Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(43,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.7 | ||
Root | \(-0.635486 - 1.26339i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.307 |
Dual form | 400.2.j.d.43.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.14628 | − | 0.828280i | 0.810541 | − | 0.585682i | ||||
\(3\) | 0.692712i | 0.399937i | 0.979802 | + | 0.199969i | \(0.0640841\pi\) | ||||
−0.979802 | + | 0.199969i | \(0.935916\pi\) | |||||||
\(4\) | 0.627905 | − | 1.89888i | 0.313952 | − | 0.949439i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.573759 | + | 0.794040i | 0.234236 | + | 0.324166i | ||||
\(7\) | 0.343872 | + | 0.343872i | 0.129971 | + | 0.129971i | 0.769100 | − | 0.639129i | \(-0.220705\pi\) |
−0.639129 | + | 0.769100i | \(0.720705\pi\) | |||||||
\(8\) | −0.853049 | − | 2.69672i | −0.301598 | − | 0.953435i | ||||
\(9\) | 2.52015 | 0.840050 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.843672 | + | 0.843672i | 0.254377 | + | 0.254377i | 0.822762 | − | 0.568386i | \(-0.192432\pi\) |
−0.568386 | + | 0.822762i | \(0.692432\pi\) | |||||||
\(12\) | 1.31538 | + | 0.434957i | 0.379716 | + | 0.125561i | ||||
\(13\) | 3.68390 | 1.02173 | 0.510865 | − | 0.859661i | \(-0.329325\pi\) | ||||
0.510865 | + | 0.859661i | \(0.329325\pi\) | |||||||
\(14\) | 0.678995 | + | 0.109350i | 0.181469 | + | 0.0292251i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.21147 | − | 2.38463i | −0.802868 | − | 0.596157i | ||||
\(17\) | −0.412137 | − | 0.412137i | −0.0999579 | − | 0.0999579i | 0.655359 | − | 0.755317i | \(-0.272517\pi\) |
−0.755317 | + | 0.655359i | \(0.772517\pi\) | |||||||
\(18\) | 2.88879 | − | 2.08739i | 0.680895 | − | 0.492003i | ||||
\(19\) | −5.37721 | − | 5.37721i | −1.23362 | − | 1.23362i | −0.962565 | − | 0.271052i | \(-0.912629\pi\) |
−0.271052 | − | 0.962565i | \(-0.587371\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.238204 | + | 0.238204i | −0.0519804 | + | 0.0519804i | ||||
\(22\) | 1.66588 | + | 0.268286i | 0.355167 | + | 0.0571987i | ||||
\(23\) | 3.08788 | − | 3.08788i | 0.643868 | − | 0.643868i | −0.307636 | − | 0.951504i | \(-0.599538\pi\) |
0.951504 | + | 0.307636i | \(0.0995380\pi\) | |||||||
\(24\) | 1.86805 | − | 0.590917i | 0.381314 | − | 0.120621i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.22278 | − | 3.05130i | 0.828154 | − | 0.598410i | ||||
\(27\) | 3.82387i | 0.735905i | ||||||||
\(28\) | 0.868890 | − | 0.437052i | 0.164205 | − | 0.0825951i | ||||
\(29\) | −4.22969 | + | 4.22969i | −0.785434 | + | 0.785434i | −0.980742 | − | 0.195308i | \(-0.937429\pi\) |
0.195308 | + | 0.980742i | \(0.437429\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.75966i | 1.57328i | 0.617411 | + | 0.786641i | \(0.288182\pi\) | ||||
−0.617411 | + | 0.786641i | \(0.711818\pi\) | |||||||
\(32\) | −5.65638 | − | 0.0734474i | −0.999916 | − | 0.0129838i | ||||
\(33\) | −0.584422 | + | 0.584422i | −0.101735 | + | 0.101735i | ||||
\(34\) | −0.813788 | − | 0.131059i | −0.139564 | − | 0.0224764i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.58241 | − | 4.78546i | 0.263736 | − | 0.797576i | ||||
\(37\) | 5.41752 | 0.890634 | 0.445317 | − | 0.895373i | \(-0.353091\pi\) | ||||
0.445317 | + | 0.895373i | \(0.353091\pi\) | |||||||
\(38\) | −10.6176 | − | 1.70994i | −1.72240 | − | 0.277389i | ||||
\(39\) | 2.55188i | 0.408628i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.54777i | 0.397895i | 0.980010 | + | 0.198948i | \(0.0637524\pi\) | ||||
−0.980010 | + | 0.198948i | \(0.936248\pi\) | |||||||
\(42\) | −0.0757484 | + | 0.470348i | −0.0116882 | + | 0.0725763i | ||||
\(43\) | −4.30732 | −0.656861 | −0.328430 | − | 0.944528i | \(-0.606520\pi\) | ||||
−0.328430 | + | 0.944528i | \(0.606520\pi\) | |||||||
\(44\) | 2.13178 | − | 1.07228i | 0.321377 | − | 0.161653i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.981939 | − | 6.09720i | 0.144779 | − | 0.898983i | ||||
\(47\) | −4.56972 | + | 4.56972i | −0.666562 | + | 0.666562i | −0.956919 | − | 0.290356i | \(-0.906226\pi\) |
0.290356 | + | 0.956919i | \(0.406226\pi\) | |||||||
\(48\) | 1.65186 | − | 2.22462i | 0.238425 | − | 0.321097i | ||||
\(49\) | − | 6.76350i | − | 0.966215i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.285492 | − | 0.285492i | 0.0399769 | − | 0.0399769i | ||||
\(52\) | 2.31314 | − | 6.99528i | 0.320775 | − | 0.970071i | ||||
\(53\) | 6.07536i | 0.834515i | 0.908788 | + | 0.417257i | \(0.137009\pi\) | ||||
−0.908788 | + | 0.417257i | \(0.862991\pi\) | |||||||
\(54\) | 3.16724 | + | 4.38322i | 0.431007 | + | 0.596481i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.633987 | − | 1.22067i | 0.0847201 | − | 0.163118i | ||||
\(57\) | 3.72486 | − | 3.72486i | 0.493369 | − | 0.493369i | ||||
\(58\) | −1.34503 | + | 8.35177i | −0.176611 | + | 1.09664i | ||||
\(59\) | −7.33694 | + | 7.33694i | −0.955189 | + | 0.955189i | −0.999038 | − | 0.0438495i | \(-0.986038\pi\) |
0.0438495 | + | 0.999038i | \(0.486038\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.81576 | − | 4.81576i | −0.616595 | − | 0.616595i | 0.328062 | − | 0.944656i | \(-0.393605\pi\) |
−0.944656 | + | 0.328062i | \(0.893605\pi\) | |||||||
\(62\) | 7.25545 | + | 10.0410i | 0.921444 | + | 1.27521i | ||||
\(63\) | 0.866609 | + | 0.866609i | 0.109183 | + | 0.109183i | ||||
\(64\) | −6.54461 | + | 4.60087i | −0.818077 | + | 0.575109i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.185845 | + | 1.15397i | −0.0228759 | + | 0.142044i | ||||
\(67\) | −14.3626 | −1.75467 | −0.877334 | − | 0.479880i | \(-0.840680\pi\) | ||||
−0.877334 | + | 0.479880i | \(0.840680\pi\) | |||||||
\(68\) | −1.04138 | + | 0.523815i | −0.126286 | + | 0.0635219i | ||||
\(69\) | 2.13901 | + | 2.13901i | 0.257507 | + | 0.257507i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.97605 | −0.353193 | −0.176596 | − | 0.984283i | \(-0.556509\pi\) | ||||
−0.176596 | + | 0.984283i | \(0.556509\pi\) | |||||||
\(72\) | −2.14981 | − | 6.79614i | −0.253358 | − | 0.800933i | ||||
\(73\) | 6.87152 | + | 6.87152i | 0.804250 | + | 0.804250i | 0.983757 | − | 0.179507i | \(-0.0574501\pi\) |
−0.179507 | + | 0.983757i | \(0.557450\pi\) | |||||||
\(74\) | 6.20998 | − | 4.48722i | 0.721895 | − | 0.521629i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.5870 | + | 6.83429i | −1.55854 | + | 0.783947i | ||||
\(77\) | 0.580231i | 0.0661234i | ||||||||
\(78\) | 2.11367 | + | 2.92517i | 0.239326 | + | 0.331210i | ||||
\(79\) | 10.1654 | 1.14369 | 0.571847 | − | 0.820360i | \(-0.306227\pi\) | ||||
0.571847 | + | 0.820360i | \(0.306227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.91161 | 0.545734 | ||||||||
\(82\) | 2.11027 | + | 2.92046i | 0.233040 | + | 0.322510i | ||||
\(83\) | − | 7.15276i | − | 0.785118i | −0.919727 | − | 0.392559i | \(-0.871590\pi\) | ||
0.919727 | − | 0.392559i | \(-0.128410\pi\) | |||||||
\(84\) | 0.302751 | + | 0.601890i | 0.0330329 | + | 0.0656716i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.93739 | + | 3.56767i | −0.532412 | + | 0.384712i | ||||
\(87\) | −2.92996 | − | 2.92996i | −0.314124 | − | 0.314124i | ||||
\(88\) | 1.55545 | − | 2.99484i | 0.165812 | − | 0.319251i | ||||
\(89\) | 1.10953 | 0.117610 | 0.0588050 | − | 0.998269i | \(-0.481271\pi\) | ||||
0.0588050 | + | 0.998269i | \(0.481271\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.26679 | + | 1.26679i | 0.132796 | + | 0.132796i | ||||
\(92\) | −3.92461 | − | 7.80240i | −0.409169 | − | 0.813457i | ||||
\(93\) | −6.06792 | −0.629214 | ||||||||
\(94\) | −1.45316 | + | 9.02318i | −0.149882 | + | 0.930670i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.0508779 | − | 3.91824i | 0.00519270 | − | 0.399904i | ||||
\(97\) | −7.15920 | − | 7.15920i | −0.726906 | − | 0.726906i | 0.243096 | − | 0.970002i | \(-0.421837\pi\) |
−0.970002 | + | 0.243096i | \(0.921837\pi\) | |||||||
\(98\) | −5.60207 | − | 7.75285i | −0.565895 | − | 0.783156i | ||||
\(99\) | 2.12618 | + | 2.12618i | 0.213689 | + | 0.213689i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.953394 | − | 0.953394i | 0.0948663 | − | 0.0948663i | −0.658081 | − | 0.752947i | \(-0.728632\pi\) |
0.752947 | + | 0.658081i | \(0.228632\pi\) | |||||||
\(102\) | 0.0907858 | − | 0.563721i | 0.00898914 | − | 0.0558167i | ||||
\(103\) | −9.59425 | + | 9.59425i | −0.945350 | + | 0.945350i | −0.998582 | − | 0.0532322i | \(-0.983048\pi\) |
0.0532322 | + | 0.998582i | \(0.483048\pi\) | |||||||
\(104\) | −3.14255 | − | 9.93446i | −0.308152 | − | 0.974154i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.03210 | + | 6.96405i | 0.488761 | + | 0.676408i | ||||
\(107\) | 5.28201i | 0.510631i | 0.966858 | + | 0.255316i | \(0.0821794\pi\) | ||||
−0.966858 | + | 0.255316i | \(0.917821\pi\) | |||||||
\(108\) | 7.26107 | + | 2.40103i | 0.698697 | + | 0.231039i | ||||
\(109\) | 1.53980 | − | 1.53980i | 0.147486 | − | 0.147486i | −0.629508 | − | 0.776994i | \(-0.716744\pi\) |
0.776994 | + | 0.629508i | \(0.216744\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.75278i | 0.356198i | ||||||||
\(112\) | −0.284329 | − | 1.92434i | −0.0268665 | − | 0.181833i | ||||
\(113\) | 2.99656 | − | 2.99656i | 0.281893 | − | 0.281893i | −0.551971 | − | 0.833863i | \(-0.686124\pi\) |
0.833863 | + | 0.551971i | \(0.186124\pi\) | |||||||
\(114\) | 1.18450 | − | 7.35494i | 0.110938 | − | 0.688854i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.37582 | + | 10.6875i | 0.499133 | + | 0.992310i | ||||
