Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1519,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1519");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.o (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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1519.19 | ||
Character | \(\chi\) | \(=\) | 3344.1519 |
Dual form | 3344.2.o.a.1519.20 |
$q$-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 \(\left(\mathbb{Z}/3344\mathbb{Z}\right)^\times\).
\(n\) | \(705\) | \(837\) | \(2433\) | \(2927\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.711963 | 0.411052 | 0.205526 | − | 0.978652i | \(-0.434109\pi\) | ||||
0.205526 | + | 0.978652i | \(0.434109\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.887508 | 0.396906 | 0.198453 | − | 0.980110i | \(-0.436408\pi\) | ||||
0.198453 | + | 0.980110i | \(0.436408\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.32992i | 0.880627i | 0.897844 | + | 0.440313i | \(0.145133\pi\) | ||||
−0.897844 | + | 0.440313i | \(0.854867\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.49311 | −0.831036 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0550862i | 0.0152782i | 0.999971 | + | 0.00763908i | \(0.00243162\pi\) | ||||
−0.999971 | + | 0.00763908i | \(0.997568\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.631873 | 0.163149 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.537779 | −0.130431 | −0.0652153 | − | 0.997871i | \(-0.520773\pi\) | ||||
−0.0652153 | + | 0.997871i | \(0.520773\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.30891 | − | 2.83745i | −0.759116 | − | 0.650956i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.65882i | 0.361983i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.34463i | − | 0.488889i | −0.969663 | − | 0.244445i | \(-0.921394\pi\) | ||
0.969663 | − | 0.244445i | \(-0.0786057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.21233 | −0.842466 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.91089 | −0.752651 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.27761i | − | 0.980028i | −0.871715 | − | 0.490014i | \(-0.836992\pi\) | ||
0.871715 | − | 0.490014i | \(-0.163008\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.62073 | −0.829908 | −0.414954 | − | 0.909842i | \(-0.636202\pi\) | ||||
−0.414954 | + | 0.909842i | \(0.636202\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.711963i | − | 0.123937i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.06782i | 0.349526i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.51560i | 0.413562i | 0.978387 | + | 0.206781i | \(0.0662987\pi\) | ||||
−0.978387 | + | 0.206781i | \(0.933701\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0392193i | 0.00628012i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 12.4472i | − | 1.94392i | −0.235144 | − | 0.971961i | \(-0.575556\pi\) | ||
0.235144 | − | 0.971961i | \(-0.424444\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.53266i | 1.45372i | 0.686787 | + | 0.726858i | \(0.259020\pi\) | ||||
−0.686787 | + | 0.726858i | \(0.740980\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.21265 | −0.329843 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.22413i | − | 0.616153i | −0.951362 | − | 0.308077i | \(-0.900315\pi\) | ||
0.951362 | − | 0.308077i | \(-0.0996853\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.57148 | 0.224497 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.382879 | −0.0536138 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.95065i | − | 0.680023i | −0.940421 | − | 0.340012i | \(-0.889569\pi\) | ||
0.940421 | − | 0.340012i | \(-0.110431\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.887508i | − | 0.119672i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.35582 | − | 2.02016i | −0.312036 | − | 0.267577i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.86465 | −0.893701 | −0.446851 | − | 0.894609i | \(-0.647454\pi\) | ||||
−0.446851 | + | 0.894609i | \(0.647454\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.13712 | −0.913815 | −0.456907 | − | 0.889514i | \(-0.651043\pi\) | ||||
−0.456907 | + | 0.889514i | \(0.651043\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 5.80874i | − | 0.731833i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0488895i | 0.00606399i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.31376 | 0.404840 | 0.202420 | − | 0.979299i | \(-0.435119\pi\) | ||||
0.202420 | + | 0.979299i | \(0.435119\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.66929i | − | 0.200959i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.62601 | 1.02372 | 0.511860 | − | 0.859069i | \(-0.328957\pi\) | ||||
0.511860 | + | 0.859069i | \(0.328957\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.5549 | −1.58648 | −0.793241 | − | 0.608908i | \(-0.791608\pi\) | ||||
−0.793241 | + | 0.608908i | \(0.791608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.99902 | −0.346297 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.32992 | 0.265519 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.6133 | 1.86914 | 0.934569 | − | 0.355781i | \(-0.115785\pi\) | ||||
0.934569 | + | 0.355781i | \(0.115785\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.69492 | 0.521658 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.87134i | − | 0.424935i | −0.977168 | − | 0.212468i | \(-0.931850\pi\) | ||
0.977168 | − | 0.212468i | \(-0.0681500\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.477284 | −0.0517687 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.75746i | − | 0.402842i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.77934i | 0.400609i | 0.979734 | + | 0.200305i | \(0.0641932\pi\) | ||||
−0.979734 | + | 0.200305i | \(0.935807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.128346 | −0.0134544 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.28979 | −0.341135 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.93668 | − | 2.51826i | −0.301297 | − | 0.258368i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 17.5949i | − | 1.78649i | −0.449566 | − | 0.893247i | \(-0.648421\pi\) | ||
0.449566 | − | 0.893247i | \(-0.351579\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.49311i | 0.250567i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.4792 | −1.24172 | −0.620862 | − | 0.783920i | \(-0.713217\pi\) | ||||
−0.620862 | + | 0.783920i | \(0.713217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.55342 | −0.448661 | −0.224331 | − | 0.974513i | \(-0.572020\pi\) | ||||
−0.224331 | + | 0.974513i | \(0.572020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.47221i | 0.143673i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.51152 | 0.822840 | 0.411420 | − | 0.911446i | \(-0.365033\pi\) | ||||
