Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(440,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, 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("441.440");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 440.3 | ||
Root | \(-0.923880 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.440 |
Dual form | 441.2.c.b.440.5 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.414214i | − 0.292893i | −0.989219 | − | 0.146447i | \(-0.953216\pi\) | ||||
0.989219 | − | 0.146447i | \(-0.0467837\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.82843 | 0.914214 | ||||||||
\(5\) | −2.93015 | −1.31040 | −0.655202 | − | 0.755454i | \(-0.727416\pi\) | ||||
−0.655202 | + | 0.755454i | \(0.727416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 1.58579i | − 0.560660i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.21371i | 0.383808i | ||||||||
\(11\) | − 4.82843i | − 1.45583i | −0.685670 | − | 0.727913i | \(-0.740491\pi\) | ||||
0.685670 | − | 0.727913i | \(-0.259509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.93015i | − 0.812678i | −0.913722 | − | 0.406339i | \(-0.866805\pi\) | ||||
0.913722 | − | 0.406339i | \(-0.133195\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 7.07401 | 1.71570 | 0.857850 | − | 0.513900i | \(-0.171800\pi\) | ||||
0.857850 | + | 0.513900i | \(0.171800\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 5.86030i | − 1.34445i | −0.740349 | − | 0.672223i | \(-0.765340\pi\) | ||||
0.740349 | − | 0.672223i | \(-0.234660\pi\) | |||||||
\(20\) | −5.35757 | −1.19799 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 2.00000i | 0.417029i | 0.978019 | + | 0.208514i | \(0.0668628\pi\) | ||||
−0.978019 | + | 0.208514i | \(0.933137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.58579 | 0.717157 | ||||||||
\(26\) | −1.21371 | −0.238028 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.828427i | 0.153835i | 0.997037 | + | 0.0769175i | \(0.0245078\pi\) | ||||
−0.997037 | + | 0.0769175i | \(0.975492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.86030i | 1.05254i | 0.850317 | + | 0.526271i | \(0.176410\pi\) | ||||
−0.850317 | + | 0.526271i | \(0.823590\pi\) | |||||||
\(32\) | − 4.41421i | − 0.780330i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 2.93015i | − 0.502517i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.41421 | −0.890091 | −0.445046 | − | 0.895508i | \(-0.646813\pi\) | ||||
−0.445046 | + | 0.895508i | \(0.646813\pi\) | |||||||
\(38\) | −2.42742 | −0.393779 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.64659i | 0.734691i | ||||||||
\(41\) | 1.21371 | 0.189549 | 0.0947747 | − | 0.995499i | \(-0.469787\pi\) | ||||
0.0947747 | + | 0.995499i | \(0.469787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.48528 | 0.683999 | 0.341999 | − | 0.939700i | \(-0.388896\pi\) | ||||
0.341999 | + | 0.939700i | \(0.388896\pi\) | |||||||
\(44\) | − 8.82843i | − 1.33094i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.828427 | 0.122145 | ||||||||
\(47\) | −5.86030 | −0.854813 | −0.427406 | − | 0.904060i | \(-0.640573\pi\) | ||||
−0.427406 | + | 0.904060i | \(0.640573\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 1.48528i | − 0.210051i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 5.35757i | − 0.742961i | ||||||||
\(53\) | 7.07107i | 0.971286i | 0.874157 | + | 0.485643i | \(0.161414\pi\) | ||||
−0.874157 | + | 0.485643i | \(0.838586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.1480i | 1.90772i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.343146 | 0.0450572 | ||||||||
\(59\) | −5.86030 | −0.762946 | −0.381473 | − | 0.924380i | \(-0.624583\pi\) | ||||
−0.381473 | + | 0.924380i | \(0.624583\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.21371i | − 0.155399i | −0.996977 | − | 0.0776997i | \(-0.975242\pi\) | ||||
0.996977 | − | 0.0776997i | \(-0.0247575\pi\) | |||||||
\(62\) | 2.42742 | 0.308282 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.17157 | 0.521447 | ||||||||
\(65\) | 8.58579i | 1.06494i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.48528 | −1.03664 | −0.518321 | − | 0.855186i | \(-0.673443\pi\) | ||||
−0.518321 | + | 0.855186i | \(0.673443\pi\) | |||||||
\(68\) | 12.9343 | 1.56852 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 0.828427i | − 0.0983162i | −0.998791 | − | 0.0491581i | \(-0.984346\pi\) | ||||
0.998791 | − | 0.0491581i | \(-0.0156538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 7.07401i | − 0.827950i | −0.910288 | − | 0.413975i | \(-0.864140\pi\) | ||||
0.910288 | − | 0.413975i | \(-0.135860\pi\) | |||||||
\(74\) | 2.24264i | 0.260702i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 10.7151i | − 1.22911i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.65685 | 0.186411 | 0.0932053 | − | 0.995647i | \(-0.470289\pi\) | ||||
0.0932053 | + | 0.995647i | \(0.470289\pi\) | |||||||
\(80\) | −8.79045 | −0.982803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 0.502734i | − 0.0555177i | ||||||||
\(83\) | 11.7206 | 1.28650 | 0.643252 | − | 0.765655i | \(-0.277585\pi\) | ||||
0.643252 | + | 0.765655i | \(0.277585\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.7279 | −2.24826 | ||||||||
\(86\) | − 1.85786i | − 0.200339i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.65685 | −0.816223 | ||||||||
\(89\) | 11.2179 | 1.18909 | 0.594546 | − | 0.804062i | \(-0.297332\pi\) | ||||
0.594546 | + | 0.804062i | \(0.297332\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.65685i | 0.381253i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.42742i | 0.250369i | ||||||||
\(95\) | 17.1716i | 1.76177i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.07401i | 0.718257i | 0.933288 | + | 0.359128i | \(0.116926\pi\) | ||||
−0.933288 | + | 0.359128i | \(0.883074\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.55635 | 0.655635 | ||||||||
\(101\) | 5.35757 | 0.533098 | 0.266549 | − | 0.963821i | \(-0.414117\pi\) | ||||
0.266549 | + | 0.963821i | \(0.414117\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.1480i | 1.39405i | 0.717049 | + | 0.697023i | \(0.245492\pi\) | ||||
−0.717049 | + | 0.697023i | \(0.754508\pi\) | |||||||
\(104\) | −4.64659 | −0.455636 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.92893 | 0.284483 | ||||||||
\(107\) | 13.3137i | 1.28708i | 0.765410 | + | 0.643542i | \(0.222536\pi\) | ||||
−0.765410 | + | 0.643542i | \(0.777464\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.41421 | −0.518588 | −0.259294 | − | 0.965798i | \(-0.583490\pi\) | ||||
