-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2243239105795984659243871407463', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.5877852522924731, -0.8090169943749475], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.9510565162951535, -0.30901699437494745], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5877852522924731, 0.8090169943749475]]]], 'bad_primes': [2, 5], 'central_character': '3200.1217', 'coefficient_field': 'CDF', 'conductor': 3200, 'conductor_radical': 10, 'conjugate': '568240828554547016679113512780', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [-0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [1.760073510670101, -0.8968022466674206], [0.5877852522924731, -0.8090169943749475]], [[1.0, 0], [0.2787682579175257, 1.760073510670101], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [-0.5, 0.36327126400268045], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0.8090169943749475, 1.5877852522924731], [-0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [-0.36327126400268045, 1.118033988749895], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0.30901699437494745, 0.04894348370484643], [0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [1.5388417685876268, -0.5], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.9510565162951535, -0.30901699437494745]], [[1.0, 0], [0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-1.760073510670101, -0.8968022466674206], [0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [-1.8090169943749475, 0.5877852522924731], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.8968022466674206, 0.14203952192020614], [0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0, -1.902113032590307], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.9510565162951535, -0.30901699437494745]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0.36327126400268045, -1.118033988749895], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.41221474770752686, 0.8090169943749475], [-0.5877852522924731, 0.8090169943749475]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-3200-200.117-c0-0-1', 'leading_term': '0.81747151783705399505279169384782', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3200/1/bz/a/1217/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.817471517837054, 0.9179730755633264, 1.027813450223656, 1.1486762529681656, 1.2810405235516042, 1.4242267874124126, 1.5765432908514943, 1.7354700564693264, 1.897838883950003, 2.0599917308230515, 2.217916593546874, 2.3673676119744234, 2.503977580134063, 2.6233695351150006, 2.72127163468235, 2.7936370860417687, 2.836768794867588, 2.84744672709003, 2.823054683072867, 2.7617022272572846, 2.6623368606619993, 2.5248411491983687, 2.350109419814649, 2.1400988074551255, 1.8978498781212267, 1.6274727631092283, 1.334095706418959, 1.0237741321580147, 0.7033597518726842, 0.380330812305451, 0.06258628010337275, -0.2417914909728957, -0.5247993341817887, -0.778793175114571, -0.9967759027381862, -1.1726826467489588, -1.3016520484424683, -1.3802716712948957, -1.406785728856401, -1.3812538555707383, -1.3056507353049176, -1.183898034382075, -1.0218222371625658, -0.8270346024284615, -0.6087324708110173, -0.3774244542911061, -0.14458550217324187, 0.0777486816478518, 0.2774350573657711, 0.4427086626246408, 0.5626816271128929, 0.6278354775460009, 0.6304852811055801, 0.565193926567156, 0.4291155681422425, 0.22224899923167915, -0.0524155226260279, -0.38886876670239234, -0.7781825395902734, -1.208740159741454, -1.6665945880077837, -2.1359454028486864, -2.599719827955258, -3.0402373539988954, -3.4399324432456053, -3.782105654929374, -4.051670544820579, -4.23586209831882, -4.3248724216748755, -4.312381041875961, -4.195950475627287, -3.977262660290175, -3.6621782456336573, -3.2606083900898835, -2.786197274867335, -2.255822661751787, -1.6889310414435674, -1.1067327820402266, -0.5312907153216595, 0.015457669289300851, 0.5126992367610239, 0.9417172908528043, 1.286787982622738, 1.5359541665399217, 1.681634214624277, 1.721030095883462, 1.6563079935694378, 1.4945354939634445, 1.2473714470825286, 0.9305173839558557, 0.5629522187713408, 0.16598417171522856, -0.23783527616595204, -0.625881698287991, -0.9766522917012898, -1.270921396805996, -1.4927937247521414, -1.6305955997262733, -1.6775515142853707, -1.6322034810699289, -1.4985436030464279, -1.2858453581473717, -1.0081955328877075, -0.6837456595669302, -0.3337182616934999, 0.018781774118339478, 0.35008772962225615, 0.6373510569422671, 0.8599028208326122, 1.000517295965872, 1.0465017621986703, 0.9905444308715261, 0.8312645934562682, 