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lfunc_lfunctions • Show schema
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{'Lhash': '423490504729869118020269322096,812798060870703874363995467788,1211250054201084681847093497632', 'a10': -15, 'a2': -3, 'a3': -1, 'a4': 6, 'a5': 5, 'a6': 3, 'a7': 1, 'a8': -10, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 255047.4402946362, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 3, 3, 1]], [11, [1, 3, 3, 1]], [19, [1]]], 'bad_primes': [2, 11, 19], 'central_character': '7942.1', 'coefficient_field': '1.1.1.1', 'conductor': 500944540888, 'conductor_radical': 418, 'degree': 6, 'euler_factors': [[1, 3, 3, 1], [1, 1, 4, 2, 12, 9, 27], [1, -5, 18, -48, 90, -125, 125], [1, -1, 14, -18, 98, -49, 343], [1, 3, 3, 1], [1, 5, 40, 116, 520, 845, 2197], [1, -4, 27, -48, 459, -1156, 4913], [1], [1, -2, 41, -124, 943, -1058, 12167], [1, 7, 68, 320, 1972, 5887, 24389], [1, -3, 68, -110, 2108, -2883, 29791], [1, -14, 127, -908, 4699, -19166, 50653], [1, -3, 98, -268, 4018, -5043, 68921], [1, 5, 62, 162, 2666, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 255047.4402946362, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 500944540888, 'conductor_radical': 418, 'degree': 6, 'dirichlet_coefficients': [1, -3, -1, 6, 5, 3, 1, -10, -3, -15, -3, -6, -5, -3, -5, 15, 4, 9, 0, 30, -1, 9, 2, 10, 7, 15, 5, 6, -7, 15, 3, -21, 3, -12, 5, -18, 14, 0, 5, -50, 3, 3, -5, -18, -15, -6, 0, -15, -13, -21, -4, -30, 16, -15, -15, -10, 0, 21, 12, -30, 6, -9, -3, 28, -25, -9, -1, 24, -2, -15, 3, 30, 4, -42, -7, 0, -3, -15, -2, 75, -3, -9, 7, -6, 20, 15, 7, 30, -16, 45, -5, 12, -3, 0, 0, 21, 14, 39, 9, 42], 'euler11': [1, 3, 3, 1, 0, 0, 0], 'euler13': [1, 5, 40, 116, 520, 845, 2197], 'euler17': [1, -4, 27, -48, 459, -1156, 4913], 'euler19': [1, 0, 0, 0, 0, 0, 0], 'euler2': [1, 3, 3, 1, 0, 0, 0], 'euler23': [1, -2, 41, -124, 943, -1058, 12167], 'euler29': [1, 7, 68, 320, 1972, 5887, 24389], 'euler3': [1, 1, 4, 2, 12, 9, 27], 'euler31': [1, -3, 68, -110, 2108, -2883, 29791], 'euler37': [1, -14, 127, -908, 4699, -19166, 50653], 'euler41': [1, -3, 98, -268, 4018, -5043, 68921], 'euler43': [1, 5, 62, 162, 2666, 9245, 79507], 'euler47': [1, 0, 89, 128, 4183, 0, 103823], 'euler5': [1, -5, 18, -48, 90, -125, 125], 'euler53': [1, -16, 223, -1752, 11819, -44944, 148877], 'euler59': [1, -12, 17, 376, 1003, -41772, 205379], 'euler61': [1, -6, 195, -740, 11895, -22326, 226981], 'euler67': [1, 1, 194, 138, 12998, 4489, 300763], 'euler7': [1, -1, 14, -18, 98, -49, 343], 'euler71': [1, -3, 182, -454, 12922, -15123, 357911], 'euler73': [1, -4, 83, -528, 6059, -21316, 389017], 'euler79': [1, 2, 121, 668, 9559, 12482, 493039], 'euler83': [1, -7, 106, -54, 8798, -48223, 571787], 'euler89': [1, 16, -13, -1576, -1157, 126736, 704969], 'euler97': [1, -14, 307, -2588, 29779, -131726, 912673], 'euler_factors': [[1, 3, 3, 1, 0, 0, 0], [1, 1, 4, 2, 12, 9, 27], [1, -5, 18, -48, 90, -125, 125], [1, -1, 14, -18, 98, -49, 343], [1, 3, 3, 1, 0, 0, 0], [1, 5, 40, 116, 520, 845, 2197], [1, -4, 27, -48, 459, -1156, 4913], [1, 0, 0, 0, 0, 0, 0], [1, -2, 41, -124, 943, -1058, 12167], [1, 7, 68, 320, 1972, 5887, 24389], [1, -3, 68, -110, 2108, -2883, 29791], [1, -14, 127, -908, 4699, -19166, 50653], [1, -3, 98, -268, 4018, -5043, 68921], [1, 5, 62, 162, 2666, 9245, 79507], [1, 0, 89, 128, 4183, 0, 103823], [1, -16, 223, -1752, 11819, -44944, 148877], [1, -12, 17, 376, 1003, -41772, 205379], [1, -6, 195, -740, 11895, -22326, 226981], [1, 1, 194, 138, 12998, 4489, 300763], [1, -3, 182, -454, 12922, -15123, 357911], [1, -4, 83, -528, 6059, -21316, 389017], [1, 2, 121, 668, 9559, 12482, 493039], [1, -7, 106, -54, 8798, -48223, 571787], [1, 16, -13, -1576, -1157, 126736, 704969], [1, -14, 307, -2588, 29779, -131726, 912673]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7942/2/a/bc'], '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': '6-7942e3-1.1-c1e3-0-0', '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': 0, 'prelabel': '6-7942e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.963491023747117, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 376298761454514145, 'z1': {'__RealLiteral__': 0, 'data': '0.33407510291370773399809401488', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '423490504729869118020269322096,812798060870703874363995467788,1211250054201084681847093497632', 'Lhash_array': ['423490504729869118020269322096', '812798060870703874363995467788', '1211250054201084681847093497632'], 'label': '6-7942e3-1.1-c1e3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7942/2/a/bc'}