Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4900,2,Mod(2549,4900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4900.2549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4900.e (of order \(2\), degree \(1\), 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: | \(39.1266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 980) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2549.3 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4900.2549 |
Dual form | 4900.2.e.r.2549.2 |
$q$-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 \(\left(\mathbb{Z}/4900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) | \(2451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.414214i | 0.239146i | 0.992825 | + | 0.119573i | \(0.0381526\pi\) | ||||
−0.992825 | + | 0.119573i | \(0.961847\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.82843 | −1.15431 | −0.577157 | − | 0.816633i | \(-0.695838\pi\) | ||||
−0.577157 | + | 0.816633i | \(0.695838\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.58579i | − 0.994518i | −0.867602 | − | 0.497259i | \(-0.834340\pi\) | ||||
0.867602 | − | 0.497259i | \(-0.165660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.41421i | 1.55568i | 0.628465 | + | 0.777838i | \(0.283683\pi\) | ||||
−0.628465 | + | 0.777838i | \(0.716317\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.65685 | −0.838940 | −0.419470 | − | 0.907769i | \(-0.637784\pi\) | ||||
−0.419470 | + | 0.907769i | \(0.637784\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 0.585786i | − 0.122145i | −0.998133 | − | 0.0610725i | \(-0.980548\pi\) | ||||
0.998133 | − | 0.0610725i | \(-0.0194521\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41421i | 0.464616i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.65685 | −1.23615 | −0.618073 | − | 0.786120i | \(-0.712087\pi\) | ||||
−0.618073 | + | 0.786120i | \(0.712087\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.58579 | 0.823632 | 0.411816 | − | 0.911267i | \(-0.364895\pi\) | ||||
0.411816 | + | 0.911267i | \(0.364895\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 1.58579i | − 0.276050i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3.41421i | − 0.561293i | −0.959811 | − | 0.280647i | \(-0.909451\pi\) | ||||
0.959811 | − | 0.280647i | \(-0.0905489\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.48528 | 0.237835 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.585786 | 0.0914845 | 0.0457422 | − | 0.998953i | \(-0.485435\pi\) | ||||
0.0457422 | + | 0.998953i | \(0.485435\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 11.6569i | − 1.77765i | −0.458243 | − | 0.888827i | \(-0.651521\pi\) | ||||
0.458243 | − | 0.888827i | \(-0.348479\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 8.89949i | − 1.29812i | −0.760735 | − | 0.649062i | \(-0.775161\pi\) | ||||
0.760735 | − | 0.649062i | \(-0.224839\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.65685 | −0.372034 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.75736i | 0.516113i | 0.966130 | + | 0.258056i | \(0.0830821\pi\) | ||||
−0.966130 | + | 0.258056i | \(0.916918\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 1.51472i | − 0.200629i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.41421 | −0.444493 | −0.222246 | − | 0.974991i | \(-0.571339\pi\) | ||||
−0.222246 | + | 0.974991i | \(0.571339\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.17157 | 0.662152 | 0.331076 | − | 0.943604i | \(-0.392588\pi\) | ||||
0.331076 | + | 0.943604i | \(0.392588\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.0711i | − 1.35255i | −0.736651 | − | 0.676273i | \(-0.763594\pi\) | ||||
0.736651 | − | 0.676273i | \(-0.236406\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.242641 | 0.0292105 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.48528 | 0.769661 | 0.384831 | − | 0.922987i | \(-0.374260\pi\) | ||||
0.384831 | + | 0.922987i | \(0.374260\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.17157i | − 0.605287i | −0.953104 | − | 0.302643i | \(-0.902131\pi\) | ||||
0.953104 | − | 0.302643i | \(-0.0978691\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.1421 | −1.47861 | −0.739303 | − | 0.673373i | \(-0.764845\pi\) | ||||
−0.739303 | + | 0.673373i | \(0.764845\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.00000i | 0.878114i | 0.898459 | + | 0.439057i | \(0.144687\pi\) | ||||
−0.898459 | + | 0.439057i | \(0.855313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 2.75736i | − 0.295620i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.9706 | −1.79888 | −0.899438 | − | 0.437048i | \(-0.856024\pi\) | ||||
−0.899438 | + | 0.437048i | \(0.856024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.89949i | 0.196968i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.7279i | 1.59693i | 0.602042 | + | 0.798464i | \(0.294354\pi\) | ||||
−0.602042 | + | 0.798464i | \(0.705646\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.8284 | −1.08830 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.82843 | −0.480446 | −0.240223 | − | 0.970718i | \(-0.577221\pi\) | ||||
−0.240223 | + | 0.970718i | \(0.577221\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.58579i | − 0.156252i | −0.996943 | − | 0.0781261i | \(-0.975106\pi\) | ||||
