Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6336,2,Mod(3169,6336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6336.3169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6336 = 2^{6} \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6336.f (of order \(2\), degree \(1\), 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: | \(50.5932147207\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\Q(\zeta_{36})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{6} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3169.11 | ||
Root | \(0.342020 + 0.939693i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6336.3169 |
Dual form | 6336.2.f.o.3169.1 |
$q$-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 \(\left(\mathbb{Z}/6336\mathbb{Z}\right)^\times\).
\(n\) | \(1729\) | \(3521\) | \(4159\) | \(4357\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.93923i | 1.76168i | 0.473416 | + | 0.880839i | \(0.343021\pi\) | ||||
−0.473416 | + | 0.880839i | \(0.656979\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.36808 | −0.517086 | −0.258543 | − | 0.966000i | \(-0.583242\pi\) | ||||
−0.258543 | + | 0.966000i | \(0.583242\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.93923i | − 1.09255i | −0.837607 | − | 0.546273i | \(-0.816046\pi\) | ||||
0.837607 | − | 0.546273i | \(-0.183954\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.06418 | 1.22824 | 0.614122 | − | 0.789211i | \(-0.289510\pi\) | ||||
0.614122 | + | 0.789211i | \(0.289510\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.06418i | 0.244139i | 0.992522 | + | 0.122070i | \(0.0389531\pi\) | ||||
−0.992522 | + | 0.122070i | \(0.961047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.20307 | 0.250857 | 0.125429 | − | 0.992103i | \(-0.459969\pi\) | ||||
0.125429 | + | 0.992103i | \(0.459969\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.5175 | −2.10351 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 6.03525i | − 1.12072i | −0.828250 | − | 0.560359i | \(-0.810663\pi\) | ||||
0.828250 | − | 0.560359i | \(-0.189337\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.60640 | −1.54576 | −0.772878 | − | 0.634555i | \(-0.781183\pi\) | ||||
−0.772878 | + | 0.634555i | \(0.781183\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 5.38919i | − 0.910939i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.325008 | −0.0507577 | −0.0253788 | − | 0.999678i | \(-0.508079\pi\) | ||||
−0.0253788 | + | 0.999678i | \(0.508079\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.5817i | 1.91869i | 0.282229 | + | 0.959347i | \(0.408926\pi\) | ||||
−0.282229 | + | 0.959347i | \(0.591074\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.13127 | −1.18607 | −0.593034 | − | 0.805177i | \(-0.702070\pi\) | ||||
−0.593034 | + | 0.805177i | \(0.702070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.12836 | −0.732622 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 8.13127i | − 1.11692i | −0.829533 | − | 0.558458i | \(-0.811393\pi\) | ||||
0.829533 | − | 0.558458i | \(-0.188607\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.93923 | −0.531166 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 5.38919i | − 0.701612i | −0.936448 | − | 0.350806i | \(-0.885908\pi\) | ||||
0.936448 | − | 0.350806i | \(-0.114092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 11.8177i | − 1.51310i | −0.653936 | − | 0.756550i | \(-0.726883\pi\) | ||||
0.653936 | − | 0.756550i | \(-0.273117\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.5175 | 1.92471 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.51754i | 0.918414i | 0.888329 | + | 0.459207i | \(0.151866\pi\) | ||||
−0.888329 | + | 0.459207i | \(0.848134\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.6036 | −1.61445 | −0.807225 | − | 0.590244i | \(-0.799032\pi\) | ||||
−0.807225 | + | 0.590244i | \(0.799032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.73917 | −0.320596 | −0.160298 | − | 0.987069i | \(-0.551245\pi\) | ||||
−0.160298 | + | 0.987069i | \(0.551245\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.36808i | − 0.155907i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.56012 | 0.625563 | 0.312781 | − | 0.949825i | \(-0.398739\pi\) | ||||
0.312781 | + | 0.949825i | \(0.398739\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.51754i | 0.386100i | 0.981189 | + | 0.193050i | \(0.0618380\pi\) | ||||
−0.981189 | + | 0.193050i | \(0.938162\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.9490i | 2.16377i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.6459 | −1.44646 | −0.723231 | − | 0.690606i | \(-0.757344\pi\) | ||||
−0.723231 | + | 0.690606i | \(0.757344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.38919i | 0.564940i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.19204 | −0.430094 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.9067 | −1.10741 | −0.553705 | − | 0.832713i | \(-0.686787\pi\) | ||||
−0.553705 | + | 0.832713i | \(0.686787\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 3.62911i | − 0.361110i | −0.983565 | − | 0.180555i | \(-0.942211\pi\) | ||||
