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lfunc_lfunctions • Show schema
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{'Lhash': '402395480491556169080906421133', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.1661232505825025, 2.019784717896268], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-0.3462406858881709, 0.19990215320193613], 'a8': [0, 0], 'a9': [-1.2196868710982038, -2.112559630066801], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.380552262766455, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-0.6194911775020762, -3.5519333722632087]]]], 'bad_primes': [2, 5, 13], 'central_character': '1300.901', 'coefficient_field': 'CDF', 'conductor': 1300, 'conductor_radical': 130, 'conjugate': '2238411965764958917227187197556', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.1661232505825025, -2.019784717896268], [-1.5, -2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.3462406858881709, -0.19990215320193613], [3.5, -6.06217782649107]], [[1.0, 0], [-1.5, 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'9.119095595915456725048507569169600'], 'prelabel': '2-1300-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.221886444734894, 'root_angle': 0.940954661722537, 'root_number': '-0.98284481829334637245386904097668614915153058844976894439 + 0.1844344413441235541922471607922735896203256524198971925*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4704773308612685', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31743406299741299603245568764', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.50642197614219762074019598255', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.76844918802942074130460817953', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.380552262766455, 'bad_primes': [2, 5, 13], 'central_character': '13.4', 'conductor': 1300, 'conductor_radical': 130, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1300/2/y/b/901/1'], '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': '2-1300-13.4-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1300-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.221886444734894, 'root_angle': 0.4704773308612685, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31743406299741299603245568764', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '402395480491556169080906421133', 'Lhash_array': ['402395480491556169080906421133'], 'label': '2-1300-13.4-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1300/2/y/b/901/1'}