Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1428,2,Mod(169,1428)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1428, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1428.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1428.d (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: | \(11.4026374086\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 43x^{10} + 647x^{8} + 4049x^{6} + 10288x^{4} + 9088x^{2} + 2304 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 169.9 | ||
Root | \(-0.981755i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1428.169 |
Dual form | 1428.2.d.c.169.4 |
$q$-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 \(\left(\mathbb{Z}/1428\mathbb{Z}\right)^\times\).
\(n\) | \(409\) | \(715\) | \(953\) | \(1261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.981755i | − | 0.439054i | −0.975606 | − | 0.219527i | \(-0.929549\pi\) | ||
0.975606 | − | 0.219527i | \(-0.0704514\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.478569i | − | 0.144294i | −0.997394 | − | 0.0721470i | \(-0.977015\pi\) | ||
0.997394 | − | 0.0721470i | \(-0.0229851\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.19199 | −1.71735 | −0.858675 | − | 0.512520i | \(-0.828712\pi\) | ||||
−0.858675 | + | 0.512520i | \(0.828712\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.981755 | 0.253488 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.75736 | + | 3.06544i | 0.668759 | + | 0.743479i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.75943 | 1.55072 | 0.775360 | − | 0.631520i | \(-0.217569\pi\) | ||||
0.775360 | + | 0.631520i | \(0.217569\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.21975i | − | 1.29691i | −0.761254 | − | 0.648454i | \(-0.775416\pi\) | ||
0.761254 | − | 0.648454i | \(-0.224584\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.03616 | 0.807232 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.43256i | − | 0.266021i | −0.991115 | − | 0.133010i | \(-0.957536\pi\) | ||
0.991115 | − | 0.133010i | \(-0.0424643\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.44411i | − | 0.438975i | −0.975615 | − | 0.219487i | \(-0.929562\pi\) | ||
0.975615 | − | 0.219487i | \(-0.0704384\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.478569 | 0.0833082 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.981755 | −0.165947 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.1488i | − | 1.66845i | −0.551422 | − | 0.834226i | \(-0.685915\pi\) | ||
0.551422 | − | 0.834226i | \(-0.314085\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.19199i | − | 0.991513i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.68008i | − | 1.19943i | −0.800215 | − | 0.599713i | \(-0.795281\pi\) | ||
0.800215 | − | 0.599713i | \(-0.204719\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.741517 | −0.113080 | −0.0565401 | − | 0.998400i | \(-0.518007\pi\) | ||||
−0.0565401 | + | 0.998400i | \(0.518007\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.981755i | 0.146351i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.44411 | 0.356510 | 0.178255 | − | 0.983984i | \(-0.442955\pi\) | ||||
0.178255 | + | 0.983984i | \(0.442955\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.06544 | + | 2.75736i | −0.429248 | + | 0.386108i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.2282 | 1.81703 | 0.908513 | − | 0.417856i | \(-0.137218\pi\) | ||||
0.908513 | + | 0.417856i | \(0.137218\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.469838 | −0.0633529 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.75943i | 0.895308i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.45048 | −0.969970 | −0.484985 | − | 0.874523i | \(-0.661175\pi\) | ||||
−0.484985 | + | 0.874523i | \(0.661175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.680410i | − | 0.0871176i | −0.999051 | − | 0.0435588i | \(-0.986130\pi\) | ||
0.999051 | − | 0.0435588i | \(-0.0138696\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.07902i | 0.754010i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.0823 | −1.84260 | −0.921299 | − | 0.388855i | \(-0.872871\pi\) | ||||
−0.921299 | + | 0.388855i | \(0.872871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.21975 | 0.748770 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.73705i | 0.443507i | 0.975103 | + | 0.221753i | \(0.0711780\pi\) | ||||
−0.975103 | + | 0.221753i | \(0.928822\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.17375i | − | 0.839624i | −0.907611 | − | 0.419812i | \(-0.862096\pi\) | ||
0.907611 | − | 0.419812i | \(-0.137904\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.03616i | 0.466055i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.478569 | −0.0545380 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.2646i | − | 1.49239i | −0.665728 | − | 0.746194i | \(-0.731879\pi\) | ||
0.665728 | − | 0.746194i | \(-0.268121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.34113 | 1.02532 | 0.512661 | − | 0.858591i | \(-0.328660\pi\) | ||||
0.512661 | + | 0.858591i | \(0.328660\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00951 | − | 2.70705i | 0.326428 | − | 0.293621i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.43256 | 0.153587 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.7765 | 1.88431 | 0.942153 | − | 0.335184i | \(-0.108798\pi\) | ||||
0.942153 | + | 0.335184i | \(0.108798\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.19199i | 0.649097i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.44411 | 0.253442 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 6.63610i | − | 0.680850i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.24673i | 0.329656i | 0.986322 | + | 0.164828i | \(0.0527068\pi\) | ||||
−0.986322 | + | 0.164828i | \(0.947293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.478569i | 0.0480980i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.99127 | 0.596153 | 0.298077 | − | 0.954542i | \(-0.403655\pi\) | ||||
0.298077 | + | 0.954542i | \(0.403655\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.01825 | −0.100331 | −0.0501653 | − | 0.998741i | \(-0.515975\pi\) | ||||
−0.0501653 | + | 0.998741i | \(0.515975\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 0.981755i | − | 0.0958094i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.6402i | 1.60867i | 0.594175 | + | 0.804336i | \(0.297479\pi\) | ||||
−0.594175 | + | 0.804336i | \(0.702521\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17.0694i | − | 1.63496i | −0.575959 | − | 0.817478i | \(-0.695371\pi\) | ||
