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lfunc_lfunctions • Show schema
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{'Lhash': '351181853238967482565669958834', 'a10': [-1.3537629792402261, -1.7796982317344217], 'a2': [-0.25881904510252074, 0.9659258262890683], 'a3': [0.0, 0.0], 'a4': [-0.8660254037844386, -0.5], 'a5': [-1.368676843451166, 1.768254421230314], 'a6': [0.0, 0.0], 'a7': [-2.561878186441203, -0.6864531911638296], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1559608545745714, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.25881904510252074, -0.9659258262890683]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.368676843451166, -1.768254421230314]]]], 'bad_primes': [2, 3, 5], 'central_character': '270.233', 'coefficient_field': 'CDF', 'conductor': 270, 'conductor_radical': 30, 'conjugate': '3553570120912203628236794626814', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.25881904510252074, -0.9659258262890683]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'7.82348914314882094992906969200747', '8.692102687829408181352324275765931', '9.411983300583221759056561928182958', '10.68761343698990942571194785610168', '11.26901122104197943662724011268135'], 'prelabel': '2-270-45.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4683190574853175, 'root_angle': 0.9282806187444029, 'root_number': '-0.9747242088717035 + 0.2234115409718839*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.464140309372', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27703363464328440497450702590', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55328551077403687300516082791', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84120360089513925311071488096', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1559608545745714, 'bad_primes': [2, 3, 5], 'central_character': '45.23', 'conductor': 270, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/270/2/m/b/233/1'], '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': '2-270-45.23-c1-0-0', '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': '2-270-45.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4683190574853175, 'root_angle': 0.46414030937220146, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.27703363464328440497450702590', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '351181853238967482565669958834', 'Lhash_array': ['351181853238967482565669958834'], 'label': '2-270-45.23-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/270/2/m/b/233/1'}