Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(37,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.v (of order \(12\), 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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Character | \(\chi\) | \(=\) | 210.193 |
Dual form | 210.3.v.a.37.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | − | 0.366025i | −0.683013 | − | 0.183013i | ||||
\(3\) | −1.67303 | + | 0.448288i | −0.557678 | + | 0.149429i | ||||
\(4\) | 1.73205 | + | 1.00000i | 0.433013 | + | 0.250000i | ||||
\(5\) | −4.60436 | + | 1.94932i | −0.920873 | + | 0.389864i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −4.28537 | + | 5.53495i | −0.612195 | + | 0.790707i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 2.59808 | − | 1.50000i | 0.288675 | − | 0.166667i | ||||
\(10\) | 7.00318 | − | 0.977504i | 0.700318 | − | 0.0977504i | ||||
\(11\) | 8.47882 | − | 14.6857i | 0.770802 | − | 1.33507i | −0.166322 | − | 0.986071i | \(-0.553189\pi\) |
0.937124 | − | 0.348996i | \(-0.113477\pi\) | |||||||
\(12\) | −3.34607 | − | 0.896575i | −0.278839 | − | 0.0747146i | ||||
\(13\) | 3.05181 | + | 3.05181i | 0.234754 | + | 0.234754i | 0.814674 | − | 0.579920i | \(-0.196916\pi\) |
−0.579920 | + | 0.814674i | \(0.696916\pi\) | |||||||
\(14\) | 7.87985 | − | 5.99233i | 0.562846 | − | 0.428023i | ||||
\(15\) | 6.82939 | − | 5.32535i | 0.455293 | − | 0.355023i | ||||
\(16\) | 2.00000 | + | 3.46410i | 0.125000 | + | 0.216506i | ||||
\(17\) | −2.87910 | − | 10.7449i | −0.169359 | − | 0.632055i | −0.997444 | − | 0.0714531i | \(-0.977236\pi\) |
0.828085 | − | 0.560602i | \(-0.189430\pi\) | |||||||
\(18\) | −4.09808 | + | 1.09808i | −0.227671 | + | 0.0610042i | ||||
\(19\) | −5.74405 | + | 3.31633i | −0.302318 | + | 0.174544i | −0.643484 | − | 0.765460i | \(-0.722512\pi\) |
0.341166 | + | 0.940003i | \(0.389178\pi\) | |||||||
\(20\) | −9.92431 | − | 1.22805i | −0.496215 | − | 0.0614023i | ||||
\(21\) | 4.68831 | − | 11.1812i | 0.223253 | − | 0.532439i | ||||
\(22\) | −16.9576 | + | 16.9576i | −0.770802 | + | 0.770802i | ||||
\(23\) | 4.49666 | − | 16.7817i | 0.195507 | − | 0.729641i | −0.796628 | − | 0.604469i | \(-0.793385\pi\) |
0.992135 | − | 0.125172i | \(-0.0399482\pi\) | |||||||
\(24\) | 4.24264 | + | 2.44949i | 0.176777 | + | 0.102062i | ||||
\(25\) | 17.4003 | − | 17.9507i | 0.696013 | − | 0.718029i | ||||
\(26\) | −3.05181 | − | 5.28588i | −0.117377 | − | 0.203303i | ||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | −12.9574 | + | 5.30145i | −0.462765 | + | 0.189337i | ||||
\(29\) | − | 35.8861i | − | 1.23745i | −0.785607 | − | 0.618725i | \(-0.787649\pi\) | ||
0.785607 | − | 0.618725i | \(-0.212351\pi\) | |||||||
\(30\) | −11.2783 | + | 4.77483i | −0.375945 | + | 0.159161i | ||||
\(31\) | 22.7901 | − | 39.4736i | 0.735165 | − | 1.27334i | −0.219486 | − | 0.975616i | \(-0.570438\pi\) |
0.954651 | − | 0.297727i | \(-0.0962286\pi\) | |||||||
\(32\) | −1.46410 | − | 5.46410i | −0.0457532 | − | 0.170753i | ||||
\(33\) | −7.60190 | + | 28.3707i | −0.230361 | + | 0.859718i | ||||
\(34\) | 15.7317i | 0.462697i | ||||||||
\(35\) | 8.94201 | − | 33.8384i | 0.255486 | − | 0.966813i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 17.7095 | + | 4.74524i | 0.478635 | + | 0.128250i | 0.490067 | − | 0.871685i | \(-0.336972\pi\) |
−0.0114320 | + | 0.999935i | \(0.503639\pi\) | |||||||
\(38\) | 9.06038 | − | 2.42772i | 0.238431 | − | 0.0638874i | ||||
\(39\) | −6.47386 | − | 3.73768i | −0.165996 | − | 0.0958380i | ||||
\(40\) | 13.1074 | + | 5.31009i | 0.327684 | + | 0.132752i | ||||
\(41\) | −42.9609 | −1.04783 | −0.523913 | − | 0.851772i | \(-0.675528\pi\) | ||||
−0.523913 | + | 0.851772i | \(0.675528\pi\) | |||||||
\(42\) | −10.4970 | + | 13.5578i | −0.249928 | + | 0.322805i | ||||
\(43\) | −1.98628 | − | 1.98628i | −0.0461926 | − | 0.0461926i | 0.683633 | − | 0.729826i | \(-0.260399\pi\) |
−0.729826 | + | 0.683633i | \(0.760399\pi\) | |||||||
\(44\) | 29.3715 | − | 16.9576i | 0.667534 | − | 0.385401i | ||||
\(45\) | −9.03851 | + | 11.9710i | −0.200856 | + | 0.266023i | ||||
\(46\) | −12.2851 | + | 21.2784i | −0.267067 | + | 0.462574i | ||||
\(47\) | 42.2437 | + | 11.3192i | 0.898801 | + | 0.240833i | 0.678501 | − | 0.734599i | \(-0.262630\pi\) |
0.220300 | + | 0.975432i | \(0.429296\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.102062 | − | 0.102062i | ||||
\(49\) | −12.2713 | − | 47.4385i | −0.250434 | − | 0.968134i | ||||
\(50\) | −30.3397 | + | 18.1522i | −0.606794 | + | 0.363044i | ||||
\(51\) | 9.63365 | + | 16.6860i | 0.188895 | + | 0.327176i | ||||
\(52\) | 2.23408 | + | 8.33769i | 0.0429630 | + | 0.160340i | ||||
\(53\) | −82.1632 | + | 22.0156i | −1.55025 | + | 0.415388i | −0.929561 | − | 0.368669i | \(-0.879813\pi\) |
−0.620688 | + | 0.784057i | \(0.713147\pi\) | |||||||
\(54\) | 6.36396 | − | 3.67423i | 0.117851 | − | 0.0680414i | ||||
\(55\) | −10.4124 | + | 84.1464i | −0.189316 | + | 1.52993i | ||||
\(56\) | 19.6406 | − | 2.49916i | 0.350725 | − | 0.0446279i | ||||
\(57\) | 8.12331 | − | 8.12331i | 0.142514 | − | 0.142514i | ||||
\(58\) | −13.1352 | + | 49.0213i | −0.226469 | + | 0.845195i | ||||
\(59\) | 22.0174 | + | 12.7117i | 0.373176 | + | 0.215453i | 0.674845 | − | 0.737960i | \(-0.264211\pi\) |
−0.301669 | + | 0.953413i | \(0.597544\pi\) | |||||||
\(60\) | 17.1542 | − | 2.39439i | 0.285903 | − | 0.0399064i | ||||
\(61\) | 42.4823 | + | 73.5814i | 0.696431 | + | 1.20625i | 0.969696 | + | 0.244314i | \(0.0785629\pi\) |
−0.273265 | + | 0.961939i | \(0.588104\pi\) | |||||||
\(62\) | −45.5802 | + | 45.5802i | −0.735165 | + | 0.735165i | ||||
\(63\) | −2.83128 | + | 20.8083i | −0.0449410 | + | 0.330290i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | −20.0006 | − | 8.10268i | −0.307701 | − | 0.124657i | ||||
\(66\) | 20.7688 | − | 35.9726i | 0.314678 | − | 0.545039i | ||||
\(67\) | −16.2919 | − | 60.8022i | −0.243163 | − | 0.907496i | −0.974298 | − | 0.225263i | \(-0.927676\pi\) |
0.731135 | − | 0.682233i | \(-0.238991\pi\) | |||||||
\(68\) | 5.75820 | − | 21.4899i | 0.0846794 | − | 0.316028i | ||||
\(69\) | 30.0922i | 0.436119i | ||||||||
\(70\) | −24.6007 | + | 42.9512i | −0.351439 | + | 0.613588i | ||||
\(71\) | 137.965 | 1.94316 | 0.971582 | − | 0.236705i | \(-0.0760674\pi\) | ||||
0.971582 | + | 0.236705i | \(0.0760674\pi\) | |||||||
\(72\) | −8.19615 | − | 2.19615i | −0.113835 | − | 0.0305021i | ||||
\(73\) | −7.00522 | + | 1.87704i | −0.0959619 | + | 0.0257129i | −0.306480 | − | 0.951877i | \(-0.599151\pi\) |
0.210519 | + | 0.977590i | \(0.432485\pi\) | |||||||
\(74\) | −22.4547 | − | 12.9642i | −0.303442 | − | 0.175193i | ||||
\(75\) | −21.0642 | + | 37.8325i | −0.280856 | + | 0.504434i | ||||
\(76\) | −13.2653 | −0.174544 | ||||||||
\(77\) | 44.9500 | + | 109.864i | 0.583766 | + | 1.42680i | ||||
\(78\) | 7.47537 | + | 7.47537i | 0.0958380 | + | 0.0958380i | ||||
\(79\) | −35.4965 | + | 20.4939i | −0.449322 | + | 0.259416i | −0.707544 | − | 0.706669i | \(-0.750197\pi\) |
0.258222 | + | 0.966086i | \(0.416863\pi\) | |||||||
\(80\) | −15.9614 | − | 12.0513i | −0.199517 | − | 0.150642i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 58.6857 | + | 15.7248i | 0.715679 | + | 0.191766i | ||||
\(83\) | −109.947 | − | 109.947i | −1.32466 | − | 1.32466i | −0.909959 | − | 0.414699i | \(-0.863887\pi\) |
−0.414699 | − | 0.909959i | \(-0.636113\pi\) | |||||||
\(84\) | 19.3016 | − | 14.6781i | 0.229781 | − | 0.174740i | ||||
\(85\) | 34.2017 | + | 43.8613i | 0.402373 | + | 0.516016i | ||||
\(86\) | 1.98628 | + | 3.44034i | 0.0230963 | + | 0.0400040i | ||||
\(87\) | 16.0873 | + | 60.0386i | 0.184911 | + | 0.690098i | ||||
\(88\) | −46.3291 | + | 12.4139i | −0.526467 | + | 0.141066i | ||||
\(89\) | −49.9706 | + | 28.8505i | −0.561467 | + | 0.324163i | −0.753734 | − | 0.657179i | \(-0.771749\pi\) |
0.192267 | + | 0.981343i | \(0.438416\pi\) | |||||||
\(90\) | 16.7285 | − | 13.0444i | 0.185873 | − | 0.144938i | ||||
\(91\) | −29.9697 | + | 3.81348i | −0.329337 | + | 0.0419064i | ||||
\(92\) | 24.5702 | − | 24.5702i | 0.267067 | − | 0.267067i | ||||
\(93\) | −20.4331 | + | 76.2572i | −0.219710 | + | 0.819970i | ||||
\(94\) | −53.5628 | − | 30.9245i | −0.569817 | − | 0.328984i | ||||
\(95\) | 19.9831 | − | 26.4666i | 0.210349 | − | 0.278595i | ||||
\(96\) | 4.89898 | + | 8.48528i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −39.7542 | + | 39.7542i | −0.409837 | + | 0.409837i | −0.881682 | − | 0.471845i | \(-0.843588\pi\) |
0.471845 | + | 0.881682i | \(0.343588\pi\) | |||||||
\(98\) | −0.600821 | + | 69.2939i | −0.00613082 | + | 0.707080i | ||||
\(99\) | − | 50.8729i | − | 0.513868i | ||||||
\(100\) | 48.0890 | − | 13.6913i | 0.480890 | − | 0.136913i | ||||
\(101\) | 36.2458 | − | 62.7796i | 0.358869 | − | 0.621580i | −0.628903 | − | 0.777484i | \(-0.716496\pi\) |
0.987772 | + | 0.155904i | \(0.0498290\pi\) | |||||||
\(102\) | −7.05232 | − | 26.3196i | −0.0691404 | − | 0.258036i | ||||
\(103\) | 40.9621 | − | 152.873i | 0.397690 | − | 1.48420i | −0.419459 | − | 0.907774i | \(-0.637780\pi\) |
0.817149 | − | 0.576426i | \(-0.195553\pi\) | |||||||
\(104\) | − | 12.2072i | − | 0.117377i | ||||||
\(105\) | 0.209093 | + | 60.6214i | 0.00199136 | + | 0.577347i | ||||
\(106\) | 120.295 | 1.13486 | ||||||||
\(107\) | 43.4424 | + | 11.6403i | 0.406003 | + | 0.108788i | 0.456040 | − | 0.889959i | \(-0.349267\pi\) |
−0.0500370 | + | 0.998747i | \(0.515934\pi\) | |||||||
\(108\) | −10.0382 | + | 2.68973i | −0.0929463 | + | 0.0249049i | ||||
\(109\) | −83.0179 | − | 47.9304i | −0.761632 | − | 0.439729i | 0.0682492 | − | 0.997668i | \(-0.478259\pi\) |
−0.829881 | + | 0.557940i | \(0.811592\pi\) | |||||||
\(110\) | 45.0233 | − | 111.135i | 0.409303 | − | 1.01032i | ||||
\(111\) | −31.7558 | −0.286088 | ||||||||
\(112\) | −27.7444 | − | 3.77505i | −0.247717 | − | 0.0337058i | ||||
\(113\) | −86.6065 | − | 86.6065i | −0.766429 | − | 0.766429i | 0.211047 | − | 0.977476i | \(-0.432313\pi\) |
−0.977476 | + | 0.211047i | \(0.932313\pi\) | |||||||
\(114\) | −14.0700 | + | 8.12331i | −0.123421 | + | 0.0712571i | ||||
\(115\) | 12.0087 | + | 86.0347i | 0.104424 | + | 0.748127i | ||||
\(116\) | 35.8861 | − | 62.1565i | 0.309363 | − | 0.535832i | ||||