\(117\) | 9.28399 | 0.858305 | ||||||||
\(118\) | −2.33313 | + | 14.4872i | −0.214782 | + | 1.33366i | ||||
\(119\) | − | 0.283445i | − | 0.0259833i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 9.57643i | − | 0.870585i | ||||||
\(122\) | −9.50899 | − | 1.53140i | −0.860904 | − | 0.138646i | ||||
\(123\) | −1.76487 | −0.159133 | ||||||||
\(124\) | 16.6335 | + | 5.50023i | 1.49373 | + | 0.493935i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.71117 | + | 0.275580i | 0.152443 | + | 0.0245506i | ||||
\(127\) | 10.5522 | − | 10.5522i | 0.936360 | − | 0.936360i | −0.0617330 | − | 0.998093i | \(-0.519663\pi\) |
0.998093 | + | 0.0617330i | \(0.0196627\pi\) | |||||||
\(128\) | −3.69113 | + | 10.6947i | −0.326253 | + | 0.945282i | ||||
\(129\) | − | 2.98373i | − | 0.262703i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.850513 | + | 0.850513i | −0.0743096 | + | 0.0743096i | −0.743285 | − | 0.668975i | \(-0.766733\pi\) |
0.668975 | + | 0.743285i | \(0.266733\pi\) | |||||||
\(132\) | 0.742784 | + | 1.47671i | 0.0646511 | + | 0.128531i | ||||
\(133\) | − | 3.69814i | − | 0.320670i | ||||||
\(134\) | −16.4635 | + | 11.8962i | −1.42223 | + | 1.02768i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.759845 | + | 1.46299i | −0.0651562 | + | 0.125451i | ||||
\(137\) | 5.50145 | − | 5.50145i | 0.470021 | − | 0.470021i | −0.431901 | − | 0.901921i | \(-0.642157\pi\) |
0.901921 | + | 0.431901i | \(0.142157\pi\) | |||||||
\(138\) | 4.22360 | + | 0.680201i | 0.359537 | + | 0.0579025i | ||||
\(139\) | 3.03517 | − | 3.03517i | 0.257440 | − | 0.257440i | −0.566572 | − | 0.824012i | \(-0.691731\pi\) |
0.824012 | + | 0.566572i | \(0.191731\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.16550 | − | 3.16550i | −0.266583 | − | 0.266583i | ||||
\(142\) | −3.41138 | + | 2.46501i | −0.286277 | + | 0.206859i | ||||
\(143\) | 3.10801 | + | 3.10801i | 0.259905 | + | 0.259905i | ||||
\(144\) | −8.09339 | − | 6.00962i | −0.674449 | − | 0.500802i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.5682 | + | 2.18513i | 1.12291 | + | 0.180842i | ||||
\(147\) | 4.68516 | 0.386425 | ||||||||
\(148\) | 3.40168 | − | 10.2872i | 0.279617 | − | 0.845603i | ||||
\(149\) | 11.1571 | + | 11.1571i | 0.914023 | + | 0.914023i | 0.996586 | − | 0.0825625i | \(-0.0263104\pi\) |
−0.0825625 | + | 0.996586i | \(0.526310\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.18265 | 0.259000 | 0.129500 | − | 0.991579i | \(-0.458663\pi\) | ||||
0.129500 | + | 0.991579i | \(0.458663\pi\) | |||||||
\(152\) | −9.91381 | + | 19.0879i | −0.804116 | + | 1.54823i | ||||
\(153\) | −1.03865 | − | 1.03865i | −0.0839696 | − | 0.0839696i | ||||
\(154\) | 0.480593 | + | 0.665105i | 0.0387273 | + | 0.0535957i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.84571 | + | 1.60234i | 0.387968 | + | 0.128290i | ||||
\(157\) | 7.05454i | 0.563014i | 0.959559 | + | 0.281507i | \(0.0908342\pi\) | ||||
−0.959559 | + | 0.281507i | \(0.909166\pi\) | |||||||
\(158\) | 11.6523 | − | 8.41978i | 0.927011 | − | 0.669842i | ||||
\(159\) | −4.20847 | −0.333754 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.12367 | 0.167369 | ||||||||
\(162\) | 5.63007 | − | 4.06819i | 0.442340 | − | 0.319627i | ||||
\(163\) | − | 16.0208i | − | 1.25484i | −0.778680 | − | 0.627422i | \(-0.784110\pi\) | ||
0.778680 | − | 0.627422i | \(-0.215890\pi\) | |||||||
\(164\) | 4.83791 | + | 1.59976i | 0.377777 | + | 0.124920i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.92449 | − | 8.19905i | −0.459830 | − | 0.636370i | ||||
\(167\) | 16.6023 | + | 16.6023i | 1.28473 | + | 1.28473i | 0.937946 | + | 0.346780i | \(0.112725\pi\) |
0.346780 | + | 0.937946i | \(0.387275\pi\) | |||||||
\(168\) | 0.845571 | + | 0.439171i | 0.0652372 | + | 0.0338827i | ||||
\(169\) | 0.571141 | 0.0439339 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.5514 | − | 13.5514i | −1.03630 | − | 1.03630i | ||||
\(172\) | −2.70459 | + | 8.17908i | −0.206223 | + | 0.623649i | ||||
\(173\) | −14.9958 | −1.14011 | −0.570054 | − | 0.821607i | \(-0.693078\pi\) | ||||
−0.570054 | + | 0.821607i | \(0.693078\pi\) | |||||||
\(174\) | −5.78537 | − | 0.931719i | −0.438588 | − | 0.0706335i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.697585 | − | 4.72127i | −0.0525825 | − | 0.355879i | ||||
\(177\) | −5.08239 | − | 5.08239i | −0.382016 | − | 0.382016i | ||||
\(178\) | 1.27183 | − | 0.919002i | 0.0953277 | − | 0.0688821i | ||||
\(179\) | −9.91310 | − | 9.91310i | −0.740940 | − | 0.740940i | 0.231819 | − | 0.972759i | \(-0.425532\pi\) |
−0.972759 | + | 0.231819i | \(0.925532\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.04015 | − | 1.04015i | 0.0773139 | − | 0.0773139i | −0.667392 | − | 0.744706i | \(-0.732590\pi\) |
0.744706 | + | 0.667392i | \(0.232590\pi\) | |||||||
\(182\) | 2.50135 | + | 0.402837i | 0.185413 | + | 0.0298602i | ||||
\(183\) | 3.33593 | − | 3.33593i | 0.246599 | − | 0.246599i | ||||
\(184\) | −10.9613 | − | 5.69304i | −0.808075 | − | 0.419696i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.95552 | + | 5.02594i | −0.510004 | + | 0.368520i | ||||
\(187\) | − | 0.695417i | − | 0.0508539i | ||||||
\(188\) | 5.80799 | + | 11.5467i | 0.423591 | + | 0.842129i | ||||
\(189\) | −1.31492 | + | 1.31492i | −0.0956466 | + | 0.0956466i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.08419i | − | 0.223164i | −0.993755 | − | 0.111582i | \(-0.964408\pi\) | ||
0.993755 | − | 0.111582i | \(-0.0355918\pi\) | |||||||
\(192\) | −3.18708 | − | 4.53353i | −0.230008 | − | 0.327179i | ||||
\(193\) | 12.0915 | − | 12.0915i | 0.870368 | − | 0.870368i | −0.122144 | − | 0.992512i | \(-0.538977\pi\) |
0.992512 | + | 0.122144i | \(0.0389770\pi\) | |||||||
\(194\) | −14.1362 | − | 2.27661i | −1.01492 | − | 0.163451i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.8431 | − | 4.24683i | −0.917362 | − | 0.303345i | ||||
\(197\) | −13.0186 | −0.927540 | −0.463770 | − | 0.885956i | \(-0.653504\pi\) | ||||
−0.463770 | + | 0.885956i | \(0.653504\pi\) | |||||||
\(198\) | 4.19827 | + | 0.676120i | 0.298358 | + | 0.0480498i | ||||
\(199\) | − | 10.6279i | − | 0.753395i | −0.926336 | − | 0.376697i | \(-0.877060\pi\) | ||
0.926336 | − | 0.376697i | \(-0.122940\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 9.94913i | − | 0.701758i | ||||||
\(202\) | 0.303177 | − | 1.88253i | 0.0213315 | − | 0.132455i | ||||
\(203\) | −2.90894 | −0.204168 | ||||||||
\(204\) | −0.362853 | − | 0.721377i | −0.0254048 | − | 0.0505065i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.05095 | + | 18.9444i | −0.212570 | + | 1.31992i | ||||
\(207\) | 7.78192 | − | 7.78192i | 0.540881 | − | 0.540881i | ||||
\(208\) | −11.8308 | − | 8.78474i | −0.820315 | − | 0.609112i | ||||
\(209\) | − | 9.07320i | − | 0.627607i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.4801 | − | 11.4801i | 0.790321 | − | 0.790321i | −0.191225 | − | 0.981546i | \(-0.561246\pi\) |
0.981546 | + | 0.191225i | \(0.0612460\pi\) | |||||||
\(212\) | 11.5364 | + | 3.81475i | 0.792321 | + | 0.261998i | ||||
\(213\) | − | 2.06155i | − | 0.141255i | ||||||
\(214\) | 4.37499 | + | 6.05465i | 0.299068 | + | 0.413888i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 10.3119 | − | 3.26195i | 0.701638 | − | 0.221948i | ||||
\(217\) | −3.01220 | + | 3.01220i | −0.204482 | + | 0.204482i | ||||
\(218\) | 0.489652 | − | 3.04042i | 0.0331634 | − | 0.205923i | ||||
\(219\) | −4.75998 | + | 4.75998i | −0.321650 | + | 0.321650i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.51827 | − | 1.51827i | −0.102130 | − | 0.102130i | ||||
\(222\) | 3.10835 | + | 4.30173i | 0.208619 | + | 0.288713i | ||||
\(223\) | −2.17863 | − | 2.17863i | −0.145892 | − | 0.145892i | 0.630388 | − | 0.776280i | \(-0.282896\pi\) |
−0.776280 | + | 0.630388i | \(0.782896\pi\) | |||||||
\(224\) | −1.91981 | − | 1.97033i | −0.128273 | − | 0.131648i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.952898 | − | 5.91688i | 0.0633859 | − | 0.393585i | ||||
\(227\) | −9.32318 | −0.618801 | −0.309401 | − | 0.950932i | \(-0.600128\pi\) | ||||
−0.309401 | + | 0.950932i | \(0.600128\pi\) | |||||||
\(228\) | −4.73419 | − | 9.41190i | −0.313530 | − | 0.623318i | ||||
\(229\) | −2.72259 | − | 2.72259i | −0.179914 | − | 0.179914i | 0.611404 | − | 0.791318i | \(-0.290605\pi\) |
−0.791318 | + | 0.611404i | \(0.790605\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.401933 | −0.0264452 | ||||||||
\(232\) | 15.0144 | + | 7.79816i | 0.985746 | + | 0.511974i | ||||
\(233\) | −12.3897 | − | 12.3897i | −0.811679 | − | 0.811679i | 0.173206 | − | 0.984886i | \(-0.444587\pi\) |
−0.984886 | + | 0.173206i | \(0.944587\pi\) | |||||||
\(234\) | 10.6420 | − | 7.68974i | 0.695691 | − | 0.502694i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.32506 | + | 18.5389i | 0.607010 | + | 1.20678i | ||||
\(237\) | 7.04168i | 0.457406i | ||||||||
\(238\) | −0.234772 | − | 0.324906i | −0.0152180 | − | 0.0210606i | ||||
\(239\) | 25.2180 | 1.63122 | 0.815609 | − | 0.578604i | \(-0.196402\pi\) | ||||
0.815609 | + | 0.578604i | \(0.196402\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0218 | 0.774391 | 0.387195 | − | 0.921998i | \(-0.373444\pi\) | ||||
0.387195 | + | 0.921998i | \(0.373444\pi\) | |||||||
\(242\) | −7.93197 | − | 10.9773i | −0.509886 | − | 0.705645i | ||||
\(243\) | 14.8740i | 0.954164i | ||||||||
