Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(1077,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.1077");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.c (of order \(2\), degree \(1\), 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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 32x^{14} + 512x^{12} - 2272x^{10} - 1087x^{8} + 72448x^{6} + 819200x^{4} + 1310720x^{2} + 1048576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1077.7 | ||
Root | \(3.90726 - 1.61844i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1077 |
Dual form | 1078.2.c.c.1077.10 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.84776i | 1.06680i | 0.845862 | + | 0.533402i | \(0.179087\pi\) | ||||
−0.845862 | + | 0.533402i | \(0.820913\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 2.47151i | − | 1.10529i | −0.833415 | − | 0.552647i | \(-0.813618\pi\) | ||
0.833415 | − | 0.552647i | \(-0.186382\pi\) | |||||||
\(6\) | 1.84776 | 0.754344 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.414214 | −0.138071 | ||||||||
\(10\) | −2.47151 | −0.781562 | ||||||||
\(11\) | −1.99049 | − | 2.65291i | −0.600155 | − | 0.799884i | ||||
\(12\) | − | 1.84776i | − | 0.533402i | ||||||
\(13\) | −1.96452 | −0.544859 | −0.272429 | − | 0.962176i | \(-0.587827\pi\) | ||||
−0.272429 | + | 0.962176i | \(0.587827\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.56676 | 1.17913 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.64974 | −1.37026 | −0.685131 | − | 0.728419i | \(-0.740255\pi\) | ||||
−0.685131 | + | 0.728419i | \(0.740255\pi\) | |||||||
\(18\) | 0.414214i | 0.0976311i | ||||||||
\(19\) | −0.906978 | −0.208075 | −0.104038 | − | 0.994573i | \(-0.533176\pi\) | ||||
−0.104038 | + | 0.994573i | \(0.533176\pi\) | |||||||
\(20\) | 2.47151i | 0.552647i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.65291 | + | 1.99049i | −0.565603 | + | 0.424374i | ||||
\(23\) | −0.936812 | −0.195339 | −0.0976694 | − | 0.995219i | \(-0.531139\pi\) | ||||
−0.0976694 | + | 0.995219i | \(0.531139\pi\) | |||||||
\(24\) | −1.84776 | −0.377172 | ||||||||
\(25\) | −1.10838 | −0.221677 | ||||||||
\(26\) | 1.96452i | 0.385273i | ||||||||
\(27\) | 4.77791i | 0.919509i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.50358i | − | 1.39338i | −0.717373 | − | 0.696689i | \(-0.754656\pi\) | ||
0.717373 | − | 0.696689i | \(-0.245344\pi\) | |||||||
\(30\) | − | 4.56676i | − | 0.833773i | ||||||
\(31\) | 4.71925i | 0.847603i | 0.905755 | + | 0.423801i | \(0.139305\pi\) | ||||
−0.905755 | + | 0.423801i | \(0.860695\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 4.90195 | − | 3.67794i | 0.853319 | − | 0.640248i | ||||
\(34\) | 5.64974i | 0.968922i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.414214 | 0.0690356 | ||||||||
\(37\) | −9.62995 | −1.58315 | −0.791577 | − | 0.611069i | \(-0.790740\pi\) | ||||
−0.791577 | + | 0.611069i | \(0.790740\pi\) | |||||||
\(38\) | 0.906978i | 0.147131i | ||||||||
\(39\) | − | 3.62995i | − | 0.581257i | ||||||
\(40\) | 2.47151 | 0.390781 | ||||||||
\(41\) | −6.93240 | −1.08266 | −0.541329 | − | 0.840811i | \(-0.682079\pi\) | ||||
−0.541329 | + | 0.840811i | \(0.682079\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.80940i | − | 1.03842i | −0.854645 | − | 0.519212i | \(-0.826225\pi\) | ||
0.854645 | − | 0.519212i | \(-0.173775\pi\) | |||||||
\(44\) | 1.99049 | + | 2.65291i | 0.300077 | + | 0.399942i | ||||
\(45\) | 1.02373i | 0.152609i | ||||||||
\(46\) | 0.936812i | 0.138125i | ||||||||
\(47\) | − | 4.00225i | − | 0.583788i | −0.956451 | − | 0.291894i | \(-0.905715\pi\) | ||
0.956451 | − | 0.291894i | \(-0.0942854\pi\) | |||||||
\(48\) | 1.84776i | 0.266701i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.10838i | 0.156749i | ||||||||
\(51\) | − | 10.4394i | − | 1.46180i | ||||||
\(52\) | 1.96452 | 0.272429 | ||||||||
\(53\) | 6.56676 | 0.902014 | 0.451007 | − | 0.892520i | \(-0.351065\pi\) | ||||
0.451007 | + | 0.892520i | \(0.351065\pi\) | |||||||
\(54\) | 4.77791 | 0.650191 | ||||||||
\(55\) | −6.55672 | + | 4.91952i | −0.884108 | + | 0.663348i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.67588i | − | 0.221975i | ||||||
\(58\) | −7.50358 | −0.985268 | ||||||||
\(59\) | − | 0.965635i | − | 0.125715i | −0.998023 | − | 0.0628575i | \(-0.979979\pi\) | ||
0.998023 | − | 0.0628575i | \(-0.0200214\pi\) | |||||||
\(60\) | −4.56676 | −0.589567 | ||||||||
\(61\) | −11.9003 | −1.52368 | −0.761838 | − | 0.647768i | \(-0.775703\pi\) | ||||
−0.761838 | + | 0.647768i | \(0.775703\pi\) | |||||||
\(62\) | 4.71925 | 0.599346 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 4.85533i | 0.602230i | ||||||||
\(66\) | −3.67794 | − | 4.90195i | −0.452724 | − | 0.603388i | ||||
\(67\) | 6.72004 | 0.820984 | 0.410492 | − | 0.911864i | \(-0.365357\pi\) | ||||
0.410492 | + | 0.911864i | \(0.365357\pi\) | |||||||
\(68\) | 5.64974 | 0.685131 | ||||||||
\(69\) | − | 1.73100i | − | 0.208388i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.5485 | −1.37055 | −0.685276 | − | 0.728284i | \(-0.740318\pi\) | ||||
−0.685276 | + | 0.728284i | \(0.740318\pi\) | |||||||
\(72\) | − | 0.414214i | − | 0.0488155i | ||||||
\(73\) | 10.8614 | 1.27123 | 0.635617 | − | 0.772004i | \(-0.280746\pi\) | ||||
0.635617 | + | 0.772004i | \(0.280746\pi\) | |||||||
\(74\) | 9.62995i | 1.11946i | ||||||||
\(75\) | − | 2.04803i | − | 0.236486i | ||||||
\(76\) | 0.906978 | 0.104038 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.62995 | −0.411011 | ||||||||
\(79\) | − | 8.48528i | − | 0.954669i | −0.878722 | − | 0.477334i | \(-0.841603\pi\) | ||
0.878722 | − | 0.477334i | \(-0.158397\pi\) | |||||||
\(80\) | − | 2.47151i | − | 0.276324i | ||||||
\(81\) | −10.0711 | −1.11901 | ||||||||
\(82\) | 6.93240i | 0.765555i | ||||||||
\(83\) | −4.83601 | −0.530821 | −0.265411 | − | 0.964135i | \(-0.585507\pi\) | ||||
−0.265411 | + | 0.964135i | \(0.585507\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.9634i | 1.51454i | ||||||||
\(86\) | −6.80940 | −0.734277 | ||||||||
\(87\) | 13.8648 | 1.48646 | ||||||||
\(88\) | 2.65291 | − | 1.99049i | 0.282802 | − | 0.212187i | ||||
\(89\) | − | 12.7340i | − | 1.34981i | −0.737906 | − | 0.674903i | \(-0.764185\pi\) | ||
0.737906 | − | 0.674903i | \(-0.235815\pi\) | |||||||
\(90\) | 1.02373 | 0.107911 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.936812 | 0.0976694 | ||||||||
\(93\) | −8.72004 | −0.904226 | ||||||||
\(94\) | −4.00225 | −0.412800 | ||||||||
\(95\) | 2.24161i | 0.229984i | ||||||||
\(96\) | 1.84776 | 0.188586 | ||||||||
\(97\) | 3.82683i | 0.388556i | 0.980946 | + | 0.194278i | \(0.0622364\pi\) | ||||
−0.980946 | + | 0.194278i | \(0.937764\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.824487 | + | 1.09887i | 0.0828641 | + | 0.110441i | ||||
\(100\) | 1.10838 | 0.110838 | ||||||||
\(101\) | −15.8293 | −1.57508 | −0.787538 | − | 0.616266i | \(-0.788645\pi\) | ||||
−0.787538 | + | 0.616266i | \(0.788645\pi\) | |||||||
\(102\) | −10.4394 | −1.03365 | ||||||||
\(103\) | 0.790221i | 0.0778628i | 0.999242 | + | 0.0389314i | \(0.0123954\pi\) | ||||
−0.999242 | + | 0.0389314i | \(0.987605\pi\) | |||||||
\(104\) | − | 1.96452i | − | 0.192637i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 6.56676i | − | 0.637820i | ||||||
\(107\) | − | 16.6117i | − | 1.60591i | −0.596040 | − | 0.802955i | \(-0.703260\pi\) | ||
0.596040 | − | 0.802955i | \(-0.296740\pi\) | |||||||
\(108\) | − | 4.77791i | − | 0.459755i | ||||||
\(109\) | − | 6.00000i | − | 0.574696i | −0.957826 | − | 0.287348i | \(-0.907226\pi\) | ||
0.957826 | − | 0.287348i | \(-0.0927736\pi\) | |||||||