0.575959 | − | 0.817478i | \(-0.304629\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.1488 | 0.963281 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.21694i | − | 0.114480i | −0.998360 | − | 0.0572402i | \(-0.981770\pi\) | ||
0.998360 | − | 0.0572402i | \(-0.0182301\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.10627 | −0.569413 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.19199 | 0.572450 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.06544 | − | 2.75736i | 0.281009 | − | 0.252767i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7710 | 0.979179 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.68008 | 0.692489 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 8.87129i | − | 0.793472i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.8584 | −0.963530 | −0.481765 | − | 0.876301i | \(-0.660004\pi\) | ||||
−0.481765 | + | 0.876301i | \(0.660004\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 0.741517i | − | 0.0652869i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8.11901i | − | 0.709361i | −0.934987 | − | 0.354681i | \(-0.884590\pi\) | ||
0.934987 | − | 0.354681i | \(-0.115410\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.75943i | − | 0.586117i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.981755 | −0.0844960 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.19870 | −0.529590 | −0.264795 | − | 0.964305i | \(-0.585304\pi\) | ||||
−0.264795 | + | 0.964305i | \(0.585304\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.2983i | 1.21276i | 0.795174 | + | 0.606382i | \(0.207380\pi\) | ||||
−0.795174 | + | 0.606382i | \(0.792620\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.44411i | 0.205831i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.96330i | 0.247803i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.40643 | −0.116797 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.38399 | −0.522997 | −0.261498 | − | 0.965204i | \(-0.584217\pi\) | ||||
−0.261498 | + | 0.965204i | \(0.584217\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.52696 | −0.612535 | −0.306268 | − | 0.951945i | \(-0.599080\pi\) | ||||
−0.306268 | + | 0.951945i | \(0.599080\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.75736 | − | 3.06544i | −0.222920 | − | 0.247826i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.39951 | −0.192734 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.81097 | −0.623383 | −0.311691 | − | 0.950183i | \(-0.600896\pi\) | ||||
−0.311691 | + | 0.950183i | \(0.600896\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.2282i | 1.04906i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.21975 | −0.490185 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.275182i | 0.0215539i | 0.999942 | + | 0.0107770i | \(0.00343048\pi\) | ||||
−0.999942 | + | 0.0107770i | \(0.996570\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 0.469838i | − | 0.0365768i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.7913i | 1.68626i | 0.537710 | + | 0.843130i | \(0.319289\pi\) | ||||
−0.537710 | + | 0.843130i | \(0.680711\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.3408 | 1.94929 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.75943 | −0.516906 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.1271i | 1.15009i | 0.818122 | + | 0.575044i | \(0.195015\pi\) | ||||
−0.818122 | + | 0.575044i | \(0.804985\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.03616i | − | 0.305105i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 7.45048i | − | 0.560012i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.93107 | −0.742283 | −0.371142 | − | 0.928576i | \(-0.621034\pi\) | ||||
−0.371142 | + | 0.928576i | \(0.621034\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5577i | 1.15640i | 0.815896 | + | 0.578199i | \(0.196244\pi\) | ||||
−0.815896 | + | 0.578199i | \(0.803756\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.680410 | 0.0502974 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.96363 | −0.732541 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.46703 | − | 1.31959i | 0.107280 | − | 0.0964980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.5252 | 1.48515 | 0.742577 | − | 0.669761i | \(-0.233603\pi\) | ||||
0.742577 | + | 0.669761i | \(0.233603\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.29708i | 0.525255i | 0.964897 | + | 0.262628i | \(0.0845891\pi\) | ||||
−0.964897 | + | 0.262628i | \(0.915411\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.07902 | −0.435328 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.5835i | 1.82275i | 0.411581 | + | 0.911373i | \(0.364977\pi\) | ||||
−0.411581 | + | 0.911373i | \(0.635023\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.0613i | − | 1.06767i | −0.845589 | − | 0.533835i | \(-0.820750\pi\) | ||
0.845589 | − | 0.533835i | \(-0.179250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 15.0823i | − | 1.06382i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.43256 | −0.100546 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.53995 | −0.526613 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.21975i | 0.432303i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.23486i | − | 0.223760i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 11.6728i | − | 0.803589i | −0.915730 | − | 0.401794i | \(-0.868387\pi\) | ||
0.915730 | − | 0.401794i | \(-0.131613\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.73705 | −0.256059 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.727988i | 0.0496484i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.44411 | −0.165917 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.17375 | 0.484757 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.0736 | − | 18.9812i | −1.14849 | − | 1.27681i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.3952 | −1.23183 | −0.615917 | − | 0.787811i | \(-0.711214\pi\) | ||||
−0.615917 | + | 0.787811i | \(0.711214\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.03616 | −0.269077 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 13.1538i | − | 0.873046i | −0.899693 | − | 0.436523i | \(-0.856210\pi\) | ||
0.899693 | − | 0.436523i | \(-0.143790\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.569823 | 0.0376550 | 0.0188275 | − | 0.999823i | \(-0.494007\pi\) | ||||
0.0188275 | + | 0.999823i | \(0.494007\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 0.478569i | − | 0.0314876i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 17.8788i | − | 1.17128i | −0.810572 | − | 0.585639i | \(-0.800844\pi\) | ||