\(244\) | −12.1684 | + | 6.12070i | −0.779000 | + | 0.391838i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.02303 | + | 1.46181i | −0.128984 | + | 0.0932015i | ||||
\(247\) | −19.8091 | − | 19.8091i | −1.26042 | − | 1.26042i | ||||
\(248\) | 23.6224 | − | 7.47242i | 1.50002 | − | 0.474499i | ||||
\(249\) | 4.95480 | 0.313998 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.48911 | + | 7.48911i | 0.472709 | + | 0.472709i | 0.902790 | − | 0.430081i | \(-0.141515\pi\) |
−0.430081 | + | 0.902790i | \(0.641515\pi\) | |||||||
\(252\) | 2.18973 | − | 1.10144i | 0.137940 | − | 0.0693840i | ||||
\(253\) | 5.21032 | 0.327570 | ||||||||
\(254\) | 3.35559 | − | 20.8360i | 0.210548 | − | 1.30737i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.62710 | + | 15.3163i | 0.289194 | + | 0.957271i | ||||
\(257\) | 10.0809 | + | 10.0809i | 0.628832 | + | 0.628832i | 0.947774 | − | 0.318942i | \(-0.103328\pi\) |
−0.318942 | + | 0.947774i | \(0.603328\pi\) | |||||||
\(258\) | −2.47137 | − | 3.42019i | −0.153861 | − | 0.212932i | ||||
\(259\) | 1.86293 | + | 1.86293i | 0.115757 | + | 0.115757i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.6595 | + | 10.6595i | −0.659804 | + | 0.659804i | ||||
\(262\) | −0.270461 | + | 1.67939i | −0.0167091 | + | 0.103753i | ||||
\(263\) | 3.83599 | − | 3.83599i | 0.236537 | − | 0.236537i | −0.578877 | − | 0.815415i | \(-0.696509\pi\) |
0.815415 | + | 0.578877i | \(0.196509\pi\) | |||||||
\(264\) | 2.07456 | + | 1.07748i | 0.127681 | + | 0.0663144i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.06310 | − | 4.23910i | −0.187811 | − | 0.259916i | ||||
\(267\) | 0.768585i | 0.0470367i | ||||||||
\(268\) | −9.01833 | + | 27.2728i | −0.550882 | + | 1.66595i | ||||
\(269\) | −13.4250 | + | 13.4250i | −0.818539 | + | 0.818539i | −0.985896 | − | 0.167357i | \(-0.946477\pi\) |
0.167357 | + | 0.985896i | \(0.446477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.3519i | − | 0.750326i | −0.926959 | − | 0.375163i | \(-0.877587\pi\) | ||
0.926959 | − | 0.375163i | \(-0.122413\pi\) | |||||||
\(272\) | 0.340773 | + | 2.30636i | 0.0206624 | + | 0.139844i | ||||
\(273\) | −0.877522 | + | 0.877522i | −0.0531100 | + | 0.0531100i | ||||
\(274\) | 1.74945 | − | 10.8629i | 0.105688 | − | 0.656253i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.40482 | − | 2.71863i | 0.325332 | − | 0.163642i | ||||
\(277\) | 6.78804 | 0.407854 | 0.203927 | − | 0.978986i | \(-0.434630\pi\) | ||||
0.203927 | + | 0.978986i | \(0.434630\pi\) | |||||||
\(278\) | 0.965177 | − | 5.99312i | 0.0578875 | − | 0.359443i | ||||
\(279\) | 22.0757i | 1.32164i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.5509i | 1.28562i | 0.766026 | + | 0.642810i | \(0.222232\pi\) | ||||
−0.766026 | + | 0.642810i | \(0.777768\pi\) | |||||||
\(282\) | −6.25046 | − | 1.00662i | −0.372210 | − | 0.0599434i | ||||
\(283\) | 9.86809 | 0.586597 | 0.293299 | − | 0.956021i | \(-0.405247\pi\) | ||||
0.293299 | + | 0.956021i | \(0.405247\pi\) | |||||||
\(284\) | −1.86868 | + | 5.65116i | −0.110886 | + | 0.335335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.13694 | + | 0.988339i | 0.362885 | + | 0.0584417i | ||||
\(287\) | −0.876108 | + | 0.876108i | −0.0517150 | + | 0.0517150i | ||||
\(288\) | −14.2549 | − | 0.185099i | −0.839979 | − | 0.0109070i | ||||
\(289\) | − | 16.6603i | − | 0.980017i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.95926 | − | 4.95926i | 0.290717 | − | 0.290717i | ||||
\(292\) | 17.3628 | − | 8.73351i | 1.01608 | − | 0.511090i | ||||
\(293\) | 14.1972i | 0.829410i | 0.909956 | + | 0.414705i | \(0.136115\pi\) | ||||
−0.909956 | + | 0.414705i | \(0.863885\pi\) | |||||||
\(294\) | 5.37049 | − | 3.88062i | 0.313214 | − | 0.226323i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.62141 | − | 14.6095i | −0.268614 | − | 0.849162i | ||||
\(297\) | −3.22610 | + | 3.22610i | −0.187197 | + | 0.187197i | ||||
\(298\) | 22.0303 | + | 3.54792i | 1.27618 | + | 0.205526i | ||||
\(299\) | 11.3755 | − | 11.3755i | 0.657859 | − | 0.657859i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.48117 | − | 1.48117i | −0.0853731 | − | 0.0853731i | ||||
\(302\) | 3.64820 | − | 2.63612i | 0.209930 | − | 0.151692i | ||||
\(303\) | 0.660428 | + | 0.660428i | 0.0379406 | + | 0.0379406i | ||||
\(304\) | 4.44611 | + | 30.0914i | 0.255002 | + | 1.72586i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.05087 | − | 0.330287i | −0.117240 | − | 0.0188813i | ||||
\(307\) | 20.4161 | 1.16521 | 0.582604 | − | 0.812756i | \(-0.302034\pi\) | ||||
0.582604 | + | 0.812756i | \(0.302034\pi\) | |||||||
\(308\) | 1.10179 | + | 0.364329i | 0.0627801 | + | 0.0207596i | ||||
\(309\) | −6.64605 | − | 6.64605i | −0.378081 | − | 0.378081i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.81074 | −0.386202 | −0.193101 | − | 0.981179i | \(-0.561854\pi\) | ||||
−0.193101 | + | 0.981179i | \(0.561854\pi\) | |||||||
\(312\) | 6.88172 | − | 2.17688i | 0.389601 | − | 0.123242i | ||||
\(313\) | 1.20933 | + | 1.20933i | 0.0683555 | + | 0.0683555i | 0.740458 | − | 0.672103i | \(-0.234609\pi\) |
−0.672103 | + | 0.740458i | \(0.734609\pi\) | |||||||
\(314\) | 5.84314 | + | 8.08646i | 0.329747 | + | 0.456345i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.38289 | − | 19.3028i | 0.359065 | − | 1.08587i | ||||
\(317\) | 3.44178i | 0.193310i | 0.995318 | + | 0.0966548i | \(0.0308143\pi\) | ||||
−0.995318 | + | 0.0966548i | \(0.969186\pi\) | |||||||
\(318\) | −4.82408 | + | 3.48580i | −0.270521 | + | 0.195474i | ||||
\(319\) | −7.13694 | −0.399592 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.65891 | −0.204221 | ||||||||
\(322\) | 2.43432 | − | 1.75899i | 0.135659 | − | 0.0980249i | ||||
\(323\) | 4.43229i | 0.246619i | ||||||||
\(324\) | 3.08402 | − | 9.32654i | 0.171334 | − | 0.518141i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.2697 | − | 18.3643i | −0.734940 | − | 1.01710i | ||||
\(327\) | 1.06664 | + | 1.06664i | 0.0589852 | + | 0.0589852i | ||||
\(328\) | 6.87063 | − | 2.17338i | 0.379367 | − | 0.120005i | ||||
\(329\) | −3.14280 | −0.173268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.48462 | − | 1.48462i | −0.0816019 | − | 0.0816019i | 0.665128 | − | 0.746730i | \(-0.268377\pi\) |
−0.746730 | + | 0.665128i | \(0.768377\pi\) | |||||||
\(332\) | −13.5822 | − | 4.49125i | −0.745421 | − | 0.246489i | ||||
\(333\) | 13.6530 | 0.748177 | ||||||||
\(334\) | 32.7822 | + | 5.27950i | 1.79376 | + | 0.288881i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.33301 | − | 0.196958i | 0.0727219 | − | 0.0107449i | ||||
\(337\) | −6.21211 | − | 6.21211i | −0.338395 | − | 0.338395i | 0.517368 | − | 0.855763i | \(-0.326912\pi\) |
−0.855763 | + | 0.517368i | \(0.826912\pi\) | |||||||
\(338\) | 0.654686 | − | 0.473065i | 0.0356102 | − | 0.0257313i | ||||
\(339\) | 2.07575 | + | 2.07575i | 0.112739 | + | 0.112739i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.39028 | + | 7.39028i | −0.400206 | + | 0.400206i | ||||
\(342\) | −26.7580 | − | 4.30930i | −1.44691 | − | 0.233020i | ||||
\(343\) | 4.73288 | − | 4.73288i | 0.255552 | − | 0.255552i | ||||
\(344\) | 3.67436 | + | 11.6156i | 0.198108 | + | 0.626274i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.1893 | + | 12.4207i | −0.924104 | + | 0.667741i | ||||
\(347\) | − | 10.1502i | − | 0.544889i | −0.962171 | − | 0.272445i | \(-0.912168\pi\) | ||
0.962171 | − | 0.272445i | \(-0.0878321\pi\) | |||||||
\(348\) | −7.40336 | + | 3.72390i | −0.396862 | + | 0.199622i | ||||
\(349\) | −3.99595 | + | 3.99595i | −0.213898 | + | 0.213898i | −0.805921 | − | 0.592023i | \(-0.798329\pi\) |
0.592023 | + | 0.805921i | \(0.298329\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.0868i | 0.751897i | ||||||||
\(352\) | −4.71016 | − | 4.83409i | −0.251053 | − | 0.257658i | ||||
\(353\) | −22.6637 | + | 22.6637i | −1.20627 | + | 1.20627i | −0.234043 | + | 0.972226i | \(0.575196\pi\) |
−0.972226 | + | 0.234043i | \(0.924804\pi\) | |||||||
\(354\) | −10.0355 | − | 1.61619i | −0.533379 | − | 0.0858994i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.696680 | − | 2.10686i | 0.0369239 | − | 0.111664i | ||||
\(357\) | 0.196346 | 0.0103917 | ||||||||
\(358\) | −19.5740 | − | 3.15234i | −1.03452 | − | 0.166606i | ||||
\(359\) | 4.31874i | 0.227934i | 0.993485 | + | 0.113967i | \(0.0363559\pi\) | ||||
−0.993485 | + | 0.113967i | \(0.963644\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.8288i | 2.04362i | ||||||||
\(362\) | 0.330766 | − | 2.05384i | 0.0173847 | − | 0.107947i | ||||
\(363\) | 6.63371 | 0.348180 | ||||||||
\(364\) | 3.20091 | − | 1.61006i | 0.167773 | − | 0.0843899i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.06082 | − | 6.58699i | 0.0554499 | − | 0.344308i | ||||
\(367\) | 6.46940 | − | 6.46940i | 0.337700 | − | 0.337700i | −0.517801 | − | 0.855501i | \(-0.673249\pi\) |
0.855501 | + | 0.517801i | \(0.173249\pi\) | |||||||
\(368\) | −17.2801 | + | 2.55320i | −0.900787 | + | 0.133095i | ||||
\(369\) | 6.42077i | 0.334252i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.08915 | + | 2.08915i | −0.108463 | + | 0.108463i | ||||
\(372\) | −3.81008 | + | 11.5222i | −0.197543 | + | 0.597400i | ||||
\(373\) | − | 16.7831i | − | 0.868995i | −0.900673 | − | 0.434497i | \(-0.856926\pi\) | ||
0.900673 | − | 0.434497i | \(-0.143074\pi\) | |||||||