\(110\) | 4.91952 | + | 6.55672i | 0.469058 | + | 0.625158i | ||||
\(111\) | − | 17.7938i | − | 1.68892i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.76421 | −0.542251 | −0.271126 | − | 0.962544i | \(-0.587396\pi\) | ||||
−0.271126 | + | 0.962544i | \(0.587396\pi\) | |||||||
\(114\) | −1.67588 | −0.156960 | ||||||||
\(115\) | 2.31534i | 0.215907i | ||||||||
\(116\) | 7.50358i | 0.696689i | ||||||||
\(117\) | 0.813729 | 0.0752293 | ||||||||
\(118\) | −0.965635 | −0.0888940 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.56676i | 0.416887i | ||||||||
\(121\) | −3.07591 | + | 10.5612i | −0.279628 | + | 0.960108i | ||||
\(122\) | 11.9003i | 1.07740i | ||||||||
\(123\) | − | 12.8094i | − | 1.15499i | ||||||
\(124\) | − | 4.71925i | − | 0.423801i | ||||||
\(125\) | − | 9.61818i | − | 0.860277i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.6371i | 1.65378i | 0.562367 | + | 0.826888i | \(0.309891\pi\) | ||||
−0.562367 | + | 0.826888i | \(0.690109\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 12.5821 | 1.10780 | ||||||||
\(130\) | 4.85533 | 0.425841 | ||||||||
\(131\) | 19.9835 | 1.74596 | 0.872982 | − | 0.487753i | \(-0.162183\pi\) | ||||
0.872982 | + | 0.487753i | \(0.162183\pi\) | |||||||
\(132\) | −4.90195 | + | 3.67794i | −0.426660 | + | 0.320124i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 6.72004i | − | 0.580523i | ||||||
\(135\) | 11.8087 | 1.01633 | ||||||||
\(136\) | − | 5.64974i | − | 0.484461i | ||||||
\(137\) | 16.4394 | 1.40451 | 0.702254 | − | 0.711926i | \(-0.252177\pi\) | ||||
0.702254 | + | 0.711926i | \(0.252177\pi\) | |||||||
\(138\) | −1.73100 | −0.147353 | ||||||||
\(139\) | 10.7109 | 0.908484 | 0.454242 | − | 0.890878i | \(-0.349910\pi\) | ||||
0.454242 | + | 0.890878i | \(0.349910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.39519 | 0.622787 | ||||||||
\(142\) | 11.5485i | 0.969126i | ||||||||
\(143\) | 3.91035 | + | 5.21169i | 0.327000 | + | 0.435824i | ||||
\(144\) | −0.414214 | −0.0345178 | ||||||||
\(145\) | −18.5452 | −1.54009 | ||||||||
\(146\) | − | 10.8614i | − | 0.898898i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.62995 | 0.791577 | ||||||||
\(149\) | 14.7635i | 1.20947i | 0.796426 | + | 0.604736i | \(0.206721\pi\) | ||||
−0.796426 | + | 0.604736i | \(0.793279\pi\) | |||||||
\(150\) | −2.04803 | −0.167221 | ||||||||
\(151\) | 10.4964i | 0.854187i | 0.904207 | + | 0.427093i | \(0.140462\pi\) | ||||
−0.904207 | + | 0.427093i | \(0.859538\pi\) | |||||||
\(152\) | − | 0.906978i | − | 0.0735656i | ||||||
\(153\) | 2.34020 | 0.189194 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.6637 | 0.936851 | ||||||||
\(156\) | 3.62995i | 0.290629i | ||||||||
\(157\) | 4.61571i | 0.368374i | 0.982891 | + | 0.184187i | \(0.0589651\pi\) | ||||
−0.982891 | + | 0.184187i | \(0.941035\pi\) | |||||||
\(158\) | −8.48528 | −0.675053 | ||||||||
\(159\) | 12.1338i | 0.962273i | ||||||||
\(160\) | −2.47151 | −0.195390 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 10.0711i | 0.791258i | ||||||||
\(163\) | 14.5746 | 1.14157 | 0.570787 | − | 0.821098i | \(-0.306638\pi\) | ||||
0.570787 | + | 0.821098i | \(0.306638\pi\) | |||||||
\(164\) | 6.93240 | 0.541329 | ||||||||
\(165\) | −9.09009 | − | 12.1152i | −0.707663 | − | 0.943170i | ||||
\(166\) | 4.83601i | 0.375347i | ||||||||
\(167\) | 7.37045 | 0.570342 | 0.285171 | − | 0.958477i | \(-0.407950\pi\) | ||||
0.285171 | + | 0.958477i | \(0.407950\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.14068 | −0.703129 | ||||||||
\(170\) | 13.9634 | 1.07094 | ||||||||
\(171\) | 0.375683 | 0.0287292 | ||||||||
\(172\) | 6.80940i | 0.519212i | ||||||||
\(173\) | −11.1489 | −0.847637 | −0.423818 | − | 0.905747i | \(-0.639310\pi\) | ||||
−0.423818 | + | 0.905747i | \(0.639310\pi\) | |||||||
\(174\) | − | 13.8648i | − | 1.05109i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.99049 | − | 2.65291i | −0.150039 | − | 0.199971i | ||||
\(177\) | 1.78426 | 0.134113 | ||||||||
\(178\) | −12.7340 | −0.954457 | ||||||||
\(179\) | 15.8087 | 1.18160 | 0.590798 | − | 0.806820i | \(-0.298813\pi\) | ||||
0.590798 | + | 0.806820i | \(0.298813\pi\) | |||||||
\(180\) | − | 1.02373i | − | 0.0763047i | ||||||
\(181\) | 16.6528i | 1.23779i | 0.785473 | + | 0.618896i | \(0.212420\pi\) | ||||
−0.785473 | + | 0.618896i | \(0.787580\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 21.9889i | − | 1.62546i | ||||||
\(184\) | − | 0.936812i | − | 0.0690627i | ||||||
\(185\) | 23.8006i | 1.74985i | ||||||||
\(186\) | 8.72004i | 0.639385i | ||||||||
\(187\) | 11.2457 | + | 14.9883i | 0.822370 | + | 1.09605i | ||||
\(188\) | 4.00225i | 0.291894i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.24161 | 0.162623 | ||||||||
\(191\) | 26.3568 | 1.90711 | 0.953557 | − | 0.301212i | \(-0.0973913\pi\) | ||||
0.953557 | + | 0.301212i | \(0.0973913\pi\) | |||||||
\(192\) | − | 1.84776i | − | 0.133351i | ||||||
\(193\) | 0.694171i | 0.0499675i | 0.999688 | + | 0.0249838i | \(0.00795341\pi\) | ||||
−0.999688 | + | 0.0249838i | \(0.992047\pi\) | |||||||
\(194\) | 3.82683 | 0.274751 | ||||||||
\(195\) | −8.97148 | −0.642461 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.74519i | 0.694316i | 0.937807 | + | 0.347158i | \(0.112853\pi\) | ||||
−0.937807 | + | 0.347158i | \(0.887147\pi\) | |||||||
\(198\) | 1.09887 | − | 0.824487i | 0.0780935 | − | 0.0585938i | ||||
\(199\) | − | 7.03460i | − | 0.498669i | −0.968417 | − | 0.249335i | \(-0.919788\pi\) | ||
0.968417 | − | 0.249335i | \(-0.0802119\pi\) | |||||||
\(200\) | − | 1.10838i | − | 0.0783746i | ||||||
\(201\) | 12.4170i | 0.875829i | ||||||||
\(202\) | 15.8293i | 1.11375i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 10.4394i | 0.730901i | ||||||||
\(205\) | 17.1335i | 1.19666i | ||||||||
\(206\) | 0.790221 | 0.0550573 | ||||||||
\(207\) | 0.388040 | 0.0269707 | ||||||||
\(208\) | −1.96452 | −0.136215 | ||||||||
\(209\) | 1.80533 | + | 2.40614i | 0.124877 | + | 0.166436i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 24.1152i | − | 1.66016i | −0.557643 | − | 0.830081i | \(-0.688294\pi\) | ||
0.557643 | − | 0.830081i | \(-0.311706\pi\) | |||||||
\(212\) | −6.56676 | −0.451007 | ||||||||
\(213\) | − | 21.3388i | − | 1.46211i | ||||||
\(214\) | −16.6117 | −1.13555 | ||||||||
\(215\) | −16.8295 | −1.14777 | ||||||||
\(216\) | −4.77791 | −0.325096 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | 20.0693i | 1.35616i | ||||||||
\(220\) | 6.55672 | − | 4.91952i | 0.442054 | − | 0.331674i | ||||
\(221\) | 11.0990 | 0.746600 | ||||||||
\(222\) | −17.7938 | −1.19424 | ||||||||
\(223\) | 2.90530i | 0.194553i | 0.995257 | + | 0.0972765i | \(0.0310131\pi\) | ||||
−0.995257 | + | 0.0972765i | \(0.968987\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.459108 | 0.0306072 | ||||||||
\(226\) | 5.76421i | 0.383429i | ||||||||
\(227\) | −14.4270 | −0.957552 | −0.478776 | − | 0.877937i | \(-0.658919\pi\) | ||||
−0.478776 | + | 0.877937i | \(0.658919\pi\) | |||||||
\(228\) | 1.67588i | 0.110988i | ||||||||
\(229\) | − | 7.09696i | − | 0.468980i | −0.972118 | − | 0.234490i | \(-0.924658\pi\) | ||
0.972118 | − | 0.234490i | \(-0.0753421\pi\) | |||||||
\(230\) | 2.31534 | 0.152669 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.50358 | 0.492634 | ||||||||
\(233\) | − | 4.16116i | − | 0.272607i | −0.990667 | − | 0.136303i | \(-0.956478\pi\) | ||
0.990667 | − | 0.136303i | \(-0.0435222\pi\) | |||||||
\(234\) | − | 0.813729i | − | 0.0531951i | ||||||
\(235\) | −9.89162 | −0.645258 | ||||||||
\(236\) | 0.965635i | 0.0628575i | ||||||||
