Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(46,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.h (of order \(5\), degree \(4\), 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: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 181.1 | ||
Root | \(1.97423 - 1.43436i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.181 |
Dual form | 225.2.h.d.46.1 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.754089 | − | 2.32085i | −0.533221 | − | 1.64109i | −0.747461 | − | 0.664306i | \(-0.768727\pi\) |
0.214240 | − | 0.976781i | \(-0.431273\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.19965 | + | 2.32468i | −1.59982 | + | 1.16234i | ||||
\(5\) | −0.824264 | + | 2.07860i | −0.368622 | + | 0.929579i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.44028 | −1.30030 | −0.650152 | − | 0.759804i | \(-0.725295\pi\) | ||||
−0.650152 | + | 0.759804i | \(0.725295\pi\) | |||||||
\(8\) | 3.85959 | + | 2.80415i | 1.36457 | + | 0.991418i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.44569 | + | 0.345540i | 1.72208 | + | 0.109269i | ||||
\(11\) | 1.00942 | + | 3.10669i | 0.304353 | + | 0.936701i | 0.979918 | + | 0.199401i | \(0.0638996\pi\) |
−0.675565 | + | 0.737300i | \(0.736100\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.998755 | + | 3.07385i | −0.277005 | + | 0.852533i | 0.711677 | + | 0.702506i | \(0.247936\pi\) |
−0.988682 | + | 0.150026i | \(0.952064\pi\) | |||||||
\(14\) | 2.59428 | + | 7.98437i | 0.693350 | + | 2.13391i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.15323 | − | 3.54927i | 0.288307 | − | 0.887317i | ||||
\(17\) | −4.08826 | − | 2.97030i | −0.991550 | − | 0.720403i | −0.0312897 | − | 0.999510i | \(-0.509961\pi\) |
−0.960260 | + | 0.279107i | \(0.909961\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.49274 | + | 1.81108i | 0.571873 | + | 0.415490i | 0.835785 | − | 0.549056i | \(-0.185013\pi\) |
−0.263912 | + | 0.964547i | \(0.585013\pi\) | |||||||
\(20\) | −2.19473 | − | 8.56695i | −0.490757 | − | 1.91563i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.44895 | − | 4.68544i | 1.37492 | − | 0.998938i | ||||
\(23\) | −0.478250 | − | 1.47190i | −0.0997219 | − | 0.306913i | 0.888734 | − | 0.458424i | \(-0.151586\pi\) |
−0.988455 | + | 0.151512i | \(0.951586\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.64118 | − | 3.42664i | −0.728235 | − | 0.685327i | ||||
\(26\) | 7.88709 | 1.54679 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 11.0077 | − | 7.99756i | 2.08026 | − | 1.51140i | ||||
\(29\) | −2.52590 | + | 1.83517i | −0.469047 | + | 0.340783i | −0.797070 | − | 0.603887i | \(-0.793618\pi\) |
0.328022 | + | 0.944670i | \(0.393618\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.02080 | − | 4.37437i | −1.08137 | − | 0.785659i | −0.103446 | − | 0.994635i | \(-0.532987\pi\) |
−0.977921 | + | 0.208976i | \(0.932987\pi\) | |||||||
\(32\) | 0.434479 | 0.0768057 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.81069 | + | 11.7281i | −0.653528 | + | 2.01135i | ||||
\(35\) | 2.83570 | − | 7.15098i | 0.479321 | − | 1.20874i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.77944 | + | 5.47655i | −0.292538 | + | 0.900339i | 0.691499 | + | 0.722377i | \(0.256950\pi\) |
−0.984037 | + | 0.177962i | \(0.943050\pi\) | |||||||
\(38\) | 2.32349 | − | 7.15098i | 0.376921 | − | 1.16004i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.01004 | + | 5.71118i | −1.42461 | + | 0.903017i | ||||
\(41\) | −1.67476 | + | 5.15437i | −0.261553 | + | 0.804977i | 0.730915 | + | 0.682469i | \(0.239094\pi\) |
−0.992468 | + | 0.122508i | \(0.960906\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.53106 | 0.385982 | 0.192991 | − | 0.981201i | \(-0.438181\pi\) | ||||
0.192991 | + | 0.981201i | \(0.438181\pi\) | |||||||
\(44\) | −10.4519 | − | 7.59371i | −1.57568 | − | 1.14480i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.05541 | + | 2.21989i | −0.450496 | + | 0.327305i | ||||
\(47\) | 5.72106 | − | 4.15659i | 0.834502 | − | 0.606301i | −0.0863273 | − | 0.996267i | \(-0.527513\pi\) |
0.920829 | + | 0.389966i | \(0.127513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.83555 | 0.690793 | ||||||||
\(50\) | −5.20693 | + | 11.0346i | −0.736371 | + | 1.56053i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.95006 | − | 12.1570i | −0.547774 | − | 1.68588i | ||||
\(53\) | −8.21277 | + | 5.96693i | −1.12811 | + | 0.819621i | −0.985419 | − | 0.170147i | \(-0.945576\pi\) |
−0.142692 | + | 0.989767i | \(0.545576\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.28960 | − | 0.462540i | −0.982929 | − | 0.0623689i | ||||
\(56\) | −13.2781 | − | 9.64708i | −1.77436 | − | 1.28915i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.16391 | + | 4.47834i | 0.809361 | + | 0.588035i | ||||
\(59\) | −0.534773 | + | 1.64586i | −0.0696215 | + | 0.214273i | −0.979814 | − | 0.199913i | \(-0.935934\pi\) |
0.910192 | + | 0.414187i | \(0.135934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.42149 | + | 7.45259i | 0.310040 | + | 0.954206i | 0.977748 | + | 0.209783i | \(0.0672756\pi\) |
−0.667708 | + | 0.744424i | \(0.732724\pi\) | |||||||
\(62\) | −5.61202 | + | 17.2720i | −0.712727 | + | 2.19355i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.63409 | − | 8.10689i | −0.329261 | − | 1.01336i | ||||
\(65\) | −5.56608 | − | 4.60968i | −0.690387 | − | 0.571760i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.49595 | + | 1.08687i | 0.182760 | + | 0.132783i | 0.675404 | − | 0.737448i | \(-0.263969\pi\) |
−0.492644 | + | 0.870231i | \(0.663969\pi\) | |||||||
\(68\) | 19.9860 | 2.42366 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −18.7347 | − | 1.18876i | −2.23923 | − | 0.142084i | ||||
\(71\) | −0.577613 | + | 0.419660i | −0.0685500 | + | 0.0498045i | −0.621533 | − | 0.783388i | \(-0.713490\pi\) |
0.552982 | + | 0.833193i | \(0.313490\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.581036 | − | 1.78825i | −0.0680052 | − | 0.209298i | 0.911279 | − | 0.411790i | \(-0.135096\pi\) |
−0.979284 | + | 0.202491i | \(0.935096\pi\) | |||||||
\(74\) | 14.0521 | 1.63352 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.1861 | −1.39784 | ||||||||
\(77\) | −3.47270 | − | 10.6879i | −0.395751 | − | 1.21800i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7868 | − | 7.83708i | 1.21361 | − | 0.881740i | 0.218058 | − | 0.975936i | \(-0.430028\pi\) |
0.995554 | + | 0.0941957i | \(0.0300279\pi\) | |||||||
\(80\) | 6.42695 | + | 5.32263i | 0.718555 | + | 0.595089i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.2254 | 1.46050 | ||||||||
\(83\) | 3.20166 | + | 2.32614i | 0.351428 | + | 0.255328i | 0.749468 | − | 0.662041i | \(-0.230309\pi\) |
−0.398040 | + | 0.917368i | \(0.630309\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.54388 | − | 6.04956i | 1.03518 | − | 0.656167i | ||||
\(86\) | −1.90864 | − | 5.87419i | −0.205814 | − | 0.633430i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.81567 | + | 14.8211i | −0.513352 | + | 1.57993i | ||||
\(89\) | −2.63713 | − | 8.11624i | −0.279535 | − | 0.860320i | −0.987984 | − | 0.154558i | \(-0.950605\pi\) |
0.708449 | − | 0.705762i | \(-0.249395\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.43600 | − | 10.5749i | 0.360191 | − | 1.10855i | ||||
\(92\) | 4.95193 | + | 3.59779i | 0.516274 | + | 0.375095i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −13.9610 | − | 10.1433i | −1.43997 | − | 1.04620i | ||||
\(95\) | −5.81919 | + | 3.68860i | −0.597037 | + | 0.378443i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.61831 | − | 6.26157i | 0.875057 | − | 0.635766i | −0.0568823 | − | 0.998381i | \(-0.518116\pi\) |
0.931939 | + | 0.362615i | \(0.118116\pi\) | |||||||
\(98\) | −3.64643 | − | 11.2226i | −0.368345 | − | 1.13365i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 19.6163 | + | 2.49946i | 1.96163 | + | 0.249946i | ||||
\(101\) | −1.76173 | −0.175299 | −0.0876496 | − | 0.996151i | \(-0.527936\pi\) | ||||
−0.0876496 | + | 0.996151i | \(0.527936\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.8749 | + | 9.35416i | −1.26860 | + | 0.921693i | −0.999146 | − | 0.0413198i | \(-0.986844\pi\) |
−0.269456 | + | 0.963013i | \(0.586844\pi\) | |||||||
\(104\) | −12.4743 | + | 9.06313i | −1.22321 | + | 0.888713i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 20.0415 | + | 14.5610i | 1.94660 | + | 1.41429i | ||||
\(107\) | 15.7807 | 1.52558 | 0.762788 | − | 0.646649i | \(-0.223830\pi\) | ||||
0.762788 | + | 0.646649i | \(0.223830\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.06539 | + | 9.43429i | −0.293611 | + | 0.903641i | 0.690074 | + | 0.723739i | \(0.257578\pi\) |
−0.983685 | + | 0.179902i | \(0.942422\pi\) | |||||||
\(110\) | 4.42352 | + | 17.2668i | 0.421766 | + | 1.64633i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.96743 | + | 12.2105i | −0.374887 | + | 1.15378i | ||||
