See the file readme.pdf for the list of references. Spherical codes Dimension: 3 Number of points: 7 Angle in degrees: 77.86954215542338680591828838037453 Cosine: 0.21013831273060308486576530161854 Number of rattlers: 0 Minimal polynomial of cosine: 3x^3-9x^2-3x+1 Known optimal: yes References: 26 Dimension: 3 Number of points: 8 Angle in degrees: 74.85849218561553500792611345605364 Cosine: 0.26120387496374144251476820691706 Number of rattlers: 0 Minimal polynomial of cosine: 7x^2+2x-1 Known optimal: yes References: 26 Dimension: 3 Number of points: 9 Angle in degrees: 70.52877936550930863075400066003756 Cosine: 0.33333333333333333333333333333334 Number of rattlers: 0 Minimal polynomial of cosine: 3x-1 Known optimal: yes References: 26 Dimension: 3 Number of points: 10 Angle in degrees: 66.14682198789054287220577533235752 Cosine: 0.40439432521625075684622475072579 Number of rattlers: 0 Minimal polynomial of cosine: 7x^3-4x^2-2x+1 Known optimal: yes References: 26, 7 Dimension: 3 Number of points: 11 Angle in degrees: 63.43494882292201064842780627954670 Cosine: 0.44721359549995793928183473374626 Number of rattlers: 0 Minimal polynomial of cosine: 5x^2-1 Known optimal: yes References: 26, 7 Dimension: 3 Number of points: 12 Angle in degrees: 63.43494882292201064842780627954670 Cosine: 0.44721359549995793928183473374626 Number of rattlers: 0 Minimal polynomial of cosine: 5x^2-1 Known optimal: yes References: 9 Dimension: 3 Number of points: 13 Angle in degrees: 57.13670307757834201767700274322533 Cosine: 0.54263648682963846368144007679523 Number of rattlers: 0 Minimal polynomial of cosine: x^8-24x^7-12x^6+8x^5+38x^4+24x^3-12x^2-8x+1 Known optimal: yes References: 26, 21 Dimension: 3 Number of points: 14 Angle in degrees: 55.67056999565952572422946524468126 Cosine: 0.56395030036050516749088520575670 Number of rattlers: 0 Minimal polynomial of cosine: 4x^4-2x^3+3x^2-1 Known optimal: yes References: 26, 22 Dimension: 3 Number of points: 15 Angle in degrees: 53.65785012993267380552604148370299 Cosine: 0.59260590292507377809642492233276 Number of rattlers: 0 Minimal polynomial of cosine: 13x^5-x^4+6x^3+2x^2-3x-1 Known optimal: no References: 26, 13 Dimension: 3 Number of points: 16 Angle in degrees: 52.24439575272065377204341696894192 Cosine: 0.61229461648269661600605156530452 Number of rattlers: 0 Minimal polynomial of cosine: 23x^6+6x^5+5x^4+4x^3-3x^2-2x-1 Known optimal: no References: 26 Dimension: 3 Number of points: 17 Angle in degrees: 51.09032855162777854657552387628875 Cosine: 0.62809441507002164642659266364200 Number of rattlers: 0 Minimal polynomial of cosine: 4x^10-92x^9+24x^8+128x^7-58x^6-78x^5+35x^4+32x^3-4x^2-6x-1 Known optimal: no References: 7 Dimension: 3 Number of points: 18 Angle in degrees: 49.55665476843424246091024211381574 Cosine: 0.64869583222311652907905517143837 Number of rattlers: 0 Minimal polynomial of cosine: 216x^11+108x^10+118x^9+209x^8-100x^7-160x^6+40x^5+46x^4-20x^3-12x^2+2x+1 Known optimal: no References: 30 Dimension: 3 Number of points: 19 Angle in degrees: 47.69191410876624840141630606242048 Cosine: 0.67311688756005104893098993946251 Number of rattlers: 1 Minimal polynomial of cosine: 26805627119546756712x^75-11948562371904894036x^74-585034737208997137002x^73+3205538219765481672033x^72-1811715795208777326138x^71-32027083460029622026050x^70+131321687130974923909328x^69-215430828926691745481942x^68+143578141387958588992206x^67-18406761611971518339214x^66+28337005985031047347118x^65+236368444777002037271073x^64-1082229764974994074739344x^63+1516092906483969195053744x^62+179570427167174666506496x^61-3217396144386747746240528x^60+3537833960550350228385744x^59+991490736993357330354848x^58-5706214109060395312919304x^57+3869375067145621202200948x^56+3222022425168550972367752x^55-6451162558970750017599320x^54+1418757773915326072392384x^53+4886013800460103250409752x^52-4187512596952067529671448x^51-1524646701886268332978696x^50+4008909869245135167286008x^49-876772290328159683949020x^48-2388289625028580376909744x^47+1571763036057352365864208x^46+929968188649714429241600x^45-1244795308423067845031536x^44-175117573311018995290304x^43+701512392486712668409464x^42-56214865908605694262284x^41-313009485469054026132306x^40+67705510705054228901124x^39+114643074677718448810196x^38-35069626854099241213472x^37-34325988490554840080772x^36+12846271813523410492212x^35+7897687687110894499948x^34-3748244298939587917724x^33-995351057402496601890x^32+1023858388193512945808x^31-197416589532207246000x^30-348107335768936904960x^29+159027821846227712400x^28+140445584391790929904x^27-44538947685690751744x^26-50311525445451632040x^25+3837870000595205380x^24+14032664738240095304x^23+2555747252845771112x^22-2415894472515188544x^21-1293572825268210408x^20-3476911855421016x^19+210842363175215224x^18+80264372524640792x^17+4168369152867604x^16-7094624800170320x^15-2960968913050640x^14-459867970025728x^13+55487582029808x^12+46737611704216x^11+11559923551036x^10+1215281611558x^9-143093193863x^8-87545738138x^7-19809266850x^6-2929239600x^5-308513494x^4-23230866x^3-1198926x^2-38178x-567 Known optimal: no References: 15 Dimension: 3 Number of points: 20 Angle in degrees: 47.43103622671058794874110898739208 Cosine: 0.67647713812965145206767190546124 Number of rattlers: 2 Minimal polynomial of cosine: 21x^3-9x^2-5x+1 Known optimal: no References: 32 Dimension: 3 Number of points: 21 Angle in degrees: 45.61322310576746718916814716981591 Cosine: 0.69949843106637709573776394272263 Number of rattlers: 0 Known optimal: no References: 13 Dimension: 3 Number of points: 22 Angle in degrees: 44.74016116716264539249224387535237 Cosine: 0.71030625857969039075297000237262 Number of rattlers: 0 Minimal polynomial of cosine: 486x^18+13113x^17+114996x^16+117476x^15+658256x^14+378752x^13-347056x^12-121388x^11+81724x^10-70886x^9-55992x^8+12716x^7+6528x^6-2392x^5-208x^4+284x^3+14x^2+5x+4 Known optimal: no References: 13 Dimension: 3 Number of points: 23 Angle in degrees: 43.70996420526255099481804509479013 Cosine: 0.72284698486839966689606899351518 Number of rattlers: 1 Known optimal: no References: 31 Dimension: 3 Number of points: 24 Angle in degrees: 43.69076710767579618171644921518231 Cosine: 0.72307846833350853703234480939452 Number of rattlers: 0 Minimal polynomial of cosine: 7x^3+x^2-3x-1 Known optimal: yes References: 24 Dimension: 3 Number of points: 25 Angle in degrees: 41.63446125970606406767024214741580 Cosine: 0.74739862857799274075800073210958 Number of rattlers: 0 Minimal polynomial of cosine: 7180192468708211294208x^89-157717648925692394471424x^88+1205728317257342942969856x^87-4502748471868607615631360x^86+14709588236775443914204275x^85-42774577964604025309919619x^84+76599134718087031860943062x^83-96976813613096908544298678x^82+145802828395781194853314467x^81-137468090597227247981340531x^80-16797985907226176343758328x^79+115349735848985688948984x^78+339218126839338276289617150x^77-646747333461837207404551454x^76+792159162552089341472707316x^75-637787712795699990727849396x^74-414892206619917407257233770x^73+102815823893140869769512778x^72-2293865907331965017528459896x^71+2827648040679434442626956408x^70+4849746030850456730367364443x^69+5806499806874699993364450197x^68+10078022791748877122055368126x^67+11682844031740411075904993890x^66+22894905408563887844082994387x^65+38975821550046544022399438301x^64+53914020128102954032910469280x^63+74786258564830258345622481760x^62+83162806722889287479097544328x^61+70573303525937791459651988984x^60+60612526812247392567994522480x^59+59040929342856659640295995280x^58+45764600807922972481345365224x^57+15540240029287467500908264344x^56-6883938325862057211571652064x^55-932115592950413390035081760x^54+16675566638557302430731767718x^53+16680771362613621478744633402x^52-561643452959277404508908148x^51-12884349400762579096060134732x^50-10651125972482084309508233562x^49-3092848177770530297429305926x^48+92246478184019273119527024x^47-934127036810783545959796336x^46-1845568512103565650446513452x^45-1289968098546903362430052756x^44-572601128519675303348402632x^43-403874112898637638902078136x^42-324627016853261845245926236x^41-8525459396392599724348260x^40+299751255675112321515406576x^39+341319612110288486423564048x^38+180717270363871094742237262x^37+19313921885905184567368466x^36-44827292888544990112811060x^35-37448192491933112216472204x^34-13807839209608231652461026x^33-545437907229853636886334x^32+2230457624090649616650016x^31+1265006708766043109778656x^30+302718932114747826739144x^29-24129911915725279878984x^28-47587451287604419553936x^27-18350236658506074372720x^26-2951950809993319277400x^25+611389996704378222552x^24+583533435395314421664x^23+206226058880426344544x^22+36181551688403418311x^21-3839476135541296535x^20-5172237488767441250x^19-1952233262605812990x^18-431384060474673065x^17-46380020052045543x^16+5050849868049864x^15+3294755930889528x^14+705390381869022x^13+76532545200642x^12-383435464204x^11-1715213031604x^10-322767548106x^9-31089390934x^8-989318200x^7+173076024x^6+31705975x^5+2786873x^4+153974x^3+5418x^2+111x+1 Known optimal: no References: 13 Dimension: 3 Number of points: 26 Angle in degrees: 41.03766160675250218608721374440023 Cosine: 0.75427817712004151970111096057049 Number of rattlers: 2 Minimal polynomial of cosine: 4747234817821577661948005859375x^101+99939112808557036746958999171875x^100+850316810773567258541926035468750x^99+3628152996699912579010320305308750x^98+7233337962611267717845078024616875x^97-3146202505453499579404619938382825x^96-90077179164620180316015417575659600x^95-469668198588166339267851664615729360x^94-1224328612356632642280038793289887740x^93-304935138654504001958379588540209420x^92+6490606391880474866453977456230821592x^91+13130580452794484863789392868632948312x^90-4074840348564687422010693188920948028x^89-43264459969987632078826343681602267500x^88-36635210258509471897616303340663605808x^87+53327980635006878169195667241327886160x^86+111157289417048245501129141267554366918x^85+8879739585524700577451912552926555086x^84-141907091623367971681651440776007716900x^83-112263952243151214026639628205474513828x^82+71909417670714501468026943137305332750x^81+151184239842717503175100864777481256966x^80+34948759553763274617255256707012683664x^79-90078016821598440349855489872005559280x^78-75184259558790918522201819774051736764x^77+8765001807488123500723651695845951668x^76+41939232272262232187849164846097458680x^75+19649030643572697658087114580721596024x^74-2833224845843688146972798172224972508x^73-7134607763337293865404542082889378828x^72-5963120337298323097956521539543243536x^71-4413873979466335365180143845073849488x^70-325429508123965571421398878246819751x^69+3393588405300353234128595212296954245x^68+3022387603727628206158664279686502674x^67+269680208491399750846721348308975378x^66-1304709949276248009764427028249473459x^65-980126426797652819777245797884668799x^64-125516615873896468152382949731949088x^63+287480390544647526105142925788209376x^62+250229582400900320393897963012824136x^61+71959887601194852897711609365038888x^60-46109262320988128125362767376303696x^59-60793077291075916066246216167373648x^58-22421383476548234784692809754303416x^57+8156350123020089520123965182953704x^56+12058074802751354300852196558581024x^55+3879322922684091227794252642941984x^54-1430159851319484523037600433647436x^53-1670357622505514271594532971398492x^52-436575105101783970721467897501432x^51+159553837064101385121997364734472x^50+158761225905353656894824803156836x^49+44063434683130225585311267442804x^48-7269558749681045001905774546912x^47-11893471658436264033464859834080x^46-5045146562803130033853577940120x^45-281654632711886265544562881336x^44+931253299707120013897750275760x^43+510613133544166375543747864496x^42+43380077536837440627584994472x^41-75103221071537433337782327352x^40-35166193439871610150930096928x^39-673113814627992473673287200x^38+4685011345265912723880814161x^37+1495777365848308117655231709x^36-120745406938471097355913518x^35-189253876351465883150238382x^34-35178602087625338436277387x^33+8085683838804366389693705x^32+4304337553016631219820912x^31+238465986405227061933808x^30-205489329180785910045900x^29-27724303010206123657372x^28+10313177989044138732408x^27+1199712746603393648888x^26-1313863861443422577804x^25-364549722930429492988x^24+56019730105601134096x^23+45719855228241214864x^22+6835252295775195622x^21-1425740919722638738x^20-753126495873013540x^19-102554745449245860x^18+12393998032376686x^17+7421545624095206x^16+1227053086474576x^15+9643830492112x^14-39555663371820x^13-9295495500540x^12-934285988008x^11+41589077464x^10+30952961972x^9+5383695300x^8+477203760x^7+6183344x^6-4419385x^5-672357x^4-54130x^3-2674x^2-77x-1 