Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(459,637)]
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([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.k (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: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 \) |
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 | 569.5 | ||
Root | \(-1.38488 + 0.286553i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.569 |
Dual form | 637.2.k.i.459.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37905i | 0.975139i | 0.873084 | + | 0.487570i | \(0.162116\pi\) | ||||
−0.873084 | + | 0.487570i | \(0.837884\pi\) | |||||||
\(3\) | 1.44060 | − | 2.49520i | 0.831732 | − | 1.44060i | −0.0649323 | − | 0.997890i | \(-0.520683\pi\) |
0.896664 | − | 0.442712i | \(-0.145984\pi\) | |||||||
\(4\) | 0.0982074 | 0.0491037 | ||||||||
\(5\) | 0.697972 | + | 0.402974i | 0.312142 | + | 0.180216i | 0.647885 | − | 0.761738i | \(-0.275654\pi\) |
−0.335742 | + | 0.941954i | \(0.608987\pi\) | |||||||
\(6\) | 3.44101 | + | 1.98667i | 1.40479 | + | 0.811054i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.89354i | 1.02302i | ||||||||
\(9\) | −2.65067 | − | 4.59109i | −0.883555 | − | 1.53036i | ||||
\(10\) | −0.555723 | + | 0.962541i | −0.175735 | + | 0.304382i | ||||
\(11\) | 4.56532 | + | 2.63579i | 1.37650 | + | 0.794720i | 0.991736 | − | 0.128296i | \(-0.0409508\pi\) |
0.384760 | + | 0.923017i | \(0.374284\pi\) | |||||||
\(12\) | 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 | ||||
\(16\) | −3.79394 | −0.948485 | ||||||||
\(17\) | −0.560102 | −0.135845 | −0.0679223 | − | 0.997691i | \(-0.521637\pi\) | ||||
−0.0679223 | + | 0.997691i | \(0.521637\pi\) | |||||||
\(18\) | 6.33136 | − | 3.65541i | 1.49232 | − | 0.861589i | ||||
\(19\) | −5.06165 | + | 2.92234i | −1.16122 | + | 0.670431i | −0.951596 | − | 0.307351i | \(-0.900558\pi\) |
−0.209625 | + | 0.977782i | \(0.567224\pi\) | |||||||
\(20\) | 0.0685460 | + | 0.0395750i | 0.0153273 | + | 0.00884925i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.63490 | + | 6.29583i | −0.774963 | + | 1.34228i | ||||
\(23\) | 1.60488 | 0.334640 | 0.167320 | − | 0.985903i | \(-0.446489\pi\) | ||||
0.167320 | + | 0.985903i | \(0.446489\pi\) | |||||||
\(24\) | 7.21995 | + | 4.16844i | 1.47377 | + | 0.850880i | ||||
\(25\) | −2.17522 | − | 3.76760i | −0.435045 | − | 0.753520i | ||||
\(26\) | 3.75219 | + | 3.26258i | 0.735864 | + | 0.639844i | ||||
\(27\) | −6.63060 | −1.27606 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.14008 | − | 1.97467i | −0.211707 | − | 0.366687i | 0.740542 | − | 0.672010i | \(-0.234569\pi\) |
−0.952249 | + | 0.305323i | \(0.901236\pi\) | |||||||
\(30\) | 1.60115 | + | 2.77328i | 0.292329 | + | 0.506329i | ||||
\(31\) | −3.01022 | + | 1.73795i | −0.540651 | + | 0.312145i | −0.745343 | − | 0.666681i | \(-0.767714\pi\) |
0.204692 | + | 0.978827i | \(0.434381\pi\) | |||||||
\(32\) | 0.555034i | 0.0981171i | ||||||||
\(33\) | 13.1536 | − | 7.59424i | 2.28975 | − | 1.32199i | ||||
\(34\) | − | 0.772411i | − | 0.132467i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.260315 | − | 0.450879i | −0.0433858 | − | 0.0751464i | ||||
\(37\) | − | 1.24196i | − | 0.204177i | −0.994775 | − | 0.102088i | \(-0.967448\pi\) | ||
0.994775 | − | 0.102088i | \(-0.0325524\pi\) | |||||||
\(38\) | −4.03007 | − | 6.98029i | −0.653764 | − | 1.13235i | ||||
\(39\) | −3.38084 | − | 9.82279i | −0.541368 | − | 1.57291i | ||||
\(40\) | −1.16602 | + | 2.01961i | −0.184364 | + | 0.319329i | ||||
\(41\) | −0.803413 | + | 0.463851i | −0.125472 | + | 0.0724413i | −0.561422 | − | 0.827529i | \(-0.689746\pi\) |
0.435950 | + | 0.899971i | \(0.356412\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.22356 | − | 3.85131i | 0.339089 | − | 0.587320i | −0.645172 | − | 0.764037i | \(-0.723214\pi\) |
0.984262 | + | 0.176717i | \(0.0565478\pi\) | |||||||
\(44\) | 0.448348 | + | 0.258854i | 0.0675910 | + | 0.0390237i | ||||
\(45\) | − | 4.27260i | − | 0.636921i | ||||||
\(46\) | 2.21321i | 0.326320i | ||||||||
\(47\) | 3.32915 | + | 1.92209i | 0.485607 | + | 0.280365i | 0.722750 | − | 0.691109i | \(-0.242878\pi\) |
−0.237143 | + | 0.971475i | \(0.576211\pi\) | |||||||
\(48\) | −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 | ||||
\(52\) | 0.232340 | − | 0.267207i | 0.0322197 | − | 0.0370549i | ||||
\(53\) | −2.72727 | − | 4.72377i | −0.374620 | − | 0.648860i | 0.615650 | − | 0.788019i | \(-0.288893\pi\) |
−0.990270 | + | 0.139159i | \(0.955560\pi\) | |||||||
\(54\) | − | 9.14396i | − | 1.24434i | ||||||
\(55\) | 2.12431 | + | 3.67941i | 0.286442 | + | 0.496132i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.8397i | 2.23048i | ||||||||
\(58\) | 2.72318 | − | 1.57223i | 0.357571 | − | 0.206444i | ||||
\(59\) | − | 10.9940i | − | 1.43129i | −0.698463 | − | 0.715646i | \(-0.746132\pi\) | ||
0.698463 | − | 0.715646i | \(-0.253868\pi\) | |||||||
\(60\) | 0.197495 | − | 0.114024i | 0.0254965 | − | 0.0147204i | ||||
\(61\) | 3.65107 | + | 6.32385i | 0.467472 | + | 0.809686i | 0.999309 | − | 0.0371610i | \(-0.0118314\pi\) |
−0.531837 | + | 0.846847i | \(0.678498\pi\) | |||||||
\(62\) | −2.39673 | − | 4.15126i | −0.304385 | − | 0.527210i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.35330 | −1.04416 | ||||||||
\(65\) | 2.74769 | − | 0.945710i | 0.340809 | − | 0.117301i | ||||
\(66\) | 10.4729 | + | 18.1396i | 1.28912 | + | 2.23283i | ||||
\(67\) | 6.36144 | + | 3.67278i | 0.777174 | + | 0.448701i | 0.835428 | − | 0.549600i | \(-0.185220\pi\) |
−0.0582541 | + | 0.998302i | \(0.518553\pi\) | |||||||
\(68\) | −0.0550061 | −0.00667047 | ||||||||
\(69\) | 2.31199 | − | 4.00448i | 0.278330 | − | 0.482083i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.06668 | − | 4.65730i | −0.957339 | − | 0.552720i | −0.0619857 | − | 0.998077i | \(-0.519743\pi\) |
−0.895353 | + | 0.445357i | \(0.853077\pi\) | |||||||
\(72\) | 13.2845 | − | 7.66982i | 1.56559 | − | 0.903896i | ||||
\(73\) | −4.33139 | + | 2.50073i | −0.506951 | + | 0.292688i | −0.731579 | − | 0.681756i | \(-0.761216\pi\) |
0.224629 | + | 0.974444i | \(0.427883\pi\) | |||||||
\(74\) | 1.71273 | 0.199101 | ||||||||
\(75\) | −12.5345 | −1.44736 | ||||||||
\(76\) | −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 | \(0.945791\pi\) | |||||||
\(80\) | −2.64806 | − | 1.52886i | −0.296062 | − | 0.170932i | ||||
\(81\) | −1.60006 | + | 2.77138i | −0.177784 | + | 0.307931i | ||||
\(82\) | −0.639676 | − | 1.10795i | −0.0706404 | − | 0.122353i | ||||
\(83\) | 5.81962i | 0.638786i | 0.947622 | + | 0.319393i | \(0.103479\pi\) | ||||
−0.947622 | + | 0.319393i | \(0.896521\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.390935 | − | 0.225707i | −0.0424029 | − | 0.0244813i | ||||
\(86\) | 5.31117 | + | 3.06641i | 0.572719 | + | 0.330659i | ||||
\(87\) | −6.56959 | −0.704334 | ||||||||
\(88\) | −7.62677 | + | 13.2100i | −0.813016 | + | 1.40819i | ||||
\(89\) | 5.00946i | 0.531001i | 0.964111 | + | 0.265501i | \(0.0855373\pi\) | ||||
−0.964111 | + | 0.265501i | \(0.914463\pi\) | |||||||
\(90\) | 5.89215 | 0.621087 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.157611 | 0.0164320 | ||||||||
\(93\) | 10.0148i | 1.03848i | ||||||||
\(94\) | −2.65067 | + | 4.59109i | −0.273395 | + | 0.473534i | ||||
\(95\) | −4.71051 | −0.483289 | ||||||||
\(96\) | 1.38492 | + | 0.799583i | 0.141348 | + | 0.0816071i | ||||
\(97\) | −9.22171 | − | 5.32416i | −0.936323 | − | 0.540586i | −0.0475172 | − | 0.998870i | \(-0.515131\pi\) |
−0.888806 | + | 0.458284i | \(0.848464\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 27.9464i | − | 2.80872i | ||||||
\(100\) | −0.213623 | − | 0.370006i | −0.0213623 | − | 0.0370006i | ||||
\(101\) | −1.95777 | + | 3.39096i | −0.194805 | + | 0.337413i | −0.946837 | − | 0.321715i | \(-0.895741\pi\) |
0.752031 | + | 0.659127i | \(0.229074\pi\) | |||||||
\(102\) | −1.92732 | − | 1.11274i | −0.190833 | − | 0.110177i | ||||
\(103\) | −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 | ||||
\(107\) | −9.67522 | −0.935339 | −0.467670 | − | 0.883903i | \(-0.654906\pi\) | ||||
−0.467670 | + | 0.883903i | \(0.654906\pi\) | |||||||
