Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2004,2,Mod(1001,2004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2004.1001");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2004 = 2^{2} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2004.h (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: | \(16.0020205651\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1001.15 | ||
Character | \(\chi\) | \(=\) | 2004.1001 |
Dual form | 2004.2.h.a.1001.13 |
$q$-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 \(\left(\mathbb{Z}/2004\mathbb{Z}\right)^\times\).
\(n\) | \(673\) | \(1003\) | \(1337\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.34740 | + | 1.08836i | −0.777921 | + | 0.628362i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.01275 | −1.34734 | −0.673672 | − | 0.739031i | \(-0.735284\pi\) | ||||
−0.673672 | + | 0.739031i | \(0.735284\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.17416 | −1.19972 | −0.599860 | − | 0.800105i | \(-0.704777\pi\) | ||||
−0.599860 | + | 0.800105i | \(0.704777\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.630964 | − | 2.93290i | 0.210321 | − | 0.977632i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.05776i | − | 1.22346i | −0.791066 | − | 0.611731i | \(-0.790474\pi\) | ||
0.791066 | − | 0.611731i | \(-0.209526\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.81029i | − | 0.779435i | −0.920934 | − | 0.389717i | \(-0.872573\pi\) | ||
0.920934 | − | 0.389717i | \(-0.127427\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.05938 | − | 3.27895i | 1.04813 | − | 0.846620i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.19734 | −0.532933 | −0.266466 | − | 0.963844i | \(-0.585856\pi\) | ||||
−0.266466 | + | 0.963844i | \(0.585856\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.15012 | −0.952104 | −0.476052 | − | 0.879417i | \(-0.657933\pi\) | ||||
−0.476052 | + | 0.879417i | \(0.657933\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.27686 | − | 3.45462i | 0.933288 | − | 0.753859i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.69008 | 0.977949 | 0.488974 | − | 0.872298i | \(-0.337371\pi\) | ||||
0.488974 | + | 0.872298i | \(0.337371\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.07667 | 0.815335 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.34187 | + | 4.63849i | 0.450694 | + | 0.892679i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.09874i | 0.389727i | 0.980830 | + | 0.194863i | \(0.0624263\pi\) | ||||
−0.980830 | + | 0.194863i | \(0.937574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.12816 | −0.921045 | −0.460523 | − | 0.887648i | \(-0.652338\pi\) | ||||
−0.460523 | + | 0.887648i | \(0.652338\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.41629 | + | 5.46742i | 0.768777 | + | 0.951756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.56296 | 1.61644 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.67475i | − | 1.26172i | −0.775896 | − | 0.630861i | \(-0.782702\pi\) | ||
0.775896 | − | 0.630861i | \(-0.217298\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.05860 | + | 3.78658i | 0.489768 | + | 0.606339i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.449127 | 0.0701419 | 0.0350710 | − | 0.999385i | \(-0.488834\pi\) | ||||
0.0350710 | + | 0.999385i | \(0.488834\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.78091i | − | 1.33908i | −0.742778 | − | 0.669538i | \(-0.766492\pi\) | ||
0.742778 | − | 0.669538i | \(-0.233508\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.90094 | + | 8.83609i | −0.283375 | + | 1.31721i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.78834i | 1.28191i | 0.767578 | + | 0.640956i | \(0.221462\pi\) | ||||
−0.767578 | + | 0.640956i | \(0.778538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.07531 | 0.439330 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.96069 | − | 2.39148i | 0.414579 | − | 0.334875i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.9061 | 1.49807 | 0.749034 | − | 0.662532i | \(-0.230518\pi\) | ||||
0.749034 | + | 0.662532i | \(0.230518\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.2250i | 1.64842i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.59187 | − | 4.51681i | 0.740661 | − | 0.598266i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.31611 | −0.952477 | −0.476238 | − | 0.879316i | \(-0.658000\pi\) | ||||
−0.476238 | + | 0.879316i | \(0.658000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.8352 | −1.77141 | −0.885707 | − | 0.464244i | \(-0.846326\pi\) | ||||
−0.885707 | + | 0.464244i | \(0.846326\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.00278 | + | 9.30949i | −0.252327 | + | 1.17289i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.46671i | 1.05017i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3620i | 1.26592i | 0.774185 | + | 0.632960i | \(0.218160\pi\) | ||||
−0.774185 | + | 0.632960i | \(0.781840\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.31940 | + | 5.10447i | −0.760767 | + | 0.614506i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.85050 | −0.694327 | −0.347163 | − | 0.937805i | \(-0.612855\pi\) | ||||
−0.347163 | + | 0.937805i | \(0.612855\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.54493i | − | 0.648985i | −0.945888 | − | 0.324492i | \(-0.894807\pi\) | ||
0.945888 | − | 0.324492i | \(-0.105193\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.49290 | + | 4.43687i | −0.634266 | + | 0.512326i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.8800i | 1.46781i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.67815i | − | 0.301315i | −0.988586 | − | 0.150658i | \(-0.951861\pi\) | ||
0.988586 | − | 0.150658i | \(-0.0481391\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.20377 | − | 3.70111i | −0.911530 | − | 0.411234i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.70992 | −0.626745 | −0.313373 | − | 0.949630i | \(-0.601459\pi\) | ||||
−0.313373 | + | 0.949630i | \(0.601459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.62003 | 0.718043 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.28418 | − | 2.82784i | −0.244889 | − | 0.303176i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.55160i | 0.800468i | 0.916413 | + | 0.400234i | \(0.131071\pi\) | ||||
−0.916413 | + | 0.400234i | \(0.868929\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.92033i | 0.935104i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.90968 | − | 5.58126i | 0.716500 | − | 0.578750i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.5033 | 1.28281 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.448156 | −0.0455033 | −0.0227517 | − | 0.999741i | \(-0.507243\pi\) | ||||
−0.0227517 | + | 0.999741i | \(0.507243\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.9010 | − | 2.56030i | −1.19610 | − | 0.257320i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.98275 | 0.794313 | 0.397156 | − | 0.917751i | \(-0.369997\pi\) | ||||
0.397156 | + | 0.917751i | \(0.369997\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.9968i | 1.47768i | 0.673881 | + | 0.738840i | \(0.264626\pi\) | ||||
