Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.14 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.33 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 1.50352i | − | 0.868058i | −0.900899 | − | 0.434029i | \(-0.857092\pi\) | ||
0.900899 | − | 0.434029i | \(-0.142908\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.31120i | 1.92803i | 0.265854 | + | 0.964013i | \(0.414346\pi\) | ||||
−0.265854 | + | 0.964013i | \(0.585654\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.93216i | − | 1.86418i | −0.362223 | − | 0.932091i | \(-0.617982\pi\) | ||
0.362223 | − | 0.932091i | \(-0.382018\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.739426 | 0.246475 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.58263i | 0.477182i | 0.971120 | + | 0.238591i | \(0.0766856\pi\) | ||||
−0.971120 | + | 0.238591i | \(0.923314\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.143694 | −0.0398535 | −0.0199267 | − | 0.999801i | \(-0.506343\pi\) | ||||
−0.0199267 | + | 0.999801i | \(0.506343\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.48198 | 1.67364 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.180560 | + | 4.11915i | −0.0437923 | + | 0.999041i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.296737 | 0.0680762 | 0.0340381 | − | 0.999421i | \(-0.489163\pi\) | ||||
0.0340381 | + | 0.999421i | \(0.489163\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.41561 | −1.61822 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.24916i | 1.30304i | 0.758631 | + | 0.651520i | \(0.225868\pi\) | ||||
−0.758631 | + | 0.651520i | \(0.774132\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.5864 | −2.71729 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.62230i | − | 1.08201i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.17923i | 1.14745i | 0.819047 | + | 0.573727i | \(0.194503\pi\) | ||||
−0.819047 | + | 0.573727i | \(0.805497\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.07702i | − | 0.732255i | −0.930565 | − | 0.366128i | \(-0.880683\pi\) | ||
0.930565 | − | 0.366128i | \(-0.119317\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.37952 | 0.414222 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 21.2635 | 3.59419 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.76874i | 1.27717i | 0.769550 | + | 0.638586i | \(0.220480\pi\) | ||||
−0.769550 | + | 0.638586i | \(0.779520\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.216046i | 0.0345951i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.59168i | 0.248579i | 0.992246 | + | 0.124290i | \(0.0396652\pi\) | ||||
−0.992246 | + | 0.124290i | \(0.960335\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.67696 | −1.01823 | −0.509113 | − | 0.860700i | \(-0.670027\pi\) | ||||
−0.509113 | + | 0.860700i | \(0.670027\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.18781i | 0.475211i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.8958 | −1.73518 | −0.867592 | − | 0.497276i | \(-0.834334\pi\) | ||||
−0.867592 | + | 0.497276i | \(0.834334\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −17.3262 | −2.47518 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.19323 | + | 0.271476i | 0.867225 | + | 0.0380142i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.38790 | 0.877445 | 0.438722 | − | 0.898623i | \(-0.355431\pi\) | ||||
0.438722 | + | 0.898623i | \(0.355431\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.82305 | −0.920020 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.446151i | − | 0.0590941i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.241773i | − | 0.0309558i | −0.999880 | − | 0.0154779i | \(-0.995073\pi\) | ||
0.999880 | − | 0.0154779i | \(-0.00492697\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 3.64697i | − | 0.459475i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.619492i | − | 0.0768386i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4554 | 1.52167 | 0.760833 | − | 0.648948i | \(-0.224791\pi\) | ||||
0.760833 | + | 0.648948i | \(0.224791\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.39574 | 1.13111 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.01095i | 0.119977i | 0.998199 | + | 0.0599886i | \(0.0191064\pi\) | ||||
−0.998199 | + | 0.0599886i | \(0.980894\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.169624i | 0.0198530i | 0.999951 | + | 0.00992651i | \(0.00315976\pi\) | ||||
−0.999951 | + | 0.00992651i | \(0.996840\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 20.4275i | 2.35876i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.80581 | 0.889555 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.2445i | − | 1.26510i | −0.774518 | − | 0.632551i | \(-0.782008\pi\) | ||
0.774518 | − | 0.632551i | \(-0.217992\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.23497 | −0.692774 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.97834 | −0.656208 | −0.328104 | − | 0.944642i | \(-0.606410\pi\) | ||||
−0.328104 | + | 0.944642i | \(0.606410\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.7585 | − | 0.778431i | −1.92618 | − | 0.0844327i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.29059 | 0.996056 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.73469 | 0.395877 | 0.197938 | − | 0.980214i | \(-0.436575\pi\) | ||||
0.197938 | + | 0.980214i | \(0.436575\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.708721i | 0.0742942i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.12989 | −0.635640 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.27929i | 0.131253i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.04072i | 0.410273i | 0.978733 | + | 0.205136i | \(0.0657638\pi\) | ||||
−0.978733 | + | 0.205136i | \(0.934236\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.17024i | 0.117614i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.71033 | −0.767206 | −0.383603 | − | 0.923498i | \(-0.625317\pi\) | ||||
−0.383603 | + | 0.923498i | \(0.625317\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.0201 | 1.47998 | 0.739988 | − | 0.672620i | \(-0.234831\pi\) | ||||
0.739988 | + | 0.672620i | \(0.234831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 31.9702i | − | 3.11997i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.34094i | 0.903023i | 0.892265 | + | 0.451512i | \(0.149115\pi\) | ||||
−0.892265 | + | 0.451512i | \(0.850885\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.42532i | 0.136521i | 0.997668 | + | 0.0682605i | \(0.0217449\pi\) | ||||
−0.997668 | + | 0.0682605i | \(0.978255\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.6805 | 1.10866 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.73563i | 0.915851i | 0.888991 | + | 0.457925i | \(0.151407\pi\) | ||||
