Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(161,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.j (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: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 161.13 | ||
Character | \(\chi\) | \(=\) | 1152.161 |
Dual form | 1152.3.j.a.737.13 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.90343 | + | 3.90343i | 0.780685 | + | 0.780685i | 0.979946 | − | 0.199261i | \(-0.0638542\pi\) |
−0.199261 | + | 0.979946i | \(0.563854\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.778757i | − | 0.111251i | −0.998452 | − | 0.0556255i | \(-0.982285\pi\) | ||
0.998452 | − | 0.0556255i | \(-0.0177153\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.29098 | + | 4.29098i | 0.390089 | + | 0.390089i | 0.874719 | − | 0.484630i | \(-0.161046\pi\) |
−0.484630 | + | 0.874719i | \(0.661046\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.44007 | − | 6.44007i | −0.495390 | − | 0.495390i | 0.414610 | − | 0.909999i | \(-0.363918\pi\) |
−0.909999 | + | 0.414610i | \(0.863918\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 31.3383i | − | 1.84343i | −0.387872 | − | 0.921713i | \(-0.626790\pi\) | ||
0.387872 | − | 0.921713i | \(-0.373210\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.11906 | − | 1.11906i | −0.0588979 | − | 0.0588979i | 0.677044 | − | 0.735942i | \(-0.263261\pi\) |
−0.735942 | + | 0.677044i | \(0.763261\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 34.2197 | 1.48781 | 0.743906 | − | 0.668285i | \(-0.232971\pi\) | ||||
0.743906 | + | 0.668285i | \(0.232971\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47346i | 0.218939i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.77471 | − | 8.77471i | 0.302576 | − | 0.302576i | −0.539445 | − | 0.842021i | \(-0.681366\pi\) |
0.842021 | + | 0.539445i | \(0.181366\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 50.8507 | 1.64035 | 0.820173 | − | 0.572116i | \(-0.193877\pi\) | ||||
0.820173 | + | 0.572116i | \(0.193877\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.03982 | − | 3.03982i | 0.0868520 | − | 0.0868520i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 29.3064 | − | 29.3064i | 0.792065 | − | 0.792065i | −0.189765 | − | 0.981830i | \(-0.560773\pi\) |
0.981830 | + | 0.189765i | \(0.0607725\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −31.4271 | −0.766513 | −0.383257 | − | 0.923642i | \(-0.625198\pi\) | ||||
−0.383257 | + | 0.923642i | \(0.625198\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −55.9022 | + | 55.9022i | −1.30005 | + | 1.30005i | −0.371696 | + | 0.928354i | \(0.621224\pi\) |
−0.928354 | + | 0.371696i | \(0.878776\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 26.5249i | 0.564359i | 0.959362 | + | 0.282180i | \(0.0910574\pi\) | ||||
−0.959362 | + | 0.282180i | \(0.908943\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.3935 | 0.987623 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.76389 | + | 9.76389i | 0.184224 | + | 0.184224i | 0.793194 | − | 0.608969i | \(-0.208417\pi\) |
−0.608969 | + | 0.793194i | \(0.708417\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 33.4991i | 0.609074i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −54.3706 | − | 54.3706i | −0.921535 | − | 0.921535i | 0.0756026 | − | 0.997138i | \(-0.475912\pi\) |
−0.997138 | + | 0.0756026i | \(0.975912\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 47.1104 | + | 47.1104i | 0.772302 | + | 0.772302i | 0.978508 | − | 0.206207i | \(-0.0661119\pi\) |
−0.206207 | + | 0.978508i | \(0.566112\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 50.2766i | − | 0.773487i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 66.1339 | + | 66.1339i | 0.987073 | + | 0.987073i | 0.999918 | − | 0.0128446i | \(-0.00408867\pi\) |
−0.0128446 | + | 0.999918i | \(0.504089\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 75.9403 | 1.06958 | 0.534791 | − | 0.844985i | \(-0.320391\pi\) | ||||
0.534791 | + | 0.844985i | \(0.320391\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 24.1992i | 0.331497i | 0.986168 | + | 0.165748i | \(0.0530039\pi\) | ||||
−0.986168 | + | 0.165748i | \(0.946996\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.34163 | − | 3.34163i | 0.0433978 | − | 0.0433978i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −80.5454 | −1.01956 | −0.509781 | − | 0.860304i | \(-0.670274\pi\) | ||||
−0.509781 | + | 0.860304i | \(0.670274\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 82.6319 | − | 82.6319i | 0.995565 | − | 0.995565i | −0.00442530 | − | 0.999990i | \(-0.501409\pi\) |
0.999990 | + | 0.00442530i | \(0.00140862\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 122.327 | − | 122.327i | 1.43914 | − | 1.43914i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −82.6445 | −0.928590 | −0.464295 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464295 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.01524 | + | 5.01524i | −0.0551126 | + | 0.0551126i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 8.73634i | − | 0.0919614i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 48.9478 | 0.504617 | 0.252308 | − | 0.967647i | \(-0.418810\pi\) | ||||
0.252308 | + | 0.967647i | \(0.418810\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −41.2778 | − | 41.2778i | −0.408691 | − | 0.408691i | 0.472591 | − | 0.881282i | \(-0.343319\pi\) |
−0.881282 | + | 0.472591i | \(0.843319\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 173.236i | 1.68190i | 0.541111 | + | 0.840951i | \(0.318004\pi\) | ||||
−0.541111 | + | 0.840951i | \(0.681996\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 53.2761 | + | 53.2761i | 0.497907 | + | 0.497907i | 0.910786 | − | 0.412879i | \(-0.135477\pi\) |
−0.412879 | + | 0.910786i | \(0.635477\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 93.1537 | + | 93.1537i | 0.854621 | + | 0.854621i | 0.990698 | − | 0.136077i | \(-0.0434494\pi\) |