0.411420 | + | 0.911446i | \(0.365033\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.9816i | − | 1.33919i | −0.742726 | − | 0.669595i | \(-0.766468\pi\) | ||
0.742726 | − | 0.669595i | \(-0.233532\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.79101i | 0.169995i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.515718i | 0.0485146i | 0.999706 | + | 0.0242573i | \(0.00772210\pi\) | ||||
−0.999706 | + | 0.0242573i | \(0.992278\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.08088i | − | 0.194043i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.137336i | − | 0.0126967i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.25298i | − | 0.114861i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 8.86192i | − | 0.799053i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.17602 | −0.731285 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.8566 | −1.31831 | −0.659157 | − | 0.752006i | \(-0.729087\pi\) | ||||
−0.659157 | + | 0.752006i | \(0.729087\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.78690i | 0.597553i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 3.47723i | − | 0.303807i | −0.988395 | − | 0.151904i | \(-0.951460\pi\) | ||
0.988395 | − | 0.151904i | \(-0.0485404\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.61103 | − | 7.70949i | 0.573249 | − | 0.668497i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.47095 | −0.298731 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.6343 | −1.07942 | −0.539709 | − | 0.841852i | \(-0.681466\pi\) | ||||
−0.539709 | + | 0.841852i | \(0.681466\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.67797i | 0.396780i | 0.980123 | + | 0.198390i | \(0.0635713\pi\) | ||||
−0.980123 | + | 0.198390i | \(0.936429\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 3.00743i | − | 0.253271i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.0550862 | 0.00460654 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.68392i | − | 0.388979i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.11883 | 0.0922799 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.88000 | 0.481709 | 0.240854 | − | 0.970561i | \(-0.422572\pi\) | ||||
0.240854 | + | 0.970561i | \(0.422572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.3497 | 1.24914 | 0.624570 | − | 0.780969i | \(-0.285274\pi\) | ||||
0.624570 | + | 0.780969i | \(0.285274\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.34074 | 0.108393 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.10094 | −0.329395 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.93139 | −0.393568 | −0.196784 | − | 0.980447i | \(-0.563050\pi\) | ||||
−0.196784 | + | 0.980447i | \(0.563050\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 3.52468i | − | 0.279525i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.46280 | 0.430529 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.5985i | 1.69173i | 0.533398 | + | 0.845864i | \(0.320915\pi\) | ||||
−0.533398 | + | 0.845864i | \(0.679085\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 0.631873i | − | 0.0491912i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.0998 | −1.09107 | −0.545537 | − | 0.838087i | \(-0.683674\pi\) | ||||
−0.545537 | + | 0.838087i | \(0.683674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9970 | 0.999767 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.24947 | + | 7.07407i | 0.630853 | + | 0.540968i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.33072i | 0.329258i | 0.986356 | + | 0.164629i | \(0.0526427\pi\) | ||||
−0.986356 | + | 0.164629i | \(0.947357\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 9.81439i | − | 0.741898i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.88738 | −0.367358 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.1073 | 1.87661 | 0.938304 | − | 0.345812i | \(-0.112396\pi\) | ||||
0.938304 | + | 0.345812i | \(0.112396\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.2246i | − | 0.759991i | −0.924988 | − | 0.379995i | \(-0.875926\pi\) | ||
0.924988 | − | 0.379995i | \(-0.124074\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.08137 | −0.375625 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.23261i | 0.164145i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.537779i | 0.0393263i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 9.11205i | − | 0.662804i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.8356i | 1.07347i | 0.843751 | + | 0.536735i | \(0.180342\pi\) | ||||
−0.843751 | + | 0.536735i | \(0.819658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.0892i | 1.51803i | 0.651073 | + | 0.759015i | \(0.274319\pi\) | ||||
−0.651073 | + | 0.759015i | \(0.725681\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0348075i | 0.00249262i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.6632 | −1.61468 | −0.807342 | − | 0.590083i | \(-0.799095\pi\) | ||||
−0.807342 | + | 0.590083i | \(0.799095\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 17.2587i | − | 1.22344i | −0.791075 | − | 0.611719i | \(-0.790478\pi\) | ||
0.791075 | − | 0.611719i | \(-0.209522\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.35927 | 0.166410 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.2964 | 0.863038 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 11.0470i | − | 0.771553i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.84542i | 0.406285i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.83745 | + | 3.30891i | −0.196271 | + | 0.228882i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.99157 | −0.550162 | −0.275081 | − | 0.961421i | \(-0.588705\pi\) | ||||
−0.275081 | + | 0.961421i | \(0.588705\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.14140 | 0.420802 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.46031i | 0.576988i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 10.7659i | − | 0.730839i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.65059 | −0.652126 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 0.0296242i | − | 0.00199274i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.6863 | −1.11740 | −0.558699 | − | 0.829371i | \(-0.688699\pi\) | ||||
−0.558699 | + | 0.829371i | \(0.688699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.5018 | 0.700120 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.2658 | −1.01322 | −0.506612 | − | 0.862174i | \(-0.669102\pi\) | ||||
−0.506612 | + | 0.862174i | \(0.669102\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.7379 | −0.775664 | −0.387832 | − | 0.921730i | \(-0.626776\pi\) | ||||
−0.387832 | + | 0.921730i | \(0.626776\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.65882 | 0.109142 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.44556 | −0.487775 | −0.243887 | − | 0.969804i | \(-0.578423\pi\) | ||||