−0.888991 | + | 0.457925i | \(0.848593\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26.9414 | −2.51230 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.106251 | −0.00982290 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.3163 | + | 0.890552i | 1.86239 | + | 0.0816368i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.49527 | 0.772297 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.39313 | 0.215781 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 37.0178i | − | 3.31098i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.8719 | −0.964721 | −0.482361 | − | 0.875973i | \(-0.660221\pi\) | ||||
−0.482361 | + | 0.875973i | \(0.660221\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.0389i | 0.883879i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.7875i | 1.81621i | 0.418742 | + | 0.908105i | \(0.362471\pi\) | ||||
−0.418742 | + | 0.908105i | \(0.637529\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.46356i | − | 0.126907i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 24.2389 | 2.08615 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.5099 | −1.41054 | −0.705268 | − | 0.708940i | \(-0.749173\pi\) | ||||
−0.705268 | + | 0.708940i | \(0.749173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.84066i | 0.156122i | 0.996949 | + | 0.0780612i | \(0.0248729\pi\) | ||||
−0.996949 | + | 0.0780612i | \(0.975127\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.8856i | 1.50624i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.227415i | − | 0.0190174i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.6399 | −2.21232 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 26.0504i | 2.14860i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.1016 | 1.48294 | 0.741471 | − | 0.670985i | \(-0.234129\pi\) | ||||
0.741471 | + | 0.670985i | \(0.234129\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.77597 | −0.470042 | −0.235021 | − | 0.971990i | \(-0.575516\pi\) | ||||
−0.235021 | + | 0.971990i | \(0.575516\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.133511 | + | 3.04581i | −0.0107937 | + | 0.246239i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.5769 | 1.41181 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.35499 | −0.347566 | −0.173783 | − | 0.984784i | \(-0.555599\pi\) | ||||
−0.173783 | + | 0.984784i | \(0.555599\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 9.60433i | − | 0.761673i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 30.8219 | 2.42911 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.3997i | 1.59783i | 0.601446 | + | 0.798914i | \(0.294592\pi\) | ||||
−0.601446 | + | 0.798914i | \(0.705408\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.2586i | 0.798631i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.6690i | 1.44465i | 0.691555 | + | 0.722324i | \(0.256926\pi\) | ||||
−0.691555 | + | 0.722324i | \(0.743074\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9794 | −0.998412 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.219415 | 0.0167791 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.2485i | 1.15932i | 0.814858 | + | 0.579661i | \(0.196815\pi\) | ||||
−0.814858 | + | 0.579661i | \(0.803185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 67.0105i | 5.06552i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1.50352i | − | 0.113012i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.07366 | −0.154992 | −0.0774962 | − | 0.996993i | \(-0.524693\pi\) | ||||
−0.0774962 | + | 0.996993i | \(0.524693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.645075i | − | 0.0479481i | −0.999713 | − | 0.0239740i | \(-0.992368\pi\) | ||
0.999713 | − | 0.0239740i | \(-0.00763190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.363510 | −0.0268715 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −33.4926 | −2.46242 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.51911 | − | 0.285761i | −0.476725 | − | 0.0208969i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −27.7301 | −2.01707 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.92528 | 0.284023 | 0.142012 | − | 0.989865i | \(-0.454643\pi\) | ||||
0.142012 | + | 0.989865i | \(0.454643\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.9594i | 1.58067i | 0.612672 | + | 0.790337i | \(0.290095\pi\) | ||||
−0.612672 | + | 0.790337i | \(0.709905\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.931419 | −0.0667003 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.36989i | − | 0.311342i | −0.987809 | − | 0.155671i | \(-0.950246\pi\) | ||
0.987809 | − | 0.155671i | \(-0.0497540\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.5589i | 1.88271i | 0.337413 | + | 0.941357i | \(0.390448\pi\) | ||||
−0.337413 | + | 0.941357i | \(0.609552\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 18.7269i | − | 1.32089i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 30.4770 | 2.13906 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.86206 | −0.479267 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.62080i | 0.321168i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.469627i | 0.0324848i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 13.3998i | − | 0.922479i | −0.887276 | − | 0.461239i | \(-0.847405\pi\) | ||
0.887276 | − | 0.461239i | \(-0.152595\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.51998 | 0.104147 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 28.7857i | − | 1.96317i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.1086 | −1.36506 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.255033 | 0.0172336 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0259454 | − | 0.591896i | 0.00174527 | − | 0.0398152i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.03682 | −0.404255 | −0.202128 | − | 0.979359i | \(-0.564786\pi\) | ||||
−0.202128 | + | 0.979359i | \(0.564786\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.0462 | −0.669745 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 17.6954i | − | 1.17448i | −0.809412 | − | 0.587241i | \(-0.800214\pi\) | ||
0.809412 | − | 0.587241i | \(-0.199786\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.1121 | 1.06472 | 0.532359 | − | 0.846519i | \(-0.321306\pi\) | ||||
0.532359 | + | 0.846519i | \(0.321306\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 11.7362i | − | 0.772185i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 17.3934i | − | 1.13948i | −0.821825 | − | 0.569739i | \(-0.807044\pi\) | ||