Known optimal: no References: 13 Dimension: 3 Number of points: 27 Angle in degrees: 40.67760068512674658008426875219181 Cosine: 0.75838921077657748391083424965931 Number of rattlers: 0 Minimal polynomial of cosine: 16x^24-128x^23+536x^22-2088x^21+4977x^20-12258x^19+20672x^18-36126x^17+51043x^16-73408x^15+104128x^14-137928x^13+175090x^12-181700x^11+155936x^10-92916x^9+32222x^8+6608x^7-16568x^6+8192x^5-1843x^4-490x^3+128x^2+2x-1 Known optimal: no References: 30 Dimension: 3 Number of points: 28 Angle in degrees: 39.35514356888495841115001709288861 Cosine: 0.77323026233796340734575992835035 Number of rattlers: 1 Known optimal: no References: 13 Dimension: 3 Number of points: 29 Angle in degrees: 38.71365119385894037633759802659374 Cosine: 0.78028141594871705893938480666397 Number of rattlers: 1 Known optimal: no References: 13 Dimension: 3 Number of points: 30 Angle in degrees: 38.59711595386765606658303351176410 Cosine: 0.78155187509498732710358610409650 Number of rattlers: 0 Minimal polynomial of cosine: 21508124014x^29+32054106929x^28-17306462662x^27-25038151480x^26+45587477052x^25+38755887413x^24-43255133604x^23-45501640088x^22+10460524458x^21+17929512405x^20-4828786226x^19-5447284224x^18+4496890016x^17+4235161545x^16-436447576x^15-1539874224x^14-487336414x^13+100621747x^12+97938998x^11+20609352x^10+665516x^9+320703x^8+272188x^7-6712x^6-34298x^5-7289x^4+386x^3+368x^2+56x+3 Known optimal: no References: 5 Dimension: 3 Number of points: 31 Angle in degrees: 37.70982914370989458237011117017694 Cosine: 0.79111861329867495834332727354269 Number of rattlers: 0 Minimal polynomial of cosine: 762939453125x^66-7749023437500000x^65-549435976806640625x^64-11954964334375000000x^63+46354290204062500000x^62+296025528806187500000x^61+490694826896712500000x^60-2924709240882350000000x^59-6800355886385641875000x^58-366339002678087500000x^57+24369506192176385375000x^56+27001547365967091000000x^55-21809158347127162000000x^54-57924024899601366500000x^53+216864844649587000000x^52+85459665184041748000000x^51+54781050077892013637500x^50-58750644174610964300000x^49-82881366173951176087500x^48+10813834042651693800000x^47+68671909889015111100000x^46+21880288415145669500000x^45-33835279909942372260000x^44-28742278663291060560000x^43+5059474474277195855000x^42+18072340935967350180000x^41+5081122618349672485000x^40-7348044648411661000000x^39-4855343931749555912000x^38+1756201950891108268000x^37+2191537623864678896000x^36-149574226224283200000x^35-601704498228424443250x^34-31377517351471092000x^33+105699566552688975850x^32+7583888617243473600x^31-11670500395907146400x^30+897723129303914400x^29+727136477631583200x^28-648477435737936000x^27-15984936748662600x^26+140013663478850400x^25-729722733211800x^24-18513532467761600x^23+83825458355200x^22+1742577366650400x^21-11081142856000x^20-124659358585600x^19+1556588076380x^18+7006344894560x^17-185033832620x^16-323267164480x^15+18407781280x^14+13515780640x^13-1414879840x^12-552613760x^11+81291880x^10+19660000x^9-3587720x^8-472000x^7+128960x^6+5280x^5-3840x^4+85x^2-1 Known optimal: no References: 28 Dimension: 3 Number of points: 32 Angle in degrees: 37.47521397487154131177437208730674 Cosine: 0.79361661487126244036481707479245 Number of rattlers: 0 Minimal polynomial of cosine: 6561x^22-4374x^21-94041x^20+1289844x^19+3605067x^18-4301046x^17+6019389x^16+238896x^15-10407366x^14+7894164x^13+7975830x^12-7790088x^11-3481466x^10+3831332x^9+843658x^8-1303376x^7-311819x^6+148290x^5+39667x^4-3660x^3-1185x^2+18x+9 Known optimal: no References: 7 Dimension: 4 Number of points: 9 Angle in degrees: 80.67611499113670774069403965727037 Cosine: 0.16201519961163454918243428113270 Number of rattlers: 0 Minimal polynomial of cosine: 16x^3-16x^2-4x+1 Known optimal: no References: 27 Dimension: 4 Number of points: 10 Angle in degrees: 80.40593177313953855556147215930090 Cosine: 0.16666666666666666666666666666667 Number of rattlers: 0 Minimal polynomial of cosine: 6x-1 Known optimal: yes References: 18, 2 Dimension: 4 Number of points: 11 Angle in degrees: 76.67904986073005406839997302465582 Cosine: 0.23040556359455544173706204865074 Number of rattlers: 0 Minimal polynomial of cosine: 8x^3-12x^2-2x+1 Known optimal: no References: 27 Dimension: 4 Number of points: 12 Angle in degrees: 75.52248781407007612122896520087283 Cosine: 0.25000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 4x-1 Known optimal: no References: 18 Dimension: 4 Number of points: 13 Angle in degrees: 72.10367061152200998823004588133241 Cosine: 0.30729565398102882232528869633144 Number of rattlers: 0 Minimal polynomial of cosine: 5632x^9+9472x^8-3072x^7-5888x^6+544x^5+944x^4+152x^3-44x^2-14x-1 Known optimal: no References: 27 Dimension: 4 Number of points: 14 Angle in degrees: 71.36618599098114419896366620681077 Cosine: 0.31951859421260363549590568166773 Number of rattlers: 0 Minimal polynomial of cosine: 58x^7+174x^6+140x^5-16x^4-54x^3-10x^2+4x+1 Known optimal: no References: 27 Dimension: 4 Number of points: 15 Angle in degrees: 69.45198696595656364825678623645506 Cosine: 0.35099217594534630329905559676410 Number of rattlers: 0 Minimal polynomial of cosine: 36x^4-18x^3+10x^2-1 Known optimal: no References: 27 Dimension: 4 Number of points: 16 Angle in degrees: 67.19300206778070795754958388500717 Cosine: 0.38762817712253427775854691441514 Number of rattlers: 0 Minimal polynomial of cosine: 256x^10+1024x^9+256x^8-1152x^7+160x^6+176x^5-144x^4+36x^3+37x^2-6x-3 Known optimal: no References: 18 Dimension: 4 Number of points: 17 Angle in degrees: 65.65315632940273003033659773645941 Cosine: 0.41225936269326378906697367932150 Number of rattlers: 0 Known optimal: no References: 27 Dimension: 4 Number of points: 18 Angle in degrees: 64.98728271299508194615697469901300 Cosine: 0.42281941407305934402640028185634 Number of rattlers: 0 Minimal polynomial of cosine: 14424x^16+42932x^15+18232x^14-62100x^13-53831x^12+41528x^11+46442x^10-18248x^9-20977x^8+6180x^7+5372x^6-1556x^5-721x^4+240x^3+34x^2-16x+1 Known optimal: no References: 27 Dimension: 4 Number of points: 19 Angle in degrees: 64.26187661462771779834845404644122 Cosine: 0.43425854591066488218653687791175 Number of rattlers: 0 Minimal polynomial of cosine: 3x^2+x-1 Known optimal: no References: 27 Dimension: 4 Number of points: 20 Angle in degrees: 64.26187661462771779834845404644122 Cosine: 0.43425854591066488218653687791175 Number of rattlers: 0 Minimal polynomial of cosine: 3x^2+x-1 Known optimal: no References: 27 Dimension: 4 Number of points: 21 Angle in degrees: 61.87603156177932859191783429796328 Cosine: 0.47138085850731791681783507846628 Number of rattlers: 0 Minimal polynomial of cosine: 16x^8-128x^7-64x^6+32x^5+72x^4+32x^3-16x^2-8x+1 Known optimal: no References: 27 Dimension: 4 Number of points: 22 Angle in degrees: 60.13988632460909789015726511015541 Cosine: 0.49788413084355235628616910040615 Number of rattlers: 0 Known optimal: no References: 27 Dimension: 4 Number of points: 23 Angle in degrees: 60.00000000000000000000000000000000 Cosine: 0.50000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 2x-1 Known optimal: no References: 27 Dimension: 4 Number of points: 24 Angle in degrees: 60.00000000000000000000000000000000 Cosine: 0.50000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 2x-1 Known optimal: yes References: 25, 14 Dimension: 4 Number of points: 25 Angle in degrees: 57.49888257759496543718680470969067 Cosine: 0.53731605665507787659607001344589 Number of rattlers: 0 Known optimal: no References: 27 Dimension: 4 Number of points: 26 Angle in degrees: 57.26259226563522993703621159690104 Cosine: 0.54078961769753707672755075220843 Number of rattlers: 0 Minimal polynomial of cosine: 3392x^6+2112x^5-496x^4-656x^3-132x^2+6x-1 Known optimal: no References: 27 Dimension: 4 Number of points: 27 Angle in degrees: 56.11061324625795902608764933134448 Cosine: 0.55759135118017018253232385918274 Number of rattlers: 3 Minimal polynomial of cosine: 794x^5+393x^4-344x^3-82x^2+6x+1 Known optimal: no References: 27 Dimension: 4 Number of points: 28 Angle in degrees: 55.43513982734237257077234003063094 Cosine: 0.56733880407434859617396405079452 Number of rattlers: 0 Known optimal: no References: 27 Dimension: 4 Number of points: 29 Angle in degrees: 55.02992450708383988500412411961470 Cosine: 0.57314853044836189190193776787666 Number of rattlers: 0 Minimal polynomial of cosine: 134217728x^58+4697620480x^57+161598144512x^56-180757725184x^55-9008861675520x^54+44334447591424x^53-83919139504128x^52+98587941797888x^51-181832408104960x^50+316581256626176x^49-90076763127808x^48-537023456608256x^47+604830226120704x^46+254556736454656x^45-752724353286144x^44+54249034416128x^43+644033914798080x^42-107040978763776x^41-560570197295104x^40+6859761270784x^39+499220015497216x^38+90040966848512x^37-380613267726336x^36-124450276397056x^35+230245747986432x^34+109643677564928x^33-105946394147840x^32-73517100673024x^31+32119186237952x^30+37184308716032x^29-1979817458176x^28-13072126472960x^27-4235166430720x^26+2344880983552x^25+2853044827712x^24+532918979008x^23-1043701990592x^22-610331035168x^21+229379699680x^20+265097468112x^19-18621871032x^18-76317870584x^17-7228205676x^16+15826810374x^15+3577929127x^14-2318270796x^13-851229809x^12+214632938x^11+128263091x^10-7704392x^9-12478145x^8-748486x^7+737925x^6+114164x^5-21803x^4-6010x^3+57x^2+120x+9 Known optimal: no References: 27 Dimension: 4 Number of points: 30 Angle in degrees: 54.25118969371278003645403260132927 Cosine: 0.58423281393058512894226706121300 Number of rattlers: 0 Known optimal: no References: 27 Dimension: 4 Number of points: 31 Angle in degrees: 53.78862671849501799323928306837474 Cosine: 0.59076583858072581074772305364896 Number of rattlers: 2 Known optimal: no References: Dimension: 4 Number of points: 32 Angle in degrees: 53.43601305266608940377321769977306 Cosine: 0.59572014923551345643989842209366 Number of rattlers: 2 Known optimal: no References: 27 Dimension: 5 Number of points: 11 Angle in degrees: 82.36548108376801990767391559984579 Cosine: 0.13285354259858991808946447681952 Number of rattlers: 0 Minimal polynomial of cosine: 45x^3-25x^2-5x+1 Known optimal: no References: 27 Dimension: 5 Number of points: 12 Angle in degrees: 81.14516188585517605543937180072117 Cosine: 0.15393160503302123094881763125084 Number of rattlers: 0 Minimal polynomial of cosine: 25x^4+30x^3+24x^2+2x-1 Known optimal: no References: 27 Dimension: 5 Number of points: 13 Angle in degrees: 79.20708470783783123366073209452406 Cosine: 0.18725985188285358701782399517981 Number of rattlers: 0 Minimal polynomial of cosine: 17x^3-5x^2-5x+1 Known optimal: no References: 27 Dimension: 5 Number of points: 14 Angle in degrees: 78.46304096718451230986262848948731 Cosine: 0.20000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 5x-1 Known optimal: no References: 27 Dimension: 5 Number of points: 15 Angle in degrees: 78.46304096718451230986262848948731 Cosine: 0.20000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 5x-1 Known optimal: no References: 27 Dimension: 