Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(559,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.u (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1231.12 | ||
Character | \(\chi\) | \(=\) | 1344.1231 |
Dual form | 1344.2.u.a.559.12 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.32544 | − | 1.32544i | 0.592756 | − | 0.592756i | −0.345619 | − | 0.938375i | \(-0.612331\pi\) |
0.938375 | + | 0.345619i | \(0.112331\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64192 | + | 0.142388i | −0.998551 | + | 0.0538175i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.18514 | − | 1.18514i | 0.357332 | − | 0.357332i | −0.505497 | − | 0.862829i | \(-0.668691\pi\) |
0.862829 | + | 0.505497i | \(0.168691\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.02086 | − | 2.02086i | −0.560487 | − | 0.560487i | 0.368959 | − | 0.929446i | \(-0.379714\pi\) |
−0.929446 | + | 0.368959i | \(0.879714\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.87446i | 0.483983i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.276387i | − | 0.0670337i | −0.999438 | − | 0.0335169i | \(-0.989329\pi\) | ||
0.999438 | − | 0.0335169i | \(-0.0106707\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.58131 | + | 4.58131i | −1.05102 | + | 1.05102i | −0.0523978 | + | 0.998626i | \(0.516686\pi\) |
−0.998626 | + | 0.0523978i | \(0.983314\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.76743 | − | 1.96880i | 0.385686 | − | 0.429628i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.81753 | 0.378981 | 0.189491 | − | 0.981883i | \(-0.439316\pi\) | ||||
0.189491 | + | 0.981883i | \(0.439316\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.48640i | 0.297280i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.64137 | + | 2.64137i | −0.490490 | + | 0.490490i | −0.908461 | − | 0.417970i | \(-0.862742\pi\) |
0.417970 | + | 0.908461i | \(0.362742\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.11326 | −1.27758 | −0.638790 | − | 0.769382i | \(-0.720565\pi\) | ||||
−0.638790 | + | 0.769382i | \(0.720565\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.67603i | 0.291760i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.31298 | + | 3.69044i | −0.559997 | + | 0.623798i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.786692 | − | 0.786692i | −0.129331 | − | 0.129331i | 0.639478 | − | 0.768809i | \(-0.279150\pi\) |
−0.768809 | + | 0.639478i | \(0.779150\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.85793 | 0.457636 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.33055 | −1.14484 | −0.572420 | − | 0.819961i | \(-0.693995\pi\) | ||||
−0.572420 | + | 0.819961i | \(0.693995\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.69851 | − | 1.69851i | 0.259020 | − | 0.259020i | −0.565635 | − | 0.824656i | \(-0.691369\pi\) |
0.824656 | + | 0.565635i | \(0.191369\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.32544 | − | 1.32544i | −0.197585 | − | 0.197585i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.5721 | −1.68796 | −0.843982 | − | 0.536372i | \(-0.819795\pi\) | ||||
−0.843982 | + | 0.536372i | \(0.819795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.95945 | − | 0.752353i | 0.994207 | − | 0.107479i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.195435 | + | 0.195435i | 0.0273664 | + | 0.0273664i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.85262 | + | 3.85262i | 0.529198 | + | 0.529198i | 0.920333 | − | 0.391135i | \(-0.127917\pi\) |
−0.391135 | + | 0.920333i | \(0.627917\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.14166i | − | 0.423621i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.47895i | − | 0.858158i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.25247 | + | 4.25247i | 0.553625 | + | 0.553625i | 0.927485 | − | 0.373860i | \(-0.121966\pi\) |
−0.373860 | + | 0.927485i | \(0.621966\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.14204 | − | 1.14204i | −0.146223 | − | 0.146223i | 0.630206 | − | 0.776428i | \(-0.282971\pi\) |
−0.776428 | + | 0.630206i | \(0.782971\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.142388 | + | 2.64192i | 0.0179392 | + | 0.332850i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.35708 | −0.664464 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.05161 | + | 3.05161i | 0.372813 | + | 0.372813i | 0.868501 | − | 0.495688i | \(-0.165084\pi\) |
−0.495688 | + | 0.868501i | \(0.665084\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.28519 | + | 1.28519i | −0.154718 | + | 0.154718i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.36612 | −0.992876 | −0.496438 | − | 0.868072i | \(-0.665359\pi\) | ||||
−0.496438 | + | 0.868072i | \(0.665359\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.9603 | −1.98505 | −0.992527 | − | 0.122024i | \(-0.961061\pi\) | ||||
−0.992527 | + | 0.122024i | \(0.961061\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.05104 | − | 1.05104i | −0.121364 | − | 0.121364i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.96228 | + | 3.29978i | −0.337583 | + | 0.376045i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.8414i | − | 1.55728i | −0.627470 | − | 0.778641i | \(-0.715909\pi\) | ||
0.627470 | − | 0.778641i | \(-0.284091\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.90941 | − | 9.90941i | 1.08770 | − | 1.08770i | 0.0919340 | − | 0.995765i | \(-0.470695\pi\) |
0.995765 | − | 0.0919340i | \(-0.0293049\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.366336 | − | 0.366336i | −0.0397347 | − | 0.0397347i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.73546i | − | 0.400484i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.94992 | −0.842690 | −0.421345 | − | 0.906901i | \(-0.638442\pi\) | ||||
−0.421345 | + | 0.906901i | \(0.638442\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.62670 | + | 5.05121i | 0.589839 | + | 0.529511i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.02983 | − | 5.02983i | 0.521569 | − | 0.521569i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.1445i | 1.24600i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1657i | 1.33678i | 0.743812 | + | 0.668388i | \(0.233016\pi\) | ||||
−0.743812 | + | 0.668388i | \(0.766984\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.18514 | − | 1.18514i | −0.119111 | − | 0.119111i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.20635 | − | 1.20635i | 0.120036 | − | 0.120036i | −0.644537 | − | 0.764573i | \(-0.722950\pi\) |
0.764573 | + | 0.644537i | \(0.222950\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.4220i | − | 1.12544i | −0.826647 | − | 0.562722i | \(-0.809754\pi\) | ||
0.826647 | − | 0.562722i | \(-0.190246\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.266900 | − | 4.95217i | −0.0260468 | − | 0.483282i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.18783 | + | 9.18783i | −0.888221 | + | 0.888221i | −0.994352 | − | 0.106131i | \(-0.966154\pi\) |
0.106131 | + | 0.994352i | \(0.466154\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.541341 | − | 0.541341i | 0.0518511 | − | 0.0518511i | −0.680706 | − | 0.732557i | \(-0.738327\pi\) |
0.732557 | + | 0.680706i | \(0.238327\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.11255 | 0.105599 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.9427 | −1.12347 | −0.561735 | − | 0.827317i | \(-0.689866\pi\) | ||||
