Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(560,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.560");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 20x^{6} + 129x^{4} + 323x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 560.2 | ||
Root | \(-2.15629i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.560 |
Dual form | 731.2.d.b.560.7 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | − | 2.15629i | − | 1.24494i | −0.782645 | − | 0.622468i | \(-0.786130\pi\) | ||
0.782645 | − | 0.622468i | \(-0.213870\pi\) | |||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | − | 2.88045i | − | 1.28818i | −0.764951 | − | 0.644089i | \(-0.777237\pi\) | ||
0.764951 | − | 0.644089i | \(-0.222763\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.59528i | − | 0.980925i | −0.871462 | − | 0.490463i | \(-0.836828\pi\) | ||
0.871462 | − | 0.490463i | \(-0.163172\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.64959 | −0.549865 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.55588i | − | 1.37365i | −0.726823 | − | 0.686825i | \(-0.759004\pi\) | ||
0.726823 | − | 0.686825i | \(-0.240996\pi\) | |||||||
\(12\) | 4.31258i | 1.24494i | ||||||||
\(13\) | 4.56150 | 1.26513 | 0.632566 | − | 0.774506i | \(-0.282002\pi\) | ||||
0.632566 | + | 0.774506i | \(0.282002\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.21109 | −1.60370 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −4.07885 | − | 0.602510i | −0.989265 | − | 0.146130i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 5.76090i | 1.28818i | ||||||||
\(21\) | −5.59619 | −1.22119 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.67790i | 0.766895i | 0.923563 | + | 0.383447i | \(0.125263\pi\) | ||||
−0.923563 | + | 0.383447i | \(0.874737\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.29700 | −0.659401 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.91187i | − | 0.560389i | ||||||
\(28\) | 5.19057i | 0.980925i | ||||||||
\(29\) | 5.76090i | 1.06977i | 0.844924 | + | 0.534886i | \(0.179646\pi\) | ||||
−0.844924 | + | 0.534886i | \(0.820354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.10756i | − | 0.558135i | −0.960272 | − | 0.279067i | \(-0.909975\pi\) | ||
0.960272 | − | 0.279067i | \(-0.0900253\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.82381 | −1.71011 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.47559 | −1.26361 | ||||||||
\(36\) | 3.29919 | 0.549865 | ||||||||
\(37\) | 1.27831i | 0.210152i | 0.994464 | + | 0.105076i | \(0.0335086\pi\) | ||||
−0.994464 | + | 0.105076i | \(0.966491\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 9.83593i | − | 1.57501i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.1948i | 1.74833i | 0.485629 | + | 0.874165i | \(0.338590\pi\) | ||||
−0.485629 | + | 0.874165i | \(0.661410\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 9.11177i | 1.37365i | ||||||||
\(45\) | 4.75158i | 0.708323i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.24578 | −0.327581 | −0.163791 | − | 0.986495i | \(-0.552372\pi\) | ||||
−0.163791 | + | 0.986495i | \(0.552372\pi\) | |||||||
\(48\) | − | 8.62517i | − | 1.24494i | ||||||
\(49\) | 0.264498 | 0.0377854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.29919 | + | 8.79518i | −0.181923 | + | 1.23157i | ||||
\(52\) | −9.12300 | −1.26513 | ||||||||
\(53\) | 11.9119 | 1.63623 | 0.818113 | − | 0.575057i | \(-0.195020\pi\) | ||||
0.818113 | + | 0.575057i | \(0.195020\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.1230 | −1.76951 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.31258i | − | 0.571216i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.297003 | 0.0386664 | 0.0193332 | − | 0.999813i | \(-0.493846\pi\) | ||||
0.0193332 | + | 0.999813i | \(0.493846\pi\) | |||||||
\(60\) | 12.4222 | 1.60370 | ||||||||
\(61\) | − | 8.38761i | − | 1.07392i | −0.843607 | − | 0.536961i | \(-0.819572\pi\) | ||
0.843607 | − | 0.536961i | \(-0.180428\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.28117i | 0.539376i | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | − | 13.1392i | − | 1.62971i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.01871 | 0.246625 | 0.123313 | − | 0.992368i | \(-0.460648\pi\) | ||||
