Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,4,Mod(5,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("124.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.e (of order \(3\), 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: | \(7.31623684071\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 29x^{6} - 58x^{5} + 824x^{4} - 1198x^{3} + 1933x^{2} + 129x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(-0.0334318 + 0.0579056i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 124.5 |
Dual form | 124.4.e.c.25.1 |
$q$-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 \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.31198 | + | 5.73652i | −0.637391 | + | 1.10399i | 0.348612 | + | 0.937267i | \(0.386653\pi\) |
−0.986003 | + | 0.166726i | \(0.946680\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.27011 | + | 12.5922i | 0.650258 | + | 1.12628i | 0.983060 | + | 0.183283i | \(0.0586725\pi\) |
−0.332802 | + | 0.942997i | \(0.607994\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.03211 | + | 6.98382i | −0.217713 | + | 0.377091i | −0.954109 | − | 0.299461i | \(-0.903193\pi\) |
0.736395 | + | 0.676552i | \(0.236526\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.43843 | − | 14.6158i | −0.312535 | − | 0.541326i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.2996 | − | 19.5714i | −0.309722 | − | 0.536455i | 0.668579 | − | 0.743641i | \(-0.266903\pi\) |
−0.978302 | + | 0.207186i | \(0.933569\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.70324 | − | 8.14624i | −0.100342 | − | 0.173797i | 0.811484 | − | 0.584375i | \(-0.198660\pi\) |
−0.911825 | + | 0.410578i | \(0.865327\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −96.3138 | −1.65787 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22.1864 | + | 38.4279i | −0.316528 | + | 0.548243i | −0.979761 | − | 0.200170i | \(-0.935851\pi\) |
0.663233 | + | 0.748413i | \(0.269184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13.0694 | + | 22.6368i | −0.157806 | + | 0.273328i | −0.934077 | − | 0.357071i | \(-0.883775\pi\) |
0.776271 | + | 0.630399i | \(0.217109\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −26.7085 | − | 46.2605i | −0.277537 | − | 0.480708i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −205.597 | −1.86391 | −0.931957 | − | 0.362568i | \(-0.881900\pi\) | ||||
−0.931957 | + | 0.362568i | \(0.881900\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −43.2089 | + | 74.8399i | −0.345671 | + | 0.598720i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −67.0553 | −0.477955 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 147.971 | 0.947502 | 0.473751 | − | 0.880659i | \(-0.342900\pi\) | ||||
0.473751 | + | 0.880659i | \(0.342900\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 170.223 | − | 28.5490i | 0.986226 | − | 0.165405i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 149.696 | 0.789657 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −117.255 | −0.566280 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.4333 | − | 30.1954i | 0.0774601 | − | 0.134165i | −0.824693 | − | 0.565580i | \(-0.808652\pi\) |
0.902153 | + | 0.431415i | \(0.141986\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 62.3081 | 0.255828 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 175.754 | + | 304.415i | 0.669468 | + | 1.15955i | 0.978053 | + | 0.208356i | \(0.0668114\pi\) |
−0.308584 | + | 0.951197i | \(0.599855\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22.1749 | − | 38.4081i | 0.0786428 | − | 0.136213i | −0.824022 | − | 0.566558i | \(-0.808275\pi\) |
0.902665 | + | 0.430345i | \(0.141608\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 122.697 | − | 212.517i | 0.406456 | − | 0.704003i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 174.136 | 0.540434 | 0.270217 | − | 0.962799i | \(-0.412905\pi\) | ||||
0.270217 | + | 0.962799i | \(0.412905\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 138.984 | + | 240.728i | 0.405202 | + | 0.701830i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −146.962 | − | 254.545i | −0.403505 | − | 0.698890i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −44.8332 | − | 77.6534i | −0.116195 | − | 0.201255i | 0.802062 | − | 0.597241i | \(-0.203736\pi\) |
−0.918257 | + | 0.395986i | \(0.870403\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 164.298 | − | 284.573i | 0.402799 | − | 0.697668i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −86.5709 | − | 149.945i | −0.201168 | − | 0.348434i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −232.918 | + | 403.425i | −0.513954 | + | 0.890194i | 0.485915 | + | 0.874006i | \(0.338486\pi\) |
−0.999869 | + | 0.0161882i | \(0.994847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 156.265 | 0.327994 | 0.163997 | − | 0.986461i | \(-0.447561\pi\) | ||||
0.163997 | + | 0.986461i | \(0.447561\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 136.099 | 0.272172 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 68.3860 | − | 118.448i | 0.130496 | − | 0.226026i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −244.979 | − | 424.316i | −0.446701 | − | 0.773709i | 0.551468 | − | 0.834196i | \(-0.314068\pi\) |
−0.998169 | + | 0.0604873i | \(0.980735\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 680.935 | − | 1179.41i | 1.18804 | − | 2.05775i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 467.320 | + | 809.423i | 0.781137 | + | 1.35297i | 0.931280 | + | 0.364305i | \(0.118693\pi\) |
−0.150143 | + | 0.988664i | \(0.547973\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 149.091 | + | 258.233i | 0.239038 | + | 0.414026i | 0.960439 | − | 0.278492i | \(-0.0898345\pi\) |
−0.721400 | + | 0.692518i | \(0.756501\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −286.214 | − | 495.737i | −0.440655 | − | 0.763237i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 182.244 | 0.269723 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −522.561 | + | 905.102i | −0.744212 | + | 1.28901i | 0.206351 | + | 0.978478i | \(0.433841\pi\) |
−0.950562 | + | 0.310534i | \(0.899492\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 449.923 | − | 779.290i | 0.617179 | − | 1.06899i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 285.827 | + | 495.067i | 0.377995 | + | 0.654707i | 0.990770 | − | 0.135550i | \(-0.0432803\pi\) |
−0.612775 | + | 0.790257i | \(0.709947\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −645.189 | −0.823300 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −490.078 | + | 848.839i | −0.603929 | + | 1.04604i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 749.227 | 0.892336 | 0.446168 | − | 0.894949i | \(-0.352788\pi\) | ||||
0.446168 | + | 0.894949i | \(0.352788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 75.8558 | 0.0873830 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −400.004 | + | 1071.04i | −0.446005 | + | 1.19421i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −380.062 | −0.410459 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1215.61 | −1.27243 | −0.636217 | − | 0.771510i | \(-0.719502\pi\) | ||||
−0.636217 | + | 0.771510i | \(0.719502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −190.701 | + | 330.304i | −0.193598 | + | 0.335321i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 597.214 | 0.588367 | 0.294183 | − | 0.955749i | \(-0.404952\pi\) | ||||
0.294183 | + | 0.955749i | \(0.404952\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 181.986 | + | 315.209i | 0.174093 | + | 0.301538i | 0.939847 | − | 0.341595i | \(-0.110967\pi\) |
−0.765754 | + | 0.643134i | \(0.777634\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 388.348 | − | 672.638i | 0.360942 | − | 0.625169i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −497.071 | + | 860.953i | −0.449100 | + | 0.777864i | −0.998328 | − | 0.0578088i | \(-0.981589\pi\) |
