Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,3,Mod(557,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.557");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.p (of order \(6\), degree \(2\), not 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: | \(16.0218395444\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.1090537426944.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - 2x^{7} - 4x^{6} - 44x^{5} + 71x^{4} + 196x^{3} + 28x^{2} + 294x + 441 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 557.2 | ||
Root | \(0.468068 - 1.22041i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.557 |
Dual form | 588.3.p.f.569.2 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −2.29094 | + | 1.93690i | −0.763648 | + | 0.645633i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.17193 | + | 4.71806i | −1.63439 | + | 0.943613i | −0.651667 | + | 0.758505i | \(0.725930\pi\) |
−0.982718 | + | 0.185108i | \(0.940737\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.49684 | − | 8.87465i | 0.166316 | − | 0.986073i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −13.4490 | − | 7.76476i | −1.22263 | − | 0.705887i | −0.257154 | − | 0.966370i | \(-0.582785\pi\) |
−0.965478 | + | 0.260483i | \(0.916118\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.22876 | −0.479135 | −0.239568 | − | 0.970880i | \(-0.577006\pi\) | ||||
−0.239568 | + | 0.970880i | \(0.577006\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.58301 | − | 26.6370i | 0.638867 | − | 1.77580i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.89489 | − | 1.67137i | −0.170288 | − | 0.0983158i | 0.412434 | − | 0.910988i | \(-0.364679\pi\) |
−0.582722 | + | 0.812672i | \(0.698012\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.46863 | + | 7.73989i | 0.235191 | + | 0.407363i | 0.959328 | − | 0.282293i | \(-0.0910951\pi\) |
−0.724137 | + | 0.689656i | \(0.757762\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −16.3439 | + | 9.43613i | −0.710602 | + | 0.410266i | −0.811284 | − | 0.584652i | \(-0.801231\pi\) |
0.100682 | + | 0.994919i | \(0.467898\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 32.0203 | − | 55.4607i | 1.28081 | − | 2.21843i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.7601 | + | 23.2306i | 0.509634 | + | 0.860391i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 41.0872i | 1.41680i | 0.705810 | + | 0.708401i | \(0.250583\pi\) | ||||
−0.705810 | + | 0.708401i | \(0.749417\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.35425 | + | 4.07768i | −0.0759435 | + | 0.131538i | −0.901496 | − | 0.432787i | \(-0.857530\pi\) |
0.825553 | + | 0.564325i | \(0.190864\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 45.8504 | − | 8.26066i | 1.38940 | − | 0.250323i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 21.9373 | + | 37.9964i | 0.592899 | + | 1.02693i | 0.993840 | + | 0.110827i | \(0.0353499\pi\) |
−0.400941 | + | 0.916104i | \(0.631317\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.2697 | − | 12.0645i | 0.365890 | − | 0.309345i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 46.5886i | − | 1.13631i | −0.822923 | − | 0.568153i | \(-0.807658\pi\) | ||
0.822923 | − | 0.568153i | \(-0.192342\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 47.8745 | 1.11336 | 0.556680 | − | 0.830727i | \(-0.312075\pi\) | ||||
0.556680 | + | 0.830727i | \(0.312075\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 29.6391 | + | 79.5852i | 0.658647 | + | 1.76856i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 21.1081 | − | 12.1868i | 0.449109 | − | 0.259293i | −0.258345 | − | 0.966053i | \(-0.583177\pi\) |
0.707454 | + | 0.706760i | \(0.249844\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.86931 | − | 1.77811i | 0.193516 | − | 0.0348649i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.86938 | − | 1.07929i | −0.0352714 | − | 0.0203639i | 0.482261 | − | 0.876028i | \(-0.339816\pi\) |
−0.517532 | + | 0.855664i | \(0.673149\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 146.539 | 2.66434 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −25.2288 | − | 9.07637i | −0.442610 | − | 0.159234i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.0668 | − | 6.38943i | −0.187573 | − | 0.108295i | 0.403273 | − | 0.915080i | \(-0.367873\pi\) |
−0.590846 | + | 0.806784i | \(0.701206\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.94837 | − | 17.2311i | −0.163088 | − | 0.282477i | 0.772887 | − | 0.634544i | \(-0.218812\pi\) |
−0.935975 | + | 0.352067i | \(0.885479\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 50.9009 | − | 29.3877i | 0.783091 | − | 0.452118i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 40.4170 | − | 70.0043i | 0.603239 | − | 1.04484i | −0.389088 | − | 0.921200i | \(-0.627210\pi\) |
0.992327 | − | 0.123640i | \(-0.0394567\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.1660 | − | 53.2740i | 0.277768 | − | 0.772087i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 65.4608i | − | 0.921983i | −0.887404 | − | 0.460992i | \(-0.847494\pi\) | ||
0.887404 | − | 0.460992i | \(-0.152506\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −50.2693 | + | 87.0689i | −0.688620 | + | 1.19273i | 0.283664 | + | 0.958924i | \(0.408450\pi\) |
−0.972284 | + | 0.233801i | \(0.924883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 34.0652 | + | 189.077i | 0.454203 | + | 2.52103i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7085 | + | 18.5477i | 0.135551 | + | 0.234781i | 0.925808 | − | 0.377995i | \(-0.123386\pi\) |
−0.790257 | + | 0.612775i | \(0.790053\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −76.5189 | − | 26.5679i | −0.944678 | − | 0.327999i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 49.3392i | − | 0.594448i | −0.954808 | − | 0.297224i | \(-0.903939\pi\) | ||
0.954808 | − | 0.297224i | \(-0.0960609\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 31.5425 | 0.371088 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −79.5819 | − | 94.1286i | −0.914734 | − | 1.08194i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −40.3469 | + | 23.2943i | −0.453336 | + | 0.261733i | −0.709238 | − | 0.704969i | \(-0.750961\pi\) |
0.255902 | + | 0.966703i | \(0.417627\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.50460 | − | 13.9017i | −0.0269312 | − | 0.149480i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −73.0346 | − | 42.1665i | −0.768785 | − | 0.443858i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −36.3320 | −0.374557 | −0.187278 | − | 0.982307i | \(-0.559967\pi\) | ||||
−0.187278 | + | 0.982307i | \(0.559967\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −89.0405 | + | 107.732i | −0.899399 | + | 1.08820i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 88.8657 | + | 51.3066i | 0.879858 | + | 0.507986i | 0.870612 | − | 0.491971i | \(-0.163723\pi\) |
0.00924658 | + | 0.999957i | \(0.497057\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −55.8745 | − | 96.7775i | −0.542471 | − | 0.939587i | −0.998761 | − | 0.0497563i | \(-0.984156\pi\) |
0.456290 | − | 0.889831i | \(-0.349178\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 26.0540 | − | 15.0423i | 0.243496 | − | 0.140582i | −0.373287 | − | 0.927716i | \(-0.621769\pi\) |
0.616782 | + | 0.787134i | \(0.288436\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 21.3542 | − | 36.9866i | 0.195911 | − | 0.339327i | −0.751288 | − | 0.659974i | \(-0.770567\pi\) |
