Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(33,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.e (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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 33.1 | ||
Root | \(1.28199 + 1.53509i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.33 |
Dual form | 128.4.e.b.97.1 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −5.49618 | − | 5.49618i | −1.05774 | − | 1.05774i | −0.998228 | − | 0.0595129i | \(-0.981045\pi\) |
−0.0595129 | − | 0.998228i | \(-0.518955\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.66372 | − | 4.66372i | 0.417136 | − | 0.417136i | −0.467079 | − | 0.884215i | \(-0.654694\pi\) |
0.884215 | + | 0.467079i | \(0.154694\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 24.8965i | − | 1.34429i | −0.740422 | − | 0.672143i | \(-0.765374\pi\) | ||
0.740422 | − | 0.672143i | \(-0.234626\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 33.4160i | 1.23763i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −22.3431 | + | 22.3431i | −0.612427 | + | 0.612427i | −0.943578 | − | 0.331151i | \(-0.892563\pi\) |
0.331151 | + | 0.943578i | \(0.392563\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.2714 | + | 11.2714i | 0.240471 | + | 0.240471i | 0.817045 | − | 0.576574i | \(-0.195611\pi\) |
−0.576574 | + | 0.817045i | \(0.695611\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −51.2653 | −0.882443 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −88.4846 | −1.26239 | −0.631196 | − | 0.775623i | \(-0.717436\pi\) | ||||
−0.631196 | + | 0.775623i | \(0.717436\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −37.8187 | − | 37.8187i | −0.456643 | − | 0.456643i | 0.440909 | − | 0.897552i | \(-0.354656\pi\) |
−0.897552 | + | 0.440909i | \(0.854656\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −136.836 | + | 136.836i | −1.42191 | + | 1.42191i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 48.1224i | 0.436270i | 0.975919 | + | 0.218135i | \(0.0699973\pi\) | ||||
−0.975919 | + | 0.218135i | \(0.930003\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 81.4994i | 0.651995i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 35.2635 | − | 35.2635i | 0.251351 | − | 0.251351i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.4432 | − | 10.4432i | −0.0668705 | − | 0.0668705i | 0.672881 | − | 0.739751i | \(-0.265057\pi\) |
−0.739751 | + | 0.672881i | \(0.765057\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −96.9578 | −0.561746 | −0.280873 | − | 0.959745i | \(-0.590624\pi\) | ||||
−0.280873 | + | 0.959745i | \(0.590624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 245.604 | 1.29558 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −116.110 | − | 116.110i | −0.560750 | − | 0.560750i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 163.279 | − | 163.279i | 0.725484 | − | 0.725484i | −0.244233 | − | 0.969717i | \(-0.578536\pi\) |
0.969717 | + | 0.244233i | \(0.0785362\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 123.899i | − | 0.508713i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 360.519i | − | 1.37326i | −0.727008 | − | 0.686629i | \(-0.759090\pi\) | ||
0.727008 | − | 0.686629i | \(-0.240910\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 100.249 | − | 100.249i | 0.355531 | − | 0.355531i | −0.506632 | − | 0.862163i | \(-0.669110\pi\) |
0.862163 | + | 0.506632i | \(0.169110\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 155.843 | + | 155.843i | 0.516260 | + | 0.516260i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 220.669 | 0.684849 | 0.342425 | − | 0.939545i | \(-0.388752\pi\) | ||||
0.342425 | + | 0.939545i | \(0.388752\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −276.837 | −0.807104 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 486.327 | + | 486.327i | 1.33528 | + | 1.33528i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 175.752 | − | 175.752i | 0.455498 | − | 0.455498i | −0.441676 | − | 0.897174i | \(-0.645616\pi\) |
0.897174 | + | 0.441676i | \(0.145616\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 208.404i | 0.510931i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 415.717i | 0.966019i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −405.008 | + | 405.008i | −0.893687 | + | 0.893687i | −0.994868 | − | 0.101181i | \(-0.967738\pi\) |
0.101181 | + | 0.994868i | \(0.467738\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −664.576 | − | 664.576i | −1.39492 | − | 1.39492i | −0.813860 | − | 0.581061i | \(-0.802638\pi\) |
−0.581061 | − | 0.813860i | \(-0.697362\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 831.942 | 1.66373 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 105.133 | 0.200619 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 107.377 | + | 107.377i | 0.195794 | + | 0.195794i | 0.798194 | − | 0.602400i | \(-0.205789\pi\) |
−0.602400 | + | 0.798194i | \(0.705789\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 264.489 | − | 264.489i | 0.461461 | − | 0.461461i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 215.050i | 0.359461i | 0.983716 | + | 0.179731i | \(0.0575226\pi\) | ||||
−0.983716 | + | 0.179731i | \(0.942477\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 668.587i | − | 1.07195i | −0.844235 | − | 0.535974i | \(-0.819945\pi\) | ||
0.844235 | − | 0.535974i | \(-0.180055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 447.935 | − | 447.935i | 0.689642 | − | 0.689642i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 556.266 | + | 556.266i | 0.823277 | + | 0.823277i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −822.956 | −1.17202 | −0.586012 | − | 0.810303i | \(-0.699303\pi\) | ||||
−0.586012 | + | 0.810303i | \(0.699303\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 514.603 | 0.705902 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −326.873 | − | 326.873i | −0.432277 | − | 0.432277i | 0.457125 | − | 0.889402i | \(-0.348879\pi\) |
−0.889402 | + | 0.457125i | \(0.848879\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −412.668 | + | 412.668i | −0.526589 | + | 0.526589i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 114.795i | 0.141463i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 262.733i | − | 0.312918i | −0.987684 | − | 0.156459i | \(-0.949992\pi\) | ||
0.987684 | − | 0.156459i | \(-0.0500079\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 280.619 | − | 280.619i | 0.323262 | − | 0.323262i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 532.898 | + | 532.898i | 0.594182 | + | 0.594182i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −352.752 | −0.380964 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −150.801 | −0.157850 | −0.0789251 | − | 0.996881i | \(-0.525149\pi\) | ||||
−0.0789251 | + | 0.996881i | \(0.525149\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −746.618 | − | 746.618i | −0.757958 | − | 0.757958i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −487.985 | + | 487.985i | −0.480755 | + | 0.480755i | −0.905373 | − | 0.424617i | \(-0.860409\pi\) |
0.424617 | + | 0.905373i | \(0.360409\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1840.58i | − | 1.76075i | −0.474275 | − | 0.880377i | \(-0.657290\pi\) | ||
0.474275 | − | 0.880377i | \(-0.342710\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1276.33i | 1.18626i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 79.4098 | − | 79.4098i | 0.0717461 | − | 0.0717461i | −0.670323 | − | 0.742069i | \(-0.733845\pi\) |
0.742069 | + | 0.670323i | \(0.233845\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −952.979 | − | 952.979i | −0.837421 | − | 0.837421i | 0.151098 | − | 0.988519i | \(-0.451719\pi\) |
