Lfunction data - 1-4033-4033.1494-r0-0-0

Formats: - HTML - YAML - JSON - 2024-06-05T07:05:43.258707

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': 'dirichlet_L_4033.1494', 'a10': [-0.984807753012208, 0.17364817766693036], 'a2': [0.5, -0.8660254037844386], 'a3': [0.9396926207859084, 0.3420201433256687], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.6427876096865394, -0.766044443118978], 'a6': [0.766044443118978, -0.6427876096865394], 'a7': [0.766044443118978, -0.6427876096865394], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [0.766044443118978, 0.6427876096865394], 'algebraic': True, 'analytic_conductor': 18.729173260907245, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.1494', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.2524', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^30', 'a^2', 'a^24', 'a^23', 'a^32', 'a^32', 'a^18', 'a^4', 'a^17', 'a^1', 'a^26', 'a^14', 'a^26', 'a^25', 'a^12', 'a^12', 'a^34', 'a^18', 'a^11', 'a^34', 'a^31', 'a^12', 'a^20', 'a^10', 'a^8', 'a^6', 'a^20', 'a^35', 'a^19', 'a^7', 'a^6', 'a^3', 'a^6', 'a^19', 'a^28', 0, 'a^12', 'a^16', 'a^5', 'a^3', 'a^28', 'a^33', 'a^25', 'a^27', 'a^6', 'a^13', 'a^14', 'a^28', 'a^4', 'a^14', 'a^2', 'a^17', 'a^0', 'a^24', 'a^14', 'a^20', 'a^29', 'a^34', 'a^13', 'a^35', 'a^1', 'a^0', 'a^0', 'a^1', 'a^33', 'a^1', 'a^0', 'a^14', 'a^13', 'a^6', 'a^22', 'a^10', 0, 'a^12', 'a^6', 'a^33', 'a^10', 'a^10', 'a^35', 'a^8', 'a^33', 'a^14', 'a^22', 'a^35', 'a^27', 'a^1', 'a^19', 'a^29', 'a^21', 'a^10', 'a^0', 'a^9', 'a^7', 'a^5', 'a^8', 'a^11', 'a^22', 'a^5', 'a^34'], 'euler_factors': [[1, 'a^30'], [1, 'a^2'], [1, 'a^23'], [1, 'a^32'], [1, 'a^1'], [1, 'a^14'], [1, 'a^12'], [1, 'a^18'], [1, 'a^12'], [1, 'a^35'], [1, 'a^7'], [0], [1, 'a^3'], [1, 'a^33'], [1, 'a^13'], [1, 'a^17'], [1, 'a^34'], [1, 'a^35'], [1, 'a^1'], [1, 'a^6'], [1, 'a^10'], [1, 'a^10'], [1, 'a^14'], [1, 'a^29'], [1, 'a^11'], [1, 'a^27']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4033-4033.1494-r0-0-0', 'leading_term': '2.65353854690243177430058590534-0.639454670054731571988167750095*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/4033/1494', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.7294997884139636, 3.0278194158651823, 2.438881065220197, 0.8201812967852573, -0.5160672795767394, -0.4060665237177334, 0.6322839891402059, 0.9205909549529456, -0.3128629199960006, -1.864083480836721, -2.0035943115825905, -0.7051452300067083, 0.3695840439041119, 0.24503283693560082, -0.018558800807317546, 0.7531721215526291, 1.3035664139099399, -0.9069354412530496, -5.546609562775244, -8.194585713275956, -5.115443958205862, 1.4154419206811681, 4.852795301437717, 2.010026929280385, -3.1128124845609153, -4.597731943176913, -1.9922447353711699, 0.11003798387817715, -0.8900253460006434, -2.3813960784721346, -1.388931970343246, 0.5445859462295547, 0.06459200416629532, -2.3287842358307853, -2.954877619537434, -0.8976181226281286, 0.5097835684280412, -0.8719106066972777, -2.575195250980895, -1.761853382302043, 0.03394488451429964, -0.3596115401025419, -2.2536857202070357, -2.301502938255995, -0.3042360779240826, 0.5686471207018602, -0.44282209053115906, -0.37522021791901794, 1.5722383454312712, 1.711784862526386, -1.5226880084564698, -3.1719542230668036, 1.162319909161641, 7.17096021528015, 7.1286273736849655, 1.813469961685673, -0.04440642660723453, 5.107865658630358, 10.275153605641218, 8.520108855493168, 2.571347261844308, -0.6972470890101546, -0.28992101925061253, 0.07048909763433962, -0.5177809705884384, -0.03218957639324785, 1.1165998687356296, 0.7252303967953352, -0.3380991727926252, 0.33975518455926657, 