Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(505,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.505");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 505.2 | ||
Root | \(0.939693 - 0.342020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.505 |
Dual form | 1368.2.s.j.577.2 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.347296 | − | 0.601535i | 0.155316 | − | 0.269015i | −0.777858 | − | 0.628440i | \(-0.783694\pi\) |
0.933174 | + | 0.359425i | \(0.117027\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.305407 | 0.115433 | 0.0577166 | − | 0.998333i | \(-0.481618\pi\) | ||||
0.0577166 | + | 0.998333i | \(0.481618\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.82295 | −1.45417 | −0.727087 | − | 0.686546i | \(-0.759126\pi\) | ||||
−0.727087 | + | 0.686546i | \(0.759126\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.75877 | + | 6.51038i | −0.911636 | + | 1.57900i | −0.0998822 | + | 0.994999i | \(0.531847\pi\) |
−0.811754 | + | 0.584000i | \(0.801487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.06418 | + | 3.10013i | 0.702971 | + | 0.711219i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.347296 | + | 0.601535i | 0.0724163 | + | 0.125429i | 0.899960 | − | 0.435973i | \(-0.143596\pi\) |
−0.827544 | + | 0.561402i | \(0.810262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.25877 | + | 3.91231i | 0.451754 | + | 0.782461i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.06418 | + | 8.77141i | 0.940394 | + | 1.62881i | 0.764721 | + | 0.644362i | \(0.222877\pi\) |
0.175674 | + | 0.984448i | \(0.443790\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.82295 | −0.327411 | −0.163706 | − | 0.986509i | \(-0.552345\pi\) | ||||
−0.163706 | + | 0.986509i | \(0.552345\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.106067 | − | 0.183713i | 0.0179286 | − | 0.0310532i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.51754 | 1.07148 | 0.535739 | − | 0.844384i | \(-0.320033\pi\) | ||||
0.535739 | + | 0.844384i | \(0.320033\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.69459 | − | 4.66717i | 0.420825 | − | 0.728890i | −0.575196 | − | 0.818016i | \(-0.695074\pi\) |
0.996020 | + | 0.0891261i | \(0.0284074\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.84730 | + | 3.19961i | −0.281710 | + | 0.487936i | −0.971806 | − | 0.235782i | \(-0.924235\pi\) |
0.690096 | + | 0.723718i | \(0.257568\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.90673 | −0.986675 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.71688 | + | 4.70578i | 0.373192 | + | 0.646388i | 0.990055 | − | 0.140683i | \(-0.0449298\pi\) |
−0.616862 | + | 0.787071i | \(0.711596\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.67499 | + | 2.90117i | −0.225856 | + | 0.391194i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.04189 | + | 3.53666i | −0.265831 | + | 0.460433i | −0.967781 | − | 0.251793i | \(-0.918980\pi\) |
0.701950 | + | 0.712226i | \(0.252313\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.194593 | − | 0.337044i | −0.0249150 | − | 0.0431541i | 0.853299 | − | 0.521422i | \(-0.174598\pi\) |
−0.878214 | + | 0.478268i | \(0.841265\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.694593 | −0.0861536 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.91147 | + | 6.77487i | 0.477863 | + | 0.827682i | 0.999678 | − | 0.0253761i | \(-0.00807834\pi\) |
−0.521815 | + | 0.853058i | \(0.674745\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.45336 | − | 9.44550i | 0.647195 | − | 1.12097i | −0.336595 | − | 0.941650i | \(-0.609275\pi\) |
0.983790 | − | 0.179325i | \(-0.0573914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.19459 | − | 3.80115i | 0.256858 | − | 0.444890i | −0.708541 | − | 0.705670i | \(-0.750646\pi\) |
0.965398 | + | 0.260779i | \(0.0839795\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.47296 | −0.167860 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.21688 | + | 12.5000i | −0.811963 | + | 1.40636i | 0.0995259 | + | 0.995035i | \(0.468267\pi\) |
−0.911489 | + | 0.411326i | \(0.865066\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.739170 | −0.0811345 | −0.0405672 | − | 0.999177i | \(-0.512916\pi\) | ||||
−0.0405672 | + | 0.999177i | \(0.512916\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.61081 | + | 4.52206i | 0.283183 | + | 0.490487i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.411474 | − | 0.712694i | −0.0436162 | − | 0.0755454i | 0.843393 | − | 0.537297i | \(-0.180555\pi\) |
−0.887009 | + | 0.461751i | \(0.847221\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.152704 | − | 0.264490i | −0.0160077 | − | 0.0277261i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.92902 | − | 0.766546i | 0.300511 | − | 0.0786459i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.45336 | + | 9.44550i | −0.553705 | + | 0.959045i | 0.444298 | + | 0.895879i | \(0.353453\pi\) |
−0.998003 | + | 0.0631663i | \(0.979880\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.75877 | + | 8.24243i | 0.473515 | + | 0.820153i | 0.999540 | − | 0.0303164i | \(-0.00965150\pi\) |
−0.526025 | + | 0.850469i | \(0.676318\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.30541 | −0.227159 | −0.113579 | − | 0.993529i | \(-0.536232\pi\) | ||||
−0.113579 | + | 0.993529i | \(0.536232\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.51754 | −0.920095 | −0.460048 | − | 0.887894i | \(-0.652168\pi\) | ||||
−0.460048 | + | 0.887894i | \(0.652168\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.75877 | + | 11.7065i | −0.647373 | + | 1.12128i | 0.336375 | + | 0.941728i | \(0.390799\pi\) |
−0.983748 | + | 0.179555i | \(0.942534\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 21.0797 | 1.98301 | 0.991504 | − | 0.130078i | \(-0.0415228\pi\) | ||||
