Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(43,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.w (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: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 267.17 | ||
Character | \(\chi\) | \(=\) | 280.267 |
Dual form | 280.2.w.a.43.17 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.205776 | + | 1.39916i | −0.145506 | + | 0.989357i | ||||
\(3\) | 1.94776 | − | 1.94776i | 1.12454 | − | 1.12454i | 0.133487 | − | 0.991051i | \(-0.457383\pi\) |
0.991051 | − | 0.133487i | \(-0.0426173\pi\) | |||||||
\(4\) | −1.91531 | − | 0.575828i | −0.957656 | − | 0.287914i | ||||
\(5\) | 2.03914 | − | 0.917560i | 0.911930 | − | 0.410345i | ||||
\(6\) | 2.32443 | + | 3.12603i | 0.948943 | + | 1.27620i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 1.19980 | − | 2.56134i | 0.424194 | − | 0.905571i | ||||
\(9\) | − | 4.58750i | − | 1.52917i | ||||||
\(10\) | 0.864211 | + | 3.04190i | 0.273287 | + | 0.961932i | ||||
\(11\) | −4.96845 | −1.49804 | −0.749022 | − | 0.662545i | \(-0.769476\pi\) | ||||
−0.749022 | + | 0.662545i | \(0.769476\pi\) | |||||||
\(12\) | −4.85213 | + | 2.60899i | −1.40069 | + | 0.753150i | ||||
\(13\) | −2.73283 | − | 2.73283i | −0.757951 | − | 0.757951i | 0.217998 | − | 0.975949i | \(-0.430047\pi\) |
−0.975949 | + | 0.217998i | \(0.930047\pi\) | |||||||
\(14\) | 0.843852 | + | 1.13486i | 0.225529 | + | 0.303305i | ||||
\(15\) | 2.18456 | − | 5.75893i | 0.564051 | − | 1.48695i | ||||
\(16\) | 3.33684 | + | 2.20578i | 0.834211 | + | 0.551446i | ||||
\(17\) | 2.50105 | + | 2.50105i | 0.606593 | + | 0.606593i | 0.942054 | − | 0.335461i | \(-0.108892\pi\) |
−0.335461 | + | 0.942054i | \(0.608892\pi\) | |||||||
\(18\) | 6.41866 | + | 0.943998i | 1.51289 | + | 0.222503i | ||||
\(19\) | 5.82728i | 1.33687i | 0.743771 | + | 0.668435i | \(0.233035\pi\) | ||||
−0.743771 | + | 0.668435i | \(0.766965\pi\) | |||||||
\(20\) | −4.43394 | + | 0.583221i | −0.991460 | + | 0.130412i | ||||
\(21\) | − | 2.75454i | − | 0.601090i | ||||||
\(22\) | 1.02239 | − | 6.95167i | 0.217974 | − | 1.48210i | ||||
\(23\) | 4.49556 | + | 4.49556i | 0.937389 | + | 0.937389i | 0.998152 | − | 0.0607632i | \(-0.0193535\pi\) |
−0.0607632 | + | 0.998152i | \(0.519353\pi\) | |||||||
\(24\) | −2.65195 | − | 7.32579i | −0.541326 | − | 1.49537i | ||||
\(25\) | 3.31617 | − | 3.74206i | 0.663233 | − | 0.748413i | ||||
\(26\) | 4.38603 | − | 3.26132i | 0.860170 | − | 0.639598i | ||||
\(27\) | −3.09207 | − | 3.09207i | −0.595069 | − | 0.595069i | ||||
\(28\) | −1.76150 | + | 0.947158i | −0.332893 | + | 0.178996i | ||||
\(29\) | 3.12482 | 0.580265 | 0.290132 | − | 0.956986i | \(-0.406301\pi\) | ||||
0.290132 | + | 0.956986i | \(0.406301\pi\) | |||||||
\(30\) | 7.60814 | + | 4.24160i | 1.38905 | + | 0.774407i | ||||
\(31\) | 4.40466i | 0.791100i | 0.918444 | + | 0.395550i | \(0.129446\pi\) | ||||
−0.918444 | + | 0.395550i | \(0.870554\pi\) | |||||||
\(32\) | −3.77289 | + | 4.21489i | −0.666959 | + | 0.745094i | ||||
\(33\) | −9.67733 | + | 9.67733i | −1.68461 | + | 1.68461i | ||||
\(34\) | −4.01403 | + | 2.98472i | −0.688400 | + | 0.511875i | ||||
\(35\) | 0.793075 | − | 2.09070i | 0.134054 | − | 0.353393i | ||||
\(36\) | −2.64161 | + | 8.78650i | −0.440269 | + | 1.46442i | ||||
\(37\) | 0.991822 | − | 0.991822i | 0.163055 | − | 0.163055i | −0.620864 | − | 0.783918i | \(-0.713218\pi\) |
0.783918 | + | 0.620864i | \(0.213218\pi\) | |||||||
\(38\) | −8.15331 | − | 1.19911i | −1.32264 | − | 0.194522i | ||||
\(39\) | −10.6458 | −1.70469 | ||||||||
\(40\) | 0.0963777 | − | 6.32382i | 0.0152387 | − | 0.999884i | ||||
\(41\) | 3.18008 | 0.496645 | 0.248322 | − | 0.968677i | \(-0.420121\pi\) | ||||
0.248322 | + | 0.968677i | \(0.420121\pi\) | |||||||
\(42\) | 3.85405 | + | 0.566819i | 0.594693 | + | 0.0874621i | ||||
\(43\) | −4.01697 | + | 4.01697i | −0.612582 | + | 0.612582i | −0.943618 | − | 0.331036i | \(-0.892602\pi\) |
0.331036 | + | 0.943618i | \(0.392602\pi\) | |||||||
\(44\) | 9.51613 | + | 2.86097i | 1.43461 | + | 0.431308i | ||||
\(45\) | −4.20931 | − | 9.35455i | −0.627487 | − | 1.39449i | ||||
\(46\) | −7.21510 | + | 5.36494i | −1.06381 | + | 0.791017i | ||||
\(47\) | −2.65726 | + | 2.65726i | −0.387602 | + | 0.387602i | −0.873831 | − | 0.486229i | \(-0.838372\pi\) |
0.486229 | + | 0.873831i | \(0.338372\pi\) | |||||||
\(48\) | 10.7957 | − | 2.20303i | 1.55822 | − | 0.317980i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 4.55337 | + | 5.40988i | 0.643944 | + | 0.765073i | ||||
\(51\) | 9.74286 | 1.36427 | ||||||||
\(52\) | 3.66058 | + | 6.80786i | 0.507631 | + | 0.944081i | ||||
\(53\) | 2.78266 | + | 2.78266i | 0.382228 | + | 0.382228i | 0.871904 | − | 0.489676i | \(-0.162885\pi\) |
−0.489676 | + | 0.871904i | \(0.662885\pi\) | |||||||
\(54\) | 4.96258 | − | 3.69003i | 0.675322 | − | 0.502150i | ||||
\(55\) | −10.1314 | + | 4.55885i | −1.36611 | + | 0.614716i | ||||
\(56\) | −0.962753 | − | 2.65953i | −0.128653 | − | 0.355395i | ||||
\(57\) | 11.3501 | + | 11.3501i | 1.50336 | + | 1.50336i | ||||
\(58\) | −0.643014 | + | 4.37213i | −0.0844318 | + | 0.574089i | ||||
\(59\) | − | 12.3297i | − | 1.60518i | −0.596528 | − | 0.802592i | \(-0.703454\pi\) | ||
0.596528 | − | 0.802592i | \(-0.296546\pi\) | |||||||
\(60\) | −7.50026 | + | 9.77221i | −0.968280 | + | 1.26159i | ||||
\(61\) | − | 0.895384i | − | 0.114642i | −0.998356 | − | 0.0573211i | \(-0.981744\pi\) | ||
0.998356 | − | 0.0573211i | \(-0.0182559\pi\) | |||||||
\(62\) | −6.16284 | − | 0.906373i | −0.782681 | − | 0.115110i | ||||
\(63\) | −3.24385 | − | 3.24385i | −0.408687 | − | 0.408687i | ||||
\(64\) | −5.12095 | − | 6.14621i | −0.640118 | − | 0.768276i | ||||
\(65\) | −8.08015 | − | 3.06508i | −1.00222 | − | 0.380176i | ||||
\(66\) | −11.5488 | − | 15.5315i | −1.42156 | − | 1.91180i | ||||
\(67\) | −3.69144 | − | 3.69144i | −0.450981 | − | 0.450981i | 0.444699 | − | 0.895680i | \(-0.353311\pi\) |
−0.895680 | + | 0.444699i | \(0.853311\pi\) | |||||||
\(68\) | −3.35011 | − | 6.23046i | −0.406261 | − | 0.755554i | ||||
\(69\) | 17.5125 | 2.10826 | ||||||||
\(70\) | 2.76204 | + | 1.53986i | 0.330126 | + | 0.184048i | ||||
\(71\) | − | 8.61057i | − | 1.02189i | −0.859614 | − | 0.510943i | \(-0.829296\pi\) | ||
0.859614 | − | 0.510943i | \(-0.170704\pi\) | |||||||
\(72\) | −11.7502 | − | 5.50410i | −1.38477 | − | 0.648665i | ||||
\(73\) | −10.7357 | + | 10.7357i | −1.25652 | + | 1.25652i | −0.303783 | + | 0.952741i | \(0.598250\pi\) |
−0.952741 | + | 0.303783i | \(0.901750\pi\) | |||||||
\(74\) | 1.18363 | + | 1.59181i | 0.137594 | + | 0.185045i | ||||
\(75\) | −0.829546 | − | 13.7477i | −0.0957877 | − | 1.58745i | ||||
\(76\) | 3.35551 | − | 11.1611i | 0.384904 | − | 1.28026i | ||||
\(77\) | −3.51322 | + | 3.51322i | −0.400369 | + | 0.400369i | ||||
\(78\) | 2.19064 | − | 14.8952i | 0.248042 | − | 1.68655i | ||||
\(79\) | −12.8846 | −1.44963 | −0.724817 | − | 0.688941i | \(-0.758076\pi\) | ||||
−0.724817 | + | 0.688941i | \(0.758076\pi\) | |||||||
\(80\) | 8.82822 | + | 1.43614i | 0.987025 | + | 0.160565i | ||||
\(81\) | 1.71732 | 0.190813 | ||||||||
\(82\) | −0.654384 | + | 4.44945i | −0.0722646 | + | 0.491359i | ||||
\(83\) | −3.46917 | + | 3.46917i | −0.380791 | + | 0.380791i | −0.871387 | − | 0.490596i | \(-0.836779\pi\) |
0.490596 | + | 0.871387i | \(0.336779\pi\) | |||||||
\(84\) | −1.58614 | + | 5.27581i | −0.173062 | + | 0.575638i | ||||
\(85\) | 7.39484 | + | 2.80512i | 0.802083 | + | 0.304258i | ||||
\(86\) | −4.79379 | − | 6.44699i | −0.516928 | − | 0.695196i | ||||
\(87\) | 6.08639 | − | 6.08639i | 0.652530 | − | 0.652530i | ||||
\(88\) | −5.96116 | + | 12.7259i | −0.635462 | + | 1.35659i | ||||
\(89\) | − | 4.83422i | − | 0.512426i | −0.966620 | − | 0.256213i | \(-0.917525\pi\) | ||
0.966620 | − | 0.256213i | \(-0.0824749\pi\) | |||||||
\(90\) | 13.9547 | − | 3.96457i | 1.47096 | − | 0.417902i | ||||
\(91\) | −3.86481 | −0.405142 | ||||||||
\(92\) | −6.02173 | − | 11.1991i | −0.627809 | − | 1.16758i | ||||
\(93\) | 8.57920 | + | 8.57920i | 0.889622 | + | 0.889622i | ||||
\(94\) | −3.17114 | − | 4.26475i | −0.327079 | − | 0.439875i | ||||
\(95\) | 5.34688 | + | 11.8826i | 0.548578 | + | 1.21913i | ||||
\(96\) | 0.860905 | + | 15.5582i | 0.0878657 | + | 1.58791i | ||||
\(97\) | −1.03935 | − | 1.03935i | −0.105530 | − | 0.105530i | 0.652370 | − | 0.757901i | \(-0.273775\pi\) |
−0.757901 | + | 0.652370i | \(0.773775\pi\) | |||||||
\(98\) | 1.39916 | + | 0.205776i | 0.141337 | + | 0.0207865i | ||||
\(99\) | 22.7928i | 2.29076i | ||||||||
\(100\) | −8.50628 | + | 5.25768i | −0.850628 | + | 0.525768i | ||||
\(101\) | − | 10.0883i | − | 1.00383i | −0.864918 | − | 0.501914i | \(-0.832629\pi\) | ||
0.864918 | − | 0.501914i | \(-0.167371\pi\) | |||||||
\(102\) | −2.00485 | + | 13.6318i | −0.198509 | + | 1.34975i | ||||
\(103\) | 7.98337 | + | 7.98337i | 0.786625 | + | 0.786625i | 0.980939 | − | 0.194315i | \(-0.0622483\pi\) |
−0.194315 | + | 0.980939i | \(0.562248\pi\) | |||||||
\(104\) | −10.2786 | + | 3.72085i | −1.00790 | + | 0.364860i | ||||
\(105\) | −2.52746 | − | 5.61689i | −0.246655 | − | 0.548152i | ||||
\(106\) | −4.46601 | + | 3.32080i | −0.433777 | + | 0.322544i | ||||
\(107\) | −11.5628 | − | 11.5628i | −1.11782 | − | 1.11782i | −0.992061 | − | 0.125759i | \(-0.959863\pi\) |
−0.125759 | − | 0.992061i | \(-0.540137\pi\) | |||||||
\(108\) | 4.14178 | + | 7.70278i | 0.398543 | + | 0.741200i | ||||
\(109\) | 0.468615 | 0.0448851 | 0.0224426 | − | 0.999748i | \(-0.492856\pi\) | ||||
0.0224426 | + | 0.999748i | \(0.492856\pi\) | |||||||
\(110\) | −4.29379 | − | 15.1135i | −0.409396 | − | 1.44102i | ||||
\(111\) | − | 3.86365i | − | 0.366722i | ||||||
\(112\) | 3.91923 | − | 0.799781i | 0.370332 | − | 0.0755722i | ||||
\(113\) | 6.78744 | − | 6.78744i | 0.638509 | − | 0.638509i | −0.311679 | − | 0.950188i | \(-0.600891\pi\) |
0.950188 | + | 0.311679i | \(0.100891\pi\) | |||||||
\(114\) | −18.2162 | + | 13.5451i | −1.70611 | + | 1.26861i | ||||