\(117\) | 12.5065 | + | 3.35111i | 0.106893 | + | 0.0286420i | ||||
\(118\) | −25.4235 | − | 25.4235i | −0.215453 | − | 0.215453i | ||||
\(119\) | 71.8107 | + | 30.1103i | 0.603451 | + | 0.253028i | ||||
\(120\) | −24.3095 | − | 3.00809i | −0.202579 | − | 0.0250674i | ||||
\(121\) | −83.2807 | − | 144.246i | −0.688270 | − | 1.19212i | ||||
\(122\) | −31.0992 | − | 116.064i | −0.254911 | − | 0.951342i | ||||
\(123\) | 71.8750 | − | 19.2588i | 0.584350 | − | 0.156576i | ||||
\(124\) | 78.9472 | − | 45.5802i | 0.636671 | − | 0.367582i | ||||
\(125\) | −45.1257 | + | 116.570i | −0.361006 | + | 0.932564i | ||||
\(126\) | 11.4840 | − | 27.3883i | 0.0911425 | − | 0.217367i | ||||
\(127\) | 46.1257 | − | 46.1257i | 0.363194 | − | 0.363194i | −0.501793 | − | 0.864988i | \(-0.667326\pi\) |
0.864988 | + | 0.501793i | \(0.167326\pi\) | |||||||
\(128\) | 2.92820 | − | 10.9282i | 0.0228766 | − | 0.0853766i | ||||
\(129\) | 4.21354 | + | 2.43269i | 0.0326631 | + | 0.0188581i | ||||
\(130\) | 24.3555 | + | 18.3892i | 0.187350 | + | 0.141455i | ||||
\(131\) | −50.4917 | − | 87.4543i | −0.385433 | − | 0.667590i | 0.606396 | − | 0.795163i | \(-0.292615\pi\) |
−0.991829 | + | 0.127573i | \(0.959281\pi\) | |||||||
\(132\) | −41.5376 | + | 41.5376i | −0.314678 | + | 0.314678i | ||||
\(133\) | 6.25965 | − | 46.0047i | 0.0470650 | − | 0.345900i | ||||
\(134\) | 89.0206i | 0.664333i | ||||||||
\(135\) | 9.75526 | − | 24.0798i | 0.0722612 | − | 0.178369i | ||||
\(136\) | −15.7317 | + | 27.2481i | −0.115674 | + | 0.200354i | ||||
\(137\) | 34.1884 | + | 127.593i | 0.249550 | + | 0.931334i | 0.971042 | + | 0.238911i | \(0.0767903\pi\) |
−0.721491 | + | 0.692423i | \(0.756543\pi\) | |||||||
\(138\) | 11.0145 | − | 41.1067i | 0.0798153 | − | 0.297875i | ||||
\(139\) | 49.7454i | 0.357880i | 0.983860 | + | 0.178940i | \(0.0572669\pi\) | ||||
−0.983860 | + | 0.178940i | \(0.942733\pi\) | |||||||
\(140\) | 49.3265 | − | 49.6679i | 0.352332 | − | 0.354771i | ||||
\(141\) | −75.7493 | −0.537229 | ||||||||
\(142\) | −188.463 | − | 50.4985i | −1.32721 | − | 0.355624i | ||||
\(143\) | 70.6937 | − | 18.9423i | 0.494362 | − | 0.132464i | ||||
\(144\) | 10.3923 | + | 6.00000i | 0.0721688 | + | 0.0416667i | ||||
\(145\) | 69.9534 | + | 165.232i | 0.482437 | + | 1.13953i | ||||
\(146\) | 10.2564 | 0.0702490 | ||||||||
\(147\) | 41.7964 | + | 73.8652i | 0.284329 | + | 0.502484i | ||||
\(148\) | 25.9285 | + | 25.9285i | 0.175193 | + | 0.175193i | ||||
\(149\) | −196.729 | + | 113.581i | −1.32033 | + | 0.762291i | −0.983780 | − | 0.179377i | \(-0.942592\pi\) |
−0.336546 | + | 0.941667i | \(0.609259\pi\) | |||||||
\(150\) | 42.6219 | − | 43.9701i | 0.284146 | − | 0.293134i | ||||
\(151\) | 99.4676 | − | 172.283i | 0.658726 | − | 1.14095i | −0.322220 | − | 0.946665i | \(-0.604429\pi\) |
0.980946 | − | 0.194282i | \(-0.0622377\pi\) | |||||||
\(152\) | 18.1208 | + | 4.85544i | 0.119215 | + | 0.0319437i | ||||
\(153\) | −23.5975 | − | 23.5975i | −0.154232 | − | 0.154232i | ||||
\(154\) | −21.1900 | − | 166.529i | −0.137597 | − | 1.08136i | ||||
\(155\) | −27.9873 | + | 226.176i | −0.180563 | + | 1.45920i | ||||
\(156\) | −7.47537 | − | 12.9477i | −0.0479190 | − | 0.0829982i | ||||
\(157\) | −71.9955 | − | 268.691i | −0.458570 | − | 1.71141i | −0.677375 | − | 0.735638i | \(-0.736882\pi\) |
0.218805 | − | 0.975769i | \(-0.429784\pi\) | |||||||
\(158\) | 55.9903 | − | 15.0026i | 0.354369 | − | 0.0949530i | ||||
\(159\) | 127.592 | − | 73.6655i | 0.802468 | − | 0.463305i | ||||
\(160\) | 17.3925 | + | 22.3047i | 0.108703 | + | 0.139404i | ||||
\(161\) | 73.6163 | + | 96.8047i | 0.457244 | + | 0.601271i | ||||
\(162\) | −9.00000 | + | 9.00000i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 54.3034 | − | 202.663i | 0.333150 | − | 1.24333i | −0.572712 | − | 0.819757i | \(-0.694109\pi\) |
0.905861 | − | 0.423574i | \(-0.139225\pi\) | |||||||
\(164\) | −74.4105 | − | 42.9609i | −0.453722 | − | 0.261957i | ||||
\(165\) | −20.3016 | − | 145.447i | −0.123040 | − | 0.881500i | ||||
\(166\) | 109.947 | + | 190.433i | 0.662329 | + | 1.14719i | ||||
\(167\) | 14.8502 | − | 14.8502i | 0.0889236 | − | 0.0889236i | −0.661246 | − | 0.750169i | \(-0.729972\pi\) |
0.750169 | + | 0.661246i | \(0.229972\pi\) | |||||||
\(168\) | −31.7391 | + | 12.9858i | −0.188923 | + | 0.0772966i | ||||
\(169\) | − | 150.373i | − | 0.889781i | ||||||
\(170\) | −30.6661 | − | 72.4344i | −0.180389 | − | 0.426085i | ||||
\(171\) | −9.94898 | + | 17.2321i | −0.0581812 | + | 0.100773i | ||||
\(172\) | −1.45406 | − | 5.42662i | −0.00845383 | − | 0.0315501i | ||||
\(173\) | −33.1178 | + | 123.597i | −0.191432 | + | 0.714435i | 0.801729 | + | 0.597687i | \(0.203914\pi\) |
−0.993162 | + | 0.116748i | \(0.962753\pi\) | |||||||
\(174\) | − | 87.9026i | − | 0.505187i | ||||||
\(175\) | 24.7896 | + | 173.235i | 0.141655 | + | 0.989916i | ||||
\(176\) | 67.8305 | 0.385401 | ||||||||
\(177\) | −42.5343 | − | 11.3970i | −0.240307 | − | 0.0643900i | ||||
\(178\) | 78.8211 | − | 21.1200i | 0.442815 | − | 0.118652i | ||||
\(179\) | −128.441 | − | 74.1555i | −0.717548 | − | 0.414277i | 0.0963015 | − | 0.995352i | \(-0.469299\pi\) |
−0.813850 | + | 0.581076i | \(0.802632\pi\) | |||||||
\(180\) | −27.6262 | + | 11.6959i | −0.153479 | + | 0.0649773i | ||||
\(181\) | −140.949 | −0.778724 | −0.389362 | − | 0.921085i | \(-0.627305\pi\) | ||||
−0.389362 | + | 0.921085i | \(0.627305\pi\) | |||||||
\(182\) | 42.3352 | + | 5.76035i | 0.232611 | + | 0.0316503i | ||||
\(183\) | −104.060 | − | 104.060i | −0.568633 | − | 0.568633i | ||||
\(184\) | −42.5568 | + | 24.5702i | −0.231287 | + | 0.133534i | ||||
\(185\) | −90.7909 | + | 12.6726i | −0.490762 | + | 0.0685006i | ||||
\(186\) | 55.8241 | − | 96.6902i | 0.300130 | − | 0.519840i | ||||
\(187\) | −182.209 | − | 48.8227i | −0.974379 | − | 0.261084i | ||||
\(188\) | 61.8490 | + | 61.8490i | 0.328984 | + | 0.328984i | ||||
\(189\) | −4.59126 | − | 36.0821i | −0.0242924 | − | 0.190911i | ||||
\(190\) | −36.9849 | + | 28.8397i | −0.194657 | + | 0.151788i | ||||
\(191\) | 81.4029 | + | 140.994i | 0.426193 | + | 0.738188i | 0.996531 | − | 0.0832220i | \(-0.0265211\pi\) |
−0.570338 | + | 0.821410i | \(0.693188\pi\) | |||||||
\(192\) | −3.58630 | − | 13.3843i | −0.0186787 | − | 0.0697097i | ||||
\(193\) | 223.493 | − | 59.8847i | 1.15799 | − | 0.310283i | 0.371829 | − | 0.928301i | \(-0.378731\pi\) |
0.786164 | + | 0.618018i | \(0.212064\pi\) | |||||||
\(194\) | 68.8562 | − | 39.7542i | 0.354929 | − | 0.204918i | ||||
\(195\) | 37.0939 | + | 4.59004i | 0.190225 | + | 0.0235387i | ||||
\(196\) | 26.1840 | − | 94.4373i | 0.133592 | − | 0.481823i | ||||
\(197\) | 175.872 | − | 175.872i | 0.892750 | − | 0.892750i | −0.102031 | − | 0.994781i | \(-0.532534\pi\) |
0.994781 | + | 0.102031i | \(0.0325340\pi\) | |||||||
\(198\) | −18.6208 | + | 69.4937i | −0.0940443 | + | 0.350978i | ||||
\(199\) | 222.868 | + | 128.673i | 1.11994 | + | 0.646598i | 0.941386 | − | 0.337332i | \(-0.109525\pi\) |
0.178555 | + | 0.983930i | \(0.442858\pi\) | |||||||
\(200\) | −70.7021 | + | 1.10083i | −0.353511 | + | 0.00550414i | ||||
\(201\) | 54.5138 | + | 94.4206i | 0.271213 | + | 0.469754i | ||||
\(202\) | −72.4916 | + | 72.4916i | −0.358869 | + | 0.358869i | ||||
\(203\) | 198.628 | + | 153.785i | 0.978461 | + | 0.757561i | ||||
\(204\) | 38.5346i | 0.188895i | ||||||||
\(205\) | 197.808 | − | 83.7445i | 0.964915 | − | 0.408510i | ||||
\(206\) | −111.911 | + | 193.835i | −0.543255 | + | 0.940945i | ||||
\(207\) | −13.4900 | − | 50.3452i | −0.0651689 | − | 0.243214i | ||||
\(208\) | −4.46815 | + | 16.6754i | −0.0214815 | + | 0.0801701i | ||||
\(209\) | 112.474i | 0.538154i | ||||||||
\(210\) | 21.9034 | − | 82.8869i | 0.104302 | − | 0.394700i | ||||
\(211\) | −269.844 | −1.27888 | −0.639441 | − | 0.768840i | \(-0.720834\pi\) | ||||
−0.639441 | + | 0.768840i | \(0.720834\pi\) | |||||||
\(212\) | −164.326 | − | 44.0311i | −0.775125 | − | 0.207694i | ||||
\(213\) | −230.819 | + | 61.8478i | −1.08366 | + | 0.290365i | ||||
\(214\) | −55.0827 | − | 31.8020i | −0.257396 | − | 0.148608i | ||||
\(215\) | 13.0175 | + | 5.27367i | 0.0605463 | + | 0.0245287i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 120.821 | + | 295.301i | 0.556777 | + | 1.36083i | ||||
\(218\) | 95.8608 | + | 95.8608i | 0.439729 | + | 0.439729i | ||||
\(219\) | 10.8785 | − | 6.28071i | 0.0496735 | − | 0.0286790i | ||||
\(220\) | −102.181 | + | 135.333i | −0.464460 | + | 0.615152i | ||||
\(221\) | 24.0050 | − | 41.5779i | 0.108620 | − | 0.188135i | ||||
\(222\) | 43.3792 | + | 11.6234i | 0.195402 | + | 0.0523578i | ||||
\(223\) | 253.501 | + | 253.501i | 1.13677 | + | 1.13677i | 0.989025 | + | 0.147749i | \(0.0472029\pi\) |
0.147749 | + | 0.989025i | \(0.452797\pi\) | |||||||
\(224\) | 36.5177 | + | 15.3119i | 0.163026 | + | 0.0683569i | ||||
\(225\) | 18.2813 | − | 72.7379i | 0.0812500 | − | 0.323279i | ||||
\(226\) | 86.6065 | + | 150.007i | 0.383215 | + | 0.663747i | ||||
\(227\) | −3.59427 | − | 13.4140i | −0.0158338 | − | 0.0590925i | 0.957557 | − | 0.288244i | \(-0.0930715\pi\) |
−0.973391 | + | 0.229152i | \(0.926405\pi\) | |||||||
\(228\) | 22.1933 | − | 5.94668i | 0.0973390 | − | 0.0260819i | ||||
\(229\) | −310.927 | + | 179.514i | −1.35776 | + | 0.783904i | −0.989322 | − | 0.145747i | \(-0.953441\pi\) |
−0.368440 | + | 0.929651i | \(0.620108\pi\) | |||||||
\(230\) | 15.0867 | − | 121.921i | 0.0655941 | − | 0.530091i | ||||
\(231\) | −124.453 | − | 163.655i | −0.538759 | − | 0.708463i | ||||
\(232\) | −71.7721 | + | 71.7721i | −0.309363 | + | 0.309363i | ||||
\(233\) | −54.9811 | + | 205.192i | −0.235970 | + | 0.880653i | 0.741739 | + | 0.670689i | \(0.234001\pi\) |
−0.977709 | + | 0.209964i | \(0.932665\pi\) | |||||||
\(234\) | −15.8576 | − | 9.15542i | −0.0677677 | − | 0.0391257i | ||||
\(235\) | −216.570 | + | 30.2288i | −0.921574 | + | 0.128633i | ||||
\(236\) | 25.4235 | + | 44.0347i | 0.107727 | + | 0.186588i | ||||
\(237\) | 50.1996 | − | 50.1996i | 0.211813 | − | 0.211813i | ||||
\(238\) | −87.0741 | − | 67.4160i | −0.365857 | − | 0.283261i | ||||
\(239\) | − | 145.882i | − | 0.610384i | −0.952291 | − | 0.305192i | \(-0.901279\pi\) | ||
0.952291 | − | 0.305192i | \(-0.0987206\pi\) | |||||||
\(240\) | 32.1063 | + | 13.0070i | 0.133776 | + | 0.0541959i | ||||