−0.673881 | + | 0.738840i | \(0.735374\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.8851 | + | 10.4079i | −1.25746 | + | 1.01571i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.7718i | 1.23470i | 0.786688 | + | 0.617350i | \(0.211794\pi\) | ||||
−0.786688 | + | 0.617350i | \(0.788206\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.04339i | 0.483069i | 0.970392 | + | 0.241534i | \(0.0776507\pi\) | ||||
−0.970392 | + | 0.241534i | \(0.922349\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.35286 | + | 10.3409i | 0.792818 | + | 0.981519i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.51829 | −0.519117 | −0.259558 | − | 0.965727i | \(-0.583577\pi\) | ||||
−0.259558 | + | 0.965727i | \(0.583577\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.1300 | −1.31763 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.24230 | − | 1.77319i | −0.762001 | − | 0.163932i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.97471 | 0.639370 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.46544 | −0.496858 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.605153 | + | 0.488810i | −0.0545649 | + | 0.0440745i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.78175 | 0.248808 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.5203 | −1.02226 | −0.511132 | − | 0.859503i | \(-0.670774\pi\) | ||||
−0.511132 | + | 0.859503i | \(0.670774\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.55675 | + | 11.8314i | 0.841425 | + | 1.04169i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.5402 | 1.61986 | 0.809931 | − | 0.586525i | \(-0.199505\pi\) | ||||
0.809931 | + | 0.586525i | \(0.199505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.1732 | 1.14226 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.05549 | − | 13.9746i | −0.607239 | − | 1.20274i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.54840i | − | 0.730339i | −0.930941 | − | 0.365170i | \(-0.881011\pi\) | ||
0.930941 | − | 0.365170i | \(-0.118989\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.46191i | − | 0.208816i | −0.994535 | − | 0.104408i | \(-0.966705\pi\) | ||
0.994535 | − | 0.104408i | \(-0.0332948\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.56484 | − | 11.8414i | −0.805505 | − | 0.997226i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.4035 | −0.953609 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.32299i | − | 0.525096i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.14367 | + | 3.34703i | −0.341764 | + | 0.276058i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.6113 | 1.19700 | 0.598501 | − | 0.801122i | \(-0.295763\pi\) | ||||
0.598501 | + | 0.801122i | \(0.295763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.8977i | 1.61926i | 0.586944 | + | 0.809628i | \(0.300331\pi\) | ||||
−0.586944 | + | 0.809628i | \(0.699669\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.38644 | + | 6.44456i | −0.112087 | + | 0.521012i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.4499 | 1.24096 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.540423 | 0.0431305 | 0.0215652 | − | 0.999767i | \(-0.493135\pi\) | ||||
0.0215652 | + | 0.999767i | \(0.493135\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.6949 | + | 11.8697i | −1.16538 | + | 0.941329i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.8871 | −1.17327 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.8121i | − | 1.55180i | −0.630855 | − | 0.775901i | \(-0.717296\pi\) | ||
0.630855 | − | 0.775901i | \(-0.282704\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.3052 | − | 16.4720i | −1.03581 | − | 1.28234i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.27036 | − | 9.92981i | 0.639980 | − | 0.768392i | ||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.10226 | 0.392481 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.61858 | + | 12.1719i | −0.200248 | + | 0.930807i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 10.9955i | − | 0.835971i | −0.908454 | − | 0.417986i | \(-0.862736\pi\) | ||
0.908454 | − | 0.417986i | \(-0.137264\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.9400 | −0.978174 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.85772 | − | 7.96253i | 0.740952 | − | 0.598501i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.5715i | 0.790153i | 0.918648 | + | 0.395076i | \(0.129282\pi\) | ||||
−0.918648 | + | 0.395076i | \(0.870718\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.81665 | 0.729666 | 0.364833 | − | 0.931073i | \(-0.381126\pi\) | ||||
0.364833 | + | 0.931073i | \(0.381126\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.6415 | − | 15.0576i | 1.37802 | − | 1.11309i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.1221i | 1.69997i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.91628i | 0.652023i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.43349 | − | 14.7233i | −0.540707 | − | 1.07097i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.8558i | 1.14728i | 0.819107 | + | 0.573641i | \(0.194470\pi\) | ||||
−0.819107 | + | 0.573641i | \(0.805530\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 18.2463i | − | 1.31340i | −0.754153 | − | 0.656699i | \(-0.771952\pi\) | ||
0.754153 | − | 0.656699i | \(-0.228048\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.21479 | − | 11.4080i | −0.659885 | − | 0.816946i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.5950 | 1.82357 | 0.911784 | − | 0.410670i | \(-0.134705\pi\) | ||||
0.911784 | + | 0.410670i | \(0.134705\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.79815 | 0.552796 | 0.276398 | − | 0.961043i | \(-0.410859\pi\) | ||||
0.276398 | + | 0.961043i | \(0.410859\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.2775 | − | 13.9617i | −0.795456 | − | 0.984785i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 6.66175i | − | 0.467563i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.35311 | −0.0945053 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.95927 | − | 13.7555i | 0.205684 | − | 0.956074i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.8402i | 1.16486i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.43732 | 0.374320 | 0.187160 | − | 0.982329i | \(-0.440072\pi\) | ||||
0.187160 | + | 0.982329i | \(0.440072\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.88296 | − | 6.36743i | 0.540131 | − | 0.436289i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 26.4547i | 1.80420i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.2776 | 1.10500 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.03485 | + | 7.47123i | 0.407798 | + | 0.504859i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.17516i | 0.415386i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.0465 | −1.67724 | −0.838619 | − | 0.544719i | \(-0.816636\pi\) | ||||
−0.838619 | + | 0.544719i | \(0.816636\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.57224 | − | 11.9565i | 0.171482 | − | 0.797098i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.55743 | 0.169743 | 0.0848714 | − | 0.996392i | \(-0.472952\pi\) | ||||
0.0848714 | + | 0.996392i | \(0.472952\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.03173 | −0.464670 | −0.232335 | − | 0.972636i | \(-0.574637\pi\) | ||||