−0.136077 | + | 0.990698i | \(0.543449\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 40.8189i | − | 0.361229i | −0.983554 | − | 0.180615i | \(-0.942191\pi\) | ||
0.983554 | − | 0.180615i | \(-0.0578087\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 133.574 | + | 133.574i | 1.16151 | + | 1.16151i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.4049 | −0.205083 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 84.1749i | − | 0.695661i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 76.2204 | − | 76.2204i | 0.609763 | − | 0.609763i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 88.9136 | 0.700107 | 0.350054 | − | 0.936730i | \(-0.386163\pi\) | ||||
0.350054 | + | 0.936730i | \(0.386163\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.0108 | + | 22.0108i | −0.168021 | + | 0.168021i | −0.786109 | − | 0.618088i | \(-0.787908\pi\) |
0.618088 | + | 0.786109i | \(0.287908\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.871475 | + | 0.871475i | −0.00655245 | + | 0.00655245i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 110.794 | 0.808715 | 0.404358 | − | 0.914601i | \(-0.367495\pi\) | ||||
0.404358 | + | 0.914601i | \(0.367495\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −30.3862 | + | 30.3862i | −0.218605 | + | 0.218605i | −0.807911 | − | 0.589305i | \(-0.799402\pi\) |
0.589305 | + | 0.807911i | \(0.299402\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 55.2684i | − | 0.386493i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 68.5029 | 0.472433 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −173.924 | − | 173.924i | −1.16727 | − | 1.16727i | −0.982846 | − | 0.184428i | \(-0.940957\pi\) |
−0.184428 | − | 0.982846i | \(-0.559043\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 26.2521i | − | 0.173855i | −0.996215 | − | 0.0869274i | \(-0.972295\pi\) | ||
0.996215 | − | 0.0869274i | \(-0.0277048\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 198.492 | + | 198.492i | 1.28059 | + | 1.28059i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −75.8493 | − | 75.8493i | −0.483117 | − | 0.483117i | 0.423009 | − | 0.906126i | \(-0.360974\pi\) |
−0.906126 | + | 0.423009i | \(0.860974\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 26.6488i | − | 0.165520i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −155.285 | − | 155.285i | −0.952672 | − | 0.952672i | 0.0462578 | − | 0.998930i | \(-0.485270\pi\) |
−0.998930 | + | 0.0462578i | \(0.985270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 236.902 | 1.41857 | 0.709286 | − | 0.704920i | \(-0.249017\pi\) | ||||
0.709286 | + | 0.704920i | \(0.249017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 86.0511i | − | 0.509178i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 68.3708 | − | 68.3708i | 0.395207 | − | 0.395207i | −0.481332 | − | 0.876539i | \(-0.659847\pi\) |
0.876539 | + | 0.481332i | \(0.159847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.26250 | 0.0243571 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 129.626 | − | 129.626i | 0.724170 | − | 0.724170i | −0.245282 | − | 0.969452i | \(-0.578880\pi\) |
0.969452 | + | 0.245282i | \(0.0788804\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −157.641 | + | 157.641i | −0.870947 | + | 0.870947i | −0.992576 | − | 0.121629i | \(-0.961188\pi\) |
0.121629 | + | 0.992576i | \(0.461188\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 228.791 | 1.23671 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 134.472 | − | 134.472i | 0.719101 | − | 0.719101i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 58.1217i | − | 0.304302i | −0.988357 | − | 0.152151i | \(-0.951380\pi\) | ||
0.988357 | − | 0.152151i | \(-0.0486200\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 312.491 | 1.61912 | 0.809561 | − | 0.587035i | \(-0.199705\pi\) | ||||
0.809561 | + | 0.587035i | \(0.199705\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −44.8306 | − | 44.8306i | −0.227567 | − | 0.227567i | 0.584109 | − | 0.811675i | \(-0.301444\pi\) |
−0.811675 | + | 0.584109i | \(0.801444\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 157.131i | 0.789601i | 0.918767 | + | 0.394801i | \(0.129186\pi\) | ||||
−0.918767 | + | 0.394801i | \(0.870814\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.83336 | − | 6.83336i | −0.0336619 | − | 0.0336619i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −122.673 | − | 122.673i | −0.598406 | − | 0.598406i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 9.60374i | − | 0.0459509i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 68.3433 | + | 68.3433i | 0.323902 | + | 0.323902i | 0.850262 | − | 0.526360i | \(-0.176444\pi\) |
−0.526360 | + | 0.850262i | \(0.676444\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −436.420 | −2.02986 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 39.6003i | − | 0.182490i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −201.820 | + | 201.820i | −0.913214 | + | 0.913214i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.75135 | −0.0168222 | −0.00841111 | − | 0.999965i | \(-0.502677\pi\) | ||||
−0.00841111 | + | 0.999965i | \(0.502677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −224.963 | + | 224.963i | −0.991028 | + | 0.991028i | −0.999960 | − | 0.00893184i | \(-0.997157\pi\) |
0.00893184 | + | 0.999960i | \(0.497157\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.3030 | + | 26.3030i | −0.114860 | + | 0.114860i | −0.762201 | − | 0.647341i | \(-0.775881\pi\) |
0.647341 | + | 0.762201i | \(0.275881\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −166.492 | −0.714557 | −0.357279 | − | 0.933998i | \(-0.616295\pi\) | ||||