0.810572 | − | 0.585639i | \(-0.199156\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2.39951i | − | 0.156527i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.2646 | 0.861631 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.89968 | −0.575673 | −0.287836 | − | 0.957680i | \(-0.592936\pi\) | ||||
−0.287836 | + | 0.957680i | \(0.592936\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2721i | 0.661686i | 0.943686 | + | 0.330843i | \(0.107333\pi\) | ||||
−0.943686 | + | 0.330843i | \(0.892667\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.981755i | 0.0627220i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −41.8543 | −2.66313 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.34113i | 0.591970i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.1953 | 1.08536 | 0.542678 | − | 0.839941i | \(-0.317410\pi\) | ||||
0.542678 | + | 0.839941i | \(0.317410\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.97658 | −0.187136 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.70705 | + | 3.00951i | 0.169522 | + | 0.188463i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.48067 | 0.529010 | 0.264505 | − | 0.964384i | \(-0.414791\pi\) | ||||
0.264505 | + | 0.964384i | \(0.414791\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.1488 | −0.630616 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.43256i | 0.0886735i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.85809 | 0.361226 | 0.180613 | − | 0.983554i | \(-0.442192\pi\) | ||||
0.180613 | + | 0.983554i | \(0.442192\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 12.9868i | − | 0.797773i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.7765i | 1.08790i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.5471i | 1.31375i | 0.754000 | + | 0.656875i | \(0.228122\pi\) | ||||
−0.754000 | + | 0.656875i | \(0.771878\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.161218 | 0.00979332 | 0.00489666 | − | 0.999988i | \(-0.498441\pi\) | ||||
0.00489666 | + | 0.999988i | \(0.498441\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.19199 | −0.374757 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.93158i | − | 0.116479i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 32.4753i | − | 1.95125i | −0.219436 | − | 0.975627i | \(-0.570422\pi\) | ||
0.219436 | − | 0.975627i | \(-0.429578\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.44411i | 0.146325i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.34113 | 0.199315 | 0.0996575 | − | 0.995022i | \(-0.468225\pi\) | ||||
0.0996575 | + | 0.995022i | \(0.468225\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5.61547i | − | 0.333805i | −0.985973 | − | 0.166902i | \(-0.946624\pi\) | ||
0.985973 | − | 0.166902i | \(-0.0533765\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.63610 | 0.393089 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.68008 | −0.453341 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.79389 | + | 16.9051i | −0.105523 | + | 0.994417i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.24673 | −0.190327 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.3747 | −1.19030 | −0.595152 | − | 0.803613i | \(-0.702908\pi\) | ||||
−0.595152 | + | 0.803613i | \(0.702908\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.31454i | 0.425869i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.478569 | −0.0277694 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 38.5127i | 2.22725i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.741517i | 0.0427403i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.99127i | 0.344189i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.667996 | −0.0382493 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.7637 | −1.01383 | −0.506914 | − | 0.861997i | \(-0.669214\pi\) | ||||
−0.506914 | + | 0.861997i | \(0.669214\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.01825i | − | 0.0579260i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.9822i | 1.30320i | 0.758562 | + | 0.651600i | \(0.225902\pi\) | ||||
−0.758562 | + | 0.651600i | \(0.774098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.6044i | 0.995062i | 0.867446 | + | 0.497531i | \(0.165760\pi\) | ||||
−0.867446 | + | 0.497531i | \(0.834240\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.981755 | 0.0553156 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 28.6237i | − | 1.60767i | −0.594855 | − | 0.803833i | \(-0.702790\pi\) | ||
0.594855 | − | 0.803833i | \(-0.297210\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.685582 | −0.0383852 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.6402 | −0.928767 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.6382 | + | 20.7207i | 1.03706 | + | 1.15293i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.9919 | −1.38630 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.0694 | 0.943943 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.44411i | − | 0.134748i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.8104 | −1.74846 | −0.874229 | − | 0.485513i | \(-0.838633\pi\) | ||||
−0.874229 | + | 0.485513i | \(0.838633\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.1488i | 0.556151i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.8071i | 0.809000i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.63820i | − | 0.470553i | −0.971928 | − | 0.235276i | \(-0.924400\pi\) | ||
0.971928 | − | 0.235276i | \(-0.0755996\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.21694 | 0.0660953 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.16967 | −0.0633414 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 6.10627i | − | 0.328751i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.9988i | 0.644131i | 0.946717 | + | 0.322065i | \(0.104377\pi\) | ||||
−0.946717 | + | 0.322065i | \(0.895623\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.48730 | −0.347257 | −0.173629 | − | 0.984811i | \(-0.555549\pi\) | ||||
−0.173629 | + | 0.984811i | \(0.555549\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.19199i | 0.330504i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.9741 | 1.00989 | 0.504946 | − | 0.863151i | \(-0.331513\pi\) | ||||
0.504946 | + | 0.863151i | \(0.331513\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.66887 | 0.194723 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.75736 | + | 3.06544i | 0.145935 | + | 0.162240i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.1374 | −1.69615 | −0.848073 | − | 0.529880i | \(-0.822237\pi\) | ||||
−0.848073 | + | 0.529880i | \(0.822237\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.6899 | 1.40473 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.7710i | 0.565329i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.04286 | −0.368640 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 8.00000i | − | 0.417597i | −0.977959 | − | 0.208798i | \(-0.933045\pi\) | ||
