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100573 bytes, as of the version from 2026-10-25 08:29 (current). Recorded here, not run.
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{
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{
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"sloane_agrees_7_decimals": true
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{
"n": 100,
"coordinate_minus_expected_cosine": "[+/- 1.44e-12]",
"squared_norm_error": "[3.9592836326593054802500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-16 +/- 5.35e-231]",
"difference_from_sloane_degrees": "[1.5264263822919576267227103226314029553777956022901242193923028286741096504818481627256870270456544581228302017913652241845320752144015140534790521566375069480681984644532489299030337014125584582041902336164810843709189e-10 +/- 2.78e-228]",
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],
"Numbers": {
"4": {
"angle": {
"number": "109.4712206344906913692459993399624359630068431009079482881711063560397464380603955633618712883605876",
"comment": "The regular tetrahedron has $\\cos(\\pi\\theta_4/180)=-1/3$ and $d_4=\\sqrt{8/3}$. Optimality is proven CITE{FejesToth}."
},
"chord": {
"number": "1.632993161855452065464856049803927594643964987104446752288461711500640251638210017693239622069760157",
"comment": "The regular tetrahedron has $\\cos(\\pi\\theta_4/180)=-1/3$ and $d_4=\\sqrt{8/3}$. Optimality is proven CITE{FejesToth}."
}
},
"5": {
"angle": {
"number": "90",
"comment": "$\\theta_n=90$ and $d_n=\\sqrt2$. Optimality is proven CITE{Schutte} CITE{FejesToth}."
},
"chord": {
"number": "1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573",
"comment": "$\\theta_n=90$ and $d_n=\\sqrt2$. Optimality is proven CITE{Schutte} CITE{FejesToth}."
}
},
"6": {
"angle": {
"number": "90",
"comment": "$\\theta_n=90$ and $d_n=\\sqrt2$. Optimality is proven CITE{Schutte} CITE{FejesToth}."
},
"chord": {
"number": "1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573",
"comment": "$\\theta_n=90$ and $d_n=\\sqrt2$. Optimality is proven CITE{Schutte} CITE{FejesToth}."
}
},
"7": {
"angle": {
"number": "77.86954215542338680591828838037453919424590740642133591865073074314973538311781413484159439425902080",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $3x^{3}-9x^{2}-3x+1$ in $(0.210138312731-10^{-10},0.210138312731+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Schutte}."
},
"chord": {
"number": "1.256870468480660034904024544082533192335643253156436631660011061050399906071854844332135412434113098",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $3x^{3}-9x^{2}-3x+1$ in $(0.210138312731-10^{-10},0.210138312731+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Schutte}."
}
},
"8": {
"angle": {
"number": "74.85849218561553500792611345605364079751084282049393387781847245319275920507463481339684227896154942",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $7x^{2}+2x-1$ in $(0.261203874964-10^{-10},0.261203874964+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Schutte}."
},
"chord": {
"number": "1.215562524131324605953884044732586661891605201667569759533735165691857679343105190624294468375968250",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $7x^{2}+2x-1$ in $(0.261203874964-10^{-10},0.261203874964+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Schutte}."
}
},
"9": {
"angle": {
"number": "70.52877936550930863075400066003756403699315689909205171182889364396025356193960443663812871163941235",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $3x-1$ in $(0.333333333334-10^{-10},0.333333333334+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Schutte}."
},
"chord": {
"number": "1.154700538379251529018297561003914911295203502540253752037204652967955344605866691387430791171499050",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $3x-1$ in $(0.333333333334-10^{-10},0.333333333334+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Schutte}."
}
},
"10": {
"angle": {
"number": "66.14682198789054287220577533235752791223071708063365606081265231850570982361238460449340260549072983",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $7x^{3}-4x^{2}-2x+1$ in $(0.404394325217-10^{-10},0.404394325217+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Danzer}."
},
"chord": {
"number": "1.091426291403821042434682867757394743310099228970515891159497186619426980252598733761621464267204957",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $7x^{3}-4x^{2}-2x+1$ in $(0.404394325217-10^{-10},0.404394325217+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Danzer}."
}
},
"11": {
"angle": {
"number": "63.43494882292201064842780627954670532879578570035477897201398368471193417851525938829142618939783528",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $5x^{2}-1$ in $(0.447213595500-10^{-10},0.447213595500+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Danzer}."
