Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1709,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2394.1709");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.b (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: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 10x^{6} + 30x^{4} + 24x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1709.3 | ||
Root | \(-0.209899i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2394.1709 |
Dual form | 2394.2.b.j.1709.6 |
$q$-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 \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | − | 2.76612i | − | 1.23705i | −0.785766 | − | 0.618523i | \(-0.787731\pi\) | ||
0.785766 | − | 0.618523i | \(-0.212269\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 2.76612i | − | 0.874724i | ||||||
\(11\) | − | 4.92827i | − | 1.48593i | −0.669331 | − | 0.742964i | \(-0.733419\pi\) | ||
0.669331 | − | 0.742964i | \(-0.266581\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.93944i | 0.815253i | 0.913149 | + | 0.407626i | \(0.133643\pi\) | ||||
−0.913149 | + | 0.407626i | \(0.866357\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 4.92827i | − | 1.19528i | −0.801764 | − | 0.597640i | \(-0.796105\pi\) | ||
0.801764 | − | 0.597640i | \(-0.203895\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.87745 | + | 3.93385i | 0.430716 | + | 0.902488i | ||||
\(20\) | − | 2.76612i | − | 0.618523i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 4.92827i | − | 1.05071i | ||||||
\(23\) | 0.685627i | 0.142963i | 0.997442 | + | 0.0714816i | \(0.0227727\pi\) | ||||
−0.997442 | + | 0.0714816i | \(0.977227\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.65142 | −0.530284 | ||||||||
\(26\) | 2.93944i | 0.576471i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −1.65142 | −0.306661 | −0.153331 | − | 0.988175i | \(-0.549000\pi\) | ||||
−0.153331 | + | 0.988175i | \(0.549000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.16215i | − | 0.388333i | −0.980969 | − | 0.194167i | \(-0.937800\pi\) | ||
0.980969 | − | 0.194167i | \(-0.0622002\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.92827i | − | 0.845191i | ||||||
\(35\) | 2.76612i | 0.467560i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.77488i | − | 1.60698i | −0.595318 | − | 0.803490i | \(-0.702974\pi\) | ||
0.595318 | − | 0.803490i | \(-0.297026\pi\) | |||||||
\(38\) | 1.87745 | + | 3.93385i | 0.304562 | + | 0.638155i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 2.76612i | − | 0.437362i | ||||||
\(41\) | −2.37594 | −0.371059 | −0.185530 | − | 0.982639i | \(-0.559400\pi\) | ||||
−0.185530 | + | 0.982639i | \(0.559400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.15699 | −1.24393 | −0.621965 | − | 0.783045i | \(-0.713665\pi\) | ||||
−0.621965 | + | 0.783045i | \(0.713665\pi\) | |||||||
\(44\) | − | 4.92827i | − | 0.742964i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.685627i | 0.101090i | ||||||||
\(47\) | − | 5.87887i | − | 0.857522i | −0.903418 | − | 0.428761i | \(-0.858950\pi\) | ||
0.903418 | − | 0.428761i | \(-0.141050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.65142 | −0.374968 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.93944i | 0.407626i | ||||||||
\(53\) | −3.47519 | −0.477354 | −0.238677 | − | 0.971099i | \(-0.576714\pi\) | ||||
−0.238677 | + | 0.971099i | \(0.576714\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.6322 | −1.83816 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.65142 | −0.216842 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.26046 | −0.545496 | −0.272748 | − | 0.962085i | \(-0.587933\pi\) | ||||
−0.272748 | + | 0.962085i | \(0.587933\pi\) | |||||||
\(62\) | − | 2.16215i | − | 0.274593i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.13083 | 1.00851 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.56450i | 0.801981i | 0.916082 | + | 0.400991i | \(0.131334\pi\) | ||||
−0.916082 | + | 0.400991i | \(0.868666\pi\) | |||||||
\(68\) | − | 4.92827i | − | 0.597640i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.76612i | 0.330615i | ||||||||
\(71\) | −11.1266 | −1.32049 | −0.660243 | − | 0.751052i | \(-0.729547\pi\) | ||||
−0.660243 | + | 0.751052i | \(0.729547\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.85415 | 0.334053 | 0.167026 | − | 0.985952i | \(-0.446584\pi\) | ||||
0.167026 | + | 0.985952i | \(0.446584\pi\) | |||||||
\(74\) | − | 9.77488i | − | 1.13631i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.87745 | + | 3.93385i | 0.215358 | + | 0.451244i | ||||
\(77\) | 4.92827i | 0.561628i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.0781i | − | 1.24638i | −0.782070 | − | 0.623191i | \(-0.785836\pi\) | ||
0.782070 | − | 0.623191i | \(-0.214164\pi\) | |||||||
\(80\) | − | 2.76612i | − | 0.309262i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.37594 | −0.262379 | ||||||||
\(83\) | − | 7.07681i | − | 0.776781i | −0.921495 | − | 0.388390i | \(-0.873031\pi\) | ||
0.921495 | − | 0.388390i | \(-0.126969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.6322 | −1.47862 | ||||||||
\(86\) | −8.15699 | −0.879591 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 4.92827i | − | 0.525355i | ||||||
\(89\) | 13.5026 | 1.43127 | 0.715634 | − | 0.698476i | \(-0.246138\pi\) | ||||
0.715634 | + | 0.698476i | \(0.246138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2.93944i | − | 0.308137i | ||||||
\(92\) | 0.685627i | 0.0714816i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 5.87887i | − | 0.606359i | ||||||
\(95\) | 10.8815 | − | 5.19325i | 1.11642 | − | 0.532816i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.11275i | 0.316052i | 0.987435 | + | 0.158026i | \(0.0505130\pi\) | ||||
−0.987435 | + | 0.158026i | \(0.949487\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.65142 | −0.265142 | ||||||||
\(101\) | 8.64499i | 0.860209i | 0.902779 | + | 0.430104i | \(0.141523\pi\) | ||||
−0.902779 | + | 0.430104i | \(0.858477\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.49761i | 0.443163i | 0.975142 | + | 0.221581i | \(0.0711218\pi\) | ||||
−0.975142 | + | 0.221581i | \(0.928878\pi\) | |||||||
\(104\) | 2.93944i | 0.288235i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.47519 | −0.337540 | ||||||||
\(107\) | 9.66678 | 0.934523 | 0.467261 | − | 0.884119i | \(-0.345241\pi\) | ||||
0.467261 | + | 0.884119i | \(0.345241\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.6895i | − | 1.40700i | −0.710694 | − | 0.703502i | \(-0.751619\pi\) | ||
0.710694 | − | 0.703502i | \(-0.248381\pi\) | |||||||
\(110\) | −13.6322 | −1.29978 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −11.0111 | −1.03584 | −0.517920 | − | 0.855429i | \(-0.673294\pi\) | ||||
−0.517920 | + | 0.855429i | \(0.673294\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.89653 | 0.176852 | ||||||||