0.996943 | − | 0.0781261i | \(-0.0248937\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 16.8284i | − 1.62687i | −0.581659 | − | 0.813433i | \(-0.697596\pi\) | ||||
0.581659 | − | 0.813433i | \(-0.302404\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.00000 | −0.862044 | −0.431022 | − | 0.902342i | \(-0.641847\pi\) | ||||
−0.431022 | + | 0.902342i | \(0.641847\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.41421 | 0.134231 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.07107i | 0.477046i | 0.971137 | + | 0.238523i | \(0.0766632\pi\) | ||||
−0.971137 | + | 0.238523i | \(0.923337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 10.1421i | − 0.937641i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.65685 | 0.332441 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.242641i | 0.0218782i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 21.8995i | − 1.94327i | −0.236494 | − | 0.971633i | \(-0.575998\pi\) | ||||
0.236494 | − | 0.971633i | \(-0.424002\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.82843 | 0.425119 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.7574 | −1.02725 | −0.513623 | − | 0.858016i | \(-0.671697\pi\) | ||||
−0.513623 | + | 0.858016i | \(0.671697\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9706i | 1.10815i | 0.832467 | + | 0.554075i | \(0.186928\pi\) | ||||
−0.832467 | + | 0.554075i | \(0.813072\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.8995 | 1.17894 | 0.589470 | − | 0.807790i | \(-0.299337\pi\) | ||||
0.589470 | + | 0.807790i | \(0.299337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.68629 | 0.310442 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.7279i | 1.14799i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.51472 | −0.287937 | −0.143968 | − | 0.989582i | \(-0.545986\pi\) | ||||
−0.143968 | + | 0.989582i | \(0.545986\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.8284 | −0.962584 | −0.481292 | − | 0.876560i | \(-0.659832\pi\) | ||||
−0.481292 | + | 0.876560i | \(0.659832\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.1421i | 1.46670i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4853i | 0.836817i | 0.908259 | + | 0.418408i | \(0.137412\pi\) | ||||
−0.908259 | + | 0.418408i | \(0.862588\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.55635 | −0.123427 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 21.5563i | − 1.68842i | −0.536010 | − | 0.844212i | \(-0.680069\pi\) | ||||
0.536010 | − | 0.844212i | \(-0.319931\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.41421i | 0.186817i | 0.995628 | + | 0.0934087i | \(0.0297763\pi\) | ||||
−0.995628 | + | 0.0934087i | \(0.970224\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.142136 | 0.0109335 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.3431 | −0.790960 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 18.5563i | − 1.41081i | −0.708803 | − | 0.705407i | \(-0.750764\pi\) | ||||
0.708803 | − | 0.705407i | \(-0.249236\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 1.41421i | − 0.106299i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.48528 | −0.484733 | −0.242366 | − | 0.970185i | \(-0.577924\pi\) | ||||
−0.242366 | + | 0.970185i | \(0.577924\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.75736 | 0.130623 | 0.0653117 | − | 0.997865i | \(-0.479196\pi\) | ||||
0.0653117 | + | 0.997865i | \(0.479196\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.14214i | 0.158351i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 24.5563i | − 1.79574i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.6569 | 1.20525 | 0.602624 | − | 0.798025i | \(-0.294122\pi\) | ||||
0.602624 | + | 0.798025i | \(0.294122\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 5.65685i | − 0.407189i | −0.979055 | − | 0.203595i | \(-0.934738\pi\) | ||||
0.979055 | − | 0.203595i | \(-0.0652625\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 27.5563i | − 1.96331i | −0.190669 | − | 0.981654i | \(-0.561066\pi\) | ||||
0.190669 | − | 0.981654i | \(-0.438934\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.7279 | 1.89469 | 0.947346 | − | 0.320212i | \(-0.103754\pi\) | ||||
0.947346 | + | 0.320212i | \(0.103754\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.58579 | 0.323456 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1.65685i | − 0.115159i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.0000 | 0.968400 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.3137 | −1.67382 | −0.836912 | − | 0.547337i | \(-0.815642\pi\) | ||||
−0.836912 | + | 0.547337i | \(0.815642\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.68629i | 0.184062i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.14214 | 0.144752 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.0000 | 1.54715 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 24.0711i | − 1.61192i | −0.591971 | − | 0.805959i | \(-0.701650\pi\) | ||||
0.591971 | − | 0.805959i | \(-0.298350\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.72792i | 0.512920i | 0.966555 | + | 0.256460i | \(0.0825562\pi\) | ||||
−0.966555 | + | 0.256460i | \(0.917444\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.8995 | −1.57932 | −0.789662 | − | 0.613543i | \(-0.789744\pi\) | ||||