\(113\) | −1.70388 | + | 5.24399i | −0.160287 | + | 0.493313i | −0.998658 | − | 0.0517868i | \(-0.983508\pi\) |
0.838371 | + | 0.545100i | \(0.183508\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.45370 | + | 0.219145i | 0.322059 | + | 0.0204353i | ||||
\(116\) | 3.81580 | − | 11.7438i | 0.354288 | − | 1.09039i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.22306 | 0.388764 | ||||||||
\(119\) | 14.0648 | + | 10.2187i | 1.28932 | + | 0.936743i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.266626 | − | 0.193715i | 0.0242387 | − | 0.0176105i | ||||
\(122\) | 15.4703 | − | 11.2398i | 1.40061 | − | 1.01761i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 29.4334 | 2.64320 | ||||||||
\(125\) | 10.1239 | − | 4.74410i | 0.905510 | − | 0.424326i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.306572 | − | 0.943532i | −0.0272039 | − | 0.0837250i | 0.936533 | − | 0.350580i | \(-0.114016\pi\) |
−0.963737 | + | 0.266855i | \(0.914016\pi\) | |||||||
\(128\) | −16.1255 | + | 11.7159i | −1.42531 | + | 1.03555i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.50105 | + | 16.3941i | −0.570179 | + | 1.43786i | ||||
\(131\) | −10.2029 | − | 7.41286i | −0.891434 | − | 0.647665i | 0.0448175 | − | 0.998995i | \(-0.485729\pi\) |
−0.936252 | + | 0.351330i | \(0.885729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.57573 | − | 6.23063i | −0.743610 | − | 0.540264i | ||||
\(134\) | 1.39438 | − | 4.29147i | 0.120456 | − | 0.370727i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.44984 | − | 22.9282i | −0.638818 | − | 1.96608i | ||||
\(137\) | −2.54650 | + | 7.83732i | −0.217562 | + | 0.669588i | 0.781400 | + | 0.624031i | \(0.214506\pi\) |
−0.998962 | + | 0.0455566i | \(0.985494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.49182 | + | 7.66904i | 0.211354 | + | 0.650479i | 0.999392 | + | 0.0348539i | \(0.0110966\pi\) |
−0.788039 | + | 0.615626i | \(0.788903\pi\) | |||||||
\(140\) | 7.55049 | + | 29.4727i | 0.638133 | + | 2.49090i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.40954 | + | 1.02409i | 0.118286 | + | 0.0859397i | ||||
\(143\) | −10.5577 | −0.882875 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.73259 | − | 6.76301i | −0.143883 | − | 0.561637i | ||||
\(146\) | −3.71209 | + | 2.69699i | −0.307215 | + | 0.223205i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.03765 | − | 21.6597i | −0.578491 | − | 1.78041i | ||||
\(149\) | 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 | \(0.479451\pi\) | |||||||
\(152\) | 4.54239 | + | 13.9800i | 0.368437 | + | 1.13393i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −22.1862 | + | 16.1192i | −1.78782 | + | 1.29892i | ||||
\(155\) | 14.0553 | − | 8.90921i | 1.12895 | − | 0.715605i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.8510 | −1.74390 | −0.871948 | − | 0.489599i | \(-0.837143\pi\) | ||||
−0.871948 | + | 0.489599i | \(0.837143\pi\) | |||||||
\(158\) | −26.3229 | − | 19.1247i | −2.09414 | − | 1.52148i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.358125 | + | 0.903108i | −0.0283123 | + | 0.0713970i | ||||
\(161\) | 1.64531 | + | 5.06376i | 0.129669 | + | 0.399080i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.13153 | − | 9.63786i | 0.245280 | − | 0.754896i | −0.750310 | − | 0.661087i | \(-0.770096\pi\) |
0.995590 | − | 0.0938092i | \(-0.0299044\pi\) | |||||||
\(164\) | −6.62363 | − | 20.3854i | −0.517219 | − | 1.59184i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.98429 | − | 9.18469i | 0.231626 | − | 0.712870i | ||||
\(167\) | −1.22250 | − | 0.888195i | −0.0945996 | − | 0.0687306i | 0.539480 | − | 0.841998i | \(-0.318621\pi\) |
−0.634080 | + | 0.773268i | \(0.718621\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.06617 | + | 1.50116i | 0.158936 | + | 0.115474i | ||||
\(170\) | −21.2370 | − | 17.5880i | −1.62881 | − | 1.34894i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.09848 | + | 5.88389i | −0.617504 | + | 0.448643i | ||||
\(173\) | 4.28153 | + | 13.1772i | 0.325518 | + | 1.00184i | 0.971206 | + | 0.238241i | \(0.0765709\pi\) |
−0.645688 | + | 0.763602i | \(0.723429\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.5267 | + | 11.7886i | 0.946928 | + | 0.891134i | ||||
\(176\) | 12.1906 | 0.918897 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.8479 | + | 12.2407i | −1.26281 | + | 0.917482i | ||||
\(179\) | 11.6949 | − | 8.49685i | 0.874119 | − | 0.635085i | −0.0575701 | − | 0.998341i | \(-0.518335\pi\) |
0.931689 | + | 0.363257i | \(0.118335\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.9068 | − | 10.1039i | −1.03369 | − | 0.751017i | −0.0646435 | − | 0.997908i | \(-0.520591\pi\) |
−0.969043 | + | 0.246891i | \(0.920591\pi\) | |||||||
\(182\) | −27.1338 | −2.01129 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.28159 | − | 7.02201i | 0.168201 | − | 0.517670i | ||||
\(185\) | −9.91684 | − | 8.21287i | −0.729101 | − | 0.603822i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.10099 | − | 15.6992i | 0.373021 | − | 1.14804i | ||||
\(188\) | −8.64262 | + | 26.5993i | −0.630328 | + | 1.93995i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.9489 | + | 10.7239i | 0.939410 | + | 0.777995i | ||||
\(191\) | −3.25778 | + | 10.0264i | −0.235725 | + | 0.725486i | 0.761300 | + | 0.648400i | \(0.224562\pi\) |
−0.997024 | + | 0.0770858i | \(0.975438\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.682908 | −0.0491568 | −0.0245784 | − | 0.999698i | \(-0.507824\pi\) | ||||
−0.0245784 | + | 0.999698i | \(0.507824\pi\) | |||||||
\(194\) | −21.0311 | − | 15.2800i | −1.50995 | − | 1.09704i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −15.4721 | + | 11.2411i | −1.10515 | + | 0.802936i | ||||
\(197\) | −18.8478 | + | 13.6937i | −1.34285 | + | 0.975639i | −0.343518 | + | 0.939146i | \(0.611619\pi\) |
−0.999334 | + | 0.0364929i | \(0.988381\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1946 | 0.722679 | 0.361339 | − | 0.932434i | \(-0.382320\pi\) | ||||
0.361339 | + | 0.932434i | \(0.382320\pi\) | |||||||
\(200\) | −4.44462 | − | 23.4358i | −0.314282 | − | 1.65716i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.32850 | + | 4.08872i | 0.0934733 | + | 0.287681i | ||||
\(203\) | 8.68980 | − | 6.31351i | 0.609905 | − | 0.443122i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.33344 | − | 7.72971i | −0.651876 | − | 0.539867i | ||||
\(206\) | 31.4184 | + | 22.8268i | 2.18902 | + | 1.59042i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.75813 | + | 7.08969i | 0.676604 | + | 0.491582i | ||||
\(209\) | −3.11023 | + | 9.57230i | −0.215139 | + | 0.662130i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.64172 | + | 17.3634i | 0.388392 | + | 1.19535i | 0.933990 | + | 0.357300i | \(0.116303\pi\) |
−0.545598 | + | 0.838047i | \(0.683697\pi\) | |||||||
\(212\) | 12.4068 | − | 38.1841i | 0.852101 | − | 2.62250i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.9000 | − | 36.6245i | −0.813470 | − | 2.50360i | ||||
\(215\) | −2.08626 | + | 5.26106i | −0.142282 | + | 0.358801i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.7133 | + | 15.0491i | 1.40611 | + | 1.02160i | ||||
\(218\) | 24.2071 | 1.63951 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 24.3994 | − | 15.4660i | 1.64501 | − | 1.04272i | ||||
\(221\) | 13.2134 | − | 9.60011i | 0.888831 | − | 0.645774i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.32262 | + | 16.3813i | 0.356429 | + | 1.09698i | 0.955176 | + | 0.296037i | \(0.0956653\pi\) |
−0.598748 | + | 0.800938i | \(0.704335\pi\) | |||||||
\(224\) | −1.49473 | −0.0998708 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.4554 | 0.895039 | ||||||||
\(227\) | 1.33767 | + | 4.11692i | 0.0887842 | + | 0.273250i | 0.985584 | − | 0.169187i | \(-0.0541142\pi\) |
−0.896800 | + | 0.442437i | \(0.854114\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.4349 | + | 11.9407i | −1.08605 | + | 0.789062i | −0.978728 | − | 0.205163i | \(-0.934228\pi\) |
−0.107322 | + | 0.994224i | \(0.534228\pi\) | |||||||
\(230\) | −2.09580 | − | 8.18077i | −0.138193 | − | 0.539424i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.8950 | −0.977906 | ||||||||
\(233\) | −0.275839 | − | 0.200409i | −0.0180708 | − | 0.0131292i | 0.578713 | − | 0.815531i | \(-0.303555\pi\) |
−0.596784 | + | 0.802402i | \(0.703555\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.92424 | + | 15.3179i | 0.255989 | + | 0.999232i | ||||
\(236\) | −2.11502 | − | 6.50936i | −0.137676 | − | 0.423723i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.1099 | − | 40.3480i | 0.849786 | − | 2.61537i | ||||
\(239\) | 2.21407 | + | 6.81421i | 0.143216 | + | 0.440774i | 0.996777 | − | 0.0802185i | \(-0.0255618\pi\) |