1.2479094207097574, -0.9507754306557115, -4.431472708820757, -3.979927005413029, 0.0686046545559115, 1.8114605172125011, -0.2981285863938915, -1.2460516564408832, 0.7156429125991108, 0.44424273484643984, -3.9505190530208276, -5.7241944988204025, -0.26095941842827247, 6.140737872738919, 5.609994819758485, 0.6987062628635714, -1.0965224897242398, 0.4056591347546366, 0.2763149774532743, -1.143142086513493, 0.22269137285738874, 2.829182660669388, 1.4340084090539984, -2.8937689977481043, -3.940043127507579, -0.9372481481084738, 0.8127514322283917, -0.38896777224614343, -0.9361764931986265, 0.17114092915811546, 0.09431479575195958, -1.1220989935707242, -0.646473101424365, 0.6761288742062929, -0.034930061646149264, -0.8357252001142148, 1.4501668977371143, 2.8250086619400028, -2.077546663803715, -7.5837150508391655, -3.0036816949495466, 9.15737187960763, 14.562738312587388, 8.149286907804301, 0.31350358478561885, -0.7435983231407125, 0.714686277354994, -0.4720459981319212, -1.464319768329831, 0.3692323728687026, 1.4969299735325543, -0.08743055389434455, -0.7873446865071698, 0.8056214311748142, 1.0861191297797386, -0.7255989107914294, -1.0275616269775392, 0.16976737699209948, -0.8342506240297054, -2.8929626404102935, -1.5283195333341502, 1.2802278054492213, -0.25326964163644405, -4.208875086973875, -3.7801338874923878, -0.12988820739819903, -0.07678377872809317, -2.932397904094425, -2.5869920823436408, -0.12725170519132928, -0.7772019693019716, -1.515566326539643, 3.712015342550266, 9.897597252865564, 7.410979461414643, -0.6765183181146046, -3.0897293781230126, 0.9664896506881212, 2.7589373518623335, 0.45643387556314036, -0.17214592641563137, 1.4783192494066009, 1.0320210179480076, -0.8972993789734749, -0.6297660326088955, 0.5421679046644085, -0.07845417650703822, -0.41148625827085067, 1.0693447465271992, 1.0407508191068098, -1.270772896711316, -1.4484122324850004, 0.6862467235598092, 0.2126446592948075, -1.3026737190559263, 2.6986418412588984, 8.522815049083908, 5.077527257477543, -5.709050836790793, -9.469155561272991, -2.916910269420523, 1.99015765666141, -0.23617084996440452, -1.7862531808846283, 1.1774513239616007, 2.692425724370902, 0.5658086299092359, -0.4442566614837896, 0.45519504997856813, 0.003492662250957337, -0.44641446823107417, 1.4131711508985791, 1.5487218466897428, -2.741711115917938, -5.355386480631724, -1.8299854629563495, 2.135498187220289, 1.4009708295130483, -0.3172248550642832, 0.18884423915994186, 0.09145376912872989, -1.0380034179933806, -0.24956438126062058, -0.15675515496587517, -4.813543702524637, -8.589159035137953, -4.62243342884418, 0.6823657145409036, -1.5469842462076264, -5.186084582112012, -0.5799685611310005, 6.248402435683253, 4.657181943768772, -1.0517163545112775, -1.3254560739924657, 0.8567176172101305, -1.4007923855123465, -4.45117517121956, -2.692570441981863, 0.27863455183698715, 0.10454959436441424, -0.6312342303978251, -0.03654153208596126, -0.2760538116368739, -0.6485553853484755, 1.0049254998839405, 1.7709528164693678, -0.41586573921621955, -0.7985492791228647, 2.005138920782576, 0.8755874653519723, -5.280943700231438, -6.828036146809268, -1.5864782242873192, 0.29394507874207176, -3.619231780847233, -3.5469138578127892, 2.0456202324937145, 3.256345145796023, -1.1721514373722568, -2.284385823825992, 0.5824770811340606, 0.49234099668382664, -1.2277594070954443, 0.8958888391467682, 3.088563185574357, 0.1455671760446082, -2.8754181414218407, -0.9306980466757345, 1.118943395074492, -0.45645445422367825, -1.3444472354040178, -0.07827736594947889, -0.7799417091885413, -2.4542837899893892, -0.6333817768845412, 2.0803219894817673, 