−0.988519 | + | 0.151098i | \(0.951719\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1794.82 | −1.53475 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −720.469 | −0.599788 | −0.299894 | − | 0.953973i | \(-0.596951\pi\) | ||||
−0.299894 | + | 0.953973i | \(0.596951\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 224.430 | + | 224.430i | 0.181984 | + | 0.181984i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −376.646 | + | 376.646i | −0.297615 | + | 0.297615i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2202.96i | 1.69702i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 332.571i | 0.249865i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1981.48 | + | 1981.48i | −1.45255 | + | 1.45255i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 963.056 | + | 963.056i | 0.689107 | + | 0.689107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2622.35 | 1.83225 | 0.916124 | − | 0.400895i | \(-0.131301\pi\) | ||||
0.916124 | + | 0.400895i | \(0.131301\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1101.97 | −0.752119 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −657.574 | − | 657.574i | −0.438569 | − | 0.438569i | 0.452961 | − | 0.891530i | \(-0.350368\pi\) |
−0.891530 | + | 0.452961i | \(0.850368\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −941.555 | + | 941.555i | −0.613858 | + | 0.613858i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 328.919i | − | 0.209695i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2511.52i | 1.56623i | 0.621874 | + | 0.783117i | \(0.286371\pi\) | ||||
−0.621874 | + | 0.783117i | \(0.713629\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1086.02 | − | 1086.02i | 0.662697 | − | 0.662697i | −0.293318 | − | 0.956015i | \(-0.594759\pi\) |
0.956015 | + | 0.293318i | \(0.0947595\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1212.84 | − | 1212.84i | −0.724393 | − | 0.724393i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −503.677 | −0.294543 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −97.4080 | −0.0557882 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1521.54 | + | 1521.54i | 0.853706 | + | 0.853706i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2284.63 | − | 2284.63i | 1.25614 | − | 1.25614i | 0.303214 | − | 0.952922i | \(-0.401940\pi\) |
0.952922 | − | 0.303214i | \(-0.0980598\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2814.39i | − | 1.51677i | −0.651809 | − | 0.758383i | \(-0.725990\pi\) | ||
0.651809 | − | 0.758383i | \(-0.274010\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2956.80i | − | 1.56237i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −452.184 | + | 452.184i | −0.234325 | + | 0.234325i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 906.308 | + | 906.308i | 0.460709 | + | 0.460709i | 0.898888 | − | 0.438179i | \(-0.144376\pi\) |
−0.438179 | + | 0.898888i | \(0.644376\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1931.93 | −0.963598 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1198.08 | 0.586472 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1392.36 | − | 1392.36i | −0.669067 | − | 0.669067i | 0.288433 | − | 0.957500i | \(-0.406866\pi\) |
−0.957500 | + | 0.288433i | \(0.906866\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1145.43 | − | 1145.43i | 0.540433 | − | 0.540433i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1221.66i | − | 0.566075i | −0.959109 | − | 0.283038i | \(-0.908658\pi\) | ||
0.959109 | − | 0.283038i | \(-0.0913421\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1942.91i | − | 0.884347i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1263.75 | − | 1263.75i | 0.565155 | − | 0.565155i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 563.418 | + | 563.418i | 0.247606 | + | 0.247606i | 0.819988 | − | 0.572381i | \(-0.193980\pi\) |
−0.572381 | + | 0.819988i | \(0.693980\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2029.05 | 0.876468 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4451.99 | 1.89058 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2202.23 | + | 2202.23i | 0.919565 | + | 0.919565i | 0.996998 | − | 0.0774329i | \(-0.0246724\pi\) |
−0.0774329 | + | 0.996998i | \(0.524672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −121.294 | + | 121.294i | −0.0498104 | + | 0.0498104i | −0.731573 | − | 0.681763i | \(-0.761214\pi\) |
0.681763 | + | 0.731573i | \(0.261214\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7305.26i | 2.95093i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1522.98i | − | 0.605251i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1977.02 | − | 1977.02i | 0.773124 | − | 0.773124i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −877.939 | − | 877.939i | −0.337887 | − | 0.337887i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3927.65 | 1.48793 | 0.743966 | − | 0.668218i | \(-0.232942\pi\) | ||||
0.743966 | + | 0.668218i | \(0.232942\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3249.02 | −1.21176 | −0.605880 | − | 0.795556i | \(-0.707179\pi\) | ||||
−0.605880 | + | 0.795556i | \(0.707179\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −577.833 | − | 577.833i | −0.212202 | − | 0.212202i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2420.90 | + | 2420.90i | −0.875545 | + | 0.875545i | −0.993070 | − | 0.117525i | \(-0.962504\pi\) |
0.117525 | + | 0.993070i | \(0.462504\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1371.30i | 0.488488i | 0.969714 | + | 0.244244i | \(0.0785397\pi\) | ||||
−0.969714 | + | 0.244244i | \(0.921460\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1180.33i | − | 0.414198i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −259.998 | + | 259.998i | −0.0898931 | + | 0.0898931i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1681.36 | − | 1681.36i | −0.572836 | − | 0.572836i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1608.06 | −0.539941 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1689.98 | 0.559321 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1620.50 | + | 1620.50i | 0.528719 | + | 0.528719i | 0.920190 | − | 0.391471i | \(-0.128034\pi\) |
−0.391471 | + | 0.920190i | \(0.628034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1181.95 | − | 1181.95i | 0.380217 | − | 0.380217i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 935.068i | − | 0.296610i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2413.91i | 0.755148i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3674.67 | + | 3674.67i | −1.13384 | + | 1.13384i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −997.347 | − | 997.347i | −0.303569 | − | 0.303569i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −419.617 | −0.126007 | −0.0630036 | − | 0.998013i | \(-0.520068\pi\) | ||||
−0.0630036 | + | 0.998013i | \(0.520068\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2723.38 | −0.806929 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2133.64 | + | 2133.64i | 0.623853 | + | 0.623853i | 0.946515 | − | 0.322661i | \(-0.104577\pi\) |
−0.322661 | + | 0.946515i | \(0.604577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1574.42 | − | 1574.42i | 0.454325 | − | 0.454325i | −0.442462 | − | 0.896787i | \(-0.645895\pi\) |
0.896787 | + | 0.442462i | \(0.145895\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 6114.67i | − | 1.74163i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1194.86i | 0.335957i | 0.985791 | + | 0.167978i | \(0.0537239\pi\) | ||||
−0.985791 | + | 0.167978i | \(0.946276\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1029.14 | − | 1029.14i | 0.285675 | − | 0.285675i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4523.12 | + | 4523.12i | 1.23970 | + | 1.23970i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4241.03 | −1.14782 | −0.573911 | − | 0.818917i | \(-0.694575\pi\) | ||||
