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lfunc_lfunctions • Show schema
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{'Lhash': '3302977817476820288962327066780', 'a10': [-6.104686356149273, 52.209372712298546], 'a2': [0.0, 4.701562118716424], 'a3': [0.0, -3.0], 'a4': [-14.104686356149273, 0.0], 'a5': [11.104686356149273, 1.2984378812835757], 'a6': [14.104686356149273, 0.0], 'a7': [0.0, -16.209372712298546], 'a8': [0.0, -28.701562118716424], 'a9': [-9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8850286500861096, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 3.0]]], [5, [[1.0, 0], [-11.104686356149273, -1.2984378812835757]]]], 'bad_primes': [3, 5], 'central_character': '15.4', 'coefficient_field': 'CDF', 'conductor': 15, 'conductor_radical': 15, 'conjugate': '6948505508091672164455243354506', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -4.701562118716424], [-8.0, 0]], [[1.0, 0], [0, 3.0]], [[1.0, 0], [-11.104686356149273, -1.2984378812835757]], [[1.0, 0], [0, 16.209372712298546], [-343.0, 0]], [[1.0, 0], 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{'__RealLiteral__': 0, 'data': '9.082106191258618449472323379130', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8850286500861096, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/15/4/b/a/4/4'], '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': '2-15-5.4-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9407596133370679, 'root_angle': -0.23147460714639062, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.60559007101968636034862575648', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3302977817476820288962327066780', 'Lhash_array': ['3302977817476820288962327066780'], 'label': '2-15-5.4-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/4/b/a/4/4'}