-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3899910271312948092933647574744', 'a10': [-144.85346791508167, 93.17261312713694], 'a2': [3.3641588869159387, -2.1638934778737404], 'a3': [0.0, 0.0], 'a4': [6.635130032830975, -14.559362947856766], 'a5': [-43.05785570308623, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -14.113867883679749], 'a8': [-9.183278859072683, -63.337724851754096], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.163956013055191, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-3.3641588869159387, 2.1638934778737404]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '108.55', 'coefficient_field': 'CDF', 'conductor': 108, 'conductor_radical': 6, 'conjugate': '201095737509968678521184219241', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.3641588869159387, 2.1638934778737404]], [[1.0, 0], [0, 0]], [[1.0, 0], [43.05785570308623, 0], [625.0, 0]], [[1.0, 0], [0, 14.113867883679749], [-2401.0, 0]], [[1.0, 0], [0, -209.4814700278462], [-14641.0, 0]], [[1.0, 0], [195.70289367364316, 0], [28561.0, 0]], [[1.0, 0], [303.68794043992756, 0], [83521.0, 0]], [[1.0, 0], [0, 274.7916756637772], [-130321.0, 0]], [[1.0, 0], [0, 466.34685499486653], [-279841.0, 0]], [[1.0, 0], [439.8348254503328, 0], [707281.0, 0]], [[1.0, 0], [0, 1220.9571406153802], [-923521.0, 0]], [[1.0, 0], [-624.1467629250103, 0], [1874161.0, 0]], [[1.0, 0], [203.59181273708424, 0], [2825761.0, 0]], [[1.0, 0], [0, 419.41815528663034], [-3418801.0, 0]], [[1.0, 0], [0, -1995.530258331503], [-4879681.0, 0]], [[1.0, 0], [206.45084526019923, 0], [7890481.0, 0]], [[1.0, 0], [0, 2321.8652011887675], [-12117361.0, 0]], [[1.0, 0], [1392.099997977272, 0], [13845841.0, 0]], [[1.0, 0], [0, -7348.268393219019], [-20151121.0, 0]], [[1.0, 0], [0, 8546.654797556412], [-25411681.0, 0]], [[1.0, 0], [3245.425001103523, 0], [28398241.0, 0]], [[1.0, 0], [0, 6157.405958127315], [-38950081.0, 0]], [[1.0, 0], [0, -213.99031453805267], [-47458321.0, 0]], [[1.0, 0], [8439.348559835871, 0], [62742241.0, 0]], [[1.0, 0], [1022.4901720751134, 0], [88529281.0, 0]], [[1.0, 0], [-2374.5188332461107, 0], [104060401.0, 0]], [[1.0, 0], [0, -8481.024139350893], [-112550881.0, 0]], [[1.0, 0], [0, -9579.92551514526], [-131079601.0, 0]], [[1.0, 0], [11549.877342682117, 0], [141158161.0, 0]], [[1.0, 0], [21853.765040681887, 0], [163047361.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 31, 'label': '2-108-4.3-c4-0-31', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/108/5/d/a/55/13', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.49485113325048513, 1.060752678484736, 1.629614466151162, 2.1842358365229932, 2.7058218615658474, 3.173910898428856, 3.5667894899752026, 3.862485038472446, 4.040345333219518, 4.083120677833293, 3.9793660866628744, 3.72588712077403, 3.329875861346088, 2.8103385543067434, 2.1984199050084308, 1.536294987621359, 0.8744361912413238, 0.2672671887026866, -0.23252728293586336, -0.58048869061569, -0.7468660416323101, -0.7221075972128584, -0.5203267237366918, -0.17982393955654116, 0.23994307896115888, 0.6650606895587188, 1.0170334354823656, 1.224677006728743, 1.2363011322243314, 1.0300917077883032, 0.6205710604870459, 0.059392637624142444, -0.5704809227004327, -1.1670386960470585, -1.6264474877198387, -1.8625456535329135, -1.8250308300811615, -1.5124911299903498, -0.9769230128545769, -0.3176737052705566, 0.33530242840132646, 0.8466963357311083, 1.105260687939178, 1.0515088453570047, 0.6973637065947966, 0.1323363303719311, -0.486905263187543, -0.9633879908120309, -1.0991620799406259, -0.7398027820013785, 0.18532665603042736, 1.6366435064639413, 3.4592846474868164, 5.402867487840523, 7.164133561993465, 8.444997093305396, 9.01417657292307, 8.75864839064982, 7.712376327599694, 6.054170344221337, 4.073327535675568, 2.109413727389048, 0.4792668755760701, -0.59178064976874, -1.017613805908447, -0.8656403354422947, -0.33335484638095725, 0.3075569301388971, 0.7855549114043985, 0.9025979934219204, 0.5867297562773403, -0.09078195802164539, -0.9389697279121572, -1.7052073434044204, -2.15152563020177, -2.1271690868012754, -1.6158204646744825, -0.7428430988624353, 0.2604664581746448, 1.1255643564084206, 1.6277188591305276, 1.654333984842845, 1.2386189593272232, 0.5470270726228977, -0.17654303654155318, -0.6924871817070362, -0.8465560301848796, -0.6226679727061121, -0.14818476104630118, 0.3523171557602779, 0.6410999139497396, 0.5613555013601088, 0.10808525650981654, -0.551766112201154, -1.1216775495253752, -1.2710224460335278, -0.7546506954663867, 0.48349174827535185, 2.2607877151202045, 4.183064338732411, 5.746459553438119, 6.486197284285118, 6.126119195096803, 4.679041881612702, 2.4611323038919046, 0.010146195211766885, -2.070797290733896, -3.295954029354272, -3.4469950567328, -2.639651789245124, -1.2826205134258881, 