Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [512,2,Mod(33,512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(512, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([0, 15]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("512.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 512 = 2^{9} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 512.i (of order \(16\), degree \(8\), 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: | \(4.08834058349\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{16})\) |
Twist minimal: | no (minimal twist has level 64) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{16}]$ |
Embedding invariants
Embedding label | 97.7 | ||
Character | \(\chi\) | \(=\) | 512.97 |
Dual form | 512.2.i.b.417.7 |
$q$-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 \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{13}{16}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.599600 | + | 3.01439i | 0.346179 | + | 1.74036i | 0.625556 | + | 0.780179i | \(0.284872\pi\) |
−0.279377 | + | 0.960181i | \(0.590128\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.78465 | − | 1.19247i | 0.798122 | − | 0.533288i | −0.0883396 | − | 0.996090i | \(-0.528156\pi\) |
0.886461 | + | 0.462802i | \(0.153156\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.99271 | + | 0.825409i | 0.753175 | + | 0.311975i | 0.726036 | − | 0.687656i | \(-0.241360\pi\) |
0.0271386 | + | 0.999632i | \(0.491360\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.95540 | + | 2.46681i | −1.98513 | + | 0.822270i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.15038 | + | 0.626650i | 0.949877 | + | 0.188942i | 0.645629 | − | 0.763651i | \(-0.276595\pi\) |
0.304247 | + | 0.952593i | \(0.401595\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0943077 | − | 0.0630144i | −0.0261563 | − | 0.0174770i | 0.542423 | − | 0.840105i | \(-0.317507\pi\) |
−0.568580 | + | 0.822628i | \(0.692507\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.66465 | + | 4.66465i | 1.20441 | + | 1.20441i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.42319 | − | 2.42319i | 0.587710 | − | 0.587710i | −0.349301 | − | 0.937011i | \(-0.613581\pi\) |
0.937011 | + | 0.349301i | \(0.113581\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.93596 | + | 2.89737i | −0.444140 | + | 0.664702i | −0.984228 | − | 0.176906i | \(-0.943391\pi\) |
0.540088 | + | 0.841609i | \(0.318391\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.29328 | + | 6.50174i | −0.282216 | + | 1.41879i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.33543 | − | 3.22402i | −0.278457 | − | 0.672255i | 0.721336 | − | 0.692585i | \(-0.243528\pi\) |
−0.999793 | + | 0.0203301i | \(0.993528\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.150405 | + | 0.363110i | −0.0300810 | + | 0.0726220i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.88424 | − | 8.80639i | −1.13242 | − | 1.69479i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.01879 | + | 0.401561i | −0.374879 | + | 0.0745681i | −0.378934 | − | 0.925424i | \(-0.623709\pi\) |
0.00405495 | + | 0.999992i | \(0.498709\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.16617i | − | 0.748266i | −0.927375 | − | 0.374133i | \(-0.877940\pi\) | ||
0.927375 | − | 0.374133i | \(-0.122060\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.87224i | 1.71854i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.54058 | − | 0.903177i | 0.767498 | − | 0.152665i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.48499 | − | 8.20886i | −0.901726 | − | 1.34953i | −0.936697 | − | 0.350140i | \(-0.886134\pi\) |
0.0349711 | − | 0.999388i | \(-0.488866\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.133403 | − | 0.322064i | 0.0213616 | − | 0.0515715i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.347569 | + | 0.839106i | 0.0542812 | + | 0.131046i | 0.948694 | − | 0.316197i | \(-0.102406\pi\) |
−0.894413 | + | 0.447243i | \(0.852406\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.925855 | + | 4.65459i | −0.141192 | + | 0.709818i | 0.843723 | + | 0.536778i | \(0.180359\pi\) |
−0.984915 | + | 0.173039i | \(0.944641\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.68675 | + | 11.5040i | −1.14587 | + | 1.71492i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.31575 | + | 8.31575i | −1.21298 | + | 1.21298i | −0.242935 | + | 0.970043i | \(0.578110\pi\) |
−0.970043 | + | 0.242935i | \(0.921890\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.66014 | − | 1.66014i | −0.237163 | − | 0.237163i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.75739 | + | 5.85150i | 1.22628 | + | 0.819374i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.565279 | − | 0.112441i | −0.0776470 | − | 0.0154450i | 0.156114 | − | 0.987739i | \(-0.450103\pi\) |
−0.233761 | + | 0.972294i | \(0.575103\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.36961 | − | 2.63838i | 0.858878 | − | 0.355759i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.89462 | − | 4.09848i | −1.31057 | − | 0.542857i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.649771 | − | 0.434163i | 0.0845930 | − | 0.0565232i | −0.512554 | − | 0.858655i | \(-0.671301\pi\) |
0.597147 | + | 0.802132i | \(0.296301\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.528753 | + | 2.65822i | 0.0676999 | + | 0.340350i | 0.999759 | − | 0.0219561i | \(-0.00698941\pi\) |
−0.932059 | + | 0.362306i | \(0.881989\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.9035 | −1.75168 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.243449 | −0.0301962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.971210 | − | 4.88260i | −0.118652 | − | 0.596505i | −0.993663 | − | 0.112401i | \(-0.964146\pi\) |
0.875011 | − | 0.484104i | \(-0.160854\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.91774 | − | 5.95864i | 1.07357 | − | 0.717336i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.38522 | + | 3.88748i | 1.11382 | + | 0.461360i | 0.862252 | − | 0.506480i | \(-0.169054\pi\) |
0.251569 | + | 0.967839i | \(0.419054\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6303 | − | 5.23165i | 1.47827 | − | 0.612318i | 0.509539 | − | 0.860447i | \(-0.329816\pi\) |
0.968727 | + | 0.248129i | \(0.0798158\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.18474 | − | 0.235659i | −0.136802 | − | 0.0272116i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.76057 | + | 3.84909i | 0.656478 | + | 0.438645i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.50532 | − | 3.50532i | −0.394379 | − | 0.394379i | 0.481866 | − | 0.876245i | \(-0.339959\pi\) |
−0.876245 | + | 0.481866i | \(0.839959\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.34353 | − | 9.34353i | 1.03817 | − | 1.03817i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.25513 | − | 12.3547i | 0.906118 | − | 1.35610i | −0.0281778 | − | 0.999603i | \(-0.508970\pi\) |
0.934296 | − | 0.356499i | \(-0.116030\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.43498 | − | 7.21413i | 0.155645 | − | 0.782483i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.42093 | − | 5.84464i | −0.259551 | − | 0.626611i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.98881 | − | 12.0441i | 0.528813 | − | 1.27667i | −0.403488 | − | 0.914985i | \(-0.632202\pi\) |
0.932301 | − | 0.361683i | \(-0.117798\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.135916 | − | 0.203412i | −0.0142478 | − | 0.0213234i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.5585 | − | 2.49803i | 1.30225 | − | 0.259034i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.47938i | 0.767368i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.06140i | − | 0.412373i | −0.978513 | − | 0.206187i | \(-0.933895\pi\) | ||
0.978513 | − | 0.206187i | \(-0.0661054\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.3076 | + | 4.03944i | −2.04099 | + | 0.405979i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.05636 | − | 4.57417i | −0.304119 | − | 0.455147i | 0.647660 | − | 0.761929i | \(-0.275748\pi\) |
−0.951780 | + | 0.306782i | \(0.900748\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.12950 | + | 12.3837i | −0.505425 | + | 1.22020i | 0.441066 | + | 0.897475i | \(0.354600\pi\) |