−0.561735 | + | 0.827317i | \(0.689866\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.40903 | − | 2.40903i | 0.224644 | − | 0.224644i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.02086 | + | 2.02086i | −0.186829 | + | 0.186829i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0393541 | + | 0.730192i | 0.00360759 | + | 0.0669366i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.19091i | 0.744628i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.18348 | − | 5.18348i | 0.467379 | − | 0.467379i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.59736 | + | 8.59736i | 0.768971 | + | 0.768971i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 18.8618i | − | 1.67371i | −0.547422 | − | 0.836857i | \(-0.684391\pi\) | ||
0.547422 | − | 0.836857i | \(-0.315609\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.40206i | 0.211489i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.80983 | + | 8.80983i | −0.769718 | + | 0.769718i | −0.978057 | − | 0.208339i | \(-0.933194\pi\) |
0.208339 | + | 0.978057i | \(0.433194\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.4511 | − | 12.7558i | 0.992937 | − | 1.10606i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.87446 | 0.161328 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.34380i | 0.371116i | 0.982633 | + | 0.185558i | \(0.0594092\pi\) | ||||
−0.982633 | + | 0.185558i | \(0.940591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.64886 | + | 1.64886i | 0.139854 | + | 0.139854i | 0.773568 | − | 0.633714i | \(-0.218470\pi\) |
−0.633714 | + | 0.773568i | \(0.718470\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.18271 | − | 8.18271i | 0.689108 | − | 0.689108i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.79000 | −0.400560 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.00197i | 0.581482i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.38908 | + | 5.45307i | −0.362005 | + | 0.449762i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.1553 | − | 10.1553i | −0.831955 | − | 0.831955i | 0.155829 | − | 0.987784i | \(-0.450195\pi\) |
−0.987784 | + | 0.155829i | \(0.950195\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.92611 | 0.726397 | 0.363198 | − | 0.931712i | \(-0.381685\pi\) | ||||
0.363198 | + | 0.931712i | \(0.381685\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.276387 | −0.0223446 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.42822 | + | 9.42822i | −0.757293 | + | 0.757293i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.83300 | + | 5.83300i | 0.465524 | + | 0.465524i | 0.900461 | − | 0.434937i | \(-0.143229\pi\) |
−0.434937 | + | 0.900461i | \(0.643229\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.44843 | −0.432089 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.80176 | + | 0.258794i | −0.378432 | + | 0.0203958i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.4751 | − | 12.4751i | −0.977129 | − | 0.977129i | 0.0226151 | − | 0.999744i | \(-0.492801\pi\) |
−0.999744 | + | 0.0226151i | \(0.992801\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.22149 | + | 2.22149i | 0.172943 | + | 0.172943i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 21.3378i | − | 1.65117i | −0.564280 | − | 0.825584i | \(-0.690846\pi\) | ||
0.564280 | − | 0.825584i | \(-0.309154\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 4.83221i | − | 0.371709i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.58131 | + | 4.58131i | 0.350341 | + | 0.350341i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.7377 | − | 10.7377i | −0.816371 | − | 0.816371i | 0.169209 | − | 0.985580i | \(-0.445879\pi\) |
−0.985580 | + | 0.169209i | \(0.945879\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.211645 | − | 3.92695i | −0.0159989 | − | 0.296849i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.01391 | −0.452033 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.41822 | − | 2.41822i | −0.180746 | − | 0.180746i | 0.610935 | − | 0.791681i | \(-0.290794\pi\) |
−0.791681 | + | 0.610935i | \(0.790794\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.318290 | − | 0.318290i | 0.0236583 | − | 0.0236583i | −0.695179 | − | 0.718837i | \(-0.744675\pi\) |
0.718837 | + | 0.695179i | \(0.244675\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.61508 | 0.119390 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.08543 | −0.153324 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.327556 | − | 0.327556i | −0.0239533 | − | 0.0239533i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.96880 | − | 1.76743i | −0.143209 | − | 0.128562i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.4401i | 1.76842i | 0.467088 | + | 0.884211i | \(0.345303\pi\) | ||||
−0.467088 | + | 0.884211i | \(0.654697\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.3910 | 1.61174 | 0.805871 | − | 0.592091i | \(-0.201698\pi\) | ||||
0.805871 | + | 0.592091i | \(0.201698\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.78803 | − | 3.78803i | 0.271266 | − | 0.271266i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.4527 | + | 13.4527i | 0.958463 | + | 0.958463i | 0.999171 | − | 0.0407083i | \(-0.0129614\pi\) |
−0.0407083 | + | 0.999171i | \(0.512961\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.64437i | 0.400119i | 0.979784 | + | 0.200059i | \(0.0641135\pi\) | ||||
−0.979784 | + | 0.200059i | \(0.935886\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.31563 | −0.304401 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.60218 | − | 7.35438i | 0.463382 | − | 0.516176i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.71623 | + | 9.71623i | −0.678611 | + | 0.678611i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.81753i | − | 0.126327i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.8589i | 0.751129i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.9095 | + | 13.9095i | 0.957568 | + | 0.957568i | 0.999136 | − | 0.0415678i | \(-0.0132353\pi\) |
−0.0415678 | + | 0.999136i | \(0.513235\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.91574 | − | 5.91574i | 0.405340 | − | 0.405340i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4.50256i | − | 0.307072i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.7926 | − | 1.01284i | 1.27573 | − | 0.0687561i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.9928 | − | 11.9928i | 0.810395 | − | 0.810395i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.558541 | + | 0.558541i | −0.0375715 | + | 0.0375715i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.4893 | 1.03724 | 0.518622 | − | 0.855004i | \(-0.326445\pi\) | ||||
0.518622 | + | 0.855004i | \(0.326445\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.48640 | 0.0990933 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.24437 | − | 4.24437i | 0.281709 | − | 0.281709i | −0.552081 | − | 0.833790i | \(-0.686166\pi\) |
0.833790 | + | 0.552081i | \(0.186166\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.39096 | + | 2.39096i | −0.157999 | + | 0.157999i | −0.781679 | − | 0.623680i | \(-0.785637\pi\) |
0.623680 | + | 0.781679i | \(0.285637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.238647 | − | 4.42795i | −0.0157018 | − | 0.291337i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.92061i | 0.191336i | 0.995413 | + | 0.0956678i | \(0.0304987\pi\) | ||||
−0.995413 | + | 0.0956678i | \(0.969501\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.3382 | + | 15.3382i | −1.00055 | + | 1.00055i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.78736 | + | 9.78736i | 0.635758 | + | 0.635758i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.83859i | 0.507036i | 0.967331 | + | 0.253518i | \(0.0815877\pi\) | ||||