\(115\) | 13.2920 | + | 5.04212i | 1.23949 | + | 0.470180i | ||||
\(116\) | −5.98501 | − | 1.79936i | −0.555694 | − | 0.167067i | ||||
\(117\) | −12.5369 | + | 12.5369i | −1.15903 | + | 1.15903i | ||||
\(118\) | 17.2512 | + | 2.53715i | 1.58810 | + | 0.233563i | ||||
\(119\) | 3.53702 | 0.324238 | ||||||||
\(120\) | −12.1295 | − | 12.5050i | −1.10727 | − | 1.14154i | ||||
\(121\) | 13.6855 | 1.24414 | ||||||||
\(122\) | 1.25279 | + | 0.184248i | 0.113422 | + | 0.0166811i | ||||
\(123\) | 6.19402 | − | 6.19402i | 0.558496 | − | 0.558496i | ||||
\(124\) | 2.53633 | − | 8.43630i | 0.227769 | − | 0.757602i | ||||
\(125\) | 3.32855 | − | 10.6734i | 0.297714 | − | 0.954655i | ||||
\(126\) | 5.20619 | − | 3.87117i | 0.463804 | − | 0.344872i | ||||
\(127\) | −10.1884 | + | 10.1884i | −0.904078 | + | 0.904078i | −0.995786 | − | 0.0917079i | \(-0.970767\pi\) |
0.0917079 | + | 0.995786i | \(0.470767\pi\) | |||||||
\(128\) | 9.65332 | − | 5.90029i | 0.853241 | − | 0.521517i | ||||
\(129\) | 15.6481i | 1.37774i | ||||||||
\(130\) | 5.95125 | − | 10.6747i | 0.521959 | − | 0.936236i | ||||
\(131\) | 0.0438076 | 0.00382749 | 0.00191375 | − | 0.999998i | \(-0.499391\pi\) | ||||
0.00191375 | + | 0.999998i | \(0.499391\pi\) | |||||||
\(132\) | 24.1076 | − | 12.9626i | 2.09830 | − | 1.12825i | ||||
\(133\) | 4.12051 | + | 4.12051i | 0.357293 | + | 0.357293i | ||||
\(134\) | 5.92454 | − | 4.40532i | 0.511802 | − | 0.380561i | ||||
\(135\) | −9.14232 | − | 3.46799i | −0.786845 | − | 0.298477i | ||||
\(136\) | 9.40680 | − | 3.40527i | 0.806627 | − | 0.292000i | ||||
\(137\) | 6.76298 | + | 6.76298i | 0.577800 | + | 0.577800i | 0.934297 | − | 0.356496i | \(-0.116029\pi\) |
−0.356496 | + | 0.934297i | \(0.616029\pi\) | |||||||
\(138\) | −3.60365 | + | 24.5028i | −0.306763 | + | 2.08582i | ||||
\(139\) | 1.07689i | 0.0913405i | 0.998957 | + | 0.0456703i | \(0.0145424\pi\) | ||||
−0.998957 | + | 0.0456703i | \(0.985458\pi\) | |||||||
\(140\) | −2.72287 | + | 3.54767i | −0.230125 | + | 0.299833i | ||||
\(141\) | 10.3514i | 0.871746i | ||||||||
\(142\) | 12.0476 | + | 1.77185i | 1.01101 | + | 0.148690i | ||||
\(143\) | 13.5779 | + | 13.5779i | 1.13544 | + | 1.13544i | ||||
\(144\) | 10.1190 | − | 15.3078i | 0.843253 | − | 1.27565i | ||||
\(145\) | 6.37194 | − | 2.86721i | 0.529161 | − | 0.238109i | ||||
\(146\) | −12.8119 | − | 17.2302i | −1.06032 | − | 1.42598i | ||||
\(147\) | −1.94776 | − | 1.94776i | −0.160648 | − | 0.160648i | ||||
\(148\) | −2.47077 | + | 1.32853i | −0.203096 | + | 0.109204i | ||||
\(149\) | −14.5524 | −1.19218 | −0.596091 | − | 0.802917i | \(-0.703280\pi\) | ||||
−0.596091 | + | 0.802917i | \(0.703280\pi\) | |||||||
\(150\) | 19.4060 | + | 1.66828i | 1.58449 | + | 0.136214i | ||||
\(151\) | − | 1.57649i | − | 0.128293i | −0.997940 | − | 0.0641465i | \(-0.979568\pi\) | ||
0.997940 | − | 0.0641465i | \(-0.0204325\pi\) | |||||||
\(152\) | 14.9257 | + | 6.99159i | 1.21063 | + | 0.567092i | ||||
\(153\) | 11.4736 | − | 11.4736i | 0.927583 | − | 0.927583i | ||||
\(154\) | −4.19264 | − | 5.63851i | −0.337852 | − | 0.454364i | ||||
\(155\) | 4.04154 | + | 8.98171i | 0.324624 | + | 0.721428i | ||||
\(156\) | 20.3900 | + | 6.13014i | 1.63250 | + | 0.490804i | ||||
\(157\) | −6.58137 | + | 6.58137i | −0.525251 | + | 0.525251i | −0.919152 | − | 0.393902i | \(-0.871125\pi\) |
0.393902 | + | 0.919152i | \(0.371125\pi\) | |||||||
\(158\) | 2.65135 | − | 18.0277i | 0.210930 | − | 1.43421i | ||||
\(159\) | 10.8399 | 0.859660 | ||||||||
\(160\) | −3.82603 | + | 12.0566i | −0.302474 | + | 0.953158i | ||||
\(161\) | 6.35768 | 0.501055 | ||||||||
\(162\) | −0.353384 | + | 2.40281i | −0.0277644 | + | 0.188783i | ||||
\(163\) | 1.84570 | − | 1.84570i | 0.144566 | − | 0.144566i | −0.631120 | − | 0.775686i | \(-0.717404\pi\) |
0.775686 | + | 0.631120i | \(0.217404\pi\) | |||||||
\(164\) | −6.09084 | − | 1.83118i | −0.475615 | − | 0.142991i | ||||
\(165\) | −10.8539 | + | 28.6129i | −0.844973 | + | 2.22751i | ||||
\(166\) | −4.14006 | − | 5.56781i | −0.321331 | − | 0.432146i | ||||
\(167\) | 6.11009 | − | 6.11009i | 0.472813 | − | 0.472813i | −0.430011 | − | 0.902824i | \(-0.641490\pi\) |
0.902824 | + | 0.430011i | \(0.141490\pi\) | |||||||
\(168\) | −7.05533 | − | 3.30491i | −0.544330 | − | 0.254979i | ||||
\(169\) | 1.93672i | 0.148979i | ||||||||
\(170\) | −5.44650 | + | 9.76936i | −0.417727 | + | 0.749276i | ||||
\(171\) | 26.7327 | 2.04430 | ||||||||
\(172\) | 10.0068 | − | 5.38066i | 0.763014 | − | 0.410272i | ||||
\(173\) | −9.08117 | − | 9.08117i | −0.690429 | − | 0.690429i | 0.271898 | − | 0.962326i | \(-0.412349\pi\) |
−0.962326 | + | 0.271898i | \(0.912349\pi\) | |||||||
\(174\) | 7.26342 | + | 9.76828i | 0.550638 | + | 0.740532i | ||||
\(175\) | −0.301156 | − | 4.99092i | −0.0227652 | − | 0.377278i | ||||
\(176\) | −16.5789 | − | 10.9593i | −1.24968 | − | 0.826090i | ||||
\(177\) | −24.0152 | − | 24.0152i | −1.80509 | − | 1.80509i | ||||
\(178\) | 6.76386 | + | 0.994766i | 0.506972 | + | 0.0745609i | ||||
\(179\) | 9.51295i | 0.711031i | 0.934670 | + | 0.355515i | \(0.115695\pi\) | ||||
−0.934670 | + | 0.355515i | \(0.884305\pi\) | |||||||
\(180\) | 2.67553 | + | 20.3407i | 0.199422 | + | 1.51611i | ||||
\(181\) | 6.48964i | 0.482371i | 0.970479 | + | 0.241186i | \(0.0775363\pi\) | ||||
−0.970479 | + | 0.241186i | \(0.922464\pi\) | |||||||
\(182\) | 0.795284 | − | 5.40749i | 0.0589504 | − | 0.400830i | ||||
\(183\) | −1.74399 | − | 1.74399i | −0.128919 | − | 0.128919i | ||||
\(184\) | 16.9085 | − | 6.12088i | 1.24651 | − | 0.451237i | ||||
\(185\) | 1.11241 | − | 2.93252i | 0.0817857 | − | 0.215603i | ||||
\(186\) | −13.7691 | + | 10.2383i | −1.00960 | + | 0.750709i | ||||
\(187\) | −12.4263 | − | 12.4263i | −0.908703 | − | 0.908703i | ||||
\(188\) | 6.61962 | − | 3.55936i | 0.482785 | − | 0.259593i | ||||
\(189\) | −4.37285 | −0.318078 | ||||||||
\(190\) | −17.7260 | + | 5.03599i | −1.28598 | + | 0.365349i | ||||
\(191\) | 11.9275i | 0.863045i | 0.902102 | + | 0.431522i | \(0.142023\pi\) | ||||
−0.902102 | + | 0.431522i | \(0.857977\pi\) | |||||||
\(192\) | −21.9457 | − | 1.99697i | −1.58379 | − | 0.144119i | ||||
\(193\) | −6.20681 | + | 6.20681i | −0.446776 | + | 0.446776i | −0.894281 | − | 0.447505i | \(-0.852313\pi\) |
0.447505 | + | 0.894281i | \(0.352313\pi\) | |||||||
\(194\) | 1.66810 | − | 1.24035i | 0.119763 | − | 0.0890520i | ||||
\(195\) | −21.7082 | + | 9.76814i | −1.55456 | + | 0.699511i | ||||
\(196\) | −0.575828 | + | 1.91531i | −0.0411306 | + | 0.136808i | ||||
\(197\) | 7.70090 | − | 7.70090i | 0.548667 | − | 0.548667i | −0.377388 | − | 0.926055i | \(-0.623178\pi\) |
0.926055 | + | 0.377388i | \(0.123178\pi\) | |||||||
\(198\) | −31.8908 | − | 4.69021i | −2.26638 | − | 0.333319i | ||||
\(199\) | −3.04511 | −0.215862 | −0.107931 | − | 0.994158i | \(-0.534423\pi\) | ||||
−0.107931 | + | 0.994158i | \(0.534423\pi\) | |||||||
\(200\) | −5.60596 | − | 12.9836i | −0.396401 | − | 0.918077i | ||||
\(201\) | −14.3800 | −1.01429 | ||||||||
\(202\) | 14.1152 | + | 2.07594i | 0.993144 | + | 0.146063i | ||||
\(203\) | 2.20958 | − | 2.20958i | 0.155082 | − | 0.155082i | ||||
\(204\) | −18.6606 | − | 5.61021i | −1.30650 | − | 0.392794i | ||||
\(205\) | 6.48462 | − | 2.91791i | 0.452905 | − | 0.203796i | ||||
\(206\) | −12.8128 | + | 9.52724i | −0.892711 | + | 0.663795i | ||||
\(207\) | 20.6234 | − | 20.6234i | 1.43343 | − | 1.43343i | ||||
\(208\) | −3.09100 | − | 15.1471i | −0.214322 | − | 1.05026i | ||||
\(209\) | − | 28.9525i | − | 2.00269i | ||||||
\(210\) | 8.37904 | − | 2.38050i | 0.578208 | − | 0.164270i | ||||
\(211\) | 27.8859 | 1.91974 | 0.959872 | − | 0.280438i | \(-0.0904796\pi\) | ||||
0.959872 | + | 0.280438i | \(0.0904796\pi\) | |||||||
\(212\) | −3.72734 | − | 6.93201i | −0.255994 | − | 0.476092i | ||||
\(213\) | −16.7713 | − | 16.7713i | −1.14915 | − | 1.14915i | ||||
\(214\) | 18.5576 | − | 13.7989i | 1.26857 | − | 0.943274i | ||||
\(215\) | −4.50534 | + | 11.8770i | −0.307262 | + | 0.810002i | ||||
\(216\) | −11.6297 | + | 4.20997i | −0.791302 | + | 0.286452i | ||||
\(217\) | 3.11456 | + | 3.11456i | 0.211430 | + | 0.211430i | ||||
\(218\) | −0.0964297 | + | 0.655668i | −0.00653104 | + | 0.0444075i | ||||
\(219\) | 41.8212i | 2.82602i | ||||||||
\(220\) | 22.0298 | − | 2.89771i | 1.48525 | − | 0.195363i | ||||
\(221\) | − | 13.6699i | − | 0.919535i | ||||||
\(222\) | 5.40588 | + | 0.795048i | 0.362819 | + | 0.0533601i | ||||
\(223\) | −18.3863 | − | 18.3863i | −1.23124 | − | 1.23124i | −0.963489 | − | 0.267748i | \(-0.913720\pi\) |
−0.267748 | − | 0.963489i | \(-0.586280\pi\) | |||||||
\(224\) | 0.312540 | + | 5.64821i | 0.0208825 | + | 0.377387i | ||||
\(225\) | −17.1667 | − | 15.2129i | −1.14445 | − | 1.01419i | ||||
\(226\) | 8.10004 | + | 10.8934i | 0.538807 | + | 0.724620i | ||||
\(227\) | −3.32486 | − | 3.32486i | −0.220679 | − | 0.220679i | 0.588105 | − | 0.808784i | \(-0.299874\pi\) |
−0.808784 | + | 0.588105i | \(0.799874\pi\) | |||||||
\(228\) | −15.2033 | − | 28.2747i | −1.00686 | − | 1.87254i | ||||
\(229\) | −25.5653 | −1.68940 | −0.844700 | − | 0.535239i | \(-0.820221\pi\) | ||||
−0.844700 | + | 0.535239i | \(0.820221\pi\) | |||||||
\(230\) | −9.78992 | + | 17.5601i | −0.645528 | + | 1.15788i | ||||
\(231\) | 13.6858i | 0.900460i | ||||||||
\(232\) | 3.74917 | − | 8.00374i | 0.246145 | − | 0.525471i | ||||
\(233\) | −6.72310 | + | 6.72310i | −0.440445 | + | 0.440445i | −0.892162 | − | 0.451716i | \(-0.850812\pi\) |
0.451716 | + | 0.892162i | \(0.350812\pi\) | |||||||
\(234\) | −14.9613 | − | 20.1209i | −0.978053 | − | 1.31534i | ||||
\(235\) | −2.98033 | + | 7.85673i | −0.194415 | + | 0.512517i | ||||
\(236\) | −7.09977 | + | 23.6151i | −0.462155 | + | 1.53721i | ||||
\(237\) | −25.0961 | + | 25.0961i | −1.63017 | + | 1.63017i | ||||
\(238\) | −0.727833 | + | 4.94886i | −0.0471784 | + | 0.320787i | ||||
\(239\) | 17.8417 | 1.15408 | 0.577040 | − | 0.816716i | \(-0.304208\pi\) | ||||
0.577040 | + | 0.816716i | \(0.304208\pi\) | |||||||
\(240\) | 19.9925 | − | 14.3980i | 1.29051 | − | 0.929385i | ||||
