Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(431,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.bl (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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 720) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 431.11 | ||
Character | \(\chi\) | \(=\) | 2880.431 |
Dual form | 2880.2.bl.c.1871.11 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.83891 | −1.45097 | −0.725485 | − | 0.688238i | \(-0.758385\pi\) | ||||
−0.725485 | + | 0.688238i | \(0.758385\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.214796 | + | 0.214796i | −0.0647635 | + | 0.0647635i | −0.738747 | − | 0.673983i | \(-0.764582\pi\) |
0.673983 | + | 0.738747i | \(0.264582\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.177819 | − | 0.177819i | −0.0493181 | − | 0.0493181i | 0.682018 | − | 0.731336i | \(-0.261103\pi\) |
−0.731336 | + | 0.682018i | \(0.761103\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.29544i | 0.314190i | 0.987583 | + | 0.157095i | \(0.0502130\pi\) | ||||
−0.987583 | + | 0.157095i | \(0.949787\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.10783 | + | 2.10783i | −0.483570 | + | 0.483570i | −0.906270 | − | 0.422700i | \(-0.861083\pi\) |
0.422700 | + | 0.906270i | \(0.361083\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.78684i | − | 0.789611i | −0.918765 | − | 0.394805i | \(-0.870812\pi\) | ||
0.918765 | − | 0.394805i | \(-0.129188\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.15157 | − | 3.15157i | 0.585232 | − | 0.585232i | −0.351105 | − | 0.936336i | \(-0.614194\pi\) |
0.936336 | + | 0.351105i | \(0.114194\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.745073i | − | 0.133819i | −0.997759 | − | 0.0669095i | \(-0.978686\pi\) | ||
0.997759 | − | 0.0669095i | \(-0.0213139\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.71452 | − | 2.71452i | −0.458837 | − | 0.458837i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.10346 | − | 7.10346i | 1.16780 | − | 1.16780i | 0.185078 | − | 0.982724i | \(-0.440746\pi\) |
0.982724 | − | 0.185078i | \(-0.0592536\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.5322 | −1.64486 | −0.822429 | − | 0.568867i | \(-0.807382\pi\) | ||||
−0.822429 | + | 0.568867i | \(0.807382\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.04046 | + | 2.04046i | 0.311167 | + | 0.311167i | 0.845362 | − | 0.534194i | \(-0.179385\pi\) |
−0.534194 | + | 0.845362i | \(0.679385\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9223 | 1.59318 | 0.796588 | − | 0.604523i | \(-0.206636\pi\) | ||||
0.796588 | + | 0.604523i | \(0.206636\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.73720 | 1.10531 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.467757 | − | 0.467757i | −0.0642514 | − | 0.0642514i | 0.674251 | − | 0.738502i | \(-0.264467\pi\) |
−0.738502 | + | 0.674251i | \(0.764467\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.303768 | −0.0409600 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.61894 | + | 1.61894i | −0.210768 | + | 0.210768i | −0.804594 | − | 0.593826i | \(-0.797617\pi\) |
0.593826 | + | 0.804594i | \(0.297617\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.34166 | + | 1.34166i | 0.171782 | + | 0.171782i | 0.787762 | − | 0.615980i | \(-0.211240\pi\) |
−0.615980 | + | 0.787762i | \(0.711240\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.251474i | − | 0.0311915i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.92451 | − | 6.92451i | 0.845964 | − | 0.845964i | −0.143663 | − | 0.989627i | \(-0.545888\pi\) |
0.989627 | + | 0.143663i | \(0.0458880\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.46318i | − | 1.00440i | −0.864753 | − | 0.502198i | \(-0.832525\pi\) | ||
0.864753 | − | 0.502198i | \(-0.167475\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.24339i | − | 0.847774i | −0.905715 | − | 0.423887i | \(-0.860665\pi\) | ||
0.905715 | − | 0.423887i | \(-0.139335\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.824582 | − | 0.824582i | 0.0939699 | − | 0.0939699i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.5416i | − | 1.41104i | −0.708689 | − | 0.705521i | \(-0.750713\pi\) | ||
0.708689 | − | 0.705521i | \(-0.249287\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.42498 | − | 9.42498i | −1.03453 | − | 1.03453i | −0.999382 | − | 0.0351442i | \(-0.988811\pi\) |
−0.0351442 | − | 0.999382i | \(-0.511189\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.916015 | + | 0.916015i | −0.0993557 | + | 0.0993557i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.41491 | −0.997979 | −0.498989 | − | 0.866608i | \(-0.666295\pi\) | ||||
−0.498989 | + | 0.866608i | \(0.666295\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.682631 | + | 0.682631i | 0.0715591 | + | 0.0715591i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.98093 | −0.305837 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.1943 | 1.84735 | 0.923674 | − | 0.383178i | \(-0.125171\pi\) | ||||
0.923674 | + | 0.383178i | \(0.125171\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.32696 | − | 7.32696i | −0.729060 | − | 0.729060i | 0.241373 | − | 0.970432i | \(-0.422402\pi\) |
−0.970432 | + | 0.241373i | \(0.922402\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.1311 | 0.998248 | 0.499124 | − | 0.866531i | \(-0.333655\pi\) | ||||
0.499124 | + | 0.866531i | \(0.333655\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.79195 | − | 7.79195i | 0.753277 | − | 0.753277i | −0.221813 | − | 0.975089i | \(-0.571197\pi\) |
0.975089 | + | 0.221813i | \(0.0711973\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.51485 | + | 8.51485i | 0.815574 | + | 0.815574i | 0.985463 | − | 0.169889i | \(-0.0543409\pi\) |
