-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '518016654759549863646041957005', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '3200.193', 'coefficient_field': 'CDF', 'conductor': 3200, 'conductor_radical': 10, 'conjugate': '2344928867911957850520368893641', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, -1.0], [0, -1.0]], [[1.0, 0], [1.0, -1.0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [2.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.0, 1.0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, -2.0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-1.0, -1.0], [0, 1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-1.0, -1.0], [0, 1.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-3200-40.13-c0-0-2', 'leading_term': '0.73571648863682245473294936786609', '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/3200/1/m/a/193/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.7357164886368225, 0.6541941147520677, 0.5745956147996553, 0.49441431513711787, 0.4111316347510331, 0.32240950968695575, 0.2262386994049441, 0.12103618870511654, 0.00569767320268569, -0.12038305540931458, -0.2573159027264488, -0.40472834860555906, -0.5617857747321174, -0.727215505923025, -0.8993338080243003, -1.076076230411621, -1.2550322094994701, -1.433484971894849, -1.608457650023285, -1.776766254342209, -1.9350798001172194, -2.0799875029507735, -2.208072560471519, -2.3159916442690833, -2.400558848699627, -2.458832492241863, -2.4882028526773436, -2.486478649339316, -2.451969873694727, -2.383564422892109, -2.280795918201399, -2.143900098931561, -1.973857278302361, -1.7724185347187704, -1.5421135913837096, -1.2862387078520212, -1.0088233645952283, -0.7145750583018878, -0.408802130563848, -0.09731521161223129, 0.21369144340383678, 0.5177767355108658, 0.8084049233255772, 1.0791098705432647, 1.323667343031385, 1.5362708172686355, 1.7117058253262076, 1.8455175535214774, 1.9341662529499764, 1.9751650274502992, 1.9671947508532734, 1.9101912379922197, 1.8054003542815755, 1.6553974915313283, 1.4640687509820127, 1.2365522392347494, 0.9791390728570435, 0.6991349705542157, 0.4046846497294037, 0.10456259403596357, -0.1920649263894331, -0.4759004685861322, -0.7377914515974425, -0.9690134806249949, -1.161552134213437, -1.308373957703718, -1.4036772720210737, -1.4431135925488752, -1.4239709716923286, -1.345311432590912, -1.2080558397889667, -1.0150110322292225, -0.7708357886447866, -0.4819441570124997, -0.1563467987345828, 0.19656679444258174, 0.5663001337308956, 0.9415683907838722, 1.3106546582988796, 1.6617928346536397, 1.9835647112598265, 2.2652977860785755, 2.4974497188478395, 2.6719652294717795, 2.7825916506004575, 2.8251402898273716, 2.797682227012871, 2.700669137766033, 2.536972143749447, 2.3118344726350766, 2.032736775163696, 1.7091771878855873, 1.3523715293540304, 0.9748822480322744, 0.5901877715598901, 0.21220661041721553, -0.14520717758669274, -0.4687788619565931, -0.7463189117257932, -0.9672002044877654, -1.122787358636612, -1.2068002033954863, -1.2155953937183286, -1.148352884979386, -1.007157324714834, -0.7969682847953912, -0.5254775098083313, -0.20285583645053695, 0.15860303173333085, 0.5449303157338361, 0.9410058692669001, 1.3311385894772079, 1.6996814252658952, 2.0316568090471794, 2.3133672076303413, 2.532965379535067, 2.680959881374148, 2.750633382850652, 2.738354380355947, 2.6437668492655684, 2.4698471073437926, 2.2228224993258725, 1.9119522456704863, 1.5491766912992617, 1.1486469916345237, 0.7261527268605379, 0.2984697904435841, -0.11734507868324646, -0.504683763917047, -0.8481090976784688, -1.1340384413015052, -1.3513578307463943, -1.4919383048162314, -1.5510296626816245, -1.527511731983566, -1.4239890870485805, -1.2467218055591662, -1.0053920142111257, -0.7127133395660876, -0.3838976200056014, -0.03600001394727339, 0.31283036579777707, 0.6441622497075672, 0.9401208278484003, 1.1842155434814785, 1.3621190762986337, 1.4623609262327768, 1.4769021360467027, 1.4015624486888179, 1.236277405786888, 0.9851703046989688, 0.6564322269002851, 