Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,3,Mod(151,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("342.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.l (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: | \(9.31882504112\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 151.7 | ||
Character | \(\chi\) | \(=\) | 342.151 |
Dual form | 342.3.l.a.265.7 |
$q$-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 \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.612372 | − | 0.353553i | ||||
\(3\) | −1.69573 | + | 2.47477i | −0.565243 | + | 0.824924i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.250000 | + | 0.433013i | ||||
\(5\) | 4.69486 | + | 8.13173i | 0.938971 | + | 1.62635i | 0.767395 | + | 0.641175i | \(0.221553\pi\) |
0.171577 | + | 0.985171i | \(0.445114\pi\) | |||||||
\(6\) | 3.82677 | − | 1.83190i | 0.637794 | − | 0.305317i | ||||
\(7\) | 5.67137 | − | 9.82311i | 0.810196 | − | 1.40330i | −0.102530 | − | 0.994730i | \(-0.532694\pi\) |
0.912726 | − | 0.408571i | \(-0.133973\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −3.24900 | − | 8.39309i | −0.361000 | − | 0.932566i | ||||
\(10\) | − | 13.2791i | − | 1.32791i | ||||||
\(11\) | 3.82304 | − | 6.62171i | 0.347549 | − | 0.601973i | −0.638264 | − | 0.769817i | \(-0.720347\pi\) |
0.985814 | + | 0.167844i | \(0.0536805\pi\) | |||||||
\(12\) | −5.98216 | − | 0.462319i | −0.498513 | − | 0.0385266i | ||||
\(13\) | 15.6637 | − | 9.04345i | 1.20490 | − | 0.695650i | 0.243260 | − | 0.969961i | \(-0.421783\pi\) |
0.961641 | + | 0.274311i | \(0.0884498\pi\) | |||||||
\(14\) | −13.8920 | + | 8.02053i | −0.992284 | + | 0.572895i | ||||
\(15\) | −28.0854 | − | 2.17052i | −1.87236 | − | 0.144701i | ||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 21.1249 | 1.24264 | 0.621320 | − | 0.783557i | \(-0.286597\pi\) | ||||
0.621320 | + | 0.783557i | \(0.286597\pi\) | |||||||
\(18\) | −1.95562 | + | 12.5768i | −0.108646 | + | 0.698710i | ||||
\(19\) | −0.118426 | − | 18.9996i | −0.00623296 | − | 0.999981i | ||||
\(20\) | −9.38971 | + | 16.2635i | −0.469486 | + | 0.813173i | ||||
\(21\) | 14.6928 | + | 30.6927i | 0.699659 | + | 1.46156i | ||||
\(22\) | −9.36451 | + | 5.40660i | −0.425659 | + | 0.245755i | ||||
\(23\) | −8.37354 | − | 14.5034i | −0.364067 | − | 0.630582i | 0.624559 | − | 0.780978i | \(-0.285279\pi\) |
−0.988626 | + | 0.150395i | \(0.951945\pi\) | |||||||
\(24\) | 6.99971 | + | 4.79625i | 0.291655 | + | 0.199844i | ||||
\(25\) | −31.5834 | + | 54.7040i | −1.26333 | + | 2.18816i | ||||
\(26\) | −25.5787 | −0.983798 | ||||||||
\(27\) | 26.2804 | + | 6.19190i | 0.973349 | + | 0.229330i | ||||
\(28\) | 22.6855 | 0.810196 | ||||||||
\(29\) | 12.3614 | + | 7.13685i | 0.426255 | + | 0.246098i | 0.697750 | − | 0.716341i | \(-0.254185\pi\) |
−0.271495 | + | 0.962440i | \(0.587518\pi\) | |||||||
\(30\) | 32.8626 | + | 22.5177i | 1.09542 | + | 0.750590i | ||||
\(31\) | −15.1408 | + | 8.74155i | −0.488413 | + | 0.281986i | −0.723916 | − | 0.689888i | \(-0.757660\pi\) |
0.235503 | + | 0.971874i | \(0.424326\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 9.90436 | + | 20.6898i | 0.300132 | + | 0.626963i | ||||
\(34\) | −25.8726 | − | 14.9376i | −0.760959 | − | 0.439340i | ||||
\(35\) | 106.505 | 3.04300 | ||||||||
\(36\) | 11.2883 | − | 14.0205i | 0.313563 | − | 0.389459i | ||||
\(37\) | − | 10.6584i | − | 0.288066i | −0.989573 | − | 0.144033i | \(-0.953993\pi\) | ||
0.989573 | − | 0.144033i | \(-0.0460071\pi\) | |||||||
\(38\) | −13.2897 | + | 23.3534i | −0.349730 | + | 0.614564i | ||||
\(39\) | −4.18096 | + | 54.0994i | −0.107204 | + | 1.38716i | ||||
\(40\) | 23.0000 | − | 13.2791i | 0.575000 | − | 0.331976i | ||||
\(41\) | 1.55194 | − | 0.896012i | 0.0378521 | − | 0.0218539i | −0.480955 | − | 0.876746i | \(-0.659710\pi\) |
0.518807 | + | 0.854892i | \(0.326376\pi\) | |||||||
\(42\) | 3.70805 | − | 47.9801i | 0.0882868 | − | 1.14238i | ||||
\(43\) | 16.7356 | − | 28.9869i | 0.389200 | − | 0.674113i | −0.603143 | − | 0.797633i | \(-0.706085\pi\) |
0.992342 | + | 0.123520i | \(0.0394183\pi\) | |||||||
\(44\) | 15.2922 | 0.347549 | ||||||||
\(45\) | 52.9968 | − | 65.8243i | 1.17771 | − | 1.46276i | ||||
\(46\) | 23.6839i | 0.514868i | ||||||||
\(47\) | −10.3261 | + | 17.8853i | −0.219704 | + | 0.380538i | −0.954717 | − | 0.297514i | \(-0.903842\pi\) |
0.735014 | + | 0.678052i | \(0.237176\pi\) | |||||||
\(48\) | −5.18140 | − | 10.8237i | −0.107946 | − | 0.225494i | ||||
\(49\) | −39.8290 | − | 68.9858i | −0.812836 | − | 1.40787i | ||||
\(50\) | 77.3631 | − | 44.6656i | 1.54726 | − | 0.893312i | ||||
\(51\) | −35.8221 | + | 52.2793i | −0.702395 | + | 1.02508i | ||||
\(52\) | 31.3274 | + | 18.0869i | 0.602451 | + | 0.347825i | ||||
\(53\) | 7.82643i | 0.147669i | 0.997271 | + | 0.0738343i | \(0.0235236\pi\) | ||||
−0.997271 | + | 0.0738343i | \(0.976476\pi\) | |||||||
\(54\) | −27.8085 | − | 26.1666i | −0.514972 | − | 0.484566i | ||||
\(55\) | 71.7946 | 1.30536 | ||||||||
\(56\) | −27.7839 | − | 16.0411i | −0.496142 | − | 0.286448i | ||||
\(57\) | 47.2206 | + | 31.9252i | 0.828431 | + | 0.560091i | ||||
\(58\) | −10.0930 | − | 17.4816i | −0.174018 | − | 0.301408i | ||||
\(59\) | 66.1193 | − | 38.1740i | 1.12067 | − | 0.647017i | 0.179095 | − | 0.983832i | \(-0.442683\pi\) |
0.941571 | + | 0.336815i | \(0.109350\pi\) | |||||||
\(60\) | −24.3259 | − | 50.8158i | −0.405432 | − | 0.846931i | ||||
\(61\) | −17.7883 | + | 30.8102i | −0.291612 | + | 0.505086i | −0.974191 | − | 0.225725i | \(-0.927525\pi\) |
0.682579 | + | 0.730811i | \(0.260858\pi\) | |||||||
\(62\) | 24.7248 | 0.398788 | ||||||||
\(63\) | −100.873 | − | 15.6851i | −1.60115 | − | 0.248970i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 147.078 | + | 84.9154i | 2.26274 | + | 1.30639i | ||||
\(66\) | 2.49957 | − | 32.3432i | 0.0378723 | − | 0.490048i | ||||
\(67\) | −96.1425 | + | 55.5079i | −1.43496 | + | 0.828476i | −0.997494 | − | 0.0707571i | \(-0.977458\pi\) |
−0.437469 | + | 0.899233i | \(0.644125\pi\) | |||||||
\(68\) | 21.1249 | + | 36.5894i | 0.310660 | + | 0.538079i | ||||
\(69\) | 50.0919 | + | 3.87125i | 0.725969 | + | 0.0561050i | ||||
\(70\) | −130.442 | − | 75.3105i | −1.86345 | − | 1.07586i | ||||
\(71\) | 54.5417i | 0.768192i | 0.923293 | + | 0.384096i | \(0.125487\pi\) | ||||
−0.923293 | + | 0.384096i | \(0.874513\pi\) | |||||||
\(72\) | −23.7393 | + | 9.18955i | −0.329712 | + | 0.127633i | ||||
\(73\) | −117.096 | −1.60405 | −0.802026 | − | 0.597289i | \(-0.796245\pi\) | ||||
−0.802026 | + | 0.597289i | \(0.796245\pi\) | |||||||
\(74\) | −7.53666 | + | 13.0539i | −0.101847 | + | 0.176404i | ||||
\(75\) | −81.8230 | − | 170.925i | −1.09097 | − | 2.27900i | ||||
\(76\) | 32.7899 | − | 19.2048i | 0.431446 | − | 0.252694i | ||||
\(77\) | −43.3638 | − | 75.1084i | −0.563167 | − | 0.975433i | ||||
\(78\) | 43.3746 | − | 63.3016i | 0.556085 | − | 0.811558i | ||||
\(79\) | 14.5702 | + | 8.41210i | 0.184433 | + | 0.106482i | 0.589374 | − | 0.807861i | \(-0.299375\pi\) |
−0.404941 | + | 0.914343i | \(0.632708\pi\) | |||||||
\(80\) | −37.5589 | −0.469486 | ||||||||
\(81\) | −59.8880 | + | 54.5383i | −0.739359 | + | 0.673312i | ||||
\(82\) | −2.53430 | −0.0309062 | ||||||||
\(83\) | −68.7574 | + | 119.091i | −0.828402 | + | 1.43483i | 0.0708894 | + | 0.997484i | \(0.477416\pi\) |
−0.899291 | + | 0.437350i | \(0.855917\pi\) | |||||||
\(84\) | −38.4685 | + | 56.1414i | −0.457958 | + | 0.668350i | ||||
\(85\) | 99.1783 | + | 171.782i | 1.16680 | + | 2.02096i | ||||
\(86\) | −40.9936 | + | 23.6677i | −0.476670 | + | 0.275206i | ||||
\(87\) | −38.6237 | + | 18.4895i | −0.443950 | + | 0.212522i | ||||
\(88\) | −18.7290 | − | 10.8132i | −0.212830 | − | 0.122877i | ||||
\(89\) | 7.70345i | 0.0865556i | 0.999063 | + | 0.0432778i | \(0.0137801\pi\) | ||||
−0.999063 | + | 0.0432778i | \(0.986220\pi\) | |||||||
\(90\) | −111.452 | + | 43.1436i | −1.23836 | + | 0.479373i | ||||
\(91\) | − | 205.155i | − | 2.25445i | ||||||
\(92\) | 16.7471 | − | 29.0068i | 0.182033 | − | 0.315291i | ||||
\(93\) | 4.04139 | − | 52.2934i | 0.0434558 | − | 0.562295i | ||||
\(94\) | 25.2936 | − | 14.6033i | 0.269081 | − | 0.155354i | ||||
\(95\) | 153.944 | − | 90.1635i | 1.62046 | − | 0.949090i | ||||
\(96\) | −1.30764 | + | 16.9201i | −0.0136212 | + | 0.176251i | ||||
\(97\) | 101.184 | + | 58.4186i | 1.04313 | + | 0.602253i | 0.920719 | − | 0.390226i | \(-0.127603\pi\) |
0.122414 | + | 0.992479i | \(0.460936\pi\) | |||||||
\(98\) | 112.653i | 1.14952i | ||||||||
\(99\) | −67.9977 | − | 10.5733i | −0.686845 | − | 0.106801i | ||||
\(100\) | −126.333 | −1.26333 | ||||||||
\(101\) | 2.91211 | − | 5.04392i | 0.0288328 | − | 0.0499398i | −0.851249 | − | 0.524762i | \(-0.824154\pi\) |
0.880082 | + | 0.474822i | \(0.157488\pi\) | |||||||
\(102\) | 80.8400 | − | 38.6987i | 0.792549 | − | 0.379399i | ||||
\(103\) | 148.585 | − | 85.7857i | 1.44257 | − | 0.832871i | 0.444554 | − | 0.895752i | \(-0.353362\pi\) |
0.998021 | + | 0.0628810i | \(0.0200289\pi\) | |||||||
\(104\) | −25.5787 | − | 44.3037i | −0.245949 | − | 0.425997i | ||||
\(105\) | −180.604 | + | 263.576i | −1.72004 | + | 2.51025i | ||||
\(106\) | 5.53412 | − | 9.58538i | 0.0522087 | − | 0.0904281i | ||||
\(107\) | 123.595i | 1.15509i | 0.816358 | + | 0.577546i | \(0.195989\pi\) | ||||
−0.816358 | + | 0.577546i | \(0.804011\pi\) | |||||||
\(108\) | 15.5557 | + | 51.7109i | 0.144035 | + | 0.478805i | ||||
\(109\) | − | 59.7721i | − | 0.548368i | −0.961677 | − | 0.274184i | \(-0.911592\pi\) | ||
0.961677 | − | 0.274184i | \(-0.0884077\pi\) | |||||||
\(110\) | −87.9300 | − | 50.7664i | −0.799364 | − | 0.461513i | ||||
\(111\) | 26.3772 | + | 18.0738i | 0.237633 | + | 0.162827i | ||||
\(112\) | 22.6855 | + | 39.2924i | 0.202549 | + | 0.350825i | ||||
\(113\) | −127.793 | + | 73.7816i | −1.13092 | + | 0.652934i | −0.944165 | − | 0.329473i | \(-0.893129\pi\) |
−0.186750 | + | 0.982407i | \(0.559796\pi\) | |||||||
\(114\) | −35.2587 | − | 72.4902i | −0.309286 | − | 0.635879i | ||||