0.821825 | − | 0.569739i | \(-0.192956\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 51.2853i | − | 3.34548i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.9063 | −1.09818 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.3331 | −0.991819 | −0.495909 | − | 0.868374i | \(-0.665165\pi\) | ||||
−0.495909 | + | 0.868374i | \(0.665165\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1882i | 0.913943i | 0.889481 | + | 0.456972i | \(0.151066\pi\) | ||||
−0.889481 | + | 0.456972i | \(0.848934\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 7.49251i | − | 0.480645i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 74.6969i | − | 4.77221i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0426393 | −0.00271307 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.98856i | 0.569627i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.6445 | −1.49243 | −0.746215 | − | 0.665705i | \(-0.768131\pi\) | ||||
−0.746215 | + | 0.665705i | \(0.768131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.89014 | −0.621788 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.17039 | + | 26.7002i | −0.0732924 | + | 1.67203i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.0533 | 0.627105 | 0.313553 | − | 0.949571i | \(-0.398481\pi\) | ||||
0.313553 | + | 0.949571i | \(0.398481\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.3167 | 2.38088 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.56908i | 0.282819i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.8706 | 0.978623 | 0.489312 | − | 0.872109i | \(-0.337248\pi\) | ||||
0.489312 | + | 0.872109i | \(0.337248\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.5395i | 1.69174i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.61519i | − | 0.343644i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.47473i | 0.455742i | 0.973691 | + | 0.227871i | \(0.0731765\pi\) | ||||
−0.973691 | + | 0.227871i | \(0.926824\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.42094 | −0.511536 | −0.255768 | − | 0.966738i | \(-0.582328\pi\) | ||||
−0.255768 | + | 0.966738i | \(0.582328\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.06558 | 0.0644916 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 21.5024i | − | 1.29664i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 11.6769i | − | 0.701600i | −0.936450 | − | 0.350800i | \(-0.885910\pi\) | ||
0.936450 | − | 0.350800i | \(-0.114090\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 3.01466i | − | 0.180483i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.5929 | 1.04950 | 0.524751 | − | 0.851256i | \(-0.324158\pi\) | ||||
0.524751 | + | 0.851256i | \(0.324158\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.765834i | 0.0455241i | 0.999741 | + | 0.0227620i | \(0.00724601\pi\) | ||||
−0.999741 | + | 0.0227620i | \(0.992754\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.92344 | 0.113935 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.85044 | 0.463397 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9348 | − | 1.48751i | −0.996164 | − | 0.0875005i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.07530 | 0.356140 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.55957 | −0.558476 | −0.279238 | − | 0.960222i | \(-0.590082\pi\) | ||||
−0.279238 | + | 0.960222i | \(0.590082\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.31120i | 0.251008i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.89805 | 0.516317 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 0.897965i | − | 0.0519307i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.9318i | 1.89816i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.5926i | 0.665979i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.04233 | 0.0596837 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.30200 | −0.359674 | −0.179837 | − | 0.983696i | \(-0.557557\pi\) | ||||
−0.179837 | + | 0.983696i | \(0.557557\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 22.5831i | − | 1.28470i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.13077i | 0.120825i | 0.998174 | + | 0.0604124i | \(0.0192416\pi\) | ||||
−0.998174 | + | 0.0604124i | \(0.980758\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 20.7160i | − | 1.17094i | −0.810695 | − | 0.585469i | \(-0.800911\pi\) | ||
0.810695 | − | 0.585469i | \(-0.199089\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 15.7228 | 0.885881 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.1861i | 1.18993i | 0.803751 | + | 0.594966i | \(0.202834\pi\) | ||||
−0.803751 | + | 0.594966i | \(0.797166\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.77946 | −0.547544 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.0443 | 0.783876 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0535789 | + | 1.22231i | −0.00298121 | + | 0.0680109i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.95229 | 0.108293 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.14300 | 0.118508 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 58.6722i | 3.23470i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.8922 | 0.653656 | 0.326828 | − | 0.945084i | \(-0.394020\pi\) | ||||
0.326828 | + | 0.945084i | \(0.394020\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.74441i | 0.314792i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 53.6976i | 2.93381i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 14.7656i | − | 0.804336i | −0.915566 | − | 0.402168i | \(-0.868257\pi\) | ||
0.915566 | − | 0.402168i | \(-0.131743\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.6377 | 0.795011 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.45244 | 0.349419 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 50.9307i | 2.75000i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 40.5069i | 2.18082i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 2.55012i | − | 0.136897i | −0.997655 | − | 0.0684487i | \(-0.978195\pi\) | ||
0.997655 | − | 0.0684487i | \(-0.0218050\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.6916 | 0.947011 | 0.473506 | − | 0.880791i | \(-0.342988\pi\) | ||||
0.473506 | + | 0.880791i | \(0.342988\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.807890i | 0.0431220i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.1137 | −0.857646 | −0.428823 | − | 0.903389i | \(-0.641072\pi\) | ||||
−0.428823 | + | 0.903389i | \(0.641072\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.35839 | −0.231319 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.33896 | − | 30.5460i | 0.0708655 | − | 1.61667i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.424780 | 0.0224190 | 0.0112095 | − | 0.999937i | \(-0.496432\pi\) | ||||