−0.259294 | + | 0.965798i | \(0.583490\pi\) | |||||||
\(110\) | 5.86030 | 0.558758 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.8995i | 1.30755i | 0.756687 | + | 0.653777i | \(0.226817\pi\) | ||||
−0.756687 | + | 0.653777i | \(0.773183\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 5.86030i | − 0.546476i | ||||||||
\(116\) | 1.51472i | 0.140638i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.42742i | 0.223462i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.3137 | −1.11943 | ||||||||
\(122\) | −0.502734 | −0.0455154 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.7151i | 0.962248i | ||||||||
\(125\) | 4.14386 | 0.370638 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.4853 | 1.46283 | 0.731416 | − | 0.681931i | \(-0.238860\pi\) | ||||
0.731416 | + | 0.681931i | \(0.238860\pi\) | |||||||
\(128\) | − 10.5563i | − 0.933058i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.55635 | 0.311912 | ||||||||
\(131\) | −8.28772 | −0.724101 | −0.362051 | − | 0.932158i | \(-0.617923\pi\) | ||||
−0.362051 | + | 0.932158i | \(0.617923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.51472i | 0.303625i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 11.2179i | − 0.961924i | ||||||||
\(137\) | 4.82843i | 0.412520i | 0.978497 | + | 0.206260i | \(0.0661293\pi\) | ||||
−0.978497 | + | 0.206260i | \(0.933871\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 8.28772i | − 0.702955i | −0.936196 | − | 0.351478i | \(-0.885679\pi\) | ||||
0.936196 | − | 0.351478i | \(-0.114321\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.343146 | −0.0287962 | ||||||||
\(143\) | −14.1480 | −1.18312 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 2.42742i | − 0.201586i | ||||||||
\(146\) | −2.93015 | −0.242501 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.89949 | −0.813733 | ||||||||
\(149\) | − 4.24264i | − 0.347571i | −0.984784 | − | 0.173785i | \(-0.944400\pi\) | ||||
0.984784 | − | 0.173785i | \(-0.0555999\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.48528 | 0.365007 | 0.182504 | − | 0.983205i | \(-0.441580\pi\) | ||||
0.182504 | + | 0.983205i | \(0.441580\pi\) | |||||||
\(152\) | −9.29319 | −0.753777 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 17.1716i | − 1.37925i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.9385i | 1.83069i | 0.402671 | + | 0.915345i | \(0.368082\pi\) | ||||
−0.402671 | + | 0.915345i | \(0.631918\pi\) | |||||||
\(158\) | − 0.686292i | − 0.0545984i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.9343i | 1.02255i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.17157 | 0.718373 | 0.359187 | − | 0.933266i | \(-0.383054\pi\) | ||||
0.359187 | + | 0.933266i | \(0.383054\pi\) | |||||||
\(164\) | 2.21918 | 0.173289 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 4.85483i | − 0.376808i | ||||||||
\(167\) | 14.1480 | 1.09481 | 0.547403 | − | 0.836869i | \(-0.315616\pi\) | ||||
0.547403 | + | 0.836869i | \(0.315616\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.41421 | 0.339555 | ||||||||
\(170\) | 8.58579i | 0.658500i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.20101 | 0.625321 | ||||||||
\(173\) | 1.21371 | 0.0922765 | 0.0461383 | − | 0.998935i | \(-0.485309\pi\) | ||||
0.0461383 | + | 0.998935i | \(0.485309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 14.4853i | − 1.09187i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 4.64659i | − 0.348277i | ||||||||
\(179\) | − 26.4853i | − 1.97960i | −0.142454 | − | 0.989801i | \(-0.545499\pi\) | ||||
0.142454 | − | 0.989801i | \(-0.454501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 9.50143i | − 0.706236i | −0.935579 | − | 0.353118i | \(-0.885121\pi\) | ||||
0.935579 | − | 0.353118i | \(-0.114879\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.17157 | 0.233811 | ||||||||
\(185\) | 15.8645 | 1.16638 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 34.1563i | − 2.49776i | ||||||||
\(188\) | −10.7151 | −0.781482 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.11270 | 0.516009 | ||||||||
\(191\) | − 15.1716i | − 1.09778i | −0.835896 | − | 0.548888i | \(-0.815051\pi\) | ||||
0.835896 | − | 0.548888i | \(-0.184949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.34315 | −0.456590 | −0.228295 | − | 0.973592i | \(-0.573315\pi\) | ||||
−0.228295 | + | 0.973592i | \(0.573315\pi\) | |||||||
\(194\) | 2.93015 | 0.210373 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.75736i | 0.552689i | 0.961059 | + | 0.276344i | \(0.0891231\pi\) | ||||
−0.961059 | + | 0.276344i | \(0.910877\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 16.5754i | − 1.17500i | −0.809224 | − | 0.587501i | \(-0.800112\pi\) | ||||
0.809224 | − | 0.587501i | \(-0.199888\pi\) | |||||||
\(200\) | − 5.68629i | − 0.402082i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 2.21918i | − 0.156141i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.55635 | −0.248386 | ||||||||
\(206\) | 5.86030 | 0.408307 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 8.79045i | − 0.609508i | ||||||||
\(209\) | −28.2960 | −1.95728 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.3137 | −1.05424 | −0.527120 | − | 0.849791i | \(-0.676728\pi\) | ||||
−0.527120 | + | 0.849791i | \(0.676728\pi\) | |||||||
\(212\) | 12.9289i | 0.887963i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.51472 | 0.376978 | ||||||||
\(215\) | −13.1426 | −0.896315 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.24264i | 0.151891i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 25.8686i | 1.74406i | ||||||||
\(221\) | − 20.7279i | − 1.39431i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3.43289i | − 0.229883i | −0.993372 | − | 0.114942i | \(-0.963332\pi\) | ||||
0.993372 | − | 0.114942i | \(-0.0366681\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.75736 | 0.382974 | ||||||||
\(227\) | 14.1480 | 0.939037 | 0.469519 | − | 0.882923i | \(-0.344427\pi\) | ||||
0.469519 | + | 0.882923i | \(0.344427\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.7946i | 1.24198i | 0.783817 | + | 0.620992i | \(0.213270\pi\) | ||||
−0.783817 | + | 0.620992i | \(0.786730\pi\) | |||||||
\(230\) | −2.42742 | −0.160059 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.31371 | 0.0862492 | ||||||||
\(233\) | − 5.17157i | − 0.338801i | −0.985547 | − | 0.169401i | \(-0.945817\pi\) | ||||