\(237\) | 15.6788 | 1.01844 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.8625i | 1.28480i | 0.766371 | + | 0.642399i | \(0.222061\pi\) | ||||
−0.766371 | + | 0.642399i | \(0.777939\pi\) | |||||||
\(240\) | 4.56676 | 0.294783 | ||||||||
\(241\) | 14.4893 | 0.933341 | 0.466670 | − | 0.884431i | \(-0.345453\pi\) | ||||
0.466670 | + | 0.884431i | \(0.345453\pi\) | |||||||
\(242\) | 10.5612 | + | 3.07591i | 0.678899 | + | 0.197727i | ||||
\(243\) | − | 4.27518i | − | 0.274253i | ||||||
\(244\) | 11.9003 | 0.761838 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −12.8094 | −0.816698 | ||||||||
\(247\) | 1.78177 | 0.113371 | ||||||||
\(248\) | −4.71925 | −0.299673 | ||||||||
\(249\) | − | 8.93578i | − | 0.566282i | ||||||
\(250\) | −9.61818 | −0.608307 | ||||||||
\(251\) | − | 14.6156i | − | 0.922529i | −0.887263 | − | 0.461264i | \(-0.847396\pi\) | ||
0.887263 | − | 0.461264i | \(-0.152604\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.86471 | + | 2.48528i | 0.117234 | + | 0.156248i | ||||
\(254\) | 18.6371 | 1.16940 | ||||||||
\(255\) | −25.8010 | −1.61572 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.1182i | 1.44207i | 0.692898 | + | 0.721035i | \(0.256334\pi\) | ||||
−0.692898 | + | 0.721035i | \(0.743666\pi\) | |||||||
\(258\) | − | 12.5821i | − | 0.783330i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 4.85533i | − | 0.301115i | ||||||
\(261\) | 3.10808i | 0.192385i | ||||||||
\(262\) | − | 19.9835i | − | 1.23458i | ||||||
\(263\) | − | 8.48528i | − | 0.523225i | −0.965173 | − | 0.261612i | \(-0.915746\pi\) | ||
0.965173 | − | 0.261612i | \(-0.0842542\pi\) | |||||||
\(264\) | 3.67794 | + | 4.90195i | 0.226362 | + | 0.301694i | ||||
\(265\) | − | 16.2299i | − | 0.996992i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.5294 | 1.43998 | ||||||||
\(268\) | −6.72004 | −0.410492 | ||||||||
\(269\) | − | 30.6005i | − | 1.86575i | −0.360203 | − | 0.932874i | \(-0.617293\pi\) | ||
0.360203 | − | 0.932874i | \(-0.382707\pi\) | |||||||
\(270\) | − | 11.8087i | − | 0.718653i | ||||||
\(271\) | −13.2016 | −0.801942 | −0.400971 | − | 0.916091i | \(-0.631327\pi\) | ||||
−0.400971 | + | 0.916091i | \(0.631327\pi\) | |||||||
\(272\) | −5.64974 | −0.342566 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 16.4394i | − | 0.993138i | ||||||
\(275\) | 2.20623 | + | 2.94045i | 0.133040 | + | 0.177316i | ||||
\(276\) | 1.73100i | 0.104194i | ||||||||
\(277\) | 3.98886i | 0.239667i | 0.992794 | + | 0.119834i | \(0.0382361\pi\) | ||||
−0.992794 | + | 0.119834i | \(0.961764\pi\) | |||||||
\(278\) | − | 10.7109i | − | 0.642395i | ||||||
\(279\) | − | 1.95478i | − | 0.117030i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.94293i | − | 0.354526i | −0.984164 | − | 0.177263i | \(-0.943276\pi\) | ||
0.984164 | − | 0.177263i | \(-0.0567243\pi\) | |||||||
\(282\) | − | 7.39519i | − | 0.440377i | ||||||
\(283\) | 21.2661 | 1.26414 | 0.632070 | − | 0.774911i | \(-0.282205\pi\) | ||||
0.632070 | + | 0.774911i | \(0.282205\pi\) | |||||||
\(284\) | 11.5485 | 0.685276 | ||||||||
\(285\) | −4.14195 | −0.245348 | ||||||||
\(286\) | 5.21169 | − | 3.91035i | 0.308174 | − | 0.231224i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.414214i | 0.0244078i | ||||||||
\(289\) | 14.9195 | 0.877621 | ||||||||
\(290\) | 18.5452i | 1.08901i | ||||||||
\(291\) | −7.07107 | −0.414513 | ||||||||
\(292\) | −10.8614 | −0.635617 | ||||||||
\(293\) | 27.7920 | 1.62362 | 0.811812 | − | 0.583919i | \(-0.198481\pi\) | ||||
0.811812 | + | 0.583919i | \(0.198481\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.38658 | −0.138952 | ||||||||
\(296\) | − | 9.62995i | − | 0.559730i | ||||||
\(297\) | 12.6754 | − | 9.51038i | 0.735501 | − | 0.551848i | ||||
\(298\) | 14.7635 | 0.855225 | ||||||||
\(299\) | 1.84038 | 0.106432 | ||||||||
\(300\) | 2.04803i | 0.118243i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.4964 | 0.604001 | ||||||||
\(303\) | − | 29.2488i | − | 1.68030i | ||||||
\(304\) | −0.906978 | −0.0520188 | ||||||||
\(305\) | 29.4117i | 1.68411i | ||||||||
\(306\) | − | 2.34020i | − | 0.133780i | ||||||
\(307\) | −16.2674 | −0.928427 | −0.464214 | − | 0.885723i | \(-0.653663\pi\) | ||||
−0.464214 | + | 0.885723i | \(0.653663\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.46014 | −0.0830644 | ||||||||
\(310\) | − | 11.6637i | − | 0.662454i | ||||||
\(311\) | − | 10.7925i | − | 0.611985i | −0.952034 | − | 0.305993i | \(-0.901012\pi\) | ||
0.952034 | − | 0.305993i | \(-0.0989883\pi\) | |||||||
\(312\) | 3.62995 | 0.205506 | ||||||||
\(313\) | − | 18.3111i | − | 1.03501i | −0.855681 | − | 0.517503i | \(-0.826862\pi\) | ||
0.855681 | − | 0.517503i | \(-0.173138\pi\) | |||||||
\(314\) | 4.61571 | 0.260480 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.48528i | 0.477334i | ||||||||
\(317\) | −0.358905 | −0.0201581 | −0.0100791 | − | 0.999949i | \(-0.503208\pi\) | ||||
−0.0100791 | + | 0.999949i | \(0.503208\pi\) | |||||||
\(318\) | 12.1338 | 0.680430 | ||||||||
\(319\) | −19.9063 | + | 14.9358i | −1.11454 | + | 0.836243i | ||||
\(320\) | 2.47151i | 0.138162i | ||||||||
\(321\) | 30.6943 | 1.71319 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.12419 | 0.285118 | ||||||||
\(324\) | 10.0711 | 0.559504 | ||||||||
\(325\) | 2.17744 | 0.120783 | ||||||||
\(326\) | − | 14.5746i | − | 0.807215i | ||||||
\(327\) | 11.0866 | 0.613088 | ||||||||
\(328\) | − | 6.93240i | − | 0.382778i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −12.1152 | + | 9.09009i | −0.666922 | + | 0.500393i | ||||
\(331\) | −28.9135 | −1.58923 | −0.794615 | − | 0.607114i | \(-0.792327\pi\) | ||||
−0.794615 | + | 0.607114i | \(0.792327\pi\) | |||||||
\(332\) | 4.83601 | 0.265411 | ||||||||
\(333\) | 3.98886 | 0.218588 | ||||||||
\(334\) | − | 7.37045i | − | 0.403293i | ||||||
\(335\) | − | 16.6087i | − | 0.907429i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7.96341i | − | 0.433795i | −0.976194 | − | 0.216897i | \(-0.930406\pi\) | ||
0.976194 | − | 0.216897i | \(-0.0695937\pi\) | |||||||
\(338\) | 9.14068i | 0.497187i | ||||||||
\(339\) | − | 10.6509i | − | 0.578476i | ||||||
\(340\) | − | 13.9634i | − | 0.757272i | ||||||
\(341\) | 12.5198 | − | 9.39362i | 0.677984 | − | 0.508693i | ||||
\(342\) | − | 0.375683i | − | 0.0203146i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.80940 | 0.367138 | ||||||||
\(345\) | −4.27820 | −0.230330 | ||||||||
\(346\) | 11.1489i | 0.599370i | ||||||||
\(347\) | 24.6810i | 1.32494i | 0.749087 | + | 0.662472i | \(0.230493\pi\) | ||||
−0.749087 | + | 0.662472i | \(0.769507\pi\) | |||||||
\(348\) | −13.8648 | −0.743231 | ||||||||
\(349\) | −11.1489 | −0.596788 | −0.298394 | − | 0.954443i | \(-0.596451\pi\) | ||||
−0.298394 | + | 0.954443i | \(0.596451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 9.38628i | − | 0.501003i | ||||||
\(352\) | −2.65291 | + | 1.99049i | −0.141401 | + | 0.106093i | ||||
\(353\) | 21.3852i | 1.13822i | 0.822261 | + | 0.569111i | \(0.192713\pi\) | ||||
−0.822261 | + | 0.569111i | \(0.807287\pi\) | |||||||
\(354\) | − | 1.78426i | − | 0.0948324i | ||||||
\(355\) | 28.5422i | 1.51486i | ||||||||
\(356\) | 12.7340i | 0.674903i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 15.8087i | − | 0.835514i | ||||||
\(359\) | − | 6.24367i | − | 0.329528i | −0.986333 | − | 0.164764i | \(-0.947314\pi\) | ||
0.986333 | − | 0.164764i | \(-0.0526863\pi\) | |||||||
\(360\) | −1.02373 | −0.0539556 | ||||||||
\(361\) | −18.1774 | −0.956705 | ||||||||
\(362\) | 16.6528 | 0.875251 | ||||||||
\(363\) | −19.5145 | − | 5.68354i | −1.02425 | − | 0.298309i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 26.8442i | − | 1.40509i | ||||||