5 Number of points: 16 Angle in degrees: 78.46304096718451230986262848948731 Cosine: 0.20000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 5x-1 Known optimal: yes References: 12, 16 Dimension: 5 Number of points: 17 Angle in degrees: 74.30741622412003388784332347892401 Cosine: 0.27047583526857362208626102246801 Number of rattlers: 0 Minimal polynomial of cosine: 9x^4-16x^3-10x^2+1 Known optimal: no References: 27 Dimension: 5 Number of points: 18 Angle in degrees: 74.00808308678895218079554484163947 Cosine: 0.27550174165981923838704223579799 Number of rattlers: 0 Minimal polynomial of cosine: 484x^5-488x^4+97x^3+17x^2-x-1 Known optimal: no References: 27 Dimension: 5 Number of points: 19 Angle in degrees: 73.03290806269132198168485098189368 Cosine: 0.29182239902449014614857168904980 Number of rattlers: 0 Minimal polynomial of cosine: 57x^6-38x^5-109x^4+32x^3+23x^2-10x+1 Known optimal: no References: 27 Dimension: 5 Number of points: 20 Angle in degrees: 72.57928983890882545220824776974176 Cosine: 0.29938569289912478230200302792897 Number of rattlers: 1 Minimal polynomial of cosine: 5x^3+13x^2-x-1 Known optimal: no References: 27 Dimension: 5 Number of points: 21 Angle in degrees: 71.64419935121190536879479200706709 Cosine: 0.31491695717530346284922041852029 Number of rattlers: 0 Minimal polynomial of cosine: 869312x^14+8798656x^13-1062776x^12-10586775x^11-968269x^10+3532907x^9+188249x^8-659974x^7-11746x^6+72246x^5-806x^4-5267x^3-97x^2+207x+21 Known optimal: no References: 27 Dimension: 5 Number of points: 22 Angle in degrees: 69.20685996353569280640998613355169 Cosine: 0.35499503416625620682992409117504 Number of rattlers: 0 Known optimal: no References: 27 Dimension: 5 Number of points: 23 Angle in degrees: 68.29840039853121657309012131409493 Cosine: 0.36977269694307633377246233586792 Number of rattlers: 2 Known optimal: no References: 27 Dimension: 5 Number of points: 24 Angle in degrees: 68.02308559289922261595581158921005 Cosine: 0.37423298246516725172655168161941 Number of rattlers: 0 Minimal polynomial of cosine: 1620x^10+5508x^9-5751x^8-2406x^7+2055x^6+276x^5+559x^4-210x^3-127x^2+48x-4 Known optimal: no References: 27 Dimension: 5 Number of points: 25 Angle in degrees: 67.68978992189891768892071915999768 Cosine: 0.37962102539378266282456421792923 Number of rattlers: 0 Known optimal: no References: 27 Dimension: 5 Number of points: 26 Angle in degrees: 67.03052523495341113770027834086652 Cosine: 0.39024065950484684004435526211173 Number of rattlers: 0 Minimal polynomial of cosine: 524800x^23+4355041x^22+12847946x^21+19153517x^20+21850072x^19+23648850x^18+22411486x^17+14303202x^16+3883390x^15-2036811x^14-4180690x^13-3335803x^12-809642x^11+335179x^10+208142x^9+70923x^8+28042x^7-4402x^6-6624x^5-798x^4+330x^3+63x^2-4x-1 Known optimal: no References: 27 Dimension: 5 Number of points: 27 Angle in degrees: 66.31805184468824442438431523624444 Cosine: 0.40165926427641808725922803276444 Number of rattlers: 0 Minimal polynomial of cosine: 1119771x^15-2830137x^14-1546771x^13+5257986x^12+1128383x^11-2395071x^10-835223x^9+3296x^8+279089x^7+182809x^6-10649x^5-22406x^4-3595x^3+127x^2+67x+4 Known optimal: no References: Dimension: 5 Number of points: 28 Angle in degrees: 65.91009009174930460688758675681090 Cosine: 0.40816969909292876817531302066075 Number of rattlers: 0 Known optimal: no References: 27 Dimension: 5 Number of points: 29 Angle in degrees: 65.73016702447021538852233536025111 Cosine: 0.41103443509195154800015221999063 Number of rattlers: 0 Minimal polynomial of cosine: 7558272x^31-140877792x^30+761392386x^29-2056857705x^28+12778454376x^27-9234224127x^26-152236269396x^25+251208094662x^24+485200038816x^23-1070947057734x^22-655636028274x^21+2081656808361x^20+417978163944x^19-2474314751169x^18+248887789152x^17+1543781797668x^16-336701441280x^15-565486924276x^14+132444694590x^13+133931442297x^12-24823009608x^11-21199487889x^10+2147658044x^9+2171347238x^8-25502752x^7-130779014x^6-8612494x^5+3809703x^4+506360x^3-29199x^2-8072x-368 Known optimal: no References: 27 Dimension: 5 Number of points: 30 Angle in degrees: 65.60469675996130765655995835525877 Cosine: 0.41302977612208581019088251209695 Number of rattlers: 0 Minimal polynomial of cosine: 269x^7-1419x^6-283x^5+405x^4+15x^3-9x^2-x-1 Known optimal: no References: 27 Dimension: 5 Number of points: 31 Angle in degrees: 64.28392571463760124123460480389348 Cosine: 0.43391186395954602878684987397560 Number of rattlers: 0 Minimal polynomial of cosine: 131813361x^20-731458980x^19+1012289262x^18+274194380x^17-1451653075x^16-56793808x^15+1045838760x^14+84095280x^13-606236238x^12-195879416x^11+142245076x^10+89397096x^9+5543250x^8-8401424x^7-3008600x^6-417936x^5-8483x^4+5244x^3+750x^2+44x+1 Known optimal: no References: 27 Dimension: 5 Number of points: 32 Angle in degrees: 63.77925174004906355623876793171895 Cosine: 0.44183074392731126949046338768223 Number of rattlers: 0 Minimal polynomial of cosine: 8x^10-40x^9+74x^8-78x^7+73x^6-10x^5-3x^4+18x^3-9x^2-2x+1 Known optimal: no References: Dimension: 6 Number of points: 13 Angle in degrees: 83.50711954519258526930790509107958 Cosine: 0.11307975214744721384507044810795 Number of rattlers: 0 Minimal polynomial of cosine: 96x^3-36x^2-6x+1 Known optimal: no References: 1 Dimension: 6 Number of points: 14 Angle in degrees: 82.38644311487112960753413014038813 Cosine: 0.13249092032347031437017906291052 Number of rattlers: 0 Minimal polynomial of cosine: 237299200x^13+463738880x^12+366062080x^11+142462784x^10+23021376x^9-2398832x^8-1849600x^7-343428x^6-1802x^5+11443x^4+1390x^3-128x^2-20x+1 Known optimal: no References: 33 Dimension: 6 Number of points: 15 Angle in degrees: 81.66567558562359971439920520487028 Cosine: 0.14494897427831780981972840747059 Number of rattlers: 0 Minimal polynomial of cosine: 20x^2+4x-1 Known optimal: no References: 33 Dimension: 6 Number of points: 16 Angle in degrees: 80.14544748501058444245852743396934 Cosine: 0.17114764942939365334044778754758 Number of rattlers: 0 Minimal polynomial of cosine: 4000000x^8+15120000x^7+9896400x^6-2451600x^5-4503600x^4-1511460x^3-87480x^2+43740x+6561 Known optimal: no References: 1 Dimension: 6 Number of points: 17 Angle in degrees: 79.43946091141681653402335194182435 Cosine: 0.18327433702314481857632435406165 Number of rattlers: 0 Minimal polynomial of cosine: 400x^4+240x^3+16x^2-8x-1 Known optimal: no References: 1 Dimension: 6 Number of points: 18 Angle in degrees: 78.59094914631781096516793437044827 Cosine: 0.19781218860197545240607808204678 Number of rattlers: 0 Minimal polynomial of cosine: 784x^8-280x^7-1191x^6+120x^5+218x^4-62x^3-31x^2+2x+1 Known optimal: no References: 33 Dimension: 6 Number of points: 19 Angle in degrees: 78.44982328103026755028504620673026 Cosine: 0.20022602589120548304270384498373 Number of rattlers: 0 Known optimal: no References: 33 Dimension: 6 Number of points: 20 Angle in degrees: 77.62637488381144200769096282034911 Cosine: 0.21428571428571428571428571428572 Number of rattlers: 0 Minimal polynomial of cosine: 14x-3 Known optimal: no References: 33 Dimension: 6 Number of points: 21 Angle in degrees: 75.94502085041603481236392354428406 Cosine: 0.24285284801369170250759542313692 Number of rattlers: 0 Known optimal: no References: 33 Dimension: 6 Number of points: 22 Angle in degrees: 75.58959971877343935476369025853277 Cosine: 0.24886569945945498664968496352672 Number of rattlers: 2 Known optimal: no References: Dimension: 6 Number of points: 23 Angle in degrees: 75.52248781407007612122896520087283 Cosine: 0.25000000000000000000000000000000 Number of rattlers: 1 Minimal polynomial of cosine: 4x-1 Known optimal: no References: 33 Dimension: 6 Number of points: 24 Angle in degrees: 75.52248781407007612122896520087283 Cosine: 0.25000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 4x-1 Known optimal: no References: 33 Dimension: 6 Number of points: 25 Angle in degrees: 75.52248781407007612122896520087283 Cosine: 0.25000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 4x-1 Known optimal: no References: 33 Dimension: 6 Number of points: 26 Angle in degrees: 75.52248781407007612122896520087283 Cosine: 0.25000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 4x-1 Known optimal: no References: 33 Dimension: 6 Number of points: 27 Angle in degrees: 75.52248781407007612122896520087283 Cosine: 0.25000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 4x-1 Known optimal: yes References: 12, 16 Dimension: 6 Number of points: 28 Angle in degrees: 72.54239687627790770975395420755505 Cosine: 0.30000000000000000000000000000000 Number of rattlers: 7 Minimal polynomial of cosine: 10x-3 Known optimal: no References: 8 Dimension: 6 Number of points: 29 Angle in degrees: 70.86198240837437246132452638327840 Cosine: 0.32784483088118687202127443197487 Number of rattlers: 2 Known optimal: no References: Dimension: 6 Number of points: 30 Angle in degrees: 70.53674616377562607328290101422838 Cosine: 0.33320223547405022827954928731378 Number of rattlers: 0 Known optimal: no References: Dimension: 6 Number of points: 31 Angle in degrees: 70.52877936550930863075400066003756 Cosine: 0.33333333333333333333333333333334 Number of rattlers: 0 Minimal polynomial of cosine: 3x-1 Known optimal: no References: 33 Dimension: 6 Number of points: 32 Angle in degrees: 70.52877936550930863075400066003756 Cosine: 0.33333333333333333333333333333334 Number of rattlers: 0 Minimal polynomial of cosine: 3x-1 Known optimal: no References: 17 Dimension: 7 Number of points: 15 Angle in degrees: 84.33558210993109390169556903708466 Cosine: 0.09870177627236447932802936506891 Number of rattlers: 0 Minimal polynomial of cosine: 175x^3-49x^2-7x+1 Known optimal: no References: 1 Dimension: 7 Number of points: 16 Angle in degrees: 83.49321458126912900808428497560837 Cosine: 0.11332087960014474124552027924541 Number of rattlers: 0 Minimal polynomial of cosine: 85823999x^12+153503984x^11+163426326x^10+92426704x^9+29708081x^8+9292960x^7+2252404x^6+410976x^5+29489x^4-3216x^3-746x^2-48x-1 Known optimal: no References: 33 Dimension: 7 Number of points: 17 Angle in degrees: 82.82839245808687789982833852129493 Cosine: 0.12484158381525719834719018255480 Number of rattlers: 0 Minimal polynomial of cosine: 125998198321917392989919022595317x^48+993033509449311326134696169231122x^47+3752248327200066770687375692539686x^46+8955158465726530265612401238780138x^45+15007364215887293115858590752506170x^44+18582312869988955755046896791034362x^43+17398454256724475463270552736728846x^42+12340249950977774848909258312869330x^41+6457098398753576023330165931609144x^40+2263122016312540000604017995134782x^39+314828563456342547964236008385066x^38-177579034616420008419141554622362x^37-137348191835973197189745676674066x^36-42702739808756989271422234943546x^35-3096465435381678859958012957294x^34+2983247678463712395049009052462x^33+1330683210419223946267107795885x^32+200508423264171416624064557236x^31-33254311832642939370952336900x^30-21993233538957427585670435292x^29-3812814026325803718729989596x^28+214098631481038052344113028x^27+228709751658607587974535244x^26+40150466235528538268095988x^25-747593026805040485716200x^24-1579936001334212279880772x^23-267450005683160048518252x^22+143104862796579626508x^21+7360876301341395343292x^20+1183398078910690852620x^19+13115715182908335396x^18-23033869432963953444x^17-3518165198645476577x^16-71920091568688102x^15+47104211363236990x^14+6917600084602194x^13+204507747167810x^12-58734651593630x^11-8591773464250x^10-343380773734x^9+37260038384x^8+6065620262x^7+321676450x^6-4131538x^5-1774922x^4-128178x^3-4950x^2-106x-1 Known optimal: no References: Dimension: 7 Number of points: 18 Angle in degrees: 82.75386890277099833164413156132155 Cosine: 0.12613198362288317391722947587285 Number of rattlers: 0 Minimal polynomial of cosine: 47x^2+2x-1 