Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4368,2,Mod(337,4368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4368.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4368.h (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: | \(34.8786556029\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1092) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.4 | ||
Root | \(2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4368.337 |
Dual form | 4368.2.h.l.337.1 |
$q$-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 \(\left(\mathbb{Z}/4368\mathbb{Z}\right)^\times\).
\(n\) | \(1093\) | \(1249\) | \(1457\) | \(2017\) | \(3823\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.56155i | 1.59277i | 0.604787 | + | 0.796387i | \(0.293258\pi\) | ||||
−0.604787 | + | 0.796387i | \(0.706742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.12311i | 1.54467i | 0.635213 | + | 0.772337i | \(0.280912\pi\) | ||||
−0.635213 | + | 0.772337i | \(0.719088\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.561553 | − | 3.56155i | 0.155747 | − | 0.987797i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.56155i | 0.919589i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.56155i | 0.358245i | 0.983827 | + | 0.179122i | \(0.0573258\pi\) | ||||
−0.983827 | + | 0.179122i | \(0.942674\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000i | 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.68466 | −1.81088 | −0.905438 | − | 0.424478i | \(-0.860458\pi\) | ||||
−0.905438 | + | 0.424478i | \(0.860458\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.68466 | −1.53693 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.56155 | 1.40415 | 0.702073 | − | 0.712105i | \(-0.252258\pi\) | ||||
0.702073 | + | 0.712105i | \(0.252258\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.56155i | 0.280463i | 0.990119 | + | 0.140232i | \(0.0447847\pi\) | ||||
−0.990119 | + | 0.140232i | \(0.955215\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.12311i | 0.891818i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.56155 | −0.602012 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.561553 | − | 3.56155i | 0.0899204 | − | 0.570305i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0000i | 1.56174i | 0.624695 | + | 0.780869i | \(0.285223\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.56155 | −0.848129 | −0.424064 | − | 0.905632i | \(-0.639397\pi\) | ||||
−0.424064 | + | 0.905632i | \(0.639397\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.56155i | 0.530925i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.438447i | − | 0.0639541i | −0.999489 | − | 0.0319770i | \(-0.989820\pi\) | ||
0.999489 | − | 0.0319770i | \(-0.0101803\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.56155 | 0.489217 | 0.244608 | − | 0.969622i | \(-0.421341\pi\) | ||||
0.244608 | + | 0.969622i | \(0.421341\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.2462 | −2.46032 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.56155i | 0.206833i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 6.87689i | − | 0.895295i | −0.894210 | − | 0.447648i | \(-0.852262\pi\) | ||
0.894210 | − | 0.447648i | \(-0.147738\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.87689 | −0.368349 | −0.184174 | − | 0.982894i | \(-0.558961\pi\) | ||||
−0.184174 | + | 0.982894i | \(0.558961\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.6847 | + | 2.00000i | 1.57334 | + | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.87689i | − | 0.595807i | −0.954596 | − | 0.297904i | \(-0.903713\pi\) | ||
0.954596 | − | 0.297904i | \(-0.0962874\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.68466 | −1.04551 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.3693i | 1.82400i | 0.410188 | + | 0.912001i | \(0.365463\pi\) | ||||
−0.410188 | + | 0.912001i | \(0.634537\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.43845i | − | 0.753563i | −0.926302 | − | 0.376782i | \(-0.877031\pi\) | ||
0.926302 | − | 0.376782i | \(-0.122969\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.68466 | −0.887348 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.12311 | −0.583832 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.68466 | −0.977100 | −0.488550 | − | 0.872536i | \(-0.662474\pi\) | ||||
−0.488550 | + | 0.872536i | \(0.662474\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.68466i | 0.733737i | 0.930273 | + | 0.366868i | \(0.119570\pi\) | ||||
−0.930273 | + | 0.366868i | \(0.880430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 7.12311i | − | 0.772609i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.56155 | 0.810684 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.68466i | − | 0.708572i | −0.935137 | − | 0.354286i | \(-0.884724\pi\) | ||
0.935137 | − | 0.354286i | \(-0.115276\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.56155 | + | 0.561553i | 0.373352 | + | 0.0588667i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.56155i | 0.161925i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.56155 | −0.570603 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.31534i | − | 0.336622i | −0.985734 | − | 0.168311i | \(-0.946169\pi\) | ||
0.985734 | − | 0.168311i | \(-0.0538313\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.12311i | 0.514891i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.3693 | 1.52930 | 0.764652 | − | 0.644443i | \(-0.222911\pi\) | ||||
0.764652 | + | 0.644443i | \(0.222911\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.2462 | 1.79785 | 0.898926 | − | 0.438100i | \(-0.144348\pi\) | ||||
0.898926 | + | 0.438100i | \(0.144348\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.56155 | −0.347572 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.4924 | −1.59438 | −0.797191 | − | 0.603727i | \(-0.793682\pi\) | ||||
−0.797191 | + | 0.603727i | \(0.793682\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.12311i | − | 0.682270i | −0.940014 | − | 0.341135i | \(-0.889189\pi\) | ||
0.940014 | − | 0.341135i | \(-0.110811\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.80776 | −0.546348 | −0.273174 | − | 0.961965i | \(-0.588074\pi\) | ||||
