Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(30,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.u (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.2346760387617129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 30.2 | ||
Root | \(-1.38488 - 0.286553i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.30 |
Dual form | 637.2.u.g.361.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.19430 | + | 0.689527i | −0.844495 | + | 0.487570i | −0.858790 | − | 0.512328i | \(-0.828783\pi\) |
0.0142944 | + | 0.999898i | \(0.495450\pi\) | |||||||
\(3\) | −2.88120 | −1.66346 | −0.831732 | − | 0.555178i | \(-0.812650\pi\) | ||||
−0.831732 | + | 0.555178i | \(0.812650\pi\) | |||||||
\(4\) | −0.0491037 | + | 0.0850501i | −0.0245518 | + | 0.0425250i | ||||
\(5\) | −0.697972 | − | 0.402974i | −0.312142 | − | 0.180216i | 0.335742 | − | 0.941954i | \(-0.391013\pi\) |
−0.647885 | + | 0.761738i | \(0.724346\pi\) | |||||||
\(6\) | 3.44101 | − | 1.98667i | 1.40479 | − | 0.811054i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.89354i | − | 1.02302i | ||||||
\(9\) | 5.30133 | 1.76711 | ||||||||
\(10\) | 1.11145 | 0.351470 | ||||||||
\(11\) | 5.27158i | 1.58944i | 0.606976 | + | 0.794720i | \(0.292382\pi\) | ||||
−0.606976 | + | 0.794720i | \(0.707618\pi\) | |||||||
\(12\) | 0.141478 | − | 0.245047i | 0.0408411 | − | 0.0707389i | ||||
\(13\) | 2.36581 | + | 2.72084i | 0.656156 | + | 0.754625i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.01100 | + | 1.16105i | 0.519237 | + | 0.299782i | ||||
\(16\) | 1.89697 | + | 3.28565i | 0.474243 | + | 0.821412i | ||||
\(17\) | 0.280051 | − | 0.485062i | 0.0679223 | − | 0.117645i | −0.830064 | − | 0.557668i | \(-0.811696\pi\) |
0.897987 | + | 0.440023i | \(0.145030\pi\) | |||||||
\(18\) | −6.33136 | + | 3.65541i | −1.49232 | + | 0.861589i | ||||
\(19\) | 5.84469i | 1.34086i | 0.741972 | + | 0.670431i | \(0.233891\pi\) | ||||
−0.741972 | + | 0.670431i | \(0.766109\pi\) | |||||||
\(20\) | 0.0685460 | − | 0.0395750i | 0.0153273 | − | 0.00884925i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.63490 | − | 6.29583i | −0.774963 | − | 1.34228i | ||||
\(23\) | −0.802438 | − | 1.38986i | −0.167320 | − | 0.289807i | 0.770157 | − | 0.637855i | \(-0.220178\pi\) |
−0.937477 | + | 0.348048i | \(0.886845\pi\) | |||||||
\(24\) | 8.33689i | 1.70176i | ||||||||
\(25\) | −2.17522 | − | 3.76760i | −0.435045 | − | 0.753520i | ||||
\(26\) | −4.70157 | − | 1.61820i | −0.922053 | − | 0.317355i | ||||
\(27\) | −6.63060 | −1.27606 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.14008 | + | 1.97467i | −0.211707 | + | 0.366687i | −0.952249 | − | 0.305323i | \(-0.901236\pi\) |
0.740542 | + | 0.672010i | \(0.234569\pi\) | |||||||
\(30\) | −3.20230 | −0.584658 | ||||||||
\(31\) | 3.01022 | − | 1.73795i | 0.540651 | − | 0.312145i | −0.204692 | − | 0.978827i | \(-0.565619\pi\) |
0.745343 | + | 0.666681i | \(0.232286\pi\) | |||||||
\(32\) | 0.480674 | + | 0.277517i | 0.0849719 | + | 0.0490585i | ||||
\(33\) | − | 15.1885i | − | 2.64398i | ||||||
\(34\) | 0.772411i | 0.132467i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.260315 | + | 0.450879i | −0.0433858 | + | 0.0751464i | ||||
\(37\) | 1.07557 | − | 0.620979i | 0.176822 | − | 0.102088i | −0.408977 | − | 0.912545i | \(-0.634114\pi\) |
0.585799 | + | 0.810457i | \(0.300781\pi\) | |||||||
\(38\) | −4.03007 | − | 6.98029i | −0.653764 | − | 1.13235i | ||||
\(39\) | −6.81636 | − | 7.83929i | −1.09149 | − | 1.25529i | ||||
\(40\) | −1.16602 | + | 2.01961i | −0.184364 | + | 0.319329i | ||||
\(41\) | −0.803413 | − | 0.463851i | −0.125472 | − | 0.0724413i | 0.435950 | − | 0.899971i | \(-0.356412\pi\) |
−0.561422 | + | 0.827529i | \(0.689746\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.22356 | + | 3.85131i | 0.339089 | + | 0.587320i | 0.984262 | − | 0.176717i | \(-0.0565478\pi\) |
−0.645172 | + | 0.764037i | \(0.723214\pi\) | |||||||
\(44\) | −0.448348 | − | 0.258854i | −0.0675910 | − | 0.0390237i | ||||
\(45\) | −3.70018 | − | 2.13630i | −0.551590 | − | 0.318461i | ||||
\(46\) | 1.91670 | + | 1.10661i | 0.282602 | + | 0.163160i | ||||
\(47\) | −3.32915 | − | 1.92209i | −0.485607 | − | 0.280365i | 0.237143 | − | 0.971475i | \(-0.423789\pi\) |
−0.722750 | + | 0.691109i | \(0.757122\pi\) | |||||||
\(48\) | −5.46556 | − | 9.46662i | −0.788885 | − | 1.36639i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.19572 | + | 2.99975i | 0.734786 | + | 0.424229i | ||||
\(51\) | −0.806883 | + | 1.39756i | −0.112986 | + | 0.195698i | ||||
\(52\) | −0.347577 | + | 0.0676087i | −0.0482003 | + | 0.00937564i | ||||
\(53\) | −2.72727 | − | 4.72377i | −0.374620 | − | 0.648860i | 0.615650 | − | 0.788019i | \(-0.288893\pi\) |
−0.990270 | + | 0.139159i | \(0.955560\pi\) | |||||||
\(54\) | 7.91890 | − | 4.57198i | 1.07763 | − | 0.622168i | ||||
\(55\) | 2.12431 | − | 3.67941i | 0.286442 | − | 0.496132i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 16.8397i | − | 2.23048i | ||||||
\(58\) | − | 3.14446i | − | 0.412887i | ||||||
\(59\) | −9.52106 | − | 5.49698i | −1.23954 | − | 0.715646i | −0.270537 | − | 0.962710i | \(-0.587201\pi\) |
−0.968999 | + | 0.247063i | \(0.920534\pi\) | |||||||
\(60\) | −0.197495 | + | 0.114024i | −0.0254965 | + | 0.0147204i | ||||
\(61\) | −7.30215 | −0.934944 | −0.467472 | − | 0.884008i | \(-0.654835\pi\) | ||||
−0.467472 | + | 0.884008i | \(0.654835\pi\) | |||||||
\(62\) | −2.39673 | + | 4.15126i | −0.304385 | + | 0.527210i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.35330 | −1.04416 | ||||||||
\(65\) | −0.554837 | − | 2.85243i | −0.0688191 | − | 0.353800i | ||||
\(66\) | 10.4729 | + | 18.1396i | 1.28912 | + | 2.23283i | ||||
\(67\) | 7.34556i | 0.897403i | 0.893682 | + | 0.448701i | \(0.148113\pi\) | ||||
−0.893682 | + | 0.448701i | \(0.851887\pi\) | |||||||
\(68\) | 0.0275031 | + | 0.0476367i | 0.00333524 | + | 0.00577680i | ||||
\(69\) | 2.31199 | + | 4.00448i | 0.278330 | + | 0.482083i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.06668 | + | 4.65730i | −0.957339 | + | 0.552720i | −0.895353 | − | 0.445357i | \(-0.853077\pi\) |
−0.0619857 | + | 0.998077i | \(0.519743\pi\) | |||||||
\(72\) | − | 15.3396i | − | 1.80779i | ||||||
\(73\) | 4.33139 | − | 2.50073i | 0.506951 | − | 0.292688i | −0.224629 | − | 0.974444i | \(-0.572117\pi\) |
0.731579 | + | 0.681756i | \(0.238784\pi\) | |||||||
\(74\) | −0.856364 | + | 1.48327i | −0.0995503 | + | 0.172426i | ||||
\(75\) | 6.26726 | + | 10.8552i | 0.723681 | + | 1.25345i | ||||
\(76\) | −0.497091 | − | 0.286996i | −0.0570202 | − | 0.0329207i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 13.5462 | + | 4.66237i | 1.53380 | + | 0.527909i | ||||
\(79\) | −5.68437 | + | 9.84562i | −0.639542 | + | 1.10772i | 0.345992 | + | 0.938238i | \(0.387543\pi\) |
−0.985533 | + | 0.169481i | \(0.945791\pi\) | |||||||
\(80\) | − | 3.05772i | − | 0.341863i | ||||||
\(81\) | 3.20012 | 0.355568 | ||||||||
\(82\) | 1.27935 | 0.141281 | ||||||||
\(83\) | − | 5.81962i | − | 0.638786i | −0.947622 | − | 0.319393i | \(-0.896521\pi\) | ||
0.947622 | − | 0.319393i | \(-0.103479\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.390935 | + | 0.225707i | −0.0424029 | + | 0.0244813i | ||||
\(86\) | −5.31117 | − | 3.06641i | −0.572719 | − | 0.330659i | ||||
\(87\) | 3.28479 | − | 5.68943i | 0.352167 | − | 0.609971i | ||||
\(88\) | 15.2535 | 1.62603 | ||||||||
\(89\) | −4.33832 | + | 2.50473i | −0.459861 | + | 0.265501i | −0.711986 | − | 0.702194i | \(-0.752204\pi\) |
0.252125 | + | 0.967695i | \(0.418871\pi\) | |||||||
\(90\) | 5.89215 | 0.621087 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.157611 | 0.0164320 | ||||||||
\(93\) | −8.67305 | + | 5.00739i | −0.899354 | + | 0.519242i | ||||
\(94\) | 5.30133 | 0.546791 | ||||||||
\(95\) | 2.35526 | − | 4.07942i | 0.241644 | − | 0.418540i | ||||
\(96\) | −1.38492 | − | 0.799583i | −0.141348 | − | 0.0816071i | ||||
\(97\) | −9.22171 | + | 5.32416i | −0.936323 | + | 0.540586i | −0.888806 | − | 0.458284i | \(-0.848464\pi\) |
−0.0475172 | + | 0.998870i | \(0.515131\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 27.9464i | 2.80872i | ||||||||
\(100\) | 0.427246 | 0.0427246 | ||||||||
\(101\) | 3.91554 | 0.389611 | 0.194805 | − | 0.980842i | \(-0.437592\pi\) | ||||
0.194805 | + | 0.980842i | \(0.437592\pi\) | |||||||
\(102\) | − | 2.22547i | − | 0.220355i | ||||||
\(103\) | −4.22690 | + | 7.32120i | −0.416488 | + | 0.721379i | −0.995583 | − | 0.0938810i | \(-0.970073\pi\) |
0.579095 | + | 0.815260i | \(0.303406\pi\) | |||||||
\(104\) | 7.87287 | − | 6.84556i | 0.771998 | − | 0.671262i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.51434 | + | 3.76106i | 0.632729 | + | 0.365306i | ||||
\(107\) | 4.83761 | + | 8.37899i | 0.467670 | + | 0.810028i | 0.999318 | − | 0.0369379i | \(-0.0117604\pi\) |
−0.531648 | + | 0.846965i | \(0.678427\pi\) | |||||||
\(108\) | 0.325587 | − | 0.563933i | 0.0313296 | − | 0.0542645i | ||||
\(109\) | 12.6126 | − | 7.28189i | 1.20807 | − | 0.697478i | 0.245731 | − | 0.969338i | \(-0.420972\pi\) |
0.962337 | + | 0.271860i | \(0.0876388\pi\) | |||||||
\(110\) | 5.85908i | 0.558641i | ||||||||
\(111\) | −3.09893 | + | 1.78917i | −0.294137 | + | 0.169820i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.75572 | − | 16.8974i | −0.917741 | − | 1.58957i | −0.802838 | − | 0.596197i | \(-0.796678\pi\) |
−0.114903 | − | 0.993377i | \(-0.536656\pi\) | |||||||
