Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,2,Mod(81,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.j (of order \(6\), degree \(2\), 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: | \(2.29170653801\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 81.19 | ||
Character | \(\chi\) | \(=\) | 287.81 |
Dual form | 287.2.j.a.163.19 |
$q$-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 \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.649153 | + | 1.12437i | 0.459020 | + | 0.795046i | 0.998909 | − | 0.0466897i | \(-0.0148672\pi\) |
−0.539889 | + | 0.841736i | \(0.681534\pi\) | |||||||
\(3\) | −0.800607 | − | 0.462230i | −0.462230 | − | 0.266869i | 0.250751 | − | 0.968052i | \(-0.419322\pi\) |
−0.712982 | + | 0.701183i | \(0.752656\pi\) | |||||||
\(4\) | 0.157202 | − | 0.272281i | 0.0786008 | − | 0.136141i | ||||
\(5\) | −1.62887 | − | 2.82129i | −0.728454 | − | 1.26172i | −0.957536 | − | 0.288313i | \(-0.906906\pi\) |
0.229082 | − | 0.973407i | \(-0.426428\pi\) | |||||||
\(6\) | − | 1.20023i | − | 0.489993i | ||||||
\(7\) | −2.18878 | + | 1.48635i | −0.827282 | + | 0.561788i | ||||
\(8\) | 3.00480 | 1.06236 | ||||||||
\(9\) | −1.07269 | − | 1.85795i | −0.357562 | − | 0.619316i | ||||
\(10\) | 2.11478 | − | 3.66290i | 0.668751 | − | 1.15831i | ||||
\(11\) | −0.320547 | − | 0.185068i | −0.0966486 | − | 0.0558001i | 0.450897 | − | 0.892576i | \(-0.351104\pi\) |
−0.547545 | + | 0.836776i | \(0.684438\pi\) | |||||||
\(12\) | −0.251713 | + | 0.145327i | −0.0726634 | + | 0.0419522i | ||||
\(13\) | − | 4.50664i | − | 1.24992i | −0.780657 | − | 0.624959i | \(-0.785116\pi\) | ||
0.780657 | − | 0.624959i | \(-0.214884\pi\) | |||||||
\(14\) | −3.09205 | − | 1.49612i | −0.826386 | − | 0.399855i | ||||
\(15\) | 3.01166i | 0.777607i | ||||||||
\(16\) | 1.63617 | + | 2.83393i | 0.409043 | + | 0.708483i | ||||
\(17\) | −2.36362 | − | 1.36464i | −0.573263 | − | 0.330973i | 0.185189 | − | 0.982703i | \(-0.440710\pi\) |
−0.758451 | + | 0.651730i | \(0.774044\pi\) | |||||||
\(18\) | 1.39267 | − | 2.41218i | 0.328256 | − | 0.568557i | ||||
\(19\) | 6.50468 | − | 3.75548i | 1.49228 | − | 0.861566i | 0.492316 | − | 0.870417i | \(-0.336151\pi\) |
0.999961 | + | 0.00885034i | \(0.00281719\pi\) | |||||||
\(20\) | −1.02425 | −0.229028 | ||||||||
\(21\) | 2.43939 | − | 0.178260i | 0.532318 | − | 0.0388996i | ||||
\(22\) | − | 0.480549i | − | 0.102453i | ||||||
\(23\) | −0.0445877 | − | 0.0772281i | −0.00929717 | − | 0.0161032i | 0.861339 | − | 0.508030i | \(-0.169626\pi\) |
−0.870637 | + | 0.491927i | \(0.836293\pi\) | |||||||
\(24\) | −2.40566 | − | 1.38891i | −0.491054 | − | 0.283510i | ||||
\(25\) | −2.80646 | + | 4.86093i | −0.561292 | + | 0.972185i | ||||
\(26\) | 5.06712 | − | 2.92550i | 0.993743 | − | 0.573738i | ||||
\(27\) | 4.75669i | 0.915426i | ||||||||
\(28\) | 0.0606253 | + | 0.829621i | 0.0114571 | + | 0.156784i | ||||
\(29\) | 3.57090i | 0.663099i | 0.943438 | + | 0.331549i | \(0.107571\pi\) | ||||
−0.943438 | + | 0.331549i | \(0.892429\pi\) | |||||||
\(30\) | −3.38621 | + | 1.95503i | −0.618234 | + | 0.356937i | ||||
\(31\) | −4.13934 | + | 7.16954i | −0.743447 | + | 1.28769i | 0.207470 | + | 0.978241i | \(0.433477\pi\) |
−0.950917 | + | 0.309447i | \(0.899856\pi\) | |||||||
\(32\) | 0.880551 | − | 1.52516i | 0.155661 | − | 0.269613i | ||||
\(33\) | 0.171088 | + | 0.296333i | 0.0297826 | + | 0.0515850i | ||||
\(34\) | − | 3.54343i | − | 0.607694i | ||||||
\(35\) | 7.75868 | + | 3.75411i | 1.31146 | + | 0.634561i | ||||
\(36\) | −0.674512 | −0.112419 | ||||||||
\(37\) | 2.96124 | + | 5.12901i | 0.486824 | + | 0.843205i | 0.999885 | − | 0.0151476i | \(-0.00482182\pi\) |
−0.513061 | + | 0.858352i | \(0.671488\pi\) | |||||||
\(38\) | 8.44506 | + | 4.87576i | 1.36997 | + | 0.790953i | ||||
\(39\) | −2.08311 | + | 3.60805i | −0.333564 | + | 0.577750i | ||||
\(40\) | −4.89444 | − | 8.47742i | −0.773879 | − | 1.34040i | ||||
\(41\) | 3.85181 | − | 5.11503i | 0.601552 | − | 0.798834i | ||||
\(42\) | 1.78397 | + | 2.62705i | 0.275272 | + | 0.405362i | ||||
\(43\) | 2.91871 | 0.445099 | 0.222549 | − | 0.974921i | \(-0.428562\pi\) | ||||
0.222549 | + | 0.974921i | \(0.428562\pi\) | |||||||
\(44\) | −0.100781 | + | 0.0581860i | −0.0151933 | + | 0.00877186i | ||||
\(45\) | −3.49454 | + | 6.05272i | −0.520935 | + | 0.902286i | ||||
\(46\) | 0.0578884 | − | 0.100266i | 0.00853518 | − | 0.0147834i | ||||
\(47\) | −2.24736 | + | 1.29752i | −0.327811 | + | 0.189262i | −0.654869 | − | 0.755742i | \(-0.727276\pi\) |
0.327058 | + | 0.945004i | \(0.393943\pi\) | |||||||
\(48\) | − | 3.02515i | − | 0.436643i | ||||||
\(49\) | 2.58153 | − | 6.50659i | 0.368789 | − | 0.929513i | ||||
\(50\) | −7.28728 | −1.03058 | ||||||||
\(51\) | 1.26155 | + | 2.18508i | 0.176653 | + | 0.305972i | ||||
\(52\) | −1.22707 | − | 0.708452i | −0.170165 | − | 0.0982446i | ||||
\(53\) | −3.42381 | − | 1.97674i | −0.470297 | − | 0.271526i | 0.246067 | − | 0.969253i | \(-0.420862\pi\) |
−0.716364 | + | 0.697727i | \(0.754195\pi\) | |||||||
\(54\) | −5.34826 | + | 3.08782i | −0.727806 | + | 0.420199i | ||||
\(55\) | 1.20581i | 0.162591i | ||||||||
\(56\) | −6.57685 | + | 4.46619i | −0.878869 | + | 0.596820i | ||||
\(57\) | −6.94359 | −0.919701 | ||||||||
\(58\) | −4.01499 | + | 2.31806i | −0.527194 | + | 0.304376i | ||||
\(59\) | 3.66047 | − | 6.34012i | 0.476553 | − | 0.825414i | −0.523086 | − | 0.852280i | \(-0.675219\pi\) |
0.999639 | + | 0.0268661i | \(0.00855278\pi\) | |||||||
\(60\) | 0.820018 | + | 0.473438i | 0.105864 | + | 0.0611205i | ||||
\(61\) | −2.07023 | − | 3.58575i | −0.265066 | − | 0.459108i | 0.702515 | − | 0.711669i | \(-0.252061\pi\) |
−0.967581 | + | 0.252561i | \(0.918727\pi\) | |||||||
\(62\) | −10.7483 | −1.36503 | ||||||||
\(63\) | 5.10943 | + | 2.47225i | 0.643728 | + | 0.311474i | ||||
\(64\) | 8.83114 | 1.10389 | ||||||||
\(65\) | −12.7146 | + | 7.34075i | −1.57705 | + | 0.910508i | ||||
\(66\) | −0.222125 | + | 0.384731i | −0.0273416 | + | 0.0473571i | ||||
\(67\) | 6.61804 | + | 3.82093i | 0.808522 | + | 0.466800i | 0.846442 | − | 0.532480i | \(-0.178740\pi\) |
−0.0379203 | + | 0.999281i | \(0.512073\pi\) | |||||||
\(68\) | −0.743131 | + | 0.429047i | −0.0901178 | + | 0.0520296i | ||||
\(69\) | 0.0824391i | 0.00992450i | ||||||||
\(70\) | 0.815569 | + | 11.1606i | 0.0974792 | + | 1.33394i | ||||
\(71\) | − | 5.81834i | − | 0.690510i | −0.938509 | − | 0.345255i | \(-0.887792\pi\) | ||
0.938509 | − | 0.345255i | \(-0.112208\pi\) | |||||||
\(72\) | −3.22321 | − | 5.58276i | −0.379859 | − | 0.657935i | ||||
\(73\) | −2.08152 | + | 3.60530i | −0.243623 | + | 0.421968i | −0.961744 | − | 0.273951i | \(-0.911669\pi\) |
0.718120 | + | 0.695919i | \(0.245003\pi\) | |||||||
\(74\) | −3.84459 | + | 6.65903i | −0.446925 | + | 0.774096i | ||||
\(75\) | 4.49374 | − | 2.59446i | 0.518892 | − | 0.299582i | ||||
\(76\) | − | 2.36147i | − | 0.270879i | ||||||
\(77\) | 0.976683 | − | 0.0713720i | 0.111303 | − | 0.00813359i | ||||
\(78\) | −5.40902 | −0.612451 | ||||||||
\(79\) | 14.6944 | − | 8.48380i | 1.65325 | − | 0.954502i | 0.677520 | − | 0.735504i | \(-0.263055\pi\) |
0.975725 | − | 0.218997i | \(-0.0702786\pi\) | |||||||
\(80\) | 5.33023 | − | 9.23224i | 0.595938 | − | 1.03220i | ||||
\(81\) | −1.01937 | + | 1.76560i | −0.113263 | + | 0.196178i | ||||
\(82\) | 8.25158 | + | 1.01041i | 0.911234 | + | 0.111581i | ||||
\(83\) | −9.85782 | −1.08204 | −0.541018 | − | 0.841011i | \(-0.681961\pi\) | ||||
−0.541018 | + | 0.841011i | \(0.681961\pi\) | |||||||
\(84\) | 0.334939 | − | 0.692222i | 0.0365448 | − | 0.0755277i | ||||
\(85\) | 8.89129i | 0.964396i | ||||||||
\(86\) | 1.89469 | + | 3.28169i | 0.204309 | + | 0.353874i | ||||
\(87\) | 1.65058 | − | 2.85888i | 0.176960 | − | 0.306504i | ||||
\(88\) | −0.963181 | − | 0.556093i | −0.102675 | − | 0.0592797i | ||||
\(89\) | 1.18830 | − | 0.686067i | 0.125960 | − | 0.0727229i | −0.435696 | − | 0.900094i | \(-0.643498\pi\) |
0.561656 | + | 0.827371i | \(0.310164\pi\) | |||||||
\(90\) | −9.07396 | −0.956479 | ||||||||
\(91\) | 6.69845 | + | 9.86406i | 0.702189 | + | 1.03403i | ||||
\(92\) | −0.0280370 | −0.00292306 | ||||||||
\(93\) | 6.62796 | − | 3.82666i | 0.687288 | − | 0.396806i | ||||
\(94\) | −2.91776 | − | 1.68457i | −0.300944 | − | 0.173750i | ||||
\(95\) | −21.1906 | − | 12.2344i | −2.17411 | − | 1.25522i | ||||
\(96\) | −1.40995 | + | 0.814035i | −0.143902 | + | 0.0830821i | ||||
\(97\) | 7.21852i | 0.732929i | 0.930432 | + | 0.366465i | \(0.119432\pi\) | ||||
−0.930432 | + | 0.366465i | \(0.880568\pi\) | |||||||
\(98\) | 8.99159 | − | 1.32119i | 0.908288 | − | 0.133461i | ||||
\(99\) | 0.794079i | 0.0798080i | ||||||||
\(100\) | 0.882359 | + | 1.52829i | 0.0882359 | + | 0.152829i | ||||
\(101\) | 14.9419 | + | 8.62671i | 1.48677 | + | 0.858389i | 0.999886 | − | 0.0150750i | \(-0.00479870\pi\) |
0.486888 | + | 0.873464i | \(0.338132\pi\) | |||||||
\(102\) | −1.63788 | + | 2.83690i | −0.162175 | + | 0.280895i | ||||
\(103\) | 4.12556 | + | 7.14567i | 0.406503 | + | 0.704084i | 0.994495 | − | 0.104783i | \(-0.0334147\pi\) |
−0.587992 | + | 0.808867i | \(0.700081\pi\) | |||||||
\(104\) | − | 13.5416i | − | 1.32786i | ||||||
\(105\) | −4.47638 | − | 6.59186i | −0.436850 | − | 0.643300i | ||||
\(106\) | − | 5.13282i | − | 0.498544i | ||||||
\(107\) | −6.84998 | − | 11.8645i | −0.662213 | − | 1.14699i | −0.980033 | − | 0.198835i | \(-0.936284\pi\) |
0.317820 | − | 0.948151i | \(-0.397049\pi\) | |||||||
\(108\) | 1.29516 | + | 0.747760i | 0.124627 | + | 0.0719532i | ||||
\(109\) | 5.60991 | + | 3.23888i | 0.537332 | + | 0.310229i | 0.743997 | − | 0.668183i | \(-0.232928\pi\) |
−0.206665 | + | 0.978412i | \(0.566261\pi\) | |||||||
\(110\) | −1.35577 | + | 0.782754i | −0.129268 | + | 0.0746327i | ||||
\(111\) | − | 5.47510i | − | 0.519673i | ||||||
