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lfunc_lfunctions • Show schema
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{'Lhash': '1143301079672468861652242381686', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 256, 'a5': -431, 'a6': 0, 'a7': -2401, 'a8': 0, 'a9': 6561, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.07145351556259, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[7, [1, 2401]], [13, [1, 28561]]], 'bad_primes': [7, 13], 'central_character': '91.90', 'coefficient_field': '1.1.1.1', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'euler_factors': [[1, 0, -256], [1, 0, -6561], [1, 431, 390625], [1, 2401], [1, 0, -214358881], [1, 28561], [1, 0, -6975757441], [1, -251233, 16983563041], [1, -375407, 78310985281], [1, 1062913, 500246412961], [1, -630433, 852891037441], [1, 0, -3512479453921], [1, 409922, 7984925229121], [1, -6653327, 11688200277601], [1, -5166913, 23811286661761], [1, -13303487, 62259690411361], [1, -22939678, 146830437604321], [1, 0, -191707312997281], [1, 0, -406067677556641], [1, 0, -645753531245761], [1, 39577007, 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'2.63090645296419318962016577961466', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.82530205555607426144551636714617', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.07145351556259, 'bad_primes': [7, 13], 'central_character': '91.90', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 256, -431, 0, -2401, 0, 6561, 0, 0, 0, -28561, 0, 0, 65536, 0, 0, 251233, -110336, 0, 0, 375407, 0, -204864, 0, 0, -614656, -1062913, 0, 630433, 0, 0, 0, 1034831, 1679616, 0, 0, 0, 0, -409922, 0, 6653327, 0, -2827791, 0, 5166913, 0, 5764801, 0, 0, -7311616, 13303487, 0, 0, 0, 0, 0, 22939678, 0, 0, 0, -15752961, 16777216, 12309791, 0, 0, 0, 0, 0, 0, 0, -39577007, 0, 0, 64315648, 0, 0, -14012113, -28246016, 43046721, 0, -37402367, 0, 0, 0, 0, 0, -4088207, 0, 68574961, 96104192, 0, 0, -108281423, 0, 174312913, 0, 0, -52445184], 'euler11': [1, 0, -214358881], 'euler13': [1, 28561, 0], 'euler17': [1, 0, -6975757441], 'euler19': [1, -251233, 16983563041], 'euler2': [1, 0, -256], 'euler23': [1, -375407, 78310985281], 'euler29': [1, 1062913, 500246412961], 'euler3': [1, 0, -6561], 'euler31': [1, -630433, 852891037441], 'euler37': [1, 0, -3512479453921], 'euler41': [1, 409922, 7984925229121], 'euler43': [1, -6653327, 11688200277601], 'euler47': [1, -5166913, 23811286661761], 'euler5': [1, 431, 390625], 'euler53': [1, -13303487, 62259690411361], 'euler59': [1, -22939678, 146830437604321], 'euler61': [1, 0, -191707312997281], 'euler67': [1, 0, -406067677556641], 'euler7': [1, 2401, 0], 'euler71': [1, 0, -645753531245761], 'euler73': [1, 39577007, 806460091894081], 'euler79': [1, 14012113, 1517108809906561], 'euler83': [1, 37402367, 2252292232139041], 'euler89': [1, 4088207, 3936588805702081], 'euler97': [1, -174312913, 7837433594376961], 'euler_factors': [[1, 0, -256], [1, 0, -6561], [1, 431, 390625], [1, 2401, 0], [1, 0, -214358881], [1, 28561, 0], [1, 0, -6975757441], [1, -251233, 16983563041], [1, -375407, 78310985281], [1, 1062913, 500246412961], [1, -630433, 852891037441], [1, 0, -3512479453921], [1, 409922, 7984925229121], [1, -6653327, 11688200277601], [1, -5166913, 23811286661761], [1, -13303487, 62259690411361], [1, -22939678, 146830437604321], [1, 0, -191707312997281], [1, 0, -406067677556641], [1, 0, -645753531245761], [1, 39577007, 806460091894081], [1, 14012113, 1517108809906561], [1, 37402367, 2252292232139041], [1, 4088207, 3936588805702081], [1, -174312913, 7837433594376961]], 'index': 34, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/9/b/a', 'ModularForm/GL2/Q/holomorphic/91/9/b/a/90/1'], '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': '2-91-91.90-c8-0-34', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-91-91.90-c8-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.0886331401688665, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c8-0', 'trace_hash': 460588017699542437, 'z1': {'__RealLiteral__': 0, 'data': '0.901905524650583925534898585636037', 'prec': 117}}
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lfunc_instances • Show schema
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id: 24566815
{'Lhash': '1143301079672468861652242381686', 'Lhash_array': ['1143301079672468861652242381686'], 'label': '2-91-91.90-c8-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/9/b/a/90/1'}
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id: 23350656
{'Lhash': '1143301079672468861652242381686', 'Lhash_array': ['1143301079672468861652242381686'], 'label': '2-91-91.90-c8-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/9/b/a'}