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{'Lhash': '1053165948566467309089995890308,1069895891170991285396296009625,1278574429883294177624830651211', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 301765.2169328456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3, 3, -1]], [5, [1]], [7, [1, -3, 3, -1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '8400.1', 'coefficient_field': '1.1.1.1', 'conductor': 592704000000, 'conductor_radical': 210, 'degree': 6, 'euler_factors': [[1], [1, -3, 3, -1], [1], [1, -3, 3, -1], [1, -2, -3, 60, -33, -242, 1331], [1, -10, 59, -252, 767, -1690, 2197], [1, -8, 19, 0, 323, -2312, 4913], [1, -2, -3, 124, -57, -722, 6859], [1, 8, 29, 64, 667, 4232, 12167], [1, 6, 99, 356, 2871, 5046, 24389], [1, -14, 145, -908, 4495, -13454, 29791], [1, -12, 95, -568, 3515, -16428, 50653], [1, 10, 143, 812, 5863, 16810, 68921], [1, 4, 81, 280, 3483, 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'5.74401165260212325499734563478155', '5.76122787194553455772750361094623', '6.24434360217085900286915605009403', '6.58238788480490738632302788536942', '6.66788761025284282990784520556412', '6.90073100734006131579281479251063', '7.04151646244583255204261642408665', '7.56633736897097594093567312434100', '7.76347363552739064434067078853558', '8.016766779038470288508058167976467', '8.066197283281715542172829684899998'], 'prelabel': '6-8400e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.18989241064103, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 1164341874406388490, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.830801443534088961792479491938', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.843999041201389317655126401699', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.00861738215017453244413305915', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 301765.2169328456, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 592704000000, 'conductor_radical': 210, 'degree': 6, 'dirichlet_coefficients': [1, 0, 3, 0, 0, 0, 3, 0, 6, 0, 2, 0, 10, 0, 0, 0, 8, 0, 2, 0, 9, 0, -8, 0, 0, 0, 10, 0, -6, 0, 14, 0, 6, 0, 0, 0, 12, 0, 30, 0, -10, 0, -4, 0, 0, 0, 0, 0, 6, 0, 24, 0, 14, 0, 0, 0, 6, 0, 8, 0, 2, 0, 18, 0, 0, 0, 16, 0, -24, 0, 18, 0, 22, 0, 0, 0, 6, 0, -4, 0, 15, 0, -8, 0, 0, 0, -18, 0, -6, 0, 30, 0, 42, 0, 0, 0, 2, 0, 12, 0], 'euler11': [1, -2, -3, 60, -33, -242, 1331], 'euler13': [1, -10, 59, -252, 767, -1690, 2197], 'euler17': [1, -8, 19, 0, 323, -2312, 4913], 'euler19': [1, -2, -3, 124, -57, -722, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 8, 29, 64, 667, 4232, 12167], 'euler29': [1, 6, 99, 356, 2871, 5046, 24389], 'euler3': [1, -3, 3, -1, 0, 0, 0], 'euler31': [1, -14, 145, -908, 4495, -13454, 29791], 'euler37': [1, -12, 95, -568, 3515, -16428, 50653], 'euler41': [1, 10, 143, 812, 5863, 16810, 68921], 'euler43': [1, 4, 81, 280, 3483, 7396, 79507], 'euler47': [1, 0, 141, 0, 6627, 0, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -14, 211, -1524, 11183, -39326, 148877], 'euler59': [1, -8, 113, -688, 6667, -27848, 205379], 'euler61': [1, -2, -29, -140, -1769, -7442, 226981], 'euler67': [1, -16, 201, -1888, 13467, -71824, 300763], 'euler7': [1, -3, 3, -1, 0, 0, 0], 'euler71': [1, -18, 161, -1204, 11431, -90738, 357911], 'euler73': [1, -22, 319, -3316, 23287, -117238, 389017], 'euler79': [1, 4, 189, 568, 14931, 24964, 493039], 'euler83': [1, 8, 185, 1072, 15355, 55112, 571787], 'euler89': [1, 6, 143, 1300, 12727, 47526, 704969], 'euler97': [1, -2, 231, -188, 22407, -18818, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, -2, -3, 60, -33, -242, 1331], [1, -10, 59, -252, 767, -1690, 2197], [1, -8, 19, 0, 323, -2312, 4913], [1, -2, -3, 124, -57, -722, 6859], [1, 8, 29, 64, 667, 4232, 12167], [1, 6, 99, 356, 2871, 5046, 24389], [1, -14, 145, -908, 4495, -13454, 29791], [1, -12, 95, -568, 3515, -16428, 50653], [1, 10, 143, 812, 5863, 16810, 68921], [1, 4, 81, 280, 3483, 7396, 79507], [1, 0, 141, 0, 6627, 0, 103823], [1, -14, 211, -1524, 11183, -39326, 148877], [1, -8, 113, -688, 6667, -27848, 205379], [1, -2, -29, -140, -1769, -7442, 226981], [1, -16, 201, -1888, 13467, -71824, 300763], [1, -18, 161, -1204, 11431, -90738, 357911], [1, -22, 319, -3316, 23287, -117238, 389017], [1, 4, 189, 568, 14931, 24964, 493039], [1, 8, 185, 1072, 15355, 55112, 571787], [1, 6, 143, 1300, 12727, 47526, 704969], [1, -2, 231, -188, 22407, -18818, 912673]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8400/2/a/dl'], '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': '6-8400e3-1.1-c1e3-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-8400e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.18989241064103, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1164341874406388490, 'z1': {'__RealLiteral__': 0, 'data': '0.830801443534088961792479491938', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1053165948566467309089995890308,1069895891170991285396296009625,1278574429883294177624830651211', 'Lhash_array': ['1053165948566467309089995890308', '1069895891170991285396296009625', '1278574429883294177624830651211'], 'label': '6-8400e3-1.1-c1e3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8400/2/a/dl'}