−0.243887 | + | 0.969804i | \(0.578423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.74895i | − | 0.244555i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.8280 | 0.768313 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 0.348169i | − | 0.0225212i | −0.999937 | − | 0.0112606i | \(-0.996416\pi\) | ||
0.999937 | − | 0.0112606i | \(-0.00358443\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.85132i | 0.376917i | 0.982081 | + | 0.188458i | \(0.0603490\pi\) | ||||
−0.982081 | + | 0.188458i | \(0.939651\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.0753 | 0.967079 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.39470 | 0.0891041 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.156304 | − | 0.182275i | 0.00994541 | − | 0.0115979i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 2.75625i | − | 0.174670i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.830707i | 0.0524338i | 0.999656 | + | 0.0262169i | \(0.00834605\pi\) | ||||
−0.999656 | + | 0.0262169i | \(0.991654\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.34463 | −0.147406 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.339808 | −0.0212796 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.28344i | 0.391950i | 0.980609 | + | 0.195975i | \(0.0627872\pi\) | ||||
−0.980609 | + | 0.195975i | \(0.937213\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.86114 | −0.364193 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.1577i | 0.814439i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.3376i | 0.637444i | 0.947848 | + | 0.318722i | \(0.103254\pi\) | ||||
−0.947848 | + | 0.318722i | \(0.896746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.39374i | − | 0.269905i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.69075i | 0.164671i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 21.8304i | − | 1.33102i | −0.746387 | − | 0.665512i | \(-0.768213\pi\) | ||
0.746387 | − | 0.665512i | \(-0.231787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.9412i | 1.63656i | 0.574817 | + | 0.818282i | \(0.305073\pi\) | ||||
−0.574817 | + | 0.818282i | \(0.694927\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0913779 | −0.00553044 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.21233i | 0.254013i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.5568 | −1.11497 | −0.557485 | − | 0.830187i | \(-0.688233\pi\) | ||||
−0.557485 | + | 0.830187i | \(0.688233\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.5200 | 0.689684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.5952i | − | 1.46723i | −0.679568 | − | 0.733613i | \(-0.737833\pi\) | ||
0.679568 | − | 0.733613i | \(-0.262167\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.20154i | 0.249756i | 0.992172 | + | 0.124878i | \(0.0398539\pi\) | ||||
−0.992172 | + | 0.124878i | \(0.960146\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.09081 | − | 1.79291i | −0.123849 | − | 0.106203i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.0009 | 1.71187 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7108 | −0.982988 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 12.5269i | − | 0.734342i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.4922i | 0.729802i | 0.931046 | + | 0.364901i | \(0.118897\pi\) | ||||
−0.931046 | + | 0.364901i | \(0.881103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.09243 | −0.354715 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.91089i | 0.226933i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.129157 | 0.00746934 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.2103 | −1.28018 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.88471 | −0.510413 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.33425 | −0.362698 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.5197 | −0.942830 | −0.471415 | − | 0.881911i | \(-0.656257\pi\) | ||||
−0.471415 | + | 0.881911i | \(0.656257\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.24186 | −0.184423 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.94014i | − | 0.450244i | −0.974331 | − | 0.225122i | \(-0.927722\pi\) | ||
0.974331 | − | 0.225122i | \(-0.0722780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.6803 | 0.773258 | 0.386629 | − | 0.922235i | \(-0.373639\pi\) | ||||
0.386629 | + | 0.922235i | \(0.373639\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 5.15530i | − | 0.290468i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 20.8148i | − | 1.16907i | −0.811367 | − | 0.584537i | \(-0.801276\pi\) | ||
0.811367 | − | 0.584537i | \(-0.198724\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.27761 | −0.295489 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.05989 | 0.338230 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.77946 | + | 1.52592i | 0.0990120 | + | 0.0849046i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.232041i | − | 0.0128713i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 9.95435i | − | 0.550477i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.84189 | 0.542601 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.5353 | −0.579072 | −0.289536 | − | 0.957167i | \(-0.593501\pi\) | ||||
−0.289536 | + | 0.957167i | \(0.593501\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 6.27166i | − | 0.343685i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.94098 | 0.160683 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 24.7712i | − | 1.34937i | −0.738105 | − | 0.674686i | \(-0.764279\pi\) | ||
0.738105 | − | 0.674686i | \(-0.235721\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.367172i | 0.0199420i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.62073i | 0.250227i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9708i | 1.07832i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 1.48151i | − | 0.0797617i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.4906i | 1.20736i | 0.797226 | + | 0.603681i | \(0.206300\pi\) | ||||
−0.797226 | + | 0.603681i | \(0.793700\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.2505 | −0.976925 | −0.488462 | − | 0.872585i | \(-0.662442\pi\) | ||||
−0.488462 | + | 0.872585i | \(0.662442\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 0.215436i | − | 0.0114991i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.3802 | 1.77665 | 0.888324 | − | 0.459217i | \(-0.151870\pi\) | ||||
0.888324 | + | 0.459217i | \(0.151870\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.65565 | 0.406320 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 0.892077i | − | 0.0472137i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 23.5969i | − | 1.24540i | −0.782462 | − | 0.622698i | \(-0.786036\pi\) | ||