−0.967331 | + | 0.253518i | \(0.918412\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 18.3656i | − | 1.18303i | −0.806293 | − | 0.591516i | \(-0.798530\pi\) | ||
0.806293 | − | 0.591516i | \(-0.201470\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.22716 | − | 10.2216i | 0.525614 | − | 0.653031i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.5164 | 1.17817 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.0140i | 0.888103i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.2774 | + | 16.2774i | 1.02742 | + | 1.02742i | 0.999613 | + | 0.0278042i | \(0.00885149\pi\) |
0.0278042 | + | 0.999613i | \(0.491149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.15402 | − | 2.15402i | 0.135422 | − | 0.135422i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.518077 | 0.0324432 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.6309i | 0.850274i | 0.905129 | + | 0.425137i | \(0.139774\pi\) | ||||
−0.905129 | + | 0.425137i | \(0.860226\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.19039 | + | 1.96636i | 0.136104 | + | 0.122184i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.64137 | + | 2.64137i | 0.163497 | + | 0.163497i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.88266 | −0.362740 | −0.181370 | − | 0.983415i | \(-0.558053\pi\) | ||||
−0.181370 | + | 0.983415i | \(0.558053\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.2129 | 0.627371 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.62144 | − | 5.62144i | 0.344027 | − | 0.344027i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.28207 | + | 7.28207i | 0.443995 | + | 0.443995i | 0.893352 | − | 0.449357i | \(-0.148347\pi\) |
−0.449357 | + | 0.893352i | \(0.648347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.65390 | 0.464941 | 0.232471 | − | 0.972603i | \(-0.425319\pi\) | ||||
0.232471 | + | 0.972603i | \(0.425319\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.55042 | + | 0.406935i | −0.456972 | + | 0.0246288i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.76159 | + | 1.76159i | 0.106228 | + | 0.106228i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.9351 | − | 20.9351i | −1.25787 | − | 1.25787i | −0.952109 | − | 0.305758i | \(-0.901090\pi\) |
−0.305758 | − | 0.952109i | \(-0.598910\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.11326i | 0.425860i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.2903i | 0.792835i | 0.918070 | + | 0.396417i | \(0.129747\pi\) | ||||
−0.918070 | + | 0.396417i | \(0.870253\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.97242 | + | 7.97242i | 0.473911 | + | 0.473911i | 0.903178 | − | 0.429267i | \(-0.141228\pi\) |
−0.429267 | + | 0.903178i | \(0.641228\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.58748 | − | 8.58748i | −0.508678 | − | 0.508678i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.3667 | − | 1.04378i | 1.14318 | − | 0.0616124i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9236 | 0.995506 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.30957 | − | 9.30957i | −0.545737 | − | 0.545737i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.7572 | − | 11.7572i | 0.686863 | − | 0.686863i | −0.274674 | − | 0.961537i | \(-0.588570\pi\) |
0.961537 | + | 0.274674i | \(0.0885701\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2728 | 0.656329 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.67603 | 0.0972534 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.67298 | − | 3.67298i | −0.212414 | − | 0.212414i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.24548 | + | 4.72917i | −0.244705 | + | 0.272585i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.70604i | 0.0980093i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.02741 | −0.173349 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0939 | − | 20.0939i | 1.14682 | − | 1.14682i | 0.159645 | − | 0.987174i | \(-0.448965\pi\) |
0.987174 | − | 0.159645i | \(-0.0510350\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.07657 | + | 8.07657i | 0.459460 | + | 0.459460i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.0652i | 1.47802i | 0.673693 | + | 0.739012i | \(0.264707\pi\) | ||||
−0.673693 | + | 0.739012i | \(0.735293\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.5651 | −0.766743 | −0.383372 | − | 0.923594i | \(-0.625237\pi\) | ||||
−0.383372 | + | 0.923594i | \(0.625237\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.69044 | + | 3.31298i | 0.207933 | + | 0.186666i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.5304 | − | 21.5304i | 1.20927 | − | 1.20927i | 0.238004 | − | 0.971264i | \(-0.423507\pi\) |
0.971264 | − | 0.238004i | \(-0.0764931\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.26077i | 0.350536i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 12.9935i | − | 0.725229i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.26621 | + | 1.26621i | 0.0704541 | + | 0.0704541i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00381 | − | 3.00381i | 0.166622 | − | 0.166622i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.765572i | 0.0423362i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.5725 | − | 1.64772i | 1.68552 | − | 0.0908420i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.85042 | + | 5.85042i | −0.321568 | + | 0.321568i | −0.849369 | − | 0.527800i | \(-0.823017\pi\) |
0.527800 | + | 0.849369i | \(0.323017\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.786692 | + | 0.786692i | −0.0431104 | + | 0.0431104i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.08947 | 0.441975 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1243 | 0.605980 | 0.302990 | − | 0.952994i | \(-0.402015\pi\) | ||||
0.302990 | + | 0.952994i | \(0.402015\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.44474 | − | 8.44474i | 0.458655 | − | 0.458655i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.43018 | + | 8.43018i | −0.456520 | + | 0.456520i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.2792 | + | 2.97859i | −0.986982 | + | 0.160829i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.40689i | 0.183421i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.7722 | − | 16.7722i | 0.900379 | − | 0.900379i | −0.0950894 | − | 0.995469i | \(-0.530314\pi\) |
0.995469 | + | 0.0950894i | \(0.0303137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.9769 | + | 11.9769i | 0.641110 | + | 0.641110i | 0.950828 | − | 0.309718i | \(-0.100235\pi\) |
−0.309718 | + | 0.950828i | \(0.600235\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.85793i | − | 0.152545i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 34.7417i | − | 1.84912i | −0.381041 | − | 0.924558i | \(-0.624434\pi\) | ||
0.381041 | − | 0.924558i | \(-0.375566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.0888 | + | 11.0888i | −0.588533 | + | 0.588533i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.544151 | − | 0.488496i | −0.0287995 | − | 0.0258540i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.2884 | −1.17634 | −0.588168 | − | 0.808739i | \(-0.700150\pi\) | ||||
−0.588168 | + | 0.808739i | \(0.700150\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 22.9768i | − | 1.20930i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.79185 | − | 5.79185i | −0.303993 | − | 0.303993i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.4799 | + | 22.4799i | −1.17665 | + | 1.17665i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35.3887 | −1.84728 | −0.923639 | − | 0.383264i | \(-0.874800\pi\) | ||||
