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lfunc_lfunctions • Show schema
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{'Lhash': '939385168667621034843892923531', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 6, 'a8': 0, 'a9': -26, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 94.40305600918502, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '1600.1', 'coefficient_field': '1.1.1.1', 'conductor': 1600, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[1], [1, -1, 27], [1], [1, -6, 343], [1, -19, 1331], [1, -12, 2197], [1, -75, 4913], [1, -91, 6859], [1, 174, 12167], [1, -272, 24389], [1, 230, 29791], [1, 182, 50653], [1, -117, 68921], [1, -372, 79507], [1, -52, 103823], [1, 402, 148877], [1, 312, 205379], [1, 170, 226981], [1, -763, 300763], [1, 52, 357911], [1, -981, 389017], [1, -1054, 493039], [1, -351, 571787], [1, -799, 704969], [1, 962, 912673], [1, 486, 1030301], [1, -1188, 1092727], [1, -1325, 1225043], [1, 126, 1295029], [1, 183, 1442897]], 'euler_factors_factorization': [[1], [[[1, -1, 27], 1]], [1], [[[1, -6, 343], 1]], [[[1, -19, 1331], 1]], [[[1, -12, 2197], 1]], [[[1, -75, 4913], 1]], [[[1, -91, 6859], 1]], [[[1, 174, 12167], 1]], [[[1, -272, 24389], 1]], [[[1, 230, 29791], 1]], [[[1, 182, 50653], 1]], [[[1, -117, 68921], 1]], [[[1, -372, 79507], 1]], [[[1, -52, 103823], 1]], [[[1, 402, 148877], 1]], [[[1, 312, 205379], 1]], [[[1, 170, 226981], 1]], [[[1, -763, 300763], 1]], [[[1, 52, 357911], 1]], [[[1, -981, 389017], 1]], [[[1, -1054, 493039], 1]], [[[1, -351, 571787], 1]], [[[1, -799, 704969], 1]], [[[1, 962, 912673], 1]], [[[1, 486, 1030301], 1]], [[[1, -1188, 1092727], 1]], [[[1, -1325, 1225043], 1]], [[[1, 126, 1295029], 1]], [[[1, 183, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 30, 'label': '2-40e2-1.1-c3-0-30', 'leading_term': '2.34562851752003718832657100014000000000000000000000000000000000000000000000000000000000000', '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/1600/4/a/bf', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.345628517520037, 2.32748033105564, 2.273307362615308, 2.183923094409028, 2.0606788772702527, 1.9054567341064457, 1.7206582861188635, 1.509188885095755, 1.274435885342513, 1.0202399150861015, 0.7508580180469959, 0.4709176357511644, 0.18536059026772148, -0.10062349853039998, -0.3816745752176888, -0.6523500866878585, -0.9072228222909439, -1.140987479039713, -1.3485742557538731, -1.5252672668357958, -1.6668250808100729, -1.76960025304927, -1.8306543582219446, -1.8478647569476911, -1.8200191722426053, -1.7468941214388614, -1.6293133619723899, -1.4691827743492198, -1.2694985275834463, -1.0343259509266591, -0.7687472643545786, -0.4787771863502462, -0.17124642190570247, 0.14634588911715773, 0.4660085445620806, 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'2-40e2-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.716123507303982, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 131327454221588115, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74104423450633238584822198309', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90673195090298212021105079156', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09031329764211998538803281526', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 94.40305600918502, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 1600, 'conductor_radical': 10, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 6, 0, -26, 0, 19, 0, 12, 0, 0, 0, 75, 0, 91, 0, 6, 0, -174, 0, 0, 0, -53, 0, 272, 0, -230, 0, 19, 0, 0, 0, -182, 0, 12, 0, 117, 0, 372, 0, 0, 0, 52, 0, -307, 0, 75, 0, -402, 0, 0, 0, 91, 0, -312, 0, -170, 0, -156, 0, 0, 0, 763, 0, -174, 0, -52, 0, 981, 0, 0, 0, 114, 0, 1054, 0, 649, 0, 351, 0, 0, 0, 272, 0, 799, 0, 72, 0, -230, 0, 0, 0, -962, 0, -494, 0], 'euler11': [1, -19, 1331], 'euler13': [1, -12, 2197], 'euler17': [1, -75, 4913], 'euler19': [1, -91, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 174, 12167], 'euler29': [1, -272, 24389], 'euler3': [1, -1, 27], 'euler31': [1, 230, 29791], 'euler37': [1, 182, 50653], 'euler41': [1, -117, 68921], 'euler43': [1, -372, 79507], 'euler47': [1, -52, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 402, 148877], 'euler59': [1, 312, 205379], 'euler61': [1, 170, 226981], 'euler67': [1, -763, 300763], 'euler7': [1, -6, 343], 'euler71': [1, 52, 357911], 'euler73': [1, -981, 389017], 'euler79': [1, -1054, 493039], 'euler83': [1, -351, 571787], 'euler89': [1, -799, 704969], 'euler97': [1, 962, 912673], 'euler_factors': [[1, 0, 0], [1, -1, 27], [1, 0, 0], [1, -6, 343], [1, -19, 1331], [1, -12, 2197], [1, -75, 4913], [1, -91, 6859], [1, 174, 12167], [1, -272, 24389], [1, 230, 29791], [1, 182, 50653], [1, -117, 68921], [1, -372, 79507], [1, -52, 103823], [1, 402, 148877], [1, 312, 205379], [1, 170, 226981], [1, -763, 300763], [1, 52, 357911], [1, -981, 389017], [1, -1054, 493039], [1, -351, 571787], [1, -799, 704969], [1, 962, 912673]], 'index': 30, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1600/4/a/bf/1/1', 'ModularForm/GL2/Q/holomorphic/1600/4/a/bf'], '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': '2-40e2-1.1-c3-0-30', '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': '2-40e2-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.716123507303982, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 131327454221588115, 'z1': {'__RealLiteral__': 0, 'data': '0.74104423450633238584822198309', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21222360
{'Lhash': '939385168667621034843892923531', 'Lhash_array': ['939385168667621034843892923531'], 'factors': ['2-40e2-1.1-c3-0-30'], 'label': '2-40e2-1.1-c3-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1600/4/a/bf'}
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id: 24591771
{'Lhash': '939385168667621034843892923531', 'Lhash_array': ['939385168667621034843892923531'], 'factors': ['2-40e2-1.1-c3-0-30'], 'label': '2-40e2-1.1-c3-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1600/4/a/bf/1/1'}