\(114\) | 11.6115 | + | 20.1116i | 1.08751 | + | 1.88363i | ||||
\(115\) | 1.29345i | 0.120615i | ||||||||
\(116\) | −0.111964 | − | 0.193927i | −0.0103956 | − | 0.0180057i | ||||
\(117\) | 12.5419 | + | 14.4241i | 1.15950 | + | 1.33351i | ||||
\(118\) | 15.1613 | 1.39571 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.35955 | − | 5.81891i | 0.306683 | − | 0.531191i | ||||
\(121\) | −16.7895 | −1.52632 | ||||||||
\(122\) | 8.72093 | − | 5.03503i | 0.789556 | − | 0.455850i | ||||
\(123\) | 2.31480 | + | 1.33645i | 0.208718 | + | 0.120503i | ||||
\(124\) | 0.341359i | 0.0306550i | ||||||||
\(125\) | 7.53598i | 0.674038i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.958656 | + | 1.66044i | −0.0850670 | + | 0.147340i | −0.905420 | − | 0.424517i | \(-0.860444\pi\) |
0.820353 | + | 0.571858i | \(0.193777\pi\) | |||||||
\(128\) | 9.01498 | − | 5.20480i | 0.796819 | − | 0.460044i | ||||
\(129\) | −6.40652 | − | 11.0964i | −0.564063 | − | 0.976985i | ||||
\(130\) | 2.62947 | + | 3.02407i | 0.230619 | + | 0.265228i | ||||
\(131\) | 7.79078 | − | 13.4940i | 0.680684 | − | 1.17898i | −0.294089 | − | 0.955778i | \(-0.595016\pi\) |
0.974772 | − | 0.223201i | \(-0.0716506\pi\) | |||||||
\(132\) | 1.29178 | + | 0.745811i | 0.112435 | + | 0.0649145i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.06496 | − | 8.77278i | −0.437546 | − | 0.757852i | ||||
\(135\) | 4.62797 | + | 2.67196i | 0.398312 | + | 0.229966i | ||||
\(136\) | −1.40355 | − | 0.810339i | −0.120353 | − | 0.0694860i | ||||
\(137\) | 6.79921 | + | 3.92553i | 0.580896 | + | 0.335380i | 0.761489 | − | 0.648178i | \(-0.224469\pi\) |
−0.180594 | + | 0.983558i | \(0.557802\pi\) | |||||||
\(138\) | −5.52240 | − | 3.18836i | −0.470098 | − | 0.271411i | ||||
\(139\) | 4.96241 | + | 8.59514i | 0.420906 | + | 0.729030i | 0.996028 | − | 0.0890370i | \(-0.0283789\pi\) |
−0.575122 | + | 0.818067i | \(0.695046\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.59197 | + | 5.53793i | 0.807790 | + | 0.466378i | ||||
\(142\) | 6.42267 | − | 11.1244i | 0.538979 | − | 0.933538i | ||||
\(143\) | −14.3431 | + | 12.4715i | −1.19943 | + | 1.04292i | ||||
\(144\) | 10.0565 | + | 17.4183i | 0.838039 | + | 1.45153i | ||||
\(145\) | 1.59148 | − | 0.918843i | 0.132165 | − | 0.0763058i | ||||
\(146\) | −3.44864 | + | 5.97322i | −0.285412 | + | 0.494347i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.121969i | 0.0100258i | ||||||||
\(149\) | − | 7.91925i | − | 0.648770i | −0.945925 | − | 0.324385i | \(-0.894843\pi\) | ||
0.945925 | − | 0.324385i | \(-0.105157\pi\) | |||||||
\(150\) | −14.9699 | − | 8.64290i | −1.22229 | − | 0.705690i | ||||
\(151\) | −1.30005 | + | 0.750582i | −0.105796 | + | 0.0610815i | −0.551965 | − | 0.833868i | \(-0.686122\pi\) |
0.446168 | + | 0.894949i | \(0.352788\pi\) | |||||||
\(152\) | 16.9118 | 1.37173 | ||||||||
\(153\) | 1.48464 | − | 2.57148i | 0.120026 | − | 0.207892i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.80140 | −0.225014 | ||||||||
\(156\) | 1.00144 | − | 0.194794i | 0.0801794 | − | 0.0155960i | ||||
\(157\) | 1.92846 | + | 3.34019i | 0.153908 | + | 0.266576i | 0.932661 | − | 0.360754i | \(-0.117481\pi\) |
−0.778753 | + | 0.627331i | \(0.784147\pi\) | |||||||
\(158\) | − | 15.6781i | − | 1.24728i | ||||||
\(159\) | 7.85782 | + | 13.6102i | 0.623166 | + | 1.07936i | ||||
\(160\) | −0.223664 | − | 0.387398i | −0.0176822 | − | 0.0306265i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.82189 | + | 2.20657i | −0.300276 | + | 0.173364i | ||||
\(163\) | − | 14.3608i | − | 1.12483i | −0.826856 | − | 0.562414i | \(-0.809873\pi\) | ||
0.826856 | − | 0.562414i | \(-0.190127\pi\) | |||||||
\(164\) | 0.0789011 | − | 0.0455536i | 0.00616114 | − | 0.00355714i | ||||
\(165\) | −6.12057 | + | 10.6011i | −0.476486 | + | 0.825297i | ||||
\(166\) | 4.01279 | + | 6.95035i | 0.311453 | + | 0.539452i | ||||
\(167\) | 3.91563 | + | 2.26069i | 0.303000 | + | 0.174937i | 0.643790 | − | 0.765202i | \(-0.277361\pi\) |
−0.340790 | + | 0.940140i | \(0.610694\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.80593 | + | 12.8740i | −0.138918 | + | 0.990304i | ||||
\(170\) | 0.311262 | − | 0.539121i | 0.0238727 | − | 0.0413487i | ||||
\(171\) | 30.9846i | 2.36945i | ||||||||
\(172\) | −0.436739 | −0.0333011 | ||||||||
\(173\) | −19.5179 | −1.48392 | −0.741960 | − | 0.670444i | \(-0.766104\pi\) | ||||
−0.741960 | + | 0.670444i | \(0.766104\pi\) | |||||||
\(174\) | 9.05982i | 0.686823i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.3206 | + | 10.0000i | −1.30559 | + | 0.753780i | ||||
\(177\) | 27.4321 | + | 15.8379i | 2.06192 | + | 1.19045i | ||||
\(178\) | 3.45416 | − | 5.98278i | 0.258900 | − | 0.448428i | ||||
\(179\) | −20.8196 | −1.55613 | −0.778065 | − | 0.628183i | \(-0.783799\pi\) | ||||
−0.778065 | + | 0.628183i | \(0.783799\pi\) | |||||||
\(180\) | 0.363385 | − | 0.209800i | 0.0270851 | − | 0.0156376i | ||||
\(181\) | −16.5522 | −1.23031 | −0.615157 | − | 0.788405i | \(-0.710907\pi\) | ||||
−0.615157 | + | 0.788405i | \(0.710907\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.0390 | 1.55525 | ||||||||
\(184\) | −4.02163 | + | 2.32189i | −0.296478 | + | 0.171172i | ||||
\(185\) | −1.00095 | −0.0735916 | ||||||||
\(186\) | 6.90546 | − | 11.9606i | 0.506333 | − | 0.876995i | ||||
\(187\) | 2.55704 | + | 1.47631i | 0.186990 | + | 0.107958i | ||||
\(188\) | 0.326948 | − | 0.188763i | 0.0238451 | − | 0.0137670i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.49606i | 0.471274i | ||||||||
\(191\) | −4.25008 | −0.307525 | −0.153762 | − | 0.988108i | \(-0.549139\pi\) | ||||
−0.153762 | + | 0.988108i | \(0.549139\pi\) | |||||||
\(192\) | 24.0676 | 1.73693 | ||||||||
\(193\) | − | 11.5972i | − | 0.834787i | −0.908726 | − | 0.417393i | \(-0.862944\pi\) | ||
0.908726 | − | 0.417393i | \(-0.137056\pi\) | |||||||
\(194\) | 7.34231 | − | 12.7172i | 0.527147 | − | 0.913045i | ||||
\(195\) | 1.59860 | + | 8.21842i | 0.114478 | + | 0.588533i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.4892 | − | 7.21066i | −0.889821 | − | 0.513738i | −0.0159371 | − | 0.999873i | \(-0.505073\pi\) |
−0.873884 | + | 0.486135i | \(0.838406\pi\) | |||||||
\(198\) | −19.2698 | − | 33.3763i | −1.36944 | − | 2.37195i | ||||
\(199\) | −3.52962 | + | 6.11348i | −0.250208 | + | 0.433373i | −0.963583 | − | 0.267409i | \(-0.913832\pi\) |
0.713375 | + | 0.700783i | \(0.247166\pi\) | |||||||
\(200\) | −10.9017 | + | 6.29410i | −0.770867 | + | 0.445060i | ||||
\(201\) | − | 21.1640i | − | 1.49280i | ||||||
\(202\) | −4.67632 | + | 2.69987i | −0.329024 | + | 0.189962i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.0792419 | − | 0.137251i | −0.00554804 | − | 0.00960949i | ||||
\(205\) | 0.373840 | + | 0.647509i | 0.0261101 | + | 0.0452240i | ||||
\(206\) | − | 11.6582i | − | 0.812268i | ||||||
\(207\) | −4.25399 | − | 7.36812i | −0.295673 | − | 0.512120i | ||||
\(208\) | −4.45186 | + | 12.9346i | −0.308681 | + | 0.896850i | ||||
\(209\) | −30.8107 | −2.13122 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.2113 | − | 22.8827i | 0.909505 | − | 1.57531i | 0.0947513 | − | 0.995501i | \(-0.469794\pi\) |
0.814754 | − | 0.579807i | \(-0.196872\pi\) | |||||||
\(212\) | 0.535677 | 0.0367904 | ||||||||
\(213\) | 23.2417 | − | 13.4186i | 1.59250 | − | 0.919429i | ||||
\(214\) | −11.5551 | − | 6.67133i | −0.789890 | − | 0.456043i | ||||
\(215\) | − | 3.58414i | − | 0.244437i | ||||||
\(216\) | 19.1859i | 1.30544i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0421 | + | 17.3935i | −0.680138 | + | 1.17803i | ||||
\(219\) | −12.4796 | + | 7.20511i | −0.843294 | + | 0.486876i | ||||
\(220\) | 0.208623 | + | 0.361345i | 0.0140654 | + | 0.0243619i | ||||
\(221\) | 1.98232 | − | 0.385590i | 0.133345 | − | 0.0259376i | ||||
\(222\) | 2.46736 | − | 4.27359i | 0.165598 | − | 0.286825i | ||||
\(223\) | −19.9191 | − | 11.5003i | −1.33388 | − | 0.770115i | −0.347987 | − | 0.937499i | \(-0.613135\pi\) |
−0.985892 | + | 0.167384i | \(0.946468\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.5316 | − | 19.9733i | −0.768772 | − | 1.33155i | ||||
\(226\) | 23.3024 | + | 13.4537i | 1.55006 | + | 0.894925i | ||||
\(227\) | 0.392628 | + | 0.226684i | 0.0260596 | + | 0.0150455i | 0.512973 | − | 0.858405i | \(-0.328544\pi\) |
−0.486914 | + | 0.873450i | \(0.661877\pi\) | |||||||
\(228\) | 1.43222 | + | 0.826893i | 0.0948511 | + | 0.0547623i | ||||
\(229\) | 15.0112 | + | 8.66674i | 0.991970 | + | 0.572714i | 0.905863 | − | 0.423571i | \(-0.139224\pi\) |
0.0861077 | + | 0.996286i | \(0.472557\pi\) | |||||||
\(230\) | −0.891867 | − | 1.54476i | −0.0588080 | − | 0.101858i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.71380 | + | 3.29886i | 0.375129 | + | 0.216581i | ||||
\(233\) | 3.90756 | − | 6.76809i | 0.255992 | − | 0.443392i | −0.709172 | − | 0.705035i | \(-0.750931\pi\) |
0.965165 | + | 0.261643i | \(0.0842644\pi\) | |||||||
\(234\) | −24.9246 | − | 8.57862i | −1.62937 | − | 0.560802i | ||||
\(235\) | 1.54910 | + | 2.68313i | 0.101052 | + | 0.175028i | ||||
\(236\) | 0.935038 | − | 0.539844i | 0.0608658 | − | 0.0351409i | ||||
\(237\) | 16.3778 | − | 28.3672i | 1.06385 | − | 1.84265i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.5314i | 0.875276i | 0.899151 | + | 0.437638i | \(0.144185\pi\) | ||||
−0.899151 | + | 0.437638i | \(0.855815\pi\) | |||||||
\(240\) | 8.80991i | 0.568677i | ||||||||
\(241\) | 19.5369 | + | 11.2796i | 1.25848 | + | 0.726583i | 0.972779 | − | 0.231736i | \(-0.0744404\pi\) |