−0.923639 | + | 0.383264i | \(0.874800\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.33055i | 0.381613i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.7269 | − | 9.62974i | −0.556912 | − | 0.499951i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.16397 | + | 6.16397i | 0.319158 | + | 0.319158i | 0.848444 | − | 0.529285i | \(-0.177540\pi\) |
−0.529285 | + | 0.848444i | \(0.677540\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1585 | −0.627862 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.6757 | 0.549827 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.14409 | + | 7.14409i | −0.366967 | + | 0.366967i | −0.866370 | − | 0.499403i | \(-0.833553\pi\) |
0.499403 | + | 0.866370i | \(0.333553\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.3373 | + | 13.3373i | 0.683291 | + | 0.683291i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.8856 | 0.811718 | 0.405859 | − | 0.913936i | \(-0.366972\pi\) | ||||
0.405859 | + | 0.913936i | \(0.366972\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.447334 | + | 8.30001i | 0.0227982 | + | 0.423007i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.69851 | − | 1.69851i | −0.0863401 | − | 0.0863401i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.30347 | + | 3.30347i | 0.167493 | + | 0.167493i | 0.785876 | − | 0.618384i | \(-0.212212\pi\) |
−0.618384 | + | 0.785876i | \(0.712212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.502342i | − | 0.0254045i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.4590i | − | 0.628472i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.3460 | − | 18.3460i | −0.923088 | − | 0.923088i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0837 | − | 11.0837i | −0.556274 | − | 0.556274i | 0.371971 | − | 0.928244i | \(-0.378682\pi\) |
−0.928244 | + | 0.371971i | \(0.878682\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.922522 | + | 17.1168i | 0.0461839 | + | 0.856914i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.6471 | −0.631566 | −0.315783 | − | 0.948831i | \(-0.602267\pi\) | ||||
−0.315783 | + | 0.948831i | \(0.602267\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.3749 | + | 14.3749i | 0.716066 | + | 0.716066i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.32544 | + | 1.32544i | −0.0658618 | + | 0.0658618i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.86467 | −0.0924284 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.39999 | 0.316459 | 0.158230 | − | 0.987402i | \(-0.449421\pi\) | ||||
0.158230 | + | 0.987402i | \(0.449421\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.07153 | − | 3.07153i | −0.151507 | − | 0.151507i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.8402 | − | 10.6292i | −0.582617 | − | 0.523028i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 26.2687i | − | 1.28948i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.33183 | −0.114190 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.92319 | + | 3.92319i | −0.191660 | + | 0.191660i | −0.796413 | − | 0.604753i | \(-0.793272\pi\) |
0.604753 | + | 0.796413i | \(0.293272\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.9120 | − | 19.9120i | −0.970449 | − | 0.970449i | 0.0291264 | − | 0.999576i | \(-0.490727\pi\) |
−0.999576 | + | 0.0291264i | \(0.990727\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.5721i | 0.562655i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.410822 | 0.0199278 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.17978 | + | 2.85455i | 0.153880 | + | 0.138142i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.38704 | − | 3.38704i | 0.163528 | − | 0.163528i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 23.6983i | − | 1.14151i | −0.821122 | − | 0.570753i | \(-0.806651\pi\) | ||
0.821122 | − | 0.570753i | \(-0.193349\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.8198i | − | 1.24082i | −0.784278 | − | 0.620410i | \(-0.786966\pi\) | ||
0.784278 | − | 0.620410i | \(-0.213034\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.95114 | − | 4.95114i | −0.237389 | − | 0.237389i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.32666 | + | 8.32666i | −0.398318 | + | 0.398318i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.7981i | 0.658548i | 0.944234 | + | 0.329274i | \(0.106804\pi\) | ||||
−0.944234 | + | 0.329274i | \(0.893196\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.752353 | − | 6.95945i | −0.0358263 | − | 0.331402i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.61155 | + | 9.61155i | −0.456658 | + | 0.456658i | −0.897557 | − | 0.440898i | \(-0.854660\pi\) |
0.440898 | + | 0.897557i | \(0.354660\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.5372 | + | 10.5372i | −0.499510 | + | 0.499510i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.3618 | 0.679288 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.2681 | −1.28686 | −0.643430 | − | 0.765505i | \(-0.722489\pi\) | ||||
−0.643430 | + | 0.765505i | \(0.722489\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.68770 | + | 8.68770i | −0.409088 | + | 0.409088i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.31171 | + | 6.31171i | −0.296550 | + | 0.296550i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.1530 | − | 0.762782i | 0.663501 | − | 0.0357598i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 15.7041i | − | 0.734607i | −0.930101 | − | 0.367303i | \(-0.880281\pi\) | ||
0.930101 | − | 0.367303i | \(-0.119719\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.195435 | − | 0.195435i | 0.00912214 | − | 0.00912214i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.60225 | + | 8.60225i | 0.400647 | + | 0.400647i | 0.878461 | − | 0.477814i | \(-0.158571\pi\) |
−0.477814 | + | 0.878461i | \(0.658571\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.85673i | − | 0.0862897i | −0.999069 | − | 0.0431449i | \(-0.986262\pi\) | ||
0.999069 | − | 0.0431449i | \(-0.0137377\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 13.3335i | − | 0.618327i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.0605 | + | 12.0605i | −0.558093 | + | 0.558093i | −0.928764 | − | 0.370671i | \(-0.879128\pi\) |
0.370671 | + | 0.928764i | \(0.379128\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.49661 | − | 7.62758i | −0.392337 | − | 0.352209i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.24911 | −0.380099 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4.02593i | − | 0.185112i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.80966 | − | 6.80966i | −0.312448 | − | 0.312448i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.85262 | − | 3.85262i | 0.176399 | − | 0.176399i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.9496 | −0.683063 | −0.341531 | − | 0.939870i | \(-0.610946\pi\) | ||||
−0.341531 | + | 0.939870i | \(0.610946\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.17959i | 0.144977i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.21236 | − | 3.57835i | 0.146168 | − | 0.162821i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.4504 | + | 17.4504i | 0.792383 | + | 0.792383i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.67317 | −0.121133 | −0.0605664 | − | 0.998164i | \(-0.519291\pi\) | ||||
−0.0605664 | + | 0.998164i | \(0.519291\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.6425 | 0.797823 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.71425 | − | 7.71425i | 0.348139 | − | 0.348139i | −0.511277 | − | 0.859416i | \(-0.670827\pi\) |