−0.789662 | + | 0.613543i | \(0.789744\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.17157i | 0.600850i | 0.953805 | + | 0.300425i | \(0.0971285\pi\) | ||||
−0.953805 | + | 0.300425i | \(0.902872\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 5.44365i | − 0.353603i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.1716 | −0.916683 | −0.458341 | − | 0.888776i | \(-0.651556\pi\) | ||||
−0.458341 | + | 0.888776i | \(0.651556\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.55635 | −0.229085 | −0.114542 | − | 0.993418i | \(-0.536540\pi\) | ||||
−0.114542 | + | 0.993418i | \(0.536540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.3431i | 0.663513i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.1127i | 0.834341i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.31371 | −0.209998 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.0711 | −1.70871 | −0.854355 | − | 0.519689i | \(-0.826048\pi\) | ||||
−0.854355 | + | 0.519689i | \(0.826048\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.24264i | 0.140994i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 25.7990i | − 1.60930i | −0.593752 | − | 0.804648i | \(-0.702354\pi\) | ||||
0.593752 | − | 0.804648i | \(-0.297646\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.8284 | −1.16545 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 10.0000i | − 0.616626i | −0.951285 | − | 0.308313i | \(-0.900236\pi\) | ||||
0.951285 | − | 0.308313i | \(-0.0997645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 7.02944i | − 0.430195i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.7279 | 1.01992 | 0.509960 | − | 0.860198i | \(-0.329660\pi\) | ||||
0.509960 | + | 0.860198i | \(0.329660\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.9706 | 1.75984 | 0.879918 | − | 0.475125i | \(-0.157597\pi\) | ||||
0.879918 | + | 0.475125i | \(0.157597\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 7.41421i | − 0.445477i | −0.974878 | − | 0.222738i | \(-0.928500\pi\) | ||||
0.974878 | − | 0.222738i | \(-0.0714996\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.9706 | 0.776527 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00000 | −0.0596550 | −0.0298275 | − | 0.999555i | \(-0.509496\pi\) | ||||
−0.0298275 | + | 0.999555i | \(0.509496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.7574i | 1.11501i | 0.830174 | + | 0.557505i | \(0.188241\pi\) | ||||
−0.830174 | + | 0.557505i | \(0.811759\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −24.1421 | −1.42013 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.51472 | −0.381900 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4142i | 0.842087i | 0.907040 | + | 0.421044i | \(0.138336\pi\) | ||||
−0.907040 | + | 0.421044i | \(0.861664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 9.24264i | − 0.536312i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.10051 | −0.121475 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2.00000i | − 0.114897i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.58579i | 0.204652i | 0.994751 | + | 0.102326i | \(0.0326284\pi\) | ||||
−0.994751 | + | 0.102326i | \(0.967372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.656854 | 0.0373671 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.97056 | 0.395264 | 0.197632 | − | 0.980276i | \(-0.436675\pi\) | ||||
0.197632 | + | 0.980276i | \(0.436675\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 16.5563i | − 0.935820i | −0.883776 | − | 0.467910i | \(-0.845007\pi\) | ||||
0.883776 | − | 0.467910i | \(-0.154993\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 14.9706i | − 0.840831i | −0.907332 | − | 0.420415i | \(-0.861884\pi\) | ||||
0.907332 | − | 0.420415i | \(-0.138116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.4853 | 1.42690 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.97056 | 0.389059 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 23.4558i | − 1.30512i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 3.72792i | − 0.206155i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.82843 | 0.265394 | 0.132697 | − | 0.991157i | \(-0.457636\pi\) | ||||
0.132697 | + | 0.991157i | \(0.457636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 9.65685i | − 0.529192i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 18.7279i | − 1.02017i | −0.860123 | − | 0.510087i | \(-0.829613\pi\) | ||||
0.860123 | − | 0.510087i | \(-0.170387\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.10051 | −0.114084 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.5563 | −0.950730 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 7.41421i | − 0.398016i | −0.979998 | − | 0.199008i | \(-0.936228\pi\) | ||||
0.979998 | − | 0.199008i | \(-0.0637719\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.0000 | −0.963518 | −0.481759 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481759 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.65685 | 0.462069 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.07107i | 0.110232i | 0.998480 | + | 0.0551159i | \(0.0175528\pi\) | ||||
−0.998480 | + | 0.0551159i | \(0.982447\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.3137 | −0.597115 | −0.298557 | − | 0.954392i | \(-0.596505\pi\) | ||||