\(241\) | −19.5797 | −1.26124 | −0.630619 | − | 0.776093i | \(-0.717199\pi\) | ||||
−0.630619 | + | 0.776093i | \(0.717199\pi\) | |||||||
\(242\) | −2.81615 | + | 19.1482i | −0.181029 | + | 1.23089i | ||||
\(243\) | 12.6211 | − | 12.6211i | 0.809646 | − | 0.809646i | ||||
\(244\) | −0.515587 | + | 1.71494i | −0.0330071 | + | 0.109788i | ||||
\(245\) | −0.917560 | − | 2.03914i | −0.0586208 | − | 0.130276i | ||||
\(246\) | 7.39186 | + | 9.94102i | 0.471287 | + | 0.633816i | ||||
\(247\) | 15.9250 | − | 15.9250i | 1.01328 | − | 1.01328i | ||||
\(248\) | 11.2818 | + | 5.28472i | 0.716398 | + | 0.335580i | ||||
\(249\) | 13.5142i | 0.856427i | ||||||||
\(250\) | 14.2488 | + | 6.85351i | 0.901176 | + | 0.433454i | ||||
\(251\) | −1.98920 | −0.125557 | −0.0627785 | − | 0.998027i | \(-0.519996\pi\) | ||||
−0.0627785 | + | 0.998027i | \(0.519996\pi\) | |||||||
\(252\) | 4.34509 | + | 8.08090i | 0.273715 | + | 0.509049i | ||||
\(253\) | −22.3360 | − | 22.3360i | −1.40425 | − | 1.40425i | ||||
\(254\) | −12.1588 | − | 16.3518i | −0.762908 | − | 1.02600i | ||||
\(255\) | 19.8670 | − | 8.93966i | 1.24412 | − | 0.559823i | ||||
\(256\) | 6.26905 | + | 14.7207i | 0.391815 | + | 0.920044i | ||||
\(257\) | −0.798299 | − | 0.798299i | −0.0497965 | − | 0.0497965i | 0.681770 | − | 0.731567i | \(-0.261210\pi\) |
−0.731567 | + | 0.681770i | \(0.761210\pi\) | |||||||
\(258\) | −21.8943 | − | 3.22001i | −1.36308 | − | 0.200469i | ||||
\(259\) | − | 1.40265i | − | 0.0871563i | ||||||
\(260\) | 13.7111 | + | 10.5234i | 0.850324 | + | 0.652632i | ||||
\(261\) | − | 14.3351i | − | 0.887323i | ||||||
\(262\) | −0.00901456 | + | 0.0612940i | −0.000556922 | + | 0.00378676i | ||||
\(263\) | 18.0156 | + | 18.0156i | 1.11089 | + | 1.11089i | 0.993030 | + | 0.117859i | \(0.0376032\pi\) |
0.117859 | + | 0.993030i | \(0.462397\pi\) | |||||||
\(264\) | 13.1761 | + | 36.3978i | 0.810930 | + | 2.24013i | ||||
\(265\) | 8.22750 | + | 3.12097i | 0.505411 | + | 0.191720i | ||||
\(266\) | −6.61316 | + | 4.91736i | −0.405479 | + | 0.301503i | ||||
\(267\) | −9.41587 | − | 9.41587i | −0.576242 | − | 0.576242i | ||||
\(268\) | 4.94463 | + | 9.19590i | 0.302041 | + | 0.561729i | ||||
\(269\) | 27.3056 | 1.66485 | 0.832427 | − | 0.554134i | \(-0.186951\pi\) | ||||
0.832427 | + | 0.554134i | \(0.186951\pi\) | |||||||
\(270\) | 6.73356 | − | 12.0780i | 0.409791 | − | 0.735041i | ||||
\(271\) | − | 22.1942i | − | 1.34820i | −0.738640 | − | 0.674100i | \(-0.764532\pi\) | ||
0.738640 | − | 0.674100i | \(-0.235468\pi\) | |||||||
\(272\) | 2.82884 | + | 13.8624i | 0.171523 | + | 0.840530i | ||||
\(273\) | −7.52770 | + | 7.52770i | −0.455597 | + | 0.455597i | ||||
\(274\) | −10.8542 | + | 8.07085i | −0.655724 | + | 0.487578i | ||||
\(275\) | −16.4762 | + | 18.5923i | −0.993552 | + | 1.12116i | ||||
\(276\) | −33.5419 | − | 10.0842i | −2.01899 | − | 0.606997i | ||||
\(277\) | 14.8136 | − | 14.8136i | 0.890064 | − | 0.890064i | −0.104464 | − | 0.994529i | \(-0.533313\pi\) |
0.994529 | + | 0.104464i | \(0.0333128\pi\) | |||||||
\(278\) | −1.50674 | − | 0.221598i | −0.0903684 | − | 0.0132906i | ||||
\(279\) | 20.2064 | 1.20973 | ||||||||
\(280\) | −4.40347 | − | 4.53977i | −0.263158 | − | 0.271303i | ||||
\(281\) | 20.8354 | 1.24294 | 0.621469 | − | 0.783439i | \(-0.286536\pi\) | ||||
0.621469 | + | 0.783439i | \(0.286536\pi\) | |||||||
\(282\) | −14.4833 | − | 2.13007i | −0.862468 | − | 0.126844i | ||||
\(283\) | −8.07810 | + | 8.07810i | −0.480193 | + | 0.480193i | −0.905193 | − | 0.425000i | \(-0.860274\pi\) |
0.425000 | + | 0.905193i | \(0.360274\pi\) | |||||||
\(284\) | −4.95821 | + | 16.4919i | −0.294216 | + | 0.978616i | ||||
\(285\) | 33.5589 | + | 12.7300i | 1.98786 | + | 0.754062i | ||||
\(286\) | −21.7917 | + | 16.2037i | −1.28857 | + | 0.958146i | ||||
\(287\) | 2.24866 | − | 2.24866i | 0.132734 | − | 0.132734i | ||||
\(288\) | 19.3358 | + | 17.3082i | 1.13937 | + | 1.01989i | ||||
\(289\) | − | 4.48952i | − | 0.264090i | ||||||
\(290\) | 2.70050 | + | 9.50539i | 0.158579 | + | 0.558176i | ||||
\(291\) | −4.04881 | −0.237346 | ||||||||
\(292\) | 26.7443 | − | 14.3804i | 1.56509 | − | 0.841547i | ||||
\(293\) | 9.50152 | + | 9.50152i | 0.555085 | + | 0.555085i | 0.927904 | − | 0.372819i | \(-0.121609\pi\) |
−0.372819 | + | 0.927904i | \(0.621609\pi\) | |||||||
\(294\) | 3.12603 | − | 2.32443i | 0.182314 | − | 0.135563i | ||||
\(295\) | −11.3132 | − | 25.1419i | −0.658680 | − | 1.46382i | ||||
\(296\) | −1.35040 | − | 3.73039i | −0.0784907 | − | 0.216824i | ||||
\(297\) | 15.3628 | + | 15.3628i | 0.891440 | + | 0.891440i | ||||
\(298\) | 2.99454 | − | 20.3612i | 0.173469 | − | 1.17949i | ||||
\(299\) | − | 24.5712i | − | 1.42099i | ||||||
\(300\) | −6.32748 | + | 26.8088i | −0.365317 | + | 1.54781i | ||||
\(301\) | 5.68085i | 0.327439i | ||||||||
\(302\) | 2.20577 | + | 0.324404i | 0.126928 | + | 0.0186674i | ||||
\(303\) | −19.6496 | − | 19.6496i | −1.12884 | − | 1.12884i | ||||
\(304\) | −12.8537 | + | 19.4447i | −0.737211 | + | 1.11523i | ||||
\(305\) | −0.821568 | − | 1.82581i | −0.0470429 | − | 0.104546i | ||||
\(306\) | 13.6924 | + | 18.4144i | 0.782742 | + | 1.05268i | ||||
\(307\) | 11.5575 | + | 11.5575i | 0.659621 | + | 0.659621i | 0.955290 | − | 0.295669i | \(-0.0955426\pi\) |
−0.295669 | + | 0.955290i | \(0.595543\pi\) | |||||||
\(308\) | 8.75194 | − | 4.70591i | 0.498688 | − | 0.268144i | ||||
\(309\) | 31.0993 | 1.76918 | ||||||||
\(310\) | −13.3985 | + | 3.80655i | −0.760985 | + | 0.216198i | ||||
\(311\) | − | 1.48399i | − | 0.0841492i | −0.999114 | − | 0.0420746i | \(-0.986603\pi\) | ||
0.999114 | − | 0.0420746i | \(-0.0133967\pi\) | |||||||
\(312\) | −12.7728 | + | 27.2675i | −0.723119 | + | 1.54372i | ||||
\(313\) | 2.82706 | − | 2.82706i | 0.159795 | − | 0.159795i | −0.622681 | − | 0.782476i | \(-0.713957\pi\) |
0.782476 | + | 0.622681i | \(0.213957\pi\) | |||||||
\(314\) | −7.85412 | − | 10.5627i | −0.443234 | − | 0.596088i | ||||
\(315\) | −9.59110 | − | 3.63823i | −0.540397 | − | 0.204991i | ||||
\(316\) | 24.6781 | + | 7.41933i | 1.38825 | + | 0.417370i | ||||
\(317\) | 9.79459 | − | 9.79459i | 0.550119 | − | 0.550119i | −0.376356 | − | 0.926475i | \(-0.622823\pi\) |
0.926475 | + | 0.376356i | \(0.122823\pi\) | |||||||
\(318\) | −2.23059 | + | 15.1668i | −0.125085 | + | 0.850511i | ||||
\(319\) | −15.5255 | −0.869262 | ||||||||
\(320\) | −16.0818 | − | 7.83420i | −0.899002 | − | 0.437945i | ||||
\(321\) | −45.0431 | −2.51406 | ||||||||
\(322\) | −1.30826 | + | 8.89543i | −0.0729064 | + | 0.495723i | ||||
\(323\) | −14.5743 | + | 14.5743i | −0.810936 | + | 0.810936i | ||||
\(324\) | −3.28921 | − | 0.988882i | −0.182734 | − | 0.0549379i | ||||
\(325\) | −19.2889 | + | 1.16391i | −1.06996 | + | 0.0645620i | ||||
\(326\) | 2.20263 | + | 2.96223i | 0.121992 | + | 0.164063i | ||||
\(327\) | 0.912747 | − | 0.912747i | 0.0504750 | − | 0.0504750i | ||||
\(328\) | 3.81547 | − | 8.14527i | 0.210674 | − | 0.449747i | ||||
\(329\) | 3.75794i | 0.207182i | ||||||||
\(330\) | −37.8007 | − | 21.0742i | −2.08086 | − | 1.16010i | ||||
\(331\) | −11.5472 | −0.634691 | −0.317345 | − | 0.948310i | \(-0.602791\pi\) | ||||
−0.317345 | + | 0.948310i | \(0.602791\pi\) | |||||||
\(332\) | 8.64219 | − | 4.64690i | 0.474302 | − | 0.255032i | ||||
\(333\) | −4.54999 | − | 4.54999i | −0.249338 | − | 0.249338i | ||||
\(334\) | 7.29170 | + | 9.80632i | 0.398984 | + | 0.536578i | ||||
\(335\) | −10.9145 | − | 4.14024i | −0.596322 | − | 0.226205i | ||||
\(336\) | 6.07592 | − | 9.19148i | 0.331469 | − | 0.501436i | ||||
\(337\) | 11.2187 | + | 11.2187i | 0.611120 | + | 0.611120i | 0.943238 | − | 0.332118i | \(-0.107763\pi\) |
−0.332118 | + | 0.943238i | \(0.607763\pi\) | |||||||
\(338\) | −2.70979 | − | 0.398531i | −0.147393 | − | 0.0216772i | ||||
\(339\) | − | 26.4406i | − | 1.43605i | ||||||
\(340\) | −12.5482 | − | 9.63084i | −0.680520 | − | 0.522305i | ||||
\(341\) | − | 21.8843i | − | 1.18510i | ||||||
\(342\) | −5.50094 | + | 37.4033i | −0.297457 | + | 2.02254i | ||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 5.46926 | + | 15.1084i | 0.294883 | + | 0.814590i | ||||
\(345\) | 35.7104 | − | 16.0688i | 1.92258 | − | 0.865114i | ||||
\(346\) | 14.5747 | − | 10.8373i | 0.783542 | − | 0.582619i | ||||
\(347\) | 14.3007 | + | 14.3007i | 0.767704 | + | 0.767704i | 0.977702 | − | 0.209998i | \(-0.0673458\pi\) |
−0.209998 | + | 0.977702i | \(0.567346\pi\) | |||||||
\(348\) | −15.1621 | + | 8.15262i | −0.812771 | + | 0.437026i | ||||
\(349\) | −16.4479 | −0.880435 | −0.440217 | − | 0.897891i | \(-0.645099\pi\) | ||||
−0.440217 | + | 0.897891i | \(0.645099\pi\) | |||||||
\(350\) | 7.04508 | + | 0.605647i | 0.376576 | + | 0.0323732i | ||||
\(351\) | 16.9002i | 0.902066i | ||||||||
\(352\) | 18.7454 | − | 20.9415i | 0.999134 | − | 1.11618i | ||||
\(353\) | −4.81028 | + | 4.81028i | −0.256025 | + | 0.256025i | −0.823435 | − | 0.567410i | \(-0.807945\pi\) |
0.567410 | + | 0.823435i | \(0.307945\pi\) | |||||||
\(354\) | 38.5429 | − | 28.6594i | 2.04853 | − | 1.52323i | ||||
\(355\) | −7.90072 | − | 17.5581i | −0.419327 | − | 0.931889i | ||||
\(356\) | −2.78368 | + | 9.25904i | −0.147535 | + | 0.490728i | ||||
\(357\) | 6.88924 | − | 6.88924i | 0.364617 | − | 0.364617i | ||||
\(358\) | −13.3102 | − | 1.95754i | −0.703464 | − | 0.103459i | ||||
\(359\) | −14.3081 | −0.755153 | −0.377576 | − | 0.925978i | \(-0.623242\pi\) | ||||
−0.377576 | + | 0.925978i | \(0.623242\pi\) | |||||||
\(360\) | −29.0106 | − | 0.442133i | −1.52899 | − | 0.0233025i | ||||
\(361\) | −14.9572 | −0.787219 | ||||||||
\(362\) | −9.08007 | − | 1.33541i | −0.477238 | − | 0.0701878i | ||||
\(363\) | 26.6560 | − | 26.6560i | 1.39908 | − | 1.39908i | ||||
\(364\) | 7.40231 | + | 2.22546i | 0.387986 | + | 0.116646i | ||||
\(365\) | −12.0410 | + | 31.7424i | −0.630253 | + | 1.66147i | ||||
\(366\) | 2.79899 | − | 2.08125i | 0.146306 | − | 0.108789i | ||||
\(367\) | −9.01109 | + | 9.01109i | −0.470375 | + | 0.470375i | −0.902036 | − | 0.431661i | \(-0.857928\pi\) |