0.859416 | + | 0.511277i | \(0.170827\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.730041 | + | 0.730041i | 0.0328794 | + | 0.0328794i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.14166 | −0.141207 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.1026 | − | 1.19123i | 0.991437 | − | 0.0534341i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.9644 | + | 10.9644i | 0.490835 | + | 0.490835i | 0.908569 | − | 0.417734i | \(-0.137176\pi\) |
−0.417734 | + | 0.908569i | \(0.637176\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.0881 | + | 15.0881i | 0.674086 | + | 0.674086i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.3842i | 0.730533i | 0.930903 | + | 0.365267i | \(0.119022\pi\) | ||||
−0.930903 | + | 0.365267i | \(0.880978\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.19790i | − | 0.142305i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.41689 | + | 3.41689i | 0.151749 | + | 0.151749i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.7512 | − | 18.7512i | −0.831133 | − | 0.831133i | 0.156539 | − | 0.987672i | \(-0.449966\pi\) |
−0.987672 | + | 0.156539i | \(0.949966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 44.8077 | − | 2.41494i | 1.98218 | − | 0.106831i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.47895 | −0.286053 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.1392 | − | 15.1392i | −0.667113 | − | 0.667113i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.7145 | + | 13.7145i | −0.603163 | + | 0.603163i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.1854 | 0.666564 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.36154 | 0.191083 | 0.0955413 | − | 0.995425i | \(-0.469542\pi\) | ||||
0.0955413 | + | 0.995425i | \(0.469542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.7720 | − | 28.7720i | −1.25811 | − | 1.25811i | −0.951994 | − | 0.306118i | \(-0.900970\pi\) |
−0.306118 | − | 0.951994i | \(-0.599030\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.92643 | + | 2.62711i | 0.127720 | + | 0.114657i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.96601i | 0.0856409i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.6966 | −0.856373 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.25247 | − | 4.25247i | 0.184542 | − | 0.184542i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.8141 | + | 14.8141i | 0.641668 | + | 0.641668i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.3559i | 1.05300i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.41987 | 0.147578 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.35625 | − | 9.13953i | 0.316856 | − | 0.393668i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.4795 | + | 11.4795i | −0.493541 | + | 0.493541i | −0.909420 | − | 0.415879i | \(-0.863474\pi\) |
0.415879 | + | 0.909420i | \(0.363474\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.450130i | 0.0193169i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.43503i | − | 0.0614701i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.5701 | + | 27.5701i | 1.17881 | + | 1.17881i | 0.980047 | + | 0.198764i | \(0.0636928\pi\) |
0.198764 | + | 0.980047i | \(0.436307\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.14204 | + | 1.14204i | −0.0487409 | + | 0.0487409i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 24.2019i | − | 1.03103i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.97085 | + | 36.5679i | 0.0838090 | + | 1.55502i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.47462 | − | 1.47462i | 0.0625942 | − | 0.0625942i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.84102 | − | 7.84102i | 0.332235 | − | 0.332235i | −0.521200 | − | 0.853435i | \(-0.674515\pi\) |
0.853435 | + | 0.521200i | \(0.174515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.86492 | −0.290355 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.463235 | 0.0195578 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.5300 | − | 20.5300i | 0.865238 | − | 0.865238i | −0.126703 | − | 0.991941i | \(-0.540439\pi\) |
0.991941 | + | 0.126703i | \(0.0404395\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.8293 | + | 15.8293i | −0.665944 | + | 0.665944i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.64192 | − | 0.142388i | 0.110950 | − | 0.00597972i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 8.26625i | − | 0.346539i | −0.984874 | − | 0.173270i | \(-0.944567\pi\) | ||
0.984874 | − | 0.173270i | \(-0.0554332\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.1033 | + | 11.1033i | −0.464659 | + | 0.464659i | −0.900179 | − | 0.435520i | \(-0.856565\pi\) |
0.435520 | + | 0.900179i | \(0.356565\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.2817 | − | 17.2817i | −0.721955 | − | 0.721955i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.70158i | 0.112664i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.00276i | 0.0417454i | 0.999782 | + | 0.0208727i | \(0.00664447\pi\) | ||||
−0.999782 | + | 0.0208727i | \(0.993356\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.8328 | + | 15.8328i | −0.657991 | + | 0.657991i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.7689 | + | 27.5908i | −1.02759 | + | 1.14466i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.13176 | 0.378199 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.35708i | 0.221488i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.42198 | − | 2.42198i | −0.0999658 | − | 0.0999658i | 0.655355 | − | 0.755321i | \(-0.272519\pi\) |
−0.755321 | + | 0.655355i | \(0.772519\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.5880 | − | 32.5880i | 1.34277 | − | 1.34277i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.0249 | −0.782582 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.2544i | 0.913881i | 0.889497 | + | 0.456940i | \(0.151055\pi\) | ||||
−0.889497 | + | 0.456940i | \(0.848945\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.01999 | + | 0.915666i | 0.0418155 | + | 0.0375387i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.99117 | − | 3.99117i | −0.163348 | − | 0.163348i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.97729 | 0.285085 | 0.142542 | − | 0.989789i | \(-0.454472\pi\) | ||||
0.142542 | + | 0.989789i | \(0.454472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.75706 | 0.397999 | 0.198999 | − | 0.980000i | \(-0.436231\pi\) | ||||
0.198999 | + | 0.980000i | \(0.436231\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.05161 | − | 3.05161i | 0.124271 | − | 0.124271i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.8566 | + | 10.8566i | 0.441383 | + | 0.441383i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.646351 | −0.0262346 | −0.0131173 | − | 0.999914i | \(-0.504175\pi\) | ||||
−0.0131173 | + | 0.999914i | \(0.504175\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.531884 | + | 9.86878i | 0.0215530 | + | 0.399903i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.3856 | + | 23.3856i | 0.946082 | + | 0.946082i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.8864 | − | 22.8864i | −0.924372 | − | 0.924372i | 0.0729627 | − | 0.997335i | \(-0.476755\pi\) |
−0.997335 | + | 0.0729627i | \(0.976755\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 13.7408i | − | 0.554084i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.2900i | 1.13891i | 0.822022 | + | 0.569456i | \(0.192846\pi\) | ||||
−0.822022 | + | 0.569456i | \(0.807154\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.0007 | − | 27.0007i | −1.08525 | − | 1.08525i | −0.996010 | − | 0.0892388i | \(-0.971557\pi\) |