0.985547 | − | 0.169401i | \(-0.0541831\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.1716 | 1.12015 | ||||||||
\(236\) | −10.7151 | −0.697496 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 11.6569i | − 0.754019i | −0.926209 | − | 0.377010i | \(-0.876952\pi\) | ||||
0.926209 | − | 0.377010i | \(-0.123048\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.3659i | 1.63396i | 0.576665 | + | 0.816980i | \(0.304354\pi\) | ||||
−0.576665 | + | 0.816980i | \(0.695646\pi\) | |||||||
\(242\) | 5.10051i | 0.327873i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 2.21918i | − 0.142068i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.1716 | −1.09260 | ||||||||
\(248\) | 9.29319 | 0.590118 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 1.71644i | − 0.108557i | ||||||||
\(251\) | −10.7151 | −0.676333 | −0.338167 | − | 0.941086i | \(-0.609807\pi\) | ||||
−0.338167 | + | 0.941086i | \(0.609807\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.65685 | 0.607121 | ||||||||
\(254\) | − 6.82843i | − 0.428454i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | −10.5069 | −0.655402 | −0.327701 | − | 0.944781i | \(-0.606274\pi\) | ||||
−0.327701 | + | 0.944781i | \(0.606274\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 15.6985i | 0.973579i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.43289i | 0.212084i | ||||||||
\(263\) | − 4.14214i | − 0.255415i | −0.991812 | − | 0.127708i | \(-0.959238\pi\) | ||||
0.991812 | − | 0.127708i | \(-0.0407619\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 20.7193i | − 1.27278i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15.5147 | −0.947712 | ||||||||
\(269\) | 2.21918 | 0.135306 | 0.0676528 | − | 0.997709i | \(-0.478449\pi\) | ||||
0.0676528 | + | 0.997709i | \(0.478449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.86030i | 0.355988i | 0.984032 | + | 0.177994i | \(0.0569608\pi\) | ||||
−0.984032 | + | 0.177994i | \(0.943039\pi\) | |||||||
\(272\) | 21.2220 | 1.28677 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | − 17.3137i | − 1.04406i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.9706 | 0.779326 | 0.389663 | − | 0.920958i | \(-0.372592\pi\) | ||||
0.389663 | + | 0.920958i | \(0.372592\pi\) | |||||||
\(278\) | −3.43289 | −0.205891 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.1716i | 0.785750i | 0.919592 | + | 0.392875i | \(0.128520\pi\) | ||||
−0.919592 | + | 0.392875i | \(0.871480\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 9.29319i | − 0.552423i | −0.961097 | − | 0.276211i | \(-0.910921\pi\) | ||||
0.961097 | − | 0.276211i | \(-0.0890790\pi\) | |||||||
\(284\) | − 1.51472i | − 0.0898820i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.86030i | 0.346527i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.0416 | 1.94363 | ||||||||
\(290\) | −1.00547 | −0.0590432 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 12.9343i | − 0.756923i | ||||||||
\(293\) | −22.9385 | −1.34008 | −0.670040 | − | 0.742325i | \(-0.733723\pi\) | ||||
−0.670040 | + | 0.742325i | \(0.733723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.1716 | 0.999768 | ||||||||
\(296\) | 8.58579i | 0.499039i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.75736 | −0.101801 | ||||||||
\(299\) | 5.86030 | 0.338910 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 1.85786i | − 0.106908i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 17.5809i | − 1.00833i | ||||||||
\(305\) | 3.55635i | 0.203636i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.4357i | 1.28048i | 0.768177 | + | 0.640238i | \(0.221164\pi\) | ||||
−0.768177 | + | 0.640238i | \(0.778836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.11270 | −0.403974 | ||||||||
\(311\) | −25.8686 | −1.46688 | −0.733438 | − | 0.679757i | \(-0.762085\pi\) | ||||
−0.733438 | + | 0.679757i | \(0.762085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.35757i | 0.302828i | 0.988470 | + | 0.151414i | \(0.0483826\pi\) | ||||
−0.988470 | + | 0.151414i | \(0.951617\pi\) | |||||||
\(314\) | 9.50143 | 0.536197 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.02944 | 0.170419 | ||||||||
\(317\) | 32.2426i | 1.81093i | 0.424424 | + | 0.905464i | \(0.360477\pi\) | ||||
−0.424424 | + | 0.905464i | \(0.639523\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | 0.223957 | ||||||||
\(320\) | −12.2233 | −0.683305 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 41.4558i | − 2.30666i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 10.5069i | − 0.582818i | ||||||||
\(326\) | − 3.79899i | − 0.210407i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 1.92468i | − 0.106273i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.6569 | 1.19037 | 0.595184 | − | 0.803589i | \(-0.297079\pi\) | ||||
0.595184 | + | 0.803589i | \(0.297079\pi\) | |||||||
\(332\) | 21.4303 | 1.17614 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 5.86030i | − 0.320661i | ||||||||
\(335\) | 24.8632 | 1.35842 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.0711 | −1.47466 | −0.737328 | − | 0.675535i | \(-0.763913\pi\) | ||||
−0.737328 | + | 0.675535i | \(0.763913\pi\) | |||||||
\(338\) | − 1.82843i | − 0.0994533i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −37.8995 | −2.05539 | ||||||||
\(341\) | 28.2960 | 1.53232 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 7.11270i | − 0.383491i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 0.502734i | − 0.0270272i | ||||||||
\(347\) | 14.9706i | 0.803662i | 0.915714 | + | 0.401831i | \(0.131626\pi\) | ||||
−0.915714 | + | 0.401831i | \(0.868374\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 11.2179i | − 0.600479i | −0.953864 | − | 0.300239i | \(-0.902933\pi\) | ||||
0.953864 | − | 0.300239i | \(-0.0970666\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −21.3137 | −1.13602 | ||||||||
\(353\) | −20.5111 | −1.09169 | −0.545847 | − | 0.837885i | \(-0.683792\pi\) | ||||
−0.545847 | + | 0.837885i | \(0.683792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.42742i | 0.128834i | ||||||||
\(356\) | 20.5111 | 1.08708 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.9706 | −0.579812 | ||||||||
\(359\) | − 34.9706i | − 1.84568i | −0.385189 | − | 0.922838i | \(-0.625864\pi\) | ||||
0.385189 | − | 0.922838i | \(-0.374136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3431 | −0.807534 | ||||||||
