Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [145,2,Mod(86,145)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(145, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("145.86");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 145 = 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 145.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.15783082931\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.16516096.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 13x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 86.1 | ||
Root | \(-2.68667i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 145.86 |
Dual form | 145.2.c.b.86.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/145\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(117\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.68667i | − | 1.89976i | −0.312613 | − | 0.949881i | \(-0.601204\pi\) | ||
0.312613 | − | 0.949881i | \(-0.398796\pi\) | |||||||
\(3\) | − | 2.31446i | − | 1.33625i | −0.744047 | − | 0.668127i | \(-0.767096\pi\) | ||
0.744047 | − | 0.668127i | \(-0.232904\pi\) | |||||||
\(4\) | −5.21819 | −2.60909 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −6.21819 | −2.53856 | ||||||||
\(7\) | 4.21819 | 1.59432 | 0.797162 | − | 0.603765i | \(-0.206333\pi\) | ||||
0.797162 | + | 0.603765i | \(0.206333\pi\) | |||||||
\(8\) | 8.64620i | 3.05689i | ||||||||
\(9\) | −2.35673 | −0.785575 | ||||||||
\(10\) | − | 2.68667i | − | 0.849599i | ||||||
\(11\) | 2.31446i | 0.697836i | 0.937153 | + | 0.348918i | \(0.113451\pi\) | ||||
−0.937153 | + | 0.348918i | \(0.886549\pi\) | |||||||
\(12\) | 12.0773i | 3.48641i | ||||||||
\(13\) | −0.643274 | −0.178412 | −0.0892061 | − | 0.996013i | \(-0.528433\pi\) | ||||
−0.0892061 | + | 0.996013i | \(0.528433\pi\) | |||||||
\(14\) | − | 11.3329i | − | 3.02884i | ||||||
\(15\) | − | 2.31446i | − | 0.597591i | ||||||
\(16\) | 12.7931 | 3.19827 | ||||||||
\(17\) | − | 0.586195i | − | 0.142173i | −0.997470 | − | 0.0710866i | \(-0.977353\pi\) | ||
0.997470 | − | 0.0710866i | \(-0.0226467\pi\) | |||||||
\(18\) | 6.33174i | 1.49241i | ||||||||
\(19\) | 5.95953i | 1.36721i | 0.729852 | + | 0.683605i | \(0.239589\pi\) | ||||
−0.729852 | + | 0.683605i | \(0.760411\pi\) | |||||||
\(20\) | −5.21819 | −1.16682 | ||||||||
\(21\) | − | 9.76282i | − | 2.13042i | ||||||
\(22\) | 6.21819 | 1.32572 | ||||||||
\(23\) | −5.57491 | −1.16245 | −0.581225 | − | 0.813743i | \(-0.697426\pi\) | ||||
−0.581225 | + | 0.813743i | \(0.697426\pi\) | |||||||
\(24\) | 20.0113 | 4.08479 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.72826i | 0.338941i | ||||||||
\(27\) | − | 1.48883i | − | 0.286526i | ||||||
\(28\) | −22.0113 | −4.15974 | ||||||||
\(29\) | −5.21819 | − | 1.33061i | −0.968993 | − | 0.247088i | ||||
\(30\) | −6.21819 | −1.13528 | ||||||||
\(31\) | 0.158221i | 0.0284174i | 0.999899 | + | 0.0142087i | \(0.00452291\pi\) | ||||
−0.999899 | + | 0.0142087i | \(0.995477\pi\) | |||||||
\(32\) | − | 17.0784i | − | 3.01907i | ||||||
\(33\) | 5.35673 | 0.932486 | ||||||||
\(34\) | −1.57491 | −0.270095 | ||||||||
\(35\) | 4.21819 | 0.713004 | ||||||||
\(36\) | 12.2978 | 2.04964 | ||||||||
\(37\) | 4.04272i | 0.664620i | 0.943170 | + | 0.332310i | \(0.107828\pi\) | ||||
−0.943170 | + | 0.332310i | \(0.892172\pi\) | |||||||
\(38\) | 16.0113 | 2.59737 | ||||||||
\(39\) | 1.48883i | 0.238404i | ||||||||
\(40\) | 8.64620i | 1.36708i | ||||||||
\(41\) | − | 9.76282i | − | 1.52470i | −0.647167 | − | 0.762349i | \(-0.724046\pi\) | ||
0.647167 | − | 0.762349i | \(-0.275954\pi\) | |||||||
\(42\) | −26.2295 | −4.04730 | ||||||||
\(43\) | 4.97568i | 0.758785i | 0.925236 | + | 0.379392i | \(0.123867\pi\) | ||||
−0.925236 | + | 0.379392i | \(0.876133\pi\) | |||||||
\(44\) | − | 12.0773i | − | 1.82072i | ||||||
\(45\) | −2.35673 | −0.351320 | ||||||||
\(46\) | 14.9779i | 2.20838i | ||||||||
\(47\) | 2.31446i | 0.337599i | 0.985650 | + | 0.168799i | \(0.0539890\pi\) | ||||
−0.985650 | + | 0.168799i | \(0.946011\pi\) | |||||||
\(48\) | − | 29.6091i | − | 4.27371i | ||||||
\(49\) | 10.7931 | 1.54187 | ||||||||
\(50\) | − | 2.68667i | − | 0.379952i | ||||||
\(51\) | −1.35673 | −0.189980 | ||||||||
\(52\) | 3.35673 | 0.465494 | ||||||||
\(53\) | 13.0796 | 1.79663 | 0.898314 | − | 0.439354i | \(-0.144793\pi\) | ||||
0.898314 | + | 0.439354i | \(0.144793\pi\) | |||||||
\(54\) | −4.00000 | −0.544331 | ||||||||
\(55\) | 2.31446i | 0.312082i | ||||||||
\(56\) | 36.4713i | 4.87368i | ||||||||
\(57\) | 13.7931 | 1.82694 | ||||||||
\(58\) | −3.57491 | + | 14.0195i | −0.469409 | + | 1.84086i | ||||
\(59\) | −2.64327 | −0.344125 | −0.172063 | − | 0.985086i | \(-0.555043\pi\) | ||||
−0.172063 | + | 0.985086i | \(0.555043\pi\) | |||||||
\(60\) | 12.0773i | 1.55917i | ||||||||
\(61\) | − | 0.983848i | − | 0.125969i | −0.998015 | − | 0.0629844i | \(-0.979938\pi\) | ||
0.998015 | − | 0.0629844i | \(-0.0200618\pi\) | |||||||
\(62\) | 0.425088 | 0.0539862 | ||||||||
\(63\) | −9.94111 | −1.25246 | ||||||||
\(64\) | −20.2978 | −2.53723 | ||||||||
\(65\) | −0.643274 | −0.0797884 | ||||||||
\(66\) | − | 14.3917i | − | 1.77150i | ||||||
\(67\) | 1.57491 | 0.192406 | 0.0962031 | − | 0.995362i | \(-0.469330\pi\) | ||||
0.0962031 | + | 0.995362i | \(0.469330\pi\) | |||||||
\(68\) | 3.05888i | 0.370943i | ||||||||
\(69\) | 12.9029i | 1.55333i | ||||||||
\(70\) | − | 11.3329i | − | 1.35454i | ||||||
\(71\) | −9.35673 | −1.11044 | −0.555220 | − | 0.831704i | \(-0.687366\pi\) | ||||
−0.555220 | + | 0.831704i | \(0.687366\pi\) | |||||||
\(72\) | − | 20.3767i | − | 2.40142i | ||||||
\(73\) | − | 9.17663i | − | 1.07404i | −0.843568 | − | 0.537022i | \(-0.819549\pi\) | ||
0.843568 | − | 0.537022i | \(-0.180451\pi\) | |||||||
\(74\) | 10.8615 | 1.26262 | ||||||||
\(75\) | − | 2.31446i | − | 0.267251i | ||||||
\(76\) | − | 31.0980i | − | 3.56718i | ||||||
\(77\) | 9.76282i | 1.11258i | ||||||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | 4.97568i | 0.559808i | 0.960028 | + | 0.279904i | \(0.0903027\pi\) | ||||
−0.960028 | + | 0.279904i | \(0.909697\pi\) | |||||||
\(80\) | 12.7931 | 1.43031 | ||||||||
\(81\) | −10.5160 | −1.16845 | ||||||||
\(82\) | −26.2295 | −2.89656 | ||||||||
\(83\) | −8.21819 | −0.902063 | −0.451032 | − | 0.892508i | \(-0.648944\pi\) | ||||
−0.451032 | + | 0.892508i | \(0.648944\pi\) | |||||||
\(84\) | 50.9442i | 5.55847i | ||||||||
\(85\) | − | 0.586195i | − | 0.0635818i | ||||||
\(86\) | 13.3680 | 1.44151 | ||||||||
\(87\) | −3.07965 | + | 12.0773i | −0.330173 | + | 1.29482i | ||||
\(88\) | −20.0113 | −2.13321 | ||||||||
\(89\) | 7.29014i | 0.772754i | 0.922341 | + | 0.386377i | \(0.126274\pi\) | ||||
−0.922341 | + | 0.386377i | \(0.873726\pi\) | |||||||
\(90\) | 6.33174i | 0.667424i | ||||||||
\(91\) | −2.71345 | −0.284447 | ||||||||
\(92\) | 29.0909 | 3.03294 | ||||||||
\(93\) | 0.366196 | 0.0379728 | ||||||||
\(94\) | 6.21819 | 0.641357 | ||||||||
\(95\) | 5.95953i | 0.611435i | ||||||||
\(96\) | −39.5273 | −4.03424 | ||||||||
\(97\) | 3.05888i | 0.310582i | 0.987869 | + | 0.155291i | \(0.0496315\pi\) | ||||
−0.987869 | + | 0.155291i | \(0.950369\pi\) | |||||||
\(98\) | − | 28.9975i | − | 2.92919i | ||||||
\(99\) | − | 5.45455i | − | 0.548203i | ||||||
\(100\) | −5.21819 | −0.521819 | ||||||||
\(101\) | 1.48883i | 0.148144i | 0.997253 | + | 0.0740722i | \(0.0235995\pi\) | ||||
−0.997253 | + | 0.0740722i | \(0.976400\pi\) | |||||||
\(102\) | 3.64507i | 0.360916i | ||||||||
\(103\) | 11.2978 | 1.11321 | 0.556604 | − | 0.830778i | \(-0.312104\pi\) | ||||
0.556604 | + | 0.830778i | \(0.312104\pi\) | |||||||
\(104\) | − | 5.56188i | − | 0.545387i | ||||||
\(105\) | − | 9.76282i | − | 0.952754i | ||||||
\(106\) | − | 35.1407i | − | 3.41316i | ||||||
