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lfunc_lfunctions • Show schema
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{'Lhash': '1886689985184053319088365530422', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -1.7320508075688772], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '3200.1599', 'coefficient_field': 'CDF', 'conductor': 3200, 'conductor_radical': 10, 'conjugate': '1219824697524091760361257207197', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 1.0], [-1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 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'-0.44721359549995793928183473374601 + 0.89442719099991587856366946749279*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.32379180882521663', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48833596958370965274205684930', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09812018185450359245456932186', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68559860862640257574997850971', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'bad_primes': [2, 5], 'central_character': '40.19', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/1/e/b/1599/2'], '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': '2-3200-40.19-c0-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3200-40.19-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48833596958370965274205684930', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1886689985184053319088365530422', 'Lhash_array': ['1886689985184053319088365530422'], 'label': '2-3200-40.19-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/1/e/b/1599/2'}