−0.232335 | + | 0.972636i | \(0.574637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.0180 | − | 17.3545i | −0.922318 | − | 1.14184i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3.24931i | − | 0.212869i | −0.994320 | − | 0.106435i | \(-0.966056\pi\) | ||
0.994320 | − | 0.106435i | \(-0.0339435\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 26.4771i | − | 1.72718i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.91478 | + | 3.60853i | 0.189335 | + | 0.234399i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.84970i | 0.249016i | 0.992219 | + | 0.124508i | \(0.0397353\pi\) | ||||
−0.992219 | + | 0.124508i | \(0.960265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2181i | 1.04470i | 0.852732 | + | 0.522349i | \(0.174944\pi\) | ||||
−0.852732 | + | 0.522349i | \(0.825056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.0819 | − | 3.94175i | 0.967502 | − | 0.252863i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.26514 | −0.591928 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.6631i | 0.742103i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.69354 | − | 6.21442i | 0.487558 | − | 0.393823i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.87277i | − | 0.181328i | −0.995882 | − | 0.0906638i | \(-0.971101\pi\) | ||
0.995882 | − | 0.0906638i | \(-0.0288989\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 19.0312i | − | 1.19648i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.91982 | + | 7.20495i | −0.558581 | + | 0.451191i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.44081 | −0.526523 | −0.263262 | − | 0.964724i | \(-0.584798\pi\) | ||||
−0.263262 | + | 0.964724i | \(0.584798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.3609i | 1.51371i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.15539 | + | 1.32423i | 0.381009 | + | 0.0819679i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.84125i | 0.606838i | 0.952857 | + | 0.303419i | \(0.0981281\pi\) | ||||
−0.952857 | + | 0.303419i | \(0.901872\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32.8574 | −2.01841 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.21883 | − | 10.1750i | −0.502984 | − | 0.622701i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.3257 | −0.934425 | −0.467212 | − | 0.884145i | \(-0.654742\pi\) | ||||
−0.467212 | + | 0.884145i | \(0.654742\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.9286i | 1.63580i | 0.575361 | + | 0.817899i | \(0.304861\pi\) | ||||
−0.575361 | + | 0.817899i | \(0.695139\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.70849 | − | 12.0192i | −0.587584 | − | 0.727437i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 16.5422i | − | 0.997531i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4453i | 0.627596i | 0.949490 | + | 0.313798i | \(0.101602\pi\) | ||||
−0.949490 | + | 0.313798i | \(0.898398\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.23569 | + | 15.0404i | −0.193716 | + | 0.900443i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.06253i | − | 0.123040i | −0.998106 | − | 0.0615200i | \(-0.980405\pi\) | ||
0.998106 | − | 0.0615200i | \(-0.0195948\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.9818 | 1.96056 | 0.980282 | − | 0.197603i | \(-0.0633157\pi\) | ||||
0.980282 | + | 0.197603i | \(0.0633157\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.8469 | + | 13.6080i | −0.997925 | + | 0.806070i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.42560 | −0.0841507 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.1717 | −0.715983 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.603844 | − | 0.487753i | 0.0353980 | − | 0.0285926i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.5875i | − | 0.852209i | −0.904674 | − | 0.426104i | \(-0.859886\pi\) | ||
0.904674 | − | 0.426104i | \(-0.140114\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.0416 | 1.28331 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.8219 | − | 9.50277i | 1.09216 | − | 0.551407i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 13.1805i | − | 0.762247i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.8720i | 1.60652i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.7559 | + | 8.68807i | −0.617913 | + | 0.499116i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 41.6820 | 2.38670 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.0182i | − | 1.25664i | −0.777954 | − | 0.628322i | \(-0.783742\pi\) | ||
0.777954 | − | 0.628322i | \(-0.216258\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.3219 | − | 20.2067i | −0.928519 | − | 1.14952i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.12088i | 0.517198i | 0.965985 | + | 0.258599i | \(0.0832608\pi\) | ||||
−0.965985 | + | 0.258599i | \(0.916739\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.4767i | 0.592179i | 0.955160 | + | 0.296089i | \(0.0956826\pi\) | ||||
−0.955160 | + | 0.296089i | \(0.904317\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.03389 | − | 28.0472i | 0.339971 | − | 1.58028i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.88166i | 0.274181i | 0.990558 | + | 0.137091i | \(0.0437752\pi\) | ||||
−0.990558 | + | 0.137091i | \(0.956225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.51620 | 0.476815 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.9003 | − | 17.2088i | −0.775840 | − | 0.960500i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.11922 | 0.507407 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 11.4566i | − | 0.635500i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.48900 | − | 6.79545i | −0.303542 | − | 0.375789i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 27.8956i | − | 1.53794i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20.1793i | − | 1.10916i | −0.832132 | − | 0.554578i | \(-0.812880\pi\) | ||
0.832132 | − | 0.554578i | \(-0.187120\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.5093 | − | 4.84250i | −1.23350 | − | 0.265367i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 31.2181i | − | 1.70563i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.1788 | 1.42605 | 0.713024 | − | 0.701140i | \(-0.247325\pi\) | ||||
0.713024 | + | 0.701140i | \(0.247325\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.43533 | − | 6.00586i | 0.403832 | − | 0.326193i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.8089i | 1.12686i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.4576 | 0.672648 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.0388 | − | 15.3785i | 1.02501 | − | 0.827951i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.6340 | −0.678227 | −0.339114 | − | 0.940745i | \(-0.610127\pi\) | ||||
−0.339114 | + | 0.940745i | \(0.610127\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.5612i | − | 0.672386i | −0.941793 | − | 0.336193i | \(-0.890861\pi\) | ||
0.941793 | − | 0.336193i | \(-0.109139\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.0355 | − | 6.58135i | 0.695785 | − | 0.351287i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 30.8243i | − | 1.64061i | −0.571923 | − | 0.820307i | \(-0.693802\pi\) | ||
0.571923 | − | 0.820307i | \(-0.306198\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.6261 | 0.935497 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.39771 | + | 7.59096i | −0.497379 | + | 0.401756i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.1337i | 1.53762i | 0.639477 | + | 0.768810i | \(0.279151\pi\) | ||||