Known optimal: no References: 1 Dimension: 7 Number of points: 19 Angle in degrees: 80.99054886891945278782199328588019 Cosine: 0.15659738541709551030242683082792 Number of rattlers: 0 Minimal polynomial of cosine: 1280x^6-352x^4-48x^3+37x^2+3x-1 Known optimal: no References: 33 Dimension: 7 Number of points: 20 Angle in degrees: 80.24003872242786137070862280615199 Cosine: 0.16952084719853722593019861519182 Number of rattlers: 0 Minimal polynomial of cosine: 23x^2+2x-1 Known optimal: no References: 8 Dimension: 7 Number of points: 21 Angle in degrees: 79.54146119500459356104591631890956 Cosine: 0.18152396080041583540526502110446 Number of rattlers: 0 Known optimal: no References: 33 Dimension: 7 Number of points: 22 Angle in degrees: 79.47036912306999346266936086218739 Cosine: 0.18274399763155681014833407039277 Number of rattlers: 0 Minimal polynomial of cosine: 19x^2+2x-1 Known optimal: no References: 33 Dimension: 7 Number of points: 23 Angle in degrees: 79.47036912306999346266936086218739 Cosine: 0.18274399763155681014833407039277 Number of rattlers: 0 Minimal polynomial of cosine: 19x^2+2x-1 Known optimal: no References: 33 Dimension: 7 Number of points: 24 Angle in degrees: 79.47036912306999346266936086218739 Cosine: 0.18274399763155681014833407039277 Number of rattlers: 0 Minimal polynomial of cosine: 19x^2+2x-1 Known optimal: no References: 33 Dimension: 7 Number of points: 25 Angle in degrees: 77.59988814551802935070031606043086 Cosine: 0.21473723385459290952279854505932 Number of rattlers: 1 Minimal polynomial of cosine: 31x^2-2x-1 Known optimal: no References: 33 Dimension: 7 Number of points: 26 Angle in degrees: 76.62452870871808904564014936022223 Cosine: 0.23133143037135692995849173196346 Number of rattlers: 0 Known optimal: no References: 33 Dimension: 7 Number of points: 27 Angle in degrees: 76.08103240866478456876439639481756 Cosine: 0.24054938200924358136050178936531 Number of rattlers: 1 Known optimal: no References: Dimension: 7 Number of points: 28 Angle in degrees: 75.67885262385933846733150735360874 Cosine: 0.24735665120702230944063342932200 Number of rattlers: 0 Known optimal: no References: Dimension: 7 Number of points: 29 Angle in degrees: 75.58560982771909589695542730493489 Cosine: 0.24893314468092960074198540286771 Number of rattlers: 0 Known optimal: no References: Dimension: 7 Number of points: 30 Angle in degrees: 75.55394961731072566588000259944602 Cosine: 0.24946828687500069590353003579697 Number of rattlers: 2 Known optimal: no References: Dimension: 7 Number of points: 31 Angle in degrees: 75.25587620303464198643062248255941 Cosine: 0.25450276751476520071094915336323 Number of rattlers: 1 Known optimal: no References: Dimension: 7 Number of points: 32 Angle in degrees: 74.59764764858858118232978881451449 Cosine: 0.26559569943123793674839332081547 Number of rattlers: 0 Known optimal: no References: Dimension: 8 Number of points: 17 Angle in degrees: 84.96677176418563658758414902955192 Cosine: 0.08773346332333854567255804176022 Number of rattlers: 0 Minimal polynomial of cosine: 288x^3-64x^2-8x+1 Known optimal: no References: 8 Dimension: 8 Number of points: 18 Angle in degrees: 84.29137305656666805537037965233645 Cosine: 0.09946957270878709385964502330429 Number of rattlers: 0 Known optimal: no References: 33 Dimension: 8 Number of points: 19 Angle in degrees: 83.60339917026873193648342462400456 Cosine: 0.11140997502603998543258143242674 Number of rattlers: 0 Minimal polynomial of cosine: 120167863410491392x^29-59590763696095232x^28-76119519931662336x^27+24767733589606400x^26+12079697995235328x^25-10338948633067520x^24-5431731731562496x^23+213918450974720x^22+1245182995202048x^21+467239418200064x^20-109683826491392x^19-132535030185984x^18-26502882410496x^17+9913949683712x^16+6281524035584x^15+851870894080x^14-327250048000x^13-152445557248x^12-14835825920x^11+5459137408x^10+1820496320x^9+106465088x^8-44725024x^7-9101472x^6-55332x^5+158896x^4+14755x^3-459x^2-127x-5 Known optimal: no References: 33 Dimension: 8 Number of points: 20 Angle in degrees: 83.13693377417703734808073144823649 Cosine: 0.11949686668719356518012001310428 Number of rattlers: 0 Minimal polynomial of cosine: 224x^3+60x^2-2x-1 Known optimal: no References: 33 Dimension: 8 Number of points: 21 Angle in degrees: 82.49562264547493543855053034509247 Cosine: 0.13060193748187072125738410345853 Number of rattlers: 0 Minimal polynomial of cosine: 28x^2+4x-1 Known optimal: no References: 33 Dimension: 8 Number of points: 22 Angle in degrees: 82.49562264547493543855053034509247 Cosine: 0.13060193748187072125738410345853 Number of rattlers: 0 Minimal polynomial of cosine: 28x^2+4x-1 Known optimal: no References: 8 Dimension: 8 Number of points: 23 Angle in degrees: 80.95733247771504282420772977150664 Cosine: 0.15716994198931666717945817456695 Number of rattlers: 0 Minimal polynomial of cosine: 5521700484255070385798883894624256x^68+93535811217563785735453865662218240x^67+667163533183396974906813981069934592x^66+2432727994101205870754617407829966848x^65+3496236871574823891927448015316451328x^64-7892400326103461562277860681894068224x^63-52077024505902658098639946831898869760x^62-125217661849986056352858508936985182208x^61-157193750240183171617639720590162001920x^60-49475927963781682363413558698300145664x^59+187362086766733535339692491507478036480x^58+368560702684960109712548233898799136768x^57+300338494898555831667286429066231545856x^56+14562039678035757842653964016694591488x^55-243587687866855077363084554498916483072x^54-278660661533650351855347063942543310848x^53-127585463700288403641753069840410607616x^52+33257584966232614951257080143896641536x^51+89178229619916210519031111271948746752x^50+57275756801171310946352817118447140864x^49+9647183632991237749212354115203497984x^48-12156553226548483263052941843312410624x^47-10818165071693813265392947808557858816x^46-3461162292477053885485911785202515968x^45+566255673527248973627570288064462848x^44+1061657563615297007053343011104620544x^43+445835150545333119788972415247187968x^42+33053501774587611045777452440748032x^41-56666678886584595816511120281174016x^40-30532343657934709446570842160889856x^39-5528445541652512341841168240214016x^38+1489432393763531468568961304494080x^37+1211648656343260942079786316201984x^36+303159349192943898167221191966720x^35-5162173267562262674537765928960x^34-28035623775117230936790449258496x^33-8866294294585555906798204813312x^32-773544276000157852115255951360x^31+354539641340874598635641765888x^30+149958850685677803955604422656x^29+21931928380082391177509175296x^28-1803570981998034168665931776x^27-1479561319797955521461551104x^26-283016190473041674402922496x^25-8240685077749556532633600x^24+8233507082377536533463040x^23+2019924053970704222003200x^22+167143293115336211709952x^21-22013601988951125637120x^20-8202940713660858552320x^19-967362691084893472768x^18+1630441179820457984x^17+17961169677979853312x^16+2751603057693476864x^15+139294803493127680x^14-17023746029512192x^13-3931081977460800x^12-320403675343232x^11-2013999223296x^10+2409317280768x^9+279388037456x^8+14292742208x^7-45762192x^6-65599328x^5-5468396x^4-255512x^3-7452x^2-128x-1 Known optimal: no References: 33 Dimension: 8 Number of points: 24 Angle in degrees: 80.92703463766069212088500837949978 Cosine: 0.15769214493936087799410602949295 Number of rattlers: 0 Minimal polynomial of cosine: 4x^4-4x^3-27x^2-2x+1 Known optimal: no References: 33 Dimension: 8 Number of points: 25 Angle in degrees: 80.54144251646111740436939861947493 Cosine: 0.16433417412503162111153267794066 Number of rattlers: 0 Minimal polynomial of cosine: 30767579136x^18+24142675968x^17-55382704128x^16-21789278208x^15+19306561536x^14+8502165504x^13-966488064x^12-884391936x^11-157079552x^10+15431680x^9+17445888x^8+1272832x^7-780672x^6-59776x^5+18624x^4+864x^3-220x^2-4x+1 Known optimal: no References: Dimension: 8 Number of points: 26 Angle in degrees: 80.05794659119825594712220494521577 Cosine: 0.17265209503507043373086916730531 Number of rattlers: 0 Minimal polynomial of cosine: 21504951447085138950750208x^40-238057277770143718264799232x^39-4383547284432462594002911232x^38-12014208460447347922176049152x^37-430476453797243831443259392x^36+13665695573901128204793413632x^35+6727353454184761158740738048x^34-2322442507908002209134018560x^33-1430918874612176982487597056x^32+513795007552116931094904832x^31+175308795674255260414640128x^30-116264106695350816430096384x^29-14871294076435946023157760x^28+16258542092999438716895232x^27-1190145923142014115774464x^26-1784184508632499620937728x^25+594147986827093357887488x^24+199702633537268172718080x^23-88069851122124093128704x^22-20657019153418800857088x^21+7741572829316890230784x^20+1653845452648483913728x^19-466768741874003869696x^18-97004979363491348480x^17+20625018126541520896x^16+4174030074526302208x^15-692874406813237248x^14-132972494382432256x^13+18040414292279296x^12+3143424127336448x^11-365646168203264x^10-54618057261056x^9+5701764259840x^8+679538786304x^7-66280071168x^6-5741376768x^5+540608256x^4+29548800x^3-2752704x^2-69984x+6561 Known optimal: no References: Dimension: 8 Number of points: 27 Angle in degrees: 79.63860105060775844503098580519417 Cosine: 0.17985645705828421512952134000393 Number of rattlers: 1 Minimal polynomial of cosine: 13221437821157376x^32-20301095675363328x^31-45539973097390080x^30+85671232651689984x^29+39058005311823872x^28-62415319523606528x^27-49397612527596544x^26-4668087974142464x^25+13372104238886400x^24+10535289848732416x^23+3184649526622336x^22-176932739052672x^21-500418041551424x^20-263444230968672x^19-102357661045348x^18-16806084814342x^17+7677522351888x^16+5338890032093x^15+1359278340599x^14+105717601621x^13-55593679261x^12-29401875175x^11-6894743533x^10-464557063x^9+180061947x^8+51312087x^7+4182309x^6-333321x^5-89679x^4-4941x^3+213x^2+33x+1 Known optimal: no References: Dimension: 8 Number of points: 28 Angle in degrees: 79.56275823883899610348089696851705 Cosine: 0.18115842002150127258095821368305 Number of rattlers: 0 Minimal polynomial of cosine: 36x^4+24x^3-36x^2+1 Known optimal: no References: Dimension: 8 Number of points: 29 Angle in degrees: 79.16814481342416346636186926617325 Cosine: 0.18792741558936484033926552129998 Number of rattlers: 0 Minimal polynomial of cosine: 1719926784x^16+6151127040x^15+5690539008x^14-883954944x^13-3468845952x^12-718437600x^11+790397772x^10+225963207x^9-100334293x^8-24178270x^7+8082650x^6+934619x^5-349129x^4+716x^3+4088x^2-64x-16 Known optimal: no References: Dimension: 8 Number of points: 30 Angle in degrees: 78.23393356566031386883522214201234 Cosine: 0.20391627940388098449483075238404 Number of rattlers: 0 Known optimal: no References: Dimension: 8 Number of points: 31 Angle in degrees: 77.30820071803608278685031586472905 Cosine: 0.21970657429991018286120539055796 Number of rattlers: 0 Known optimal: no References: Dimension: 8 Number of points: 32 Angle in degrees: 76.86033910977556120802212334482103 Cosine: 0.22732545202384657669029760629103 Number of rattlers: 0 Minimal polynomial of cosine: 95x^2-4x-4 Known optimal: no References: Dimension: 9 Number of points: 19 Angle in degrees: 85.46505241660988144988439695603464 Cosine: 0.07906715121746358947508550780826 Number of rattlers: 0 Minimal polynomial of cosine: 441x^3-81x^2-9x+1 Known optimal: no References: 8 Dimension: 9 Number of points: 20 Angle in degrees: 85.00504887023442958036688945019129 Cosine: 0.08706795832124714750492273563902 Number of rattlers: 0 Minimal polynomial of cosine: 63x^2+6x-1 Known optimal: no References: Dimension: 9 Number of points: 21 Angle in degrees: 85.00504887023442958036688945019129 Cosine: 0.08706795832124714750492273563902 Number of rattlers: 0 Minimal polynomial of cosine: 63x^2+6x-1 Known optimal: no References: Dimension: 9 Number of points: 22 Angle in degrees: 