Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,3,Mod(7,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.d (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.17166513675\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 37x^{10} + 483x^{8} + 2718x^{6} + 6923x^{4} + 7253x^{2} + 1849 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 7.4 | ||
Root | \(1.51156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.7 |
Dual form | 43.3.d.a.37.3 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.51156i | 0.755782i | 0.925850 | + | 0.377891i | \(0.123351\pi\) | ||||
−0.925850 | + | 0.377891i | \(0.876649\pi\) | |||||||
\(3\) | −3.66976 | + | 2.11873i | −1.22325 | + | 0.706245i | −0.965610 | − | 0.259996i | \(-0.916279\pi\) |
−0.257642 | + | 0.966240i | \(0.582946\pi\) | |||||||
\(4\) | 1.71518 | 0.428794 | ||||||||
\(5\) | −4.51092 | + | 2.60438i | −0.902184 | + | 0.520876i | −0.877908 | − | 0.478829i | \(-0.841061\pi\) |
−0.0242756 | + | 0.999705i | \(0.507728\pi\) | |||||||
\(6\) | −3.20260 | − | 5.54707i | −0.533767 | − | 0.924512i | ||||
\(7\) | 1.23619 | + | 0.713712i | 0.176598 | + | 0.101959i | 0.585693 | − | 0.810533i | \(-0.300822\pi\) |
−0.409095 | + | 0.912492i | \(0.634156\pi\) | |||||||
\(8\) | 8.63885i | 1.07986i | ||||||||
\(9\) | 4.47807 | − | 7.75625i | 0.497564 | − | 0.861805i | ||||
\(10\) | −3.93669 | − | 6.81854i | −0.393669 | − | 0.681854i | ||||
\(11\) | 19.5852 | 1.78048 | 0.890238 | − | 0.455496i | \(-0.150538\pi\) | ||||
0.890238 | + | 0.455496i | \(0.150538\pi\) | |||||||
\(12\) | −6.29427 | + | 3.63400i | −0.524523 | + | 0.302833i | ||||
\(13\) | 4.99698 | − | 8.65502i | 0.384383 | − | 0.665771i | −0.607300 | − | 0.794472i | \(-0.707748\pi\) |
0.991683 | + | 0.128701i | \(0.0410808\pi\) | |||||||
\(14\) | −1.07882 | + | 1.86857i | −0.0770587 | + | 0.133469i | ||||
\(15\) | 11.0360 | − | 19.1149i | 0.735732 | − | 1.27433i | ||||
\(16\) | −6.19747 | −0.387342 | ||||||||
\(17\) | −12.5438 | + | 21.7264i | −0.737868 | + | 1.27802i | 0.215586 | + | 0.976485i | \(0.430834\pi\) |
−0.953454 | + | 0.301540i | \(0.902499\pi\) | |||||||
\(18\) | 11.7241 | + | 6.76889i | 0.651337 | + | 0.376049i | ||||
\(19\) | 9.29850 | − | 5.36849i | 0.489395 | − | 0.282552i | −0.234929 | − | 0.972013i | \(-0.575486\pi\) |
0.724323 | + | 0.689460i | \(0.242152\pi\) | |||||||
\(20\) | −7.73701 | + | 4.46697i | −0.386851 | + | 0.223348i | ||||
\(21\) | −6.04866 | −0.288032 | ||||||||
\(22\) | 29.6043i | 1.34565i | ||||||||
\(23\) | −16.7391 | − | 28.9930i | −0.727788 | − | 1.26057i | −0.957816 | − | 0.287381i | \(-0.907215\pi\) |
0.230029 | − | 0.973184i | \(-0.426118\pi\) | |||||||
\(24\) | −18.3034 | − | 31.7025i | −0.762643 | − | 1.32094i | ||||
\(25\) | 1.06559 | − | 1.84565i | 0.0426235 | − | 0.0738261i | ||||
\(26\) | 13.0826 | + | 7.55325i | 0.503178 | + | 0.290510i | ||||
\(27\) | − | 0.185841i | − | 0.00688300i | ||||||
\(28\) | 2.12027 | + | 1.22414i | 0.0757241 | + | 0.0437193i | ||||
\(29\) | 13.9164 | + | 8.03462i | 0.479875 | + | 0.277056i | 0.720364 | − | 0.693596i | \(-0.243975\pi\) |
−0.240490 | + | 0.970652i | \(0.577308\pi\) | |||||||
\(30\) | 28.8934 | + | 16.6816i | 0.963112 | + | 0.556053i | ||||
\(31\) | 3.71424 | + | 6.43325i | 0.119814 | + | 0.207524i | 0.919694 | − | 0.392636i | \(-0.128437\pi\) |
−0.799880 | + | 0.600160i | \(0.795103\pi\) | |||||||
\(32\) | 25.1875i | 0.787110i | ||||||||
\(33\) | −71.8730 | + | 41.4959i | −2.17797 | + | 1.25745i | ||||
\(34\) | −32.8409 | − | 18.9607i | −0.965908 | − | 0.557667i | ||||
\(35\) | −7.43511 | −0.212432 | ||||||||
\(36\) | 7.68068 | − | 13.3033i | 0.213352 | − | 0.369537i | ||||
\(37\) | 18.9142 | − | 10.9201i | 0.511194 | − | 0.295138i | −0.222130 | − | 0.975017i | \(-0.571301\pi\) |
0.733324 | + | 0.679879i | \(0.237968\pi\) | |||||||
\(38\) | 8.11482 | + | 14.0553i | 0.213548 | + | 0.369876i | ||||
\(39\) | 42.3491i | 1.08587i | ||||||||
\(40\) | −22.4989 | − | 38.9692i | −0.562471 | − | 0.974229i | ||||
\(41\) | −22.3015 | −0.543940 | −0.271970 | − | 0.962306i | \(-0.587675\pi\) | ||||
−0.271970 | + | 0.962306i | \(0.587675\pi\) | |||||||
\(42\) | − | 9.14294i | − | 0.217689i | ||||||
\(43\) | 35.8442 | − | 23.7528i | 0.833586 | − | 0.552390i | ||||
\(44\) | 33.5921 | 0.763457 | ||||||||
\(45\) | 46.6504i | 1.03668i | ||||||||
\(46\) | 43.8248 | − | 25.3022i | 0.952712 | − | 0.550049i | ||||
\(47\) | 78.3686 | 1.66742 | 0.833709 | − | 0.552204i | \(-0.186213\pi\) | ||||
0.833709 | + | 0.552204i | \(0.186213\pi\) | |||||||
\(48\) | 22.7432 | − | 13.1308i | 0.473817 | − | 0.273558i | ||||
\(49\) | −23.4812 | − | 40.6707i | −0.479209 | − | 0.830014i | ||||
\(50\) | 2.78982 | + | 1.61070i | 0.0557964 | + | 0.0322141i | ||||
\(51\) | − | 106.308i | − | 2.08446i | ||||||
\(52\) | 8.57070 | − | 14.8449i | 0.164821 | − | 0.285478i | ||||
\(53\) | −13.1640 | − | 22.8006i | −0.248376 | − | 0.430201i | 0.714699 | − | 0.699432i | \(-0.246564\pi\) |
−0.963076 | + | 0.269231i | \(0.913230\pi\) | |||||||
\(54\) | 0.280911 | 0.00520205 | ||||||||
\(55\) | −88.3474 | + | 51.0074i | −1.60632 | + | 0.927407i | ||||
\(56\) | −6.16565 | + | 10.6792i | −0.110101 | + | 0.190700i | ||||
\(57\) | −22.7488 | + | 39.4021i | −0.399102 | + | 0.691265i | ||||
\(58\) | −12.1448 | + | 21.0355i | −0.209394 | + | 0.362680i | ||||
\(59\) | 39.1712 | 0.663919 | 0.331959 | − | 0.943294i | \(-0.392290\pi\) | ||||
0.331959 | + | 0.943294i | \(0.392290\pi\) | |||||||
\(60\) | 18.9286 | − | 32.7854i | 0.315477 | − | 0.546423i | ||||
\(61\) | −27.5478 | − | 15.9047i | −0.451603 | − | 0.260733i | 0.256904 | − | 0.966437i | \(-0.417298\pi\) |
−0.708507 | + | 0.705704i | \(0.750631\pi\) | |||||||
\(62\) | −9.72426 | + | 5.61430i | −0.156843 | + | 0.0905533i | ||||
\(63\) | 11.0715 | − | 6.39211i | 0.175737 | − | 0.101462i | ||||
\(64\) | −62.8625 | −0.982226 | ||||||||
\(65\) | 52.0561i | 0.800864i | ||||||||
\(66\) | −62.7237 | − | 108.641i | −0.950359 | − | 1.64607i | ||||
\(67\) | 61.2076 | + | 106.015i | 0.913546 | + | 1.58231i | 0.809016 | + | 0.587787i | \(0.200001\pi\) |
0.104530 | + | 0.994522i | \(0.466666\pi\) | |||||||
\(68\) | −21.5147 | + | 37.2646i | −0.316393 | + | 0.548009i | ||||
\(69\) | 122.857 | + | 70.9315i | 1.78054 | + | 1.02799i | ||||
\(70\) | − | 11.2386i | − | 0.160552i | ||||||
\(71\) | −110.307 | − | 63.6857i | −1.55362 | − | 0.896982i | −0.997843 | − | 0.0656495i | \(-0.979088\pi\) |
−0.555776 | − | 0.831332i | \(-0.687579\pi\) | |||||||
\(72\) | 67.0051 | + | 38.6854i | 0.930626 | + | 0.537297i | ||||
\(73\) | 14.9276 | + | 8.61845i | 0.204488 | + | 0.118061i | 0.598747 | − | 0.800938i | \(-0.295666\pi\) |
−0.394259 | + | 0.918999i | \(0.628999\pi\) | |||||||
\(74\) | 16.5064 | + | 28.5900i | 0.223060 | + | 0.386351i | ||||
\(75\) | 9.03079i | 0.120411i | ||||||||
\(76\) | 15.9486 | − | 9.20790i | 0.209849 | − | 0.121157i | ||||
\(77\) | 24.2110 | + | 13.9782i | 0.314428 | + | 0.181535i | ||||
\(78\) | −64.0134 | −0.820684 | ||||||||
\(79\) | −18.2494 | + | 31.6090i | −0.231006 | + | 0.400113i | −0.958104 | − | 0.286419i | \(-0.907535\pi\) |
0.727099 | + | 0.686533i | \(0.240868\pi\) | |||||||
\(80\) | 27.9563 | − | 16.1406i | 0.349454 | − | 0.201757i | ||||
\(81\) | 40.6964 | + | 70.4882i | 0.502425 | + | 0.870225i | ||||
\(82\) | − | 33.7102i | − | 0.411100i | ||||||
\(83\) | −42.8675 | − | 74.2487i | −0.516476 | − | 0.894562i | −0.999817 | − | 0.0191303i | \(-0.993910\pi\) |
0.483341 | − | 0.875432i | \(-0.339423\pi\) | |||||||
\(84\) | −10.3745 | −0.123506 | ||||||||
\(85\) | − | 130.675i | − | 1.53735i | ||||||
\(86\) | 35.9038 | + | 54.1808i | 0.417487 | + | 0.630009i | ||||
\(87\) | −68.0929 | −0.782677 | ||||||||
\(88\) | 169.194i | 1.92266i | ||||||||
\(89\) | −11.1803 | + | 6.45493i | −0.125621 | + | 0.0725273i | −0.561494 | − | 0.827481i | \(-0.689773\pi\) |
0.435873 | + | 0.900008i | \(0.356440\pi\) | |||||||
\(90\) | −70.5150 | −0.783501 | ||||||||
\(91\) | 12.3544 | − | 7.13281i | 0.135763 | − | 0.0783825i | ||||
\(92\) | −28.7105 | − | 49.7281i | −0.312071 | − | 0.540523i | ||||
\(93\) | −27.2607 | − | 15.7390i | −0.293126 | − | 0.169236i | ||||
\(94\) | 118.459i | 1.26020i | ||||||||
\(95\) | −27.9632 | + | 48.4336i | −0.294349 | + | 0.509828i | ||||
\(96\) | −53.3657 | − | 92.4321i | −0.555893 | − | 0.962834i | ||||
\(97\) | −113.142 | −1.16642 | −0.583208 | − | 0.812323i | \(-0.698203\pi\) | ||||
−0.583208 | + | 0.812323i | \(0.698203\pi\) | |||||||
\(98\) | 61.4763 | − | 35.4934i | 0.627310 | − | 0.362177i | ||||
\(99\) | 87.7041 | − | 151.908i | 0.885900 | − | 1.53442i | ||||
\(100\) | 1.82767 | − | 3.16562i | 0.0182767 | − | 0.0316562i | ||||
\(101\) | 34.0992 | − | 59.0615i | 0.337616 | − | 0.584768i | −0.646368 | − | 0.763026i | \(-0.723713\pi\) |
0.983984 | + | 0.178258i | \(0.0570462\pi\) | |||||||
\(102\) | 160.691 | 1.57540 | ||||||||
\(103\) | 31.5613 | − | 54.6657i | 0.306420 | − | 0.530735i | −0.671156 | − | 0.741316i | \(-0.734202\pi\) |
0.977576 | + | 0.210581i | \(0.0675355\pi\) | |||||||
\(104\) | 74.7695 | + | 43.1682i | 0.718937 | + | 0.415079i | ||||
\(105\) | 27.2850 | − | 15.7530i | 0.259857 | − | 0.150029i | ||||
\(106\) | 34.4646 | − | 19.8982i | 0.325138 | − | 0.187718i | ||||
\(107\) | −109.460 | −1.02299 | −0.511497 | − | 0.859285i | \(-0.670909\pi\) | ||||
−0.511497 | + | 0.859285i | \(0.670909\pi\) | |||||||
\(108\) | − | 0.318750i | − | 0.00295139i | ||||||
\(109\) | 17.3755 | + | 30.0953i | 0.159408 | + | 0.276103i | 0.934655 | − | 0.355555i | \(-0.115708\pi\) |
−0.775247 | + | 0.631658i | \(0.782375\pi\) | |||||||
\(110\) | −77.1009 | − | 133.543i | −0.700918 | − | 1.21402i | ||||