0.983565 | − | 0.180555i | \(-0.0577894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.3426 | 1.11762 | 0.558808 | − | 0.829297i | \(-0.311259\pi\) | ||||
0.558808 | + | 0.829297i | \(0.311259\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.90673i | 0.861046i | 0.902580 | + | 0.430523i | \(0.141671\pi\) | ||||
−0.902580 | + | 0.430523i | \(0.858329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 16.0097i | − 1.53345i | −0.641973 | − | 0.766727i | \(-0.721884\pi\) | ||||
0.641973 | − | 0.766727i | \(-0.278116\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.51754 | −0.330902 | −0.165451 | − | 0.986218i | \(-0.552908\pi\) | ||||
−0.165451 | + | 0.986218i | \(0.552908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.73917i | 0.441930i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.92820 | −0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 21.7349i | − 1.94403i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.36808 | −0.121398 | −0.0606988 | − | 0.998156i | \(-0.519333\pi\) | ||||
−0.0606988 | + | 0.998156i | \(0.519333\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.6459i | 1.19225i | 0.802893 | + | 0.596124i | \(0.203293\pi\) | ||||
−0.802893 | + | 0.596124i | \(0.796707\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.45588i | − 0.126241i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.2959 | 1.22138 | 0.610691 | − | 0.791869i | \(-0.290892\pi\) | ||||
0.610691 | + | 0.791869i | \(0.290892\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 13.2317i | − 1.12230i | −0.827714 | − | 0.561151i | \(-0.810359\pi\) | ||||
0.827714 | − | 0.561151i | \(-0.189641\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.93923 | 0.329415 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23.7743 | 1.97434 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.72167i | 0.796430i | 0.917292 | + | 0.398215i | \(0.130370\pi\) | ||||
−0.917292 | + | 0.398215i | \(0.869630\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.3170 | −1.73476 | −0.867378 | − | 0.497649i | \(-0.834197\pi\) | ||||
−0.867378 | + | 0.497649i | \(0.834197\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 33.9026i | − 2.72312i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 0.950259i | − 0.0758389i | −0.999281 | − | 0.0379195i | \(-0.987927\pi\) | ||||
0.999281 | − | 0.0379195i | \(-0.0120730\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.64590 | −0.129715 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 22.3851i | − 1.75333i | −0.481098 | − | 0.876667i | \(-0.659762\pi\) | ||||
0.481098 | − | 0.876667i | \(-0.340238\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.78590 | −0.138197 | −0.0690986 | − | 0.997610i | \(-0.522012\pi\) | ||||
−0.0690986 | + | 0.997610i | \(0.522012\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.51754 | −0.193657 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 7.82115i | − 0.594631i | −0.954779 | − | 0.297316i | \(-0.903909\pi\) | ||||
0.954779 | − | 0.297316i | \(-0.0960914\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.3888 | 1.08769 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 20.2567i | − 1.51406i | −0.653381 | − | 0.757029i | \(-0.726650\pi\) | ||||
0.653381 | − | 0.757029i | \(-0.273350\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.35640i | 0.249479i | 0.992190 | + | 0.124740i | \(0.0398095\pi\) | ||||
−0.992190 | + | 0.124740i | \(0.960190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.06418i | 0.370329i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.62565 | 0.551773 | 0.275886 | − | 0.961190i | \(-0.411029\pi\) | ||||
0.275886 | + | 0.961190i | \(0.411029\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.51754 | 0.397161 | 0.198581 | − | 0.980085i | \(-0.436367\pi\) | ||||
0.198581 | + | 0.980085i | \(0.436367\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 17.4855i | − 1.24579i | −0.782305 | − | 0.622896i | \(-0.785956\pi\) | ||||
0.782305 | − | 0.622896i | \(-0.214044\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.15052 | 0.506887 | 0.253444 | − | 0.967350i | \(-0.418437\pi\) | ||||
0.253444 | + | 0.967350i | \(0.418437\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.25671i | 0.579508i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1.28028i | − 0.0894186i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.06418 | −0.0736107 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.71419i | 0.668753i | 0.942440 | + | 0.334376i | \(0.108526\pi\) | ||||
−0.942440 | + | 0.334376i | \(0.891474\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −49.5623 | −3.38012 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.7743 | 0.799288 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 19.9490i | − 1.34191i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3426 | −0.759554 | −0.379777 | − | 0.925078i | \(-0.623999\pi\) | ||||
−0.379777 | + | 0.925078i | \(0.623999\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 28.5134i | − 1.89250i | −0.323433 | − | 0.946251i | \(-0.604837\pi\) | ||||
