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lfunc_lfunctions • Show schema
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{'Lhash': '525732631702215874435862617182', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -3.4641016151377544], 'a6': [0, 0], 'a7': [-2.0, 1.7320508075688772], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.19568209498026, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.0, -1.7320508075688772]]]], 'bad_primes': [2, 3, 7], 'central_character': '4032.3583', 'coefficient_field': 'CDF', 'conductor': 4032, 'conductor_radical': 42, 'conjugate': '1174642478203702575409928680383', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-5.0, 0]], [[1.0, 0], [2.0, -1.7320508075688772]], [[1.0, 0], [0, -3.4641016151377544], [-11.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-13.0, 0]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], [2.0, 0], [19.0, 0]], [[1.0, 0], [0, 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'6.27874542988212070303393365280899', '7.04821121628172993232073123278327', '7.19223352513606076732536581837686', '8.438706800639572008712255992784060'], 'prelabel': '2-4032-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': -0.227185525828505, 'root_number': '0.7559289460184544544290330724683601216315026237378429087 - 0.6546536707079771437982924562468583555692080823954245575*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11359276291425252', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41472991974883482330920704373', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.07195135518234775470214142646', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94825323482482435308327660990', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.19568209498026, 'bad_primes': [2, 3, 7], 'central_character': '28.27', 'conductor': 4032, 'conductor_radical': 42, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4032/2/b/b/3583/1'], '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': '2-4032-28.27-c1-0-15', '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': '2-4032-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': -0.1135927629142525, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41472991974883482330920704373', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '525732631702215874435862617182', 'Lhash_array': ['525732631702215874435862617182'], 'label': '2-4032-28.27-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4032/2/b/b/3583/1'}