\(116\) | −1.65142 | −0.153331 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.92827i | 0.451774i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.2878 | −1.20798 | ||||||||
\(122\) | −4.26046 | −0.385724 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 2.16215i | − | 0.194167i | ||||||
\(125\) | − | 6.49645i | − | 0.581060i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.56818i | − | 0.139154i | −0.997577 | − | 0.0695768i | \(-0.977835\pi\) | ||
0.997577 | − | 0.0695768i | \(-0.0221649\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.13083 | 0.713121 | ||||||||
\(131\) | 15.8330i | 1.38334i | 0.722214 | + | 0.691669i | \(0.243124\pi\) | ||||
−0.722214 | + | 0.691669i | \(0.756876\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.87745 | − | 3.93385i | −0.162795 | − | 0.341108i | ||||
\(134\) | 6.56450i | 0.567086i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 4.92827i | − | 0.422595i | ||||||
\(137\) | − | 5.61390i | − | 0.479627i | −0.970819 | − | 0.239814i | \(-0.922914\pi\) | ||
0.970819 | − | 0.239814i | \(-0.0770864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.0770 | 1.87255 | 0.936273 | − | 0.351273i | \(-0.114251\pi\) | ||||
0.936273 | + | 0.351273i | \(0.114251\pi\) | |||||||
\(140\) | 2.76612i | 0.233780i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.1266 | −0.933725 | ||||||||
\(143\) | 14.4863 | 1.21141 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.56803i | 0.379354i | ||||||||
\(146\) | 2.85415 | 0.236211 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 9.77488i | − | 0.803490i | ||||||
\(149\) | − | 1.37125i | − | 0.112338i | −0.998421 | − | 0.0561688i | \(-0.982112\pi\) | ||
0.998421 | − | 0.0561688i | \(-0.0178885\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.8358i | 1.85835i | 0.369636 | + | 0.929177i | \(0.379482\pi\) | ||||
−0.369636 | + | 0.929177i | \(0.620518\pi\) | |||||||
\(152\) | 1.87745 | + | 3.93385i | 0.152281 | + | 0.319078i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.92827i | 0.397131i | ||||||||
\(155\) | −5.98076 | −0.480386 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.53595 | 0.441817 | 0.220908 | − | 0.975295i | \(-0.429098\pi\) | ||||
0.220908 | + | 0.975295i | \(0.429098\pi\) | |||||||
\(158\) | − | 11.0781i | − | 0.881325i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 2.76612i | − | 0.218681i | ||||||
\(161\) | − | 0.685627i | − | 0.0540350i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.9200 | −1.71691 | −0.858454 | − | 0.512891i | \(-0.828574\pi\) | ||||
−0.858454 | + | 0.512891i | \(0.828574\pi\) | |||||||
\(164\) | −2.37594 | −0.185530 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 7.07681i | − | 0.549267i | ||||||
\(167\) | 17.7892 | 1.37657 | 0.688284 | − | 0.725442i | \(-0.258364\pi\) | ||||
0.688284 | + | 0.725442i | \(0.258364\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.35972 | 0.335363 | ||||||||
\(170\) | −13.6322 | −1.04554 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.15699 | −0.621965 | ||||||||
\(173\) | 9.66678 | 0.734952 | 0.367476 | − | 0.930033i | \(-0.380222\pi\) | ||||
0.367476 | + | 0.930033i | \(0.380222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.65142 | 0.200429 | ||||||||
\(176\) | − | 4.92827i | − | 0.371482i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.5026 | 1.01206 | ||||||||
\(179\) | 14.4295 | 1.07851 | 0.539254 | − | 0.842143i | \(-0.318706\pi\) | ||||
0.539254 | + | 0.842143i | \(0.318706\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.5880i | − | 0.861331i | −0.902512 | − | 0.430666i | \(-0.858279\pi\) | ||
0.902512 | − | 0.430666i | \(-0.141721\pi\) | |||||||
\(182\) | − | 2.93944i | − | 0.217886i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.685627i | 0.0505451i | ||||||||
\(185\) | −27.0385 | −1.98791 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.2878 | −1.77610 | ||||||||
\(188\) | − | 5.87887i | − | 0.428761i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.8815 | − | 5.19325i | 0.789428 | − | 0.376758i | ||||
\(191\) | − | 3.36772i | − | 0.243680i | −0.992550 | − | 0.121840i | \(-0.961121\pi\) | ||
0.992550 | − | 0.121840i | \(-0.0388794\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 16.0064i | − | 1.15216i | −0.817392 | − | 0.576081i | \(-0.804581\pi\) | ||
0.817392 | − | 0.576081i | \(-0.195419\pi\) | |||||||
\(194\) | 3.11275i | 0.223483i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 5.87887i | 0.418852i | 0.977824 | + | 0.209426i | \(0.0671596\pi\) | ||||
−0.977824 | + | 0.209426i | \(0.932840\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.43368 | 0.526959 | 0.263480 | − | 0.964665i | \(-0.415130\pi\) | ||||
0.263480 | + | 0.964665i | \(0.415130\pi\) | |||||||
\(200\) | −2.65142 | −0.187484 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.64499i | 0.608260i | ||||||||
\(203\) | 1.65142 | 0.115907 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.57214i | 0.459018i | ||||||||
\(206\) | 4.49761i | 0.313363i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.93944i | 0.203813i | ||||||||
\(209\) | 19.3871 | − | 9.25256i | 1.34103 | − | 0.640013i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.18208i | 0.494435i | 0.968960 | + | 0.247217i | \(0.0795161\pi\) | ||||
−0.968960 | + | 0.247217i | \(0.920484\pi\) | |||||||
\(212\) | −3.47519 | −0.238677 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.66678 | 0.660807 | ||||||||
\(215\) | 22.5632i | 1.53880i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.16215i | 0.146776i | ||||||||
\(218\) | − | 14.6895i | − | 0.994902i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13.6322 | −0.919082 | ||||||||
\(221\) | 14.4863 | 0.974456 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.7653i | 1.72537i | 0.505742 | + | 0.862685i | \(0.331219\pi\) | ||||
−0.505742 | + | 0.862685i | \(0.668781\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.0111 | −0.732450 | ||||||||
\(227\) | 16.9350 | 1.12402 | 0.562009 | − | 0.827131i | \(-0.310029\pi\) | ||||
0.562009 | + | 0.827131i | \(0.310029\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.2878 | 0.679839 | 0.339919 | − | 0.940455i | \(-0.389600\pi\) | ||||
0.339919 | + | 0.940455i | \(0.389600\pi\) | |||||||
\(230\) | 1.89653 | 0.125053 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.65142 | −0.108421 | ||||||||
\(233\) | − | 3.97169i | − | 0.260194i | −0.991501 | − | 0.130097i | \(-0.958471\pi\) | ||
0.991501 | − | 0.130097i | \(-0.0415289\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.2617 | −1.06079 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.92827i | 0.319452i | ||||||||
\(239\) | − | 16.8753i | − | 1.09157i | −0.837924 | − | 0.545786i | \(-0.816231\pi\) | ||