−0.298557 | + | 0.954392i | \(0.596505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.62742 | −0.296180 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.51472i | 0.0795021i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.7279i | 1.02979i | 0.857254 | + | 0.514895i | \(0.172169\pi\) | ||||
−0.857254 | + | 0.514895i | \(0.827831\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.65685 | 0.0862524 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 16.4853i | − 0.853576i | −0.904352 | − | 0.426788i | \(-0.859645\pi\) | ||||
0.904352 | − | 0.426788i | \(-0.140355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.8701i | 1.22937i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.0000 | −0.719132 | −0.359566 | − | 0.933120i | \(-0.617075\pi\) | ||||
−0.359566 | + | 0.933120i | \(0.617075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.07107 | 0.464725 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.51472i | 0.179594i | 0.995960 | + | 0.0897969i | \(0.0286218\pi\) | ||||
−0.995960 | + | 0.0897969i | \(0.971378\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 32.9706i | − 1.67599i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.1421 | −0.666333 | −0.333166 | − | 0.942868i | \(-0.608117\pi\) | ||||
−0.333166 | + | 0.942868i | \(0.608117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.75736 | 0.190018 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 4.87006i | − 0.245662i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.4142i | 0.723429i | 0.932289 | + | 0.361714i | \(0.117808\pi\) | ||||
−0.932289 | + | 0.361714i | \(0.882192\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.514719 | 0.0257038 | 0.0128519 | − | 0.999917i | \(-0.495909\pi\) | ||||
0.0128519 | + | 0.999917i | \(0.495909\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 16.4437i | − 0.819117i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.0711i | 0.647909i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.8284 | −1.62326 | −0.811631 | − | 0.584171i | \(-0.801420\pi\) | ||||
−0.811631 | + | 0.584171i | \(0.801420\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.37258 | −0.265010 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.75736i | 0.281939i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.55635 | 0.466858 | 0.233429 | − | 0.972374i | \(-0.425005\pi\) | ||||
0.233429 | + | 0.972374i | \(0.425005\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3137 | 0.990030 | 0.495015 | − | 0.868885i | \(-0.335163\pi\) | ||||
0.495015 | + | 0.868885i | \(0.335163\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 25.1716i | − 1.22388i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.68629 | −0.274537 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.82843 | −0.473419 | −0.236709 | − | 0.971581i | \(-0.576069\pi\) | ||||
−0.236709 | + | 0.971581i | \(0.576069\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.2843i | 1.07091i | 0.844563 | + | 0.535457i | \(0.179861\pi\) | ||||
−0.844563 | + | 0.535457i | \(0.820139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.14214i | 0.102472i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.2426 | −1.15704 | −0.578519 | − | 0.815669i | \(-0.696369\pi\) | ||||
−0.578519 | + | 0.815669i | \(0.696369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.4558i | 1.68456i | 0.539042 | + | 0.842279i | \(0.318786\pi\) | ||||
−0.539042 | + | 0.842279i | \(0.681214\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 1.45584i | − 0.0688591i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.8284 | −1.12453 | −0.562267 | − | 0.826956i | \(-0.690070\pi\) | ||||
−0.562267 | + | 0.826956i | \(0.690070\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.24264 | −0.105602 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 4.89949i | − 0.230198i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 15.0711i | − 0.704995i | −0.935813 | − | 0.352497i | \(-0.885333\pi\) | ||||
0.935813 | − | 0.352497i | \(-0.114667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.4853 | −0.722791 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.3431 | 1.04062 | 0.520312 | − | 0.853976i | \(-0.325816\pi\) | ||||
0.520312 | + | 0.853976i | \(0.325816\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.4558i | 0.625346i | 0.949861 | + | 0.312673i | \(0.101224\pi\) | ||||
−0.949861 | + | 0.312673i | \(0.898776\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.899495i | 0.0416237i | 0.999783 | + | 0.0208118i | \(0.00662509\pi\) | ||||
−0.999783 | + | 0.0208118i | \(0.993375\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.34315 | −0.200122 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 44.6274i | 2.05197i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.6274i | 0.486596i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.41421 | −0.430146 | −0.215073 | − | 0.976598i | \(-0.568999\pi\) | ||||
−0.215073 | + | 0.976598i | \(0.568999\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.2426 | −0.558216 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 7.41421i | − 0.335970i | −0.985790 | − | 0.167985i | \(-0.946274\pi\) | ||||
0.985790 | − | 0.167985i | \(-0.0537260\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.92893 | 0.403780 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.2843 | 0.780028 | 0.390014 | − | 0.920809i | \(-0.372470\pi\) | ||||
