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lfunc_lfunctions • Show schema
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{'Lhash': '295587910169362223008797415696', 'a10': [-654722.746215848, 0], 'a2': [-39.191835884530846, -22.627416997969522], 'a3': [0, 0], 'a4': [1024.0, 1773.6200269505302], 'a5': [12529.1925876762, -7233.732713223518], 'a6': [0, 0], 'a7': [-48617.54290962262, 84208.05445862641], 'a8': [0, -92681.90002368316], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 148.06699839875827, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '6.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [39.191835884530846, 22.627416997969522]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.107', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1829960225089308919759557260247', 'degree': 2, 'euler_factors': [[[1.0, 0], [39.191835884530846, 22.627416997969522]], [[1.0, 0], [0, 0]], [[1.0, 0], [-12529.1925876762, 7233.732713223518], [122070312.5, -211431983.3458102]], [[1.0, 0], [48617.54290962262, -84208.05445862641], 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'c12-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.23317774638859020419994233908', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.14926742678328889574990515537', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.50942246125231692004158020395', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 148.06699839875827, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/13/d/c/107/2'], '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': '2-162-9.2-c12-0-9', 'motivic_weight': 12, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [12], 'order_of_vanishing': 0, 'prelabel': '2-162-9.2-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.16827836625865, 'root_angle': -0.3888888888888889, 'self_dual': False, 'spectral_label': 'c12-0', 'z1': {'__RealLiteral__': 0, 'data': '0.23317774638859020419994233908', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '295587910169362223008797415696', 'Lhash_array': ['295587910169362223008797415696'], 'label': '2-162-9.2-c12-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/13/d/c/107/2'}