−0.639477 | + | 0.768810i | \(0.720849\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.77647 | −0.0934987 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.36413 | − | 5.94835i | 0.386517 | − | 0.312207i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.7055i | 0.874405i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.9558 | 0.989485 | 0.494742 | − | 0.869040i | \(-0.335262\pi\) | ||||
0.494742 | + | 0.869040i | \(0.335262\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.283383 | − | 1.31724i | 0.0147524 | − | 0.0685730i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −34.6177 | −1.79726 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.1417i | 1.25001i | 0.780621 | + | 0.625005i | \(0.214903\pi\) | ||||
−0.780621 | + | 0.625005i | \(0.785097\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.74813 | + | 3.02754i | −0.193553 | + | 0.156341i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.89808 | 0.303766 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.87437i | − | 0.147647i | −0.997271 | − | 0.0738233i | \(-0.976480\pi\) | ||
0.997271 | − | 0.0738233i | \(-0.0235201\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.5225 | − | 12.5382i | 0.795240 | − | 0.642352i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.2016i | 0.521280i | 0.965436 | + | 0.260640i | \(0.0839335\pi\) | ||||
−0.965436 | + | 0.260640i | \(0.916067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 38.8042i | − | 1.97765i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.7535 | − | 5.54044i | −1.30912 | − | 0.281636i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.8123 | −1.81575 | −0.907877 | − | 0.419237i | \(-0.862298\pi\) | ||||
−0.907877 | + | 0.419237i | \(0.862298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3057 | −0.521181 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.9810 | + | 20.1783i | −1.26012 | + | 1.01786i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.06859i | 0.405975i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.9019 | 0.647528 | 0.323764 | − | 0.946138i | \(-0.395052\pi\) | ||||
0.323764 | + | 0.946138i | \(0.395052\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.7495 | + | 14.3371i | −0.888587 | + | 0.717752i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.3427 | 1.21562 | 0.607809 | − | 0.794084i | \(-0.292049\pi\) | ||||
0.607809 | + | 0.794084i | \(0.292049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.4116i | 0.717895i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.7159 | + | 11.1505i | 1.22814 | + | 0.554074i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.1423 | −1.54367 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.12084 | 0.352103 | 0.176051 | − | 0.984381i | \(-0.443668\pi\) | ||||
0.176051 | + | 0.984381i | \(0.443668\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.30370 | + | 11.5181i | 0.458918 | + | 0.568146i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.2225 | 1.14271 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.2026 | 0.844441 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.67943 | + | 3.31717i | 0.131212 | + | 0.162443i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.60372i | 0.176053i | 0.996118 | + | 0.0880267i | \(0.0280561\pi\) | ||||
−0.996118 | + | 0.0880267i | \(0.971944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.88137 | 0.189166 | 0.0945832 | − | 0.995517i | \(-0.469848\pi\) | ||||
0.0945832 | + | 0.995517i | \(0.469848\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.7753 | + | 5.54513i | 1.25324 | + | 0.269614i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.95783 | −0.434518 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.9152 | 2.12520 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.3651 | − | 12.4111i | 0.741832 | − | 0.599212i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.7404i | 1.38438i | 0.721718 | + | 0.692188i | \(0.243353\pi\) | ||||
−0.721718 | + | 0.692188i | \(0.756647\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.5388 | 0.650634 | 0.325317 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325317 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.88166 | + | 8.51958i | 0.329950 | + | 0.408483i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.4644 | −0.931109 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7.32987i | − | 0.349835i | −0.984583 | − | 0.174918i | \(-0.944034\pi\) | ||
0.984583 | − | 0.174918i | \(-0.0559659\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.94041 | − | 9.01956i | 0.0924005 | − | 0.429503i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.8926 | −1.08766 | −0.543829 | − | 0.839196i | \(-0.683026\pi\) | ||||
−0.543829 | + | 0.839196i | \(0.683026\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 22.7511i | − | 1.07851i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.6872 | + | 15.9022i | −0.931172 | + | 0.752151i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15.0367i | − | 0.709625i | −0.934937 | − | 0.354813i | \(-0.884545\pi\) | ||
0.934937 | − | 0.354813i | \(-0.115455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.82245i | − | 0.0858159i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.6558 | − | 26.8102i | −1.01748 | − | 1.25965i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 26.8747i | − | 1.25991i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 36.6485i | − | 1.71434i | −0.515032 | − | 0.857171i | \(-0.672220\pi\) | ||
0.515032 | − | 0.857171i | \(-0.327780\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.14589 | − | 10.1923i | −0.240189 | − | 0.475738i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 24.3754i | − | 1.13528i | −0.823278 | − | 0.567639i | \(-0.807857\pi\) | ||
0.823278 | − | 0.567639i | \(-0.192143\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.8499i | 1.48019i | 0.672503 | + | 0.740095i | \(0.265219\pi\) | ||||
−0.672503 | + | 0.740095i | \(0.734781\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.8171 | + | 16.8150i | −0.965372 | + | 0.779775i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 7.82188i | − | 0.361953i | −0.983487 | − | 0.180977i | \(-0.942074\pi\) | ||
0.983487 | − | 0.180977i | \(-0.0579258\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 32.8907i | − | 1.51875i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.728165 | + | 0.588172i | −0.0335521 | + | 0.0271016i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35.6308 | −1.63831 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.9187 | −0.776283 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.88136 | − | 31.9864i | 0.315076 | − | 1.46456i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.41249 | 0.384377 | 0.192188 | − | 0.981358i | \(-0.438442\pi\) | ||||
0.192188 | + | 0.981358i | \(0.438442\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.5683 | −0.983430 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.0588 | − | 16.2024i | 0.912708 | − | 0.737236i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.35018 | 0.0613086 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 19.3033i | − | 0.874718i | −0.899287 | − | 0.437359i | \(-0.855914\pi\) | ||
