Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(989,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.989");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.ba (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 989.5 | ||
Character | \(\chi\) | \(=\) | 1386.989 |
Dual form | 1386.2.ba.a.1187.5 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.78334 | − | 1.02961i | −0.797535 | − | 0.460457i | 0.0450733 | − | 0.998984i | \(-0.485648\pi\) |
−0.842609 | + | 0.538526i | \(0.818981\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.289722 | − | 2.62984i | 0.109504 | − | 0.993986i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.78334 | − | 1.02961i | 0.563943 | − | 0.325592i | ||||
\(11\) | 1.29385 | − | 3.05384i | 0.390109 | − | 0.920768i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.97891i | 1.93560i | 0.251719 | + | 0.967800i | \(0.419004\pi\) | ||||
−0.251719 | + | 0.967800i | \(0.580996\pi\) | |||||||
\(14\) | 2.13265 | + | 1.56583i | 0.569974 | + | 0.418485i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.66515 | − | 4.61618i | −0.646394 | − | 1.11959i | −0.983978 | − | 0.178292i | \(-0.942943\pi\) |
0.337584 | − | 0.941295i | \(-0.390390\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.36851 | + | 4.25421i | 1.69045 | + | 0.975983i | 0.954149 | + | 0.299331i | \(0.0967636\pi\) |
0.736303 | + | 0.676652i | \(0.236570\pi\) | |||||||
\(20\) | 2.05923i | 0.460457i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.99778 | + | 2.64743i | 0.425929 | + | 0.564433i | ||||
\(23\) | −1.35506 | − | 0.782344i | −0.282549 | − | 0.163130i | 0.352028 | − | 0.935990i | \(-0.385492\pi\) |
−0.634577 | + | 0.772860i | \(0.718826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.379791 | − | 0.657818i | −0.0759582 | − | 0.131564i | ||||
\(26\) | −6.04391 | − | 3.48945i | −1.18531 | − | 0.684338i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.42237 | + | 1.06401i | −0.457785 | + | 0.201080i | ||||
\(29\) | 2.87708 | 0.534260 | 0.267130 | − | 0.963660i | \(-0.413925\pi\) | ||||
0.267130 | + | 0.963660i | \(0.413925\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.39314 | − | 7.60915i | −0.789032 | − | 1.36664i | −0.926561 | − | 0.376145i | \(-0.877249\pi\) |
0.137529 | − | 0.990498i | \(-0.456084\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.33030 | 0.914139 | ||||||||
\(35\) | −3.22439 | + | 4.39161i | −0.545022 | + | 0.742317i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.82231 | + | 3.15633i | −0.299585 | + | 0.518897i | −0.976041 | − | 0.217586i | \(-0.930182\pi\) |
0.676456 | + | 0.736483i | \(0.263515\pi\) | |||||||
\(38\) | −7.36851 | + | 4.25421i | −1.19533 | + | 0.690124i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.78334 | − | 1.02961i | −0.281971 | − | 0.162796i | ||||
\(41\) | −2.42621 | −0.378910 | −0.189455 | − | 0.981889i | \(-0.560672\pi\) | ||||
−0.189455 | + | 0.981889i | \(0.560672\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.55213i | − | 1.15169i | −0.817559 | − | 0.575844i | \(-0.804673\pi\) | ||
0.817559 | − | 0.575844i | \(-0.195327\pi\) | |||||||
\(44\) | −3.29163 | + | 0.406418i | −0.496232 | + | 0.0612698i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.35506 | − | 0.782344i | 0.199793 | − | 0.115350i | ||||
\(47\) | −10.2450 | − | 5.91497i | −1.49439 | − | 0.862787i | −0.494412 | − | 0.869228i | \(-0.664616\pi\) |
−0.999979 | + | 0.00644106i | \(0.997950\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.83212 | − | 1.52384i | −0.976018 | − | 0.217692i | ||||
\(50\) | 0.759582 | 0.107421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.04391 | − | 3.48945i | 0.838140 | − | 0.483900i | ||||
\(53\) | −9.93207 | + | 5.73428i | −1.36427 | + | 0.787664i | −0.990190 | − | 0.139730i | \(-0.955376\pi\) |
−0.374085 | + | 0.927395i | \(0.622043\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.45165 | + | 4.11389i | −0.735101 | + | 0.554717i | ||||
\(56\) | 0.289722 | − | 2.62984i | 0.0387157 | − | 0.351427i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.43854 | + | 2.49162i | −0.188890 | + | 0.327166i | ||||
\(59\) | 3.49197 | − | 2.01609i | 0.454616 | − | 0.262473i | −0.255162 | − | 0.966898i | \(-0.582129\pi\) |
0.709778 | + | 0.704426i | \(0.248795\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.39206 | − | 2.53576i | −0.562346 | − | 0.324670i | 0.191741 | − | 0.981446i | \(-0.438587\pi\) |
−0.754086 | + | 0.656775i | \(0.771920\pi\) | |||||||
\(62\) | 8.78629 | 1.11586 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.18558 | − | 12.4458i | 0.891261 | − | 1.54371i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.75461 | − | 8.23523i | −0.580868 | − | 1.00609i | −0.995377 | − | 0.0960479i | \(-0.969380\pi\) |
0.414508 | − | 0.910045i | \(-0.363954\pi\) | |||||||
\(68\) | −2.66515 | + | 4.61618i | −0.323197 | + | 0.559794i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.19105 | − | 4.98821i | −0.261880 | − | 0.596205i | ||||
\(71\) | − | 3.30443i | − | 0.392163i | −0.980588 | − | 0.196082i | \(-0.937178\pi\) | ||
0.980588 | − | 0.196082i | \(-0.0628217\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.828178 | + | 0.478149i | −0.0969309 | + | 0.0559631i | −0.547682 | − | 0.836687i | \(-0.684490\pi\) |
0.450751 | + | 0.892650i | \(0.351156\pi\) | |||||||
\(74\) | −1.82231 | − | 3.15633i | −0.211839 | − | 0.366915i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 8.50842i | − | 0.975983i | ||||||
\(77\) | −7.65627 | − | 4.28737i | −0.872513 | − | 0.488592i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.75287 | + | 4.47612i | 0.872266 | + | 0.503603i | 0.868101 | − | 0.496388i | \(-0.165341\pi\) |
0.00416551 | + | 0.999991i | \(0.498674\pi\) | |||||||
\(80\) | 1.78334 | − | 1.02961i | 0.199384 | − | 0.115114i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.21310 | − | 2.10116i | 0.133965 | − | 0.232034i | ||||
\(83\) | −7.50706 | −0.824007 | −0.412003 | − | 0.911182i | \(-0.635171\pi\) | ||||
−0.412003 | + | 0.911182i | \(0.635171\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.9763i | 1.19055i | ||||||||
\(86\) | 6.54033 | + | 3.77606i | 0.705262 | + | 0.407183i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.29385 | − | 3.05384i | 0.137925 | − | 0.325541i | ||||
\(89\) | 2.99174 | + | 1.72728i | 0.317124 | + | 0.183092i | 0.650110 | − | 0.759840i | \(-0.274723\pi\) |
−0.332986 | + | 0.942932i | \(0.608056\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.3534 | + | 2.02194i | 1.92396 | + | 0.211957i | ||||
\(92\) | 1.56469i | 0.163130i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.2450 | − | 5.91497i | 1.05669 | − | 0.610082i | ||||
\(95\) | −8.76039 | − | 15.1734i | −0.898797 | − | 1.55676i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.95332 | −0.604468 | −0.302234 | − | 0.953234i | \(-0.597732\pi\) | ||||
−0.302234 | + | 0.953234i | \(0.597732\pi\) | |||||||
\(98\) | 4.73575 | − | 5.15487i | 0.478383 | − | 0.520721i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.379791 | + | 0.657818i | −0.0379791 | + | 0.0657818i | ||||
\(101\) | −1.95460 | − | 3.38547i | −0.194490 | − | 0.336867i | 0.752243 | − | 0.658886i | \(-0.228972\pi\) |
−0.946733 | + | 0.322019i | \(0.895639\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.72042 | − | 2.97985i | 0.169518 | − | 0.293614i | −0.768733 | − | 0.639570i | \(-0.779112\pi\) |
0.938250 | + | 0.345957i | \(0.112446\pi\) | |||||||
\(104\) | 6.97891i | 0.684338i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 11.4686i | − | 1.11393i | ||||||
\(107\) | −1.00997 | + | 1.74932i | −0.0976377 | + | 0.169114i | −0.910706 | − | 0.413054i | \(-0.864462\pi\) |
0.813069 | + | 0.582168i | \(0.197795\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.05488 | + | 1.76373i | −0.292604 | + | 0.168935i | −0.639116 | − | 0.769111i | \(-0.720699\pi\) |
0.346512 | + | 0.938046i | \(0.387366\pi\) | |||||||
\(110\) | −0.836906 | − | 6.77821i | −0.0797959 | − | 0.646277i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.13265 | + | 1.56583i | 0.201516 | + | 0.147957i | ||||
\(113\) | − | 7.60125i | − | 0.715065i | −0.933901 | − | 0.357533i | \(-0.883618\pi\) | ||
0.933901 | − | 0.357533i | \(-0.116382\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.61102 | + | 2.79038i | 0.150229 | + | 0.260204i | ||||
\(116\) | −1.43854 | − | 2.49162i | −0.133565 | − | 0.231342i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.03218i | 0.371193i | ||||||||
