Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(719,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.719");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.bq (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 719.16 | ||
Character | \(\chi\) | \(=\) | 1120.719 |
Dual form | 1120.2.bq.b.1039.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.653375 | − | 1.13168i | −0.377226 | − | 0.653375i | 0.613431 | − | 0.789748i | \(-0.289789\pi\) |
−0.990658 | + | 0.136373i | \(0.956455\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.67181 | − | 1.48495i | −0.747654 | − | 0.664088i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.03631 | + | 2.43435i | 0.391687 | + | 0.920099i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.646203 | − | 1.11926i | 0.215401 | − | 0.373085i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.168671 | − | 0.292146i | −0.0508561 | − | 0.0880853i | 0.839477 | − | 0.543396i | \(-0.182862\pi\) |
−0.890333 | + | 0.455310i | \(0.849528\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.29865i | − | 0.360182i | −0.983650 | − | 0.180091i | \(-0.942361\pi\) | ||
0.983650 | − | 0.180091i | \(-0.0576391\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.588166 | + | 2.86217i | −0.151864 | + | 0.739010i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.41832 | − | 5.92071i | −0.829065 | − | 1.43598i | −0.898773 | − | 0.438415i | \(-0.855540\pi\) |
0.0697076 | − | 0.997567i | \(-0.477793\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.551990 | + | 0.318691i | 0.126635 | + | 0.0731128i | 0.561979 | − | 0.827151i | \(-0.310040\pi\) |
−0.435344 | + | 0.900264i | \(0.643373\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.07781 | − | 2.76331i | 0.453415 | − | 0.603003i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.51602 | + | 2.62582i | −0.316111 | + | 0.547521i | −0.979673 | − | 0.200601i | \(-0.935711\pi\) |
0.663562 | + | 0.748121i | \(0.269044\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.589869 | + | 4.96508i | 0.117974 | + | 0.993017i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.60910 | −1.07947 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.90687i | − | 1.09688i | −0.836191 | − | 0.548439i | \(-0.815222\pi\) | ||
0.836191 | − | 0.548439i | \(-0.184778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.08115 | + | 1.87261i | 0.194181 | + | 0.336331i | 0.946632 | − | 0.322318i | \(-0.104462\pi\) |
−0.752451 | + | 0.658648i | \(0.771129\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.220410 | + | 0.381762i | −0.0383685 | + | 0.0664562i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.88238 | − | 5.60862i | 0.318180 | − | 0.948030i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.30421 | + | 7.45510i | −0.707607 | + | 1.22561i | 0.258135 | + | 0.966109i | \(0.416892\pi\) |
−0.965742 | + | 0.259503i | \(0.916441\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.46966 | + | 0.848507i | −0.235334 | + | 0.135870i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.28231i | − | 0.824959i | −0.910967 | − | 0.412479i | \(-0.864663\pi\) | ||
0.910967 | − | 0.412479i | \(-0.135337\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.6010i | − | 1.61664i | −0.588744 | − | 0.808320i | \(-0.700377\pi\) | ||
0.588744 | − | 0.808320i | \(-0.299623\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.74236 | + | 0.911602i | −0.408807 | + | 0.135894i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.78384 | − | 4.49400i | −1.13539 | − | 0.655517i | −0.190105 | − | 0.981764i | \(-0.560883\pi\) |
−0.945285 | + | 0.326247i | \(0.894216\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.85214 | + | 5.04547i | −0.693163 | + | 0.720781i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.46689 | + | 7.73688i | −0.625490 | + | 1.08338i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.63168 | + | 6.29026i | 0.498850 | + | 0.864034i | 0.999999 | − | 0.00132737i | \(-0.000422515\pi\) |
−0.501149 | + | 0.865361i | \(0.667089\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.151837 | + | 0.738878i | −0.0204737 | + | 0.0996303i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.832900i | − | 0.110320i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.50354 | + | 4.33217i | −0.976877 | + | 0.564000i | −0.901326 | − | 0.433142i | \(-0.857405\pi\) |
−0.0755513 | + | 0.997142i | \(0.524072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.97207 | + | 6.87982i | −0.508571 | + | 0.880871i | 0.491380 | + | 0.870945i | \(0.336493\pi\) |
−0.999951 | + | 0.00992531i | \(0.996841\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.39433 | + | 0.413194i | 0.427645 | + | 0.0520575i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.92843 | + | 2.17110i | −0.239192 | + | 0.269291i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9447 | + | 6.31895i | −1.33711 | + | 0.771983i | −0.986378 | − | 0.164492i | \(-0.947401\pi\) |
−0.350735 | + | 0.936475i | \(0.614068\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.96211 | 0.476981 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.53507i | 0.419536i | 0.977751 | + | 0.209768i | \(0.0672708\pi\) | ||||
−0.977751 | + | 0.209768i | \(0.932729\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.93618 | − | 10.2818i | −0.694777 | − | 1.20339i | −0.970256 | − | 0.242082i | \(-0.922170\pi\) |
0.275479 | − | 0.961307i | \(-0.411164\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.23347 | − | 3.91160i | 0.604309 | − | 0.451673i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.536392 | − | 0.713356i | 0.0611275 | − | 0.0812945i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.96466 | − | 5.17575i | −1.00860 | − | 0.582317i | −0.0978208 | − | 0.995204i | \(-0.531187\pi\) |
−0.910782 | + | 0.412887i | \(0.864521\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.72624 | + | 2.98993i | 0.191804 | + | 0.332214i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.76821 | 0.413615 | 0.206807 | − | 0.978382i | \(-0.433693\pi\) | ||||
0.206807 | + | 0.978382i | \(0.433693\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.07716 | + | 14.9743i | −0.333765 | + | 1.62419i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.68467 | + | 3.85940i | −0.716672 | + | 0.413771i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.43915 | − | 3.71765i | −0.682549 | − | 0.394070i | 0.118266 | − | 0.992982i | \(-0.462266\pi\) |
−0.800815 | + | 0.598912i | \(0.795600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.16138 | − | 1.34580i | 0.331403 | − | 0.141078i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.41279 | − | 2.44703i | 0.146500 | − | 0.253745i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.449580 | − | 1.35247i | −0.0461259 | − | 0.138760i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.03558 | 0.612820 | 0.306410 | − | 0.951900i | \(-0.400872\pi\) | ||||
0.306410 | + | 0.951900i | \(0.400872\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.435982 | −0.0438178 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.757059 | − | 1.31127i | −0.0753302 | − | 0.130476i | 0.825900 | − | 0.563817i | \(-0.190668\pi\) |
−0.901230 | + | 0.433341i | \(0.857334\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.60049 | + | 3.81079i | 0.650366 | + | 0.375489i | 0.788596 | − | 0.614911i | \(-0.210808\pi\) |
−0.138231 | + | 0.990400i | \(0.544142\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.57706 | + | 1.53428i | −0.739445 | + | 0.149731i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.68270 | − | 0.971509i | −0.162673 | − | 0.0939193i | 0.416453 | − | 0.909157i | \(-0.363273\pi\) |
−0.579126 | + | 0.815238i | \(0.696606\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.32933 | + | 0.767488i | −0.127326 | + | 0.0735120i | −0.562310 | − | 0.826926i | \(-0.690087\pi\) |
0.434984 | + | 0.900438i | \(0.356754\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.2490 | 1.06771 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.74556i | 0.634569i | 0.948330 | + | 0.317285i | \(0.102771\pi\) | ||||