\(107\) | −2.93164 | −0.283412 | −0.141706 | − | 0.989909i | \(-0.545259\pi\) | ||||
−0.141706 | + | 0.989909i | \(0.545259\pi\) | |||||||
\(108\) | 7.76901i | 0.747573i | ||||||||
\(109\) | −17.0796 | −1.63593 | −0.817967 | − | 0.575265i | \(-0.804899\pi\) | ||||
−0.817967 | + | 0.575265i | \(0.804899\pi\) | |||||||
\(110\) | 6.21819 | 0.592881 | ||||||||
\(111\) | 9.35673 | 0.888101 | ||||||||
\(112\) | 53.9637 | 5.09909 | ||||||||
\(113\) | − | 13.4891i | − | 1.26895i | −0.772944 | − | 0.634474i | \(-0.781217\pi\) | ||
0.772944 | − | 0.634474i | \(-0.218783\pi\) | |||||||
\(114\) | − | 37.0575i | − | 3.47075i | ||||||
\(115\) | −5.57491 | −0.519863 | ||||||||
\(116\) | 27.2295 | + | 6.94338i | 2.52819 | + | 0.644677i | ||||
\(117\) | 1.51602 | 0.140156 | ||||||||
\(118\) | 7.10160i | 0.653755i | ||||||||
\(119\) | − | 2.47268i | − | 0.226670i | ||||||
\(120\) | 20.0113 | 1.82677 | ||||||||
\(121\) | 5.64327 | 0.513025 | ||||||||
\(122\) | −2.64327 | −0.239311 | ||||||||
\(123\) | −22.5957 | −2.03738 | ||||||||
\(124\) | − | 0.825627i | − | 0.0741435i | ||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 26.7085i | 2.37938i | ||||||||
\(127\) | − | 11.0934i | − | 0.984383i | −0.870487 | − | 0.492192i | \(-0.836196\pi\) | ||
0.870487 | − | 0.492192i | \(-0.163804\pi\) | |||||||
\(128\) | 20.3767i | 1.80106i | ||||||||
\(129\) | 11.5160 | 1.01393 | ||||||||
\(130\) | 1.72826i | 0.151579i | ||||||||
\(131\) | 7.13192i | 0.623119i | 0.950227 | + | 0.311559i | \(0.100851\pi\) | ||||
−0.950227 | + | 0.311559i | \(0.899149\pi\) | |||||||
\(132\) | −27.9524 | −2.43294 | ||||||||
\(133\) | 25.1384i | 2.17978i | ||||||||
\(134\) | − | 4.23127i | − | 0.365526i | ||||||
\(135\) | − | 1.48883i | − | 0.128138i | ||||||
\(136\) | 5.06836 | 0.434608 | ||||||||
\(137\) | − | 14.7894i | − | 1.26354i | −0.775154 | − | 0.631772i | \(-0.782328\pi\) | ||
0.775154 | − | 0.631772i | \(-0.217672\pi\) | |||||||
\(138\) | 34.6658 | 2.95095 | ||||||||
\(139\) | 3.56363 | 0.302263 | 0.151131 | − | 0.988514i | \(-0.451708\pi\) | ||||
0.151131 | + | 0.988514i | \(0.451708\pi\) | |||||||
\(140\) | −22.0113 | −1.86029 | ||||||||
\(141\) | 5.35673 | 0.451118 | ||||||||
\(142\) | 25.1384i | 2.10957i | ||||||||
\(143\) | − | 1.48883i | − | 0.124502i | ||||||
\(144\) | −30.1498 | −2.51249 | ||||||||
\(145\) | −5.21819 | − | 1.33061i | −0.433347 | − | 0.110501i | ||||
\(146\) | −24.6546 | −2.04043 | ||||||||
\(147\) | − | 24.9802i | − | 2.06033i | ||||||
\(148\) | − | 21.0957i | − | 1.73406i | ||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | −6.21819 | −0.507713 | ||||||||
\(151\) | 4.50655 | 0.366738 | 0.183369 | − | 0.983044i | \(-0.441300\pi\) | ||||
0.183369 | + | 0.983044i | \(0.441300\pi\) | |||||||
\(152\) | −51.5273 | −4.17942 | ||||||||
\(153\) | 1.38150i | 0.111688i | ||||||||
\(154\) | 26.2295 | 2.11363 | ||||||||
\(155\) | 0.158221i | 0.0127086i | ||||||||
\(156\) | − | 7.76901i | − | 0.622018i | ||||||
\(157\) | 16.9456i | 1.35241i | 0.736714 | + | 0.676205i | \(0.236376\pi\) | ||||
−0.736714 | + | 0.676205i | \(0.763624\pi\) | |||||||
\(158\) | 13.3680 | 1.06350 | ||||||||
\(159\) | − | 30.2723i | − | 2.40075i | ||||||
\(160\) | − | 17.0784i | − | 1.35017i | ||||||
\(161\) | −23.5160 | −1.85332 | ||||||||
\(162\) | 28.2531i | 2.21977i | ||||||||
\(163\) | 11.0934i | 0.868905i | 0.900695 | + | 0.434453i | \(0.143058\pi\) | ||||
−0.900695 | + | 0.434453i | \(0.856942\pi\) | |||||||
\(164\) | 50.9442i | 3.97808i | ||||||||
\(165\) | 5.35673 | 0.417021 | ||||||||
\(166\) | 22.0795i | 1.71370i | ||||||||
\(167\) | −5.57491 | −0.431400 | −0.215700 | − | 0.976460i | \(-0.569203\pi\) | ||||
−0.215700 | + | 0.976460i | \(0.569203\pi\) | |||||||
\(168\) | 84.4113 | 6.51248 | ||||||||
\(169\) | −12.5862 | −0.968169 | ||||||||
\(170\) | −1.57491 | −0.120790 | ||||||||
\(171\) | − | 14.0450i | − | 1.07405i | ||||||
\(172\) | − | 25.9640i | − | 1.97974i | ||||||
\(173\) | 7.79310 | 0.592498 | 0.296249 | − | 0.955111i | \(-0.404264\pi\) | ||||
0.296249 | + | 0.955111i | \(0.404264\pi\) | |||||||
\(174\) | 32.4477 | + | 8.27399i | 2.45985 | + | 0.627250i | ||||
\(175\) | 4.21819 | 0.318865 | ||||||||
\(176\) | 29.6091i | 2.23187i | ||||||||
\(177\) | 6.11775i | 0.459838i | ||||||||
\(178\) | 19.5862 | 1.46805 | ||||||||
\(179\) | −4.43637 | −0.331590 | −0.165795 | − | 0.986160i | \(-0.553019\pi\) | ||||
−0.165795 | + | 0.986160i | \(0.553019\pi\) | |||||||
\(180\) | 12.2978 | 0.916626 | ||||||||
\(181\) | 13.5160 | 1.00464 | 0.502319 | − | 0.864682i | \(-0.332480\pi\) | ||||
0.502319 | + | 0.864682i | \(0.332480\pi\) | |||||||
\(182\) | 7.29014i | 0.540381i | ||||||||
\(183\) | −2.27708 | −0.168326 | ||||||||
\(184\) | − | 48.2018i | − | 3.55348i | ||||||
\(185\) | 4.04272i | 0.297227i | ||||||||
\(186\) | − | 0.983848i | − | 0.0721393i | ||||||
\(187\) | 1.35673 | 0.0992136 | ||||||||
\(188\) | − | 12.0773i | − | 0.880827i | ||||||
\(189\) | − | 6.28017i | − | 0.456816i | ||||||
\(190\) | 16.0113 | 1.16158 | ||||||||
\(191\) | − | 11.5723i | − | 0.837342i | −0.908138 | − | 0.418671i | \(-0.862496\pi\) | ||
0.908138 | − | 0.418671i | \(-0.137504\pi\) | |||||||
\(192\) | 46.9785i | 3.39038i | ||||||||
\(193\) | − | 9.84404i | − | 0.708589i | −0.935134 | − | 0.354295i | \(-0.884721\pi\) | ||
0.935134 | − | 0.354295i | \(-0.115279\pi\) | |||||||
\(194\) | 8.21819 | 0.590031 | ||||||||
\(195\) | 1.48883i | 0.106618i | ||||||||
\(196\) | −56.3204 | −4.02289 | ||||||||
\(197\) | −5.14982 | −0.366910 | −0.183455 | − | 0.983028i | \(-0.558728\pi\) | ||||
−0.183455 | + | 0.983028i | \(0.558728\pi\) | |||||||
\(198\) | −14.6546 | −1.04145 | ||||||||
\(199\) | −17.7931 | −1.26132 | −0.630660 | − | 0.776060i | \(-0.717216\pi\) | ||||
−0.630660 | + | 0.776060i | \(0.717216\pi\) | |||||||
\(200\) | 8.64620i | 0.611379i | ||||||||
\(201\) | − | 3.64507i | − | 0.257104i | ||||||
\(202\) | 4.00000 | 0.281439 | ||||||||
\(203\) | −22.0113 | − | 5.61277i | −1.54489 | − | 0.393939i | ||||
\(204\) | 7.07965 | 0.495674 | ||||||||
\(205\) | − | 9.76282i | − | 0.681865i | ||||||
\(206\) | − | 30.3535i | − | 2.11483i | ||||||
\(207\) | 13.1385 | 0.913192 | ||||||||
\(208\) | −8.22947 | −0.570611 | ||||||||
\(209\) | −13.7931 | −0.954089 | ||||||||
\(210\) | −26.2295 | −1.81001 | ||||||||
\(211\) | 18.8624i | 1.29854i | 0.760556 | + | 0.649272i | \(0.224926\pi\) | ||||
−0.760556 | + | 0.649272i | \(0.775074\pi\) | |||||||
\(212\) | −68.2520 | −4.68757 | ||||||||
\(213\) | 21.6558i | 1.48383i | ||||||||
\(214\) | 7.87634i | 0.538415i | ||||||||
\(215\) | 4.97568i | 0.339339i | ||||||||
\(216\) | 12.8727 | 0.875879 | ||||||||
\(217\) | 0.667406i | 0.0453065i | ||||||||
\(218\) | 45.8873i | 3.10788i | ||||||||
\(219\) | −21.2389 | −1.43519 | ||||||||
\(220\) | − | 12.0773i | − | 0.814250i | ||||||
\(221\) | 0.377084i | 0.0253654i | ||||||||
\(222\) | − | 25.1384i | − | 1.68718i | ||||||
\(223\) | 13.5749 | 0.909043 | 0.454522 | − | 0.890736i | \(-0.349810\pi\) | ||||
0.454522 | + | 0.890736i | \(0.349810\pi\) | |||||||
\(224\) | − | 72.0399i | − | 4.81337i | ||||||
\(225\) | −2.35673 | −0.157115 | ||||||||
\(226\) | −36.2408 | −2.41070 | ||||||||
\(227\) | 7.00181 | 0.464727 | 0.232363 | − | 0.972629i | \(-0.425354\pi\) | ||||
0.232363 | + | 0.972629i | \(0.425354\pi\) | |||||||
\(228\) | −71.9750 | −4.76666 | ||||||||
\(229\) | − | 24.1546i | − | 1.59618i | −0.602539 | − | 0.798089i | \(-0.705844\pi\) | ||
0.602539 | − | 0.798089i | \(-0.294156\pi\) | |||||||
\(230\) | 14.9779i | 0.987616i | ||||||||
\(231\) | 22.5957 | 1.48669 | ||||||||
\(232\) | 11.5047 | − | 45.1175i | 0.755323 | − | 2.96211i | ||||
\(233\) | 5.14982 | 0.337376 | 0.168688 | − | 0.985669i | \(-0.446047\pi\) | ||||