0.431661 | + | 0.902036i | \(0.357928\pi\) | |||||||
\(368\) | 5.08475 | + | 24.9172i | 0.265061 | + | 1.29890i | ||||
\(369\) | − | 14.5886i | − | 0.759453i | ||||||
\(370\) | 3.87416 | + | 2.15988i | 0.201408 | + | 0.112287i | ||||
\(371\) | 3.93528 | 0.204310 | ||||||||
\(372\) | −11.4917 | − | 21.3720i | −0.595817 | − | 1.10809i | ||||
\(373\) | 19.1338 | + | 19.1338i | 0.990713 | + | 0.990713i | 0.999957 | − | 0.00924424i | \(-0.00294258\pi\) |
−0.00924424 | + | 0.999957i | \(0.502943\pi\) | |||||||
\(374\) | 19.9435 | − | 14.8294i | 1.03125 | − | 0.766811i | ||||
\(375\) | −14.3059 | − | 27.2723i | −0.738754 | − | 1.40834i | ||||
\(376\) | 3.61797 | + | 9.99436i | 0.186583 | + | 0.515420i | ||||
\(377\) | −8.53961 | − | 8.53961i | −0.439812 | − | 0.439812i | ||||
\(378\) | 0.899827 | − | 6.11832i | 0.0462821 | − | 0.314693i | ||||
\(379\) | − | 9.38553i | − | 0.482102i | −0.970512 | − | 0.241051i | \(-0.922508\pi\) | ||
0.970512 | − | 0.241051i | \(-0.0774921\pi\) | |||||||
\(380\) | −3.39859 | − | 25.8378i | −0.174344 | − | 1.32545i | ||||
\(381\) | 39.6892i | 2.03334i | ||||||||
\(382\) | −16.6885 | − | 2.45440i | −0.853860 | − | 0.125578i | ||||
\(383\) | −23.3553 | − | 23.3553i | −1.19340 | − | 1.19340i | −0.976107 | − | 0.217291i | \(-0.930278\pi\) |
−0.217291 | − | 0.976107i | \(-0.569722\pi\) | |||||||
\(384\) | 7.30998 | − | 30.2946i | 0.373036 | − | 1.54597i | ||||
\(385\) | −3.94035 | + | 10.3875i | −0.200819 | + | 0.529398i | ||||
\(386\) | −7.40712 | − | 9.96155i | −0.377013 | − | 0.507029i | ||||
\(387\) | 18.4279 | + | 18.4279i | 0.936740 | + | 0.936740i | ||||
\(388\) | 1.39220 | + | 2.58918i | 0.0706781 | + | 0.131445i | ||||
\(389\) | −24.7781 | −1.25630 | −0.628150 | − | 0.778092i | \(-0.716188\pi\) | ||||
−0.628150 | + | 0.778092i | \(0.716188\pi\) | |||||||
\(390\) | −9.20019 | − | 32.3833i | −0.465870 | − | 1.63979i | ||||
\(391\) | 22.4872i | 1.13723i | ||||||||
\(392\) | −2.56134 | − | 1.19980i | −0.129367 | − | 0.0605992i | ||||
\(393\) | 0.0853266 | − | 0.0853266i | 0.00430416 | − | 0.00430416i | ||||
\(394\) | 9.19015 | + | 12.3595i | 0.462993 | + | 0.622661i | ||||
\(395\) | −26.2735 | + | 11.8224i | −1.32196 | + | 0.594851i | ||||
\(396\) | 13.1247 | − | 43.6553i | 0.659543 | − | 2.19376i | ||||
\(397\) | 1.32585 | − | 1.32585i | 0.0665427 | − | 0.0665427i | −0.673052 | − | 0.739595i | \(-0.735017\pi\) |
0.739595 | + | 0.673052i | \(0.235017\pi\) | |||||||
\(398\) | 0.626610 | − | 4.26060i | 0.0314091 | − | 0.213565i | ||||
\(399\) | 16.0515 | 0.803579 | ||||||||
\(400\) | 19.3197 | − | 5.17194i | 0.965985 | − | 0.258597i | ||||
\(401\) | 7.01726 | 0.350425 | 0.175213 | − | 0.984531i | \(-0.443939\pi\) | ||||
0.175213 | + | 0.984531i | \(0.443939\pi\) | |||||||
\(402\) | 2.95907 | − | 20.1200i | 0.147585 | − | 1.00350i | ||||
\(403\) | 12.0372 | − | 12.0372i | 0.599615 | − | 0.599615i | ||||
\(404\) | −5.80915 | + | 19.3223i | −0.289016 | + | 0.961322i | ||||
\(405\) | 3.50185 | − | 1.57575i | 0.174009 | − | 0.0782994i | ||||
\(406\) | 2.63689 | + | 3.54625i | 0.130867 | + | 0.175997i | ||||
\(407\) | −4.92782 | + | 4.92782i | −0.244263 | + | 0.244263i | ||||
\(408\) | 11.6895 | − | 24.9548i | 0.578717 | − | 1.23545i | ||||
\(409\) | 8.59601i | 0.425046i | 0.977156 | + | 0.212523i | \(0.0681680\pi\) | ||||
−0.977156 | + | 0.212523i | \(0.931832\pi\) | |||||||
\(410\) | 2.74826 | + | 9.67347i | 0.135727 | + | 0.477739i | ||||
\(411\) | 26.3453 | 1.29952 | ||||||||
\(412\) | −10.6936 | − | 19.8877i | −0.526836 | − | 0.979796i | ||||
\(413\) | −8.71838 | − | 8.71838i | −0.429004 | − | 0.429004i | ||||
\(414\) | 24.6117 | + | 33.0993i | 1.20960 | + | 1.62674i | ||||
\(415\) | −3.89094 | + | 10.2573i | −0.190999 | + | 0.503511i | ||||
\(416\) | 21.8292 | − | 1.20791i | 1.07027 | − | 0.0592225i | ||||
\(417\) | 2.09752 | + | 2.09752i | 0.102716 | + | 0.102716i | ||||
\(418\) | 40.5093 | + | 5.95774i | 1.98138 | + | 0.291403i | ||||
\(419\) | − | 2.83105i | − | 0.138306i | −0.997606 | − | 0.0691530i | \(-0.977970\pi\) | ||
0.997606 | − | 0.0691530i | \(-0.0220297\pi\) | |||||||
\(420\) | 1.60651 | + | 12.2135i | 0.0783896 | + | 0.595957i | ||||
\(421\) | − | 8.77852i | − | 0.427839i | −0.976851 | − | 0.213920i | \(-0.931377\pi\) | ||
0.976851 | − | 0.213920i | \(-0.0686230\pi\) | |||||||
\(422\) | −5.73825 | + | 39.0169i | −0.279334 | + | 1.89931i | ||||
\(423\) | 12.1902 | + | 12.1902i | 0.592708 | + | 0.592708i | ||||
\(424\) | 10.4660 | − | 3.78871i | 0.508274 | − | 0.183996i | ||||
\(425\) | 17.6530 | − | 1.06519i | 0.856295 | − | 0.0516694i | ||||
\(426\) | 26.9169 | − | 20.0146i | 1.30413 | − | 0.969712i | ||||
\(427\) | −0.633132 | − | 0.633132i | −0.0306394 | − | 0.0306394i | ||||
\(428\) | 15.4882 | + | 28.8046i | 0.748651 | + | 1.39232i | ||||
\(429\) | 52.8930 | 2.55370 | ||||||||
\(430\) | −15.6907 | − | 8.74770i | −0.756673 | − | 0.421851i | ||||
\(431\) | − | 10.2783i | − | 0.495086i | −0.968877 | − | 0.247543i | \(-0.920377\pi\) | ||
0.968877 | − | 0.247543i | \(-0.0796232\pi\) | |||||||
\(432\) | −3.49732 | − | 17.1382i | −0.168265 | − | 0.824561i | ||||
\(433\) | −5.26399 | + | 5.26399i | −0.252971 | + | 0.252971i | −0.822188 | − | 0.569216i | \(-0.807247\pi\) |
0.569216 | + | 0.822188i | \(0.307247\pi\) | |||||||
\(434\) | −4.99869 | + | 3.71688i | −0.239945 | + | 0.178416i | ||||
\(435\) | 6.82636 | − | 17.9956i | 0.327299 | − | 0.862824i | ||||
\(436\) | −0.897543 | − | 0.269842i | −0.0429845 | − | 0.0129231i | ||||
\(437\) | −26.1969 | + | 26.1969i | −1.25317 | + | 1.25317i | ||||
\(438\) | −58.5147 | − | 8.60581i | −2.79594 | − | 0.411201i | ||||
\(439\) | 13.1390 | 0.627092 | 0.313546 | − | 0.949573i | \(-0.398483\pi\) | ||||
0.313546 | + | 0.949573i | \(0.398483\pi\) | |||||||
\(440\) | −0.478848 | + | 31.4196i | −0.0228282 | + | 1.49787i | ||||
\(441\) | −4.58750 | −0.218453 | ||||||||
\(442\) | 19.1264 | + | 2.81293i | 0.909749 | + | 0.133798i | ||||
\(443\) | −12.0683 | + | 12.0683i | −0.573383 | + | 0.573383i | −0.933072 | − | 0.359689i | \(-0.882883\pi\) |
0.359689 | + | 0.933072i | \(0.382883\pi\) | |||||||
\(444\) | −2.22480 | + | 7.40011i | −0.105584 | + | 0.351193i | ||||
\(445\) | −4.43569 | − | 9.85764i | −0.210272 | − | 0.467297i | ||||
\(446\) | 29.5089 | − | 21.9420i | 1.39729 | − | 1.03898i | ||||
\(447\) | −28.3446 | + | 28.3446i | −1.34065 | + | 1.34065i | ||||
\(448\) | −7.96708 | − | 0.724973i | −0.376409 | − | 0.0342517i | ||||
\(449\) | 32.4383i | 1.53086i | 0.643520 | + | 0.765429i | \(0.277473\pi\) | ||||
−0.643520 | + | 0.765429i | \(0.722527\pi\) | |||||||
\(450\) | 24.8179 | − | 20.8886i | 1.16993 | − | 0.984698i | ||||
\(451\) | −15.8001 | −0.743996 | ||||||||
\(452\) | −16.9085 | + | 9.09167i | −0.795308 | + | 0.427636i | ||||
\(453\) | −3.07062 | − | 3.07062i | −0.144270 | − | 0.144270i | ||||
\(454\) | 5.33620 | − | 3.96785i | 0.250440 | − | 0.186220i | ||||
\(455\) | −7.88087 | + | 3.54619i | −0.369461 | + | 0.166248i | ||||
\(456\) | 42.6894 | − | 15.4536i | 1.99912 | − | 0.723682i | ||||
\(457\) | 2.77670 | + | 2.77670i | 0.129888 | + | 0.129888i | 0.769062 | − | 0.639174i | \(-0.220724\pi\) |
−0.639174 | + | 0.769062i | \(0.720724\pi\) | |||||||
\(458\) | 5.26072 | − | 35.7700i | 0.245817 | − | 1.67142i | ||||
\(459\) | − | 15.4668i | − | 0.721929i | ||||||
\(460\) | −22.5550 | − | 17.3111i | −1.05163 | − | 0.807137i | ||||
\(461\) | − | 11.4770i | − | 0.534535i | −0.963622 | − | 0.267267i | \(-0.913879\pi\) | ||
0.963622 | − | 0.267267i | \(-0.0861207\pi\) | |||||||
\(462\) | −19.1487 | − | 2.81621i | −0.890877 | − | 0.131022i | ||||
\(463\) | 16.7196 | + | 16.7196i | 0.777027 | + | 0.777027i | 0.979324 | − | 0.202297i | \(-0.0648407\pi\) |
−0.202297 | + | 0.979324i | \(0.564841\pi\) | |||||||
\(464\) | 10.4270 | + | 6.89268i | 0.484063 | + | 0.319985i | ||||
\(465\) | 25.3661 | + | 9.62224i | 1.17632 | + | 0.446221i | ||||
\(466\) | −8.02326 | − | 10.7902i | −0.371670 | − | 0.499845i | ||||
\(467\) | 9.99558 | + | 9.99558i | 0.462540 | + | 0.462540i | 0.899487 | − | 0.436947i | \(-0.143940\pi\) |
−0.436947 | + | 0.899487i | \(0.643940\pi\) | |||||||
\(468\) | 31.2311 | − | 16.7929i | 1.44366 | − | 0.776254i | ||||
\(469\) | −5.22049 | −0.241060 | ||||||||
\(470\) | −10.3796 | − | 5.78669i | −0.478774 | − | 0.266920i | ||||
\(471\) | 25.6378i | 1.18133i | ||||||||
\(472\) | −31.5805 | − | 14.7932i | −1.45361 | − | 0.680910i | ||||
\(473\) | 19.9581 | − | 19.9581i | 0.917674 | − | 0.917674i | ||||
\(474\) | −29.9494 | − | 40.2777i | −1.37562 | − | 1.85002i | ||||
\(475\) | 21.8060 | + | 19.3242i | 1.00053 | + | 0.886656i | ||||
\(476\) | −6.77449 | − | 2.03671i | −0.310508 | − | 0.0933526i | ||||
\(477\) | 12.7655 | − | 12.7655i | 0.584491 | − | 0.584491i | ||||
\(478\) | −3.67138 | + | 24.9634i | −0.167925 | + | 1.14180i | ||||
\(479\) | 3.47313 | 0.158691 | 0.0793457 | − | 0.996847i | \(-0.474717\pi\) | ||||
0.0793457 | + | 0.996847i | \(0.474717\pi\) | |||||||
\(480\) | 16.0311 | + | 30.9355i | 0.731718 | + | 1.41200i | ||||
\(481\) | −5.42096 | −0.247175 | ||||||||
\(482\) | 4.02903 | − | 27.3952i | 0.183517 | − | 1.24782i | ||||
\(483\) | 12.3832 | − | 12.3832i | 0.563456 | − | 0.563456i | ||||
\(484\) | −26.2120 | − | 7.88050i | −1.19145 | − | 0.358204i | ||||
\(485\) | −3.07305 | − | 1.16572i | −0.139540 | − | 0.0529324i | ||||
\(486\) | 15.0619 | + | 20.2561i | 0.683221 | + | 0.918837i | ||||
\(487\) | 11.9556 | − | 11.9556i | 0.541760 | − | 0.541760i | −0.382285 | − | 0.924045i | \(-0.624863\pi\) |
0.924045 | + | 0.382285i | \(0.124863\pi\) | |||||||
\(488\) | −2.29338 | − | 1.07428i | −0.103817 | − | 0.0486305i | ||||
\(489\) | − | 7.18993i | − | 0.325140i | ||||||
\(490\) | 3.04190 | − | 0.864211i | 0.137419 | − | 0.0390411i | ||||
\(491\) | −9.41030 | −0.424681 | −0.212340 | − | 0.977196i | \(-0.568109\pi\) | ||||
−0.212340 | + | 0.977196i | \(0.568109\pi\) | |||||||
\(492\) | −15.4302 | + | 8.29679i | −0.695646 | + | 0.374048i | ||||