−0.853561 | + | 0.520993i | \(0.825562\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.88194 | + | 11.9474i | −0.250058 | + | 0.769599i | 0.744705 | + | 0.667393i | \(0.232590\pi\) |
−0.994763 | + | 0.102206i | \(0.967410\pi\) | |||||||
\(242\) | −0.650643 | − | 0.472720i | −0.0418249 | − | 0.0303876i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −25.0728 | − | 18.2165i | −1.60512 | − | 1.16619i | ||||
\(245\) | −3.98577 | + | 10.0512i | −0.254642 | + | 0.642147i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.05662 | + | 5.85348i | −0.512631 | + | 0.372448i | ||||
\(248\) | −10.9714 | − | 33.7665i | −0.696684 | − | 2.14417i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −18.6447 | − | 19.9186i | −1.17919 | − | 1.25976i | ||||
\(251\) | −17.0160 | −1.07404 | −0.537022 | − | 0.843568i | \(-0.680451\pi\) | ||||
−0.537022 | + | 0.843568i | \(0.680451\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.08998 | − | 2.97154i | 0.257135 | − | 0.186819i | ||||
\(254\) | −1.95861 | + | 1.42301i | −0.122894 | + | 0.0892879i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 25.5586 | + | 18.5694i | 1.59741 | + | 1.16059i | ||||
\(257\) | −4.13200 | −0.257747 | −0.128874 | − | 0.991661i | \(-0.541136\pi\) | ||||
−0.128874 | + | 0.991661i | \(0.541136\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.12177 | − | 18.8409i | 0.380388 | − | 1.17072i | ||||
\(260\) | 28.5255 | + | 1.81000i | 1.76908 | + | 0.112252i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.51020 | + | 29.2694i | −0.587542 | + | 1.80827i | ||||
\(263\) | 0.320676 | − | 0.986940i | 0.0197737 | − | 0.0608573i | −0.940683 | − | 0.339287i | \(-0.889814\pi\) |
0.960456 | + | 0.278430i | \(0.0898141\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.63338 | − | 21.9894i | −0.346056 | − | 1.35080i | ||||
\(266\) | −7.99348 | + | 24.6014i | −0.490112 | + | 1.50841i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.31315 | −0.446722 | ||||||||
\(269\) | −12.7741 | − | 9.28093i | −0.778851 | − | 0.565869i | 0.125783 | − | 0.992058i | \(-0.459856\pi\) |
−0.904634 | + | 0.426189i | \(0.859856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0838 | − | 8.05286i | 0.673294 | − | 0.489176i | −0.197832 | − | 0.980236i | \(-0.563390\pi\) |
0.871126 | + | 0.491059i | \(0.163390\pi\) | |||||||
\(272\) | −15.2571 | + | 11.0849i | −0.925096 | + | 0.672122i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.1095 | 1.21486 | ||||||||
\(275\) | 6.96999 | − | 14.7709i | 0.420306 | − | 0.890720i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.15691 | + | 6.63827i | 0.129596 | + | 0.398855i | 0.994710 | − | 0.102719i | \(-0.0327543\pi\) |
−0.865114 | + | 0.501574i | \(0.832754\pi\) | |||||||
\(278\) | 15.9196 | − | 11.5663i | 0.954795 | − | 0.693699i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 30.9971 | − | 19.6481i | 1.85243 | − | 1.17420i | ||||
\(281\) | 6.43834 | + | 4.67773i | 0.384079 | + | 0.279050i | 0.763025 | − | 0.646369i | \(-0.223713\pi\) |
−0.378946 | + | 0.925419i | \(0.623713\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.4868 | + | 16.3376i | 1.33670 | + | 0.971169i | 0.999558 | + | 0.0297149i | \(0.00945992\pi\) |
0.337141 | + | 0.941454i | \(0.390540\pi\) | |||||||
\(284\) | 0.872582 | − | 2.68553i | 0.0517782 | − | 0.159357i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.96141 | + | 24.5027i | 0.470768 | + | 1.44888i | ||||
\(287\) | 5.76163 | − | 17.7325i | 0.340099 | − | 1.04672i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.63794 | + | 8.11876i | 0.155173 | + | 0.477574i | ||||
\(290\) | −14.3894 | + | 9.12098i | −0.844973 | + | 0.535602i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.01621 | + | 4.37103i | 0.352072 | + | 0.255795i | ||||
\(293\) | 14.2098 | 0.830146 | 0.415073 | − | 0.909788i | \(-0.363756\pi\) | ||||
0.415073 | + | 0.909788i | \(0.363756\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.98030 | − | 2.46821i | −0.173520 | − | 0.143705i | ||||
\(296\) | −22.2250 | + | 16.1474i | −1.29180 | + | 0.938548i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.4107 | − | 44.3517i | −0.834791 | − | 2.56922i | ||||
\(299\) | 5.00206 | 0.289276 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.70755 | −0.501895 | ||||||||
\(302\) | −1.19561 | − | 3.67971i | −0.0687997 | − | 0.211744i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.30270 | − | 6.75881i | 0.533547 | − | 0.387644i | ||||
\(305\) | −17.4869 | − | 1.10958i | −1.00130 | − | 0.0635345i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.2911 | −1.32930 | −0.664648 | − | 0.747157i | \(-0.731418\pi\) | ||||
−0.664648 | + | 0.747157i | \(0.731418\pi\) | |||||||
\(308\) | 35.9573 | + | 26.1245i | 2.04886 | + | 1.48858i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −31.2759 | − | 25.9019i | −1.77635 | − | 1.47113i | ||||
\(311\) | 2.33284 | + | 7.17976i | 0.132283 | + | 0.407127i | 0.995158 | − | 0.0982923i | \(-0.0313380\pi\) |
−0.862874 | + | 0.505419i | \(0.831338\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.78241 | + | 30.1072i | −0.552934 | + | 1.70176i | 0.148402 | + | 0.988927i | \(0.452587\pi\) |
−0.701337 | + | 0.712830i | \(0.747413\pi\) | |||||||
\(314\) | 16.4776 | + | 50.7127i | 0.929883 | + | 2.86188i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.2953 | + | 50.1518i | −0.916682 | + | 2.82126i | ||||
\(317\) | 20.9019 | + | 15.1861i | 1.17397 | + | 0.852938i | 0.991479 | − | 0.130270i | \(-0.0415844\pi\) |
0.182490 | + | 0.983208i | \(0.441584\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.25100 | − | 5.99471i | −0.461968 | − | 0.335639i | ||||
\(320\) | 19.0222 | + | 1.20700i | 1.06337 | + | 0.0674733i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.5115 | − | 7.63705i | 0.585783 | − | 0.425596i | ||||
\(323\) | −4.81152 | − | 14.8083i | −0.267720 | − | 0.823959i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.1696 | − | 7.77006i | 0.785988 | − | 0.431006i | ||||
\(326\) | −24.7295 | −1.36964 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −20.9175 | + | 15.1975i | −1.15498 | + | 0.839139i | ||||
\(329\) | −19.6821 | + | 14.2999i | −1.08511 | + | 0.788376i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.2679 | − | 11.8193i | −0.894166 | − | 0.649650i | 0.0427948 | − | 0.999084i | \(-0.486374\pi\) |
−0.936961 | + | 0.349434i | \(0.886374\pi\) | |||||||
\(332\) | −15.6517 | −0.859001 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.13949 | + | 3.50700i | −0.0623504 | + | 0.191895i | ||||
\(335\) | −3.49224 | + | 2.21362i | −0.190801 | + | 0.120943i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.04564 | − | 3.21816i | 0.0569599 | − | 0.175304i | −0.918529 | − | 0.395354i | \(-0.870622\pi\) |
0.975489 | + | 0.220050i | \(0.0706219\pi\) | |||||||
\(338\) | 1.92589 | − | 5.92729i | 0.104755 | − | 0.322402i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −16.4737 | + | 41.5429i | −0.893414 | + | 2.25298i | ||||
\(341\) | 7.51225 | − | 23.1203i | 0.406811 | − | 1.25204i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.44633 | 0.402064 | ||||||||
\(344\) | 9.76882 | + | 7.09747i | 0.526700 | + | 0.382670i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 27.3536 | − | 19.8735i | 1.47054 | − | 1.06841i | ||||
\(347\) | −23.6204 | + | 17.1612i | −1.26801 | + | 0.921262i | −0.999121 | − | 0.0419100i | \(-0.986656\pi\) |
−0.268887 | + | 0.963172i | \(0.586656\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.3979 | −1.09187 | −0.545937 | − | 0.837826i | \(-0.683826\pi\) | ||||
−0.545937 | + | 0.837826i | \(0.683826\pi\) | |||||||
\(350\) | 17.9133 | − | 37.9622i | 0.957506 | − | 2.02916i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.438573 | + | 1.34979i | 0.0233760 | + | 0.0719440i | ||||
\(353\) | −1.50757 | + | 1.09532i | −0.0802400 | + | 0.0582978i | −0.627182 | − | 0.778873i | \(-0.715792\pi\) |
0.546942 | + | 0.837170i | \(0.315792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.396201 | − | 1.54654i | −0.0210282 | − | 0.0820818i | ||||
\(356\) | 27.3055 | + | 19.8386i | 1.44719 | + | 1.05145i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −28.5389 | − | 20.7347i | −1.50833 | − | 1.09586i | ||||
\(359\) | −1.18599 | + | 3.65011i | −0.0625943 | + | 0.192645i | −0.977463 | − | 0.211105i | \(-0.932294\pi\) |
0.914869 | + | 0.403751i | \(0.132294\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.93759 | − | 9.04097i | −0.154610 | − | 0.475841i | ||||
\(362\) | −12.9626 | + | 39.8949i | −0.681301 | + | 2.09683i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.5893 | + | 41.8236i | 0.712274 | + | 2.19215i | ||||
\(365\) | 4.19598 | + | 0.266244i | 0.219628 | + | 0.0139358i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.7335 | − | 15.0638i | −1.08228 | − | 0.786324i | −0.104203 | − | 0.994556i | \(-0.533229\pi\) |
