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lfunc_lfunctions • Show schema
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{'Lhash': '2013011540144349442718837675624', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [12.446221994724903, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 104.07936925012649, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.1', 'coefficient_field': 'CDF', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-12.446221994724903, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-51.123553963074315, 0], [1331.0, 0]], [[1.0, 0], [37.23110997362451, 0], [2197.0, 0]], [[1.0, 0], [-22.215112021100392, 0], [4913.0, 0]], [[1.0, 0], [54.3386659841747, 0], [6859.0, 0]], [[1.0, 0], [176.92443989449805, 0], [12167.0, 0]], [[1.0, 0], 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'6.87097750727987642237460499924515', '7.66784074350945642071579570999027', '8.805448595766898552985203162744848'], 'prelabel': '2-42e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.201929682669181, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58798610577861464682137493355', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13333575779049972860808218319', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50876373457885020965654768839', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 104.07936925012649, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/4/a/y/1/2'], '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': '2-42e2-1.1-c3-0-50', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-42e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.201929682669181, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58798610577861464682137493355', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2013011540144349442718837675624', 'Lhash_array': ['2013011540144349442718837675624'], 'factors': ['2-42e2-1.1-c3-0-50'], 'label': '2-42e2-1.1-c3-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/4/a/y/1/2'}