Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(118,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.118");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.m (of order \(4\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 118.9 | ||
Character | \(\chi\) | \(=\) | 525.118 |
Dual form | 525.2.m.c.307.9 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.11266 | − | 1.11266i | 0.786769 | − | 0.786769i | −0.194194 | − | 0.980963i | \(-0.562209\pi\) |
0.980963 | + | 0.194194i | \(0.0622091\pi\) | |||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | − | 0.476024i | − | 0.238012i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.57354i | 0.642394i | ||||||||
\(7\) | −2.09141 | − | 1.62049i | −0.790480 | − | 0.612488i | ||||
\(8\) | 1.69567 | + | 1.69567i | 0.599509 | + | 0.599509i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.20147 | 1.56830 | 0.784151 | − | 0.620569i | \(-0.213099\pi\) | ||||
0.784151 | + | 0.620569i | \(0.213099\pi\) | |||||||
\(12\) | 0.336600 | + | 0.336600i | 0.0971679 | + | 0.0971679i | ||||
\(13\) | 2.22988 | − | 2.22988i | 0.618456 | − | 0.618456i | −0.326679 | − | 0.945135i | \(-0.605930\pi\) |
0.945135 | + | 0.326679i | \(0.105930\pi\) | |||||||
\(14\) | −4.13009 | + | 0.523976i | −1.10381 | + | 0.140039i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.72545 | 1.18136 | ||||||||
\(17\) | 3.11335 | + | 3.11335i | 0.755099 | + | 0.755099i | 0.975426 | − | 0.220327i | \(-0.0707125\pi\) |
−0.220327 | + | 0.975426i | \(0.570713\pi\) | |||||||
\(18\) | −1.11266 | − | 1.11266i | −0.262256 | − | 0.262256i | ||||
\(19\) | 4.13009 | 0.947507 | 0.473753 | − | 0.880658i | \(-0.342899\pi\) | ||||
0.473753 | + | 0.880658i | \(0.342899\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.62471 | − | 0.332992i | 0.572759 | − | 0.0726649i | ||||
\(22\) | 5.78747 | − | 5.78747i | 1.23389 | − | 1.23389i | ||||
\(23\) | −2.97914 | − | 2.97914i | −0.621194 | − | 0.621194i | 0.324643 | − | 0.945837i | \(-0.394756\pi\) |
−0.945837 | + | 0.324643i | \(0.894756\pi\) | |||||||
\(24\) | −2.39804 | −0.489497 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 4.96218i | − | 0.973164i | ||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | −0.771392 | + | 0.995562i | −0.145779 | + | 0.188144i | ||||
\(29\) | − | 0.249425i | − | 0.0463171i | −0.999732 | − | 0.0231585i | \(-0.992628\pi\) | ||
0.999732 | − | 0.0231585i | \(-0.00737225\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.4242i | 1.87225i | 0.351669 | + | 0.936124i | \(0.385614\pi\) | ||||
−0.351669 | + | 0.936124i | \(0.614386\pi\) | |||||||
\(32\) | 1.86648 | − | 1.86648i | 0.329951 | − | 0.329951i | ||||
\(33\) | −3.67800 | + | 3.67800i | −0.640257 | + | 0.640257i | ||||
\(34\) | 6.92820 | 1.18818 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.476024 | −0.0793373 | ||||||||
\(37\) | −1.69567 | + | 1.69567i | −0.278766 | + | 0.278766i | −0.832616 | − | 0.553850i | \(-0.813158\pi\) |
0.553850 | + | 0.832616i | \(0.313158\pi\) | |||||||
\(38\) | 4.59538 | − | 4.59538i | 0.745469 | − | 0.745469i | ||||
\(39\) | 3.15352i | 0.504967i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.92820i | − | 1.08200i | −0.841021 | − | 0.541002i | \(-0.818045\pi\) | ||
0.841021 | − | 0.541002i | \(-0.181955\pi\) | |||||||
\(42\) | 2.54990 | − | 3.29092i | 0.393459 | − | 0.507800i | ||||
\(43\) | −4.39191 | − | 4.39191i | −0.669760 | − | 0.669760i | 0.287900 | − | 0.957660i | \(-0.407043\pi\) |
−0.957660 | + | 0.287900i | \(0.907043\pi\) | |||||||
\(44\) | − | 2.47602i | − | 0.373275i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.62954 | −0.977473 | ||||||||
\(47\) | −3.11335 | − | 3.11335i | −0.454129 | − | 0.454129i | 0.442593 | − | 0.896722i | \(-0.354059\pi\) |
−0.896722 | + | 0.442593i | \(0.854059\pi\) | |||||||
\(48\) | −3.34140 | + | 3.34140i | −0.482289 | + | 0.482289i | ||||
\(49\) | 1.74802 | + | 6.77823i | 0.249717 | + | 0.968319i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.40294 | −0.616536 | ||||||||
\(52\) | −1.06147 | − | 1.06147i | −0.147200 | − | 0.147200i | ||||
\(53\) | −4.89898 | − | 4.89898i | −0.672927 | − | 0.672927i | 0.285463 | − | 0.958390i | \(-0.407853\pi\) |
−0.958390 | + | 0.285463i | \(0.907853\pi\) | |||||||
\(54\) | 1.57354 | 0.214131 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.798528 | − | 6.29415i | −0.106708 | − | 0.841092i | ||||
\(57\) | −2.92041 | + | 2.92041i | −0.386818 | + | 0.386818i | ||||
\(58\) | −0.277525 | − | 0.277525i | −0.0364409 | − | 0.0364409i | ||||
\(59\) | −11.8904 | −1.54800 | −0.773998 | − | 0.633188i | \(-0.781746\pi\) | ||||
−0.773998 | + | 0.633188i | \(0.781746\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.16407i | − | 0.277080i | −0.990357 | − | 0.138540i | \(-0.955759\pi\) | ||
0.990357 | − | 0.138540i | \(-0.0442410\pi\) | |||||||
\(62\) | 11.5986 | + | 11.5986i | 1.47303 | + | 1.47303i | ||||
\(63\) | −1.62049 | + | 2.09141i | −0.204163 | + | 0.263493i | ||||
\(64\) | 5.29738i | 0.662172i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.18472i | 1.00747i | ||||||||
\(67\) | −2.50822 | + | 2.50822i | −0.306428 | + | 0.306428i | −0.843522 | − | 0.537094i | \(-0.819522\pi\) |
0.537094 | + | 0.843522i | \(0.319522\pi\) | |||||||
\(68\) | 1.48203 | − | 1.48203i | 0.179722 | − | 0.179722i | ||||
\(69\) | 4.21314 | 0.507203 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.798528 | −0.0947678 | −0.0473839 | − | 0.998877i | \(-0.515088\pi\) | ||||
−0.0473839 | + | 0.998877i | \(0.515088\pi\) | |||||||
\(72\) | 1.69567 | − | 1.69567i | 0.199836 | − | 0.199836i | ||||
\(73\) | 5.94178 | − | 5.94178i | 0.695433 | − | 0.695433i | −0.267989 | − | 0.963422i | \(-0.586359\pi\) |
0.963422 | + | 0.267989i | \(0.0863592\pi\) | |||||||
\(74\) | 3.77340i | 0.438649i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.96602i | − | 0.225518i | ||||||
\(77\) | −10.8784 | − | 8.42894i | −1.23971 | − | 0.960567i | ||||
\(78\) | 3.50879 | + | 3.50879i | 0.397293 | + | 0.397293i | ||||
\(79\) | − | 5.29738i | − | 0.596002i | −0.954566 | − | 0.298001i | \(-0.903680\pi\) | ||
0.954566 | − | 0.298001i | \(-0.0963198\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −7.70873 | − | 7.70873i | −0.851287 | − | 0.851287i | ||||
\(83\) | 4.59538 | − | 4.59538i | 0.504409 | − | 0.504409i | −0.408396 | − | 0.912805i | \(-0.633912\pi\) |
0.912805 | + | 0.408396i | \(0.133912\pi\) | |||||||
\(84\) | −0.158512 | − | 1.24943i | −0.0172951 | − | 0.136323i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.77340 | −1.05389 | ||||||||
\(87\) | 0.176370 | + | 0.176370i | 0.0189089 | + | 0.0189089i | ||||
\(88\) | 8.81997 | + | 8.81997i | 0.940212 | + | 0.940212i | ||||
\(89\) | −6.29415 | −0.667179 | −0.333590 | − | 0.942718i | \(-0.608260\pi\) | ||||
−0.333590 | + | 0.942718i | \(0.608260\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.27708 | + | 1.05010i | −0.867674 | + | 0.110080i | ||||
\(92\) | −1.41814 | + | 1.41814i | −0.147852 | + | 0.147852i | ||||
\(93\) | −7.37105 | − | 7.37105i | −0.764342 | − | 0.764342i | ||||
\(94\) | −6.92820 | −0.714590 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.63960i | 0.269404i | ||||||||
\(97\) | 12.1972 | + | 12.1972i | 1.23844 | + | 1.23844i | 0.960640 | + | 0.277797i | \(0.0896041\pi\) |
0.277797 | + | 0.960640i | \(0.410396\pi\) | |||||||
\(98\) | 9.48682 | + | 5.59692i | 0.958313 | + | 0.565374i | ||||
\(99\) | − | 5.20147i | − | 0.522768i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.29415i | 0.626292i | 0.949705 | + | 0.313146i | \(0.101383\pi\) | ||||
−0.949705 | + | 0.313146i | \(0.898617\pi\) | |||||||
\(102\) | −4.89898 | + | 4.89898i | −0.485071 | + | 0.485071i | ||||
\(103\) | −10.5372 | + | 10.5372i | −1.03826 | + | 1.03826i | −0.0390188 | + | 0.999238i | \(0.512423\pi\) |
−0.999238 | + | 0.0390188i | \(0.987577\pi\) | |||||||
\(104\) | 7.56225 | 0.741540 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.9018 | −1.05888 | ||||||||
\(107\) | −10.8573 | + | 10.8573i | −1.04961 | + | 1.04961i | −0.0509079 | + | 0.998703i | \(0.516212\pi\) |
−0.998703 | + | 0.0509079i | \(0.983788\pi\) | |||||||
\(108\) | 0.336600 | − | 0.336600i | 0.0323893 | − | 0.0323893i | ||||
\(109\) | − | 15.9018i | − | 1.52312i | −0.648097 | − | 0.761558i | \(-0.724435\pi\) | ||
0.648097 | − | 0.761558i | \(-0.275565\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.39804i | − | 0.227611i | ||||||
\(112\) | −9.88287 | − | 7.65755i | −0.933843 | − | 0.723570i | ||||
\(113\) | 8.47834 | + | 8.47834i | 0.797575 | + | 0.797575i | 0.982713 | − | 0.185138i | \(-0.0592731\pi\) |