0.991504 | + | 0.130078i | \(0.0415228\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.482459 | 0.0449895 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.14796 | + | 1.98832i | −0.105233 | + | 0.182269i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.2608 | 1.11462 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.61081 | 0.591289 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.69459 | − | 8.13127i | −0.416578 | − | 0.721534i | 0.579015 | − | 0.815317i | \(-0.303437\pi\) |
−0.995593 | + | 0.0937831i | \(0.970104\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.06418 | + | 7.03936i | −0.355089 | + | 0.615032i | −0.987133 | − | 0.159900i | \(-0.948883\pi\) |
0.632044 | + | 0.774932i | \(0.282216\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.935822 | + | 0.946803i | 0.0811461 | + | 0.0820982i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.67499 | − | 4.63322i | −0.228540 | − | 0.395843i | 0.728836 | − | 0.684689i | \(-0.240062\pi\) |
−0.957376 | + | 0.288846i | \(0.906729\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.97565 | − | 12.0822i | −0.591667 | − | 1.02480i | −0.994008 | − | 0.109308i | \(-0.965137\pi\) |
0.402341 | − | 0.915490i | \(-0.368197\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.41147 | + | 4.17680i | 0.201658 | + | 0.349281i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.03508 | 0.584232 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.34730 | − | 9.26179i | 0.438068 | − | 0.758755i | −0.559473 | − | 0.828849i | \(-0.688996\pi\) |
0.997540 | + | 0.0700934i | \(0.0223297\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.6459 | −1.43600 | −0.718001 | − | 0.696042i | \(-0.754943\pi\) | ||||
−0.718001 | + | 0.696042i | \(0.754943\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.633103 | + | 1.09657i | −0.0508521 | + | 0.0880784i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.95336 | + | 13.7756i | −0.634747 | + | 1.09941i | 0.351821 | + | 0.936067i | \(0.385563\pi\) |
−0.986569 | + | 0.163348i | \(0.947771\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.106067 | + | 0.183713i | 0.00835924 | + | 0.0144786i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.17705 | −0.170520 | −0.0852599 | − | 0.996359i | \(-0.527172\pi\) | ||||
−0.0852599 | + | 0.996359i | \(0.527172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.47565 | − | 9.48411i | −0.423719 | − | 0.733902i | 0.572581 | − | 0.819848i | \(-0.305942\pi\) |
−0.996300 | + | 0.0859458i | \(0.972609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.06418 | + | 8.77141i | −0.385022 | + | 0.666878i | −0.991772 | − | 0.128015i | \(-0.959140\pi\) |
0.606750 | + | 0.794893i | \(0.292473\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.689845 | + | 1.19485i | 0.0521474 | + | 0.0903219i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.69459 | −0.649864 | −0.324932 | − | 0.945737i | \(-0.605341\pi\) | ||||
−0.324932 | + | 0.945737i | \(0.605341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.93582 | − | 6.81704i | −0.292547 | − | 0.506707i | 0.681864 | − | 0.731479i | \(-0.261170\pi\) |
−0.974411 | + | 0.224772i | \(0.927836\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.26352 | − | 3.92053i | 0.166417 | − | 0.288243i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.1284 | − | 31.3992i | 1.32568 | − | 2.29614i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8580 | −1.00273 | −0.501366 | − | 0.865235i | \(-0.667169\pi\) | ||||
−0.501366 | + | 0.865235i | \(0.667169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.04664 | + | 1.81283i | −0.0753386 | + | 0.130490i | −0.901233 | − | 0.433334i | \(-0.857337\pi\) |
0.825895 | + | 0.563824i | \(0.190670\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.0446 | −1.00063 | −0.500317 | − | 0.865842i | \(-0.666783\pi\) | ||||
−0.500317 | + | 0.865842i | \(0.666783\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.9953 | + | 19.0443i | 0.779433 | + | 1.35002i | 0.932269 | + | 0.361766i | \(0.117826\pi\) |
−0.152836 | + | 0.988252i | \(0.548841\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.54664 | + | 2.67885i | 0.108553 | + | 0.188019i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.87164 | − | 3.24178i | −0.130721 | − | 0.226416i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.7784 | − | 14.9518i | −1.02224 | − | 1.03424i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.97565 | − | 13.8142i | 0.549067 | − | 0.951011i | −0.449272 | − | 0.893395i | \(-0.648317\pi\) |
0.998339 | − | 0.0576162i | \(-0.0183500\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.28312 | + | 2.22243i | 0.0875080 | + | 0.151568i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.556742 | −0.0377941 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.51754 | 0.505685 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.2520 | − | 22.9531i | 0.887417 | − | 1.53705i | 0.0444991 | − | 0.999009i | \(-0.485831\pi\) |
0.842918 | − | 0.538042i | \(-0.180836\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.65539 | −0.176245 | −0.0881223 | − | 0.996110i | \(-0.528087\pi\) | ||||
−0.0881223 | + | 0.996110i | \(0.528087\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2567 | 1.40468 | 0.702342 | − | 0.711840i | \(-0.252138\pi\) | ||||
0.702342 | + | 0.711840i | \(0.252138\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.75877 | − | 11.7065i | 0.442782 | − | 0.766921i | −0.555113 | − | 0.831775i | \(-0.687325\pi\) |
0.997895 | + | 0.0648544i | \(0.0206583\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.16756 | −0.271861 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.4688 | 1.58276 | 0.791379 | − | 0.611326i | \(-0.209364\pi\) | ||||
0.791379 | + | 0.611326i | \(0.209364\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.93376 | − | 10.2776i | −0.382227 | − | 0.662037i | 0.609153 | − | 0.793053i | \(-0.291510\pi\) |
