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lfunc_lfunctions • Show schema
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{'Lhash': '2394341142619288493232479316952', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.5877852522924731, 0.8090169943749475], 'a5': [-0.8090169943749475, -0.5877852522924731], 'a6': [0.0, 0.0], 'a7': [0.30901699437494745, -0.04894348370484643], 'a8': [0.0, 0.0], 'a9': [-0.9510565162951535, -0.30901699437494745], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5215229382014875, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [11, [[1.0, 0], [0.5877852522924731, 0.8090169943749475]]], [19, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.607', 'coefficient_field': 'CDF', 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': '461685078631830788227249620967', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.5877852522924731, -0.8090169943749475]], [[1.0, 0], [0, 0], 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'9.651433540513964990730755844116530', '10.40845825294976579252552074640140'], 'prelabel': '2-1045-1045.607-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7221654507115994, 'root_angle': 0.6307900744816596, 'root_number': '-0.39942461651203531902312301653461 + 0.91676604197811205924817835809530*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3153950372408298', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88880212117456364992933003052', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.19737034919313375151934384878', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.41031743435027963341026339995', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5215229382014875, 'bad_primes': [5, 11, 19], 'central_character': '1045.607', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1045/1/br/b/607/1'], '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': '2-1045-1045.607-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1045-1045.607-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7221654507115994, 'root_angle': 0.3153950372408298, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.88880212117456364992933003052', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2394341142619288493232479316952', 'Lhash_array': ['2394341142619288493232479316952'], 'label': '2-1045-1045.607-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/1/br/b/607/1'}