Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(118,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.118");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.m (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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.7 | ||
Character | \(\chi\) | \(=\) | 525.307 |
Dual form | 525.2.m.c.118.7 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.653796 | + | 0.653796i | 0.462303 | + | 0.462303i | 0.899410 | − | 0.437106i | \(-0.143997\pi\) |
−0.437106 | + | 0.899410i | \(0.643997\pi\) | |||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | − | 1.14510i | − | 0.572551i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 0.924607i | − | 0.377469i | ||||||
\(7\) | −2.53981 | − | 0.741188i | −0.959958 | − | 0.280143i | ||||
\(8\) | 2.05625 | − | 2.05625i | 0.726996 | − | 0.726996i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.746568 | −0.225099 | −0.112549 | − | 0.993646i | \(-0.535902\pi\) | ||||
−0.112549 | + | 0.993646i | \(0.535902\pi\) | |||||||
\(12\) | −0.809710 | + | 0.809710i | −0.233743 | + | 0.233743i | ||||
\(13\) | −4.26864 | − | 4.26864i | −1.18391 | − | 1.18391i | −0.978723 | − | 0.205186i | \(-0.934220\pi\) |
−0.205186 | − | 0.978723i | \(-0.565780\pi\) | |||||||
\(14\) | −1.17593 | − | 2.14510i | −0.314281 | − | 0.573303i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.398534 | 0.0996336 | ||||||||
\(17\) | −5.29845 | + | 5.29845i | −1.28506 | + | 1.28506i | −0.347313 | + | 0.937749i | \(0.612906\pi\) |
−0.937749 | + | 0.347313i | \(0.887094\pi\) | |||||||
\(18\) | −0.653796 | + | 0.653796i | −0.154101 | + | 0.154101i | ||||
\(19\) | 1.17593 | 0.269777 | 0.134889 | − | 0.990861i | \(-0.456932\pi\) | ||||
0.134889 | + | 0.990861i | \(0.456932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.27182 | + | 2.32002i | 0.277534 | + | 0.506269i | ||||
\(22\) | −0.488103 | − | 0.488103i | −0.104064 | − | 0.104064i | ||||
\(23\) | 3.19815 | − | 3.19815i | 0.666861 | − | 0.666861i | −0.290127 | − | 0.956988i | \(-0.593698\pi\) |
0.956988 | + | 0.290127i | \(0.0936976\pi\) | |||||||
\(24\) | −2.90798 | −0.593589 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 5.58164i | − | 1.09465i | ||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | −0.848736 | + | 2.90834i | −0.160396 | + | 0.549625i | ||||
\(29\) | − | 2.45636i | − | 0.456135i | −0.973645 | − | 0.228068i | \(-0.926759\pi\) | ||
0.973645 | − | 0.228068i | \(-0.0732407\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.87436i | − | 0.875461i | −0.899106 | − | 0.437730i | \(-0.855782\pi\) | ||
0.899106 | − | 0.437730i | \(-0.144218\pi\) | |||||||
\(32\) | −3.85195 | − | 3.85195i | −0.680935 | − | 0.680935i | ||||
\(33\) | 0.527903 | + | 0.527903i | 0.0918962 | + | 0.0918962i | ||||
\(34\) | −6.92820 | −1.18818 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.14510 | 0.190850 | ||||||||
\(37\) | −2.05625 | − | 2.05625i | −0.338046 | − | 0.338046i | 0.517585 | − | 0.855632i | \(-0.326831\pi\) |
−0.855632 | + | 0.517585i | \(0.826831\pi\) | |||||||
\(38\) | 0.768819 | + | 0.768819i | 0.124719 | + | 0.124719i | ||||
\(39\) | 6.03677i | 0.966657i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.92820i | − | 1.08200i | −0.841021 | − | 0.541002i | \(-0.818045\pi\) | ||
0.841021 | − | 0.541002i | \(-0.181955\pi\) | |||||||
\(42\) | −0.685307 | + | 2.34833i | −0.105745 | + | 0.362355i | ||||
\(43\) | −6.64484 | + | 6.64484i | −1.01333 | + | 1.01333i | −0.0134193 | + | 0.999910i | \(0.504272\pi\) |
−0.999910 | + | 0.0134193i | \(0.995728\pi\) | |||||||
\(44\) | 0.854897i | 0.128881i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.18188 | 0.616584 | ||||||||
\(47\) | 5.29845 | − | 5.29845i | 0.772858 | − | 0.772858i | −0.205747 | − | 0.978605i | \(-0.565962\pi\) |
0.978605 | + | 0.205747i | \(0.0659624\pi\) | |||||||
\(48\) | −0.281806 | − | 0.281806i | −0.0406753 | − | 0.0406753i | ||||
\(49\) | 5.90128 | + | 3.76496i | 0.843040 | + | 0.537851i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.49314 | 1.04925 | ||||||||
\(52\) | −4.88804 | + | 4.88804i | −0.677849 | + | 0.677849i | ||||
\(53\) | 4.89898 | − | 4.89898i | 0.672927 | − | 0.672927i | −0.285463 | − | 0.958390i | \(-0.592147\pi\) |
0.958390 | + | 0.285463i | \(0.0921474\pi\) | |||||||
\(54\) | 0.924607 | 0.125823 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.74657 | + | 3.69843i | −0.901548 | + | 0.494223i | ||||
\(57\) | −0.831509 | − | 0.831509i | −0.110136 | − | 0.110136i | ||||
\(58\) | 1.60596 | − | 1.60596i | 0.210873 | − | 0.210873i | ||||
\(59\) | 12.5098 | 1.62864 | 0.814321 | − | 0.580414i | \(-0.197109\pi\) | ||||
0.814321 | + | 0.580414i | \(0.197109\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.52249i | 0.322972i | 0.986875 | + | 0.161486i | \(0.0516287\pi\) | ||||
−0.986875 | + | 0.161486i | \(0.948371\pi\) | |||||||
\(62\) | 3.18683 | − | 3.18683i | 0.404728 | − | 0.404728i | ||||
\(63\) | 0.741188 | − | 2.53981i | 0.0933809 | − | 0.319986i | ||||
\(64\) | − | 5.83384i | − | 0.729230i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.690282i | 0.0849678i | ||||||||
\(67\) | 6.47915 | + | 6.47915i | 0.791554 | + | 0.791554i | 0.981747 | − | 0.190192i | \(-0.0609112\pi\) |
−0.190192 | + | 0.981747i | \(0.560911\pi\) | |||||||
\(68\) | 6.06727 | + | 6.06727i | 0.735764 | + | 0.735764i | ||||
\(69\) | −4.52287 | −0.544490 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.74657 | −0.800670 | −0.400335 | − | 0.916369i | \(-0.631106\pi\) | ||||
−0.400335 | + | 0.916369i | \(0.631106\pi\) | |||||||
\(72\) | 2.05625 | + | 2.05625i | 0.242332 | + | 0.242332i | ||||
\(73\) | −2.47002 | − | 2.47002i | −0.289094 | − | 0.289094i | 0.547628 | − | 0.836722i | \(-0.315531\pi\) |
−0.836722 | + | 0.547628i | \(0.815531\pi\) | |||||||
\(74\) | − | 2.68874i | − | 0.312560i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.34656i | − | 0.154461i | ||||||
\(77\) | 1.89614 | + | 0.553347i | 0.216085 | + | 0.0630598i | ||||
\(78\) | −3.94682 | + | 3.94682i | −0.446889 | + | 0.446889i | ||||
\(79\) | 5.83384i | 0.656359i | 0.944615 | + | 0.328179i | \(0.106435\pi\) | ||||
−0.944615 | + | 0.328179i | \(0.893565\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 4.52963 | − | 4.52963i | 0.500214 | − | 0.500214i | ||||
\(83\) | 0.768819 | + | 0.768819i | 0.0843888 | + | 0.0843888i | 0.748041 | − | 0.663652i | \(-0.230995\pi\) |
−0.663652 | + | 0.748041i | \(0.730995\pi\) | |||||||
\(84\) | 2.65666 | − | 1.45636i | 0.289865 | − | 0.158902i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.68874 | −0.936931 | ||||||||
\(87\) | −1.73691 | + | 1.73691i | −0.186216 | + | 0.186216i | ||||
\(88\) | −1.53513 | + | 1.53513i | −0.163646 | + | 0.163646i | ||||
\(89\) | −3.69843 | −0.392032 | −0.196016 | − | 0.980601i | \(-0.562801\pi\) | ||||
−0.196016 | + | 0.980601i | \(0.562801\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.67768 | + | 14.0054i | 0.804840 | + | 1.46817i | ||||
\(92\) | −3.66221 | − | 3.66221i | −0.381812 | − | 0.381812i | ||||
\(93\) | −3.44669 | + | 3.44669i | −0.357405 | + | 0.357405i | ||||
\(94\) | 6.92820 | 0.714590 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.44748i | 0.555981i | ||||||||
\(97\) | 10.2839 | − | 10.2839i | 1.04417 | − | 1.04417i | 0.0451941 | − | 0.998978i | \(-0.485609\pi\) |
0.998978 | − | 0.0451941i | \(-0.0143906\pi\) | |||||||
\(98\) | 1.39672 | + | 6.31974i | 0.141090 | + | 0.638390i | ||||
\(99\) | − | 0.746568i | − | 0.0750329i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 3.69843i | − | 0.368007i | −0.982926 | − | 0.184004i | \(-0.941094\pi\) | ||
0.982926 | − | 0.184004i | \(-0.0589058\pi\) | |||||||
\(102\) | 4.89898 | + | 4.89898i | 0.485071 | + | 0.485071i | ||||
\(103\) | 1.70120 | + | 1.70120i | 0.167624 | + | 0.167624i | 0.785934 | − | 0.618310i | \(-0.212182\pi\) |
−0.618310 | + | 0.785934i | \(0.712182\pi\) | |||||||
\(104\) | −17.5548 | −1.72139 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.40586 | 0.622192 | ||||||||
\(107\) | 11.2953 | + | 11.2953i | 1.09196 | + | 1.09196i | 0.995320 | + | 0.0966367i | \(0.0308085\pi\) |
0.0966367 | + | 0.995320i | \(0.469192\pi\) | |||||||
\(108\) | −0.809710 | − | 0.809710i | −0.0779144 | − | 0.0779144i | ||||
\(109\) | − | 1.40586i | − | 0.134657i | −0.997731 | − | 0.0673286i | \(-0.978552\pi\) | ||
0.997731 | − | 0.0673286i | \(-0.0214476\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.90798i | 0.276013i | ||||||||
\(112\) | −1.01220 | − | 0.295389i | −0.0956441 | − | 0.0279116i | ||||
\(113\) | 10.2813 | − | 10.2813i | 0.967181 | − | 0.967181i | −0.0322977 | − | 0.999478i | \(-0.510282\pi\) |