−0.573911 | + | 0.818917i | \(0.694575\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5571.19 | −1.48910 | −0.744548 | − | 0.667569i | \(-0.767335\pi\) | ||||
−0.744548 | + | 0.667569i | \(0.767335\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3780.46 | − | 3780.46i | −0.998012 | − | 0.998012i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1291.09 | + | 1291.09i | −0.336672 | + | 0.336672i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 852.541i | − | 0.219619i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3593.11i | 0.914474i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 482.728 | − | 482.728i | 0.121393 | − | 0.121393i | −0.643801 | − | 0.765193i | \(-0.722643\pi\) |
0.765193 | + | 0.643801i | \(0.222643\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1075.20 | − | 1075.20i | −0.267184 | − | 0.267184i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4536.19 | 1.11399 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8093.12 | 1.96434 | 0.982169 | − | 0.188002i | \(-0.0602013\pi\) | ||||
0.982169 | + | 0.188002i | \(0.0602013\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4065.08 | − | 4065.08i | −0.975257 | − | 0.975257i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 348.969 | − | 348.969i | 0.0827610 | − | 0.0827610i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 410.300i | − | 0.0961984i | −0.998843 | − | 0.0480992i | \(-0.984684\pi\) | ||
0.998843 | − | 0.0480992i | \(-0.0153164\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1639.32i | − | 0.380009i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1444.03 | + | 1444.03i | −0.330986 | + | 0.330986i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.77962 | + | 4.77962i | 0.00108334 | + | 0.00108334i | 0.707648 | − | 0.706565i | \(-0.249756\pi\) |
−0.706565 | + | 0.707648i | \(0.749756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2833.98 | −0.635247 | −0.317623 | − | 0.948217i | \(-0.602885\pi\) | ||||
−0.317623 | + | 0.948217i | \(0.602885\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3084.67 | −0.683855 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1820.95 | − | 1820.95i | −0.399300 | − | 0.399300i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1525.80 | + | 1525.80i | −0.330962 | + | 0.330962i | −0.852952 | − | 0.521989i | \(-0.825190\pi\) |
0.521989 | + | 0.852952i | \(0.325190\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 3239.94i | − | 0.695234i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4750.23i | 1.00845i | 0.863572 | + | 0.504226i | \(0.168222\pi\) | ||||
−0.863572 | + | 0.504226i | \(0.831778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −644.104 | + | 644.104i | −0.135293 | + | 0.135293i | −0.771510 | − | 0.636217i | \(-0.780498\pi\) |
0.636217 | + | 0.771510i | \(0.280498\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1938.79 | + | 1938.79i | 0.402961 | + | 0.402961i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8975.67 | −1.84605 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2916.53 | 0.593635 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 828.827 | + | 828.827i | 0.166965 | + | 0.166965i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1433.16 | − | 1433.16i | 0.285755 | − | 0.285755i | −0.549644 | − | 0.835399i | \(-0.685237\pi\) |
0.835399 | + | 0.549644i | \(0.185237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3777.69i | 0.745578i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1575.79i | 0.307868i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −542.407 | + | 542.407i | −0.104910 | + | 0.104910i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2495.85 | − | 2495.85i | −0.477935 | − | 0.477935i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5364.10 | 1.01703 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6198.79 | −1.16374 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 231.211 | + | 231.211i | 0.0429834 | + | 0.0429834i | 0.728272 | − | 0.685288i | \(-0.240324\pi\) |
−0.685288 | + | 0.728272i | \(0.740324\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10116.2 | + | 10116.2i | −1.86242 | + | 1.86242i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 871.410i | 0.158885i | 0.996839 | + | 0.0794423i | \(0.0253140\pi\) | ||||
−0.996839 | + | 0.0794423i | \(0.974686\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3515.02i | − | 0.634762i | −0.948298 | − | 0.317381i | \(-0.897197\pi\) | ||
0.948298 | − | 0.317381i | \(-0.102803\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3879.95 | − | 3879.95i | 0.694001 | − | 0.694001i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4723.77 | − | 4723.77i | −0.836951 | − | 0.836951i | 0.151506 | − | 0.988456i | \(-0.451588\pi\) |
−0.988456 | + | 0.151506i | \(0.951588\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 466.665 | 0.0819067 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −872.901 | −0.151778 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3346.38 | + | 3346.38i | 0.576462 | + | 0.576462i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −918.613 | + | 918.613i | −0.156786 | + | 0.156786i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10475.5i | 1.77155i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 5493.90i | − | 0.920633i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1820.26 | − | 1820.26i | 0.302268 | − | 0.302268i | −0.539633 | − | 0.841901i | \(-0.681437\pi\) |
0.841901 | + | 0.539633i | \(0.181437\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5456.13 | + | 5456.13i | 0.897880 | + | 0.897880i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1001.55 | 0.163345 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 74.0970 | 0.0119772 | 0.00598861 | − | 0.999982i | \(-0.498094\pi\) | ||||
0.00598861 | + | 0.999982i | \(0.498094\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3959.83 | + | 3959.83i | 0.634420 | + | 0.634420i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2166.34 | − | 2166.34i | 0.344029 | − | 0.344029i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1647.24i | − | 0.259307i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 2467.01i | − | 0.384984i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2102.73 | + | 2102.73i | −0.325305 | + | 0.325305i | −0.850798 | − | 0.525493i | \(-0.823881\pi\) |
0.525493 | + | 0.850798i | \(0.323881\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6612.85 | + | 6612.85i | 1.01426 | + | 1.01426i | 0.999897 | + | 0.0143661i | \(0.00457302\pi\) |
0.0143661 | + | 0.999897i | \(0.495427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 794.940 | 0.120885 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2216.90 | 0.334259 | 0.167130 | − | 0.985935i | \(-0.446550\pi\) | ||||
0.167130 | + | 0.985935i | \(0.446550\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1002.93 | + | 1002.93i | 0.149944 | + | 0.149944i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12107.9 | − | 12107.9i | 1.79500 | − | 1.79500i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2082.23i | − | 0.306117i | −0.988217 | − | 0.153059i | \(-0.951088\pi\) | ||
0.988217 | − | 0.153059i | \(-0.0489123\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 3998.49i | − | 0.582955i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1827.87 | − | 1827.87i | 0.264293 | − | 0.264293i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3118.10 | − | 3118.10i | −0.447148 | − | 0.447148i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4509.22 | 0.641360 | 0.320680 | − | 0.947188i | \(-0.396089\pi\) | ||||
