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lfunc_lfunctions • Show schema
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{'Lhash': '390624722165454776388525877224', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -34, '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, 34, 343], [1, 18, 1331], [1, 12, 2197], [1, 106, 4913], [1, 44, 6859], [1, -56, 12167], [1, 270, 24389], [1, -204, 29791], [1, 120, 50653], [1, 80, 68921], [1, 536, 79507], [1, 536, 103823], [1, -542, 148877], [1, -174, 205379], [1, -186, 226981], [1, 332, 300763], [1, -132, 357911], [1, -602, 389017], [1, 548, 493039], [1, 492, 571787], [1, -1052, 704969], [1, 482, 912673], [1, 1214, 1030301], [1, 898, 1092727], [1, -1364, 1225043], [1, -218, 1295029], [1, -1386, 1442897]], 'euler_factors_factorization': [[1], [1], [1], [[[1, 34, 343], 1]], [[[1, 18, 1331], 1]], [[[1, 12, 2197], 1]], [[[1, 106, 4913], 1]], [[[1, 44, 6859], 1]], [[[1, -56, 12167], 1]], [[[1, 270, 24389], 1]], [[[1, -204, 29791], 1]], [[[1, 120, 50653], 1]], [[[1, 80, 68921], 1]], [[[1, 536, 79507], 1]], [[[1, 536, 103823], 1]], [[[1, -542, 148877], 1]], [[[1, -174, 205379], 1]], [[[1, -186, 226981], 1]], [[[1, 332, 300763], 1]], [[[1, -132, 357911], 1]], [[[1, -602, 389017], 1]], [[[1, 548, 493039], 1]], [[[1, 492, 571787], 1]], [[[1, -1052, 704969], 1]], [[[1, 482, 912673], 1]], [[[1, 1214, 1030301], 1]], [[[1, 898, 1092727], 1]], [[[1, -1364, 1225043], 1]], [[[1, -218, 1295029], 1]], [[[1, -1386, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-1800-1.1-c3-0-3', 'leading_term': '0.496843713415839064237088027322520000000000000000000000000000000000000000000000000000000000', '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/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.49684371341583905, 0.4828304360652224, 0.4409658710168466, 0.3717749678913772, 0.2761297545665173, 0.15524483205643286, 0.010670731473951532, -0.15571518010620608, -0.3417206161851275, -0.5448535174574461, -0.7623408478500595, -0.9911514442644361, -1.2280232815485137, -1.4694954438374603, -1.7119449964836289, -1.9516288314254817, -2.184730416014784, -2.4074112148431985, -2.6158663805119144, -2.8063841277008454, -2.9754080209256255, -3.119601225979063, -3.2359116044104206, -3.3216363757441894, -3.374484939645608, -3.392638345835676, -3.3748038287812534, -3.3202627920119423, -3.2289106375909133, -3.1012868931409403, -2.9385941941920946, -2.7427048345601133, -2.516153801734114, -2.2621174661548205, -1.9843773895857235, 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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': 227023750330029897, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30814857192914688972266718032', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.04650628620539726469342120586', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97919958800080101311492941657', '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, -34, 0, 0, 0, -18, 0, -12, 0, 0, 0, -106, 0, -44, 0, 0, 0, 56, 0, 0, 0, 0, 0, -270, 0, 204, 0, 0, 0, 0, 0, -120, 0, 0, 0, -80, 0, -536, 0, 0, 0, -536, 0, 813, 0, 0, 0, 542, 0, 0, 0, 0, 0, 174, 0, 186, 0, 0, 0, 0, 0, -332, 0, 0, 0, 132, 0, 602, 0, 0, 0, 612, 0, -548, 0, 0, 0, -492, 0, 0, 0, 0, 0, 1052, 0, 408, 0, 0, 0, 0, 0, -482, 0, 0, 0], 'euler11': [1, 18, 1331], 'euler13': [1, 12, 2197], 'euler17': [1, 106, 4913], 'euler19': [1, 44, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -56, 12167], 'euler29': [1, 270, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -204, 29791], 'euler37': [1, 120, 50653], 'euler41': [1, 80, 68921], 'euler43': [1, 536, 79507], 'euler47': [1, 536, 103823], 'euler5': [1, 0, 0], 'euler53': [1, -542, 148877], 'euler59': [1, -174, 205379], 'euler61': [1, -186, 226981], 'euler67': [1, 332, 300763], 'euler7': [1, 34, 343], 'euler71': [1, -132, 357911], 'euler73': [1, -602, 389017], 'euler79': [1, 548, 493039], 'euler83': [1, 492, 571787], 'euler89': [1, -1052, 704969], 'euler97': [1, 482, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 34, 343], [1, 18, 1331], [1, 12, 2197], [1, 106, 4913], [1, 44, 6859], [1, -56, 12167], [1, 270, 24389], [1, -204, 29791], [1, 120, 50653], [1, 80, 68921], [1, 536, 79507], [1, 536, 103823], [1, -542, 148877], [1, -174, 205379], [1, -186, 226981], [1, 332, 300763], [1, -132, 357911], [1, -602, 389017], [1, 548, 493039], [1, 492, 571787], [1, -1052, 704969], [1, 482, 912673]], 'index': 3, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/1800/4/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': '2-1800-1.1-c3-0-3', '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': 227023750330029897, 'z1': {'__RealLiteral__': 0, 'data': '0.30814857192914688972266718032', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21274185
{'Lhash': '390624722165454776388525877224', 'Lhash_array': ['390624722165454776388525877224'], 'label': '2-1800-1.1-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/4/a/a'}
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id: 24592233
{'Lhash': '390624722165454776388525877224', 'Lhash_array': ['390624722165454776388525877224'], 'label': '2-1800-1.1-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/4/a/a/1/1'}