0.899287 | − | 0.437359i | \(-0.144086\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.5626 | + | 26.6948i | 0.975094 | + | 1.20718i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.6151i | − | 0.704701i | −0.935868 | − | 0.352350i | \(-0.885383\pi\) | ||
0.935868 | − | 0.352350i | \(-0.114617\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.61164i | − | 0.207698i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 35.8548 | + | 7.71356i | 1.61155 | + | 0.346699i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.5704 | 0.832998 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0615i | 1.43527i | 0.696419 | + | 0.717635i | \(0.254776\pi\) | ||||
−0.696419 | + | 0.717635i | \(0.745224\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.336311 | + | 22.3805i | −0.0150253 | + | 0.999887i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 20.3177i | − | 0.905920i | −0.891531 | − | 0.452960i | \(-0.850368\pi\) | ||
0.891531 | − | 0.452960i | \(-0.149632\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.0500 | −1.07021 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.87477 | + | 5.55307i | −0.305319 | + | 0.246620i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 18.7036i | − | 0.829020i | −0.910045 | − | 0.414510i | \(-0.863953\pi\) | ||
0.910045 | − | 0.414510i | \(-0.136047\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.6005i | 0.778600i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.71907 | − | 19.2503i | −0.429107 | − | 0.849923i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 45.1817i | − | 1.99094i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.6610 | 1.56837 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.9670 | + | 14.8153i | 0.525293 | + | 0.650319i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.04946 | −0.352653 | −0.176327 | − | 0.984332i | \(-0.556421\pi\) | ||||
−0.176327 | + | 0.984332i | \(0.556421\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.7013 | −1.60483 | −0.802417 | − | 0.596764i | \(-0.796453\pi\) | ||||
−0.802417 | + | 0.596764i | \(0.796453\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.4354 | − | 14.0833i | 0.760942 | − | 0.614648i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.2683 | 0.490855 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00317 | −0.0436161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.61621 | + | 21.4574i | −0.200326 | + | 0.931172i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.26218i | − | 0.0546711i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 38.4784i | − | 1.66357i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.5056 | − | 14.2441i | −0.496502 | − | 0.614676i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 12.4789i | − | 0.537503i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 12.6561i | − | 0.544127i | −0.962279 | − | 0.272063i | \(-0.912294\pi\) | ||
0.962279 | − | 0.272063i | \(-0.0877061\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.2269 | + | 10.6840i | −0.567622 | + | 0.458495i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 15.1945i | − | 0.650860i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 26.1871i | − | 1.11968i | −0.828601 | − | 0.559840i | \(-0.810863\pi\) | ||
0.828601 | − | 0.559840i | \(-0.189137\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.72952 | + | 40.5772i | −0.372567 | + | 1.73179i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.71004i | − | 0.371060i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.50088i | 0.361494i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −25.1651 | − | 31.1547i | −1.06820 | − | 1.32244i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.4856i | 0.740887i | 0.928855 | + | 0.370443i | \(0.120794\pi\) | ||||
−0.928855 | + | 0.370443i | \(0.879206\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.6769 | −1.04372 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.70408 | − | 12.0138i | −0.409707 | − | 0.507222i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.4515i | 1.40981i | 0.709300 | + | 0.704907i | \(0.249011\pi\) | ||||
−0.709300 | + | 0.704907i | \(0.750989\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.6252 | 0.699428 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.0401 | + | 11.7479i | 1.09358 | + | 0.493366i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.72419 | 0.365737 | 0.182868 | − | 0.983137i | \(-0.441462\pi\) | ||||
0.182868 | + | 0.983137i | \(0.441462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.97889i | 0.166511i | 0.996528 | + | 0.0832556i | \(0.0265318\pi\) | ||||
−0.996528 | + | 0.0832556i | \(0.973468\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.2567 | − | 21.3640i | −0.720909 | − | 0.892495i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.1199 | 0.797356 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.1199 | −1.37880 | −0.689401 | − | 0.724380i | \(-0.742126\pi\) | ||||
−0.689401 | + | 0.724380i | \(0.742126\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.8585 | + | 24.5850i | 0.825290 | + | 1.02172i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.1242 | 0.751919 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 44.2543i | − | 1.83283i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.8320 | + | 5.34220i | 1.02668 | + | 0.220873i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.8588 | −0.819659 | −0.409829 | − | 0.912162i | \(-0.634412\pi\) | ||||
−0.409829 | + | 0.912162i | \(0.634412\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.2825 | 0.876930 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −34.4867 | + | 27.8565i | −1.41859 | + | 1.14586i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.73548 | −0.235528 | −0.117764 | − | 0.993042i | \(-0.537573\pi\) | ||||
−0.117764 | + | 0.993042i | \(0.537573\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.0131 | −0.861452 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.5072 | + | 8.48716i | −0.430032 | + | 0.347356i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.7361i | 1.09241i | 0.837653 | + | 0.546203i | \(0.183927\pi\) | ||||
−0.837653 | + | 0.546203i | \(0.816073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.7890 | −1.05196 | −0.525978 | − | 0.850498i | \(-0.676301\pi\) | ||||
−0.525978 | + | 0.850498i | \(0.676301\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.3907 | + | 6.53805i | 1.23760 | + | 0.266250i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.4660 | 0.669439 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.0071i | 1.29913i | 0.760307 | + | 0.649564i | \(0.225048\pi\) | ||||
−0.760307 | + | 0.649564i | \(0.774952\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.25035 | + | 8.97603i | 0.293799 | + | 0.363727i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.6978 | 0.999167 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.7394 | 0.756879 | 0.378439 | − | 0.925626i | \(-0.376461\pi\) | ||||