\(108\) | −0.651174 | −0.0626592 | ||||||||
\(109\) | −12.6126 | + | 7.28189i | −1.20807 | + | 0.697478i | −0.962337 | − | 0.271860i | \(-0.912361\pi\) |
−0.245731 | + | 0.969338i | \(0.579028\pi\) | |||||||
\(110\) | −5.07411 | + | 2.92954i | −0.483798 | + | 0.279321i | ||||
\(111\) | −3.09893 | − | 1.78917i | −0.294137 | − | 0.169820i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.75572 | + | 16.8974i | −0.917741 | + | 1.58957i | −0.114903 | + | 0.993377i | \(0.536656\pi\) |
−0.802838 | + | 0.596197i | \(0.796678\pi\) | |||||||
\(114\) | −23.2229 | −2.17502 | ||||||||
\(115\) | 1.12016 | + | 0.646723i | 0.104455 | + | 0.0603073i | ||||
\(116\) | −0.111964 | − | 0.193927i | −0.0103956 | − | 0.0180057i | ||||
\(117\) | −18.7626 | − | 3.64958i | −1.73460 | − | 0.337404i | ||||
\(118\) | 15.1613 | 1.39571 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.35955 | + | 5.81891i | 0.306683 | + | 0.531191i | ||||
\(121\) | 8.39477 | + | 14.5402i | 0.763161 | + | 1.32183i | ||||
\(122\) | −8.72093 | + | 5.03503i | −0.789556 | + | 0.455850i | ||||
\(123\) | 2.67290i | 0.241007i | ||||||||
\(124\) | −0.295626 | + | 0.170680i | −0.0265480 | + | 0.0153275i | ||||
\(125\) | − | 7.53598i | − | 0.674038i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.958656 | − | 1.66044i | −0.0850670 | − | 0.147340i | 0.820353 | − | 0.571858i | \(-0.193777\pi\) |
−0.905420 | + | 0.424517i | \(0.860444\pi\) | |||||||
\(128\) | − | 10.4096i | − | 0.920087i | ||||||
\(129\) | −6.40652 | − | 11.0964i | −0.564063 | − | 0.976985i | ||||
\(130\) | 1.30419 | + | 3.78922i | 0.114385 | + | 0.332337i | ||||
\(131\) | 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 | ||||
\(136\) | − | 1.62068i | − | 0.138972i | ||||||
\(137\) | 7.85105i | 0.670761i | 0.942083 | + | 0.335380i | \(0.108865\pi\) | ||||
−0.942083 | + | 0.335380i | \(0.891135\pi\) | |||||||
\(138\) | 5.52240 | + | 3.18836i | 0.470098 | + | 0.271411i | ||||
\(139\) | 4.96241 | − | 8.59514i | 0.420906 | − | 0.729030i | −0.575122 | − | 0.818067i | \(-0.695046\pi\) |
0.996028 | + | 0.0890370i | \(0.0283789\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.59197 | − | 5.53793i | 0.807790 | − | 0.466378i | ||||
\(142\) | 6.42267 | − | 11.1244i | 0.538979 | − | 0.933538i | ||||
\(143\) | 17.9722 | − | 6.18574i | 1.50291 | − | 0.517278i | ||||
\(144\) | 10.0565 | + | 17.4183i | 0.838039 | + | 1.45153i | ||||
\(145\) | − | 1.83769i | − | 0.152612i | ||||||
\(146\) | −3.44864 | − | 5.97322i | −0.285412 | − | 0.494347i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 0.121969i | − | 0.0100258i | ||||||
\(149\) | 6.85827 | − | 3.95962i | 0.561851 | − | 0.324385i | −0.192037 | − | 0.981388i | \(-0.561509\pi\) |
0.753888 | + | 0.657003i | \(0.228176\pi\) | |||||||
\(150\) | − | 17.2858i | − | 1.41138i | ||||||
\(151\) | 1.30005 | − | 0.750582i | 0.105796 | − | 0.0610815i | −0.446168 | − | 0.894949i | \(-0.647212\pi\) |
0.551965 | + | 0.833868i | \(0.313878\pi\) | |||||||
\(152\) | −8.45592 | − | 14.6461i | −0.685866 | − | 1.18795i | ||||
\(153\) | 1.48464 | + | 2.57148i | 0.120026 | + | 0.207892i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.80140 | −0.225014 | ||||||||
\(156\) | −0.332024 | − | 0.964671i | −0.0265832 | − | 0.0772355i | ||||
\(157\) | 1.92846 | + | 3.34019i | 0.153908 | + | 0.266576i | 0.932661 | − | 0.360754i | \(-0.117481\pi\) |
−0.778753 | + | 0.627331i | \(0.784147\pi\) | |||||||
\(158\) | −13.5777 | − | 7.83906i | −1.08018 | − | 0.623642i | ||||
\(159\) | −15.7156 | −1.24633 | ||||||||
\(160\) | −0.223664 | + | 0.387398i | −0.0176822 | + | 0.0306265i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.82189 | − | 2.20657i | −0.300276 | − | 0.173364i | ||||
\(163\) | 12.4369 | − | 7.18042i | 0.974130 | − | 0.562414i | 0.0736372 | − | 0.997285i | \(-0.476539\pi\) |
0.900493 | + | 0.434871i | \(0.143206\pi\) | |||||||
\(164\) | −0.0789011 | + | 0.0455536i | −0.00616114 | + | 0.00355714i | ||||
\(165\) | 12.2411 | 0.952971 | ||||||||
\(166\) | −8.02557 | −0.622905 | ||||||||
\(167\) | 3.91563 | − | 2.26069i | 0.303000 | − | 0.174937i | −0.340790 | − | 0.940140i | \(-0.610694\pi\) |
0.643790 | + | 0.765202i | \(0.277361\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.80593 | − | 12.8740i | −0.138918 | − | 0.990304i | ||||
\(170\) | 0.311262 | − | 0.539121i | 0.0238727 | − | 0.0413487i | ||||
\(171\) | 26.8335 | + | 15.4923i | 2.05201 | + | 1.18473i | ||||
\(172\) | 0.218370 | − | 0.378227i | 0.0166505 | − | 0.0288396i | ||||
\(173\) | 9.75896 | + | 16.9030i | 0.741960 | + | 1.28511i | 0.951602 | + | 0.307334i | \(0.0994369\pi\) |
−0.209642 | + | 0.977778i | \(0.567230\pi\) | |||||||
\(174\) | − | 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 | ||||
\(178\) | −6.90832 | −0.517800 | ||||||||
\(179\) | 10.4098 | − | 18.0303i | 0.778065 | − | 1.34765i | −0.154990 | − | 0.987916i | \(-0.549535\pi\) |
0.933055 | − | 0.359733i | \(-0.117132\pi\) | |||||||
\(180\) | − | 0.419601i | − | 0.0312752i | ||||||
\(181\) | −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 | ||||||||
\(184\) | 4.64378i | 0.342344i | ||||||||
\(185\) | 0.500477 | − | 0.866851i | 0.0367958 | − | 0.0637322i | ||||
\(186\) | −13.8109 | −1.01267 | ||||||||
\(187\) | −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 | ||||||
\(191\) | 2.12504 | + | 3.68068i | 0.153762 | + | 0.266324i | 0.932608 | − | 0.360892i | \(-0.117528\pi\) |
−0.778845 | + | 0.627216i | \(0.784194\pi\) | |||||||
\(192\) | −12.0338 | + | 20.8431i | −0.868463 | + | 1.50422i | ||||
\(193\) | −10.0435 | − | 5.79861i | −0.722946 | − | 0.417393i | 0.0928898 | − | 0.995676i | \(-0.470390\pi\) |
−0.815836 | + | 0.578283i | \(0.803723\pi\) | |||||||
\(194\) | 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 | −0.873884 | − | 0.486135i | \(-0.838406\pi\) |
−0.0159371 | + | 0.999873i | \(0.505073\pi\) | |||||||
\(198\) | 38.5396 | 2.73889 | ||||||||
\(199\) | 7.05924 | 0.500416 | 0.250208 | − | 0.968192i | \(-0.419501\pi\) | ||||
0.250208 | + | 0.968192i | \(0.419501\pi\) | |||||||
\(200\) | 10.9017 | − | 6.29410i | 0.770867 | − | 0.445060i | ||||
\(201\) | 18.3286 | − | 10.5820i | 1.29280 | − | 0.746398i | ||||
\(202\) | −4.67632 | − | 2.69987i | −0.329024 | − | 0.189962i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.0792419 | + | 0.137251i | −0.00554804 | + | 0.00960949i | ||||
\(205\) | −0.747680 | −0.0522202 | ||||||||
\(206\) | −10.0963 | − | 5.82912i | −0.703445 | − | 0.406134i | ||||
\(207\) | −4.25399 | − | 7.36812i | −0.295673 | − | 0.512120i | ||||
\(208\) | −8.97572 | + | 10.3227i | −0.622354 | + | 0.715751i | ||||
\(209\) | −30.8107 | −2.13122 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.2113 | + | 22.8827i | 0.909505 | + | 1.57531i | 0.814754 | + | 0.579807i | \(0.196872\pi\) |
0.0947513 | + | 0.995501i | \(0.469794\pi\) | |||||||
\(212\) | −0.267838 | − | 0.463909i | −0.0183952 | − | 0.0318614i | ||||
\(213\) | −23.2417 | + | 13.4186i | −1.59250 | + | 0.919429i | ||||
\(214\) | − | 13.3427i | − | 0.912086i | ||||||
\(215\) | 3.10396 | − | 1.79207i | 0.211688 | − | 0.122218i | ||||
\(216\) | − | 19.1859i | − | 1.30544i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0421 | − | 17.3935i | −0.680138 | − | 1.17803i | ||||
\(219\) | 14.4102i | 0.973752i | ||||||||
\(220\) | 0.208623 | + | 0.361345i | 0.0140654 | + | 0.0243619i | ||||
\(221\) | −1.32509 | + | 1.52395i | −0.0891353 | + | 0.102512i | ||||
\(222\) | 2.46736 | − | 4.27359i | 0.165598 | − | 0.286825i | ||||
\(223\) | −19.9191 | + | 11.5003i | −1.33388 | + | 0.770115i | −0.985892 | − | 0.167384i | \(-0.946468\pi\) |
−0.347987 | + | 0.937499i | \(0.613135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.5316 | + | 19.9733i | −0.768772 | + | 1.33155i | ||||
\(226\) | −23.3024 | − | 13.4537i | −1.55006 | − | 0.894925i | ||||
\(227\) | 0.453367i | 0.0300911i | 0.999887 | + | 0.0150455i | \(0.00478932\pi\) | ||||
−0.999887 | + | 0.0150455i | \(0.995211\pi\) | |||||||
\(228\) | 1.65379i | 0.109525i | ||||||||
\(229\) | −15.0112 | − | 8.66674i | −0.991970 | − | 0.572714i | −0.0861077 | − | 0.996286i | \(-0.527443\pi\) |
−0.905863 | + | 0.423571i | \(0.860776\pi\) | |||||||
