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lfunc_lfunctions • Show schema
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{'Lhash': '1312443311107289952496720235959', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.0, 0], 'a6': [0, 0], 'a7': [0, -1.446492442036953], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.11613287362019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [0.9998117901077787, -4.690455882359569]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '8280.1241', 'coefficient_field': 'CDF', 'conductor': 8280, 'conductor_radical': 690, 'conjugate': '236304401506030114089452228524', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 1.446492442036953], [-7.0, 0]], [[1.0, 0], [1.3613673325590805, 0], [11.0, 0]], [[1.0, 0], [1.075585819268115, 0], [13.0, 0]], [[1.0, 0], [0.32462292843283247, 0], [17.0, 0]], [[1.0, 0], [0, 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'2.34649660295967480829790560721575', '2.80212910098265346420976093074888', '3.91683530805089434064500675522934', '4.47890512410066951261852674021794', '5.38024008857241655184097961073854', '5.88178367104836020417910971312365', '6.83505647773143220448330233034045', '7.31004079056284749861661440888405', '8.190412126891768674426645102395281'], 'prelabel': '2-8280-69.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.7627633218094466, 'root_number': '-0.734883795930789323993519341763512370001340582141699846 + 0.678193045141539322030288408587815632474567673831837821*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3813816609047233', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03533521845135876971233883743', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34649660295967480829790560722', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80212910098265346420976093075', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 66.11613287362019, 'bad_primes': [2, 3, 5, 23], 'central_character': '69.68', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'index': 72, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8280/2/p/a/1241/18'], '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': '2-8280-69.68-c1-0-72', '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': '2-8280-69.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.3813816609047233, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03533521845135876971233883743', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1312443311107289952496720235959', 'Lhash_array': ['1312443311107289952496720235959'], 'label': '2-8280-69.68-c1-0-72', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/p/a/1241/18'}