-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '413157409872098519130347381000', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.0, -1.4142135623730951], 'a4': [0, 0], 'a5': [0, 1.4142135623730951], 'a6': [0, 0], 'a7': [0, 4.242640687119285], 'a8': [0, 0], 'a9': [-1.0, 2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.930660344511594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 1.4142135623730951]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '2496.1535', 'coefficient_field': 'CDF', 'conductor': 2496, 'conductor_radical': 78, 'conjugate': '1797781526381589643473938349572', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 1.4142135623730951]], [[1.0, 0], [0, -1.4142135623730951], [-5.0, 0]], [[1.0, 0], [0, -4.242640687119285], [-7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 5.656854249492381], [-17.0, 0]], [[1.0, 0], [0, -4.242640687119285], [-19.0, 0]], [[1.0, 0], [-6.0, 0], [23.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-29.0, 0]], [[1.0, 0], [0, -4.242640687119285], [-31.0, 0]], [[1.0, 0], [2.0, 0], [37.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-41.0, 0]], [[1.0, 0], [0, -8.48528137423857], [-43.0, 0]], [[1.0, 0], [12.0, 0], [47.0, 0]], [[1.0, 0], [0, -5.656854249492381], [-53.0, 0]], [[1.0, 0], [0, 0], [59.0, 0]], [[1.0, 0], [8.0, 0], [61.0, 0]], [[1.0, 0], [0, -4.242640687119285], [-67.0, 0]], [[1.0, 0], [12.0, 0], [71.0, 0]], [[1.0, 0], [-2.0, 0], [73.0, 0]], [[1.0, 0], [0, -8.48528137423857], [-79.0, 0]], [[1.0, 0], [-12.0, 0], [83.0, 0]], [[1.0, 0], [0, -7.0710678118654755], [-89.0, 0]], [[1.0, 0], [10.0, 0], [97.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-101.0, 0]], [[1.0, 0], [0, 8.48528137423857], [-103.0, 0]], [[1.0, 0], [12.0, 0], [107.0, 0]], [[1.0, 0], [2.0, 0], [109.0, 0]], [[1.0, 0], [0, 14.142135623730951], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-2496-12.11-c1-0-7', 'leading_term': '0.846014815761063994774387044490445929334939844986558894', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2496/2/d/b/1535/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.846014815761064, 0.7201265341490609, 0.5913312989618684, 0.4600620115998791, 0.32679663235834455, 0.192099825132654, 0.0566618077053211, -0.07866773443634871, -0.212852436651231, -0.34465007824161253, -0.4726023345615366, -0.5950339506670046, -0.7100614851002706, -0.8156114922182459, -0.9094477885583943, -0.9892072696600384, -1.052443593037823, -1.0966779066647159, -1.1194556699856884, -1.1184084801574363, -1.0913196781760333, -1.0361923697398576, -0.9513183588225438, -0.8353463646474125, -0.6873477828378987, -0.5068781671962626, -0.29403255795295186, -0.049492772976452604, 0.22543518307135765, 0.5287953449911414, 0.857969253479004, 1.2096780589803071, 1.5800003937142202, 1.9644068192047632, 2.3578112805535714, 2.7546395763462312, 3.1489143931161174, 3.5343559663840165, 3.904496929023065, 4.252809406270844, 4.572841930623182, 4.858363295483923, 5.103510060611025, 5.302934081773314, 5.451946177602566, 5.546651883086185, 5.5840751842848775, 5.562266192961797, 5.480388910091645, 5.3387855473248855, 5.139014325062776, 4.883858240188792, 4.577302986529752, 4.224483003058127, 3.831595500520263, 3.405783254236595, 2.9549879231985257, 2.487776634104701, 2.013145522131804, 1.5403048151133687, 1.0784508511415523, 0.6365310989376114, 0.22300877517554935, -0.15436600397479064, -0.4887714613430531, -0.7745087949840354, -1.0071695359184594, -1.1837695032747655, -1.3028440161436121, -1.3645000231070736, -1.3704220086634884, -1.3238299007145078, -1.2293886972184611, -1.0930711084373321, -0.9219761235747788, -0.7241080024242127, -0.508121706803125, -0.2830421653550437, -0.05796595259567304, 0.15824509358121294, 0.35726813888856773, 0.5316110032920021, 0.6748807283771613, 0.782019003065466, 0.8494951766100135, 0.8754487440415855, 0.8597746902919556, 0.8041468867595697, 0.7119767961817723, 0.5883069940500014, 0.4396413825624363, 0.27371637305742114, 0.09921965626255472, -0.07453462463550832, -0.23796352531059178, -0.38159336890376944, -0.4964445913863262, -0.5744089563538763, -0.6086044826467174, -0.5936937296323893, -0.5261519504353042, -0.40447304465296274, -0.22930318867781974, -0.0034944409580939676, 0.26792656254563213, 0.5778765840881542, 0.9174188734628782, 1.2760464215479201, 1.6420370955253192, 2.0028692337959195, 2.3456834664809443, 2.6577741689902132, 2.927092165233461, 3.14273916953386, 3.295434065348704, 3.3779315108996544, 3.3853745531917925, 3.3155649070504496, 3.1691372662545922, 2.949627378766643, 