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lfunc_lfunctions • Show schema
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{'Lhash': '251195918322112379177736832068', 'a10': [1.0157530031696416, -1.75933580943049], 'a2': [0.5, -0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, -0.8660254037844386], 'a5': [2.031506006339283, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.1284163748308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2646.361', 'coefficient_field': 'CDF', 'conductor': 2646, 'conductor_radical': 42, 'conjugate': '2070469838393021731878936969432', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.031506006339283, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.0, 0], [11.0, 0]], [[1.0, 0], [2.1213203435596424, -3.6742346141747673], [-6.5, -11.258330249197702]], [[1.0, 0], 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[-33.5, 58.023702053557386]], [[1.0, 0], [-2.127016653792583, 0], [71.0, 0]], [[1.0, 0], [-7.688360255831663, 13.316630589993693], [-36.5, -63.21985447626402]], [[1.0, 0], [2.9364916731037085, -5.0861527738185615], [-39.5, -68.41600689897065]], [[1.0, 0], [4.152826349898926, 7.192906233035747], [-41.5, 71.88010851410841]], [[1.0, 0], [3.5355339059327378, 6.123724356957945], [-44.5, 77.07626093681505]], [[1.0, 0], [8.92294514376404, 15.454994342149297], [-48.5, 84.00446416709055]], [[1.0, 0], [7.867988930272382, 0], [101.0, 0]], [[1.0, 0], [-18.025518961968796, 0], [103.0, 0]], [[1.0, 0], [-7.872983346207417, -13.636407162774878], [-53.5, 92.66471820493493]], [[1.0, 0], [4.563508326896292, -7.904228282948018], [-54.5, -94.39676901250381]], [[1.0, 0], [1.9364916731037085, -3.3541019662496847], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-2646-63.4-c1-0-3', 'leading_term': '0.778704276917802589026977985506790053920457474651518022', 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'8.009285895039084831601900775832563', '8.285105313873410247597283097384214'], 'prelabel': '2-2646-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': -0.5248982233154194, 'root_number': '-0.078140336492527298346139886342682677919850565453259880 - 0.996942369353833113831848668223404828255714820167589171*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2624491116577097', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19815863951540491637027979659', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09118273767723836306348849653', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81535614753016922363766570043', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.1284163748308, 'bad_primes': [2, 3, 7], 'central_character': '63.4', 'conductor': 2646, 'conductor_radical': 42, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2646/2/h/s/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': '2-2646-63.4-c1-0-3', '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': '2-2646-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': -0.2624491116577097, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.19815863951540491637027979659', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '251195918322112379177736832068', 'Lhash_array': ['251195918322112379177736832068'], 'label': '2-2646-63.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2646/2/h/s/361/3'}