−0.169889 | + | 0.985463i | \(0.554341\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0710i | 1.13554i | 0.823187 | + | 0.567771i | \(0.192194\pi\) | ||||
−0.823187 | + | 0.567771i | \(0.807806\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.67770 | − | 2.67770i | 0.249697 | − | 0.249697i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.97307i | − | 0.455881i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9077i | 0.991611i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.72800i | − | 0.863221i | −0.902060 | − | 0.431610i | \(-0.857946\pi\) | ||
0.902060 | − | 0.431610i | \(-0.142054\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.6884 | − | 13.6884i | −1.19596 | − | 1.19596i | −0.975366 | − | 0.220595i | \(-0.929200\pi\) |
−0.220595 | − | 0.975366i | \(-0.570800\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.09178 | − | 8.09178i | 0.701646 | − | 0.701646i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.3237 | 1.05288 | 0.526442 | − | 0.850211i | \(-0.323526\pi\) | ||||
0.526442 | + | 0.850211i | \(0.323526\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.97240 | + | 1.97240i | 0.167297 | + | 0.167297i | 0.785790 | − | 0.618493i | \(-0.212257\pi\) |
−0.618493 | + | 0.785790i | \(0.712257\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.0763897 | 0.00638803 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.45699 | 0.370133 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.05302 | − | 6.05302i | −0.495883 | − | 0.495883i | 0.414271 | − | 0.910154i | \(-0.364037\pi\) |
−0.910154 | + | 0.414271i | \(0.864037\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.2195 | 1.80820 | 0.904098 | − | 0.427325i | \(-0.140544\pi\) | ||||
0.904098 | + | 0.427325i | \(0.140544\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.526846 | − | 0.526846i | 0.0423173 | − | 0.0423173i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.1205 | − | 16.1205i | −1.28656 | − | 1.28656i | −0.936864 | − | 0.349693i | \(-0.886286\pi\) |
−0.349693 | − | 0.936864i | \(-0.613714\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.5373i | 1.14570i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.2959 | + | 10.2959i | −0.806437 | + | 0.806437i | −0.984093 | − | 0.177656i | \(-0.943149\pi\) |
0.177656 | + | 0.984093i | \(0.443149\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.1651i | 1.79257i | 0.443482 | + | 0.896283i | \(0.353743\pi\) | ||||
−0.443482 | + | 0.896283i | \(0.646257\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.9368i | − | 0.995135i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.0819 | − | 14.0819i | 1.07063 | − | 1.07063i | 0.0733180 | − | 0.997309i | \(-0.476641\pi\) |
0.997309 | − | 0.0733180i | \(-0.0233588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.83891i | − | 0.290194i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.68257 | − | 6.68257i | −0.499479 | − | 0.499479i | 0.411797 | − | 0.911276i | \(-0.364901\pi\) |
−0.911276 | + | 0.411797i | \(0.864901\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.3416 | + | 16.3416i | −1.21467 | + | 1.21467i | −0.245190 | + | 0.969475i | \(0.578850\pi\) |
−0.969475 | + | 0.245190i | \(0.921150\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.0458 | 0.738583 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.278256 | − | 0.278256i | −0.0203481 | − | 0.0203481i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.67079 | 0.482681 | 0.241341 | − | 0.970440i | \(-0.422413\pi\) | ||||
0.241341 | + | 0.970440i | \(0.422413\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.38312 | 0.603430 | 0.301715 | − | 0.953398i | \(-0.402441\pi\) | ||||
0.301715 | + | 0.953398i | \(0.402441\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.31421 | − | 8.31421i | −0.592363 | − | 0.592363i | 0.345906 | − | 0.938269i | \(-0.387572\pi\) |
−0.938269 | + | 0.345906i | \(0.887572\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.6248 | 0.753174 | 0.376587 | − | 0.926381i | \(-0.377098\pi\) | ||||
0.376587 | + | 0.926381i | \(0.377098\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.0986 | + | 12.0986i | −0.849154 | + | 0.849154i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.44741 | − | 7.44741i | −0.520150 | − | 0.520150i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 0.905509i | − | 0.0626354i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6632 | − | 11.6632i | 0.802929 | − | 0.802929i | −0.180623 | − | 0.983552i | \(-0.557812\pi\) |
0.983552 | + | 0.180623i | \(0.0578115\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.88565i | 0.196800i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.86027i | 0.194167i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.230354 | − | 0.230354i | 0.0154953 | − | 0.0154953i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.5818i | 0.775574i | 0.921749 | + | 0.387787i | \(0.126760\pi\) | ||||
−0.921749 | + | 0.387787i | \(0.873240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.349583 | + | 0.349583i | 0.0232026 | + | 0.0232026i | 0.718613 | − | 0.695410i | \(-0.244777\pi\) |
−0.695410 | + | 0.718613i | \(0.744777\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.3899 | + | 12.3899i | −0.818746 | + | 0.818746i | −0.985926 | − | 0.167181i | \(-0.946534\pi\) |
0.167181 | + | 0.985926i | \(0.446534\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.97429 | −0.391389 | −0.195694 | − | 0.980665i | \(-0.562696\pi\) | ||||
