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lfunc_lfunctions • Show schema
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{'Lhash': '265206681019408519693402762032', 'a10': [302923.8329936595, 335523.8577313153], 'a2': [-33.59020361004495, 30.326526695876716], 'a3': [342.7710133470081, 244.24379707387703], 'a4': [208.60355712855383, -2037.3484129999254], 'a5': [0, -9988.741408848706], 'a6': [-18920.814162210663, 2190.855412638723], 'a7': [0, -16807.0], 'a8': [54778.66507791653, 74761.16936138338], 'a9': [57836.93518186956, 167439.38765346765], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.54082716700547, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [33.59020361004495, -30.326526695876716]]], [3, [[1.0, 0], [-342.7710133470081, -244.24379707387703]]], [7, [[1.0, 0], [0, 16807.0]]]], 'bad_primes': [2, 3, 7], 'central_character': '84.71', 'coefficient_field': 'CDF', 'conductor': 84, 'conductor_radical': 42, 'conjugate': '1375258476681950938533870925067', 'degree': 2, 'euler_factors': [[[1.0, 0], [33.59020361004495, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 8.033730588400726, 'root_angle': -0.7704546931113911, 'root_number': '-0.7510549619118725 - 0.6602396869225264*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3852273465556955', 'prec': 64}, 'spectral_label': 'c11-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20921118245963073478939990863541', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.13210774413664490369447825197925', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.60822337422359246124355037822946', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.54082716700547, 'bad_primes': [2, 3, 7], 'central_character': '12.11', 'conductor': 84, 'conductor_radical': 42, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/84/12/e/a/71/30'], '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': '2-84-12.11-c11-0-15', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'prelabel': '2-84-12.11-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.033730588400726, 'root_angle': -0.38522734655569557, 'self_dual': False, 'spectral_label': 'c11-0', 'z1': {'__RealLiteral__': 0, 'data': '0.20921118245963073478939990863541', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '265206681019408519693402762032', 'Lhash_array': ['265206681019408519693402762032'], 'label': '2-84-12.11-c11-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/84/12/e/a/71/30'}