0.168688 | + | 0.985669i | \(0.446047\pi\) | |||||||
\(234\) | − | 4.07305i | − | 0.266263i | ||||||
\(235\) | 2.31446i | 0.150979i | ||||||||
\(236\) | 13.7931 | 0.897854 | ||||||||
\(237\) | 11.5160 | 0.748046 | ||||||||
\(238\) | −6.64327 | −0.430620 | ||||||||
\(239\) | 14.6433 | 0.947195 | 0.473597 | − | 0.880741i | \(-0.342955\pi\) | ||||
0.473597 | + | 0.880741i | \(0.342955\pi\) | |||||||
\(240\) | − | 29.6091i | − | 1.91126i | ||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | − | 15.1616i | − | 0.974625i | ||||||
\(243\) | 19.8724i | 1.27482i | ||||||||
\(244\) | 5.13390i | 0.328665i | ||||||||
\(245\) | 10.7931 | 0.689546 | ||||||||
\(246\) | 60.7071i | 3.87054i | ||||||||
\(247\) | − | 3.83361i | − | 0.243927i | ||||||
\(248\) | −1.36801 | −0.0868688 | ||||||||
\(249\) | 19.0207i | 1.20539i | ||||||||
\(250\) | − | 2.68667i | − | 0.169920i | ||||||
\(251\) | 22.6354i | 1.42873i | 0.699771 | + | 0.714367i | \(0.253285\pi\) | ||||
−0.699771 | + | 0.714367i | \(0.746715\pi\) | |||||||
\(252\) | 51.8746 | 3.26779 | ||||||||
\(253\) | − | 12.9029i | − | 0.811199i | ||||||
\(254\) | −29.8044 | −1.87009 | ||||||||
\(255\) | −1.35673 | −0.0849615 | ||||||||
\(256\) | 14.1498 | 0.884364 | ||||||||
\(257\) | 10.9204 | 0.681193 | 0.340596 | − | 0.940210i | \(-0.389371\pi\) | ||||
0.340596 | + | 0.940210i | \(0.389371\pi\) | |||||||
\(258\) | − | 30.9397i | − | 1.92622i | ||||||
\(259\) | 17.0530i | 1.05962i | ||||||||
\(260\) | 3.35673 | 0.208175 | ||||||||
\(261\) | 12.2978 | + | 3.13589i | 0.761217 | + | 0.194107i | ||||
\(262\) | 19.1611 | 1.18378 | ||||||||
\(263\) | − | 9.92105i | − | 0.611758i | −0.952070 | − | 0.305879i | \(-0.901050\pi\) | ||
0.952070 | − | 0.305879i | \(-0.0989503\pi\) | |||||||
\(264\) | 46.3153i | 2.85051i | ||||||||
\(265\) | 13.0796 | 0.803476 | ||||||||
\(266\) | 67.5386 | 4.14106 | ||||||||
\(267\) | 16.8727 | 1.03260 | ||||||||
\(268\) | −8.21819 | −0.502006 | ||||||||
\(269\) | 12.4240i | 0.757508i | 0.925497 | + | 0.378754i | \(0.123647\pi\) | ||||
−0.925497 | + | 0.378754i | \(0.876353\pi\) | |||||||
\(270\) | −4.00000 | −0.243432 | ||||||||
\(271\) | 27.2643i | 1.65619i | 0.560587 | + | 0.828095i | \(0.310575\pi\) | ||||
−0.560587 | + | 0.828095i | \(0.689425\pi\) | |||||||
\(272\) | − | 7.49925i | − | 0.454709i | ||||||
\(273\) | 6.28017i | 0.380093i | ||||||||
\(274\) | −39.7342 | −2.40043 | ||||||||
\(275\) | 2.31446i | 0.139567i | ||||||||
\(276\) | − | 67.3298i | − | 4.05278i | ||||||
\(277\) | −2.92035 | −0.175467 | −0.0877335 | − | 0.996144i | \(-0.527962\pi\) | ||||
−0.0877335 | + | 0.996144i | \(0.527962\pi\) | |||||||
\(278\) | − | 9.57428i | − | 0.574227i | ||||||
\(279\) | − | 0.372884i | − | 0.0223240i | ||||||
\(280\) | 36.4713i | 2.17958i | ||||||||
\(281\) | −18.3662 | −1.09564 | −0.547818 | − | 0.836598i | \(-0.684541\pi\) | ||||
−0.547818 | + | 0.836598i | \(0.684541\pi\) | |||||||
\(282\) | − | 14.3917i | − | 0.857016i | ||||||
\(283\) | −14.8615 | −0.883422 | −0.441711 | − | 0.897157i | \(-0.645628\pi\) | ||||
−0.441711 | + | 0.897157i | \(0.645628\pi\) | |||||||
\(284\) | 48.8251 | 2.89724 | ||||||||
\(285\) | 13.7931 | 0.817033 | ||||||||
\(286\) | −4.00000 | −0.236525 | ||||||||
\(287\) | − | 41.1814i | − | 2.43086i | ||||||
\(288\) | 40.2491i | 2.37170i | ||||||||
\(289\) | 16.6564 | 0.979787 | ||||||||
\(290\) | −3.57491 | + | 14.0195i | −0.209926 | + | 0.823256i | ||||
\(291\) | 7.07965 | 0.415016 | ||||||||
\(292\) | 47.8854i | 2.80228i | ||||||||
\(293\) | − | 1.57004i | − | 0.0917229i | −0.998948 | − | 0.0458615i | \(-0.985397\pi\) | ||
0.998948 | − | 0.0458615i | \(-0.0146033\pi\) | |||||||
\(294\) | −67.1135 | −3.91414 | ||||||||
\(295\) | −2.64327 | −0.153897 | ||||||||
\(296\) | −34.9542 | −2.03167 | ||||||||
\(297\) | 3.44584 | 0.199948 | ||||||||
\(298\) | − | 16.1200i | − | 0.933807i | ||||||
\(299\) | 3.58620 | 0.207395 | ||||||||
\(300\) | 12.0773i | 0.697282i | ||||||||
\(301\) | 20.9884i | 1.20975i | ||||||||
\(302\) | − | 12.1076i | − | 0.696714i | ||||||
\(303\) | 3.44584 | 0.197959 | ||||||||
\(304\) | 76.2409i | 4.37271i | ||||||||
\(305\) | − | 0.983848i | − | 0.0563350i | ||||||
\(306\) | 3.71164 | 0.212180 | ||||||||
\(307\) | − | 4.65924i | − | 0.265917i | −0.991122 | − | 0.132958i | \(-0.957552\pi\) | ||
0.991122 | − | 0.132958i | \(-0.0424477\pi\) | |||||||
\(308\) | − | 50.9442i | − | 2.90282i | ||||||
\(309\) | − | 26.1484i | − | 1.48753i | ||||||
\(310\) | 0.425088 | 0.0241434 | ||||||||
\(311\) | 21.6516i | 1.22775i | 0.789404 | + | 0.613874i | \(0.210390\pi\) | ||||
−0.789404 | + | 0.613874i | \(0.789610\pi\) | |||||||
\(312\) | −12.8727 | −0.728776 | ||||||||
\(313\) | 11.3567 | 0.641920 | 0.320960 | − | 0.947093i | \(-0.395994\pi\) | ||||
0.320960 | + | 0.947093i | \(0.395994\pi\) | |||||||
\(314\) | 45.5273 | 2.56925 | ||||||||
\(315\) | −9.94111 | −0.560118 | ||||||||
\(316\) | − | 25.9640i | − | 1.46059i | ||||||
\(317\) | 9.36517i | 0.526000i | 0.964796 | + | 0.263000i | \(0.0847120\pi\) | ||||
−0.964796 | + | 0.263000i | \(0.915288\pi\) | |||||||
\(318\) | −81.3317 | −4.56085 | ||||||||
\(319\) | 3.07965 | − | 12.0773i | 0.172427 | − | 0.676198i | ||||
\(320\) | −20.2978 | −1.13468 | ||||||||
\(321\) | 6.78516i | 0.378711i | ||||||||
\(322\) | 63.1797i | 3.52087i | ||||||||
\(323\) | 3.49345 | 0.194381 | ||||||||
\(324\) | 54.8746 | 3.04859 | ||||||||
\(325\) | −0.643274 | −0.0356824 | ||||||||
\(326\) | 29.8044 | 1.65071 | ||||||||
\(327\) | 39.5302i | 2.18602i | ||||||||
\(328\) | 84.4113 | 4.66084 | ||||||||
\(329\) | 9.76282i | 0.538242i | ||||||||
\(330\) | − | 14.3917i | − | 0.792239i | ||||||
\(331\) | − | 18.5115i | − | 1.01748i | −0.860919 | − | 0.508741i | \(-0.830111\pi\) | ||
0.860919 | − | 0.508741i | \(-0.169889\pi\) | |||||||
\(332\) | 42.8840 | 2.35357 | ||||||||
\(333\) | − | 9.52759i | − | 0.522109i | ||||||
\(334\) | 14.9779i | 0.819556i | ||||||||
\(335\) | 1.57491 | 0.0860467 | ||||||||
\(336\) | − | 124.897i | − | 6.81368i | ||||||
\(337\) | − | 18.8116i | − | 1.02473i | −0.858768 | − | 0.512365i | \(-0.828769\pi\) | ||
0.858768 | − | 0.512365i | \(-0.171231\pi\) | |||||||
\(338\) | 33.8149i | 1.83929i | ||||||||
\(339\) | −31.2200 | −1.69564 | ||||||||
\(340\) | 3.05888i | 0.165891i | ||||||||
\(341\) | −0.366196 | −0.0198306 | ||||||||
\(342\) | −37.7342 | −2.04043 | ||||||||
\(343\) | 16.0000 | 0.863919 | ||||||||
\(344\) | −43.0208 | −2.31952 | ||||||||
\(345\) | 12.9029i | 0.694669i | ||||||||
\(346\) | − | 20.9375i | − | 1.12561i | ||||||
\(347\) | −25.2313 | −1.35449 | −0.677243 | − | 0.735759i | \(-0.736826\pi\) | ||||
−0.677243 | + | 0.735759i | \(0.736826\pi\) | |||||||
\(348\) | 16.0702 | − | 63.0215i | 0.861452 | − | 3.37831i | ||||
\(349\) | 2.85018 | 0.152566 | 0.0762832 | − | 0.997086i | \(-0.475695\pi\) | ||||
0.0762832 | + | 0.997086i | \(0.475695\pi\) | |||||||
\(350\) | − | 11.3329i | − | 0.605767i | ||||||
\(351\) | 0.957728i | 0.0511197i | ||||||||
\(352\) | 39.5273 | 2.10681 | ||||||||
\(353\) | −30.0927 | −1.60168 | −0.800838 | − | 0.598881i | \(-0.795612\pi\) | ||||
−0.800838 | + | 0.598881i | \(0.795612\pi\) | |||||||
\(354\) | 16.4364 | 0.873583 | ||||||||
\(355\) | −9.35673 | −0.496603 | ||||||||
\(356\) | − | 38.0413i | − | 2.01619i | ||||||
\(357\) | −5.72292 | −0.302889 | ||||||||
\(358\) | 11.9191i | 0.629942i | ||||||||
\(359\) | 23.6193i | 1.24658i | 0.781992 | + | 0.623289i | \(0.214204\pi\) | ||||
−0.781992 | + | 0.623289i | \(0.785796\pi\) | |||||||
\(360\) | − | 20.3767i | − | 1.07395i | ||||||
\(361\) | −16.5160 | −0.869264 | ||||||||
\(362\) | − | 36.3131i | − | 1.90857i | ||||||
\(363\) | − | 13.0611i | − | 0.685532i | ||||||