1.1486659601954674, -0.42506967078422736, 0.370478452932786, 0.0008830019429534384, -1.961027595024206, -1.016041144858594, 0.12185320629431429, -3.98454665549776, -5.335381389249635, 6.345675257523562, 20.187607018265616, 17.644004525571898, 3.2678562126315267, -3.8904798133467606, -1.0288625631103467, 0.8596909407967896, -0.43120808488627, -0.05410164106510508, 0.7848139806850764, -0.14927437002864158, 0.06673465448863704, 1.3600805063129457, -0.2560871262615931, -2.774224230460014, -1.5836098038630726, 0.3988849188888349, -0.5944937934431741, -0.9575080255941745, 0.6232035671146502, -1.3262976664854669, -5.9006381279881515, -5.161416536238336, -0.34902381469886534, 0.45113753356291875, -0.8553793216167458, 1.7435026627673944, 3.058341329024702, -2.18233252087671, -5.328476215914812, 0.06696982693832097, 4.739738259882252, 1.9928981204833367, -0.6637735939556071, 0.6881655591256259, -0.40577130891526675, -3.588903565186149, -1.2293160096348985, 3.9418253200613687, 3.1640636323388556, -0.8551624679205879, -0.6374941650202344, 1.2099105069340643, -0.06103713154028001, -1.2635504806446933, -0.13438063214493523, 0.058592800090580356, -0.6499204378594514, 0.2552323843117097, 0.5919358476654192, -0.46213871523730987, 1.1046863409915741, 2.5831616283629835, -3.596579104980861, -11.6536333096171, -8.768540596855019, 0.3296732998626399, 1.3333266529491923, -2.516970288389382, 0.6958993889428701, 6.120448960838463, 3.2087523347591604, -2.1305541819151284, -0.6591149700178416, 2.2660168715571003, 0.3383193470294589, -1.5352133158190657, -0.24956486116729898, -0.0036440729642845805, -0.870541166672006, 0.15495704683868966, 0.518048354456044, -0.8980059984105495, 0.9906223360392895, 5.3168244170079095, 4.535363042709288, 0.10224935944896842, -0.15551738785427477, 1.8030972626570956, 0.02941449093258488, -1.9725989623654345, -0.4586454318020107, 0.016806343636714387, -1.2104211317924864, 0.9260240599311742, 2.745498870728478, -2.013487289495236, -5.640508328650057, -0.31997096239335227, 3.6457589319207715, -2.582361418890165, -7.718114925142066, -2.7244124810865338, 2.1228528536755578, -0.6508194517664428, -2.7769276082392285, 0.09902964550814822, 1.4963491199834738, 0.04178491528199364, -0.037864132148626654, -0.1420646783765152, -2.050035283003039, -1.9827690245459693, 0.06292832294921978, -0.38397981515483876, -1.6115034150013852, -0.1714640979334992, 0.20382073654321692, -1.9788985532566623, -1.3759895942910418, 0.656602485257696, -1.738197777750294, -2.0479019859541716, 7.519069422026197, 14.879420984124174, 6.695244179936107, -5.584102834235023, -5.933045643146106, -0.25087871810466195, 0.5633000395086321, -0.10021196269225943, 1.2641021105917354, 0.22752555164746877, -1.8379124484442597, 0.20810181813446785, 2.137245266147648, -0.38931416510124556, -1.3383960173946656, 1.6907300859330017, 1.4461488917888645, -2.4942199463463717, -2.6546256485706667, 0.18226124365104093, 0.3369037566032693, -0.34453984815090877, 0.2984432076382874, -1.1233143038789728, -3.0039713677687057, -0.3777913205071277, 2.643793182853021, 1.0678122474530403, 0.03293700515379829, 1.218068854133448, -2.310614538842579, -6.626234455015789, -0.06805704411984047, 10.208882684541475, 7.661146875129469, -1.8106625607298579, -1.5329399860617017, 4.592273223840224, 3.9587543117613846, 0.06227732415578577, 0.15306664235675244, 0.07941096190761632, -2.518076900563706, -2.5085619441729636, -0.22608243532028713, -0.00914411708904487, -0.27611784789974025, 0.4985085082363766, 0.05127254694573222, 0.5992867516519412, 4.250747727905174, 4.203548965988662, -2.005990262980387, -4.359433109192043, 0.07727047700075336, 