0.390014 | + | 0.920809i | \(0.372470\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 42.6985i | − 1.92304i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.6274 | 0.610047 | 0.305023 | − | 0.952345i | \(-0.401336\pi\) | ||||
0.305023 | + | 0.952345i | \(0.401336\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 39.0416i | − 1.74078i | −0.492363 | − | 0.870390i | \(-0.663867\pi\) | ||||
0.492363 | − | 0.870390i | \(-0.336133\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.0588745i | 0.00261471i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.0711 | 1.55450 | 0.777249 | − | 0.629193i | \(-0.216615\pi\) | ||||
0.777249 | + | 0.629193i | \(0.216615\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 8.82843i | − 0.389785i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.0711i | 1.49844i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.68629 | 0.337391 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.68629 | 0.292932 | 0.146466 | − | 0.989216i | \(-0.453210\pi\) | ||||
0.146466 | + | 0.989216i | \(0.453210\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.85786i | − 0.0812387i | −0.999175 | − | 0.0406194i | \(-0.987067\pi\) | ||||
0.999175 | − | 0.0406194i | \(-0.0129331\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.4142i | 1.28130i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.6569 | 0.985081 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.65685 | −0.419072 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 2.10051i | − 0.0909830i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 2.68629i | − 0.115922i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.9706 | 0.686628 | 0.343314 | − | 0.939221i | \(-0.388450\pi\) | ||||
0.343314 | + | 0.939221i | \(0.388450\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.727922i | 0.0312381i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.51472i | 0.321306i | 0.987011 | + | 0.160653i | \(0.0513600\pi\) | ||||
−0.987011 | + | 0.160653i | \(0.948640\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.6274 | 0.624283 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.3431 | 1.03705 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 7.79899i | − 0.330454i | −0.986256 | − | 0.165227i | \(-0.947164\pi\) | ||||
0.986256 | − | 0.165227i | \(-0.0528356\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.7990 | −1.76791 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.1716 | 0.429444 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.6274i | 0.869342i | 0.900589 | + | 0.434671i | \(0.143135\pi\) | ||||
−0.900589 | + | 0.434671i | \(0.856865\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.7990 | 1.33308 | 0.666542 | − | 0.745468i | \(-0.267774\pi\) | ||||
0.666542 | + | 0.745468i | \(0.267774\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.82843 | 0.202063 | 0.101032 | − | 0.994883i | \(-0.467786\pi\) | ||||
0.101032 | + | 0.994883i | \(0.467786\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.89949i | 0.288231i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 14.0711i | − 0.585786i | −0.956145 | − | 0.292893i | \(-0.905382\pi\) | ||||
0.956145 | − | 0.292893i | \(-0.0946180\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.34315 | 0.0973778 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 14.3848i | − 0.595757i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 30.8284i | − 1.27243i | −0.771514 | − | 0.636213i | \(-0.780500\pi\) | ||||
0.771514 | − | 0.636213i | \(-0.219500\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.7696 | −0.690977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.4142 | 0.469518 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 17.7279i | − 0.727999i | −0.931399 | − | 0.363999i | \(-0.881411\pi\) | ||||
0.931399 | − | 0.363999i | \(-0.118589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.0711i | 0.453109i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.7990 | 0.522953 | 0.261476 | − | 0.965210i | \(-0.415791\pi\) | ||||
0.261476 | + | 0.965210i | \(0.415791\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.6569 | 1.61764 | 0.808818 | − | 0.588058i | \(-0.200108\pi\) | ||||
0.808818 | + | 0.588058i | \(0.200108\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 31.3137i | − 1.27519i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.9289i | 0.565358i | 0.959215 | + | 0.282679i | \(0.0912231\pi\) | ||||
−0.959215 | + | 0.282679i | \(0.908777\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.9117 | −1.29101 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.3137i | 1.66864i | 0.551277 | + | 0.834322i | \(0.314141\pi\) | ||||
−0.551277 | + | 0.834322i | \(0.685859\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.8701i | 1.64537i | 0.568500 | + | 0.822683i | \(0.307524\pi\) | ||||
−0.568500 | + | 0.822683i | \(0.692476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.8701 | −0.436905 | −0.218452 | − | 0.975848i | \(-0.570101\pi\) | ||||
