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lfunc_lfunctions • Show schema
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{'Lhash': '2781717273802398972337870016212,3148031125513573942404559604944', 'a10': 3, 'a2': -1, 'a3': 0, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': -1, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.110407724657517, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 1]], [3, [1]], [7, [1, 1, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '378.1', 'coefficient_field': '1.1.1.1', 'conductor': 142884, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, 1, 1], [1], [1, 3, 4, 15, 25], [1, 1, 1], [1, 6, 25, 66, 121], [1, 2, -9, 26, 169], [1, 12, 70, 204, 289], [1, 14, 87, 266, 361], [1, -3, -14, -69, 529], [1, -6, 7, -174, 841], [1, 2, -27, 62, 961], [1, -4, 78, -148, 1369], [1, 0, -41, 0, 1681], [1, 2, -39, 86, 1849], [1, 0, -47, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, -59, 0, 3481], [1, 5, -36, 305, 3721], [1, 8, -3, 536, 4489], [1, 6, 151, 426, 5041], [1, -4, 150, -292, 5329], [1, 5, -54, 395, 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'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1585192518253189222, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.19438800668068560131758197913', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48335868333655857253174963387', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41515839077614286366190499300', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 9.110407724657517, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 142884, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 0, -3, 0, -1, 1, 0, 3, -6, 0, -2, 1, 0, -1, -12, 0, -14, 0, 0, 6, 3, 0, 5, 2, 0, 0, 6, 0, -2, 0, 0, 12, 3, 0, 4, 14, 0, -3, 0, 0, -2, 0, 0, -3, 0, 0, 0, -5, 0, 0, -12, 0, 18, -1, 0, -6, 0, 0, -5, 2, 0, 1, 6, 0, -8, 0, 0, -3, -6, 0, 4, -4, 0, 0, 6, 0, -5, 3, 0, 0, 12, 0, 36, 2, 0, -6, 0, 0, 2, 0, 0, 0, 42, 0, -2, 0, 0, 0], 'euler11': [1, 6, 25, 66, 121], 'euler13': [1, 2, -9, 26, 169], 'euler17': [1, 12, 70, 204, 289], 'euler19': [1, 14, 87, 266, 361], 'euler2': [1, 1, 1, 0, 0], 'euler23': [1, -3, -14, -69, 529], 'euler29': [1, -6, 7, -174, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 2, -27, 62, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, -41, 0, 1681], 'euler43': [1, 2, -39, 86, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, 3, 4, 15, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, 5, -36, 305, 3721], 'euler67': [1, 8, -3, 536, 4489], 'euler7': [1, 1, 1, 0, 0], 'euler71': [1, 6, 151, 426, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 5, -54, 395, 6241], 'euler83': [1, -12, 61, -996, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 2, -93, 194, 9409], 'euler_factors': [[1, 1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 3, 4, 15, 25], [1, 1, 1, 0, 0], [1, 6, 25, 66, 121], [1, 2, -9, 26, 169], [1, 12, 70, 204, 289], [1, 14, 87, 266, 361], [1, -3, -14, -69, 529], [1, -6, 7, -174, 841], [1, 2, -27, 62, 961], [1, -4, 78, -148, 1369], [1, 0, -41, 0, 1681], [1, 2, -39, 86, 1849], [1, 0, -47, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, -59, 0, 3481], [1, 5, -36, 305, 3721], [1, 8, -3, 536, 4489], [1, 6, 151, 426, 5041], [1, -4, 150, -292, 5329], [1, 5, -54, 395, 6241], [1, -12, 61, -996, 6889], [1, 0, 178, 0, 7921], [1, 2, -93, 194, 9409]], 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/f/a'], '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': '4-378e2-1.1-c1e2-0-31', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-378e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1585192518253189222, 'z1': {'__RealLiteral__': 0, 'data': '2.19438800668068560131758197913', 'prec': 103}}
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{'Lhash': '2781717273802398972337870016212,3148031125513573942404559604944', 'Lhash_array': ['2781717273802398972337870016212', '3148031125513573942404559604944'], 'label': '4-378e2-1.1-c1e2-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/f/a'}