1.3708123482511811, -1.5996719710827603, -0.7004132630797993, 1.201526949507519, -2.3246036260058798, -4.413556864412915, -0.4118269109379812, 0.1309534050037844, -4.724915235482504, -3.350752424799496, 3.981478612954003, 4.967901168492626, 0.43915302385791566, -0.3321434834561307, 0.4530976451419873, -1.5556405653313101, -1.4832532271424106, 1.0106503280387962, -0.832795929849633, -4.507336975826145, -2.7909251257979726, 0.5653744727872964, -0.07482649609041728, -0.9042818678032969, 0.37634057830274903, 0.30388432105135355, -0.09772138502166271, 1.2198279646979893, 0.7515497515922431, -0.5536586442242273, 2.211580229618826, 3.3256215509912783, -2.7797518060253537, -3.6327504496458163, 8.902514645989228, 17.250450103353153, 8.64122921265955, -1.166941561547742, 0.7421049241626347, 3.6753975853359253, 0.23335837957164526, -1.6882478041829903, -0.005832770528545491, -0.21860703499284698, -0.7436817247644953, 0.6873946339880213, -0.06523206814722562, -2.258656823254068, -1.0145129920770481, 0.4773101957226489, -1.325922330066221, -1.2417024951196405, 1.656495275928953, 0.9343297781449795, -1.6765341543339827, -0.23749521841091767, 1.1607444752751621, -0.7422835739656279, 0.6278398643844444, 4.920129369395045, 3.4993796121704714, -0.3386130829592734, 1.7475589002167582, 3.4302501923523874, -1.59442560727708, -4.256689839384886, -0.6967056278774102, -0.03911950882610511, -1.1636874867565532, 4.579428622984792, 9.510539195870953, 2.8727066294899513, -5.465503728748493, -3.8322446849689493, 0.7400658970175332, 0.5950371270567659, -0.20143611748216758, 0.10367335673172771, -0.8888319335988596, -0.7918435131110673, 0.9662638860735826, 0.3498764137198267, -0.7263391437646285, 1.2834911420881008, 1.8341936010112732, -0.6839256151683706, -0.41605017993530147, 0.45055334130056285, -3.7017913114231615, -4.623942061175816, 3.6626961755482115, 7.5968083373472295, 0.37722820079367075, -2.8688015958231468, 3.057659931685879, 3.517569885216197, -3.452899377168992, -4.550521971530581, 0.014593995007916081, 0.7857755959479784, -0.2814626638057435, 0.7830259380255842, 0.40268018508475617, -0.38351969758166393, 2.3564976367312, 3.7439208623086793, 0.7682093163303498, -0.03243607318449164, 1.7272209129923077, -0.3027451817914689, -2.5430932736384344, 0.8766623649126996, 3.7459989791813766, 1.428837164659761, -0.09859744858040279, 0.6710579614179575, -0.17942910473496718, -0.4206536616601842, 0.19314711707553822, -3.4329905795515736, -5.1574620051874565, 3.942347125082023, 11.407963254712495, 3.2165411685530203, -6.83665707338973, -3.2080815528172613, 2.9112275071513363, 0.3091668130564398, -2.1800089784779937, -0.02761715195979428, -0.5854202859830486, -2.685205436082743, -0.6727399411736265, 0.9581651350120672, -0.992237661394942, -1.3253728857819365, 0.12911885384360164, -0.4954151977730883, -0.7463091489750073, 0.6315474400005291, 0.1817115007255386, -0.10362622266687825, 1.5036631359689225, -1.2895783832871126, -6.697004921473566, -3.180128922829713, 5.220869024739589, 4.065281566228951, -2.064321394825947, -1.047873461459712, 0.9521632547975292, -2.663329455635909, -2.549374825322774, 3.100466457647185, 3.172840792535916, -1.0833965502177714, -0.5281278995872913, 0.8462144561402846, -1.620360429339426, -1.4653529053691963, 1.064289891356064, -1.717798867696392, -5.543117900705932, -2.99148379339902, 0.12758243983566403, -0.8380641825647157, -0.3548150900519217, 1.8137738879932768, 0.9538281215775507, -0.11916055892317082, 0.8836174414629696, 0.23889148154478468, -0.04617423226122498, 3.366125127786881, 4.095285701226854, 0.012466512029319764, -0.7537354719434111, 0.803854028458722, -1.2574416211503192, 