\(241\) | −132.371 | + | 229.274i | −0.549258 | + | 0.951343i | 0.449068 | + | 0.893498i | \(0.351756\pi\) |
−0.998326 | + | 0.0578448i | \(0.981577\pi\) | |||||||
\(242\) | 60.9657 | + | 227.527i | 0.251924 | + | 0.940195i | ||||
\(243\) | −4.03459 | + | 15.0573i | −0.0166032 | + | 0.0619642i | ||||
\(244\) | 169.929i | 0.696431i | ||||||||
\(245\) | 148.974 | + | 194.504i | 0.608058 | + | 0.793892i | ||||
\(246\) | −105.232 | −0.427774 | ||||||||
\(247\) | −27.6505 | − | 7.40893i | −0.111945 | − | 0.0299957i | ||||
\(248\) | −124.527 | + | 33.3670i | −0.502127 | + | 0.134544i | ||||
\(249\) | 233.232 | + | 134.657i | 0.936674 | + | 0.540789i | ||||
\(250\) | 104.311 | − | 142.721i | 0.417242 | − | 0.570884i | ||||
\(251\) | −301.864 | −1.20265 | −0.601323 | − | 0.799006i | \(-0.705359\pi\) | ||||
−0.601323 | + | 0.799006i | \(0.705359\pi\) | |||||||
\(252\) | −25.7122 | + | 33.2097i | −0.102033 | + | 0.131784i | ||||
\(253\) | −208.326 | − | 208.326i | −0.823423 | − | 0.823423i | ||||
\(254\) | −79.8921 | + | 46.1257i | −0.314536 | + | 0.181597i | ||||
\(255\) | −76.8831 | − | 58.0492i | −0.301502 | − | 0.227644i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −114.284 | − | 30.6224i | −0.444687 | − | 0.119153i | 0.0295256 | − | 0.999564i | \(-0.490600\pi\) |
−0.474212 | + | 0.880411i | \(0.657267\pi\) | |||||||
\(258\) | −4.86538 | − | 4.86538i | −0.0188581 | − | 0.0188581i | ||||
\(259\) | −102.156 | + | 77.6860i | −0.394426 | + | 0.299946i | ||||
\(260\) | −26.5393 | − | 34.0348i | −0.102074 | − | 0.130903i | ||||
\(261\) | −53.8291 | − | 93.2347i | −0.206242 | − | 0.357221i | ||||
\(262\) | 36.9625 | + | 137.946i | 0.141078 | + | 0.526511i | ||||
\(263\) | −328.455 | + | 88.0092i | −1.24888 | + | 0.334636i | −0.821903 | − | 0.569628i | \(-0.807087\pi\) |
−0.426975 | + | 0.904264i | \(0.640421\pi\) | |||||||
\(264\) | 71.9452 | − | 41.5376i | 0.272520 | − | 0.157339i | ||||
\(265\) | 335.394 | − | 261.530i | 1.26564 | − | 0.986905i | ||||
\(266\) | −25.3897 | + | 60.5524i | −0.0954501 | + | 0.227641i | ||||
\(267\) | 70.6691 | − | 70.6691i | 0.264678 | − | 0.264678i | ||||
\(268\) | 32.5838 | − | 121.604i | 0.121581 | − | 0.453748i | ||||
\(269\) | 319.982 | + | 184.742i | 1.18953 | + | 0.686773i | 0.958199 | − | 0.286103i | \(-0.0923600\pi\) |
0.231327 | + | 0.972876i | \(0.425693\pi\) | |||||||
\(270\) | −22.1397 | + | 29.3229i | −0.0819990 | + | 0.108603i | ||||
\(271\) | 137.014 | + | 237.315i | 0.505586 | + | 0.875700i | 0.999979 | + | 0.00646203i | \(0.00205694\pi\) |
−0.494393 | + | 0.869238i | \(0.664610\pi\) | |||||||
\(272\) | 31.4634 | − | 31.4634i | 0.115674 | − | 0.115674i | ||||
\(273\) | 48.4307 | − | 19.8151i | 0.177402 | − | 0.0725829i | ||||
\(274\) | − | 186.809i | − | 0.681784i | ||||||
\(275\) | −116.086 | − | 407.738i | −0.422130 | − | 1.48268i | ||||
\(276\) | −30.0922 | + | 52.1212i | −0.109030 | + | 0.188845i | ||||
\(277\) | −14.5626 | − | 54.3485i | −0.0525727 | − | 0.196204i | 0.934645 | − | 0.355583i | \(-0.115718\pi\) |
−0.987218 | + | 0.159379i | \(0.949051\pi\) | |||||||
\(278\) | 18.2081 | − | 67.9534i | 0.0654967 | − | 0.244437i | ||||
\(279\) | − | 136.741i | − | 0.490110i | ||||||
\(280\) | −85.5609 | + | 49.7929i | −0.305575 | + | 0.177832i | ||||
\(281\) | 535.008 | 1.90394 | 0.951971 | − | 0.306187i | \(-0.0990534\pi\) | ||||
0.951971 | + | 0.306187i | \(0.0990534\pi\) | |||||||
\(282\) | 103.475 | + | 27.7262i | 0.366934 | + | 0.0983197i | ||||
\(283\) | 195.681 | − | 52.4326i | 0.691452 | − | 0.185274i | 0.104054 | − | 0.994572i | \(-0.466819\pi\) |
0.587399 | + | 0.809298i | \(0.300152\pi\) | |||||||
\(284\) | 238.962 | + | 137.965i | 0.841414 | + | 0.485791i | ||||
\(285\) | −21.5678 | + | 53.2376i | −0.0756764 | + | 0.186799i | ||||
\(286\) | −103.503 | −0.361898 | ||||||||
\(287\) | 184.103 | − | 237.786i | 0.641474 | − | 0.828524i | ||||
\(288\) | −12.0000 | − | 12.0000i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | 143.117 | − | 82.6285i | 0.495214 | − | 0.285912i | ||||
\(290\) | −35.0788 | − | 251.316i | −0.120961 | − | 0.866609i | ||||
\(291\) | 48.6887 | − | 84.3313i | 0.167315 | − | 0.289798i | ||||
\(292\) | −14.0104 | − | 3.75408i | −0.0479809 | − | 0.0128565i | ||||
\(293\) | −225.228 | − | 225.228i | −0.768696 | − | 0.768696i | 0.209181 | − | 0.977877i | \(-0.432920\pi\) |
−0.977877 | + | 0.209181i | \(0.932920\pi\) | |||||||
\(294\) | −30.0584 | − | 116.200i | −0.102239 | − | 0.395239i | ||||
\(295\) | −126.155 | − | 15.6106i | −0.427645 | − | 0.0529172i | ||||
\(296\) | −25.9285 | − | 44.9095i | −0.0875963 | − | 0.151721i | ||||
\(297\) | 22.8057 | + | 85.1120i | 0.0767869 | + | 0.286573i | ||||
\(298\) | 310.310 | − | 83.1473i | 1.04131 | − | 0.279018i | ||||
\(299\) | 64.9375 | − | 37.4917i | 0.217182 | − | 0.125390i | ||||
\(300\) | −74.3168 | + | 44.4636i | −0.247723 | + | 0.148212i | ||||
\(301\) | 19.5059 | − | 2.48202i | 0.0648037 | − | 0.00824592i | ||||
\(302\) | −198.935 | + | 198.935i | −0.658726 | + | 0.658726i | ||||
\(303\) | −32.4971 | + | 121.281i | −0.107251 | + | 0.400267i | ||||
\(304\) | −22.9762 | − | 13.2653i | −0.0755796 | − | 0.0436359i | ||||
\(305\) | −339.037 | − | 255.984i | −1.11160 | − | 0.839293i | ||||
\(306\) | 23.5975 | + | 40.8721i | 0.0771161 | + | 0.133569i | ||||
\(307\) | 294.340 | − | 294.340i | 0.958762 | − | 0.958762i | −0.0404208 | − | 0.999183i | \(-0.512870\pi\) |
0.999183 | + | 0.0404208i | \(0.0128699\pi\) | |||||||
\(308\) | −32.0079 | + | 235.239i | −0.103922 | + | 0.763764i | ||||
\(309\) | 274.124i | 0.887132i | ||||||||
\(310\) | 121.018 | − | 298.718i | 0.390379 | − | 0.963607i | ||||
\(311\) | −116.986 | + | 202.625i | −0.376160 | + | 0.651529i | −0.990500 | − | 0.137513i | \(-0.956089\pi\) |
0.614340 | + | 0.789042i | \(0.289422\pi\) | |||||||
\(312\) | 5.47235 | + | 20.4231i | 0.0175396 | + | 0.0654586i | ||||
\(313\) | 36.7853 | − | 137.285i | 0.117525 | − | 0.438609i | −0.881938 | − | 0.471365i | \(-0.843762\pi\) |
0.999463 | + | 0.0327556i | \(0.0104283\pi\) | |||||||
\(314\) | 393.391i | 1.25284i | ||||||||
\(315\) | −27.5257 | − | 101.328i | −0.0873830 | − | 0.321676i | ||||
\(316\) | −81.9755 | −0.259416 | ||||||||
\(317\) | −67.7680 | − | 18.1584i | −0.213779 | − | 0.0572820i | 0.150340 | − | 0.988634i | \(-0.451963\pi\) |
−0.364119 | + | 0.931352i | \(0.618630\pi\) | |||||||
\(318\) | −201.258 | + | 53.9269i | −0.632887 | + | 0.169581i | ||||
\(319\) | −527.014 | − | 304.271i | −1.65208 | − | 0.953829i | ||||
\(320\) | −15.5945 | − | 36.8349i | −0.0487329 | − | 0.115109i | ||||
\(321\) | −77.8987 | −0.242675 | ||||||||
\(322\) | −65.1287 | − | 159.183i | −0.202263 | − | 0.494357i | ||||
\(323\) | 52.1714 | + | 52.1714i | 0.161521 | + | 0.161521i | ||||
\(324\) | 15.5885 | − | 9.00000i | 0.0481125 | − | 0.0277778i | ||||
\(325\) | 107.885 | − | 1.67976i | 0.331952 | − | 0.00516848i | ||||
\(326\) | −148.360 | + | 256.966i | −0.455091 | + | 0.788240i | ||||
\(327\) | 160.378 | + | 42.9732i | 0.490454 | + | 0.131417i | ||||
\(328\) | 85.9218 | + | 85.9218i | 0.261957 | + | 0.261957i | ||||
\(329\) | −243.680 | + | 185.310i | −0.740670 | + | 0.563252i | ||||
\(330\) | −25.5050 | + | 206.116i | −0.0772879 | + | 0.624593i | ||||
\(331\) | 127.726 | + | 221.227i | 0.385878 | + | 0.668360i | 0.991891 | − | 0.127095i | \(-0.0405652\pi\) |
−0.606013 | + | 0.795455i | \(0.707232\pi\) | |||||||
\(332\) | −80.4865 | − | 300.380i | −0.242429 | − | 0.904758i | ||||
\(333\) | 53.1285 | − | 14.2357i | 0.159545 | − | 0.0427499i | ||||
\(334\) | −25.7214 | + | 14.8502i | −0.0770101 | + | 0.0444618i | ||||
\(335\) | 193.537 | + | 248.197i | 0.577721 | + | 0.740888i | ||||
\(336\) | 48.1095 | − | 6.12168i | 0.143183 | − | 0.0182193i | ||||
\(337\) | 2.44497 | − | 2.44497i | 0.00725510 | − | 0.00725510i | −0.703470 | − | 0.710725i | \(-0.748367\pi\) |
0.710725 | + | 0.703470i | \(0.248367\pi\) | |||||||
\(338\) | −55.0403 | + | 205.413i | −0.162841 | + | 0.607732i | ||||
\(339\) | 183.720 | + | 106.071i | 0.541947 | + | 0.312893i | ||||
\(340\) | 15.3778 | + | 110.172i | 0.0452288 | + | 0.324035i | ||||
\(341\) | −386.466 | − | 669.379i | −1.13333 | − | 1.96299i | ||||
\(342\) | 19.8980 | − | 19.8980i | 0.0581812 | − | 0.0581812i | ||||
\(343\) | 315.157 | + | 135.371i | 0.918825 | + | 0.394666i | ||||
\(344\) | 7.94513i | 0.0230963i | ||||||||
\(345\) | −58.6593 | − | 138.555i | −0.170027 | − | 0.401610i | ||||
\(346\) | 90.4795 | − | 156.715i | 0.261501 | − | 0.452934i | ||||
\(347\) | 136.632 | + | 509.917i | 0.393752 | + | 1.46950i | 0.823896 | + | 0.566741i | \(0.191796\pi\) |
−0.430145 | + | 0.902760i | \(0.641537\pi\) | |||||||
\(348\) | −32.1746 | + | 120.077i | −0.0924557 | + | 0.345049i | ||||
\(349\) | − | 74.0257i | − | 0.212108i | −0.994360 | − | 0.106054i | \(-0.966178\pi\) | ||
0.994360 | − | 0.106054i | \(-0.0338216\pi\) | |||||||
\(350\) | 29.5452 | − | 245.717i | 0.0844150 | − | 0.702050i | ||||
\(351\) | −22.4261 | −0.0638920 | ||||||||
\(352\) | −92.6583 | − | 24.8277i | −0.263234 | − | 0.0705332i | ||||
\(353\) | 277.271 | − | 74.2945i | 0.785470 | − | 0.210466i | 0.156275 | − | 0.987714i | \(-0.450051\pi\) |
0.629195 | + | 0.777248i | \(0.283385\pi\) | |||||||
\(354\) | 53.9313 | + | 31.1373i | 0.152348 | + | 0.0879584i | ||||
\(355\) | −635.239 | + | 268.937i | −1.78941 | + | 0.757569i | ||||
\(356\) | −115.402 | −0.324163 | ||||||||
\(357\) | −133.640 | − | 18.1837i | −0.374341 | − | 0.0509348i | ||||
\(358\) | 148.311 | + | 148.311i | 0.414277 | + | 0.414277i | ||||
\(359\) | 571.100 | − | 329.725i | 1.59081 | − | 0.918453i | 0.597638 | − | 0.801766i | \(-0.296106\pi\) |
0.993169 | − | 0.116687i | \(-0.0372273\pi\) | |||||||
\(360\) | 42.0191 | − | 5.86502i | 0.116720 | − | 0.0162917i | ||||
\(361\) | −158.504 | + | 274.537i | −0.439069 | + | 0.760490i | ||||
\(362\) | 192.540 | + | 51.5910i | 0.531879 | + | 0.142516i | ||||
\(363\) | 203.995 | + | 203.995i | 0.561970 | + | 0.561970i | ||||
\(364\) | −55.7225 | − | 23.3645i | −0.153084 | − | 0.0641883i | ||||
\(365\) | 28.5956 | − | 22.2980i | 0.0783442 | − | 0.0610904i | ||||
\(366\) | 104.060 | + | 180.237i | 0.284317 | + | 0.492451i | ||||