\(493\) | 7.81533 | + | 7.81533i | 0.351985 | + | 0.351985i | ||||
\(494\) | 19.0046 | + | 25.5586i | 0.855059 | + | 1.14994i | ||||
\(495\) | 20.9138 | + | 46.4776i | 0.940003 | + | 2.08901i | ||||
\(496\) | −9.71572 | + | 14.6977i | −0.436249 | + | 0.659944i | ||||
\(497\) | −6.08859 | − | 6.08859i | −0.273111 | − | 0.273111i | ||||
\(498\) | −18.9086 | − | 2.78090i | −0.847312 | − | 0.124615i | ||||
\(499\) | − | 34.1095i | − | 1.52695i | −0.645838 | − | 0.763475i | \(-0.723492\pi\) | ||
0.645838 | − | 0.763475i | \(-0.276508\pi\) | |||||||
\(500\) | −12.5212 | + | 18.5262i | −0.559967 | + | 0.828515i | ||||
\(501\) | − | 23.8019i | − | 1.06339i | ||||||
\(502\) | 0.409329 | − | 2.78321i | 0.0182693 | − | 0.124221i | ||||
\(503\) | 8.89616 | + | 8.89616i | 0.396660 | + | 0.396660i | 0.877053 | − | 0.480393i | \(-0.159506\pi\) |
−0.480393 | + | 0.877053i | \(0.659506\pi\) | |||||||
\(504\) | −12.2006 | + | 4.41663i | −0.543458 | + | 0.196733i | ||||
\(505\) | −9.25666 | − | 20.5715i | −0.411916 | − | 0.915421i | ||||
\(506\) | 35.8479 | − | 26.6554i | 1.59363 | − | 1.18498i | ||||
\(507\) | 3.77226 | + | 3.77226i | 0.167532 | + | 0.167532i | ||||
\(508\) | 25.3808 | − | 13.6473i | 1.12609 | − | 0.605499i | ||||
\(509\) | −22.3517 | −0.990721 | −0.495361 | − | 0.868687i | \(-0.664964\pi\) | ||||
−0.495361 | + | 0.868687i | \(0.664964\pi\) | |||||||
\(510\) | 8.41988 | + | 29.6368i | 0.372839 | + | 1.31234i | ||||
\(511\) | 15.1826i | 0.671640i | ||||||||
\(512\) | −21.8867 | + | 5.74225i | −0.967264 | + | 0.253774i | ||||
\(513\) | 18.0183 | − | 18.0183i | 0.795529 | − | 0.795529i | ||||
\(514\) | 1.28122 | − | 0.952679i | 0.0565122 | − | 0.0420209i | ||||
\(515\) | 23.6044 | + | 8.95396i | 1.04013 | + | 0.394559i | ||||
\(516\) | 9.01064 | − | 29.9711i | 0.396671 | − | 1.31940i | ||||
\(517\) | 13.2025 | − | 13.2025i | 0.580645 | − | 0.580645i | ||||
\(518\) | 1.96253 | + | 0.288631i | 0.0862288 | + | 0.0126817i | ||||
\(519\) | −35.3758 | −1.55283 | ||||||||
\(520\) | −17.5453 | + | 17.0185i | −0.769413 | + | 0.746313i | ||||
\(521\) | 17.4188 | 0.763132 | 0.381566 | − | 0.924342i | \(-0.375385\pi\) | ||||
0.381566 | + | 0.924342i | \(0.375385\pi\) | |||||||
\(522\) | 20.0572 | + | 2.94983i | 0.877879 | + | 0.129110i | ||||
\(523\) | −24.9080 | + | 24.9080i | −1.08915 | + | 1.08915i | −0.0935346 | + | 0.995616i | \(0.529817\pi\) |
−0.995616 | + | 0.0935346i | \(0.970183\pi\) | |||||||
\(524\) | −0.0839053 | − | 0.0252257i | −0.00366542 | − | 0.00110199i | ||||
\(525\) | −10.3077 | − | 9.13452i | −0.449864 | − | 0.398663i | ||||
\(526\) | −28.9139 | + | 21.4996i | −1.26071 | + | 0.937426i | ||||
\(527\) | −11.0163 | + | 11.0163i | −0.479876 | + | 0.479876i | ||||
\(528\) | −53.6378 | + | 10.9456i | −2.33429 | + | 0.476348i | ||||
\(529\) | 17.4201i | 0.757396i | ||||||||
\(530\) | −6.05977 | + | 10.8694i | −0.263220 | + | 0.472136i | ||||
\(531\) | −56.5623 | −2.45460 | ||||||||
\(532\) | −5.51935 | − | 10.2648i | −0.239294 | − | 0.445034i | ||||
\(533\) | −8.69061 | − | 8.69061i | −0.376432 | − | 0.376432i | ||||
\(534\) | 15.1119 | − | 11.2368i | 0.653956 | − | 0.486263i | ||||
\(535\) | −34.1878 | − | 12.9686i | −1.47807 | − | 0.560681i | ||||
\(536\) | −13.8840 | + | 5.02604i | −0.599699 | + | 0.217092i | ||||
\(537\) | 18.5289 | + | 18.5289i | 0.799581 | + | 0.799581i | ||||
\(538\) | −5.61885 | + | 38.2050i | −0.242246 | + | 1.64714i | ||||
\(539\) | 4.96845i | 0.214006i | ||||||||
\(540\) | 15.5134 | + | 11.9067i | 0.667591 | + | 0.512383i | ||||
\(541\) | 33.9788i | 1.46086i | 0.682986 | + | 0.730431i | \(0.260681\pi\) | ||||
−0.682986 | + | 0.730431i | \(0.739319\pi\) | |||||||
\(542\) | 31.0533 | + | 4.56703i | 1.33385 | + | 0.196171i | ||||
\(543\) | 12.6402 | + | 12.6402i | 0.542445 | + | 0.542445i | ||||
\(544\) | −19.9778 | + | 1.10546i | −0.856542 | + | 0.0473962i | ||||
\(545\) | 0.955570 | − | 0.429982i | 0.0409321 | − | 0.0184184i | ||||
\(546\) | −8.98345 | − | 12.0815i | −0.384456 | − | 0.517040i | ||||
\(547\) | −6.09800 | − | 6.09800i | −0.260732 | − | 0.260732i | 0.564620 | − | 0.825351i | \(-0.309023\pi\) |
−0.825351 | + | 0.564620i | \(0.809023\pi\) | |||||||
\(548\) | −9.05890 | − | 16.8475i | −0.386977 | − | 0.719691i | ||||
\(549\) | −4.10758 | −0.175307 | ||||||||
\(550\) | −22.6232 | − | 26.8787i | −0.964656 | − | 1.14611i | ||||
\(551\) | 18.2092i | 0.775738i | ||||||||
\(552\) | 21.0116 | − | 44.8555i | 0.894311 | − | 1.90918i | ||||
\(553\) | −9.11081 | + | 9.11081i | −0.387431 | + | 0.387431i | ||||
\(554\) | 17.6784 | + | 23.7750i | 0.751082 | + | 1.01010i | ||||
\(555\) | −3.54514 | − | 7.87852i | −0.150483 | − | 0.334425i | ||||
\(556\) | 0.620103 | − | 2.06258i | 0.0262982 | − | 0.0874728i | ||||
\(557\) | 25.0294 | − | 25.0294i | 1.06053 | − | 1.06053i | 0.0624840 | − | 0.998046i | \(-0.480098\pi\) |
0.998046 | − | 0.0624840i | \(-0.0199023\pi\) | |||||||
\(558\) | −4.15799 | + | 28.2720i | −0.176022 | + | 1.19685i | ||||
\(559\) | 21.9554 | 0.928614 | ||||||||
\(560\) | 7.25800 | − | 5.22699i | 0.306706 | − | 0.220881i | ||||
\(561\) | −48.4069 | −2.04374 | ||||||||
\(562\) | −4.28743 | + | 29.1522i | −0.180854 | + | 1.22971i | ||||
\(563\) | −13.6166 | + | 13.6166i | −0.573870 | + | 0.573870i | −0.933208 | − | 0.359338i | \(-0.883003\pi\) |
0.359338 | + | 0.933208i | \(0.383003\pi\) | |||||||
\(564\) | 5.96063 | − | 19.8262i | 0.250988 | − | 0.834833i | ||||
\(565\) | 7.61264 | − | 20.0684i | 0.320266 | − | 0.844285i | ||||
\(566\) | −9.64030 | − | 12.9649i | −0.405212 | − | 0.544954i | ||||
\(567\) | 1.21433 | − | 1.21433i | 0.0509970 | − | 0.0509970i | ||||
\(568\) | −22.0546 | − | 10.3310i | −0.925391 | − | 0.433479i | ||||
\(569\) | − | 27.0676i | − | 1.13473i | −0.823465 | − | 0.567367i | \(-0.807962\pi\) | ||
0.823465 | − | 0.567367i | \(-0.192038\pi\) | |||||||
\(570\) | −24.7170 | + | 44.3348i | −1.03528 | + | 1.85698i | ||||
\(571\) | 7.52462 | 0.314895 | 0.157448 | − | 0.987527i | \(-0.449673\pi\) | ||||
0.157448 | + | 0.987527i | \(0.449673\pi\) | |||||||
\(572\) | −18.1874 | − | 33.8245i | −0.760454 | − | 1.41427i | ||||
\(573\) | 23.2319 | + | 23.2319i | 0.970526 | + | 0.970526i | ||||
\(574\) | 2.68351 | + | 3.60895i | 0.112008 | + | 0.150635i | ||||
\(575\) | 31.7307 | − | 1.91465i | 1.32326 | − | 0.0798465i | ||||
\(576\) | −28.1958 | + | 23.4924i | −1.17482 | + | 0.978848i | ||||
\(577\) | −21.6199 | − | 21.6199i | −0.900049 | − | 0.900049i | 0.0953910 | − | 0.995440i | \(-0.469590\pi\) |
−0.995440 | + | 0.0953910i | \(0.969590\pi\) | |||||||
\(578\) | 6.28158 | + | 0.923837i | 0.261279 | + | 0.0384265i | ||||
\(579\) | 24.1787i | 1.00483i | ||||||||
\(580\) | −13.8553 | + | 1.82246i | −0.575309 | + | 0.0756737i | ||||
\(581\) | 4.90615i | 0.203541i | ||||||||
\(582\) | 0.833149 | − | 5.66495i | 0.0345351 | − | 0.234820i | ||||
\(583\) | −13.8255 | − | 13.8255i | −0.572595 | − | 0.572595i | ||||
\(584\) | 14.6171 | + | 40.3787i | 0.604862 | + | 1.67088i | ||||
\(585\) | −14.0611 | + | 37.0677i | −0.581354 | + | 1.53256i | ||||
\(586\) | −15.2494 | + | 11.3390i | −0.629945 | + | 0.468409i | ||||
\(587\) | 22.1254 | + | 22.1254i | 0.913215 | + | 0.913215i | 0.996524 | − | 0.0833088i | \(-0.0265488\pi\) |
−0.0833088 | + | 0.996524i | \(0.526549\pi\) | |||||||
\(588\) | 2.60899 | + | 4.85213i | 0.107593 | + | 0.200099i | ||||
\(589\) | −25.6672 | −1.05760 | ||||||||
\(590\) | 37.5055 | − | 10.6554i | 1.54408 | − | 0.438677i | ||||
\(591\) | − | 29.9990i | − | 1.23399i | ||||||
\(592\) | 5.49730 | − | 1.12181i | 0.225938 | − | 0.0461062i | ||||
\(593\) | −28.6255 | + | 28.6255i | −1.17551 | + | 1.17551i | −0.194630 | + | 0.980877i | \(0.562351\pi\) |
−0.980877 | + | 0.194630i | \(0.937649\pi\) | |||||||
\(594\) | −24.6563 | + | 18.3337i | −1.01166 | + | 0.752243i | ||||
\(595\) | 7.21246 | − | 3.24542i | 0.295682 | − | 0.133049i | ||||
\(596\) | 27.8724 | + | 8.37970i | 1.14170 | + | 0.343246i | ||||
\(597\) | −5.93113 | + | 5.93113i | −0.242745 | + | 0.242745i | ||||
\(598\) | 34.3791 | + | 5.05617i | 1.40587 | + | 0.206762i | ||||
\(599\) | 20.4804 | 0.836805 | 0.418403 | − | 0.908262i | \(-0.362590\pi\) | ||||
0.418403 | + | 0.908262i | \(0.362590\pi\) | |||||||
\(600\) | −36.2079 | − | 14.3698i | −1.47818 | − | 0.586644i | ||||
\(601\) | 23.8646 | 0.973459 | 0.486729 | − | 0.873553i | \(-0.338190\pi\) | ||||
0.486729 | + | 0.873553i | \(0.338190\pi\) | |||||||
\(602\) | −7.94843 | − | 1.16898i | −0.323954 | − | 0.0476442i | ||||
\(603\) | −16.9345 | + | 16.9345i | −0.689626 | + | 0.689626i | ||||
\(604\) | −0.907788 | + | 3.01947i | −0.0369374 | + | 0.122861i | ||||
\(605\) | 27.9066 | − | 12.5573i | 1.13456 | − | 0.510525i | ||||
\(606\) | 31.5364 | − | 23.4496i | 1.28108 | − | 0.952575i | ||||
\(607\) | 21.2236 | − | 21.2236i | 0.861440 | − | 0.861440i | −0.130066 | − | 0.991505i | \(-0.541519\pi\) |
0.991505 | + | 0.130066i | \(0.0415189\pi\) | |||||||
\(608\) | −24.5613 | − | 21.9857i | −0.996094 | − | 0.891637i | ||||
\(609\) | − | 8.60746i | − | 0.348792i | ||||||
\(610\) | 2.72366 | − | 0.773800i | 0.110278 | − | 0.0313302i | ||||
\(611\) | 14.5237 | 0.587566 | ||||||||
\(612\) | −28.5823 | + | 15.3687i | −1.15537 | + | 0.621241i | ||||
\(613\) | 19.6848 | + | 19.6848i | 0.795062 | + | 0.795062i | 0.982312 | − | 0.187250i | \(-0.0599575\pi\) |
−0.187250 | + | 0.982312i | \(0.559958\pi\) | |||||||
\(614\) | −18.5491 | + | 13.7926i | −0.748580 | + | 0.556622i | ||||
\(615\) | 6.94707 | − | 18.3138i | 0.280133 | − | 0.738485i | ||||
\(616\) | 4.78339 | + | 13.2137i | 0.192728 | + | 0.532397i | ||||
\(617\) | 2.42500 | + | 2.42500i | 0.0976268 | + | 0.0976268i | 0.754233 | − | 0.656607i | \(-0.228009\pi\) |
−0.656607 | + | 0.754233i | \(0.728009\pi\) | |||||||
\(618\) | −6.39949 | + | 43.5130i | −0.257425 | + | 1.75035i | ||||
\(619\) | − | 19.1625i | − | 0.770207i | −0.922873 | − | 0.385104i | \(-0.874166\pi\) | ||
0.922873 | − | 0.385104i | \(-0.125834\pi\) | |||||||
\(620\) | −2.56889 | − | 19.5300i | −0.103169 | − | 0.784344i | ||||