−0.978079 | + | 0.208232i | \(0.933229\pi\) | |||||||
\(368\) | −5.77570 | −0.301079 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.5826 | + | 29.2087i | −0.602153 | + | 1.51849i | ||||
\(371\) | 28.2543 | − | 20.5279i | 1.46689 | − | 1.06576i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.62437 | + | 20.3877i | 0.342997 | + | 1.05564i | 0.962648 | + | 0.270758i | \(0.0872742\pi\) |
−0.619651 | + | 0.784878i | \(0.712726\pi\) | |||||||
\(374\) | −40.2821 | −2.08294 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 33.7366 | 1.73983 | ||||||||
\(377\) | −3.11829 | − | 9.59712i | −0.160600 | − | 0.494277i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.9304 | − | 15.2068i | 1.07512 | − | 0.781120i | 0.0982945 | − | 0.995157i | \(-0.468661\pi\) |
0.976826 | + | 0.214037i | \(0.0686613\pi\) | |||||||
\(380\) | 10.0445 | − | 25.3300i | 0.515274 | − | 1.29940i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 25.7264 | 1.31628 | ||||||||
\(383\) | −11.7579 | − | 8.54263i | −0.600802 | − | 0.436508i | 0.245362 | − | 0.969432i | \(-0.421093\pi\) |
−0.846163 | + | 0.532924i | \(0.821093\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.0783 | + | 1.59127i | 1.27811 | + | 0.0810986i | ||||
\(386\) | 0.514974 | + | 1.58493i | 0.0262115 | + | 0.0806706i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.0194 | + | 40.0696i | −0.660960 | + | 2.03423i | ||||
\(389\) | −7.13973 | − | 21.9738i | −0.361999 | − | 1.11412i | −0.951839 | − | 0.306598i | \(-0.900809\pi\) |
0.589840 | − | 0.807520i | \(-0.299191\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.41677 | + | 7.43806i | −0.122221 | + | 0.376159i | ||||
\(392\) | 18.6632 | + | 13.5596i | 0.942635 | + | 0.684864i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 45.9940 | + | 33.4166i | 2.31715 | + | 1.68350i | ||||
\(395\) | 7.39898 | + | 28.8813i | 0.372283 | + | 1.45318i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.2733 | + | 8.19052i | −0.565790 | + | 0.411070i | −0.833573 | − | 0.552409i | \(-0.813709\pi\) |
0.267784 | + | 0.963479i | \(0.413709\pi\) | |||||||
\(398\) | −7.68766 | − | 23.6602i | −0.385348 | − | 1.18598i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.3611 | + | 8.97182i | −0.818057 | + | 0.448591i | ||||
\(401\) | 27.5822 | 1.37739 | 0.688694 | − | 0.725052i | \(-0.258184\pi\) | ||||
0.688694 | + | 0.725052i | \(0.258184\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.4594 | − | 14.1381i | 0.969344 | − | 0.704270i | ||||
\(404\) | 5.63693 | − | 4.09547i | 0.280448 | − | 0.203757i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.2056 | − | 15.4068i | −1.05242 | − | 0.764625i | ||||
\(407\) | −18.8101 | −0.932383 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.08288 | − | 12.5658i | 0.201886 | − | 0.621340i | −0.797941 | − | 0.602735i | \(-0.794078\pi\) |
0.999827 | − | 0.0186048i | \(-0.00592242\pi\) | |||||||
\(410\) | −10.9012 | + | 27.4904i | −0.538374 | + | 1.35765i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 19.4497 | − | 59.8601i | 0.958218 | − | 2.94909i | ||||
\(413\) | 1.83977 | − | 5.66223i | 0.0905292 | − | 0.278620i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.47415 | + | 4.73763i | −0.366891 | + | 0.232561i | ||||
\(416\) | −0.433937 | + | 1.33552i | −0.0212755 | + | 0.0654794i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 24.5612 | 1.20133 | ||||||||
\(419\) | −7.15797 | − | 5.20057i | −0.349690 | − | 0.254064i | 0.399049 | − | 0.916930i | \(-0.369340\pi\) |
−0.748739 | + | 0.662865i | \(0.769340\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.3192 | − | 22.0282i | 1.47767 | − | 1.07359i | 0.499367 | − | 0.866390i | \(-0.333566\pi\) |
0.978299 | − | 0.207197i | \(-0.0664341\pi\) | |||||||
\(422\) | 36.0435 | − | 26.1871i | 1.75457 | − | 1.27477i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −48.4301 | −2.35197 | ||||||||
\(425\) | 4.70796 | + | 24.8244i | 0.228370 | + | 1.20416i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.33062 | − | 25.6390i | −0.403147 | − | 1.24076i | ||||
\(428\) | −50.4926 | + | 36.6850i | −2.44065 | + | 1.77324i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.7833 | + | 0.874582i | 0.664691 | + | 0.0421761i | ||||
\(431\) | −21.5397 | − | 15.6495i | −1.03753 | − | 0.753809i | −0.0677274 | − | 0.997704i | \(-0.521575\pi\) |
−0.969802 | + | 0.243895i | \(0.921575\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.3133 | − | 20.5708i | −1.36065 | − | 0.988571i | −0.998403 | − | 0.0564887i | \(-0.982010\pi\) |
−0.362248 | − | 0.932082i | \(-0.617990\pi\) | |||||||
\(434\) | 19.3069 | − | 59.4206i | 0.926762 | − | 2.85228i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.1235 | − | 37.3124i | −0.580613 | − | 1.78694i | ||||
\(437\) | 1.47358 | − | 4.53521i | 0.0704909 | − | 0.216949i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.19701 | + | 19.0724i | 0.295767 | + | 0.910277i | 0.982963 | + | 0.183805i | \(0.0588415\pi\) |
−0.687196 | + | 0.726472i | \(0.741159\pi\) | |||||||
\(440\) | −26.8378 | − | 22.2264i | −1.27944 | − | 1.05960i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −32.2445 | − | 23.4270i | −1.53371 | − | 1.11431i | ||||
\(443\) | −4.14871 | −0.197111 | −0.0985556 | − | 0.995132i | \(-0.531422\pi\) | ||||
−0.0985556 | + | 0.995132i | \(0.531422\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.0441 | + | 1.20839i | 0.902778 | + | 0.0572832i | ||||
\(446\) | 34.0048 | − | 24.7060i | 1.61018 | − | 1.16986i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.06201 | + | 27.8900i | 0.428140 | + | 1.31768i | ||||
\(449\) | 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 | ||||||||
\(452\) | −6.73880 | − | 20.7399i | −0.316967 | − | 0.975523i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.54602 | − | 6.20905i | 0.401085 | − | 0.291405i | ||||
\(455\) | 19.1489 | + | 15.8586i | 0.897713 | + | 0.743463i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.5774 | 0.962571 | 0.481285 | − | 0.876564i | \(-0.340170\pi\) | ||||
0.481285 | + | 0.876564i | \(0.340170\pi\) | |||||||
\(458\) | 40.1059 | + | 29.1386i | 1.87402 | + | 1.36156i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11.5601 | + | 7.32757i | −0.538991 | + | 0.341650i | ||||
\(461\) | −8.86541 | − | 27.2849i | −0.412903 | − | 1.27079i | −0.914113 | − | 0.405460i | \(-0.867111\pi\) |
0.501210 | − | 0.865326i | \(-0.332889\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.3853 | − | 38.1181i | 0.575594 | − | 1.77150i | −0.0585520 | − | 0.998284i | \(-0.518648\pi\) |
0.634146 | − | 0.773213i | \(-0.281352\pi\) | |||||||
\(464\) | 3.60058 | + | 11.0815i | 0.167153 | + | 0.514444i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.257111 | + | 0.791307i | −0.0119105 | + | 0.0366566i | ||||
\(467\) | −6.58694 | − | 4.78569i | −0.304807 | − | 0.221456i | 0.424858 | − | 0.905260i | \(-0.360324\pi\) |
−0.729665 | + | 0.683805i | \(0.760324\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.14650 | − | 3.73915i | −0.237643 | − | 0.172658i | ||||
\(470\) | 32.5914 | − | 20.6586i | 1.50333 | − | 0.952912i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.67925 | + | 4.85276i | −0.307438 | + | 0.223366i | ||||
\(473\) | 2.55491 | + | 7.86319i | 0.117475 | + | 0.361550i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.87059 | − | 15.1362i | −0.131712 | − | 0.694495i | ||||
\(476\) | −68.7575 | −3.15149 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.1451 | − | 10.2770i | 0.646983 | − | 0.470061i | ||||
\(479\) | −22.7027 | + | 16.4945i | −1.03731 | + | 0.753652i | −0.969759 | − | 0.244064i | \(-0.921519\pi\) |
−0.0675535 | + | 0.997716i | \(0.521519\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.0569 | − | 10.9395i | −0.686534 | − | 0.498796i | ||||
\(482\) | 30.6554 | 1.39631 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.402784 | + | 1.23964i | −0.0183084 | + | 0.0563473i | ||||
\(485\) | 5.91155 | + | 23.0752i | 0.268429 | + | 1.04779i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.70239 | + | 14.4725i | −0.213086 | + | 0.655810i | 0.786198 | + | 0.617974i | \(0.212046\pi\) |
−0.999284 | + | 0.0378360i | \(0.987954\pi\) | |||||||
\(488\) | −11.5522 | + | 35.5541i | −0.522945 | + | 1.60946i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 26.3329 | + | 1.67088i | 1.18960 | + | 0.0754826i | ||||
\(491\) | −2.56246 | + | 7.88645i | −0.115642 | + | 0.355910i | −0.992080 | − | 0.125604i | \(-0.959913\pi\) |
0.876438 | + | 0.481514i | \(0.159913\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.7775 | 0.710585 | ||||||||
\(494\) | 19.6604 | + | 14.2842i | 0.884565 | + | 0.642674i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.4691 | + | 16.3248i | −1.00889 | + | 0.733005i | ||||
