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lfunc_lfunctions • Show schema
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{'Lhash': '3205761247173331381803112720859', 'a10': 4, 'a2': -1, 'a3': 1, 'a4': 1, 'a5': -4, 'a6': -1, 'a7': 0, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.3476018194256443, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '294.1', 'coefficient_field': '1.1.1.1', 'conductor': 294, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, 4, 5], [1], [1, 4, 11], [1, 4, 13], [1, 0, 17], [1, 4, 19], [1, 0, 23], [1, -2, 29], [1, 8, 31], [1, 6, 37], [1, 0, 41], [1, -4, 43], [1, -8, 47], [1, 10, 53], [1, 4, 59], [1, -4, 61], [1, -4, 67], [1, -8, 71], [1, -16, 73], [1, 8, 79], [1, -12, 83], [1, 8, 89], [1, 8, 97], [1, 4, 101], [1, -8, 103], [1, -4, 107], [1, 14, 109], [1, 14, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -1], 1]], [[[1, 4, 5], 1]], [1], [[[1, 4, 11], 1]], [[[1, 4, 13], 1]], [[[1, 0, 17], 1]], [[[1, 4, 19], 1]], [[[1, 0, 23], 1]], [[[1, -2, 29], 1]], [[[1, 8, 31], 1]], [[[1, 6, 37], 1]], [[[1, 0, 41], 1]], [[[1, -4, 43], 1]], [[[1, -8, 47], 1]], [[[1, 10, 53], 1]], [[[1, 4, 59], 1]], [[[1, -4, 61], 1]], [[[1, -4, 67], 1]], [[[1, -8, 71], 1]], [[[1, -16, 73], 1]], [[[1, 8, 79], 1]], [[[1, -12, 83], 1]], [[[1, 8, 89], 1]], [[[1, 8, 97], 1]], [[[1, 4, 101], 1]], [[[1, -8, 103], 1]], [[[1, -4, 107], 1]], [[[1, 14, 109], 1]], [[[1, 14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-294-1.1-c1-0-6', '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/294/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-2.7058827403200052e-120, 0.15556732487201053, 0.3160256782228306, 0.4853178498511095, 0.6656624712369519, 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0.11688196987978877, 0.8997970510186925, 1.2496783089983245, 1.1185880024779695, 0.6398456711757878, 0.08561246007576154, -0.2216073782775783, -0.01724461879938013, 0.8103390411505202], 'positive_zeros': ['2.52889971936759396667083662828712', '3.77980943086478052006597909549280', '5.02209723965846660973920127041189', '6.94059953288016050503047892712810', '7.69885140727101440087412366745780', '8.236567804687403362610493554922803', '9.234982336494788048482584951325829', '10.47310858692444357093438177285371', '11.10546510557791154808322951719276'], 'prelabel': '2-294-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.5321885717579427, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1337916839818329096, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.52889971936759396667083662829', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.77980943086478052006597909549', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.02209723965846660973920127041', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.3476018194256443, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 294, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, -4, -1, 0, -1, 1, 4, -4, 1, -4, 0, -4, 1, 0, -1, -4, -4, 0, 4, 0, -1, 11, 4, 1, 0, 2, 4, -8, -1, -4, 0, 0, 1, -6, 4, -4, 4, 0, 0, 4, -4, -4, 0, 8, 1, 0, -11, 0, -4, -10, -1, 16, 0, -4, -2, -4, -4, 4, 8, 0, 1, 16, 4, 4, 0, 0, 0, 8, -1, 16, 6, 11, -4, 0, 4, -8, -4, 1, 0, 12, 0, 0, -4, 2, 4, -8, 4, 0, 0, -8, -8, 16, -1, -8, 0, -4, 11], 'euler11': [1, 4, 11], 'euler13': [1, 4, 13], 'euler17': [1, 0, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 6, 37], 'euler41': [1, 0, 41], 'euler43': [1, -4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 4, 5], 'euler53': [1, 10, 53], 'euler59': [1, 4, 59], 'euler61': [1, -4, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -8, 71], 'euler73': [1, -16, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 8, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 4, 5], [1, 0, 0], [1, 4, 11], [1, 4, 13], [1, 0, 17], [1, 4, 19], [1, 0, 23], [1, -2, 29], [1, 8, 31], [1, 6, 37], [1, 0, 41], [1, -4, 43], [1, -8, 47], [1, 10, 53], [1, 4, 59], [1, -4, 61], [1, -4, 67], [1, -8, 71], [1, -16, 73], [1, 8, 79], [1, -12, 83], [1, 8, 89], [1, 8, 97]], 'index': 6, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/294/c', 'ModularForm/GL2/Q/holomorphic/294/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/294/2/a/c'], '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': '2-294-1.1-c1-0-6', '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': '2-294-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.5321885717579427, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1337916839818329096, 'z1': {'__RealLiteral__': 0, 'data': '2.52889971936759396667083662829', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10198905
{'Lhash': '3205761247173331381803112720859', 'Lhash_array': ['3205761247173331381803112720859'], 'factors': ['2-294-1.1-c1-0-6'], 'label': '2-294-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/294/2/a/c'}
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id: 24548897
{'Lhash': '3205761247173331381803112720859', 'Lhash_array': ['3205761247173331381803112720859'], 'factors': ['2-294-1.1-c1-0-6'], 'label': '2-294-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/294/2/a/c/1/1'}
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id: 103810
{'Lhash': '1337916839818329096', 'Lhash_array': ['1337916839818329096'], 'factors': ['2-294-1.1-c1-0-6'], 'label': '2-294-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/294/c'}