\(367\) | −101.239 | − | 377.829i | −0.275856 | − | 1.02951i | −0.955266 | − | 0.295749i | \(-0.904431\pi\) |
0.679410 | − | 0.733759i | \(-0.262236\pi\) | |||||||
\(368\) | 67.1270 | − | 17.9866i | 0.182410 | − | 0.0488767i | ||||
\(369\) | −111.616 | + | 64.4414i | −0.302482 | + | 0.174638i | ||||
\(370\) | 128.661 | + | 15.9207i | 0.347733 | + | 0.0430289i | ||||
\(371\) | 230.244 | − | 549.114i | 0.620605 | − | 1.48009i | ||||
\(372\) | −111.648 | + | 111.648i | −0.300130 | + | 0.300130i | ||||
\(373\) | 7.60446 | − | 28.3802i | 0.0203873 | − | 0.0760864i | −0.954983 | − | 0.296661i | \(-0.904127\pi\) |
0.975370 | + | 0.220575i | \(0.0707934\pi\) | |||||||
\(374\) | 231.032 | + | 133.386i | 0.617731 | + | 0.356647i | ||||
\(375\) | 23.2397 | − | 215.255i | 0.0619725 | − | 0.574015i | ||||
\(376\) | −61.8490 | − | 107.126i | −0.164492 | − | 0.284909i | ||||
\(377\) | 109.517 | − | 109.517i | 0.290497 | − | 0.290497i | ||||
\(378\) | −6.93520 | + | 50.9696i | −0.0183471 | + | 0.134840i | ||||
\(379\) | 469.896i | 1.23983i | 0.784668 | + | 0.619916i | \(0.212833\pi\) | ||||
−0.784668 | + | 0.619916i | \(0.787167\pi\) | |||||||
\(380\) | 61.0783 | − | 25.8583i | 0.160732 | − | 0.0680482i | ||||
\(381\) | −56.4922 | + | 97.8474i | −0.148274 | + | 0.256817i | ||||
\(382\) | −59.5911 | − | 222.397i | −0.155998 | − | 0.582191i | ||||
\(383\) | 140.563 | − | 524.588i | 0.367005 | − | 1.36968i | −0.497678 | − | 0.867362i | \(-0.665814\pi\) |
0.864683 | − | 0.502318i | \(-0.167519\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | −421.125 | − | 418.230i | −1.09383 | − | 1.08631i | ||||
\(386\) | −327.216 | −0.847709 | ||||||||
\(387\) | −8.13994 | − | 2.18109i | −0.0210334 | − | 0.00563589i | ||||
\(388\) | −108.610 | + | 29.1021i | −0.279924 | + | 0.0750053i | ||||
\(389\) | 329.553 | + | 190.268i | 0.847180 | + | 0.489120i | 0.859699 | − | 0.510802i | \(-0.170651\pi\) |
−0.0125180 | + | 0.999922i | \(0.503985\pi\) | |||||||
\(390\) | −48.9912 | − | 19.8474i | −0.125618 | − | 0.0508909i | ||||
\(391\) | −193.265 | −0.494284 | ||||||||
\(392\) | −70.3345 | + | 119.420i | −0.179425 | + | 0.304642i | ||||
\(393\) | 123.679 | + | 123.679i | 0.314705 | + | 0.314705i | ||||
\(394\) | −304.619 | + | 175.872i | −0.773145 | + | 0.446375i | ||||
\(395\) | 123.489 | − | 163.555i | 0.312632 | − | 0.414064i | ||||
\(396\) | 50.8729 | − | 88.1145i | 0.128467 | − | 0.222511i | ||||
\(397\) | 329.585 | + | 88.3122i | 0.830190 | + | 0.222449i | 0.648797 | − | 0.760962i | \(-0.275273\pi\) |
0.181393 | + | 0.983411i | \(0.441939\pi\) | |||||||
\(398\) | −257.346 | − | 257.346i | −0.646598 | − | 0.646598i | ||||
\(399\) | 10.1507 | + | 79.7735i | 0.0254405 | + | 0.199934i | ||||
\(400\) | 96.9838 | + | 24.3750i | 0.242460 | + | 0.0609375i | ||||
\(401\) | −216.181 | − | 374.437i | −0.539105 | − | 0.933757i | −0.998952 | − | 0.0457593i | \(-0.985429\pi\) |
0.459848 | − | 0.887998i | \(-0.347904\pi\) | |||||||
\(402\) | −39.9068 | − | 148.934i | −0.0992708 | − | 0.370484i | ||||
\(403\) | 190.017 | − | 50.9148i | 0.471506 | − | 0.126340i | ||||
\(404\) | 125.559 | − | 72.4916i | 0.310790 | − | 0.179435i | ||||
\(405\) | −5.52621 | + | 44.6594i | −0.0136450 | + | 0.110270i | ||||
\(406\) | −215.041 | − | 282.777i | −0.529658 | − | 0.696495i | ||||
\(407\) | 219.843 | − | 219.843i | 0.540155 | − | 0.540155i | ||||
\(408\) | 14.1046 | − | 52.6392i | 0.0345702 | − | 0.129018i | ||||
\(409\) | 219.191 | + | 126.550i | 0.535918 | + | 0.309413i | 0.743423 | − | 0.668821i | \(-0.233201\pi\) |
−0.207505 | + | 0.978234i | \(0.566534\pi\) | |||||||
\(410\) | −300.863 | + | 41.9944i | −0.733812 | + | 0.102425i | ||||
\(411\) | −114.397 | − | 198.141i | −0.278337 | − | 0.482094i | ||||
\(412\) | 223.821 | − | 223.821i | 0.543255 | − | 0.543255i | ||||
\(413\) | −164.711 | + | 67.3905i | −0.398817 | + | 0.163173i | ||||
\(414\) | 73.7105i | 0.178045i | ||||||||
\(415\) | 720.555 | + | 291.913i | 1.73628 | + | 0.703405i | ||||
\(416\) | 12.2072 | − | 21.1435i | 0.0293443 | − | 0.0508258i | ||||
\(417\) | −22.3002 | − | 83.2256i | −0.0534778 | − | 0.199582i | ||||
\(418\) | 41.1684 | − | 153.643i | 0.0984890 | − | 0.367566i | ||||
\(419\) | − | 456.021i | − | 1.08835i | −0.838970 | − | 0.544177i | \(-0.816842\pi\) | ||
0.838970 | − | 0.544177i | \(-0.183158\pi\) | |||||||
\(420\) | −60.2593 | + | 105.208i | −0.143474 | + | 0.250496i | ||||
\(421\) | 87.9279 | 0.208855 | 0.104427 | − | 0.994533i | \(-0.466699\pi\) | ||||
0.104427 | + | 0.994533i | \(0.466699\pi\) | |||||||
\(422\) | 368.614 | + | 98.7698i | 0.873493 | + | 0.234052i | ||||
\(423\) | 126.731 | − | 33.9575i | 0.299600 | − | 0.0802777i | ||||
\(424\) | 208.358 | + | 120.295i | 0.491409 | + | 0.283715i | ||||
\(425\) | −242.977 | − | 135.283i | −0.571710 | − | 0.318314i | ||||
\(426\) | 337.943 | 0.793293 | ||||||||
\(427\) | −589.321 | − | 80.1862i | −1.38014 | − | 0.187790i | ||||
\(428\) | 63.6040 | + | 63.6040i | 0.148608 | + | 0.148608i | ||||
\(429\) | −109.781 | + | 63.3823i | −0.255900 | + | 0.147744i | ||||
\(430\) | −15.8519 | − | 11.9687i | −0.0368648 | − | 0.0278342i | ||||
\(431\) | −368.932 | + | 639.009i | −0.855991 | + | 1.48262i | 0.0197313 | + | 0.999805i | \(0.493719\pi\) |
−0.875722 | + | 0.482815i | \(0.839614\pi\) | |||||||
\(432\) | −20.0764 | − | 5.37945i | −0.0464731 | − | 0.0124524i | ||||
\(433\) | 29.1869 | + | 29.1869i | 0.0674062 | + | 0.0674062i | 0.740006 | − | 0.672600i | \(-0.234823\pi\) |
−0.672600 | + | 0.740006i | \(0.734823\pi\) | |||||||
\(434\) | −56.9562 | − | 447.612i | −0.131236 | − | 1.03136i | ||||
\(435\) | −191.106 | − | 245.080i | −0.439324 | − | 0.563403i | ||||
\(436\) | −95.8608 | − | 166.036i | −0.219864 | − | 0.380816i | ||||
\(437\) | 29.8248 | + | 111.308i | 0.0682489 | + | 0.254708i | ||||
\(438\) | −17.1592 | + | 4.59780i | −0.0391763 | + | 0.0104973i | ||||
\(439\) | −353.707 | + | 204.213i | −0.805710 | + | 0.465177i | −0.845464 | − | 0.534033i | \(-0.820676\pi\) |
0.0397539 | + | 0.999210i | \(0.487343\pi\) | |||||||
\(440\) | 189.118 | − | 147.468i | 0.429813 | − | 0.335155i | ||||
\(441\) | −103.040 | − | 104.842i | −0.233650 | − | 0.237737i | ||||
\(442\) | −48.0100 | + | 48.0100i | −0.108620 | + | 0.108620i | ||||
\(443\) | −153.503 | + | 572.880i | −0.346507 | + | 1.29318i | 0.544334 | + | 0.838869i | \(0.316782\pi\) |
−0.890841 | + | 0.454314i | \(0.849884\pi\) | |||||||
\(444\) | −55.0026 | − | 31.7558i | −0.123880 | − | 0.0715221i | ||||
\(445\) | 173.844 | − | 230.247i | 0.390660 | − | 0.517409i | ||||
\(446\) | −253.501 | − | 439.076i | −0.568387 | − | 0.984475i | ||||
\(447\) | 278.216 | − | 278.216i | 0.622408 | − | 0.622408i | ||||
\(448\) | −44.2796 | − | 34.2829i | −0.0988383 | − | 0.0765244i | ||||
\(449\) | − | 176.194i | − | 0.392415i | −0.980562 | − | 0.196208i | \(-0.937137\pi\) | ||
0.980562 | − | 0.196208i | \(-0.0628627\pi\) | |||||||
\(450\) | −51.5966 | + | 92.6704i | −0.114659 | + | 0.205934i | ||||
\(451\) | −364.258 | + | 630.913i | −0.807667 | + | 1.39892i | ||||
\(452\) | −63.4004 | − | 236.613i | −0.140266 | − | 0.523481i | ||||
\(453\) | −89.1802 | + | 332.825i | −0.196866 | + | 0.734713i | ||||
\(454\) | 19.6394i | 0.0432587i | ||||||||
\(455\) | 130.558 | − | 75.9791i | 0.286940 | − | 0.166987i | ||||
\(456\) | −32.4932 | −0.0712571 | ||||||||
\(457\) | 50.1945 | + | 13.4496i | 0.109835 | + | 0.0294302i | 0.313318 | − | 0.949648i | \(-0.398559\pi\) |
−0.203483 | + | 0.979078i | \(0.565226\pi\) | |||||||
\(458\) | 490.442 | − | 131.413i | 1.07083 | − | 0.286929i | ||||
\(459\) | 50.0579 | + | 28.9010i | 0.109059 | + | 0.0629650i | ||||
\(460\) | −65.2349 | + | 161.025i | −0.141815 | + | 0.350055i | ||||
\(461\) | −420.947 | −0.913117 | −0.456558 | − | 0.889693i | \(-0.650918\pi\) | ||||
−0.456558 | + | 0.889693i | \(0.650918\pi\) | |||||||
\(462\) | 110.105 | + | 269.110i | 0.238322 | + | 0.582489i | ||||
\(463\) | −45.3241 | − | 45.3241i | −0.0978921 | − | 0.0978921i | 0.656465 | − | 0.754357i | \(-0.272051\pi\) |
−0.754357 | + | 0.656465i | \(0.772051\pi\) | |||||||
\(464\) | 124.313 | − | 71.7721i | 0.267916 | − | 0.154681i | ||||
\(465\) | −54.5683 | − | 390.946i | −0.117351 | − | 0.840745i | ||||
\(466\) | 150.211 | − | 260.173i | 0.322342 | − | 0.558312i | ||||
\(467\) | −512.522 | − | 137.330i | −1.09748 | − | 0.294068i | −0.335741 | − | 0.941954i | \(-0.608987\pi\) |
−0.761737 | + | 0.647886i | \(0.775653\pi\) | |||||||
\(468\) | 18.3108 | + | 18.3108i | 0.0391257 | + | 0.0391257i | ||||
\(469\) | 406.354 | + | 170.385i | 0.866426 | + | 0.363294i | ||||
\(470\) | 306.904 | + | 37.9767i | 0.652988 | + | 0.0808015i | ||||
\(471\) | 240.902 | + | 417.254i | 0.511468 | + | 0.885889i | ||||
\(472\) | −18.6113 | − | 69.4582i | −0.0394306 | − | 0.147157i | ||||
\(473\) | −46.0114 | + | 12.3287i | −0.0972756 | + | 0.0260649i | ||||
\(474\) | −86.9482 | + | 50.1996i | −0.183435 | + | 0.105906i | ||||
\(475\) | −40.4178 | + | 160.815i | −0.0850900 | + | 0.338558i | ||||
\(476\) | 94.2694 | + | 123.963i | 0.198045 | + | 0.260427i | ||||
\(477\) | −180.443 | + | 180.443i | −0.378287 | + | 0.378287i | ||||
\(478\) | −53.3964 | + | 199.278i | −0.111708 | + | 0.416900i | ||||
\(479\) | −287.563 | − | 166.025i | −0.600340 | − | 0.346607i | 0.168835 | − | 0.985644i | \(-0.445999\pi\) |
−0.769175 | + | 0.639038i | \(0.779333\pi\) | |||||||
\(480\) | −39.0972 | − | 29.5196i | −0.0814525 | − | 0.0614993i | ||||
\(481\) | 39.5644 | + | 68.5275i | 0.0822544 | + | 0.142469i | ||||
\(482\) | 264.742 | − | 264.742i | 0.549258 | − | 0.549258i | ||||
\(483\) | −166.559 | − | 128.956i | −0.344842 | − | 0.266990i | ||||
\(484\) | − | 333.123i | − | 0.688270i | ||||||
\(485\) | 105.549 | − | 260.536i | 0.217627 | − | 0.537188i | ||||
\(486\) | 11.0227 | − | 19.0919i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 192.469 | + | 718.303i | 0.395213 | + | 1.47496i | 0.821417 | + | 0.570328i | \(0.193184\pi\) |
−0.426204 | + | 0.904627i | \(0.640149\pi\) | |||||||
\(488\) | 62.1984 | − | 232.127i | 0.127456 | − | 0.475671i | ||||
\(489\) | 363.405i | 0.743160i | ||||||||
\(490\) | −132.309 | − | 320.225i | −0.270019 | − | 0.653521i | ||||
\(491\) | 46.6728 | 0.0950567 | 0.0475284 | − | 0.998870i | \(-0.484866\pi\) | ||||