83.74144061078498175599806682372632 Cosine: 0.10901537523956808103629964436986 Number of rattlers: 0 Minimal polynomial of cosine: 662x^4+23x^3-67x^2-3x+1 Known optimal: no References: Dimension: 9 Number of points: 23 Angle in degrees: 83.43834176274170463729335671391570 Cosine: 0.11427236968530968639282662571064 Number of rattlers: 0 Minimal polynomial of cosine: 138601725696x^16+190276978176x^15+81726705216x^14-1109579904x^13-12081367908x^12-3601545032x^11-18274696x^10+190659516x^9+28416823x^8-4404944x^7-1681516x^6-103944x^5+21190x^4+3320x^3+28x^2-20x-1 Known optimal: no References: Dimension: 9 Number of points: 24 Angle in degrees: 82.69572003011940237898366484162956 Cosine: 0.12713870233144916446935012832137 Number of rattlers: 0 Known optimal: no References: Dimension: 9 Number of points: 25 Angle in degrees: 82.21526716285776604011270317876021 Cosine: 0.13545157071140596843926701196576 Number of rattlers: 0 Known optimal: no References: Dimension: 9 Number of points: 26 Angle in degrees: 81.56646252404429792600612337711779 Cosine: 0.14666206355598451422693622189428 Number of rattlers: 0 Known optimal: no References: Dimension: 9 Number of points: 27 Angle in degrees: 81.37451515992256032311509112656080 Cosine: 0.14997512190732167370329398866647 Number of rattlers: 0 Known optimal: no References: Dimension: 9 Number of points: 28 Angle in degrees: 81.36025988047509994374351806034096 Cosine: 0.15022110482233484500666951280126 Number of rattlers: 0 Minimal polynomial of cosine: 31x^2+2x-1 Known optimal: no References: Dimension: 9 Number of points: 29 Angle in degrees: 81.36025988047509994374351806034096 Cosine: 0.15022110482233484500666951280126 Number of rattlers: 0 Minimal polynomial of cosine: 31x^2+2x-1 Known optimal: no References: Dimension: 9 Number of points: 30 Angle in degrees: 81.36025988047509994374351806034096 Cosine: 0.15022110482233484500666951280126 Number of rattlers: 0 Minimal polynomial of cosine: 31x^2+2x-1 Known optimal: no References: Dimension: 9 Number of points: 31 Angle in degrees: 81.36025988047509994374351806034096 Cosine: 0.15022110482233484500666951280126 Number of rattlers: 0 Minimal polynomial of cosine: 31x^2+2x-1 Known optimal: no References: Dimension: 9 Number of points: 32 Angle in degrees: 81.36025988047509994374351806034096 Cosine: 0.15022110482233484500666951280126 Number of rattlers: 0 Minimal polynomial of cosine: 31x^2+2x-1 Known optimal: no References: 8 Dimension: 10 Number of points: 21 Angle in degrees: 85.86922756255215254252562467970065 Cosine: 0.07203313984214689097267814366206 Number of rattlers: 0 Minimal polynomial of cosine: 640x^3-100x^2-10x+1 Known optimal: no References: 8 Dimension: 10 Number of points: 22 Angle in degrees: 85.18399762239600994758481562639966 Cosine: 0.08395615471838847066948704055021 Number of rattlers: 0 Known optimal: no References: Dimension: 10 Number of points: 23 Angle in degrees: 85.01716307608855479434686116116361 Cosine: 0.08685732654080788416875987795916 Number of rattlers: 0 Known optimal: no References: Dimension: 10 Number of points: 24 Angle in degrees: 84.33510092628997408494182728050967 Cosine: 0.09871013349961574400220437104983 Number of rattlers: 1 Minimal polynomial of cosine: 613376x^8-228096x^7+40432x^6+16416x^5-8016x^4-216x^3+184x^2-1 Known optimal: no References: Dimension: 10 Number of points: 25 Angle in degrees: 84.00300089438494881057341225491142 Cosine: 0.10447637455518529630303057158420 Number of rattlers: 2 Known optimal: no References: Dimension: 10 Number of points: 26 Angle in degrees: 84.00292729231194909345418912755366 Cosine: 0.10447765212347525953178684587436 Number of rattlers: 2 Known optimal: no References: Dimension: 10 Number of points: 27 Angle in degrees: 82.86472401968381046705342077791511 Cosine: 0.12421241419098055856947587657933 Number of rattlers: 0 Known optimal: no References: Dimension: 10 Number of points: 28 Angle in degrees: 82.63217553629403240068661445184869 Cosine: 0.12823868446883383035640365542200 Number of rattlers: 0 Minimal polynomial of cosine: 92x^2-4x-1 Known optimal: no References: Dimension: 10 Number of points: 29 Angle in degrees: 82.49375262123563187253908379588596 Cosine: 0.13063429594350723450192868698071 Number of rattlers: 0 Minimal polynomial of cosine: 1048576x^13-7405568x^12+18612224x^11-25821184x^10+20357120x^9-9419776x^8+2347264x^7-166976x^6-60544x^5+15040x^4-568x^3-193x^2+26x-1 Known optimal: no References: Dimension: 10 Number of points: 30 Angle in degrees: 82.04243958547137508091683068558780 Cosine: 0.13843956089234491690957456895262 Number of rattlers: 0 Known optimal: no References: Dimension: 10 Number of points: 31 Angle in degrees: 81.71396932030560284629358122094045 Cosine: 0.14411493980324056199859132544531 Number of rattlers: 0 Minimal polynomial of cosine: 959694194388174715650339807402327771168x^64+16107292953152423257277423816358360385392x^63+90540360244591566249018316892243447613528x^62+197058346307242646657595663152311339442076x^61+110405400463645381591070759245747231918560x^60-231897028414934384777400732287564996612562x^59-405735069243610607042833386198372411316935x^58-131314557942710280076668264989757432652988x^57+209537900575210032585084408163105462618139x^56+210830041975412142706676211944399890537162x^55+12196374941154735183281887131247546733379x^54-82295757165824737663523081072999487026036x^53-41231303614626322543563814030707770027195x^52+9156198499440249037424682434288515225252x^51+15337364364034556712929671684745864103220x^50+3349834213299982669145540080060318503880x^49-2405686782841821113345262209462393244104x^48-1557149990243945648975295000094522637720x^47-48914578112423383986426975468405651416x^46+267789482303019988591473799301416789912x^45+93535355396355910767374749317692812216x^44-12615564052098176183836359396286826528x^43-17229133395243803394018113369780083040x^42-3358091308966245759721406950529646656x^41+1174967263348410092631693698246588608x^40+710048011698346101077459614492683808x^39+64026431151951375068677542096278416x^38-54662126163915752135256681251244992x^37-19859292602021158568093495091482096x^36-40118060335053859972863078980960x^35+1649498991816031541073987253690048x^34+387713961615344659578498501245344x^33-34993864858022141679005910084992x^32-35138048715209584513403387475008x^31-5243941450438182024018844229408x^30+1126722087398806589581281058048x^29+547408488266046553233758386336x^28+45348153507504662342436320128x^27-20809637725839678960316429376x^26-6299562017865557489004060032x^25-156647541799059189427658432x^24+262338263422946097751312768x^23+53014741185582228659637376x^22-1751480937140358197161088x^21-2353390159896238148690816x^20-314394317620977309238016x^19+32149138600220987153152x^18+14991210112852493639680x^17+1196716877062717284352x^16-256470594625851341312x^15-65366033814250521344x^14-2059597736935583744x^13+1203662104675501312x^12+177536820602930176x^11-3171102199536896x^10-3214914911171072x^9-249279077636864x^8+19586713318912x^7+4250558639872x^6+120626781184x^5-24882871040x^4-2182530048x^3+5866496x^2+7569408x+262144 Known optimal: no References: Dimension: 10 Number of points: 32 Angle in degrees: 81.54924887861374196351888585409882 Cosine: 0.14695924301669103564198244582096 Number of rattlers: 1 Minimal polynomial of cosine: 279x^4-420x^3+102x^2-1 Known optimal: no References: Dimension: 11 Number of points: 23 Angle in degrees: 86.20417042912042729212060451488947 Cosine: 0.06620127253123946651867717228392 Number of rattlers: 0 Minimal polynomial of cosine: 891x^3-121x^2-11x+1 Known optimal: no References: 8 Dimension: 11 Number of points: 24 Angle in degrees: 85.56679287692953277928081849687661 Cosine: 0.07729688069488853395571677916567 Number of rattlers: 0 Minimal polynomial of cosine: 308630377356759397764211223357x^54+1250056903993285440424882267506x^53+451292039064668138547999818511x^52-4547920040343804083169631697844x^51-5626565634710479301047529020265x^50+5722895114255640051007214751066x^49+13093586798768786756663935291581x^48-940135003800188601980533517648x^47-14738379000277117807078073016026x^46-4925238025492962657346761070868x^45+8878363958398281004073370302658x^44+5106412855379130112779751480344x^43-3379635397470323334474380551414x^42-2370821188042526192163815183732x^41+1538348642180283379811015956718x^40+1219388950591311271201663654384x^39-505541072768961703685592384689x^38-611940725177500458452809285866x^37-11356880213393086675575963211x^36+163048424579837532740090246132x^35+50880875111703587831629192277x^34-16303369047447452177010246050x^33-12499571953118467066476229657x^32-936846628550057753763599008x^31+1247140951992854755720566404x^30+371862130936411858661327240x^29-34711506423203157368176532x^28-36077756575137545648092848x^27-4099277399042241746375556x^26+1552870132400598980647432x^25+473345318816097215337556x^24-7366716486805066825376x^23-22133129409250421557877x^22-2551020705972905876482x^21+490281481175088474633x^20+137021779722001436404x^19-13758402687375279x^18-3558603380932936714x^17-315632746296438725x^16+47960610546958320x^15+9442533113071350x^14-135212425888820x^13-145622650373710x^12-6616087859176x^11+1290440327642x^10+125025072044x^9-5672798754x^8-1117518672x^7-2083511x^6+5657402x^5+151123x^4-15540x^3-669x^2+18x+1 Known optimal: no References: Dimension: 11 Number of points: 25 Angle in degrees: 85.20339725620965291421448003411845 Cosine: 0.08361875782883598879744264452381 Number of rattlers: 0 Known optimal: no References: Dimension: 11 Number of points: 26 Angle in degrees: 84.78132887746403773861380695926107 Cosine: 0.09095710678149019861518700080992 Number of rattlers: 0 Known optimal: no References: Dimension: 11 Number of points: 27 Angle in degrees: 84.45774803217907043974444006213338 Cosine: 0.09657976733774336498968777561990 Number of rattlers: 0 Known optimal: no References: Dimension: 11 Number of points: 28 Angle in degrees: 84.14207380255381358035583049749578 Cosine: 0.10206207261596575409155350311275 Number of rattlers: 4 Minimal polynomial of cosine: 96x^2-1 Known optimal: no References: Dimension: 11 Number of points: 29 Angle in degrees: 83.76699904422190494849921443855078 Cosine: 0.10857194419424991594861451754294 Number of rattlers: 3 Known optimal: no References: Dimension: 11 Number of points: 30 Angle in degrees: 83.62062979155719613171583346115651 Cosine: 0.11111111111111111111111111111112 Number of rattlers: 0 Minimal polynomial of cosine: 9x-1 Known optimal: no References: Dimension: 11 Number of points: 31 Angle in degrees: 83.28777079774670717422873522594895 Cosine: 0.11688271662887820937338660035349 Number of rattlers: 1 Minimal polynomial of cosine: 1880159x^4+662980x^3+23850x^2-9500x-625 Known optimal: no References: Dimension: 11 Number of points: 32 Angle in degrees: 82.69679003267851774601464010418772 Cosine: 0.12712017879076092950462557449550 Number of rattlers: 0 Known optimal: no References: Dimension: 12 Number of points: 25 Angle in degrees: 86.48660351232267423604065825066232 Cosine: 0.06128191457415120417840411389235 Number of rattlers: 0 Minimal polynomial of cosine: 1200x^3-144x^2-12x+1 Known optimal: no References: 8 Dimension: 12 Number of points: 26 Angle in degrees: 85.90395624184766728749502089192657 Cosine: 0.07142857142857142857142857142858 Number of rattlers: 0 Minimal polynomial of cosine: 14x-1 Known optimal: no References: 8 Dimension: 12 Number of points: 27 Angle in degrees: 85.71228435477866652047950625107686 Cosine: 0.07476492618150171900046741798712 Number of rattlers: 0 Known optimal: no References: Dimension: 12 Number of points: 28 Angle in degrees: 85.26241849962199173241062883459952 Cosine: 0.08259220626797780620169942560462 Number of rattlers: 0 Known optimal: no References: Dimension: 12 Number of points: 29 Angle in degrees: 85.16146608689673106871449037115439 Cosine: 