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lfunc_lfunctions • Show schema
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{'Lhash': '1195077647125011802202877341628', 'a10': [5889.141491677434, 0.0], 'a2': [16.300656527108504, 0.0], 'a3': [-27.0, 0.0], 'a4': [137.71140321476514, 0.0], 'a5': [361.28247238898666, 0.0], 'a6': [-440.1177262319297, 0.0], 'a7': [685.7529386236413, 0.0], 'a8': [158.3022482001439, 0.0], 'a9': [729.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 147.1333470030214, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [27.0, 0]]], [157, [[1.0, 0], [3869893.0, 0]]]], 'bad_primes': [3, 157], 'central_character': '471.1', 'coefficient_field': 'CDF', 'conductor': 471, 'conductor_radical': 471, 'degree': 2, 'euler_factors': [[[1.0, 0], [-16.300656527108504, 0], [128.0, 0]], [[1.0, 0], [27.0, 0]], [[1.0, 0], [-361.28247238898666, 0], [78125.0, 0]], [[1.0, 0], [-685.7529386236413, 0], [823543.0, 0]], [[1.0, 0], [2074.7592556670556, 0], [19487171.0, 0]], [[1.0, 0], [1380.8744087809873, 0], [62748517.0, 0]], [[1.0, 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'prelabel': '2-471-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.129853544170325, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.942750034520433726819742337424', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.15959239260740852059470834778', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06054182814397123409630401979', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 147.1333470030214, 'bad_primes': [3, 157], 'central_character': '1.1', 'conductor': 471, 'conductor_radical': 471, 'degree': 2, 'index': 96, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/471/8/a/c/1/40'], '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': '2-471-1.1-c7-0-96', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-471-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.129853544170325, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.942750034520433726819742337424', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1195077647125011802202877341628', 'Lhash_array': ['1195077647125011802202877341628'], 'label': '2-471-1.1-c7-0-96', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/471/8/a/c/1/40'}