0.0475284 | + | 0.998870i | \(0.484866\pi\) | |||||||
\(492\) | 143.750 | + | 38.5177i | 0.292175 | + | 0.0782880i | ||||
\(493\) | −385.594 | + | 103.320i | −0.782137 | + | 0.209573i | ||||
\(494\) | 35.0594 | + | 20.2416i | 0.0709705 | + | 0.0409748i | ||||
\(495\) | 99.1675 | + | 234.237i | 0.200338 | + | 0.473207i | ||||
\(496\) | 182.321 | 0.367582 | ||||||||
\(497\) | −591.229 | + | 763.627i | −1.18959 | + | 1.53647i | ||||
\(498\) | −269.313 | − | 269.313i | −0.540789 | − | 0.540789i | ||||
\(499\) | −216.276 | + | 124.867i | −0.433418 | + | 0.250234i | −0.700802 | − | 0.713356i | \(-0.747174\pi\) |
0.267384 | + | 0.963590i | \(0.413841\pi\) | |||||||
\(500\) | −194.730 | + | 156.780i | −0.389461 | + | 0.313560i | ||||
\(501\) | −18.1878 | + | 31.5021i | −0.0363029 | + | 0.0628785i | ||||
\(502\) | 412.354 | + | 110.490i | 0.821422 | + | 0.220099i | ||||
\(503\) | −77.7709 | − | 77.7709i | −0.154614 | − | 0.154614i | 0.625561 | − | 0.780175i | \(-0.284870\pi\) |
−0.780175 | + | 0.625561i | \(0.784870\pi\) | |||||||
\(504\) | 47.2791 | − | 35.9540i | 0.0938077 | − | 0.0713372i | ||||
\(505\) | −44.5115 | + | 359.715i | −0.0881416 | + | 0.712306i | ||||
\(506\) | 208.326 | + | 360.831i | 0.411712 | + | 0.713106i | ||||
\(507\) | 67.4104 | + | 251.579i | 0.132959 | + | 0.496211i | ||||
\(508\) | 126.018 | − | 33.7664i | 0.248066 | − | 0.0664692i | ||||
\(509\) | 269.664 | − | 155.690i | 0.529791 | − | 0.305875i | −0.211140 | − | 0.977456i | \(-0.567718\pi\) |
0.740931 | + | 0.671581i | \(0.234384\pi\) | |||||||
\(510\) | 83.7768 | + | 107.438i | 0.164268 | + | 0.210663i | ||||
\(511\) | 19.6306 | − | 46.8173i | 0.0384160 | − | 0.0916190i | ||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 8.92002 | − | 33.2900i | 0.0173879 | − | 0.0648927i | ||||
\(514\) | 144.907 | + | 83.6620i | 0.281920 | + | 0.162767i | ||||
\(515\) | 109.393 | + | 783.729i | 0.212414 | + | 1.52180i | ||||
\(516\) | 4.86538 | + | 8.42708i | 0.00942903 | + | 0.0163316i | ||||
\(517\) | 524.407 | − | 524.407i | 1.01433 | − | 1.01433i | ||||
\(518\) | 167.983 | − | 68.7293i | 0.324292 | − | 0.132682i | ||||
\(519\) | − | 221.629i | − | 0.427030i | ||||||
\(520\) | 23.7958 | + | 56.2065i | 0.0457611 | + | 0.108089i | ||||
\(521\) | 146.921 | − | 254.474i | 0.281997 | − | 0.488434i | −0.689879 | − | 0.723924i | \(-0.742336\pi\) |
0.971877 | + | 0.235491i | \(0.0756698\pi\) | |||||||
\(522\) | 39.4056 | + | 147.064i | 0.0754897 | + | 0.281732i | ||||
\(523\) | 7.45680 | − | 27.8292i | 0.0142577 | − | 0.0532106i | −0.958430 | − | 0.285326i | \(-0.907898\pi\) |
0.972688 | + | 0.232116i | \(0.0745647\pi\) | |||||||
\(524\) | − | 201.967i | − | 0.385433i | ||||||
\(525\) | −119.133 | − | 278.715i | −0.226920 | − | 0.530887i | ||||
\(526\) | 480.891 | 0.914242 | ||||||||
\(527\) | −489.757 | − | 131.230i | −0.929330 | − | 0.249013i | ||||
\(528\) | −113.483 | + | 30.4076i | −0.214929 | + | 0.0575902i | ||||
\(529\) | 196.720 | + | 113.577i | 0.371872 | + | 0.214700i | ||||
\(530\) | −553.883 | + | 234.494i | −1.04506 | + | 0.442441i | ||||
\(531\) | 76.2704 | 0.143635 | ||||||||
\(532\) | 56.8467 | − | 73.4228i | 0.106855 | − | 0.138013i | ||||
\(533\) | −131.108 | − | 131.108i | −0.245982 | − | 0.245982i | ||||
\(534\) | −122.402 | + | 70.6691i | −0.229218 | + | 0.132339i | ||||
\(535\) | −222.715 | + | 31.0866i | −0.416290 | + | 0.0581058i | ||||
\(536\) | −89.0206 | + | 154.188i | −0.166083 | + | 0.287665i | ||||
\(537\) | 248.129 | + | 66.4860i | 0.462066 | + | 0.123810i | ||||
\(538\) | −369.484 | − | 369.484i | −0.686773 | − | 0.686773i | ||||
\(539\) | −800.716 | − | 222.010i | −1.48556 | − | 0.411892i | ||||
\(540\) | 40.9764 | − | 31.9521i | 0.0758822 | − | 0.0591706i | ||||
\(541\) | 429.327 | + | 743.616i | 0.793580 | + | 1.37452i | 0.923737 | + | 0.383028i | \(0.125119\pi\) |
−0.130157 | + | 0.991493i | \(0.541548\pi\) | |||||||
\(542\) | −100.301 | − | 374.329i | −0.185057 | − | 0.690643i | ||||
\(543\) | 235.812 | − | 63.1858i | 0.434277 | − | 0.116364i | ||||
\(544\) | −54.4962 | + | 31.4634i | −0.100177 | + | 0.0578371i | ||||
\(545\) | 475.676 | + | 58.8607i | 0.872800 | + | 0.108001i | ||||
\(546\) | −73.4104 | + | 9.34108i | −0.134451 | + | 0.0171082i | ||||
\(547\) | −579.972 | + | 579.972i | −1.06028 | + | 1.06028i | −0.0622157 | + | 0.998063i | \(0.519817\pi\) |
−0.998063 | + | 0.0622157i | \(0.980183\pi\) | |||||||
\(548\) | −68.3767 | + | 255.185i | −0.124775 | + | 0.465667i | ||||
\(549\) | 220.744 | + | 127.447i | 0.402084 | + | 0.232144i | ||||
\(550\) | 9.33373 | + | 599.470i | 0.0169704 | + | 1.08995i | ||||
\(551\) | 119.010 | + | 206.131i | 0.215989 | + | 0.374104i | ||||
\(552\) | 60.1844 | − | 60.1844i | 0.109030 | − | 0.109030i | ||||
\(553\) | 38.6827 | − | 284.295i | 0.0699506 | − | 0.514095i | ||||
\(554\) | 79.5717i | 0.143631i | ||||||||
\(555\) | 146.215 | − | 61.9021i | 0.263451 | − | 0.111535i | ||||
\(556\) | −49.7454 | + | 86.1615i | −0.0894701 | + | 0.154967i | ||||
\(557\) | 235.011 | + | 877.073i | 0.421923 | + | 1.57464i | 0.770552 | + | 0.637377i | \(0.219981\pi\) |
−0.348629 | + | 0.937261i | \(0.613353\pi\) | |||||||
\(558\) | −50.0505 | + | 186.791i | −0.0896963 | + | 0.334751i | ||||
\(559\) | − | 12.1235i | − | 0.0216878i | ||||||
\(560\) | 135.104 | − | 36.7009i | 0.241257 | − | 0.0655373i | ||||
\(561\) | 326.728 | 0.582403 | ||||||||
\(562\) | −730.834 | − | 195.826i | −1.30042 | − | 0.348446i | ||||
\(563\) | −89.3163 | + | 23.9322i | −0.158644 | + | 0.0425084i | −0.337267 | − | 0.941409i | \(-0.609502\pi\) |
0.178623 | + | 0.983918i | \(0.442836\pi\) | |||||||
\(564\) | −131.202 | − | 75.7493i | −0.232627 | − | 0.134307i | ||||
\(565\) | 567.591 | + | 229.944i | 1.00459 | + | 0.406981i | ||||
\(566\) | −286.497 | −0.506178 | ||||||||
\(567\) | 23.8565 | + | 58.3084i | 0.0420750 | + | 0.102837i | ||||
\(568\) | −275.929 | − | 275.929i | −0.485791 | − | 0.485791i | ||||
\(569\) | 579.130 | − | 334.361i | 1.01780 | − | 0.587628i | 0.104336 | − | 0.994542i | \(-0.466728\pi\) |
0.913467 | + | 0.406914i | \(0.133395\pi\) | |||||||
\(570\) | 48.9484 | − | 64.8296i | 0.0858744 | − | 0.113736i | ||||
\(571\) | 47.9078 | − | 82.9787i | 0.0839016 | − | 0.145322i | −0.821021 | − | 0.570898i | \(-0.806595\pi\) |
0.904923 | + | 0.425576i | \(0.139929\pi\) | |||||||
\(572\) | 141.387 | + | 37.8847i | 0.247181 | + | 0.0662319i | ||||
\(573\) | −199.396 | − | 199.396i | −0.347985 | − | 0.347985i | ||||
\(574\) | −338.525 | + | 257.436i | −0.589766 | + | 0.448494i | ||||
\(575\) | −223.001 | − | 372.726i | −0.387829 | − | 0.648219i | ||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −110.186 | − | 411.220i | −0.190964 | − | 0.712686i | −0.993275 | − | 0.115780i | \(-0.963063\pi\) |
0.802311 | − | 0.596906i | \(-0.203603\pi\) | |||||||
\(578\) | −225.745 | + | 60.4883i | −0.390563 | + | 0.104651i | ||||
\(579\) | −347.065 | + | 200.378i | −0.599421 | + | 0.346076i | ||||
\(580\) | −44.0697 | + | 356.144i | −0.0759823 | + | 0.614042i | ||||
\(581\) | 1079.71 | − | 137.387i | 1.85836 | − | 0.236467i | ||||
\(582\) | −97.3774 | + | 97.3774i | −0.167315 | + | 0.167315i | ||||
\(583\) | −373.332 | + | 1393.29i | −0.640364 | + | 2.38987i | ||||
\(584\) | 17.7645 | + | 10.2564i | 0.0304187 | + | 0.0175622i | ||||
\(585\) | −64.1170 | + | 8.94945i | −0.109602 | + | 0.0152982i | ||||
\(586\) | 225.228 | + | 390.106i | 0.384348 | + | 0.665710i | ||||
\(587\) | 139.731 | − | 139.731i | 0.238042 | − | 0.238042i | −0.577997 | − | 0.816039i | \(-0.696165\pi\) |
0.816039 | + | 0.577997i | \(0.196165\pi\) | |||||||
\(588\) | −1.47170 | + | 169.735i | −0.00250290 | + | 0.288664i | ||||
\(589\) | 302.318i | 0.513273i | ||||||||
\(590\) | 166.617 | + | 67.5004i | 0.282402 | + | 0.114408i | ||||
\(591\) | −215.398 | + | 373.081i | −0.364464 | + | 0.631270i | ||||
\(592\) | 18.9810 | + | 70.8380i | 0.0320625 | + | 0.119659i | ||||
\(593\) | −96.1240 | + | 358.740i | −0.162098 | + | 0.604957i | 0.836295 | + | 0.548280i | \(0.184717\pi\) |
−0.998393 | + | 0.0566772i | \(0.981949\pi\) | |||||||
\(594\) | − | 124.613i | − | 0.209786i | ||||||
\(595\) | −389.337 | + | 1.34289i | −0.654348 | + | 0.00225695i | ||||
\(596\) | −454.325 | −0.762291 | ||||||||
\(597\) | −430.548 | − | 115.365i | −0.721186 | − | 0.193241i | ||||
\(598\) | −102.429 | + | 27.4458i | −0.171286 | + | 0.0458960i | ||||
\(599\) | −612.367 | − | 353.550i | −1.02232 | − | 0.590234i | −0.107542 | − | 0.994201i | \(-0.534298\pi\) |
−0.914774 | + | 0.403966i | \(0.867631\pi\) | |||||||
\(600\) | 117.793 | − | 33.5366i | 0.196322 | − | 0.0558944i | ||||
\(601\) | −568.154 | −0.945347 | −0.472674 | − | 0.881238i | \(-0.656711\pi\) | ||||
−0.472674 | + | 0.881238i | \(0.656711\pi\) | |||||||
\(602\) | −27.5541 | − | 3.74915i | −0.0457709 | − | 0.00622783i | ||||
\(603\) | −133.531 | − | 133.531i | −0.221444 | − | 0.221444i | ||||
\(604\) | 344.566 | − | 198.935i | 0.570473 | − | 0.329363i | ||||
\(605\) | 664.637 | + | 501.822i | 1.09857 | + | 0.829459i | ||||
\(606\) | 88.7838 | − | 153.778i | 0.146508 | − | 0.253759i | ||||
\(607\) | −256.981 | − | 68.8578i | −0.423362 | − | 0.113439i | 0.0408466 | − | 0.999165i | \(-0.486995\pi\) |
−0.464209 | + | 0.885726i | \(0.653661\pi\) | |||||||
\(608\) | 26.5306 | + | 26.5306i | 0.0436359 | + | 0.0436359i | ||||
\(609\) | −401.250 | − | 168.245i | −0.658867 | − | 0.276264i | ||||
\(610\) | 369.437 | + | 473.777i | 0.605634 | + | 0.776684i | ||||
\(611\) | 94.3756 | + | 163.463i | 0.154461 | + | 0.267534i | ||||
\(612\) | −17.2746 | − | 64.4696i | −0.0282265 | − | 0.105343i | ||||
\(613\) | 794.625 | − | 212.919i | 1.29629 | − | 0.347340i | 0.456243 | − | 0.889855i | \(-0.349195\pi\) |
0.840046 | + | 0.542515i | \(0.182528\pi\) | |||||||
\(614\) | −509.812 | + | 294.340i | −0.830312 | + | 0.479381i | ||||
\(615\) | −293.397 | + | 228.782i | −0.477068 | + | 0.372003i | ||||
\(616\) | 129.827 | − | 309.627i | 0.210758 | − | 0.502642i | ||||
\(617\) | −49.7691 | + | 49.7691i | −0.0806631 | + | 0.0806631i | −0.746287 | − | 0.665624i | \(-0.768165\pi\) |
0.665624 | + | 0.746287i | \(0.268165\pi\) | |||||||
\(618\) | 100.336 | − | 374.460i | 0.162356 | − | 0.605922i | ||||
