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lfunc_lfunctions • Show schema
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{'Lhash': '1097424038543134717125537984004', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.806641746768046, 1.043065098825747], 'a4': [0, 0], 'a5': [-1.9845305813597276, 1.1457692653630833], 'a6': [0, 0], 'a7': [1.7266519576509893, 0], 'a8': [0, 0], 'a9': [0.6759696007767309, -1.1708136929173483], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.7098088857877, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [3.5554062050090973, 2.5217229660259686]]]], 'bad_primes': [2, 19], 'central_character': '1216.1185', 'coefficient_field': 'CDF', 'conductor': 1216, 'conductor_radical': 38, 'conjugate': '706510522748614147387496413414', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.806641746768046, -1.043065098825747], [1.5, -2.598076211353316]], [[1.0, 0], [1.9845305813597276, -1.1457692653630833], [2.5, -4.330127018922194]], [[1.0, 0], [-1.7266519576509893, 0], [7.0, 0]], [[1.0, 0], [0, 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'7.950380823623311917714049966050881', '8.766179632918727170183029272473159', '9.826826863999850893413740085806890'], 'prelabel': '2-1216-152.45-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.11605662429098, 'root_angle': 0.014123954545545124, 'root_number': '0.99901573709883304609754315733776516288339979590454016175 + 0.0443571530745075457220682332268481786308115757889023949*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.007061977272772562', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.865714920456435802549219491760', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.12912607980476620803560387792', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87649306391167744169734925422', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.7098088857877, 'bad_primes': [2, 19], 'central_character': '152.45', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1216/2/t/d/1185/4'], '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': '2-1216-152.45-c1-0-18', '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': '2-1216-152.45-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.11605662429098, 'root_angle': 0.007061977272772562, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.865714920456435802549219491760', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1097424038543134717125537984004', 'Lhash_array': ['1097424038543134717125537984004'], 'label': '2-1216-152.45-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/2/t/d/1185/4'}