0.999478 | + | 0.0322977i | \(0.0102825\pi\) | |||||||
\(114\) | − | 1.08727i | − | 0.101833i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.81279 | −0.261161 | ||||||||
\(117\) | 4.26864 | − | 4.26864i | 0.394636 | − | 0.394636i | ||||
\(118\) | 8.17888 | + | 8.17888i | 0.752927 | + | 0.752927i | ||||
\(119\) | 17.3842 | − | 9.52991i | 1.59361 | − | 0.873605i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4426 | −0.949331 | ||||||||
\(122\) | −1.64920 | + | 1.64920i | −0.149311 | + | 0.149311i | ||||
\(123\) | −4.89898 | + | 4.89898i | −0.441726 | + | 0.441726i | ||||
\(124\) | −5.58164 | −0.501246 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.14510 | − | 1.17593i | 0.191101 | − | 0.104760i | ||||
\(127\) | 5.48195 | + | 5.48195i | 0.486444 | + | 0.486444i | 0.907182 | − | 0.420738i | \(-0.138229\pi\) |
−0.420738 | + | 0.907182i | \(0.638229\pi\) | |||||||
\(128\) | −3.88976 | + | 3.88976i | −0.343809 | + | 0.343809i | ||||
\(129\) | 9.39723 | 0.827380 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.3304i | 1.33942i | 0.742623 | + | 0.669710i | \(0.233581\pi\) | ||||
−0.742623 | + | 0.669710i | \(0.766419\pi\) | |||||||
\(132\) | 0.604504 | − | 0.604504i | 0.0526153 | − | 0.0526153i | ||||
\(133\) | −2.98664 | − | 0.871587i | −0.258975 | − | 0.0755761i | ||||
\(134\) | 8.47208i | 0.731876i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.7899i | 1.86847i | ||||||||
\(137\) | −11.4610 | − | 11.4610i | −0.979177 | − | 0.979177i | 0.0206102 | − | 0.999788i | \(-0.493439\pi\) |
−0.999788 | + | 0.0206102i | \(0.993439\pi\) | |||||||
\(138\) | −2.95703 | − | 2.95703i | −0.251719 | − | 0.251719i | ||||
\(139\) | −12.5098 | −1.06107 | −0.530536 | − | 0.847663i | \(-0.678009\pi\) | ||||
−0.530536 | + | 0.847663i | \(0.678009\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.49314 | −0.631036 | ||||||||
\(142\) | −4.41088 | − | 4.41088i | −0.370153 | − | 0.370153i | ||||
\(143\) | 3.18683 | + | 3.18683i | 0.266496 | + | 0.266496i | ||||
\(144\) | 0.398534i | 0.0332112i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 3.22978i | − | 0.267298i | ||||||
\(147\) | −1.51061 | − | 6.83506i | −0.124593 | − | 0.563746i | ||||
\(148\) | −2.35462 | + | 2.35462i | −0.193549 | + | 0.193549i | ||||
\(149\) | 2.45636i | 0.201233i | 0.994925 | + | 0.100617i | \(0.0320815\pi\) | ||||
−0.994925 | + | 0.100617i | \(0.967918\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7833 | −1.04029 | −0.520147 | − | 0.854077i | \(-0.674123\pi\) | ||||
−0.520147 | + | 0.854077i | \(0.674123\pi\) | |||||||
\(152\) | 2.41801 | − | 2.41801i | 0.196127 | − | 0.196127i | ||||
\(153\) | −5.29845 | − | 5.29845i | −0.428354 | − | 0.428354i | ||||
\(154\) | 0.877913 | + | 1.60147i | 0.0707443 | + | 0.129050i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.91273 | 0.553461 | ||||||||
\(157\) | −9.56709 | + | 9.56709i | −0.763537 | + | 0.763537i | −0.976960 | − | 0.213423i | \(-0.931539\pi\) |
0.213423 | + | 0.976960i | \(0.431539\pi\) | |||||||
\(158\) | −3.81414 | + | 3.81414i | −0.303437 | + | 0.303437i | ||||
\(159\) | −6.92820 | −0.549442 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.4931 | + | 5.75227i | −0.826975 | + | 0.453342i | ||||
\(162\) | −0.653796 | − | 0.653796i | −0.0513670 | − | 0.0513670i | ||||
\(163\) | 10.1744 | − | 10.1744i | 0.796919 | − | 0.796919i | −0.185689 | − | 0.982608i | \(-0.559452\pi\) |
0.982608 | + | 0.185689i | \(0.0594518\pi\) | |||||||
\(164\) | −7.93350 | −0.619503 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.00530i | 0.0780265i | ||||||||
\(167\) | 16.6642 | − | 16.6642i | 1.28951 | − | 1.28951i | 0.354428 | − | 0.935083i | \(-0.384675\pi\) |
0.935083 | − | 0.354428i | \(-0.115325\pi\) | |||||||
\(168\) | 7.38573 | + | 2.15536i | 0.569821 | + | 0.166290i | ||||
\(169\) | 23.4426i | 1.80328i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.17593i | 0.0899258i | ||||||||
\(172\) | 7.60903 | + | 7.60903i | 0.580183 | + | 0.580183i | ||||
\(173\) | −6.83609 | − | 6.83609i | −0.519738 | − | 0.519738i | 0.397754 | − | 0.917492i | \(-0.369790\pi\) |
−0.917492 | + | 0.397754i | \(0.869790\pi\) | |||||||
\(174\) | −2.27117 | −0.172177 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.297533 | −0.0224274 | ||||||||
\(177\) | −8.84580 | − | 8.84580i | −0.664891 | − | 0.664891i | ||||
\(178\) | −2.41801 | − | 2.41801i | −0.181238 | − | 0.181238i | ||||
\(179\) | − | 16.0735i | − | 1.20139i | −0.799477 | − | 0.600697i | \(-0.794890\pi\) | ||
0.799477 | − | 0.600697i | \(-0.205110\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 26.6643i | − | 1.98194i | −0.134086 | − | 0.990970i | \(-0.542810\pi\) | ||
0.134086 | − | 0.990970i | \(-0.457190\pi\) | |||||||
\(182\) | −4.13705 | + | 14.1763i | −0.306658 | + | 1.05082i | ||||
\(183\) | 1.78367 | − | 1.78367i | 0.131853 | − | 0.131853i | ||||
\(184\) | − | 13.1524i | − | 0.969610i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.50686 | −0.330459 | ||||||||
\(187\) | 3.95565 | − | 3.95565i | 0.289266 | − | 0.289266i | ||||
\(188\) | −6.06727 | − | 6.06727i | −0.442501 | − | 0.442501i | ||||
\(189\) | −2.32002 | + | 1.27182i | −0.168756 | + | 0.0925112i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.89900 | 0.137407 | 0.0687034 | − | 0.997637i | \(-0.478114\pi\) | ||||
0.0687034 | + | 0.997637i | \(0.478114\pi\) | |||||||
\(192\) | −4.12515 | + | 4.12515i | −0.297707 | + | 0.297707i | ||||
\(193\) | 3.67423 | − | 3.67423i | 0.264477 | − | 0.264477i | −0.562393 | − | 0.826870i | \(-0.690119\pi\) |
0.826870 | + | 0.562393i | \(0.190119\pi\) | |||||||
\(194\) | 13.4471 | 0.965449 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.31126 | − | 6.75757i | 0.307947 | − | 0.482684i | ||||
\(197\) | 6.33446 | + | 6.33446i | 0.451311 | + | 0.451311i | 0.895790 | − | 0.444478i | \(-0.146611\pi\) |
−0.444478 | + | 0.895790i | \(0.646611\pi\) | |||||||
\(198\) | 0.488103 | − | 0.488103i | 0.0346880 | − | 0.0346880i | ||||
\(199\) | 8.98205 | 0.636721 | 0.318360 | − | 0.947970i | \(-0.396868\pi\) | ||||
0.318360 | + | 0.947970i | \(0.396868\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 9.16290i | − | 0.646301i | ||||||
\(202\) | 2.41801 | − | 2.41801i | 0.170131 | − | 0.170131i | ||||
\(203\) | −1.82063 | + | 6.23870i | −0.127783 | + | 0.437871i | ||||
\(204\) | − | 8.58041i | − | 0.600749i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.22448i | 0.154987i | ||||||||
\(207\) | 3.19815 | + | 3.19815i | 0.222287 | + | 0.222287i | ||||
\(208\) | −1.70120 | − | 1.70120i | −0.117957 | − | 0.117957i | ||||
\(209\) | −0.877913 | −0.0607265 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.442636 | 0.0304723 | 0.0152362 | − | 0.999884i | \(-0.495150\pi\) | ||||
0.0152362 | + | 0.999884i | \(0.495150\pi\) | |||||||
\(212\) | −5.60983 | − | 5.60983i | −0.385285 | − | 0.385285i | ||||
\(213\) | 4.77054 | + | 4.77054i | 0.326872 | + | 0.326872i | ||||
\(214\) | 14.7696i | 1.00963i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 2.90798i | − | 0.197863i | ||||||
\(217\) | −3.61282 | + | 12.3799i | −0.245254 | + | 0.840406i | ||||
\(218\) | 0.919147 | − | 0.919147i | 0.0622525 | − | 0.0622525i | ||||
\(219\) | 3.49314i | 0.236044i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 45.2344 | 3.04279 | ||||||||
\(222\) | −1.90123 | + | 1.90123i | −0.127602 | + | 0.127602i | ||||
\(223\) | −6.32825 | − | 6.32825i | −0.423771 | − | 0.423771i | 0.462729 | − | 0.886500i | \(-0.346870\pi\) |
−0.886500 | + | 0.462729i | \(0.846870\pi\) | |||||||
\(224\) | 6.92820 | + | 12.6382i | 0.462910 | + | 0.844428i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.4437 | 0.894262 | ||||||||
\(227\) | −3.95565 | + | 3.95565i | −0.262546 | + | 0.262546i | −0.826088 | − | 0.563542i | \(-0.809438\pi\) |
0.563542 | + | 0.826088i | \(0.309438\pi\) | |||||||
\(228\) | −0.952164 | + | 0.952164i | −0.0630586 | + | 0.0630586i | ||||
\(229\) | −14.1544 | −0.935351 | −0.467675 | − | 0.883900i | \(-0.654908\pi\) | ||||
−0.467675 | + | 0.883900i | \(0.654908\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.949499 | − | 1.73205i | −0.0624725 | − | 0.113961i | ||||
\(232\) | −5.05091 | − | 5.05091i | −0.331608 | − | 0.331608i | ||||
\(233\) | −20.4106 | + | 20.4106i | −1.33714 | + | 1.33714i | −0.438330 | + | 0.898814i | \(0.644430\pi\) |
−0.898814 | + | 0.438330i | \(0.855570\pi\) | |||||||
\(234\) | 5.58164 | 0.364883 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 14.3251i | − | 0.932482i | ||||||
\(237\) | 4.12515 | − | 4.12515i | 0.267957 | − | 0.267957i | ||||