0.378439 | + | 0.925626i | \(0.376461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.82318 | − | 1.47266i | 0.0735176 | − | 0.0593835i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.39733i | 0.177030i | 0.996075 | + | 0.0885150i | \(0.0282121\pi\) | ||||
−0.996075 | + | 0.0885150i | \(0.971788\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.39703i | 0.257118i | 0.991702 | + | 0.128559i | \(0.0410352\pi\) | ||||
−0.991702 | + | 0.128559i | \(0.958965\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.9836 | + | 21.7549i | 0.440756 | + | 0.872994i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 23.9700i | − | 0.960338i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.7641 | −1.15056 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.3281 | − | 22.6905i | −0.731956 | − | 0.906171i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.8640i | 0.672413i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.5355 | −0.897124 | −0.448562 | − | 0.893752i | \(-0.648064\pi\) | ||||
−0.448562 | + | 0.893752i | \(0.648064\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.32623 | + | 5.91773i | −0.291192 | + | 0.235209i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 34.7079 | 1.37734 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 8.64252i | − | 0.342429i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.69146 | + | 17.1589i | −0.146032 | + | 0.678796i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.1224 | −0.439306 | −0.219653 | − | 0.975578i | \(-0.570493\pi\) | ||||
−0.219653 | + | 0.975578i | \(0.570493\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 36.8683i | − | 1.45394i | −0.686667 | − | 0.726972i | \(-0.740927\pi\) | ||
0.686667 | − | 0.726972i | \(-0.259073\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −28.7921 | − | 35.6450i | −1.13369 | − | 1.40352i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.9225 | 1.72677 | 0.863387 | − | 0.504543i | \(-0.168339\pi\) | ||||
0.863387 | + | 0.504543i | \(0.168339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.6871i | 1.16532i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.9324 | + | 17.7158i | −0.859600 | + | 0.694338i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.48149i | 0.175374i | 0.996148 | + | 0.0876872i | \(0.0279476\pi\) | ||||
−0.996148 | + | 0.0876872i | \(0.972052\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −55.8569 | −2.18251 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.2627 | − | 3.49865i | −0.634468 | − | 0.136495i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.8073 | −0.888447 | −0.444224 | − | 0.895916i | \(-0.646520\pi\) | ||||
−0.444224 | + | 0.895916i | \(0.646520\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.7339i | 1.27320i | 0.771194 | + | 0.636601i | \(0.219660\pi\) | ||||
−0.771194 | + | 0.636601i | \(0.780340\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.72077 | − | 8.32040i | −0.261013 | − | 0.323138i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −39.6875 | −1.53901 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.84326i | 0.381133i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 33.7476 | − | 27.2595i | 1.30476 | − | 1.05391i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 56.1399i | 2.16726i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.6438i | 1.10414i | 0.833798 | + | 0.552069i | \(0.186162\pi\) | ||||
−0.833798 | + | 0.552069i | \(0.813838\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.54706 | + | 18.9096i | 0.367466 | + | 0.727832i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.77741i | 0.337343i | 0.985672 | + | 0.168672i | \(0.0539477\pi\) | ||||
−0.985672 | + | 0.168672i | \(0.946052\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.42252 | 0.0545913 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.44588 | + | 2.78340i | −0.132046 | + | 0.106660i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.9621 | −0.495979 | −0.247990 | − | 0.968763i | \(-0.579770\pi\) | ||||
−0.247990 | + | 0.968763i | \(0.579770\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.7542i | 0.984018i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.47455 | − | 7.65303i | 0.361477 | − | 0.291981i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 30.6493i | − | 1.16765i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 27.1220i | − | 1.03177i | −0.856658 | − | 0.515885i | \(-0.827463\pi\) | ||
0.856658 | − | 0.515885i | \(-0.172537\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 37.7757 | + | 8.12682i | 1.43498 | + | 0.308712i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.41712i | 0.281347i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.986884 | −0.0373809 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.53640 | + | 4.37811i | 0.133759 | + | 0.165596i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.6669i | 1.87589i | 0.346779 | + | 0.937947i | \(0.387275\pi\) | ||||
−0.346779 | + | 0.937947i | \(0.612725\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.8512i | 1.20129i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 28.8165 | + | 35.6752i | 1.08529 | + | 1.34361i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25.3385 | −0.952954 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.93531i | − | 0.0726821i | −0.999339 | − | 0.0363410i | \(-0.988430\pi\) | ||
0.999339 | − | 0.0363410i | \(-0.0115703\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.85473 | − | 1.68982i | −0.294575 | − | 0.0633730i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.0515 | −0.900735 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.3559 | 1.28484 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.18984 | − | 5.18707i | −0.156472 | − | 0.193715i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.0805 | 0.562408 | 0.281204 | − | 0.959648i | \(-0.409266\pi\) | ||||
0.281204 | + | 0.959648i | \(0.409266\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 47.6023i | − | 1.77280i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.6510 | − | 21.8522i | −0.656448 | − | 0.812692i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.55588i | 0.317758i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 44.3277i | − | 1.64402i | −0.569471 | − | 0.822011i | \(-0.692852\pi\) | ||
0.569471 | − | 0.822011i | \(-0.307148\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.0313 | + | 21.7255i | −0.593750 | + | 0.804650i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.2946i | 0.713637i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.5739 | −0.612172 | −0.306086 | − | 0.952004i | \(-0.599020\pi\) | ||||
−0.306086 | + | 0.952004i | \(0.599020\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.4838 | − | 10.0838i | 0.460473 | − | 0.371945i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.0465 | 1.54880 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 32.7848i | − | 1.20601i | −0.797739 | − | 0.603003i | \(-0.793971\pi\) | ||
0.797739 | − | 0.603003i | \(-0.206029\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.6936 | − | 15.7148i | −0.466309 | − | 0.577297i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.9115i | 0.473676i | 0.971549 | + | 0.236838i | \(0.0761111\pi\) | ||||