−0.185138 | + | 0.982713i | \(0.559273\pi\) | |||||||
\(114\) | 6.49885i | 0.608673i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.118732 | −0.0110240 | ||||||||
\(117\) | −2.22988 | − | 2.22988i | −0.206152 | − | 0.206152i | ||||
\(118\) | −13.2300 | + | 13.2300i | −1.21792 | + | 1.21792i | ||||
\(119\) | −1.46615 | − | 11.5565i | −0.134401 | − | 1.05938i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.0553 | 1.45957 | ||||||||
\(122\) | −2.40787 | − | 2.40787i | −0.217998 | − | 0.217998i | ||||
\(123\) | 4.89898 | + | 4.89898i | 0.441726 | + | 0.441726i | ||||
\(124\) | 4.96218 | 0.445617 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.523976 | + | 4.13009i | 0.0466795 | + | 0.367937i | ||||
\(127\) | −12.3288 | + | 12.3288i | −1.09400 | + | 1.09400i | −0.0989036 | + | 0.995097i | \(0.531534\pi\) |
−0.995097 | + | 0.0989036i | \(0.968466\pi\) | |||||||
\(128\) | 9.62714 | + | 9.62714i | 0.850927 | + | 0.850927i | ||||
\(129\) | 6.21110 | 0.546857 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 15.8863i | − | 1.38799i | −0.719979 | − | 0.693996i | \(-0.755848\pi\) | ||
0.719979 | − | 0.693996i | \(-0.244152\pi\) | |||||||
\(132\) | 1.75081 | + | 1.75081i | 0.152389 | + | 0.152389i | ||||
\(133\) | −8.63772 | − | 6.69277i | −0.748985 | − | 0.580337i | ||||
\(134\) | 5.58159i | 0.482176i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.5584i | 0.905377i | ||||||||
\(137\) | 3.95713 | − | 3.95713i | 0.338081 | − | 0.338081i | −0.517564 | − | 0.855645i | \(-0.673161\pi\) |
0.855645 | + | 0.517564i | \(0.173161\pi\) | |||||||
\(138\) | 4.68779 | − | 4.68779i | 0.399052 | − | 0.399052i | ||||
\(139\) | 11.8904 | 1.00853 | 0.504265 | − | 0.863549i | \(-0.331764\pi\) | ||||
0.504265 | + | 0.863549i | \(0.331764\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.40294 | 0.370795 | ||||||||
\(142\) | −0.888490 | + | 0.888490i | −0.0745604 | + | 0.0745604i | ||||
\(143\) | 11.5986 | − | 11.5986i | 0.969926 | − | 0.969926i | ||||
\(144\) | − | 4.72545i | − | 0.393787i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 13.2224i | − | 1.09429i | ||||||
\(147\) | −6.02897 | − | 3.55690i | −0.497261 | − | 0.293368i | ||||
\(148\) | 0.807178 | + | 0.807178i | 0.0663496 | + | 0.0663496i | ||||
\(149\) | 0.249425i | 0.0204337i | 0.999948 | + | 0.0102169i | \(0.00325218\pi\) | ||||
−0.999948 | + | 0.0102169i | \(0.996748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.35499 | 0.191647 | 0.0958233 | − | 0.995398i | \(-0.469452\pi\) | ||||
0.0958233 | + | 0.995398i | \(0.469452\pi\) | |||||||
\(152\) | 7.00325 | + | 7.00325i | 0.568039 | + | 0.568039i | ||||
\(153\) | 3.11335 | − | 3.11335i | 0.251700 | − | 0.251700i | ||||
\(154\) | −21.4825 | + | 2.72545i | −1.73111 | + | 0.219623i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.50115 | 0.120188 | ||||||||
\(157\) | 5.34323 | + | 5.34323i | 0.426436 | + | 0.426436i | 0.887412 | − | 0.460976i | \(-0.152501\pi\) |
−0.460976 | + | 0.887412i | \(0.652501\pi\) | |||||||
\(158\) | −5.89418 | − | 5.89418i | −0.468916 | − | 0.468916i | ||||
\(159\) | 6.92820 | 0.549442 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.40294 | + | 11.0583i | 0.110568 | + | 0.871515i | ||||
\(162\) | −1.11266 | + | 1.11266i | −0.0874188 | + | 0.0874188i | ||||
\(163\) | 15.2130 | + | 15.2130i | 1.19158 | + | 1.19158i | 0.976625 | + | 0.214951i | \(0.0689593\pi\) |
0.214951 | + | 0.976625i | \(0.431041\pi\) | |||||||
\(164\) | −3.29799 | −0.257530 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 10.2262i | − | 0.793706i | ||||||
\(167\) | −4.74468 | − | 4.74468i | −0.367154 | − | 0.367154i | 0.499284 | − | 0.866438i | \(-0.333596\pi\) |
−0.866438 | + | 0.499284i | \(0.833596\pi\) | |||||||
\(168\) | 5.01528 | + | 3.88599i | 0.386938 | + | 0.299811i | ||||
\(169\) | 3.05531i | 0.235024i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 4.13009i | − | 0.315836i | ||||||
\(172\) | −2.09065 | + | 2.09065i | −0.159411 | + | 0.159411i | ||||
\(173\) | −6.07741 | + | 6.07741i | −0.462057 | + | 0.462057i | −0.899329 | − | 0.437272i | \(-0.855945\pi\) |
0.437272 | + | 0.899329i | \(0.355945\pi\) | |||||||
\(174\) | 0.392480 | 0.0297538 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 24.5793 | 1.85273 | ||||||||
\(177\) | 8.40777 | − | 8.40777i | 0.631967 | − | 0.631967i | ||||
\(178\) | −7.00325 | + | 7.00325i | −0.524916 | + | 0.524916i | ||||
\(179\) | − | 2.30704i | − | 0.172436i | −0.996276 | − | 0.0862181i | \(-0.972522\pi\) | ||
0.996276 | − | 0.0862181i | \(-0.0274782\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.134178i | − | 0.00997334i | −0.999988 | − | 0.00498667i | \(-0.998413\pi\) | ||
0.999988 | − | 0.00498667i | \(-0.00158731\pi\) | |||||||
\(182\) | −8.04117 | + | 10.3780i | −0.596052 | + | 0.769267i | ||||
\(183\) | 1.53023 | + | 1.53023i | 0.113118 | + | 0.113118i | ||||
\(184\) | − | 10.1033i | − | 0.744823i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −16.4029 | −1.20272 | ||||||||
\(187\) | 16.1940 | + | 16.1940i | 1.18422 | + | 1.18422i | ||||
\(188\) | −1.48203 | + | 1.48203i | −0.108088 | + | 0.108088i | ||||
\(189\) | −0.332992 | − | 2.62471i | −0.0242216 | − | 0.190920i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −27.3047 | −1.97570 | −0.987851 | − | 0.155405i | \(-0.950332\pi\) | ||||
−0.987851 | + | 0.155405i | \(0.950332\pi\) | |||||||
\(192\) | −3.74581 | − | 3.74581i | −0.270331 | − | 0.270331i | ||||
\(193\) | −3.67423 | − | 3.67423i | −0.264477 | − | 0.264477i | 0.562393 | − | 0.826870i | \(-0.309881\pi\) |
−0.826870 | + | 0.562393i | \(0.809881\pi\) | |||||||
\(194\) | 27.1426 | 1.94873 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.22660 | − | 0.832098i | 0.230471 | − | 0.0594356i | ||||
\(197\) | 11.9871 | − | 11.9871i | 0.854048 | − | 0.854048i | −0.136581 | − | 0.990629i | \(-0.543611\pi\) |
0.990629 | + | 0.136581i | \(0.0436115\pi\) | |||||||
\(198\) | −5.78747 | − | 5.78747i | −0.411298 | − | 0.411298i | ||||
\(199\) | −24.2806 | −1.72121 | −0.860605 | − | 0.509274i | \(-0.829914\pi\) | ||||
−0.860605 | + | 0.509274i | \(0.829914\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 3.54716i | − | 0.250197i | ||||||
\(202\) | 7.00325 | + | 7.00325i | 0.492747 | + | 0.492747i | ||||
\(203\) | −0.404191 | + | 0.521651i | −0.0283687 | + | 0.0366127i | ||||
\(204\) | 2.09591i | 0.146743i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 23.4485i | 1.63374i | ||||||||
\(207\) | −2.97914 | + | 2.97914i | −0.207065 | + | 0.207065i | ||||
\(208\) | 10.5372 | − | 10.5372i | 0.730621 | − | 0.730621i | ||||
\(209\) | 21.4825 | 1.48598 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.0553 | −1.79372 | −0.896861 | − | 0.442313i | \(-0.854158\pi\) | ||||
−0.896861 | + | 0.442313i | \(0.854158\pi\) | |||||||
\(212\) | −2.33203 | + | 2.33203i | −0.160164 | + | 0.160164i | ||||
\(213\) | 0.564644 | − | 0.564644i | 0.0386888 | − | 0.0386888i | ||||
\(214\) | 24.1609i | 1.65160i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.39804i | 0.163166i | ||||||||
\(217\) | 16.8924 | − | 21.8014i | 1.14673 | − | 1.47998i | ||||
\(218\) | −17.6933 | − | 17.6933i | −1.19834 | − | 1.19834i | ||||
\(219\) | 8.40294i | 0.567818i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.8848 | 0.933991 | ||||||||
\(222\) | −2.66820 | − | 2.66820i | −0.179078 | − | 0.179078i | ||||
\(223\) | 3.99683 | − | 3.99683i | 0.267647 | − | 0.267647i | −0.560504 | − | 0.828152i | \(-0.689393\pi\) |
0.828152 | + | 0.560504i | \(0.189393\pi\) | |||||||
\(224\) | −6.92820 | + | 0.878968i | −0.462910 | + | 0.0587285i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.8670 | 1.25501 | ||||||||
\(227\) | −16.1940 | − | 16.1940i | −1.07483 | − | 1.07483i | −0.996963 | − | 0.0778711i | \(-0.975188\pi\) |
−0.0778711 | − | 0.996963i | \(-0.524812\pi\) | |||||||
\(228\) | 1.39019 | + | 1.39019i | 0.0920673 | + | 0.0920673i | ||||
\(229\) | −11.7562 | −0.776872 | −0.388436 | − | 0.921476i | \(-0.626985\pi\) | ||||
−0.388436 | + | 0.921476i | \(0.626985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.6524 | − | 1.73205i | 0.898260 | − | 0.113961i | ||||
\(232\) | 0.422942 | − | 0.422942i | 0.0277675 | − | 0.0277675i | ||||
\(233\) | −12.4806 | − | 12.4806i | −0.817634 | − | 0.817634i | 0.168131 | − | 0.985765i | \(-0.446227\pi\) |
−0.985765 | + | 0.168131i | \(0.946227\pi\) | |||||||
\(234\) | −4.96218 | −0.324388 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.66011i | 0.368441i | ||||||||
\(237\) | 3.74581 | + | 3.74581i | 0.243317 | + | 0.243317i | ||||
\(238\) | −14.4897 | − | 11.2271i | −0.939230 | − | 0.727744i | ||||
