Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(215,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.l (of order \(6\), degree \(2\), not 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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 215.3 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.215 |
Dual form | 1134.2.l.e.269.1 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.22474 | − | 2.12132i | −0.547723 | − | 0.948683i | −0.998430 | − | 0.0560116i | \(-0.982162\pi\) |
0.450708 | − | 0.892672i | \(-0.351172\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.62132 | + | 2.09077i | −0.612801 | + | 0.790237i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.12132 | − | 1.22474i | 0.670820 | − | 0.387298i | ||||
\(11\) | 3.67423 | + | 2.12132i | 1.10782 | + | 0.639602i | 0.938265 | − | 0.345918i | \(-0.112432\pi\) |
0.169559 | + | 0.985520i | \(0.445766\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.621320 | − | 0.358719i | −0.172323 | − | 0.0994909i | 0.411358 | − | 0.911474i | \(-0.365055\pi\) |
−0.583681 | + | 0.811983i | \(0.698388\pi\) | |||||||
\(14\) | −2.09077 | − | 1.62132i | −0.558782 | − | 0.433316i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.22474 | − | 2.12132i | −0.297044 | − | 0.514496i | 0.678414 | − | 0.734680i | \(-0.262668\pi\) |
−0.975458 | + | 0.220184i | \(0.929334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.24264 | − | 2.44949i | −0.973329 | − | 0.561951i | −0.0730792 | − | 0.997326i | \(-0.523283\pi\) |
−0.900249 | + | 0.435375i | \(0.856616\pi\) | |||||||
\(20\) | 1.22474 | + | 2.12132i | 0.273861 | + | 0.474342i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.12132 | + | 3.67423i | −0.452267 | + | 0.783349i | ||||
\(23\) | 5.19615 | − | 3.00000i | 1.08347 | − | 0.625543i | 0.151642 | − | 0.988436i | \(-0.451544\pi\) |
0.931831 | + | 0.362892i | \(0.118211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0.358719 | − | 0.621320i | 0.0703507 | − | 0.121851i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.62132 | − | 2.09077i | 0.306401 | − | 0.395118i | ||||
\(29\) | −1.52192 | + | 0.878680i | −0.282613 | + | 0.163167i | −0.634606 | − | 0.772836i | \(-0.718838\pi\) |
0.351993 | + | 0.936003i | \(0.385504\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.08052i | − | 1.63091i | −0.578821 | − | 0.815455i | \(-0.696487\pi\) | ||
0.578821 | − | 0.815455i | \(-0.303513\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.12132 | − | 1.22474i | 0.363803 | − | 0.210042i | ||||
\(35\) | 6.42090 | + | 0.878680i | 1.08533 | + | 0.148524i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.62132 | + | 4.54026i | −0.430942 | + | 0.746414i | −0.996955 | − | 0.0779826i | \(-0.975152\pi\) |
0.566012 | + | 0.824397i | \(0.308485\pi\) | |||||||
\(38\) | 2.44949 | − | 4.24264i | 0.397360 | − | 0.688247i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.12132 | + | 1.22474i | −0.335410 | + | 0.193649i | ||||
\(41\) | 1.22474 | − | 2.12132i | 0.191273 | − | 0.331295i | −0.754399 | − | 0.656416i | \(-0.772072\pi\) |
0.945672 | + | 0.325121i | \(0.105405\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.50000 | − | 6.06218i | −0.533745 | − | 0.924473i | −0.999223 | − | 0.0394140i | \(-0.987451\pi\) |
0.465478 | − | 0.885059i | \(-0.345882\pi\) | |||||||
\(44\) | −3.67423 | − | 2.12132i | −0.553912 | − | 0.319801i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | + | 5.19615i | 0.442326 | + | 0.766131i | ||||
\(47\) | 12.8418 | 1.87317 | 0.936584 | − | 0.350443i | \(-0.113969\pi\) | ||||
0.936584 | + | 0.350443i | \(0.113969\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74264 | − | 6.77962i | −0.248949 | − | 0.968517i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.621320 | + | 0.358719i | 0.0861616 | + | 0.0497454i | ||||
\(53\) | 12.5446 | − | 7.24264i | 1.72314 | − | 0.994853i | 0.810905 | − | 0.585178i | \(-0.198975\pi\) |
0.912231 | − | 0.409675i | \(-0.134358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10.3923i | − | 1.40130i | ||||||
\(56\) | 2.09077 | + | 1.62132i | 0.279391 | + | 0.216658i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.878680 | − | 1.52192i | −0.115376 | − | 0.199838i | ||||
\(59\) | −2.44949 | −0.318896 | −0.159448 | − | 0.987206i | \(-0.550971\pi\) | ||||
−0.159448 | + | 0.987206i | \(0.550971\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.18154i | − | 0.535391i | −0.963504 | − | 0.267696i | \(-0.913738\pi\) | ||
0.963504 | − | 0.267696i | \(-0.0862622\pi\) | |||||||
\(62\) | 9.08052 | 1.15323 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.75736i | 0.217974i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.4853 | 1.64749 | 0.823745 | − | 0.566961i | \(-0.191881\pi\) | ||||
0.823745 | + | 0.566961i | \(0.191881\pi\) | |||||||
\(68\) | 1.22474 | + | 2.12132i | 0.148522 | + | 0.257248i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.878680 | + | 6.42090i | −0.105022 | + | 0.767444i | ||||
\(71\) | − | 12.7279i | − | 1.51053i | −0.655422 | − | 0.755263i | \(-0.727509\pi\) | ||
0.655422 | − | 0.755263i | \(-0.272491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.75736 | + | 2.74666i | −0.556807 | + | 0.321473i | −0.751863 | − | 0.659320i | \(-0.770844\pi\) |
0.195056 | + | 0.980792i | \(0.437511\pi\) | |||||||
\(74\) | −4.54026 | − | 2.62132i | −0.527795 | − | 0.304722i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.24264 | + | 2.44949i | 0.486664 | + | 0.280976i | ||||
\(77\) | −10.3923 | + | 4.24264i | −1.18431 | + | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.757359 | 0.0852096 | 0.0426048 | − | 0.999092i | \(-0.486434\pi\) | ||||
0.0426048 | + | 0.999092i | \(0.486434\pi\) | |||||||
\(80\) | −1.22474 | − | 2.12132i | −0.136931 | − | 0.237171i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.12132 | + | 1.22474i | 0.234261 | + | 0.135250i | ||||
\(83\) | −7.64564 | − | 13.2426i | −0.839218 | − | 1.45357i | −0.890549 | − | 0.454887i | \(-0.849680\pi\) |
0.0513309 | − | 0.998682i | \(-0.483654\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | + | 5.19615i | −0.325396 | + | 0.563602i | ||||
\(86\) | 6.06218 | − | 3.50000i | 0.653701 | − | 0.377415i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.12132 | − | 3.67423i | 0.226134 | − | 0.391675i | ||||
\(89\) | −1.52192 | + | 2.63604i | −0.161323 | + | 0.279420i | −0.935343 | − | 0.353741i | \(-0.884909\pi\) |
0.774020 | + | 0.633161i | \(0.218243\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.75736 | − | 0.717439i | 0.184221 | − | 0.0752080i | ||||
\(92\) | −5.19615 | + | 3.00000i | −0.541736 | + | 0.312772i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.8418i | 1.32453i | ||||||||
\(95\) | 12.0000i | 1.23117i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.74264 | + | 1.58346i | −0.278473 | + | 0.160776i | −0.632732 | − | 0.774371i | \(-0.718066\pi\) |
0.354259 | + | 0.935147i | \(0.384733\pi\) | |||||||
\(98\) | 6.77962 | − | 1.74264i | 0.684845 | − | 0.176033i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −3.67423 | + | 6.36396i | −0.365600 | + | 0.633238i | −0.988872 | − | 0.148767i | \(-0.952470\pi\) |
0.623272 | + | 0.782005i | \(0.285803\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.62132 | + | 5.55487i | −0.948017 | + | 0.547338i | −0.892464 | − | 0.451118i | \(-0.851025\pi\) |
−0.0555525 | + | 0.998456i | \(0.517692\pi\) | |||||||
\(104\) | −0.358719 | + | 0.621320i | −0.0351753 | + | 0.0609255i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.24264 | + | 12.5446i | 0.703467 | + | 1.21844i | ||||
\(107\) | 2.15232 | + | 1.24264i | 0.208072 | + | 0.120131i | 0.600415 | − | 0.799688i | \(-0.295002\pi\) |
−0.392343 | + | 0.919819i | \(0.628335\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.86396 | + | 15.3528i | 0.849013 | + | 1.47053i | 0.882090 | + | 0.471082i | \(0.156136\pi\) |
−0.0330761 | + | 0.999453i | \(0.510530\pi\) | |||||||
\(110\) | 10.3923 | 0.990867 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.62132 | + | 2.09077i | −0.153200 | + | 0.197559i | ||||
\(113\) | −8.87039 | − | 5.12132i | −0.834456 | − | 0.481773i | 0.0209200 | − | 0.999781i | \(-0.493340\pi\) |
−0.855376 | + | 0.518008i | \(0.826674\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.7279 | − | 7.34847i | −1.18688 | − | 0.685248i | ||||