0.782462 | − | 0.622698i | \(-0.213964\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.89775 | + | 18.7777i | 0.152513 | + | 0.988301i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.711963 | −0.0373684 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.0301 | −0.629683 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.74050i | 0.404051i | 0.979380 | + | 0.202025i | \(0.0647523\pi\) | ||||
−0.979380 | + | 0.202025i | \(0.935248\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 31.0321i | 1.61547i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5346 | 0.598847 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 35.3793i | − | 1.83187i | −0.401323 | − | 0.915936i | \(-0.631450\pi\) | ||
0.401323 | − | 0.915936i | \(-0.368550\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.82102 | −0.300596 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.290724 | 0.0149730 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.5036 | 1.00183 | 0.500917 | − | 0.865496i | \(-0.332996\pi\) | ||||
0.500917 | + | 0.865496i | \(0.332996\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.5774 | −0.541895 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.8221 | −1.57493 | −0.787467 | − | 0.616357i | \(-0.788608\pi\) | ||||
−0.787467 | + | 0.616357i | \(0.788608\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.06782 | 0.105386 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 23.7660i | − | 1.20809i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.3756 | 1.23589 | 0.617946 | − | 0.786220i | \(-0.287965\pi\) | ||||
0.617946 | + | 0.786220i | \(0.287965\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.26089i | 0.0637662i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.47566i | − | 0.124881i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.7444 | 0.741872 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.60268 | −0.481945 | −0.240972 | − | 0.970532i | \(-0.577466\pi\) | ||||
−0.240972 | + | 0.970532i | \(0.577466\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.70681 | − | 5.48887i | 0.235635 | − | 0.274787i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.4337i | 1.41991i | 0.704246 | + | 0.709956i | \(0.251285\pi\) | ||||
−0.704246 | + | 0.709956i | \(0.748715\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.254539i | − | 0.0126795i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.16678 | 0.207049 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.51560 | 0.124694 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.08938i | − | 0.202207i | −0.994876 | − | 0.101103i | \(-0.967763\pi\) | ||
0.994876 | − | 0.101103i | \(-0.0322373\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.99512 | −0.443696 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 15.9941i | − | 0.787017i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3.43585i | − | 0.168659i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.33054i | 0.163097i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 3.79345i | − | 0.185322i | −0.995698 | − | 0.0926611i | \(-0.970463\pi\) | ||
0.995698 | − | 0.0926611i | \(-0.0295373\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 30.3197i | − | 1.47769i | −0.673875 | − | 0.738846i | \(-0.735371\pi\) | ||
0.673875 | − | 0.738846i | \(-0.264629\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.5312i | 0.512046i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.26530 | 0.109883 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 16.6289i | − | 0.804729i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0392193 | 0.00189353 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.0264 | −0.723797 | −0.361899 | − | 0.932217i | \(-0.617871\pi\) | ||||
−0.361899 | + | 0.932217i | \(0.617871\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3689i | 1.21915i | 0.792727 | + | 0.609577i | \(0.208661\pi\) | ||||
−0.792727 | + | 0.609577i | \(0.791339\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 3.33478i | − | 0.159890i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.65277 | + | 7.75817i | −0.318245 | + | 0.371124i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5729 | 1.07735 | 0.538673 | − | 0.842515i | \(-0.318926\pi\) | ||||
0.538673 | + | 0.842515i | \(0.318926\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.91787 | −0.186565 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 15.5170i | − | 0.737233i | −0.929582 | − | 0.368617i | \(-0.879832\pi\) | ||
0.929582 | − | 0.368617i | \(-0.120168\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.35420i | 0.159004i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.18634 | 0.198007 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.5368i | 1.44112i | 0.693391 | + | 0.720561i | \(0.256116\pi\) | ||||
−0.693391 | + | 0.720561i | \(0.743884\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.4472 | −0.586114 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.9284 | 0.513461 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.113908 | −0.00534011 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.49042 | −0.0697188 | −0.0348594 | − | 0.999392i | \(-0.511098\pi\) | ||||
−0.0348594 | + | 0.999392i | \(0.511098\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.10320 | 0.0981688 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.3751 | 0.622939 | 0.311470 | − | 0.950256i | \(-0.399179\pi\) | ||||
0.311470 | + | 0.950256i | \(0.399179\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.12253i | 0.145116i | 0.997364 | + | 0.0725581i | \(0.0231163\pi\) | ||||
−0.997364 | + | 0.0725581i | \(0.976884\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.91972 | −0.135399 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 40.7800i | − | 1.88707i | −0.331268 | − | 0.943537i | \(-0.607477\pi\) | ||
0.331268 | − | 0.943537i | \(-0.392523\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.72078i | 0.356513i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.51097 | −0.161777 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.53266 | 0.438312 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.9382 | + | 11.9523i | 0.639529 | + | 0.548408i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.3425i | 0.565124i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.7350i | 0.627568i | 0.949494 | + | 0.313784i | \(0.101597\pi\) | ||||
−0.949494 | + | 0.313784i | \(0.898403\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.138575 | −0.00631846 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.88931 | 0.176970 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 15.6156i | − | 0.709070i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.9267 | 1.22017 | 0.610083 | − | 0.792338i | \(-0.291136\pi\) | ||||
