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lfunc_lfunctions • Show schema
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{'Lhash': '832608619465044188278633375089', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 106.20343801033316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.1', 'coefficient_field': '1.1.1.1', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 0, 343], [1, 4, 1331], [1, 54, 2197], [1, -114, 4913], [1, -44, 6859], [1, -96, 12167], [1, 134, 24389], [1, 272, 29791], [1, -98, 50653], [1, -6, 68921], [1, 12, 79507], [1, 200, 103823], [1, -654, 148877], [1, 36, 205379], [1, 442, 226981], [1, -188, 300763], [1, -632, 357911], [1, -390, 389017], [1, -688, 493039], [1, -1188, 571787], [1, -694, 704969], [1, -1726, 912673], [1, 1182, 1030301], [1, 1968, 1092727], [1, -796, 1225043], [1, -342, 1295029], [1, -114, 1442897]], 'euler_factors_factorization': [[1], [1], [1], [[[1, 0, 343], 1]], [[[1, 4, 1331], 1]], [[[1, 54, 2197], 1]], [[[1, -114, 4913], 1]], [[[1, -44, 6859], 1]], [[[1, -96, 12167], 1]], [[[1, 134, 24389], 1]], [[[1, 272, 29791], 1]], [[[1, -98, 50653], 1]], [[[1, -6, 68921], 1]], [[[1, 12, 79507], 1]], [[[1, 200, 103823], 1]], [[[1, -654, 148877], 1]], [[[1, 36, 205379], 1]], [[[1, 442, 226981], 1]], [[[1, -188, 300763], 1]], [[[1, -632, 357911], 1]], [[[1, -390, 389017], 1]], [[[1, -688, 493039], 1]], [[[1, -1188, 571787], 1]], [[[1, -694, 704969], 1]], [[[1, -1726, 912673], 1]], [[[1, 1182, 1030301], 1]], [[[1, 1968, 1092727], 1]], [[[1, -796, 1225043], 1]], [[[1, -342, 1295029], 1]], [[[1, -114, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-1800-1.1-c3-0-16', 'leading_term': '1.953187726231845019448156460882000000000000000000000000000000000000000000000000000000000000', '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/1800/4/a/s', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.9531877262318451, 1.934573645742593, 1.8790361525391288, 1.7874875197348499, 1.661441473048735, 1.5030025579874509, 1.3148502178117423, 1.1002166398824282, 0.86285728680144, 0.6070129740055771, 0.3373623964457084, 0.058964148090046034, -0.22281248141394677, -0.5023683140732618, -0.7739666578199924, -1.031836723155298, -1.2702870188630169, -1.4838270945941132, -1.6672954224979994, -1.8159906527702874, -1.9258029649092896, -1.9933417935943287, -2.0160558605982066, -1.9923412155292783, -1.9216328993767973, -1.80447591319098, -1.6425714127028934, -1.4387944658917207, -1.1971803059399457, -0.9228767814158245, -0.6220616363818163, -0.30182432545385707, 0.029986744830211878, 0.36494939123355635, 0.6942817844698487, 1.0090807782965827, 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True, 'rational': True, 'root_analytic_conductor': 10.305505228291, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1207887307228405128, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65681238924601170841980941923', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86975000775240846554078848643', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00098549697199502841337192071', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 106.20343801033316, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -54, 0, 0, 0, 114, 0, 44, 0, 0, 0, 96, 0, 0, 0, 0, 0, -134, 0, -272, 0, 0, 0, 0, 0, 98, 0, 0, 0, 6, 0, -12, 0, 0, 0, -200, 0, -343, 0, 0, 0, 654, 0, 0, 0, 0, 0, -36, 0, -442, 0, 0, 0, 0, 0, 188, 0, 0, 0, 632, 0, 390, 0, 0, 0, 0, 0, 688, 0, 0, 0, 1188, 0, 0, 0, 0, 0, 694, 0, 0, 0, 0, 0, 0, 0, 1726, 0, 0, 0], 'euler11': [1, 4, 1331], 'euler13': [1, 54, 2197], 'euler17': [1, -114, 4913], 'euler19': [1, -44, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -96, 12167], 'euler29': [1, 134, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 272, 29791], 'euler37': [1, -98, 50653], 'euler41': [1, -6, 68921], 'euler43': [1, 12, 79507], 'euler47': [1, 200, 103823], 'euler5': [1, 0, 0], 'euler53': [1, -654, 148877], 'euler59': [1, 36, 205379], 'euler61': [1, 442, 226981], 'euler67': [1, -188, 300763], 'euler7': [1, 0, 343], 'euler71': [1, -632, 357911], 'euler73': [1, -390, 389017], 'euler79': [1, -688, 493039], 'euler83': [1, -1188, 571787], 'euler89': [1, -694, 704969], 'euler97': [1, -1726, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 343], [1, 4, 1331], [1, 54, 2197], [1, -114, 4913], [1, -44, 6859], [1, -96, 12167], [1, 134, 24389], [1, 272, 29791], [1, -98, 50653], [1, -6, 68921], [1, 12, 79507], [1, 200, 103823], [1, -654, 148877], [1, 36, 205379], [1, 442, 226981], [1, -188, 300763], [1, -632, 357911], [1, -390, 389017], [1, -688, 493039], [1, -1188, 571787], [1, -694, 704969], [1, -1726, 912673]], 'index': 16, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/4/a/s/1/1', 'ModularForm/GL2/Q/holomorphic/1800/4/a/s'], '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': '2-1800-1.1-c3-0-16', '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': '2-1800-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.305505228291, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1207887307228405128, 'z1': {'__RealLiteral__': 0, 'data': '0.65681238924601170841980941923', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21050099
{'Lhash': '832608619465044188278633375089', 'Lhash_array': ['832608619465044188278633375089'], 'label': '2-1800-1.1-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/4/a/s'}
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id: 24592251
{'Lhash': '832608619465044188278633375089', 'Lhash_array': ['832608619465044188278633375089'], 'label': '2-1800-1.1-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/4/a/s/1/1'}