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lfunc_lfunctions • Show schema
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{'Lhash': '1381013655729051838041804408650', 'a10': [-0.05495813208737119, 0.0951902770644083], 'a2': [-0.38541756336001515, -0.2225209339563144], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.9009688679024191, -1.5605238552448022], 'a5': [0.0, -0.24697960371746705], 'a6': [0.38541756336001515, -0.2225209339563144], 'a7': [-1.5181601965329372, 0.8765101981412665], 'a8': [0.0, 1.6920214716300959], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.316', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '1217568359412883293862506523725', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.38541756336001515, 0.2225209339563144], [1.0, 1.7320508075688772]], [[1.0, 0], [0.5, 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'9.879804735010014335325649209805728', '11.15721665176891362752950688406735'], 'prelabel': '2-507-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.10634284185188345, 'root_number': '0.944710445966118 + 0.32790573841044407*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0531714209259', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08942768258099858910050036241', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23334605440969161790327674890', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95282526567200115913145536904', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '13.4', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/j/h/316/3'], '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': '2-507-13.4-c1-0-8', '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': '2-507-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.05317142092594172, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08942768258099858910050036241', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1381013655729051838041804408650', 'Lhash_array': ['1381013655729051838041804408650'], 'label': '2-507-13.4-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/j/h/316/3'}