\(119\) | −12.9120 | + | 5.67151i | −1.18364 | + | 0.519907i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.65192 | − | 7.90241i | −0.695629 | − | 0.718401i | ||||
\(122\) | 4.39206 | − | 2.53576i | 0.397638 | − | 0.229577i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.39314 | + | 7.60915i | −0.394516 | + | 0.683322i | ||||
\(125\) | 11.8603i | 1.06082i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.33932i | − | 0.562523i | −0.959631 | − | 0.281262i | \(-0.909247\pi\) | ||
0.959631 | − | 0.281262i | \(-0.0907529\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.18558 | + | 12.4458i | 0.630217 | + | 1.09157i | ||||
\(131\) | −6.50013 | + | 11.2586i | −0.567919 | + | 0.983664i | 0.428853 | + | 0.903374i | \(0.358918\pi\) |
−0.996772 | + | 0.0802898i | \(0.974415\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.3227 | − | 18.1455i | 1.15523 | − | 1.57341i | ||||
\(134\) | 9.50922 | 0.821472 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.66515 | − | 4.61618i | −0.228535 | − | 0.395834i | ||||
\(137\) | 7.97258 | − | 4.60297i | 0.681144 | − | 0.393258i | −0.119142 | − | 0.992877i | \(-0.538014\pi\) |
0.800286 | + | 0.599619i | \(0.204681\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.5202i | 1.57087i | 0.618946 | + | 0.785433i | \(0.287560\pi\) | ||||
−0.618946 | + | 0.785433i | \(0.712440\pi\) | |||||||
\(140\) | 5.41544 | + | 0.596603i | 0.457688 | + | 0.0504221i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.86172 | + | 1.65221i | 0.240150 | + | 0.138651i | ||||
\(143\) | 21.3125 | + | 9.02964i | 1.78224 | + | 0.755096i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.13082 | − | 2.96228i | −0.426092 | − | 0.246004i | ||||
\(146\) | − | 0.956297i | − | 0.0791437i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.64461 | 0.299585 | ||||||||
\(149\) | 6.04969 | − | 10.4784i | 0.495610 | − | 0.858422i | −0.504377 | − | 0.863483i | \(-0.668278\pi\) |
0.999987 | + | 0.00506166i | \(0.00161118\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.47659 | + | 2.58456i | −0.364300 | + | 0.210329i | −0.670965 | − | 0.741489i | \(-0.734120\pi\) |
0.306665 | + | 0.951817i | \(0.400787\pi\) | |||||||
\(152\) | 7.36851 | + | 4.25421i | 0.597665 | + | 0.345062i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.54111 | − | 4.48683i | 0.607680 | − | 0.361559i | ||||
\(155\) | 18.0930i | 1.45326i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.478738 | + | 0.829198i | 0.0382074 | + | 0.0661772i | 0.884497 | − | 0.466546i | \(-0.154502\pi\) |
−0.846289 | + | 0.532724i | \(0.821169\pi\) | |||||||
\(158\) | −7.75287 | + | 4.47612i | −0.616785 | + | 0.356101i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.05923i | 0.162796i | ||||||||
\(161\) | −2.45003 | + | 3.33693i | −0.193089 | + | 0.262987i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.54401 | − | 14.7987i | 0.669219 | − | 1.15912i | −0.308904 | − | 0.951093i | \(-0.599962\pi\) |
0.978123 | − | 0.208027i | \(-0.0667043\pi\) | |||||||
\(164\) | 1.21310 | + | 2.10116i | 0.0947274 | + | 0.164073i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.75353 | − | 6.50130i | 0.291330 | − | 0.504599i | ||||
\(167\) | 17.6200 | 1.36348 | 0.681738 | − | 0.731596i | \(-0.261224\pi\) | ||||
0.681738 | + | 0.731596i | \(0.261224\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −35.7051 | −2.74655 | ||||||||
\(170\) | −9.50576 | − | 5.48815i | −0.729058 | − | 0.420922i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.54033 | + | 3.77606i | −0.498696 | + | 0.287922i | ||||
\(173\) | −8.05455 | + | 13.9509i | −0.612376 | + | 1.06067i | 0.378462 | + | 0.925617i | \(0.376453\pi\) |
−0.990839 | + | 0.135050i | \(0.956880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.83999 | + | 0.808206i | −0.139090 | + | 0.0610947i | ||||
\(176\) | 1.99778 | + | 2.64743i | 0.150589 | + | 0.199557i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.99174 | + | 1.72728i | −0.224241 | + | 0.129465i | ||||
\(179\) | 7.99155 | − | 4.61392i | 0.597316 | − | 0.344861i | −0.170669 | − | 0.985328i | \(-0.554593\pi\) |
0.767985 | + | 0.640468i | \(0.221259\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.46346 | 0.406096 | 0.203048 | − | 0.979169i | \(-0.434915\pi\) | ||||
0.203048 | + | 0.979169i | \(0.434915\pi\) | |||||||
\(182\) | −10.9278 | + | 14.8836i | −0.810019 | + | 1.10324i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.35506 | − | 0.782344i | −0.0998963 | − | 0.0576752i | ||||
\(185\) | 6.49959 | − | 3.75254i | 0.477859 | − | 0.275892i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.5454 | + | 2.16633i | −1.28304 | + | 0.158418i | ||||
\(188\) | 11.8299i | 0.862787i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.5208 | 1.27109 | ||||||||
\(191\) | −17.8512 | − | 10.3064i | −1.29167 | − | 0.745746i | −0.312720 | − | 0.949845i | \(-0.601240\pi\) |
−0.978950 | + | 0.204099i | \(0.934573\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.2631 | − | 6.50274i | 0.810734 | − | 0.468077i | −0.0364770 | − | 0.999334i | \(-0.511614\pi\) |
0.847211 | + | 0.531257i | \(0.178280\pi\) | |||||||
\(194\) | 2.97666 | − | 5.15573i | 0.213712 | − | 0.370160i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.09637 | + | 6.67871i | 0.149741 | + | 0.477051i | ||||
\(197\) | −18.4806 | −1.31669 | −0.658345 | − | 0.752716i | \(-0.728743\pi\) | ||||
−0.658345 | + | 0.752716i | \(0.728743\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.65478 | + | 9.79436i | 0.400856 | + | 0.694304i | 0.993829 | − | 0.110919i | \(-0.0353793\pi\) |
−0.592973 | + | 0.805222i | \(0.702046\pi\) | |||||||
\(200\) | −0.379791 | − | 0.657818i | −0.0268553 | − | 0.0465147i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.90921 | 0.275051 | ||||||||
\(203\) | 0.833552 | − | 7.56626i | 0.0585039 | − | 0.531048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.32676 | + | 2.49806i | 0.302194 | + | 0.174472i | ||||
\(206\) | 1.72042 | + | 2.97985i | 0.119867 | + | 0.207616i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.04391 | − | 3.48945i | −0.419070 | − | 0.241950i | ||||
\(209\) | 22.5254 | − | 16.9980i | 1.55812 | − | 1.17578i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 21.8547i | − | 1.50454i | −0.658854 | − | 0.752271i | \(-0.728959\pi\) | ||
0.658854 | − | 0.752271i | \(-0.271041\pi\) | |||||||
\(212\) | 9.93207 | + | 5.73428i | 0.682137 | + | 0.393832i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.00997 | − | 1.74932i | −0.0690403 | − | 0.119581i | ||||
\(215\) | −7.77577 | + | 13.4680i | −0.530303 | + | 0.918512i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.2836 | + | 9.34873i | −1.44483 | + | 0.634633i | ||||
\(218\) | − | 3.52747i | − | 0.238910i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.28856 | + | 2.66432i | 0.423975 | + | 0.179629i | ||||
\(221\) | 32.2159 | − | 18.5998i | 2.16707 | − | 1.25116i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.3441 | −1.22841 | −0.614207 | − | 0.789145i | \(-0.710524\pi\) | ||||
−0.614207 | + | 0.789145i | \(0.710524\pi\) | |||||||
\(224\) | −2.42237 | + | 1.06401i | −0.161851 | + | 0.0710924i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.58287 | + | 3.80062i | 0.437886 | + | 0.252814i | ||||
\(227\) | −0.871542 | − | 1.50956i | −0.0578463 | − | 0.100193i | 0.835652 | − | 0.549259i | \(-0.185090\pi\) |
−0.893498 | + | 0.449066i | \(0.851757\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.1778 | − | 24.5567i | 0.936895 | − | 1.62275i | 0.165676 | − | 0.986180i | \(-0.447019\pi\) |
0.771219 | − | 0.636570i | \(-0.219647\pi\) | |||||||
\(230\) | −3.22205 | −0.212456 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.87708 | 0.188890 | ||||||||
\(233\) | 10.4076 | − | 18.0264i | 0.681823 | − | 1.18095i | −0.292601 | − | 0.956235i | \(-0.594521\pi\) |
0.974424 | − | 0.224717i | \(-0.0721458\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1803 | + | 21.0968i | 0.794553 | + | 1.37621i | ||||
\(236\) | −3.49197 | − | 2.01609i | −0.227308 | − | 0.131236i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.54430 | − | 14.0178i | 0.100102 | − | 0.908642i | ||||
\(239\) | 7.45803 | 0.482420 | 0.241210 | − | 0.970473i | \(-0.422456\pi\) | ||||
0.241210 | + | 0.970473i | \(0.422456\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.76722 | − | 3.32971i | 0.371500 | − | 0.214485i | −0.302614 | − | 0.953113i | \(-0.597859\pi\) |
0.674113 | + | 0.738628i | \(0.264526\pi\) | |||||||