−0.357279 | + | 0.933998i | \(0.616295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −103.538 | + | 103.538i | −0.440587 | + | 0.440587i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 247.174i | − | 1.03420i | −0.855925 | − | 0.517100i | \(-0.827011\pi\) | ||
0.855925 | − | 0.517100i | \(-0.172989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7552 | 0.0612247 | 0.0306124 | − | 0.999531i | \(-0.490254\pi\) | ||||
0.0306124 | + | 0.999531i | \(0.490254\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 188.901 | + | 188.901i | 0.771023 | + | 0.771023i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.4136i | 0.0583548i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 41.5560 | + | 41.5560i | 0.165562 | + | 0.165562i | 0.785025 | − | 0.619464i | \(-0.212650\pi\) |
−0.619464 | + | 0.785025i | \(0.712650\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 146.836 | + | 146.836i | 0.580379 | + | 0.580379i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 189.265i | 0.736439i | 0.929739 | + | 0.368220i | \(0.120033\pi\) | ||||
−0.929739 | + | 0.368220i | \(0.879967\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.8226 | − | 22.8226i | −0.0881180 | − | 0.0881180i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −57.5273 | −0.218735 | −0.109368 | − | 0.994001i | \(-0.534883\pi\) | ||||
−0.109368 | + | 0.994001i | \(0.534883\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 76.2252i | 0.287642i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −121.413 | + | 121.413i | −0.451350 | + | 0.451350i | −0.895803 | − | 0.444452i | \(-0.853398\pi\) |
0.444452 | + | 0.895803i | \(0.353398\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −217.759 | −0.803539 | −0.401769 | − | 0.915741i | \(-0.631605\pi\) | ||||
−0.401769 | + | 0.915741i | \(0.631605\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −23.4865 | + | 23.4865i | −0.0854056 | + | 0.0854056i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −56.8037 | + | 56.8037i | −0.205068 | + | 0.205068i | −0.802167 | − | 0.597100i | \(-0.796320\pi\) |
0.597100 | + | 0.802167i | \(0.296320\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −58.9828 | −0.209903 | −0.104952 | − | 0.994477i | \(-0.533469\pi\) | ||||
−0.104952 | + | 0.994477i | \(0.533469\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 170.002 | − | 170.002i | 0.600713 | − | 0.600713i | −0.339789 | − | 0.940502i | \(-0.610356\pi\) |
0.940502 | + | 0.339789i | \(0.110356\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.4740i | 0.0852753i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −693.086 | −2.39822 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −46.1968 | − | 46.1968i | −0.157668 | − | 0.157668i | 0.623864 | − | 0.781533i | \(-0.285562\pi\) |
−0.781533 | + | 0.623864i | \(0.785562\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 424.463i | − | 1.43886i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −220.377 | − | 220.377i | −0.737046 | − | 0.737046i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 43.5342 | + | 43.5342i | 0.144632 | + | 0.144632i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 367.784i | 1.20585i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −361.635 | − | 361.635i | −1.17796 | − | 1.17796i | −0.980262 | − | 0.197701i | \(-0.936653\pi\) |
−0.197701 | − | 0.980262i | \(-0.563347\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −175.216 | −0.563395 | −0.281697 | − | 0.959503i | \(-0.590897\pi\) | ||||
−0.281697 | + | 0.959503i | \(0.590897\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 432.899i | 1.38307i | 0.722345 | + | 0.691533i | \(0.243064\pi\) | ||||
−0.722345 | + | 0.691533i | \(0.756936\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 180.916 | − | 180.916i | 0.570714 | − | 0.570714i | −0.361614 | − | 0.932328i | \(-0.617774\pi\) |
0.932328 | + | 0.361614i | \(0.117774\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 75.3043 | 0.236064 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −35.0694 | + | 35.0694i | −0.108574 | + | 0.108574i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 35.2495 | − | 35.2495i | 0.108460 | − | 0.108460i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.6564 | 0.0627855 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −98.3525 | + | 98.3525i | −0.297137 | + | 0.297137i | −0.839892 | − | 0.542754i | \(-0.817382\pi\) |
0.542754 | + | 0.839892i | \(0.317382\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 516.297i | 1.54119i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −384.266 | −1.14026 | −0.570128 | − | 0.821556i | \(-0.693106\pi\) | ||||
−0.570128 | + | 0.821556i | \(0.693106\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 218.200 | + | 218.200i | 0.639881 | + | 0.639881i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 75.8459i | − | 0.221125i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −380.232 | − | 380.232i | −1.09577 | − | 1.09577i | −0.994900 | − | 0.100869i | \(-0.967838\pi\) |
−0.100869 | − | 0.994900i | \(-0.532162\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −260.199 | − | 260.199i | −0.745555 | − | 0.745555i | 0.228086 | − | 0.973641i | \(-0.426753\pi\) |
−0.973641 | + | 0.228086i | \(0.926753\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 97.9162i | 0.277383i | 0.990336 | + | 0.138692i | \(0.0442897\pi\) | ||||
−0.990336 | + | 0.138692i | \(0.955710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 296.427 | + | 296.427i | 0.835006 | + | 0.835006i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 126.839 | 0.353311 | 0.176656 | − | 0.984273i | \(-0.443472\pi\) | ||||
0.176656 | + | 0.984273i | \(0.443472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 358.495i | − | 0.993062i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −94.4600 | + | 94.4600i | −0.258794 | + | 0.258794i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −354.084 | −0.964807 | −0.482404 | − | 0.875949i | \(-0.660236\pi\) | ||||
