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lfunc_lfunctions • Show schema
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{'Lhash': '2257581768502049631203711134423', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.7098088857877, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [19, [1, 1]]], 'bad_primes': [2, 19], 'central_character': '1216.1', 'coefficient_field': '1.1.1.1', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, 0, 5], [1, -3, 7], [1, 2, 11], [1, 1, 13], [1, 5, 17], [1, 1], [1, 1, 23], [1, -3, 29], [1, -4, 31], [1, 2, 37], [1, 8, 41], [1, -8, 43], [1, 8, 47], [1, 9, 53], [1, 1, 59], [1, 14, 61], [1, 13, 67], [1, -10, 71], [1, -9, 73], [1, 10, 79], [1, 10, 83], [1, 12, 89], [1, -14, 97], [1, -14, 101], [1, -6, 103], [1, 15, 107], [1, 7, 109], [1, 18, 113]], 'euler_factors_factorization': [[1], [[[1, 1, 3], 1]], [[[1, 0, 5], 1]], [[[1, -3, 7], 1]], [[[1, 2, 11], 1]], [[[1, 1, 13], 1]], [[[1, 5, 17], 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0.3382643883206204, 0.9076071059923411, 1.4764902337553707, 2.009243910179792, 2.4724360268903274, 2.8370785993733882, 3.080556618019318, 3.1881505167237854, 3.154048911148458], 'positive_zeros': ['1.78091799751097958894751684260535', '2.89182953598080292522833763992257', '4.41313931480294198592546395455815', '4.99527268882455447172353841145527', '5.90719710332910393553929521875013', '6.72377104864689556277323751664492', '7.87598676263742878936605339825175', '8.346693816906368374834545094569225', '9.279291644452987911454471213218352'], 'prelabel': '2-1216-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.11605662429098, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1809907073493533625, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78091799751097958894751684261', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89182953598080292522833763992', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.41313931480294198592546395456', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.7098088857877, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 3, 0, -2, 0, -2, 0, -1, 0, 0, 0, -5, 0, -1, 0, -3, 0, -1, 0, -5, 0, 5, 0, 3, 0, 4, 0, 2, 0, 0, 0, -2, 0, 1, 0, -8, 0, 8, 0, 0, 0, -8, 0, 2, 0, 5, 0, -9, 0, 0, 0, 1, 0, -1, 0, -14, 0, -6, 0, 0, 0, -13, 0, 1, 0, 10, 0, 9, 0, 5, 0, -6, 0, -10, 0, 1, 0, -10, 0, 0, 0, -3, 0, -12, 0, -3, 0, -4, 0, 0, 0, 14, 0, 4, 0], 'euler11': [1, 2, 11], 'euler13': [1, 1, 13], 'euler17': [1, 5, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 1, 23], 'euler29': [1, -3, 29], 'euler3': [1, 1, 3], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 8, 41], 'euler43': [1, -8, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 5], 'euler53': [1, 9, 53], 'euler59': [1, 1, 59], 'euler61': [1, 14, 61], 'euler67': [1, 13, 67], 'euler7': [1, -3, 7], 'euler71': [1, -10, 71], 'euler73': [1, -9, 73], 'euler79': [1, 10, 79], 'euler83': [1, 10, 83], 'euler89': [1, 12, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 0, 5], [1, -3, 7], [1, 2, 11], [1, 1, 13], [1, 5, 17], [1, 1, 0], [1, 1, 23], [1, -3, 29], [1, -4, 31], [1, 2, 37], [1, 8, 41], [1, -8, 43], [1, 8, 47], [1, 9, 53], [1, 1, 59], [1, 14, 61], [1, 13, 67], [1, -10, 71], [1, -9, 73], [1, 10, 79], [1, 10, 83], [1, 12, 89], [1, -14, 97]], 'index': 27, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1216/f', 'ModularForm/GL2/Q/holomorphic/1216/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/1216/2/a/f'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1216-1.1-c1-0-27', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1216-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.11605662429098, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1809907073493533625, 'z1': {'__RealLiteral__': 0, 'data': '1.78091799751097958894751684261', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20709640
{'Lhash': '2257581768502049631203711134423', 'Lhash_array': ['2257581768502049631203711134423'], 'label': '2-1216-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/2/a/f'}
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id: 24552227
{'Lhash': '2257581768502049631203711134423', 'Lhash_array': ['2257581768502049631203711134423'], 'label': '2-1216-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/2/a/f/1/1'}
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id: 42747
{'Lhash': '1809907073493533625', 'Lhash_array': ['1809907073493533625'], 'label': '2-1216-1.1-c1-0-27', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1216/f'}