\(242\) | 10.6696 | − | 2.67555i | 0.685871 | − | 0.171991i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.07151i | 0.324670i | ||||||||
\(245\) | 10.6151 | + | 9.75198i | 0.678171 | + | 0.623031i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.6897 | + | 51.4242i | −1.88911 | + | 3.27204i | ||||
\(248\) | −4.39314 | − | 7.60915i | −0.278965 | − | 0.483181i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.2713 | − | 5.93015i | −0.649615 | − | 0.375055i | ||||
\(251\) | 19.8684i | 1.25408i | 0.778986 | + | 0.627042i | \(0.215734\pi\) | ||||
−0.778986 | + | 0.627042i | \(0.784266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.14240 | + | 3.12591i | −0.260430 | + | 0.196524i | ||||
\(254\) | 5.49001 | + | 3.16966i | 0.344474 | + | 0.198882i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 19.1251 | + | 11.0419i | 1.19299 | + | 0.688773i | 0.958983 | − | 0.283463i | \(-0.0914832\pi\) |
0.234006 | + | 0.972235i | \(0.424817\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.77267 | + | 5.70683i | 0.482970 | + | 0.354605i | ||||
\(260\) | −14.3712 | −0.891261 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.50013 | − | 11.2586i | −0.401579 | − | 0.695556i | ||||
\(263\) | −5.60069 | − | 9.70067i | −0.345353 | − | 0.598169i | 0.640065 | − | 0.768321i | \(-0.278907\pi\) |
−0.985418 | + | 0.170152i | \(0.945574\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.6164 | 1.45074 | ||||||||
\(266\) | 9.05308 | + | 20.6105i | 0.555080 | + | 1.26371i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.75461 | + | 8.23523i | −0.290434 | + | 0.503047i | ||||
\(269\) | 3.35811 | − | 1.93880i | 0.204747 | − | 0.118211i | −0.394121 | − | 0.919059i | \(-0.628951\pi\) |
0.598868 | + | 0.800848i | \(0.295617\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.49796 | + | 1.44220i | 0.151740 | + | 0.0876073i | 0.573948 | − | 0.818892i | \(-0.305411\pi\) |
−0.422207 | + | 0.906499i | \(0.638745\pi\) | |||||||
\(272\) | 5.33030 | 0.323197 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.20594i | 0.556151i | ||||||||
\(275\) | −2.50026 | + | 0.308708i | −0.150772 | + | 0.0186158i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.4381 | + | 10.6453i | −1.10784 | + | 0.639612i | −0.938269 | − | 0.345906i | \(-0.887572\pi\) |
−0.169571 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(278\) | −16.0390 | − | 9.26012i | −0.961955 | − | 0.555385i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.22439 | + | 4.39161i | −0.192694 | + | 0.262449i | ||||
\(281\) | −14.7696 | −0.881078 | −0.440539 | − | 0.897733i | \(-0.645213\pi\) | ||||
−0.440539 | + | 0.897733i | \(0.645213\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.509546 | + | 0.294187i | −0.0302894 | + | 0.0174876i | −0.515068 | − | 0.857149i | \(-0.672233\pi\) |
0.484779 | + | 0.874637i | \(0.338900\pi\) | |||||||
\(284\) | −2.86172 | + | 1.65221i | −0.169812 | + | 0.0980408i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.4761 | + | 13.9423i | −1.09252 | + | 0.824428i | ||||
\(287\) | −0.702924 | + | 6.38054i | −0.0414923 | + | 0.376631i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.70605 | + | 9.88317i | −0.335650 | + | 0.581363i | ||||
\(290\) | 5.13082 | − | 2.96228i | 0.301292 | − | 0.173951i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.828178 | + | 0.478149i | 0.0484654 | + | 0.0279815i | ||||
\(293\) | 1.57886 | 0.0922380 | 0.0461190 | − | 0.998936i | \(-0.485315\pi\) | ||||
0.0461190 | + | 0.998936i | \(0.485315\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.30318 | −0.483430 | ||||||||
\(296\) | −1.82231 | + | 3.15633i | −0.105919 | + | 0.183458i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.04969 | + | 10.4784i | 0.350449 | + | 0.606996i | ||||
\(299\) | 5.45991 | − | 9.45683i | 0.315754 | − | 0.546903i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.8609 | − | 2.18801i | −1.14476 | − | 0.126115i | ||||
\(302\) | − | 5.16913i | − | 0.297450i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.36851 | + | 4.25421i | −0.422613 | + | 0.243996i | ||||
\(305\) | 5.22170 | + | 9.04425i | 0.298994 | + | 0.517872i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.9956i | 0.855842i | 0.903816 | + | 0.427921i | \(0.140754\pi\) | ||||
−0.903816 | + | 0.427921i | \(0.859246\pi\) | |||||||
\(308\) | 0.115158 | + | 8.77421i | 0.00656171 | + | 0.499957i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.6690 | − | 9.04648i | −0.889937 | − | 0.513806i | ||||
\(311\) | −9.46660 | + | 5.46555i | −0.536802 | + | 0.309923i | −0.743782 | − | 0.668422i | \(-0.766970\pi\) |
0.206980 | + | 0.978345i | \(0.433637\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.10928 | − | 10.5816i | 0.345317 | − | 0.598107i | −0.640094 | − | 0.768296i | \(-0.721105\pi\) |
0.985411 | + | 0.170190i | \(0.0544380\pi\) | |||||||
\(314\) | −0.957476 | −0.0540335 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 8.95224i | − | 0.503603i | ||||||
\(317\) | 19.9526 | + | 11.5197i | 1.12065 | + | 0.647008i | 0.941567 | − | 0.336826i | \(-0.109353\pi\) |
0.179084 | + | 0.983834i | \(0.442687\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.72250 | − | 8.78615i | 0.208420 | − | 0.491930i | ||||
\(320\) | −1.78334 | − | 1.02961i | −0.0996919 | − | 0.0575572i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.66485 | − | 3.79025i | −0.0927785 | − | 0.211222i | ||||
\(323\) | − | 45.3525i | − | 2.52348i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.59085 | − | 2.65053i | 0.254654 | − | 0.147025i | ||||
\(326\) | 8.54401 | + | 14.7987i | 0.473209 | + | 0.819622i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.42621 | −0.133965 | ||||||||
\(329\) | −18.5236 | + | 25.2291i | −1.02124 | + | 1.39092i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.855231 | + | 1.48130i | −0.0470077 | + | 0.0814198i | −0.888572 | − | 0.458737i | \(-0.848302\pi\) |
0.841564 | + | 0.540157i | \(0.181635\pi\) | |||||||
\(332\) | 3.75353 | + | 6.50130i | 0.206002 | + | 0.356805i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.81000 | + | 15.2594i | −0.482062 | + | 0.834956i | ||||
\(335\) | 19.5817i | 1.06986i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.45772i | 0.242828i | 0.992602 | + | 0.121414i | \(0.0387428\pi\) | ||||
−0.992602 | + | 0.121414i | \(0.961257\pi\) | |||||||
\(338\) | 17.8526 | − | 30.9216i | 0.971052 | − | 1.68191i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.50576 | − | 5.48815i | 0.515522 | − | 0.297637i | ||||
\(341\) | −28.9212 | + | 3.57090i | −1.56617 | + | 0.193375i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.98688 | + | 17.5259i | −0.323261 | + | 0.946310i | ||||
\(344\) | − | 7.55213i | − | 0.407183i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.05455 | − | 13.9509i | −0.433016 | − | 0.750005i | ||||
\(347\) | −9.27272 | − | 16.0608i | −0.497786 | − | 0.862190i | 0.502211 | − | 0.864745i | \(-0.332520\pi\) |
−0.999997 | + | 0.00255476i | \(0.999187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 16.0494i | − | 0.859104i | −0.903042 | − | 0.429552i | \(-0.858671\pi\) | ||
0.903042 | − | 0.429552i | \(-0.141329\pi\) | |||||||
\(350\) | 0.220067 | − | 1.99758i | 0.0117631 | − | 0.106775i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.29163 | + | 0.406418i | −0.175444 | + | 0.0216621i | ||||
\(353\) | 5.81710 | − | 3.35850i | 0.309613 | − | 0.178755i | −0.337140 | − | 0.941454i | \(-0.609460\pi\) |
0.646753 | + | 0.762699i | \(0.276126\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.40228 | + | 5.89292i | −0.180574 | + | 0.312764i | ||||
\(356\) | − | 3.45457i | − | 0.183092i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.22784i | 0.487707i | ||||||||
\(359\) | −17.4909 | + | 30.2952i | −0.923136 | + | 1.59892i | −0.128605 | + | 0.991696i | \(0.541050\pi\) |
−0.794531 | + | 0.607223i | \(0.792283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.6966 | + | 46.2399i | 1.40509 | + | 2.43368i | ||||
\(362\) | −2.73173 | + | 4.73150i | −0.143577 | + | 0.248682i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.42565 | − | 16.9055i | −0.389210 | − | 0.886089i | ||||
\(365\) | 1.96923 | 0.103074 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.89294 | + | 3.27867i | 0.0988107 | + | 0.171145i | 0.911193 | − | 0.411981i | \(-0.135163\pi\) |
−0.812382 | + | 0.583126i | \(0.801830\pi\) | |||||||
\(368\) | 1.35506 | − | 0.782344i | 0.0706374 | − | 0.0407825i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.50508i | 0.390171i | ||||||||
