Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(49,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.i (of order \(10\), degree \(4\), 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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 274.5 | ||
Character | \(\chi\) | \(=\) | 375.274 |
Dual form | 375.2.i.d.349.5 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.32085 | + | 0.754089i | 1.64109 | + | 0.533221i | 0.976781 | − | 0.214240i | \(-0.0687273\pi\) |
0.664306 | + | 0.747461i | \(0.268727\pi\) | |||||||
\(3\) | 0.587785 | − | 0.809017i | 0.339358 | − | 0.467086i | ||||
\(4\) | 3.19965 | + | 2.32468i | 1.59982 | + | 1.16234i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.97423 | − | 1.43436i | 0.805976 | − | 0.585576i | ||||
\(7\) | − | 3.44028i | − | 1.30030i | −0.759804 | − | 0.650152i | \(-0.774705\pi\) | ||
0.759804 | − | 0.650152i | \(-0.225295\pi\) | |||||||
\(8\) | 2.80415 | + | 3.85959i | 0.991418 | + | 1.36457i | ||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00942 | + | 3.10669i | −0.304353 | + | 0.936701i | 0.675565 | + | 0.737300i | \(0.263900\pi\) |
−0.979918 | + | 0.199401i | \(0.936100\pi\) | |||||||
\(12\) | 3.76141 | − | 1.22216i | 1.08583 | − | 0.352806i | ||||
\(13\) | −3.07385 | + | 0.998755i | −0.852533 | + | 0.277005i | −0.702506 | − | 0.711677i | \(-0.747936\pi\) |
−0.150026 | + | 0.988682i | \(0.547936\pi\) | |||||||
\(14\) | 2.59428 | − | 7.98437i | 0.693350 | − | 2.13391i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.15323 | + | 3.54927i | 0.288307 | + | 0.887317i | ||||
\(17\) | 2.97030 | + | 4.08826i | 0.720403 | + | 0.991550i | 0.999510 | + | 0.0312897i | \(0.00996144\pi\) |
−0.279107 | + | 0.960260i | \(0.590039\pi\) | |||||||
\(18\) | − | 2.44028i | − | 0.575180i | ||||||
\(19\) | −2.49274 | + | 1.81108i | −0.571873 | + | 0.415490i | −0.835785 | − | 0.549056i | \(-0.814987\pi\) |
0.263912 | + | 0.964547i | \(0.414987\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.78325 | − | 2.02215i | −0.607354 | − | 0.441269i | ||||
\(22\) | −4.68544 | + | 6.44895i | −0.998938 | + | 1.37492i | ||||
\(23\) | −1.47190 | − | 0.478250i | −0.306913 | − | 0.0997219i | 0.151512 | − | 0.988455i | \(-0.451586\pi\) |
−0.458424 | + | 0.888734i | \(0.651586\pi\) | |||||||
\(24\) | 4.77071 | 0.973817 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.88709 | −1.54679 | ||||||||
\(27\) | −0.951057 | − | 0.309017i | −0.183031 | − | 0.0594703i | ||||
\(28\) | 7.99756 | − | 11.0077i | 1.51140 | − | 2.08026i | ||||
\(29\) | −2.52590 | − | 1.83517i | −0.469047 | − | 0.340783i | 0.328022 | − | 0.944670i | \(-0.393618\pi\) |
−0.797070 | + | 0.603887i | \(0.793618\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.02080 | + | 4.37437i | −1.08137 | + | 0.785659i | −0.977921 | − | 0.208976i | \(-0.932987\pi\) |
−0.103446 | + | 0.994635i | \(0.532987\pi\) | |||||||
\(32\) | − | 0.434479i | − | 0.0768057i | ||||||
\(33\) | 1.92004 | + | 2.64270i | 0.334236 | + | 0.460036i | ||||
\(34\) | 3.81069 | + | 11.7281i | 0.653528 | + | 2.01135i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.22216 | − | 3.76141i | 0.203693 | − | 0.626902i | ||||
\(37\) | 5.47655 | − | 1.77944i | 0.900339 | − | 0.292538i | 0.177962 | − | 0.984037i | \(-0.443050\pi\) |
0.722377 | + | 0.691499i | \(0.243050\pi\) | |||||||
\(38\) | −7.15098 | + | 2.32349i | −1.16004 | + | 0.376921i | ||||
\(39\) | −0.998755 | + | 3.07385i | −0.159929 | + | 0.492210i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.67476 | + | 5.15437i | 0.261553 | + | 0.804977i | 0.992468 | + | 0.122508i | \(0.0390938\pi\) |
−0.730915 | + | 0.682469i | \(0.760906\pi\) | |||||||
\(42\) | −4.93461 | − | 6.79191i | −0.761427 | − | 1.04801i | ||||
\(43\) | − | 2.53106i | − | 0.385982i | −0.981201 | − | 0.192991i | \(-0.938181\pi\) | ||
0.981201 | − | 0.192991i | \(-0.0618189\pi\) | |||||||
\(44\) | −10.4519 | + | 7.59371i | −1.57568 | + | 1.14480i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.05541 | − | 2.21989i | −0.450496 | − | 0.327305i | ||||
\(47\) | 4.15659 | − | 5.72106i | 0.606301 | − | 0.834502i | −0.389966 | − | 0.920829i | \(-0.627513\pi\) |
0.996267 | + | 0.0863273i | \(0.0275131\pi\) | |||||||
\(48\) | 3.54927 | + | 1.15323i | 0.512293 | + | 0.166454i | ||||
\(49\) | −4.83555 | −0.690793 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.05337 | 0.707614 | ||||||||
\(52\) | −12.1570 | − | 3.95006i | −1.68588 | − | 0.547774i | ||||
\(53\) | 5.96693 | − | 8.21277i | 0.819621 | − | 1.12811i | −0.170147 | − | 0.985419i | \(-0.554424\pi\) |
0.989767 | − | 0.142692i | \(-0.0455759\pi\) | |||||||
\(54\) | −1.97423 | − | 1.43436i | −0.268659 | − | 0.195192i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 13.2781 | − | 9.64708i | 1.77436 | − | 1.28915i | ||||
\(57\) | 3.08119i | 0.408114i | ||||||||
\(58\) | −4.47834 | − | 6.16391i | −0.588035 | − | 0.809361i | ||||
\(59\) | −0.534773 | − | 1.64586i | −0.0696215 | − | 0.214273i | 0.910192 | − | 0.414187i | \(-0.135934\pi\) |
−0.979814 | + | 0.199913i | \(0.935934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.42149 | − | 7.45259i | 0.310040 | − | 0.954206i | −0.667708 | − | 0.744424i | \(-0.732724\pi\) |
0.977748 | − | 0.209783i | \(-0.0672756\pi\) | |||||||
\(62\) | −17.2720 | + | 5.61202i | −2.19355 | + | 0.712727i | ||||
\(63\) | −3.27190 | + | 1.06311i | −0.412221 | + | 0.133939i | ||||
\(64\) | 2.63409 | − | 8.10689i | 0.329261 | − | 1.01336i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.46328 | + | 7.58119i | 0.303209 | + | 0.933180i | ||||
\(67\) | 1.08687 | + | 1.49595i | 0.132783 | + | 0.182760i | 0.870231 | − | 0.492644i | \(-0.163969\pi\) |
−0.737448 | + | 0.675404i | \(0.763969\pi\) | |||||||
\(68\) | 19.9860i | 2.42366i | ||||||||
\(69\) | −1.25207 | + | 0.909685i | −0.150732 | + | 0.109513i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.577613 | + | 0.419660i | 0.0685500 | + | 0.0498045i | 0.621533 | − | 0.783388i | \(-0.286510\pi\) |
−0.552982 | + | 0.833193i | \(0.686510\pi\) | |||||||
\(72\) | 2.80415 | − | 3.85959i | 0.330473 | − | 0.454857i | ||||
\(73\) | 1.78825 | + | 0.581036i | 0.209298 | + | 0.0680052i | 0.411790 | − | 0.911279i | \(-0.364904\pi\) |
−0.202491 | + | 0.979284i | \(0.564904\pi\) | |||||||
\(74\) | 14.0521 | 1.63352 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.1861 | −1.39784 | ||||||||
\(77\) | 10.6879 | + | 3.47270i | 1.21800 | + | 0.395751i | ||||
\(78\) | −4.63591 | + | 6.38079i | −0.524914 | + | 0.722482i | ||||
\(79\) | −10.7868 | − | 7.83708i | −1.21361 | − | 0.881740i | −0.218058 | − | 0.975936i | \(-0.569972\pi\) |
−0.995554 | + | 0.0941957i | \(0.969972\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 13.2254i | 1.46050i | ||||||||
\(83\) | 2.32614 | + | 3.20166i | 0.255328 | + | 0.351428i | 0.917368 | − | 0.398040i | \(-0.130309\pi\) |
−0.662041 | + | 0.749468i | \(0.730309\pi\) | |||||||
\(84\) | −4.20457 | − | 12.9403i | −0.458756 | − | 1.41190i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.90864 | − | 5.87419i | 0.205814 | − | 0.633430i | ||||
\(87\) | −2.96937 | + | 0.964807i | −0.318350 | + | 0.103438i | ||||
\(88\) | −14.8211 | + | 4.81567i | −1.57993 | + | 0.513352i | ||||
\(89\) | −2.63713 | + | 8.11624i | −0.279535 | + | 0.860320i | 0.708449 | + | 0.705762i | \(0.249395\pi\) |
−0.987984 | + | 0.154558i | \(0.950605\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.43600 | + | 10.5749i | 0.360191 | + | 1.10855i | ||||
\(92\) | −3.59779 | − | 4.95193i | −0.375095 | − | 0.516274i | ||||
\(93\) | 7.44212i | 0.771712i | ||||||||
\(94\) | 13.9610 | − | 10.1433i | 1.43997 | − | 1.04620i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.351501 | − | 0.255380i | −0.0358749 | − | 0.0260646i | ||||
\(97\) | −6.26157 | + | 8.61831i | −0.635766 | + | 0.875057i | −0.998381 | − | 0.0568823i | \(-0.981884\pi\) |
0.362615 | + | 0.931939i | \(0.381884\pi\) | |||||||
\(98\) | −11.2226 | − | 3.64643i | −1.13365 | − | 0.368345i | ||||
\(99\) | 3.26656 | 0.328302 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.76173 | 0.175299 | 0.0876496 | − | 0.996151i | \(-0.472064\pi\) | ||||
0.0876496 | + | 0.996151i | \(0.472064\pi\) | |||||||
\(102\) | 11.7281 | + | 3.81069i | 1.16126 | + | 0.377315i | ||||
\(103\) | −9.35416 | + | 12.8749i | −0.921693 | + | 1.26860i | 0.0413198 | + | 0.999146i | \(0.486844\pi\) |
−0.963013 | + | 0.269456i | \(0.913156\pi\) | |||||||
\(104\) | −12.4743 | − | 9.06313i | −1.22321 | − | 0.888713i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 20.0415 | − | 14.5610i | 1.94660 | − | 1.41429i | ||||
\(107\) | − | 15.7807i | − | 1.52558i | −0.646649 | − | 0.762788i | \(-0.723830\pi\) | ||
0.646649 | − | 0.762788i | \(-0.276170\pi\) | |||||||
\(108\) | −2.32468 | − | 3.19965i | −0.223692 | − | 0.307886i | ||||
\(109\) | 3.06539 | + | 9.43429i | 0.293611 | + | 0.903641i | 0.983685 | + | 0.179902i | \(0.0575781\pi\) |
−0.690074 | + | 0.723739i | \(0.742422\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.77944 | − | 5.47655i | 0.168897 | − | 0.519811i | ||||
\(112\) | 12.2105 | − | 3.96743i | 1.15378 | − | 0.374887i | ||||
\(113\) | 5.24399 | − | 1.70388i | 0.493313 | − | 0.160287i | −0.0517868 | − | 0.998658i | \(-0.516492\pi\) |
0.545100 | + | 0.838371i | \(0.316492\pi\) | |||||||
