Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(116,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.89539436150784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 116.6 | ||
Root | \(-0.147520 + 0.550552i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.116 |
Dual form | 637.2.r.d.324.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.14878 | − | 1.24060i | 1.51941 | − | 0.877235i | 0.519677 | − | 0.854363i | \(-0.326052\pi\) |
0.999738 | − | 0.0228716i | \(-0.00728089\pi\) | |||||||
\(3\) | 0.837565 | − | 1.45071i | 0.483569 | − | 0.837565i | −0.516253 | − | 0.856436i | \(-0.672674\pi\) |
0.999822 | + | 0.0188705i | \(0.00600703\pi\) | |||||||
\(4\) | 2.07816 | − | 3.59948i | 1.03908 | − | 1.79974i | ||||
\(5\) | 0.584680 | − | 0.337565i | 0.261477 | − | 0.150964i | −0.363531 | − | 0.931582i | \(-0.618429\pi\) |
0.625008 | + | 0.780618i | \(0.285096\pi\) | |||||||
\(6\) | − | 4.15633i | − | 1.69681i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 5.35026i | − | 1.89160i | ||||||
\(9\) | 0.0969683 | + | 0.167954i | 0.0323228 | + | 0.0559847i | ||||
\(10\) | 0.837565 | − | 1.45071i | 0.264861 | − | 0.458753i | ||||
\(11\) | 3.88083 | + | 2.24060i | 1.17011 | + | 0.675565i | 0.953707 | − | 0.300738i | \(-0.0972329\pi\) |
0.216407 | + | 0.976303i | \(0.430566\pi\) | |||||||
\(12\) | −3.48119 | − | 6.02961i | −1.00493 | − | 1.74060i | ||||
\(13\) | −3.28726 | + | 1.48119i | −0.911721 | + | 0.410809i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.13093i | − | 0.292006i | ||||||
\(16\) | −2.48119 | − | 4.29755i | −0.620299 | − | 1.07439i | ||||
\(17\) | −1.64363 | + | 2.84685i | −0.398639 | + | 0.690462i | −0.993558 | − | 0.113323i | \(-0.963851\pi\) |
0.594920 | + | 0.803785i | \(0.297184\pi\) | |||||||
\(18\) | 0.416726 | + | 0.240597i | 0.0982234 | + | 0.0567093i | ||||
\(19\) | −4.52007 | + | 2.60966i | −1.03698 | + | 0.598698i | −0.918975 | − | 0.394315i | \(-0.870982\pi\) |
−0.118000 | + | 0.993014i | \(0.537648\pi\) | |||||||
\(20\) | − | 2.80606i | − | 0.627455i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.1187 | 2.37052 | ||||||||
\(23\) | −2.38423 | − | 4.12960i | −0.497145 | − | 0.861081i | 0.502849 | − | 0.864374i | \(-0.332285\pi\) |
−0.999995 | + | 0.00329297i | \(0.998952\pi\) | |||||||
\(24\) | −7.76166 | − | 4.48119i | −1.58434 | − | 0.914720i | ||||
\(25\) | −2.27210 | + | 3.93539i | −0.454420 | + | 0.787078i | ||||
\(26\) | −5.22602 | + | 7.26092i | −1.02491 | + | 1.42398i | ||||
\(27\) | 5.35026 | 1.02966 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.31265 | −1.72932 | −0.864658 | − | 0.502361i | \(-0.832465\pi\) | ||||
−0.864658 | + | 0.502361i | \(0.832465\pi\) | |||||||
\(30\) | −1.40303 | − | 2.43012i | −0.256157 | − | 0.443678i | ||||
\(31\) | −1.41813 | − | 0.818760i | −0.254704 | − | 0.147054i | 0.367212 | − | 0.930137i | \(-0.380312\pi\) |
−0.621916 | + | 0.783084i | \(0.713646\pi\) | |||||||
\(32\) | −1.39614 | − | 0.806063i | −0.246806 | − | 0.142493i | ||||
\(33\) | 6.50089 | − | 3.75329i | 1.13166 | − | 0.653365i | ||||
\(34\) | 8.15633i | 1.39880i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.806063 | 0.134344 | ||||||||
\(37\) | 1.25018 | − | 0.721791i | 0.205528 | − | 0.118662i | −0.393703 | − | 0.919238i | \(-0.628806\pi\) |
0.599231 | + | 0.800576i | \(0.295473\pi\) | |||||||
\(38\) | −6.47508 | + | 11.2152i | −1.05040 | + | 1.81934i | ||||
\(39\) | −0.604516 | + | 6.00944i | −0.0968001 | + | 0.962281i | ||||
\(40\) | −1.80606 | − | 3.12819i | −0.285564 | − | 0.494611i | ||||
\(41\) | − | 7.92478i | − | 1.23764i | −0.785532 | − | 0.618821i | \(-0.787611\pi\) | ||
0.785532 | − | 0.618821i | \(-0.212389\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.61213 | −0.703343 | −0.351671 | − | 0.936124i | \(-0.614387\pi\) | ||||
−0.351671 | + | 0.936124i | \(0.614387\pi\) | |||||||
\(44\) | 16.1300 | − | 9.31265i | 2.43169 | − | 1.40393i | ||||
\(45\) | 0.113391 | + | 0.0654663i | 0.0169033 | + | 0.00975914i | ||||
\(46\) | −10.2463 | − | 5.91573i | −1.51074 | − | 0.872227i | ||||
\(47\) | 6.81481 | − | 3.93453i | 0.994043 | − | 0.573911i | 0.0875623 | − | 0.996159i | \(-0.472092\pi\) |
0.906480 | + | 0.422248i | \(0.138759\pi\) | |||||||
\(48\) | −8.31265 | −1.19983 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 11.2750i | 1.59453i | ||||||||
\(51\) | 2.75329 | + | 4.76884i | 0.385538 | + | 0.667772i | ||||
\(52\) | −1.49992 | + | 14.9106i | −0.208002 | + | 2.06773i | ||||
\(53\) | 1.57816 | − | 2.73346i | 0.216777 | − | 0.375469i | −0.737044 | − | 0.675845i | \(-0.763779\pi\) |
0.953821 | + | 0.300376i | \(0.0971121\pi\) | |||||||
\(54\) | 11.4965 | − | 6.63752i | 1.56448 | − | 0.903252i | ||||
\(55\) | 3.02539 | 0.407944 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.74306i | 1.15805i | ||||||||
\(58\) | −20.0108 | + | 11.5532i | −2.62755 | + | 1.51702i | ||||
\(59\) | 2.20334 | + | 1.27210i | 0.286850 | + | 0.165613i | 0.636521 | − | 0.771260i | \(-0.280373\pi\) |
−0.349670 | + | 0.936873i | \(0.613706\pi\) | |||||||
\(60\) | −4.07077 | − | 2.35026i | −0.525535 | − | 0.303417i | ||||
\(61\) | −1.15633 | − | 2.00281i | −0.148052 | − | 0.256434i | 0.782455 | − | 0.622707i | \(-0.213967\pi\) |
−0.930508 | + | 0.366273i | \(0.880634\pi\) | |||||||
\(62\) | −4.06300 | −0.516002 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.92478 | 0.740597 | ||||||||
\(65\) | −1.42200 | + | 1.97569i | −0.176377 | + | 0.245054i | ||||
\(66\) | 9.31265 | − | 16.1300i | 1.14631 | − | 1.98546i | ||||
\(67\) | 6.36551 | + | 3.67513i | 0.777671 | + | 0.448989i | 0.835604 | − | 0.549332i | \(-0.185118\pi\) |
−0.0579331 | + | 0.998320i | \(0.518451\pi\) | |||||||
\(68\) | 6.83146 | + | 11.8324i | 0.828436 | + | 1.43489i | ||||
\(69\) | −7.98778 | −0.961616 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.75623i | − | 0.920496i | −0.887791 | − | 0.460248i | \(-0.847761\pi\) | ||
0.887791 | − | 0.460248i | \(-0.152239\pi\) | |||||||
\(72\) | 0.898598 | − | 0.518806i | 0.105901 | − | 0.0611418i | ||||
\(73\) | 13.1152 | + | 7.57205i | 1.53502 | + | 0.886242i | 0.999119 | + | 0.0419581i | \(0.0133596\pi\) |
0.535896 | + | 0.844284i | \(0.319974\pi\) | |||||||
\(74\) | 1.79090 | − | 3.10194i | 0.208188 | − | 0.360593i | ||||
\(75\) | 3.80606 | + | 6.59230i | 0.439486 | + | 0.761213i | ||||
\(76\) | 21.6932i | 2.48838i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.15633 | + | 13.6629i | 0.697067 | + | 1.54702i | ||||
\(79\) | −7.33146 | − | 12.6985i | −0.824853 | − | 1.42869i | −0.902031 | − | 0.431670i | \(-0.857924\pi\) |
0.0771782 | − | 0.997017i | \(-0.475409\pi\) | |||||||
\(80\) | −2.90141 | − | 1.67513i | −0.324388 | − | 0.187285i | ||||
\(81\) | 4.19029 | − | 7.25779i | 0.465588 | − | 0.806422i | ||||
\(82\) | −9.83146 | − | 17.0286i | −1.08570 | − | 1.88049i | ||||
\(83\) | − | 1.45088i | − | 0.159254i | −0.996825 | − | 0.0796272i | \(-0.974627\pi\) | ||
0.996825 | − | 0.0796272i | \(-0.0253730\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.21933i | 0.240720i | ||||||||
\(86\) | −9.91043 | + | 5.72179i | −1.06867 | + | 0.616997i | ||||
\(87\) | −7.79995 | + | 13.5099i | −0.836243 | + | 1.44842i | ||||
\(88\) | 11.9878 | − | 20.7634i | 1.27790 | − | 2.21339i | ||||
\(89\) | −6.74967 | + | 3.89692i | −0.715463 | + | 0.413073i | −0.813081 | − | 0.582151i | \(-0.802211\pi\) |
0.0976173 | + | 0.995224i | \(0.468878\pi\) | |||||||
\(90\) | 0.324869 | 0.0342442 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −19.8192 | −2.06630 | ||||||||
\(93\) | −2.37556 | + | 1.37153i | −0.246334 | + | 0.142221i | ||||
\(94\) | 9.76234 | − | 16.9089i | 1.00691 | − | 1.74402i | ||||
\(95\) | −1.76187 | + | 3.05164i | −0.180764 | + | 0.313092i | ||||
\(96\) | −2.33872 | + | 1.35026i | −0.238695 | + | 0.137811i | ||||
\(97\) | − | 17.9805i | − | 1.82564i | −0.408360 | − | 0.912821i | \(-0.633899\pi\) | ||
0.408360 | − | 0.912821i | \(-0.366101\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.869067i | 0.0873446i | ||||||||
\(100\) | 9.44358 | + | 16.3568i | 0.944358 | + | 1.63568i | ||||
\(101\) | 4.66902 | − | 8.08698i | 0.464585 | − | 0.804685i | −0.534598 | − | 0.845107i | \(-0.679537\pi\) |
0.999183 | + | 0.0404219i | \(0.0128702\pi\) | |||||||
\(102\) | 11.8324 | + | 6.83146i | 1.17159 | + | 0.676415i | ||||
\(103\) | 3.11871 | + | 5.40177i | 0.307296 | + | 0.532252i | 0.977770 | − | 0.209681i | \(-0.0672425\pi\) |
−0.670474 | + | 0.741933i | \(0.733909\pi\) | |||||||
\(104\) | 7.92478 | + | 17.5877i | 0.777088 | + | 1.72461i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 7.83146i | − | 0.760658i | ||||||
\(107\) | −3.62236 | − | 6.27411i | −0.350187 | − | 0.606541i | 0.636095 | − | 0.771611i | \(-0.280549\pi\) |
−0.986282 | + | 0.165069i | \(0.947215\pi\) | |||||||
\(108\) | 11.1187 | − | 19.2582i | 1.06990 | − | 1.85312i | ||||
\(109\) | 4.15159 | + | 2.39692i | 0.397650 | + | 0.229584i | 0.685470 | − | 0.728101i | \(-0.259597\pi\) |
−0.287819 | + | 0.957685i | \(0.592930\pi\) | |||||||
\(110\) | 6.50089 | − | 3.75329i | 0.619836 | − | 0.357862i | ||||
\(111\) | − | 2.41819i | − | 0.229524i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.34297 | −0.878912 | −0.439456 | − | 0.898264i | \(-0.644829\pi\) | ||||
−0.439456 | + | 0.898264i | \(0.644829\pi\) | |||||||