0.837924 | − | 0.545786i | \(-0.183769\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.88015i | 0.636436i | 0.948018 | + | 0.318218i | \(0.103084\pi\) | ||||
−0.948018 | + | 0.318218i | \(0.896916\pi\) | |||||||
\(242\) | −13.2878 | −0.854174 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.26046 | −0.272748 | ||||||||
\(245\) | − | 2.76612i | − | 0.176721i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.5633 | + | 5.51864i | −0.735756 | + | 0.351142i | ||||
\(248\) | − | 2.16215i | − | 0.137297i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 6.49645i | − | 0.410872i | ||||||
\(251\) | − | 10.6202i | − | 0.670342i | −0.942157 | − | 0.335171i | \(-0.891206\pi\) | ||
0.942157 | − | 0.335171i | \(-0.108794\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.37895 | 0.212433 | ||||||||
\(254\) | − | 1.56818i | − | 0.0983965i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.18857 | −0.323654 | −0.161827 | − | 0.986819i | \(-0.551739\pi\) | ||||
−0.161827 | + | 0.986819i | \(0.551739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.77488i | 0.607382i | ||||||||
\(260\) | 8.13083 | 0.504253 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.8330i | 0.978168i | ||||||||
\(263\) | 1.13990i | 0.0702890i | 0.999382 | + | 0.0351445i | \(0.0111891\pi\) | ||||
−0.999382 | + | 0.0351445i | \(0.988811\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.61280i | 0.590510i | ||||||||
\(266\) | −1.87745 | − | 3.93385i | −0.115114 | − | 0.241200i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.56450i | 0.400991i | ||||||||
\(269\) | −8.79339 | −0.536143 | −0.268071 | − | 0.963399i | \(-0.586386\pi\) | ||||
−0.268071 | + | 0.963399i | \(0.586386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.88452 | −0.600442 | −0.300221 | − | 0.953870i | \(-0.597060\pi\) | ||||
−0.300221 | + | 0.953870i | \(0.597060\pi\) | |||||||
\(272\) | − | 4.92827i | − | 0.298820i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 5.61390i | − | 0.339148i | ||||||
\(275\) | 13.0669i | 0.787965i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.3687 | 1.58434 | 0.792171 | − | 0.610299i | \(-0.208951\pi\) | ||||
0.792171 | + | 0.610299i | \(0.208951\pi\) | |||||||
\(278\) | 22.0770 | 1.32409 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.76612i | 0.165307i | ||||||||
\(281\) | 12.9504 | 0.772555 | 0.386278 | − | 0.922383i | \(-0.373761\pi\) | ||||
0.386278 | + | 0.922383i | \(0.373761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.88151 | 0.409063 | 0.204532 | − | 0.978860i | \(-0.434433\pi\) | ||||
0.204532 | + | 0.978860i | \(0.434433\pi\) | |||||||
\(284\) | −11.1266 | −0.660243 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.4863 | 0.856595 | ||||||||
\(287\) | 2.37594 | 0.140247 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.28782 | −0.428696 | ||||||||
\(290\) | 4.56803i | 0.268244i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.85415 | 0.167026 | ||||||||
\(293\) | −2.67792 | −0.156446 | −0.0782228 | − | 0.996936i | \(-0.524925\pi\) | ||||
−0.0782228 | + | 0.996936i | \(0.524925\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 9.77488i | − | 0.568153i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 1.37125i | − | 0.0794346i | ||||||
\(299\) | −2.01536 | −0.116551 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.15699 | 0.470161 | ||||||||
\(302\) | 22.8358i | 1.31405i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.87745 | + | 3.93385i | 0.107679 | + | 0.225622i | ||||
\(305\) | 11.7850i | 0.674804i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 29.0597i | − | 1.65852i | −0.558861 | − | 0.829261i | \(-0.688761\pi\) | ||
0.558861 | − | 0.829261i | \(-0.311239\pi\) | |||||||
\(308\) | 4.92827i | 0.280814i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.98076 | −0.339684 | ||||||||
\(311\) | 13.1562i | 0.746020i | 0.927827 | + | 0.373010i | \(0.121674\pi\) | ||||
−0.927827 | + | 0.373010i | \(0.878326\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.50979 | −0.0853383 | −0.0426692 | − | 0.999089i | \(-0.513586\pi\) | ||||
−0.0426692 | + | 0.999089i | \(0.513586\pi\) | |||||||
\(314\) | 5.53595 | 0.312411 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 11.0781i | − | 0.623191i | ||||||
\(317\) | 27.1573 | 1.52531 | 0.762654 | − | 0.646807i | \(-0.223896\pi\) | ||||
0.762654 | + | 0.646807i | \(0.223896\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.13865i | 0.455677i | ||||||||
\(320\) | − | 2.76612i | − | 0.154631i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 0.685627i | − | 0.0382085i | ||||||
\(323\) | 19.3871 | − | 9.25256i | 1.07873 | − | 0.514826i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 7.79369i | − | 0.432316i | ||||||
\(326\) | −21.9200 | −1.21404 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.37594 | −0.131189 | ||||||||
\(329\) | 5.87887i | 0.324113i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.35655i | 0.294423i | 0.989105 | + | 0.147211i | \(0.0470298\pi\) | ||||
−0.989105 | + | 0.147211i | \(0.952970\pi\) | |||||||
\(332\) | − | 7.07681i | − | 0.388390i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.7892 | 0.973380 | ||||||||
\(335\) | 18.1582 | 0.992088 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.8875i | − | 0.974397i | −0.873291 | − | 0.487198i | \(-0.838019\pi\) | ||
0.873291 | − | 0.487198i | \(-0.161981\pi\) | |||||||
\(338\) | 4.35972 | 0.237137 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.6322 | −0.739309 | ||||||||
\(341\) | −10.6556 | −0.577035 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −8.15699 | −0.439795 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.66678 | 0.519689 | ||||||||
\(347\) | 18.5992i | 0.998455i | 0.866471 | + | 0.499228i | \(0.166383\pi\) | ||||
−0.866471 | + | 0.499228i | \(0.833617\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7507 | −0.682528 | −0.341264 | − | 0.939968i | \(-0.610855\pi\) | ||||
−0.341264 | + | 0.939968i | \(0.610855\pi\) | |||||||
\(350\) | 2.65142 | 0.141724 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.92827i | − | 0.262678i | ||||||
\(353\) | − | 17.5745i | − | 0.935398i | −0.883888 | − | 0.467699i | \(-0.845083\pi\) | ||
0.883888 | − | 0.467699i | \(-0.154917\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.7776i | 1.63350i | ||||||||
\(356\) | 13.5026 | 0.715634 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.4295 | 0.762621 | ||||||||
\(359\) | − | 17.6290i | − | 0.930422i | −0.885200 | − | 0.465211i | \(-0.845978\pi\) | ||
0.885200 | − | 0.465211i | \(-0.154022\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.9504 | + | 14.7712i | −0.628968 | + | 0.777432i | ||||
\(362\) | − | 11.5880i | − | 0.609053i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 2.93944i | − | 0.154068i | ||||||