0.977959 | − | 0.208798i | \(-0.0669552\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.68008i | 0.399809i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 13.2282i | − | 0.686771i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.7800 | 0.765279 | 0.382639 | − | 0.923898i | \(-0.375015\pi\) | ||||
0.382639 | + | 0.923898i | \(0.375015\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.87129 | 0.458111 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.87043i | 0.456851i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.33707i | − | 0.479613i | −0.970821 | − | 0.239807i | \(-0.922916\pi\) | ||
0.970821 | − | 0.239807i | \(-0.0770840\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 10.8584i | − | 0.556294i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.7417 | 1.36644 | 0.683219 | − | 0.730214i | \(-0.260580\pi\) | ||||
0.683219 | + | 0.730214i | \(0.260580\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.469838i | 0.0239451i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.741517 | 0.0376934 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.8581 | −1.31106 | −0.655529 | − | 0.755170i | \(-0.727554\pi\) | ||||
−0.655529 | + | 0.755170i | \(0.727554\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.0663 | − | 17.1501i | 0.964224 | − | 0.867319i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.11901 | 0.409550 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.0226 | −0.655239 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.01327i | 0.301798i | 0.988549 | + | 0.150899i | \(0.0482168\pi\) | ||||
−0.988549 | + | 0.150899i | \(0.951783\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.75943 | 0.338395 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 6.26543i | − | 0.312880i | −0.987687 | − | 0.156440i | \(-0.949998\pi\) | ||
0.987687 | − | 0.156440i | \(-0.0500018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.1339i | 0.753873i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 0.981755i | − | 0.0487838i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.85690 | −0.240748 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.3872 | −0.513613 | −0.256807 | − | 0.966463i | \(-0.582670\pi\) | ||||
−0.256807 | + | 0.966463i | \(0.582670\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.19870i | − | 0.305759i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.45048i | 0.366614i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 9.17070i | − | 0.450172i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.2983 | −0.700189 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.3933i | 1.53366i | 0.641848 | + | 0.766832i | \(0.278168\pi\) | ||||
−0.641848 | + | 0.766832i | \(0.721832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.1560 | 1.61593 | 0.807963 | − | 0.589233i | \(-0.200570\pi\) | ||||
0.807963 | + | 0.589233i | \(0.200570\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.44411 | −0.118837 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.1292 | + | 12.3726i | 0.539843 | + | 0.600160i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.680410 | −0.0329274 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.96330 | −0.143069 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.8257i | − | 0.762299i | −0.924513 | − | 0.381149i | \(-0.875528\pi\) | ||
0.924513 | − | 0.381149i | \(-0.124472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.87360 | 0.378381 | 0.189191 | − | 0.981940i | \(-0.439414\pi\) | ||||
0.189191 | + | 0.981940i | \(0.439414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 1.40643i | − | 0.0674330i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 42.0420i | − | 2.01114i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.3850i | 1.92747i | 0.266859 | + | 0.963736i | \(0.414014\pi\) | ||||
−0.266859 | + | 0.963736i | \(0.585986\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.2583 | −1.24757 | −0.623784 | − | 0.781597i | \(-0.714406\pi\) | ||||
−0.623784 | + | 0.781597i | \(0.714406\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 17.4522i | − | 0.827312i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 6.38399i | − | 0.301952i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 16.0822i | − | 0.758968i | −0.925198 | − | 0.379484i | \(-0.876102\pi\) | ||
0.925198 | − | 0.379484i | \(-0.123898\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.67545 | −0.173070 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 7.52696i | − | 0.353648i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.07902 | 0.284989 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.6042 | −1.05738 | −0.528691 | − | 0.848814i | \(-0.677317\pi\) | ||||
−0.528691 | + | 0.848814i | \(0.677317\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.06544 | − | 2.75736i | 0.143083 | − | 0.128703i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.9582 | 1.20899 | 0.604496 | − | 0.796608i | \(-0.293374\pi\) | ||||
0.604496 | + | 0.796608i | \(0.293374\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.36125 | 0.435054 | 0.217527 | − | 0.976054i | \(-0.430201\pi\) | ||||
0.217527 | + | 0.976054i | \(0.430201\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 2.39951i | − | 0.111275i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.7677 | −0.498269 | −0.249134 | − | 0.968469i | \(-0.580146\pi\) | ||||
−0.249134 | + | 0.968469i | \(0.580146\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.0823i | 0.696436i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7.81097i | − | 0.359910i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.354867i | 0.0163168i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.2821 | 1.25179 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.2282 | −0.605675 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.3883i | 0.885872i | 0.896553 | + | 0.442936i | \(0.146063\pi\) | ||||
−0.896553 | + | 0.442936i | \(0.853937\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 62.8413i | 2.86532i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 6.21975i | − | 0.283009i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.18749 | 0.144737 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.8727i | 0.764576i | 0.924043 | + | 0.382288i | \(0.124864\pi\) | ||||
−0.924043 | + | 0.382288i | \(0.875136\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.275182 | −0.0124442 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.40112 | −0.0632318 | −0.0316159 | − | 0.999500i | \(-0.510065\pi\) | ||||