0.610083 | + | 0.792338i | \(0.291136\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.3774i | 0.695388i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.7745i | 1.25345i | 0.779242 | + | 0.626723i | \(0.215604\pi\) | ||||
−0.779242 | + | 0.626723i | \(0.784396\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.83819i | 0.127826i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.21265i | 0.0994514i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.0979i | 0.901514i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13.0780i | − | 0.585450i | −0.956197 | − | 0.292725i | \(-0.905438\pi\) | ||
0.956197 | − | 0.292725i | \(-0.0945621\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.0385 | −0.448488 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 24.8338i | − | 1.10728i | −0.832755 | − | 0.553642i | \(-0.813238\pi\) | ||
0.832755 | − | 0.553642i | \(-0.186762\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.0754 | −0.492847 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.25336 | 0.410956 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.0888i | 1.24501i | 0.782614 | + | 0.622507i | \(0.213886\pi\) | ||||
−0.782614 | + | 0.622507i | \(0.786114\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 31.5818i | − | 1.39710i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.9408 | + | 11.0970i | 0.571349 | + | 0.489943i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.04119 | −0.178076 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.22413 | −0.185777 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.08331i | 0.135342i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 23.8899i | − | 1.04663i | −0.852138 | − | 0.523317i | \(-0.824694\pi\) | ||
0.852138 | − | 0.523317i | \(-0.175306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.7408 | −1.03811 | −0.519057 | − | 0.854739i | \(-0.673717\pi\) | ||||
−0.519057 | + | 0.854739i | \(0.673717\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 6.98748i | − | 0.304959i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.48494 | 0.108245 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.5027 | 0.760987 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.1143 | 0.742698 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.685668 | 0.0296996 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.55404 | 0.326590 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.8755 | 0.771383 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.57148i | − | 0.0676884i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.19316 | −0.0942913 | −0.0471457 | − | 0.998888i | \(-0.515012\pi\) | ||||
−0.0471457 | + | 0.998888i | \(0.515012\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 7.27956i | − | 0.312396i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 12.4087i | − | 0.531532i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.4939 | −0.448688 | −0.224344 | − | 0.974510i | \(-0.572024\pi\) | ||||
−0.224344 | + | 0.974510i | \(0.572024\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.7936 | 0.759413 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.9750 | + | 17.4631i | −0.637955 | + | 0.743954i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 38.7076i | 1.64601i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.58954i | 0.0674721i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.87419 | −0.164155 | −0.0820773 | − | 0.996626i | \(-0.526155\pi\) | ||||
−0.0820773 | + | 0.996626i | \(0.526155\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.525118 | −0.0222101 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.382879i | 0.0161652i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.7084 | 1.12562 | 0.562812 | − | 0.826585i | \(-0.309719\pi\) | ||||
0.562812 | + | 0.826585i | \(0.309719\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.457703i | 0.0192557i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.9388i | 0.459386i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.8604i | 0.790669i | 0.918537 | + | 0.395335i | \(0.129371\pi\) | ||||
−0.918537 | + | 0.395335i | \(0.870629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.4837i | 0.940914i | 0.882423 | + | 0.470457i | \(0.155911\pi\) | ||||
−0.882423 | + | 0.470457i | \(0.844089\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.5624i | 0.441252i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.87636i | 0.411873i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.3471 | 1.01358 | 0.506791 | − | 0.862069i | \(-0.330832\pi\) | ||||
0.506791 | + | 0.862069i | \(0.330832\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.0147i | 0.623990i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.01991 | 0.374209 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.95065 | −0.205035 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 0.121887i | − | 0.00503940i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.65715i | 0.398593i | 0.979939 | + | 0.199297i | \(0.0638657\pi\) | ||||
−0.979939 | + | 0.199297i | \(0.936134\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.2896 | + | 13.1111i | 0.629996 | + | 0.540234i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.1353 | −0.663719 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.6414 | 1.50468 | 0.752341 | − | 0.658774i | \(-0.228925\pi\) | ||||
0.752341 | + | 0.658774i | \(0.228925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.11203i | − | 0.0455889i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 12.2876i | − | 0.502897i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.63445 | 0.393653 | 0.196827 | − | 0.980438i | \(-0.436936\pi\) | ||||
0.196827 | + | 0.980438i | \(0.436936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.62962i | 0.311219i | 0.987819 | + | 0.155609i | \(0.0497341\pi\) | ||||
−0.987819 | + | 0.155609i | \(0.950266\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.26155 | −0.336436 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.887508 | −0.0360823 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.8697 | −0.928251 | −0.464126 | − | 0.885769i | \(-0.653631\pi\) | ||||
−0.464126 | + | 0.885769i | \(0.653631\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.75458 | 0.354754 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.232692 | 0.00941369 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.2107 | 1.54331 | 0.771657 | − | 0.636039i | \(-0.219428\pi\) | ||||