−0.273174 | + | 0.961965i | \(0.588074\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 30.9309i | − | 2.88432i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.561553 | − | 3.56155i | 0.0519156 | − | 0.329266i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.00000i | − | 0.183340i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.2462 | −1.38602 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.0000i | 0.901670i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 9.56155i | − | 0.855211i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.4924 | 1.81841 | 0.909204 | − | 0.416350i | \(-0.136691\pi\) | ||||
0.909204 | + | 0.416350i | \(0.136691\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.56155 | −0.489667 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.1231 | −1.32131 | −0.660656 | − | 0.750689i | \(-0.729722\pi\) | ||||
−0.660656 | + | 0.750689i | \(0.729722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.56155 | −0.135404 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.56155i | 0.306530i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 19.3693i | − | 1.65483i | −0.561589 | − | 0.827416i | \(-0.689810\pi\) | ||
0.561589 | − | 0.827416i | \(-0.310190\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.2462 | −1.88690 | −0.943450 | − | 0.331516i | \(-0.892440\pi\) | ||||
−0.943450 | + | 0.331516i | \(0.892440\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 0.438447i | − | 0.0369239i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.2462 | + | 2.87689i | 1.52582 | + | 0.240578i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 26.9309i | 2.23649i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.3693i | 1.58680i | 0.608703 | + | 0.793398i | \(0.291690\pi\) | ||||
−0.608703 | + | 0.793398i | \(0.708310\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000i | 0.976546i | 0.872691 | + | 0.488273i | \(0.162373\pi\) | ||||
−0.872691 | + | 0.488273i | \(0.837627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.56155 | −0.446715 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.24621 | 0.658119 | 0.329060 | − | 0.944309i | \(-0.393268\pi\) | ||||
0.329060 | + | 0.944309i | \(0.393268\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.56155 | 0.282450 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 8.68466i | − | 0.684447i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.1231i | − | 1.18453i | −0.805742 | − | 0.592267i | \(-0.798233\pi\) | ||
0.805742 | − | 0.592267i | \(-0.201767\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18.2462 | −1.42047 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.56155i | − | 0.275601i | −0.990460 | − | 0.137801i | \(-0.955997\pi\) | ||
0.990460 | − | 0.137801i | \(-0.0440033\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3693 | − | 4.00000i | −0.951486 | − | 0.307692i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.56155i | 0.119415i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.1231 | −0.997731 | −0.498866 | − | 0.866679i | \(-0.666250\pi\) | ||||
−0.498866 | + | 0.866679i | \(0.666250\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 7.68466i | − | 0.580906i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.87689i | − | 0.516899i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.43845 | −0.481232 | −0.240616 | − | 0.970620i | \(-0.577349\pi\) | ||||
−0.240616 | + | 0.970620i | \(0.577349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.36932 | −0.547757 | −0.273879 | − | 0.961764i | \(-0.588307\pi\) | ||||
−0.273879 | + | 0.961764i | \(0.588307\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.87689 | −0.212666 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 10.2462i | − | 0.749277i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0000 | 1.15772 | 0.578860 | − | 0.815427i | \(-0.303498\pi\) | ||||
0.578860 | + | 0.815427i | \(0.303498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.36932i | 0.674418i | 0.941430 | + | 0.337209i | \(0.109483\pi\) | ||||
−0.941430 | + | 0.337209i | \(0.890517\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.6847 | + | 2.00000i | 0.908367 | + | 0.143223i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.36932i | − | 0.240054i | −0.992771 | − | 0.120027i | \(-0.961702\pi\) | ||
0.992771 | − | 0.120027i | \(-0.0382981\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.6155 | −1.10696 | −0.553478 | − | 0.832864i | \(-0.686700\pi\) | ||||
−0.553478 | + | 0.832864i | \(0.686700\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.87689i | − | 0.343990i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.56155i | 0.530717i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −35.6155 | −2.48750 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.68466 | −0.603625 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.56155 | 0.107502 | 0.0537509 | − | 0.998554i | \(-0.482882\pi\) | ||||
0.0537509 | + | 0.998554i | \(0.482882\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.3693i | 1.05309i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 19.8078i | − | 1.35088i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.56155 | −0.106005 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 6.43845i | − | 0.435070i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.12311 | + | 7.12311i | −0.0755483 | + | 0.479152i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.43845i | 0.431150i | 0.976487 | + | 0.215575i | \(0.0691626\pi\) | ||||
−0.976487 | + | 0.215575i | \(0.930837\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.68466 | −0.512311 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.12311i | − | 0.0745431i | −0.999305 | − | 0.0372716i | \(-0.988133\pi\) | ||
0.999305 | − | 0.0372716i | \(-0.0118667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.36932i | 0.354814i | 0.984138 | + | 0.177407i | \(0.0567710\pi\) | ||||
−0.984138 | + | 0.177407i | \(0.943229\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.12311 | −0.337076 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.31534 | −0.348220 | −0.174110 | − | 0.984726i | \(-0.555705\pi\) | ||||
−0.174110 | + | 0.984726i | \(0.555705\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.56155 | 0.101864 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.68466 | −0.564129 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.24621i | − | 0.533403i | −0.963779 | − | 0.266702i | \(-0.914066\pi\) | ||
0.963779 | − | 0.266702i | \(-0.0859338\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0540i | 0.905296i | 0.891689 | + | 0.452648i | \(0.149521\pi\) | ||||