−0.946491 | + | 0.322730i | \(0.895400\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.44506 | + | 13.1455i | 0.531384 | + | 1.28287i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.35370 | + | 6.80550i | −0.130867 | + | 0.657913i | 0.858540 | + | 0.512746i | \(0.171372\pi\) |
−0.989407 | + | 0.145167i | \(0.953628\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0688 | − | 16.5656i | 1.06020 | − | 1.58670i | 0.281225 | − | 0.959642i | \(-0.409259\pi\) |
0.778973 | − | 0.627057i | \(-0.215741\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.4559 | − | 21.4559i | 2.03651 | − | 2.03651i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.43123 | + | 6.43123i | 0.605000 | + | 0.605000i | 0.941635 | − | 0.336635i | \(-0.109289\pi\) |
−0.336635 | + | 0.941635i | \(0.609289\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.22783 | − | 4.16130i | −0.580748 | − | 0.388044i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.717085 | + | 0.142637i | 0.0662945 | + | 0.0131868i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.82884 | − | 2.82860i | 0.625999 | − | 0.259297i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.630442 | − | 0.261137i | −0.0573129 | − | 0.0237398i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.32099 | + | 1.55084i | −0.209277 | + | 0.139834i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.25827 | + | 11.3531i | 0.201986 | + | 1.01545i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.12090 | −0.454406 | −0.227203 | − | 0.973847i | \(-0.572958\pi\) | ||||
−0.227203 | + | 0.973847i | \(0.572958\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.5859 | −1.28422 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.39632 | + | 12.0471i | 0.209368 | + | 1.05256i | 0.932312 | + | 0.361656i | \(0.117789\pi\) |
−0.722944 | + | 0.690907i | \(0.757211\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.24933 | + | 4.17567i | −0.541886 | + | 0.362076i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −21.0027 | − | 8.69960i | −1.80762 | − | 0.748742i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.03177 | + | 0.427371i | −0.0881496 | + | 0.0365128i | −0.426323 | − | 0.904571i | \(-0.640191\pi\) |
0.338173 | + | 0.941084i | \(0.390191\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.00073 | − | 0.596882i | −0.254518 | − | 0.0506269i | 0.0661819 | − | 0.997808i | \(-0.478918\pi\) |
−0.320700 | + | 0.947181i | \(0.603918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30.0531 | − | 20.0808i | −2.53093 | − | 1.69111i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.257618 | − | 0.257618i | −0.0215431 | − | 0.0215431i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.12399 | + | 3.12399i | −0.259433 | + | 0.259433i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.00890 | − | 5.99974i | 0.330648 | − | 0.494850i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.649276 | − | 3.26413i | 0.0531907 | − | 0.267408i | −0.945034 | − | 0.326973i | \(-0.893971\pi\) |
0.998224 | + | 0.0595651i | \(0.0189714\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.38074 | − | 3.33339i | −0.112363 | − | 0.271268i | 0.857688 | − | 0.514171i | \(-0.171900\pi\) |
−0.970051 | + | 0.242903i | \(0.921900\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.45353 | + | 20.4086i | −0.683427 | + | 1.64994i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.96802 | − | 7.43517i | −0.399041 | − | 0.597207i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8431 | − | 2.95247i | 1.18460 | − | 0.235633i | 0.436805 | − | 0.899556i | \(-0.356110\pi\) |
0.747800 | + | 0.663924i | \(0.231110\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 1.77139i | − | 0.140481i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.52683i | − | 0.593197i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.0586 | + | 2.79643i | −1.10115 | + | 0.219033i | −0.712027 | − | 0.702152i | \(-0.752223\pi\) |
−0.389126 | + | 0.921185i | \(0.627223\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.7723 | + | 17.6185i | 0.916474 | + | 1.37160i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.52271 | − | 6.09036i | 0.195213 | − | 0.471286i | −0.795716 | − | 0.605670i | \(-0.792905\pi\) |
0.990929 | + | 0.134383i | \(0.0429053\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.96996 | − | 11.9985i | −0.382305 | − | 0.922965i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.38217 | − | 22.0307i | 0.335113 | − | 1.68473i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.9283 | + | 16.3554i | −0.830866 | + | 1.24348i | 0.136637 | + | 0.990621i | \(0.456371\pi\) |
−0.967503 | + | 0.252858i | \(0.918629\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.599428 | + | 0.599428i | −0.0453125 | + | 0.0453125i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.69834 | + | 1.69834i | 0.127655 | + | 0.127655i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.59347 | − | 1.06472i | −0.119102 | − | 0.0795812i | 0.494593 | − | 0.869125i | \(-0.335317\pi\) |
−0.613694 | + | 0.789544i | \(0.710317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.2000 | + | 3.81912i | 1.42713 | + | 0.283873i | 0.847408 | − | 0.530943i | \(-0.178162\pi\) |
0.579720 | + | 0.814816i | \(0.303162\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.69588 | + | 3.18774i | −0.568896 | + | 0.235644i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.5776 | − | 8.10931i | −1.43937 | − | 0.596209i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.15247 | − | 6.11549i | 0.669295 | − | 0.447209i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.45674 | − | 22.4055i | −0.324180 | − | 1.62976i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.6604 | 0.916073 | 0.458037 | − | 0.888933i | \(-0.348553\pi\) | ||||
0.458037 | + | 0.888933i | \(0.348553\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.31378 | 0.454476 | 0.227238 | − | 0.973839i | \(-0.427030\pi\) | ||||
0.227238 | + | 0.973839i | \(0.427030\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.145972 | − | 0.733852i | −0.0104533 | − | 0.0525522i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.2658 | + | 12.8730i | −1.37263 | + | 0.917163i | −0.999942 | − | 0.0107926i | \(-0.996565\pi\) |
−0.372690 | + | 0.927956i | \(0.621565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.5609 | − | 5.61712i | −0.961309 | − | 0.398187i | −0.153839 | − | 0.988096i | \(-0.549164\pi\) |
−0.807470 | + | 0.589909i | \(0.799164\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.1357 | − | 5.85522i | 0.997059 | − | 0.412995i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.35431 | − | 0.866127i | −0.305613 | − | 0.0607902i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.62090 | + | 1.08305i | 0.113208 | + | 0.0756434i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.9061 | + | 15.9061i | 1.10555 | + | 1.10555i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.91466 | + | 7.91466i | −0.547469 | + | 0.547469i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.35601 | + | 2.02941i | −0.0933516 | + | 0.139711i | −0.875206 | − | 0.483751i | \(-0.839274\pi\) |
0.781854 | + | 0.623461i | \(0.214274\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.09103 | + | 30.6217i | −0.417350 | + | 2.09816i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.89811 | + | 9.41088i | 0.265849 | + | 0.641817i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.43879 | − | 8.30198i | 0.233440 | − | 0.563575i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23.3434 | + | 34.9358i | 1.57740 | + | 2.36074i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.381221 | + | 0.0758296i | −0.0256437 | + | 0.00510085i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 7.01617i | − | 0.469838i | −0.972015 | − | 0.234919i | \(-0.924518\pi\) | ||
0.972015 | − | 0.234919i | \(-0.0754824\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 2.53349i | − | 0.168899i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9611 | − | 3.37378i | 1.12575 | − | 0.223925i | 0.403110 | − | 0.915151i | \(-0.367929\pi\) |
0.722638 | + | 0.691226i | \(0.242929\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.93254 | − | 2.89225i | −0.127706 | − | 0.191126i | 0.762107 | − | 0.647451i | \(-0.224165\pi\) |