\(366\) | −21.9889 | −1.14938 | ||||||||
\(367\) | − | 28.7533i | − | 1.50091i | −0.660921 | − | 0.750456i | \(-0.729834\pi\) | ||
0.660921 | − | 0.750456i | \(-0.270166\pi\) | |||||||
\(368\) | −0.936812 | −0.0488347 | ||||||||
\(369\) | 2.87149 | 0.149484 | ||||||||
\(370\) | 23.8006 | 1.23733 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.72004 | 0.452113 | ||||||||
\(373\) | 12.3589i | 0.639920i | 0.947431 | + | 0.319960i | \(0.103669\pi\) | ||||
−0.947431 | + | 0.319960i | \(0.896331\pi\) | |||||||
\(374\) | 14.9883 | − | 11.2457i | 0.775025 | − | 0.581503i | ||||
\(375\) | 17.7721 | 0.917747 | ||||||||
\(376\) | 4.00225 | 0.206400 | ||||||||
\(377\) | 14.7409i | 0.759195i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.7822 | −1.22161 | −0.610805 | − | 0.791781i | \(-0.709154\pi\) | ||||
−0.610805 | + | 0.791781i | \(0.709154\pi\) | |||||||
\(380\) | − | 2.24161i | − | 0.114992i | ||||||
\(381\) | −34.4369 | −1.76425 | ||||||||
\(382\) | − | 26.3568i | − | 1.34853i | ||||||
\(383\) | − | 31.8645i | − | 1.62820i | −0.580724 | − | 0.814100i | \(-0.697231\pi\) | ||
0.580724 | − | 0.814100i | \(-0.302769\pi\) | |||||||
\(384\) | −1.84776 | −0.0942931 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.694171 | 0.0353324 | ||||||||
\(387\) | 2.82055i | 0.143376i | ||||||||
\(388\) | − | 3.82683i | − | 0.194278i | ||||||
\(389\) | 21.0155 | 1.06553 | 0.532763 | − | 0.846264i | \(-0.321154\pi\) | ||||
0.532763 | + | 0.846264i | \(0.321154\pi\) | |||||||
\(390\) | 8.97148i | 0.454289i | ||||||||
\(391\) | 5.29274 | 0.267665 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.9246i | 1.86260i | ||||||||
\(394\) | 9.74519 | 0.490955 | ||||||||
\(395\) | −20.9715 | −1.05519 | ||||||||
\(396\) | −0.824487 | − | 1.09887i | −0.0414320 | − | 0.0552205i | ||||
\(397\) | − | 8.31805i | − | 0.417471i | −0.977972 | − | 0.208735i | \(-0.933065\pi\) | ||
0.977972 | − | 0.208735i | \(-0.0669347\pi\) | |||||||
\(398\) | −7.03460 | −0.352612 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.10838 | −0.0554192 | ||||||||
\(401\) | −30.6820 | −1.53219 | −0.766093 | − | 0.642730i | \(-0.777802\pi\) | ||||
−0.766093 | + | 0.642730i | \(0.777802\pi\) | |||||||
\(402\) | 12.4170 | 0.619305 | ||||||||
\(403\) | − | 9.27105i | − | 0.461824i | ||||||
\(404\) | 15.8293 | 0.787538 | ||||||||
\(405\) | 24.8908i | 1.23683i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.1683 | + | 25.5474i | 0.950138 | + | 1.26634i | ||||
\(408\) | 10.4394 | 0.516825 | ||||||||
\(409\) | 9.57877 | 0.473640 | 0.236820 | − | 0.971554i | \(-0.423895\pi\) | ||||
0.236820 | + | 0.971554i | \(0.423895\pi\) | |||||||
\(410\) | 17.1335 | 0.846165 | ||||||||
\(411\) | 30.3760i | 1.49834i | ||||||||
\(412\) | − | 0.790221i | − | 0.0389314i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 0.388040i | − | 0.0190711i | ||||||
\(415\) | 11.9523i | 0.586714i | ||||||||
\(416\) | 1.96452i | 0.0963183i | ||||||||
\(417\) | 19.7911i | 0.969175i | ||||||||
\(418\) | 2.40614 | − | 1.80533i | 0.117688 | − | 0.0883016i | ||||
\(419\) | − | 10.3074i | − | 0.503550i | −0.967786 | − | 0.251775i | \(-0.918986\pi\) | ||
0.967786 | − | 0.251775i | \(-0.0810143\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.8805 | −1.26134 | −0.630669 | − | 0.776052i | \(-0.717219\pi\) | ||||
−0.630669 | + | 0.776052i | \(0.717219\pi\) | |||||||
\(422\) | −24.1152 | −1.17391 | ||||||||
\(423\) | 1.65779i | 0.0806043i | ||||||||
\(424\) | 6.56676i | 0.318910i | ||||||||
\(425\) | 6.26208 | 0.303756 | ||||||||
\(426\) | −21.3388 | −1.03387 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.6117i | 0.802955i | ||||||||
\(429\) | −9.62995 | + | 7.22538i | −0.464938 | + | 0.348845i | ||||
\(430\) | 16.8295i | 0.811593i | ||||||||
\(431\) | 17.0858i | 0.822994i | 0.911411 | + | 0.411497i | \(0.134994\pi\) | ||||
−0.911411 | + | 0.411497i | \(0.865006\pi\) | |||||||
\(432\) | 4.77791i | 0.229877i | ||||||||
\(433\) | − | 1.92881i | − | 0.0926926i | −0.998925 | − | 0.0463463i | \(-0.985242\pi\) | ||
0.998925 | − | 0.0463463i | \(-0.0147578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 34.2671i | − | 1.64298i | ||||||
\(436\) | 6.00000i | 0.287348i | ||||||||
\(437\) | 0.849668 | 0.0406451 | ||||||||
\(438\) | 20.0693 | 0.958949 | ||||||||
\(439\) | 10.4234 | 0.497481 | 0.248741 | − | 0.968570i | \(-0.419983\pi\) | ||||
0.248741 | + | 0.968570i | \(0.419983\pi\) | |||||||
\(440\) | −4.91952 | − | 6.55672i | −0.234529 | − | 0.312579i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 11.0990i | − | 0.527926i | ||||||
\(443\) | 15.9254 | 0.756637 | 0.378318 | − | 0.925675i | \(-0.376502\pi\) | ||||
0.378318 | + | 0.925675i | \(0.376502\pi\) | |||||||
\(444\) | 17.7938i | 0.844458i | ||||||||
\(445\) | −31.4724 | −1.49193 | ||||||||
\(446\) | 2.90530 | 0.137570 | ||||||||
\(447\) | −27.2794 | −1.29027 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.4404 | 0.492712 | 0.246356 | − | 0.969179i | \(-0.420767\pi\) | ||||
0.246356 | + | 0.969179i | \(0.420767\pi\) | |||||||
\(450\) | − | 0.459108i | − | 0.0216426i | ||||||
\(451\) | 13.7989 | + | 18.3911i | 0.649763 | + | 0.866001i | ||||
\(452\) | 5.76421 | 0.271126 | ||||||||
\(453\) | −19.3949 | −0.911250 | ||||||||
\(454\) | 14.4270i | 0.677092i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.67588 | 0.0784801 | ||||||||
\(457\) | − | 18.0582i | − | 0.844725i | −0.906427 | − | 0.422363i | \(-0.861201\pi\) | ||
0.906427 | − | 0.422363i | \(-0.138799\pi\) | |||||||
\(458\) | −7.09696 | −0.331619 | ||||||||
\(459\) | − | 26.9939i | − | 1.25997i | ||||||
\(460\) | − | 2.31534i | − | 0.107953i | ||||||
\(461\) | 11.4500 | 0.533281 | 0.266641 | − | 0.963796i | \(-0.414086\pi\) | ||||
0.266641 | + | 0.963796i | \(0.414086\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.6805 | −1.23995 | −0.619975 | − | 0.784622i | \(-0.712857\pi\) | ||||
−0.619975 | + | 0.784622i | \(0.712857\pi\) | |||||||
\(464\) | − | 7.50358i | − | 0.348345i | ||||||
\(465\) | 21.5517i | 0.999437i | ||||||||
\(466\) | −4.16116 | −0.192762 | ||||||||
\(467\) | − | 9.71626i | − | 0.449615i | −0.974403 | − | 0.224807i | \(-0.927825\pi\) | ||
0.974403 | − | 0.224807i | \(-0.0721753\pi\) | |||||||
\(468\) | −0.813729 | −0.0376146 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.89162i | 0.456266i | ||||||||
\(471\) | −8.52872 | −0.392983 | ||||||||
\(472\) | 0.965635 | 0.0444470 | ||||||||
\(473\) | −18.0648 | + | 13.5540i | −0.830619 | + | 0.623215i | ||||
\(474\) | − | 15.6788i | − | 0.720149i | ||||||
\(475\) | 1.00528 | 0.0461254 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.72004 | −0.124542 | ||||||||
\(478\) | 19.8625 | 0.908489 | ||||||||
\(479\) | −19.2084 | −0.877653 | −0.438826 | − | 0.898572i | \(-0.644606\pi\) | ||||
−0.438826 | + | 0.898572i | \(0.644606\pi\) | |||||||
\(480\) | − | 4.56676i | − | 0.208443i | ||||||
\(481\) | 18.9182 | 0.862595 | ||||||||
\(482\) | − | 14.4893i | − | 0.659972i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.07591 | − | 10.5612i | 0.139814 | − | 0.480054i | ||||
\(485\) | 9.45808 | 0.429469 | ||||||||
\(486\) | −4.27518 | −0.193926 | ||||||||
\(487\) | 0.362596 | 0.0164308 | 0.00821539 | − | 0.999966i | \(-0.497385\pi\) | ||||
0.00821539 | + | 0.999966i | \(0.497385\pi\) | |||||||
\(488\) | − | 11.9003i | − | 0.538701i | ||||||
\(489\) | 26.9304i | 1.21784i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.04374i | 0.0471033i | 0.999723 | + | 0.0235516i | \(0.00749741\pi\) | ||||
−0.999723 | + | 0.0235516i | \(0.992503\pi\) | |||||||
\(492\) | 12.8094i | 0.577493i | ||||||||