\(374\) | −0.576000 | − | 0.797141i | −0.0297842 | − | 0.0412192i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.2215 | + | 8.42507i | 0.836558 | + | 0.434490i | ||||
\(377\) | −15.5818 | + | 15.5818i | −0.802502 | + | 0.802502i | ||||
\(378\) | −0.418142 | + | 2.59639i | −0.0215069 | + | 0.133544i | ||||
\(379\) | −7.31046 | + | 7.31046i | −0.375513 | + | 0.375513i | −0.869480 | − | 0.493967i | \(-0.835546\pi\) |
0.493967 | + | 0.869480i | \(0.335546\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.30966 | + | 7.30966i | 0.374485 | + | 0.374485i | ||||
\(382\) | −2.55457 | − | 3.53533i | −0.130703 | − | 0.180883i | ||||
\(383\) | 5.31492 | + | 5.31492i | 0.271580 | + | 0.271580i | 0.829736 | − | 0.558156i | \(-0.188491\pi\) |
−0.558156 | + | 0.829736i | \(0.688491\pi\) | |||||||
\(384\) | −7.40831 | − | 2.55689i | −0.378054 | − | 0.130481i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.84508 | − | 23.8754i | 0.195710 | − | 1.21523i | ||||
\(387\) | −10.8551 | −0.551796 | ||||||||
\(388\) | −18.0897 | + | 9.09915i | −0.918367 | + | 0.461939i | ||||
\(389\) | −1.28845 | − | 1.28845i | −0.0653271 | − | 0.0653271i | 0.673688 | − | 0.739016i | \(-0.264709\pi\) |
−0.739016 | + | 0.673688i | \(0.764709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.54526 | −0.128719 | ||||||||
\(392\) | −18.2393 | + | 5.76960i | −0.921223 | + | 0.291409i | ||||
\(393\) | −0.589160 | − | 0.589160i | −0.0297192 | − | 0.0297192i | ||||
\(394\) | −14.9230 | + | 10.7831i | −0.751809 | + | 0.543244i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.37239 | − | 2.70232i | 0.269973 | − | 0.135797i | ||||
\(397\) | − | 9.53832i | − | 0.478715i | −0.970932 | − | 0.239357i | \(-0.923063\pi\) | ||
0.970932 | − | 0.239357i | \(-0.0769367\pi\) | |||||||
\(398\) | −8.80291 | − | 12.1826i | −0.441250 | − | 0.610657i | ||||
\(399\) | 2.56175 | 0.128248 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.6103 | −1.22898 | −0.614491 | − | 0.788924i | \(-0.710638\pi\) | ||||
−0.614491 | + | 0.788924i | \(0.710638\pi\) | |||||||
\(402\) | −8.24067 | − | 11.4045i | −0.411007 | − | 0.568803i | ||||
\(403\) | 32.2697i | 1.60747i | ||||||||
\(404\) | −1.21174 | − | 2.40902i | −0.0602862 | − | 0.119853i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.33446 | + | 2.40942i | −0.165486 | + | 0.119578i | ||||
\(407\) | 4.57061 | + | 4.57061i | 0.226557 | + | 0.226557i | ||||
\(408\) | −1.01343 | − | 0.526354i | −0.0501724 | − | 0.0260584i | ||||
\(409\) | −16.9457 | −0.837911 | −0.418955 | − | 0.908007i | \(-0.637604\pi\) | ||||
−0.418955 | + | 0.908007i | \(0.637604\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.81092 | + | 3.81092i | 0.187979 | + | 0.187979i | ||||
\(412\) | 12.1940 | + | 24.2426i | 0.600757 | + | 1.19435i | ||||
\(413\) | −5.04594 | −0.248294 | ||||||||
\(414\) | 2.47463 | − | 15.3659i | 0.121622 | − | 0.755190i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −20.8375 | − | 0.270573i | −1.02164 | − | 0.0132659i | ||||
\(417\) | 2.10250 | + | 2.10250i | 0.102960 | + | 0.102960i | ||||
\(418\) | −7.51515 | − | 10.4004i | −0.367578 | − | 0.508701i | ||||
\(419\) | −6.56956 | − | 6.56956i | −0.320944 | − | 0.320944i | 0.528185 | − | 0.849129i | \(-0.322873\pi\) |
−0.849129 | + | 0.528185i | \(0.822873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.8805 | − | 13.8805i | 0.676493 | − | 0.676493i | −0.282712 | − | 0.959205i | \(-0.591234\pi\) |
0.959205 | + | 0.282712i | \(0.0912341\pi\) | |||||||
\(422\) | 3.65064 | − | 22.6681i | 0.177710 | − | 1.10346i | ||||
\(423\) | −11.5164 | + | 11.5164i | −0.559946 | + | 0.559946i | ||||
\(424\) | 16.3836 | − | 5.18258i | 0.795656 | − | 0.251688i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.70754 | − | 2.36311i | −0.0827305 | − | 0.114493i | ||||
\(427\) | − | 3.31201i | − | 0.160279i | ||||||
\(428\) | 10.0299 | + | 3.31660i | 0.484813 | + | 0.160314i | ||||
\(429\) | −2.15295 | + | 2.15295i | −0.103946 | + | 0.103946i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12.3740i | − | 0.596035i | −0.954560 | − | 0.298017i | \(-0.903675\pi\) | ||
0.954560 | − | 0.298017i | \(-0.0963254\pi\) | |||||||
\(432\) | 9.11852 | − | 12.2803i | 0.438715 | − | 0.590834i | ||||
\(433\) | 0.145326 | − | 0.145326i | 0.00698392 | − | 0.00698392i | −0.703606 | − | 0.710590i | \(-0.748428\pi\) |
0.710590 | + | 0.703606i | \(0.248428\pi\) | |||||||
\(434\) | −0.957873 | + | 5.94777i | −0.0459794 | + | 0.285502i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.95704 | − | 3.89074i | −0.0937253 | − | 0.186332i | ||||
\(437\) | −33.2084 | −1.58857 | ||||||||
\(438\) | −1.51366 | + | 9.39886i | −0.0723256 | + | 0.449095i | ||||
\(439\) | − | 3.65842i | − | 0.174607i | −0.996182 | − | 0.0873035i | \(-0.972175\pi\) | ||
0.996182 | − | 0.0873035i | \(-0.0278250\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 17.0450i | − | 0.811669i | ||||||
\(442\) | −2.99792 | − | 0.482807i | −0.142596 | − | 0.0229648i | ||||
\(443\) | −3.94027 | −0.187208 | −0.0936039 | − | 0.995610i | \(-0.529839\pi\) | ||||
−0.0936039 | + | 0.995610i | \(0.529839\pi\) | |||||||
\(444\) | 7.12607 | + | 2.35639i | 0.338188 | + | 0.111829i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.30184 | − | 0.692800i | −0.203698 | − | 0.0328050i | ||||
\(447\) | −7.72864 | + | 7.72864i | −0.365552 | + | 0.365552i | ||||
\(448\) | −3.83262 | − | 0.668398i | −0.181074 | − | 0.0315788i | ||||
\(449\) | 38.0014i | 1.79340i | 0.442642 | + | 0.896698i | \(0.354041\pi\) | ||||
−0.442642 | + | 0.896698i | \(0.645959\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.14949 | + | 2.14949i | −0.101215 | + | 0.101215i | ||||
\(452\) | −3.80855 | − | 7.57165i | −0.179139 | − | 0.356140i | ||||
\(453\) | 2.20466i | 0.103584i | ||||||||
\(454\) | −10.6870 | + | 7.72221i | −0.501564 | + | 0.362421i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.2224 | − | 6.86742i | −0.619195 | − | 0.321596i | ||||
\(457\) | −18.1142 | + | 18.1142i | −0.847348 | + | 0.847348i | −0.989801 | − | 0.142454i | \(-0.954501\pi\) |
0.142454 | + | 0.989801i | \(0.454501\pi\) | |||||||
\(458\) | −5.37592 | − | 0.865778i | −0.251200 | − | 0.0404551i | ||||
\(459\) | 1.57596 | − | 1.57596i | 0.0735595 | − | 0.0735595i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.4144 | + | 12.4144i | 0.578197 | + | 0.578197i | 0.934406 | − | 0.356209i | \(-0.115931\pi\) |
−0.356209 | + | 0.934406i | \(0.615931\pi\) | |||||||
\(462\) | −0.460726 | + | 0.332913i | −0.0214349 | + | 0.0154885i | ||||
\(463\) | 8.56578 | + | 8.56578i | 0.398085 | + | 0.398085i | 0.877557 | − | 0.479472i | \(-0.159172\pi\) |
−0.479472 | + | 0.877557i | \(0.659172\pi\) | |||||||
\(464\) | 23.6698 | − | 3.49729i | 1.09884 | − | 0.162358i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.4643 | − | 3.93991i | −1.13329 | − | 0.182513i | ||||
\(467\) | 34.3465 | 1.58937 | 0.794684 | − | 0.607023i | \(-0.207636\pi\) | ||||
0.794684 | + | 0.607023i | \(0.207636\pi\) | |||||||
\(468\) | 5.82946 | − | 17.6292i | 0.269467 | − | 0.814908i | ||||
\(469\) | −4.93889 | − | 4.93889i | −0.228057 | − | 0.228057i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.88677 | −0.225170 | ||||||||
\(472\) | 26.0445 | + | 13.5269i | 1.19879 | + | 0.622627i | ||||
\(473\) | −3.63397 | − | 3.63397i | −0.167090 | − | 0.167090i | ||||
\(474\) | 5.83248 | + | 8.07172i | 0.267895 | + | 0.370746i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.538227 | − | 0.177976i | −0.0246696 | − | 0.00815753i | ||||
\(477\) | 15.3108i | 0.701034i | ||||||||
\(478\) | 28.9068 | − | 20.8876i | 1.32217 | − | 0.955375i | ||||
\(479\) | −23.4504 | −1.07148 | −0.535738 | − | 0.844384i | \(-0.679966\pi\) | ||||
−0.535738 | + | 0.844384i | \(0.679966\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.9576 | 0.909988 | ||||||||
\(482\) | 13.7803 | − | 9.95740i | 0.627675 | − | 0.453547i | ||||
\(483\) | 1.47109i | 0.0669370i | ||||||||
\(484\) | −18.1845 | − | 6.01309i | −0.826567 | − | 0.273322i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.3198 | + | 17.0497i | 0.558837 | + | 0.773389i | ||||
\(487\) | 5.31215 | + | 5.31215i | 0.240716 | + | 0.240716i | 0.817146 | − | 0.576430i | \(-0.195555\pi\) |
−0.576430 | + | 0.817146i | \(0.695555\pi\) | |||||||
\(488\) | −8.87868 | + | 17.0948i | −0.401919 | + | 0.773847i | ||||
\(489\) | 11.0978 | 0.501859 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.71980 | − | 3.71980i | −0.167872 | − | 0.167872i | 0.618171 | − | 0.786044i | \(-0.287874\pi\) |
−0.786044 | + | 0.618171i | \(0.787874\pi\) | |||||||
\(492\) | −1.10817 | + | 3.35128i | −0.0499602 | + | 0.151087i | ||||
\(493\) | 3.48642 | 0.157021 | ||||||||
\(494\) | −39.1142 | − | 6.29925i | −1.75983 | − | 0.283417i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.8885 | − | 28.1314i | 0.937923 | − | 1.26314i | ||||
\(497\) | −1.02338 | − | 1.02338i | −0.0459050 | − | 0.0459050i | ||||
\(498\) | 5.67958 | − | 4.10396i | 0.254508 | − | 0.183903i | ||||
\(499\) | 13.6065 | + | 13.6065i | 0.609111 | + | 0.609111i | 0.942714 | − | 0.333603i | \(-0.108264\pi\) |
−0.333603 | + | 0.942714i | \(0.608264\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.5006 | + | 11.5006i | −0.513810 | + | 0.513810i | ||||
\(502\) | 14.7877 | + | 2.38152i | 0.660007 | + | 0.106292i | ||||
\(503\) | 9.31208 | − | 9.31208i | 0.415205 | − | 0.415205i | −0.468342 | − | 0.883547i | \(-0.655148\pi\) |
0.883547 | + | 0.468342i | \(0.155148\pi\) | |||||||
