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lfunc_lfunctions • Show schema
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{'Lhash': '1213448928619097515133350123347', 'a10': [-1.008305652725687, -0.09721213586853254], 'a2': [0.13999052999805425, 0.43084654953545004], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [1.4520025879924279, -1.054941630950345], 'a5': [-0.8918785576321787, 2.05050058240322], 'a6': [-0.3664999656380178, -0.26627781154852337], 'a7': [1.0, 0.0], 'a8': [1.3907845047838983, 1.0104640900163775], 'a9': [0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.192146106117222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]], [5, [[1.0, 0], [0.8918785576321787, -2.05050058240322]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.106', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': '2207757350178486370771684216918', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.957242420269928204560380259700', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.48993433067969466378883561724', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85265043370401468201090784919', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.192146106117222, 'bad_primes': [3, 5, 7], 'central_character': '25.6', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/2/n/c/106/4'], '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': '2-525-25.6-c1-0-6', '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': '2-525-25.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0474731026602577, 'root_angle': -0.2294058643036516, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.957242420269928204560380259700', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1213448928619097515133350123347', 'Lhash_array': ['1213448928619097515133350123347'], 'label': '2-525-25.6-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/2/n/c/106/4'}