−0.0316159 | + | 0.999500i | \(0.510065\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.39145 | − | 3.95010i | 0.197781 | − | 0.177904i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.469838 | 0.0211176 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.73705 | 0.167630 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.8565i | 1.96328i | 0.190732 | + | 0.981642i | \(0.438914\pi\) | ||||
−0.190732 | + | 0.981642i | \(0.561086\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.7913 | −0.973562 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 42.2970i | − | 1.88593i | −0.332889 | − | 0.942966i | \(-0.608023\pi\) | ||
0.332889 | − | 0.942966i | \(-0.391977\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 5.88196i | − | 0.261744i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.3408i | 1.12542i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 43.2398 | 1.91657 | 0.958286 | − | 0.285810i | \(-0.0922628\pi\) | ||||
0.958286 | + | 0.285810i | \(0.0922628\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.17375 | −0.317348 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 6.75943i | − | 0.298436i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.999667i | 0.0440506i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.16967i | − | 0.0514422i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.1271 | −0.664004 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.0895i | − | 0.836325i | −0.908372 | − | 0.418162i | \(-0.862674\pi\) | ||
0.908372 | − | 0.418162i | \(-0.137326\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.455302 | 0.0199090 | 0.00995448 | − | 0.999950i | \(-0.496831\pi\) | ||||
0.00995448 | + | 0.999950i | \(0.496831\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.03616 | 0.176152 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.49227 | − | 6.73929i | 0.326369 | − | 0.293568i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.6853 | −0.681971 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.45048 | 0.323323 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 47.5550i | 2.05984i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.3366 | 0.706294 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 9.93107i | − | 0.428558i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.478569i | 0.0206134i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 14.2190i | − | 0.611322i | −0.952140 | − | 0.305661i | \(-0.901122\pi\) | ||
0.952140 | − | 0.305661i | \(-0.0988775\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.5577 | −0.667646 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.7580 | −0.717834 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.5565i | − | 0.793420i | −0.917944 | − | 0.396710i | \(-0.870152\pi\) | ||
0.917944 | − | 0.396710i | \(-0.129848\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.680410i | 0.0290392i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 9.68332i | − | 0.412523i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.2646 | −0.564070 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 9.96363i | − | 0.422933i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −45.3071 | −1.91972 | −0.959861 | − | 0.280477i | \(-0.909507\pi\) | ||||
−0.959861 | + | 0.280477i | \(0.909507\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.59147 | 0.194198 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.31959 | + | 1.46703i | 0.0557131 | + | 0.0619379i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.6705 | 1.03974 | 0.519869 | − | 0.854246i | \(-0.325981\pi\) | ||||
0.519869 | + | 0.854246i | \(0.325981\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.19474 | −0.0502631 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.3661 | 1.52455 | 0.762273 | − | 0.647255i | \(-0.224083\pi\) | ||||
0.762273 | + | 0.647255i | \(0.224083\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 25.8299i | − | 1.08095i | −0.841361 | − | 0.540473i | \(-0.818245\pi\) | ||
0.841361 | − | 0.540473i | \(-0.181755\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.5252i | 0.857454i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 25.1039i | − | 1.04691i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.8676 | 1.49319 | 0.746595 | − | 0.665279i | \(-0.231688\pi\) | ||||
0.746595 | + | 0.665279i | \(0.231688\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.29708 | −0.303256 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 9.34113i | − | 0.387535i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.33059i | − | 0.262186i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 6.07902i | − | 0.251337i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.2130 | −1.08193 | −0.540963 | − | 0.841046i | \(-0.681940\pi\) | ||||
−0.540963 | + | 0.841046i | \(0.681940\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 16.5208i | − | 0.680726i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.5835 | −1.05236 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.25752 | 0.174835 | 0.0874177 | − | 0.996172i | \(-0.472139\pi\) | ||||
0.0874177 | + | 0.996172i | \(0.472139\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.70705 | − | 3.00951i | −0.110978 | − | 0.123378i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.0613 | 0.616420 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.5605 | 0.717502 | 0.358751 | − | 0.933433i | \(-0.383203\pi\) | ||||
0.358751 | + | 0.933433i | \(0.383203\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.19927i | − | 0.252873i | −0.991975 | − | 0.126437i | \(-0.959646\pi\) | ||
0.991975 | − | 0.126437i | \(-0.0403541\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.0823 | 0.614199 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 10.5745i | − | 0.429913i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.8262i | 0.642366i | 0.947017 | + | 0.321183i | \(0.104080\pi\) | ||||
−0.947017 | + | 0.321183i | \(0.895920\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 1.43256i | − | 0.0580505i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.1339 | −0.612252 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.6250 | −1.19654 | −0.598271 | − | 0.801294i | \(-0.704146\pi\) | ||||
−0.598271 | + | 0.801294i | \(0.704146\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 7.53995i | − | 0.304040i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.4121i | − | 0.902278i | −0.892454 | − | 0.451139i | \(-0.851018\pi\) | ||