−0.948330 | + | 0.317285i | \(0.897229\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.43368 | − | 2.13865i | 0.599944 | − | 0.199430i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.45353 | − | 0.839193i | −0.134378 | − | 0.0775834i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.8707 | − | 14.4571i | 0.996512 | − | 1.32528i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.44310 | − | 9.42773i | 0.494827 | − | 0.857066i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.97788 | + | 3.45133i | −0.539007 | + | 0.311196i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.38674 | − | 9.17658i | 0.571247 | − | 0.820778i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.49296 | 0.398686 | 0.199343 | − | 0.979930i | \(-0.436119\pi\) | ||||
0.199343 | + | 0.979930i | \(0.436119\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.9969 | + | 6.92644i | −1.05627 | + | 0.609839i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.26159 | + | 2.46043i | 0.372336 | + | 0.214969i | 0.674479 | − | 0.738294i | \(-0.264368\pi\) |
−0.302142 | + | 0.953263i | \(0.597702\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.203777 | + | 1.67400i | −0.0176697 | + | 0.145154i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.37732 | + | 8.32921i | 0.807072 | + | 0.716864i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.2291 | − | 8.21516i | 1.21567 | − | 0.701868i | 0.251682 | − | 0.967810i | \(-0.419016\pi\) |
0.963989 | + | 0.265942i | \(0.0856829\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.85042i | − | 0.835502i | −0.908562 | − | 0.417751i | \(-0.862818\pi\) | ||
0.908562 | − | 0.417751i | \(-0.137182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.7451i | 0.989113i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.379396 | + | 0.219044i | −0.0317267 | + | 0.0183174i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.77138 | + | 9.87513i | −0.728423 | + | 0.820085i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.88011 | + | 2.19448i | 0.732419 | + | 0.180998i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.5917 | − | 7.26981i | −1.03155 | − | 0.595566i | −0.114122 | − | 0.993467i | \(-0.536405\pi\) |
−0.917428 | + | 0.397901i | \(0.869739\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.58039 | + | 3.79919i | −0.535504 | + | 0.309174i | −0.743255 | − | 0.669008i | \(-0.766719\pi\) |
0.207751 | + | 0.978182i | \(0.433386\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.83572 | −0.714326 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.973249 | − | 4.73609i | 0.0781732 | − | 0.380412i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.6636 | − | 9.04339i | 1.25009 | − | 0.721741i | 0.278964 | − | 0.960302i | \(-0.410009\pi\) |
0.971128 | + | 0.238561i | \(0.0766756\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.74570 | − | 8.21979i | 0.376358 | − | 0.651872i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.96322 | − | 0.969367i | −0.627589 | − | 0.0763968i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.40416 | + | 3.69745i | 0.501613 | + | 0.289606i | 0.729379 | − | 0.684109i | \(-0.239809\pi\) |
−0.227766 | + | 0.973716i | \(0.573142\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.935378 | − | 0.310934i | 0.0728191 | − | 0.0242062i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 18.7215i | − | 1.44872i | −0.689424 | − | 0.724358i | \(-0.742136\pi\) | ||
0.689424 | − | 0.724358i | \(-0.257864\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.3135 | 0.870269 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.713395 | − | 0.411879i | 0.0545547 | − | 0.0314971i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.41281 | − | 4.85714i | −0.639614 | − | 0.369281i | 0.144852 | − | 0.989453i | \(-0.453729\pi\) |
−0.784466 | + | 0.620172i | \(0.787063\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.4755 | + | 6.58129i | −0.867465 | + | 0.497499i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.80524 | + | 5.66106i | 0.737007 | + | 0.425511i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.19445 | − | 2.06885i | −0.0892775 | − | 0.154633i | 0.817928 | − | 0.575320i | \(-0.195122\pi\) |
−0.907206 | + | 0.420687i | \(0.861789\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.87158 | 0.733749 | 0.366874 | − | 0.930270i | \(-0.380428\pi\) | ||||
0.366874 | + | 0.930270i | \(0.380428\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.3810 | 0.767385 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.2662 | − | 6.07197i | 1.34296 | − | 0.446420i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.15314 | + | 1.99730i | −0.0843260 | + | 0.146057i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.81274 | − | 13.6545i | −0.422815 | − | 0.993220i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.1524 | − | 6.43881i | −0.806956 | − | 0.465896i | 0.0389418 | − | 0.999241i | \(-0.487601\pi\) |
−0.845898 | + | 0.533345i | \(0.820935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.28850 | − | 2.47597i | 0.308693 | − | 0.178224i | −0.337649 | − | 0.941272i | \(-0.609632\pi\) |
0.646341 | + | 0.763048i | \(0.276298\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.71697 | + | 0.763823i | 0.266178 | + | 0.0546985i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.56633 | 0.467831 | 0.233916 | − | 0.972257i | \(-0.424846\pi\) | ||||
0.233916 | + | 0.972257i | \(0.424846\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8184 | − | 23.9342i | −0.979560 | − | 1.69665i | −0.663983 | − | 0.747748i | \(-0.731135\pi\) |
−0.315577 | − | 0.948900i | \(-0.602198\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.3020 | + | 8.25729i | 1.00879 | + | 0.582424i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.3794 | − | 6.12132i | 1.00924 | − | 0.429632i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.84395 | + | 8.83100i | −0.547845 | + | 0.616784i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.95931 | + | 3.39362i | 0.136181 | + | 0.235873i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 0.215015i | − | 0.0148729i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2713 | 1.12016 | 0.560080 | − | 0.828439i | \(-0.310770\pi\) | ||||
0.560080 | + | 0.828439i | \(0.310770\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.00056 | − | 2.30973i | 0.274114 | − | 0.158260i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.7419 | + | 17.7228i | −1.07359 | + | 1.20869i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.43819 | + | 4.57250i | −0.233399 | + | 0.310401i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.75709 | + | 13.4357i | −0.524176 | + | 0.907899i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.68895 | + | 4.43921i | −0.517214 | + | 0.298614i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.78444i | − | 0.119495i | −0.998214 | − | 0.0597475i | \(-0.980970\pi\) | ||
0.998214 | − | 0.0597475i | \(-0.0190296\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.93838 | + | 2.54824i | 0.395892 | + | 0.169882i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.5973 | + | 18.3551i | 0.703368 | + | 1.21827i | 0.967277 | + | 0.253722i | \(0.0816547\pi\) |
−0.263909 | + | 0.964548i | \(0.585012\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.07746 | − | 7.06236i | 0.269446 | − | 0.466694i | −0.699273 | − | 0.714855i | \(-0.746493\pi\) |
0.968719 | + | 0.248161i | \(0.0798261\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.15775 | − | 0.140934i | −0.0761746 | − | 0.00927279i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.4709 | + | 13.5509i | 1.53763 | + | 0.887750i | 0.998977 | + | 0.0452221i | \(0.0143995\pi\) |
0.538652 | + | 0.842528i | \(0.318934\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.33971 | + | 19.0717i | 0.413557 | + | 1.24410i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.5268i | 0.878661i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.6789i | 1.20824i | 0.796894 | + | 0.604119i | \(0.206475\pi\) | ||||