\(362\) | −3.93562 | −0.206852 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.7279i | 1.08495i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 20.0083i | − 1.04443i | −0.852815 | − | 0.522213i | \(-0.825107\pi\) | ||||
0.852815 | − | 0.522213i | \(-0.174893\pi\) | |||||||
\(368\) | 6.00000i | 0.312772i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 6.57128i | − 0.341624i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6274 | 1.17160 | 0.585802 | − | 0.810454i | \(-0.300780\pi\) | ||||
0.585802 | + | 0.810454i | \(0.300780\pi\) | |||||||
\(374\) | −14.1480 | −0.731577 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.29319i | 0.479260i | ||||||||
\(377\) | 2.42742 | 0.125018 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 31.3970i | 1.61063i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.28427 | −0.321531 | ||||||||
\(383\) | 23.4412 | 1.19779 | 0.598895 | − | 0.800828i | \(-0.295607\pi\) | ||||
0.598895 | + | 0.800828i | \(0.295607\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.62742i | 0.133732i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.9343i | 0.656640i | ||||||||
\(389\) | 25.7990i | 1.30806i | 0.756468 | + | 0.654030i | \(0.226923\pi\) | ||||
−0.756468 | + | 0.654030i | \(0.773077\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.1480i | 0.715496i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.21320 | 0.161879 | ||||||||
\(395\) | −4.85483 | −0.244273 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7891i | 0.892812i | 0.894831 | + | 0.446406i | \(0.147296\pi\) | ||||
−0.894831 | + | 0.446406i | \(0.852704\pi\) | |||||||
\(398\) | −6.86577 | −0.344150 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.7574 | 0.537868 | ||||||||
\(401\) | 5.17157i | 0.258256i | 0.991628 | + | 0.129128i | \(0.0412178\pi\) | ||||
−0.991628 | + | 0.129128i | \(0.958782\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.1716 | 0.855377 | ||||||||
\(404\) | 9.79592 | 0.487365 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.1421i | 1.29582i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 9.50143i | − 0.469815i | −0.972018 | − | 0.234908i | \(-0.924521\pi\) | ||||
0.972018 | − | 0.234908i | \(-0.0754788\pi\) | |||||||
\(410\) | 1.47309i | 0.0727506i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 25.8686i | 1.27446i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −34.3431 | −1.68584 | ||||||||
\(416\) | −12.9343 | −0.634157 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11.7206i | 0.573274i | ||||||||
\(419\) | −19.0029 | −0.928350 | −0.464175 | − | 0.885743i | \(-0.653649\pi\) | ||||
−0.464175 | + | 0.885743i | \(0.653649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.686292 | −0.0334478 | −0.0167239 | − | 0.999860i | \(-0.505324\pi\) | ||||
−0.0167239 | + | 0.999860i | \(0.505324\pi\) | |||||||
\(422\) | 6.34315i | 0.308780i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.2132 | 0.544561 | ||||||||
\(425\) | 25.3659 | 1.23043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 24.3431i | 1.17667i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.44382i | 0.262524i | ||||||||
\(431\) | 35.4558i | 1.70785i | 0.520398 | + | 0.853924i | \(0.325784\pi\) | ||||
−0.520398 | + | 0.853924i | \(0.674216\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.21371i | 0.0583271i | 0.999575 | + | 0.0291636i | \(0.00928436\pi\) | ||||
−0.999575 | + | 0.0291636i | \(0.990716\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.89949 | −0.474100 | ||||||||
\(437\) | 11.7206 | 0.560673 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.8632i | 1.18665i | 0.804962 | + | 0.593327i | \(0.202186\pi\) | ||||
−0.804962 | + | 0.593327i | \(0.797814\pi\) | |||||||
\(440\) | 22.4357 | 1.06958 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.58579 | −0.408384 | ||||||||
\(443\) | − 19.1716i | − 0.910869i | −0.890269 | − | 0.455434i | \(-0.849484\pi\) | ||||
0.890269 | − | 0.455434i | \(-0.150516\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.8701 | −1.55819 | ||||||||
\(446\) | −1.42195 | −0.0673312 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7574i | 0.743636i | 0.928306 | + | 0.371818i | \(0.121265\pi\) | ||||
−0.928306 | + | 0.371818i | \(0.878735\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 5.86030i | − 0.275951i | ||||||||
\(452\) | 25.4142i | 1.19538i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 5.86030i | − 0.275038i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.6274 | −0.777798 | −0.388899 | − | 0.921280i | \(-0.627144\pi\) | ||||
−0.388899 | + | 0.921280i | \(0.627144\pi\) | |||||||
\(458\) | 7.78498 | 0.363768 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 10.7151i | − 0.499596i | ||||||||
\(461\) | −10.5069 | −0.489355 | −0.244677 | − | 0.969605i | \(-0.578682\pi\) | ||||
−0.244677 | + | 0.969605i | \(0.578682\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.4853 | 0.952032 | 0.476016 | − | 0.879437i | \(-0.342080\pi\) | ||||
0.476016 | + | 0.879437i | \(0.342080\pi\) | |||||||
\(464\) | 2.48528i | 0.115376i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.14214 | −0.0992325 | ||||||||
\(467\) | −14.1480 | −0.654692 | −0.327346 | − | 0.944904i | \(-0.606154\pi\) | ||||
−0.327346 | + | 0.944904i | \(0.606154\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 7.11270i | − 0.328084i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.29319i | 0.427754i | ||||||||
\(473\) | − 21.6569i | − 0.995783i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 21.0138i | − 0.964179i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.82843 | −0.220847 | ||||||||
\(479\) | −42.4441 | −1.93932 | −0.969659 | − | 0.244460i | \(-0.921389\pi\) | ||||
−0.969659 | + | 0.244460i | \(0.921389\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.8645i | 0.723357i | ||||||||
\(482\) | 10.5069 | 0.478576 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22.5147 | −1.02340 | ||||||||
\(485\) | − 20.7279i | − 0.941206i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.4558 | −1.87854 | −0.939272 | − | 0.343174i | \(-0.888498\pi\) | ||||
−0.939272 | + | 0.343174i | \(0.888498\pi\) | |||||||
\(488\) | −1.92468 | −0.0871263 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 25.3137i | − 1.14239i | −0.820814 | − | 0.571196i | \(-0.806480\pi\) | ||||
0.820814 | − | 0.571196i | \(-0.193520\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.86030i | 0.263935i | ||||||||