0.0112095 | + | 0.999937i | \(0.496432\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9119 | −0.995366 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 12.7728i | − | 0.670399i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.731284 | −0.0382771 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.9082i | 1.35240i | 0.736719 | + | 0.676199i | \(0.236374\pi\) | ||||
−0.736719 | + | 0.676199i | \(0.763626\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.17693i | 0.0612686i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 31.5061i | − | 1.63572i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.8854 | 0.667178 | 0.333589 | − | 0.942719i | \(-0.391740\pi\) | ||||
0.333589 | + | 0.942719i | \(0.391740\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −55.6571 | −2.87412 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.887916i | − | 0.0457300i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 22.9050i | − | 1.17655i | −0.808661 | − | 0.588274i | \(-0.799808\pi\) | ||
0.808661 | − | 0.588274i | \(-0.200192\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.3461i | 0.837434i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.2399 | 1.85177 | 0.925885 | − | 0.377804i | \(-0.123321\pi\) | ||||
0.925885 | + | 0.377804i | \(0.123321\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 33.6524i | 1.71509i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.93712 | −0.250968 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.1675 | 0.819725 | 0.409863 | − | 0.912147i | \(-0.365577\pi\) | ||||
0.409863 | + | 0.912147i | \(0.365577\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.7412 | − | 1.12835i | −1.30179 | − | 0.0570631i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.2544 | 1.57658 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 48.4772 | 2.43915 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 26.4855i | − | 1.32927i | −0.747168 | − | 0.664635i | \(-0.768587\pi\) | ||
0.747168 | − | 0.664635i | \(-0.231413\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.20049 | −0.110162 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.0998i | 1.45318i | 0.687074 | + | 0.726588i | \(0.258895\pi\) | ||||
−0.687074 | + | 0.726588i | \(0.741105\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.585843i | 0.0291829i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 26.8802i | − | 1.33569i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.2951 | −0.609444 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 40.4080 | 1.99805 | 0.999023 | − | 0.0441909i | \(-0.0140710\pi\) | ||||
0.999023 | + | 0.0441909i | \(0.0140710\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.8230i | 1.22443i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 4.93216i | − | 0.242696i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 25.7738i | − | 1.26519i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.76746 | 0.135523 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.1646i | 0.691986i | 0.938237 | + | 0.345993i | \(0.112458\pi\) | ||||
−0.938237 | + | 0.345993i | \(0.887542\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.0232 | 1.56072 | 0.780358 | − | 0.625333i | \(-0.215037\pi\) | ||||
0.780358 | + | 0.625333i | \(0.215037\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.79609 | −0.427680 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.45317 | − | 55.9646i | 0.118996 | − | 2.71468i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.19246 | −0.0577074 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.341923 | −0.0165082 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 18.1644i | − | 0.874949i | −0.899231 | − | 0.437475i | \(-0.855873\pi\) | ||
0.899231 | − | 0.437475i | \(-0.144127\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.10107 | 0.100971 | 0.0504854 | − | 0.998725i | \(-0.483923\pi\) | ||||
0.0504854 | + | 0.998725i | \(0.483923\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 40.0536i | 1.92042i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.85436i | 0.0887061i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.43081i | 0.259199i | 0.991566 | + | 0.129599i | \(0.0413691\pi\) | ||||
−0.991566 | + | 0.129599i | \(0.958631\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.8115 | −0.610071 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.1788 | −1.76642 | −0.883209 | − | 0.468979i | \(-0.844622\pi\) | ||||
−0.883209 | + | 0.468979i | \(0.844622\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.1010i | 0.763261i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 27.2161i | − | 1.28728i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.5969i | 0.641676i | 0.947134 | + | 0.320838i | \(0.103964\pi\) | ||||
−0.947134 | + | 0.320838i | \(0.896036\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.51905 | −0.118618 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.68429i | 0.408024i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.05544 | −0.143241 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.6533 | 1.20001 | 0.600005 | − | 0.799996i | \(-0.295165\pi\) | ||||
0.600005 | + | 0.799996i | \(0.295165\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.1591 | + | 1.01516i | 1.08097 | + | 0.0473838i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.6479 | 1.00824 | 0.504121 | − | 0.863633i | \(-0.331817\pi\) | ||||
0.504121 | + | 0.863633i | \(0.331817\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.07378 | 0.375220 | 0.187610 | − | 0.982244i | \(-0.439926\pi\) | ||||
0.187610 | + | 0.982244i | \(0.439926\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 26.4272i | − | 1.22553i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.5973 | −1.13823 | −0.569114 | − | 0.822259i | \(-0.692714\pi\) | ||||
−0.569114 | + | 0.822259i | \(0.692714\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 61.4319i | − | 2.83666i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.54782i | 0.301708i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10.5672i | − | 0.485880i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.03160 | −0.184983 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.72338 | 0.216269 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 19.0113i | − | 0.868647i | −0.900757 | − | 0.434323i | \(-0.856988\pi\) | ||
0.900757 | − | 0.434323i | \(-0.143012\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1.11632i | − | 0.0508997i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 46.3413i | − | 2.10860i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.4203 | −0.791017 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.22891i | − | 0.101001i | −0.998724 | − | 0.0505007i | \(-0.983918\pi\) | ||
