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lfunc_lfunctions • Show schema
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{'Lhash': '1995607516281693954876784581931', 'a10': 0, 'a2': -4, 'a3': 0, 'a4': 8, 'a5': 0, 'a6': 0, 'a7': -6, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.1', 'coefficient_field': '1.1.1.1', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, 4, 8], [1], [1], [1, 6, 343], [1, 32, 1331], [1, -38, 2197], [1, -26, 4913], [1, -100, 6859], [1, 78, 12167], [1, -50, 24389], [1, 108, 29791], [1, 266, 50653], [1, 22, 68921], [1, 442, 79507], [1, 514, 103823], [1, -2, 148877], [1, 500, 205379], [1, 518, 226981], [1, 126, 300763], [1, 412, 357911], [1, -878, 389017], [1, -600, 493039], [1, -282, 571787], [1, -150, 704969], [1, 386, 912673], [1, 702, 1030301], [1, -598, 1092727], [1, 1194, 1225043], [1, 550, 1295029], [1, -1562, 1442897]], 'euler_factors_factorization': [[[[1, 4, 8], 1]], [1], [1], [[[1, 6, 343], 1]], [[[1, 32, 1331], 1]], [[[1, -38, 2197], 1]], [[[1, -26, 4913], 1]], [[[1, -100, 6859], 1]], [[[1, 78, 12167], 1]], [[[1, -50, 24389], 1]], [[[1, 108, 29791], 1]], [[[1, 266, 50653], 1]], [[[1, 22, 68921], 1]], [[[1, 442, 79507], 1]], [[[1, 514, 103823], 1]], [[[1, -2, 148877], 1]], [[[1, 500, 205379], 1]], [[[1, 518, 226981], 1]], [[[1, 126, 300763], 1]], [[[1, 412, 357911], 1]], [[[1, -878, 389017], 1]], [[[1, -600, 493039], 1]], [[[1, -282, 571787], 1]], [[[1, -150, 704969], 1]], [[[1, 386, 912673], 1]], [[[1, 702, 1030301], 1]], [[[1, -598, 1092727], 1]], [[[1, 1194, 1225043], 1]], [[[1, 550, 1295029], 1]], [[[1, -1562, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-15e2-1.1-c3-0-9', '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/225/4/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [5.637387123491209e-120, 0.18103990033748152, 0.35499577335192384, 0.5146790984299479, 0.6527373747285405, 0.7616796486292742, 0.8340176902213763, 0.8625407458071498, 0.840726917365572, 0.7632782406269798, 0.6267503502490811, 0.4302320534010714, 0.17601607775228792, -0.12980918357618265, -0.47692459976184004, -0.8505816129940749, -1.2317147475837074, -1.5974270802209893, -1.9218885359380442, -2.1776562407976665, -2.337387916072623, -2.375875704124325, -2.2722822901573574, -2.01241816064484, -1.5908634737865368, -1.012715730378553, -0.2947403169888838, 0.5342808749385376, 1.4341648168418595, 2.35500144166481, 3.239892184416541, 4.028653877343609, 4.662277252290881, 5.087822115488787, 5.263341371566988, 5.16236648975603, 4.777469327672931, 4.122447959245977, 3.232771096747149, 2.16405468722391, 0.9885264594363103, 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 2052512481258298677, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57425675175983214824376213776', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.29610350142201987915407042625', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.10283943943181689170567094516', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, -4, 0, 8, 0, 0, -6, 0, 0, 0, -32, 0, 38, 24, 0, -64, 26, 0, 100, 0, 0, 128, -78, 0, 0, -152, 0, -48, 50, 0, -108, 256, 0, -104, 0, 0, -266, -400, 0, 0, -22, 0, -442, -256, 0, 312, -514, 0, -307, 0, 0, 304, 2, 0, 0, 0, 0, -200, -500, 0, -518, 432, 0, -512, 0, 0, -126, 208, 0, 0, -412, 0, 878, 1064, 0, 800, 192, 0, 600, 0, 0, 88, 282, 0, 0, 1768, 0, 0, 150, 0, -228, -624, 0, 2056, 0, 0, -386, 1228, 0, 0], 'euler11': [1, 32, 1331], 'euler13': [1, -38, 2197], 'euler17': [1, -26, 4913], 'euler19': [1, -100, 6859], 'euler2': [1, 4, 8], 'euler23': [1, 78, 12167], 'euler29': [1, -50, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 108, 29791], 'euler37': [1, 266, 50653], 'euler41': [1, 22, 68921], 'euler43': [1, 442, 79507], 'euler47': [1, 514, 103823], 'euler5': [1, 0, 0], 'euler53': [1, -2, 148877], 'euler59': [1, 500, 205379], 'euler61': [1, 518, 226981], 'euler67': [1, 126, 300763], 'euler7': [1, 6, 343], 'euler71': [1, 412, 357911], 'euler73': [1, -878, 389017], 'euler79': [1, -600, 493039], 'euler83': [1, -282, 571787], 'euler89': [1, -150, 704969], 'euler97': [1, 386, 912673], 'euler_factors': [[1, 4, 8], [1, 0, 0], [1, 0, 0], [1, 6, 343], [1, 32, 1331], [1, -38, 2197], [1, -26, 4913], [1, -100, 6859], [1, 78, 12167], [1, -50, 24389], [1, 108, 29791], [1, 266, 50653], [1, 22, 68921], [1, 442, 79507], [1, 514, 103823], [1, -2, 148877], [1, 500, 205379], [1, 518, 226981], [1, 126, 300763], [1, 412, 357911], [1, -878, 389017], [1, -600, 493039], [1, -282, 571787], [1, -150, 704969], [1, 386, 912673]], 'index': 9, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/225/4/a/b'], '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': '2-15e2-1.1-c3-0-9', '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': '2-15e2-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 2052512481258298677, 'z1': {'__RealLiteral__': 0, 'data': '1.57425675175983214824376213776', 'prec': 103}}
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lfunc_instances • Show schema
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id: 17111031
{'Lhash': '1995607516281693954876784581931', 'Lhash_array': ['1995607516281693954876784581931'], 'label': '2-15e2-1.1-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/a/b'}
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id: 24553995
{'Lhash': '1995607516281693954876784581931', 'Lhash_array': ['1995607516281693954876784581931'], 'label': '2-15e2-1.1-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/a/b/1/1'}