0.947199 | + | 0.320647i | \(0.103900\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −123.852 | − | 44.5574i | −1.11579 | − | 0.401418i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 92.2027i | − | 0.815953i | −0.912992 | − | 0.407977i | \(-0.866234\pi\) | ||
0.912992 | − | 0.407977i | \(-0.133766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 89.0405 | − | 154.223i | 0.774265 | − | 1.34107i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.32346 | + | 55.2781i | −0.0796877 | + | 0.472462i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 60.0830 | + | 104.067i | 0.496554 | + | 0.860056i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 90.2374 | + | 106.732i | 0.733637 | + | 0.867738i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 368.391i | 2.94713i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 159.579 | 1.25653 | 0.628264 | − | 0.778000i | \(-0.283766\pi\) | ||||
0.628264 | + | 0.778000i | \(0.283766\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −109.678 | + | 92.7281i | −0.850215 | + | 0.718823i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 217.747 | − | 125.716i | 1.66219 | − | 0.959667i | 0.690526 | − | 0.723307i | \(-0.257379\pi\) |
0.971666 | − | 0.236359i | \(-0.0759543\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −222.050 | − | 124.917i | −1.64482 | − | 0.925313i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 194.075 | + | 112.049i | 1.41661 | + | 0.817879i | 0.995999 | − | 0.0893636i | \(-0.0284833\pi\) |
0.420608 | + | 0.907242i | \(0.361817\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −70.5163 | −0.507312 | −0.253656 | − | 0.967295i | \(-0.581633\pi\) | ||||
−0.253656 | + | 0.967295i | \(0.581633\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.7530 | + | 68.8036i | −0.175553 | + | 0.487968i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 83.7703 | + | 48.3648i | 0.585806 | + | 0.338215i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −193.852 | − | 335.762i | −1.33691 | − | 2.31560i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −194.257 | + | 112.154i | −1.30374 | + | 0.752713i | −0.981043 | − | 0.193790i | \(-0.937922\pi\) |
−0.322694 | + | 0.946503i | \(0.604589\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0405 | − | 17.3907i | 0.0664935 | − | 0.115170i | −0.830862 | − | 0.556478i | \(-0.812152\pi\) |
0.897356 | + | 0.441308i | \(0.145486\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.1660 | + | 23.1894i | −0.125268 | + | 0.151565i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 44.4300i | − | 0.286645i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 92.8412 | − | 160.806i | 0.591345 | − | 1.02424i | −0.402707 | − | 0.915329i | \(-0.631930\pi\) |
0.994052 | − | 0.108910i | \(-0.0347362\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.37312 | − | 1.14822i | 0.0400825 | − | 0.00722149i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −101.184 | − | 175.256i | −0.620763 | − | 1.07519i | −0.989344 | − | 0.145597i | \(-0.953490\pi\) |
0.368581 | − | 0.929595i | \(-0.379844\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −335.712 | + | 283.830i | −2.03462 | + | 1.72018i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 207.595i | − | 1.24308i | −0.783381 | − | 0.621541i | \(-0.786507\pi\) | ||
0.783381 | − | 0.621541i | \(-0.213493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −130.203 | −0.770430 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 75.3777 | − | 28.0721i | 0.440805 | − | 0.164164i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −148.451 | + | 85.7084i | −0.858100 | + | 0.495424i | −0.863376 | − | 0.504562i | \(-0.831654\pi\) |
0.00527553 | + | 0.999986i | \(0.498321\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 37.7291 | − | 6.79749i | 0.213159 | − | 0.0384039i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −26.0540 | − | 15.0423i | −0.145553 | − | 0.0840353i | 0.425455 | − | 0.904980i | \(-0.360114\pi\) |
−0.571008 | + | 0.820944i | \(0.693448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −253.978 | −1.40319 | −0.701596 | − | 0.712575i | \(-0.747529\pi\) | ||||
−0.701596 | + | 0.712575i | \(0.747529\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 56.1660 | + | 20.2064i | 0.306918 | + | 0.110418i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −358.539 | − | 207.003i | −1.93805 | − | 1.11893i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.9555 | + | 44.9563i | 0.138800 | + | 0.240408i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 183.703 | − | 106.061i | 0.961795 | − | 0.555292i | 0.0650698 | − | 0.997881i | \(-0.479273\pi\) |
0.896725 | + | 0.442588i | \(0.145940\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −82.3098 | + | 142.565i | −0.426476 | + | 0.738677i | −0.996557 | − | 0.0829108i | \(-0.973578\pi\) |
0.570081 | + | 0.821588i | \(0.306912\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −59.6902 | + | 165.915i | −0.306104 | + | 0.850849i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 173.193i | 0.879153i | 0.898205 | + | 0.439576i | \(0.144871\pi\) | ||||
−0.898205 | + | 0.439576i | \(0.855129\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 70.1255 | − | 121.461i | 0.352389 | − | 0.610356i | −0.634278 | − | 0.773105i | \(-0.718703\pi\) |
0.986668 | + | 0.162749i | \(0.0520359\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 42.9982 | + | 238.660i | 0.213921 | + | 1.18736i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 219.808 | + | 380.718i | 1.07223 | + | 1.85716i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 59.2782 | + | 159.170i | 0.286368 | + | 0.768939i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 138.791i | − | 0.664073i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −256.243 | −1.21442 | −0.607211 | − | 0.794540i | \(-0.707712\pi\) | ||||
−0.607211 | + | 0.794540i | \(0.707712\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 126.791 | + | 149.967i | 0.595263 | + | 0.704071i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −391.227 | + | 225.875i | −1.81966 | + | 1.05058i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −53.4797 | − | 296.837i | −0.244200 | − | 1.35542i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.0316 | + | 10.4105i | 0.0815909 | + | 0.0471065i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 185.875 | 0.833518 | 0.416759 | − | 0.909017i | \(-0.363166\pi\) | ||||
0.416759 | + | 0.909017i | \(0.363166\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −444.265 | − | 367.185i | −1.97451 | − | 1.63193i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −68.6014 | − | 39.6070i | −0.302209 | − | 0.174480i | 0.341226 | − | 0.939981i | \(-0.389158\pi\) |
−0.643435 | + | 0.765501i | \(0.722491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −87.3654 | − | 151.321i | −0.381508 | − | 0.660791i | 0.609770 | − | 0.792578i | \(-0.291262\pi\) |
−0.991278 | + | 0.131787i | \(0.957929\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 271.030 | − | 156.479i | 1.16322 | − | 0.671585i | 0.211146 | − | 0.977454i | \(-0.432280\pi\) |
0.952074 | + | 0.305869i | \(0.0989470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −114.996 | + | 199.179i | −0.489345 | + | 0.847570i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −60.4575 | − | 21.7504i | −0.255095 | − | 0.0917737i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 238.654i | 0.998552i | 0.866443 | + | 0.499276i | \(0.166401\pi\) | ||||