\(114\) | −2.32349 | + | 7.15098i | −0.217615 | + | 0.669751i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.81580 | − | 11.7438i | −0.354288 | − | 1.09039i | ||||
\(117\) | 1.89974 | + | 2.61477i | 0.175631 | + | 0.241736i | ||||
\(118\) | − | 4.22306i | − | 0.388764i | ||||||
\(119\) | 14.0648 | − | 10.2187i | 1.28932 | − | 0.936743i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.266626 | + | 0.193715i | 0.0242387 | + | 0.0176105i | ||||
\(122\) | 11.2398 | − | 15.4703i | 1.01761 | − | 1.40061i | ||||
\(123\) | 5.15437 | + | 1.67476i | 0.464754 | + | 0.151008i | ||||
\(124\) | −29.4334 | −2.64320 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.39527 | −0.747910 | ||||||||
\(127\) | −0.943532 | − | 0.306572i | −0.0837250 | − | 0.0272039i | 0.266855 | − | 0.963737i | \(-0.414016\pi\) |
−0.350580 | + | 0.936533i | \(0.614016\pi\) | |||||||
\(128\) | 11.7159 | − | 16.1255i | 1.03555 | − | 1.42531i | ||||
\(129\) | −2.04767 | − | 1.48772i | −0.180287 | − | 0.130986i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2029 | − | 7.41286i | 0.891434 | − | 0.647665i | −0.0448175 | − | 0.998995i | \(-0.514271\pi\) |
0.936252 | + | 0.351330i | \(0.114271\pi\) | |||||||
\(132\) | 12.9192i | 1.12447i | ||||||||
\(133\) | 6.23063 | + | 8.57573i | 0.540264 | + | 0.743610i | ||||
\(134\) | 1.39438 | + | 4.29147i | 0.120456 | + | 0.370727i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.44984 | + | 22.9282i | −0.638818 | + | 1.96608i | ||||
\(137\) | −7.83732 | + | 2.54650i | −0.669588 | + | 0.217562i | −0.624031 | − | 0.781400i | \(-0.714506\pi\) |
−0.0455566 | + | 0.998962i | \(0.514506\pi\) | |||||||
\(138\) | −3.59186 | + | 1.16706i | −0.305759 | + | 0.0993471i | ||||
\(139\) | −2.49182 | + | 7.66904i | −0.211354 | + | 0.650479i | 0.788039 | + | 0.615626i | \(0.211097\pi\) |
−0.999392 | + | 0.0348539i | \(0.988903\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.18525 | − | 6.72551i | −0.184031 | − | 0.566390i | ||||
\(142\) | 1.02409 | + | 1.40954i | 0.0859397 | + | 0.118286i | ||||
\(143\) | − | 10.5577i | − | 0.882875i | ||||||
\(144\) | 3.01919 | − | 2.19357i | 0.251599 | − | 0.182797i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.71209 | + | 2.69699i | 0.307215 | + | 0.223205i | ||||
\(147\) | −2.84226 | + | 3.91204i | −0.234426 | + | 0.322660i | ||||
\(148\) | 21.6597 | + | 7.03765i | 1.78041 | + | 0.578491i | ||||
\(149\) | 19.1101 | 1.56556 | 0.782781 | − | 0.622298i | \(-0.213801\pi\) | ||||
0.782781 | + | 0.622298i | \(0.213801\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.58550 | 0.129026 | 0.0645132 | − | 0.997917i | \(-0.479451\pi\) | ||||
0.0645132 | + | 0.997917i | \(0.479451\pi\) | |||||||
\(152\) | −13.9800 | − | 4.54239i | −1.13393 | − | 0.368437i | ||||
\(153\) | 2.97030 | − | 4.08826i | 0.240134 | − | 0.330517i | ||||
\(154\) | 22.1862 | + | 16.1192i | 1.78782 | + | 1.29892i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10.3414 | + | 7.51345i | −0.827973 | + | 0.601558i | ||||
\(157\) | − | 21.8510i | − | 1.74390i | −0.489599 | − | 0.871948i | \(-0.662857\pi\) | ||
0.489599 | − | 0.871948i | \(-0.337143\pi\) | |||||||
\(158\) | −19.1247 | − | 26.3229i | −1.52148 | − | 2.09414i | ||||
\(159\) | −3.13700 | − | 9.65469i | −0.248780 | − | 0.765667i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.64531 | + | 5.06376i | −0.129669 | + | 0.399080i | ||||
\(162\) | −2.32085 | + | 0.754089i | −0.182343 | + | 0.0592468i | ||||
\(163\) | 9.63786 | − | 3.13153i | 0.754896 | − | 0.245280i | 0.0938092 | − | 0.995590i | \(-0.470096\pi\) |
0.661087 | + | 0.750310i | \(0.270096\pi\) | |||||||
\(164\) | −6.62363 | + | 20.3854i | −0.517219 | + | 1.59184i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.98429 | + | 9.18469i | 0.231626 | + | 0.712870i | ||||
\(167\) | 0.888195 | + | 1.22250i | 0.0687306 | + | 0.0945996i | 0.841998 | − | 0.539480i | \(-0.181379\pi\) |
−0.773268 | + | 0.634080i | \(0.781379\pi\) | |||||||
\(168\) | − | 16.4126i | − | 1.26626i | ||||||
\(169\) | −2.06617 | + | 1.50116i | −0.158936 | + | 0.115474i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.49274 | + | 1.81108i | 0.190624 | + | 0.138497i | ||||
\(172\) | 5.88389 | − | 8.09848i | 0.448643 | − | 0.617504i | ||||
\(173\) | 13.1772 | + | 4.28153i | 1.00184 | + | 0.325518i | 0.763602 | − | 0.645688i | \(-0.223429\pi\) |
0.238241 | + | 0.971206i | \(0.423429\pi\) | |||||||
\(174\) | −7.61901 | −0.577595 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.1906 | −0.918897 | ||||||||
\(177\) | −1.64586 | − | 0.534773i | −0.123711 | − | 0.0401960i | ||||
\(178\) | −12.2407 | + | 16.8479i | −0.917482 | + | 1.26281i | ||||
\(179\) | 11.6949 | + | 8.49685i | 0.874119 | + | 0.635085i | 0.931689 | − | 0.363257i | \(-0.118335\pi\) |
−0.0575701 | + | 0.998341i | \(0.518335\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.9068 | + | 10.1039i | −1.03369 | + | 0.751017i | −0.969043 | − | 0.246891i | \(-0.920591\pi\) |
−0.0646435 | + | 0.997908i | \(0.520591\pi\) | |||||||
\(182\) | 27.1338i | 2.01129i | ||||||||
\(183\) | −4.60595 | − | 6.33955i | −0.340482 | − | 0.468633i | ||||
\(184\) | −2.28159 | − | 7.02201i | −0.168201 | − | 0.517670i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.61202 | + | 17.2720i | −0.411493 | + | 1.26645i | ||||
\(187\) | −15.6992 | + | 5.10099i | −1.14804 | + | 0.373021i | ||||
\(188\) | 26.5993 | − | 8.64262i | 1.93995 | − | 0.630328i | ||||
\(189\) | −1.06311 | + | 3.27190i | −0.0773296 | + | 0.237996i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.25778 | + | 10.0264i | 0.235725 | + | 0.725486i | 0.997024 | + | 0.0770858i | \(0.0245615\pi\) |
−0.761300 | + | 0.648400i | \(0.775438\pi\) | |||||||
\(192\) | −5.01034 | − | 6.89613i | −0.361590 | − | 0.497686i | ||||
\(193\) | 0.682908i | 0.0491568i | 0.999698 | + | 0.0245784i | \(0.00782434\pi\) | ||||
−0.999698 | + | 0.0245784i | \(0.992176\pi\) | |||||||
\(194\) | −21.0311 | + | 15.2800i | −1.50995 | + | 1.09704i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −15.4721 | − | 11.2411i | −1.10515 | − | 0.802936i | ||||
\(197\) | −13.6937 | + | 18.8478i | −0.975639 | + | 1.34285i | −0.0364929 | + | 0.999334i | \(0.511619\pi\) |
−0.939146 | + | 0.343518i | \(0.888381\pi\) | |||||||
\(198\) | 7.58119 | + | 2.46328i | 0.538772 | + | 0.175058i | ||||
\(199\) | −10.1946 | −0.722679 | −0.361339 | − | 0.932434i | \(-0.617680\pi\) | ||||
−0.361339 | + | 0.932434i | \(0.617680\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.84910 | 0.130425 | ||||||||
\(202\) | 4.08872 | + | 1.32850i | 0.287681 | + | 0.0934733i | ||||
\(203\) | −6.31351 | + | 8.68980i | −0.443122 | + | 0.609905i | ||||
\(204\) | 16.1690 | + | 11.7475i | 1.13206 | + | 0.822488i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −31.4184 | + | 22.8268i | −2.18902 | + | 1.59042i | ||||
\(207\) | 1.54765i | 0.107569i | ||||||||
\(208\) | −7.08969 | − | 9.75813i | −0.491582 | − | 0.676604i | ||||
\(209\) | −3.11023 | − | 9.57230i | −0.215139 | − | 0.662130i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.64172 | − | 17.3634i | 0.388392 | − | 1.19535i | −0.545598 | − | 0.838047i | \(-0.683697\pi\) |
0.933990 | − | 0.357300i | \(-0.116303\pi\) | |||||||
\(212\) | 38.1841 | − | 12.4068i | 2.62250 | − | 0.852101i | ||||
\(213\) | 0.679025 | − | 0.220629i | 0.0465260 | − | 0.0151172i | ||||
\(214\) | 11.9000 | − | 36.6245i | 0.813470 | − | 2.50360i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.47423 | − | 4.53722i | −0.100309 | − | 0.308718i | ||||
\(217\) | 15.0491 | + | 20.7133i | 1.02160 | + | 1.40611i | ||||
\(218\) | 24.2071i | 1.63951i | ||||||||
\(219\) | 1.52117 | − | 1.10520i | 0.102791 | − | 0.0746823i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.2134 | − | 9.60011i | −0.888831 | − | 0.645774i | ||||
\(222\) | 8.25961 | − | 11.3684i | 0.554349 | − | 0.762996i | ||||
\(223\) | −16.3813 | − | 5.32262i | −1.09698 | − | 0.356429i | −0.296037 | − | 0.955176i | \(-0.595665\pi\) |
−0.800938 | + | 0.598748i | \(0.795665\pi\) | |||||||
\(224\) | −1.49473 | −0.0998708 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.4554 | 0.895039 | ||||||||
\(227\) | −4.11692 | − | 1.33767i | −0.273250 | − | 0.0887842i | 0.169187 | − | 0.985584i | \(-0.445886\pi\) |
−0.442437 | + | 0.896800i | \(0.645886\pi\) | |||||||
\(228\) | −7.16279 | + | 9.85874i | −0.474367 | + | 0.652911i | ||||
\(229\) | 16.4349 | + | 11.9407i | 1.08605 | + | 0.789062i | 0.978728 | − | 0.205163i | \(-0.0657723\pi\) |
0.107322 | + | 0.994224i | \(0.465772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.09165 | − | 6.60547i | 0.598187 | − | 0.434608i | ||||
\(232\) | − | 14.8950i | − | 0.977906i | ||||||
\(233\) | −0.200409 | − | 0.275839i | −0.0131292 | − | 0.0180708i | 0.802402 | − | 0.596784i | \(-0.203555\pi\) |
−0.815531 | + | 0.578713i | \(0.803555\pi\) | |||||||
\(234\) | 2.43724 | + | 7.50107i | 0.159328 | + | 0.490360i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.11502 | − | 6.50936i | 0.137676 | − | 0.423723i | ||||
\(237\) | −12.6807 | + | 4.12020i | −0.823697 | + | 0.267635i | ||||
\(238\) | 40.3480 | − | 13.1099i | 2.61537 | − | 0.849786i | ||||
\(239\) | 2.21407 | − | 6.81421i | 0.143216 | − | 0.440774i | −0.853561 | − | 0.520993i | \(-0.825562\pi\) |