\(493\) | 42.3932i | 1.90930i | ||||||||
\(494\) | − | 1.78177i | − | 0.0801658i | ||||||
\(495\) | 2.71588 | − | 2.03773i | 0.122070 | − | 0.0915893i | ||||
\(496\) | 4.71925i | 0.211901i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −8.93578 | −0.400422 | ||||||||
\(499\) | 19.6008 | 0.877453 | 0.438727 | − | 0.898621i | \(-0.355430\pi\) | ||||
0.438727 | + | 0.898621i | \(0.355430\pi\) | |||||||
\(500\) | 9.61818i | 0.430138i | ||||||||
\(501\) | 13.6188i | 0.608443i | ||||||||
\(502\) | −14.6156 | −0.652326 | ||||||||
\(503\) | −36.6503 | −1.63415 | −0.817077 | − | 0.576529i | \(-0.804407\pi\) | ||||
−0.817077 | + | 0.576529i | \(0.804407\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.1224i | 1.74092i | ||||||||
\(506\) | 2.48528 | − | 1.86471i | 0.110484 | − | 0.0828966i | ||||
\(507\) | − | 16.8898i | − | 0.750101i | ||||||
\(508\) | − | 18.6371i | − | 0.826888i | ||||||
\(509\) | − | 37.0949i | − | 1.64420i | −0.569342 | − | 0.822101i | \(-0.692802\pi\) | ||
0.569342 | − | 0.822101i | \(-0.307198\pi\) | |||||||
\(510\) | 25.8010i | 1.14249i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 4.33346i | − | 0.191327i | ||||||
\(514\) | 23.1182 | 1.01970 | ||||||||
\(515\) | 1.95304 | 0.0860614 | ||||||||
\(516\) | −12.5821 | −0.553898 | ||||||||
\(517\) | −10.6176 | + | 7.96643i | −0.466963 | + | 0.350363i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 20.6005i | − | 0.904262i | ||||||
\(520\) | −4.85533 | −0.212920 | ||||||||
\(521\) | 19.4850i | 0.853653i | 0.904333 | + | 0.426827i | \(0.140369\pi\) | ||||
−0.904333 | + | 0.426827i | \(0.859631\pi\) | |||||||
\(522\) | 3.10808 | 0.136037 | ||||||||
\(523\) | 43.0327 | 1.88169 | 0.940844 | − | 0.338841i | \(-0.110035\pi\) | ||||
0.940844 | + | 0.338841i | \(0.110035\pi\) | |||||||
\(524\) | −19.9835 | −0.872982 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.48528 | −0.369976 | ||||||||
\(527\) | − | 26.6625i | − | 1.16144i | ||||||
\(528\) | 4.90195 | − | 3.67794i | 0.213330 | − | 0.160062i | ||||
\(529\) | −22.1224 | −0.961843 | ||||||||
\(530\) | −16.2299 | −0.704980 | ||||||||
\(531\) | 0.399979i | 0.0173576i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.6188 | 0.589896 | ||||||||
\(534\) | − | 23.5294i | − | 1.01822i | ||||||
\(535\) | −41.0560 | −1.77500 | ||||||||
\(536\) | 6.72004i | 0.290262i | ||||||||
\(537\) | 29.2106i | 1.26053i | ||||||||
\(538\) | −30.6005 | −1.31928 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −11.8087 | −0.508164 | ||||||||
\(541\) | − | 19.6188i | − | 0.843478i | −0.906717 | − | 0.421739i | \(-0.861420\pi\) | ||
0.906717 | − | 0.421739i | \(-0.138580\pi\) | |||||||
\(542\) | 13.2016i | 0.567059i | ||||||||
\(543\) | −30.7703 | −1.32048 | ||||||||
\(544\) | 5.64974i | 0.242231i | ||||||||
\(545\) | −14.8291 | −0.635208 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.5800i | 1.82059i | 0.413959 | + | 0.910295i | \(0.364146\pi\) | ||||
−0.413959 | + | 0.910295i | \(0.635854\pi\) | |||||||
\(548\) | −16.4394 | −0.702254 | ||||||||
\(549\) | 4.92926 | 0.210376 | ||||||||
\(550\) | 2.94045 | − | 2.20623i | 0.125381 | − | 0.0940738i | ||||
\(551\) | 6.80558i | 0.289927i | ||||||||
\(552\) | 1.73100 | 0.0736764 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.98886 | 0.169470 | ||||||||
\(555\) | −43.9777 | −1.86675 | ||||||||
\(556\) | −10.7109 | −0.454242 | ||||||||
\(557\) | − | 8.86441i | − | 0.375597i | −0.982208 | − | 0.187799i | \(-0.939865\pi\) | ||
0.982208 | − | 0.187799i | \(-0.0601352\pi\) | |||||||
\(558\) | −1.95478 | −0.0827524 | ||||||||
\(559\) | 13.3772i | 0.565795i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.6947 | + | 20.7794i | −1.16927 | + | 0.877308i | ||||
\(562\) | −5.94293 | −0.250687 | ||||||||
\(563\) | −16.2674 | −0.685588 | −0.342794 | − | 0.939411i | \(-0.611373\pi\) | ||||
−0.342794 | + | 0.939411i | \(0.611373\pi\) | |||||||
\(564\) | −7.39519 | −0.311394 | ||||||||
\(565\) | 14.2463i | 0.599347i | ||||||||
\(566\) | − | 21.2661i | − | 0.893882i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 11.5485i | − | 0.484563i | ||||||
\(569\) | 43.1112i | 1.80732i | 0.428254 | + | 0.903659i | \(0.359129\pi\) | ||||
−0.428254 | + | 0.903659i | \(0.640871\pi\) | |||||||
\(570\) | 4.14195i | 0.173487i | ||||||||
\(571\) | − | 4.79826i | − | 0.200801i | −0.994947 | − | 0.100400i | \(-0.967988\pi\) | ||
0.994947 | − | 0.100400i | \(-0.0320124\pi\) | |||||||
\(572\) | −3.91035 | − | 5.21169i | −0.163500 | − | 0.217912i | ||||
\(573\) | 48.7011i | 2.03452i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.03835 | 0.0433021 | ||||||||
\(576\) | 0.414214 | 0.0172589 | ||||||||
\(577\) | − | 1.91203i | − | 0.0795988i | −0.999208 | − | 0.0397994i | \(-0.987328\pi\) | ||
0.999208 | − | 0.0397994i | \(-0.0126719\pi\) | |||||||
\(578\) | − | 14.9195i | − | 0.620571i | ||||||
\(579\) | −1.28266 | −0.0533056 | ||||||||
\(580\) | 18.5452 | 0.770047 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.07107i | 0.293105i | ||||||||
\(583\) | −13.0711 | − | 17.4211i | −0.541348 | − | 0.721507i | ||||
\(584\) | 10.8614i | 0.449449i | ||||||||
\(585\) | − | 2.01114i | − | 0.0831505i | ||||||
\(586\) | − | 27.7920i | − | 1.14808i | ||||||
\(587\) | 1.71510i | 0.0707896i | 0.999373 | + | 0.0353948i | \(0.0112689\pi\) | ||||
−0.999373 | + | 0.0353948i | \(0.988731\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.28026i | − | 0.176365i | ||||||
\(590\) | 2.38658i | 0.0982540i | ||||||||
\(591\) | −18.0068 | −0.740699 | ||||||||
\(592\) | −9.62995 | −0.395789 | ||||||||
\(593\) | 14.0391 | 0.576517 | 0.288258 | − | 0.957553i | \(-0.406924\pi\) | ||||
0.288258 | + | 0.957553i | \(0.406924\pi\) | |||||||
\(594\) | −9.51038 | − | 12.6754i | −0.390215 | − | 0.520077i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 14.7635i | − | 0.604736i | ||||||
\(597\) | 12.9982 | 0.531983 | ||||||||
\(598\) | − | 1.84038i | − | 0.0752588i | ||||||
\(599\) | 6.07034 | 0.248027 | 0.124014 | − | 0.992281i | \(-0.460423\pi\) | ||||
0.124014 | + | 0.992281i | \(0.460423\pi\) | |||||||
\(600\) | 2.04803 | 0.0836104 | ||||||||
\(601\) | 18.3373 | 0.747995 | 0.373998 | − | 0.927430i | \(-0.377987\pi\) | ||||
0.373998 | + | 0.927430i | \(0.377987\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.78353 | −0.113354 | ||||||||
\(604\) | − | 10.4964i | − | 0.427093i | ||||||
\(605\) | 26.1021 | + | 7.60216i | 1.06120 | + | 0.309072i | ||||
\(606\) | −29.2488 | −1.18815 | ||||||||
\(607\) | 0.212923 | 0.00864229 | 0.00432114 | − | 0.999991i | \(-0.498625\pi\) | ||||
0.00432114 | + | 0.999991i | \(0.498625\pi\) | |||||||
\(608\) | 0.906978i | 0.0367828i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 29.4117 | 1.19085 | ||||||||
\(611\) | 7.86248i | 0.318082i | ||||||||
\(612\) | −2.34020 | −0.0945969 | ||||||||
\(613\) | − | 16.8899i | − | 0.682175i | −0.940032 | − | 0.341087i | \(-0.889205\pi\) | ||
0.940032 | − | 0.341087i | \(-0.110795\pi\) | |||||||
\(614\) | 16.2674i | 0.656497i | ||||||||
\(615\) | −31.6586 | −1.27660 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.0864 | 1.33201 | 0.666004 | − | 0.745948i | \(-0.268003\pi\) | ||||
0.666004 | + | 0.745948i | \(0.268003\pi\) | |||||||
\(618\) | 1.46014i | 0.0587354i | ||||||||
\(619\) | − | 14.2494i | − | 0.572733i | −0.958120 | − | 0.286366i | \(-0.907553\pi\) | ||
0.958120 | − | 0.286366i | \(-0.0924475\pi\) | |||||||
\(620\) | −11.6637 | −0.468426 | ||||||||
\(621\) | − | 4.47600i | − | 0.179616i | ||||||
\(622\) | −10.7925 | −0.432739 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 3.62995i | − | 0.145314i | ||||||