\(112\) | −7.79344 | − | 3.77093i | −0.736411 | − | 0.356320i | ||||
\(113\) | 11.3001 | 1.06302 | 0.531510 | − | 0.847052i | \(-0.321625\pi\) | ||||
0.531510 | + | 0.847052i | \(0.321625\pi\) | |||||||
\(114\) | −4.50745 | − | 7.80713i | −0.422161 | − | 0.731205i | ||||
\(115\) | −0.145255 | + | 0.251590i | −0.0135451 | + | 0.0234608i | ||||
\(116\) | 0.972288 | + | 0.561351i | 0.0902746 | + | 0.0521201i | ||||
\(117\) | −8.37311 | + | 4.83422i | −0.774094 | + | 0.446923i | ||||
\(118\) | 9.50482 | 0.874990 | ||||||||
\(119\) | 7.20178 | − | 0.526277i | 0.660187 | − | 0.0482437i | ||||
\(120\) | 9.04944i | 0.826097i | ||||||||
\(121\) | −5.43150 | − | 9.40763i | −0.493773 | − | 0.855239i | ||||
\(122\) | 2.68780 | − | 4.65540i | 0.243342 | − | 0.421480i | ||||
\(123\) | −5.44811 | + | 2.31470i | −0.491239 | + | 0.208710i | ||||
\(124\) | 1.30142 | + | 2.25413i | 0.116871 | + | 0.202427i | ||||
\(125\) | 1.99672 | 0.178592 | ||||||||
\(126\) | 0.537089 | + | 7.34974i | 0.0478477 | + | 0.654767i | ||||
\(127\) | 4.82132 | 0.427823 | 0.213911 | − | 0.976853i | \(-0.431380\pi\) | ||||
0.213911 | + | 0.976853i | \(0.431380\pi\) | |||||||
\(128\) | 3.97165 | + | 6.87911i | 0.351048 | + | 0.608033i | ||||
\(129\) | −2.33674 | − | 1.34912i | −0.205738 | − | 0.118783i | ||||
\(130\) | −16.5074 | − | 9.53054i | −1.44779 | − | 0.835884i | ||||
\(131\) | −2.00722 | − | 3.47661i | −0.175372 | − | 0.303753i | 0.764918 | − | 0.644128i | \(-0.222779\pi\) |
−0.940290 | + | 0.340375i | \(0.889446\pi\) | |||||||
\(132\) | 0.107581 | 0.00936375 | ||||||||
\(133\) | −8.65537 | + | 17.8882i | −0.750516 | + | 1.55110i | ||||
\(134\) | 9.92146i | 0.857083i | ||||||||
\(135\) | 13.4200 | − | 7.74805i | 1.15501 | − | 0.666846i | ||||
\(136\) | −7.10222 | − | 4.10047i | −0.609010 | − | 0.351612i | ||||
\(137\) | −18.1498 | − | 10.4788i | −1.55064 | − | 0.895262i | −0.998090 | − | 0.0617811i | \(-0.980322\pi\) |
−0.552549 | − | 0.833480i | \(-0.686345\pi\) | |||||||
\(138\) | −0.0926916 | + | 0.0535155i | −0.00789044 | + | 0.00455555i | ||||
\(139\) | 11.4687 | 0.972761 | 0.486381 | − | 0.873747i | \(-0.338317\pi\) | ||||
0.486381 | + | 0.873747i | \(0.338317\pi\) | |||||||
\(140\) | 2.24185 | − | 1.52239i | 0.189471 | − | 0.128665i | ||||
\(141\) | 2.39900 | 0.202033 | ||||||||
\(142\) | 6.54195 | − | 3.77699i | 0.548988 | − | 0.316958i | ||||
\(143\) | −0.834035 | + | 1.44459i | −0.0697455 | + | 0.120803i | ||||
\(144\) | 3.51020 | − | 6.07984i | 0.292517 | − | 0.506653i | ||||
\(145\) | 10.0745 | − | 5.81654i | 0.836645 | − | 0.483037i | ||||
\(146\) | −5.40490 | −0.447312 | ||||||||
\(147\) | −5.07433 | + | 4.01596i | −0.418524 | + | 0.331231i | ||||
\(148\) | 1.86205 | 0.153059 | ||||||||
\(149\) | −5.27942 | + | 3.04808i | −0.432507 | + | 0.249708i | −0.700414 | − | 0.713737i | \(-0.747001\pi\) |
0.267907 | + | 0.963445i | \(0.413668\pi\) | |||||||
\(150\) | 5.83424 | + | 3.36840i | 0.476364 | + | 0.275029i | ||||
\(151\) | −2.85099 | − | 1.64602i | −0.232010 | − | 0.133951i | 0.379489 | − | 0.925196i | \(-0.376100\pi\) |
−0.611499 | + | 0.791245i | \(0.709433\pi\) | |||||||
\(152\) | 19.5453 | − | 11.2845i | 1.58533 | − | 0.915292i | ||||
\(153\) | 5.85532i | 0.473374i | ||||||||
\(154\) | 0.714265 | + | 1.05182i | 0.0575571 | + | 0.0847579i | ||||
\(155\) | 26.9698 | 2.16627 | ||||||||
\(156\) | 0.654936 | + | 1.13438i | 0.0524368 | + | 0.0908233i | ||||
\(157\) | 17.5828 | + | 10.1514i | 1.40326 | + | 0.810171i | 0.994725 | − | 0.102573i | \(-0.0327075\pi\) |
0.408532 | + | 0.912744i | \(0.366041\pi\) | |||||||
\(158\) | 19.0778 | + | 11.0146i | 1.51775 | + | 0.876271i | ||||
\(159\) | 1.82742 | + | 3.16518i | 0.144924 | + | 0.251015i | ||||
\(160\) | −5.73723 | −0.453567 | ||||||||
\(161\) | 0.212381 | + | 0.102763i | 0.0167379 | + | 0.00809882i | ||||
\(162\) | −2.64691 | −0.207961 | ||||||||
\(163\) | 7.62545 | + | 13.2077i | 0.597271 | + | 1.03450i | 0.993222 | + | 0.116233i | \(0.0370818\pi\) |
−0.395951 | + | 0.918272i | \(0.629585\pi\) | |||||||
\(164\) | −0.787215 | − | 1.85287i | −0.0614712 | − | 0.144685i | ||||
\(165\) | 0.557362 | − | 0.965379i | 0.0433905 | − | 0.0751546i | ||||
\(166\) | −6.39923 | − | 11.0838i | −0.496677 | − | 0.860269i | ||||
\(167\) | 4.99262i | 0.386341i | 0.981165 | + | 0.193170i | \(0.0618770\pi\) | ||||
−0.981165 | + | 0.193170i | \(0.938123\pi\) | |||||||
\(168\) | 7.32988 | − | 0.535637i | 0.565513 | − | 0.0413253i | ||||
\(169\) | −7.30985 | −0.562296 | ||||||||
\(170\) | −9.99706 | + | 5.77181i | −0.766740 | + | 0.442677i | ||||
\(171\) | −13.9550 | − | 8.05690i | −1.06716 | − | 0.616127i | ||||
\(172\) | 0.458826 | − | 0.794709i | 0.0349851 | − | 0.0605960i | ||||
\(173\) | −3.93376 | − | 6.81347i | −0.299078 | − | 0.518018i | 0.676847 | − | 0.736124i | \(-0.263346\pi\) |
−0.975925 | + | 0.218105i | \(0.930012\pi\) | |||||||
\(174\) | 4.28590 | 0.324914 | ||||||||
\(175\) | −1.08232 | − | 14.8109i | −0.0818156 | − | 1.11960i | ||||
\(176\) | − | 1.21121i | − | 0.0912985i | ||||||
\(177\) | −5.86119 | + | 3.38396i | −0.440554 | + | 0.254354i | ||||
\(178\) | 1.54278 | + | 0.890724i | 0.115636 | + | 0.0667626i | ||||
\(179\) | −15.6160 | − | 9.01589i | −1.16719 | − | 0.673879i | −0.214176 | − | 0.976795i | \(-0.568707\pi\) |
−0.953017 | + | 0.302916i | \(0.902040\pi\) | |||||||
\(180\) | 1.09869 | + | 1.90299i | 0.0818919 | + | 0.141841i | ||||
\(181\) | − | 2.39196i | − | 0.177793i | −0.996041 | − | 0.0888966i | \(-0.971666\pi\) | ||
0.996041 | − | 0.0888966i | \(-0.0283341\pi\) | |||||||
\(182\) | −6.74249 | + | 13.9348i | −0.499787 | + | 1.03292i | ||||
\(183\) | 3.82770i | 0.282952i | ||||||||
\(184\) | −0.133977 | − | 0.232055i | −0.00987692 | − | 0.0171073i | ||||
\(185\) | 9.64696 | − | 16.7090i | 0.709259 | − | 1.22847i | ||||
\(186\) | 8.60512 | + | 4.96817i | 0.630958 | + | 0.364284i | ||||
\(187\) | 0.505102 | + | 0.874862i | 0.0369367 | + | 0.0639762i | ||||
\(188\) | 0.815886i | 0.0595046i | ||||||||
\(189\) | −7.07011 | − | 10.4114i | −0.514275 | − | 0.757315i | ||||
\(190\) | − | 31.7680i | − | 2.30469i | ||||||
\(191\) | 10.6743 | − | 6.16280i | 0.772364 | − | 0.445924i | −0.0613535 | − | 0.998116i | \(-0.519542\pi\) |
0.833717 | + | 0.552192i | \(0.186208\pi\) | |||||||
\(192\) | −7.07027 | − | 4.08202i | −0.510252 | − | 0.294594i | ||||
\(193\) | −0.821104 | − | 0.474065i | −0.0591044 | − | 0.0341239i | 0.470157 | − | 0.882583i | \(-0.344197\pi\) |
−0.529261 | + | 0.848459i | \(0.677531\pi\) | |||||||
\(194\) | −8.11625 | + | 4.68592i | −0.582713 | + | 0.336429i | ||||
\(195\) | 13.5725 | 0.971945 | ||||||||
\(196\) | −1.36580 | − | 1.72575i | −0.0975573 | − | 0.123268i | ||||
\(197\) | −13.4798 | −0.960395 | −0.480197 | − | 0.877160i | \(-0.659435\pi\) | ||||
−0.480197 | + | 0.877160i | \(0.659435\pi\) | |||||||
\(198\) | −0.892835 | + | 0.515479i | −0.0634510 | + | 0.0366335i | ||||
\(199\) | −18.3342 | − | 10.5852i | −1.29968 | − | 0.750368i | −0.319328 | − | 0.947644i | \(-0.603457\pi\) |
−0.980348 | + | 0.197276i | \(0.936790\pi\) | |||||||
\(200\) | −8.43285 | + | 14.6061i | −0.596293 | + | 1.03281i | ||||
\(201\) | −3.53230 | − | 6.11812i | −0.249149 | − | 0.431539i | ||||
\(202\) | 22.4002i | 1.57607i | ||||||||
\(203\) | −5.30760 | − | 7.81591i | −0.372521 | − | 0.548569i | ||||
\(204\) | 0.793274 | 0.0555403 | ||||||||
\(205\) | −20.7051 | − | 2.53535i | −1.44611 | − | 0.177077i | ||||
\(206\) | −5.35623 | + | 9.27727i | −0.373186 | + | 0.646378i | ||||
\(207\) | −0.0956571 | + | 0.165683i | −0.00664863 | + | 0.0115158i | ||||
\(208\) | 12.7715 | − | 7.37365i | 0.885546 | − | 0.511270i | ||||
\(209\) | −2.78008 | −0.192302 | ||||||||
\(210\) | 4.50581 | − | 9.31221i | 0.310930 | − | 0.642604i | ||||
\(211\) | 4.58129i | 0.315389i | 0.987488 | + | 0.157694i | \(0.0504061\pi\) | ||||
−0.987488 | + | 0.157694i | \(0.949594\pi\) | |||||||
\(212\) | −1.07646 | + | 0.621493i | −0.0739314 | + | 0.0426843i | ||||
\(213\) | −2.68942 | + | 4.65820i | −0.184276 | + | 0.319175i | ||||
\(214\) | 8.89337 | − | 15.4038i | 0.607938 | − | 1.05298i | ||||
\(215\) | −4.75421 | − | 8.23453i | −0.324234 | − | 0.561590i | ||||
\(216\) | 14.2929i | 0.972510i | ||||||||
\(217\) | −1.59635 | − | 21.8451i | −0.108367 | − | 1.48294i | ||||
\(218\) | 8.41012i | 0.569605i | ||||||||
\(219\) | 3.33296 | − | 1.92428i | 0.225220 | − | 0.130031i | ||||
\(220\) | 0.328319 | + | 0.189555i | 0.0221353 | + | 0.0127798i | ||||
\(221\) | −6.14994 | + | 10.6520i | −0.413690 | + | 0.716532i | ||||
\(222\) | 6.15601 | − | 3.55417i | 0.413164 | − | 0.238540i | ||||
\(223\) | 10.6545 | 0.713477 | 0.356739 | − | 0.934204i | \(-0.383889\pi\) | ||||
0.356739 | + | 0.934204i | \(0.383889\pi\) | |||||||
\(224\) | 0.339587 | + | 4.64705i | 0.0226896 | + | 0.310494i | ||||
\(225\) | 12.0418 | 0.802786 | ||||||||
\(226\) | 7.33546 | + | 12.7054i | 0.487948 | + | 0.845150i | ||||
\(227\) | 8.41999 | + | 4.86128i | 0.558854 | + | 0.322655i | 0.752686 | − | 0.658380i | \(-0.228758\pi\) |
−0.193831 | + | 0.981035i | \(0.562091\pi\) | |||||||
\(228\) | −1.09154 | + | 1.89061i | −0.0722892 | + | 0.125209i | ||||
\(229\) | −18.5636 | + | 10.7177i | −1.22672 | + | 0.708245i | −0.966341 | − | 0.257263i | \(-0.917179\pi\) |
−0.260374 | + | 0.965508i | \(0.583846\pi\) | |||||||
\(230\) | −0.377171 | −0.0248699 | ||||||||
\(231\) | −0.814929 | − | 0.394312i | −0.0536184 | − | 0.0259438i | ||||
\(232\) | 10.7298i | 0.704448i | ||||||||
\(233\) | 20.0911 | − | 11.5996i | 1.31621 | − | 0.759917i | 0.333097 | − | 0.942893i | \(-0.391906\pi\) |
0.983117 | + | 0.182976i | \(0.0585731\pi\) | |||||||
\(234\) | −10.8708 | − | 6.27629i | −0.710650 | − | 0.410294i | ||||
\(235\) | 7.32134 | + | 4.22698i | 0.477591 | + | 0.275737i | ||||
\(236\) | −1.15086 | − | 1.99335i | −0.0749149 | − | 0.129756i | ||||
\(237\) | −15.6859 | −1.01891 | ||||||||
