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lfunc_lfunctions • Show schema
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{'Lhash': '1127568220768854303605565940114', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-4.724756408574553, 0.0], 'a4': [0.0, 0.0], 'a5': [-4.308491017559558, 4.308491017559558], 'a6': [0.0, 0.0], 'a7': [-7.524039764470431, -7.524039764470431], 'a8': [0.0, 0.0], 'a9': [13.32332312036631, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.667589498694176, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-7.6318141379258675, 10.524039764470432]]]], 'bad_primes': [2, 13], 'central_character': '208.161', 'coefficient_field': 'CDF', 'conductor': 208, 'conductor_radical': 26, 'conjugate': '826576421130771549087203603417', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [4.724756408574553, 0], [9.0, 0]], [[1.0, 0], [4.308491017559558, -4.308491017559558], [0, -25.0]], [[1.0, 0], [7.524039764470431, 7.524039764470431], [0, 49.0]], [[1.0, 0], [-13.557287190604542, 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'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.889494487334164089952446533773', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.65096594340045462682627227246', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.87382175909109043794458198961', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.667589498694176, 'bad_primes': [2, 13], 'central_character': '13.5', 'conductor': 208, 'conductor_radical': 26, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/208/3/t/f/161/1'], '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': '2-208-13.5-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-208-13.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3806699684530352, 'root_angle': 0.053066126007733014, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.889494487334164089952446533773', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1127568220768854303605565940114', 'Lhash_array': ['1127568220768854303605565940114'], 'factors': ['2-208-13.5-c2-0-3'], 'label': '2-208-13.5-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/208/3/t/f/161/1'}