\(625\) | −29.3134 | −1.17254 | ||||||||
\(626\) | −18.3111 | −0.731860 | ||||||||
\(627\) | −4.44596 | + | 3.33581i | −0.177554 | + | 0.133220i | ||||
\(628\) | − | 4.61571i | − | 0.184187i | ||||||
\(629\) | 54.4067 | 2.16934 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.3751 | −0.771312 | −0.385656 | − | 0.922643i | \(-0.626025\pi\) | ||||
−0.385656 | + | 0.922643i | \(0.626025\pi\) | |||||||
\(632\) | 8.48528 | 0.337526 | ||||||||
\(633\) | 44.5591 | 1.77107 | ||||||||
\(634\) | 0.358905i | 0.0142539i | ||||||||
\(635\) | 46.0619 | 1.82791 | ||||||||
\(636\) | − | 12.1338i | − | 0.481136i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 14.9358 | + | 19.9063i | 0.591313 | + | 0.788100i | ||||
\(639\) | 4.78353 | 0.189234 | ||||||||
\(640\) | 2.47151 | 0.0976952 | ||||||||
\(641\) | −36.5087 | −1.44201 | −0.721003 | − | 0.692932i | \(-0.756319\pi\) | ||||
−0.721003 | + | 0.692932i | \(0.756319\pi\) | |||||||
\(642\) | − | 30.6943i | − | 1.21141i | ||||||
\(643\) | − | 2.49558i | − | 0.0984161i | −0.998789 | − | 0.0492080i | \(-0.984330\pi\) | ||
0.998789 | − | 0.0492080i | \(-0.0156697\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 31.0969i | − | 1.22444i | ||||||
\(646\) | − | 5.12419i | − | 0.201609i | ||||||
\(647\) | − | 4.21517i | − | 0.165715i | −0.996561 | − | 0.0828577i | \(-0.973595\pi\) | ||
0.996561 | − | 0.0828577i | \(-0.0264047\pi\) | |||||||
\(648\) | − | 10.0711i | − | 0.395629i | ||||||
\(649\) | −2.56175 | + | 1.92209i | −0.100557 | + | 0.0754485i | ||||
\(650\) | − | 2.17744i | − | 0.0854062i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.5746 | −0.570787 | ||||||||
\(653\) | −10.7972 | −0.422528 | −0.211264 | − | 0.977429i | \(-0.567758\pi\) | ||||
−0.211264 | + | 0.977429i | \(0.567758\pi\) | |||||||
\(654\) | − | 11.0866i | − | 0.433519i | ||||||
\(655\) | − | 49.3894i | − | 1.92981i | ||||||
\(656\) | −6.93240 | −0.270665 | ||||||||
\(657\) | −4.49895 | −0.175521 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.1591i | 1.64229i | 0.570723 | + | 0.821143i | \(0.306663\pi\) | ||||
−0.570723 | + | 0.821143i | \(0.693337\pi\) | |||||||
\(660\) | 9.09009 | + | 12.1152i | 0.353831 | + | 0.471585i | ||||
\(661\) | − | 8.98122i | − | 0.349329i | −0.984628 | − | 0.174664i | \(-0.944116\pi\) | ||
0.984628 | − | 0.174664i | \(-0.0558841\pi\) | |||||||
\(662\) | 28.9135i | 1.12375i | ||||||||
\(663\) | 20.5083i | 0.796476i | ||||||||
\(664\) | − | 4.83601i | − | 0.187674i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 3.98886i | − | 0.154565i | ||||||
\(667\) | 7.02944i | 0.272181i | ||||||||
\(668\) | −7.37045 | −0.285171 | ||||||||
\(669\) | −5.36829 | −0.207550 | ||||||||
\(670\) | −16.6087 | −0.641649 | ||||||||
\(671\) | 23.6874 | + | 31.5704i | 0.914441 | + | 1.21876i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 26.4282i | − | 1.01873i | −0.860550 | − | 0.509366i | \(-0.829880\pi\) | ||
0.860550 | − | 0.509366i | \(-0.170120\pi\) | |||||||
\(674\) | −7.96341 | −0.306739 | ||||||||
\(675\) | − | 5.29576i | − | 0.203834i | ||||||
\(676\) | 9.14068 | 0.351565 | ||||||||
\(677\) | 11.7138 | 0.450197 | 0.225099 | − | 0.974336i | \(-0.427730\pi\) | ||||
0.225099 | + | 0.974336i | \(0.427730\pi\) | |||||||
\(678\) | −10.6509 | −0.409044 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −13.9634 | −0.535472 | ||||||||
\(681\) | − | 26.6576i | − | 1.02152i | ||||||
\(682\) | −9.39362 | − | 12.5198i | −0.359700 | − | 0.479407i | ||||
\(683\) | 35.9868 | 1.37700 | 0.688498 | − | 0.725238i | \(-0.258270\pi\) | ||||
0.688498 | + | 0.725238i | \(0.258270\pi\) | |||||||
\(684\) | −0.375683 | −0.0143646 | ||||||||
\(685\) | − | 40.6301i | − | 1.55240i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.1135 | 0.500310 | ||||||||
\(688\) | − | 6.80940i | − | 0.259606i | ||||||
\(689\) | −12.9005 | −0.491470 | ||||||||
\(690\) | 4.27820i | 0.162868i | ||||||||
\(691\) | − | 5.91057i | − | 0.224849i | −0.993660 | − | 0.112424i | \(-0.964138\pi\) | ||
0.993660 | − | 0.112424i | \(-0.0358616\pi\) | |||||||
\(692\) | 11.1489 | 0.423818 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.6810 | 0.936877 | ||||||||
\(695\) | − | 26.4721i | − | 1.00414i | ||||||
\(696\) | 13.8648i | 0.525544i | ||||||||
\(697\) | 39.1662 | 1.48353 | ||||||||
\(698\) | 11.1489i | 0.421993i | ||||||||
\(699\) | 7.68882 | 0.290818 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 39.6167i | − | 1.49630i | −0.663527 | − | 0.748152i | \(-0.730941\pi\) | ||
0.663527 | − | 0.748152i | \(-0.269059\pi\) | |||||||
\(702\) | −9.38628 | −0.354262 | ||||||||
\(703\) | 8.73416 | 0.329415 | ||||||||
\(704\) | 1.99049 | + | 2.65291i | 0.0750194 | + | 0.0999855i | ||||
\(705\) | − | 18.2773i | − | 0.688364i | ||||||
\(706\) | 21.3852 | 0.804844 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.78426 | −0.0670567 | ||||||||
\(709\) | −20.4023 | −0.766226 | −0.383113 | − | 0.923701i | \(-0.625148\pi\) | ||||
−0.383113 | + | 0.923701i | \(0.625148\pi\) | |||||||
\(710\) | 28.5422 | 1.07117 | ||||||||
\(711\) | 3.51472i | 0.131812i | ||||||||
\(712\) | 12.7340 | 0.477229 | ||||||||
\(713\) | − | 4.42105i | − | 0.165570i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.8808 | − | 9.66448i | 0.481714 | − | 0.361431i | ||||
\(716\) | −15.8087 | −0.590798 | ||||||||
\(717\) | −36.7011 | −1.37063 | ||||||||
\(718\) | −6.24367 | −0.233012 | ||||||||
\(719\) | − | 28.7190i | − | 1.07104i | −0.844524 | − | 0.535518i | \(-0.820116\pi\) | ||
0.844524 | − | 0.535518i | \(-0.179884\pi\) | |||||||
\(720\) | 1.02373i | 0.0381523i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.1774i | 0.676492i | ||||||||
\(723\) | 26.7728i | 0.995692i | ||||||||
\(724\) | − | 16.6528i | − | 0.618896i | ||||||
\(725\) | 8.31685i | 0.308880i | ||||||||
\(726\) | −5.68354 | + | 19.5145i | −0.210936 | + | 0.724252i | ||||
\(727\) | − | 9.15820i | − | 0.339659i | −0.985473 | − | 0.169829i | \(-0.945678\pi\) | ||
0.985473 | − | 0.169829i | \(-0.0543217\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.3137 | −0.826434 | ||||||||
\(730\) | −26.8442 | −0.993548 | ||||||||
\(731\) | 38.4714i | 1.42291i | ||||||||
\(732\) | 21.9889i | 0.812732i | ||||||||
\(733\) | −44.7097 | −1.65139 | −0.825695 | − | 0.564116i | \(-0.809217\pi\) | ||||
−0.825695 | + | 0.564116i | \(0.809217\pi\) | |||||||
\(734\) | −28.7533 | −1.06130 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.936812i | 0.0345313i | ||||||||
\(737\) | −13.3762 | − | 17.8277i | −0.492717 | − | 0.656692i | ||||
\(738\) | − | 2.87149i | − | 0.105701i | ||||||
\(739\) | − | 21.7013i | − | 0.798296i | −0.916887 | − | 0.399148i | \(-0.869306\pi\) | ||
0.916887 | − | 0.399148i | \(-0.130694\pi\) | |||||||
\(740\) | − | 23.8006i | − | 0.874926i | ||||||
\(741\) | 3.29229i | 0.120945i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.20708i | − | 0.301089i | −0.988603 | − | 0.150544i | \(-0.951897\pi\) | ||
0.988603 | − | 0.150544i | \(-0.0481026\pi\) | |||||||
\(744\) | − | 8.72004i | − | 0.319692i | ||||||
\(745\) | 36.4882 | 1.33682 | ||||||||
\(746\) | 12.3589 | 0.452492 | ||||||||
\(747\) | 2.00314 | 0.0732911 | ||||||||
\(748\) | −11.2457 | − | 14.9883i | −0.411185 | − | 0.548026i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 17.7721i | − | 0.648945i | ||||||
\(751\) | −19.4206 | −0.708669 | −0.354335 | − | 0.935119i | \(-0.615293\pi\) | ||||
−0.354335 | + | 0.935119i | \(0.615293\pi\) | |||||||
\(752\) | − | 4.00225i | − | 0.145947i | ||||||
\(753\) | 27.0061 | 0.984158 | ||||||||
\(754\) | 14.7409 | 0.536832 | ||||||||