0.285701 | + | 0.958319i | \(0.407774\pi\) | |||||||
\(242\) | 20.0517 | − | 11.5768i | 1.28897 | − | 0.744188i | ||||
\(243\) | 10.6716 | 0.684585 | ||||||||
\(244\) | 0.358563 | − | 0.621049i | 0.0229546 | − | 0.0397586i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.68607 | −0.235015 | ||||||||
\(247\) | −15.9024 | + | 13.8274i | −1.01185 | + | 0.879815i | ||||
\(248\) | −5.02884 | − | 8.71020i | −0.319331 | − | 0.553098i | ||||
\(249\) | 16.7675i | 1.06260i | ||||||||
\(250\) | −5.19626 | − | 9.00019i | −0.328641 | − | 0.569222i | ||||
\(251\) | 3.36618 | + | 5.83039i | 0.212471 | + | 0.368011i | 0.952487 | − | 0.304578i | \(-0.0985154\pi\) |
−0.740016 | + | 0.672589i | \(0.765182\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.32677 | − | 4.23011i | 0.460630 | − | 0.265945i | ||||
\(254\) | − | 2.64408i | − | 0.165904i | ||||||
\(255\) | 1.12636 | − | 0.650306i | 0.0705356 | − | 0.0407238i | ||||
\(256\) | 1.17560 | − | 2.03620i | 0.0734750 | − | 0.127262i | ||||
\(257\) | −8.26907 | − | 14.3225i | −0.515811 | − | 0.893410i | −0.999832 | − | 0.0183536i | \(-0.994158\pi\) |
0.484021 | − | 0.875056i | \(-0.339176\pi\) | |||||||
\(258\) | 15.3026 | + | 8.83494i | 0.952696 | + | 0.550039i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.269844 | + | 0.0928757i | 0.0167350 | + | 0.00575991i | ||||
\(261\) | −6.04392 | + | 10.4684i | −0.374110 | + | 0.647977i | ||||
\(262\) | 21.4878i | 1.32752i | ||||||||
\(263\) | −10.0227 | −0.618028 | −0.309014 | − | 0.951057i | \(-0.599999\pi\) | ||||
−0.309014 | + | 0.951057i | \(0.599999\pi\) | |||||||
\(264\) | −43.9485 | −2.70485 | ||||||||
\(265\) | 4.39608i | 0.270049i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.4996 | − | 7.21663i | 0.764962 | − | 0.441651i | ||||
\(268\) | −0.624740 | − | 0.360694i | −0.0381621 | − | 0.0220329i | ||||
\(269\) | −7.86149 | + | 13.6165i | −0.479323 | + | 0.830212i | −0.999719 | − | 0.0237130i | \(-0.992451\pi\) |
0.520395 | + | 0.853925i | \(0.325785\pi\) | |||||||
\(270\) | −7.36956 | −0.448497 | ||||||||
\(271\) | 4.51734 | − | 2.60809i | 0.274409 | − | 0.158430i | −0.356481 | − | 0.934303i | \(-0.616023\pi\) |
0.630890 | + | 0.775873i | \(0.282690\pi\) | |||||||
\(272\) | 2.12499 | 0.128847 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.8270 | −0.654085 | ||||||||
\(275\) | 19.8612 | − | 11.4669i | 1.19767 | − | 0.691478i | ||||
\(276\) | −0.454108 | −0.0273341 | ||||||||
\(277\) | −9.63619 | + | 16.6904i | −0.578983 | + | 1.00283i | 0.416614 | + | 0.909084i | \(0.363217\pi\) |
−0.995596 | + | 0.0937439i | \(0.970117\pi\) | |||||||
\(278\) | −11.8532 | − | 6.84343i | −0.710906 | − | 0.410442i | ||||
\(279\) | 15.9582 | − | 9.21345i | 0.955390 | − | 0.551595i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.14283i | 0.127831i | 0.997955 | + | 0.0639153i | \(0.0203588\pi\) | ||||
−0.997955 | + | 0.0639153i | \(0.979641\pi\) | |||||||
\(282\) | −15.2742 | −0.909566 | ||||||||
\(283\) | −15.7502 | −0.936255 | −0.468127 | − | 0.883661i | \(-0.655071\pi\) | ||||
−0.468127 | + | 0.883661i | \(0.655071\pi\) | |||||||
\(284\) | − | 0.914762i | − | 0.0542812i | ||||||
\(285\) | −6.78597 | + | 11.7537i | −0.401966 | + | 0.696226i | ||||
\(286\) | 8.53048 | − | 24.7847i | 0.504418 | − | 1.46555i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.54821 | + | 1.47121i | 0.150155 | + | 0.0866919i | ||||
\(289\) | 8.34314 | + | 14.4507i | 0.490773 | + | 0.850044i | ||||
\(290\) | −1.26714 | + | 2.19474i | −0.0744087 | + | 0.128880i | ||||
\(291\) | 26.5696 | − | 15.3400i | 1.55754 | − | 0.899246i | ||||
\(292\) | 0.491180i | 0.0287441i | ||||||||
\(293\) | 20.0474 | − | 11.5744i | 1.17118 | − | 0.676182i | 0.217223 | − | 0.976122i | \(-0.430300\pi\) |
0.953958 | + | 0.299940i | \(0.0969668\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.43029 | + | 7.67348i | 0.257941 | + | 0.446767i | ||||
\(296\) | −1.79683 | − | 3.11220i | −0.104439 | − | 0.180893i | ||||
\(297\) | − | 34.9537i | − | 2.02822i | ||||||
\(298\) | 5.46054 | + | 9.45793i | 0.316320 | + | 0.547883i | ||||
\(299\) | 1.88318 | − | 5.47145i | 0.108907 | − | 0.316422i | ||||
\(300\) | −1.23098 | −0.0710708 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.03509 | − | 1.79283i | 0.0595629 | − | 0.103166i | ||||
\(303\) | −11.2815 | −0.648103 | ||||||||
\(304\) | −19.2036 | + | 11.0872i | −1.10140 | + | 0.635894i | ||||
\(305\) | 5.09669 | + | 2.94258i | 0.291836 | + | 0.168491i | ||||
\(306\) | 4.09481i | 0.234085i | ||||||||
\(307\) | 4.23590i | 0.241756i | 0.992667 | + | 0.120878i | \(0.0385709\pi\) | ||||
−0.992667 | + | 0.120878i | \(0.961429\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.1785 | − | 21.0939i | 0.692813 | − | 1.19999i | ||||
\(310\) | 3.34570 | − | 1.93164i | 0.190023 | − | 0.109710i | ||||
\(311\) | −13.6251 | − | 23.5993i | −0.772606 | − | 1.33819i | −0.936130 | − | 0.351654i | \(-0.885619\pi\) |
0.163524 | − | 0.986539i | \(-0.447714\pi\) | |||||||
\(312\) | −22.6833 | + | 19.7234i | −1.28419 | + | 1.11662i | ||||
\(313\) | 1.34849 | − | 2.33565i | 0.0762209 | − | 0.132018i | −0.825396 | − | 0.564555i | \(-0.809048\pi\) |
0.901617 | + | 0.432536i | \(0.142381\pi\) | |||||||
\(314\) | −4.60631 | − | 2.65945i | −0.259949 | − | 0.150082i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.558247 | − | 0.966913i | −0.0314039 | − | 0.0543931i | ||||
\(317\) | −20.8456 | − | 12.0352i | −1.17081 | − | 0.675966i | −0.216937 | − | 0.976186i | \(-0.569607\pi\) |
−0.953870 | + | 0.300220i | \(0.902940\pi\) | |||||||
\(318\) | −18.7691 | − | 10.8364i | −1.05252 | − | 0.607674i | ||||
\(319\) | −10.4096 | − | 6.01000i | −0.582828 | − | 0.336496i | ||||
\(320\) | 5.83037 | + | 3.36617i | 0.325928 | + | 0.188174i | ||||
\(321\) | −13.9381 | − | 24.1416i | −0.777951 | − | 1.34745i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.83504 | + | 1.63681i | 0.157746 | + | 0.0910745i | ||||
\(324\) | −0.157138 | + | 0.272170i | −0.00872986 | + | 0.0151206i | ||||
\(325\) | 5.10487 | − | 14.8318i | 0.283167 | − | 0.822722i | ||||
\(326\) | 9.90220 | + | 17.1511i | 0.548432 | + | 0.949912i | ||||
\(327\) | −36.3394 | + | 20.9806i | −2.00958 | + | 1.16023i | ||||
\(328\) | −1.34217 | + | 2.32471i | −0.0741091 | + | 0.128361i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 16.8812i | − | 0.929279i | ||||||
\(331\) | − | 0.619723i | − | 0.0340631i | −0.999855 | − | 0.0170315i | \(-0.994578\pi\) | ||
0.999855 | − | 0.0170315i | \(-0.00542157\pi\) | |||||||
\(332\) | 0.494959 | + | 0.285765i | 0.0271644 | + | 0.0156834i | ||||
\(333\) | 5.70194 | − | 3.29201i | 0.312464 | − | 0.180401i | ||||
\(334\) | −6.23523 | −0.341177 | ||||||||
\(335\) | 2.96007 | − | 5.12699i | 0.161726 | − | 0.280117i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.72118 | −0.311652 | −0.155826 | − | 0.987784i | \(-0.549804\pi\) | ||||
−0.155826 | + | 0.987784i | \(0.549804\pi\) | |||||||
\(338\) | −6.72012 | − | 16.6206i | −0.365527 | − | 0.904039i | ||||
\(339\) | 28.1082 | + | 48.6848i | 1.52663 | + | 2.64420i | ||||
\(340\) | − | 0.0443321i | − | 0.00240425i | ||||||
\(341\) | 9.16174 | + | 15.8686i | 0.496136 | + | 0.859333i | ||||
\(342\) | −21.3647 | − | 37.0048i | −1.15527 | − | 2.00099i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.1439 | − | 6.43396i | 0.600841 | − | 0.346896i | ||||
\(345\) | − | 3.72668i | − | 0.200638i | ||||||
\(346\) | 23.3102 | − | 13.4581i | 1.25316 | − | 0.723514i | ||||
\(347\) | 0.932429 | − | 1.61501i | 0.0500554 | − | 0.0866985i | −0.839912 | − | 0.542722i | \(-0.817394\pi\) |
0.889968 | + | 0.456024i | \(0.150727\pi\) | |||||||
\(348\) | 0.322591 | + | 0.558744i | 0.0172927 | + | 0.0299518i | ||||
\(349\) | 19.3273 | + | 11.1586i | 1.03457 | + | 0.597307i | 0.918290 | − | 0.395909i | \(-0.129571\pi\) |
0.116277 | + | 0.993217i | \(0.462904\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.6867 | − | 18.0408i | −0.837295 | − | 0.962947i | ||||
\(352\) | −1.46295 | + | 2.53391i | −0.0779756 | + | 0.135058i | ||||
\(353\) | − | 2.33199i | − | 0.124119i | −0.998072 | − | 0.0620597i | \(-0.980233\pi\) | ||
0.998072 | − | 0.0620597i | \(-0.0197669\pi\) | |||||||
\(354\) | −43.6827 | −2.32171 | ||||||||
\(355\) | 7.50708 | 0.398435 | ||||||||
\(356\) | − | 0.491966i | − | 0.0260741i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.8648 | − | 14.3557i | 1.31415 | − | 0.758722i | ||||
\(359\) | 2.83281 | + | 1.63553i | 0.149510 | + | 0.0863197i | 0.572889 | − | 0.819633i | \(-0.305823\pi\) |
−0.423379 | + | 0.905953i | \(0.639156\pi\) | |||||||
\(360\) | −6.18147 | + | 10.7066i | −0.325792 | + | 0.564289i | ||||
\(361\) | −15.1603 | −0.797913 | ||||||||
\(362\) | 19.7682 | − | 11.4132i | 1.03899 | − | 0.599863i | ||||
\(363\) | 48.3741 | 2.53898 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.03092 | −0.210988 | ||||||||
\(366\) | −25.1268 | + | 14.5070i | −1.31340 | + | 0.758291i | ||||
\(367\) | −4.15290 | −0.216780 | −0.108390 | − | 0.994108i | \(-0.534569\pi\) | ||||
−0.108390 | + | 0.994108i | \(0.534569\pi\) | |||||||
\(368\) | 3.04440 | − | 5.27306i | 0.158700 | − | 0.274877i | ||||
\(369\) | −4.25916 | − | 2.45903i | −0.221723 | − | 0.128012i | ||||
\(370\) | 1.19544 | − | 0.690185i | 0.0621477 | − | 0.0358810i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 0.983525i | − | 0.0509934i | ||||||
\(373\) | −11.1089 | −0.575198 | −0.287599 | − | 0.957751i | \(-0.592857\pi\) | ||||