0.323433 | − | 0.946251i | \(-0.395163\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2292i | 1.40287i | 0.712734 | + | 0.701434i | \(0.247457\pi\) | ||||
−0.712734 | + | 0.701434i | \(0.752543\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.325008 | 0.0212920 | 0.0106460 | − | 0.999943i | \(-0.496611\pi\) | ||||
0.0106460 | + | 0.999943i | \(0.496611\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 32.0310i | − 2.08947i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0705 | −0.780776 | −0.390388 | − | 0.920650i | \(-0.627659\pi\) | ||||
−0.390388 | + | 0.920650i | \(0.627659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.73917 | −0.176445 | −0.0882227 | − | 0.996101i | \(-0.528119\pi\) | ||||
−0.0882227 | + | 0.996101i | \(0.528119\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 20.2018i | − 1.29064i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.19204 | 0.266733 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 17.3892i | − 1.09760i | −0.835955 | − | 0.548798i | \(-0.815086\pi\) | ||||
0.835955 | − | 0.548798i | \(-0.184914\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.20307i | 0.0756364i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.3892 | 1.08471 | 0.542354 | − | 0.840150i | \(-0.317533\pi\) | ||||
0.542354 | + | 0.840150i | \(0.317533\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.19204 | −0.258492 | −0.129246 | − | 0.991613i | \(-0.541256\pi\) | ||||
−0.129246 | + | 0.991613i | \(0.541256\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.0310 | 1.96765 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0318i | 0.611649i | 0.952088 | + | 0.305825i | \(0.0989321\pi\) | ||||
−0.952088 | + | 0.305825i | \(0.901068\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.72448 | 0.286992 | 0.143496 | − | 0.989651i | \(-0.454166\pi\) | ||||
0.143496 | + | 0.989651i | \(0.454166\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 10.5175i | − 0.634232i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 0.252811i | − 0.0151899i | −0.999971 | − | 0.00759497i | \(-0.997582\pi\) | ||||
0.999971 | − | 0.00759497i | \(-0.00241758\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.2276 | 1.32599 | 0.662994 | − | 0.748625i | \(-0.269285\pi\) | ||||
0.662994 | + | 0.748625i | \(0.269285\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 9.06418i | − 0.538809i | −0.963027 | − | 0.269405i | \(-0.913173\pi\) | ||||
0.963027 | − | 0.269405i | \(-0.0868269\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.444637 | 0.0262461 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.64590 | 0.508582 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 19.3860i | − 1.13254i | −0.824218 | − | 0.566272i | \(-0.808385\pi\) | ||||
0.824218 | − | 0.566272i | \(-0.191615\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.2292 | 1.23601 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 4.73917i | − 0.274073i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 17.2128i | − 0.992130i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 46.5526 | 2.66560 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 15.3601i | − 0.876647i | −0.898817 | − | 0.438323i | \(-0.855572\pi\) | ||||
0.898817 | − | 0.438323i | \(-0.144428\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.4877 | 0.651406 | 0.325703 | − | 0.945472i | \(-0.394399\pi\) | ||||
0.325703 | + | 0.945472i | \(0.394399\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.1676 | 0.800798 | 0.400399 | − | 0.916341i | \(-0.368872\pi\) | ||||
0.400399 | + | 0.916341i | \(0.368872\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.75151i | 0.491534i | 0.969329 | + | 0.245767i | \(0.0790398\pi\) | ||||
−0.969329 | + | 0.245767i | \(0.920960\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.03525 | 0.337909 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.38919i | 0.299862i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 41.4310i | 2.29818i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.1242 | 0.613299 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.90673i | 0.269698i | 0.990866 | + | 0.134849i | \(0.0430549\pi\) | ||||
−0.990866 | + | 0.134849i | \(0.956945\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −29.6133 | −1.61795 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.9959 | −1.47056 | −0.735280 | − | 0.677764i | \(-0.762949\pi\) | ||||
−0.735280 | + | 0.677764i | \(0.762949\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 8.60640i | − 0.466063i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.5926 | 0.895914 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.8093i | 1.65393i | 0.562252 | + | 0.826966i | \(0.309935\pi\) | ||||
−0.562252 | + | 0.826966i | \(0.690065\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.31899i | 0.177662i | 0.996047 | + | 0.0888308i | \(0.0283131\pi\) | ||||
−0.996047 | + | 0.0888308i | \(0.971687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.3269 | −1.82704 | −0.913518 | − | 0.406799i | \(-0.866645\pi\) | ||||