\(504\) | 1.59774 | − | 3.07626i | 0.0711691 | − | 0.137028i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.97247 | − | 4.31560i | 0.265509 | − | 0.191852i | ||||
\(507\) | 0.395636i | 0.0175708i | ||||||||
\(508\) | −13.4116 | − | 26.6632i | −0.595044 | − | 1.18299i | ||||
\(509\) | 7.94836 | − | 7.94836i | 0.352305 | − | 0.352305i | −0.508662 | − | 0.860966i | \(-0.669860\pi\) |
0.860966 | + | 0.508662i | \(0.169860\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.72585i | 0.209059i | ||||||||
\(512\) | 17.9902 | + | 13.7242i | 0.795060 | + | 0.606531i | ||||
\(513\) | 20.5618 | − | 20.5618i | 0.907824 | − | 0.907824i | ||||
\(514\) | 19.9054 | + | 3.20571i | 0.877989 | + | 0.141398i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.66575 | − | 1.87350i | −0.249421 | − | 0.0824762i | ||||
\(517\) | −7.71069 | −0.339116 | ||||||||
\(518\) | 3.67847 | + | 0.592408i | 0.161623 | + | 0.0260289i | ||||
\(519\) | − | 10.3878i | − | 0.455972i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 29.3979i | − | 1.28795i | −0.765048 | − | 0.643974i | \(-0.777285\pi\) | ||
0.765048 | − | 0.643974i | \(-0.222715\pi\) | |||||||
\(522\) | −3.38968 | + | 21.0477i | −0.148362 | + | 0.921233i | ||||
\(523\) | 19.5121 | 0.853205 | 0.426602 | − | 0.904439i | \(-0.359710\pi\) | ||||
0.426602 | + | 0.904439i | \(0.359710\pi\) | |||||||
\(524\) | 1.08098 | + | 2.14906i | 0.0472228 | + | 0.0938821i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.21984 | − | 7.57438i | 0.0531874 | − | 0.330259i | ||||
\(527\) | 3.61018 | − | 3.61018i | 0.157262 | − | 0.157262i | ||||
\(528\) | 3.27048 | − | 0.483226i | 0.142329 | − | 0.0210297i | ||||
\(529\) | 3.92999i | 0.170869i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.4902 | + | 18.4902i | −0.802406 | + | 0.802406i | ||||
\(532\) | −7.02232 | − | 2.32208i | −0.304456 | − | 0.100675i | ||||
\(533\) | 9.38575i | 0.406542i | ||||||||
\(534\) | 0.636604 | + | 0.881012i | 0.0275485 | + | 0.0381251i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.2520 | + | 38.7319i | 0.529205 | + | 1.67296i | ||||
\(537\) | 6.86692 | − | 6.86692i | 0.296329 | − | 0.296329i | ||||
\(538\) | −4.26913 | + | 26.5085i | −0.184055 | + | 1.14286i | ||||
\(539\) | 5.70618 | − | 5.70618i | 0.245783 | − | 0.245783i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.47183 | + | 8.47183i | 0.364232 | + | 0.364232i | 0.865369 | − | 0.501136i | \(-0.167084\pi\) |
−0.501136 | + | 0.865369i | \(0.667084\pi\) | |||||||
\(542\) | −10.2309 | − | 14.1587i | −0.439453 | − | 0.608170i | ||||
\(543\) | 0.720526 | + | 0.720526i | 0.0309207 | + | 0.0309207i | ||||
\(544\) | 2.30093 | + | 2.36147i | 0.0986516 | + | 0.101247i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.279050 | + | 1.73272i | −0.0119422 | + | 0.0741534i | ||||
\(547\) | −9.97988 | −0.426709 | −0.213355 | − | 0.976975i | \(-0.568439\pi\) | ||||
−0.213355 | + | 0.976975i | \(0.568439\pi\) | |||||||
\(548\) | −6.99219 | − | 13.9010i | −0.298692 | − | 0.593820i | ||||
\(549\) | −12.1364 | − | 12.1364i | −0.517971 | − | 0.517971i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 45.4879 | 1.93785 | ||||||||
\(552\) | 3.94364 | − | 7.59300i | 0.167852 | − | 0.323180i | ||||
\(553\) | 3.49559 | + | 3.49559i | 0.148648 | + | 0.148648i | ||||
\(554\) | 7.78098 | − | 5.62240i | 0.330582 | − | 0.238873i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.85762 | − | 7.66922i | −0.163600 | − | 0.325247i | ||||
\(557\) | − | 13.4866i | − | 0.571445i | −0.958312 | − | 0.285722i | \(-0.907766\pi\) | ||
0.958312 | − | 0.285722i | \(-0.0922335\pi\) | |||||||
\(558\) | 18.2848 | + | 25.3048i | 0.774059 | + | 1.07124i | ||||
\(559\) | −15.8678 | −0.671135 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.481724 | 0.0203384 | ||||||||
\(562\) | 17.8502 | + | 24.7033i | 0.752965 | + | 1.04205i | ||||
\(563\) | − | 20.3451i | − | 0.857445i | −0.903436 | − | 0.428723i | \(-0.858964\pi\) | ||
0.903436 | − | 0.428723i | \(-0.141036\pi\) | |||||||
\(564\) | −7.99853 | + | 4.02327i | −0.336799 | + | 0.169410i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.3116 | − | 8.17354i | 0.475461 | − | 0.343560i | ||||
\(567\) | 1.68896 | + | 1.68896i | 0.0709298 | + | 0.0709298i | ||||
\(568\) | 2.53872 | + | 8.02559i | 0.106522 | + | 0.336746i | ||||
\(569\) | −17.1460 | −0.718797 | −0.359399 | − | 0.933184i | \(-0.617018\pi\) | ||||
−0.359399 | + | 0.933184i | \(0.617018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.24329 | + | 6.24329i | 0.261274 | + | 0.261274i | 0.825571 | − | 0.564298i | \(-0.190853\pi\) |
−0.564298 | + | 0.825571i | \(0.690853\pi\) | |||||||
\(572\) | 7.85325 | − | 3.95019i | 0.328361 | − | 0.165166i | ||||
\(573\) | 2.13645 | 0.0892516 | ||||||||
\(574\) | −0.278600 | + | 1.72993i | −0.0116285 | + | 0.0722057i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −16.4934 | + | 11.5949i | −0.687225 | + | 0.483120i | ||||
\(577\) | 10.0373 | + | 10.0373i | 0.417859 | + | 0.417859i | 0.884465 | − | 0.466606i | \(-0.154523\pi\) |
−0.466606 | + | 0.884465i | \(0.654523\pi\) | |||||||
\(578\) | −13.7994 | − | 19.0973i | −0.573979 | − | 0.794343i | ||||
\(579\) | 8.37596 | + | 8.37596i | 0.348093 | + | 0.348093i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.45963 | − | 2.45963i | 0.102043 | − | 0.102043i | ||||
\(582\) | 1.57703 | − | 9.79235i | 0.0653701 | − | 0.405906i | ||||
\(583\) | −5.12561 | + | 5.12561i | −0.212281 | + | 0.212281i | ||||
\(584\) | 12.6688 | − | 24.3923i | 0.524240 | − | 1.00936i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.7593 | + | 16.2739i | 0.485771 | + | 0.672270i | ||||
\(587\) | − | 30.6857i | − | 1.26654i | −0.773933 | − | 0.633268i | \(-0.781713\pi\) | ||
0.773933 | − | 0.633268i | \(-0.218287\pi\) | |||||||
\(588\) | 2.94183 | − | 8.89655i | 0.121319 | − | 0.366887i | ||||
\(589\) | 47.1025 | − | 47.1025i | 1.94083 | − | 1.94083i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 9.01817i | − | 0.370958i | ||||||
\(592\) | −17.3982 | − | 12.9188i | −0.715062 | − | 0.530958i | ||||
\(593\) | 2.10671 | − | 2.10671i | 0.0865123 | − | 0.0865123i | −0.662526 | − | 0.749039i | \(-0.730516\pi\) |
0.749039 | + | 0.662526i | \(0.230516\pi\) | |||||||
\(594\) | −1.02589 | + | 6.37011i | −0.0420928 | + | 0.261369i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 28.1915 | − | 14.1803i | 1.15477 | − | 0.580850i | ||||
\(597\) | 7.36210 | 0.301311 | ||||||||
\(598\) | 3.61737 | − | 22.4615i | 0.147925 | − | 0.918518i | ||||
\(599\) | − | 32.1322i | − | 1.31289i | −0.754375 | − | 0.656444i | \(-0.772060\pi\) | ||
0.754375 | − | 0.656444i | \(-0.227940\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.9811i | 0.611091i | 0.952177 | + | 0.305546i | \(0.0988388\pi\) | ||||
−0.952177 | + | 0.305546i | \(0.901161\pi\) | |||||||
\(602\) | −2.92465 | − | 0.471008i | −0.119200 | − | 0.0191968i | ||||
\(603\) | −36.1959 | −1.47401 | ||||||||
\(604\) | 1.99840 | − | 6.04345i | 0.0813136 | − | 0.245905i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.30405 | + | 0.210014i | 0.0529735 | + | 0.00853125i | ||||
\(607\) | −27.3357 | + | 27.3357i | −1.10952 | + | 1.10952i | −0.116310 | + | 0.993213i | \(0.537107\pi\) |
−0.993213 | + | 0.116310i | \(0.962893\pi\) | |||||||
\(608\) | 30.0206 | + | 30.8105i | 1.21750 | + | 1.24953i | ||||
\(609\) | − | 2.01506i | − | 0.0816544i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.8344 | + | 16.8344i | −0.681047 | + | 0.681047i | ||||
\(612\) | −2.62443 | + | 1.32009i | −0.106086 | + | 0.0533616i | ||||
\(613\) | − | 48.3829i | − | 1.95417i | −0.212859 | − | 0.977083i | \(-0.568277\pi\) | ||
0.212859 | − | 0.977083i | \(-0.431723\pi\) | |||||||
\(614\) | 23.4025 | − | 16.9103i | 0.944449 | − | 0.682442i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.56472 | − | 0.494965i | 0.0630444 | − | 0.0199427i | ||||
\(617\) | 31.1565 | − | 31.1565i | 1.25432 | − | 1.25432i | 0.300549 | − | 0.953766i | \(-0.402830\pi\) |
0.953766 | − | 0.300549i | \(-0.0971699\pi\) | |||||||
\(618\) | −13.1230 | − | 2.11343i | −0.527885 | − | 0.0850146i | ||||
\(619\) | 0.198272 | − | 0.198272i | 0.00796922 | − | 0.00796922i | −0.703111 | − | 0.711080i | \(-0.748206\pi\) |
0.711080 | + | 0.703111i | \(0.248206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.8077 | + | 11.8077i | 0.473825 | + | 0.473825i | ||||
\(622\) | −7.80700 | + | 5.64120i | −0.313032 | + | 0.226191i | ||||
\(623\) | 0.381537 | + | 0.381537i | 0.0152859 | + | 0.0152859i | ||||
\(624\) | 6.08529 | − | 8.19530i | 0.243607 | − | 0.328075i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.38790 | + | 0.384565i | 0.0954395 | + | 0.0153703i | ||||
\(627\) | 6.28512 | 0.251003 | ||||||||
\(628\) | 13.3957 | + | 4.42958i | 0.534547 | + | 0.176759i | ||||
\(629\) | −2.23276 | − | 2.23276i | −0.0890259 | − | 0.0890259i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.3314 | −1.28709 | −0.643547 | − | 0.765407i | \(-0.722538\pi\) | ||||
−0.643547 | + | 0.765407i | \(0.722538\pi\) | |||||||
\(632\) | −8.67157 | − | 27.4132i | −0.344936 | − | 1.09044i | ||||
\(633\) | 7.95239 | + | 7.95239i | 0.316079 | + | 0.316079i | ||||
\(634\) | 2.85076 | + | 3.94523i | 0.113218 | + | 0.156685i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.64252 | + | 7.99138i | −0.104783 | + | 0.316879i | ||||
\(637\) | − | 24.9161i | − | 0.987212i | ||||||