\(364\) | 14.1593 | 0.742149 | ||||||||
\(365\) | − | 9.17663i | − | 0.480327i | ||||||
\(366\) | 6.11775i | 0.319780i | ||||||||
\(367\) | − | 17.2112i | − | 0.898417i | −0.893427 | − | 0.449208i | \(-0.851706\pi\) | ||
0.893427 | − | 0.449208i | \(-0.148294\pi\) | |||||||
\(368\) | −71.3204 | −3.71783 | ||||||||
\(369\) | 23.0083i | 1.19776i | ||||||||
\(370\) | 10.8615 | 0.564660 | ||||||||
\(371\) | 55.1724 | 2.86441 | ||||||||
\(372\) | −1.91088 | −0.0990746 | ||||||||
\(373\) | 22.8727 | 1.18431 | 0.592153 | − | 0.805826i | \(-0.298278\pi\) | ||||
0.592153 | + | 0.805826i | \(0.298278\pi\) | |||||||
\(374\) | − | 3.64507i | − | 0.188482i | ||||||
\(375\) | − | 2.31446i | − | 0.119518i | ||||||
\(376\) | −20.0113 | −1.03200 | ||||||||
\(377\) | 3.35673 | + | 0.855948i | 0.172880 | + | 0.0440836i | ||||
\(378\) | −16.8727 | −0.867840 | ||||||||
\(379\) | − | 27.2643i | − | 1.40047i | −0.713910 | − | 0.700237i | \(-0.753077\pi\) | ||
0.713910 | − | 0.700237i | \(-0.246923\pi\) | |||||||
\(380\) | − | 31.0980i | − | 1.59529i | ||||||
\(381\) | −25.6753 | −1.31539 | ||||||||
\(382\) | −31.0909 | −1.59075 | ||||||||
\(383\) | 37.2313 | 1.90243 | 0.951215 | − | 0.308529i | \(-0.0998367\pi\) | ||||
0.951215 | + | 0.308529i | \(0.0998367\pi\) | |||||||
\(384\) | 47.1611 | 2.40668 | ||||||||
\(385\) | 9.76282i | 0.497560i | ||||||||
\(386\) | −26.4477 | −1.34615 | ||||||||
\(387\) | − | 11.7263i | − | 0.596082i | ||||||
\(388\) | − | 15.9618i | − | 0.810337i | ||||||
\(389\) | − | 23.6496i | − | 1.19908i | −0.800344 | − | 0.599541i | \(-0.795350\pi\) | ||
0.800344 | − | 0.599541i | \(-0.204650\pi\) | |||||||
\(390\) | 4.00000 | 0.202548 | ||||||||
\(391\) | 3.26799i | 0.165269i | ||||||||
\(392\) | 93.3193i | 4.71334i | ||||||||
\(393\) | 16.5066 | 0.832645 | ||||||||
\(394\) | 13.8359i | 0.697041i | ||||||||
\(395\) | 4.97568i | 0.250354i | ||||||||
\(396\) | 28.4628i | 1.43031i | ||||||||
\(397\) | −30.0226 | −1.50679 | −0.753395 | − | 0.657568i | \(-0.771585\pi\) | ||||
−0.753395 | + | 0.657568i | \(0.771585\pi\) | |||||||
\(398\) | 47.8042i | 2.39621i | ||||||||
\(399\) | 58.1819 | 2.91274 | ||||||||
\(400\) | 12.7931 | 0.639655 | ||||||||
\(401\) | −32.3698 | −1.61647 | −0.808236 | − | 0.588859i | \(-0.799577\pi\) | ||||
−0.808236 | + | 0.588859i | \(0.799577\pi\) | |||||||
\(402\) | −9.79310 | −0.488435 | ||||||||
\(403\) | − | 0.101780i | − | 0.00507000i | ||||||
\(404\) | − | 7.76901i | − | 0.386523i | ||||||
\(405\) | −10.5160 | −0.522545 | ||||||||
\(406\) | −15.0796 | + | 59.1370i | −0.748390 | + | 2.93492i | ||||
\(407\) | −9.35673 | −0.463796 | ||||||||
\(408\) | − | 11.7305i | − | 0.580747i | ||||||
\(409\) | − | 24.5055i | − | 1.21172i | −0.795571 | − | 0.605860i | \(-0.792829\pi\) | ||
0.795571 | − | 0.605860i | \(-0.207171\pi\) | |||||||
\(410\) | −26.2295 | −1.29538 | ||||||||
\(411\) | −34.2295 | −1.68842 | ||||||||
\(412\) | −58.9542 | −2.90447 | ||||||||
\(413\) | −11.1498 | −0.548647 | ||||||||
\(414\) | − | 35.2989i | − | 1.73485i | ||||||
\(415\) | −8.21819 | −0.403415 | ||||||||
\(416\) | 10.9861i | 0.538638i | ||||||||
\(417\) | − | 8.24787i | − | 0.403900i | ||||||
\(418\) | 37.0575i | 1.81254i | ||||||||
\(419\) | 6.22947 | 0.304330 | 0.152165 | − | 0.988355i | \(-0.451376\pi\) | ||||
0.152165 | + | 0.988355i | \(0.451376\pi\) | |||||||
\(420\) | 50.9442i | 2.48582i | ||||||||
\(421\) | − | 32.9074i | − | 1.60381i | −0.597452 | − | 0.801905i | \(-0.703820\pi\) | ||
0.597452 | − | 0.801905i | \(-0.296180\pi\) | |||||||
\(422\) | 50.6771 | 2.46692 | ||||||||
\(423\) | − | 5.45455i | − | 0.265209i | ||||||
\(424\) | 113.089i | 5.49210i | ||||||||
\(425\) | − | 0.586195i | − | 0.0284346i | ||||||
\(426\) | 58.1819 | 2.81892 | ||||||||
\(427\) | − | 4.15006i | − | 0.200835i | ||||||
\(428\) | 15.2978 | 0.739449 | ||||||||
\(429\) | −3.44584 | −0.166367 | ||||||||
\(430\) | 13.3680 | 0.644663 | ||||||||
\(431\) | 3.00947 | 0.144961 | 0.0724806 | − | 0.997370i | \(-0.476908\pi\) | ||||
0.0724806 | + | 0.997370i | \(0.476908\pi\) | |||||||
\(432\) | − | 19.0468i | − | 0.916389i | ||||||
\(433\) | − | 34.3150i | − | 1.64908i | −0.565807 | − | 0.824538i | \(-0.691435\pi\) | ||
0.565807 | − | 0.824538i | \(-0.308565\pi\) | |||||||
\(434\) | 1.79310 | 0.0860715 | ||||||||
\(435\) | −3.07965 | + | 12.0773i | −0.147658 | + | 0.579061i | ||||
\(436\) | 89.1248 | 4.26830 | ||||||||
\(437\) | − | 33.2239i | − | 1.58931i | ||||||
\(438\) | 57.0620i | 2.72653i | ||||||||
\(439\) | 29.8157 | 1.42302 | 0.711512 | − | 0.702674i | \(-0.248011\pi\) | ||||
0.711512 | + | 0.702674i | \(0.248011\pi\) | |||||||
\(440\) | −20.0113 | −0.954001 | ||||||||
\(441\) | −25.4364 | −1.21126 | ||||||||
\(442\) | 1.01310 | 0.0481883 | ||||||||
\(443\) | − | 27.9579i | − | 1.32832i | −0.747591 | − | 0.664159i | \(-0.768790\pi\) | ||
0.747591 | − | 0.664159i | \(-0.231210\pi\) | |||||||
\(444\) | −48.8251 | −2.31714 | ||||||||
\(445\) | 7.29014i | 0.345586i | ||||||||
\(446\) | − | 36.4713i | − | 1.72697i | ||||||
\(447\) | − | 13.8868i | − | 0.656821i | ||||||
\(448\) | −85.6201 | −4.04517 | ||||||||
\(449\) | − | 4.27796i | − | 0.201889i | −0.994892 | − | 0.100945i | \(-0.967814\pi\) | ||
0.994892 | − | 0.100945i | \(-0.0321865\pi\) | |||||||
\(450\) | 6.33174i | 0.298481i | ||||||||
\(451\) | 22.5957 | 1.06399 | ||||||||
\(452\) | 70.3887i | 3.31081i | ||||||||
\(453\) | − | 10.4302i | − | 0.490055i | ||||||
\(454\) | − | 18.8116i | − | 0.882870i | ||||||
\(455\) | −2.71345 | −0.127209 | ||||||||
\(456\) | 119.258i | 5.58476i | ||||||||
\(457\) | −10.3662 | −0.484910 | −0.242455 | − | 0.970163i | \(-0.577953\pi\) | ||||
−0.242455 | + | 0.970163i | \(0.577953\pi\) | |||||||
\(458\) | −64.8953 | −3.03236 | ||||||||
\(459\) | −0.872747 | −0.0407363 | ||||||||
\(460\) | 29.0909 | 1.35637 | ||||||||
\(461\) | 13.0915i | 0.609730i | 0.952396 | + | 0.304865i | \(0.0986113\pi\) | ||||
−0.952396 | + | 0.304865i | \(0.901389\pi\) | |||||||
\(462\) | − | 60.7071i | − | 2.82435i | ||||||
\(463\) | −33.4571 | −1.55488 | −0.777442 | − | 0.628954i | \(-0.783483\pi\) | ||||
−0.777442 | + | 0.628954i | \(0.783483\pi\) | |||||||
\(464\) | −66.7568 | − | 17.0226i | −3.09911 | − | 0.790257i | ||||
\(465\) | 0.366196 | 0.0169820 | ||||||||
\(466\) | − | 13.8359i | − | 0.640934i | ||||||
\(467\) | 32.5868i | 1.50794i | 0.656911 | + | 0.753968i | \(0.271863\pi\) | ||||
−0.656911 | + | 0.753968i | \(0.728137\pi\) | |||||||
\(468\) | −7.91088 | −0.365681 | ||||||||
\(469\) | 6.64327 | 0.306758 | ||||||||
\(470\) | 6.21819 | 0.286824 | ||||||||
\(471\) | 39.2200 | 1.80716 | ||||||||
\(472\) | − | 22.8543i | − | 1.05195i | ||||||
\(473\) | −11.5160 | −0.529507 | ||||||||
\(474\) | − | 30.9397i | − | 1.42111i | ||||||
\(475\) | 5.95953i | 0.273442i | ||||||||
\(476\) | 12.9029i | 0.591404i | ||||||||
\(477\) | −30.8251 | −1.41139 | ||||||||
\(478\) | − | 39.3416i | − | 1.79944i | ||||||
\(479\) | 36.5222i | 1.66874i | 0.551204 | + | 0.834370i | \(0.314169\pi\) | ||||
−0.551204 | + | 0.834370i | \(0.685831\pi\) | |||||||
\(480\) | −39.5273 | −1.80417 | ||||||||
\(481\) | − | 2.60058i | − | 0.118576i | ||||||
\(482\) | − | 5.37334i | − | 0.244749i | ||||||
\(483\) | 54.4269i | 2.47651i | ||||||||
\(484\) | −29.4477 | −1.33853 | ||||||||
\(485\) | 3.05888i | 0.138896i | ||||||||
\(486\) | 53.3906 | 2.42185 | ||||||||
\(487\) | 25.9411 | 1.17550 | 0.587752 | − | 0.809041i | \(-0.300013\pi\) | ||||
0.587752 | + | 0.809041i | \(0.300013\pi\) | |||||||
\(488\) | 8.50655 | 0.385073 | ||||||||
\(489\) | 25.6753 | 1.16108 | ||||||||
\(490\) | − | 28.9975i | − | 1.30997i | ||||||
\(491\) | − | 26.3411i | − | 1.18876i | −0.804185 | − | 0.594379i | \(-0.797398\pi\) | ||