\(238\) | 17.5963 | + | 5.13510i | 1.14060 | + | 0.332859i | ||||
\(239\) | − | 14.9863i | − | 0.969381i | −0.874686 | − | 0.484691i | \(-0.838932\pi\) | ||
0.874686 | − | 0.484691i | \(-0.161068\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 7.63549i | − | 0.491845i | −0.969290 | − | 0.245922i | \(-0.920909\pi\) | ||
0.969290 | − | 0.245922i | \(-0.0790909\pi\) | |||||||
\(242\) | −6.82735 | − | 6.82735i | −0.438879 | − | 0.438879i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 2.88852 | 0.184918 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.40586 | −0.408423 | ||||||||
\(247\) | −5.01963 | − | 5.01963i | −0.319392 | − | 0.319392i | ||||
\(248\) | −10.0229 | − | 10.0229i | −0.636456 | − | 0.636456i | ||||
\(249\) | − | 1.08727i | − | 0.0689032i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 15.3304i | − | 0.967644i | −0.875167 | − | 0.483822i | \(-0.839248\pi\) | ||
0.875167 | − | 0.483822i | \(-0.160752\pi\) | |||||||
\(252\) | −2.90834 | − | 0.848736i | −0.183208 | − | 0.0534654i | ||||
\(253\) | −2.38764 | + | 2.38764i | −0.150110 | + | 0.150110i | ||||
\(254\) | 7.16815i | 0.449770i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.7539 | −1.04712 | ||||||||
\(257\) | −19.0822 | + | 19.0822i | −1.19031 | + | 1.19031i | −0.213334 | + | 0.976979i | \(0.568432\pi\) |
−0.976979 | + | 0.213334i | \(0.931568\pi\) | |||||||
\(258\) | 6.14387 | + | 6.14387i | 0.382500 | + | 0.382500i | ||||
\(259\) | 3.69843 | + | 6.74657i | 0.229809 | + | 0.419211i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.45636 | 0.152045 | ||||||||
\(262\) | −10.0229 | + | 10.0229i | −0.619218 | + | 0.619218i | ||||
\(263\) | 9.76015 | − | 9.76015i | 0.601837 | − | 0.601837i | −0.338963 | − | 0.940800i | \(-0.610076\pi\) |
0.940800 | + | 0.338963i | \(0.110076\pi\) | |||||||
\(264\) | 2.17101 | 0.133616 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.38282 | − | 2.52249i | −0.0847859 | − | 0.154664i | ||||
\(267\) | 2.61518 | + | 2.61518i | 0.160047 | + | 0.160047i | ||||
\(268\) | 7.41929 | − | 7.41929i | 0.453206 | − | 0.453206i | ||||
\(269\) | 4.57634 | 0.279024 | 0.139512 | − | 0.990220i | \(-0.455447\pi\) | ||||
0.139512 | + | 0.990220i | \(0.455447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.05029i | − | 0.367529i | −0.982970 | − | 0.183764i | \(-0.941172\pi\) | ||
0.982970 | − | 0.183764i | \(-0.0588284\pi\) | |||||||
\(272\) | −2.11161 | + | 2.11161i | −0.128035 | + | 0.128035i | ||||
\(273\) | 4.47438 | − | 15.3323i | 0.270802 | − | 0.927951i | ||||
\(274\) | − | 14.9863i | − | 0.905354i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.17915i | 0.311748i | ||||||||
\(277\) | −11.3403 | − | 11.3403i | −0.681374 | − | 0.681374i | 0.278936 | − | 0.960310i | \(-0.410018\pi\) |
−0.960310 | + | 0.278936i | \(0.910018\pi\) | |||||||
\(278\) | −8.17888 | − | 8.17888i | −0.490537 | − | 0.490537i | ||||
\(279\) | 4.87436 | 0.291820 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.1976 | 1.68213 | 0.841064 | − | 0.540936i | \(-0.181930\pi\) | ||||
0.841064 | + | 0.540936i | \(0.181930\pi\) | |||||||
\(282\) | −4.89898 | − | 4.89898i | −0.291730 | − | 0.291730i | ||||
\(283\) | 20.1120 | + | 20.1120i | 1.19553 | + | 1.19553i | 0.975490 | + | 0.220043i | \(0.0706198\pi\) |
0.220043 | + | 0.975490i | \(0.429380\pi\) | |||||||
\(284\) | 7.72551i | 0.458425i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.16708i | 0.246404i | ||||||||
\(287\) | −5.13510 | + | 17.5963i | −0.303115 | + | 1.03868i | ||||
\(288\) | 3.85195 | − | 3.85195i | 0.226978 | − | 0.226978i | ||||
\(289\) | − | 39.1471i | − | 2.30277i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.5436 | −0.852563 | ||||||||
\(292\) | −2.82843 | + | 2.82843i | −0.165521 | + | 0.165521i | ||||
\(293\) | −3.18683 | − | 3.18683i | −0.186177 | − | 0.186177i | 0.607864 | − | 0.794041i | \(-0.292027\pi\) |
−0.794041 | + | 0.607864i | \(0.792027\pi\) | |||||||
\(294\) | 3.48110 | − | 5.45636i | 0.203022 | − | 0.318222i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.45636 | −0.491516 | ||||||||
\(297\) | −0.527903 | + | 0.527903i | −0.0306321 | + | 0.0306321i | ||||
\(298\) | −1.60596 | + | 1.60596i | −0.0930307 | + | 0.0930307i | ||||
\(299\) | −27.3035 | −1.57901 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.8017 | − | 11.9516i | 1.25663 | − | 0.688877i | ||||
\(302\) | −8.35769 | − | 8.35769i | −0.480931 | − | 0.480931i | ||||
\(303\) | −2.61518 | + | 2.61518i | −0.150238 | + | 0.150238i | ||||
\(304\) | 0.468649 | 0.0268789 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 6.92820i | − | 0.396059i | ||||||
\(307\) | 3.49982 | − | 3.49982i | 0.199746 | − | 0.199746i | −0.600145 | − | 0.799891i | \(-0.704891\pi\) |
0.799891 | + | 0.600145i | \(0.204891\pi\) | |||||||
\(308\) | 0.633640 | − | 2.17128i | 0.0361050 | − | 0.123720i | ||||
\(309\) | − | 2.40586i | − | 0.136865i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.6822i | 1.00267i | 0.865254 | + | 0.501333i | \(0.167157\pi\) | ||||
−0.865254 | + | 0.501333i | \(0.832843\pi\) | |||||||
\(312\) | 12.4131 | + | 12.4131i | 0.702756 | + | 0.702756i | ||||
\(313\) | −7.09707 | − | 7.09707i | −0.401150 | − | 0.401150i | 0.477488 | − | 0.878638i | \(-0.341547\pi\) |
−0.878638 | + | 0.477488i | \(0.841547\pi\) | |||||||
\(314\) | −12.5098 | −0.705971 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.68035 | 0.375799 | ||||||||
\(317\) | 18.9133 | + | 18.9133i | 1.06228 | + | 1.06228i | 0.997927 | + | 0.0643487i | \(0.0204970\pi\) |
0.0643487 | + | 0.997927i | \(0.479503\pi\) | |||||||
\(318\) | −4.52963 | − | 4.52963i | −0.254009 | − | 0.254009i | ||||
\(319\) | 1.83384i | 0.102675i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 15.9739i | − | 0.891579i | ||||||
\(322\) | −10.6212 | − | 3.09956i | −0.591895 | − | 0.172732i | ||||
\(323\) | −6.23061 | + | 6.23061i | −0.346681 | + | 0.346681i | ||||
\(324\) | 1.14510i | 0.0636168i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.3039 | 0.736837 | ||||||||
\(327\) | −0.994095 | + | 0.994095i | −0.0549736 | + | 0.0549736i | ||||
\(328\) | −14.2461 | − | 14.2461i | −0.786612 | − | 0.786612i | ||||
\(329\) | −17.3842 | + | 9.52991i | −0.958422 | + | 0.525401i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.2260 | −1.05676 | −0.528378 | − | 0.849009i | \(-0.677199\pi\) | ||||
−0.528378 | + | 0.849009i | \(0.677199\pi\) | |||||||
\(332\) | 0.880377 | − | 0.880377i | 0.0483169 | − | 0.0483169i | ||||
\(333\) | 2.05625 | − | 2.05625i | 0.112682 | − | 0.112682i | ||||
\(334\) | 21.7899 | 1.19229 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.506864 | + | 0.924607i | 0.0276517 | + | 0.0504414i | ||||
\(337\) | −4.77833 | − | 4.77833i | −0.260292 | − | 0.260292i | 0.564881 | − | 0.825173i | \(-0.308922\pi\) |
−0.825173 | + | 0.564881i | \(0.808922\pi\) | |||||||
\(338\) | −15.3267 | + | 15.3267i | −0.833662 | + | 0.833662i | ||||
\(339\) | −14.5399 | −0.789700 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.63904i | 0.197065i | ||||||||
\(342\) | −0.768819 | + | 0.768819i | −0.0415730 | + | 0.0415730i | ||||
\(343\) | −12.1976 | − | 13.9362i | −0.658608 | − | 0.752486i | ||||
\(344\) | 27.3270i | 1.47337i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 8.93881i | − | 0.480553i | ||||||
\(347\) | −13.7826 | − | 13.7826i | −0.739888 | − | 0.739888i | 0.232668 | − | 0.972556i | \(-0.425254\pi\) |
−0.972556 | + | 0.232668i | \(0.925254\pi\) | |||||||
\(348\) | 1.98894 | + | 1.98894i | 0.106618 | + | 0.106618i | ||||
\(349\) | −14.3931 | −0.770443 | −0.385221 | − | 0.922824i | \(-0.625875\pi\) | ||||
−0.385221 | + | 0.922824i | \(0.625875\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.03677 | −0.322219 | ||||||||
\(352\) | 2.87574 | + | 2.87574i | 0.153278 | + | 0.153278i | ||||
\(353\) | 9.82808 | + | 9.82808i | 0.523096 | + | 0.523096i | 0.918505 | − | 0.395409i | \(-0.129397\pi\) |
−0.395409 | + | 0.918505i | \(0.629397\pi\) | |||||||
\(354\) | − | 11.5667i | − | 0.614762i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.23508i | 0.224459i | ||||||||
\(357\) | −19.0312 | − | 5.55382i | −1.00724 | − | 0.293939i | ||||
\(358\) | 10.5088 | − | 10.5088i | 0.555408 | − | 0.555408i | ||||
\(359\) | 18.7466i | 0.989406i | 0.869062 | + | 0.494703i | \(0.164723\pi\) | ||||
−0.869062 | + | 0.494703i | \(0.835277\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6172 | −0.927220 | ||||||||
\(362\) | 17.4330 | − | 17.4330i | 0.916257 | − | 0.916257i | ||||
\(363\) | 7.38406 | + | 7.38406i | 0.387563 | + | 0.387563i | ||||
\(364\) | 16.0376 | − | 8.79173i | 0.840601 | − | 0.460812i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.33231 | 0.121912 | ||||||||