−0.889813 | + | 0.456326i | \(0.849165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.14863 | + | 19.6725i | −0.536141 | + | 1.29436i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0866 | + | 24.3511i | 0.660794 | + | 1.59530i | 0.796563 | + | 0.604556i | \(0.206650\pi\) |
−0.135769 | + | 0.990741i | \(0.543350\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.92448 | + | 24.7570i | −0.321238 | + | 1.61497i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.46462 | − | 12.6682i | 0.549836 | − | 0.822888i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.2250 | + | 11.2250i | −0.726085 | + | 0.726085i | −0.969838 | − | 0.243752i | \(-0.921622\pi\) |
0.243752 | + | 0.969838i | \(0.421622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.1085 | − | 15.1085i | −0.973222 | − | 0.973222i | 0.0264284 | − | 0.999651i | \(-0.491587\pi\) |
−0.999651 | + | 0.0264284i | \(0.991587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.34826 | + | 4.90995i | 0.471391 | + | 0.314973i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.94245 | − | 0.983113i | −0.315761 | − | 0.0628088i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.365152 | − | 0.151251i | 0.0232341 | − | 0.00962387i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 42.1916 | + | 17.4763i | 2.67378 | + | 1.10752i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.246229 | − | 0.164525i | 0.0155419 | − | 0.0103847i | −0.547775 | − | 0.836626i | \(-0.684525\pi\) |
0.563317 | + | 0.826241i | \(0.309525\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.18679 | − | 10.9938i | −0.137483 | − | 0.691172i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 22.6066 | 1.41568 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.958734 | 0.0598042 | 0.0299021 | − | 0.999553i | \(-0.490480\pi\) | ||||
0.0299021 | + | 0.999553i | \(0.490480\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.15434 | − | 20.8853i | −0.258138 | − | 1.29775i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.0321 | − | 7.37142i | 0.682870 | − | 0.456279i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.44089 | + | 1.83948i | 0.273837 | + | 0.113427i | 0.515376 | − | 0.856964i | \(-0.327652\pi\) |
−0.241539 | + | 0.970391i | \(0.577652\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.14291 | + | 0.473409i | −0.0702084 | + | 0.0290813i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 39.2968 | + | 7.81663i | 2.40493 | + | 0.478370i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.61121 | + | 2.41293i | 0.220179 | + | 0.147119i | 0.660769 | − | 0.750590i | \(-0.270230\pi\) |
−0.440589 | + | 0.897709i | \(0.645230\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.6599 | − | 10.6599i | −0.647540 | − | 0.647540i | 0.304858 | − | 0.952398i | \(-0.401391\pi\) |
−0.952398 | + | 0.304858i | \(0.901391\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.531669 | − | 0.531669i | 0.0321781 | − | 0.0321781i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.701377 | + | 1.04968i | −0.0422946 | + | 0.0632984i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.0750905 | + | 0.377506i | −0.00451175 | + | 0.0226821i | −0.982976 | − | 0.183736i | \(-0.941181\pi\) |
0.978464 | + | 0.206418i | \(0.0661808\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.2771 | + | 24.8112i | 0.615276 | + | 1.48541i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.58445 | + | 3.82519i | −0.0945201 | + | 0.228192i | −0.964067 | − | 0.265658i | \(-0.914411\pi\) |
0.869547 | + | 0.493850i | \(0.164411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.06218 | − | 7.57609i | −0.300915 | − | 0.450352i | 0.649941 | − | 0.759985i | \(-0.274794\pi\) |
−0.950856 | + | 0.309633i | \(0.899794\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −22.5458 | + | 4.48464i | −1.33550 | + | 0.265647i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.95898i | 0.115635i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.25630i | 0.309194i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.2427 | − | 2.43522i | 0.717678 | − | 0.142755i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.97915 | − | 14.9349i | −0.582988 | − | 0.872504i | 0.416338 | − | 0.909210i | \(-0.363313\pi\) |
−0.999326 | + | 0.0367064i | \(0.988313\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.641891 | − | 1.54966i | 0.0373723 | − | 0.0902248i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.0191 | − | 31.4309i | −0.755445 | − | 1.82381i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.0772181 | + | 0.388202i | −0.00446564 | + | 0.0224503i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.68690 | + | 8.51105i | −0.327787 | + | 0.490568i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.9557 | − | 11.9557i | 0.686840 | − | 0.686840i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.11348 | + | 4.11348i | 0.235537 | + | 0.235537i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.6650 | − | 13.1398i | −1.12234 | − | 0.749925i | −0.151219 | − | 0.988500i | \(-0.548320\pi\) |
−0.971124 | + | 0.238575i | \(0.923320\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −40.4050 | − | 8.03706i | −2.29856 | − | 0.457213i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.33022 | + | 2.20785i | −0.302249 | + | 0.125196i | −0.528654 | − | 0.848838i | \(-0.677303\pi\) |
0.226404 | + | 0.974033i | \(0.427303\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.66540 | + | 2.76090i | 0.376751 | + | 0.156055i | 0.563020 | − | 0.826444i | \(-0.309640\pi\) |
−0.186269 | + | 0.982499i | \(0.559640\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −24.8130 | + | 16.5795i | −1.39806 | + | 0.934151i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.63635 | + | 33.3632i | 0.372734 | + | 1.87386i | 0.476366 | + | 0.879247i | \(0.341954\pi\) |
−0.103632 | + | 0.994616i | \(0.533046\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.61159 | −0.370178 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.3261 | −1.19031 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.32968 | + | 11.7121i | 0.129627 | + | 0.651678i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0370655 | − | 0.0247664i | 0.00205603 | − | 0.00137379i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 56.5721 | + | 23.4330i | 3.12845 | + | 1.29585i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.4348 | + | 9.70702i | −1.29200 | + | 0.535165i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.2233 | − | 2.82918i | −0.781781 | − | 0.155506i | −0.211964 | − | 0.977277i | \(-0.567986\pi\) |
−0.569817 | + | 0.821772i | \(0.692986\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 52.9150 | + | 35.3567i | 2.89972 | + | 1.93753i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.55562 | − | 7.55562i | −0.412808 | − | 0.412808i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.7689 | + | 22.7689i | −1.24030 | + | 1.24030i | −0.280423 | + | 0.959877i | \(0.590475\pi\) |
−0.959877 | + | 0.280423i | \(0.909525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.5301 | + | 23.2424i | −0.843479 | + | 1.26236i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.61073 | − | 13.1250i | 0.141379 | − | 0.710760i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.71575 | − | 18.6275i | −0.416611 | − | 1.00579i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.80959 | − | 21.2682i | 0.474293 | − | 1.14504i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.44427 | − | 8.14793i | −0.292264 | − | 0.437404i | 0.656060 | − | 0.754709i | \(-0.272222\pi\) |
−0.948323 | + | 0.317305i | \(0.897222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.0492 | + | 6.57390i | −1.76909 | + | 0.351893i | −0.968822 | − | 0.247756i | \(-0.920307\pi\) |
−0.800263 | + | 0.599649i | \(0.795307\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.20130i | 0.0641208i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.4677i | 0.929711i | 0.885387 | + | 0.464856i | \(0.153894\pi\) | ||||
−0.885387 | + | 0.464856i | \(0.846106\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.3851 | − | 4.25376i | 1.13500 | − | 0.225766i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.6211 | + | 18.8888i | 0.667979 | + | 0.999701i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.92204 | − | 16.7113i | 0.365331 | − | 0.881987i | −0.629171 | − | 0.777267i | \(-0.716605\pi\) |