0.771657 | + | 0.636039i | \(0.219428\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 7.86503i | − | 0.317148i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.6009 | 0.507294 | 0.253647 | − | 0.967297i | \(-0.418370\pi\) | ||||
0.253647 | + | 0.967297i | \(0.418370\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 37.7476i | − | 1.51720i | −0.651554 | − | 0.758602i | \(-0.725883\pi\) | ||
0.651554 | − | 0.758602i | \(-0.274117\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.16959i | 0.367963i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.80556 | −0.352787 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.8054 | 0.552215 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.02016 | + | 2.35582i | −0.0806774 | + | 0.0940824i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.35284i | − | 0.0539411i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 35.1749i | − | 1.40029i | −0.714000 | − | 0.700146i | \(-0.753118\pi\) | ||
0.714000 | − | 0.700146i | \(-0.246882\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.68970 | −0.226145 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.1854 | −0.523246 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0865668i | 0.00342990i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21.5056 | −0.850748 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.8964i | 1.49682i | 0.663238 | + | 0.748409i | \(0.269182\pi\) | ||||
−0.663238 | + | 0.748409i | \(0.730818\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.8841i | 1.45457i | 0.686337 | + | 0.727284i | \(0.259217\pi\) | ||||
−0.686337 | + | 0.727284i | \(0.740783\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.02343i | 0.237172i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.5863i | 1.51698i | 0.651682 | + | 0.758492i | \(0.274063\pi\) | ||||
−0.651682 | + | 0.758492i | \(0.725937\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.86465i | 0.269461i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 7.66495i | − | 0.300413i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.82383 | −0.345303 | −0.172652 | − | 0.984983i | \(-0.555233\pi\) | ||||
−0.172652 | + | 0.984983i | \(0.555233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3.08607i | − | 0.120583i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 33.7939 | 1.31842 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.3489 | −1.33804 | −0.669021 | − | 0.743243i | \(-0.733287\pi\) | ||||
−0.669021 | + | 0.743243i | \(0.733287\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 12.1440i | − | 0.472345i | −0.971711 | − | 0.236173i | \(-0.924107\pi\) | ||
0.971711 | − | 0.236173i | \(-0.0758931\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 0.0210914i | − | 0.000819120i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.86734 | − | 6.84223i | 0.227526 | − | 0.265330i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.3741 | −0.479125 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.8800 | −0.459309 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.13712i | 0.275526i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.5180i | 0.945099i | 0.881304 | + | 0.472550i | \(0.156666\pi\) | ||||
−0.881304 | + | 0.472550i | \(0.843334\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.4740 | 0.634083 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.9924i | 1.42173i | 0.703327 | + | 0.710866i | \(0.251697\pi\) | ||||
−0.703327 | + | 0.710866i | \(0.748303\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.9948 | 1.57323 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.8687 | −0.416488 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.5821 | −0.902345 | −0.451173 | − | 0.892437i | \(-0.648994\pi\) | ||||
−0.451173 | + | 0.892437i | \(0.648994\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.2130 | −0.428427 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.35697 | −0.318838 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.272712 | 0.0103895 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8.28297i | − | 0.315099i | −0.987511 | − | 0.157550i | \(-0.949641\pi\) | ||
0.987511 | − | 0.157550i | \(-0.0503594\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.80874 | −0.220656 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.15173i | 0.157484i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.69383i | 0.253547i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.30096 | −0.200501 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.40604 | −0.241953 | −0.120976 | − | 0.992655i | \(-0.538603\pi\) | ||||
−0.120976 | + | 0.992655i | \(0.538603\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.13788 | − | 8.32388i | 0.269210 | − | 0.313941i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 2.66911i | − | 0.100525i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 29.0755i | − | 1.09350i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.8898 | −1.12254 | −0.561268 | − | 0.827634i | \(-0.689686\pi\) | ||||
−0.561268 | + | 0.827634i | \(0.689686\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.4187 | −1.55332 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.8339i | 0.405733i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0488895 | 0.00182836 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 0.247884i | − | 0.00925738i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 43.9435i | − | 1.63881i | −0.573212 | − | 0.819407i | \(-0.694303\pi\) | ||
0.573212 | − | 0.819407i | \(-0.305697\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 10.6091i | − | 0.395103i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.16592i | 0.154932i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.2310i | 0.825640i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.462251i | 0.0171439i | 0.999963 | + | 0.00857197i | \(0.00272858\pi\) | ||||
−0.999963 | + | 0.00857197i | \(0.997271\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.35172 | −0.124138 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 5.12647i | − | 0.189609i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.69709 | 0.284299 | 0.142149 | − | 0.989845i | \(-0.454599\pi\) | ||||
0.142149 | + | 0.989845i | \(0.454599\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.992975 | 0.0366264 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.31376i | − | 0.122064i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.6855i | 0.503428i | 0.967802 | + | 0.251714i | \(0.0809943\pi\) | ||||
−0.967802 | + | 0.251714i | \(0.919006\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.111283 | − | 0.129773i | 0.00408808 | − | 0.00476734i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.9287 | −1.35478 | −0.677392 | − | 0.735622i | \(-0.736890\pi\) | ||||