\(114\) | 10.8466 | + | 18.7869i | 1.01588 | + | 1.75955i | ||||
\(115\) | −2.78802 | − | 1.60966i | −0.259984 | − | 0.150102i | ||||
\(116\) | −19.3532 | + | 33.5207i | −1.79690 | + | 3.11232i | ||||
\(117\) | −0.567532 | − | 0.408479i | −0.0524684 | − | 0.0377639i | ||||
\(118\) | 6.31265 | 0.581127 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.05079 | −0.552359 | ||||||||
\(121\) | 4.54055 | + | 7.86447i | 0.412777 | + | 0.714951i | ||||
\(122\) | −4.96937 | − | 2.86907i | −0.449906 | − | 0.259753i | ||||
\(123\) | −11.4965 | − | 6.63752i | −1.03661 | − | 0.598485i | ||||
\(124\) | −5.89422 | + | 3.40303i | −0.529317 | + | 0.305601i | ||||
\(125\) | 6.44358i | 0.576332i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.38058 | −0.122507 | −0.0612533 | − | 0.998122i | \(-0.519510\pi\) | ||||
−0.0612533 | + | 0.998122i | \(0.519510\pi\) | |||||||
\(128\) | 15.5233 | − | 8.96239i | 1.37208 | − | 0.792171i | ||||
\(129\) | −3.86296 | + | 6.69084i | −0.340114 | + | 0.589096i | ||||
\(130\) | −0.604516 | + | 6.00944i | −0.0530196 | + | 0.527063i | ||||
\(131\) | 6.24965 | + | 10.8247i | 0.546034 | + | 0.945759i | 0.998541 | + | 0.0539980i | \(0.0171965\pi\) |
−0.452507 | + | 0.891761i | \(0.649470\pi\) | |||||||
\(132\) | − | 31.1998i | − | 2.71560i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 18.2374 | 1.57547 | ||||||||
\(135\) | 3.12819 | − | 1.80606i | 0.269232 | − | 0.155441i | ||||
\(136\) | 15.2314 | + | 8.79384i | 1.30608 | + | 0.754066i | ||||
\(137\) | 2.77661 | + | 1.60308i | 0.237222 | + | 0.136960i | 0.613899 | − | 0.789384i | \(-0.289600\pi\) |
−0.376677 | + | 0.926345i | \(0.622933\pi\) | |||||||
\(138\) | −17.1640 | + | 9.90962i | −1.46109 | + | 0.843563i | ||||
\(139\) | 0.249646 | 0.0211747 | 0.0105874 | − | 0.999944i | \(-0.496630\pi\) | ||||
0.0105874 | + | 0.999944i | \(0.496630\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 13.1817i | − | 1.11010i | ||||||
\(142\) | −9.62236 | − | 16.6664i | −0.807491 | − | 1.39861i | ||||
\(143\) | −16.0760 | − | 1.61716i | −1.34435 | − | 0.135234i | ||||
\(144\) | 0.481194 | − | 0.833453i | 0.0400995 | − | 0.0694544i | ||||
\(145\) | −5.44492 | + | 3.14363i | −0.452176 | + | 0.261064i | ||||
\(146\) | 37.5755 | 3.10977 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 6.00000i | − | 0.493197i | ||||||
\(149\) | 3.49241 | − | 2.01634i | 0.286109 | − | 0.165185i | −0.350077 | − | 0.936721i | \(-0.613844\pi\) |
0.636186 | + | 0.771536i | \(0.280511\pi\) | |||||||
\(150\) | 16.3568 | + | 9.44358i | 1.33552 | + | 0.771065i | ||||
\(151\) | 1.35931 | + | 0.784795i | 0.110619 | + | 0.0638657i | 0.554289 | − | 0.832325i | \(-0.312990\pi\) |
−0.443670 | + | 0.896190i | \(0.646324\pi\) | |||||||
\(152\) | 13.9624 | + | 24.1836i | 1.13250 | + | 1.96155i | ||||
\(153\) | −0.637519 | −0.0515404 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.10554 | −0.0887991 | ||||||||
\(156\) | 20.3746 | + | 14.6645i | 1.63127 | + | 1.17410i | ||||
\(157\) | 1.44969 | − | 2.51094i | 0.115698 | − | 0.200395i | −0.802361 | − | 0.596840i | \(-0.796423\pi\) |
0.918059 | + | 0.396445i | \(0.129756\pi\) | |||||||
\(158\) | −31.5073 | − | 18.1908i | −2.50659 | − | 1.44718i | ||||
\(159\) | −2.64363 | − | 4.57890i | −0.209653 | − | 0.363130i | ||||
\(160\) | −1.08840 | −0.0860453 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 20.7938i | − | 1.63372i | ||||||
\(163\) | −14.9606 | + | 8.63752i | −1.17181 | + | 0.676543i | −0.954105 | − | 0.299473i | \(-0.903189\pi\) |
−0.217702 | + | 0.976015i | \(0.569856\pi\) | |||||||
\(164\) | −28.5251 | − | 16.4690i | −2.22744 | − | 1.28601i | ||||
\(165\) | 2.53396 | − | 4.38895i | 0.197269 | − | 0.341680i | ||||
\(166\) | −1.79995 | − | 3.11761i | −0.139704 | − | 0.241974i | ||||
\(167\) | 16.2931i | 1.26080i | 0.776270 | + | 0.630400i | \(0.217109\pi\) | ||||
−0.776270 | + | 0.630400i | \(0.782891\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.61213 | − | 9.73813i | 0.662471 | − | 0.749087i | ||||
\(170\) | 2.75329 | + | 4.76884i | 0.211168 | + | 0.365754i | ||||
\(171\) | −0.876607 | − | 0.506109i | −0.0670358 | − | 0.0387032i | ||||
\(172\) | −9.58475 | + | 16.6013i | −0.730830 | + | 1.26584i | ||||
\(173\) | 1.08721 | + | 1.88311i | 0.0826592 | + | 0.143170i | 0.904391 | − | 0.426704i | \(-0.140325\pi\) |
−0.821732 | + | 0.569874i | \(0.806992\pi\) | |||||||
\(174\) | 38.7064i | 2.93432i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 22.2374i | − | 1.67621i | ||||||
\(177\) | 3.69088 | − | 2.13093i | 0.277424 | − | 0.160171i | ||||
\(178\) | −9.66902 | + | 16.7472i | −0.724724 | + | 1.25526i | ||||
\(179\) | 0.275746 | − | 0.477607i | 0.0206102 | − | 0.0356980i | −0.855536 | − | 0.517743i | \(-0.826772\pi\) |
0.876147 | + | 0.482045i | \(0.160106\pi\) | |||||||
\(180\) | 0.471290 | − | 0.272099i | 0.0351278 | − | 0.0202811i | ||||
\(181\) | −0.511511 | −0.0380203 | −0.0190102 | − | 0.999819i | \(-0.506051\pi\) | ||||
−0.0190102 | + | 0.999819i | \(0.506051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.87399 | −0.286374 | ||||||||
\(184\) | −22.0944 | + | 12.7562i | −1.62882 | + | 0.940402i | ||||
\(185\) | 0.487304 | − | 0.844035i | 0.0358273 | − | 0.0620547i | ||||
\(186\) | −3.40303 | + | 5.89422i | −0.249522 | + | 0.432185i | ||||
\(187\) | −12.7573 | + | 7.36542i | −0.932905 | + | 0.538613i | ||||
\(188\) | − | 32.7064i | − | 2.38536i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.74306i | 0.634288i | ||||||||
\(191\) | 8.27210 | + | 14.3277i | 0.598548 | + | 1.03672i | 0.993036 | + | 0.117814i | \(0.0375888\pi\) |
−0.394488 | + | 0.918901i | \(0.629078\pi\) | |||||||
\(192\) | 4.96239 | − | 8.59511i | 0.358130 | − | 0.620299i | ||||
\(193\) | 6.41802 | + | 3.70545i | 0.461979 | + | 0.266724i | 0.712876 | − | 0.701290i | \(-0.247392\pi\) |
−0.250897 | + | 0.968014i | \(0.580725\pi\) | |||||||
\(194\) | −22.3065 | − | 38.6361i | −1.60152 | − | 2.77391i | ||||
\(195\) | 1.67513 | + | 3.71767i | 0.119959 | + | 0.266228i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.14903i | − | 0.509347i | −0.967027 | − | 0.254674i | \(-0.918032\pi\) | ||
0.967027 | − | 0.254674i | \(-0.0819681\pi\) | |||||||
\(198\) | 1.07816 | + | 1.86743i | 0.0766217 | + | 0.132713i | ||||
\(199\) | 2.55031 | − | 4.41726i | 0.180787 | − | 0.313131i | −0.761362 | − | 0.648327i | \(-0.775469\pi\) |
0.942149 | + | 0.335195i | \(0.108802\pi\) | |||||||
\(200\) | 21.0554 | + | 12.1563i | 1.48884 | + | 0.859582i | ||||
\(201\) | 10.6631 | − | 6.15633i | 0.752115 | − | 0.434234i | ||||
\(202\) | − | 23.1695i | − | 1.63020i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 22.8872 | 1.60242 | ||||||||
\(205\) | −2.67513 | − | 4.63346i | −0.186839 | − | 0.323615i | ||||
\(206\) | 13.4028 | + | 7.73813i | 0.933820 | + | 0.539141i | ||||
\(207\) | 0.462389 | − | 0.800881i | 0.0321382 | − | 0.0556650i | ||||
\(208\) | 14.5218 | + | 10.4520i | 1.00691 | + | 0.724718i | ||||
\(209\) | −23.3888 | −1.61784 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.193937 | 0.0133511 | 0.00667557 | − | 0.999978i | \(-0.497875\pi\) | ||||
0.00667557 | + | 0.999978i | \(0.497875\pi\) | |||||||
\(212\) | −6.55936 | − | 11.3611i | −0.450498 | − | 0.780286i | ||||
\(213\) | −11.2520 | − | 6.49635i | −0.770975 | − | 0.445123i | ||||
\(214\) | −15.5673 | − | 8.98778i | −1.06416 | − | 0.614392i | ||||
\(215\) | −2.69662 | + | 1.55689i | −0.183908 | + | 0.106179i | ||||
\(216\) | − | 28.6253i | − | 1.94771i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 11.8945 | 0.805594 | ||||||||
\(219\) | 21.9696 | − | 12.6842i | 1.48457 | − | 0.857117i | ||||
\(220\) | 6.28726 | − | 10.8898i | 0.423887 | − | 0.734194i | ||||
\(221\) | 1.18630 | − | 11.7929i | 0.0797989 | − | 0.793274i | ||||
\(222\) | −3.00000 | − | 5.19615i | −0.201347 | − | 0.348743i | ||||
\(223\) | 5.83875i | 0.390992i | 0.980705 | + | 0.195496i | \(0.0626316\pi\) | ||||
−0.980705 | + | 0.195496i | \(0.937368\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.881286 | −0.0587524 | ||||||||
\(226\) | −20.0760 | + | 11.5909i | −1.33543 | + | 0.771012i | ||||
\(227\) | 3.19334 | + | 1.84367i | 0.211949 | + | 0.122369i | 0.602217 | − | 0.798332i | \(-0.294284\pi\) |
−0.390268 | + | 0.920701i | \(0.627618\pi\) | |||||||
\(228\) | 31.4705 | + | 18.1695i | 2.08418 | + | 1.20330i | ||||
\(229\) | −4.89913 | + | 2.82852i | −0.323744 | + | 0.186914i | −0.653060 | − | 0.757306i | \(-0.726515\pi\) |
0.329316 | + | 0.944220i | \(0.393182\pi\) | |||||||
\(230\) | −7.98778 | −0.526699 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 49.8251i | 3.27118i | ||||||||
\(233\) | 5.16291 | + | 8.94243i | 0.338234 | + | 0.585838i | 0.984101 | − | 0.177612i | \(-0.0568373\pi\) |
−0.645867 | + | 0.763450i | \(0.723504\pi\) | |||||||
\(234\) | −1.72626 | − | 0.173652i | −0.112849 | − | 0.0113520i | ||||
\(235\) | 2.65633 | − | 4.60089i | 0.173280 | − | 0.300129i | ||||
\(236\) | 9.15780 | − | 5.28726i | 0.596122 | − | 0.344171i | ||||
\(237\) | −24.5623 | −1.59549 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.2882i | 1.44170i | 0.693089 | + | 0.720852i | \(0.256249\pi\) | ||||
−0.693089 | + | 0.720852i | \(0.743751\pi\) | |||||||
\(240\) | −4.86024 | + | 2.80606i | −0.313727 | + | 0.181131i | ||||