−0.482404 | + | 0.875949i | \(0.660236\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.60369 | − | 7.60369i | 0.0204951 | − | 0.0204951i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −77.4388 | + | 77.4388i | −0.207611 | + | 0.207611i | −0.803251 | − | 0.595640i | \(-0.796898\pi\) |
0.595640 | + | 0.803251i | \(0.296898\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −113.019 | −0.299786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 209.955 | − | 209.955i | 0.553971 | − | 0.553971i | −0.373614 | − | 0.927584i | \(-0.621881\pi\) |
0.927584 | + | 0.373614i | \(0.121881\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 579.620i | 1.51337i | 0.653781 | + | 0.756684i | \(0.273182\pi\) | ||||
−0.653781 | + | 0.756684i | \(0.726818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.0876 | 0.0677601 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 420.113 | + | 420.113i | 1.07998 | + | 1.07998i | 0.996510 | + | 0.0834708i | \(0.0266005\pi\) |
0.0834708 | + | 0.996510i | \(0.473399\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1072.38i | − | 2.74267i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −314.403 | − | 314.403i | −0.795957 | − | 0.795957i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0474 | − | 13.0474i | −0.0328650 | − | 0.0328650i | 0.690483 | − | 0.723348i | \(-0.257398\pi\) |
−0.723348 | + | 0.690483i | \(0.757398\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 152.424i | − | 0.380110i | −0.981773 | − | 0.190055i | \(-0.939133\pi\) | ||
0.981773 | − | 0.190055i | \(-0.0608666\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −327.482 | − | 327.482i | −0.812610 | − | 0.812610i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 251.507 | 0.617952 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 43.2426i | − | 0.105728i | −0.998602 | − | 0.0528639i | \(-0.983165\pi\) | ||
0.998602 | − | 0.0528639i | \(-0.0168349\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −42.3415 | + | 42.3415i | −0.102522 | + | 0.102522i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 645.095 | 1.55445 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −81.3896 | + | 81.3896i | −0.194247 | + | 0.194247i | −0.797528 | − | 0.603281i | \(-0.793860\pi\) |
0.603281 | + | 0.797528i | \(0.293860\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −198.570 | + | 198.570i | −0.471663 | + | 0.471663i | −0.902452 | − | 0.430789i | \(-0.858235\pi\) |
0.430789 | + | 0.902452i | \(0.358235\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 171.529 | 0.403597 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.6875 | − | 36.6875i | 0.0859193 | − | 0.0859193i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 395.497i | − | 0.917627i | −0.888533 | − | 0.458813i | \(-0.848275\pi\) | ||
0.888533 | − | 0.458813i | \(-0.151725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −672.683 | −1.55354 | −0.776770 | − | 0.629784i | \(-0.783143\pi\) | ||||
−0.776770 | + | 0.629784i | \(0.783143\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −38.2939 | − | 38.2939i | −0.0876290 | − | 0.0876290i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.8920i | 0.0612574i | 0.999531 | + | 0.0306287i | \(0.00975095\pi\) | ||||
−0.999531 | + | 0.0306287i | \(0.990249\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 524.214 | + | 524.214i | 1.18333 | + | 1.18333i | 0.978877 | + | 0.204451i | \(0.0655408\pi\) |
0.204451 | + | 0.978877i | \(0.434459\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −322.597 | − | 322.597i | −0.724937 | − | 0.724937i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 518.381i | − | 1.15452i | −0.816559 | − | 0.577262i | \(-0.804121\pi\) | ||
0.816559 | − | 0.577262i | \(-0.195879\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −134.853 | − | 134.853i | −0.299009 | − | 0.299009i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −39.1533 | −0.0860511 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 853.516i | 1.86765i | 0.357729 | + | 0.933825i | \(0.383551\pi\) | ||||
−0.357729 | + | 0.933825i | \(0.616449\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 331.810 | − | 331.810i | 0.719761 | − | 0.719761i | −0.248795 | − | 0.968556i | \(-0.580034\pi\) |
0.968556 | + | 0.248795i | \(0.0800345\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −164.893 | −0.356141 | −0.178070 | − | 0.984018i | \(-0.556986\pi\) | ||||
−0.178070 | + | 0.984018i | \(0.556986\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −105.253 | + | 105.253i | −0.225380 | + | 0.225380i | −0.810760 | − | 0.585379i | \(-0.800946\pi\) |
0.585379 | + | 0.810760i | \(0.300946\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 51.5022 | − | 51.5022i | 0.109813 | − | 0.109813i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −479.751 | −1.01427 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.12514 | − | 6.12514i | 0.0128950 | − | 0.0128950i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 678.054i | 1.41556i | 0.706432 | + | 0.707781i | \(0.250304\pi\) | ||||
−0.706432 | + | 0.707781i | \(0.749696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −377.470 | −0.784762 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 191.064 | + | 191.064i | 0.393947 | + | 0.393947i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.72273i | − | 0.0158578i | −0.999969 | − | 0.00792888i | \(-0.997476\pi\) | ||
0.999969 | − | 0.00792888i | \(-0.00252387\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −296.311 | − | 296.311i | −0.603484 | − | 0.603484i | 0.337751 | − | 0.941235i | \(-0.390334\pi\) |