\(497\) | 1.98715 | − | 1.44375i | 0.0891360 | − | 0.0647611i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.4006 | −1.09232 | −0.546160 | − | 0.837681i | \(-0.683911\pi\) | ||||
−0.546160 | + | 0.837681i | \(0.683911\pi\) | |||||||
\(500\) | −21.3644 | + | 38.7143i | −0.955445 | + | 1.73136i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.8316 | + | 39.4916i | 0.572703 | + | 1.76260i | ||||
\(503\) | 8.47295 | − | 6.15596i | 0.377790 | − | 0.274481i | −0.382644 | − | 0.923896i | \(-0.624986\pi\) |
0.760434 | + | 0.649415i | \(0.224986\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.45214 | − | 3.66195i | 0.0646192 | − | 0.162954i | ||||
\(506\) | −9.98070 | − | 7.25141i | −0.443696 | − | 0.322364i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.17433 | + | 2.30629i | 0.140838 | + | 0.102325i | ||||
\(509\) | 3.41769 | − | 10.5186i | 0.151486 | − | 0.466227i | −0.846302 | − | 0.532704i | \(-0.821176\pi\) |
0.997788 | + | 0.0664770i | \(0.0211759\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.99893 | + | 6.15207i | 0.0884274 | + | 0.272152i | ||||
\(512\) | 11.5045 | − | 35.4071i | 0.508431 | − | 1.56479i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.11590 | + | 9.58974i | 0.137436 | + | 0.422985i | ||||
\(515\) | −8.83126 | − | 34.4721i | −0.389152 | − | 1.51902i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.6882 | + | 13.5778i | 0.821906 | + | 0.597150i | ||||
\(518\) | −48.3432 | −2.12408 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.55650 | − | 33.3996i | −0.375227 | − | 1.46467i | ||||
\(521\) | −33.5105 | + | 24.3468i | −1.46812 | + | 1.06665i | −0.486967 | + | 0.873420i | \(0.661897\pi\) |
−0.981153 | + | 0.193231i | \(0.938103\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.21576 | + | 12.9748i | 0.184342 | + | 0.567347i | 0.999936 | − | 0.0112775i | \(-0.00358982\pi\) |
−0.815594 | + | 0.578624i | \(0.803590\pi\) | |||||||
\(524\) | 49.8783 | 2.17894 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.53235 | −0.110416 | ||||||||
\(527\) | 11.6214 | + | 35.7671i | 0.506238 | + | 1.55804i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.6696 | − | 12.1112i | 0.724766 | − | 0.526573i | ||||
\(530\) | −46.7860 | + | 29.6562i | −2.03225 | + | 1.28818i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 41.9235 | 1.81762 | ||||||||
\(533\) | −14.1711 | − | 10.2959i | −0.613818 | − | 0.445965i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.0075 | + | 32.8018i | −0.562361 | + | 1.41814i | ||||
\(536\) | 2.72600 | + | 8.38976i | 0.117745 | + | 0.362382i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.9068 | + | 36.6454i | −0.513339 | + | 1.57990i | ||||
\(539\) | 4.88112 | + | 15.0225i | 0.210245 | + | 0.647066i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.53011 | − | 13.9423i | 0.194765 | − | 0.599424i | −0.805214 | − | 0.592984i | \(-0.797950\pi\) |
0.999979 | − | 0.00644072i | \(-0.00205016\pi\) | |||||||
\(542\) | −27.0476 | − | 19.6513i | −1.16180 | − | 0.844094i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.77626 | − | 1.29053i | −0.0761566 | − | 0.0553310i | ||||
\(545\) | −17.0834 | − | 14.1481i | −0.731775 | − | 0.606037i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.5298 | + | 15.6423i | −0.920549 | + | 0.668818i | −0.943661 | − | 0.330915i | \(-0.892643\pi\) |
0.0231115 | + | 0.999733i | \(0.492643\pi\) | |||||||
\(548\) | −10.0714 | − | 30.9965i | −0.430227 | − | 1.32410i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −39.5370 | − | 5.03770i | −1.68586 | − | 0.214808i | ||||
\(551\) | −9.62005 | −0.409828 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −37.1097 | + | 26.9618i | −1.57806 | + | 1.14653i | ||||
\(554\) | 13.7799 | − | 10.0117i | 0.585453 | − | 0.425356i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.8010 | − | 18.7455i | −1.09421 | − | 0.794988i | ||||
\(557\) | 10.3141 | 0.437020 | 0.218510 | − | 0.975835i | \(-0.429880\pi\) | ||||
0.218510 | + | 0.975835i | \(0.429880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.52790 | + | 7.78008i | −0.106919 | + | 0.329063i | ||||
\(560\) | −22.1105 | − | 18.3114i | −0.934341 | − | 0.773797i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00121 | − | 18.4698i | 0.253146 | − | 0.779103i | ||||
\(563\) | 10.6311 | − | 32.7193i | 0.448049 | − | 1.37895i | −0.431056 | − | 0.902325i | \(-0.641859\pi\) |
0.879105 | − | 0.476628i | \(-0.158141\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.49573 | − | 7.86412i | −0.399488 | − | 0.330846i | ||||
\(566\) | 20.9600 | − | 64.5083i | 0.881016 | − | 2.71149i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.40614 | −0.142918 | ||||||||
\(569\) | −9.87387 | − | 7.17378i | −0.413934 | − | 0.300741i | 0.361259 | − | 0.932466i | \(-0.382347\pi\) |
−0.775193 | + | 0.631725i | \(0.782347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.0308 | + | 24.7248i | −1.42415 | + | 1.03470i | −0.433076 | + | 0.901357i | \(0.642572\pi\) |
−0.991070 | + | 0.133345i | \(0.957428\pi\) | |||||||
\(572\) | 33.7808 | − | 24.5432i | 1.41245 | − | 1.02620i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −45.4992 | −1.89910 | ||||||||
\(575\) | −3.30228 | + | 6.99824i | −0.137715 | + | 0.291847i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.41863 | + | 16.6768i | 0.225581 | + | 0.694266i | 0.998232 | + | 0.0594353i | \(0.0189300\pi\) |
−0.772652 | + | 0.634830i | \(0.781070\pi\) | |||||||
\(578\) | 16.8532 | − | 12.2445i | 0.700999 | − | 0.509305i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21.2655 | + | 17.6115i | 0.883001 | + | 0.731279i | ||||
\(581\) | −11.0146 | − | 8.00260i | −0.456964 | − | 0.332004i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.8275 | − | 19.4913i | −1.11108 | − | 0.807249i | ||||
\(584\) | 2.77196 | − | 8.53120i | 0.114704 | − | 0.353024i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.7155 | − | 32.9788i | −0.442651 | − | 1.36234i | ||||
\(587\) | 6.77115 | − | 20.8395i | 0.279475 | − | 0.860137i | −0.708525 | − | 0.705686i | \(-0.750639\pi\) |
0.988000 | − | 0.154451i | \(-0.0493610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.08595 | − | 21.8083i | −0.291971 | − | 0.898595i | ||||
\(590\) | −3.48092 | + | 8.77807i | −0.143307 | + | 0.361387i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.3856 | + | 12.6314i | 0.714545 | + | 0.519148i | ||||
\(593\) | 38.0061 | 1.56072 | 0.780361 | − | 0.625330i | \(-0.215035\pi\) | ||||
0.780361 | + | 0.625330i | \(0.215035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.8336 | + | 20.8122i | −1.34605 | + | 0.853218i | ||||
\(596\) | −61.1456 | + | 44.4249i | −2.50462 | + | 1.81971i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.77200 | − | 11.6090i | −0.154248 | − | 0.474728i | ||||
\(599\) | −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 | \(0.484941\pi\) | |||||||
\(602\) | 6.56626 | + | 20.2089i | 0.267621 | + | 0.823653i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.07305 | + | 3.68579i | −0.206420 | + | 0.149973i | ||||
\(605\) | 0.182887 | + | 0.713882i | 0.00743539 | + | 0.0290234i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.2134 | 1.30750 | 0.653752 | − | 0.756709i | \(-0.273194\pi\) | ||||
0.653752 | + | 0.756709i | \(0.273194\pi\) | |||||||
\(608\) | 1.08304 | + | 0.786876i | 0.0439231 | + | 0.0319120i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.6115 | + | 41.4212i | 0.429648 | + | 1.67709i | ||||
\(611\) | 7.06281 | + | 21.7371i | 0.285731 | + | 0.879389i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.01843 | − | 24.6782i | 0.323861 | − | 0.996742i | −0.648091 | − | 0.761563i | \(-0.724432\pi\) |
0.971952 | − | 0.235179i | \(-0.0755677\pi\) | |||||||
\(614\) | 17.5636 | + | 54.0552i | 0.708809 | + | 2.18149i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.5673 | − | 50.9888i | 0.667514 | − | 2.05440i | ||||
\(617\) | 1.54016 | + | 1.11899i | 0.0620043 | + | 0.0450488i | 0.618356 | − | 0.785898i | \(-0.287799\pi\) |
−0.556351 | + | 0.830947i | \(0.687799\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.0829 | + | 11.6849i | 0.646425 | + | 0.469655i | 0.862052 | − | 0.506821i | \(-0.169179\pi\) |
−0.215627 | + | 0.976476i | \(0.569179\pi\) | |||||||
\(620\) | −24.2609 | + | 61.1804i | −0.974343 | + | 2.45706i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.9039 | − | 10.8283i | 0.597594 | − | 0.434177i | ||||
\(623\) | 9.07246 | + | 27.9222i | 0.363480 | + | 1.11868i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.51633 | + | 24.9540i | 0.0606533 | + | 0.998159i | ||||
\(626\) | 77.2509 | 3.08757 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 69.9154 | − | 50.7965i | 2.78993 | − | 2.02700i | ||||