−0.891689 | + | 0.452648i | \(0.850479\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 3.56155i | − | 0.227539i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.56155 | + | 0.876894i | 0.353873 | + | 0.0557955i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.68466i | 0.423623i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00000 | 0.252478 | 0.126239 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126239 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 44.4924i | − | 2.79721i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 7.12311i | − | 0.446066i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.3693 | 1.20822 | 0.604112 | − | 0.796899i | \(-0.293528\pi\) | ||||
0.604112 | + | 0.796899i | \(0.293528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.56155 | 0.468048 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.0540 | 0.619955 | 0.309977 | − | 0.950744i | \(-0.399679\pi\) | ||||
0.309977 | + | 0.950744i | \(0.399679\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.6847i | 0.779212i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.68466i | − | 0.409094i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.7386i | 1.62426i | 0.583479 | + | 0.812128i | \(0.301691\pi\) | ||||
−0.583479 | + | 0.812128i | \(0.698309\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.56155 | + | 0.561553i | 0.215555 | + | 0.0339867i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 39.3693i | − | 2.37406i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.43845 | 0.507017 | 0.253509 | − | 0.967333i | \(-0.418415\pi\) | ||||
0.253509 | + | 0.967333i | \(0.418415\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.56155i | 0.0934877i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.0000i | − | 1.07379i | −0.843649 | − | 0.536895i | \(-0.819597\pi\) | ||
0.843649 | − | 0.536895i | \(-0.180403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.2462 | 1.56018 | 0.780088 | − | 0.625670i | \(-0.215174\pi\) | ||||
0.780088 | + | 0.625670i | \(0.215174\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.56155 | −0.329438 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0000 | −0.590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 3.31534i | − | 0.194349i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.9309i | 1.22279i | 0.791324 | + | 0.611397i | \(0.209392\pi\) | ||||
−0.791324 | + | 0.611397i | \(0.790608\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.4924 | 1.42600 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.12311i | 0.297273i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.87689 | + | 30.9309i | −0.282038 | + | 1.78878i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 5.56155i | − | 0.320563i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.3693 | 0.882944 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 10.2462i | − | 0.586696i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.8078i | 0.673905i | 0.941522 | + | 0.336952i | \(0.109396\pi\) | ||||
−0.941522 | + | 0.336952i | \(0.890604\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.2462 | 1.03799 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.6155 | −0.885475 | −0.442738 | − | 0.896651i | \(-0.645993\pi\) | ||||
−0.442738 | + | 0.896651i | \(0.645993\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.1231 | −1.42004 | −0.710021 | − | 0.704181i | \(-0.751315\pi\) | ||||
−0.710021 | + | 0.704181i | \(0.751315\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.56155 | −0.200671 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000i | 0.336994i | 0.985702 | + | 0.168497i | \(0.0538913\pi\) | ||||
−0.985702 | + | 0.168497i | \(0.946109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 38.7386i | 2.16895i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.4924 | −0.920517 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.12311i | − | 0.173774i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.31534 | + | 27.3693i | −0.239372 | + | 1.51818i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 7.12311i | − | 0.393909i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.438447 | 0.0241724 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.75379i | 0.536117i | 0.963403 | + | 0.268058i | \(0.0863820\pi\) | ||||
−0.963403 | + | 0.268058i | \(0.913618\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.3693 | 0.948987 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.6847 | 0.582030 | 0.291015 | − | 0.956718i | \(-0.406007\pi\) | ||||
0.291015 | + | 0.956718i | \(0.406007\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.80776 | −0.315434 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.00000 | −0.433224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 30.9309i | − | 1.66526i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.4924 | 1.31482 | 0.657411 | − | 0.753532i | \(-0.271652\pi\) | ||||
0.657411 | + | 0.753532i | \(0.271652\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 35.4233i | − | 1.89617i | −0.318024 | − | 0.948083i | \(-0.603019\pi\) | ||
0.318024 | − | 0.948083i | \(-0.396981\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.561553 | − | 3.56155i | 0.0299735 | − | 0.190102i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.7538i | 0.625591i | 0.949820 | + | 0.312796i | \(0.101265\pi\) | ||||
−0.949820 | + | 0.312796i | \(0.898735\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −54.7386 | −2.90523 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 2.00000i | − | 0.105851i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.75379i | 0.198117i | 0.995082 | + | 0.0990587i | \(0.0315832\pi\) | ||||
−0.995082 | + | 0.0990587i | \(0.968417\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.5616 | 0.871661 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.2462 | −0.800219 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.9309 | 1.20026 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.3693 | −0.697873 | −0.348936 | − | 0.937146i | \(-0.613457\pi\) | ||||
−0.348936 | + | 0.937146i | \(0.613457\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.0000i | 0.520579i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.56155i | 0.184907i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 9.56155i | − | 0.493756i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.24621 | − | 26.9309i | 0.218691 | − | 1.38701i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.9848i | 1.48885i | 0.667705 | + | 0.744426i | \(0.267277\pi\) | ||||