\(116\) | 1.52192 | − | 0.878680i | 0.141307 | − | 0.0815834i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 2.44949i | − | 0.225494i | ||||||
\(119\) | 6.42090 | + | 0.878680i | 0.588603 | + | 0.0805484i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 4.18154 | 0.378579 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.08052i | 0.815455i | ||||||||
\(125\) | −9.79796 | −0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.72792 | −0.685742 | −0.342871 | − | 0.939382i | \(-0.611399\pi\) | ||||
−0.342871 | + | 0.939382i | \(0.611399\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.75736 | −0.154131 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000 | − | 4.89898i | 1.04053 | − | 0.424795i | ||||
\(134\) | 13.4853i | 1.16495i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.12132 | + | 1.22474i | −0.181902 | + | 0.105021i | ||||
\(137\) | −5.19615 | − | 3.00000i | −0.443937 | − | 0.256307i | 0.261329 | − | 0.965250i | \(-0.415839\pi\) |
−0.705266 | + | 0.708942i | \(0.749173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.98528 | + | 4.03295i | 0.592484 | + | 0.342071i | 0.766079 | − | 0.642746i | \(-0.222205\pi\) |
−0.173595 | + | 0.984817i | \(0.555538\pi\) | |||||||
\(140\) | −6.42090 | − | 0.878680i | −0.542665 | − | 0.0742620i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.7279 | 1.06810 | ||||||||
\(143\) | −1.52192 | − | 2.63604i | −0.127269 | − | 0.220437i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.72792 | + | 2.15232i | 0.309587 | + | 0.178740i | ||||
\(146\) | −2.74666 | − | 4.75736i | −0.227315 | − | 0.393722i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.62132 | − | 4.54026i | 0.215471 | − | 0.373207i | ||||
\(149\) | 14.0665 | − | 8.12132i | 1.15238 | − | 0.665324i | 0.202911 | − | 0.979197i | \(-0.434960\pi\) |
0.949465 | + | 0.313873i | \(0.101627\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.37868 | + | 7.58410i | −0.356332 | + | 0.617185i | −0.987345 | − | 0.158587i | \(-0.949306\pi\) |
0.631013 | + | 0.775772i | \(0.282639\pi\) | |||||||
\(152\) | −2.44949 | + | 4.24264i | −0.198680 | + | 0.344124i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.24264 | − | 10.3923i | −0.341882 | − | 0.837436i | ||||
\(155\) | −19.2627 | + | 11.1213i | −1.54722 | + | 0.893286i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.3923i | − | 0.829396i | −0.909959 | − | 0.414698i | \(-0.863887\pi\) | ||
0.909959 | − | 0.414698i | \(-0.136113\pi\) | |||||||
\(158\) | 0.757359i | 0.0602523i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.12132 | − | 1.22474i | 0.167705 | − | 0.0968246i | ||||
\(161\) | −2.15232 | + | 15.7279i | −0.169626 | + | 1.23953i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.74264 | − | 8.21449i | 0.371472 | − | 0.643409i | −0.618320 | − | 0.785926i | \(-0.712186\pi\) |
0.989792 | + | 0.142518i | \(0.0455197\pi\) | |||||||
\(164\) | −1.22474 | + | 2.12132i | −0.0956365 | + | 0.165647i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.2426 | − | 7.64564i | 1.02783 | − | 0.593417i | ||||
\(167\) | 0.297173 | − | 0.514719i | 0.0229959 | − | 0.0398301i | −0.854298 | − | 0.519783i | \(-0.826013\pi\) |
0.877294 | + | 0.479953i | \(0.159346\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.24264 | − | 10.8126i | −0.480203 | − | 0.831736i | ||||
\(170\) | −5.19615 | − | 3.00000i | −0.398527 | − | 0.230089i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.50000 | + | 6.06218i | 0.266872 | + | 0.462237i | ||||
\(173\) | 20.7846 | 1.58022 | 0.790112 | − | 0.612962i | \(-0.210022\pi\) | ||||
0.790112 | + | 0.612962i | \(0.210022\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | − | 2.44949i | −0.0755929 | − | 0.185164i | ||||
\(176\) | 3.67423 | + | 2.12132i | 0.276956 | + | 0.159901i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.63604 | − | 1.52192i | −0.197579 | − | 0.114073i | ||||
\(179\) | −5.82655 | + | 3.36396i | −0.435497 | + | 0.251434i | −0.701686 | − | 0.712487i | \(-0.747569\pi\) |
0.266189 | + | 0.963921i | \(0.414236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.79796i | 0.728277i | 0.931345 | + | 0.364138i | \(0.118636\pi\) | ||||
−0.931345 | + | 0.364138i | \(0.881364\pi\) | |||||||
\(182\) | 0.717439 | + | 1.75736i | 0.0531801 | + | 0.130264i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | 12.8418 | 0.944148 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 10.3923i | − | 0.759961i | ||||||
\(188\) | −12.8418 | −0.936584 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0000 | −0.870572 | ||||||||
\(191\) | 21.2132i | 1.53493i | 0.641089 | + | 0.767467i | \(0.278483\pi\) | ||||
−0.641089 | + | 0.767467i | \(0.721517\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.48528 | −0.106913 | −0.0534564 | − | 0.998570i | \(-0.517024\pi\) | ||||
−0.0534564 | + | 0.998570i | \(0.517024\pi\) | |||||||
\(194\) | −1.58346 | − | 2.74264i | −0.113686 | − | 0.196910i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.74264 | + | 6.77962i | 0.124474 | + | 0.484258i | ||||
\(197\) | 16.9706i | 1.20910i | 0.796566 | + | 0.604551i | \(0.206648\pi\) | ||||
−0.796566 | + | 0.604551i | \(0.793352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.1066 | + | 10.4539i | −1.28354 | + | 0.741054i | −0.977494 | − | 0.210962i | \(-0.932340\pi\) |
−0.306049 | + | 0.952016i | \(0.599007\pi\) | |||||||
\(200\) | 0.866025 | + | 0.500000i | 0.0612372 | + | 0.0353553i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.36396 | − | 3.67423i | −0.447767 | − | 0.258518i | ||||
\(203\) | 0.630399 | − | 4.60660i | 0.0442453 | − | 0.323320i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | −5.55487 | − | 9.62132i | −0.387026 | − | 0.670349i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.621320 | − | 0.358719i | −0.0430808 | − | 0.0248727i | ||||
\(209\) | −10.3923 | − | 18.0000i | −0.718851 | − | 1.24509i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.74264 | + | 3.01834i | −0.119968 | + | 0.207791i | −0.919755 | − | 0.392493i | \(-0.871613\pi\) |
0.799787 | + | 0.600284i | \(0.204946\pi\) | |||||||
\(212\) | −12.5446 | + | 7.24264i | −0.861568 | + | 0.497427i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.24264 | + | 2.15232i | −0.0849452 | + | 0.147129i | ||||
\(215\) | −8.57321 | + | 14.8492i | −0.584688 | + | 1.01271i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.9853 | + | 14.7224i | 1.28880 | + | 0.999424i | ||||
\(218\) | −15.3528 | + | 8.86396i | −1.03982 | + | 0.600343i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.3923i | 0.700649i | ||||||||
\(221\) | 1.75736i | 0.118213i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.00000 | − | 5.19615i | 0.602685 | − | 0.347960i | −0.167412 | − | 0.985887i | \(-0.553541\pi\) |
0.770097 | + | 0.637927i | \(0.220208\pi\) | |||||||
\(224\) | −2.09077 | − | 1.62132i | −0.139695 | − | 0.108329i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.12132 | − | 8.87039i | 0.340665 | − | 0.590049i | ||||
\(227\) | 12.5446 | − | 21.7279i | 0.832616 | − | 1.44213i | −0.0633412 | − | 0.997992i | \(-0.520176\pi\) |
0.895957 | − | 0.444141i | \(-0.146491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.86396 | − | 2.80821i | 0.321420 | − | 0.185572i | −0.330606 | − | 0.943769i | \(-0.607253\pi\) |
0.652025 | + | 0.758197i | \(0.273920\pi\) | |||||||
\(230\) | 7.34847 | − | 12.7279i | 0.484544 | − | 0.839254i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.878680 | + | 1.52192i | 0.0576881 | + | 0.0999188i | ||||
\(233\) | −17.7408 | − | 10.2426i | −1.16224 | − | 0.671018i | −0.210398 | − | 0.977616i | \(-0.567476\pi\) |
−0.951839 | + | 0.306598i | \(0.900809\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.7279 | − | 27.2416i | −1.02598 | − | 1.77704i | ||||
\(236\) | 2.44949 | 0.159448 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.878680 | + | 6.42090i | −0.0569563 | + | 0.416205i | ||||
\(239\) | −14.0665 | − | 8.12132i | −0.909889 | − | 0.525325i | −0.0294934 | − | 0.999565i | \(-0.509389\pi\) |
−0.880395 | + | 0.474240i | \(0.842723\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.985281 | + | 0.568852i | 0.0634676 | + | 0.0366430i | 0.531398 | − | 0.847122i | \(-0.321667\pi\) |
−0.467930 | + | 0.883765i | \(0.655000\pi\) | |||||||
\(242\) | −6.06218 | + | 3.50000i | −0.389692 | + | 0.224989i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.18154i | 0.267696i | ||||||||