\(371\) | 12.2027 | + | 27.7811i | 0.633533 | + | 1.44232i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.3482 | − | 9.43867i | −0.846480 | − | 0.488716i | 0.0129814 | − | 0.999916i | \(-0.495868\pi\) |
−0.859462 | + | 0.511200i | \(0.829201\pi\) | |||||||
\(374\) | 6.89659 | − | 16.2779i | 0.356614 | − | 0.841710i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.2450 | − | 5.91497i | −0.528347 | − | 0.305041i | ||||
\(377\) | 20.0789i | 1.03411i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.1679 | 0.727755 | 0.363878 | − | 0.931447i | \(-0.381453\pi\) | ||||
0.363878 | + | 0.931447i | \(0.381453\pi\) | |||||||
\(380\) | −8.76039 | + | 15.1734i | −0.449399 | + | 0.778381i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.8512 | − | 10.3064i | 0.913349 | − | 0.527322i | ||||
\(383\) | 23.0987 | + | 13.3360i | 1.18029 | + | 0.681439i | 0.956081 | − | 0.293103i | \(-0.0946879\pi\) |
0.224206 | + | 0.974542i | \(0.428021\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.23941 | + | 15.5289i | 0.470884 | + | 0.791424i | ||||
\(386\) | 13.0055i | 0.661961i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.97666 | + | 5.15573i | 0.151117 | + | 0.261742i | ||||
\(389\) | 2.99247 | − | 1.72771i | 0.151724 | − | 0.0875981i | −0.422216 | − | 0.906495i | \(-0.638748\pi\) |
0.573940 | + | 0.818897i | \(0.305414\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.34026i | 0.421785i | ||||||||
\(392\) | −6.83212 | − | 1.52384i | −0.345074 | − | 0.0769657i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.24031 | − | 16.0047i | 0.465520 | − | 0.806305i | ||||
\(395\) | −9.21735 | − | 15.9649i | −0.463775 | − | 0.803283i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.1910 | − | 19.3833i | 0.561659 | − | 0.972822i | −0.435693 | − | 0.900096i | \(-0.643497\pi\) |
0.997352 | − | 0.0727269i | \(-0.0231701\pi\) | |||||||
\(398\) | −11.3096 | −0.566897 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.759582 | 0.0379791 | ||||||||
\(401\) | −5.81710 | − | 3.35850i | −0.290492 | − | 0.167716i | 0.347672 | − | 0.937616i | \(-0.386972\pi\) |
−0.638164 | + | 0.769901i | \(0.720306\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 53.1035 | − | 30.6593i | 2.64528 | − | 1.52725i | ||||
\(404\) | −1.95460 | + | 3.38547i | −0.0972451 | + | 0.168434i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.13580 | + | 4.50501i | 0.304515 | + | 0.223580i | ||||
\(407\) | 7.28114 | + | 9.64884i | 0.360913 | + | 0.478275i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.30162 | − | 0.751492i | 0.0643611 | − | 0.0371589i | −0.467474 | − | 0.884007i | \(-0.654836\pi\) |
0.531835 | + | 0.846848i | \(0.321503\pi\) | |||||||
\(410\) | −4.32676 | + | 2.49806i | −0.213683 | + | 0.123370i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.44084 | −0.169518 | ||||||||
\(413\) | −4.29030 | − | 9.76744i | −0.211112 | − | 0.480624i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.3877 | + | 7.72937i | 0.657175 | + | 0.379420i | ||||
\(416\) | 6.04391 | − | 3.48945i | 0.296327 | − | 0.171085i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.45797 | + | 28.0066i | 0.169135 | + | 1.36985i | ||||
\(419\) | 15.6194i | 0.763058i | 0.924357 | + | 0.381529i | \(0.124602\pi\) | ||||
−0.924357 | + | 0.381529i | \(0.875398\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.70442 | 0.472965 | 0.236482 | − | 0.971636i | \(-0.424005\pi\) | ||||
0.236482 | + | 0.971636i | \(0.424005\pi\) | |||||||
\(422\) | 18.9267 | + | 10.9274i | 0.921339 | + | 0.531936i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.93207 | + | 5.73428i | −0.482344 | + | 0.278481i | ||||
\(425\) | −2.02440 | + | 3.50637i | −0.0981979 | + | 0.170084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.94111 | + | 10.8158i | −0.384297 | + | 0.523411i | ||||
\(428\) | 2.01995 | 0.0976377 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.77577 | − | 13.4680i | −0.374981 | − | 0.649486i | ||||
\(431\) | 11.7521 | + | 20.3553i | 0.566081 | + | 0.980480i | 0.996948 | + | 0.0780652i | \(0.0248742\pi\) |
−0.430868 | + | 0.902415i | \(0.641792\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.3720 | −0.882902 | −0.441451 | − | 0.897285i | \(-0.645536\pi\) | ||||
−0.441451 | + | 0.897285i | \(0.645536\pi\) | |||||||
\(434\) | 2.54558 | − | 23.1065i | 0.122192 | − | 1.10915i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.05488 | + | 1.76373i | 0.146302 | + | 0.0844675i | ||||
\(437\) | −6.65651 | − | 11.5294i | −0.318424 | − | 0.551527i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.8078 | + | 6.81724i | 0.563556 | + | 0.325369i | 0.754571 | − | 0.656218i | \(-0.227845\pi\) |
−0.191016 | + | 0.981587i | \(0.561178\pi\) | |||||||
\(440\) | −5.45165 | + | 4.11389i | −0.259897 | + | 0.196122i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 37.1997i | 1.76941i | ||||||||
\(443\) | 18.9667 | + | 10.9504i | 0.901133 | + | 0.520270i | 0.877568 | − | 0.479453i | \(-0.159165\pi\) |
0.0235656 | + | 0.999722i | \(0.492498\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.55687 | − | 6.16068i | −0.168612 | − | 0.292044i | ||||
\(446\) | 9.17207 | − | 15.8865i | 0.434310 | − | 0.752247i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.289722 | − | 2.62984i | 0.0136881 | − | 0.124248i | ||||
\(449\) | − | 34.6012i | − | 1.63293i | −0.577395 | − | 0.816465i | \(-0.695931\pi\) | ||
0.577395 | − | 0.816465i | \(-0.304069\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.13914 | + | 7.40926i | −0.147816 | + | 0.348888i | ||||
\(452\) | −6.58287 | + | 3.80062i | −0.309632 | + | 0.178766i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.74308 | 0.0818070 | ||||||||
\(455\) | −30.6486 | − | 22.5027i | −1.43683 | − | 1.05494i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.7285 | − | 13.1223i | −1.06319 | − | 0.613835i | −0.136879 | − | 0.990588i | \(-0.543707\pi\) |
−0.926314 | + | 0.376753i | \(0.877041\pi\) | |||||||
\(458\) | 14.1778 | + | 24.5567i | 0.662485 | + | 1.14746i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.61102 | − | 2.79038i | 0.0751144 | − | 0.130102i | ||||
\(461\) | 42.1747 | 1.96427 | 0.982136 | − | 0.188175i | \(-0.0602571\pi\) | ||||
0.982136 | + | 0.188175i | \(0.0602571\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.1308 | 1.21440 | 0.607200 | − | 0.794549i | \(-0.292293\pi\) | ||||
0.607200 | + | 0.794549i | \(0.292293\pi\) | |||||||
\(464\) | −1.43854 | + | 2.49162i | −0.0667826 | + | 0.115671i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.4076 | + | 18.0264i | 0.482121 | + | 0.835059i | ||||
\(467\) | −4.98050 | − | 2.87549i | −0.230470 | − | 0.133062i | 0.380319 | − | 0.924855i | \(-0.375814\pi\) |
−0.610789 | + | 0.791794i | \(0.709148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.0349 | + | 10.1179i | −1.06365 | + | 0.467203i | ||||
\(470\) | −24.3605 | −1.12367 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.49197 | − | 2.01609i | 0.160731 | − | 0.0927981i | ||||
\(473\) | −23.0630 | − | 9.77129i | −1.06044 | − | 0.449285i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.46285i | − | 0.296536i | ||||||
\(476\) | 11.3677 | + | 8.34633i | 0.521036 | + | 0.382553i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.72902 | + | 6.45884i | −0.170561 | + | 0.295421i | ||||
\(479\) | 6.97303 | + | 12.0776i | 0.318606 | + | 0.551842i | 0.980197 | − | 0.198023i | \(-0.0634520\pi\) |
−0.661591 | + | 0.749865i | \(0.730119\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.0277 | − | 12.7177i | −1.00438 | − | 0.579877i | ||||
\(482\) | 6.65942i | 0.303328i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.01773 | + | 10.5780i | −0.137169 | + | 0.480817i | ||||
\(485\) | 10.6168 | + | 6.12962i | 0.482085 | + | 0.278332i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.77700 | − | 13.4702i | −0.352410 | − | 0.610391i | 0.634261 | − | 0.773119i | \(-0.281304\pi\) |
−0.986671 | + | 0.162727i | \(0.947971\pi\) | |||||||
\(488\) | −4.39206 | − | 2.53576i | −0.198819 | − | 0.114788i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.7530 | + | 4.31691i | −0.621297 | + | 0.195018i | ||||
\(491\) | 14.7267 | 0.664609 | 0.332304 | − | 0.943172i | \(-0.392174\pi\) | ||||
0.332304 | + | 0.943172i | \(0.392174\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.66785 | − | 13.2811i | −0.345343 | − | 0.598151i | ||||
\(494\) | −29.6897 | − | 51.4242i | −1.33580 | − | 2.31368i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.78629 | 0.394516 | ||||||||