\(230\) | −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 | \(0.0842644\pi\) | |||||||
\(234\) | 5.03298 | − | 25.8746i | 0.329016 | − | 1.69148i | ||||
\(235\) | 1.54910 | + | 2.68313i | 0.101052 | + | 0.175028i | ||||
\(236\) | − | 1.07969i | − | 0.0702818i | ||||||
\(237\) | 16.3778 | + | 28.3672i | 1.06385 | + | 1.84265i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 13.5314i | − | 0.875276i | −0.899151 | − | 0.437638i | \(-0.855815\pi\) | ||
0.899151 | − | 0.437638i | \(-0.144185\pi\) | |||||||
\(240\) | −7.62961 | + | 4.40496i | −0.492489 | + | 0.284339i | ||||
\(241\) | 22.5592i | 1.45317i | 0.687078 | + | 0.726583i | \(0.258893\pi\) | ||||
−0.687078 | + | 0.726583i | \(0.741107\pi\) | |||||||
\(242\) | −20.0517 | + | 11.5768i | −1.28897 | + | 0.744188i | ||||
\(243\) | −5.33581 | − | 9.24189i | −0.342292 | − | 0.592868i | ||||
\(244\) | 0.358563 | + | 0.621049i | 0.0229546 | + | 0.0397586i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.68607 | −0.235015 | ||||||||
\(247\) | −4.02364 | + | 20.6856i | −0.256018 | + | 1.31619i | ||||
\(248\) | −5.02884 | − | 8.71020i | −0.319331 | − | 0.553098i | ||||
\(249\) | 14.5211 | + | 8.38375i | 0.920236 | + | 0.531299i | ||||
\(250\) | 10.3925 | 0.657281 | ||||||||
\(251\) | 3.36618 | − | 5.83039i | 0.212471 | − | 0.368011i | −0.740016 | − | 0.672589i | \(-0.765182\pi\) |
0.952487 | + | 0.304578i | \(0.0985154\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.32677 | + | 4.23011i | 0.460630 | + | 0.265945i | ||||
\(254\) | 2.28984 | − | 1.32204i | 0.143677 | − | 0.0829521i | ||||
\(255\) | −1.12636 | + | 0.650306i | −0.0705356 | + | 0.0407238i | ||||
\(256\) | −2.35120 | −0.146950 | ||||||||
\(257\) | 16.5381 | 1.03162 | 0.515811 | − | 0.856703i | \(-0.327491\pi\) | ||||
0.515811 | + | 0.856703i | \(0.327491\pi\) | |||||||
\(258\) | 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 | ||||
\(262\) | 18.6090 | + | 10.7439i | 1.14967 | + | 0.663761i | ||||
\(263\) | 5.01137 | − | 8.67994i | 0.309014 | − | 0.535228i | −0.669133 | − | 0.743143i | \(-0.733334\pi\) |
0.978147 | + | 0.207915i | \(0.0666676\pi\) | |||||||
\(264\) | 21.9743 | + | 38.0606i | 1.35242 | + | 2.34247i | ||||
\(265\) | − | 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 | ||||
\(269\) | 15.7230 | 0.958647 | 0.479323 | − | 0.877638i | \(-0.340882\pi\) | ||||
0.479323 | + | 0.877638i | \(0.340882\pi\) | |||||||
\(270\) | 3.68478 | − | 6.38223i | 0.224249 | − | 0.388410i | ||||
\(271\) | − | 5.21618i | − | 0.316860i | −0.987370 | − | 0.158430i | \(-0.949357\pi\) | ||
0.987370 | − | 0.158430i | \(-0.0506433\pi\) | |||||||
\(272\) | 2.12499 | 0.128847 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.8270 | −0.654085 | ||||||||
\(275\) | − | 22.9337i | − | 1.38296i | ||||||
\(276\) | 0.227054 | − | 0.393269i | 0.0136671 | − | 0.0236720i | ||||
\(277\) | 19.2724 | 1.15797 | 0.578983 | − | 0.815340i | \(-0.303450\pi\) | ||||
0.578983 | + | 0.815340i | \(0.303450\pi\) | |||||||
\(278\) | 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 | \(-0.979641\pi\) | ||
0.997955 | − | 0.0639153i | \(-0.0203588\pi\) | |||||||
\(282\) | 7.63711 | + | 13.2279i | 0.454783 | + | 0.787707i | ||||
\(283\) | 7.87512 | − | 13.6401i | 0.468127 | − | 0.810820i | −0.531209 | − | 0.847241i | \(-0.678262\pi\) |
0.999337 | + | 0.0364203i | \(0.0115955\pi\) | |||||||
\(284\) | −0.792207 | − | 0.457381i | −0.0470089 | − | 0.0271406i | ||||
\(285\) | −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 | ||||
\(289\) | −16.6863 | −0.981546 | ||||||||
\(290\) | 2.53427 | 0.148817 | ||||||||
\(291\) | −26.5696 | + | 15.3400i | −1.55754 | + | 0.899246i | ||||
\(292\) | −0.425374 | + | 0.245590i | −0.0248932 | + | 0.0143721i | ||||
\(293\) | 20.0474 | + | 11.5744i | 1.17118 | + | 0.676182i | 0.953958 | − | 0.299940i | \(-0.0969668\pi\) |
0.217223 | + | 0.976122i | \(0.430300\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.43029 | − | 7.67348i | 0.257941 | − | 0.446767i | ||||
\(296\) | 3.59366 | 0.208877 | ||||||||
\(297\) | −30.2708 | − | 17.4769i | −1.75649 | − | 1.01411i | ||||
\(298\) | 5.46054 | + | 9.45793i | 0.316320 | + | 0.547883i | ||||
\(299\) | 3.79682 | − | 4.36661i | 0.219576 | − | 0.252528i | ||||
\(300\) | −1.23098 | −0.0710708 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.03509 | + | 1.79283i | 0.0595629 | + | 0.103166i | ||||
\(303\) | 5.64073 | + | 9.77003i | 0.324052 | + | 0.561274i | ||||
\(304\) | 19.2036 | − | 11.0872i | 1.10140 | − | 0.635894i | ||||
\(305\) | 5.88515i | 0.336983i | ||||||||
\(306\) | −3.54621 | + | 2.04740i | −0.202723 | + | 0.117042i | ||||
\(307\) | − | 4.23590i | − | 0.241756i | −0.992667 | − | 0.120878i | \(-0.961429\pi\) | ||
0.992667 | − | 0.120878i | \(-0.0385709\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.1785 | + | 21.0939i | 0.692813 | + | 1.19999i | ||||
\(310\) | − | 3.86328i | − | 0.219420i | ||||||
\(311\) | −13.6251 | − | 23.5993i | −0.772606 | − | 1.33819i | −0.936130 | − | 0.351654i | \(-0.885619\pi\) |
0.163524 | − | 0.986539i | \(-0.447714\pi\) | |||||||
\(312\) | 28.4227 | − | 9.78261i | 1.60912 | − | 0.553831i | ||||
\(313\) | 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 | 0.953870 | − | 0.300220i | \(-0.0970600\pi\) |
0.216937 | + | 0.976186i | \(0.430393\pi\) | |||||||
\(318\) | − | 21.6727i | − | 1.21535i | ||||||
\(319\) | − | 12.0200i | − | 0.672991i | ||||||
\(320\) | −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 | ||||
\(325\) | −15.3972 | − | 2.99497i | −0.854082 | − | 0.166131i | ||||
\(326\) | 9.90220 | + | 17.1511i | 0.548432 | + | 0.949912i | ||||
\(327\) | 41.9612i | 2.32046i | ||||||||
\(328\) | −1.34217 | − | 2.32471i | −0.0741091 | − | 0.128361i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 16.8812i | 0.929279i | ||||||||
\(331\) | 0.536696 | − | 0.309862i | 0.0294995 | − | 0.0170315i | −0.485178 | − | 0.874416i | \(-0.661245\pi\) |
0.514677 | + | 0.857384i | \(0.327912\pi\) | |||||||
\(332\) | 0.571530i | 0.0313668i | ||||||||
\(333\) | −5.70194 | + | 3.29201i | −0.312464 | + | 0.180401i | ||||
\(334\) | 3.11762 | + | 5.39987i | 0.170588 | + | 0.295468i | ||||
\(335\) | 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 | \(0.549804\pi\) | |||||||
\(338\) | 17.7539 | − | 2.49048i | 0.965684 | − | 0.135464i | ||||
\(339\) | 28.1082 | + | 48.6848i | 1.52663 | + | 2.64420i | ||||
\(340\) | −0.0383927 | − | 0.0221660i | −0.00208214 | − | 0.00120212i | ||||
\(341\) | −18.3235 | −0.992272 | ||||||||
\(342\) | −21.3647 | + | 37.0048i | −1.15527 | + | 2.00099i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.1439 | + | 6.43396i | 0.600841 | + | 0.346896i | ||||
\(345\) | 3.22740 | − | 1.86334i | 0.173757 | − | 0.100319i | ||||
\(346\) | −23.3102 | + | 13.4581i | −1.25316 | + | 0.723514i | ||||
\(347\) | −1.86486 | −0.100111 | −0.0500554 | − | 0.998746i | \(-0.515940\pi\) | ||||
−0.0500554 | + | 0.998746i | \(0.515940\pi\) | |||||||
\(348\) | −0.645182 | −0.0345854 | ||||||||
\(349\) | 19.3273 | − | 11.1586i | 1.03457 | − | 0.597307i | 0.116277 | − | 0.993217i | \(-0.462904\pi\) |
0.918290 | + | 0.395909i | \(0.129571\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.6867 | + | 18.0408i | −0.837295 | + | 0.962947i | ||||
\(352\) | −1.46295 | + | 2.53391i | −0.0779756 | + | 0.135058i | ||||
\(353\) | −2.01956 | − | 1.16600i | −0.107491 | − | 0.0620597i | 0.445291 | − | 0.895386i | \(-0.353100\pi\) |
−0.552781 | + | 0.833326i | \(0.686434\pi\) | |||||||
\(354\) | 21.8414 | − | 37.8304i | 1.16086 | − | 2.01066i | ||||
\(355\) | −3.75354 | − | 6.50133i | −0.199217 | − | 0.345055i | ||||
\(356\) | 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 | 0.423379 | − | 0.905953i | \(-0.360844\pi\) |
−0.572889 | + | 0.819633i | \(0.694177\pi\) | |||||||
\(360\) | 12.3629 | 0.651585 | ||||||||
\(361\) | 7.58017 | − | 13.1292i | 0.398956 | − | 0.691013i | ||||
\(362\) | − | 22.8264i | − | 1.19973i | ||||||
\(363\) | 48.3741 | 2.53898 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.03092 | −0.210988 | ||||||||
\(366\) | 29.0139i | 1.51658i | ||||||||
\(367\) | 2.07645 | − | 3.59652i | 0.108390 | − | 0.187737i | −0.806728 | − | 0.590923i | \(-0.798764\pi\) |