0.804185 | − | 0.594379i | \(-0.202602\pi\) | |||||||
\(492\) | 117.908 | 5.31572 | ||||||||
\(493\) | −0.779998 | + | 3.05888i | −0.0351294 | + | 0.137765i | ||||
\(494\) | −10.2996 | −0.463403 | ||||||||
\(495\) | − | 5.45455i | − | 0.245164i | ||||||
\(496\) | 2.02414i | 0.0908865i | ||||||||
\(497\) | −39.4684 | −1.77040 | ||||||||
\(498\) | 51.1022 | 2.28995 | ||||||||
\(499\) | −21.0131 | −0.940676 | −0.470338 | − | 0.882486i | \(-0.655868\pi\) | ||||
−0.470338 | + | 0.882486i | \(0.655868\pi\) | |||||||
\(500\) | −5.21819 | −0.233364 | ||||||||
\(501\) | 12.9029i | 0.576460i | ||||||||
\(502\) | 60.8139 | 2.71426 | ||||||||
\(503\) | 14.5500i | 0.648751i | 0.945928 | + | 0.324375i | \(0.105154\pi\) | ||||
−0.945928 | + | 0.324375i | \(0.894846\pi\) | |||||||
\(504\) | − | 85.9528i | − | 3.82864i | ||||||
\(505\) | 1.48883i | 0.0662522i | ||||||||
\(506\) | −34.6658 | −1.54108 | ||||||||
\(507\) | 29.1303i | 1.29372i | ||||||||
\(508\) | 57.8876i | 2.56835i | ||||||||
\(509\) | −12.2295 | −0.542062 | −0.271031 | − | 0.962571i | \(-0.587365\pi\) | ||||
−0.271031 | + | 0.962571i | \(0.587365\pi\) | |||||||
\(510\) | 3.64507i | 0.161406i | ||||||||
\(511\) | − | 38.7087i | − | 1.71237i | ||||||
\(512\) | 2.73756i | 0.120984i | ||||||||
\(513\) | 8.87275 | 0.391741 | ||||||||
\(514\) | − | 29.3394i | − | 1.29410i | ||||||
\(515\) | 11.2978 | 0.497842 | ||||||||
\(516\) | −60.0927 | −2.64544 | ||||||||
\(517\) | −5.35673 | −0.235589 | ||||||||
\(518\) | 45.8157 | 2.01302 | ||||||||
\(519\) | − | 18.0368i | − | 0.791728i | ||||||
\(520\) | − | 5.56188i | − | 0.243905i | ||||||
\(521\) | 17.5160 | 0.767391 | 0.383695 | − | 0.923460i | \(-0.374651\pi\) | ||||
0.383695 | + | 0.923460i | \(0.374651\pi\) | |||||||
\(522\) | 8.42509 | − | 33.0402i | 0.368756 | − | 1.44613i | ||||
\(523\) | −10.8840 | −0.475926 | −0.237963 | − | 0.971274i | \(-0.576480\pi\) | ||||
−0.237963 | + | 0.971274i | \(0.576480\pi\) | |||||||
\(524\) | − | 37.2157i | − | 1.62578i | ||||||
\(525\) | − | 9.76282i | − | 0.426085i | ||||||
\(526\) | −26.6546 | −1.16219 | ||||||||
\(527\) | 0.0927485 | 0.00404019 | ||||||||
\(528\) | 68.5291 | 2.98235 | ||||||||
\(529\) | 8.07965 | 0.351289 | ||||||||
\(530\) | − | 35.1407i | − | 1.52641i | ||||||
\(531\) | 6.22947 | 0.270336 | ||||||||
\(532\) | − | 131.177i | − | 5.68724i | ||||||
\(533\) | 6.28017i | 0.272025i | ||||||||
\(534\) | − | 45.3315i | − | 1.96168i | ||||||
\(535\) | −2.93164 | −0.126746 | ||||||||
\(536\) | 13.6170i | 0.588165i | ||||||||
\(537\) | 10.2678i | 0.443089i | ||||||||
\(538\) | 33.3793 | 1.43908 | ||||||||
\(539\) | 24.9802i | 1.07597i | ||||||||
\(540\) | 7.76901i | 0.334325i | ||||||||
\(541\) | 35.7572i | 1.53732i | 0.639657 | + | 0.768661i | \(0.279077\pi\) | ||||
−0.639657 | + | 0.768661i | \(0.720923\pi\) | |||||||
\(542\) | 73.2502 | 3.14637 | ||||||||
\(543\) | − | 31.2823i | − | 1.34245i | ||||||
\(544\) | −10.0113 | −0.429230 | ||||||||
\(545\) | −17.0796 | −0.731612 | ||||||||
\(546\) | 16.8727 | 0.722087 | ||||||||
\(547\) | 12.6320 | 0.540105 | 0.270052 | − | 0.962846i | \(-0.412959\pi\) | ||||
0.270052 | + | 0.962846i | \(0.412959\pi\) | |||||||
\(548\) | 77.1738i | 3.29670i | ||||||||
\(549\) | 2.31866i | 0.0989580i | ||||||||
\(550\) | 6.21819 | 0.265144 | ||||||||
\(551\) | 7.92982 | − | 31.0980i | 0.337822 | − | 1.32482i | ||||
\(552\) | −111.561 | −4.74836 | ||||||||
\(553\) | 20.9884i | 0.892516i | ||||||||
\(554\) | 7.84602i | 0.333345i | ||||||||
\(555\) | 9.35673 | 0.397171 | ||||||||
\(556\) | −18.5957 | −0.788632 | ||||||||
\(557\) | −21.0095 | −0.890200 | −0.445100 | − | 0.895481i | \(-0.646832\pi\) | ||||
−0.445100 | + | 0.895481i | \(0.646832\pi\) | |||||||
\(558\) | −1.00181 | −0.0424102 | ||||||||
\(559\) | − | 3.20073i | − | 0.135376i | ||||||
\(560\) | 53.9637 | 2.28038 | ||||||||
\(561\) | − | 3.14009i | − | 0.132575i | ||||||
\(562\) | 49.3439i | 2.08145i | ||||||||
\(563\) | − | 45.6782i | − | 1.92511i | −0.271090 | − | 0.962554i | \(-0.587384\pi\) | ||
0.271090 | − | 0.962554i | \(-0.412616\pi\) | |||||||
\(564\) | −27.9524 | −1.17701 | ||||||||
\(565\) | − | 13.4891i | − | 0.567491i | ||||||
\(566\) | 39.9278i | 1.67829i | ||||||||
\(567\) | −44.3585 | −1.86288 | ||||||||
\(568\) | − | 80.9001i | − | 3.39449i | ||||||
\(569\) | 38.5463i | 1.61595i | 0.589220 | + | 0.807973i | \(0.299435\pi\) | ||||
−0.589220 | + | 0.807973i | \(0.700565\pi\) | |||||||
\(570\) | − | 37.0575i | − | 1.55217i | ||||||
\(571\) | −25.7229 | −1.07647 | −0.538235 | − | 0.842795i | \(-0.680909\pi\) | ||||
−0.538235 | + | 0.842795i | \(0.680909\pi\) | |||||||
\(572\) | 7.76901i | 0.324839i | ||||||||
\(573\) | −26.7836 | −1.11890 | ||||||||
\(574\) | −110.641 | −4.61806 | ||||||||
\(575\) | −5.57491 | −0.232490 | ||||||||
\(576\) | 47.8364 | 1.99318 | ||||||||
\(577\) | 31.7145i | 1.32029i | 0.751138 | + | 0.660145i | \(0.229505\pi\) | ||||
−0.751138 | + | 0.660145i | \(0.770495\pi\) | |||||||
\(578\) | − | 44.7502i | − | 1.86136i | ||||||
\(579\) | −22.7836 | −0.946855 | ||||||||
\(580\) | 27.2295 | + | 6.94338i | 1.13064 | + | 0.288308i | ||||
\(581\) | −34.6658 | −1.43818 | ||||||||
\(582\) | − | 19.0207i | − | 0.788432i | ||||||
\(583\) | 30.2723i | 1.25375i | ||||||||
\(584\) | 79.3430 | 3.28324 | ||||||||
\(585\) | 1.51602 | 0.0626798 | ||||||||
\(586\) | −4.21819 | −0.174252 | ||||||||
\(587\) | 37.5975 | 1.55181 | 0.775907 | − | 0.630847i | \(-0.217293\pi\) | ||||
0.775907 | + | 0.630847i | \(0.217293\pi\) | |||||||
\(588\) | 130.351i | 5.37560i | ||||||||
\(589\) | −0.942924 | −0.0388525 | ||||||||
\(590\) | 7.10160i | 0.292368i | ||||||||
\(591\) | 11.9191i | 0.490285i | ||||||||
\(592\) | 51.7190i | 2.12564i | ||||||||
\(593\) | 36.2295 | 1.48777 | 0.743883 | − | 0.668310i | \(-0.232982\pi\) | ||||
0.743883 | + | 0.668310i | \(0.232982\pi\) | |||||||
\(594\) | − | 9.25784i | − | 0.379854i | ||||||
\(595\) | − | 2.47268i | − | 0.101370i | ||||||
\(596\) | −31.3091 | −1.28247 | ||||||||
\(597\) | 41.1814i | 1.68544i | ||||||||
\(598\) | − | 9.63492i | − | 0.394001i | ||||||
\(599\) | − | 3.48685i | − | 0.142469i | −0.997460 | − | 0.0712344i | \(-0.977306\pi\) | ||
0.997460 | − | 0.0712344i | \(-0.0226938\pi\) | |||||||
\(600\) | 20.0113 | 0.816957 | ||||||||
\(601\) | − | 4.81746i | − | 0.196508i | −0.995161 | − | 0.0982542i | \(-0.968674\pi\) | ||
0.995161 | − | 0.0982542i | \(-0.0313258\pi\) | |||||||
\(602\) | 56.3888 | 2.29823 | ||||||||
\(603\) | −3.71164 | −0.151150 | ||||||||
\(604\) | −23.5160 | −0.956853 | ||||||||
\(605\) | 5.64327 | 0.229432 | ||||||||
\(606\) | − | 9.25784i | − | 0.376074i | ||||||
\(607\) | − | 7.57626i | − | 0.307511i | −0.988109 | − | 0.153756i | \(-0.950863\pi\) | ||
0.988109 | − | 0.153756i | \(-0.0491368\pi\) | |||||||
\(608\) | 101.779 | 4.12770 | ||||||||
\(609\) | −12.9905 | + | 50.9442i | −0.526403 | + | 2.06436i | ||||
\(610\) | −2.64327 | −0.107023 | ||||||||
\(611\) | − | 1.48883i | − | 0.0602317i | ||||||
\(612\) | − | 7.20893i | − | 0.291404i | ||||||
\(613\) | 4.15930 | 0.167992 | 0.0839962 | − | 0.996466i | \(-0.473232\pi\) | ||||
0.0839962 | + | 0.996466i | \(0.473232\pi\) | |||||||
\(614\) | −12.5178 | −0.505179 | ||||||||
\(615\) | −22.5957 | −0.911145 | ||||||||
\(616\) | −84.4113 | −3.40103 | ||||||||
\(617\) | − | 25.7246i | − | 1.03563i | −0.855491 | − | 0.517817i | \(-0.826745\pi\) | ||
0.855491 | − | 0.517817i | \(-0.173255\pi\) | |||||||
\(618\) | −70.2520 | −2.82595 | ||||||||
\(619\) | − | 31.1997i | − | 1.25402i | −0.779010 | − | 0.627012i | \(-0.784278\pi\) | ||
0.779010 | − | 0.627012i | \(-0.215722\pi\) | |||||||
\(620\) | − | 0.825627i | − | 0.0331580i | ||||||
\(621\) | 8.30011i | 0.333072i | ||||||||
\(622\) | 58.1706 | 2.33243 | ||||||||