\(621\) | − | 27.8012i | − | 1.11562i | ||||||
\(622\) | 2.07634 | + | 0.305369i | 0.0832537 | + | 0.0122442i | ||||
\(623\) | −3.41831 | − | 3.41831i | −0.136952 | − | 0.136952i | ||||
\(624\) | −35.5233 | − | 23.4823i | −1.42207 | − | 0.940043i | ||||
\(625\) | −3.00609 | − | 24.8186i | −0.120244 | − | 0.992744i | ||||
\(626\) | 3.37377 | + | 4.53726i | 0.134843 | + | 0.181345i | ||||
\(627\) | −56.3925 | − | 56.3925i | −2.25210 | − | 2.25210i | ||||
\(628\) | 16.3951 | − | 8.81564i | 0.654237 | − | 0.351782i | ||||
\(629\) | 4.96119 | 0.197816 | ||||||||
\(630\) | 7.06410 | − | 12.6708i | 0.281441 | − | 0.504819i | ||||
\(631\) | 1.62356i | 0.0646329i | 0.999478 | + | 0.0323164i | \(0.0102884\pi\) | ||||
−0.999478 | + | 0.0323164i | \(0.989712\pi\) | |||||||
\(632\) | −15.4590 | + | 33.0019i | −0.614927 | + | 1.31275i | ||||
\(633\) | 54.3149 | − | 54.3149i | 2.15882 | − | 2.15882i | ||||
\(634\) | 11.6887 | + | 15.7197i | 0.464219 | + | 0.624310i | ||||
\(635\) | −11.4271 | + | 30.1241i | −0.453472 | + | 1.19544i | ||||
\(636\) | −20.7618 | − | 6.24192i | −0.823259 | − | 0.247508i | ||||
\(637\) | −2.73283 | + | 2.73283i | −0.108279 | + | 0.108279i | ||||
\(638\) | 3.19478 | − | 21.7227i | 0.126483 | − | 0.860011i | ||||
\(639\) | −39.5010 | −1.56264 | ||||||||
\(640\) | 14.2706 | − | 20.8890i | 0.564094 | − | 0.825711i | ||||
\(641\) | −29.5662 | −1.16779 | −0.583897 | − | 0.811828i | \(-0.698473\pi\) | ||||
−0.583897 | + | 0.811828i | \(0.698473\pi\) | |||||||
\(642\) | 9.26879 | − | 63.0226i | 0.365810 | − | 2.48730i | ||||
\(643\) | 14.8816 | − | 14.8816i | 0.586875 | − | 0.586875i | −0.349909 | − | 0.936784i | \(-0.613788\pi\) |
0.936784 | + | 0.349909i | \(0.113788\pi\) | |||||||
\(644\) | −12.1769 | − | 3.66093i | −0.479839 | − | 0.144261i | ||||
\(645\) | 14.3581 | + | 31.9087i | 0.565350 | + | 1.25640i | ||||
\(646\) | −17.3928 | − | 23.3909i | −0.684309 | − | 0.920301i | ||||
\(647\) | 11.9683 | − | 11.9683i | 0.470521 | − | 0.470521i | −0.431562 | − | 0.902083i | \(-0.642037\pi\) |
0.902083 | + | 0.431562i | \(0.142037\pi\) | |||||||
\(648\) | 2.06045 | − | 4.39865i | 0.0809420 | − | 0.172795i | ||||
\(649\) | 61.2593i | 2.40464i | ||||||||
\(650\) | 2.34071 | − | 27.2279i | 0.0918101 | − | 1.06797i | ||||
\(651\) | 12.1328 | 0.475523 | ||||||||
\(652\) | −4.59789 | + | 2.47228i | −0.180067 | + | 0.0968219i | ||||
\(653\) | −10.4874 | − | 10.4874i | −0.410405 | − | 0.410405i | 0.471475 | − | 0.881880i | \(-0.343722\pi\) |
−0.881880 | + | 0.471475i | \(0.843722\pi\) | |||||||
\(654\) | 1.08926 | + | 1.46490i | 0.0425934 | + | 0.0572822i | ||||
\(655\) | 0.0893298 | − | 0.0401962i | 0.00349040 | − | 0.00157059i | ||||
\(656\) | 10.6114 | + | 7.01456i | 0.414306 | + | 0.273873i | ||||
\(657\) | 49.2503 | + | 49.2503i | 1.92144 | + | 1.92144i | ||||
\(658\) | −5.25797 | − | 0.773294i | −0.204977 | − | 0.0301461i | ||||
\(659\) | − | 45.3348i | − | 1.76599i | −0.469380 | − | 0.882996i | \(-0.655522\pi\) | ||
0.469380 | − | 0.882996i | \(-0.344478\pi\) | |||||||
\(660\) | 37.2647 | − | 48.5527i | 1.45053 | − | 1.88991i | ||||
\(661\) | 11.7352i | 0.456444i | 0.973609 | + | 0.228222i | \(0.0732913\pi\) | ||||
−0.973609 | + | 0.228222i | \(0.926709\pi\) | |||||||
\(662\) | 2.37613 | − | 16.1564i | 0.0923511 | − | 0.627936i | ||||
\(663\) | −26.6256 | − | 26.6256i | −1.03405 | − | 1.03405i | ||||
\(664\) | 4.72341 | + | 13.0481i | 0.183304 | + | 0.506363i | ||||
\(665\) | 12.1831 | + | 4.62147i | 0.472440 | + | 0.179213i | ||||
\(666\) | 7.30245 | − | 5.42989i | 0.282964 | − | 0.210404i | ||||
\(667\) | 14.0478 | + | 14.0478i | 0.543934 | + | 0.543934i | ||||
\(668\) | −15.2211 | + | 8.18437i | −0.588922 | + | 0.316663i | ||||
\(669\) | −71.6240 | −2.76914 | ||||||||
\(670\) | 8.03880 | − | 14.4192i | 0.310566 | − | 0.557061i | ||||
\(671\) | 4.44867i | 0.171739i | ||||||||
\(672\) | 11.6101 | + | 10.3926i | 0.447869 | + | 0.400903i | ||||
\(673\) | 10.7808 | − | 10.7808i | 0.415570 | − | 0.415570i | −0.468103 | − | 0.883674i | \(-0.655063\pi\) |
0.883674 | + | 0.468103i | \(0.155063\pi\) | |||||||
\(674\) | −18.0053 | + | 13.3882i | −0.693538 | + | 0.515695i | ||||
\(675\) | −21.8245 | + | 1.31691i | −0.840027 | + | 0.0506878i | ||||
\(676\) | 1.11522 | − | 3.70943i | 0.0428931 | − | 0.142670i | ||||
\(677\) | −34.4843 | + | 34.4843i | −1.32534 | + | 1.32534i | −0.415953 | + | 0.909386i | \(0.636552\pi\) |
−0.909386 | + | 0.415953i | \(0.863448\pi\) | |||||||
\(678\) | 36.9946 | + | 5.44083i | 1.42077 | + | 0.208954i | ||||
\(679\) | −1.46987 | −0.0564084 | ||||||||
\(680\) | 16.0572 | − | 15.5751i | 0.615766 | − | 0.597279i | ||||
\(681\) | −12.9520 | −0.496323 | ||||||||
\(682\) | 30.6197 | + | 4.50327i | 1.17249 | + | 0.172439i | ||||
\(683\) | 29.0992 | − | 29.0992i | 1.11345 | − | 1.11345i | 0.120769 | − | 0.992681i | \(-0.461464\pi\) |
0.992681 | − | 0.120769i | \(-0.0385361\pi\) | |||||||
\(684\) | −51.2014 | − | 15.3934i | −1.95773 | − | 0.588582i | ||||
\(685\) | 19.9961 | + | 7.58520i | 0.764011 | + | 0.289816i | ||||
\(686\) | 1.13486 | − | 0.843852i | 0.0433293 | − | 0.0322184i | ||||
\(687\) | −49.7949 | + | 49.7949i | −1.89979 | + | 1.89979i | ||||
\(688\) | −22.2645 | + | 4.54343i | −0.848828 | + | 0.173217i | ||||
\(689\) | − | 15.2091i | − | 0.579421i | ||||||
\(690\) | 15.1345 | + | 53.2712i | 0.576160 | + | 2.02800i | ||||
\(691\) | −43.5975 | −1.65853 | −0.829263 | − | 0.558859i | \(-0.811239\pi\) | ||||
−0.829263 | + | 0.558859i | \(0.811239\pi\) | |||||||
\(692\) | 12.1641 | + | 22.6225i | 0.462409 | + | 0.859978i | ||||
\(693\) | 16.1169 | + | 16.1169i | 0.612232 | + | 0.612232i | ||||
\(694\) | −22.9518 | + | 17.0663i | −0.871238 | + | 0.647828i | ||||
\(695\) | 0.988111 | + | 2.19593i | 0.0374812 | + | 0.0832962i | ||||
\(696\) | −8.28686 | − | 22.8918i | −0.314113 | − | 0.867711i | ||||
\(697\) | 7.95353 | + | 7.95353i | 0.301261 | + | 0.301261i | ||||
\(698\) | 3.38458 | − | 23.0133i | 0.128108 | − | 0.871065i | ||||
\(699\) | 26.1899i | 0.990594i | ||||||||
\(700\) | −2.29711 | + | 9.73259i | −0.0868225 | + | 0.367857i | ||||
\(701\) | − | 7.31961i | − | 0.276458i | −0.990400 | − | 0.138229i | \(-0.955859\pi\) | ||
0.990400 | − | 0.138229i | \(-0.0441409\pi\) | |||||||
\(702\) | −23.6461 | − | 3.47766i | −0.892466 | − | 0.131256i | ||||
\(703\) | 5.77962 | + | 5.77962i | 0.217983 | + | 0.217983i | ||||
\(704\) | 25.4432 | + | 30.5371i | 0.958925 | + | 1.15091i | ||||
\(705\) | 9.49804 | + | 21.1079i | 0.357717 | + | 0.794971i | ||||
\(706\) | −5.74052 | − | 7.72020i | −0.216047 | − | 0.290553i | ||||
\(707\) | −7.13354 | − | 7.13354i | −0.268284 | − | 0.268284i | ||||
\(708\) | 32.1679 | + | 59.8251i | 1.20894 | + | 2.24837i | ||||
\(709\) | −19.4599 | −0.730832 | −0.365416 | − | 0.930844i | \(-0.619073\pi\) | ||||
−0.365416 | + | 0.930844i | \(0.619073\pi\) | |||||||
\(710\) | 26.1925 | − | 7.44135i | 0.982986 | − | 0.279269i | ||||
\(711\) | 59.1083i | 2.21673i | ||||||||
\(712\) | −12.3821 | − | 5.80011i | −0.464038 | − | 0.217368i | ||||
\(713\) | −19.8014 | + | 19.8014i | −0.741569 | + | 0.741569i | ||||
\(714\) | 8.22153 | + | 11.0568i | 0.307683 | + | 0.413791i | ||||
\(715\) | 40.1458 | + | 15.2287i | 1.50137 | + | 0.569521i | ||||
\(716\) | 5.47782 | − | 18.2203i | 0.204716 | − | 0.680923i | ||||
\(717\) | 34.7512 | − | 34.7512i | 1.29781 | − | 1.29781i | ||||
\(718\) | 2.94426 | − | 20.0194i | 0.109879 | − | 0.747116i | ||||
\(719\) | −4.16036 | −0.155155 | −0.0775776 | − | 0.996986i | \(-0.524719\pi\) | ||||
−0.0775776 | + | 0.996986i | \(0.524719\pi\) | |||||||
\(720\) | 6.58829 | − | 40.4995i | 0.245531 | − | 1.50933i | ||||
\(721\) | 11.2902 | 0.420469 | ||||||||
\(722\) | 3.07783 | − | 20.9275i | 0.114545 | − | 0.778841i | ||||
\(723\) | −38.1364 | + | 38.1364i | −1.41831 | + | 1.41831i | ||||
\(724\) | 3.73692 | − | 12.4297i | 0.138882 | − | 0.461946i | ||||
\(725\) | 10.3624 | − | 11.6933i | 0.384851 | − | 0.434278i | ||||
\(726\) | 31.8109 | + | 42.7812i | 1.18061 | + | 1.58776i | ||||
\(727\) | −1.53832 | + | 1.53832i | −0.0570531 | + | 0.0570531i | −0.735058 | − | 0.678005i | \(-0.762845\pi\) |
0.678005 | + | 0.735058i | \(0.262845\pi\) | |||||||
\(728\) | −4.63701 | + | 9.89909i | −0.171859 | + | 0.366885i | ||||
\(729\) | − | 44.0138i | − | 1.63014i | ||||||
\(730\) | −41.9350 | − | 23.3791i | −1.55208 | − | 0.865299i | ||||
\(731\) | −20.0932 | −0.743176 | ||||||||
\(732\) | 2.33604 | + | 4.34452i | 0.0863427 | + | 0.160578i | ||||
\(733\) | 23.9118 | + | 23.9118i | 0.883201 | + | 0.883201i | 0.993859 | − | 0.110658i | \(-0.0352957\pi\) |
−0.110658 | + | 0.993859i | \(0.535296\pi\) | |||||||
\(734\) | −10.7537 | − | 14.4622i | −0.396927 | − | 0.533811i | ||||
\(735\) | −5.75893 | − | 2.18456i | −0.212421 | − | 0.0805787i | ||||
\(736\) | −35.9095 | + | 1.98703i | −1.32364 | + | 0.0732429i | ||||
\(737\) | 18.3407 | + | 18.3407i | 0.675590 | + | 0.675590i | ||||
\(738\) | 20.4119 | + | 3.00199i | 0.751371 | + | 0.110505i | ||||
\(739\) | − | 19.4344i | − | 0.714906i | −0.933931 | − | 0.357453i | \(-0.883645\pi\) | ||
0.933931 | − | 0.357453i | \(-0.116355\pi\) | |||||||
\(740\) | −3.81923 | + | 4.97614i | −0.140398 | + | 0.182926i | ||||
\(741\) | − | 62.0359i | − | 2.27894i | ||||||
\(742\) | −0.809787 | + | 5.50610i | −0.0297282 | + | 0.202135i | ||||
\(743\) | 20.4921 | + | 20.4921i | 0.751783 | + | 0.751783i | 0.974812 | − | 0.223029i | \(-0.0715944\pi\) |
−0.223029 | + | 0.974812i | \(0.571594\pi\) | |||||||
\(744\) | 32.2676 | − | 11.6809i | 1.18299 | − | 0.428243i | ||||
\(745\) | −29.6744 | + | 13.3527i | −1.08719 | + | 0.489206i | ||||
\(746\) | −30.7087 | + | 22.8341i | −1.12432 | + | 0.836015i | ||||
\(747\) | 15.9148 | + | 15.9148i | 0.582293 | + | 0.582293i | ||||
\(748\) | 16.6449 | + | 30.9557i | 0.608597 | + | 1.13185i | ||||
\(749\) | −16.3523 | −0.597500 | ||||||||
\(750\) | 41.1022 | − | 14.4043i | 1.50084 | − | 0.525971i | ||||
\(751\) | − | 50.5961i | − | 1.84628i | −0.384465 | − | 0.923140i | \(-0.625614\pi\) | ||