1.6770339713730964, 13.331601289825482, 14.782438008755317, -0.7606540232599965, -10.70013539199856, -4.550036690781317, 0.9800277856485593, -1.3038717090745762, -1.6783869005347503, 0.6170171850062127, 0.13889000832549608, -0.4864468028592074, 0.24713371849113153, -0.45384811432003563, -0.4639893443339957, 0.713311795353993, -1.6825607384771937, -4.330051798805518, -0.8169892895550698, 2.5726722649795404, -0.10823204437552576, -1.7187091769098624, 0.30004417516314275, -0.46807408052289023, -1.6667785840008515, 0.8604063094205023, -0.025254809158567128, -4.692759359597541, -2.068949356708889, 4.57469889594878, 2.8247977786753453, -1.5156396775179763, 1.2762430526337138, 3.2324190742325456, 0.05482024730269135, 1.5587136309021035, 6.400630992163479, 4.061959410149538], 'positive_zeros': ['1.09721213516161293407968671959', '1.69156711016238051377739638297', '2.441628469789687545588697653176', '3.60276236126109851118894090708', '4.23996414287272205994929954223', '4.39715665017877291471524056835', '5.23126205533553175206223585696', '6.4932276858230025400165286831', '7.30389261585460274579392583993', '8.39254490948301011040937234536', '8.5726940633997568793256306805', '9.576693396379053645234360421537', '10.0101323398672730139787969855', '11.069362160194061583398552947931', '11.426623672402651699810845558722', '12.49003507311231623407915407473', '12.73241599656566240656724412785', '13.80196993983135068300087235189', '14.25716577026496490597392753739', '14.76059011051581225666663286512', '15.49751643512647439722146125068', '16.19293548956003068110219106108', '17.33730108947365279261980668479', '17.50643764491949095941407701935', '18.94219610886776698912674519426', '19.48541455159648932282787930408', '19.73414703409280218719014959346', '20.32074201606798933252188229427', '21.11681216164113208189624851378', '21.483459425450297185978204758109', '22.10020890466675841954107824371', '23.11947349748324840337677619314', '23.71347610724167369724534898359', '24.27178041780637810878657491038', '24.73083766812069201290186318257', '25.63559428296045665286102710429', '26.61908033532359430704258021609', '27.10599078210247267191729823147', '27.5540496507410915932219569510', '28.10032243127983402564424456789', '28.85517770215930072820845639849', '29.78830427479968062974561854642', '30.236411160704126978948774946249', '30.88729825646701340484969124142', '31.2755178239979559580720335127', '32.00253985292245039197862484509', '32.49288593055781656004143831834', '32.971599153871007654283034369608', '33.65470574988947159447097758371', '34.4576256054483487325301183989', '35.64735650810712828775974952659', '36.06437674074842030886269118241', '36.48698743718017747483829709363', '37.1385400886227540174228842690', '37.79822449988268879591368931946', '38.29799294724991027443216665437', '38.94225276124345102144290477840', '39.62214355792503933699609169976', '39.85809755488326644916508894186', '40.76918707513372137921508196084', '41.22925793944954477779879029093', '42.203269533509601763657375826741', '42.48982378155211363471342051659', '43.473893340942091819920231732225', '43.59408015995002682825511493843', '44.19831372678581075822890453895', '45.28250046080262586704319117805', '45.87075712742182130924661998864', '46.632315813032891969613214329661', '46.91504561834323561376892186372', '47.65181495955670691691056602218', '48.25913604607957253912537297568', '48.72805336064649357018945101852', '49.17081829121496667786971534048', '49.83503743360043540331429830802', '50.51518114248961007319781709815', '50.96755135330989568957756230387', '51.41530555929510628392855285642', '52.3366451215135199342101968799', '53.2536838717559745248265932926', '53.72921438697686671944805079478', '54.27237569796752462631995586311', '55.08485220779019081033483234189', '55.46904663137538516501957780771', '55.938457605797683030829676104916', '56.3558804901488182205217418312', '57.01300834886730609386800356218', '57.92531873145391478129071222651', '58.64900574043517972259838977317', '58.995391356351751626662651712512', '59.39959986872143389062404237394', '60.05584867429606832885309483974', '60.28832742937161024566745608418', '61.49125959199946360458906175861', '61.76896676223253597658758159123', '62.52239657171346739640139692098', '63.36477571824546998879522416084', '63.89965892166159245924891572745', '64.254530832903027977726989136163', '65.264040400863151878014683017273', '65.6519721127880483828639662626', '66.274643155445986572985120893592', '66.43392296692821841780627437414', '67.033632814527856381527330974842', '67.75967595430820717119568374789', '68.224638008071811433952907812468', '68.802493675982216144884935683774', '69.80193697987991916397695167433', '70.03647679642911241272845790993', '70.82543069138211062604040913870', '71.48210770383661230081025784674', '72.11778330200175387858328371200', '72.568965475341759425721101429161', '73.04267691962614347549282481001', '73.76018928971193810776871181203', '74.46722030273911535021826010561', '74.93609424043652590327771023092', '75.65954022690828815424941411755', '75.76443675844881262410138766649', '76.62051243726114546556306930217', '77.359987279017699662274310921957', '77.709869517367309476512840635116', '78.12514944967325231031827984821', '78.897116171705754506758451840842', '79.08544567936262723124146453002', '79.86884451742273107276787620277', '81.02360089404053038169936015445', '81.65305445742618454638145317927', '82.0832261552314578167926466982', '82.51250413133866220095729715880', '83.08043739288138956160223628867', '83.42218017114801137661328284138', '84.03591045978785600873656176569', '84.89027921591592855912329303691', '85.197290488268290098815315409112', '85.79902922911604817828220283094', '86.13761518902528779624509103254', '87.219513198252562380732790767903', '87.57652812421436554411848111645', '87.96875540844859945588072857993', '88.64490203921228936229753652293', '89.3721318751260125717199238765', '90.164049866014922834615828784935', '90.496335817668245914702924667966', '90.89737231948600859224780653235', '91.629746221599910318122141817007', '92.41541702542513618710353544330', '92.895564360925844491673342324225', '93.42869292978905280194723087844', '94.099681249366098362582537445265', '94.39677924767455423178007342565', '94.939167342698151905304338441166', '95.46780694240412118017680296343', '95.80232998812171854698568533430', '96.43069420203094449831502906038', '97.48478554386461181078827938274', '97.90741683903574864723872656268', '98.40392516633775277654041158374', '99.21846904915474384837455323852', '99.7380477919380019064132672448', '100.34607741305064629584317304526', '100.9978386453615033705407343716', '101.248806747181489556333461478638', '101.84267715397978960656024958947', '102.299741574820410658938394678938', '102.72991463092521990359680065098', '103.76039910874579903197696844466', '104.0840791931140565386048879239', '104.690439012564601776440636245334', '105.39822055854836568530383041458', '105.62937051637075785097365570460', '106.165160839978390090685879847347', '106.77683598086224665878250228642', '107.51353294125939235333709908671', '108.02998423822255042075645357581', '108.872574017542214985562205656499', '109.32848645855897464418296109934', '109.990718905758441880442424526787', '110.63644901537902732731534572765