0.994502 | − | 0.104720i | \(-0.0333947\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.62417 | + | 6.33532i | 0.138114 | + | 0.333438i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.409158 | − | 2.05698i | 0.0214752 | − | 0.107963i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.3022 | − | 24.3979i | 0.853295 | − | 1.27705i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.7264 | + | 22.7264i | −1.18631 | + | 1.18631i | −0.208226 | + | 0.978081i | \(0.566769\pi\) |
−0.978081 | + | 0.208226i | \(0.933231\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.13983 | − | 4.13983i | −0.215511 | − | 0.215511i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.03363 | − | 0.690649i | −0.0536633 | − | 0.0358567i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.36804 | + | 0.868856i | 0.226168 | + | 0.0449877i | 0.306873 | − | 0.951750i | \(-0.400717\pi\) |
−0.0807051 | + | 0.996738i | \(0.525717\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −32.8686 | + | 13.6146i | −1.69733 | + | 0.703057i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.215691 | + | 0.0893422i | 0.0111087 | + | 0.00460136i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0406 | − | 12.7225i | 0.978052 | − | 0.653513i | 0.0397061 | − | 0.999211i | \(-0.487358\pi\) |
0.938346 | + | 0.345698i | \(0.112358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.07049 | − | 15.4364i | −0.157306 | − | 0.790830i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.58576 | −0.489809 | −0.244905 | − | 0.969547i | \(-0.578757\pi\) | ||||
−0.244905 | + | 0.969547i | \(0.578757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.8705 | 0.757873 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.96814 | − | 30.0038i | −0.303377 | − | 1.52518i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.2676 | − | 6.86062i | 0.520590 | − | 0.347847i | −0.267349 | − | 0.963600i | \(-0.586148\pi\) |
0.787940 | + | 0.615752i | \(0.211148\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0484 | − | 4.57641i | −0.558743 | − | 0.231439i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −34.8779 | + | 14.4469i | −1.75936 | + | 0.728751i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.4358 | − | 2.07580i | −0.525081 | − | 0.104445i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.79289 | − | 4.53886i | −0.340925 | − | 0.227799i | 0.373307 | − | 0.927708i | \(-0.378224\pi\) |
−0.714232 | + | 0.699909i | \(0.753224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.3342 | − | 16.3342i | −0.817733 | − | 0.817733i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.63465 | − | 6.63465i | 0.331319 | − | 0.331319i | −0.521769 | − | 0.853087i | \(-0.674728\pi\) |
0.853087 | + | 0.521769i | \(0.174728\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.262529 | + | 0.392902i | −0.0130775 | + | 0.0195718i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.53311 | − | 27.8168i | 0.274943 | − | 1.38223i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.1357 | − | 29.2982i | −0.601546 | − | 1.45226i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.09518 | + | 7.47242i | −0.153047 | + | 0.369487i | −0.981743 | − | 0.190211i | \(-0.939083\pi\) |
0.828697 | + | 0.559698i | \(0.189083\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.90691 | − | 2.85389i | −0.0940610 | − | 0.140772i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.65317 | − | 0.328836i | 0.0813471 | − | 0.0161809i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 31.8928i | − | 1.56556i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 9.40326i | − | 0.460480i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.86945 | − | 0.570769i | 0.140182 | − | 0.0278839i | −0.124501 | − | 0.992220i | \(-0.539733\pi\) |
0.264682 | + | 0.964336i | \(0.414733\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.9038 | + | 17.8153i | 0.580157 | + | 0.868266i | 0.999212 | − | 0.0396948i | \(-0.0126386\pi\) |
−0.419055 | + | 0.907961i | \(0.637639\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.0103 | − | 70.0371i | 1.41053 | − | 3.40532i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.515424 | + | 1.24434i | 0.0250018 | + | 0.0603596i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.14047 | + | 5.73351i | −0.0551910 | + | 0.277464i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.622093 | − | 0.931028i | 0.0300349 | − | 0.0449505i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.75609 | − | 8.75609i | 0.421766 | − | 0.421766i | −0.464045 | − | 0.885811i | \(-0.653603\pi\) |
0.885811 | + | 0.464045i | \(0.153603\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.9449 | − | 13.9449i | −0.670149 | − | 0.670149i | 0.287601 | − | 0.957750i | \(-0.407142\pi\) |
−0.957750 | + | 0.287601i | \(0.907142\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.2901 | − | 7.54378i | −0.541317 | − | 0.361696i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.9265 | + | 2.37233i | 0.570523 | + | 0.113484i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.84033 | + | 4.07600i | −0.469653 | + | 0.194537i | −0.604942 | − | 0.796270i | \(-0.706804\pi\) |
0.135289 | + | 0.990806i | \(0.456804\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.9821 | + | 5.79156i | 0.665813 | + | 0.275789i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.3602 | + | 10.9315i | −0.777294 | + | 0.519371i | −0.879790 | − | 0.475362i | \(-0.842317\pi\) |
0.102496 | + | 0.994733i | \(0.467317\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.45885 | − | 27.4435i | −0.258774 | − | 1.30095i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.2287 | 0.483800 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.9457 | 1.46042 | 0.730209 | − | 0.683224i | \(-0.239423\pi\) | ||||
0.730209 | + | 0.683224i | \(0.239423\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.569150 | + | 2.86131i | 0.0268002 | + | 0.134734i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.22026 | − | 6.16078i | 0.433206 | − | 0.289459i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.485125 | − | 0.200945i | −0.0227430 | − | 0.00942046i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.3997 | − | 15.0773i | 1.70271 | − | 0.705285i | 0.702727 | − | 0.711459i | \(-0.251965\pi\) |
0.999981 | + | 0.00617459i | \(0.00196544\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −35.5982 | − | 7.08092i | −1.66158 | − | 0.330509i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.22960 | − | 4.83066i | −0.336716 | − | 0.224986i | 0.375704 | − | 0.926740i | \(-0.377401\pi\) |
−0.712420 | + | 0.701753i | \(0.752401\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.2338 | + | 25.2338i | 1.17271 | + | 1.17271i | 0.981560 | + | 0.191154i | \(0.0612228\pi\) |
0.191154 | + | 0.981560i | \(0.438777\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.4337 | − | 19.4337i | 0.901216 | − | 0.901216i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.5128 | + | 30.6996i | −0.949220 | + | 1.42061i | −0.0423942 | + | 0.999101i | \(0.513499\pi\) |
−0.906825 | + | 0.421507i | \(0.861501\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.09480 | − | 10.5313i | 0.0967289 | − | 0.486289i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.7998 | + | 42.9725i | 0.820171 | + | 1.98007i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.83360 | + | 14.0835i | −0.268229 | + | 0.647562i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.760886 | − | 1.13875i | −0.0349118 | − | 0.0522493i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.64383 | − | 0.724804i | 0.166840 | − | 0.0331865i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.3832i | 1.02271i | 0.859368 | + | 0.511357i | \(0.170857\pi\) | ||||
−0.859368 | + | 0.511357i | \(0.829143\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.11979i | 0.0510581i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.6888 | − | 4.51309i | 1.03238 | − | 0.205353i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.84310 | − | 7.24821i | −0.219914 | − | 0.329124i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.3025 | + | 32.1150i | −0.602792 | + | 1.45527i | 0.267902 | + | 0.963446i | \(0.413670\pi\) |