\(494\) | 7.11270i | 0.320015i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.5809i | 0.789406i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.1421 | 1.17028 | 0.585141 | − | 0.810931i | \(-0.301039\pi\) | ||||
0.585141 | + | 0.810931i | \(0.301039\pi\) | |||||||
\(500\) | 7.57675 | 0.338842 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.43835i | 0.198093i | ||||||||
\(503\) | 4.85483 | 0.216466 | 0.108233 | − | 0.994126i | \(-0.465481\pi\) | ||||
0.108233 | + | 0.994126i | \(0.465481\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6985 | −0.698573 | ||||||||
\(506\) | − 4.00000i | − 0.177822i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 30.1421 | 1.33734 | ||||||||
\(509\) | 26.0769 | 1.15584 | 0.577918 | − | 0.816095i | \(-0.303865\pi\) | ||||
0.577918 | + | 0.816095i | \(0.303865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 22.7574i | − 1.00574i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.35210i | 0.191963i | ||||||||
\(515\) | − 41.4558i | − 1.82676i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.2960i | 1.24446i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 13.6152 | 0.597067 | ||||||||
\(521\) | 3.93562 | 0.172423 | 0.0862113 | − | 0.996277i | \(-0.472524\pi\) | ||||
0.0862113 | + | 0.996277i | \(0.472524\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 31.7289i | − 1.38741i | −0.720260 | − | 0.693705i | \(-0.755977\pi\) | ||||
0.720260 | − | 0.693705i | \(-0.244023\pi\) | |||||||
\(524\) | −15.1535 | −0.661983 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.71573 | −0.0748093 | ||||||||
\(527\) | 41.4558i | 1.80584i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0000 | 0.826087 | ||||||||
\(530\) | −8.58221 | −0.372788 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3.55635i | − 0.154043i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 39.0112i | − 1.68660i | ||||||||
\(536\) | 13.4558i | 0.581204i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 0.919213i | − 0.0396301i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.9706 | −0.643635 | −0.321817 | − | 0.946802i | \(-0.604294\pi\) | ||||
−0.321817 | + | 0.946802i | \(0.604294\pi\) | |||||||
\(542\) | 2.42742 | 0.104266 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 31.2262i | − 1.33881i | ||||||||
\(545\) | 15.8645 | 0.679559 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.6274 | 0.796451 | 0.398225 | − | 0.917288i | \(-0.369626\pi\) | ||||
0.398225 | + | 0.917288i | \(0.369626\pi\) | |||||||
\(548\) | 8.82843i | 0.377132i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.17157 | −0.305797 | ||||||||
\(551\) | 4.85483 | 0.206823 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 5.37258i | − 0.228259i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 15.1535i | − 0.642651i | ||||||||
\(557\) | − 13.4142i | − 0.568378i | −0.958768 | − | 0.284189i | \(-0.908276\pi\) | ||||
0.958768 | − | 0.284189i | \(-0.0917244\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 13.1426i | − 0.555871i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.45584 | 0.230141 | ||||||||
\(563\) | 14.1480 | 0.596268 | 0.298134 | − | 0.954524i | \(-0.403636\pi\) | ||||
0.298134 | + | 0.954524i | \(0.403636\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 40.7276i | − 1.71342i | ||||||||
\(566\) | −3.84936 | −0.161801 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.31371 | −0.0551220 | ||||||||
\(569\) | − 37.1127i | − 1.55585i | −0.628360 | − | 0.777923i | \(-0.716274\pi\) | ||||
0.628360 | − | 0.777923i | \(-0.283726\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.3137 | 0.473464 | 0.236732 | − | 0.971575i | \(-0.423924\pi\) | ||||
0.236732 | + | 0.971575i | \(0.423924\pi\) | |||||||
\(572\) | −25.8686 | −1.08162 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.17157i | 0.299075i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.5098i | 1.22851i | 0.789109 | + | 0.614254i | \(0.210543\pi\) | ||||
−0.789109 | + | 0.614254i | \(0.789457\pi\) | |||||||
\(578\) | − 13.6863i | − 0.569275i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 4.43835i | − 0.184293i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.1421 | 1.41402 | ||||||||
\(584\) | −11.2179 | −0.464199 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.50143i | 0.392500i | ||||||||
\(587\) | 17.5809 | 0.725642 | 0.362821 | − | 0.931859i | \(-0.381814\pi\) | ||||
0.362821 | + | 0.931859i | \(0.381814\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.3431 | 1.41508 | ||||||||
\(590\) | − 7.11270i | − 0.292825i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.2426 | −0.667568 | ||||||||
\(593\) | −23.6494 | −0.971166 | −0.485583 | − | 0.874190i | \(-0.661393\pi\) | ||||
−0.485583 | + | 0.874190i | \(0.661393\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 7.75736i | − 0.317754i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 2.42742i | − 0.0992645i | ||||||||
\(599\) | − 10.4853i | − 0.428417i | −0.976788 | − | 0.214208i | \(-0.931283\pi\) | ||||
0.976788 | − | 0.214208i | \(-0.0687172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 40.5194i | − 1.65282i | −0.563069 | − | 0.826410i | \(-0.690379\pi\) | ||||
0.563069 | − | 0.826410i | \(-0.309621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.20101 | 0.333694 | ||||||||
\(605\) | 36.0810 | 1.46690 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 3.43289i | − 0.139337i | −0.997570 | − | 0.0696683i | \(-0.977806\pi\) | ||||
0.997570 | − | 0.0696683i | \(-0.0221941\pi\) | |||||||
\(608\) | −25.8686 | −1.04911 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.47309 | 0.0596436 | ||||||||
\(611\) | 17.1716i | 0.694687i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.8701 | 1.73151 | 0.865753 | − | 0.500472i | \(-0.166840\pi\) | ||||
0.865753 | + | 0.500472i | \(0.166840\pi\) | |||||||
\(614\) | 9.29319 | 0.375043 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 13.5147i | − 0.544082i | −0.962286 | − | 0.272041i | \(-0.912301\pi\) | ||||
0.962286 | − | 0.272041i | \(-0.0876986\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.8715i | 1.80354i | 0.432219 | + | 0.901769i | \(0.357731\pi\) | ||||
−0.432219 | + | 0.901769i | \(0.642269\pi\) | |||||||
\(620\) | − 31.3970i | − 1.26093i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.7151i | 0.429638i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.0711 | −1.20284 | ||||||||
\(626\) | 2.21918 | 0.0886962 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 41.9413i | 1.67364i | ||||||||
