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{'Lhash': '1274429571248283026096507439409,2187325275491356305160090830331,2438282609341218371466027592460', 'a10': 0, 'a2': 2, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 3, 'a8': -5, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33199.30369666823, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [7, [1, -3, 3, -1]], [23, [1, -3, 3, -1]]], 'bad_primes': [5, 7, 23], 'central_character': '4025.1', 'coefficient_field': '1.1.1.1', 'conductor': 65207515625, 'conductor_radical': 805, 'degree': 6, 'euler_factors': [[1, -2, 5, -7, 10, -8, 8], [1, 0, 2, -7, 6, 0, 27], [1], [1, -3, 3, -1], [1, 7, 47, 161, 517, 847, 1331], [1, 5, 17, 33, 221, 845, 2197], [1, 5, 43, 129, 731, 1445, 4913], [1, 6, 62, 215, 1178, 2166, 6859], [1, -3, 3, -1], [1, 12, 107, 592, 3103, 10092, 24389], [1, 4, 96, 247, 2976, 3844, 29791], [1, 3, 93, 195, 3441, 4107, 50653], [1, -1, 58, 87, 2378, -1681, 68921], [1, 2, 128, 171, 5504, 3698, 79507], 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'6.88624394833029820502249280570892', '7.17314791331029379251449891840623', '7.46006098675106934615307436056617', '7.60106236153447593219611580102587', '7.68505204303610114232881314017007', '8.102894225367344336857283854337843', '8.377314658512906070524025900943309'], 'prelabel': '6-4025e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.669196311080202, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 1963993231152417781, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00534766521534650807430766966', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.72549539683691036272509663868', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.92346582638956421991183983702', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33199.30369666823, 'bad_primes': [5, 7, 23], 'central_character': '1.1', 'conductor': 65207515625, 'conductor_radical': 805, 'degree': 6, 'dirichlet_coefficients': [1, 2, 0, -1, 0, 0, 3, -5, -2, 0, -7, 0, -5, 6, 0, -1, -5, -4, -6, 0, 0, -14, 3, 0, 0, -10, 7, -3, -12, 0, -4, 4, 0, -10, 0, 2, -3, -12, 0, 0, 1, 0, -2, 7, 0, 6, -12, 0, 6, 0, 0, 5, 9, 14, 0, -15, 0, -24, -21, 0, -9, -8, -6, -4, 0, 0, -13, 5, 0, 0, -16, 10, 9, -6, 0, 6, -21, 0, -18, 0, -2, 2, 29, 0, 0, -4, 0, 35, 7, 0, -15, -3, 0, -24, 0, 0, -1, 12, 14, 0], 'euler11': [1, 7, 47, 161, 517, 847, 1331], 'euler13': [1, 5, 17, 33, 221, 845, 2197], 'euler17': [1, 5, 43, 129, 731, 1445, 4913], 'euler19': [1, 6, 62, 215, 1178, 2166, 6859], 'euler2': [1, -2, 5, -7, 10, -8, 8], 'euler23': [1, -3, 3, -1, 0, 0, 0], 'euler29': [1, 12, 107, 592, 3103, 10092, 24389], 'euler3': [1, 0, 2, -7, 6, 0, 27], 'euler31': [1, 4, 96, 247, 2976, 3844, 29791], 'euler37': [1, 3, 93, 195, 3441, 4107, 50653], 'euler41': [1, -1, 58, 87, 2378, -1681, 68921], 'euler43': [1, 2, 128, 171, 5504, 3698, 79507], 'euler47': [1, 12, 140, 1087, 6580, 26508, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -9, 11, 419, 583, -25281, 148877], 'euler59': [1, 21, 303, 2681, 17877, 73101, 205379], 'euler61': [1, 9, 161, 887, 9821, 33489, 226981], 'euler67': [1, 13, 185, 1365, 12395, 58357, 300763], 'euler7': [1, -3, 3, -1, 0, 0, 0], 'euler71': [1, 16, 198, 1809, 14058, 80656, 357911], 'euler73': [1, -9, 197, -1285, 14381, -47961, 389017], 'euler79': [1, 18, 282, 2493, 22278, 112338, 493039], 'euler83': [1, -29, 443, -4603, 36769, -199781, 571787], 'euler89': [1, -7, 253, -1155, 22517, -55447, 704969], 'euler97': [1, 1, 142, 277, 13774, 9409, 912673], 'euler_factors': [[1, -2, 5, -7, 10, -8, 8], [1, 0, 2, -7, 6, 0, 27], [1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, 7, 47, 161, 517, 847, 1331], [1, 5, 17, 33, 221, 845, 2197], [1, 5, 43, 129, 731, 1445, 4913], [1, 6, 62, 215, 1178, 2166, 6859], [1, -3, 3, -1, 0, 0, 0], [1, 12, 107, 592, 3103, 10092, 24389], [1, 4, 96, 247, 2976, 3844, 29791], [1, 3, 93, 195, 3441, 4107, 50653], [1, -1, 58, 87, 2378, -1681, 68921], [1, 2, 128, 171, 5504, 3698, 79507], [1, 12, 140, 1087, 6580, 26508, 103823], [1, -9, 11, 419, 583, -25281, 148877], [1, 21, 303, 2681, 17877, 73101, 205379], [1, 9, 161, 887, 9821, 33489, 226981], [1, 13, 185, 1365, 12395, 58357, 300763], [1, 16, 198, 1809, 14058, 80656, 357911], [1, -9, 197, -1285, 14381, -47961, 389017], [1, 18, 282, 2493, 22278, 112338, 493039], [1, -29, 443, -4603, 36769, -199781, 571787], [1, -7, 253, -1155, 22517, -55447, 704969], [1, 1, 142, 277, 13774, 9409, 912673]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4025/2/a/k'], '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': '6-4025e3-1.1-c1e3-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-4025e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.669196311080202, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1963993231152417781, 'z1': {'__RealLiteral__': 0, 'data': '1.00534766521534650807430766966', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1274429571248283026096507439409,2187325275491356305160090830331,2438282609341218371466027592460', 'Lhash_array': ['1274429571248283026096507439409', '2187325275491356305160090830331', '2438282609341218371466027592460'], 'label': '6-4025e3-1.1-c1e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4025/2/a/k'}