0.915118 | + | 0.403186i | \(0.132097\pi\) | |||||||
\(368\) | −6.08880 | −0.317401 | ||||||||
\(369\) | 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 | ||||||||
\(373\) | 5.55446 | + | 9.62061i | 0.287599 | + | 0.498136i | 0.973236 | − | 0.229807i | \(-0.0738096\pi\) |
−0.685637 | + | 0.727944i | \(0.740476\pi\) | |||||||
\(374\) | 2.03591 | − | 3.52630i | 0.105275 | − | 0.182341i | ||||
\(375\) | −18.8037 | − | 10.8563i | −0.971021 | − | 0.560619i | ||||
\(376\) | −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 | −0.599648 | − | 0.800264i | \(-0.704693\pi\) |
0.393225 | + | 0.919442i | \(0.371359\pi\) | |||||||
\(380\) | −0.462607 | −0.0237312 | ||||||||
\(381\) | −5.52416 | −0.283012 | ||||||||
\(382\) | −5.07586 | + | 2.93055i | −0.259703 | + | 0.149940i | ||||
\(383\) | 3.17773 | − | 1.83466i | 0.162374 | − | 0.0937469i | −0.416611 | − | 0.909085i | \(-0.636782\pi\) |
0.578985 | + | 0.815338i | \(0.303449\pi\) | |||||||
\(384\) | −25.9740 | − | 14.9961i | −1.32548 | − | 0.765266i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.99661 | − | 13.8505i | 0.407017 | − | 0.704973i | ||||
\(387\) | −23.5756 | −1.19842 | ||||||||
\(388\) | −0.905640 | − | 0.522872i | −0.0459769 | − | 0.0265448i | ||||
\(389\) | 8.44156 | + | 14.6212i | 0.428004 | + | 0.741324i | 0.996696 | − | 0.0812262i | \(-0.0258836\pi\) |
−0.568692 | + | 0.822551i | \(0.692550\pi\) | |||||||
\(390\) | 11.3337 | + | 2.20455i | 0.573902 | + | 0.111632i | ||||
\(391\) | −0.898894 | −0.0454590 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.4468 | − | 38.8790i | −1.13229 | − | 1.96119i | ||||
\(394\) | −9.94390 | − | 17.2233i | −0.500966 | − | 0.867699i | ||||
\(395\) | −7.93506 | + | 4.58131i | −0.399256 | + | 0.230511i | ||||
\(396\) | − | 2.74454i | − | 0.137918i | ||||||
\(397\) | 14.4700 | − | 8.35428i | 0.726230 | − | 0.419289i | −0.0908114 | − | 0.995868i | \(-0.528946\pi\) |
0.817041 | + | 0.576579i | \(0.195613\pi\) | |||||||
\(398\) | 9.73508i | 0.487976i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.25267 | + | 14.2940i | 0.412633 | + | 0.714702i | ||||
\(401\) | − | 25.3134i | − | 1.26409i | −0.774931 | − | 0.632046i | \(-0.782215\pi\) | ||
0.774931 | − | 0.632046i | \(-0.217785\pi\) | |||||||
\(402\) | 14.5932 | + | 25.2761i | 0.727842 | + | 1.26066i | ||||
\(403\) | −2.39291 | + | 12.3020i | −0.119199 | + | 0.612805i | ||||
\(404\) | −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 | ||||
\(409\) | − | 5.73343i | − | 0.283500i | −0.989903 | − | 0.141750i | \(-0.954727\pi\) | ||
0.989903 | − | 0.141750i | \(-0.0452729\pi\) | |||||||
\(410\) | − | 1.03109i | − | 0.0509220i | ||||||
\(411\) | 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 | ||||
\(416\) | 1.51016 | + | 1.31310i | 0.0740416 | + | 0.0643801i | ||||
\(417\) | −14.2977 | − | 24.7643i | −0.700161 | − | 1.21272i | ||||
\(418\) | − | 42.4897i | − | 2.07824i | ||||||
\(419\) | −17.1729 | − | 29.7443i | −0.838950 | − | 1.45310i | −0.890773 | − | 0.454448i | \(-0.849836\pi\) |
0.0518229 | − | 0.998656i | \(-0.483497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.94167i | − | 0.143368i | −0.997427 | − | 0.0716842i | \(-0.977163\pi\) | ||
0.997427 | − | 0.0716842i | \(-0.0228374\pi\) | |||||||
\(422\) | −31.5565 | + | 18.2191i | −1.53614 | + | 0.886894i | ||||
\(423\) | − | 20.3793i | − | 0.990873i | ||||||
\(424\) | 13.6684 | − | 7.89148i | 0.663798 | − | 0.383244i | ||||
\(425\) | 1.21835 | + | 2.11024i | 0.0590985 | + | 0.102362i | ||||
\(426\) | −18.5050 | − | 32.0516i | −0.896571 | − | 1.55291i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.950178 | −0.0459286 | ||||||||
\(429\) | 10.4562 | − | 53.7554i | 0.504829 | − | 2.59533i | ||||
\(430\) | 2.47137 | + | 4.28053i | 0.119180 | + | 0.206426i | ||||
\(431\) | 34.3773 | + | 19.8478i | 1.65590 | + | 0.956033i | 0.974578 | + | 0.224048i | \(0.0719273\pi\) |
0.681321 | + | 0.731985i | \(0.261406\pi\) | |||||||
\(432\) | 25.1561 | 1.21032 | ||||||||
\(433\) | 4.91827 | − | 8.51869i | 0.236357 | − | 0.409382i | −0.723309 | − | 0.690524i | \(-0.757380\pi\) |
0.959666 | + | 0.281142i | \(0.0907133\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.58538 | − | 2.64737i | −0.219852 | − | 0.126932i | ||||
\(436\) | −1.23865 | + | 0.715135i | −0.0593206 | + | 0.0342488i | ||||
\(437\) | −8.12331 | + | 4.69000i | −0.388591 | + | 0.224353i | ||||
\(438\) | −19.8725 | −0.949544 | ||||||||
\(439\) | 28.5465 | 1.36245 | 0.681226 | − | 0.732073i | \(-0.261447\pi\) | ||||
0.681226 | + | 0.732073i | \(0.261447\pi\) | |||||||
\(440\) | −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 | \(0.191942\pi\) | |||||||
\(444\) | −0.304337 | − | 0.175709i | −0.0144432 | − | 0.00833880i | ||||
\(445\) | −2.01868 | + | 3.49646i | −0.0956947 | + | 0.165748i | ||||
\(446\) | −15.8595 | − | 27.4695i | −0.750969 | − | 1.30072i | ||||
\(447\) | − | 22.8170i | − | 1.07921i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7487 | + | 9.09253i | 0.743228 | + | 0.429103i | 0.823242 | − | 0.567691i | \(-0.192163\pi\) |
−0.0800136 | + | 0.996794i | \(0.525496\pi\) | |||||||
\(450\) | −27.5443 | − | 15.9027i | −1.29845 | − | 0.749660i | ||||
\(451\) | −4.89045 | −0.230282 | ||||||||
\(452\) | −0.958084 | + | 1.65945i | −0.0450645 | + | 0.0780539i | ||||
\(453\) | − | 4.32516i | − | 0.203214i | ||||||
\(454\) | −0.625219 | −0.0293430 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −48.7265 | −2.28183 | ||||||||
\(457\) | − | 8.72932i | − | 0.408341i | −0.978935 | − | 0.204170i | \(-0.934550\pi\) | ||
0.978935 | − | 0.204170i | \(-0.0654496\pi\) | |||||||
\(458\) | 11.9519 | − | 20.7013i | 0.558476 | − | 0.967309i | ||||
\(459\) | 3.71381 | 0.173346 | ||||||||
\(460\) | 0.110008 | + | 0.0635130i | 0.00512914 | + | 0.00296131i | ||||
\(461\) | 1.96695 | + | 1.13562i | 0.0916099 | + | 0.0528910i | 0.545105 | − | 0.838368i | \(-0.316490\pi\) |
−0.453495 | + | 0.891259i | \(0.649823\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.48326i | − | 0.254829i | −0.991850 | − | 0.127414i | \(-0.959332\pi\) | ||
0.991850 | − | 0.127414i | \(-0.0406678\pi\) | |||||||
\(464\) | 4.32538 | + | 7.49178i | 0.200801 | + | 0.347797i | ||||
\(465\) | −4.03570 | + | 6.99003i | −0.187151 | + | 0.324155i | ||||
\(466\) | 9.33356 | + | 5.38873i | 0.432369 | + | 0.249628i | ||||
\(467\) | −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 | ||||
\(471\) | 11.1126 | 0.512040 | ||||||||
\(472\) | 31.8115 | 1.46424 | ||||||||
\(473\) | 20.3025 | − | 11.7217i | 0.933510 | − | 0.538962i | ||||
\(474\) | −39.1200 | + | 22.5859i | −1.79684 | + | 1.03741i | ||||
\(475\) | 22.0204 | + | 12.7135i | 1.01037 | + | 0.583335i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.4582 | + | 25.0423i | −0.661994 | + | 1.14661i | ||||
\(478\) | 18.6606 | 0.853516 | ||||||||
\(479\) | 28.6961 | + | 16.5677i | 1.31116 | + | 0.756997i | 0.982288 | − | 0.187378i | \(-0.0599991\pi\) |
0.328869 | + | 0.944375i | \(0.393332\pi\) | |||||||
\(480\) | 0.644422 | + | 1.11617i | 0.0294137 | + | 0.0509461i | ||||
\(481\) | −3.37917 | − | 2.93823i | −0.154077 | − | 0.133972i | ||||
\(482\) | −31.1104 | −1.41704 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.824428 | + | 1.42795i | 0.0374740 | + | 0.0649069i | ||||
\(485\) | −4.29100 | − | 7.43222i | −0.194844 | − | 0.337480i | ||||
\(486\) | 12.7451 | − | 7.35838i | 0.578129 | − | 0.333783i | ||||
\(487\) | − | 15.9563i | − | 0.723048i | −0.932363 | − | 0.361524i | \(-0.882257\pi\) | ||
0.932363 | − | 0.361524i | \(-0.117743\pi\) | |||||||
\(488\) | −18.2983 | + | 10.5645i | −0.828326 | + | 0.478234i | ||||
\(489\) | − | 41.3765i | − | 1.87111i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.8464 | − | 27.4468i | −0.715138 | − | 1.23866i | −0.962906 | − | 0.269836i | \(-0.913031\pi\) |
0.247769 | − | 0.968819i | \(-0.420303\pi\) | |||||||
\(492\) | 0.262498i | 0.0118343i | ||||||||
\(493\) | 0.638559 | + | 1.10602i | 0.0287593 | + | 0.0498125i | ||||
\(494\) | −28.5266 | − | 5.54882i | −1.28347 | − | 0.249653i | ||||
\(495\) | 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 | 0.889620 | − | 0.456701i | \(-0.150969\pi\) |