\(623\) | 30.7512i | 1.23202i | ||||||||
\(624\) | 19.0468i | 0.762482i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − | 30.5118i | − | 1.21949i | ||||||
\(627\) | 31.9236i | 1.27490i | ||||||||
\(628\) | − | 88.4255i | − | 3.52856i | ||||||
\(629\) | 2.36983 | 0.0944912 | ||||||||
\(630\) | 26.7085i | 1.06409i | ||||||||
\(631\) | 22.1593 | 0.882148 | 0.441074 | − | 0.897471i | \(-0.354598\pi\) | ||||
0.441074 | + | 0.897471i | \(0.354598\pi\) | |||||||
\(632\) | −43.0208 | −1.71127 | ||||||||
\(633\) | 43.6564 | 1.73519 | ||||||||
\(634\) | 25.1611 | 0.999275 | ||||||||
\(635\) | − | 11.0934i | − | 0.440230i | ||||||
\(636\) | 157.967i | 6.26378i | ||||||||
\(637\) | −6.94292 | −0.275089 | ||||||||
\(638\) | −32.4477 | − | 8.27399i | −1.28462 | − | 0.327570i | ||||
\(639\) | 22.0512 | 0.872333 | ||||||||
\(640\) | 20.3767i | 0.805461i | ||||||||
\(641\) | 22.3754i | 0.883776i | 0.897070 | + | 0.441888i | \(0.145691\pi\) | ||||
−0.897070 | + | 0.441888i | \(0.854309\pi\) | |||||||
\(642\) | 18.2295 | 0.719460 | ||||||||
\(643\) | −20.1480 | −0.794560 | −0.397280 | − | 0.917697i | \(-0.630046\pi\) | ||||
−0.397280 | + | 0.917697i | \(0.630046\pi\) | |||||||
\(644\) | 122.711 | 4.83549 | ||||||||
\(645\) | 11.5160 | 0.453443 | ||||||||
\(646\) | − | 9.38574i | − | 0.369277i | ||||||
\(647\) | 34.9542 | 1.37419 | 0.687096 | − | 0.726567i | \(-0.258885\pi\) | ||||
0.687096 | + | 0.726567i | \(0.258885\pi\) | |||||||
\(648\) | − | 90.9236i | − | 3.57182i | ||||||
\(649\) | − | 6.11775i | − | 0.240143i | ||||||
\(650\) | 1.72826i | 0.0677881i | ||||||||
\(651\) | 1.54468 | 0.0605410 | ||||||||
\(652\) | − | 57.8876i | − | 2.26705i | ||||||
\(653\) | − | 17.3227i | − | 0.677890i | −0.940806 | − | 0.338945i | \(-0.889930\pi\) | ||
0.940806 | − | 0.338945i | \(-0.110070\pi\) | |||||||
\(654\) | 106.204 | 4.15292 | ||||||||
\(655\) | 7.13192i | 0.278667i | ||||||||
\(656\) | − | 124.897i | − | 4.87640i | ||||||
\(657\) | 21.6268i | 0.843742i | ||||||||
\(658\) | 26.2295 | 1.02253 | ||||||||
\(659\) | 17.1851i | 0.669435i | 0.942318 | + | 0.334718i | \(0.108641\pi\) | ||||
−0.942318 | + | 0.334718i | \(0.891359\pi\) | |||||||
\(660\) | −27.9524 | −1.08805 | ||||||||
\(661\) | 24.0891 | 0.936958 | 0.468479 | − | 0.883475i | \(-0.344802\pi\) | ||||
0.468479 | + | 0.883475i | \(0.344802\pi\) | |||||||
\(662\) | −49.7342 | −1.93297 | ||||||||
\(663\) | 0.872747 | 0.0338947 | ||||||||
\(664\) | − | 71.0561i | − | 2.75751i | ||||||
\(665\) | 25.1384i | 0.974826i | ||||||||
\(666\) | −25.5975 | −0.991882 | ||||||||
\(667\) | 29.0909 | + | 7.41804i | 1.12641 | + | 0.287228i | ||||
\(668\) | 29.0909 | 1.12556 | ||||||||
\(669\) | − | 31.4186i | − | 1.21471i | ||||||
\(670\) | − | 4.23127i | − | 0.163468i | ||||||
\(671\) | 2.27708 | 0.0879056 | ||||||||
\(672\) | −166.734 | −6.43189 | ||||||||
\(673\) | −31.4495 | −1.21229 | −0.606144 | − | 0.795355i | \(-0.707285\pi\) | ||||
−0.606144 | + | 0.795355i | \(0.707285\pi\) | |||||||
\(674\) | −50.5404 | −1.94674 | ||||||||
\(675\) | − | 1.48883i | − | 0.0573052i | ||||||
\(676\) | 65.6771 | 2.52604 | ||||||||
\(677\) | 29.0187i | 1.11528i | 0.830083 | + | 0.557640i | \(0.188293\pi\) | ||||
−0.830083 | + | 0.557640i | \(0.811707\pi\) | |||||||
\(678\) | 83.8778i | 3.22131i | ||||||||
\(679\) | 12.9029i | 0.495168i | ||||||||
\(680\) | 5.06836 | 0.194363 | ||||||||
\(681\) | − | 16.2054i | − | 0.620993i | ||||||
\(682\) | 0.983848i | 0.0376735i | ||||||||
\(683\) | 12.2884 | 0.470201 | 0.235101 | − | 0.971971i | \(-0.424458\pi\) | ||||
0.235101 | + | 0.971971i | \(0.424458\pi\) | |||||||
\(684\) | 73.2893i | 2.80229i | ||||||||
\(685\) | − | 14.7894i | − | 0.565074i | ||||||
\(686\) | − | 42.9867i | − | 1.64124i | ||||||
\(687\) | −55.9048 | −2.13290 | ||||||||
\(688\) | 63.6544i | 2.42680i | ||||||||
\(689\) | −8.41380 | −0.320540 | ||||||||
\(690\) | 34.6658 | 1.31971 | ||||||||
\(691\) | −41.6753 | −1.58540 | −0.792702 | − | 0.609609i | \(-0.791326\pi\) | ||||
−0.792702 | + | 0.609609i | \(0.791326\pi\) | |||||||
\(692\) | −40.6658 | −1.54588 | ||||||||
\(693\) | − | 23.0083i | − | 0.874013i | ||||||
\(694\) | 67.7881i | 2.57320i | ||||||||
\(695\) | 3.56363 | 0.135176 | ||||||||
\(696\) | −104.423 | − | 26.6273i | −3.95813 | − | 1.00930i | ||||
\(697\) | −5.72292 | −0.216771 | ||||||||
\(698\) | − | 7.65748i | − | 0.289840i | ||||||
\(699\) | − | 11.9191i | − | 0.450820i | ||||||
\(700\) | −22.0113 | −0.831948 | ||||||||
\(701\) | 27.8157 | 1.05058 | 0.525292 | − | 0.850922i | \(-0.323956\pi\) | ||||
0.525292 | + | 0.850922i | \(0.323956\pi\) | |||||||
\(702\) | 2.57310 | 0.0971153 | ||||||||
\(703\) | −24.0927 | −0.908675 | ||||||||
\(704\) | − | 46.9785i | − | 1.77057i | ||||||
\(705\) | 5.35673 | 0.201746 | ||||||||
\(706\) | 80.8492i | 3.04280i | ||||||||
\(707\) | 6.28017i | 0.236190i | ||||||||
\(708\) | − | 31.9236i | − | 1.19976i | ||||||
\(709\) | −0.643274 | −0.0241587 | −0.0120793 | − | 0.999927i | \(-0.503845\pi\) | ||||
−0.0120793 | + | 0.999927i | \(0.503845\pi\) | |||||||
\(710\) | 25.1384i | 0.943428i | ||||||||
\(711\) | − | 11.7263i | − | 0.439771i | ||||||
\(712\) | −63.0320 | −2.36223 | ||||||||
\(713\) | − | 0.882069i | − | 0.0330337i | ||||||
\(714\) | 15.3756i | 0.575417i | ||||||||
\(715\) | − | 1.48883i | − | 0.0556792i | ||||||
\(716\) | 23.1498 | 0.865150 | ||||||||
\(717\) | − | 33.8913i | − | 1.26569i | ||||||
\(718\) | 63.4571 | 2.36820 | ||||||||
\(719\) | 21.2389 | 0.792079 | 0.396039 | − | 0.918233i | \(-0.370384\pi\) | ||||
0.396039 | + | 0.918233i | \(0.370384\pi\) | |||||||
\(720\) | −30.1498 | −1.12362 | ||||||||
\(721\) | 47.6564 | 1.77482 | ||||||||
\(722\) | 44.3731i | 1.65139i | ||||||||
\(723\) | − | 4.62892i | − | 0.172151i | ||||||
\(724\) | −70.5291 | −2.62119 | ||||||||
\(725\) | −5.21819 | − | 1.33061i | −0.193799 | − | 0.0494177i | ||||
\(726\) | −35.0909 | −1.30235 | ||||||||
\(727\) | 19.0771i | 0.707531i | 0.935334 | + | 0.353765i | \(0.115099\pi\) | ||||
−0.935334 | + | 0.353765i | \(0.884901\pi\) | |||||||
\(728\) | − | 23.4610i | − | 0.869524i | ||||||
\(729\) | 14.4458 | 0.535031 | ||||||||
\(730\) | −24.6546 | −0.912506 | ||||||||
\(731\) | 2.91672 | 0.107879 | ||||||||
\(732\) | 11.8822 | 0.439179 | ||||||||
\(733\) | 39.4835i | 1.45836i | 0.684324 | + | 0.729178i | \(0.260097\pi\) | ||||
−0.684324 | + | 0.729178i | \(0.739903\pi\) | |||||||
\(734\) | −46.2408 | −1.70678 | ||||||||
\(735\) | − | 24.9802i | − | 0.921408i | ||||||
\(736\) | 95.2107i | 3.50951i | ||||||||
\(737\) | 3.64507i | 0.134268i | ||||||||
\(738\) | 61.8157 | 2.27547 | ||||||||
\(739\) | 5.95953i | 0.219225i | 0.993974 | + | 0.109612i | \(0.0349610\pi\) | ||||
−0.993974 | + | 0.109612i | \(0.965039\pi\) | |||||||
\(740\) | − | 21.0957i | − | 0.775493i | ||||||
\(741\) | −8.87275 | −0.325948 | ||||||||
\(742\) | − | 148.230i | − | 5.44169i | ||||||
\(743\) | − | 18.0065i | − | 0.660594i | −0.943877 | − | 0.330297i | \(-0.892851\pi\) | ||
0.943877 | − | 0.330297i | \(-0.107149\pi\) | |||||||
\(744\) | 3.16621i | 0.116079i | ||||||||
\(745\) | 6.00000 | 0.219823 | ||||||||
\(746\) | − | 61.4515i | − | 2.24990i | ||||||
\(747\) | 19.3680 | 0.708638 | ||||||||
\(748\) | −7.07965 | −0.258858 | ||||||||
\(749\) | −12.3662 | −0.451851 | ||||||||
\(750\) | −6.21819 | −0.227056 | ||||||||
\(751\) | − | 25.8623i | − | 0.943727i | −0.881671 | − | 0.471864i | \(-0.843581\pi\) | ||
0.881671 | − | 0.471864i | \(-0.156419\pi\) | |||||||
\(752\) | 29.6091i | 1.07973i | ||||||||
\(753\) | 52.3888 | 1.90915 | ||||||||
\(754\) | 2.29965 | − | 9.01841i | 0.0837483 | − | 0.328431i | ||||
\(755\) | 4.50655 | 0.164010 | ||||||||
\(756\) | 32.7711i | 1.19187i | ||||||||