−0.991380 | + | 0.131016i | \(0.958176\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.39868 | + | 4.15464i | −0.153246 | + | 0.265430i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.15270 | − | 4.20372i | 0.0733448 | − | 0.267476i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.69459 | + | 6.39922i | 0.233201 | + | 0.403915i | 0.958748 | − | 0.284257i | \(-0.0917468\pi\) |
−0.725548 | + | 0.688172i | \(0.758413\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.67499 | − | 2.90117i | −0.105306 | − | 0.182395i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.67230 | + | 4.62857i | 0.166694 | + | 0.288722i | 0.937255 | − | 0.348643i | \(-0.113358\pi\) |
−0.770562 | + | 0.637365i | \(0.780024\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.99050 | 0.123684 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0642 | + | 20.8958i | −0.743909 | + | 1.28849i | 0.206794 | + | 0.978385i | \(0.433697\pi\) |
−0.950703 | + | 0.310104i | \(0.899636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.77425 | 0.231850 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.80066 | + | 3.11883i | −0.109788 | + | 0.190159i | −0.915684 | − | 0.401898i | \(-0.868351\pi\) |
0.805896 | + | 0.592057i | \(0.201684\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.38919 | + | 16.2625i | −0.570352 | + | 0.987879i | 0.426177 | + | 0.904640i | \(0.359860\pi\) |
−0.996530 | + | 0.0832396i | \(0.973473\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.8939 | − | 18.8688i | −0.656929 | − | 1.13783i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.1284 | 1.20940 | 0.604698 | − | 0.796455i | \(-0.293294\pi\) | ||||
0.604698 | + | 0.796455i | \(0.293294\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.17024 | − | 12.4192i | −0.427741 | − | 0.740869i | 0.568931 | − | 0.822385i | \(-0.307357\pi\) |
−0.996672 | + | 0.0815162i | \(0.974024\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.38919 | + | 5.87024i | −0.201466 | + | 0.348950i | −0.949001 | − | 0.315273i | \(-0.897904\pi\) |
0.747535 | + | 0.664223i | \(0.231237\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.822948 | − | 1.42539i | 0.0485771 | − | 0.0841380i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.7567 | − | 34.2196i | −1.16216 | − | 2.01292i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.7784 | −0.980203 | −0.490101 | − | 0.871665i | \(-0.663040\pi\) | ||||
−0.490101 | + | 0.871665i | \(0.663040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.41828 | + | 2.45654i | 0.0825755 | + | 0.143025i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.347296 | − | 0.601535i | 0.0200847 | − | 0.0347877i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.564178 | + | 0.977185i | −0.0325187 | + | 0.0563240i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.270325 | −0.0154788 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.58172 | − | 14.8640i | 0.489785 | − | 0.848332i | −0.510146 | − | 0.860088i | \(-0.670409\pi\) |
0.999931 | + | 0.0117559i | \(0.00374210\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.1729 | 0.690264 | 0.345132 | − | 0.938554i | \(-0.387834\pi\) | ||||
0.345132 | + | 0.938554i | \(0.387834\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.85204 | − | 3.20783i | −0.104684 | − | 0.181318i | 0.808925 | − | 0.587912i | \(-0.200050\pi\) |
−0.913609 | + | 0.406594i | \(0.866716\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.7811 | + | 20.4054i | 0.661690 | + | 1.14608i | 0.980171 | + | 0.198152i | \(0.0634939\pi\) |
−0.318481 | + | 0.947929i | \(0.603173\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.4243 | − | 42.3041i | −1.36750 | − | 2.36857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −31.7006 | + | 8.29628i | −1.76387 | + | 0.461618i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.25877 | − | 3.91231i | 0.125294 | − | 0.217016i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.916222 | − | 1.58694i | −0.0505129 | − | 0.0874910i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.30541 | −0.236647 | −0.118323 | − | 0.992975i | \(-0.537752\pi\) | ||||
−0.118323 | + | 0.992975i | \(0.537752\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.43376 | 0.296878 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.77631 | + | 16.9331i | −0.532550 | + | 0.922403i | 0.466728 | + | 0.884401i | \(0.345433\pi\) |
−0.999278 | + | 0.0380021i | \(0.987901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.79199 | 0.476113 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.24722 | −0.229328 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.8452 | − | 29.1768i | 0.904300 | − | 1.56629i | 0.0824452 | − | 0.996596i | \(-0.473727\pi\) |
0.821855 | − | 0.569697i | \(-0.192940\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.5567 | 0.672147 | 0.336073 | − | 0.941836i | \(-0.390901\pi\) | ||||
0.336073 | + | 0.941836i | \(0.390901\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.65951 | 0.301225 | 0.150613 | − | 0.988593i | \(-0.451875\pi\) | ||||
0.150613 | + | 0.988593i | \(0.451875\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.78787 | − | 6.56078i | −0.201039 | − | 0.348210i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3892 | − | 19.7266i | 0.601098 | − | 1.04113i | −0.391557 | − | 0.920154i | \(-0.628063\pi\) |
0.992655 | − | 0.120979i | \(-0.0386033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.221629 | + | 18.9987i | −0.0116647 | + | 0.999932i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.52435 | − | 2.64025i | −0.0797880 | − | 0.138197i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.5574 | + | 23.4821i | 0.707689 | + | 1.22575i | 0.965712 | + | 0.259615i | \(0.0835955\pi\) |
