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lfunc_lfunctions • Show schema
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{'Lhash': '650016755170993620390047241541', 'a10': [0.0240055331703113, -3.162186543260408], 'a2': [-1.260073510670101, 0.6420395219202062], 'a3': [0.0, 0.0], 'a4': [1.1755705045849463, -1.618033988749895], 'a5': [-1.0302487364574218, 1.9845874989598937], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.4424634841649486, 2.793604493334841], 'a9': [0.0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.547732965744995, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.260073510670101, -0.6420395219202062]]], [5, [[1.0, 0], [1.0302487364574218, -1.9845874989598937]]], [41, [[1.0, 0], [5.991350558975557, -2.2591410933058773]]]], 'bad_primes': [2, 5, 41], 'central_character': '820.107', 'coefficient_field': 'CDF', 'conductor': 820, 'conductor_radical': 410, 'conjugate': '2008047282468503918873958919865', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.260073510670101, -0.6420395219202062]], [[1.0, 0], [0, 0], [0, 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-34.91892036436906]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-820-820.107-c1-0-34', '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/820/2/bm/b/107/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7439732757955617, 0.5728044953862744, 0.395303427298347, 0.21062205893924757, 0.019727143720136394, -0.17328832047039772, -0.3605174746150734, -0.5302255799292055, -0.667477915752835, -0.7553511552063036, -0.7766526804151195, -0.7160376629339517, -0.5623580143103851, -0.31101127724855465, 0.034002452952245174, 0.4586443153616864, 0.9383484237102121, 1.4387578229376663, 1.9178553537965224, 2.329502827754048, 2.6282050478464063, 2.774700363242424, 2.741776324977958, 2.5195523742656185, 2.11939645240682, 1.5756785477207298, 0.9447292282706905, 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'7.42149079566663528673978495362903', '8.628038496888344254052781668932099', '9.006262811760259636994062239010008', '9.588633940329196941011251956645903'], 'prelabel': '2-820-820.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.558853838292644, 'root_angle': -0.7800579257155896, 'root_number': '-0.7706292277987092 - 0.6372837619635111*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.390028962858', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51277280589301483373833396966', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.73894478823022643574852889811', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43750302314832882994527045876', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.547732965744995, 'bad_primes': [2, 5, 41], 'central_character': '820.107', 'conductor': 820, 'conductor_radical': 410, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/820/2/bm/b/107/1'], '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': '2-820-820.107-c1-0-34', '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': '2-820-820.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.558853838292644, 'root_angle': -0.3900289628577948, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51277280589301483373833396966', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '650016755170993620390047241541', 'Lhash_array': ['650016755170993620390047241541'], 'label': '2-820-820.107-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/820/2/bm/b/107/1'}