0.0492955 | + | 0.998784i | \(0.484302\pi\) | |||||||
\(500\) | − | 0.740089i | − | 0.0330978i | ||||||
\(501\) | − | 13.0270i | − | 0.582004i | ||||||
\(502\) | 8.04043 | + | 4.64215i | 0.358862 | + | 0.207189i | ||||
\(503\) | 0.427249 | − | 0.740017i | 0.0190501 | − | 0.0329957i | −0.856343 | − | 0.516407i | \(-0.827269\pi\) |
0.875393 | + | 0.483411i | \(0.160602\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.73294 | + | 1.57786i | −0.121614 | + | 0.0702139i | ||||
\(506\) | −5.83356 | + | 10.1040i | −0.259333 | + | 0.449179i | ||||
\(507\) | −34.7246 | − | 14.0401i | −1.54218 | − | 0.623542i | ||||
\(508\) | −0.0941471 | − | 0.163068i | −0.00417710 | − | 0.00723495i | ||||
\(509\) | − | 1.30000i | − | 0.0576215i | −0.999585 | − | 0.0288108i | \(-0.990828\pi\) | ||
0.999585 | − | 0.0288108i | \(-0.00917202\pi\) | |||||||
\(510\) | −0.896808 | − | 1.55332i | −0.0397113 | − | 0.0687820i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 24.0616i | − | 1.06338i | ||||||
\(513\) | 33.5618 | − | 19.3769i | 1.48179 | − | 0.855511i | ||||
\(514\) | 22.8070i | 1.00597i | ||||||||
\(515\) | −5.90051 | + | 3.40666i | −0.260007 | + | 0.150115i | ||||
\(516\) | −0.629167 | − | 1.08975i | −0.0276976 | − | 0.0479736i | ||||
\(517\) | 10.1324 | + | 17.5499i | 0.445624 | + | 0.771844i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 56.2351 | 2.46845 | ||||||||
\(520\) | 2.73645 | + | 7.95057i | 0.120001 | + | 0.348655i | ||||
\(521\) | −12.5228 | − | 21.6901i | −0.548632 | − | 0.950259i | −0.998369 | − | 0.0570974i | \(-0.981815\pi\) |
0.449736 | − | 0.893161i | \(-0.351518\pi\) | |||||||
\(522\) | −14.4365 | − | 8.33490i | −0.631867 | − | 0.364809i | ||||
\(523\) | −12.8239 | −0.560752 | −0.280376 | − | 0.959890i | \(-0.590459\pi\) | ||||
−0.280376 | + | 0.959890i | \(0.590459\pi\) | |||||||
\(524\) | 0.765112 | − | 1.32521i | 0.0334241 | − | 0.0578922i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.9701 | + | 6.91095i | 0.521922 | + | 0.301332i | ||||
\(527\) | 1.68603 | − | 0.973429i | 0.0734446 | − | 0.0424032i | ||||
\(528\) | −49.9040 | + | 28.8121i | −2.17179 | + | 1.25389i | ||||
\(529\) | −20.4244 | −0.888016 | ||||||||
\(530\) | 6.06244 | 0.263335 | ||||||||
\(531\) | −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 | ||||
\(535\) | −6.75303 | − | 3.89886i | −0.291959 | − | 0.168563i | ||||
\(536\) | −10.6273 | + | 18.4071i | −0.459031 | + | 0.795066i | ||||
\(537\) | −29.9928 | − | 51.9490i | −1.29428 | − | 2.24176i | ||||
\(538\) | 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 | −0.142014 | − | 0.989865i | \(-0.545358\pi\) |
−0.928255 | + | 0.371944i | \(0.878691\pi\) | |||||||
\(542\) | 7.19340 | 0.308983 | ||||||||
\(543\) | −23.8451 | + | 41.3009i | −1.02329 | + | 1.77239i | ||||
\(544\) | − | 0.310876i | − | 0.0133287i | ||||||
\(545\) | −11.7376 | −0.502785 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.88085 | −0.379718 | −0.189859 | − | 0.981811i | \(-0.560803\pi\) | ||||
−0.189859 | + | 0.981811i | \(0.560803\pi\) | |||||||
\(548\) | 0.771031i | 0.0329368i | ||||||||
\(549\) | 19.3556 | − | 33.5248i | 0.826075 | − | 1.43080i | ||||
\(550\) | 31.6269 | 1.34857 | ||||||||
\(551\) | 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 | ||||||||
\(555\) | −1.44198 | − | 2.49757i | −0.0612084 | − | 0.106016i | ||||
\(556\) | 0.487345 | − | 0.844106i | 0.0206680 | − | 0.0357981i | ||||
\(557\) | 33.5389 | + | 19.3637i | 1.42109 | + | 0.820465i | 0.996392 | − | 0.0848711i | \(-0.0270478\pi\) |
0.424695 | + | 0.905336i | \(0.360381\pi\) | |||||||
\(558\) | −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 | ||||
\(562\) | 2.95508 | 0.124653 | ||||||||
\(563\) | 6.90882 | 0.291172 | 0.145586 | − | 0.989346i | \(-0.453493\pi\) | ||||
0.145586 | + | 0.989346i | \(0.453493\pi\) | |||||||
\(564\) | 0.942002 | − | 0.543865i | 0.0396655 | − | 0.0229009i | ||||
\(565\) | −13.6184 | + | 7.86260i | −0.572932 | + | 0.330782i | ||||
\(566\) | 18.8105 | + | 10.8602i | 0.790663 | + | 0.456489i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.4761 | − | 23.3413i | 0.565444 | − | 0.979379i | ||||
\(569\) | 2.83745 | 0.118952 | 0.0594759 | − | 0.998230i | \(-0.481057\pi\) | ||||
0.0594759 | + | 0.998230i | \(0.481057\pi\) | |||||||
\(570\) | −16.2089 | − | 9.35823i | −0.678917 | − | 0.391973i | ||||
\(571\) | −23.3362 | − | 40.4195i | −0.976589 | − | 1.69150i | −0.674588 | − | 0.738195i | \(-0.735679\pi\) |
−0.302001 | − | 0.953307i | \(-0.597655\pi\) | |||||||
\(572\) | 1.76500 | − | 0.607485i | 0.0737985 | − | 0.0254002i | ||||
\(573\) | 12.2453 | 0.511557 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.49096 | − | 6.04653i | −0.145583 | − | 0.252158i | ||||
\(576\) | 22.1418 | + | 38.3507i | 0.922576 | + | 1.59795i | ||||
\(577\) | 9.88033 | − | 5.70441i | 0.411323 | − | 0.237478i | −0.280035 | − | 0.959990i | \(-0.590346\pi\) |
0.691358 | + | 0.722512i | \(0.257013\pi\) | |||||||
\(578\) | − | 23.0113i | − | 0.957144i | ||||||
\(579\) | −28.9373 | + | 16.7070i | −1.20259 | + | 0.694318i | ||||
\(580\) | − | 0.180474i | − | 0.00749379i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −21.1547 | − | 36.6410i | −0.876890 | − | 1.51882i | ||||
\(583\) | − | 28.7541i | − | 1.19087i | ||||||
\(584\) | −7.23597 | − | 12.5331i | −0.299426 | − | 0.518622i | ||||
\(585\) | −11.6251 | − | 10.1081i | −0.480637 | − | 0.417920i | ||||
\(586\) | −15.9617 | + | 27.6465i | −0.659371 | + | 1.14206i | ||||
\(587\) | 40.2191 | − | 23.2205i | 1.66002 | − | 0.958413i | 0.687318 | − | 0.726356i | \(-0.258788\pi\) |
0.972702 | − | 0.232057i | \(-0.0745456\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.1578 | − | 17.5938i | 0.418544 | − | 0.724939i | ||||
\(590\) | 10.5821 | + | 6.10961i | 0.435660 | + | 0.251529i | ||||
\(591\) | 41.5508i | 1.70917i | ||||||||
\(592\) | 4.71191i | 0.193658i | ||||||||
\(593\) | −17.5462 | − | 10.1303i | −0.720535 | − | 0.416001i | 0.0944146 | − | 0.995533i | \(-0.469902\pi\) |
−0.814950 | + | 0.579532i | \(0.803235\pi\) | |||||||
\(594\) | 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 | ||||
\(598\) | 6.02179 | + | 5.23603i | 0.246249 | + | 0.214117i | ||||
\(599\) | 19.4938 | + | 33.7642i | 0.796494 | + | 1.37957i | 0.921886 | + | 0.387462i | \(0.126648\pi\) |
−0.125391 | + | 0.992107i | \(0.540019\pi\) | |||||||
\(600\) | − | 36.2692i | − | 1.48068i | ||||||
\(601\) | 9.56951 | + | 16.5749i | 0.390348 | + | 0.676103i | 0.992495 | − | 0.122282i | \(-0.0390212\pi\) |
−0.602147 | + | 0.798385i | \(0.705688\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 38.9412i | − | 1.58581i | ||||||
\(604\) | 0.127674 | − | 0.0737127i | 0.00519499 | − | 0.00299933i | ||||
\(605\) | 13.5315i | 0.550134i | ||||||||
\(606\) | −13.4734 | + | 7.77888i | −0.547320 | + | 0.315995i | ||||
\(607\) | 21.6668 | + | 37.5280i | 0.879428 | + | 1.52321i | 0.851970 | + | 0.523590i | \(0.175408\pi\) |
0.0274572 | + | 0.999623i | \(0.491259\pi\) | |||||||
\(608\) | −1.62200 | − | 2.80939i | −0.0657808 | − | 0.113936i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.11595 | −0.328605 | ||||||||
\(611\) | 13.1058 | − | 4.51081i | 0.530205 | − | 0.182488i | ||||
\(612\) | 0.145803 | + | 0.252538i | 0.00589373 | + | 0.0102082i | ||||
\(613\) | 8.92834 | + | 5.15478i | 0.360612 | + | 0.208200i | 0.669349 | − | 0.742948i | \(-0.266573\pi\) |
−0.308737 | + | 0.951147i | \(0.599906\pi\) | |||||||
\(614\) | 5.84154 | 0.235745 | ||||||||
\(615\) | −1.07711 | + | 1.86561i | −0.0434332 | + | 0.0752285i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.58684 | − | 5.53497i | −0.385952 | − | 0.222829i | 0.294453 | − | 0.955666i | \(-0.404863\pi\) |
−0.680405 | + | 0.732837i | \(0.738196\pi\) | |||||||
\(618\) | −29.0896 | + | 16.7949i | −1.17015 | + | 0.675589i | ||||
\(619\) | −29.2384 | + | 16.8808i | −1.17519 | + | 0.678498i | −0.954897 | − | 0.296936i | \(-0.904035\pi\) |
−0.220295 | + | 0.975433i | \(0.570702\pi\) | |||||||
\(620\) | −0.275118 | −0.0110490 | ||||||||
\(621\) | −10.6413 | −0.427020 | ||||||||
\(622\) | 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 | ||||