0.996777 | + | 0.0802185i | \(0.0255618\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.88194 | − | 11.9474i | −0.250058 | − | 0.769599i | −0.994763 | − | 0.102206i | \(-0.967410\pi\) |
0.744705 | − | 0.667393i | \(-0.232590\pi\) | |||||||
\(242\) | 0.472720 | + | 0.650643i | 0.0303876 | + | 0.0418249i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 25.0728 | − | 18.2165i | 1.60512 | − | 1.16619i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.6996 | + | 7.77370i | 0.682181 | + | 0.495633i | ||||
\(247\) | 5.85348 | − | 8.05662i | 0.372448 | − | 0.512631i | ||||
\(248\) | −33.7665 | − | 10.9714i | −2.14417 | − | 0.696684i | ||||
\(249\) | 3.95747 | 0.250795 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.0160 | 1.07404 | 0.537022 | − | 0.843568i | \(-0.319549\pi\) | ||||
0.537022 | + | 0.843568i | \(0.319549\pi\) | |||||||
\(252\) | −12.9403 | − | 4.20457i | −0.815164 | − | 0.264863i | ||||
\(253\) | 2.97154 | − | 4.08998i | 0.186819 | − | 0.257135i | ||||
\(254\) | −1.95861 | − | 1.42301i | −0.122894 | − | 0.0892879i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 25.5586 | − | 18.5694i | 1.59741 | − | 1.16059i | ||||
\(257\) | 4.13200i | 0.257747i | 0.991661 | + | 0.128874i | \(0.0411361\pi\) | ||||
−0.991661 | + | 0.128874i | \(0.958864\pi\) | |||||||
\(258\) | −3.63045 | − | 4.99689i | −0.226022 | − | 0.311093i | ||||
\(259\) | −6.12177 | − | 18.8409i | −0.380388 | − | 1.17072i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.964807 | + | 2.96937i | −0.0597201 | + | 0.183799i | ||||
\(262\) | 29.2694 | − | 9.51020i | 1.80827 | − | 0.587542i | ||||
\(263\) | −0.986940 | + | 0.320676i | −0.0608573 | + | 0.0197737i | −0.339287 | − | 0.940683i | \(-0.610186\pi\) |
0.278430 | + | 0.960456i | \(0.410186\pi\) | |||||||
\(264\) | −4.81567 | + | 14.8211i | −0.296384 | + | 0.912176i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.99348 | + | 24.6014i | 0.490112 | + | 1.50841i | ||||
\(267\) | 5.01611 | + | 6.90408i | 0.306981 | + | 0.422523i | ||||
\(268\) | 7.31315i | 0.446722i | ||||||||
\(269\) | −12.7741 | + | 9.28093i | −0.778851 | + | 0.565869i | −0.904634 | − | 0.426189i | \(-0.859856\pi\) |
0.125783 | + | 0.992058i | \(0.459856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0838 | + | 8.05286i | 0.673294 | + | 0.489176i | 0.871126 | − | 0.491059i | \(-0.163390\pi\) |
−0.197832 | + | 0.980236i | \(0.563390\pi\) | |||||||
\(272\) | −11.0849 | + | 15.2571i | −0.672122 | + | 0.925096i | ||||
\(273\) | 10.5749 | + | 3.43600i | 0.640023 | + | 0.207956i | ||||
\(274\) | −20.1095 | −1.21486 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.12092 | −0.368436 | ||||||||
\(277\) | 6.63827 | + | 2.15691i | 0.398855 | + | 0.129596i | 0.501574 | − | 0.865114i | \(-0.332754\pi\) |
−0.102719 | + | 0.994710i | \(0.532754\pi\) | |||||||
\(278\) | −11.5663 | + | 15.9196i | −0.693699 | + | 0.954795i | ||||
\(279\) | 6.02080 | + | 4.37437i | 0.360456 | + | 0.261886i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.43834 | + | 4.67773i | −0.384079 | + | 0.279050i | −0.763025 | − | 0.646369i | \(-0.776287\pi\) |
0.378946 | + | 0.925419i | \(0.376287\pi\) | |||||||
\(282\) | − | 17.2567i | − | 1.02762i | ||||||
\(283\) | −16.3376 | − | 22.4868i | −0.971169 | − | 1.33670i | −0.941454 | − | 0.337141i | \(-0.890540\pi\) |
−0.0297149 | − | 0.999558i | \(-0.509460\pi\) | |||||||
\(284\) | 0.872582 | + | 2.68553i | 0.0517782 | + | 0.159357i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.96141 | − | 24.5027i | 0.470768 | − | 1.44888i | ||||
\(287\) | 17.7325 | − | 5.76163i | 1.04672 | − | 0.340099i | ||||
\(288\) | −0.413214 | + | 0.134261i | −0.0243488 | + | 0.00791142i | ||||
\(289\) | −2.63794 | + | 8.11876i | −0.155173 | + | 0.477574i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.29190 | + | 10.1314i | 0.192975 | + | 0.593915i | ||||
\(292\) | 4.37103 | + | 6.01621i | 0.255795 | + | 0.352072i | ||||
\(293\) | 14.2098i | 0.830146i | 0.909788 | + | 0.415073i | \(0.136244\pi\) | ||||
−0.909788 | + | 0.415073i | \(0.863756\pi\) | |||||||
\(294\) | −9.54649 | + | 6.93593i | −0.556763 | + | 0.404512i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 22.2250 | + | 16.1474i | 1.29180 | + | 0.938548i | ||||
\(297\) | 1.92004 | − | 2.64270i | 0.111412 | − | 0.153345i | ||||
\(298\) | 44.3517 | + | 14.4107i | 2.56922 | + | 0.834791i | ||||
\(299\) | 5.00206 | 0.289276 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.70755 | −0.501895 | ||||||||
\(302\) | 3.67971 | + | 1.19561i | 0.211744 | + | 0.0687997i | ||||
\(303\) | 1.03552 | − | 1.42527i | 0.0594892 | − | 0.0818798i | ||||
\(304\) | −9.30270 | − | 6.75881i | −0.533547 | − | 0.387644i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.97652 | − | 7.24837i | 0.570320 | − | 0.414362i | ||||
\(307\) | − | 23.2911i | − | 1.32930i | −0.747157 | − | 0.664648i | \(-0.768582\pi\) | ||
0.747157 | − | 0.664648i | \(-0.231418\pi\) | |||||||
\(308\) | 26.1245 | + | 35.9573i | 1.48858 | + | 2.04886i | ||||
\(309\) | 4.91777 | + | 15.1354i | 0.279762 | + | 0.861020i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.33284 | + | 7.17976i | −0.132283 | + | 0.407127i | −0.995158 | − | 0.0982923i | \(-0.968662\pi\) |
0.862874 | + | 0.505419i | \(0.168662\pi\) | |||||||
\(312\) | −14.6645 | + | 4.76477i | −0.830211 | + | 0.269752i | ||||
\(313\) | −30.1072 | + | 9.78241i | −1.70176 | + | 0.552934i | −0.988927 | − | 0.148402i | \(-0.952587\pi\) |
−0.712830 | + | 0.701337i | \(0.752587\pi\) | |||||||
\(314\) | 16.4776 | − | 50.7127i | 0.929883 | − | 2.86188i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.2953 | − | 50.1518i | −0.916682 | − | 2.82126i | ||||
\(317\) | −15.1861 | − | 20.9019i | −0.852938 | − | 1.17397i | −0.983208 | − | 0.182490i | \(-0.941584\pi\) |
0.130270 | − | 0.991479i | \(-0.458416\pi\) | |||||||
\(318\) | − | 24.7726i | − | 1.38918i | ||||||
\(319\) | 8.25100 | − | 5.99471i | 0.461968 | − | 0.335639i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.7668 | − | 9.27565i | −0.712575 | − | 0.517716i | ||||
\(322\) | −7.63705 | + | 10.5115i | −0.425596 | + | 0.585783i | ||||
\(323\) | −14.8083 | − | 4.81152i | −0.823959 | − | 0.267720i | ||||
\(324\) | −3.95498 | −0.219721 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.7295 | 1.36964 | ||||||||
\(327\) | 9.43429 | + | 3.06539i | 0.521717 | + | 0.169516i | ||||
\(328\) | −15.1975 | + | 20.9175i | −0.839139 | + | 1.15498i | ||||
\(329\) | −19.6821 | − | 14.2999i | −1.08511 | − | 0.788376i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.2679 | + | 11.8193i | −0.894166 | + | 0.649650i | −0.936961 | − | 0.349434i | \(-0.886374\pi\) |
0.0427948 | + | 0.999084i | \(0.486374\pi\) | |||||||
\(332\) | 15.6517i | 0.859001i | ||||||||
\(333\) | −3.38469 | − | 4.65863i | −0.185480 | − | 0.255291i | ||||
\(334\) | 1.13949 | + | 3.50700i | 0.0623504 | + | 0.191895i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.96743 | − | 12.2105i | 0.216441 | − | 0.666137i | ||||
\(337\) | −3.21816 | + | 1.04564i | −0.175304 | + | 0.0569599i | −0.395354 | − | 0.918529i | \(-0.629378\pi\) |
0.220050 | + | 0.975489i | \(0.429378\pi\) | |||||||
\(338\) | −5.92729 | + | 1.92589i | −0.322402 | + | 0.104755i | ||||
\(339\) | 1.70388 | − | 5.24399i | 0.0925419 | − | 0.284815i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.51225 | − | 23.1203i | −0.406811 | − | 1.25204i | ||||
\(342\) | 4.41955 | + | 6.08299i | 0.238982 | + | 0.328930i | ||||
\(343\) | − | 7.44633i | − | 0.402064i | ||||||
\(344\) | 9.76882 | − | 7.09747i | 0.526700 | − | 0.382670i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 27.3536 | + | 19.8735i | 1.47054 | + | 1.06841i | ||||
\(347\) | −17.1612 | + | 23.6204i | −0.921262 | + | 1.26801i | 0.0419100 | + | 0.999121i | \(0.486656\pi\) |
−0.963172 | + | 0.268887i | \(0.913344\pi\) | |||||||
\(348\) | −11.7438 | − | 3.81580i | −0.629534 | − | 0.204548i | ||||
\(349\) | 20.3979 | 1.09187 | 0.545937 | − | 0.837826i | \(-0.316174\pi\) | ||||
0.545937 | + | 0.837826i | \(0.316174\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.23204 | 0.172513 | ||||||||
\(352\) | 1.34979 | + | 0.438573i | 0.0719440 | + | 0.0233760i | ||||
\(353\) | 1.09532 | − | 1.50757i | 0.0582978 | − | 0.0802400i | −0.778873 | − | 0.627182i | \(-0.784208\pi\) |
0.837170 | + | 0.546942i | \(0.184208\pi\) | |||||||
\(354\) | −3.41653 | − | 2.48225i | −0.181586 | − | 0.131930i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −27.3055 | + | 19.8386i | −1.44719 | + | 1.05145i | ||||
\(357\) | − | 17.3850i | − | 0.920113i | ||||||
\(358\) | 20.7347 | + | 28.5389i | 1.09586 | + | 1.50833i | ||||
\(359\) | −1.18599 | − | 3.65011i | −0.0625943 | − | 0.192645i | 0.914869 | − | 0.403751i | \(-0.132294\pi\) |
−0.977463 | + | 0.211105i | \(0.932294\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.93759 | + | 9.04097i | −0.154610 | + | 0.475841i | ||||
\(362\) | −39.8949 | + | 12.9626i | −2.09683 | + | 0.681301i | ||||
\(363\) | 0.313438 | − | 0.101842i | 0.0164512 | − | 0.00534532i | ||||
\(364\) | −13.5893 | + | 41.8236i | −0.712274 | + | 2.19215i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.90913 | − | 18.1864i | −0.308875 | − | 0.950620i | ||||
\(367\) | −15.0638 | − | 20.7335i | −0.786324 | − | 1.08228i | −0.994556 | − | 0.104203i | \(-0.966771\pi\) |
0.208232 | − | 0.978079i | \(-0.433229\pi\) | |||||||
\(368\) | − | 5.77570i | − | 0.301079i | ||||||