\(115\) | 78.6251 | − | 136.183i | 0.683697 | − | 1.18420i | ||||
\(116\) | 28.5474i | 0.246098i | ||||||||
\(117\) | −126.794 | − | 102.085i | −1.08371 | − | 0.872520i | ||||
\(118\) | −107.972 | −0.915020 | ||||||||
\(119\) | 119.807 | − | 207.512i | 1.00678 | − | 1.74380i | ||||
\(120\) | −6.13916 | + | 79.4375i | −0.0511597 | + | 0.661979i | ||||
\(121\) | 31.2687 | + | 54.1589i | 0.258419 | + | 0.447594i | ||||
\(122\) | 43.5723 | − | 25.1565i | 0.357150 | − | 0.206200i | ||||
\(123\) | −0.414243 | + | 5.36009i | −0.00336783 | + | 0.0435780i | ||||
\(124\) | −30.2816 | − | 17.4831i | −0.244207 | − | 0.140993i | ||||
\(125\) | −358.374 | −2.86699 | ||||||||
\(126\) | 112.452 | + | 90.5379i | 0.892477 | + | 0.718555i | ||||
\(127\) | − | 2.73827i | − | 0.0215612i | −0.999942 | − | 0.0107806i | \(-0.996568\pi\) | ||
0.999942 | − | 0.0107806i | \(-0.00343164\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 43.3569 | + | 90.5707i | 0.336100 | + | 0.702098i | ||||
\(130\) | −120.089 | − | 207.999i | −0.923758 | − | 1.60000i | ||||
\(131\) | −63.4682 | − | 109.930i | −0.484490 | − | 0.839161i | 0.515351 | − | 0.856979i | \(-0.327661\pi\) |
−0.999841 | + | 0.0178179i | \(0.994328\pi\) | |||||||
\(132\) | −25.9314 | + | 37.8447i | −0.196450 | + | 0.286702i | ||||
\(133\) | −187.307 | − | 106.591i | −1.40832 | − | 0.801434i | ||||
\(134\) | 157.000 | 1.17164 | ||||||||
\(135\) | 73.0319 | + | 242.775i | 0.540977 | + | 1.79834i | ||||
\(136\) | − | 59.7502i | − | 0.439340i | ||||||
\(137\) | 24.8292 | − | 43.0054i | 0.181235 | − | 0.313908i | −0.761066 | − | 0.648674i | \(-0.775324\pi\) |
0.942301 | + | 0.334766i | \(0.108657\pi\) | |||||||
\(138\) | −58.6124 | − | 40.1616i | −0.424727 | − | 0.291026i | ||||
\(139\) | −88.0079 | − | 152.434i | −0.633151 | − | 1.09665i | −0.986904 | − | 0.161310i | \(-0.948428\pi\) |
0.353753 | − | 0.935339i | \(-0.384905\pi\) | |||||||
\(140\) | 106.505 | + | 184.472i | 0.760751 | + | 1.31766i | ||||
\(141\) | −26.7518 | − | 55.8833i | −0.189729 | − | 0.396336i | ||||
\(142\) | 38.5668 | − | 66.7996i | 0.271597 | − | 0.470420i | ||||
\(143\) | − | 138.294i | − | 0.967091i | ||||||
\(144\) | 35.5725 | + | 5.53133i | 0.247031 | + | 0.0384120i | ||||
\(145\) | 134.026i | 0.924317i | ||||||||
\(146\) | 143.413 | + | 82.7993i | 0.982278 | + | 0.567118i | ||||
\(147\) | 238.263 | + | 18.4137i | 1.62084 | + | 0.125263i | ||||
\(148\) | 18.4610 | − | 10.6584i | 0.124736 | − | 0.0720165i | ||||
\(149\) | 28.8271 | + | 49.9300i | 0.193471 | + | 0.335101i | 0.946398 | − | 0.323003i | \(-0.104692\pi\) |
−0.752928 | + | 0.658103i | \(0.771359\pi\) | |||||||
\(150\) | −20.6498 | + | 267.197i | −0.137665 | + | 1.78131i | ||||
\(151\) | −28.5137 | − | 16.4624i | −0.188832 | − | 0.109022i | 0.402603 | − | 0.915375i | \(-0.368105\pi\) |
−0.591436 | + | 0.806352i | \(0.701439\pi\) | |||||||
\(152\) | −53.7391 | + | 0.334960i | −0.353547 | + | 0.00220368i | ||||
\(153\) | −68.6347 | − | 177.303i | −0.448593 | − | 1.15884i | ||||
\(154\) | 122.651i | 0.796438i | ||||||||
\(155\) | −142.168 | − | 82.0807i | −0.917212 | − | 0.529553i | ||||
\(156\) | −97.8838 | + | 46.8577i | −0.627461 | + | 0.300370i | ||||
\(157\) | 85.3745 | + | 147.873i | 0.543786 | + | 0.941866i | 0.998682 | + | 0.0513209i | \(0.0163431\pi\) |
−0.454896 | + | 0.890545i | \(0.650324\pi\) | |||||||
\(158\) | −11.8965 | − | 20.6054i | −0.0752944 | − | 0.130414i | ||||
\(159\) | −19.3686 | − | 13.2715i | −0.121815 | − | 0.0834687i | ||||
\(160\) | 46.0000 | + | 26.5581i | 0.287500 | + | 0.165988i | ||||
\(161\) | −189.958 | −1.17986 | ||||||||
\(162\) | 111.912 | − | 24.4482i | 0.690815 | − | 0.150915i | ||||
\(163\) | 59.4491 | 0.364718 | 0.182359 | − | 0.983232i | \(-0.441627\pi\) | ||||
0.182359 | + | 0.983232i | \(0.441627\pi\) | |||||||
\(164\) | 3.10388 | + | 1.79202i | 0.0189261 | + | 0.0109270i | ||||
\(165\) | −121.744 | + | 177.675i | −0.737844 | + | 1.07682i | ||||
\(166\) | 168.420 | − | 97.2376i | 1.01458 | − | 0.585769i | ||||
\(167\) | 29.9680 | − | 17.3020i | 0.179449 | − | 0.103605i | −0.407585 | − | 0.913167i | \(-0.633629\pi\) |
0.587034 | + | 0.809562i | \(0.300296\pi\) | |||||||
\(168\) | 86.8121 | − | 41.5576i | 0.516739 | − | 0.247367i | ||||
\(169\) | 79.0680 | − | 136.950i | 0.467858 | − | 0.810354i | ||||
\(170\) | − | 280.519i | − | 1.65011i | ||||||
\(171\) | −159.081 | + | 62.7237i | −0.930298 | + | 0.366805i | ||||
\(172\) | 66.9423 | 0.389200 | ||||||||
\(173\) | −161.923 | − | 93.4862i | −0.935971 | − | 0.540383i | −0.0472756 | − | 0.998882i | \(-0.515054\pi\) |
−0.888695 | + | 0.458499i | \(0.848387\pi\) | |||||||
\(174\) | 60.3782 | + | 4.66620i | 0.347001 | + | 0.0268173i | ||||
\(175\) | 358.242 | + | 620.493i | 2.04710 | + | 3.54568i | ||||
\(176\) | 15.2922 | + | 26.4868i | 0.0868874 | + | 0.150493i | ||||
\(177\) | −17.6486 | + | 228.363i | −0.0997094 | + | 1.29019i | ||||
\(178\) | 5.44716 | − | 9.43476i | 0.0306020 | − | 0.0530043i | ||||
\(179\) | 169.146i | 0.944948i | 0.881345 | + | 0.472474i | \(0.156639\pi\) | ||||
−0.881345 | + | 0.472474i | \(0.843361\pi\) | |||||||
\(180\) | 167.008 | + | 25.9688i | 0.927822 | + | 0.144271i | ||||
\(181\) | − | 275.892i | − | 1.52426i | −0.647421 | − | 0.762132i | \(-0.724153\pi\) | ||
0.647421 | − | 0.762132i | \(-0.275847\pi\) | |||||||
\(182\) | −145.067 | + | 251.263i | −0.797069 | + | 1.38056i | ||||
\(183\) | −46.0842 | − | 96.2679i | −0.251826 | − | 0.526054i | ||||
\(184\) | −41.0218 | + | 23.6839i | −0.222945 | + | 0.128717i | ||||
\(185\) | 86.6716 | − | 50.0398i | 0.468495 | − | 0.270486i | ||||
\(186\) | −41.9267 | + | 61.1884i | −0.225412 | + | 0.328970i | ||||
\(187\) | 80.7614 | − | 139.883i | 0.431879 | − | 0.748037i | ||||
\(188\) | −41.3043 | −0.219704 | ||||||||
\(189\) | 209.870 | − | 223.039i | 1.11042 | − | 1.18010i | ||||
\(190\) | −252.297 | + | 1.57259i | −1.32788 | + | 0.00827678i | ||||
\(191\) | 109.421 | − | 189.522i | 0.572883 | − | 0.992263i | −0.423385 | − | 0.905950i | \(-0.639158\pi\) |
0.996268 | − | 0.0863132i | \(-0.0275086\pi\) | |||||||
\(192\) | 13.5658 | − | 19.7982i | 0.0706554 | − | 0.103116i | ||||
\(193\) | −319.126 | + | 184.247i | −1.65350 | + | 0.954649i | −0.677884 | + | 0.735169i | \(0.737103\pi\) |
−0.975617 | + | 0.219480i | \(0.929564\pi\) | |||||||
\(194\) | −82.6163 | − | 143.096i | −0.425857 | − | 0.737607i | ||||
\(195\) | −459.551 | + | 219.990i | −2.35667 | + | 1.12816i | ||||
\(196\) | 79.6579 | − | 137.972i | 0.406418 | − | 0.703937i | ||||
\(197\) | 246.260 | 1.25005 | 0.625025 | − | 0.780605i | \(-0.285089\pi\) | ||||
0.625025 | + | 0.780605i | \(0.285089\pi\) | |||||||
\(198\) | 75.8034 | + | 61.0312i | 0.382845 | + | 0.308238i | ||||
\(199\) | −9.55232 | −0.0480016 | −0.0240008 | − | 0.999712i | \(-0.507640\pi\) | ||||
−0.0240008 | + | 0.999712i | \(0.507640\pi\) | |||||||
\(200\) | 154.726 | + | 89.3312i | 0.773631 | + | 0.446656i | ||||
\(201\) | 25.6624 | − | 332.057i | 0.127673 | − | 1.65203i | ||||
\(202\) | −7.13318 | + | 4.11835i | −0.0353128 | + | 0.0203879i | ||||
\(203\) | 140.212 | − | 80.9515i | 0.690700 | − | 0.398776i | ||||
\(204\) | −126.373 | − | 9.76644i | −0.619473 | − | 0.0478747i | ||||
\(205\) | 14.5723 | + | 8.41329i | 0.0710842 | + | 0.0410405i | ||||
\(206\) | −242.639 | −1.17786 | ||||||||
\(207\) | −94.5228 | + | 117.401i | −0.456632 | + | 0.567156i | ||||
\(208\) | 72.3476i | 0.347825i | ||||||||
\(209\) | −126.263 | − | 71.8522i | −0.604128 | − | 0.343791i | ||||
\(210\) | 407.570 | − | 195.107i | 1.94081 | − | 0.929081i | ||||
\(211\) | 120.321 | − | 69.4672i | 0.570241 | − | 0.329229i | −0.187005 | − | 0.982359i | \(-0.559878\pi\) |
0.757245 | + | 0.653130i | \(0.226545\pi\) | |||||||
\(212\) | −13.5558 | + | 7.82643i | −0.0639423 | + | 0.0369171i | ||||
\(213\) | −134.978 | − | 92.4879i | −0.633700 | − | 0.434216i | ||||
\(214\) | 87.3947 | − | 151.372i | 0.408386 | − | 0.707346i | ||||
\(215\) | 314.285 | 1.46179 | ||||||||
\(216\) | 17.5133 | − | 74.3322i | 0.0810803 | − | 0.344131i | ||||
\(217\) | 198.306i | 0.913855i | ||||||||
\(218\) | −42.2652 | + | 73.2055i | −0.193877 | + | 0.335805i | ||||
\(219\) | 198.563 | − | 289.786i | 0.906680 | − | 1.32322i | ||||
\(220\) | 71.7946 | + | 124.352i | 0.326339 | + | 0.565236i | ||||
\(221\) | 330.894 | − | 191.042i | 1.49726 | − | 0.864443i | ||||
\(222\) | −19.5252 | − | 40.7874i | −0.0879514 | − | 0.183727i | ||||
\(223\) | −75.1582 | − | 43.3926i | −0.337032 | − | 0.194586i | 0.321927 | − | 0.946765i | \(-0.395670\pi\) |
−0.658959 | + | 0.752179i | \(0.729003\pi\) | |||||||
\(224\) | − | 64.1643i | − | 0.286448i | ||||||
\(225\) | 561.750 | + | 87.3490i | 2.49667 | + | 0.388218i | ||||
\(226\) | 208.686 | 0.923388 | ||||||||
\(227\) | −76.1650 | − | 43.9739i | −0.335529 | − | 0.193717i | 0.322764 | − | 0.946479i | \(-0.395388\pi\) |
−0.658293 | + | 0.752762i | \(0.728721\pi\) | |||||||
\(228\) | −8.07545 | + | 113.714i | −0.0354186 | + | 0.498744i | ||||
\(229\) | 100.571 | + | 174.195i | 0.439177 | + | 0.760676i | 0.997626 | − | 0.0688623i | \(-0.0219369\pi\) |
−0.558450 | + | 0.829538i | \(0.688604\pi\) | |||||||
\(230\) | −192.591 | + | 111.193i | −0.837354 | + | 0.483447i | ||||
\(231\) | 259.409 | + | 20.0479i | 1.12298 | + | 0.0867875i | ||||
\(232\) | 20.1861 | − | 34.9633i | 0.0870089 | − | 0.150704i | ||||
\(233\) | 123.948 | 0.531966 | 0.265983 | − | 0.963978i | \(-0.414303\pi\) | ||||
0.265983 | + | 0.963978i | \(0.414303\pi\) | |||||||
\(234\) | 83.1052 | + | 214.685i | 0.355151 | + | 0.917456i | ||||
\(235\) | −193.918 | −0.825182 | ||||||||
\(236\) | 132.239 | + | 76.3480i | 0.560333 | + | 0.323508i | ||||
\(237\) | −45.5252 | + | 21.7932i | −0.192089 | + | 0.0919546i | ||||
\(238\) | −293.466 | + | 169.433i | −1.23305 | + | 0.711903i | ||||
\(239\) | −20.1831 | − | 34.9582i | −0.0844482 | − | 0.146269i | 0.820708 | − | 0.571348i | \(-0.193579\pi\) |
−0.905156 | + | 0.425080i | \(0.860246\pi\) | |||||||