0.08434800930948543817609523562697 Number of rattlers: 1 Minimal polynomial of cosine: 496x^4+92x^3-57x^2-8x+1 Known optimal: no References: Dimension: 12 Number of points: 30 Angle in degrees: 84.88548639117046286003528177685698 Cosine: 0.08914660143341378396187447349699 Number of rattlers: 2 Minimal polynomial of cosine: 3856x^4+1456x^3+100x^2-12x-1 Known optimal: no References: Dimension: 12 Number of points: 31 Angle in degrees: 84.33544882119447216179621892107059 Cosine: 0.09870409124008622425851938202713 Number of rattlers: 2 Minimal polynomial of cosine: 863x^2+6x-9 Known optimal: no References: Dimension: 12 Number of points: 32 Angle in degrees: 84.33544882119447216179621892107059 Cosine: 0.09870409124008622425851938202713 Number of rattlers: 2 Minimal polynomial of cosine: 863x^2+6x-9 Known optimal: no References: Dimension: 13 Number of points: 27 Angle in degrees: 86.72820743221797881588476373812048 Cosine: 0.05707252378225744920008530386950 Number of rattlers: 0 Minimal polynomial of cosine: 1573x^3-169x^2-13x+1 Known optimal: no References: 8 Dimension: 13 Number of points: 28 Angle in degrees: 86.17744627072565592258954502500064 Cosine: 0.06666666666666666666666666666667 Number of rattlers: 0 Minimal polynomial of cosine: 15x-1 Known optimal: no References: 8 Dimension: 13 Number of points: 29 Angle in degrees: 86.09521508953741869233276895693838 Cosine: 0.06809860947842661920489059247239 Number of rattlers: 0 Minimal polynomial of cosine: 2576x^4-640x^3-184x^2+1 Known optimal: no References: Dimension: 13 Number of points: 30 Angle in degrees: 85.88755834693804299033436911861864 Cosine: 0.07171403472725743246612172136228 Number of rattlers: 0 Minimal polynomial of cosine: 55x^2+10x-1 Known optimal: no References: Dimension: 13 Number of points: 31 Angle in degrees: 85.88755834693804299033436911861864 Cosine: 0.07171403472725743246612172136228 Number of rattlers: 0 Minimal polynomial of cosine: 55x^2+10x-1 Known optimal: no References: Dimension: 13 Number of points: 32 Angle in degrees: 85.88755834693804299033436911861864 Cosine: 0.07171403472725743246612172136228 Number of rattlers: 0 Minimal polynomial of cosine: 55x^2+10x-1 Known optimal: no References: 27 Dimension: 14 Number of points: 29 Angle in degrees: 86.93740093073654695880034161794277 Cosine: 0.05342698734150995608695304765938 Number of rattlers: 0 Minimal polynomial of cosine: 2016x^3-196x^2-14x+1 Known optimal: no References: 8 Dimension: 14 Number of points: 30 Angle in degrees: 86.41667830152802708533930034951524 Cosine: 0.06250000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 16x-1 Known optimal: no References: Dimension: 14 Number of points: 31 Angle in degrees: 86.12460899190957035070816310747061 Cosine: 0.06758677109098814555067432244432 Number of rattlers: 0 Known optimal: no References: Dimension: 14 Number of points: 32 Angle in degrees: 85.90382237711584907584146688399887 Cosine: 0.07143090184092342423297534986236 Number of rattlers: 0 Known optimal: no References: Dimension: 15 Number of points: 31 Angle in degrees: 87.12041292542000784714168523646969 Cosine: 0.05023712037295819182915747580845 Number of rattlers: 0 Minimal polynomial of cosine: 2535x^3-225x^2-15x+1 Known optimal: no References: 8 Dimension: 15 Number of points: 32 Angle in degrees: 86.62327786108254877209601095926377 Cosine: 0.05890080848833338725817955269602 Number of rattlers: 0 Known optimal: no References: Real projective codes Dimension: 3 Number of lines: 4 Angle in degrees: 70.52877936550930863075400066003756 Cosine: 0.33333333333333333333333333333334 Number of rattlers: 0 Minimal polynomial of cosine: 3x-1 Known optimal: yes References: 10, 34 Dimension: 3 Number of lines: 5 Angle in degrees: 63.43494882292201064842780627954670 Cosine: 0.44721359549995793928183473374626 Number of rattlers: 0 Minimal polynomial of cosine: 5x^2-1 Known optimal: yes References: 10 Dimension: 3 Number of lines: 6 Angle in degrees: 63.43494882292201064842780627954670 Cosine: 0.44721359549995793928183473374626 Number of rattlers: 0 Minimal polynomial of cosine: 5x^2-1 Known optimal: yes References: 10, 34 Dimension: 3 Number of lines: 7 Angle in degrees: 54.73561031724534568462299966998121 Cosine: 0.57735026918962576450914878050196 Number of rattlers: 0 Minimal polynomial of cosine: 3x^2-1 Known optimal: yes References: 10 Dimension: 3 Number of lines: 8 Angle in degrees: 49.63993310860389742493923002240324 Cosine: 0.64758897873417862734156471888316 Number of rattlers: 0 Minimal polynomial of cosine: 1537x^9+677x^8-584x^7-80x^6+146x^5-78x^4-80x^3-8x^2+5x+1 Known optimal: yes References: 6, 20 Dimension: 3 Number of lines: 9 Angle in degrees: 47.98213263901537661792294942878183 Cosine: 0.66936231928109901015298754554435 Number of rattlers: 0 Minimal polynomial of cosine: 13x^3+x^2-5x-1 Known optimal: no References: 6 Dimension: 3 Number of lines: 10 Angle in degrees: 46.67462012128404521093686093105504 Cosine: 0.68614066163450716496265286705474 Number of rattlers: 1 Minimal polynomial of cosine: 2x^2+3x-3 Known optimal: no References: 6 Dimension: 3 Number of lines: 11 Angle in degrees: 44.40312667538491787697365266830151 Cosine: 0.71443449739467850485464566840562 Number of rattlers: 0 Minimal polynomial of cosine: 5x^6+200x^5-115x^4-40x^3+15x^2-1 Known optimal: no References: 6 Dimension: 3 Number of lines: 12 Angle in degrees: 41.88204094448767774526036007277152 Cosine: 0.74452083820543412912980911157876 Number of rattlers: 0 Minimal polynomial of cosine: 17x^2-14x+1 Known optimal: no References: 6 Dimension: 3 Number of lines: 13 Angle in degrees: 39.81307975076508498806899179892640 Cosine: 0.76813737631458482294245319830313 Number of rattlers: 0 Minimal polynomial of cosine: x^5+13x^4+42x^3+42x^2-75x+9 Known optimal: no References: 6 Dimension: 3 Number of lines: 14 Angle in degrees: 38.68242186271878245469605694479806 Cosine: 0.78062219278523604521158858789220 Number of rattlers: 0 Minimal polynomial of cosine: 620141535144576532186425x^111+38068438093151880625170885x^110+922116325587625144662971112x^109+10663557538128920052284890668x^108+50176131816106177685896714351x^107-98709885374933604095613917541x^106+2961785945665870386284091194362x^105+174080475200140381482803232275038x^104+2704704670021673953617843745818691x^103+21380223943815998056386032213631863x^102+99466665211595135365371862858912068x^101+309353592251396003499135857985252096x^100+755537713372765069837359237866871781x^99+1440840991427446102154881766696385241x^98+1600625727651295242251048883983268498x^97+307661698789790518649588145669522894x^96-3057465648903772890793207844826201586x^95-11923148857522071724362634811048565322x^94-16589273082501028743242944835188645664x^93+8894868791840835519910357478295141272x^92+44821410812003253974206447254229369506x^91+29318903867953318764538973102713372042x^90-32571370242172886135753568200778386852x^89-65772341967031219603220346757894593452x^88-24743775302375785823448963535586900814x^87+56247470617886464426998386905230910634x^86+74405793352398862368630270078424953064x^85-14286028472166047422524070113282007408x^84-82789874598037368812893197707275347906x^83-20858000772573730428579518221863117770x^82+62244797249468694342196204772393015900x^81+34649234244419355459112562193984660356x^80-34718687624576487968820925353864680893x^79-32998860315109915337509073487060566585x^78+11541857159419463316205752250128325224x^77+23478764061836294629594372361889587156x^76+2394009483330911805451255977810811893x^75-12473355053608259568392427976990003751x^74-6847663920621925634792157473551521298x^73+4895557248841765788205919951266851130x^72+5930738264586504382504504562645381689x^71-1672392252209499709848111662037372075x^70-3953221357369824521777778924116053412x^69+801995693843009178209852480337607952x^68+2569217872503329101456945826896845119x^67-475012972888121224058133068924529381x^66-1659323592493843267526005745035054842x^65+184276921775900325616093971801613498x^64+954985119797274478297532130858815988x^63-8884204604629115575638559177116572x^62-453904331192783852256415943237352576x^61-31405790075434835463785956213280432x^60+177298296343911155099318925133197612x^59+16750926870808195594172933786091804x^58-60172302464800532610287856426348248x^57-2878975228931469663981518529175432x^56+19516110769132448717224535938728684x^55-1067553044131580007194584483639620x^54-6435291055556297347593517082117072x^53+918789098615574340952942921840160x^52+2082570540530861090274905556393652x^51-358172111770713539887205958714236x^50-610777845630980377597692820162328x^49+103272865554644876742076341382616x^48+154021435316860522471117280495279x^47-27602188795679222138509275947645x^46-33114371997454266655042242192712x^45+7907525869485973932320356782228x^44+6307681987383613840138674501353x^43-2320368653738625585053302319587x^42-1156871119610599917377001793610x^41+615606472938367740198340920946x^40+219748883306607459461001520645x^39-138572612709006885889495955407x^38-42361618635382916161883716292x^37+26424914542182366544738900128x^36+7674354737025496810478766227x^35-4415272110503818412420418561x^34-1262229004375640691994295554x^33+674713083105582064474928610x^32+195334967058175960822097438x^31-95311788729136547777624698x^30-30030418915580598914273120x^29+11822288844652217230953624x^28+4511358943150103661564690x^27-1153425151184092000767558x^26-604506189177915799021124x^25+70760404626329892081908x^24+65687390075031664235842x^23+7343723994949039610x^22-5379133889506557699224x^21-540586377304220037808x^20+308257696805237141806x^19+63172625967714800614x^18-10717093810505457668x^17-4064941144887620764x^16+101114077682589621x^15+163436080812387153x^14+9632704778109688x^13-4045809265043476x^12-521652283212333x^11+54579688576271x^10+12739420398882x^9-189803577290x^8-173364006241x^7-4932311133x^6+1320832676x^5+72580432x^4-5150167x^3-385171x^2+7722x+726 Known optimal: no References: 6 Dimension: 3 Number of lines: 15 Angle in degrees: 38.13494231207122157184699263557831 Cosine: 0.78655857113558130772653953634602 Number of rattlers: 0 Minimal polynomial of cosine: 725x^12+13490x^11+2464x^10-19426x^9+4429x^8+6132x^7-4728x^6+252x^5+1119x^4-454x^3+88x^2+6x-1 Known optimal: no References: 6 Dimension: 3 Number of lines: 16 Angle in degrees: 37.37736814064969564285713849493751 Cosine: 0.79465447229176612295553092832760 Number of rattlers: 0 Minimal polynomial of cosine: 45x^4-30x^2+1 Known optimal: no References: 6 Dimension: 4 Number of lines: 5 Angle in degrees: 75.52248781407007612122896520087283 Cosine: 0.25000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 4x-1 Known optimal: yes References: 34 Dimension: 4 Number of lines: 6 Angle in degrees: 70.52877936550930863075400066003756 Cosine: 0.33333333333333333333333333333334 Number of rattlers: 0 Minimal polynomial of cosine: 3x-1 Known optimal: yes References: 6, 11, 4 Dimension: 4 Number of lines: 7 Angle in degrees: 67.02134330823037957099598718897022 Cosine: 0.39038820320220756872767623199676 Number of rattlers: 0 Minimal polynomial of cosine: 4x^2+x-1 Known optimal: no References: 6 Dimension: 4 Number of lines: 8 Angle in degrees: 65.53019947929780834865078988055737 Cosine: 0.41421356237309504880168872420970 Number of rattlers: 0 Minimal polynomial of cosine: x^2+2x-1 Known optimal: no References: 6 Dimension: 4 Number of lines: 9 Angle in degrees: 64.26187661462771779834845404644122 Cosine: 0.43425854591066488218653687791175 Number of rattlers: 0 Minimal polynomial of cosine: 3x^2+x-1 Known optimal: no References: 6 Dimension: 4 Number of lines: 10 Angle in degrees: 64.26187661462771779834845404644122 Cosine: 0.43425854591066488218653687791175 Number of rattlers: 0 Minimal polynomial of cosine: 3x^2+x-1 Known optimal: no References: 6 Dimension: 4 Number of lines: 11 Angle in degrees: 60.00000000000000000000000000000000 Cosine: 