−0.667705 | + | 0.744426i | \(0.732723\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.4924 | 1.04986 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.1231i | 1.48812i | 0.668112 | + | 0.744061i | \(0.267103\pi\) | ||||
−0.668112 | + | 0.744061i | \(0.732897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 18.2462i | − | 0.929913i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.56155 | −0.282710 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.2462 | −0.620908 | −0.310454 | − | 0.950588i | \(-0.600481\pi\) | ||||
−0.310454 | + | 0.950588i | \(0.600481\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.3693 | 0.878404 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.1231 | −0.762860 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 30.9309i | − | 1.55630i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.0540i | 1.30761i | 0.756662 | + | 0.653806i | \(0.226829\pi\) | ||||
−0.756662 | + | 0.653806i | \(0.773171\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.56155 | −0.0781754 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.4924i | 1.52272i | 0.648330 | + | 0.761359i | \(0.275468\pi\) | ||||
−0.648330 | + | 0.761359i | \(0.724532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.56155 | + | 0.876894i | 0.277041 | + | 0.0436812i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.56155i | 0.176975i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.56155i | − | 0.0772138i | −0.999254 | − | 0.0386069i | \(-0.987708\pi\) | ||
0.999254 | − | 0.0386069i | \(-0.0122920\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 19.3693i | − | 0.955418i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.87689 | 0.338390 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23.8078 | −1.16868 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.2462 | −1.08940 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.00000 | 0.195413 | 0.0977064 | − | 0.995215i | \(-0.468849\pi\) | ||||
0.0977064 | + | 0.995215i | \(0.468849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.3693i | 1.43137i | 0.698422 | + | 0.715686i | \(0.253886\pi\) | ||||
−0.698422 | + | 0.715686i | \(0.746114\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 0.438447i | − | 0.0213180i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.3693 | 0.745521 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2.87689i | − | 0.139223i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.2462 | + | 2.87689i | 0.880935 | + | 0.138898i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17.1231i | − | 0.824791i | −0.911005 | − | 0.412395i | \(-0.864692\pi\) | ||
0.911005 | − | 0.412395i | \(-0.135308\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.7386 | −1.38109 | −0.690545 | − | 0.723289i | \(-0.742629\pi\) | ||||
−0.690545 | + | 0.723289i | \(0.742629\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26.9309i | 1.29124i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 13.5616i | − | 0.648737i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2462 | 0.489025 | 0.244512 | − | 0.969646i | \(-0.421372\pi\) | ||||
0.244512 | + | 0.969646i | \(0.421372\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.6847 | 1.74294 | 0.871470 | − | 0.490448i | \(-0.163167\pi\) | ||||
0.871470 | + | 0.490448i | \(0.163167\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.8078 | 1.12860 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.3693i | 0.916137i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0000i | 0.471929i | 0.971762 | + | 0.235965i | \(0.0758249\pi\) | ||||
−0.971762 | + | 0.235965i | \(0.924175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −51.2311 | −2.41238 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0000i | 0.563809i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | + | 12.6847i | −0.0937614 | + | 0.594666i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.3693i | 1.37384i | 0.726734 | + | 0.686919i | \(0.241037\pi\) | ||||
−0.726734 | + | 0.686919i | \(0.758963\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.00000 | −0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.2462i | 0.942960i | 0.881877 | + | 0.471480i | \(0.156280\pi\) | ||||
−0.881877 | + | 0.471480i | \(0.843720\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.6155i | − | 1.09751i | −0.835984 | − | 0.548753i | \(-0.815103\pi\) | ||
0.835984 | − | 0.548753i | \(-0.184897\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.56155 | −0.257911 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.87689 | −0.410774 | −0.205387 | − | 0.978681i | \(-0.565845\pi\) | ||||
−0.205387 | + | 0.978681i | \(0.565845\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.87689 | 0.225194 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.24621 | 0.379965 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 28.4924i | − | 1.31008i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 12.0000i | − | 0.550598i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.56155 | 0.163072 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 18.3002i | − | 0.836157i | −0.908411 | − | 0.418078i | \(-0.862704\pi\) | ||
0.908411 | − | 0.418078i | \(-0.137296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 8.68466i | − | 0.395166i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.8078 | 0.536163 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.2462i | − | 0.464300i | −0.972680 | − | 0.232150i | \(-0.925424\pi\) | ||
0.972680 | − | 0.232150i | \(-0.0745760\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 15.1231i | − | 0.683890i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2462 | 0.462405 | 0.231203 | − | 0.972906i | \(-0.425734\pi\) | ||||
0.231203 | + | 0.972906i | \(0.425734\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.1231 | −0.681110 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.2462 | −0.820106 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.3693 | −0.689408 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.384472i | − | 0.0172113i | −0.999963 | − | 0.00860566i | \(-0.997261\pi\) | ||
0.999963 | − | 0.00860566i | \(-0.00273930\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 3.56155i | − | 0.159118i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.49242 | 0.200307 | 0.100154 | − | 0.994972i | \(-0.468067\pi\) | ||||
