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lfunc_lfunctions • Show schema
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{'Lhash': '821673138042235668772690321338', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-22.293950585835702, 0.0], 'a4': [0.0, 0.0], 'a5': [-24.121856501341018, 0.0], 'a6': [0.0, 0.0], 'a7': [-222.16655606711623, 0.0], 'a8': [0.0, 0.0], 'a9': [254.02023272368405, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 164.8745667677441, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [257, [[1.0, 0], [-66049.0, 0]]]], 'bad_primes': [2, 257], 'central_character': '1028.1', 'coefficient_field': 'CDF', 'conductor': 1028, 'conductor_radical': 514, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [22.293950585835702, 0], [243.0, 0]], [[1.0, 0], [24.121856501341018, 0], [3125.0, 0]], [[1.0, 0], [222.16655606711623, 0], [16807.0, 0]], [[1.0, 0], [158.6866135610151, 0], [161051.0, 0]], [[1.0, 0], [403.52229068631283, 0], [371293.0, 0]], [[1.0, 0], [1697.0702607870314, 0], [1419857.0, 0]], [[1.0, 0], 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[254194901951.0, 0]], [[1.0, 0], [909465.0705078853, 0], [267785184193.0, 0]], [[1.0, 0], [963362.1857293283, 0], [296709280757.0, 0]], [[1.0, 0], [-915739.6580993814, 0], [312079600999.0, 0]], [[1.0, 0], [-552163.9060997401, 0], [418227202051.0, 0]], [[1.0, 0], [1073522.9043014639, 0], [551473077343.0, 0]], [[1.0, 0], [-1188002.8328549971, 0], [602738989907.0, 0]], [[1.0, 0], [-76366.04544641991, 0], [629763392149.0, 0]], [[1.0, 0], [97225.99886788092, 0], [686719856393.0, 0]], [[1.0, 0], [356101.21255255595, 0], [779811265199.0, 0]], [[1.0, 0], [780291.4304213686, 0], [812990017201.0, 0]], [[1.0, 0], [1025734.4546573681, 0], [996250626251.0, 0]], [[1.0, 0], [-66049.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-1028-1.1-c5-0-34', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64818581547178742158833969982', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40065520541199370323996554287', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52254098359476097061512948814', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 164.8745667677441, 'bad_primes': [2, 257], 'central_character': '1.1', 'conductor': 1028, 'conductor_radical': 514, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1028/6/a/a/1/7'], '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': '2-1028-1.1-c5-0-34', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-1028-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.84034916845115, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64818581547178742158833969982', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '821673138042235668772690321338', 'Lhash_array': ['821673138042235668772690321338'], 'label': '2-1028-1.1-c5-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1028/6/a/a/1/7'}