\(245\) | −12.2474 | + | 12.0000i | −0.782461 | + | 0.766652i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.75736 | + | 3.04384i | 0.111818 | + | 0.193675i | ||||
\(248\) | −9.08052 | −0.576614 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 9.79796i | − | 0.619677i | ||||||
\(251\) | −15.2913 | −0.965177 | −0.482589 | − | 0.875847i | \(-0.660303\pi\) | ||||
−0.482589 | + | 0.875847i | \(0.660303\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.4558 | 1.60040 | ||||||||
\(254\) | − | 7.72792i | − | 0.484893i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.5446 | + | 21.7279i | 0.782512 | + | 1.35535i | 0.930474 | + | 0.366358i | \(0.119395\pi\) |
−0.147962 | + | 0.988993i | \(0.547271\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.24264 | − | 12.8418i | −0.325762 | − | 0.797950i | ||||
\(260\) | − | 1.75736i | − | 0.108987i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.82655 | − | 3.36396i | −0.359281 | − | 0.207431i | 0.309485 | − | 0.950904i | \(-0.399843\pi\) |
−0.668765 | + | 0.743474i | \(0.733177\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30.7279 | − | 17.7408i | −1.88760 | − | 1.08981i | ||||
\(266\) | 4.89898 | + | 12.0000i | 0.300376 | + | 0.735767i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.4853 | −0.823745 | ||||||||
\(269\) | 4.89898 | + | 8.48528i | 0.298696 | + | 0.517357i | 0.975838 | − | 0.218496i | \(-0.0701150\pi\) |
−0.677142 | + | 0.735853i | \(0.736782\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.3492 | − | 9.43924i | −0.993146 | − | 0.573393i | −0.0869326 | − | 0.996214i | \(-0.527706\pi\) |
−0.906213 | + | 0.422821i | \(0.861040\pi\) | |||||||
\(272\) | −1.22474 | − | 2.12132i | −0.0742611 | − | 0.128624i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.00000 | − | 5.19615i | 0.181237 | − | 0.313911i | ||||
\(275\) | −3.67423 | + | 2.12132i | −0.221565 | + | 0.127920i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8640 | + | 20.5490i | −0.712836 | + | 1.23467i | 0.250952 | + | 0.968000i | \(0.419256\pi\) |
−0.963788 | + | 0.266669i | \(0.914077\pi\) | |||||||
\(278\) | −4.03295 | + | 6.98528i | −0.241881 | + | 0.418949i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.878680 | − | 6.42090i | 0.0525112 | − | 0.383722i | ||||
\(281\) | −11.9142 | + | 6.87868i | −0.710743 | + | 0.410348i | −0.811336 | − | 0.584580i | \(-0.801259\pi\) |
0.100593 | + | 0.994928i | \(0.467926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.03668i | 0.358844i | 0.983772 | + | 0.179422i | \(0.0574227\pi\) | ||||
−0.983772 | + | 0.179422i | \(0.942577\pi\) | |||||||
\(284\) | 12.7279i | 0.755263i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.63604 | − | 1.52192i | 0.155872 | − | 0.0899929i | ||||
\(287\) | 2.44949 | + | 6.00000i | 0.144589 | + | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.50000 | − | 9.52628i | 0.323529 | − | 0.560369i | ||||
\(290\) | −2.15232 | + | 3.72792i | −0.126388 | + | 0.218911i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.75736 | − | 2.74666i | 0.278403 | − | 0.160736i | ||||
\(293\) | 6.42090 | − | 11.1213i | 0.375113 | − | 0.649714i | −0.615231 | − | 0.788347i | \(-0.710937\pi\) |
0.990344 | + | 0.138632i | \(0.0442706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | + | 5.19615i | 0.174667 | + | 0.302532i | ||||
\(296\) | 4.54026 | + | 2.62132i | 0.263897 | + | 0.152361i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.12132 | + | 14.0665i | 0.470455 | + | 0.814853i | ||||
\(299\) | −4.30463 | −0.248943 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.3492 | + | 2.51104i | 1.05763 | + | 0.144734i | ||||
\(302\) | −7.58410 | − | 4.37868i | −0.436416 | − | 0.251965i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.24264 | − | 2.44949i | −0.243332 | − | 0.140488i | ||||
\(305\) | −8.87039 | + | 5.12132i | −0.507917 | + | 0.293246i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 26.8213i | − | 1.53077i | −0.643571 | − | 0.765386i | \(-0.722548\pi\) | ||
0.643571 | − | 0.765386i | \(-0.277452\pi\) | |||||||
\(308\) | 10.3923 | − | 4.24264i | 0.592157 | − | 0.241747i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.1213 | − | 19.2627i | −0.631649 | − | 1.09405i | ||||
\(311\) | 17.1464 | 0.972285 | 0.486142 | − | 0.873880i | \(-0.338404\pi\) | ||||
0.486142 | + | 0.873880i | \(0.338404\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.1903i | 1.14122i | 0.821221 | + | 0.570611i | \(0.193293\pi\) | ||||
−0.821221 | + | 0.570611i | \(0.806707\pi\) | |||||||
\(314\) | 10.3923 | 0.586472 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.757359 | −0.0426048 | ||||||||
\(317\) | − | 22.2426i | − | 1.24927i | −0.780916 | − | 0.624636i | \(-0.785248\pi\) | ||
0.780916 | − | 0.624636i | \(-0.214752\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.45584 | −0.417447 | ||||||||
\(320\) | 1.22474 | + | 2.12132i | 0.0684653 | + | 0.118585i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.7279 | − | 2.15232i | −0.876483 | − | 0.119944i | ||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.621320 | − | 0.358719i | 0.0344647 | − | 0.0198982i | ||||
\(326\) | 8.21449 | + | 4.74264i | 0.454959 | + | 0.262671i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.12132 | − | 1.22474i | −0.117130 | − | 0.0676252i | ||||
\(329\) | −20.8207 | + | 26.8492i | −1.14788 | + | 1.48025i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | 0.549650 | 0.274825 | − | 0.961494i | \(-0.411380\pi\) | ||||
0.274825 | + | 0.961494i | \(0.411380\pi\) | |||||||
\(332\) | 7.64564 | + | 13.2426i | 0.419609 | + | 0.726784i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.514719 | + | 0.297173i | 0.0281642 | + | 0.0162606i | ||||
\(335\) | −16.5160 | − | 28.6066i | −0.902367 | − | 1.56295i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7279 | − | 18.5813i | 0.584387 | − | 1.01219i | −0.410564 | − | 0.911832i | \(-0.634668\pi\) |
0.994952 | − | 0.100357i | \(-0.0319984\pi\) | |||||||
\(338\) | 10.8126 | − | 6.24264i | 0.588126 | − | 0.339555i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.00000 | − | 5.19615i | 0.162698 | − | 0.281801i | ||||
\(341\) | 19.2627 | − | 33.3640i | 1.04313 | − | 1.80676i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | + | 7.34847i | 0.917914 | + | 0.396780i | ||||
\(344\) | −6.06218 | + | 3.50000i | −0.326851 | + | 0.188707i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.7846i | 1.11739i | ||||||||
\(347\) | 4.97056i | 0.266834i | 0.991060 | + | 0.133417i | \(0.0425949\pi\) | ||||
−0.991060 | + | 0.133417i | \(0.957405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.106602 | − | 0.0615465i | 0.00570626 | − | 0.00329451i | −0.497144 | − | 0.867668i | \(-0.665618\pi\) |
0.502850 | + | 0.864373i | \(0.332285\pi\) | |||||||
\(350\) | 2.44949 | − | 1.00000i | 0.130931 | − | 0.0534522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.12132 | + | 3.67423i | −0.113067 | + | 0.195837i | ||||
\(353\) | 5.49333 | − | 9.51472i | 0.292380 | − | 0.506417i | −0.681992 | − | 0.731360i | \(-0.738886\pi\) |
0.974372 | + | 0.224942i | \(0.0722194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.0000 | + | 15.5885i | −1.43301 | + | 0.827349i | ||||
\(356\) | 1.52192 | − | 2.63604i | 0.0806615 | − | 0.139710i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.36396 | − | 5.82655i | −0.177791 | − | 0.307943i | ||||
\(359\) | 12.5446 | + | 7.24264i | 0.662080 | + | 0.382252i | 0.793069 | − | 0.609132i | \(-0.208482\pi\) |
−0.130989 | + | 0.991384i | \(0.541815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.50000 | + | 4.33013i | 0.131579 | + | 0.227901i | ||||
\(362\) | −9.79796 | −0.514969 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.75736 | + | 0.717439i | −0.0921107 | + | 0.0376040i | ||||
\(365\) | 11.6531 | + | 6.72792i | 0.609951 | + | 0.352156i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.9706 | + | 14.9941i | 1.35565 | + | 0.782686i | 0.989034 | − | 0.147685i | \(-0.0471823\pi\) |
0.366618 | + | 0.930372i | \(0.380516\pi\) | |||||||
\(368\) | 5.19615 | − | 3.00000i | 0.270868 | − | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.8418i | 0.667613i | ||||||||
\(371\) | −5.19615 | + | 37.9706i | −0.269771 | + | 1.97133i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | + | 19.0526i | 0.569558 | + | 0.986504i | 0.996610 | + | 0.0822766i | \(0.0262191\pi\) |