\(241\) | −25.4840 | − | 14.7132i | −1.64157 | − | 0.947762i | −0.980275 | − | 0.197637i | \(-0.936673\pi\) |
−0.661296 | − | 0.750125i | \(-0.729993\pi\) | |||||||
\(242\) | 19.5133 | + | 11.2660i | 1.25436 | + | 0.724205i | ||||
\(243\) | 1.00611 | + | 1.74263i | 0.0645419 | + | 0.111790i | ||||
\(244\) | −9.61213 | −0.615353 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −32.9380 | −2.10005 | ||||||||
\(247\) | 10.9932 | − | 15.2737i | 0.699482 | − | 0.971845i | ||||
\(248\) | −4.38058 | + | 7.58739i | −0.278167 | + | 0.481799i | ||||
\(249\) | −2.10480 | − | 1.21520i | −0.133386 | − | 0.0770105i | ||||
\(250\) | 7.99389 | + | 13.8458i | 0.505578 | + | 0.875687i | ||||
\(251\) | 21.5247 | 1.35863 | 0.679313 | − | 0.733849i | \(-0.262278\pi\) | ||||
0.679313 | + | 0.733849i | \(0.262278\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 21.3684i | − | 1.34342i | ||||||
\(254\) | −2.96656 | + | 1.71274i | −0.186138 | + | 0.107467i | ||||
\(255\) | 3.21959 | + | 1.85883i | 0.201619 | + | 0.116405i | ||||
\(256\) | 16.3127 | − | 28.2543i | 1.01954 | − | 1.76590i | ||||
\(257\) | 0.330979 | + | 0.573272i | 0.0206459 | + | 0.0357597i | 0.876164 | − | 0.482014i | \(-0.160094\pi\) |
−0.855518 | + | 0.517773i | \(0.826761\pi\) | |||||||
\(258\) | 19.1695i | 1.19344i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.15633 | + | 9.22425i | 0.257764 | + | 0.572064i | ||||
\(261\) | −0.903032 | − | 1.56410i | −0.0558963 | − | 0.0968152i | ||||
\(262\) | 26.8582 | + | 15.5066i | 1.65930 | + | 0.958000i | ||||
\(263\) | −2.59332 | + | 4.49176i | −0.159911 | + | 0.276974i | −0.934836 | − | 0.355079i | \(-0.884454\pi\) |
0.774925 | + | 0.632053i | \(0.217787\pi\) | |||||||
\(264\) | −20.0811 | − | 34.7815i | −1.23591 | − | 2.14065i | ||||
\(265\) | − | 2.13093i | − | 0.130902i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.0557i | 0.798996i | ||||||||
\(268\) | 26.4571 | − | 15.2750i | 1.61613 | − | 0.933072i | ||||
\(269\) | 13.6253 | − | 23.5997i | 0.830749 | − | 1.43890i | −0.0666957 | − | 0.997773i | \(-0.521246\pi\) |
0.897445 | − | 0.441127i | \(-0.145421\pi\) | |||||||
\(270\) | 4.48119 | − | 7.76166i | 0.272717 | − | 0.472359i | ||||
\(271\) | −16.2476 | + | 9.38058i | −0.986974 | + | 0.569830i | −0.904368 | − | 0.426753i | \(-0.859657\pi\) |
−0.0826055 | + | 0.996582i | \(0.526324\pi\) | |||||||
\(272\) | 16.3127 | 0.989100 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.95509 | 0.480585 | ||||||||
\(275\) | −17.6353 | + | 10.1817i | −1.06345 | + | 0.613981i | ||||
\(276\) | −16.5999 | + | 28.7519i | −0.999197 | + | 1.73066i | ||||
\(277\) | 7.71203 | − | 13.3576i | 0.463371 | − | 0.802583i | −0.535755 | − | 0.844373i | \(-0.679973\pi\) |
0.999126 | + | 0.0417908i | \(0.0133063\pi\) | |||||||
\(278\) | 0.536434 | − | 0.309711i | 0.0321732 | − | 0.0185752i | ||||
\(279\) | − | 0.317575i | − | 0.0190127i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.8446i | 1.48211i | 0.671446 | + | 0.741053i | \(0.265673\pi\) | ||||
−0.671446 | + | 0.741053i | \(0.734327\pi\) | |||||||
\(282\) | −16.3532 | − | 28.3246i | −0.973819 | − | 1.68670i | ||||
\(283\) | −11.4436 | + | 19.8209i | −0.680250 | + | 1.17823i | 0.294654 | + | 0.955604i | \(0.404796\pi\) |
−0.974904 | + | 0.222624i | \(0.928538\pi\) | |||||||
\(284\) | −27.9184 | − | 16.1187i | −1.65665 | − | 0.956470i | ||||
\(285\) | 2.95135 | + | 5.11190i | 0.174823 | + | 0.302803i | ||||
\(286\) | −36.5501 | + | 16.4690i | −2.16125 | + | 0.973831i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 0.312650i | − | 0.0184231i | ||||||
\(289\) | 3.09697 | + | 5.36411i | 0.182175 | + | 0.315536i | ||||
\(290\) | −7.79995 | + | 13.5099i | −0.458029 | + | 0.793330i | ||||
\(291\) | −26.0844 | − | 15.0598i | −1.52909 | − | 0.882823i | ||||
\(292\) | 54.5110 | − | 31.4719i | 3.19001 | − | 1.84175i | ||||
\(293\) | 25.2193i | 1.47333i | 0.676258 | + | 0.736664i | \(0.263600\pi\) | ||||
−0.676258 | + | 0.736664i | \(0.736400\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.71767 | 0.100006 | ||||||||
\(296\) | −3.86177 | − | 6.68879i | −0.224461 | − | 0.388778i | ||||
\(297\) | 20.7634 | + | 11.9878i | 1.20482 | + | 0.695602i | ||||
\(298\) | 5.00294 | − | 8.66535i | 0.289813 | − | 0.501970i | ||||
\(299\) | 13.9543 | + | 10.0436i | 0.806998 | + | 0.580834i | ||||
\(300\) | 31.6385 | 1.82665 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.89446 | 0.224101 | ||||||||
\(303\) | −7.82122 | − | 13.5468i | −0.449317 | − | 0.778241i | ||||
\(304\) | 22.4304 | + | 12.9502i | 1.28647 | + | 0.742743i | ||||
\(305\) | −1.35216 | − | 0.780671i | −0.0774245 | − | 0.0447011i | ||||
\(306\) | −1.36989 | + | 0.790905i | −0.0783112 | + | 0.0452130i | ||||
\(307\) | 7.24965i | 0.413759i | 0.978366 | + | 0.206880i | \(0.0663308\pi\) | ||||
−0.978366 | + | 0.206880i | \(0.933669\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.4485 | 0.594395 | ||||||||
\(310\) | −2.37556 | + | 1.37153i | −0.134923 | + | 0.0778977i | ||||
\(311\) | 10.1199 | − | 17.5282i | 0.573847 | − | 0.993932i | −0.422319 | − | 0.906447i | \(-0.638784\pi\) |
0.996166 | − | 0.0874846i | \(-0.0278829\pi\) | |||||||
\(312\) | 32.1521 | + | 3.23432i | 1.82025 | + | 0.183107i | ||||
\(313\) | −16.5684 | − | 28.6973i | −0.936502 | − | 1.62207i | −0.771934 | − | 0.635703i | \(-0.780710\pi\) |
−0.164568 | − | 0.986366i | \(-0.552623\pi\) | |||||||
\(314\) | − | 7.19394i | − | 0.405977i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −60.9438 | −3.42836 | ||||||||
\(317\) | −14.7338 | + | 8.50659i | −0.827535 | + | 0.477778i | −0.853008 | − | 0.521898i | \(-0.825224\pi\) |
0.0254730 | + | 0.999676i | \(0.491891\pi\) | |||||||
\(318\) | −11.3611 | − | 6.55936i | −0.637101 | − | 0.367830i | ||||
\(319\) | −36.1408 | − | 20.8659i | −2.02350 | − | 1.16827i | ||||
\(320\) | 3.46410 | − | 2.00000i | 0.193649 | − | 0.111803i | ||||
\(321\) | −12.1359 | −0.677357 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 17.1573i | − | 0.954657i | ||||||
\(324\) | −17.4162 | − | 30.1658i | −0.967567 | − | 1.67588i | ||||
\(325\) | 1.63990 | − | 16.3021i | 0.0909651 | − | 0.904276i | ||||
\(326\) | −21.4314 | + | 37.1202i | −1.18697 | + | 2.05590i | ||||
\(327\) | 6.95446 | − | 4.01516i | 0.384582 | − | 0.222039i | ||||
\(328\) | −42.3996 | −2.34113 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 12.5745i | − | 0.692204i | ||||||
\(331\) | 9.38458 | − | 5.41819i | 0.515823 | − | 0.297811i | −0.219401 | − | 0.975635i | \(-0.570410\pi\) |
0.735224 | + | 0.677824i | \(0.237077\pi\) | |||||||
\(332\) | −5.22241 | − | 3.01516i | −0.286617 | − | 0.165478i | ||||
\(333\) | 0.242456 | + | 0.139982i | 0.0132865 | + | 0.00767095i | ||||
\(334\) | 20.2132 | + | 35.0103i | 1.10602 | + | 1.91568i | ||||
\(335\) | 4.96239 | 0.271124 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.96968 | −0.161769 | −0.0808845 | − | 0.996723i | \(-0.525774\pi\) | ||||
−0.0808845 | + | 0.996723i | \(0.525774\pi\) | |||||||
\(338\) | 6.42444 | − | 31.6093i | 0.349443 | − | 1.71932i | ||||
\(339\) | −7.82535 | + | 13.5539i | −0.425014 | + | 0.736147i | ||||
\(340\) | 7.98844 | + | 4.61213i | 0.433234 | + | 0.250128i | ||||
\(341\) | −3.66902 | − | 6.35493i | −0.198689 | − | 0.344139i | ||||
\(342\) | −2.51151 | −0.135807 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 24.6761i | 1.33045i | ||||||||
\(345\) | −4.67030 | + | 2.69640i | −0.251440 | + | 0.145169i | ||||
\(346\) | 4.67235 | + | 2.69758i | 0.251187 | + | 0.145023i | ||||
\(347\) | −15.3684 | + | 26.6188i | −0.825017 | + | 1.42897i | 0.0768897 | + | 0.997040i | \(0.475501\pi\) |
−0.901906 | + | 0.431931i | \(0.857832\pi\) | |||||||
\(348\) | 32.4191 | + | 56.1516i | 1.73785 | + | 3.01004i | ||||
\(349\) | 2.00492i | 0.107321i | 0.998559 | + | 0.0536606i | \(0.0170889\pi\) | ||||
−0.998559 | + | 0.0536606i | \(0.982911\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.5877 | + | 7.92478i | −0.938761 | + | 0.422993i | ||||
\(352\) | −3.61213 | − | 6.25639i | −0.192527 | − | 0.333467i | ||||
\(353\) | 14.9429 | + | 8.62729i | 0.795330 | + | 0.459184i | 0.841836 | − | 0.539734i | \(-0.181475\pi\) |
−0.0465055 | + | 0.998918i | \(0.514809\pi\) | |||||||
\(354\) | 5.28726 | − | 9.15780i | 0.281015 | − | 0.486732i | ||||
\(355\) | −2.61824 | − | 4.53492i | −0.138962 | − | 0.240688i | ||||
\(356\) | 32.3938i | 1.71687i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 1.36836i | − | 0.0723201i | ||||||
\(359\) | 6.15441 | − | 3.55325i | 0.324817 | − | 0.187533i | −0.328721 | − | 0.944427i | \(-0.606617\pi\) |
0.653538 | + | 0.756894i | \(0.273284\pi\) | |||||||
\(360\) | 0.350262 | − | 0.606671i | 0.0184604 | − | 0.0319744i | ||||
\(361\) | 4.12070 | − | 7.13726i | 0.216879 | − | 0.375645i | ||||
\(362\) | −1.09912 | + | 0.634580i | −0.0577687 | + | 0.0333528i | ||||
\(363\) | 15.2120 | 0.798425 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.2243 | 0.535162 | ||||||||
\(366\) | −8.32435 | + | 4.80606i | −0.435121 | + | 0.251217i | ||||
\(367\) | −13.6314 | + | 23.6103i | −0.711554 | + | 1.23245i | 0.252720 | + | 0.967539i | \(0.418675\pi\) |
−0.964274 | + | 0.264908i | \(0.914658\pi\) | |||||||
\(368\) | −11.8315 | + | 20.4927i | −0.616757 | + | 1.06825i | ||||
\(369\) | 1.33100 | − | 0.768452i | 0.0692890 | − | 0.0400040i | ||||