−0.941235 | + | 0.337751i | \(0.890334\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −274.984 | − | 274.984i | −0.557777 | − | 0.557777i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 59.1390i | − | 0.118992i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −555.542 | − | 555.542i | −1.11331 | − | 1.11331i | −0.992700 | − | 0.120612i | \(-0.961514\pi\) |
−0.120612 | − | 0.992700i | \(-0.538486\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −322.916 | −0.641979 | −0.320990 | − | 0.947083i | \(-0.604015\pi\) | ||||
−0.320990 | + | 0.947083i | \(0.604015\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 322.250i | − | 0.638118i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −522.344 | + | 522.344i | −1.02622 | + | 1.02622i | −0.0265686 | + | 0.999647i | \(0.508458\pi\) |
−0.999647 | + | 0.0265686i | \(0.991542\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.8453 | 0.0368793 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −676.213 | + | 676.213i | −1.31304 | + | 1.31304i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −113.818 | + | 113.818i | −0.220150 | + | 0.220150i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 80.4109 | 0.154340 | 0.0771698 | − | 0.997018i | \(-0.475412\pi\) | ||||
0.0771698 | + | 0.997018i | \(0.475412\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −133.868 | + | 133.868i | −0.255962 | + | 0.255962i | −0.823410 | − | 0.567447i | \(-0.807931\pi\) |
0.567447 | + | 0.823410i | \(0.307931\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1593.57i | − | 3.02386i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 641.985 | 1.21358 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 202.392 | + | 202.392i | 0.379723 | + | 0.379723i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 415.918i | 0.777417i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 207.656 | + | 207.656i | 0.385261 | + | 0.385261i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 643.791 | + | 643.791i | 1.19000 | + | 1.19000i | 0.977066 | + | 0.212936i | \(0.0683025\pi\) |
0.212936 | + | 0.977066i | \(0.431698\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 727.237i | 1.33438i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 543.953 | + | 543.953i | 0.994429 | + | 0.994429i | 0.999985 | − | 0.00555539i | \(-0.00176834\pi\) |
−0.00555539 | + | 0.999985i | \(0.501768\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.6389 | −0.0356422 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 62.7252i | 0.113427i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −436.430 | + | 436.430i | −0.783537 | + | 0.783537i | −0.980426 | − | 0.196889i | \(-0.936916\pi\) |
0.196889 | + | 0.980426i | \(0.436916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 720.027 | 1.28806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 525.339 | − | 525.339i | 0.933107 | − | 0.933107i | −0.0647918 | − | 0.997899i | \(-0.520638\pi\) |
0.997899 | + | 0.0647918i | \(0.0206383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 159.334 | − | 159.334i | 0.282006 | − | 0.282006i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 848.985 | 1.49207 | 0.746033 | − | 0.665909i | \(-0.231956\pi\) | ||||
0.746033 | + | 0.665909i | \(0.231956\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −503.454 | + | 503.454i | −0.881706 | + | 0.881706i | −0.993708 | − | 0.112002i | \(-0.964274\pi\) |
0.112002 | + | 0.993708i | \(0.464274\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 187.300i | 0.325739i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 891.580 | 1.54520 | 0.772600 | − | 0.634894i | \(-0.218956\pi\) | ||||
0.772600 | + | 0.634894i | \(0.218956\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −64.3501 | − | 64.3501i | −0.110758 | − | 0.110758i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 83.7934i | 0.143728i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −121.737 | − | 121.737i | −0.207388 | − | 0.207388i | 0.595768 | − | 0.803156i | \(-0.296848\pi\) |
−0.803156 | + | 0.595768i | \(0.796848\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −56.9050 | − | 56.9050i | −0.0966129 | − | 0.0966129i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 207.925i | 0.350632i | 0.984512 | + | 0.175316i | \(0.0560947\pi\) | ||||
−0.984512 | + | 0.175316i | \(0.943905\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −95.2626 | − | 95.2626i | −0.160105 | − | 0.160105i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −689.528 | −1.15113 | −0.575566 | − | 0.817755i | \(-0.695218\pi\) | ||||
−0.575566 | + | 0.817755i | \(0.695218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 542.421i | − | 0.902531i | −0.892390 | − | 0.451266i | \(-0.850973\pi\) | ||
0.892390 | − | 0.451266i | \(-0.149027\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 328.571 | − | 328.571i | 0.543092 | − | 0.543092i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1018.93 | −1.67864 | −0.839318 | − | 0.543641i | \(-0.817045\pi\) | ||||
−0.839318 | + | 0.543641i | \(0.817045\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 170.822 | − | 170.822i | 0.279578 | − | 0.279578i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −169.481 | + | 169.481i | −0.276478 | + | 0.276478i | −0.831701 | − | 0.555223i | \(-0.812633\pi\) |
0.555223 | + | 0.831701i | \(0.312633\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −834.597 | −1.35267 | −0.676335 | − | 0.736594i | \(-0.736433\pi\) | ||||
−0.676335 | + | 0.736594i | \(0.736433\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 322.772 | − | 322.772i | 0.521441 | − | 0.521441i | −0.396565 | − | 0.918007i | \(-0.629798\pi\) |
0.918007 | + | 0.396565i | \(0.129798\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 64.3600i | 0.103307i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 731.878 | 1.17100 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −918.411 | − | 918.411i | −1.46011 | − | 1.46011i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1006.06i | 1.59439i | 0.603723 | + | 0.797194i | \(0.293683\pi\) | ||||