\(497\) | −8.69011 | − | 0.957363i | −0.389805 | − | 0.0429436i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.51020 | − | 6.07984i | 0.157138 | − | 0.272171i | −0.776697 | − | 0.629874i | \(-0.783107\pi\) |
0.933835 | + | 0.357703i | \(0.116440\pi\) | |||||||
\(500\) | 10.2713 | − | 5.93015i | 0.459347 | − | 0.265204i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.2066 | − | 9.93421i | −0.767966 | − | 0.443385i | ||||
\(503\) | 20.7055 | 0.923213 | 0.461607 | − | 0.887085i | \(-0.347273\pi\) | ||||
0.461607 | + | 0.887085i | \(0.347273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.04994i | 0.358218i | ||||||||
\(506\) | −0.635917 | − | 5.15037i | −0.0282699 | − | 0.228962i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.49001 | + | 3.16966i | −0.243580 | + | 0.140631i | ||||
\(509\) | −19.4116 | − | 11.2073i | −0.860403 | − | 0.496754i | 0.00374431 | − | 0.999993i | \(-0.498808\pi\) |
−0.864147 | + | 0.503239i | \(0.832141\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.01751 | + | 2.31651i | 0.0450122 | + | 0.102476i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.1251 | + | 11.0419i | −0.843571 | + | 0.487036i | ||||
\(515\) | −6.13620 | + | 3.54273i | −0.270393 | + | 0.156112i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.3189 | + | 23.6336i | −1.37740 | + | 1.03941i | ||||
\(518\) | −8.82859 | + | 3.87792i | −0.387906 | + | 0.170386i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.18558 | − | 12.4458i | 0.315108 | − | 0.545784i | ||||
\(521\) | −20.0520 | + | 11.5770i | −0.878494 | + | 0.507199i | −0.870161 | − | 0.492767i | \(-0.835986\pi\) |
−0.00833225 | + | 0.999965i | \(0.502652\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.0181 | − | 10.4027i | −0.787875 | − | 0.454880i | 0.0513386 | − | 0.998681i | \(-0.483651\pi\) |
−0.839214 | + | 0.543801i | \(0.816985\pi\) | |||||||
\(524\) | 13.0003 | 0.567919 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.2014 | 0.488403 | ||||||||
\(527\) | −23.4168 | + | 40.5590i | −1.02005 | + | 1.76678i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.2759 | − | 17.7983i | −0.446777 | − | 0.773841i | ||||
\(530\) | −11.8082 | + | 20.4524i | −0.512915 | + | 0.888395i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −22.3758 | − | 2.46507i | −0.970114 | − | 0.106875i | ||||
\(533\) | − | 16.9323i | − | 0.733418i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.60226 | − | 2.07976i | 0.155739 | − | 0.0899160i | ||||
\(536\) | −4.75461 | − | 8.23523i | −0.205368 | − | 0.355708i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.87761i | 0.167175i | ||||||||
\(539\) | −13.4933 | + | 18.8926i | −0.581197 | + | 0.813763i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.4366 | + | 9.48967i | 0.706664 | + | 0.407993i | 0.809825 | − | 0.586672i | \(-0.199562\pi\) |
−0.103160 | + | 0.994665i | \(0.532896\pi\) | |||||||
\(542\) | −2.49796 | + | 1.44220i | −0.107297 | + | 0.0619477i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.66515 | + | 4.61618i | −0.114267 | + | 0.197917i | ||||
\(545\) | 7.26386 | 0.311149 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 27.3881i | − | 1.17103i | −0.810661 | − | 0.585515i | \(-0.800892\pi\) | ||
0.810661 | − | 0.585515i | \(-0.199108\pi\) | |||||||
\(548\) | −7.97258 | − | 4.60297i | −0.340572 | − | 0.196629i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.982783 | − | 2.31965i | 0.0419060 | − | 0.0989100i | ||||
\(551\) | 21.1998 | + | 12.2397i | 0.903142 | + | 0.521429i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.0177 | − | 19.0920i | 0.596092 | − | 0.811874i | ||||
\(554\) | − | 21.2905i | − | 0.904548i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.0390 | − | 9.26012i | 0.680205 | − | 0.392717i | ||||
\(557\) | −5.98411 | − | 10.3648i | −0.253555 | − | 0.439170i | 0.710947 | − | 0.703245i | \(-0.248266\pi\) |
−0.964502 | + | 0.264076i | \(0.914933\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52.7056 | 2.22921 | ||||||||
\(560\) | −2.19105 | − | 4.98821i | −0.0925886 | − | 0.210790i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.38478 | − | 12.7908i | 0.311508 | − | 0.539548i | ||||
\(563\) | 3.34982 | + | 5.80206i | 0.141178 | + | 0.244527i | 0.927940 | − | 0.372728i | \(-0.121578\pi\) |
−0.786762 | + | 0.617256i | \(0.788244\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.82635 | + | 13.5556i | −0.329257 | + | 0.570290i | ||||
\(566\) | − | 0.588373i | − | 0.0247312i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 3.30443i | − | 0.138651i | ||||||
\(569\) | 7.52076 | − | 13.0263i | 0.315287 | − | 0.546092i | −0.664212 | − | 0.747544i | \(-0.731233\pi\) |
0.979498 | + | 0.201452i | \(0.0645660\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.3794 | − | 14.0755i | 1.02025 | − | 0.589040i | 0.106072 | − | 0.994358i | \(-0.466173\pi\) |
0.914176 | + | 0.405318i | \(0.132839\pi\) | |||||||
\(572\) | −2.83635 | − | 22.9720i | −0.118594 | − | 0.960507i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.17424 | − | 3.79902i | −0.215969 | − | 0.158568i | ||||
\(575\) | 1.18851i | 0.0495643i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.3717 | − | 19.6964i | −0.473410 | − | 0.819970i | 0.526127 | − | 0.850406i | \(-0.323644\pi\) |
−0.999537 | + | 0.0304358i | \(0.990310\pi\) | |||||||
\(578\) | −5.70605 | − | 9.88317i | −0.237340 | − | 0.411086i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.92456i | 0.246004i | ||||||||
\(581\) | −2.17496 | + | 19.7424i | −0.0902324 | + | 0.819051i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.66103 | + | 37.7503i | 0.193040 | + | 1.56346i | ||||
\(584\) | −0.828178 | + | 0.478149i | −0.0342702 | + | 0.0197859i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.789430 | + | 1.36733i | −0.0326110 | + | 0.0564840i | ||||
\(587\) | − | 18.9106i | − | 0.780523i | −0.920704 | − | 0.390261i | \(-0.872385\pi\) | ||
0.920704 | − | 0.390261i | \(-0.127615\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 74.7574i | − | 3.08033i | ||||||
\(590\) | 4.15159 | − | 7.19077i | 0.170918 | − | 0.296039i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.82231 | − | 3.15633i | −0.0748963 | − | 0.129724i | ||||
\(593\) | 16.7412 | − | 28.9966i | 0.687479 | − | 1.19075i | −0.285171 | − | 0.958477i | \(-0.592051\pi\) |
0.972651 | − | 0.232273i | \(-0.0746162\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.8659 | + | 3.18007i | 1.18339 | + | 0.130370i | ||||
\(596\) | −12.0994 | −0.495610 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.45991 | + | 9.45683i | 0.223272 | + | 0.386719i | ||||
\(599\) | 7.22458 | − | 4.17111i | 0.295188 | − | 0.170427i | −0.345091 | − | 0.938569i | \(-0.612152\pi\) |
0.640279 | + | 0.768142i | \(0.278819\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 18.8871i | − | 0.770420i | −0.922829 | − | 0.385210i | \(-0.874129\pi\) | ||
0.922829 | − | 0.385210i | \(-0.125871\pi\) | |||||||
\(602\) | 11.8253 | − | 16.1060i | 0.481964 | − | 0.656433i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.47659 | + | 2.58456i | 0.182150 | + | 0.105164i | ||||
\(605\) | 5.50957 | + | 21.9712i | 0.223996 | + | 0.893258i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.0729 | + | 19.6720i | 1.38298 | + | 0.798461i | 0.992511 | − | 0.122157i | \(-0.0389812\pi\) |
0.390464 | + | 0.920618i | \(0.372314\pi\) | |||||||
\(608\) | − | 8.50842i | − | 0.345062i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.4434 | −0.422841 | ||||||||
\(611\) | 41.2800 | − | 71.4991i | 1.67001 | − | 2.89254i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.07950 | + | 4.66470i | −0.326328 | + | 0.188405i | −0.654210 | − | 0.756313i | \(-0.726999\pi\) |
0.327882 | + | 0.944719i | \(0.393665\pi\) | |||||||
\(614\) | −12.9865 | − | 7.49778i | −0.524094 | − | 0.302586i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.65627 | − | 4.28737i | −0.308480 | − | 0.172743i | ||||
\(617\) | 46.3271i | 1.86506i | 0.361093 | + | 0.932530i | \(0.382404\pi\) | ||||
−0.361093 | + | 0.932530i | \(0.617596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.3541 | + | 21.3979i | 0.496552 | + | 0.860053i | 0.999992 | − | 0.00397706i | \(-0.00126594\pi\) |
−0.503440 | + | 0.864030i | \(0.667933\pi\) | |||||||
\(620\) | 15.6690 | − | 9.04648i | 0.629281 | − | 0.363315i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 10.9311i | − | 0.438297i | ||||||
\(623\) | 5.40925 | − | 7.36737i | 0.216717 | − | 0.295168i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.3126 | − | 17.8619i | 0.412502 | − | 0.714475i | ||||
