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lfunc_lfunctions • Show schema
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{'Lhash': '1033067703796321035941880448742', 'a10': [3.367360361204188, 0.0], 'a2': [-0.8864861007560895, 0.0], 'a3': [-3.3561675879923083, 0.0], 'a4': [-1.2141423931662643, 0.0], 'a5': [-3.79854840175401, 0.0], 'a6': [2.9751959185632715, 0.0], 'a7': [-4.5603065680705726, 0.0], 'a8': [2.8492925573928076, 0.0], 'a9': [8.263860878690108, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.008995322734426, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [-1.0, 0]]], [59, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [17, 59], 'central_character': '1003.1', 'coefficient_field': 'CDF', 'conductor': 1003, 'conductor_radical': 1003, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8864861007560895, 0], [2.0, 0]], [[1.0, 0], [3.3561675879923083, 0], [3.0, 0]], [[1.0, 0], [3.79854840175401, 0], [5.0, 0]], [[1.0, 0], [4.5603065680705726, 0], [7.0, 0]], [[1.0, 0], [-3.9117398161910057, 0], [11.0, 0]], [[1.0, 0], [4.651758164229767, 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'5.11186169705653967787848694719687', '6.33678897473865506820971363422768', '7.06124618799932755303339097501241', '7.55737133299301944878412072109880', '8.966611999535779394465055392519651', '9.716251255818472618407651108566745'], 'prelabel': '2-1003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8300168414224016, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.814946723971357906412223086233', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.58829404354048512652502267686', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29763240810814151572853015251', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.008995322734426, 'bad_primes': [17, 59], 'central_character': '1.1', 'conductor': 1003, 'conductor_radical': 1003, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1003/2/a/h/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': '2-1003-1.1-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8300168414224016, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.814946723971357906412223086233', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1033067703796321035941880448742', 'Lhash_array': ['1033067703796321035941880448742'], 'label': '2-1003-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1003/2/a/h/1/7'}