−0.258023 | + | 0.966139i | \(0.583071\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.829755 | + | 1.43718i | 0.0430788 | + | 0.0746146i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.9418 | −0.721879 | −0.360940 | − | 0.932589i | \(-0.617544\pi\) | ||||
−0.360940 | + | 0.932589i | \(0.617544\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.06418 | − | 8.77141i | 0.260818 | − | 0.451751i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.08378 | 0.0556699 | 0.0278350 | − | 0.999613i | \(-0.491139\pi\) | ||||
0.0278350 | + | 0.999613i | \(0.491139\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.5398 | − | 28.6478i | 0.845146 | − | 1.46384i | −0.0403487 | − | 0.999186i | \(-0.512847\pi\) |
0.885495 | − | 0.464650i | \(-0.153820\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.511555 | + | 0.886039i | −0.0260713 | + | 0.0451567i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.41147 | − | 2.44474i | −0.0715646 | − | 0.123953i | 0.828023 | − | 0.560695i | \(-0.189466\pi\) |
−0.899587 | + | 0.436741i | \(0.856133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.22163 | −0.264069 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.01279 | + | 8.68241i | 0.252221 | + | 0.436860i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.7567 | − | 25.5594i | 0.740618 | − | 1.28279i | −0.211596 | − | 0.977357i | \(-0.567866\pi\) |
0.952214 | − | 0.305431i | \(-0.0988005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.1506 | − | 19.3135i | 0.556837 | − | 0.964469i | −0.440922 | − | 0.897546i | \(-0.645348\pi\) |
0.997758 | − | 0.0669236i | \(-0.0213184\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.911474 | + | 1.57872i | 0.0454038 | + | 0.0786416i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.4338 | −1.55811 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.8871 | − | 25.7853i | −0.736121 | − | 1.27500i | −0.954230 | − | 0.299075i | \(-0.903322\pi\) |
0.218109 | − | 0.975924i | \(-0.430011\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.623608 | + | 1.08012i | −0.0306857 | + | 0.0531493i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.256711 | + | 0.444637i | −0.0126015 | + | 0.0218264i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 40.1147 | 1.95973 | 0.979867 | − | 0.199653i | \(-0.0639815\pi\) | ||||
0.979867 | + | 0.199653i | \(0.0639815\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0155 | + | 29.4717i | −0.829284 | + | 1.43636i | 0.0693170 | + | 0.997595i | \(0.477918\pi\) |
−0.898601 | + | 0.438767i | \(0.855415\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −33.9608 | −1.64734 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0594300 | − | 0.102936i | −0.00287602 | − | 0.00498141i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.12836 | + | 8.88257i | 0.247024 | + | 0.427858i | 0.962699 | − | 0.270575i | \(-0.0872140\pi\) |
−0.715675 | + | 0.698434i | \(0.753881\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.9979 | − | 27.7092i | −0.768812 | − | 1.33162i | −0.938208 | − | 0.346073i | \(-0.887515\pi\) |
0.169396 | − | 0.985548i | \(-0.445818\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.800660 | + | 2.91987i | −0.0383007 | + | 0.139677i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.05943 | + | 10.4952i | −0.289201 | + | 0.500911i | −0.973619 | − | 0.228179i | \(-0.926723\pi\) |
0.684418 | + | 0.729089i | \(0.260056\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.45336 | + | 4.24935i | 0.116563 | + | 0.201893i | 0.918403 | − | 0.395645i | \(-0.129479\pi\) |
−0.801841 | + | 0.597538i | \(0.796146\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.571614 | −0.0270971 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.12836 | 0.289215 | 0.144607 | − | 0.989489i | \(-0.453808\pi\) | ||||
0.144607 | + | 0.989489i | \(0.453808\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.9959 | + | 22.5095i | −0.611952 | + | 1.05993i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.212134 | −0.00994498 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.9959 | 1.40315 | 0.701574 | − | 0.712597i | \(-0.252481\pi\) | ||||
0.701574 | + | 0.712597i | \(0.252481\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.53983 | + | 14.7914i | −0.397740 | + | 0.688905i | −0.993447 | − | 0.114297i | \(-0.963539\pi\) |
0.595707 | + | 0.803202i | \(0.296872\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.3756 | 1.31872 | 0.659362 | − | 0.751825i | \(-0.270826\pi\) | ||||
0.659362 | + | 0.751825i | \(0.270826\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.61081 | −0.305912 | −0.152956 | − | 0.988233i | \(-0.548879\pi\) | ||||
−0.152956 | + | 0.988233i | \(0.548879\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.19459 | + | 2.06910i | 0.0551612 | + | 0.0955419i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.90941 | − | 15.4316i | 0.409655 | − | 0.709544i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.20739 | + | 18.9905i | −0.238931 | + | 0.871343i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.45336 | + | 9.44550i | 0.249171 | + | 0.431576i | 0.963296 | − | 0.268442i | \(-0.0865087\pi\) |
−0.714125 | + | 0.700018i | \(0.753175\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.25877 | − | 5.64436i | −0.148587 | − | 0.257360i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.78787 | + | 6.56078i | 0.171998 | + | 0.297910i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.8324 | 0.536179 | 0.268090 | − | 0.963394i | \(-0.413608\pi\) | ||||
0.268090 | + | 0.963394i | \(0.413608\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.45336 | + | 12.9096i | −0.336366 | + | 0.582602i | −0.983746 | − | 0.179565i | \(-0.942531\pi\) |