\(111\) | −46.2736 | + | 80.1483i | −0.416879 | + | 0.722056i | ||||
\(112\) | −7.66123 | − | 4.42321i | −0.0684038 | − | 0.0394930i | ||||
\(113\) | − | 25.0080i | − | 0.221310i | −0.993859 | − | 0.110655i | \(-0.964705\pi\) | ||
0.993859 | − | 0.110655i | \(-0.0352949\pi\) | |||||||
\(114\) | −59.5588 | − | 34.3863i | −0.522445 | − | 0.301634i | ||||
\(115\) | 151.018 | + | 87.1900i | 1.31320 | + | 0.758174i | ||||
\(116\) | 23.8690 | + | 13.7808i | 0.205767 | + | 0.118800i | ||||
\(117\) | −44.7537 | − | 77.5156i | −0.382510 | − | 0.662527i | ||||
\(118\) | 59.2098i | 0.501778i | ||||||||
\(119\) | −31.0128 | + | 17.9053i | −0.260612 | + | 0.150464i | ||||
\(120\) | 165.131 | + | 95.3382i | 1.37609 | + | 0.794485i | ||||
\(121\) | 262.582 | 2.17010 | ||||||||
\(122\) | 24.0410 | − | 41.6402i | 0.197057 | − | 0.341313i | ||||
\(123\) | 81.8412 | − | 47.2510i | 0.665375 | − | 0.384155i | ||||
\(124\) | 6.37056 | + | 11.0341i | 0.0513755 | + | 0.0889850i | ||||
\(125\) | − | 119.118i | − | 0.952946i | ||||||
\(126\) | 9.66208 | + | 16.7352i | 0.0766831 | + | 0.132819i | ||||
\(127\) | −27.5460 | −0.216897 | −0.108449 | − | 0.994102i | \(-0.534588\pi\) | ||||
−0.108449 | + | 0.994102i | \(0.534588\pi\) | |||||||
\(128\) | 5.72951i | 0.0447618i | ||||||||
\(129\) | −81.2135 | + | 163.111i | −0.629562 | + | 1.26443i | ||||
\(130\) | −78.6862 | −0.605278 | ||||||||
\(131\) | − | 30.8157i | − | 0.235234i | −0.993059 | − | 0.117617i | \(-0.962474\pi\) | ||
0.993059 | − | 0.117617i | \(-0.0375256\pi\) | |||||||
\(132\) | −123.275 | + | 71.1728i | −0.933900 | + | 0.539188i | ||||
\(133\) | 15.3262 | 0.115235 | ||||||||
\(134\) | −160.248 | + | 92.5192i | −1.19588 | + | 0.690442i | ||||
\(135\) | 0.484001 | + | 0.838314i | 0.00358519 | + | 0.00620973i | ||||
\(136\) | −187.691 | − | 108.364i | −1.38008 | − | 0.796792i | ||||
\(137\) | − | 171.866i | − | 1.25450i | −0.778819 | − | 0.627249i | \(-0.784181\pi\) | ||
0.778819 | − | 0.627249i | \(-0.215819\pi\) | |||||||
\(138\) | −107.217 | + | 185.706i | −0.776938 | + | 1.34570i | ||||
\(139\) | 30.8690 | + | 53.4666i | 0.222079 | + | 0.384652i | 0.955439 | − | 0.295188i | \(-0.0953824\pi\) |
−0.733360 | + | 0.679840i | \(0.762049\pi\) | |||||||
\(140\) | −12.7525 | −0.0910894 | ||||||||
\(141\) | −287.594 | + | 166.042i | −2.03967 | + | 1.17761i | ||||
\(142\) | 96.2650 | − | 166.736i | 0.677923 | − | 1.17420i | ||||
\(143\) | 97.8671 | − | 169.511i | 0.684385 | − | 1.18539i | ||||
\(144\) | −27.7527 | + | 48.0691i | −0.192727 | + | 0.333814i | ||||
\(145\) | −83.7008 | −0.577247 | ||||||||
\(146\) | −13.0273 | + | 22.5640i | −0.0892283 | + | 0.154548i | ||||
\(147\) | 172.341 | + | 99.5010i | 1.17239 | + | 0.676877i | ||||
\(148\) | 32.4411 | − | 18.7299i | 0.219197 | − | 0.126553i | ||||
\(149\) | −180.832 | + | 104.403i | −1.21364 | + | 0.700694i | −0.963550 | − | 0.267529i | \(-0.913793\pi\) |
−0.250088 | + | 0.968223i | \(0.580459\pi\) | |||||||
\(150\) | −13.6506 | −0.0910041 | ||||||||
\(151\) | − | 154.264i | − | 1.02162i | −0.859694 | − | 0.510810i | \(-0.829346\pi\) | ||
0.859694 | − | 0.510810i | \(-0.170654\pi\) | |||||||
\(152\) | 46.3776 | + | 80.3283i | 0.305116 | + | 0.528476i | ||||
\(153\) | 112.344 | + | 194.585i | 0.734272 | + | 1.27180i | ||||
\(154\) | −21.1290 | + | 36.5964i | −0.137201 | + | 0.237639i | ||||
\(155\) | −33.5092 | − | 19.3466i | −0.216189 | − | 0.124817i | ||||
\(156\) | 72.6361i | 0.465616i | ||||||||
\(157\) | 137.667 | + | 79.4818i | 0.876857 | + | 0.506254i | 0.869621 | − | 0.493720i | \(-0.164363\pi\) |
0.00723635 | + | 0.999974i | \(0.497697\pi\) | |||||||
\(158\) | −47.7790 | − | 27.5852i | −0.302399 | − | 0.174590i | ||||
\(159\) | 96.6170 | + | 55.7818i | 0.607654 | + | 0.350829i | ||||
\(160\) | −65.5979 | − | 113.619i | −0.409987 | − | 0.710118i | ||||
\(161\) | − | 47.7876i | − | 0.296818i | ||||||
\(162\) | −106.547 | + | 61.5152i | −0.657700 | + | 0.379723i | ||||
\(163\) | −34.1370 | − | 19.7090i | −0.209429 | − | 0.120914i | 0.391617 | − | 0.920128i | \(-0.371916\pi\) |
−0.601046 | + | 0.799214i | \(0.705249\pi\) | |||||||
\(164\) | −38.2510 | −0.233238 | ||||||||
\(165\) | 216.142 | − | 374.369i | 1.30995 | − | 2.26891i | ||||
\(166\) | 112.232 | − | 64.7969i | 0.676094 | − | 0.390343i | ||||
\(167\) | 99.7184 | + | 172.717i | 0.597116 | + | 1.03424i | 0.993244 | + | 0.116041i | \(0.0370203\pi\) |
−0.396128 | + | 0.918195i | \(0.629646\pi\) | |||||||
\(168\) | − | 52.2535i | − | 0.311033i | ||||||
\(169\) | 34.5604 | + | 59.8603i | 0.204499 | + | 0.354203i | ||||
\(170\) | 197.523 | 1.16190 | ||||||||
\(171\) | − | 96.1619i | − | 0.562351i | ||||||
\(172\) | 61.4790 | − | 40.7402i | 0.357436 | − | 0.236862i | ||||
\(173\) | −86.0652 | −0.497487 | −0.248743 | − | 0.968569i | \(-0.580018\pi\) | ||||
−0.248743 | + | 0.968569i | \(0.580018\pi\) | |||||||
\(174\) | − | 102.927i | − | 0.591533i | ||||||
\(175\) | 2.63453 | − | 1.52105i | 0.0150545 | − | 0.00869169i | ||||
\(176\) | −121.379 | −0.689653 | ||||||||
\(177\) | −143.749 | + | 82.9934i | −0.812140 | + | 0.468889i | ||||
\(178\) | −9.75704 | − | 16.8997i | −0.0548148 | − | 0.0949421i | ||||
\(179\) | −70.6225 | − | 40.7739i | −0.394539 | − | 0.227787i | 0.289586 | − | 0.957152i | \(-0.406482\pi\) |
−0.684125 | + | 0.729365i | \(0.739816\pi\) | |||||||
\(180\) | 80.0136i | 0.444520i | ||||||||
\(181\) | −84.7687 | + | 146.824i | −0.468335 | + | 0.811181i | −0.999345 | − | 0.0361849i | \(-0.988479\pi\) |
0.531010 | + | 0.847366i | \(0.321813\pi\) | |||||||
\(182\) | 10.7817 | + | 18.6744i | 0.0592401 | + | 0.102607i | ||||
\(183\) | 134.791 | 0.736566 | ||||||||
\(184\) | 250.466 | − | 144.607i | 1.36123 | − | 0.785906i | ||||
\(185\) | −56.8802 | + | 98.5194i | −0.307461 | + | 0.532537i | ||||
\(186\) | 23.7904 | − | 41.2063i | 0.127906 | − | 0.221539i | ||||
\(187\) | −245.672 | + | 425.517i | −1.31376 | + | 2.27549i | ||||
\(188\) | 134.416 | 0.714978 | ||||||||
\(189\) | 0.132637 | − | 0.229734i | 0.000701783 | − | 0.00121552i | ||||
\(190\) | −73.2105 | − | 42.2681i | −0.385319 | − | 0.222464i | ||||
\(191\) | 85.6498 | − | 49.4499i | 0.448428 | − | 0.258900i | −0.258738 | − | 0.965948i | \(-0.583307\pi\) |
0.707166 | + | 0.707047i | \(0.249973\pi\) | |||||||
\(192\) | 230.690 | − | 133.189i | 1.20151 | − | 0.693692i | ||||
\(193\) | −243.765 | −1.26303 | −0.631515 | − | 0.775363i | \(-0.717567\pi\) | ||||
−0.631515 | + | 0.775363i | \(0.717567\pi\) | |||||||
\(194\) | − | 171.022i | − | 0.881556i | ||||||
\(195\) | −110.293 | − | 191.033i | −0.565606 | − | 0.979658i | ||||
\(196\) | −40.2744 | − | 69.7573i | −0.205482 | − | 0.355905i | ||||
\(197\) | 160.733 | − | 278.398i | 0.815903 | − | 1.41319i | −0.0927748 | − | 0.995687i | \(-0.529574\pi\) |
0.908678 | − | 0.417498i | \(-0.137093\pi\) | |||||||
\(198\) | 229.619 | + | 132.570i | 1.15969 | + | 0.669547i | ||||
\(199\) | 39.2071i | 0.197021i | 0.995136 | + | 0.0985103i | \(0.0314077\pi\) | ||||
−0.995136 | + | 0.0985103i | \(0.968592\pi\) | |||||||
\(200\) | 15.9443 | + | 9.20546i | 0.0797216 | + | 0.0460273i | ||||
\(201\) | −449.234 | − | 259.365i | −2.23499 | − | 1.29037i | ||||
\(202\) | 89.2753 | + | 51.5431i | 0.441957 | + | 0.255164i | ||||
\(203\) | 11.4688 | + | 19.8645i | 0.0564966 | + | 0.0978549i | ||||
\(204\) | − | 182.336i | − | 0.893804i | ||||||
\(205\) | 100.600 | − | 58.0817i | 0.490734 | − | 0.283325i | ||||
\(206\) | 82.6307 | + | 47.7069i | 0.401120 | + | 0.231587i | ||||
\(207\) | −299.836 | −1.44848 | ||||||||
\(208\) | −30.9687 | + | 53.6393i | −0.148888 | + | 0.257881i | ||||
\(209\) | 182.113 | − | 105.143i | 0.871355 | − | 0.503077i | ||||
\(210\) | 23.8117 | + | 41.2431i | 0.113389 | + | 0.196396i | ||||
\(211\) | 378.026i | 1.79159i | 0.444466 | + | 0.895796i | \(0.353394\pi\) | ||||
−0.444466 | + | 0.895796i | \(0.646606\pi\) | |||||||
\(212\) | −22.5785 | − | 39.1071i | −0.106502 | − | 0.184467i | ||||
\(213\) | 539.732 | 2.53396 | ||||||||
\(214\) | − | 165.456i | − | 0.773161i | ||||||
\(215\) | −99.8289 | + | 200.499i | −0.464320 | + | 0.932552i | ||||
\(216\) | 1.60545 | 0.00743266 | ||||||||
\(217\) | 10.6036i | 0.0488644i | ||||||||
\(218\) | −45.4909 | + | 26.2642i | −0.208674 | + | 0.120478i | ||||
\(219\) | −73.0408 | −0.333520 | ||||||||
\(220\) | −151.531 | + | 87.4866i | −0.688778 | + | 0.397666i | ||||
\(221\) | 125.362 | + | 217.133i | 0.567248 | + | 0.982502i | ||||
\(222\) | −121.149 | − | 69.9455i | −0.545717 | − | 0.315070i | ||||
\(223\) | − | 222.482i | − | 0.997678i | −0.866695 | − | 0.498839i | \(-0.833760\pi\) | ||
0.866695 | − | 0.498839i | \(-0.166240\pi\) | |||||||
\(224\) | −17.9766 | + | 31.1365i | −0.0802529 | + | 0.139002i | ||||
\(225\) | −9.54356 | − | 16.5299i | −0.0424158 | − | 0.0734664i | ||||
\(226\) | 37.8012 | 0.167262 | ||||||||
\(227\) | −175.306 | + | 101.213i | −0.772271 | + | 0.445871i | −0.833684 | − | 0.552241i | \(-0.813773\pi\) |
0.0614129 | + | 0.998112i | \(0.480439\pi\) | |||||||
\(228\) | −39.0182 | + | 67.5815i | −0.171132 | + | 0.296410i | ||||
\(229\) | 70.4417 | − | 122.009i | 0.307606 | − | 0.532789i | −0.670232 | − | 0.742151i | \(-0.733806\pi\) |
0.977838 | + | 0.209363i | \(0.0671389\pi\) | |||||||
\(230\) | −131.793 | + | 228.273i | −0.573014 | + | 0.992490i | ||||
\(231\) | −118.465 | −0.512833 | ||||||||
\(232\) | −69.4098 | + | 120.221i | −0.299180 | + | 0.518196i | ||||
\(233\) | 43.7817 | + | 25.2774i | 0.187904 | + | 0.108487i | 0.591001 | − | 0.806671i | \(-0.298733\pi\) |
−0.403097 | + | 0.915157i | \(0.632066\pi\) | |||||||
\(234\) | 117.170 | − | 67.6480i | 0.500726 | − | 0.289094i | ||||
\(235\) | −353.515 | + | 204.102i | −1.50432 | + | 0.868518i | ||||
