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lfunc_lfunctions • Show schema
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{'Lhash': '1749887495782961313942543777773', 'a10': 10, 'a2': 2, 'a3': 0, 'a4': 4, 'a5': 5, 'a6': 0, 'a7': 8, 'a8': 8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.930515701549973, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1]], [5, [1, -5]]], 'bad_primes': [2, 3, 5], 'central_character': '270.1', 'coefficient_field': '1.1.1.1', 'conductor': 270, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1, -2], [1], [1, -5], [1, -8, 343], [1, -18, 1331], [1, -8, 2197], [1, -15, 4913], [1, -23, 6859], [1, -63, 12167], [1, -156, 24389], [1, 85, 29791], [1, -74, 50653], [1, -246, 68921], [1, 190, 79507], [1, -288, 103823], [1, 177, 148877], [1, -792, 205379], [1, 907, 226981], [1, 322, 300763], [1, 270, 357911], [1, -254, 389017], [1, 1123, 493039], [1, 771, 571787], [1, 198, 704969], [1, 1192, 912673], [1, 1692, 1030301], [1, -1748, 1092727], [1, 948, 1225043], [1, -593, 1295029], [1, 1062, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [1], [[[1, -5], 1]], [[[1, -8, 343], 1]], [[[1, -18, 1331], 1]], [[[1, -8, 2197], 1]], [[[1, -15, 4913], 1]], [[[1, -23, 6859], 1]], [[[1, -63, 12167], 1]], [[[1, -156, 24389], 1]], [[[1, 85, 29791], 1]], [[[1, -74, 50653], 1]], [[[1, -246, 68921], 1]], [[[1, 190, 79507], 1]], [[[1, -288, 103823], 1]], [[[1, 177, 148877], 1]], [[[1, -792, 205379], 1]], [[[1, 907, 226981], 1]], [[[1, 322, 300763], 1]], [[[1, 270, 357911], 1]], [[[1, -254, 389017], 1]], [[[1, 1123, 493039], 1]], [[[1, 771, 571787], 1]], [[[1, 198, 704969], 1]], [[[1, 1192, 912673], 1]], [[[1, 1692, 1030301], 1]], [[[1, -1748, 1092727], 1]], [[[1, 948, 1225043], 1]], [[[1, -593, 1295029], 1]], [[[1, 1062, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-270-1.1-c3-0-8', 'leading_term': '3.34207104043201712300345843840000000000000000000000000000000000000000000000000000000000000', '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/270/4/a/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [3.342071040432017, 3.331888640395952, 3.301362847376542, 3.2505606042145216, 3.179602435036893, 3.0886754618066234, 2.978050818691381, 2.848104692165395, 2.6993420435715567, 2.5324219319531167, 2.348183251108527, 2.1476696272705533, 1.9321521926255014, 1.7031489543903984, 1.4624395183385477, 1.2120739984635946, 0.9543750500020047, 0.6919321005679863, 0.42758702303046187, 0.1644106931679681, -0.0943298961567547, -0.3452140364999964, -0.5847190127356094, -0.8092806103242997, -1.0153615964671505, -1.1995270274818162, -1.358524912312749, -1.489370450218072, -1.5894317703267433, -1.6565148437559225, -1.688945027639892, -1.6856425471211138, -1.646189138014421, -1.5708830704044487, -1.4607798612324892, 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True, 'rational': True, 'root_analytic_conductor': 3.991305012342451, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1125462651684481670, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38041783395827634040710503882', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87345634784495729641931328210', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24491218427357514486926764281', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.930515701549973, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 270, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 4, 5, 0, 8, 8, 0, 10, 18, 0, 8, 16, 0, 16, 15, 0, 23, 20, 0, 36, 63, 0, 25, 16, 0, 32, 156, 0, -85, 32, 0, 30, 40, 0, 74, 46, 0, 40, 246, 0, -190, 72, 0, 126, 288, 0, -279, 50, 0, 32, -177, 0, 90, 64, 0, 312, 792, 0, -907, -170, 0, 64, 40, 0, -322, 60, 0, 80, -270, 0, 254, 148, 0, 92, 144, 0, -1123, 80, 0, 492, -771, 0, 75, -380, 0, 144, -198, 0, 64, 252, 0, 576, 115, 0, -1192, -558, 0, 100], 'euler11': [1, -18, 1331], 'euler13': [1, -8, 2197], 'euler17': [1, -15, 4913], 'euler19': [1, -23, 6859], 'euler2': [1, -2, 0], 'euler23': [1, -63, 12167], 'euler29': [1, -156, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 85, 29791], 'euler37': [1, -74, 50653], 'euler41': [1, -246, 68921], 'euler43': [1, 190, 79507], 'euler47': [1, -288, 103823], 'euler5': [1, -5, 0], 'euler53': [1, 177, 148877], 'euler59': [1, -792, 205379], 'euler61': [1, 907, 226981], 'euler67': [1, 322, 300763], 'euler7': [1, -8, 343], 'euler71': [1, 270, 357911], 'euler73': [1, -254, 389017], 'euler79': [1, 1123, 493039], 'euler83': [1, 771, 571787], 'euler89': [1, 198, 704969], 'euler97': [1, 1192, 912673], 'euler_factors': [[1, -2, 0], [1, 0, 0], [1, -5, 0], [1, -8, 343], [1, -18, 1331], [1, -8, 2197], [1, -15, 4913], [1, -23, 6859], [1, -63, 12167], [1, -156, 24389], [1, 85, 29791], [1, -74, 50653], [1, -246, 68921], [1, 190, 79507], [1, -288, 103823], [1, 177, 148877], [1, -792, 205379], [1, 907, 226981], [1, 322, 300763], [1, 270, 357911], [1, -254, 389017], [1, 1123, 493039], [1, 771, 571787], [1, 198, 704969], [1, 1192, 912673]], 'index': 8, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/270/4/a/l/1/1', 'ModularForm/GL2/Q/holomorphic/270/4/a/l'], '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': '2-270-1.1-c3-0-8', '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': '2-270-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.991305012342451, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1125462651684481670, 'z1': {'__RealLiteral__': 0, 'data': '1.38041783395827634040710503882', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20642868
{'Lhash': '1749887495782961313942543777773', 'Lhash_array': ['1749887495782961313942543777773'], 'label': '2-270-1.1-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/270/4/a/l'}
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id: 24555412
{'Lhash': '1749887495782961313942543777773', 'Lhash_array': ['1749887495782961313942543777773'], 'label': '2-270-1.1-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/270/4/a/l/1/1'}