\(239\) | − | 8.80589i | − | 0.569606i | −0.958586 | − | 0.284803i | \(-0.908072\pi\) | ||
0.958586 | − | 0.284803i | \(-0.0919281\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 22.3146i | − | 1.43741i | −0.695314 | − | 0.718706i | \(-0.744735\pi\) | ||
0.695314 | − | 0.718706i | \(-0.255265\pi\) | |||||||
\(242\) | 17.8641 | − | 17.8641i | 1.14835 | − | 1.14835i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −1.03015 | −0.0659484 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.9018 | 0.695073 | ||||||||
\(247\) | 9.20958 | − | 9.20958i | 0.585991 | − | 0.585991i | ||||
\(248\) | −17.6760 | + | 17.6760i | −1.12243 | + | 1.12243i | ||||
\(249\) | 6.49885i | 0.411848i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.8863i | 1.00273i | 0.865235 | + | 0.501367i | \(0.167169\pi\) | ||||
−0.865235 | + | 0.501367i | \(0.832831\pi\) | |||||||
\(252\) | 0.995562 | + | 0.771392i | 0.0627145 | + | 0.0485931i | ||||
\(253\) | −15.4959 | − | 15.4959i | −0.974220 | − | 0.974220i | ||||
\(254\) | 27.4354i | 1.72145i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.8287 | 0.676795 | ||||||||
\(257\) | −2.25858 | − | 2.25858i | −0.140886 | − | 0.140886i | 0.633146 | − | 0.774032i | \(-0.281763\pi\) |
−0.774032 | + | 0.633146i | \(0.781763\pi\) | |||||||
\(258\) | 6.91084 | − | 6.91084i | 0.430250 | − | 0.430250i | ||||
\(259\) | 6.29415 | − | 0.798528i | 0.391100 | − | 0.0496181i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.249425 | −0.0154390 | ||||||||
\(262\) | −17.6760 | − | 17.6760i | −1.09203 | − | 1.09203i | ||||
\(263\) | −2.03730 | − | 2.03730i | −0.125625 | − | 0.125625i | 0.641499 | − | 0.767124i | \(-0.278313\pi\) |
−0.767124 | + | 0.641499i | \(0.778313\pi\) | |||||||
\(264\) | −12.4733 | −0.767680 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −17.0576 | + | 2.16407i | −1.04587 | + | 0.132688i | ||||
\(267\) | 4.45064 | − | 4.45064i | 0.272375 | − | 0.272375i | ||||
\(268\) | 1.19397 | + | 1.19397i | 0.0729334 | + | 0.0729334i | ||||
\(269\) | −15.1884 | −0.926052 | −0.463026 | − | 0.886345i | \(-0.653236\pi\) | ||||
−0.463026 | + | 0.886345i | \(0.653236\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.5543i | 0.884112i | 0.896987 | + | 0.442056i | \(0.145751\pi\) | ||||
−0.896987 | + | 0.442056i | \(0.854249\pi\) | |||||||
\(272\) | 14.7120 | + | 14.7120i | 0.892045 | + | 0.892045i | ||||
\(273\) | 5.11025 | − | 6.59531i | 0.309286 | − | 0.399166i | ||||
\(274\) | − | 8.80589i | − | 0.531983i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 2.00556i | − | 0.120720i | ||||||
\(277\) | −0.353463 | + | 0.353463i | −0.0212375 | + | 0.0212375i | −0.717646 | − | 0.696408i | \(-0.754780\pi\) |
0.696408 | + | 0.717646i | \(0.254780\pi\) | |||||||
\(278\) | 13.2300 | − | 13.2300i | 0.793480 | − | 0.793480i | ||||
\(279\) | 10.4242 | 0.624083 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.03829 | 0.360214 | 0.180107 | − | 0.983647i | \(-0.442356\pi\) | ||||
0.180107 | + | 0.983647i | \(0.442356\pi\) | |||||||
\(282\) | 4.89898 | − | 4.89898i | 0.291730 | − | 0.291730i | ||||
\(283\) | 1.37510 | − | 1.37510i | 0.0817412 | − | 0.0817412i | −0.665054 | − | 0.746795i | \(-0.731591\pi\) |
0.746795 | + | 0.665054i | \(0.231591\pi\) | |||||||
\(284\) | 0.380118i | 0.0225559i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 25.8107i | − | 1.52622i | ||||||
\(287\) | −11.2271 | + | 14.4897i | −0.662714 | + | 0.855302i | ||||
\(288\) | −1.86648 | − | 1.86648i | −0.109984 | − | 0.109984i | ||||
\(289\) | 2.38592i | 0.140348i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.2494 | −1.01118 | ||||||||
\(292\) | −2.82843 | − | 2.82843i | −0.165521 | − | 0.165521i | ||||
\(293\) | −11.5986 | + | 11.5986i | −0.677599 | + | 0.677599i | −0.959456 | − | 0.281857i | \(-0.909050\pi\) |
0.281857 | + | 0.959456i | \(0.409050\pi\) | |||||||
\(294\) | −10.6658 | + | 2.75057i | −0.622043 | + | 0.160417i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.75057 | −0.334245 | ||||||||
\(297\) | 3.67800 | + | 3.67800i | 0.213419 | + | 0.213419i | ||||
\(298\) | 0.277525 | + | 0.277525i | 0.0160766 | + | 0.0160766i | ||||
\(299\) | −13.2862 | −0.768362 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.06825 | + | 16.3023i | 0.119212 | + | 0.939652i | ||||
\(302\) | 2.62030 | − | 2.62030i | 0.150782 | − | 0.150782i | ||||
\(303\) | −4.45064 | − | 4.45064i | −0.255683 | − | 0.255683i | ||||
\(304\) | 19.5165 | 1.11935 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 6.92820i | − | 0.396059i | ||||||
\(307\) | −6.82526 | − | 6.82526i | −0.389538 | − | 0.389538i | 0.484985 | − | 0.874523i | \(-0.338825\pi\) |
−0.874523 | + | 0.484985i | \(0.838825\pi\) | |||||||
\(308\) | −4.01237 | + | 5.17839i | −0.228626 | + | 0.295066i | ||||
\(309\) | − | 14.9018i | − | 0.847733i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 24.1465i | − | 1.36922i | −0.728909 | − | 0.684610i | \(-0.759972\pi\) | ||
0.728909 | − | 0.684610i | \(-0.240028\pi\) | |||||||
\(312\) | −5.34732 | + | 5.34732i | −0.302732 | + | 0.302732i | ||||
\(313\) | −0.598552 | + | 0.598552i | −0.0338322 | + | 0.0338322i | −0.723820 | − | 0.689988i | \(-0.757616\pi\) |
0.689988 | + | 0.723820i | \(0.257616\pi\) | |||||||
\(314\) | 11.8904 | 0.671013 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.52168 | −0.141855 | ||||||||
\(317\) | 13.5399 | − | 13.5399i | 0.760479 | − | 0.760479i | −0.215930 | − | 0.976409i | \(-0.569278\pi\) |
0.976409 | + | 0.215930i | \(0.0692783\pi\) | |||||||
\(318\) | 7.70873 | − | 7.70873i | 0.432284 | − | 0.432284i | ||||
\(319\) | − | 1.29738i | − | 0.0726392i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 15.3545i | − | 0.857004i | ||||||
\(322\) | 13.8651 | + | 10.7431i | 0.772673 | + | 0.598690i | ||||
\(323\) | 12.8584 | + | 12.8584i | 0.715461 | + | 0.715461i | ||||
\(324\) | 0.476024i | 0.0264458i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 33.8538 | 1.87499 | ||||||||
\(327\) | 11.2443 | + | 11.2443i | 0.621809 | + | 0.621809i | ||||
\(328\) | 11.7479 | − | 11.7479i | 0.648671 | − | 0.648671i | ||||
\(329\) | 1.46615 | + | 11.5565i | 0.0808313 | + | 0.637128i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.4103 | 1.23178 | 0.615891 | − | 0.787831i | \(-0.288796\pi\) | ||||
0.615891 | + | 0.787831i | \(0.288796\pi\) | |||||||
\(332\) | −2.18751 | − | 2.18751i | −0.120055 | − | 0.120055i | ||||
\(333\) | 1.69567 | + | 1.69567i | 0.0929220 | + | 0.0929220i | ||||
\(334\) | −10.5584 | −0.577731 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.4029 | − | 1.57354i | 0.676636 | − | 0.0858436i | ||||
\(337\) | 0.588382 | − | 0.588382i | 0.0320512 | − | 0.0320512i | −0.690900 | − | 0.722951i | \(-0.742785\pi\) |
0.722951 | + | 0.690900i | \(0.242785\pi\) | |||||||
\(338\) | 3.39953 | + | 3.39953i | 0.184910 | + | 0.184910i | ||||
\(339\) | −11.9902 | −0.651217 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 54.2214i | 2.93625i | ||||||||
\(342\) | −4.59538 | − | 4.59538i | −0.248490 | − | 0.248490i | ||||
\(343\) | 7.32823 | − | 17.0087i | 0.395687 | − | 0.918385i | ||||
\(344\) | − | 14.8944i | − | 0.803054i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.5242i | 0.727064i | ||||||||
\(347\) | 21.0674 | − | 21.0674i | 1.13096 | − | 1.13096i | 0.140940 | − | 0.990018i | \(-0.454988\pi\) |
0.990018 | − | 0.140940i | \(-0.0450124\pi\) | |||||||
\(348\) | 0.0839564 | − | 0.0839564i | 0.00450053 | − | 0.00450053i | ||||
\(349\) | 23.1467 | 1.23902 | 0.619508 | − | 0.784990i | \(-0.287332\pi\) | ||||
0.619508 | + | 0.784990i | \(0.287332\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.15352 | 0.168322 | ||||||||
\(352\) | 9.70846 | − | 9.70846i | 0.517462 | − | 0.517462i | ||||
\(353\) | −10.8221 | + | 10.8221i | −0.576001 | + | 0.576001i | −0.933799 | − | 0.357798i | \(-0.883528\pi\) |
0.357798 | + | 0.933799i | \(0.383528\pi\) | |||||||
\(354\) | − | 18.7100i | − | 0.994424i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.99617i | 0.158796i | ||||||||
\(357\) | 9.20838 | + | 7.13493i | 0.487359 | + | 0.377621i | ||||
\(358\) | −2.56695 | − | 2.56695i | −0.135668 | − | 0.135668i | ||||
\(359\) | − | 12.7985i | − | 0.675480i | −0.941239 | − | 0.337740i | \(-0.890337\pi\) | ||
0.941239 | − | 0.337740i | \(-0.109663\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.94239 | −0.102231 | ||||||||
\(362\) | −0.149294 | − | 0.149294i | −0.00784671 | − | 0.00784671i | ||||
\(363\) | −11.3528 | + | 11.3528i | −0.595869 | + | 0.595869i | ||||
\(364\) | 0.499871 | + | 3.94009i | 0.0262004 | + | 0.206517i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.40524 | 0.177995 | ||||||||