\(629\) | 23.5418 | − | 17.1041i | 0.938673 | − | 0.681986i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.6152 | + | 19.3371i | 1.05953 | + | 0.769796i | 0.974002 | − | 0.226539i | \(-0.0727412\pi\) |
0.0855315 | + | 0.996335i | \(0.472741\pi\) | |||||||
\(632\) | 63.6090 | 2.53023 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.4828 | − | 59.9618i | 0.773760 | − | 2.38139i | ||||
\(635\) | 2.21393 | + | 0.140478i | 0.0878570 | + | 0.00557471i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.82953 | + | 14.8638i | −0.191353 | + | 0.588923i | ||||
\(638\) | −7.69080 | + | 23.6699i | −0.304482 | + | 0.937099i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.0610 | − | 43.1755i | −0.437223 | − | 1.70666i | ||||
\(641\) | 12.5963 | − | 38.7673i | 0.497523 | − | 1.53122i | −0.315465 | − | 0.948937i | \(-0.602161\pi\) |
0.812988 | − | 0.582280i | \(-0.197839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.9947 | 0.985695 | 0.492847 | − | 0.870116i | \(-0.335956\pi\) | ||||
0.492847 | + | 0.870116i | \(0.335956\pi\) | |||||||
\(644\) | −17.0360 | − | 12.3774i | −0.671314 | − | 0.487738i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30.7396 | + | 22.3336i | −1.20943 | + | 0.878705i | ||||
\(647\) | −25.9073 | + | 18.8228i | −1.01852 | + | 0.739999i | −0.965979 | − | 0.258620i | \(-0.916732\pi\) |
−0.0525420 | + | 0.998619i | \(0.516732\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.65299 | −0.221899 | ||||||||
\(650\) | −28.7183 | − | 27.0262i | −1.12642 | − | 1.06005i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.3852 | + | 38.1176i | 0.485040 | + | 1.49280i | ||||
\(653\) | −36.1446 | + | 26.2606i | −1.41445 | + | 1.02766i | −0.421791 | + | 0.906693i | \(0.638599\pi\) |
−0.992657 | + | 0.120964i | \(0.961401\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.8183 | − | 15.0977i | 0.930658 | − | 0.589915i | ||||
\(656\) | 16.3629 | + | 11.8883i | 0.638862 | + | 0.464161i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 48.0298 | + | 34.8957i | 1.87240 | + | 1.36038i | ||||
\(659\) | 7.42307 | − | 22.8458i | 0.289162 | − | 0.889948i | −0.695959 | − | 0.718082i | \(-0.745020\pi\) |
0.985120 | − | 0.171866i | \(-0.0549796\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.7095 | + | 36.0382i | 0.455447 | + | 1.40172i | 0.870610 | + | 0.491974i | \(0.163725\pi\) |
−0.415163 | + | 0.909747i | \(0.636275\pi\) | |||||||
\(662\) | −15.1634 | + | 46.6682i | −0.589343 | + | 1.81381i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.83423 | + | 17.9559i | 0.226412 | + | 0.696824i | ||||
\(665\) | 20.0197 | − | 12.6898i | 0.776329 | − | 0.492091i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.90920 | + | 2.84020i | 0.151365 | + | 0.109973i | ||||
\(668\) | 5.97633 | 0.231231 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.77093 | + | 6.43568i | 0.300217 | + | 0.248632i | ||||
\(671\) | −20.7085 | + | 15.0456i | −0.799444 | + | 0.580830i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.69418 | − | 17.5249i | −0.219494 | − | 0.675534i | −0.998804 | − | 0.0488951i | \(-0.984430\pi\) |
0.779310 | − | 0.626639i | \(-0.215570\pi\) | |||||||
\(674\) | −8.25737 | −0.318062 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.1008 | −0.388491 | ||||||||
\(677\) | 7.05064 | + | 21.6996i | 0.270978 | + | 0.833985i | 0.990256 | + | 0.139262i | \(0.0444730\pi\) |
−0.719277 | + | 0.694723i | \(0.755527\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.6494 | + | 21.5416i | −1.13784 | + | 0.826690i | ||||
\(680\) | 53.7993 | + | 3.41368i | 2.06311 | + | 0.130909i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −59.3236 | −2.27162 | ||||||||
\(683\) | 26.0555 | + | 18.9304i | 0.996987 | + | 0.724353i | 0.961440 | − | 0.275015i | \(-0.0886828\pi\) |
0.0355465 | + | 0.999368i | \(0.488683\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.1917 | − | 11.7532i | −0.542237 | − | 0.449066i | ||||
\(686\) | −5.61519 | − | 17.2818i | −0.214389 | − | 0.659822i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.91888 | − | 8.98339i | 0.111281 | − | 0.342489i | ||||
\(689\) | −10.1389 | − | 31.2043i | −0.386261 | − | 1.18879i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.59466 | − | 23.3740i | 0.288915 | − | 0.889188i | −0.696283 | − | 0.717767i | \(-0.745164\pi\) |
0.985198 | − | 0.171421i | \(-0.0548358\pi\) | |||||||
\(692\) | −44.3321 | − | 32.2092i | −1.68525 | − | 1.22441i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 57.6404 | + | 41.8782i | 2.18800 | + | 1.58967i | ||||
\(695\) | −17.9948 | − | 1.14181i | −0.682582 | − | 0.0433113i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.1568 | − | 16.0979i | 0.839251 | − | 0.609751i | ||||
\(698\) | 15.3818 | + | 47.3404i | 0.582211 | + | 1.79186i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −67.4857 | − | 8.59884i | −2.55072 | − | 0.325006i | ||||
\(701\) | 3.66355 | 0.138370 | 0.0691852 | − | 0.997604i | \(-0.477960\pi\) | ||||
0.0691852 | + | 0.997604i | \(0.477960\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.3541 | + | 10.4289i | −0.541377 | + | 0.393333i | ||||
\(704\) | 22.5267 | − | 16.3666i | 0.849005 | − | 0.616838i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.67890 | + | 2.67288i | 0.138457 | + | 0.100595i | ||||
\(707\) | 6.06087 | 0.227942 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.24980 | + | 25.3903i | −0.309828 | + | 0.953552i | 0.668003 | + | 0.744158i | \(0.267149\pi\) |
−0.977831 | + | 0.209394i | \(0.932851\pi\) | |||||||
\(710\) | −3.29051 | + | 2.08575i | −0.123491 | + | 0.0782768i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.5810 | − | 38.7202i | 0.471492 | − | 1.45110i | ||||
\(713\) | −3.55919 | + | 10.9541i | −0.133293 | + | 0.410233i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.70230 | − | 21.9452i | 0.325447 | − | 0.820703i | ||||
\(716\) | −17.6671 | + | 54.3739i | −0.660252 | + | 2.03205i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.36569 | 0.349524 | ||||||||
\(719\) | 14.4570 | + | 10.5036i | 0.539156 | + | 0.391720i | 0.823771 | − | 0.566922i | \(-0.191866\pi\) |
−0.284616 | + | 0.958642i | \(0.591866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.2933 | − | 32.1810i | 1.64957 | − | 1.19848i | ||||
\(722\) | −18.7675 | + | 13.6354i | −0.698455 | + | 0.507457i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 67.9853 | 2.52665 | ||||||||
\(725\) | 15.4857 | + | 1.97315i | 0.575125 | + | 0.0732808i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.5290 | − | 32.4050i | −0.390500 | − | 1.20184i | −0.932411 | − | 0.361400i | \(-0.882299\pi\) |
0.541910 | − | 0.840436i | \(-0.317701\pi\) | |||||||
\(728\) | 42.9152 | − | 31.1797i | 1.59054 | − | 1.15560i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.54623 | − | 9.93900i | −0.0942402 | − | 0.367859i | ||||
\(731\) | −10.3476 | − | 7.51799i | −0.382721 | − | 0.278063i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.5068 | + | 23.6176i | 1.20067 | + | 0.872335i | 0.994350 | − | 0.106150i | \(-0.0338525\pi\) |
0.206316 | + | 0.978485i | \(0.433853\pi\) | |||||||
\(734\) | −19.3258 | + | 59.4788i | −0.713330 | + | 2.19540i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.207789 | − | 0.639509i | −0.00765921 | − | 0.0235726i | ||||
\(737\) | −1.86652 | + | 5.74457i | −0.0687542 | + | 0.211604i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.78203 | + | 14.7176i | 0.175910 | + | 0.541395i | 0.999674 | − | 0.0255381i | \(-0.00812990\pi\) |
−0.823764 | + | 0.566933i | \(0.808130\pi\) | |||||||
\(740\) | 50.8227 | + | 3.22481i | 1.86828 | + | 0.118546i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −68.9484 | − | 50.0939i | −2.53118 | − | 1.83901i | ||||
\(743\) | 17.1140 | 0.627853 | 0.313926 | − | 0.949447i | \(-0.398355\pi\) | ||||
0.313926 | + | 0.949447i | \(0.398355\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.7518 | + | 39.7223i | −0.577101 | + | 1.45531i | ||||
\(746\) | 42.3214 | − | 30.7483i | 1.54950 | − | 1.12577i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20.1743 | + | 62.0902i | 0.737647 | + | 2.27024i | ||||
\(749\) | −54.2900 | −1.98371 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.1559 | −0.407086 | −0.203543 | − | 0.979066i | \(-0.565246\pi\) | ||||
−0.203543 | + | 0.979066i | \(0.565246\pi\) | |||||||
\(752\) | −8.15518 | − | 25.0991i | −0.297389 | − | 0.915268i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −19.9220 | + | 14.4742i | −0.725516 | + | 0.527118i | ||||
\(755\) | −1.30687 | + | 3.29563i | −0.0475620 | + | 0.119940i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.6773 | 0.896911 | 0.448456 | − | 0.893805i | \(-0.351974\pi\) | ||||
0.448456 | + | 0.893805i | \(0.351974\pi\) | |||||||
\(758\) | −51.0760 | − | 37.1089i | −1.85516 | − | 1.34786i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −32.8031 | − | 2.08143i | −1.18989 | − | 0.0755012i | ||||