0.549228 | + | 0.835673i | \(0.314922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2004.47 | −1.76141 | −0.880706 | − | 0.473664i | \(-0.842931\pi\) | ||||
−0.880706 | + | 0.473664i | \(0.842931\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 115.478 | + | 200.013i | 0.0987447 | + | 0.171031i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −72.7745 | − | 126.049i | −0.0605845 | − | 0.104935i | 0.834142 | − | 0.551549i | \(-0.185963\pi\) |
−0.894727 | + | 0.446614i | \(0.852630\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1494.72 | − | 2588.92i | −1.21203 | − | 2.09929i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −79.3759 | + | 137.483i | −0.0627205 | + | 0.108635i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −178.916 | − | 309.891i | −0.137825 | − | 0.238720i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 410.140 | − | 710.383i | 0.308144 | − | 0.533721i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2328.38 | −1.70685 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 560.995 | 0.401415 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −40.9997 | + | 71.0136i | −0.0286467 | + | 0.0496176i | −0.879993 | − | 0.474986i | \(-0.842453\pi\) |
0.851347 | + | 0.524604i | \(0.175786\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 146.886 | + | 254.414i | 0.100252 | + | 0.173642i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1294.29 | − | 2241.78i | 0.863226 | − | 1.49515i | −0.00557139 | − | 0.999984i | \(-0.501773\pi\) |
0.868798 | − | 0.495167i | \(-0.164893\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −105.394 | − | 182.548i | −0.0687130 | − | 0.119014i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −487.499 | − | 844.373i | −0.310794 | − | 0.538311i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1070.86 | + | 1854.79i | 0.667811 | + | 1.15668i | 0.978515 | + | 0.206175i | \(0.0661017\pi\) |
−0.310704 | + | 0.950507i | \(0.600565\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −254.389 | −0.155230 | −0.0776150 | − | 0.996983i | \(-0.524730\pi\) | ||||
−0.0776150 | + | 0.996983i | \(0.524730\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −576.737 | + | 998.937i | −0.344468 | + | 0.596636i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −106.289 | + | 184.098i | −0.0621562 | + | 0.107658i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1075.77 | + | 1863.28i | 0.616121 | + | 1.06715i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1841.25 | −1.03309 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1240.05 | + | 2147.83i | −0.681805 | + | 1.18092i | 0.292625 | + | 0.956227i | \(0.405471\pi\) |
−0.974430 | + | 0.224693i | \(0.927862\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2779.12 | 1.49776 | 0.748880 | − | 0.662706i | \(-0.230592\pi\) | ||||
0.748880 | + | 0.662706i | \(0.230592\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 748.872 | 0.395704 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1597.04 | + | 1935.93i | 0.827593 | + | 1.00321i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 101.582 | 0.0516377 | 0.0258188 | − | 0.999667i | \(-0.491781\pi\) | ||||
0.0258188 | + | 0.999667i | \(0.491781\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 593.947 | 0.296246 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 828.991 | − | 1435.86i | 0.405799 | − | 0.702865i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2303.54 | 1.10692 | 0.553458 | − | 0.832877i | \(-0.313308\pi\) | ||||
0.553458 | + | 0.832877i | \(0.313308\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1088.30 | + | 1885.00i | 0.513481 | + | 0.889375i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1292.05 | − | 2237.90i | 0.598695 | − | 1.03697i | −0.394319 | − | 0.918974i | \(-0.629019\pi\) |
0.993014 | − | 0.117997i | \(-0.0376472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1054.26 | − | 1826.03i | 0.479863 | − | 0.831147i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 441.140 | 0.197279 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1547.93 | + | 2681.09i | 0.680270 | + | 1.17826i | 0.974898 | + | 0.222651i | \(0.0714709\pi\) |
−0.294628 | + | 0.955612i | \(0.595196\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −348.446 | − | 603.526i | −0.150514 | − | 0.260699i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1542.84 | − | 2672.27i | −0.655179 | − | 1.13480i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 621.702 | − | 1076.82i | 0.259599 | − | 0.449638i | −0.706536 | − | 0.707677i | \(-0.749743\pi\) |
0.966134 | + | 0.258039i | \(0.0830764\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2067.19 | − | 3580.48i | −0.848911 | − | 1.47036i | −0.882181 | − | 0.470911i | \(-0.843925\pi\) |
0.0332697 | − | 0.999446i | \(-0.489408\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −517.545 | + | 896.414i | −0.209060 | + | 0.362103i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 506.969 | 0.201476 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1002.78 | 0.392144 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 270.374 | − | 468.302i | 0.104057 | − | 0.180233i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1679.13 | + | 2908.34i | 0.636113 | + | 1.10178i | 0.986278 | + | 0.165092i | \(0.0527922\pi\) |
−0.350165 | + | 0.936688i | \(0.613874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1063.13 | − | 1841.40i | 0.396508 | − | 0.686773i | −0.596784 | − | 0.802402i | \(-0.703555\pi\) |
0.993292 | + | 0.115629i | \(0.0368885\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 452.986 | + | 784.596i | 0.166354 | + | 0.288134i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2262.95 | − | 3919.54i | −0.818418 | − | 1.41754i | −0.906847 | − | 0.421460i | \(-0.861518\pi\) |
0.0884289 | − | 0.996082i | \(-0.471815\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2314.66 | − | 4009.11i | −0.824533 | − | 1.42813i | −0.902276 | − | 0.431160i | \(-0.858105\pi\) |
0.0777425 | − | 0.996973i | \(-0.475229\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3245.46 | 1.13889 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −596.636 | + | 1033.40i | −0.206284 | + | 0.357294i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2555.50 | + | 4426.26i | −0.870654 | + | 1.50802i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1734.92 | + | 3004.97i | 0.582538 | + | 1.00898i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 590.712 | 0.195504 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1624.65 | − | 2813.98i | 0.530074 | − | 0.918115i | −0.469311 | − | 0.883033i | \(-0.655498\pi\) |
0.999384 | − | 0.0350817i | \(-0.0111691\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6191.03 | −1.99156 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 644.856 | 0.204553 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −486.978 | + | 1303.92i | −0.152342 | + | 0.407907i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1975.15 | −0.609443 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 417.391 | 0.127044 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1385.70 | − | 2400.10i | 0.416113 | − | 0.720729i | −0.579431 | − | 0.815021i | \(-0.696725\pi\) |
0.995545 | + | 0.0942919i | \(0.0300587\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1458.46 | 0.432136 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2217.13 | + | 3840.18i | 0.648264 | + | 1.12283i | 0.983537 | + | 0.180705i | \(0.0578380\pi\) |
−0.335273 | + | 0.942121i | \(0.608829\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1173.98 | + | 2033.39i | −0.338772 | + | 0.586770i | −0.984202 | − | 0.177049i | \(-0.943345\pi\) |
0.645430 | + | 0.763819i | \(0.276678\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −603.590 | + | 1045.45i | −0.171919 | + | 0.297772i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5784.03 | −1.62629 | −0.813143 | − | 0.582064i | \(-0.802245\pi\) | ||||
