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lfunc_lfunctions • Show schema
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{'Lhash': '706342561218425145858768742413', 'a10': [-2715092985.541209, 242603079.9044738], 'a2': [-88.26966822486315, 88.26966822486315], 'a3': [0, 0], 'a4': [0, 2081568.9313429452], 'a5': [16753750.891592119, 14005320.03438698], 'a6': [0, 0], 'a7': [637624944.8102171, 637624944.8102171], 'a8': [-368854310.21393293, -368854310.21393293], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 125.76480492917796, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-16753750.891592119, -14005320.03438698]]]], 'bad_primes': [3, 5], 'central_character': '45.17', 'coefficient_field': 'CDF', 'conductor': 45, 'conductor_radical': 15, 'conjugate': '1641781589964885061664003961670', 'degree': 2, 'euler_factors': [[[1.0, 0], [88.26966822486315, -88.26966822486315], [0, -2097152.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-16753750.891592119, -14005320.03438698]], [[1.0, 0], [-637624944.8102171, 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3793308429735117', 'prec': 64}, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55720603223889480793093386240', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.41874210645177708049879432038', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.29121245689482727838676087994', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 125.76480492917796, 'bad_primes': [3, 5], 'central_character': '15.2', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/22/f/a/17/20'], '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': '2-45-15.2-c21-0-14', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'prelabel': '2-45-15.2-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.214490845739629, 'root_angle': -0.3793308429735117, 'self_dual': False, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55720603223889480793093386240', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '706342561218425145858768742413', 'Lhash_array': ['706342561218425145858768742413'], 'label': '2-45-15.2-c21-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/22/f/a/17/20'}