\(365\) | − | 7.89491i | − | 0.413239i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.1925 | 1.68043 | 0.840217 | − | 0.542251i | \(-0.182428\pi\) | ||||
0.840217 | + | 0.542251i | \(0.182428\pi\) | |||||||
\(368\) | 0.685627i | 0.0357408i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −27.0385 | −1.40566 | ||||||||
\(371\) | 3.47519 | 0.180423 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 23.4458i | − | 1.21398i | −0.794711 | − | 0.606988i | \(-0.792378\pi\) | ||
0.794711 | − | 0.606988i | \(-0.207622\pi\) | |||||||
\(374\) | −24.2878 | −1.25589 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 5.87887i | − | 0.303180i | ||||||
\(377\) | − | 4.85425i | − | 0.250007i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.27600i | − | 0.0655435i | −0.999463 | − | 0.0327717i | \(-0.989567\pi\) | ||
0.999463 | − | 0.0327717i | \(-0.0104334\pi\) | |||||||
\(380\) | 10.8815 | − | 5.19325i | 0.558210 | − | 0.266408i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 3.36772i | − | 0.172308i | ||||||
\(383\) | 9.66343 | 0.493778 | 0.246889 | − | 0.969044i | \(-0.420592\pi\) | ||||
0.246889 | + | 0.969044i | \(0.420592\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.6322 | 0.694760 | ||||||||
\(386\) | − | 16.0064i | − | 0.814702i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.11275i | 0.158026i | ||||||||
\(389\) | 27.3098i | 1.38466i | 0.721579 | + | 0.692332i | \(0.243416\pi\) | ||||
−0.721579 | + | 0.692332i | \(0.756584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.37895 | 0.170881 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.87887i | 0.296173i | ||||||||
\(395\) | −30.6433 | −1.54183 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.6018 | 1.13435 | 0.567176 | − | 0.823597i | \(-0.308036\pi\) | ||||
0.567176 | + | 0.823597i | \(0.308036\pi\) | |||||||
\(398\) | 7.43368 | 0.372617 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.65142 | −0.132571 | ||||||||
\(401\) | 28.1771 | 1.40710 | 0.703549 | − | 0.710647i | \(-0.251598\pi\) | ||||
0.703549 | + | 0.710647i | \(0.251598\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.35549 | 0.316590 | ||||||||
\(404\) | 8.64499i | 0.430104i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.65142 | 0.0819587 | ||||||||
\(407\) | −48.1732 | −2.38786 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.9581i | 1.18465i | 0.805699 | + | 0.592325i | \(0.201790\pi\) | ||||
−0.805699 | + | 0.592325i | \(0.798210\pi\) | |||||||
\(410\) | 6.57214i | 0.324575i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.49761i | 0.221581i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.5753 | −0.960914 | ||||||||
\(416\) | 2.93944i | 0.144118i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 19.3871 | − | 9.25256i | 0.948253 | − | 0.452558i | ||||
\(419\) | 29.5796i | 1.44506i | 0.691340 | + | 0.722529i | \(0.257021\pi\) | ||||
−0.691340 | + | 0.722529i | \(0.742979\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 15.2467i | − | 0.743079i | −0.928417 | − | 0.371540i | \(-0.878830\pi\) | ||
0.928417 | − | 0.371540i | \(-0.121170\pi\) | |||||||
\(422\) | 7.18208i | 0.349618i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.47519 | −0.168770 | ||||||||
\(425\) | 13.0669i | 0.633839i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.26046 | 0.206178 | ||||||||
\(428\) | 9.66678 | 0.467261 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 22.5632i | 1.08809i | ||||||||
\(431\) | −23.7215 | −1.14262 | −0.571312 | − | 0.820733i | \(-0.693565\pi\) | ||||
−0.571312 | + | 0.820733i | \(0.693565\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.8306i | 0.664656i | 0.943164 | + | 0.332328i | \(0.107834\pi\) | ||||
−0.943164 | + | 0.332328i | \(0.892166\pi\) | |||||||
\(434\) | 2.16215i | 0.103786i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 14.6895i | − | 0.703502i | ||||||
\(437\) | −2.69716 | + | 1.28723i | −0.129022 | + | 0.0615765i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.5039i | 1.40815i | 0.710128 | + | 0.704073i | \(0.248637\pi\) | ||||
−0.710128 | + | 0.704073i | \(0.751363\pi\) | |||||||
\(440\) | −13.6322 | −0.649889 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.4863 | 0.689044 | ||||||||
\(443\) | 0.257341i | 0.0122267i | 0.999981 | + | 0.00611333i | \(0.00194594\pi\) | ||||
−0.999981 | + | 0.00611333i | \(0.998054\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 37.3497i | − | 1.77055i | ||||||
\(446\) | 25.7653i | 1.22002i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −22.3687 | −1.05564 | −0.527822 | − | 0.849355i | \(-0.676991\pi\) | ||||
−0.527822 | + | 0.849355i | \(0.676991\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.7093i | 0.551368i | ||||||||
\(452\) | −11.0111 | −0.517920 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.9350 | 0.794800 | ||||||||
\(455\) | −8.13083 | −0.381179 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.2990 | −1.55766 | −0.778830 | − | 0.627235i | \(-0.784186\pi\) | ||||
−0.778830 | + | 0.627235i | \(0.784186\pi\) | |||||||
\(458\) | 10.2878 | 0.480718 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.89653 | 0.0884260 | ||||||||
\(461\) | 1.90481i | 0.0887157i | 0.999016 | + | 0.0443578i | \(0.0141242\pi\) | ||||
−0.999016 | + | 0.0443578i | \(0.985876\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.22888 | −0.243007 | −0.121503 | − | 0.992591i | \(-0.538772\pi\) | ||||
−0.121503 | + | 0.992591i | \(0.538772\pi\) | |||||||
\(464\) | −1.65142 | −0.0766653 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 3.97169i | − | 0.183985i | ||||||
\(467\) | 31.1342i | 1.44072i | 0.693601 | + | 0.720359i | \(0.256023\pi\) | ||||
−0.693601 | + | 0.720359i | \(0.743977\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.56450i | − | 0.303120i | ||||||
\(470\) | −16.2617 | −0.750095 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 40.1998i | 1.84839i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.97790 | − | 10.4303i | −0.228402 | − | 0.478575i | ||||
\(476\) | 4.92827i | 0.225887i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 16.8753i | − | 0.771858i | ||||||
\(479\) | 7.25013i | 0.331267i | 0.986187 | + | 0.165633i | \(0.0529668\pi\) | ||||
−0.986187 | + | 0.165633i | \(0.947033\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.7326 | 1.31010 | ||||||||
\(482\) | 9.88015i | 0.450028i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.2878 | −0.603992 | ||||||||
\(485\) | 8.61025 | 0.390971 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.2637i | 0.736978i | 0.929632 | + | 0.368489i | \(0.120125\pi\) | ||||
−0.929632 | + | 0.368489i | \(0.879875\pi\) | |||||||
\(488\) | −4.26046 | −0.192862 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 2.76612i | − | 0.124961i | ||||||
\(491\) | 31.7282i | 1.43187i | 0.698166 | + | 0.715936i | \(0.254000\pi\) | ||||
