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lfunc_lfunctions • Show schema
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{'Lhash': '1735131995476389890702948039281', 'a10': [-80.54841337063525, 0.0], 'a2': [5.069370691082129, 0.0], 'a3': [91.52951577955487, 0.0], 'a4': [-102.3014807963975, 0.0], 'a5': [-15.889233255783283, 0.0], 'a6': [463.9970446618147, 0.0], 'a7': [343.0, 0.0], 'a8': [-1167.4835768620712, 0.0], 'a9': [6190.652258839784, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.427037319055092, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-343.0, 0]]], [13, [[1.0, 0], [-2197.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '91.1', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'euler_factors': [[[1.0, 0], [-5.069370691082129, 0], [128.0, 0]], [[1.0, 0], [-91.52951577955487, 0], [2187.0, 0]], [[1.0, 0], [15.889233255783283, 0], [78125.0, 0]], [[1.0, 0], [-343.0, 0]], [[1.0, 0], [579.100795464297, 0], [19487171.0, 0]], [[1.0, 0], [-2197.0, 0]], [[1.0, 0], 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0.5539864136575469, 0.8403458878278547, 1.0462100501827554, 1.1510088505901914, 1.143825251605629, 1.0245833117744965], 'positive_zeros': ['1.36877779662944549026067084813695', '3.08258049307173903683321344673365', '3.84969856016893263449107447325743', '5.27495524703005699123453113375397', '7.46933215813166924124029306664042', '8.219394093027801447613748356538239', '9.312040463911508798050286439493574', '9.958574289516056350248779225240636', '11.98468323624242149189932443755848', '13.21617165068745411664291797352103'], 'prelabel': '2-91-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.331701165580746, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36877779662944549026067084814', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08258049307173903683321344673', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84969856016893263449107447326', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.427037319055092, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/8/a/e/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': '2-91-1.1-c7-0-22', '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': '2-91-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.331701165580746, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36877779662944549026067084814', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1735131995476389890702948039281', 'Lhash_array': ['1735131995476389890702948039281'], 'label': '2-91-1.1-c7-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/8/a/e/1/7'}