−0.603723 | + | 0.797194i | \(0.706317\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 347.068 | + | 347.068i | 0.546563 | + | 0.546563i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −311.658 | − | 311.658i | −0.489258 | − | 0.489258i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 257.206i | − | 0.401257i | −0.979667 | − | 0.200628i | \(-0.935702\pi\) | ||
0.979667 | − | 0.200628i | \(-0.0642984\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 311.891 | + | 311.891i | 0.485056 | + | 0.485056i | 0.906742 | − | 0.421686i | \(-0.138562\pi\) |
−0.421686 | + | 0.906742i | \(0.638562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 855.255 | 1.32188 | 0.660939 | − | 0.750440i | \(-0.270158\pi\) | ||||
0.660939 | + | 0.750440i | \(0.270158\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 466.607i | − | 0.718962i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 171.197 | − | 171.197i | 0.262170 | − | 0.262170i | −0.563765 | − | 0.825935i | \(-0.690648\pi\) |
0.825935 | + | 0.563765i | \(0.190648\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −171.835 | −0.262343 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 510.283 | − | 510.283i | 0.774330 | − | 0.774330i | −0.204530 | − | 0.978860i | \(-0.565567\pi\) |
0.978860 | + | 0.204530i | \(0.0655667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −491.063 | + | 491.063i | −0.742910 | + | 0.742910i | −0.973137 | − | 0.230227i | \(-0.926053\pi\) |
0.230227 | + | 0.973137i | \(0.426053\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.80348 | −0.0102308 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 300.268 | − | 300.268i | 0.450176 | − | 0.450176i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 404.300i | 0.602534i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −200.282 | −0.297596 | −0.148798 | − | 0.988868i | \(-0.547540\pi\) | ||||
−0.148798 | + | 0.988868i | \(0.547540\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −818.346 | − | 818.346i | −1.20878 | − | 1.20878i | −0.971422 | − | 0.237361i | \(-0.923718\pi\) |
−0.237361 | − | 0.971422i | \(-0.576282\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 38.1184i | − | 0.0561391i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −559.041 | − | 559.041i | −0.818508 | − | 0.818508i | 0.167383 | − | 0.985892i | \(-0.446468\pi\) |
−0.985892 | + | 0.167383i | \(0.946468\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 432.476 | + | 432.476i | 0.631352 | + | 0.631352i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 125.760i | − | 0.182526i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 558.744 | + | 558.744i | 0.808602 | + | 0.808602i | 0.984422 | − | 0.175820i | \(-0.0562577\pi\) |
−0.175820 | + | 0.984422i | \(0.556258\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −237.220 | −0.341324 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 984.869i | 1.41301i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 452.428 | − | 452.428i | 0.645404 | − | 0.645404i | −0.306475 | − | 0.951879i | \(-0.599149\pi\) |
0.951879 | + | 0.306475i | \(0.0991495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −65.5913 | −0.0933019 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −32.1454 | + | 32.1454i | −0.0454673 | + | 0.0454673i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 693.360 | − | 693.360i | 0.977941 | − | 0.977941i | −0.0218205 | − | 0.999762i | \(-0.506946\pi\) |
0.999762 | + | 0.0218205i | \(0.00694622\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1740.09 | 2.44052 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 215.736 | − | 215.736i | 0.301729 | − | 0.301729i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 641.528i | − | 0.892251i | −0.894970 | − | 0.446125i | \(-0.852804\pi\) | ||
0.894970 | − | 0.446125i | \(-0.147196\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 134.909 | 0.187113 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 48.0281 | + | 48.0281i | 0.0662456 | + | 0.0662456i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 644.665i | 0.886747i | 0.896337 | + | 0.443373i | \(0.146218\pi\) | ||||
−0.896337 | + | 0.443373i | \(0.853782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1751.88 | + | 1751.88i | 2.39655 | + | 2.39655i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 748.983 | + | 748.983i | 1.02180 | + | 1.02180i | 0.999757 | + | 0.0220473i | \(0.00701846\pi\) |
0.0220473 | + | 0.999757i | \(0.492982\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 567.559i | 0.770093i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 387.245 | + | 387.245i | 0.524013 | + | 0.524013i | 0.918781 | − | 0.394768i | \(-0.129175\pi\) |
−0.394768 | + | 0.918781i | \(0.629175\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 245.165 | 0.329966 | 0.164983 | − | 0.986296i | \(-0.447243\pi\) | ||||
0.164983 | + | 0.986296i | \(0.447243\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1357.80i | − | 1.82255i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 41.4891 | − | 41.4891i | 0.0553926 | − | 0.0553926i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −547.753 | −0.729365 | −0.364683 | − | 0.931132i | \(-0.618822\pi\) | ||||
−0.364683 | + | 0.931132i | \(0.618822\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 102.473 | − | 102.473i | 0.135726 | − | 0.135726i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 876.755 | − | 876.755i | 1.15820 | − | 1.15820i | 0.173334 | − | 0.984863i | \(-0.444546\pi\) |
0.984863 | − | 0.173334i | \(-0.0554540\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −876.682 | −1.15201 | −0.576007 | − | 0.817445i | \(-0.695390\pi\) | ||||