\(238\) | 5.26679 | + | 7.75580i | 0.341395 | + | 0.502734i | ||||
\(239\) | 27.7775i | 1.79677i | 0.439204 | + | 0.898387i | \(0.355261\pi\) | ||||
−0.439204 | + | 0.898387i | \(0.644739\pi\) | |||||||
\(240\) | −8.53484 | + | 4.92759i | −0.550922 | + | 0.318075i | ||||
\(241\) | 11.9356 | − | 20.6730i | 0.768838 | − | 1.33167i | −0.169355 | − | 0.985555i | \(-0.554168\pi\) |
0.938193 | − | 0.346112i | \(-0.112498\pi\) | |||||||
\(242\) | 7.05175 | − | 12.2140i | 0.453303 | − | 0.785144i | ||||
\(243\) | 13.9905 | − | 8.07741i | 0.897490 | − | 0.518166i | ||||
\(244\) | −1.30178 | −0.0833377 | ||||||||
\(245\) | −22.5620 | + | 3.31518i | −1.44143 | + | 0.211799i | ||||
\(246\) | −6.13923 | − | 4.62307i | −0.391423 | − | 0.294756i | ||||
\(247\) | −16.9246 | − | 29.3143i | −1.07689 | − | 1.86522i | ||||
\(248\) | −12.4379 | + | 21.5431i | −0.789807 | + | 1.36799i | ||||
\(249\) | 7.89224 | + | 4.55659i | 0.500150 | + | 0.288762i | ||||
\(250\) | 1.29618 | + | 2.24505i | 0.0819775 | + | 0.141989i | ||||
\(251\) | −13.1080 | −0.827369 | −0.413685 | − | 0.910420i | \(-0.635758\pi\) | ||||
−0.413685 | + | 0.910420i | \(0.635758\pi\) | |||||||
\(252\) | 1.47636 | − | 1.00256i | 0.0930019 | − | 0.0631554i | ||||
\(253\) | 0.0330070i | 0.00207513i | ||||||||
\(254\) | 3.12977 | + | 5.42092i | 0.196379 | + | 0.340139i | ||||
\(255\) | 4.10983 | − | 7.11843i | 0.257367 | − | 0.445773i | ||||
\(256\) | 3.67472 | − | 6.36480i | 0.229670 | − | 0.397800i | ||||
\(257\) | −23.4392 | + | 13.5326i | −1.46210 | + | 0.844143i | −0.999108 | − | 0.0422210i | \(-0.986557\pi\) |
−0.462990 | + | 0.886364i | \(0.653223\pi\) | |||||||
\(258\) | − | 3.50313i | − | 0.218095i | ||||||
\(259\) | −14.1050 | − | 6.82485i | −0.876443 | − | 0.424076i | ||||
\(260\) | 4.61591i | 0.286267i | ||||||||
\(261\) | 6.63453 | − | 3.83045i | 0.410667 | − | 0.237099i | ||||
\(262\) | 2.60599 | − | 4.51370i | 0.160998 | − | 0.278858i | ||||
\(263\) | 14.6829 | + | 8.47715i | 0.905384 | + | 0.522724i | 0.878943 | − | 0.476927i | \(-0.158249\pi\) |
0.0264410 | + | 0.999650i | \(0.491583\pi\) | |||||||
\(264\) | 0.514086 | + | 0.890423i | 0.0316398 | + | 0.0548017i | ||||
\(265\) | 12.8794i | 0.791177i | ||||||||
\(266\) | −25.7315 | + | 1.88035i | −1.57770 | + | 0.115292i | ||||
\(267\) | −1.26848 | −0.0776299 | ||||||||
\(268\) | 2.08073 | − | 1.20131i | 0.127101 | − | 0.0733818i | ||||
\(269\) | −8.61346 | + | 14.9189i | −0.525172 | + | 0.909624i | 0.474399 | + | 0.880310i | \(0.342666\pi\) |
−0.999570 | + | 0.0293139i | \(0.990668\pi\) | |||||||
\(270\) | 17.4233 | + | 10.0593i | 1.06035 | + | 0.612192i | ||||
\(271\) | 15.0859 | + | 26.1295i | 0.916401 | + | 1.58725i | 0.804837 | + | 0.593496i | \(0.202253\pi\) |
0.111564 | + | 0.993757i | \(0.464414\pi\) | |||||||
\(272\) | − | 8.93113i | − | 0.541530i | ||||||
\(273\) | −0.803357 | − | 10.9935i | −0.0486214 | − | 0.665354i | ||||
\(274\) | − | 27.2093i | − | 1.64377i | ||||||
\(275\) | 1.79920 | − | 1.03877i | 0.108496 | − | 0.0626402i | ||||
\(276\) | 0.0224466 | + | 0.0129596i | 0.00135113 | + | 0.000780074i | ||||
\(277\) | −3.06362 | + | 5.30635i | −0.184075 | + | 0.318828i | −0.943265 | − | 0.332042i | \(-0.892262\pi\) |
0.759189 | + | 0.650870i | \(0.225596\pi\) | |||||||
\(278\) | 7.44493 | + | 12.8950i | 0.446517 | + | 0.773390i | ||||
\(279\) | 17.7608 | 1.06331 | ||||||||
\(280\) | 23.3133 | + | 11.2804i | 1.39324 | + | 0.674131i | ||||
\(281\) | 13.8056i | 0.823574i | 0.911280 | + | 0.411787i | \(0.135095\pi\) | ||||
−0.911280 | + | 0.411787i | \(0.864905\pi\) | |||||||
\(282\) | 1.55732 | + | 2.69736i | 0.0927370 | + | 0.160625i | ||||
\(283\) | −11.8443 | + | 20.5150i | −0.704073 | + | 1.21949i | 0.262952 | + | 0.964809i | \(0.415304\pi\) |
−0.967025 | + | 0.254682i | \(0.918029\pi\) | |||||||
\(284\) | −1.58423 | − | 0.914653i | −0.0940065 | − | 0.0542747i | ||||
\(285\) | 11.3102 | + | 19.5899i | 0.669960 | + | 1.16040i | ||||
\(286\) | −2.16567 | −0.128058 | ||||||||
\(287\) | −0.828050 | + | 16.9208i | −0.0488782 | + | 0.998805i | ||||
\(288\) | −3.77822 | −0.222634 | ||||||||
\(289\) | −4.77552 | − | 8.27145i | −0.280913 | − | 0.486556i | ||||
\(290\) | 13.0798 | + | 7.55164i | 0.768074 | + | 0.443448i | ||||
\(291\) | 3.33662 | − | 5.77919i | 0.195596 | − | 0.338782i | ||||
\(292\) | 0.654436 | + | 1.13352i | 0.0382980 | + | 0.0663341i | ||||
\(293\) | 3.71283i | 0.216906i | 0.994102 | + | 0.108453i | \(0.0345896\pi\) | ||||
−0.994102 | + | 0.108453i | \(0.965410\pi\) | |||||||
\(294\) | −7.80942 | − | 3.09843i | −0.455455 | − | 0.180704i | ||||
\(295\) | −23.8498 | −1.38859 | ||||||||
\(296\) | 8.89793 | + | 15.4117i | 0.517182 | + | 0.895785i | ||||
\(297\) | 0.880312 | − | 1.52474i | 0.0510809 | − | 0.0884747i | ||||
\(298\) | −6.85430 | − | 3.95733i | −0.397059 | − | 0.229242i | ||||
\(299\) | −0.348040 | + | 0.200941i | −0.0201276 | + | 0.0116207i | ||||
\(300\) | − | 1.63141i | − | 0.0941897i | ||||||
\(301\) | −6.38841 | + | 4.33822i | −0.368222 | + | 0.250051i | ||||
\(302\) | − | 4.27408i | − | 0.245945i | ||||||
\(303\) | −7.97505 | − | 13.8132i | −0.458155 | − | 0.793547i | ||||
\(304\) | 21.2856 | + | 12.2892i | 1.22081 | + | 0.704835i | ||||
\(305\) | −6.74430 | + | 11.6815i | −0.386178 | + | 0.668879i | ||||
\(306\) | −6.58351 | + | 3.80099i | −0.376354 | + | 0.217288i | ||||
\(307\) | 17.3521 | 0.990338 | 0.495169 | − | 0.868797i | \(-0.335106\pi\) | ||||
0.495169 | + | 0.868797i | \(0.335106\pi\) | |||||||
\(308\) | 0.134103 | − | 0.277152i | 0.00764122 | − | 0.0157922i | ||||
\(309\) | − | 7.62783i | − | 0.433932i | ||||||
\(310\) | 17.5075 | + | 30.3239i | 0.994361 | + | 1.72228i | ||||
\(311\) | 13.7214 | + | 7.92203i | 0.778067 | + | 0.449217i | 0.835745 | − | 0.549118i | \(-0.185036\pi\) |
−0.0576779 | + | 0.998335i | \(0.518370\pi\) | |||||||
\(312\) | −6.25933 | + | 10.8415i | −0.354365 | + | 0.613778i | ||||
\(313\) | −20.0741 | + | 11.5898i | −1.13465 | + | 0.655092i | −0.945101 | − | 0.326779i | \(-0.894037\pi\) |
−0.189552 | + | 0.981871i | \(0.560703\pi\) | |||||||
\(314\) | 26.3593i | 1.48754i | ||||||||
\(315\) | −1.34768 | − | 18.4422i | −0.0759331 | − | 1.03910i | ||||
\(316\) | − | 5.33467i | − | 0.300098i | ||||||
\(317\) | 9.96567 | − | 5.75368i | 0.559728 | − | 0.323159i | −0.193309 | − | 0.981138i | \(-0.561922\pi\) |
0.753036 | + | 0.657979i | \(0.228589\pi\) | |||||||
\(318\) | −2.37255 | + | 4.10937i | −0.133046 | + | 0.230442i | ||||
\(319\) | 0.660858 | − | 1.14464i | 0.0370010 | − | 0.0640875i | ||||
\(320\) | −14.3848 | − | 24.9152i | −0.804135 | − | 1.39280i | ||||
\(321\) | 12.6651i | 0.706896i | ||||||||
\(322\) | 0.0223248 | + | 0.305502i | 0.00124411 | + | 0.0170250i | ||||
\(323\) | −20.4995 | −1.14062 | ||||||||
\(324\) | 0.320493 | + | 0.555110i | 0.0178052 | + | 0.0308395i | ||||
\(325\) | 21.9065 | + | 12.6477i | 1.21515 | + | 0.701569i | ||||
\(326\) | −9.90016 | + | 17.1476i | −0.548319 | + | 0.949717i | ||||
\(327\) | −2.99422 | − | 5.18614i | −0.165581 | − | 0.286794i | ||||
\(328\) | 11.5739 | − | 15.3697i | 0.639064 | − | 0.848647i | ||||
\(329\) | 2.99042 | − | 6.18034i | 0.164867 | − | 0.340733i | ||||
\(330\) | 1.44725 | 0.0796685 | ||||||||
\(331\) | −1.55916 | + | 0.900183i | −0.0856993 | + | 0.0494785i | −0.542237 | − | 0.840225i | \(-0.682423\pi\) |
0.456538 | + | 0.889704i | \(0.349089\pi\) | |||||||
\(332\) | −1.54967 | + | 2.68410i | −0.0850490 | + | 0.147309i | ||||
\(333\) | 6.35296 | − | 11.0036i | 0.348140 | − | 0.602996i | ||||
\(334\) | −5.61353 | + | 3.24097i | −0.307159 | + | 0.177338i | ||||
\(335\) | − | 24.8952i | − | 1.36017i | ||||||
\(336\) | 4.49644 | + | 6.62140i | 0.245301 | + | 0.361227i | ||||
\(337\) | −32.4253 | −1.76632 | −0.883158 | − | 0.469075i | \(-0.844587\pi\) | ||||
−0.883158 | + | 0.469075i | \(0.844587\pi\) | |||||||
\(338\) | −4.74521 | − | 8.21894i | −0.258105 | − | 0.447051i | ||||
\(339\) | −9.04690 | − | 5.22323i | −0.491360 | − | 0.283687i | ||||
\(340\) | 2.42093 | + | 1.39773i | 0.131293 | + | 0.0758023i | ||||
\(341\) | 2.65371 | − | 1.53212i | 0.143706 | − | 0.0829688i | ||||
\(342\) | − | 20.9206i | − | 1.13126i | ||||||
\(343\) | 4.02068 | + | 18.0786i | 0.217096 | + | 0.976150i | ||||
\(344\) | 8.77014 | 0.472854 | ||||||||
\(345\) | 0.232585 | − | 0.134283i | 0.0125219 | − | 0.00722954i | ||||
\(346\) | 5.10722 | − | 8.84596i | 0.274566 | − | 0.475562i | ||||
\(347\) | 3.41052 | + | 1.96907i | 0.183087 | + | 0.105705i | 0.588742 | − | 0.808321i | \(-0.299623\pi\) |
−0.405656 | + | 0.914026i | \(0.632957\pi\) | |||||||
\(348\) | −0.518947 | − | 0.898842i | −0.0278185 | − | 0.0481830i | ||||
\(349\) | −17.9009 | −0.958211 | −0.479106 | − | 0.877757i | \(-0.659039\pi\) | ||||
−0.479106 | + | 0.877757i | \(0.659039\pi\) | |||||||
\(350\) | 15.9503 | − | 10.8314i | 0.852577 | − | 0.578965i | ||||
\(351\) | 21.4367 | 1.14421 | ||||||||
\(352\) | −0.564516 | + | 0.325924i | −0.0300888 | + | 0.0173718i | ||||
\(353\) | 12.4338 | − | 21.5360i | 0.661784 | − | 1.14624i | −0.318362 | − | 0.947969i | \(-0.603133\pi\) |
0.980146 | − | 0.198275i | \(-0.0635338\pi\) | |||||||
\(354\) | −7.60962 | − | 4.39342i | −0.404447 | − | 0.233507i | ||||
\(355\) | −16.4152 | + | 9.47735i | −0.871231 | + | 0.503005i | ||||
\(356\) | − | 0.431403i | − | 0.0228643i | ||||||
\(357\) | −6.00906 | − | 2.90754i | −0.318033 | − | 0.153883i | ||||
\(358\) | − | 23.4108i | − | 1.23730i | ||||||
\(359\) | −15.9680 | − | 27.6574i | −0.842760 | − | 1.45970i | −0.887552 | − | 0.460707i | \(-0.847596\pi\) |
0.0447917 | − | 0.998996i | \(-0.485738\pi\) | |||||||
\(360\) | −10.5004 | + | 18.1872i | −0.553420 | + | 0.958551i | ||||
\(361\) | 18.7073 | − | 32.4019i | 0.984593 | − | 1.70537i | ||||
\(362\) | 2.68944 | − | 1.55275i | 0.141354 | − | 0.0816106i | ||||