−0.866443 | + | 0.499276i | \(0.833599\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 73.1255 | − | 126.657i | 0.303425 | − | 0.525548i | −0.673484 | − | 0.739202i | \(-0.735203\pi\) |
0.976909 | + | 0.213654i | \(0.0685364\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 226.760 | − | 87.3439i | 0.933168 | − | 0.359440i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.8340 | − | 48.2099i | −0.112688 | − | 0.195182i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 95.5651 | + | 113.033i | 0.383796 | + | 0.453949i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 38.3366i | − | 0.152735i | −0.997080 | − | 0.0763677i | \(-0.975668\pi\) | ||
0.997080 | − | 0.0763677i | \(-0.0243323\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 293.077 | 1.15841 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −72.2620 | + | 61.0946i | −0.283381 | + | 0.239587i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 204.811 | − | 118.248i | 0.796930 | − | 0.460108i | −0.0454667 | − | 0.998966i | \(-0.514478\pi\) |
0.842396 | + | 0.538858i | \(0.181144\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 364.635 | + | 61.5011i | 1.39707 | + | 0.235636i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −72.0091 | − | 41.5745i | −0.273799 | − | 0.158078i | 0.356814 | − | 0.934175i | \(-0.383863\pi\) |
−0.630613 | + | 0.776098i | \(0.717196\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.3686 | 0.0768627 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 47.3137 | − | 131.514i | 0.177205 | − | 0.492561i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 288.731 | + | 166.699i | 1.07335 | + | 0.619698i | 0.929094 | − | 0.369843i | \(-0.120588\pi\) |
0.144254 | + | 0.989541i | \(0.453922\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −109.225 | − | 189.183i | −0.403044 | − | 0.698092i | 0.591048 | − | 0.806636i | \(-0.298714\pi\) |
−0.994092 | + | 0.108544i | \(0.965381\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −861.278 | + | 497.259i | −3.13192 | + | 1.80822i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −48.6235 | + | 84.2184i | −0.175536 | + | 0.304038i | −0.940347 | − | 0.340218i | \(-0.889499\pi\) |
0.764811 | + | 0.644255i | \(0.222833\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 32.6640 | + | 26.9968i | 0.117075 | + | 0.0967627i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 386.079i | 1.37395i | 0.726682 | + | 0.686974i | \(0.241061\pi\) | ||||
−0.726682 | + | 0.686974i | \(0.758939\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −132.675 | + | 229.800i | −0.468817 | + | 0.812015i | −0.999365 | − | 0.0356404i | \(-0.988653\pi\) |
0.530548 | + | 0.847655i | \(0.321986\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 248.990 | − | 44.8595i | 0.873651 | − | 0.157402i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −138.913 | − | 240.604i | −0.480668 | − | 0.832541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 83.2346 | − | 70.3715i | 0.286030 | − | 0.241826i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 250.458i | − | 0.854807i | −0.904061 | − | 0.427403i | \(-0.859428\pi\) | ||
0.904061 | − | 0.427403i | \(-0.140572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 120.583 | 0.408756 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.67971 | − | 419.271i | −0.0157566 | − | 1.41169i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 101.802 | − | 58.7753i | 0.340475 | − | 0.196573i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −302.962 | + | 54.5833i | −0.999875 | + | 0.180143i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 162.595 | + | 93.8741i | 0.533097 | + | 0.307784i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 407.225 | 1.32647 | 0.663233 | − | 0.748413i | \(-0.269184\pi\) | ||||
0.663233 | + | 0.748413i | \(0.269184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 315.454 | + | 113.488i | 1.02089 | + | 0.367276i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −89.5601 | − | 51.7075i | −0.287975 | − | 0.166262i | 0.349054 | − | 0.937103i | \(-0.386503\pi\) |
−0.637028 | + | 0.770841i | \(0.719836\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −129.642 | − | 224.546i | −0.414191 | − | 0.717400i | 0.581152 | − | 0.813795i | \(-0.302602\pi\) |
−0.995343 | + | 0.0963950i | \(0.969269\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 197.996 | − | 114.313i | 0.624592 | − | 0.360608i | −0.154063 | − | 0.988061i | \(-0.549236\pi\) |
0.778655 | + | 0.627453i | \(0.215902\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 319.033 | − | 552.581i | 1.00010 | − | 1.73223i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.5529 | + | 84.9252i | −0.0951804 | + | 0.264564i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 29.8749i | − | 0.0924919i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −199.446 | + | 345.451i | −0.613681 | + | 1.06293i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.7180 | + | 126.095i | 0.0694741 | + | 0.385613i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.8157 | + | 53.3744i | 0.0930988 | + | 0.161252i | 0.908814 | − | 0.417203i | \(-0.136989\pi\) |
−0.815715 | + | 0.578454i | \(0.803656\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 370.042 | − | 137.811i | 1.11124 | − | 0.413846i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 762.760i | 2.27690i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 269.195 | 0.798797 | 0.399399 | − | 0.916777i | \(-0.369219\pi\) | ||||
0.399399 | + | 0.916777i | \(0.369219\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 178.587 | + | 211.231i | 0.526806 | + | 0.623101i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 63.3244 | − | 36.5604i | 0.185702 | − | 0.107215i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 94.7271 | + | 525.778i | 0.274571 | + | 1.52399i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −265.059 | − | 153.032i | −0.763858 | − | 0.441014i | 0.0668211 | − | 0.997765i | \(-0.478714\pi\) |
−0.830679 | + | 0.556751i | \(0.812048\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −418.759 | −1.19988 | −0.599942 | − | 0.800044i | \(-0.704810\pi\) | ||||
−0.599942 | + | 0.800044i | \(0.704810\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −85.7085 | − | 144.697i | −0.244184 | − | 0.412244i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 225.919 | + | 130.434i | 0.639997 | + | 0.369503i | 0.784614 | − | 0.619985i | \(-0.212861\pi\) |
−0.144616 | + | 0.989488i | \(0.546195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 308.848 | + | 534.941i | 0.869995 | + | 1.50688i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 604.723 | − | 349.137i | 1.68446 | − | 0.972526i | 0.725834 | − | 0.687870i | \(-0.241454\pi\) |
0.958630 | − | 0.284656i | \(-0.0918795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 140.563 | − | 243.462i | 0.389370 | − | 0.674409i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −339.214 | − | 122.036i | −0.934473 | − | 0.336189i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 948.695i | − | 2.59916i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 245.808 | − | 425.752i | 0.669776 | − | 1.16009i | −0.308190 | − | 0.951325i | \(-0.599723\pi\) |
0.977967 | − | 0.208762i | \(-0.0669433\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −413.457 | − | 69.7357i | −1.12048 | − | 0.188986i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −95.4575 | − | 165.337i | −0.255918 | − | 0.443263i | 0.709226 | − | 0.704981i | \(-0.249044\pi\) |