−0.677392 | + | 0.735622i | \(0.736890\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.21855 | 0.191193 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.65168i | 0.353136i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.8312i | 0.724615i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.9950 | 1.34997 | 0.674983 | − | 0.737834i | \(-0.264151\pi\) | ||||
0.674983 | + | 0.737834i | \(0.264151\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.591433i | 0.0215530i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.6230 | 0.495791 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.2818 | −0.555426 | −0.277713 | − | 0.960664i | \(-0.589576\pi\) | ||||
−0.277713 | + | 0.960664i | \(0.589576\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.66929 | −0.0605914 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.3286 | 1.09941 | 0.549706 | − | 0.835358i | \(-0.314740\pi\) | ||||
0.549706 | + | 0.835358i | \(0.314740\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.5759 | 1.17933 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.18992 | 0.0430216 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 0.378148i | − | 0.0136541i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.48948 | −0.125834 | −0.0629170 | − | 0.998019i | \(-0.520040\pi\) | ||||
−0.0629170 | + | 0.998019i | \(0.520040\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.47358i | 0.161112i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 43.1010i | 1.55024i | 0.631817 | + | 0.775118i | \(0.282309\pi\) | ||||
−0.631817 | + | 0.775118i | \(0.717691\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.4641 | 0.699169 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.17291 | −0.149702 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −35.3182 | + | 41.1865i | −1.26541 | + | 1.47566i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 8.62601i | − | 0.308663i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.6402i | 0.737619i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.37665 | −0.156209 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.4792 | −1.15776 | −0.578879 | − | 0.815413i | \(-0.696510\pi\) | ||||
−0.578879 | + | 0.815413i | \(0.696510\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.35999i | 0.262023i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.20158 | −0.0427233 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.393157i | − | 0.0139614i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 3.12818i | − | 0.110945i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 33.2354i | − | 1.17726i | −0.808404 | − | 0.588628i | \(-0.799668\pi\) | ||
0.808404 | − | 0.588628i | \(-0.200332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.27165i | 0.0803653i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 9.42231i | − | 0.332921i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.5549i | 0.478342i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.84828 | 0.170879 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 15.5425i | − | 0.547120i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.09578 | 0.284633 | 0.142316 | − | 0.989821i | \(-0.454545\pi\) | ||||
0.142316 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.1041 | 1.19756 | 0.598779 | − | 0.800915i | \(-0.295653\pi\) | ||||
0.598779 | + | 0.800915i | \(0.295653\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.1812i | 0.672713i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.1689i | 0.671457i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.0484 | − | 31.5427i | 0.946305 | − | 1.10354i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.319982 | 0.0111811 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.2388 | 0.985539 | 0.492770 | − | 0.870160i | \(-0.335985\pi\) | ||||
0.492770 | + | 0.870160i | \(0.335985\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.9408i | 1.39225i | 0.717922 | + | 0.696124i | \(0.245094\pi\) | ||||
−0.717922 | + | 0.696124i | \(0.754906\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.99902i | 0.104413i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.23108 | −0.216676 | −0.108338 | − | 0.994114i | \(-0.534553\pi\) | ||||
−0.108338 | + | 0.994114i | \(0.534553\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 43.8585i | − | 1.52327i | −0.648008 | − | 0.761634i | \(-0.724398\pi\) | ||
0.648008 | − | 0.761634i | \(-0.275602\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.2117 | −0.458310 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.845109 | −0.0292813 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.5137 | −0.433054 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.0712 | 0.624631 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.61542 | 0.331961 | 0.165981 | − | 0.986129i | \(-0.446921\pi\) | ||||
0.165981 | + | 0.986129i | \(0.446921\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.14683 | 0.0395457 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 17.5109i | − | 0.603106i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.5349 | 0.396813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.32992i | − | 0.0800570i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.99134i | 0.102663i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.89815 | 0.202186 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.8247 | −1.08966 | −0.544829 | − | 0.838547i | \(-0.683405\pi\) | ||||
−0.544829 | + | 0.838547i | \(0.683405\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.32147 | + | 6.27830i | 0.250389 | + | 0.214713i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.0170i | 0.547132i | 0.961853 | + | 0.273566i | \(0.0882032\pi\) | ||||
−0.961853 | + | 0.273566i | \(0.911797\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 13.6556i | − | 0.465924i | −0.972486 | − | 0.232962i | \(-0.925158\pi\) | ||
0.972486 | − | 0.232962i | \(-0.0748418\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.6476 | 0.703667 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.0815 | 1.29631 | 0.648155 | − | 0.761508i | \(-0.275541\pi\) | ||||
0.648155 | + | 0.761508i | \(0.275541\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.84355i | 0.130684i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.8975 | −0.404059 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 16.6133i | − | 0.563566i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.182542i | 0.00618521i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 43.8661i | 1.48464i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 19.0495i | − | 0.643989i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 20.8231i | − | 0.703146i | −0.936161 | − | 0.351573i | \(-0.885647\pi\) | ||