−0.913518 | + | 0.406799i | \(0.866645\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 53.5877i | − 2.84414i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.8495 | 1.15317 | 0.576586 | − | 0.817037i | \(-0.304385\pi\) | ||||
0.576586 | + | 0.817037i | \(0.304385\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.8675 | 0.940396 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 10.7902i | − 0.564786i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.8149 | 0.877730 | 0.438865 | − | 0.898553i | \(-0.355381\pi\) | ||||
0.438865 | + | 0.898553i | \(0.355381\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.1242i | 0.577542i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.2943i | 1.36147i | 0.732530 | + | 0.680735i | \(0.238339\pi\) | ||||
−0.732530 | + | 0.680735i | \(0.761661\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.7743 | −1.22444 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.3500i | 0.788476i | 0.919008 | + | 0.394238i | \(0.128991\pi\) | ||||
−0.919008 | + | 0.394238i | \(0.871009\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.67539 | −0.341097 | −0.170548 | − | 0.985349i | \(-0.554554\pi\) | ||||
−0.170548 | + | 0.985349i | \(0.554554\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.38919 | 0.274658 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 1.53309i | − 0.0777308i | −0.999244 | − | 0.0388654i | \(-0.987626\pi\) | ||||
0.999244 | − | 0.0388654i | \(-0.0123744\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.09256 | 0.308114 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.9026i | 1.10204i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.0195i | 1.60701i | 0.595297 | + | 0.803506i | \(0.297034\pi\) | ||||
−0.595297 | + | 0.803506i | \(0.702966\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.6067 | 0.979112 | 0.489556 | − | 0.871972i | \(-0.337159\pi\) | ||||
0.489556 | + | 0.871972i | \(0.337159\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.9026i | 1.68881i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.55674 | −0.373657 | −0.186828 | − | 0.982393i | \(-0.559821\pi\) | ||||
−0.186828 | + | 0.982393i | \(0.559821\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.37284i | 0.362794i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.8564 | −0.680184 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 31.4593i | − 1.53689i | −0.639916 | − | 0.768445i | \(-0.721031\pi\) | ||||
0.639916 | − | 0.768445i | \(-0.278969\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 6.42258i | − 0.313017i | −0.987677 | − | 0.156509i | \(-0.949976\pi\) | ||||
0.987677 | − | 0.156509i | \(-0.0500239\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −53.2627 | −2.58362 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.1676i | 0.782403i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.4918 | −1.80592 | −0.902958 | − | 0.429729i | \(-0.858609\pi\) | ||||
−0.902958 | + | 0.429729i | \(0.858609\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.08915 | 0.100398 | 0.0501992 | − | 0.998739i | \(-0.484014\pi\) | ||||
0.0501992 | + | 0.998739i | \(0.484014\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.28028i | 0.0612441i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.6181 | −1.69996 | −0.849979 | − | 0.526816i | \(-0.823386\pi\) | ||||
−0.849979 | + | 0.526816i | \(0.823386\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 19.0351i | − 0.904384i | −0.891921 | − | 0.452192i | \(-0.850642\pi\) | ||||
0.891921 | − | 0.452192i | \(-0.149358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 53.7543i | − 2.54820i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.6459 | 1.77662 | 0.888310 | − | 0.459245i | \(-0.151880\pi\) | ||||
0.888310 | + | 0.459245i | \(0.151880\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 0.325008i | − 0.0153040i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.2292 | −0.995242 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.2918 | −1.74444 | −0.872218 | − | 0.489117i | \(-0.837319\pi\) | ||||
−0.872218 | + | 0.489117i | \(0.837319\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.31553i | 0.340718i | 0.985382 | + | 0.170359i | \(0.0544928\pi\) | ||||
−0.985382 | + | 0.170359i | \(0.945507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.6272 | −1.00510 | −0.502550 | − | 0.864548i | \(-0.667605\pi\) | ||||
−0.502550 | + | 0.864548i | \(0.667605\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 4.96492i | − 0.229749i | −0.993380 | − | 0.114875i | \(-0.963353\pi\) | ||||
0.993380 | − | 0.114875i | \(-0.0366466\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 10.2846i | − 0.474899i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.5817 | −0.578508 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 11.1925i | − 0.513549i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.5471 | 1.21297 | 0.606485 | − | 0.795095i | \(-0.292579\pi\) | ||||