\(626\) | 3.22098 | + | 1.85964i | 0.128736 | + | 0.0743260i | ||||
\(627\) | −44.3860 | + | 76.8787i | −1.77260 | + | 3.07024i | ||||
\(628\) | 0.189389 | + | 0.328031i | 0.00755745 | + | 0.0130899i | ||||
\(629\) | 0.695623i | 0.0277363i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4264 | + | 19.2987i | 1.33068 | + | 0.768271i | 0.985405 | − | 0.170229i | \(-0.0544507\pi\) |
0.345280 | + | 0.938500i | \(0.387784\pi\) | |||||||
\(632\) | −28.4887 | − | 16.4480i | −1.13322 | − | 0.654265i | ||||
\(633\) | 76.1290 | 3.02586 | ||||||||
\(634\) | −16.5972 | + | 28.7473i | −0.659161 | + | 1.14170i | ||||
\(635\) | − | 1.54525i | − | 0.0613215i | ||||||
\(636\) | −1.54339 | −0.0611995 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.5763 | 0.656260 | ||||||||
\(639\) | 49.3798i | 1.95343i | ||||||||
\(640\) | 4.19480 | − | 7.26560i | 0.165814 | − | 0.287198i | ||||
\(641\) | −19.5228 | −0.771105 | −0.385553 | − | 0.922686i | \(-0.625989\pi\) | ||||
−0.385553 | + | 0.922686i | \(0.625989\pi\) | |||||||
\(642\) | −33.2926 | − | 19.2215i | −1.31395 | − | 0.758611i | ||||
\(643\) | −10.8009 | − | 6.23589i | −0.425945 | − | 0.245920i | 0.271673 | − | 0.962390i | \(-0.412423\pi\) |
−0.697618 | + | 0.716470i | \(0.745757\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 10.3266i | − | 0.406611i | ||||||
\(646\) | 2.25725 | + | 3.90967i | 0.0888103 | + | 0.153824i | ||||
\(647\) | −17.9695 | + | 31.1241i | −0.706455 | + | 1.22362i | 0.259709 | + | 0.965687i | \(0.416373\pi\) |
−0.966164 | + | 0.257929i | \(0.916960\pi\) | |||||||
\(648\) | −8.01911 | − | 4.62984i | −0.315021 | − | 0.181877i | ||||
\(649\) | 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 | ||||
\(653\) | 4.85888 | 0.190143 | 0.0950713 | − | 0.995470i | \(-0.469692\pi\) | ||||
0.0950713 | + | 0.995470i | \(0.469692\pi\) | |||||||
\(654\) | −57.8668 | −2.26277 | ||||||||
\(655\) | 10.8755 | − | 6.27897i | 0.424941 | − | 0.245340i | ||||
\(656\) | 3.04810 | − | 1.75982i | 0.119008 | − | 0.0687095i | ||||
\(657\) | 22.9621 | + | 13.2572i | 0.895838 | + | 0.517212i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.8103 | − | 20.4560i | 0.460063 | − | 0.796853i | −0.538900 | − | 0.842370i | \(-0.681160\pi\) |
0.998964 | + | 0.0455166i | \(0.0144934\pi\) | |||||||
\(660\) | 1.20217 | 0.0467944 | ||||||||
\(661\) | −14.1970 | − | 8.19662i | −0.552198 | − | 0.318812i | 0.197810 | − | 0.980240i | \(-0.436617\pi\) |
−0.750008 | + | 0.661429i | \(0.769950\pi\) | |||||||
\(662\) | 0.427316 | + | 0.740134i | 0.0166081 | + | 0.0287661i | ||||
\(663\) | 1.89362 | + | 5.50176i | 0.0735419 | + | 0.213671i | ||||
\(664\) | −16.8393 | −0.653492 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.53987 | − | 7.86328i | −0.175916 | − | 0.304696i | ||||
\(667\) | −1.82968 | − | 3.16910i | −0.0708456 | − | 0.122708i | ||||
\(668\) | 0.384544 | − | 0.222016i | 0.0148784 | − | 0.00859007i | ||||
\(669\) | 66.2692i | 2.56212i | ||||||||
\(670\) | −7.07040 | + | 4.08210i | −0.273154 | + | 0.157705i | ||||
\(671\) | 38.4939i | 1.48604i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.12678 | − | 12.3439i | −0.274717 | − | 0.475824i | 0.695347 | − | 0.718675i | \(-0.255251\pi\) |
−0.970064 | + | 0.242851i | \(0.921918\pi\) | |||||||
\(674\) | − | 7.88982i | − | 0.303904i | ||||||
\(675\) | 14.4230 | + | 24.9814i | 0.555143 | + | 0.961536i | ||||
\(676\) | −0.177356 | − | 1.26432i | −0.00682138 | − | 0.0486276i | ||||
\(677\) | −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 | ||||
\(682\) | − | 25.2691i | − | 0.967604i | ||||||
\(683\) | 2.22201i | 0.0850230i | 0.999096 | + | 0.0425115i | \(0.0135359\pi\) | ||||
−0.999096 | + | 0.0425115i | \(0.986464\pi\) | |||||||
\(684\) | 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 | ||||
\(689\) | −19.3048 | − | 3.75506i | −0.735455 | − | 0.143056i | ||||
\(690\) | 2.56965 | + | 4.45076i | 0.0978249 | + | 0.169438i | ||||
\(691\) | 2.64015i | 0.100436i | 0.998738 | + | 0.0502179i | \(0.0159916\pi\) | ||||
−0.998738 | + | 0.0502179i | \(0.984008\pi\) | |||||||
\(692\) | 0.958402 | + | 1.66000i | 0.0364330 | + | 0.0631038i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 2.57174i | − | 0.0976220i | ||||||
\(695\) | 6.92724 | − | 3.99944i | 0.262765 | − | 0.151708i | ||||
\(696\) | − | 19.0094i | − | 0.720549i | ||||||
\(697\) | 0.449993 | − | 0.259804i | 0.0170447 | − | 0.00984077i | ||||
\(698\) | 15.3884 | + | 26.6534i | 0.582458 | + | 1.00885i | ||||
\(699\) | −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 | \(0.553754\pi\) | |||||||
\(702\) | −24.8793 | − | 21.6328i | −0.939007 | − | 0.816479i | ||||
\(703\) | 3.62943 | + | 6.28635i | 0.136886 | + | 0.237094i | ||||
\(704\) | −38.1355 | − | 22.0175i | −1.43729 | − | 0.829818i | ||||
\(705\) | 8.92656 | 0.336194 | ||||||||
\(706\) | 1.60797 | − | 2.78509i | 0.0605168 | − | 0.104818i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.69403 | − | 1.55540i | −0.101248 | − | 0.0584556i | ||||
\(709\) | −35.1558 | + | 20.2972i | −1.32030 | + | 0.762278i | −0.983777 | − | 0.179396i | \(-0.942586\pi\) |
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(710\) | 8.96569 | − | 5.17634i | 0.336476 | − | 0.194265i | ||||
\(711\) | 60.2695 | 2.26028 | ||||||||
\(712\) | −14.4951 | −0.543226 | ||||||||
\(713\) | −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 | ||||
\(717\) | −33.7636 | − | 19.4934i | −1.26092 | − | 0.727995i | ||||
\(718\) | 2.25548 | − | 3.90661i | 0.0841738 | − | 0.145793i | ||||
\(719\) | −7.25674 | − | 12.5690i | −0.270631 | − | 0.468746i | 0.698393 | − | 0.715715i | \(-0.253899\pi\) |
−0.969024 | + | 0.246968i | \(0.920566\pi\) | |||||||
\(720\) | 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 | ||||
\(724\) | −1.62555 | −0.0604129 | ||||||||
\(725\) | −4.95984 | + | 8.59070i | −0.184204 | + | 0.319051i | ||||
\(726\) | 66.7105i | 2.47586i | ||||||||
\(727\) | −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 | ||||||||
\(730\) | − | 5.55885i | − | 0.205742i | ||||||
\(731\) | −1.24542 | + | 2.15713i | −0.0460635 | + | 0.0797842i | ||||
\(732\) | 2.06618 | 0.0763683 | ||||||||
\(733\) | 11.4873 | + | 6.63218i | 0.424292 | + | 0.244965i | 0.696912 | − | 0.717157i | \(-0.254557\pi\) |
−0.272620 | + | 0.962122i | \(0.587890\pi\) | |||||||
\(734\) | 4.95980 | + | 2.86354i | 0.183069 | + | 0.105695i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.890761i | 0.0328339i | ||||||||
\(737\) | 19.3613 | + | 33.5348i | 0.713184 | + | 1.23527i | ||||
\(738\) | −3.39113 | + | 5.87361i | −0.124829 | + | 0.216211i | ||||
\(739\) | −6.28279 | − | 3.62737i | −0.231116 | − | 0.133435i | 0.379971 | − | 0.924999i | \(-0.375934\pi\) |
−0.611087 | + | 0.791564i | \(0.709267\pi\) | |||||||
\(740\) | 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 | −0.999435 | − | 0.0336128i | \(-0.989299\pi\) |
−0.470608 | + | 0.882342i | \(0.655965\pi\) | |||||||
\(744\) | −28.9782 | −1.06239 | ||||||||
\(745\) | 6.38250 | 0.233837 | ||||||||
\(746\) | −13.2673 | + | 7.65991i | −0.485752 | + | 0.280449i | ||||
\(747\) | 26.7184 | − | 15.4259i | 0.977574 | − | 0.564403i | ||||
\(748\) | −0.251121 | − | 0.144985i | −0.00918188 | − | 0.00530116i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14.9715 | − | 25.9314i | 0.546681 | − | 0.946880i | ||||
\(751\) | 36.0260 | 1.31461 | 0.657305 | − | 0.753625i | \(-0.271697\pi\) | ||||
0.657305 | + | 0.753625i | \(0.271697\pi\) | |||||||
\(752\) | −12.6306 | − | 7.29229i | −0.460591 | − | 0.265922i | ||||
\(753\) | −9.69865 | − | 16.7985i | −0.353438 | − | 0.612173i | ||||
\(754\) | 2.16473 | − | 11.1289i | 0.0788349 | − | 0.405291i | ||||
\(755\) | 1.20986 | 0.0440313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.28132 | + | 9.14751i | 0.191953 | + | 0.332472i | 0.945897 | − | 0.324466i | \(-0.105185\pi\) |
−0.753945 | + | 0.656938i | \(0.771851\pi\) | |||||||
\(758\) | −3.19961 | − | 5.54189i | −0.116215 | − | 0.201291i | ||||
\(759\) | 21.1099 | − | 12.1878i | 0.766242 | − | 0.442390i | ||||
\(760\) | − | 13.6301i | − | 0.494415i | ||||||
\(761\) | −6.76541 | + | 3.90601i | −0.245246 | + | 0.141593i | −0.617585 | − | 0.786504i | \(-0.711889\pi\) |