\(367\) | 23.7612 | − | 23.7612i | 1.24033 | − | 1.24033i | 0.280461 | − | 0.959865i | \(-0.409513\pi\) |
0.959865 | − | 0.280461i | \(-0.0904873\pi\) | |||||||
\(368\) | 1.27457 | − | 1.27457i | 0.0664418 | − | 0.0664418i | ||||
\(369\) | 6.92820 | 0.360668 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.0735 | + | 8.81142i | −0.834497 | + | 0.457466i | ||||
\(372\) | 3.94682 | + | 3.94682i | 0.204633 | + | 0.204633i | ||||
\(373\) | 5.83433 | − | 5.83433i | 0.302090 | − | 0.302090i | −0.539741 | − | 0.841831i | \(-0.681478\pi\) |
0.841831 | + | 0.539741i | \(0.181478\pi\) | |||||||
\(374\) | 5.17238 | 0.267457 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 21.7899i | − | 1.12373i | ||||||
\(377\) | −10.4853 | + | 10.4853i | −0.540022 | + | 0.540022i | ||||
\(378\) | −2.34833 | − | 0.685307i | −0.120785 | − | 0.0352484i | ||||
\(379\) | 4.60879i | 0.236738i | 0.992970 | + | 0.118369i | \(0.0377665\pi\) | ||||
−0.992970 | + | 0.118369i | \(0.962233\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 7.75265i | − | 0.397180i | ||||||
\(382\) | 1.24156 | + | 1.24156i | 0.0635236 | + | 0.0635236i | ||||
\(383\) | −0.306401 | − | 0.306401i | −0.0156564 | − | 0.0156564i | 0.699235 | − | 0.714892i | \(-0.253524\pi\) |
−0.714892 | + | 0.699235i | \(0.753524\pi\) | |||||||
\(384\) | 5.50095 | 0.280719 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.80440 | 0.244537 | ||||||||
\(387\) | −6.64484 | − | 6.64484i | −0.337776 | − | 0.337776i | ||||
\(388\) | −11.7761 | − | 11.7761i | −0.597842 | − | 0.597842i | ||||
\(389\) | 9.26809i | 0.469911i | 0.972006 | + | 0.234955i | \(0.0754944\pi\) | ||||
−0.972006 | + | 0.234955i | \(0.924506\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.8905i | 1.71392i | ||||||||
\(392\) | 19.8762 | − | 4.39283i | 1.00390 | − | 0.221871i | ||||
\(393\) | 10.8402 | − | 10.8402i | 0.546816 | − | 0.546816i | ||||
\(394\) | 8.28288i | 0.417285i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.854897 | −0.0429602 | ||||||||
\(397\) | −20.1120 | + | 20.1120i | −1.00939 | + | 1.00939i | −0.00943590 | + | 0.999955i | \(0.503004\pi\) |
−0.999955 | + | 0.00943590i | \(0.996996\pi\) | |||||||
\(398\) | 5.87242 | + | 5.87242i | 0.294358 | + | 0.294358i | ||||
\(399\) | 1.49557 | + | 2.72818i | 0.0748722 | + | 0.136580i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.03677 | 0.251524 | 0.125762 | − | 0.992060i | \(-0.459862\pi\) | ||||
0.125762 | + | 0.992060i | \(0.459862\pi\) | |||||||
\(402\) | 5.99067 | − | 5.99067i | 0.298787 | − | 0.298787i | ||||
\(403\) | −20.8069 | + | 20.8069i | −1.03647 | + | 1.03647i | ||||
\(404\) | −4.23508 | −0.210703 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.26915 | + | 2.88852i | −0.261504 | + | 0.143355i | ||||
\(407\) | 1.53513 | + | 1.53513i | 0.0760938 | + | 0.0760938i | ||||
\(408\) | 15.4078 | − | 15.4078i | 0.762799 | − | 0.762799i | ||||
\(409\) | 19.7361 | 0.975886 | 0.487943 | − | 0.872876i | \(-0.337747\pi\) | ||||
0.487943 | + | 0.872876i | \(0.337747\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.2083i | 0.799495i | ||||||||
\(412\) | 1.94805 | − | 1.94805i | 0.0959736 | − | 0.0959736i | ||||
\(413\) | −31.7726 | − | 9.27215i | −1.56343 | − | 0.456252i | ||||
\(414\) | 4.18188i | 0.205528i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 32.8852i | 1.61233i | ||||||||
\(417\) | 8.84580 | + | 8.84580i | 0.433180 | + | 0.433180i | ||||
\(418\) | −0.573976 | − | 0.573976i | −0.0280741 | − | 0.0280741i | ||||
\(419\) | 2.22448 | 0.108673 | 0.0543364 | − | 0.998523i | \(-0.482696\pi\) | ||||
0.0543364 | + | 0.998523i | \(0.482696\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0230 | −1.07334 | −0.536669 | − | 0.843793i | \(-0.680318\pi\) | ||||
−0.536669 | + | 0.843793i | \(0.680318\pi\) | |||||||
\(422\) | 0.289393 | + | 0.289393i | 0.0140874 | + | 0.0140874i | ||||
\(423\) | 5.29845 | + | 5.29845i | 0.257619 | + | 0.257619i | ||||
\(424\) | − | 20.1471i | − | 0.978429i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.23792i | 0.302228i | ||||||||
\(427\) | 1.86964 | − | 6.40666i | 0.0904784 | − | 0.310040i | ||||
\(428\) | 12.9343 | − | 12.9343i | 0.625201 | − | 0.625201i | ||||
\(429\) | − | 4.50686i | − | 0.217593i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.8990 | 1.24751 | 0.623755 | − | 0.781620i | \(-0.285606\pi\) | ||||
0.623755 | + | 0.781620i | \(0.285606\pi\) | |||||||
\(432\) | 0.281806 | − | 0.281806i | 0.0135584 | − | 0.0135584i | ||||
\(433\) | 19.5900 | + | 19.5900i | 0.941436 | + | 0.941436i | 0.998378 | − | 0.0569417i | \(-0.0181349\pi\) |
−0.0569417 | + | 0.998378i | \(0.518135\pi\) | |||||||
\(434\) | −10.4560 | + | 5.73191i | −0.501904 | + | 0.275141i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.60986 | −0.0770981 | ||||||||
\(437\) | 3.76081 | − | 3.76081i | 0.179904 | − | 0.179904i | ||||
\(438\) | −2.28380 | + | 2.28380i | −0.109124 | + | 0.109124i | ||||
\(439\) | −17.2568 | −0.823623 | −0.411811 | − | 0.911269i | \(-0.635104\pi\) | ||||
−0.411811 | + | 0.911269i | \(0.635104\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.76496 | + | 5.90128i | −0.179284 | + | 0.281013i | ||||
\(442\) | 29.5740 | + | 29.5740i | 1.40669 | + | 1.40669i | ||||
\(443\) | −1.16594 | + | 1.16594i | −0.0553955 | + | 0.0553955i | −0.734262 | − | 0.678866i | \(-0.762472\pi\) |
0.678866 | + | 0.734262i | \(0.262472\pi\) | |||||||
\(444\) | 3.32994 | 0.158032 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 8.27477i | − | 0.391822i | ||||||
\(447\) | 1.73691 | − | 1.73691i | 0.0821531 | − | 0.0821531i | ||||
\(448\) | −4.32397 | + | 14.8169i | −0.204289 | + | 0.700031i | ||||
\(449\) | − | 17.0368i | − | 0.804015i | −0.915636 | − | 0.402008i | \(-0.868313\pi\) | ||
0.915636 | − | 0.402008i | \(-0.131687\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.17238i | 0.243558i | ||||||||
\(452\) | −11.7731 | − | 11.7731i | −0.553761 | − | 0.553761i | ||||
\(453\) | 9.03919 | + | 9.03919i | 0.424698 | + | 0.424698i | ||||
\(454\) | −5.17238 | −0.242752 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.41959 | −0.160137 | ||||||||
\(457\) | −26.8069 | − | 26.8069i | −1.25397 | − | 1.25397i | −0.953923 | − | 0.300052i | \(-0.902996\pi\) |
−0.300052 | − | 0.953923i | \(-0.597004\pi\) | |||||||
\(458\) | −9.25410 | − | 9.25410i | −0.432416 | − | 0.432416i | ||||
\(459\) | 7.49314i | 0.349750i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.4218i | 1.55661i | 0.627886 | + | 0.778305i | \(0.283920\pi\) | ||||
−0.627886 | + | 0.778305i | \(0.716080\pi\) | |||||||
\(462\) | 0.511629 | − | 1.75319i | 0.0238031 | − | 0.0815656i | ||||
\(463\) | −14.8626 | + | 14.8626i | −0.690725 | + | 0.690725i | −0.962391 | − | 0.271666i | \(-0.912425\pi\) |
0.271666 | + | 0.962391i | \(0.412425\pi\) | |||||||
\(464\) | − | 0.978945i | − | 0.0454464i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.6887 | −1.23633 | ||||||||
\(467\) | −1.34279 | + | 1.34279i | −0.0621371 | + | 0.0621371i | −0.737492 | − | 0.675355i | \(-0.763990\pi\) |
0.675355 | + | 0.737492i | \(0.263990\pi\) | |||||||
\(468\) | −4.88804 | − | 4.88804i | −0.225950 | − | 0.225950i | ||||
\(469\) | −11.6536 | − | 21.2581i | −0.538111 | − | 0.981607i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.5299 | 0.623425 | ||||||||
\(472\) | 25.7234 | − | 25.7234i | 1.18402 | − | 1.18402i | ||||
\(473\) | 4.96083 | − | 4.96083i | 0.228099 | − | 0.228099i | ||||
\(474\) | 5.39401 | 0.247755 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.9127 | − | 19.9067i | −0.500184 | − | 0.912422i | ||||
\(477\) | 4.89898 | + | 4.89898i | 0.224309 | + | 0.224309i | ||||
\(478\) | 9.79796 | − | 9.79796i | 0.448148 | − | 0.448148i | ||||
\(479\) | 17.2136 | 0.786508 | 0.393254 | − | 0.919430i | \(-0.371349\pi\) | ||||
0.393254 | + | 0.919430i | \(0.371349\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.5548i | 0.800431i | ||||||||
\(482\) | 4.99205 | − | 4.99205i | 0.227381 | − | 0.227381i | ||||
\(483\) | 11.4872 | + | 3.35230i | 0.522687 | + | 0.152535i | ||||
\(484\) | 11.9579i | 0.543540i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.924607i | 0.0419410i | ||||||||
\(487\) | 18.8923 | + | 18.8923i | 0.856092 | + | 0.856092i | 0.990875 | − | 0.134784i | \(-0.0430339\pi\) |
−0.134784 | + | 0.990875i | \(0.543034\pi\) | |||||||
\(488\) | 5.18689 | + | 5.18689i | 0.234799 | + | 0.234799i | ||||
\(489\) | −14.3887 | −0.650682 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.9947 | −0.857217 | −0.428609 | − | 0.903490i | \(-0.640996\pi\) | ||||
−0.428609 | + | 0.903490i | \(0.640996\pi\) | |||||||