0.100154 | + | 0.994972i | \(0.468067\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 54.7386i | 2.43584i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.3693 | − | 4.00000i | −0.549341 | − | 0.177646i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.3153i | 1.29938i | 0.760199 | + | 0.649690i | \(0.225101\pi\) | ||||
−0.760199 | + | 0.649690i | \(0.774899\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.43845 | 0.284820 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.56155i | 0.0689442i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 64.9848i | 2.86357i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.24621 | 0.0987883 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.1231 | −0.576040 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.36932 | −0.147612 | −0.0738062 | − | 0.997273i | \(-0.523515\pi\) | ||||
−0.0738062 | + | 0.997273i | \(0.523515\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.2462 | −0.972759 | −0.486379 | − | 0.873748i | \(-0.661683\pi\) | ||||
−0.486379 | + | 0.873748i | \(0.661683\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 7.68466i | − | 0.335386i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 3.12311i | − | 0.136045i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 52.4233 | 2.27927 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.87689i | − | 0.298432i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.6155 | + | 5.61553i | 1.54268 | + | 0.243236i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 58.7386i | − | 2.53949i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.43845 | −0.277840 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 5.12311i | − | 0.220668i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 44.9848i | − | 1.93405i | −0.254682 | − | 0.967025i | \(-0.581971\pi\) | ||
0.254682 | − | 0.967025i | \(-0.418029\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.36932 | −0.316248 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.3693 | 1.08670 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.1771 | 0.563411 | 0.281706 | − | 0.959501i | \(-0.409100\pi\) | ||||
0.281706 | + | 0.959501i | \(0.409100\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.87689 | −0.122783 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.8078i | 0.503028i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 8.68466i | − | 0.369309i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 5.12311i | − | 0.217073i | −0.994092 | − | 0.108536i | \(-0.965384\pi\) | ||
0.994092 | − | 0.108536i | \(-0.0346164\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.12311 | + | 19.8078i | −0.132093 | + | 0.837779i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 10.2462i | − | 0.432595i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.3693 | 0.900609 | 0.450305 | − | 0.892875i | \(-0.351315\pi\) | ||||
0.450305 | + | 0.892875i | \(0.351315\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 20.6847i | − | 0.870210i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.4233 | 1.23349 | 0.616744 | − | 0.787164i | \(-0.288451\pi\) | ||||
0.616744 | + | 0.787164i | \(0.288451\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.80776 | −0.326745 | −0.163372 | − | 0.986564i | \(-0.552237\pi\) | ||||
−0.163372 | + | 0.986564i | \(0.552237\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0000 | 0.668410 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 66.7386 | 2.78319 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 7.61553i | − | 0.317039i | −0.987356 | − | 0.158519i | \(-0.949328\pi\) | ||
0.987356 | − | 0.158519i | \(-0.0506720\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.36932i | 0.389376i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.68466 | −0.277326 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.2462i | 0.755681i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.6847 | + | 2.00000i | 0.524446 | + | 0.0826898i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 15.5616i | − | 0.642294i | −0.947029 | − | 0.321147i | \(-0.895932\pi\) | ||
0.947029 | − | 0.321147i | \(-0.104068\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.43845 | −0.100474 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 3.36932i | − | 0.138595i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.4233i | 1.53679i | 0.639976 | + | 0.768395i | \(0.278944\pi\) | ||||
−0.639976 | + | 0.768395i | \(0.721056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.12311 | 0.292019 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.6155 | −0.639101 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.4384 | 0.753375 | 0.376687 | − | 0.926340i | \(-0.377063\pi\) | ||||
0.376687 | + | 0.926340i | \(0.377063\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.4924 | −0.427995 | −0.213997 | − | 0.976834i | \(-0.568648\pi\) | ||||
−0.213997 | + | 0.976834i | \(0.568648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.87689i | − | 0.198602i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 54.3002i | − | 2.20762i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.4924 | 1.31883 | 0.659413 | − | 0.751781i | \(-0.270805\pi\) | ||||
0.659413 | + | 0.751781i | \(0.270805\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.56155i | 0.306410i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.56155 | − | 0.246211i | −0.0631737 | − | 0.00996064i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3.12311i | − | 0.126141i | −0.998009 | − | 0.0630705i | \(-0.979911\pi\) | ||
0.998009 | − | 0.0630705i | \(-0.0200893\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −35.6155 | −1.43616 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 19.8617i | − | 0.799604i | −0.916602 | − | 0.399802i | \(-0.869079\pi\) | ||
0.916602 | − | 0.399802i | \(-0.130921\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.2462i | 0.572604i | 0.958139 | + | 0.286302i | \(0.0924260\pi\) | ||||
−0.958139 | + | 0.286302i | \(0.907574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.68466 | −0.348503 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.68466 | 0.267815 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.36932 | −0.174773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.00000 | −0.319489 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7386i | 0.905211i | 0.891711 | + | 0.452605i | \(0.149505\pi\) | ||||