0.320680 | + | 0.947188i | \(0.396089\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12047.1 | 1.69959 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4375.61 | − | 4375.61i | −0.612320 | − | 0.612320i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8661.56 | − | 8661.56i | 1.20236 | − | 1.20236i | 0.228908 | − | 0.973448i | \(-0.426485\pi\) |
0.973448 | − | 0.228908i | \(-0.0735154\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 10586.3i | − | 1.45779i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 235.418i | − | 0.0321609i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3522.46 | + | 3522.46i | −0.477405 | + | 0.477405i | −0.904301 | − | 0.426896i | \(-0.859607\pi\) |
0.426896 | + | 0.904301i | \(0.359607\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14412.9 | − | 14412.9i | −1.93804 | − | 1.93804i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3044.88 | 0.406229 | 0.203115 | − | 0.979155i | \(-0.434894\pi\) | ||||
0.203115 | + | 0.979155i | \(0.434894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5188.54 | 0.686837 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3349.92 | + | 3349.92i | 0.440016 | + | 0.440016i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1932.73 | + | 1932.73i | −0.251911 | + | 0.251911i | −0.821754 | − | 0.569843i | \(-0.807004\pi\) |
0.569843 | + | 0.821754i | \(0.307004\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4258.09i | − | 0.550744i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7228.29i | 0.927784i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3838.04 | + | 3838.04i | −0.488893 | + | 0.488893i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 672.457 | + | 672.457i | 0.0850117 | + | 0.0850117i | 0.748334 | − | 0.663322i | \(-0.230854\pi\) |
−0.663322 | + | 0.748334i | \(0.730854\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10349.9 | 1.29861 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7606.74 | −0.947288 | −0.473644 | − | 0.880716i | \(-0.657062\pi\) | ||||
−0.473644 | + | 0.880716i | \(0.657062\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1092.85 | − | 1092.85i | −0.135084 | − | 0.135084i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2399.96 | − | 2399.96i | 0.294457 | − | 0.294457i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7296.32i | 0.888612i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4981.58i | 0.602257i | 0.953584 | + | 0.301129i | \(0.0973634\pi\) | ||||
−0.953584 | + | 0.301129i | \(0.902637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13803.8 | − | 13803.8i | 1.65667 | − | 1.65667i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10083.3 | + | 10083.3i | 1.20137 | + | 1.20137i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3048.89 | −0.360637 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11937.9 | −1.40192 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3433.38 | + | 3433.38i | 0.400314 | + | 0.400314i | 0.878344 | − | 0.478030i | \(-0.158649\pi\) |
−0.478030 | + | 0.878344i | \(0.658649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7973.72 | + | 7973.72i | −0.923077 | + | 0.923077i | −0.997246 | − | 0.0741686i | \(-0.976370\pi\) |
0.0741686 | + | 0.997246i | \(0.476370\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7373.88i | 0.847590i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 7211.44i | − | 0.823074i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16545.6 | + | 16545.6i | −1.87517 | + | 1.87517i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2768.30 | + | 2768.30i | 0.311550 | + | 0.311550i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4800.16 | 0.536463 | 0.268232 | − | 0.963354i | \(-0.413561\pi\) | ||||
0.268232 | + | 0.963354i | \(0.413561\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6242.32 | 0.692810 | 0.346405 | − | 0.938085i | \(-0.387402\pi\) | ||||
0.346405 | + | 0.938085i | \(0.387402\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 535.372 | + | 535.372i | 0.0590095 | + | 0.0590095i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1819.93 | − | 1819.93i | 0.199220 | − | 0.199220i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4929.27i | 0.535903i | 0.963432 | + | 0.267951i | \(0.0863466\pi\) | ||||
−0.963432 | + | 0.267951i | \(0.913653\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 9250.77i | − | 0.998896i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7670.67 | − | 7670.67i | 0.822674 | − | 0.822674i | −0.163817 | − | 0.986491i | \(-0.552381\pi\) |
0.986491 | + | 0.163817i | \(0.0523807\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1225.32 | − | 1225.32i | −0.130529 | − | 0.130529i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25113.5 | −2.65733 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11515.2 | −1.21032 | −0.605162 | − | 0.796102i | \(-0.706892\pi\) | ||||
−0.605162 | + | 0.796102i | \(0.706892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8055.12 | + | 8055.12i | 0.841021 | + | 0.841021i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15468.4 | + | 15468.4i | −1.60434 | + | 1.60434i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 2617.46i | − | 0.269689i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4829.89i | 0.494383i | 0.968967 | + | 0.247191i | \(0.0795076\pi\) | ||||
−0.968967 | + | 0.247191i | \(0.920492\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3120.28 | + | 3120.28i | −0.317303 | + | 0.317303i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8265.79 | − | 8265.79i | −0.835090 | − | 0.835090i | 0.153118 | − | 0.988208i | \(-0.451069\pi\) |
−0.988208 | + | 0.153118i | \(0.951069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5043.86 | −0.506281 | −0.253141 | − | 0.967430i | \(-0.581464\pi\) | ||||
−0.253141 | + | 0.967430i | \(0.581464\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4970.57 | 0.495709 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12438.8 | − | 12438.8i | −1.23255 | − | 1.23255i | −0.962982 | − | 0.269564i | \(-0.913120\pi\) |
−0.269564 | − | 0.962982i | \(-0.586880\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2673.31 | − | 2673.31i | 0.263203 | − | 0.263203i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 9962.47i | − | 0.974621i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4479.75i | 0.435474i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3082.20 | − | 3082.20i | 0.297729 | − | 0.297729i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5872.93 | + | 5872.93i | 0.563738 | + | 0.563738i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13059.7 | 1.24575 | 0.622875 | − | 0.782321i | \(-0.285964\pi\) | ||||
0.622875 | + | 0.782321i | \(0.285964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3680.77 | 0.348916 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6584.87 | − | 6584.87i | −0.620335 | − | 0.620335i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −703.292 | + | 703.292i | −0.0658450 | + | 0.0658450i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15549.3i | 1.44683i | 0.690414 | + | 0.723414i | \(0.257428\pi\) | ||||
−0.690414 | + | 0.723414i | \(0.742572\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15305.3i | 1.41540i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8628.34 | − | 8628.34i | 0.793058 | − | 0.793058i | −0.188932 | − | 0.981990i | \(-0.560503\pi\) |
0.981990 | + | 0.188932i | \(0.0605027\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 924.059 | + | 924.059i | 0.0844169 | + | 0.0844169i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6964.03 | −0.632344 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5354.00 | 0.483219 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1732.42 | − | 1732.42i | −0.155418 | − | 0.155418i | 0.625115 | − | 0.780533i | \(-0.285052\pi\) |