0.606485 | + | 0.795095i | \(0.292579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 42.9641i | − 1.95090i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5069 | 0.476114 | 0.238057 | − | 0.971251i | \(-0.423489\pi\) | ||||
0.238057 | + | 0.971251i | \(0.423489\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 26.7202i | − 1.20586i | −0.797792 | − | 0.602932i | \(-0.793999\pi\) | ||||
0.797792 | − | 0.602932i | \(-0.206001\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 30.5636i | − 1.37651i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.6108 | 0.834809 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.8135i | 1.51370i | 0.653590 | + | 0.756849i | \(0.273262\pi\) | ||||
−0.653590 | + | 0.756849i | \(0.726738\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.6133 | −1.32039 | −0.660197 | − | 0.751093i | \(-0.729527\pi\) | ||||
−0.660197 | + | 0.751093i | \(0.729527\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.2959 | 0.636160 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.65895i | 0.117856i | 0.998262 | + | 0.0589280i | \(0.0187682\pi\) | ||||
−0.998262 | + | 0.0589280i | \(0.981232\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.74741 | 0.165775 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 44.6810i | 1.96888i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 8.13127i | − 0.357613i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.6851 | −1.38815 | −0.694075 | − | 0.719903i | \(-0.744186\pi\) | ||||
−0.694075 | + | 0.719903i | \(0.744186\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 18.4534i | − 0.806909i | −0.915000 | − | 0.403455i | \(-0.867809\pi\) | ||||
0.915000 | − | 0.403455i | \(-0.132191\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −43.5844 | −1.89856 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.5526 | −0.937071 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.28028i | 0.0554551i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.0857 | −1.51689 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5.12836i | − 0.220894i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 14.1092i | − 0.606603i | −0.952895 | − | 0.303301i | \(-0.901911\pi\) | ||||
0.952895 | − | 0.303301i | \(-0.0980889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 63.0660 | 2.70145 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.0411i | 1.54100i | 0.637437 | + | 0.770502i | \(0.279995\pi\) | ||||
−0.637437 | + | 0.770502i | \(0.720005\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.42258 | 0.273611 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.60670 | −0.323470 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 43.5270i | − 1.84430i | −0.386832 | − | 0.922150i | \(-0.626431\pi\) | ||||
0.386832 | − | 0.922150i | \(-0.373569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 49.5623 | 2.09626 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.0351i | 0.802233i | 0.916027 | + | 0.401117i | \(0.131378\pi\) | ||||
−0.916027 | + | 0.401117i | \(0.868622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 13.8564i | − 0.582943i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.00599 | 0.377551 | 0.188775 | − | 0.982020i | \(-0.439548\pi\) | ||||
0.188775 | + | 0.982020i | \(0.439548\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.93170i | 0.164537i | 0.996610 | + | 0.0822683i | \(0.0262165\pi\) | ||||
−0.996610 | + | 0.0822683i | \(0.973784\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.6533 | −0.527681 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.99588 | −0.124720 | −0.0623601 | − | 0.998054i | \(-0.519863\pi\) | ||||
−0.0623601 | + | 0.998054i | \(0.519863\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 4.81228i | − 0.199647i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.13127 | 0.336763 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 14.8675i | − 0.613648i | −0.951766 | − | 0.306824i | \(-0.900734\pi\) | ||||
0.951766 | − | 0.306824i | \(-0.0992664\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 9.15874i | − 0.377379i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 46.8776 | 1.92503 | 0.962517 | − | 0.271222i | \(-0.0874278\pi\) | ||||
0.962517 | + | 0.271222i | \(0.0874278\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 27.2918i | − 1.11885i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.2472 | 0.418689 | 0.209345 | − | 0.977842i | \(-0.432867\pi\) | ||||
0.209345 | + | 0.977842i | \(0.432867\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.0310 | −1.71448 | −0.857239 | − | 0.514918i | \(-0.827822\pi\) | ||||
−0.857239 | + | 0.514918i | \(0.827822\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.93923i | − 0.160153i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.4650 | −0.668292 | −0.334146 | − | 0.942521i | \(-0.608448\pi\) | ||||
−0.334146 | + | 0.942521i | \(0.608448\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.0310i | 1.29583i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 11.3121i | − 0.456890i | −0.973557 | − | 0.228445i | \(-0.926636\pi\) | ||||