−0.427051 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(374\) | 10.3923 | 0.537373 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 12.8418i | − | 0.662265i | ||||||
\(377\) | 1.26080 | 0.0649344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.48528 | −0.384493 | −0.192247 | − | 0.981347i | \(-0.561577\pi\) | ||||
−0.192247 | + | 0.981347i | \(0.561577\pi\) | |||||||
\(380\) | − | 12.0000i | − | 0.615587i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.2132 | −1.08536 | ||||||||
\(383\) | 2.74666 | + | 4.75736i | 0.140348 | + | 0.243090i | 0.927628 | − | 0.373506i | \(-0.121845\pi\) |
−0.787280 | + | 0.616596i | \(0.788511\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.7279 | + | 16.8493i | 1.10736 | + | 0.858718i | ||||
\(386\) | − | 1.48528i | − | 0.0755988i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.74264 | − | 1.58346i | 0.139236 | − | 0.0803882i | ||||
\(389\) | 13.4361 | + | 7.75736i | 0.681239 | + | 0.393314i | 0.800322 | − | 0.599571i | \(-0.204662\pi\) |
−0.119082 | + | 0.992884i | \(0.537995\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.7279 | − | 7.34847i | −0.643679 | − | 0.371628i | ||||
\(392\) | −6.77962 | + | 1.74264i | −0.342422 | + | 0.0880166i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16.9706 | −0.854965 | ||||||||
\(395\) | −0.927572 | − | 1.60660i | −0.0466712 | − | 0.0808369i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.1360 | − | 7.58410i | −0.659279 | − | 0.380635i | 0.132723 | − | 0.991153i | \(-0.457628\pi\) |
−0.792002 | + | 0.610518i | \(0.790961\pi\) | |||||||
\(398\) | −10.4539 | − | 18.1066i | −0.524004 | − | 0.907602i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −17.1104 | + | 9.87868i | −0.854451 | + | 0.493318i | −0.862150 | − | 0.506653i | \(-0.830883\pi\) |
0.00769892 | + | 0.999970i | \(0.497549\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.25736 | + | 5.64191i | −0.162261 | + | 0.281044i | ||||
\(404\) | 3.67423 | − | 6.36396i | 0.182800 | − | 0.316619i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.60660 | + | 0.630399i | 0.228622 | + | 0.0312862i | ||||
\(407\) | −19.2627 | + | 11.1213i | −0.954816 | + | 0.551263i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.76127i | − | 0.185983i | −0.995667 | − | 0.0929915i | \(-0.970357\pi\) | ||
0.995667 | − | 0.0929915i | \(-0.0296430\pi\) | |||||||
\(410\) | − | 6.00000i | − | 0.296319i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.62132 | − | 5.55487i | 0.474008 | − | 0.273669i | ||||
\(413\) | 3.97141 | − | 5.12132i | 0.195420 | − | 0.252004i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.7279 | + | 32.4377i | −0.919318 | + | 1.59230i | ||||
\(416\) | 0.358719 | − | 0.621320i | 0.0175877 | − | 0.0304627i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.0000 | − | 10.3923i | 0.880409 | − | 0.508304i | ||||
\(419\) | 3.97141 | − | 6.87868i | 0.194016 | − | 0.336045i | −0.752562 | − | 0.658522i | \(-0.771182\pi\) |
0.946577 | + | 0.322476i | \(0.104515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.7279 | + | 20.3134i | 0.571584 | + | 0.990012i | 0.996404 | + | 0.0847344i | \(0.0270042\pi\) |
−0.424820 | + | 0.905278i | \(0.639662\pi\) | |||||||
\(422\) | −3.01834 | − | 1.74264i | −0.146931 | − | 0.0848304i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.24264 | − | 12.5446i | −0.351734 | − | 0.609221i | ||||
\(425\) | 2.44949 | 0.118818 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.74264 | + | 6.77962i | 0.423086 | + | 0.328089i | ||||
\(428\) | −2.15232 | − | 1.24264i | −0.104036 | − | 0.0600653i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.8492 | − | 8.57321i | −0.716094 | − | 0.413437i | ||||
\(431\) | −1.52192 | + | 0.878680i | −0.0733082 | + | 0.0423245i | −0.536206 | − | 0.844087i | \(-0.680143\pi\) |
0.462898 | + | 0.886412i | \(0.346810\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.57258i | − | 0.123630i | −0.998088 | − | 0.0618152i | \(-0.980311\pi\) | ||
0.998088 | − | 0.0618152i | \(-0.0196889\pi\) | |||||||
\(434\) | −14.7224 | + | 18.9853i | −0.706699 | + | 0.911323i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.86396 | − | 15.3528i | −0.424507 | − | 0.735267i | ||||
\(437\) | −29.3939 | −1.40610 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.30463i | − | 0.205449i | −0.994710 | − | 0.102724i | \(-0.967244\pi\) | ||
0.994710 | − | 0.102724i | \(-0.0327560\pi\) | |||||||
\(440\) | −10.3923 | −0.495434 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.75736 | −0.0835891 | ||||||||
\(443\) | − | 25.4558i | − | 1.20944i | −0.796437 | − | 0.604722i | \(-0.793284\pi\) | ||
0.796437 | − | 0.604722i | \(-0.206716\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.45584 | 0.353441 | ||||||||
\(446\) | 5.19615 | + | 9.00000i | 0.246045 | + | 0.426162i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.62132 | − | 2.09077i | 0.0766002 | − | 0.0987796i | ||||
\(449\) | 5.27208i | 0.248805i | 0.992232 | + | 0.124402i | \(0.0397014\pi\) | ||||
−0.992232 | + | 0.124402i | \(0.960299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | − | 5.19615i | 0.423793 | − | 0.244677i | ||||
\(452\) | 8.87039 | + | 5.12132i | 0.417228 | + | 0.240887i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.7279 | + | 12.5446i | 1.01974 | + | 0.588748i | ||||
\(455\) | −3.67423 | − | 2.84924i | −0.172251 | − | 0.133575i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0000 | −1.07589 | −0.537947 | − | 0.842978i | \(-0.680800\pi\) | ||||
−0.537947 | + | 0.842978i | \(0.680800\pi\) | |||||||
\(458\) | 2.80821 | + | 4.86396i | 0.131219 | + | 0.227278i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.7279 | + | 7.34847i | 0.593442 | + | 0.342624i | ||||
\(461\) | 10.7255 | + | 18.5772i | 0.499538 | + | 0.865225i | 1.00000 | 0.000533648i | \(-0.000169865\pi\) | |
−0.500462 | + | 0.865758i | \(0.666837\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0000 | − | 19.0526i | 0.511213 | − | 0.885448i | −0.488702 | − | 0.872451i | \(-0.662530\pi\) |
0.999916 | − | 0.0129968i | \(-0.00413714\pi\) | |||||||
\(464\) | −1.52192 | + | 0.878680i | −0.0706533 | + | 0.0407917i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.2426 | − | 17.7408i | 0.474481 | − | 0.821825i | ||||
\(467\) | 8.87039 | − | 15.3640i | 0.410473 | − | 0.710959i | −0.584469 | − | 0.811416i | \(-0.698697\pi\) |
0.994941 | + | 0.100457i | \(0.0320304\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.8640 | + | 28.1946i | −1.00958 | + | 1.30191i | ||||
\(470\) | 27.2416 | − | 15.7279i | 1.25656 | − | 0.725475i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.44949i | 0.112747i | ||||||||
\(473\) | − | 29.6985i | − | 1.36554i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.24264 | − | 2.44949i | 0.194666 | − | 0.112390i | ||||
\(476\) | −6.42090 | − | 0.878680i | −0.294301 | − | 0.0402742i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.12132 | − | 14.0665i | 0.371461 | − | 0.643389i | ||||
\(479\) | 1.22474 | − | 2.12132i | 0.0559600 | − | 0.0969256i | −0.836688 | − | 0.547679i | \(-0.815511\pi\) |
0.892648 | + | 0.450754i | \(0.148845\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.25736 | − | 1.88064i | 0.148523 | − | 0.0857497i | ||||
\(482\) | −0.568852 | + | 0.985281i | −0.0259105 | + | 0.0448783i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.50000 | − | 6.06218i | −0.159091 | − | 0.275554i | ||||
\(485\) | 6.71807 | + | 3.87868i | 0.305052 | + | 0.176122i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0000 | − | 19.0526i | −0.498458 | − | 0.863354i | 0.501541 | − | 0.865134i | \(-0.332767\pi\) |
−0.999998 | + | 0.00178012i | \(0.999433\pi\) | |||||||
\(488\) | −4.18154 | −0.189289 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12.0000 | − | 12.2474i | −0.542105 | − | 0.553283i | ||||
\(491\) | −30.2854 | − | 17.4853i | −1.36676 | − | 0.789100i | −0.376248 | − | 0.926519i | \(-0.622786\pi\) |
−0.990513 | + | 0.137419i | \(0.956119\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.72792 | + | 2.15232i | 0.167897 | + | 0.0969355i | ||||
\(494\) | −3.04384 | + | 1.75736i | −0.136949 | + | 0.0790673i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 9.08052i | − | 0.407727i | ||||||
\(497\) | 26.6112 | + | 20.6360i | 1.19367 | + | 0.925653i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.2279 | + | 21.1794i | 0.547397 | + | 0.948119i | 0.998452 | + | 0.0556231i | \(0.0177145\pi\) |
−0.451055 | + | 0.892496i | \(0.648952\pi\) | |||||||
