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lfunc_lfunctions • Show schema
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{'Lhash': '1315138425350208478053907889752', 'a10': [-1.7770288385086555, 1.3572650835811622], 'a2': [0.8660254037844386, 0.5], 'a3': [0.25881904510252074, 0.9659258262890683], 'a4': [0.5, 0.8660254037844386], 'a5': [-0.8603195756154693, 2.0639404613052235], 'a6': [-0.25881904510252074, 0.9659258262890683], 'a7': [0.2598474499097465, 0.45006898546088986], 'a8': [0.0, 1.0], 'a9': [-0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [5, [[1.0, 0], [0.8603195756154693, -2.0639404613052235]]], [13, [[1.0, 0], [3.1448986209496708, 1.7634093863731304]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.7', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '3321268125800675484466735891037', 'degree': 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'2.62106265471268997003509163512885', '4.05425286940499104606651857960038', '5.00494150106440324947210712185950', '6.08435009031708084783507311489679', '7.31934482760910469861535925545023', '8.126070114049493383249732940336200', '9.231744202066045550603715610880073', '10.12413777031959871299630632283258', '11.42795069188445794928133438535109'], 'prelabel': '2-390-65.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.6460382215748208, 'root_number': '-0.4428658934705656 - 0.896587865410032*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.323019110787', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03746128871270151968926580658', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62106265471268997003509163513', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05425286940499104606651857960', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.7', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bd/b/7/3'], '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': '2-390-65.7-c1-0-1', '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': '2-390-65.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.3230191107874104, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03746128871270151968926580658', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1315138425350208478053907889752', 'Lhash_array': ['1315138425350208478053907889752'], 'label': '2-390-65.7-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bd/b/7/3'}