-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3378913249027043515946088410912', 'a10': [0.0, 0.0], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.8660254037844386, -0.5], 'a4': [-4.582907174201562e-80, 2.6459426906140066e-80], 'a5': [0.0, 0.0], 'a6': [-0.8660254037844386, -0.5], 'a7': [0.5, -0.8660254037844386], 'a8': [-1.0, 1.3229713455367871e-80], 'a9': [4.582907174201562e-80, -2.6459426906140066e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2011232000911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0, -1.0]]], [31, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [13, 31], 'central_character': '403.185', 'coefficient_field': 'CDF', 'conductor': 403, 'conductor_radical': 403, 'conjugate': '2036370334805404539195999589538', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, 0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.8660254037844386, -0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-0.8660254037844386, -0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.8660254037844386, -0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, 0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0.8660254037844386, -0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 2.0], [-1.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, -0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.8660254037844386, -0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-403-403.185-c0-0-1', 'leading_term': '0.85068033303021052173913893424667', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/403/1/p/a/185/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [0.8506803330302105, 0.8907277469344929, 0.9483187981807443, 1.0236670639104346, 1.1160813996504055, 1.2242561134798282, 1.346532420845795, 1.4810684419055027, 1.6259185102724218, 1.779050351720315, 1.9383300623701256, 2.101496412975693, 2.266137332602969, 2.4296753464494487, 2.589365144486559, 2.7423045097014778, 2.885458813887493, 3.01569872931568, 3.129850444766783, 3.224757380690162, 3.297352109239224, 3.344736878040992, 3.3642708098496734, 3.3536615127863993, 3.311058502742191, 3.2351455290351603, 3.1252286265029015, 2.981316512290156, 2.80418982359951, 2.595455672180519, 2.3575840886548876, 2.093923158077979, 1.8086900165601734, 1.5069353916007895, 1.1944800247130276, 0.8778221064315247, 0.5640157667634818, 0.26052167762248685, -0.0249680899174603, -0.28472768564354445, -0.5112131854734341, -0.6972909110934441, -0.8364719070844022, -0.9231452746384399, -0.952802407686264, -0.9222437608858373, -0.8297596407823928, -0.6752766856223872, -0.46046221035113477, -0.188779454154451, 0.13451202205783883, 0.5024149970663635, 0.9063146722872928, 1.3361604375676959, 1.780707287678176, 2.227812449047425, 2.6647803428444408, 3.078746651187957, 3.457090073311355, 3.787858465023978, 4.060194552008353, 4.26474539170565, 4.394039313054999, 4.442814253378831, 4.408282279729585, 4.290316643773364, 4.0915499606695604, 3.8173749774789045, 3.475842827030548, 3.077457539005865, 2.6348697623389277, 2.1624769781094857, 1.6759417669941752, 1.191643745155126, 0.7260843986923581, 0.2952670366386881, -0.08592373147708757, -0.4043173574243307, -0.6490017629298328, -0.8117919946273366, -0.8876004898734616, -0.8746896265789281, -0.7747915951625354, -0.5930859080277406, -0.33803085366092395, -0.02105166290194188, 0.3439052001687326, 0.7409356921624429, 1.1528377913328443, 1.5618397526759606, 1.9503655031873224, 2.301802781494284, 2.601238296502075, 2.8361245482020214, 2.996845087359354, 3.0771488689758977, 3.07442986494869, 2.9898350404162986, 2.8281918758057922, 2.5977554664761238, 2.309784427147461, 1.9779639006617842, 1.6177024333017875, 1.245336852291415, 0.8772851194745963, 0.5291910532127996, 0.2151065082293761, -0.053244112683871074, -0.26707533984126475, -0.4209920515801836, -0.5132525933014641, -0.5458250749615597, -0.524229437551325, -0.45716984173499947, -0.3559740981135362, -0.23386854156166903, -0.10512725794130914, 0.015856760553928657, 0.11552471247658906, 0.18207217578951715, 0.20627911585765019, 0.1821957159375237, 0.10763666001968725, -0.015553760084882306, -0.18149091718219307, -0.3805042127791104, -0.5996514559361922, -0.8234719806494136, -1.0349415726823132, -1.216578143168368, -1.3516354023866628, -1.4253133822806912, -1.4259102029828283, -1.345839442900837, -1.1824420740423407, -0.9385311120390594, -0.6226205680519813, -0.24880736381777832, 0.16370528661717174, 0.5914329968345091, 1.0077518249132051, 1.3843032948764393, 