\(367\) | −4.14612 | − | 4.14612i | −0.216426 | − | 0.216426i | 0.590565 | − | 0.806990i | \(-0.298905\pi\) |
−0.806990 | + | 0.590565i | \(0.798905\pi\) | |||||||
\(368\) | −14.0778 | − | 14.0778i | −0.733855 | − | 0.733855i | ||||
\(369\) | −6.92820 | −0.360668 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.30704 | + | 18.1845i | 0.119776 | + | 0.944094i | ||||
\(372\) | −3.50879 | + | 3.50879i | −0.181923 | + | 0.181923i | ||||
\(373\) | 22.8670 | + | 22.8670i | 1.18401 | + | 1.18401i | 0.978697 | + | 0.205310i | \(0.0658203\pi\) |
0.205310 | + | 0.978697i | \(0.434180\pi\) | |||||||
\(374\) | 36.0369 | 1.86342 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 10.5584i | − | 0.544509i | ||||||
\(377\) | −0.556187 | − | 0.556187i | −0.0286451 | − | 0.0286451i | ||||
\(378\) | −3.29092 | − | 2.54990i | −0.169267 | − | 0.131153i | ||||
\(379\) | 21.3527i | 1.09681i | 0.836212 | + | 0.548407i | \(0.184766\pi\) | ||||
−0.836212 | + | 0.548407i | \(0.815234\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 17.4355i | − | 0.893248i | ||||||
\(382\) | −30.3809 | + | 30.3809i | −1.55442 | + | 1.55442i | ||||
\(383\) | −21.7152 | + | 21.7152i | −1.10960 | + | 1.10960i | −0.116394 | + | 0.993203i | \(0.537133\pi\) |
−0.993203 | + | 0.116394i | \(0.962867\pi\) | |||||||
\(384\) | −13.6148 | −0.694779 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.17635 | −0.416165 | ||||||||
\(387\) | −4.39191 | + | 4.39191i | −0.223253 | + | 0.223253i | ||||
\(388\) | 5.80615 | − | 5.80615i | 0.294763 | − | 0.294763i | ||||
\(389\) | 28.0530i | 1.42234i | 0.703018 | + | 0.711172i | \(0.251835\pi\) | ||||
−0.703018 | + | 0.711172i | \(0.748165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 18.5502i | − | 0.938126i | ||||||
\(392\) | −8.52957 | + | 14.4577i | −0.430808 | + | 0.730223i | ||||
\(393\) | 11.2333 | + | 11.2333i | 0.566645 | + | 0.566645i | ||||
\(394\) | − | 26.6752i | − | 1.34388i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.47602 | −0.124425 | ||||||||
\(397\) | −1.37510 | − | 1.37510i | −0.0690143 | − | 0.0690143i | 0.671757 | − | 0.740771i | \(-0.265540\pi\) |
−0.740771 | + | 0.671757i | \(0.765540\pi\) | |||||||
\(398\) | −27.0161 | + | 27.0161i | −1.35419 | + | 1.35419i | ||||
\(399\) | 10.8403 | − | 1.37529i | 0.542693 | − | 0.0688505i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.15352 | −0.207417 | −0.103708 | − | 0.994608i | \(-0.533071\pi\) | ||||
−0.103708 | + | 0.994608i | \(0.533071\pi\) | |||||||
\(402\) | −3.94678 | − | 3.94678i | −0.196848 | − | 0.196848i | ||||
\(403\) | 23.2448 | + | 23.2448i | 1.15790 | + | 1.15790i | ||||
\(404\) | 2.99617 | 0.149065 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.130693 | + | 1.03015i | 0.00648618 | + | 0.0511254i | ||||
\(407\) | −8.81997 | + | 8.81997i | −0.437189 | + | 0.437189i | ||||
\(408\) | −7.46593 | − | 7.46593i | −0.369619 | − | 0.369619i | ||||
\(409\) | 6.79403 | 0.335943 | 0.167971 | − | 0.985792i | \(-0.446278\pi\) | ||||
0.167971 | + | 0.985792i | \(0.446278\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.59623i | 0.276042i | ||||||||
\(412\) | 5.01594 | + | 5.01594i | 0.247117 | + | 0.247117i | ||||
\(413\) | 24.8677 | + | 19.2683i | 1.22366 | + | 0.948129i | ||||
\(414\) | 6.62954i | 0.325824i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 8.32404i | − | 0.408120i | ||||||
\(417\) | −8.40777 | + | 8.40777i | −0.411730 | + | 0.411730i | ||||
\(418\) | 23.9027 | − | 23.9027i | 1.16912 | − | 1.16912i | ||||
\(419\) | −23.4485 | −1.14554 | −0.572768 | − | 0.819717i | \(-0.694131\pi\) | ||||
−0.572768 | + | 0.819717i | \(0.694131\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.9594 | 0.534129 | 0.267064 | − | 0.963679i | \(-0.413946\pi\) | ||||
0.267064 | + | 0.963679i | \(0.413946\pi\) | |||||||
\(422\) | −28.9907 | + | 28.9907i | −1.41125 | + | 1.41125i | ||||
\(423\) | −3.11335 | + | 3.11335i | −0.151376 | + | 0.151376i | ||||
\(424\) | − | 16.6141i | − | 0.806851i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 1.25651i | − | 0.0608783i | ||||||
\(427\) | −3.50685 | + | 4.52596i | −0.169708 | + | 0.219027i | ||||
\(428\) | 5.16831 | + | 5.16831i | 0.249820 | + | 0.249820i | ||||
\(429\) | 16.4029i | 0.791942i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.30474 | −0.159184 | −0.0795919 | − | 0.996828i | \(-0.525362\pi\) | ||||
−0.0795919 | + | 0.996828i | \(0.525362\pi\) | |||||||
\(432\) | 3.34140 | + | 3.34140i | 0.160763 | + | 0.160763i | ||||
\(433\) | 12.3328 | − | 12.3328i | 0.592677 | − | 0.592677i | −0.345676 | − | 0.938354i | \(-0.612351\pi\) |
0.938354 | + | 0.345676i | \(0.112351\pi\) | |||||||
\(434\) | −5.46206 | − | 43.0530i | −0.262187 | − | 2.06661i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.56963 | −0.362520 | ||||||||
\(437\) | −12.3041 | − | 12.3041i | −0.588586 | − | 0.588586i | ||||
\(438\) | 9.34962 | + | 9.34962i | 0.446742 | + | 0.446742i | ||||
\(439\) | 33.1749 | 1.58335 | 0.791675 | − | 0.610942i | \(-0.209209\pi\) | ||||
0.791675 | + | 0.610942i | \(0.209209\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.77823 | − | 1.74802i | 0.322773 | − | 0.0832390i | ||||
\(442\) | 15.4490 | − | 15.4490i | 0.734835 | − | 0.734835i | ||||
\(443\) | 14.8596 | + | 14.8596i | 0.705999 | + | 0.705999i | 0.965691 | − | 0.259692i | \(-0.0836211\pi\) |
−0.259692 | + | 0.965691i | \(0.583621\pi\) | |||||||
\(444\) | −1.14152 | −0.0541742 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 8.89422i | − | 0.421154i | ||||||
\(447\) | −0.176370 | − | 0.176370i | −0.00834202 | − | 0.00834202i | ||||
\(448\) | 8.58435 | − | 11.0790i | 0.405573 | − | 0.523434i | ||||
\(449\) | 7.84648i | 0.370298i | 0.982710 | + | 0.185149i | \(0.0592768\pi\) | ||||
−0.982710 | + | 0.185149i | \(0.940723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 36.0369i | − | 1.69691i | ||||||
\(452\) | 4.03589 | − | 4.03589i | 0.189832 | − | 0.189832i | ||||
\(453\) | −1.66523 | + | 1.66523i | −0.0782394 | + | 0.0782394i | ||||
\(454\) | −36.0369 | −1.69129 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.90409 | −0.463802 | ||||||||
\(457\) | −6.52235 | + | 6.52235i | −0.305103 | + | 0.305103i | −0.843006 | − | 0.537904i | \(-0.819216\pi\) |
0.537904 | + | 0.843006i | \(0.319216\pi\) | |||||||
\(458\) | −13.0807 | + | 13.0807i | −0.611219 | + | 0.611219i | ||||
\(459\) | 4.40294i | 0.205512i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.966276i | 0.0450039i | 0.999747 | + | 0.0225020i | \(0.00716320\pi\) | ||||
−0.999747 | + | 0.0225020i | \(0.992837\pi\) | |||||||
\(462\) | 13.2633 | − | 17.1176i | 0.617063 | − | 0.796384i | ||||
\(463\) | 7.79681 | + | 7.79681i | 0.362348 | + | 0.362348i | 0.864677 | − | 0.502328i | \(-0.167523\pi\) |
−0.502328 | + | 0.864677i | \(0.667523\pi\) | |||||||
\(464\) | − | 1.17865i | − | 0.0547173i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.7734 | −1.28658 | ||||||||
\(467\) | 19.3074 | + | 19.3074i | 0.893438 | + | 0.893438i | 0.994845 | − | 0.101407i | \(-0.0323343\pi\) |
−0.101407 | + | 0.994845i | \(0.532334\pi\) | |||||||
\(468\) | −1.06147 | + | 1.06147i | −0.0490666 | + | 0.0490666i | ||||
\(469\) | 9.31027 | − | 1.18118i | 0.429908 | − | 0.0545417i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.55646 | −0.348183 | ||||||||
\(472\) | −20.1621 | − | 20.1621i | −0.928038 | − | 0.928038i | ||||
\(473\) | −22.8444 | − | 22.8444i | −1.05039 | − | 1.05039i | ||||
\(474\) | 8.33563 | 0.382868 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.50115 | + | 0.697921i | −0.252145 | + | 0.0319891i | ||||
\(477\) | −4.89898 | + | 4.89898i | −0.224309 | + | 0.224309i | ||||
\(478\) | −9.79796 | − | 9.79796i | −0.448148 | − | 0.448148i | ||||
\(479\) | 4.62996 | 0.211548 | 0.105774 | − | 0.994390i | \(-0.466268\pi\) | ||||
0.105774 | + | 0.994390i | \(0.466268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.56225i | 0.344809i | ||||||||
\(482\) | −24.8286 | − | 24.8286i | −1.13091 | − | 1.13091i | ||||
\(483\) | −8.81142 | − | 6.82736i | −0.400934 | − | 0.310656i | ||||
\(484\) | − | 7.64271i | − | 0.347396i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.57354i | − | 0.0713772i | ||||||
\(487\) | −7.85554 | + | 7.85554i | −0.355968 | + | 0.355968i | −0.862325 | − | 0.506356i | \(-0.830992\pi\) |
0.506356 | + | 0.862325i | \(0.330992\pi\) | |||||||
\(488\) | 3.66954 | − | 3.66954i | 0.166112 | − | 0.166112i | ||||
\(489\) | −21.5145 | −0.972918 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.48919 | −0.247724 | −0.123862 | − | 0.992299i | \(-0.539528\pi\) | ||||
−0.123862 | + | 0.992299i | \(0.539528\pi\) | |||||||