\(236\) | 67.1855 | 0.284684 | ||||||||
\(237\) | − | 154.663i | − | 0.652586i | ||||||
\(238\) | −27.0649 | − | 46.8778i | −0.113718 | − | 0.196966i | ||||
\(239\) | −5.88438 | − | 10.1920i | −0.0246208 | − | 0.0426445i | 0.853452 | − | 0.521171i | \(-0.174505\pi\) |
−0.878073 | + | 0.478526i | \(0.841171\pi\) | |||||||
\(240\) | −68.3952 | + | 118.464i | −0.284980 | + | 0.493600i | ||||
\(241\) | 131.634 | + | 75.9987i | 0.546198 | + | 0.315348i | 0.747587 | − | 0.664164i | \(-0.231212\pi\) |
−0.201389 | + | 0.979511i | \(0.564546\pi\) | |||||||
\(242\) | 396.909i | 1.64012i | ||||||||
\(243\) | −297.243 | − | 171.613i | −1.22322 | − | 0.706228i | ||||
\(244\) | −47.2493 | − | 27.2794i | −0.193645 | − | 0.111801i | ||||
\(245\) | 211.844 | + | 122.308i | 0.864669 | + | 0.499217i | ||||
\(246\) | 71.4229 | + | 123.708i | 0.290337 | + | 0.502879i | ||||
\(247\) | − | 107.305i | − | 0.434433i | ||||||
\(248\) | −55.5759 | + | 32.0867i | −0.224096 | + | 0.129382i | ||||
\(249\) | 314.626 | + | 181.650i | 1.26356 | + | 0.729517i | ||||
\(250\) | 180.055 | 0.720219 | ||||||||
\(251\) | −21.4395 | + | 37.1344i | −0.0854165 | + | 0.147946i | −0.905569 | − | 0.424200i | \(-0.860555\pi\) |
0.820152 | + | 0.572146i | \(0.193889\pi\) | |||||||
\(252\) | 18.9895 | − | 10.9636i | 0.0753551 | − | 0.0435063i | ||||
\(253\) | −327.840 | − | 567.835i | −1.29581 | − | 2.24441i | ||||
\(254\) | − | 41.6375i | − | 0.163927i | ||||||
\(255\) | 276.865 | + | 479.545i | 1.08575 | + | 1.88057i | ||||
\(256\) | −260.110 | −1.01606 | ||||||||
\(257\) | 169.737i | 0.660455i | 0.943901 | + | 0.330227i | \(0.107125\pi\) | ||||
−0.943901 | + | 0.330227i | \(0.892875\pi\) | |||||||
\(258\) | −246.553 | − | 122.759i | −0.955632 | − | 0.475812i | ||||
\(259\) | 31.1752 | 0.120368 | ||||||||
\(260\) | 89.2854i | 0.343405i | ||||||||
\(261\) | 124.637 | − | 71.9592i | 0.477536 | − | 0.275706i | ||||
\(262\) | 46.5799 | 0.177786 | ||||||||
\(263\) | 241.781 | − | 139.592i | 0.919319 | − | 0.530769i | 0.0359012 | − | 0.999355i | \(-0.488570\pi\) |
0.883418 | + | 0.468586i | \(0.155237\pi\) | |||||||
\(264\) | −358.477 | − | 620.901i | −1.35787 | − | 2.35190i | ||||
\(265\) | 118.763 | + | 68.5679i | 0.448162 | + | 0.258747i | ||||
\(266\) | 23.1666i | 0.0870923i | ||||||||
\(267\) | 27.3526 | − | 47.3760i | 0.102444 | − | 0.177438i | ||||
\(268\) | 104.982 | + | 181.834i | 0.391723 | + | 0.678484i | ||||
\(269\) | −112.264 | −0.417337 | −0.208668 | − | 0.977986i | \(-0.566913\pi\) | ||||
−0.208668 | + | 0.977986i | \(0.566913\pi\) | |||||||
\(270\) | −1.26717 | + | 0.731598i | −0.00469320 | + | 0.00270962i | ||||
\(271\) | −16.6159 | + | 28.7796i | −0.0613133 | + | 0.106198i | −0.895053 | − | 0.445960i | \(-0.852862\pi\) |
0.833739 | + | 0.552158i | \(0.186196\pi\) | |||||||
\(272\) | 77.7396 | − | 134.649i | 0.285807 | − | 0.495033i | ||||
\(273\) | −30.2251 | + | 52.3513i | −0.110715 | + | 0.191763i | ||||
\(274\) | 259.787 | 0.948127 | ||||||||
\(275\) | 20.8698 | − | 36.1476i | 0.0758902 | − | 0.131446i | ||||
\(276\) | 210.721 | + | 121.660i | 0.763482 | + | 0.440797i | ||||
\(277\) | 81.5518 | − | 47.0839i | 0.294411 | − | 0.169978i | −0.345519 | − | 0.938412i | \(-0.612297\pi\) |
0.639929 | + | 0.768434i | \(0.278964\pi\) | |||||||
\(278\) | −80.8182 | + | 46.6604i | −0.290713 | + | 0.167843i | ||||
\(279\) | 66.5305 | 0.238460 | ||||||||
\(280\) | − | 64.2308i | − | 0.229396i | ||||||
\(281\) | −38.5912 | − | 66.8420i | −0.137335 | − | 0.237872i | 0.789152 | − | 0.614198i | \(-0.210520\pi\) |
−0.926487 | + | 0.376326i | \(0.877187\pi\) | |||||||
\(282\) | −250.984 | − | 434.716i | −0.890013 | − | 1.54155i | ||||
\(283\) | 82.1091 | − | 142.217i | 0.290138 | − | 0.502534i | −0.683704 | − | 0.729759i | \(-0.739632\pi\) |
0.973842 | + | 0.227225i | \(0.0729654\pi\) | |||||||
\(284\) | −189.196 | − | 109.232i | −0.666182 | − | 0.384620i | ||||
\(285\) | − | 236.986i | − | 0.831530i | ||||||
\(286\) | 256.226 | + | 147.932i | 0.895896 | + | 0.517246i | ||||
\(287\) | −27.5688 | − | 15.9169i | −0.0960586 | − | 0.0554595i | ||||
\(288\) | 195.361 | + | 112.792i | 0.678336 | + | 0.391637i | ||||
\(289\) | −170.192 | − | 294.781i | −0.588898 | − | 1.02000i | ||||
\(290\) | − | 126.519i | − | 0.436273i | ||||||
\(291\) | 415.205 | − | 239.719i | 1.42682 | − | 0.823775i | ||||
\(292\) | 25.6034 | + | 14.7822i | 0.0876830 | + | 0.0506238i | ||||
\(293\) | 177.674 | 0.606394 | 0.303197 | − | 0.952928i | \(-0.401946\pi\) | ||||
0.303197 | + | 0.952928i | \(0.401946\pi\) | |||||||
\(294\) | −150.402 | + | 260.504i | −0.511572 | + | 0.886068i | ||||
\(295\) | −176.698 | + | 102.017i | −0.598977 | + | 0.345819i | ||||
\(296\) | 94.3372 | + | 163.397i | 0.318707 | + | 0.552016i | ||||
\(297\) | − | 3.63974i | − | 0.0122550i | ||||||
\(298\) | −157.812 | − | 273.339i | −0.529572 | − | 0.917245i | ||||
\(299\) | −334.580 | −1.11900 | ||||||||
\(300\) | 15.4894i | 0.0516313i | ||||||||
\(301\) | 61.2627 | − | 3.78043i | 0.203531 | − | 0.0125596i | ||||
\(302\) | 233.181 | 0.772121 | ||||||||
\(303\) | 288.989i | 0.953757i | ||||||||
\(304\) | −57.6272 | + | 33.2711i | −0.189563 | + | 0.109444i | ||||
\(305\) | 165.688 | 0.543238 | ||||||||
\(306\) | −294.128 | + | 169.815i | −0.961201 | + | 0.554950i | ||||
\(307\) | −120.549 | − | 208.796i | −0.392666 | − | 0.680118i | 0.600134 | − | 0.799900i | \(-0.295114\pi\) |
−0.992800 | + | 0.119781i | \(0.961781\pi\) | |||||||
\(308\) | 41.5261 | + | 23.9751i | 0.134825 | + | 0.0778412i | ||||
\(309\) | 267.480i | 0.865630i | ||||||||
\(310\) | 29.2436 | − | 50.6513i | 0.0943341 | − | 0.163391i | ||||
\(311\) | 23.5430 | + | 40.7777i | 0.0757009 | + | 0.131118i | 0.901391 | − | 0.433006i | \(-0.142547\pi\) |
−0.825690 | + | 0.564124i | \(0.809214\pi\) | |||||||
\(312\) | −365.848 | −1.17259 | ||||||||
\(313\) | 3.18599 | − | 1.83943i | 0.0101789 | − | 0.00587678i | −0.494902 | − | 0.868949i | \(-0.664796\pi\) |
0.505081 | + | 0.863072i | \(0.331463\pi\) | |||||||
\(314\) | −120.142 | + | 208.092i | −0.382617 | + | 0.662713i | ||||
\(315\) | −33.2949 | + | 57.6685i | −0.105698 | + | 0.183075i | ||||
\(316\) | −31.3010 | + | 54.2149i | −0.0990538 | + | 0.171566i | ||||
\(317\) | −78.3317 | −0.247103 | −0.123552 | − | 0.992338i | \(-0.539428\pi\) | ||||
−0.123552 | + | 0.992338i | \(0.539428\pi\) | |||||||
\(318\) | −84.3178 | + | 146.043i | −0.265150 | + | 0.459254i | ||||
\(319\) | 272.555 | + | 157.360i | 0.854405 | + | 0.493291i | ||||
\(320\) | 283.567 | − | 163.718i | 0.886148 | − | 0.511618i | ||||
\(321\) | 401.693 | − | 231.918i | 1.25138 | − | 0.722484i | ||||
\(322\) | 72.2341 | 0.224329 | ||||||||
\(323\) | 269.364i | 0.833945i | ||||||||
\(324\) | 69.8014 | + | 120.900i | 0.215437 | + | 0.373147i | ||||
\(325\) | −10.6494 | − | 18.4454i | −0.0327675 | − | 0.0567550i | ||||
\(326\) | 29.7914 | − | 51.6002i | 0.0913847 | − | 0.158283i | ||||
\(327\) | −127.528 | − | 73.6282i | −0.389993 | − | 0.225163i | ||||
\(328\) | − | 192.660i | − | 0.587377i | ||||||
\(329\) | 96.8782 | + | 55.9326i | 0.294463 | + | 0.170008i | ||||
\(330\) | 565.883 | + | 326.713i | 1.71480 | + | 0.990039i | ||||
\(331\) | −65.0459 | − | 37.5543i | −0.196513 | − | 0.113457i | 0.398515 | − | 0.917162i | \(-0.369526\pi\) |
−0.595028 | + | 0.803705i | \(0.702859\pi\) | |||||||
\(332\) | −73.5253 | − | 127.349i | −0.221462 | − | 0.383583i | ||||
\(333\) | − | 195.604i | − | 0.587400i | ||||||
\(334\) | −261.073 | + | 150.731i | −0.781657 | + | 0.451290i | ||||
\(335\) | −552.205 | − | 318.816i | −1.64837 | − | 0.951688i | ||||
\(336\) | 37.4864 | 0.111567 | ||||||||
\(337\) | −131.845 | + | 228.363i | −0.391232 | + | 0.677634i | −0.992612 | − | 0.121329i | \(-0.961284\pi\) |
0.601380 | + | 0.798963i | \(0.294618\pi\) | |||||||
\(338\) | −90.4827 | + | 52.2402i | −0.267700 | + | 0.154557i | ||||
\(339\) | 52.9854 | + | 91.7734i | 0.156299 | + | 0.270718i | ||||
\(340\) | − | 224.130i | − | 0.659206i | ||||||
\(341\) | 72.7442 | + | 125.997i | 0.213326 | + | 0.369492i | ||||
\(342\) | 145.355 | 0.425014 | ||||||||
\(343\) | − | 136.979i | − | 0.399356i | ||||||
\(344\) | 205.197 | + | 309.653i | 0.596502 | + | 0.900153i | ||||
\(345\) | −738.930 | −2.14183 | ||||||||
\(346\) | − | 130.093i | − | 0.375991i | ||||||
\(347\) | 508.938 | − | 293.836i | 1.46668 | − | 0.846789i | 0.467376 | − | 0.884059i | \(-0.345199\pi\) |
0.999305 | + | 0.0372699i | \(0.0118661\pi\) | |||||||
\(348\) | −116.791 | −0.335607 | ||||||||
\(349\) | 384.482 | − | 221.981i | 1.10167 | − | 0.636048i | 0.165009 | − | 0.986292i | \(-0.447235\pi\) |
0.936659 | + | 0.350244i | \(0.113901\pi\) | |||||||
\(350\) | 2.29916 | + | 3.98226i | 0.00656902 | + | 0.0113779i | ||||
\(351\) | −1.60846 | − | 0.928644i | −0.00458250 | − | 0.00264571i | ||||
\(352\) | 493.304i | 1.40143i | ||||||||
\(353\) | −298.730 | + | 517.416i | −0.846262 | + | 1.46577i | 0.0382591 | + | 0.999268i | \(0.487819\pi\) |
−0.884521 | + | 0.466501i | \(0.845515\pi\) | |||||||
\(354\) | −125.450 | − | 217.285i | −0.354378 | − | 0.613801i | ||||
\(355\) | 663.447 | 1.86887 | ||||||||
\(356\) | −19.1761 | + | 11.0713i | −0.0538655 | + | 0.0310993i | ||||
\(357\) | 75.8730 | − | 131.416i | 0.212529 | − | 0.368112i | ||||
\(358\) | 61.6324 | − | 106.750i | 0.172158 | − | 0.298186i | ||||
\(359\) | 127.194 | − | 220.307i | 0.354302 | − | 0.613668i | −0.632697 | − | 0.774400i | \(-0.718052\pi\) |
0.986998 | + | 0.160731i | \(0.0513853\pi\) | |||||||
\(360\) | −403.006 | −1.11946 | ||||||||
\(361\) | −122.859 | + | 212.797i | −0.340329 | + | 0.589466i | ||||
\(362\) | −221.933 | − | 128.133i | −0.613076 | − | 0.353959i | ||||
