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lfunc_lfunctions • Show schema
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{'Lhash': '1153370815747812115758067663507,2016014943840749015663358036764', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 3, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1138.1713270202724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [13, [1]]], 'bad_primes': [5, 13], 'central_character': '4225.1', 'coefficient_field': '1.1.1.1', 'conductor': 17850625, 'conductor_radical': 65, 'degree': 4, 'euler_factors': [[1, 1, 3, 2, 4], [1, 0, 1, 0, 9], [1], [1, 4, 13, 28, 49], [1, -4, 21, -44, 121], [1], [1, 2, 15, 34, 289], [1, -4, 37, -76, 361], [1, 12, 77, 276, 529], [1, 6, 47, 174, 841], [1, 0, 62, 0, 961], [1, 6, 83, 222, 1369], [1, -6, 11, -246, 1681], [1, -8, 97, -344, 1849], [1, 8, 30, 376, 2209], [1, 12, 142, 636, 2809], [1, -12, 109, -708, 3481], [1, -2, -57, -122, 3721], [1, 8, 105, 536, 4489], [1, 8, 153, 568, 5041], [1, -12, 182, -876, 5329], [1, 0, 158, 0, 6241], [1, 0, 86, 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'rational': True, 'root_analytic_conductor': 5.808338390107018, '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': 1604204615396489704, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.909849145766315883704496109797', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.59035537353730054684932430914', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.08057816170988343724375407856', 'prec': 103}}
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lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1138.1713270202724, 'bad_primes': [5, 13], 'central_character': '1.1', 'conductor': 17850625, 'conductor_radical': 65, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, -2, 0, 0, -4, 3, -1, 0, 4, 0, 0, 4, 0, 1, -2, 1, 4, 0, 0, -4, -12, 0, 0, 0, 0, 8, -6, 0, 0, -2, 0, 2, 0, 2, -6, -4, 0, 0, 6, 0, 8, -8, 0, 12, -8, 0, 3, 0, 0, 0, -12, 0, 0, -12, 0, 6, 12, 0, 2, 0, 4, 1, 0, 0, -8, 4, 0, 0, -8, -3, 12, 6, 0, -8, -16, 0, 0, 0, -8, -6, 0, 0, 0, -8, 0, 12, -18, 0, 0, 24, 0, 8, 0, 0, -2, -3, -4, 0], 'euler11': [1, -4, 21, -44, 121], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, 2, 15, 34, 289], 'euler19': [1, -4, 37, -76, 361], 'euler2': [1, 1, 3, 2, 4], 'euler23': [1, 12, 77, 276, 529], 'euler29': [1, 6, 47, 174, 841], 'euler3': [1, 0, 1, 0, 9], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 6, 83, 222, 1369], 'euler41': [1, -6, 11, -246, 1681], 'euler43': [1, -8, 97, -344, 1849], 'euler47': [1, 8, 30, 376, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, -12, 109, -708, 3481], 'euler61': [1, -2, -57, -122, 3721], 'euler67': [1, 8, 105, 536, 4489], 'euler7': [1, 4, 13, 28, 49], 'euler71': [1, 8, 153, 568, 5041], 'euler73': [1, -12, 182, -876, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 86, 0, 6889], 'euler89': [1, 18, 259, 1602, 7921], 'euler97': [1, 2, 175, 194, 9409], 'euler_factors': [[1, 1, 3, 2, 4], [1, 0, 1, 0, 9], [1, 0, 0, 0, 0], [1, 4, 13, 28, 49], [1, -4, 21, -44, 121], [1, 0, 0, 0, 0], [1, 2, 15, 34, 289], [1, -4, 37, -76, 361], [1, 12, 77, 276, 529], [1, 6, 47, 174, 841], [1, 0, 62, 0, 961], [1, 6, 83, 222, 1369], [1, -6, 11, -246, 1681], [1, -8, 97, -344, 1849], [1, 8, 30, 376, 2209], [1, 12, 142, 636, 2809], [1, -12, 109, -708, 3481], [1, -2, -57, -122, 3721], [1, 8, 105, 536, 4489], [1, 8, 153, 568, 5041], [1, -12, 182, -876, 5329], [1, 0, 158, 0, 6241], [1, 0, 86, 0, 6889], [1, 18, 259, 1602, 7921], [1, 2, 175, 194, 9409]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4225/2/a/u'], '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': '4-65e4-1.1-c1e2-0-3', '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': '4-65e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.808338390107018, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1604204615396489704, 'z1': {'__RealLiteral__': 0, 'data': '0.909849145766315883704496109797', 'prec': 107}}
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{'Lhash': '1153370815747812115758067663507,2016014943840749015663358036764', 'Lhash_array': ['1153370815747812115758067663507', '2016014943840749015663358036764'], 'factors': ['2-65e2-1.1-c1-0-89', '2-65e2-1.1-c1-0-193'], 'label': '4-65e4-1.1-c1e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4225/2/a/u'}