\(369\) | 4.38457 | − | 3.18557i | 0.228251 | − | 0.165834i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.2543 | − | 20.5279i | −1.46689 | − | 1.06576i | ||||
\(372\) | −17.3005 | + | 23.8122i | −0.896991 | + | 1.23460i | ||||
\(373\) | −20.3877 | − | 6.62437i | −1.05564 | − | 0.342997i | −0.270758 | − | 0.962648i | \(-0.587274\pi\) |
−0.784878 | + | 0.619651i | \(0.787274\pi\) | |||||||
\(374\) | −40.2821 | −2.08294 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 33.7366 | 1.73983 | ||||||||
\(377\) | 9.59712 | + | 3.11829i | 0.494277 | + | 0.160600i | ||||
\(378\) | −4.93461 | + | 6.79191i | −0.253809 | + | 0.349338i | ||||
\(379\) | −20.9304 | − | 15.2068i | −1.07512 | − | 0.781120i | −0.0982945 | − | 0.995157i | \(-0.531339\pi\) |
−0.976826 | + | 0.214037i | \(0.931339\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.802617 | + | 0.583135i | −0.0411193 | + | 0.0298749i | ||||
\(382\) | 25.7264i | 1.31628i | ||||||||
\(383\) | −8.54263 | − | 11.7579i | −0.436508 | − | 0.600802i | 0.532924 | − | 0.846163i | \(-0.321093\pi\) |
−0.969432 | + | 0.245362i | \(0.921093\pi\) | |||||||
\(384\) | −6.15940 | − | 18.9567i | −0.314321 | − | 0.967379i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.514974 | + | 1.58493i | −0.0262115 | + | 0.0806706i | ||||
\(387\) | −2.40718 | + | 0.782139i | −0.122364 | + | 0.0397584i | ||||
\(388\) | −40.0696 | + | 13.0194i | −2.03423 | + | 0.660960i | ||||
\(389\) | −7.13973 | + | 21.9738i | −0.361999 | + | 1.11412i | 0.589840 | + | 0.807520i | \(0.299191\pi\) |
−0.951839 | + | 0.306598i | \(0.900809\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.41677 | − | 7.43806i | −0.122221 | − | 0.376159i | ||||
\(392\) | −13.5596 | − | 18.6632i | −0.684864 | − | 0.942635i | ||||
\(393\) | − | 12.6115i | − | 0.636167i | ||||||
\(394\) | −45.9940 | + | 33.4166i | −2.31715 | + | 1.68350i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.4519 | + | 7.59371i | 0.525225 | + | 0.381598i | ||||
\(397\) | 8.19052 | − | 11.2733i | 0.411070 | − | 0.565790i | −0.552409 | − | 0.833573i | \(-0.686291\pi\) |
0.963479 | + | 0.267784i | \(0.0862912\pi\) | |||||||
\(398\) | −23.6602 | − | 7.68766i | −1.18598 | − | 0.385348i | ||||
\(399\) | 10.6002 | 0.530673 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.5822 | −1.37739 | −0.688694 | − | 0.725052i | \(-0.741816\pi\) | ||||
−0.688694 | + | 0.725052i | \(0.741816\pi\) | |||||||
\(402\) | 4.29147 | + | 1.39438i | 0.214039 | + | 0.0695456i | ||||
\(403\) | 14.1381 | − | 19.4594i | 0.704270 | − | 0.969344i | ||||
\(404\) | 5.63693 | + | 4.09547i | 0.280448 | + | 0.203757i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.2056 | + | 15.4068i | −1.05242 | + | 0.764625i | ||||
\(407\) | 18.8101i | 0.932383i | ||||||||
\(408\) | 14.1704 | + | 19.5039i | 0.701541 | + | 0.965588i | ||||
\(409\) | −4.08288 | − | 12.5658i | −0.201886 | − | 0.621340i | −0.999827 | − | 0.0186048i | \(-0.994078\pi\) |
0.797941 | − | 0.602735i | \(-0.205922\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.54650 | + | 7.83732i | −0.125610 | + | 0.386587i | ||||
\(412\) | −59.8601 | + | 19.4497i | −2.94909 | + | 0.958218i | ||||
\(413\) | −5.66223 | + | 1.83977i | −0.278620 | + | 0.0905292i | ||||
\(414\) | −1.16706 | + | 3.59186i | −0.0573581 | + | 0.176530i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.433937 | + | 1.33552i | 0.0212755 | + | 0.0654794i | ||||
\(417\) | 4.73973 | + | 6.52367i | 0.232105 | + | 0.319466i | ||||
\(418\) | − | 24.5612i | − | 1.20133i | ||||||
\(419\) | −7.15797 | + | 5.20057i | −0.349690 | + | 0.254064i | −0.748739 | − | 0.662865i | \(-0.769340\pi\) |
0.399049 | + | 0.916930i | \(0.369340\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.3192 | + | 22.0282i | 1.47767 | + | 1.07359i | 0.978299 | + | 0.207197i | \(0.0664341\pi\) |
0.499367 | + | 0.866390i | \(0.333566\pi\) | |||||||
\(422\) | 26.1871 | − | 36.0435i | 1.27477 | − | 1.75457i | ||||
\(423\) | −6.72551 | − | 2.18525i | −0.327005 | − | 0.106250i | ||||
\(424\) | 48.4301 | 2.35197 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.74229 | 0.0844140 | ||||||||
\(427\) | −25.6390 | − | 8.33062i | −1.24076 | − | 0.403147i | ||||
\(428\) | 36.6850 | − | 50.4926i | 1.77324 | − | 2.44065i | ||||
\(429\) | −8.54132 | − | 6.20563i | −0.412379 | − | 0.299611i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.5397 | − | 15.6495i | 1.03753 | − | 0.753809i | 0.0677274 | − | 0.997704i | \(-0.478425\pi\) |
0.969802 | + | 0.243895i | \(0.0784252\pi\) | |||||||
\(432\) | − | 3.73192i | − | 0.179552i | ||||||
\(433\) | 20.5708 | + | 28.3133i | 0.988571 | + | 1.36065i | 0.932082 | + | 0.362248i | \(0.117990\pi\) |
0.0564887 | + | 0.998403i | \(0.482010\pi\) | |||||||
\(434\) | 19.3069 | + | 59.4206i | 0.926762 | + | 2.85228i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.1235 | + | 37.3124i | −0.580613 | + | 1.78694i | ||||
\(437\) | 4.53521 | − | 1.47358i | 0.216949 | − | 0.0704909i | ||||
\(438\) | 4.36383 | − | 1.41789i | 0.208512 | − | 0.0677496i | ||||
\(439\) | −6.19701 | + | 19.0724i | −0.295767 | + | 0.910277i | 0.687196 | + | 0.726472i | \(0.258841\pi\) |
−0.982963 | + | 0.183805i | \(0.941159\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.49427 | + | 4.59888i | 0.0711556 | + | 0.218994i | ||||
\(442\) | −23.4270 | − | 32.2445i | −1.11431 | − | 1.53371i | ||||
\(443\) | − | 4.14871i | − | 0.197111i | −0.995132 | − | 0.0985556i | \(-0.968578\pi\) | ||
0.995132 | − | 0.0985556i | \(-0.0314222\pi\) | |||||||
\(444\) | 18.4248 | − | 13.3864i | 0.874402 | − | 0.635291i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −34.0048 | − | 24.7060i | −1.61018 | − | 1.16986i | ||||
\(447\) | 11.2326 | − | 15.4604i | 0.531286 | − | 0.731252i | ||||
\(448\) | −27.8900 | − | 9.06201i | −1.31768 | − | 0.428140i | ||||
\(449\) | 8.34804 | 0.393969 | 0.196984 | − | 0.980407i | \(-0.436885\pi\) | ||||
0.196984 | + | 0.980407i | \(0.436885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.7035 | −0.833627 | ||||||||
\(452\) | 20.7399 | + | 6.73880i | 0.975523 | + | 0.316967i | ||||
\(453\) | 0.931936 | − | 1.28270i | 0.0437862 | − | 0.0602665i | ||||
\(454\) | −8.54602 | − | 6.20905i | −0.401085 | − | 0.291405i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.8921 | + | 8.64014i | −0.556900 | + | 0.404612i | ||||
\(457\) | 20.5774i | 0.962571i | 0.876564 | + | 0.481285i | \(0.159830\pi\) | ||||
−0.876564 | + | 0.481285i | \(0.840170\pi\) | |||||||
\(458\) | 29.1386 | + | 40.1059i | 1.36156 | + | 1.87402i | ||||
\(459\) | −1.56158 | − | 4.80604i | −0.0728882 | − | 0.224327i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.86541 | − | 27.2849i | 0.412903 | − | 1.27079i | −0.501210 | − | 0.865326i | \(-0.667111\pi\) |
0.914113 | − | 0.405460i | \(-0.132889\pi\) | |||||||
\(462\) | 26.0815 | − | 8.47438i | 1.21342 | − | 0.394264i | ||||
\(463\) | 38.1181 | − | 12.3853i | 1.77150 | − | 0.575594i | 0.773213 | − | 0.634146i | \(-0.218648\pi\) |
0.998284 | + | 0.0585520i | \(0.0186483\pi\) | |||||||
\(464\) | 3.60058 | − | 11.0815i | 0.167153 | − | 0.514444i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.257111 | − | 0.791307i | −0.0119105 | − | 0.0366566i | ||||
\(467\) | 4.78569 | + | 6.58694i | 0.221456 | + | 0.304807i | 0.905260 | − | 0.424858i | \(-0.139676\pi\) |
−0.683805 | + | 0.729665i | \(0.739676\pi\) | |||||||
\(468\) | 12.7827i | 0.590878i | ||||||||
\(469\) | 5.14650 | − | 3.73915i | 0.237643 | − | 0.172658i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.6778 | − | 12.8437i | −0.814550 | − | 0.591805i | ||||
\(472\) | 4.85276 | − | 6.67925i | 0.223366 | − | 0.307438i | ||||
\(473\) | 7.86319 | + | 2.55491i | 0.361550 | + | 0.117475i | ||||
\(474\) | −32.5369 | −1.49447 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 68.7575 | 3.15149 | ||||||||
\(477\) | −9.65469 | − | 3.13700i | −0.442058 | − | 0.143633i | ||||
\(478\) | 10.2770 | − | 14.1451i | 0.470061 | − | 0.646983i | ||||
\(479\) | −22.7027 | − | 16.4945i | −1.03731 | − | 0.753652i | −0.0675535 | − | 0.997716i | \(-0.521519\pi\) |
−0.969759 | + | 0.244064i | \(0.921519\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.0569 | + | 10.9395i | −0.686534 | + | 0.498796i | ||||
\(482\) | − | 30.6554i | − | 1.39631i | ||||||
\(483\) | 3.12957 | + | 4.30749i | 0.142401 | + | 0.195998i | ||||
\(484\) | 0.402784 | + | 1.23964i | 0.0183084 | + | 0.0563473i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.754089 | + | 2.32085i | −0.0342062 | + | 0.105276i | ||||
\(487\) | 14.4725 | − | 4.70239i | 0.655810 | − | 0.213086i | 0.0378360 | − | 0.999284i | \(-0.487954\pi\) |
0.617974 | + | 0.786198i | \(0.287954\pi\) | |||||||
\(488\) | 35.5541 | − | 11.5522i | 1.60946 | − | 0.522945i | ||||
\(489\) | 3.13153 | − | 9.63786i | 0.141613 | − | 0.435839i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.56246 | + | 7.88645i | 0.115642 | + | 0.355910i | 0.992080 | − | 0.125604i | \(-0.0400869\pi\) |
−0.876438 | + | 0.481514i | \(0.840087\pi\) | |||||||
\(492\) | 12.5989 | + | 17.3409i | 0.568002 | + | 0.781788i | ||||
\(493\) | − | 15.7775i | − | 0.710585i | ||||||
\(494\) | 19.6604 | − | 14.2842i | 0.884565 | − | 0.642674i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.4691 | − | 16.3248i | −1.00889 | − | 0.733005i | ||||
