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lfunc_lfunctions • Show schema
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{'Lhash': '986038097346875814018145349139', 'a10': -20, 'a2': -4, 'a3': -2, 'a4': 8, 'a5': 5, 'a6': 8, 'a7': 0, 'a8': 0, 'a9': -23, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.455467951406456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -5]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '245.1', 'coefficient_field': '1.1.1.1', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'euler_factors': [[1, 4, 8], [1, 2, 27], [1, -5], [1], [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, 2, 27], 1]], [[[1, -5], 1]], [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': 6, 'label': '2-245-1.1-c3-0-6', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/245/4/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7117047454018506, 0.6916387636381033, 0.6319204045351974, 0.534042221538757, 0.4006621911085751, 0.2358290150408311, 0.045240298154321505, -0.16351651788587326, -0.3807959955698732, -0.5948552254023792, -0.7919942054207373, -0.9569173894951757, -1.073342765568612, -1.1248649702978735, -1.0960547266057177, -0.9737493840022396, -0.7484602998267116, -0.4157946764877487, 0.022234673612374262, 0.556154881124184, 1.1683829349851582, 1.8331207767055653, 2.5169119026460534, 3.1799341824106895, 3.778045766912884, 4.265529919906282, 4.598405556995015, 4.738090435931288, 4.655132096611604, 4.332667389424668, 3.7692441272316493, 2.9806459892010397, 2.0004095312882386, 0.8788113795076274, -0.31976901258610113, -1.5210488950450072, -2.646369339133148, -3.619144749509046, -4.371681614909058, -4.851708763050495, -5.0279188126502605, 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'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 24811122809532280, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77784690605546061366834461245', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24428123059458504388370733691', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21700883997275093707582999933', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.455467951406456, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'dirichlet_coefficients': [1, -4, -2, 8, 5, 8, 0, 0, -23, -20, 32, -16, 38, 0, -10, -64, -26, 92, -100, 40, 0, -128, -78, 0, 25, -152, 100, 0, -50, 40, 108, 256, -64, 104, 0, -184, 266, 400, -76, 0, -22, 0, 442, 256, -115, 312, 514, 128, 0, -100, 52, 304, 2, -400, 160, 0, 200, 200, -500, -80, 518, -432, 0, -512, 190, 256, 126, -208, 156, 0, 412, 0, 878, -1064, -50, -800, 0, 304, 600, -320, 421, 88, -282, 0, -130, -1768, 100, 0, 150, 460, 0, -624, -216, -2056, -500, -512, -386, 0, -736, 200], '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, 2, 27], 'euler31': [1, -108, 29791], 'euler37': [1, -266, 50653], 'euler41': [1, 22, 68921], 'euler43': [1, -442, 79507], 'euler47': [1, -514, 103823], 'euler5': [1, -5, 0], 'euler53': [1, -2, 148877], 'euler59': [1, 500, 205379], 'euler61': [1, -518, 226981], 'euler67': [1, -126, 300763], 'euler7': [1, 0, 0], '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, 2, 27], [1, -5, 0], [1, 0, 0], [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': 6, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/245/4/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': '2-245-1.1-c3-0-6', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-245-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.802034712020191, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 24811122809532280, 'z1': {'__RealLiteral__': 0, 'data': '0.77784690605546061366834461245', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19210718
{'Lhash': '986038097346875814018145349139', 'Lhash_array': ['986038097346875814018145349139'], 'label': '2-245-1.1-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/4/a/a'}
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id: 24554666
{'Lhash': '986038097346875814018145349139', 'Lhash_array': ['986038097346875814018145349139'], 'label': '2-245-1.1-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/4/a/a/1/1'}