−0.870695 | + | 0.491824i | \(0.836330\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.8591 | − | 40.7014i | −0.762393 | − | 1.84058i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.09965 | − | 25.6377i | 0.230144 | − | 1.15701i | −0.676933 | − | 0.736045i | \(-0.736691\pi\) |
0.907076 | − | 0.420966i | \(-0.138309\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.91884 | + | 5.86496i | −0.176496 | + | 0.264144i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −31.4252 | + | 31.4252i | −1.41246 | + | 1.41246i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.4933 | + | 15.4933i | 0.694969 | + | 0.694969i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.9332 | + | 18.6644i | 1.25046 | + | 0.835532i | 0.991468 | − | 0.130347i | \(-0.0416091\pi\) |
0.258994 | + | 0.965879i | \(0.416609\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.8714 | + | 3.95266i | 0.887787 | + | 0.176592i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.0549 | − | 8.30702i | 0.894205 | − | 0.370392i | 0.112216 | − | 0.993684i | \(-0.464205\pi\) |
0.781989 | + | 0.623292i | \(0.214205\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.9091 | − | 4.51870i | −0.485449 | − | 0.201079i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.1883 | − | 22.1757i | 1.47395 | − | 0.984859i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.581805 | + | 2.92493i | 0.0257881 | + | 0.129645i | 0.991535 | − | 0.129841i | \(-0.0414467\pi\) |
−0.965747 | + | 0.259486i | \(0.916447\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.4868 | 1.30442 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 36.9071 | 1.62949 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.61280 | + | 28.2174i | 0.247329 | + | 1.24341i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.4089 | + | 20.9868i | −1.38136 | + | 0.922996i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −55.8543 | − | 23.1356i | −2.45173 | − | 1.01554i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.7789 | + | 7.77848i | −0.822719 | + | 0.340781i | −0.754016 | − | 0.656856i | \(-0.771886\pi\) |
−0.0687028 | + | 0.997637i | \(0.521886\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.4384 | − | 2.67306i | −0.587620 | − | 0.116885i | −0.107679 | − | 0.994186i | \(-0.534342\pi\) |
−0.479941 | + | 0.877301i | \(0.659342\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.16633 | − | 1.44750i | −0.0945464 | − | 0.0631739i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.0954 | − | 10.0954i | −0.439763 | − | 0.439763i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.65252 | − | 7.65252i | 0.332718 | − | 0.332718i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.79865 | + | 4.18848i | −0.121451 | + | 0.181764i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.0200973 | − | 0.101036i | 0.000870511 | − | 0.00437635i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.69946 | + | 13.7597i | 0.246409 | + | 0.594884i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.25405 | − | 5.44176i | 0.0972694 | − | 0.234829i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.18976 | − | 6.27041i | −0.180466 | − | 0.270086i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.53938 | + | 1.49968i | −0.324143 | + | 0.0644761i | −0.354480 | − | 0.935064i | \(-0.615342\pi\) |
0.0303365 | + | 0.999540i | \(0.490342\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 60.1664i | 2.58199i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 42.7631i | − | 1.83177i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.2900 | + | 4.63267i | −0.995809 | + | 0.198079i | −0.665986 | − | 0.745964i | \(-0.731989\pi\) |
−0.329823 | + | 0.944043i | \(0.606989\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.70626 | − | 14.5264i | −0.414253 | − | 0.619974i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.74482 | − | 6.62658i | 0.116933 | − | 0.282302i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.09178 | − | 9.87842i | −0.174000 | − | 0.420073i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.7059 | − | 63.8770i | 0.539336 | − | 2.71143i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.86803 | − | 11.7753i | 0.333379 | − | 0.498937i | −0.626473 | − | 0.779443i | \(-0.715502\pi\) |
0.959852 | + | 0.280506i | \(0.0905023\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.380621 | − | 0.380621i | 0.0160986 | − | 0.0160986i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.9223 | + | 23.9223i | 1.01000 | + | 1.01000i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.80935 | + | 3.88168i | 0.244835 | + | 0.163593i | 0.671933 | − | 0.740612i | \(-0.265464\pi\) |
−0.427098 | + | 0.904205i | \(0.640464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.1466 | + | 3.80849i | 0.805502 | + | 0.160224i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.3312 | − | 10.9067i | 1.10581 | − | 0.458040i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.1266 | − | 7.09406i | −0.717983 | − | 0.297398i | −0.00637952 | − | 0.999980i | \(-0.502031\pi\) |
−0.711603 | + | 0.702581i | \(0.752031\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.16513 | + | 0.778514i | −0.0487591 | + | 0.0325798i | −0.579711 | − | 0.814822i | \(-0.696835\pi\) |
0.530952 | + | 0.847402i | \(0.321835\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.59116 | + | 38.1634i | 0.317125 | + | 1.59430i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.37153 | 0.0571968 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.1108 | 1.17027 | 0.585135 | − | 0.810936i | \(-0.301042\pi\) | ||||
0.585135 | + | 0.810936i | \(0.301042\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.78574 | + | 19.0322i | 0.157330 | + | 0.790952i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.6478 | − | 17.8055i | 1.10554 | − | 0.738695i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.71038 | − | 0.708464i | −0.0708369 | − | 0.0293416i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.44984 | − | 0.600543i | 0.0599435 | − | 0.0248294i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.1359 | − | 2.21507i | −0.459629 | − | 0.0914258i | −0.0401553 | − | 0.999193i | \(-0.512785\pi\) |
−0.419473 | + | 0.907768i | \(0.637785\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0709 | + | 8.06554i | 0.497374 | + | 0.332335i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −50.3561 | − | 50.3561i | −2.07137 | − | 2.07137i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.38627 | − | 5.38627i | 0.221188 | − | 0.221188i | −0.587811 | − | 0.808998i | \(-0.700010\pi\) |
0.808998 | + | 0.587811i | \(0.200010\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.81411 | − | 13.1913i | 0.361343 | − | 0.540789i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.80108 | − | 44.2460i | 0.360204 | − | 1.81087i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.9367 | − | 26.4036i | −0.446863 | − | 1.07882i | −0.973491 | − | 0.228727i | \(-0.926544\pi\) |
0.526627 | − | 0.850096i | \(-0.323456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.76796 | + | 21.1677i | −0.357653 | + | 0.863450i | 0.637977 | + | 0.770056i | \(0.279772\pi\) |
−0.995629 | + | 0.0933942i | \(0.970228\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.8284 | + | 26.6821i | 0.726029 | + | 1.08658i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.43652 | + | 0.285741i | −0.0584028 | + | 0.0116170i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 27.1652i | − | 1.10260i | −0.834306 | − | 0.551301i | \(-0.814132\pi\) | ||
0.834306 | − | 0.551301i | \(-0.185868\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 13.6449i | − | 0.552921i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.30825 | − | 0.260227i | 0.0529262 | − | 0.0105277i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.77987 | + | 7.15358i | 0.193057 | + | 0.288930i | 0.915352 | − | 0.402655i | \(-0.131913\pi\) |
−0.722295 | + | 0.691585i | \(0.756913\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.29285 | + | 5.53542i | −0.0924564 | + | 0.223210i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.84308 | − | 9.27803i | −0.154717 | − | 0.373519i | 0.827448 | − | 0.561543i | \(-0.189792\pi\) |