\(497\) | 1.44375 | − | 1.98715i | 0.0647611 | − | 0.0891360i | ||||
\(498\) | 9.18469 | + | 2.98429i | 0.411576 | + | 0.133729i | ||||
\(499\) | 24.4006 | 1.09232 | 0.546160 | − | 0.837681i | \(-0.316089\pi\) | ||||
0.546160 | + | 0.837681i | \(0.316089\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.51109 | 0.0675104 | ||||||||
\(502\) | 39.4916 | + | 12.8316i | 1.76260 | + | 0.572703i | ||||
\(503\) | −6.15596 | + | 8.47295i | −0.274481 | + | 0.377790i | −0.923896 | − | 0.382644i | \(-0.875014\pi\) |
0.649415 | + | 0.760434i | \(0.275014\pi\) | |||||||
\(504\) | −13.2781 | − | 9.64708i | −0.591452 | − | 0.429715i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.98070 | − | 7.25141i | 0.443696 | − | 0.322364i | ||||
\(507\) | 2.55393i | 0.113424i | ||||||||
\(508\) | −2.30629 | − | 3.17433i | −0.102325 | − | 0.140838i | ||||
\(509\) | 3.41769 | + | 10.5186i | 0.151486 | + | 0.466227i | 0.997788 | − | 0.0664770i | \(-0.0211759\pi\) |
−0.846302 | + | 0.532704i | \(0.821176\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.99893 | − | 6.15207i | 0.0884274 | − | 0.272152i | ||||
\(512\) | 35.4071 | − | 11.5045i | 1.56479 | − | 0.508431i | ||||
\(513\) | 2.93039 | − | 0.952141i | 0.129380 | − | 0.0420381i | ||||
\(514\) | −3.11590 | + | 9.58974i | −0.137436 | + | 0.422985i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.09335 | − | 9.52034i | −0.136177 | − | 0.419110i | ||||
\(517\) | 13.5778 | + | 18.6882i | 0.597150 | + | 0.821906i | ||||
\(518\) | − | 48.3432i | − | 2.12408i | ||||||
\(519\) | 11.2092 | − | 8.14395i | 0.492029 | − | 0.357480i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.5105 | + | 24.3468i | 1.46812 | + | 1.06665i | 0.981153 | + | 0.193231i | \(0.0618968\pi\) |
0.486967 | + | 0.873420i | \(0.338103\pi\) | |||||||
\(522\) | −4.47834 | + | 6.16391i | −0.196012 | + | 0.269787i | ||||
\(523\) | −12.9748 | − | 4.21576i | −0.567347 | − | 0.184342i | 0.0112775 | − | 0.999936i | \(-0.496410\pi\) |
−0.578624 | + | 0.815594i | \(0.696410\pi\) | |||||||
\(524\) | 49.8783 | 2.17894 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.53235 | −0.110416 | ||||||||
\(527\) | −35.7671 | − | 11.6214i | −1.55804 | − | 0.506238i | ||||
\(528\) | −7.16543 | + | 9.86236i | −0.311835 | + | 0.429204i | ||||
\(529\) | −16.6696 | − | 12.1112i | −0.724766 | − | 0.526573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.40005 | + | 1.01720i | −0.0607572 | + | 0.0441427i | ||||
\(532\) | 41.9235i | 1.81762i | ||||||||
\(533\) | −10.2959 | − | 14.1711i | −0.445965 | − | 0.613818i | ||||
\(534\) | 6.43533 | + | 19.8059i | 0.278484 | + | 0.857086i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.72600 | + | 8.38976i | −0.117745 | + | 0.362382i | ||||
\(537\) | 13.7482 | − | 4.46706i | 0.593278 | − | 0.192768i | ||||
\(538\) | −36.6454 | + | 11.9068i | −1.57990 | + | 0.513339i | ||||
\(539\) | 4.88112 | − | 15.0225i | 0.210245 | − | 0.647066i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.53011 | + | 13.9423i | 0.194765 | + | 0.599424i | 0.999979 | + | 0.00644072i | \(0.00205016\pi\) |
−0.805214 | + | 0.592984i | \(0.797950\pi\) | |||||||
\(542\) | 19.6513 | + | 27.0476i | 0.844094 | + | 1.16180i | ||||
\(543\) | 17.1898i | 0.737685i | ||||||||
\(544\) | 1.77626 | − | 1.29053i | 0.0761566 | − | 0.0553310i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 21.9517 | + | 15.9489i | 0.939447 | + | 0.682548i | ||||
\(547\) | 15.6423 | − | 21.5298i | 0.668818 | − | 0.920549i | −0.330915 | − | 0.943661i | \(-0.607357\pi\) |
0.999733 | + | 0.0231115i | \(0.00735726\pi\) | |||||||
\(548\) | −30.9965 | − | 10.0714i | −1.32410 | − | 0.430227i | ||||
\(549\) | −7.83611 | −0.334437 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.62005 | 0.409828 | ||||||||
\(552\) | −7.02201 | − | 2.28159i | −0.298877 | − | 0.0971109i | ||||
\(553\) | −26.9618 | + | 37.1097i | −1.14653 | + | 1.57806i | ||||
\(554\) | 13.7799 | + | 10.0117i | 0.585453 | + | 0.425356i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.8010 | + | 18.7455i | −1.09421 | + | 0.794988i | ||||
\(557\) | − | 10.3141i | − | 0.437020i | −0.975835 | − | 0.218510i | \(-0.929880\pi\) | ||
0.975835 | − | 0.218510i | \(-0.0701197\pi\) | |||||||
\(558\) | 10.6747 | + | 14.6925i | 0.451896 | + | 0.621981i | ||||
\(559\) | 2.52790 | + | 7.78008i | 0.106919 | + | 0.329063i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.10099 | + | 15.6992i | −0.215364 | + | 0.662822i | ||||
\(562\) | −18.4698 | + | 6.00121i | −0.779103 | + | 0.253146i | ||||
\(563\) | −32.7193 | + | 10.6311i | −1.37895 | + | 0.448049i | −0.902325 | − | 0.431056i | \(-0.858141\pi\) |
−0.476628 | + | 0.879105i | \(0.658141\pi\) | |||||||
\(564\) | 8.64262 | − | 26.5993i | 0.363920 | − | 1.12003i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.9600 | − | 64.5083i | −0.881016 | − | 2.71149i | ||||
\(567\) | 2.02215 | + | 2.78325i | 0.0849222 | + | 0.116885i | ||||
\(568\) | 3.40614i | 0.142918i | ||||||||
\(569\) | −9.87387 | + | 7.17378i | −0.413934 | + | 0.300741i | −0.775193 | − | 0.631725i | \(-0.782347\pi\) |
0.361259 | + | 0.932466i | \(0.382347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.0308 | − | 24.7248i | −1.42415 | − | 1.03470i | −0.991070 | − | 0.133345i | \(-0.957428\pi\) |
−0.433076 | − | 0.901357i | \(-0.642572\pi\) | |||||||
\(572\) | 24.5432 | − | 33.7808i | 1.02620 | − | 1.41245i | ||||
\(573\) | 10.0264 | + | 3.25778i | 0.418859 | + | 0.136096i | ||||
\(574\) | 45.4992 | 1.89910 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.52409 | −0.355170 | ||||||||
\(577\) | 16.6768 | + | 5.41863i | 0.694266 | + | 0.225581i | 0.634830 | − | 0.772652i | \(-0.281070\pi\) |
0.0594353 | + | 0.998232i | \(0.481070\pi\) | |||||||
\(578\) | −12.2445 | + | 16.8532i | −0.509305 | + | 0.700999i | ||||
\(579\) | 0.552485 | + | 0.401404i | 0.0229605 | + | 0.0166818i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.0146 | − | 8.00260i | 0.456964 | − | 0.332004i | ||||
\(582\) | 25.9959i | 1.07756i | ||||||||
\(583\) | 19.4913 | + | 26.8275i | 0.807249 | + | 1.11108i | ||||
\(584\) | 2.77196 | + | 8.53120i | 0.114704 | + | 0.353024i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.7155 | + | 32.9788i | −0.442651 | + | 1.36234i | ||||
\(587\) | 20.8395 | − | 6.77115i | 0.860137 | − | 0.279475i | 0.154451 | − | 0.988000i | \(-0.450639\pi\) |
0.705686 | + | 0.708525i | \(0.250639\pi\) | |||||||
\(588\) | −18.1885 | + | 5.90980i | −0.750081 | + | 0.243716i | ||||
\(589\) | 7.08595 | − | 21.8083i | 0.291971 | − | 0.898595i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.19923 | + | 22.1569i | 0.296137 | + | 0.911415i | ||||
\(592\) | 12.6314 | + | 17.3856i | 0.519148 | + | 0.714545i | ||||
\(593\) | 38.0061i | 1.56072i | 0.625330 | + | 0.780361i | \(0.284965\pi\) | ||||
−0.625330 | + | 0.780361i | \(0.715035\pi\) | |||||||
\(594\) | 6.44895 | − | 4.68544i | 0.264604 | − | 0.192246i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 61.1456 | + | 44.4249i | 2.50462 | + | 1.81971i | ||||
\(597\) | −5.99226 | + | 8.24764i | −0.245247 | + | 0.337553i | ||||
\(598\) | 11.6090 | + | 3.77200i | 0.474728 | + | 0.154248i | ||||
\(599\) | −16.3154 | −0.666629 | −0.333314 | − | 0.942816i | \(-0.608167\pi\) | ||||
−0.333314 | + | 0.942816i | \(0.608167\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.31871 | 0.0945822 | 0.0472911 | − | 0.998881i | \(-0.484941\pi\) | ||||
0.0472911 | + | 0.998881i | \(0.484941\pi\) | |||||||
\(602\) | −20.2089 | − | 6.56626i | −0.823653 | − | 0.267621i | ||||
\(603\) | 1.08687 | − | 1.49595i | 0.0442609 | − | 0.0609199i | ||||
\(604\) | 5.07305 | + | 3.68579i | 0.206420 | + | 0.149973i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.47807 | − | 2.52697i | 0.141287 | − | 0.102651i | ||||
\(607\) | 32.2134i | 1.30750i | 0.756709 | + | 0.653752i | \(0.226806\pi\) | ||||
−0.756709 | + | 0.653752i | \(0.773194\pi\) | |||||||
\(608\) | 0.786876 | + | 1.08304i | 0.0319120 | + | 0.0439231i | ||||
\(609\) | 3.31921 | + | 10.2155i | 0.134501 | + | 0.413952i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.06281 | + | 21.7371i | −0.285731 | + | 0.879389i | ||||
\(612\) | 19.0078 | − | 6.17601i | 0.768345 | − | 0.249651i | ||||
\(613\) | 24.6782 | − | 8.01843i | 0.996742 | − | 0.323861i | 0.235179 | − | 0.971952i | \(-0.424432\pi\) |
0.761563 | + | 0.648091i | \(0.224432\pi\) | |||||||
\(614\) | 17.5636 | − | 54.0552i | 0.708809 | − | 2.18149i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.5673 | + | 50.9888i | 0.667514 | + | 2.05440i | ||||
\(617\) | −1.11899 | − | 1.54016i | −0.0450488 | − | 0.0620043i | 0.785898 | − | 0.618356i | \(-0.212201\pi\) |
−0.830947 | + | 0.556351i | \(0.812201\pi\) | |||||||
\(618\) | 38.8353i | 1.56218i | ||||||||
\(619\) | −16.0829 | + | 11.6849i | −0.646425 | + | 0.469655i | −0.862052 | − | 0.506821i | \(-0.830821\pi\) |
0.215627 | + | 0.976476i | \(0.430821\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.25207 | + | 0.909685i | 0.0502440 | + | 0.0365044i | ||||
\(622\) | −10.8283 | + | 14.9039i | −0.434177 | + | 0.597594i | ||||
\(623\) | 27.9222 | + | 9.07246i | 1.11868 | + | 0.363480i | ||||
\(624\) | −12.0617 | −0.482855 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −77.2509 | −3.08757 | ||||||||
\(627\) | −9.57230 | − | 3.11023i | −0.382281 | − | 0.124211i | ||||