\(363\) | 10.0424i | 0.527090i | ||||||||
\(364\) | 3.73881 | − | 0.273216i | 0.195967 | − | 0.0143204i | ||||
\(365\) | 13.5621 | 0.709874 | ||||||||
\(366\) | −4.30374 | + | 2.48476i | −0.224960 | + | 0.129881i | ||||
\(367\) | −8.11670 | + | 14.0585i | −0.423688 | + | 0.733849i | −0.996297 | − | 0.0859794i | \(-0.972598\pi\) |
0.572609 | + | 0.819829i | \(0.305931\pi\) | |||||||
\(368\) | 0.145906 | − | 0.252717i | 0.00760588 | − | 0.0131738i | ||||
\(369\) | −13.6352 | − | 1.66964i | −0.709822 | − | 0.0869181i | ||||
\(370\) | 25.0494 | 1.30226 | ||||||||
\(371\) | 10.4321 | − | 0.762335i | 0.541608 | − | 0.0395785i | ||||
\(372\) | − | 2.40623i | − | 0.124757i | ||||||
\(373\) | 0.209226 | + | 0.362391i | 0.0108333 | + | 0.0187639i | 0.871391 | − | 0.490589i | \(-0.163218\pi\) |
−0.860558 | + | 0.509353i | \(0.829885\pi\) | |||||||
\(374\) | −0.655776 | + | 1.13584i | −0.0339094 | + | 0.0587328i | ||||
\(375\) | −1.59859 | − | 0.922946i | −0.0825508 | − | 0.0476607i | ||||
\(376\) | −6.75288 | + | 3.89878i | −0.348253 | + | 0.201064i | ||||
\(377\) | 16.0928 | 0.828819 | ||||||||
\(378\) | 7.11659 | − | 14.7080i | 0.366038 | − | 0.756496i | ||||
\(379\) | 5.51123 | 0.283093 | 0.141546 | − | 0.989932i | \(-0.454793\pi\) | ||||
0.141546 | + | 0.989932i | \(0.454793\pi\) | |||||||
\(380\) | −6.66240 | + | 3.84654i | −0.341774 | + | 0.197323i | ||||
\(381\) | −3.85998 | − | 2.22856i | −0.197753 | − | 0.114173i | ||||
\(382\) | 13.8585 | + | 8.00119i | 0.709061 | + | 0.409377i | ||||
\(383\) | −4.73045 | + | 2.73113i | −0.241715 | + | 0.139554i | −0.615965 | − | 0.787774i | \(-0.711234\pi\) |
0.374250 | + | 0.927328i | \(0.377900\pi\) | |||||||
\(384\) | − | 7.34328i | − | 0.374735i | ||||||
\(385\) | −1.79225 | − | 2.63925i | −0.0913417 | − | 0.134509i | ||||
\(386\) | − | 1.23096i | − | 0.0626543i | ||||||
\(387\) | −3.13086 | − | 5.42281i | −0.159150 | − | 0.275657i | ||||
\(388\) | 1.96547 | + | 1.13476i | 0.0997814 | + | 0.0576088i | ||||
\(389\) | −0.298408 | + | 0.516858i | −0.0151299 | + | 0.0262057i | −0.873491 | − | 0.486840i | \(-0.838150\pi\) |
0.858361 | + | 0.513046i | \(0.171483\pi\) | |||||||
\(390\) | 8.81061 | + | 15.2604i | 0.446143 | + | 0.772742i | ||||
\(391\) | 0.243384i | 0.0123085i | ||||||||
\(392\) | 7.75698 | − | 19.5510i | 0.391786 | − | 0.987475i | ||||
\(393\) | 3.71120i | 0.187205i | ||||||||
\(394\) | −8.75044 | − | 15.1562i | −0.440841 | − | 0.763558i | ||||
\(395\) | −47.8705 | − | 27.6381i | −2.40863 | − | 1.39062i | ||||
\(396\) | 0.216213 | + | 0.124831i | 0.0108651 | + | 0.00627297i | ||||
\(397\) | 5.33287 | − | 3.07894i | 0.267649 | − | 0.154527i | −0.360170 | − | 0.932887i | \(-0.617281\pi\) |
0.627819 | + | 0.778359i | \(0.283948\pi\) | |||||||
\(398\) | − | 27.4858i | − | 1.37774i | ||||||
\(399\) | 15.1980 | − | 10.3206i | 0.760851 | − | 0.516676i | ||||
\(400\) | −18.3674 | −0.918370 | ||||||||
\(401\) | 3.49391 | + | 6.05163i | 0.174478 | + | 0.302204i | 0.939980 | − | 0.341228i | \(-0.110843\pi\) |
−0.765503 | + | 0.643433i | \(0.777510\pi\) | |||||||
\(402\) | 4.58600 | − | 7.94318i | 0.228729 | − | 0.396170i | ||||
\(403\) | 32.3106 | + | 18.6545i | 1.60951 | + | 0.929248i | ||||
\(404\) | 4.69778 | − | 2.71226i | 0.233723 | − | 0.134940i | ||||
\(405\) | 6.64170 | 0.330029 | ||||||||
\(406\) | 5.34249 | − | 11.0414i | 0.265144 | − | 0.547976i | ||||
\(407\) | − | 2.19212i | − | 0.108659i | ||||||
\(408\) | 3.79072 | + | 6.56572i | 0.187669 | + | 0.325052i | ||||
\(409\) | 11.1621 | − | 19.3333i | 0.551929 | − | 0.955970i | −0.446206 | − | 0.894930i | \(-0.647225\pi\) |
0.998135 | − | 0.0610394i | \(-0.0194415\pi\) | |||||||
\(410\) | −10.5901 | − | 24.9259i | −0.523009 | − | 1.23100i | ||||
\(411\) | 9.68721 | + | 16.7787i | 0.477835 | + | 0.827634i | ||||
\(412\) | 2.59418 | 0.127806 | ||||||||
\(413\) | 1.41167 | + | 19.3179i | 0.0694638 | + | 0.950571i | ||||
\(414\) | −0.248384 | −0.0122074 | ||||||||
\(415\) | 16.0571 | + | 27.8118i | 0.788214 | + | 1.36523i | ||||
\(416\) | −6.87335 | − | 3.96833i | −0.336994 | − | 0.194563i | ||||
\(417\) | −9.18191 | − | 5.30118i | −0.449640 | − | 0.259600i | ||||
\(418\) | −1.80469 | − | 3.12582i | −0.0882705 | − | 0.152889i | ||||
\(419\) | −22.7835 | −1.11304 | −0.556522 | − | 0.830833i | \(-0.687865\pi\) | ||||
−0.556522 | + | 0.830833i | \(0.687865\pi\) | |||||||
\(420\) | −2.49853 | + | 0.182583i | −0.121916 | + | 0.00890912i | ||||
\(421\) | − | 32.2607i | − | 1.57229i | −0.618041 | − | 0.786146i | \(-0.712074\pi\) | ||
0.618041 | − | 0.786146i | \(-0.287926\pi\) | |||||||
\(422\) | −5.15104 | + | 2.97395i | −0.250749 | + | 0.144770i | ||||
\(423\) | 4.82143 | + | 2.78365i | 0.234426 | + | 0.135346i | ||||
\(424\) | −10.2879 | − | 5.93971i | −0.499624 | − | 0.288458i | ||||
\(425\) | 13.2668 | − | 7.65960i | 0.643535 | − | 0.371545i | ||||
\(426\) | −6.98337 | −0.338345 | ||||||||
\(427\) | 9.86097 | + | 4.77133i | 0.477206 | + | 0.230901i | ||||
\(428\) | −4.30731 | −0.208202 | ||||||||
\(429\) | 1.33547 | − | 0.771033i | 0.0644770 | − | 0.0372258i | ||||
\(430\) | 6.17241 | − | 10.6909i | 0.297660 | − | 0.515562i | ||||
\(431\) | −13.8335 | + | 23.9604i | −0.666338 | + | 1.15413i | 0.312583 | + | 0.949890i | \(0.398806\pi\) |
−0.978921 | + | 0.204240i | \(0.934528\pi\) | |||||||
\(432\) | −13.4802 | + | 7.78277i | −0.648564 | + | 0.374449i | ||||
\(433\) | −30.9523 | −1.48747 | −0.743735 | − | 0.668474i | \(-0.766948\pi\) | ||||
−0.743735 | + | 0.668474i | \(0.766948\pi\) | |||||||
\(434\) | 23.5256 | − | 15.9757i | 1.12926 | − | 0.766856i | ||||
\(435\) | −10.7543 | −0.515630 | ||||||||
\(436\) | 1.76377 | − | 1.01832i | 0.0844695 | − | 0.0487685i | ||||
\(437\) | −0.580057 | − | 0.334896i | −0.0277479 | − | 0.0160203i | ||||
\(438\) | 4.32719 | + | 2.49831i | 0.206761 | + | 0.119374i | ||||
\(439\) | −25.3040 | + | 14.6092i | −1.20769 | + | 0.697261i | −0.962255 | − | 0.272151i | \(-0.912265\pi\) |
−0.245438 | + | 0.969412i | \(0.578932\pi\) | |||||||
\(440\) | 3.62322i | 0.172730i | ||||||||
\(441\) | −14.8581 | + | 2.18319i | −0.707527 | + | 0.103961i | ||||
\(442\) | −15.9690 | −0.759568 | ||||||||
\(443\) | 14.5625 | + | 25.2230i | 0.691884 | + | 1.19838i | 0.971220 | + | 0.238185i | \(0.0765525\pi\) |
−0.279335 | + | 0.960194i | \(0.590114\pi\) | |||||||
\(444\) | −1.49077 | − | 0.860694i | −0.0707486 | − | 0.0408467i | ||||
\(445\) | −3.87119 | − | 2.23503i | −0.183512 | − | 0.105951i | ||||
\(446\) | 6.91639 | + | 11.9795i | 0.327501 | + | 0.567248i | ||||
\(447\) | 5.63566 | 0.266557 | ||||||||
\(448\) | −19.3294 | + | 13.1262i | −0.913230 | + | 0.620153i | ||||
\(449\) | 40.1417 | 1.89441 | 0.947203 | − | 0.320636i | \(-0.103897\pi\) | ||||
0.947203 | + | 0.320636i | \(0.103897\pi\) | |||||||
\(450\) | 7.81696 | + | 13.5394i | 0.368495 | + | 0.638252i | ||||
\(451\) | −2.18132 | + | 0.926761i | −0.102714 | + | 0.0436395i | ||||
\(452\) | 1.77639 | − | 3.07679i | 0.0835542 | − | 0.144720i | ||||
\(453\) | 1.52168 | + | 2.63563i | 0.0714949 | + | 0.123833i | ||||
\(454\) | 12.6229i | 0.592420i | ||||||||
\(455\) | 16.9185 | − | 34.9656i | 0.793149 | − | 1.63921i | ||||
\(456\) | −20.8641 | −0.977051 | ||||||||
\(457\) | −21.6179 | + | 12.4811i | −1.01124 | + | 0.583840i | −0.911555 | − | 0.411179i | \(-0.865117\pi\) |
−0.0996860 | + | 0.995019i | \(0.531784\pi\) | |||||||
\(458\) | −24.1012 | − | 13.9148i | −1.12617 | − | 0.650197i | ||||
\(459\) | 6.49117 | − | 11.2430i | 0.302982 | − | 0.524780i | ||||
\(460\) | 0.0456687 | + | 0.0791006i | 0.00212932 | + | 0.00368808i | ||||
\(461\) | 34.4081 | 1.60255 | 0.801273 | − | 0.598299i | \(-0.204157\pi\) | ||||
0.801273 | + | 0.598299i | \(0.204157\pi\) | |||||||
\(462\) | −0.0856630 | − | 1.17225i | −0.00398540 | − | 0.0545379i | ||||
\(463\) | − | 33.8366i | − | 1.57252i | −0.617896 | − | 0.786260i | \(-0.712015\pi\) | ||
0.617896 | − | 0.786260i | \(-0.287985\pi\) | |||||||
\(464\) | −10.1197 | + | 5.84260i | −0.469794 | + | 0.271236i | ||||
\(465\) | −21.5922 | − | 12.4663i | −1.00132 | − | 0.578110i | ||||
\(466\) | 26.0844 | + | 15.0599i | 1.20834 | + | 0.697634i | ||||
\(467\) | 13.6860 | + | 23.7049i | 0.633314 | + | 1.09693i | 0.986870 | + | 0.161518i | \(0.0516391\pi\) |
−0.353556 | + | 0.935413i | \(0.615028\pi\) | |||||||
\(468\) | 3.03979i | 0.140514i | ||||||||
\(469\) | −20.1647 | + | 1.47355i | −0.931118 | + | 0.0680423i | ||||
\(470\) | 10.9758i | 0.506276i | ||||||||
\(471\) | −9.38458 | − | 16.2546i | −0.432419 | − | 0.748971i | ||||
\(472\) | 10.9990 | − | 19.0508i | 0.506270 | − | 0.876885i | ||||
\(473\) | −0.935583 | − | 0.540159i | −0.0430182 | − | 0.0248366i | ||||
\(474\) | −10.1825 | − | 17.6367i | −0.467699 | − | 0.810078i | ||||
\(475\) | 42.1584i | 1.93436i | ||||||||
\(476\) | 0.988837 | − | 2.04364i | 0.0453233 | − | 0.0936702i | ||||
\(477\) | 8.48169i | 0.388350i | ||||||||
\(478\) | −31.2320 | + | 18.0318i | −1.42852 | + | 0.824756i | ||||
\(479\) | 2.20712 | + | 1.27428i | 0.100846 | + | 0.0582234i | 0.549575 | − | 0.835445i | \(-0.314790\pi\) |
−0.448729 | + | 0.893668i | \(0.648123\pi\) | |||||||
\(480\) | 4.59326 | + | 2.65192i | 0.209653 | + | 0.121043i | ||||
\(481\) | 23.1146 | − | 13.3452i | 1.05394 | − | 0.608491i | ||||
\(482\) | 30.9921 | 1.41165 | ||||||||
\(483\) | −0.122533 | − | 0.180441i | −0.00557546 | − | 0.00821035i | ||||
\(484\) | −3.41536 | −0.155244 | ||||||||
\(485\) | 20.3655 | − | 11.7581i | 0.924752 | − | 0.533906i | ||||
\(486\) | 18.1639 | + | 10.4869i | 0.823932 | + | 0.475697i | ||||
\(487\) | 0.141019 | − | 0.244252i | 0.00639018 | − | 0.0110681i | −0.862813 | − | 0.505524i | \(-0.831299\pi\) |
0.869203 | + | 0.494456i | \(0.164633\pi\) | |||||||
\(488\) | −6.22065 | − | 10.7745i | −0.281595 | − | 0.487738i | ||||
\(489\) | − | 14.0989i | − | 0.637573i | ||||||