\(363\) | −963.610 | + | 556.341i | −2.65457 | + | 1.53262i | ||||
\(364\) | 21.1899 | − | 12.2340i | 0.0582141 | − | 0.0336099i | ||||
\(365\) | −89.7829 | −0.245980 | ||||||||
\(366\) | 203.746i | 0.556683i | ||||||||
\(367\) | −142.193 | − | 246.286i | −0.387447 | − | 0.671078i | 0.604658 | − | 0.796485i | \(-0.293310\pi\) |
−0.992105 | + | 0.125407i | \(0.959976\pi\) | |||||||
\(368\) | 103.740 | + | 179.683i | 0.281903 | + | 0.488270i | ||||
\(369\) | −99.8679 | + | 172.976i | −0.270645 | + | 0.468770i | ||||
\(370\) | −148.918 | − | 85.9781i | −0.402482 | − | 0.232373i | ||||
\(371\) | − | 37.5811i | − | 0.101297i | ||||||
\(372\) | −46.7568 | − | 26.9951i | −0.125690 | − | 0.0725674i | ||||
\(373\) | −229.260 | − | 132.363i | −0.614637 | − | 0.354861i | 0.160141 | − | 0.987094i | \(-0.448805\pi\) |
−0.774778 | + | 0.632233i | \(0.782138\pi\) | |||||||
\(374\) | −643.196 | − | 371.350i | −1.71978 | − | 0.992913i | ||||
\(375\) | 252.380 | + | 437.135i | 0.673013 | + | 1.16569i | ||||
\(376\) | 677.015i | 1.80057i | ||||||||
\(377\) | 139.080 | − | 80.2976i | 0.368911 | − | 0.212991i | ||||
\(378\) | 0.347258 | + | 0.200489i | 0.000918671 | + | 0.000530395i | ||||
\(379\) | −98.0731 | −0.258768 | −0.129384 | − | 0.991595i | \(-0.541300\pi\) | ||||
−0.129384 | + | 0.991595i | \(0.541300\pi\) | |||||||
\(380\) | −47.9617 | + | 83.0722i | −0.126215 | + | 0.218611i | ||||
\(381\) | 101.087 | − | 58.3626i | 0.265320 | − | 0.153183i | ||||
\(382\) | 74.7467 | + | 129.465i | 0.195672 | + | 0.338914i | ||||
\(383\) | − | 439.727i | − | 1.14811i | −0.818816 | − | 0.574056i | \(-0.805369\pi\) | ||
0.818816 | − | 0.574056i | \(-0.194631\pi\) | |||||||
\(384\) | −12.1393 | − | 21.0259i | −0.0316128 | − | 0.0547550i | ||||
\(385\) | −145.618 | −0.378230 | ||||||||
\(386\) | − | 368.466i | − | 0.954576i | ||||||
\(387\) | −23.7197 | − | 384.383i | −0.0612911 | − | 0.993238i | ||||
\(388\) | −194.059 | −0.500152 | ||||||||
\(389\) | 279.833i | 0.719366i | 0.933075 | + | 0.359683i | \(0.117115\pi\) | ||||
−0.933075 | + | 0.359683i | \(0.882885\pi\) | |||||||
\(390\) | 288.759 | − | 166.715i | 0.740408 | − | 0.427475i | ||||
\(391\) | 839.886 | 2.14804 | ||||||||
\(392\) | 351.348 | − | 202.851i | 0.896296 | − | 0.517477i | ||||
\(393\) | 65.2903 | + | 113.086i | 0.166133 | + | 0.287751i | ||||
\(394\) | 420.816 | + | 242.958i | 1.06806 | + | 0.616645i | ||||
\(395\) | − | 190.114i | − | 0.481301i | ||||||
\(396\) | 150.428 | − | 260.549i | 0.379868 | − | 0.657951i | ||||
\(397\) | −108.633 | − | 188.157i | −0.273634 | − | 0.473948i | 0.696156 | − | 0.717891i | \(-0.254892\pi\) |
−0.969790 | + | 0.243943i | \(0.921559\pi\) | |||||||
\(398\) | −59.2640 | −0.148905 | ||||||||
\(399\) | −56.2435 | + | 32.4722i | −0.140961 | + | 0.0813840i | ||||
\(400\) | −6.60396 | + | 11.4384i | −0.0165099 | + | 0.0285960i | ||||
\(401\) | −203.564 | + | 352.583i | −0.507641 | + | 0.879260i | 0.492320 | + | 0.870414i | \(0.336149\pi\) |
−0.999961 | + | 0.00884561i | \(0.997184\pi\) | |||||||
\(402\) | 392.047 | − | 679.046i | 0.975242 | − | 1.68917i | ||||
\(403\) | 74.2399 | 0.184218 | ||||||||
\(404\) | 58.4861 | − | 101.301i | 0.144768 | − | 0.250745i | ||||
\(405\) | −367.156 | − | 211.978i | −0.906559 | − | 0.523402i | ||||
\(406\) | −30.0265 | + | 17.3358i | −0.0739570 | + | 0.0426991i | ||||
\(407\) | 370.439 | − | 213.873i | 0.910169 | − | 0.525486i | ||||
\(408\) | 918.375 | 2.25092 | ||||||||
\(409\) | − | 63.1215i | − | 0.154331i | −0.997018 | − | 0.0771656i | \(-0.975413\pi\) | ||
0.997018 | − | 0.0771656i | \(-0.0245870\pi\) | |||||||
\(410\) | 87.7941 | + | 152.064i | 0.214132 | + | 0.370888i | ||||
\(411\) | 364.139 | + | 630.707i | 0.885983 | + | 1.53457i | ||||
\(412\) | 54.1331 | − | 93.7613i | 0.131391 | − | 0.227576i | ||||
\(413\) | 48.4229 | + | 27.9570i | 0.117247 | + | 0.0676924i | ||||
\(414\) | − | 453.221i | − | 1.09474i | ||||||
\(415\) | 386.743 | + | 223.286i | 0.931912 | + | 0.538040i | ||||
\(416\) | 217.999 | + | 125.862i | 0.524035 | + | 0.302552i | ||||
\(417\) | −226.563 | − | 130.806i | −0.543317 | − | 0.313684i | ||||
\(418\) | 158.931 | + | 275.276i | 0.380217 | + | 0.658555i | ||||
\(419\) | − | 182.446i | − | 0.435432i | −0.976012 | − | 0.217716i | \(-0.930139\pi\) | ||
0.976012 | − | 0.217716i | \(-0.0698606\pi\) | |||||||
\(420\) | 46.7986 | − | 27.0192i | 0.111425 | − | 0.0643314i | ||||
\(421\) | −310.193 | − | 179.090i | −0.736800 | − | 0.425392i | 0.0841044 | − | 0.996457i | \(-0.473197\pi\) |
−0.820905 | + | 0.571065i | \(0.806530\pi\) | |||||||
\(422\) | −571.410 | −1.35405 | ||||||||
\(423\) | 350.940 | − | 607.847i | 0.829646 | − | 1.43699i | ||||
\(424\) | 196.971 | − | 113.721i | 0.464555 | − | 0.268211i | ||||
\(425\) | 26.7330 | + | 46.3028i | 0.0629011 | + | 0.108948i | ||||
\(426\) | 815.840i | 1.91512i | ||||||||
\(427\) | −22.7028 | − | 39.3224i | −0.0531681 | − | 0.0920898i | ||||
\(428\) | −187.744 | −0.438654 | ||||||||
\(429\) | 829.417i | 1.93337i | ||||||||
\(430\) | −303.067 | − | 150.898i | −0.704806 | − | 0.350925i | ||||
\(431\) | −201.977 | −0.468624 | −0.234312 | − | 0.972161i | \(-0.575284\pi\) | ||||
−0.234312 | + | 0.972161i | \(0.575284\pi\) | |||||||
\(432\) | 1.15175i | 0.00266608i | ||||||||
\(433\) | −404.038 | + | 233.272i | −0.933114 | + | 0.538734i | −0.887795 | − | 0.460239i | \(-0.847764\pi\) |
−0.0453190 | + | 0.998973i | \(0.514430\pi\) | |||||||
\(434\) | −16.0280 | −0.0369308 | ||||||||
\(435\) | 307.161 | − | 177.340i | 0.706118 | − | 0.407677i | ||||
\(436\) | 29.8020 | + | 51.6187i | 0.0683533 | + | 0.118391i | ||||
\(437\) | −311.297 | − | 179.728i | −0.712351 | − | 0.411276i | ||||
\(438\) | − | 110.406i | − | 0.252068i | ||||||
\(439\) | 319.089 | − | 552.679i | 0.726855 | − | 1.25895i | −0.231351 | − | 0.972870i | \(-0.574315\pi\) |
0.958206 | − | 0.286079i | \(-0.0923520\pi\) | |||||||
\(440\) | −440.645 | − | 763.220i | −1.00147 | − | 1.73459i | ||||
\(441\) | −420.603 | −0.953747 | ||||||||
\(442\) | −328.210 | + | 189.492i | −0.742557 | + | 0.428716i | ||||
\(443\) | −181.021 | + | 313.538i | −0.408626 | + | 0.707761i | −0.994736 | − | 0.102470i | \(-0.967325\pi\) |
0.586110 | + | 0.810231i | \(0.300659\pi\) | |||||||
\(444\) | −79.3674 | + | 137.468i | −0.178755 | + | 0.309613i | ||||
\(445\) | 33.6222 | − | 58.2353i | 0.0755555 | − | 0.130866i | ||||
\(446\) | 336.296 | 0.754027 | ||||||||
\(447\) | 442.406 | − | 766.270i | 0.989723 | − | 1.71425i | ||||
\(448\) | −77.7096 | − | 44.8657i | −0.173459 | − | 0.100147i | ||||
\(449\) | −613.878 | + | 354.423i | −1.36721 | + | 0.789360i | −0.990571 | − | 0.137000i | \(-0.956254\pi\) |
−0.376640 | + | 0.926360i | \(0.622921\pi\) | |||||||
\(450\) | 24.9860 | − | 14.4257i | 0.0555245 | − | 0.0320571i | ||||
\(451\) | −436.781 | −0.968472 | ||||||||
\(452\) | − | 42.8932i | − | 0.0948964i | ||||||
\(453\) | 326.845 | + | 566.113i | 0.721513 | + | 1.24970i | ||||
\(454\) | −152.990 | − | 264.986i | −0.336981 | − | 0.583669i | ||||
\(455\) | −37.1531 | + | 64.3510i | −0.0816551 | + | 0.141431i | ||||
\(456\) | −340.389 | − | 196.524i | −0.746467 | − | 0.430973i | ||||
\(457\) | 444.549i | 0.972755i | 0.873749 | + | 0.486378i | \(0.161682\pi\) | ||||
−0.873749 | + | 0.486378i | \(0.838318\pi\) | |||||||
\(458\) | 184.424 | + | 106.477i | 0.402672 | + | 0.232483i | ||||
\(459\) | 4.03766 | + | 2.33115i | 0.00879665 | + | 0.00507875i | ||||
\(460\) | 259.022 | + | 149.546i | 0.563090 | + | 0.325100i | ||||
\(461\) | 250.340 | + | 433.602i | 0.543038 | + | 0.940569i | 0.998728 | + | 0.0504301i | \(0.0160592\pi\) |
−0.455690 | + | 0.890139i | \(0.650607\pi\) | |||||||
\(462\) | − | 179.067i | − | 0.387590i | ||||||
\(463\) | −756.342 | + | 436.674i | −1.63357 | + | 0.943141i | −0.650588 | + | 0.759431i | \(0.725478\pi\) |
−0.982980 | + | 0.183710i | \(0.941189\pi\) | |||||||
\(464\) | −86.2463 | − | 49.7943i | −0.185876 | − | 0.107315i | ||||
\(465\) | 163.961 | 0.352604 | ||||||||
\(466\) | −38.2084 | + | 66.1788i | −0.0819922 | + | 0.142015i | ||||
\(467\) | −19.1619 | + | 11.0631i | −0.0410320 | + | 0.0236898i | −0.520376 | − | 0.853937i | \(-0.674208\pi\) |
0.479344 | + | 0.877627i | \(0.340875\pi\) | |||||||
\(468\) | −76.7604 | − | 132.953i | −0.164018 | − | 0.284087i | ||||
\(469\) | 174.738i | 0.372576i | ||||||||
\(470\) | −308.513 | − | 534.360i | −0.656410 | − | 1.13694i | ||||
\(471\) | −673.604 | −1.43016 | ||||||||
\(472\) | 338.394i | 0.716937i | ||||||||
\(473\) | 702.017 | − | 465.204i | 1.48418 | − | 0.983518i | ||||
\(474\) | 233.783 | 0.493213 | ||||||||
\(475\) | − | 22.8824i | − | 0.0481735i | ||||||
\(476\) | −53.1924 | + | 30.7107i | −0.111749 | + | 0.0645182i | ||||
\(477\) | −235.797 | −0.494332 | ||||||||
\(478\) | 15.4059 | − | 8.89461i | 0.0322300 | − | 0.0186080i | ||||
\(479\) | 366.668 | + | 635.088i | 0.765487 | + | 1.32586i | 0.939989 | + | 0.341205i | \(0.110835\pi\) |
−0.174502 | + | 0.984657i | \(0.555832\pi\) | |||||||
\(480\) | 481.456 | + | 277.969i | 1.00303 | + | 0.579102i | ||||
\(481\) | − | 218.270i | − | 0.453784i | ||||||
\(482\) | −114.877 | + | 198.973i | −0.238334 | + | 0.412806i | ||||
\(483\) | 101.249 | + | 175.369i | 0.209626 | + | 0.363083i | ||||
\(484\) | 450.373 | 0.930523 | ||||||||
\(485\) | 510.376 | − | 294.666i | 1.05232 | − | 0.607558i | ||||
\(486\) | 259.405 | − | 449.302i | 0.533754 | − | 0.924490i | ||||
\(487\) | −237.862 | + | 411.988i | −0.488422 | + | 0.845972i | −0.999911 | − | 0.0133179i | \(-0.995761\pi\) |
0.511489 | + | 0.859290i | \(0.329094\pi\) | |||||||
\(488\) | 137.398 | − | 237.981i | 0.281554 | − | 0.487666i | ||||
\(489\) | 167.033 | 0.341580 | ||||||||
