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lfunc_lfunctions • Show schema
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{'Lhash': '2229149208781783493286783128936', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [0.8660254037844386, -0.5], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.8660254037844386, -0.5], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7607013645692327, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-0.8660254037844386, 0.5]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '3528.2419', 'coefficient_field': 'CDF', 'conductor': 3528, 'conductor_radical': 42, 'conjugate': '1903913294753448817483138066608', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], 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'2.72372848457672153679145536314274', '3.17711767920968668380279876334599', '4.37610181681956975406612854119562', '4.83694006765172745712026721794710', '5.43779420884832283705897081469010', '6.80845903876148038916726024043067', '7.21770322760282856111854020336219', '7.86693213849887474889753796690052', '8.898461096579013213885228000290820'], 'prelabel': '2-3528-504.403-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3269142265305744, 'root_angle': 0.18187631611433, 'root_number': '0.84115477925641530262327173010849 + 0.54079445016946248661107852846760*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09093815805716499', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75848866271229996519326139013', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72372848457672153679145536314', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17711767920968668380279876335', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7607013645692327, 'bad_primes': [2, 3, 7], 'central_character': '504.403', 'conductor': 3528, 'conductor_radical': 42, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3528/1/ce/d/2419/2'], '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': '2-3528-504.403-c0-0-9', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3528-504.403-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3269142265305744, 'root_angle': 0.090938158057165, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75848866271229996519326139013', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2229149208781783493286783128936', 'Lhash_array': ['2229149208781783493286783128936'], 'label': '2-3528-504.403-c0-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3528/1/ce/d/2419/2'}