\(370\) | − | 2.41819i | − | 0.125716i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 11.4010i | 0.591117i | ||||||||
\(373\) | 2.95945 | + | 5.12592i | 0.153234 | + | 0.265410i | 0.932415 | − | 0.361390i | \(-0.117698\pi\) |
−0.779180 | + | 0.626800i | \(0.784364\pi\) | |||||||
\(374\) | −18.2750 | + | 31.6533i | −0.944980 | + | 1.63675i | ||||
\(375\) | 9.34774 | + | 5.39692i | 0.482715 | + | 0.278696i | ||||
\(376\) | −21.0508 | − | 36.4610i | −1.08561 | − | 1.88033i | ||||
\(377\) | 30.6131 | − | 13.7938i | 1.57665 | − | 0.710419i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 28.9706i | − | 1.48812i | −0.668112 | − | 0.744061i | \(-0.732897\pi\) | ||
0.668112 | − | 0.744061i | \(-0.267103\pi\) | |||||||
\(380\) | 7.32288 | + | 12.6836i | 0.375656 | + | 0.650655i | ||||
\(381\) | −1.15633 | + | 2.00281i | −0.0592403 | + | 0.102607i | ||||
\(382\) | 35.5498 | + | 20.5247i | 1.81889 | + | 1.05013i | ||||
\(383\) | −20.1128 | + | 11.6121i | −1.02772 | + | 0.593352i | −0.916329 | − | 0.400425i | \(-0.868862\pi\) |
−0.111386 | + | 0.993777i | \(0.535529\pi\) | |||||||
\(384\) | − | 30.0263i | − | 1.53228i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.3879 | 0.935918 | ||||||||
\(387\) | −0.447230 | − | 0.774625i | −0.0227340 | − | 0.0393764i | ||||
\(388\) | −64.7205 | − | 37.3664i | −3.28568 | − | 1.89699i | ||||
\(389\) | 8.06594 | − | 13.9706i | 0.408960 | − | 0.708339i | −0.585814 | − | 0.810446i | \(-0.699225\pi\) |
0.994773 | + | 0.102107i | \(0.0325584\pi\) | |||||||
\(390\) | 8.21161 | + | 5.91028i | 0.415811 | + | 0.299278i | ||||
\(391\) | 15.6751 | 0.792725 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.9380 | 1.05618 | ||||||||
\(394\) | −8.86907 | − | 15.3617i | −0.446817 | − | 0.773910i | ||||
\(395\) | −8.57312 | − | 4.94969i | −0.431360 | − | 0.249046i | ||||
\(396\) | 3.12819 | + | 1.80606i | 0.157198 | + | 0.0907581i | ||||
\(397\) | 20.8329 | − | 12.0279i | 1.04557 | − | 0.603661i | 0.124165 | − | 0.992262i | \(-0.460375\pi\) |
0.921406 | + | 0.388601i | \(0.127041\pi\) | |||||||
\(398\) | − | 12.6556i | − | 0.634369i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.5501 | 1.12750 | ||||||||
\(401\) | −2.40387 | + | 1.38787i | −0.120043 | + | 0.0693071i | −0.558819 | − | 0.829289i | \(-0.688745\pi\) |
0.438776 | + | 0.898596i | \(0.355412\pi\) | |||||||
\(402\) | 15.2750 | − | 26.4571i | 0.761850 | − | 1.31956i | ||||
\(403\) | 5.87451 | + | 0.590943i | 0.292630 | + | 0.0294370i | ||||
\(404\) | −19.4060 | − | 33.6121i | −0.965483 | − | 1.67227i | ||||
\(405\) | − | 5.65799i | − | 0.281148i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.46898 | 0.320655 | ||||||||
\(408\) | 25.5146 | − | 14.7308i | 1.26316 | − | 0.729285i | ||||
\(409\) | −17.4339 | − | 10.0655i | −0.862051 | − | 0.497705i | 0.00264770 | − | 0.999996i | \(-0.499157\pi\) |
−0.864699 | + | 0.502291i | \(0.832491\pi\) | |||||||
\(410\) | −11.4965 | − | 6.63752i | −0.567773 | − | 0.327804i | ||||
\(411\) | 4.65119 | − | 2.68536i | 0.229426 | − | 0.132459i | ||||
\(412\) | 25.9248 | 1.27722 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 2.29455i | − | 0.112771i | ||||||
\(415\) | −0.489766 | − | 0.848300i | −0.0240417 | − | 0.0416414i | ||||
\(416\) | 5.78342 | + | 0.581779i | 0.283555 | + | 0.0285241i | ||||
\(417\) | 0.209095 | − | 0.362163i | 0.0102394 | − | 0.0177352i | ||||
\(418\) | −50.2574 | + | 29.0161i | −2.45817 | + | 1.41922i | ||||
\(419\) | 0.385503 | 0.0188331 | 0.00941654 | − | 0.999956i | \(-0.497003\pi\) | ||||
0.00941654 | + | 0.999956i | \(0.497003\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.6810i | 0.764246i | 0.924112 | + | 0.382123i | \(0.124807\pi\) | ||||
−0.924112 | + | 0.382123i | \(0.875193\pi\) | |||||||
\(422\) | 0.416726 | − | 0.240597i | 0.0202859 | − | 0.0117121i | ||||
\(423\) | 1.32164 | + | 0.763050i | 0.0642604 | + | 0.0371008i | ||||
\(424\) | −14.6247 | − | 8.44358i | −0.710239 | − | 0.410057i | ||||
\(425\) | −7.46898 | − | 12.9366i | −0.362299 | − | 0.627519i | ||||
\(426\) | −32.2374 | −1.56191 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −30.1114 | −1.45549 | ||||||||
\(429\) | −15.8108 | + | 21.9671i | −0.763351 | + | 1.06058i | ||||
\(430\) | −3.86296 | + | 6.69084i | −0.186288 | + | 0.322661i | ||||
\(431\) | −1.33100 | − | 0.768452i | −0.0641119 | − | 0.0370150i | 0.467601 | − | 0.883939i | \(-0.345118\pi\) |
−0.531713 | + | 0.846924i | \(0.678452\pi\) | |||||||
\(432\) | −13.2750 | − | 22.9930i | −0.638696 | − | 1.10625i | ||||
\(433\) | −26.0362 | −1.25122 | −0.625610 | − | 0.780136i | \(-0.715150\pi\) | ||||
−0.625610 | + | 0.780136i | \(0.715150\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.5320i | 0.504970i | ||||||||
\(436\) | 17.2554 | − | 9.96239i | 0.826382 | − | 0.477112i | ||||
\(437\) | 21.5537 | + | 12.4441i | 1.03106 | + | 0.595280i | ||||
\(438\) | 31.4719 | − | 54.5110i | 1.50379 | − | 2.60463i | ||||
\(439\) | −9.56230 | − | 16.5624i | −0.456384 | − | 0.790479i | 0.542383 | − | 0.840131i | \(-0.317522\pi\) |
−0.998767 | + | 0.0496519i | \(0.984189\pi\) | |||||||
\(440\) | − | 16.1866i | − | 0.771668i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0811 | − | 26.8119i | −0.574639 | − | 1.27531i | ||||
\(443\) | 6.30900 | + | 10.9275i | 0.299750 | + | 0.519182i | 0.976079 | − | 0.217418i | \(-0.0697635\pi\) |
−0.676329 | + | 0.736600i | \(0.736430\pi\) | |||||||
\(444\) | −8.70424 | − | 5.02539i | −0.413085 | − | 0.238495i | ||||
\(445\) | −2.63093 | + | 4.55691i | −0.124718 | + | 0.216018i | ||||
\(446\) | 7.24354 | + | 12.5462i | 0.342991 | + | 0.594079i | ||||
\(447\) | − | 6.75528i | − | 0.319514i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.02302i | 0.0482794i | 0.999709 | + | 0.0241397i | \(0.00768466\pi\) | ||||
−0.999709 | + | 0.0241397i | \(0.992315\pi\) | |||||||
\(450\) | −1.89369 | + | 1.09332i | −0.0892693 | + | 0.0515397i | ||||
\(451\) | 17.7562 | − | 30.7547i | 0.836108 | − | 1.44818i | ||||
\(452\) | −19.4162 | + | 33.6299i | −0.913261 | + | 1.58182i | ||||
\(453\) | 2.27701 | − | 1.31464i | 0.106983 | − | 0.0617669i | ||||
\(454\) | 9.14903 | 0.429385 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 46.7777 | 2.19056 | ||||||||
\(457\) | 24.7094 | − | 14.2660i | 1.15586 | − | 0.667335i | 0.205550 | − | 0.978647i | \(-0.434102\pi\) |
0.950308 | + | 0.311312i | \(0.100768\pi\) | |||||||
\(458\) | −7.01810 | + | 12.1557i | −0.327934 | + | 0.567999i | ||||
\(459\) | −8.79384 | + | 15.2314i | −0.410462 | + | 0.710940i | ||||
\(460\) | −11.5879 | + | 6.69029i | −0.540290 | + | 0.311936i | ||||
\(461\) | − | 25.3503i | − | 1.18068i | −0.807155 | − | 0.590340i | \(-0.798994\pi\) | ||
0.807155 | − | 0.590340i | \(-0.201006\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 39.6810i | − | 1.84413i | −0.387032 | − | 0.922066i | \(-0.626500\pi\) | ||
0.387032 | − | 0.922066i | \(-0.373500\pi\) | |||||||
\(464\) | 23.1065 | + | 40.0216i | 1.07269 | + | 1.85796i | ||||
\(465\) | −0.925962 | + | 1.60381i | −0.0429405 | + | 0.0743751i | ||||
\(466\) | 22.1879 | + | 12.8102i | 1.02783 | + | 0.593421i | ||||
\(467\) | −0.975792 | − | 1.69012i | −0.0451543 | − | 0.0782095i | 0.842565 | − | 0.538595i | \(-0.181045\pi\) |
−0.887719 | + | 0.460385i | \(0.847711\pi\) | |||||||
\(468\) | −2.64974 | + | 1.19394i | −0.122484 | + | 0.0551897i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 13.1817i | − | 0.608027i | ||||||
\(471\) | −2.42842 | − | 4.20615i | −0.111896 | − | 0.193809i | ||||
\(472\) | 6.80606 | − | 11.7884i | 0.313274 | − | 0.542607i | ||||
\(473\) | −17.8989 | − | 10.3339i | −0.822991 | − | 0.475154i | ||||
\(474\) | −52.7789 | + | 30.4719i | −2.42422 | + | 1.39962i | ||||
\(475\) | − | 23.7177i | − | 1.08824i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.612127 | 0.0280274 | ||||||||
\(478\) | 27.6507 | + | 47.8924i | 1.26471 | + | 2.19055i | ||||
\(479\) | 22.6351 | + | 13.0684i | 1.03423 | + | 0.597111i | 0.918192 | − | 0.396135i | \(-0.129649\pi\) |
0.116034 | + | 0.993245i | \(0.462982\pi\) | |||||||
\(480\) | −0.911603 | + | 1.57894i | −0.0416088 | + | 0.0720686i | ||||
\(481\) | −3.04055 | + | 4.22447i | −0.138637 | + | 0.192619i | ||||
\(482\) | −73.0127 | −3.32564 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 37.7440 | 1.71564 | ||||||||
\(485\) | −6.06959 | − | 10.5128i | −0.275606 | − | 0.477363i | ||||
\(486\) | 4.32381 | + | 2.49635i | 0.196132 | + | 0.113237i | ||||
\(487\) | 18.1540 | + | 10.4812i | 0.822634 | + | 0.474948i | 0.851324 | − | 0.524640i | \(-0.175800\pi\) |
−0.0286896 | + | 0.999588i | \(0.509133\pi\) | |||||||
\(488\) | −10.7156 | + | 6.18664i | −0.485071 | + | 0.280056i | ||||
\(489\) | 28.9380i | 1.30862i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.95651 | 0.133425 | 0.0667127 | − | 0.997772i | \(-0.478749\pi\) | ||||
0.0667127 | + | 0.997772i | \(0.478749\pi\) | |||||||
\(492\) | −47.7833 | + | 27.5877i | −2.15424 | + | 1.24375i | ||||
\(493\) | 15.3065 | − | 26.5117i | 0.689372 | − | 1.19403i | ||||
\(494\) | 4.67342 | − | 46.4580i | 0.210267 | − | 2.09025i | ||||
\(495\) | 0.293367 | + | 0.508127i | 0.0131859 | + | 0.0228386i | ||||
\(496\) | 8.12601i | 0.364869i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.03032 | −0.270225 | ||||||||
\(499\) | −2.47205 | + | 1.42724i | −0.110664 | + | 0.0638920i | −0.554311 | − | 0.832310i | \(-0.687018\pi\) |