−0.195694 | + | 0.980665i | \(0.562696\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.72320 | + | 7.72320i | 0.503806 | + | 0.503806i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.4047 | −0.867081 | −0.433540 | − | 0.901134i | \(-0.642736\pi\) | ||||
−0.433540 | + | 0.901134i | \(0.642736\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.7309 | −1.01332 | −0.506660 | − | 0.862146i | \(-0.669120\pi\) | ||||
−0.506660 | + | 0.862146i | \(0.669120\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.47103 | + | 5.47103i | 0.349531 | + | 0.349531i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.749626 | 0.0476975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.53586 | + | 1.53586i | −0.0969423 | + | 0.0969423i | −0.753915 | − | 0.656972i | \(-0.771837\pi\) |
0.656972 | + | 0.753915i | \(0.271837\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.813399 | + | 0.813399i | 0.0511379 | + | 0.0511379i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 8.67880i | − | 0.541368i | −0.962668 | − | 0.270684i | \(-0.912750\pi\) | ||
0.962668 | − | 0.270684i | \(-0.0872499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.2695 | + | 27.2695i | −1.69445 | + | 1.69445i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2.30739i | − | 0.142279i | −0.997466 | − | 0.0711397i | \(-0.977336\pi\) | ||
0.997466 | − | 0.0711397i | \(-0.0226636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.661508i | − | 0.0406361i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.59842 | − | 7.59842i | 0.463284 | − | 0.463284i | −0.436446 | − | 0.899730i | \(-0.643763\pi\) |
0.899730 | + | 0.436446i | \(0.143763\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 29.5935i | − | 1.79768i | −0.438282 | − | 0.898838i | \(-0.644413\pi\) | ||
0.438282 | − | 0.898838i | \(-0.355587\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.214796 | − | 0.214796i | −0.0129527 | − | 0.0129527i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8775 | − | 14.8775i | 0.893902 | − | 0.893902i | −0.100986 | − | 0.994888i | \(-0.532200\pi\) |
0.994888 | + | 0.100986i | \(0.0321998\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.6466 | 0.814086 | 0.407043 | − | 0.913409i | \(-0.366560\pi\) | ||||
0.407043 | + | 0.913409i | \(0.366560\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.19089 | − | 8.19089i | −0.486898 | − | 0.486898i | 0.420428 | − | 0.907326i | \(-0.361880\pi\) |
−0.907326 | + | 0.420428i | \(0.861880\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 40.4323 | 2.38664 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.3218 | 0.901284 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.3315 | − | 18.3315i | −1.07094 | − | 1.07094i | −0.997284 | − | 0.0736556i | \(-0.976533\pi\) |
−0.0736556 | − | 0.997284i | \(-0.523467\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.28952 | −0.133301 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.673372 | + | 0.673372i | −0.0389421 | + | 0.0389421i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.83314 | − | 7.83314i | −0.451495 | − | 0.451495i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.89739i | 0.108645i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.859523 | − | 0.859523i | 0.0490556 | − | 0.0490556i | −0.682153 | − | 0.731209i | \(-0.738956\pi\) |
0.731209 | + | 0.682153i | \(0.238956\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.04247i | 0.115818i | 0.998322 | + | 0.0579089i | \(0.0184433\pi\) | ||||
−0.998322 | + | 0.0579089i | \(0.981557\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.51059i | 0.537571i | 0.963200 | + | 0.268785i | \(0.0866222\pi\) | ||||
−0.963200 | + | 0.268785i | \(0.913378\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.7157 | − | 13.7157i | 0.770349 | − | 0.770349i | −0.207818 | − | 0.978167i | \(-0.566636\pi\) |
0.978167 | + | 0.207818i | \(0.0666363\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.35389i | 0.0758033i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.73057 | − | 2.73057i | −0.151933 | − | 0.151933i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.177819 | − | 0.177819i | 0.00986362 | − | 0.00986362i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −41.9295 | −2.31165 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.51338 | + | 4.51338i | 0.248078 | + | 0.248078i | 0.820181 | − | 0.572104i | \(-0.193872\pi\) |
−0.572104 | + | 0.820181i | \(0.693872\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.79274 | 0.535035 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.8857 | 0.756405 | 0.378202 | − | 0.925723i | \(-0.376542\pi\) | ||||
0.378202 | + | 0.925723i | \(0.376542\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.160039 | + | 0.160039i | 0.00866659 | + | 0.00866659i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.83006 | −0.152809 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.3358 | + | 17.3358i | −0.930632 | + | 0.930632i | −0.997745 | − | 0.0671132i | \(-0.978621\pi\) |
0.0671132 | + | 0.997745i | \(0.478621\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.2056 | − | 17.2056i | −0.920994 | − | 0.920994i | 0.0761058 | − | 0.997100i | \(-0.475751\pi\) |
−0.997100 | + | 0.0761058i | \(0.975751\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4.28779i | − | 0.228216i | −0.993468 | − | 0.114108i | \(-0.963599\pi\) | ||
0.993468 | − | 0.114108i | \(-0.0364010\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.98437 | − | 5.98437i | 0.317618 | − | 0.317618i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.4890i | 0.711921i | 0.934501 | + | 0.355960i | \(0.115846\pi\) | ||||