−0.218452 | + | 0.975848i | \(0.570101\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.41421 | 0.0567504 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.79899i | 0.231589i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.8995 | 0.873190 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.4853 | −1.57188 | −0.785942 | − | 0.618300i | \(-0.787822\pi\) | ||||
−0.785942 | + | 0.618300i | \(0.787822\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 10.0711i | − 0.400289i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.3431 | 0.725644 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.3137 | 1.55280 | 0.776399 | − | 0.630242i | \(-0.217044\pi\) | ||||
0.776399 | + | 0.630242i | \(0.217044\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 4.21320i | − 0.166153i | −0.996543 | − | 0.0830763i | \(-0.973525\pi\) | ||||
0.996543 | − | 0.0830763i | \(-0.0264745\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.1127i | 1.38042i | 0.723608 | + | 0.690211i | \(0.242482\pi\) | ||||
−0.723608 | + | 0.690211i | \(0.757518\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.0711 | 0.513084 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.6863i | 1.04432i | 0.852849 | + | 0.522158i | \(0.174873\pi\) | ||||
−0.852849 | + | 0.522158i | \(0.825127\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 14.6274i | − 0.570670i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.6569 | 0.804677 | 0.402338 | − | 0.915491i | \(-0.368198\pi\) | ||||
0.402338 | + | 0.915491i | \(0.368198\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.1421 | −1.32798 | −0.663988 | − | 0.747744i | \(-0.731137\pi\) | ||||
−0.663988 | + | 0.747744i | \(0.731137\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.52691i | 0.369995i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.89949i | 0.150989i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.97056 | 0.385484 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.7990 | −0.764332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.5147i | 1.06061i | 0.847806 | + | 0.530307i | \(0.177923\pi\) | ||||
−0.847806 | + | 0.530307i | \(0.822077\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 10.2721i | − 0.394788i | −0.980324 | − | 0.197394i | \(-0.936752\pi\) | ||||
0.980324 | − | 0.197394i | \(-0.0632478\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.20101 | −0.122663 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 35.1127i | − 1.34355i | −0.740755 | − | 0.671775i | \(-0.765532\pi\) | ||||
0.740755 | − | 0.671775i | \(-0.234468\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 9.89949i | − 0.377689i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.4731 | 0.513284 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.51472 | 0.133706 | 0.0668531 | − | 0.997763i | \(-0.478704\pi\) | ||||
0.0668531 | + | 0.997763i | \(0.478704\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.75736i | 0.142320i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.79899 | −0.143691 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.514719 | 0.0194407 | 0.00972033 | − | 0.999953i | \(-0.496906\pi\) | ||||
0.00972033 | + | 0.999953i | \(0.496906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.4853i | 0.470891i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.62742 | −0.136231 | −0.0681153 | − | 0.997677i | \(-0.521699\pi\) | ||||
−0.0681153 | + | 0.997677i | \(0.521699\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −37.1716 | −1.39404 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2.68629i | − 0.100602i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 5.87006i | − 0.219221i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.7574 | −0.587650 | −0.293825 | − | 0.955859i | \(-0.594928\pi\) | ||||
−0.293825 | + | 0.955859i | \(0.594928\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1.47309i | − 0.0547847i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 18.0000i | − 0.667583i | −0.942647 | − | 0.333792i | \(-0.891672\pi\) | ||||
0.942647 | − | 0.333792i | \(-0.108328\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.1716 | 0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 74.7696 | 2.76545 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.6985i | 1.13387i | 0.823761 | + | 0.566937i | \(0.191872\pi\) | ||||
−0.823761 | + | 0.566937i | \(0.808128\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.3848i | 1.56126i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.6569 | −0.759875 | −0.379937 | − | 0.925012i | \(-0.624054\pi\) | ||||
−0.379937 | + | 0.925012i | \(0.624054\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.43146 | −0.199530 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.92893i | 0.327571i | 0.986496 | + | 0.163785i | \(0.0523705\pi\) | ||||
−0.986496 | + | 0.163785i | \(0.947630\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.6274i | 0.827894i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.14214 | 0.0416771 | 0.0208386 | − | 0.999783i | \(-0.493366\pi\) | ||||
0.0208386 | + | 0.999783i | \(0.493366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 11.2132i | − 0.408632i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.1716i | 1.35102i | 0.737349 | + | 0.675512i | \(0.236077\pi\) | ||||