\(492\) | 5.60983 | + | 5.60983i | 0.252911 | + | 0.252911i | ||||
\(493\) | 13.0149 | + | 13.0149i | 0.586162 | + | 0.586162i | ||||
\(494\) | − | 6.56363i | − | 0.295312i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.94260i | − | 0.0872253i | ||||||
\(497\) | 17.1350 | + | 5.00048i | 0.768610 | + | 0.224302i | ||||
\(498\) | 0.710855 | − | 0.710855i | 0.0318542 | − | 0.0318542i | ||||
\(499\) | 5.52991i | 0.247553i | 0.992310 | + | 0.123776i | \(0.0395006\pi\) | ||||
−0.992310 | + | 0.123776i | \(0.960499\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.5667 | −1.05288 | ||||||||
\(502\) | 10.0229 | − | 10.0229i | 0.447345 | − | 0.447345i | ||||
\(503\) | 6.37367 | + | 6.37367i | 0.284188 | + | 0.284188i | 0.834777 | − | 0.550589i | \(-0.185597\pi\) |
−0.550589 | + | 0.834777i | \(0.685597\pi\) | |||||||
\(504\) | −3.69843 | − | 6.74657i | −0.164741 | − | 0.300516i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.12206 | −0.138792 | ||||||||
\(507\) | 16.5764 | − | 16.5764i | 0.736186 | − | 0.736186i | ||||
\(508\) | 6.27740 | − | 6.27740i | 0.278514 | − | 0.278514i | ||||
\(509\) | 12.5098 | 0.554489 | 0.277245 | − | 0.960799i | \(-0.410579\pi\) | ||||
0.277245 | + | 0.960799i | \(0.410579\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.44264 | + | 8.10414i | 0.196531 | + | 0.358506i | ||||
\(512\) | −3.17411 | − | 3.17411i | −0.140277 | − | 0.140277i | ||||
\(513\) | 0.831509 | − | 0.831509i | 0.0367120 | − | 0.0367120i | ||||
\(514\) | −24.9517 | −1.10057 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 10.7608i | − | 0.473717i | ||||||
\(517\) | −3.95565 | + | 3.95565i | −0.173969 | + | 0.173969i | ||||
\(518\) | −1.99286 | + | 6.82889i | −0.0875613 | + | 0.300044i | ||||
\(519\) | 9.66769i | 0.424364i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 16.2083i | − | 0.710097i | −0.934848 | − | 0.355049i | \(-0.884464\pi\) | ||
0.934848 | − | 0.355049i | \(-0.115536\pi\) | |||||||
\(522\) | 1.60596 | + | 1.60596i | 0.0702909 | + | 0.0702909i | ||||
\(523\) | 15.2760 | + | 15.2760i | 0.667971 | + | 0.667971i | 0.957246 | − | 0.289275i | \(-0.0934143\pi\) |
−0.289275 | + | 0.957246i | \(0.593414\pi\) | |||||||
\(524\) | 17.5548 | 0.766886 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.7623 | 0.556462 | ||||||||
\(527\) | 25.8265 | + | 25.8265i | 1.12502 | + | 1.12502i | ||||
\(528\) | 0.210388 | + | 0.210388i | 0.00915595 | + | 0.00915595i | ||||
\(529\) | 2.54364i | 0.110593i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.5098i | 0.542881i | ||||||||
\(532\) | −0.998056 | + | 3.42001i | −0.0432712 | + | 0.148276i | ||||
\(533\) | −29.5740 | + | 29.5740i | −1.28099 | + | 1.28099i | ||||
\(534\) | 3.41959i | 0.147980i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 26.6456 | 1.15091 | ||||||||
\(537\) | −11.3657 | + | 11.3657i | −0.490467 | + | 0.490467i | ||||
\(538\) | 2.99199 | + | 2.99199i | 0.128994 | + | 0.128994i | ||||
\(539\) | −4.40571 | − | 2.81080i | −0.189767 | − | 0.121070i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.7412 | 0.805749 | 0.402874 | − | 0.915255i | \(-0.368011\pi\) | ||||
0.402874 | + | 0.915255i | \(0.368011\pi\) | |||||||
\(542\) | 3.95565 | − | 3.95565i | 0.169910 | − | 0.169910i | ||||
\(543\) | −18.8545 | + | 18.8545i | −0.809123 | + | 0.809123i | ||||
\(544\) | 40.8187 | 1.75009 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.9495 | − | 7.09883i | 0.554187 | − | 0.303802i | ||||
\(547\) | −13.6589 | − | 13.6589i | −0.584012 | − | 0.584012i | 0.351992 | − | 0.936003i | \(-0.385505\pi\) |
−0.936003 | + | 0.351992i | \(0.885505\pi\) | |||||||
\(548\) | −13.1240 | + | 13.1240i | −0.560629 | + | 0.560629i | ||||
\(549\) | −2.52249 | −0.107657 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.88852i | − | 0.123055i | ||||||
\(552\) | −9.30017 | + | 9.30017i | −0.395842 | + | 0.395842i | ||||
\(553\) | 4.32397 | − | 14.8169i | 0.183874 | − | 0.630077i | ||||
\(554\) | − | 14.8285i | − | 0.630003i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.3251i | 0.607518i | ||||||||
\(557\) | 7.45231 | + | 7.45231i | 0.315765 | + | 0.315765i | 0.847138 | − | 0.531373i | \(-0.178324\pi\) |
−0.531373 | + | 0.847138i | \(0.678324\pi\) | |||||||
\(558\) | 3.18683 | + | 3.18683i | 0.134909 | + | 0.134909i | ||||
\(559\) | 56.7289 | 2.39938 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.59414 | −0.236185 | ||||||||
\(562\) | 18.4355 | + | 18.4355i | 0.777653 | + | 0.777653i | ||||
\(563\) | 31.9855 | + | 31.9855i | 1.34803 | + | 1.34803i | 0.887800 | + | 0.460229i | \(0.152233\pi\) |
0.460229 | + | 0.887800i | \(0.347767\pi\) | |||||||
\(564\) | 8.58041i | 0.361300i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 26.2982i | 1.10540i | ||||||||
\(567\) | 2.53981 | + | 0.741188i | 0.106662 | + | 0.0311270i | ||||
\(568\) | −13.8727 | + | 13.8727i | −0.582084 | + | 0.582084i | ||||
\(569\) | 3.13777i | 0.131542i | 0.997835 | + | 0.0657712i | \(0.0209507\pi\) | ||||
−0.997835 | + | 0.0657712i | \(0.979049\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.5951 | 0.485238 | 0.242619 | − | 0.970122i | \(-0.421993\pi\) | ||||
0.242619 | + | 0.970122i | \(0.421993\pi\) | |||||||
\(572\) | 3.64925 | − | 3.64925i | 0.152583 | − | 0.152583i | ||||
\(573\) | −1.34279 | − | 1.34279i | −0.0560961 | − | 0.0560961i | ||||
\(574\) | −14.8617 | + | 8.14709i | −0.620316 | + | 0.340053i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.83384 | 0.243077 | ||||||||
\(577\) | −7.09707 | + | 7.09707i | −0.295455 | + | 0.295455i | −0.839231 | − | 0.543776i | \(-0.816994\pi\) |
0.543776 | + | 0.839231i | \(0.316994\pi\) | |||||||
\(578\) | 25.5942 | − | 25.5942i | 1.06458 | − | 1.06458i | ||||
\(579\) | −5.19615 | −0.215945 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.38282 | − | 2.52249i | −0.0573689 | − | 0.104651i | ||||
\(582\) | −9.50857 | − | 9.50857i | −0.394143 | − | 0.394143i | ||||
\(583\) | −3.65742 | + | 3.65742i | −0.151475 | + | 0.151475i | ||||
\(584\) | −10.1580 | −0.420340 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 4.16708i | − | 0.172140i | ||||||
\(587\) | −10.9033 | + | 10.9033i | −0.450027 | + | 0.450027i | −0.895363 | − | 0.445336i | \(-0.853084\pi\) |
0.445336 | + | 0.895363i | \(0.353084\pi\) | |||||||
\(588\) | −7.82685 | + | 1.72980i | −0.322774 | + | 0.0713359i | ||||
\(589\) | − | 5.73191i | − | 0.236179i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 8.95827i | − | 0.368494i | ||||||
\(592\) | −0.819488 | − | 0.819488i | −0.0336808 | − | 0.0336808i | ||||
\(593\) | 10.5969 | + | 10.5969i | 0.435162 | + | 0.435162i | 0.890380 | − | 0.455218i | \(-0.150439\pi\) |
−0.455218 | + | 0.890380i | \(0.650439\pi\) | |||||||
\(594\) | −0.690282 | −0.0283226 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.81279 | 0.115216 | ||||||||
\(597\) | −6.35127 | − | 6.35127i | −0.259940 | − | 0.259940i | ||||
\(598\) | −17.8509 | − | 17.8509i | −0.729979 | − | 0.729979i | ||||
\(599\) | − | 0.0926102i | − | 0.00378395i | −0.999998 | − | 0.00189198i | \(-0.999398\pi\) | ||
0.999998 | − | 0.00189198i | \(-0.000602235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 25.6590i | − | 1.04665i | −0.852133 | − | 0.523326i | \(-0.824691\pi\) | ||
0.852133 | − | 0.523326i | \(-0.175309\pi\) | |||||||
\(602\) | 22.0678 | + | 6.43999i | 0.899415 | + | 0.262474i | ||||
\(603\) | −6.47915 | + | 6.47915i | −0.263851 | + | 0.263851i | ||||
\(604\) | 14.6382i | 0.595622i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.41959 | −0.138911 | ||||||||
\(607\) | 11.0073 | − | 11.0073i | 0.446773 | − | 0.446773i | −0.447507 | − | 0.894280i | \(-0.647688\pi\) |
0.894280 | + | 0.447507i | \(0.147688\pi\) | |||||||
\(608\) | −4.52963 | − | 4.52963i | −0.183701 | − | 0.183701i | ||||
\(609\) | 5.69880 | − | 3.12405i | 0.230927 | − | 0.126593i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −45.2344 | −1.82999 | ||||||||
\(612\) | −6.06727 | + | 6.06727i | −0.245255 | + | 0.245255i | ||||
\(613\) | 6.16876 | − | 6.16876i | 0.249154 | − | 0.249154i | −0.571469 | − | 0.820623i | \(-0.693626\pi\) |
0.820623 | + | 0.571469i | \(0.193626\pi\) | |||||||
\(614\) | 4.57634 | 0.184686 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.03677 | − | 2.76113i | 0.202937 | − | 0.111249i | ||||
\(617\) | −27.9729 | − | 27.9729i | −1.12615 | − | 1.12615i | −0.990798 | − | 0.135347i | \(-0.956785\pi\) |
−0.135347 | − | 0.990798i | \(-0.543215\pi\) | |||||||
\(618\) | 1.57294 | − | 1.57294i | 0.0632730 | − | 0.0632730i | ||||
\(619\) | −28.0788 | −1.12858 | −0.564292 | − | 0.825575i | \(-0.690851\pi\) | ||||