},
"chord": {
"number": "1.051462224238267212051338169695753214570995864486683563057871046482422292806428036743265257663105142",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $5x^{2}-1$ in $(0.447213595500-10^{-10},0.447213595500+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Danzer}."
}
},
"12": {
"angle": {
"number": "63.43494882292201064842780627954670532879578570035477897201398368471193417851525938829142618939783528",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $5x^{2}-1$ in $(0.447213595500-10^{-10},0.447213595500+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{FejesToth}."
},
"chord": {
"number": "1.051462224238267212051338169695753214570995864486683563057871046482422292806428036743265257663105142",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $5x^{2}-1$ in $(0.447213595500-10^{-10},0.447213595500+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{FejesToth}."
}
},
"13": {
"angle": {
"number": "57.13670307757834201767700274322533597760711636528224555516565534861346950278936664449157529803315396",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $x^{8}-24x^{7}-12x^{6}+8x^{5}+38x^{4}+24x^{3}-12x^{2}-8x+1$ in $(0.542636486830-10^{-10},0.542636486830+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Musin13}."
},
"chord": {
"number": "0.9564136272244990720875205665808557947269876360823935179447247145199889402438175360251024534129268150",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $x^{8}-24x^{7}-12x^{6}+8x^{5}+38x^{4}+24x^{3}-12x^{2}-8x+1$ in $(0.542636486830-10^{-10},0.542636486830+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Musin13}."
}
},
"14": {
"angle": {
"number": "55.67056999565952572422946524468126528134983339933129590091570352836575510701258072290020366120459492",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $4x^{4}-2x^{3}+3x^{2}-1$ in $(0.563950300361-10^{-10},0.563950300361+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Musin14}."
},
"chord": {
"number": "0.9338626233440278688077841691123048999950999946977422766327774075751129850007292358699087911906913833",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $4x^{4}-2x^{3}+3x^{2}-1$ in $(0.563950300361-10^{-10},0.563950300361+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Musin14}."
}
},
"15": {
"angle": {
"number": "53.65785012993267380552604148370299303169577018942255647465603609403395050000327059497239044377493759",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $13x^{5}-x^{4}+6x^{3}+2x^{2}-3x-1$ in $(0.592605902926-10^{-10},0.592605902926+10^{-10})$ CITE{Cohn}. Cohn marks this configuration as optimal, citing the 2026 preprint CITE{Tammes15}; that proof claim is distinguished here from the established published cases."
},
"chord": {
"number": "0.9026561882299663511276264760307219938239215614122841771344488235999651726273727841908295218026690448",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $13x^{5}-x^{4}+6x^{3}+2x^{2}-3x-1$ in $(0.592605902926-10^{-10},0.592605902926+10^{-10})$ CITE{Cohn}. Cohn marks this configuration as optimal, citing the 2026 preprint CITE{Tammes15}; that proof claim is distinguished here from the established published cases."
}
},
"16": {
"angle": {
"number": "52.24439575272065377204341696894192408372344517847959576403435169874430504823078187364332134385647256",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $23x^{6}+6x^{5}+5x^{4}+4x^{3}-3x^{2}-2x-1$ in $(0.612294616483-10^{-10},0.612294616483+10^{-10})$ CITE{Cohn}."
},
"chord": {
"number": "0.8805741121760318749621097470943480162399443231658259154473708725447978848627326948539161468949108172",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $23x^{6}+6x^{5}+5x^{4}+4x^{3}-3x^{2}-2x-1$ in $(0.612294616483-10^{-10},0.612294616483+10^{-10})$ CITE{Cohn}."
}
},
"17": {
"angle": {
"number": "51.09032855162777854657552387628875512696140109538242717714956916962016320304792956793687517468126625",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $4x^{10}-92x^{9}+24x^{8}+128x^{7}-58x^{6}-78x^{5}+35x^{4}+32x^{3}-4x^{2}-6x-1$ in $(0.628094415071-10^{-10},0.628094415071+10^{-10})$ CITE{Cohn}."