\(619\) | −309.731 | − | 178.823i | −0.500373 | − | 0.288891i | 0.228494 | − | 0.973545i | \(-0.426620\pi\) |
−0.728868 | + | 0.684655i | \(0.759953\pi\) | |||||||
\(620\) | −274.651 | + | 363.761i | −0.442986 | + | 0.586712i | ||||
\(621\) | 45.1383 | + | 78.1818i | 0.0726865 | + | 0.125897i | ||||
\(622\) | 233.972 | − | 233.972i | 0.376160 | − | 0.376160i | ||||
\(623\) | 54.4560 | − | 400.219i | 0.0874093 | − | 0.642407i | ||||
\(624\) | − | 29.9015i | − | 0.0479190i | ||||||
\(625\) | −19.4577 | − | 624.697i | −0.0311324 | − | 0.999515i | ||||
\(626\) | −100.499 | + | 174.070i | −0.160542 | + | 0.278067i | ||||
\(627\) | −50.4208 | − | 188.173i | −0.0804159 | − | 0.300116i | ||||
\(628\) | 143.991 | − | 537.382i | 0.229285 | − | 0.855703i | ||||
\(629\) | − | 203.949i | − | 0.324244i | ||||||
\(630\) | 0.512171 | + | 148.492i | 0.000812970 | + | 0.235701i | ||||
\(631\) | −35.2671 | −0.0558908 | −0.0279454 | − | 0.999609i | \(-0.508896\pi\) | ||||
−0.0279454 | + | 0.999609i | \(0.508896\pi\) | |||||||
\(632\) | 111.981 | + | 30.0051i | 0.177185 | + | 0.0474765i | ||||
\(633\) | 451.458 | − | 120.968i | 0.713204 | − | 0.191102i | ||||
\(634\) | 85.9264 | + | 49.6096i | 0.135531 | + | 0.0782486i | ||||
\(635\) | −122.466 | + | 302.293i | −0.192860 | + | 0.476052i | ||||
\(636\) | 294.662 | 0.463305 | ||||||||
\(637\) | 107.324 | − | 182.223i | 0.168483 | − | 0.286064i | ||||
\(638\) | 608.543 | + | 608.543i | 0.953829 | + | 0.953829i | ||||
\(639\) | 358.443 | − | 206.947i | 0.560943 | − | 0.323861i | ||||
\(640\) | 7.82003 | + | 56.0254i | 0.0122188 | + | 0.0875397i | ||||
\(641\) | 154.470 | − | 267.550i | 0.240983 | − | 0.417394i | −0.720012 | − | 0.693962i | \(-0.755864\pi\) |
0.960995 | + | 0.276567i | \(0.0891969\pi\) | |||||||
\(642\) | 106.412 | + | 28.5129i | 0.165750 | + | 0.0444126i | ||||
\(643\) | 356.455 | + | 356.455i | 0.554362 | + | 0.554362i | 0.927697 | − | 0.373335i | \(-0.121786\pi\) |
−0.373335 | + | 0.927697i | \(0.621786\pi\) | |||||||
\(644\) | 30.7025 | + | 241.287i | 0.0476746 | + | 0.374669i | ||||
\(645\) | −24.1428 | − | 2.98745i | −0.0374306 | − | 0.00463171i | ||||
\(646\) | −52.1714 | − | 90.3636i | −0.0807607 | − | 0.139882i | ||||
\(647\) | −79.7113 | − | 297.486i | −0.123201 | − | 0.459794i | 0.876568 | − | 0.481278i | \(-0.159827\pi\) |
−0.999769 | + | 0.0214847i | \(0.993161\pi\) | |||||||
\(648\) | −24.5885 | + | 6.58846i | −0.0379452 | + | 0.0101674i | ||||
\(649\) | 373.362 | − | 215.561i | 0.575289 | − | 0.332143i | ||||
\(650\) | −147.988 | − | 37.1939i | −0.227674 | − | 0.0572214i | ||||
\(651\) | −334.516 | − | 439.886i | −0.513850 | − | 0.675708i | ||||
\(652\) | 296.719 | − | 296.719i | 0.455091 | − | 0.455091i | ||||
\(653\) | −6.40777 | + | 23.9141i | −0.00981282 | + | 0.0366219i | −0.970659 | − | 0.240462i | \(-0.922701\pi\) |
0.960846 | + | 0.277083i | \(0.0893679\pi\) | |||||||
\(654\) | −203.352 | − | 117.405i | −0.310935 | − | 0.179518i | ||||
\(655\) | 402.958 | + | 304.247i | 0.615204 | + | 0.464499i | ||||
\(656\) | −85.9218 | − | 148.821i | −0.130978 | − | 0.226861i | ||||
\(657\) | −15.3845 | + | 15.3845i | −0.0234163 | + | 0.0234163i | ||||
\(658\) | 400.702 | − | 163.945i | 0.608969 | − | 0.249156i | ||||
\(659\) | 392.819i | 0.596083i | 0.954553 | + | 0.298042i | \(0.0963334\pi\) | ||||
−0.954553 | + | 0.298042i | \(0.903667\pi\) | |||||||
\(660\) | 110.284 | − | 272.224i | 0.167097 | − | 0.412460i | ||||
\(661\) | 630.880 | − | 1092.72i | 0.954433 | − | 1.65313i | 0.218772 | − | 0.975776i | \(-0.429795\pi\) |
0.735661 | − | 0.677350i | \(-0.236872\pi\) | |||||||
\(662\) | −93.5016 | − | 348.953i | −0.141241 | − | 0.527119i | ||||
\(663\) | −21.5223 | + | 80.3224i | −0.0324620 | + | 0.121150i | ||||
\(664\) | 439.786i | 0.662329i | ||||||||
\(665\) | 60.8561 | + | 224.024i | 0.0915129 | + | 0.336879i | ||||
\(666\) | −77.7855 | −0.116795 | ||||||||
\(667\) | −602.231 | − | 161.367i | −0.902895 | − | 0.241930i | ||||
\(668\) | 40.5716 | − | 10.8711i | 0.0607360 | − | 0.0162741i | ||||
\(669\) | −537.756 | − | 310.474i | −0.803821 | − | 0.464086i | ||||
\(670\) | −173.529 | − | 409.883i | −0.258999 | − | 0.611766i | ||||
\(671\) | 1440.80 | 2.14724 | ||||||||
\(672\) | −67.9595 | − | 9.24694i | −0.101130 | − | 0.0137603i | ||||
\(673\) | −848.161 | − | 848.161i | −1.26027 | − | 1.26027i | −0.950962 | − | 0.309306i | \(-0.899903\pi\) |
−0.309306 | − | 0.950962i | \(-0.600097\pi\) | |||||||
\(674\) | −4.23481 | + | 2.44497i | −0.00628310 | + | 0.00362755i | ||||
\(675\) | 2.02235 | + | 129.888i | 0.00299608 | + | 0.192427i | ||||
\(676\) | 150.373 | − | 260.454i | 0.222445 | − | 0.385286i | ||||
\(677\) | −734.564 | − | 196.826i | −1.08503 | − | 0.290732i | −0.328374 | − | 0.944548i | \(-0.606501\pi\) |
−0.756654 | + | 0.653815i | \(0.773167\pi\) | |||||||
\(678\) | −212.142 | − | 212.142i | −0.312893 | − | 0.312893i | ||||
\(679\) | −49.6761 | − | 390.398i | −0.0731607 | − | 0.574961i | ||||
\(680\) | 19.3192 | − | 156.126i | 0.0284106 | − | 0.229597i | ||||
\(681\) | 12.0267 | + | 20.8308i | 0.0176603 | + | 0.0305885i | ||||
\(682\) | 282.913 | + | 1055.85i | 0.414828 | + | 1.54816i | ||||
\(683\) | 223.339 | − | 59.8436i | 0.326997 | − | 0.0876187i | −0.0915857 | − | 0.995797i | \(-0.529194\pi\) |
0.418583 | + | 0.908179i | \(0.362527\pi\) | |||||||
\(684\) | −34.4643 | + | 19.8980i | −0.0503864 | + | 0.0290906i | ||||
\(685\) | −406.134 | − | 520.839i | −0.592897 | − | 0.760349i | ||||
\(686\) | −380.963 | − | 300.275i | −0.555340 | − | 0.437719i | ||||
\(687\) | 439.718 | − | 439.718i | 0.640055 | − | 0.640055i | ||||
\(688\) | 2.90812 | − | 10.8532i | 0.00422692 | − | 0.0157751i | ||||
\(689\) | −317.933 | − | 183.559i | −0.461442 | − | 0.266413i | ||||
\(690\) | 29.4152 | + | 210.741i | 0.0426308 | + | 0.305422i | ||||
\(691\) | −536.360 | − | 929.003i | −0.776209 | − | 1.34443i | −0.934112 | − | 0.356979i | \(-0.883807\pi\) |
0.157904 | − | 0.987455i | \(-0.449526\pi\) | |||||||
\(692\) | −180.959 | + | 180.959i | −0.261501 | + | 0.261501i | ||||
\(693\) | 281.579 | + | 218.009i | 0.406319 | + | 0.314587i | ||||
\(694\) | − | 746.570i | − | 1.07575i | ||||||
\(695\) | −96.9695 | − | 229.046i | −0.139525 | − | 0.329562i | ||||
\(696\) | 87.9026 | − | 152.252i | 0.126297 | − | 0.218752i | ||||
\(697\) | 123.689 | + | 461.612i | 0.177459 | + | 0.662285i | ||||
\(698\) | −27.0953 | + | 101.121i | −0.0388185 | + | 0.144872i | ||||
\(699\) | − | 367.941i | − | 0.526382i | ||||||
\(700\) | −130.298 | + | 324.842i | −0.186141 | + | 0.464060i | ||||
\(701\) | 708.751 | 1.01106 | 0.505528 | − | 0.862810i | \(-0.331298\pi\) | ||||
0.505528 | + | 0.862810i | \(0.331298\pi\) | |||||||
\(702\) | 30.6346 | + | 8.20852i | 0.0436391 | + | 0.0116930i | ||||
\(703\) | −117.461 | + | 31.4736i | −0.167085 | + | 0.0447704i | ||||
\(704\) | 117.486 | + | 67.8305i | 0.166883 | + | 0.0963502i | ||||
\(705\) | 348.777 | − | 147.659i | 0.494719 | − | 0.209446i | ||||
\(706\) | −405.953 | −0.575004 | ||||||||
\(707\) | 192.155 | + | 469.652i | 0.271790 | + | 0.664289i | ||||
\(708\) | −62.2745 | − | 62.2745i | −0.0879584 | − | 0.0879584i | ||||
\(709\) | 328.423 | − | 189.615i | 0.463220 | − | 0.267440i | −0.250177 | − | 0.968200i | \(-0.580489\pi\) |
0.713397 | + | 0.700760i | \(0.247156\pi\) | |||||||
\(710\) | 966.190 | − | 134.861i | 1.36083 | − | 0.189945i | ||||
\(711\) | −61.4817 | + | 106.489i | −0.0864721 | + | 0.149774i | ||||
\(712\) | 157.642 | + | 42.2401i | 0.221408 | + | 0.0593260i | ||||
\(713\) | −559.957 | − | 559.957i | −0.785354 | − | 0.785354i | ||||
\(714\) | 175.900 | + | 73.7550i | 0.246358 | + | 0.103298i | ||||
\(715\) | −288.575 | + | 225.022i | −0.403601 | + | 0.314716i | ||||
\(716\) | −148.311 | − | 256.882i | −0.207138 | − | 0.358774i | ||||
\(717\) | 65.3970 | + | 244.065i | 0.0912092 | + | 0.340397i | ||||
\(718\) | −900.824 | + | 241.375i | −1.25463 | + | 0.336177i | ||||
\(719\) | 498.664 | − | 287.904i | 0.693552 | − | 0.400422i | −0.111390 | − | 0.993777i | \(-0.535530\pi\) |
0.804941 | + | 0.593355i | \(0.202197\pi\) | |||||||
\(720\) | −59.5459 | − | 7.36827i | −0.0827026 | − | 0.0102337i | ||||
\(721\) | 670.605 | + | 881.838i | 0.930103 | + | 1.22308i | ||||
\(722\) | 317.008 | − | 317.008i | 0.439069 | − | 0.439069i | ||||
\(723\) | 118.681 | − | 442.923i | 0.164150 | − | 0.612618i | ||||
\(724\) | −244.131 | − | 140.949i | −0.337198 | − | 0.194681i | ||||
\(725\) | −644.181 | − | 624.429i | −0.888526 | − | 0.861281i | ||||
\(726\) | −203.995 | − | 353.330i | −0.280985 | − | 0.486681i | ||||
\(727\) | 841.342 | − | 841.342i | 1.15728 | − | 1.15728i | 0.172220 | − | 0.985058i | \(-0.444906\pi\) |
0.985058 | − | 0.172220i | \(-0.0550941\pi\) | |||||||
\(728\) | 67.5663 | + | 52.3124i | 0.0928109 | + | 0.0718577i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −47.2240 | + | 19.9929i | −0.0646904 | + | 0.0273875i | ||||
\(731\) | −15.6238 | + | 27.0612i | −0.0213732 | + | 0.0370194i | ||||
\(732\) | −76.1771 | − | 284.297i | −0.104067 | − | 0.388384i | ||||
\(733\) | 116.341 | − | 434.189i | 0.158718 | − | 0.592345i | −0.840040 | − | 0.542525i | \(-0.817469\pi\) |
0.998758 | − | 0.0498201i | \(-0.0158648\pi\) | |||||||
\(734\) | 553.181i | 0.753652i | ||||||||
\(735\) | −336.432 | − | 258.628i | −0.457731 | − | 0.351874i | ||||
\(736\) | −98.2807 | −0.133534 | ||||||||
\(737\) | −1031.06 | − | 276.272i | −1.39900 | − | 0.374860i | ||||
\(738\) | 176.057 | − | 47.1743i | 0.238560 | − | 0.0639219i | ||||
\(739\) | −725.131 | − | 418.655i | −0.981233 | − | 0.566515i | −0.0785910 | − | 0.996907i | \(-0.525042\pi\) |
−0.902642 | + | 0.430392i | \(0.858375\pi\) | |||||||
\(740\) | −169.927 | − | 68.8413i | −0.229631 | − | 0.0930288i | ||||
\(741\) | 49.5815 | 0.0669116 | ||||||||
\(742\) | −515.509 | + | 665.828i | −0.694756 | + | 0.897342i | ||||
\(743\) | 241.494 | + | 241.494i | 0.325025 | + | 0.325025i | 0.850691 | − | 0.525666i | \(-0.176184\pi\) |
−0.525666 | + | 0.850691i | \(0.676184\pi\) | |||||||
\(744\) | 193.380 | − | 111.648i | 0.259920 | − | 0.150065i | ||||
\(745\) | 684.404 | − | 906.456i | 0.918663 | − | 1.21672i | ||||
\(746\) | −20.7758 | + | 35.9847i | −0.0278495 | + | 0.0482368i | ||||
\(747\) | −450.569 | − | 120.730i | −0.603172 | − | 0.161619i | ||||
