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lfunc_lfunctions • Show schema
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{'Lhash': '1232174232931306468803073770996', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.207928927189314, 0.3536238856195162], 'a6': [0, 0], 'a7': [0, -1.6557265539237704], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.36998814595924, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.207928927189314, -0.3536238856195162]]], [13, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '4680.2809', 'coefficient_field': 'CDF', 'conductor': 4680, 'conductor_radical': 390, 'conjugate': '1179955549542067876713339139833', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.207928927189314, -0.3536238856195162]], [[1.0, 0], [0, 1.6557265539237704], [-7.0, 0]], [[1.0, 0], [-2.948478782684738, 0], [11.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 1.4673790716938901], 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'2.74987326316847345178145792211274', '3.78880324415242888171106329853075', '4.71022832893870307432706222536855', '5.50180073112236378860051855482506', '6.13301564415279927914005732504823', '6.66867562971390741102083084349705', '7.62067797065872935077353098203115', '8.496799465786426347216678813968863'], 'prelabel': '2-4680-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.113099716670687, 'root_angle': 0.050551475063327626, 'root_number': '0.98741583413669798352400716481124676294801063547452911603 + 0.15814540934256971711713763023816017632073170535886985720*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.025275737531663817', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.972014080780196275614306854551', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.98297838439118852706239349516', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.74987326316847345178145792211', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.36998814595924, 'bad_primes': [2, 3, 5, 13], 'central_character': '5.4', 'conductor': 4680, 'conductor_radical': 390, 'degree': 2, 'index': 58, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4680/2/l/g/2809/8'], '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': '2-4680-5.4-c1-0-58', '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': '2-4680-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.113099716670687, 'root_angle': 0.025275737531663813, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.972014080780196275614306854551', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1232174232931306468803073770996', 'Lhash_array': ['1232174232931306468803073770996'], 'label': '2-4680-5.4-c1-0-58', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4680/2/l/g/2809/8'}