−0.813143 | + | 0.582064i | \(0.802245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1265.99 | + | 2192.76i | 0.351422 | + | 0.608680i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3461.42 | − | 5995.36i | −0.948708 | − | 1.64321i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1012.16 | + | 1753.11i | 0.273937 | + | 0.474473i | 0.969866 | − | 0.243637i | \(-0.0783407\pi\) |
−0.695929 | + | 0.718110i | \(0.745007\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1111.44 | − | 1925.07i | 0.297071 | − | 0.514542i | −0.678394 | − | 0.734699i | \(-0.737324\pi\) |
0.975464 | + | 0.220157i | \(0.0706569\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2075.03 | + | 3594.06i | 0.547791 | + | 0.948802i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2020.86 | + | 3500.23i | −0.526971 | + | 0.912741i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 245.873 | 0.0633382 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3786.61 | −0.963723 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1428.08 | − | 2473.50i | 0.359121 | − | 0.622015i | −0.628693 | − | 0.777653i | \(-0.716410\pi\) |
0.987814 | + | 0.155638i | \(0.0497433\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2323.16 | + | 4023.83i | 0.577296 | + | 0.999906i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2136.85 | − | 3701.14i | 0.524764 | − | 0.908918i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 95.4369 | + | 165.302i | 0.0231642 | + | 0.0401215i | 0.877375 | − | 0.479805i | \(-0.159293\pi\) |
−0.854211 | + | 0.519927i | \(0.825959\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 140.586 | + | 243.502i | 0.0337282 | + | 0.0584190i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1248.64 | − | 2162.72i | −0.296127 | − | 0.512907i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 240.843 | 0.0564678 | 0.0282339 | − | 0.999601i | \(-0.491012\pi\) | ||||
0.0282339 | + | 0.999601i | \(0.491012\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 651.885 | − | 1129.10i | 0.151113 | − | 0.261735i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2481.43 | + | 4297.95i | −0.568767 | + | 0.985133i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 964.105 | + | 1669.88i | 0.218522 | + | 0.378492i | 0.954356 | − | 0.298670i | \(-0.0965430\pi\) |
−0.735834 | + | 0.677162i | \(0.763210\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6571.59 | −1.47305 | −0.736523 | − | 0.676412i | \(-0.763534\pi\) | ||||
−0.736523 | + | 0.676412i | \(0.763534\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −251.233 | + | 435.148i | −0.0556971 | + | 0.0964703i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1952.97 | 0.428248 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8626.52 | −1.87118 | −0.935591 | − | 0.353086i | \(-0.885132\pi\) | ||||
−0.935591 | + | 0.353086i | \(0.885132\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1853.68 | − | 2247.04i | −0.397768 | − | 0.482174i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3100.09 | 0.658135 | 0.329067 | − | 0.944306i | \(-0.393266\pi\) | ||||
0.329067 | + | 0.944306i | \(0.393266\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 720.027 | 0.151241 | 0.0756204 | − | 0.997137i | \(-0.475906\pi\) | ||||
0.0756204 | + | 0.997137i | \(0.475906\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1258.76 | − | 2180.24i | 0.261623 | − | 0.453144i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2834.64 | −0.583009 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1472.03 | + | 2549.63i | 0.299620 | + | 0.518956i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4026.06 | − | 6973.35i | 0.811038 | − | 1.40476i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1450.44 | + | 2512.24i | −0.289201 | + | 0.500910i | −0.973619 | − | 0.228179i | \(-0.926723\pi\) |
0.684418 | + | 0.729089i | \(0.260056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6773.34 | −1.33681 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 757.695 | + | 1312.37i | 0.148033 | + | 0.256401i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 966.973 | + | 1674.85i | 0.187028 | + | 0.323943i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 178.823 | + | 309.731i | 0.0342432 | + | 0.0593110i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1977.96 | + | 3425.93i | −0.375020 | + | 0.649553i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1136.06 | + | 1967.71i | 0.213281 | + | 0.369413i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1909.53 | − | 3307.41i | 0.354993 | − | 0.614865i | −0.632124 | − | 0.774867i | \(-0.717817\pi\) |
0.987117 | + | 0.160002i | \(0.0511501\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2410.94 | −0.443862 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2936.50 | −0.535413 | −0.267707 | − | 0.963500i | \(-0.586266\pi\) | ||||
−0.267707 | + | 0.963500i | \(0.586266\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2513.05 | + | 4352.72i | −0.453820 | + | 0.786040i | −0.998620 | − | 0.0525265i | \(-0.983273\pi\) |
0.544799 | + | 0.838567i | \(0.316606\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 989.452 | + | 1713.78i | 0.176982 | + | 0.306542i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −471.163 | + | 816.078i | −0.0834799 | + | 0.144591i | −0.904742 | − | 0.425959i | \(-0.859937\pi\) |
0.821263 | + | 0.570550i | \(0.193270\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1672.01 | − | 2896.01i | −0.293463 | − | 0.508292i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3292.58 | − | 5702.92i | −0.572505 | − | 0.991607i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −579.923 | − | 1004.46i | −0.0999002 | − | 0.173032i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 812.886 | 0.138741 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6638.78 | − | 11498.7i | 1.12271 | − | 1.94459i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −702.137 | + | 1216.14i | −0.117660 | + | 0.203793i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2540.45 | + | 4400.19i | 0.421860 | + | 0.730683i | 0.996121 | − | 0.0879889i | \(-0.0280440\pi\) |
−0.574261 | + | 0.818672i | \(0.694711\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −588.440 | −0.0968358 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3562.05 | − | 6169.65i | 0.580942 | − | 1.00622i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8615.39 | 1.39261 | 0.696306 | − | 0.717745i | \(-0.254826\pi\) | ||||
0.696306 | + | 0.717745i | \(0.254826\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 964.111 | 0.154464 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2482.19 | − | 3008.92i | −0.394189 | − | 0.477836i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5007.62 | −0.788298 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19801.9 | 3.09014 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5082.62 | − | 8803.36i | 0.786310 | − | 1.36193i | −0.141904 | − | 0.989880i | \(-0.545322\pi\) |
0.928213 | − | 0.372048i | \(-0.121344\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9573.66 | 1.46838 | 0.734192 | − | 0.678941i | \(-0.237561\pi\) | ||||
0.734192 | + | 0.678941i | \(0.237561\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 315.377 | + | 546.249i | 0.0479589 | + | 0.0830672i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1408.79 | − | 2440.10i | 0.212415 | − | 0.367913i | −0.740055 | − | 0.672546i | \(-0.765201\pi\) |
0.952470 | + | 0.304633i | \(0.0985340\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6794.94 | + | 11769.2i | −1.01588 | + | 1.75956i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2370.26 | 0.351393 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2690.56 | + | 4660.18i | 0.395549 | + | 0.685111i | 0.993171 | − | 0.116667i | \(-0.0372210\pi\) |