−0.796894 | + | 0.604119i | \(0.793525\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.4676 | + | 10.0849i | −1.12518 | + | 0.649625i | −0.942719 | − | 0.333587i | \(-0.891741\pi\) |
−0.182465 | + | 0.983212i | \(0.558408\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.15789 | + | 10.6658i | −0.395029 | + | 0.684210i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.6041 | − | 1.22987i | 0.996908 | − | 0.0785736i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.413870 | − | 0.716843i | 0.0263339 | − | 0.0456116i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.46205 | − | 4.26440i | −0.156026 | − | 0.270245i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 21.5319i | − | 1.35908i | −0.733637 | − | 0.679542i | \(-0.762179\pi\) | ||
0.733637 | − | 0.679542i | \(-0.237821\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.02283 | 0.0643047 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.9566 | − | 6.30147i | 1.18711 | − | 0.394613i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.89663 | − | 8.48121i | 0.305443 | − | 0.529043i | −0.671917 | − | 0.740627i | \(-0.734529\pi\) |
0.977360 | + | 0.211583i | \(0.0678620\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.6088 | − | 2.75219i | −1.40484 | − | 0.171013i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.61130 | − | 3.81703i | −0.409229 | − | 0.236268i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.74263 | − | 15.1427i | −0.539094 | − | 0.933737i | −0.998953 | − | 0.0457458i | \(-0.985434\pi\) |
0.459860 | − | 0.887992i | \(-0.347900\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.26923 | − | 15.9089i | 0.200827 | − | 0.977279i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.71606i | 0.594613i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.86300 | − | 17.0832i | −0.601358 | − | 1.04158i | −0.992616 | − | 0.121301i | \(-0.961293\pi\) |
0.391258 | − | 0.920281i | \(-0.372040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.58340 | + | 4.47458i | −0.156930 | + | 0.271811i | −0.933760 | − | 0.357899i | \(-0.883493\pi\) |
0.776830 | + | 0.629710i | \(0.216826\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.58858 | − | 2.69835i | −0.217191 | − | 0.163312i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.35104 | − | 1.00979i | 0.0814705 | − | 0.0608927i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.49971 | − | 12.9899i | −0.450614 | − | 0.780486i | 0.547810 | − | 0.836603i | \(-0.315462\pi\) |
−0.998424 | + | 0.0561162i | \(0.982128\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.79457 | 0.167307 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.7107 | 1.41446 | 0.707232 | − | 0.706981i | \(-0.249944\pi\) | ||||
0.707232 | + | 0.706981i | \(0.249944\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.91985 | + | 10.2535i | 0.351899 | + | 0.609506i | 0.986582 | − | 0.163266i | \(-0.0522028\pi\) |
−0.634683 | + | 0.772772i | \(0.718869\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.23681 | + | 1.39245i | −0.0732624 | + | 0.0824814i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.8590 | − | 5.47409i | 0.759043 | − | 0.323125i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8699 | + | 25.7553i | −0.874697 | + | 1.51502i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.94349 | − | 6.83033i | −0.231172 | − | 0.400401i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5.93168i | − | 0.346533i | −0.984875 | − | 0.173266i | \(-0.944568\pi\) | ||
0.984875 | − | 0.173266i | \(-0.0554321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.9775 | + | 3.89980i | 1.10491 | + | 0.227055i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.946090 | + | 1.63868i | 0.0548977 | + | 0.0950856i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.41002 | + | 1.96878i | 0.197207 | + | 0.113857i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.8066 | − | 10.9859i | 1.48747 | − | 0.633216i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.989287 | + | 1.71350i | −0.0568331 | + | 0.0984377i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.8567 | − | 5.60342i | 0.965211 | − | 0.320851i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.83855 | −0.504443 | −0.252221 | − | 0.967670i | \(-0.581161\pi\) | ||||
−0.252221 | + | 0.967670i | \(0.581161\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 9.95951i | − | 0.566577i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.3386 | + | 19.6391i | 0.642955 | + | 1.11363i | 0.984770 | + | 0.173864i | \(0.0556253\pi\) |
−0.341814 | + | 0.939768i | \(0.611041\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.2270 | + | 17.7137i | −0.578064 | + | 1.00124i | 0.417637 | + | 0.908614i | \(0.362858\pi\) |
−0.995701 | + | 0.0926229i | \(0.970475\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.06109 | − | 5.73117i | −0.285160 | − | 0.322915i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.04378 | − | 1.80788i | 0.0586245 | − | 0.101541i | −0.835224 | − | 0.549910i | \(-0.814662\pi\) |
0.893848 | + | 0.448370i | \(0.147995\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.72567 | + | 0.996314i | −0.0966188 | + | 0.0557829i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.53904i | 0.141715i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.35756i | − | 0.242461i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.44792 | − | 0.766035i | 0.357666 | − | 0.0424920i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.73710 | + | 1.00291i | 0.0960617 | + | 0.0554613i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.87354 | − | 23.6058i | 0.158424 | − | 1.30143i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.62025 | − | 11.4666i | 0.363882 | − | 0.630262i | −0.624714 | − | 0.780854i | \(-0.714784\pi\) |
0.988596 | + | 0.150591i | \(0.0481178\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.56278 | + | 9.63502i | 0.304839 | + | 0.527996i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.6808 | + | 5.68830i | 1.51236 | + | 0.310785i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0464i | 0.710681i | 0.934737 | + | 0.355341i | \(0.115635\pi\) | ||||
−0.934737 | + | 0.355341i | \(0.884365\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.63381 | − | 4.40738i | 0.414612 | − | 0.239376i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.364717 | − | 0.631708i | 0.0197505 | − | 0.0342089i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.3107 | − | 6.58317i | −0.934692 | − | 0.355458i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.62387 | − | 5.88351i | −0.356617 | − | 0.316758i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.2014 | − | 12.8180i | 1.19184 | − | 0.688107i | 0.233113 | − | 0.972450i | \(-0.425109\pi\) |
0.958723 | + | 0.284343i | \(0.0917754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.9774 | 1.33701 | 0.668505 | − | 0.743708i | \(-0.266935\pi\) | ||||
0.668505 | + | 0.743708i | \(0.266935\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.28427i | 0.388806i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.78385 | + | 8.28587i | 0.254619 | + | 0.441012i | 0.964792 | − | 0.263015i | \(-0.0847168\pi\) |
−0.710173 | + | 0.704027i | \(0.751383\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.24939 | − | 5.90995i | 0.278609 | − | 0.313668i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −23.4634 | − | 2.85621i | −1.24181 | − | 0.151167i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.0899 | − | 9.86683i | −0.901968 | − | 0.520752i | −0.0241299 | − | 0.999709i | \(-0.507682\pi\) |
−0.877838 | + | 0.478957i | \(0.841015\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.29687 | − | 16.1027i | −0.489309 | − | 0.847508i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.2255 | −0.746647 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.34373 | + | 26.0040i | −0.279703 | + | 1.36111i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.78783 | + | 5.07365i | −0.458721 | + | 0.264843i | −0.711506 | − | 0.702680i | \(-0.751987\pi\) |