0.973557 | − | 0.228445i | \(-0.0733641\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.2526 | −1.33870 | −0.669349 | − | 0.742948i | \(-0.733427\pi\) | ||||
−0.669349 | + | 0.742948i | \(0.733427\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.9377i | 1.48465i | 0.670039 | + | 0.742326i | \(0.266277\pi\) | ||||
−0.670039 | + | 0.742326i | \(0.733723\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.6687 | 0.747945 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 33.0310 | 1.32124 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.4766 | −1.73078 | −0.865389 | − | 0.501101i | \(-0.832929\pi\) | ||||
−0.865389 | + | 0.501101i | \(0.832929\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 5.38919i | − 0.213863i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.2018i | 0.800424i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.74329 | 0.147851 | 0.0739255 | − | 0.997264i | \(-0.476447\pi\) | ||||
0.0739255 | + | 0.997264i | \(0.476447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.6459i | 1.32686i | 0.748236 | + | 0.663432i | \(0.230901\pi\) | ||||
−0.748236 | + | 0.663432i | \(0.769099\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.70869 | −0.0671756 | −0.0335878 | − | 0.999436i | \(-0.510693\pi\) | ||||
−0.0335878 | + | 0.999436i | \(0.510693\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.38919 | 0.211544 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.3385i | 1.38290i | 0.722424 | + | 0.691450i | \(0.243028\pi\) | ||||
−0.722424 | + | 0.691450i | \(0.756972\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −53.7543 | −2.10036 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 22.1284i | − 0.861998i | −0.902352 | − | 0.430999i | \(-0.858161\pi\) | ||||
0.902352 | − | 0.430999i | \(-0.141839\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 11.2349i | − 0.436985i | −0.975839 | − | 0.218493i | \(-0.929886\pi\) | ||||
0.975839 | − | 0.218493i | \(-0.0701140\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.73505 | 0.222396 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 7.26083i | − 0.281140i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.8177 | 0.456217 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.29179 | −0.203984 | −0.101992 | − | 0.994785i | \(-0.532522\pi\) | ||||
−0.101992 | + | 0.994785i | \(0.532522\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.2537i | 0.509380i | 0.967023 | + | 0.254690i | \(0.0819734\pi\) | ||||
−0.967023 | + | 0.254690i | \(0.918027\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.9213 | 0.572626 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 30.1593i | − 1.15401i | −0.816739 | − | 0.577007i | \(-0.804220\pi\) | ||||
0.816739 | − | 0.577007i | \(-0.195780\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 56.3149i | 2.15168i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32.0310 | −1.22028 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 10.6108i | − 0.403654i | −0.979421 | − | 0.201827i | \(-0.935312\pi\) | ||||
0.979421 | − | 0.201827i | \(-0.0646879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 52.1229 | 1.97713 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.64590 | −0.0623428 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.4829i | 1.30240i | 0.758905 | + | 0.651201i | \(0.225734\pi\) | ||||
−0.758905 | + | 0.651201i | \(0.774266\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.96492i | 0.186725i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 46.0303i | − 1.72870i | −0.502887 | − | 0.864352i | \(-0.667729\pi\) | ||||
0.502887 | − | 0.864352i | \(-0.332271\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.3541 | −0.387764 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.5175i | 0.580323i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.7887 | 0.961757 | 0.480878 | − | 0.876787i | \(-0.340318\pi\) | ||||
0.480878 | + | 0.876787i | \(0.340318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.5175 | −0.577903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 63.4760i | 2.35744i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.15052 | −0.265198 | −0.132599 | − | 0.991170i | \(-0.542332\pi\) | ||||
−0.132599 | + | 0.991170i | \(0.542332\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 63.7161i | 2.35662i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.8000i | 0.989879i | 0.868927 | + | 0.494940i | \(0.164810\pi\) | ||||
−0.868927 | + | 0.494940i | \(0.835190\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.51754 | −0.276912 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.0993i | 1.47508i | 0.675306 | + | 0.737538i | \(0.264012\pi\) | ||||
−0.675306 | + | 0.737538i | \(0.735988\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.8205 | −1.31413 | −0.657063 | − | 0.753835i | \(-0.728202\pi\) | ||||
−0.657063 | + | 0.753835i | \(0.728202\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.2959 | −1.40305 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 12.1851i | − 0.445235i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.1782 | −0.444389 | −0.222195 | − | 0.975002i | \(-0.571322\pi\) | ||||