\(490\) | −18.3736 | − | 23.2158i | −0.830036 | − | 1.04878i | ||||
\(491\) | 11.2078 | 0.505802 | 0.252901 | − | 0.967492i | \(-0.418615\pi\) | ||||
0.252901 | + | 0.967492i | \(0.418615\pi\) | |||||||
\(492\) | −0.226202 | + | 1.84729i | −0.0101980 | + | 0.0832824i | ||||
\(493\) | 4.87298 | − | 8.44025i | 0.219468 | − | 0.380130i | ||||
\(494\) | 21.9733 | − | 38.0589i | 0.988626 | − | 1.71235i | ||||
\(495\) | 2.24033 | − | 1.29345i | 0.100695 | − | 0.0581365i | ||||
\(496\) | −27.0907 | −1.21641 | ||||||||
\(497\) | 8.64810 | + | 12.7351i | 0.387920 | + | 0.571247i | ||||
\(498\) | 11.8317i | 0.530190i | ||||||||
\(499\) | 25.0096 | − | 14.4393i | 1.11958 | − | 0.646392i | 0.178289 | − | 0.983978i | \(-0.442944\pi\) |
0.941295 | + | 0.337586i | \(0.109610\pi\) | |||||||
\(500\) | 0.313888 | − | 0.543670i | 0.0140375 | − | 0.0243137i | ||||
\(501\) | 2.30774 | − | 3.99713i | 0.103102 | − | 0.178578i | ||||
\(502\) | −8.50909 | − | 14.7382i | −0.379779 | − | 0.657797i | ||||
\(503\) | 10.8826i | 0.485231i | 0.970123 | + | 0.242615i | \(0.0780053\pi\) | ||||
−0.970123 | + | 0.242615i | \(0.921995\pi\) | |||||||
\(504\) | 15.3528 | + | 7.42863i | 0.683870 | + | 0.330897i | ||||
\(505\) | − | 56.2073i | − | 2.50119i | ||||||
\(506\) | −0.0371119 | + | 0.0214266i | −0.00164983 | + | 0.000952527i | ||||
\(507\) | 5.85231 | + | 3.37883i | 0.259910 | + | 0.150059i | ||||
\(508\) | 0.757919 | − | 1.31275i | 0.0336272 | − | 0.0582440i | ||||
\(509\) | 6.70359 | − | 3.87032i | 0.297131 | − | 0.171549i | −0.344022 | − | 0.938962i | \(-0.611790\pi\) |
0.641153 | + | 0.767413i | \(0.278456\pi\) | |||||||
\(510\) | 10.6716 | 0.472547 | ||||||||
\(511\) | −0.802744 | − | 10.9851i | −0.0355113 | − | 0.485951i | ||||
\(512\) | 25.4284 | 1.12379 | ||||||||
\(513\) | 17.8637 | + | 30.9408i | 0.788701 | + | 1.36607i | ||||
\(514\) | −30.4313 | − | 17.5695i | −1.34227 | − | 0.774957i | ||||
\(515\) | 13.4400 | − | 23.2788i | 0.592238 | − | 1.02579i | ||||
\(516\) | −0.734678 | + | 0.424166i | −0.0323424 | + | 0.0186729i | ||||
\(517\) | 0.960514 | 0.0422433 | ||||||||
\(518\) | −1.48268 | − | 20.2896i | −0.0651451 | − | 0.891472i | ||||
\(519\) | 7.27321i | 0.319258i | ||||||||
\(520\) | −38.2047 | + | 22.0575i | −1.67539 | + | 0.967286i | ||||
\(521\) | −3.95840 | − | 2.28539i | −0.173421 | − | 0.100125i | 0.410777 | − | 0.911736i | \(-0.365257\pi\) |
−0.584198 | + | 0.811611i | \(0.698591\pi\) | |||||||
\(522\) | 8.61365 | + | 4.97309i | 0.377009 | + | 0.217666i | ||||
\(523\) | −3.49436 | − | 6.05241i | −0.152798 | − | 0.264653i | 0.779457 | − | 0.626455i | \(-0.215495\pi\) |
−0.932255 | + | 0.361802i | \(0.882162\pi\) | |||||||
\(524\) | −1.26215 | −0.0551375 | ||||||||
\(525\) | −5.97953 | + | 12.3580i | −0.260968 | + | 0.539346i | ||||
\(526\) | 22.0119i | 0.959763i | ||||||||
\(527\) | 19.5677 | − | 11.2974i | 0.852381 | − | 0.492123i | ||||
\(528\) | −0.559859 | + | 0.969704i | −0.0243647 | + | 0.0422010i | ||||
\(529\) | 11.4960 | − | 19.9117i | 0.499827 | − | 0.865726i | ||||
\(530\) | −14.4812 | + | 8.36072i | −0.629023 | + | 0.363166i | ||||
\(531\) | −15.7061 | −0.681589 | ||||||||
\(532\) | 3.50997 | + | 5.16874i | 0.152177 | + | 0.224093i | ||||
\(533\) | −23.0516 | − | 17.3588i | −0.998477 | − | 0.751891i | ||||
\(534\) | −0.823439 | − | 1.42624i | −0.0356337 | − | 0.0617194i | ||||
\(535\) | −22.3155 | + | 38.6516i | −0.964784 | + | 1.67105i | ||||
\(536\) | 19.8859 | + | 11.4811i | 0.858940 | + | 0.495909i | ||||
\(537\) | 8.33484 | + | 14.4364i | 0.359675 | + | 0.622975i | ||||
\(538\) | −22.3658 | −0.964258 | ||||||||
\(539\) | −2.03166 | + | 1.60791i | −0.0875099 | + | 0.0692576i | ||||
\(540\) | − | 4.87203i | − | 0.209659i | ||||||
\(541\) | 11.5132 | + | 19.9414i | 0.494990 | + | 0.857348i | 0.999983 | − | 0.00577557i | \(-0.00183843\pi\) |
−0.504993 | + | 0.863123i | \(0.668505\pi\) | |||||||
\(542\) | −19.5861 | + | 33.9240i | −0.841293 | + | 1.45716i | ||||
\(543\) | −1.10564 | + | 1.91502i | −0.0474474 | + | 0.0821814i | ||||
\(544\) | −4.16258 | + | 2.40327i | −0.178469 | + | 0.103039i | ||||
\(545\) | − | 21.1029i | − | 0.903950i | ||||||
\(546\) | 11.8392 | − | 8.03970i | 0.506669 | − | 0.344067i | ||||
\(547\) | 23.4712i | 1.00355i | 0.864997 | + | 0.501777i | \(0.167320\pi\) | ||||
−0.864997 | + | 0.501777i | \(0.832680\pi\) | |||||||
\(548\) | −5.70634 | + | 3.29456i | −0.243763 | + | 0.140737i | ||||
\(549\) | −4.44142 | + | 7.69277i | −0.189555 | + | 0.328320i | ||||
\(550\) | 2.33592 | + | 1.34864i | 0.0996038 | + | 0.0575063i | ||||
\(551\) | 13.4104 | + | 23.2275i | 0.571303 | + | 0.989527i | ||||
\(552\) | 0.247713i | 0.0105434i | ||||||||
\(553\) | −19.5529 | + | 40.4102i | −0.831472 | + | 1.71841i | ||||
\(554\) | −7.95504 | −0.337977 | ||||||||
\(555\) | −15.4468 | + | 8.91824i | −0.655682 | + | 0.378558i | ||||
\(556\) | 1.80290 | − | 3.12271i | 0.0764598 | − | 0.132432i | ||||
\(557\) | 28.1303 | + | 16.2411i | 1.19192 | + | 0.688155i | 0.958742 | − | 0.284278i | \(-0.0917540\pi\) |
0.233178 | + | 0.972434i | \(0.425087\pi\) | |||||||
\(558\) | 11.5295 | + | 19.9697i | 0.488083 | + | 0.845384i | ||||
\(559\) | − | 13.1536i | − | 0.556337i | ||||||
\(560\) | 2.05562 | + | 28.1299i | 0.0868658 | + | 1.18871i | ||||
\(561\) | − | 0.933893i | − | 0.0394290i | ||||||
\(562\) | −15.5226 | + | 8.96196i | −0.654780 | + | 0.378037i | ||||
\(563\) | −2.14320 | − | 1.23738i | −0.0903250 | − | 0.0521492i | 0.454157 | − | 0.890922i | \(-0.349940\pi\) |
−0.544482 | + | 0.838772i | \(0.683274\pi\) | |||||||
\(564\) | 0.377127 | − | 0.653203i | 0.0158799 | − | 0.0275048i | ||||
\(565\) | −18.4064 | − | 31.8808i | −0.774361 | − | 1.34123i | ||||
\(566\) | −30.7552 | −1.29274 | ||||||||
\(567\) | −0.393123 | − | 5.37965i | −0.0165096 | − | 0.225924i | ||||
\(568\) | − | 17.4830i | − | 0.733569i | ||||||
\(569\) | 1.17007 | + | 2.02661i | 0.0490517 | + | 0.0849600i | 0.889509 | − | 0.456918i | \(-0.151047\pi\) |
−0.840457 | + | 0.541878i | \(0.817713\pi\) | |||||||
\(570\) | −14.6841 | + | 25.4337i | −0.615050 | + | 1.06530i | ||||
\(571\) | 26.7501 | + | 15.4442i | 1.11946 | + | 0.646319i | 0.941262 | − | 0.337676i | \(-0.109641\pi\) |
0.178195 | + | 0.983995i | \(0.442974\pi\) | |||||||
\(572\) | 0.262223 | + | 0.454184i | 0.0109641 | + | 0.0189904i | ||||
\(573\) | −11.3945 | −0.476013 | ||||||||
\(574\) | −19.5627 | + | 10.0532i | −0.816532 | + | 0.419611i | ||||
\(575\) | 0.500533 | 0.0208737 | ||||||||
\(576\) | −9.47304 | − | 16.4078i | −0.394710 | − | 0.683658i | ||||
\(577\) | 29.6939 | + | 17.1438i | 1.23617 | + | 0.713705i | 0.968310 | − | 0.249752i | \(-0.0803490\pi\) |
0.267864 | + | 0.963457i | \(0.413682\pi\) | |||||||
\(578\) | 6.20009 | − | 10.7389i | 0.257890 | − | 0.446678i | ||||
\(579\) | 0.438254 | + | 0.759079i | 0.0182132 | + | 0.0315462i | ||||
\(580\) | − | 3.65748i | − | 0.151868i | ||||||
\(581\) | 21.5766 | − | 14.6522i | 0.895149 | − | 0.607875i | ||||
\(582\) | 8.66390 | 0.359130 | ||||||||
\(583\) | 0.731662 | + | 1.26728i | 0.0303024 | + | 0.0524852i | ||||
\(584\) | −6.25455 | + | 10.8332i | −0.258815 | + | 0.448281i | ||||
\(585\) | 27.2775 | + | 15.7487i | 1.12778 | + | 0.651127i | ||||
\(586\) | −4.17457 | + | 2.41019i | −0.172450 | + | 0.0995641i | ||||
\(587\) | − | 16.2051i | − | 0.668854i | −0.942422 | − | 0.334427i | \(-0.891457\pi\) | ||
0.942422 | − | 0.334427i | \(-0.108543\pi\) | |||||||
\(588\) | 0.295777 | + | 2.01296i | 0.0121976 | + | 0.0830131i | ||||
\(589\) | 62.1808i | 2.56212i | ||||||||
\(590\) | −15.4821 | − | 26.8159i | −0.637390 | − | 1.10399i | ||||
\(591\) | 10.7920 | + | 6.23077i | 0.443924 | + | 0.256299i | ||||
\(592\) | −9.69019 | + | 16.7839i | −0.398264 | + | 0.689814i | ||||
\(593\) | 10.3926 | − | 6.00019i | 0.426774 | − | 0.246398i | −0.271197 | − | 0.962524i | \(-0.587420\pi\) |
0.697972 | + | 0.716126i | \(0.254086\pi\) | |||||||
\(594\) | 2.28583 | 0.0937886 | ||||||||
\(595\) | −13.2156 | − | 19.4611i | −0.541786 | − | 0.797827i | ||||
\(596\) | 1.91665i | 0.0785091i | ||||||||
\(597\) | 9.78564 | + | 16.9492i | 0.400500 | + | 0.693686i | ||||
\(598\) | −0.451862 | − | 0.260882i | −0.0184780 | − | 0.0106683i | ||||
\(599\) | −11.1823 | + | 19.3684i | −0.456898 | + | 0.791371i | −0.998795 | − | 0.0490739i | \(-0.984373\pi\) |
0.541897 | + | 0.840445i | \(0.317706\pi\) | |||||||
\(600\) | 13.5028 | − | 7.79584i | 0.551249 | − | 0.318264i | ||||
\(601\) | − | 5.86294i | − | 0.239154i | −0.992825 | − | 0.119577i | \(-0.961846\pi\) | ||
0.992825 | − | 0.119577i | \(-0.0381539\pi\) | |||||||
\(602\) | −9.02480 | − | 4.36674i | −0.367824 | − | 0.177975i | ||||
\(603\) | − | 16.3946i | − | 0.667640i | ||||||
\(604\) | −0.896361 | + | 0.517514i | −0.0364724 | + | 0.0210574i | ||||
\(605\) | −17.6945 | + | 30.6477i | −0.719382 | + | 1.24601i | ||||
\(606\) | 10.3541 | − | 17.9337i | 0.420605 | − | 0.728509i | ||||
\(607\) | −1.13344 | − | 1.96317i | −0.0460047 | − | 0.0796825i | 0.842106 | − | 0.539312i | \(-0.181316\pi\) |
−0.888111 | + | 0.459629i | \(0.847982\pi\) | |||||||
\(608\) | − | 13.2276i | − | 0.536449i | ||||||
\(609\) | 0.636550 | + | 8.71080i | 0.0257943 | + | 0.352980i | ||||
\(610\) | −17.5123 | −0.709053 | ||||||||
\(611\) | 5.84744 | + | 10.1281i | 0.236562 | + | 0.409738i | ||||
\(612\) | 1.59429 | + | 0.920465i | 0.0644454 | + | 0.0372076i | ||||
\(613\) | −2.45166 | + | 4.24641i | −0.0990218 | + | 0.171511i | −0.911280 | − | 0.411787i | \(-0.864905\pi\) |
0.812258 | + | 0.583298i | \(0.198238\pi\) | |||||||
\(614\) | 11.2642 | + | 19.5101i | 0.454585 | + | 0.787364i | ||||
\(615\) | 15.4047 | + | 11.6003i | 0.621179 | + | 0.467771i | ||||
\(616\) | 2.93474 | − | 0.214459i | 0.118244 | − | 0.00864079i | ||||
\(617\) | 20.9232 | 0.842337 | 0.421169 | − | 0.906982i | \(-0.361620\pi\) | ||||
0.421169 | + | 0.906982i | \(0.361620\pi\) | |||||||