−0.971549 | + | 0.236838i | \(0.923889\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44.0201 | −1.61277 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.60276 | + | 16.7466i | −0.131818 | + | 0.612726i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 40.5399i | − | 1.48130i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.63472i | 0.0596516i | 0.999555 | + | 0.0298258i | \(0.00949526\pi\) | ||||
−0.999555 | + | 0.0298258i | \(0.990505\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.12659 | + | 3.87076i | 0.113939 | + | 0.141058i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 59.9470i | − | 2.18169i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.159682 | 0.00580372 | 0.00290186 | − | 0.999996i | \(-0.499076\pi\) | ||||
0.00290186 | + | 0.999996i | \(0.499076\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.7127 | + | 25.6426i | 0.751825 | + | 0.930769i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.6281i | 1.61777i | 0.587970 | + | 0.808883i | \(0.299927\pi\) | ||||
−0.587970 | + | 0.808883i | \(0.700073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 16.0085i | − | 0.579548i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.17701 | − | 19.4159i | 0.151020 | − | 0.701982i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.5604i | 0.742394i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.1447i | 0.510071i | 0.966932 | + | 0.255036i | \(0.0820872\pi\) | ||||
−0.966932 | + | 0.255036i | \(0.917913\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.3731 | − | 9.18660i | 0.409593 | − | 0.330847i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.6410 | −0.382730 | −0.191365 | − | 0.981519i | \(-0.561291\pi\) | ||||
−0.191365 | + | 0.981519i | \(0.561291\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.9058 | −0.750960 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −26.5133 | − | 32.8238i | −0.951160 | − | 1.17755i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.86393 | −0.0667824 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.7400i | 0.849482i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.73500 | + | 4.91499i | −0.347901 | + | 0.175647i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.62816 | −0.0581115 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.0013i | 1.71106i | 0.517753 | + | 0.855530i | \(0.326769\pi\) | ||||
−0.517753 | + | 0.855530i | \(0.673231\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.7108 | − | 13.2601i | −0.381314 | − | 0.472072i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.5159 | 0.622795 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.8809i | 1.38070i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 44.2719 | − | 35.7605i | 1.57016 | − | 1.26829i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.3959 | 0.899569 | 0.449784 | − | 0.893137i | \(-0.351501\pi\) | ||||
0.449784 | + | 0.893137i | \(0.351501\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 19.3110i | − | 0.683173i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.1481 | + | 4.76479i | 0.782563 | + | 0.168356i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.5000 | −0.794008 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 44.8510 | 1.58079 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.6498 | − | 16.6798i | 0.726908 | − | 0.587157i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.3601i | 0.856454i | 0.903671 | + | 0.428227i | \(0.140862\pi\) | ||||
−0.903671 | + | 0.428227i | \(0.859138\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.7712i | 0.869835i | 0.900470 | + | 0.434918i | \(0.143223\pi\) | ||||
−0.900470 | + | 0.434918i | \(0.856777\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.3079 | − | 36.2836i | −1.02787 | − | 1.27252i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 59.6889i | 2.09081i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.4418i | 1.27494i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 26.1624 | + | 5.62841i | 0.914188 | + | 0.196673i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.7159 | 0.583389 | 0.291694 | − | 0.956512i | \(-0.405781\pi\) | ||||
0.291694 | + | 0.956512i | \(0.405781\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.32039i | 0.185457i | 0.995691 | + | 0.0927286i | \(0.0295589\pi\) | ||||
−0.995691 | + | 0.0927286i | \(0.970441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.0038 | + | 22.2889i | 0.626811 | + | 0.776000i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.1772 | 0.458217 | 0.229108 | − | 0.973401i | \(-0.426419\pi\) | ||||
0.229108 | + | 0.973401i | \(0.426419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 29.3203i | − | 1.01833i | −0.860667 | − | 0.509167i | \(-0.829953\pi\) | ||
0.860667 | − | 0.509167i | \(-0.170047\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.3682 | − | 14.0740i | −0.394358 | − | 0.488220i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.75749 | −0.234133 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.9166 | + | 29.9160i | −0.862273 | + | 1.03529i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.0095 | − | 23.7869i | −0.415109 | − | 0.822197i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 54.2464i | − | 1.87280i | −0.350941 | − | 0.936398i | \(-0.614138\pi\) | ||
0.350941 | − | 0.936398i | \(-0.385862\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.5953 | 0.848113 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.24476 | + | 2.77905i | 0.0773137 | + | 0.0957154i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.3718 | −0.528807 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.3482 | 0.596091 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −44.4396 | + | 35.8959i | −1.52516 | + | 1.23194i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 35.9952i | − | 1.23390i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0438 | 0.549328 | 0.274664 | − | 0.961540i | \(-0.411433\pi\) | ||||
0.274664 | + | 0.961540i | \(0.411433\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.88913 | − | 36.6709i | 0.269803 | − | 1.25412i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.5609i | 1.38553i | 0.721162 | + | 0.692767i | \(0.243609\pi\) | ||||
−0.721162 | + | 0.692767i | \(0.756391\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.1289 | 1.64214 | 0.821069 | − | 0.570829i | \(-0.193378\pi\) | ||||
0.821069 | + | 0.570829i | \(0.193378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.92086 | − | 1.55156i | 0.0654626 | − | 0.0528771i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 6.26818i | − | 0.213371i | −0.994293 | − | 0.106686i | \(-0.965976\pi\) | ||
0.994293 | − | 0.106686i | \(-0.0340238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.1267i | 1.12634i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.4001 | − | 13.2471i | 0.556978 | − | 0.449897i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.8673 | −0.368647 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.1202 | 0.986702 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.282770 | + | 1.31439i | −0.00957033 | + | 0.0444855i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.82974 | −0.298500 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.90778 | −0.0981888 | −0.0490944 | − | 0.998794i | \(-0.515634\pi\) | ||||