−0.982165 | + | 0.188023i | \(0.939792\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.956021 | − | 4.80624i | 0.0384257 | − | 0.193179i | −0.956805 | − | 0.290732i | \(-0.906101\pi\) |
0.995230 | + | 0.0975524i | \(0.0311013\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.5340 | + | 30.7313i | −0.824000 | + | 1.23320i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.8826 | − | 19.8826i | 0.796578 | − | 0.796578i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.1789 | + | 16.1789i | 0.647155 | + | 0.647155i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −28.6035 | − | 19.1123i | −1.14231 | − | 0.763270i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.1828 | − | 6.60047i | −1.32308 | − | 0.263178i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.21091 | − | 1.74421i | 0.167634 | − | 0.0694361i | −0.297289 | − | 0.954788i | \(-0.596082\pi\) |
0.464922 | + | 0.885352i | \(0.346082\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.93051 | − | 2.87071i | −0.275463 | − | 0.114101i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.13903 | + | 6.10650i | −0.362671 | + | 0.242329i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0519513 | + | 0.261177i | 0.00205839 | + | 0.0103482i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −65.4825 | −2.59045 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.0849 | −0.714310 | −0.357155 | − | 0.934045i | \(-0.616253\pi\) | ||||
−0.357155 | + | 0.934045i | \(0.616253\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.42112 | + | 7.14443i | 0.0560433 | + | 0.281749i | 0.998637 | − | 0.0521929i | \(-0.0166211\pi\) |
−0.942594 | + | 0.333942i | \(0.891621\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −26.0308 | + | 17.3932i | −1.02496 | + | 0.684857i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.05247 | + | 1.26437i | 0.120005 | + | 0.0497076i | 0.441878 | − | 0.897075i | \(-0.354312\pi\) |
−0.321873 | + | 0.946783i | \(0.604312\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.31910 | − | 0.960601i | 0.0910325 | − | 0.0377069i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.0873 | + | 5.38800i | 1.06164 | + | 0.211172i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.1827 | − | 6.80383i | −0.398478 | − | 0.266254i | 0.340145 | − | 0.940373i | \(-0.389524\pi\) |
−0.738623 | + | 0.674118i | \(0.764524\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.6424 | + | 18.6424i | 0.728420 | + | 0.728420i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −62.3131 | + | 62.3131i | −2.43107 | + | 2.43107i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.7692 | − | 22.1037i | 0.575328 | − | 0.861039i | −0.423669 | − | 0.905817i | \(-0.639258\pi\) |
0.998997 | + | 0.0447783i | \(0.0142581\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.82505 | + | 14.2025i | −0.109882 | + | 0.552412i | 0.886149 | + | 0.463400i | \(0.153371\pi\) |
−0.996031 | + | 0.0890116i | \(0.971629\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.457161 | − | 1.10368i | −0.0177546 | − | 0.0428635i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.17355 | + | 14.9043i | −0.239400 | + | 0.577962i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.99060 | + | 5.97235i | 0.154516 | + | 0.231250i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.1495 | − | 4.20690i | 0.817687 | − | 0.162648i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.70576i | 0.336082i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 26.9629i | − | 1.03934i | −0.854366 | − | 0.519671i | \(-0.826054\pi\) | ||
0.854366 | − | 0.519671i | \(-0.173946\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.08271 | − | 0.812101i | 0.157144 | − | 0.0312578i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.17925 | + | 13.7377i | 0.352787 | + | 0.527984i | 0.964842 | − | 0.262832i | \(-0.0846566\pi\) |
−0.612054 | + | 0.790816i | \(0.709657\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.35232 | − | 8.09321i | 0.128650 | − | 0.310589i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.3398 | + | 49.1045i | 0.779422 | + | 1.88169i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.67420 | − | 18.4714i | 0.140589 | − | 0.706790i | −0.844611 | − | 0.535381i | \(-0.820168\pi\) |
0.985200 | − | 0.171409i | \(-0.0548320\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.33172 | + | 1.99306i | −0.0508823 | + | 0.0761508i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.55964 | − | 7.55964i | 0.288418 | − | 0.288418i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0462248 | + | 0.0462248i | 0.00176102 | + | 0.00176102i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.5013 | + | 15.0349i | 0.855989 | + | 0.571953i | 0.904309 | − | 0.426879i | \(-0.140387\pi\) |
−0.0483204 | + | 0.998832i | \(0.515387\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −43.8015 | − | 8.71266i | −1.66388 | − | 0.330967i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.06703 | + | 2.51304i | −0.230135 | + | 0.0953252i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.87554 | + | 1.19109i | 0.108919 | + | 0.0451156i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −67.3560 | + | 45.0058i | −2.54764 | + | 1.70228i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.62224 | + | 23.2376i | 0.174579 | + | 0.877670i | 0.964423 | + | 0.264362i | \(0.0851615\pi\) |
−0.789844 | + | 0.613308i | \(0.789838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.4028 | 1.29753 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −77.5801 | −2.92184 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.31489 | − | 11.6378i | −0.0870605 | − | 0.437683i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.3280 | + | 10.9100i | −0.613211 | + | 0.409734i | −0.823024 | − | 0.568007i | \(-0.807715\pi\) |
0.209813 | + | 0.977742i | \(0.432715\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.5226 | + | 12.2286i | 1.10718 | + | 0.458610i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.4318 | + | 5.56364i | −0.503025 | + | 0.208360i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.766959 | − | 0.152558i | −0.0286826 | − | 0.00570533i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −40.5671 | − | 27.1061i | −1.51501 | − | 1.01229i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.45757 | + | 3.45757i | 0.128946 | + | 0.128946i | 0.768634 | − | 0.639689i | \(-0.220937\pi\) |
−0.639689 | + | 0.768634i | \(0.720937\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.4433 | + | 20.4433i | −0.761347 | + | 0.761347i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.4838 | − | 54.6019i | 1.35685 | − | 2.03067i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.157825 | − | 0.793438i | 0.00586146 | − | 0.0294676i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0936 | + | 34.0251i | 0.522704 | + | 1.26192i | 0.936217 | + | 0.351421i | \(0.114302\pi\) |
−0.413513 | + | 0.910498i | \(0.635698\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.77554 | − | 11.5292i | 0.176872 | − | 0.427007i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.03542 | + | 13.5225i | 0.334187 | + | 0.500146i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.93170 | − | 1.97554i | 0.366836 | − | 0.0729681i | −0.00823071 | − | 0.999966i | \(-0.502620\pi\) |
0.375066 | + | 0.926998i | \(0.377620\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 15.4879i | − | 0.571281i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 15.9907i | − | 0.589025i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.0664 | + | 9.36209i | −1.73137 | + | 0.344390i | −0.957384 | − | 0.288817i | \(-0.906738\pi\) |
−0.773982 | + | 0.633207i | \(0.781738\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.674875 | + | 1.01002i | 0.0247922 | + | 0.0371041i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.63374 | + | 20.8437i | −0.316741 | + | 0.764681i | 0.682682 | + | 0.730716i | \(0.260814\pi\) |
−0.999423 | + | 0.0339651i | \(0.989186\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.73364 | − | 6.59958i | −0.100153 | − | 0.241790i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.6860 | + | 93.9409i | −0.683685 | + | 3.43712i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.31486 | + | 12.4441i | −0.303818 | + | 0.454696i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.86892 | − | 6.86892i | 0.250650 | − | 0.250650i | −0.570587 | − | 0.821237i | \(-0.693284\pi\) |