0.647381 | + | 0.762167i | \(0.275864\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −76.1403 | −3.42919 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.66550 | − | 2.88473i | 0.0747077 | − | 0.129398i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.9115 | + | 34.4877i | −0.891360 | + | 1.54388i | −0.0531141 | + | 0.998588i | \(0.516915\pi\) |
−0.838246 | + | 0.545292i | \(0.816419\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.06418 | − | 8.77141i | −0.225801 | − | 0.391098i | 0.730759 | − | 0.682636i | \(-0.239166\pi\) |
−0.956559 | + | 0.291538i | \(0.905833\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.61081 | 0.294177 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.5175 | + | 21.6810i | 0.554830 | + | 0.960994i | 0.997917 | + | 0.0645153i | \(0.0205501\pi\) |
−0.443086 | + | 0.896479i | \(0.646117\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.670245 | − | 1.16090i | 0.0296499 | − | 0.0513551i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.800660 | + | 1.38678i | −0.0352813 | + | 0.0611090i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.4688 | + | 25.0608i | 0.636339 | + | 1.10217i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.9162 | −1.04779 | −0.523894 | − | 0.851783i | \(-0.675521\pi\) | ||||
−0.523894 | + | 0.851783i | \(0.675521\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.4290 | + | 31.9200i | 0.805845 | + | 1.39576i | 0.915719 | + | 0.401818i | \(0.131622\pi\) |
−0.109875 | + | 0.993945i | \(0.535045\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.85204 | − | 11.8681i | 0.298480 | − | 0.516982i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2588 | − | 19.5008i | 0.489512 | − | 0.847859i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.38919 | −0.233432 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.30541 | + | 5.72513i | −0.142905 | + | 0.247519i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33.3108 | 1.43480 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.2101 | − | 19.4164i | −0.481959 | − | 0.834777i | 0.517827 | − | 0.855485i | \(-0.326741\pi\) |
−0.999786 | + | 0.0207084i | \(0.993408\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.69459 | + | 8.13127i | 0.201094 | + | 0.348305i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.18779 | + | 5.52141i | 0.136300 | + | 0.236078i | 0.926093 | − | 0.377295i | \(-0.123146\pi\) |
−0.789793 | + | 0.613373i | \(0.789812\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.6750 | + | 42.5768i | −0.497371 | + | 1.81383i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.20409 | + | 3.81759i | −0.0937274 | + | 0.162341i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.97090 | − | 15.5381i | −0.380109 | − | 0.658369i | 0.610968 | − | 0.791655i | \(-0.290780\pi\) |
−0.991078 | + | 0.133286i | \(0.957447\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.69459 | 0.156265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.5175 | 0.738276 | 0.369138 | − | 0.929375i | \(-0.379653\pi\) | ||||
0.369138 | + | 0.929375i | \(0.379653\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.32089 | − | 12.6802i | 0.307992 | − | 0.533458i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.6810 | −0.531614 | −0.265807 | − | 0.964026i | \(-0.585638\pi\) | ||||
−0.265807 | + | 0.964026i | \(0.585638\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.0256 | 1.63317 | 0.816585 | − | 0.577225i | \(-0.195865\pi\) | ||||
0.816585 | + | 0.577225i | \(0.195865\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.56893 | + | 2.71746i | −0.0654287 | + | 0.113326i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.2959 | 1.17797 | 0.588987 | − | 0.808142i | \(-0.299527\pi\) | ||||
0.588987 | + | 0.808142i | \(0.299527\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.225748 | −0.00936560 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.1034 | − | 22.6957i | −0.542686 | − | 0.939961i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.8648 | − | 22.2826i | 0.530989 | − | 0.919699i | −0.468357 | − | 0.883539i | \(-0.655154\pi\) |
0.999346 | − | 0.0361602i | \(-0.0115127\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.58584 | − | 5.65138i | −0.230160 | − | 0.232861i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.49525 | − | 11.2501i | −0.266728 | − | 0.461987i | 0.701287 | − | 0.712879i | \(-0.252609\pi\) |
−0.968015 | + | 0.250893i | \(0.919276\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.797362 | + | 1.38107i | 0.0326886 | + | 0.0566184i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.18984 | − | 8.98908i | −0.212051 | − | 0.367284i | 0.740305 | − | 0.672271i | \(-0.234681\pi\) |
−0.952356 | + | 0.304987i | \(0.901348\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.29591 | −0.297606 | −0.148803 | − | 0.988867i | \(-0.547542\pi\) | ||||
−0.148803 | + | 0.988867i | \(0.547542\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.25814 | − | 7.37532i | 0.173118 | − | 0.299849i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.1147 | 1.58762 | 0.793809 | − | 0.608167i | \(-0.208095\pi\) | ||||
0.793809 | + | 0.608167i | \(0.208095\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.00000 | + | 5.19615i | −0.121367 | + | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.3209 | + | 35.1968i | −0.820753 | + | 1.42159i | 0.0843693 | + | 0.996435i | \(0.473112\pi\) |
−0.905122 | + | 0.425151i | \(0.860221\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.38238 | − | 14.5187i | −0.337462 | − | 0.584501i | 0.646493 | − | 0.762920i | \(-0.276235\pi\) |
−0.983955 | + | 0.178419i | \(0.942902\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0797 | −0.565909 | −0.282955 | − | 0.959133i | \(-0.591315\pi\) | ||||