−0.576007 | + | 0.817445i | \(0.695390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 72.5441 | − | 72.5441i | 0.0950774 | − | 0.0950774i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 700.300i | 0.913038i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −155.364 | −0.202034 | −0.101017 | − | 0.994885i | \(-0.532210\pi\) | ||||
−0.101017 | + | 0.994885i | \(0.532210\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −336.932 | − | 336.932i | −0.435876 | − | 0.435876i | 0.454746 | − | 0.890621i | \(-0.349730\pi\) |
−0.890621 | + | 0.454746i | \(0.849730\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 278.330i | 0.359135i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.1688 | + | 35.1688i | 0.0451460 | + | 0.0451460i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 325.858 | + | 325.858i | 0.417232 | + | 0.417232i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 592.144i | − | 0.754324i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −201.318 | − | 201.318i | −0.255804 | − | 0.255804i | 0.567541 | − | 0.823345i | \(-0.307895\pi\) |
−0.823345 | + | 0.567541i | \(0.807895\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.7880 | −0.0401871 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 606.788i | − | 0.765181i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 571.213 | − | 571.213i | 0.716704 | − | 0.716704i | −0.251225 | − | 0.967929i | \(-0.580833\pi\) |
0.967929 | + | 0.251225i | \(0.0808333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 831.243 | 1.04035 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −103.839 | + | 103.839i | −0.129313 | + | 0.129313i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 104.022 | − | 104.022i | 0.129219 | − | 0.129219i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −554.891 | −0.685898 | −0.342949 | − | 0.939354i | \(-0.611426\pi\) | ||||
−0.342949 | + | 0.939354i | \(0.611426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −570.087 | + | 570.087i | −0.702944 | + | 0.702944i | −0.965041 | − | 0.262098i | \(-0.915586\pi\) |
0.262098 | + | 0.965041i | \(0.415586\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1212.29i | − | 1.48747i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 125.116 | 0.153141 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 150.698 | + | 150.698i | 0.183554 | + | 0.183554i | 0.792903 | − | 0.609348i | \(-0.208569\pi\) |
−0.609348 | + | 0.792903i | \(0.708569\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 742.019i | 0.901603i | 0.892624 | + | 0.450801i | \(0.148862\pi\) | ||||
−0.892624 | + | 0.450801i | \(0.851138\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 248.150 | + | 248.150i | 0.300061 | + | 0.300061i | 0.841037 | − | 0.540977i | \(-0.181945\pi\) |
−0.540977 | + | 0.841037i | \(0.681945\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −373.174 | − | 373.174i | −0.450150 | − | 0.450150i | 0.445255 | − | 0.895404i | \(-0.353113\pi\) |
−0.895404 | + | 0.445255i | \(0.853113\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1516.57i | − | 1.82061i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 924.728 | + | 924.728i | 1.10746 | + | 1.10746i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1227.49 | 1.46304 | 0.731520 | − | 0.681820i | \(-0.238811\pi\) | ||||
0.731520 | + | 0.681820i | \(0.238811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 687.009i | 0.816895i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 335.894 | − | 335.894i | 0.397508 | − | 0.397508i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −65.5518 | −0.0773929 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1002.86 | − | 1002.86i | 1.17844 | − | 1.17844i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.4613 | + | 24.4613i | −0.0286768 | + | 0.0286768i | −0.721300 | − | 0.692623i | \(-0.756455\pi\) |
0.692623 | + | 0.721300i | \(0.256455\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 839.732 | 0.979850 | 0.489925 | − | 0.871764i | \(-0.337024\pi\) | ||||
0.489925 | + | 0.871764i | \(0.337024\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 483.229 | − | 483.229i | 0.562548 | − | 0.562548i | −0.367482 | − | 0.930031i | \(-0.619780\pi\) |
0.930031 | + | 0.367482i | \(0.119780\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 21.1881i | − | 0.0245517i | −0.999925 | − | 0.0122758i | \(-0.996092\pi\) | ||
0.999925 | − | 0.0122758i | \(-0.00390761\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 533.761 | 0.617064 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −345.619 | − | 345.619i | −0.397720 | − | 0.397720i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 851.813i | − | 0.977971i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −59.3571 | − | 59.3571i | −0.0678367 | − | 0.0678367i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −350.528 | − | 350.528i | −0.399690 | − | 0.399690i | 0.478434 | − | 0.878124i | \(-0.341205\pi\) |
−0.878124 | + | 0.478434i | \(0.841205\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 472.491i | − | 0.536312i | −0.963375 | − | 0.268156i | \(-0.913586\pi\) | ||
0.963375 | − | 0.268156i | \(-0.0864143\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −294.850 | − | 294.850i | −0.333919 | − | 0.333919i | 0.520154 | − | 0.854073i | \(-0.325875\pi\) |
−0.854073 | + | 0.520154i | \(0.825875\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 189.405 | 0.213535 | 0.106767 | − | 0.994284i | \(-0.465950\pi\) | ||||
0.106767 | + | 0.994284i | \(0.465950\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 69.2421i | − | 0.0778876i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.6829 | − | 29.6829i | 0.0332396 | − | 0.0332396i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1011.97 | 1.13070 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 446.200 | − | 446.200i | 0.496330 | − | 0.496330i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 305.983 | − | 305.983i | 0.339604 | − | 0.339604i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1230.68 | −1.35987 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1025.20 | + | 1025.20i | −1.13032 | + | 1.13032i | −0.140200 | + | 0.990123i | \(0.544774\pi\) |