\(240\) | 63.6897 | − | 92.9496i | 0.265374 | − | 0.387290i | ||||
\(241\) | 145.375 | + | 83.9323i | 0.603216 | + | 0.348267i | 0.770306 | − | 0.637675i | \(-0.220104\pi\) |
−0.167090 | + | 0.985942i | \(0.553437\pi\) | |||||||
\(242\) | − | 88.4411i | − | 0.365459i | ||||||
\(243\) | −33.4158 | − | 240.691i | −0.137514 | − | 0.990500i | ||||
\(244\) | −71.1532 | −0.291612 | ||||||||
\(245\) | 373.983 | − | 647.757i | 1.52646 | − | 2.64391i | ||||
\(246\) | 4.29750 | − | 6.27183i | 0.0174695 | − | 0.0254952i | ||||
\(247\) | −173.677 | − | 296.534i | −0.703147 | − | 1.20054i | ||||
\(248\) | 24.7248 | + | 42.8247i | 0.0996970 | + | 0.172680i | ||||
\(249\) | −178.130 | − | 372.105i | −0.715381 | − | 1.49440i | ||||
\(250\) | 438.917 | + | 253.409i | 1.75567 | + | 1.01364i | ||||
\(251\) | −81.5710 | −0.324984 | −0.162492 | − | 0.986710i | \(-0.551953\pi\) | ||||
−0.162492 | + | 0.986710i | \(0.551953\pi\) | |||||||
\(252\) | −73.7051 | − | 190.401i | −0.292481 | − | 0.755561i | ||||
\(253\) | −128.050 | −0.506125 | ||||||||
\(254\) | −1.93625 | + | 3.35369i | −0.00762304 | + | 0.0132035i | ||||
\(255\) | −593.301 | − | 45.8520i | −2.32667 | − | 0.179812i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −280.685 | + | 162.054i | −1.09216 | + | 0.630559i | −0.934151 | − | 0.356879i | \(-0.883841\pi\) |
−0.158009 | + | 0.987438i | \(0.550507\pi\) | |||||||
\(258\) | 10.9420 | − | 141.584i | 0.0424109 | − | 0.548775i | ||||
\(259\) | −104.699 | − | 60.4480i | −0.404243 | − | 0.233390i | ||||
\(260\) | 339.662i | 1.30639i | ||||||||
\(261\) | 19.7382 | − | 126.938i | 0.0756251 | − | 0.486352i | ||||
\(262\) | 179.515i | 0.685172i | ||||||||
\(263\) | −145.409 | + | 251.855i | −0.552885 | + | 0.957625i | 0.445179 | + | 0.895441i | \(0.353140\pi\) |
−0.998065 | + | 0.0621839i | \(0.980193\pi\) | |||||||
\(264\) | 58.5196 | − | 28.0138i | 0.221665 | − | 0.106113i | ||||
\(265\) | −63.6424 | + | 36.7440i | −0.240160 | + | 0.138657i | ||||
\(266\) | 154.032 | + | 262.993i | 0.579069 | + | 0.988694i | ||||
\(267\) | −19.0643 | − | 13.0630i | −0.0714018 | − | 0.0489250i | ||||
\(268\) | −192.285 | − | 111.016i | −0.717481 | − | 0.414238i | ||||
\(269\) | 412.277i | 1.53263i | 0.642465 | + | 0.766315i | \(0.277912\pi\) | ||||
−0.642465 | + | 0.766315i | \(0.722088\pi\) | |||||||
\(270\) | 82.2226 | − | 348.979i | 0.304528 | − | 1.29252i | ||||
\(271\) | 80.0609 | 0.295428 | 0.147714 | − | 0.989030i | \(-0.452809\pi\) | ||||
0.147714 | + | 0.989030i | \(0.452809\pi\) | |||||||
\(272\) | −42.2498 | + | 73.1788i | −0.155330 | + | 0.269040i | ||||
\(273\) | 507.712 | + | 347.888i | 1.85975 | + | 1.27431i | ||||
\(274\) | −60.8189 | + | 35.1138i | −0.221967 | + | 0.128153i | ||||
\(275\) | 241.489 | + | 418.271i | 0.878142 | + | 1.52099i | ||||
\(276\) | 43.3867 | + | 90.6329i | 0.157198 | + | 0.328380i | ||||
\(277\) | −29.3529 | + | 50.8407i | −0.105967 | + | 0.183540i | −0.914133 | − | 0.405415i | \(-0.867127\pi\) |
0.808166 | + | 0.588955i | \(0.200461\pi\) | |||||||
\(278\) | 248.924i | 0.895410i | ||||||||
\(279\) | 122.561 | + | 98.6770i | 0.439287 | + | 0.353681i | ||||
\(280\) | − | 301.242i | − | 1.07586i | ||||||
\(281\) | 438.013 | + | 252.887i | 1.55877 | + | 0.899953i | 0.997376 | + | 0.0724018i | \(0.0230664\pi\) |
0.561390 | + | 0.827552i | \(0.310267\pi\) | |||||||
\(282\) | −6.75138 | + | 87.3592i | −0.0239410 | + | 0.309784i | ||||
\(283\) | 208.876 | + | 361.784i | 0.738078 | + | 1.27839i | 0.953359 | + | 0.301837i | \(0.0975999\pi\) |
−0.215281 | + | 0.976552i | \(0.569067\pi\) | |||||||
\(284\) | −94.4689 | + | 54.5417i | −0.332637 | + | 0.192048i | ||||
\(285\) | −37.9131 | + | 533.869i | −0.133028 | + | 1.87322i | ||||
\(286\) | −97.7887 | + | 169.375i | −0.341918 | + | 0.592220i | ||||
\(287\) | − | 20.3265i | − | 0.0708240i | ||||||
\(288\) | −39.6560 | − | 31.9280i | −0.137695 | − | 0.110861i | ||||
\(289\) | 157.261 | 0.544156 | ||||||||
\(290\) | 94.7707 | − | 164.148i | 0.326795 | − | 0.566026i | ||||
\(291\) | −316.153 | + | 151.345i | −1.08644 | + | 0.520086i | ||||
\(292\) | −117.096 | − | 202.816i | −0.401013 | − | 0.694575i | ||||
\(293\) | −281.151 | + | 162.323i | −0.959559 | + | 0.554002i | −0.896037 | − | 0.443979i | \(-0.853567\pi\) |
−0.0635219 | + | 0.997980i | \(0.520233\pi\) | |||||||
\(294\) | −278.791 | − | 191.030i | −0.948270 | − | 0.649761i | ||||
\(295\) | 620.841 | + | 358.443i | 2.10455 | + | 1.21506i | ||||
\(296\) | −30.1466 | −0.101847 | ||||||||
\(297\) | 141.472 | − | 150.349i | 0.476337 | − | 0.506227i | ||||
\(298\) | − | 81.5354i | − | 0.273609i | ||||||
\(299\) | −262.321 | − | 151.451i | −0.877329 | − | 0.506526i | ||||
\(300\) | 214.227 | − | 312.646i | 0.714091 | − | 1.04215i | ||||
\(301\) | −189.827 | − | 328.791i | −0.630656 | − | 1.09233i | ||||
\(302\) | 23.2813 | + | 40.3245i | 0.0770905 | + | 0.133525i | ||||
\(303\) | 7.54441 | + | 15.7599i | 0.0248990 | + | 0.0520130i | ||||
\(304\) | 66.0535 | + | 37.5890i | 0.217281 | + | 0.123648i | ||||
\(305\) | −334.054 | −1.09526 | ||||||||
\(306\) | −41.3123 | + | 265.683i | −0.135008 | + | 0.868246i | ||||
\(307\) | 50.8776i | 0.165725i | 0.996561 | + | 0.0828625i | \(0.0264062\pi\) | ||||
−0.996561 | + | 0.0828625i | \(0.973594\pi\) | |||||||
\(308\) | 86.7277 | − | 150.217i | 0.281583 | − | 0.487717i | ||||
\(309\) | −39.6604 | + | 513.184i | −0.128351 | + | 1.66079i | ||||
\(310\) | 116.080 | + | 201.056i | 0.374450 | + | 0.648567i | ||||
\(311\) | 81.1604 | + | 140.574i | 0.260966 | + | 0.452006i | 0.966499 | − | 0.256671i | \(-0.0826256\pi\) |
−0.705533 | + | 0.708677i | \(0.749292\pi\) | |||||||
\(312\) | 153.016 | + | 11.8255i | 0.490436 | + | 0.0379024i | ||||
\(313\) | 11.8965 | − | 20.6054i | 0.0380081 | − | 0.0658320i | −0.846396 | − | 0.532555i | \(-0.821232\pi\) |
0.884404 | + | 0.466723i | \(0.154565\pi\) | |||||||
\(314\) | − | 241.475i | − | 0.769030i | ||||||
\(315\) | −346.035 | − | 893.908i | −1.09852 | − | 2.83780i | ||||
\(316\) | 33.6484i | 0.106482i | ||||||||
\(317\) | −395.572 | − | 228.384i | −1.24786 | − | 0.720453i | −0.277179 | − | 0.960818i | \(-0.589400\pi\) |
−0.970683 | + | 0.240365i | \(0.922733\pi\) | |||||||
\(318\) | 14.3373 | + | 29.9499i | 0.0450857 | + | 0.0941821i | ||||
\(319\) | 94.5163 | − | 54.5690i | 0.296289 | − | 0.171063i | ||||
\(320\) | −37.5589 | − | 65.0538i | −0.117371 | − | 0.203293i | ||||
\(321\) | −305.869 | − | 209.583i | −0.952863 | − | 0.652908i | ||||
\(322\) | 232.650 | + | 134.321i | 0.722515 | + | 0.417144i | ||||
\(323\) | −2.50174 | − | 401.365i | −0.00774532 | − | 1.24262i | ||||
\(324\) | −154.351 | − | 49.1909i | −0.476392 | − | 0.151824i | ||||
\(325\) | 1142.49i | 3.51535i | ||||||||
\(326\) | −72.8099 | − | 42.0368i | −0.223343 | − | 0.128947i | ||||
\(327\) | 147.922 | + | 101.357i | 0.452362 | + | 0.309961i | ||||
\(328\) | −2.53430 | − | 4.38954i | −0.00772654 | − | 0.0133828i | ||||
\(329\) | 117.126 | + | 202.868i | 0.356006 | + | 0.616621i | ||||
\(330\) | 274.741 | − | 131.521i | 0.832548 | − | 0.398547i | ||||
\(331\) | −398.307 | − | 229.963i | −1.20334 | − | 0.694752i | −0.242048 | − | 0.970264i | \(-0.577819\pi\) |
−0.961297 | + | 0.275513i | \(0.911152\pi\) | |||||||
\(332\) | −275.029 | −0.828402 | ||||||||
\(333\) | −89.4573 | + | 34.6292i | −0.268641 | + | 0.103992i | ||||
\(334\) | −48.9376 | −0.146520 | ||||||||
\(335\) | −902.751 | − | 521.203i | −2.69478 | − | 1.55583i | ||||
\(336\) | −135.708 | − | 10.4879i | −0.403894 | − | 0.0312141i | ||||
\(337\) | 111.183 | − | 64.1915i | 0.329920 | − | 0.190479i | −0.325886 | − | 0.945409i | \(-0.605662\pi\) |
0.655805 | + | 0.754930i | \(0.272329\pi\) | |||||||
\(338\) | −193.676 | + | 111.819i | −0.573007 | + | 0.330825i | ||||
\(339\) | 34.1106 | − | 441.373i | 0.100621 | − | 1.30199i | ||||
\(340\) | −198.357 | + | 343.564i | −0.583402 | + | 1.01048i | ||||
\(341\) | 133.677i | 0.392016i | ||||||||
\(342\) | 239.186 | + | 35.6667i | 0.699374 | + | 0.104289i | ||||
\(343\) | −347.745 | −1.01383 | ||||||||
\(344\) | −81.9873 | − | 47.3354i | −0.238335 | − | 0.137603i | ||||
\(345\) | 203.694 | + | 425.508i | 0.590418 | + | 1.23336i | ||||
\(346\) | 132.209 | + | 228.994i | 0.382108 | + | 0.661831i | ||||
\(347\) | −128.415 | − | 222.420i | −0.370071 | − | 0.640981i | 0.619505 | − | 0.784992i | \(-0.287333\pi\) |
−0.989576 | + | 0.144011i | \(0.954000\pi\) | |||||||
\(348\) | −70.6483 | − | 48.4087i | −0.203012 | − | 0.139105i | ||||
\(349\) | 229.402 | − | 397.336i | 0.657312 | − | 1.13850i | −0.323997 | − | 0.946058i | \(-0.605027\pi\) |
0.981309 | − | 0.192439i | \(-0.0616399\pi\) | |||||||
\(350\) | − | 1013.26i | − | 2.89503i | ||||||
\(351\) | 467.645 | − | 140.678i | 1.33232 | − | 0.400791i | ||||
\(352\) | − | 43.2528i | − | 0.122877i | ||||||
\(353\) | −226.280 | + | 391.928i | −0.641020 | + | 1.11028i | 0.344186 | + | 0.938901i | \(0.388155\pi\) |
−0.985206 | + | 0.171377i | \(0.945178\pi\) | |||||||
\(354\) | 183.092 | − | 267.207i | 0.517209 | − | 0.754822i | ||||
\(355\) | −443.518 | + | 256.065i | −1.24935 | + | 0.721310i | ||||
\(356\) | −13.3428 | + | 7.70345i | −0.0374797 | + | 0.0216389i | ||||
\(357\) | 310.384 | + | 648.380i | 0.869424 | + | 1.81619i | ||||
\(358\) | 119.604 | − | 207.160i | 0.334090 | − | 0.578660i | ||||
\(359\) | 459.016 | 1.27860 | 0.639299 | − | 0.768959i | \(-0.279225\pi\) | ||||
0.639299 | + | 0.768959i | \(0.279225\pi\) | |||||||
\(360\) | −186.179 | − | 149.898i | −0.517165 | − | 0.416382i | ||||
\(361\) | −360.972 | + | 4.50011i | −0.999922 | + | 0.0124657i | ||||
\(362\) | −195.085 | + | 337.897i | −0.538909 | + | 0.933418i | ||||
\(363\) | −187.054 | − | 14.4561i | −0.515301 | − | 0.0398240i | ||||
\(364\) | 355.339 | − | 205.155i | 0.976206 | − | 0.563613i | ||||
\(365\) | −549.748 | − | 952.192i | −1.50616 | − | 2.60874i | ||||
\(366\) | −11.6303 | + | 150.490i | −0.0317768 | + | 0.411175i | ||||
\(367\) | −349.240 | + | 604.902i | −0.951608 | + | 1.64823i | −0.209662 | + | 0.977774i | \(0.567236\pi\) |