−0.0892388 | − | 0.996010i | \(-0.528443\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.28519 | + | 1.28519i | 0.0515728 | + | 0.0515728i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.0030 | − | 1.13197i | 0.841468 | − | 0.0453514i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.3586 | 0.614345 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.67843 | − | 7.67843i | −0.306647 | − | 0.306647i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.217431 | + | 0.217431i | −0.00866956 | + | 0.00866956i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.2622 | −1.24453 | −0.622265 | − | 0.782807i | \(-0.713787\pi\) | ||||
−0.622265 | + | 0.782807i | \(0.713787\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.6710 | −0.781851 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.0002 | − | 25.0002i | −0.992104 | − | 0.992104i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.5845 | − | 12.5437i | −0.617481 | − | 0.497000i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.36612i | 0.330959i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.0504 | 0.515458 | 0.257729 | − | 0.966217i | \(-0.417026\pi\) | ||||
0.257729 | + | 0.966217i | \(0.417026\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.786696 | − | 0.786696i | 0.0310242 | − | 0.0310242i | −0.691424 | − | 0.722449i | \(-0.743017\pi\) |
0.722449 | + | 0.691424i | \(0.243017\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.18379 | + | 3.18379i | 0.125362 | + | 0.125362i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.9721i | 0.903125i | 0.892239 | + | 0.451563i | \(0.149133\pi\) | ||||
−0.892239 | + | 0.451563i | \(0.850867\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0795 | 0.395656 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.5722 | + | 14.0046i | −0.492744 | + | 0.548883i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.7129 | + | 11.7129i | −0.458362 | + | 0.458362i | −0.898118 | − | 0.439756i | \(-0.855065\pi\) |
0.439756 | + | 0.898118i | \(0.355065\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.3539i | 0.912511i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.9603i | 0.661685i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.8441 | − | 28.8441i | −1.12361 | − | 1.12361i | −0.991195 | − | 0.132413i | \(-0.957728\pi\) |
−0.132413 | − | 0.991195i | \(-0.542272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5775 | + | 20.5775i | −0.800371 | + | 0.800371i | −0.983153 | − | 0.182782i | \(-0.941490\pi\) |
0.182782 | + | 0.983153i | \(0.441490\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 0.789896i | − | 0.0306770i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.72923 | − | 32.0848i | −0.0670567 | − | 1.24420i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.80077 | + | 4.80077i | −0.185887 | + | 0.185887i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.9526 | + | 10.9526i | −0.423453 | + | 0.423453i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.70694 | −0.104500 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.3585 | 0.746215 | 0.373108 | − | 0.927788i | \(-0.378292\pi\) | ||||
0.373108 | + | 0.927788i | \(0.378292\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.05104 | + | 1.05104i | −0.0404547 | + | 0.0404547i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.0458 | + | 26.0458i | −1.00102 | + | 1.00102i | −0.00102364 | + | 0.999999i | \(0.500326\pi\) |
−0.999999 | + | 0.00102364i | \(0.999674\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.87464 | − | 34.7828i | −0.0719420 | − | 1.33484i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00245i | 0.230014i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.8826 | − | 21.8826i | 0.837315 | − | 0.837315i | −0.151189 | − | 0.988505i | \(-0.548310\pi\) |
0.988505 | + | 0.151189i | \(0.0483103\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.75746 | + | 5.75746i | 0.219981 | + | 0.219981i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.38133i | − | 0.129006i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 15.5713i | − | 0.593218i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.1294 | + | 12.1294i | −0.461424 | + | 0.461424i | −0.899122 | − | 0.437698i | \(-0.855794\pi\) |
0.437698 | + | 0.899122i | \(0.355794\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.29978 | + | 2.96228i | 0.125348 | + | 0.112528i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.37093 | 0.165799 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.02607i | 0.0767429i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.06518 | − | 2.06518i | −0.0781125 | − | 0.0781125i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.76393 | + | 1.76393i | −0.0666225 | + | 0.0666225i | −0.739633 | − | 0.673010i | \(-0.765001\pi\) |
0.673010 | + | 0.739633i | \(0.265001\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.20815 | 0.271861 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 21.6914i | − | 0.816947i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.01531 | + | 3.35885i | −0.113402 | + | 0.126322i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.0457 | + | 24.0457i | 0.903055 | + | 0.903055i | 0.995699 | − | 0.0926439i | \(-0.0295318\pi\) |
−0.0926439 | + | 0.995699i | \(0.529532\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.8414 | −0.519094 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.9286 | −0.484178 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.34887 | + | 6.34887i | −0.237434 | + | 0.237434i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.54272 | − | 5.54272i | −0.206997 | − | 0.206997i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.8470 | −0.814754 | −0.407377 | − | 0.913260i | \(-0.633556\pi\) | ||||
−0.407377 | + | 0.913260i | \(0.633556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.62635 | + | 30.1760i | 0.0605685 | + | 1.12381i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.9864 | + | 12.9864i | 0.482971 | + | 0.482971i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.92613 | − | 3.92613i | −0.145813 | − | 0.145813i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.6131i | 1.58043i | 0.612829 | + | 0.790216i | \(0.290031\pi\) | ||||
−0.612829 | + | 0.790216i | \(0.709969\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.469446 | − | 0.469446i | −0.0173631 | − | 0.0173631i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.0115 | − | 27.0115i | −0.997693 | − | 0.997693i | 0.00230393 | − | 0.999997i | \(-0.499267\pi\) |
−0.999997 | + | 0.00230393i | \(0.999267\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.41026 | + | 13.0452i | 0.0520180 | + | 0.481180i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.23314 | 0.266436 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.43265 | + | 1.43265i | 0.0527008 | + | 0.0527008i | 0.732966 | − | 0.680265i | \(-0.238135\pi\) |
−0.680265 | + | 0.732966i | \(0.738135\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.0931 | + | 13.0931i | −0.480986 | + | 0.480986i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.5309 | 0.789892 | 0.394946 | − | 0.918704i | \(-0.370763\pi\) | ||||
0.394946 | + | 0.918704i | \(0.370763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.9206 | −0.986293 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.90941 | − | 9.90941i | −0.362566 | − | 0.362566i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.9652 | − | 25.5817i | 0.839132 | − | 0.934735i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.47866i | 0.163429i | 0.996656 | + | 0.0817143i | \(0.0260395\pi\) | ||||