−0.282955 | + | 0.959133i | \(0.591315\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.125667 | − | 0.217662i | −0.00503475 | − | 0.00872044i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.99794 | + | 15.5849i | −0.359918 | + | 0.623396i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.4979 | + | 42.4317i | −0.976797 | + | 1.69186i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.4486 | − | 18.0975i | −0.415953 | − | 0.720451i | 0.579575 | − | 0.814919i | \(-0.303219\pi\) |
−0.995528 | + | 0.0944674i | \(0.969885\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.52166 | −0.258804 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.45336 | + | 5.98140i | 0.136827 | + | 0.236992i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.69459 | − | 2.93512i | 0.0669324 | − | 0.115930i | −0.830617 | − | 0.556844i | \(-0.812012\pi\) |
0.897550 | + | 0.440914i | \(0.145345\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.82770 | − | 15.2900i | 0.348130 | − | 0.602979i | −0.637787 | − | 0.770213i | \(-0.720150\pi\) |
0.985917 | + | 0.167233i | \(0.0534833\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.6500 | 0.654580 | 0.327290 | − | 0.944924i | \(-0.393865\pi\) | ||||
0.327290 | + | 0.944924i | \(0.393865\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.84793 | − | 17.0571i | 0.386565 | − | 0.669550i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.5877 | 1.39265 | 0.696327 | − | 0.717724i | \(-0.254816\pi\) | ||||
0.696327 | + | 0.717724i | \(0.254816\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.82295 | + | 4.88949i | 0.110302 | + | 0.191048i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.4561 | + | 35.4309i | 0.796855 | + | 1.38019i | 0.921655 | + | 0.388011i | \(0.126838\pi\) |
−0.124800 | + | 0.992182i | \(0.539829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.645897 | + | 1.11873i | 0.0251225 | + | 0.0435134i | 0.878313 | − | 0.478085i | \(-0.158669\pi\) |
−0.853191 | + | 0.521599i | \(0.825336\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.894543 | − | 0.234109i | 0.0346889 | − | 0.00907834i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.51754 | + | 6.09256i | −0.136200 | + | 0.235905i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.938511 | + | 1.62555i | 0.0362308 | + | 0.0627536i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.99588 | 0.308219 | 0.154109 | − | 0.988054i | \(-0.450749\pi\) | ||||
0.154109 | + | 0.988054i | \(0.450749\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −46.7701 | −1.79752 | −0.898761 | − | 0.438439i | \(-0.855532\pi\) | ||||
−0.898761 | + | 0.438439i | \(0.855532\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.66550 | + | 2.88473i | −0.0639159 | + | 0.110706i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.69047 | 0.217740 | 0.108870 | − | 0.994056i | \(-0.465277\pi\) | ||||
0.108870 | + | 0.994056i | \(0.465277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.71606 | −0.141983 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.71688 | − | 4.70578i | 0.103505 | − | 0.179276i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.8485 | −1.09745 | −0.548725 | − | 0.836003i | \(-0.684887\pi\) | ||||
−0.548725 | + | 0.836003i | \(0.684887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.69047 | −0.367581 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.2567 | + | 35.0857i | 0.767278 | + | 1.32896i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.7716 | + | 39.4415i | −0.860070 | + | 1.48969i | 0.0117902 | + | 0.999930i | \(0.496247\pi\) |
−0.871860 | + | 0.489755i | \(0.837086\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.9709 | + | 20.2052i | 0.753217 | + | 0.762055i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.45336 | + | 2.51730i | 0.0546593 | + | 0.0946728i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.1013 | + | 26.1563i | 0.567142 | + | 0.982319i | 0.996847 | + | 0.0793493i | \(0.0252842\pi\) |
−0.429705 | + | 0.902969i | \(0.641382\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.633103 | − | 1.09657i | −0.0237099 | − | 0.0410668i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.34998 | 0.125282 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.0770 | + | 31.3102i | −0.674157 | + | 1.16767i | 0.302557 | + | 0.953131i | \(0.402160\pi\) |
−0.976714 | + | 0.214543i | \(0.931174\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.704088 | −0.0262216 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.8776 | + | 39.6252i | −0.849654 | + | 1.47164i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.65064 | − | 6.32310i | 0.135395 | − | 0.234511i | −0.790353 | − | 0.612651i | \(-0.790103\pi\) |
0.925748 | + | 0.378140i | \(0.123436\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.8871 | − | 24.0532i | −0.513634 | − | 0.889640i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.4986 | 1.90214 | 0.951071 | − | 0.308972i | \(-0.0999849\pi\) | ||||
0.951071 | + | 0.308972i | \(0.0999849\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.8648 | − | 32.6749i | −0.694895 | − | 1.20359i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.3452 | + | 28.3108i | −0.601269 | + | 1.04143i | 0.391360 | + | 0.920238i | \(0.372005\pi\) |
−0.992629 | + | 0.121191i | \(0.961329\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.7965 | + | 39.4848i | −0.836324 | + | 1.44856i | 0.0566239 | + | 0.998396i | \(0.481966\pi\) |
−0.892948 | + | 0.450160i | \(0.851367\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.71419 | − | 6.43317i | −0.136078 | − | 0.235693i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.90673 | −0.106209 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.15270 | + | 15.8529i | 0.333987 | + | 0.578482i | 0.983290 | − | 0.182048i | \(-0.0582725\pi\) |
−0.649303 | + | 0.760530i | \(0.724939\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.12836 | + | 10.6146i | −0.223034 | + | 0.386306i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.7121 | − | 27.2142i | 0.571067 | − | 0.989117i | −0.425390 | − | 0.905010i | \(-0.639863\pi\) |