0.252785 | + | 0.967522i | \(0.418653\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.91226 | − | 3.41345i | −0.307780 | − | 0.177697i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.5492 | + | 15.3594i | −0.599603 | + | 0.797422i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.28187 | − | 16.0767i | 0.480597 | − | 0.832419i | −0.519155 | − | 0.854680i | \(-0.673753\pi\) |
0.999752 | + | 0.0222614i | \(0.00708662\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.5579 | − | 1.23199i | −0.751765 | − | 0.0636195i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.67097 | −0.395075 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.9371 | −1.22956 | −0.614782 | − | 0.788697i | \(-0.710756\pi\) | ||||
−0.614782 | + | 0.788697i | \(0.710756\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.93559 | − | 5.08459i | −0.150395 | − | 0.260491i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.1286 | + | 11.0439i | 0.977428 | + | 0.564318i | 0.901493 | − | 0.432794i | \(-0.142472\pi\) |
0.0759355 | + | 0.997113i | \(0.475806\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.95604 | + | 0.396080i | −0.0996889 | + | 0.0201861i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.8653 | − | 6.85041i | −0.603145 | − | 0.348226i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.69778 | + | 1.55757i | −0.136783 | + | 0.0789717i | −0.566830 | − | 0.823835i | \(-0.691830\pi\) |
0.430047 | + | 0.902807i | \(0.358497\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.7289 | 1.04831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.43032i | − | 0.324367i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.30146 | + | 21.9649i | 0.367376 | + | 1.10517i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.1570 | + | 12.2150i | 1.06184 | + | 0.613054i | 0.925941 | − | 0.377668i | \(-0.123274\pi\) |
0.135900 | + | 0.990723i | \(0.456607\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.02757 | − | 0.863139i | 0.101506 | − | 0.0432110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.5658 | + | 21.7647i | −0.627508 | + | 1.08688i | 0.360542 | + | 0.932743i | \(0.382592\pi\) |
−0.988050 | + | 0.154133i | \(0.950742\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.43187 | − | 1.40404i | 0.121140 | − | 0.0699402i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.55395 | − | 7.56194i | 0.0772165 | − | 0.375756i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.90397 | 0.143945 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.63575 | − | 5.56320i | 0.476457 | − | 0.275083i | −0.242482 | − | 0.970156i | \(-0.577961\pi\) |
0.718939 | + | 0.695073i | \(0.244628\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.5938 | − | 10.7352i | −0.917166 | − | 0.529526i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.3220 | − | 13.7768i | −0.901566 | − | 0.677912i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.29971 | − | 5.59559i | −0.309241 | − | 0.274677i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.1475 | + | 6.43602i | −0.545896 | + | 0.315173i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.05377i | 0.198040i | 0.995085 | + | 0.0990198i | \(0.0315707\pi\) | ||||
−0.995085 | + | 0.0990198i | \(0.968429\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.4223i | 1.09279i | 0.837526 | + | 0.546397i | \(0.184001\pi\) | ||||
−0.837526 | + | 0.546397i | \(0.815999\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.0599 | + | 5.80807i | −0.489128 | + | 0.282398i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 27.3805 | − | 20.4647i | 1.32815 | − | 0.992684i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.8642 | − | 2.53981i | −1.00969 | − | 0.122910i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.495776 | + | 0.286236i | 0.0239363 | + | 0.0138196i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.0817 | + | 8.13005i | −0.678289 | + | 0.391611i | −0.799210 | − | 0.601052i | \(-0.794749\pi\) |
0.120921 | + | 0.992662i | \(0.461415\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.53783 | 0.121960 | 0.0609801 | − | 0.998139i | \(-0.480577\pi\) | ||||
0.0609801 | + | 0.998139i | \(0.480577\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.9065 | + | 3.47422i | 0.810603 | + | 0.166576i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.67365 | + | 0.966283i | −0.0800616 | + | 0.0462236i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.3888 | − | 19.7261i | 0.543560 | − | 0.941473i | −0.455136 | − | 0.890422i | \(-0.650409\pi\) |
0.998696 | − | 0.0510514i | \(-0.0162572\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.51170 | + | 8.69118i | 0.119605 | + | 0.413866i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.64896 | − | 0.952029i | −0.0783446 | − | 0.0452323i | 0.460316 | − | 0.887755i | \(-0.347736\pi\) |
−0.538661 | + | 0.842523i | \(0.681069\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.24451 | + | 15.7770i | 0.248613 | + | 0.747900i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.9996i | 0.898652i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.8903 | −1.08026 | −0.540130 | − | 0.841582i | \(-0.681625\pi\) | ||||
−0.540130 | + | 0.841582i | \(0.681625\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.54321 | + | 0.890970i | −0.0726667 | + | 0.0419542i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.59892 | + | 4.96459i | 0.404012 | + | 0.233257i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.28365 | − | 2.44456i | −0.341463 | − | 0.114603i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.0413 | − | 18.4990i | −1.49883 | − | 0.865349i | −0.498829 | − | 0.866701i | \(-0.666236\pi\) |
−0.999999 | + | 0.00135206i | \(0.999570\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.1737 | + | 33.2098i | 0.894952 | + | 1.55010i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.04683 | −0.328204 | −0.164102 | − | 0.986443i | \(-0.552473\pi\) | ||||
−0.164102 | + | 0.986443i | \(0.552473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.8182 | −1.71109 | −0.855543 | − | 0.517731i | \(-0.826777\pi\) | ||||
−0.855543 | + | 0.517731i | \(0.826777\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.99563 | + | 1.99304i | −0.278041 | + | 0.0924249i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.6516 | − | 23.6452i | 0.631719 | − | 1.09417i | −0.355481 | − | 0.934683i | \(-0.615683\pi\) |
0.987200 | − | 0.159486i | \(-0.0509837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.7247 | − | 20.0950i | −1.23403 | − | 0.927901i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.4684 | − | 11.8174i | −0.943134 | − | 0.544519i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.09704 | + | 1.78808i | −0.142402 | + | 0.0822160i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.25673 | + | 2.92866i | −0.0576626 | + | 0.134376i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.38722 | 0.429811 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.50010 | − | 14.7226i | −0.388379 | − | 0.672693i | 0.603852 | − | 0.797096i | \(-0.293632\pi\) |
−0.992232 | + | 0.124403i | \(0.960298\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.68159 | + | 5.58967i | 0.441443 | + | 0.254867i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.10595 | + | 9.64516i | 0.186827 | + | 0.438870i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.0903 | − | 8.96251i | −0.458177 | − | 0.406966i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.8165 | + | 34.3232i | 0.897973 | + | 1.55533i | 0.830082 | + | 0.557642i | \(0.188294\pi\) |
0.0678912 | + | 0.997693i | \(0.478373\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 9.66327i | − | 0.436988i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.8252 | 1.93267 | 0.966337 | − | 0.257280i | \(-0.0828263\pi\) | ||||
0.966337 | + | 0.257280i | \(0.0828263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.9728 | + | 20.1916i | −1.57510 | + | 0.909383i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.728876 | + | 0.647409i | 0.0327606 | + | 0.0290989i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.60561 | + | 3.66342i | −0.386014 | + | 0.164327i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.363871 | − | 0.630243i | 0.0162891 | − | 0.0282136i | −0.857766 | − | 0.514040i | \(-0.828148\pi\) |