−0.564292 | + | 0.825575i | \(0.690851\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 4.52287i | − | 0.181497i | ||||||
\(622\) | −11.5606 | + | 11.5606i | −0.463536 | + | 0.463536i | ||||
\(623\) | 9.39330 | + | 2.74123i | 0.376335 | + | 0.109825i | ||||
\(624\) | 2.40586i | 0.0963116i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 9.28007i | − | 0.370906i | ||||||
\(627\) | 0.620778 | + | 0.620778i | 0.0247915 | + | 0.0247915i | ||||
\(628\) | 10.9553 | + | 10.9553i | 0.437164 | + | 0.437164i | ||||
\(629\) | 21.7899 | 0.868821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.79707 | 0.0715402 | 0.0357701 | − | 0.999360i | \(-0.488612\pi\) | ||||
0.0357701 | + | 0.999360i | \(0.488612\pi\) | |||||||
\(632\) | 11.9959 | + | 11.9959i | 0.477170 | + | 0.477170i | ||||
\(633\) | −0.312991 | − | 0.312991i | −0.0124403 | − | 0.0124403i | ||||
\(634\) | 24.7308i | 0.982188i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.93350i | 0.314584i | ||||||||
\(637\) | −9.11921 | − | 41.2617i | −0.361316 | − | 1.63485i | ||||
\(638\) | −1.19896 | + | 1.19896i | −0.0474672 | + | 0.0474672i | ||||
\(639\) | − | 6.74657i | − | 0.266890i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.9220 | −0.628883 | −0.314441 | − | 0.949277i | \(-0.601817\pi\) | ||||
−0.314441 | + | 0.949277i | \(0.601817\pi\) | |||||||
\(642\) | 10.4437 | − | 10.4437i | 0.412180 | − | 0.412180i | ||||
\(643\) | 4.94004 | + | 4.94004i | 0.194816 | + | 0.194816i | 0.797773 | − | 0.602957i | \(-0.206011\pi\) |
−0.602957 | + | 0.797773i | \(0.706011\pi\) | |||||||
\(644\) | 6.58694 | + | 12.0157i | 0.259562 | + | 0.473486i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.14709 | −0.320543 | ||||||||
\(647\) | 18.5082 | − | 18.5082i | 0.727632 | − | 0.727632i | −0.242515 | − | 0.970148i | \(-0.577972\pi\) |
0.970148 | + | 0.242515i | \(0.0779724\pi\) | |||||||
\(648\) | −2.05625 | + | 2.05625i | −0.0807773 | + | 0.0807773i | ||||
\(649\) | −9.33945 | −0.366606 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.3086 | − | 6.19930i | 0.443219 | − | 0.242970i | ||||
\(652\) | −11.6507 | − | 11.6507i | −0.456277 | − | 0.456277i | ||||
\(653\) | 21.5903 | − | 21.5903i | 0.844895 | − | 0.844895i | −0.144596 | − | 0.989491i | \(-0.546188\pi\) |
0.989491 | + | 0.144596i | \(0.0461883\pi\) | |||||||
\(654\) | −1.29987 | −0.0508289 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 2.76113i | − | 0.107804i | ||||||
\(657\) | 2.47002 | − | 2.47002i | 0.0963647 | − | 0.0963647i | ||||
\(658\) | −17.5963 | − | 5.13510i | −0.685976 | − | 0.200187i | ||||
\(659\) | − | 29.1608i | − | 1.13594i | −0.823048 | − | 0.567972i | \(-0.807728\pi\) | ||
0.823048 | − | 0.567972i | \(-0.192272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 5.92290i | − | 0.230374i | −0.993344 | − | 0.115187i | \(-0.963253\pi\) | ||
0.993344 | − | 0.115187i | \(-0.0367468\pi\) | |||||||
\(662\) | −12.5699 | − | 12.5699i | −0.488541 | − | 0.488541i | ||||
\(663\) | −31.9855 | − | 31.9855i | −1.24222 | − | 1.24222i | ||||
\(664\) | 3.16177 | 0.122701 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.68874 | 0.104187 | ||||||||
\(667\) | −7.85582 | − | 7.85582i | −0.304179 | − | 0.304179i | ||||
\(668\) | −19.0822 | − | 19.0822i | −0.738312 | − | 0.738312i | ||||
\(669\) | 8.94950i | 0.346008i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.88321i | − | 0.0727007i | ||||||
\(672\) | 4.03761 | − | 13.8356i | 0.155754 | − | 0.533718i | ||||
\(673\) | 22.9220 | − | 22.9220i | 0.883576 | − | 0.883576i | −0.110320 | − | 0.993896i | \(-0.535187\pi\) |
0.993896 | + | 0.110320i | \(0.0351875\pi\) | |||||||
\(674\) | − | 6.24810i | − | 0.240668i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26.8442 | 1.03247 | ||||||||
\(677\) | −21.3886 | + | 21.3886i | −0.822032 | + | 0.822032i | −0.986399 | − | 0.164367i | \(-0.947442\pi\) |
0.164367 | + | 0.986399i | \(0.447442\pi\) | |||||||
\(678\) | −9.50613 | − | 9.50613i | −0.365081 | − | 0.365081i | ||||
\(679\) | −33.7415 | + | 18.4969i | −1.29488 | + | 0.709845i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.59414 | 0.214368 | ||||||||
\(682\) | −2.37919 | + | 2.37919i | −0.0911039 | + | 0.0911039i | ||||
\(683\) | 19.1030 | − | 19.1030i | 0.730957 | − | 0.730957i | −0.239852 | − | 0.970809i | \(-0.577099\pi\) |
0.970809 | + | 0.239852i | \(0.0770991\pi\) | |||||||
\(684\) | 1.34656 | 0.0514871 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.13671 | − | 17.0862i | 0.0433999 | − | 0.652354i | ||||
\(687\) | 10.0087 | + | 10.0087i | 0.381855 | + | 0.381855i | ||||
\(688\) | −2.64820 | + | 2.64820i | −0.100962 | + | 0.100962i | ||||
\(689\) | −41.8240 | −1.59337 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.58694i | 0.250579i | 0.992120 | + | 0.125290i | \(0.0399860\pi\) | ||||
−0.992120 | + | 0.125290i | \(0.960014\pi\) | |||||||
\(692\) | −7.82802 | + | 7.82802i | −0.297577 | + | 0.297577i | ||||
\(693\) | −0.553347 | + | 1.89614i | −0.0210199 | + | 0.0720285i | ||||
\(694\) | − | 18.0220i | − | 0.684105i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.14306i | 0.270757i | ||||||||
\(697\) | 36.7087 | + | 36.7087i | 1.39044 | + | 1.39044i | ||||
\(698\) | −9.41012 | − | 9.41012i | −0.356178 | − | 0.356178i | ||||
\(699\) | 28.8650 | 1.09177 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | −3.94682 | − | 3.94682i | −0.148963 | − | 0.148963i | ||||
\(703\) | −2.41801 | − | 2.41801i | −0.0911972 | − | 0.0911972i | ||||
\(704\) | 4.35536i | 0.164149i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.8511i | 0.483658i | ||||||||
\(707\) | −2.74123 | + | 9.39330i | −0.103095 | + | 0.353272i | ||||
\(708\) | −10.1293 | + | 10.1293i | −0.380684 | + | 0.380684i | ||||
\(709\) | 38.5897i | 1.44927i | 0.689134 | + | 0.724634i | \(0.257991\pi\) | ||||
−0.689134 | + | 0.724634i | \(0.742009\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.83384 | −0.218786 | ||||||||
\(712\) | −7.60490 | + | 7.60490i | −0.285006 | + | 0.285006i | ||||
\(713\) | −15.5889 | − | 15.5889i | −0.583810 | − | 0.583810i | ||||
\(714\) | −8.81142 | − | 16.0735i | −0.329759 | − | 0.601537i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.4059 | −0.687859 | ||||||||
\(717\) | −10.5969 | + | 10.5969i | −0.395748 | + | 0.395748i | ||||
\(718\) | −12.2564 | + | 12.2564i | −0.457406 | + | 0.457406i | ||||
\(719\) | 13.9838 | 0.521508 | 0.260754 | − | 0.965405i | \(-0.416029\pi\) | ||||
0.260754 | + | 0.965405i | \(0.416029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.05982 | − | 5.58164i | −0.113954 | − | 0.207871i | ||||
\(722\) | −11.5180 | − | 11.5180i | −0.428657 | − | 0.428657i | ||||
\(723\) | −5.39910 | + | 5.39910i | −0.200795 | + | 0.200795i | ||||
\(724\) | −30.5333 | −1.13476 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.65533i | 0.358343i | ||||||||
\(727\) | −25.4104 | + | 25.4104i | −0.942421 | + | 0.942421i | −0.998430 | − | 0.0560096i | \(-0.982162\pi\) |
0.0560096 | + | 0.998430i | \(0.482162\pi\) | |||||||
\(728\) | 44.5860 | + | 13.0114i | 1.65247 | + | 0.482236i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 70.4147i | − | 2.60438i | ||||||
\(732\) | −2.04249 | − | 2.04249i | −0.0754926 | − | 0.0754926i | ||||
\(733\) | −25.5078 | − | 25.5078i | −0.942154 | − | 0.942154i | 0.0562621 | − | 0.998416i | \(-0.482082\pi\) |
−0.998416 | + | 0.0562621i | \(0.982082\pi\) | |||||||
\(734\) | 31.0700 | 1.14681 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.6382 | −0.908178 | ||||||||
\(737\) | −4.83713 | − | 4.83713i | −0.178178 | − | 0.178178i | ||||
\(738\) | 4.52963 | + | 4.52963i | 0.166738 | + | 0.166738i | ||||
\(739\) | − | 41.4005i | − | 1.52294i | −0.648198 | − | 0.761471i | \(-0.724477\pi\) | ||
0.648198 | − | 0.761471i | \(-0.275523\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.09883i | 0.260782i | ||||||||
\(742\) | −16.2697 | − | 4.74795i | −0.597279 | − | 0.174303i | ||||
\(743\) | 17.9474 | − | 17.9474i | 0.658425 | − | 0.658425i | −0.296582 | − | 0.955007i | \(-0.595847\pi\) |
0.955007 | + | 0.296582i | \(0.0958470\pi\) | |||||||
\(744\) | 14.1745i | 0.519664i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.62892 | 0.279315 | ||||||||
\(747\) | −0.768819 | + | 0.768819i | −0.0281296 | + | 0.0281296i | ||||
\(748\) | −4.52963 | − | 4.52963i | −0.165620 | − | 0.165620i | ||||
\(749\) | −20.3160 | − | 37.0598i | −0.742329 | − | 1.35414i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.0000 | 1.16770 | 0.583848 | − | 0.811863i | \(-0.301546\pi\) | ||||
0.583848 | + | 0.811863i | \(0.301546\pi\) | |||||||
\(752\) | 2.11161 | − | 2.11161i | 0.0770026 | − | 0.0770026i | ||||
