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lfunc_lfunctions • Show schema
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{'Lhash': '1099417282374560632586117963184', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.179056282979259, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1, -1]]], 'bad_primes': [2, 5, 7], 'central_character': '1400.1', 'coefficient_field': '1.1.1.1', 'conductor': 1400, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1], [1, -1], [1, 1, 11], [1, -6, 13], [1, 7, 17], [1, -1, 19], [1, -8, 23], [1, 6, 29], [1, -4, 31], [1, -8, 37], [1, 5, 41], [1, 0, 43], [1, -6, 47], [1, -4, 53], [1, 4, 59], [1, -6, 61], [1, 5, 67], [1, -14, 71], [1, -15, 73], [1, -14, 79], [1, -1, 83], [1, 3, 89], [1, 6, 97], [1, 0, 101], [1, -4, 103], [1, -9, 107], [1, 10, 109], [1, -1, 113]], 'euler_factors_factorization': [[1], [[[1, 1, 3], 1]], [1], [[[1, -1], 1]], [[[1, 1, 11], 1]], [[[1, -6, 13], 1]], [[[1, 7, 17], 1]], [[[1, -1, 19], 1]], [[[1, -8, 23], 1]], [[[1, 6, 29], 1]], [[[1, -4, 31], 1]], [[[1, -8, 37], 1]], [[[1, 5, 41], 1]], [[[1, 0, 43], 1]], [[[1, -6, 47], 1]], [[[1, -4, 53], 1]], [[[1, 4, 59], 1]], [[[1, -6, 61], 1]], [[[1, 5, 67], 1]], [[[1, -14, 71], 1]], [[[1, -15, 73], 1]], [[[1, -14, 79], 1]], [[[1, -1, 83], 1]], [[[1, 3, 89], 1]], [[[1, 6, 97], 1]], [[[1, 0, 101], 1]], [[[1, -4, 103], 1]], [[[1, -9, 107], 1]], [[[1, 10, 109], 1]], [[[1, -1, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-1400-1.1-c1-0-5', 'leading_term': '1.325053665352846937476212013339000000000000000000000000000000000000000000000000000000000000', '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/1400/2/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': 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4.8160465369313386, 5.012547631192125, 5.046745463478137, 4.914122273992995, 4.620221532612401, 4.180375331575632, 3.6187906416075117, 2.9670489640470126, 2.2621137135015297, 1.543973605570298, 0.8530760146648183, 0.22771984554855143, -0.29841827081225186, -0.6984581340037496], 'positive_zeros': ['0.867287312589620648077715338683064', '2.34689818796577333300960201246678', '3.52438399205802001718955909069403', '4.61143092669363740989497297698730', '5.43872973785191668777901933330089', '6.25749628912076697704085671911225', '6.93407948236618105259838358209406', '8.119081850079968697907109335927491', '8.733118585358889207850399364953923', '9.404941766502201303772246076860121'], 'prelabel': '2-1400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.343509575727167, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1292913301824818699, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.867287312589620648077715338683', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.34689818796577333300960201247', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52438399205802001718955909069', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.179056282979259, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 1400, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 1, 0, -2, 0, -1, 0, 6, 0, 0, 0, -7, 0, 1, 0, -1, 0, 8, 0, 0, 0, 5, 0, -6, 0, 4, 0, 1, 0, 0, 0, 8, 0, -6, 0, -5, 0, 0, 0, 0, 0, 6, 0, 1, 0, 7, 0, 4, 0, 0, 0, -1, 0, -4, 0, 6, 0, -2, 0, 0, 0, -5, 0, -8, 0, 14, 0, 15, 0, 0, 0, -1, 0, 14, 0, 1, 0, 1, 0, 0, 0, 6, 0, -3, 0, 6, 0, -4, 0, 0, 0, -6, 0, 2, 0], 'euler11': [1, 1, 11], 'euler13': [1, -6, 13], 'euler17': [1, 7, 17], 'euler19': [1, -1, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 3], 'euler31': [1, -4, 31], 'euler37': [1, -8, 37], 'euler41': [1, 5, 41], 'euler43': [1, 0, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 0], 'euler53': [1, -4, 53], 'euler59': [1, 4, 59], 'euler61': [1, -6, 61], 'euler67': [1, 5, 67], 'euler7': [1, -1, 0], 'euler71': [1, -14, 71], 'euler73': [1, -15, 73], 'euler79': [1, -14, 79], 'euler83': [1, -1, 83], 'euler89': [1, 3, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 0, 0], [1, -1, 0], [1, 1, 11], [1, -6, 13], [1, 7, 17], [1, -1, 19], [1, -8, 23], [1, 6, 29], [1, -4, 31], [1, -8, 37], [1, 5, 41], [1, 0, 43], [1, -6, 47], [1, -4, 53], [1, 4, 59], [1, -6, 61], [1, 5, 67], [1, -14, 71], [1, -15, 73], [1, -14, 79], [1, -1, 83], [1, 3, 89], [1, 6, 97]], 'index': 5, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1400/e', 'ModularForm/GL2/Q/holomorphic/1400/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/1400/2/a/e'], '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': '2-1400-1.1-c1-0-5', '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': '2-1400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.343509575727167, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1292913301824818699, 'z1': {'__RealLiteral__': 0, 'data': '0.867287312589620648077715338683', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20618619
{'Lhash': '1099417282374560632586117963184', 'Lhash_array': ['1099417282374560632586117963184'], 'factors': ['2-1400-1.1-c1-0-5'], 'label': '2-1400-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1400/2/a/e'}
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id: 24552964
{'Lhash': '1099417282374560632586117963184', 'Lhash_array': ['1099417282374560632586117963184'], 'factors': ['2-1400-1.1-c1-0-5'], 'label': '2-1400-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1400/2/a/e/1/1'}
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id: 38715
{'Lhash': '1292913301824818699', 'Lhash_array': ['1292913301824818699'], 'factors': ['2-1400-1.1-c1-0-5'], 'label': '2-1400-1.1-c1-0-5', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1400/e'}