0.892454 | − | 0.451139i | \(-0.148982\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 23.2873i | − | 0.935995i | −0.883730 | − | 0.467998i | \(-0.844976\pi\) | ||
0.883730 | − | 0.467998i | \(-0.155024\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.21975 | −0.249590 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 17.7765i | − | 0.712201i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.4714 | 0.458854 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.23486 | 0.129188 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.1106 | − | 27.9839i | 1.24046 | − | 1.11579i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.2209 | 1.64098 | 0.820489 | − | 0.571662i | \(-0.193701\pi\) | ||||
0.820489 | + | 0.571662i | \(0.193701\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.6728 | 0.463952 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.6603i | 0.423042i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.19199 | 0.245336 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 3.73705i | − | 0.147836i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 23.5909i | − | 0.931783i | −0.884842 | − | 0.465891i | \(-0.845734\pi\) | ||
0.884842 | − | 0.465891i | \(-0.154266\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.7061i | 0.934877i | 0.884026 | + | 0.467438i | \(0.154823\pi\) | ||||
−0.884026 | + | 0.467438i | \(0.845177\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.727988 | −0.0286645 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.8664 | 0.623771 | 0.311885 | − | 0.950120i | \(-0.399039\pi\) | ||||
0.311885 | + | 0.950120i | \(0.399039\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.56557i | 0.139961i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 2.44411i | − | 0.0957921i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.4040i | 1.11153i | 0.831338 | + | 0.555767i | \(0.187575\pi\) | ||||
−0.831338 | + | 0.555767i | \(0.812425\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.97088 | −0.311448 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.17375i | 0.279875i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.37006 | −0.209188 | −0.104594 | − | 0.994515i | \(-0.533354\pi\) | ||||
−0.104594 | + | 0.994515i | \(0.533354\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.0808 | 0.430993 | 0.215496 | − | 0.976505i | \(-0.430863\pi\) | ||||
0.215496 | + | 0.976505i | \(0.430863\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.9812 | − | 17.0736i | 0.737169 | − | 0.663083i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.63610 | −0.257337 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.91020 | −0.345004 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 18.3952i | − | 0.711199i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.325624 | −0.0125706 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0526i | 1.15844i | 0.815170 | + | 0.579222i | \(0.196643\pi\) | ||||
−0.815170 | + | 0.579222i | \(0.803357\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 4.03616i | − | 0.155352i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.19473i | 0.199650i | 0.995005 | + | 0.0998248i | \(0.0318282\pi\) | ||||
−0.995005 | + | 0.0998248i | \(0.968172\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.24673 | 0.124598 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.1538 | 0.504054 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.2719i | 1.23485i | 0.786629 | + | 0.617426i | \(0.211824\pi\) | ||||
−0.786629 | + | 0.617426i | \(0.788176\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.08560i | 0.232519i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.569823i | 0.0217401i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −81.9086 | −3.12047 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 43.0141i | − | 1.63633i | −0.574981 | − | 0.818167i | \(-0.694991\pi\) | ||
0.574981 | − | 0.818167i | \(-0.305009\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.478569 | 0.0181793 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.0374 | 0.532469 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.5428 | − | 21.1768i | 0.891749 | − | 0.802127i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.8788 | 0.676237 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.3405 | 1.25925 | 0.629626 | − | 0.776898i | \(-0.283208\pi\) | ||||
0.629626 | + | 0.776898i | \(0.283208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 68.6001i | − | 2.58730i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.39951 | 0.0903709 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 5.99127i | − | 0.225325i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.00000i | 0.300446i | 0.988652 | + | 0.150223i | \(0.0479992\pi\) | ||||
−0.988652 | + | 0.150223i | \(0.952001\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.2646i | 0.497463i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.2017 | −0.569310 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.90923 | 0.108799 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 8.89968i | − | 0.332365i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 18.1701i | − | 0.677629i | −0.940853 | − | 0.338814i | \(-0.889974\pi\) | ||
0.940853 | − | 0.338814i | \(-0.110026\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.01825i | 0.0379214i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.2721 | −0.382025 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 5.78206i | − | 0.214740i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.03407 | 0.260879 | 0.130440 | − | 0.991456i | \(-0.458361\pi\) | ||||
0.130440 | + | 0.991456i | \(0.458361\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.04463 | − | 2.27308i | −0.0756234 | − | 0.0840729i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.27611 | −0.0471342 | −0.0235671 | − | 0.999722i | \(-0.507502\pi\) | ||||
−0.0235671 | + | 0.999722i | \(0.507502\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.981755 | −0.0362126 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.21793i | 0.265876i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.1114 | −1.14445 | −0.572226 | − | 0.820096i | \(-0.693920\pi\) | ||||
−0.572226 | + | 0.820096i | \(0.693920\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 41.8543i | − | 1.53756i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 14.8570i | − | 0.545049i | −0.962149 | − | 0.272524i | \(-0.912141\pi\) | ||
0.962149 | − | 0.272524i | \(-0.0878585\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.26751i | 0.229624i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.34113 | −0.341774 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.6402 | 0.608021 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 20.0765i | − | 0.732601i | −0.930497 | − | 0.366301i | \(-0.880624\pi\) | ||