0.5734249492684229, 0.2277848351874954, -0.1894062663181798, -0.6572541926619797, -1.1513629604265103, -1.6452144240198618, -2.1117081572302205, -2.52477311033959, -2.860955704150999, -3.1008877064106657, -3.2305417706950066, -3.24219282673243, -3.1350191574229944, -2.9152971965528374, -2.5961677346766, -2.1969769750440706, -1.7422222021604747, -1.2601570871951486, -0.781134240398192, -0.3357810263188425, 0.04688240951453056, 0.34126748334201745, 0.5268690702833042, 0.5896380004939757, 0.5229820373347629, 0.3283243030834941, 0.015174284296015868, -0.39930372658343216, -0.8912084198398346, -1.431257901261888, -1.9865081795077546, -2.522332305419839, -3.004539865506873, -3.4015049471700975, -3.6861673734875424, -3.837777388982085, -3.8432679414207627, -3.6981605531685835, -3.406939270153566, -2.9828606004124647, -2.4472036132190746, -1.8280011213980658, -1.1583276732705519, -0.4742505608753599, 0.1874259405812852, 0.7914771182649126, 1.3064828941404618, 1.70681302792486, 1.9742380181489827, 2.0990546086491095, 2.0806461345674303, 1.927435281812169, 1.6562277481909262, 1.2909870360709, 0.8611203030238245, 0.3993900479520909, -0.06040611476840613, -0.48582731674261065, -0.8480855449763753, -1.124083140862667, -1.298044923138167, -1.3626249278574334, -1.3194035063931124, -1.1787329033972194, -0.9589355649141845, -0.684906080415494, -0.3862115057204438, -0.09482263439788365, 0.1573622703030044, 0.3410219820148205, 0.43176064693770466, 0.4121237519067255, 0.2731267483651185, 0.015174314901691875, -0.35170921675551536, -0.8083685294607101, -1.3277029103005047, -1.8764747316711992, -2.4176193320498465, -2.9128953328744056, -3.32568603058039, -3.6237475171664295, -3.781699006087928, -3.7830658034312963, -3.6217146803194105, -3.3025631984393384, -2.8414959711706, -2.2644782798462413, -1.6059167503399248, -0.9063735414401716, -0.20979040969760224, 0.43958177814833777, 1.0003271663929492, 1.4368524329882646, 1.7219952140342718, 1.839055455167232, 1.7830915014619904, 1.5613750688958592, 1.1929603929997243, 0.7073883560621962, 0.14261136631750682, -0.4577157395684023, -1.0473840921361552, -1.5809884186604528, -2.017245407163866, -2.3220245013865006, -2.470861927341093, -2.450765589039446, -2.2611704749840507, -1.9139676042601854, -1.4325995806316467, -0.8502871877887138, -0.20751863042761032, 0.4510092769632485, 1.0797650739447144, 1.635812965844955, 2.082034725796697, 2.389893152289514, 2.5415215478640527, 2.5309754858534848, 2.364548347166858, 2.060125725347593, 1.6456300574212828, 1.1566796842006895, 0.6336501026152956, 0.11837422709067963, -0.3492511019395298, -0.7344760254728574, -1.0104628821409034, -1.160377397325086, -1.1786312745664007, -1.071170245588465, -0.8547797159426644, -0.5554614127612161, -0.20601227428840233, 0.15699523144572713, 0.49657985058409493, 0.7787816970961307, 0.9758631563659642, 1.0690031117128063, 1.050245656455621, 0.9235235705873834, 0.7046519059900833, 0.4202720581041872], 'positive_zeros': ['1.76960363162539352839939916410230', '2.73289589462564306078027304816315', '3.27105938648442573324135962377273', '4.62718449959383427598071017230635', '5.35604736326213731318133543229017', '6.14916671452523482012374719017032', '6.71274017716045485443569827645784', '7.78508216438129598431138658010116', '8.146938425186109621599093753143224', '9.182229580049751600256388493749507'], 'prelabel': '2-3200-200.117-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': 0.6799999999999999, 'root_number': '-0.53582679497899661827130876786751 + 0.84432792550201507854855806396698*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.34', 'prec': 14}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.76960363162539352839939916410', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73289589462564306078027304816', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27105938648442573324135962377', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'bad_primes': [2, 5], 'central_character': '200.117', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/1/bz/a/1217/1'], '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': '2-3200-200.117-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3200-200.117-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': 0.33999999999999997, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76960363162539352839939916410', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2243239105795984659243871407463', 'Lhash_array': ['2243239105795984659243871407463'], 'label': '2-3200-200.117-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/1/bz/a/1217/1'}