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lfunc_lfunctions • Show schema
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{'Lhash': '2258133486996029392438679995901', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.13417688936339, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [11, [1, 1]]], 'bad_primes': [2, 5, 11], 'central_character': '4400.1', 'coefficient_field': '1.1.1.1', 'conductor': 4400, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1], [1, 0, 7], [1, 1], [1, -2, 13], [1, 6, 17], [1, 4, 19], [1, 2, 23], [1, 10, 29], [1, -8, 31], [1, 8, 37], [1, 2, 41], [1, 0, 43], [1, -2, 47], [1, 0, 53], [1, -12, 59], [1, 10, 61], [1, 6, 67], [1, 0, 71], [1, 6, 73], [1, 12, 79], [1, -16, 83], [1, -18, 89], [1, -12, 97], [1, -2, 101], [1, 14, 103], [1, -12, 107], [1, -2, 109], [1, 12, 113]], 'euler_factors_factorization': [[1], [[[1, -2, 3], 1]], [1], [[[1, 0, 7], 1]], [[[1, 1], 1]], [[[1, -2, 13], 1]], [[[1, 6, 17], 1]], [[[1, 4, 19], 1]], [[[1, 2, 23], 1]], [[[1, 10, 29], 1]], [[[1, -8, 31], 1]], [[[1, 8, 37], 1]], [[[1, 2, 41], 1]], [[[1, 0, 43], 1]], [[[1, -2, 47], 1]], [[[1, 0, 53], 1]], [[[1, -12, 59], 1]], [[[1, 10, 61], 1]], [[[1, 6, 67], 1]], [[[1, 0, 71], 1]], [[[1, 6, 73], 1]], [[[1, 12, 79], 1]], [[[1, -16, 83], 1]], [[[1, -18, 89], 1]], [[[1, -12, 97], 1]], [[[1, -2, 101], 1]], [[[1, 14, 103], 1]], [[[1, -12, 107], 1]], [[[1, -2, 109], 1]], [[[1, 12, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 90, 'label': '2-4400-1.1-c1-0-90', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4400/2/a/ba', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.470065816127549e-58, 0.25213185362732354, 0.5036454256340777, 0.7538571627239053, 1.001957373061003, 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-4.210895523274711, -3.7380951351725824, -3.196527026566764, -2.6184833805177963, -2.0365012047521978, -1.4814415084187802, -0.9807094531380552, -0.5567224682933065], 'positive_zeros': ['1.78135322666156763674745180324568', '2.39205859293039716070712786825090', '3.35384730409316744338498807656211', '4.03622799462293727086828674779596', '4.85769740309940293341350504865556', '5.91622166242744518172165511635280', '6.58547960716893830705713223683427', '7.44768565041909769092975201089765', '8.137296030013542999760814973380457'], 'prelabel': '2-4400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.927408952431357, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1124443262653287824, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78135322666156763674745180325', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39205859293039716070712786825', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35384730409316744338498807656', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 35.13417688936339, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 4400, 'conductor_radical': 110, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 2, 0, 0, 0, -6, 0, -4, 0, 0, 0, -2, 0, 0, 0, -4, 0, -10, 0, 8, 0, -2, 0, 0, 0, -8, 0, 4, 0, -2, 0, 0, 0, 0, 0, 2, 0, -7, 0, -12, 0, 0, 0, 0, 0, -8, 0, 12, 0, -10, 0, 0, 0, 0, 0, -6, 0, -4, 0, 0, 0, -6, 0, 0, 0, 0, 0, -12, 0, -11, 0, 16, 0, 0, 0, -20, 0, 18, 0, 0, 0, 16, 0, 0, 0, 12, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, 10, 29], 'euler3': [1, -2, 3], 'euler31': [1, -8, 31], 'euler37': [1, 8, 37], 'euler41': [1, 2, 41], 'euler43': [1, 0, 43], 'euler47': [1, -2, 47], 'euler5': [1, 0, 0], 'euler53': [1, 0, 53], 'euler59': [1, -12, 59], 'euler61': [1, 10, 61], 'euler67': [1, 6, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, 12, 79], 'euler83': [1, -16, 83], 'euler89': [1, -18, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 0, 0], [1, 0, 7], [1, 1, 0], [1, -2, 13], [1, 6, 17], [1, 4, 19], [1, 2, 23], [1, 10, 29], [1, -8, 31], [1, 8, 37], [1, 2, 41], [1, 0, 43], [1, -2, 47], [1, 0, 53], [1, -12, 59], [1, 10, 61], [1, 6, 67], [1, 0, 71], [1, 6, 73], [1, 12, 79], [1, -16, 83], [1, -18, 89], [1, -12, 97]], 'index': 90, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4400/ba', 'ModularForm/GL2/Q/holomorphic/4400/2/a/ba/1/1', 'ModularForm/GL2/Q/holomorphic/4400/2/a/ba'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-4400-1.1-c1-0-90', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.927408952431357, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1124443262653287824, 'z1': {'__RealLiteral__': 0, 'data': '1.78135322666156763674745180325', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20102699
{'Lhash': '2258133486996029392438679995901', 'Lhash_array': ['2258133486996029392438679995901'], 'label': '2-4400-1.1-c1-0-90', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4400/2/a/ba'}
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id: 24565774
{'Lhash': '2258133486996029392438679995901', 'Lhash_array': ['2258133486996029392438679995901'], 'label': '2-4400-1.1-c1-0-90', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4400/2/a/ba/1/1'}
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id: 38079
{'Lhash': '1124443262653287824', 'Lhash_array': ['1124443262653287824'], 'label': '2-4400-1.1-c1-0-90', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4400/ba'}