−0.780533 | + | 0.625115i | \(0.785052\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6714.44 | + | 6714.44i | −0.598761 | + | 0.598761i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 16579.6i | − | 1.46968i | −0.678241 | − | 0.734839i | \(-0.737258\pi\) | ||
0.678241 | − | 0.734839i | \(-0.262742\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4551.65i | 0.401081i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10678.6 | + | 10678.6i | −0.935410 | + | 0.935410i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7830.92 | + | 7830.92i | 0.681924 | + | 0.681924i | 0.960434 | − | 0.278509i | \(-0.0898403\pi\) |
−0.278509 | + | 0.960434i | \(0.589840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16645.5 | −1.44100 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2667.24 | −0.229555 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8583.95 | − | 8583.95i | −0.734474 | − | 0.734474i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4930.44 | + | 4930.44i | −0.419420 | + | 0.419420i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 6193.30i | − | 0.523807i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3400.02i | − | 0.285907i | −0.989729 | − | 0.142953i | \(-0.954340\pi\) | ||
0.989729 | − | 0.142953i | \(-0.0456599\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2019.50 | − | 2019.50i | 0.168847 | − | 0.168847i | −0.617626 | − | 0.786472i | \(-0.711905\pi\) |
0.786472 | + | 0.617626i | \(0.211905\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11152.0 | − | 11152.0i | −0.927075 | − | 0.927075i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8579.28 | 0.709144 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9851.23 | 0.809668 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13533.7 | − | 13533.7i | −1.10605 | − | 1.10605i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4063.56 | − | 4063.56i | 0.330229 | − | 0.330229i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 740.691i | − | 0.0598558i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 24207.7i | − | 1.94532i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6185.39 | − | 6185.39i | 0.494293 | − | 0.494293i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13432.6 | + | 13432.6i | 1.06749 | + | 1.06749i | 0.997551 | + | 0.0699388i | \(0.0222804\pi\) |
0.0699388 | + | 0.997551i | \(0.477720\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1333.30 | 0.105373 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8888.86 | −0.698637 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5376.46 | + | 5376.46i | 0.420257 | + | 0.420257i | 0.885292 | − | 0.465035i | \(-0.153958\pi\) |
−0.465035 | + | 0.885292i | \(0.653958\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 22207.5 | − | 22207.5i | 1.72640 | − | 1.72640i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 789.894i | 0.0610719i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20488.7i | 1.57553i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8370.55 | + | 8370.55i | −0.640198 | + | 0.640198i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2076.28 | + | 2076.28i | 0.157944 | + | 0.157944i | 0.781655 | − | 0.623711i | \(-0.214376\pi\) |
−0.623711 | + | 0.781655i | \(0.714376\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2259.90 | 0.170990 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21732.1 | −1.63553 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16643.1 | + | 16643.1i | 1.24587 | + | 1.24587i | 0.957528 | + | 0.288339i | \(0.0931031\pi\) |
0.288339 | + | 0.957528i | \(0.406897\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3360.07 | + | 3360.07i | −0.250193 | + | 0.250193i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 12811.8i | − | 0.948934i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5659.60i | 0.416982i | 0.978024 | + | 0.208491i | \(0.0668551\pi\) | ||||
−0.978024 | + | 0.208491i | \(0.933145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4872.67 | + | 4872.67i | −0.357119 | + | 0.357119i | −0.862750 | − | 0.505631i | \(-0.831260\pi\) |
0.505631 | + | 0.862750i | \(0.331260\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21587.1 | − | 21587.1i | −1.57385 | − | 1.57385i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3921.95 | −0.284446 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10652.2 | 0.768556 | 0.384278 | − | 0.923217i | \(-0.374450\pi\) | ||||
0.384278 | + | 0.923217i | \(0.374450\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17857.2 | + | 17857.2i | 1.28173 | + | 1.28173i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8138.01 | + | 8138.01i | −0.581104 | + | 0.581104i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7853.69i | 0.557919i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3513.14i | 0.248291i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9903.95 | + | 9903.95i | −0.696388 | + | 0.696388i | −0.963630 | − | 0.267242i | \(-0.913888\pi\) |
0.267242 | + | 0.963630i | \(0.413888\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3666.82 | + | 3666.82i | 0.256517 | + | 0.256517i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26611.5 | 1.85220 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3528.04 | −0.244316 | −0.122158 | − | 0.992511i | \(-0.538981\pi\) | ||||
−0.122158 | + | 0.992511i | \(0.538981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10274.0 | + | 10274.0i | 0.707887 | + | 0.707887i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7536.93 | − | 7536.93i | 0.516693 | − | 0.516693i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19024.9i | 1.29772i | 0.760907 | + | 0.648861i | \(0.224754\pi\) | ||||
−0.760907 | + | 0.648861i | \(0.775246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1065.92i | 0.0723460i | 0.999346 | + | 0.0361730i | \(0.0115167\pi\) | ||||
−0.999346 | + | 0.0361730i | \(0.988483\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3588.11 | + | 3588.11i | −0.242320 | + | 0.242320i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1551.02 | + | 1551.02i | 0.104228 | + | 0.104228i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12909.7 | 0.863242 | 0.431621 | − | 0.902055i | \(-0.357942\pi\) | ||||
0.431621 | + | 0.902055i | \(0.357942\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2858.00 | 0.190167 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2487.25 | + | 2487.25i | 0.164687 | + | 0.164687i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8763.41 | − | 8763.41i | 0.577408 | − | 0.577408i | −0.356781 | − | 0.934188i | \(-0.616126\pi\) |
0.934188 | + | 0.356781i | \(0.116126\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18482.1i | 1.21182i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 18921.2i | − | 1.23459i | −0.786733 | − | 0.617293i | \(-0.788229\pi\) | ||
0.786733 | − | 0.617293i | \(-0.211771\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15116.6 | − | 15116.6i | 0.981565 | − | 0.981565i | −0.0182677 | − | 0.999833i | \(-0.505815\pi\) |
0.999833 | + | 0.0182677i | \(0.00581513\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1696.97 | + | 1696.97i | 0.109657 | + | 0.109657i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6541.15 | −0.420651 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1204.57 | −0.0770926 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9288.42 | − | 9288.42i | −0.591617 | − | 0.591617i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14447.7 | + | 14447.7i | −0.915845 | + | 0.915845i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9602.80i | − | 0.605834i | −0.953017 | − | 0.302917i | \(-0.902039\pi\) | ||