\(761\) | 12.4372 | + | 38.2779i | 0.450850 | + | 1.38757i | 0.875939 | + | 0.482422i | \(0.160243\pi\) |
−0.425089 | + | 0.905151i | \(0.639757\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.5458 | − | 32.4566i | 0.381784 | − | 1.17501i | ||||
\(764\) | −12.8845 | − | 39.6543i | −0.466143 | − | 1.43464i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.9596 | + | 33.7302i | −0.395987 | + | 1.21872i | ||||
\(767\) | −4.52503 | − | 3.28763i | −0.163389 | − | 0.118709i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.8801 | − | 12.9907i | −0.644773 | − | 0.468455i | 0.216714 | − | 0.976235i | \(-0.430466\pi\) |
−0.861487 | + | 0.507780i | \(0.830466\pi\) | |||||||
\(770\) | −15.2182 | − | 59.4028i | −0.548424 | − | 2.14073i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.18507 | − | 1.58754i | 0.0786423 | − | 0.0571370i | ||||
\(773\) | −1.51429 | − | 4.66049i | −0.0544651 | − | 0.167626i | 0.920124 | − | 0.391628i | \(-0.128088\pi\) |
−0.974589 | + | 0.224002i | \(0.928088\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.93343 | + | 36.5589i | 0.249056 | + | 1.31324i | ||||
\(776\) | 50.8215 | 1.82439 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −45.6139 | + | 33.1405i | −1.63534 | + | 1.18814i | ||||
\(779\) | −13.5097 | + | 9.81537i | −0.484035 | + | 0.351672i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.88681 | − | 1.37085i | −0.0675153 | − | 0.0490528i | ||||
\(782\) | 19.0851 | 0.682481 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.57648 | − | 17.1627i | 0.199160 | − | 0.612952i | ||||
\(785\) | 18.0110 | − | 45.4194i | 0.642839 | − | 1.62109i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.15411 | + | 3.55198i | −0.0411395 | + | 0.126614i | −0.969517 | − | 0.245024i | \(-0.921204\pi\) |
0.928377 | + | 0.371639i | \(0.121204\pi\) | |||||||
\(788\) | 28.4728 | − | 87.6303i | 1.01430 | − | 3.12170i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 61.4496 | − | 38.9510i | 2.18628 | − | 1.38581i | ||||
\(791\) | 5.86182 | − | 18.0408i | 0.208422 | − | 0.641458i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.3266 | −0.899375 | ||||||||
\(794\) | 27.5100 | + | 19.9872i | 0.976294 | + | 0.709319i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −32.6193 | + | 23.6993i | −1.15616 | + | 0.839998i | ||||
\(797\) | 2.70538 | − | 1.96557i | 0.0958295 | − | 0.0696242i | −0.538839 | − | 0.842409i | \(-0.681137\pi\) |
0.634668 | + | 0.772785i | \(0.281137\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.7355 | −1.26423 | ||||||||
\(800\) | −1.58201 | − | 1.48880i | −0.0559326 | − | 0.0526370i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.7994 | − | 64.0140i | −0.734453 | − | 2.26041i | ||||
\(803\) | 4.96901 | − | 3.61019i | 0.175352 | − | 0.127401i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.8817 | − | 0.753920i | −0.418775 | − | 0.0265722i | ||||
\(806\) | −47.4866 | − | 34.5010i | −1.67264 | − | 1.21525i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.79957 | − | 4.94017i | −0.239208 | − | 0.173795i | ||||
\(809\) | −10.5954 | + | 32.6094i | −0.372516 | + | 1.14649i | 0.572624 | + | 0.819818i | \(0.305926\pi\) |
−0.945140 | + | 0.326667i | \(0.894074\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.07152 | − | 3.29778i | −0.0376260 | − | 0.115801i | 0.930479 | − | 0.366344i | \(-0.119391\pi\) |
−0.968105 | + | 0.250543i | \(0.919391\pi\) | |||||||
\(812\) | −13.1274 | + | 40.4020i | −0.460682 | + | 1.41783i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.1845 | + | 43.6554i | 0.497167 | + | 1.53012i | ||||
\(815\) | 17.4521 | + | 14.4534i | 0.611320 | + | 0.506279i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.30926 | + | 4.58394i | 0.220733 | + | 0.160372i | ||||
\(818\) | −32.2422 | −1.12732 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 47.8328 | + | 3.03510i | 1.67040 | + | 0.105990i | ||||
\(821\) | −11.8771 | + | 8.62922i | −0.414514 | + | 0.301162i | −0.775427 | − | 0.631438i | \(-0.782465\pi\) |
0.360913 | + | 0.932600i | \(0.382465\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.44912 | − | 19.8483i | −0.224802 | − | 0.691870i | −0.998312 | − | 0.0580851i | \(-0.981501\pi\) |
0.773510 | − | 0.633785i | \(-0.218499\pi\) | |||||||
\(824\) | −75.9223 | −2.64488 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.5285 | −0.505512 | ||||||||
\(827\) | −13.9946 | − | 43.0710i | −0.486641 | − | 1.49773i | −0.829590 | − | 0.558372i | \(-0.811426\pi\) |
0.342950 | − | 0.939354i | \(-0.388574\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.81291 | − | 5.67641i | 0.271354 | − | 0.197150i | −0.443784 | − | 0.896134i | \(-0.646364\pi\) |
0.715137 | + | 0.698984i | \(0.246364\pi\) | |||||||
\(830\) | 16.6315 | + | 13.7738i | 0.577287 | + | 0.478094i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 27.5502 | 0.955131 | ||||||||
\(833\) | −19.7690 | − | 14.3630i | −0.684955 | − | 0.497649i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.85386 | − | 1.80897i | 0.0987620 | − | 0.0626022i | ||||
\(836\) | −12.3009 | − | 37.8583i | −0.425436 | − | 1.30936i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.67198 | + | 20.5342i | −0.230480 | + | 0.709344i | ||||
\(839\) | 7.77848 | + | 23.9397i | 0.268543 | + | 0.826490i | 0.990856 | + | 0.134924i | \(0.0430789\pi\) |
−0.722313 | + | 0.691566i | \(0.756921\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.94919 | + | 18.3097i | −0.205144 | + | 0.631370i | ||||
\(842\) | −73.9874 | − | 53.7550i | −2.54977 | − | 1.85252i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −58.4159 | − | 42.4416i | −2.01076 | − | 1.46090i | ||||
\(845\) | −4.82340 | + | 3.05740i | −0.165930 | + | 0.105178i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.917269 | + | 0.666435i | −0.0315177 | + | 0.0228990i | ||||
\(848\) | 11.7070 | + | 36.0305i | 0.402021 | + | 1.23729i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 54.0633 | − | 29.6462i | 1.85436 | − | 1.01686i | ||||
\(851\) | 8.91196 | 0.305498 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.59571 | − | 1.88589i | 0.0888753 | − | 0.0645717i | −0.542460 | − | 0.840081i | \(-0.682507\pi\) |
0.631336 | + | 0.775510i | \(0.282507\pi\) | |||||||
\(854\) | −53.2222 | + | 38.6682i | −1.82123 | + | 1.32320i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 60.9069 | + | 44.2514i | 2.08175 | + | 1.51248i | ||||
\(857\) | −19.4569 | −0.664634 | −0.332317 | − | 0.943168i | \(-0.607830\pi\) | ||||
−0.332317 | + | 0.943168i | \(0.607830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.20173 | − | 16.0093i | 0.177481 | − | 0.546230i | −0.822257 | − | 0.569116i | \(-0.807286\pi\) |
0.999738 | + | 0.0228862i | \(0.00728553\pi\) | |||||||
\(860\) | −5.55498 | − | 21.6834i | −0.189423 | − | 0.739398i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.0772 | + | 61.7914i | −0.683833 | + | 2.10462i | ||||
\(863\) | −1.17803 | + | 3.62560i | −0.0401006 | + | 0.123417i | −0.969103 | − | 0.246657i | \(-0.920668\pi\) |
0.929002 | + | 0.370074i | \(0.120668\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.9192 | − | 1.96189i | −1.05129 | − | 0.0667063i | ||||
\(866\) | −26.3910 | + | 81.2231i | −0.896802 | + | 2.76007i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −101.259 | −3.43697 | ||||||||
\(869\) | 35.2358 | + | 25.6003i | 1.19529 | + | 0.868431i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.83497 | + | 3.51281i | −0.163827 | + | 0.119027i | ||||
\(872\) | −38.2863 | + | 27.8166i | −1.29654 | + | 0.941990i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.6367 | −0.393619 | ||||||||
\(875\) | −34.8291 | + | 16.3211i | −1.17744 | + | 0.551753i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.95569 | − | 24.4851i | −0.268644 | − | 0.826803i | −0.990831 | − | 0.135105i | \(-0.956863\pi\) |
0.722187 | − | 0.691698i | \(-0.243137\pi\) | |||||||
\(878\) | 39.5911 | − | 28.7646i | 1.33613 | − | 0.970759i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.0482 | + | 25.3393i | −0.338726 | + | 0.854188i | ||||
\(881\) | 36.6110 | + | 26.5995i | 1.23346 | + | 0.896159i | 0.997144 | − | 0.0755181i | \(-0.0240611\pi\) |
0.236313 | + | 0.971677i | \(0.424061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.9186 | − | 26.0964i | −1.20876 | − | 0.878212i | −0.213639 | − | 0.976913i | \(-0.568531\pi\) |
−0.995117 | + | 0.0987003i | \(0.968531\pi\) | |||||||
\(884\) | −19.9611 | + | 61.4340i | −0.671365 | + | 2.06625i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.12850 | + | 9.62853i | 0.105104 | + | 0.323477i | ||||
\(887\) | 12.0495 | − | 37.0844i | 0.404581 | − | 1.24517i | −0.516664 | − | 0.856189i | \(-0.672826\pi\) |