0.998724 | − | 0.0505007i | \(-0.0160817\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 30.6713 | 1.38701 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.68008 | −0.0758208 | −0.0379104 | − | 0.999281i | \(-0.512070\pi\) | ||||
−0.0379104 | + | 0.999281i | \(0.512070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.4532 | − | 1.11572i | −1.14635 | − | 0.0502496i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.04515 | −0.226762 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.98615 | 0.223659 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 14.7992i | − | 0.662502i | −0.943543 | − | 0.331251i | \(-0.892529\pi\) | ||
0.943543 | − | 0.331251i | \(-0.107471\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.0692 | 1.25404 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 35.9433i | − | 1.60263i | −0.598240 | − | 0.801317i | \(-0.704133\pi\) | ||
0.598240 | − | 0.801317i | \(-0.295867\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 33.2408i | − | 1.47919i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.5147i | 0.866679i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.44784 | 0.418768 | 0.209384 | − | 0.977833i | \(-0.432854\pi\) | ||||
0.209384 | + | 0.977833i | \(0.432854\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.836615 | 0.0370096 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1.66835i | − | 0.0736594i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 64.7547i | 2.85343i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 18.8267i | − | 0.827999i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.9264 | 1.00636 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.49939i | − | 0.328554i | −0.986414 | − | 0.164277i | \(-0.947471\pi\) | ||
0.986414 | − | 0.164277i | \(-0.0525291\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.8814 | 1.39408 | 0.697038 | − | 0.717034i | \(-0.254501\pi\) | ||||
0.697038 | + | 0.717034i | \(0.254501\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 100.752 | 4.39716 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.7939 | + | 0.736148i | 0.731553 | + | 0.0320671i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.0520 | −0.697914 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.739426 | 0.0320884 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.228715i | − | 0.00990674i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.2707 | −1.74105 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.11779i | 0.134542i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 27.4211i | − | 1.18111i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.9009i | 1.28554i | 0.766058 | + | 0.642771i | \(0.222215\pi\) | ||||
−0.766058 | + | 0.642771i | \(0.777785\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.969884 | −0.0416217 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.14485 | −0.263216 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.5398i | 0.493404i | 0.969091 | + | 0.246702i | \(0.0793469\pi\) | ||||
−0.969091 | + | 0.246702i | \(0.920653\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 0.178773i | − | 0.00762986i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.83361i | 0.0781143i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −55.4596 | −2.35838 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 50.3568i | 2.13753i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.6636 | 1.25689 | 0.628444 | − | 0.777855i | \(-0.283692\pi\) | ||||
0.628444 | + | 0.777855i | \(0.283692\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.959437 | 0.0405799 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.429647 | + | 9.80161i | −0.0181397 | + | 0.413824i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.39522 | −0.353816 | −0.176908 | − | 0.984227i | \(-0.556610\pi\) | ||||
−0.176908 | + | 0.984227i | \(0.556610\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41.9722 | −1.76578 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30.7519i | 1.29146i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.7721 | 0.535436 | 0.267718 | − | 0.963497i | \(-0.413730\pi\) | ||||
0.267718 | + | 0.963497i | \(0.413730\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 18.3722i | − | 0.768853i | −0.923156 | − | 0.384426i | \(-0.874399\pi\) | ||
0.923156 | − | 0.384426i | \(-0.125601\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.90174i | − | 0.246549i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 84.9038i | − | 3.54074i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.8464 | −0.659695 | −0.329848 | − | 0.944034i | \(-0.606997\pi\) | ||||
−0.329848 | + | 0.944034i | \(0.606997\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 33.0165 | 1.37212 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.4862i | 1.22329i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.1097i | 0.418701i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 0.458069i | − | 0.0189388i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −43.0686 | −1.77763 | −0.888816 | − | 0.458264i | \(-0.848471\pi\) | ||||
−0.888816 | + | 0.458264i | \(0.848471\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.20981i | − | 0.0498492i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.57022 | −0.270263 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −44.5851 | −1.83089 | −0.915446 | − | 0.402440i | \(-0.868162\pi\) | ||||
−0.915446 | + | 0.402440i | \(0.868162\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.83935 | + | 87.5877i | −0.157398 | + | 3.59075i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 39.9319 | 1.63430 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.1693 | 1.15097 | 0.575483 | − | 0.817814i | \(-0.304814\pi\) | ||||
0.575483 | + | 0.817814i | \(0.304814\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 40.3029i | − | 1.64399i | −0.569495 | − | 0.821995i | \(-0.692861\pi\) | ||
0.569495 | − | 0.821995i | \(-0.307139\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.20983 | 0.375053 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 36.6248i | 1.48901i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 17.9363i | − | 0.728013i | −0.931396 | − | 0.364006i | \(-0.881409\pi\) | ||
0.931396 | − | 0.364006i | \(-0.118591\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 45.8227i | − | 1.85683i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.70936 | 0.0691531 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.4913 | 0.666077 | 0.333039 | − | 0.942913i | \(-0.391926\pi\) | ||||
0.333039 | + | 0.942913i | \(0.391926\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.3172i | 0.416032i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.31424i | − | 0.254202i | −0.991890 | − | 0.127101i | \(-0.959433\pi\) | ||