\(638\) | −8.18092 | + | 5.91139i | −0.323886 | + | 0.234034i | ||||
\(639\) | −7.50010 | −0.296700 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −46.5662 | −1.83926 | −0.919628 | − | 0.392790i | \(-0.871510\pi\) | ||||
−0.919628 | + | 0.392790i | \(0.871510\pi\) | |||||||
\(642\) | −4.19413 | + | 3.03060i | −0.165529 | + | 0.119608i | ||||
\(643\) | − | 40.2247i | − | 1.58631i | −0.609021 | − | 0.793154i | \(-0.708437\pi\) | ||
0.609021 | − | 0.793154i | \(-0.291563\pi\) | |||||||
\(644\) | 1.33346 | − | 4.03259i | 0.0525458 | − | 0.158906i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.67118 | + | 5.08064i | 0.144441 | + | 0.199895i | ||||
\(647\) | 10.7938 | + | 10.7938i | 0.424349 | + | 0.424349i | 0.886698 | − | 0.462349i | \(-0.152993\pi\) |
−0.462349 | + | 0.886698i | \(0.652993\pi\) | |||||||
\(648\) | −4.18984 | − | 13.2452i | −0.164593 | − | 0.520322i | ||||
\(649\) | −12.3799 | −0.485956 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.08659 | − | 2.08659i | −0.0817799 | − | 0.0817799i | ||||
\(652\) | −30.4215 | − | 10.0595i | −1.19140 | − | 0.393961i | ||||
\(653\) | 3.92443 | 0.153575 | 0.0767875 | − | 0.997047i | \(-0.475534\pi\) | ||||
0.0767875 | + | 0.997047i | \(0.475534\pi\) | |||||||
\(654\) | 2.10614 | + | 0.339188i | 0.0823564 | + | 0.0132633i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.07549 | − | 8.18210i | 0.237208 | − | 0.319457i | ||||
\(657\) | 17.3173 | + | 17.3173i | 0.675610 | + | 0.675610i | ||||
\(658\) | −3.60252 | + | 2.60312i | −0.140441 | + | 0.101480i | ||||
\(659\) | 34.6142 | + | 34.6142i | 1.34838 | + | 1.34838i | 0.887425 | + | 0.460952i | \(0.152492\pi\) |
0.460952 | + | 0.887425i | \(0.347508\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.7641 | − | 21.7641i | 0.846525 | − | 0.846525i | −0.143173 | − | 0.989698i | \(-0.545730\pi\) |
0.989698 | + | 0.143173i | \(0.0457304\pi\) | |||||||
\(662\) | −2.93146 | − | 0.472104i | −0.113934 | − | 0.0183489i | ||||
\(663\) | 1.05173 | − | 1.05173i | 0.0408456 | − | 0.0408456i | ||||
\(664\) | −19.2890 | + | 6.10166i | −0.748559 | + | 0.236790i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.6501 | − | 11.3085i | 0.606428 | − | 0.438194i | ||||
\(667\) | 26.1216i | 1.01143i | ||||||||
\(668\) | 41.9505 | − | 21.1011i | 1.62311 | − | 0.816426i | ||||
\(669\) | 1.50917 | − | 1.50917i | 0.0583477 | − | 0.0583477i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 8.12584i | − | 0.313695i | ||||||
\(672\) | 1.36487 | − | 1.32988i | 0.0526510 | − | 0.0513012i | ||||
\(673\) | −29.4450 | + | 29.4450i | −1.13502 | + | 1.13502i | −0.145691 | + | 0.989330i | \(0.546541\pi\) |
−0.989330 | + | 0.145691i | \(0.953459\pi\) | |||||||
\(674\) | −12.2662 | − | 1.97544i | −0.472475 | − | 0.0760910i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.358622 | − | 1.08453i | 0.0137932 | − | 0.0417126i | ||||
\(677\) | 34.7351 | 1.33498 | 0.667490 | − | 0.744619i | \(-0.267369\pi\) | ||||
0.667490 | + | 0.744619i | \(0.267369\pi\) | |||||||
\(678\) | 4.09869 | + | 0.660084i | 0.157409 | + | 0.0253504i | ||||
\(679\) | − | 4.92370i | − | 0.188954i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 6.45828i | − | 0.247482i | ||||||
\(682\) | −2.35009 | + | 14.5925i | −0.0899897 | + | 0.558777i | ||||
\(683\) | 22.2693 | 0.852110 | 0.426055 | − | 0.904697i | \(-0.359903\pi\) | ||||
0.426055 | + | 0.904697i | \(0.359903\pi\) | |||||||
\(684\) | −34.2414 | + | 17.2234i | −1.30925 | + | 0.658554i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.50505 | − | 9.34535i | 0.0574629 | − | 0.356807i | ||||
\(687\) | 1.88597 | − | 1.88597i | 0.0719543 | − | 0.0719543i | ||||
\(688\) | 13.8328 | + | 10.2714i | 0.527372 | + | 0.391592i | ||||
\(689\) | 22.3810i | 0.852650i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.7043 | − | 15.7043i | 0.597420 | − | 0.597420i | −0.342205 | − | 0.939625i | \(-0.611174\pi\) |
0.939625 | + | 0.342205i | \(0.111174\pi\) | |||||||
\(692\) | −9.41591 | + | 28.4751i | −0.357939 | + | 1.08246i | ||||
\(693\) | 1.46227i | 0.0555470i | ||||||||
\(694\) | −8.40717 | − | 11.6349i | −0.319132 | − | 0.441655i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.40188 | + | 10.4007i | −0.204758 | + | 0.394237i | ||||
\(697\) | 1.05003 | − | 1.05003i | 0.0397728 | − | 0.0397728i | ||||
\(698\) | −1.27070 | + | 7.89023i | −0.0480968 | + | 0.298650i | ||||
\(699\) | 8.58253 | − | 8.58253i | 0.324621 | − | 0.324621i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.5588 | − | 21.5588i | −0.814266 | − | 0.814266i | 0.171004 | − | 0.985270i | \(-0.445299\pi\) |
−0.985270 | + | 0.171004i | \(0.945299\pi\) | |||||||
\(702\) | 11.6678 | + | 16.1474i | 0.440373 | + | 0.609443i | ||||
\(703\) | −29.1311 | − | 29.1311i | −1.09870 | − | 1.09870i | ||||
\(704\) | −9.40314 | − | 1.63988i | −0.354394 | − | 0.0618053i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.20702 | + | 44.7509i | −0.271240 | + | 1.68422i | ||||
\(707\) | 0.655691 | 0.0246598 | ||||||||
\(708\) | −12.8421 | + | 6.45958i | −0.482635 | + | 0.242766i | ||||
\(709\) | −2.96687 | − | 2.96687i | −0.111423 | − | 0.111423i | 0.649197 | − | 0.760620i | \(-0.275105\pi\) |
−0.760620 | + | 0.649197i | \(0.775105\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.6183 | 0.960760 | ||||||||
\(712\) | −0.946485 | − | 2.99210i | −0.0354710 | − | 0.112134i | ||||
\(713\) | 27.0488 | + | 27.0488i | 1.01299 | + | 1.01299i | ||||
\(714\) | 0.225067 | − | 0.162629i | 0.00842290 | − | 0.00608624i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.0482 | + | 12.5993i | −0.936096 | + | 0.470857i | ||||
\(717\) | 17.4688i | 0.652385i | ||||||||
\(718\) | 3.57712 | + | 4.95047i | 0.133497 | + | 0.184750i | ||||
\(719\) | −25.8357 | −0.963509 | −0.481755 | − | 0.876306i | \(-0.660000\pi\) | ||||
−0.481755 | + | 0.876306i | \(0.660000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.59839 | −0.245737 | ||||||||
\(722\) | 32.1611 | + | 44.5085i | 1.19691 | + | 1.65644i | ||||
\(723\) | 8.32763i | 0.309708i | ||||||||
\(724\) | −1.32201 | − | 2.62824i | −0.0491320 | − | 0.0976777i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.60407 | − | 5.49457i | 0.282214 | − | 0.203923i | ||||
\(727\) | −28.9620 | − | 28.9620i | −1.07414 | − | 1.07414i | −0.997022 | − | 0.0771198i | \(-0.975428\pi\) |
−0.0771198 | − | 0.997022i | \(-0.524572\pi\) | |||||||
\(728\) | 2.33555 | − | 4.49682i | 0.0865612 | − | 0.166663i | ||||
\(729\) | 4.43146 | 0.164128 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.77521 | + | 1.77521i | 0.0656584 | + | 0.0656584i | ||||
\(732\) | −4.23988 | − | 8.42918i | −0.156711 | − | 0.311551i | ||||
\(733\) | −21.1673 | −0.781832 | −0.390916 | − | 0.920426i | \(-0.627842\pi\) | ||||
−0.390916 | + | 0.920426i | \(0.627842\pi\) | |||||||
\(734\) | 2.05725 | − | 12.7742i | 0.0759346 | − | 0.471504i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.6930 | + | 17.2394i | −0.652173 | + | 0.635453i | ||||
\(737\) | −12.1173 | − | 12.1173i | −0.446347 | − | 0.446347i | ||||
\(738\) | 5.31820 | + | 7.35999i | 0.195765 | + | 0.270925i | ||||
\(739\) | 2.23302 | + | 2.23302i | 0.0821431 | + | 0.0821431i | 0.746985 | − | 0.664841i | \(-0.231501\pi\) |
−0.664841 | + | 0.746985i | \(0.731501\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.7220 | − | 13.7220i | 0.504091 | − | 0.504091i | ||||
\(742\) | −0.664344 | + | 4.12514i | −0.0243888 | + | 0.151439i | ||||
\(743\) | 18.4514 | − | 18.4514i | 0.676915 | − | 0.676915i | −0.282386 | − | 0.959301i | \(-0.591126\pi\) |
0.959301 | + | 0.282386i | \(0.0911258\pi\) | |||||||
\(744\) | 5.17624 | + | 16.3635i | 0.189770 | + | 0.599915i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.9011 | − | 19.2381i | −0.508955 | − | 0.704356i | ||||
\(747\) | − | 18.0260i | − | 0.659538i | ||||||
\(748\) | −1.32051 | − | 0.436655i | −0.0482827 | − | 0.0159657i | ||||
\(749\) | −1.81634 | + | 1.81634i | −0.0663675 | + | 0.0663675i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 42.4243i | − | 1.54808i | −0.633134 | − | 0.774042i | \(-0.718232\pi\) | ||
0.633134 | − | 0.774042i | \(-0.281768\pi\) | |||||||
\(752\) | 25.5726 | − | 3.77845i | 0.932537 | − | 0.137786i | ||||
\(753\) | −5.18780 | + | 5.18780i | −0.189054 | + | 0.189054i | ||||
\(754\) | −4.95496 | + | 30.7671i | −0.180449 | + | 1.12047i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.67123 | + | 3.32253i | 0.0607821 | + | 0.120839i | ||||
\(757\) | 19.7595 | 0.718170 | 0.359085 | − | 0.933305i | \(-0.383089\pi\) | ||||
0.359085 | + | 0.933305i | \(0.383089\pi\) | |||||||
\(758\) | −2.32471 | + | 14.4349i | −0.0844372 | + | 0.524300i | ||||
\(759\) | 3.60925i | 0.131007i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 48.0351i | − | 1.74127i | −0.491928 | − | 0.870636i | \(-0.663708\pi\) | ||
0.491928 | − | 0.870636i | \(-0.336292\pi\) | |||||||
\(762\) | 14.4333 | + | 2.32445i | 0.522865 | + | 0.0842061i | ||||
\(763\) | 1.05899 | 0.0383379 | ||||||||
\(764\) | −5.85649 | − | 1.93657i | −0.211880 | − | 0.0700628i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.4946 | + | 1.69013i | 0.379186 | + | 0.0610669i | ||||
\(767\) | −27.0286 | + | 27.0286i | −0.975946 | + | 0.975946i | ||||
\(768\) | −10.6098 | + | 3.20525i | −0.382848 | + | 0.115659i | ||||
\(769\) | 24.0184i | 0.866127i | 0.901363 | + | 0.433064i | \(0.142567\pi\) | ||||