0.384465 | − | 0.923140i | \(-0.374386\pi\) | |||||||
\(752\) | −14.7282 | + | 3.00553i | −0.537083 | + | 0.109600i | ||||
\(753\) | −3.87447 | + | 3.87447i | −0.141194 | + | 0.141194i | ||||
\(754\) | 13.7055 | − | 10.1911i | 0.499127 | − | 0.371136i | ||||
\(755\) | −1.44653 | − | 3.21468i | −0.0526444 | − | 0.116994i | ||||
\(756\) | 8.37537 | + | 2.51801i | 0.304609 | + | 0.0915791i | ||||
\(757\) | −17.3973 | + | 17.3973i | −0.632315 | + | 0.632315i | −0.948648 | − | 0.316333i | \(-0.897548\pi\) |
0.316333 | + | 0.948648i | \(0.397548\pi\) | |||||||
\(758\) | 13.1319 | + | 1.93132i | 0.476971 | + | 0.0701486i | ||||
\(759\) | −87.0100 | −3.15826 | ||||||||
\(760\) | 36.8507 | + | 0.561620i | 1.33671 | + | 0.0203721i | ||||
\(761\) | 33.2640 | 1.20582 | 0.602910 | − | 0.797809i | \(-0.294008\pi\) | ||||
0.602910 | + | 0.797809i | \(0.294008\pi\) | |||||||
\(762\) | −55.5316 | − | 8.16709i | −2.01170 | − | 0.295862i | ||||
\(763\) | 0.331361 | − | 0.331361i | 0.0119961 | − | 0.0119961i | ||||
\(764\) | 6.86820 | − | 22.8449i | 0.248483 | − | 0.826500i | ||||
\(765\) | 12.8685 | − | 33.9239i | 0.465261 | − | 1.22652i | ||||
\(766\) | 37.4838 | − | 27.8719i | 1.35434 | − | 1.00705i | ||||
\(767\) | −33.6949 | + | 33.6949i | −1.21665 | + | 1.21665i | ||||
\(768\) | 40.8829 | + | 16.4618i | 1.47523 | + | 0.594012i | ||||
\(769\) | − | 45.8098i | − | 1.65194i | −0.563712 | − | 0.825971i | \(-0.690627\pi\) | ||
0.563712 | − | 0.825971i | \(-0.309373\pi\) | |||||||
\(770\) | −13.7230 | − | 7.65070i | −0.494544 | − | 0.275712i | ||||
\(771\) | −3.10978 | −0.111996 | ||||||||
\(772\) | 15.4620 | − | 8.31392i | 0.556491 | − | 0.299225i | ||||
\(773\) | −22.8403 | − | 22.8403i | −0.821510 | − | 0.821510i | 0.164814 | − | 0.986325i | \(-0.447298\pi\) |
−0.986325 | + | 0.164814i | \(0.947298\pi\) | |||||||
\(774\) | −29.5756 | + | 21.9916i | −1.06307 | + | 0.790470i | ||||
\(775\) | 16.4825 | + | 14.6066i | 0.592070 | + | 0.524684i | ||||
\(776\) | −3.90916 | + | 1.41512i | −0.140331 | + | 0.0507999i | ||||
\(777\) | −2.73202 | − | 2.73202i | −0.0980105 | − | 0.0980105i | ||||
\(778\) | 5.09874 | − | 34.6686i | 0.182799 | − | 1.24293i | ||||
\(779\) | 18.5312i | 0.663949i | ||||||||
\(780\) | 47.2027 | − | 6.20884i | 1.69013 | − | 0.222312i | ||||
\(781\) | 42.7812i | 1.53083i | ||||||||
\(782\) | −31.4633 | − | 4.62733i | −1.12512 | − | 0.165473i | ||||
\(783\) | −9.66217 | − | 9.66217i | −0.345298 | − | 0.345298i | ||||
\(784\) | 2.20578 | − | 3.33684i | 0.0787779 | − | 0.119173i | ||||
\(785\) | −7.38152 | + | 19.4591i | −0.263458 | + | 0.694526i | ||||
\(786\) | 0.101828 | + | 0.136944i | 0.00363207 | + | 0.00488463i | ||||
\(787\) | −23.4151 | − | 23.4151i | −0.834657 | − | 0.834657i | 0.153492 | − | 0.988150i | \(-0.450948\pi\) |
−0.988150 | + | 0.153492i | \(0.950948\pi\) | |||||||
\(788\) | −19.1840 | + | 10.3152i | −0.683403 | + | 0.367465i | ||||
\(789\) | 70.1800 | 2.49847 | ||||||||
\(790\) | −11.1350 | − | 39.1937i | −0.396167 | − | 1.39445i | ||||
\(791\) | − | 9.59889i | − | 0.341297i | ||||||
\(792\) | 58.3801 | + | 27.3468i | 2.07445 | + | 0.971728i | ||||
\(793\) | −2.44693 | + | 2.44693i | −0.0868931 | + | 0.0868931i | ||||
\(794\) | 1.58226 | + | 2.12792i | 0.0561522 | + | 0.0755169i | ||||
\(795\) | 22.1041 | − | 9.94627i | 0.783950 | − | 0.352758i | ||||
\(796\) | 5.83233 | + | 1.75346i | 0.206722 | + | 0.0621497i | ||||
\(797\) | 13.9493 | − | 13.9493i | 0.494111 | − | 0.494111i | −0.415488 | − | 0.909599i | \(-0.636389\pi\) |
0.909599 | + | 0.415488i | \(0.136389\pi\) | |||||||
\(798\) | −3.30301 | + | 22.4586i | −0.116925 | + | 0.795027i | ||||
\(799\) | −13.2919 | −0.470233 | ||||||||
\(800\) | 3.26085 | + | 28.0957i | 0.115289 | + | 0.993332i | ||||
\(801\) | −22.1770 | −0.783585 | ||||||||
\(802\) | −1.44398 | + | 9.81829i | −0.0509888 | + | 0.346696i | ||||
\(803\) | 53.3400 | − | 53.3400i | 1.88233 | − | 1.88233i | ||||
\(804\) | 27.5423 | + | 8.28044i | 0.971342 | + | 0.292029i | ||||
\(805\) | 12.9642 | − | 5.83356i | 0.456928 | − | 0.205606i | ||||
\(806\) | 14.3650 | + | 19.3189i | 0.505986 | + | 0.680481i | ||||
\(807\) | 53.1847 | − | 53.1847i | 1.87219 | − | 1.87219i | ||||
\(808\) | −25.8397 | − | 12.1040i | −0.909037 | − | 0.425818i | ||||
\(809\) | − | 44.2402i | − | 1.55540i | −0.628635 | − | 0.777701i | \(-0.716386\pi\) | ||
0.628635 | − | 0.777701i | \(-0.283614\pi\) | |||||||
\(810\) | 1.48413 | + | 5.22391i | 0.0521469 | + | 0.183550i | ||||
\(811\) | 9.19726 | 0.322959 | 0.161480 | − | 0.986876i | \(-0.448373\pi\) | ||||
0.161480 | + | 0.986876i | \(0.448373\pi\) | |||||||
\(812\) | −5.50438 | + | 2.95970i | −0.193166 | + | 0.103865i | ||||
\(813\) | −43.2288 | − | 43.2288i | −1.51610 | − | 1.51610i | ||||
\(814\) | −5.88079 | − | 7.90885i | −0.206122 | − | 0.277205i | ||||
\(815\) | 2.07009 | − | 5.45716i | 0.0725121 | − | 0.191156i | ||||
\(816\) | 32.5104 | + | 21.4906i | 1.13809 | + | 0.752322i | ||||
\(817\) | −23.4080 | − | 23.4080i | −0.818942 | − | 0.818942i | ||||
\(818\) | −12.0272 | − | 1.76885i | −0.420522 | − | 0.0618465i | ||||
\(819\) | 17.7298i | 0.619530i | ||||||||
\(820\) | −14.1003 | + | 1.85469i | −0.492403 | + | 0.0647686i | ||||
\(821\) | 33.5623i | 1.17133i | 0.810552 | + | 0.585666i | \(0.199167\pi\) | ||||
−0.810552 | + | 0.585666i | \(0.800833\pi\) | |||||||
\(822\) | −5.42122 | + | 36.8613i | −0.189087 | + | 1.28569i | ||||
\(823\) | −15.2780 | − | 15.2780i | −0.532556 | − | 0.532556i | 0.388776 | − | 0.921332i | \(-0.372898\pi\) |
−0.921332 | + | 0.388776i | \(0.872898\pi\) | |||||||
\(824\) | 30.0266 | − | 10.8697i | 1.04603 | − | 0.378663i | ||||
\(825\) | 4.12156 | + | 68.3048i | 0.143494 | + | 2.37807i | ||||
\(826\) | 13.9925 | − | 10.4044i | 0.486860 | − | 0.362015i | ||||
\(827\) | 0.689674 | + | 0.689674i | 0.0239823 | + | 0.0239823i | 0.718996 | − | 0.695014i | \(-0.244602\pi\) |
−0.695014 | + | 0.718996i | \(0.744602\pi\) | |||||||
\(828\) | −51.3758 | + | 27.6247i | −1.78543 | + | 0.960025i | ||||
\(829\) | 57.4990 | 1.99702 | 0.998512 | − | 0.0545294i | \(-0.0173659\pi\) | ||||
0.998512 | + | 0.0545294i | \(0.0173659\pi\) | |||||||
\(830\) | −13.5510 | − | 7.55477i | −0.470360 | − | 0.262230i | ||||
\(831\) | − | 57.7066i | − | 2.00182i | ||||||
\(832\) | −2.80188 | + | 30.7912i | −0.0971377 | + | 1.06749i | ||||
\(833\) | 2.50105 | − | 2.50105i | 0.0866562 | − | 0.0866562i | ||||
\(834\) | −3.36639 | + | 2.50315i | −0.116568 | + | 0.0866769i | ||||
\(835\) | 6.85294 | − | 18.0657i | 0.237156 | − | 0.625189i | ||||
\(836\) | −16.6717 | + | 55.4532i | −0.576603 | + | 1.91789i | ||||
\(837\) | 13.6195 | − | 13.6195i | 0.470759 | − | 0.470759i | ||||
\(838\) | 3.96110 | + | 0.582563i | 0.136834 | + | 0.0201243i | ||||
\(839\) | −16.0870 | −0.555384 | −0.277692 | − | 0.960670i | \(-0.589570\pi\) | ||||
−0.277692 | + | 0.960670i | \(0.589570\pi\) | |||||||
\(840\) | −17.4192 | − | 0.265477i | −0.601021 | − | 0.00915981i | ||||
\(841\) | −19.2355 | −0.663293 | ||||||||
\(842\) | 12.2826 | + | 1.80641i | 0.423286 | + | 0.0622530i | ||||
\(843\) | 40.5823 | − | 40.5823i | 1.39773 | − | 1.39773i | ||||
\(844\) | −53.4102 | − | 16.0575i | −1.83846 | − | 0.552722i | ||||
\(845\) | 1.77706 | + | 3.94924i | 0.0611327 | + | 0.135858i | ||||
\(846\) | −19.5645 | + | 14.5476i | −0.672643 | + | 0.500158i | ||||
\(847\) | 9.67711 | − | 9.67711i | 0.332509 | − | 0.332509i | ||||
\(848\) | 3.14736 | + | 15.4233i | 0.108081 | + | 0.529637i | ||||
\(849\) | 31.4683i | 1.07999i | ||||||||
\(850\) | −2.14218 | + | 24.9186i | −0.0734762 | + | 0.854700i | ||||
\(851\) | 8.91759 | 0.305691 | ||||||||
\(852\) | 22.4649 | + | 41.7796i | 0.769634 | + | 1.43135i | ||||
\(853\) | 10.7040 | + | 10.7040i | 0.366497 | + | 0.366497i | 0.866198 | − | 0.499701i | \(-0.166557\pi\) |
−0.499701 | + | 0.866198i | \(0.666557\pi\) | |||||||
\(854\) | 1.01614 | − | 0.755571i | 0.0347715 | − | 0.0258551i | ||||
\(855\) | 54.5116 | − | 24.5288i | 1.86426 | − | 0.838868i | ||||
\(856\) | −43.4894 | + | 15.7432i | −1.48644 | + | 0.538092i | ||||
\(857\) | −13.5293 | − | 13.5293i | −0.462152 | − | 0.462152i | 0.437208 | − | 0.899360i | \(-0.355967\pi\) |
−0.899360 | + | 0.437208i | \(0.855967\pi\) | |||||||
\(858\) | −10.8841 | + | 74.0059i | −0.371577 | + | 2.52652i | ||||
\(859\) | 24.1069i | 0.822518i | 0.911518 | + | 0.411259i | \(0.134911\pi\) | ||||
−0.911518 | + | 0.411259i | \(0.865089\pi\) | |||||||
\(860\) | 15.4682 | − | 20.1538i | 0.527462 | − | 0.687238i | ||||
\(861\) | − | 8.75966i | − | 0.298528i | ||||||
\(862\) | 14.3810 | + | 2.11502i | 0.489817 | + | 0.0720379i | ||||
\(863\) | 18.5324 | + | 18.5324i | 0.630852 | + | 0.630852i | 0.948282 | − | 0.317430i | \(-0.102820\pi\) |
−0.317430 | + | 0.948282i | \(0.602820\pi\) | |||||||
\(864\) | 24.6988 | − | 1.36669i | 0.840269 | − | 0.0464957i | ||||
\(865\) | −26.8503 | − | 10.1852i | −0.912937 | − | 0.346308i | ||||
\(866\) | −6.28198 | − | 8.44839i | −0.213470 | − | 0.287088i | ||||
\(867\) | −8.74450 | − | 8.74450i | −0.296979 | − | 0.296979i | ||||
\(868\) | −4.17191 | − | 7.75882i | −0.141604 | − | 0.263351i | ||||
\(869\) | 64.0166 | 2.17162 | ||||||||
\(870\) | 23.7741 | + | 13.2543i | 0.806017 | + | 0.449361i | ||||
\(871\) | 20.1762i | 0.683643i | ||||||||
\(872\) | 0.562245 | − | 1.20028i | 0.0190400 | − | 0.0406467i | ||||
\(873\) | −4.76804 | + | 4.76804i | −0.161374 | + | 0.161374i | ||||
\(874\) | −31.2630 | − | 42.0444i | −1.05749 | − | 1.42217i | ||||
\(875\) | −5.19357 | − | 9.90085i | −0.175575 | − | 0.334710i | ||||
\(876\) | 24.0818 | − | 80.1007i | 0.813650 | − | 2.70635i | ||||
\(877\) | 0.359005 | − | 0.359005i | 0.0121227 | − | 0.0121227i | −0.701019 | − | 0.713142i | \(-0.747271\pi\) |
0.713142 | + | 0.701019i | \(0.247271\pi\) | |||||||
\(878\) | −2.70370 | + | 18.3837i | −0.0912454 | + | 0.620418i | ||||
\(879\) | 37.0133 | 1.24843 | ||||||||
\(880\) | −43.8626 | − | 7.13538i | −1.47861 | − | 0.240534i | ||||