\(490\) | −184.876 | + | 320.215i | −0.377299 | + | 0.653501i | ||||
\(491\) | 40.6876 | + | 23.4910i | 0.0828669 | + | 0.0478432i | 0.540861 | − | 0.841112i | \(-0.318099\pi\) |
−0.457994 | + | 0.888955i | \(0.651432\pi\) | |||||||
\(492\) | 140.372 | − | 81.0438i | 0.285309 | − | 0.164723i | ||||
\(493\) | −349.127 | + | 201.569i | −0.708168 | + | 0.408861i | ||||
\(494\) | 162.198 | 0.328337 | ||||||||
\(495\) | 913.659i | 1.84578i | ||||||||
\(496\) | −23.0189 | − | 39.8699i | −0.0464090 | − | 0.0803828i | ||||
\(497\) | −90.9065 | − | 157.455i | −0.182910 | − | 0.316810i | ||||
\(498\) | −274.575 | + | 475.578i | −0.551356 | + | 0.954976i | ||||
\(499\) | −476.488 | − | 275.101i | −0.954886 | − | 0.551304i | −0.0602909 | − | 0.998181i | \(-0.519203\pi\) |
−0.894595 | + | 0.446877i | \(0.852536\pi\) | |||||||
\(500\) | − | 204.309i | − | 0.408617i | ||||||
\(501\) | −731.885 | − | 422.554i | −1.46085 | − | 0.843421i | ||||
\(502\) | −56.1310 | − | 32.4072i | −0.111815 | − | 0.0645563i | ||||
\(503\) | −515.731 | − | 297.757i | −1.02531 | − | 0.591963i | −0.109672 | − | 0.993968i | \(-0.534980\pi\) |
−0.915638 | + | 0.402005i | \(0.868313\pi\) | |||||||
\(504\) | 55.2205 | + | 95.6446i | 0.109564 | + | 0.189771i | ||||
\(505\) | 355.229i | 0.703424i | ||||||||
\(506\) | 858.319 | − | 495.550i | 1.69628 | − | 0.979349i | ||||
\(507\) | −253.656 | − | 146.449i | −0.500308 | − | 0.288853i | ||||
\(508\) | −47.2462 | −0.0930043 | ||||||||
\(509\) | −2.32623 | + | 4.02916i | −0.00457021 | + | 0.00791583i | −0.868301 | − | 0.496037i | \(-0.834788\pi\) |
0.863731 | + | 0.503953i | \(0.168121\pi\) | |||||||
\(510\) | −724.862 | + | 418.499i | −1.42130 | + | 0.820587i | ||||
\(511\) | 12.3022 | + | 21.3080i | 0.0240747 | + | 0.0416986i | ||||
\(512\) | − | 370.255i | − | 0.723155i | ||||||
\(513\) | −0.997686 | − | 1.72804i | −0.00194481 | − | 0.00336851i | ||||
\(514\) | −256.568 | −0.499160 | ||||||||
\(515\) | 328.790i | 0.638427i | ||||||||
\(516\) | −139.295 | + | 279.764i | −0.269952 | + | 0.542179i | ||||
\(517\) | 1534.87 | 2.96880 | ||||||||
\(518\) | 47.1234i | 0.0909718i | ||||||||
\(519\) | 315.838 | − | 182.349i | 0.608552 | − | 0.351347i | ||||
\(520\) | −449.705 | −0.864818 | ||||||||
\(521\) | 428.671 | − | 247.493i | 0.822785 | − | 0.475035i | −0.0285906 | − | 0.999591i | \(-0.509102\pi\) |
0.851376 | + | 0.524556i | \(0.175769\pi\) | |||||||
\(522\) | 108.771 | + | 188.397i | 0.208373 | + | 0.360913i | ||||
\(523\) | 531.027 | + | 306.589i | 1.01535 | + | 0.586212i | 0.912753 | − | 0.408511i | \(-0.133952\pi\) |
0.102596 | + | 0.994723i | \(0.467285\pi\) | |||||||
\(524\) | − | 52.8543i | − | 0.100867i | ||||||
\(525\) | −6.44539 | + | 11.1637i | −0.0122769 | + | 0.0212643i | ||||
\(526\) | 211.003 | + | 365.467i | 0.401146 | + | 0.694805i | ||||
\(527\) | −186.362 | −0.353628 | ||||||||
\(528\) | 445.431 | − | 257.170i | 0.843620 | − | 0.487064i | ||||
\(529\) | −295.896 | + | 512.507i | −0.559350 | + | 0.968822i | ||||
\(530\) | −103.645 | + | 179.518i | −0.195556 | + | 0.338713i | ||||
\(531\) | 175.412 | − | 303.822i | 0.330342 | − | 0.572169i | ||||
\(532\) | 26.2872 | 0.0494119 | ||||||||
\(533\) | −111.440 | + | 193.020i | −0.209081 | + | 0.362139i | ||||
\(534\) | 71.6119 | + | 41.3452i | 0.134105 | + | 0.0774254i | ||||
\(535\) | 493.767 | − | 285.076i | 0.922929 | − | 0.532853i | ||||
\(536\) | −915.845 | + | 528.763i | −1.70867 | + | 0.986499i | ||||
\(537\) | 345.557 | 0.643495 | ||||||||
\(538\) | − | 169.693i | − | 0.315415i | ||||||
\(539\) | −459.885 | − | 796.545i | −0.853220 | − | 1.47782i | ||||
\(540\) | 0.830146 | + | 1.43786i | 0.00153731 | + | 0.00266269i | ||||
\(541\) | 392.586 | − | 679.979i | 0.725668 | − | 1.25689i | −0.233031 | − | 0.972469i | \(-0.574864\pi\) |
0.958699 | − | 0.284424i | \(-0.0918024\pi\) | |||||||
\(542\) | −43.5022 | − | 25.1160i | −0.0802623 | − | 0.0463394i | ||||
\(543\) | − | 718.410i | − | 1.32304i | ||||||
\(544\) | −547.235 | − | 315.946i | −1.00595 | − | 0.580783i | ||||
\(545\) | −156.759 | − | 90.5049i | −0.287631 | − | 0.166064i | ||||
\(546\) | −79.1324 | − | 45.6871i | −0.144931 | − | 0.0836760i | ||||
\(547\) | 81.3090 | + | 140.831i | 0.148645 | + | 0.257461i | 0.930727 | − | 0.365715i | \(-0.119175\pi\) |
−0.782082 | + | 0.623176i | \(0.785842\pi\) | |||||||
\(548\) | − | 294.781i | − | 0.537921i | ||||||
\(549\) | −246.722 | + | 142.445i | −0.449402 | + | 0.259463i | ||||
\(550\) | 54.6393 | + | 31.5460i | 0.0993442 | + | 0.0573564i | ||||
\(551\) | 172.535 | 0.313131 | ||||||||
\(552\) | −612.767 | + | 1061.34i | −1.11008 | + | 1.92272i | ||||
\(553\) | −45.1194 | + | 26.0497i | −0.0815902 | + | 0.0471061i | ||||
\(554\) | 71.1704 | + | 123.271i | 0.128466 | + | 0.222510i | ||||
\(555\) | − | 482.056i | − | 0.868570i | ||||||
\(556\) | 52.9457 | + | 91.7046i | 0.0952260 | + | 0.164936i | ||||
\(557\) | 46.2986 | 0.0831213 | 0.0415607 | − | 0.999136i | \(-0.486767\pi\) | ||||
0.0415607 | + | 0.999136i | \(0.486767\pi\) | |||||||
\(558\) | 100.565i | 0.180224i | ||||||||
\(559\) | −26.4683 | − | 428.924i | −0.0473493 | − | 0.767307i | ||||
\(560\) | 46.0789 | 0.0822837 | ||||||||
\(561\) | − | 2082.06i | − | 3.71133i | ||||||
\(562\) | 101.036 | − | 58.3331i | 0.179779 | − | 0.103796i | ||||
\(563\) | −246.469 | −0.437778 | −0.218889 | − | 0.975750i | \(-0.570243\pi\) | ||||
−0.218889 | + | 0.975750i | \(0.570243\pi\) | |||||||
\(564\) | −493.274 | + | 284.792i | −0.874599 | + | 0.504950i | ||||
\(565\) | 65.1304 | + | 112.809i | 0.115275 | + | 0.199662i | ||||
\(566\) | 214.970 | + | 124.113i | 0.379806 | + | 0.219281i | ||||
\(567\) | 116.182i | 0.204907i | ||||||||
\(568\) | 550.171 | − | 952.925i | 0.968612 | − | 1.67768i | ||||
\(569\) | 424.894 | + | 735.938i | 0.746738 | + | 1.29339i | 0.949378 | + | 0.314135i | \(0.101715\pi\) |
−0.202640 | + | 0.979253i | \(0.564952\pi\) | |||||||
\(570\) | 358.220 | 0.628456 | ||||||||
\(571\) | 175.177 | − | 101.138i | 0.306790 | − | 0.177125i | −0.338699 | − | 0.940895i | \(-0.609987\pi\) |
0.645489 | + | 0.763770i | \(0.276654\pi\) | |||||||
\(572\) | 167.859 | − | 290.741i | 0.293460 | − | 0.508288i | ||||
\(573\) | −209.542 | + | 362.938i | −0.365694 | + | 0.633400i | ||||
\(574\) | 24.0594 | − | 41.6720i | 0.0419153 | − | 0.0725994i | ||||
\(575\) | −71.3480 | −0.124084 | ||||||||
\(576\) | −281.503 | + | 487.577i | −0.488720 | + | 0.846487i | ||||
\(577\) | −634.982 | − | 366.607i | −1.10049 | − | 0.635368i | −0.164140 | − | 0.986437i | \(-0.552485\pi\) |
−0.936349 | + | 0.351069i | \(0.885818\pi\) | |||||||
\(578\) | 445.580 | − | 257.256i | 0.770899 | − | 0.445079i | ||||
\(579\) | 894.558 | − | 516.473i | 1.54500 | − | 0.892009i | ||||
\(580\) | −143.561 | −0.247520 | ||||||||
\(581\) | − | 122.380i | − | 0.210637i | ||||||
\(582\) | 362.350 | + | 627.608i | 0.622594 | + | 1.07836i | ||||
\(583\) | −257.819 | − | 446.556i | −0.442228 | − | 0.765962i | ||||
\(584\) | −74.4535 | + | 128.957i | −0.127489 | + | 0.220817i | ||||
\(585\) | 403.760 | + | 233.111i | 0.690189 | + | 0.398481i | ||||
\(586\) | 268.565i | 0.458302i | ||||||||
\(587\) | 549.572 | + | 317.295i | 0.936238 | + | 0.540537i | 0.888779 | − | 0.458336i | \(-0.151554\pi\) |
0.0474590 | + | 0.998873i | \(0.484888\pi\) | |||||||
\(588\) | 295.595 | + | 170.662i | 0.502712 | + | 0.290241i | ||||
\(589\) | 69.0736 | + | 39.8797i | 0.117273 | + | 0.0677074i | ||||
\(590\) | −154.205 | − | 267.091i | −0.261364 | − | 0.452696i | ||||
\(591\) | 1362.20i | 2.30491i | ||||||||
\(592\) | −117.220 | + | 67.6771i | −0.198007 | + | 0.114319i | ||||
\(593\) | 577.047 | + | 333.158i | 0.973098 | + | 0.561818i | 0.900179 | − | 0.435520i | \(-0.143435\pi\) |
0.0729186 | + | 0.997338i | \(0.476769\pi\) | |||||||
\(594\) | 5.50170 | 0.00926213 | ||||||||
\(595\) | 93.2642 | − | 161.538i | 0.156747 | − | 0.271493i | ||||
\(596\) | −310.158 | + | 179.070i | −0.520400 | + | 0.300453i | ||||
\(597\) | −83.0694 | − | 143.881i | −0.139145 | − | 0.241006i | ||||
\(598\) | − | 505.739i | − | 0.845718i | ||||||
\(599\) | −354.761 | − | 614.463i | −0.592255 | − | 1.02582i | −0.993928 | − | 0.110032i | \(-0.964905\pi\) |
0.401673 | − | 0.915783i | \(-0.368429\pi\) | |||||||
\(600\) | −78.0157 | −0.130026 | ||||||||
\(601\) | − | 389.979i | − | 0.648884i | −0.945906 | − | 0.324442i | \(-0.894824\pi\) | ||
0.945906 | − | 0.324442i | \(-0.105176\pi\) | |||||||
\(602\) | 5.71435 | + | 92.6025i | 0.00949228 | + | 0.153825i | ||||
\(603\) | 1096.37 | 1.81819 | ||||||||
\(604\) | − | 264.591i | − | 0.438064i | ||||||
\(605\) | −1184.48 | + | 683.862i | −1.95782 | + | 1.13035i | ||||
\(606\) | −436.825 | −0.720833 | ||||||||
\(607\) | −818.471 | + | 472.545i | −1.34839 | + | 0.778492i | −0.988021 | − | 0.154319i | \(-0.950682\pi\) |
−0.360366 | + | 0.932811i | \(0.617348\pi\) | |||||||
\(608\) | 135.219 | + | 234.206i | 0.222400 | + | 0.385208i | ||||
\(609\) | −84.1754 | − | 48.5987i | −0.138219 | − | 0.0798008i | ||||
\(610\) | 250.448i | 0.410570i | ||||||||
\(611\) | 391.607 | − | 678.283i | 0.640927 | − | 1.11012i | ||||
\(612\) | 192.689 | + | 333.747i | 0.314851 | + | 0.545339i | ||||
\(613\) | −89.2278 | −0.145559 | −0.0727796 | − | 0.997348i | \(-0.523187\pi\) | ||||
−0.0727796 | + | 0.997348i | \(0.523187\pi\) | |||||||
\(614\) | 315.609 | − | 182.217i | 0.514021 | − | 0.296770i | ||||
\(615\) | −246.119 | + | 426.291i | −0.400194 | + | 0.693156i | ||||
\(616\) | −120.756 | + | 209.155i | −0.196032 | + | 0.339537i | ||||
\(617\) | −46.9205 | + | 81.2687i | −0.0760462 | + | 0.131716i | −0.901541 | − | 0.432694i | \(-0.857563\pi\) |
0.825495 | + | 0.564410i | \(0.190896\pi\) | |||||||
