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lfunc_lfunctions • Show schema
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{'Lhash': '1415725132049094761812383278123', 'a10': [0.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [1.618033988749895, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [-1.618033988749895, 0.0], 'a7': [3.23606797749979, 0.0], 'a8': [-1.0, 0.0], 'a9': [-0.38196601125010515, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.772324373936879, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 37], 'central_character': '1850.1', 'coefficient_field': 'CDF', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.618033988749895, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.23606797749979, 0], [7.0, 0]], [[1.0, 0], [1.381966011250105, 0], [11.0, 0]], [[1.0, 0], [-2.8541019662496847, 0], [13.0, 0]], [[1.0, 0], [-4.47213595499958, 0], [17.0, 0]], [[1.0, 0], [-4.47213595499958, 0], 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[[1.0, 0], [-6.944271909999159, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-1850-1.1-c1-0-22', 'leading_term': '2.05518222577290909863265332904', '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/1850/2/a/t/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.055182225772909, 2.050574922653544, 2.0366351773618647, 2.013019870227179, 1.9791909138611357, 1.9344630874440276, 1.8780657857019436, 1.8092143829615948, 1.7271867219621015, 1.6314004569070284, 1.5214874613847378, 1.3973621021734317, 1.2592807614635735, 1.1078904941862164, 0.9442651125941945, 0.7699273100350398, 0.586855701901077, 0.39747591160368007, 0.2046350972376421, 0.01155962616570863, -0.17820402434349011, -0.3608646265689352, -0.5324768110709804, 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'5.36115706059252588801950825631277', '5.98503522449555619853665348234279', '7.43754249445562827816109448724539', '7.83845619818879868059911359685194', '8.345416302891367089728665455620692', '9.163989806725291634246632017565516'], 'prelabel': '2-1850-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11681020921238536563500437236', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16233851146825294382014338910', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.12247841847445430566933046554', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.772324373936879, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1850/2/a/t/1/2'], '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': '2-1850-1.1-c1-0-22', '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': '2-1850-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11681020921238536563500437236', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1415725132049094761812383278123', 'Lhash_array': ['1415725132049094761812383278123'], 'label': '2-1850-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/t/1/2'}