−0.934501 | + | 0.355960i | \(0.884154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.1141i | 0.532320i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.12185 | − | 5.12185i | 0.268090 | − | 0.268090i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.03456i | 0.262802i | 0.991329 | + | 0.131401i | \(0.0419475\pi\) | ||||
−0.991329 | + | 0.131401i | \(0.958052\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.79568 | + | 1.79568i | 0.0932268 | + | 0.0932268i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.45718 | − | 1.45718i | 0.0754501 | − | 0.0754501i | −0.668375 | − | 0.743825i | \(-0.733010\pi\) |
0.743825 | + | 0.668375i | \(0.233010\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.12082 | −0.0577251 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.5423 | + | 26.5423i | 1.36339 | + | 1.36339i | 0.869561 | + | 0.493826i | \(0.164402\pi\) |
0.493826 | + | 0.869561i | \(0.335598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.12655 | −0.0575642 | −0.0287821 | − | 0.999586i | \(-0.509163\pi\) | ||||
−0.0287821 | + | 0.999586i | \(0.509163\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.16614 | 0.0594318 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.36402 | − | 6.36402i | −0.322668 | − | 0.322668i | 0.527121 | − | 0.849790i | \(-0.323271\pi\) |
−0.849790 | + | 0.527121i | \(0.823271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.90563 | 0.248088 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.86827 | − | 8.86827i | 0.446211 | − | 0.446211i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.54196 | + | 6.54196i | 0.328331 | + | 0.328331i | 0.851952 | − | 0.523620i | \(-0.175419\pi\) |
−0.523620 | + | 0.851952i | \(0.675419\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.60993i | 0.479897i | 0.970786 | + | 0.239949i | \(0.0771306\pi\) | ||||
−0.970786 | + | 0.239949i | \(0.922869\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.132488 | + | 0.132488i | −0.00659970 | + | 0.00659970i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.05159i | 0.151262i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.6444i | 0.625224i | 0.949881 | + | 0.312612i | \(0.101204\pi\) | ||||
−0.949881 | + | 0.312612i | \(0.898796\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.21495 | − | 6.21495i | 0.305818 | − | 0.305818i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 13.3289i | − | 0.654292i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.73617 | + | 3.73617i | 0.182524 | + | 0.182524i | 0.792455 | − | 0.609931i | \(-0.208803\pi\) |
−0.609931 | + | 0.792455i | \(0.708803\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.9508 | − | 16.9508i | 0.826130 | − | 0.826130i | −0.160849 | − | 0.986979i | \(-0.551423\pi\) |
0.986979 | + | 0.160849i | \(0.0514232\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.29544 | −0.0628381 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.15051 | − | 5.15051i | −0.249251 | − | 0.249251i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0390 | 0.724402 | 0.362201 | − | 0.932100i | \(-0.382025\pi\) | ||||
0.362201 | + | 0.932100i | \(0.382025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.1574 | −1.30510 | −0.652552 | − | 0.757744i | \(-0.726302\pi\) | ||||
−0.652552 | + | 0.757744i | \(0.726302\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.98203 | + | 7.98203i | 0.381832 | + | 0.381832i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.6307 | −0.793738 | −0.396869 | − | 0.917875i | \(-0.629903\pi\) | ||||
−0.396869 | + | 0.917875i | \(0.629903\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.2352 | + | 26.2352i | −1.24647 | + | 1.24647i | −0.289204 | + | 0.957268i | \(0.593390\pi\) |
−0.957268 | + | 0.289204i | \(0.906610\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.65735 | − | 6.65735i | −0.315589 | − | 0.315589i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 27.7821i | − | 1.31112i | −0.755143 | − | 0.655560i | \(-0.772433\pi\) | ||
0.755143 | − | 0.655560i | \(-0.227567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.26228 | − | 2.26228i | 0.106527 | − | 0.106527i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.965385i | 0.0452580i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 22.0885i | − | 1.03326i | −0.856210 | − | 0.516628i | \(-0.827187\pi\) | ||
0.856210 | − | 0.516628i | \(-0.172813\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.9897 | − | 19.9897i | 0.931015 | − | 0.931015i | −0.0667540 | − | 0.997769i | \(-0.521264\pi\) |
0.997769 | + | 0.0667540i | \(0.0212643\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.90536i | 0.274445i | 0.990540 | + | 0.137223i | \(0.0438176\pi\) | ||||
−0.990540 | + | 0.137223i | \(0.956182\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.4037 | + | 13.4037i | 0.620248 | + | 0.620248i | 0.945595 | − | 0.325346i | \(-0.105481\pi\) |
−0.325346 | + | 0.945595i | \(0.605481\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.5826 | + | 26.5826i | −1.22747 | + | 1.22747i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.876567 | −0.0403046 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.10783 | − | 2.10783i | −0.0967140 | − | 0.0967140i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.3524 | −0.838544 | −0.419272 | − | 0.907861i | \(-0.637715\pi\) | ||||
−0.419272 | + | 0.907861i | \(0.637715\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.52626 | −0.115188 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.8653 | + | 12.8653i | 0.584183 | + | 0.584183i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.0699 | −1.49854 | −0.749270 | − | 0.662265i | \(-0.769595\pi\) | ||||
