Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(719,2880)]
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, 1, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.719");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.u (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 720) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2159.31 | ||
Character | \(\chi\) | \(=\) | 2880.2159 |
Dual form | 2880.2.u.a.719.31 |
$q$-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 | ||||||||
\(5\) | 1.11222 | − | 1.93984i | 0.497400 | − | 0.867521i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.78786i | 0.675747i | 0.941191 | + | 0.337874i | \(0.109708\pi\) | ||||
−0.941191 | + | 0.337874i | \(0.890292\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.34421 | − | 3.34421i | 1.00832 | − | 1.00832i | 0.00835103 | − | 0.999965i | \(-0.497342\pi\) |
0.999965 | − | 0.00835103i | \(-0.00265824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.90349 | − | 2.90349i | 0.805282 | − | 0.805282i | −0.178634 | − | 0.983916i | \(-0.557168\pi\) |
0.983916 | + | 0.178634i | \(0.0571677\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.56733 | 1.10774 | 0.553870 | − | 0.832603i | \(-0.313151\pi\) | ||||
0.553870 | + | 0.832603i | \(0.313151\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0693845 | + | 0.0693845i | −0.0159179 | + | 0.0159179i | −0.715021 | − | 0.699103i | \(-0.753583\pi\) |
0.699103 | + | 0.715021i | \(0.253583\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.07695 | 0.224560 | 0.112280 | − | 0.993677i | \(-0.464185\pi\) | ||||
0.112280 | + | 0.993677i | \(0.464185\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.52593 | − | 4.31505i | −0.505186 | − | 0.863010i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.23988 | − | 1.23988i | 0.230239 | − | 0.230239i | −0.582553 | − | 0.812792i | \(-0.697946\pi\) |
0.812792 | + | 0.582553i | \(0.197946\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.56612i | 1.53852i | 0.638935 | + | 0.769261i | \(0.279375\pi\) | ||||
−0.638935 | + | 0.769261i | \(0.720625\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.46816 | + | 1.98849i | 0.586225 | + | 0.336117i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.62458 | − | 7.62458i | −1.25347 | − | 1.25347i | −0.954153 | − | 0.299321i | \(-0.903240\pi\) |
−0.299321 | − | 0.954153i | \(-0.596760\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.91601 | −1.23627 | −0.618137 | − | 0.786071i | \(-0.712112\pi\) | ||||
−0.618137 | + | 0.786071i | \(0.712112\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.35179 | + | 2.35179i | −0.358645 | + | 0.358645i | −0.863313 | − | 0.504668i | \(-0.831615\pi\) |
0.504668 | + | 0.863313i | \(0.331615\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.32188i | 0.922141i | 0.887364 | + | 0.461070i | \(0.152534\pi\) | ||||
−0.887364 | + | 0.461070i | \(0.847466\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.80356 | 0.543365 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.61429 | − | 3.61429i | 0.496461 | − | 0.496461i | −0.413874 | − | 0.910334i | \(-0.635824\pi\) |
0.910334 | + | 0.413874i | \(0.135824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.76772 | − | 10.2067i | −0.373199 | − | 1.37627i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.25080 | − | 2.25080i | 0.293030 | − | 0.293030i | −0.545246 | − | 0.838276i | \(-0.683564\pi\) |
0.838276 | + | 0.545246i | \(0.183564\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.29893 | + | 4.29893i | 0.550421 | + | 0.550421i | 0.926562 | − | 0.376141i | \(-0.122749\pi\) |
−0.376141 | + | 0.926562i | \(0.622749\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.40297 | − | 8.86160i | −0.298052 | − | 1.09915i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.85271 | − | 5.85271i | −0.715022 | − | 0.715022i | 0.252559 | − | 0.967581i | \(-0.418728\pi\) |
−0.967581 | + | 0.252559i | \(0.918728\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.1431i | 1.79716i | 0.438812 | + | 0.898579i | \(0.355399\pi\) | ||||
−0.438812 | + | 0.898579i | \(0.644601\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.88118 | 0.805381 | 0.402691 | − | 0.915336i | \(-0.368075\pi\) | ||||
0.402691 | + | 0.915336i | \(0.368075\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.97897 | + | 5.97897i | 0.681367 | + | 0.681367i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.9721i | − | 1.45947i | −0.683730 | − | 0.729735i | \(-0.739643\pi\) | ||
0.683730 | − | 0.729735i | \(-0.260357\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.88840 | − | 6.88840i | 0.756100 | − | 0.756100i | −0.219510 | − | 0.975610i | \(-0.570446\pi\) |
0.975610 | + | 0.219510i | \(0.0704459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.07987 | − | 8.85986i | 0.550989 | − | 0.960987i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.31609 | −0.669504 | −0.334752 | − | 0.942306i | \(-0.608653\pi\) | ||||
−0.334752 | + | 0.942306i | \(0.608653\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.19103 | + | 5.19103i | 0.544167 | + | 0.544167i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0574238 | + | 0.211766i | 0.00589155 | + | 0.0217267i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.56728i | − | 0.463737i | −0.972747 | − | 0.231869i | \(-0.925516\pi\) | ||
0.972747 | − | 0.231869i | \(-0.0744839\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.24690 | + | 6.24690i | 0.621589 | + | 0.621589i | 0.945938 | − | 0.324348i | \(-0.105145\pi\) |
−0.324348 | + | 0.945938i | \(0.605145\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.8548i | − | 1.36515i | −0.730815 | − | 0.682576i | \(-0.760860\pi\) | ||
0.730815 | − | 0.682576i | \(-0.239140\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.922209 | − | 0.922209i | −0.0891533 | − | 0.0891533i | 0.661124 | − | 0.750277i | \(-0.270080\pi\) |