−0.891711 | + | 0.452605i | \(0.850495\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.56155 | 0.0620662 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 72.9848i | 2.89632i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.561553 | + | 3.56155i | −0.0222495 | + | 0.141114i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.3693i | 0.608001i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.3153 | 0.841905 | 0.420953 | − | 0.907083i | \(-0.361696\pi\) | ||||
0.420953 | + | 0.907083i | \(0.361696\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.2462i | 1.50828i | 0.656712 | + | 0.754142i | \(0.271947\pi\) | ||||
−0.656712 | + | 0.754142i | \(0.728053\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 19.8078i | − | 0.779930i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.3693 | −0.682858 | −0.341429 | − | 0.939908i | \(-0.610911\pi\) | ||||
−0.341429 | + | 0.939908i | \(0.610911\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.2311 | 1.38294 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.56155 | −0.0612021 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.2462 | −1.10536 | −0.552680 | − | 0.833394i | \(-0.686395\pi\) | ||||
−0.552680 | + | 0.833394i | \(0.686395\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 53.8617i | − | 2.10455i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6.43845i | − | 0.251188i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.6695 | −1.77903 | −0.889516 | − | 0.456905i | \(-0.848958\pi\) | ||||
−0.889516 | + | 0.456905i | \(0.848958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.0540i | 1.63571i | 0.575424 | + | 0.817855i | \(0.304837\pi\) | ||||
−0.575424 | + | 0.817855i | \(0.695163\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.12311 | + | 7.12311i | −0.0436178 | + | 0.276638i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 5.56155i | − | 0.215668i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −65.6695 | −2.54273 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.43845i | 0.248925i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 14.7386i | − | 0.568979i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.1771 | 1.35598 | 0.677988 | − | 0.735073i | \(-0.262852\pi\) | ||||
0.677988 | + | 0.735073i | \(0.262852\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.68466 | −0.295783 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.7386 | −1.71945 | −0.859723 | − | 0.510761i | \(-0.829364\pi\) | ||||
−0.859723 | + | 0.510761i | \(0.829364\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.31534 | 0.127231 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1.12311i | − | 0.0430375i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 23.3693i | − | 0.894202i | −0.894483 | − | 0.447101i | \(-0.852456\pi\) | ||
0.894483 | − | 0.447101i | \(-0.147544\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 68.9848 | 2.63578 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.36932i | 0.204852i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00000 | − | 12.6847i | 0.0761939 | − | 0.483247i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.9309i | 0.872331i | 0.899866 | + | 0.436166i | \(0.143664\pi\) | ||||
−0.899866 | + | 0.436166i | \(0.856336\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.12311 | −0.194611 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 79.2311i | − | 3.00541i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 20.0000i | − | 0.757554i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.31534 | −0.201045 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −47.6695 | −1.80045 | −0.900226 | − | 0.435423i | \(-0.856599\pi\) | ||||
−0.900226 | + | 0.435423i | \(0.856599\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.56155 | 0.0588115 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.3693i | 0.578023i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 34.2462i | − | 1.28614i | −0.765806 | − | 0.643072i | \(-0.777660\pi\) | ||
0.765806 | − | 0.643072i | \(-0.222340\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.68466 | −0.325700 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 13.5616i | − | 0.507884i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.2462 | + | 64.9848i | −0.383187 | + | 2.43030i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 8.24621i | − | 0.307960i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 50.3542 | 1.87789 | 0.938947 | − | 0.344063i | \(-0.111803\pi\) | ||||
0.938947 | + | 0.344063i | \(0.111803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.2462i | 0.679524i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.0540i | 0.522673i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −58.1080 | −2.15808 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.6155 | 0.875851 | 0.437926 | − | 0.899011i | \(-0.355713\pi\) | ||||
0.437926 | + | 0.899011i | \(0.355713\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.1231 | 0.411403 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.4384i | 1.41976i | 0.704324 | + | 0.709878i | \(0.251250\pi\) | ||||
−0.704324 | + | 0.709878i | \(0.748750\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 3.56155i | − | 0.131370i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.9848 | 0.920329 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 33.7538i | − | 1.24165i | −0.783948 | − | 0.620827i | \(-0.786797\pi\) | ||
0.783948 | − | 0.620827i | \(-0.213203\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.56155 | + | 0.876894i | 0.204309 | + | 0.0322135i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 20.7386i | − | 0.760827i | −0.924817 | − | 0.380413i | \(-0.875782\pi\) | ||
0.924817 | − | 0.380413i | \(-0.124218\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −68.9848 | −2.52741 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.68466i | 0.244579i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 16.4924i | − | 0.602620i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.5616 | −1.22468 | −0.612339 | − | 0.790595i | \(-0.709771\pi\) | ||||
−0.612339 | + | 0.790595i | \(0.709771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.00000 | 0.145768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −42.7386 | −1.55542 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.0540 | 1.01964 | 0.509820 | − | 0.860281i | \(-0.329712\pi\) | ||||