−0.222195 | + | 0.975002i | \(0.571322\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 83.9728i | − 3.05608i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 45.6605i | − 1.65956i | −0.558092 | − | 0.829779i | \(-0.688466\pi\) | ||||
0.558092 | − | 0.829779i | \(-0.311534\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.5858 | −0.709986 | −0.354993 | − | 0.934869i | \(-0.615517\pi\) | ||||
−0.354993 | + | 0.934869i | \(0.615517\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.9026i | 0.792928i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.2292 | −0.766544 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.5526 | −1.17388 | −0.586939 | − | 0.809631i | \(-0.699667\pi\) | ||||
−0.586939 | + | 0.809631i | \(0.699667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 5.21951i | − 0.187733i | −0.995585 | − | 0.0938664i | \(-0.970077\pi\) | ||||
0.995585 | − | 0.0938664i | \(-0.0299226\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 90.5182 | 3.25151 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 0.345866i | − 0.0123919i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 13.6036i | − 0.486775i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.74329 | 0.133604 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.93170i | 0.140150i | 0.997542 | + | 0.0700750i | \(0.0223239\pi\) | ||||
−0.997542 | + | 0.0700750i | \(0.977676\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.81228 | 0.171105 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −46.5526 | −1.65313 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 19.6962i | − 0.697674i | −0.937183 | − | 0.348837i | \(-0.886577\pi\) | ||||
0.937183 | − | 0.348837i | \(-0.113423\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.1782 | −1.45678 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.73917i | − 0.0966632i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 6.48357i | − 0.228516i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.3952 | 0.506107 | 0.253054 | − | 0.967452i | \(-0.418565\pi\) | ||||
0.253054 | + | 0.967452i | \(0.418565\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 15.3601i | − 0.539366i | −0.962949 | − | 0.269683i | \(-0.913081\pi\) | ||||
0.962949 | − | 0.269683i | \(-0.0869189\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 88.1799 | 3.08881 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.3892 | −0.468428 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.41501i | 0.188985i | 0.995526 | + | 0.0944927i | \(0.0301229\pi\) | ||||
−0.995526 | + | 0.0944927i | \(0.969877\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.4723 | −1.20163 | −0.600815 | − | 0.799388i | \(-0.705157\pi\) | ||||
−0.600815 | + | 0.799388i | \(0.705157\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 37.6459i | − 1.30908i | −0.756029 | − | 0.654538i | \(-0.772863\pi\) | ||||
0.756029 | − | 0.654538i | \(-0.227137\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.8646i | 1.55821i | 0.626892 | + | 0.779107i | \(0.284327\pi\) | ||||
−0.626892 | + | 0.779107i | \(0.715673\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.9709 | −0.899838 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 7.03508i | − 0.243459i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.8272 | 1.54761 | 0.773804 | − | 0.633425i | \(-0.218352\pi\) | ||||
0.773804 | + | 0.633425i | \(0.218352\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.42427 | −0.256009 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 9.91718i | − 0.341161i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.36808 | 0.0470078 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.89080i | 0.235936i | 0.993017 | + | 0.117968i | \(0.0376381\pi\) | ||||
−0.993017 | + | 0.117968i | \(0.962362\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.1533 | −1.13250 | −0.566248 | − | 0.824235i | \(-0.691606\pi\) | ||||
−0.566248 | + | 0.824235i | \(0.691606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 34.6418i | − 1.18196i | −0.806685 | − | 0.590981i | \(-0.798741\pi\) | ||||
0.806685 | − | 0.590981i | \(-0.201259\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.5318 | 0.698911 | 0.349455 | − | 0.936953i | \(-0.386367\pi\) | ||||
0.349455 | + | 0.936953i | \(0.386367\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.8093 | 1.04755 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.56012i | 0.188614i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.6133 | 1.00341 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.7351i | 1.00523i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.7182i | 1.17235i | 0.810184 | + | 0.586176i | \(0.199367\pi\) | ||||
−0.810184 | + | 0.586176i | \(0.800633\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.83656 | 0.230330 | 0.115165 | − | 0.993346i | \(-0.463260\pi\) | ||||
0.115165 | + | 0.993346i | \(0.463260\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.55262i | 0.220513i | 0.993903 | + | 0.110257i | \(0.0351673\pi\) | ||||