\(618\) | −404.313 | −0.654228 | ||||||||
\(619\) | 113.587 | − | 196.739i | 0.183501 | − | 0.317834i | −0.759569 | − | 0.650427i | \(-0.774590\pi\) |
0.943071 | + | 0.332593i | \(0.107923\pi\) | |||||||
\(620\) | −57.4742 | − | 33.1827i | −0.0927003 | − | 0.0535206i | ||||
\(621\) | −5.38809 | + | 3.11082i | −0.00867648 | + | 0.00500937i | ||||
\(622\) | −61.6380 | + | 35.5867i | −0.0990965 | + | 0.0572134i | ||||
\(623\) | −18.4278 | −0.0295792 | ||||||||
\(624\) | − | 262.457i | − | 0.420605i | ||||||
\(625\) | 336.869 | + | 583.474i | 0.538990 | + | 0.933558i | ||||
\(626\) | 2.78042 | + | 4.81582i | 0.00444156 | + | 0.00769301i | ||||
\(627\) | −445.541 | + | 771.699i | −0.710591 | + | 1.23078i | ||||
\(628\) | 236.122 | + | 136.325i | 0.375991 | + | 0.217078i | ||||
\(629\) | 547.917i | 0.871092i | ||||||||
\(630\) | −87.1697 | − | 50.3274i | −0.138365 | − | 0.0798848i | ||||
\(631\) | −405.265 | − | 233.980i | −0.642259 | − | 0.370808i | 0.143225 | − | 0.989690i | \(-0.454253\pi\) |
−0.785484 | + | 0.618882i | \(0.787586\pi\) | |||||||
\(632\) | −273.065 | − | 157.654i | −0.432065 | − | 0.249453i | ||||
\(633\) | −800.936 | − | 1387.26i | −1.26530 | − | 2.19157i | ||||
\(634\) | − | 118.403i | − | 0.186756i | ||||||
\(635\) | 124.258 | − | 71.7402i | 0.195681 | − | 0.112977i | ||||
\(636\) | 165.715 | + | 95.6756i | 0.260558 | + | 0.150433i | ||||
\(637\) | −469.341 | −0.736799 | ||||||||
\(638\) | −237.859 | + | 411.985i | −0.372820 | + | 0.645744i | ||||
\(639\) | −987.924 | + | 570.378i | −1.54605 | + | 0.892611i | ||||
\(640\) | −14.9218 | − | 25.8454i | −0.0233153 | − | 0.0403834i | ||||
\(641\) | 1181.26i | 1.84283i | 0.388577 | + | 0.921416i | \(0.372967\pi\) | ||||
−0.388577 | + | 0.921416i | \(0.627033\pi\) | |||||||
\(642\) | 350.558 | + | 607.184i | 0.546041 | + | 0.945770i | ||||
\(643\) | 1130.33 | 1.75790 | 0.878948 | − | 0.476917i | \(-0.158246\pi\) | ||||
0.878948 | + | 0.476917i | \(0.158246\pi\) | |||||||
\(644\) | − | 81.9642i | − | 0.127274i | ||||||
\(645\) | −58.4559 | − | 947.292i | −0.0906293 | − | 1.46867i | ||||
\(646\) | −407.161 | −0.630280 | ||||||||
\(647\) | 1275.13i | 1.97084i | 0.170149 | + | 0.985418i | \(0.445575\pi\) | ||||
−0.170149 | + | 0.985418i | \(0.554425\pi\) | |||||||
\(648\) | −608.937 | + | 351.570i | −0.939718 | + | 0.542546i | ||||
\(649\) | 767.178 | 1.18209 | ||||||||
\(650\) | 27.8814 | − | 16.0973i | 0.0428944 | − | 0.0247651i | ||||
\(651\) | −22.4662 | − | 38.9125i | −0.0345102 | − | 0.0597735i | ||||
\(652\) | −58.5509 | − | 33.8044i | −0.0898020 | − | 0.0518472i | ||||
\(653\) | 185.383i | 0.283894i | 0.989874 | + | 0.141947i | \(0.0453363\pi\) | ||||
−0.989874 | + | 0.141947i | \(0.954664\pi\) | |||||||
\(654\) | 111.294 | − | 192.766i | 0.170174 | − | 0.294750i | ||||
\(655\) | 80.2558 | + | 139.007i | 0.122528 | + | 0.212225i | ||||
\(656\) | 138.213 | 0.210691 | ||||||||
\(657\) | 133.694 | − | 77.1881i | 0.203491 | − | 0.117486i | ||||
\(658\) | −84.5458 | + | 146.438i | −0.128489 | + | 0.222549i | ||||
\(659\) | 119.493 | − | 206.969i | 0.181325 | − | 0.314065i | −0.761007 | − | 0.648744i | \(-0.775295\pi\) |
0.942332 | + | 0.334679i | \(0.108628\pi\) | |||||||
\(660\) | 370.722 | − | 642.109i | 0.561700 | − | 0.972892i | ||||
\(661\) | −1149.01 | −1.73829 | −0.869144 | − | 0.494559i | \(-0.835330\pi\) | ||||
−0.869144 | + | 0.494559i | \(0.835330\pi\) | |||||||
\(662\) | 56.7657 | − | 98.3211i | 0.0857488 | − | 0.148521i | ||||
\(663\) | −920.094 | − | 531.217i | −1.38777 | − | 0.801232i | ||||
\(664\) | 641.423 | − | 370.326i | 0.965999 | − | 0.557720i | ||||
\(665\) | −69.1353 | + | 39.9153i | −0.103963 | + | 0.0600230i | ||||
\(666\) | 295.668 | 0.443946 | ||||||||
\(667\) | − | 537.969i | − | 0.806551i | ||||||
\(668\) | 171.035 | + | 296.241i | 0.256040 | + | 0.443474i | ||||
\(669\) | 471.381 | + | 816.455i | 0.704605 | + | 1.22041i | ||||
\(670\) | 481.910 | − | 834.693i | 0.719269 | − | 1.24581i | ||||
\(671\) | −539.530 | − | 311.498i | −0.804068 | − | 0.464229i | ||||
\(672\) | − | 152.351i | − | 0.226713i | ||||||
\(673\) | 106.943 | + | 61.7437i | 0.158905 | + | 0.0917440i | 0.577344 | − | 0.816501i | \(-0.304089\pi\) |
−0.418439 | + | 0.908245i | \(0.637423\pi\) | |||||||
\(674\) | −345.185 | − | 199.292i | −0.512143 | − | 0.295686i | ||||
\(675\) | −0.342998 | − | 0.198030i | −0.000508145 | − | 0.000293378i | ||||
\(676\) | 59.2771 | + | 102.671i | 0.0876880 | + | 0.151880i | ||||
\(677\) | − | 444.331i | − | 0.656323i | −0.944622 | − | 0.328162i | \(-0.893571\pi\) | ||
0.944622 | − | 0.328162i | \(-0.106429\pi\) | |||||||
\(678\) | −138.721 | + | 80.0908i | −0.204604 | + | 0.118128i | ||||
\(679\) | −139.865 | − | 80.7510i | −0.205987 | − | 0.118926i | ||||
\(680\) | 1128.88 | 1.66012 | ||||||||
\(681\) | 428.886 | − | 742.852i | 0.629788 | − | 1.09083i | ||||
\(682\) | −190.452 | + | 109.957i | −0.279255 | + | 0.161228i | ||||
\(683\) | 162.804 | + | 281.985i | 0.238366 | + | 0.412863i | 0.960246 | − | 0.279156i | \(-0.0900547\pi\) |
−0.721879 | + | 0.692019i | \(0.756721\pi\) | |||||||
\(684\) | − | 164.935i | − | 0.241132i | ||||||
\(685\) | 447.605 | + | 775.274i | 0.653438 | + | 1.13179i | ||||
\(686\) | 207.053 | 0.301826 | ||||||||
\(687\) | 596.989i | 0.868980i | ||||||||
\(688\) | −222.143 | + | 147.207i | −0.322883 | + | 0.213964i | ||||
\(689\) | −263.120 | −0.381887 | ||||||||
\(690\) | − | 1116.94i | − | 1.61875i | ||||||
\(691\) | 6.60671 | − | 3.81439i | 0.00956109 | − | 0.00552010i | −0.495212 | − | 0.868772i | \(-0.664910\pi\) |
0.504773 | + | 0.863252i | \(0.331576\pi\) | |||||||
\(692\) | −147.617 | −0.213319 | ||||||||
\(693\) | 216.837 | − | 125.191i | 0.312896 | − | 0.180651i | ||||
\(694\) | 444.151 | + | 769.293i | 0.639988 | + | 1.10849i | ||||
\(695\) | −278.495 | − | 160.789i | −0.400712 | − | 0.231351i | ||||
\(696\) | − | 588.244i | − | 0.845178i | ||||||
\(697\) | 279.745 | − | 484.533i | 0.401356 | − | 0.695169i | ||||
\(698\) | 335.538 | + | 581.169i | 0.480714 | + | 0.832620i | ||||
\(699\) | −214.224 | −0.306472 | ||||||||
\(700\) | 4.51868 | − | 2.60886i | 0.00645526 | − | 0.00372694i | ||||
\(701\) | 154.353 | − | 267.347i | 0.220189 | − | 0.381379i | −0.734676 | − | 0.678418i | \(-0.762666\pi\) |
0.954865 | + | 0.297039i | \(0.0959991\pi\) | |||||||
\(702\) | 1.40371 | − | 2.43129i | 0.00199958 | − | 0.00346337i | ||||
\(703\) | 117.249 | − | 203.081i | 0.166784 | − | 0.288878i | ||||
\(704\) | −1231.18 | −1.74883 | ||||||||
\(705\) | 864.875 | − | 1498.01i | 1.22677 | − | 2.12483i | ||||
\(706\) | −782.108 | − | 451.550i | −1.10780 | − | 0.639589i | ||||
\(707\) | 84.3058 | − | 48.6740i | 0.119244 | − | 0.0688458i | ||||
\(708\) | −246.554 | + | 142.348i | −0.348241 | + | 0.201057i | ||||
\(709\) | −85.3563 | −0.120390 | −0.0601949 | − | 0.998187i | \(-0.519172\pi\) | ||||
−0.0601949 | + | 0.998187i | \(0.519172\pi\) | |||||||
\(710\) | 1002.84i | 1.41245i | ||||||||
\(711\) | 163.445 | + | 283.094i | 0.229880 | + | 0.398164i | ||||
\(712\) | −55.7632 | − | 96.5847i | −0.0783191 | − | 0.135653i | ||||
\(713\) | 124.346 | − | 215.374i | 0.174398 | − | 0.302067i | ||||
\(714\) | 198.643 | + | 114.687i | 0.278212 | + | 0.160626i | ||||
\(715\) | 1019.53i | 1.42592i | ||||||||
\(716\) | −121.130 | − | 69.9345i | −0.169176 | − | 0.0976738i | ||||
\(717\) | 43.1885 | + | 24.9349i | 0.0602349 | + | 0.0347767i | ||||
\(718\) | 333.008 | + | 192.262i | 0.463800 | + | 0.267775i | ||||
\(719\) | −253.076 | − | 438.341i | −0.351984 | − | 0.609654i | 0.634613 | − | 0.772830i | \(-0.281159\pi\) |
−0.986597 | + | 0.163176i | \(0.947826\pi\) | |||||||
\(720\) | − | 289.115i | − | 0.401548i | ||||||
\(721\) | 78.0311 | − | 45.0513i | 0.108226 | − | 0.0624845i | ||||
\(722\) | −321.657 | − | 185.709i | −0.445508 | − | 0.257214i | ||||
\(723\) | −644.085 | −0.890850 | ||||||||
\(724\) | −145.393 | + | 251.828i | −0.200819 | + | 0.347829i | ||||
\(725\) | 29.6582 | − | 17.1232i | 0.0409079 | − | 0.0236182i | ||||
\(726\) | −840.944 | − | 1456.56i | −1.15833 | − | 2.00628i | ||||
\(727\) | 230.282i | 0.316757i | 0.987379 | + | 0.158378i | \(0.0506265\pi\) | ||||
−0.987379 | + | 0.158378i | \(0.949373\pi\) | |||||||
\(728\) | 61.6193 | + | 106.728i | 0.0846419 | + | 0.146604i | ||||
\(729\) | 721.878 | 0.990230 | ||||||||
\(730\) | − | 135.713i | − | 0.185908i | ||||||
\(731\) | 66.4424 | + | 1076.71i | 0.0908925 | + | 1.47293i | ||||
\(732\) | 231.191 | 0.315835 | ||||||||
\(733\) | 500.013i | 0.682147i | 0.940037 | + | 0.341073i | \(0.110790\pi\) | ||||
−0.940037 | + | 0.341073i | \(0.889210\pi\) | |||||||
\(734\) | 372.277 | − | 214.934i | 0.507189 | − | 0.292826i | ||||
\(735\) | −1036.55 | −1.41028 | ||||||||
\(736\) | 730.262 | − | 421.617i | 0.992204 | − | 0.572849i | ||||
\(737\) | 1198.77 | + | 2076.32i | 1.62655 | + | 2.81726i | ||||
\(738\) | −261.465 | − | 150.957i | −0.354288 | − | 0.204548i | ||||
\(739\) | − | 865.575i | − | 1.17128i | −0.810572 | − | 0.585639i | \(-0.800843\pi\) | ||
0.810572 | − | 0.585639i | \(-0.199157\pi\) | |||||||
\(740\) | −97.5595 | + | 168.978i | −0.131837 | + | 0.228349i | ||||
\(741\) | 227.351 | + | 393.783i | 0.306816 | + | 0.531421i | ||||
\(742\) | 56.8062 | 0.0765582 | ||||||||
\(743\) | 1045.99 | − | 603.905i | 1.40780 | − | 0.812793i | 0.412622 | − | 0.910902i | \(-0.364613\pi\) |
0.995176 | + | 0.0981096i | \(0.0312796\pi\) | |||||||
\(744\) | 135.967 | − | 235.501i | 0.182751 | − | 0.316534i | ||||
\(745\) | 543.812 | − | 941.910i | 0.729949 | − | 1.26431i | ||||
\(746\) | 200.075 | − | 346.540i | 0.268197 | − | 0.464531i | ||||
\(747\) | −767.855 | −1.02792 | ||||||||