−0.749270 | + | 0.662265i | \(0.769595\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.13752 | + | 8.13752i | −0.367241 | + | 0.367241i | −0.866470 | − | 0.499229i | \(-0.833617\pi\) |
0.499229 | + | 0.866470i | \(0.333617\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.08267 | + | 4.08267i | 0.183874 | + | 0.183874i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.4894i | 1.45735i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.1350 | + | 16.1350i | −0.722304 | + | 0.722304i | −0.969074 | − | 0.246770i | \(-0.920631\pi\) |
0.246770 | + | 0.969074i | \(0.420631\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 4.24518i | − | 0.189283i | −0.995511 | − | 0.0946417i | \(-0.969829\pi\) | ||
0.995511 | − | 0.0946417i | \(-0.0301705\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 10.3619i | − | 0.461098i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.1649 | + | 20.1649i | −0.893795 | + | 0.893795i | −0.994878 | − | 0.101083i | \(-0.967769\pi\) |
0.101083 | + | 0.994878i | \(0.467769\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.8067i | 1.23010i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.16378 | + | 7.16378i | 0.315674 | + | 0.315674i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.34606 | + | 2.34606i | −0.103180 | + | 0.103180i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.7970 | 0.516836 | 0.258418 | − | 0.966033i | \(-0.416799\pi\) | ||||
0.258418 | + | 0.966033i | \(0.416799\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.70782 | − | 6.70782i | −0.293313 | − | 0.293313i | 0.545075 | − | 0.838387i | \(-0.316501\pi\) |
−0.838387 | + | 0.545075i | \(0.816501\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.965198 | 0.0420447 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.65984 | 0.376515 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.87283 | + | 1.87283i | 0.0811213 | + | 0.0811213i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.0195 | 0.476414 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.66192 | + | 1.66192i | −0.0715840 | + | 0.0715840i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.14915 | − | 2.14915i | −0.0923994 | − | 0.0923994i | 0.659396 | − | 0.751796i | \(-0.270812\pi\) |
−0.751796 | + | 0.659396i | \(0.770812\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.0418i | 0.515815i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.5780 | + | 24.5780i | −1.05088 | + | 1.05088i | −0.0522461 | + | 0.998634i | \(0.516638\pi\) |
−0.998634 | + | 0.0522461i | \(0.983362\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.2860i | 0.566001i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 48.1461i | 2.04738i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.51628 | − | 5.51628i | 0.233732 | − | 0.233732i | −0.580516 | − | 0.814249i | \(-0.697149\pi\) |
0.814249 | + | 0.580516i | \(0.197149\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.725666i | − | 0.0306924i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.2621 | − | 13.2621i | −0.558931 | − | 0.558931i | 0.370072 | − | 0.929003i | \(-0.379333\pi\) |
−0.929003 | + | 0.370072i | \(0.879333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.53547 | + | 8.53547i | −0.359090 | + | 0.359090i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.2485 | −0.681174 | −0.340587 | − | 0.940213i | \(-0.610626\pi\) | ||||
−0.340587 | + | 0.940213i | \(0.610626\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.5062 | − | 19.5062i | −0.816307 | − | 0.816307i | 0.169264 | − | 0.985571i | \(-0.445861\pi\) |
−0.985571 | + | 0.169264i | \(0.945861\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.78684 | 0.157922 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.61350 | −0.316954 | −0.158477 | − | 0.987363i | \(-0.550658\pi\) | ||||
−0.158477 | + | 0.987363i | \(0.550658\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.1816 | + | 36.1816i | 1.50107 | + | 1.50107i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.200945 | 0.00832228 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.8450 | − | 14.8450i | 0.612719 | − | 0.612719i | −0.330935 | − | 0.943654i | \(-0.607364\pi\) |
0.943654 | + | 0.330935i | \(0.107364\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.57049 | + | 1.57049i | 0.0647109 | + | 0.0647109i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.5714i | 1.41968i | 0.704364 | + | 0.709839i | \(0.251232\pi\) | ||||
−0.704364 | + | 0.709839i | \(0.748768\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.51649 | − | 3.51649i | 0.144162 | − | 0.144162i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.69952i | − | 0.0694406i | −0.999397 | − | 0.0347203i | \(-0.988946\pi\) | ||
0.999397 | − | 0.0347203i | \(-0.0110540\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.54584i | − | 0.0630561i | −0.999503 | − | 0.0315281i | \(-0.989963\pi\) | ||
0.999503 | − | 0.0315281i | \(-0.0100374\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.71293 | + | 7.71293i | −0.313575 | + | 0.313575i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.11308i | − | 0.0857674i | −0.999080 | − | 0.0428837i | \(-0.986346\pi\) | ||
0.999080 | − | 0.0428837i | \(-0.0136545\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.94219 | − | 1.94219i | −0.0785724 | − | 0.0785724i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.2409 | + | 12.2409i | −0.494405 | + | 0.494405i | −0.909691 | − | 0.415286i | \(-0.863682\pi\) |
0.415286 | + | 0.909691i | \(0.363682\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.9584 | 0.884013 | 0.442007 | − | 0.897012i | \(-0.354267\pi\) | ||||
0.442007 | + | 0.897012i | \(0.354267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.0983 | + | 24.0983i | 0.968593 | + | 0.968593i | 0.999522 | − | 0.0309290i | \(-0.00984657\pi\) |