−0.287599 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(374\) | −4.07183 | −0.210549 | ||||||||
\(375\) | − | 21.7127i | − | 1.12124i | ||||||
\(376\) | −5.56165 | + | 9.63305i | −0.286820 | + | 0.496787i | ||||
\(377\) | −8.06996 | + | 1.56972i | −0.415624 | + | 0.0808447i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.01862 | − | 2.32015i | −0.206422 | − | 0.119178i | 0.393225 | − | 0.919442i | \(-0.371359\pi\) |
−0.599648 | + | 0.800264i | \(0.704693\pi\) | |||||||
\(380\) | 0.231304 | + | 0.400630i | 0.0118656 | + | 0.0205519i | ||||
\(381\) | 2.76208 | − | 4.78407i | 0.141506 | − | 0.245095i | ||||
\(382\) | 5.07586 | − | 2.93055i | 0.259703 | − | 0.149940i | ||||
\(383\) | − | 3.66933i | − | 0.187494i | −0.995596 | − | 0.0937469i | \(-0.970116\pi\) | ||
0.995596 | − | 0.0937469i | \(-0.0298845\pi\) | |||||||
\(384\) | −25.9740 | + | 14.9961i | −1.32548 | + | 0.765266i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.99661 | + | 13.8505i | 0.407017 | + | 0.704973i | ||||
\(387\) | 11.7878 | + | 20.4171i | 0.599208 | + | 1.03786i | ||||
\(388\) | − | 1.04574i | − | 0.0530896i | ||||||
\(389\) | 8.44156 | + | 14.6212i | 0.428004 | + | 0.741324i | 0.996696 | − | 0.0812262i | \(-0.0258836\pi\) |
−0.568692 | + | 0.822551i | \(0.692550\pi\) | |||||||
\(390\) | −7.57603 | − | 8.71296i | −0.383627 | − | 0.441198i | ||||
\(391\) | −0.898894 | −0.0454590 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.4468 | + | 38.8790i | −1.13229 | + | 1.96119i | ||||
\(394\) | 19.8878 | 1.00193 | ||||||||
\(395\) | 7.93506 | − | 4.58131i | 0.399256 | − | 0.230511i | ||||
\(396\) | −2.37684 | − | 1.37227i | −0.119441 | − | 0.0689592i | ||||
\(397\) | − | 16.7086i | − | 0.838578i | −0.907853 | − | 0.419289i | \(-0.862279\pi\) | ||
0.907853 | − | 0.419289i | \(-0.137721\pi\) | |||||||
\(398\) | − | 9.73508i | − | 0.487976i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.25267 | − | 14.2940i | 0.412633 | − | 0.714702i | ||||
\(401\) | 21.9221 | − | 12.6567i | 1.09474 | − | 0.632046i | 0.159902 | − | 0.987133i | \(-0.448882\pi\) |
0.934833 | + | 0.355087i | \(0.115549\pi\) | |||||||
\(402\) | 14.5932 | + | 25.2761i | 0.727842 | + | 1.26066i | ||||
\(403\) | 11.8503 | + | 4.07867i | 0.590304 | + | 0.203173i | ||||
\(404\) | −0.192267 | + | 0.333017i | −0.00956566 | + | 0.0165682i | ||||
\(405\) | −2.23359 | − | 1.28956i | −0.110988 | − | 0.0640789i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.27354 | + | 5.66994i | 0.162263 | + | 0.281048i | ||||
\(408\) | 4.04391 | + | 2.33475i | 0.200203 | + | 0.115587i | ||||
\(409\) | −4.96529 | − | 2.86671i | −0.245518 | − | 0.141750i | 0.372192 | − | 0.928156i | \(-0.378606\pi\) |
−0.617710 | + | 0.786406i | \(0.711940\pi\) | |||||||
\(410\) | −0.892951 | − | 0.515546i | −0.0440997 | − | 0.0254610i | ||||
\(411\) | −19.5899 | − | 11.3102i | −0.966299 | − | 0.557893i | ||||
\(412\) | −0.415112 | − | 0.718996i | −0.0204511 | − | 0.0354224i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 10.1610 | + | 5.86648i | 0.499388 | + | 0.288322i | ||||
\(415\) | −2.34516 | + | 4.06193i | −0.115119 | + | 0.199392i | ||||
\(416\) | 0.382101 | + | 1.96439i | 0.0187340 | + | 0.0963120i | ||||
\(417\) | −14.2977 | − | 24.7643i | −0.700161 | − | 1.21272i | ||||
\(418\) | 36.7971 | − | 21.2448i | 1.79981 | − | 1.03912i | ||||
\(419\) | −17.1729 | + | 29.7443i | −0.838950 | + | 1.45310i | 0.0518229 | + | 0.998656i | \(0.483497\pi\) |
−0.890773 | + | 0.454448i | \(0.849836\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.94167i | 0.143368i | 0.997427 | + | 0.0716842i | \(0.0228374\pi\) | ||||
−0.997427 | + | 0.0716842i | \(0.977163\pi\) | |||||||
\(422\) | 36.4383i | 1.77379i | ||||||||
\(423\) | −17.6489 | − | 10.1896i | −0.858121 | − | 0.495437i | ||||
\(424\) | −13.6684 | + | 7.89148i | −0.663798 | + | 0.383244i | ||||
\(425\) | −2.43669 | −0.118197 | ||||||||
\(426\) | −18.5050 | + | 32.0516i | −0.896571 | + | 1.55291i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.950178 | −0.0459286 | ||||||||
\(429\) | 41.3254 | − | 35.9330i | 1.99521 | − | 1.73486i | ||||
\(430\) | 2.47137 | + | 4.28053i | 0.119180 | + | 0.206426i | ||||
\(431\) | 39.6955i | 1.91207i | 0.293258 | + | 0.956033i | \(0.405261\pi\) | ||||
−0.293258 | + | 0.956033i | \(0.594739\pi\) | |||||||
\(432\) | −12.5781 | − | 21.7858i | −0.605162 | − | 1.04817i | ||||
\(433\) | 4.91827 | + | 8.51869i | 0.236357 | + | 0.409382i | 0.959666 | − | 0.281142i | \(-0.0907133\pi\) |
−0.723309 | + | 0.690524i | \(0.757380\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.58538 | + | 2.64737i | −0.219852 | + | 0.126932i | ||||
\(436\) | 1.43027i | 0.0684975i | ||||||||
\(437\) | 8.12331 | − | 4.69000i | 0.388591 | − | 0.224353i | ||||
\(438\) | 9.93624 | − | 17.2101i | 0.474772 | − | 0.822329i | ||||
\(439\) | −14.2733 | − | 24.7220i | −0.681226 | − | 1.17992i | −0.974607 | − | 0.223922i | \(-0.928114\pi\) |
0.293381 | − | 0.955996i | \(-0.405220\pi\) | |||||||
\(440\) | −10.6465 | − | 6.14678i | −0.507554 | − | 0.293036i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.10161 | + | 1.82737i | −0.0999632 | + | 0.0869193i | ||||
\(443\) | −1.66951 | + | 2.89167i | −0.0793207 | + | 0.137387i | −0.902957 | − | 0.429731i | \(-0.858608\pi\) |
0.823636 | + | 0.567118i | \(0.191942\pi\) | |||||||
\(444\) | − | 0.351419i | − | 0.0166776i | ||||||
\(445\) | 4.03736 | 0.191389 | ||||||||
\(446\) | 31.7190 | 1.50194 | ||||||||
\(447\) | 22.8170i | 1.07921i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7487 | − | 9.09253i | 0.743228 | − | 0.429103i | −0.0800136 | − | 0.996794i | \(-0.525496\pi\) |
0.823242 | + | 0.567691i | \(0.192163\pi\) | |||||||
\(450\) | 27.5443 | + | 15.9027i | 1.29845 | + | 0.749660i | ||||
\(451\) | 2.44523 | − | 4.23526i | 0.115141 | − | 0.199430i | ||||
\(452\) | 1.91617 | 0.0901289 | ||||||||
\(453\) | 3.74570 | − | 2.16258i | 0.175988 | − | 0.101607i | ||||
\(454\) | −0.625219 | −0.0293430 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −48.7265 | −2.28183 | ||||||||
\(457\) | 7.55982 | − | 4.36466i | 0.353633 | − | 0.204170i | −0.312651 | − | 0.949868i | \(-0.601217\pi\) |
0.666284 | + | 0.745698i | \(0.267884\pi\) | |||||||
\(458\) | −23.9038 | −1.11695 | ||||||||
\(459\) | −1.85691 | + | 3.21625i | −0.0866729 | + | 0.150122i | ||||
\(460\) | −0.110008 | − | 0.0635130i | −0.00512914 | − | 0.00296131i | ||||
\(461\) | 1.96695 | − | 1.13562i | 0.0916099 | − | 0.0528910i | −0.453495 | − | 0.891259i | \(-0.649823\pi\) |
0.545105 | + | 0.838368i | \(0.316490\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.48326i | 0.254829i | 0.991850 | + | 0.127414i | \(0.0406678\pi\) | ||||
−0.991850 | + | 0.127414i | \(0.959332\pi\) | |||||||
\(464\) | −8.65077 | −0.401602 | ||||||||
\(465\) | 8.07139 | 0.374302 | ||||||||
\(466\) | 10.7775i | 0.499257i | ||||||||
\(467\) | −9.44095 | + | 16.3522i | −0.436875 | + | 0.756690i | −0.997447 | − | 0.0714164i | \(-0.977248\pi\) |
0.560572 | + | 0.828106i | \(0.310581\pi\) | |||||||
\(468\) | −1.84262 | + | 0.358416i | −0.0851753 | + | 0.0165678i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.70018 | − | 2.13630i | −0.170677 | − | 0.0985401i | ||||
\(471\) | −5.55629 | − | 9.62377i | −0.256020 | − | 0.443440i | ||||
\(472\) | −15.9058 | + | 27.5496i | −0.732122 | + | 1.26807i | ||||
\(473\) | −20.3025 | + | 11.7217i | −0.933510 | + | 0.538962i | ||||
\(474\) | 45.1718i | 2.07481i | ||||||||
\(475\) | 22.0204 | − | 12.7135i | 1.01037 | − | 0.583335i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.4582 | − | 25.0423i | −0.661994 | − | 1.14661i | ||||
\(478\) | −9.33030 | − | 16.1606i | −0.426758 | − | 0.739166i | ||||
\(479\) | 33.1354i | 1.51399i | 0.653418 | + | 0.756997i | \(0.273334\pi\) | ||||
−0.653418 | + | 0.756997i | \(0.726666\pi\) | |||||||
\(480\) | 0.644422 | + | 1.11617i | 0.0294137 | + | 0.0509461i | ||||
\(481\) | 4.23417 | + | 1.45733i | 0.193061 | + | 0.0664485i | ||||
\(482\) | −31.1104 | −1.41704 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.824428 | − | 1.42795i | 0.0374740 | − | 0.0649069i | ||||
\(485\) | 8.58199 | 0.389688 | ||||||||
\(486\) | −12.7451 | + | 7.35838i | −0.578129 | + | 0.333783i | ||||
\(487\) | −13.8185 | − | 7.97814i | −0.626178 | − | 0.361524i | 0.153093 | − | 0.988212i | \(-0.451077\pi\) |
−0.779270 | + | 0.626688i | \(0.784410\pi\) | |||||||
\(488\) | 21.1291i | 0.956469i | ||||||||
\(489\) | 41.3765i | 1.87111i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.8464 | + | 27.4468i | −0.715138 | + | 1.23866i | 0.247769 | + | 0.968819i | \(0.420303\pi\) |
−0.962906 | + | 0.269836i | \(0.913031\pi\) | |||||||
\(492\) | −0.227330 | + | 0.131249i | −0.0102488 | + | 0.00591717i | ||||
\(493\) | 0.638559 | + | 1.10602i | 0.0287593 | + | 0.0498125i | ||||
\(494\) | 9.45788 | − | 27.4792i | 0.425530 | − | 1.23635i | ||||
\(495\) | 11.2617 | − | 19.5058i | 0.506174 | − | 0.876720i | ||||
\(496\) | 11.4206 | + | 6.59368i | 0.512800 | + | 0.296065i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −11.5617 | − | 20.0254i | −0.518090 | − | 0.897358i | ||||
\(499\) | −20.9738 | − | 12.1092i | −0.938916 | − | 0.542083i | −0.0492955 | − | 0.998784i | \(-0.515698\pi\) |
−0.889620 | + | 0.456701i | \(0.849031\pi\) | |||||||
\(500\) | −0.640935 | − | 0.370044i | −0.0286635 | − | 0.0165489i | ||||
\(501\) | −11.2817 | − | 6.51351i | −0.504030 | − | 0.291002i | ||||