−0.741946 | + | 0.670460i | \(0.766097\pi\) | |||||||
\(368\) | 66.9883 | 0.182033 | ||||||||
\(369\) | −12.5626 | − | 10.1144i | −0.0340449 | − | 0.0274104i | ||||
\(370\) | −141.534 | −0.382524 | ||||||||
\(371\) | 76.8799 | + | 44.3866i | 0.207223 | + | 0.119640i | ||||
\(372\) | 94.6162 | − | 45.2935i | 0.254345 | − | 0.121757i | ||||
\(373\) | 461.435 | − | 266.409i | 1.23709 | − | 0.714234i | 0.268592 | − | 0.963254i | \(-0.413442\pi\) |
0.968498 | + | 0.249020i | \(0.0801083\pi\) | |||||||
\(374\) | −197.824 | + | 114.214i | −0.528942 | + | 0.305385i | ||||
\(375\) | 607.706 | − | 886.895i | 1.62055 | − | 2.36505i | ||||
\(376\) | 50.5873 | + | 29.2066i | 0.134541 | + | 0.0776770i | ||||
\(377\) | 258.167 | 0.684793 | ||||||||
\(378\) | −414.749 | + | 124.765i | −1.09722 | + | 0.330067i | ||||
\(379\) | − | 182.927i | − | 0.482657i | −0.970443 | − | 0.241329i | \(-0.922417\pi\) | ||
0.970443 | − | 0.241329i | \(-0.0775832\pi\) | |||||||
\(380\) | 310.112 | + | 176.475i | 0.816083 | + | 0.464408i | ||||
\(381\) | 6.77661 | + | 4.64338i | 0.0177864 | + | 0.0121873i | ||||
\(382\) | −268.025 | + | 154.744i | −0.701636 | + | 0.405090i | ||||
\(383\) | −376.937 | + | 217.625i | −0.984170 | + | 0.568211i | −0.903527 | − | 0.428532i | \(-0.859031\pi\) |
−0.0806435 | + | 0.996743i | \(0.525698\pi\) | |||||||
\(384\) | −30.6141 | + | 14.6552i | −0.0797243 | + | 0.0381646i | ||||
\(385\) | 407.174 | − | 705.246i | 1.05759 | − | 1.83181i | ||||
\(386\) | 521.130 | 1.35008 | ||||||||
\(387\) | −297.663 | − | 46.2850i | −0.769156 | − | 0.119600i | ||||
\(388\) | 233.674i | 0.602253i | ||||||||
\(389\) | −158.195 | + | 274.002i | −0.406672 | + | 0.704376i | −0.994514 | − | 0.104599i | \(-0.966644\pi\) |
0.587843 | + | 0.808975i | \(0.299977\pi\) | |||||||
\(390\) | 718.389 | + | 55.5192i | 1.84202 | + | 0.142357i | ||||
\(391\) | −176.890 | − | 306.383i | −0.452404 | − | 0.783587i | ||||
\(392\) | −195.121 | + | 112.653i | −0.497758 | + | 0.287381i | ||||
\(393\) | 379.677 | + | 29.3425i | 0.966099 | + | 0.0746630i | ||||
\(394\) | −301.606 | − | 174.132i | −0.765496 | − | 0.441960i | ||||
\(395\) | 157.974i | 0.399935i | ||||||||
\(396\) | −49.6842 | − | 128.349i | −0.125465 | − | 0.324113i | ||||
\(397\) | 555.614 | 1.39953 | 0.699766 | − | 0.714372i | \(-0.253288\pi\) | ||||
0.699766 | + | 0.714372i | \(0.253288\pi\) | |||||||
\(398\) | 11.6992 | + | 6.75451i | 0.0293949 | + | 0.0169711i | ||||
\(399\) | 581.410 | − | 282.793i | 1.45717 | − | 0.708755i | ||||
\(400\) | −126.333 | − | 218.816i | −0.315834 | − | 0.547040i | ||||
\(401\) | −237.374 | + | 137.048i | −0.591954 | + | 0.341765i | −0.765870 | − | 0.642996i | \(-0.777691\pi\) |
0.173916 | + | 0.984761i | \(0.444358\pi\) | |||||||
\(402\) | −266.230 | + | 388.539i | −0.662263 | + | 0.966516i | ||||
\(403\) | −158.108 | + | 273.850i | −0.392327 | + | 0.679530i | ||||
\(404\) | 11.6484 | 0.0288328 | ||||||||
\(405\) | −724.656 | − | 230.944i | −1.78927 | − | 0.570232i | ||||
\(406\) | −228.965 | −0.563954 | ||||||||
\(407\) | −70.5771 | − | 40.7477i | −0.173408 | − | 0.100117i | ||||
\(408\) | 147.868 | + | 101.320i | 0.362422 | + | 0.248334i | ||||
\(409\) | 638.552 | − | 368.668i | 1.56125 | − | 0.901389i | 0.564121 | − | 0.825692i | \(-0.309215\pi\) |
0.997131 | − | 0.0756974i | \(-0.0241183\pi\) | |||||||
\(410\) | −11.8982 | − | 20.6083i | −0.0290200 | − | 0.0502641i | ||||
\(411\) | 64.3250 | + | 134.372i | 0.156509 | + | 0.326940i | ||||
\(412\) | 297.170 | + | 171.571i | 0.721287 | + | 0.416436i | ||||
\(413\) | − | 865.996i | − | 2.09684i | ||||||
\(414\) | 198.782 | − | 76.9490i | 0.480149 | − | 0.185867i | ||||
\(415\) | −1291.22 | −3.11138 | ||||||||
\(416\) | 51.1575 | − | 88.6074i | 0.122975 | − | 0.212998i | ||||
\(417\) | 526.478 | + | 40.6877i | 1.26254 | + | 0.0975725i | ||||
\(418\) | 103.832 | + | 177.282i | 0.248403 | + | 0.424119i | ||||
\(419\) | 38.7513 | + | 67.1193i | 0.0924852 | + | 0.160189i | 0.908556 | − | 0.417762i | \(-0.137186\pi\) |
−0.816071 | + | 0.577952i | \(0.803852\pi\) | |||||||
\(420\) | −637.131 | − | 49.2394i | −1.51698 | − | 0.117237i | ||||
\(421\) | −370.966 | − | 214.177i | −0.881153 | − | 0.508734i | −0.0101148 | − | 0.999949i | \(-0.503220\pi\) |
−0.871038 | + | 0.491215i | \(0.836553\pi\) | |||||||
\(422\) | −196.483 | −0.465600 | ||||||||
\(423\) | 183.662 | + | 28.5585i | 0.434190 | + | 0.0675142i | ||||
\(424\) | 22.1365 | 0.0522087 | ||||||||
\(425\) | −667.195 | + | 1155.62i | −1.56987 | + | 2.71909i | ||||
\(426\) | 99.9150 | + | 208.718i | 0.234542 | + | 0.489949i | ||||
\(427\) | 201.768 | + | 349.473i | 0.472525 | + | 0.818438i | ||||
\(428\) | −214.072 | + | 123.595i | −0.500169 | + | 0.288773i | ||||
\(429\) | 342.246 | + | 234.509i | 0.797777 | + | 0.546642i | ||||
\(430\) | −384.918 | − | 222.233i | −0.895159 | − | 0.516820i | ||||
\(431\) | 725.938i | 1.68431i | 0.539236 | + | 0.842155i | \(0.318713\pi\) | ||||
−0.539236 | + | 0.842155i | \(0.681287\pi\) | |||||||
\(432\) | −74.0102 | + | 78.6542i | −0.171320 | + | 0.182070i | ||||
\(433\) | − | 315.242i | − | 0.728043i | −0.931391 | − | 0.364021i | \(-0.881404\pi\) | ||
0.931391 | − | 0.364021i | \(-0.118596\pi\) | |||||||
\(434\) | 140.224 | − | 242.875i | 0.323096 | − | 0.559619i | ||||
\(435\) | −331.684 | − | 227.272i | −0.762492 | − | 0.522464i | ||||
\(436\) | 103.528 | − | 59.7721i | 0.237450 | − | 0.137092i | ||||
\(437\) | −274.568 | + | 160.812i | −0.628301 | + | 0.367990i | ||||
\(438\) | −448.098 | + | 214.508i | −1.02306 | + | 0.489745i | ||||
\(439\) | −243.573 | − | 140.627i | −0.554837 | − | 0.320335i | 0.196234 | − | 0.980557i | \(-0.437129\pi\) |
−0.751071 | + | 0.660222i | \(0.770462\pi\) | |||||||
\(440\) | − | 203.066i | − | 0.461513i | ||||||
\(441\) | −449.600 | + | 558.423i | −1.01950 | + | 1.26626i | ||||
\(442\) | −540.348 | −1.22251 | ||||||||
\(443\) | 83.3663 | − | 144.395i | 0.188186 | − | 0.325948i | −0.756460 | − | 0.654040i | \(-0.773073\pi\) |
0.944645 | + | 0.328093i | \(0.106406\pi\) | |||||||
\(444\) | −4.92760 | + | 63.7605i | −0.0110982 | + | 0.143605i | ||||
\(445\) | −62.6424 | + | 36.1666i | −0.140769 | + | 0.0812732i | ||||
\(446\) | 61.3664 | + | 106.290i | 0.137593 | + | 0.238318i | ||||
\(447\) | −172.448 | − | 13.3273i | −0.385791 | − | 0.0298150i | ||||
\(448\) | −45.3710 | + | 78.5849i | −0.101275 | + | 0.175413i | ||||
\(449\) | − | 294.066i | − | 0.654936i | −0.944862 | − | 0.327468i | \(-0.893805\pi\) | ||
0.944862 | − | 0.327468i | \(-0.106195\pi\) | |||||||
\(450\) | −626.235 | − | 504.197i | −1.39163 | − | 1.12044i | ||||
\(451\) | − | 13.7020i | − | 0.0303813i | ||||||
\(452\) | −255.587 | − | 147.563i | −0.565458 | − | 0.326467i | ||||
\(453\) | 89.0922 | − | 42.6491i | 0.196672 | − | 0.0941482i | ||||
\(454\) | 62.1884 | + | 107.714i | 0.136979 | + | 0.237254i | ||||
\(455\) | 1668.27 | − | 963.174i | 3.66652 | − | 2.11687i | ||||
\(456\) | 90.2980 | − | 133.560i | 0.198022 | − | 0.292895i | ||||
\(457\) | 334.386 | − | 579.173i | 0.731697 | − | 1.26734i | −0.224460 | − | 0.974483i | \(-0.572062\pi\) |
0.956157 | − | 0.292853i | \(-0.0946047\pi\) | |||||||
\(458\) | − | 284.459i | − | 0.621089i | ||||||
\(459\) | 555.171 | + | 130.803i | 1.20952 | + | 0.284974i | ||||
\(460\) | 314.500 | 0.683697 | ||||||||
\(461\) | 76.9781 | − | 133.330i | 0.166981 | − | 0.289219i | −0.770376 | − | 0.637590i | \(-0.779932\pi\) |
0.937357 | + | 0.348370i | \(0.113265\pi\) | |||||||
\(462\) | −303.534 | − | 207.984i | −0.657001 | − | 0.450181i | ||||
\(463\) | 72.5534 | + | 125.666i | 0.156703 | + | 0.271417i | 0.933678 | − | 0.358114i | \(-0.116580\pi\) |
−0.776975 | + | 0.629532i | \(0.783247\pi\) | |||||||
\(464\) | −49.4456 | + | 28.5474i | −0.106564 | + | 0.0615246i | ||||
\(465\) | 444.209 | − | 212.646i | 0.955289 | − | 0.457304i | ||||
\(466\) | −151.805 | − | 87.6446i | −0.325762 | − | 0.188078i | ||||
\(467\) | 147.528 | 0.315906 | 0.157953 | − | 0.987447i | \(-0.449511\pi\) | ||||
0.157953 | + | 0.987447i | \(0.449511\pi\) | |||||||
\(468\) | 50.0224 | − | 321.698i | 0.106885 | − | 0.687390i | ||||
\(469\) | 1259.22i | 2.68491i | ||||||||
\(470\) | 237.500 | + | 137.121i | 0.505319 | + | 0.291746i | ||||
\(471\) | −510.724 | − | 39.4702i | −1.08434 | − | 0.0838009i | ||||
\(472\) | −107.972 | − | 187.014i | −0.228755 | − | 0.396215i | ||||
\(473\) | −127.962 | − | 221.636i | −0.270532 | − | 0.468575i | ||||
\(474\) | 71.1669 | + | 5.49998i | 0.150141 | + | 0.0116033i | ||||
\(475\) | 1043.10 | + | 593.594i | 2.19599 | + | 1.24967i | ||||
\(476\) | 479.229 | 1.00678 | ||||||||
\(477\) | 65.6880 | − | 25.4280i | 0.137711 | − | 0.0533083i | ||||
\(478\) | 57.0865i | 0.119428i | ||||||||
\(479\) | 249.268 | − | 431.745i | 0.520392 | − | 0.901346i | −0.479327 | − | 0.877637i | \(-0.659119\pi\) |
0.999719 | − | 0.0237093i | \(-0.00754763\pi\) | |||||||
\(480\) | −143.729 | + | 68.8041i | −0.299435 | + | 0.143342i | ||||
\(481\) | −96.3891 | − | 166.951i | −0.200393 | − | 0.347091i | ||||
\(482\) | −118.698 | − | 205.591i | −0.246262 | − | 0.426538i | ||||
\(483\) | 322.117 | − | 470.103i | 0.666910 | − | 0.973297i | ||||
\(484\) | −62.5373 | + | 108.318i | −0.129209 | + | 0.223797i | ||||
\(485\) | 1097.07i | 2.26199i | ||||||||
\(486\) | −129.269 | + | 318.414i | −0.265985 | + | 0.655173i | ||||
\(487\) | − | 439.949i | − | 0.903386i | −0.892173 | − | 0.451693i | \(-0.850820\pi\) | ||
0.892173 | − | 0.451693i | \(-0.149180\pi\) | |||||||
\(488\) | 87.1445 | + | 50.3129i | 0.178575 | + | 0.103100i | ||||
\(489\) | −100.810 | + | 147.123i | −0.206155 | + | 0.300865i | ||||
\(490\) | −916.066 | + | 528.891i | −1.86952 | + | 1.07937i | ||||
\(491\) | −104.929 | − | 181.742i | −0.213704 | − | 0.370146i | 0.739167 | − | 0.673522i | \(-0.235219\pi\) |
−0.952871 | + | 0.303376i | \(0.901886\pi\) | |||||||
\(492\) | −9.69819 | + | 4.64260i | −0.0197118 | + | 0.00943617i | ||||