−0.965145 | + | 0.261717i | \(0.915711\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −713.537 | − | 843.964i | −1.90277 | − | 2.25057i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 255.922i | − | 0.678839i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −333.454 | −0.879825 | −0.439912 | − | 0.898041i | \(-0.644991\pi\) | ||||
−0.439912 | + | 0.898041i | \(0.644991\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −365.587 | + | 309.089i | −0.959545 | + | 0.811256i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.3183 | − | 8.84405i | 0.0399957 | − | 0.0230915i | −0.479869 | − | 0.877340i | \(-0.659316\pi\) |
0.519865 | + | 0.854249i | \(0.325982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 71.6606 | − | 424.870i | 0.185169 | − | 1.09785i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −439.051 | − | 253.486i | −1.12867 | − | 0.651636i | −0.185068 | − | 0.982726i | \(-0.559250\pi\) |
−0.943599 | + | 0.331090i | \(0.892584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 63.0850 | 0.161343 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −255.346 | + | 709.763i | −0.649736 | + | 1.80601i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −175.018 | − | 101.047i | −0.443084 | − | 0.255815i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 322.797 | + | 559.100i | 0.813090 | + | 1.40831i | 0.910691 | + | 0.413088i | \(0.135550\pi\) |
−0.0976014 | + | 0.995226i | \(0.531117\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −60.7928 | + | 35.0987i | −0.151603 | + | 0.0875280i | −0.573883 | − | 0.818938i | \(-0.694563\pi\) |
0.422280 | + | 0.906466i | \(0.361230\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.6640 | − | 25.3989i | 0.0363872 | − | 0.0630245i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 750.656 | − | 143.910i | 1.85347 | − | 0.355334i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 681.350i | − | 1.67408i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −240.933 | + | 417.309i | −0.589079 | + | 1.02031i | 0.405274 | + | 0.914195i | \(0.367176\pi\) |
−0.994353 | + | 0.106120i | \(0.966157\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −661.644 | + | 119.205i | −1.60984 | + | 0.290037i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 232.786 | + | 403.196i | 0.560929 | + | 0.971558i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 161.549 | − | 136.583i | 0.387407 | − | 0.327537i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 168.074i | − | 0.401131i | −0.979680 | − | 0.200566i | \(-0.935722\pi\) | ||
0.979680 | − | 0.200566i | \(-0.0642780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 453.336 | 1.07681 | 0.538404 | − | 0.842687i | \(-0.319028\pi\) | ||||
0.538404 | + | 0.842687i | \(0.319028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −76.5579 | − | 205.569i | −0.180988 | − | 0.485979i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −185.391 | + | 107.035i | −0.436213 | + | 0.251848i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −285.591 | + | 51.4536i | −0.665713 | + | 0.119938i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 620.041 | + | 357.981i | 1.43861 | + | 0.830582i | 0.997753 | − | 0.0669956i | \(-0.0213413\pi\) |
0.440857 | + | 0.897577i | \(0.354675\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 255.992 | 0.591206 | 0.295603 | − | 0.955311i | \(-0.404479\pi\) | ||||
0.295603 | + | 0.955311i | \(0.404479\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1094.44 | + | 393.739i | 2.51596 | + | 0.905148i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −146.069 | − | 84.3331i | −0.334254 | − | 0.192982i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 405.956 | + | 703.136i | 0.924728 | + | 1.60168i | 0.791998 | + | 0.610523i | \(0.209041\pi\) |
0.132730 | + | 0.991152i | \(0.457626\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.4745 | + | 8.35684i | −0.0326738 | + | 0.0188642i | −0.516248 | − | 0.856439i | \(-0.672672\pi\) |
0.483574 | + | 0.875303i | \(0.339338\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 219.808 | − | 380.718i | 0.493950 | − | 0.855547i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 227.800 | − | 633.195i | 0.509620 | − | 1.41654i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.6369i | 0.0437348i | 0.999761 | + | 0.0218674i | \(0.00696117\pi\) | ||||
−0.999761 | + | 0.0218674i | \(0.993039\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −361.749 | + | 626.568i | −0.802104 | + | 1.38929i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.6818 | + | 59.2886i | 0.0235800 | + | 0.130880i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −176.148 | − | 305.097i | −0.385444 | − | 0.667608i | 0.606387 | − | 0.795170i | \(-0.292618\pi\) |
−0.991831 | + | 0.127562i | \(0.959285\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00731 | − | 90.2483i | −0.00219457 | − | 0.196619i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.3850i | 0.0246962i | 0.999924 | + | 0.0123481i | \(0.00393063\pi\) | ||||
−0.999924 | + | 0.0123481i | \(0.996069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −482.081 | −1.04121 | −0.520606 | − | 0.853797i | \(-0.674294\pi\) | ||||
−0.520606 | + | 0.853797i | \(0.674294\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 86.0564 | + | 101.787i | 0.185068 | + | 0.218896i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 652.878 | − | 376.939i | 1.39803 | − | 0.807151i | 0.403840 | − | 0.914830i | \(-0.367675\pi\) |
0.994186 | + | 0.107679i | \(0.0343418\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 98.7705 | + | 548.221i | 0.209704 | + | 1.16395i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −643.862 | − | 371.734i | −1.36123 | − | 0.785907i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 572.346 | 1.20494 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.3765 | + | 14.9746i | −0.0259465 | + | 0.0313933i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 461.367 | + | 266.370i | 0.963187 | + | 0.556096i | 0.897153 | − | 0.441721i | \(-0.145632\pi\) |
0.0660347 | + | 0.997817i | \(0.478965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −136.642 | − | 236.671i | −0.284079 | − | 0.492039i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 296.903 | − | 171.417i | 0.612170 | − | 0.353437i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −164.373 | + | 284.702i | −0.337521 | + | 0.584603i | −0.983966 | − | 0.178358i | \(-0.942922\pi\) |
0.646445 | + | 0.762960i | \(0.276255\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 571.261 | + | 205.519i | 1.16822 | + | 0.420283i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 451.540i | 0.919634i | 0.888014 | + | 0.459817i | \(0.152085\pi\) | ||||
−0.888014 | + | 0.459817i | \(0.847915\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 68.6719 | − | 118.943i | 0.139294 | − | 0.241264i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 219.345 | − | 1300.48i | 0.443121 | − | 2.62723i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 96.4091 | + | 166.985i | 0.193205 | + | 0.334640i | 0.946310 | − | 0.323259i | \(-0.104779\pi\) |
−0.753106 | + | 0.657899i | \(0.771445\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 402.090 | + | 475.588i | 0.802575 | + | 0.949277i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 271.662i | − | 0.540083i | −0.962849 | − | 0.270041i | \(-0.912963\pi\) | ||