−0.901363 | + | 0.433064i | \(0.857433\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.98319 | + | 6.98319i | −0.251493 | + | 0.251493i | ||||
\(772\) | −15.3680 | − | 30.5527i | −0.553107 | − | 1.09962i | ||||
\(773\) | 22.4630i | 0.807937i | 0.914773 | + | 0.403969i | \(0.132370\pi\) | ||||
−0.914773 | + | 0.403969i | \(0.867630\pi\) | |||||||
\(774\) | −12.4430 | + | 8.99106i | −0.447253 | + | 0.323177i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.1992 | + | 25.4135i | −0.473824 | + | 0.912292i | ||||
\(777\) | −1.29048 | + | 1.29048i | −0.0462956 | + | 0.0462956i | ||||
\(778\) | −2.54412 | − | 0.409725i | −0.0912113 | − | 0.0146893i | ||||
\(779\) | 13.6999 | − | 13.6999i | 0.490850 | − | 0.490850i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.51081 | − | 2.51081i | −0.0898440 | − | 0.0898440i | ||||
\(782\) | −2.91757 | + | 2.10819i | −0.104332 | + | 0.0753886i | ||||
\(783\) | −16.1738 | − | 16.1738i | −0.578005 | − | 0.578005i | ||||
\(784\) | −16.1284 | + | 21.7208i | −0.576016 | + | 0.775743i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.16333 | − | 0.187352i | −0.0414946 | − | 0.00668261i | ||||
\(787\) | −26.1054 | −0.930556 | −0.465278 | − | 0.885165i | \(-0.654046\pi\) | ||||
−0.465278 | + | 0.885165i | \(0.654046\pi\) | |||||||
\(788\) | −8.17446 | + | 24.7208i | −0.291203 | + | 0.880642i | ||||
\(789\) | 2.65724 | + | 2.65724i | 0.0946001 | + | 0.0946001i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.06087 | 0.0732759 | ||||||||
\(792\) | 3.91998 | − | 7.54745i | 0.139290 | − | 0.268187i | ||||
\(793\) | −17.7408 | − | 17.7408i | −0.629994 | − | 0.629994i | ||||
\(794\) | −7.90040 | − | 10.9336i | −0.280375 | − | 0.388018i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.1812 | − | 6.67333i | −0.715302 | − | 0.236530i | ||||
\(797\) | − | 43.4888i | − | 1.54045i | −0.637770 | − | 0.770227i | \(-0.720143\pi\) | ||
0.637770 | − | 0.770227i | \(-0.279857\pi\) | |||||||
\(798\) | 2.93647 | − | 2.12185i | 0.103950 | − | 0.0751125i | ||||
\(799\) | 3.76670 | 0.133256 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.79618 | 0.0987983 | ||||||||
\(802\) | −28.2103 | + | 20.3842i | −0.996139 | + | 0.719793i | ||||
\(803\) | 11.5946i | 0.409165i | ||||||||
\(804\) | −18.8922 | − | 6.24710i | −0.666276 | − | 0.220318i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.7284 | + | 36.9901i | 0.941467 | + | 1.30292i | ||||
\(807\) | −9.29969 | − | 9.29969i | −0.327364 | − | 0.327364i | ||||
\(808\) | −3.38433 | − | 1.75775i | −0.119060 | − | 0.0618373i | ||||
\(809\) | 36.6271 | 1.28774 | 0.643870 | − | 0.765135i | \(-0.277328\pi\) | ||||
0.643870 | + | 0.765135i | \(0.277328\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.7904 | + | 18.7904i | 0.659821 | + | 0.659821i | 0.955338 | − | 0.295516i | \(-0.0954917\pi\) |
−0.295516 | + | 0.955338i | \(0.595492\pi\) | |||||||
\(812\) | −1.82654 | + | 5.52373i | −0.0640990 | + | 0.193845i | ||||
\(813\) | 8.55633 | 0.300084 | ||||||||
\(814\) | 9.02493 | + | 1.45344i | 0.316324 | + | 0.0509431i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.59764 | + | 0.236058i | −0.0559287 | + | 0.00826367i | ||||
\(817\) | 23.1614 | + | 23.1614i | 0.810314 | + | 0.810314i | ||||
\(818\) | −19.4245 | + | 14.0358i | −0.679161 | + | 0.490750i | ||||
\(819\) | 3.19250 | + | 3.19250i | 0.111555 | + | 0.111555i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.91048 | − | 3.91048i | 0.136477 | − | 0.136477i | −0.635568 | − | 0.772045i | \(-0.719234\pi\) |
0.772045 | + | 0.635568i | \(0.219234\pi\) | |||||||
\(822\) | 7.52488 | + | 1.21186i | 0.262460 | + | 0.0422686i | ||||
\(823\) | −35.4412 | + | 35.4412i | −1.23540 | + | 1.23540i | −0.273542 | + | 0.961860i | \(0.588195\pi\) |
−0.961860 | + | 0.273542i | \(0.911805\pi\) | |||||||
\(824\) | 34.0574 | + | 17.6887i | 1.18645 | + | 0.616214i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.78405 | + | 4.17945i | −0.201253 | + | 0.145422i | ||||
\(827\) | 44.0700i | 1.53246i | 0.642565 | + | 0.766232i | \(0.277870\pi\) | ||||
−0.642565 | + | 0.766232i | \(0.722130\pi\) | |||||||
\(828\) | −9.89061 | − | 19.6632i | −0.343723 | − | 0.683344i | ||||
\(829\) | 15.1609 | − | 15.1609i | 0.526561 | − | 0.526561i | −0.392984 | − | 0.919545i | \(-0.628557\pi\) |
0.919545 | + | 0.392984i | \(0.128557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.70216i | 0.163116i | ||||||||
\(832\) | −24.1097 | + | 16.9492i | −0.835854 | + | 0.587607i | ||||
\(833\) | −2.78749 | + | 2.78749i | −0.0965808 | + | 0.0965808i | ||||
\(834\) | 4.15151 | + | 0.668590i | 0.143755 | + | 0.0231514i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −17.2289 | − | 5.69711i | −0.595874 | − | 0.197039i | ||||
\(837\) | −33.4958 | −1.15779 | ||||||||
\(838\) | −12.9720 | − | 2.08910i | −0.448109 | − | 0.0721669i | ||||
\(839\) | 40.3143i | 1.39180i | 0.718137 | + | 0.695901i | \(0.244995\pi\) | ||||
−0.718137 | + | 0.695901i | \(0.755005\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 6.78056i | − | 0.233812i | ||||||
\(842\) | 4.41396 | − | 27.4078i | 0.152115 | − | 0.944535i | ||||
\(843\) | −14.9286 | −0.514168 | ||||||||
\(844\) | −14.5909 | − | 29.0077i | −0.502238 | − | 0.998485i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.66218 | + | 22.7398i | −0.125908 | + | 0.781809i | ||||
\(847\) | 3.29307 | − | 3.29307i | 0.113151 | − | 0.113151i | ||||
\(848\) | 14.4875 | − | 19.5108i | 0.497502 | − | 0.670005i | ||||
\(849\) | 6.83575i | 0.234602i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.7286 | − | 16.7286i | 0.573450 | − | 0.573450i | ||||
\(852\) | −3.91463 | − | 1.29446i | −0.134113 | − | 0.0443473i | ||||
\(853\) | 28.6203i | 0.979941i | 0.871739 | + | 0.489971i | \(0.162992\pi\) | ||||
−0.871739 | + | 0.489971i | \(0.837008\pi\) | |||||||
\(854\) | −2.74327 | − | 3.79648i | −0.0938728 | − | 0.129913i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.2441 | − | 4.50582i | 0.486854 | − | 0.154006i | ||||
\(857\) | 7.19794 | − | 7.19794i | 0.245877 | − | 0.245877i | −0.573399 | − | 0.819276i | \(-0.694376\pi\) |
0.819276 | + | 0.573399i | \(0.194376\pi\) | |||||||
\(858\) | −0.684634 | + | 4.25113i | −0.0233730 | + | 0.145131i | ||||
\(859\) | −18.8135 | + | 18.8135i | −0.641910 | + | 0.641910i | −0.951025 | − | 0.309115i | \(-0.899967\pi\) |
0.309115 | + | 0.951025i | \(0.399967\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.606890 | − | 0.606890i | −0.0206828 | − | 0.0206828i | ||||
\(862\) | −10.2491 | − | 14.1840i | −0.349087 | − | 0.483110i | ||||
\(863\) | −19.2328 | − | 19.2328i | −0.654691 | − | 0.654691i | 0.299428 | − | 0.954119i | \(-0.403204\pi\) |
−0.954119 | + | 0.299428i | \(0.903204\pi\) | |||||||
\(864\) | 0.280854 | − | 21.6293i | 0.00955484 | − | 0.735843i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.0462133 | − | 0.286955i | 0.00157039 | − | 0.00975112i | ||||
\(867\) | 11.5408 | 0.391945 | ||||||||
\(868\) | 3.82843 | + | 7.61118i | 0.129945 | + | 0.258340i | ||||
\(869\) | 8.57624 | + | 8.57624i | 0.290929 | + | 0.290929i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52.9103 | −1.79280 | ||||||||
\(872\) | −5.46593 | − | 2.83888i | −0.185100 | − | 0.0961367i | ||||
\(873\) | −18.0423 | − | 18.0423i | −0.610638 | − | 0.610638i | ||||
\(874\) | −38.0660 | + | 27.5058i | −1.28760 | + | 0.930398i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.04981 | + | 12.0274i | 0.204404 | + | 0.406369i | ||||
\(877\) | − | 35.4397i | − | 1.19671i | −0.801229 | − | 0.598357i | \(-0.795820\pi\) | ||
0.801229 | − | 0.598357i | \(-0.204180\pi\) | |||||||
\(878\) | −3.03020 | − | 4.19357i | −0.102264 | − | 0.141526i | ||||
\(879\) | −9.83458 | −0.331712 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.2010 | 1.01750 | 0.508748 | − | 0.860915i | \(-0.330108\pi\) | ||||
0.508748 | + | 0.860915i | \(0.330108\pi\) | |||||||
\(882\) | −14.1181 | − | 19.5384i | −0.475380 | − | 0.657891i | ||||
\(883\) | 28.9931i | 0.975696i | 0.872928 | + | 0.487848i | \(0.162218\pi\) | ||||
−0.872928 | + | 0.487848i | \(0.837782\pi\) | |||||||
\(884\) | −3.83634 | + | 1.92968i | −0.129030 | + | 0.0649023i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.51664 | + | 3.26364i | −0.151740 | + | 0.109644i | ||||
\(887\) | −5.33418 | − | 5.33418i | −0.179104 | − | 0.179104i | 0.611861 | − | 0.790965i | \(-0.290421\pi\) |
−0.790965 | + | 0.611861i | \(0.790421\pi\) | |||||||
\(888\) | 10.1202 | − | 3.20131i | 0.339612 | − | 0.107429i | ||||
\(889\) | 7.25724 | 0.243400 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.14379 | + | 4.14379i | 0.138822 | + | 0.138822i | ||||
\(892\) | −5.50493 | + | 2.76898i | −0.184319 | + | 0.0927125i | ||||
\(893\) | 49.1447 | 1.64456 | ||||||||
\(894\) | −2.45769 | + | 15.2606i | −0.0821974 | + | 0.510392i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.94687 | + | 2.40831i | −0.165263 | + | 0.0804561i | ||||
\(897\) | 7.87991 | + | 7.87991i | 0.263103 | + | 0.263103i | ||||
\(898\) | 31.4758 | + | 43.5602i | 1.05036 | + | 1.45362i | ||||
\(899\) | −37.0507 | − | 37.0507i | −1.23571 | − | 1.23571i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.50388 | − | 2.50388i | 0.0834163 | − | 0.0834163i | ||||
\(902\) | −0.683531 | + | 4.24428i | −0.0227591 | + | 0.141319i | ||||
\(903\) | 1.02602 | − | 1.02602i | 0.0341439 | − | 0.0341439i | ||||
