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lfunc_lfunctions • Show schema
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{'Lhash': '481654921894136719995128902530', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.7320508075688773, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -1.2679491924311228], 'a8': [0, 0], 'a9': [-2.4641016151377544, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.776064323404867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '1600.1249', 'coefficient_field': 'CDF', 'conductor': 1600, 'conductor_radical': 10, 'conjugate': '1416162511768545027347894259759', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7320508075688773, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.2679491924311228], [-7.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-11.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [13.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-17.0, 0]], [[1.0, 0], [0, -2.0], [-19.0, 0]], [[1.0, 0], [0, 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'4.94660877963680126888018262217189', '6.00179148015105020610291146293846', '6.78240567349042639481273147221343', '7.56005340835900278208472656377065', '8.544129746210144621426521497578627', '9.213346771569086706404723342912629'], 'prelabel': '2-40e2-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5743620862197027, 'root_angle': -0.4357497156829001, 'root_number': '0.2004803702726738430713491402645067130815609233997908969 - 0.9796977192661681367853993514228391276150947994632357227*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.21787485784145005', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37995873768956443100235724700', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26450784827701981890912682445', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90645131554751467910927678800', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.776064323404867, 'bad_primes': [2, 5], 'central_character': '40.29', 'conductor': 1600, 'conductor_radical': 10, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1600/2/f/i/1249/1'], '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': '2-40e2-40.29-c1-0-4', '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': '2-40e2-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5743620862197027, 'root_angle': -0.21787485784145005, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37995873768956443100235724700', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '481654921894136719995128902530', 'Lhash_array': ['481654921894136719995128902530'], 'label': '2-40e2-40.29-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1600/2/f/i/1249/1'}