\(748\) | −421.371 | + | 729.836i | −0.563331 | + | 0.975717i | ||||
\(749\) | −135.313 | − | 78.1232i | −0.180659 | − | 0.104303i | ||||
\(750\) | −660.757 | + | 381.488i | −0.881009 | + | 0.508651i | ||||
\(751\) | 405.939 | − | 234.369i | 0.540532 | − | 0.312076i | −0.204763 | − | 0.978812i | \(-0.565642\pi\) |
0.745294 | + | 0.666735i | \(0.232309\pi\) | |||||||
\(752\) | −485.688 | −0.645861 | ||||||||
\(753\) | − | 181.699i | − | 0.241300i | ||||||
\(754\) | 121.375 | + | 210.228i | 0.160975 | + | 0.278817i | ||||
\(755\) | 401.763 | + | 695.874i | 0.532137 | + | 0.921688i | ||||
\(756\) | 0.227496 | − | 0.394034i | 0.000300920 | − | 0.000521209i | ||||
\(757\) | 591.471 | + | 341.486i | 0.781336 | + | 0.451104i | 0.836903 | − | 0.547351i | \(-0.184364\pi\) |
−0.0555678 | + | 0.998455i | \(0.517697\pi\) | |||||||
\(758\) | − | 148.244i | − | 0.195572i | ||||||
\(759\) | 2406.18 | + | 1389.21i | 3.17020 | + | 1.83032i | ||||
\(760\) | −418.411 | − | 241.570i | −0.550541 | − | 0.317855i | ||||
\(761\) | −284.325 | − | 164.155i | −0.373620 | − | 0.215710i | 0.301419 | − | 0.953492i | \(-0.402540\pi\) |
−0.675039 | + | 0.737782i | \(0.735873\pi\) | |||||||
\(762\) | 88.2188 | + | 152.799i | 0.115773 | + | 0.200524i | ||||
\(763\) | 49.6044i | 0.0650124i | ||||||||
\(764\) | 146.904 | − | 84.8153i | 0.192283 | − | 0.111015i | ||||
\(765\) | −1013.55 | − | 585.171i | −1.32490 | − | 0.764930i | ||||
\(766\) | 664.675 | 0.867723 | ||||||||
\(767\) | 195.738 | − | 339.028i | 0.255199 | − | 0.442018i | ||||
\(768\) | 954.541 | − | 551.105i | 1.24289 | − | 0.717584i | ||||
\(769\) | −278.216 | − | 481.884i | −0.361789 | − | 0.626637i | 0.626466 | − | 0.779449i | \(-0.284501\pi\) |
−0.988255 | + | 0.152811i | \(0.951167\pi\) | |||||||
\(770\) | − | 220.111i | − | 0.285859i | ||||||
\(771\) | −359.627 | − | 622.893i | −0.466443 | − | 0.807903i | ||||
\(772\) | −418.100 | −0.541580 | ||||||||
\(773\) | − | 440.683i | − | 0.570095i | −0.958513 | − | 0.285047i | \(-0.907991\pi\) | ||
0.958513 | − | 0.285047i | \(-0.0920093\pi\) | |||||||
\(774\) | 581.019 | − | 35.8538i | 0.750671 | − | 0.0463227i | ||||
\(775\) | 15.8314 | 0.0204276 | ||||||||
\(776\) | − | 977.420i | − | 1.25956i | ||||||
\(777\) | −114.406 | + | 66.0521i | −0.147240 | + | 0.0850091i | ||||
\(778\) | −422.986 | −0.543683 | ||||||||
\(779\) | −207.371 | + | 119.726i | −0.266201 | + | 0.153691i | ||||
\(780\) | −189.172 | − | 327.656i | −0.242528 | − | 0.420071i | ||||
\(781\) | −2160.39 | − | 1247.30i | −2.76618 | − | 1.59705i | ||||
\(782\) | 1269.54i | 1.62345i | ||||||||
\(783\) | 1.49316 | − | 2.58623i | 0.00190698 | − | 0.00330298i | ||||
\(784\) | 145.524 | + | 252.056i | 0.185618 | + | 0.321499i | ||||
\(785\) | −828.004 | −1.05478 | ||||||||
\(786\) | −170.937 | + | 98.6904i | −0.217477 | + | 0.125560i | ||||
\(787\) | 81.7718 | − | 141.633i | 0.103903 | − | 0.179966i | −0.809386 | − | 0.587277i | \(-0.800200\pi\) |
0.913290 | + | 0.407311i | \(0.133533\pi\) | |||||||
\(788\) | 275.685 | − | 477.500i | 0.349854 | − | 0.605965i | ||||
\(789\) | −591.518 | + | 1024.54i | −0.749706 | + | 1.29853i | ||||
\(790\) | 287.369 | 0.363759 | ||||||||
\(791\) | 17.8485 | − | 30.9146i | 0.0225645 | − | 0.0390829i | ||||
\(792\) | 1312.31 | + | 757.663i | 1.65696 | + | 0.956645i | ||||
\(793\) | −275.311 | + | 158.951i | −0.347177 | + | 0.200443i | ||||
\(794\) | 284.412 | − | 164.205i | 0.358201 | − | 0.206807i | ||||
\(795\) | −581.108 | −0.730954 | ||||||||
\(796\) | 67.2471i | 0.0844812i | ||||||||
\(797\) | 527.628 | + | 913.878i | 0.662017 | + | 1.14665i | 0.980085 | + | 0.198579i | \(0.0636327\pi\) |
−0.318068 | + | 0.948068i | \(0.603034\pi\) | |||||||
\(798\) | −49.0838 | − | 85.0156i | −0.0615085 | − | 0.106536i | ||||
\(799\) | −983.037 | + | 1702.67i | −1.23033 | + | 2.13100i | ||||
\(800\) | 46.4874 | + | 26.8395i | 0.0581093 | + | 0.0335494i | ||||
\(801\) | 115.623i | 0.144348i | ||||||||
\(802\) | −532.952 | − | 307.700i | −0.664529 | − | 0.383666i | ||||
\(803\) | 292.360 | + | 168.794i | 0.364085 | + | 0.210205i | ||||
\(804\) | −770.515 | − | 444.857i | −0.958352 | − | 0.553305i | ||||
\(805\) | 124.457 | + | 215.566i | 0.154605 | + | 0.267784i | ||||
\(806\) | 112.218i | 0.139229i | ||||||||
\(807\) | 411.980 | − | 237.857i | 0.510508 | − | 0.294742i | ||||
\(808\) | 510.224 | + | 294.578i | 0.631465 | + | 0.364577i | ||||
\(809\) | −1278.56 | −1.58042 | −0.790209 | − | 0.612837i | \(-0.790028\pi\) | ||||
−0.790209 | + | 0.612837i | \(0.790028\pi\) | |||||||
\(810\) | 320.418 | − | 554.980i | 0.395578 | − | 0.685160i | ||||
\(811\) | −1346.24 | + | 777.252i | −1.65998 | + | 0.958387i | −0.687252 | + | 0.726419i | \(0.741183\pi\) |
−0.972723 | + | 0.231968i | \(0.925484\pi\) | |||||||
\(812\) | 19.6710 | + | 34.0712i | 0.0242254 | + | 0.0419596i | ||||
\(813\) | − | 140.819i | − | 0.173209i | ||||||
\(814\) | 323.283 | + | 559.942i | 0.397153 | + | 0.687889i | ||||
\(815\) | 205.319 | 0.251925 | ||||||||
\(816\) | 658.838i | 0.807400i | ||||||||
\(817\) | 205.780 | − | 413.294i | 0.251873 | − | 0.505868i | ||||
\(818\) | 95.4121 | 0.116641 | ||||||||
\(819\) | − | 127.765i | − | 0.156001i | ||||||
\(820\) | 172.547 | − | 99.6202i | 0.210423 | − | 0.121488i | ||||
\(821\) | −271.907 | −0.331189 | −0.165595 | − | 0.986194i | \(-0.552954\pi\) | ||||
−0.165595 | + | 0.986194i | \(0.552954\pi\) | |||||||
\(822\) | −953.354 | + | 550.419i | −1.15980 | + | 0.669610i | ||||
\(823\) | −311.057 | − | 538.766i | −0.377955 | − | 0.654637i | 0.612810 | − | 0.790230i | \(-0.290039\pi\) |
−0.990765 | + | 0.135594i | \(0.956706\pi\) | |||||||
\(824\) | 472.249 | + | 272.653i | 0.573118 | + | 0.330890i | ||||
\(825\) | 176.870i | 0.214388i | ||||||||
\(826\) | −42.2587 | + | 73.1943i | −0.0511607 | + | 0.0886129i | ||||
\(827\) | −529.310 | − | 916.791i | −0.640036 | − | 1.10857i | −0.985424 | − | 0.170115i | \(-0.945586\pi\) |
0.345388 | − | 0.938460i | \(-0.387747\pi\) | |||||||
\(828\) | −514.271 | −0.621100 | ||||||||
\(829\) | 269.501 | − | 155.597i | 0.325092 | − | 0.187692i | −0.328568 | − | 0.944480i | \(-0.606566\pi\) |
0.653660 | + | 0.756788i | \(0.273233\pi\) | |||||||
\(830\) | −337.512 | + | 584.587i | −0.406641 | + | 0.704322i | ||||
\(831\) | −199.517 | + | 345.573i | −0.240092 | + | 0.415852i | ||||
\(832\) | −314.122 | + | 544.076i | −0.377551 | + | 0.653938i | ||||
\(833\) | 1178.17 | 1.41437 | ||||||||
\(834\) | 197.722 | − | 342.465i | 0.237077 | − | 0.410629i | ||||
\(835\) | −899.643 | − | 519.409i | −1.07742 | − | 0.622047i | ||||
\(836\) | 312.356 | − | 180.339i | 0.373632 | − | 0.215716i | ||||
\(837\) | 1.19556 | − | 0.690258i | 0.00142839 | − | 0.000824681i | ||||
\(838\) | 275.779 | 0.329091 | ||||||||
\(839\) | − | 827.992i | − | 0.986879i | −0.869780 | − | 0.493440i | \(-0.835739\pi\) | ||
0.869780 | − | 0.493440i | \(-0.164261\pi\) | |||||||
\(840\) | 136.088 | + | 235.711i | 0.162010 | + | 0.280609i | ||||
\(841\) | −291.390 | − | 504.702i | −0.346480 | − | 0.600121i | ||||
\(842\) | 270.706 | − | 468.876i | 0.321504 | − | 0.556860i | ||||
\(843\) | 283.241 | + | 163.529i | 0.335991 | + | 0.193985i | ||||
\(844\) | 648.380i | 0.768223i | ||||||||
\(845\) | −311.798 | − | 180.017i | −0.368992 | − | 0.213037i | ||||
\(846\) | 918.799 | + | 530.469i | 1.08605 | + | 0.627032i | ||||
\(847\) | 324.599 | + | 187.408i | 0.383234 | + | 0.221260i | ||||
\(848\) | 81.5833 | + | 141.306i | 0.0962067 | + | 0.166635i | ||||
\(849\) | 695.869i | 0.819634i | ||||||||
\(850\) | −69.9897 | + | 40.4086i | −0.0823408 | + | 0.0475395i | ||||
\(851\) | −633.213 | − | 365.586i | −0.744082 | − | 0.429596i | ||||
\(852\) | 925.736 | 1.08654 | ||||||||
\(853\) | −764.869 | + | 1324.79i | −0.896682 | + | 1.55310i | −0.0649722 | + | 0.997887i | \(0.520696\pi\) |
−0.831709 | + | 0.555211i | \(0.812637\pi\) | |||||||
\(854\) | 59.4382 | − | 34.3167i | 0.0695998 | − | 0.0401835i | ||||
\(855\) | 250.442 | + | 433.779i | 0.292915 | + | 0.507343i | ||||
\(856\) | − | 945.612i | − | 1.10469i | ||||||
\(857\) | −622.430 | − | 1078.08i | −0.726289 | − | 1.25797i | −0.958441 | − | 0.285290i | \(-0.907910\pi\) |
0.232152 | − | 0.972679i | \(-0.425423\pi\) | |||||||
\(858\) | −1253.72 | −1.46121 | ||||||||
\(859\) | − | 158.942i | − | 0.185032i | −0.995711 | − | 0.0925159i | \(-0.970509\pi\) | ||
0.995711 | − | 0.0925159i | \(-0.0294909\pi\) | |||||||
\(860\) | −171.224 | + | 343.890i | −0.199098 | + | 0.399873i | ||||
\(861\) | 134.894 | 0.156672 | ||||||||
\(862\) | − | 305.301i | − | 0.354177i | ||||||
\(863\) | −320.063 | + | 184.788i | −0.370872 | + | 0.214123i | −0.673839 | − | 0.738878i | \(-0.735356\pi\) |
0.302967 | + | 0.953001i | \(0.402023\pi\) | |||||||
\(864\) | 4.68088 | 0.00541768 | ||||||||
\(865\) | 388.233 | − | 224.146i | 0.448824 | − | 0.259129i | ||||
\(866\) | −352.605 | − | 610.730i | −0.407165 | − | 0.705231i | ||||
\(867\) | 1249.12 | + | 721.182i | 1.44074 | + | 0.831813i | ||||
\(868\) | 18.1870i | 0.0209528i | ||||||||
\(869\) | −357.420 | + | 619.069i | −0.411300 | + | 0.712393i | ||||
\(870\) | 268.060 | + | 464.294i | 0.308115 | + | 0.533671i | ||||
\(871\) | 1223.41 | 1.40461 | ||||||||
\(872\) | −259.989 | + | 150.104i | −0.298152 | + | 0.172138i | ||||
\(873\) | −506.659 | + | 877.560i | −0.580366 | + | 1.00522i | ||||
\(874\) | 271.670 | − | 470.546i | 0.310835 | − | 0.538382i | ||||
\(875\) | 85.0161 | − | 147.252i | 0.0971612 | − | 0.168288i | ||||
\(876\) | −125.278 | −0.143011 | ||||||||
\(877\) | 411.371 | − | 712.516i | 0.469067 | − | 0.812447i | −0.530308 | − | 0.847805i | \(-0.677924\pi\) |
0.999375 | + | 0.0353577i | \(0.0112571\pi\) | |||||||