},
"chord": {
"number": "0.8624448793169084073408845262983338825653241623297785110129646186099117287685098483793368096561656861",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $4x^{10}-92x^{9}+24x^{8}+128x^{7}-58x^{6}-78x^{5}+35x^{4}+32x^{3}-4x^{2}-6x-1$ in $(0.628094415071-10^{-10},0.628094415071+10^{-10})$ CITE{Cohn}."
}
},
"18": {
"angle": {
"number": "49.55665476843424246091024211381574183273081464780093027384950985046921349197025762588699604800221768",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $216x^{11}+108x^{10}+118x^{9}+209x^{8}-100x^{7}-160x^{6}+40x^{5}+46x^{4}-20x^{3}-12x^{2}+2x+1$ in $(0.648695832224-10^{-10},0.648695832224+10^{-10})$ CITE{Cohn}."
},
"chord": {
"number": "0.8382173557936908656657105762753363318752035308224810456154185138534639771572551133316250127721611622",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $216x^{11}+108x^{10}+118x^{9}+209x^{8}-100x^{7}-160x^{6}+40x^{5}+46x^{4}-20x^{3}-12x^{2}+2x+1$ in $(0.648695832224-10^{-10},0.648695832224+10^{-10})$ CITE{Cohn}."
}
},
"19": {
"angle": {
"number": "47.69191410876624840141630606242048882455884334136696319819462117952532994830283236056716513807861562",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
},
"chord": {
"number": "0.8085581147202085326048189225383308759118591759714600683835929868359128245208954494958900105844163022",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
}
},
"20": {
"angle": {
"number": "47.43103622671058794874110898739208056495251708472259489802058097854051803072851876177063163448720652",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $21x^{3}-9x^{2}-5x+1$ in $(0.676477138130-10^{-10},0.676477138130+10^{-10})$ CITE{Cohn}."
},
"chord": {
"number": "0.8043915239115197786798331800377488477071546465562427822662686942369865463034830685161557357134335496",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $21x^{3}-9x^{2}-5x+1$ in $(0.676477138130-10^{-10},0.676477138130+10^{-10})$ CITE{Cohn}."
}
},
"21": {
"angle": {
"number": "45.61322311"
},
"chord": {
"number": "0.7752439215"
}
},
"22": {
"angle": {
"number": "44.74016116716264539249224387535237040533603841148933744771629301307369978526494619388751795720465498",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $486x^{18}+13113x^{17}+114996x^{16}+117476x^{15}+658256x^{14}+378752x^{13}-347056x^{12}-121388x^{11}+81724x^{10}-70886x^{9}-55992x^{8}+12716x^{7}+6528x^{6}-2392x^{5}-208x^{4}+284x^{3}+14x^{2}+5x+4$ in $(0.710306258580-10^{-10},0.710306258580+10^{-10})$ CITE{Cohn}."
},
"chord": {
"number": "0.7611750671433078531679774887287235136368490028296560006502358555380840221519648322824553029290166432",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $486x^{18}+13113x^{17}+114996x^{16}+117476x^{15}+658256x^{14}+378752x^{13}-347056x^{12}-121388x^{11}+81724x^{10}-70886x^{9}-55992x^{8}+12716x^{7}+6528x^{6}-2392x^{5}-208x^{4}+284x^{3}+14x^{2}+5x+4$ in $(0.710306258580-10^{-10},0.710306258580+10^{-10})$ CITE{Cohn}."
}
},
"23": {
"angle": {
"number": "43.70996421"
},
"chord": {
"number": "0.7445173136"
}
},
"24": {
"angle": {
"number": "43.69076710767579618171644921518231448443934426057622589508560623880706548956391472616352325219452075",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $7x^{3}+x^{2}-3x-1$ in $(0.723078468334-10^{-10},0.723078468334+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Robinson}."
},
"chord": {
"number": "0.7442063311562075967551192250788305032776327199015088815823724075583781520771015804522782613296565679",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $7x^{3}+x^{2}-3x-1$ in $(0.723078468334-10^{-10},0.723078468334+10^{-10})$ CITE{Cohn}. Optimality is proven CITE{Robinson}."