−0.737349 | + | 0.675512i | \(0.763923\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.928932 | −0.0337181 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.8701 | −0.684039 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.2426i | 0.442056i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.1421 | −1.01483 | −0.507416 | − | 0.861701i | \(-0.669399\pi\) | ||||
−0.507416 | + | 0.861701i | \(0.669399\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.6863 | 0.384857 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 43.7279i | 1.57278i | 0.617728 | + | 0.786392i | \(0.288053\pi\) | ||||
−0.617728 | + | 0.786392i | \(0.711947\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.14214 | −0.0767500 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.8284 | −0.888431 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 16.0711i | − 0.574333i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 43.7279i | − 1.55873i | −0.626569 | − | 0.779366i | \(-0.715541\pi\) | ||||
0.626569 | − | 0.779366i | \(-0.284459\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.14214 | 0.147464 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 18.5442i | − 0.658522i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 35.3848i | − 1.25339i | −0.779263 | − | 0.626697i | \(-0.784407\pi\) | ||||
0.779263 | − | 0.626697i | \(-0.215593\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 57.0833 | 2.01946 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −48.0000 | −1.69600 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.7990i | 0.698691i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.92893i | 0.243910i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.02944 | −0.211984 | −0.105992 | − | 0.994367i | \(-0.533802\pi\) | ||||
−0.105992 | + | 0.994367i | \(0.533802\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.5563 | −0.686716 | −0.343358 | − | 0.939205i | \(-0.611564\pi\) | ||||
−0.343358 | + | 0.939205i | \(0.611564\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.0000i | 0.420858i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.6274i | 1.49134i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.8284 | 1.66922 | 0.834612 | − | 0.550839i | \(-0.185692\pi\) | ||||
0.834612 | + | 0.550839i | \(0.185692\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 36.5269i | − 1.27325i | −0.771174 | − | 0.636624i | \(-0.780330\pi\) | ||||
0.771174 | − | 0.636624i | \(-0.219670\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 10.0416i | − 0.349182i | −0.984641 | − | 0.174591i | \(-0.944140\pi\) | ||||
0.984641 | − | 0.174591i | \(-0.0558603\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.7279 | −0.789373 | −0.394687 | − | 0.918816i | \(-0.629147\pi\) | ||||
−0.394687 | + | 0.918816i | \(0.629147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.07107 | 0.106534 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.0711i | 0.382672i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.3848 | −0.772808 | −0.386404 | − | 0.922330i | \(-0.626283\pi\) | ||||
−0.386404 | + | 0.922330i | \(0.626283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.3137 | 0.528059 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 0.414214i | − 0.0142663i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.76955 | −0.266650 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.00000 | −0.0685591 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.2843i | 1.03691i | 0.855104 | + | 0.518457i | \(0.173493\pi\) | ||||
−0.855104 | + | 0.518457i | \(0.826507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 20.8284i | − 0.711486i | −0.934584 | − | 0.355743i | \(-0.884228\pi\) | ||||
0.934584 | − | 0.355743i | \(-0.115772\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.4558 | 1.55093 | 0.775467 | − | 0.631388i | \(-0.217515\pi\) | ||||
0.775467 | + | 0.631388i | \(0.217515\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.7574i | 0.672548i | 0.941764 | + | 0.336274i | \(0.109167\pi\) | ||||
−0.941764 | + | 0.336274i | \(0.890833\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 10.0000i | − 0.339618i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.3137 | 1.70678 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.6985 | −1.34513 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 44.4853i | 1.50560i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.6863i | 0.360850i | 0.983589 | + | 0.180425i | \(0.0577474\pi\) | ||||
−0.983589 | + | 0.180425i | \(0.942253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.97056 | −0.201382 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −56.2843 | −1.89627 | −0.948133 | − | 0.317875i | \(-0.897031\pi\) | ||||
−0.948133 | + | 0.317875i | \(0.897031\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.11270i | 0.239361i | 0.992812 | + | 0.119681i | \(0.0381871\pi\) | ||||
−0.992812 | + | 0.119681i | \(0.961813\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 57.5980i | 1.93395i | 0.254870 | + | 0.966975i | \(0.417967\pi\) | ||||
−0.254870 | + | 0.966975i | \(0.582033\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.6569 | −0.960041 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32.5442i | 1.08905i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 0.870058i | − 0.0290504i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.5269 | −1.01813 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.1005 | −0.802904 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.5269i | 0.747994i | 0.927430 | + | 0.373997i | \(0.122013\pi\) | ||||