0.509820 | + | 0.860281i | \(0.329712\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 44.4924i | − | 1.61497i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.93087i | 0.178744i | 0.995998 | + | 0.0893719i | \(0.0284860\pi\) | ||||
−0.995998 | + | 0.0893719i | \(0.971514\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.12311 | 0.257874 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 7.12311i | − | 0.257536i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.4924 | − | 3.86174i | −0.884370 | − | 0.139439i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.82292i | 0.101797i | 0.998704 | + | 0.0508985i | \(0.0162085\pi\) | ||||
−0.998704 | + | 0.0508985i | \(0.983791\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.3693 | 0.697569 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.2462i | 1.15982i | 0.814682 | + | 0.579908i | \(0.196911\pi\) | ||||
−0.814682 | + | 0.579908i | \(0.803089\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 12.0000i | − | 0.431053i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.6155 | −0.559484 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −78.7386 | −2.81749 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.56155 | 0.270228 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29.3693i | 1.04824i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 11.8078i | − | 0.420901i | −0.977604 | − | 0.210451i | \(-0.932507\pi\) | ||
0.977604 | − | 0.210451i | \(-0.0674931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.0540 | 0.357931 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.80776i | − | 0.206500i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.61553 | + | 10.2462i | −0.0573691 | + | 0.363854i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.6847i | 0.449878i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.2311 | 1.46048 | 0.730239 | − | 0.683191i | \(-0.239408\pi\) | ||||
0.730239 | + | 0.683191i | \(0.239408\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.876894i | 0.0310223i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 6.68466i | − | 0.236191i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.9848 | 1.16401 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30.9309 | 1.09017 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.0000 | 0.352017 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 54.6847 | 1.92261 | 0.961305 | − | 0.275486i | \(-0.0888387\pi\) | ||||
0.961305 | + | 0.275486i | \(0.0888387\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.0000i | − | 1.26413i | −0.774915 | − | 0.632065i | \(-0.782207\pi\) | ||
0.774915 | − | 0.632065i | \(-0.217793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.7386i | 0.937765i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 53.8617 | 1.88669 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8.68466i | − | 0.303838i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.56155 | + | 0.561553i | 0.124451 | + | 0.0196222i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.4924i | 1.34339i | 0.740826 | + | 0.671697i | \(0.234434\pi\) | ||||
−0.740826 | + | 0.671697i | \(0.765566\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.73863 | 0.234894 | 0.117447 | − | 0.993079i | \(-0.462529\pi\) | ||||
0.117447 | + | 0.993079i | \(0.462529\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 39.3693i | − | 1.37066i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 32.7386i | − | 1.13843i | −0.822187 | − | 0.569217i | \(-0.807246\pi\) | ||
0.822187 | − | 0.569217i | \(-0.192754\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.7386 | 0.998134 | 0.499067 | − | 0.866563i | \(-0.333676\pi\) | ||||
0.499067 | + | 0.866563i | \(0.333676\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.43845 | 0.292726 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000 | 0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.6847 | 0.438971 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.56155i | 0.0539752i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 5.12311i | − | 0.176869i | −0.996082 | − | 0.0884346i | \(-0.971814\pi\) | ||
0.996082 | − | 0.0884346i | \(-0.0281864\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1771 | 0.971623 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 18.0000i | − | 0.619953i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.2462 | − | 44.0540i | 0.490085 | − | 1.51550i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 15.2462i | − | 0.523866i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.2462 | 0.900768 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 17.0691i | − | 0.584436i | −0.956352 | − | 0.292218i | \(-0.905607\pi\) | ||
0.956352 | − | 0.292218i | \(-0.0943933\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.56155 | −0.190201 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.630683 | 0.0215437 | 0.0107719 | − | 0.999942i | \(-0.496571\pi\) | ||||
0.0107719 | + | 0.999942i | \(0.496571\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.12311 | −0.243037 | −0.121519 | − | 0.992589i | \(-0.538776\pi\) | ||||
−0.121519 | + | 0.992589i | \(0.538776\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.0000 | −0.340799 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 34.1080i | − | 1.16105i | −0.814243 | − | 0.580524i | \(-0.802848\pi\) | ||
0.814243 | − | 0.580524i | \(-0.197152\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 46.7386i | − | 1.58916i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 44.4924i | − | 1.50930i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.3693 | − | 2.73863i | −0.588537 | − | 0.0927951i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.31534i | − | 0.112207i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.56155 | 0.323239 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 31.6155i | − | 1.06758i | −0.845617 | − | 0.533790i | \(-0.820767\pi\) | ||
0.845617 | − | 0.533790i | \(-0.179233\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.9309i | 0.705981i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.7538 | −0.800285 | −0.400143 | − | 0.916453i | \(-0.631039\pi\) | ||||
−0.400143 | + | 0.916453i | \(0.631039\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.2462 | −0.883255 | −0.441628 | − | 0.897198i | \(-0.645599\pi\) | ||||