}
},
"25": {
"angle": {
"number": "41.63446125970606406767024214741580439206152387118051048191563247810318655999535762806209426164383366",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
},
"chord": {
"number": "0.7107761552303330599427222043473561053795135178734944886026131510343220056811048133280791217219247887",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
}
},
"26": {
"angle": {
"number": "41.03766160675250218608721374440023245934261213702983507114556637137177434726900940710701626633877561",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
},
"chord": {
"number": "0.7010304171431628833141504526901419067964211066931217182959544662804611207665636461719674450599193749",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
}
},
"27": {
"angle": {
"number": "40.67760068512674658008426875219181826237202623047945250561214975101720910728948644177296019178585591",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
},
"chord": {
"number": "0.6951414089570876888852481195205176391528617110516831083289331865074355279714766615139851438523810348",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
}
},
"28": {
"angle": {
"number": "39.35514357"
},
"chord": {
"number": "0.6734533951"
}
},
"29": {
"angle": {
"number": "38.71365119"
},
"chord": {
"number": "0.6629005718"
}
},
"30": {
"angle": {
"number": "38.59711595386765606658303351176410722068094792113867161902240174454545275938897731504661824649471709",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
},
"chord": {
"number": "0.6609812779572696382718134325081396164782068706854392768941802836820873489371734658926068123699771659",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
}
},
"31": {
"angle": {
"number": "37.70982914370989458237011117017694655887335581557542773980966980224966084907075333286193910627414486",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
},
"chord": {
"number": "0.6463457073444907495878761799859959746226221969240235534291369756195496148457204439825550738103842041",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
}
},
"32": {
"angle": {
"number": "37.47521397487154131177437208730674048457529757692086861566553292771657980069388220402500232544887019",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
},
"chord": {
"number": "0.6424692757303458159434634750035208230179756704754858423655962813857269946389544403723583796118628602",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
}
},
"33": {
"angle": {
"number": "36.25455298"
},
"chord": {
"number": "0.6222578024"
}
},
"34": {
"angle": {
"number": "35.80778440"
},
"chord": {
"number": "0.6148425210"
}
},
"35": {
"angle": {
"number": "35.31980759"
},
"chord": {
"number": "0.6067326075"
}
},
"36": {
"angle": {
"number": "35.18973226"
},
"chord": {
"number": "0.6045689617"
}
},
"37": {
"angle": {
"number": "34.42240801"
},
"chord": {
"number": "0.5917896920"
}
},
"38": {
"angle": {
"number": "34.25066067222863122268183736668475604863630632810011398334707877088116648114477850843863955089954015",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $363x^{14}+7685x^{12}+34299x^{10}-77139x^{8}+68985x^{6}-31833x^{4}+6561x^{2}-729$ in $(0.826583259422-10^{-10},0.826583259422+10^{-10})$ CITE{Cohn}."
},
"chord": {
"number": "0.5889257008796497051926213773453604457703941908248557329352616866483774123559375006793547196752065076",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $363x^{14}+7685x^{12}+34299x^{10}-77139x^{8}+68985x^{6}-31833x^{4}+6561x^{2}-729$ in $(0.826583259422-10^{-10},0.826583259422+10^{-10})$ CITE{Cohn}."
}
},
"39": {
"angle": {
"number": "33.48904658"
},
"chord": {
"number": "0.5762094716"
}
},
"40": {
"angle": {
"number": "33.15835626"
},
"chord": {
"number": "0.5706801688"
}
},
"41": {
"angle": {
"number": "32.72909442"
},
"chord": {
"number": "0.5634956202"
}
},
"42": {
"angle": {
"number": "32.50638634974149291094556186886744874622303767263225252061844035564707386377695798244050963969050693",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
},
"chord": {
"number": "0.5597650370666593981132760330640500424180665121937637350403067449216294517833435746995413308835462916",
"comment": "The cosine $c_n=\\cos(\\pi\\theta_n/180)$ is algebraic. Its polynomial and isolating interval are specified in the attached sources.json and generate.py CITE{Cohn}."
}
},
"43": {
"angle": {
"number": "32.09062441"
},
"chord": {
"number": "0.5527949612"
}
},
"44": {
"angle": {
"number": "31.98342303"
},
"chord": {
"number": "0.5509965911"
}
},
"45": {
"angle": {
"number": "31.32308143"
},
"chord": {
"number": "0.5399083736"
}
},
"46": {
"angle": {
"number": "30.95916349"
},
"chord": {
"number": "0.5337899084"
}
},
"47": {
"angle": {
"number": "30.78181596"
},
"chord": {
"number": "0.5308062520"
}
},
"48": {
"angle": {
"number": "30.76278555063470255272279475166525256460496249397517001625032210918509447938903220881838309834643441",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $34x^{5}+15x^{4}-12x^{3}-14x^{2}-6x-1$ in $(0.859292295076-10^{-10},0.859292295076+10^{-10})$ CITE{Cohn}."