−0.0309290 | + | 0.999522i | \(0.509847\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.1430 | 1.44804 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.20211 | + | 9.20211i | 0.366912 | + | 0.366912i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.7381 | −0.546904 | −0.273452 | − | 0.961886i | \(-0.588165\pi\) | ||||
−0.273452 | + | 0.961886i | \(0.588165\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.87874 | − | 6.87874i | 0.272974 | − | 0.272974i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.37582 | − | 1.37582i | −0.0545121 | − | 0.0545121i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.1567i | 1.50710i | 0.657391 | + | 0.753549i | \(0.271660\pi\) | ||||
−0.657391 | + | 0.753549i | \(0.728340\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.775769 | + | 0.775769i | −0.0305933 | + | 0.0305933i | −0.722238 | − | 0.691645i | \(-0.756886\pi\) |
0.691645 | + | 0.722238i | \(0.256886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.67247i | 0.0657514i | 0.999459 | + | 0.0328757i | \(0.0104666\pi\) | ||||
−0.999459 | + | 0.0328757i | \(0.989533\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.695483i | − | 0.0273001i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.3372 | + | 24.3372i | −0.952390 | + | 0.952390i | −0.998917 | − | 0.0465271i | \(-0.985185\pi\) |
0.0465271 | + | 0.998917i | \(0.485185\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 19.3583i | − | 0.756392i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.5973 | − | 22.5973i | −0.880265 | − | 0.880265i | 0.113296 | − | 0.993561i | \(-0.463859\pi\) |
−0.993561 | + | 0.113296i | \(0.963859\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.4472 | + | 11.4472i | −0.445245 | + | 0.445245i | −0.893770 | − | 0.448525i | \(-0.851950\pi\) |
0.448525 | + | 0.893770i | \(0.351950\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.4435 | 0.443760 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.9345 | − | 11.9345i | −0.462105 | − | 0.462105i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.576367 | −0.0222504 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.0206 | −1.58123 | −0.790614 | − | 0.612315i | \(-0.790238\pi\) | ||||
−0.790614 | + | 0.612315i | \(0.790238\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.7765 | + | 13.7765i | 0.529473 | + | 0.529473i | 0.920415 | − | 0.390943i | \(-0.127851\pi\) |
−0.390943 | + | 0.920415i | \(0.627851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −69.8461 | −2.68045 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.6321 | − | 25.6321i | 0.980784 | − | 0.980784i | −0.0190347 | − | 0.999819i | \(-0.506059\pi\) |
0.999819 | + | 0.0190347i | \(0.00605929\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.71416 | + | 8.71416i | 0.332951 | + | 0.332951i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.166352i | 0.00633751i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.44050 | + | 6.44050i | −0.245008 | + | 0.245008i | −0.818918 | − | 0.573910i | \(-0.805426\pi\) |
0.573910 | + | 0.818918i | \(0.305426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.78939i | 0.105808i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 13.6439i | − | 0.516799i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0706 | + | 13.0706i | −0.493670 | + | 0.493670i | −0.909460 | − | 0.415791i | \(-0.863505\pi\) |
0.415791 | + | 0.909460i | \(0.363505\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.9458i | 1.12943i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.1275 | + | 28.1275i | 1.05784 | + | 1.05784i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.6678 | + | 24.6678i | −0.926420 | + | 0.926420i | −0.997473 | − | 0.0710527i | \(-0.977364\pi\) |
0.0710527 | + | 0.997473i | \(0.477364\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.82147 | −0.105665 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0540157 | + | 0.0540157i | 0.00202007 | + | 0.00202007i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.8290 | −1.33620 | −0.668099 | − | 0.744072i | \(-0.732892\pi\) | ||||
−0.668099 | + | 0.744072i | \(0.732892\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.8924 | −1.44843 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.15157 | + | 3.15157i | 0.117046 | + | 0.117046i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.5183 | 1.39148 | 0.695739 | − | 0.718295i | \(-0.255077\pi\) | ||||
0.695739 | + | 0.718295i | \(0.255077\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.64330 | + | 2.64330i | −0.0977658 | + | 0.0977658i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.8396 | + | 20.8396i | 0.769727 | + | 0.769727i | 0.978058 | − | 0.208331i | \(-0.0668032\pi\) |
−0.208331 | + | 0.978058i | \(0.566803\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.97472i | 0.109575i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.45480 | − | 9.45480i | 0.347801 | − | 0.347801i | −0.511489 | − | 0.859290i | \(-0.670906\pi\) |
0.859290 | + | 0.511489i | \(0.170906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.3935i | 0.931597i | 0.884891 | + | 0.465799i | \(0.154233\pi\) | ||||
−0.884891 | + | 0.465799i | \(0.845767\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 8.56026i | − | 0.313624i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.9126 | + | 29.9126i | −1.09298 | + | 1.09298i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.3845i | 0.816823i | 0.912798 | + | 0.408412i | \(0.133917\pi\) | ||||