\(629\) | −38.3002 | −1.52713 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.8284 | −1.06802 | −0.534011 | − | 0.845477i | \(-0.679316\pi\) | ||||
−0.534011 | + | 0.845477i | \(0.679316\pi\) | |||||||
\(632\) | − 2.62742i | − 0.104513i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.3553 | 0.530408 | ||||||||
\(635\) | −48.3044 | −1.91690 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 1.65685i | − 0.0655955i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 30.9317i | 1.22268i | ||||||||
\(641\) | 24.4853i | 0.967110i | 0.875314 | + | 0.483555i | \(0.160655\pi\) | ||||
−0.875314 | + | 0.483555i | \(0.839345\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5.86030i | − 0.231108i | −0.993301 | − | 0.115554i | \(-0.963136\pi\) | ||||
0.993301 | − | 0.115554i | \(-0.0368643\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.1716 | −0.675606 | ||||||||
\(647\) | 10.7151 | 0.421255 | 0.210628 | − | 0.977566i | \(-0.432449\pi\) | ||||
0.210628 | + | 0.977566i | \(0.432449\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.2960i | 1.11072i | ||||||||
\(650\) | −4.35210 | −0.170703 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.7696 | 0.656746 | ||||||||
\(653\) | − 21.5147i | − 0.841936i | −0.907075 | − | 0.420968i | \(-0.861690\pi\) | ||||
0.907075 | − | 0.420968i | \(-0.138310\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.2843 | 0.948865 | ||||||||
\(656\) | 3.64113 | 0.142162 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.45584i | 0.134621i | 0.997732 | + | 0.0673103i | \(0.0214417\pi\) | ||||
−0.997732 | + | 0.0673103i | \(0.978558\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 22.9385i | − 0.892203i | −0.894982 | − | 0.446102i | \(-0.852812\pi\) | ||||
0.894982 | − | 0.446102i | \(-0.147188\pi\) | |||||||
\(662\) | − 8.97056i | − 0.348651i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 18.5864i | − 0.721291i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.65685 | −0.0641537 | ||||||||
\(668\) | 25.8686 | 1.00089 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 10.2987i | − 0.397872i | ||||||||
\(671\) | −5.86030 | −0.226234 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.1005 | −0.697723 | −0.348862 | − | 0.937174i | \(-0.613432\pi\) | ||||
−0.348862 | + | 0.937174i | \(0.613432\pi\) | |||||||
\(674\) | 11.2132i | 0.431916i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.07107 | 0.310426 | ||||||||
\(677\) | −46.0852 | −1.77120 | −0.885599 | − | 0.464451i | \(-0.846252\pi\) | ||||
−0.885599 | + | 0.464451i | \(0.846252\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 32.8701i | 1.26051i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 11.7206i | − 0.448805i | ||||||||
\(683\) | − 34.7696i | − 1.33042i | −0.746656 | − | 0.665210i | \(-0.768342\pi\) | ||||
0.746656 | − | 0.665210i | \(-0.231658\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 14.1480i | − 0.540568i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.4558 | 0.512999 | ||||||||
\(689\) | 20.7193 | 0.789342 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 8.28772i | − 0.315280i | −0.987497 | − | 0.157640i | \(-0.949611\pi\) | ||||
0.987497 | − | 0.157640i | \(-0.0503885\pi\) | |||||||
\(692\) | 2.21918 | 0.0843605 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.20101 | 0.235387 | ||||||||
\(695\) | 24.2843i | 0.921155i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.58579 | 0.325210 | ||||||||
\(698\) | −4.64659 | −0.175876 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.7696i | 1.23769i | 0.785514 | + | 0.618844i | \(0.212399\pi\) | ||||
−0.785514 | + | 0.618844i | \(0.787601\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.7289i | 1.19668i | ||||||||
\(704\) | − 20.1421i | − 0.759135i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.49596i | 0.319750i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.27208 | −0.273109 | −0.136554 | − | 0.990633i | \(-0.543603\pi\) | ||||
−0.136554 | + | 0.990633i | \(0.543603\pi\) | |||||||
\(710\) | 1.00547 | 0.0377346 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 17.7891i | − 0.666676i | ||||||||
\(713\) | −11.7206 | −0.438940 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41.4558 | 1.55036 | ||||||||
\(716\) | − 48.4264i | − 1.80978i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.4853 | −0.540586 | ||||||||
\(719\) | 11.7206 | 0.437105 | 0.218552 | − | 0.975825i | \(-0.429867\pi\) | ||||
0.218552 | + | 0.975825i | \(0.429867\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.35534i | 0.236521i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 17.3727i | − 0.645650i | ||||||||
\(725\) | 2.97056i | 0.110324i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.0138i | 0.779358i | 0.920951 | + | 0.389679i | \(0.127414\pi\) | ||||
−0.920951 | + | 0.389679i | \(0.872586\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.58579 | 0.317774 | ||||||||
\(731\) | 31.7289 | 1.17354 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 37.7975i | − 1.39608i | −0.716058 | − | 0.698041i | \(-0.754055\pi\) | ||||
0.716058 | − | 0.698041i | \(-0.245945\pi\) | |||||||
\(734\) | −8.28772 | −0.305905 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.82843 | 0.325420 | ||||||||
\(737\) | 40.9706i | 1.50917i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1716 | −0.484524 | −0.242262 | − | 0.970211i | \(-0.577889\pi\) | ||||
−0.242262 | + | 0.970211i | \(0.577889\pi\) | |||||||
\(740\) | 29.0070 | 1.06632 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 32.4264i | − 1.18961i | −0.803870 | − | 0.594805i | \(-0.797229\pi\) | ||||
0.803870 | − | 0.594805i | \(-0.202771\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.4316i | 0.455458i | ||||||||
\(746\) | − 9.37258i | − 0.343155i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 62.4524i | − 2.28349i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.3137 | 1.58054 | 0.790270 | − | 0.612759i | \(-0.209940\pi\) | ||||
0.790270 | + | 0.612759i | \(0.209940\pi\) | |||||||
\(752\) | −17.5809 | −0.641110 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 1.00547i | − 0.0366170i | ||||||||
\(755\) | −13.1426 | −0.478306 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.8701 | −1.70352 | −0.851761 | − | 0.523931i | \(-0.824465\pi\) | ||||
−0.851761 | + | 0.523931i | \(0.824465\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27.2304 | 0.987752 | ||||||||