0.953017 | − | 0.302917i | \(-0.0979605\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 17813.1i | − | 1.11849i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12229.9 | − | 12229.9i | 0.764297 | − | 0.764297i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3120.34 | − | 3120.34i | −0.194085 | − | 0.194085i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7186.12 | −0.444880 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4450.84 | 0.274256 | 0.137128 | − | 0.990553i | \(-0.456213\pi\) | ||||
0.137128 | + | 0.990553i | \(0.456213\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6491.27 | − | 6491.27i | −0.398119 | − | 0.398119i | 0.479450 | − | 0.877569i | \(-0.340836\pi\) |
−0.877569 | + | 0.479450i | \(0.840836\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5139.30 | + | 5139.30i | −0.313736 | + | 0.313736i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 5546.17i | − | 0.337005i | −0.985701 | − | 0.168503i | \(-0.946107\pi\) | ||
0.985701 | − | 0.168503i | \(-0.0538932\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 18098.3i | − | 1.09464i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13267.3 | − | 13267.3i | 0.798750 | − | 0.798750i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6327.58 | − | 6327.58i | −0.379200 | − | 0.379200i | 0.491614 | − | 0.870813i | \(-0.336407\pi\) |
−0.870813 | + | 0.491614i | \(0.836407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6133.49 | −0.365886 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22341.5 | 1.32667 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15135.2 | − | 15135.2i | −0.894663 | − | 0.894663i | 0.100294 | − | 0.994958i | \(-0.468022\pi\) |
−0.994958 | + | 0.100294i | \(0.968022\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23460.1 | − | 23460.1i | 1.38047 | − | 1.38047i | 0.536694 | − | 0.843777i | \(-0.319673\pi\) |
0.843777 | − | 0.536694i | \(-0.180327\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10963.2i | 0.642195i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8782.30i | 0.512125i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 502.550 | − | 502.550i | 0.0291736 | − | 0.0291736i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2306.29 | + | 2306.29i | 0.133283 | + | 0.133283i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29697.4 | 1.70858 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30638.5 | 1.75487 | 0.877436 | − | 0.479694i | \(-0.159252\pi\) | ||||
0.877436 | + | 0.479694i | \(0.159252\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2873.96 | + | 2873.96i | 0.163879 | + | 0.163879i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12468.9 | − | 12468.9i | 0.707855 | − | 0.707855i | −0.258229 | − | 0.966084i | \(-0.583139\pi\) |
0.966084 | + | 0.258229i | \(0.0831388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3754.41i | 0.212196i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 23453.8i | − | 1.31975i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13838.5 | + | 13838.5i | −0.775280 | + | 0.775280i | −0.979024 | − | 0.203744i | \(-0.934689\pi\) |
0.203744 | + | 0.979024i | \(0.434689\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11713.1 | + | 11713.1i | 0.653333 | + | 0.653333i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17306.6 | −0.961116 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3961.95 | 0.219068 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 106.012 | + | 106.012i | 0.00583628 | + | 0.00583628i | 0.710019 | − | 0.704183i | \(-0.248686\pi\) |
−0.704183 | + | 0.710019i | \(0.748686\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18588.2 | + | 18588.2i | −1.01891 | + | 1.01891i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 10129.8i | − | 0.552870i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31900.4i | 1.73359i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6567.17 | − | 6567.17i | 0.355355 | − | 0.355355i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7839.35 | − | 7839.35i | −0.422380 | − | 0.422380i | 0.463643 | − | 0.886022i | \(-0.346542\pi\) |
−0.886022 | + | 0.463643i | \(0.846542\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12350.0 | −0.662574 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11312.7 | −0.604341 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12149.1 | + | 12149.1i | 0.646273 | + | 0.646273i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2728.30 | + | 2728.30i | −0.144518 | + | 0.144518i | −0.775664 | − | 0.631146i | \(-0.782585\pi\) |
0.631146 | + | 0.775664i | \(0.282585\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 27499.9i | − | 1.45053i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4665.84i | − | 0.245073i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2349.01 | + | 2349.01i | −0.122864 | + | 0.122864i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23309.5 | + | 23309.5i | 1.21410 | + | 1.21410i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32717.8 | −1.69704 | −0.848519 | − | 0.529166i | \(-0.822505\pi\) | ||||
−0.848519 | + | 0.529166i | \(0.822505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45824.0 | −2.36696 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30620.3 | + | 30620.3i | 1.57508 | + | 1.57508i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 851.111 | − | 851.111i | 0.0435993 | − | 0.0435993i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25847.2i | 1.31859i | 0.751883 | + | 0.659297i | \(0.229146\pi\) | ||||
−0.751883 | + | 0.659297i | \(0.770854\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27662.0i | 1.40537i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8870.50 | + | 8870.50i | −0.448820 | + | 0.448820i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10131.9 | − | 10131.9i | −0.510547 | − | 0.510547i | 0.404147 | − | 0.914694i | \(-0.367568\pi\) |
−0.914694 | + | 0.404147i | \(0.867568\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14192.1 | 0.712223 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4798.27 | −0.239819 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19163.7 | − | 19163.7i | −0.953921 | − | 0.953921i | 0.0450633 | − | 0.998984i | \(-0.485651\pi\) |
−0.998984 | + | 0.0450633i | \(0.985651\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4685.72 | + | 4685.72i | −0.232300 | + | 0.232300i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23322.1i | − | 1.15155i | −0.817607 | − | 0.575777i | \(-0.804699\pi\) | ||
0.817607 | − | 0.575777i | \(-0.195301\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 21309.8i | − | 1.04796i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10922.8 | − | 10922.8i | 0.534999 | − | 0.534999i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1977.03 | − | 1977.03i | −0.0964473 | − | 0.0964473i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25994.0 | 1.26303 | 0.631515 | − | 0.775364i | \(-0.282434\pi\) | ||||
0.631515 | + | 0.775364i | \(0.282434\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5306.32 | −0.256804 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13125.5 | − | 13125.5i | −0.632698 | − | 0.632698i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22145.0 | + | 22145.0i | −1.06324 | + | 1.06324i | −0.0653808 | + | 0.997860i | \(0.520826\pi\) |
−0.997860 | + | 0.0653808i | \(0.979174\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11819.0i | 0.565222i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16497.5i | 0.785853i | 0.919570 | + | 0.392926i | \(0.128537\pi\) | ||||