0.874055 | + | 0.485827i | \(0.161481\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.1868 | + | 12.2322i | −0.946555 | + | 0.546494i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.71017i | 0.210016i | 0.994471 | + | 0.105008i | \(0.0334868\pi\) | ||||
−0.994471 | + | 0.105008i | \(0.966513\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.681503 | + | 3.31637i | −0.0303265 | + | 0.147577i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.39196 | − | 12.8032i | −0.328288 | − | 0.568612i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.9005 | + | 29.2726i | −0.749103 | + | 1.29749i | 0.199150 | + | 0.979969i | \(0.436182\pi\) |
−0.948253 | + | 0.317516i | \(0.897151\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.8777 | − | 25.1058i | 0.835101 | − | 1.11061i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.09617 | − | 1.78757i | −0.136699 | − | 0.0789232i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.37591 | − | 16.1723i | −0.236891 | − | 0.712636i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.03202i | 0.133348i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.6941i | 0.557210i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.19800 | + | 0.691667i | −0.0524855 | + | 0.0303025i | −0.526013 | − | 0.850476i | \(-0.676314\pi\) |
0.473528 | + | 0.880779i | \(0.342980\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.5809 | + | 18.3267i | −0.462671 | + | 0.801370i | −0.999093 | − | 0.0425801i | \(-0.986442\pi\) |
0.536422 | + | 0.843950i | \(0.319776\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.9457 | + | 8.68650i | 0.652284 | + | 0.379110i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.39145 | − | 12.8024i | 0.321977 | − | 0.557680i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.90339 | + | 11.9570i | 0.300147 | + | 0.519871i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.1978i | 0.485945i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.85989 | −0.297135 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.37051 | + | 4.12290i | 0.0592525 | + | 0.178248i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.56085 | + | 2.70347i | −0.0673556 | + | 0.116663i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.29243 | + | 0.566512i | 0.0987418 | + | 0.0244014i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.03605 | + | 1.17551i | 0.0875366 | + | 0.0505393i | 0.543129 | − | 0.839649i | \(-0.317239\pi\) |
−0.455593 | + | 0.890188i | \(0.650573\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.44984 | − | 11.1715i | −0.276789 | − | 0.479413i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.36206 | + | 0.690890i | 0.144015 | + | 0.0295945i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 37.9822i | − | 1.62400i | −0.583656 | − | 0.812001i | \(-0.698378\pi\) | ||
0.583656 | − | 0.812001i | \(-0.301622\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.13352 | + | 8.89152i | 0.219093 | + | 0.379481i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.88247 | − | 3.26053i | 0.0801958 | − | 0.138903i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.30947 | − | 27.1868i | 0.140733 | − | 1.15610i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.8062 | − | 16.7042i | −0.798279 | − | 0.709055i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.5827 | − | 21.7938i | −0.533144 | − | 0.923433i | −0.999251 | − | 0.0387043i | \(-0.987677\pi\) |
0.466106 | − | 0.884729i | \(-0.345656\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.7670 | −0.582284 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.01373 | 0.127240 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.7306 | − | 39.3705i | −0.957980 | − | 1.65927i | −0.727396 | − | 0.686218i | \(-0.759269\pi\) |
−0.230585 | − | 0.973052i | \(-0.574064\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0168 | − | 11.2773i | 0.421410 | − | 0.474438i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.48963 | + | 7.30074i | −0.230543 | + | 0.306602i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.41670 | + | 9.38201i | −0.227080 | + | 0.393314i | −0.956941 | − | 0.290281i | \(-0.906251\pi\) |
0.729861 | + | 0.683595i | \(0.239585\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.714547 | − | 1.23763i | −0.0299029 | − | 0.0517933i | 0.850687 | − | 0.525673i | \(-0.176186\pi\) |
−0.880590 | + | 0.473880i | \(0.842853\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.8278i | 0.702993i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.9316 | − | 5.97826i | −0.580990 | − | 0.249311i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.32076 | + | 12.6799i | 0.304767 | + | 0.527872i | 0.977209 | − | 0.212277i | \(-0.0680880\pi\) |
−0.672442 | + | 0.740149i | \(0.734755\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.60399 | − | 3.23547i | −0.232894 | − | 0.134461i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.90502 | + | 9.17314i | 0.162007 | + | 0.380566i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.22512 | − | 2.12196i | 0.0507391 | − | 0.0878827i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.18385 | + | 3.56138i | 0.0489464 | + | 0.147245i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.7299 | 0.855616 | 0.427808 | − | 0.903870i | \(-0.359286\pi\) | ||||
0.427808 | + | 0.903870i | \(0.359286\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.37821i | 0.0567884i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.29027 | − | 7.43097i | −0.176478 | − | 0.305669i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.830997 | + | 1.43933i | −0.0341249 | + | 0.0591061i | −0.882583 | − | 0.470156i | \(-0.844198\pi\) |
0.848459 | + | 0.529262i | \(0.177531\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −39.6416 | + | 8.02706i | −1.62515 | + | 0.329077i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.0572 | + | 31.2760i | −0.739031 | + | 1.28004i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.9015 | − | 18.4183i | 1.30346 | − | 0.752553i | 0.322464 | − | 0.946582i | \(-0.395489\pi\) |
0.980996 | + | 0.194029i | \(0.0621555\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 36.8443i | − | 1.50291i | −0.659785 | − | 0.751455i | \(-0.729353\pi\) | ||
0.659785 | − | 0.751455i | \(-0.270647\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.3333i | 0.665143i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.0995 | + | 7.67861i | −0.939127 | + | 0.312180i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.7562 | − | 9.67418i | −0.680112 | − | 0.392663i | 0.119785 | − | 0.992800i | \(-0.461779\pi\) |
−0.799897 | + | 0.600137i | \(0.795113\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.3225 | − | 12.2733i | −0.661421 | − | 0.497340i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.83615 | + | 10.1085i | −0.236105 | + | 0.408946i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.61363 | + | 11.4551i | 0.267122 | + | 0.462669i | 0.968117 | − | 0.250497i | \(-0.0805940\pi\) |
−0.700995 | + | 0.713166i | \(0.747261\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.1189 | + | 3.10688i | 0.609652 | + | 0.125281i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.0831i | − | 0.486448i | −0.969970 | − | 0.243224i | \(-0.921795\pi\) | ||
0.969970 | − | 0.243224i | \(-0.0782049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.4861 | − | 6.05415i | 0.421472 | − | 0.243337i | −0.274235 | − | 0.961663i | \(-0.588425\pi\) |
0.695707 | + | 0.718326i | \(0.255091\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.50348 | − | 14.7285i | 0.341233 | − | 0.591033i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.37713 | − | 19.5278i | 0.0952376 | − | 0.782364i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.3041 | + | 5.85749i | −0.972164 | + | 0.234300i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.243328 | + | 0.140486i | −0.00971760 | + | 0.00561046i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 58.8527 | 2.34661 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.98549i | 0.158660i | 0.996848 | + | 0.0793299i | \(0.0252780\pi\) | ||||