\(492\) | 2.33203 | − | 2.33203i | 0.105136 | − | 0.105136i | ||||
\(493\) | 0.776548 | − | 0.776548i | 0.0349740 | − | 0.0349740i | ||||
\(494\) | − | 20.4943i | − | 0.922080i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 49.2592i | 2.21180i | ||||||||
\(497\) | 1.67005 | + | 1.29401i | 0.0749120 | + | 0.0580441i | ||||
\(498\) | 7.23101 | + | 7.23101i | 0.324029 | + | 0.324029i | ||||
\(499\) | 15.5565i | 0.696403i | 0.937420 | + | 0.348201i | \(0.113207\pi\) | ||||
−0.937420 | + | 0.348201i | \(0.886793\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.70998 | 0.299780 | ||||||||
\(502\) | 17.6760 | + | 17.6760i | 0.788920 | + | 0.788920i | ||||
\(503\) | 23.1973 | − | 23.1973i | 1.03432 | − | 1.03432i | 0.0349251 | − | 0.999390i | \(-0.488881\pi\) |
0.999390 | − | 0.0349251i | \(-0.0111193\pi\) | |||||||
\(504\) | −6.29415 | + | 0.798528i | −0.280364 | + | 0.0355692i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −34.4834 | −1.53297 | ||||||||
\(507\) | −2.16043 | − | 2.16043i | −0.0959482 | − | 0.0959482i | ||||
\(508\) | 5.86878 | + | 5.86878i | 0.260385 | + | 0.260385i | ||||
\(509\) | −11.8904 | −0.527032 | −0.263516 | − | 0.964655i | \(-0.584882\pi\) | ||||
−0.263516 | + | 0.964655i | \(0.584882\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.0553 | + | 2.79812i | −0.975670 | + | 0.123781i | ||||
\(512\) | −7.20561 | + | 7.20561i | −0.318446 | + | 0.318446i | ||||
\(513\) | 2.92041 | + | 2.92041i | 0.128939 | + | 0.128939i | ||||
\(514\) | −5.02606 | −0.221690 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 2.95663i | − | 0.130158i | ||||||
\(517\) | −16.1940 | − | 16.1940i | −0.712212 | − | 0.712212i | ||||
\(518\) | 6.11476 | − | 7.89174i | 0.268667 | − | 0.346743i | ||||
\(519\) | − | 8.59476i | − | 0.377268i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.59623i | − | 0.245175i | −0.992458 | − | 0.122588i | \(-0.960881\pi\) | ||
0.992458 | − | 0.122588i | \(-0.0391193\pi\) | |||||||
\(522\) | −0.277525 | + | 0.277525i | −0.0121470 | + | 0.0121470i | ||||
\(523\) | −12.6314 | + | 12.6314i | −0.552333 | + | 0.552333i | −0.927113 | − | 0.374781i | \(-0.877718\pi\) |
0.374781 | + | 0.927113i | \(0.377718\pi\) | |||||||
\(524\) | −7.56225 | −0.330359 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.53364 | −0.197676 | ||||||||
\(527\) | −32.4543 | + | 32.4543i | −1.41373 | + | 1.41373i | ||||
\(528\) | −17.3802 | + | 17.3802i | −0.756375 | + | 0.756375i | ||||
\(529\) | − | 5.24943i | − | 0.228236i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.8904i | 0.515999i | ||||||||
\(532\) | −3.18592 | + | 4.11176i | −0.138127 | + | 0.178267i | ||||
\(533\) | −15.4490 | − | 15.4490i | −0.669172 | − | 0.669172i | ||||
\(534\) | − | 9.90409i | − | 0.428592i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.50621 | −0.367412 | ||||||||
\(537\) | 1.63132 | + | 1.63132i | 0.0703968 | + | 0.0703968i | ||||
\(538\) | −16.8995 | + | 16.8995i | −0.728589 | + | 0.728589i | ||||
\(539\) | 9.09227 | + | 35.2568i | 0.391632 | + | 1.51862i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.712283 | −0.0306234 | −0.0153117 | − | 0.999883i | \(-0.504874\pi\) | ||||
−0.0153117 | + | 0.999883i | \(0.504874\pi\) | |||||||
\(542\) | 16.1940 | + | 16.1940i | 0.695592 | + | 0.695592i | ||||
\(543\) | 0.0948778 | + | 0.0948778i | 0.00407160 | + | 0.00407160i | ||||
\(544\) | 11.6220 | 0.498291 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.65237 | − | 13.0243i | −0.0707149 | − | 0.557389i | ||||
\(547\) | −14.8234 | + | 14.8234i | −0.633803 | + | 0.633803i | −0.949020 | − | 0.315216i | \(-0.897923\pi\) |
0.315216 | + | 0.949020i | \(0.397923\pi\) | |||||||
\(548\) | −1.88369 | − | 1.88369i | −0.0804672 | − | 0.0804672i | ||||
\(549\) | −2.16407 | −0.0923602 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.03015i | − | 0.0438858i | ||||||
\(552\) | 7.14409 | + | 7.14409i | 0.304073 | + | 0.304073i | ||||
\(553\) | −8.58435 | + | 11.0790i | −0.365044 | + | 0.471127i | ||||
\(554\) | 0.786567i | 0.0334180i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 5.66011i | − | 0.240042i | ||||||
\(557\) | 17.4971 | − | 17.4971i | 0.741375 | − | 0.741375i | −0.231468 | − | 0.972843i | \(-0.574353\pi\) |
0.972843 | + | 0.231468i | \(0.0743528\pi\) | |||||||
\(558\) | 11.5986 | − | 11.5986i | 0.491009 | − | 0.491009i | ||||
\(559\) | −19.5868 | −0.828434 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.9018 | −0.966915 | ||||||||
\(562\) | 6.71856 | − | 6.71856i | 0.283406 | − | 0.283406i | ||||
\(563\) | 9.81802 | − | 9.81802i | 0.413780 | − | 0.413780i | −0.469273 | − | 0.883053i | \(-0.655484\pi\) |
0.883053 | + | 0.469273i | \(0.155484\pi\) | |||||||
\(564\) | − | 2.09591i | − | 0.0882535i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 3.06004i | − | 0.128623i | ||||||
\(567\) | 2.09141 | + | 1.62049i | 0.0878311 | + | 0.0680542i | ||||
\(568\) | −1.35404 | − | 1.35404i | −0.0568141 | − | 0.0568141i | ||||
\(569\) | − | 23.1512i | − | 0.970550i | −0.874362 | − | 0.485275i | \(-0.838720\pi\) | ||
0.874362 | − | 0.485275i | \(-0.161280\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.1586 | −1.59689 | −0.798443 | − | 0.602070i | \(-0.794343\pi\) | ||||
−0.798443 | + | 0.602070i | \(0.794343\pi\) | |||||||
\(572\) | −5.52122 | − | 5.52122i | −0.230854 | − | 0.230854i | ||||
\(573\) | 19.3074 | − | 19.3074i | 0.806577 | − | 0.806577i | ||||
\(574\) | 3.63021 | + | 28.6141i | 0.151522 | + | 1.19433i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.29738 | 0.220724 | ||||||||
\(577\) | −0.598552 | − | 0.598552i | −0.0249180 | − | 0.0249180i | 0.694538 | − | 0.719456i | \(-0.255609\pi\) |
−0.719456 | + | 0.694538i | \(0.755609\pi\) | |||||||
\(578\) | 2.65472 | + | 2.65472i | 0.110422 | + | 0.110422i | ||||
\(579\) | 5.19615 | 0.215945 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.0576 | + | 2.16407i | −0.707669 | + | 0.0897807i | ||||
\(582\) | −19.1927 | + | 19.1927i | −0.795565 | + | 0.795565i | ||||
\(583\) | −25.4819 | − | 25.4819i | −1.05535 | − | 1.05535i | ||||
\(584\) | 20.1506 | 0.833836 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.8107i | 1.06623i | ||||||||
\(587\) | −15.4885 | − | 15.4885i | −0.639280 | − | 0.639280i | 0.311098 | − | 0.950378i | \(-0.399303\pi\) |
−0.950378 | + | 0.311098i | \(0.899303\pi\) | |||||||
\(588\) | −1.69317 | + | 2.86993i | −0.0698250 | + | 0.118354i | ||||
\(589\) | 43.0530i | 1.77397i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.9524i | 0.697327i | ||||||||
\(592\) | −8.01279 | + | 8.01279i | −0.329324 | + | 0.329324i | ||||
\(593\) | −6.22670 | + | 6.22670i | −0.255700 | + | 0.255700i | −0.823303 | − | 0.567603i | \(-0.807871\pi\) |
0.567603 | + | 0.823303i | \(0.307871\pi\) | |||||||
\(594\) | 8.18472 | 0.335823 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.118732 | 0.00486346 | ||||||||
\(597\) | 17.1690 | − | 17.1690i | 0.702681 | − | 0.702681i | ||||
\(598\) | −14.7831 | + | 14.7831i | −0.604524 | + | 0.604524i | ||||
\(599\) | 19.0097i | 0.776714i | 0.921509 | + | 0.388357i | \(0.126957\pi\) | ||||
−0.921509 | + | 0.388357i | \(0.873043\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10.3604i | − | 0.422608i | −0.977420 | − | 0.211304i | \(-0.932229\pi\) | ||
0.977420 | − | 0.211304i | \(-0.0677710\pi\) | |||||||
\(602\) | 20.4402 | + | 15.8377i | 0.833081 | + | 0.645497i | ||||
\(603\) | 2.50822 | + | 2.50822i | 0.102143 | + | 0.102143i | ||||
\(604\) | − | 1.12103i | − | 0.0456141i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.90409 | −0.402326 | ||||||||
\(607\) | −10.4015 | − | 10.4015i | −0.422185 | − | 0.422185i | 0.463770 | − | 0.885955i | \(-0.346496\pi\) |
−0.885955 | + | 0.463770i | \(0.846496\pi\) | |||||||
\(608\) | 7.70873 | − | 7.70873i | 0.312630 | − | 0.312630i | ||||
\(609\) | −0.0830567 | − | 0.654669i | −0.00336563 | − | 0.0265285i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.8848 | −0.561718 | ||||||||
\(612\) | −1.48203 | − | 1.48203i | −0.0599075 | − | 0.0599075i | ||||
\(613\) | 5.08700 | + | 5.08700i | 0.205462 | + | 0.205462i | 0.802335 | − | 0.596873i | \(-0.203591\pi\) |
−0.596873 | + | 0.802335i | \(0.703591\pi\) | |||||||
\(614\) | −15.1884 | −0.612953 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.15352 | − | 32.7389i | −0.167350 | − | 1.31909i | ||||
\(617\) | 8.33721 | − | 8.33721i | 0.335643 | − | 0.335643i | −0.519081 | − | 0.854725i | \(-0.673726\pi\) |
0.854725 | + | 0.519081i | \(0.173726\pi\) | |||||||
\(618\) | −16.5806 | − | 16.5806i | −0.666971 | − | 0.666971i | ||||
\(619\) | 30.9070 | 1.24226 | 0.621129 | − | 0.783708i | \(-0.286674\pi\) | ||||