0.821237 | + | 0.570587i | \(0.193284\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.643583 | + | 0.643583i | 0.0234535 | + | 0.0234535i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.43910 | − | 4.30247i | −0.234343 | − | 0.156583i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.6195 | + | 4.10147i | 0.749428 | + | 0.149070i | 0.555005 | − | 0.831847i | \(-0.312716\pi\) |
0.194423 | + | 0.980918i | \(0.437716\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 31.8283 | − | 13.1837i | 1.15529 | − | 0.478539i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.27046 | − | 0.940453i | −0.0823039 | − | 0.0340914i | 0.341152 | − | 0.940008i | \(-0.389183\pi\) |
−0.423456 | + | 0.905917i | \(0.639183\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.7303 | − | 23.8743i | 1.29353 | − | 0.864306i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.25000 | + | 46.5029i | 0.334435 | + | 1.68132i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.0886369 | −0.00320049 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.66124 | −0.132028 | −0.0660139 | − | 0.997819i | \(-0.521028\pi\) | ||||
−0.0660139 | + | 0.997819i | \(0.521028\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.574857 | + | 2.89000i | 0.0207030 | + | 0.104081i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.7598 | − | 23.8939i | 1.28619 | − | 0.859404i | 0.290938 | − | 0.956742i | \(-0.406033\pi\) |
0.995251 | + | 0.0973381i | \(0.0310328\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.51278 | + | 0.626613i | 0.0543406 | + | 0.0225086i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 60.4654 | − | 25.0456i | 2.16919 | − | 0.898506i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.10408 | − | 0.617440i | −0.111215 | − | 0.0221221i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.1310 | + | 18.1283i | 0.970822 | + | 0.648682i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.4153 | + | 15.4153i | 0.550899 | + | 0.550899i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.9690 | − | 22.9690i | 0.819799 | − | 0.819799i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.0932 | + | 25.5818i | −0.609308 | + | 0.911894i | −0.999963 | − | 0.00864361i | \(-0.997249\pi\) |
0.390655 | + | 0.920537i | \(0.372249\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.88215 | + | 14.4895i | −0.102607 | + | 0.515842i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.50721 | + | 18.1240i | 0.266926 | + | 0.644415i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.117641 | − | 0.284010i | 0.00417754 | − | 0.0100855i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.11233 | − | 3.16132i | −0.0749166 | − | 0.112121i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.59248 | − | 0.714589i | 0.127252 | − | 0.0253120i | −0.131053 | − | 0.991375i | \(-0.541836\pi\) |
0.258306 | + | 0.966063i | \(0.416836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.3013i | 1.42576i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 84.0337i | 2.96919i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 43.0688 | − | 8.56691i | 1.51986 | − | 0.302320i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.97550 | − | 13.4328i | −0.316345 | − | 0.473444i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.10825 | + | 12.3324i | −0.179819 | + | 0.434121i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.56231 | − | 11.0144i | −0.160402 | − | 0.387245i | 0.823161 | − | 0.567808i | \(-0.192208\pi\) |
−0.983564 | + | 0.180562i | \(0.942208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.413214 | + | 2.07737i | −0.0145099 | + | 0.0729462i | −0.987362 | − | 0.158482i | \(-0.949340\pi\) |
0.972852 | + | 0.231428i | \(0.0743399\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.7413 | − | 38.5246i | 0.902788 | − | 1.35112i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.7551 | + | 21.7551i | −0.762047 | + | 0.762047i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.6936 | − | 11.6936i | −0.409109 | − | 0.409109i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.31121 | + | 0.876123i | 0.0458174 | + | 0.0306142i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.0479 | + | 9.15949i | 1.60708 | + | 0.319668i | 0.915403 | − | 0.402538i | \(-0.131872\pi\) |
0.691678 | + | 0.722206i | \(0.256872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.8242 | − | 18.1526i | 1.52761 | − | 0.632759i | 0.548515 | − | 0.836141i | \(-0.315193\pi\) |
0.979099 | + | 0.203382i | \(0.0651933\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.58471 | − | 1.48483i | −0.124804 | − | 0.0516953i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.79161 | − | 5.20619i | 0.270941 | − | 0.181037i | −0.412676 | − | 0.910878i | \(-0.635406\pi\) |
0.683617 | + | 0.729841i | \(0.260406\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.9119 | − | 54.8578i | −0.378986 | − | 1.90529i | −0.422747 | − | 0.906248i | \(-0.638934\pi\) |
0.0437617 | − | 0.999042i | \(-0.486066\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.18297 | −0.0410369 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.04568 | −0.278766 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.76040 | − | 13.8774i | −0.0955274 | − | 0.480249i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −36.6889 | + | 24.5147i | −1.26815 | + | 0.847354i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.4928 | + | 15.9443i | 1.32892 | + | 0.550457i | 0.930347 | − | 0.366680i | \(-0.119506\pi\) |
0.398573 | + | 0.917137i | \(0.369506\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.8783 | + | 9.47649i | −0.788906 | + | 0.326775i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.4807 | − | 2.48256i | −0.429857 | − | 0.0855038i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.1776 | − | 15.4867i | −0.797332 | − | 0.532760i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.04074 | − | 1.04074i | −0.0357604 | − | 0.0357604i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.8020 | − | 19.8020i | 0.679604 | − | 0.679604i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.1407 | + | 28.6461i | −0.656135 | + | 0.981976i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.22130 | − | 16.1946i | 0.110295 | − | 0.554491i | −0.885636 | − | 0.464379i | \(-0.846277\pi\) |
0.995932 | − | 0.0901121i | \(-0.0287225\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.4502 | − | 44.5427i | −0.630984 | − | 1.52333i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.26603 | + | 7.88490i | −0.111566 | + | 0.269343i | −0.969794 | − | 0.243924i | \(-0.921565\pi\) |
0.858229 | + | 0.513267i | \(0.171565\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.93549 | + | 5.88988i | 0.134277 | + | 0.200960i | 0.892515 | − | 0.451019i | \(-0.148939\pi\) |
−0.758237 | + | 0.651979i | \(0.773939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.90515 | + | 1.17461i | −0.201247 | + | 0.0400305i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.7071i | 0.602756i | 0.953505 | + | 0.301378i | \(0.0974466\pi\) | ||||
−0.953505 | + | 0.301378i | \(0.902553\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 42.2205i | 1.43554i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.8446 | + | 3.15168i | −0.538110 | + | 0.107037i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.84650 | − | 13.2397i | −0.300097 | − | 0.449127i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.216082 | + | 0.521667i | −0.00732165 | + | 0.0176760i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.0187 | + | 24.1873i | 0.339082 | + | 0.818616i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.87086 | + | 24.4875i | −0.164665 | + | 0.827827i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.3455 | + | 34.9391i | −0.788323 | + | 1.17981i | 0.191804 | + | 0.981433i | \(0.438566\pi\) |
−0.980126 | + | 0.198375i | \(0.936434\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 39.0360 | − | 39.0360i | 1.31665 | − | 1.31665i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.0191 | − | 22.0191i | −0.741844 | − | 0.741844i | 0.231089 | − | 0.972933i | \(-0.425771\pi\) |