−0.996848 | + | 0.0793299i | \(0.974722\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.6312 | − | 18.4138i | −0.422554 | − | 0.731884i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.51136 | − | 6.67181i | −0.298079 | − | 0.264763i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.55231 | + | 6.30125i | 0.259612 | + | 0.249664i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.95665 | + | 2.28437i | 0.156523 | + | 0.0903684i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.32962 | − | 5.76707i | −0.131512 | − | 0.227786i | 0.792748 | − | 0.609550i | \(-0.208650\pi\) |
−0.924260 | + | 0.381764i | \(0.875317\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.3506 | −0.881421 | −0.440711 | − | 0.897649i | \(-0.645273\pi\) | ||||
−0.440711 | + | 0.897649i | \(0.645273\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 30.3419 | + | 6.23516i | 1.19471 | + | 0.245509i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.62380 | + | 5.55631i | −0.378351 | + | 0.218441i | −0.677100 | − | 0.735891i | \(-0.736764\pi\) |
0.298750 | + | 0.954331i | \(0.403430\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.53125 | + | 1.46142i | 0.0993603 | + | 0.0573657i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.42102 | + | 0.903366i | 0.290853 | + | 0.0354057i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.41053 | − | 12.8354i | 0.289997 | − | 0.502289i | −0.683812 | − | 0.729658i | \(-0.739679\pi\) |
0.973809 | + | 0.227369i | \(0.0730125\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.47094 | − | 10.4416i | −0.135621 | − | 0.407986i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.3439 | −0.598622 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.263237 | 0.0102542 | 0.00512712 | − | 0.999987i | \(-0.498368\pi\) | ||||
0.00512712 | + | 0.999987i | \(0.498368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.3229 | + | 23.0759i | 0.518199 | + | 0.897547i | 0.999776 | + | 0.0211434i | \(0.00673066\pi\) |
−0.481577 | + | 0.876404i | \(0.659936\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.0475 | + | 5.80094i | 0.390214 | + | 0.225290i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.82647 | − | 2.49600i | 0.109606 | − | 0.0967909i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.5103 | + | 8.95490i | 0.600563 | + | 0.346735i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.01941 | + | 1.16591i | −0.0780750 | + | 0.0450766i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.67988 | 0.103456 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.5349i | − | 1.40832i | −0.710043 | − | 0.704158i | \(-0.751324\pi\) | ||
0.710043 | − | 0.704158i | \(-0.248676\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.30863 | − | 27.8496i | −0.127349 | − | 1.07193i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.0196 | − | 9.82627i | −0.654116 | − | 0.377654i | 0.135915 | − | 0.990720i | \(-0.456602\pi\) |
−0.790031 | + | 0.613066i | \(0.789936\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.25470 | + | 14.6927i | 0.240033 | + | 0.563855i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.8480 | − | 23.9855i | 0.530658 | − | 0.919126i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.62027 | − | 3.24486i | 0.215054 | − | 0.124161i | −0.388604 | − | 0.921405i | \(-0.627043\pi\) |
0.603658 | + | 0.797244i | \(0.293709\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −35.9873 | − | 7.39526i | −1.37500 | − | 0.282558i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.6564 | −0.406568 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.16886 | − | 4.71630i | 0.311209 | − | 0.179677i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.9183 | + | 8.61308i | 0.567518 | + | 0.327657i | 0.756158 | − | 0.654390i | \(-0.227074\pi\) |
−0.188639 | + | 0.982046i | \(0.560408\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.451810 | − | 1.06133i | −0.0171629 | − | 0.0403167i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.6274 | + | 16.4680i | −0.554847 | + | 0.624667i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.2750 | + | 18.0566i | −1.18463 | + | 0.683944i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 35.4153i | − | 1.33953i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 20.0480i | − | 0.757201i | −0.925560 | − | 0.378600i | \(-0.876405\pi\) | ||
0.925560 | − | 0.378600i | \(-0.123595\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.75176 | + | 2.74343i | −0.179216 | + | 0.103470i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.4408 | − | 19.6355i | 0.656858 | − | 0.739514i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.40754 | − | 3.20182i | 0.0905447 | − | 0.120417i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.6342 | − | 7.87172i | −0.512044 | − | 0.295629i | 0.221630 | − | 0.975131i | \(-0.428862\pi\) |
−0.733673 | + | 0.679502i | \(0.762196\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.5860 | + | 6.68917i | −0.434508 | + | 0.250863i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.55617 | −0.245531 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.959546 | + | 0.197183i | 0.0358850 | + | 0.00737423i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.1385 | − | 12.2043i | 0.789432 | − | 0.455779i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.4051 | + | 19.7541i | −0.425337 | + | 0.736705i | −0.996452 | − | 0.0841652i | \(-0.973178\pi\) |
0.571115 | + | 0.820870i | \(0.306511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.43669 | + | 20.0171i | −0.0907471 | + | 0.745474i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.8257 | + | 13.1784i | 0.848898 | + | 0.490111i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.3281 | − | 3.48427i | 1.08922 | − | 0.129403i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 43.1926i | − | 1.60193i | −0.598714 | − | 0.800963i | \(-0.704321\pi\) | ||
0.598714 | − | 0.800963i | \(-0.295679\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.4511 | 0.979669 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −62.7655 | + | 36.2377i | −2.32147 | + | 1.34030i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.9526 | + | 7.47818i | 0.478415 | + | 0.276213i | 0.719756 | − | 0.694227i | \(-0.244254\pi\) |
−0.241341 | + | 0.970440i | \(0.577587\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.5871 | − | 16.8552i | −0.427398 | − | 0.621715i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.69211 | + | 2.13164i | 0.136001 | + | 0.0785200i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.37228 | + | 2.37687i | 0.0504803 | + | 0.0874344i | 0.890161 | − | 0.455645i | \(-0.150591\pi\) |
−0.839681 | + | 0.543080i | \(0.817258\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.08165 | −0.0397353 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.5678 | 0.754559 | 0.377279 | − | 0.926099i | \(-0.376860\pi\) | ||||
0.377279 | + | 0.926099i | \(0.376860\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.2556 | + | 30.8517i | 0.375735 | + | 1.13032i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.43503 | − | 4.21759i | 0.0890930 | − | 0.154314i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.621200 | − | 5.10307i | 0.0226982 | − | 0.186462i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.6827 | + | 18.2920i | 1.15612 | + | 0.667486i | 0.950371 | − | 0.311119i | \(-0.100704\pi\) |
0.205748 | + | 0.978605i | \(0.434037\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.3672 | + | 14.0684i | −0.887991 | + | 0.512682i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.6427 | + | 3.42002i | 0.605691 | + | 0.124467i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.7609 | −1.26341 | −0.631704 | − | 0.775210i | \(-0.717644\pi\) | ||||
−0.631704 | + | 0.775210i | \(0.717644\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.668291 | − | 1.15751i | −0.0242574 | − | 0.0420151i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.09181 | − | 4.09446i | −0.257078 | − | 0.148424i | 0.365923 | − | 0.930645i | \(-0.380753\pi\) |