\(881\) | 33.8357 | 1.13995 | 0.569977 | − | 0.821660i | \(-0.306952\pi\) | ||||
0.569977 | + | 0.821660i | \(0.306952\pi\) | |||||||
\(882\) | 0.943998 | − | 6.41866i | 0.0317861 | − | 0.216128i | ||||
\(883\) | 25.4680 | − | 25.4680i | 0.857068 | − | 0.857068i | −0.133924 | − | 0.990992i | \(-0.542758\pi\) |
0.990992 | + | 0.133924i | \(0.0427577\pi\) | |||||||
\(884\) | −7.87150 | + | 26.1821i | −0.264747 | + | 0.880599i | ||||
\(885\) | −71.0056 | − | 26.9349i | −2.38683 | − | 0.905405i | ||||
\(886\) | −14.4022 | − | 19.3689i | −0.483850 | − | 0.650711i | ||||
\(887\) | −9.87786 | + | 9.87786i | −0.331666 | + | 0.331666i | −0.853219 | − | 0.521553i | \(-0.825353\pi\) |
0.521553 | + | 0.853219i | \(0.325353\pi\) | |||||||
\(888\) | −9.89614 | − | 4.63562i | −0.332093 | − | 0.155561i | ||||
\(889\) | 14.4086i | 0.483250i | ||||||||
\(890\) | 14.7052 | − | 4.17778i | 0.492919 | − | 0.140040i | ||||
\(891\) | −8.53242 | −0.285847 | ||||||||
\(892\) | 24.6281 | + | 45.8028i | 0.824611 | + | 1.53359i | ||||
\(893\) | −15.4846 | − | 15.4846i | −0.518173 | − | 0.518173i | ||||
\(894\) | −33.8260 | − | 45.4913i | −1.13131 | − | 1.52146i | ||||
\(895\) | 8.72870 | + | 19.3982i | 0.291768 | + | 0.648411i | ||||
\(896\) | 2.65379 | − | 10.9981i | 0.0886569 | − | 0.367420i | ||||
\(897\) | −47.8587 | − | 47.8587i | −1.59796 | − | 1.59796i | ||||
\(898\) | −45.3865 | − | 6.67503i | −1.51457 | − | 0.222749i | ||||
\(899\) | 13.7638i | 0.459048i | ||||||||
\(900\) | 24.1196 | + | 39.0226i | 0.803987 | + | 1.30075i | ||||
\(901\) | 13.9192i | 0.463714i | ||||||||
\(902\) | 3.25127 | − | 22.1069i | 0.108256 | − | 0.736078i | ||||
\(903\) | 11.0649 | + | 11.0649i | 0.368217 | + | 0.368217i | ||||
\(904\) | −9.24137 | − | 25.5286i | −0.307363 | − | 0.849067i | ||||
\(905\) | 5.95464 | + | 13.2333i | 0.197939 | + | 0.439889i | ||||
\(906\) | 4.92815 | − | 3.66443i | 0.163727 | − | 0.121743i | ||||
\(907\) | −9.49904 | − | 9.49904i | −0.315411 | − | 0.315411i | 0.531591 | − | 0.847001i | \(-0.321594\pi\) |
−0.847001 | + | 0.531591i | \(0.821594\pi\) | |||||||
\(908\) | 4.45360 | + | 8.28270i | 0.147798 | + | 0.274871i | ||||
\(909\) | −46.2803 | −1.53502 | ||||||||
\(910\) | −3.34001 | − | 11.7563i | −0.110720 | − | 0.389719i | ||||
\(911\) | − | 42.0078i | − | 1.39178i | −0.718148 | − | 0.695890i | \(-0.755010\pi\) | ||
0.718148 | − | 0.695890i | \(-0.244990\pi\) | |||||||
\(912\) | 12.8377 | + | 62.9094i | 0.425098 | + | 2.08314i | ||||
\(913\) | 17.2364 | − | 17.2364i | 0.570441 | − | 0.570441i | ||||
\(914\) | −4.45643 | + | 3.31367i | −0.147405 | + | 0.109607i | ||||
\(915\) | −5.15645 | − | 1.95602i | −0.170467 | − | 0.0646640i | ||||
\(916\) | 48.9655 | + | 14.7212i | 1.61787 | + | 0.486403i | ||||
\(917\) | 0.0309767 | − | 0.0309767i | 0.00102294 | − | 0.00102294i | ||||
\(918\) | 21.6406 | + | 3.18270i | 0.714246 | + | 0.105045i | ||||
\(919\) | 43.7978 | 1.44476 | 0.722378 | − | 0.691498i | \(-0.243049\pi\) | ||||
0.722378 | + | 0.691498i | \(0.243049\pi\) | |||||||
\(920\) | 28.8624 | − | 27.9958i | 0.951565 | − | 0.922996i | ||||
\(921\) | 45.0224 | 1.48354 | ||||||||
\(922\) | 16.0581 | + | 2.36168i | 0.528846 | + | 0.0777778i | ||||
\(923\) | −23.5312 | + | 23.5312i | −0.774540 | + | 0.774540i | ||||
\(924\) | 7.88068 | − | 26.2126i | 0.259255 | − | 0.862331i | ||||
\(925\) | −0.422415 | − | 7.00051i | −0.0138889 | − | 0.230175i | ||||
\(926\) | −26.8340 | + | 19.9530i | −0.881819 | + | 0.655695i | ||||
\(927\) | 36.6237 | − | 36.6237i | 1.20288 | − | 1.20288i | ||||
\(928\) | −11.7896 | + | 13.1708i | −0.387013 | + | 0.432352i | ||||
\(929\) | − | 6.69434i | − | 0.219634i | −0.993952 | − | 0.109817i | \(-0.964973\pi\) | ||
0.993952 | − | 0.109817i | \(-0.0350265\pi\) | |||||||
\(930\) | −18.6828 | + | 33.5113i | −0.612634 | + | 1.09888i | ||||
\(931\) | 5.82728 | 0.190981 | ||||||||
\(932\) | 16.7482 | − | 9.00549i | 0.548605 | − | 0.294985i | ||||
\(933\) | −2.89045 | − | 2.89045i | −0.0946289 | − | 0.0946289i | ||||
\(934\) | −16.0423 | + | 11.9286i | −0.524920 | + | 0.390316i | ||||
\(935\) | −36.7409 | − | 13.9371i | −1.20156 | − | 0.455792i | ||||
\(936\) | 17.0694 | + | 47.1530i | 0.557932 | + | 1.54124i | ||||
\(937\) | −30.7721 | − | 30.7721i | −1.00528 | − | 1.00528i | −0.999986 | − | 0.00529627i | \(-0.998314\pi\) |
−0.00529627 | − | 0.999986i | \(-0.501686\pi\) | |||||||
\(938\) | 1.07425 | − | 7.30431i | 0.0350755 | − | 0.238494i | ||||
\(939\) | − | 11.0128i | − | 0.359390i | ||||||
\(940\) | 10.2324 | − | 13.3319i | 0.333744 | − | 0.434840i | ||||
\(941\) | 57.1321i | 1.86245i | 0.364439 | + | 0.931227i | \(0.381261\pi\) | ||||
−0.364439 | + | 0.931227i | \(0.618739\pi\) | |||||||
\(942\) | −35.8715 | − | 5.27565i | −1.16876 | − | 0.171890i | ||||
\(943\) | 14.2962 | + | 14.2962i | 0.465549 | + | 0.465549i | ||||
\(944\) | 27.1965 | − | 41.1421i | 0.885172 | − | 1.33906i | ||||
\(945\) | −8.91684 | + | 4.01235i | −0.290065 | + | 0.130522i | ||||
\(946\) | 23.8177 | + | 32.0315i | 0.774381 | + | 1.04143i | ||||
\(947\) | 10.4235 | + | 10.4235i | 0.338719 | + | 0.338719i | 0.855885 | − | 0.517166i | \(-0.173013\pi\) |
−0.517166 | + | 0.855885i | \(0.673013\pi\) | |||||||
\(948\) | 62.5179 | − | 33.6158i | 2.03049 | − | 1.09179i | ||||
\(949\) | 58.6780 | 1.90477 | ||||||||
\(950\) | −31.5249 | + | 26.5337i | −1.02280 | + | 0.860868i | ||||
\(951\) | − | 38.1549i | − | 1.23726i | ||||||
\(952\) | 4.24372 | − | 9.05951i | 0.137540 | − | 0.293620i | ||||
\(953\) | −30.0029 | + | 30.0029i | −0.971888 | + | 0.971888i | −0.999616 | − | 0.0277275i | \(-0.991173\pi\) |
0.0277275 | + | 0.999616i | \(0.491173\pi\) | |||||||
\(954\) | 15.2342 | + | 20.4878i | 0.493224 | + | 0.663318i | ||||
\(955\) | 10.9442 | + | 24.3218i | 0.354146 | + | 0.787036i | ||||
\(956\) | −34.1723 | − | 10.2737i | −1.10521 | − | 0.332276i | ||||
\(957\) | −30.2399 | + | 30.2399i | −0.977518 | + | 0.977518i | ||||
\(958\) | −0.714687 | + | 4.85948i | −0.0230905 | + | 0.157003i | ||||
\(959\) | 9.56429 | 0.308847 | ||||||||
\(960\) | −46.5826 | + | 16.0644i | −1.50345 | + | 0.518476i | ||||
\(961\) | 11.5990 | 0.374160 | ||||||||
\(962\) | 1.11550 | − | 7.58481i | 0.0359653 | − | 0.244544i | ||||
\(963\) | −53.0445 | + | 53.0445i | −1.70933 | + | 1.70933i | ||||
\(964\) | 37.5012 | + | 11.2745i | 1.20783 | + | 0.363128i | ||||
\(965\) | −6.96142 | + | 18.3517i | −0.224096 | + | 0.590761i | ||||
\(966\) | 14.7780 | + | 19.8743i | 0.475473 | + | 0.639445i | ||||
\(967\) | 9.86610 | − | 9.86610i | 0.317272 | − | 0.317272i | −0.530446 | − | 0.847719i | \(-0.677976\pi\) |
0.847719 | + | 0.530446i | \(0.177976\pi\) | |||||||
\(968\) | 16.4199 | − | 35.0532i | 0.527755 | − | 1.12665i | ||||
\(969\) | 56.7743i | 1.82385i | ||||||||
\(970\) | 2.26339 | − | 4.05983i | 0.0726730 | − | 0.130353i | ||||
\(971\) | −2.71827 | −0.0872336 | −0.0436168 | − | 0.999048i | \(-0.513888\pi\) | ||||
−0.0436168 | + | 0.999048i | \(0.513888\pi\) | |||||||
\(972\) | −31.4410 | + | 16.9058i | −1.00847 | + | 0.542254i | ||||
\(973\) | 0.761476 | + | 0.761476i | 0.0244118 | + | 0.0244118i | ||||
\(974\) | 14.2677 | + | 19.1880i | 0.457165 | + | 0.614823i | ||||
\(975\) | −35.3031 | + | 39.8372i | −1.13061 | + | 1.27581i | ||||
\(976\) | 1.97502 | − | 2.98775i | 0.0632189 | − | 0.0956357i | ||||
\(977\) | −5.94180 | − | 5.94180i | −0.190095 | − | 0.190095i | 0.605642 | − | 0.795737i | \(-0.292916\pi\) |
−0.795737 | + | 0.605642i | \(0.792916\pi\) | |||||||
\(978\) | 10.0599 | + | 1.47951i | 0.321679 | + | 0.0473097i | ||||
\(979\) | 24.0186i | 0.767637i | ||||||||
\(980\) | 0.583221 | + | 4.43394i | 0.0186303 | + | 0.141637i | ||||
\(981\) | − | 2.14977i | − | 0.0686369i | ||||||
\(982\) | 1.93641 | − | 13.1665i | 0.0617935 | − | 0.420161i | ||||
\(983\) | 31.0579 | + | 31.0579i | 0.990594 | + | 0.990594i | 0.999956 | − | 0.00936180i | \(-0.00298000\pi\) |
−0.00936180 | + | 0.999956i | \(0.502980\pi\) | |||||||
\(984\) | −8.43339 | − | 23.2966i | −0.268847 | − | 0.742668i | ||||
\(985\) | 8.63716 | − | 22.7692i | 0.275203 | − | 0.725488i | ||||
\(986\) | −12.5431 | + | 9.32671i | −0.399454 | + | 0.297023i | ||||
\(987\) | 7.31955 | + | 7.31955i | 0.232984 | + | 0.232984i | ||||
\(988\) | −39.6713 | + | 21.3312i | −1.26211 | + | 0.678637i | ||||
\(989\) | −36.1170 | −1.14845 | ||||||||
\(990\) | −69.3333 | + | 19.6978i | −2.20356 | + | 0.626036i | ||||
\(991\) | − | 7.18404i | − | 0.228209i | −0.993469 | − | 0.114104i | \(-0.963600\pi\) | ||
0.993469 | − | 0.114104i | \(-0.0363998\pi\) | |||||||
\(992\) | −18.5652 | − | 16.6183i | −0.589444 | − | 0.527632i | ||||
\(993\) | −22.4911 | + | 22.4911i | −0.713733 | + | 0.713733i | ||||
\(994\) | 9.77182 | − | 7.26605i | 0.309943 | − | 0.230465i | ||||
\(995\) | −6.20939 | + | 2.79407i | −0.196851 | + | 0.0885780i | ||||
\(996\) | 7.78185 | − | 25.8839i | 0.246577 | − | 0.820163i | ||||
\(997\) | 9.91715 | − | 9.91715i | 0.314079 | − | 0.314079i | −0.532408 | − | 0.846488i | \(-0.678713\pi\) |
0.846488 | + | 0.532408i | \(0.178713\pi\) | |||||||
\(998\) | 47.7247 | + | 7.01891i | 1.51070 | + | 0.222180i | ||||
\(999\) | −6.13357 | −0.194057 |
(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 | 280.2.w.a.267.17 | yes | 72 | |
4.3 | odd | 2 | 1120.2.bi.a.687.5 | 72 | |||
5.3 | odd | 4 | inner | 280.2.w.a.43.36 | yes | 72 | |
8.3 | odd | 2 | inner | 280.2.w.a.267.36 | yes | 72 | |
8.5 | even | 2 | 1120.2.bi.a.687.6 | 72 | |||
20.3 | even | 4 | 1120.2.bi.a.463.6 | 72 | |||
40.3 | even | 4 | inner | 280.2.w.a.43.17 | ✓ | 72 | |
40.13 | odd | 4 | 1120.2.bi.a.463.5 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.w.a.43.17 | ✓ | 72 | 40.3 | even | 4 | inner | |
280.2.w.a.43.36 | yes | 72 | 5.3 | odd | 4 | inner | |
280.2.w.a.267.17 | yes | 72 | 1.1 | even | 1 | trivial | |
280.2.w.a.267.36 | yes | 72 | 8.3 | odd | 2 | inner | |
1120.2.bi.a.463.5 | 72 | 40.13 | odd | 4 | |||
1120.2.bi.a.463.6 | 72 | 20.3 | even | 4 | |||
1120.2.bi.a.687.5 | 72 | 4.3 | odd | 2 | |||
1120.2.bi.a.687.6 | 72 | 8.5 | even | 2 |