−0.750277 | + | 0.661124i | \(0.770080\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.28662 | − | 2.28662i | −0.219019 | − | 0.219019i | 0.589066 | − | 0.808085i | \(-0.299496\pi\) |
−0.808085 | + | 0.589066i | \(0.799496\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.53772 | 0.709089 | 0.354544 | − | 0.935039i | \(-0.384636\pi\) | ||||
0.354544 | + | 0.935039i | \(0.384636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.19781 | − | 2.08911i | 0.111696 | − | 0.194811i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.16574i | 0.748552i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 11.3674i | − | 1.03340i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1799 | + | 0.100608i | −0.999960 | + | 0.00899866i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.00277854 | 0.000246555 | 0.000123278 | − | 1.00000i | \(-0.499961\pi\) | ||||
0.000123278 | 1.00000i | \(0.499961\pi\) | ||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.71989 | + | 8.71989i | 0.761860 | + | 0.761860i | 0.976658 | − | 0.214798i | \(-0.0689095\pi\) |
−0.214798 | + | 0.976658i | \(0.568909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.124050 | − | 0.124050i | −0.0107565 | − | 0.0107565i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 23.1771i | − | 1.98016i | −0.140516 | − | 0.990078i | \(-0.544876\pi\) | ||
0.140516 | − | 0.990078i | \(-0.455124\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.85331 | + | 7.85331i | 0.666109 | + | 0.666109i | 0.956813 | − | 0.290704i | \(-0.0938894\pi\) |
−0.290704 | + | 0.956813i | \(0.593889\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 19.4197i | − | 1.62396i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.02614 | − | 3.78417i | −0.0852164 | − | 0.314258i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.6076 | + | 13.6076i | 1.11478 | + | 1.11478i | 0.992495 | + | 0.122285i | \(0.0390222\pi\) |
0.122285 | + | 0.992495i | \(0.460978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2447 | −1.24059 | −0.620297 | − | 0.784367i | \(-0.712988\pi\) | ||||
−0.620297 | + | 0.784367i | \(0.712988\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.6169 | + | 9.52742i | 1.33470 | + | 0.765261i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.76894 | − | 5.76894i | 0.460411 | − | 0.460411i | −0.438379 | − | 0.898790i | \(-0.644447\pi\) |
0.898790 | + | 0.438379i | \(0.144447\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.92544i | 0.151746i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.4511 | − | 10.4511i | −0.818594 | − | 0.818594i | 0.167311 | − | 0.985904i | \(-0.446492\pi\) |
−0.985904 | + | 0.167311i | \(0.946492\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.41872 | 0.728842 | 0.364421 | − | 0.931234i | \(-0.381267\pi\) | ||||
0.364421 | + | 0.931234i | \(0.381267\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 3.86046i | − | 0.296958i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.21995 | + | 6.21995i | 0.472894 | + | 0.472894i | 0.902850 | − | 0.429956i | \(-0.141471\pi\) |
−0.429956 | + | 0.902850i | \(0.641471\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.71471 | − | 4.51601i | 0.583177 | − | 0.341378i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.4020 | − | 18.4020i | −1.37543 | − | 1.37543i | −0.852179 | − | 0.523251i | \(-0.824719\pi\) |
−0.523251 | − | 0.852179i | \(-0.675281\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.5731 | + | 18.5731i | −1.38053 | + | 1.38053i | −0.536851 | + | 0.843677i | \(0.680386\pi\) |
−0.843677 | + | 0.536851i | \(0.819614\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.2707 | + | 6.31023i | −1.71089 | + | 0.463937i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.2741 | − | 15.2741i | 1.11695 | − | 1.11695i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.73383 | 0.342528 | 0.171264 | − | 0.985225i | \(-0.445215\pi\) | ||||
0.171264 | + | 0.985225i | \(0.445215\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 16.7218i | − | 1.20366i | −0.798625 | − | 0.601829i | \(-0.794439\pi\) | ||
0.798625 | − | 0.601829i | \(-0.205561\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.93066 | + | 7.93066i | −0.565036 | + | 0.565036i | −0.930734 | − | 0.365698i | \(-0.880830\pi\) |
0.365698 | + | 0.930734i | \(0.380830\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.34717 | 0.166386 | 0.0831932 | − | 0.996533i | \(-0.473488\pi\) | ||||
0.0831932 | + | 0.996533i | \(0.473488\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.21672 | + | 2.21672i | 0.155583 | + | 0.155583i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.80435 | + | 15.3558i | −0.614922 | + | 1.07249i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.464072i | 0.0321006i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.00077 | − | 3.00077i | 0.206581 | − | 0.206581i | −0.596231 | − | 0.802813i | \(-0.703336\pi\) |
0.802813 | + | 0.596231i | \(0.203336\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.94638 | + | 7.17781i | 0.132742 | + | 0.489522i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.3150 | −1.03965 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.2612 | − | 13.2612i | 0.892042 | − | 0.892042i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.6842 | −1.65298 | −0.826489 | − | 0.562952i | \(-0.809665\pi\) | ||||
−0.826489 | + | 0.562952i | \(0.809665\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.05360 | − | 5.05360i | 0.335419 | − | 0.335419i | −0.519221 | − | 0.854640i | \(-0.673778\pi\) |
0.854640 | + | 0.519221i | \(0.173778\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.4816 | + | 13.4816i | −0.890886 | + | 0.890886i | −0.994606 | − | 0.103720i | \(-0.966925\pi\) |
0.103720 | + | 0.994606i | \(0.466925\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.8466i | 0.776096i | 0.921639 | + | 0.388048i | \(0.126851\pi\) | ||||
