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lfunc_lfunctions • Show schema
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{'Lhash': '1217568359412883293862506523725', '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': '507.361', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '1381013655729051838041804408650', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.38541756336001515, -0.2225209339563144], [1.0, -1.7320508075688772]], [[1.0, 0], [0.5, 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'group': 'GL2', 'index': 10, 'label': '2-507-13.10-c1-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/507/2/j/h/361/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0070506955015177, 0.9748416882506405, 0.9232057786100708, 0.8475893548755776, 0.741764342316731, 0.5991657726020168, 0.4142686144857911, 0.18385976329091253, -0.09186703005052632, -0.40844133776983793, -0.7565295657959978, -1.1217086331673185, -1.4846848693242611, -1.8220321106667823, -2.107490558338068, -2.3138161071583805, -2.415103214602458, -2.3894299362788383, -2.2216006034894047, -1.9057004357622787, -1.4471384646982783, -0.8638510262651794, -0.18637584013878386, 0.5434097815922131, 1.2749656316328466, 1.9530965539137835, 2.523025615852855, 2.93608615291904, 3.1554338624399856, 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'9.770488072029371480900139810156454', '10.76264392909579892476641162455545'], 'prelabel': '2-507-13.10-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': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.960492078174909365181795592660', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.78245625435021061829802838446', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.41541194307444616245635208037', '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': '13.10', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/j/h/361/3'], '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': '2-507-13.10-c1-0-10', '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': '2-507-13.10-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': '0.960492078174909365181795592660', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1217568359412883293862506523725', 'Lhash_array': ['1217568359412883293862506523725'], 'label': '2-507-13.10-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/j/h/361/3'}