−0.919570 | + | 0.392926i | \(0.871463\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23725.9 | + | 23725.9i | −1.12573 | + | 1.12573i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13789.7 | − | 13789.7i | −0.651723 | − | 0.651723i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9130.02 | −0.429812 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24867.3 | −1.16611 | −0.583055 | − | 0.812433i | \(-0.698143\pi\) | ||||
−0.583055 | + | 0.812433i | \(0.698143\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44481.2 | − | 44481.2i | −2.07776 | − | 2.07776i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1881.72 | + | 1881.72i | −0.0875559 | + | 0.0875559i | −0.749528 | − | 0.661972i | \(-0.769720\pi\) |
0.661972 | + | 0.749528i | \(0.269720\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7902.00i | − | 0.366256i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 44684.8i | 2.06314i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13634.4 | + | 13634.4i | −0.627089 | + | 0.627089i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4804.89 | − | 4804.89i | −0.220144 | − | 0.220144i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −736.525 | −0.0336159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8453.54 | 0.384356 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7790.94 | + | 7790.94i | 0.352881 | + | 0.352881i | 0.861180 | − | 0.508300i | \(-0.169726\pi\) |
−0.508300 | + | 0.861180i | \(0.669726\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2255.08 | + | 2255.08i | −0.101753 | + | 0.101753i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17937.2i | 0.806286i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 14981.4i | − | 0.670877i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9009.98 | + | 9009.98i | −0.401951 | + | 0.401951i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4209.84 | + | 4209.84i | 0.187102 | + | 0.187102i | 0.794442 | − | 0.607340i | \(-0.207763\pi\) |
−0.607340 | + | 0.794442i | \(0.707763\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19525.8 | −0.864549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8779.50 | 0.387276 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14938.3 | + | 14938.3i | 0.656490 | + | 0.656490i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5587.51 | − | 5587.51i | 0.244639 | − | 0.244639i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 52.5393i | − | 0.00229178i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27554.3i | 1.19747i | 0.800946 | + | 0.598737i | \(0.204330\pi\) | ||||
−0.800946 | + | 0.598737i | \(0.795670\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3406.54 | + | 3406.54i | −0.147497 | + | 0.147497i | −0.776999 | − | 0.629502i | \(-0.783259\pi\) |
0.629502 | + | 0.776999i | \(0.283259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15576.1 | + | 15576.1i | 0.671926 | + | 0.671926i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12987.1 | −0.558184 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7582.59 | −0.324701 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9377.16 | + | 9377.16i | 0.400079 | + | 0.400079i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9839.14 | − | 9839.14i | 0.418256 | − | 0.418256i | −0.466346 | − | 0.884602i | \(-0.654430\pi\) |
0.884602 | + | 0.466346i | \(0.154430\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 36653.5i | − | 1.55244i | −0.630461 | − | 0.776221i | \(-0.717134\pi\) | ||
0.630461 | − | 0.776221i | \(-0.282866\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20016.5i | 0.844711i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22223.2 | − | 22223.2i | 0.934431 | − | 0.934431i | −0.0635475 | − | 0.997979i | \(-0.520241\pi\) |
0.997979 | + | 0.0635475i | \(0.0202414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14715.5 | − | 14715.5i | −0.616516 | − | 0.616516i | 0.328120 | − | 0.944636i | \(-0.393585\pi\) |
−0.944636 | + | 0.328120i | \(0.893585\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16772.2 | 0.700145 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24495.8 | 1.01888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5697.46 | − | 5697.46i | −0.236130 | − | 0.236130i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3419.07 | + | 3419.07i | −0.141195 | + | 0.141195i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 11010.0i | − | 0.453050i | −0.974005 | − | 0.226525i | \(-0.927263\pi\) | ||
0.974005 | − | 0.226525i | \(-0.0727365\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 24170.9i | − | 0.991057i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26108.1 | − | 26108.1i | 1.06668 | − | 1.06668i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9061.20 | − | 9061.20i | −0.368893 | − | 0.368893i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8279.85 | 0.335890 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7080.22 | 0.286210 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7857.37 | + | 7857.37i | 0.316507 | + | 0.316507i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12809.9 | + | 12809.9i | −0.514190 | + | 0.514190i | −0.915808 | − | 0.401617i | \(-0.868448\pi\) |
0.401617 | + | 0.915808i | \(0.368448\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 11787.6i | − | 0.471493i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 38510.8i | − | 1.53501i | −0.641043 | − | 0.767505i | \(-0.721498\pi\) | ||
0.641043 | − | 0.767505i | \(-0.278502\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23234.6 | + | 23234.6i | −0.922882 | + | 0.922882i | −0.997232 | − | 0.0743503i | \(-0.976312\pi\) |
0.0743503 | + | 0.997232i | \(0.476312\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 49331.9 | + | 49331.9i | 1.95264 | + | 1.95264i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22079.5 | −0.870911 | −0.435456 | − | 0.900210i | \(-0.643413\pi\) | ||||
−0.435456 | + | 0.900210i | \(0.643413\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5255.26 | 0.206571 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16029.8 | − | 16029.8i | −0.627912 | − | 0.627912i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18387.4 | − | 18387.4i | 0.717779 | − | 0.717779i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2420.58i | 0.0941656i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 5039.15i | − | 0.195360i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23976.7 | − | 23976.7i | 0.926356 | − | 0.926356i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4082.13 | − | 4082.13i | −0.157176 | − | 0.157176i | 0.624138 | − | 0.781314i | \(-0.285450\pi\) |
−0.781314 | + | 0.624138i | \(0.785450\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15753.9 | −0.604510 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7132.59 | 0.272762 | 0.136381 | − | 0.990656i | \(-0.456453\pi\) | ||||
0.136381 | + | 0.990656i | \(0.456453\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19170.0 | − | 19170.0i | −0.730601 | − | 0.730601i | 0.240138 | − | 0.970739i | \(-0.422807\pi\) |
−0.970739 | + | 0.240138i | \(0.922807\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20762.9 | − | 20762.9i | 0.788628 | − | 0.788628i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45045.7i | 1.70517i | 0.522589 | + | 0.852585i | \(0.324966\pi\) | ||||