−0.921639 | + | 0.388048i | \(0.873149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.2634 | + | 7.03132i | 0.799977 | + | 0.458673i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.8620 | −1.60819 | −0.804093 | − | 0.594503i | \(-0.797349\pi\) | ||||
−0.804093 | + | 0.594503i | \(0.797349\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8396 | 1.21356 | 0.606782 | − | 0.794868i | \(-0.292460\pi\) | ||||
0.606782 | + | 0.794868i | \(0.292460\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.23039 | − | 7.37828i | 0.270270 | − | 0.471381i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.402914i | 0.0256368i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.6723 | − | 21.6723i | 1.36795 | − | 1.36795i | 0.504582 | − | 0.863364i | \(-0.331647\pi\) |
0.863364 | − | 0.504582i | \(-0.168353\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.60155 | − | 3.60155i | 0.226428 | − | 0.226428i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.914423 | 0.0570402 | 0.0285201 | − | 0.999593i | \(-0.490921\pi\) | ||||
0.0285201 | + | 0.999593i | \(0.490921\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.6317 | − | 13.6317i | 0.847031 | − | 0.847031i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.19643 | −0.0737752 | −0.0368876 | − | 0.999319i | \(-0.511744\pi\) | ||||
−0.0368876 | + | 0.999319i | \(0.511744\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.99124 | − | 11.0310i | −0.183751 | − | 0.677630i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.54542 | − | 7.54542i | 0.460053 | − | 0.460053i | −0.438620 | − | 0.898673i | \(-0.644533\pi\) |
0.898673 | + | 0.438620i | \(0.144533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.45852i | − | 0.270836i | −0.990789 | − | 0.135418i | \(-0.956762\pi\) | ||
0.990789 | − | 0.135418i | \(-0.0432377\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22.8777 | − | 5.98318i | −1.37957 | − | 0.360800i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.28152 | + | 5.28152i | 0.317336 | + | 0.317336i | 0.847743 | − | 0.530407i | \(-0.177961\pi\) |
−0.530407 | + | 0.847743i | \(0.677961\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.3280 | 1.57060 | 0.785298 | − | 0.619118i | \(-0.212510\pi\) | ||||
0.785298 | + | 0.619118i | \(0.212510\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.6186 | + | 13.6186i | −0.809540 | + | 0.809540i | −0.984564 | − | 0.175024i | \(-0.944000\pi\) |
0.175024 | + | 0.984564i | \(0.444000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 14.1527i | − | 0.835409i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.86046 | 0.227086 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.23746 | + | 9.23746i | −0.539658 | + | 0.539658i | −0.923429 | − | 0.383770i | \(-0.874625\pi\) |
0.383770 | + | 0.923429i | \(0.374625\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.86280 | − | 6.86958i | −0.108457 | − | 0.399962i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.12692 | − | 3.12692i | 0.180834 | − | 0.180834i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.20468 | − | 4.20468i | −0.242353 | − | 0.242353i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.1206 | − | 3.55786i | 0.751282 | − | 0.203723i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.37148 | − | 2.37148i | −0.135348 | − | 0.135348i | 0.636187 | − | 0.771535i | \(-0.280511\pi\) |
−0.771535 | + | 0.636187i | \(0.780511\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5352i | 0.824214i | 0.911135 | + | 0.412107i | \(0.135207\pi\) | ||||
−0.911135 | + | 0.412107i | \(0.864793\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.2104 | 1.19888 | 0.599442 | − | 0.800418i | \(-0.295389\pi\) | ||||
0.599442 | + | 0.800418i | \(0.295389\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.575423 | + | 0.575423i | 0.0323190 | + | 0.0323190i | 0.723082 | − | 0.690763i | \(-0.242725\pi\) |
−0.690763 | + | 0.723082i | \(0.742725\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.29280i | − | 0.464308i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.316902 | + | 0.316902i | −0.0176329 | + | 0.0176329i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.8627 | − | 5.19468i | −1.10178 | − | 0.288149i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.3026 | −0.623134 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.54595 | − | 5.54595i | −0.304833 | − | 0.304833i | 0.538068 | − | 0.842901i | \(-0.319154\pi\) |
−0.842901 | + | 0.538068i | \(0.819154\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.8628 | + | 4.84380i | −0.975949 | + | 0.264645i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3650i | 0.891460i | 0.895167 | + | 0.445730i | \(0.147056\pi\) | ||||
−0.895167 | + | 0.445730i | \(0.852944\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.6469 | + | 28.6469i | 1.55132 | + | 1.55132i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.3152i | 1.04293i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.6768 | + | 18.6768i | 1.00262 | + | 1.00262i | 0.999997 | + | 0.00262421i | \(0.000835314\pi\) |
0.00262421 | + | 0.999997i | \(0.499165\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.2350 | + | 15.2350i | 0.815511 | + | 0.815511i | 0.985454 | − | 0.169943i | \(-0.0543583\pi\) |
−0.169943 | + | 0.985454i | \(0.554358\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.23255 | 0.438175 | 0.219087 | − | 0.975705i | \(-0.429692\pi\) | ||||
0.219087 | + | 0.975705i | \(0.429692\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.3752 | + | 16.8425i | 1.55907 | + | 0.893906i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 4.96843i | − | 0.262224i | −0.991368 | − | 0.131112i | \(-0.958145\pi\) | ||
0.991368 | − | 0.131112i | \(-0.0418547\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9904i | 0.999493i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.65339 | − | 13.3484i | 0.400597 | − | 0.698685i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.3790 | 1.32477 | 0.662385 | − | 0.749163i | \(-0.269544\pi\) | ||||