−0.927430 | + | 0.373997i | \(0.877987\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.6569 | −0.452969 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.5980 | −1.84204 | −0.921022 | − | 0.389511i | \(-0.872644\pi\) | ||||
−0.921022 | + | 0.389511i | \(0.872644\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 30.6274i | − 1.01362i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.5147 | 0.610744 | 0.305372 | − | 0.952233i | \(-0.401219\pi\) | ||||
0.305372 | + | 0.952233i | \(0.401219\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.48528 | −0.0489417 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 23.2548i | − 0.765442i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 4.48528i | − 0.147316i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.2721 | 0.697914 | 0.348957 | − | 0.937139i | \(-0.386536\pi\) | ||||
0.348957 | + | 0.937139i | \(0.386536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.88730i | 0.0945260i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 7.72792i | − 0.252460i | −0.992001 | − | 0.126230i | \(-0.959712\pi\) | ||||
0.992001 | − | 0.126230i | \(-0.0402878\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.85786 | 0.223798 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.00000 | −0.130396 | −0.0651981 | − | 0.997872i | \(-0.520768\pi\) | ||||
−0.0651981 | + | 0.997872i | \(0.520768\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 0.343146i | − 0.0111744i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 32.0416i | − 1.04121i | −0.853797 | − | 0.520607i | \(-0.825706\pi\) | ||||
0.853797 | − | 0.520607i | \(-0.174294\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.5442 | −0.601969 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.20101 | 0.201082 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.8701i | 1.25912i | 0.776950 | + | 0.629562i | \(0.216766\pi\) | ||||
−0.776950 | + | 0.629562i | \(0.783234\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.5563i | 0.341238i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.97056 | −0.321631 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 47.5980i | − 1.53382i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 7.45584i | − 0.239764i | −0.992788 | − | 0.119882i | \(-0.961748\pi\) | ||||
0.992788 | − | 0.119882i | \(-0.0382516\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.71573 | 0.312114 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.5269 | −0.722923 | −0.361462 | − | 0.932387i | \(-0.617722\pi\) | ||||
−0.361462 | + | 0.932387i | \(0.617722\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 8.14214i | − 0.260490i | −0.991482 | − | 0.130245i | \(-0.958424\pi\) | ||||
0.991482 | − | 0.130245i | \(-0.0415764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 64.9706 | 2.07647 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.4558 | −0.812743 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.0122i | 1.33998i | 0.742370 | + | 0.669990i | \(0.233702\pi\) | ||||
−0.742370 | + | 0.669990i | \(0.766298\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.82843 | −0.217131 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.3137 | 0.804116 | 0.402058 | − | 0.915614i | \(-0.368295\pi\) | ||||
0.402058 | + | 0.915614i | \(0.368295\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.00000i | 0.0634681i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 50.8406i | − 1.61014i | −0.593181 | − | 0.805069i | \(-0.702128\pi\) | ||||
0.593181 | − | 0.805069i | \(-0.297872\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.24264 | 0.260786 |
(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 | 4900.2.e.r.2549.3 | 4 | ||
5.2 | odd | 4 | 4900.2.a.x.1.2 | 2 | |||
5.3 | odd | 4 | 980.2.a.k.1.1 | yes | 2 | ||
5.4 | even | 2 | inner | 4900.2.e.r.2549.2 | 4 | ||
7.6 | odd | 2 | 4900.2.e.q.2549.2 | 4 | |||
15.8 | even | 4 | 8820.2.a.bl.1.2 | 2 | |||
20.3 | even | 4 | 3920.2.a.bo.1.2 | 2 | |||
35.3 | even | 12 | 980.2.i.l.961.1 | 4 | |||
35.13 | even | 4 | 980.2.a.j.1.2 | ✓ | 2 | ||
35.18 | odd | 12 | 980.2.i.k.961.2 | 4 | |||
35.23 | odd | 12 | 980.2.i.k.361.2 | 4 | |||
35.27 | even | 4 | 4900.2.a.z.1.1 | 2 | |||
35.33 | even | 12 | 980.2.i.l.361.1 | 4 | |||
35.34 | odd | 2 | 4900.2.e.q.2549.3 | 4 | |||
105.83 | odd | 4 | 8820.2.a.bg.1.2 | 2 | |||
140.83 | odd | 4 | 3920.2.a.bx.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
980.2.a.j.1.2 | ✓ | 2 | 35.13 | even | 4 | ||
980.2.a.k.1.1 | yes | 2 | 5.3 | odd | 4 | ||
980.2.i.k.361.2 | 4 | 35.23 | odd | 12 | |||
980.2.i.k.961.2 | 4 | 35.18 | odd | 12 | |||
980.2.i.l.361.1 | 4 | 35.33 | even | 12 | |||
980.2.i.l.961.1 | 4 | 35.3 | even | 12 | |||
3920.2.a.bo.1.2 | 2 | 20.3 | even | 4 | |||
3920.2.a.bx.1.1 | 2 | 140.83 | odd | 4 | |||
4900.2.a.x.1.2 | 2 | 5.2 | odd | 4 | |||
4900.2.a.z.1.1 | 2 | 35.27 | even | 4 | |||
4900.2.e.q.2549.2 | 4 | 7.6 | odd | 2 | |||
4900.2.e.q.2549.3 | 4 | 35.34 | odd | 2 | |||
4900.2.e.r.2549.2 | 4 | 5.4 | even | 2 | inner | ||
4900.2.e.r.2549.3 | 4 | 1.1 | even | 1 | trivial | ||
8820.2.a.bg.1.2 | 2 | 105.83 | odd | 4 | |||
8820.2.a.bl.1.2 | 2 | 15.8 | even | 4 |