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lfunc_lfunctions • Show schema
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{'Lhash': '3469541751692430070299591573202', 'a10': [-1.4233396472651387, 1.724559146136528], 'a2': [0.0, -1.0], 'a3': [1.13990478581479, 0.6581243349407118], 'a4': [-1.0, 0.0], 'a5': [-1.724559146136528, -1.4233396472651387], 'a6': [0.6581243349407118, -1.13990478581479], 'a7': [-3.465261560592412, 2.0006696948204916], 'a8': [0.0, 1.0], 'a9': [-0.6337447195176917, -1.0976780532331296], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.433567286915058, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [1.724559146136528, 1.4233396472651387]]], [43, [[1.0, 0], [-0.07438804506879719, 6.5570165791120925]]]], 'bad_primes': [2, 5, 43], 'central_character': '430.49', 'coefficient_field': 'CDF', 'conductor': 430, 'conductor_radical': 430, 'conjugate': '131235200403051929460818092015', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [-1.13990478581479, -0.6581243349407118], [1.5, 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12.070754537394578], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-430-215.49-c1-0-21', '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/430/2/j/a/49/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.18935253014394365, 0.4247023208497162, 0.6738527482471608, 0.9422855097604428, 1.2328785501080295, 1.5450665730014257, 1.874412345975378, 2.212529851294126, 2.5473046291007906, 2.863393470665938, 3.1430137198238324, 3.3670355440337145, 3.516369826418828, 3.573607299526623, 3.524819354363934, 3.3613851265639494, 3.0816700347340684, 2.692354700249983, 2.2092063728867695, 1.6571027238548708, 1.0691632185307716, 0.4849163866237782, -0.05247135357189052, -0.49976564911426313, -0.8177740602364181, -0.9756271146113727, -0.9547778607131031, 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'8.579619009731374777029165714283327', '9.958417217202214540556941026651439', '10.47019389770147007386301733765934', '11.71489953659753999118676087717316'], 'prelabel': '2-430-215.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8529887444113249, 'root_angle': -0.8738125537264204, 'root_number': '-0.9224455172631206 - 0.38612726876144576*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.436906276863', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.73698584694218535339866465185', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.59708227941249503273224801157', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.96759421645839883818236669320', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.433567286915058, 'bad_primes': [2, 5, 43], 'central_character': '215.49', 'conductor': 430, 'conductor_radical': 430, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/430/2/j/a/49/8'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-430-215.49-c1-0-21', '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': '2-430-215.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8529887444113249, 'root_angle': -0.4369062768632102, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.73698584694218535339866465185', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3469541751692430070299591573202', 'Lhash_array': ['3469541751692430070299591573202'], 'label': '2-430-215.49-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/430/2/j/a/49/8'}