0.443646 | + | 0.896202i | \(0.353685\pi\) | |||||||
\(500\) | 23.1936 | + | 13.3908i | 1.03725 | + | 0.598855i | ||||
\(501\) | 23.6366 | + | 13.6466i | 1.05600 | + | 0.609684i | ||||
\(502\) | 46.2518 | − | 26.7035i | 2.06432 | − | 1.19183i | ||||
\(503\) | −23.8641 | −1.06405 | −0.532025 | − | 0.846729i | \(-0.678569\pi\) | ||||
−0.532025 | + | 0.846729i | \(0.678569\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 6.30440i | − | 0.280542i | ||||||
\(506\) | −26.5095 | − | 45.9158i | −1.17849 | − | 2.04121i | ||||
\(507\) | −6.91395 | − | 20.6500i | −0.307059 | − | 0.917098i | ||||
\(508\) | −2.86907 | + | 4.96937i | −0.127294 | + | 0.220480i | ||||
\(509\) | 9.69506 | − | 5.59745i | 0.429726 | − | 0.248102i | −0.269504 | − | 0.962999i | \(-0.586860\pi\) |
0.699230 | + | 0.714897i | \(0.253526\pi\) | |||||||
\(510\) | 9.22425 | 0.408457 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 45.1002i | − | 1.99316i | ||||||
\(513\) | −24.1836 | + | 13.9624i | −1.06773 | + | 0.616455i | ||||
\(514\) | 1.42240 | + | 0.821222i | 0.0627393 | + | 0.0362226i | ||||
\(515\) | 3.64690 | + | 2.10554i | 0.160702 | + | 0.0927812i | ||||
\(516\) | 16.0557 | + | 27.8093i | 0.706813 | + | 1.22424i | ||||
\(517\) | 35.2628 | 1.55086 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.64244 | 0.159886 | ||||||||
\(520\) | 10.5705 | + | 7.60805i | 0.463545 | + | 0.333635i | ||||
\(521\) | −13.2447 | + | 22.9405i | −0.580262 | + | 1.00504i | 0.415186 | + | 0.909736i | \(0.363716\pi\) |
−0.995448 | + | 0.0953065i | \(0.969617\pi\) | |||||||
\(522\) | −3.88083 | − | 2.24060i | −0.169859 | − | 0.0980683i | ||||
\(523\) | −6.47627 | − | 11.2172i | −0.283188 | − | 0.490495i | 0.688981 | − | 0.724780i | \(-0.258059\pi\) |
−0.972168 | + | 0.234285i | \(0.924725\pi\) | |||||||
\(524\) | 51.9511 | 2.26950 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.8691i | 0.561118i | ||||||||
\(527\) | 4.66177 | − | 2.69147i | 0.203070 | − | 0.117242i | ||||
\(528\) | −32.2600 | − | 18.6253i | −1.40393 | − | 0.810562i | ||||
\(529\) | 0.130933 | − | 0.226782i | 0.00569272 | − | 0.00986008i | ||||
\(530\) | −2.64363 | − | 4.57890i | −0.114832 | − | 0.198895i | ||||
\(531\) | 0.493413i | 0.0214123i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.7381 | + | 26.0508i | 0.508435 | + | 1.12838i | ||||
\(534\) | 16.1969 | + | 28.0538i | 0.700907 | + | 1.21401i | ||||
\(535\) | −4.23585 | − | 2.44557i | −0.183132 | − | 0.105731i | ||||
\(536\) | 19.6629 | − | 34.0572i | 0.849308 | − | 1.47105i | ||||
\(537\) | −0.461911 | − | 0.800053i | −0.0199329 | − | 0.0345249i | ||||
\(538\) | − | 67.6140i | − | 2.91505i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 15.0132i | − | 0.646064i | ||||||
\(541\) | 24.3295 | − | 14.0467i | 1.04601 | − | 0.603913i | 0.124479 | − | 0.992222i | \(-0.460274\pi\) |
0.921529 | + | 0.388309i | \(0.126941\pi\) | |||||||
\(542\) | −23.2750 | + | 40.3136i | −0.999749 | + | 1.73162i | ||||
\(543\) | −0.428424 | + | 0.742053i | −0.0183854 | + | 0.0318445i | ||||
\(544\) | 4.58948 | − | 2.64974i | 0.196772 | − | 0.113607i | ||||
\(545\) | 3.23647 | 0.138635 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.8192 | 0.633625 | 0.316812 | − | 0.948488i | \(-0.397387\pi\) | ||||
0.316812 | + | 0.948488i | \(0.397387\pi\) | |||||||
\(548\) | 11.5405 | − | 6.66291i | 0.492986 | − | 0.284625i | ||||
\(549\) | 0.224254 | − | 0.388419i | 0.00957092 | − | 0.0165773i | ||||
\(550\) | −25.2628 | + | 43.7565i | −1.07721 | + | 1.86578i | ||||
\(551\) | 42.0938 | − | 24.3029i | 1.79326 | − | 1.03534i | ||||
\(552\) | 42.7367i | 1.81900i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 38.2701i | − | 1.62594i | ||||||
\(555\) | −0.816297 | − | 1.41387i | −0.0346499 | − | 0.0600154i | ||||
\(556\) | 0.518806 | − | 0.898598i | 0.0220023 | − | 0.0381090i | ||||
\(557\) | 15.9244 | + | 9.19394i | 0.674737 | + | 0.389560i | 0.797869 | − | 0.602831i | \(-0.205961\pi\) |
−0.123132 | + | 0.992390i | \(0.539294\pi\) | |||||||
\(558\) | −0.393983 | − | 0.682398i | −0.0166786 | − | 0.0288882i | ||||
\(559\) | 15.1612 | − | 6.83146i | 0.641253 | − | 0.288940i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.6761i | 1.04183i | ||||||||
\(562\) | 30.8222 | + | 53.3856i | 1.30016 | + | 2.25193i | ||||
\(563\) | 7.66784 | − | 13.2811i | 0.323161 | − | 0.559731i | −0.657978 | − | 0.753037i | \(-0.728588\pi\) |
0.981138 | + | 0.193307i | \(0.0619212\pi\) | |||||||
\(564\) | −47.4474 | − | 27.3938i | −1.99789 | − | 1.15349i | ||||
\(565\) | −5.46265 | + | 3.15386i | −0.229815 | + | 0.132684i | ||||
\(566\) | 56.7875i | 2.38696i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −41.4979 | −1.74121 | ||||||||
\(569\) | 0.661250 | + | 1.14532i | 0.0277210 | + | 0.0480142i | 0.879553 | − | 0.475801i | \(-0.157842\pi\) |
−0.851832 | + | 0.523815i | \(0.824508\pi\) | |||||||
\(570\) | 12.6836 | + | 7.32288i | 0.531258 | + | 0.306722i | ||||
\(571\) | −18.9587 | + | 32.8375i | −0.793399 | + | 1.37421i | 0.130452 | + | 0.991455i | \(0.458357\pi\) |
−0.923851 | + | 0.382752i | \(0.874976\pi\) | |||||||
\(572\) | −39.2296 | + | 54.5047i | −1.64027 | + | 2.27896i | ||||
\(573\) | 27.7137 | 1.15776 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.6688 | 0.903651 | ||||||||
\(576\) | 0.574515 | + | 0.995090i | 0.0239381 | + | 0.0414621i | ||||
\(577\) | −11.1394 | − | 6.43136i | −0.463741 | − | 0.267741i | 0.249875 | − | 0.968278i | \(-0.419611\pi\) |
−0.713616 | + | 0.700537i | \(0.752944\pi\) | |||||||
\(578\) | 13.3094 | + | 7.68418i | 0.553598 | + | 0.319620i | ||||
\(579\) | 10.7510 | − | 6.20711i | 0.446798 | − | 0.257959i | ||||
\(580\) | 26.1319i | 1.08507i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −74.7328 | −3.09777 | ||||||||
\(583\) | 12.2492 | − | 7.07205i | 0.507308 | − | 0.292895i | ||||
\(584\) | 40.5125 | − | 70.1697i | 1.67642 | − | 2.90364i | ||||
\(585\) | −0.469713 | − | 0.0472505i | −0.0194203 | − | 0.00195357i | ||||
\(586\) | 31.2870 | + | 54.1907i | 1.29246 | + | 2.23860i | ||||
\(587\) | 31.0240i | 1.28050i | 0.768168 | + | 0.640248i | \(0.221169\pi\) | ||||
−0.768168 | + | 0.640248i | \(0.778831\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.54675 | 0.352163 | ||||||||
\(590\) | 3.69088 | − | 2.13093i | 0.151951 | − | 0.0877291i | ||||
\(591\) | −10.3711 | − | 5.98778i | −0.426612 | − | 0.246304i | ||||
\(592\) | −6.20388 | − | 3.58181i | −0.254978 | − | 0.147211i | ||||
\(593\) | −9.88295 | + | 5.70593i | −0.405844 | + | 0.234314i | −0.689003 | − | 0.724759i | \(-0.741951\pi\) |
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(594\) | 59.4880 | 2.44082 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 16.7612i | − | 0.686564i | ||||||
\(597\) | −4.27210 | − | 7.39949i | −0.174845 | − | 0.302841i | ||||
\(598\) | 42.4447 | + | 4.26970i | 1.73569 | + | 0.174601i | ||||
\(599\) | −3.68664 | + | 6.38545i | −0.150632 | + | 0.260902i | −0.931460 | − | 0.363844i | \(-0.881464\pi\) |
0.780828 | + | 0.624746i | \(0.214798\pi\) | |||||||
\(600\) | 35.2705 | − | 20.3634i | 1.43991 | − | 0.831334i | ||||
\(601\) | −17.2144 | −0.702190 | −0.351095 | − | 0.936340i | \(-0.614191\pi\) | ||||
−0.351095 | + | 0.936340i | \(0.614191\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.42548i | 0.0580502i | ||||||||
\(604\) | 5.64972 | − | 3.26187i | 0.229884 | − | 0.132723i | ||||
\(605\) | 5.30954 | + | 3.06547i | 0.215864 | + | 0.124629i | ||||
\(606\) | −33.6121 | − | 19.4060i | −1.36540 | − | 0.788314i | ||||
\(607\) | 16.2132 | + | 28.0821i | 0.658074 | + | 1.13982i | 0.981114 | + | 0.193433i | \(0.0619621\pi\) |
−0.323039 | + | 0.946386i | \(0.604705\pi\) | |||||||
\(608\) | 8.41422 | 0.341242 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.87399 | −0.156853 | ||||||||
\(611\) | −16.5742 | + | 23.0279i | −0.670522 | + | 0.931609i | ||||
\(612\) | −1.32487 | + | 2.29474i | −0.0535547 | + | 0.0927594i | ||||
\(613\) | 30.9163 | + | 17.8496i | 1.24870 | + | 0.720937i | 0.970850 | − | 0.239688i | \(-0.0770452\pi\) |
0.277849 | + | 0.960625i | \(0.410378\pi\) | |||||||
\(614\) | 8.99389 | + | 15.5779i | 0.362964 | + | 0.628672i | ||||
\(615\) | −8.96239 | −0.361398 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.3733i | 0.820198i | 0.912041 | + | 0.410099i | \(0.134506\pi\) | ||||
−0.912041 | + | 0.410099i | \(0.865494\pi\) | |||||||
\(618\) | 22.4515 | − | 12.9624i | 0.903132 | − | 0.521424i | ||||
\(619\) | 34.6512 | + | 20.0059i | 1.39275 | + | 0.804104i | 0.993619 | − | 0.112790i | \(-0.0359787\pi\) |
0.399130 | + | 0.916894i | \(0.369312\pi\) | |||||||
\(620\) | −2.29749 | + | 3.97937i | −0.0922695 | + | 0.159815i | ||||
\(621\) | −12.7562 | − | 22.0944i | −0.511890 | − | 0.886620i | ||||
\(622\) | − | 50.2189i | − | 2.01359i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 27.3258 | − | 12.3127i | 1.09391 | − | 0.492900i | ||||
\(625\) | −9.18536 | − | 15.9095i | −0.367415 | − | 0.636381i | ||||
\(626\) | −71.2036 | − | 41.1094i | −2.84587 | − | 1.64306i | ||||
\(627\) | −19.5897 | + | 33.9303i | −0.782336 | + | 1.35505i | ||||
\(628\) | −6.02539 | − | 10.4363i | −0.240439 | − | 0.416453i | ||||
\(629\) | 4.74543i | 0.189213i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.3879i | 0.652391i | 0.945302 | + | 0.326195i | \(0.105767\pi\) | ||||