\(500\) | 9.79796 | 0.438178 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 15.2913i | − | 0.682483i | ||||||
\(503\) | 0.594346 | 0.0265006 | 0.0132503 | − | 0.999912i | \(-0.495782\pi\) | ||||
0.0132503 | + | 0.999912i | \(0.495782\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | 25.4558i | 1.13165i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.72792 | 0.342871 | ||||||||
\(509\) | −4.60181 | − | 7.97056i | −0.203971 | − | 0.353289i | 0.745833 | − | 0.666133i | \(-0.232052\pi\) |
−0.949805 | + | 0.312844i | \(0.898718\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.97056 | − | 14.3998i | 0.0871726 | − | 0.637008i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.7279 | + | 12.5446i | −0.958378 | + | 0.553320i | ||||
\(515\) | 23.5673 | + | 13.6066i | 1.03850 | + | 0.599579i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 47.1838 | + | 27.2416i | 2.07514 | + | 1.19808i | ||||
\(518\) | 12.8418 | − | 5.24264i | 0.564236 | − | 0.230348i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.75736 | 0.0770653 | ||||||||
\(521\) | −14.9941 | − | 25.9706i | −0.656904 | − | 1.13779i | −0.981413 | − | 0.191908i | \(-0.938532\pi\) |
0.324509 | − | 0.945883i | \(-0.394801\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.7426 | + | 13.7078i | 1.03819 | + | 0.599401i | 0.919321 | − | 0.393508i | \(-0.128739\pi\) |
0.118872 | + | 0.992910i | \(0.462072\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.36396 | − | 5.82655i | 0.146676 | − | 0.254050i | ||||
\(527\) | −19.2627 | + | 11.1213i | −0.839096 | + | 0.484452i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | 17.7408 | − | 30.7279i | 0.770610 | − | 1.33474i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.0000 | + | 4.89898i | −0.520266 | + | 0.212398i | ||||
\(533\) | −1.52192 | + | 0.878680i | −0.0659216 | + | 0.0380598i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6.08767i | − | 0.263193i | ||||||
\(536\) | − | 13.4853i | − | 0.582475i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.48528 | + | 4.89898i | −0.365826 | + | 0.211210i | ||||
\(539\) | 7.97887 | − | 28.6066i | 0.343674 | − | 1.23217i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.72792 | − | 4.72490i | 0.117283 | − | 0.203139i | −0.801407 | − | 0.598119i | \(-0.795915\pi\) |
0.918690 | + | 0.394980i | \(0.129248\pi\) | |||||||
\(542\) | 9.43924 | − | 16.3492i | 0.405450 | − | 0.702260i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.12132 | − | 1.22474i | 0.0909509 | − | 0.0525105i | ||||
\(545\) | 21.7122 | − | 37.6066i | 0.930048 | − | 1.61089i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.9853 | − | 34.6155i | −0.854509 | − | 1.48005i | −0.877100 | − | 0.480308i | \(-0.840525\pi\) |
0.0225909 | − | 0.999745i | \(-0.492808\pi\) | |||||||
\(548\) | 5.19615 | + | 3.00000i | 0.221969 | + | 0.128154i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.12132 | − | 3.67423i | −0.0904534 | − | 0.156670i | ||||
\(551\) | 8.60927 | 0.366767 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.22792 | + | 1.58346i | −0.0522166 | + | 0.0673358i | ||||
\(554\) | −20.5490 | − | 11.8640i | −0.873043 | − | 0.504051i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.98528 | − | 4.03295i | −0.296242 | − | 0.171035i | ||||
\(557\) | 18.3712 | − | 10.6066i | 0.778412 | − | 0.449416i | −0.0574555 | − | 0.998348i | \(-0.518299\pi\) |
0.835867 | + | 0.548932i | \(0.184965\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.02207i | 0.212411i | ||||||||
\(560\) | 6.42090 | + | 0.878680i | 0.271332 | + | 0.0371310i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.87868 | − | 11.9142i | −0.290160 | − | 0.502571i | ||||
\(563\) | 45.8739 | 1.93335 | 0.966676 | − | 0.256002i | \(-0.0824054\pi\) | ||||
0.966676 | + | 0.256002i | \(0.0824054\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.0892i | 1.05551i | ||||||||
\(566\) | −6.03668 | −0.253741 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.7279 | −0.534052 | ||||||||
\(569\) | − | 10.2426i | − | 0.429394i | −0.976681 | − | 0.214697i | \(-0.931124\pi\) | ||
0.976681 | − | 0.214697i | \(-0.0688764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0000 | −0.920671 | −0.460336 | − | 0.887745i | \(-0.652271\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | 1.52192 | + | 2.63604i | 0.0636346 | + | 0.110218i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.00000 | + | 2.44949i | −0.250435 | + | 0.102240i | ||||
\(575\) | 6.00000i | 0.250217i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.7426 | − | 13.7078i | 0.988419 | − | 0.570664i | 0.0836177 | − | 0.996498i | \(-0.473353\pi\) |
0.904801 | + | 0.425834i | \(0.140019\pi\) | |||||||
\(578\) | 9.52628 | + | 5.50000i | 0.396241 | + | 0.228770i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.72792 | − | 2.15232i | −0.154794 | − | 0.0893701i | ||||
\(581\) | 40.0834 | + | 5.48528i | 1.66294 | + | 0.227568i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 61.4558 | 2.54524 | ||||||||
\(584\) | 2.74666 | + | 4.75736i | 0.113658 | + | 0.196861i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.1213 | + | 6.42090i | 0.459418 | + | 0.265245i | ||||
\(587\) | 16.2189 | + | 28.0919i | 0.669424 | + | 1.15948i | 0.978065 | + | 0.208298i | \(0.0667923\pi\) |
−0.308642 | + | 0.951178i | \(0.599874\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.2426 | + | 38.5254i | −0.916492 | + | 1.58741i | ||||
\(590\) | −5.19615 | + | 3.00000i | −0.213922 | + | 0.123508i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.62132 | + | 4.54026i | −0.107736 | + | 0.186604i | ||||
\(593\) | −0.927572 | + | 1.60660i | −0.0380908 | + | 0.0659752i | −0.884442 | − | 0.466650i | \(-0.845461\pi\) |
0.846352 | + | 0.532625i | \(0.178794\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | − | 14.6969i | −0.245976 | − | 0.602516i | ||||
\(596\) | −14.0665 | + | 8.12132i | −0.576188 | + | 0.332662i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 4.30463i | − | 0.176030i | ||||||
\(599\) | − | 3.51472i | − | 0.143608i | −0.997419 | − | 0.0718038i | \(-0.977124\pi\) | ||
0.997419 | − | 0.0718038i | \(-0.0228755\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.9558 | + | 20.7591i | −1.46667 | + | 0.846782i | −0.999305 | − | 0.0372826i | \(-0.988130\pi\) |
−0.467365 | + | 0.884065i | \(0.654796\pi\) | |||||||
\(602\) | −2.51104 | + | 18.3492i | −0.102342 | + | 0.747859i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.37868 | − | 7.58410i | 0.178166 | − | 0.308592i | ||||
\(605\) | 8.57321 | − | 14.8492i | 0.348551 | − | 0.603708i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.2426 | + | 18.0379i | −1.26810 | + | 0.732138i | −0.974628 | − | 0.223830i | \(-0.928144\pi\) |
−0.293471 | + | 0.955968i | \(0.594811\pi\) | |||||||
\(608\) | 2.44949 | − | 4.24264i | 0.0993399 | − | 0.172062i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.12132 | − | 8.87039i | −0.207356 | − | 0.359151i | ||||
\(611\) | −7.97887 | − | 4.60660i | −0.322790 | − | 0.186363i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.1066 | + | 24.4334i | 0.569760 | + | 0.986854i | 0.996589 | + | 0.0825214i | \(0.0262973\pi\) |
−0.426829 | + | 0.904332i | \(0.640369\pi\) | |||||||
\(614\) | 26.8213 | 1.08242 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.24264 | + | 10.3923i | 0.170941 | + | 0.418718i | ||||
\(617\) | −3.67423 | − | 2.12132i | −0.147919 | − | 0.0854011i | 0.424214 | − | 0.905562i | \(-0.360551\pi\) |
−0.572133 | + | 0.820161i | \(0.693884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.0147 | + | 6.35935i | 0.442719 | + | 0.255604i | 0.704750 | − | 0.709455i | \(-0.251059\pi\) |
−0.262031 | + | 0.965059i | \(0.584392\pi\) | |||||||
\(620\) | 19.2627 | − | 11.1213i | 0.773608 | − | 0.446643i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.1464i | 0.687509i | ||||||||
\(623\) | −3.04384 | − | 7.45584i | −0.121949 | − | 0.298712i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | −20.1903 | −0.806965 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.3923i | 0.414698i | ||||||||
\(629\) | 12.8418 | 0.512036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.7574 | −0.587481 | −0.293741 | − | 0.955885i | \(-0.594900\pi\) | ||||
−0.293741 | + | 0.955885i | \(0.594900\pi\) | |||||||
\(632\) | − | 0.757359i | − | 0.0301261i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.2426 | 0.883368 | ||||||||
