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lfunc_lfunctions • Show schema
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{'Lhash': '2672492263909657951117787086828', 'a10': -18, 'a2': -2, 'a3': 0, 'a4': 4, 'a5': 9, 'a6': 0, 'a7': -31, 'a8': -8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.558309420929984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '162.1', 'coefficient_field': '1.1.1.1', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1, 2], [1], [1, -9, 125], [1, 31, 343], [1, -15, 1331], [1, 37, 2197], [1, -42, 4913], [1, 28, 6859], [1, 195, 12167], [1, 111, 24389], [1, 205, 29791], [1, 166, 50653], [1, -261, 68921], [1, 43, 79507], [1, 177, 103823], [1, 114, 148877], [1, 159, 205379], [1, -191, 226981], [1, 421, 300763], [1, 156, 357911], [1, -182, 389017], [1, -1133, 493039], [1, -1083, 571787], [1, -1050, 704969], [1, 901, 912673], [1, 387, 1030301], [1, -551, 1092727], [1, -12, 1225043], [1, 502, 1295029], [1, -1401, 1442897]], 'euler_factors_factorization': [[[[1, 2], 1]], [1], [[[1, -9, 125], 1]], [[[1, 31, 343], 1]], [[[1, -15, 1331], 1]], [[[1, 37, 2197], 1]], [[[1, -42, 4913], 1]], [[[1, 28, 6859], 1]], [[[1, 195, 12167], 1]], [[[1, 111, 24389], 1]], [[[1, 205, 29791], 1]], [[[1, 166, 50653], 1]], [[[1, -261, 68921], 1]], [[[1, 43, 79507], 1]], [[[1, 177, 103823], 1]], [[[1, 114, 148877], 1]], [[[1, 159, 205379], 1]], [[[1, -191, 226981], 1]], [[[1, 421, 300763], 1]], [[[1, 156, 357911], 1]], [[[1, -182, 389017], 1]], [[[1, -1133, 493039], 1]], [[[1, -1083, 571787], 1]], [[[1, -1050, 704969], 1]], [[[1, 901, 912673], 1]], [[[1, 387, 1030301], 1]], [[[1, -551, 1092727], 1]], [[[1, -12, 1225043], 1]], [[[1, 502, 1295029], 1]], [[[1, -1401, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-162-1.1-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/162/4/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-4.501493200464891e-120, 0.23387281013334868, 0.46335617006233387, 0.6838615660357686, 0.8904350069002408, 1.0776530706360905, 1.2396059439265001, 1.3699849094677414, 1.462283508145187, 1.51011271319229, 1.5076211804152728, 1.4500021347428405, 1.334058889427536, 1.1587916978361923, 0.9259601756924215, 0.6405687181360866, 0.31121817344215713, -0.049733396331363956, -0.42625372426971203, -0.7990061282255405, -1.1460333155352873, -1.4437608651578435, -1.6682994685521395, -1.796994922323395, -1.810143483990971, -1.6927603674659795, -1.4362641564810814, -1.0399232224979071, -0.511905150985449, 0.1302205634040686, 0.8596509626352482, 1.641271878929961, 2.4333598747155603, 3.1900211679358255, 3.8642496022860415, 4.4114105951845115, 4.792890921171579, 4.979603564124912, 4.955010665100211, 4.717332334691139, 4.280648874800979, 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 884454523556432232, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.10822466650392394975477454917', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.60114648545183038779602919539', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.73320443153005755121658124085', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.558309420929984, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 4, 9, 0, -31, -8, 0, -18, 15, 0, -37, 62, 0, 16, 42, 0, -28, 36, 0, -30, -195, 0, -44, 74, 0, -124, -111, 0, -205, -32, 0, -84, -279, 0, -166, 56, 0, -72, 261, 0, -43, 60, 0, 390, -177, 0, 618, 88, 0, -148, -114, 0, 135, 248, 0, 222, -159, 0, 191, 410, 0, 64, -333, 0, -421, 168, 0, 558, -156, 0, 182, 332, 0, -112, -465, 0, 1133, 144, 0, -522, 1083, 0, 378, 86, 0, -120, 1050, 0, 1147, -780, 0, 354, -252, 0, -901, -1236, 0, -176], 'euler11': [1, -15, 1331], 'euler13': [1, 37, 2197], 'euler17': [1, -42, 4913], 'euler19': [1, 28, 6859], 'euler2': [1, 2, 0], 'euler23': [1, 195, 12167], 'euler29': [1, 111, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 205, 29791], 'euler37': [1, 166, 50653], 'euler41': [1, -261, 68921], 'euler43': [1, 43, 79507], 'euler47': [1, 177, 103823], 'euler5': [1, -9, 125], 'euler53': [1, 114, 148877], 'euler59': [1, 159, 205379], 'euler61': [1, -191, 226981], 'euler67': [1, 421, 300763], 'euler7': [1, 31, 343], 'euler71': [1, 156, 357911], 'euler73': [1, -182, 389017], 'euler79': [1, -1133, 493039], 'euler83': [1, -1083, 571787], 'euler89': [1, -1050, 704969], 'euler97': [1, 901, 912673], 'euler_factors': [[1, 2, 0], [1, 0, 0], [1, -9, 125], [1, 31, 343], [1, -15, 1331], [1, 37, 2197], [1, -42, 4913], [1, 28, 6859], [1, 195, 12167], [1, 111, 24389], [1, 205, 29791], [1, 166, 50653], [1, -261, 68921], [1, 43, 79507], [1, 177, 103823], [1, 114, 148877], [1, 159, 205379], [1, -191, 226981], [1, 421, 300763], [1, 156, 357911], [1, -182, 389017], [1, -1133, 493039], [1, -1083, 571787], [1, -1050, 704969], [1, 901, 912673]], 'index': 9, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/162/4/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': '2-162-1.1-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': '2-162-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.0916515684873, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 884454523556432232, 'z1': {'__RealLiteral__': 0, 'data': '2.10822466650392394975477454917', 'prec': 103}}
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lfunc_instances • Show schema
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id: 12610366
{'Lhash': '2672492263909657951117787086828', 'Lhash_array': ['2672492263909657951117787086828'], 'label': '2-162-1.1-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/4/a/a'}
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id: 24552154
{'Lhash': '2672492263909657951117787086828', 'Lhash_array': ['2672492263909657951117787086828'], 'label': '2-162-1.1-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/4/a/a/1/1'}