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lfunc_lfunctions • Show schema
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{'Lhash': '3118380548549554088210376619119', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.1661232505825025, -2.019784717896268], 'a4': [0.0, 0.0], 'a5': [0.0, -1.0], 'a6': [0.0, 0.0], 'a7': [0.3462406858881709, -0.19990215320193613], 'a8': [0.0, 0.0], 'a9': [-1.2196868710982038, -2.112559630066801], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [0.6194911775020762, 3.5519333722632087]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.121', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '1711786637032853571891086332443', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.1661232505825025, 2.019784717896268], [-1.5, -2.598076211353316]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-0.3462406858881709, 0.19990215320193613], [3.5, -6.06217782649107]], 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'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.44095466172253694, 'root_number': '0.1844344413441235 + 0.9828448182933464*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.220477330861', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.45996850235239659036784096039', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.81196785478660970369013151617', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61980104263590401138682521249', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '13.4', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/x/a/121/4'], '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': '2-260-13.4-c1-0-3', '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': '2-260-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.22047733086126847, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.45996850235239659036784096039', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3118380548549554088210376619119', 'Lhash_array': ['3118380548549554088210376619119'], 'label': '2-260-13.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/x/a/121/4'}