2.663427526164342, 2.3196273602018582, 1.9297426058957774, 1.5073387627342691, 1.067561435530158, 0.6265891134493884, 0.2010279045377548, -0.19272924826831758, -0.5391541457714153, -0.8242197268674345, -1.0359950746271473, -1.1651736819555727, -1.2055115566289414, -1.154154715011656, -1.0118395325272638, -0.7829541549512175, -0.47545455596684616, -0.10063464741478263, 0.3272441228136467, 0.7914522635681676, 1.2734037137037952, 1.753357047745677, 2.211179816147142, 2.6271460721369233, 2.9827349616447383, 3.2613973818419293, 3.4492582246632773, 3.5357236335998676, 3.513965973584741, 3.3812637423853418, 3.1391792764350517, 2.793563609965788, 2.354384973557304, 1.8353848712880818, 1.2535731357482855, 0.6285804987538877, -0.01810629099204506, -0.6639962278538217, -1.286497786426489, -1.8638368523887017, -2.375949785941138, -2.8053129801167955, -3.1376724214322476, -3.362640570359578, -3.4741332195522205, -3.4706256508295854, -3.355215123887288, -3.135485161778293, -2.823175880362085, -2.433673345970248, -1.985339234995929, -1.498709519863917, -0.9955971568407995, -0.49813848927087506, -0.027826055910949443, 0.3954284636422479, 0.7541584100374212, 1.0340936392486022, 1.2247644659702195, 1.3199297611544754, 1.3178089216865214, 1.2211065049370062, 1.0368280416384654, 0.7758954508928995, 0.45258010640668517, 0.08378047287218679, -0.3118210971494455, -0.7146817355020376, -1.1053567636668318, -1.4654468777879106, -1.7784872254349269, -2.030734355935439, -2.211811809355067, -2.3151819022630855, -2.338419763304667, -2.2832754690091086, -2.1555207576623685, -1.9645877329324892, -1.7230176601158704, -1.445747858937318, -1.1492732899782707, -0.8507262559376155, -0.5669223145457714, -0.313422750430306, -0.10366362134737568, 0.0518015470990623, 0.14590378738929916, 0.17547151166505343, 0.1414298105498068, 0.048772949921574806, -0.09369129465730303, -0.2738146373036949, -0.4767759645302438, -0.6859102267102077, -0.8836558286908478, -1.0525706841973292, -1.1763625017632504, -1.2408770965490739, -1.2349897238289678, -1.1513486026562427, -0.986926780634278, -0.7433479679948906, -0.4269634865043422, -0.04867046229086274, 0.3765248233532206, 0.8301806472969854, 1.2912996441614053, 1.7373719018854437, 2.14552880332784, 2.493747926773266, 2.7620452447102424, 2.9335901364443377, 2.995681467746318, 2.9405291172083627, 2.7657945870005074, 2.4748562929627465, 2.076779197476994, 1.585983913056249, 1.0216264583821704, 0.4067156352858982, -0.23299034562324844, -0.8702536492766383, -1.4777286306704631, -2.0293645368402773, -2.5017649002688263, -2.875430325682994, -3.1358162525002586, -3.2741459522368555, -3.2879310972021667, -3.181167123014725, -2.9641875464502463, -2.653179507836683, -2.2693811179716823, -1.8379987075252602, -1.3868978303956014, -0.945134968030673, -0.5414065549993962], 'positive_zeros': ['0.32592372835047223712539166839346', '1.38065508868933377644396312671839', '3.17779129694635953876009540049201', '3.97426791652236557253659632781327', '4.70066714191072884606691469289568', '5.23117870242481600587779957832089', '6.42372197197166788844178362494794', '6.96948567783300939658450681800598', '7.920460628607853711662591199969212', '8.839088466692589603269792597625612'], 'prelabel': '2-2496-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.464376814798634, 'root_angle': -0.3479566380076518, 'root_number': '-0.5773502691896257645091487805019574556476017512701268761 - 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3479566380076518', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.32592372835047223712539166839', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.38065508868933377644396312672', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17779129694635953876009540049', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 19.930660344511594, 'bad_primes': [2, 3, 13], 'central_character': '12.11', 'conductor': 2496, 'conductor_radical': 78, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2496/2/d/b/1535/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-2496-12.11-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2496-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.464376814798634, 'root_angle': -0.3479566380076518, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.32592372835047223712539166839', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '413157409872098519130347381000', 'Lhash_array': ['413157409872098519130347381000'], 'factors': ['2-2496-12.11-c1-0-7'], 'label': '2-2496-12.11-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2496/2/d/b/1535/1'}