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lfunc_lfunctions • Show schema
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{'Lhash': '1328309946743757553762744778833', 'a10': [-2.302775637731995, -3.160879749278794e-61], 'a2': [1.1513878188659974, 1.9942622014918188], 'a3': [0.0, 0.0], 'a4': [-1.6513878188659974, 2.8602876052762576], 'a5': [-0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [1.3027756377319946, 2.2564735954147603], 'a8': [-3.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.233941281861857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [3, 5], 'central_character': '405.271', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '3324242674055141679128370364587', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.1513878188659974, -1.9942622014918188], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.3027756377319946, -2.2564735954147603], 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-0.8888888888888888, 'root_number': '-0.9396926207859083 - 0.3420201433256689*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.444444444444', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04785178700235456643805987958', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56383472050128163536341837559', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68591498923956038649469511012', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.233941281861857, 'bad_primes': [3, 5], 'central_character': '9.4', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/2/e/k/271/2'], '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': '2-405-9.4-c1-0-2', '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': '2-405-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': -0.4444444444444444, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04785178700235456643805987958', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1328309946743757553762744778833', 'Lhash_array': ['1328309946743757553762744778833'], 'label': '2-405-9.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/2/e/k/271/2'}