−0.623001 | + | 0.782221i | \(0.714087\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.24592 | − | 2.44070i | −0.117510 | − | 0.0883593i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.7716 | + | 13.1206i | 0.534069 | + | 0.474375i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.62598 | + | 9.74449i | 0.203142 | + | 0.351853i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.2850i | 1.05604i | 0.849231 | + | 0.528021i | \(0.177066\pi\) | ||||
−0.849231 | + | 0.528021i | \(0.822934\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.7973 | −0.460885 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.5234 | + | 8.38511i | −0.522372 | + | 0.301591i | −0.737904 | − | 0.674905i | \(-0.764185\pi\) |
0.215533 | + | 0.976497i | \(0.430851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.65992 | + | 6.47260i | −0.311074 | + | 0.232503i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.6574 | + | 27.3841i | 0.418209 | + | 0.982400i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.68343 | − | 2.91578i | 0.0603151 | − | 0.104469i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.03276 | − | 0.596262i | 0.0369549 | − | 0.0213359i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.1322i | 1.18405i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −39.6154 | − | 8.14083i | −1.41394 | − | 0.290559i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.115323 | − | 0.199746i | −0.00411083 | − | 0.00712017i | 0.863963 | − | 0.503556i | \(-0.167975\pi\) |
−0.868074 | + | 0.496436i | \(0.834642\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.4244 | + | 19.7877i | −0.406720 | + | 0.704460i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.4211 | + | 6.99047i | −0.583866 | + | 0.248552i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.93450 | + | 5.15834i | 0.317273 | + | 0.183178i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20.1398 | + | 6.69479i | −0.714287 | + | 0.237440i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 25.6496i | − | 0.908554i | −0.890860 | − | 0.454277i | \(-0.849898\pi\) | ||
0.890860 | − | 0.454277i | \(-0.150102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 61.4478i | 2.17387i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.32200 | + | 4.80471i | −0.294043 | + | 0.169766i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.00252 | + | 3.46846i | −0.0706673 | + | 0.122399i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.8735 | + | 13.4455i | 0.418486 | + | 0.473893i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.8885 | + | 22.3235i | −0.453696 | + | 0.785824i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.0378 | + | 22.5821i | 0.458385 | + | 0.793946i | 0.998876 | − | 0.0474041i | \(-0.0150948\pi\) |
−0.540491 | + | 0.841350i | \(0.681762\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.3763i | 0.575051i | 0.957773 | + | 0.287525i | \(0.0928325\pi\) | ||||
−0.957773 | + | 0.287525i | \(0.907167\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.75171 | 0.236793 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.21601 | − | 15.6913i | −0.182709 | − | 0.549641i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.37845 | − | 5.85165i | 0.118197 | − | 0.204723i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.536595 | − | 4.40805i | 0.0187501 | − | 0.154030i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.7768 | − | 20.0784i | −1.21372 | − | 0.700740i | −0.250150 | − | 0.968207i | \(-0.580480\pi\) |
−0.963567 | + | 0.267467i | \(0.913813\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.4665 | + | 47.5734i | 0.957422 | + | 1.65830i | 0.728725 | + | 0.684806i | \(0.240113\pi\) |
0.228697 | + | 0.973498i | \(0.426553\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.02549 | − | 0.869166i | −0.0705186 | − | 0.0302605i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.3142i | 1.26277i | 0.775471 | + | 0.631384i | \(0.217513\pi\) | ||||
−0.775471 | + | 0.631384i | \(0.782487\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.57148 | + | 4.45393i | 0.0893111 | + | 0.154691i | 0.907220 | − | 0.420656i | \(-0.138200\pi\) |
−0.817909 | + | 0.575348i | \(0.804867\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.80025 | + | 16.9745i | −0.339967 | + | 0.588840i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 46.4589 | + | 11.4811i | 1.60971 | + | 0.397796i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.8005 | + | 31.2988i | −0.962075 | + | 1.08314i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.06429 | − | 10.5037i | −0.209612 | − | 0.363059i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.7304 | −1.19903 | −0.599514 | − | 0.800365i | \(-0.704639\pi\) | ||||
−0.599514 | + | 0.800365i | \(0.704639\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.89106 | −0.203140 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.4920 | − | 26.8329i | −0.533573 | − | 0.924175i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.9140 | − | 16.7999i | −0.650661 | − | 0.577936i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.5911 | + | 3.48041i | 0.982403 | + | 0.119588i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.73576 | − | 13.3987i | 0.265491 | − | 0.459843i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.0505 | − | 22.6041i | −0.447365 | − | 0.774859i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.93358i | 0.0662045i | 0.999452 | + | 0.0331023i | \(0.0105387\pi\) | ||||
−0.999452 | + | 0.0331023i | \(0.989461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.80428 | − | 0.370772i | −0.0617049 | − | 0.0126801i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.25417 | + | 10.8325i | 0.213638 | + | 0.370032i | 0.952850 | − | 0.303440i | \(-0.0981353\pi\) |
−0.739212 | + | 0.673473i | \(0.764802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.9495 | − | 6.32172i | −0.373594 | − | 0.215694i | 0.301434 | − | 0.953487i | \(-0.402535\pi\) |
−0.675027 | + | 0.737793i | \(0.735868\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.5967 | − | 10.9756i | −0.497453 | − | 0.374048i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.6283 | − | 39.1934i | 0.770276 | − | 1.33416i | −0.167135 | − | 0.985934i | \(-0.553452\pi\) |
0.937411 | − | 0.348224i | \(-0.113215\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.85199 | + | 20.6128i | 0.232975 | + | 0.700855i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.8624 | 1.31983 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.49199i | 0.118458i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.20612 | + | 14.2134i | 0.278054 | + | 0.481603i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.90021 | − | 6.75536i | 0.132002 | − | 0.228634i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.9576 | + | 6.03783i | 0.978947 | + | 0.204116i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.2278 | − | 36.7676i | 0.716810 | − | 1.24155i | −0.245447 | − | 0.969410i | \(-0.578935\pi\) |
0.962257 | − | 0.272142i | \(-0.0877320\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.71276 | + | 3.87561i | −0.226416 | + | 0.130721i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 12.5917i | − | 0.424225i | −0.977245 | − | 0.212113i | \(-0.931966\pi\) | ||
0.977245 | − | 0.212113i | \(-0.0680344\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.44218i | 0.317755i | 0.987298 | + | 0.158877i | \(0.0507874\pi\) | ||||
−0.987298 | + | 0.158877i | \(0.949213\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.98609 | − | 24.0245i | −0.268450 | − | 0.807573i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.38100 | + | 3.68407i | 0.214253 | + | 0.123699i | 0.603286 | − | 0.797525i | \(-0.293858\pi\) |