−0.993903 | + | 0.110257i | \(0.964833\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.5800 | 1.16108 | 0.580542 | − | 0.814230i | \(-0.302841\pi\) | ||||
0.580542 | + | 0.814230i | \(0.302841\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.87164 | 0.0627729 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 8.65312i | − 0.289566i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 79.7959 | 2.66728 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 51.9418i | 1.73236i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 41.1782i | − 1.37185i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.2216 | −0.439502 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.8675i | 1.02494i | 0.858705 | + | 0.512470i | \(0.171269\pi\) | ||||
−0.858705 | + | 0.512470i | \(0.828731\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.1395 | −1.29675 | −0.648375 | − | 0.761321i | \(-0.724551\pi\) | ||||
−0.648375 | + | 0.761321i | \(0.724551\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.51754 | −0.116414 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 18.6687i | − 0.616494i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.8932 | −1.11803 | −0.559016 | − | 0.829157i | \(-0.688821\pi\) | ||||
−0.559016 | + | 0.829157i | \(0.688821\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 53.5877i | 1.76386i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45.3310 | 1.48726 | 0.743631 | − | 0.668590i | \(-0.233102\pi\) | ||||
0.743631 | + | 0.668590i | \(0.233102\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 5.45748i | − 0.178862i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.9490 | −0.652401 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.8135 | 1.30065 | 0.650324 | − | 0.759657i | \(-0.274633\pi\) | ||||
0.650324 | + | 0.759657i | \(0.274633\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.5560i | 0.963499i | 0.876309 | + | 0.481749i | \(0.159998\pi\) | ||||
−0.876309 | + | 0.481749i | \(0.840002\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.391007 | −0.0127329 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 36.7701i | − 1.19487i | −0.801918 | − | 0.597434i | \(-0.796187\pi\) | ||||
0.801918 | − | 0.597434i | \(-0.203813\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.7902i | 0.350265i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.9317 | −0.645651 | −0.322826 | − | 0.946458i | \(-0.604633\pi\) | ||||
−0.322826 | + | 0.946458i | \(0.604633\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.0392i | 0.972046i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.5580 | −0.631559 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.0702 | 1.38936 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.7349i | 0.699670i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.91652 | −0.286736 | −0.143368 | − | 0.989669i | \(-0.545793\pi\) | ||||
−0.143368 | + | 0.989669i | \(0.545793\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 19.0351i | − 0.610865i | −0.952214 | − | 0.305432i | \(-0.901199\pi\) | ||||
0.952214 | − | 0.305432i | \(-0.0988010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.1021i | 0.580326i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.4201 | −1.19718 | −0.598588 | − | 0.801057i | \(-0.704271\pi\) | ||||
−0.598588 | + | 0.801057i | \(0.704271\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 13.6459i | − 0.436125i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −61.1646 | −1.95085 | −0.975424 | − | 0.220338i | \(-0.929284\pi\) | ||||
−0.975424 | + | 0.220338i | \(0.929284\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 68.8795 | 2.19468 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.1367i | 0.481319i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.5510 | −0.621059 | −0.310530 | − | 0.950564i | \(-0.600506\pi\) | ||||
−0.310530 | + | 0.950564i | \(0.600506\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.1676i | 0.892972i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.82462i | 0.121127i | 0.998164 | + | 0.0605634i | \(0.0192897\pi\) | ||||
−0.998164 | + | 0.0605634i | \(0.980710\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6336.2.f.o.3169.11 | yes | 12 | |
3.2 | odd | 2 | 6336.2.f.m.3169.1 | ✓ | 12 | ||
4.3 | odd | 2 | inner | 6336.2.f.o.3169.12 | yes | 12 | |
8.3 | odd | 2 | inner | 6336.2.f.o.3169.2 | yes | 12 | |
8.5 | even | 2 | inner | 6336.2.f.o.3169.1 | yes | 12 | |
12.11 | even | 2 | 6336.2.f.m.3169.2 | yes | 12 | ||
24.5 | odd | 2 | 6336.2.f.m.3169.11 | yes | 12 | ||
24.11 | even | 2 | 6336.2.f.m.3169.12 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6336.2.f.m.3169.1 | ✓ | 12 | 3.2 | odd | 2 | ||
6336.2.f.m.3169.2 | yes | 12 | 12.11 | even | 2 | ||
6336.2.f.m.3169.11 | yes | 12 | 24.5 | odd | 2 | ||
6336.2.f.m.3169.12 | yes | 12 | 24.11 | even | 2 | ||
6336.2.f.o.3169.1 | yes | 12 | 8.5 | even | 2 | inner | |
6336.2.f.o.3169.2 | yes | 12 | 8.3 | odd | 2 | inner | |
6336.2.f.o.3169.11 | yes | 12 | 1.1 | even | 1 | trivial | |
6336.2.f.o.3169.12 | yes | 12 | 4.3 | odd | 2 | inner |