\(502\) | −8.04043 | − | 4.64215i | −0.358862 | − | 0.207189i | ||||
\(503\) | 0.427249 | + | 0.740017i | 0.0190501 | + | 0.0329957i | 0.875393 | − | 0.483411i | \(-0.160602\pi\) |
−0.856343 | + | 0.516407i | \(0.827269\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.73294 | − | 1.57786i | −0.121614 | − | 0.0702139i | ||||
\(506\) | −5.83356 | + | 10.1040i | −0.259333 | + | 0.449179i | ||||
\(507\) | 5.20326 | − | 37.0925i | 0.231085 | − | 1.64733i | ||||
\(508\) | −0.0941471 | − | 0.163068i | −0.00417710 | − | 0.00723495i | ||||
\(509\) | 1.12583 | − | 0.650000i | 0.0499017 | − | 0.0288108i | −0.474842 | − | 0.880071i | \(-0.657495\pi\) |
0.524743 | + | 0.851261i | \(0.324161\pi\) | |||||||
\(510\) | −0.896808 | + | 1.55332i | −0.0397113 | + | 0.0687820i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.0616i | 1.06338i | ||||||||
\(513\) | − | 38.7538i | − | 1.71102i | ||||||
\(514\) | 19.7514 | + | 11.4035i | 0.871199 | + | 0.502987i | ||||
\(515\) | 5.90051 | − | 3.40666i | 0.260007 | − | 0.150115i | ||||
\(516\) | 1.25833 | 0.0553951 | ||||||||
\(517\) | 10.1324 | − | 17.5499i | 0.445624 | − | 0.771844i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 56.2351 | 2.46845 | ||||||||
\(520\) | −8.25362 | + | 1.60545i | −0.361945 | + | 0.0704034i | ||||
\(521\) | −12.5228 | − | 21.6901i | −0.548632 | − | 0.950259i | −0.998369 | − | 0.0570974i | \(-0.981815\pi\) |
0.449736 | − | 0.893161i | \(-0.351518\pi\) | |||||||
\(522\) | − | 16.6698i | − | 0.729618i | ||||||
\(523\) | 6.41197 | + | 11.1059i | 0.280376 | + | 0.485625i | 0.971477 | − | 0.237133i | \(-0.0762076\pi\) |
−0.691101 | + | 0.722758i | \(0.742874\pi\) | |||||||
\(524\) | 0.765112 | + | 1.32521i | 0.0334241 | + | 0.0578922i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.9701 | − | 6.91095i | 0.521922 | − | 0.301332i | ||||
\(527\) | − | 1.94686i | − | 0.0848065i | ||||||
\(528\) | 49.9040 | − | 28.8121i | 2.17179 | − | 1.25389i | ||||
\(529\) | 10.2122 | − | 17.6880i | 0.444008 | − | 0.769045i | ||||
\(530\) | −3.03122 | − | 5.25022i | −0.131668 | − | 0.228055i | ||||
\(531\) | −50.4743 | − | 29.1413i | −2.19040 | − | 1.26463i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.638656 | − | 3.28334i | −0.0276632 | − | 0.142217i | ||||
\(534\) | −9.95213 | + | 17.2376i | −0.430671 | + | 0.745944i | ||||
\(535\) | − | 7.79773i | − | 0.337125i | ||||||
\(536\) | 21.2547 | 0.918063 | ||||||||
\(537\) | 59.9855 | 2.58857 | ||||||||
\(538\) | − | 21.6828i | − | 0.934814i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.454501 | + | 0.262406i | −0.0195586 | + | 0.0112922i | ||||
\(541\) | 24.8938 | + | 14.3725i | 1.07027 | + | 0.617920i | 0.928255 | − | 0.371944i | \(-0.121309\pi\) |
0.142014 | + | 0.989865i | \(0.454642\pi\) | |||||||
\(542\) | −3.59670 | + | 6.22966i | −0.154491 | + | 0.267587i | ||||
\(543\) | 47.6902 | 2.04658 | ||||||||
\(544\) | 0.269226 | − | 0.155438i | 0.0115430 | − | 0.00666434i | ||||
\(545\) | −11.7376 | −0.502785 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.88085 | −0.379718 | −0.189859 | − | 0.981811i | \(-0.560803\pi\) | ||||
−0.189859 | + | 0.981811i | \(0.560803\pi\) | |||||||
\(548\) | −0.667733 | + | 0.385516i | −0.0285241 | + | 0.0164684i | ||||
\(549\) | −38.7111 | −1.65215 | ||||||||
\(550\) | −15.8134 | + | 27.3897i | −0.674287 | + | 1.16790i | ||||
\(551\) | −11.5413 | − | 6.66339i | −0.491677 | − | 0.283870i | ||||
\(552\) | 11.5871 | − | 6.68983i | 0.493181 | − | 0.284738i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 26.5777i | − | 1.12918i | ||||||
\(555\) | 2.88395 | 0.122417 | ||||||||
\(556\) | −0.974690 | −0.0413361 | ||||||||
\(557\) | 38.7273i | 1.64093i | 0.571696 | + | 0.820465i | \(0.306286\pi\) | ||||
−0.571696 | + | 0.820465i | \(0.693714\pi\) | |||||||
\(558\) | −12.7059 | + | 22.0072i | −0.537882 | + | 0.931639i | ||||
\(559\) | −5.21830 | + | 15.1614i | −0.220711 | + | 0.641259i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.36736 | − | 4.25355i | −0.311050 | − | 0.179585i | ||||
\(562\) | −1.47754 | − | 2.55918i | −0.0623263 | − | 0.107952i | ||||
\(563\) | −3.45441 | + | 5.98321i | −0.145586 | + | 0.252162i | −0.929591 | − | 0.368592i | \(-0.879840\pi\) |
0.784005 | + | 0.620754i | \(0.213173\pi\) | |||||||
\(564\) | −0.942002 | + | 0.543865i | −0.0396655 | + | 0.0229009i | ||||
\(565\) | 15.7252i | 0.661565i | ||||||||
\(566\) | 18.8105 | − | 10.8602i | 0.790663 | − | 0.456489i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.4761 | + | 23.3413i | 0.565444 | + | 0.979379i | ||||
\(569\) | −1.41872 | − | 2.45730i | −0.0594759 | − | 0.103015i | 0.834754 | − | 0.550623i | \(-0.185610\pi\) |
−0.894230 | + | 0.447607i | \(0.852276\pi\) | |||||||
\(570\) | − | 18.7165i | − | 0.783946i | ||||||
\(571\) | −23.3362 | − | 40.4195i | −0.976589 | − | 1.69150i | −0.674588 | − | 0.738195i | \(-0.735679\pi\) |
−0.302001 | − | 0.953307i | \(-0.597655\pi\) | |||||||
\(572\) | −0.356404 | − | 1.83228i | −0.0149020 | − | 0.0766115i | ||||
\(573\) | 12.2453 | 0.511557 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.49096 | + | 6.04653i | −0.145583 | + | 0.252158i | ||||
\(576\) | −44.2836 | −1.84515 | ||||||||
\(577\) | −9.88033 | + | 5.70441i | −0.411323 | + | 0.237478i | −0.691358 | − | 0.722512i | \(-0.742987\pi\) |
0.280035 | + | 0.959990i | \(0.409654\pi\) | |||||||
\(578\) | −19.9284 | − | 11.5057i | −0.828911 | − | 0.478572i | ||||
\(579\) | 33.4140i | 1.38864i | ||||||||
\(580\) | 0.180474i | 0.00749379i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −21.1547 | + | 36.6410i | −0.876890 | + | 1.51882i | ||||
\(583\) | 24.9017 | − | 14.3770i | 1.03132 | − | 0.595436i | ||||
\(584\) | −7.23597 | − | 12.5331i | −0.299426 | − | 0.518622i | ||||
\(585\) | −2.94138 | − | 15.1217i | −0.121611 | − | 0.625204i | ||||
\(586\) | −15.9617 | + | 27.6465i | −0.659371 | + | 1.14206i | ||||
\(587\) | 40.2191 | + | 23.2205i | 1.66002 | + | 0.958413i | 0.972702 | + | 0.232057i | \(0.0745456\pi\) |
0.687318 | + | 0.726356i | \(0.258788\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.1578 | + | 17.5938i | 0.418544 | + | 0.724939i | ||||
\(590\) | −10.5821 | − | 6.10961i | −0.435660 | − | 0.251529i | ||||
\(591\) | 35.9840 | + | 20.7754i | 1.48018 | + | 0.854585i | ||||
\(592\) | 4.08064 | + | 2.35596i | 0.167713 | + | 0.0968292i | ||||
\(593\) | 17.5462 | + | 10.1303i | 0.720535 | + | 0.416001i | 0.814950 | − | 0.579532i | \(-0.196765\pi\) |
−0.0944146 | + | 0.995533i | \(0.530098\pi\) | |||||||
\(594\) | 24.1016 | + | 41.7451i | 0.988899 | + | 1.71282i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.673533 | + | 0.388864i | 0.0275890 | + | 0.0159285i | ||||
\(597\) | 10.1696 | − | 17.6142i | 0.416212 | − | 0.720901i | ||||
\(598\) | 1.52364 | + | 7.83304i | 0.0623061 | + | 0.320317i | ||||
\(599\) | 19.4938 | + | 33.7642i | 0.796494 | + | 1.37957i | 0.921886 | + | 0.387462i | \(0.126648\pi\) |
−0.125391 | + | 0.992107i | \(0.540019\pi\) | |||||||
\(600\) | 31.4100 | − | 18.1346i | 1.28231 | − | 0.740342i | ||||
\(601\) | 9.56951 | − | 16.5749i | 0.390348 | − | 0.676103i | −0.602147 | − | 0.798385i | \(-0.705688\pi\) |
0.992495 | + | 0.122282i | \(0.0390212\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 38.9412i | 1.58581i | ||||||||
\(604\) | − | 0.147425i | − | 0.00599865i | ||||||
\(605\) | 11.7186 | + | 6.76575i | 0.476430 | + | 0.275067i | ||||
\(606\) | 13.4734 | − | 7.77888i | 0.547320 | − | 0.315995i | ||||
\(607\) | −43.3336 | −1.75886 | −0.879428 | − | 0.476033i | \(-0.842074\pi\) | ||||
−0.879428 | + | 0.476033i | \(0.842074\pi\) | |||||||
\(608\) | −1.62200 | + | 2.80939i | −0.0657808 | + | 0.113936i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.11595 | −0.328605 | ||||||||
\(611\) | −2.64644 | − | 13.6054i | −0.107063 | − | 0.550415i | ||||
\(612\) | 0.145803 | + | 0.252538i | 0.00589373 | + | 0.0102082i | ||||
\(613\) | 10.3096i | 0.416399i | 0.978086 | + | 0.208200i | \(0.0667604\pi\) | ||||
−0.978086 | + | 0.208200i | \(0.933240\pi\) | |||||||
\(614\) | −2.92077 | − | 5.05892i | −0.117873 | − | 0.204161i | ||||
\(615\) | −1.07711 | − | 1.86561i | −0.0434332 | − | 0.0752285i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.58684 | + | 5.53497i | −0.385952 | + | 0.222829i | −0.680405 | − | 0.732837i | \(-0.738196\pi\) |
0.294453 | + | 0.955666i | \(0.404863\pi\) | |||||||
\(618\) | 33.5898i | 1.35118i | ||||||||
\(619\) | 29.2384 | − | 16.8808i | 1.17519 | − | 0.678498i | 0.220295 | − | 0.975433i | \(-0.429298\pi\) |
0.954897 | + | 0.296936i | \(0.0959647\pi\) | |||||||
\(620\) | 0.137559 | − | 0.238259i | 0.00552450 | − | 0.00956871i | ||||
\(621\) | 5.32065 | + | 9.21563i | 0.213510 | + | 0.369810i | ||||
\(622\) | 32.5447 | + | 18.7897i | 1.30492 | + | 0.753399i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 12.8267 | − | 37.2671i | 0.513480 | − | 1.49188i | ||||
\(625\) | −7.83931 | + | 13.5781i | −0.313573 | + | 0.543124i | ||||
\(626\) | 3.71927i | 0.148652i | ||||||||
\(627\) | 88.7719 | 3.54521 | ||||||||
\(628\) | −0.378778 | −0.0151149 | ||||||||
\(629\) | − | 0.695623i | − | 0.0277363i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4264 | − | 19.2987i | 1.33068 | − | 0.768271i | 0.345280 | − | 0.938500i | \(-0.387784\pi\) |
0.985405 | + | 0.170229i | \(0.0544507\pi\) | |||||||
\(632\) | 28.4887 | + | 16.4480i | 1.13322 | + | 0.654265i | ||||
\(633\) | −38.0645 | + | 65.9296i | −1.51293 | + | 2.62047i | ||||