−0.945302 | + | 0.326195i | \(0.894233\pi\) | |||||||
\(632\) | −67.9401 | + | 39.2252i | −2.70251 | + | 1.56030i | ||||
\(633\) | 0.162435 | − | 0.281345i | 0.00645619 | − | 0.0111825i | ||||
\(634\) | −21.1065 | + | 36.5575i | −0.838246 | + | 1.45188i | ||||
\(635\) | −0.807198 | + | 0.466036i | −0.0320327 | + | 0.0184941i | ||||
\(636\) | −21.9756 | −0.871388 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −103.545 | −4.09937 | ||||||||
\(639\) | 1.30269 | − | 0.752109i | 0.0515336 | − | 0.0297530i | ||||
\(640\) | 6.05079 | − | 10.4803i | 0.239178 | − | 0.414269i | ||||
\(641\) | −4.11942 | + | 7.13505i | −0.162707 | + | 0.281817i | −0.935839 | − | 0.352428i | \(-0.885356\pi\) |
0.773131 | + | 0.634246i | \(0.218689\pi\) | |||||||
\(642\) | −26.0773 | + | 15.0557i | −1.02919 | + | 0.594201i | ||||
\(643\) | 30.4847i | 1.20220i | 0.799174 | + | 0.601100i | \(0.205271\pi\) | ||||
−0.799174 | + | 0.601100i | \(0.794729\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.21600i | 0.205380i | ||||||||
\(646\) | −21.2853 | − | 36.8672i | −0.837458 | − | 1.45052i | ||||
\(647\) | −14.4194 | + | 24.9751i | −0.566884 | + | 0.981872i | 0.429988 | + | 0.902835i | \(0.358518\pi\) |
−0.996872 | + | 0.0790373i | \(0.974815\pi\) | |||||||
\(648\) | −38.8311 | − | 22.4191i | −1.52543 | − | 0.880707i | ||||
\(649\) | 5.70052 | + | 9.87360i | 0.223765 | + | 0.387573i | ||||
\(650\) | −16.7005 | − | 37.0640i | −0.655048 | − | 1.45377i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 71.8007i | 2.81193i | ||||||||
\(653\) | −10.7259 | − | 18.5778i | −0.419738 | − | 0.727007i | 0.576175 | − | 0.817326i | \(-0.304545\pi\) |
−0.995913 | + | 0.0903194i | \(0.971211\pi\) | |||||||
\(654\) | 9.96239 | − | 17.2554i | 0.389560 | − | 0.674738i | ||||
\(655\) | 7.30809 | + | 4.21933i | 0.285551 | + | 0.164863i | ||||
\(656\) | −34.0572 | + | 19.6629i | −1.32971 | + | 0.767708i | ||||
\(657\) | 2.93700i | 0.114583i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −50.6589 | −1.97339 | −0.986696 | − | 0.162575i | \(-0.948020\pi\) | ||||
−0.986696 | + | 0.162575i | \(0.948020\pi\) | |||||||
\(660\) | −10.5320 | − | 18.2419i | −0.409957 | − | 0.710066i | ||||
\(661\) | 13.4647 | + | 7.77385i | 0.523717 | + | 0.302368i | 0.738454 | − | 0.674304i | \(-0.235556\pi\) |
−0.214737 | + | 0.976672i | \(0.568890\pi\) | |||||||
\(662\) | 13.4436 | − | 23.2850i | 0.522500 | − | 0.904996i | ||||
\(663\) | −16.1144 | − | 11.5983i | −0.625830 | − | 0.450439i | ||||
\(664\) | −7.76257 | −0.301246 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.694644 | 0.0269169 | ||||||||
\(667\) | 22.2035 | + | 38.4575i | 0.859722 | + | 1.48908i | ||||
\(668\) | 58.6469 | + | 33.8598i | 2.26912 | + | 1.31007i | ||||
\(669\) | 8.47031 | + | 4.89034i | 0.327481 | + | 0.189071i | ||||
\(670\) | 10.6631 | − | 6.15633i | 0.411950 | − | 0.237840i | ||||
\(671\) | − | 10.3634i | − | 0.400076i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.8700 | 1.03576 | 0.517882 | − | 0.855452i | \(-0.326721\pi\) | ||||
0.517882 | + | 0.855452i | \(0.326721\pi\) | |||||||
\(674\) | −6.38119 | + | 3.68418i | −0.245794 | + | 0.141909i | ||||
\(675\) | −12.1563 | + | 21.0554i | −0.467897 | + | 0.810422i | ||||
\(676\) | −17.1549 | − | 51.2366i | −0.659802 | − | 1.97064i | ||||
\(677\) | 8.18783 | + | 14.1817i | 0.314684 | + | 0.545048i | 0.979370 | − | 0.202074i | \(-0.0647682\pi\) |
−0.664686 | + | 0.747122i | \(0.731435\pi\) | |||||||
\(678\) | 38.8324i | 1.49135i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11.8740 | 0.455347 | ||||||||
\(681\) | 5.34926 | − | 3.08840i | 0.204984 | − | 0.118348i | ||||
\(682\) | −15.7678 | − | 9.10356i | −0.603781 | − | 0.348593i | ||||
\(683\) | −13.6821 | − | 7.89938i | −0.523532 | − | 0.302262i | 0.214846 | − | 0.976648i | \(-0.431075\pi\) |
−0.738379 | + | 0.674386i | \(0.764408\pi\) | |||||||
\(684\) | −3.64346 | + | 2.10356i | −0.139311 | + | 0.0804314i | ||||
\(685\) | 2.16457 | 0.0827041 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.47627i | 0.361542i | ||||||||
\(688\) | 11.4436 | + | 19.8209i | 0.436283 | + | 0.755663i | ||||
\(689\) | −1.13905 | + | 11.3231i | −0.0433942 | + | 0.431377i | ||||
\(690\) | −6.69029 | + | 11.5879i | −0.254695 | + | 0.441145i | ||||
\(691\) | −6.55423 | + | 3.78409i | −0.249335 | + | 0.143953i | −0.619460 | − | 0.785029i | \(-0.712648\pi\) |
0.370125 | + | 0.928982i | \(0.379315\pi\) | |||||||
\(692\) | 9.03761 | 0.343558 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 76.2638i | 2.89493i | ||||||||
\(695\) | 0.145963 | − | 0.0842720i | 0.00553671 | − | 0.00319662i | ||||
\(696\) | 72.2816 | + | 41.7318i | 2.73983 | + | 1.58184i | ||||
\(697\) | 22.5606 | + | 13.0254i | 0.854545 | + | 0.493372i | ||||
\(698\) | 2.48730 | + | 4.30814i | 0.0941458 | + | 0.163065i | ||||
\(699\) | 17.2971 | 0.654237 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.6629 | −1.23366 | −0.616831 | − | 0.787096i | \(-0.711584\pi\) | ||||
−0.616831 | + | 0.787096i | \(0.711584\pi\) | |||||||
\(702\) | −27.9606 | + | 38.8478i | −1.05530 | + | 1.46622i | ||||
\(703\) | −3.76727 | + | 6.52510i | −0.142085 | + | 0.246099i | ||||
\(704\) | 22.9930 | + | 13.2750i | 0.866583 | + | 0.500322i | ||||
\(705\) | −4.44969 | − | 7.70709i | −0.167585 | − | 0.290266i | ||||
\(706\) | 42.8119 | 1.61125 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 17.7137i | − | 0.665722i | ||||||
\(709\) | −21.6692 | + | 12.5107i | −0.813803 | + | 0.469850i | −0.848275 | − | 0.529556i | \(-0.822359\pi\) |
0.0344715 | + | 0.999406i | \(0.489025\pi\) | |||||||
\(710\) | −11.2520 | − | 6.49635i | −0.422281 | − | 0.243804i | ||||
\(711\) | 1.42184 | − | 2.46269i | 0.0533231 | − | 0.0923583i | ||||
\(712\) | 20.8496 | + | 36.1125i | 0.781370 | + | 1.35337i | ||||
\(713\) | 7.80843i | 0.292428i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.94525 | + | 4.48119i | −0.371931 | + | 0.167587i | ||||
\(716\) | −1.14609 | − | 1.98509i | −0.0428314 | − | 0.0741862i | ||||
\(717\) | 32.3336 | + | 18.6678i | 1.20752 | + | 0.697163i | ||||
\(718\) | 8.81630 | − | 15.2703i | 0.329021 | − | 0.569882i | ||||
\(719\) | 0.925962 | + | 1.60381i | 0.0345326 | + | 0.0598121i | 0.882775 | − | 0.469796i | \(-0.155672\pi\) |
−0.848243 | + | 0.529608i | \(0.822339\pi\) | |||||||
\(720\) | − | 0.649738i | − | 0.0242143i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 20.4485i | − | 0.761015i | ||||||
\(723\) | −42.6891 | + | 24.6466i | −1.58763 | + | 0.916616i | ||||
\(724\) | −1.06300 | + | 1.84118i | −0.0395062 | + | 0.0684268i | ||||
\(725\) | 21.1593 | − | 36.6489i | 0.785835 | − | 1.36111i | ||||
\(726\) | 32.6873 | − | 18.8720i | 1.21314 | − | 0.700406i | ||||
\(727\) | 10.8265 | 0.401534 | 0.200767 | − | 0.979639i | \(-0.435657\pi\) | ||||
0.200767 | + | 0.979639i | \(0.435657\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.5125 | 1.05602 | ||||||||
\(730\) | 21.9696 | − | 12.6842i | 0.813133 | − | 0.469463i | ||||
\(731\) | 7.58062 | − | 13.1300i | 0.280380 | − | 0.485632i | ||||
\(732\) | −8.05079 | + | 13.9444i | −0.297566 | + | 0.515399i | ||||
\(733\) | 20.2879 | − | 11.7132i | 0.749350 | − | 0.432638i | −0.0761088 | − | 0.997100i | \(-0.524250\pi\) |
0.825459 | + | 0.564462i | \(0.190916\pi\) | |||||||
\(734\) | 67.6444i | 2.49680i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.68735i | 0.283359i | ||||||||
\(737\) | 16.4690 | + | 28.5251i | 0.606643 | + | 1.05074i | ||||
\(738\) | 1.90668 | − | 3.30246i | 0.0701858 | − | 0.121565i | ||||
\(739\) | 0.416726 | + | 0.240597i | 0.0153295 | + | 0.00885051i | 0.507645 | − | 0.861566i | \(-0.330516\pi\) |
−0.492316 | + | 0.870417i | \(0.663849\pi\) | |||||||
\(740\) | −2.02539 | − | 3.50808i | −0.0744549 | − | 0.128960i | ||||
\(741\) | −12.9502 | − | 28.7407i | −0.475736 | − | 1.05582i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.7889i | 0.505866i | 0.967484 | + | 0.252933i | \(0.0813953\pi\) | ||||
−0.967484 | + | 0.252933i | \(0.918605\pi\) | |||||||
\(744\) | 7.33804 | + | 12.7099i | 0.269026 | + | 0.465966i | ||||
\(745\) | 1.36130 | − | 2.35783i | 0.0498740 | − | 0.0863843i | ||||
\(746\) | 12.7184 | + | 7.34297i | 0.465653 | + | 0.268845i | ||||
\(747\) | 0.243681 | − | 0.140689i | 0.00891581 | − | 0.00514754i | ||||
\(748\) | 61.2262i | 2.23865i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 26.7816 | 0.977927 | ||||||||
\(751\) | −13.2308 | − | 22.9165i | −0.482800 | − | 0.836235i | 0.517005 | − | 0.855983i | \(-0.327047\pi\) |
−0.999805 | + | 0.0197480i | \(0.993714\pi\) | |||||||
\(752\) | −33.8177 | − | 19.5247i | −1.23321 | − | 0.711992i | ||||
\(753\) | 18.0283 | − | 31.2260i | 0.656989 | − | 1.13794i | ||||
\(754\) | 48.6681 | − | 67.6184i | 1.77239 | − | 2.46252i | ||||
\(755\) | 1.05968 | 0.0385657 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.1114 | −0.767308 | −0.383654 | − | 0.923477i | \(-0.625334\pi\) | ||||
−0.383654 | + | 0.923477i | \(0.625334\pi\) | |||||||
\(758\) | −35.9409 | − | 62.2514i | −1.30543 | − | 2.26107i | ||||
\(759\) | −30.9992 | − | 17.8974i | −1.12520 | − | 0.649634i | ||||
\(760\) | 16.3271 | + | 9.42644i | 0.592245 | + | 0.341933i | ||||
\(761\) | −24.7031 | + | 14.2623i | −0.895487 | + | 0.517010i | −0.875733 | − | 0.482795i | \(-0.839621\pi\) |
