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lfunc_lfunctions • Show schema
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{'Lhash': '2386126959370411788297431757418', 'a10': [38321953.60901647, 1.3412961869027268e-70], 'a2': [71.0487698111873, 123.06007912824222], 'a3': [0, 0], 'a4': [6288.144616633842, -10891.385961350534], 'a5': [134843.83231003644, -233556.36864828086], 'a6': [0, 0], 'a7': [-263672.3872651247, -456693.971296173], 'a8': [6443311.935972668, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38.52724637697854, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '7.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '27.10', 'coefficient_field': 'CDF', 'conductor': 27, 'conductor_radical': 3, 'conjugate': '881784550271684776121114010773', 'degree': 2, 'euler_factors': [[[1.0, 0], [-71.0487698111873, -123.06007912824222], [-16384.0, 28377.920431208484]], [[1.0, 0], [0, 0]], [[1.0, 0], [-134843.83231003644, 233556.36864828086], [-15258789062.5, -26428997918.226276]], [[1.0, 0], [263672.3872651247, 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'prelabel': '2-3e3-9.4-c15-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.207032010307224, 'root_angle': 0.20961463188991114, 'root_number': '0.25103442427577466462648250971135085588785171551884938097 + 0.96797815978901629128844693410517799624953282220560505420*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.20961463188991114', 'prec': 64}, 'spectral_label': 'c15-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88232227314120350077103342782', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.74884848618905091167695173045', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11318073749337559399484443099', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 38.52724637697854, 'bad_primes': [3], 'central_character': '9.4', 'conductor': 27, 'conductor_radical': 3, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/27/16/c/a/10/9'], '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': '2-3e3-9.4-c15-0-12', 'motivic_weight': 15, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [15], 'order_of_vanishing': 0, 'prelabel': '2-3e3-9.4-c15-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.207032010307224, 'root_angle': 0.20961463188991114, 'self_dual': False, 'spectral_label': 'c15-0', 'z1': {'__RealLiteral__': 0, 'data': '1.88232227314120350077103342782', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2386126959370411788297431757418', 'Lhash_array': ['2386126959370411788297431757418'], 'factors': ['2-3e3-9.4-c15-0-12'], 'label': '2-3e3-9.4-c15-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/27/16/c/a/10/9'}