\(755\) | 25.9421 | 0.944128 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.7958 | 1.62813 | 0.814065 | − | 0.580774i | \(-0.197250\pi\) | ||||
0.814065 | + | 0.580774i | \(0.197250\pi\) | |||||||
\(758\) | 23.7822i | 0.863808i | ||||||||
\(759\) | −4.59220 | + | 3.44554i | −0.166686 | + | 0.125065i | ||||
\(760\) | −2.24161 | −0.0813117 | ||||||||
\(761\) | −3.83578 | −0.139047 | −0.0695235 | − | 0.997580i | \(-0.522148\pi\) | ||||
−0.0695235 | + | 0.997580i | \(0.522148\pi\) | |||||||
\(762\) | 34.4369i | 1.24752i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −26.3568 | −0.953557 | ||||||||
\(765\) | − | 5.78383i | − | 0.209115i | ||||||
\(766\) | −31.8645 | −1.15131 | ||||||||
\(767\) | 1.89701i | 0.0684969i | ||||||||
\(768\) | 1.84776i | 0.0666753i | ||||||||
\(769\) | −37.6267 | −1.35685 | −0.678427 | − | 0.734667i | \(-0.737338\pi\) | ||||
−0.678427 | + | 0.734667i | \(0.737338\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −42.7168 | −1.53841 | ||||||||
\(772\) | − | 0.694171i | − | 0.0249838i | ||||||
\(773\) | − | 28.5737i | − | 1.02772i | −0.857873 | − | 0.513861i | \(-0.828215\pi\) | ||
0.857873 | − | 0.513861i | \(-0.171785\pi\) | |||||||
\(774\) | 2.82055 | 0.101382 | ||||||||
\(775\) | − | 5.23075i | − | 0.187894i | ||||||
\(776\) | −3.82683 | −0.137375 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 21.0155i | − | 0.753441i | ||||||
\(779\) | 6.28754 | 0.225274 | ||||||||
\(780\) | 8.97148 | 0.321230 | ||||||||
\(781\) | 22.9871 | + | 30.6371i | 0.822543 | + | 1.09628i | ||||
\(782\) | − | 5.29274i | − | 0.189268i | ||||||
\(783\) | 35.8514 | 1.28122 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.4078 | 0.407162 | ||||||||
\(786\) | 36.9246 | 1.31706 | ||||||||
\(787\) | −23.2666 | −0.829364 | −0.414682 | − | 0.909966i | \(-0.636107\pi\) | ||||
−0.414682 | + | 0.909966i | \(0.636107\pi\) | |||||||
\(788\) | − | 9.74519i | − | 0.347158i | ||||||
\(789\) | 15.6788 | 0.558178 | ||||||||
\(790\) | 20.9715i | 0.746132i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.09887 | + | 0.824487i | −0.0390468 | + | 0.0292969i | ||||
\(793\) | 23.3783 | 0.830188 | ||||||||
\(794\) | −8.31805 | −0.295196 | ||||||||
\(795\) | 29.9889 | 1.06360 | ||||||||
\(796\) | 7.03460i | 0.249335i | ||||||||
\(797\) | 26.8026i | 0.949396i | 0.880149 | + | 0.474698i | \(0.157443\pi\) | ||||
−0.880149 | + | 0.474698i | \(0.842557\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.6117i | 0.799943i | ||||||||
\(800\) | 1.10838i | 0.0391873i | ||||||||
\(801\) | 5.27461i | 0.186369i | ||||||||
\(802\) | 30.6820i | 1.08342i | ||||||||
\(803\) | −21.6196 | − | 28.8144i | −0.762938 | − | 1.01684i | ||||
\(804\) | − | 12.4170i | − | 0.437915i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.27105 | −0.326559 | ||||||||
\(807\) | 56.5424 | 1.99039 | ||||||||
\(808\) | − | 15.8293i | − | 0.556873i | ||||||
\(809\) | 1.08760i | 0.0382380i | 0.999817 | + | 0.0191190i | \(0.00608614\pi\) | ||||
−0.999817 | + | 0.0191190i | \(0.993914\pi\) | |||||||
\(810\) | 24.8908 | 0.874573 | ||||||||
\(811\) | 23.7806 | 0.835051 | 0.417525 | − | 0.908665i | \(-0.362897\pi\) | ||||
0.417525 | + | 0.908665i | \(0.362897\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 24.3934i | − | 0.855515i | ||||||
\(814\) | 25.5474 | − | 19.1683i | 0.895437 | − | 0.671849i | ||||
\(815\) | − | 36.0214i | − | 1.26178i | ||||||
\(816\) | − | 10.4394i | − | 0.365451i | ||||||
\(817\) | 6.17598i | 0.216070i | ||||||||
\(818\) | − | 9.57877i | − | 0.334914i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 17.1335i | − | 0.598329i | ||||||
\(821\) | − | 43.3894i | − | 1.51430i | −0.653240 | − | 0.757151i | \(-0.726591\pi\) | ||
0.653240 | − | 0.757151i | \(-0.273409\pi\) | |||||||
\(822\) | 30.3760 | 1.05948 | ||||||||
\(823\) | 6.80007 | 0.237035 | 0.118518 | − | 0.992952i | \(-0.462186\pi\) | ||||
0.118518 | + | 0.992952i | \(0.462186\pi\) | |||||||
\(824\) | −0.790221 | −0.0275287 | ||||||||
\(825\) | −5.43324 | + | 4.07658i | −0.189161 | + | 0.141928i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36.3112i | − | 1.26266i | −0.775513 | − | 0.631332i | \(-0.782509\pi\) | ||
0.775513 | − | 0.631332i | \(-0.217491\pi\) | |||||||
\(828\) | −0.388040 | −0.0134853 | ||||||||
\(829\) | − | 34.2337i | − | 1.18899i | −0.804101 | − | 0.594493i | \(-0.797353\pi\) | ||
0.804101 | − | 0.594493i | \(-0.202647\pi\) | |||||||
\(830\) | 11.9523 | 0.414869 | ||||||||
\(831\) | −7.37045 | −0.255678 | ||||||||
\(832\) | 1.96452 | 0.0681073 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 19.7911 | 0.685310 | ||||||||
\(835\) | − | 18.2162i | − | 0.630396i | ||||||
\(836\) | −1.80533 | − | 2.40614i | −0.0624386 | − | 0.0832179i | ||||
\(837\) | −22.5482 | −0.779379 | ||||||||
\(838\) | −10.3074 | −0.356064 | ||||||||
\(839\) | − | 17.3286i | − | 0.598250i | −0.954214 | − | 0.299125i | \(-0.903305\pi\) | ||
0.954214 | − | 0.299125i | \(-0.0966947\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3036 | −0.941505 | ||||||||
\(842\) | 25.8805i | 0.891900i | ||||||||
\(843\) | 10.9811 | 0.378209 | ||||||||
\(844\) | 24.1152i | 0.830081i | ||||||||
\(845\) | 22.5913i | 0.777165i | ||||||||
\(846\) | 1.65779 | 0.0569958 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.56676 | 0.225504 | ||||||||
\(849\) | 39.2947i | 1.34859i | ||||||||
\(850\) | − | 6.26208i | − | 0.214788i | ||||||
\(851\) | 9.02145 | 0.309251 | ||||||||
\(852\) | 21.3388i | 0.731055i | ||||||||
\(853\) | −9.22034 | −0.315698 | −0.157849 | − | 0.987463i | \(-0.550456\pi\) | ||||
−0.157849 | + | 0.987463i | \(0.550456\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.928505i | − | 0.0317542i | ||||||
\(856\) | 16.6117 | 0.567775 | ||||||||
\(857\) | 8.86098 | 0.302685 | 0.151343 | − | 0.988481i | \(-0.451640\pi\) | ||||
0.151343 | + | 0.988481i | \(0.451640\pi\) | |||||||
\(858\) | 7.22538 | + | 9.62995i | 0.246670 | + | 0.328761i | ||||
\(859\) | 44.3311i | 1.51256i | 0.654249 | + | 0.756279i | \(0.272985\pi\) | ||||
−0.654249 | + | 0.756279i | \(0.727015\pi\) | |||||||
\(860\) | 16.8295 | 0.573883 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.0858 | 0.581945 | ||||||||
\(863\) | 4.90306 | 0.166902 | 0.0834511 | − | 0.996512i | \(-0.473406\pi\) | ||||
0.0834511 | + | 0.996512i | \(0.473406\pi\) | |||||||
\(864\) | 4.77791 | 0.162548 | ||||||||
\(865\) | 27.5547i | 0.936888i | ||||||||
\(866\) | −1.92881 | −0.0655436 | ||||||||
\(867\) | 27.5677i | 0.936249i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.5107 | + | 16.8899i | −0.763624 | + | 0.572949i | ||||
\(870\) | −34.2671 | −1.16176 | ||||||||
\(871\) | −13.2016 | −0.447320 | ||||||||
\(872\) | 6.00000 | 0.203186 | ||||||||
\(873\) | − | 1.58513i | − | 0.0536484i | ||||||
\(874\) | − | 0.849668i | − | 0.0287404i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 20.0693i | − | 0.678079i | ||||||
\(877\) | 14.7157i | 0.496915i | 0.968643 | + | 0.248458i | \(0.0799237\pi\) | ||||
−0.968643 | + | 0.248458i | \(0.920076\pi\) | |||||||
\(878\) | − | 10.4234i | − | 0.351772i | ||||||
\(879\) | 51.3529i | 1.73209i | ||||||||
\(880\) | −6.55672 | + | 4.91952i | −0.221027 | + | 0.165837i | ||||
\(881\) | − | 33.3550i | − | 1.12376i | −0.827219 | − | 0.561880i | \(-0.810078\pi\) | ||
0.827219 | − | 0.561880i | \(-0.189922\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.3385 | 1.52576 | 0.762882 | − | 0.646538i | \(-0.223784\pi\) | ||||
0.762882 | + | 0.646538i | \(0.223784\pi\) | |||||||
\(884\) | −11.0990 | −0.373300 | ||||||||
\(885\) | − | 4.40983i | − | 0.148235i | ||||||
\(886\) | − | 15.9254i | − | 0.535023i | ||||||