0.372340 | + | 0.928097i | \(0.378556\pi\) | |||||||
\(762\) | − | 7.61813i | − | 0.275976i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.208695 | + | 0.361470i | 0.00755031 | + | 0.0130775i | ||||
\(765\) | 2.39309i | 0.0865223i | ||||||||
\(766\) | 2.53010 | + | 4.38226i | 0.0914163 | + | 0.158338i | ||||
\(767\) | −29.9128 | − | 26.0096i | −1.08009 | − | 0.939152i | ||||
\(768\) | −3.38714 | + | 5.86671i | −0.122223 | + | 0.211696i | ||||
\(769\) | −21.9030 | + | 12.6457i | −0.789844 | + | 0.456017i | −0.839908 | − | 0.542729i | \(-0.817391\pi\) |
0.0500637 | + | 0.998746i | \(0.484058\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.8249 | − | 41.2659i | 0.858032 | − | 1.48615i | ||||
\(772\) | −0.986345 | − | 0.569467i | −0.0354993 | − | 0.0204956i | ||||
\(773\) | 46.6004i | 1.67610i | 0.545592 | + | 0.838051i | \(0.316305\pi\) | ||||
−0.545592 | + | 0.838051i | \(0.683695\pi\) | |||||||
\(774\) | − | 32.5121i | − | 1.16862i | ||||||
\(775\) | 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 | ||||
\(780\) | 0.156994 | − | 0.807110i | 0.00562129 | − | 0.0288992i | ||||
\(781\) | −24.5513 | − | 42.5241i | −0.878515 | − | 1.52163i | ||||
\(782\) | − | 1.23962i | − | 0.0443289i | ||||||
\(783\) | 7.55940 | + | 13.0933i | 0.270151 | + | 0.467915i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.10848i | 0.110946i | ||||||||
\(786\) | 53.6163 | − | 30.9554i | 1.91243 | − | 1.10414i | ||||
\(787\) | − | 39.7332i | − | 1.41633i | −0.706045 | − | 0.708167i | \(-0.749522\pi\) | ||
0.706045 | − | 0.708167i | \(-0.250478\pi\) | |||||||
\(788\) | −1.22653 | + | 0.708140i | −0.0436935 | + | 0.0252265i | ||||
\(789\) | −14.4388 | − | 25.0087i | −0.514034 | − | 0.890333i | ||||
\(790\) | −6.31788 | − | 10.9429i | −0.224780 | − | 0.389330i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 80.8641 | 2.87338 | ||||||||
\(793\) | 25.8439 | + | 5.02700i | 0.917744 | + | 0.178514i | ||||
\(794\) | 11.5210 | + | 19.9550i | 0.408865 | + | 0.708175i | ||||
\(795\) | −10.9691 | − | 6.33300i | −0.389033 | − | 0.224608i | ||||
\(796\) | 0.693270 | 0.0245723 | ||||||||
\(797\) | 1.39299 | − | 2.41273i | 0.0493422 | − | 0.0854632i | −0.840299 | − | 0.542123i | \(-0.817621\pi\) |
0.889642 | + | 0.456659i | \(0.150954\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.86467 | − | 1.07656i | −0.0659671 | − | 0.0380861i | ||||
\(800\) | 2.09115 | − | 1.20732i | 0.0739332 | − | 0.0426853i | ||||
\(801\) | 22.9989 | − | 13.2784i | 0.812625 | − | 0.469169i | ||||
\(802\) | 34.9086 | 1.23267 | ||||||||
\(803\) | −26.3656 | −0.930421 | ||||||||
\(804\) | 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 | ||||
\(808\) | −9.81188 | − | 5.66489i | −0.345181 | − | 0.199290i | ||||
\(809\) | 20.7293 | − | 35.9042i | 0.728803 | − | 1.26232i | −0.228586 | − | 0.973524i | \(-0.573410\pi\) |
0.957389 | − | 0.288801i | \(-0.0932565\pi\) | |||||||
\(810\) | −1.77838 | − | 3.08024i | −0.0624859 | − | 0.108229i | ||||
\(811\) | − | 27.8622i | − | 0.978375i | −0.872179 | − | 0.489188i | \(-0.837293\pi\) | ||
0.872179 | − | 0.489188i | \(-0.162707\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.0154 | − | 7.51443i | −0.456469 | − | 0.263543i | ||||
\(814\) | 7.81915 | + | 4.51439i | 0.274061 | + | 0.158229i | ||||
\(815\) | 11.5741 | 0.405423 | ||||||||
\(816\) | 3.06127 | − | 5.30227i | 0.107166 | − | 0.185617i | ||||
\(817\) | 25.9920i | 0.909344i | ||||||||
\(818\) | 7.90671 | 0.276452 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0734276 | −0.00256420 | ||||||||
\(821\) | 22.4202i | 0.782469i | 0.920291 | + | 0.391235i | \(0.127952\pi\) | ||||
−0.920291 | + | 0.391235i | \(0.872048\pi\) | |||||||
\(822\) | −15.5974 | + | 27.0156i | −0.544023 | + | 0.942276i | ||||
\(823\) | 2.36166 | 0.0823221 | 0.0411611 | − | 0.999153i | \(-0.486894\pi\) | ||||
0.0411611 | + | 0.999153i | \(0.486894\pi\) | |||||||
\(824\) | −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 | \(0.271443\pi\) | ||||
−0.657904 | + | 0.753102i | \(0.728557\pi\) | |||||||
\(828\) | −0.417773 | − | 0.723604i | −0.0145186 | − | 0.0251470i | ||||
\(829\) | 27.4640 | − | 47.5690i | 0.953864 | − | 1.65214i | 0.216917 | − | 0.976190i | \(-0.430400\pi\) |
0.736947 | − | 0.675951i | \(-0.236267\pi\) | |||||||
\(830\) | −5.60162 | − | 3.23410i | −0.194435 | − | 0.112257i | ||||
\(831\) | 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 | ||||
\(835\) | 3.64400 | 0.126106 | ||||||||
\(836\) | −3.02584 | −0.104651 | ||||||||
\(837\) | 19.9596 | − | 11.5237i | 0.689903 | − | 0.398316i | ||||
\(838\) | 41.0190 | − | 23.6824i | 1.41698 | − | 0.818093i | ||||
\(839\) | 12.7661 | + | 7.37052i | 0.440735 | + | 0.254459i | 0.703910 | − | 0.710290i | \(-0.251436\pi\) |
−0.263174 | + | 0.964748i | \(0.584769\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.9004 | − | 20.6122i | 0.410360 | − | 0.710765i | ||||
\(842\) | 4.05673 | 0.139804 | ||||||||
\(843\) | −5.34678 | − | 3.08697i | −0.184153 | − | 0.106321i | ||||
\(844\) | 1.29745 | + | 2.24725i | 0.0446600 | + | 0.0773535i | ||||
\(845\) | 3.92738 | − | 9.71340i | 0.135106 | − | 0.334151i | ||||
\(846\) | 28.1041 | 0.966239 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.3471 | + | 17.9217i | 0.355321 | + | 0.615434i | ||||
\(849\) | −22.6898 | − | 39.2999i | −0.778713 | − | 1.34877i | ||||
\(850\) | −2.91013 | + | 1.68017i | −0.0998168 | + | 0.0576292i | ||||
\(851\) | − | 1.99319i | − | 0.0683256i | ||||||
\(852\) | −2.28251 | + | 1.31781i | −0.0781975 | + | 0.0451474i | ||||
\(853\) | − | 24.1038i | − | 0.825297i | −0.910890 | − | 0.412649i | \(-0.864604\pi\) | ||
0.910890 | − | 0.412649i | \(-0.135396\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.4860 | + | 21.6264i | 0.427012 | + | 0.739607i | ||||
\(856\) | − | 27.9957i | − | 0.956873i | ||||||
\(857\) | 9.29249 | + | 16.0951i | 0.317425 | + | 0.549797i | 0.979950 | − | 0.199243i | \(-0.0638483\pi\) |
−0.662525 | + | 0.749040i | \(0.730515\pi\) | |||||||
\(858\) | 74.1316 | + | 14.4196i | 2.53081 | + | 0.492278i | ||||
\(859\) | 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 | 0.199357 | − | 0.979927i | \(-0.436115\pi\) |
−0.748963 | + | 0.662612i | \(0.769448\pi\) | |||||||
\(864\) | − | 3.68021i | − | 0.125203i | ||||||
\(865\) | 15.7304i | 0.534851i | ||||||||
\(866\) | 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 | ||||
\(871\) | 25.0430 | − | 8.61938i | 0.848549 | − | 0.292056i | ||||
\(872\) | −21.0705 | − | 36.4951i | −0.713536 | − | 1.23588i | ||||
\(873\) | 56.4502i | 1.91055i | ||||||||
\(874\) | −6.46776 | − | 11.2025i | −0.218775 | − | 0.378930i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.41519i | 0.0478148i | ||||||||
\(877\) | −32.6941 | + | 18.8759i | −1.10400 | + | 0.637395i | −0.937269 | − | 0.348608i | \(-0.886655\pi\) |
−0.166731 | + | 0.986002i | \(0.553321\pi\) | |||||||
\(878\) | 39.3673i | 1.32858i | ||||||||
\(879\) | 57.7606 | − | 33.3481i | 1.94822 | − | 1.12480i | ||||
\(880\) | −8.05950 | − | 13.9595i | −0.271686 | − | 0.470574i | ||||
\(881\) | −14.9149 | − | 25.8334i | −0.502497 | − | 0.870350i | −0.999996 | − | 0.00288515i | \(-0.999082\pi\) |
0.497499 | − | 0.867464i | \(-0.334252\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.3979 | −1.09028 | −0.545138 | − | 0.838346i | \(-0.683523\pi\) | ||||
−0.545138 | + | 0.838346i | \(0.683523\pi\) | |||||||
\(884\) | −0.130134 | + | 0.149663i | −0.00437687 | + | 0.00503371i | ||||
\(885\) | −12.7646 | − | 22.1089i | −0.429076 | − | 0.743181i | ||||
\(886\) | −3.98777 | − | 2.30234i | −0.133972 | − | 0.0773487i | ||||
\(887\) | 25.9198 | 0.870302 | 0.435151 | − | 0.900358i | \(-0.356695\pi\) | ||||
0.435151 | + | 0.900358i | \(0.356695\pi\) | |||||||
\(888\) | 5.17703 | − | 8.96688i | 0.173730 | − | 0.300909i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.82181 | − | 2.78387i | −0.161627 | − | 0.0933156i | ||||
\(891\) | −14.6096 | + | 8.43483i | −0.489439 | + | 0.282577i | ||||
\(892\) | −1.95620 | + | 1.12941i | −0.0654984 | + | 0.0378155i | ||||
\(893\) | −22.4680 | −0.751863 | ||||||||
\(894\) | 31.4658 | 1.05238 | ||||||||