0.123313 | + | 0.992368i | \(0.460648\pi\) | |||||||
\(68\) | 8.15769 | + | 1.20502i | 0.989265 | + | 0.146130i | ||||
\(69\) | 7.93062 | 0.954734 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.58842i | 0.425868i | 0.977067 | + | 0.212934i | \(0.0683019\pi\) | ||||
−0.977067 | + | 0.212934i | \(0.931698\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.19704i | 0.374185i | 0.982342 | + | 0.187092i | \(0.0599064\pi\) | ||||
−0.982342 | + | 0.187092i | \(0.940094\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.10930i | 0.820911i | ||||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | −11.8238 | −1.34745 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.02456i | 0.115272i | 0.998338 | + | 0.0576358i | \(0.0183562\pi\) | ||||
−0.998338 | + | 0.0576358i | \(0.981644\pi\) | |||||||
\(80\) | − | 11.5218i | − | 1.28818i | ||||||
\(81\) | −11.2276 | −1.24751 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.61490 | 0.616316 | 0.308158 | − | 0.951335i | \(-0.400287\pi\) | ||||
0.308158 | + | 0.951335i | \(0.400287\pi\) | |||||||
\(84\) | 11.1924 | 1.22119 | ||||||||
\(85\) | −1.73550 | + | 11.7489i | −0.188242 | + | 1.27435i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.4222 | 1.33180 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.2298 | −1.19036 | −0.595179 | − | 0.803593i | \(-0.702919\pi\) | ||||
−0.595179 | + | 0.803593i | \(0.702919\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 11.8384i | − | 1.24100i | ||||||
\(92\) | − | 7.35579i | − | 0.766895i | ||||||
\(93\) | −6.70081 | −0.694842 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 5.76090i | − | 0.591056i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.08301i | 0.211497i | 0.994393 | + | 0.105749i | \(0.0337239\pi\) | ||||
−0.994393 | + | 0.105749i | \(0.966276\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.51536i | 0.755322i | ||||||||
\(100\) | 6.59401 | 0.659401 | ||||||||
\(101\) | 14.8238 | 1.47502 | 0.737512 | − | 0.675334i | \(-0.236000\pi\) | ||||
0.737512 | + | 0.675334i | \(0.236000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.9303 | 1.76672 | 0.883362 | − | 0.468692i | \(-0.155274\pi\) | ||||
0.883362 | + | 0.468692i | \(0.155274\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 16.1196i | 1.57311i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 9.98975i | − | 0.965746i | −0.875690 | − | 0.482873i | \(-0.839593\pi\) | ||
0.875690 | − | 0.482873i | \(-0.160407\pi\) | |||||||
\(108\) | 5.82374i | 0.560389i | ||||||||
\(109\) | − | 20.3903i | − | 1.95303i | −0.215440 | − | 0.976517i | \(-0.569119\pi\) | ||
0.215440 | − | 0.976517i | \(-0.430881\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.75640 | 0.261626 | ||||||||
\(112\) | − | 10.3811i | − | 0.980925i | ||||||
\(113\) | 6.93929i | 0.652793i | 0.945233 | + | 0.326397i | \(0.105834\pi\) | ||||
−0.945233 | + | 0.326397i | \(0.894166\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.5940 | 0.987896 | ||||||||
\(116\) | − | 11.5218i | − | 1.06977i | ||||||
\(117\) | −7.52462 | −0.695652 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.56369 | + | 10.5858i | −0.143343 | + | 0.970396i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.75607 | −0.886915 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 24.1392 | 2.17656 | ||||||||
\(124\) | 6.21513i | 0.558135i | ||||||||
\(125\) | − | 4.90540i | − | 0.438752i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.3157 | −0.915372 | −0.457686 | − | 0.889114i | \(-0.651322\pi\) | ||||
−0.457686 | + | 0.889114i | \(0.651322\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 2.15629i | − | 0.189851i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2362i | 0.894345i | 0.894448 | + | 0.447172i | \(0.147569\pi\) | ||||
−0.894448 | + | 0.447172i | \(0.852431\pi\) | |||||||
\(132\) | 19.6476 | 1.71011 | ||||||||
\(133\) | − | 5.19057i | − | 0.450079i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.38750 | −0.721881 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.59401 | −0.563364 | −0.281682 | − | 0.959508i | \(-0.590892\pi\) | ||||
−0.281682 | + | 0.959508i | \(0.590892\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.27358i | − | 0.616937i | −0.951235 | − | 0.308468i | \(-0.900184\pi\) | ||
