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lfunc_lfunctions • Show schema
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{'Lhash': '2565803025918536464231439950447', 'a10': [-347.676117269262, 0.0], 'a2': [9.273153101288923, 0.0], 'a3': [9.0, 0.0], 'a4': [53.99136843994438, 0.0], 'a5': [-37.492761466532535, 0.0], 'a6': [83.45837791160031, 0.0], 'a7': [154.850391171128, 0.0], 'a8': [203.92932645045755, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.066483567095666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-9.0, 0]]], [23, [[1.0, 0], [529.0, 0]]]], 'bad_primes': [3, 23], 'central_character': '69.1', 'coefficient_field': 'CDF', 'conductor': 69, 'conductor_radical': 69, 'conjugate': '2565803025918536464231439950447', 'degree': 2, 'euler_factors': [[[1.0, 0], [-9.273153101288923, 0], [32.0, 0]], [[1.0, 0], [-9.0, 0]], [[1.0, 0], [37.492761466532535, 0], [3125.0, 0]], [[1.0, 0], [-154.850391171128, 0], [16807.0, 0]], [[1.0, 0], [-521.2893230431707, 0], [161051.0, 0]], [[1.0, 0], [28.851100501744234, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.066483567095666, 'bad_primes': [3, 23], 'central_character': '1.1', 'conductor': 69, 'conductor_radical': 69, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/69/6/a/e/1/4'], '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': '2-69-1.1-c5-0-12', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-69-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.326632466488546, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.02406169764490789053824577434', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2565803025918536464231439950447', 'Lhash_array': ['2565803025918536464231439950447'], 'label': '2-69-1.1-c5-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/69/6/a/e/1/4'}