0.50000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 2x-1 Known optimal: yes References: 6 Dimension: 4 Number of lines: 12 Angle in degrees: 60.00000000000000000000000000000000 Cosine: 0.50000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 2x-1 Known optimal: yes References: 25, 6 Dimension: 4 Number of lines: 13 Angle in degrees: 55.46460289540390742225599065742296 Cosine: 0.56691527068179906330992487897558 Number of rattlers: 1 Minimal polynomial of cosine: 11x^2-8x+1 Known optimal: no References: 6 Dimension: 4 Number of lines: 14 Angle in degrees: 53.83756185561468502789580068152968 Cosine: 0.59007651527101322282935291615497 Number of rattlers: 0 Minimal polynomial of cosine: 1024x^14-3008x^13+960x^12+5888x^11-5744x^10-3812x^9+6328x^8+552x^7-2728x^6-57x^5+605x^4+68x^3-56x^2-15x-1 Known optimal: no References: 6 Dimension: 4 Number of lines: 15 Angle in degrees: 52.50159006899752919534622790929021 Cosine: 0.60873941168052296928961201448826 Number of rattlers: 0 Minimal polynomial of cosine: 768x^10-256x^9-1984x^8+768x^7+1632x^6-728x^5-388x^4+240x^3-51x^2-18x+18 Known optimal: no References: 6 Dimension: 4 Number of lines: 16 Angle in degrees: 51.82729237298775250653169866714976 Cosine: 0.61803398874989484820458683436564 Number of rattlers: 1 Minimal polynomial of cosine: x^2+x-1 Known optimal: no References: 6 Dimension: 5 Number of lines: 6 Angle in degrees: 78.46304096718451230986262848948731 Cosine: 0.20000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 5x-1 Known optimal: yes References: 34 Dimension: 5 Number of lines: 7 Angle in degrees: 73.36891411676058928587218034313065 Cosine: 0.28620826421558111221120097995740 Number of rattlers: 0 Minimal polynomial of cosine: x^3-9x^2-x+1 Known optimal: yes References: 6, 19 Dimension: 5 Number of lines: 8 Angle in degrees: 70.80389108835636555759053705322263 Cosine: 0.32880251120576348843092644566680 Number of rattlers: 0 Minimal polynomial of cosine: 169x^7+27x^6-15x^5-21x^4-29x^3-7x^2+3x+1 Known optimal: no References: 6 Dimension: 5 Number of lines: 9 Angle in degrees: 70.52877936550930863075400066003756 Cosine: 0.33333333333333333333333333333334 Number of rattlers: 0 Minimal polynomial of cosine: 3x-1 Known optimal: no References: 6 Dimension: 5 Number of lines: 10 Angle in degrees: 70.52877936550930863075400066003756 Cosine: 0.33333333333333333333333333333334 Number of rattlers: 0 Minimal polynomial of cosine: 3x-1 Known optimal: yes References: 17, 34 Dimension: 5 Number of lines: 11 Angle in degrees: 67.25433424996223115606845660045316 Cosine: 0.38664119885581345037571121632975 Number of rattlers: 1 Minimal polynomial of cosine: 29x^5+43x^4-38x^3-10x^2+9x-1 Known optimal: no References: 6 Dimension: 5 Number of lines: 12 Angle in degrees: 67.02134330823037957099598718897022 Cosine: 0.39038820320220756872767623199676 Number of rattlers: 0 Minimal polynomial of cosine: 4x^2+x-1 Known optimal: no References: 6 Dimension: 5 Number of lines: 13 Angle in degrees: 65.73191170546411112226621768142922 Cosine: 0.41100667568798964514107873257679 Number of rattlers: 0 Minimal polynomial of cosine: 81x^7+189x^6-119x^5-75x^4+43x^3+15x^2-5x-1 Known optimal: no References: 6 Dimension: 5 Number of lines: 14 Angle in degrees: 65.72412595762296659871704684626071 Cosine: 0.41113055081625813204082106348155 Number of rattlers: 0 Minimal polynomial of cosine: 49x^4-26x^3-16x^2+10x-1 Known optimal: no References: 6 Dimension: 5 Number of lines: 15 Angle in degrees: 65.53019947929780834865078988055737 Cosine: 0.41421356237309504880168872420970 Number of rattlers: 0 Minimal polynomial of cosine: x^2+2x-1 Known optimal: no References: 6 Dimension: 5 Number of lines: 16 Angle in degrees: 63.43494882292201064842780627954670 Cosine: 0.44721359549995793928183473374626 Number of rattlers: 0 Minimal polynomial of cosine: 5x^2-1 Known optimal: yes References: 6 Dimension: 6 Number of lines: 7 Angle in degrees: 80.40593177313953855556147215930090 Cosine: 0.16666666666666666666666666666667 Number of rattlers: 0 Minimal polynomial of cosine: 6x-1 Known optimal: yes References: 34 Dimension: 6 Number of lines: 8 Angle in degrees: 76.05778989196194115112700228626424 Cosine: 0.24094310926034164895054811006593 Number of rattlers: 0 Minimal polynomial of cosine: 106x^6-264x^5-53x^4+84x^3+20x^2-4x-1 Known optimal: yes References: 6, 19 Dimension: 6 Number of lines: 9 Angle in degrees: 73.84373286559096880698918614084805 Cosine: 0.27825804947907715858960015942485 Number of rattlers: 0 Minimal polynomial of cosine: 18x^7-185x^6-222x^5+75x^4+150x^3+33x^2-10x-3 Known optimal: no References: 6 Dimension: 6 Number of lines: 10 Angle in degrees: 73.69345147611278435400760510932453 Cosine: 0.28077640640441513745535246399352 Number of rattlers: 0 Minimal polynomial of cosine: 2x^2+3x-1 Known optimal: no References: 6 Dimension: 6 Number of lines: 11 Angle in degrees: 71.56505117707798935157219372045329 Cosine: 0.31622776601683793319988935444328 Number of rattlers: 0 Minimal polynomial of cosine: 10x^2-1 Known optimal: no References: 6 Dimension: 6 Number of lines: 12 Angle in degrees: 71.56505117707798935157219372045329 Cosine: 0.31622776601683793319988935444328 Number of rattlers: 0 Minimal polynomial of cosine: 10x^2-1 Known optimal: no References: 6 Dimension: 6 Number of lines: 13 Angle in degrees: 70.52877936550930863075400066003756 Cosine: 0.33333333333333333333333333333334 Number of rattlers: 1 Minimal polynomial of cosine: 3x-1 Known optimal: no References: 6 Dimension: 6 Number of lines: 14 Angle in degrees: 70.52877936550930863075400066003756 Cosine: 0.33333333333333333333333333333334 Number of rattlers: 0 Minimal polynomial of cosine: 3x-1 Known optimal: no References: 6 Dimension: 6 Number of lines: 15 Angle in degrees: 70.52877936550930863075400066003756 Cosine: 0.33333333333333333333333333333334 Number of rattlers: 0 Minimal polynomial of cosine: 3x-1 Known optimal: no References: 6 Dimension: 6 Number of lines: 16 Angle in degrees: 70.52877936550930863075400066003756 Cosine: 0.33333333333333333333333333333334 Number of rattlers: 0 Minimal polynomial of cosine: 3x-1 Known optimal: yes References: 17, 34 Dimension: 7 Number of lines: 8 Angle in degrees: 81.78678929826181121096505051973983 Cosine: 0.14285714285714285714285714285715 Number of rattlers: 0 Minimal polynomial of cosine: 7x-1 Known optimal: yes References: 34 Dimension: 7 Number of lines: 9 Angle in degrees: 78.46304096718451230986262848948731 Cosine: 0.20000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 5x-1 Known optimal: yes References: 6, 4 Dimension: 7 Number of lines: 10 Angle in degrees: 76.34541525402449498693660266570047 Cosine: 0.23606797749978969640917366873128 Number of rattlers: 0 Minimal polynomial of cosine: x^2+4x-1 Known optimal: no References: 6 Dimension: 7 Number of lines: 11 Angle in degrees: 75.01791891615368019750800037747615 Cosine: 0.25851694486106515028856211348079 Number of rattlers: 0 Minimal polynomial of cosine: 76x^5-44x^4-31x^3+13x^2+3x-1 Known optimal: no References: 6 Dimension: 7 Number of lines: 12 Angle in degrees: 74.17337986812765503557560221279313 Cosine: 0.27272727272727272727272727272728 Number of rattlers: 0 Minimal polynomial of cosine: 11x-3 Known optimal: no References: 6 Dimension: 7 Number of lines: 13 Angle in degrees: 73.89788624801398471639314920558475 Cosine: 0.27735009811261456100917086672850 Number of rattlers: 0 Minimal polynomial of cosine: 13x^2-1 Known optimal: no References: 6 Dimension: 7 Number of lines: 14 Angle in degrees: 73.89788624801398471639314920558475 Cosine: 0.27735009811261456100917086672850 Number of rattlers: 0 Minimal polynomial of cosine: 13x^2-1 Known optimal: yes References: 17, 34 Dimension: 7 Number of lines: 15 Angle in degrees: 71.56775080024527214955571530032924 Cosine: 0.31618306625810221110773896871360 Number of rattlers: 0 Minimal polynomial of cosine: 5152x^8+4848x^7-3364x^6-2896x^5+1057x^4+572x^3-158x^2-36x+9 Known optimal: no References: 6 Dimension: 7 Number of lines: 16 Angle in degrees: 70.98610673394449611283192399424235 Cosine: 0.32579741728791719861570522781737 Number of rattlers: 0 Known optimal: no References: 6 Dimension: 8 Number of lines: 9 Angle in degrees: 82.81924421854171867696100437385144 Cosine: 0.12500000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 8x-1 Known optimal: yes References: 34 Dimension: 8 Number of lines: 10 Angle in degrees: 79.47036912306999346266936086218739 Cosine: 0.18274399763155681014833407039277 Number of rattlers: 0 Minimal polynomial of cosine: 19x^2+2x-1 Known optimal: no References: 6 Dimension: 8 Number of lines: 11 Angle in degrees: 77.86960404819235407696671759498103 Cosine: 0.21013725661767148165690452663564 Number of rattlers: 0 Minimal polynomial of cosine: 253342x^19-1560445x^18+25746x^17+10280209x^16+2786088x^15-26799812x^14-30699504x^13-4439348x^12+10256804x^11+5384474x^10-355532x^9-890634x^8-141496x^7+53068x^6+16672x^5-724x^4-690x^3-37x^2+10x+1 Known optimal: no References: Dimension: 8 Number of lines: 12 Angle in degrees: 76.60503138478824299023379147831469 Cosine: 0.23166247903553998491149327366707 Number of rattlers: 0 Minimal polynomial of cosine: 10x^2+2x-1 Known optimal: no References: 6 Dimension: 8 Number of lines: 13 Angle in degrees: 76.16887099561858389080144521373411 Cosine: 0.23906104311673605013508516180858 Number of rattlers: 0 Known optimal: no References: Dimension: 8 Number of lines: 14 Angle in degrees: 75.03494156434741140472444326408931 Cosine: 0.25822993164268312301618267398557 Number of rattlers: 0 Minimal polynomial of cosine: 1856x^11+7264x^10+184x^9-9760x^8-1448x^7+1785x^6+186x^5-17x^4+16x^3-17x^2-2x+1 Known optimal: no References: 6 Dimension: 8 Number of lines: 15 Angle in degrees: 74.33780449221571330243299474093471 Cosine: 0.26996519072292358265868340141656 Number of rattlers: 0 Known optimal: no References: Dimension: 8 Number of lines: 16 Angle in degrees: 74.10046152634479034474470141857092 Cosine: 0.27395147170889821586916164817386 Number of rattlers: 0 Minimal polynomial of cosine: 9x^4-14x^2+1 Known optimal: no References: 6 Dimension: 9 Number of lines: 10 Angle in degrees: 83.62062979155719613171583346115651 Cosine: 0.11111111111111111111111111111112 Number of rattlers: 0 Minimal polynomial of cosine: 9x-1 Known optimal: yes References: 34 Dimension: 9 Number of lines: 11 Angle in degrees: 80.62041468644675388022795488969295 Cosine: 0.16297443277324822659060918082968 Number of rattlers: 0 Minimal polynomial of cosine: 4049x^6-2188x^5-907x^4+208x^3+59x^2-4x-1 Known optimal: no References: 6 Dimension: 9 Number of lines: 12 Angle in degrees: 79.47036912306999346266936086218739 Cosine: 0.18274399763155681014833407039277 Number of rattlers: 0 Minimal polynomial of cosine: 19x^2+2x-1 Known optimal: yes References: 6, 4 Dimension: 9 Number of lines: 13 Angle in degrees: 77.94349477004604359437339329793022 Cosine: 0.20887624097518068198468149347108 Number of rattlers: 0 Known optimal: no References: Dimension: 9 Number of lines: 14 Angle in degrees: 77.23815708490940583219193003600005 Cosine: 0.22089903147727419339287508022539 Number of rattlers: 0 Minimal polynomial of cosine: 1948x^8-3089x^7+369x^6+1239x^5-231x^4-139x^3+27x^2+5x-1 Known optimal: no References: 6 Dimension: 9 Number of lines: 15 Angle in degrees: 76.50822887158298627567314413407969 Cosine: 0.23330570880288229977333738574545 Number of rattlers: 0 Known optimal: no References: Dimension: 9 Number of lines: 16 Angle in degrees: 75.96375653207352141710767984083657 Cosine: 0.24253562503633297351890646211613 Number of rattlers: 0 Minimal polynomial of cosine: 17x^2-1 Known optimal: no References: 6 Dimension: 10 Number of lines: 11 Angle in degrees: 84.26082952273321368748509109606960 Cosine: 0.10000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 