0.951235 | − | 0.308468i | \(-0.0998164\pi\) | |||||||
\(140\) | 14.9512 | 1.26361 | ||||||||
\(141\) | 4.84257i | 0.407818i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 20.7817i | − | 1.73785i | ||||||
\(144\) | −6.59838 | −0.549865 | ||||||||
\(145\) | 16.5940 | 1.37806 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 0.570334i | − | 0.0470404i | ||||||
\(148\) | − | 2.55661i | − | 0.210152i | ||||||
\(149\) | −10.3154 | −0.845069 | −0.422535 | − | 0.906347i | \(-0.638859\pi\) | ||||
−0.422535 | + | 0.906347i | \(0.638859\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.59401 | 0.211097 | 0.105549 | − | 0.994414i | \(-0.466340\pi\) | ||||
0.105549 | + | 0.994414i | \(0.466340\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.72844 | + | 0.993898i | 0.543962 | + | 0.0803519i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.95118 | −0.718976 | ||||||||
\(156\) | 19.6719i | 1.57501i | ||||||||
\(157\) | −8.52900 | −0.680688 | −0.340344 | − | 0.940301i | \(-0.610544\pi\) | ||||
−0.340344 | + | 0.940301i | \(0.610544\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 25.6855i | − | 2.03700i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.54519 | 0.752266 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.83099i | 0.456719i | 0.973577 | + | 0.228359i | \(0.0733361\pi\) | ||||
−0.973577 | + | 0.228359i | \(0.926664\pi\) | |||||||
\(164\) | − | 22.3895i | − | 1.74833i | ||||||
\(165\) | 28.2970i | 2.20292i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.67790i | 0.284604i | 0.989823 | + | 0.142302i | \(0.0454505\pi\) | ||||
−0.989823 | + | 0.142302i | \(0.954550\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.80729 | 0.600560 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.29919 | −0.252295 | ||||||||
\(172\) | −2.00000 | −0.152499 | ||||||||
\(173\) | 21.3326i | 1.62189i | 0.585123 | + | 0.810944i | \(0.301046\pi\) | ||||
−0.585123 | + | 0.810944i | \(0.698954\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.55666i | 0.646823i | ||||||||
\(176\) | − | 18.2235i | − | 1.37365i | ||||||
\(177\) | − | 0.640424i | − | 0.0481372i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.8238 | 0.883753 | 0.441877 | − | 0.897076i | \(-0.354313\pi\) | ||||
0.441877 | + | 0.897076i | \(0.354313\pi\) | |||||||
\(180\) | − | 9.50315i | − | 0.708323i | ||||||
\(181\) | 9.53553i | 0.708770i | 0.935100 | + | 0.354385i | \(0.115310\pi\) | ||||
−0.935100 | + | 0.354385i | \(0.884690\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.0861 | −1.33696 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.68210 | 0.270713 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.74497 | + | 18.5827i | −0.200732 | + | 1.35890i | ||||
\(188\) | 4.49157 | 0.327581 | ||||||||
\(189\) | −7.55713 | −0.549700 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.9094 | −1.65767 | −0.828833 | − | 0.559497i | \(-0.810994\pi\) | ||||
−0.828833 | + | 0.559497i | \(0.810994\pi\) | |||||||
\(192\) | 17.2503i | 1.24494i | ||||||||
\(193\) | − | 3.61506i | − | 0.260218i | −0.991500 | − | 0.130109i | \(-0.958467\pi\) | ||
0.991500 | − | 0.130109i | \(-0.0415327\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −28.3319 | −2.02889 | ||||||||
\(196\) | −0.528996 | −0.0377854 | ||||||||
\(197\) | 18.1607i | 1.29390i | 0.762534 | + | 0.646948i | \(0.223955\pi\) | ||||
−0.762534 | + | 0.646948i | \(0.776045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 22.2195i | − | 1.57510i | −0.616250 | − | 0.787550i | \(-0.711349\pi\) | ||
0.616250 | − | 0.787550i | \(-0.288651\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.35293i | − | 0.307032i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.9512 | 1.04937 | ||||||||
\(204\) | 2.59838 | − | 17.5904i | 0.181923 | − | 1.23157i | ||||
\(205\) | 32.2460 | 2.25216 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.06704i | − | 0.421688i | ||||||
\(208\) | 18.2460 | 1.26513 | ||||||||
\(209\) | − | 9.11177i | − | 0.630274i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 21.5791i | − | 1.48557i | −0.669532 | − | 0.742783i | \(-0.733505\pi\) | ||
0.669532 | − | 0.742783i | \(-0.266495\pi\) | |||||||
