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lfunc_lfunctions • Show schema
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{'Lhash': '3891086467807824706157110476030', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -1.0], 'a4': [-0.8660254037844386, -0.5], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5, -0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [7, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [-0.8660254037844386, -0.5]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.215', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '1480018905331736138009334215360', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [0.5, 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['3.06952599328811000904381042251916', '3.93353428475640900203245746300063', '5.25547027501461647727713418139136', '6.04903113434626166223002293017963', '7.980561807734962318510237680934002', '8.609382485427544086735652332057726', '9.650958419204735814008440258435660', '10.12765993759472145699502311956132', '11.60352512859213456000844825589732', '12.22157640284510323689059769177520'], 'prelabel': '2-273-273.215-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': 0.5321366699282929, 'root_number': '-0.10078889899226260502936526010691 + 0.99490783384187275482613836397968*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.26606833496414645', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.06952599328811000904381042252', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93353428475640900203245746300', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.25547027501461647727713418139', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'bad_primes': [3, 7, 13], 'central_character': '273.215', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/1/ch/a/215/1'], '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': '2-273-273.215-c0-0-0', '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': '2-273-273.215-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': 0.26606833496414645, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.06952599328811000904381042252', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3891086467807824706157110476030', 'Lhash_array': ['3891086467807824706157110476030'], 'label': '2-273-273.215-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/1/ch/a/215/1'}