\(895\) | 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 | ||||
\(899\) | 6.86376 | + | 3.96280i | 0.228919 | + | 0.132167i | ||||
\(900\) | −1.13249 | + | 1.96152i | −0.0377495 | + | 0.0653841i | ||||
\(901\) | 1.52755 | + | 2.64579i | 0.0508901 | + | 0.0881442i | ||||
\(902\) | − | 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 | ||||
\(906\) | 5.96463 | 0.198162 | ||||||||
\(907\) | 7.77113 | − | 13.4600i | 0.258036 | − | 0.446931i | −0.707680 | − | 0.706533i | \(-0.750258\pi\) |
0.965716 | + | 0.259602i | \(0.0835914\pi\) | |||||||
\(908\) | 0.0445240i | 0.00147758i | ||||||||
\(909\) | 20.7576 | 0.688485 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.6358 | 0.783090 | 0.391545 | − | 0.920159i | \(-0.371941\pi\) | ||||
0.391545 | + | 0.920159i | \(0.371941\pi\) | |||||||
\(912\) | − | 63.8889i | − | 2.11557i | ||||||
\(913\) | −15.3393 | + | 26.5684i | −0.507656 | + | 0.879287i | ||||
\(914\) | 12.0382 | 0.398189 | ||||||||
\(915\) | 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 | ||||||||
\(919\) | −22.2409 | − | 38.5223i | −0.733659 | − | 1.27073i | −0.955309 | − | 0.295608i | \(-0.904478\pi\) |
0.221651 | − | 0.975126i | \(-0.428856\pi\) | |||||||
\(920\) | −1.87132 | + | 3.24123i | −0.0616957 | + | 0.106860i | ||||
\(921\) | −10.5694 | − | 6.10224i | −0.348273 | − | 0.201076i | ||||
\(922\) | −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 | ||||
\(926\) | 7.56171 | 0.248493 | ||||||||
\(927\) | 44.8163 | 1.47196 | ||||||||
\(928\) | 1.09601 | − | 0.632782i | 0.0359783 | − | 0.0207721i | ||||
\(929\) | 2.54846 | − | 1.47135i | 0.0836121 | − | 0.0482735i | −0.457611 | − | 0.889152i | \(-0.651295\pi\) |
0.541223 | + | 0.840879i | \(0.317961\pi\) | |||||||
\(930\) | −9.63964 | − | 5.56545i | −0.316096 | − | 0.182498i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.383751 | − | 0.664676i | 0.0125702 | − | 0.0217722i | ||||
\(933\) | −78.5131 | −2.57040 | ||||||||
\(934\) | −22.5506 | − | 13.0196i | −0.737878 | − | 0.426014i | ||||
\(935\) | −1.18983 | − | 2.06085i | −0.0389116 | − | 0.0673968i | ||||
\(936\) | 10.5602 | − | 54.2903i | 0.345172 | − | 1.77453i | ||||
\(937\) | 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 | ||||
\(940\) | 0.152133 | + | 0.263503i | 0.00496205 | + | 0.00859451i | ||||
\(941\) | 19.1125 | − | 11.0346i | 0.623050 | − | 0.359718i | −0.155006 | − | 0.987914i | \(-0.549540\pi\) |
0.778056 | + | 0.628196i | \(0.216206\pi\) | |||||||
\(942\) | 15.3248i | 0.499311i | ||||||||
\(943\) | −1.28938 | + | 0.744423i | −0.0419879 | + | 0.0242417i | ||||
\(944\) | 41.7105i | 1.35756i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.1648 | + | 27.9983i | 0.525563 | + | 0.910302i | ||||
\(947\) | 51.1717i | 1.66286i | 0.555631 | + | 0.831429i | \(0.312477\pi\) | ||||
−0.555631 | + | 0.831429i | \(0.687523\pi\) | |||||||
\(948\) | 1.60842 | + | 2.78587i | 0.0522392 | + | 0.0904809i | ||||
\(949\) | −3.44314 | + | 17.7012i | −0.111769 | + | 0.574607i | ||||
\(950\) | −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 | −0.208758 | − | 0.977967i | \(-0.566942\pi\) |
0.951324 | − | 0.308194i | \(-0.0997245\pi\) | |||||||
\(954\) | −34.5347 | − | 19.9386i | −1.11810 | − | 0.645536i | ||||
\(955\) | 3.42534i | 0.110842i | ||||||||
\(956\) | − | 1.32889i | − | 0.0429793i | ||||||
\(957\) | −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 | ||||
\(962\) | 4.05198 | − | 4.66006i | 0.130641 | − | 0.150246i | ||||
\(963\) | 25.6458 | + | 44.4198i | 0.826424 | + | 1.43141i | ||||
\(964\) | 2.21548i | 0.0713559i | ||||||||
\(965\) | −4.67338 | − | 8.09453i | −0.150441 | − | 0.260572i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.2609i | 0.619387i | 0.950836 | + | 0.309694i | \(0.100227\pi\) | ||||
−0.950836 | + | 0.309694i | \(0.899773\pi\) | |||||||
\(968\) | −42.0726 | + | 24.2906i | −1.35226 | + | 0.780730i | ||||
\(969\) | − | 9.43196i | − | 0.302998i | ||||||
\(970\) | 10.2494 | − | 5.91752i | 0.329090 | − | 0.190000i | ||||
\(971\) | 23.6663 | + | 40.9912i | 0.759487 | + | 1.31547i | 0.943112 | + | 0.332474i | \(0.107883\pi\) |
−0.183625 | + | 0.982996i | \(0.558783\pi\) | |||||||
\(972\) | −0.524016 | − | 0.907622i | −0.0168078 | − | 0.0291120i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 22.0046 | 0.705072 | ||||||||
\(975\) | −29.6542 | + | 34.1044i | −0.949696 | + | 1.09222i | ||||
\(976\) | −13.8520 | − | 23.9923i | −0.443390 | − | 0.767975i | ||||
\(977\) | 41.4454 | + | 23.9285i | 1.32596 | + | 0.765541i | 0.984672 | − | 0.174418i | \(-0.0558045\pi\) |
0.341285 | + | 0.939960i | \(0.389138\pi\) | |||||||
\(978\) | 57.0605 | 1.82459 | ||||||||
\(979\) | −13.2039 | + | 22.8698i | −0.421998 | + | 0.730921i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 66.8635 | + | 38.6037i | 2.13479 | + | 1.23252i | ||||
\(982\) | 37.8506 | − | 21.8531i | 1.20786 | − | 0.697359i | ||||
\(983\) | −13.6560 | + | 7.88432i | −0.435560 | + | 0.251471i | −0.701712 | − | 0.712460i | \(-0.747581\pi\) |
0.266152 | + | 0.963931i | \(0.414248\pi\) | |||||||
\(984\) | −7.73414 | −0.246555 | ||||||||
\(985\) | −11.6228 | −0.370335 | ||||||||
\(986\) | −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 | ||||
\(990\) | 26.8995 | + | 15.5305i | 0.854924 | + | 0.493590i | ||||
\(991\) | 6.06892 | − | 10.5117i | 0.192786 | − | 0.333914i | −0.753387 | − | 0.657578i | \(-0.771581\pi\) |
0.946172 | + | 0.323663i | \(0.104914\pi\) | |||||||
\(992\) | −0.964622 | − | 1.67077i | −0.0306268 | − | 0.0530471i | ||||
\(993\) | − | 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 | ||||
\(997\) | −33.7876 | −1.07006 | −0.535032 | − | 0.844832i | \(-0.679701\pi\) | ||||
−0.535032 | + | 0.844832i | \(0.679701\pi\) | |||||||
\(998\) | −16.6993 | + | 28.9240i | −0.528607 | + | 0.915574i | ||||
\(999\) | 8.23493i | 0.260542i |
(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.k.i.569.5 | 12 | ||
7.2 | even | 3 | 637.2.q.i.491.5 | 12 | |||
7.3 | odd | 6 | 91.2.u.b.88.2 | yes | 12 | ||
7.4 | even | 3 | 637.2.u.g.361.2 | 12 | |||
7.5 | odd | 6 | 637.2.q.g.491.5 | 12 | |||
7.6 | odd | 2 | 91.2.k.b.23.5 | yes | 12 | ||
13.4 | even | 6 | 637.2.u.g.30.2 | 12 | |||
21.17 | even | 6 | 819.2.do.e.361.5 | 12 | |||
21.20 | even | 2 | 819.2.bm.f.478.2 | 12 | |||
91.2 | odd | 12 | 8281.2.a.co.1.10 | 12 | |||
91.4 | even | 6 | inner | 637.2.k.i.459.2 | 12 | ||
91.17 | odd | 6 | 91.2.k.b.4.2 | ✓ | 12 | ||
91.24 | even | 12 | 1183.2.e.j.508.10 | 24 | |||
91.30 | even | 6 | 637.2.q.i.589.5 | 12 | |||
91.37 | odd | 12 | 8281.2.a.co.1.3 | 12 | |||
91.41 | even | 12 | 1183.2.e.j.170.3 | 24 | |||
91.54 | even | 12 | 8281.2.a.cp.1.10 | 12 | |||
91.69 | odd | 6 | 91.2.u.b.30.2 | yes | 12 | ||
91.76 | even | 12 | 1183.2.e.j.170.10 | 24 | |||
91.80 | even | 12 | 1183.2.e.j.508.3 | 24 | |||
91.82 | odd | 6 | 637.2.q.g.589.5 | 12 | |||
91.89 | even | 12 | 8281.2.a.cp.1.3 | 12 | |||
273.17 | even | 6 | 819.2.bm.f.550.5 | 12 | |||
273.251 | even | 6 | 819.2.do.e.667.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.2 | ✓ | 12 | 91.17 | odd | 6 | ||
91.2.k.b.23.5 | yes | 12 | 7.6 | odd | 2 | ||
91.2.u.b.30.2 | yes | 12 | 91.69 | odd | 6 | ||
91.2.u.b.88.2 | yes | 12 | 7.3 | odd | 6 | ||
637.2.k.i.459.2 | 12 | 91.4 | even | 6 | inner | ||
637.2.k.i.569.5 | 12 | 1.1 | even | 1 | trivial | ||
637.2.q.g.491.5 | 12 | 7.5 | odd | 6 | |||
637.2.q.g.589.5 | 12 | 91.82 | odd | 6 | |||
637.2.q.i.491.5 | 12 | 7.2 | even | 3 | |||
637.2.q.i.589.5 | 12 | 91.30 | even | 6 | |||
637.2.u.g.30.2 | 12 | 13.4 | even | 6 | |||
637.2.u.g.361.2 | 12 | 7.4 | even | 3 | |||
819.2.bm.f.478.2 | 12 | 21.20 | even | 2 | |||
819.2.bm.f.550.5 | 12 | 273.17 | even | 6 | |||
819.2.do.e.361.5 | 12 | 21.17 | even | 6 | |||
819.2.do.e.667.5 | 12 | 273.251 | even | 6 | |||
1183.2.e.j.170.3 | 24 | 91.41 | even | 12 | |||
1183.2.e.j.170.10 | 24 | 91.76 | even | 12 | |||
1183.2.e.j.508.3 | 24 | 91.80 | even | 12 | |||
1183.2.e.j.508.10 | 24 | 91.24 | even | 12 | |||
8281.2.a.co.1.3 | 12 | 91.37 | odd | 12 | |||
8281.2.a.co.1.10 | 12 | 91.2 | odd | 12 | |||
8281.2.a.cp.1.3 | 12 | 91.89 | even | 12 | |||
8281.2.a.cp.1.10 | 12 | 91.54 | even | 12 |