\(748\) | −266.772 | − | 266.772i | −0.356647 | − | 0.356647i | ||||
\(749\) | −250.595 | + | 190.568i | −0.334573 | + | 0.254430i | ||||
\(750\) | −110.535 | + | 285.538i | −0.147380 | + | 0.380718i | ||||
\(751\) | 157.587 | + | 272.949i | 0.209836 | + | 0.363447i | 0.951663 | − | 0.307145i | \(-0.0993735\pi\) |
−0.741826 | + | 0.670592i | \(0.766040\pi\) | |||||||
\(752\) | 45.2766 | + | 168.975i | 0.0602083 | + | 0.224700i | ||||
\(753\) | 505.028 | − | 135.322i | 0.670688 | − | 0.179710i | ||||
\(754\) | −189.690 | + | 109.517i | −0.251578 | + | 0.145248i | ||||
\(755\) | −122.151 | + | 987.147i | −0.161789 | + | 1.30748i | ||||
\(756\) | 28.1298 | − | 67.0873i | 0.0372088 | − | 0.0887399i | ||||
\(757\) | −650.017 | + | 650.017i | −0.858675 | + | 0.858675i | −0.991182 | − | 0.132507i | \(-0.957697\pi\) |
0.132507 | + | 0.991182i | \(0.457697\pi\) | |||||||
\(758\) | 171.994 | − | 641.890i | 0.226905 | − | 0.846821i | ||||
\(759\) | 441.926 | + | 255.146i | 0.582248 | + | 0.336161i | ||||
\(760\) | −92.8993 | + | 12.9669i | −0.122236 | + | 0.0170617i | ||||
\(761\) | 349.979 | + | 606.182i | 0.459894 | + | 0.796560i | 0.998955 | − | 0.0457070i | \(-0.0145541\pi\) |
−0.539061 | + | 0.842267i | \(0.681221\pi\) | |||||||
\(762\) | 112.984 | − | 112.984i | 0.148274 | − | 0.148274i | ||||
\(763\) | 621.054 | − | 254.100i | 0.813964 | − | 0.333028i | ||||
\(764\) | 325.612i | 0.426193i | ||||||||
\(765\) | 154.651 | + | 62.6525i | 0.202158 | + | 0.0818987i | ||||
\(766\) | −384.025 | + | 665.150i | −0.501338 | + | 0.868343i | ||||
\(767\) | 28.3990 | + | 105.986i | 0.0370260 | + | 0.138183i | ||||
\(768\) | 7.17260 | − | 26.7685i | 0.00933933 | − | 0.0348548i | ||||
\(769\) | − | 272.975i | − | 0.354974i | −0.984123 | − | 0.177487i | \(-0.943203\pi\) | ||
0.984123 | − | 0.177487i | \(-0.0567967\pi\) | |||||||
\(770\) | 422.185 | + | 725.455i | 0.548292 | + | 0.942150i | ||||
\(771\) | 204.929 | 0.265797 | ||||||||
\(772\) | 446.985 | + | 119.769i | 0.578996 | + | 0.155142i | ||||
\(773\) | −831.312 | + | 222.749i | −1.07544 | + | 0.288162i | −0.752725 | − | 0.658335i | \(-0.771261\pi\) |
−0.322711 | + | 0.946498i | \(0.604594\pi\) | |||||||
\(774\) | 10.3210 | + | 5.95885i | 0.0133347 | + | 0.00769877i | ||||
\(775\) | −312.025 | − | 1095.95i | −0.402613 | − | 1.41413i | ||||
\(776\) | 159.017 | 0.204918 | ||||||||
\(777\) | 136.085 | − | 175.767i | 0.175142 | − | 0.226212i | ||||
\(778\) | −380.535 | − | 380.535i | −0.489120 | − | 0.489120i | ||||
\(779\) | 246.770 | − | 142.472i | 0.316777 | − | 0.182891i | ||||
\(780\) | 59.6585 | + | 45.0441i | 0.0764853 | + | 0.0577489i | ||||
\(781\) | 1169.78 | − | 2026.11i | 1.49779 | − | 2.59425i | ||||
\(782\) | 264.005 | + | 70.7400i | 0.337602 | + | 0.0904603i | ||||
\(783\) | 131.854 | + | 131.854i | 0.168396 | + | 0.168396i | ||||
\(784\) | 139.789 | − | 137.386i | 0.178303 | − | 0.175237i | ||||
\(785\) | 855.257 | + | 1096.81i | 1.08950 | + | 1.39721i | ||||
\(786\) | −123.679 | − | 214.218i | −0.157352 | − | 0.272542i | ||||
\(787\) | −149.860 | − | 559.283i | −0.190419 | − | 0.710652i | −0.993405 | − | 0.114655i | \(-0.963424\pi\) |
0.802987 | − | 0.595997i | \(-0.203243\pi\) | |||||||
\(788\) | 480.491 | − | 128.747i | 0.609760 | − | 0.163385i | ||||
\(789\) | 510.062 | − | 294.484i | 0.646466 | − | 0.373238i | ||||
\(790\) | −228.555 | + | 178.220i | −0.289310 | + | 0.225595i | ||||
\(791\) | 850.503 | − | 108.222i | 1.07522 | − | 0.136817i | ||||
\(792\) | −101.746 | + | 101.746i | −0.128467 | + | 0.128467i | ||||
\(793\) | −94.9086 | + | 354.204i | −0.119683 | + | 0.446663i | ||||
\(794\) | −417.898 | − | 241.273i | −0.526319 | − | 0.303871i | ||||
\(795\) | −443.884 | + | 587.901i | −0.558345 | + | 0.739498i | ||||
\(796\) | 257.346 | + | 445.736i | 0.323299 | + | 0.559970i | ||||
\(797\) | −934.809 | + | 934.809i | −1.17291 | + | 1.17291i | −0.191396 | + | 0.981513i | \(0.561302\pi\) |
−0.981513 | + | 0.191396i | \(0.938698\pi\) | |||||||
\(798\) | 15.3329 | − | 112.688i | 0.0192142 | − | 0.141213i | ||||
\(799\) | − | 486.495i | − | 0.608879i | ||||||
\(800\) | −123.560 | − | 68.7954i | −0.154451 | − | 0.0859943i | ||||
\(801\) | −86.5516 | + | 149.912i | −0.108054 | + | 0.187156i | ||||
\(802\) | 158.256 | + | 590.618i | 0.197326 | + | 0.736431i | ||||
\(803\) | −31.8302 | + | 118.792i | −0.0396391 | + | 0.147935i | ||||
\(804\) | 218.055i | 0.271213i | ||||||||
\(805\) | −527.659 | − | 302.222i | −0.655477 | − | 0.375431i | ||||
\(806\) | −278.204 | −0.345166 | ||||||||
\(807\) | −618.158 | − | 165.635i | −0.765996 | − | 0.205248i | ||||
\(808\) | −198.051 | + | 53.0676i | −0.245112 | + | 0.0656777i | ||||
\(809\) | −185.686 | − | 107.206i | −0.229525 | − | 0.132516i | 0.380828 | − | 0.924646i | \(-0.375639\pi\) |
−0.610353 | + | 0.792130i | \(0.708972\pi\) | |||||||
\(810\) | 23.8954 | − | 58.9831i | 0.0295005 | − | 0.0728187i | ||||
\(811\) | −527.675 | −0.650647 | −0.325324 | − | 0.945603i | \(-0.605473\pi\) | ||||
−0.325324 | + | 0.945603i | \(0.605473\pi\) | |||||||
\(812\) | 190.248 | + | 464.991i | 0.234296 | + | 0.572649i | ||||
\(813\) | −335.614 | − | 335.614i | −0.412809 | − | 0.412809i | ||||
\(814\) | −380.779 | + | 219.843i | −0.467788 | + | 0.270077i | ||||
\(815\) | 145.022 | + | 1038.99i | 0.177941 | + | 1.27483i | ||||
\(816\) | −38.5346 | + | 66.7439i | −0.0472238 | + | 0.0817940i | ||||
\(817\) | 17.9965 | + | 4.82214i | 0.0220275 | + | 0.00590225i | ||||
\(818\) | −253.100 | − | 253.100i | −0.309413 | − | 0.309413i | ||||
\(819\) | −72.1433 | + | 54.8622i | −0.0880870 | + | 0.0669869i | ||||
\(820\) | 426.357 | + | 52.7579i | 0.519948 | + | 0.0643390i | ||||
\(821\) | −6.70379 | − | 11.6113i | −0.00816539 | − | 0.0141429i | 0.861914 | − | 0.507055i | \(-0.169266\pi\) |
−0.870079 | + | 0.492912i | \(0.835932\pi\) | |||||||
\(822\) | 83.7441 | + | 312.537i | 0.101878 | + | 0.380215i | ||||
\(823\) | −555.346 | + | 148.804i | −0.674782 | + | 0.180807i | −0.579908 | − | 0.814682i | \(-0.696912\pi\) |
−0.0948742 | + | 0.995489i | \(0.530245\pi\) | |||||||
\(824\) | −387.670 | + | 223.821i | −0.470473 | + | 0.271628i | ||||
\(825\) | 376.999 | + | 630.119i | 0.456969 | + | 0.763780i | ||||
\(826\) | 249.666 | − | 31.7687i | 0.302260 | − | 0.0384609i | ||||
\(827\) | 485.728 | − | 485.728i | 0.587337 | − | 0.587337i | −0.349572 | − | 0.936909i | \(-0.613673\pi\) |
0.936909 | + | 0.349572i | \(0.113673\pi\) | |||||||
\(828\) | 26.9799 | − | 100.690i | 0.0325845 | − | 0.121607i | ||||
\(829\) | 80.3994 | + | 46.4186i | 0.0969836 | + | 0.0559935i | 0.547707 | − | 0.836670i | \(-0.315501\pi\) |
−0.450724 | + | 0.892663i | \(0.648834\pi\) | |||||||
\(830\) | −877.449 | − | 662.502i | −1.05717 | − | 0.798195i | ||||
\(831\) | 48.7275 | + | 84.3986i | 0.0586372 | + | 0.101563i | ||||
\(832\) | −24.4144 | + | 24.4144i | −0.0293443 | + | 0.0293443i | ||||
\(833\) | −474.394 | + | 268.434i | −0.569501 | + | 0.322250i | ||||
\(834\) | 121.851i | 0.146104i | ||||||||
\(835\) | −39.4281 | + | 97.3238i | −0.0472192 | + | 0.116555i | ||||
\(836\) | −112.474 | + | 194.811i | −0.134538 | + | 0.233028i | ||||
\(837\) | 61.2992 | + | 228.772i | 0.0732367 | + | 0.273323i | ||||
\(838\) | −166.915 | + | 622.936i | −0.199183 | + | 0.743360i | ||||
\(839\) | 1256.89i | 1.49808i | 0.662527 | + | 0.749038i | \(0.269484\pi\) | ||||
−0.662527 | + | 0.749038i | \(0.730516\pi\) | |||||||
\(840\) | 120.825 | − | 121.661i | 0.143839 | − | 0.144835i | ||||
\(841\) | −446.810 | −0.531284 | ||||||||
\(842\) | −120.112 | − | 32.1839i | −0.142651 | − | 0.0382231i | ||||
\(843\) | −895.086 | + | 239.837i | −1.06179 | + | 0.284505i | ||||
\(844\) | −467.384 | − | 269.844i | −0.553772 | − | 0.319720i | ||||
\(845\) | 293.125 | + | 692.372i | 0.346893 | + | 0.819375i | ||||
\(846\) | −185.547 | −0.219323 | ||||||||
\(847\) | 1155.28 | + | 157.194i | 1.36397 | + | 0.185589i | ||||
\(848\) | −240.591 | − | 240.591i | −0.283715 | − | 0.283715i | ||||
\(849\) | −303.876 | + | 175.443i | −0.357922 | + | 0.206646i | ||||
\(850\) | 282.395 | + | 273.736i | 0.332230 | + | 0.322043i | ||||
\(851\) | 159.267 | − | 275.858i | 0.187153 | − | 0.324158i | ||||
\(852\) | −461.639 | − | 123.696i | −0.541829 | − | 0.145183i | ||||
\(853\) | −74.9889 | − | 74.9889i | −0.0879119 | − | 0.0879119i | 0.661783 | − | 0.749695i | \(-0.269800\pi\) |
−0.749695 | + | 0.661783i | \(0.769800\pi\) | |||||||
\(854\) | 775.678 | + | 325.243i | 0.908288 | + | 0.380847i | ||||
\(855\) | 12.2178 | − | 98.7368i | 0.0142898 | − | 0.115482i | ||||
\(856\) | −63.6040 | − | 110.165i | −0.0743038 | − | 0.128698i | ||||
\(857\) | −162.704 | − | 607.221i | −0.189853 | − | 0.708542i | −0.993539 | − | 0.113489i | \(-0.963797\pi\) |
0.803686 | − | 0.595054i | \(-0.202869\pi\) | |||||||
\(858\) | 173.164 | − | 46.3990i | 0.201822 | − | 0.0540781i | ||||
\(859\) | 1187.28 | − | 685.475i | 1.38216 | − | 0.797991i | 0.389746 | − | 0.920922i | \(-0.372563\pi\) |
0.992415 | + | 0.122931i | \(0.0392293\pi\) | |||||||
\(860\) | 17.2732 | + | 22.1517i | 0.0200852 | + | 0.0257578i | ||||
\(861\) | −201.414 | + | 480.355i | −0.233930 | + | 0.557904i | ||||
\(862\) | 737.864 | − | 737.864i | 0.855991 | − | 0.855991i | ||||
\(863\) | −201.325 | + | 751.357i | −0.233286 | + | 0.870634i | 0.745629 | + | 0.666362i | \(0.232149\pi\) |
−0.978914 | + | 0.204272i | \(0.934517\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | −88.4441 | − | 633.644i | −0.102247 | − | 0.732536i | ||||
\(866\) | −29.1869 | − | 50.5532i | −0.0337031 | − | 0.0583755i | ||||
\(867\) | −202.398 | + | 202.398i | −0.233446 | + | 0.233446i | ||||
\(868\) | −86.0337 | + | 632.297i | −0.0991172 | + | 0.728452i | ||||
\(869\) | 695.056i | 0.799834i | ||||||||
\(870\) | 171.350 | + | 404.735i | 0.196954 | + | 0.465213i | ||||
\(871\) | 135.837 | − | 235.276i | 0.155955 | − | 0.270122i | ||||
\(872\) | 70.1750 | + | 261.897i | 0.0804759 | + | 0.300340i | ||||
\(873\) | −43.6531 | + | 162.916i | −0.0500035 | + | 0.186616i | ||||
\(874\) | − | 162.966i | − | 0.186459i | ||||||
\(875\) | −451.831 | − | 749.315i | −0.516379 | − | 0.856360i | ||||
\(876\) | 25.1228 | 0.0286790 | ||||||||
\(877\) | −394.106 | − | 105.600i | −0.449380 | − | 0.120411i | 0.0270295 | − | 0.999635i | \(-0.491395\pi\) |