1.692590870424024, 1.9056805674240578, 1.9999076461981304, 1.9564860806965165, 1.7629183466167282, 1.4141102418553824, 0.9131088058115681, 0.2714004026636305, -0.4912702355722984, -1.3475719988056172, -2.263733247857699, -3.2011149463975683, -4.118136670883193, -4.972456631522151, -5.723287402318766, -6.333716067521829, -6.772892018160601, -7.0179483212924385, -7.055533594395297, -6.88285028829046, -6.508121337438374, -5.950438917477517, -5.238984782572186, -4.411649247758722, -3.513113046312162, -2.5924906851695257, -1.7006632913480544, -0.8874512794933033, -0.1987908463198516, 0.32591781691354543, 0.6561291449882188, 0.7719928637778801, 0.6655980182229874, 0.3415358306628188, -0.1832629189385203, -0.880416417630098, -1.71166185940231, -2.6310197177344996, -3.5874268056610017, -4.527681815506171, -5.399525620011958, -6.154668239302944, -6.751575921516693, -7.157845365093533, -7.352017044564966, -7.32471443285278, -7.079038491729878, -6.630194414494699, -6.004377145668907, -5.236990378441939, -4.3703172830170045, -3.450797149623935, -2.5260879140377894, -1.6421083053340635, -0.8402540523883125, -0.15497003748686675, 0.3881647550566166, 0.7737185408893263, 0.9969776541797529, 1.0637801413611827, 0.9896366779190777, 0.7982132874252774, 0.5192948426576941, 0.1863842677466835, -0.165882910133236, -0.5043173528573796, -0.7995590799628998, -1.0280922901208644, -1.1737481369940226, -1.2285914824388058, -1.193135159606, -1.075877049947938, -0.8922074222510307, -0.6627825345234651, -0.4115017216553129, -0.16325585765429387, 0.05836726538271588, 0.233231943658262, 0.34648097968952135, 0.3898883726217089, 0.36262520346447413, 0.27137305800453443, 0.1297724583987891, -0.04275154829365006, -0.22269262069921766, -0.3845562769686452, -0.5031699257198897, -0.5560162275689052, -0.5253912790503649, -0.40020036395232117, -0.17723086831212098, 0.13821748463729489, 0.5324136926312176, 0.9839985061431988, 1.4654600800942494, 1.9451756306729424, 2.3898627545450455, 2.767246129640226, 3.0487225625029146, 3.211802010409438, 3.2421151484046877, 3.134808655685192, 2.895195580372101, 2.5385864913483114, 2.0892931366901037, 1.5788647488203362, 1.0436823791526157, 0.5220932362859002, 0.051310036309889784, -0.33567406636423086, -0.6128988942625995, -0.7637384777482763, -0.7824854421422451, -0.6750676704576363, -0.4588140802340699], 'positive_zeros': ['2.66549256429074363496068972055175', '3.48762579600775443326674568583201', '5.32693212338431208144727800978034', '5.98085371872081457354262675499124', '7.50834843972665177469714238890288', '8.216775647198376174303104780644793', '8.640817716924347589576077843595234', '9.675764230718966348357525302388251', '10.50276671636804297753257264728318', '11.97706412431208658778877458540084'], 'prelabel': '2-403-403.185-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.44846761320200146, 'root_angle': 0.29064619097038336, 'root_number': '-0.25262040749347358192731521544581 + 0.96756546533959724442040989300710*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2906461909703833', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.66549256429074363496068972055', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.48762579600775443326674568583', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.32693212338431208144727800978', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.2011232000911, 'bad_primes': [13, 31], 'central_character': '403.185', 'conductor': 403, 'conductor_radical': 403, 'degree': 2, 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/403/1/p/a/185/2', 'ArtinRepresentation/2.403.16t60.a.b'], 'is_instance_Artin': True, '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': '2-403-403.185-c0-0-1', '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': '2-403-403.185-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.44846761320200146, 'root_angle': 0.29064619097038336, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.66549256429074363496068972055', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24603166
{'Lhash': '3378913249027043515946088410912', 'Lhash_array': ['3378913249027043515946088410912'], 'factors': ['2-403-403.185-c0-0-1'], 'label': '2-403-403.185-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.403.16t60.a.b'}
-
id: 19810524
{'Lhash': '3378913249027043515946088410912', 'Lhash_array': ['3378913249027043515946088410912'], 'factors': ['2-403-403.185-c0-0-1'], 'label': '2-403-403.185-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/403/1/p/a/185/2'}