\(618\) | 8.57647 | − | 4.95163i | 0.344996 | − | 0.199184i | ||||
\(619\) | 2.48094 | − | 4.29712i | 0.0997175 | − | 0.172716i | −0.811850 | − | 0.583866i | \(-0.801539\pi\) |
0.911568 | + | 0.411150i | \(0.134873\pi\) | |||||||
\(620\) | 4.23970 | − | 7.34338i | 0.170271 | − | 0.294917i | ||||
\(621\) | 0.367350 | − | 0.212090i | 0.0147413 | − | 0.00851087i | ||||
\(622\) | 20.5704i | 0.824799i | ||||||||
\(623\) | −1.58120 | + | 3.26788i | −0.0633494 | + | 0.130925i | ||||
\(624\) | −13.6333 | −0.545769 | ||||||||
\(625\) | 10.7799 | + | 18.6713i | 0.431195 | + | 0.746852i | ||||
\(626\) | −26.0623 | − | 15.0470i | −1.04166 | − | 0.601401i | ||||
\(627\) | 2.22575 | + | 1.28504i | 0.0888878 | + | 0.0513194i | ||||
\(628\) | 5.52808 | − | 3.19164i | 0.220594 | − | 0.127360i | ||||
\(629\) | − | 16.1641i | − | 0.644504i | ||||||
\(630\) | 19.8609 | − | 13.4871i | 0.791278 | − | 0.537338i | ||||
\(631\) | −42.3254 | −1.68495 | −0.842474 | − | 0.538738i | \(-0.818901\pi\) | ||||
−0.842474 | + | 0.538738i | \(0.818901\pi\) | |||||||
\(632\) | 44.1537 | − | 25.4921i | 1.75634 | − | 1.01402i | ||||
\(633\) | 2.11761 | − | 3.66781i | 0.0841674 | − | 0.145782i | ||||
\(634\) | 12.9385 | + | 7.47003i | 0.513853 | + | 0.296673i | ||||
\(635\) | −7.85332 | − | 13.6023i | −0.311649 | − | 0.539793i | ||||
\(636\) | 1.14909 | 0.0455645 | ||||||||
\(637\) | −29.3229 | − | 11.6340i | −1.16182 | − | 0.460957i | ||||
\(638\) | 1.71599 | 0.0679368 | ||||||||
\(639\) | −10.8102 | + | 6.24126i | −0.427644 | + | 0.246900i | ||||
\(640\) | 12.9386 | − | 22.4104i | 0.511445 | − | 0.885848i | ||||
\(641\) | −13.0008 | − | 7.50602i | −0.513501 | − | 0.296470i | 0.220770 | − | 0.975326i | \(-0.429143\pi\) |
−0.734272 | + | 0.678856i | \(0.762476\pi\) | |||||||
\(642\) | −14.2402 | + | 8.22157i | −0.562015 | + | 0.324479i | ||||
\(643\) | − | 2.19624i | − | 0.0866113i | −0.999062 | − | 0.0433057i | \(-0.986211\pi\) | ||
0.999062 | − | 0.0433057i | \(-0.0137889\pi\) | |||||||
\(644\) | 0.0613669 | − | 0.0416728i | 0.00241819 | − | 0.00164214i | ||||
\(645\) | 8.79016i | 0.346112i | ||||||||
\(646\) | −13.3073 | − | 23.0489i | −0.523569 | − | 0.906848i | ||||
\(647\) | 1.70654 | − | 2.95581i | 0.0670909 | − | 0.116205i | −0.830529 | − | 0.556976i | \(-0.811962\pi\) |
0.897620 | + | 0.440771i | \(0.145295\pi\) | |||||||
\(648\) | −3.06300 | + | 5.30528i | −0.120326 | + | 0.208411i | ||||
\(649\) | −2.34671 | + | 1.35487i | −0.0921163 | + | 0.0531834i | ||||
\(650\) | 32.8412i | 1.28814i | ||||||||
\(651\) | −8.81941 | + | 18.2272i | −0.345660 | + | 0.714380i | ||||
\(652\) | 4.79493 | 0.187784 | ||||||||
\(653\) | −40.7253 | + | 23.5128i | −1.59370 | + | 0.920126i | −0.601041 | + | 0.799218i | \(0.705247\pi\) |
−0.992664 | + | 0.120908i | \(0.961419\pi\) | |||||||
\(654\) | 3.88741 | − | 6.73320i | 0.152010 | − | 0.263289i | ||||
\(655\) | −6.53902 | + | 11.3259i | −0.255501 | + | 0.442540i | ||||
\(656\) | 20.7979 | + | 2.54671i | 0.812021 | + | 0.0994324i | ||||
\(657\) | 8.93127 | 0.348442 | ||||||||
\(658\) | 8.89020 | − | 0.649660i | 0.346576 | − | 0.0253264i | ||||
\(659\) | 15.9862i | 0.622734i | 0.950290 | + | 0.311367i | \(0.100787\pi\) | ||||
−0.950290 | + | 0.311367i | \(0.899213\pi\) | |||||||
\(660\) | −0.175236 | − | 0.303518i | −0.00682106 | − | 0.0118144i | ||||
\(661\) | 8.92876 | − | 15.4651i | 0.347288 | − | 0.601521i | −0.638478 | − | 0.769640i | \(-0.720436\pi\) |
0.985767 | + | 0.168119i | \(0.0537691\pi\) | |||||||
\(662\) | −2.02427 | − | 1.16871i | −0.0786754 | − | 0.0454233i | ||||
\(663\) | 9.84737 | − | 5.68538i | 0.382440 | − | 0.220802i | ||||
\(664\) | −29.6208 | −1.14951 | ||||||||
\(665\) | 64.5662 | − | 4.71823i | 2.50377 | − | 0.182965i | ||||
\(666\) | 16.4962 | 0.639213 | ||||||||
\(667\) | 0.275773 | − | 0.159218i | 0.0106780 | − | 0.00616494i | ||||
\(668\) | 1.35940 | + | 0.784848i | 0.0525967 | + | 0.0303667i | ||||
\(669\) | −8.53005 | − | 4.92483i | −0.329791 | − | 0.190405i | ||||
\(670\) | 27.9913 | − | 16.1608i | 1.08140 | − | 0.624346i | ||||
\(671\) | 1.53254i | 0.0591629i | ||||||||
\(672\) | 1.87613 | − | 3.87742i | 0.0723733 | − | 0.149575i | ||||
\(673\) | − | 0.243849i | − | 0.00939969i | −0.999989 | − | 0.00469985i | \(-0.998504\pi\) | ||
0.999989 | − | 0.00469985i | \(-0.00149601\pi\) | |||||||
\(674\) | −21.0489 | − | 36.4578i | −0.810775 | − | 1.40430i | ||||
\(675\) | −23.1219 | − | 13.3495i | −0.889964 | − | 0.513821i | ||||
\(676\) | −1.14912 | + | 1.99033i | −0.0441969 | + | 0.0765513i | ||||
\(677\) | −18.1476 | − | 31.4326i | −0.697470 | − | 1.20805i | −0.969341 | − | 0.245720i | \(-0.920976\pi\) |
0.271871 | − | 0.962334i | \(-0.412358\pi\) | |||||||
\(678\) | − | 13.5627i | − | 0.520872i | ||||||
\(679\) | −10.7292 | − | 15.7998i | −0.411751 | − | 0.606339i | ||||
\(680\) | 26.7166i | 1.02453i | ||||||||
\(681\) | −4.49407 | − | 7.78395i | −0.172213 | − | 0.298282i | ||||
\(682\) | 3.44532 | + | 1.98916i | 0.131928 | + | 0.0761687i | ||||
\(683\) | −0.320128 | − | 0.184826i | −0.0122494 | − | 0.00707217i | 0.493863 | − | 0.869540i | \(-0.335584\pi\) |
−0.506112 | + | 0.862468i | \(0.668918\pi\) | |||||||
\(684\) | −4.38749 | + | 2.53312i | −0.167760 | + | 0.0968561i | ||||
\(685\) | 68.2744i | 2.60863i | ||||||||
\(686\) | −17.7169 | + | 16.2565i | −0.676433 | + | 0.620674i | ||||
\(687\) | 19.8162 | 0.756034 | ||||||||
\(688\) | 4.77551 | + | 8.27142i | 0.182065 | + | 0.315345i | ||||
\(689\) | −8.90846 | + | 15.4299i | −0.339385 | + | 0.587833i | ||||
\(690\) | 0.301966 | + | 0.174340i | 0.0114956 | + | 0.00663701i | ||||
\(691\) | −2.41961 | + | 1.39696i | −0.0920464 | + | 0.0531430i | −0.545317 | − | 0.838230i | \(-0.683591\pi\) |
0.453270 | + | 0.891373i | \(0.350257\pi\) | |||||||
\(692\) | −2.47357 | −0.0940311 | ||||||||
\(693\) | −1.18028 | − | 1.73807i | −0.0448351 | − | 0.0660237i | ||||
\(694\) | 5.11290i | 0.194083i | ||||||||
\(695\) | −18.6810 | − | 32.3565i | −0.708612 | − | 1.22735i | ||||
\(696\) | 4.95966 | − | 8.59038i | 0.187995 | − | 0.325617i | ||||
\(697\) | −16.0844 | + | 6.83367i | −0.609240 | + | 0.258844i | ||||
\(698\) | −11.6204 | − | 20.1271i | −0.439838 | − | 0.761822i | ||||
\(699\) | −21.4468 | −0.811192 | ||||||||
\(700\) | −4.20287 | − | 2.03360i | −0.158853 | − | 0.0768629i | ||||
\(701\) | −25.9392 | −0.979709 | −0.489854 | − | 0.871804i | \(-0.662950\pi\) | ||||
−0.489854 | + | 0.871804i | \(0.662950\pi\) | |||||||
\(702\) | 13.9157 | + | 24.1027i | 0.525215 | + | 0.909699i | ||||
\(703\) | 38.5238 | + | 22.2417i | 1.45295 | + | 0.838863i | ||||
\(704\) | −2.83080 | − | 1.63436i | −0.106690 | − | 0.0615973i | ||||
\(705\) | −3.90767 | − | 6.76829i | −0.147171 | − | 0.254908i | ||||
\(706\) | 32.2857 | 1.21509 | ||||||||
\(707\) | −45.5268 | + | 3.32691i | −1.71221 | + | 0.125122i | ||||
\(708\) | 2.12786i | 0.0799698i | ||||||||
\(709\) | −22.3462 | + | 12.9016i | −0.839230 | + | 0.484530i | −0.857002 | − | 0.515313i | \(-0.827676\pi\) |
0.0177726 | + | 0.999842i | \(0.494343\pi\) | |||||||
\(710\) | −21.3120 | − | 12.3045i | −0.799825 | − | 0.461779i | ||||
\(711\) | −31.5249 | − | 18.2009i | −1.18228 | − | 0.682587i | ||||
\(712\) | 3.57061 | − | 2.06149i | 0.133814 | − | 0.0772578i | ||||
\(713\) | 0.738254 | 0.0276478 | ||||||||
\(714\) | −0.631654 | − | 8.64382i | −0.0236391 | − | 0.323487i | ||||
\(715\) | 5.43415 | 0.203226 | ||||||||
\(716\) | −4.90972 | + | 2.83463i | −0.183485 | + | 0.105935i | ||||
\(717\) | 12.8396 | − | 22.2388i | 0.479503 | − | 0.830524i | ||||
\(718\) | 20.7314 | − | 35.9078i | 0.773688 | − | 1.34007i | ||||
\(719\) | −1.71154 | + | 0.988158i | −0.0638297 | + | 0.0368521i | −0.531575 | − | 0.847011i | \(-0.678400\pi\) |
0.467746 | + | 0.883863i | \(0.345066\pi\) | |||||||
\(720\) | −22.8707 | −0.852340 | ||||||||
\(721\) | −19.6509 | − | 9.50829i | −0.731838 | − | 0.354107i | ||||
\(722\) | 48.5755 | 1.80779 | ||||||||
\(723\) | −19.1114 | + | 11.0340i | −0.710761 | + | 0.410358i | ||||
\(724\) | −0.651286 | − | 0.376020i | −0.0242049 | − | 0.0139747i | ||||
\(725\) | −17.3579 | − | 10.0216i | −0.644655 | − | 0.372192i | ||||
\(726\) | −11.2913 | + | 6.51906i | −0.419061 | + | 0.241945i | ||||
\(727\) | − | 31.9543i | − | 1.18512i | −0.805527 | − | 0.592560i | \(-0.798117\pi\) | ||
0.805527 | − | 0.592560i | \(-0.201883\pi\) | |||||||
\(728\) | 20.1275 | + | 29.6395i | 0.745976 | + | 1.09851i | ||||
\(729\) | −8.81828 | −0.326603 | ||||||||
\(730\) | 8.80389 | + | 15.2488i | 0.325847 | + | 0.564383i | ||||
\(731\) | −6.89873 | − | 3.98298i | −0.255159 | − | 0.147316i | ||||
\(732\) | 1.04221 | + | 0.601721i | 0.0385212 | + | 0.0222402i | ||||
\(733\) | 0.726003 | + | 1.25747i | 0.0268155 | + | 0.0464458i | 0.879122 | − | 0.476597i | \(-0.158130\pi\) |
−0.852306 | + | 0.523043i | \(0.824797\pi\) | |||||||
\(734\) | −21.0759 | −0.777926 | ||||||||
\(735\) | 19.5956 | + | 7.77468i | 0.722796 | + | 0.286773i | ||||
\(736\) | −0.157047 | −0.00578882 | ||||||||
\(737\) | −1.41426 | − | 2.44957i | −0.0520950 | − | 0.0902312i | ||||
\(738\) | −6.97407 | − | 16.4148i | −0.256719 | − | 0.604239i | ||||
\(739\) | −20.5305 | + | 35.5599i | −0.755227 | + | 1.30809i | 0.190034 | + | 0.981778i | \(0.439140\pi\) |
−0.945261 | + | 0.326315i | \(0.894193\pi\) | |||||||
\(740\) | −3.03304 | − | 5.25337i | −0.111497 | − | 0.193118i | ||||
\(741\) | 31.2923i | 1.14955i | ||||||||
\(742\) | 7.62917 | + | 11.2346i | 0.280076 | + | 0.412436i | ||||
\(743\) | −6.51918 | −0.239165 | −0.119583 | − | 0.992824i | \(-0.538156\pi\) | ||||
−0.119583 | + | 0.992824i | \(0.538156\pi\) | |||||||
\(744\) | 19.9157 | − | 11.4983i | 0.730146 | − | 0.421550i | ||||
\(745\) | 17.1990 | + | 9.92986i | 0.630124 | + | 0.363802i | ||||
\(746\) | −0.271640 | + | 0.470494i | −0.00994544 | + | 0.0172260i | ||||