\(493\) | 261.133 | + | 150.765i | 0.529682 | + | 0.305812i | ||||
\(494\) | 3.02919 | + | 485.987i | 0.00613197 | + | 0.983779i | ||||
\(495\) | −233.260 | − | 602.579i | −0.471233 | − | 1.21733i | ||||
\(496\) | − | 69.9324i | − | 0.140993i | ||||||
\(497\) | 535.769 | + | 309.326i | 1.07801 | + | 0.622387i | ||||
\(498\) | −44.9548 | + | 581.691i | −0.0902707 | + | 1.16805i | ||||
\(499\) | 208.841 | + | 361.723i | 0.418519 | + | 0.724897i | 0.995791 | − | 0.0916557i | \(-0.0292159\pi\) |
−0.577272 | + | 0.816552i | \(0.695883\pi\) | |||||||
\(500\) | −358.374 | − | 620.723i | −0.716749 | − | 1.24145i | ||||
\(501\) | −7.99907 | + | 103.504i | −0.0159662 | + | 0.206594i | ||||
\(502\) | 99.9037 | + | 57.6794i | 0.199011 | + | 0.114899i | ||||
\(503\) | −422.202 | −0.839367 | −0.419684 | − | 0.907671i | \(-0.637859\pi\) | ||||
−0.419684 | + | 0.907671i | \(0.637859\pi\) | |||||||
\(504\) | −44.3643 | + | 285.311i | −0.0880243 | + | 0.566093i | ||||
\(505\) | 54.6878 | 0.108293 | ||||||||
\(506\) | 156.828 | + | 90.5448i | 0.309937 | + | 0.178942i | ||||
\(507\) | 204.841 | + | 427.905i | 0.404027 | + | 0.843994i | ||||
\(508\) | 4.74283 | − | 2.73827i | 0.00933628 | − | 0.00539030i | ||||
\(509\) | −145.016 | + | 83.7250i | −0.284904 | + | 0.164489i | −0.635641 | − | 0.771985i | \(-0.719264\pi\) |
0.350738 | + | 0.936474i | \(0.385931\pi\) | |||||||
\(510\) | 694.220 | + | 475.684i | 1.36122 | + | 0.932714i | ||||
\(511\) | −664.094 | + | 1150.25i | −1.29960 | + | 2.25097i | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 114.532 | − | 500.052i | 0.223258 | − | 0.974759i | ||||
\(514\) | 458.357 | 0.891745 | ||||||||
\(515\) | 1395.17 | + | 805.503i | 2.70907 | + | 1.56408i | ||||
\(516\) | −113.516 | + | 165.667i | −0.219992 | + | 0.321060i | ||||
\(517\) | 78.9541 | + | 136.753i | 0.152716 | + | 0.264512i | ||||
\(518\) | 85.4864 | + | 148.067i | 0.165032 | + | 0.285843i | ||||
\(519\) | 505.935 | − | 242.195i | 0.974826 | − | 0.466657i | ||||
\(520\) | 240.177 | − | 415.999i | 0.461879 | − | 0.799998i | ||||
\(521\) | − | 293.382i | − | 0.563113i | −0.959545 | − | 0.281556i | \(-0.909149\pi\) | ||
0.959545 | − | 0.281556i | \(-0.0908506\pi\) | |||||||
\(522\) | −113.933 | + | 141.510i | −0.218262 | + | 0.271091i | ||||
\(523\) | 138.278i | 0.264394i | 0.991223 | + | 0.132197i | \(0.0422032\pi\) | ||||
−0.991223 | + | 0.132197i | \(0.957797\pi\) | |||||||
\(524\) | 126.936 | − | 219.860i | 0.242245 | − | 0.419581i | ||||
\(525\) | −2143.06 | − | 165.622i | −4.08202 | − | 0.315471i | ||||
\(526\) | 356.177 | − | 205.639i | 0.677143 | − | 0.390949i | ||||
\(527\) | −319.848 | + | 184.664i | −0.606922 | + | 0.350407i | ||||
\(528\) | −91.4803 | − | 7.06986i | −0.173258 | − | 0.0133899i | ||||
\(529\) | 124.268 | − | 215.238i | 0.234911 | − | 0.406877i | ||||
\(530\) | 103.928 | 0.196090 | ||||||||
\(531\) | −535.219 | − | 430.918i | −1.00795 | − | 0.811522i | ||||
\(532\) | −2.68656 | − | 431.016i | −0.00504992 | − | 0.810181i | ||||
\(533\) | 16.2061 | − | 28.0698i | 0.0304054 | − | 0.0526637i | ||||
\(534\) | 14.1120 | + | 29.4793i | 0.0264269 | + | 0.0552047i | ||||
\(535\) | −1005.04 | + | 580.260i | −1.87858 | + | 1.08460i | ||||
\(536\) | 157.000 | + | 271.932i | 0.292911 | + | 0.507336i | ||||
\(537\) | −418.597 | − | 286.825i | −0.779510 | − | 0.534126i | ||||
\(538\) | 291.524 | − | 504.935i | 0.541867 | − | 0.938540i | ||||
\(539\) | −609.072 | −1.13000 | ||||||||
\(540\) | −347.467 | + | 369.270i | −0.643458 | + | 0.683834i | ||||
\(541\) | 680.631 | 1.25810 | 0.629049 | − | 0.777366i | \(-0.283444\pi\) | ||||
0.629049 | + | 0.777366i | \(0.283444\pi\) | |||||||
\(542\) | −98.0541 | − | 56.6116i | −0.180912 | − | 0.104449i | ||||
\(543\) | 682.770 | + | 467.838i | 1.25740 | + | 0.861581i | ||||
\(544\) | 103.490 | − | 59.7502i | 0.190240 | − | 0.109835i | ||||
\(545\) | 486.050 | − | 280.621i | 0.891835 | − | 0.514901i | ||||
\(546\) | −375.824 | − | 785.081i | −0.688323 | − | 1.43788i | ||||
\(547\) | 452.278 | + | 261.123i | 0.826833 | + | 0.477372i | 0.852767 | − | 0.522291i | \(-0.174923\pi\) |
−0.0259341 | + | 0.999664i | \(0.508256\pi\) | |||||||
\(548\) | 99.3168 | 0.181235 | ||||||||
\(549\) | 316.387 | + | 49.1965i | 0.576298 | + | 0.0896112i | ||||
\(550\) | − | 683.034i | − | 1.24188i | ||||||
\(551\) | 134.134 | − | 235.707i | 0.243437 | − | 0.427781i | ||||
\(552\) | 10.9495 | − | 141.681i | 0.0198361 | − | 0.256669i | ||||
\(553\) | 165.266 | − | 95.4164i | 0.298854 | − | 0.172543i | ||||
\(554\) | 71.8996 | − | 41.5113i | 0.129783 | − | 0.0749301i | ||||
\(555\) | −23.1344 | + | 299.346i | −0.0416836 | + | 0.539363i | ||||
\(556\) | 176.016 | − | 304.868i | 0.316575 | − | 0.548324i | ||||
\(557\) | −740.279 | −1.32905 | −0.664523 | − | 0.747268i | \(-0.731365\pi\) | ||||
−0.664523 | + | 0.747268i | \(0.731365\pi\) | |||||||
\(558\) | −80.3309 | − | 207.518i | −0.143962 | − | 0.371896i | ||||
\(559\) | − | 605.389i | − | 1.08299i | ||||||
\(560\) | −213.010 | + | 368.945i | −0.380376 | + | 0.658830i | ||||
\(561\) | 209.229 | + | 437.070i | 0.372957 | + | 0.779090i | ||||
\(562\) | −357.636 | − | 619.444i | −0.636363 | − | 1.10221i | ||||
\(563\) | −127.632 | + | 73.6883i | −0.226699 | + | 0.130885i | −0.609049 | − | 0.793133i | \(-0.708449\pi\) |
0.382349 | + | 0.924018i | \(0.375115\pi\) | |||||||
\(564\) | 70.0410 | − | 102.219i | 0.124186 | − | 0.181239i | ||||
\(565\) | −1199.94 | − | 692.788i | −2.12379 | − | 1.22617i | ||||
\(566\) | − | 590.791i | − | 1.04380i | ||||||
\(567\) | 196.088 | + | 897.594i | 0.345834 | + | 1.58306i | ||||
\(568\) | 154.267 | 0.271597 | ||||||||
\(569\) | −290.015 | − | 167.440i | −0.509693 | − | 0.294271i | 0.223015 | − | 0.974815i | \(-0.428410\pi\) |
−0.732707 | + | 0.680544i | \(0.761744\pi\) | |||||||
\(570\) | 423.936 | − | 627.045i | 0.743748 | − | 1.10008i | ||||
\(571\) | 372.211 | + | 644.689i | 0.651859 | + | 1.12905i | 0.982671 | + | 0.185356i | \(0.0593439\pi\) |
−0.330812 | + | 0.943697i | \(0.607323\pi\) | |||||||
\(572\) | 239.532 | − | 138.294i | 0.418763 | − | 0.241773i | ||||
\(573\) | 283.476 | + | 592.170i | 0.494723 | + | 1.03346i | ||||
\(574\) | −14.3730 | + | 24.8947i | −0.0250400 | + | 0.0433706i | ||||
\(575\) | 1057.86 | 1.83975 | ||||||||
\(576\) | 25.9920 | + | 67.1448i | 0.0451249 | + | 0.116571i | ||||
\(577\) | −558.799 | −0.968455 | −0.484228 | − | 0.874942i | \(-0.660899\pi\) | ||||
−0.484228 | + | 0.874942i | \(0.660899\pi\) | |||||||
\(578\) | −192.605 | − | 111.200i | −0.333226 | − | 0.192388i | ||||
\(579\) | 85.1810 | − | 1102.20i | 0.147118 | − | 1.90362i | ||||
\(580\) | −232.140 | + | 134.026i | −0.400241 | + | 0.231079i | ||||
\(581\) | 779.897 | + | 1350.82i | 1.34234 | + | 2.32499i | ||||
\(582\) | 494.224 | + | 38.1951i | 0.849183 | + | 0.0656273i | ||||
\(583\) | 51.8243 | + | 29.9208i | 0.0888925 | + | 0.0513221i | ||||
\(584\) | 331.197i | 0.567118i | ||||||||
\(585\) | 234.848 | − | 1510.33i | 0.401449 | − | 2.58176i | ||||
\(586\) | 459.117 | 0.783477 | ||||||||
\(587\) | −173.031 | + | 299.699i | −0.294772 | + | 0.510560i | −0.974932 | − | 0.222504i | \(-0.928577\pi\) |
0.680160 | + | 0.733064i | \(0.261910\pi\) | |||||||
\(588\) | 206.370 | + | 431.098i | 0.350969 | + | 0.733160i | ||||
\(589\) | 167.879 | + | 286.635i | 0.285024 | + | 0.486646i | ||||
\(590\) | −506.915 | − | 878.002i | −0.859178 | − | 1.48814i | ||||
\(591\) | −417.590 | + | 609.437i | −0.706583 | + | 1.03120i | ||||
\(592\) | 36.9219 | + | 21.3169i | 0.0623681 | + | 0.0360082i | ||||
\(593\) | 187.654 | 0.316449 | 0.158225 | − | 0.987403i | \(-0.449423\pi\) | ||||
0.158225 | + | 0.987403i | \(0.449423\pi\) | |||||||
\(594\) | −279.580 | + | 84.1036i | −0.470674 | + | 0.141589i | ||||
\(595\) | 2249.91 | 3.78136 | ||||||||
\(596\) | −57.6542 | + | 99.8600i | −0.0967353 | + | 0.167550i | ||||
\(597\) | 16.1982 | − | 23.6398i | 0.0271326 | − | 0.0395977i | ||||
\(598\) | 214.185 | + | 370.979i | 0.358168 | + | 0.620365i | ||||
\(599\) | −590.699 | + | 341.040i | −0.986143 | + | 0.569350i | −0.904119 | − | 0.427281i | \(-0.859472\pi\) |
−0.0820236 | + | 0.996630i | \(0.526138\pi\) | |||||||
\(600\) | −483.448 | + | 231.430i | −0.805747 | + | 0.385717i | ||||
\(601\) | 6.79494 | + | 3.92306i | 0.0113061 | + | 0.00652755i | 0.505642 | − | 0.862743i | \(-0.331256\pi\) |
−0.494336 | + | 0.869271i | \(0.664589\pi\) | |||||||
\(602\) | 536.913i | 0.891882i | ||||||||
\(603\) | 778.250 | + | 626.588i | 1.29063 | + | 1.03912i | ||||
\(604\) | − | 65.8496i | − | 0.109022i | ||||||
\(605\) | −293.604 | + | 508.537i | −0.485296 | + | 0.840556i | ||||
\(606\) | 1.90399 | − | 24.6366i | 0.00314190 | − | 0.0406545i | ||||
\(607\) | −781.844 | + | 451.398i | −1.28805 | + | 0.743653i | −0.978305 | − | 0.207168i | \(-0.933575\pi\) |
−0.309740 | + | 0.950821i | \(0.600242\pi\) | |||||||
\(608\) | −54.3192 | − | 92.7438i | −0.0893409 | − | 0.152539i | ||||
\(609\) | −37.4254 | + | 484.265i | −0.0614539 | + | 0.795181i | ||||
\(610\) | 409.131 | + | 236.212i | 0.670707 | + | 0.387233i | ||||
\(611\) | 373.534i | 0.611348i | ||||||||
\(612\) | 238.463 | − | 296.182i | 0.389646 | − | 0.483957i | ||||
\(613\) | −481.589 | −0.785627 | −0.392814 | − | 0.919618i | \(-0.628498\pi\) | ||||
−0.392814 | + | 0.919618i | \(0.628498\pi\) | |||||||
\(614\) | 35.9759 | − | 62.3120i | 0.0585926 | − | 0.101485i | ||||
\(615\) | −45.5316 | + | 21.7963i | −0.0740351 | + | 0.0354412i | ||||
\(616\) | −212.439 | + | 122.651i | −0.344868 | + | 0.199109i | ||||
\(617\) | 120.361 | + | 208.471i | 0.195075 | + | 0.337879i | 0.946925 | − | 0.321455i | \(-0.104172\pi\) |
−0.751850 | + | 0.659334i | \(0.770838\pi\) | |||||||
\(618\) | 411.450 | − | 600.475i | 0.665776 | − | 0.971643i | ||||
\(619\) | 539.689 | − | 934.768i | 0.871872 | − | 1.51013i | 0.0118142 | − | 0.999930i | \(-0.496239\pi\) |
0.860058 | − | 0.510197i | \(-0.170427\pi\) | |||||||
\(620\) | − | 328.323i | − | 0.529553i | ||||||