0.621129 | + | 0.783708i | \(0.286674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 4.21314i | − | 0.169068i | ||||||
\(622\) | −26.8668 | − | 26.8668i | −1.07726 | − | 1.07726i | ||||
\(623\) | 13.1637 | + | 10.1996i | 0.527392 | + | 0.408639i | ||||
\(624\) | 14.9018i | 0.596549i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.33197i | 0.0532362i | ||||||||
\(627\) | −15.1904 | + | 15.1904i | −0.606648 | + | 0.606648i | ||||
\(628\) | 2.54350 | − | 2.54350i | 0.101497 | − | 0.101497i | ||||
\(629\) | −10.5584 | −0.420992 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.4509 | 0.416044 | 0.208022 | − | 0.978124i | \(-0.433297\pi\) | ||||
0.208022 | + | 0.978124i | \(0.433297\pi\) | |||||||
\(632\) | 8.98259 | − | 8.98259i | 0.357308 | − | 0.357308i | ||||
\(633\) | 18.4239 | − | 18.4239i | 0.732284 | − | 0.732284i | ||||
\(634\) | − | 30.1307i | − | 1.19664i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 3.29799i | − | 0.130774i | ||||||
\(637\) | 19.0125 | + | 11.2167i | 0.753302 | + | 0.444424i | ||||
\(638\) | −1.44354 | − | 1.44354i | −0.0571503 | − | 0.0571503i | ||||
\(639\) | 0.798528i | 0.0315893i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.2641 | 1.82732 | 0.913662 | − | 0.406475i | \(-0.133242\pi\) | ||||
0.913662 | + | 0.406475i | \(0.133242\pi\) | |||||||
\(642\) | −17.0843 | − | 17.0843i | −0.674264 | − | 0.674264i | ||||
\(643\) | −11.8836 | + | 11.8836i | −0.468642 | + | 0.468642i | −0.901474 | − | 0.432833i | \(-0.857514\pi\) |
0.432833 | + | 0.901474i | \(0.357514\pi\) | |||||||
\(644\) | 5.26401 | − | 0.667835i | 0.207431 | − | 0.0263164i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.6141 | 1.12581 | ||||||||
\(647\) | 26.1613 | + | 26.1613i | 1.02851 | + | 1.02851i | 0.999582 | + | 0.0289263i | \(0.00920880\pi\) |
0.0289263 | + | 0.999582i | \(0.490791\pi\) | |||||||
\(648\) | −1.69567 | − | 1.69567i | −0.0666121 | − | 0.0666121i | ||||
\(649\) | −61.8475 | −2.42773 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.47119 | + | 27.3606i | 0.136047 | + | 1.07235i | ||||
\(652\) | 7.24176 | − | 7.24176i | 0.283609 | − | 0.283609i | ||||
\(653\) | 0.0451641 | + | 0.0451641i | 0.00176741 | + | 0.00176741i | 0.707990 | − | 0.706223i | \(-0.249602\pi\) |
−0.706223 | + | 0.707990i | \(0.749602\pi\) | |||||||
\(654\) | 25.0221 | 0.978441 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 32.7389i | − | 1.27824i | ||||||
\(657\) | −5.94178 | − | 5.94178i | −0.231811 | − | 0.231811i | ||||
\(658\) | 14.4897 | + | 11.2271i | 0.564869 | + | 0.437678i | ||||
\(659\) | 16.1918i | 0.630743i | 0.948968 | + | 0.315372i | \(0.102129\pi\) | ||||
−0.948968 | + | 0.315372i | \(0.897871\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 17.1544i | − | 0.667229i | −0.942710 | − | 0.333614i | \(-0.891732\pi\) | ||
0.942710 | − | 0.333614i | \(-0.108268\pi\) | |||||||
\(662\) | 24.9350 | − | 24.9350i | 0.969128 | − | 0.969128i | ||||
\(663\) | −9.81802 | + | 9.81802i | −0.381300 | + | 0.381300i | ||||
\(664\) | 15.5845 | 0.604795 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.77340 | 0.146216 | ||||||||
\(667\) | −0.743073 | + | 0.743073i | −0.0287719 | + | 0.0287719i | ||||
\(668\) | −2.25858 | + | 2.25858i | −0.0873870 | + | 0.0873870i | ||||
\(669\) | 5.65237i | 0.218533i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 11.2563i | − | 0.434546i | ||||||
\(672\) | 4.27746 | − | 5.52050i | 0.165006 | − | 0.212958i | ||||
\(673\) | −7.91427 | − | 7.91427i | −0.305073 | − | 0.305073i | 0.537922 | − | 0.842995i | \(-0.319210\pi\) |
−0.842995 | + | 0.537922i | \(0.819210\pi\) | |||||||
\(674\) | − | 1.30934i | − | 0.0504338i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.45440 | 0.0559385 | ||||||||
\(677\) | −16.0447 | − | 16.0447i | −0.616649 | − | 0.616649i | 0.328022 | − | 0.944670i | \(-0.393618\pi\) |
−0.944670 | + | 0.328022i | \(0.893618\pi\) | |||||||
\(678\) | −13.3410 | + | 13.3410i | −0.512358 | + | 0.512358i | ||||
\(679\) | −5.74393 | − | 45.2748i | −0.220432 | − | 1.73749i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.9018 | 0.877599 | ||||||||
\(682\) | 60.3300 | + | 60.3300i | 2.31015 | + | 2.31015i | ||||
\(683\) | 10.2553 | + | 10.2553i | 0.392409 | + | 0.392409i | 0.875545 | − | 0.483136i | \(-0.160502\pi\) |
−0.483136 | + | 0.875545i | \(0.660502\pi\) | |||||||
\(684\) | −1.96602 | −0.0751726 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.7711 | − | 27.0788i | −0.411243 | − | 1.03387i | ||||
\(687\) | 8.31290 | − | 8.31290i | 0.317157 | − | 0.317157i | ||||
\(688\) | −20.7537 | − | 20.7537i | −0.791229 | − | 0.791229i | ||||
\(689\) | −21.8482 | −0.832351 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 5.26401i | − | 0.200252i | −0.994975 | − | 0.100126i | \(-0.968075\pi\) | ||
0.994975 | − | 0.100126i | \(-0.0319246\pi\) | |||||||
\(692\) | 2.89299 | + | 2.89299i | 0.109975 | + | 0.109975i | ||||
\(693\) | −8.42894 | + | 10.8784i | −0.320189 | + | 0.413237i | ||||
\(694\) | − | 46.8817i | − | 1.77961i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.598130i | 0.0226721i | ||||||||
\(697\) | 21.5699 | − | 21.5699i | 0.817020 | − | 0.817020i | ||||
\(698\) | 25.7544 | − | 25.7544i | 0.974820 | − | 0.974820i | ||||
\(699\) | 17.6503 | 0.667595 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 3.50879 | − | 3.50879i | 0.132431 | − | 0.132431i | ||||
\(703\) | −7.00325 | + | 7.00325i | −0.264133 | + | 0.264133i | ||||
\(704\) | 27.5542i | 1.03849i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.0826i | 0.906361i | ||||||||
\(707\) | 10.1996 | − | 13.1637i | 0.383596 | − | 0.495071i | ||||
\(708\) | −4.00230 | − | 4.00230i | −0.150416 | − | 0.150416i | ||||
\(709\) | 24.6694i | 0.926478i | 0.886233 | + | 0.463239i | \(0.153313\pi\) | ||||
−0.886233 | + | 0.463239i | \(0.846687\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.29738 | −0.198667 | ||||||||
\(712\) | −10.6728 | − | 10.6728i | −0.399980 | − | 0.399980i | ||||
\(713\) | 31.0553 | − | 31.0553i | 1.16303 | − | 1.16303i | ||||
\(714\) | 18.1845 | − | 2.30704i | 0.680539 | − | 0.0863388i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.09821 | −0.0410418 | ||||||||
\(717\) | 6.22670 | + | 6.22670i | 0.232541 | + | 0.232541i | ||||
\(718\) | −14.2404 | − | 14.2404i | −0.531447 | − | 0.531447i | ||||
\(719\) | 17.8523 | 0.665779 | 0.332890 | − | 0.942966i | \(-0.391976\pi\) | ||||
0.332890 | + | 0.942966i | \(0.391976\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 39.1129 | − | 4.96218i | 1.45664 | − | 0.184801i | ||||
\(722\) | −2.16121 | + | 2.16121i | −0.0804321 | + | 0.0804321i | ||||
\(723\) | 15.7788 | + | 15.7788i | 0.586821 | + | 0.586821i | ||||
\(724\) | −0.0638717 | −0.00237377 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25.2637i | 0.937622i | ||||||||
\(727\) | 1.73825 | + | 1.73825i | 0.0644682 | + | 0.0644682i | 0.738606 | − | 0.674138i | \(-0.235485\pi\) |
−0.674138 | + | 0.738606i | \(0.735485\pi\) | |||||||
\(728\) | −15.8158 | − | 12.2546i | −0.586172 | − | 0.454184i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 27.3471i | − | 1.01147i | ||||||
\(732\) | 0.728424 | − | 0.728424i | 0.0269233 | − | 0.0269233i | ||||
\(733\) | −12.5108 | + | 12.5108i | −0.462097 | + | 0.462097i | −0.899342 | − | 0.437245i | \(-0.855954\pi\) |
0.437245 | + | 0.899342i | \(0.355954\pi\) | |||||||
\(734\) | −9.22645 | −0.340554 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.1210 | −0.409927 | ||||||||
\(737\) | −13.0464 | + | 13.0464i | −0.480572 | + | 0.480572i | ||||
\(738\) | −7.70873 | + | 7.70873i | −0.283762 | + | 0.283762i | ||||
\(739\) | 10.5874i | 0.389464i | 0.980857 | + | 0.194732i | \(0.0623836\pi\) | ||||
−0.980857 | + | 0.194732i | \(0.937616\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.0243i | 0.478460i | ||||||||
\(742\) | 22.8002 | + | 17.6663i | 0.837020 | + | 0.648549i | ||||
\(743\) | 12.5060 | + | 12.5060i | 0.458802 | + | 0.458802i | 0.898262 | − | 0.439460i | \(-0.144830\pi\) |
−0.439460 | + | 0.898262i | \(0.644830\pi\) | |||||||
\(744\) | − | 24.9977i | − | 0.916460i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 50.8863 | 1.86308 | ||||||||
\(747\) | −4.59538 | − | 4.59538i | −0.168136 | − | 0.168136i | ||||
\(748\) | 7.70873 | − | 7.70873i | 0.281859 | − | 0.281859i | ||||
\(749\) | 40.3011 | − | 5.11293i | 1.47257 | − | 0.186822i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.0000 | 1.16770 | 0.583848 | − | 0.811863i | \(-0.301546\pi\) | ||||
0.583848 | + | 0.811863i | \(0.301546\pi\) | |||||||
\(752\) | −14.7120 | − | 14.7120i | −0.536491 | − | 0.536491i | ||||