\(747\) | 10.5744 | + | 18.3153i | 0.386895 | + | 0.670122i | ||||
\(748\) | 0.317611 | 0.0116130 | ||||||||
\(749\) | 32.6279 | + | 15.7874i | 1.19220 | + | 0.576858i | ||||
\(750\) | − | 2.39653i | − | 0.0875090i | ||||||
\(751\) | 15.7514 | − | 9.09405i | 0.574775 | − | 0.331847i | −0.184279 | − | 0.982874i | \(-0.558995\pi\) |
0.759054 | + | 0.651027i | \(0.225662\pi\) | |||||||
\(752\) | −7.35414 | − | 4.24592i | −0.268178 | − | 0.154833i | ||||
\(753\) | 10.4943 | + | 6.05891i | 0.382435 | + | 0.220799i | ||||
\(754\) | 10.4467 | + | 18.0941i | 0.380445 | + | 0.658950i | ||||
\(755\) | 10.7246i | 0.390310i | ||||||||
\(756\) | −3.94625 | + | 0.288376i | −0.143524 | + | 0.0104881i | ||||
\(757\) | − | 14.6557i | − | 0.532670i | −0.963881 | − | 0.266335i | \(-0.914187\pi\) | ||
0.963881 | − | 0.266335i | \(-0.0858127\pi\) | |||||||
\(758\) | 3.57763 | + | 6.19664i | 0.129945 | + | 0.225072i | ||||
\(759\) | 0.0152568 | − | 0.0264256i | 0.000553788 | − | 0.000959189i | ||||
\(760\) | −63.6736 | − | 36.7620i | −2.30968 | − | 1.33350i | ||||
\(761\) | 10.6602 | + | 18.4639i | 0.386431 | + | 0.669317i | 0.991967 | − | 0.126501i | \(-0.0403746\pi\) |
−0.605536 | + | 0.795818i | \(0.707041\pi\) | |||||||
\(762\) | − | 5.78670i | − | 0.209630i | ||||||
\(763\) | −17.0930 | + | 1.24909i | −0.618808 | + | 0.0452199i | ||||
\(764\) | − | 3.87521i | − | 0.140200i | ||||||
\(765\) | 16.5196 | − | 9.53757i | 0.597266 | − | 0.344831i | ||||
\(766\) | −6.14157 | − | 3.54584i | −0.221904 | − | 0.128116i | ||||
\(767\) | −28.5727 | − | 16.4964i | −1.03170 | − | 0.595652i | ||||
\(768\) | −5.88401 | + | 3.39713i | −0.212321 | + | 0.122583i | ||||
\(769\) | 30.0535 | 1.08376 | 0.541879 | − | 0.840457i | \(-0.317713\pi\) | ||||
0.541879 | + | 0.840457i | \(0.317713\pi\) | |||||||
\(770\) | 1.80404 | − | 3.72843i | 0.0650130 | − | 0.134363i | ||||
\(771\) | 25.0208 | 0.901101 | ||||||||
\(772\) | −0.258158 | + | 0.149047i | −0.00929130 | + | 0.00536434i | ||||
\(773\) | 34.9028 | + | 20.1511i | 1.25537 | + | 0.724786i | 0.972170 | − | 0.234276i | \(-0.0752718\pi\) |
0.283197 | + | 0.959062i | \(0.408605\pi\) | |||||||
\(774\) | 4.06481 | − | 7.04046i | 0.146107 | − | 0.253064i | ||||
\(775\) | −23.2338 | − | 40.2420i | −0.834581 | − | 1.44554i | ||||
\(776\) | 21.6902i | 0.778633i | ||||||||
\(777\) | 8.13791 | + | 11.9838i | 0.291946 | + | 0.429916i | ||||
\(778\) | −0.774850 | −0.0277797 | ||||||||
\(779\) | 5.84543 | − | 47.7371i | 0.209434 | − | 1.71036i | ||||
\(780\) | 2.13362 | − | 3.69553i | 0.0763957 | − | 0.132321i | ||||
\(781\) | −1.07679 | + | 1.86505i | −0.0385305 | + | 0.0667369i | ||||
\(782\) | −0.273653 | + | 0.157993i | −0.00978580 | + | 0.00564983i | ||||
\(783\) | −16.9857 | −0.607018 | ||||||||
\(784\) | 22.6631 | − | 3.33003i | 0.809395 | − | 0.118930i | ||||
\(785\) | − | 66.1415i | − | 2.36069i | ||||||
\(786\) | −4.17274 | + | 2.40913i | −0.148837 | + | 0.0859309i | ||||
\(787\) | −1.71536 | + | 2.97109i | −0.0611459 | + | 0.105908i | −0.894978 | − | 0.446110i | \(-0.852809\pi\) |
0.833832 | + | 0.552018i | \(0.186142\pi\) | |||||||
\(788\) | −2.11904 | + | 3.67029i | −0.0754878 | + | 0.130749i | ||||
\(789\) | −7.83680 | − | 13.5737i | −0.278997 | − | 0.483238i | ||||
\(790\) | − | 71.7653i | − | 2.55329i | ||||||
\(791\) | −24.7333 | + | 16.7958i | −0.879417 | + | 0.597191i | ||||
\(792\) | 2.38605i | 0.0847846i | ||||||||
\(793\) | −16.1597 | + | 9.32981i | −0.573848 | + | 0.331311i | ||||
\(794\) | 6.92370 | + | 3.99740i | 0.245713 | + | 0.141862i | ||||
\(795\) | 5.95327 | − | 10.3114i | 0.211141 | − | 0.365706i | ||||
\(796\) | −5.76433 | + | 3.32803i | −0.204311 | + | 0.117959i | ||||
\(797\) | 23.1970 | 0.821680 | 0.410840 | − | 0.911707i | \(-0.365235\pi\) | ||||
0.410840 | + | 0.911707i | \(0.365235\pi\) | |||||||
\(798\) | 21.4700 | + | 10.3885i | 0.760028 | + | 0.367747i | ||||
\(799\) | 7.08256 | 0.250563 | ||||||||
\(800\) | 4.94246 | + | 8.56059i | 0.174742 | + | 0.302663i | ||||
\(801\) | −2.54935 | − | 1.47187i | −0.0900769 | − | 0.0520059i | ||||
\(802\) | −4.53617 | + | 7.85687i | −0.160178 | + | 0.277436i | ||||
\(803\) | 1.33445 | − | 0.770445i | 0.0470917 | − | 0.0271884i | ||||
\(804\) | −2.22113 | −0.0783332 | ||||||||
\(805\) | −0.0560181 | − | 0.766575i | −0.00197438 | − | 0.0270182i | ||||
\(806\) | 48.4385i | 1.70618i | ||||||||
\(807\) | 13.7920 | − | 7.96280i | 0.485501 | − | 0.280304i | ||||
\(808\) | 44.8974 | + | 25.9215i | 1.57949 | + | 0.911917i | ||||
\(809\) | −6.08020 | − | 3.51040i | −0.213768 | − | 0.123419i | 0.389293 | − | 0.921114i | \(-0.372719\pi\) |
−0.603061 | + | 0.797695i | \(0.706053\pi\) | |||||||
\(810\) | 4.31147 | + | 7.46769i | 0.151490 | + | 0.262388i | ||||
\(811\) | 54.4055 | 1.91043 | 0.955217 | − | 0.295905i | \(-0.0956212\pi\) | ||||
0.955217 | + | 0.295905i | \(0.0956212\pi\) | |||||||
\(812\) | −2.96249 | + | 0.216486i | −0.103963 | + | 0.00759719i | ||||
\(813\) | − | 27.8926i | − | 0.978236i | ||||||
\(814\) | 2.46474 | − | 1.42302i | 0.0863892 | − | 0.0498769i | ||||
\(815\) | 24.8418 | − | 43.0272i | 0.870170 | − | 1.50718i | ||||
\(816\) | −4.12824 | + | 7.15032i | −0.144517 | + | 0.250311i | ||||
\(817\) | 18.9853 | − | 10.9612i | 0.664211 | − | 0.383482i | ||||
\(818\) | 28.9836 | 1.01339 | ||||||||
\(819\) | 11.1416 | − | 23.0264i | 0.389318 | − | 0.804608i | ||||
\(820\) | −3.94520 | + | 5.23905i | −0.137773 | + | 0.182956i | ||||
\(821\) | 15.9540 | + | 27.6331i | 0.556798 | + | 0.964402i | 0.997761 | + | 0.0668771i | \(0.0213035\pi\) |
−0.440963 | + | 0.897525i | \(0.645363\pi\) | |||||||
\(822\) | −12.5770 | + | 21.7839i | −0.438672 | + | 0.759802i | ||||
\(823\) | −9.05242 | − | 5.22642i | −0.315548 | − | 0.182182i | 0.333859 | − | 0.942623i | \(-0.391649\pi\) |
−0.649406 | + | 0.760442i | \(0.724983\pi\) | |||||||
\(824\) | 12.3965 | + | 21.4713i | 0.431852 | + | 0.747989i | ||||
\(825\) | −1.92061 | −0.0668669 | ||||||||
\(826\) | −20.8040 | + | 14.1275i | −0.723863 | + | 0.491558i | ||||
\(827\) | − | 27.9280i | − | 0.971153i | −0.874194 | − | 0.485577i | \(-0.838610\pi\) | ||
0.874194 | − | 0.485577i | \(-0.161390\pi\) | |||||||
\(828\) | 0.0300749 | + | 0.0520913i | 0.00104518 | + | 0.00181030i | ||||
\(829\) | 4.03014 | − | 6.98040i | 0.139972 | − | 0.242439i | −0.787514 | − | 0.616297i | \(-0.788632\pi\) |
0.927486 | + | 0.373858i | \(0.121965\pi\) | |||||||
\(830\) | −20.8471 | + | 36.1082i | −0.723613 | + | 1.25333i | ||||
\(831\) | 4.90551 | − | 2.83220i | 0.170170 | − | 0.0982479i | ||||
\(832\) | − | 39.7988i | − | 1.37977i | ||||||
\(833\) | −14.9809 | + | 11.8563i | −0.519057 | + | 0.410796i | ||||
\(834\) | − | 13.7651i | − | 0.476646i | ||||||
\(835\) | 14.0856 | − | 8.13235i | 0.487454 | − | 0.281432i | ||||
\(836\) | −0.437032 | + | 0.756962i | −0.0151151 | + | 0.0261801i | ||||
\(837\) | −34.1033 | − | 19.6896i | −1.17878 | − | 0.680571i | ||||
\(838\) | −14.7899 | − | 25.6169i | −0.510910 | − | 0.884922i | ||||
\(839\) | 3.51083i | 0.121207i | 0.998162 | + | 0.0606037i | \(0.0193026\pi\) | ||||
−0.998162 | + | 0.0606037i | \(0.980697\pi\) | |||||||
\(840\) | −13.4506 | − | 19.8072i | −0.464091 | − | 0.683415i | ||||
\(841\) | 16.2487 | 0.560300 | ||||||||
\(842\) | 36.2728 | − | 20.9421i | 1.25004 | − | 0.721713i | ||||
\(843\) | 6.38138 | − | 11.0529i | 0.219786 | − | 0.380681i | ||||
\(844\) | 1.24740 | + | 0.720185i | 0.0429372 | + | 0.0247898i | ||||
\(845\) | 11.9068 | + | 20.6232i | 0.409607 | + | 0.709460i | ||||
\(846\) | 7.22806i | 0.248506i | ||||||||
\(847\) | 25.8714 | + | 12.5181i | 0.888952 | + | 0.430128i | ||||
\(848\) | − | 12.9371i | − | 0.444263i | ||||||
\(849\) | 18.9653 | − | 10.9496i | 0.650888 | − | 0.375790i | ||||
\(850\) | 17.2244 | + | 9.94450i | 0.590791 | + | 0.341094i | ||||
\(851\) | 0.264069 | − | 0.457381i | 0.00905218 | − | 0.0156788i | ||||
\(852\) | 0.845561 | + | 1.46455i | 0.0289684 | + | 0.0501748i | ||||
\(853\) | −4.80855 | −0.164642 | −0.0823208 | − | 0.996606i | \(-0.526233\pi\) | ||||
−0.0823208 | + | 0.996606i | \(0.526233\pi\) | |||||||
\(854\) | 1.03656 | + | 14.1847i | 0.0354702 | + | 0.485389i | ||||
\(855\) | 52.4947i | 1.79528i | ||||||||
\(856\) | −20.5828 | − | 35.6505i | −0.703507 | − | 1.21851i | ||||
\(857\) | −11.1155 | + | 19.2526i | −0.379698 | + | 0.657657i | −0.991018 | − | 0.133727i | \(-0.957306\pi\) |
0.611320 | + | 0.791384i | \(0.290639\pi\) | |||||||
\(858\) | 1.73385 | + | 1.00104i | 0.0591925 | + | 0.0341748i | ||||
\(859\) | 0.862437 | + | 1.49378i | 0.0294260 | + | 0.0509673i | 0.880363 | − | 0.474300i | \(-0.157299\pi\) |
−0.850937 | + | 0.525267i | \(0.823965\pi\) | |||||||
\(860\) | −2.98948 | −0.101940 | ||||||||
\(861\) | 8.48426 | − | 13.1642i | 0.289143 | − | 0.448634i | ||||
\(862\) | −35.9203 | −1.22345 | ||||||||
\(863\) | 12.7774 | + | 22.1311i | 0.434948 | + | 0.753353i | 0.997291 | − | 0.0735512i | \(-0.0234332\pi\) |
−0.562343 | + | 0.826904i | \(0.690100\pi\) | |||||||
\(864\) | 7.25472 | + | 4.18851i | 0.246810 | + | 0.142496i | ||||
\(865\) | −12.8152 | + | 22.1966i | −0.435729 | + | 0.754706i | ||||
\(866\) | −20.0927 | − | 34.8016i | −0.682779 | − | 1.18261i | ||||
\(867\) | 8.82957i | 0.299868i | ||||||||
\(868\) | −6.19895 | − | 2.99942i | −0.210406 | − | 0.101807i | ||||
\(869\) | −6.28032 | −0.213045 | ||||||||
\(870\) | −6.98120 | − | 12.0918i | −0.236685 | − | 0.409950i | ||||
\(871\) | 17.2196 | − | 29.8251i | 0.583462 | − | 1.01059i | ||||
\(872\) | 16.8567 | + | 9.73221i | 0.570839 | + | 0.329574i | ||||
\(873\) | 13.4116 | − | 7.74320i | 0.453915 | − | 0.262068i | ||||
\(874\) | − | 0.869595i | − | 0.0294145i | ||||||
\(875\) | −4.37039 | + | 2.96783i | −0.147746 | + | 0.100331i | ||||
\(876\) | − | 1.21000i | − | 0.0408822i | ||||||
\(877\) | −9.59661 | − | 16.6218i | −0.324054 | − | 0.561279i | 0.657266 | − | 0.753659i | \(-0.271713\pi\) |