0.962849 | − | 0.270041i | \(-0.0870374\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −968.272 | −1.91737 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 298.287 | − | 252.189i | 0.588337 | − | 0.497415i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 560.786 | − | 323.770i | 1.10174 | − | 0.636091i | 0.165064 | − | 0.986283i | \(-0.447217\pi\) |
0.936678 | + | 0.350192i | \(0.113884\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −118.313 | + | 210.311i | −0.230630 | + | 0.409962i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 913.205 | + | 527.239i | 1.77321 | + | 1.02377i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −378.510 | −0.732127 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 174.085 | − | 483.888i | 0.335424 | − | 0.932347i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 832.329 | + | 480.546i | 1.59756 | + | 0.922352i | 0.991955 | + | 0.126588i | \(0.0404025\pi\) |
0.605606 | + | 0.795765i | \(0.292931\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 146.720 | + | 254.126i | 0.280535 | + | 0.485900i | 0.971517 | − | 0.236972i | \(-0.0761549\pi\) |
−0.690982 | + | 0.722872i | \(0.742822\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.6306 | − | 7.86963i | 0.0258645 | − | 0.0149329i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −86.4190 | + | 149.682i | −0.163363 | + | 0.282953i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −73.2693 | + | 88.6502i | −0.137984 | + | 0.166950i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 290.189i | 0.544444i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −141.941 | + | 245.849i | −0.265311 | + | 0.459532i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 88.8238 | − | 16.0030i | 0.165407 | − | 0.0298007i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.4536 | + | 18.1061i | 0.0193227 | + | 0.0334679i | 0.875525 | − | 0.483173i | \(-0.160516\pi\) |
−0.856202 | + | 0.516641i | \(0.827182\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 581.849 | − | 491.929i | 1.07154 | − | 0.905947i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 403.003i | 0.739455i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 465.689 | 0.851351 | 0.425675 | − | 0.904876i | \(-0.360037\pi\) | ||||
0.425675 | + | 0.904876i | \(0.360037\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −167.811 | + | 62.4961i | −0.305667 | + | 0.113836i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −318.011 | + | 183.604i | −0.577152 | + | 0.333219i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1222.34 | − | 220.223i | 2.20241 | − | 0.396798i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −217.416 | − | 125.525i | −0.390334 | − | 0.225359i | 0.291971 | − | 0.956427i | \(-0.405689\pi\) |
−0.682305 | + | 0.731068i | \(0.739022\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −298.199 | −0.533450 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −146.539 | − | 52.7191i | −0.261210 | − | 0.0939734i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −384.262 | − | 221.854i | −0.682526 | − | 0.394057i | 0.118280 | − | 0.992980i | \(-0.462262\pi\) |
−0.800806 | + | 0.598924i | \(0.795595\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 435.018 | + | 753.474i | 0.769944 | + | 1.33358i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −900.055 | + | 519.647i | −1.58182 | + | 0.913263i | −0.587224 | + | 0.809424i | \(0.699779\pi\) |
−0.994594 | + | 0.103839i | \(0.966887\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −507.095 | + | 878.315i | −0.888083 | + | 1.53820i | −0.0459442 | + | 0.998944i | \(0.514630\pi\) |
−0.842139 | + | 0.539261i | \(0.818704\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −215.423 | + | 598.793i | −0.375957 | + | 1.04501i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1208.59i | 2.10189i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 479.280 | − | 830.137i | 0.830641 | − | 1.43871i | −0.0668902 | − | 0.997760i | \(-0.521308\pi\) |
0.897531 | − | 0.440952i | \(-0.145359\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −87.5665 | − | 486.034i | −0.151237 | − | 0.839436i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.7608 | + | 29.0306i | 0.0287493 | + | 0.0497952i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −184.615 | − | 495.717i | −0.315581 | − | 0.847379i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 327.341i | − | 0.557651i | −0.960342 | − | 0.278826i | \(-0.910055\pi\) | ||
0.960342 | − | 0.278826i | \(-0.0899451\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.0810 | −0.0714449 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −335.457 | − | 396.775i | −0.567610 | − | 0.671363i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −671.604 | + | 387.751i | −1.13255 | + | 0.653880i | −0.944576 | − | 0.328293i | \(-0.893527\pi\) |
−0.187977 | + | 0.982173i | \(0.560193\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 74.6040 | + | 414.086i | 0.124965 | + | 0.693612i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −81.9009 | − | 47.2855i | −0.136729 | − | 0.0789408i | 0.430075 | − | 0.902793i | \(-0.358487\pi\) |
−0.566804 | + | 0.823852i | \(0.691820\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −61.6314 | −0.102548 | −0.0512740 | − | 0.998685i | \(-0.516328\pi\) | ||||
−0.0512740 | + | 0.998685i | \(0.516328\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −560.766 | − | 463.472i | −0.929960 | − | 0.768611i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −981.988 | − | 566.951i | −1.62312 | − | 0.937109i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −95.0993 | − | 164.717i | −0.156671 | − | 0.271362i | 0.776995 | − | 0.629507i | \(-0.216743\pi\) |
−0.933666 | + | 0.358144i | \(0.883410\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −131.477 | + | 75.9085i | −0.215184 | + | 0.124237i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.3908 | − | 26.6577i | 0.0251074 | − | 0.0434873i | −0.853199 | − | 0.521586i | \(-0.825341\pi\) |
0.878306 | + | 0.478099i | \(0.158674\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1240.98 | − | 446.458i | −2.01785 | − | 0.725949i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 60.7242i | 0.0984184i | 0.998788 | + | 0.0492092i | \(0.0156701\pi\) | ||||
−0.998788 | + | 0.0492092i | \(0.984330\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.0151 | − | 71.0402i | 0.0662602 | − | 0.114766i | −0.830992 | − | 0.556284i | \(-0.812227\pi\) |
0.897252 | + | 0.441518i | \(0.145560\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −444.100 | − | 249.834i | −0.715137 | − | 0.402310i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −937.588 | − | 1623.95i | −1.50014 | − | 2.59832i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 268.825 | + | 317.963i | 0.428748 | + | 0.507118i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 146.661i | − | 0.233165i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −230.761 | −0.365707 | −0.182853 | − | 0.983140i | \(-0.558533\pi\) | ||||
−0.182853 | + | 0.983140i | \(0.558533\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 587.038 | − | 496.317i | 0.927391 | − | 0.784071i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1304.07 | + | 752.904i | −2.05365 | + | 1.18568i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −580.942 | − | 97.9845i | −0.909142 | − | 0.153340i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −779.922 | − | 450.288i | −1.21673 | − | 0.702478i | −0.252511 | − | 0.967594i | \(-0.581256\pi\) |