−0.996656 | + | 0.0817143i | \(0.973960\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −23.0197 | −0.838883 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.8311 | − | 11.8311i | 0.430576 | − | 0.430576i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.9860 | − | 13.9860i | −0.508329 | − | 0.508329i | 0.405684 | − | 0.914013i | \(-0.367033\pi\) |
−0.914013 | + | 0.405684i | \(0.867033\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.04624i | 0.110572i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.8043 | −0.971653 | −0.485827 | − | 0.874055i | \(-0.661481\pi\) | ||||
−0.485827 | + | 0.874055i | \(0.661481\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.35310 | + | 1.50726i | −0.0489854 | + | 0.0545664i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.366336 | + | 0.366336i | −0.0132449 | + | 0.0132449i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 17.1873i | − | 0.620599i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.2390i | − | 1.12651i | −0.826285 | − | 0.563253i | \(-0.809550\pi\) | ||
0.826285 | − | 0.563253i | \(-0.190450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.63852 | − | 9.63852i | −0.347123 | − | 0.347123i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.9282 | + | 21.9282i | −0.788703 | + | 0.788703i | −0.981282 | − | 0.192578i | \(-0.938315\pi\) |
0.192578 | + | 0.981282i | \(0.438315\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10.5731i | − | 0.379799i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.93926 | + | 0.158413i | −0.105446 | + | 0.00568305i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.5835 | − | 33.5835i | 1.20325 | − | 1.20325i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.91499 | + | 9.91499i | −0.354786 | + | 0.354786i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.73546 | −0.133495 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.4626 | 0.551885 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.9965 | − | 33.9965i | 1.21184 | − | 1.21184i | 0.241424 | − | 0.970420i | \(-0.422385\pi\) |
0.970420 | − | 0.241424i | \(-0.0776145\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.15967 | − | 4.15967i | 0.148088 | − | 0.148088i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.5515 | − | 1.70049i | 1.12184 | − | 0.0604624i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.61580i | 0.163912i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.22159 | + | 7.22159i | −0.256123 | + | 0.256123i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.75244 | − | 4.75244i | −0.168340 | − | 0.168340i | 0.617909 | − | 0.786249i | \(-0.287980\pi\) |
−0.786249 | + | 0.617909i | \(0.787980\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.19838i | 0.113151i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.94992i | 0.280897i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.1003 | + | 20.1003i | −0.709323 | + | 0.709323i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.02145 | + | 6.70748i | −0.212228 | + | 0.236408i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.2984 | −0.362521 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 32.4123i | − | 1.13956i | −0.821798 | − | 0.569778i | \(-0.807029\pi\) | ||
0.821798 | − | 0.569778i | \(-0.192971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.225151 | − | 0.225151i | −0.00790612 | − | 0.00790612i | 0.703143 | − | 0.711049i | \(-0.251780\pi\) |
−0.711049 | + | 0.703143i | \(0.751780\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.41212 | + | 5.41212i | −0.189811 | + | 0.189811i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.0702 | −1.15840 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.5628i | 0.544473i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.05121 | − | 5.62670i | 0.176504 | − | 0.196613i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.0047 | − | 37.0047i | −1.29147 | − | 1.29147i | −0.933875 | − | 0.357599i | \(-0.883595\pi\) |
−0.357599 | − | 0.933875i | \(-0.616405\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.21299 | 0.0422821 | 0.0211411 | − | 0.999777i | \(-0.493270\pi\) | ||||
0.0211411 | + | 0.999777i | \(0.493270\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.49126 | −0.0867345 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.1226 | + | 22.1226i | −0.769278 | + | 0.769278i | −0.977979 | − | 0.208701i | \(-0.933076\pi\) |
0.208701 | + | 0.977979i | \(0.433076\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.0435 | + | 27.0435i | 0.939258 | + | 0.939258i | 0.998258 | − | 0.0589998i | \(-0.0187911\pi\) |
−0.0589998 | + | 0.998258i | \(0.518791\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.6067 | 1.02704 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.207941 | − | 1.92350i | −0.00720472 | − | 0.0666454i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.2820 | − | 28.2820i | −0.978740 | − | 0.978740i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.02983 | − | 5.02983i | −0.173856 | − | 0.173856i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.8066i | 0.649277i | 0.945838 | + | 0.324639i | \(0.105243\pi\) | ||||
−0.945838 | + | 0.324639i | \(0.894757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.0463i | 0.518839i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.39768 | − | 9.39768i | −0.323673 | − | 0.323673i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.40483 | − | 6.40483i | −0.220333 | − | 0.220333i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.16628 | − | 21.6397i | −0.0400740 | − | 0.743549i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.2747 | −0.386947 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.42984 | − | 1.42984i | −0.0490141 | − | 0.0490141i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.4226 | − | 13.4226i | 0.459581 | − | 0.459581i | −0.438937 | − | 0.898518i | \(-0.644645\pi\) |
0.898518 | + | 0.438937i | \(0.144645\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.1445 | 0.415334 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.2069 | −0.485297 | −0.242649 | − | 0.970114i | \(-0.578016\pi\) | ||||
−0.242649 | + | 0.970114i | \(0.578016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.7166 | + | 12.7166i | 0.433886 | + | 0.433886i | 0.889948 | − | 0.456062i | \(-0.150741\pi\) |
−0.456062 | + | 0.889948i | \(0.650741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.9563 | + | 14.4324i | −0.441549 | + | 0.491855i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 0.417666i | − | 0.0142175i | −0.999975 | − | 0.00710875i | \(-0.997737\pi\) | ||
0.999975 | − | 0.00710875i | \(-0.00226281\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.4644 | −0.967818 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.9668 | + | 11.9668i | −0.406414 | + | 0.406414i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.4040 | − | 16.4040i | −0.556466 | − | 0.556466i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 12.3338i | − | 0.417914i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.1657 | 0.445592 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.9377 | − | 21.4893i | −0.809241 | − | 0.726472i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.3450 | + | 37.3450i | −1.26105 | + | 1.26105i | −0.310468 | + | 0.950584i | \(0.600486\pi\) |
−0.950584 | + | 0.310468i | \(0.899514\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.6272i | 0.560821i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 40.8076i | − | 1.37484i | −0.726259 | − | 0.687421i | \(-0.758743\pi\) | ||
0.726259 | − | 0.687421i | \(-0.241257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.1593 | − | 38.1593i | −1.28416 | − | 1.28416i | −0.938277 | − | 0.345886i | \(-0.887579\pi\) |