0.930497 | − | 0.366301i | \(-0.119376\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.1953i | 0.626631i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.38963i | 0.268936i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.5851 | 1.03894 | 0.519472 | − | 0.854488i | \(-0.326129\pi\) | ||||
0.519472 | + | 0.854488i | \(0.326129\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 2.97658i | − | 0.108043i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.61218 | −0.348441 | −0.174221 | − | 0.984707i | \(-0.555741\pi\) | ||||
−0.174221 | + | 0.984707i | \(0.555741\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.0694 | −0.617956 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.00951 | + | 2.70705i | −0.108809 | + | 0.0978738i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 46.1333 | 1.66578 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.7410 | 0.603695 | 0.301847 | − | 0.953356i | \(-0.402397\pi\) | ||||
0.301847 | + | 0.953356i | \(0.402397\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.48067i | 0.305424i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.1130 | −1.19099 | −0.595496 | − | 0.803358i | \(-0.703045\pi\) | ||||
−0.595496 | + | 0.803358i | \(0.703045\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 9.86480i | − | 0.354354i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 10.1488i | − | 0.364086i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 51.9129i | − | 1.85997i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.78844 | 0.0639954 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.43256 | −0.0511957 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.66845i | 0.273699i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.30644i | 0.331739i | 0.986148 | + | 0.165869i | \(0.0530430\pi\) | ||||
−0.986148 | + | 0.165869i | \(0.946957\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.85809i | 0.208554i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.21694 | −0.0432695 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.21310i | 0.149611i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.9868 | 0.460594 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.29134 | 0.0811633 | 0.0405816 | − | 0.999176i | \(-0.487079\pi\) | ||||
0.0405816 | + | 0.999176i | \(0.487079\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.73929 | + | 7.49227i | 0.238419 | + | 0.265058i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.7765 | −0.628102 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.43314 | −0.121153 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.10627i | 0.215218i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.5471 | −0.758494 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.0582i | 0.810685i | 0.914165 | + | 0.405342i | \(0.132848\pi\) | ||||
−0.914165 | + | 0.405342i | \(0.867152\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.9136i | 1.12064i | 0.828277 | + | 0.560319i | \(0.189322\pi\) | ||||
−0.828277 | + | 0.560319i | \(0.810678\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.161218i | 0.00565418i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.270162 | 0.00946335 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.01223 | −0.175356 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 6.19199i | − | 0.216366i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 8.99462i | − | 0.313914i | −0.987605 | − | 0.156957i | \(-0.949832\pi\) | ||
0.987605 | − | 0.156957i | \(-0.0501685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 23.9666i | − | 0.835423i | −0.908580 | − | 0.417711i | \(-0.862832\pi\) | ||
0.908580 | − | 0.417711i | \(-0.137168\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.93158 | 0.0672490 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.3456i | 1.19431i | 0.802125 | + | 0.597157i | \(0.203703\pi\) | ||||
−0.802125 | + | 0.597157i | \(0.796297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.60897 | 0.0906134 | 0.0453067 | − | 0.998973i | \(-0.485573\pi\) | ||||
0.0453067 | + | 0.998973i | \(0.485573\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.4753 | 1.12656 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.75736 | − | 3.06544i | −0.0955370 | − | 0.106211i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.3937 | 0.740359 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.44411 | −0.0844807 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 7.08425i | − | 0.244576i | −0.992495 | − | 0.122288i | \(-0.960977\pi\) | ||
0.992495 | − | 0.122288i | \(-0.0390231\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.9478 | 0.929233 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.34113i | 0.115075i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 24.8784i | − | 0.855844i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.7710i | − | 0.370095i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.61547 | 0.192722 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −63.1230 | −2.16383 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.2509i | 1.10425i | 0.833762 | + | 0.552125i | \(0.186183\pi\) | ||||
−0.833762 | + | 0.552125i | \(0.813817\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.63610i | 0.226950i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.4904i | 0.939053i | 0.882918 | + | 0.469527i | \(0.155575\pi\) | ||||
−0.882918 | + | 0.469527i | \(0.844425\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.7376 | −0.434602 | −0.217301 | − | 0.976105i | \(-0.569725\pi\) | ||||
−0.217301 | + | 0.976105i | \(0.569725\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 7.68008i | − | 0.261736i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.3637 | −0.488947 | −0.244474 | − | 0.969656i | \(-0.578615\pi\) | ||||
−0.244474 | + | 0.969656i | \(0.578615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.8511 | 0.504951 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.9051 | − | 1.79389i | −0.574127 | − | 0.0609238i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.34805 | −0.215343 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 93.3896 | 3.16439 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.24673i | − | 0.109885i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.87129 | −0.299904 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.6010i | 0.830718i | 0.909657 | + | 0.415359i | \(0.136344\pi\) | ||||