−0.0197536 | + | 0.999805i | \(0.506288\pi\) | |||||||
\(762\) | 5.73813i | 0.207871i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 68.7631 | 2.48776 | ||||||||
\(765\) | −0.372745 | + | 0.215205i | −0.0134766 | + | 0.00778074i | ||||
\(766\) | −28.8119 | + | 49.9037i | −1.04102 | + | 1.80310i | ||||
\(767\) | −9.12717 | − | 0.918143i | −0.329563 | − | 0.0331522i | ||||
\(768\) | −27.3258 | − | 47.3297i | −0.986036 | − | 1.70786i | ||||
\(769\) | − | 25.8388i | − | 0.931769i | −0.884845 | − | 0.465885i | \(-0.845736\pi\) | ||
0.884845 | − | 0.465885i | \(-0.154264\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.10886 | 0.0399348 | ||||||||
\(772\) | 26.6754 | − | 15.4010i | 0.960069 | − | 0.554296i | ||||
\(773\) | 23.7300 | + | 13.7005i | 0.853509 | + | 0.492774i | 0.861833 | − | 0.507192i | \(-0.169316\pi\) |
−0.00832435 | + | 0.999965i | \(0.502650\pi\) | |||||||
\(774\) | −1.92200 | − | 1.10966i | −0.0690847 | − | 0.0398861i | ||||
\(775\) | 6.44428 | − | 3.72061i | 0.231485 | − | 0.133648i | ||||
\(776\) | −96.2003 | −3.45339 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 40.0263i | − | 1.43501i | ||||||
\(779\) | 20.6810 | + | 35.8206i | 0.740974 | + | 1.28340i | ||||
\(780\) | 16.8629 | + | 1.69631i | 0.603788 | + | 0.0607377i | ||||
\(781\) | 17.3786 | − | 30.1006i | 0.621855 | − | 1.07708i | ||||
\(782\) | 33.6824 | − | 19.4465i | 1.20448 | − | 0.695406i | ||||
\(783\) | −49.8251 | −1.78060 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.95746i | − | 0.0698649i | ||||||
\(786\) | 44.9910 | − | 25.9756i | 1.60478 | − | 0.926518i | ||||
\(787\) | −26.8676 | − | 15.5120i | −0.957725 | − | 0.552943i | −0.0622528 | − | 0.998060i | \(-0.519828\pi\) |
−0.895472 | + | 0.445118i | \(0.853162\pi\) | |||||||
\(788\) | −25.7328 | − | 14.8568i | −0.916694 | − | 0.529253i | ||||
\(789\) | 4.34415 | + | 7.52429i | 0.154656 | + | 0.267872i | ||||
\(790\) | −24.5623 | −0.873887 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.64974 | 0.165221 | ||||||||
\(793\) | 6.76770 | + | 4.87102i | 0.240328 | + | 0.172975i | ||||
\(794\) | 29.8434 | − | 51.6904i | 1.05910 | − | 1.83442i | ||||
\(795\) | −3.09136 | − | 1.78480i | −0.109639 | − | 0.0633002i | ||||
\(796\) | −10.5999 | − | 18.3596i | −0.375704 | − | 0.650738i | ||||
\(797\) | 16.1378 | 0.571629 | 0.285815 | − | 0.958285i | \(-0.407736\pi\) | ||||
0.285815 | + | 0.958285i | \(0.407736\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.8677i | 0.915132i | ||||||||
\(800\) | 6.34435 | − | 3.66291i | 0.224307 | − | 0.129503i | ||||
\(801\) | −1.30901 | − | 0.755756i | −0.0462515 | − | 0.0267033i | ||||
\(802\) | −3.44358 | + | 5.96446i | −0.121597 | + | 0.210612i | ||||
\(803\) | 33.9318 | + | 58.7717i | 1.19743 | + | 2.07401i | ||||
\(804\) | − | 51.1754i | − | 1.80482i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.3561 | − | 6.01810i | 0.470450 | − | 0.211978i | ||||
\(807\) | −22.8242 | − | 39.5326i | −0.803449 | − | 1.39161i | ||||
\(808\) | −43.2675 | − | 24.9805i | −1.52214 | − | 0.878810i | ||||
\(809\) | 5.17513 | − | 8.96359i | 0.181948 | − | 0.315143i | −0.760596 | − | 0.649226i | \(-0.775093\pi\) |
0.942544 | + | 0.334083i | \(0.108426\pi\) | |||||||
\(810\) | −7.01928 | − | 12.1578i | −0.246632 | − | 0.427180i | ||||
\(811\) | − | 46.3752i | − | 1.62845i | −0.580547 | − | 0.814227i | \(-0.697161\pi\) | ||
0.580547 | − | 0.814227i | \(-0.302839\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.4274i | 1.10221i | ||||||||
\(814\) | 13.9004 | − | 8.02539i | 0.487208 | − | 0.281290i | ||||
\(815\) | −5.83146 | + | 10.1004i | −0.204267 | + | 0.353801i | ||||
\(816\) | 13.6629 | − | 23.6649i | 0.478298 | − | 0.828436i | ||||
\(817\) | 20.8471 | − | 12.0361i | 0.729349 | − | 0.421090i | ||||
\(818\) | −49.9488 | −1.74642 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.2374 | −0.776565 | ||||||||
\(821\) | 48.0980 | − | 27.7694i | 1.67863 | − | 0.969159i | 0.716098 | − | 0.698000i | \(-0.245926\pi\) |
0.962534 | − | 0.271159i | \(-0.0874071\pi\) | |||||||
\(822\) | 6.66291 | − | 11.5405i | 0.232396 | − | 0.402521i | ||||
\(823\) | −10.4162 | + | 18.0414i | −0.363086 | + | 0.628884i | −0.988467 | − | 0.151436i | \(-0.951610\pi\) |
0.625381 | + | 0.780320i | \(0.284944\pi\) | |||||||
\(824\) | 28.9009 | − | 16.6859i | 1.00681 | − | 0.581282i | ||||
\(825\) | 34.1114i | 1.18761i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2.47295i | − | 0.0859927i | −0.999075 | − | 0.0429964i | \(-0.986310\pi\) | ||
0.999075 | − | 0.0429964i | \(-0.0136904\pi\) | |||||||
\(828\) | −1.92184 | − | 3.32872i | −0.0667885 | − | 0.115681i | ||||
\(829\) | 17.2811 | − | 29.9318i | 0.600199 | − | 1.03958i | −0.392591 | − | 0.919713i | \(-0.628421\pi\) |
0.992791 | − | 0.119862i | \(-0.0382453\pi\) | |||||||
\(830\) | −2.10480 | − | 1.21520i | −0.0730585 | − | 0.0421804i | ||||
\(831\) | −12.9187 | − | 22.3758i | −0.448144 | − | 0.776208i | ||||
\(832\) | −19.4763 | + | 8.77575i | −0.675218 | + | 0.304244i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 1.03761i | − | 0.0359295i | ||||||
\(835\) | 5.50000 | + | 9.52628i | 0.190335 | + | 0.329670i | ||||
\(836\) | −48.6058 | + | 84.1877i | −1.68107 | + | 2.91169i | ||||
\(837\) | −7.58739 | − | 4.38058i | −0.262258 | − | 0.151415i | ||||
\(838\) | 0.828361 | − | 0.478255i | 0.0286153 | − | 0.0165210i | ||||
\(839\) | − | 39.9149i | − | 1.37802i | −0.724754 | − | 0.689008i | \(-0.758046\pi\) | ||
0.724754 | − | 0.689008i | \(-0.241954\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.7255 | 1.99053 | ||||||||
\(842\) | 19.4538 | + | 33.6950i | 0.670423 | + | 1.16121i | ||||
\(843\) | 36.0423 | + | 20.8090i | 1.24136 | + | 0.716700i | ||||
\(844\) | 0.403032 | − | 0.698071i | 0.0138729 | − | 0.0240286i | ||||
\(845\) | 1.74808 | − | 8.60085i | 0.0601359 | − | 0.295878i | ||||
\(846\) | 3.78655 | 0.130184 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15.6629 | −0.537867 | ||||||||
\(849\) | 19.1695 | + | 33.2025i | 0.657896 | + | 1.13951i | ||||
\(850\) | −32.0983 | − | 18.5320i | −1.10096 | − | 0.635642i | ||||
\(851\) | −5.96142 | − | 3.44183i | −0.204355 | − | 0.117984i | ||||
\(852\) | −46.7670 | + | 27.0010i | −1.60221 | + | 0.925037i | ||||
\(853\) | − | 32.6507i | − | 1.11794i | −0.829188 | − | 0.558969i | \(-0.811197\pi\) | ||
0.829188 | − | 0.558969i | \(-0.188803\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.683380 | −0.0233711 | ||||||||
\(856\) | −33.5681 | + | 19.3806i | −1.14734 | + | 0.662415i | ||||
\(857\) | 3.81828 | − | 6.61346i | 0.130430 | − | 0.225911i | −0.793412 | − | 0.608684i | \(-0.791698\pi\) |
0.923842 | + | 0.382773i | \(0.125031\pi\) | |||||||
\(858\) | −6.72144 | + | 66.8173i | −0.229466 | + | 2.28110i | ||||
\(859\) | −4.48119 | − | 7.76166i | −0.152896 | − | 0.264824i | 0.779395 | − | 0.626533i | \(-0.215527\pi\) |
−0.932291 | + | 0.361709i | \(0.882193\pi\) | |||||||
\(860\) | 12.9419i | 0.441316i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.81336 | −0.129883 | ||||||||
\(863\) | −40.5318 | + | 23.4010i | −1.37972 | + | 0.796581i | −0.992125 | − | 0.125250i | \(-0.960027\pi\) |
−0.387593 | + | 0.921830i | \(0.626694\pi\) | |||||||
\(864\) | −7.46973 | − | 4.31265i | −0.254125 | − | 0.146719i | ||||
\(865\) | 1.27134 | + | 0.734010i | 0.0432270 | + | 0.0249571i | ||||
\(866\) | −55.9460 | + | 32.3004i | −1.90112 | + | 1.09761i | ||||
\(867\) | 10.3757 | 0.352376 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 65.7074i | − | 2.22897i | ||||||
\(870\) | 13.0659 | + | 22.6309i | 0.442977 | + | 0.767259i | ||||
\(871\) | −26.3687 | − | 2.65254i | −0.893468 | − | 0.0898779i | ||||
\(872\) | 12.8242 | − | 22.2121i | 0.434281 | − | 0.752197i | ||||
\(873\) | 3.01989 | − | 1.74354i | 0.102208 | − | 0.0590098i | ||||
\(874\) | 61.7523 | 2.08880 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 105.439i | − | 3.56246i | ||||||
\(877\) | 8.95522 | − | 5.17030i | 0.302396 | − | 0.174589i | −0.341123 | − | 0.940019i | \(-0.610807\pi\) |
0.643519 | + | 0.765430i | \(0.277474\pi\) | |||||||
\(878\) | −41.0945 | − | 23.7259i | −1.38687 | − | 0.800711i | ||||
\(879\) | 36.5858 | + | 21.1228i | 1.23401 | + | 0.712456i | ||||
\(880\) | −7.50659 | − | 13.0018i | −0.253047 | − | 0.438290i | ||||
\(881\) | 15.1538 | 0.510543 | 0.255272 | − | 0.966869i | \(-0.417835\pi\) | ||||
0.255272 | + | 0.966869i | \(0.417835\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.5983 | 1.73642 | 0.868211 | − | 0.496196i | \(-0.165270\pi\) | ||||
0.868211 | + | 0.496196i | \(0.165270\pi\) | |||||||
\(884\) | −39.9829 | − | 28.7775i | −1.34477 | − | 0.967893i | ||||
\(885\) | 1.43866 | − | 2.49183i | 0.0483600 | − | 0.0837619i | ||||
\(886\) | 27.1133 | + | 15.6539i | 0.910889 | + | 0.525902i | ||||
\(887\) | 2.09332 | + | 3.62574i | 0.0702868 | + | 0.121740i | 0.899027 | − | 0.437893i | \(-0.144275\pi\) |
−0.828740 | + | 0.559634i | \(0.810942\pi\) | |||||||
\(888\) | −12.9380 | −0.434169 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13.0557i | 0.437628i | ||||||||
\(891\) | 32.5236 | − | 18.7775i | 1.08958 | − | 0.629070i | ||||
\(892\) | 21.0165 | + | 12.1339i | 0.703684 | + | 0.406272i | ||||
\(893\) | −20.5356 | + | 35.5687i | −0.687199 | + | 1.19026i | ||||