\(753\) | −10.8402 | + | 10.8402i | −0.395039 | + | 0.395039i | ||||
\(754\) | −13.7105 | −0.499308 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.45636 | + | 2.65666i | 0.0529674 | + | 0.0966217i | ||||
\(757\) | 16.7226 | + | 16.7226i | 0.607794 | + | 0.607794i | 0.942369 | − | 0.334575i | \(-0.108593\pi\) |
−0.334575 | + | 0.942369i | \(0.608593\pi\) | |||||||
\(758\) | −3.01321 | + | 3.01321i | −0.109445 | + | 0.109445i | ||||
\(759\) | 3.37663 | 0.122564 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.8564i | 0.502294i | 0.967949 | + | 0.251147i | \(0.0808078\pi\) | ||||
−0.967949 | + | 0.251147i | \(0.919192\pi\) | |||||||
\(762\) | 5.06865 | − | 5.06865i | 0.183618 | − | 0.183618i | ||||
\(763\) | −1.04201 | + | 3.57062i | −0.0377232 | + | 0.129265i | ||||
\(764\) | − | 2.17455i | − | 0.0786724i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 0.400647i | − | 0.0144760i | ||||||
\(767\) | −53.4001 | − | 53.4001i | −1.92816 | − | 1.92816i | ||||
\(768\) | 11.8468 | + | 11.8468i | 0.427484 | + | 0.427484i | ||||
\(769\) | 22.4972 | 0.811270 | 0.405635 | − | 0.914035i | \(-0.367050\pi\) | ||||
0.405635 | + | 0.914035i | \(0.367050\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.9863 | 0.971887 | ||||||||
\(772\) | −4.20738 | − | 4.20738i | −0.151427 | − | 0.151427i | ||||
\(773\) | −14.2461 | − | 14.2461i | −0.512398 | − | 0.512398i | 0.402862 | − | 0.915261i | \(-0.368015\pi\) |
−0.915261 | + | 0.402862i | \(0.868015\pi\) | |||||||
\(774\) | − | 8.68874i | − | 0.312310i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 42.2926i | − | 1.51822i | ||||||
\(777\) | 2.15536 | − | 7.38573i | 0.0773232 | − | 0.264961i | ||||
\(778\) | −6.05943 | + | 6.05943i | −0.217241 | + | 0.217241i | ||||
\(779\) | − | 8.14709i | − | 0.291900i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.03677 | 0.180230 | ||||||||
\(782\) | −22.1575 | + | 22.1575i | −0.792349 | + | 0.792349i | ||||
\(783\) | −1.73691 | − | 1.73691i | −0.0620721 | − | 0.0620721i | ||||
\(784\) | 2.35186 | + | 1.50046i | 0.0839951 | + | 0.0535880i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 14.1745 | 0.505589 | ||||||||
\(787\) | −19.8056 | + | 19.8056i | −0.705993 | + | 0.705993i | −0.965690 | − | 0.259697i | \(-0.916377\pi\) |
0.259697 | + | 0.965690i | \(0.416377\pi\) | |||||||
\(788\) | 7.25360 | − | 7.25360i | 0.258399 | − | 0.258399i | ||||
\(789\) | −13.8029 | −0.491398 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.7328 | + | 18.4921i | −1.19940 | + | 0.657504i | ||||
\(792\) | −1.53513 | − | 1.53513i | −0.0545486 | − | 0.0545486i | ||||
\(793\) | 10.7676 | − | 10.7676i | 0.382370 | − | 0.382370i | ||||
\(794\) | −26.2982 | −0.933290 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 10.2854i | − | 0.364555i | ||||||
\(797\) | −30.9103 | + | 30.9103i | −1.09490 | + | 1.09490i | −0.0999020 | + | 0.994997i | \(0.531853\pi\) |
−0.994997 | + | 0.0999020i | \(0.968147\pi\) | |||||||
\(798\) | −0.805875 | + | 2.76147i | −0.0285277 | + | 0.0977550i | ||||
\(799\) | 56.1471i | 1.98634i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.69843i | − | 0.130677i | ||||||
\(802\) | 3.29302 | + | 3.29302i | 0.116281 | + | 0.116281i | ||||
\(803\) | 1.84404 | + | 1.84404i | 0.0650747 | + | 0.0650747i | ||||
\(804\) | −10.4925 | −0.370041 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27.2069 | −0.958323 | ||||||||
\(807\) | −3.23596 | − | 3.23596i | −0.113911 | − | 0.113911i | ||||
\(808\) | −7.60490 | − | 7.60490i | −0.267540 | − | 0.267540i | ||||
\(809\) | 6.15150i | 0.216275i | 0.994136 | + | 0.108138i | \(0.0344887\pi\) | ||||
−0.994136 | + | 0.108138i | \(0.965511\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.4704i | 1.21042i | 0.796066 | + | 0.605209i | \(0.206911\pi\) | ||||
−0.796066 | + | 0.605209i | \(0.793089\pi\) | |||||||
\(812\) | 7.14395 | + | 2.08480i | 0.250703 | + | 0.0731623i | ||||
\(813\) | −4.27820 | + | 4.27820i | −0.150043 | + | 0.150043i | ||||
\(814\) | 2.00733i | 0.0703568i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.98627 | 0.104540 | ||||||||
\(817\) | −7.81388 | + | 7.81388i | −0.273373 | + | 0.273373i | ||||
\(818\) | 12.9034 | + | 12.9034i | 0.451155 | + | 0.451155i | ||||
\(819\) | −14.0054 | + | 7.67768i | −0.489389 | + | 0.268280i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00000 | 0.209401 | 0.104701 | − | 0.994504i | \(-0.466612\pi\) | ||||
0.104701 | + | 0.994504i | \(0.466612\pi\) | |||||||
\(822\) | −10.5969 | + | 10.5969i | −0.369609 | + | 0.369609i | ||||
\(823\) | −7.92839 | + | 7.92839i | −0.276366 | + | 0.276366i | −0.831657 | − | 0.555290i | \(-0.812607\pi\) |
0.555290 | + | 0.831657i | \(0.312607\pi\) | |||||||
\(824\) | 6.99621 | 0.243724 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.7107 | − | 26.8349i | −0.511852 | − | 0.933706i | ||||
\(827\) | 3.24014 | + | 3.24014i | 0.112671 | + | 0.112671i | 0.761195 | − | 0.648524i | \(-0.224613\pi\) |
−0.648524 | + | 0.761195i | \(0.724613\pi\) | |||||||
\(828\) | 3.66221 | − | 3.66221i | 0.127271 | − | 0.127271i | ||||
\(829\) | 17.0862 | 0.593428 | 0.296714 | − | 0.954966i | \(-0.404109\pi\) | ||||
0.296714 | + | 0.954966i | \(0.404109\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.0376i | 0.556340i | ||||||||
\(832\) | −24.9026 | + | 24.9026i | −0.863342 | + | 0.863342i | ||||
\(833\) | −51.2160 | + | 11.3192i | −1.77453 | + | 0.392187i | ||||
\(834\) | 11.5667i | 0.400522i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.00530i | 0.0347691i | ||||||||
\(837\) | −3.44669 | − | 3.44669i | −0.119135 | − | 0.119135i | ||||
\(838\) | 1.45435 | + | 1.45435i | 0.0502398 | + | 0.0502398i | ||||
\(839\) | 14.2657 | 0.492506 | 0.246253 | − | 0.969206i | \(-0.420801\pi\) | ||||
0.246253 | + | 0.969206i | \(0.420801\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.9663 | 0.791941 | ||||||||
\(842\) | −14.3986 | − | 14.3986i | −0.496208 | − | 0.496208i | ||||
\(843\) | −19.9387 | − | 19.9387i | −0.686726 | − | 0.686726i | ||||
\(844\) | − | 0.506864i | − | 0.0174470i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.92820i | 0.238197i | ||||||||
\(847\) | 26.5223 | + | 7.73996i | 0.911318 | + | 0.265948i | ||||
\(848\) | 1.95241 | − | 1.95241i | 0.0670461 | − | 0.0670461i | ||||
\(849\) | − | 28.4426i | − | 0.976149i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.1524 | −0.450860 | ||||||||
\(852\) | 5.46276 | − | 5.46276i | 0.187151 | − | 0.187151i | ||||
\(853\) | −7.45548 | − | 7.45548i | −0.255271 | − | 0.255271i | 0.567857 | − | 0.823127i | \(-0.307773\pi\) |
−0.823127 | + | 0.567857i | \(0.807773\pi\) | |||||||
\(854\) | 5.41101 | − | 2.96628i | 0.185161 | − | 0.101504i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 46.4520 | 1.58770 | ||||||||
\(857\) | 22.1575 | − | 22.1575i | 0.756884 | − | 0.756884i | −0.218870 | − | 0.975754i | \(-0.570237\pi\) |
0.975754 | + | 0.218870i | \(0.0702370\pi\) | |||||||
\(858\) | 2.94657 | − | 2.94657i | 0.100594 | − | 0.100594i | ||||
\(859\) | −27.3716 | −0.933905 | −0.466953 | − | 0.884282i | \(-0.654648\pi\) | ||||
−0.466953 | + | 0.884282i | \(0.654648\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.0735 | − | 8.81142i | 0.547785 | − | 0.300292i | ||||
\(862\) | 16.9327 | + | 16.9327i | 0.576728 | + | 0.576728i | ||||
\(863\) | 30.8534 | − | 30.8534i | 1.05026 | − | 1.05026i | 0.0515936 | − | 0.998668i | \(-0.483570\pi\) |
0.998668 | − | 0.0515936i | \(-0.0164301\pi\) | |||||||
\(864\) | −5.44748 | −0.185327 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 25.6157i | 0.870458i | ||||||||
\(867\) | −27.6812 | + | 27.6812i | −0.940102 | + | 0.940102i | ||||
\(868\) | 14.1763 | + | 4.13705i | 0.481175 | + | 0.140420i | ||||
\(869\) | − | 4.35536i | − | 0.147746i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 55.3144i | − | 1.87426i | ||||||
\(872\) | −2.89081 | − | 2.89081i | −0.0978952 | − | 0.0978952i | ||||
\(873\) | 10.2839 | + | 10.2839i | 0.348057 | + | 0.348057i | ||||
\(874\) | 4.91760 | 0.166340 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.00000 | 0.135147 | ||||||||
\(877\) | 1.54236 | + | 1.54236i | 0.0520819 | + | 0.0520819i | 0.732668 | − | 0.680586i | \(-0.238275\pi\) |
−0.680586 | + | 0.732668i | \(0.738275\pi\) | |||||||
\(878\) | −11.2824 | − | 11.2824i | −0.380764 | − | 0.380764i | ||||
\(879\) | 4.50686i | 0.152013i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 14.3251i | − | 0.482623i | −0.970448 | − | 0.241312i | \(-0.922422\pi\) | ||
0.970448 | − | 0.241312i | \(-0.0775776\pi\) | |||||||
\(882\) | −6.31974 | + | 1.39672i | −0.212797 | + | 0.0470300i | ||||