0.936161 | − | 0.351573i | \(-0.114353\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.89399i | 0.299987i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.0286 | −1.14645 | −0.573226 | − | 0.819397i | \(-0.694308\pi\) | ||||
−0.573226 | + | 0.819397i | \(0.694308\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 45.1054i | − | 1.51792i | −0.651138 | − | 0.758959i | \(-0.725708\pi\) | ||
0.651138 | − | 0.758959i | \(-0.274292\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.33759 | −0.145806 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.7218 | 1.30015 | 0.650075 | − | 0.759870i | \(-0.274737\pi\) | ||||
0.650075 | + | 0.759870i | \(0.274737\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 34.6147i | − | 1.16094i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 4.69492i | − | 0.157286i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.9858 | + | 13.9773i | −0.401088 | + | 0.467731i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.2829 | 0.744836 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0919549 | 0.00307028 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.3864i | 0.813333i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.66236i | 0.0886959i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.8129 | −0.526221 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 9.07444i | − | 0.301645i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.79264 | 0.225546 | 0.112773 | − | 0.993621i | \(-0.464027\pi\) | ||||
0.112773 | + | 0.993621i | \(0.464027\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31.1119 | 1.03192 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.6986 | 0.652645 | 0.326322 | − | 0.945259i | \(-0.394190\pi\) | ||||
0.326322 | + | 0.945259i | \(0.394190\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.87134 | −0.128123 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.50975 | −0.149088 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.10167 | 0.267541 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.6293i | 1.60413i | 0.597235 | + | 0.802066i | \(0.296266\pi\) | ||||
−0.597235 | + | 0.802066i | \(0.703734\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.7614 | −0.387552 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.475174i | 0.0156406i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 10.5965i | − | 0.348412i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.3522 | 0.372854 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.7546 | 1.10745 | 0.553727 | − | 0.832698i | \(-0.313205\pi\) | ||||
0.553727 | + | 0.832698i | \(0.313205\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.19988 | − | 4.45899i | −0.170419 | − | 0.146138i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 5.65308i | − | 0.185074i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.477284i | 0.0156088i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.0164 | −0.523233 | −0.261616 | − | 0.965172i | \(-0.584256\pi\) | ||||
−0.261616 | + | 0.965172i | \(0.584256\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.73989 | 0.317849 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.82145i | 0.222373i | 0.993800 | + | 0.111186i | \(0.0354651\pi\) | ||||
−0.993800 | + | 0.111186i | \(0.964535\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.1840 | −0.950363 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 8.08702i | − | 0.263071i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.08216i | 0.100157i | 0.998745 | + | 0.0500784i | \(0.0159471\pi\) | ||||
−0.998745 | + | 0.0500784i | \(0.984053\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 0.746688i | − | 0.0242385i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 14.8194i | − | 0.480550i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.3471i | 0.983037i | 0.870867 | + | 0.491519i | \(0.163558\pi\) | ||||
−0.870867 | + | 0.491519i | \(0.836442\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.1668i | 0.426066i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.75746 | −0.121462 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 29.4368i | − | 0.950563i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.64882 | −0.311252 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.2202 | −0.683810 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.7168i | 0.602515i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50.2143i | − | 1.61478i | −0.590016 | − | 0.807391i | \(-0.700879\pi\) | ||
0.590016 | − | 0.807391i | \(-0.299121\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.26691 | + | 1.08640i | 0.0406991 | + | 0.0349002i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.8802 | 1.85746 | 0.928732 | − | 0.370752i | \(-0.120900\pi\) | ||||
0.928732 | + | 0.370752i | \(0.120900\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.8993 | −0.349415 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 0.165205i | − | 0.00529079i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.5595i | 0.849714i | 0.905261 | + | 0.424857i | \(0.139676\pi\) | ||||
−0.905261 | + | 0.424857i | \(0.860324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.77934 | 0.120788 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34.8575i | 1.11292i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.3968 | 0.746243 | 0.373121 | − | 0.927783i | \(-0.378288\pi\) | ||||
0.373121 | + | 0.927783i | \(0.378288\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.1138 | −0.640877 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.00706 | 0.223037 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.3506 | 0.710707 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.0983 | 0.670210 | 0.335105 | − | 0.942181i | \(-0.391228\pi\) | ||||
0.335105 | + | 0.942181i | \(0.391228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.50074 | −0.238029 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 15.3172i | − | 0.485589i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.87104 | −0.312619 | −0.156309 | − | 0.987708i | \(-0.549960\pi\) | ||||
−0.156309 | + | 0.987708i | \(0.549960\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 9.83822i | − | 0.311268i |
(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 | 3344.2.o.a.1519.19 | yes | 36 | |
4.3 | odd | 2 | inner | 3344.2.o.a.1519.17 | ✓ | 36 | |
19.18 | odd | 2 | inner | 3344.2.o.a.1519.18 | yes | 36 | |
76.75 | even | 2 | inner | 3344.2.o.a.1519.20 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3344.2.o.a.1519.17 | ✓ | 36 | 4.3 | odd | 2 | inner | |
3344.2.o.a.1519.18 | yes | 36 | 19.18 | odd | 2 | inner | |
3344.2.o.a.1519.19 | yes | 36 | 1.1 | even | 1 | trivial | |
3344.2.o.a.1519.20 | yes | 36 | 76.75 | even | 2 | inner |