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lfunc_lfunctions • Show schema
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{'Lhash': '1379315974321276971441071211098', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': -2, 'a5': 1, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.361294003886016, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [5, [1, -1]], [23, [1]]], 'bad_primes': [3, 5, 23], 'central_character': '7935.1', 'coefficient_field': '1.1.1.1', 'conductor': 7935, 'conductor_radical': 345, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, -1], [1, -1], [1, -3, 7], [1, -4, 11], [1, 0, 13], [1, -3, 17], [1, -8, 19], [1], [1, -9, 29], [1, 5, 31], [1, -9, 37], [1, -7, 41], [1, 4, 43], [1, 2, 47], [1, 13, 53], [1, 3, 59], [1, -14, 61], [1, 13, 67], [1, 13, 71], [1, 4, 73], [1, 0, 79], [1, -1, 83], [1, -8, 89], [1, 10, 97], [1, -9, 101], [1, 8, 103], [1, 11, 107], [1, -16, 109], [1, 1, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, -3, 7], 1]], [[[1, -4, 11], 1]], [[[1, 0, 13], 1]], [[[1, -3, 17], 1]], [[[1, -8, 19], 1]], [1], [[[1, -9, 29], 1]], [[[1, 5, 31], 1]], [[[1, -9, 37], 1]], [[[1, -7, 41], 1]], [[[1, 4, 43], 1]], [[[1, 2, 47], 1]], [[[1, 13, 53], 1]], [[[1, 3, 59], 1]], [[[1, -14, 61], 1]], [[[1, 13, 67], 1]], [[[1, 13, 71], 1]], [[[1, 4, 73], 1]], [[[1, 0, 79], 1]], [[[1, -1, 83], 1]], [[[1, -8, 89], 1]], [[[1, 10, 97], 1]], [[[1, -9, 101], 1]], [[[1, 8, 103], 1]], [[[1, 11, 107], 1]], [[[1, -16, 109], 1]], [[[1, 1, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 206, 'label': '2-7935-1.1-c1-0-206', 'leading_term': '3.38348124366234081851246215402000000000000000000000000000000000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/7935/2/a/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 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-3.019432798654794, -2.8189595361281623, -2.483238952634979, -2.03523923815002, -1.503353406111208, -0.9199090044984891, -0.31946855284867437, 0.2629892360459969, 0.7939102824784511, 1.2429290358272087, 1.584460106084565, 1.7990312484289086, 1.8742851276625654], 'positive_zeros': ['1.08808844808888442616464545029827', '1.44916460017560560616018639189708', '2.81115829937462615855121342452581', '3.53725605521994980339182259647367', '4.38823825915169226440286241800758', '4.90307351654083838200647110312088', '5.63250647392578322865911031083666', '6.39266474337588345916140481734150', '7.47953200977075673945869485544763', '7.84090507307028456710160148083384'], 'prelabel': '2-7935-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.959980779115362, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1256892091577714846, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08808844808888442616464545030', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.44916460017560560616018639190', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81115829937462615855121342453', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.361294003886016, 'bad_primes': [3, 5, 23], 'central_character': '1.1', 'conductor': 7935, 'conductor_radical': 345, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, -2, 1, 0, 3, 0, 1, 0, 4, -2, 0, 0, 1, 4, 3, 0, 8, -2, 3, 0, 0, 0, 1, 0, 1, -6, 9, 0, -5, 0, 4, 0, 3, -2, 9, 0, 0, 0, 7, 0, -4, -8, 1, 0, -2, 4, 2, 0, 3, 0, -13, 0, 4, 0, 8, 0, -3, -2, 14, 0, 3, -8, 0, 0, -13, -6, 0, 0, -13, 0, -4, 0, 1, -16, 12, 0, 0, 4, 1, 0, 1, -6, 3, 0, 9, 0, 8, 0, 0, 0, -5, 0, 8, 0, -10, 0, 4, -2], 'euler11': [1, -4, 11], 'euler13': [1, 0, 13], 'euler17': [1, -3, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 2], 'euler23': [1, 0, 0], 'euler29': [1, -9, 29], 'euler3': [1, -1, 0], 'euler31': [1, 5, 31], 'euler37': [1, -9, 37], 'euler41': [1, -7, 41], 'euler43': [1, 4, 43], 'euler47': [1, 2, 47], 'euler5': [1, -1, 0], 'euler53': [1, 13, 53], 'euler59': [1, 3, 59], 'euler61': [1, -14, 61], 'euler67': [1, 13, 67], 'euler7': [1, -3, 7], 'euler71': [1, 13, 71], 'euler73': [1, 4, 73], 'euler79': [1, 0, 79], 'euler83': [1, -1, 83], 'euler89': [1, -8, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 2], [1, -1, 0], [1, -1, 0], [1, -3, 7], [1, -4, 11], [1, 0, 13], [1, -3, 17], [1, -8, 19], [1, 0, 0], [1, -9, 29], [1, 5, 31], [1, -9, 37], [1, -7, 41], [1, 4, 43], [1, 2, 47], [1, 13, 53], [1, 3, 59], [1, -14, 61], [1, 13, 67], [1, 13, 71], [1, 4, 73], [1, 0, 79], [1, -1, 83], [1, -8, 89], [1, 10, 97]], 'index': 206, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7935/i', 'ModularForm/GL2/Q/holomorphic/7935/2/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/7935/2/a/i'], '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': '2-7935-1.1-c1-0-206', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-7935-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.959980779115362, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1256892091577714846, 'z1': {'__RealLiteral__': 0, 'data': '1.08808844808888442616464545030', 'prec': 103}}
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lfunc_instances • Show schema
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id: 22119099
{'Lhash': '1379315974321276971441071211098', 'Lhash_array': ['1379315974321276971441071211098'], 'label': '2-7935-1.1-c1-0-206', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7935/2/a/i'}
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id: 24581795
{'Lhash': '1379315974321276971441071211098', 'Lhash_array': ['1379315974321276971441071211098'], 'label': '2-7935-1.1-c1-0-206', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7935/2/a/i/1/1'}
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id: 23708
{'Lhash': '1256892091577714846', 'Lhash_array': ['1256892091577714846'], 'label': '2-7935-1.1-c1-0-206', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7935/i'}