\(753\) | −11.2333 | − | 11.2333i | −0.409365 | − | 0.409365i | ||||
\(754\) | −1.23769 | −0.0450741 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.24943 | + | 0.158512i | −0.0454412 | + | 0.00576503i | ||||
\(757\) | 13.7308 | − | 13.7308i | 0.499054 | − | 0.499054i | −0.412090 | − | 0.911143i | \(-0.635201\pi\) |
0.911143 | + | 0.412090i | \(0.135201\pi\) | |||||||
\(758\) | 23.7583 | + | 23.7583i | 0.862940 | + | 0.862940i | ||||
\(759\) | 21.9145 | 0.795448 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.8564i | 0.502294i | 0.967949 | + | 0.251147i | \(0.0808078\pi\) | ||||
−0.967949 | + | 0.251147i | \(0.919192\pi\) | |||||||
\(762\) | −19.3998 | − | 19.3998i | −0.702780 | − | 0.702780i | ||||
\(763\) | −25.7687 | + | 33.2572i | −0.932890 | + | 1.20399i | ||||
\(764\) | 12.9977i | 0.470240i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 48.3233i | 1.74599i | ||||||||
\(767\) | −26.5141 | + | 26.5141i | −0.957368 | + | 0.957368i | ||||
\(768\) | −7.65706 | + | 7.65706i | −0.276300 | + | 0.276300i | ||||
\(769\) | −25.9448 | −0.935595 | −0.467797 | − | 0.883836i | \(-0.654952\pi\) | ||||
−0.467797 | + | 0.883836i | \(0.654952\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.19411 | 0.115033 | ||||||||
\(772\) | −1.74902 | + | 1.74902i | −0.0629487 | + | 0.0629487i | ||||
\(773\) | 11.7479 | − | 11.7479i | 0.422544 | − | 0.422544i | −0.463535 | − | 0.886079i | \(-0.653419\pi\) |
0.886079 | + | 0.463535i | \(0.153419\pi\) | |||||||
\(774\) | 9.77340i | 0.351298i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 41.3647i | 1.48491i | ||||||||
\(777\) | −3.88599 | + | 5.01528i | −0.139409 | + | 0.179922i | ||||
\(778\) | 31.2135 | + | 31.2135i | 1.11906 | + | 1.11906i | ||||
\(779\) | − | 28.6141i | − | 1.02521i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.15352 | −0.148625 | ||||||||
\(782\) | −20.6401 | − | 20.6401i | −0.738089 | − | 0.738089i | ||||
\(783\) | 0.176370 | − | 0.176370i | 0.00630296 | − | 0.00630296i | ||||
\(784\) | 8.26017 | + | 32.0302i | 0.295006 | + | 1.14394i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 24.9977 | 0.891638 | ||||||||
\(787\) | 20.3401 | + | 20.3401i | 0.725048 | + | 0.725048i | 0.969629 | − | 0.244581i | \(-0.0786505\pi\) |
−0.244581 | + | 0.969629i | \(0.578650\pi\) | |||||||
\(788\) | −5.70616 | − | 5.70616i | −0.203273 | − | 0.203273i | ||||
\(789\) | 2.88117 | 0.102572 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.99264 | − | 31.4708i | −0.141962 | − | 1.11897i | ||||
\(792\) | 8.81997 | − | 8.81997i | 0.313404 | − | 0.313404i | ||||
\(793\) | −4.82560 | − | 4.82560i | −0.171362 | − | 0.171362i | ||||
\(794\) | −3.06004 | −0.108597 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.5582i | 0.409668i | ||||||||
\(797\) | 16.4926 | + | 16.4926i | 0.584198 | + | 0.584198i | 0.936054 | − | 0.351856i | \(-0.114449\pi\) |
−0.351856 | + | 0.936054i | \(0.614449\pi\) | |||||||
\(798\) | 10.5313 | − | 13.5918i | 0.372805 | − | 0.481144i | ||||
\(799\) | − | 19.3859i | − | 0.685825i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.29415i | 0.222393i | ||||||||
\(802\) | −4.62145 | + | 4.62145i | −0.163189 | + | 0.163189i | ||||
\(803\) | 30.9060 | − | 30.9060i | 1.09065 | − | 1.09065i | ||||
\(804\) | −1.68853 | −0.0595499 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 51.7270 | 1.82201 | ||||||||
\(807\) | 10.7398 | − | 10.7398i | 0.378059 | − | 0.378059i | ||||
\(808\) | −10.6728 | + | 10.6728i | −0.375467 | + | 0.375467i | ||||
\(809\) | − | 49.9571i | − | 1.75640i | −0.478295 | − | 0.878199i | \(-0.658745\pi\) | ||
0.478295 | − | 0.878199i | \(-0.341255\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.5449i | 1.00235i | 0.865347 | + | 0.501174i | \(0.167098\pi\) | ||||
−0.865347 | + | 0.501174i | \(0.832902\pi\) | |||||||
\(812\) | 0.248318 | + | 0.192405i | 0.00871426 | + | 0.00675208i | ||||
\(813\) | −10.2915 | − | 10.2915i | −0.360937 | − | 0.360937i | ||||
\(814\) | 19.6272i | 0.687935i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −20.8059 | −0.728352 | ||||||||
\(817\) | −18.1390 | − | 18.1390i | −0.634602 | − | 0.634602i | ||||
\(818\) | 7.55944 | − | 7.55944i | 0.264310 | − | 0.264310i | ||||
\(819\) | 1.05010 | + | 8.27708i | 0.0366934 | + | 0.289225i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00000 | 0.209401 | 0.104701 | − | 0.994504i | \(-0.466612\pi\) | ||||
0.104701 | + | 0.994504i | \(0.466612\pi\) | |||||||
\(822\) | 6.22670 | + | 6.22670i | 0.217181 | + | 0.217181i | ||||
\(823\) | −16.8020 | − | 16.8020i | −0.585680 | − | 0.585680i | 0.350778 | − | 0.936459i | \(-0.385917\pi\) |
−0.936459 | + | 0.350778i | \(0.885917\pi\) | |||||||
\(824\) | −35.7350 | −1.24489 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 49.1083 | − | 6.23028i | 1.70870 | − | 0.216779i | ||||
\(827\) | 39.8118 | − | 39.8118i | 1.38439 | − | 1.38439i | 0.547751 | − | 0.836641i | \(-0.315484\pi\) |
0.836641 | − | 0.547751i | \(-0.184516\pi\) | |||||||
\(828\) | 1.41814 | + | 1.41814i | 0.0492838 | + | 0.0492838i | ||||
\(829\) | −27.0788 | −0.940484 | −0.470242 | − | 0.882537i | \(-0.655833\pi\) | ||||
−0.470242 | + | 0.882537i | \(0.655833\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 0.499871i | − | 0.0173403i | ||||||
\(832\) | 11.8125 | + | 11.8125i | 0.409524 | + | 0.409524i | ||||
\(833\) | −15.6608 | + | 26.5452i | −0.542615 | + | 0.919737i | ||||
\(834\) | 18.7100i | 0.647874i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 10.2262i | − | 0.353680i | ||||||
\(837\) | −7.37105 | + | 7.37105i | −0.254781 | + | 0.254781i | ||||
\(838\) | −26.0903 | + | 26.0903i | −0.901273 | + | 0.901273i | ||||
\(839\) | −54.8554 | −1.89382 | −0.946910 | − | 0.321498i | \(-0.895814\pi\) | ||||
−0.946910 | + | 0.321498i | \(0.895814\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9378 | 0.997855 | ||||||||
\(842\) | 12.1941 | − | 12.1941i | 0.420236 | − | 0.420236i | ||||
\(843\) | −4.26972 | + | 4.26972i | −0.147057 | + | 0.147057i | ||||
\(844\) | 12.4029i | 0.426927i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.92820i | 0.238197i | ||||||||
\(847\) | −33.5783 | − | 26.0175i | −1.15376 | − | 0.893972i | ||||
\(848\) | −23.1499 | − | 23.1499i | −0.794970 | − | 0.794970i | ||||
\(849\) | 1.94469i | 0.0667414i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.1033 | 0.346336 | ||||||||
\(852\) | −0.268784 | − | 0.268784i | −0.00920839 | − | 0.00920839i | ||||
\(853\) | −9.36876 | + | 9.36876i | −0.320780 | + | 0.320780i | −0.849066 | − | 0.528286i | \(-0.822835\pi\) |
0.528286 | + | 0.849066i | \(0.322835\pi\) | |||||||
\(854\) | 1.13392 | + | 8.93779i | 0.0388020 | + | 0.305845i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36.8206 | −1.25850 | ||||||||
\(857\) | 20.6401 | + | 20.6401i | 0.705052 | + | 0.705052i | 0.965491 | − | 0.260438i | \(-0.0838670\pi\) |
−0.260438 | + | 0.965491i | \(0.583867\pi\) | |||||||
\(858\) | 18.2509 | + | 18.2509i | 0.623075 | + | 0.623075i | ||||
\(859\) | 15.5206 | 0.529556 | 0.264778 | − | 0.964309i | \(-0.414701\pi\) | ||||
0.264778 | + | 0.964309i | \(0.414701\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.30704 | − | 18.1845i | −0.0786237 | − | 0.619728i | ||||
\(862\) | −3.67705 | + | 3.67705i | −0.125241 | + | 0.125241i | ||||
\(863\) | −22.6925 | − | 22.6925i | −0.772462 | − | 0.772462i | 0.206074 | − | 0.978536i | \(-0.433931\pi\) |
−0.978536 | + | 0.206074i | \(0.933931\pi\) | |||||||
\(864\) | 2.63960 | 0.0898012 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 27.4445i | − | 0.932601i | ||||||
\(867\) | −1.68710 | − | 1.68710i | −0.0572970 | − | 0.0572970i | ||||
\(868\) | −10.3780 | − | 8.04117i | −0.352252 | − | 0.272935i | ||||
\(869\) | − | 27.5542i | − | 0.934711i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.1860i | 0.379024i | ||||||||
\(872\) | 26.9642 | − | 26.9642i | 0.913121 | − | 0.913121i | ||||
\(873\) | 12.1972 | − | 12.1972i | 0.412812 | − | 0.412812i | ||||
\(874\) | −27.3806 | −0.926162 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.00000 | 0.135147 | ||||||||
\(877\) | 10.1514 | − | 10.1514i | 0.342789 | − | 0.342789i | −0.514626 | − | 0.857415i | \(-0.672069\pi\) |
0.857415 | + | 0.514626i | \(0.172069\pi\) | |||||||
\(878\) | 36.9123 | − | 36.9123i | 1.24573 | − | 1.24573i | ||||
\(879\) | − | 16.4029i | − | 0.553258i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.66011i | 0.190694i | 0.995444 | + | 0.0953469i | \(0.0303960\pi\) | ||||
−0.995444 | + | 0.0953469i | \(0.969604\pi\) | |||||||
\(882\) | 5.59692 | − | 9.48682i | 0.188458 | − | 0.319438i | ||||
