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lfunc_lfunctions • Show schema
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{'Lhash': '1954141679480347227293039366546', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': -8, 'a6': 0, 'a7': -12, 'a8': 0, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.31346688440881, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': '1.1.1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1, -3], [1, 8, 125], [1, 12, 343], [1, 12, 1331], [1, -20, 2197], [1, -62, 4913], [1, -108, 6859], [1, -72, 12167], [1, 128, 24389], [1, 204, 29791], [1, 228, 50653], [1, -22, 68921], [1, 204, 79507], [1, 600, 103823], [1, -256, 148877], [1, 828, 205379], [1, 84, 226981], [1, -348, 300763], [1, 456, 357911], [1, 822, 389017], [1, 1356, 493039], [1, -108, 571787], [1, -938, 704969], [1, -1278, 912673], [1, -608, 1030301], [1, 948, 1092727], [1, -1044, 1225043], [1, -1780, 1295029], [1, 622, 1442897]], 'euler_factors_factorization': [[1], [[[1, -3], 1]], [[[1, 8, 125], 1]], [[[1, 12, 343], 1]], [[[1, 12, 1331], 1]], [[[1, -20, 2197], 1]], [[[1, -62, 4913], 1]], [[[1, -108, 6859], 1]], [[[1, -72, 12167], 1]], [[[1, 128, 24389], 1]], [[[1, 204, 29791], 1]], [[[1, 228, 50653], 1]], [[[1, -22, 68921], 1]], [[[1, 204, 79507], 1]], [[[1, 600, 103823], 1]], [[[1, -256, 148877], 1]], [[[1, 828, 205379], 1]], [[[1, 84, 226981], 1]], [[[1, -348, 300763], 1]], [[[1, 456, 357911], 1]], [[[1, 822, 389017], 1]], [[[1, 1356, 493039], 1]], [[[1, -108, 571787], 1]], [[[1, -938, 704969], 1]], [[[1, -1278, 912673], 1]], [[[1, -608, 1030301], 1]], [[[1, 948, 1092727], 1]], [[[1, -1044, 1225043], 1]], [[[1, -1780, 1295029], 1]], [[[1, 622, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 35, 'label': '2-768-1.1-c3-0-35', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/768/4/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.453657475062876e-60, 0.23481663747159479, 0.4669282642457639, 0.6936424641971651, 0.9122927115620642, 1.1202530312145933, 1.314954612351703, 1.4939048567681323, 1.654709206058585, 1.7950959314760606, 1.9129438919221846, 2.006313076267425, 2.0734775527530593, 2.1129602574746587, 2.123568872566863, 2.104431879051155, 2.0550337252881867, 1.9752479350002476, 1.8653668937352248, 1.726127003645383, 1.558727887084366, 1.3648443525610434, 1.1466299139642167, 0.9067107766792386, 0.6481693721934729, 0.3745167348023027, 0.08965326757882022, -0.2021822640034903, -0.496475348785159, -0.7885094456662772, -1.0734499202363277, -1.3464369492161687, -1.602685767279786, -1.8375922726631106, -2.046841676361897, -2.2265175874205485, -2.3732086865854014, -2.484109964797753, -2.5571154031254704, -2.5908989569226573, -2.5849807875793998, 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True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1581314946346314174, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54154597420497502404888668768', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.19587389648295029777001640025', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55584382040405851196106792860', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.31346688440881, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, -8, 0, -12, 0, 9, 0, -12, 0, 20, 0, -24, 0, 62, 0, 108, 0, -36, 0, 72, 0, -61, 0, 27, 0, -128, 0, -204, 0, -36, 0, 96, 0, -228, 0, 60, 0, 22, 0, -204, 0, -72, 0, -600, 0, -199, 0, 186, 0, 256, 0, 96, 0, 324, 0, -828, 0, -84, 0, -108, 0, -160, 0, 348, 0, 216, 0, -456, 0, -822, 0, -183, 0, 144, 0, -1356, 0, 81, 0, 108, 0, -496, 0, -384, 0, 938, 0, -240, 0, -612, 0, -864, 0, 1278, 0, -108, 0], 'euler11': [1, 12, 1331], 'euler13': [1, -20, 2197], 'euler17': [1, -62, 4913], 'euler19': [1, -108, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -72, 12167], 'euler29': [1, 128, 24389], 'euler3': [1, -3, 0], 'euler31': [1, 204, 29791], 'euler37': [1, 228, 50653], 'euler41': [1, -22, 68921], 'euler43': [1, 204, 79507], 'euler47': [1, 600, 103823], 'euler5': [1, 8, 125], 'euler53': [1, -256, 148877], 'euler59': [1, 828, 205379], 'euler61': [1, 84, 226981], 'euler67': [1, -348, 300763], 'euler7': [1, 12, 343], 'euler71': [1, 456, 357911], 'euler73': [1, 822, 389017], 'euler79': [1, 1356, 493039], 'euler83': [1, -108, 571787], 'euler89': [1, -938, 704969], 'euler97': [1, -1278, 912673], 'euler_factors': [[1, 0, 0], [1, -3, 0], [1, 8, 125], [1, 12, 343], [1, 12, 1331], [1, -20, 2197], [1, -62, 4913], [1, -108, 6859], [1, -72, 12167], [1, 128, 24389], [1, 204, 29791], [1, 228, 50653], [1, -22, 68921], [1, 204, 79507], [1, 600, 103823], [1, -256, 148877], [1, 828, 205379], [1, 84, 226981], [1, -348, 300763], [1, 456, 357911], [1, 822, 389017], [1, 1356, 493039], [1, -108, 571787], [1, -938, 704969], [1, -1278, 912673]], 'index': 35, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/4/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/768/4/a/c'], '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': '2-768-1.1-c3-0-35', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-768-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1581314946346314174, 'z1': {'__RealLiteral__': 0, 'data': '1.54154597420497502404888668768', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20121222
{'Lhash': '1954141679480347227293039366546', 'Lhash_array': ['1954141679480347227293039366546'], 'label': '2-768-1.1-c3-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/4/a/c'}
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id: 24571389
{'Lhash': '1954141679480347227293039366546', 'Lhash_array': ['1954141679480347227293039366546'], 'label': '2-768-1.1-c3-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/4/a/c/1/1'}