', '110.956390834271671565656090271516', '111.21088855807251227419371293860', '112.17288184861864267631907330048', '112.42377489101584423446002710990', '113.1546849567547764624888906174', '113.47471377207196747078696589882', '114.2234580547996245257031689824', '114.52707117897043569817383519993', '115.09660836379092544493207333601', '116.08625355472857961967015314439', '116.896496110057190784051764285585', '117.324939559180498424331022026875', '117.5349516854536203380605649970', '118.15117039753575494650550555678', '118.730847874601131385004184814790', '119.33738212332893241688025148788', '119.83797485885488303851443035256', '120.42917938310446798630479058768', '121.22290912810616427653163523315', '121.653958879979470544720191843806', '122.035645536054748362265606390', '122.338331291966618226383773276482', '123.15264016798041501715563595494', '123.92611989662772670870087527631', '124.05095277302565006915195645518', '124.55096201414927879474515790330', '125.31432755770125875609760639962', '126.17492995943788563809976248589', '126.63729226610610105634635571933', '127.50961990225023919460287845192', '127.77365406151285179293951651931', '128.13762568833962919178776126623', '129.11582145307871851886919435693', '129.37089193021598728681319729157', '129.8012556459767318897888179973', '130.332989430421600583786439380824', '130.52029056624073085528933087108', '131.468890149837112470161029265079', '132.182200484061052140898315392139', '132.64288845564163755126713909754', '133.19531703528967192530983218089', '133.59169053119643021654597224148', '134.40769839573979338864419482215', '134.69851998992639212266860054343', '135.45381772704707830853452591609', '136.29381471430539607762632193134', '136.63404124089479316655920442799', '136.97630416343226480044585282124', '137.66524909632348506078433435550', '138.05885951027720624611191671838', '138.979529895130181351722254579691', '139.36195911138997100597396182782', '139.91000052957615105415684814438', '140.41520076603140152365898498374', '140.66202771445008921641678919685', '141.36849268409095954937147769416', '141.677303598992609053688249441012', '142.378154082808451459734633561870', '142.93005150802463998396324552988', '143.994660881827151089826801715672', '144.328984889345675683773473392119', '145.017511086623035017847189020696', '145.62640520684364319898839739260', '145.8802266261300437113004565112', '146.41911959185039740789039120551', '146.86650130030540369856218670111', '147.633685392304707536440771562147', '147.93574038242013037027917015054', '148.56837867328101966414161546820', '149.15404995352165103279596194065', '149.71437885799785676529344249744', '150.1978385506631620082645918225', '150.57398674793679762134235381613', '151.50725473374441221759863232770', '151.71853397533873554899422185050', '152.418917696752730764939085118230', '153.19880834426467503483028998034', '153.43120167042679232597165887065', '153.85796675773579517520828507204', '154.77275038609023434248817081085', '155.54858102650791311576792504452', '156.07800796023370028215067547323', '156.3948427646920608961924871164', '156.62997827183927225873428062127', '157.32092224899234189690336930125', '157.871163976019073293719239174747', '158.277714389160468160291384316973', '158.9724901812706933591984913088', '159.43882894605317884604602630545', '159.74792249766789053677929392713', '160.5060207198882100029981700133', '161.2644660484152073391481045057', '161.73118291220760251449515091814', '162.348547259125319156873363929325', '163.12372108640951108544493963912', '163.60029829284129097599279702946', '163.872244789948782850790338154409', '164.45491724343554805481967419