−0.597622 | + | 0.801778i | \(0.703888\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3087.88 | + | 5348.37i | 0.450194 | + | 0.779760i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2716.75 | + | 4705.55i | 0.392816 | + | 0.680378i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2167.82 | + | 3754.77i | −0.310873 | + | 0.538448i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 569.058 | + | 985.638i | 0.0809390 | + | 0.140190i | 0.903654 | − | 0.428264i | \(-0.140875\pi\) |
−0.822715 | + | 0.568455i | \(0.807541\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2966.18 | − | 5137.58i | 0.418464 | − | 0.724801i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 723.090 | 0.101189 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6628.38 | −0.920119 | −0.460060 | − | 0.887888i | \(-0.652172\pi\) | ||||
−0.460060 | + | 0.887888i | \(0.652172\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1858.00 | + | 3218.16i | −0.255858 | + | 0.443160i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −695.943 | − | 1205.41i | −0.0950740 | − | 0.164673i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −767.668 | + | 1329.64i | −0.104043 | + | 0.180209i | −0.913347 | − | 0.407182i | \(-0.866511\pi\) |
0.809304 | + | 0.587391i | \(0.199845\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −271.580 | − | 470.391i | −0.0365183 | − | 0.0632516i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4413.24 | + | 7643.95i | 0.588788 | + | 1.01981i | 0.994391 | + | 0.105762i | \(0.0337281\pi\) |
−0.405603 | + | 0.914049i | \(0.632939\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1324.94 | + | 2294.86i | 0.175390 | + | 0.303784i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −748.486 | −0.0983144 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6508.83 | − | 11273.6i | 0.848357 | − | 1.46940i | −0.0343162 | − | 0.999411i | \(-0.510925\pi\) |
0.882673 | − | 0.469987i | \(-0.155741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4561.46 | − | 7900.68i | 0.589982 | − | 1.02188i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8573.33 | + | 14849.4i | 1.10043 | + | 1.90599i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15196.3 | −1.93572 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 444.201 | − | 769.379i | 0.0561557 | − | 0.0972646i | −0.836581 | − | 0.547843i | \(-0.815449\pi\) |
0.892737 | + | 0.450579i | \(0.148782\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1396.25 | 0.175188 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8784.47 | −1.09395 | −0.546977 | − | 0.837148i | \(-0.684221\pi\) | ||||
−0.546977 | + | 0.837148i | \(0.684221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1033.17 | − | 1252.41i | −0.127707 | − | 0.154806i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13084.0 | 1.60530 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −787.956 | −0.0959645 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7158.51 | − | 12398.9i | 0.865442 | − | 1.49899i | −0.00116619 | − | 0.999999i | \(-0.500371\pi\) |
0.866608 | − | 0.498990i | \(-0.166295\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14186.7 | −1.70263 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1878.30 | − | 3253.31i | −0.223789 | − | 0.387615i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4155.98 | + | 7198.38i | −0.491589 | + | 0.851456i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 842.530 | − | 1459.31i | 0.0989422 | − | 0.171373i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 710.070 | 0.0827904 | 0.0413952 | − | 0.999143i | \(-0.486820\pi\) | ||||
0.0413952 | + | 0.999143i | \(0.486820\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5497.80 | − | 9522.48i | −0.636453 | − | 1.10237i | −0.986205 | − | 0.165526i | \(-0.947068\pi\) |
0.349753 | − | 0.936842i | \(-0.386266\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1469.44 | − | 2545.14i | −0.168904 | − | 0.292551i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1917.29 | − | 3320.85i | −0.218829 | − | 0.379023i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −630.076 | + | 1091.32i | −0.0714087 | + | 0.123683i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −704.054 | − | 1219.46i | −0.0792356 | − | 0.137240i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1401.22 | + | 2426.98i | −0.156600 | + | 0.271238i | −0.933640 | − | 0.358212i | \(-0.883387\pi\) |
0.777041 | + | 0.629450i | \(0.216720\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7065.63 | −0.784186 | −0.392093 | − | 0.919926i | \(-0.628249\pi\) | ||||
−0.392093 | + | 0.919926i | \(0.628249\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14251.7 | −1.57084 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2687.03 | − | 4654.07i | 0.294137 | − | 0.509461i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1193.21 | + | 2066.70i | 0.129724 | + | 0.224688i | 0.923570 | − | 0.383431i | \(-0.125258\pi\) |
−0.793846 | + | 0.608119i | \(0.791924\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2345.62 | − | 4062.73i | 0.253279 | − | 0.438692i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1971.10 | + | 3414.05i | 0.211399 | + | 0.366154i | 0.952153 | − | 0.305623i | \(-0.0988646\pi\) |
−0.740753 | + | 0.671777i | \(0.765531\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5446.96 | + | 9434.41i | 0.580249 | + | 1.00502i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8214.05 | − | 14227.1i | −0.869152 | − | 1.50542i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9890.55 | −1.03956 | −0.519782 | − | 0.854299i | \(-0.673987\pi\) | ||||
−0.519782 | + | 0.854299i | \(0.673987\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3971.89 | − | 6879.52i | 0.414699 | − | 0.718279i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9204.40 | + | 15942.5i | −0.954659 | + | 1.65352i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 551.480 | + | 955.191i | 0.0568215 | + | 0.0984177i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18623.9 | 1.90633 | 0.953163 | − | 0.302458i | \(-0.0978073\pi\) | ||||
0.953163 | + | 0.302458i | \(0.0978073\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1487.71 | − | 2576.79i | 0.151286 | − | 0.262036i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16497.4 | −1.66673 | −0.833363 | − | 0.552726i | \(-0.813588\pi\) | ||||
−0.833363 | + | 0.552726i | \(0.813588\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5453.00 | 0.547349 | 0.273674 | − | 0.961822i | \(-0.411761\pi\) | ||||
0.273674 | + | 0.961822i | \(0.411761\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16394.8 | + | 2749.66i | −1.63504 | + | 0.274221i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9875.95 | 0.978596 | 0.489298 | − | 0.872117i | \(-0.337253\pi\) | ||||
0.489298 | + | 0.872117i | \(0.337253\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3951.13 | 0.389011 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −336.437 | + | 582.727i | −0.0329134 | + | 0.0570077i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1002.27 | −0.0974298 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1129.42 | − | 1956.22i | −0.109098 | − | 0.188963i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −756.644 | + | 1310.55i | −0.0726297 | + | 0.125798i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4012.39 | + | 6949.67i | −0.382737 | + | 0.662919i | −0.991452 | − | 0.130469i | \(-0.958352\pi\) |
0.608716 | + | 0.793388i | \(0.291685\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −327.972 | −0.0310899 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5491.21 | + | 9511.05i | 0.517306 | + | 0.896000i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8837.58 | − | 15307.1i | −0.827410 | − | 1.43312i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9581.32 | + | 16595.3i | 0.891522 | + | 1.54416i | 0.838051 | + | 0.545592i | \(0.183695\pi\) |