0.662385 | + | 0.749163i | \(0.269544\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.46184 | + | 6.46184i | 0.335482 | + | 0.335482i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.85715 | − | 2.85715i | −0.147938 | − | 0.147938i | 0.629259 | − | 0.777196i | \(-0.283359\pi\) |
−0.777196 | + | 0.629259i | \(0.783359\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.19992i | − | 0.370815i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.96148 | + | 8.96148i | 0.460320 | + | 0.460320i | 0.898760 | − | 0.438440i | \(-0.144469\pi\) |
−0.438440 | + | 0.898760i | \(0.644469\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.83688i | 0.502641i | 0.967904 | + | 0.251321i | \(0.0808648\pi\) | ||||
−0.967904 | + | 0.251321i | \(0.919135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.2482 | − | 4.94829i | 0.930012 | − | 0.252188i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.69886 | + | 8.69886i | 0.441050 | + | 0.441050i | 0.892365 | − | 0.451315i | \(-0.149045\pi\) |
−0.451315 | + | 0.892365i | \(0.649045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.91879 | 0.248754 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −25.1637 | − | 14.4278i | −1.26612 | − | 0.725941i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.52696 | − | 2.52696i | 0.126824 | − | 0.126824i | −0.640845 | − | 0.767670i | \(-0.721416\pi\) |
0.767670 | + | 0.640845i | \(0.221416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.5176i | 0.575161i | 0.957757 | + | 0.287580i | \(0.0928508\pi\) | ||||
−0.957757 | + | 0.287580i | \(0.907149\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.8716 | + | 24.8716i | 1.23894 | + | 1.23894i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −50.9963 | −2.52779 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 17.5055i | − | 0.865591i | −0.901492 | − | 0.432795i | \(-0.857527\pi\) | ||
0.901492 | − | 0.432795i | \(-0.142473\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.02412 | + | 4.02412i | 0.198014 | + | 0.198014i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.70095 | − | 21.0238i | −0.279849 | − | 1.03202i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.30068 | − | 3.30068i | −0.161249 | − | 0.161249i | 0.621871 | − | 0.783120i | \(-0.286373\pi\) |
−0.783120 | + | 0.621871i | \(0.786373\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.14311 | + | 6.14311i | −0.299397 | + | 0.299397i | −0.840778 | − | 0.541381i | \(-0.817902\pi\) |
0.541381 | + | 0.840778i | \(0.317902\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.5368 | − | 19.7082i | −0.559615 | − | 0.955990i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.68588 | + | 7.68588i | −0.371946 | + | 0.371946i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.73359 | 0.420682 | 0.210341 | − | 0.977628i | \(-0.432543\pi\) | ||||
0.210341 | + | 0.977628i | \(0.432543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.28479i | 0.109800i | 0.998492 | + | 0.0548999i | \(0.0174840\pi\) | ||||
−0.998492 | + | 0.0548999i | \(0.982516\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.0747238 | + | 0.0747238i | −0.00357452 | + | 0.00357452i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.7235 | −1.32317 | −0.661585 | − | 0.749870i | \(-0.730116\pi\) | ||||
−0.661585 | + | 0.749870i | \(0.730116\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.8575 | − | 15.8575i | −0.753410 | − | 0.753410i | 0.221704 | − | 0.975114i | \(-0.428838\pi\) |
−0.975114 | + | 0.221704i | \(0.928838\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.02488 | + | 12.2522i | −0.333011 | + | 0.580809i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.7098i | − | 1.07174i | −0.844301 | − | 0.535870i | \(-0.819984\pi\) | ||
0.844301 | − | 0.535870i | \(-0.180016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.4728 | + | 26.4728i | −1.24655 | + | 1.24655i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.8433 | − | 4.29618i | 0.742746 | − | 0.201408i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.3185 | −1.09079 | −0.545397 | − | 0.838178i | \(-0.683621\pi\) | ||||
−0.545397 | + | 0.838178i | \(0.683621\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.98422 | + | 6.98422i | −0.325288 | + | 0.325288i | −0.850791 | − | 0.525504i | \(-0.823877\pi\) |
0.525504 | + | 0.850791i | \(0.323877\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.177929 | 0.00826905 | 0.00413453 | − | 0.999991i | \(-0.498684\pi\) | ||||
0.00413453 | + | 0.999991i | \(0.498684\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.8586 | − | 25.8586i | 1.19659 | − | 1.19659i | 0.221414 | − | 0.975180i | \(-0.428933\pi\) |
0.975180 | − | 0.221414i | \(-0.0710672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4638 | − | 10.4638i | 0.483175 | − | 0.483175i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.7298i | 0.723255i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.474658 | + | 0.124137i | 0.0217788 | + | 0.00569581i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.74528 | −0.308200 | −0.154100 | − | 0.988055i | \(-0.549248\pi\) | ||||
−0.154100 | + | 0.988055i | \(0.549248\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −44.2757 | −2.01880 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.85978 | − | 5.07982i | −0.402302 | − | 0.230663i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.5084i | 1.24652i | 0.782014 | + | 0.623261i | \(0.214193\pi\) | ||||
−0.782014 | + | 0.623261i | \(0.785807\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.96277 | + | 1.96277i | −0.0885786 | + | 0.0885786i | −0.750008 | − | 0.661429i | \(-0.769950\pi\) |
0.661429 | + | 0.750008i | \(0.269950\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.66291 | − | 5.66291i | 0.255045 | − | 0.255045i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27.0738 | −1.21442 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0400 | − | 10.0400i | 0.449452 | − | 0.449452i | −0.445720 | − | 0.895172i | \(-0.647052\pi\) |