10x-1 Known optimal: yes References: 34 Dimension: 10 Number of lines: 12 Angle in degrees: 81.78678929826181121096505051973983 Cosine: 0.14285714285714285714285714285715 Number of rattlers: 0 Minimal polynomial of cosine: 7x-1 Known optimal: yes References: 6, 4 Dimension: 10 Number of lines: 13 Angle in degrees: 80.05285623285759709241063942360213 Cosine: 0.17273960369212825269887122191439 Number of rattlers: 0 Minimal polynomial of cosine: 158x^5+349x^4+28x^3-38x^2-2x+1 Known optimal: no References: 6 Dimension: 10 Number of lines: 14 Angle in degrees: 79.01542372329351652480222333147543 Cosine: 0.19054473957762242321193235020642 Number of rattlers: 0 Minimal polynomial of cosine: 549015032919966508138027677096272016384x^84+6679897366741564542669179503619975672064x^83+18204064532670051706624005126594893268688x^82-41226321918585187491952527852914749154016x^81-309676799344329854634732833082047900405236x^80-579652469384463466729523793166508168989480x^79-192320984680828074315720279289724524876700x^78+666328606894112719661461254657260924647220x^77+587319582007024096311992585097072551804177x^76+80312374966214657933447293494421807794492x^75+2117541861269578856193675291427554785273940x^74+5286369783964828558083256333782184510699248x^73+2534334899699302962701778809962982615210610x^72-6297049932420282222611439739978276109843368x^71-9802003955724905080624132914886440867996208x^70-1929830066518532099787375282493559591156308x^69+7086823290090363698800387877121569083312433x^68+6185599716298329793884998682501500713427508x^67-867377281960267872274356507202018967474336x^66-3974253940801766931040571033044776837124432x^65-1498608885690605597844613947637139884584848x^64+1135174130289385494946009148938906599199328x^63+1074843147381610865468532766471926842907312x^62-22202563069898216309133559416849738786480x^61-374290714054113911200079956872967073797772x^60-112100868233691328004222130939184365552144x^59+75275899513599253611133723575145116852080x^58+50678941219684140032931956675205952160064x^57-5837133601845912913148056289317706852904x^56-13156305721385501065221404387866967338272x^55-1649424560328248413889887322927979395296x^54+2332435342712987636490040781587079396080x^53+765706373259878222807975540929574968868x^52-279806299002221725089130530892838273776x^51-176640311484655516515375758032493104960x^50+16604438108394935632249969053954942720x^49+29027747985771283279368340885400824024x^48+1668920470547361202117583624215987024x^47-3688461843479356164813539358115017704x^46-662983163324571663170459343027357288x^45+369431596736882303173053445262213774x^44+115755045621998306943652746110878216x^43-28385004177461287479632112465009096x^42-14652999255367573451274364798989408x^41+1452163571194008771261145895186892x^40+1485754346810150787463719085821648x^39-7379388250356194259006074509696x^38-124963368353449649563667836142232x^37-8595845904149874765548708108162x^36+8820521741431326201447090963032x^35+1204719378524791044255058393376x^34-521322383365384812529934319968x^33-109317168634861476450418321600x^32+25369212319556138374915759328x^31+7724557381519704131426927152x^30-972249943822614131528769776x^29-448475949668100785117076860x^28+25610068999288549600832048x^27+21850929779394410065205232x^26-150866740923546977602240x^25-901283007918243133519848x^24-29722602900362174616992x^23+31555579259631052209504x^22+2109704230628849486000x^21-937022607598102968940x^20-91179355041979527344x^19+23526026748878333680x^18+2963522946411978080x^17-497284457682777476x^16-76438056501634920x^15+8812660024804516x^14+1588832748571348x^13-130696299179927x^12-26567284875108x^11+1627657985044x^10+352162805488x^9-17173264174x^8-3590525032x^7+153787696x^6+26625356x^5-1123687x^4-128492x^3+5888x^2+304x-16 Known optimal: no References: Dimension: 10 Number of lines: 15 Angle in degrees: 78.77156770908704590339727960620247 Cosine: 0.19472111361678885284305008159890 Number of rattlers: 0 Minimal polynomial of cosine: 6x^3-7x^2-4x+1 Known optimal: no References: 6 Dimension: 10 Number of lines: 16 Angle in degrees: 78.46304096718451230986262848948731 Cosine: 0.20000000000000000000000000000000 Number of rattlers: 0 Minimal polynomial of cosine: 5x-1 Known optimal: yes References: 17, 34 Dimension: 11 Number of lines: 12 Angle in degrees: 84.78409142954587633484654697408818 Cosine: 0.09090909090909090909090909090910 Number of rattlers: 0 Minimal polynomial of cosine: 11x-1 Known optimal: yes References: 34 Dimension: 11 Number of lines: 13 Angle in degrees: 82.24200454869299084712048468871350 Cosine: 0.13498920127459953264187217399185 Number of rattlers: 0 Minimal polynomial of cosine: 89x^5-103x^4-138x^3-42x^2+x+1 Known optimal: no References: 6 Dimension: 11 Number of lines: 14 Angle in degrees: 80.92225381731771444800119529035526 Cosine: 0.15777454145867061988851120512478 Number of rattlers: 0 Minimal polynomial of cosine: x^3+21x^2+3x-1 Known optimal: no References: 6 Dimension: 11 Number of lines: 15 Angle in degrees: 79.96359256915856914076881879627022 Cosine: 0.17427391850565105193695154876787 Number of rattlers: 0 Minimal polynomial of cosine: 56804217966753831884369680610237588x^102+1600767894577143349780727874680377018x^101-119793196992507134288097116999737852x^100-168022541921533968359827412672799934309x^99-653885871887580416485634237875361334891x^98+4994343133448723885894806139085769150055x^97+35446290707750888838886455999836728899093x^96-6061953235029491167281725903713329807640x^95-567637511262670817012819045044697346126400x^94-1242461101478910803255462315650155808347488x^93+2278555040840862532930301456876363083641744x^92+11494956728294826376804968311653369223964620x^91+2630874135855686604348490957207179431757548x^90-50296707037580177515274724752254764261603588x^89-61521380634972578331527592018768514167195012x^88+132079119883804959048921323322692815942006584x^87+350987288350152189263202300865185186153583656x^86-37665368355328390267160535755087392588525988x^85-1005758748570082536631735923999977089340505640x^84-989976730078590865527021958209274930400398938x^83+1087476080043401308036810026389888824853577490x^82+2960452474557604157692410349447282402917951390x^81+1136914055774743115176352064191544027693484898x^80-3251142669458335581407562546976898231437864392x^79-4463732895049600472699456055058893044012614336x^78-123565557960623671688561244156132166380169104x^77+4593319744578910101776486387177287034656020336x^76+3843492688090437311298558642441871247949799292x^75-955313863742274971332078551203809105424279028x^74-3712331342416720013874232619686842478217345364x^73-1984891358390696612488477039914073470667858948x^72+1035018610243312986427603873317460507309162280x^71+1853823388849186286410163118867561714587912012x^70+611282155501781669821412107441137205517811102x^69-546347019162344173921534156224905517767290612x^68-589649802205120542447796066231576085721956923x^67-94891438402597778337928984391978442017762125x^66+175264449859949293950316487504858075704529945x^65+117884670956060375844254459222633924142534115x^64-3432153868968725422962012083142161465496176x^63-36932196599284014404681237962912501063013760x^62-13479316384600292427760721476875223342643584x^61+4944441452470433182580896530998085276123808x^60+5075831587233456840963800980300870618776088x^59+367396342393728762421720633194291593873176x^58-1109446027409578471247747242824158524584584x^57-400959503814562787254663694205168223273288x^56+146752206708282813042050160850566209326000x^55+133230298888610036838327690359159238963632x^54+5414390795068923736893176368054795007208x^53-26990849401661740105367348018546828806128x^52-8991063359222013182710942090473440575660x^51+2600459064601787134398534467170025696860x^50+2390878792698730287828733366594353817700x^49+233296176249026521082513008258331246460x^48-319900048226765126551188105043451948304x^47-121798368740858405356898983244181304960x^46+13262550429305590351432434036357274016x^45+19545978719442464304001213515367397856x^44+3163046484855372501004870409201812696x^43-1531780808658161335589835595243830472x^42-698866178424527285277186431160230984x^41+3048220965773324442199214674410776x^40+68317001297518552399078243732428752x^39+13785389733351449375230464832499436x^38-3109281201146908634185249451512042x^37-1703235166922386593857840782474532x^36-78607582360814049603459048076587x^35+107229862220629305934154247193931x^34+23621440518159344580601589849865x^33-2851584494233929503039217720277x^32-1853610867779236699663443114488x^31-126092783528327696342528400448x^30+78458448985800856872788812384x^29+17474851859899444805097891024x^28-1215253823468863444334657764x^27-925310149949245113758556804x^26-70385384513181660664387956x^25+26806903970696673359808844x^24+5820984243113426700190872x^23-222651906722604007805016x^22-211488114069384377092996x^21-16944189234589443313512x^20+4100843461203584393574x^19+878068974333937025714x^18-10829382020002712610x^17-21238203293887769534x^16-1825329535109191592x^15+250291913808649536x^14+56478894987291248x^13+765723885884336x^12-814344881005908x^11-79159581446340x^10+4048031918748x^9+1238555073644x^8+54140641672x^7-7108003916x^6-949035822x^5-22092908x^4+3556459x^3+345165x^2+12951x+189 Known optimal: no References: Dimension: 11 Number of lines: 16 Angle in degrees: 79.72373706200256566250187720629029 Cosine: 0.17839458616266547701324680749673 Number of rattlers: 0 Minimal polynomial of cosine: 9x^2+4x-1 Known optimal: no References: 6 Dimension: 12 Number of lines: 13 Angle in degrees: 85.21980815280084115760897153997236 Cosine: 0.08333333333333333333333333333334 Number of rattlers: 0 Minimal polynomial of cosine: 12x-1 Known optimal: yes References: 34 Dimension: 12 Number of lines: 14 Angle in degrees: 82.93741873504045562259719782856134 Cosine: 0.12295337815830641009836335476174 Number of rattlers: 0 Minimal polynomial of cosine: 32666x^6-8248x^5-3781x^4+388x^3+116x^2-4x-1 Known optimal: no References: Dimension: 12 Number of lines: 15 Angle in degrees: 81.59287205432104507399220453738513 Cosine: 0.14620609896519678926426427287249 Number of rattlers: 0 Minimal polynomial of cosine: 18898x^6+2762x^5-2709x^4-312x^3+92x^2+6x-1 Known optimal: no References: Dimension: 12 Number of lines: 16 Angle in degrees: 80.71566582334384874476081260487622 Cosine: 0.16133398878131368888992070727444 Number of rattlers: 0 Minimal polynomial of cosine: 9814x^8+284x^7-6059x^6-180x^5+917x^4-108x^3-65x^2+4x+1 Known optimal: no References: 6 Dimension: 13 Number of lines: 14 Angle in degrees: 85.58827421422982354574618634815500 Cosine: 0.07692307692307692307692307692308 Number of rattlers: 0 Minimal polynomial of cosine: 13x-1 Known optimal: yes References: 34 Dimension: 13 Number of lines: 15 Angle in degrees: 83.62062979155719613171583346115651 Cosine: 0.11111111111111111111111111111112 Number of rattlers: 0 Minimal polynomial of cosine: 9x-1 Known optimal: yes References: 6, 4 Dimension: 13 Number of lines: 16 Angle in degrees: 82.24156501008816166112574485178805 Cosine: 0.13499680245071983220881421251035 Number of rattlers: 0 Minimal polynomial of cosine: 11579x^8-18738x^7-22330x^6-2658x^5+1988x^4+282x^3-70x^2-6x+1 Known optimal: no References: 6 Dimension: 14 Number of lines: 15 Angle in degrees: 85.90395624184766728749502089192657 Cosine: 0.07142857142857142857142857142858 Number of rattlers: 0 Minimal polynomial of cosine: 14x-1 Known optimal: yes References: 34 Dimension: 14 Number of lines: 16 Angle in degrees: 83.89024189667627996319554855956316 Cosine: 0.10643341651544703618977147422985 Number of rattlers: 0 Minimal polynomial of cosine: 1078x^5-398x^4-397x^3-71x^2+3x+1 Known optimal: no References: 6 Dimension: 15 Number of lines: 16 Angle in degrees: 86.17744627072565592258954502500064 Cosine: 0.06666666666666666666666666666667 Number of rattlers: 0 Minimal polynomial of cosine: 15x-1 Known optimal: yes References: 34