0.0534712 | + | 0.998569i | \(0.482971\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7629.28 | + | 13214.3i | −0.705538 | + | 1.22203i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9062.63 | − | 15696.9i | −0.832975 | − | 1.44275i | −0.895669 | − | 0.444722i | \(-0.853302\pi\) |
0.0626937 | − | 0.998033i | \(-0.480031\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3282.94 | + | 5686.22i | −0.299911 | + | 0.519461i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5545.67 | −0.503554 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7537.15 | −0.680256 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2476.37 | − | 4289.19i | 0.222159 | − | 0.384791i | −0.733304 | − | 0.679901i | \(-0.762023\pi\) |
0.955463 | + | 0.295110i | \(0.0953562\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8558.51 | + | 14823.8i | 0.763206 | + | 1.32191i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4865.54 | + | 8427.36i | −0.431300 | + | 0.747033i | −0.996986 | − | 0.0775880i | \(-0.975278\pi\) |
0.565686 | + | 0.824621i | \(0.308611\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4341.81 | + | 7520.24i | 0.382590 | + | 0.662666i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6983.37 | + | 12095.6i | 0.611721 | + | 1.05953i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1189.71 | + | 2060.63i | 0.103601 | + | 0.179442i | 0.913166 | − | 0.407588i | \(-0.133630\pi\) |
−0.809565 | + | 0.587031i | \(0.800297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2404.61 | −0.208167 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 876.369 | − | 1517.92i | 0.0754243 | − | 0.130639i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2646.11 | + | 4583.20i | −0.226411 | + | 0.392156i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1967.67 | − | 3408.10i | −0.167385 | − | 0.289919i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20506.8 | −1.73439 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10280.5 | − | 17806.3i | 0.864482 | − | 1.49733i | −0.00307815 | − | 0.999995i | \(-0.500980\pi\) |
0.867560 | − | 0.497332i | \(-0.165687\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 563.267 | 0.0470936 | 0.0235468 | − | 0.999723i | \(-0.492504\pi\) | ||||
0.0235468 | + | 0.999723i | \(0.492504\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4616.18 | 0.383746 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2679.55 | + | 7174.72i | −0.221486 | + | 0.593047i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30103.3 | 2.47418 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7861.83 | 0.642513 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1653.23 | − | 2863.47i | 0.134351 | − | 0.232703i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14455.0 | −1.16812 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4118.13 | + | 7132.80i | 0.330932 | + | 0.573190i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3140.92 | − | 5440.24i | 0.251000 | − | 0.434745i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1301.29 | + | 2253.90i | −0.103414 | + | 0.179118i | −0.913089 | − | 0.407760i | \(-0.866310\pi\) |
0.809675 | + | 0.586878i | \(0.199643\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27386.0 | 2.16435 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14572.7 | − | 25240.7i | −1.14537 | − | 1.98384i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11531.9 | − | 19973.8i | −0.901401 | − | 1.56127i | −0.825677 | − | 0.564144i | \(-0.809206\pi\) |
−0.0757244 | − | 0.997129i | \(-0.524127\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1318.63 | − | 2283.93i | −0.102509 | − | 0.177551i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1933.89 | + | 3349.59i | −0.149522 | + | 0.258979i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4214.05 | − | 7298.94i | −0.324050 | − | 0.561271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1679.07 | + | 2908.24i | −0.128419 | + | 0.222428i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1134.19 | 0.0862788 | 0.0431394 | − | 0.999069i | \(-0.486264\pi\) | ||||
0.0431394 | + | 0.999069i | \(0.486264\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −417.175 | −0.0315646 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3321.20 | + | 5752.49i | −0.249949 | + | 0.432924i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4721.71 | − | 8178.25i | −0.353457 | − | 0.612206i | 0.633395 | − | 0.773828i | \(-0.281661\pi\) |
−0.986853 | + | 0.161622i | \(0.948327\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1058.16 | − | 1832.78i | 0.0787911 | − | 0.136470i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3628.28 | + | 6284.37i | 0.268736 | + | 0.465465i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3430.12 | − | 5941.15i | −0.252721 | − | 0.437726i | 0.711553 | − | 0.702632i | \(-0.247992\pi\) |
−0.964274 | + | 0.264907i | \(0.914659\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6211.21 | − | 10758.1i | −0.455221 | − | 0.788465i | 0.543480 | − | 0.839422i | \(-0.317106\pi\) |
−0.998701 | + | 0.0509568i | \(0.983773\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22245.0 | −1.62181 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8883.63 | − | 15386.9i | 0.644301 | − | 1.11596i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11258.7 | − | 19500.6i | 0.812313 | − | 1.40697i | −0.0989284 | − | 0.995095i | \(-0.531541\pi\) |
0.911241 | − | 0.411873i | \(-0.135125\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7042.16 | + | 12197.4i | 0.505462 | + | 0.875485i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4609.94 | −0.329178 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1013.19 | + | 1754.90i | −0.0719762 | + | 0.124666i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2308.28 | −0.163138 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14384.0 | 1.01140 | 0.505698 | − | 0.862711i | \(-0.331235\pi\) | ||||
0.505698 | + | 0.862711i | \(0.331235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1578.45 | + | 4226.43i | −0.110423 | + | 0.295665i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29979.4 | 2.08661 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2115.81 | −0.146520 | −0.0732598 | − | 0.997313i | \(-0.523340\pi\) | ||||
−0.0732598 | + | 0.997313i | \(0.523340\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2601.47 | − | 4505.88i | 0.179244 | − | 0.310459i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30664.5 | 2.10220 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7643.57 | + | 13239.1i | 0.521382 | + | 0.903061i | 0.999691 | + | 0.0248686i | \(0.00791675\pi\) |
−0.478308 | + | 0.878192i | \(0.658750\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5175.74 | + | 8964.65i | −0.351286 | + | 0.608446i | −0.986475 | − | 0.163911i | \(-0.947589\pi\) |
0.635189 | + | 0.772357i | \(0.280922\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4134.48 | + | 7161.13i | −0.279219 | + | 0.483621i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11927.0 | 0.801492 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1517.64 | + | 2628.63i | 0.101481 | + | 0.175771i | 0.912295 | − | 0.409533i | \(-0.134309\pi\) |
−0.810814 | + | 0.585304i | \(0.800975\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3952.09 | − | 6845.23i | −0.262967 | − | 0.455472i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −819.005 | − | 1418.56i | −0.0542281 | − | 0.0939259i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14234.5 | + | 24654.9i | −0.937892 | + | 1.62448i | −0.168498 | + | 0.985702i | \(0.553892\pi\) |
−0.769394 | + | 0.638774i | \(0.779442\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16927.6 | − | 29319.4i | −1.10989 | − | 1.92239i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 470.158 | − | 814.338i | 0.0306773 | − | 0.0531346i | −0.850279 | − | 0.526332i | \(-0.823567\pi\) |