−0.698166 | + | 0.715936i | \(0.746000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.13865i | 0.366546i | ||||||||
\(494\) | −11.5633 | + | 5.51864i | −0.520258 | + | 0.248295i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2.16215i | − | 0.0970833i | ||||||
\(497\) | 11.1266 | 0.499097 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.29171 | 0.102591 | 0.0512954 | − | 0.998684i | \(-0.483665\pi\) | ||||
0.0512954 | + | 0.998684i | \(0.483665\pi\) | |||||||
\(500\) | − | 6.49645i | − | 0.290530i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 10.6202i | − | 0.474004i | ||||||
\(503\) | − | 21.0239i | − | 0.937410i | −0.883355 | − | 0.468705i | \(-0.844721\pi\) | ||
0.883355 | − | 0.468705i | \(-0.155279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.9131 | 1.06412 | ||||||||
\(506\) | 3.37895 | 0.150213 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 1.56818i | − | 0.0695768i | ||||||
\(509\) | −40.6364 | −1.80118 | −0.900588 | − | 0.434673i | \(-0.856864\pi\) | ||||
−0.900588 | + | 0.434673i | \(0.856864\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.85415 | −0.126260 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.18857 | −0.228858 | ||||||||
\(515\) | 12.4409 | 0.548213 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.9727 | −1.27422 | ||||||||
\(518\) | 9.77488i | 0.429484i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.13083 | 0.356561 | ||||||||
\(521\) | −40.8857 | −1.79124 | −0.895619 | − | 0.444823i | \(-0.853267\pi\) | ||||
−0.895619 | + | 0.444823i | \(0.853267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.1427i | 0.837053i | 0.908205 | + | 0.418526i | \(0.137453\pi\) | ||||
−0.908205 | + | 0.418526i | \(0.862547\pi\) | |||||||
\(524\) | 15.8330i | 0.691669i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.13990i | 0.0497018i | ||||||||
\(527\) | −10.6556 | −0.464167 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.5299 | 0.979562 | ||||||||
\(530\) | 9.61280i | 0.417553i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.87745 | − | 3.93385i | −0.0813977 | − | 0.170554i | ||||
\(533\) | − | 6.98392i | − | 0.302507i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 26.7395i | − | 1.15605i | ||||||
\(536\) | 6.56450i | 0.283543i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.79339 | −0.379110 | ||||||||
\(539\) | − | 4.92827i | − | 0.212276i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.2190 | 1.94412 | 0.972058 | − | 0.234742i | \(-0.0754246\pi\) | ||||
0.972058 | + | 0.234742i | \(0.0754246\pi\) | |||||||
\(542\) | −9.88452 | −0.424577 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 4.92827i | − | 0.211298i | ||||||
\(545\) | −40.6330 | −1.74053 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0274i | 0.813555i | 0.913527 | + | 0.406777i | \(0.133348\pi\) | ||||
−0.913527 | + | 0.406777i | \(0.866652\pi\) | |||||||
\(548\) | − | 5.61390i | − | 0.239814i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13.0669i | 0.557175i | ||||||||
\(551\) | −3.10046 | − | 6.49645i | −0.132084 | − | 0.276758i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.0781i | 0.471088i | ||||||||
\(554\) | 26.3687 | 1.12030 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.0770 | 0.936273 | ||||||||
\(557\) | − | 26.1219i | − | 1.10682i | −0.832909 | − | 0.553410i | \(-0.813326\pi\) | ||
0.832909 | − | 0.553410i | \(-0.186674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 23.9770i | − | 1.01412i | ||||||
\(560\) | 2.76612i | 0.116890i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.9504 | 0.546279 | ||||||||
\(563\) | 23.9615 | 1.00986 | 0.504929 | − | 0.863161i | \(-0.331519\pi\) | ||||
0.504929 | + | 0.863161i | \(0.331519\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.4581i | 1.28138i | ||||||||
\(566\) | 6.88151 | 0.289251 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.1266 | −0.466862 | ||||||||
\(569\) | −28.0316 | −1.17515 | −0.587573 | − | 0.809171i | \(-0.699916\pi\) | ||||
−0.587573 | + | 0.809171i | \(0.699916\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.54017 | −0.357395 | −0.178697 | − | 0.983904i | \(-0.557188\pi\) | ||||
−0.178697 | + | 0.983904i | \(0.557188\pi\) | |||||||
\(572\) | 14.4863 | 0.605704 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.37594 | 0.0991698 | ||||||||
\(575\) | − | 1.81789i | − | 0.0758111i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.2424 | 1.59205 | 0.796027 | − | 0.605262i | \(-0.206932\pi\) | ||||
0.796027 | + | 0.605262i | \(0.206932\pi\) | |||||||
\(578\) | −7.28782 | −0.303134 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.56803i | 0.189677i | ||||||||
\(581\) | 7.07681i | 0.293596i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.1267i | 0.709314i | ||||||||
\(584\) | 2.85415 | 0.118105 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.67792 | −0.110624 | ||||||||
\(587\) | 20.0697i | 0.828366i | 0.910194 | + | 0.414183i | \(0.135933\pi\) | ||||
−0.910194 | + | 0.414183i | \(0.864067\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.50557 | − | 4.05932i | 0.350466 | − | 0.167261i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 9.77488i | − | 0.401745i | ||||||
\(593\) | − | 32.8000i | − | 1.34693i | −0.739217 | − | 0.673467i | \(-0.764804\pi\) | ||
0.739217 | − | 0.673467i | \(-0.235196\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.6322 | 0.558865 | ||||||||
\(596\) | − | 1.37125i | − | 0.0561688i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.01536 | −0.0824141 | ||||||||
\(599\) | 5.73230 | 0.234215 | 0.117108 | − | 0.993119i | \(-0.462638\pi\) | ||||
0.117108 | + | 0.993119i | \(0.462638\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.3428i | 0.789010i | 0.918894 | + | 0.394505i | \(0.129084\pi\) | ||||
−0.918894 | + | 0.394505i | \(0.870916\pi\) | |||||||
\(602\) | 8.15699 | 0.332454 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 22.8358i | 0.929177i | ||||||||
\(605\) | 36.7557i | 1.49433i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.9940i | 0.811532i | 0.913977 | + | 0.405766i | \(0.132995\pi\) | ||||
−0.913977 | + | 0.405766i | \(0.867005\pi\) | |||||||
\(608\) | 1.87745 | + | 3.93385i | 0.0761405 | + | 0.159539i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.7850i | 0.477159i | ||||||||
\(611\) | 17.2806 | 0.699097 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.43790 | 0.260024 | 0.130012 | − | 0.991512i | \(-0.458498\pi\) | ||||
0.130012 | + | 0.991512i | \(0.458498\pi\) | |||||||
\(614\) | − | 29.0597i | − | 1.17275i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.92827i | 0.198566i | ||||||||
\(617\) | − | 32.9557i | − | 1.32675i | −0.748289 | − | 0.663373i | \(-0.769124\pi\) | ||
0.748289 | − | 0.663373i | \(-0.230876\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.8995 | 0.518476 | 0.259238 | − | 0.965813i | \(-0.416529\pi\) | ||||