},
"chord": {
"number": "0.5304860128680869911358365318309447191565187367298696885292842813336946860025663196956216413275569364",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $34x^{5}+15x^{4}-12x^{3}-14x^{2}-6x-1$ in $(0.859292295076-10^{-10},0.859292295076+10^{-10})$ CITE{Cohn}."
}
},
"49": {
"angle": {
"number": "29.92358511"
},
"chord": {
"number": "0.5163497283"
}
},
"50": {
"angle": {
"number": "29.75295639697365612330731744297445625024915826185666920679022507054042258853757167946710208712158170",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $386x^{12}+1679x^{11}+6433x^{10}-743x^{9}-2287x^{8}-19290x^{7}+8490x^{6}+19170x^{5}-5580x^{4}-6885x^{3}-1755x^{2}+2997x-567$ in $(0.868173209127-10^{-10},0.868173209127+10^{-10})$ CITE{Cohn}."
},
"chord": {
"number": "0.5134720846805647881992541205653954233345131537543003582529503063769833734110944962677356138605248128",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $386x^{12}+1679x^{11}+6433x^{10}-743x^{9}-2287x^{8}-19290x^{7}+8490x^{6}+19170x^{5}-5580x^{4}-6885x^{3}-1755x^{2}+2997x-567$ in $(0.868173209127-10^{-10},0.868173209127+10^{-10})$ CITE{Cohn}."
}
},
"51": {
"angle": {
"number": "29.36840688"
},
"chord": {
"number": "0.5069825146"
}
},
"52": {
"angle": {
"number": "29.19475790534553237106281307477898182637601182239826492917397555907891150912476625291156229181265596",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $448001x^{16}+1243448x^{15}+2260200x^{14}+2517944x^{13}+1365340x^{12}-424904x^{11}-1782664x^{10}-1847944x^{9}-864186x^{8}-12568x^{7}+192280x^{6}+95976x^{5}+19676x^{4}+936x^{3}-248x^{2}-24x+1$ in $(0.872966708781-10^{-10},0.872966708781+10^{-10})$ CITE{Cohn}."
},
"chord": {
"number": "0.5040501784938189268309565236802392569339516330211263126733164376069960843951079997625282798520778085",
"comment": "With $c_n=\\cos(\\pi\\theta_n/180)$, $c_n$ is the unique zero of $448001x^{16}+1243448x^{15}+2260200x^{14}+2517944x^{13}+1365340x^{12}-424904x^{11}-1782664x^{10}-1847944x^{9}-864186x^{8}-12568x^{7}+192280x^{6}+95976x^{5}+19676x^{4}+936x^{3}-248x^{2}-24x+1$ in $(0.872966708781-10^{-10},0.872966708781+10^{-10})$ CITE{Cohn}."
}
},
"53": {
"angle": {
"number": "28.81389721"
},
"chord": {
"number": "0.4976147024"
}
},
"54": {
"angle": {
"number": "28.71692053"
},
"chord": {
"number": "0.4959751882"
}
},
"55": {
"angle": {
"number": "28.26279142"
},
"chord": {
"number": "0.4882928496"
}
},
"56": {
"angle": {
"number": "28.14804665"
},
"chord": {
"number": "0.4863505353"
}
},
"57": {
"angle": {
"number": "27.82667595"
},
"chord": {
"number": "0.4809080211"
}
},
"58": {
"angle": {
"number": "27.55641596"
},
"chord": {
"number": "0.4763281533"
}
},
"59": {
"angle": {
"number": "27.39497567"
},
"chord": {
"number": "0.4735910955"
}
},
"60": {
"angle": {
"number": "27.19283000"
},
"chord": {
"number": "0.4701625940"
}
},
"61": {
"angle": {
"number": "26.87327787"
},
"chord": {
"number": "0.4647398341"
}
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