−0.981321 | + | 0.192380i | \(0.938379\pi\) | |||||||
\(878\) | −32.8523 | − | 18.9673i | −1.10871 | − | 0.640114i | ||||
\(879\) | 1.71618 | − | 2.97251i | 0.0578854 | − | 0.100260i | ||||
\(880\) | −3.41718 | + | 1.97291i | −0.115193 | + | 0.0665068i | ||||
\(881\) | 5.58798 | 0.188264 | 0.0941320 | − | 0.995560i | \(-0.469992\pi\) | ||||
0.0941320 | + | 0.995560i | \(0.469992\pi\) | |||||||
\(882\) | −12.0999 | − | 15.2887i | −0.407423 | − | 0.514796i | ||||
\(883\) | 17.4028i | 0.585651i | 0.956166 | + | 0.292826i | \(0.0945956\pi\) | ||||
−0.956166 | + | 0.292826i | \(0.905404\pi\) | |||||||
\(884\) | 1.93356 | + | 3.34903i | 0.0650327 | + | 0.112640i | ||||
\(885\) | 19.0943 | + | 11.0241i | 0.641847 | + | 0.370571i | ||||
\(886\) | −18.9065 | + | 32.7471i | −0.635178 | + | 1.10016i | ||||
\(887\) | −22.7517 | + | 13.1357i | −0.763927 | + | 0.441053i | −0.830704 | − | 0.556714i | \(-0.812062\pi\) |
0.0667769 | + | 0.997768i | \(0.478728\pi\) | |||||||
\(888\) | − | 16.4516i | − | 0.552079i | ||||||
\(889\) | −10.5528 | + | 7.16617i | −0.353930 | + | 0.240346i | ||||
\(890\) | − | 5.80351i | − | 0.194534i | ||||||
\(891\) | 0.653512 | − | 0.377305i | 0.0218935 | − | 0.0126402i | ||||
\(892\) | 1.67490 | − | 2.90102i | 0.0560799 | − | 0.0971332i | ||||
\(893\) | −9.74558 | + | 16.8798i | −0.326124 | + | 0.564863i | ||||
\(894\) | 3.65840 | + | 6.33654i | 0.122355 | + | 0.211925i | ||||
\(895\) | 58.7430i | 1.96356i | ||||||||
\(896\) | −18.9178 | − | 9.15359i | −0.632001 | − | 0.305800i | ||||
\(897\) | 0.371524 | 0.0124048 | ||||||||
\(898\) | 26.0581 | + | 45.1340i | 0.869570 | + | 1.50614i | ||||
\(899\) | −25.6017 | − | 14.7811i | −0.853864 | − | 0.492979i | ||||
\(900\) | 1.89299 | − | 3.27875i | 0.0630996 | − | 0.109292i | ||||
\(901\) | 5.39507 | + | 9.34454i | 0.179736 | + | 0.311312i | ||||
\(902\) | −2.45802 | − | 1.85099i | −0.0818433 | − | 0.0616311i | ||||
\(903\) | 7.11986 | − | 0.520290i | 0.236934 | − | 0.0173142i | ||||
\(904\) | 33.9544 | 1.12931 | ||||||||
\(905\) | −6.74842 | + | 3.89620i | −0.224325 | + | 0.129514i | ||||
\(906\) | −1.97561 | + | 3.42185i | −0.0656352 | + | 0.113683i | ||||
\(907\) | 16.1717 | − | 28.0103i | 0.536974 | − | 0.930065i | −0.462091 | − | 0.886832i | \(-0.652901\pi\) |
0.999065 | − | 0.0432332i | \(-0.0137658\pi\) | |||||||
\(908\) | 2.64727 | − | 1.52840i | 0.0878528 | − | 0.0507218i | ||||
\(909\) | − | 37.0150i | − | 1.22771i | ||||||
\(910\) | 50.2968 | − | 3.67548i | 1.66732 | − | 0.121841i | ||||
\(911\) | −15.6606 | −0.518859 | −0.259429 | − | 0.965762i | \(-0.583534\pi\) | ||||
−0.259429 | + | 0.965762i | \(0.583534\pi\) | |||||||
\(912\) | −11.3609 | − | 19.6777i | −0.376197 | − | 0.651593i | ||||
\(913\) | 3.15990 | + | 1.82437i | 0.104577 | + | 0.0603777i | ||||
\(914\) | −28.0666 | − | 16.2042i | −0.928360 | − | 0.535989i | ||||
\(915\) | 10.7991 | − | 6.23484i | 0.357006 | − | 0.206118i | ||||
\(916\) | 6.73935i | 0.222674i | ||||||||
\(917\) | 9.56083 | + | 4.62611i | 0.315727 | + | 0.152767i | ||||
\(918\) | 16.8550 | 0.556299 | ||||||||
\(919\) | −45.2344 | + | 26.1161i | −1.49214 | + | 0.861489i | −0.999959 | − | 0.00900168i | \(-0.997135\pi\) |
−0.492184 | + | 0.870491i | \(0.663801\pi\) | |||||||
\(920\) | −0.436463 | + | 0.755977i | −0.0143898 | + | 0.0249238i | ||||
\(921\) | −13.8922 | − | 8.02068i | −0.457764 | − | 0.264290i | ||||
\(922\) | 22.3361 | + | 38.6873i | 0.735601 | + | 1.27410i | ||||
\(923\) | −26.2212 | −0.863082 | ||||||||
\(924\) | −0.235472 | + | 0.159903i | −0.00774646 | + | 0.00526044i | ||||
\(925\) | −33.2423 | −1.09300 | ||||||||
\(926\) | 38.0447 | − | 21.9651i | 1.25023 | − | 0.721818i | ||||
\(927\) | 8.85085 | − | 15.3301i | 0.290700 | − | 0.503508i | ||||
\(928\) | 5.44618 | + | 3.14436i | 0.178780 | + | 0.103219i | ||||
\(929\) | 29.7342 | − | 17.1670i | 0.975547 | − | 0.563232i | 0.0746243 | − | 0.997212i | \(-0.476224\pi\) |
0.900923 | + | 0.433979i | \(0.142891\pi\) | |||||||
\(930\) | − | 32.3701i | − | 1.06146i | ||||||
\(931\) | −7.64337 | − | 52.0182i | −0.250501 | − | 1.70483i | ||||
\(932\) | − | 7.29392i | − | 0.238920i | ||||||
\(933\) | −7.32361 | − | 12.6849i | −0.239764 | − | 0.415284i | ||||
\(934\) | −17.7686 | + | 30.7762i | −0.581408 | + | 1.00703i | ||||
\(935\) | 1.64549 | − | 2.85008i | 0.0538134 | − | 0.0932075i | ||||
\(936\) | −25.1595 | + | 14.5259i | −0.822365 | + | 0.474793i | ||||
\(937\) | − | 20.3893i | − | 0.666089i | −0.942911 | − | 0.333045i | \(-0.891924\pi\) | ||
0.942911 | − | 0.333045i | \(-0.108076\pi\) | |||||||
\(938\) | −14.7468 | − | 21.7159i | −0.481499 | − | 0.709049i | ||||
\(939\) | 21.4286 | 0.699295 | ||||||||
\(940\) | 2.30185 | − | 1.32897i | 0.0750781 | − | 0.0433464i | ||||
\(941\) | 17.4846 | − | 30.2843i | 0.569982 | − | 0.987239i | −0.426584 | − | 0.904448i | \(-0.640283\pi\) |
0.996567 | − | 0.0827909i | \(-0.0263834\pi\) | |||||||
\(942\) | 12.1841 | − | 21.1034i | 0.396978 | − | 0.687586i | ||||
\(943\) | −0.566767 | − | 0.0694009i | −0.0184565 | − | 0.00226001i | ||||
\(944\) | 23.9566 | 0.779722 | ||||||||
\(945\) | −17.8572 | + | 36.9056i | −0.580894 | + | 1.20054i | ||||
\(946\) | − | 1.40258i | − | 0.0456019i | ||||||
\(947\) | 12.2589 | + | 21.2330i | 0.398360 | + | 0.689980i | 0.993524 | − | 0.113624i | \(-0.0362460\pi\) |
−0.595163 | + | 0.803605i | \(0.702913\pi\) | |||||||
\(948\) | −2.46584 | + | 4.27097i | −0.0800869 | + | 0.138715i | ||||
\(949\) | 16.2478 | + | 9.38067i | 0.527426 | + | 0.304509i | ||||
\(950\) | −47.4014 | + | 27.3672i | −1.53791 | + | 0.887910i | ||||
\(951\) | −10.6381 | −0.344964 | ||||||||
\(952\) | 21.6399 | − | 1.58136i | 0.701354 | − | 0.0512521i | ||||
\(953\) | −19.9080 | −0.644883 | −0.322442 | − | 0.946589i | \(-0.604504\pi\) | ||||
−0.322442 | + | 0.946589i | \(0.604504\pi\) | |||||||
\(954\) | −9.53651 | + | 5.50591i | −0.308756 | + | 0.178260i | ||||
\(955\) | −34.7741 | − | 20.0768i | −1.12526 | − | 0.649671i | ||||
\(956\) | 7.56328 | + | 4.36666i | 0.244614 | + | 0.141228i | ||||
\(957\) | −1.05817 | + | 0.610938i | −0.0342059 | + | 0.0197488i | ||||
\(958\) | 3.30881i | 0.106903i | ||||||||
\(959\) | 55.3010 | − | 4.04117i | 1.78576 | − | 0.130496i | ||||
\(960\) | 26.5964i | 0.858394i | ||||||||
\(961\) | −18.7682 | − | 32.5076i | −0.605427 | − | 1.04863i | ||||
\(962\) | 30.0099 | + | 17.3262i | 0.967557 | + | 0.558619i | ||||
\(963\) | −14.6958 | + | 25.4538i | −0.473564 | + | 0.820237i | ||||
\(964\) | −3.75259 | − | 6.49967i | −0.120863 | − | 0.209340i | ||||
\(965\) | 3.08877i | 0.0994309i | ||||||||
\(966\) | 0.123339 | − | 0.254906i | 0.00396836 | − | 0.00820147i | ||||
\(967\) | − | 34.7675i | − | 1.11805i | −0.829152 | − | 0.559023i | \(-0.811176\pi\) | ||
0.829152 | − | 0.559023i | \(-0.188824\pi\) | |||||||
\(968\) | −16.3206 | − | 28.2681i | −0.524563 | − | 0.908570i | ||||
\(969\) | 16.4120 | + | 9.47549i | 0.527230 | + | 0.304397i | ||||
\(970\) | 26.4407 | + | 15.2655i | 0.848959 | + | 0.490147i | ||||
\(971\) | 6.10264 | − | 3.52336i | 0.195843 | − | 0.113070i | −0.398872 | − | 0.917007i | \(-0.630598\pi\) |
0.594715 | + | 0.803937i | \(0.297265\pi\) | |||||||
\(972\) | − | 5.07913i | − | 0.162913i | ||||||
\(973\) | −25.1024 | + | 17.0465i | −0.804747 | + | 0.546485i | ||||
\(974\) | 0.366171 | 0.0117329 | ||||||||
\(975\) | −11.6923 | − | 20.2517i | −0.374454 | − | 0.648573i | ||||
\(976\) | 6.77452 | − | 11.7338i | 0.216847 | − | 0.375590i | ||||
\(977\) | −42.6007 | − | 24.5955i | −1.36292 | − | 0.786880i | −0.372906 | − | 0.927869i | \(-0.621639\pi\) |
−0.990011 | + | 0.140989i | \(0.954972\pi\) | |||||||
\(978\) | 15.8523 | − | 9.15231i | 0.506900 | − | 0.292659i | ||||
\(979\) | −0.507876 | −0.0162318 | ||||||||
\(980\) | −2.64412 | + | 6.66435i | −0.0844633 | + | 0.212885i | ||||
\(981\) | − | 13.8972i | − | 0.443704i | ||||||
\(982\) | 7.27558 | + | 12.6017i | 0.232173 | + | 0.402136i | ||||
\(983\) | 14.0331 | − | 24.3061i | 0.447587 | − | 0.775243i | −0.550642 | − | 0.834742i | \(-0.685617\pi\) |
0.998228 | + | 0.0594989i | \(0.0189503\pi\) | |||||||
\(984\) | −16.3705 | + | 6.95522i | −0.521872 | + | 0.221724i | ||||
\(985\) | 21.9569 | + | 38.0304i | 0.699604 | + | 1.21175i | ||||
\(986\) | 12.6532 | 0.402961 | ||||||||
\(987\) | −5.25089 | + | 3.56576i | −0.167138 | + | 0.113499i | ||||
\(988\) | −10.6423 | −0.338577 | ||||||||
\(989\) | −0.130138 | − | 0.225406i | −0.00413816 | − | 0.00716750i | ||||
\(990\) | 2.90863 | + | 1.67930i | 0.0924424 | + | 0.0533716i | ||||
\(991\) | 11.5589 | + | 6.67353i | 0.367180 | + | 0.211992i | 0.672226 | − | 0.740346i | \(-0.265338\pi\) |
−0.305046 | + | 0.952338i | \(0.598672\pi\) | |||||||
\(992\) | 7.28980 | + | 12.6263i | 0.231451 | + | 0.400885i | ||||
\(993\) | 1.66437 | 0.0528171 | ||||||||
\(994\) | −8.70495 | + | 17.9906i | −0.276104 | + | 0.570628i | ||||
\(995\) | 68.9681i | 2.18644i | ||||||||
\(996\) | 2.48135 | − | 1.43261i | 0.0786244 | − | 0.0453938i | ||||
\(997\) | −12.1719 | − | 7.02743i | −0.385487 | − | 0.222561i | 0.294716 | − | 0.955585i | \(-0.404775\pi\) |
−0.680203 | + | 0.733024i | \(0.738108\pi\) | |||||||
\(998\) | 32.4701 | + | 18.7466i | 1.02782 | + | 0.593414i | ||||
\(999\) | −24.3972 | + | 14.0857i | −0.771892 | + | 0.445652i |
(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 | 287.2.j.a.81.19 | ✓ | 52 | |
7.2 | even | 3 | inner | 287.2.j.a.163.20 | yes | 52 | |
41.40 | even | 2 | inner | 287.2.j.a.81.20 | yes | 52 | |
287.163 | even | 6 | inner | 287.2.j.a.163.19 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.j.a.81.19 | ✓ | 52 | 1.1 | even | 1 | trivial | |
287.2.j.a.81.20 | yes | 52 | 41.40 | even | 2 | inner | |
287.2.j.a.163.19 | yes | 52 | 287.163 | even | 6 | inner | |
287.2.j.a.163.20 | yes | 52 | 7.2 | even | 3 | inner |