0.895172 | + | 0.445720i | \(0.147052\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.8104 | −0.704952 | −0.352476 | − | 0.935821i | \(-0.614660\pi\) | ||||
−0.352476 | + | 0.935821i | \(0.614660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.0659 | − | 5.17003i | 0.848421 | − | 0.230063i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.6015 | + | 16.6015i | −0.735849 | + | 0.735849i | −0.971772 | − | 0.235922i | \(-0.924189\pi\) |
0.235922 | + | 0.971772i | \(0.424189\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.3026i | 0.544234i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.8760 | − | 15.4096i | −1.18430 | − | 0.679027i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.1417 | + | 21.1417i | 0.929809 | + | 0.929809i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.96468 | −0.348939 | −0.174469 | − | 0.984663i | \(-0.555821\pi\) | ||||
−0.174469 | + | 0.984663i | \(0.555821\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.2514 | + | 15.2514i | −0.666897 | + | 0.666897i | −0.956997 | − | 0.290099i | \(-0.906312\pi\) |
0.290099 | + | 0.956997i | \(0.406312\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.1243i | 1.70428i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8402 | −0.949573 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.9840 | + | 22.9840i | −0.995549 | + | 0.995549i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.81463 | + | 0.763235i | −0.121687 | + | 0.0329975i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.7199 | − | 12.7199i | 0.547884 | − | 0.547884i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.80924 | − | 6.80924i | −0.292752 | − | 0.292752i | 0.545414 | − | 0.838167i | \(-0.316372\pi\) |
−0.838167 | + | 0.545414i | \(0.816372\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.97890 | + | 1.89245i | −0.298943 | + | 0.0810635i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.8809 | − | 24.8809i | −1.06383 | − | 1.06383i | −0.997819 | − | 0.0660132i | \(-0.978972\pi\) |
−0.0660132 | − | 0.997819i | \(-0.521028\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.172056i | 0.00732985i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.1922 | 0.986233 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.05959 | − | 3.05959i | −0.129639 | − | 0.129639i | 0.639310 | − | 0.768949i | \(-0.279220\pi\) |
−0.768949 | + | 0.639310i | \(0.779220\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.6568i | 0.577621i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.0945 | + | 32.0945i | −1.35262 | + | 1.35262i | −0.469906 | + | 0.882716i | \(0.655712\pi\) |
−0.882716 | + | 0.469906i | \(0.844288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.38360 | − | 14.6219i | 0.352701 | − | 0.615150i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.4585 | −1.19304 | −0.596521 | − | 0.802597i | \(-0.703451\pi\) | ||||
−0.596521 | + | 0.802597i | \(0.703451\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.7837 | + | 26.7837i | 1.12086 | + | 1.12086i | 0.991612 | + | 0.129250i | \(0.0412571\pi\) |
0.129250 | + | 0.991612i | \(0.458743\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.72031 | − | 4.64710i | −0.113445 | − | 0.193798i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.4904i | 1.39423i | 0.716962 | + | 0.697113i | \(0.245532\pi\) | ||||
−0.716962 | + | 0.697113i | \(0.754468\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.3155 | + | 12.3155i | 0.510933 | + | 0.510933i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 24.1738i | − | 1.00118i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.3666 | + | 12.3666i | 0.510425 | + | 0.510425i | 0.914657 | − | 0.404232i | \(-0.132461\pi\) |
−0.404232 | + | 0.914657i | \(0.632461\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.594357 | − | 0.594357i | −0.0244900 | − | 0.0244900i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.1105 | −0.990099 | −0.495050 | − | 0.868865i | \(-0.664850\pi\) | ||||
−0.495050 | + | 0.868865i | \(0.664850\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.8402 | + | 9.08210i | 0.649385 | + | 0.372330i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.0184i | 0.736213i | 0.929784 | + | 0.368107i | \(0.119994\pi\) | ||||
−0.929784 | + | 0.368107i | \(0.880006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.8361i | 0.768342i | 0.923262 | + | 0.384171i | \(0.125513\pi\) | ||||
−0.923262 | + | 0.384171i | \(0.874487\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.0510 | − | 12.6431i | −0.896499 | − | 0.514015i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.4336 | 0.423486 | 0.211743 | − | 0.977325i | \(-0.432086\pi\) | ||||
0.211743 | + | 0.977325i | \(0.432086\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.3555 | + | 18.3555i | 0.742583 | + | 0.742583i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.35631 | + | 9.35631i | 0.377898 | + | 0.377898i | 0.870343 | − | 0.492445i | \(-0.163897\pi\) |
−0.492445 | + | 0.870343i | \(0.663897\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.8927i | 0.921626i | 0.887497 | + | 0.460813i | \(0.152442\pi\) | ||||
−0.887497 | + | 0.460813i | \(0.847558\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.9542 | − | 32.9542i | −1.32454 | − | 1.32454i | −0.910057 | − | 0.414484i | \(-0.863962\pi\) |
−0.414484 | − | 0.910057i | \(-0.636038\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 11.2923i | − | 0.452415i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.2393 | + | 21.7991i | −0.489573 | + | 0.871962i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.8239 | − | 34.8239i | −1.38852 | − | 1.38852i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.9668 | −0.595817 | −0.297908 | − | 0.954594i | \(-0.596289\pi\) | ||||