\(626\) | 6.10928 | + | 10.5816i | 0.244176 | + | 0.422925i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.478738 | − | 0.829198i | 0.0191037 | − | 0.0330886i | ||||
\(629\) | 19.4269 | 0.774600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.6824 | −0.624306 | −0.312153 | − | 0.950032i | \(-0.601050\pi\) | ||||
−0.312153 | + | 0.950032i | \(0.601050\pi\) | |||||||
\(632\) | 7.75287 | + | 4.47612i | 0.308393 | + | 0.178051i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −19.9526 | + | 11.5197i | −0.792420 | + | 0.457504i | ||||
\(635\) | −6.52705 | + | 11.3052i | −0.259018 | + | 0.448632i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.6348 | − | 47.6807i | 0.421364 | − | 1.88918i | ||||
\(638\) | 5.74778 | + | 7.61686i | 0.227557 | + | 0.301554i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.78334 | − | 1.02961i | 0.0704928 | − | 0.0406991i | ||||
\(641\) | 21.5853 | − | 12.4623i | 0.852568 | − | 0.492231i | −0.00894816 | − | 0.999960i | \(-0.502848\pi\) |
0.861517 | + | 0.507729i | \(0.169515\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.4327 | −0.884658 | −0.442329 | − | 0.896853i | \(-0.645848\pi\) | ||||
−0.442329 | + | 0.896853i | \(0.645848\pi\) | |||||||
\(644\) | 4.11488 | + | 0.453324i | 0.162149 | + | 0.0178635i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 39.2764 | + | 22.6762i | 1.54531 | + | 0.892184i | ||||
\(647\) | 23.0631 | − | 13.3155i | 0.906705 | − | 0.523486i | 0.0273356 | − | 0.999626i | \(-0.491298\pi\) |
0.879370 | + | 0.476140i | \(0.157964\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.63875 | − | 13.2725i | −0.0643266 | − | 0.520989i | ||||
\(650\) | 5.30106i | 0.207924i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.0880 | −0.669219 | ||||||||
\(653\) | −5.78961 | − | 3.34263i | −0.226565 | − | 0.130807i | 0.382421 | − | 0.923988i | \(-0.375090\pi\) |
−0.608986 | + | 0.793181i | \(0.708424\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.1839 | − | 13.3852i | 0.905871 | − | 0.523005i | ||||
\(656\) | 1.21310 | − | 2.10116i | 0.0473637 | − | 0.0820364i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.5872 | − | 28.6565i | −0.490701 | − | 1.11715i | ||||
\(659\) | 1.73849 | 0.0677218 | 0.0338609 | − | 0.999427i | \(-0.489220\pi\) | ||||
0.0338609 | + | 0.999427i | \(0.489220\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.9433 | + | 24.1506i | 0.542333 | + | 0.939349i | 0.998770 | + | 0.0495927i | \(0.0157923\pi\) |
−0.456436 | + | 0.889756i | \(0.650874\pi\) | |||||||
\(662\) | −0.855231 | − | 1.48130i | −0.0332395 | − | 0.0575725i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.50706 | −0.291330 | ||||||||
\(665\) | −42.4418 | + | 18.6424i | −1.64582 | + | 0.722920i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.89861 | − | 2.25087i | −0.150955 | − | 0.0871539i | ||||
\(668\) | −8.81000 | − | 15.2594i | −0.340869 | − | 0.590403i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.9582 | − | 9.79083i | −0.655153 | − | 0.378253i | ||||
\(671\) | −13.4265 | + | 10.1318i | −0.518323 | + | 0.391133i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.61388i | 0.139305i | 0.997571 | + | 0.0696525i | \(0.0221890\pi\) | ||||
−0.997571 | + | 0.0696525i | \(0.977811\pi\) | |||||||
\(674\) | −3.86050 | − | 2.22886i | −0.148701 | − | 0.0858526i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.8526 | + | 30.9216i | 0.686637 | + | 1.18929i | ||||
\(677\) | −7.73709 | + | 13.4010i | −0.297361 | + | 0.515044i | −0.975531 | − | 0.219861i | \(-0.929440\pi\) |
0.678171 | + | 0.734904i | \(0.262773\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.72480 | + | 15.6563i | −0.0661919 | + | 0.600833i | ||||
\(680\) | 10.9763i | 0.420922i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.3681 | − | 26.8319i | 0.435307 | − | 1.02745i | ||||
\(683\) | −22.4201 | + | 12.9442i | −0.857879 | + | 0.495297i | −0.863302 | − | 0.504688i | \(-0.831607\pi\) |
0.00542219 | + | 0.999985i | \(0.498274\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.9571 | −0.724315 | ||||||||
\(686\) | −12.1844 | − | 13.9477i | −0.465204 | − | 0.532527i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.54033 | + | 3.77606i | 0.249348 | + | 0.143961i | ||||
\(689\) | −40.0190 | − | 69.3150i | −1.52460 | − | 2.64069i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.4617 | − | 38.9047i | 0.854481 | − | 1.48001i | −0.0226438 | − | 0.999744i | \(-0.507208\pi\) |
0.877125 | − | 0.480262i | \(-0.159458\pi\) | |||||||
\(692\) | 16.1091 | 0.612376 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.5454 | 0.703976 | ||||||||
\(695\) | 19.0687 | − | 33.0279i | 0.723317 | − | 1.25282i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.46621 | + | 11.1998i | 0.244925 | + | 0.424223i | ||||
\(698\) | 13.8992 | + | 8.02470i | 0.526092 | + | 0.303739i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.61992 | + | 1.18937i | 0.0612273 | + | 0.0449541i | ||||
\(701\) | −10.0235 | −0.378583 | −0.189292 | − | 0.981921i | \(-0.560619\pi\) | ||||
−0.189292 | + | 0.981921i | \(0.560619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.8554 | + | 15.5049i | −1.01287 | + | 0.584780i | ||||
\(704\) | 1.29385 | − | 3.05384i | 0.0487637 | − | 0.115096i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.71701i | 0.252798i | ||||||||
\(707\) | −9.46954 | + | 4.15945i | −0.356139 | + | 0.156432i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.17467 | − | 15.8910i | 0.344562 | − | 0.596799i | −0.640712 | − | 0.767781i | \(-0.721361\pi\) |
0.985274 | + | 0.170982i | \(0.0546941\pi\) | |||||||
\(710\) | −3.40228 | − | 5.89292i | −0.127685 | − | 0.221158i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.99174 | + | 1.72728i | 0.112120 | + | 0.0647327i | ||||
\(713\) | 13.7478i | 0.514859i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.7104 | − | 38.0466i | −1.07371 | − | 1.42286i | ||||
\(716\) | −7.99155 | − | 4.61392i | −0.298658 | − | 0.172430i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17.4909 | − | 30.2952i | −0.652756 | − | 1.13061i | ||||
\(719\) | −40.5198 | − | 23.3941i | −1.51113 | − | 0.872454i | −0.999915 | − | 0.0130036i | \(-0.995861\pi\) |
−0.511219 | − | 0.859450i | \(-0.670806\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.33810 | − | 5.38776i | −0.273285 | − | 0.200651i | ||||
\(722\) | −53.3933 | −1.98709 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.73173 | − | 4.73150i | −0.101524 | − | 0.175845i | ||||
\(725\) | −1.09269 | − | 1.89259i | −0.0405815 | − | 0.0702892i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.15090 | −0.228124 | −0.114062 | − | 0.993474i | \(-0.536386\pi\) | ||||
−0.114062 | + | 0.993474i | \(0.536386\pi\) | |||||||
\(728\) | 18.3534 | + | 2.02194i | 0.680223 | + | 0.0749381i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.984617 | + | 1.70541i | −0.0364423 | + | 0.0631199i | ||||
\(731\) | −34.8619 | + | 20.1276i | −1.28942 | + | 0.744444i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.6845 | + | 10.7875i | 0.690128 | + | 0.398446i | 0.803660 | − | 0.595089i | \(-0.202883\pi\) |
−0.113532 | + | 0.993534i | \(0.536216\pi\) | |||||||
\(734\) | −3.78588 | −0.139739 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.56469i | 0.0576752i | ||||||||
\(737\) | −31.3008 | + | 3.86472i | −1.15298 | + | 0.142359i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.3942 | − | 12.3520i | 0.787000 | − | 0.454375i | −0.0519053 | − | 0.998652i | \(-0.516529\pi\) |
0.838905 | + | 0.544277i | \(0.183196\pi\) | |||||||
\(740\) | −6.49959 | − | 3.75254i | −0.238930 | − | 0.137946i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.1605 | − | 3.32269i | −1.10723 | − | 0.121980i | ||||
\(743\) | −10.6465 | −0.390583 | −0.195292 | − | 0.980745i | \(-0.562565\pi\) | ||||
−0.195292 | + | 0.980745i | \(0.562565\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.5774 | + | 12.4577i | −0.790533 | + | 0.456414i | ||||
\(746\) | 16.3482 | − | 9.43867i | 0.598552 | − | 0.345574i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.6488 | + | 14.1116i | 0.389358 | + | 0.515970i | ||||
\(749\) | 4.30783 | + | 3.16288i | 0.157405 | + | 0.115569i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.2351 | − | 26.3879i | 0.555935 | − | 0.962908i | −0.441895 | − | 0.897067i | \(-0.645694\pi\) |
0.997830 | − | 0.0658410i | \(-0.0209730\pi\) | |||||||
\(752\) | 10.2450 | − | 5.91497i | 0.373598 | − | 0.215697i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17.3888 | − | 10.0394i | −0.633263 | − | 0.365615i | ||||
