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lfunc_lfunctions • Show schema
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{'Lhash': '1451517802641274973356573920560', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-70.63885286567391, 70.63885286567391], 'a4': [0, 0], 'a5': [1004.8959264865707, -2959.0216587464674], 'a6': [0, 0], 'a7': [-2611.7421665784805, -2611.7421665784805], 'a8': [0, 0], 'a9': [0, 49069.304931643346], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.82858021389796, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1004.8959264865707, 2959.0216587464674]]]], 'bad_primes': [2, 5], 'central_character': '80.17', 'coefficient_field': 'CDF', 'conductor': 80, 'conductor_radical': 10, 'conjugate': '634981749128463685789011301458', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [70.63885286567391, -70.63885286567391], [0, -59049.0]], [[1.0, 0], [-1004.8959264865707, 2959.0216587464674]], [[1.0, 0], [2611.7421665784805, 2611.7421665784805], [0, 282475249.0]], [[1.0, 0], [15694.746432983424, 0], 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'2-80-5.2-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.129416540916792, 'root_angle': 0.42800124513509624, 'root_number': '0.2242669488838113 + 0.9745277500606876*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21400062256754812', 'prec': 64}, 'spectral_label': 'c10-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14504564773601013598493108239914', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.67926200792948349869455472441842', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.98142651388087361952430007375033', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 50.82858021389796, 'bad_primes': [2, 5], 'central_character': '5.2', 'conductor': 80, 'conductor_radical': 10, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/80/11/p/d/17/2'], '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': '2-80-5.2-c10-0-22', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'prelabel': '2-80-5.2-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.129416540916792, 'root_angle': 0.21400062256754812, 'self_dual': False, 'spectral_label': 'c10-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14504564773601013598493108239914', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '1451517802641274973356573920560', 'Lhash_array': ['1451517802641274973356573920560'], 'label': '2-80-5.2-c10-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/80/11/p/d/17/2'}