0.259238 | + | 0.965813i | \(0.416529\pi\) | |||||||
\(620\) | −5.98076 | −0.240193 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.1562i | 0.527516i | ||||||||
\(623\) | −13.5026 | −0.540968 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2271 | −1.24908 | ||||||||
\(626\) | −1.50979 | −0.0603433 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.53595 | 0.220908 | ||||||||
\(629\) | −48.1732 | −1.92079 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0307 | 0.797410 | 0.398705 | − | 0.917079i | \(-0.369460\pi\) | ||||
0.398705 | + | 0.917079i | \(0.369460\pi\) | |||||||
\(632\) | − | 11.0781i | − | 0.440663i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27.1573 | 1.07856 | ||||||||
\(635\) | −4.33778 | −0.172140 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.93944i | 0.116465i | ||||||||
\(638\) | 8.13865i | 0.322212i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 2.76612i | − | 0.109341i | ||||||
\(641\) | −2.95641 | −0.116771 | −0.0583857 | − | 0.998294i | \(-0.518595\pi\) | ||||
−0.0583857 | + | 0.998294i | \(0.518595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.45292 | −0.136170 | −0.0680849 | − | 0.997680i | \(-0.521689\pi\) | ||||
−0.0680849 | + | 0.997680i | \(0.521689\pi\) | |||||||
\(644\) | − | 0.685627i | − | 0.0270175i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.3871 | − | 9.25256i | 0.762774 | − | 0.364037i | ||||
\(647\) | − | 19.8964i | − | 0.782208i | −0.920346 | − | 0.391104i | \(-0.872093\pi\) | ||
0.920346 | − | 0.391104i | \(-0.127907\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 7.79369i | − | 0.305693i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21.9200 | −0.858454 | ||||||||
\(653\) | − | 6.90350i | − | 0.270155i | −0.990835 | − | 0.135077i | \(-0.956872\pi\) | ||
0.990835 | − | 0.135077i | \(-0.0431283\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.7961 | 1.71125 | ||||||||
\(656\) | −2.37594 | −0.0927649 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.87887i | 0.229182i | ||||||||
\(659\) | 25.4214 | 0.990275 | 0.495138 | − | 0.868815i | \(-0.335118\pi\) | ||||
0.495138 | + | 0.868815i | \(0.335118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 14.4866i | − | 0.563465i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(662\) | 5.35655i | 0.208188i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 7.07681i | − | 0.274634i | ||||||
\(665\) | −10.8815 | + | 5.19325i | −0.421967 | + | 0.201385i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.13226i | − | 0.0438413i | ||||||
\(668\) | 17.7892 | 0.688284 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.1582 | 0.701512 | ||||||||
\(671\) | 20.9967i | 0.810569i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.1465i | − | 1.39334i | −0.717390 | − | 0.696672i | \(-0.754663\pi\) | ||
0.717390 | − | 0.696672i | \(-0.245337\pi\) | |||||||
\(674\) | − | 17.8875i | − | 0.689003i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.35972 | 0.167681 | ||||||||
\(677\) | 42.5564 | 1.63558 | 0.817788 | − | 0.575520i | \(-0.195200\pi\) | ||||
0.817788 | + | 0.575520i | \(0.195200\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.11275i | − | 0.119456i | ||||||
\(680\) | −13.6322 | −0.522770 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.6556 | −0.408026 | ||||||||
\(683\) | 14.0355 | 0.537053 | 0.268526 | − | 0.963272i | \(-0.413463\pi\) | ||||
0.268526 | + | 0.963272i | \(0.413463\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.5287 | −0.593322 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.15699 | −0.310982 | ||||||||
\(689\) | − | 10.2151i | − | 0.389164i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.90410 | −0.338728 | −0.169364 | − | 0.985554i | \(-0.554171\pi\) | ||||
−0.169364 | + | 0.985554i | \(0.554171\pi\) | |||||||
\(692\) | 9.66678 | 0.367476 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.5992i | 0.706014i | ||||||||
\(695\) | − | 61.0676i | − | 2.31643i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.7093i | 0.443520i | ||||||||
\(698\) | −12.7507 | −0.482620 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.65142 | 0.100214 | ||||||||
\(701\) | − | 47.9871i | − | 1.81245i | −0.422798 | − | 0.906224i | \(-0.638952\pi\) | ||
0.422798 | − | 0.906224i | \(-0.361048\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.4529 | − | 18.3518i | 1.45028 | − | 0.692152i | ||||
\(704\) | − | 4.92827i | − | 0.185741i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 17.5745i | − | 0.661426i | ||||||
\(707\) | − | 8.64499i | − | 0.325128i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.3533 | −0.914609 | −0.457305 | − | 0.889310i | \(-0.651185\pi\) | ||||
−0.457305 | + | 0.889310i | \(0.651185\pi\) | |||||||
\(710\) | 30.7776i | 1.15506i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.5026 | 0.506030 | ||||||||
\(713\) | 1.48243 | 0.0555173 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 40.0709i | − | 1.49857i | ||||||
\(716\) | 14.4295 | 0.539254 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 17.6290i | − | 0.657908i | ||||||
\(719\) | − | 8.86512i | − | 0.330613i | −0.986242 | − | 0.165307i | \(-0.947139\pi\) | ||
0.986242 | − | 0.165307i | \(-0.0528614\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 4.49761i | − | 0.167500i | ||||||
\(722\) | −11.9504 | + | 14.7712i | −0.444747 | + | 0.549727i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 11.5880i | − | 0.430666i | ||||||
\(725\) | 4.37862 | 0.162618 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.1573 | −0.710506 | −0.355253 | − | 0.934770i | \(-0.615605\pi\) | ||||
−0.355253 | + | 0.934770i | \(0.615605\pi\) | |||||||
\(728\) | − | 2.93944i | − | 0.108943i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 7.89491i | − | 0.292204i | ||||||
\(731\) | 40.1998i | 1.48684i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.2220 | 1.48563 | 0.742816 | − | 0.669495i | \(-0.233490\pi\) | ||||
0.742816 | + | 0.669495i | \(0.233490\pi\) | |||||||
\(734\) | 32.1925 | 1.18825 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.685627i | 0.0252726i | ||||||||
\(737\) | 32.3516 | 1.19169 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.6138 | 1.75150 | 0.875752 | − | 0.482762i | \(-0.160366\pi\) | ||||
0.875752 | + | 0.482762i | \(0.160366\pi\) | |||||||
\(740\) | −27.0385 | −0.993955 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.47519 | 0.127578 | ||||||||
\(743\) | −39.8593 | −1.46229 | −0.731147 | − | 0.682220i | \(-0.761015\pi\) | ||||
−0.731147 | + | 0.682220i | \(0.761015\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.79305 | −0.138967 | ||||||||
\(746\) | − | 23.4458i | − | 0.858411i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −24.2878 | −0.888051 | ||||||||