0.921245 | − | 0.388984i | \(-0.127174\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.05470 | + | 3.24602i | 0.0353734 | + | 0.108868i | ||||
\(890\) | −11.5565 | − | 45.1097i | −0.387374 | − | 1.51208i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −55.1119 | − | 40.0411i | −1.84528 | − | 1.34068i | ||||
\(893\) | 21.7890 | 0.729142 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.02188 | + | 31.3127i | 0.268142 | + | 1.04667i | ||||
\(896\) | 55.4764 | − | 40.3059i | 1.85334 | − | 1.34653i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.29517 | − | 19.3745i | −0.210072 | − | 0.646537i | ||||
\(899\) | 23.2356 | 0.774952 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51.2995 | 1.70903 | ||||||||
\(902\) | 13.3500 | + | 41.0872i | 0.444508 | + | 1.36805i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.2812 | + | 15.4617i | −0.707803 | + | 0.514249i | ||||
\(905\) | 32.4649 | − | 20.5785i | 1.07917 | − | 0.684052i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.0201 | 0.365915 | 0.182958 | − | 0.983121i | \(-0.441433\pi\) | ||||
0.182958 | + | 0.983121i | \(0.441433\pi\) | |||||||
\(908\) | −13.8506 | − | 10.0630i | −0.459648 | − | 0.333954i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 22.3654 | − | 56.4004i | 0.741407 | − | 1.86966i | ||||
\(911\) | 16.3540 | + | 50.3325i | 0.541833 | + | 1.66759i | 0.728404 | + | 0.685148i | \(0.240263\pi\) |
−0.186571 | + | 0.982441i | \(0.559737\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.99477 | + | 12.2946i | −0.132207 | + | 0.406893i | ||||
\(914\) | −15.5172 | − | 47.7570i | −0.513263 | − | 1.57966i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.8277 | − | 76.4119i | 0.820331 | − | 2.52472i | ||||
\(917\) | 35.1010 | + | 25.5023i | 1.15914 | + | 0.842162i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.5129 | + | 27.9812i | 1.27042 | + | 0.923016i | 0.999219 | − | 0.0395064i | \(-0.0125786\pi\) |
0.271203 | + | 0.962522i | \(0.412579\pi\) | |||||||
\(920\) | 12.7153 | + | 10.5305i | 0.419212 | + | 0.347181i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −56.6388 | + | 41.1505i | −1.86530 | + | 1.35522i | ||||
\(923\) | −0.713080 | − | 2.19463i | −0.0234713 | − | 0.0722372i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.2454 | − | 13.8436i | 0.830063 | − | 0.455175i | ||||
\(926\) | −97.8059 | −3.21410 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.09745 | + | 0.797343i | −0.0360255 | + | 0.0261741i | ||||
\(929\) | 17.5465 | − | 12.7483i | 0.575682 | − | 0.418258i | −0.261483 | − | 0.965208i | \(-0.584211\pi\) |
0.837165 | + | 0.546951i | \(0.184211\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0538 | + | 8.75757i | 0.395046 | + | 0.287018i | ||||
\(932\) | 1.34848 | 0.0441708 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.13972 | + | 18.8961i | −0.200898 | + | 0.618300i | ||||
\(935\) | 28.4279 | + | 23.5433i | 0.929692 | + | 0.769947i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.680112 | − | 2.09317i | 0.0222183 | − | 0.0683809i | −0.939333 | − | 0.343008i | \(-0.888554\pi\) |
0.961551 | + | 0.274627i | \(0.0885543\pi\) | |||||||
\(938\) | −4.79708 | + | 14.7639i | −0.156630 | + | 0.482058i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −48.1655 | − | 39.8894i | −1.57098 | − | 1.30105i | ||||
\(941\) | 5.18833 | − | 15.9680i | 0.169135 | − | 0.520543i | −0.830183 | − | 0.557492i | \(-0.811764\pi\) |
0.999317 | + | 0.0369489i | \(0.0117639\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.38767 | 0.273140 | ||||||||
\(944\) | 5.22489 | + | 3.79611i | 0.170056 | + | 0.123553i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.3226 | − | 11.8591i | 0.530695 | − | 0.385572i | ||||
\(947\) | 29.6207 | − | 21.5207i | 0.962544 | − | 0.699329i | 0.00880418 | − | 0.999961i | \(-0.497198\pi\) |
0.953740 | + | 0.300632i | \(0.0971975\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.07711 | 0.197271 | ||||||||
\(950\) | −32.9641 | + | 18.0762i | −1.06950 | + | 0.586470i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 25.6295 | + | 78.8796i | 0.830658 | + | 2.55650i | ||||
\(953\) | 35.5383 | − | 25.8201i | 1.15120 | − | 0.836394i | 0.162558 | − | 0.986699i | \(-0.448026\pi\) |
0.988640 | + | 0.150305i | \(0.0480256\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.1557 | − | 15.0360i | −0.587503 | − | 0.486555i | ||||
\(956\) | −22.9251 | − | 16.6561i | −0.741450 | − | 0.538695i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 55.4010 | + | 40.2512i | 1.78993 | + | 1.30046i | ||||
\(959\) | 8.76068 | − | 26.9626i | 0.282897 | − | 0.870668i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.53541 | + | 23.1916i | 0.243078 | + | 0.748116i | ||||
\(962\) | −14.0346 | + | 43.1940i | −0.452493 | + | 1.39263i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.3530 | − | 47.2517i | −0.494487 | − | 1.52188i | ||||
\(965\) | 0.562897 | − | 1.41950i | 0.0181203 | − | 0.0456952i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.8059 | − | 14.3899i | −0.636916 | − | 0.462747i | 0.221873 | − | 0.975076i | \(-0.428783\pi\) |
−0.858789 | + | 0.512329i | \(0.828783\pi\) | |||||||
\(968\) | 1.57227 | 0.0505348 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 49.0962 | − | 31.1206i | 1.57639 | − | 0.999221i | ||||
\(971\) | −15.8773 | + | 11.5355i | −0.509526 | + | 0.370192i | −0.812644 | − | 0.582761i | \(-0.801972\pi\) |
0.303118 | + | 0.952953i | \(0.401972\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.57257 | − | 26.3837i | −0.274824 | − | 0.845822i | ||||
\(974\) | 37.1344 | 1.18986 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.2438 | 0.936070 | ||||||||
\(977\) | −9.43236 | − | 29.0298i | −0.301768 | − | 0.928746i | −0.980864 | − | 0.194696i | \(-0.937628\pi\) |
0.679096 | − | 0.734050i | \(-0.262372\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.5526 | − | 16.3854i | 0.720785 | − | 0.523681i | ||||
\(980\) | −10.6127 | − | 41.4259i | −0.339011 | − | 1.32330i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 20.2356 | 0.645743 | ||||||||
\(983\) | 8.38590 | + | 6.09271i | 0.267469 | + | 0.194327i | 0.713433 | − | 0.700723i | \(-0.247139\pi\) |
−0.445964 | + | 0.895051i | \(0.647139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.9283 | − | 50.4644i | −0.411929 | − | 1.60793i | ||||
\(986\) | −11.8977 | − | 36.6173i | −0.378899 | − | 1.16613i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.1709 | − | 37.4582i | 0.387208 | − | 1.19170i | ||||
\(989\) | −1.21048 | − | 3.72546i | −0.0384909 | − | 0.118463i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.12376 | + | 9.61395i | −0.0992295 | + | 0.305397i | −0.988333 | − | 0.152309i | \(-0.951329\pi\) |
0.889103 | + | 0.457707i | \(0.151329\pi\) | |||||||
\(992\) | −2.61591 | − | 1.90057i | −0.0830552 | − | 0.0603431i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.84921 | − | 3.52316i | −0.153808 | − | 0.111748i | ||||
\(995\) | −8.40308 | + | 21.1906i | −0.266395 | + | 0.671787i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.2838 | + | 12.5574i | −0.547382 | + | 0.397697i | −0.826819 | − | 0.562467i | \(-0.809852\pi\) |
0.279437 | + | 0.960164i | \(0.409852\pi\) | |||||||
\(998\) | 18.4002 | + | 56.6300i | 0.582448 | + | 1.79259i | ||||
\(999\) | 0 | 0 |
(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 | 225.2.h.d.181.1 | 12 | ||
3.2 | odd | 2 | 75.2.g.c.31.3 | ✓ | 12 | ||
15.2 | even | 4 | 375.2.i.d.349.2 | 24 | |||
15.8 | even | 4 | 375.2.i.d.349.5 | 24 | |||
15.14 | odd | 2 | 375.2.g.c.151.1 | 12 | |||
25.11 | even | 5 | 5625.2.a.p.1.1 | 6 | |||
25.14 | even | 10 | 5625.2.a.q.1.6 | 6 | |||
25.21 | even | 5 | inner | 225.2.h.d.46.1 | 12 | ||
75.2 | even | 20 | 1875.2.b.f.1249.11 | 12 | |||
75.11 | odd | 10 | 1875.2.a.j.1.6 | 6 | |||
75.14 | odd | 10 | 1875.2.a.k.1.1 | 6 | |||
75.23 | even | 20 | 1875.2.b.f.1249.2 | 12 | |||
75.29 | odd | 10 | 375.2.g.c.226.1 | 12 | |||
75.47 | even | 20 | 375.2.i.d.274.5 | 24 | |||
75.53 | even | 20 | 375.2.i.d.274.2 | 24 | |||
75.71 | odd | 10 | 75.2.g.c.46.3 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.31.3 | ✓ | 12 | 3.2 | odd | 2 | ||
75.2.g.c.46.3 | yes | 12 | 75.71 | odd | 10 | ||
225.2.h.d.46.1 | 12 | 25.21 | even | 5 | inner | ||
225.2.h.d.181.1 | 12 | 1.1 | even | 1 | trivial | ||
375.2.g.c.151.1 | 12 | 15.14 | odd | 2 | |||
375.2.g.c.226.1 | 12 | 75.29 | odd | 10 | |||
375.2.i.d.274.2 | 24 | 75.53 | even | 20 | |||
375.2.i.d.274.5 | 24 | 75.47 | even | 20 | |||
375.2.i.d.349.2 | 24 | 15.2 | even | 4 | |||
375.2.i.d.349.5 | 24 | 15.8 | even | 4 | |||
1875.2.a.j.1.6 | 6 | 75.11 | odd | 10 | |||
1875.2.a.k.1.1 | 6 | 75.14 | odd | 10 | |||
1875.2.b.f.1249.2 | 12 | 75.23 | even | 20 | |||
1875.2.b.f.1249.11 | 12 | 75.2 | even | 20 | |||
5625.2.a.p.1.1 | 6 | 25.11 | even | 5 | |||
5625.2.a.q.1.6 | 6 | 25.14 | even | 10 |