0.996457 | − | 0.0841071i | \(-0.0268038\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.5580 | −1.39773 | −0.698863 | − | 0.715255i | \(-0.746310\pi\) | ||||
−0.698863 | + | 0.715255i | \(0.746310\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.06418 | + | 3.57526i | −0.0747283 | + | 0.129433i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.08378 | 0.147457 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.37164 | − | 12.7681i | −0.265828 | − | 0.460428i | 0.701952 | − | 0.712224i | \(-0.252312\pi\) |
−0.967780 | + | 0.251796i | \(0.918979\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.95130 | − | 3.37976i | −0.0701835 | − | 0.121561i | 0.828798 | − | 0.559548i | \(-0.189025\pi\) |
−0.898982 | + | 0.437986i | \(0.855692\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.11762 | − | 7.13193i | −0.147909 | − | 0.256186i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.7256 | − | 5.94745i | 0.814228 | − | 0.213090i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.3013 | + | 45.5552i | −0.941134 | + | 1.63009i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.52435 | + | 9.56845i | 0.197172 | + | 0.341513i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.7879 | −0.384546 | −0.192273 | − | 0.981341i | \(-0.561586\pi\) | ||||
−0.192273 | + | 0.981341i | \(0.561586\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.43788 | 0.228905 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.194593 | + | 0.337044i | −0.00691019 | + | 0.0119688i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.5526 | 1.71982 | 0.859911 | − | 0.510444i | \(-0.170519\pi\) | ||||
0.859911 | + | 0.510444i | \(0.170519\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.1052 | 1.59571 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.5844 | + | 18.3327i | −0.373516 | + | 0.646948i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.147347 | 0.00519328 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.8972 | 1.26208 | 0.631040 | − | 0.775751i | \(-0.282628\pi\) | ||||
0.631040 | + | 0.775751i | \(0.282628\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.17705 | + | 5.50282i | 0.111561 | + | 0.193230i | 0.916400 | − | 0.400264i | \(-0.131082\pi\) |
−0.804839 | + | 0.593494i | \(0.797748\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.756082 | + | 1.30957i | −0.0264844 | + | 0.0458723i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.5797 | + | 4.07732i | −0.545063 | + | 0.142647i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.93582 | − | 12.0132i | −0.242062 | − | 0.419263i | 0.719240 | − | 0.694762i | \(-0.244490\pi\) |
−0.961301 | + | 0.275499i | \(0.911157\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.95130 | − | 5.11181i | −0.102876 | − | 0.178186i | 0.809992 | − | 0.586440i | \(-0.199471\pi\) |
−0.912868 | + | 0.408254i | \(0.866138\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.9709 | + | 20.7342i | 0.416269 | + | 0.720999i | 0.995561 | − | 0.0941211i | \(-0.0300041\pi\) |
−0.579292 | + | 0.815120i | \(0.696671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.4593 | 0.710583 | 0.355291 | − | 0.934756i | \(-0.384382\pi\) | ||||
0.355291 | + | 0.934756i | \(0.384382\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.9608 | − | 44.9654i | 0.899488 | − | 1.55796i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.60670 | −0.263241 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.3628 | + | 24.8771i | −0.495858 | + | 0.858852i | −0.999989 | − | 0.00477600i | \(-0.998480\pi\) |
0.504130 | + | 0.863628i | \(0.331813\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −36.7918 | + | 63.7253i | −1.26868 | + | 2.19742i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.16756 | − | 7.21842i | −0.143368 | − | 0.248321i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.74455 | 0.128664 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.26352 | + | 3.92053i | 0.0775924 | + | 0.134394i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.22369 | − | 2.11949i | 0.0418983 | − | 0.0725700i | −0.844316 | − | 0.535846i | \(-0.819993\pi\) |
0.886214 | + | 0.463276i | \(0.153326\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.0351 | + | 17.3813i | −0.342792 | + | 0.593733i | −0.984950 | − | 0.172839i | \(-0.944706\pi\) |
0.642158 | + | 0.766572i | \(0.278039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.5128 | − | 38.9933i | −0.768127 | − | 1.33043i | −0.938578 | − | 0.345068i | \(-0.887856\pi\) |
0.170451 | − | 0.985366i | \(-0.445478\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.5918 | 0.632873 | 0.316437 | − | 0.948614i | \(-0.397514\pi\) | ||||
0.316437 | + | 0.948614i | \(0.397514\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.51754 | + | 6.09256i | 0.119600 | + | 0.207153i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.8066 | − | 60.2869i | 1.18073 | − | 2.04509i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.91147 | − | 6.77487i | 0.132535 | − | 0.229558i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.01899 | 0.0682544 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.86959 | + | 6.70232i | −0.130667 | + | 0.226321i | −0.923934 | − | 0.382553i | \(-0.875045\pi\) |
0.793267 | + | 0.608874i | \(0.208378\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.0487 | −0.507003 | −0.253502 | − | 0.967335i | \(-0.581582\pi\) | ||||
−0.253502 | + | 0.967335i | \(0.581582\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.281059 | + | 0.486809i | 0.00945839 | + | 0.0163824i | 0.870716 | − | 0.491786i | \(-0.163656\pi\) |
