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lfunc_lfunctions • Show schema
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{'Lhash': '942924800684781313074880303061', 'a10': [-1.5073053991587197, 0.0], 'a2': [1.5073053991587197, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.2719695663330275, 0.0], 'a5': [-1.0, 0.0], 'a6': [-1.5073053991587197, 0.0], 'a7': [-1.0, 0.0], 'a8': [-2.6046696025768115, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.283872088139223, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 7, 23], 'central_character': '2415.1', 'coefficient_field': 'CDF', 'conductor': 2415, 'conductor_radical': 2415, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.5073053991587197, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.6072433390655756, 0], [11.0, 0]], [[1.0, 0], [2.8325477584760588, 0], [13.0, 0]], [[1.0, 0], [-4.57881780756296, 0], [17.0, 0]], [[1.0, 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'3.56739021502311175519561526305883', '4.11825698821944310413665899212180', '4.99619304612251397410161853764462', '5.71204201583698888701973657383210', '6.38175817475512509346457257906252', '7.23810972903887522767024790962136', '7.988620683778637857115793294075415', '9.261526052368250607273924792677370'], 'prelabel': '2-2415-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.391340579838829, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74383651182353871892617623803', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46356460733964575322142628518', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56739021502311175519561526306', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.283872088139223, 'bad_primes': [3, 5, 7, 23], 'central_character': '1.1', 'conductor': 2415, 'conductor_radical': 2415, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2415/2/a/p/1/5'], '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': '2-2415-1.1-c1-0-17', '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': '2-2415-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.391340579838829, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74383651182353871892617623803', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '942924800684781313074880303061', 'Lhash_array': ['942924800684781313074880303061'], 'label': '2-2415-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2415/2/a/p/1/5'}