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lfunc_lfunctions • Show schema
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{'Lhash': '1403320294998124738225065457450', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 9, 'a6': 0, 'a7': 31, 'a8': 0, 'a9': -23, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 71.74632256698062, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [19, [1, -19]]], 'bad_primes': [2, 19], 'central_character': '1216.1', 'coefficient_field': '1.1.1.1', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'euler_factors': [[1], [1, 2, 27], [1, -9, 125], [1, -31, 343], [1, -57, 1331], [1, -52, 2197], [1, -69, 4913], [1, -19], [1, -72, 12167], [1, -150, 24389], [1, 32, 29791], [1, -226, 50653], [1, 258, 68921], [1, 67, 79507], [1, 579, 103823], [1, -432, 148877], [1, 330, 205379], [1, -13, 226981], [1, 856, 300763], [1, 642, 357911], [1, 487, 389017], [1, -700, 493039], [1, 12, 571787], [1, 600, 704969], [1, -1424, 912673], [1, 1062, 1030301], [1, 1178, 1092727], [1, -114, 1225043], [1, 1460, 1295029], [1, 822, 1442897]], 'euler_factors_factorization': [[1], [[[1, 2, 27], 1]], [[[1, -9, 125], 1]], [[[1, -31, 343], 1]], [[[1, -57, 1331], 1]], [[[1, -52, 2197], 1]], [[[1, -69, 4913], 1]], [[[1, -19], 1]], [[[1, -72, 12167], 1]], [[[1, -150, 24389], 1]], [[[1, 32, 29791], 1]], [[[1, -226, 50653], 1]], [[[1, 258, 68921], 1]], [[[1, 67, 79507], 1]], [[[1, 579, 103823], 1]], [[[1, -432, 148877], 1]], [[[1, 330, 205379], 1]], [[[1, -13, 226981], 1]], [[[1, 856, 300763], 1]], [[[1, 642, 357911], 1]], [[[1, 487, 389017], 1]], [[[1, -700, 493039], 1]], [[[1, 12, 571787], 1]], [[[1, 600, 704969], 1]], [[[1, -1424, 912673], 1]], [[[1, 1062, 1030301], 1]], [[[1, 1178, 1092727], 1]], [[[1, -114, 1225043], 1]], [[[1, 1460, 1295029], 1]], [[[1, 822, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 57, 'label': '2-1216-1.1-c3-0-57', 'leading_term': '3.30342368801775813261006042361000000000000000000000000000000000000000000000000000000000000', '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/1216/4/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [3.3034236880177583, 3.288601501710352, 3.24433414251424, 3.17121886325859, 3.070249805152374, 2.9428156448116423, 2.790695460064005, 2.616052032473982, 2.421421660736985, 2.209699469723701, 1.9841191716861513, 1.748226272950009, 1.505843822564261, 1.2610299674254972, 1.018026807369109, 0.7812003273216196, 0.5549715134456858, 0.34373912605888096, 0.15179499217923062, -0.01676691824267898, -0.15814597010903947, -0.26893285224277025, -0.3462076875832847, -0.38763557520706343, -0.3915566388705181, -0.3570674979713348, -0.2840910079521144, -0.17343114911789764, -0.02681008412462574, 0.15311533936433078, 0.362759990941056, 0.5976416257450313, 0.8524380811513136, 1.1210710659356946, 1.3968163229096604, 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'primitive': True, 'rational': True, 'root_analytic_conductor': 8.470320098259606, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1929826342342224901, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10702451822723800626756830215', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.65006164214392016088048213028', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.12733224881032251138485402995', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 71.74632256698062, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, 9, 0, 31, 0, -23, 0, 57, 0, 52, 0, -18, 0, 69, 0, 19, 0, -62, 0, 72, 0, -44, 0, 100, 0, 150, 0, -32, 0, -114, 0, 279, 0, 226, 0, -104, 0, -258, 0, -67, 0, -207, 0, -579, 0, 618, 0, -138, 0, 432, 0, 513, 0, -38, 0, -330, 0, 13, 0, -713, 0, 468, 0, -856, 0, -144, 0, -642, 0, -487, 0, 88, 0, 1767, 0, 700, 0, 421, 0, -12, 0, 621, 0, -300, 0, -600, 0, 1612, 0, 64, 0, 171, 0, 1424, 0, -1311, 0], 'euler11': [1, -57, 1331], 'euler13': [1, -52, 2197], 'euler17': [1, -69, 4913], 'euler19': [1, -19, 0], 'euler2': [1, 0, 0], 'euler23': [1, -72, 12167], 'euler29': [1, -150, 24389], 'euler3': [1, 2, 27], 'euler31': [1, 32, 29791], 'euler37': [1, -226, 50653], 'euler41': [1, 258, 68921], 'euler43': [1, 67, 79507], 'euler47': [1, 579, 103823], 'euler5': [1, -9, 125], 'euler53': [1, -432, 148877], 'euler59': [1, 330, 205379], 'euler61': [1, -13, 226981], 'euler67': [1, 856, 300763], 'euler7': [1, -31, 343], 'euler71': [1, 642, 357911], 'euler73': [1, 487, 389017], 'euler79': [1, -700, 493039], 'euler83': [1, 12, 571787], 'euler89': [1, 600, 704969], 'euler97': [1, -1424, 912673], 'euler_factors': [[1, 0, 0], [1, 2, 27], [1, -9, 125], [1, -31, 343], [1, -57, 1331], [1, -52, 2197], [1, -69, 4913], [1, -19, 0], [1, -72, 12167], [1, -150, 24389], [1, 32, 29791], [1, -226, 50653], [1, 258, 68921], [1, 67, 79507], [1, 579, 103823], [1, -432, 148877], [1, 330, 205379], [1, -13, 226981], [1, 856, 300763], [1, 642, 357911], [1, 487, 389017], [1, -700, 493039], [1, 12, 571787], [1, 600, 704969], [1, -1424, 912673]], 'index': 57, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1216/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/1216/4/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': '2-1216-1.1-c3-0-57', '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': '2-1216-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.470320098259606, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1929826342342224901, 'z1': {'__RealLiteral__': 0, 'data': '1.10702451822723800626756830215', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20338304
{'Lhash': '1403320294998124738225065457450', 'Lhash_array': ['1403320294998124738225065457450'], 'label': '2-1216-1.1-c3-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/4/a/b'}
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id: 24586528
{'Lhash': '1403320294998124738225065457450', 'Lhash_array': ['1403320294998124738225065457450'], 'label': '2-1216-1.1-c3-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/4/a/b/1/1'}