\(761\) | 17.0782 | 0.619083 | 0.309542 | − | 0.950886i | \(-0.399824\pi\) | ||||
0.309542 | + | 0.950886i | \(0.399824\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 27.7401i | − 1.00360i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 9.70967i | − 0.350825i | ||||||||
\(767\) | 17.1716i | 0.620030i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.0961i | 1.73439i | 0.497968 | + | 0.867195i | \(0.334080\pi\) | ||||
−0.497968 | + | 0.867195i | \(0.665920\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.5980 | −0.417420 | ||||||||
\(773\) | −24.6549 | −0.886776 | −0.443388 | − | 0.896330i | \(-0.646224\pi\) | ||||
−0.443388 | + | 0.896330i | \(0.646224\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.0138i | 0.754838i | ||||||||
\(776\) | 11.2179 | 0.402698 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.6863 | 0.383122 | ||||||||
\(779\) | − 7.11270i | − 0.254839i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 5.86030 | 0.209564 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 67.2132i | − 2.39894i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.7206i | 0.417794i | 0.977938 | + | 0.208897i | \(0.0669874\pi\) | ||||
−0.977938 | + | 0.208897i | \(0.933013\pi\) | |||||||
\(788\) | 14.1838i | 0.505276i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.01094i | 0.0715460i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.55635 | −0.126290 | ||||||||
\(794\) | 7.36851 | 0.261498 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 30.3070i | − 1.07420i | ||||||||
\(797\) | 51.2345 | 1.81482 | 0.907410 | − | 0.420247i | \(-0.138056\pi\) | ||||
0.907410 | + | 0.420247i | \(0.138056\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.4558 | −1.46660 | ||||||||
\(800\) | − 15.8284i | − 0.559619i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.14214 | 0.0756414 | ||||||||
\(803\) | −34.1563 | −1.20535 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 7.11270i | − 0.250534i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 8.49596i | − 0.298887i | ||||||||
\(809\) | − 16.0416i | − 0.563994i | −0.959415 | − | 0.281997i | \(-0.909003\pi\) | ||||
0.959415 | − | 0.281997i | \(-0.0909968\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.28772i | 0.291021i | 0.989357 | + | 0.145511i | \(0.0464825\pi\) | ||||
−0.989357 | + | 0.145511i | \(0.953518\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.8284 | 0.379536 | ||||||||
\(815\) | −26.8741 | −0.941359 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 26.2851i | − 0.919599i | ||||||||
\(818\) | −3.93562 | −0.137606 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.50253 | −0.227078 | ||||||||
\(821\) | 23.7574i | 0.829138i | 0.910018 | + | 0.414569i | \(0.136068\pi\) | ||||
−0.910018 | + | 0.414569i | \(0.863932\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.9411 | −1.46198 | −0.730988 | − | 0.682390i | \(-0.760940\pi\) | ||||
−0.730988 | + | 0.682390i | \(0.760940\pi\) | |||||||
\(824\) | 22.4357 | 0.781586 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.6569i | 1.37900i | 0.724284 | + | 0.689502i | \(0.242171\pi\) | ||||
−0.724284 | + | 0.689502i | \(0.757829\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 36.0810i | − 1.25315i | −0.779363 | − | 0.626573i | \(-0.784457\pi\) | ||||
0.779363 | − | 0.626573i | \(-0.215543\pi\) | |||||||
\(830\) | 14.2254i | 0.493771i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 12.2233i | − 0.423768i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.4558 | −1.43464 | ||||||||
\(836\) | −51.7373 | −1.78937 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.87124i | 0.271907i | ||||||||
\(839\) | 17.5809 | 0.606960 | 0.303480 | − | 0.952838i | \(-0.401851\pi\) | ||||
0.303480 | + | 0.952838i | \(0.401851\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.3137 | 0.976335 | ||||||||
\(842\) | 0.284271i | 0.00979663i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.0000 | −0.963800 | ||||||||
\(845\) | −12.9343 | −0.444954 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 21.2132i | 0.728464i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 10.5069i | − 0.360384i | ||||||||
\(851\) | − 10.8284i | − 0.371194i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0727i | 0.550319i | 0.961399 | + | 0.275159i | \(0.0887306\pi\) | ||||
−0.961399 | + | 0.275159i | \(0.911269\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.1127 | 0.721617 | ||||||||
\(857\) | 0.502734 | 0.0171731 | 0.00858654 | − | 0.999963i | \(-0.497267\pi\) | ||||
0.00858654 | + | 0.999963i | \(0.497267\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.29319i | 0.317079i | 0.987353 | + | 0.158540i | \(0.0506786\pi\) | ||||
−0.987353 | + | 0.158540i | \(0.949321\pi\) | |||||||
\(860\) | −24.0302 | −0.819423 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.6863 | 0.500217 | ||||||||
\(863\) | − 10.6863i | − 0.363766i | −0.983320 | − | 0.181883i | \(-0.941781\pi\) | ||||
0.983320 | − | 0.181883i | \(-0.0582191\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.55635 | −0.120919 | ||||||||
\(866\) | 0.502734 | 0.0170836 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 8.00000i | − 0.271381i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.8632i | 0.842456i | ||||||||
\(872\) | 8.58579i | 0.290751i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 4.85483i | − 0.164217i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.5269 | −1.09836 | −0.549178 | − | 0.835705i | \(-0.685059\pi\) | ||||
−0.549178 | + | 0.835705i | \(0.685059\pi\) | |||||||
\(878\) | 10.2987 | 0.347563 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 42.4441i | 1.43079i | ||||||||
\(881\) | 23.6494 | 0.796770 | 0.398385 | − | 0.917218i | \(-0.369571\pi\) | ||||
0.398385 | + | 0.917218i | \(0.369571\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.4558 | 0.452825 | 0.226413 | − | 0.974031i | \(-0.427300\pi\) | ||||
0.226413 | + | 0.974031i | \(0.427300\pi\) | |||||||
\(884\) | − 37.8995i | − 1.27470i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.94113 | −0.266787 | ||||||||
\(887\) | 50.7318 | 1.70341 | 0.851703 | − | 0.524024i | \(-0.175570\pi\) | ||||
0.851703 | + | 0.524024i | \(0.175570\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13.6152i | 0.456383i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 6.27678i | − 0.210162i | ||||||||
\(893\) | 34.3431i | 1.14925i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 77.6059i | 2.59408i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.52691 | 0.217806 | ||||||||