\(635\) | 9.46473 | + | 16.3934i | 0.375596 | + | 0.650552i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.34924 | + | 4.83743i | −0.0534589 | + | 0.191666i | ||||
\(638\) | − | 7.45584i | − | 0.295180i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.12132 | + | 1.22474i | −0.0838525 | + | 0.0484123i | ||||
\(641\) | 28.7635 | + | 16.6066i | 1.13609 | + | 0.655921i | 0.945459 | − | 0.325741i | \(-0.105614\pi\) |
0.190630 | + | 0.981662i | \(0.438947\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.50000 | − | 0.866025i | −0.0591542 | − | 0.0341527i | 0.470131 | − | 0.882597i | \(-0.344207\pi\) |
−0.529285 | + | 0.848444i | \(0.677540\pi\) | |||||||
\(644\) | 2.15232 | − | 15.7279i | 0.0848132 | − | 0.619767i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | 10.3923 | + | 18.0000i | 0.408564 | + | 0.707653i | 0.994729 | − | 0.102538i | \(-0.0326965\pi\) |
−0.586165 | + | 0.810191i | \(0.699363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | − | 5.19615i | −0.353281 | − | 0.203967i | ||||
\(650\) | 0.358719 | + | 0.621320i | 0.0140701 | + | 0.0243702i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.74264 | + | 8.21449i | −0.185736 | + | 0.321704i | ||||
\(653\) | −2.15232 | + | 1.24264i | −0.0842267 | + | 0.0486283i | −0.541522 | − | 0.840687i | \(-0.682152\pi\) |
0.457295 | + | 0.889315i | \(0.348818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.22474 | − | 2.12132i | 0.0478183 | − | 0.0828236i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −26.8492 | − | 20.8207i | −1.04669 | − | 0.811674i | ||||
\(659\) | 19.2627 | − | 11.1213i | 0.750368 | − | 0.433225i | −0.0754589 | − | 0.997149i | \(-0.524042\pi\) |
0.825827 | + | 0.563924i | \(0.190709\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 4.89898i | − | 0.190548i | −0.995451 | − | 0.0952741i | \(-0.969627\pi\) | ||
0.995451 | − | 0.0952741i | \(-0.0303728\pi\) | |||||||
\(662\) | 10.0000i | 0.388661i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.2426 | + | 7.64564i | −0.513914 | + | 0.296708i | ||||
\(665\) | −25.0892 | − | 19.4558i | −0.972919 | − | 0.754465i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.27208 | + | 9.13151i | −0.204136 | + | 0.353573i | ||||
\(668\) | −0.297173 | + | 0.514719i | −0.0114980 | + | 0.0199151i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 28.6066 | − | 16.5160i | 1.10517 | − | 0.638070i | ||||
\(671\) | 8.87039 | − | 15.3640i | 0.342437 | − | 0.593119i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.7279 | + | 39.3659i | 0.876097 | + | 1.51744i | 0.855590 | + | 0.517655i | \(0.173195\pi\) |
0.0205075 | + | 0.999790i | \(0.493472\pi\) | |||||||
\(674\) | 18.5813 | + | 10.7279i | 0.715725 | + | 0.413224i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.24264 | + | 10.8126i | 0.240102 | + | 0.415868i | ||||
\(677\) | 14.6969 | 0.564849 | 0.282425 | − | 0.959289i | \(-0.408861\pi\) | ||||
0.282425 | + | 0.959289i | \(0.408861\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.13604 | − | 8.30153i | 0.0435972 | − | 0.318584i | ||||
\(680\) | 5.19615 | + | 3.00000i | 0.199263 | + | 0.115045i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 33.3640 | + | 19.2627i | 1.27757 | + | 0.737607i | ||||
\(683\) | −8.87039 | + | 5.12132i | −0.339416 | + | 0.195962i | −0.660014 | − | 0.751254i | \(-0.729450\pi\) |
0.320598 | + | 0.947215i | \(0.396116\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6969i | 0.561541i | ||||||||
\(686\) | −7.34847 | + | 17.0000i | −0.280566 | + | 0.649063i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.50000 | − | 6.06218i | −0.133436 | − | 0.231118i | ||||
\(689\) | −10.3923 | −0.395915 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.57258i | − | 0.0978657i | −0.998802 | − | 0.0489328i | \(-0.984418\pi\) | ||
0.998802 | − | 0.0489328i | \(-0.0155820\pi\) | |||||||
\(692\) | −20.7846 | −0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.97056 | −0.188680 | ||||||||
\(695\) | − | 19.7574i | − | 0.749439i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.00000 | −0.227266 | ||||||||
\(698\) | 0.0615465 | + | 0.106602i | 0.00232957 | + | 0.00403493i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | + | 2.44949i | 0.0377964 | + | 0.0925820i | ||||
\(701\) | 20.4853i | 0.773718i | 0.922139 | + | 0.386859i | \(0.126440\pi\) | ||||
−0.922139 | + | 0.386859i | \(0.873560\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.2426 | − | 12.8418i | 0.838897 | − | 0.484337i | ||||
\(704\) | −3.67423 | − | 2.12132i | −0.138478 | − | 0.0799503i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.51472 | + | 5.49333i | 0.358091 | + | 0.206744i | ||||
\(707\) | −7.34847 | − | 18.0000i | −0.276368 | − | 0.676960i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.2132 | 0.608900 | 0.304450 | − | 0.952528i | \(-0.401527\pi\) | ||||
0.304450 | + | 0.952528i | \(0.401527\pi\) | |||||||
\(710\) | −15.5885 | − | 27.0000i | −0.585024 | − | 1.01329i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.63604 | + | 1.52192i | 0.0987897 | + | 0.0570363i | ||||
\(713\) | −27.2416 | − | 47.1838i | −1.02020 | − | 1.76705i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.72792 | + | 6.45695i | −0.139416 | + | 0.241476i | ||||
\(716\) | 5.82655 | − | 3.36396i | 0.217748 | − | 0.125717i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.24264 | + | 12.5446i | −0.270293 | + | 0.468161i | ||||
\(719\) | 26.3140 | − | 45.5772i | 0.981346 | − | 1.69974i | 0.324181 | − | 0.945995i | \(-0.394911\pi\) |
0.657166 | − | 0.753746i | \(-0.271755\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.98528 | − | 29.1222i | 0.148420 | − | 1.08457i | ||||
\(722\) | −4.33013 | + | 2.50000i | −0.161151 | + | 0.0930404i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 9.79796i | − | 0.364138i | ||||||
\(725\) | − | 1.75736i | − | 0.0652667i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.3198 | − | 14.0410i | 0.901972 | − | 0.520754i | 0.0241323 | − | 0.999709i | \(-0.492318\pi\) |
0.877839 | + | 0.478955i | \(0.158984\pi\) | |||||||
\(728\) | −0.717439 | − | 1.75736i | −0.0265901 | − | 0.0651321i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.72792 | + | 11.6531i | −0.249012 | + | 0.431301i | ||||
\(731\) | −8.57321 | + | 14.8492i | −0.317092 | + | 0.549219i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.13604 | + | 0.655892i | −0.0419606 | + | 0.0242259i | −0.520834 | − | 0.853658i | \(-0.674379\pi\) |
0.478873 | + | 0.877884i | \(0.341045\pi\) | |||||||
\(734\) | −14.9941 | + | 25.9706i | −0.553443 | + | 0.958591i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | 49.5481 | + | 28.6066i | 1.82513 | + | 1.05374i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.22792 | + | 7.32298i | 0.155527 | + | 0.269380i | 0.933251 | − | 0.359226i | \(-0.116959\pi\) |
−0.777724 | + | 0.628606i | \(0.783626\pi\) | |||||||
\(740\) | −12.8418 | −0.472074 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −37.9706 | − | 5.19615i | −1.39394 | − | 0.190757i | ||||
\(743\) | −16.2189 | − | 9.36396i | −0.595012 | − | 0.343530i | 0.172065 | − | 0.985086i | \(-0.444956\pi\) |
−0.767077 | + | 0.641555i | \(0.778290\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.4558 | − | 19.8931i | −1.26236 | − | 0.728826i | ||||
\(746\) | −19.0526 | + | 11.0000i | −0.697564 | + | 0.402739i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.3923i | 0.379980i | ||||||||
\(749\) | −6.08767 | + | 2.48528i | −0.222439 | + | 0.0908102i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.7279 | − | 46.2941i | −0.975316 | − | 1.68930i | −0.678889 | − | 0.734241i | \(-0.737538\pi\) |
−0.296427 | − | 0.955056i | \(-0.595795\pi\) | |||||||
\(752\) | 12.8418 | 0.468292 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.26080i | 0.0459156i | ||||||||
\(755\) | 21.4511 | 0.780684 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.7574 | 1.19059 | 0.595293 | − | 0.803509i | \(-0.297036\pi\) | ||||
0.595293 | + | 0.803509i | \(0.297036\pi\) | |||||||
\(758\) | − | 7.48528i | − | 0.271878i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | 0.435286 | ||||||||
\(761\) | 12.2474 | + | 21.2132i | 0.443970 | + | 0.768978i | 0.997980 | − | 0.0635319i | \(-0.0202365\pi\) |
−0.554010 | + | 0.832510i | \(0.686903\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.4706 | − | 6.35935i | −1.68235 | − | 0.230224i | ||||