\(887\) | −15.9534 | −0.535664 | −0.267832 | − | 0.963466i | \(-0.586307\pi\) | ||||
−0.267832 | + | 0.963466i | \(0.586307\pi\) | |||||||
\(888\) | 17.7938 | 0.597122 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 31.4724i | 1.05496i | ||||||||
\(891\) | 20.0463 | + | 26.7177i | 0.671578 | + | 0.895076i | ||||
\(892\) | − | 2.90530i | − | 0.0972765i | ||||||
\(893\) | 3.62995i | 0.121472i | ||||||||
\(894\) | 27.2794i | 0.912358i | ||||||||
\(895\) | − | 39.0714i | − | 1.30601i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.40058i | 0.113542i | ||||||||
\(898\) | − | 10.4404i | − | 0.348400i | ||||||
\(899\) | 35.4113 | 1.18103 | ||||||||
\(900\) | −0.459108 | −0.0153036 | ||||||||
\(901\) | −37.1005 | −1.23600 | ||||||||
\(902\) | 18.3911 | − | 13.7989i | 0.612355 | − | 0.459452i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 5.76421i | − | 0.191715i | ||||||
\(905\) | 41.1576 | 1.36812 | ||||||||
\(906\) | 19.3949i | 0.644351i | ||||||||
\(907\) | −16.1841 | −0.537385 | −0.268692 | − | 0.963226i | \(-0.586591\pi\) | ||||
−0.268692 | + | 0.963226i | \(0.586591\pi\) | |||||||
\(908\) | 14.4270 | 0.478776 | ||||||||
\(909\) | 6.55672 | 0.217473 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.2957 | −1.30193 | −0.650963 | − | 0.759110i | \(-0.725635\pi\) | ||||
−0.650963 | + | 0.759110i | \(0.725635\pi\) | |||||||
\(912\) | − | 1.67588i | − | 0.0554938i | ||||||
\(913\) | 9.62602 | + | 12.8295i | 0.318575 | + | 0.424595i | ||||
\(914\) | −18.0582 | −0.597311 | ||||||||
\(915\) | −54.3458 | −1.79662 | ||||||||
\(916\) | 7.09696i | 0.234490i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −26.9939 | −0.890933 | ||||||||
\(919\) | 14.2893i | 0.471362i | 0.971830 | + | 0.235681i | \(0.0757320\pi\) | ||||
−0.971830 | + | 0.235681i | \(0.924268\pi\) | |||||||
\(920\) | −2.31534 | −0.0763346 | ||||||||
\(921\) | − | 30.0582i | − | 0.990450i | ||||||
\(922\) | − | 11.4500i | − | 0.377087i | ||||||
\(923\) | 22.6872 | 0.746757 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.6737 | 0.350949 | ||||||||
\(926\) | 26.6805i | 0.876777i | ||||||||
\(927\) | − | 0.327320i | − | 0.0107506i | ||||||
\(928\) | −7.50358 | −0.246317 | ||||||||
\(929\) | − | 21.2116i | − | 0.695930i | −0.937508 | − | 0.347965i | \(-0.886873\pi\) | ||
0.937508 | − | 0.347965i | \(-0.113127\pi\) | |||||||
\(930\) | 21.5517 | 0.706709 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.16116i | 0.136303i | ||||||||
\(933\) | 19.9419 | 0.652869 | ||||||||
\(934\) | −9.71626 | −0.317926 | ||||||||
\(935\) | 37.0437 | − | 27.7940i | 1.21146 | − | 0.908961i | ||||
\(936\) | 0.813729i | 0.0265976i | ||||||||
\(937\) | −50.6154 | −1.65353 | −0.826767 | − | 0.562544i | \(-0.809823\pi\) | ||||
−0.826767 | + | 0.562544i | \(0.809823\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.8345 | 1.10415 | ||||||||
\(940\) | 9.89162 | 0.322629 | ||||||||
\(941\) | −34.5874 | −1.12752 | −0.563759 | − | 0.825939i | \(-0.690645\pi\) | ||||
−0.563759 | + | 0.825939i | \(0.690645\pi\) | |||||||
\(942\) | 8.52872i | 0.277881i | ||||||||
\(943\) | 6.49435 | 0.211485 | ||||||||
\(944\) | − | 0.965635i | − | 0.0314288i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.5540 | + | 18.0648i | 0.440680 | + | 0.587336i | ||||
\(947\) | 1.70338 | 0.0553525 | 0.0276763 | − | 0.999617i | \(-0.491189\pi\) | ||||
0.0276763 | + | 0.999617i | \(0.491189\pi\) | |||||||
\(948\) | −15.6788 | −0.509222 | ||||||||
\(949\) | −21.3375 | −0.692643 | ||||||||
\(950\) | − | 1.00528i | − | 0.0326156i | ||||||
\(951\) | − | 0.663170i | − | 0.0215047i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.2050i | 0.330573i | 0.986246 | + | 0.165287i | \(0.0528549\pi\) | ||||
−0.986246 | + | 0.165287i | \(0.947145\pi\) | |||||||
\(954\) | 2.72004i | 0.0880646i | ||||||||
\(955\) | − | 65.1413i | − | 2.10792i | ||||||
\(956\) | − | 19.8625i | − | 0.642399i | ||||||
\(957\) | −27.5977 | − | 36.7821i | −0.892108 | − | 1.18900i | ||||
\(958\) | 19.2084i | 0.620594i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4.56676 | −0.147392 | ||||||||
\(961\) | 8.72865 | 0.281569 | ||||||||
\(962\) | − | 18.9182i | − | 0.609947i | ||||||
\(963\) | 6.88077i | 0.221730i | ||||||||
\(964\) | −14.4893 | −0.466670 | ||||||||
\(965\) | 1.71565 | 0.0552289 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.7361i | 0.956249i | 0.878292 | + | 0.478124i | \(0.158683\pi\) | ||||
−0.878292 | + | 0.478124i | \(0.841317\pi\) | |||||||
\(968\) | −10.5612 | − | 3.07591i | −0.339450 | − | 0.0988635i | ||||
\(969\) | 9.46827i | 0.304165i | ||||||||
\(970\) | − | 9.45808i | − | 0.303681i | ||||||
\(971\) | 35.6308i | 1.14345i | 0.820447 | + | 0.571723i | \(0.193725\pi\) | ||||
−0.820447 | + | 0.571723i | \(0.806275\pi\) | |||||||
\(972\) | 4.27518i | 0.137126i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 0.362596i | − | 0.0116183i | ||||||
\(975\) | 4.02338i | 0.128851i | ||||||||
\(976\) | −11.9003 | −0.380919 | ||||||||
\(977\) | −27.6432 | −0.884385 | −0.442193 | − | 0.896920i | \(-0.645799\pi\) | ||||
−0.442193 | + | 0.896920i | \(0.645799\pi\) | |||||||
\(978\) | 26.9304 | 0.861140 | ||||||||
\(979\) | −33.7823 | + | 25.3470i | −1.07969 | + | 0.810093i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.48528i | 0.0793489i | ||||||||
\(982\) | 1.04374 | 0.0333070 | ||||||||
\(983\) | 43.2786i | 1.38037i | 0.723631 | + | 0.690187i | \(0.242472\pi\) | ||||
−0.723631 | + | 0.690187i | \(0.757528\pi\) | |||||||
\(984\) | 12.8094 | 0.408349 | ||||||||
\(985\) | 24.0854 | 0.767424 | ||||||||
\(986\) | 42.3932 | 1.35008 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.78177 | −0.0566857 | ||||||||
\(989\) | 6.37913i | 0.202845i | ||||||||
\(990\) | −2.03773 | − | 2.71588i | −0.0647634 | − | 0.0863164i | ||||
\(991\) | −3.49673 | −0.111077 | −0.0555386 | − | 0.998457i | \(-0.517688\pi\) | ||||
−0.0555386 | + | 0.998457i | \(0.517688\pi\) | |||||||
\(992\) | 4.71925 | 0.149836 | ||||||||
\(993\) | − | 53.4252i | − | 1.69540i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.3861 | −0.551177 | ||||||||
\(996\) | 8.93578i | 0.283141i | ||||||||
\(997\) | 16.1304 | 0.510856 | 0.255428 | − | 0.966828i | \(-0.417784\pi\) | ||||
0.255428 | + | 0.966828i | \(0.417784\pi\) | |||||||
\(998\) | − | 19.6008i | − | 0.620453i | ||||||
\(999\) | − | 46.0110i | − | 1.45573i |
(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 | 1078.2.c.c.1077.7 | yes | 16 | |
7.2 | even | 3 | 1078.2.i.d.1011.5 | 32 | |||
7.3 | odd | 6 | 1078.2.i.d.901.9 | 32 | |||
7.4 | even | 3 | 1078.2.i.d.901.10 | 32 | |||
7.5 | odd | 6 | 1078.2.i.d.1011.6 | 32 | |||
7.6 | odd | 2 | inner | 1078.2.c.c.1077.2 | ✓ | 16 | |
11.10 | odd | 2 | inner | 1078.2.c.c.1077.15 | yes | 16 | |
77.10 | even | 6 | 1078.2.i.d.901.5 | 32 | |||
77.32 | odd | 6 | 1078.2.i.d.901.6 | 32 | |||
77.54 | even | 6 | 1078.2.i.d.1011.10 | 32 | |||
77.65 | odd | 6 | 1078.2.i.d.1011.9 | 32 | |||
77.76 | even | 2 | inner | 1078.2.c.c.1077.10 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1078.2.c.c.1077.2 | ✓ | 16 | 7.6 | odd | 2 | inner | |
1078.2.c.c.1077.7 | yes | 16 | 1.1 | even | 1 | trivial | |
1078.2.c.c.1077.10 | yes | 16 | 77.76 | even | 2 | inner | |
1078.2.c.c.1077.15 | yes | 16 | 11.10 | odd | 2 | inner | |
1078.2.i.d.901.5 | 32 | 77.10 | even | 6 | |||
1078.2.i.d.901.6 | 32 | 77.32 | odd | 6 | |||
1078.2.i.d.901.9 | 32 | 7.3 | odd | 6 | |||
1078.2.i.d.901.10 | 32 | 7.4 | even | 3 | |||
1078.2.i.d.1011.5 | 32 | 7.2 | even | 3 | |||
1078.2.i.d.1011.6 | 32 | 7.5 | odd | 6 | |||
1078.2.i.d.1011.9 | 32 | 77.65 | odd | 6 | |||
1078.2.i.d.1011.10 | 32 | 77.54 | even | 6 |