0.991890 | − | 0.127101i | \(-0.0405672\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 42.7568i | − | 1.71854i | −0.511520 | − | 0.859271i | \(-0.670917\pi\) | ||
0.511520 | − | 0.859271i | \(-0.329083\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 35.1347 | 1.40991 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 18.4201i | − | 0.737987i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 91.6590 | 3.66636 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.706094 | 0.0281987 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32.0006 | − | 1.40272i | −1.27595 | − | 0.0559303i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.5154 | −1.13518 | −0.567591 | − | 0.823311i | \(-0.692124\pi\) | ||||
−0.567591 | + | 0.823311i | \(0.692124\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.1468 | −0.800765 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 46.8707i | − | 1.86001i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.48967 | 0.0986444 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.747520i | 0.0295714i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.3593i | 0.488162i | 0.969755 | + | 0.244081i | \(0.0784862\pi\) | ||||
−0.969755 | + | 0.244081i | \(0.921514\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 15.3362i | − | 0.604800i | −0.953181 | − | 0.302400i | \(-0.902212\pi\) | ||
0.953181 | − | 0.302400i | \(-0.0977879\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −43.2799 | −1.70414 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −46.9121 | −1.84430 | −0.922152 | − | 0.386828i | \(-0.873571\pi\) | ||||
−0.922152 | + | 0.386828i | \(0.873571\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.58263i | 0.0621238i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.2336i | 1.18495i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 20.0020i | − | 0.782740i | −0.920233 | − | 0.391370i | \(-0.872001\pi\) | ||
0.920233 | − | 0.391370i | \(-0.127999\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −89.6190 | −3.50170 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.125425i | 0.00489328i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.4677 | −1.30372 | −0.651858 | − | 0.758341i | \(-0.726010\pi\) | ||||
−0.651858 | + | 0.758341i | \(0.726010\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.9379 | 0.736601 | 0.368300 | − | 0.929707i | \(-0.379940\pi\) | ||||
0.368300 | + | 0.929707i | \(0.379940\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.889928 | − | 0.0390094i | −0.0345619 | − | 0.00151500i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.30969 | 0.244679 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.6150 | −1.49518 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.07648i | 0.350917i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.382638 | 0.0147716 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 28.1073i | − | 1.08346i | −0.840553 | − | 0.541729i | \(-0.817770\pi\) | ||
0.840553 | − | 0.541729i | \(-0.182230\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 76.3871i | 2.94014i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 30.2847i | − | 1.16394i | −0.813212 | − | 0.581968i | \(-0.802283\pi\) | ||
0.813212 | − | 0.581968i | \(-0.197717\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.9295 | 0.764823 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.6053 | −1.01952 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.4526i | 0.782599i | 0.920263 | + | 0.391299i | \(0.127974\pi\) | ||||
−0.920263 | + | 0.391299i | \(0.872026\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 71.1775i | − | 2.71955i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 24.2249i | − | 0.924237i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.917900 | −0.0349692 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 23.3610i | − | 0.888696i | −0.895854 | − | 0.444348i | \(-0.853435\pi\) | ||
0.895854 | − | 0.444348i | \(-0.146565\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.77183 | 0.219254 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.93543 | −0.301008 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.55638 | − | 0.287394i | −0.248341 | − | 0.0108858i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.1513 | −0.989134 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.457933 | −0.0172959 | −0.00864794 | − | 0.999963i | \(-0.502753\pi\) | ||||
−0.00864794 | + | 0.999963i | \(0.502753\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.30527i | 0.0869451i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −77.1084 | −2.90407 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.0286i | 1.43021i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.24043i | 0.271920i | 0.990714 | + | 0.135960i | \(0.0434119\pi\) | ||||
−0.990714 | + | 0.135960i | \(0.956588\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 8.31446i | − | 0.311817i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.4780 | 0.954158 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.980430 | 0.0366660 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.0537i | 0.860956i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 42.6305i | 1.58985i | 0.606707 | + | 0.794925i | \(0.292490\pi\) | ||||
−0.606707 | + | 0.794925i | \(0.707510\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 74.0817i | − | 2.75895i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.3323 | 0.793356 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 83.9536i | − | 3.11796i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.88783 | 0.181280 | 0.0906398 | − | 0.995884i | \(-0.471109\pi\) | ||||
0.0906398 | + | 0.995884i | \(0.471109\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.9700 | −1.11000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.20559 | − | 27.5034i | 0.0445904 | − | 1.01725i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.6680 | −0.985007 | −0.492503 | − | 0.870311i | \(-0.663918\pi\) | ||||
−0.492503 | + | 0.870311i | \(0.663918\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −112.308 | −4.14255 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.7123i | 0.726112i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.74907 | 0.321840 | 0.160920 | − | 0.986967i | \(-0.448554\pi\) | ||||
0.160920 | + | 0.986967i | \(0.448554\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0641091i | 0.00235510i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.87111i | − | 0.105331i | −0.998612 | − | 0.0526655i | \(-0.983228\pi\) | ||