\(883\) | 28.5666 | − | 28.5666i | 0.961341 | − | 0.961341i | −0.0379391 | − | 0.999280i | \(-0.512079\pi\) |
0.999280 | + | 0.0379391i | \(0.0120793\pi\) | |||||||
\(884\) | − | 51.7980i | − | 1.74216i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.52457 | −0.0512191 | ||||||||
\(887\) | 38.9332 | − | 38.9332i | 1.30725 | − | 1.30725i | 0.383854 | − | 0.923394i | \(-0.374596\pi\) |
0.923394 | − | 0.383854i | \(-0.125404\pi\) | |||||||
\(888\) | 5.97955 | + | 5.97955i | 0.200661 | + | 0.200661i | ||||
\(889\) | −9.85996 | − | 17.9863i | −0.330693 | − | 0.603240i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.746568 | 0.0250110 | ||||||||
\(892\) | −7.24650 | + | 7.24650i | −0.242631 | + | 0.242631i | ||||
\(893\) | 6.23061 | − | 6.23061i | 0.208500 | − | 0.208500i | ||||
\(894\) | 2.27117 | 0.0759593 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12.7623 | − | 6.99621i | 0.426358 | − | 0.233727i | ||||
\(897\) | 19.3065 | + | 19.3065i | 0.644626 | + | 0.644626i | ||||
\(898\) | 11.1386 | − | 11.1386i | 0.371699 | − | 0.371699i | ||||
\(899\) | −11.9732 | −0.399328 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51.9140i | 1.72951i | ||||||||
\(902\) | −3.38168 | + | 3.38168i | −0.112598 | + | 0.112598i | ||||
\(903\) | −23.8672 | − | 6.96511i | −0.794250 | − | 0.231784i | ||||
\(904\) | − | 42.2818i | − | 1.40627i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.8196i | 0.392679i | ||||||||
\(907\) | −14.5312 | − | 14.5312i | −0.482502 | − | 0.482502i | 0.423428 | − | 0.905930i | \(-0.360827\pi\) |
−0.905930 | + | 0.423428i | \(0.860827\pi\) | |||||||
\(908\) | 4.52963 | + | 4.52963i | 0.150321 | + | 0.150321i | ||||
\(909\) | 3.69843 | 0.122669 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.3407 | −0.607655 | −0.303827 | − | 0.952727i | \(-0.598265\pi\) | ||||
−0.303827 | + | 0.952727i | \(0.598265\pi\) | |||||||
\(912\) | −0.331385 | − | 0.331385i | −0.0109733 | − | 0.0109733i | ||||
\(913\) | −0.573976 | − | 0.573976i | −0.0189958 | − | 0.0189958i | ||||
\(914\) | − | 35.0525i | − | 1.15943i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.2083i | 0.535536i | ||||||||
\(917\) | 11.3627 | − | 38.9362i | 0.375229 | − | 1.28579i | ||||
\(918\) | −4.89898 | + | 4.89898i | −0.161690 | + | 0.161690i | ||||
\(919\) | − | 7.36375i | − | 0.242908i | −0.992597 | − | 0.121454i | \(-0.961244\pi\) | ||
0.992597 | − | 0.121454i | \(-0.0387557\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.94950 | −0.163092 | ||||||||
\(922\) | −21.8511 | + | 21.8511i | −0.719626 | + | 0.719626i | ||||
\(923\) | 28.7987 | + | 28.7987i | 0.947921 | + | 0.947921i | ||||
\(924\) | −1.98338 | + | 1.08727i | −0.0652483 | + | 0.0357687i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −19.4342 | −0.638649 | ||||||||
\(927\) | −1.70120 | + | 1.70120i | −0.0558748 | + | 0.0558748i | ||||
\(928\) | −9.46178 | + | 9.46178i | −0.310598 | + | 0.310598i | ||||
\(929\) | 46.8010 | 1.53549 | 0.767745 | − | 0.640755i | \(-0.221379\pi\) | ||||
0.767745 | + | 0.640755i | \(0.221379\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.93950 | + | 4.42733i | 0.227433 | + | 0.145100i | ||||
\(932\) | 23.3723 | + | 23.3723i | 0.765584 | + | 0.765584i | ||||
\(933\) | 12.5032 | − | 12.5032i | 0.409337 | − | 0.409337i | ||||
\(934\) | −1.75583 | −0.0574524 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 17.5548i | − | 0.573798i | ||||||
\(937\) | −3.80623 | + | 3.80623i | −0.124344 | + | 0.124344i | −0.766540 | − | 0.642196i | \(-0.778023\pi\) |
0.642196 | + | 0.766540i | \(0.278023\pi\) | |||||||
\(938\) | 6.27941 | − | 21.5175i | 0.205030 | − | 0.702571i | ||||
\(939\) | 10.0368i | 0.327538i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 42.6339i | − | 1.38983i | −0.719094 | − | 0.694913i | \(-0.755443\pi\) | ||
0.719094 | − | 0.694913i | \(-0.244557\pi\) | |||||||
\(942\) | 8.84580 | + | 8.84580i | 0.288212 | + | 0.288212i | ||||
\(943\) | −22.1575 | − | 22.1575i | −0.721546 | − | 0.721546i | ||||
\(944\) | 4.98560 | 0.162268 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.48674 | 0.210902 | ||||||||
\(947\) | 15.1940 | + | 15.1940i | 0.493739 | + | 0.493739i | 0.909482 | − | 0.415743i | \(-0.136478\pi\) |
−0.415743 | + | 0.909482i | \(0.636478\pi\) | |||||||
\(948\) | −4.72372 | − | 4.72372i | −0.153419 | − | 0.153419i | ||||
\(949\) | 21.0873i | 0.684522i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 26.7474i | − | 0.867345i | ||||||
\(952\) | 16.1504 | − | 55.3423i | 0.523438 | − | 1.79365i | ||||
\(953\) | 7.74170 | − | 7.74170i | 0.250778 | − | 0.250778i | −0.570511 | − | 0.821290i | \(-0.693255\pi\) |
0.821290 | + | 0.570511i | \(0.193255\pi\) | |||||||
\(954\) | 6.40586i | 0.207397i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −17.1608 | −0.555021 | ||||||||
\(957\) | 1.29672 | − | 1.29672i | 0.0419171 | − | 0.0419171i | ||||
\(958\) | 11.2542 | + | 11.2542i | 0.363605 | + | 0.363605i | ||||
\(959\) | 20.6140 | + | 37.6035i | 0.665660 | + | 1.21428i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.24063 | 0.233569 | ||||||||
\(962\) | −11.4773 | + | 11.4773i | −0.370042 | + | 0.370042i | ||||
\(963\) | −11.2953 | + | 11.2953i | −0.363985 | + | 0.363985i | ||||
\(964\) | −8.74342 | −0.281606 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.31859 | + | 9.70202i | 0.171123 | + | 0.312157i | ||||
\(967\) | −18.8514 | − | 18.8514i | −0.606221 | − | 0.606221i | 0.335735 | − | 0.941956i | \(-0.391015\pi\) |
−0.941956 | + | 0.335735i | \(0.891015\pi\) | |||||||
\(968\) | −21.4727 | + | 21.4727i | −0.690159 | + | 0.690159i | ||||
\(969\) | 8.81142 | 0.283064 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 7.33747i | − | 0.235471i | −0.993045 | − | 0.117735i | \(-0.962437\pi\) | ||
0.993045 | − | 0.117735i | \(-0.0375634\pi\) | |||||||
\(972\) | 0.809710 | − | 0.809710i | 0.0259715 | − | 0.0259715i | ||||
\(973\) | 31.7726 | + | 9.27215i | 1.01858 | + | 0.297251i | ||||
\(974\) | 24.7034i | 0.791548i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.00530i | 0.0321789i | ||||||||
\(977\) | 18.0848 | + | 18.0848i | 0.578585 | + | 0.578585i | 0.934513 | − | 0.355928i | \(-0.115835\pi\) |
−0.355928 | + | 0.934513i | \(0.615835\pi\) | |||||||
\(978\) | −9.40730 | − | 9.40730i | −0.300812 | − | 0.300812i | ||||
\(979\) | 2.76113 | 0.0882460 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.40586 | 0.0448857 | ||||||||
\(982\) | −12.4186 | − | 12.4186i | −0.396294 | − | 0.396294i | ||||
\(983\) | −7.87248 | − | 7.87248i | −0.251093 | − | 0.251093i | 0.570326 | − | 0.821419i | \(-0.306817\pi\) |
−0.821419 | + | 0.570326i | \(0.806817\pi\) | |||||||
\(984\) | 20.1471i | 0.642266i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 17.0182i | 0.541969i | ||||||||
\(987\) | 19.0312 | + | 5.55382i | 0.605768 | + | 0.176780i | ||||
\(988\) | −5.74800 | + | 5.74800i | −0.182868 | + | 0.182868i | ||||
\(989\) | 42.5025i | 1.35150i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.85689 | 0.154284 | 0.0771421 | − | 0.997020i | \(-0.475420\pi\) | ||||
0.0771421 | + | 0.997020i | \(0.475420\pi\) | |||||||
\(992\) | −18.7758 | + | 18.7758i | −0.596131 | + | 0.596131i | ||||
\(993\) | 13.5948 | + | 13.5948i | 0.431419 | + | 0.431419i | ||||
\(994\) | 7.93350 | + | 14.4721i | 0.251635 | + | 0.459027i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.24504 | −0.0394506 | ||||||||
\(997\) | 24.6275 | − | 24.6275i | 0.779960 | − | 0.779960i | −0.199864 | − | 0.979824i | \(-0.564050\pi\) |
0.979824 | + | 0.199864i | \(0.0640500\pi\) | |||||||
\(998\) | −3.61543 | + | 3.61543i | −0.114444 | + | 0.114444i | ||||
\(999\) | −2.90798 | −0.0920045 |
(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 | 525.2.m.c.307.7 | yes | 24 | |
5.2 | odd | 4 | inner | 525.2.m.c.118.5 | ✓ | 24 | |
5.3 | odd | 4 | inner | 525.2.m.c.118.8 | yes | 24 | |
5.4 | even | 2 | inner | 525.2.m.c.307.6 | yes | 24 | |
7.6 | odd | 2 | inner | 525.2.m.c.307.8 | yes | 24 | |
35.13 | even | 4 | inner | 525.2.m.c.118.7 | yes | 24 | |
35.27 | even | 4 | inner | 525.2.m.c.118.6 | yes | 24 | |
35.34 | odd | 2 | inner | 525.2.m.c.307.5 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.m.c.118.5 | ✓ | 24 | 5.2 | odd | 4 | inner | |
525.2.m.c.118.6 | yes | 24 | 35.27 | even | 4 | inner | |
525.2.m.c.118.7 | yes | 24 | 35.13 | even | 4 | inner | |
525.2.m.c.118.8 | yes | 24 | 5.3 | odd | 4 | inner | |
525.2.m.c.307.5 | yes | 24 | 35.34 | odd | 2 | inner | |
525.2.m.c.307.6 | yes | 24 | 5.4 | even | 2 | inner | |
525.2.m.c.307.7 | yes | 24 | 1.1 | even | 1 | trivial | |
525.2.m.c.307.8 | yes | 24 | 7.6 | odd | 2 | inner |