0.880956 | + | 0.473197i | \(0.156900\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25961.5 | −1.68575 | −0.842876 | − | 0.538108i | \(-0.819139\pi\) | ||||
−0.842876 | + | 0.538108i | \(0.819139\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13786.4 | 0.890868 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3020.96 | + | 5232.46i | −0.194274 | + | 0.336492i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9479.60 | + | 16419.1i | 0.606694 | + | 1.05083i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1956.43 | + | 3388.63i | −0.124613 | + | 0.215836i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 773.564 | + | 1339.85i | 0.0490366 | + | 0.0849339i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9698.27 | + | 16797.9i | 0.611857 | + | 1.05977i | 0.990927 | + | 0.134400i | \(0.0429107\pi\) |
−0.379070 | + | 0.925368i | \(0.623756\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10761.6 | + | 18639.7i | 0.675729 | + | 1.17040i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1192.29 | −0.0745111 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1307.35 | − | 2264.40i | 0.0813173 | − | 0.140846i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7886.90 | − | 13660.5i | 0.488265 | − | 0.845699i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −681.241 | − | 1179.94i | −0.0419773 | − | 0.0727067i | 0.844273 | − | 0.535913i | \(-0.180032\pi\) |
−0.886251 | + | 0.463206i | \(0.846699\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11817.0 | 0.724752 | 0.362376 | − | 0.932032i | \(-0.381966\pi\) | ||||
0.362376 | + | 0.932032i | \(0.381966\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2135.75 | + | 3699.23i | −0.130380 | + | 0.225825i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9822.78 | 0.596868 | 0.298434 | − | 0.954430i | \(-0.403536\pi\) | ||||
0.298434 | + | 0.954430i | \(0.403536\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10527.5 | 0.636732 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5867.11 | − | 7112.12i | −0.353226 | − | 0.428181i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30236.8 | 1.81203 | 0.906016 | − | 0.423243i | \(-0.139108\pi\) | ||||
0.906016 | + | 0.423243i | \(0.139108\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37638.5 | 2.24528 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2516.19 | − | 4358.17i | 0.149415 | − | 0.258795i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4483.62 | −0.265034 | −0.132517 | − | 0.991181i | \(-0.542306\pi\) | ||||
−0.132517 | + | 0.991181i | \(0.542306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5593.01 | − | 9687.37i | −0.329112 | − | 0.570038i | 0.653224 | − | 0.757164i | \(-0.273416\pi\) |
−0.982336 | + | 0.187127i | \(0.940083\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1382.39 | + | 2394.37i | −0.0809767 | + | 0.140256i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1532.45 | − | 2654.29i | 0.0893624 | − | 0.154780i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30422.5 | −1.76606 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9178.81 | + | 15898.2i | 0.530453 | + | 0.918772i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1765.72 | − | 3058.32i | −0.101587 | − | 0.175954i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2325.43 | − | 4027.77i | −0.133193 | − | 0.230697i | 0.791713 | − | 0.610894i | \(-0.209190\pi\) |
−0.924906 | + | 0.380197i | \(0.875856\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2897.38 | − | 5018.41i | 0.165215 | − | 0.286161i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8173.67 | − | 14157.2i | −0.464017 | − | 0.803702i | 0.535139 | − | 0.844764i | \(-0.320259\pi\) |
−0.999157 | + | 0.0410621i | \(0.986926\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4901.46 | − | 8489.57i | 0.277026 | − | 0.479823i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29372.3 | −1.65279 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6320.40 | 0.354090 | 0.177045 | − | 0.984203i | \(-0.443346\pi\) | ||||
0.177045 | + | 0.984203i | \(0.443346\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15570.6 | + | 26969.0i | −0.868498 | + | 1.50428i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7776.39 | − | 13469.1i | −0.431860 | − | 0.748004i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −421.722 | + | 730.445i | −0.0233184 | + | 0.0403886i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3839.67 | + | 6650.51i | 0.211386 | + | 0.366132i | 0.952149 | − | 0.305635i | \(-0.0988688\pi\) |
−0.740762 | + | 0.671767i | \(0.765535\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1537.86 | − | 2663.65i | −0.0842977 | − | 0.146008i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1849.43 | − | 3203.31i | −0.100940 | − | 0.174832i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15597.4 | −0.847623 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19156.6 | − | 33180.2i | 1.03658 | − | 1.79541i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6090.54 | − | 10549.1i | 0.328155 | − | 0.568381i | −0.653991 | − | 0.756502i | \(-0.726907\pi\) |
0.982146 | + | 0.188121i | \(0.0602399\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 455.685 | + | 789.270i | 0.0244473 | + | 0.0423440i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16771.7 | −0.895972 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2408.03 | + | 4170.84i | −0.128095 | + | 0.221868i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1886.15 | 0.0999094 | 0.0499547 | − | 0.998751i | \(-0.484092\pi\) | ||||
0.0499547 | + | 0.998751i | \(0.484092\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17638.4 | 0.930367 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −34997.5 | + | 5869.61i | −1.83824 | + | 0.308301i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3090.93 | −0.161670 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13409.0 | −0.698420 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9816.14 | + | 17002.1i | −0.509152 | + | 0.881877i | 0.490792 | + | 0.871277i | \(0.336708\pi\) |
−0.999944 | + | 0.0106002i | \(0.996626\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2935.15 | −0.151610 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7362.13 | + | 12751.6i | 0.378701 | + | 0.655929i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6393.67 | + | 11074.2i | −0.327524 | + | 0.567288i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15442.3 | + | 26746.9i | −0.787790 | + | 1.36449i | 0.139528 | + | 0.990218i | \(0.455441\pi\) |
−0.927318 | + | 0.374274i | \(0.877892\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3193.96 | −0.162270 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 983.961 | + | 1704.27i | 0.0497854 | + | 0.0862308i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7406.60 | − | 12828.6i | −0.373218 | − | 0.646433i | 0.616841 | − | 0.787088i | \(-0.288412\pi\) |
−0.990059 | + | 0.140655i | \(0.955079\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13386.1 | − | 23185.4i | −0.671773 | − | 1.16355i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5536.31 | + | 9589.18i | −0.276707 | + | 0.479270i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1650.29 | + | 2858.38i | 0.0821473 | + | 0.142283i | 0.904172 | − | 0.427168i | \(-0.140489\pi\) |
−0.822025 | + | 0.569452i | \(0.807156\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −814.327 | + | 1410.46i | −0.0403712 | + | 0.0699249i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3851.25 | −0.190160 | −0.0950799 | − | 0.995470i | \(-0.530311\pi\) | ||||