\(634\) | 33.1945 | 1.31832 | ||||||||
\(635\) | 1.33823 | − | 0.772627i | 0.0531060 | − | 0.0306608i | ||||
\(636\) | −1.54339 | −0.0611995 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.5763 | 0.656260 | ||||||||
\(639\) | −42.7641 | + | 24.6899i | −1.69172 | + | 0.976717i | ||||
\(640\) | −8.38960 | −0.331628 | ||||||||
\(641\) | 9.76141 | − | 16.9073i | 0.385553 | − | 0.667797i | −0.606293 | − | 0.795241i | \(-0.707344\pi\) |
0.991846 | + | 0.127445i | \(0.0406775\pi\) | |||||||
\(642\) | 33.2926 | + | 19.2215i | 1.31395 | + | 0.758611i | ||||
\(643\) | −10.8009 | + | 6.23589i | −0.425945 | + | 0.245920i | −0.697618 | − | 0.716470i | \(-0.745757\pi\) |
0.271673 | + | 0.962390i | \(0.412423\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.3266i | 0.406611i | ||||||||
\(646\) | −4.51450 | −0.177621 | ||||||||
\(647\) | 35.9391 | 1.41291 | 0.706455 | − | 0.707758i | \(-0.250293\pi\) | ||||
0.706455 | + | 0.707758i | \(0.250293\pi\) | |||||||
\(648\) | − | 9.25967i | − | 0.363754i | ||||||
\(649\) | 28.9778 | − | 50.1910i | 1.13748 | − | 1.97017i | ||||
\(650\) | 4.13023 | + | 21.2336i | 0.162001 | + | 0.832849i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.22139 | + | 0.705171i | 0.0478334 | + | 0.0276166i | ||||
\(653\) | −2.42944 | − | 4.20791i | −0.0950713 | − | 0.164668i | 0.814567 | − | 0.580069i | \(-0.196975\pi\) |
−0.909638 | + | 0.415401i | \(0.863641\pi\) | |||||||
\(654\) | 28.9334 | − | 50.1141i | 1.13138 | − | 1.95962i | ||||
\(655\) | −10.8755 | + | 6.27897i | −0.424941 | + | 0.245340i | ||||
\(656\) | − | 3.51964i | − | 0.137419i | ||||||
\(657\) | 22.9621 | − | 13.2572i | 0.895838 | − | 0.517212i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.8103 | + | 20.4560i | 0.460063 | + | 0.796853i | 0.998964 | − | 0.0455166i | \(-0.0144934\pi\) |
−0.538900 | + | 0.842370i | \(0.681160\pi\) | |||||||
\(660\) | −0.601085 | − | 1.04111i | −0.0233972 | − | 0.0405251i | ||||
\(661\) | − | 16.3932i | − | 0.637623i | −0.947818 | − | 0.318812i | \(-0.896716\pi\) | ||
0.947818 | − | 0.318812i | \(-0.103284\pi\) | |||||||
\(662\) | 0.427316 | + | 0.740134i | 0.0166081 | + | 0.0287661i | ||||
\(663\) | −5.71147 | + | 1.11096i | −0.221815 | + | 0.0431462i | ||||
\(664\) | −16.8393 | −0.653492 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.53987 | + | 7.86328i | −0.175916 | + | 0.304696i | ||||
\(667\) | 3.65936 | 0.141691 | ||||||||
\(668\) | −0.384544 | + | 0.222016i | −0.0148784 | + | 0.00859007i | ||||
\(669\) | 57.3908 | + | 33.1346i | 2.21886 | + | 1.28106i | ||||
\(670\) | 8.16420i | 0.315410i | ||||||||
\(671\) | − | 38.4939i | − | 1.48604i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.12678 | + | 12.3439i | −0.274717 | + | 0.475824i | −0.970064 | − | 0.242851i | \(-0.921918\pi\) |
0.695347 | + | 0.718675i | \(0.255251\pi\) | |||||||
\(674\) | 6.83278 | − | 3.94491i | 0.263189 | − | 0.151952i | ||||
\(675\) | 14.4230 | + | 24.9814i | 0.555143 | + | 0.961536i | ||||
\(676\) | −1.00625 | − | 0.785753i | −0.0387020 | − | 0.0302213i | ||||
\(677\) | −5.13574 | + | 8.89537i | −0.197383 | + | 0.341877i | −0.947679 | − | 0.319225i | \(-0.896577\pi\) |
0.750296 | + | 0.661102i | \(0.229911\pi\) | |||||||
\(678\) | −67.1391 | − | 38.7628i | −2.57846 | − | 1.48867i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.653092 | + | 1.13119i | 0.0250449 | + | 0.0433791i | ||||
\(681\) | −1.13124 | − | 0.653122i | −0.0433492 | − | 0.0250277i | ||||
\(682\) | −21.8837 | − | 12.6345i | −0.837969 | − | 0.483802i | ||||
\(683\) | 1.92432 | + | 1.11101i | 0.0736321 | + | 0.0425115i | 0.536364 | − | 0.843987i | \(-0.319797\pi\) |
−0.462732 | + | 0.886498i | \(0.653131\pi\) | |||||||
\(684\) | −2.63524 | − | 1.52146i | −0.100761 | − | 0.0581744i | ||||
\(685\) | −3.16377 | − | 5.47981i | −0.120881 | − | 0.209373i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.2504 | − | 24.9706i | −1.65011 | − | 0.952689i | ||||
\(688\) | −8.43604 | + | 14.6117i | −0.321621 | + | 0.557064i | ||||
\(689\) | 6.40044 | − | 18.5960i | 0.243837 | − | 0.708451i | ||||
\(690\) | 2.56965 | + | 4.45076i | 0.0978249 | + | 0.169438i | ||||
\(691\) | −2.28643 | + | 1.32007i | −0.0869800 | + | 0.0502179i | −0.542859 | − | 0.839824i | \(-0.682658\pi\) |
0.455879 | + | 0.890042i | \(0.349325\pi\) | |||||||
\(692\) | 0.958402 | − | 1.66000i | 0.0364330 | − | 0.0631038i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.57174i | 0.0976220i | ||||||||
\(695\) | − | 7.99889i | − | 0.303415i | ||||||
\(696\) | −16.4626 | − | 9.50469i | −0.624014 | − | 0.360274i | ||||
\(697\) | −0.449993 | + | 0.259804i | −0.0170447 | + | 0.00984077i | ||||
\(698\) | −30.7767 | −1.16492 | ||||||||
\(699\) | −11.2585 | + | 19.5002i | −0.425834 | + | 0.737566i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.89991 | −0.336145 | −0.168072 | − | 0.985775i | \(-0.553754\pi\) | ||||
−0.168072 | + | 0.985775i | \(0.553754\pi\) | |||||||
\(702\) | 31.1742 | + | 10.7296i | 1.17659 | + | 0.404965i | ||||
\(703\) | 3.62943 | + | 6.28635i | 0.136886 | + | 0.237094i | ||||
\(704\) | − | 44.0351i | − | 1.65964i | ||||||
\(705\) | −4.46328 | − | 7.73063i | −0.168097 | − | 0.291152i | ||||
\(706\) | 1.60797 | + | 2.78509i | 0.0605168 | + | 0.104818i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.69403 | + | 1.55540i | −0.101248 | + | 0.0584556i | ||||
\(709\) | 40.5944i | 1.52456i | 0.647250 | + | 0.762278i | \(0.275919\pi\) | ||||
−0.647250 | + | 0.762278i | \(0.724081\pi\) | |||||||
\(710\) | −8.96569 | + | 5.17634i | −0.336476 | + | 0.194265i | ||||
\(711\) | −30.1347 | + | 52.1949i | −1.13014 | + | 1.95746i | ||||
\(712\) | 7.24754 | + | 12.5531i | 0.271613 | + | 0.470448i | ||||
\(713\) | −4.83103 | − | 2.78920i | −0.180923 | − | 0.104456i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.0368 | − | 2.92487i | 0.562344 | − | 0.109384i | ||||
\(716\) | 1.02232 | − | 1.77071i | 0.0382059 | − | 0.0661745i | ||||
\(717\) | − | 38.9868i | − | 1.45599i | ||||||
\(718\) | −4.51096 | −0.168348 | ||||||||
\(719\) | 14.5135 | 0.541262 | 0.270631 | − | 0.962683i | \(-0.412768\pi\) | ||||
0.270631 | + | 0.962683i | \(0.412768\pi\) | |||||||
\(720\) | − | 16.2100i | − | 0.604110i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.1059 | − | 10.4535i | 0.673834 | − | 0.389038i | ||||
\(723\) | −56.2896 | − | 32.4988i | −2.09343 | − | 1.20864i | ||||
\(724\) | 0.812773 | − | 1.40776i | 0.0302065 | − | 0.0523191i | ||||
\(725\) | 9.91969 | 0.368408 | ||||||||
\(726\) | −57.7730 | + | 33.3552i | −2.14416 | + | 1.23793i | ||||
\(727\) | −30.6942 | −1.13839 | −0.569193 | − | 0.822204i | \(-0.692744\pi\) | ||||
−0.569193 | + | 0.822204i | \(0.692744\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.3475 | −1.49435 | ||||||||
\(730\) | 4.81411 | − | 2.77943i | 0.178178 | − | 0.102871i | ||||
\(731\) | 2.49084 | 0.0921269 | ||||||||
\(732\) | −1.03309 | + | 1.78937i | −0.0381842 | + | 0.0661369i | ||||
\(733\) | −11.4873 | − | 6.63218i | −0.424292 | − | 0.244965i | 0.272620 | − | 0.962122i | \(-0.412110\pi\) |
−0.696912 | + | 0.717157i | \(0.745443\pi\) | |||||||
\(734\) | 4.95980 | − | 2.86354i | 0.183069 | − | 0.105695i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 0.890761i | − | 0.0328339i | ||||||
\(737\) | −38.7227 | −1.42637 | ||||||||
\(738\) | 6.78227 | 0.249659 | ||||||||
\(739\) | − | 7.25474i | − | 0.266870i | −0.991058 | − | 0.133435i | \(-0.957399\pi\) | ||
0.991058 | − | 0.133435i | \(-0.0426008\pi\) | |||||||
\(740\) | 0.0491505 | − | 0.0851312i | 0.00180681 | − | 0.00312948i | ||||
\(741\) | 45.8182 | − | 39.8395i | 1.68317 | − | 1.46354i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.0705 | − | 23.1347i | −1.47004 | − | 0.848730i | −0.470608 | − | 0.882342i | \(-0.655965\pi\) |
−0.999435 | + | 0.0336128i | \(0.989299\pi\) | |||||||
\(744\) | 14.4891 | + | 25.0959i | 0.531196 | + | 0.920059i | ||||
\(745\) | −3.19125 | + | 5.52741i | −0.116918 | + | 0.202509i | ||||
\(746\) | 13.2673 | − | 7.65991i | 0.485752 | − | 0.280449i | ||||
\(747\) | − | 30.8517i | − | 1.12881i | ||||||
\(748\) | −0.251121 | + | 0.144985i | −0.00918188 | + | 0.00530116i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14.9715 | + | 25.9314i | 0.546681 | + | 0.946880i | ||||
\(751\) | −18.0130 | − | 31.1995i | −0.657305 | − | 1.13848i | −0.981311 | − | 0.192430i | \(-0.938363\pi\) |
0.324006 | − | 0.946055i | \(-0.394970\pi\) | |||||||
\(752\) | − | 14.5846i | − | 0.531845i | ||||||
\(753\) | −9.69865 | − | 16.7985i | −0.353438 | − | 0.612173i | ||||
\(754\) | 8.55556 | − | 7.43917i | 0.311575 | − | 0.270919i | ||||
\(755\) | 1.20986 | 0.0440313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.28132 | − | 9.14751i | 0.191953 | − | 0.332472i | −0.753945 | − | 0.656938i | \(-0.771851\pi\) |
0.945897 | + | 0.324466i | \(0.105185\pi\) | |||||||
\(758\) | 6.39923 | 0.232430 | ||||||||
\(759\) | −21.1099 | + | 12.1878i | −0.766242 | + | 0.442390i | ||||
\(760\) | −11.8040 | − | 6.81504i | −0.428176 | − | 0.247207i | ||||
\(761\) | 7.81202i | 0.283185i | 0.989925 | + | 0.141593i | \(0.0452223\pi\) | ||||
−0.989925 | + | 0.141593i | \(0.954778\pi\) | |||||||
\(762\) | 7.61813i | 0.275976i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.208695 | − | 0.361470i | 0.00755031 | − | 0.0130775i | ||||
\(765\) | −2.07248 | + | 1.19654i | −0.0749305 | + | 0.0432612i | ||||
\(766\) | 2.53010 | + | 4.38226i | 0.0914163 | + | 0.158338i | ||||