−0.522589 | + | 0.852585i | \(0.675034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 65287.3i | − | 2.46306i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11497.8 | + | 11497.8i | −0.432314 | + | 0.432314i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8345.43 | − | 8345.43i | −0.312731 | − | 0.312731i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20541.1 | 0.767167 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5962.34 | 0.221936 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1012.55 | + | 1012.55i | 0.0375643 | + | 0.0375643i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15551.4 | + | 15551.4i | −0.575017 | + | 0.575017i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27435.3i | 1.01106i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1131.36i | 0.0415554i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33658.2 | − | 33658.2i | 1.23220 | − | 1.23220i | 0.269079 | − | 0.963118i | \(-0.413281\pi\) |
0.963118 | − | 0.269079i | \(-0.0867192\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16306.5 | − | 16306.5i | −0.594997 | − | 0.594997i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42503.8 | −1.54579 | −0.772895 | − | 0.634534i | \(-0.781192\pi\) | ||||
−0.772895 | + | 0.634534i | \(0.781192\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14606.7 | 0.529477 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 34069.7 | + | 34069.7i | 1.23094 | + | 1.23094i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16371.3 | + | 16371.3i | −0.589562 | + | 0.589562i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8819.41i | 0.316568i | 0.987394 | + | 0.158284i | \(0.0505961\pi\) | ||||
−0.987394 | + | 0.158284i | \(0.949404\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 2541.55i | − | 0.0909305i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2423.92 | + | 2423.92i | −0.0864402 | + | 0.0864402i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13307.1 | + | 13307.1i | 0.473012 | + | 0.473012i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 61504.8 | 2.17916 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14155.6 | −0.499925 | −0.249963 | − | 0.968256i | \(-0.580418\pi\) | ||||
−0.249963 | + | 0.968256i | \(0.580418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10469.6 | + | 10469.6i | 0.368558 | + | 0.368558i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4789.43 | − | 4789.43i | 0.168059 | − | 0.168059i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 18440.6i | − | 0.644996i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38518.7i | 1.34296i | 0.741023 | + | 0.671479i | \(0.234341\pi\) | ||||
−0.741023 | + | 0.671479i | \(0.765659\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19319.2 | + | 19319.2i | −0.671414 | + | 0.671414i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27998.2 | − | 27998.2i | −0.969942 | − | 0.969942i | 0.0296196 | − | 0.999561i | \(-0.490570\pi\) |
−0.999561 | + | 0.0296196i | \(0.990570\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17349.0 | 0.599112 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8188.93 | −0.281890 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32839.5 | + | 32839.5i | 1.12687 | + | 1.12687i | 0.990684 | + | 0.136181i | \(0.0434829\pi\) |
0.136181 | + | 0.990684i | \(0.456517\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7535.92 | − | 7535.92i | 0.257773 | − | 0.257773i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 51925.4i | 1.77055i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20600.1i | 0.700211i | 0.936710 | + | 0.350106i | \(0.113854\pi\) | ||||
−0.936710 | + | 0.350106i | \(0.886146\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18317.5 | − | 18317.5i | 0.620670 | − | 0.620670i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2564.88 | − | 2564.88i | −0.0866360 | − | 0.0866360i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 62528.2 | 2.10547 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20390.2 | −0.684441 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2653.56 | + | 2653.56i | 0.0887951 | + | 0.0887951i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15152.5 | + | 15152.5i | −0.505469 | + | 0.505469i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 38210.9i | − | 1.27071i | −0.772219 | − | 0.635356i | \(-0.780853\pi\) | ||
0.772219 | − | 0.635356i | \(-0.219147\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 36784.6i | − | 1.21950i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37224.9 | + | 37224.9i | −1.23028 | + | 1.23028i | −0.266427 | + | 0.963855i | \(0.585843\pi\) |
−0.963855 | + | 0.266427i | \(0.914157\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27038.1 | − | 27038.1i | −0.890854 | − | 0.890854i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10097.7 | 0.331678 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7985.95 | 0.261508 | 0.130754 | − | 0.991415i | \(-0.458260\pi\) | ||||
0.130754 | + | 0.991415i | \(0.458260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5870.28 | + | 5870.28i | 0.191639 | + | 0.191639i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 31844.8 | − | 31844.8i | 1.03642 | − | 1.03642i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10703.1i | 0.347279i | 0.984809 | + | 0.173639i | \(0.0555527\pi\) | ||||
−0.984809 | + | 0.173639i | \(0.944447\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22580.9i | 0.730442i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −30195.4 | + | 30195.4i | −0.973791 | + | 0.973791i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4824.23 | + | 4824.23i | 0.155108 | + | 0.155108i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23945.4 | −0.767558 | −0.383779 | − | 0.923425i | \(-0.625377\pi\) | ||||
−0.383779 | + | 0.923425i | \(0.625377\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20009.0 | −0.639442 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6395.37 | + | 6395.37i | 0.203766 | + | 0.203766i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14292.5 | − | 14292.5i | 0.454010 | − | 0.454010i | −0.442673 | − | 0.896683i | \(-0.645970\pi\) |
0.896683 | + | 0.442673i | \(0.145970\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 11515.6i | − | 0.364702i |
(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 | 128.4.e.b.33.1 | 10 | ||
4.3 | odd | 2 | 128.4.e.a.33.5 | 10 | |||
8.3 | odd | 2 | 64.4.e.a.17.1 | 10 | |||
8.5 | even | 2 | 16.4.e.a.13.1 | yes | 10 | ||
16.3 | odd | 4 | 64.4.e.a.49.1 | 10 | |||
16.5 | even | 4 | inner | 128.4.e.b.97.1 | 10 | ||
16.11 | odd | 4 | 128.4.e.a.97.5 | 10 | |||
16.13 | even | 4 | 16.4.e.a.5.1 | ✓ | 10 | ||
24.5 | odd | 2 | 144.4.k.a.109.5 | 10 | |||
24.11 | even | 2 | 576.4.k.a.145.4 | 10 | |||
32.3 | odd | 8 | 1024.4.b.k.513.9 | 10 | |||
32.5 | even | 8 | 1024.4.a.n.1.9 | 10 | |||
32.11 | odd | 8 | 1024.4.a.m.1.9 | 10 | |||
32.13 | even | 8 | 1024.4.b.j.513.9 | 10 | |||
32.19 | odd | 8 | 1024.4.b.k.513.2 | 10 | |||
32.21 | even | 8 | 1024.4.a.n.1.2 | 10 | |||
32.27 | odd | 8 | 1024.4.a.m.1.2 | 10 | |||
32.29 | even | 8 | 1024.4.b.j.513.2 | 10 | |||
48.29 | odd | 4 | 144.4.k.a.37.5 | 10 | |||
48.35 | even | 4 | 576.4.k.a.433.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.1 | ✓ | 10 | 16.13 | even | 4 | ||
16.4.e.a.13.1 | yes | 10 | 8.5 | even | 2 | ||
64.4.e.a.17.1 | 10 | 8.3 | odd | 2 | |||
64.4.e.a.49.1 | 10 | 16.3 | odd | 4 | |||
128.4.e.a.33.5 | 10 | 4.3 | odd | 2 | |||
128.4.e.a.97.5 | 10 | 16.11 | odd | 4 | |||
128.4.e.b.33.1 | 10 | 1.1 | even | 1 | trivial | ||
128.4.e.b.97.1 | 10 | 16.5 | even | 4 | inner | ||
144.4.k.a.37.5 | 10 | 48.29 | odd | 4 | |||
144.4.k.a.109.5 | 10 | 24.5 | odd | 2 | |||
576.4.k.a.145.4 | 10 | 24.11 | even | 2 | |||
576.4.k.a.433.4 | 10 | 48.35 | even | 4 | |||
1024.4.a.m.1.2 | 10 | 32.27 | odd | 8 | |||
1024.4.a.m.1.9 | 10 | 32.11 | odd | 8 | |||
1024.4.a.n.1.2 | 10 | 32.21 | even | 8 | |||
1024.4.a.n.1.9 | 10 | 32.5 | even | 8 | |||
1024.4.b.j.513.2 | 10 | 32.29 | even | 8 | |||
1024.4.b.j.513.9 | 10 | 32.13 | even | 8 | |||
1024.4.b.k.513.2 | 10 | 32.19 | odd | 8 | |||
1024.4.b.k.513.9 | 10 | 32.3 | odd | 8 |