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lfunc_lfunctions • Show schema
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{'Lhash': '1621461278029008385237960643953', 'a10': 0, 'a2': -2, 'a3': -1, 'a4': 4, 'a5': 0, 'a6': 2, 'a7': 18, 'a8': -8, 'a9': -26, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.85219650660174, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2]], [5, [1]], [23, [1, -23]]], 'bad_primes': [2, 5, 23], 'central_character': '1150.1', 'coefficient_field': '1.1.1.1', 'conductor': 1150, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[1, 2], [1, 1, 27], [1], [1, -18, 343], [1, 32, 1331], [1, -47, 2197], [1, 20, 4913], [1, -36, 6859], [1, -23], [1, 27, 24389], [1, 33, 29791], [1, 56, 50653], [1, 157, 68921], [1, 18, 79507], [1, 65, 103823], [1, -14, 148877], [1, 744, 205379], [1, -552, 226981], [1, -156, 300763], [1, -699, 357911], [1, -609, 389017], [1, 644, 493039], [1, 512, 571787], [1, 102, 704969], [1, 578, 912673], [1, 6, 1030301], [1, -160, 1092727], [1, 380, 1225043], [1, -250, 1295029], [1, -390, 1442897]], 'euler_factors_factorization': [[[[1, 2], 1]], [[[1, 1, 27], 1]], [1], [[[1, -18, 343], 1]], [[[1, 32, 1331], 1]], [[[1, -47, 2197], 1]], [[[1, 20, 4913], 1]], [[[1, -36, 6859], 1]], [[[1, -23], 1]], [[[1, 27, 24389], 1]], [[[1, 33, 29791], 1]], [[[1, 56, 50653], 1]], [[[1, 157, 68921], 1]], [[[1, 18, 79507], 1]], [[[1, 65, 103823], 1]], [[[1, -14, 148877], 1]], [[[1, 744, 205379], 1]], [[[1, -552, 226981], 1]], [[[1, -156, 300763], 1]], [[[1, -699, 357911], 1]], [[[1, -609, 389017], 1]], [[[1, 644, 493039], 1]], [[[1, 512, 571787], 1]], [[[1, 102, 704969], 1]], [[[1, 578, 912673], 1]], [[[1, 6, 1030301], 1]], [[[1, -160, 1092727], 1]], [[[1, 380, 1225043], 1]], [[[1, -250, 1295029], 1]], [[[1, -390, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 65, 'label': '2-1150-1.1-c3-0-65', '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/1150/4/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.0404103667674096e-60, 0.1530320257117171, 0.30405346794002386, 0.4510700706406825, 0.5921204395729709, 0.725292975228347, 0.8487433659549802, 0.9607127592854365, 1.0595466738333266, 1.1437146484954956, 1.2118305524604758, 1.2626734013274972, 1.29520844430426, 1.3086082078832242, 1.3022731055057777, 1.275851153349231, 1.22925627221189, 1.1626846070281944, 1.076628261073965, 0.9718858233860255, 0.8495690669574077, 0.71110521315244, 0.5582341953931341, 0.3930004129509961, 0.2177385436331044, 0.03505308179298934, -0.15220861556349485, -0.3409898582793866, -0.5280646631813797, -0.7100840786211899, -0.8836283964533627, -1.045264677826246, -1.191608840630595, -1.3193913804628747, -1.4255256282603614, -1.5071772913221897, -1.561833885333082, -1.5873725483392291, -1.5821246383335066, -1.5449354588490143, -1.475217435956571, 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1776546685338618634, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27910741156678225549380618519', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41704504641600854839838949231', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50425058643302021168851113884', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 67.85219650660174, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 1150, 'conductor_radical': 230, 'degree': 2, 'dirichlet_coefficients': [1, -2, -1, 4, 0, 2, 18, -8, -26, 0, -32, -4, 47, -36, 0, 16, -20, 52, 36, 0, -18, 64, 23, 8, 0, -94, 53, 72, -27, 0, -33, -32, 32, 40, 0, -104, -56, -72, -47, 0, -157, 36, -18, -128, 0, -46, -65, -16, -19, 0, 20, 188, 14, -106, 0, -144, -36, 54, -744, 0, 552, 66, -468, 64, 0, -64, 156, -80, -23, 0, 699, 208, 609, 112, 0, 144, -576, 94, -644, 0, 649, 314, -512, -72, 0, 36, 27, 256, -102, 0, 846, 92, 33, 130, 0, 32, -578, 38, 832, 0], 'euler11': [1, 32, 1331], 'euler13': [1, -47, 2197], 'euler17': [1, 20, 4913], 'euler19': [1, -36, 6859], 'euler2': [1, 2, 0], 'euler23': [1, -23, 0], 'euler29': [1, 27, 24389], 'euler3': [1, 1, 27], 'euler31': [1, 33, 29791], 'euler37': [1, 56, 50653], 'euler41': [1, 157, 68921], 'euler43': [1, 18, 79507], 'euler47': [1, 65, 103823], 'euler5': [1, 0, 0], 'euler53': [1, -14, 148877], 'euler59': [1, 744, 205379], 'euler61': [1, -552, 226981], 'euler67': [1, -156, 300763], 'euler7': [1, -18, 343], 'euler71': [1, -699, 357911], 'euler73': [1, -609, 389017], 'euler79': [1, 644, 493039], 'euler83': [1, 512, 571787], 'euler89': [1, 102, 704969], 'euler97': [1, 578, 912673], 'euler_factors': [[1, 2, 0], [1, 1, 27], [1, 0, 0], [1, -18, 343], [1, 32, 1331], [1, -47, 2197], [1, 20, 4913], [1, -36, 6859], [1, -23, 0], [1, 27, 24389], [1, 33, 29791], [1, 56, 50653], [1, 157, 68921], [1, 18, 79507], [1, 65, 103823], [1, -14, 148877], [1, 744, 205379], [1, -552, 226981], [1, -156, 300763], [1, -699, 357911], [1, -609, 389017], [1, 644, 493039], [1, 512, 571787], [1, 102, 704969], [1, 578, 912673]], 'index': 65, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1150/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/1150/4/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': '2-1150-1.1-c3-0-65', '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': '2-1150-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.237244472917006, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1776546685338618634, 'z1': {'__RealLiteral__': 0, 'data': '1.27910741156678225549380618519', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20131801
{'Lhash': '1621461278029008385237960643953', 'Lhash_array': ['1621461278029008385237960643953'], 'label': '2-1150-1.1-c3-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1150/4/a/b'}
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id: 24584318
{'Lhash': '1621461278029008385237960643953', 'Lhash_array': ['1621461278029008385237960643953'], 'label': '2-1150-1.1-c3-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1150/4/a/b/1/1'}