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lfunc_lfunctions • Show schema
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{'Lhash': '2837640267450346313656783427287', 'a10': -336, 'a2': -4, 'a3': 10, 'a4': 16, 'a5': 84, 'a6': -40, 'a7': 49, 'a8': -64, 'a9': -143, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.2453734773817295, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 4]], [7, [1, -49]]], 'bad_primes': [2, 7], 'central_character': '14.1', 'coefficient_field': '1.1.1.1', 'conductor': 14, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1, 4], [1, -10, 243], [1, -84, 3125], [1, -49], [1, 336, 161051], [1, -584, 371293], [1, 1458, 1419857], [1, -470, 2476099], [1, 4200, 6436343], [1, -4866, 20511149], [1, 7372, 28629151], [1, -14330, 69343957], [1, -6222, 115856201], [1, -3704, 147008443], [1, 1812, 229345007], [1, 37242, 418195493], [1, -34302, 714924299], [1, -24476, 844596301], [1, 17452, 1350125107], [1, -28224, 1804229351], [1, -3602, 2073071593], [1, -42872, 3077056399], [1, 35202, 3939040643], [1, -26730, 5584059449], [1, 16978, 8587340257], [1, -99204, 10510100501], [1, 131644, 11592740743], [1, -48852, 14025517307], [1, 56374, 15386239549], [1, -8742, 18424351793]], 'euler_factors_factorization': [[[[1, 4], 1]], [[[1, -10, 243], 1]], [[[1, -84, 3125], 1]], [[[1, -49], 1]], [[[1, 336, 161051], 1]], [[[1, -584, 371293], 1]], [[[1, 1458, 1419857], 1]], [[[1, -470, 2476099], 1]], [[[1, 4200, 6436343], 1]], [[[1, -4866, 20511149], 1]], [[[1, 7372, 28629151], 1]], [[[1, -14330, 69343957], 1]], [[[1, -6222, 115856201], 1]], [[[1, -3704, 147008443], 1]], [[[1, 1812, 229345007], 1]], [[[1, 37242, 418195493], 1]], [[[1, -34302, 714924299], 1]], [[[1, -24476, 844596301], 1]], [[[1, 17452, 1350125107], 1]], [[[1, -28224, 1804229351], 1]], [[[1, -3602, 2073071593], 1]], [[[1, -42872, 3077056399], 1]], [[[1, 35202, 3939040643], 1]], [[[1, -26730, 5584059449], 1]], [[[1, 16978, 8587340257], 1]], [[[1, -99204, 10510100501], 1]], [[[1, 131644, 11592740743], 1]], [[[1, -48852, 14025517307], 1]], [[[1, 56374, 15386239549], 1]], [[[1, -8742, 18424351793], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-14-1.1-c5-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/14/6/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.2985965382222935, 1.2928939534532307, 1.2755573963496214, 1.245911107042479, 1.2028644179270456, 1.1449655045565907, 1.070477291781349, 0.9774760141170524, 0.8639727711475303, 0.728057943996994, 0.5680674422700199, 0.38276836098014017, 0.171559726614045, -0.06531835055849108, -0.3265765047787016, -0.6096811660171437, -0.9106878263439995, -1.2241198423211261, -1.5429116408094015, -1.8584355747311947, -2.1606305068400786, -2.438247146612794, -2.679219980998145, -2.87116821832224, -3.002018594171129, -3.0607314969915342, 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'14.34092229903959090081539461126570', '16.03645682248407660920089837922871', '17.64934176165743027115248287728248', '18.22409149997367053031732153522263'], 'prelabel': '2-14-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.4984570322107102, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 1660554801592053743, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.23850347007247423417292537660', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.97738936838904106726730651498', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.262777881296668124181083957358', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.2453734773817295, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 14, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, -4, 10, 16, 84, -40, 49, -64, -143, -336, -336, 160, 584, -196, 840, 256, -1458, 572, 470, 1344, 490, 1344, -4200, -640, 3931, -2336, -3860, 784, 4866, -3360, -7372, -1024, -3360, 5832, 4116, -2288, 14330, -1880, 5840, -5376, 6222, -1960, 3704, -5376, -12012, 16800, -1812, 2560, 2401, -15724, -14580, 9344, -37242, 15440, -28224, -3136, 4700, -19464, 34302, 13440, 24476, 29488, -7007, 4096, 49056, 13440, -17452, -23328, -42000, -16464, 28224, 9152, 3602, -57320, 39310, 7520, -16464, -23360, 42872, 21504, -3851, -24888, -35202, 7840, -122472, -14816, 48660, 21504, 26730, 48048, 28616, -67200, -73720, 7248, 39480, -10240, -16978, -9604, 48048, 62896], 'euler11': [1, 336, 161051], 'euler13': [1, -584, 371293], 'euler17': [1, 1458, 1419857], 'euler19': [1, -470, 2476099], 'euler2': [1, 4, 0], 'euler23': [1, 4200, 6436343], 'euler29': [1, -4866, 20511149], 'euler3': [1, -10, 243], 'euler31': [1, 7372, 28629151], 'euler37': [1, -14330, 69343957], 'euler41': [1, -6222, 115856201], 'euler43': [1, -3704, 147008443], 'euler47': [1, 1812, 229345007], 'euler5': [1, -84, 3125], 'euler53': [1, 37242, 418195493], 'euler59': [1, -34302, 714924299], 'euler61': [1, -24476, 844596301], 'euler67': [1, 17452, 1350125107], 'euler7': [1, -49, 0], 'euler71': [1, -28224, 1804229351], 'euler73': [1, -3602, 2073071593], 'euler79': [1, -42872, 3077056399], 'euler83': [1, 35202, 3939040643], 'euler89': [1, -26730, 5584059449], 'euler97': [1, 16978, 8587340257], 'euler_factors': [[1, 4, 0], [1, -10, 243], [1, -84, 3125], [1, -49, 0], [1, 336, 161051], [1, -584, 371293], [1, 1458, 1419857], [1, -470, 2476099], [1, 4200, 6436343], [1, -4866, 20511149], [1, 7372, 28629151], [1, -14330, 69343957], [1, -6222, 115856201], [1, -3704, 147008443], [1, 1812, 229345007], [1, 37242, 418195493], [1, -34302, 714924299], [1, -24476, 844596301], [1, 17452, 1350125107], [1, -28224, 1804229351], [1, -3602, 2073071593], [1, -42872, 3077056399], [1, 35202, 3939040643], [1, -26730, 5584059449], [1, 16978, 8587340257]], 'index': 0, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/14/6/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/14/6/a/a'], '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': '2-14-1.1-c5-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-14-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.4984570322107102, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1660554801592053743, 'z1': {'__RealLiteral__': 0, 'data': '2.23850347007247423417292537660', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9973863
{'Lhash': '2837640267450346313656783427287', 'Lhash_array': ['2837640267450346313656783427287'], 'factors': ['2-14-1.1-c5-0-0'], 'label': '2-14-1.1-c5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/6/a/a'}
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id: 24548864
{'Lhash': '2837640267450346313656783427287', 'Lhash_array': ['2837640267450346313656783427287'], 'factors': ['2-14-1.1-c5-0-0'], 'label': '2-14-1.1-c5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/6/a/a/1/1'}