\(628\) | 50.7965 | − | 69.9154i | 2.02700 | − | 2.78993i | ||||
\(629\) | 23.5418 | + | 17.1041i | 0.938673 | + | 0.681986i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.6152 | − | 19.3371i | 1.05953 | − | 0.769796i | 0.0855315 | − | 0.996335i | \(-0.472741\pi\) |
0.974002 | + | 0.226539i | \(0.0727412\pi\) | |||||||
\(632\) | − | 63.6090i | − | 2.53023i | ||||||
\(633\) | −10.7312 | − | 14.7702i | −0.426526 | − | 0.587063i | ||||
\(634\) | −19.4828 | − | 59.9618i | −0.773760 | − | 2.38139i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12.4068 | − | 38.1841i | 0.491961 | − | 1.51410i | ||||
\(637\) | 14.8638 | − | 4.82953i | 0.588923 | − | 0.191353i | ||||
\(638\) | 23.6699 | − | 7.69080i | 0.937099 | − | 0.304482i | ||||
\(639\) | 0.220629 | − | 0.679025i | 0.00872793 | − | 0.0268618i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5963 | − | 38.7673i | −0.497523 | − | 1.53122i | −0.812988 | − | 0.582280i | \(-0.802161\pi\) |
0.315465 | − | 0.948937i | \(-0.397839\pi\) | |||||||
\(642\) | −22.6352 | − | 31.1547i | −0.893341 | − | 1.22958i | ||||
\(643\) | − | 24.9947i | − | 0.985695i | −0.870116 | − | 0.492847i | \(-0.835956\pi\) | ||
0.870116 | − | 0.492847i | \(-0.164044\pi\) | |||||||
\(644\) | −17.0360 | + | 12.3774i | −0.671314 | + | 0.487738i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30.7396 | − | 22.3336i | −1.20943 | − | 0.878705i | ||||
\(647\) | −18.8228 | + | 25.9073i | −0.739999 | + | 1.01852i | 0.258620 | + | 0.965979i | \(0.416732\pi\) |
−0.998619 | + | 0.0525420i | \(0.983268\pi\) | |||||||
\(648\) | −4.53722 | − | 1.47423i | −0.178239 | − | 0.0579132i | ||||
\(649\) | 5.65299 | 0.221899 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.6030 | 1.00346 | ||||||||
\(652\) | 38.1176 | + | 12.3852i | 1.49280 | + | 0.485040i | ||||
\(653\) | 26.2606 | − | 36.1446i | 1.02766 | − | 1.41445i | 0.120964 | − | 0.992657i | \(-0.461401\pi\) |
0.906693 | − | 0.421791i | \(-0.138599\pi\) | |||||||
\(654\) | 19.5840 | + | 14.2286i | 0.765794 | + | 0.556382i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −16.3629 | + | 11.8883i | −0.638862 | + | 0.464161i | ||||
\(657\) | − | 1.88027i | − | 0.0733564i | ||||||
\(658\) | −34.8957 | − | 48.0298i | −1.36038 | − | 1.87240i | ||||
\(659\) | 7.42307 | + | 22.8458i | 0.289162 | + | 0.889948i | 0.985120 | + | 0.171866i | \(0.0549796\pi\) |
−0.695959 | + | 0.718082i | \(0.745020\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.7095 | − | 36.0382i | 0.455447 | − | 1.40172i | −0.415163 | − | 0.909747i | \(-0.636275\pi\) |
0.870610 | − | 0.491974i | \(-0.163725\pi\) | |||||||
\(662\) | −46.6682 | + | 15.1634i | −1.81381 | + | 0.589343i | ||||
\(663\) | −15.5333 | + | 5.04708i | −0.603264 | + | 0.196012i | ||||
\(664\) | −5.83423 | + | 17.9559i | −0.226412 | + | 0.696824i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.34233 | − | 13.3643i | −0.168262 | − | 0.517857i | ||||
\(667\) | 2.84020 | + | 3.90920i | 0.109973 | + | 0.151365i | ||||
\(668\) | 5.97633i | 0.231231i | ||||||||
\(669\) | −13.9348 | + | 10.1242i | −0.538750 | + | 0.391425i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.7085 | + | 15.0456i | 0.799444 | + | 0.580830i | ||||
\(672\) | −0.878580 | + | 1.20926i | −0.0338920 | + | 0.0466483i | ||||
\(673\) | 17.5249 | + | 5.69418i | 0.675534 | + | 0.219494i | 0.626639 | − | 0.779310i | \(-0.284430\pi\) |
0.0488951 | + | 0.998804i | \(0.484430\pi\) | |||||||
\(674\) | −8.25737 | −0.318062 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.1008 | −0.388491 | ||||||||
\(677\) | −21.6996 | − | 7.05064i | −0.833985 | − | 0.270978i | −0.139262 | − | 0.990256i | \(-0.544473\pi\) |
−0.694723 | + | 0.719277i | \(0.744473\pi\) | |||||||
\(678\) | 7.90887 | − | 10.8856i | 0.303738 | − | 0.418060i | ||||
\(679\) | 29.6494 | + | 21.5416i | 1.13784 | + | 0.826690i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.50206 | + | 2.54440i | −0.134199 | + | 0.0975015i | ||||
\(682\) | − | 59.3236i | − | 2.27162i | ||||||
\(683\) | 18.9304 | + | 26.0555i | 0.724353 | + | 0.996987i | 0.999368 | + | 0.0355465i | \(0.0113172\pi\) |
−0.275015 | + | 0.961440i | \(0.588683\pi\) | |||||||
\(684\) | 3.76570 | + | 11.5896i | 0.143985 | + | 0.443141i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.61519 | − | 17.2818i | 0.214389 | − | 0.659822i | ||||
\(687\) | 19.3204 | − | 6.27758i | 0.737120 | − | 0.239505i | ||||
\(688\) | 8.98339 | − | 2.91888i | 0.342489 | − | 0.111281i | ||||
\(689\) | −10.1389 | + | 31.2043i | −0.386261 | + | 1.18879i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.59466 | + | 23.3740i | 0.288915 | + | 0.889188i | 0.985198 | + | 0.171421i | \(0.0548358\pi\) |
−0.696283 | + | 0.717767i | \(0.745164\pi\) | |||||||
\(692\) | 32.2092 | + | 44.3321i | 1.22441 | + | 1.68525i | ||||
\(693\) | − | 11.2379i | − | 0.426893i | ||||||
\(694\) | −57.6404 | + | 41.8782i | −2.18800 | + | 1.58967i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.0503 | − | 8.75508i | −0.456767 | − | 0.331860i | ||||
\(697\) | −16.0979 | + | 22.1568i | −0.609751 | + | 0.839251i | ||||
\(698\) | 47.3404 | + | 15.3818i | 1.79186 | + | 0.582211i | ||||
\(699\) | −0.340956 | −0.0128961 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.66355 | −0.138370 | −0.0691852 | − | 0.997604i | \(-0.522040\pi\) | ||||
−0.0691852 | + | 0.997604i | \(0.522040\pi\) | |||||||
\(702\) | 7.50107 | + | 2.43724i | 0.283109 | + | 0.0919879i | ||||
\(703\) | −10.4289 | + | 14.3541i | −0.393333 | + | 0.541377i | ||||
\(704\) | 22.5267 | + | 16.3666i | 0.849005 | + | 0.616838i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.67890 | − | 2.67288i | 0.138457 | − | 0.100595i | ||||
\(707\) | − | 6.06087i | − | 0.227942i | ||||||
\(708\) | −4.02300 | − | 5.53719i | −0.151194 | − | 0.208100i | ||||
\(709\) | 8.24980 | + | 25.3903i | 0.309828 | + | 0.953552i | 0.977831 | + | 0.209394i | \(0.0671491\pi\) |
−0.668003 | + | 0.744158i | \(0.732851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.12020 | + | 12.6807i | −0.154519 | + | 0.475562i | ||||
\(712\) | −38.7202 | + | 12.5810i | −1.45110 | + | 0.471492i | ||||
\(713\) | 10.9541 | − | 3.55919i | 0.410233 | − | 0.133293i | ||||
\(714\) | 13.1099 | − | 40.3480i | 0.490624 | − | 1.50999i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 17.6671 | + | 54.3739i | 0.660252 | + | 2.03205i | ||||
\(717\) | −4.21141 | − | 5.79651i | −0.157278 | − | 0.216475i | ||||
\(718\) | − | 9.36569i | − | 0.349524i | ||||||
\(719\) | 14.4570 | − | 10.5036i | 0.539156 | − | 0.391720i | −0.284616 | − | 0.958642i | \(-0.591866\pi\) |
0.823771 | + | 0.566922i | \(0.191866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.2933 | + | 32.1810i | 1.64957 | + | 1.19848i | ||||
\(722\) | −13.6354 | + | 18.7675i | −0.507457 | + | 0.698455i | ||||
\(723\) | −11.9474 | − | 3.88194i | −0.444328 | − | 0.144371i | ||||
\(724\) | −67.9853 | −2.52665 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.804239 | 0.0298481 | ||||||||
\(727\) | −32.4050 | − | 10.5290i | −1.20184 | − | 0.390500i | −0.361400 | − | 0.932411i | \(-0.617701\pi\) |
−0.840436 | + | 0.541910i | \(0.817701\pi\) | |||||||
\(728\) | −31.1797 | + | 42.9152i | −1.15560 | + | 1.59054i | ||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.3476 | − | 7.51799i | 0.382721 | − | 0.278063i | ||||
\(732\) | − | 30.9917i | − | 1.14549i | ||||||
\(733\) | −23.6176 | − | 32.5068i | −0.872335 | − | 1.20067i | −0.978485 | − | 0.206316i | \(-0.933853\pi\) |
0.106150 | − | 0.994350i | \(-0.466147\pi\) | |||||||
\(734\) | −19.3258 | − | 59.4788i | −0.713330 | − | 2.19540i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.207789 | + | 0.639509i | −0.00765921 | + | 0.0235726i | ||||
\(737\) | −5.74457 | + | 1.86652i | −0.211604 | + | 0.0687542i | ||||
\(738\) | 12.5781 | − | 4.08688i | 0.463007 | − | 0.150440i | ||||
\(739\) | −4.78203 | + | 14.7176i | −0.175910 | + | 0.541395i | −0.999674 | − | 0.0255381i | \(-0.991870\pi\) |
0.823764 | + | 0.566933i | \(0.191870\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.07736 | − | 9.47113i | −0.113050 | − | 0.347931i | ||||
\(742\) | −50.0939 | − | 68.9484i | −1.83901 | − | 2.53118i | ||||
\(743\) | 17.1140i | 0.627853i | 0.949447 | + | 0.313926i | \(0.101645\pi\) | ||||
−0.949447 | + | 0.313926i | \(0.898355\pi\) | |||||||
\(744\) | −28.7235 | + | 20.8688i | −1.05305 | + | 0.765089i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −42.3214 | − | 30.7483i | −1.54950 | − | 1.12577i | ||||
\(747\) | 2.32614 | − | 3.20166i | 0.0851092 | − | 0.117143i | ||||
\(748\) | −62.0902 | − | 20.1743i | −2.27024 | − | 0.737647i | ||||
\(749\) | −54.2900 | −1.98371 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.1559 | −0.407086 | −0.203543 | − | 0.979066i | \(-0.565246\pi\) | ||||
−0.203543 | + | 0.979066i | \(0.565246\pi\) | |||||||
\(752\) | 25.0991 | + | 8.15518i | 0.915268 | + | 0.297389i | ||||
\(753\) | 10.0018 | − | 13.7663i | 0.364485 | − | 0.501671i | ||||
\(754\) | 19.9220 | + | 14.4742i | 0.725516 | + | 0.527118i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11.0077 | + | 7.99756i | −0.400346 | + | 0.290868i | ||||
\(757\) | 24.6773i | 0.896911i | 0.893805 | + | 0.448456i | \(0.148026\pi\) | ||||
−0.893805 | + | 0.448456i | \(0.851974\pi\) | |||||||