0.998612 | − | 0.0526655i | \(-0.0167717\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 78.0397i | 2.85915i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.42054 | −0.161739 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46.0711 | 1.68340 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 13.0671i | − | 0.476825i | −0.971164 | − | 0.238413i | \(-0.923373\pi\) | ||
0.971164 | − | 0.238413i | \(-0.0766271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 35.5500i | 1.29552i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 24.9014i | − | 0.906254i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.3683 | −0.631262 | −0.315631 | − | 0.948882i | \(-0.602216\pi\) | ||||
−0.315631 | + | 0.948882i | \(0.602216\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.8700i | 0.539748i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.3288 | 0.664419 | 0.332209 | − | 0.943206i | \(-0.392206\pi\) | ||||
0.332209 | + | 0.943206i | \(0.392206\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.02992 | 0.254500 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.1311 | − | 0.575592i | −0.474755 | − | 0.0208106i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.143694 | −0.00518848 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.99518 | 0.252253 | 0.126126 | − | 0.992014i | \(-0.459746\pi\) | ||||
0.126126 | + | 0.992014i | \(0.459746\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 15.1153i | − | 0.544364i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −49.6691 | −1.78647 | −0.893237 | − | 0.449587i | \(-0.851571\pi\) | ||||
−0.893237 | + | 0.449587i | \(0.851571\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 55.3922i | 1.98975i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 57.6099i | − | 2.06674i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.472312i | 0.0169223i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.59996 | −0.0572510 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 34.7415 | 1.24156 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 18.7752i | − | 0.670117i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.5635i | 0.768657i | 0.923196 | + | 0.384328i | \(0.125567\pi\) | ||||
−0.923196 | + | 0.384328i | \(0.874433\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 23.8618i | − | 0.849501i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.0177 | 1.70731 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0347412i | 0.00123370i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 41.4062 | 1.46853 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.0795 | 0.357036 | 0.178518 | − | 0.983937i | \(-0.442870\pi\) | ||||
0.178518 | + | 0.983937i | \(0.442870\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.14791 | − | 49.0007i | 0.0759877 | − | 1.73352i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.76153 | 0.0975739 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.268453 | −0.00947351 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 132.879i | 4.68338i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.2384 | 0.395611 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.9211i | 1.64966i | 0.565383 | + | 0.824828i | \(0.308728\pi\) | ||||
−0.565383 | + | 0.824828i | \(0.691272\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.75936i | 0.0968941i | 0.998826 | + | 0.0484471i | \(0.0154272\pi\) | ||||
−0.998826 | + | 0.0484471i | \(0.984573\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.6611i | 0.444043i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −87.9471 | −3.08065 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.98130 | −0.0693170 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.524047i | 0.0183117i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 7.08149i | − | 0.247146i | −0.992336 | − | 0.123573i | \(-0.960565\pi\) | ||
0.992336 | − | 0.123573i | \(-0.0394353\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 4.94122i | − | 0.172240i | −0.996285 | − | 0.0861200i | \(-0.972553\pi\) | ||
0.996285 | − | 0.0861200i | \(-0.0274468\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −32.3292 | −1.12556 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.4685i | 1.51155i | 0.654832 | + | 0.755774i | \(0.272739\pi\) | ||||
−0.654832 | + | 0.755774i | \(0.727261\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.72742 | −0.337847 | −0.168924 | − | 0.985629i | \(-0.554029\pi\) | ||||
−0.168924 | + | 0.985629i | \(0.554029\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.5565 | −0.609029 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.12843 | − | 71.3694i | 0.108394 | − | 2.47280i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −80.4856 | −2.78532 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.9223 | −0.792310 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 5.50925i | − | 0.190200i | −0.995468 | − | 0.0951002i | \(-0.969683\pi\) | ||
0.995468 | − | 0.0951002i | \(-0.0303172\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.18282 | −0.316649 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 26.4512i | − | 0.911029i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 55.9566i | − | 1.92496i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 41.9001i | − | 1.43970i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.15145 | 0.0395175 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −48.5481 | −1.66421 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 25.1521i | − | 0.861192i | −0.902545 | − | 0.430596i | \(-0.858303\pi\) | ||
0.902545 | − | 0.430596i | \(-0.141697\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.945944i | 0.0323506i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.2189i | 1.10058i | 0.834974 | + | 0.550289i | \(0.185482\pi\) | ||||
−0.834974 | + | 0.550289i | \(0.814518\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.7655 | 1.11794 | 0.558972 | − | 0.829186i | \(-0.311196\pi\) | ||||
0.558972 | + | 0.829186i | \(0.311196\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 11.8033i | − | 0.402255i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.7835 | 0.571318 | 0.285659 | − | 0.958331i | \(-0.407788\pi\) | ||||
0.285659 | + | 0.958331i | \(0.407788\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −65.7393 | −2.23520 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.23650 | + | 25.4618i | −0.0759555 | + | 0.864728i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.7959 | 0.603685 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.78976 | −0.0606436 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.98781i | 0.101122i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −182.578 | −6.17226 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.0193i | 1.11498i | 0.830182 | + | 0.557492i | \(0.188236\pi\) | ||||
