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lfunc_lfunctions • Show schema
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{'Lhash': '894793981648036126087461622556', 'a10': [-3.0, 0.0], 'a2': [-1.5, -0.8660254037844386], 'a3': [1.0, 0.0], 'a4': [0.5, 0.8660254037844386], 'a5': [1.5, -0.8660254037844386], 'a6': [-1.5, -0.8660254037844386], 'a7': [0.0, 0.0], 'a8': [0.0, 1.7320508075688772], 'a9': [-2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, -3.4641016151377544]]]], 'bad_primes': [7, 13], 'central_character': '637.361', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '2055603045079721287417864356048', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5, 0.8660254037844386], [1.0, 1.7320508075688772]], [[1.0, 0], [-1.0, 0], [3.0, 0]], [[1.0, 0], [-1.5, 0.8660254037844386], [2.5, -4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -5.196152422706632], [-11.0, 0]], [[1.0, 0], [-1.0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '91.88', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/u/a/361/1'], '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': '2-637-91.88-c1-0-12', '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': '2-637-91.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.06286009541689613, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70586799034918320325363066594', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '894793981648036126087461622556', 'Lhash_array': ['894793981648036126087461622556'], 'factors': ['2-637-91.88-c1-0-12'], 'label': '2-637-91.88-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/u/a/361/1'}