\(757\) | − | 53.0193i | − | 1.92702i | −0.267676 | − | 0.963509i | \(-0.586256\pi\) | ||
0.267676 | − | 0.963509i | \(-0.413744\pi\) | |||||||
\(758\) | −73.2502 | −2.66057 | ||||||||
\(759\) | −29.8633 | −1.08397 | ||||||||
\(760\) | −51.5273 | −1.86909 | ||||||||
\(761\) | −34.8953 | −1.26495 | −0.632477 | − | 0.774579i | \(-0.717962\pi\) | ||||
−0.632477 | + | 0.774579i | \(0.717962\pi\) | |||||||
\(762\) | 68.9811i | 2.49892i | ||||||||
\(763\) | −72.0451 | −2.60821 | ||||||||
\(764\) | 60.3864i | 2.18470i | ||||||||
\(765\) | 1.38150i | 0.0499483i | ||||||||
\(766\) | − | 100.028i | − | 3.61416i | ||||||
\(767\) | 1.70035 | 0.0613961 | ||||||||
\(768\) | − | 32.7492i | − | 1.18174i | ||||||
\(769\) | − | 30.5888i | − | 1.10306i | −0.834155 | − | 0.551530i | \(-0.814044\pi\) | ||
0.834155 | − | 0.551530i | \(-0.185956\pi\) | |||||||
\(770\) | 26.2295 | 0.945245 | ||||||||
\(771\) | − | 25.2747i | − | 0.910247i | ||||||
\(772\) | 51.3680i | 1.84878i | ||||||||
\(773\) | 11.9658i | 0.430378i | 0.976572 | + | 0.215189i | \(0.0690368\pi\) | ||||
−0.976572 | + | 0.215189i | \(0.930963\pi\) | |||||||
\(774\) | −31.5047 | −1.13241 | ||||||||
\(775\) | 0.158221i | 0.00568347i | ||||||||
\(776\) | −26.4477 | −0.949416 | ||||||||
\(777\) | 39.4684 | 1.41592 | ||||||||
\(778\) | −63.5386 | −2.27797 | ||||||||
\(779\) | 58.1819 | 2.08458 | ||||||||
\(780\) | − | 7.76901i | − | 0.278175i | ||||||
\(781\) | − | 21.6558i | − | 0.774904i | ||||||
\(782\) | 8.78000 | 0.313972 | ||||||||
\(783\) | −1.98106 | + | 7.76901i | −0.0707973 | + | 0.277642i | ||||
\(784\) | 138.077 | 4.93133 | ||||||||
\(785\) | 16.9456i | 0.604816i | ||||||||
\(786\) | − | 44.3476i | − | 1.58183i | ||||||
\(787\) | −21.2087 | −0.756009 | −0.378005 | − | 0.925804i | \(-0.623390\pi\) | ||||
−0.378005 | + | 0.925804i | \(0.623390\pi\) | |||||||
\(788\) | 26.8727 | 0.957302 | ||||||||
\(789\) | −22.9619 | −0.817464 | ||||||||
\(790\) | 13.3680 | 0.475613 | ||||||||
\(791\) | − | 56.8996i | − | 2.02312i | ||||||
\(792\) | 47.1611 | 1.67580 | ||||||||
\(793\) | 0.632884i | 0.0224744i | ||||||||
\(794\) | 80.6607i | 2.86254i | ||||||||
\(795\) | − | 30.2723i | − | 1.07365i | ||||||
\(796\) | 92.8477 | 3.29090 | ||||||||
\(797\) | − | 8.32068i | − | 0.294734i | −0.989082 | − | 0.147367i | \(-0.952920\pi\) | ||
0.989082 | − | 0.147367i | \(-0.0470798\pi\) | |||||||
\(798\) | − | 156.315i | − | 5.53350i | ||||||
\(799\) | 1.35673 | 0.0479975 | ||||||||
\(800\) | − | 17.0784i | − | 0.603813i | ||||||
\(801\) | − | 17.1809i | − | 0.607056i | ||||||
\(802\) | 86.9670i | 3.07091i | ||||||||
\(803\) | 21.2389 | 0.749506 | ||||||||
\(804\) | 19.0207i | 0.670807i | ||||||||
\(805\) | −23.5160 | −0.828831 | ||||||||
\(806\) | −0.273448 | −0.00963179 | ||||||||
\(807\) | 28.7550 | 1.01222 | ||||||||
\(808\) | −12.8727 | −0.452862 | ||||||||
\(809\) | 23.4610i | 0.824846i | 0.910992 | + | 0.412423i | \(0.135317\pi\) | ||||
−0.910992 | + | 0.412423i | \(0.864683\pi\) | |||||||
\(810\) | 28.2531i | 0.992711i | ||||||||
\(811\) | −7.00947 | −0.246136 | −0.123068 | − | 0.992398i | \(-0.539273\pi\) | ||||
−0.123068 | + | 0.992398i | \(0.539273\pi\) | |||||||
\(812\) | 114.859 | + | 29.2885i | 4.03076 | + | 1.02782i | ||||
\(813\) | 63.1022 | 2.21309 | ||||||||
\(814\) | 25.1384i | 0.881101i | ||||||||
\(815\) | 11.0934i | 0.388586i | ||||||||
\(816\) | −17.3567 | −0.607607 | ||||||||
\(817\) | −29.6527 | −1.03742 | ||||||||
\(818\) | −65.8382 | −2.30198 | ||||||||
\(819\) | 6.39486 | 0.223455 | ||||||||
\(820\) | 50.9442i | 1.77905i | ||||||||
\(821\) | 1.44584 | 0.0504603 | 0.0252302 | − | 0.999682i | \(-0.491968\pi\) | ||||
0.0252302 | + | 0.999682i | \(0.491968\pi\) | |||||||
\(822\) | 91.9632i | 3.20759i | ||||||||
\(823\) | − | 47.1671i | − | 1.64414i | −0.569386 | − | 0.822070i | \(-0.692819\pi\) | ||
0.569386 | − | 0.822070i | \(-0.307181\pi\) | |||||||
\(824\) | 97.6833i | 3.40296i | ||||||||
\(825\) | 5.35673 | 0.186497 | ||||||||
\(826\) | 29.9559i | 1.04230i | ||||||||
\(827\) | 20.1366i | 0.700219i | 0.936709 | + | 0.350109i | \(0.113856\pi\) | ||||
−0.936709 | + | 0.350109i | \(0.886144\pi\) | |||||||
\(828\) | −68.5593 | −2.38260 | ||||||||
\(829\) | − | 12.8011i | − | 0.444602i | −0.974978 | − | 0.222301i | \(-0.928643\pi\) | ||
0.974978 | − | 0.222301i | \(-0.0713567\pi\) | |||||||
\(830\) | 22.0795i | 0.766392i | ||||||||
\(831\) | 6.75904i | 0.234468i | ||||||||
\(832\) | 13.0571 | 0.452673 | ||||||||
\(833\) | − | 6.32686i | − | 0.219213i | ||||||
\(834\) | −22.1593 | −0.767314 | ||||||||
\(835\) | −5.57491 | −0.192928 | ||||||||
\(836\) | 71.9750 | 2.48931 | ||||||||
\(837\) | 0.235565 | 0.00814231 | ||||||||
\(838\) | − | 16.7365i | − | 0.578154i | ||||||
\(839\) | 16.8341i | 0.581178i | 0.956848 | + | 0.290589i | \(0.0938512\pi\) | ||||
−0.956848 | + | 0.290589i | \(0.906149\pi\) | |||||||
\(840\) | 84.4113 | 2.91247 | ||||||||
\(841\) | 25.4589 | + | 13.8868i | 0.877895 | + | 0.478854i | ||||
\(842\) | −88.4113 | −3.04686 | ||||||||
\(843\) | 42.5078i | 1.46405i | ||||||||
\(844\) | − | 98.4278i | − | 3.38802i | ||||||
\(845\) | −12.5862 | −0.432978 | ||||||||
\(846\) | −14.6546 | −0.503834 | ||||||||
\(847\) | 23.8044 | 0.817928 | ||||||||
\(848\) | 167.329 | 5.74611 | ||||||||
\(849\) | 34.3963i | 1.18048i | ||||||||
\(850\) | −1.57491 | −0.0540190 | ||||||||
\(851\) | − | 22.5378i | − | 0.772587i | ||||||
\(852\) | − | 113.004i | − | 3.87145i | ||||||
\(853\) | 40.1164i | 1.37356i | 0.726866 | + | 0.686779i | \(0.240976\pi\) | ||||
−0.726866 | + | 0.686779i | \(0.759024\pi\) | |||||||
\(854\) | −11.1498 | −0.381539 | ||||||||
\(855\) | − | 14.0450i | − | 0.480328i | ||||||
\(856\) | − | 25.3475i | − | 0.866361i | ||||||
\(857\) | 15.2389 | 0.520552 | 0.260276 | − | 0.965534i | \(-0.416186\pi\) | ||||
0.260276 | + | 0.965534i | \(0.416186\pi\) | |||||||
\(858\) | 9.25784i | 0.316057i | ||||||||
\(859\) | 10.7770i | 0.367706i | 0.982954 | + | 0.183853i | \(0.0588571\pi\) | ||||
−0.982954 | + | 0.183853i | \(0.941143\pi\) | |||||||
\(860\) | − | 25.9640i | − | 0.885367i | ||||||
\(861\) | −95.3128 | −3.24825 | ||||||||
\(862\) | − | 8.08545i | − | 0.275392i | ||||||
\(863\) | −32.1004 | −1.09271 | −0.546355 | − | 0.837554i | \(-0.683985\pi\) | ||||
−0.546355 | + | 0.837554i | \(0.683985\pi\) | |||||||
\(864\) | −25.4269 | −0.865041 | ||||||||
\(865\) | 7.79310 | 0.264973 | ||||||||
\(866\) | −92.1932 | −3.13285 | ||||||||
\(867\) | − | 38.5505i | − | 1.30924i | ||||||
\(868\) | − | 3.48265i | − | 0.118209i | ||||||
\(869\) | −11.5160 | −0.390654 | ||||||||
\(870\) | 32.4477 | + | 8.27399i | 1.10008 | + | 0.280515i | ||||
\(871\) | −1.01310 | −0.0343276 | ||||||||
\(872\) | − | 147.674i | − | 5.00087i | ||||||
\(873\) | − | 7.20893i | − | 0.243985i | ||||||
\(874\) | −89.2615 | −3.01932 | ||||||||
\(875\) | 4.21819 | 0.142601 | ||||||||
\(876\) | 110.829 | 3.74456 | ||||||||
\(877\) | 28.2520 | 0.954004 | 0.477002 | − | 0.878902i | \(-0.341723\pi\) | ||||
0.477002 | + | 0.878902i | \(0.341723\pi\) | |||||||
\(878\) | − | 80.1048i | − | 2.70341i | ||||||
\(879\) | −3.63380 | −0.122565 | ||||||||
\(880\) | 29.6091i | 0.998123i | ||||||||
\(881\) | 8.59043i | 0.289419i | 0.989474 | + | 0.144710i | \(0.0462248\pi\) | ||||
−0.989474 | + | 0.144710i | \(0.953775\pi\) | |||||||
\(882\) | 68.3391i | 2.30110i | ||||||||
\(883\) | −34.7913 | −1.17082 | −0.585410 | − | 0.810737i | \(-0.699066\pi\) | ||||
−0.585410 | + | 0.810737i | \(0.699066\pi\) | |||||||
\(884\) | − | 1.96770i | − | 0.0661808i | ||||||
\(885\) | 6.11775i | 0.205646i | ||||||||
\(886\) | −75.1135 | −2.52349 | ||||||||
\(887\) | 40.3558i | 1.35501i | 0.735516 | + | 0.677507i | \(0.236940\pi\) | ||||
