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lfunc_lfunctions • Show schema
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{'Lhash': '1722388300303132752410513122640', 'a10': [0, 0], 'a2': [0, 0], 'a3': [5.522949432546196, 0], 'a4': [0, 0], 'a5': [0, -2.23606797749979], 'a6': [0, 0], 'a7': [0, 3.7820337469633207], 'a8': [0, 0], 'a9': [21.50297043446235, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.136368642294634, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 2.23606797749979]]], [23, [[1.0, 0], [-13.195673548562947, 18.838104989614962]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.321', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'conjugate': '1195919204455620556755342300791', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-5.522949432546196, 0], [9.0, 0]], [[1.0, 0], [0, 2.23606797749979]], [[1.0, 0], [0, -3.7820337469633207], [-49.0, 0]], [[1.0, 0], [0, 2.9761623708631344], [-121.0, 0]], [[1.0, 0], [0.3838647814145041, 0], [169.0, 0]], 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0.3560110709692123], 'positive_zeros': ['1.35872479371920922527173219394870', '2.26347371842522641187664818929748', '3.30490051261860158498225737902179', '3.79934079444435066777260830588097', '4.76024246290362915829028181665287', '6.15881049255274779542918390117343', '7.10020575604916173223651453320007', '7.74057989296443135628542133026949', '8.215566444668180843057428851054963', '9.174110309876906000671724552886670'], 'prelabel': '2-1840-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.080703965164385, 'root_angle': 0.19450215313482422, 'root_number': '0.81904804302673752705363006015446749857187873983377011101 + 0.57372493689404116102782134730509940352173454613127701236*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09725107656741212', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35872479371920922527173219395', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26347371842522641187664818930', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30490051261860158498225737902', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 50.136368642294634, 'bad_primes': [2, 5, 23], 'central_character': '23.22', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 77, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/3/k/e/321/48'], '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': '2-1840-23.22-c2-0-77', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1840-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.080703965164385, 'root_angle': 0.09725107656741211, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35872479371920922527173219395', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1722388300303132752410513122640', 'Lhash_array': ['1722388300303132752410513122640'], 'label': '2-1840-23.22-c2-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/3/k/e/321/48'}