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lfunc_lfunctions • Show schema
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{'Lhash': '16737092008769434709136479341', 'a10': [-2738.095342193591, -4742.520248646991], 'a2': [-10.21992154235009, 17.70142336071804], 'a3': [30.491770748539007, 52.81329614921206], 'a4': [-144.8935926635829, -250.96306418451468], 'a5': [-133.9587261432127, 232.0233197972496], 'a6': [-1246.4940189495765, -3.5003493241285724e-59], 'a7': [0.0, 0.0], 'a8': [3306.9046812025754, 0.0], 'a9': [-765.9961667629179, 1326.7442792363765], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.306866248721972, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]]], 'bad_primes': [7], 'central_character': '49.30', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '4303496252097571532503563924495', 'degree': 2, 'euler_factors': [[[1.0, 0], [10.21992154235009, -17.70142336071804], [-64.0, -110.85125168440814]], [[1.0, 0], [-30.491770748539007, -52.81329614921206], [-1093.5, 1893.9975580765674]], 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['0.01320323755280521912318816233513', '1.49939679535123775563189655974532', '2.48652988545325765918896121454428', '4.33652367399940888884472520201346', '7.41172828300296364631579352713125', '8.293799247004782825243085211270639', '9.272540044940082332469582305997983', '10.65182219876307935276517950989893', '12.00694088391867019795561898243530', '12.83601175339037221209736752854135'], 'prelabel': '2-7e2-7.2-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.912399040067612, 'root_angle': 0.051601452080239404, 'root_number': '0.9478990257184787 + 0.3185709293735992*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0516014520802', 'prec': 50}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.01320323755280521912318816234', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.49939679535123775563189655975', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.48652988545325765918896121454', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.306866248721972, 'bad_primes': [7], 'central_character': '7.2', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/8/c/h/30/2'], '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': '2-7e2-7.2-c7-0-0', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-7e2-7.2-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.912399040067612, 'root_angle': 0.051601452080239404, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.01320323755280521912318816234', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '16737092008769434709136479341', 'Lhash_array': ['16737092008769434709136479341'], 'factors': ['2-7e2-7.2-c7-0-0'], 'label': '2-7e2-7.2-c7-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/8/c/h/30/2'}