\(899\) | −4.85483 | −0.161918 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.0208i | 1.66643i | ||||||||
\(902\) | −2.42742 | −0.0808241 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.0416 | 0.733094 | ||||||||
\(905\) | 27.8406i | 0.925454i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.7696 | 0.955277 | 0.477639 | − | 0.878556i | \(-0.341493\pi\) | ||||
0.477639 | + | 0.878556i | \(0.341493\pi\) | |||||||
\(908\) | 25.8686 | 0.858481 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.4853i | 1.40760i | 0.710398 | + | 0.703800i | \(0.248515\pi\) | ||||
−0.710398 | + | 0.703800i | \(0.751485\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 56.5921i | − 1.87292i | ||||||||
\(914\) | 6.88730i | 0.227812i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 34.3646i | 1.13544i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.4558 | −1.36750 | −0.683751 | − | 0.729715i | \(-0.739653\pi\) | ||||
−0.683751 | + | 0.729715i | \(0.739653\pi\) | |||||||
\(920\) | −9.29319 | −0.306387 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.35210i | 0.143329i | ||||||||
\(923\) | −2.42742 | −0.0798994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.4142 | −0.638335 | ||||||||
\(926\) | − 8.48528i | − 0.278844i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.65685 | 0.120042 | ||||||||
\(929\) | 0.502734 | 0.0164942 | 0.00824709 | − | 0.999966i | \(-0.497375\pi\) | ||||
0.00824709 | + | 0.999966i | \(0.497375\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 9.45584i | − 0.309736i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.86030i | 0.191755i | ||||||||
\(935\) | 100.083i | 3.27307i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 51.2345i | − 1.67376i | −0.547387 | − | 0.836879i | \(-0.684378\pi\) | ||||
0.547387 | − | 0.836879i | \(-0.315622\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 31.3970 | 1.02406 | ||||||||
\(941\) | −4.64659 | −0.151475 | −0.0757373 | − | 0.997128i | \(-0.524131\pi\) | ||||
−0.0757373 | + | 0.997128i | \(0.524131\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.42742i | 0.0790476i | ||||||||
\(944\) | −17.5809 | −0.572210 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.97056 | −0.291658 | ||||||||
\(947\) | − 10.9706i | − 0.356495i | −0.983986 | − | 0.178248i | \(-0.942957\pi\) | ||||
0.983986 | − | 0.178248i | \(-0.0570428\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.7279 | −0.672857 | ||||||||
\(950\) | −8.70420 | −0.282401 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.3848i | 0.336396i | 0.985753 | + | 0.168198i | \(0.0537948\pi\) | ||||
−0.985753 | + | 0.168198i | \(0.946205\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.4550i | 1.43853i | ||||||||
\(956\) | − 21.3137i | − 0.689335i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.5809i | 0.568013i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.34315 | −0.107843 | ||||||||
\(962\) | 6.57128 | 0.211866 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 46.3797i | 1.49379i | ||||||||
\(965\) | 18.5864 | 0.598317 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.1127 | −0.614623 | −0.307311 | − | 0.951609i | \(-0.599429\pi\) | ||||
−0.307311 | + | 0.951609i | \(0.599429\pi\) | |||||||
\(968\) | 19.5269i | 0.627619i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.58579 | −0.275673 | ||||||||
\(971\) | 4.85483 | 0.155799 | 0.0778995 | − | 0.996961i | \(-0.475179\pi\) | ||||
0.0778995 | + | 0.996961i | \(0.475179\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 17.1716i | 0.550213i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 3.64113i | − 0.116550i | ||||||||
\(977\) | 44.8284i | 1.43419i | 0.696976 | + | 0.717094i | \(0.254528\pi\) | ||||
−0.696976 | + | 0.717094i | \(0.745472\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 54.1647i | − 1.73111i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.4853 | −0.334599 | ||||||||
\(983\) | −31.7289 | −1.01200 | −0.505998 | − | 0.862535i | \(-0.668876\pi\) | ||||
−0.505998 | + | 0.862535i | \(0.668876\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 22.7302i | − 0.724246i | ||||||||
\(986\) | 2.42742 | 0.0773047 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.3970 | −0.998871 | ||||||||
\(989\) | 8.97056i | 0.285247i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.3970 | −1.88681 | −0.943403 | − | 0.331647i | \(-0.892396\pi\) | ||||
−0.943403 | + | 0.331647i | \(0.892396\pi\) | |||||||
\(992\) | 25.8686 | 0.821330 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.5685i | 1.53973i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.5139i | 1.25142i | 0.780056 | + | 0.625709i | \(0.215190\pi\) | ||||
−0.780056 | + | 0.625709i | \(0.784810\pi\) | |||||||
\(998\) | − 10.8284i | − 0.342768i | ||||||||
\(999\) | 0 | 0 |
(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 | 441.2.c.b.440.3 | ✓ | 8 | |
3.2 | odd | 2 | inner | 441.2.c.b.440.6 | yes | 8 | |
4.3 | odd | 2 | 7056.2.k.g.881.4 | 8 | |||
7.2 | even | 3 | 441.2.p.c.80.4 | 16 | |||
7.3 | odd | 6 | 441.2.p.c.215.5 | 16 | |||
7.4 | even | 3 | 441.2.p.c.215.6 | 16 | |||
7.5 | odd | 6 | 441.2.p.c.80.3 | 16 | |||
7.6 | odd | 2 | inner | 441.2.c.b.440.4 | yes | 8 | |
12.11 | even | 2 | 7056.2.k.g.881.5 | 8 | |||
21.2 | odd | 6 | 441.2.p.c.80.5 | 16 | |||
21.5 | even | 6 | 441.2.p.c.80.6 | 16 | |||
21.11 | odd | 6 | 441.2.p.c.215.3 | 16 | |||
21.17 | even | 6 | 441.2.p.c.215.4 | 16 | |||
21.20 | even | 2 | inner | 441.2.c.b.440.5 | yes | 8 | |
28.27 | even | 2 | 7056.2.k.g.881.6 | 8 | |||
84.83 | odd | 2 | 7056.2.k.g.881.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.c.b.440.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
441.2.c.b.440.4 | yes | 8 | 7.6 | odd | 2 | inner | |
441.2.c.b.440.5 | yes | 8 | 21.20 | even | 2 | inner | |
441.2.c.b.440.6 | yes | 8 | 3.2 | odd | 2 | inner | |
441.2.p.c.80.3 | 16 | 7.5 | odd | 6 | |||
441.2.p.c.80.4 | 16 | 7.2 | even | 3 | |||
441.2.p.c.80.5 | 16 | 21.2 | odd | 6 | |||
441.2.p.c.80.6 | 16 | 21.5 | even | 6 | |||
441.2.p.c.215.3 | 16 | 21.11 | odd | 6 | |||
441.2.p.c.215.4 | 16 | 21.17 | even | 6 | |||
441.2.p.c.215.5 | 16 | 7.3 | odd | 6 | |||
441.2.p.c.215.6 | 16 | 7.4 | even | 3 | |||
7056.2.k.g.881.3 | 8 | 84.83 | odd | 2 | |||
7056.2.k.g.881.4 | 8 | 4.3 | odd | 2 | |||
7056.2.k.g.881.5 | 8 | 12.11 | even | 2 | |||
7056.2.k.g.881.6 | 8 | 28.27 | even | 2 |