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lfunc_lfunctions • Show schema
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{'Lhash': '2061878280225208273409967042535,2618398101965784908856321269776', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 60.612674220014505, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1, 1]], [5, [1]], [13, [1, 7, 13]]], 'bad_primes': [3, 5, 13], 'central_character': '975.1', 'coefficient_field': '1.1.1.1', 'conductor': 950625, 'conductor_radical': 195, 'degree': 4, 'euler_factors': [[1, 0, 2, 0, 4], [1, 1, 1], [1], [1, -3, 10, -21, 49], [1, 6, 23, 66, 121], [1, 7, 13], [1, 0, -17, 0, 289], [1, -6, 31, -114, 361], [1, 6, 13, 138, 529], [1, 6, 7, 174, 841], [1, 0, -59, 0, 961], [1, 0, 37, 0, 1369], [1, 12, 89, 492, 1681], [1, 1, -42, 43, 1849], [1, 0, -82, 0, 2209], [1, 24, 250, 1272, 2809], [1, 6, 71, 354, 3481], [1, 1, -60, 61, 3721], [1, 15, 142, 1005, 4489], [1, 18, 179, 1278, 5041], [1, 0, -143, 0, 5329], [1, 22, 279, 1738, 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'4-975e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.790235509249146, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 2182621060596501205, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62653516659400084362747731031', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.06555189694570825403784157666', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04759202969689392374417843759', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 60.612674220014505, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 950625, 'conductor_radical': 195, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, -2, 0, 0, 3, 0, 0, 0, -6, 2, -7, 0, 0, 0, 0, 0, 6, 0, -3, 0, -6, 0, 0, 0, 1, -6, -6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 7, 0, -12, 0, -1, 12, 0, 0, 0, 0, -1, 0, 0, 14, -24, 0, 0, 0, -6, 0, -6, 0, -1, 0, 0, 8, 0, 0, -15, 0, 6, 0, -18, 0, 0, 0, 0, -12, -18, 0, -22, 0, -1, 0, 0, 6, 0, 0, 6, 0, 12, 0, -21, 12, 0, 0, 0, 0, 9, 0, 0, 0], 'euler11': [1, 6, 23, 66, 121], 'euler13': [1, 7, 13, 0, 0], 'euler17': [1, 0, -17, 0, 289], 'euler19': [1, -6, 31, -114, 361], 'euler2': [1, 0, 2, 0, 4], 'euler23': [1, 6, 13, 138, 529], 'euler29': [1, 6, 7, 174, 841], 'euler3': [1, 1, 1, 0, 0], 'euler31': [1, 0, -59, 0, 961], 'euler37': [1, 0, 37, 0, 1369], 'euler41': [1, 12, 89, 492, 1681], 'euler43': [1, 1, -42, 43, 1849], 'euler47': [1, 0, -82, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 24, 250, 1272, 2809], 'euler59': [1, 6, 71, 354, 3481], 'euler61': [1, 1, -60, 61, 3721], 'euler67': [1, 15, 142, 1005, 4489], 'euler7': [1, -3, 10, -21, 49], 'euler71': [1, 18, 179, 1278, 5041], 'euler73': [1, 0, -143, 0, 5329], 'euler79': [1, 22, 279, 1738, 6241], 'euler83': [1, 0, 26, 0, 6889], 'euler89': [1, -12, 137, -1068, 7921], 'euler97': [1, -9, 124, -873, 9409], 'euler_factors': [[1, 0, 2, 0, 4], [1, 1, 1, 0, 0], [1, 0, 0, 0, 0], [1, -3, 10, -21, 49], [1, 6, 23, 66, 121], [1, 7, 13, 0, 0], [1, 0, -17, 0, 289], [1, -6, 31, -114, 361], [1, 6, 13, 138, 529], [1, 6, 7, 174, 841], [1, 0, -59, 0, 961], [1, 0, 37, 0, 1369], [1, 12, 89, 492, 1681], [1, 1, -42, 43, 1849], [1, 0, -82, 0, 2209], [1, 24, 250, 1272, 2809], [1, 6, 71, 354, 3481], [1, 1, -60, 61, 3721], [1, 15, 142, 1005, 4489], [1, 18, 179, 1278, 5041], [1, 0, -143, 0, 5329], [1, 22, 279, 1738, 6241], [1, 0, 26, 0, 6889], [1, -12, 137, -1068, 7921], [1, -9, 124, -873, 9409]], 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/975/2/bc/c'], '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': '4-975e2-1.1-c1e2-0-36', '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': '4-975e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.790235509249146, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2182621060596501205, 'z1': {'__RealLiteral__': 0, 'data': '1.62653516659400084362747731031', 'prec': 103}}
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{'Lhash': '2061878280225208273409967042535,2618398101965784908856321269776', 'Lhash_array': ['2061878280225208273409967042535', '2618398101965784908856321269776'], 'label': '4-975e2-1.1-c1e2-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/975/2/bc/c'}