\(764\) | − | 21.2132i | − | 0.767467i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.75736 | + | 2.74666i | −0.171890 | + | 0.0992410i | ||||
\(767\) | 1.52192 | + | 0.878680i | 0.0549533 | + | 0.0317273i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.9706 | − | 20.1903i | −1.26107 | − | 0.728080i | −0.287789 | − | 0.957694i | \(-0.592920\pi\) |
−0.973282 | + | 0.229614i | \(0.926254\pi\) | |||||||
\(770\) | −16.8493 | + | 21.7279i | −0.607205 | + | 0.783020i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.48528 | 0.0534564 | ||||||||
\(773\) | −4.89898 | − | 8.48528i | −0.176204 | − | 0.305194i | 0.764373 | − | 0.644774i | \(-0.223049\pi\) |
−0.940577 | + | 0.339580i | \(0.889715\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.86396 | + | 4.54026i | 0.282482 | + | 0.163091i | ||||
\(776\) | 1.58346 | + | 2.74264i | 0.0568431 | + | 0.0984551i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.75736 | + | 13.4361i | −0.278115 | + | 0.481709i | ||||
\(779\) | −10.3923 | + | 6.00000i | −0.372343 | + | 0.214972i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0000 | − | 46.7654i | 0.966136 | − | 1.67340i | ||||
\(782\) | 7.34847 | − | 12.7279i | 0.262781 | − | 0.455150i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.74264 | − | 6.77962i | −0.0622372 | − | 0.242129i | ||||
\(785\) | −22.0454 | + | 12.7279i | −0.786834 | + | 0.454279i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28.2562i | − | 1.00722i | −0.863930 | − | 0.503612i | \(-0.832004\pi\) | ||
0.863930 | − | 0.503612i | \(-0.167996\pi\) | |||||||
\(788\) | − | 16.9706i | − | 0.604551i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.60660 | − | 0.927572i | 0.0571603 | − | 0.0330015i | ||||
\(791\) | 25.0892 | − | 10.2426i | 0.892071 | − | 0.364186i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.50000 | + | 2.59808i | −0.0532666 | + | 0.0922604i | ||||
\(794\) | 7.58410 | − | 13.1360i | 0.269149 | − | 0.466181i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.1066 | − | 10.4539i | 0.641771 | − | 0.370527i | ||||
\(797\) | −8.87039 | + | 15.3640i | −0.314205 | + | 0.544219i | −0.979268 | − | 0.202568i | \(-0.935071\pi\) |
0.665063 | + | 0.746787i | \(0.268405\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.7279 | − | 27.2416i | −0.556414 | − | 0.963737i | ||||
\(800\) | −0.866025 | − | 0.500000i | −0.0306186 | − | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.87868 | − | 17.1104i | −0.348828 | − | 0.604188i | ||||
\(803\) | −23.3062 | −0.822458 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 36.0000 | − | 14.6969i | 1.26883 | − | 0.517999i | ||||
\(806\) | −5.64191 | − | 3.25736i | −0.198728 | − | 0.114736i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.36396 | + | 3.67423i | 0.223883 | + | 0.129259i | ||||
\(809\) | −12.5446 | + | 7.24264i | −0.441045 | + | 0.254638i | −0.704041 | − | 0.710159i | \(-0.748623\pi\) |
0.262996 | + | 0.964797i | \(0.415290\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | −0.630399 | + | 4.60660i | −0.0221227 | + | 0.161660i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.1213 | − | 19.2627i | −0.389802 | − | 0.675157i | ||||
\(815\) | −23.2341 | −0.813855 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.2929i | 1.19976i | ||||||||
\(818\) | 3.76127 | 0.131510 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | 22.9706i | 0.801678i | 0.916148 | + | 0.400839i | \(0.131281\pi\) | ||||
−0.916148 | + | 0.400839i | \(0.868719\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.75736 | −0.0961155 | −0.0480578 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480578 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(824\) | 5.55487 | + | 9.62132i | 0.193513 | + | 0.335175i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.12132 | + | 3.97141i | 0.178194 | + | 0.138183i | ||||
\(827\) | − | 3.51472i | − | 0.122219i | −0.998131 | − | 0.0611094i | \(-0.980536\pi\) | ||
0.998131 | − | 0.0611094i | \(-0.0194638\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.48528 | − | 4.89898i | 0.294706 | − | 0.170149i | −0.345356 | − | 0.938472i | \(-0.612242\pi\) |
0.640062 | + | 0.768323i | \(0.278909\pi\) | |||||||
\(830\) | −32.4377 | − | 18.7279i | −1.12593 | − | 0.650056i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.621320 | + | 0.358719i | 0.0215404 | + | 0.0124364i | ||||
\(833\) | −12.2474 | + | 12.0000i | −0.424349 | + | 0.415775i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.45584 | −0.0503816 | ||||||||
\(836\) | 10.3923 | + | 18.0000i | 0.359425 | + | 0.622543i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.87868 | + | 3.97141i | 0.237620 | + | 0.137190i | ||||
\(839\) | 7.64564 | + | 13.2426i | 0.263957 | + | 0.457187i | 0.967290 | − | 0.253674i | \(-0.0816390\pi\) |
−0.703333 | + | 0.710861i | \(0.748306\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.9558 | + | 22.4402i | −0.446753 | + | 0.773799i | ||||
\(842\) | −20.3134 | + | 11.7279i | −0.700045 | + | 0.404171i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.74264 | − | 3.01834i | 0.0599842 | − | 0.103896i | ||||
\(845\) | −15.2913 | + | 26.4853i | −0.526036 | + | 0.911121i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.3492 | − | 2.51104i | −0.630487 | − | 0.0862802i | ||||
\(848\) | 12.5446 | − | 7.24264i | 0.430784 | − | 0.248713i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.44949i | 0.0840168i | ||||||||
\(851\) | 31.4558i | 1.07829i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.5147 | + | 15.8856i | −0.942086 | + | 0.543914i | −0.890614 | − | 0.454761i | \(-0.849725\pi\) |
−0.0514724 | + | 0.998674i | \(0.516391\pi\) | |||||||
\(854\) | −6.77962 | + | 8.74264i | −0.231994 | + | 0.299167i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.24264 | − | 2.15232i | 0.0424726 | − | 0.0735647i | ||||
\(857\) | −13.7694 | + | 23.8492i | −0.470353 | + | 0.814675i | −0.999425 | − | 0.0339020i | \(-0.989207\pi\) |
0.529073 | + | 0.848577i | \(0.322540\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.4706 | + | 14.1281i | −0.834925 | + | 0.482044i | −0.855536 | − | 0.517743i | \(-0.826772\pi\) |
0.0206111 | + | 0.999788i | \(0.493439\pi\) | |||||||
\(860\) | 8.57321 | − | 14.8492i | 0.292344 | − | 0.506355i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.878680 | − | 1.52192i | −0.0299279 | − | 0.0518367i | ||||
\(863\) | −32.4377 | − | 18.7279i | −1.10419 | − | 0.637506i | −0.166874 | − | 0.985978i | \(-0.553367\pi\) |
−0.937319 | + | 0.348472i | \(0.886700\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.4558 | − | 44.0908i | −0.865525 | − | 1.49913i | ||||
\(866\) | 2.57258 | 0.0874199 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −18.9853 | − | 14.7224i | −0.644402 | − | 0.499712i | ||||
\(869\) | 2.78272 | + | 1.60660i | 0.0943972 | + | 0.0545002i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.37868 | − | 4.83743i | −0.283901 | − | 0.163910i | ||||
\(872\) | 15.3528 | − | 8.86396i | 0.519912 | − | 0.300172i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 29.3939i | − | 0.994263i | ||||||
\(875\) | 15.8856 | − | 20.4853i | 0.537032 | − | 0.692529i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1066 | + | 40.0218i | 0.780254 | + | 1.35144i | 0.931793 | + | 0.362989i | \(0.118244\pi\) |
−0.151539 | + | 0.988451i | \(0.548423\pi\) | |||||||
\(878\) | 4.30463 | 0.145274 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 10.3923i | − | 0.350325i | ||||||
\(881\) | 25.0892 | 0.845278 | 0.422639 | − | 0.906298i | \(-0.361104\pi\) | ||||
0.422639 | + | 0.906298i | \(0.361104\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00000 | −0.0673054 | −0.0336527 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336527 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(884\) | − | 1.75736i | − | 0.0591064i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.4558 | 0.855206 | ||||||||
\(887\) | 4.60181 | + | 7.97056i | 0.154514 | + | 0.267625i | 0.932882 | − | 0.360183i | \(-0.117286\pi\) |
−0.778368 | + | 0.627808i | \(0.783952\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.5294 | − | 16.1573i | 0.420224 | − | 0.541899i | ||||
\(890\) | 7.45584i | 0.249920i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.00000 | + | 5.19615i | −0.301342 | + | 0.173980i | ||||