−0.964217 | + | 0.265116i | \(0.914590\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −440.051 | −0.684372 | −0.342186 | − | 0.939632i | \(-0.611167\pi\) | ||||
−0.342186 | + | 0.939632i | \(0.611167\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 458.782 | − | 1275.23i | 0.711289 | − | 1.97711i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −698.320 | − | 403.175i | −1.07932 | − | 0.623146i | −0.148607 | − | 0.988896i | \(-0.547479\pi\) |
−0.930713 | + | 0.365750i | \(0.880812\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 99.2248 | + | 171.862i | 0.152889 | + | 0.264811i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 295.397 | − | 170.547i | 0.452368 | − | 0.261175i | −0.256462 | − | 0.966554i | \(-0.582557\pi\) |
0.708830 | + | 0.705379i | \(0.249223\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1186.28 | + | 2054.69i | −1.81111 | + | 3.13693i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 697.461 | + | 576.451i | 1.06159 | + | 0.877398i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 648.132i | − | 0.983509i | −0.870734 | − | 0.491755i | \(-0.836356\pi\) | ||
0.870734 | − | 0.491755i | \(-0.163644\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −587.357 | + | 1017.33i | −0.888589 | + | 1.53908i | −0.0470455 | + | 0.998893i | \(0.514981\pi\) |
−0.841544 | + | 0.540189i | \(0.818353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −61.4735 | + | 11.0754i | −0.0927203 | + | 0.0167050i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −387.705 | − | 671.524i | −0.581266 | − | 1.00678i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −425.828 | + | 360.020i | −0.636514 | + | 0.538147i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 308.987i | 0.460487i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.4980 | −0.0200565 | −0.0100283 | − | 0.999950i | \(-0.503192\pi\) | ||||
−0.0100283 | + | 0.999950i | \(0.503192\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1728.99 | − | 19.2981i | 2.56146 | − | 0.0285898i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −110.700 | + | 63.9129i | −0.163516 | + | 0.0944061i | −0.579525 | − | 0.814955i | \(-0.696762\pi\) |
0.416009 | + | 0.909361i | \(0.363429\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 233.877 | − | 42.1365i | 0.343431 | − | 0.0618745i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −599.478 | − | 346.109i | −0.877713 | − | 0.506748i | −0.00780909 | − | 0.999970i | \(-0.502486\pi\) |
−0.869904 | + | 0.493222i | \(0.835819\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2114.62 | −3.08704 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 493.243 | + | 177.450i | 0.717967 | + | 0.258298i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.6439 | + | 6.72262i | 0.0168997 | + | 0.00975707i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −659.139 | − | 1141.66i | −0.953892 | − | 1.65219i | −0.736884 | − | 0.676019i | \(-0.763704\pi\) |
−0.217007 | − | 0.976170i | \(-0.569630\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 576.254 | − | 332.701i | 0.829143 | − | 0.478706i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −77.8666 | + | 134.869i | −0.111717 | + | 0.193499i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −317.830 | + | 883.444i | −0.454692 | + | 1.26387i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 489.285i | − | 0.697981i | −0.937126 | − | 0.348991i | \(-0.886525\pi\) | ||
0.937126 | − | 0.348991i | \(-0.113475\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −196.059 | + | 339.584i | −0.278889 | + | 0.483050i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −122.340 | − | 679.044i | −0.173532 | − | 0.963182i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −279.059 | − | 483.344i | −0.393595 | − | 0.681726i | 0.599326 | − | 0.800505i | \(-0.295435\pi\) |
−0.992921 | + | 0.118779i | \(0.962102\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 180.633 | − | 67.2713i | 0.254055 | − | 0.0946150i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 88.8600i | − | 0.124628i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −912.753 | −1.27658 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −462.249 | − | 546.742i | −0.644698 | − | 0.762542i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.3244 | + | 18.6625i | −0.0449575 | + | 0.0259562i | −0.522310 | − | 0.852756i | \(-0.674930\pi\) |
0.477353 | + | 0.878712i | \(0.341596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 77.7956 | + | 431.801i | 0.107601 | + | 0.597235i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2278.73 | + | 1315.62i | 3.14307 | + | 1.81465i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1010.66 | 1.39017 | 0.695087 | − | 0.718926i | \(-0.255366\pi\) | ||||
0.695087 | + | 0.718926i | \(0.255366\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −350.318 | + | 639.311i | −0.480545 | + | 0.876970i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −138.592 | − | 80.0159i | −0.189592 | − | 0.109461i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 108.369 | + | 187.701i | 0.147844 | + | 0.256072i | 0.930430 | − | 0.366469i | \(-0.119433\pi\) |
−0.782587 | + | 0.622542i | \(0.786100\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1087.13 | + | 627.657i | −1.47508 | + | 0.851637i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 293.383 | − | 508.154i | 0.397000 | − | 0.687624i | −0.596354 | − | 0.802721i | \(-0.703385\pi\) |
0.993354 | + | 0.115097i | \(0.0367180\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 157.144 | + | 56.5345i | 0.212070 | + | 0.0762948i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 380.578i | 0.512218i | 0.966648 | + | 0.256109i | \(0.0824406\pi\) | ||||
−0.966648 | + | 0.256109i | \(0.917559\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1058.30 | − | 1833.03i | 1.42054 | − | 2.46045i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −437.868 | − | 73.8530i | −0.586169 | − | 0.0988661i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 670.320 | + | 1161.03i | 0.892570 | + | 1.54598i | 0.836783 | + | 0.547534i | \(0.184433\pi\) |
0.0557869 | + | 0.998443i | \(0.482233\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 74.2541 | + | 87.8270i | 0.0986111 | + | 0.116636i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 189.487i | 0.250976i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 487.210 | 0.643607 | 0.321803 | − | 0.946806i | \(-0.395711\pi\) | ||||
0.321803 | + | 0.946806i | \(0.395711\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −671.423 | + | 567.661i | −0.884615 | + | 0.747906i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 576.981 | − | 333.120i | 0.758188 | − | 0.437740i | −0.0704570 | − | 0.997515i | \(-0.522446\pi\) |
0.828645 | + | 0.559775i | \(0.189112\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 47.2141 | − | 279.929i | 0.0617178 | − | 0.365920i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 68.9325 | + | 39.7982i | 0.0898729 | + | 0.0518882i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 129.409 | 0.168282 | 0.0841412 | − | 0.996454i | \(-0.473185\pi\) | ||||
0.0841412 | + | 0.996454i | \(0.473185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −240.176 | + | 667.597i | −0.311513 | + | 0.865884i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −145.738 | − | 84.1419i | −0.188536 | − | 0.108851i | 0.402761 | − | 0.915305i | \(-0.368051\pi\) |
