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lfunc_lfunctions • Show schema
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{'Lhash': '2155041176204560134517490019205', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': -3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.762974500266903, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [11, [1, 1]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.1', 'coefficient_field': '1.1.1.1', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[1, -1, 2], [1], [1], [1, -2, 7], [1, 1], [1, -2, 13], [1, 2, 17], [1, 6, 19], [1, 4, 23], [1, 6, 29], [1, -4, 31], [1, -6, 37], [1, 10, 41], [1, 6, 43], [1, -8, 47], [1, 0, 53], [1, -4, 59], [1, 6, 61], [1, 8, 67], [1, 0, 71], [1, -2, 73], [1, 10, 79], [1, 12, 83], [1, 0, 89], [1, 2, 97], [1, 14, 101], [1, 8, 103], [1, 12, 107], [1, 2, 109], [1, 12, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [1], [1], [[[1, -2, 7], 1]], [[[1, 1], 1]], [[[1, -2, 13], 1]], [[[1, 2, 17], 1]], [[[1, 6, 19], 1]], [[[1, 4, 23], 1]], [[[1, 6, 29], 1]], [[[1, -4, 31], 1]], [[[1, -6, 37], 1]], [[[1, 10, 41], 1]], [[[1, 6, 43], 1]], [[[1, -8, 47], 1]], [[[1, 0, 53], 1]], [[[1, -4, 59], 1]], [[[1, 6, 61], 1]], [[[1, 8, 67], 1]], [[[1, 0, 71], 1]], [[[1, -2, 73], 1]], [[[1, 10, 79], 1]], [[[1, 12, 83], 1]], [[[1, 0, 89], 1]], [[[1, 2, 97], 1]], [[[1, 14, 101], 1]], [[[1, 8, 103], 1]], [[[1, 12, 107], 1]], [[[1, 2, 109], 1]], [[[1, 12, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 67, 'label': '2-2475-1.1-c1-0-67', '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/2475/2/a/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.2719502906800166e-60, 0.20113872038642394, 0.4020633575734931, 0.6025060441452692, 0.8020943165302202, 1.0003060082489639, 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1.8584727470349784, 1.6375190765403234, 1.367721357882079, 1.066637091195901, 0.7530993291609502, 0.44608456031578364, 0.16358341573238938], 'positive_zeros': ['1.70002773304928331393197381104331', '2.82049928275954817840186820476583', '3.98159649274510364542505380475534', '4.42806580035514350183447341926319', '5.32946274439723089843787755674533', '6.02983209069794989603640383675980', '6.81603726027801660997015654357843', '8.037404731553225089340453872858137', '8.426508541426244909616098012576463'], 'prelabel': '2-2475-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.445556714323517, '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': 1556033467662516423, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70002773304928331393197381104', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82049928275954817840186820477', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98159649274510364542505380476', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.762974500266903, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, 0, 0, 2, -3, 0, 0, -1, 0, 2, 2, 0, -1, -2, 0, -6, 0, 0, -1, -4, 0, 0, 2, 0, -2, -6, 0, 4, 5, 0, -2, 0, 0, 6, -6, 0, 0, -10, 0, -6, 1, 0, -4, 8, 0, -3, 0, 0, -2, 0, 0, 0, -6, 0, -6, 4, 0, -6, 4, 0, 7, 0, 0, -8, 2, 0, 0, 0, 0, 2, 6, 0, 6, -2, 0, -10, 0, 0, -10, -12, 0, 0, -6, 0, 3, 0, 0, 4, 4, 0, 8, 0, 0, -2, -3, 0, 0], 'euler11': [1, 1, 0], 'euler13': [1, -2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 6, 19], 'euler2': [1, -1, 2], 'euler23': [1, 4, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, 10, 41], 'euler43': [1, 6, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 0, 53], 'euler59': [1, -4, 59], 'euler61': [1, 6, 61], 'euler67': [1, 8, 67], 'euler7': [1, -2, 7], 'euler71': [1, 0, 71], 'euler73': [1, -2, 73], 'euler79': [1, 10, 79], 'euler83': [1, 12, 83], 'euler89': [1, 0, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 2], [1, 0, 0], [1, 0, 0], [1, -2, 7], [1, 1, 0], [1, -2, 13], [1, 2, 17], [1, 6, 19], [1, 4, 23], [1, 6, 29], [1, -4, 31], [1, -6, 37], [1, 10, 41], [1, 6, 43], [1, -8, 47], [1, 0, 53], [1, -4, 59], [1, 6, 61], [1, 8, 67], [1, 0, 71], [1, -2, 73], [1, 10, 79], [1, 12, 83], [1, 0, 89], [1, 2, 97]], 'index': 67, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2475/j', 'ModularForm/GL2/Q/holomorphic/2475/2/a/j/1/1', 'ModularForm/GL2/Q/holomorphic/2475/2/a/j'], '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': '2-2475-1.1-c1-0-67', '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': '2-2475-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.445556714323517, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1556033467662516423, 'z1': {'__RealLiteral__': 0, 'data': '1.70002773304928331393197381104', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20620972
{'Lhash': '2155041176204560134517490019205', 'Lhash_array': ['2155041176204560134517490019205'], 'label': '2-2475-1.1-c1-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/2/a/j'}
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id: 24557389
{'Lhash': '2155041176204560134517490019205', 'Lhash_array': ['2155041176204560134517490019205'], 'label': '2-2475-1.1-c1-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/2/a/j/1/1'}
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id: 25333
{'Lhash': '1556033467662516423', 'Lhash_array': ['1556033467662516423'], 'label': '2-2475-1.1-c1-0-67', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2475/j'}