\(893\) | −54.4831 | − | 31.4558i | −1.82321 | − | 1.05263i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.2721 | + | 8.23999i | 0.477063 | + | 0.275432i | ||||
\(896\) | 2.09077 | + | 1.62132i | 0.0698477 | + | 0.0541645i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.27208 | −0.175932 | ||||||||
\(899\) | 7.97887 | + | 13.8198i | 0.266110 | + | 0.460916i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.7279 | − | 17.7408i | −1.02370 | − | 0.591031i | ||||
\(902\) | 5.19615 | + | 9.00000i | 0.173013 | + | 0.299667i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.12132 | + | 8.87039i | −0.170333 | + | 0.295025i | ||||
\(905\) | 20.7846 | − | 12.0000i | 0.690904 | − | 0.398893i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.74264 | − | 11.6786i | 0.223886 | − | 0.387781i | −0.732099 | − | 0.681198i | \(-0.761459\pi\) |
0.955985 | + | 0.293417i | \(0.0947924\pi\) | |||||||
\(908\) | −12.5446 | + | 21.7279i | −0.416308 | + | 0.721066i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.84924 | − | 3.67423i | 0.0944515 | − | 0.121800i | ||||
\(911\) | −8.87039 | + | 5.12132i | −0.293889 | + | 0.169677i | −0.639694 | − | 0.768629i | \(-0.720939\pi\) |
0.345805 | + | 0.938306i | \(0.387606\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 64.8754i | − | 2.14706i | ||||||
\(914\) | − | 23.0000i | − | 0.760772i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.86396 | + | 2.80821i | −0.160710 | + | 0.0927858i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.8640 | + | 22.2810i | −0.424343 | + | 0.734983i | −0.996359 | − | 0.0852590i | \(-0.972828\pi\) |
0.572016 | + | 0.820243i | \(0.306162\pi\) | |||||||
\(920\) | −7.34847 | + | 12.7279i | −0.242272 | + | 0.419627i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.5772 | + | 10.7255i | −0.611806 | + | 0.353227i | ||||
\(923\) | −4.56575 | + | 7.90812i | −0.150284 | + | 0.260299i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.62132 | − | 4.54026i | −0.0861885 | − | 0.149283i | ||||
\(926\) | 19.0526 | + | 11.0000i | 0.626106 | + | 0.361482i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.878680 | − | 1.52192i | −0.0288441 | − | 0.0499594i | ||||
\(929\) | −28.7274 | −0.942516 | −0.471258 | − | 0.881995i | \(-0.656200\pi\) | ||||
−0.471258 | + | 0.881995i | \(0.656200\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.21320 | + | 33.0321i | −0.301951 | + | 1.08258i | ||||
\(932\) | 17.7408 | + | 10.2426i | 0.581118 | + | 0.335509i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.3640 | + | 8.87039i | 0.502724 | + | 0.290248i | ||||
\(935\) | −22.0454 | + | 12.7279i | −0.720962 | + | 0.416248i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.5033i | 1.09451i | 0.836967 | + | 0.547253i | \(0.184326\pi\) | ||||
−0.836967 | + | 0.547253i | \(0.815674\pi\) | |||||||
\(938\) | −28.1946 | − | 21.8640i | −0.920587 | − | 0.713884i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.7279 | + | 27.2416i | 0.512988 | + | 0.888522i | ||||
\(941\) | −42.2357 | −1.37684 | −0.688422 | − | 0.725311i | \(-0.741696\pi\) | ||||
−0.688422 | + | 0.725311i | \(0.741696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 14.6969i | − | 0.478598i | ||||||
\(944\) | −2.44949 | −0.0797241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.6985 | 0.965581 | ||||||||
\(947\) | − | 16.2426i | − | 0.527815i | −0.964548 | − | 0.263907i | \(-0.914989\pi\) | ||
0.964548 | − | 0.263907i | \(-0.0850114\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.94113 | 0.127934 | ||||||||
\(950\) | 2.44949 | + | 4.24264i | 0.0794719 | + | 0.137649i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.878680 | − | 6.42090i | 0.0284782 | − | 0.208102i | ||||
\(953\) | − | 1.02944i | − | 0.0333467i | −0.999861 | − | 0.0166734i | \(-0.994692\pi\) | ||
0.999861 | − | 0.0166734i | \(-0.00530755\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.0000 | − | 25.9808i | 1.45617 | − | 0.840718i | ||||
\(956\) | 14.0665 | + | 8.12132i | 0.454944 | + | 0.262662i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.12132 | + | 1.22474i | 0.0685367 | + | 0.0395697i | ||||
\(959\) | 14.6969 | − | 6.00000i | 0.474589 | − | 0.193750i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −51.4558 | −1.65987 | ||||||||
\(962\) | 1.88064 | + | 3.25736i | 0.0606342 | + | 0.105021i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.985281 | − | 0.568852i | −0.0317338 | − | 0.0183215i | ||||
\(965\) | 1.81909 | + | 3.15076i | 0.0585586 | + | 0.101426i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.3492 | − | 36.9780i | 0.686545 | − | 1.18913i | −0.286403 | − | 0.958109i | \(-0.592460\pi\) |
0.972948 | − | 0.231022i | \(-0.0742070\pi\) | |||||||
\(968\) | 6.06218 | − | 3.50000i | 0.194846 | − | 0.112494i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.87868 | + | 6.71807i | −0.124537 | + | 0.215704i | ||||
\(971\) | −20.1903 | + | 34.9706i | −0.647936 | + | 1.12226i | 0.335679 | + | 0.941977i | \(0.391034\pi\) |
−0.983615 | + | 0.180282i | \(0.942299\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.7574 | + | 8.06591i | −0.633392 | + | 0.258581i | ||||
\(974\) | 19.0526 | − | 11.0000i | 0.610483 | − | 0.352463i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 4.18154i | − | 0.133848i | ||||||
\(977\) | 6.00000i | 0.191957i | 0.995383 | + | 0.0959785i | \(0.0305980\pi\) | ||||
−0.995383 | + | 0.0959785i | \(0.969402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.1838 | + | 6.45695i | −0.357435 | + | 0.206365i | ||||
\(980\) | 12.2474 | − | 12.0000i | 0.391230 | − | 0.383326i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.4853 | − | 30.2854i | 0.557978 | − | 0.966446i | ||||
\(983\) | 11.6170 | − | 20.1213i | 0.370526 | − | 0.641770i | −0.619120 | − | 0.785296i | \(-0.712511\pi\) |
0.989647 | + | 0.143526i | \(0.0458440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.0000 | − | 20.7846i | 1.14706 | − | 0.662253i | ||||
\(986\) | −2.15232 | + | 3.72792i | −0.0685437 | + | 0.118721i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.75736 | − | 3.04384i | −0.0559090 | − | 0.0968373i | ||||
\(989\) | −36.3731 | − | 21.0000i | −1.15660 | − | 0.667761i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.1066 | + | 17.5051i | 0.321047 | + | 0.556069i | 0.980704 | − | 0.195497i | \(-0.0626320\pi\) |
−0.659658 | + | 0.751566i | \(0.729299\pi\) | |||||||
\(992\) | 9.08052 | 0.288307 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.6360 | + | 26.6112i | −0.654535 | + | 0.844055i | ||||
\(995\) | 44.3519 | + | 25.6066i | 1.40605 | + | 0.811784i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.8640 | − | 9.73641i | −0.534087 | − | 0.308355i | 0.208592 | − | 0.978003i | \(-0.433112\pi\) |
−0.742679 | + | 0.669647i | \(0.766445\pi\) | |||||||
\(998\) | −21.1794 | + | 12.2279i | −0.670422 | + | 0.387068i | ||||
\(999\) | 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 | 1134.2.l.e.215.3 | 8 | ||
3.2 | odd | 2 | inner | 1134.2.l.e.215.2 | 8 | ||
7.3 | odd | 6 | 1134.2.t.f.1025.1 | 8 | |||
9.2 | odd | 6 | 1134.2.t.f.593.1 | 8 | |||
9.4 | even | 3 | 378.2.k.d.215.1 | ✓ | 8 | ||
9.5 | odd | 6 | 378.2.k.d.215.4 | yes | 8 | ||
9.7 | even | 3 | 1134.2.t.f.593.4 | 8 | |||
21.17 | even | 6 | 1134.2.t.f.1025.4 | 8 | |||
63.5 | even | 6 | 2646.2.d.d.2645.4 | 8 | |||
63.23 | odd | 6 | 2646.2.d.d.2645.2 | 8 | |||
63.31 | odd | 6 | 378.2.k.d.269.4 | yes | 8 | ||
63.38 | even | 6 | inner | 1134.2.l.e.269.1 | 8 | ||
63.40 | odd | 6 | 2646.2.d.d.2645.5 | 8 | |||
63.52 | odd | 6 | inner | 1134.2.l.e.269.4 | 8 | ||
63.58 | even | 3 | 2646.2.d.d.2645.7 | 8 | |||
63.59 | even | 6 | 378.2.k.d.269.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.k.d.215.1 | ✓ | 8 | 9.4 | even | 3 | ||
378.2.k.d.215.4 | yes | 8 | 9.5 | odd | 6 | ||
378.2.k.d.269.1 | yes | 8 | 63.59 | even | 6 | ||
378.2.k.d.269.4 | yes | 8 | 63.31 | odd | 6 | ||
1134.2.l.e.215.2 | 8 | 3.2 | odd | 2 | inner | ||
1134.2.l.e.215.3 | 8 | 1.1 | even | 1 | trivial | ||
1134.2.l.e.269.1 | 8 | 63.38 | even | 6 | inner | ||
1134.2.l.e.269.4 | 8 | 63.52 | odd | 6 | inner | ||
1134.2.t.f.593.1 | 8 | 9.2 | odd | 6 | |||
1134.2.t.f.593.4 | 8 | 9.7 | even | 3 | |||
1134.2.t.f.1025.1 | 8 | 7.3 | odd | 6 | |||
1134.2.t.f.1025.4 | 8 | 21.17 | even | 6 | |||
2646.2.d.d.2645.2 | 8 | 63.23 | odd | 6 | |||
2646.2.d.d.2645.4 | 8 | 63.5 | even | 6 | |||
2646.2.d.d.2645.5 | 8 | 63.40 | odd | 6 | |||
2646.2.d.d.2645.7 | 8 | 63.58 | even | 3 |