−0.591297 | + | 0.806454i | \(0.701384\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 150.767 | + | 261.137i | 0.194538 | + | 0.336950i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 360.590 | − | 208.187i | 0.462889 | − | 0.267249i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −508.288 | + | 880.380i | −0.650816 | + | 1.12725i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −954.480 | + | 565.366i | −1.21900 | + | 0.722051i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1752.12i | 2.23200i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −143.643 | + | 248.796i | −0.182519 | + | 0.316132i | −0.942738 | − | 0.333535i | \(-0.891758\pi\) |
0.760219 | + | 0.649667i | \(0.225092\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 245.494 | − | 44.2296i | 0.311146 | − | 0.0560578i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 61.9660 | + | 107.328i | 0.0781412 | + | 0.135345i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −46.6633 | + | 39.4519i | −0.0586960 | + | 0.0496251i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 107.769i | 0.135219i | 0.997712 | + | 0.0676094i | \(0.0215372\pi\) | ||||
−0.997712 | + | 0.0676094i | \(0.978463\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −81.4744 | −0.101970 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 146.336 | + | 392.932i | 0.182691 | + | 0.490552i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1352.14 | − | 780.658i | 1.68386 | − | 0.972177i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −984.344 | + | 177.345i | −1.21976 | + | 0.219758i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 145.589 | + | 84.0556i | 0.179961 | + | 0.103901i | 0.587274 | − | 0.809388i | \(-0.300201\pi\) |
−0.407313 | + | 0.913289i | \(0.633534\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1013.65 | −1.24987 | −0.624936 | − | 0.780676i | \(-0.714875\pi\) | ||||
−0.624936 | + | 0.780676i | \(0.714875\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 616.656 | + | 221.850i | 0.758495 | + | 0.272878i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1653.74 | + | 954.788i | 2.02913 | + | 1.17152i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 213.933 | + | 370.543i | 0.261852 | + | 0.453541i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 116.575 | − | 67.3048i | 0.141992 | − | 0.0819790i | −0.427321 | − | 0.904100i | \(-0.640543\pi\) |
0.569313 | + | 0.822121i | \(0.307209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −160.073 | + | 277.255i | −0.194500 | + | 0.336883i | −0.946736 | − | 0.322010i | \(-0.895642\pi\) |
0.752237 | + | 0.658893i | \(0.228975\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1010.00 | − | 2807.40i | 1.22424 | − | 3.40291i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1244.18i | − | 1.50444i | −0.658910 | − | 0.752222i | \(-0.728982\pi\) | ||
0.658910 | − | 0.752222i | \(-0.271018\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 460.870 | − | 798.250i | 0.555935 | − | 0.962907i | −0.441895 | − | 0.897067i | \(-0.645694\pi\) |
0.997830 | − | 0.0658406i | \(-0.0209729\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −51.7289 | − | 287.118i | −0.0622489 | − | 0.345510i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 979.446 | + | 1696.45i | 1.17299 | + | 2.03168i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −127.122 | + | 1.41887i | −0.151878 | + | 0.00169519i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 494.231i | 0.589072i | 0.955640 | + | 0.294536i | \(0.0951650\pi\) | ||||
−0.955640 | + | 0.294536i | \(0.904835\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −847.162 | −1.00733 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −747.797 | − | 884.486i | −0.887066 | − | 1.04921i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1064.01 | − | 614.304i | 1.25918 | − | 0.726987i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −141.148 | − | 783.437i | −0.166253 | − | 0.922777i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −717.079 | − | 414.005i | −0.842630 | − | 0.486493i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1063.29 | 1.24653 | 0.623265 | − | 0.782011i | \(-0.285806\pi\) | ||||
0.623265 | + | 0.782011i | \(0.285806\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −483.535 | + | 585.040i | −0.565538 | + | 0.684257i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −184.365 | − | 106.443i | −0.215128 | − | 0.124204i | 0.388564 | − | 0.921422i | \(-0.372971\pi\) |
−0.603693 | + | 0.797217i | \(0.706305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 112.025 | + | 194.034i | 0.130414 | + | 0.225883i | 0.923836 | − | 0.382788i | \(-0.125036\pi\) |
−0.793422 | + | 0.608672i | \(0.791703\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −812.247 | + | 468.951i | −0.941190 | + | 0.543396i | −0.890333 | − | 0.455310i | \(-0.849529\pi\) |
−0.0508567 | + | 0.998706i | \(0.516195\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 808.755 | − | 1400.81i | 0.934977 | − | 1.61943i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 784.269 | + | 282.151i | 0.904577 | + | 0.325433i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 332.596i | − | 0.382734i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −251.748 | + | 436.040i | −0.289033 | + | 0.500620i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −54.3833 | + | 322.434i | −0.0622947 | + | 0.369340i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −797.634 | − | 1381.54i | −0.909503 | − | 1.57531i | −0.814756 | − | 0.579804i | \(-0.803129\pi\) |
−0.0947465 | − | 0.995501i | \(-0.530204\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 485.113 | + | 573.786i | 0.551891 | + | 0.652771i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.6704i | 0.0586497i | 0.999570 | + | 0.0293249i | \(0.00933573\pi\) | ||||
−0.999570 | + | 0.0293249i | \(0.990664\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1503.98 | −1.70326 | −0.851629 | − | 0.524145i | \(-0.824385\pi\) | ||||
−0.851629 | + | 0.524145i | \(0.824385\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −276.249 | + | 233.557i | −0.312146 | + | 0.263906i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −749.104 | + | 432.495i | −0.844537 | + | 0.487593i | −0.858804 | − | 0.512305i | \(-0.828792\pi\) |
0.0142671 | + | 0.999898i | \(0.495458\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 822.807 | + | 951.462i | 0.923464 | + | 1.06786i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 188.649 | + | 108.916i | 0.211253 | + | 0.121967i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 283.882 | 0.317187 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −119.380 | + | 331.831i | −0.133089 | + | 0.369934i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −167.541 | − | 96.7296i | −0.186363 | − | 0.107597i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.60778 | + | 6.24885i | 0.00400419 | + | 0.00693546i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2075.49 | − | 1198.28i | 2.29336 | − | 1.32407i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 362.948 | − | 628.644i | 0.400163 | − | 0.693102i | −0.593582 | − | 0.804773i | \(-0.702287\pi\) |
0.993745 | + | 0.111671i | \(0.0356202\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 588.346 | − | 711.854i | 0.647246 | − | 0.783118i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1418.21i | − | 1.55676i | −0.627794 | − | 0.778379i | \(-0.716042\pi\) | ||