−0.297908 | + | 0.954594i | \(0.596289\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.00309035 | − | 0.00538991i | 0.000122637 | − | 0.000213892i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.0436 | − | 11.0436i | 0.437562 | − | 0.437562i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 3.08889i | − | 0.122004i | −0.998138 | − | 0.0610019i | \(-0.980570\pi\) | ||
0.998138 | − | 0.0610019i | \(-0.0194296\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.1306 | − | 18.1306i | −0.715001 | − | 0.715001i | 0.252576 | − | 0.967577i | \(-0.418722\pi\) |
−0.967577 | + | 0.252576i | \(0.918722\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.79255 | −0.267043 | −0.133521 | − | 0.991046i | \(-0.542628\pi\) | ||||
−0.133521 | + | 0.991046i | \(0.542628\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 15.0543i | − | 0.590933i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.2088 | − | 12.2088i | −0.477769 | − | 0.477769i | 0.426649 | − | 0.904417i | \(-0.359694\pi\) |
−0.904417 | + | 0.426649i | \(0.859694\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.6136 | − | 7.21672i | 1.03988 | − | 0.281981i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.8761 | + | 24.8761i | 0.969034 | + | 0.969034i | 0.999535 | − | 0.0305007i | \(-0.00971017\pi\) |
−0.0305007 | + | 0.999535i | \(0.509710\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.1349 | + | 21.1349i | −0.822052 | + | 0.822052i | −0.986402 | − | 0.164350i | \(-0.947447\pi\) |
0.164350 | + | 0.986402i | \(0.447447\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.378607 | + | 0.102666i | −0.0146818 | + | 0.00398120i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.33529 | − | 1.33529i | 0.0517025 | − | 0.0517025i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.7530 | 1.11000 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.6471i | 1.87521i | 0.347705 | + | 0.937604i | \(0.386961\pi\) | ||||
−0.347705 | + | 0.937604i | \(0.613039\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.69556 | − | 8.69556i | 0.334197 | − | 0.334197i | −0.519981 | − | 0.854178i | \(-0.674061\pi\) |
0.854178 | + | 0.519981i | \(0.174061\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.16566 | 0.313369 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.4514 | − | 26.4514i | −1.01213 | − | 1.01213i | −0.999925 | − | 0.0122093i | \(-0.996114\pi\) |
−0.0122093 | − | 0.999925i | \(-0.503886\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −44.9599 | − | 25.7781i | −1.71783 | − | 0.984930i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 20.9881i | − | 0.799582i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.89820 | + | 8.89820i | −0.338503 | + | 0.338503i | −0.855804 | − | 0.517301i | \(-0.826937\pi\) |
0.517301 | + | 0.855804i | \(0.326937\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.9688 | − | 6.49953i | 0.909187 | − | 0.246541i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.1550 | −1.36947 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.7989 | − | 15.7989i | 0.596716 | − | 0.596716i | −0.342721 | − | 0.939437i | \(-0.611349\pi\) |
0.939437 | + | 0.342721i | \(0.111349\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.05806 | 0.0399053 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.1686 | + | 11.1686i | −0.420037 | + | 0.420037i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.9259 | − | 18.9259i | 0.710776 | − | 0.710776i | −0.255922 | − | 0.966697i | \(-0.582379\pi\) |
0.966697 | + | 0.255922i | \(0.0823790\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.22531i | 0.345490i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −37.6711 | − | 21.5990i | −1.40882 | − | 0.807757i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.6789 | 0.398256 | 0.199128 | − | 0.979973i | \(-0.436189\pi\) | ||||
0.199128 | + | 0.979973i | \(0.436189\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.7704 | 0.922498 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.48197 | − | 2.21828i | −0.315012 | − | 0.0823850i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.2573i | 1.19636i | 0.801363 | + | 0.598179i | \(0.204109\pi\) | ||||
−0.801363 | + | 0.598179i | \(0.795891\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.7414 | + | 10.7414i | −0.397285 | + | 0.397285i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.6986 | + | 29.6986i | −1.09694 | + | 1.09694i | −0.102175 | + | 0.994766i | \(0.532580\pi\) |
−0.994766 | + | 0.102175i | \(0.967420\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −39.1453 | −1.44194 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.7806 | + | 19.7806i | −0.727640 | + | 0.727640i | −0.970149 | − | 0.242509i | \(-0.922030\pi\) |
0.242509 | + | 0.970149i | \(0.422030\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.3449 | 1.25999 | 0.629996 | − | 0.776598i | \(-0.283056\pi\) | ||||
0.629996 | + | 0.776598i | \(0.283056\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.5312 | − | 11.2619i | 1.52159 | − | 0.412604i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.64878 | − | 1.64878i | 0.0602451 | − | 0.0602451i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.4556i | 1.76817i | 0.467326 | + | 0.884085i | \(0.345217\pi\) | ||||
−0.467326 | + | 0.884085i | \(0.654783\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.9554 | + | 29.5722i | −0.617071 | + | 1.07624i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.8358 | + | 24.8358i | 0.902672 | + | 0.902672i | 0.995667 | − | 0.0929947i | \(-0.0296440\pi\) |
−0.0929947 | + | 0.995667i | \(0.529644\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.2421 | 0.951274 | 0.475637 | − | 0.879642i | \(-0.342218\pi\) | ||||