−0.909657 | + | 0.415359i | \(0.863656\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 20.3747i | − | 0.687222i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 53.9581i | − | 1.81789i | −0.416911 | − | 0.908947i | \(-0.636887\pi\) | ||
0.416911 | − | 0.908947i | \(-0.363113\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.7546 | 0.597490 | 0.298745 | − | 0.954333i | \(-0.403432\pi\) | ||||
0.298745 | + | 0.954333i | \(0.403432\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.31454 | −0.245876 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 26.2348i | − | 0.880880i | −0.897782 | − | 0.440440i | \(-0.854823\pi\) | ||
0.897782 | − | 0.440440i | \(-0.145177\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.8584i | 0.364180i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 0.478569i | − | 0.0160327i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.5208 | 0.552846 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.74988i | 0.325903i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −38.5127 | −1.28590 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.50134 | −0.116776 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.4748 | + | 40.5502i | 1.21515 | + | 1.35092i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.741517 | −0.0246761 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.2739 | 0.507721 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.2658i | 0.805734i | 0.915259 | + | 0.402867i | \(0.131986\pi\) | ||||
−0.915259 | + | 0.402867i | \(0.868014\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.99127 | −0.198718 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.6008i | 0.550008i | 0.961443 | + | 0.275004i | \(0.0886793\pi\) | ||||
−0.961443 | + | 0.275004i | \(0.911321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 4.47038i | − | 0.147948i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 0.667996i | − | 0.0220833i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.11901 | −0.268113 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.4120 | 1.00320 | 0.501600 | − | 0.865100i | \(-0.332745\pi\) | ||||
0.501600 | + | 0.865100i | \(0.332745\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 17.7637i | − | 0.585334i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 23.1398i | − | 0.761656i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 40.9622i | − | 1.34683i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.01825 | 0.0334436 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.6790i | 0.908118i | 0.890972 | + | 0.454059i | \(0.150025\pi\) | ||||
−0.890972 | + | 0.454059i | \(0.849975\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.75943 | −0.221531 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.9822 | −0.752403 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.29551 | − | 1.44026i | −0.0423678 | − | 0.0471016i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.78940 | 0.254469 | 0.127234 | − | 0.991873i | \(-0.459390\pi\) | ||||
0.127234 | + | 0.991873i | \(0.459390\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.6044 | −0.574499 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.16746i | 0.0380582i | 0.999819 | + | 0.0190291i | \(0.00605752\pi\) | ||||
−0.999819 | + | 0.0190291i | \(0.993942\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47.7682 | −1.55555 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.981755i | 0.0319365i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.8703i | 0.385734i | 0.981225 | + | 0.192867i | \(0.0617786\pi\) | ||||
−0.981225 | + | 0.192867i | \(0.938221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.4198i | 1.44193i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.6237 | 0.928187 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.7585 | −0.640041 | −0.320021 | − | 0.947411i | \(-0.603690\pi\) | ||||
−0.320021 | + | 0.947411i | \(0.603690\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 20.1507i | − | 0.652063i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.685582i | − | 0.0221617i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.19870i | 0.200166i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.0263 | 0.807301 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 16.6402i | − | 0.536224i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.16394 | 0.230615 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.6197 | 0.405823 | 0.202912 | − | 0.979197i | \(-0.434960\pi\) | ||||
0.202912 | + | 0.979197i | \(0.434960\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.7207 | + | 18.6382i | −0.665643 | + | 0.598745i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.7951 | 1.63009 | 0.815046 | − | 0.579396i | \(-0.196711\pi\) | ||||
0.815046 | + | 0.579396i | \(0.196711\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.2983 | 0.458381 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 24.9919i | − | 0.800380i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.6003 | −0.691054 | −0.345527 | − | 0.938409i | \(-0.612300\pi\) | ||||
−0.345527 | + | 0.938409i | \(0.612300\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 8.50729i | − | 0.271894i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.0694i | 0.544986i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 30.3369i | − | 0.967596i | −0.875180 | − | 0.483798i | \(-0.839257\pi\) | ||
0.875180 | − | 0.483798i | \(-0.160743\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.1167 | 0.800284 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.44411 | 0.0777968 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.61205i | 0.146655i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 12.6099i | − | 0.400568i | −0.979738 | − | 0.200284i | \(-0.935814\pi\) | ||
0.979738 | − | 0.200284i | \(-0.0641865\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 31.8104i | − | 1.00947i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.7865 | −0.468765 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.4095i | 1.46980i | 0.678174 | + | 0.734901i | \(0.262771\pi\) | ||||
−0.678174 | + | 0.734901i | \(0.737229\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.1488 | −0.321094 |
(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 | 1428.2.d.c.169.9 | yes | 12 | |
3.2 | odd | 2 | 4284.2.d.f.3025.8 | 12 | |||
17.16 | even | 2 | inner | 1428.2.d.c.169.4 | ✓ | 12 | |
51.50 | odd | 2 | 4284.2.d.f.3025.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1428.2.d.c.169.4 | ✓ | 12 | 17.16 | even | 2 | inner | |
1428.2.d.c.169.9 | yes | 12 | 1.1 | even | 1 | trivial | |
4284.2.d.f.3025.5 | 12 | 51.50 | odd | 2 | |||
4284.2.d.f.3025.8 | 12 | 3.2 | odd | 2 |