−0.830182 | + | 0.557492i | \(0.811764\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.3730i | 0.484790i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 27.0787i | − | 0.912304i | −0.889902 | − | 0.456152i | \(-0.849227\pi\) | ||
0.889902 | − | 0.456152i | \(-0.150773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.2722 | −0.480299 | −0.240150 | − | 0.970736i | \(-0.577197\pi\) | ||||
−0.240150 | + | 0.970736i | \(0.577197\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.48198 | 0.217889 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 37.1589i | − | 1.24767i | −0.781555 | − | 0.623836i | \(-0.785573\pi\) | ||
0.781555 | − | 0.623836i | \(-0.214427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 53.6218i | 1.79842i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 9.86768i | − | 0.330580i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.52994 | −0.118125 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 8.93995i | − | 0.298829i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.35011 | −0.0450788 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.1929 | 0.840229 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.15340 | + | 26.3127i | −0.0384253 | + | 0.876603i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 49.5137 | 1.64771 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.78105 | 0.0924451 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 40.9545i | − | 1.35987i | −0.733271 | − | 0.679936i | \(-0.762007\pi\) | ||
0.733271 | − | 0.679936i | \(-0.237993\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.70122 | −0.189098 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 16.5692i | − | 0.548962i | −0.961592 | − | 0.274481i | \(-0.911494\pi\) | ||
0.961592 | − | 0.274481i | \(-0.0885061\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 9.46153i | − | 0.313131i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 1.56717i | − | 0.0518089i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 102.527 | 3.38575 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.9072 | 1.87720 | 0.938598 | − | 0.345014i | \(-0.112126\pi\) | ||||
0.938598 | + | 0.345014i | \(0.112126\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.47518i | 0.312218i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 0.145267i | − | 0.00478151i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 105.549i | − | 3.47044i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.1063 | 0.364778 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.0882i | 1.34806i | 0.738704 | + | 0.674030i | \(0.235438\pi\) | ||||
−0.738704 | + | 0.674030i | \(0.764562\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.14134 | −0.168501 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.20366 | 0.104883 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.23197 | − | 28.1052i | 0.0402898 | − | 0.919138i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.4899 | 1.45342 | 0.726712 | − | 0.686943i | \(-0.241048\pi\) | ||||
0.726712 | + | 0.686943i | \(0.241048\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.1469 | −1.01644 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 56.9747i | − | 1.85732i | −0.370930 | − | 0.928661i | \(-0.620961\pi\) | ||
0.370930 | − | 0.928661i | \(-0.379039\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.94668 | −0.323909 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 119.550i | − | 3.88896i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.6216i | 0.540129i | 0.962842 | + | 0.270064i | \(0.0870450\pi\) | ||||
−0.962842 | + | 0.270064i | \(0.912955\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 0.0243739i | − | 0.000791211i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.8538 | 1.03293 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.0168 | −1.45824 | −0.729119 | − | 0.684387i | \(-0.760070\pi\) | ||||
−0.729119 | + | 0.684387i | \(0.760070\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.9227i | 0.547604i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.7036i | 0.475300i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 81.4296i | 2.62950i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.3779 | 0.463802 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.90694i | 0.222573i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −94.6715 | −3.04758 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.2016 | −1.13201 | −0.566004 | − | 0.824403i | \(-0.691511\pi\) | ||||
−0.566004 | + | 0.824403i | \(0.691511\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.83776 | + | 0.0805570i | 0.0590374 | + | 0.00258786i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.9567 | 1.18600 | 0.592998 | − | 0.805204i | \(-0.297944\pi\) | ||||
0.592998 | + | 0.805204i | \(0.297944\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.07841 | 0.291041 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 2.93530i | − | 0.0940049i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.6388 | −1.52410 | −0.762051 | − | 0.647517i | \(-0.775807\pi\) | ||||
−0.762051 | + | 0.647517i | \(0.775807\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.91066i | 0.188905i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.05392i | 0.0336491i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 48.2389i | − | 1.53858i | −0.638899 | − | 0.769291i | \(-0.720610\pi\) | ||
0.638899 | − | 0.769291i | \(-0.279390\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.8395 | 0.600276 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 88.2148 | 2.80791 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 41.7254i | − | 1.32679i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24.5705i | − | 0.780509i | −0.920707 | − | 0.390254i | \(-0.872387\pi\) | ||
0.920707 | − | 0.390254i | \(-0.127613\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 17.8802i | − | 0.567411i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −114.501 | −3.62992 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 44.8184i | − | 1.41941i | −0.704497 | − | 0.709707i | \(-0.748827\pi\) | ||
0.704497 | − | 0.709707i | \(-0.251173\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 43.6782 | 1.38192 |
(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 | 4012.2.b.b.237.14 | ✓ | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.33 | yes | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.14 | ✓ | 46 | 1.1 | even | 1 | trivial | |
4012.2.b.b.237.33 | yes | 46 | 17.16 | even | 2 | inner |