−0.389033 | + | 0.921224i | \(0.627191\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.65609 | + | 10.9375i | 0.156160 | + | 0.366831i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.582330 | − | 1.00863i | 0.0195088 | − | 0.0337902i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.86440 | − | 4.96128i | −0.0958535 | − | 0.166023i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.07524 | + | 5.23241i | −0.0359414 | + | 0.174900i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 5.14540i | − | 0.171800i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.0612 | − | 6.38622i | 0.368913 | − | 0.212992i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.8285 | − | 43.0043i | 0.827158 | − | 1.43268i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29.2939 | − | 22.0269i | −0.974839 | − | 0.733008i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.5034 | − | 14.6588i | −0.548590 | − | 0.487274i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.0520 | − | 16.7732i | 0.964657 | − | 0.556945i | 0.0670537 | − | 0.997749i | \(-0.478640\pi\) |
0.897603 | + | 0.440804i | \(0.145307\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.95686 | −0.0649048 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 49.7262i | − | 1.64750i | −0.566951 | − | 0.823751i | \(-0.691877\pi\) | ||
0.566951 | − | 0.823751i | \(-0.308123\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.635586 | − | 1.10087i | −0.0210348 | − | 0.0364334i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.3550 | − | 15.4152i | −0.573739 | − | 0.509611i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.57324 | + | 12.9240i | −0.0519530 | + | 0.426787i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.1509 | + | 8.74736i | 0.499781 | + | 0.288549i | 0.728623 | − | 0.684915i | \(-0.240161\pi\) |
−0.228842 | + | 0.973464i | \(0.573494\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.77489 | + | 10.0024i | 0.190289 | + | 0.329590i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.59083 | 0.151109 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39.5541 | − | 16.9732i | −1.30053 | − | 0.558076i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.53051 | − | 4.92509i | 0.280179 | − | 0.161761i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.5419 | − | 8.39576i | −0.477104 | − | 0.275456i | 0.242105 | − | 0.970250i | \(-0.422162\pi\) |
−0.719209 | + | 0.694794i | \(0.755496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.28628 | + | 1.23871i | −0.140477 | + | 0.0405971i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.8168 | − | 25.6634i | 0.485079 | − | 0.840182i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.89371 | − | 1.62674i | 0.160041 | − | 0.0532002i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.8764 | 1.43338 | 0.716690 | − | 0.697392i | \(-0.245656\pi\) | ||||
0.716690 | + | 0.697392i | \(0.245656\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.7283 | 0.872244 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.66745 | − | 2.88811i | −0.0543573 | − | 0.0941495i | 0.837566 | − | 0.546336i | \(-0.183978\pi\) |
−0.891924 | + | 0.452186i | \(0.850644\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.8704 | + | 8.00807i | 0.451682 | + | 0.260779i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.5585 | + | 31.4593i | −0.343467 | + | 1.02337i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.9434 | − | 8.05021i | −0.453099 | − | 0.261597i | 0.256039 | − | 0.966666i | \(-0.417582\pi\) |
−0.709138 | + | 0.705070i | \(0.750916\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.3524 | + | 7.70903i | −0.433438 | + | 0.250246i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.72791 | −0.0884587 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.07172i | 0.0995026i | 0.998762 | + | 0.0497513i | \(0.0158429\pi\) | ||||
−0.998762 | + | 0.0497513i | \(0.984157\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.08327 | + | 27.3251i | 0.293928 | + | 0.884219i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.25501 | + | 1.30193i | 0.0728943 | + | 0.0420855i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34.7442 | + | 26.1251i | 1.12195 | + | 0.843625i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.1622 | − | 22.7976i | 0.424588 | − | 0.735408i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.17473 | + | 1.25558i | −0.0700798 | + | 0.0404606i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.8462 | − | 2.22886i | −0.349152 | − | 0.0717494i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.1674 | 0.616383 | 0.308192 | − | 0.951324i | \(-0.400276\pi\) | ||||
0.308192 | + | 0.951324i | \(0.400276\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.93136 | + | 2.84712i | −0.158418 | + | 0.0914627i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.7871 | + | 21.2390i | 1.18055 | + | 0.681593i | 0.956143 | − | 0.292901i | \(-0.0946206\pi\) |
0.224412 | + | 0.974494i | \(0.427954\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.9794 | − | 10.2081i | 0.768744 | − | 0.327255i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.07981 | − | 6.79646i | −0.162684 | − | 0.217661i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.83162 | − | 2.78954i | 0.154577 | − | 0.0892452i | −0.420716 | − | 0.907192i | \(-0.638221\pi\) |
0.575293 | + | 0.817947i | \(0.304888\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.50823i | 0.0801634i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.98381i | 0.0633382i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.32060 | + | 1.33980i | −0.0740156 | + | 0.0427329i | −0.536551 | − | 0.843868i | \(-0.680273\pi\) |
0.462535 | + | 0.886601i | \(0.346940\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.9776 | − | 9.75064i | −0.349776 | − | 0.310681i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28.5916 | + | 12.1715i | −0.910081 | + | 0.387422i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.8363 | + | 16.0713i | 0.885143 | + | 0.511038i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.289819 | − | 0.167327i | 0.00920640 | − | 0.00531532i | −0.495390 | − | 0.868671i | \(-0.664975\pi\) |
0.504596 | + | 0.863356i | \(0.331641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.3020 | −0.549063 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.4393 | + | 60.5328i | −0.394352 | + | 1.91902i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.3710 | + | 15.2253i | −0.835179 | + | 0.482191i | −0.855623 | − | 0.517600i | \(-0.826825\pi\) |
0.0204437 | + | 0.999791i | \(0.493492\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.1427 | − | 41.8164i | 0.763842 | − | 1.32301i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1120.2.bq.b.719.16 | 80 | ||
4.3 | odd | 2 | 280.2.ba.b.19.14 | yes | 80 | ||
5.4 | even | 2 | inner | 1120.2.bq.b.719.26 | 80 | ||
7.3 | odd | 6 | inner | 1120.2.bq.b.1039.25 | 80 | ||
8.3 | odd | 2 | inner | 1120.2.bq.b.719.15 | 80 | ||
8.5 | even | 2 | 280.2.ba.b.19.1 | ✓ | 80 | ||
20.19 | odd | 2 | 280.2.ba.b.19.27 | yes | 80 | ||
28.3 | even | 6 | 280.2.ba.b.59.40 | yes | 80 | ||
35.24 | odd | 6 | inner | 1120.2.bq.b.1039.15 | 80 | ||
40.19 | odd | 2 | inner | 1120.2.bq.b.719.25 | 80 | ||
40.29 | even | 2 | 280.2.ba.b.19.40 | yes | 80 | ||
56.3 | even | 6 | inner | 1120.2.bq.b.1039.26 | 80 | ||
56.45 | odd | 6 | 280.2.ba.b.59.27 | yes | 80 | ||
140.59 | even | 6 | 280.2.ba.b.59.1 | yes | 80 | ||
280.59 | even | 6 | inner | 1120.2.bq.b.1039.16 | 80 | ||
280.269 | odd | 6 | 280.2.ba.b.59.14 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.ba.b.19.1 | ✓ | 80 | 8.5 | even | 2 | ||
280.2.ba.b.19.14 | yes | 80 | 4.3 | odd | 2 | ||
280.2.ba.b.19.27 | yes | 80 | 20.19 | odd | 2 | ||
280.2.ba.b.19.40 | yes | 80 | 40.29 | even | 2 | ||
280.2.ba.b.59.1 | yes | 80 | 140.59 | even | 6 | ||
280.2.ba.b.59.14 | yes | 80 | 280.269 | odd | 6 | ||
280.2.ba.b.59.27 | yes | 80 | 56.45 | odd | 6 | ||
280.2.ba.b.59.40 | yes | 80 | 28.3 | even | 6 | ||
1120.2.bq.b.719.15 | 80 | 8.3 | odd | 2 | inner | ||
1120.2.bq.b.719.16 | 80 | 1.1 | even | 1 | trivial | ||
1120.2.bq.b.719.25 | 80 | 40.19 | odd | 2 | inner | ||
1120.2.bq.b.719.26 | 80 | 5.4 | even | 2 | inner | ||
1120.2.bq.b.1039.15 | 80 | 35.24 | odd | 6 | inner | ||
1120.2.bq.b.1039.16 | 80 | 280.59 | even | 6 | inner | ||
1120.2.bq.b.1039.25 | 80 | 7.3 | odd | 6 | inner | ||
1120.2.bq.b.1039.26 | 80 | 56.3 | even | 6 | inner |