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lfunc_lfunctions • Show schema
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{'Lhash': '3451197577958015070876261933361', 'a10': 0, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': 1, 'a7': -4, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [19, [1, -1]]], 'bad_primes': [2, 3, 19], 'central_character': '114.1', 'coefficient_field': '1.1.1.1', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, 0, 5], [1, 4, 7], [1, 0, 11], [1, 4, 13], [1, -6, 17], [1, -1], [1, 6, 23], [1, -6, 29], [1, -2, 31], [1, 4, 37], [1, -6, 41], [1, 4, 43], [1, -6, 47], [1, -6, 53], [1, 12, 59], [1, -14, 61], [1, -8, 67], [1, 0, 71], [1, -14, 73], [1, 10, 79], [1, 12, 83], [1, 6, 89], [1, 10, 97], [1, 0, 101], [1, 10, 103], [1, -12, 107], [1, 16, 109], [1, 18, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1], 1]], [[[1, 0, 5], 1]], [[[1, 4, 7], 1]], [[[1, 0, 11], 1]], [[[1, 4, 13], 1]], [[[1, -6, 17], 1]], [[[1, -1], 1]], [[[1, 6, 23], 1]], [[[1, -6, 29], 1]], [[[1, -2, 31], 1]], [[[1, 4, 37], 1]], [[[1, -6, 41], 1]], [[[1, 4, 43], 1]], [[[1, -6, 47], 1]], [[[1, -6, 53], 1]], [[[1, 12, 59], 1]], [[[1, -14, 61], 1]], [[[1, -8, 67], 1]], [[[1, 0, 71], 1]], [[[1, -14, 73], 1]], [[[1, 10, 79], 1]], [[[1, 12, 83], 1]], [[[1, 6, 89], 1]], [[[1, 10, 97], 1]], [[[1, 0, 101], 1]], [[[1, 10, 103], 1]], [[[1, -12, 107], 1]], [[[1, 16, 109], 1]], [[[1, 18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-114-1.1-c1-0-2', '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/114/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5744353565575322, 1.5846769548768653, 1.6145238257246606, 1.6614605975667276, 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-2.40288906283984, -1.6985956360426033, -0.8739076099974374, -0.11026965835468298, 0.43944749929324484, 0.6881661787039451, 0.6337763493950722, 0.3554474486972121, -0.011813273477242136, -0.3175567951845959], 'positive_zeros': ['2.72251484544452322835217288407985', '3.89674503164637365373404147868612', '5.61719283222003359694793802525626', '6.84732233829542762166868447521870', '7.973335490421157373200340268575066', '9.659160529040683538070775225453843', '10.14217150491024881359990946724127', '12.03323217483777155326327378475295', '12.53921727142600454148846778560071', '13.70443556114571377556292054916466'], 'prelabel': '2-114-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1277823241558919606, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.72251484544452322835217288408', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.89674503164637365373404147869', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.61719283222003359694793802526', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, -4, 1, 1, 0, 0, 1, -4, -4, 0, 1, 6, 1, 1, 0, -4, 0, -6, 1, -5, -4, 1, -4, 6, 0, 2, 1, 0, 6, 0, 1, -4, 1, -4, 0, 6, -4, -4, 0, 0, -6, 6, 1, 9, -5, 6, -4, 6, 1, 0, -4, 1, 6, -12, 0, 14, 2, -4, 1, 0, 0, 8, 6, -6, 0, 0, 1, 14, -4, -5, 1, 0, -4, -10, 0, 1, 6, -12, -4, 0, -4, 6, 0, -6, 0, 16, -6, 2, 6, 0, 1, -10, 9, 0, -5], 'euler11': [1, 0, 11], 'euler13': [1, 4, 13], 'euler17': [1, -6, 17], 'euler19': [1, -1, 0], 'euler2': [1, -1, 0], 'euler23': [1, 6, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -2, 31], 'euler37': [1, 4, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 5], 'euler53': [1, -6, 53], 'euler59': [1, 12, 59], 'euler61': [1, -14, 61], 'euler67': [1, -8, 67], 'euler7': [1, 4, 7], 'euler71': [1, 0, 71], 'euler73': [1, -14, 73], 'euler79': [1, 10, 79], 'euler83': [1, 12, 83], 'euler89': [1, 6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 0, 5], [1, 4, 7], [1, 0, 11], [1, 4, 13], [1, -6, 17], [1, -1, 0], [1, 6, 23], [1, -6, 29], [1, -2, 31], [1, 4, 37], [1, -6, 41], [1, 4, 43], [1, -6, 47], [1, -6, 53], [1, 12, 59], [1, -14, 61], [1, -8, 67], [1, 0, 71], [1, -14, 73], [1, 10, 79], [1, 12, 83], [1, 6, 89], [1, 10, 97]], 'index': 2, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/114/c', 'ModularForm/GL2/Q/holomorphic/114/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/114/2/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': '2-114-1.1-c1-0-2', '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': '2-114-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1277823241558919606, 'z1': {'__RealLiteral__': 0, 'data': '2.72251484544452322835217288408', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9969068
{'Lhash': '3451197577958015070876261933361', 'Lhash_array': ['3451197577958015070876261933361'], 'label': '2-114-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/a/c'}
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id: 24546875
{'Lhash': '3451197577958015070876261933361', 'Lhash_array': ['3451197577958015070876261933361'], 'label': '2-114-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/a/c/1/1'}
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id: 22067
{'Lhash': '1277823241558919606', 'Lhash_array': ['1277823241558919606'], 'label': '2-114-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/114/c'}