−0.476409 | + | 0.879224i | \(0.658062\pi\) | |||||||
\(878\) | 557.919 | − | 149.494i | 0.635443 | − | 0.170267i | ||||
\(879\) | 477.781 | + | 275.847i | 0.543550 | + | 0.313819i | ||||
\(880\) | −312.316 | + | 132.223i | −0.354905 | + | 0.150254i | ||||
\(881\) | 175.519 | 0.199227 | 0.0996134 | − | 0.995026i | \(-0.468239\pi\) | ||||
0.0996134 | + | 0.995026i | \(0.468239\pi\) | |||||||
\(882\) | 102.380 | + | 180.932i | 0.116077 | + | 0.205138i | ||||
\(883\) | 528.630 | + | 528.630i | 0.598675 | + | 0.598675i | 0.939960 | − | 0.341285i | \(-0.110862\pi\) |
−0.341285 | + | 0.939960i | \(0.610862\pi\) | |||||||
\(884\) | 83.1558 | − | 48.0100i | 0.0940677 | − | 0.0543100i | ||||
\(885\) | 218.060 | − | 30.4368i | 0.246395 | − | 0.0343918i | ||||
\(886\) | 419.377 | − | 726.383i | 0.473338 | − | 0.819845i | ||||
\(887\) | 1006.63 | + | 269.726i | 1.13487 | + | 0.304088i | 0.776888 | − | 0.629639i | \(-0.216797\pi\) |
0.357985 | + | 0.933727i | \(0.383464\pi\) | |||||||
\(888\) | 63.5116 | + | 63.5116i | 0.0715221 | + | 0.0715221i | ||||
\(889\) | 57.6379 | + | 452.969i | 0.0648345 | + | 0.509526i | ||||
\(890\) | −321.751 | + | 250.892i | −0.361518 | + | 0.281901i | ||||
\(891\) | −76.3094 | − | 132.172i | −0.0856446 | − | 0.148341i | ||||
\(892\) | 185.575 | + | 692.577i | 0.208044 | + | 0.776431i | ||||
\(893\) | −280.188 | + | 75.0761i | −0.313760 | + | 0.0840718i | ||||
\(894\) | −481.885 | + | 278.216i | −0.539021 | + | 0.311204i | ||||
\(895\) | 735.942 | + | 91.0664i | 0.822282 | + | 0.101750i | ||||
\(896\) | 47.9386 | + | 63.0388i | 0.0535029 | + | 0.0703558i | ||||
\(897\) | −91.8355 | + | 91.8355i | −0.102381 | + | 0.102381i | ||||
\(898\) | −64.4916 | + | 240.686i | −0.0718170 | + | 0.268025i | ||||
\(899\) | −1416.55 | − | 817.847i | −1.57570 | − | 0.909730i | ||||
\(900\) | 104.402 | − | 107.704i | 0.116002 | − | 0.119672i | ||||
\(901\) | 473.112 | + | 819.454i | 0.525096 | + | 0.909494i | ||||
\(902\) | 728.515 | − | 728.515i | 0.807667 | − | 0.807667i | ||||
\(903\) | −31.5214 | + | 12.8968i | −0.0349074 | + | 0.0142821i | ||||
\(904\) | 346.426i | 0.383215i | ||||||||
\(905\) | 648.981 | − | 274.755i | 0.717106 | − | 0.303596i | ||||
\(906\) | 243.645 | − | 422.005i | 0.268924 | − | 0.465790i | ||||
\(907\) | 233.926 | + | 873.023i | 0.257912 | + | 0.962539i | 0.966448 | + | 0.256864i | \(0.0826893\pi\) |
−0.708536 | + | 0.705675i | \(0.750644\pi\) | |||||||
\(908\) | 7.18854 | − | 26.8280i | 0.00791689 | − | 0.0295462i | ||||
\(909\) | − | 217.475i | − | 0.239246i | ||||||
\(910\) | −206.155 | + | 56.0020i | −0.226544 | + | 0.0615406i | ||||
\(911\) | −1543.49 | −1.69428 | −0.847140 | − | 0.531370i | \(-0.821678\pi\) | ||||
−0.847140 | + | 0.531370i | \(0.821678\pi\) | |||||||
\(912\) | 44.3866 | + | 11.8934i | 0.0486695 | + | 0.0130410i | ||||
\(913\) | −2546.86 | + | 682.430i | −2.78956 | + | 0.747459i | ||||
\(914\) | −63.6441 | − | 36.7450i | −0.0696325 | − | 0.0402024i | ||||
\(915\) | 681.975 | + | 276.284i | 0.745328 | + | 0.301949i | ||||
\(916\) | −718.056 | −0.783904 | ||||||||
\(917\) | 700.430 | + | 95.3043i | 0.763828 | + | 0.103931i | ||||
\(918\) | −57.8019 | − | 57.8019i | −0.0629650 | − | 0.0629650i | ||||
\(919\) | 1140.39 | − | 658.405i | 1.24090 | − | 0.716436i | 0.271625 | − | 0.962403i | \(-0.412439\pi\) |
0.969278 | + | 0.245967i | \(0.0791055\pi\) | |||||||
\(920\) | 148.052 | − | 196.087i | 0.160926 | − | 0.213138i | ||||
\(921\) | −360.491 | + | 624.389i | −0.391413 | + | 0.677947i | ||||
\(922\) | 575.024 | + | 154.077i | 0.623670 | + | 0.167112i | ||||
\(923\) | 421.041 | + | 421.041i | 0.456166 | + | 0.456166i | ||||
\(924\) | −51.9046 | − | 407.912i | −0.0561738 | − | 0.441463i | ||||
\(925\) | 393.331 | − | 235.330i | 0.425223 | − | 0.254410i | ||||
\(926\) | 45.3241 | + | 78.5036i | 0.0489461 | + | 0.0847771i | ||||
\(927\) | −122.886 | − | 458.618i | −0.132563 | − | 0.494734i | ||||
\(928\) | −196.085 | + | 52.5409i | −0.211299 | + | 0.0566173i | ||||
\(929\) | 963.700 | − | 556.392i | 1.03735 | − | 0.598915i | 0.118270 | − | 0.992981i | \(-0.462265\pi\) |
0.919082 | + | 0.394066i | \(0.128932\pi\) | |||||||
\(930\) | −68.5546 | + | 554.016i | −0.0737146 | + | 0.595716i | ||||
\(931\) | 227.809 | + | 231.794i | 0.244692 | + | 0.248973i | ||||
\(932\) | −300.422 | + | 300.422i | −0.322342 | + | 0.322342i | ||||
\(933\) | 104.887 | − | 391.442i | 0.112419 | − | 0.419552i | ||||
\(934\) | 649.852 | + | 375.192i | 0.695773 | + | 0.401705i | ||||
\(935\) | 934.126 | − | 130.385i | 0.999066 | − | 0.139450i | ||||
\(936\) | −18.3108 | − | 31.7153i | −0.0195629 | − | 0.0338839i | ||||
\(937\) | −1008.35 | + | 1008.35i | −1.07614 | + | 1.07614i | −0.0792913 | + | 0.996851i | \(0.525266\pi\) |
−0.996851 | + | 0.0792913i | \(0.974734\pi\) | |||||||
\(938\) | −492.724 | − | 381.486i | −0.525293 | − | 0.406701i | ||||
\(939\) | 246.172i | 0.262164i | ||||||||
\(940\) | −405.339 | − | 164.212i | −0.431211 | − | 0.174694i | ||||
\(941\) | −350.515 | + | 607.110i | −0.372492 | + | 0.645176i | −0.989948 | − | 0.141430i | \(-0.954830\pi\) |
0.617456 | + | 0.786606i | \(0.288163\pi\) | |||||||
\(942\) | −176.352 | − | 658.156i | −0.187210 | − | 0.698679i | ||||
\(943\) | −193.180 | + | 720.959i | −0.204857 | + | 0.764538i | ||||
\(944\) | 101.694i | 0.107727i | ||||||||
\(945\) | 91.4754 | + | 157.185i | 0.0967993 | + | 0.166334i | ||||
\(946\) | 67.3653 | 0.0712107 | ||||||||
\(947\) | 58.9346 | + | 15.7915i | 0.0622330 | + | 0.0166753i | 0.289801 | − | 0.957087i | \(-0.406411\pi\) |
−0.227568 | + | 0.973762i | \(0.573077\pi\) | |||||||
\(948\) | 137.148 | − | 36.7486i | 0.144671 | − | 0.0387644i | ||||
\(949\) | −27.1069 | − | 15.6502i | −0.0285637 | − | 0.0164912i | ||||
\(950\) | 114.074 | − | 204.884i | 0.120078 | − | 0.215667i | ||||
\(951\) | 121.518 | 0.127779 | ||||||||
\(952\) | −83.4007 | − | 203.842i | −0.0876057 | − | 0.214120i | ||||
\(953\) | 102.107 | + | 102.107i | 0.107142 | + | 0.107142i | 0.758646 | − | 0.651503i | \(-0.225861\pi\) |
−0.651503 | + | 0.758646i | \(0.725861\pi\) | |||||||
\(954\) | 312.536 | − | 180.443i | 0.327606 | − | 0.189144i | ||||
\(955\) | −649.651 | − | 490.507i | −0.680262 | − | 0.513620i | ||||
\(956\) | 145.882 | − | 252.675i | 0.152596 | − | 0.264304i | ||||
\(957\) | 1018.11 | + | 272.802i | 1.06386 | + | 0.285060i | ||||
\(958\) | 332.049 | + | 332.049i | 0.346607 | + | 0.346607i | ||||
\(959\) | −852.729 | − | 357.551i | −0.889185 | − | 0.372837i | ||||
\(960\) | 42.6028 | + | 54.6352i | 0.0443779 | + | 0.0569116i | ||||
\(961\) | −558.278 | − | 966.966i | −0.580934 | − | 1.00621i | ||||
\(962\) | −28.9631 | − | 108.092i | −0.0301072 | − | 0.112362i | ||||
\(963\) | 130.327 | − | 34.9210i | 0.135334 | − | 0.0362628i | ||||
\(964\) | −458.547 | + | 264.742i | −0.475671 | + | 0.274629i | ||||
\(965\) | −912.307 | + | 711.389i | −0.945396 | + | 0.737190i | ||||
\(966\) | 180.322 | + | 237.122i | 0.186669 | + | 0.245468i | ||||
\(967\) | 1.00086 | − | 1.00086i | 0.00103501 | − | 0.00103501i | −0.706589 | − | 0.707624i | \(-0.749767\pi\) |
0.707624 | + | 0.706589i | \(0.249767\pi\) | |||||||
\(968\) | −121.931 | + | 455.054i | −0.125962 | + | 0.470097i | ||||
\(969\) | −110.672 | − | 63.8967i | −0.114213 | − | 0.0659409i | ||||
\(970\) | −239.546 | + | 317.265i | −0.246954 | + | 0.327078i | ||||
\(971\) | −362.599 | − | 628.039i | −0.373428 | − | 0.646796i | 0.616662 | − | 0.787228i | \(-0.288484\pi\) |
−0.990090 | + | 0.140431i | \(0.955151\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −275.338 | − | 213.177i | −0.282978 | − | 0.219093i | ||||
\(974\) | − | 1051.67i | − | 1.07974i | ||||||
\(975\) | −179.741 | + | 51.1736i | −0.184350 | + | 0.0524857i | ||||
\(976\) | −169.929 | + | 294.326i | −0.174108 | + | 0.301563i | ||||
\(977\) | −276.413 | − | 1031.59i | −0.282920 | − | 1.05587i | −0.950346 | − | 0.311196i | \(-0.899270\pi\) |
0.667425 | − | 0.744677i | \(-0.267396\pi\) | |||||||
\(978\) | 133.016 | − | 496.421i | 0.136008 | − | 0.507588i | ||||
\(979\) | 978.473i | 0.999462i | ||||||||
\(980\) | 63.5274 | + | 485.864i | 0.0648238 | + | 0.495780i | ||||
\(981\) | −287.583 | −0.293152 | ||||||||
\(982\) | −63.7563 | − | 17.0834i | −0.0649249 | − | 0.0173966i | ||||
\(983\) | 1063.81 | − | 285.048i | 1.08221 | − | 0.289977i | 0.326709 | − | 0.945125i | \(-0.394060\pi\) |
0.755501 | + | 0.655147i | \(0.227393\pi\) | |||||||
\(984\) | −182.268 | − | 105.232i | −0.185231 | − | 0.106943i | ||||
\(985\) | −466.948 | + | 1152.61i | −0.474059 | + | 1.17016i | ||||
\(986\) | 564.548 | 0.572564 | ||||||||
\(987\) | 324.613 | − | 419.268i | 0.328889 | − | 0.424791i | ||||
\(988\) | −40.4832 | − | 40.4832i | −0.0409748 | − | 0.0409748i | ||||
\(989\) | −42.2649 | + | 24.4017i | −0.0427350 | + | 0.0246731i | ||||
\(990\) | −49.7285 | − | 356.272i | −0.0502308 | − | 0.359871i | ||||
\(991\) | 245.356 | − | 424.969i | 0.247584 | − | 0.428828i | −0.715271 | − | 0.698847i | \(-0.753697\pi\) |
0.962855 | + | 0.270019i | \(0.0870300\pi\) | |||||||
\(992\) | −249.055 | − | 66.7341i | −0.251063 | − | 0.0672722i | ||||
\(993\) | −312.863 | − | 312.863i | −0.315068 | − | 0.315068i | ||||
\(994\) | 1087.14 | − | 826.729i | 1.09370 | − | 0.831719i | ||||
\(995\) | −1276.99 | − | 158.016i | −1.28341 | − | 0.158810i | ||||
\(996\) | 269.313 | + | 466.464i | 0.270395 | + | 0.468337i | ||||
\(997\) | 434.835 | + | 1622.83i | 0.436144 | + | 1.62771i | 0.738315 | + | 0.674456i | \(0.235622\pi\) |
−0.302171 | + | 0.953254i | \(0.597711\pi\) | |||||||
\(998\) | 341.143 | − | 91.4089i | 0.341826 | − | 0.0915921i | ||||
\(999\) | −82.5040 | + | 47.6337i | −0.0825866 | + | 0.0476814i |
(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 | 210.3.v.a.193.1 | yes | 32 | |
5.2 | odd | 4 | inner | 210.3.v.a.67.7 | yes | 32 | |
7.2 | even | 3 | inner | 210.3.v.a.163.7 | yes | 32 | |
35.2 | odd | 12 | inner | 210.3.v.a.37.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.v.a.37.1 | ✓ | 32 | 35.2 | odd | 12 | inner | |
210.3.v.a.67.7 | yes | 32 | 5.2 | odd | 4 | inner | |
210.3.v.a.163.7 | yes | 32 | 7.2 | even | 3 | inner | |
210.3.v.a.193.1 | yes | 32 | 1.1 | even | 1 | trivial |