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lfunc_lfunctions • Show schema
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{'Lhash': '2250152821918995926365957349566', 'a10': [-2.2192169375852875, -0.27400033564683673], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.43431886095114186, 1.6209000557551039], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.346899720108267, -1.7848980766341453], 'a6': [1.186581194803962, -1.186581194803962], 'a7': [-0.6328455666844436, -2.3618118082110615], 'a8': [1.0, 0.0], 'a9': [0.15939209358431433, -0.0920250681376019], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [5, [[1.0, 0], [-1.346899720108267, 1.7848980766341453]]], [37, [[1.0, 0], [-5.952751033740892, 1.2509017268741554]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.103', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': '1390067861385373386257826143914', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 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'6.92664898741843367060212817334215', '7.59148900048829736443579047260953', '8.575509155584551179024433351532613', '9.796334025695685596006800098819043', '10.21325713440623753226378825980033', '11.64259007753022259423602534779203'], 'prelabel': '2-370-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': 0.30582286930847835, 'root_number': '0.5728883177240243 + 0.8196334396639374*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.152911434654', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77505759198463330078897552248', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91118011217007532789242216703', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.99740689577046792175691146950', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '185.103', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/q/d/103/2'], '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': '2-370-185.103-c1-0-12', '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': '2-370-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': 0.15291143465423918, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77505759198463330078897552248', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2250152821918995926365957349566', 'Lhash_array': ['2250152821918995926365957349566'], 'label': '2-370-185.103-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/q/d/103/2'}