0.475637 | + | 0.879642i | \(0.342218\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.08816 | − | 4.08816i | 0.148001 | − | 0.148001i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 13.0704i | − | 0.471943i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.4168 | 0.916552 | 0.458276 | − | 0.888810i | \(-0.348467\pi\) | ||||
0.458276 | + | 0.888810i | \(0.348467\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.1984 | − | 30.1984i | 1.08616 | − | 1.08616i | 0.0902412 | − | 0.995920i | \(-0.471236\pi\) |
0.995920 | − | 0.0902412i | \(-0.0287638\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.9633 | − | 21.6374i | 1.32776 | − | 0.777240i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.549249 | − | 0.549249i | 0.0196789 | − | 0.0196789i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.6417 | + | 50.6417i | 1.81210 | + | 1.81210i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.77447 | − | 17.6071i | −0.170408 | − | 0.628425i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.3428 | + | 19.3428i | 0.689496 | + | 0.689496i | 0.962120 | − | 0.272625i | \(-0.0878917\pi\) |
−0.272625 | + | 0.962120i | \(0.587892\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.4764i | 0.479165i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.9637 | 0.886489 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.3328 | + | 32.3328i | 1.14529 | + | 1.14529i | 0.987468 | + | 0.157820i | \(0.0504466\pi\) |
0.157820 | + | 0.987468i | \(0.449553\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.8741i | 1.02149i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.0121 | − | 23.0121i | 0.812079 | − | 0.812079i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.73504 | + | 2.14151i | 0.131643 | + | 0.0754784i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.09587 | 0.144003 | 0.0720015 | − | 0.997405i | \(-0.477061\pi\) | ||||
0.0720015 | + | 0.997405i | \(0.477061\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.34586 | − | 1.34586i | −0.0472594 | − | 0.0472594i | 0.683082 | − | 0.730342i | \(-0.260639\pi\) |
−0.730342 | + | 0.683082i | \(0.760639\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −31.8974 | + | 8.64950i | −1.11732 | + | 0.302979i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 0.326356i | − | 0.0114178i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.3658 | − | 16.3658i | −0.571171 | − | 0.571171i | 0.361285 | − | 0.932456i | \(-0.382338\pi\) |
−0.932456 | + | 0.361285i | \(0.882338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.6816i | 1.17407i | 0.809562 | + | 0.587034i | \(0.199705\pi\) | ||||
−0.809562 | + | 0.587034i | \(0.800295\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.94113 | − | 1.94113i | −0.0674997 | − | 0.0674997i | 0.672551 | − | 0.740051i | \(-0.265199\pi\) |
−0.740051 | + | 0.672551i | \(0.765199\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.5836 | − | 31.5836i | −1.09695 | − | 1.09695i | −0.994766 | − | 0.102179i | \(-0.967419\pi\) |
−0.102179 | − | 0.994766i | \(-0.532581\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.3721 | 0.601907 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.4757 | − | 18.2708i | 0.362526 | − | 0.632286i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 25.0492i | − | 0.864795i | −0.901683 | − | 0.432398i | \(-0.857668\pi\) | ||
0.901683 | − | 0.432398i | \(-0.142332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.9254i | 0.893980i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.48866 | − | 4.29368i | −0.257618 | − | 0.147707i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.3234 | 0.698319 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.21131 | − | 8.21131i | −0.281480 | − | 0.281480i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.21199 | − | 5.21199i | −0.178455 | − | 0.178455i | 0.612227 | − | 0.790682i | \(-0.290274\pi\) |
−0.790682 | + | 0.612227i | \(0.790274\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 42.7298i | − | 1.45962i | −0.683649 | − | 0.729811i | \(-0.739608\pi\) | ||
0.683649 | − | 0.729811i | \(-0.260392\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.0244 | + | 12.0244i | 0.410268 | + | 0.410268i | 0.881832 | − | 0.471564i | \(-0.156310\pi\) |
−0.471564 | + | 0.881832i | \(0.656310\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.21809i | 0.0755047i | 0.999287 | + | 0.0377523i | \(0.0120198\pi\) | ||||
−0.999287 | + | 0.0377523i | \(0.987980\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.9836 | − | 5.14773i | 0.645463 | − | 0.175028i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −43.3812 | − | 43.3812i | −1.47161 | − | 1.47161i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.9865 | −1.15159 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.179873 | − | 19.9881i | −0.00608082 | − | 0.675720i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.6890 | − | 37.6890i | 1.27267 | − | 1.27267i | 0.327984 | − | 0.944683i | \(-0.393631\pi\) |
0.944683 | − | 0.327984i | \(-0.106369\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.4850i | 0.555395i | 0.960669 | + | 0.277698i | \(0.0895713\pi\) | ||||
−0.960669 | + | 0.277698i | \(0.910429\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.2952 | + | 25.2952i | 0.851251 | + | 0.851251i | 0.990287 | − | 0.139036i | \(-0.0444004\pi\) |
−0.139036 | + | 0.990287i | \(0.544400\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51.1894 | −1.71877 | −0.859386 | − | 0.511327i | \(-0.829154\pi\) | ||||
−0.859386 | + | 0.511327i | \(0.829154\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.00496763i | 0.000166609i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.438641 | − | 0.438641i | −0.0146785 | − | 0.0146785i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −56.1639 | + | 15.2298i | −1.87735 | + | 0.509076i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.6209 | + | 10.6209i | 0.354228 | + | 0.354228i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.5076 | − | 16.5076i | 0.549949 | − | 0.549949i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.3714 | + | 56.6862i | 0.510963 | + | 1.88431i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.4729 | + | 12.4729i | −0.414156 | + | 0.414156i | −0.883183 | − | 0.469028i | \(-0.844604\pi\) |