0.627794 | − | 0.778379i | \(-0.283958\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −383.107 | + | 663.561i | −0.419614 | + | 0.726792i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −554.320 | + | 99.8693i | −0.605814 | + | 0.109147i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −88.8261 | − | 153.851i | −0.0966552 | − | 0.167412i | 0.813643 | − | 0.581365i | \(-0.197481\pi\) |
−0.910298 | + | 0.413953i | \(0.864148\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −932.929 | + | 788.753i | −1.01295 | + | 0.856410i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 407.740i | 0.441755i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2809.75 | 3.03756 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −942.502 | + | 351.006i | −1.01672 | + | 0.378648i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −870.145 | + | 502.378i | −0.936647 | + | 0.540773i | −0.888908 | − | 0.458087i | \(-0.848535\pi\) |
−0.0477390 | + | 0.998860i | \(0.515202\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 305.329 | − | 55.0098i | 0.327255 | − | 0.0589602i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −424.214 | − | 244.920i | −0.453704 | − | 0.261946i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 943.357 | 1.00678 | 0.503392 | − | 0.864058i | \(-0.332085\pi\) | ||||
0.503392 | + | 0.864058i | \(0.332085\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 731.925 | + | 263.319i | 0.779473 | + | 0.280425i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1224.73 | + | 707.099i | 1.30152 | + | 0.751434i | 0.980665 | − | 0.195694i | \(-0.0626961\pi\) |
0.320856 | + | 0.947128i | \(0.396029\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 439.616 | + | 761.437i | 0.466188 | + | 0.807462i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 213.677 | − | 123.367i | 0.225636 | − | 0.130271i | −0.382921 | − | 0.923781i | \(-0.625082\pi\) |
0.608557 | + | 0.793510i | \(0.291749\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 313.115 | − | 542.331i | 0.329942 | − | 0.571477i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −232.184 | + | 645.382i | −0.244148 | + | 0.678635i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1753.94i | − | 1.84044i | −0.391406 | − | 0.920218i | \(-0.628011\pi\) | ||
0.391406 | − | 0.920218i | \(-0.371989\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1000.80 | + | 1733.44i | −1.04796 | + | 1.81512i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 339.408 | + | 1883.87i | 0.354658 | + | 1.96851i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 469.415 | + | 813.051i | 0.488465 | + | 0.846046i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −94.4965 | − | 253.737i | −0.0981272 | − | 0.263486i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1553.37i | − | 1.60971i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.97638 | −0.00411208 | −0.00205604 | − | 0.999998i | \(-0.500654\pi\) | ||||
−0.00205604 | + | 0.999998i | \(0.500654\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 57.8646 | + | 68.4417i | 0.0597158 | + | 0.0706312i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −707.336 | + | 408.381i | −0.728462 | + | 0.420577i | −0.817859 | − | 0.575419i | \(-0.804839\pi\) |
0.0893975 | + | 0.995996i | \(0.471506\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −212.184 | − | 1177.72i | −0.217625 | − | 1.20791i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 85.5224 | + | 49.3764i | 0.0875357 | + | 0.0505388i | 0.543129 | − | 0.839649i | \(-0.317239\pi\) |
−0.455593 | + | 0.890188i | \(0.650573\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 723.498 | 0.739017 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −296.280 | − | 244.875i | −0.302018 | − | 0.249617i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 910.492 | + | 525.673i | 0.926238 | + | 0.534764i | 0.885620 | − | 0.464411i | \(-0.153734\pi\) |
0.0406179 | + | 0.999175i | \(0.487067\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −817.136 | − | 1415.32i | −0.829580 | − | 1.43687i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −782.454 | + | 451.750i | −0.791157 | + | 0.456775i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 64.1255 | − | 111.069i | 0.0647079 | − | 0.112077i | −0.831856 | − | 0.554991i | \(-0.812722\pi\) |
0.896564 | + | 0.442913i | \(0.146055\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −173.978 | − | 62.5907i | −0.175204 | − | 0.0630319i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1323.43i | 1.33008i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 656.222 | − | 1136.61i | 0.658196 | − | 1.14003i | −0.322886 | − | 0.946438i | \(-0.604653\pi\) |
0.981082 | − | 0.193591i | \(-0.0620136\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −580.819 | + | 1032.45i | −0.581400 | + | 1.03348i |
(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 | 588.3.p.f.557.2 | 8 | ||
3.2 | odd | 2 | inner | 588.3.p.f.557.3 | 8 | ||
7.2 | even | 3 | inner | 588.3.p.f.569.3 | 8 | ||
7.3 | odd | 6 | 588.3.c.h.197.1 | 4 | |||
7.4 | even | 3 | 84.3.c.a.29.4 | yes | 4 | ||
7.5 | odd | 6 | 588.3.p.h.569.2 | 8 | |||
7.6 | odd | 2 | 588.3.p.h.557.3 | 8 | |||
21.2 | odd | 6 | inner | 588.3.p.f.569.2 | 8 | ||
21.5 | even | 6 | 588.3.p.h.569.3 | 8 | |||
21.11 | odd | 6 | 84.3.c.a.29.3 | ✓ | 4 | ||
21.17 | even | 6 | 588.3.c.h.197.2 | 4 | |||
21.20 | even | 2 | 588.3.p.h.557.2 | 8 | |||
28.11 | odd | 6 | 336.3.d.a.113.1 | 4 | |||
35.4 | even | 6 | 2100.3.g.a.701.1 | 4 | |||
35.18 | odd | 12 | 2100.3.e.a.449.4 | 8 | |||
35.32 | odd | 12 | 2100.3.e.a.449.5 | 8 | |||
56.11 | odd | 6 | 1344.3.d.g.449.4 | 4 | |||
56.53 | even | 6 | 1344.3.d.a.449.1 | 4 | |||
63.4 | even | 3 | 2268.3.bg.a.2213.1 | 8 | |||
63.11 | odd | 6 | 2268.3.bg.a.701.1 | 8 | |||
63.25 | even | 3 | 2268.3.bg.a.701.4 | 8 | |||
63.32 | odd | 6 | 2268.3.bg.a.2213.4 | 8 | |||
84.11 | even | 6 | 336.3.d.a.113.2 | 4 | |||
105.32 | even | 12 | 2100.3.e.a.449.3 | 8 | |||
105.53 | even | 12 | 2100.3.e.a.449.6 | 8 | |||
105.74 | odd | 6 | 2100.3.g.a.701.2 | 4 | |||
168.11 | even | 6 | 1344.3.d.g.449.3 | 4 | |||
168.53 | odd | 6 | 1344.3.d.a.449.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.3.c.a.29.3 | ✓ | 4 | 21.11 | odd | 6 | ||
84.3.c.a.29.4 | yes | 4 | 7.4 | even | 3 | ||
336.3.d.a.113.1 | 4 | 28.11 | odd | 6 | |||
336.3.d.a.113.2 | 4 | 84.11 | even | 6 | |||
588.3.c.h.197.1 | 4 | 7.3 | odd | 6 | |||
588.3.c.h.197.2 | 4 | 21.17 | even | 6 | |||
588.3.p.f.557.2 | 8 | 1.1 | even | 1 | trivial | ||
588.3.p.f.557.3 | 8 | 3.2 | odd | 2 | inner | ||
588.3.p.f.569.2 | 8 | 21.2 | odd | 6 | inner | ||
588.3.p.f.569.3 | 8 | 7.2 | even | 3 | inner | ||
588.3.p.h.557.2 | 8 | 21.20 | even | 2 | |||
588.3.p.h.557.3 | 8 | 7.6 | odd | 2 | |||
588.3.p.h.569.2 | 8 | 7.5 | odd | 6 | |||
588.3.p.h.569.3 | 8 | 21.5 | even | 6 | |||
1344.3.d.a.449.1 | 4 | 56.53 | even | 6 | |||
1344.3.d.a.449.2 | 4 | 168.53 | odd | 6 | |||
1344.3.d.g.449.3 | 4 | 168.11 | even | 6 | |||
1344.3.d.g.449.4 | 4 | 56.11 | odd | 6 | |||
2100.3.e.a.449.3 | 8 | 105.32 | even | 12 | |||
2100.3.e.a.449.4 | 8 | 35.18 | odd | 12 | |||
2100.3.e.a.449.5 | 8 | 35.32 | odd | 12 | |||
2100.3.e.a.449.6 | 8 | 105.53 | even | 12 | |||
2100.3.g.a.701.1 | 4 | 35.4 | even | 6 | |||
2100.3.g.a.701.2 | 4 | 105.74 | odd | 6 | |||
2268.3.bg.a.701.1 | 8 | 63.11 | odd | 6 | |||
2268.3.bg.a.701.4 | 8 | 63.25 | even | 3 | |||
2268.3.bg.a.2213.1 | 8 | 63.4 | even | 3 | |||
2268.3.bg.a.2213.4 | 8 | 63.32 | odd | 6 |