\(767\) | −7.56855 | − | 38.9101i | −0.273285 | − | 1.40496i | ||||
\(768\) | −3.38714 | + | 5.86671i | −0.122223 | + | 0.211696i | ||||
\(769\) | −21.9030 | − | 12.6457i | −0.789844 | − | 0.456017i | 0.0500637 | − | 0.998746i | \(-0.484058\pi\) |
−0.839908 | + | 0.542729i | \(0.817391\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.8249 | + | 41.2659i | 0.858032 | + | 1.48615i | ||||
\(772\) | 0.986345 | + | 0.569467i | 0.0354993 | + | 0.0204956i | ||||
\(773\) | 40.3572 | + | 23.3002i | 1.45155 | + | 0.838051i | 0.998569 | − | 0.0534716i | \(-0.0170287\pi\) |
0.452977 | + | 0.891522i | \(0.350362\pi\) | |||||||
\(774\) | −28.1563 | − | 16.2560i | −1.01206 | − | 0.584311i | ||||
\(775\) | −13.0958 | − | 7.56086i | −0.470415 | − | 0.271594i | ||||
\(776\) | 15.4057 | + | 26.6834i | 0.553032 | + | 0.957879i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.1634 | − | 11.6414i | −0.722895 | − | 0.417363i | ||||
\(779\) | 2.71106 | − | 4.69570i | 0.0971339 | − | 0.168241i | ||||
\(780\) | −0.777475 | − | 0.267594i | −0.0278381 | − | 0.00958140i | ||||
\(781\) | −24.5513 | − | 42.5241i | −0.878515 | − | 1.52163i | ||||
\(782\) | 1.07355 | − | 0.619812i | 0.0383899 | − | 0.0221644i | ||||
\(783\) | 7.55940 | − | 13.0933i | 0.270151 | − | 0.467915i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 3.10848i | − | 0.110946i | ||||||
\(786\) | − | 61.9108i | − | 2.20829i | ||||||
\(787\) | −34.4099 | − | 19.8666i | −1.22658 | − | 0.708167i | −0.260268 | − | 0.965536i | \(-0.583811\pi\) |
−0.966313 | + | 0.257369i | \(0.917144\pi\) | |||||||
\(788\) | 1.22653 | − | 0.708140i | 0.0436935 | − | 0.0252265i | ||||
\(789\) | 28.8775 | 1.02807 | ||||||||
\(790\) | −6.31788 | + | 10.9429i | −0.224780 | + | 0.389330i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 80.8641 | 2.87338 | ||||||||
\(793\) | −17.2755 | − | 19.8680i | −0.613470 | − | 0.705533i | ||||
\(794\) | 11.5210 | + | 19.9550i | 0.408865 | + | 0.708175i | ||||
\(795\) | − | 12.6660i | − | 0.449217i | ||||||
\(796\) | −0.346635 | − | 0.600389i | −0.0122861 | − | 0.0212802i | ||||
\(797\) | 1.39299 | + | 2.41273i | 0.0493422 | + | 0.0854632i | 0.889642 | − | 0.456659i | \(-0.150954\pi\) |
−0.840299 | + | 0.542123i | \(0.817621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.86467 | + | 1.07656i | −0.0659671 | + | 0.0380861i | ||||
\(800\) | − | 2.41465i | − | 0.0853706i | ||||||
\(801\) | −22.9989 | + | 13.2784i | −0.812625 | + | 0.469169i | ||||
\(802\) | −17.4543 | + | 30.2317i | −0.616333 | + | 1.06752i | ||||
\(803\) | 13.1828 | + | 22.8333i | 0.465210 | + | 0.805768i | ||||
\(804\) | 1.80000 | + | 1.03923i | 0.0634812 | + | 0.0366509i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.9651 | + | 3.29995i | −0.597570 | + | 0.116236i | ||||
\(807\) | 22.6505 | − | 39.2319i | 0.797337 | − | 1.38103i | ||||
\(808\) | − | 11.3298i | − | 0.398580i | ||||||
\(809\) | −41.4586 | −1.45761 | −0.728803 | − | 0.684723i | \(-0.759923\pi\) | ||||
−0.728803 | + | 0.684723i | \(0.759923\pi\) | |||||||
\(810\) | 3.55676 | 0.124972 | ||||||||
\(811\) | 27.8622i | 0.978375i | 0.872179 | + | 0.489188i | \(0.162707\pi\) | ||||
−0.872179 | + | 0.489188i | \(0.837293\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.0154 | + | 7.51443i | −0.456469 | + | 0.263543i | ||||
\(814\) | −7.81915 | − | 4.51439i | −0.274061 | − | 0.158229i | ||||
\(815\) | −5.78705 | + | 10.0235i | −0.202712 | + | 0.351107i | ||||
\(816\) | −6.12254 | −0.214332 | ||||||||
\(817\) | −22.5097 | + | 12.9960i | −0.787515 | + | 0.454672i | ||||
\(818\) | 7.90671 | 0.276452 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0734276 | −0.00256420 | ||||||||
\(821\) | −19.4164 | + | 11.2101i | −0.677638 | + | 0.391235i | −0.798965 | − | 0.601378i | \(-0.794619\pi\) |
0.121326 | + | 0.992613i | \(0.461285\pi\) | |||||||
\(822\) | 31.1949 | 1.08805 | ||||||||
\(823\) | −1.18083 | + | 2.04525i | −0.0411611 | + | 0.0712931i | −0.885872 | − | 0.463930i | \(-0.846439\pi\) |
0.844711 | + | 0.535223i | \(0.179772\pi\) | |||||||
\(824\) | 21.1842 | + | 12.2307i | 0.737987 | + | 0.426077i | ||||
\(825\) | −57.2241 | + | 33.0384i | −1.99229 | + | 1.15025i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 43.3148i | − | 1.50620i | −0.657904 | − | 0.753102i | \(-0.728557\pi\) | ||
0.657904 | − | 0.753102i | \(-0.271443\pi\) | |||||||
\(828\) | 0.835546 | 0.0290372 | ||||||||
\(829\) | −54.9280 | −1.90773 | −0.953864 | − | 0.300239i | \(-0.902933\pi\) | ||||
−0.953864 | + | 0.300239i | \(0.902933\pi\) | |||||||
\(830\) | − | 6.46820i | − | 0.224514i | ||||||
\(831\) | 27.7638 | − | 48.0884i | 0.963117 | − | 1.66817i | ||||
\(832\) | −19.7623 | − | 22.7280i | −0.685134 | − | 0.787951i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 34.1514 | + | 19.7173i | 1.18257 | + | 0.682755i | ||||
\(835\) | −1.82200 | − | 3.15579i | −0.0630529 | − | 0.109211i | ||||
\(836\) | 1.51292 | − | 2.62045i | 0.0523254 | − | 0.0906303i | ||||
\(837\) | −19.9596 | + | 11.5237i | −0.689903 | + | 0.398316i | ||||
\(838\) | − | 47.3647i | − | 1.63619i | ||||||
\(839\) | 12.7661 | − | 7.37052i | 0.440735 | − | 0.254459i | −0.263174 | − | 0.964748i | \(-0.584769\pi\) |
0.703910 | + | 0.710290i | \(0.251436\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.9004 | + | 20.6122i | 0.410360 | + | 0.710765i | ||||
\(842\) | −2.02837 | − | 3.51323i | −0.0699021 | − | 0.121074i | ||||
\(843\) | − | 6.17393i | − | 0.212642i | ||||||
\(844\) | 1.29745 | + | 2.24725i | 0.0446600 | + | 0.0773535i | ||||
\(845\) | 6.44836 | − | 8.25791i | 0.221830 | − | 0.284081i | ||||
\(846\) | 28.1041 | 0.966239 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.3471 | − | 17.9217i | 0.355321 | − | 0.615434i | ||||
\(849\) | 45.3796 | 1.55743 | ||||||||
\(850\) | 2.91013 | − | 1.68017i | 0.0998168 | − | 0.0576292i | ||||
\(851\) | −1.72615 | − | 0.996594i | −0.0591717 | − | 0.0341628i | ||||
\(852\) | 2.63562i | 0.0902947i | ||||||||
\(853\) | 24.1038i | 0.825297i | 0.910890 | + | 0.412649i | \(0.135396\pi\) | ||||
−0.910890 | + | 0.412649i | \(0.864604\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.4860 | − | 21.6264i | 0.427012 | − | 0.739607i | ||||
\(856\) | 24.2450 | − | 13.9978i | 0.828676 | − | 0.478436i | ||||
\(857\) | 9.29249 | + | 16.0951i | 0.317425 | + | 0.549797i | 0.979950 | − | 0.199243i | \(-0.0638483\pi\) |
−0.662525 | + | 0.749040i | \(0.730515\pi\) | |||||||
\(858\) | −24.5780 | + | 71.4097i | −0.839080 | + | 2.43789i | ||||
\(859\) | 14.7487 | − | 25.5456i | 0.503221 | − | 0.871604i | −0.496772 | − | 0.867881i | \(-0.665482\pi\) |
0.999993 | − | 0.00372294i | \(-0.00118505\pi\) | |||||||
\(860\) | 0.304832 | + | 0.175995i | 0.0103947 | + | 0.00600137i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.3712 | − | 47.4083i | −0.932266 | − | 1.61473i | ||||
\(863\) | 16.1457 | + | 9.32173i | 0.549606 | + | 0.317315i | 0.748963 | − | 0.662612i | \(-0.230552\pi\) |
−0.199357 | + | 0.979927i | \(0.563885\pi\) | |||||||
\(864\) | −3.18716 | − | 1.84010i | −0.108429 | − | 0.0626016i | ||||
\(865\) | 13.6230 | + | 7.86522i | 0.463194 | + | 0.267425i | ||||
\(866\) | −11.7477 | − | 6.78256i | −0.399204 | − | 0.230481i | ||||
\(867\) | −24.0383 | − | 41.6355i | −0.816383 | − | 1.41402i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −51.9020 | − | 29.9656i | −1.76065 | − | 1.01651i | ||||
\(870\) | 3.65087 | − | 6.32350i | 0.123776 | − | 0.214387i | ||||
\(871\) | −19.9861 | + | 17.3782i | −0.677203 | + | 0.588836i | ||||
\(872\) | −21.0705 | − | 36.4951i | −0.713536 | − | 1.23588i | ||||
\(873\) | −48.8873 | + | 28.2251i | −1.65459 | + | 0.955276i | ||||
\(874\) | −6.46776 | + | 11.2025i | −0.218775 | + | 0.378930i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 1.41519i | − | 0.0478148i | ||||||
\(877\) | 37.7518i | 1.27479i | 0.770538 | + | 0.637395i | \(0.219988\pi\) | ||||
−0.770538 | + | 0.637395i | \(0.780012\pi\) | |||||||
\(878\) | 34.0930 | + | 19.6836i | 1.15058 | + | 0.664290i | ||||
\(879\) | −57.7606 | + | 33.3481i | −1.94822 | + | 1.12480i | ||||
\(880\) | 16.1190 | 0.543372 | ||||||||
\(881\) | −14.9149 | + | 25.8334i | −0.502497 | + | 0.870350i | 0.497499 | + | 0.867464i | \(0.334252\pi\) |
−0.999996 | + | 0.00288515i | \(0.999082\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.3979 | −1.09028 | −0.545138 | − | 0.838346i | \(-0.683523\pi\) | ||||
−0.545138 | + | 0.838346i | \(0.683523\pi\) | |||||||
\(884\) | −0.0645449 | + | 0.187531i | −0.00217088 | + | 0.00630734i | ||||
\(885\) | −12.7646 | − | 22.1089i | −0.429076 | − | 0.743181i | ||||
\(886\) | − | 4.60468i | − | 0.154697i | ||||||
\(887\) | −12.9599 | − | 22.4472i | −0.435151 | − | 0.753703i | 0.562157 | − | 0.827030i | \(-0.309972\pi\) |
−0.997308 | + | 0.0733272i | \(0.976638\pi\) | |||||||
\(888\) | 5.17703 | + | 8.96688i | 0.173730 | + | 0.300909i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.82181 | + | 2.78387i | −0.161627 | + | 0.0933156i | ||||
\(891\) | 16.8697i | 0.565155i | ||||||||
\(892\) | 1.95620 | − | 1.12941i | 0.0654984 | − | 0.0378155i | ||||
\(893\) | 11.2340 | − | 19.4579i | 0.375931 | − | 0.651132i | ||||
\(894\) | −15.7329 | − | 27.2502i | −0.526188 | − | 0.911384i | ||||
\(895\) | 14.5315 | + | 8.38976i | 0.485734 | + | 0.280439i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.42583 | + | 15.7644i | −0.181163 | + | 0.526357i | ||||