−0.345886 | − | 0.938277i | \(-0.612421\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.97109 | + | 7.97109i | −0.267945 | + | 0.267945i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.0533i | 1.14340i | 0.820464 | + | 0.571698i | \(0.193715\pi\) | ||||
−0.820464 | + | 0.571698i | \(0.806285\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.68569 | + | 49.8313i | 0.0900750 | + | 1.67129i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.18514 | + | 1.18514i | −0.0397035 | + | 0.0397035i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 53.0153 | − | 53.0153i | 1.77409 | − | 1.77409i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.41042 | −0.214277 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.19438 | 0.173435 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.7888 | − | 18.7888i | 0.626640 | − | 0.626640i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.06482 | − | 1.06482i | 0.0354741 | − | 0.0354741i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.342023 | − | 6.34603i | −0.0113818 | − | 0.211183i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 0.843750i | − | 0.0280472i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.29406 | − | 1.29406i | 0.0429685 | − | 0.0429685i | −0.685296 | − | 0.728265i | \(-0.740327\pi\) |
0.728265 | + | 0.685296i | \(0.240327\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.20635 | − | 1.20635i | −0.0400121 | − | 0.0400121i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.1193i | 0.699715i | 0.936803 | + | 0.349857i | \(0.113770\pi\) | ||||
−0.936803 | + | 0.349857i | \(0.886230\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23.4880i | − | 0.777339i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.14070 | − | 2.14070i | 0.0707694 | − | 0.0707694i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.0204 | − | 24.5292i | 0.727178 | − | 0.810027i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.462843 | −0.0152678 | −0.00763389 | − | 0.999971i | \(-0.502430\pi\) | ||||
−0.00763389 | + | 0.999971i | \(0.502430\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.4171i | 0.936374i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.9068 | + | 16.9068i | 0.556494 | + | 0.556494i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.16934 | − | 1.16934i | 0.0384476 | − | 0.0384476i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.4220 | −0.375148 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 7.13095i | − | 0.233959i | −0.993134 | − | 0.116980i | \(-0.962679\pi\) | ||
0.993134 | − | 0.116980i | \(-0.0373212\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.4366 | + | 35.3301i | −0.931973 | + | 1.15790i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.4309 | − | 18.4309i | −0.603400 | − | 0.603400i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.868315 | −0.0283969 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.02900 | 0.164290 | 0.0821452 | − | 0.996620i | \(-0.473823\pi\) | ||||
0.0821452 | + | 0.996620i | \(0.473823\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.59195 | − | 9.59195i | 0.313022 | − | 0.313022i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.2671 | + | 38.2671i | 1.24747 | + | 1.24747i | 0.956833 | + | 0.290639i | \(0.0938679\pi\) |
0.290639 | + | 0.956833i | \(0.406132\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.3235 | −0.433873 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.95217 | + | 0.266900i | −0.161094 | + | 0.00868226i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.42949 | + | 4.42949i | 0.143939 | + | 0.143939i | 0.775404 | − | 0.631465i | \(-0.217546\pi\) |
−0.631465 | + | 0.775404i | \(0.717546\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.2745 | + | 34.2745i | 1.11260 | + | 1.11260i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.4486i | 0.987363i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 40.8007i | − | 1.32166i | −0.750534 | − | 0.660832i | \(-0.770204\pi\) | ||
0.750534 | − | 0.660832i | \(-0.229796\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.3939 | + | 32.3939i | 1.04824 | + | 1.04824i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.42703 | − | 4.42703i | −0.143106 | − | 0.143106i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.618504 | − | 11.4760i | −0.0199725 | − | 0.370578i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.5985 | 0.632208 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.18783 | + | 9.18783i | 0.296074 | + | 0.296074i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.6780 | − | 29.6780i | 0.955370 | − | 0.955370i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.09367 | 0.0673278 | 0.0336639 | − | 0.999433i | \(-0.489282\pi\) | ||||
0.0336639 | + | 0.999433i | \(0.489282\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.79070 | −0.0575255 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.1592 | + | 12.1592i | 0.390208 | + | 0.390208i | 0.874762 | − | 0.484554i | \(-0.161018\pi\) |
−0.484554 | + | 0.874762i | \(0.661018\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.59092 | − | 4.12136i | −0.147178 | − | 0.132125i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.24803i | 0.136046i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.8415 | 1.46660 | 0.733300 | − | 0.679906i | \(-0.237979\pi\) | ||||
0.733300 | + | 0.679906i | \(0.237979\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.42173 | + | 9.42173i | −0.301120 | + | 0.301120i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.541341 | − | 0.541341i | −0.0172837 | − | 0.0172837i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 7.70439i | − | 0.245732i | −0.992423 | − | 0.122866i | \(-0.960791\pi\) | ||
0.992423 | − | 0.122866i | \(-0.0392085\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.6615 | 1.13627 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.4529 | + | 22.7832i | −0.651024 | + | 0.725196i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.08709 | − | 3.08709i | 0.0981639 | − | 0.0981639i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.61965i | 0.210280i | 0.994457 | + | 0.105140i | \(0.0335291\pi\) | ||||
−0.994457 | + | 0.105140i | \(0.966471\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.27375i | − | 0.262559i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.48130 | + | 7.48130i | 0.237173 | + | 0.237173i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.8831 | − | 20.8831i | 0.661376 | − | 0.661376i | −0.294329 | − | 0.955704i | \(-0.595096\pi\) |
0.955704 | + | 0.294329i | \(0.0950960\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.11255i | − | 0.0351995i |
(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 | 1344.2.u.a.1231.12 | 64 | ||
4.3 | odd | 2 | 336.2.u.a.139.6 | yes | 64 | ||
7.6 | odd | 2 | inner | 1344.2.u.a.1231.21 | 64 | ||
16.3 | odd | 4 | inner | 1344.2.u.a.559.21 | 64 | ||
16.13 | even | 4 | 336.2.u.a.307.5 | yes | 64 | ||
28.27 | even | 2 | 336.2.u.a.139.5 | ✓ | 64 | ||
112.13 | odd | 4 | 336.2.u.a.307.6 | yes | 64 | ||
112.83 | even | 4 | inner | 1344.2.u.a.559.12 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.u.a.139.5 | ✓ | 64 | 28.27 | even | 2 | ||
336.2.u.a.139.6 | yes | 64 | 4.3 | odd | 2 | ||
336.2.u.a.307.5 | yes | 64 | 16.13 | even | 4 | ||
336.2.u.a.307.6 | yes | 64 | 112.13 | odd | 4 | ||
1344.2.u.a.559.12 | 64 | 112.83 | even | 4 | inner | ||
1344.2.u.a.559.21 | 64 | 16.3 | odd | 4 | inner | ||
1344.2.u.a.1231.12 | 64 | 1.1 | even | 1 | trivial | ||
1344.2.u.a.1231.21 | 64 | 7.6 | odd | 2 | inner |