−0.441628 | + | 0.897198i | \(0.645599\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.4924 | 0.823304 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.8617 | 0.465432 | 0.232716 | − | 0.972545i | \(-0.425239\pi\) | ||||
0.232716 | + | 0.972545i | \(0.425239\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.4924i | 0.687294i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.12311i | 0.171630i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.684658 | 0.0229112 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 22.9309i | − | 0.766494i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.87689 | + | 30.9309i | −0.162835 | + | 1.03275i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.8078i | 0.393811i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.12311 | −0.237305 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 5.56155i | − | 0.185077i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 26.2462i | − | 0.872454i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.4384 | 1.54196 | 0.770982 | − | 0.636857i | \(-0.219766\pi\) | ||||
0.770982 | + | 0.636857i | \(0.219766\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.3693 | 0.509768 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.19224 | −0.138895 | −0.0694475 | − | 0.997586i | \(-0.522124\pi\) | ||||
−0.0694475 | + | 0.997586i | \(0.522124\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.2462 | −1.13338 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 10.2462i | − | 0.338729i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 15.1231i | − | 0.499409i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.4924 | 0.675983 | 0.337991 | − | 0.941149i | \(-0.390253\pi\) | ||||
0.337991 | + | 0.941149i | \(0.390253\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.8078i | 0.389079i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 54.7386 | + | 8.63068i | 1.80174 | + | 0.284082i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.2462 | 0.599284 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.0691i | 0.363166i | 0.983376 | + | 0.181583i | \(0.0581222\pi\) | ||||
−0.983376 | + | 0.181583i | \(0.941878\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.56155i | − | 0.0511778i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.6155 | −0.511229 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 36.4924 | 1.19343 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.8617 | −1.04088 | −0.520439 | − | 0.853899i | \(-0.674232\pi\) | ||||
−0.520439 | + | 0.853899i | \(0.674232\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.1231 | −0.819862 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 15.0691i | − | 0.491240i | −0.969366 | − | 0.245620i | \(-0.921009\pi\) | ||
0.969366 | − | 0.245620i | \(-0.0789915\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 86.8466i | − | 2.82811i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.56155 | −0.115857 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 14.4924i | − | 0.470940i | −0.971882 | − | 0.235470i | \(-0.924337\pi\) | ||
0.971882 | − | 0.235470i | \(-0.0756630\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.9309 | − | 3.61553i | −0.744368 | − | 0.117365i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00000i | 0.194563i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.6847 | −1.51226 | −0.756132 | − | 0.654419i | \(-0.772913\pi\) | ||||
−0.756132 | + | 0.654419i | \(0.772913\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 56.9848i | 1.84399i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 38.7386i | 1.25224i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.3693 | 0.625468 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.5616 | 0.921340 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.4924 | −0.531461 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.3693 | −1.07420 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.4924i | 1.04489i | 0.852674 | + | 0.522443i | \(0.174979\pi\) | ||||
−0.852674 | + | 0.522443i | \(0.825021\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 3.12311i | − | 0.100329i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.4773 | 1.84453 | 0.922267 | − | 0.386554i | \(-0.126335\pi\) | ||||
0.922267 | + | 0.386554i | \(0.126335\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 22.2462i | − | 0.713181i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.31534 | + | 27.3693i | −0.138202 | + | 0.876520i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.6307i | 1.17192i | 0.810340 | + | 0.585960i | \(0.199282\pi\) | ||||
−0.810340 | + | 0.585960i | \(0.800718\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.2462 | 1.09451 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 7.12311i | − | 0.227423i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.4384i | 1.03463i | 0.855796 | + | 0.517313i | \(0.173068\pi\) | ||||
−0.855796 | + | 0.517313i | \(0.826932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0000 | 0.382352 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.438447 | 0.0139559 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.3002 | 1.53586 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.2462 | 0.579610 | 0.289805 | − | 0.957086i | \(-0.406410\pi\) | ||||
0.289805 | + | 0.957086i | \(0.406410\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.75379i | 0.309527i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 55.6155i | − | 1.76313i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.1080 | −0.953528 | −0.476764 | − | 0.879031i | \(-0.658190\pi\) | ||||
−0.476764 | + | 0.879031i | \(0.658190\pi\) | |||||||
\(998\) | 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 | 4368.2.h.l.337.4 | 4 | ||
4.3 | odd | 2 | 1092.2.e.e.337.4 | yes | 4 | ||
12.11 | even | 2 | 3276.2.e.e.2521.1 | 4 | |||
13.12 | even | 2 | inner | 4368.2.h.l.337.1 | 4 | ||
28.27 | even | 2 | 7644.2.e.i.4705.1 | 4 | |||
52.51 | odd | 2 | 1092.2.e.e.337.1 | ✓ | 4 | ||
156.155 | even | 2 | 3276.2.e.e.2521.4 | 4 | |||
364.363 | even | 2 | 7644.2.e.i.4705.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1092.2.e.e.337.1 | ✓ | 4 | 52.51 | odd | 2 | ||
1092.2.e.e.337.4 | yes | 4 | 4.3 | odd | 2 | ||
3276.2.e.e.2521.1 | 4 | 12.11 | even | 2 | |||
3276.2.e.e.2521.4 | 4 | 156.155 | even | 2 | |||
4368.2.h.l.337.1 | 4 | 13.12 | even | 2 | inner | ||
4368.2.h.l.337.4 | 4 | 1.1 | even | 1 | trivial | ||
7644.2.e.i.4705.1 | 4 | 28.27 | even | 2 | |||
7644.2.e.i.4705.4 | 4 | 364.363 | even | 2 |