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lfunc_lfunctions • Show schema
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{'Lhash': '2393329132536544004456650098505', 'a10': [249.45540041582538, 231.46078630021074], 'a2': [-0.9105189619701578, 1.890712106515866], 'a3': [23.861923628149945, 1.7882039668565024], 'a4': [37.1575998293405, 46.59415642873543], 'a5': [47.79737220408979, -154.9552748566673], 'a6': [-25.107712821569553, 43.487834268807], 'a7': [360.4080941985264, -208.08171020363923], 'a8': [-252.86755720469424, 57.715369816949405], 'a9': [-154.66394650953947, -23.3118390650619], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.892325595653594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-22129.467813971616, -76365.23884117953]]]], 'bad_primes': [43], 'central_character': '43.3', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '1939422557006218553283766864504', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9105189619701578, -1.890712106515866], [-39.90334731895894, -50.03721487795391]], 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0.015581958226999662*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00248004603991', 'prec': 57}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88800378598459704145438481885', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93122336362543680930777504887', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.55349892682987316795705996186', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.892325595653594, 'bad_primes': [43], 'central_character': '43.3', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/7/h/a/3/9'], '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': '2-43-43.3-c6-0-15', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-43-43.3-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1452067651672113, 'root_angle': -0.0024800460399140804, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.88800378598459704145438481885', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2393329132536544004456650098505', 'Lhash_array': ['2393329132536544004456650098505'], 'label': '2-43-43.3-c6-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/7/h/a/3/9'}