\(758\) | −37.1089 | − | 51.0760i | −1.34786 | − | 1.85516i | ||||
\(759\) | −1.56223 | − | 4.80806i | −0.0567054 | − | 0.174521i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.4372 | + | 38.2779i | −0.450850 | + | 1.38757i | 0.425089 | + | 0.905151i | \(0.360243\pi\) |
−0.875939 | + | 0.482422i | \(0.839757\pi\) | |||||||
\(762\) | −2.30249 | + | 0.748123i | −0.0834103 | + | 0.0271016i | ||||
\(763\) | 32.4566 | − | 10.5458i | 1.17501 | − | 0.381784i | ||||
\(764\) | −12.8845 | + | 39.6543i | −0.466143 | + | 1.43464i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.9596 | − | 33.7302i | −0.395987 | − | 1.21872i | ||||
\(767\) | 3.28763 | + | 4.52503i | 0.118709 | + | 0.163389i | ||||
\(768\) | − | 31.5921i | − | 1.13998i | ||||||
\(769\) | 17.8801 | − | 12.9907i | 0.644773 | − | 0.468455i | −0.216714 | − | 0.976235i | \(-0.569534\pi\) |
0.861487 | + | 0.507780i | \(0.169534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.34286 | + | 2.42873i | 0.120390 | + | 0.0874685i | ||||
\(772\) | −1.58754 | + | 2.18507i | −0.0571370 | + | 0.0786423i | ||||
\(773\) | −4.66049 | − | 1.51429i | −0.167626 | − | 0.0544651i | 0.224002 | − | 0.974589i | \(-0.428088\pi\) |
−0.391628 | + | 0.920124i | \(0.628088\pi\) | |||||||
\(774\) | −6.17649 | −0.222009 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −50.8215 | −1.82439 | ||||||||
\(777\) | −18.8409 | − | 6.12177i | −0.675913 | − | 0.219617i | ||||
\(778\) | −33.1405 | + | 45.6139i | −1.18814 | + | 1.63534i | ||||
\(779\) | −13.5097 | − | 9.81537i | −0.484035 | − | 0.351672i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.88681 | + | 1.37085i | −0.0675153 | + | 0.0490528i | ||||
\(782\) | − | 19.0851i | − | 0.682481i | ||||||
\(783\) | 1.83517 | + | 2.52590i | 0.0655837 | + | 0.0902682i | ||||
\(784\) | −5.57648 | − | 17.1627i | −0.199160 | − | 0.612952i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.51020 | − | 29.2694i | 0.339218 | − | 1.04400i | ||||
\(787\) | 3.55198 | − | 1.15411i | 0.126614 | − | 0.0411395i | −0.245024 | − | 0.969517i | \(-0.578796\pi\) |
0.371639 | + | 0.928377i | \(0.378796\pi\) | |||||||
\(788\) | −87.6303 | + | 28.4728i | −3.12170 | + | 1.01430i | ||||
\(789\) | −0.320676 | + | 0.986940i | −0.0114164 | + | 0.0351360i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.86182 | − | 18.0408i | −0.208422 | − | 0.641458i | ||||
\(792\) | 9.15994 | + | 12.6076i | 0.325484 | + | 0.447991i | ||||
\(793\) | 25.3266i | 0.899375i | ||||||||
\(794\) | 27.5100 | − | 19.9872i | 0.976294 | − | 0.709319i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −32.6193 | − | 23.6993i | −1.15616 | − | 0.839998i | ||||
\(797\) | 1.96557 | − | 2.70538i | 0.0696242 | − | 0.0958295i | −0.772785 | − | 0.634668i | \(-0.781137\pi\) |
0.842409 | + | 0.538839i | \(0.181137\pi\) | |||||||
\(798\) | 24.6014 | + | 7.99348i | 0.870880 | + | 0.282966i | ||||
\(799\) | 35.7355 | 1.26423 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.53392 | 0.301531 | ||||||||
\(802\) | −64.0140 | − | 20.7994i | −2.26041 | − | 0.734453i | ||||
\(803\) | −3.61019 | + | 4.96901i | −0.127401 | + | 0.175352i | ||||
\(804\) | 5.91646 | + | 4.29856i | 0.208658 | + | 0.151599i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 47.4866 | − | 34.5010i | 1.67264 | − | 1.21525i | ||||
\(807\) | 15.7897i | 0.555823i | ||||||||
\(808\) | 4.94017 | + | 6.79957i | 0.173795 | + | 0.239208i | ||||
\(809\) | −10.5954 | − | 32.6094i | −0.372516 | − | 1.14649i | −0.945140 | − | 0.326667i | \(-0.894074\pi\) |
0.572624 | − | 0.819818i | \(-0.305926\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.07152 | + | 3.29778i | −0.0376260 | + | 0.115801i | −0.968105 | − | 0.250543i | \(-0.919391\pi\) |
0.930479 | + | 0.366344i | \(0.119391\pi\) | |||||||
\(812\) | −40.4020 | + | 13.1274i | −1.41783 | + | 0.460682i | ||||
\(813\) | 13.0298 | − | 4.23364i | 0.456975 | − | 0.148480i | ||||
\(814\) | −14.1845 | + | 43.6554i | −0.497167 | + | 1.53012i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.82768 | + | 17.9358i | 0.204010 | + | 0.627877i | ||||
\(817\) | 4.58394 | + | 6.30926i | 0.160372 | + | 0.220733i | ||||
\(818\) | − | 32.2422i | − | 1.12732i | ||||||
\(819\) | 8.99556 | − | 6.53566i | 0.314330 | − | 0.228374i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.8771 | + | 8.62922i | 0.414514 | + | 0.301162i | 0.775427 | − | 0.631438i | \(-0.217535\pi\) |
−0.360913 | + | 0.932600i | \(0.617535\pi\) | |||||||
\(822\) | −11.8201 | + | 16.2689i | −0.412273 | + | 0.567445i | ||||
\(823\) | 19.8483 | + | 6.44912i | 0.691870 | + | 0.224802i | 0.633785 | − | 0.773510i | \(-0.281501\pi\) |
0.0580851 | + | 0.998312i | \(0.481501\pi\) | |||||||
\(824\) | −75.9223 | −2.64488 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.5285 | −0.505512 | ||||||||
\(827\) | 43.0710 | + | 13.9946i | 1.49773 | + | 0.486641i | 0.939354 | − | 0.342950i | \(-0.111426\pi\) |
0.558372 | + | 0.829590i | \(0.311426\pi\) | |||||||
\(828\) | −3.59779 | + | 4.95193i | −0.125032 | + | 0.172091i | ||||
\(829\) | −7.81291 | − | 5.67641i | −0.271354 | − | 0.197150i | 0.443784 | − | 0.896134i | \(-0.353636\pi\) |
−0.715137 | + | 0.698984i | \(0.753636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.64685 | − | 4.10268i | 0.195887 | − | 0.142320i | ||||
\(832\) | 27.5502i | 0.955131i | ||||||||
\(833\) | −14.3630 | − | 19.7690i | −0.497649 | − | 0.684955i | ||||
\(834\) | 6.08075 | + | 18.7146i | 0.210559 | + | 0.648035i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.3009 | − | 37.8583i | 0.425436 | − | 1.30936i | ||||
\(837\) | 7.07787 | − | 2.29974i | 0.244647 | − | 0.0794907i | ||||
\(838\) | −20.5342 | + | 6.67198i | −0.709344 | + | 0.230480i | ||||
\(839\) | 7.77848 | − | 23.9397i | 0.268543 | − | 0.826490i | −0.722313 | − | 0.691566i | \(-0.756921\pi\) |
0.990856 | − | 0.134924i | \(-0.0430789\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.94919 | − | 18.3097i | −0.205144 | − | 0.631370i | ||||
\(842\) | 53.7550 | + | 73.9874i | 1.85252 | + | 2.54977i | ||||
\(843\) | 7.95823i | 0.274096i | ||||||||
\(844\) | 58.4159 | − | 42.4416i | 2.01076 | − | 1.46090i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13.9610 | − | 10.1433i | −0.479989 | − | 0.348733i | ||||
\(847\) | 0.666435 | − | 0.917269i | 0.0228990 | − | 0.0315177i | ||||
\(848\) | 36.0305 | + | 11.7070i | 1.23729 | + | 0.402021i | ||||
\(849\) | −27.7952 | −0.953928 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.91196 | −0.305498 | ||||||||
\(852\) | 2.68553 | + | 0.872582i | 0.0920048 | + | 0.0298942i | ||||
\(853\) | 1.88589 | − | 2.59571i | 0.0645717 | − | 0.0888753i | −0.775510 | − | 0.631336i | \(-0.782507\pi\) |
0.840081 | + | 0.542460i | \(0.182507\pi\) | |||||||
\(854\) | −53.2222 | − | 38.6682i | −1.82123 | − | 1.32320i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 60.9069 | − | 44.2514i | 2.08175 | − | 1.51248i | ||||
\(857\) | 19.4569i | 0.664634i | 0.943168 | + | 0.332317i | \(0.107830\pi\) | ||||
−0.943168 | + | 0.332317i | \(0.892170\pi\) | |||||||
\(858\) | −15.1435 | − | 20.8432i | −0.516991 | − | 0.711577i | ||||
\(859\) | −5.20173 | − | 16.0093i | −0.177481 | − | 0.546230i | 0.822257 | − | 0.569116i | \(-0.192714\pi\) |
−0.999738 | + | 0.0228862i | \(0.992714\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.76163 | − | 17.7325i | 0.196356 | − | 0.604322i | ||||
\(862\) | 61.7914 | − | 20.0772i | 2.10462 | − | 0.683833i | ||||
\(863\) | 3.62560 | − | 1.17803i | 0.123417 | − | 0.0401006i | −0.246657 | − | 0.969103i | \(-0.579332\pi\) |
0.370074 | + | 0.929002i | \(0.379332\pi\) | |||||||
\(864\) | −0.134261 | + | 0.413214i | −0.00456766 | + | 0.0140578i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 26.3910 | + | 81.2231i | 0.896802 | + | 2.76007i | ||||
\(867\) | 5.01767 | + | 6.90623i | 0.170409 | + | 0.234548i | ||||
\(868\) | 101.259i | 3.43697i | ||||||||
\(869\) | 35.2358 | − | 25.6003i | 1.19529 | − | 0.868431i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.83497 | − | 3.51281i | −0.163827 | − | 0.119027i | ||||
\(872\) | −27.8166 | + | 38.2863i | −0.941990 | + | 1.29654i | ||||
\(873\) | 10.1314 | + | 3.29190i | 0.342897 | + | 0.111414i | ||||
\(874\) | 11.6367 | 0.393619 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.43645 | 0.251254 | ||||||||
\(877\) | −24.4851 | − | 7.95569i | −0.826803 | − | 0.268644i | −0.135105 | − | 0.990831i | \(-0.543137\pi\) |
−0.691698 | + | 0.722187i | \(0.743137\pi\) | |||||||
\(878\) | −28.7646 | + | 39.5911i | −0.970759 | + | 1.33613i | ||||
\(879\) | 11.4960 | + | 8.35231i | 0.387749 | + | 0.281717i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.6110 | + | 26.5995i | −1.23346 | + | 0.896159i | −0.997144 | − | 0.0755181i | \(-0.975939\pi\) |
−0.236313 | + | 0.971677i | \(0.575939\pi\) | |||||||
\(882\) | 11.8001i | 0.397330i | ||||||||
\(883\) | 26.0964 | + | 35.9186i | 0.878212 | + | 1.20876i | 0.976913 | + | 0.213639i | \(0.0685315\pi\) |
−0.0987003 | + | 0.995117i | \(0.531469\pi\) | |||||||
\(884\) | −19.9611 | − | 61.4340i | −0.671365 | − | 2.06625i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.12850 | − | 9.62853i | 0.105104 | − | 0.323477i | ||||
\(887\) | 37.0844 | − | 12.0495i | 1.24517 | − | 0.404581i | 0.388984 | − | 0.921245i | \(-0.372826\pi\) |
0.856189 | + | 0.516664i | \(0.172826\pi\) | |||||||