\(621\) | −130.257 | − | 433.003i | −0.209753 | − | 0.697268i | ||||
\(622\) | − | 229.556i | − | 0.369062i | ||||||
\(623\) | 75.6718 | + | 43.6891i | 0.121464 | + | 0.0701270i | ||||
\(624\) | −179.044 | − | 122.682i | −0.286929 | − | 0.196606i | ||||
\(625\) | −892.932 | − | 1546.60i | −1.42869 | − | 2.47457i | ||||
\(626\) | −29.1404 | + | 16.8242i | −0.0465502 | + | 0.0268758i | ||||
\(627\) | 391.926 | − | 190.629i | 0.625081 | − | 0.304034i | ||||
\(628\) | −170.749 | + | 295.746i | −0.271893 | + | 0.470933i | ||||
\(629\) | − | 225.158i | − | 0.357962i | ||||||
\(630\) | −208.284 | + | 1339.49i | −0.330609 | + | 2.12618i | ||||
\(631\) | −1069.71 | −1.69526 | −0.847628 | − | 0.530591i | \(-0.821970\pi\) | ||||
−0.847628 | + | 0.530591i | \(0.821970\pi\) | |||||||
\(632\) | 23.7930 | − | 41.2107i | 0.0376472 | − | 0.0652068i | ||||
\(633\) | −32.1160 | + | 415.564i | −0.0507362 | + | 0.656500i | ||||
\(634\) | 322.983 | + | 559.424i | 0.509438 | + | 0.882372i | ||||
\(635\) | 22.2669 | − | 12.8558i | 0.0350660 | − | 0.0202454i | ||||
\(636\) | 3.61831 | − | 46.8190i | 0.00568916 | − | 0.0736148i | ||||
\(637\) | −1247.74 | − | 720.383i | −1.95877 | − | 1.13090i | ||||
\(638\) | −154.344 | −0.241919 | ||||||||
\(639\) | 457.773 | − | 177.206i | 0.716390 | − | 0.277317i | ||||
\(640\) | 106.232i | 0.165988i | ||||||||
\(641\) | 134.017 | + | 77.3747i | 0.209075 | + | 0.120709i | 0.600881 | − | 0.799338i | \(-0.294816\pi\) |
−0.391807 | + | 0.920048i | \(0.628150\pi\) | |||||||
\(642\) | 226.414 | + | 472.968i | 0.352669 | + | 0.736711i | ||||
\(643\) | −254.826 | − | 441.371i | −0.396307 | − | 0.686425i | 0.596960 | − | 0.802271i | \(-0.296375\pi\) |
−0.993267 | + | 0.115847i | \(0.963042\pi\) | |||||||
\(644\) | −189.958 | − | 329.017i | −0.294966 | − | 0.510896i | ||||
\(645\) | −532.942 | + | 777.783i | −0.826267 | + | 1.20586i | ||||
\(646\) | −280.744 | + | 493.339i | −0.434588 | + | 0.763682i | ||||
\(647\) | −215.440 | −0.332983 | −0.166492 | − | 0.986043i | \(-0.553244\pi\) | ||||
−0.166492 | + | 0.986043i | \(0.553244\pi\) | |||||||
\(648\) | 154.257 | + | 169.389i | 0.238052 | + | 0.261403i | ||||
\(649\) | − | 583.764i | − | 0.899482i | ||||||
\(650\) | 807.862 | − | 1399.26i | 1.24287 | − | 2.15271i | ||||
\(651\) | −490.763 | − | 336.274i | −0.753861 | − | 0.516550i | ||||
\(652\) | 59.4491 | + | 102.969i | 0.0911796 | + | 0.157928i | ||||
\(653\) | 92.8163 | + | 160.763i | 0.142138 | + | 0.246191i | 0.928302 | − | 0.371828i | \(-0.121269\pi\) |
−0.786163 | + | 0.618019i | \(0.787936\pi\) | |||||||
\(654\) | −109.497 | − | 228.734i | −0.167426 | − | 0.349746i | ||||
\(655\) | 595.948 | − | 1032.21i | 0.909844 | − | 1.57590i | ||||
\(656\) | 7.16810i | 0.0109270i | ||||||||
\(657\) | 380.444 | + | 982.796i | 0.579062 | + | 1.49588i | ||||
\(658\) | − | 331.283i | − | 0.503469i | ||||||
\(659\) | −1072.33 | − | 619.112i | −1.62721 | − | 0.939472i | −0.984919 | − | 0.173013i | \(-0.944650\pi\) |
−0.642294 | − | 0.766459i | \(-0.722017\pi\) | |||||||
\(660\) | −429.487 | − | 33.1920i | −0.650738 | − | 0.0502909i | ||||
\(661\) | 694.069 | − | 400.721i | 1.05003 | − | 0.606234i | 0.127371 | − | 0.991855i | \(-0.459346\pi\) |
0.922657 | + | 0.385621i | \(0.126013\pi\) | |||||||
\(662\) | 325.216 | + | 563.291i | 0.491264 | + | 0.850893i | ||||
\(663\) | −88.3223 | + | 1142.84i | −0.133216 | + | 1.72375i | ||||
\(664\) | 336.841 | + | 194.475i | 0.507290 | + | 0.292884i | ||||
\(665\) | −12.6130 | − | 2023.56i | −0.0189669 | − | 3.04295i | ||||
\(666\) | 134.049 | + | 20.8439i | 0.201275 | + | 0.0312971i | ||||
\(667\) | − | 239.043i | − | 0.358385i | ||||||
\(668\) | 59.9361 | + | 34.6041i | 0.0897246 | + | 0.0518025i | ||||
\(669\) | 234.835 | − | 112.417i | 0.351024 | − | 0.168038i | ||||
\(670\) | 737.093 | + | 1276.68i | 1.10014 | + | 1.90550i | ||||
\(671\) | 136.011 | + | 235.578i | 0.202699 | + | 0.351085i | ||||
\(672\) | 158.792 | + | 108.805i | 0.236298 | + | 0.161913i | ||||
\(673\) | 721.063 | + | 416.306i | 1.07142 | + | 0.618582i | 0.928568 | − | 0.371162i | \(-0.121041\pi\) |
0.142848 | + | 0.989745i | \(0.454374\pi\) | |||||||
\(674\) | −181.561 | −0.269378 | ||||||||
\(675\) | −1168.75 | + | 1242.08i | −1.73147 | + | 1.84012i | ||||
\(676\) | 316.272 | 0.467858 | ||||||||
\(677\) | 35.8927 | + | 20.7226i | 0.0530173 | + | 0.0306095i | 0.526274 | − | 0.850315i | \(-0.323588\pi\) |
−0.473257 | + | 0.880924i | \(0.656922\pi\) | |||||||
\(678\) | −353.875 | + | 516.450i | −0.521939 | + | 0.761725i | ||||
\(679\) | 1147.70 | − | 662.627i | 1.69029 | − | 0.975887i | ||||
\(680\) | 485.873 | − | 280.519i | 0.714518 | − | 0.412527i | ||||
\(681\) | 237.981 | − | 113.923i | 0.349458 | − | 0.167288i | ||||
\(682\) | 94.5242 | − | 163.721i | 0.138599 | − | 0.240060i | ||||
\(683\) | 519.839i | 0.761111i | 0.924758 | + | 0.380556i | \(0.124267\pi\) | ||||
−0.924758 | + | 0.380556i | \(0.875733\pi\) | |||||||
\(684\) | −267.722 | − | 212.813i | −0.391406 | − | 0.311129i | ||||
\(685\) | 466.278 | 0.680698 | ||||||||
\(686\) | 425.899 | + | 245.893i | 0.620844 | + | 0.358445i | ||||
\(687\) | −601.635 | − | 46.4961i | −0.875742 | − | 0.0676799i | ||||
\(688\) | 66.9423 | + | 115.947i | 0.0972999 | + | 0.168528i | ||||
\(689\) | 70.7779 | + | 122.591i | 0.102726 | + | 0.177926i | ||||
\(690\) | 51.4065 | − | 665.173i | 0.0745022 | − | 0.964019i | ||||
\(691\) | −482.416 | + | 835.570i | −0.698142 | + | 1.20922i | 0.270967 | + | 0.962589i | \(0.412656\pi\) |
−0.969110 | + | 0.246630i | \(0.920677\pi\) | |||||||
\(692\) | − | 373.945i | − | 0.540383i | ||||||
\(693\) | −489.503 | + | 607.983i | −0.706353 | + | 0.877321i | ||||
\(694\) | 363.211i | 0.523359i | ||||||||
\(695\) | 826.369 | − | 1431.31i | 1.18902 | − | 2.05944i | ||||
\(696\) | 52.2961 | + | 109.244i | 0.0751380 | + | 0.156960i | ||||
\(697\) | 32.7845 | − | 18.9282i | 0.0470366 | − | 0.0271566i | ||||
\(698\) | −561.917 | + | 324.423i | −0.805039 | + | 0.464790i | ||||
\(699\) | −210.183 | + | 306.743i | −0.300690 | + | 0.438832i | ||||
\(700\) | −716.484 | + | 1240.99i | −1.02355 | + | 1.77284i | ||||
\(701\) | −903.971 | −1.28955 | −0.644773 | − | 0.764374i | \(-0.723048\pi\) | ||||
−0.644773 | + | 0.764374i | \(0.723048\pi\) | |||||||
\(702\) | −672.220 | − | 158.381i | −0.957578 | − | 0.225614i | ||||
\(703\) | −202.506 | + | 1.26224i | −0.288060 | + | 0.00179550i | ||||
\(704\) | −30.5844 | + | 52.9737i | −0.0434437 | + | 0.0752467i | ||||
\(705\) | 328.832 | − | 479.902i | 0.466429 | − | 0.680713i | ||||
\(706\) | 554.270 | − | 320.008i | 0.785085 | − | 0.453269i | ||||
\(707\) | −33.0313 | − | 57.2120i | −0.0467204 | − | 0.0809221i | ||||
\(708\) | −413.185 | + | 197.795i | −0.583595 | + | 0.279371i | ||||
\(709\) | 122.373 | − | 211.957i | 0.172600 | − | 0.298952i | −0.766728 | − | 0.641972i | \(-0.778117\pi\) |
0.939328 | + | 0.343020i | \(0.111450\pi\) | |||||||
\(710\) | 724.262 | 1.02009 | ||||||||
\(711\) | 23.2651 | − | 149.620i | 0.0327216 | − | 0.210436i | ||||
\(712\) | 21.7886 | 0.0306020 | ||||||||
\(713\) | 253.564 | + | 146.395i | 0.355630 | + | 0.205323i | ||||
\(714\) | 78.3321 | − | 1013.58i | 0.109709 | − | 1.41957i | ||||
\(715\) | 1124.57 | − | 649.271i | 1.57282 | − | 0.908071i | ||||
\(716\) | −292.969 | + | 169.146i | −0.409174 | + | 0.236237i | ||||
\(717\) | 120.739 | + | 9.33104i | 0.168394 | + | 0.0130140i | ||||
\(718\) | −562.178 | − | 324.574i | −0.782978 | − | 0.452052i | ||||
\(719\) | −385.608 | −0.536311 | −0.268155 | − | 0.963376i | \(-0.586414\pi\) | ||||
−0.268155 | + | 0.963376i | \(0.586414\pi\) | |||||||
\(720\) | 122.029 | + | 315.235i | 0.169484 | + | 0.437826i | ||||
\(721\) | − | 1946.09i | − | 2.69916i | ||||||
\(722\) | 445.281 | + | 249.734i | 0.616732 | + | 0.345892i | ||||
\(723\) | −454.230 | + | 217.443i | −0.628257 | + | 0.300752i | ||||
\(724\) | 477.859 | − | 275.892i | 0.660026 | − | 0.381066i | ||||
\(725\) | −780.828 | + | 450.811i | −1.07700 | + | 0.621809i | ||||
\(726\) | 218.872 | + | 149.972i | 0.301476 | + | 0.206573i | ||||
\(727\) | −239.797 | + | 415.340i | −0.329844 | + | 0.571307i | −0.982481 | − | 0.186364i | \(-0.940329\pi\) |
0.652637 | + | 0.757671i | \(0.273663\pi\) | |||||||
\(728\) | −580.266 | −0.797069 | ||||||||
\(729\) | 652.321 | + | 325.451i | 0.894816 | + | 0.446435i | ||||
\(730\) | 1554.92i | 2.13003i | ||||||||
\(731\) | 353.537 | − | 612.344i | 0.483635 | − | 0.837681i | ||||
\(732\) | 120.657 | − | 176.088i | 0.164832 | − | 0.240557i | ||||
\(733\) | −193.320 | − | 334.839i | −0.263737 | − | 0.456807i | 0.703495 | − | 0.710701i | \(-0.251622\pi\) |
−0.967232 | + | 0.253894i | \(0.918289\pi\) | |||||||
\(734\) | 855.460 | − | 493.900i | 1.16548 | − | 0.672889i | ||||
\(735\) | 968.877 | + | 2023.94i | 1.31820 | + | 2.75366i | ||||
\(736\) | −82.0436 | − | 47.3679i | −0.111472 | − | 0.0643585i | ||||
\(737\) | 848.837i | 1.15175i | ||||||||
\(738\) | 8.23395 | + | 21.2707i | 0.0111571 | + | 0.0288220i | ||||
\(739\) | −210.976 | −0.285489 | −0.142744 | − | 0.989760i | \(-0.545593\pi\) | ||||
−0.142744 | + | 0.989760i | \(0.545593\pi\) | |||||||
\(740\) | 173.343 | + | 100.080i | 0.234247 | + | 0.135243i | ||||
\(741\) | 1028.36 | + | 73.0299i | 1.38780 | + | 0.0985559i | ||||
\(742\) | −62.7722 | − | 108.725i | −0.0845986 | − | 0.146529i | ||||
\(743\) | 886.789 | − | 511.988i | 1.19352 | − | 0.689082i | 0.234420 | − | 0.972135i | \(-0.424681\pi\) |
0.959104 | + | 0.283054i | \(0.0913475\pi\) | |||||||
\(744\) | −147.908 | − | 11.4308i | −0.198801 | − | 0.0153639i | ||||
\(745\) | −270.678 | + | 468.829i | −0.363327 | + | 0.629300i | ||||
\(746\) | −753.520 | −1.01008 | ||||||||
\(747\) | 1222.94 | + | 190.160i | 1.63713 | + | 0.254565i | ||||
\(748\) | 323.046 | 0.431879 | ||||||||
\(749\) | 1214.08 | + | 700.952i | 1.62094 | + | 0.935851i | ||||
\(750\) | −1371.41 | + | 656.507i | −1.82855 | + | 0.875342i | ||||
\(751\) | −582.160 | + | 336.110i | −0.775180 | + | 0.447550i | −0.834719 | − | 0.550676i | \(-0.814370\pi\) |