003', '164.76515475131902176491917227721', '165.72091430129491344329178742631', '165.94385441648379510234160752323', '166.53675951038582032989897387333', '167.13102416373989900371821992405', '168.0175289105685747229140647477', '168.180946347908384627168347724834', '168.7087599697652029732197448901', '169.17380337374156624446182666789', '169.4157852301765642470422749171', '170.20785776191383414492629822600', '171.01340876058537683039743433985', '171.68594796310646870613166543513', '172.208123850557859125099137258550', '172.81720965741071503756050511036', '173.04471198329273882150699558789', '173.81961850439729894171029556742', '174.24144861825307638142913920010', '174.95178113426929924931769878170', '175.18043106474221979714882559805', '175.78707455030405727102440008019', '176.296517379713565972917745477634', '176.586711185517888061684054291285', '177.11167448492315955272676895687', '177.91956301406901827849645404519', '178.621198099399386423959620399890', '179.150480338507830959796754040254', '179.48953870876575082941686447179', '180.142645882570874255792107374797', '180.83944467301722478037022922635', '181.31299577944923990016953630637', '181.69759063731551967850306001641', '182.33563926568190488059429918055', '182.696432248515265942564184309019', '183.71139572676701712159256954706', '183.88116884630081116913272742214', '184.421348369254117007615391904', '185.18445709160955897595638949317', '185.37263537996273838871383597925', '185.987806057859739269588396401993', '186.25759163559315388824418456376', '187.18857046817113167830973957990', '187.60875375879323061757822631923', '187.97181095522254452940875214647', '188.36828573745124630075381722962', '189.36131478899506047387773990629', '190.19385073258639572178414556543', '190.497303587130141949813700799460', '191.14359427025165808529728422927', '191.59326807457234454324568653061', '192.05804321640337243924950272123', '192.37012595722261230649715987337', '192.91027930768895443416756150757', '193.28776000664136820375959709565', '194.11052851956835136938712870421', '194.67855272410546343341957436073', '195.25777750110902425265907225713', '195.558300529947964027874505728619', '196.15444110092529763872576747343', '196.5606773667651953478117663680', '197.27327472328294386945397662931', '197.969715577020570312769597717767', '198.34967502910464071440047638013', '199.069880288564225695645064676745', '199.25032040991303865631641297611'], 'prelabel': '1-4033-4033.1494-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': -0.15054349194294311, 'root_number': '0.890230068648543346304053539152-0.455511168769778685672556376684*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.53549225971061444670349648085-0.637753896063379345732163115045*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.09721213516', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.69156711016', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.44162846979', 'prec': 44}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 18.729173260907245, 'bad_primes': [37, 109], 'central_character': '4033.1494', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/1494'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-4033-4033.1494-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4033-4033.1494-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': -0.07527174597147156, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09721213516', 'prec': 44}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': 'dirichlet_L_4033.1494', 'Lhash_array': ['dirichlet_L_4033.1494'], 'label': '1-4033-4033.1494-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/1494'}