\(898\) | −12.5391 | + | 21.7184i | −0.418435 | + | 0.724751i | ||||
\(899\) | 7.92559i | 0.264333i | ||||||||
\(900\) | 2.26497 | 0.0754991 | ||||||||
\(901\) | −3.05510 | −0.101780 | ||||||||
\(902\) | 6.74420i | 0.224557i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −48.8934 | + | 28.2286i | −1.62617 | + | 0.938869i | ||||
\(905\) | 11.5529 | + | 6.67010i | 0.384033 | + | 0.221722i | ||||
\(906\) | −2.98231 | + | 5.16552i | −0.0990808 | + | 0.171613i | ||||
\(907\) | −15.5423 | −0.516072 | −0.258036 | − | 0.966135i | \(-0.583075\pi\) | ||||
−0.258036 | + | 0.966135i | \(0.583075\pi\) | |||||||
\(908\) | −0.0385589 | + | 0.0222620i | −0.00127962 | + | 0.000738791i | ||||
\(909\) | 20.7576 | 0.688485 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.6358 | 0.783090 | 0.391545 | − | 0.920159i | \(-0.371941\pi\) | ||||
0.391545 | + | 0.920159i | \(0.371941\pi\) | |||||||
\(912\) | 55.3294 | − | 31.9445i | 1.83214 | − | 1.05779i | ||||
\(913\) | 30.6786 | 1.01531 | ||||||||
\(914\) | −6.01911 | + | 10.4254i | −0.199094 | + | 0.344842i | ||||
\(915\) | −14.6846 | − | 8.47816i | −0.485458 | − | 0.280279i | ||||
\(916\) | −1.47421 | + | 0.851138i | −0.0487094 | + | 0.0281224i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 5.12155i | − | 0.169036i | ||||||
\(919\) | 44.4817 | 1.46732 | 0.733659 | − | 0.679518i | \(-0.237811\pi\) | ||||
0.733659 | + | 0.679518i | \(0.237811\pi\) | |||||||
\(920\) | 3.74264 | 0.123391 | ||||||||
\(921\) | − | 12.2045i | − | 0.402151i | ||||||
\(922\) | −1.56608 | + | 2.71253i | −0.0515761 | + | 0.0893324i | ||||
\(923\) | −31.7560 | − | 10.9299i | −1.04526 | − | 0.359761i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.67920 | − | 2.70154i | −0.153851 | − | 0.0888259i | ||||
\(926\) | −3.78086 | − | 6.54864i | −0.124247 | − | 0.215202i | ||||
\(927\) | −22.4082 | + | 38.8121i | −0.735981 | + | 1.27476i | ||||
\(928\) | −1.09601 | + | 0.632782i | −0.0359783 | + | 0.0207721i | ||||
\(929\) | − | 2.94270i | − | 0.0965470i | −0.998834 | − | 0.0482735i | \(-0.984628\pi\) | ||
0.998834 | − | 0.0482735i | \(-0.0153719\pi\) | |||||||
\(930\) | −9.63964 | + | 5.56545i | −0.316096 | + | 0.182498i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.383751 | + | 0.664676i | 0.0125702 | + | 0.0217722i | ||||
\(933\) | 39.2566 | + | 67.9944i | 1.28520 | + | 2.22604i | ||||
\(934\) | − | 26.0392i | − | 0.852028i | ||||||
\(935\) | −1.18983 | − | 2.06085i | −0.0389116 | − | 0.0673968i | ||||
\(936\) | 41.7367 | − | 36.2906i | 1.36421 | − | 1.18619i | ||||
\(937\) | 0.951020 | 0.0310685 | 0.0155342 | − | 0.999879i | \(-0.495055\pi\) | ||||
0.0155342 | + | 0.999879i | \(0.495055\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.88526 | + | 6.72947i | −0.126791 | + | 0.219608i | ||||
\(940\) | −0.304267 | −0.00992409 | ||||||||
\(941\) | −19.1125 | + | 11.0346i | −0.623050 | + | 0.359718i | −0.778056 | − | 0.628196i | \(-0.783794\pi\) |
0.155006 | + | 0.987914i | \(0.450460\pi\) | |||||||
\(942\) | 13.2717 | + | 7.66242i | 0.432416 | + | 0.249655i | ||||
\(943\) | 1.48885i | 0.0484835i | ||||||||
\(944\) | − | 41.7105i | − | 1.35756i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.1648 | − | 27.9983i | 0.525563 | − | 0.910302i | ||||
\(947\) | −44.3160 | + | 25.5859i | −1.44008 | + | 0.831429i | −0.997854 | − | 0.0654762i | \(-0.979143\pi\) |
−0.442223 | + | 0.896905i | \(0.645810\pi\) | |||||||
\(948\) | 1.60842 | + | 2.78587i | 0.0522392 | + | 0.0904809i | ||||
\(949\) | 17.0513 | + | 5.86878i | 0.553509 | + | 0.190509i | ||||
\(950\) | −17.5326 | + | 30.3674i | −0.568833 | + | 0.985248i | ||||
\(951\) | 60.0605 | + | 34.6759i | 1.94759 | + | 1.12444i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.9235 | + | 39.7047i | 0.742565 | + | 1.28616i | 0.951324 | + | 0.308194i | \(0.0997245\pi\) |
−0.208758 | + | 0.977967i | \(0.566942\pi\) | |||||||
\(954\) | 34.5347 | + | 19.9386i | 1.11810 | + | 0.645536i | ||||
\(955\) | 2.96644 | + | 1.71267i | 0.0959916 | + | 0.0554208i | ||||
\(956\) | −1.15085 | − | 0.664444i | −0.0372212 | − | 0.0214896i | ||||
\(957\) | 29.9923 | + | 17.3160i | 0.969512 | + | 0.559748i | ||||
\(958\) | −22.8478 | − | 39.5735i | −0.738177 | − | 1.27856i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −16.7985 | − | 9.69861i | −0.542169 | − | 0.313021i | ||||
\(961\) | −9.45905 | + | 16.3836i | −0.305131 | + | 0.528502i | ||||
\(962\) | −6.06172 | + | 1.17909i | −0.195438 | + | 0.0380154i | ||||
\(963\) | 25.6458 | + | 44.4198i | 0.826424 | + | 1.43141i | ||||
\(964\) | −1.91866 | + | 1.10774i | −0.0617960 | + | 0.0356779i | ||||
\(965\) | −4.67338 | + | 8.09453i | −0.150441 | + | 0.260572i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 19.2609i | − | 0.619387i | −0.950836 | − | 0.309694i | \(-0.899773\pi\) | ||
0.950836 | − | 0.309694i | \(-0.100227\pi\) | |||||||
\(968\) | 48.5813i | 1.56146i | ||||||||
\(969\) | −8.16832 | − | 4.71598i | −0.262404 | − | 0.151499i | ||||
\(970\) | −10.2494 | + | 5.91752i | −0.329090 | + | 0.190000i | ||||
\(971\) | −47.3326 | −1.51897 | −0.759487 | − | 0.650522i | \(-0.774550\pi\) | ||||
−0.759487 | + | 0.650522i | \(0.774550\pi\) | |||||||
\(972\) | −0.524016 | + | 0.907622i | −0.0168078 | + | 0.0291120i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 22.0046 | 0.705072 | ||||||||
\(975\) | −14.7082 | + | 42.7335i | −0.471039 | + | 1.36857i | ||||
\(976\) | −13.8520 | − | 23.9923i | −0.443390 | − | 0.767975i | ||||
\(977\) | 47.8571i | 1.53108i | 0.643387 | + | 0.765541i | \(0.277529\pi\) | ||||
−0.643387 | + | 0.765541i | \(0.722471\pi\) | |||||||
\(978\) | −28.5302 | − | 49.4158i | −0.912297 | − | 1.58014i | ||||
\(979\) | −13.2039 | − | 22.8698i | −0.421998 | − | 0.730921i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 66.8635 | − | 38.6037i | 2.13479 | − | 1.23252i | ||||
\(982\) | − | 43.7061i | − | 1.39472i | ||||||
\(983\) | 13.6560 | − | 7.88432i | 0.435560 | − | 0.251471i | −0.266152 | − | 0.963931i | \(-0.585752\pi\) |
0.701712 | + | 0.712460i | \(0.252419\pi\) | |||||||
\(984\) | 3.86707 | − | 6.69796i | 0.123278 | − | 0.213523i | ||||
\(985\) | 5.81142 | + | 10.0657i | 0.185167 | + | 0.320719i | ||||
\(986\) | −1.52526 | − | 0.880608i | −0.0485741 | − | 0.0280443i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.395151 | − | 2.03148i | −0.0125714 | − | 0.0646300i | ||||
\(989\) | 3.56853 | − | 6.18088i | 0.113473 | − | 0.196541i | ||||
\(990\) | 31.0609i | 0.987181i | ||||||||
\(991\) | −12.1378 | −0.385571 | −0.192786 | − | 0.981241i | \(-0.561752\pi\) | ||||
−0.192786 | + | 0.981241i | \(0.561752\pi\) | |||||||
\(992\) | 1.92924 | 0.0612536 | ||||||||
\(993\) | 1.78555i | 0.0566627i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.92715 | − | 2.84469i | 0.156201 | − | 0.0901828i | ||||
\(996\) | −1.42608 | − | 0.823346i | −0.0451870 | − | 0.0260887i | ||||
\(997\) | 16.8938 | − | 29.2609i | 0.535032 | − | 0.926703i | −0.464129 | − | 0.885767i | \(-0.653633\pi\) |
0.999162 | − | 0.0409358i | \(-0.0130339\pi\) | |||||||
\(998\) | 33.3986 | 1.05721 | ||||||||
\(999\) | −7.13166 | + | 4.11746i | −0.225636 | + | 0.130271i |
(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 | 637.2.u.g.30.2 | 12 | ||
7.2 | even | 3 | 637.2.q.i.589.5 | 12 | |||
7.3 | odd | 6 | 91.2.k.b.4.2 | ✓ | 12 | ||
7.4 | even | 3 | 637.2.k.i.459.2 | 12 | |||
7.5 | odd | 6 | 637.2.q.g.589.5 | 12 | |||
7.6 | odd | 2 | 91.2.u.b.30.2 | yes | 12 | ||
13.10 | even | 6 | 637.2.k.i.569.5 | 12 | |||
21.17 | even | 6 | 819.2.bm.f.550.5 | 12 | |||
21.20 | even | 2 | 819.2.do.e.667.5 | 12 | |||
91.6 | even | 12 | 1183.2.e.j.170.10 | 24 | |||
91.10 | odd | 6 | 91.2.u.b.88.2 | yes | 12 | ||
91.19 | even | 12 | 8281.2.a.cp.1.3 | 12 | |||
91.20 | even | 12 | 1183.2.e.j.170.3 | 24 | |||
91.23 | even | 6 | 637.2.q.i.491.5 | 12 | |||
91.33 | even | 12 | 8281.2.a.cp.1.10 | 12 | |||
91.45 | even | 12 | 1183.2.e.j.508.10 | 24 | |||
91.58 | odd | 12 | 8281.2.a.co.1.3 | 12 | |||
91.59 | even | 12 | 1183.2.e.j.508.3 | 24 | |||
91.62 | odd | 6 | 91.2.k.b.23.5 | yes | 12 | ||
91.72 | odd | 12 | 8281.2.a.co.1.10 | 12 | |||
91.75 | odd | 6 | 637.2.q.g.491.5 | 12 | |||
91.88 | even | 6 | inner | 637.2.u.g.361.2 | 12 | ||
273.62 | even | 6 | 819.2.bm.f.478.2 | 12 | |||
273.101 | even | 6 | 819.2.do.e.361.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.2 | ✓ | 12 | 7.3 | odd | 6 | ||
91.2.k.b.23.5 | yes | 12 | 91.62 | odd | 6 | ||
91.2.u.b.30.2 | yes | 12 | 7.6 | odd | 2 | ||
91.2.u.b.88.2 | yes | 12 | 91.10 | odd | 6 | ||
637.2.k.i.459.2 | 12 | 7.4 | even | 3 | |||
637.2.k.i.569.5 | 12 | 13.10 | even | 6 | |||
637.2.q.g.491.5 | 12 | 91.75 | odd | 6 | |||
637.2.q.g.589.5 | 12 | 7.5 | odd | 6 | |||
637.2.q.i.491.5 | 12 | 91.23 | even | 6 | |||
637.2.q.i.589.5 | 12 | 7.2 | even | 3 | |||
637.2.u.g.30.2 | 12 | 1.1 | even | 1 | trivial | ||
637.2.u.g.361.2 | 12 | 91.88 | even | 6 | inner | ||
819.2.bm.f.478.2 | 12 | 273.62 | even | 6 | |||
819.2.bm.f.550.5 | 12 | 21.17 | even | 6 | |||
819.2.do.e.361.5 | 12 | 273.101 | even | 6 | |||
819.2.do.e.667.5 | 12 | 21.20 | even | 2 | |||
1183.2.e.j.170.3 | 24 | 91.20 | even | 12 | |||
1183.2.e.j.170.10 | 24 | 91.6 | even | 12 | |||
1183.2.e.j.508.3 | 24 | 91.59 | even | 12 | |||
1183.2.e.j.508.10 | 24 | 91.45 | even | 12 | |||
8281.2.a.co.1.3 | 12 | 91.58 | odd | 12 | |||
8281.2.a.co.1.10 | 12 | 91.72 | odd | 12 | |||
8281.2.a.cp.1.3 | 12 | 91.19 | even | 12 | |||
8281.2.a.cp.1.10 | 12 | 91.33 | even | 12 |