\(888\) | 26.1270 | − | 8.48919i | 0.876766 | − | 0.284878i | ||||
\(889\) | −1.05470 | + | 3.24602i | −0.0353734 | + | 0.108868i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00942 | − | 3.10669i | −0.0338170 | − | 0.104078i | ||||
\(892\) | −40.0411 | − | 55.1119i | −1.34068 | − | 1.84528i | ||||
\(893\) | 21.7890i | 0.729142i | ||||||||
\(894\) | 37.7278 | − | 27.4108i | 1.26181 | − | 0.916755i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −55.4764 | − | 40.3059i | −1.85334 | − | 1.34653i | ||||
\(897\) | 2.94014 | − | 4.04675i | 0.0981683 | − | 0.135117i | ||||
\(898\) | 19.3745 | + | 6.29517i | 0.646537 | + | 0.210072i | ||||
\(899\) | 23.2356 | 0.774952 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51.2995 | 1.70903 | ||||||||
\(902\) | −41.0872 | − | 13.3500i | −1.36805 | − | 0.444508i | ||||
\(903\) | −5.11817 | + | 7.04455i | −0.170322 | + | 0.234428i | ||||
\(904\) | 21.2812 | + | 15.4617i | 0.707803 | + | 0.514249i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.13015 | − | 2.27419i | 0.103992 | − | 0.0755548i | ||||
\(907\) | 11.0201i | 0.365915i | 0.983121 | + | 0.182958i | \(0.0585671\pi\) | ||||
−0.983121 | + | 0.182958i | \(0.941433\pi\) | |||||||
\(908\) | −10.0630 | − | 13.8506i | −0.333954 | − | 0.459648i | ||||
\(909\) | −0.544406 | − | 1.67551i | −0.0180568 | − | 0.0555731i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.3540 | + | 50.3325i | −0.541833 | + | 1.66759i | 0.186571 | + | 0.982441i | \(0.440263\pi\) |
−0.728404 | + | 0.685148i | \(0.759737\pi\) | |||||||
\(912\) | −10.9360 | + | 3.55332i | −0.362127 | + | 0.117662i | ||||
\(913\) | −12.2946 | + | 3.99477i | −0.406893 | + | 0.132207i | ||||
\(914\) | −15.5172 | + | 47.7570i | −0.513263 | + | 1.57966i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.8277 | + | 76.4119i | 0.820331 | + | 2.52472i | ||||
\(917\) | −25.5023 | − | 35.1010i | −0.842162 | − | 1.15914i | ||||
\(918\) | − | 12.3317i | − | 0.407005i | ||||||
\(919\) | −38.5129 | + | 27.9812i | −1.27042 | + | 0.923016i | −0.999219 | − | 0.0395064i | \(-0.987421\pi\) |
−0.271203 | + | 0.962522i | \(0.587421\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.8429 | − | 13.6902i | −0.620896 | − | 0.451107i | ||||
\(922\) | 41.1505 | − | 56.6388i | 1.35522 | − | 1.86530i | ||||
\(923\) | −2.19463 | − | 0.713080i | −0.0722372 | − | 0.0234713i | ||||
\(924\) | 44.4457 | 1.46216 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 97.8059 | 3.21410 | ||||||||
\(927\) | 15.1354 | + | 4.91777i | 0.497110 | + | 0.161521i | ||||
\(928\) | −0.797343 | + | 1.09745i | −0.0261741 | + | 0.0360255i | ||||
\(929\) | 17.5465 | + | 12.7483i | 0.575682 | + | 0.418258i | 0.837165 | − | 0.546951i | \(-0.184211\pi\) |
−0.261483 | + | 0.965208i | \(0.584211\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0538 | − | 8.75757i | 0.395046 | − | 0.287018i | ||||
\(932\) | − | 1.34848i | − | 0.0441708i | ||||||
\(933\) | 4.43733 | + | 6.10746i | 0.145272 | + | 0.199949i | ||||
\(934\) | 6.13972 | + | 18.8961i | 0.200898 | + | 0.618300i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.76477 | + | 14.6645i | −0.155741 | + | 0.479323i | ||||
\(937\) | −2.09317 | + | 0.680112i | −0.0683809 | + | 0.0222183i | −0.343008 | − | 0.939333i | \(-0.611446\pi\) |
0.274627 | + | 0.961551i | \(0.411446\pi\) | |||||||
\(938\) | 14.7639 | − | 4.79708i | 0.482058 | − | 0.156630i | ||||
\(939\) | −9.78241 | + | 30.1072i | −0.319237 | + | 0.982510i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.18833 | − | 15.9680i | −0.169135 | − | 0.520543i | 0.830183 | − | 0.557492i | \(-0.188236\pi\) |
−0.999317 | + | 0.0369489i | \(0.988236\pi\) | |||||||
\(942\) | −31.3422 | − | 43.1388i | −1.02118 | − | 1.40554i | ||||
\(943\) | − | 8.38767i | − | 0.273140i | ||||||
\(944\) | 5.22489 | − | 3.79611i | 0.170056 | − | 0.123553i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.3226 | + | 11.8591i | 0.530695 | + | 0.385572i | ||||
\(947\) | 21.5207 | − | 29.6207i | 0.699329 | − | 0.962544i | −0.300632 | − | 0.953740i | \(-0.597198\pi\) |
0.999961 | − | 0.00880418i | \(-0.00280249\pi\) | |||||||
\(948\) | −50.1518 | − | 16.2953i | −1.62885 | − | 0.529247i | ||||
\(949\) | −6.07711 | −0.197271 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.8362 | −0.837796 | ||||||||
\(952\) | 78.8796 | + | 25.6295i | 2.55650 | + | 0.830658i | ||||
\(953\) | −25.8201 | + | 35.5383i | −0.836394 | + | 1.15120i | 0.150305 | + | 0.988640i | \(0.451974\pi\) |
−0.986699 | + | 0.162558i | \(0.948026\pi\) | |||||||
\(954\) | −20.0415 | − | 14.5610i | −0.648867 | − | 0.471430i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22.9251 | − | 16.6561i | 0.741450 | − | 0.538695i | ||||
\(957\) | − | 10.1988i | − | 0.329680i | ||||||
\(958\) | −40.2512 | − | 55.4010i | −1.30046 | − | 1.78993i | ||||
\(959\) | 8.76068 | + | 26.9626i | 0.282897 | + | 0.870668i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.53541 | − | 23.1916i | 0.243078 | − | 0.748116i | ||||
\(962\) | −43.1940 | + | 14.0346i | −1.39263 | + | 0.452493i | ||||
\(963\) | −15.0083 | + | 4.87650i | −0.483636 | + | 0.157143i | ||||
\(964\) | 15.3530 | − | 47.2517i | 0.494487 | − | 1.52188i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.01503 | + | 12.3570i | 0.129182 | + | 0.397580i | ||||
\(967\) | −14.3899 | − | 19.8059i | −0.462747 | − | 0.636916i | 0.512329 | − | 0.858789i | \(-0.328783\pi\) |
−0.975076 | + | 0.221873i | \(0.928783\pi\) | |||||||
\(968\) | 1.57227i | 0.0505348i | ||||||||
\(969\) | −12.5967 | + | 9.15206i | −0.404665 | + | 0.294007i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.8773 | + | 11.5355i | 0.509526 | + | 0.370192i | 0.812644 | − | 0.582761i | \(-0.198028\pi\) |
−0.303118 | + | 0.952953i | \(0.598028\pi\) | |||||||
\(972\) | −2.32468 | + | 3.19965i | −0.0745642 | + | 0.102629i | ||||
\(973\) | 26.3837 | + | 8.57257i | 0.845822 | + | 0.274824i | ||||
\(974\) | 37.1344 | 1.18986 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.2438 | 0.936070 | ||||||||
\(977\) | 29.0298 | + | 9.43236i | 0.928746 | + | 0.301768i | 0.734050 | − | 0.679096i | \(-0.237628\pi\) |
0.194696 | + | 0.980864i | \(0.437628\pi\) | |||||||
\(978\) | 14.5356 | − | 20.0066i | 0.464798 | − | 0.639739i | ||||
\(979\) | −22.5526 | − | 16.3854i | −0.720785 | − | 0.523681i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.02529 | − | 5.83071i | 0.256228 | − | 0.186160i | ||||
\(982\) | 20.2356i | 0.645743i | ||||||||
\(983\) | 6.09271 | + | 8.38590i | 0.194327 | + | 0.267469i | 0.895051 | − | 0.445964i | \(-0.147139\pi\) |
−0.700723 | + | 0.713433i | \(0.747139\pi\) | |||||||
\(984\) | 7.98977 | + | 24.5900i | 0.254705 | + | 0.783901i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.8977 | − | 36.6173i | 0.378899 | − | 1.16613i | ||||
\(987\) | −23.1376 | + | 7.51788i | −0.736479 | + | 0.239297i | ||||
\(988\) | 37.4582 | − | 12.1709i | 1.19170 | − | 0.387208i | ||||
\(989\) | −1.21048 | + | 3.72546i | −0.0384909 | + | 0.118463i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.12376 | − | 9.61395i | −0.0992295 | − | 0.305397i | 0.889103 | − | 0.457707i | \(-0.151329\pi\) |
−0.988333 | + | 0.152309i | \(0.951329\pi\) | |||||||
\(992\) | 1.90057 | + | 2.61591i | 0.0603431 | + | 0.0830552i | ||||
\(993\) | 20.1083i | 0.638116i | ||||||||
\(994\) | 4.84921 | − | 3.52316i | 0.153808 | − | 0.111748i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 12.6625 | + | 9.19986i | 0.401227 | + | 0.291509i | ||||
\(997\) | 12.5574 | − | 17.2838i | 0.397697 | − | 0.547382i | −0.562467 | − | 0.826819i | \(-0.690148\pi\) |
0.960164 | + | 0.279437i | \(0.0901478\pi\) | |||||||
\(998\) | 56.6300 | + | 18.4002i | 1.79259 | + | 0.582448i | ||||
\(999\) | −5.75838 | −0.182187 |
(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 | 375.2.i.d.274.5 | 24 | ||
5.2 | odd | 4 | 375.2.g.c.226.1 | 12 | |||
5.3 | odd | 4 | 75.2.g.c.46.3 | yes | 12 | ||
5.4 | even | 2 | inner | 375.2.i.d.274.2 | 24 | ||
15.8 | even | 4 | 225.2.h.d.46.1 | 12 | |||
25.6 | even | 5 | inner | 375.2.i.d.349.2 | 24 | ||
25.8 | odd | 20 | 75.2.g.c.31.3 | ✓ | 12 | ||
25.9 | even | 10 | 1875.2.b.f.1249.2 | 12 | |||
25.12 | odd | 20 | 1875.2.a.k.1.1 | 6 | |||
25.13 | odd | 20 | 1875.2.a.j.1.6 | 6 | |||
25.16 | even | 5 | 1875.2.b.f.1249.11 | 12 | |||
25.17 | odd | 20 | 375.2.g.c.151.1 | 12 | |||
25.19 | even | 10 | inner | 375.2.i.d.349.5 | 24 | ||
75.8 | even | 20 | 225.2.h.d.181.1 | 12 | |||
75.38 | even | 20 | 5625.2.a.p.1.1 | 6 | |||
75.62 | even | 20 | 5625.2.a.q.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.31.3 | ✓ | 12 | 25.8 | odd | 20 | ||
75.2.g.c.46.3 | yes | 12 | 5.3 | odd | 4 | ||
225.2.h.d.46.1 | 12 | 15.8 | even | 4 | |||
225.2.h.d.181.1 | 12 | 75.8 | even | 20 | |||
375.2.g.c.151.1 | 12 | 25.17 | odd | 20 | |||
375.2.g.c.226.1 | 12 | 5.2 | odd | 4 | |||
375.2.i.d.274.2 | 24 | 5.4 | even | 2 | inner | ||
375.2.i.d.274.5 | 24 | 1.1 | even | 1 | trivial | ||
375.2.i.d.349.2 | 24 | 25.6 | even | 5 | inner | ||
375.2.i.d.349.5 | 24 | 25.19 | even | 10 | inner | ||
1875.2.a.j.1.6 | 6 | 25.13 | odd | 20 | |||
1875.2.a.k.1.1 | 6 | 25.12 | odd | 20 | |||
1875.2.b.f.1249.2 | 12 | 25.9 | even | 10 | |||
1875.2.b.f.1249.11 | 12 | 25.16 | even | 5 | |||
5625.2.a.p.1.1 | 6 | 75.38 | even | 20 | |||
5625.2.a.q.1.6 | 6 | 75.62 | even | 20 |