0.0595396 | + | 0.998226i | \(0.481037\pi\) | |||||||
\(752\) | −41.3043 | − | 71.5412i | −0.0549260 | − | 0.0951345i | ||||
\(753\) | 138.323 | − | 201.870i | 0.183695 | − | 0.268087i | ||||
\(754\) | −316.189 | − | 182.552i | −0.419349 | − | 0.242111i | ||||
\(755\) | − | 309.154i | − | 0.409476i | ||||||
\(756\) | 596.184 | + | 140.466i | 0.788604 | + | 0.185802i | ||||
\(757\) | 208.644 | 0.275620 | 0.137810 | − | 0.990459i | \(-0.455994\pi\) | ||||
0.137810 | + | 0.990459i | \(0.455994\pi\) | |||||||
\(758\) | −129.349 | + | 224.039i | −0.170645 | + | 0.295566i | ||||
\(759\) | 217.138 | − | 316.894i | 0.286084 | − | 0.417515i | ||||
\(760\) | −255.021 | − | 435.419i | −0.335554 | − | 0.572920i | ||||
\(761\) | 323.299 | + | 559.971i | 0.424835 | + | 0.735835i | 0.996405 | − | 0.0847178i | \(-0.0269989\pi\) |
−0.571570 | + | 0.820553i | \(0.693666\pi\) | |||||||
\(762\) | −5.01625 | − | 10.4787i | −0.00658301 | − | 0.0137516i | ||||
\(763\) | −587.147 | − | 338.990i | −0.769525 | − | 0.444285i | ||||
\(764\) | 437.683 | 0.572883 | ||||||||
\(765\) | 1119.55 | − | 1390.53i | 1.46347 | − | 1.81769i | ||||
\(766\) | 615.536 | 0.803571 | ||||||||
\(767\) | 690.449 | − | 1195.89i | 0.900195 | − | 1.55918i | ||||
\(768\) | 47.8573 | + | 3.69855i | 0.0623142 | + | 0.00481582i | ||||
\(769\) | −643.423 | − | 1114.44i | −0.836701 | − | 1.44921i | −0.892638 | − | 0.450774i | \(-0.851148\pi\) |
0.0559376 | − | 0.998434i | \(-0.482185\pi\) | |||||||
\(770\) | −997.368 | + | 575.831i | −1.29528 | + | 0.747832i | ||||
\(771\) | 74.9205 | − | 969.431i | 0.0971731 | − | 1.25737i | ||||
\(772\) | −638.251 | − | 368.495i | −0.826750 | − | 0.477325i | ||||
\(773\) | 63.3904i | 0.0820057i | 0.999159 | + | 0.0410028i | \(0.0130553\pi\) | ||||
−0.999159 | + | 0.0410028i | \(0.986945\pi\) | |||||||
\(774\) | 331.833 | + | 267.167i | 0.428725 | + | 0.345177i | ||||
\(775\) | − | 1104.35i | − | 1.42497i | ||||||
\(776\) | 165.233 | − | 286.191i | 0.212929 | − | 0.368803i | ||||
\(777\) | 327.136 | − | 156.603i | 0.421025 | − | 0.201548i | ||||
\(778\) | 387.498 | − | 223.722i | 0.498069 | − | 0.287560i | ||||
\(779\) | −17.2077 | − | 29.3801i | −0.0220895 | − | 0.0377152i | ||||
\(780\) | −840.585 | − | 575.975i | −1.07767 | − | 0.738429i | ||||
\(781\) | 361.159 | + | 208.515i | 0.462431 | + | 0.266985i | ||||
\(782\) | 500.321i | 0.639796i | ||||||||
\(783\) | 280.672 | + | 264.100i | 0.358457 | + | 0.337292i | ||||
\(784\) | 318.632 | 0.406418 | ||||||||
\(785\) | −801.642 | + | 1388.48i | −1.02120 | + | 1.76877i | ||||
\(786\) | −444.259 | − | 304.409i | −0.565215 | − | 0.387289i | ||||
\(787\) | −74.7615 | + | 43.1636i | −0.0949956 | + | 0.0548457i | −0.546745 | − | 0.837299i | \(-0.684133\pi\) |
0.451750 | + | 0.892145i | \(0.350800\pi\) | |||||||
\(788\) | 246.260 | + | 426.535i | 0.312513 | + | 0.541288i | ||||
\(789\) | −376.711 | − | 786.933i | −0.477453 | − | 0.997380i | ||||
\(790\) | 111.705 | − | 193.478i | 0.141399 | − | 0.244909i | ||||
\(791\) | 1673.77i | 2.11602i | ||||||||
\(792\) | −29.9057 | + | 192.326i | −0.0377597 | + | 0.242836i | ||||
\(793\) | 643.471i | 0.811438i | ||||||||
\(794\) | −680.486 | − | 392.879i | −0.857035 | − | 0.494809i | ||||
\(795\) | 16.9874 | − | 219.808i | 0.0213678 | − | 0.276489i | ||||
\(796\) | −9.55232 | − | 16.5451i | −0.0120004 | − | 0.0207853i | ||||
\(797\) | 1244.32 | − | 718.409i | 1.56126 | − | 0.901392i | 0.564126 | − | 0.825689i | \(-0.309213\pi\) |
0.997130 | − | 0.0757027i | \(-0.0241200\pi\) | |||||||
\(798\) | −912.044 | − | 64.7694i | −1.14291 | − | 0.0811647i | ||||
\(799\) | −218.137 | + | 377.825i | −0.273013 | + | 0.472872i | ||||
\(800\) | 357.325i | 0.446656i | ||||||||
\(801\) | 64.6558 | − | 25.0285i | 0.0807188 | − | 0.0312465i | ||||
\(802\) | 387.629 | 0.483328 | ||||||||
\(803\) | −447.663 | + | 775.374i | −0.557488 | + | 0.965597i | ||||
\(804\) | 600.802 | − | 287.609i | 0.747267 | − | 0.357722i | ||||
\(805\) | −891.825 | − | 1544.69i | −1.10786 | − | 1.91886i | ||||
\(806\) | 387.283 | − | 223.598i | 0.480500 | − | 0.277417i | ||||
\(807\) | −1020.29 | − | 699.112i | −1.26430 | − | 0.866309i | ||||
\(808\) | −14.2664 | − | 8.23669i | −0.0176564 | − | 0.0101939i | ||||
\(809\) | −684.177 | −0.845707 | −0.422854 | − | 0.906198i | \(-0.638972\pi\) | ||||
−0.422854 | + | 0.906198i | \(0.638972\pi\) | |||||||
\(810\) | 724.217 | + | 795.257i | 0.894095 | + | 0.981799i | ||||
\(811\) | 1024.06i | 1.26272i | 0.775492 | + | 0.631358i | \(0.217502\pi\) | ||||
−0.775492 | + | 0.631358i | \(0.782498\pi\) | |||||||
\(812\) | 280.424 | + | 161.903i | 0.345350 | + | 0.199388i | ||||
\(813\) | −135.762 | + | 198.132i | −0.166989 | + | 0.243705i | ||||
\(814\) | 57.6259 | + | 99.8110i | 0.0707935 | + | 0.122618i | ||||
\(815\) | 279.105 | + | 483.424i | 0.342460 | + | 0.593158i | ||||
\(816\) | −109.457 | − | 228.650i | −0.134138 | − | 0.280208i | ||||
\(817\) | −552.722 | − | 314.537i | −0.676526 | − | 0.384990i | ||||
\(818\) | −1042.75 | −1.27476 | ||||||||
\(819\) | −1721.89 | + | 666.548i | −2.10243 | + | 0.813856i | ||||
\(820\) | 33.6532i | 0.0410405i | ||||||||
\(821\) | 145.846 | − | 252.613i | 0.177644 | − | 0.307689i | −0.763429 | − | 0.645892i | \(-0.776486\pi\) |
0.941073 | + | 0.338203i | \(0.109819\pi\) | |||||||
\(822\) | 16.2338 | − | 210.056i | 0.0197491 | − | 0.255543i | ||||
\(823\) | 78.0236 | + | 135.141i | 0.0948039 | + | 0.164205i | 0.909527 | − | 0.415645i | \(-0.136444\pi\) |
−0.814723 | + | 0.579851i | \(0.803111\pi\) | |||||||
\(824\) | −242.639 | − | 420.262i | −0.294464 | − | 0.510027i | ||||
\(825\) | −1444.63 | − | 111.645i | −1.75106 | − | 0.135327i | ||||
\(826\) | −612.352 | + | 1060.62i | −0.741346 | + | 1.28405i | ||||
\(827\) | − | 900.483i | − | 1.08886i | −0.838808 | − | 0.544428i | \(-0.816747\pi\) | ||
0.838808 | − | 0.544428i | \(-0.183253\pi\) | |||||||
\(828\) | −297.868 | − | 46.3168i | −0.359744 | − | 0.0559382i | ||||
\(829\) | 588.063i | 0.709364i | 0.934987 | + | 0.354682i | \(0.115411\pi\) | ||||
−0.934987 | + | 0.354682i | \(0.884589\pi\) | |||||||
\(830\) | 1581.42 | + | 913.033i | 1.90532 | + | 1.10004i | ||||
\(831\) | −76.0446 | − | 158.854i | −0.0915097 | − | 0.191160i | ||||
\(832\) | −125.310 | + | 72.3476i | −0.150613 | + | 0.0869563i | ||||
\(833\) | −841.383 | − | 1457.32i | −1.01006 | − | 1.74948i | ||||
\(834\) | −616.030 | − | 422.108i | −0.738645 | − | 0.506125i | ||||
\(835\) | 281.391 | + | 162.461i | 0.336995 | + | 0.194564i | ||||
\(836\) | −1.81099 | − | 290.546i | −0.00216626 | − | 0.347543i | ||||
\(837\) | −452.034 | + | 135.981i | −0.540064 | + | 0.162463i | ||||
\(838\) | − | 109.605i | − | 0.130794i | ||||||
\(839\) | −124.060 | − | 71.6259i | −0.147866 | − | 0.0853705i | 0.424242 | − | 0.905549i | \(-0.360541\pi\) |
−0.572108 | + | 0.820179i | \(0.693874\pi\) | |||||||
\(840\) | 745.505 | + | 510.825i | 0.887506 | + | 0.608125i | ||||
\(841\) | −318.631 | − | 551.885i | −0.378871 | − | 0.656224i | ||||
\(842\) | 302.892 | + | 524.624i | 0.359729 | + | 0.623069i | ||||
\(843\) | −1368.59 | + | 655.154i | −1.62348 | + | 0.777170i | ||||
\(844\) | 240.642 | + | 138.934i | 0.285120 | + | 0.164614i | ||||
\(845\) | 1484.85 | 1.75722 | ||||||||
\(846\) | −204.746 | − | 164.846i | −0.242016 | − | 0.194853i | ||||
\(847\) | 709.345 | 0.837480 | ||||||||
\(848\) | −27.1116 | − | 15.6529i | −0.0319712 | − | 0.0184586i | ||||
\(849\) | −1249.53 | − | 96.5674i | −1.47177 | − | 0.113743i | ||||
\(850\) | 1634.29 | − | 943.556i | 1.92269 | − | 1.11007i | ||||
\(851\) | −154.584 | + | 89.2489i | −0.181649 | + | 0.104875i | ||||
\(852\) | 25.2156 | − | 326.277i | 0.0295958 | − | 0.382954i | ||||
\(853\) | 48.9522 | − | 84.7877i | 0.0573883 | − | 0.0993994i | −0.835904 | − | 0.548876i | \(-0.815056\pi\) |
0.893292 | + | 0.449476i | \(0.148389\pi\) | |||||||
\(854\) | − | 570.687i | − | 0.668252i | ||||||
\(855\) | −1256.91 | − | 999.124i | −1.47008 | − | 1.16857i | ||||
\(856\) | 349.579 | 0.408386 | ||||||||
\(857\) | 417.160 | + | 240.847i | 0.486767 | + | 0.281035i | 0.723232 | − | 0.690605i | \(-0.242656\pi\) |
−0.236465 | + | 0.971640i | \(0.575989\pi\) | |||||||
\(858\) | −253.341 | − | 529.219i | −0.295269 | − | 0.616805i | ||||
\(859\) | −815.301 | − | 1412.14i | −0.949128 | − | 1.64394i | −0.747266 | − | 0.664525i | \(-0.768634\pi\) |
−0.201862 | − | 0.979414i | \(-0.564699\pi\) | |||||||
\(860\) | 314.285 | + | 544.357i | 0.365447 | + | 0.632973i | ||||
\(861\) | 50.3034 | + | 34.4682i | 0.0584244 | + | 0.0400328i | ||||
\(862\) | 513.315 | − | 889.088i | 0.595493 | − | 1.03142i | ||||
\(863\) | 1042.37i | 1.20784i | 0.797044 | + | 0.603921i | \(0.206396\pi\) | ||||
−0.797044 | + | 0.603921i | \(0.793604\pi\) | |||||||
\(864\) | 146.261 | − | 43.9983i | 0.169283 | − | 0.0509239i | ||||
\(865\) | − | 1755.62i | − | 2.02962i | ||||||
\(866\) | −222.910 | + | 386.092i | −0.257402 | + | 0.445833i | ||||
\(867\) | −266.672 | + | 389.185i | −0.307580 | + | 0.448887i | ||||
\(868\) | −343.477 | + | 198.306i | −0.395711 | + | 0.228464i | ||||
\(869\) | 111.405 | − | 64.3197i | 0.128199 | − | 0.0740158i | ||||
\(870\) | 245.522 | + | 512.886i | 0.282210 | + | 0.589524i | ||||
\(871\) | −1003.97 | + | 1738.92i | −1.15266 | + | 1.99646i | ||||
\(872\) | −169.061 | −0.193877 | ||||||||
\(873\) | 161.566 | − | 1039.05i | 0.185070 | − | 1.19020i | ||||
\(874\) | 449.986 | − | 2.80480i | 0.514858 | − | 0.00320915i | ||||
\(875\) | −2032.48 | + | 3520.35i | −2.32283 | + | 4.02326i | ||||
\(876\) | 700.486 | + | 54.1356i | 0.799642 | + | 0.0617987i | ||||
\(877\) | −375.107 | + | 216.568i | −0.427716 | + | 0.246942i | −0.698373 | − | 0.715734i | \(-0.746092\pi\) |
0.270657 | + | 0.962676i | \(0.412759\pi\) | |||||||
\(878\) | 198.877 | + | 344.465i | 0.226511 | + | 0.392329i | ||||
\(879\) | 75.0448 | − | 971.040i | 0.0853752 | − | 1.10471i | ||||
\(880\) | −143.589 | + | 248.704i | −0.163169 | + | 0.282618i | ||||