\(894\) | −8.38058 | − | 14.5156i | −0.280288 | − | 0.485474i | ||||
\(895\) | − | 0.372330i | − | 0.0124456i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.2579 | − | 11.8315i | 0.876726 | − | 0.395041i | ||||
\(898\) | 1.26916 | + | 2.19825i | 0.0423524 | + | 0.0733565i | ||||
\(899\) | 13.2066 | + | 7.62482i | 0.440464 | + | 0.254302i | ||||
\(900\) | −1.83146 | + | 3.17217i | −0.0610485 | + | 0.105739i | ||||
\(901\) | 5.18783 | + | 8.98558i | 0.172832 | + | 0.299353i | ||||
\(902\) | − | 88.1133i | − | 2.93385i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 49.9873i | 1.66255i | ||||||||
\(905\) | −0.299071 | + | 0.172669i | −0.00994145 | + | 0.00573970i | ||||
\(906\) | 3.26187 | − | 5.64972i | 0.108368 | − | 0.187699i | ||||
\(907\) | −4.80242 | + | 8.31803i | −0.159462 | + | 0.276196i | −0.934675 | − | 0.355504i | \(-0.884309\pi\) |
0.775213 | + | 0.631700i | \(0.217642\pi\) | |||||||
\(908\) | 13.2726 | − | 7.66291i | 0.440465 | − | 0.254303i | ||||
\(909\) | 1.81099 | 0.0600667 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.82653 | −0.0605157 | −0.0302578 | − | 0.999542i | \(-0.509633\pi\) | ||||
−0.0302578 | + | 0.999542i | \(0.509633\pi\) | |||||||
\(912\) | 37.5738 | − | 21.6932i | 1.24419 | − | 0.718335i | ||||
\(913\) | 3.25083 | − | 5.63060i | 0.107587 | − | 0.186346i | ||||
\(914\) | 35.3967 | − | 61.3089i | 1.17082 | − | 2.02792i | ||||
\(915\) | −2.26505 | + | 1.30773i | −0.0748802 | + | 0.0432321i | ||||
\(916\) | 23.5125i | 0.776874i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 43.6385i | 1.44028i | ||||||||
\(919\) | −7.89209 | − | 13.6695i | −0.260336 | − | 0.450915i | 0.705995 | − | 0.708217i | \(-0.250500\pi\) |
−0.966331 | + | 0.257301i | \(0.917167\pi\) | |||||||
\(920\) | −8.61213 | + | 14.9166i | −0.283933 | + | 0.491787i | ||||
\(921\) | 10.5171 | + | 6.07205i | 0.346550 | + | 0.200081i | ||||
\(922\) | −31.4495 | − | 54.4721i | −1.03573 | − | 1.79394i | ||||
\(923\) | 11.4885 | + | 25.4967i | 0.378148 | + | 0.839235i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.55993i | 0.215689i | ||||||||
\(926\) | −49.2281 | − | 85.2657i | −1.61774 | − | 2.80200i | ||||
\(927\) | −0.604833 | + | 1.04760i | −0.0198653 | + | 0.0344077i | ||||
\(928\) | 13.0018 | + | 7.50659i | 0.426805 | + | 0.246416i | ||||
\(929\) | 14.5502 | − | 8.40057i | 0.477377 | − | 0.275614i | −0.241946 | − | 0.970290i | \(-0.577786\pi\) |
0.719323 | + | 0.694676i | \(0.244452\pi\) | |||||||
\(930\) | 4.59498i | 0.150675i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 42.9175 | 1.40581 | ||||||||
\(933\) | −16.9522 | − | 29.3620i | −0.554989 | − | 0.961268i | ||||
\(934\) | −4.19352 | − | 2.42113i | −0.137216 | − | 0.0792218i | ||||
\(935\) | −4.97262 | + | 8.61284i | −0.162622 | + | 0.281670i | ||||
\(936\) | −2.18547 | + | 3.03645i | −0.0714343 | + | 0.0992493i | ||||
\(937\) | 38.3004 | 1.25122 | 0.625610 | − | 0.780136i | \(-0.284850\pi\) | ||||
0.625610 | + | 0.780136i | \(0.284850\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −55.5085 | −1.81145 | ||||||||
\(940\) | −11.0406 | − | 19.1228i | −0.360103 | − | 0.623717i | ||||
\(941\) | −39.1873 | − | 22.6248i | −1.27747 | − | 0.737548i | −0.301088 | − | 0.953596i | \(-0.597350\pi\) |
−0.976383 | + | 0.216048i | \(0.930683\pi\) | |||||||
\(942\) | −10.4363 | − | 6.02539i | −0.340033 | − | 0.196318i | ||||
\(943\) | −32.7262 | + | 18.8945i | −1.06571 | + | 0.615288i | ||||
\(944\) | − | 12.6253i | − | 0.410919i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −51.2809 | −1.66729 | ||||||||
\(947\) | −4.10212 | + | 2.36836i | −0.133301 | + | 0.0769614i | −0.565168 | − | 0.824976i | \(-0.691188\pi\) |
0.431867 | + | 0.901938i | \(0.357855\pi\) | |||||||
\(948\) | −51.0444 | + | 88.4116i | −1.65785 | + | 2.87147i | ||||
\(949\) | −54.3287 | − | 5.46516i | −1.76358 | − | 0.177407i | ||||
\(950\) | −29.4241 | − | 50.9640i | −0.954643 | − | 1.65349i | ||||
\(951\) | 28.4993i | 0.924153i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.8007 | −1.45124 | −0.725618 | − | 0.688098i | \(-0.758446\pi\) | ||||
−0.725618 | + | 0.688098i | \(0.758446\pi\) | |||||||
\(954\) | 1.31532 | − | 0.759403i | 0.0425852 | − | 0.0245866i | ||||
\(955\) | 9.67307 | + | 5.58475i | 0.313013 | + | 0.180718i | ||||
\(956\) | 80.2260 | + | 46.3185i | 2.59470 | + | 1.49805i | ||||
\(957\) | −60.5406 | + | 34.9531i | −1.95700 | + | 1.12987i | ||||
\(958\) | 64.8505 | 2.09522 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 6.70052i | − | 0.216258i | ||||||
\(961\) | −14.1593 | − | 24.5246i | −0.456750 | − | 0.791115i | ||||
\(962\) | −1.29259 | + | 12.8495i | −0.0416749 | + | 0.414286i | ||||
\(963\) | 0.702508 | − | 1.21678i | 0.0226380 | − | 0.0392102i | ||||
\(964\) | −105.920 | + | 61.1529i | −3.41145 | + | 1.96960i | ||||
\(965\) | 5.00332 | 0.161063 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40.6843i | − | 1.30832i | −0.756356 | − | 0.654160i | \(-0.773022\pi\) | ||
0.756356 | − | 0.654160i | \(-0.226978\pi\) | |||||||
\(968\) | 42.0769 | − | 24.2931i | 1.35240 | − | 0.780811i | ||||
\(969\) | −24.8902 | − | 14.3703i | −0.799587 | − | 0.461642i | ||||
\(970\) | −26.0844 | − | 15.0598i | −0.837520 | − | 0.483542i | ||||
\(971\) | −20.7054 | − | 35.8629i | −0.664469 | − | 1.15089i | −0.979429 | − | 0.201790i | \(-0.935324\pi\) |
0.314959 | − | 0.949105i | \(-0.398009\pi\) | |||||||
\(972\) | 8.36344 | 0.268257 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 52.0118 | 1.66656 | ||||||||
\(975\) | −22.2760 | − | 16.0331i | −0.713402 | − | 0.513469i | ||||
\(976\) | −5.73813 | + | 9.93874i | −0.183673 | + | 0.318131i | ||||
\(977\) | −43.8271 | − | 25.3036i | −1.40215 | − | 0.809534i | −0.407540 | − | 0.913187i | \(-0.633613\pi\) |
−0.994613 | + | 0.103653i | \(0.966947\pi\) | |||||||
\(978\) | 35.9003 | + | 62.1812i | 1.14797 | + | 1.98834i | ||||
\(979\) | −34.9257 | −1.11623 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.929702i | 0.0296831i | ||||||||
\(982\) | 6.35288 | − | 3.66784i | 0.202729 | − | 0.117045i | ||||
\(983\) | −21.2567 | − | 12.2726i | −0.677984 | − | 0.391434i | 0.121111 | − | 0.992639i | \(-0.461354\pi\) |
−0.799095 | + | 0.601205i | \(0.794688\pi\) | |||||||
\(984\) | −35.5125 | + | 61.5094i | −1.13210 | + | 1.96085i | ||||
\(985\) | −2.41327 | − | 4.17990i | −0.0768930 | − | 0.133183i | ||||
\(986\) | − | 75.9570i | − | 2.41896i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −32.1319 | − | 71.3112i | −1.02225 | − | 2.26871i | ||||
\(989\) | 10.9964 | + | 19.0462i | 0.349664 | + | 0.605635i | ||||
\(990\) | 1.26076 | + | 0.727901i | 0.0400696 | + | 0.0231342i | ||||
\(991\) | 15.8271 | − | 27.4133i | 0.502764 | − | 0.870814i | −0.497230 | − | 0.867619i | \(-0.665650\pi\) |
0.999995 | − | 0.00319506i | \(-0.00101702\pi\) | |||||||
\(992\) | 1.31994 | + | 2.28621i | 0.0419083 | + | 0.0725873i | ||||
\(993\) | − | 18.1524i | − | 0.576048i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 3.44358i | − | 0.109169i | ||||||
\(996\) | −8.74822 | + | 5.05079i | −0.277198 | + | 0.160040i | ||||
\(997\) | −14.5926 | + | 25.2751i | −0.462153 | + | 0.800472i | −0.999068 | − | 0.0431642i | \(-0.986256\pi\) |
0.536915 | + | 0.843636i | \(0.319589\pi\) | |||||||
\(998\) | −3.54126 | + | 6.13364i | −0.112097 | + | 0.194157i | ||||
\(999\) | 6.68879 | − | 3.86177i | 0.211624 | − | 0.122181i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 637.2.r.d.116.6 | 12 | ||
7.2 | even | 3 | inner | 637.2.r.d.324.1 | 12 | ||
7.3 | odd | 6 | 91.2.c.a.64.6 | yes | 6 | ||
7.4 | even | 3 | 637.2.c.d.246.6 | 6 | |||
7.5 | odd | 6 | 637.2.r.e.324.1 | 12 | |||
7.6 | odd | 2 | 637.2.r.e.116.6 | 12 | |||
13.12 | even | 2 | inner | 637.2.r.d.116.1 | 12 | ||
21.17 | even | 6 | 819.2.c.b.64.1 | 6 | |||
28.3 | even | 6 | 1456.2.k.c.337.1 | 6 | |||
91.12 | odd | 6 | 637.2.r.e.324.6 | 12 | |||
91.18 | odd | 12 | 8281.2.a.bi.1.3 | 3 | |||
91.25 | even | 6 | 637.2.c.d.246.1 | 6 | |||
91.31 | even | 12 | 1183.2.a.j.1.3 | 3 | |||
91.38 | odd | 6 | 91.2.c.a.64.1 | ✓ | 6 | ||
91.51 | even | 6 | inner | 637.2.r.d.324.6 | 12 | ||
91.60 | odd | 12 | 8281.2.a.be.1.1 | 3 | |||
91.73 | even | 12 | 1183.2.a.h.1.1 | 3 | |||
91.90 | odd | 2 | 637.2.r.e.116.1 | 12 | |||
273.38 | even | 6 | 819.2.c.b.64.6 | 6 | |||
364.311 | even | 6 | 1456.2.k.c.337.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.c.a.64.1 | ✓ | 6 | 91.38 | odd | 6 | ||
91.2.c.a.64.6 | yes | 6 | 7.3 | odd | 6 | ||
637.2.c.d.246.1 | 6 | 91.25 | even | 6 | |||
637.2.c.d.246.6 | 6 | 7.4 | even | 3 | |||
637.2.r.d.116.1 | 12 | 13.12 | even | 2 | inner | ||
637.2.r.d.116.6 | 12 | 1.1 | even | 1 | trivial | ||
637.2.r.d.324.1 | 12 | 7.2 | even | 3 | inner | ||
637.2.r.d.324.6 | 12 | 91.51 | even | 6 | inner | ||
637.2.r.e.116.1 | 12 | 91.90 | odd | 2 | |||
637.2.r.e.116.6 | 12 | 7.6 | odd | 2 | |||
637.2.r.e.324.1 | 12 | 7.5 | odd | 6 | |||
637.2.r.e.324.6 | 12 | 91.12 | odd | 6 | |||
819.2.c.b.64.1 | 6 | 21.17 | even | 6 | |||
819.2.c.b.64.6 | 6 | 273.38 | even | 6 | |||
1183.2.a.h.1.1 | 3 | 91.73 | even | 12 | |||
1183.2.a.j.1.3 | 3 | 91.31 | even | 12 | |||
1456.2.k.c.337.1 | 6 | 28.3 | even | 6 | |||
1456.2.k.c.337.2 | 6 | 364.311 | even | 6 | |||
8281.2.a.be.1.1 | 3 | 91.60 | odd | 12 | |||
8281.2.a.bi.1.3 | 3 | 91.18 | odd | 12 |