−0.735516 | + | 0.677507i | \(0.763060\pi\) | |||||||
\(888\) | 80.9001i | 2.71483i | ||||||||
\(889\) | − | 46.7942i | − | 1.56943i | ||||||
\(890\) | 19.5862 | 0.656531 | ||||||||
\(891\) | − | 24.3389i | − | 0.815384i | ||||||
\(892\) | −70.8364 | −2.37178 | ||||||||
\(893\) | −13.7931 | −0.461568 | ||||||||
\(894\) | −37.3091 | −1.24780 | ||||||||
\(895\) | −4.43637 | −0.148292 | ||||||||
\(896\) | 85.9528i | 2.87148i | ||||||||
\(897\) | − | 8.30011i | − | 0.277133i | ||||||
\(898\) | −11.4934 | −0.383541 | ||||||||
\(899\) | 0.210531 | − | 0.825627i | 0.00702160 | − | 0.0275362i | ||||
\(900\) | 12.2978 | 0.409928 | ||||||||
\(901\) | − | 7.66723i | − | 0.255432i | ||||||
\(902\) | − | 60.7071i | − | 2.02132i | ||||||
\(903\) | 48.5767 | 1.61653 | ||||||||
\(904\) | 116.630 | 3.87904 | ||||||||
\(905\) | 13.5160 | 0.449288 | ||||||||
\(906\) | −28.0226 | −0.930988 | ||||||||
\(907\) | − | 8.59463i | − | 0.285380i | −0.989767 | − | 0.142690i | \(-0.954425\pi\) | ||
0.989767 | − | 0.142690i | \(-0.0455752\pi\) | |||||||
\(908\) | −36.5368 | −1.21252 | ||||||||
\(909\) | − | 3.50877i | − | 0.116379i | ||||||
\(910\) | 7.29014i | 0.241666i | ||||||||
\(911\) | 12.9332i | 0.428497i | 0.976779 | + | 0.214249i | \(0.0687303\pi\) | ||||
−0.976779 | + | 0.214249i | \(0.931270\pi\) | |||||||
\(912\) | 176.456 | 5.84306 | ||||||||
\(913\) | − | 19.0207i | − | 0.629492i | ||||||
\(914\) | 27.8505i | 0.921214i | ||||||||
\(915\) | −2.27708 | −0.0752779 | ||||||||
\(916\) | 126.043i | 4.16458i | ||||||||
\(917\) | 30.0838i | 0.993454i | ||||||||
\(918\) | 2.34478i | 0.0773893i | ||||||||
\(919\) | 52.1153 | 1.71913 | 0.859563 | − | 0.511030i | \(-0.170736\pi\) | ||||
0.859563 | + | 0.511030i | \(0.170736\pi\) | |||||||
\(920\) | − | 48.2018i | − | 1.58917i | ||||||
\(921\) | −10.7836 | −0.355333 | ||||||||
\(922\) | 35.1724 | 1.15834 | ||||||||
\(923\) | 6.01894 | 0.198116 | ||||||||
\(924\) | −117.908 | −3.87890 | ||||||||
\(925\) | 4.04272i | 0.132924i | ||||||||
\(926\) | 89.8882i | 2.95391i | ||||||||
\(927\) | −26.6259 | −0.874509 | ||||||||
\(928\) | −22.7247 | + | 89.1184i | −0.745976 | + | 2.92545i | ||||
\(929\) | −26.5993 | −0.872695 | −0.436347 | − | 0.899778i | \(-0.643728\pi\) | ||||
−0.436347 | + | 0.899778i | \(0.643728\pi\) | |||||||
\(930\) | − | 0.983848i | − | 0.0322617i | ||||||
\(931\) | 64.3218i | 2.10806i | ||||||||
\(932\) | −26.8727 | −0.880246 | ||||||||
\(933\) | 50.1117 | 1.64058 | ||||||||
\(934\) | 87.5499 | 2.86472 | ||||||||
\(935\) | 1.35673 | 0.0443697 | ||||||||
\(936\) | 13.1078i | 0.428443i | ||||||||
\(937\) | −14.5291 | −0.474646 | −0.237323 | − | 0.971431i | \(-0.576270\pi\) | ||||
−0.237323 | + | 0.971431i | \(0.576270\pi\) | |||||||
\(938\) | − | 17.8483i | − | 0.582767i | ||||||
\(939\) | − | 26.2847i | − | 0.857768i | ||||||
\(940\) | − | 12.0773i | − | 0.393918i | ||||||
\(941\) | 3.14619 | 0.102563 | 0.0512815 | − | 0.998684i | \(-0.483669\pi\) | ||||
0.0512815 | + | 0.998684i | \(0.483669\pi\) | |||||||
\(942\) | − | 105.371i | − | 3.43318i | ||||||
\(943\) | 54.4269i | 1.77238i | ||||||||
\(944\) | −33.8157 | −1.10061 | ||||||||
\(945\) | − | 6.28017i | − | 0.204294i | ||||||
\(946\) | 30.9397i | 1.00594i | ||||||||
\(947\) | − | 51.7960i | − | 1.68314i | −0.540145 | − | 0.841572i | \(-0.681631\pi\) | ||
0.540145 | − | 0.841572i | \(-0.318369\pi\) | |||||||
\(948\) | −60.0927 | −1.95172 | ||||||||
\(949\) | 5.90309i | 0.191622i | ||||||||
\(950\) | 16.0113 | 0.519475 | ||||||||
\(951\) | 21.6753 | 0.702870 | ||||||||
\(952\) | 21.3793 | 0.692907 | ||||||||
\(953\) | −10.5542 | −0.341883 | −0.170941 | − | 0.985281i | \(-0.554681\pi\) | ||||
−0.170941 | + | 0.985281i | \(0.554681\pi\) | |||||||
\(954\) | 82.8169i | 2.68130i | ||||||||
\(955\) | − | 11.5723i | − | 0.374471i | ||||||
\(956\) | −76.4113 | −2.47132 | ||||||||
\(957\) | −27.9524 | − | 7.12772i | −0.903573 | − | 0.230407i | ||||
\(958\) | 98.1230 | 3.17021 | ||||||||
\(959\) | − | 62.3844i | − | 2.01450i | ||||||
\(960\) | 46.9785i | 1.51623i | ||||||||
\(961\) | 30.9750 | 0.999192 | ||||||||
\(962\) | −6.98690 | −0.225267 | ||||||||
\(963\) | 6.90907 | 0.222642 | ||||||||
\(964\) | −10.4364 | −0.336133 | ||||||||
\(965\) | − | 9.84404i | − | 0.316891i | ||||||
\(966\) | 146.227 | 4.70478 | ||||||||
\(967\) | 21.0448i | 0.676755i | 0.941010 | + | 0.338378i | \(0.109878\pi\) | ||||
−0.941010 | + | 0.338378i | \(0.890122\pi\) | |||||||
\(968\) | 48.7929i | 1.56826i | ||||||||
\(969\) | − | 8.08545i | − | 0.259742i | ||||||
\(970\) | 8.21819 | 0.263870 | ||||||||
\(971\) | 1.01417i | 0.0325462i | 0.999868 | + | 0.0162731i | \(0.00518012\pi\) | ||||
−0.999868 | + | 0.0162731i | \(0.994820\pi\) | |||||||
\(972\) | − | 103.698i | − | 3.32611i | ||||||
\(973\) | 15.0320 | 0.481905 | ||||||||
\(974\) | − | 69.6952i | − | 2.23318i | ||||||
\(975\) | 1.48883i | 0.0476808i | ||||||||
\(976\) | − | 12.5865i | − | 0.402883i | ||||||
\(977\) | 9.95239 | 0.318405 | 0.159203 | − | 0.987246i | \(-0.449108\pi\) | ||||
0.159203 | + | 0.987246i | \(0.449108\pi\) | |||||||
\(978\) | − | 68.9811i | − | 2.20577i | ||||||
\(979\) | −16.8727 | −0.539255 | ||||||||
\(980\) | −56.3204 | −1.79909 | ||||||||
\(981\) | 40.2520 | 1.28515 | ||||||||
\(982\) | −70.7699 | −2.25836 | ||||||||
\(983\) | − | 15.4059i | − | 0.491372i | −0.969349 | − | 0.245686i | \(-0.920987\pi\) | ||
0.969349 | − | 0.245686i | \(-0.0790133\pi\) | |||||||
\(984\) | − | 195.367i | − | 6.22806i | ||||||
\(985\) | −5.14982 | −0.164087 | ||||||||
\(986\) | 8.21819 | + | 2.09560i | 0.261720 | + | 0.0667374i | ||||
\(987\) | 22.5957 | 0.719228 | ||||||||
\(988\) | 20.0045i | 0.636428i | ||||||||
\(989\) | − | 27.7390i | − | 0.882049i | ||||||
\(990\) | −14.6546 | −0.465752 | ||||||||
\(991\) | −8.92035 | −0.283364 | −0.141682 | − | 0.989912i | \(-0.545251\pi\) | ||||
−0.141682 | + | 0.989912i | \(0.545251\pi\) | |||||||
\(992\) | 2.70217 | 0.0857938 | ||||||||
\(993\) | −42.8441 | −1.35962 | ||||||||
\(994\) | 106.039i | 3.36334i | ||||||||
\(995\) | −17.7931 | −0.564079 | ||||||||
\(996\) | − | 99.2534i | − | 3.14496i | ||||||
\(997\) | − | 1.19296i | − | 0.0377814i | −0.999822 | − | 0.0188907i | \(-0.993987\pi\) | ||
0.999822 | − | 0.0188907i | \(-0.00601345\pi\) | |||||||
\(998\) | 56.4552i | 1.78706i | ||||||||
\(999\) | 6.01894 | 0.190431 |
(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 | 145.2.c.b.86.1 | ✓ | 6 | |
3.2 | odd | 2 | 1305.2.d.b.811.6 | 6 | |||
4.3 | odd | 2 | 2320.2.g.i.1681.5 | 6 | |||
5.2 | odd | 4 | 725.2.d.c.724.12 | 12 | |||
5.3 | odd | 4 | 725.2.d.c.724.1 | 12 | |||
5.4 | even | 2 | 725.2.c.e.376.6 | 6 | |||
29.12 | odd | 4 | 4205.2.a.m.1.6 | 6 | |||
29.17 | odd | 4 | 4205.2.a.m.1.1 | 6 | |||
29.28 | even | 2 | inner | 145.2.c.b.86.6 | yes | 6 | |
87.86 | odd | 2 | 1305.2.d.b.811.1 | 6 | |||
116.115 | odd | 2 | 2320.2.g.i.1681.2 | 6 | |||
145.28 | odd | 4 | 725.2.d.c.724.11 | 12 | |||
145.57 | odd | 4 | 725.2.d.c.724.2 | 12 | |||
145.144 | even | 2 | 725.2.c.e.376.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
145.2.c.b.86.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
145.2.c.b.86.6 | yes | 6 | 29.28 | even | 2 | inner | |
725.2.c.e.376.1 | 6 | 145.144 | even | 2 | |||
725.2.c.e.376.6 | 6 | 5.4 | even | 2 | |||
725.2.d.c.724.1 | 12 | 5.3 | odd | 4 | |||
725.2.d.c.724.2 | 12 | 145.57 | odd | 4 | |||
725.2.d.c.724.11 | 12 | 145.28 | odd | 4 | |||
725.2.d.c.724.12 | 12 | 5.2 | odd | 4 | |||
1305.2.d.b.811.1 | 6 | 87.86 | odd | 2 | |||
1305.2.d.b.811.6 | 6 | 3.2 | odd | 2 | |||
2320.2.g.i.1681.2 | 6 | 116.115 | odd | 2 | |||
2320.2.g.i.1681.5 | 6 | 4.3 | odd | 2 | |||
4205.2.a.m.1.1 | 6 | 29.17 | odd | 4 | |||
4205.2.a.m.1.6 | 6 | 29.12 | odd | 4 |