−0.912798 | + | 0.408412i | \(0.866083\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.7115 | + | 15.7115i | 0.571802 | + | 0.571802i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.57143 | − | 7.57143i | 0.275188 | − | 0.275188i | −0.555996 | − | 0.831185i | \(-0.687663\pi\) |
0.831185 | + | 0.555996i | \(0.187663\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.42940 | 0.196816 | 0.0984078 | − | 0.995146i | \(-0.468625\pi\) | ||||
0.0984078 | + | 0.995146i | \(0.468625\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.6877 | − | 32.6877i | −1.18337 | − | 1.18337i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.575756 | 0.0207893 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.9314 | 0.646624 | 0.323312 | − | 0.946292i | \(-0.395204\pi\) | ||||
0.323312 | + | 0.946292i | \(0.395204\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.2317 | − | 32.2317i | −1.15930 | − | 1.15930i | −0.984627 | − | 0.174668i | \(-0.944115\pi\) |
−0.174668 | − | 0.984627i | \(-0.555885\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.745073 | 0.0267638 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.2002 | − | 22.2002i | 0.795405 | − | 0.795405i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.81786 | + | 1.81786i | 0.0650481 | + | 0.0650481i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 22.7979i | − | 0.813690i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.7312 | − | 14.7312i | 0.525109 | − | 0.525109i | −0.394001 | − | 0.919110i | \(-0.628909\pi\) |
0.919110 | + | 0.394001i | \(0.128909\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 46.3394i | − | 1.64764i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.477146i | − | 0.0169439i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.3916 | − | 10.3916i | 0.368089 | − | 0.368089i | −0.498691 | − | 0.866780i | \(-0.666186\pi\) |
0.866780 | + | 0.498691i | \(0.166186\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.1491i | 0.500561i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.55585 | + | 1.55585i | 0.0549048 | + | 0.0549048i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.2794 | + | 10.2794i | −0.362303 | + | 0.362303i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.9148 | 1.40333 | 0.701666 | − | 0.712506i | \(-0.252440\pi\) | ||||
0.701666 | + | 0.712506i | \(0.252440\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.303197 | + | 0.303197i | 0.0106467 | + | 0.0106467i | 0.712410 | − | 0.701763i | \(-0.247604\pi\) |
−0.701763 | + | 0.712410i | \(0.747604\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.5606 | −0.510036 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.60191 | −0.300943 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.2299 | − | 38.2299i | −1.33423 | − | 1.33423i | −0.901544 | − | 0.432688i | \(-0.857565\pi\) |
−0.432688 | − | 0.901544i | \(-0.642435\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.3498 | 0.430487 | 0.215243 | − | 0.976560i | \(-0.430946\pi\) | ||||
0.215243 | + | 0.976560i | \(0.430946\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.8655 | − | 11.8655i | 0.412605 | − | 0.412605i | −0.470040 | − | 0.882645i | \(-0.655761\pi\) |
0.882645 | + | 0.470040i | \(0.155761\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.36024 | + | 2.36024i | 0.0819746 | + | 0.0819746i | 0.746905 | − | 0.664931i | \(-0.231539\pi\) |
−0.664931 | + | 0.746905i | \(0.731539\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.0231i | 0.347279i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.3802 | + | 16.3802i | −0.566859 | + | 0.566859i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.6899i | 0.955963i | 0.878370 | + | 0.477982i | \(0.158631\pi\) | ||||
−0.878370 | + | 0.477982i | \(0.841369\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.13522i | 0.315008i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.14767 | − | 9.14767i | 0.314689 | − | 0.314689i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 41.8737i | − | 1.43880i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.8997 | − | 26.8997i | −0.922109 | − | 0.922109i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.9953 | − | 22.9953i | 0.787343 | − | 0.787343i | −0.193715 | − | 0.981058i | \(-0.562054\pi\) |
0.981058 | + | 0.193715i | \(0.0620536\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.9441 | 0.612958 | 0.306479 | − | 0.951877i | \(-0.400849\pi\) | ||||
0.306479 | + | 0.951877i | \(0.400849\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.3836 | − | 18.3836i | −0.627242 | − | 0.627242i | 0.320131 | − | 0.947373i | \(-0.396273\pi\) |
−0.947373 | + | 0.320131i | \(0.896273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.1838 | 1.16363 | 0.581815 | − | 0.813321i | \(-0.302343\pi\) | ||||
0.581815 | + | 0.813321i | \(0.302343\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.9148 | 0.677124 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.69389 | + | 2.69389i | 0.0913840 | + | 0.0913840i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.46262 | −0.0834427 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.71452 | − | 2.71452i | 0.0917674 | − | 0.0917674i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.60130 | + | 8.60130i | 0.290445 | + | 0.290445i | 0.837256 | − | 0.546811i | \(-0.184158\pi\) |
−0.546811 | + | 0.837256i | \(0.684158\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 32.5526i | − | 1.09673i | −0.836240 | − | 0.548363i | \(-0.815251\pi\) | ||
0.836240 | − | 0.548363i | \(-0.184749\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.9330 | − | 27.9330i | 0.940020 | − | 0.940020i | −0.0582798 | − | 0.998300i | \(-0.518562\pi\) |