−0.861257 | + | 0.508169i | \(0.830323\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.43107 | + | 2.47869i | 0.0480508 | + | 0.0832264i | 0.889050 | − | 0.457809i | \(-0.151366\pi\) |
−0.841000 | + | 0.541036i | \(0.818032\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.43376 | − | 2.48335i | −0.0480869 | − | 0.0832889i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.91622 | − | 25.2223i | 0.231443 | − | 0.844033i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.01960 | + | 5.23010i | −0.100934 | + | 0.174823i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.23173 | − | 15.9898i | −0.307896 | − | 0.533291i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.8485 | −1.36086 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.46759 | −0.181749 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.0351 | − | 29.5056i | 0.565641 | − | 0.979718i | −0.431349 | − | 0.902185i | \(-0.641962\pi\) |
0.996990 | − | 0.0775332i | \(-0.0247044\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.90261 | 0.195562 | 0.0977811 | − | 0.995208i | \(-0.468826\pi\) | ||||
0.0977811 | + | 0.995208i | \(0.468826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.56498 | 0.117984 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.24123 | + | 2.14987i | −0.0409890 | + | 0.0709950i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.394562 | −0.0130154 | −0.00650770 | − | 0.999979i | \(-0.502071\pi\) | ||||
−0.00650770 | + | 0.999979i | \(0.502071\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.9067 | −0.358999 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.7216 | + | 25.4986i | 0.484044 | + | 0.838389i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.8999 | + | 29.2715i | −0.554468 | + | 0.960367i | 0.443476 | + | 0.896286i | \(0.353745\pi\) |
−0.997945 | + | 0.0640813i | \(0.979588\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.1634 | − | 21.4118i | −0.693604 | − | 0.701742i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.5918 | − | 21.8097i | −0.411797 | − | 0.713253i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.8601 | − | 36.1307i | −0.681469 | − | 1.18034i | −0.974532 | − | 0.224247i | \(-0.928008\pi\) |
0.293063 | − | 0.956093i | \(-0.405325\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.73917 | + | 8.20848i | 0.154493 | + | 0.267589i | 0.932874 | − | 0.360203i | \(-0.117292\pi\) |
−0.778382 | + | 0.627791i | \(0.783959\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.74329 | 0.121898 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.71007 | − | 6.42604i | 0.120561 | − | 0.208818i | −0.799428 | − | 0.600762i | \(-0.794864\pi\) |
0.919989 | + | 0.391944i | \(0.128197\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.38919 | −0.142479 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.909415 | − | 1.57515i | 0.0294588 | − | 0.0510242i | −0.850920 | − | 0.525295i | \(-0.823955\pi\) |
0.880379 | + | 0.474271i | \(0.157288\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.81284 | + | 8.33609i | −0.155740 | + | 0.269750i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.816962 | − | 1.41502i | −0.0263811 | − | 0.0456934i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6769 | −0.892802 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.726986 | + | 1.25918i | 0.0234025 | + | 0.0405343i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.95067 | + | 5.11072i | −0.0948873 | + | 0.164350i | −0.909562 | − | 0.415569i | \(-0.863582\pi\) |
0.814674 | + | 0.579919i | \(0.196916\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.6851 | − | 39.2917i | 0.727999 | − | 1.26093i | −0.229728 | − | 0.973255i | \(-0.573784\pi\) |
0.957727 | − | 0.287677i | \(-0.0928830\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.13041 | − | 3.68999i | −0.0682980 | − | 0.118296i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.2377 | 1.15935 | 0.579674 | − | 0.814849i | \(-0.303180\pi\) | ||||
0.579674 | + | 0.814849i | \(0.303180\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.98452 | + | 3.43729i | 0.0634255 | + | 0.109856i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.32770 | + | 7.49579i | −0.138032 | + | 0.239079i | −0.926752 | − | 0.375675i | \(-0.877411\pi\) |
0.788720 | + | 0.614753i | \(0.210744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.87763 | + | 8.44830i | −0.155414 | + | 0.269185i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.56624 | −0.0816016 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.9020 | + | 51.7917i | −0.949868 | + | 1.64522i | −0.204169 | + | 0.978936i | \(0.565449\pi\) |
−0.745699 | + | 0.666283i | \(0.767884\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.2744 | 0.484232 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.52498 | + | 13.0336i | 0.238318 | + | 0.412780i | 0.960232 | − | 0.279204i | \(-0.0900705\pi\) |
−0.721913 | + | 0.691983i | \(0.756737\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1368.2.s.j.505.2 | 6 | ||
3.2 | odd | 2 | 456.2.q.f.49.2 | ✓ | 6 | ||
4.3 | odd | 2 | 2736.2.s.x.1873.2 | 6 | |||
12.11 | even | 2 | 912.2.q.k.49.2 | 6 | |||
19.7 | even | 3 | inner | 1368.2.s.j.577.2 | 6 | ||
57.8 | even | 6 | 8664.2.a.z.1.2 | 3 | |||
57.11 | odd | 6 | 8664.2.a.x.1.2 | 3 | |||
57.26 | odd | 6 | 456.2.q.f.121.2 | yes | 6 | ||
76.7 | odd | 6 | 2736.2.s.x.577.2 | 6 | |||
228.83 | even | 6 | 912.2.q.k.577.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.q.f.49.2 | ✓ | 6 | 3.2 | odd | 2 | ||
456.2.q.f.121.2 | yes | 6 | 57.26 | odd | 6 | ||
912.2.q.k.49.2 | 6 | 12.11 | even | 2 | |||
912.2.q.k.577.2 | 6 | 228.83 | even | 6 | |||
1368.2.s.j.505.2 | 6 | 1.1 | even | 1 | trivial | ||
1368.2.s.j.577.2 | 6 | 19.7 | even | 3 | inner | ||
2736.2.s.x.577.2 | 6 | 76.7 | odd | 6 | |||
2736.2.s.x.1873.2 | 6 | 4.3 | odd | 2 | |||
8664.2.a.x.1.2 | 3 | 57.11 | odd | 6 | |||
8664.2.a.z.1.2 | 3 | 57.8 | even | 6 |