\(881\) | 569.865 | 0.646839 | 0.323419 | − | 0.946256i | \(-0.395168\pi\) | ||||
0.323419 | + | 0.946256i | \(0.395168\pi\) | |||||||
\(882\) | 945.510 | − | 366.010i | 1.07201 | − | 0.414978i | ||||
\(883\) | −1130.40 | −1.28018 | −0.640090 | − | 0.768300i | \(-0.721103\pi\) | ||||
−0.640090 | + | 0.768300i | \(0.721103\pi\) | |||||||
\(884\) | 661.789 | + | 382.084i | 0.748630 | + | 0.432221i | ||||
\(885\) | −1939.84 | + | 928.618i | −2.19191 | + | 1.04929i | ||||
\(886\) | −204.205 | + | 117.898i | −0.230480 | + | 0.133068i | ||||
\(887\) | 582.034 | − | 336.037i | 0.656182 | − | 0.378847i | −0.134638 | − | 0.990895i | \(-0.542987\pi\) |
0.790821 | + | 0.612048i | \(0.209654\pi\) | |||||||
\(888\) | 51.1205 | − | 74.6060i | 0.0575682 | − | 0.0840158i | ||||
\(889\) | −26.8984 | − | 15.5298i | −0.0302569 | − | 0.0174688i | ||||
\(890\) | 102.295 | 0.114938 | ||||||||
\(891\) | 132.182 | + | 605.063i | 0.148352 | + | 0.679083i | ||||
\(892\) | − | 173.570i | − | 0.194586i | ||||||
\(893\) | 341.037 | + | 194.074i | 0.381900 | + | 0.217328i | ||||
\(894\) | 201.781 | + | 138.262i | 0.225706 | + | 0.154656i | ||||
\(895\) | −1375.45 | + | 794.115i | −1.53681 | + | 0.887279i | ||||
\(896\) | 111.136 | − | 64.1643i | 0.124035 | − | 0.0716119i | ||||
\(897\) | 819.634 | − | 392.365i | 0.913750 | − | 0.437419i | ||||
\(898\) | −207.936 | + | 360.156i | −0.231555 | + | 0.401065i | ||||
\(899\) | −249.549 | −0.277585 | ||||||||
\(900\) | 410.457 | + | 1060.33i | 0.456063 | + | 1.17814i | ||||
\(901\) | 165.333i | 0.183499i | ||||||||
\(902\) | −9.68876 | + | 16.7814i | −0.0107414 | + | 0.0186047i | ||||
\(903\) | 1135.58 | + | 87.7608i | 1.25756 | + | 0.0971881i | ||||
\(904\) | 208.686 | + | 361.454i | 0.230847 | + | 0.399839i | ||||
\(905\) | 2243.48 | − | 1295.27i | 2.47898 | − | 1.43124i | ||||
\(906\) | −139.273 | − | 10.7634i | −0.153723 | − | 0.0118801i | ||||
\(907\) | −1299.82 | − | 750.453i | −1.43310 | − | 0.827401i | −0.435745 | − | 0.900070i | \(-0.643515\pi\) |
−0.997356 | + | 0.0726693i | \(0.976848\pi\) | |||||||
\(908\) | − | 175.895i | − | 0.193717i | ||||||
\(909\) | −51.7956 | − | 8.05393i | −0.0569808 | − | 0.00886021i | ||||
\(910\) | −2724.27 | −2.99370 | ||||||||
\(911\) | −1530.99 | − | 883.916i | −1.68056 | − | 0.970270i | −0.961290 | − | 0.275537i | \(-0.911144\pi\) |
−0.719267 | − | 0.694733i | \(-0.755522\pi\) | |||||||
\(912\) | −205.033 | + | 99.7265i | −0.224817 | + | 0.109349i | ||||
\(913\) | 525.725 | + | 910.582i | 0.575821 | + | 0.997352i | ||||
\(914\) | −819.074 | + | 472.893i | −0.896142 | + | 0.517388i | ||||
\(915\) | 566.466 | − | 826.708i | 0.619088 | − | 0.903506i | ||||
\(916\) | −201.143 | + | 348.390i | −0.219588 | + | 0.380338i | ||||
\(917\) | −1439.81 | −1.57013 | ||||||||
\(918\) | −587.451 | − | 552.766i | −0.639925 | − | 0.602141i | ||||
\(919\) | −423.196 | −0.460496 | −0.230248 | − | 0.973132i | \(-0.573954\pi\) | ||||
−0.230248 | + | 0.973132i | \(0.573954\pi\) | |||||||
\(920\) | −385.183 | − | 222.385i | −0.418677 | − | 0.241723i | ||||
\(921\) | −125.910 | − | 86.2746i | −0.136710 | − | 0.0936749i | ||||
\(922\) | −188.557 | + | 108.864i | −0.204509 | + | 0.118073i | ||||
\(923\) | 493.245 | + | 854.325i | 0.534393 | + | 0.925596i | ||||
\(924\) | 224.685 | + | 469.358i | 0.243166 | + | 0.507963i | ||||
\(925\) | 583.059 | + | 336.629i | 0.630334 | + | 0.363924i | ||||
\(926\) | − | 205.212i | − | 0.221611i | ||||||
\(927\) | −1202.76 | − | 968.372i | −1.29748 | − | 1.04463i | ||||
\(928\) | 80.7443 | 0.0870089 | ||||||||
\(929\) | 630.955 | − | 1092.85i | 0.679176 | − | 1.17637i | −0.296053 | − | 0.955171i | \(-0.595671\pi\) |
0.975229 | − | 0.221196i | \(-0.0709961\pi\) | |||||||
\(930\) | −694.407 | − | 53.6658i | −0.746674 | − | 0.0577052i | ||||
\(931\) | −1305.99 | + | 764.905i | −1.40278 | + | 0.821595i | ||||
\(932\) | 123.948 | + | 214.684i | 0.132992 | + | 0.230348i | ||||
\(933\) | −485.515 | − | 37.5220i | −0.520380 | − | 0.0402165i | ||||
\(934\) | −180.684 | − | 104.318i | −0.193452 | − | 0.111690i | ||||
\(935\) | 1516.65 | 1.62209 | ||||||||
\(936\) | −288.740 | + | 358.627i | −0.308483 | + | 0.383149i | ||||
\(937\) | −90.0561 | −0.0961111 | −0.0480555 | − | 0.998845i | \(-0.515302\pi\) | ||||
−0.0480555 | + | 0.998845i | \(0.515302\pi\) | |||||||
\(938\) | 890.406 | − | 1542.23i | 0.949260 | − | 1.64417i | ||||
\(939\) | 30.8204 | + | 64.3824i | 0.0328225 | + | 0.0685649i | ||||
\(940\) | −193.918 | − | 335.876i | −0.206296 | − | 0.357314i | ||||
\(941\) | −1039.21 | + | 599.990i | −1.10437 | + | 0.637609i | −0.937366 | − | 0.348347i | \(-0.886743\pi\) |
−0.167005 | + | 0.985956i | \(0.553410\pi\) | |||||||
\(942\) | 597.597 | + | 409.477i | 0.634391 | + | 0.434689i | ||||
\(943\) | −25.9904 | − | 15.0056i | −0.0275614 | − | 0.0159126i | ||||
\(944\) | 305.392i | 0.323508i | ||||||||
\(945\) | 2799.00 | + | 659.469i | 2.96190 | + | 0.697851i | ||||
\(946\) | 361.930i | 0.382590i | ||||||||
\(947\) | 681.001 | − | 1179.53i | 0.719114 | − | 1.24554i | −0.242237 | − | 0.970217i | \(-0.577881\pi\) |
0.961351 | − | 0.275325i | \(-0.0887856\pi\) | |||||||
\(948\) | −83.2722 | − | 57.0586i | −0.0878398 | − | 0.0601884i | ||||
\(949\) | −1834.16 | + | 1058.95i | −1.93272 | + | 1.11586i | ||||
\(950\) | −857.792 | − | 1464.58i | −0.902939 | − | 1.54166i | ||||
\(951\) | 1235.98 | − | 591.674i | 1.29967 | − | 0.622160i | ||||
\(952\) | −586.933 | − | 338.866i | −0.616526 | − | 0.355951i | ||||
\(953\) | 1125.78i | 1.18130i | 0.806927 | + | 0.590651i | \(0.201129\pi\) | ||||
−0.806927 | + | 0.590651i | \(0.798871\pi\) | |||||||
\(954\) | −98.4314 | − | 15.3055i | −0.103178 | − | 0.0160435i | ||||
\(955\) | 2054.86 | 2.15168 | ||||||||
\(956\) | 40.3662 | − | 69.9164i | 0.0422241 | − | 0.0731343i | ||||
\(957\) | −25.2283 | + | 326.441i | −0.0263619 | + | 0.341108i | ||||
\(958\) | −610.579 | + | 352.518i | −0.637348 | + | 0.367973i | ||||
\(959\) | −281.631 | − | 487.800i | −0.293672 | − | 0.508655i | ||||
\(960\) | 224.683 | + | 17.3642i | 0.234045 | + | 0.0180877i | ||||
\(961\) | −327.670 | + | 567.542i | −0.340968 | + | 0.590574i | ||||
\(962\) | 272.629i | 0.283399i | ||||||||
\(963\) | 1037.34 | − | 401.559i | 1.07720 | − | 0.416987i | ||||
\(964\) | 335.729i | 0.348267i | ||||||||
\(965\) | −2996.50 | − | 1730.03i | −3.10518 | − | 1.79278i | ||||
\(966\) | −726.924 | + | 347.984i | −0.752510 | + | 0.360232i | ||||
\(967\) | −17.3355 | − | 30.0259i | −0.0179270 | − | 0.0310506i | 0.856923 | − | 0.515445i | \(-0.172373\pi\) |
−0.874850 | + | 0.484394i | \(0.839040\pi\) | |||||||
\(968\) | 153.185 | − | 88.4411i | 0.158249 | − | 0.0913648i | ||||
\(969\) | 997.530 | + | 674.416i | 1.02944 | + | 0.695992i | ||||
\(970\) | 775.744 | − | 1343.63i | 0.799736 | − | 1.38518i | ||||
\(971\) | − | 829.722i | − | 0.854503i | −0.904133 | − | 0.427251i | \(-0.859482\pi\) | ||
0.904133 | − | 0.427251i | \(-0.140518\pi\) | |||||||
\(972\) | 383.474 | − | 298.569i | 0.394521 | − | 0.307170i | ||||
\(973\) | −1996.50 | −2.05190 | ||||||||
\(974\) | −311.091 | + | 538.826i | −0.319395 | + | 0.553209i | ||||
\(975\) | −2827.40 | − | 1937.35i | −2.89990 | − | 1.98703i | ||||
\(976\) | −71.1532 | − | 123.241i | −0.0729029 | − | 0.126272i | ||||
\(977\) | 320.514 | − | 185.049i | 0.328059 | − | 0.189405i | −0.326920 | − | 0.945052i | \(-0.606011\pi\) |
0.654979 | + | 0.755647i | \(0.272677\pi\) | |||||||
\(978\) | 227.498 | − | 108.905i | 0.232615 | − | 0.111355i | ||||
\(979\) | 51.0100 | + | 29.4506i | 0.0521042 | + | 0.0300824i | ||||
\(980\) | 1495.93 | 1.52646 | ||||||||
\(981\) | −501.673 | + | 194.199i | −0.511389 | + | 0.197960i | ||||
\(982\) | 296.783i | 0.302223i | ||||||||
\(983\) | 75.4062 | + | 43.5358i | 0.0767103 | + | 0.0442887i | 0.537865 | − | 0.843031i | \(-0.319231\pi\) |
−0.461154 | + | 0.887320i | \(0.652565\pi\) | |||||||
\(984\) | 15.1606 | + | 1.17166i | 0.0154071 | + | 0.00119071i | ||||
\(985\) | 1156.15 | + | 2002.52i | 1.17376 | + | 2.03301i | ||||
\(986\) | −213.214 | − | 369.298i | −0.216242 | − | 0.374541i | ||||
\(987\) | −700.667 | − | 54.1496i | −0.709896 | − | 0.0548629i | ||||
\(988\) | 339.934 | − | 597.352i | 0.344063 | − | 0.604607i | ||||
\(989\) | −560.544 | −0.566779 | ||||||||
\(990\) | −140.403 | + | 902.945i | −0.141821 | + | 0.912066i | ||||
\(991\) | 615.381i | 0.620970i | 0.950578 | + | 0.310485i | \(0.100491\pi\) | ||||
−0.950578 | + | 0.310485i | \(0.899509\pi\) | |||||||
\(992\) | −49.4497 | + | 85.6494i | −0.0498485 | + | 0.0863401i | ||||
\(993\) | 1244.53 | − | 595.765i | 1.25330 | − | 0.599964i | ||||
\(994\) | −437.453 | − | 757.691i | −0.440094 | − | 0.762265i | ||||
\(995\) | −44.8468 | − | 77.6769i | −0.0450721 | − | 0.0780672i | ||||
\(996\) | 466.376 | − | 680.635i | 0.468249 | − | 0.683369i | ||||
\(997\) | 304.693 | − | 527.744i | 0.305610 | − | 0.529332i | −0.671787 | − | 0.740745i | \(-0.734473\pi\) |
0.977397 | + | 0.211412i | \(0.0678062\pi\) | |||||||
\(998\) | − | 590.692i | − | 0.591876i | ||||||
\(999\) | 65.9960 | − | 280.108i | 0.0660621 | − | 0.280389i |
(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 | 342.3.l.a.151.7 | ✓ | 80 | |
3.2 | odd | 2 | 1026.3.l.a.721.25 | 80 | |||
9.4 | even | 3 | inner | 342.3.l.a.265.34 | yes | 80 | |
9.5 | odd | 6 | 1026.3.l.a.37.6 | 80 | |||
19.18 | odd | 2 | inner | 342.3.l.a.151.34 | yes | 80 | |
57.56 | even | 2 | 1026.3.l.a.721.6 | 80 | |||
171.94 | odd | 6 | inner | 342.3.l.a.265.7 | yes | 80 | |
171.113 | even | 6 | 1026.3.l.a.37.25 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
342.3.l.a.151.7 | ✓ | 80 | 1.1 | even | 1 | trivial | |
342.3.l.a.151.34 | yes | 80 | 19.18 | odd | 2 | inner | |
342.3.l.a.265.7 | yes | 80 | 171.94 | odd | 6 | inner | |
342.3.l.a.265.34 | yes | 80 | 9.4 | even | 3 | inner | |
1026.3.l.a.37.6 | 80 | 9.5 | odd | 6 | |||
1026.3.l.a.37.25 | 80 | 171.113 | even | 6 | |||
1026.3.l.a.721.6 | 80 | 57.56 | even | 2 | |||
1026.3.l.a.721.25 | 80 | 3.2 | odd | 2 |