−0.990123 | + | 0.140200i | \(0.955226\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1115.84i | 1.22485i | 0.790528 | + | 0.612426i | \(0.209806\pi\) | ||||
−0.790528 | + | 0.612426i | \(0.790194\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 709.144 | 0.776719 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.1410 | + | 17.1410i | 0.0186925 | + | 0.0186925i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1169.50i | 1.27258i | 0.771450 | + | 0.636290i | \(0.219532\pi\) | ||||
−0.771450 | + | 0.636290i | \(0.780468\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −489.060 | − | 489.060i | −0.529859 | − | 0.529859i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 160.408 | + | 160.408i | 0.173414 | + | 0.173414i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 115.506i | − | 0.124334i | −0.998066 | − | 0.0621671i | \(-0.980199\pi\) | ||
0.998066 | − | 0.0621671i | \(-0.0198012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −54.1553 | − | 54.1553i | −0.0581689 | − | 0.0581689i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1049.80 | 1.12278 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 666.120i | 0.710907i | 0.934694 | + | 0.355454i | \(0.115674\pi\) | ||||
−0.934694 | + | 0.355454i | \(0.884326\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −559.735 | + | 559.735i | −0.594830 | + | 0.594830i | −0.938932 | − | 0.344102i | \(-0.888183\pi\) |
0.344102 | + | 0.938932i | \(0.388183\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1075.42 | −1.14043 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −871.120 | + | 871.120i | −0.919873 | + | 0.919873i | −0.997020 | − | 0.0771466i | \(-0.975419\pi\) |
0.0771466 | + | 0.997020i | \(0.475419\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 155.845 | − | 155.845i | 0.164220 | − | 0.164220i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 264.384 | 0.277423 | 0.138711 | − | 0.990333i | \(-0.455704\pi\) | ||||
0.138711 | + | 0.990333i | \(0.455704\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 226.874 | − | 226.874i | 0.237564 | − | 0.237564i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 86.2816i | − | 0.0899703i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1624.80 | 1.69073 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1219.78 | + | 1219.78i | 1.26402 | + | 1.26402i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 92.8445i | − | 0.0960129i | −0.998847 | − | 0.0480065i | \(-0.984713\pi\) | ||
0.998847 | − | 0.0480065i | \(-0.0152868\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1086.25 | − | 1086.25i | −1.11870 | − | 1.11870i | −0.991933 | − | 0.126764i | \(-0.959541\pi\) |
−0.126764 | − | 0.991933i | \(-0.540459\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.6634 | + | 23.6634i | 0.0243201 | + | 0.0243201i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 626.473i | 0.641222i | 0.947211 | + | 0.320611i | \(0.103888\pi\) | ||||
−0.947211 | + | 0.320611i | \(0.896112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −354.626 | − | 354.626i | −0.362233 | − | 0.362233i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −204.267 | −0.207800 | −0.103900 | − | 0.994588i | \(-0.533132\pi\) | ||||
−0.103900 | + | 0.994588i | \(0.533132\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 349.986i | − | 0.355316i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1912.95 | + | 1912.95i | −1.93423 | + | 1.93423i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1147.30 | 1.15772 | 0.578859 | − | 0.815428i | \(-0.303498\pi\) | ||||
0.578859 | + | 0.815428i | \(0.303498\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −613.348 | + | 613.348i | −0.616430 | + | 0.616430i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −514.690 | + | 514.690i | −0.516239 | + | 0.516239i | −0.916431 | − | 0.400192i | \(-0.868943\pi\) |
0.400192 | + | 0.916431i | \(0.368943\pi\) | |||||||
\(998\) | 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 | 1152.3.j.a.161.13 | 32 | ||
3.2 | odd | 2 | inner | 1152.3.j.a.161.4 | 32 | ||
4.3 | odd | 2 | 1152.3.j.b.161.13 | 32 | |||
8.3 | odd | 2 | 576.3.j.a.17.4 | 32 | |||
8.5 | even | 2 | 144.3.j.a.125.12 | yes | 32 | ||
12.11 | even | 2 | 1152.3.j.b.161.4 | 32 | |||
16.3 | odd | 4 | 576.3.j.a.305.13 | 32 | |||
16.5 | even | 4 | inner | 1152.3.j.a.737.4 | 32 | ||
16.11 | odd | 4 | 1152.3.j.b.737.4 | 32 | |||
16.13 | even | 4 | 144.3.j.a.53.5 | ✓ | 32 | ||
24.5 | odd | 2 | 144.3.j.a.125.5 | yes | 32 | ||
24.11 | even | 2 | 576.3.j.a.17.13 | 32 | |||
48.5 | odd | 4 | inner | 1152.3.j.a.737.13 | 32 | ||
48.11 | even | 4 | 1152.3.j.b.737.13 | 32 | |||
48.29 | odd | 4 | 144.3.j.a.53.12 | yes | 32 | ||
48.35 | even | 4 | 576.3.j.a.305.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.j.a.53.5 | ✓ | 32 | 16.13 | even | 4 | ||
144.3.j.a.53.12 | yes | 32 | 48.29 | odd | 4 | ||
144.3.j.a.125.5 | yes | 32 | 24.5 | odd | 2 | ||
144.3.j.a.125.12 | yes | 32 | 8.5 | even | 2 | ||
576.3.j.a.17.4 | 32 | 8.3 | odd | 2 | |||
576.3.j.a.17.13 | 32 | 24.11 | even | 2 | |||
576.3.j.a.305.4 | 32 | 48.35 | even | 4 | |||
576.3.j.a.305.13 | 32 | 16.3 | odd | 4 | |||
1152.3.j.a.161.4 | 32 | 3.2 | odd | 2 | inner | ||
1152.3.j.a.161.13 | 32 | 1.1 | even | 1 | trivial | ||
1152.3.j.a.737.4 | 32 | 16.5 | even | 4 | inner | ||
1152.3.j.a.737.13 | 32 | 48.5 | odd | 4 | inner | ||
1152.3.j.b.161.4 | 32 | 12.11 | even | 2 | |||
1152.3.j.b.161.13 | 32 | 4.3 | odd | 2 | |||
1152.3.j.b.737.4 | 32 | 16.11 | odd | 4 | |||
1152.3.j.b.737.13 | 32 | 48.11 | even | 4 |