0.262012162401272, -0.18287181983086342, -0.6603807872440952, -1.1508350834020917, -1.6335921574389238, -2.087982548345861, -2.4942609531856026, -2.8345277512443663, -3.0935769025839863, -3.259628815361947, -3.324911504587641, -3.286059966333546, -3.144311889967036, -2.9054872651008674, -2.5797496776669573, -2.1811576477438366, -1.7270247289289449, -1.237116749679431, -0.7327230374182083, -0.23564527962768508, 0.23284753329504118, 0.6530471552686801, 1.007766193290555, 1.2831818872032907, 1.4695201753709313, 1.5615439366900696, 1.558818527947999, 1.4657384934041127, 1.2913110988339471, 1.0487045592117472, 0.7545808754774388, 0.42824445338548955, 0.0906475540718598, -0.23669841341170247, -0.5328511516535532, -0.7785477870236341, -0.9572397486454036, -1.0559977086422518, -1.0662379310962862, -0.9842298575769927, -0.8113554769417014, -0.5541034725830294, -0.223794695734217, 0.1639505087489055, 0.5899789224977724, 1.032568170288537, 1.4685397501206592, 1.8744649843337866, 2.227901715134347, 2.508596969776484, 2.6995916078224576, 2.7881671582419507, 2.7665824988025136, 2.632558388173157, 2.3894806330783553, 2.0463072193328165, 1.617180308628794, 1.1207597838873937, 0.5793101683606587, 0.017586418566094913, -0.5384244673282217, -1.062840535579693, -1.5312300271146104, -1.9218925690788675, -2.217006881078758, -2.403581785526087, -2.474157167446607, -2.427214445216233, -2.2672714326246903, -2.004653392182871, -1.6549496939791257, -1.2381828426345398, -0.7777327530033618, -0.29907312987389895, 0.17161217261448497, 0.6088575303950619, 0.9893100657927403, 1.2930127137255831, 1.504503612637152, 1.6136690712227373, 1.6163004842733468, 1.5143216570973876, 1.315671186429566, 1.033843840947622, 0.6871142109357301, 0.29748415838620945, -0.11058825818045222, -0.5116076370071065, -0.8805279067464348, -1.1942220991135548, -1.4328505223281396, -1.581047517658893, -1.628856511860812, -1.5723567799758693, -1.4139424784742016, -1.1622341595717285, -0.831624034739309, -0.4414775202078633, -0.015033839174384984, 0.42193351678225166, 0.8426209325985226, 1.2207773574566099, 1.53227382217757, 1.7565677045778167, 1.8779746726503137], 'positive_zeros': ['0.40864308719317885893019546827959', '1.99630123309310964539548613851534', '3.01384498110321250829265305199424', '3.78070882516106446624104476266456', '4.85389042418997605937052989960679', '5.46263949197854850011078557800706', '6.43461904558354509306971422289502', '7.11457656648307350791939560277057', '7.74922393383044929538967402886911', '8.708610726679551382837449125380241'], 'prelabel': '2-3200-40.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': -0.6762081911747834, 'root_number': '-0.52573111211913360602566908484825 - 0.85065080835203993218154049706283*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3381040955873917', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40864308719317885893019546828', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.99630123309310964539548613852', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01384498110321250829265305199', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'bad_primes': [2, 5], 'central_character': '40.13', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'index': 2, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/1/m/a/193/1', 'ArtinRepresentation/2.3200.8t17.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': '2-3200-40.13-c0-0-2', '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': '2-3200-40.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': -0.3381040955873917, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40864308719317885893019546828', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24601480
{'Lhash': '518016654759549863646041957005', 'Lhash_array': ['518016654759549863646041957005'], 'label': '2-3200-40.13-c0-0-2', 'type': 'Artin', 'url': 'ArtinRepresentation/2.3200.8t17.a.b'}
-
id: 19913654
{'Lhash': '518016654759549863646041957005', 'Lhash_array': ['518016654759549863646041957005'], 'label': '2-3200-40.13-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/1/m/a/193/1'}