−0.0490944 | + | 0.998794i | \(0.515634\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.8763 | + | 19.6551i | 0.535496 | + | 0.662951i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.84456 | −0.230599 | −0.115300 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115300 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.9179 | 1.17508 | 0.587541 | − | 0.809194i | \(-0.300096\pi\) | ||||
0.587541 | + | 0.809194i | \(0.300096\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29.6989 | + | 23.9891i | −0.998316 | + | 0.806386i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.7480 | 0.931686 | 0.465843 | − | 0.884867i | \(-0.345751\pi\) | ||||
0.465843 | + | 0.884867i | \(0.345751\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.5674 | 1.22643 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.0182 | + | 33.2889i | −0.503129 | + | 1.11522i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 36.4727i | − | 1.22051i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 31.8494i | − | 1.06461i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.3451 | + | 17.7594i | 0.478968 | + | 0.592968i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 10.7627i | − | 0.358956i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.9644 | −0.798369 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.3347 | − | 37.5547i | −1.00947 | − | 1.24974i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.5751 | −0.983111 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −49.1492 | −1.63197 | −0.815986 | − | 0.578071i | \(-0.803806\pi\) | ||||
−0.815986 | + | 0.578071i | \(0.803806\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.03683 | − | 23.4126i | 0.167061 | − | 0.776546i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 37.7917i | − | 1.25210i | −0.779785 | − | 0.626048i | \(-0.784672\pi\) | ||
0.779785 | − | 0.626048i | \(-0.215328\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.1695i | 0.766799i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −56.1623 | + | 45.3648i | −1.85667 | + | 1.49972i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −58.8495 | −1.94338 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.81977 | −0.0930157 | −0.0465078 | − | 0.998918i | \(-0.514809\pi\) | ||||
−0.0465078 | + | 0.998918i | \(0.514809\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.9636 | + | 29.6673i | 0.789628 | + | 0.977569i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.4416i | 0.541183i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 31.2875i | − | 1.02873i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 43.9841 | + | 9.46246i | 1.44463 | + | 0.310788i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.0753i | 0.363370i | 0.983357 | + | 0.181685i | \(0.0581552\pi\) | ||||
−0.983357 | + | 0.181685i | \(0.941845\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.7629 | −0.418288 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.92676 | − | 12.2895i | −0.324988 | − | 0.402339i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 26.8625i | − | 0.878499i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.1524i | 1.70374i | 0.523749 | + | 0.851872i | \(0.324533\pi\) | ||||
−0.523749 | + | 0.851872i | \(0.675467\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.4024 | − | 14.1163i | −0.372103 | − | 0.460668i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.7815 | 1.00345 | 0.501724 | − | 0.865028i | \(-0.332699\pi\) | ||||
0.501724 | + | 0.865028i | \(0.332699\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.10644 | 0.0685952 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 22.3953 | + | 44.3578i | 0.728518 | + | 1.44296i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 48.2547i | − | 1.56807i | −0.620719 | − | 0.784033i | \(-0.713159\pi\) | ||
0.620719 | − | 0.784033i | \(-0.286841\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.5829 | −0.505841 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.31298 | − | 6.57754i | −0.172285 | − | 0.213291i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.5920 | 0.990973 | 0.495487 | − | 0.868616i | \(-0.334990\pi\) | ||||
0.495487 | + | 0.868616i | \(0.334990\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 47.7695i | − | 1.54578i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.4747 | + | 9.26865i | −0.370925 | + | 0.299613i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.1340i | 0.876203i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.70196 | −0.151676 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 37.4585 | + | 8.05858i | 1.20708 | + | 0.259684i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 54.9716i | 1.76960i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.4597 | −0.850887 | −0.425443 | − | 0.904985i | \(-0.639882\pi\) | ||||
−0.425443 | + | 0.904985i | \(0.639882\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.2872 | + | 9.92496i | −0.394723 | + | 0.318836i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.5318 | −0.947722 | −0.473861 | − | 0.880600i | \(-0.657140\pi\) | ||||
−0.473861 | + | 0.880600i | \(0.657140\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.81450i | 0.250521i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.4689 | + | 15.4367i | 0.399324 | + | 0.494369i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.1580 | 0.836868 | 0.418434 | − | 0.908247i | \(-0.362579\pi\) | ||||
0.418434 | + | 0.908247i | \(0.362579\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.6426 | 0.979342 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.7917 | + | 3.18220i | 0.472264 | + | 0.101600i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.6040 | 0.402005 | 0.201003 | − | 0.979591i | \(-0.435580\pi\) | ||||
0.201003 | + | 0.979591i | \(0.435580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −77.1114 | −2.45697 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 30.3604 | + | 37.5865i | 0.966381 | + | 1.19639i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 41.1831i | − | 1.30955i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.9747i | 1.68280i | 0.540415 | + | 0.841399i | \(0.318267\pi\) | ||||
−0.540415 | + | 0.841399i | \(0.681733\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.9623 | + | 27.1896i | 0.696952 | + | 0.862836i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.4939 | −0.744807 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.3828 | 1.88067 | 0.940336 | − | 0.340248i | \(-0.110511\pi\) | ||||
0.940336 | + | 0.340248i | \(0.110511\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 35.5993 | − | 17.9733i | 1.12631 | − | 0.568650i |
(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 | 2004.2.h.a.1001.15 | yes | 56 | |
3.2 | odd | 2 | inner | 2004.2.h.a.1001.14 | yes | 56 | |
167.166 | odd | 2 | inner | 2004.2.h.a.1001.16 | yes | 56 | |
501.500 | even | 2 | inner | 2004.2.h.a.1001.13 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.h.a.1001.13 | ✓ | 56 | 501.500 | even | 2 | inner | |
2004.2.h.a.1001.14 | yes | 56 | 3.2 | odd | 2 | inner | |
2004.2.h.a.1001.15 | yes | 56 | 1.1 | even | 1 | trivial | |
2004.2.h.a.1001.16 | yes | 56 | 167.166 | odd | 2 | inner |