−0.0950799 | + | 0.995470i | \(0.530311\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36061.2 | −1.77340 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4823.86 | − | 8355.18i | 0.236273 | − | 0.409237i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4008.49 | − | 6942.91i | −0.195550 | − | 0.338703i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10665.5 | − | 18473.2i | 0.518230 | − | 0.897601i | −0.481546 | − | 0.876421i | \(-0.659924\pi\) |
0.999776 | − | 0.0211799i | \(-0.00674227\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9459.51 | + | 16384.4i | 0.457801 | + | 0.792934i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20204.5 | + | 34995.2i | 0.973930 | + | 1.68690i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11493.4 | − | 19907.2i | −0.551830 | − | 0.955797i | −0.998143 | − | 0.0609200i | \(-0.980597\pi\) |
0.446313 | − | 0.894877i | \(-0.352737\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −30777.1 | −1.47185 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4053.56 | + | 7020.97i | −0.193090 | + | 0.334441i | −0.946273 | − | 0.323370i | \(-0.895184\pi\) |
0.753183 | + | 0.657811i | \(0.228518\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8082.26 | − | 13998.9i | 0.383483 | − | 0.664212i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5444.38 | + | 9429.94i | 0.257310 | + | 0.445674i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4381.86 | 0.206284 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3911.06 | + | 6774.15i | −0.183402 | + | 0.317662i | −0.943037 | − | 0.332688i | \(-0.892044\pi\) |
0.759635 | + | 0.650350i | \(0.225378\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1264.34 | −0.0590585 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29299.4 | −1.36329 | −0.681646 | − | 0.731682i | \(-0.738736\pi\) | ||||
−0.681646 | + | 0.731682i | \(0.738736\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5218.55 | + | 13973.1i | −0.241878 | + | 0.647648i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1862.48 | −0.0859922 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9187.98 | −0.422585 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10561.0 | − | 18292.2i | 0.483871 | − | 0.838090i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9922.25 | −0.452864 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 738.511 | + | 1279.14i | 0.0335778 | + | 0.0581585i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12076.9 | − | 20917.8i | 0.547007 | − | 0.947445i | −0.451470 | − | 0.892286i | \(-0.649100\pi\) |
0.998478 | − | 0.0551585i | \(-0.0175664\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −797.669 | + | 1381.60i | −0.0359921 | + | 0.0623401i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1173.74 | 0.0527603 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −734.949 | − | 1272.97i | −0.0329115 | − | 0.0570044i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4318.06 | + | 7479.10i | 0.192636 | + | 0.333656i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2282.82 | − | 3953.96i | −0.101457 | − | 0.175729i | 0.810828 | − | 0.585285i | \(-0.199017\pi\) |
−0.912285 | + | 0.409555i | \(0.865684\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3863.45 | + | 6691.70i | −0.171063 | + | 0.296289i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6322.30 | − | 10950.5i | −0.278886 | − | 0.483044i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3369.33 | − | 5835.85i | 0.148071 | − | 0.256467i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24107.4 | 1.05550 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12772.4 | −0.557137 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11967.6 | + | 20728.4i | −0.520096 | + | 0.900832i | 0.479632 | + | 0.877470i | \(0.340770\pi\) |
−0.999727 | + | 0.0233619i | \(0.992563\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4799.14 | + | 8312.36i | 0.207794 | + | 0.359909i | 0.951019 | − | 0.309132i | \(-0.100038\pi\) |
−0.743225 | + | 0.669041i | \(0.766705\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21765.0 | − | 37698.0i | 0.938906 | − | 1.62623i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16747.0 | + | 29006.6i | 0.719781 | + | 1.24670i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 579.624 | + | 1003.94i | 0.0248206 | + | 0.0429906i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −640.104 | − | 1108.69i | −0.0273102 | − | 0.0473027i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16451.6 | 0.699348 | 0.349674 | − | 0.936871i | \(-0.386292\pi\) | ||||
0.349674 | + | 0.936871i | \(0.386292\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4406.07 | + | 7631.54i | −0.186617 | + | 0.323230i | −0.944120 | − | 0.329601i | \(-0.893086\pi\) |
0.757503 | + | 0.652832i | \(0.226419\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6468.18 | + | 11203.2i | −0.272961 | + | 0.472783i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9798.52 | + | 16971.5i | 0.412005 | + | 0.713613i | 0.995109 | − | 0.0987844i | \(-0.0314954\pi\) |
−0.583104 | + | 0.812397i | \(0.698162\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12302.4 | 0.515418 | 0.257709 | − | 0.966223i | \(-0.417032\pi\) | ||||
0.257709 | + | 0.966223i | \(0.417032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28570.9 | − | 49486.2i | 1.19267 | − | 2.06577i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12334.2 | −0.513031 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 37573.5 | 1.55723 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11414.4 | + | 1914.36i | −0.471372 | + | 0.0790562i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8585.46 | −0.353281 | −0.176641 | − | 0.984275i | \(-0.556523\pi\) | ||||
−0.176641 | + | 0.984275i | \(0.556523\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2493.53 | −0.102240 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10267.4 | + | 17783.7i | −0.419489 | + | 0.726577i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30658.3 | 1.24814 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3307.46 | + | 5728.68i | 0.134174 | + | 0.232397i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2384.71 | + | 4130.45i | −0.0963995 | + | 0.166969i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3584.25 | + | 6208.10i | −0.144379 | + | 0.250072i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 946.881 | 0.0380077 | 0.0190039 | − | 0.999819i | \(-0.493951\pi\) | ||||
0.0190039 | + | 0.999819i | \(0.493951\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3207.13 | + | 5554.91i | 0.128283 | + | 0.222192i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10504.9 | − | 18194.9i | −0.418715 | − | 0.725236i | 0.577095 | − | 0.816677i | \(-0.304186\pi\) |
−0.995811 | + | 0.0914408i | \(0.970853\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −95.4124 | − | 165.259i | −0.00378979 | − | 0.00656411i | 0.864124 | − | 0.503278i | \(-0.167873\pi\) |
−0.867914 | + | 0.496714i | \(0.834540\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9388.28 | − | 16261.0i | 0.371605 | − | 0.643638i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14503.1 | + | 25120.1i | 0.572064 | + | 0.990844i | 0.996354 | + | 0.0853178i | \(0.0271905\pi\) |
−0.424290 | + | 0.905527i | \(0.639476\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22507.2 | + | 38983.6i | −0.884702 | + | 1.53235i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19501.4 | −0.763899 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23618.9 | 0.921996 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2304.39 | + | 3991.32i | −0.0896455 | + | 0.155271i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10257.8 | + | 17767.0i | 0.397680 | + | 0.688801i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2261.99 | + | 3917.88i | −0.0873934 | + | 0.151370i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13651.2 | − | 23644.6i | −0.525620 | − | 0.910400i | −0.999555 | − | 0.0298401i | \(-0.990500\pi\) |