\(749\) | −9.66678 | −0.353216 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.3831i | 1.72904i | 0.502603 | + | 0.864518i | \(0.332376\pi\) | ||||
−0.502603 | + | 0.864518i | \(0.667624\pi\) | |||||||
\(752\) | − | 5.87887i | − | 0.214380i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 4.85425i | − | 0.176781i | ||||||
\(755\) | 63.1667 | 2.29887 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.0966 | 1.42099 | 0.710495 | − | 0.703703i | \(-0.248471\pi\) | ||||
0.710495 | + | 0.703703i | \(0.248471\pi\) | |||||||
\(758\) | − | 1.27600i | − | 0.0463462i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.8815 | − | 5.19325i | 0.394714 | − | 0.188379i | ||||
\(761\) | 53.0230i | 1.92208i | 0.276404 | + | 0.961041i | \(0.410857\pi\) | ||||
−0.276404 | + | 0.961041i | \(0.589143\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.6895i | 0.531797i | ||||||||
\(764\) | − | 3.36772i | − | 0.121840i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.66343 | 0.349154 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.90410 | 0.104725 | 0.0523623 | − | 0.998628i | \(-0.483325\pi\) | ||||
0.0523623 | + | 0.998628i | \(0.483325\pi\) | |||||||
\(770\) | 13.6322 | 0.491270 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 16.0064i | − | 0.576081i | ||||||
\(773\) | −38.0162 | −1.36735 | −0.683675 | − | 0.729787i | \(-0.739619\pi\) | ||||
−0.683675 | + | 0.729787i | \(0.739619\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.73277i | 0.205927i | ||||||||
\(776\) | 3.11275i | 0.111741i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.3098i | 0.979105i | ||||||||
\(779\) | −4.46070 | − | 9.34660i | −0.159821 | − | 0.334877i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 54.8349i | 1.96215i | ||||||||
\(782\) | 3.37895 | 0.120831 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | − | 15.3131i | − | 0.546548i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 53.0094i | − | 1.88958i | −0.327674 | − | 0.944791i | \(-0.606265\pi\) | ||
0.327674 | − | 0.944791i | \(-0.393735\pi\) | |||||||
\(788\) | 5.87887i | 0.209426i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −30.6433 | −1.09024 | ||||||||
\(791\) | 11.0111 | 0.391511 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 12.5234i | − | 0.444718i | ||||||
\(794\) | 22.6018 | 0.802108 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.43368 | 0.263480 | ||||||||
\(797\) | −46.9727 | −1.66386 | −0.831928 | − | 0.554883i | \(-0.812763\pi\) | ||||
−0.831928 | + | 0.554883i | \(0.812763\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.9727 | −1.02498 | ||||||||
\(800\) | −2.65142 | −0.0937419 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.1771 | 0.994969 | ||||||||
\(803\) | − | 14.0660i | − | 0.496378i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.89653 | −0.0668438 | ||||||||
\(806\) | 6.35549 | 0.223863 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.64499i | 0.304130i | ||||||||
\(809\) | 3.41453i | 0.120049i | 0.998197 | + | 0.0600243i | \(0.0191178\pi\) | ||||
−0.998197 | + | 0.0600243i | \(0.980882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 19.5025i | − | 0.684827i | −0.939549 | − | 0.342413i | \(-0.888756\pi\) | ||
0.939549 | − | 0.342413i | \(-0.111244\pi\) | |||||||
\(812\) | 1.65142 | 0.0579535 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −48.1732 | −1.68847 | ||||||||
\(815\) | 60.6334i | 2.12389i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.3143 | − | 32.0884i | −0.535780 | − | 1.12263i | ||||
\(818\) | 23.9581i | 0.837675i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.57214i | 0.229509i | ||||||||
\(821\) | − | 48.8484i | − | 1.70482i | −0.522873 | − | 0.852411i | \(-0.675140\pi\) | ||
0.522873 | − | 0.852411i | \(-0.324860\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.9774 | −1.63753 | −0.818765 | − | 0.574129i | \(-0.805341\pi\) | ||||
−0.818765 | + | 0.574129i | \(0.805341\pi\) | |||||||
\(824\) | 4.49761i | 0.156682i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.8896 | 1.56097 | 0.780483 | − | 0.625177i | \(-0.214973\pi\) | ||||
0.780483 | + | 0.625177i | \(0.214973\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 25.7689i | − | 0.894989i | −0.894287 | − | 0.447495i | \(-0.852316\pi\) | ||
0.894287 | − | 0.447495i | \(-0.147684\pi\) | |||||||
\(830\) | −19.5753 | −0.679469 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.93944i | 0.101907i | ||||||||
\(833\) | − | 4.92827i | − | 0.170754i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 49.2070i | − | 1.70288i | ||||||
\(836\) | 19.3871 | − | 9.25256i | 0.670516 | − | 0.320007i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 29.5796i | 1.02181i | ||||||||
\(839\) | −35.2764 | −1.21788 | −0.608938 | − | 0.793218i | \(-0.708404\pi\) | ||||
−0.608938 | + | 0.793218i | \(0.708404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.2728 | −0.905959 | ||||||||
\(842\) | − | 15.2467i | − | 0.525436i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.18208i | 0.247217i | ||||||||
\(845\) | − | 12.0595i | − | 0.414859i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.2878 | 0.456575 | ||||||||
\(848\) | −3.47519 | −0.119339 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.0669i | 0.448192i | ||||||||
\(851\) | 6.70192 | 0.229739 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.9046 | −1.57175 | −0.785873 | − | 0.618388i | \(-0.787786\pi\) | ||||
−0.785873 | + | 0.618388i | \(0.787786\pi\) | |||||||
\(854\) | 4.26046 | 0.145790 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.66678 | 0.330404 | ||||||||
\(857\) | −34.4307 | −1.17613 | −0.588065 | − | 0.808814i | \(-0.700110\pi\) | ||||
−0.588065 | + | 0.808814i | \(0.700110\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.0920 | 1.67500 | 0.837499 | − | 0.546439i | \(-0.184017\pi\) | ||||
0.837499 | + | 0.546439i | \(0.184017\pi\) | |||||||
\(860\) | 22.5632i | 0.769399i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.7215 | −0.807958 | ||||||||
\(863\) | 44.5324 | 1.51590 | 0.757950 | − | 0.652312i | \(-0.226201\pi\) | ||||
0.757950 | + | 0.652312i | \(0.226201\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 26.7395i | − | 0.909169i | ||||||
\(866\) | 13.8306i | 0.469983i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.16215i | 0.0733881i | ||||||||
\(869\) | −54.5958 | −1.85203 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.2959 | −0.653818 | ||||||||
\(872\) | − | 14.6895i | − | 0.497451i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.69716 | + | 1.28723i | −0.0912327 | + | 0.0435412i | ||||
\(875\) | 6.49645i | 0.219620i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 28.3876i | − | 0.958583i | −0.877656 | − | 0.479291i | \(-0.840894\pi\) | ||
0.877656 | − | 0.479291i | \(-0.159106\pi\) | |||||||