\(212\) | −23.8238 | −1.63623 | ||||||||
\(213\) | 7.73769 | 0.530178 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2.88045i | − | 0.196445i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.06501 | −0.547489 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.89374 | 0.465836 | ||||||||
\(220\) | 26.2460 | 1.76951 | ||||||||
\(221\) | −18.6057 | − | 2.74835i | −1.25155 | − | 0.184874i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.6146 | 1.17956 | 0.589779 | − | 0.807564i | \(-0.299215\pi\) | ||||
0.589779 | + | 0.807564i | \(0.299215\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.43872 | 0.362581 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.22295i | 0.346659i | 0.984864 | + | 0.173330i | \(0.0554526\pi\) | ||||
−0.984864 | + | 0.173330i | \(0.944547\pi\) | |||||||
\(228\) | 8.62517i | 0.571216i | ||||||||
\(229\) | 24.2273 | 1.60098 | 0.800492 | − | 0.599343i | \(-0.204572\pi\) | ||||
0.800492 | + | 0.599343i | \(0.204572\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 25.4956i | 1.67749i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.27391i | − | 0.279993i | −0.990152 | − | 0.139997i | \(-0.955291\pi\) | ||
0.990152 | − | 0.139997i | \(-0.0447092\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.46888i | 0.421983i | ||||||||
\(236\) | −0.594005 | −0.0386664 | ||||||||
\(237\) | 2.20924 | 0.143506 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.842309 | −0.0544844 | −0.0272422 | − | 0.999629i | \(-0.508673\pi\) | ||||
−0.0272422 | + | 0.999629i | \(0.508673\pi\) | |||||||
\(240\) | −24.8444 | −1.60370 | ||||||||
\(241\) | − | 5.40819i | − | 0.348372i | −0.984713 | − | 0.174186i | \(-0.944271\pi\) | ||
0.984713 | − | 0.174186i | \(-0.0557294\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.4744i | 0.992685i | ||||||||
\(244\) | 16.7752i | 1.07392i | ||||||||
\(245\) | − | 0.761873i | − | 0.0486743i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.12300 | 0.580483 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 12.1074i | − | 0.767273i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.17367 | 0.326559 | 0.163280 | − | 0.986580i | \(-0.447793\pi\) | ||||
0.163280 | + | 0.986580i | \(0.447793\pi\) | |||||||
\(252\) | − | 8.56233i | − | 0.539376i | ||||||
\(253\) | 16.7561 | 1.05344 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 25.3341 | + | 3.74225i | 1.58648 | + | 0.234349i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 5.40599 | 0.337217 | 0.168608 | − | 0.985683i | \(-0.446073\pi\) | ||||
0.168608 | + | 0.985683i | \(0.446073\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.31757 | 0.206144 | ||||||||
\(260\) | 26.2784i | 1.62971i | ||||||||
\(261\) | − | 9.50315i | − | 0.588230i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.7214 | −1.70937 | −0.854687 | − | 0.519144i | \(-0.826251\pi\) | ||||
−0.854687 | + | 0.519144i | \(0.826251\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 34.3117i | − | 2.10775i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.2147i | 1.48192i | ||||||||
\(268\) | −4.03743 | −0.246625 | ||||||||
\(269\) | 6.31185i | 0.384841i | 0.981313 | + | 0.192420i | \(0.0616337\pi\) | ||||
−0.981313 | + | 0.192420i | \(0.938366\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0905 | −0.673700 | −0.336850 | − | 0.941558i | \(-0.609361\pi\) | ||||
−0.336850 | + | 0.941558i | \(0.609361\pi\) | |||||||
\(272\) | −16.3154 | − | 2.41004i | −0.989265 | − | 0.146130i | ||||
\(273\) | −25.5270 | −1.54497 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.0208i | 0.905786i | ||||||||
\(276\) | −15.8612 | −0.954734 | ||||||||
\(277\) | 17.0290i | 1.02317i | 0.859232 | + | 0.511586i | \(0.170942\pi\) | ||||
−0.859232 | + | 0.511586i | \(0.829058\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.12622i | 0.306899i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.63088 | −0.156945 | −0.0784726 | − | 0.996916i | \(-0.525004\pi\) | ||||
−0.0784726 | + | 0.996916i | \(0.525004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.5563i | 1.45972i | 0.683597 | + | 0.729860i | \(0.260415\pi\) | ||||
−0.683597 | + | 0.729860i | \(0.739585\pi\) | |||||||
\(284\) | − | 7.17685i | − | 0.425868i | ||||||