\(755\) | 10.6444 | 0.387390 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.9876 | 1.59876 | 0.799379 | − | 0.600827i | \(-0.205162\pi\) | ||||
0.799379 | + | 0.600827i | \(0.205162\pi\) | |||||||
\(758\) | −7.08394 | + | 12.2697i | −0.257300 | + | 0.445657i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.76039 | − | 15.1734i | −0.317773 | − | 0.550399i | ||||
\(761\) | −2.85261 | + | 4.94087i | −0.103407 | + | 0.179106i | −0.913086 | − | 0.407766i | \(-0.866308\pi\) |
0.809679 | + | 0.586873i | \(0.199641\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.75327 | + | 8.54483i | 0.135878 | + | 0.309344i | ||||
\(764\) | 20.6128i | 0.745746i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.0987 | + | 13.3360i | −0.834589 | + | 0.481850i | ||||
\(767\) | 14.0701 | + | 24.3702i | 0.508042 | + | 0.879955i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4.02217i | − | 0.145043i | −0.997367 | − | 0.0725215i | \(-0.976895\pi\) | ||
0.997367 | − | 0.0725215i | \(-0.0231046\pi\) | |||||||
\(770\) | −18.0681 | + | 0.237136i | −0.651129 | + | 0.00854578i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.2631 | − | 6.50274i | −0.405367 | − | 0.234039i | ||||
\(773\) | −13.6864 | + | 7.90184i | −0.492265 | + | 0.284210i | −0.725514 | − | 0.688208i | \(-0.758398\pi\) |
0.233248 | + | 0.972417i | \(0.425064\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.33695 | + | 5.77977i | −0.119867 | + | 0.207616i | ||||
\(776\) | −5.95332 | −0.213712 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.45541i | 0.123882i | ||||||||
\(779\) | −17.8775 | − | 10.3216i | −0.640529 | − | 0.369810i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0912 | − | 4.27542i | −0.361091 | − | 0.152987i | ||||
\(782\) | −7.22287 | − | 4.17013i | −0.258289 | − | 0.149123i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.73575 | − | 5.15487i | 0.169134 | − | 0.184103i | ||||
\(785\) | − | 1.97166i | − | 0.0703716i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.40102 | − | 5.42768i | 0.335110 | − | 0.193476i | −0.322997 | − | 0.946400i | \(-0.604691\pi\) |
0.658108 | + | 0.752924i | \(0.271357\pi\) | |||||||
\(788\) | 9.24031 | + | 16.0047i | 0.329172 | + | 0.570143i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 18.4347 | 0.655877 | ||||||||
\(791\) | −19.9901 | − | 2.20225i | −0.710765 | − | 0.0783028i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.6968 | − | 30.6518i | 0.628432 | − | 1.08848i | ||||
\(794\) | 11.1910 | + | 19.3833i | 0.397153 | + | 0.687889i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.65478 | − | 9.79436i | 0.200428 | − | 0.347152i | ||||
\(797\) | − | 53.5614i | − | 1.89724i | −0.316414 | − | 0.948621i | \(-0.602479\pi\) | ||
0.316414 | − | 0.948621i | \(-0.397521\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 63.0571i | 2.23080i | ||||||||
\(800\) | −0.379791 | + | 0.657818i | −0.0134276 | + | 0.0232574i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.81710 | − | 3.35850i | 0.205409 | − | 0.118593i | ||||
\(803\) | 0.388656 | + | 3.14778i | 0.0137154 | + | 0.111083i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.80499 | − | 3.42830i | 0.275090 | − | 0.120832i | ||||
\(806\) | 61.3187i | 2.15986i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.95460 | − | 3.38547i | −0.0687627 | − | 0.119100i | ||||
\(809\) | 11.3084 | + | 19.5867i | 0.397582 | + | 0.688632i | 0.993427 | − | 0.114468i | \(-0.0365162\pi\) |
−0.595845 | + | 0.803099i | \(0.703183\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.51083i | − | 0.158396i | −0.996859 | − | 0.0791982i | \(-0.974764\pi\) | ||
0.996859 | − | 0.0791982i | \(-0.0252360\pi\) | |||||||
\(812\) | −6.96935 | + | 3.06125i | −0.244576 | + | 0.107429i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.9967 | + | 1.48123i | −0.420484 | + | 0.0519172i | ||||
\(815\) | −30.4738 | + | 17.5941i | −1.06745 | + | 0.616293i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32.1283 | − | 55.6479i | 1.12403 | − | 1.94687i | ||||
\(818\) | 1.50298i | 0.0525506i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 4.99611i | − | 0.174472i | ||||||
\(821\) | 14.1814 | − | 24.5629i | 0.494935 | − | 0.857253i | −0.505048 | − | 0.863091i | \(-0.668525\pi\) |
0.999983 | + | 0.00583875i | \(0.00185854\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.18222 | − | 2.04767i | −0.0412097 | − | 0.0713772i | 0.844685 | − | 0.535264i | \(-0.179788\pi\) |
−0.885895 | + | 0.463887i | \(0.846454\pi\) | |||||||
\(824\) | 1.72042 | − | 2.97985i | 0.0599336 | − | 0.103808i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.6040 | + | 1.16821i | 0.368960 | + | 0.0406472i | ||||
\(827\) | −31.0362 | −1.07923 | −0.539617 | − | 0.841911i | \(-0.681431\pi\) | ||||
−0.539617 | + | 0.841911i | \(0.681431\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.1654 | + | 19.3391i | 0.387791 | + | 0.671674i | 0.992152 | − | 0.125037i | \(-0.0399049\pi\) |
−0.604361 | + | 0.796711i | \(0.706572\pi\) | |||||||
\(830\) | −13.3877 | + | 7.72937i | −0.464693 | + | 0.268290i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.97891i | 0.241950i | ||||||||
\(833\) | 11.1743 | + | 35.5996i | 0.387167 | + | 1.23345i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.4225 | − | 18.1418i | −1.08742 | − | 0.627823i | ||||
\(836\) | −25.9834 | − | 11.0086i | −0.898655 | − | 0.380740i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.5268 | − | 7.80971i | −0.467276 | − | 0.269782i | ||||
\(839\) | 39.0283i | 1.34741i | 0.739003 | + | 0.673703i | \(0.235297\pi\) | ||||
−0.739003 | + | 0.673703i | \(0.764703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.7224 | −0.714566 | ||||||||
\(842\) | −4.85221 | + | 8.40428i | −0.167218 | + | 0.289631i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18.9267 | + | 10.9274i | −0.651485 | + | 0.376135i | ||||
\(845\) | 63.6745 | + | 36.7625i | 2.19047 | + | 1.26467i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.9990 | + | 17.8338i | −0.790255 | + | 0.612778i | ||||
\(848\) | − | 11.4686i | − | 0.393832i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.02440 | − | 3.50637i | −0.0694364 | − | 0.120267i | ||||
\(851\) | 4.93866 | − | 2.85134i | 0.169295 | − | 0.0977426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.6365i | 1.32289i | 0.749995 | + | 0.661444i | \(0.230056\pi\) | ||||
−0.749995 | + | 0.661444i | \(0.769944\pi\) | |||||||
\(854\) | −5.39616 | − | 12.2851i | −0.184653 | − | 0.420387i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.00997 | + | 1.74932i | −0.0345202 | + | 0.0597907i | ||||
\(857\) | 6.30291 | + | 10.9170i | 0.215303 | + | 0.372916i | 0.953366 | − | 0.301815i | \(-0.0975926\pi\) |
−0.738063 | + | 0.674732i | \(0.764259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.7546 | − | 25.5558i | 0.503421 | − | 0.871951i | −0.496571 | − | 0.867996i | \(-0.665408\pi\) |
0.999992 | − | 0.00395510i | \(-0.00125895\pi\) | |||||||
\(860\) | 15.5515 | 0.530303 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.5043 | −0.800559 | ||||||||
\(863\) | 1.60259 | + | 0.925254i | 0.0545527 | + | 0.0314960i | 0.527028 | − | 0.849848i | \(-0.323306\pi\) |
−0.472476 | + | 0.881344i | \(0.656640\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.7281 | − | 16.5862i | 0.976784 | − | 0.563946i | ||||
\(866\) | 9.18600 | − | 15.9106i | 0.312153 | − | 0.540665i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.7381 | + | 13.7578i | 0.636011 | + | 0.466970i | ||||
\(869\) | 23.7004 | − | 17.8846i | 0.803981 | − | 0.606695i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 57.4729 | − | 33.1820i | 1.94739 | − | 1.12433i | ||||
\(872\) | −3.05488 | + | 1.76373i | −0.103451 | + | 0.0597275i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.3130 | 0.450320 | ||||||||
\(875\) | 31.1907 | + | 3.43618i | 1.05444 | + | 0.116164i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0961 | + | 8.13840i | 0.475992 | + | 0.274814i | 0.718745 | − | 0.695274i | \(-0.244717\pi\) |
−0.242753 | + | 0.970088i | \(0.578050\pi\) | |||||||
\(878\) | −11.8078 | + | 6.81724i | −0.398494 | + | 0.230071i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.836906 | − | 6.77821i | −0.0282121 | − | 0.228494i | ||||
\(881\) | 30.0489i | 1.01237i | 0.862424 | + | 0.506187i | \(0.168945\pi\) | ||||
−0.862424 | + | 0.506187i | \(0.831055\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.4464 | −1.02460 | −0.512302 | − | 0.858805i | \(-0.671207\pi\) | ||||