\(878\) | 835.409 | + | 482.324i | 0.951491 | + | 0.549344i | ||||
\(879\) | −652.018 | + | 376.443i | −0.741773 | + | 0.428263i | ||||
\(880\) | 547.531 | − | 316.117i | 0.622194 | − | 0.359224i | ||||
\(881\) | 1688.29 | 1.91634 | 0.958169 | − | 0.286205i | \(-0.0923937\pi\) | ||||
0.958169 | + | 0.286205i | \(0.0923937\pi\) | |||||||
\(882\) | − | 635.768i | − | 0.720825i | ||||||
\(883\) | 299.386 | + | 518.552i | 0.339055 | + | 0.587261i | 0.984255 | − | 0.176753i | \(-0.0565592\pi\) |
−0.645200 | + | 0.764014i | \(0.723226\pi\) | |||||||
\(884\) | 215.017 | + | 372.421i | 0.243232 | + | 0.421291i | ||||
\(885\) | 432.293 | − | 748.753i | 0.488466 | − | 0.846048i | ||||
\(886\) | −473.933 | − | 273.625i | −0.534913 | − | 0.308832i | ||||
\(887\) | − | 1583.51i | − | 1.78524i | −0.450810 | − | 0.892620i | \(-0.648865\pi\) | ||
0.450810 | − | 0.892620i | \(-0.351135\pi\) | |||||||
\(888\) | −692.389 | − | 399.751i | −0.779717 | − | 0.450170i | ||||
\(889\) | −34.0519 | − | 19.6599i | −0.0383036 | − | 0.0221146i | ||||
\(890\) | 88.0264 | + | 50.8221i | 0.0989061 | + | 0.0571035i | ||||
\(891\) | 797.049 | + | 1380.53i | 0.894555 | + | 1.54941i | ||||
\(892\) | − | 381.596i | − | 0.427798i | ||||||
\(893\) | 728.711 | − | 420.721i | 0.816025 | − | 0.471133i | ||||
\(894\) | 1158.27 | + | 668.725i | 1.29560 | + | 0.748015i | ||||
\(895\) | 424.763 | 0.474596 | ||||||||
\(896\) | −4.08922 | + | 7.08274i | −0.00456386 | + | 0.00790484i | ||||
\(897\) | 1227.83 | − | 708.887i | 1.36882 | − | 0.790286i | ||||
\(898\) | −535.732 | − | 927.915i | −0.596584 | − | 1.03331i | ||||
\(899\) | 119.370i | 0.132781i | ||||||||
\(900\) | −16.3689 | − | 28.3517i | −0.0181876 | − | 0.0315019i | ||||
\(901\) | 660.502 | 0.733076 | ||||||||
\(902\) | − | 660.222i | − | 0.731953i | ||||||
\(903\) | −216.809 | + | 143.673i | −0.240099 | + | 0.159106i | ||||
\(904\) | 216.041 | 0.238983 | ||||||||
\(905\) | − | 883.080i | − | 0.975779i | ||||||
\(906\) | −855.716 | + | 494.048i | −0.944499 | + | 0.545307i | ||||
\(907\) | 1250.79 | 1.37904 | 0.689518 | − | 0.724269i | \(-0.257822\pi\) | ||||
0.689518 | + | 0.724269i | \(0.257822\pi\) | |||||||
\(908\) | −300.680 | + | 173.598i | −0.331145 | + | 0.191187i | ||||
\(909\) | −305.397 | − | 528.964i | −0.335971 | − | 0.581918i | ||||
\(910\) | −97.2707 | − | 56.1593i | −0.106891 | − | 0.0617135i | ||||
\(911\) | − | 170.898i | − | 0.187594i | −0.995591 | − | 0.0937970i | \(-0.970100\pi\) | ||
0.995591 | − | 0.0937970i | \(-0.0299005\pi\) | |||||||
\(912\) | 140.985 | − | 244.193i | 0.154589 | − | 0.267756i | ||||
\(913\) | −839.570 | − | 1454.18i | −0.919573 | − | 1.59275i | ||||
\(914\) | −671.964 | −0.735191 | ||||||||
\(915\) | −608.033 | + | 351.048i | −0.664517 | + | 0.383659i | ||||
\(916\) | 120.820 | − | 209.266i | 0.131899 | − | 0.228457i | ||||
\(917\) | 21.9935 | − | 38.0939i | 0.0239842 | − | 0.0415419i | ||||
\(918\) | −3.52367 | + | 6.10318i | −0.00383843 | + | 0.00664835i | ||||
\(919\) | −169.349 | −0.184275 | −0.0921377 | − | 0.995746i | \(-0.529370\pi\) | ||||
−0.0921377 | + | 0.995746i | \(0.529370\pi\) | |||||||
\(920\) | −753.222 | + | 1304.62i | −0.818719 | + | 1.41806i | ||||
\(921\) | 884.768 | + | 510.821i | 0.960660 | + | 0.554637i | ||||
\(922\) | −655.417 | + | 378.405i | −0.710865 | + | 0.410418i | ||||
\(923\) | −1102.40 | + | 636.473i | −1.19437 | + | 0.689569i | ||||
\(924\) | −203.187 | −0.219900 | ||||||||
\(925\) | − | 46.5454i | − | 0.0503193i | ||||||
\(926\) | −660.061 | − | 1143.26i | −0.712809 | − | 1.23462i | ||||
\(927\) | −282.667 | − | 489.594i | −0.304927 | − | 0.528149i | ||||
\(928\) | −202.372 | + | 350.519i | −0.218073 | + | 0.377714i | ||||
\(929\) | −850.652 | − | 491.124i | −0.915665 | − | 0.528659i | −0.0334152 | − | 0.999442i | \(-0.510638\pi\) |
−0.882249 | + | 0.470782i | \(0.843972\pi\) | |||||||
\(930\) | 247.837i | 0.266492i | ||||||||
\(931\) | −436.680 | − | 252.118i | −0.469044 | − | 0.270803i | ||||
\(932\) | 75.0933 | + | 43.3551i | 0.0805722 | + | 0.0465184i | ||||
\(933\) | −172.794 | − | 99.7627i | −0.185203 | − | 0.106927i | ||||
\(934\) | −16.7227 | − | 28.9645i | −0.0179043 | − | 0.0310112i | ||||
\(935\) | − | 2559.30i | − | 2.73722i | ||||||
\(936\) | 669.646 | − | 386.620i | 0.715434 | − | 0.413056i | ||||
\(937\) | 999.637 | + | 577.141i | 1.06685 | + | 0.615945i | 0.927319 | − | 0.374273i | \(-0.122108\pi\) |
0.139530 | + | 0.990218i | \(0.455441\pi\) | |||||||
\(938\) | −264.128 | −0.281587 | ||||||||
\(939\) | −7.79453 | + | 13.5005i | −0.00830089 | + | 0.0143776i | ||||
\(940\) | −606.339 | + | 350.070i | −0.645042 | + | 0.372415i | ||||
\(941\) | 832.384 | + | 1441.73i | 0.884574 | + | 1.53213i | 0.846201 | + | 0.532864i | \(0.178884\pi\) |
0.0383733 | + | 0.999263i | \(0.487782\pi\) | |||||||
\(942\) | − | 1018.19i | − | 1.08089i | ||||||
\(943\) | 373.308 | + | 646.588i | 0.395873 | + | 0.685672i | ||||
\(944\) | −242.763 | −0.257164 | ||||||||
\(945\) | 1.38175i | 0.00146217i | ||||||||
\(946\) | 703.185 | + | 1061.14i | 0.743325 | + | 1.12172i | ||||
\(947\) | −451.815 | −0.477101 | −0.238551 | − | 0.971130i | \(-0.576672\pi\) | ||||
−0.238551 | + | 0.971130i | \(0.576672\pi\) | |||||||
\(948\) | − | 265.274i | − | 0.279825i | ||||||
\(949\) | 149.186 | − | 86.1325i | 0.157203 | − | 0.0907613i | ||||
\(950\) | 34.5882 | 0.0364086 | ||||||||
\(951\) | 287.458 | − | 165.964i | 0.302270 | − | 0.174515i | ||||
\(952\) | −154.681 | − | 267.915i | −0.162480 | − | 0.281423i | ||||
\(953\) | 538.083 | + | 310.662i | 0.564620 | + | 0.325984i | 0.754998 | − | 0.655727i | \(-0.227638\pi\) |
−0.190378 | + | 0.981711i | \(0.560971\pi\) | |||||||
\(954\) | − | 356.421i | − | 0.373607i | ||||||
\(955\) | −257.573 | + | 446.129i | −0.269710 | + | 0.467151i | ||||
\(956\) | −10.0927 | − | 17.4811i | −0.0105573 | − | 0.0182857i | ||||
\(957\) | −1333.61 | −1.39354 | ||||||||
\(958\) | −959.976 | + | 554.242i | −1.00206 | + | 0.578541i | ||||
\(959\) | 122.663 | − | 212.459i | 0.127907 | − | 0.221542i | ||||
\(960\) | −693.749 | + | 1201.61i | −0.722655 | + | 1.25167i | ||||
\(961\) | 452.909 | − | 784.461i | 0.471289 | − | 0.816297i | ||||
\(962\) | 329.929 | 0.342962 | ||||||||
\(963\) | −490.171 | + | 849.002i | −0.509005 | + | 0.881622i | ||||
\(964\) | 225.775 | + | 130.351i | 0.234206 | + | 0.135219i | ||||
\(965\) | 1099.60 | − | 634.856i | 1.13949 | − | 0.657882i | ||||
\(966\) | −265.081 | + | 153.045i | −0.274411 | + | 0.158431i | ||||
\(967\) | 19.2812 | 0.0199392 | 0.00996961 | − | 0.999950i | \(-0.496827\pi\) | ||||
0.00996961 | + | 0.999950i | \(0.496827\pi\) | |||||||
\(968\) | 2268.40i | 2.34339i | ||||||||
\(969\) | −570.711 | − | 988.501i | −0.588969 | − | 1.02012i | ||||
\(970\) | 445.406 | + | 771.465i | 0.459181 | + | 0.795325i | ||||
\(971\) | 454.351 | − | 786.958i | 0.467920 | − | 0.810462i | −0.531408 | − | 0.847116i | \(-0.678337\pi\) |
0.999328 | + | 0.0366546i | \(0.0116701\pi\) | |||||||
\(972\) | −509.824 | − | 294.347i | −0.524510 | − | 0.302826i | ||||
\(973\) | 88.1262i | 0.0905716i | ||||||||
\(974\) | −622.746 | − | 359.543i | −0.639370 | − | 0.369140i | ||||
\(975\) | 78.1617 | + | 45.1267i | 0.0801659 | + | 0.0462838i | ||||
\(976\) | 170.727 | + | 98.5691i | 0.174925 | + | 0.100993i | ||||
\(977\) | −464.004 | − | 803.679i | −0.474928 | − | 0.822599i | 0.524660 | − | 0.851312i | \(-0.324192\pi\) |
−0.999588 | + | 0.0287130i | \(0.990859\pi\) | |||||||
\(978\) | 252.480i | 0.258160i | ||||||||
\(979\) | −218.968 | + | 126.421i | −0.223665 | + | 0.129133i | ||||
\(980\) | 363.349 | + | 209.780i | 0.370765 | + | 0.214061i | ||||
\(981\) | 311.235 | 0.317263 | ||||||||
\(982\) | −35.5082 | + | 61.5019i | −0.0361590 | + | 0.0626293i | ||||
\(983\) | 895.385 | − | 516.951i | 0.910869 | − | 0.525891i | 0.0301586 | − | 0.999545i | \(-0.490399\pi\) |
0.880711 | + | 0.473654i | \(0.157065\pi\) | |||||||
\(984\) | 408.195 | + | 707.014i | 0.414832 | + | 0.718510i | ||||
\(985\) | 1674.44i | 1.69994i | ||||||||
\(986\) | −304.684 | − | 527.728i | −0.309010 | − | 0.535221i | ||||
\(987\) | −474.026 | −0.480269 | ||||||||
\(988\) | − | 184.047i | − | 0.186282i | ||||||
\(989\) | −1288.66 | − | 641.630i | −1.30300 | − | 0.648766i | ||||
\(990\) | −1381.05 | −1.39500 | ||||||||
\(991\) | 1837.99i | 1.85469i | 0.374212 | + | 0.927343i | \(0.377913\pi\) | ||||
−0.374212 | + | 0.927343i | \(0.622087\pi\) | |||||||
\(992\) | −162.038 | + | 93.5524i | −0.163344 | + | 0.0943069i | ||||
\(993\) | 318.270 | 0.320514 | ||||||||
\(994\) | 238.003 | − | 137.411i | 0.239439 | − | 0.138240i | ||||
\(995\) | −102.110 | − | 176.860i | −0.102623 | − | 0.177749i | ||||
\(996\) | 539.639 | + | 311.561i | 0.541807 | + | 0.312812i | ||||
\(997\) | 1108.28i | 1.11161i | 0.831312 | + | 0.555806i | \(0.187590\pi\) | ||||
−0.831312 | + | 0.555806i | \(0.812410\pi\) | |||||||
\(998\) | 415.832 | − | 720.242i | 0.416666 | − | 0.721686i | ||||
\(999\) | −2.02940 | − | 3.51503i | −0.00203144 | − | 0.00351855i |
(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 | 43.3.d.a.7.4 | ✓ | 12 | |
3.2 | odd | 2 | 387.3.j.c.136.3 | 12 | |||
4.3 | odd | 2 | 688.3.t.c.609.6 | 12 | |||
43.37 | odd | 6 | inner | 43.3.d.a.37.3 | yes | 12 | |
129.80 | even | 6 | 387.3.j.c.37.4 | 12 | |||
172.123 | even | 6 | 688.3.t.c.209.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.3.d.a.7.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
43.3.d.a.37.3 | yes | 12 | 43.37 | odd | 6 | inner | |
387.3.j.c.37.4 | 12 | 129.80 | even | 6 | |||
387.3.j.c.136.3 | 12 | 3.2 | odd | 2 | |||
688.3.t.c.209.6 | 12 | 172.123 | even | 6 | |||
688.3.t.c.609.6 | 12 | 4.3 | odd | 2 |