0.473935 | − | 0.880560i | \(-0.342833\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9607.68 | − | 16641.0i | −0.368668 | − | 0.638552i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5329.69 | + | 9231.29i | 0.203816 | + | 0.353019i | 0.949755 | − | 0.312995i | \(-0.101332\pi\) |
−0.745939 | + | 0.666014i | \(0.767999\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30383.9 | 1.15798 | 0.578992 | − | 0.815333i | \(-0.303446\pi\) | ||||
0.578992 | + | 0.815333i | \(0.303446\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22433.2 | − | 38855.4i | 0.852071 | − | 1.47583i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21863.4 | + | 37868.5i | −0.827622 | + | 1.43348i | 0.0722761 | + | 0.997385i | \(0.476974\pi\) |
−0.899899 | + | 0.436099i | \(0.856360\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −330.631 | − | 572.669i | −0.0124736 | − | 0.0216048i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20335.8 | −0.764617 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2275.85 | + | 3941.89i | −0.0852838 | + | 0.147716i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18079.3 | 0.675224 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12810.4 | −0.476841 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25188.1 | − | 4224.43i | 0.934451 | − | 0.156722i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3978.74 | 0.147116 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2369.04 | −0.0873053 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30057.4 | − | 52060.9i | 1.10402 | − | 1.91222i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10279.2 | −0.376312 | −0.188156 | − | 0.982139i | \(-0.560251\pi\) | ||||
−0.188156 | + | 0.982139i | \(0.560251\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5039.55 | − | 8728.76i | −0.183885 | − | 0.318498i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21156.9 | − | 36644.8i | 0.769438 | − | 1.33271i | −0.168430 | − | 0.985714i | \(-0.553870\pi\) |
0.937868 | − | 0.346992i | \(-0.112797\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6459.44 | − | 11188.1i | 0.234147 | − | 0.405555i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15050.4 | −0.543773 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10437.4 | + | 18078.2i | 0.375872 | + | 0.651029i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7250.48 | − | 12558.2i | −0.260252 | − | 0.450769i | 0.706057 | − | 0.708155i | \(-0.250472\pi\) |
−0.966309 | + | 0.257386i | \(0.917139\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12648.7 | + | 21908.1i | 0.452538 | + | 0.783819i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4395.84 | − | 7613.81i | 0.156761 | − | 0.271519i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1506.55 | + | 2609.42i | 0.0535514 | + | 0.0927537i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3071.35 | − | 5319.74i | 0.108820 | − | 0.188482i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6146.06 | 0.217057 | 0.108528 | − | 0.994093i | \(-0.465386\pi\) | ||||
0.108528 | + | 0.994093i | \(0.465386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7265.74 | −0.255773 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9725.62 | − | 16845.3i | 0.341267 | − | 0.591093i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7290.35 | + | 12627.3i | 0.254995 | + | 0.441664i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9541.44 | + | 16526.3i | −0.332663 | + | 0.576189i | −0.983033 | − | 0.183428i | \(-0.941280\pi\) |
0.650370 | + | 0.759617i | \(0.274614\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16646.3 | − | 28832.3i | −0.578522 | − | 1.00203i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3486.71 | − | 6039.17i | −0.120790 | − | 0.209215i | 0.799289 | − | 0.600946i | \(-0.205210\pi\) |
−0.920080 | + | 0.391732i | \(0.871876\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36134.6 | − | 62587.0i | −1.24783 | − | 2.16131i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7862.59 | 0.270656 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8133.14 | + | 14087.0i | −0.279083 | + | 0.483386i | −0.971157 | − | 0.238441i | \(-0.923364\pi\) |
0.692074 | + | 0.721826i | \(0.256697\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1402.42 | − | 2429.07i | 0.0479710 | − | 0.0830883i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3120.96 | − | 5405.67i | −0.106419 | − | 0.184323i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42228.7 | −1.43539 | −0.717693 | − | 0.696360i | \(-0.754802\pi\) | ||||
−0.717693 | + | 0.696360i | \(0.754802\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24414.9 | + | 42287.9i | −0.827275 | + | 1.43288i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22150.7 | 0.748202 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17271.4 | −0.581565 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28160.9 | − | 9719.41i | 0.945282 | − | 0.326253i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16778.0 | 0.561437 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30916.4 | 1.03133 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8635.30 | − | 14956.8i | 0.287169 | − | 0.497392i | −0.685964 | − | 0.727636i | \(-0.740619\pi\) |
0.973133 | + | 0.230244i | \(0.0739525\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7682.77 | 0.254702 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26409.4 | + | 45742.4i | 0.872829 | + | 1.51178i | 0.859058 | + | 0.511879i | \(0.171050\pi\) |
0.0137709 | + | 0.999905i | \(0.495616\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1025.72 | − | 1776.60i | 0.0337957 | − | 0.0585358i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2692.26 | + | 4663.13i | −0.0884322 | + | 0.153169i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37685.4 | 1.23405 | 0.617023 | − | 0.786945i | \(-0.288339\pi\) | ||||
0.617023 | + | 0.786945i | \(0.288339\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8465.94 | − | 14663.4i | −0.276376 | − | 0.478698i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16914.6 | + | 29297.0i | 0.550502 | + | 0.953497i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4794.72 | − | 8304.70i | −0.155573 | − | 0.269460i | 0.777695 | − | 0.628642i | \(-0.216389\pi\) |
−0.933267 | + | 0.359182i | \(0.883056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32903.7 | − | 56991.0i | 1.06437 | − | 1.84354i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4650.93 | − | 8055.65i | −0.149991 | − | 0.259791i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4559.11 | + | 7896.60i | −0.146584 | + | 0.253890i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9963.12 | 0.319363 | 0.159682 | − | 0.987169i | \(-0.448953\pi\) | ||||
0.159682 | + | 0.987169i | \(0.448953\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33655.7 | −1.07556 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33655.7 | − | 58293.4i | 1.07232 | − | 1.85731i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5599.52 | + | 9698.65i | 0.177872 | + | 0.308084i | 0.941151 | − | 0.337985i | \(-0.109745\pi\) |
−0.763279 | + | 0.646069i | \(0.776412\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1169.00 | + | 2024.76i | −0.0370224 | + | 0.0641248i |
(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 | 124.4.e.c.5.1 | ✓ | 8 | |
3.2 | odd | 2 | 1116.4.i.e.253.1 | 8 | |||
4.3 | odd | 2 | 496.4.i.e.129.4 | 8 | |||
31.25 | even | 3 | inner | 124.4.e.c.25.1 | yes | 8 | |
93.56 | odd | 6 | 1116.4.i.e.397.1 | 8 | |||
124.87 | odd | 6 | 496.4.i.e.273.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.4.e.c.5.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
124.4.e.c.25.1 | yes | 8 | 31.25 | even | 3 | inner | |
496.4.i.e.129.4 | 8 | 4.3 | odd | 2 | |||
496.4.i.e.273.4 | 8 | 124.87 | odd | 6 | |||
1116.4.i.e.253.1 | 8 | 3.2 | odd | 2 | |||
1116.4.i.e.397.1 | 8 | 93.56 | odd | 6 |