\(883\) | 18.2373 | + | 18.2373i | 0.613735 | + | 0.613735i | 0.943917 | − | 0.330182i | \(-0.107110\pi\) |
−0.330182 | + | 0.943917i | \(0.607110\pi\) | |||||||
\(884\) | − | 6.60948i | − | 0.222301i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33.0673 | 1.11092 | ||||||||
\(887\) | 9.11254 | + | 9.11254i | 0.305969 | + | 0.305969i | 0.843344 | − | 0.537375i | \(-0.180584\pi\) |
−0.537375 | + | 0.843344i | \(0.680584\pi\) | |||||||
\(888\) | 4.06627 | − | 4.06627i | 0.136455 | − | 0.136455i | ||||
\(889\) | 45.7632 | − | 5.80589i | 1.53485 | − | 0.194723i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.20147 | −0.174256 | ||||||||
\(892\) | −1.90258 | − | 1.90258i | −0.0637033 | − | 0.0637033i | ||||
\(893\) | −12.8584 | − | 12.8584i | −0.430290 | − | 0.430290i | ||||
\(894\) | −0.392480 | −0.0131265 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.53364 | − | 35.7350i | −0.151458 | − | 1.19382i | ||||
\(897\) | 9.39478 | − | 9.39478i | 0.313683 | − | 0.313683i | ||||
\(898\) | 8.73046 | + | 8.73046i | 0.291339 | + | 0.291339i | ||||
\(899\) | 2.60007 | 0.0867171 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 30.5045i | − | 1.01625i | ||||||
\(902\) | −40.0968 | − | 40.0968i | −1.33508 | − | 1.33508i | ||||
\(903\) | −12.9900 | − | 10.0650i | −0.432279 | − | 0.334943i | ||||
\(904\) | 28.7529i | 0.956306i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.70567i | 0.123113i | ||||||||
\(907\) | 21.5971 | − | 21.5971i | 0.717119 | − | 0.717119i | −0.250895 | − | 0.968014i | \(-0.580725\pi\) |
0.968014 | + | 0.250895i | \(0.0807250\pi\) | |||||||
\(908\) | −7.70873 | + | 7.70873i | −0.255823 | + | 0.255823i | ||||
\(909\) | 6.29415 | 0.208764 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.7003 | −0.984016 | −0.492008 | − | 0.870591i | \(-0.663737\pi\) | ||||
−0.492008 | + | 0.870591i | \(0.663737\pi\) | |||||||
\(912\) | −13.8003 | + | 13.8003i | −0.456972 | + | 0.456972i | ||||
\(913\) | 23.9027 | − | 23.9027i | 0.791065 | − | 0.791065i | ||||
\(914\) | 14.5143i | 0.480091i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.59623i | 0.184905i | ||||||||
\(917\) | −25.7436 | + | 33.2248i | −0.850129 | + | 1.09718i | ||||
\(918\) | 4.89898 | + | 4.89898i | 0.161690 | + | 0.161690i | ||||
\(919\) | − | 14.2591i | − | 0.470364i | −0.971951 | − | 0.235182i | \(-0.924431\pi\) | ||
0.971951 | − | 0.235182i | \(-0.0755686\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.65237 | 0.318056 | ||||||||
\(922\) | 1.07514 | + | 1.07514i | 0.0354077 | + | 0.0354077i | ||||
\(923\) | −1.78062 | + | 1.78062i | −0.0586097 | + | 0.0586097i | ||||
\(924\) | −0.824497 | − | 6.49885i | −0.0271240 | − | 0.213796i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.3504 | 0.570169 | ||||||||
\(927\) | 10.5372 | + | 10.5372i | 0.346086 | + | 0.346086i | ||||
\(928\) | −0.465548 | − | 0.465548i | −0.0152823 | − | 0.0152823i | ||||
\(929\) | 54.9832 | 1.80394 | 0.901970 | − | 0.431799i | \(-0.142121\pi\) | ||||
0.901970 | + | 0.431799i | \(0.142121\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.21947 | + | 27.9947i | 0.236609 | + | 0.917489i | ||||
\(932\) | −5.94108 | + | 5.94108i | −0.194606 | + | 0.194606i | ||||
\(933\) | 17.0741 | + | 17.0741i | 0.558982 | + | 0.558982i | ||||
\(934\) | 42.9651 | 1.40586 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 7.56225i | − | 0.247180i | ||||||
\(937\) | −14.8900 | − | 14.8900i | −0.486434 | − | 0.486434i | 0.420745 | − | 0.907179i | \(-0.361769\pi\) |
−0.907179 | + | 0.420745i | \(0.861769\pi\) | |||||||
\(938\) | 9.04492 | − | 11.6734i | 0.295327 | − | 0.381150i | ||||
\(939\) | − | 0.846480i | − | 0.0276238i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.1725i | 0.950997i | 0.879716 | + | 0.475499i | \(0.157732\pi\) | ||||
−0.879716 | + | 0.475499i | \(0.842268\pi\) | |||||||
\(942\) | −8.40777 | + | 8.40777i | −0.273940 | + | 0.273940i | ||||
\(943\) | −20.6401 | + | 20.6401i | −0.672134 | + | 0.672134i | ||||
\(944\) | −56.1874 | −1.82874 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −50.8361 | −1.65282 | ||||||||
\(947\) | 6.00345 | − | 6.00345i | 0.195086 | − | 0.195086i | −0.602804 | − | 0.797890i | \(-0.705950\pi\) |
0.797890 | + | 0.602804i | \(0.205950\pi\) | |||||||
\(948\) | 1.78309 | − | 1.78309i | 0.0579122 | − | 0.0579122i | ||||
\(949\) | − | 26.4989i | − | 0.860189i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.1484i | 0.620928i | ||||||||
\(952\) | 17.1098 | − | 22.0820i | 0.554532 | − | 0.715682i | ||||
\(953\) | −11.4936 | − | 11.4936i | −0.372315 | − | 0.372315i | 0.496005 | − | 0.868320i | \(-0.334800\pi\) |
−0.868320 | + | 0.496005i | \(0.834800\pi\) | |||||||
\(954\) | 10.9018i | 0.352959i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.19181 | −0.135573 | ||||||||
\(957\) | 0.917385 | + | 0.917385i | 0.0296548 | + | 0.0296548i | ||||
\(958\) | 5.15157 | − | 5.15157i | 0.166440 | − | 0.166440i | ||||
\(959\) | −14.6885 | + | 1.86350i | −0.474317 | + | 0.0601757i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −77.6648 | −2.50532 | ||||||||
\(962\) | 8.41421 | + | 8.41421i | 0.271285 | + | 0.271285i | ||||
\(963\) | 10.8573 | + | 10.8573i | 0.349870 | + | 0.349870i | ||||
\(964\) | −10.6223 | −0.342121 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −17.4006 | + | 2.20759i | −0.559857 | + | 0.0710280i | ||||
\(967\) | −31.4854 | + | 31.4854i | −1.01250 | + | 1.01250i | −0.0125799 | + | 0.999921i | \(0.504004\pi\) |
−0.999921 | + | 0.0125799i | \(0.995996\pi\) | |||||||
\(968\) | 27.2245 | + | 27.2245i | 0.875028 | + | 0.875028i | ||||
\(969\) | −18.1845 | −0.584172 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 47.9272i | − | 1.53806i | −0.639214 | − | 0.769029i | \(-0.720740\pi\) | ||
0.639214 | − | 0.769029i | \(-0.279260\pi\) | |||||||
\(972\) | −0.336600 | − | 0.336600i | −0.0107964 | − | 0.0107964i | ||||
\(973\) | −24.8677 | − | 19.2683i | −0.797222 | − | 0.617712i | ||||
\(974\) | 17.4811i | 0.560130i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 10.2262i | − | 0.327332i | ||||||
\(977\) | −20.9607 | + | 20.9607i | −0.670592 | + | 0.670592i | −0.957853 | − | 0.287260i | \(-0.907256\pi\) |
0.287260 | + | 0.957853i | \(0.407256\pi\) | |||||||
\(978\) | −23.9383 | + | 23.9383i | −0.765462 | + | 0.765462i | ||||
\(979\) | −32.7389 | −1.04634 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.9018 | −0.507705 | ||||||||
\(982\) | −6.10760 | + | 6.10760i | −0.194901 | + | 0.194901i | ||||
\(983\) | 34.9452 | − | 34.9452i | 1.11458 | − | 1.11458i | 0.122055 | − | 0.992523i | \(-0.461051\pi\) |
0.992523 | − | 0.122055i | \(-0.0389485\pi\) | |||||||
\(984\) | 16.6141i | 0.529637i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 1.72807i | − | 0.0550329i | ||||||
\(987\) | −9.20838 | − | 7.13493i | −0.293106 | − | 0.227107i | ||||
\(988\) | −4.38398 | − | 4.38398i | −0.139473 | − | 0.139473i | ||||
\(989\) | 26.1682i | 0.832102i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.6620 | −0.910479 | −0.455240 | − | 0.890369i | \(-0.650446\pi\) | ||||
−0.455240 | + | 0.890369i | \(0.650446\pi\) | |||||||
\(992\) | 19.4567 | + | 19.4567i | 0.617750 | + | 0.617750i | ||||
\(993\) | −15.8465 | + | 15.8465i | −0.502873 | + | 0.502873i | ||||
\(994\) | 3.29799 | − | 0.418410i | 0.104606 | − | 0.0132711i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.09361 | 0.0980247 | ||||||||
\(997\) | 14.6983 | + | 14.6983i | 0.465501 | + | 0.465501i | 0.900453 | − | 0.434953i | \(-0.143235\pi\) |
−0.434953 | + | 0.900453i | \(0.643235\pi\) | |||||||
\(998\) | 17.3091 | + | 17.3091i | 0.547908 | + | 0.547908i | ||||
\(999\) | −2.39804 | −0.0758705 |
(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 | 525.2.m.c.118.9 | yes | 24 | |
5.2 | odd | 4 | inner | 525.2.m.c.307.10 | yes | 24 | |
5.3 | odd | 4 | inner | 525.2.m.c.307.3 | yes | 24 | |
5.4 | even | 2 | inner | 525.2.m.c.118.4 | yes | 24 | |
7.6 | odd | 2 | inner | 525.2.m.c.118.10 | yes | 24 | |
35.13 | even | 4 | inner | 525.2.m.c.307.4 | yes | 24 | |
35.27 | even | 4 | inner | 525.2.m.c.307.9 | yes | 24 | |
35.34 | odd | 2 | inner | 525.2.m.c.118.3 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.m.c.118.3 | ✓ | 24 | 35.34 | odd | 2 | inner | |
525.2.m.c.118.4 | yes | 24 | 5.4 | even | 2 | inner | |
525.2.m.c.118.9 | yes | 24 | 1.1 | even | 1 | trivial | |
525.2.m.c.118.10 | yes | 24 | 7.6 | odd | 2 | inner | |
525.2.m.c.307.3 | yes | 24 | 5.3 | odd | 4 | inner | |
525.2.m.c.307.4 | yes | 24 | 35.13 | even | 4 | inner | |
525.2.m.c.307.9 | yes | 24 | 35.27 | even | 4 | inner | |
525.2.m.c.307.10 | yes | 24 | 5.2 | odd | 4 | inner |