−0.512302 | + | 0.858805i | \(0.671207\pi\) | |||||||
\(884\) | −32.2159 | − | 18.5998i | −1.08354 | − | 0.625580i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.9667 | + | 10.9504i | −0.637197 | + | 0.367886i | ||||
\(887\) | 1.84407 | − | 3.19402i | 0.0619178 | − | 0.107245i | −0.833405 | − | 0.552663i | \(-0.813612\pi\) |
0.895323 | + | 0.445418i | \(0.146945\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.6714 | − | 1.83664i | −0.559141 | − | 0.0615988i | ||||
\(890\) | 7.11374 | 0.238453 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.17207 | + | 15.8865i | 0.307104 | + | 0.531919i | ||||
\(893\) | −50.3271 | − | 87.1690i | −1.68413 | − | 2.91700i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.0022 | −0.635174 | ||||||||
\(896\) | 2.13265 | + | 1.56583i | 0.0712468 | + | 0.0523106i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.9655 | + | 17.3006i | 0.999961 | + | 0.577328i | ||||
\(899\) | −12.6394 | − | 21.8921i | −0.421548 | − | 0.730143i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 52.9409 | + | 30.5654i | 1.76372 | + | 1.01828i | ||||
\(902\) | −4.84703 | − | 6.42320i | −0.161389 | − | 0.213869i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 7.60125i | − | 0.252814i | ||||||
\(905\) | −9.74323 | − | 5.62526i | −0.323876 | − | 0.186990i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.3787 | − | 17.9765i | −0.344620 | − | 0.596899i | 0.640665 | − | 0.767820i | \(-0.278659\pi\) |
−0.985285 | + | 0.170922i | \(0.945325\pi\) | |||||||
\(908\) | −0.871542 | + | 1.50956i | −0.0289231 | + | 0.0500964i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 34.8123 | − | 15.2911i | 1.15401 | − | 0.506895i | ||||
\(911\) | − | 30.1614i | − | 0.999290i | −0.866230 | − | 0.499645i | \(-0.833464\pi\) | ||
0.866230 | − | 0.499645i | \(-0.166536\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.71298 | + | 22.9254i | −0.321453 | + | 0.758719i | ||||
\(914\) | 22.7285 | − | 13.1223i | 0.751791 | − | 0.434047i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28.3556 | −0.936895 | ||||||||
\(917\) | 27.7250 | + | 20.3561i | 0.915559 | + | 0.672219i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.7967 | + | 24.7087i | 1.41173 | + | 0.815065i | 0.995552 | − | 0.0942164i | \(-0.0300346\pi\) |
0.416182 | + | 0.909281i | \(0.363368\pi\) | |||||||
\(920\) | 1.61102 | + | 2.79038i | 0.0531139 | + | 0.0919960i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −21.0873 | + | 36.5244i | −0.694475 | + | 1.20287i | ||||
\(923\) | 23.0613 | 0.759071 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.76838 | 0.0910238 | ||||||||
\(926\) | −13.0654 | + | 22.6299i | −0.429356 | + | 0.743666i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.43854 | − | 2.49162i | −0.0472224 | − | 0.0817916i | ||||
\(929\) | −6.64222 | − | 3.83488i | −0.217924 | − | 0.125818i | 0.387065 | − | 0.922053i | \(-0.373489\pi\) |
−0.604989 | + | 0.796234i | \(0.706822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.8598 | − | 40.2938i | −1.43745 | − | 1.32057i | ||||
\(932\) | −20.8151 | −0.681823 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.98050 | − | 2.87549i | 0.162967 | − | 0.0940889i | ||||
\(935\) | 33.5199 | + | 14.2017i | 1.09622 | + | 0.464444i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.93121i | 0.0630899i | 0.999502 | + | 0.0315449i | \(0.0100427\pi\) | ||||
−0.999502 | + | 0.0315449i | \(0.989957\pi\) | |||||||
\(938\) | 2.75503 | − | 25.0077i | 0.0899548 | − | 0.816532i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.1803 | − | 21.0968i | 0.397276 | − | 0.688103i | ||||
\(941\) | 6.36930 | + | 11.0319i | 0.207633 | + | 0.359631i | 0.950968 | − | 0.309288i | \(-0.100091\pi\) |
−0.743335 | + | 0.668919i | \(0.766757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.28765 | + | 1.89813i | 0.107061 | + | 0.0618115i | ||||
\(944\) | 4.03218i | 0.131236i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.9937 | − | 15.0875i | 0.650051 | − | 0.490537i | ||||
\(947\) | 41.3900 | + | 23.8965i | 1.34499 | + | 0.776532i | 0.987535 | − | 0.157397i | \(-0.0503101\pi\) |
0.357458 | + | 0.933929i | \(0.383643\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.33695 | − | 5.77977i | −0.108322 | − | 0.187619i | ||||
\(950\) | 5.59699 | + | 3.23142i | 0.181590 | + | 0.104841i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.9120 | + | 5.67151i | −0.418479 | + | 0.183815i | ||||
\(953\) | 44.7647 | 1.45007 | 0.725036 | − | 0.688711i | \(-0.241823\pi\) | ||||
0.725036 | + | 0.688711i | \(0.241823\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.2233 | + | 36.7598i | 0.686768 | + | 1.18952i | ||||
\(956\) | −3.72902 | − | 6.45884i | −0.120605 | − | 0.208894i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.9461 | −0.450577 | ||||||||
\(959\) | −9.79525 | − | 22.3002i | −0.316305 | − | 0.720111i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0994 | + | 40.0094i | −0.745142 | + | 1.29062i | ||||
\(962\) | 22.0277 | − | 12.7177i | 0.710202 | − | 0.410035i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.76722 | − | 3.32971i | −0.185750 | − | 0.107243i | ||||
\(965\) | −26.7812 | −0.862118 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.10584i | − | 0.0998771i | −0.998752 | − | 0.0499386i | \(-0.984097\pi\) | ||
0.998752 | − | 0.0499386i | \(-0.0159026\pi\) | |||||||
\(968\) | −7.65192 | − | 7.90241i | −0.245942 | − | 0.253993i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.6168 | + | 6.12962i | −0.340885 | + | 0.196810i | ||||
\(971\) | −9.39097 | − | 5.42188i | −0.301370 | − | 0.173996i | 0.341688 | − | 0.939813i | \(-0.389001\pi\) |
−0.643058 | + | 0.765817i | \(0.722335\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.7053 | + | 5.36571i | 1.56142 | + | 0.172017i | ||||
\(974\) | 15.5540 | 0.498383 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.39206 | − | 2.53576i | 0.140586 | − | 0.0811676i | ||||
\(977\) | 37.0400 | − | 21.3850i | 1.18501 | − | 0.684168i | 0.227844 | − | 0.973698i | \(-0.426832\pi\) |
0.957169 | + | 0.289530i | \(0.0934989\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.14571 | − | 6.90147i | 0.292298 | − | 0.220572i | ||||
\(980\) | 3.13794 | − | 14.0689i | 0.100238 | − | 0.449414i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.36337 | + | 12.7537i | −0.234975 | + | 0.406988i | ||||
\(983\) | −32.8275 | + | 18.9529i | −1.04703 | + | 0.604505i | −0.921817 | − | 0.387624i | \(-0.873296\pi\) |
−0.125216 | + | 0.992129i | \(0.539962\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.9573 | + | 19.0279i | 1.05011 | + | 0.606279i | ||||
\(986\) | 15.3357 | 0.488388 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 59.3795 | 1.88911 | ||||||||
\(989\) | −5.90836 | + | 10.2336i | −0.187875 | + | 0.325409i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.09256 | − | 1.89236i | −0.0347062 | − | 0.0601129i | 0.848151 | − | 0.529755i | \(-0.177716\pi\) |
−0.882857 | + | 0.469642i | \(0.844383\pi\) | |||||||
\(992\) | −4.39314 | + | 7.60915i | −0.139482 | + | 0.241591i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.17416 | − | 7.04718i | 0.164114 | − | 0.223523i | ||||
\(995\) | − | 23.2889i | − | 0.738309i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.6710 | + | 9.04768i | −0.496307 | + | 0.286543i | −0.727187 | − | 0.686439i | \(-0.759173\pi\) |
0.230880 | + | 0.972982i | \(0.425839\pi\) | |||||||
\(998\) | 3.51020 | + | 6.07984i | 0.111113 | + | 0.192454i | ||||
\(999\) | 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 | 1386.2.ba.a.989.5 | ✓ | 32 | |
3.2 | odd | 2 | 1386.2.ba.b.989.12 | yes | 32 | ||
7.4 | even | 3 | inner | 1386.2.ba.a.1187.12 | yes | 32 | |
11.10 | odd | 2 | 1386.2.ba.b.989.5 | yes | 32 | ||
21.11 | odd | 6 | 1386.2.ba.b.1187.5 | yes | 32 | ||
33.32 | even | 2 | inner | 1386.2.ba.a.989.12 | yes | 32 | |
77.32 | odd | 6 | 1386.2.ba.b.1187.12 | yes | 32 | ||
231.32 | even | 6 | inner | 1386.2.ba.a.1187.5 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.ba.a.989.5 | ✓ | 32 | 1.1 | even | 1 | trivial | |
1386.2.ba.a.989.12 | yes | 32 | 33.32 | even | 2 | inner | |
1386.2.ba.a.1187.5 | yes | 32 | 231.32 | even | 6 | inner | |
1386.2.ba.a.1187.12 | yes | 32 | 7.4 | even | 3 | inner | |
1386.2.ba.b.989.5 | yes | 32 | 11.10 | odd | 2 | ||
1386.2.ba.b.989.12 | yes | 32 | 3.2 | odd | 2 | ||
1386.2.ba.b.1187.5 | yes | 32 | 21.11 | odd | 6 | ||
1386.2.ba.b.1187.12 | yes | 32 | 77.32 | odd | 6 |