\(904\) | −10.6371 | − | 5.52467i | −0.353785 | − | 0.183748i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.82607 | + | 2.52715i | 0.0606672 | + | 0.0839589i | ||||
\(907\) | − | 26.2683i | − | 0.872226i | −0.899892 | − | 0.436113i | \(-0.856355\pi\) | ||
0.899892 | − | 0.436113i | \(-0.143645\pi\) | |||||||
\(908\) | −5.85407 | + | 17.7036i | −0.194274 | + | 0.587514i | ||||
\(909\) | 2.40270 | − | 2.40270i | 0.0796924 | − | 0.0796924i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.5196i | 1.11055i | 0.831665 | + | 0.555277i | \(0.187388\pi\) | ||||
−0.831665 | + | 0.555277i | \(0.812612\pi\) | |||||||
\(912\) | −20.8447 | + | 3.07988i | −0.690236 | + | 0.101985i | ||||
\(913\) | 6.03459 | − | 6.03459i | 0.199716 | − | 0.199716i | ||||
\(914\) | −5.76028 | + | 35.7676i | −0.190533 | + | 1.18309i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.87940 | + | 3.46034i | −0.227302 | + | 0.114333i | ||||
\(917\) | −0.584935 | −0.0193163 | ||||||||
\(918\) | 0.501151 | − | 3.11182i | 0.0165405 | − | 0.102705i | ||||
\(919\) | − | 25.7545i | − | 0.849564i | −0.905296 | − | 0.424782i | \(-0.860351\pi\) | ||
0.905296 | − | 0.424782i | \(-0.139649\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.1425i | 0.466011i | ||||||||
\(922\) | 24.5130 | + | 3.94775i | 0.807292 | + | 0.130012i | ||||
\(923\) | −10.9635 | −0.360868 | ||||||||
\(924\) | −0.252375 | + | 0.763221i | −0.00830254 | + | 0.0251081i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.9136 | + | 2.72390i | 0.555816 | + | 0.0895128i | ||||
\(927\) | −24.1790 | + | 24.1790i | −0.794141 | + | 0.794141i | ||||
\(928\) | 24.2354 | − | 23.6141i | 0.795565 | − | 0.775170i | ||||
\(929\) | 9.06425i | 0.297388i | 0.988883 | + | 0.148694i | \(0.0475070\pi\) | ||||
−0.988883 | + | 0.148694i | \(0.952493\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.3688 | + | 36.3688i | −1.19194 | + | 1.19194i | ||||
\(932\) | −31.3062 | + | 15.7470i | −1.02547 | + | 0.515811i | ||||
\(933\) | − | 4.71788i | − | 0.154456i | ||||||
\(934\) | 39.3707 | − | 28.4486i | 1.28825 | − | 0.930865i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.91970 | − | 25.0363i | −0.258864 | − | 0.818338i | ||||
\(937\) | 3.38621 | − | 3.38621i | 0.110623 | − | 0.110623i | −0.649629 | − | 0.760251i | \(-0.725076\pi\) |
0.760251 | + | 0.649629i | \(0.225076\pi\) | |||||||
\(938\) | −9.75212 | − | 1.57055i | −0.318418 | − | 0.0512804i | ||||
\(939\) | −0.837719 | + | 0.837719i | −0.0273379 | + | 0.0273379i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.9347 | − | 16.9347i | −0.552054 | − | 0.552054i | 0.374979 | − | 0.927033i | \(-0.377650\pi\) |
−0.927033 | + | 0.374979i | \(0.877650\pi\) | |||||||
\(942\) | −5.60159 | + | 4.04761i | −0.182510 | + | 0.131878i | ||||
\(943\) | 7.86722 | + | 7.86722i | 0.256192 | + | 0.256192i | ||||
\(944\) | 41.0583 | − | 6.06651i | 1.33633 | − | 0.197448i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.17548 | − | 1.15559i | −0.233295 | − | 0.0375716i | ||||
\(947\) | 1.08633 | 0.0353011 | 0.0176505 | − | 0.999844i | \(-0.494381\pi\) | ||||
0.0176505 | + | 0.999844i | \(0.494381\pi\) | |||||||
\(948\) | 13.3713 | + | 4.42150i | 0.434279 | + | 0.143604i | ||||
\(949\) | 25.3140 | + | 25.3140i | 0.821727 | + | 0.821727i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.38416 | −0.0773117 | ||||||||
\(952\) | −0.764372 | + | 0.241792i | −0.0247734 | + | 0.00783654i | ||||
\(953\) | −10.7914 | − | 10.7914i | −0.349567 | − | 0.349567i | 0.510381 | − | 0.859948i | \(-0.329504\pi\) |
−0.859948 | + | 0.510381i | \(0.829504\pi\) | |||||||
\(954\) | 12.6816 | + | 17.5504i | 0.410583 | + | 0.568217i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.8345 | − | 47.8859i | 0.512124 | − | 1.54874i | ||||
\(957\) | − | 4.94385i | − | 0.159812i | ||||||
\(958\) | −26.8807 | + | 19.4235i | −0.868475 | + | 0.627544i | ||||
\(959\) | 3.78359 | 0.122178 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −45.7317 | −1.47522 | ||||||||
\(962\) | 22.8770 | − | 16.5305i | 0.737583 | − | 0.532964i | ||||
\(963\) | 13.3115i | 0.428956i | ||||||||
\(964\) | 7.54853 | − | 22.8279i | 0.243122 | − | 0.735237i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.21848 | + | 1.68628i | 0.0392038 | + | 0.0542552i | ||||
\(967\) | 31.4724 | + | 31.4724i | 1.01208 | + | 1.01208i | 0.999926 | + | 0.0121587i | \(0.00387033\pi\) |
0.0121587 | + | 0.999926i | \(0.496130\pi\) | |||||||
\(968\) | −25.8250 | + | 8.16917i | −0.830046 | + | 0.262567i | ||||
\(969\) | −3.07030 | −0.0986323 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.1234 | − | 23.1234i | −0.742066 | − | 0.742066i | 0.230909 | − | 0.972975i | \(-0.425830\pi\) |
−0.972975 | + | 0.230909i | \(0.925830\pi\) | |||||||
\(972\) | 28.2438 | + | 9.33942i | 0.905921 | + | 0.299562i | ||||
\(973\) | 2.08742 | 0.0669196 | ||||||||
\(974\) | 10.4891 | + | 1.68925i | 0.336094 | + | 0.0541271i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.98188 | + | 26.9495i | 0.127457 | + | 0.862632i | ||||
\(977\) | −15.3820 | − | 15.3820i | −0.492114 | − | 0.492114i | 0.416858 | − | 0.908972i | \(-0.363131\pi\) |
−0.908972 | + | 0.416858i | \(0.863131\pi\) | |||||||
\(978\) | 12.7211 | − | 9.19207i | 0.406777 | − | 0.293930i | ||||
\(979\) | 0.936080 | + | 0.936080i | 0.0299173 | + | 0.0299173i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.88052 | − | 3.88052i | 0.123896 | − | 0.123896i | ||||
\(982\) | −7.34496 | − | 1.18289i | −0.234387 | − | 0.0377475i | ||||
\(983\) | 38.5198 | − | 38.5198i | 1.22859 | − | 1.22859i | 0.264093 | − | 0.964497i | \(-0.414927\pi\) |
0.964497 | − | 0.264093i | \(-0.0850726\pi\) | |||||||
\(984\) | 1.50552 | + | 4.75937i | 0.0479943 | + | 0.151723i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.99641 | − | 2.88773i | 0.127272 | − | 0.0919642i | ||||
\(987\) | − | 2.17705i | − | 0.0692964i | ||||||
\(988\) | −50.0533 | + | 25.1769i | −1.59241 | + | 0.800982i | ||||
\(989\) | −13.3005 | + | 13.3005i | −0.422931 | + | 0.422931i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.0556i | 0.700619i | 0.936634 | + | 0.350310i | \(0.113924\pi\) | ||||
−0.936634 | + | 0.350310i | \(0.886076\pi\) | |||||||
\(992\) | 0.643375 | − | 49.5480i | 0.0204272 | − | 1.57315i | ||||
\(993\) | 1.02841 | − | 1.02841i | 0.0326356 | − | 0.0326356i | ||||
\(994\) | −2.02073 | − | 0.325433i | −0.0640936 | − | 0.0103221i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.11114 | − | 9.40856i | 0.0985804 | − | 0.298122i | ||||
\(997\) | −0.840040 | −0.0266043 | −0.0133022 | − | 0.999912i | \(-0.504234\pi\) | ||||
−0.0133022 | + | 0.999912i | \(0.504234\pi\) | |||||||
\(998\) | 26.8668 | + | 4.32684i | 0.850455 | + | 0.136964i | ||||
\(999\) | 20.7159i | 0.655422i |
(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 | 400.2.j.d.307.7 | 18 | ||
4.3 | odd | 2 | 1600.2.j.d.1007.4 | 18 | |||
5.2 | odd | 4 | 80.2.s.b.3.7 | yes | 18 | ||
5.3 | odd | 4 | 400.2.s.d.243.3 | 18 | |||
5.4 | even | 2 | 80.2.j.b.67.3 | yes | 18 | ||
15.2 | even | 4 | 720.2.z.g.163.3 | 18 | |||
15.14 | odd | 2 | 720.2.bd.g.307.7 | 18 | |||
16.5 | even | 4 | 1600.2.s.d.207.6 | 18 | |||
16.11 | odd | 4 | 400.2.s.d.107.3 | 18 | |||
20.3 | even | 4 | 1600.2.s.d.943.6 | 18 | |||
20.7 | even | 4 | 320.2.s.b.303.4 | 18 | |||
20.19 | odd | 2 | 320.2.j.b.47.6 | 18 | |||
40.19 | odd | 2 | 640.2.j.c.607.4 | 18 | |||
40.27 | even | 4 | 640.2.s.c.223.6 | 18 | |||
40.29 | even | 2 | 640.2.j.d.607.6 | 18 | |||
40.37 | odd | 4 | 640.2.s.d.223.4 | 18 | |||
80.19 | odd | 4 | 640.2.s.d.287.4 | 18 | |||
80.27 | even | 4 | 80.2.j.b.43.3 | ✓ | 18 | ||
80.29 | even | 4 | 640.2.s.c.287.6 | 18 | |||
80.37 | odd | 4 | 320.2.j.b.143.4 | 18 | |||
80.43 | even | 4 | inner | 400.2.j.d.43.7 | 18 | ||
80.53 | odd | 4 | 1600.2.j.d.143.6 | 18 | |||
80.59 | odd | 4 | 80.2.s.b.27.7 | yes | 18 | ||
80.67 | even | 4 | 640.2.j.d.543.4 | 18 | |||
80.69 | even | 4 | 320.2.s.b.207.4 | 18 | |||
80.77 | odd | 4 | 640.2.j.c.543.6 | 18 | |||
240.59 | even | 4 | 720.2.z.g.667.3 | 18 | |||
240.107 | odd | 4 | 720.2.bd.g.523.7 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.j.b.43.3 | ✓ | 18 | 80.27 | even | 4 | ||
80.2.j.b.67.3 | yes | 18 | 5.4 | even | 2 | ||
80.2.s.b.3.7 | yes | 18 | 5.2 | odd | 4 | ||
80.2.s.b.27.7 | yes | 18 | 80.59 | odd | 4 | ||
320.2.j.b.47.6 | 18 | 20.19 | odd | 2 | |||
320.2.j.b.143.4 | 18 | 80.37 | odd | 4 | |||
320.2.s.b.207.4 | 18 | 80.69 | even | 4 | |||
320.2.s.b.303.4 | 18 | 20.7 | even | 4 | |||
400.2.j.d.43.7 | 18 | 80.43 | even | 4 | inner | ||
400.2.j.d.307.7 | 18 | 1.1 | even | 1 | trivial | ||
400.2.s.d.107.3 | 18 | 16.11 | odd | 4 | |||
400.2.s.d.243.3 | 18 | 5.3 | odd | 4 | |||
640.2.j.c.543.6 | 18 | 80.77 | odd | 4 | |||
640.2.j.c.607.4 | 18 | 40.19 | odd | 2 | |||
640.2.j.d.543.4 | 18 | 80.67 | even | 4 | |||
640.2.j.d.607.6 | 18 | 40.29 | even | 2 | |||
640.2.s.c.223.6 | 18 | 40.27 | even | 4 | |||
640.2.s.c.287.6 | 18 | 80.29 | even | 4 | |||
640.2.s.d.223.4 | 18 | 40.37 | odd | 4 | |||
640.2.s.d.287.4 | 18 | 80.19 | odd | 4 | |||
720.2.z.g.163.3 | 18 | 15.2 | even | 4 | |||
720.2.z.g.667.3 | 18 | 240.59 | even | 4 | |||
720.2.bd.g.307.7 | 18 | 15.14 | odd | 2 | |||
720.2.bd.g.523.7 | 18 | 240.107 | odd | 4 | |||
1600.2.j.d.143.6 | 18 | 80.53 | odd | 4 | |||
1600.2.j.d.1007.4 | 18 | 4.3 | odd | 2 | |||
1600.2.s.d.207.6 | 18 | 16.5 | even | 4 | |||
1600.2.s.d.943.6 | 18 | 20.3 | even | 4 |