0.998300 | + | 0.0582798i | \(0.0185616\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 13.7416i | − | 0.461397i | −0.973025 | − | 0.230698i | \(-0.925899\pi\) | ||
0.973025 | − | 0.230698i | \(-0.0741010\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.3449i | 1.25251i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23.0223 | + | 23.0223i | −0.770412 | + | 0.770412i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 9.45058i | − | 0.315898i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.34815 | − | 2.34815i | −0.0783152 | − | 0.0783152i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.605951 | − | 0.605951i | 0.0201872 | − | 0.0201872i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.1106 | −0.768222 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.7473 | − | 19.7473i | −0.655697 | − | 0.655697i | 0.298662 | − | 0.954359i | \(-0.403460\pi\) |
−0.954359 | + | 0.298662i | \(0.903460\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0800 | −1.59296 | −0.796481 | − | 0.604663i | \(-0.793308\pi\) | ||||
−0.796481 | + | 0.604663i | \(0.793308\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.04890 | 0.133999 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 52.5485 | + | 52.5485i | 1.73530 | + | 1.73530i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.1967 | −0.468305 | −0.234152 | − | 0.972200i | \(-0.575232\pi\) | ||||
−0.234152 | + | 0.972200i | \(0.575232\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.50491 | + | 1.50491i | −0.0495349 | + | 0.0495349i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.10346 | + | 7.10346i | 0.233560 | + | 0.233560i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 19.9508i | − | 0.654565i | −0.944927 | − | 0.327282i | \(-0.893867\pi\) | ||
0.944927 | − | 0.327282i | \(-0.106133\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.3087 | + | 16.3087i | −0.534497 | + | 0.534497i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 0.393513i | − | 0.0128692i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 53.8894i | − | 1.76049i | −0.474519 | − | 0.880245i | \(-0.657378\pi\) | ||
0.474519 | − | 0.880245i | \(-0.342622\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.2221 | + | 16.2221i | −0.528825 | + | 0.528825i | −0.920222 | − | 0.391397i | \(-0.871992\pi\) |
0.391397 | + | 0.920222i | \(0.371992\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.8839i | 1.29880i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.4793 | + | 21.4793i | 0.697983 | + | 0.697983i | 0.963975 | − | 0.265992i | \(-0.0856996\pi\) |
−0.265992 | + | 0.963975i | \(0.585700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.28801 | + | 1.28801i | −0.0418106 | + | 0.0418106i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.12681 | −0.133680 | −0.0668402 | − | 0.997764i | \(-0.521292\pi\) | ||||
−0.0668402 | + | 0.997764i | \(0.521292\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.71696 | + | 4.71696i | 0.152637 | + | 0.152637i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −47.3095 | −1.52770 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.4449 | 0.982092 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.92776 | + | 5.92776i | 0.190821 | + | 0.190821i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.2853 | 1.42412 | 0.712060 | − | 0.702119i | \(-0.247763\pi\) | ||||
0.712060 | + | 0.702119i | \(0.247763\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.12262 | − | 2.12262i | 0.0681181 | − | 0.0681181i | −0.672227 | − | 0.740345i | \(-0.734662\pi\) |
0.740345 | + | 0.672227i | \(0.234662\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.57185 | − | 7.57185i | −0.242742 | − | 0.242742i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.40556i | 0.0449677i | 0.999747 | + | 0.0224839i | \(0.00715744\pi\) | ||||
−0.999747 | + | 0.0224839i | \(0.992843\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.02229 | − | 2.02229i | 0.0646326 | − | 0.0646326i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 42.6887i | − | 1.36156i | −0.732488 | − | 0.680780i | \(-0.761641\pi\) | ||
0.732488 | − | 0.680780i | \(-0.238359\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 11.7581i | − | 0.374643i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.72690 | − | 7.72690i | 0.245701 | − | 0.245701i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.2269i | 1.65904i | 0.558474 | + | 0.829522i | \(0.311387\pi\) | ||||
−0.558474 | + | 0.829522i | \(0.688613\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.51289 | + | 7.51289i | 0.238175 | + | 0.238175i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0768 | − | 21.0768i | 0.667509 | − | 0.667509i | −0.289629 | − | 0.957139i | \(-0.593532\pi\) |
0.957139 | + | 0.289629i | \(0.0935320\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2880.2.bl.c.431.11 | 32 | ||
3.2 | odd | 2 | inner | 2880.2.bl.c.431.2 | 32 | ||
4.3 | odd | 2 | 720.2.bl.c.611.13 | yes | 32 | ||
12.11 | even | 2 | 720.2.bl.c.611.4 | yes | 32 | ||
16.5 | even | 4 | 720.2.bl.c.251.4 | ✓ | 32 | ||
16.11 | odd | 4 | inner | 2880.2.bl.c.1871.2 | 32 | ||
48.5 | odd | 4 | 720.2.bl.c.251.13 | yes | 32 | ||
48.11 | even | 4 | inner | 2880.2.bl.c.1871.11 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.bl.c.251.4 | ✓ | 32 | 16.5 | even | 4 | ||
720.2.bl.c.251.13 | yes | 32 | 48.5 | odd | 4 | ||
720.2.bl.c.611.4 | yes | 32 | 12.11 | even | 2 | ||
720.2.bl.c.611.13 | yes | 32 | 4.3 | odd | 2 | ||
2880.2.bl.c.431.2 | 32 | 3.2 | odd | 2 | inner | ||
2880.2.bl.c.431.11 | 32 | 1.1 | even | 1 | trivial | ||
2880.2.bl.c.1871.2 | 32 | 16.11 | odd | 4 | inner | ||
2880.2.bl.c.1871.11 | 32 | 48.11 | even | 4 | inner |