\(878\) | 29.5039i | 0.995709i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.6322 | −0.459541 | ||||||||
\(881\) | − | 4.25028i | − | 0.143195i | −0.997434 | − | 0.0715977i | \(-0.977190\pi\) | ||
0.997434 | − | 0.0715977i | \(-0.0228098\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.7742 | −0.766411 | −0.383206 | − | 0.923663i | \(-0.625180\pi\) | ||||
−0.383206 | + | 0.923663i | \(0.625180\pi\) | |||||||
\(884\) | 14.4863 | 0.487228 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.257341i | 0.00864555i | ||||||||
\(887\) | 2.41531 | 0.0810980 | 0.0405490 | − | 0.999178i | \(-0.487089\pi\) | ||||
0.0405490 | + | 0.999178i | \(0.487089\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.56818i | 0.0525951i | ||||||||
\(890\) | − | 37.3497i | − | 1.25196i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25.7653i | 0.862685i | ||||||||
\(893\) | 23.1266 | − | 11.0373i | 0.773903 | − | 0.369348i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 39.9136i | − | 1.33417i | ||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.3687 | −0.746453 | ||||||||
\(899\) | 3.57062i | 0.119087i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.1267i | 0.570572i | ||||||||
\(902\) | 11.7093i | 0.389876i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.0111 | −0.366225 | ||||||||
\(905\) | −32.0539 | −1.06551 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.5971i | 1.61364i | 0.590798 | + | 0.806819i | \(0.298813\pi\) | ||||
−0.590798 | + | 0.806819i | \(0.701187\pi\) | |||||||
\(908\) | 16.9350 | 0.562009 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.13083 | −0.269535 | ||||||||
\(911\) | −17.0111 | −0.563604 | −0.281802 | − | 0.959473i | \(-0.590932\pi\) | ||||
−0.281802 | + | 0.959473i | \(0.590932\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.8764 | −1.15424 | ||||||||
\(914\) | −33.2990 | −1.10143 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.2878 | 0.339919 | ||||||||
\(917\) | − | 15.8330i | − | 0.522853i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.5480 | −1.07366 | −0.536829 | − | 0.843691i | \(-0.680378\pi\) | ||||
−0.536829 | + | 0.843691i | \(0.680378\pi\) | |||||||
\(920\) | 1.89653 | 0.0625267 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.90481i | 0.0627315i | ||||||||
\(923\) | − | 32.7060i | − | 1.07653i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.9173i | 0.852157i | ||||||||
\(926\) | −5.22888 | −0.171832 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.65142 | −0.0542106 | ||||||||
\(929\) | 27.0725i | 0.888220i | 0.895972 | + | 0.444110i | \(0.146480\pi\) | ||||
−0.895972 | + | 0.444110i | \(0.853520\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.87745 | + | 3.93385i | 0.0615308 | + | 0.128927i | ||||
\(932\) | − | 3.97169i | − | 0.130097i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31.1342i | 1.01874i | ||||||||
\(935\) | 67.1830i | 2.19712i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.6523 | −0.576676 | −0.288338 | − | 0.957529i | \(-0.593103\pi\) | ||||
−0.288338 | + | 0.957529i | \(0.593103\pi\) | |||||||
\(938\) | − | 6.56450i | − | 0.214339i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16.2617 | −0.530397 | ||||||||
\(941\) | −4.06075 | −0.132377 | −0.0661884 | − | 0.997807i | \(-0.521084\pi\) | ||||
−0.0661884 | + | 0.997807i | \(0.521084\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.62901i | − | 0.0530478i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.1998i | 1.30701i | ||||||||
\(947\) | − | 3.87644i | − | 0.125967i | −0.998015 | − | 0.0629836i | \(-0.979938\pi\) | ||
0.998015 | − | 0.0629836i | \(-0.0200616\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.38958i | 0.272337i | ||||||||
\(950\) | −4.97790 | − | 10.4303i | −0.161505 | − | 0.338404i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.92827i | 0.159726i | ||||||||
\(953\) | 54.0854 | 1.75200 | 0.876000 | − | 0.482312i | \(-0.160203\pi\) | ||||
0.876000 | + | 0.482312i | \(0.160203\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.31552 | −0.301443 | ||||||||
\(956\) | − | 16.8753i | − | 0.545786i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.25013i | 0.234241i | ||||||||
\(959\) | 5.61390i | 0.181282i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.3251 | 0.849197 | ||||||||
\(962\) | 28.7326 | 0.926377 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.88015i | 0.318218i | ||||||||
\(965\) | −44.2755 | −1.42528 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.18771 | 0.198983 | 0.0994916 | − | 0.995038i | \(-0.468278\pi\) | ||||
0.0994916 | + | 0.995038i | \(0.468278\pi\) | |||||||
\(968\) | −13.2878 | −0.427087 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.61025 | 0.276458 | ||||||||
\(971\) | 12.7588 | 0.409449 | 0.204725 | − | 0.978820i | \(-0.434370\pi\) | ||||
0.204725 | + | 0.978820i | \(0.434370\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.0770 | −0.707756 | ||||||||
\(974\) | 16.2637i | 0.521122i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.26046 | −0.136374 | ||||||||
\(977\) | −44.6980 | −1.43002 | −0.715009 | − | 0.699116i | \(-0.753577\pi\) | ||||
−0.715009 | + | 0.699116i | \(0.753577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 66.5442i | − | 2.12676i | ||||||
\(980\) | − | 2.76612i | − | 0.0883605i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 31.7282i | 1.01249i | ||||||||
\(983\) | −5.35159 | −0.170689 | −0.0853447 | − | 0.996351i | \(-0.527199\pi\) | ||||
−0.0853447 | + | 0.996351i | \(0.527199\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.2617 | 0.518140 | ||||||||
\(986\) | 8.13865i | 0.259187i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.5633 | + | 5.51864i | −0.367878 | + | 0.175571i | ||||
\(989\) | − | 5.59265i | − | 0.177836i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15.9323i | − | 0.506107i | −0.967452 | − | 0.253054i | \(-0.918565\pi\) | ||
0.967452 | − | 0.253054i | \(-0.0814349\pi\) | |||||||
\(992\) | − | 2.16215i | − | 0.0686483i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11.1266 | 0.352915 | ||||||||
\(995\) | − | 20.5624i | − | 0.651873i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.2767 | 0.547158 | 0.273579 | − | 0.961850i | \(-0.411792\pi\) | ||||
0.273579 | + | 0.961850i | \(0.411792\pi\) | |||||||
\(998\) | 2.29171 | 0.0725427 | ||||||||
\(999\) | 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 | 2394.2.b.j.1709.3 | yes | 8 | |
3.2 | odd | 2 | 2394.2.b.i.1709.6 | yes | 8 | ||
19.18 | odd | 2 | 2394.2.b.i.1709.3 | ✓ | 8 | ||
57.56 | even | 2 | inner | 2394.2.b.j.1709.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2394.2.b.i.1709.3 | ✓ | 8 | 19.18 | odd | 2 | ||
2394.2.b.i.1709.6 | yes | 8 | 3.2 | odd | 2 | ||
2394.2.b.j.1709.3 | yes | 8 | 1.1 | even | 1 | trivial | |
2394.2.b.j.1709.6 | yes | 8 | 57.56 | even | 2 | inner |