0.05978483466131658, 0.8565693597457819, 0.7871963285147897, -0.15357362462213137, -1.6594369133737361, -3.2236349411852405, -4.318318452697301, -4.578725502378825, -3.926856764612605, -2.5911532435929217, -1.016557914631676, 0.30052271541614467, 0.9904110672164097, 0.9353092757469584, 0.2959931932841041, -0.5672866008712489, -1.2462290285273443, -1.447132408988438, -1.100200825580464, -0.3732167008407168, 0.4133899516156576, 0.9324553833504636, 0.9941290625268184, 0.6260316204218799, 0.05454909343634827, -0.40524267733274416, -0.5032751463590087, -0.1833269178281629, 0.37303632842664136, 0.8123234346087135, 0.761905607379221, 0.0066445805788418, -1.3884190073153477, -3.0684407680119437, -4.505548924459078, -5.200813456934578, -4.8901449298623785, -3.665627799765197, -1.9545502111840125, -0.35612026236573807, 0.6028219204827082, 0.6932006223537791, 0.09248391487385732, -0.6765233610432402, -0.9604235426328224, -0.26041569576964285, 1.5298254299004295, 4.037517993552642, 6.520568375397396, 8.138311587795318, 8.278618784088733, 6.80915291051761, 4.147617989649223, 1.1178646985974534, -1.3536582483503226, -2.5802343246131954, -2.3585781251891866, -1.0175011875342355, 0.743300249776307, 2.15184357189883, 2.671807338021467, 2.191913691664888, 1.0240914976053732, -0.27673979257569925, -1.1809889374606468, -1.415656381871306, -1.0560995973438863, -0.4448166178841353, 0.013637425484881832, 0.07505256307561803, -0.21664912186262708, -0.5593016320933009, -0.5636946393041626, 0.02168000933167444, 1.148419129238535, 2.4553464562488307, 3.4184259312174623, 3.594880592719374, 2.842941153164288, 1.4064713515051441, -0.18276745145170484, -1.3431793759211244, -1.7084573762758268, -1.2896232625956556, -0.45176415434482264, 0.28570541006918276, 0.5264882361891549, 0.21051844557349292, -0.3518586929457016, -0.6516743370149074, -0.2799218909252065, 0.7980009183854828, 2.141783962528256, 2.981528880865172, 2.5607686743611655, 0.5245660153254751, -2.835674898642667, -6.61413632071104, -9.608906859060275, -10.80044750374259, -9.78135572833099, -6.941476685562088, -3.3182309890981676, -0.17311470310032315, 1.5191762684860275, 1.4427429033808599, 0.013045194417169325, -1.8701973991942162, -3.262189118525356, -3.5923617754097115, -2.8707058218792887, -1.5992019747031294, -0.4535829832653215, 0.08969314344878399, -0.011992548851010629, -0.38460467457948977, -0.4843390459315209, 0.06783451893216934, 1.2487548608295584, 2.621933846563202, 3.5583984805230138, 3.569945411026578, 2.5748664970637356, 0.9527180926965534, -0.6416848670267513, -1.6053694984842493, -1.6802767481246548, -1.0567927842143345, -0.2364650990460644, 0.2652364491377448, 0.20779947883588828, -0.2561024365176467, -0.6981547496951797, -0.6977111257392288, -0.12339082804679209, 0.7579030792069156, 1.4197381017494692, 1.3941290017780534, 0.5887727295343115, -0.5897858502099762, -1.4023551746776965, -1.1676065123943786, 0.3237927634122515, 2.6047504162532764, 4.674726720796209, 5.448481554249794], 'positive_zeros': ['3.07648674690865398081628016939346', '4.12062893023030389456105580021884', '5.46620297252736245817391043635283', '6.93849255350193216306503593680160', '7.947230808525174524942889841820349', '8.761015127851082360788251854751911', '10.96498452387400413376552702937917', '11.69176705422377020446731570163917', '12.46030950601739772502375178400119', '13.66485321247732278917401542075565'], 'prelabel': '2-108-4.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.341250666001459, 'root_angle': -0.8638880548125384, 'root_number': '-0.909960184241048 - 0.4146956270519357*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.431944027406', 'prec': 50}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.07648674690865398081628016939', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.12062893023030389456105580022', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.46620297252736245817391043635', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.163956013055191, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 108, 'conductor_radical': 6, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/108/5/d/a/55/13'], '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': '2-108-4.3-c4-0-31', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-108-4.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.341250666001459, 'root_angle': -0.4319440274062692, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '3.07648674690865398081628016939', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3899910271312948092933647574744', 'Lhash_array': ['3899910271312948092933647574744'], 'label': '2-108-4.3-c4-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/108/5/d/a/55/13'}