−0.972933 | + | 0.231089i | \(0.925771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.7422 | + | 25.2185i | 1.27012 | + | 0.848670i | 0.993668 | − | 0.112356i | \(-0.0358398\pi\) |
0.276457 | + | 0.961026i | \(0.410840\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.05617 | + | 1.00573i | 0.169961 | + | 0.0338074i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.8061 | + | 18.5593i | −1.50444 | + | 0.623160i | −0.974402 | − | 0.224812i | \(-0.927823\pi\) |
−0.530040 | + | 0.847973i | \(0.677823\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.2045 | − | 4.22683i | −0.342247 | − | 0.141763i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.2908 | − | 23.5806i | 1.18229 | − | 0.789979i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.99485 | − | 40.1928i | −0.267537 | − | 1.34500i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.11345 | −0.137497 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.21649 | −0.0406175 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.67297 | + | 8.41060i | 0.0557968 | + | 0.280509i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.64224 | + | 1.09731i | −0.0547111 | + | 0.0365568i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29.0655 | − | 12.0393i | −0.967239 | − | 0.400644i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 38.8196 | − | 16.0796i | 1.29041 | − | 0.534504i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.1400 | + | 9.37673i | 1.56526 | + | 0.311349i | 0.900212 | − | 0.435453i | \(-0.143412\pi\) |
0.665047 | + | 0.746802i | \(0.268412\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.4855 | + | 19.7016i | 0.977972 | + | 0.653460i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.2741 | + | 36.2741i | 1.20182 | + | 1.20182i | 0.973614 | + | 0.228202i | \(0.0732847\pi\) |
0.228202 | + | 0.973614i | \(0.426715\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.7489 | − | 33.7489i | 1.11693 | − | 1.11693i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.93321 | + | 14.8661i | −0.328382 | + | 0.491458i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.16862 | + | 25.9844i | −0.170683 | + | 0.858081i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.2124 | + | 27.0692i | 0.369864 | + | 0.892932i | 0.993772 | + | 0.111433i | \(0.0355442\pi\) |
−0.623907 | + | 0.781498i | \(0.714456\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.8172 | − | 67.1567i | 0.916609 | − | 2.21289i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.640131 | − | 0.958024i | −0.0210702 | − | 0.0315337i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.80569 | − | 0.756999i | 0.125130 | − | 0.0248900i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 86.4036i | − | 2.83787i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.1312i | 1.38228i | 0.722722 | + | 0.691139i | \(0.242891\pi\) | ||||
−0.722722 | + | 0.691139i | \(0.757109\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.02402 | − | 1.59608i | 0.262976 | − | 0.0523093i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.85133 | − | 14.7436i | −0.322518 | − | 0.482682i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.04148 | − | 21.8281i | 0.295688 | − | 0.713854i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.2961 | + | 27.2713i | 0.369028 | + | 0.890913i | 0.993910 | + | 0.110194i | \(0.0351472\pi\) |
−0.624882 | + | 0.780719i | \(0.714853\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.32586 | + | 21.7476i | −0.141169 | + | 0.709705i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.97461 | − | 10.4382i | 0.227366 | − | 0.340277i | −0.700193 | − | 0.713953i | \(-0.746903\pi\) |
0.927559 | + | 0.373676i | \(0.121903\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.24114 | − | 2.24114i | 0.0729815 | − | 0.0729815i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −34.6716 | − | 34.6716i | −1.12787 | − | 1.12787i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.5016 | + | 8.35333i | 0.406249 | + | 0.271447i | 0.741861 | − | 0.670553i | \(-0.233943\pi\) |
−0.335612 | + | 0.942000i | \(0.608943\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.52080 | − | 0.302507i | −0.0493674 | − | 0.00981979i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −96.5906 | + | 40.0091i | −3.13216 | + | 1.29738i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.7086 | + | 17.6905i | 1.38347 | + | 0.573051i | 0.945407 | − | 0.325893i | \(-0.105665\pi\) |
0.438062 | + | 0.898945i | \(0.355665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.5944 | − | 15.0971i | 0.731138 | − | 0.488531i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.96431 | − | 19.9299i | −0.128148 | − | 0.644243i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.40877 | −0.0777832 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6430 | 0.440098 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.72606 | − | 43.8688i | −0.281193 | − | 1.41365i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.2679 | − | 7.52898i | 0.362727 | − | 0.242367i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.3386 | − | 14.6377i | −1.13641 | − | 0.470718i | −0.266457 | − | 0.963847i | \(-0.585853\pi\) |
−0.869956 | + | 0.493129i | \(0.835853\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.9079 | + | 14.0451i | −1.08928 | + | 0.451194i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.620988 | − | 0.123522i | −0.0199285 | − | 0.00396402i | 0.185116 | − | 0.982717i | \(-0.440734\pi\) |
−0.205044 | + | 0.978753i | \(0.565734\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.48692 | − | 3.66624i | −0.175903 | − | 0.117534i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0968801 | + | 0.0968801i | 0.00310265 | + | 0.00310265i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.4692 | − | 14.4692i | 0.462911 | − | 0.462911i | −0.436697 | − | 0.899608i | \(-0.643852\pi\) |
0.899608 | + | 0.436697i | \(0.143852\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.2641 | − | 34.8172i | 0.743524 | − | 1.11276i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.0549 | + | 125.960i | −0.799942 | + | 4.02158i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.41367 | − | 15.4840i | −0.204564 | − | 0.493862i | 0.787987 | − | 0.615692i | \(-0.211124\pi\) |
−0.992551 | + | 0.121831i | \(0.961124\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.0322 | + | 45.9477i | −0.606415 | + | 1.46402i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −43.3123 | − | 64.8214i | −1.37864 | − | 2.06329i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.2429 | − | 3.23091i | 0.516494 | − | 0.102737i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 53.4671i | − | 1.69844i | −0.528041 | − | 0.849219i | \(-0.677073\pi\) | ||
0.528041 | − | 0.849219i | \(-0.322927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 44.5709i | − | 1.41441i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.8998 | + | 6.14636i | −0.979590 | + | 0.194853i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.9595 | + | 26.8783i | 0.568783 | + | 0.851244i | 0.998666 | − | 0.0516411i | \(-0.0164452\pi\) |
−0.429883 | + | 0.902885i | \(0.641445\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40.0155 | + | 96.6059i | −1.26603 | + | 3.05648i |
(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 | 512.2.i.b.97.7 | 56 | ||
4.3 | odd | 2 | 512.2.i.a.97.1 | 56 | |||
8.3 | odd | 2 | 256.2.i.a.177.7 | 56 | |||
8.5 | even | 2 | 64.2.i.a.21.6 | ✓ | 56 | ||
24.5 | odd | 2 | 576.2.bd.a.469.2 | 56 | |||
64.3 | odd | 16 | 512.2.i.a.417.1 | 56 | |||
64.29 | even | 16 | 64.2.i.a.61.6 | yes | 56 | ||
64.35 | odd | 16 | 256.2.i.a.81.7 | 56 | |||
64.61 | even | 16 | inner | 512.2.i.b.417.7 | 56 | ||
192.29 | odd | 16 | 576.2.bd.a.253.2 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
64.2.i.a.21.6 | ✓ | 56 | 8.5 | even | 2 | ||
64.2.i.a.61.6 | yes | 56 | 64.29 | even | 16 | ||
256.2.i.a.81.7 | 56 | 64.35 | odd | 16 | |||
256.2.i.a.177.7 | 56 | 8.3 | odd | 2 | |||
512.2.i.a.97.1 | 56 | 4.3 | odd | 2 | |||
512.2.i.a.417.1 | 56 | 64.3 | odd | 16 | |||
512.2.i.b.97.7 | 56 | 1.1 | even | 1 | trivial | ||
512.2.i.b.417.7 | 56 | 64.61 | even | 16 | inner | ||
576.2.bd.a.253.2 | 56 | 192.29 | odd | 16 | |||
576.2.bd.a.469.2 | 56 | 24.5 | odd | 2 |