0.469028 | + | 0.883183i | \(0.344604\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.2168 | 1.36557 | 0.682786 | − | 0.730618i | \(-0.260768\pi\) | ||||
0.682786 | + | 0.730618i | \(0.260768\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 46.0725i | − | 1.52478i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.5899 | + | 15.5899i | −0.514825 | + | 0.514825i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.4592 | 1.20268 | 0.601339 | − | 0.798994i | \(-0.294634\pi\) | ||||
0.601339 | + | 0.798994i | \(0.294634\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 43.9678 | + | 43.9678i | 1.44722 | + | 1.44722i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.6413 | + | 52.1596i | −0.448523 | + | 1.71500i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.1770i | 0.760413i | 0.924902 | + | 0.380206i | \(0.124147\pi\) | ||||
−0.924902 | + | 0.380206i | \(0.875853\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.263908 | + | 0.263908i | −0.00864924 | + | 0.00864924i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.6411 | − | 46.6174i | −0.413407 | − | 1.52455i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.1100 | −1.08166 | −0.540829 | − | 0.841133i | \(-0.681889\pi\) | ||||
−0.540829 | + | 0.841133i | \(0.681889\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7810 | + | 11.7810i | −0.384050 | + | 0.384050i | −0.872559 | − | 0.488509i | \(-0.837541\pi\) |
0.488509 | + | 0.872559i | \(0.337541\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.52517 | −0.277618 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.78760 | + | 3.78760i | −0.123080 | + | 0.123080i | −0.765964 | − | 0.642884i | \(-0.777738\pi\) |
0.642884 | + | 0.765964i | \(0.277738\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.9794 | − | 19.9794i | 0.648559 | − | 0.648559i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 33.8756i | − | 1.09734i | −0.836039 | − | 0.548670i | \(-0.815134\pi\) | ||
0.836039 | − | 0.548670i | \(-0.184866\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.26506 | − | 9.18286i | 0.170373 | − | 0.297150i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 41.4375 | 1.33809 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −42.3785 | −1.36705 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.4375 | − | 18.5983i | −1.04420 | − | 0.598700i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.8455i | 1.28134i | 0.767814 | + | 0.640672i | \(0.221344\pi\) | ||||
−0.767814 | + | 0.640672i | \(0.778656\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.4598 | + | 10.4598i | −0.335670 | + | 0.335670i | −0.854735 | − | 0.519065i | \(-0.826280\pi\) |
0.519065 | + | 0.854735i | \(0.326280\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.0406 | + | 14.0406i | −0.450122 | + | 0.450122i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.8272 | 1.05024 | 0.525118 | − | 0.851030i | \(-0.324021\pi\) | ||||
0.525118 | + | 0.851030i | \(0.324021\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.1223 | + | 21.1223i | −0.675071 | + | 0.675071i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.96088 | −0.158227 | −0.0791137 | − | 0.996866i | \(-0.525209\pi\) | ||||
−0.0791137 | + | 0.996866i | \(0.525209\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.56354 | + | 24.2048i | 0.209132 | + | 0.771229i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.53277 | + | 2.53277i | −0.0805373 | + | 0.0805373i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 53.9675i | − | 1.71433i | −0.515039 | − | 0.857166i | \(-0.672223\pi\) | ||
0.515039 | − | 0.857166i | \(-0.327777\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.61057 | − | 4.55312i | 0.0827606 | − | 0.144344i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.14670 | + | 3.14670i | 0.0996570 | + | 0.0996570i | 0.755177 | − | 0.655520i | \(-0.227551\pi\) |
−0.655520 | + | 0.755177i | \(0.727551\pi\) | |||||||
\(998\) | 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.u.a.2159.31 | 96 | ||
3.2 | odd | 2 | inner | 2880.2.u.a.2159.18 | 96 | ||
4.3 | odd | 2 | 720.2.u.a.179.13 | ✓ | 96 | ||
5.4 | even | 2 | inner | 2880.2.u.a.2159.7 | 96 | ||
12.11 | even | 2 | 720.2.u.a.179.36 | yes | 96 | ||
15.14 | odd | 2 | inner | 2880.2.u.a.2159.42 | 96 | ||
16.5 | even | 4 | 720.2.u.a.539.14 | yes | 96 | ||
16.11 | odd | 4 | inner | 2880.2.u.a.719.42 | 96 | ||
20.19 | odd | 2 | 720.2.u.a.179.35 | yes | 96 | ||
48.5 | odd | 4 | 720.2.u.a.539.35 | yes | 96 | ||
48.11 | even | 4 | inner | 2880.2.u.a.719.7 | 96 | ||
60.59 | even | 2 | 720.2.u.a.179.14 | yes | 96 | ||
80.59 | odd | 4 | inner | 2880.2.u.a.719.18 | 96 | ||
80.69 | even | 4 | 720.2.u.a.539.36 | yes | 96 | ||
240.59 | even | 4 | inner | 2880.2.u.a.719.31 | 96 | ||
240.149 | odd | 4 | 720.2.u.a.539.13 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.u.a.179.13 | ✓ | 96 | 4.3 | odd | 2 | ||
720.2.u.a.179.14 | yes | 96 | 60.59 | even | 2 | ||
720.2.u.a.179.35 | yes | 96 | 20.19 | odd | 2 | ||
720.2.u.a.179.36 | yes | 96 | 12.11 | even | 2 | ||
720.2.u.a.539.13 | yes | 96 | 240.149 | odd | 4 | ||
720.2.u.a.539.14 | yes | 96 | 16.5 | even | 4 | ||
720.2.u.a.539.35 | yes | 96 | 48.5 | odd | 4 | ||
720.2.u.a.539.36 | yes | 96 | 80.69 | even | 4 | ||
2880.2.u.a.719.7 | 96 | 48.11 | even | 4 | inner | ||
2880.2.u.a.719.18 | 96 | 80.59 | odd | 4 | inner | ||
2880.2.u.a.719.31 | 96 | 240.59 | even | 4 | inner | ||
2880.2.u.a.719.42 | 96 | 16.11 | odd | 4 | inner | ||
2880.2.u.a.2159.7 | 96 | 5.4 | even | 2 | inner | ||
2880.2.u.a.2159.18 | 96 | 3.2 | odd | 2 | inner | ||
2880.2.u.a.2159.31 | 96 | 1.1 | even | 1 | trivial | ||
2880.2.u.a.2159.42 | 96 | 15.14 | odd | 2 | inner |