\(285\) | −12.4222 | −0.735827 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.0536 | 1.71498 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.2740 | + | 4.91509i | 0.957292 | + | 0.289123i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.49157 | 0.263300 | ||||||||
\(292\) | − | 6.39407i | − | 0.374185i | ||||||
\(293\) | −27.4731 | −1.60499 | −0.802497 | − | 0.596656i | \(-0.796496\pi\) | ||||
−0.802497 | + | 0.596656i | \(0.796496\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 0.855502i | − | 0.0498092i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.2661 | −0.769779 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.7767i | 0.970223i | ||||||||
\(300\) | − | 14.2186i | − | 0.820911i | ||||||
\(301\) | − | 2.59528i | − | 0.149590i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 31.9645i | − | 1.83631i | ||||||
\(304\) | 8.00000 | 0.458831 | ||||||||
\(305\) | −24.1601 | −1.38340 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.49157 | 0.199274 | 0.0996372 | − | 0.995024i | \(-0.468232\pi\) | ||||
0.0996372 | + | 0.995024i | \(0.468232\pi\) | |||||||
\(308\) | 23.6476 | 1.34745 | ||||||||
\(309\) | − | 38.6629i | − | 2.19946i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.3174i | 1.32221i | 0.750295 | + | 0.661103i | \(0.229912\pi\) | ||||
−0.750295 | + | 0.661103i | \(0.770088\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.91873i | 0.108453i | 0.998529 | + | 0.0542265i | \(0.0172693\pi\) | ||||
−0.998529 | + | 0.0542265i | \(0.982731\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.3317 | 0.694812 | ||||||||
\(316\) | − | 2.04911i | − | 0.115272i | ||||||
\(317\) | − | 16.1405i | − | 0.906542i | −0.891373 | − | 0.453271i | \(-0.850257\pi\) | ||
0.891373 | − | 0.453271i | \(-0.149743\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.2460 | 1.46949 | ||||||||
\(320\) | 23.0436i | 1.28818i | ||||||||
\(321\) | −21.5408 | −1.20229 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.15769 | − | 1.20502i | −0.453906 | − | 0.0670492i | ||||
\(324\) | 22.4552 | 1.24751 | ||||||||
\(325\) | −15.0393 | −0.834229 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −43.9674 | −2.43140 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.82845i | 0.321333i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.6146 | −1.07811 | −0.539057 | − | 0.842269i | \(-0.681219\pi\) | ||||
−0.539057 | + | 0.842269i | \(0.681219\pi\) | |||||||
\(332\) | −11.2298 | −0.616316 | ||||||||
\(333\) | − | 2.10869i | − | 0.115555i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 5.81481i | − | 0.317697i | ||||||
\(336\) | −22.3848 | −1.22119 | ||||||||
\(337\) | 23.0242i | 1.25421i | 0.778935 | + | 0.627105i | \(0.215760\pi\) | ||||
−0.778935 | + | 0.627105i | \(0.784240\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.9631 | 0.812685 | ||||||||
\(340\) | 3.47100 | − | 23.4978i | 0.188242 | − | 1.27435i | ||||
\(341\) | −14.1577 | −0.766682 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.8534i | − | 1.01799i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 22.8438i | − | 1.22987i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 33.8717i | − | 1.81833i | −0.416437 | − | 0.909165i | \(-0.636721\pi\) | ||
0.416437 | − | 0.909165i | \(-0.363279\pi\) | |||||||
\(348\) | −24.8444 | −1.33180 | ||||||||
\(349\) | −25.3690 | −1.35797 | −0.678986 | − | 0.734151i | \(-0.737580\pi\) | ||||
−0.678986 | + | 0.734151i | \(0.737580\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 13.2825i | − | 0.708967i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.208909 | −0.0111191 | −0.00555955 | − | 0.999985i | \(-0.501770\pi\) | ||||
−0.00555955 | + | 0.999985i | \(0.501770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.3363 | 0.548593 | ||||||||
\(356\) | 22.4596 | 1.19036 | ||||||||
\(357\) | 22.8260 | + | 3.37176i | 1.20808 | + | 0.178453i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.1601 | 1.75012 | 0.875061 | − | 0.484012i | \(-0.160821\pi\) | ||||
0.875061 | + | 0.484012i | \(0.160821\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.0369i | 1.10415i | ||||||||
\(364\) | 23.6768i | 1.24100i | ||||||||
\(365\) | 9.20891 | 0.482016 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.92613i | 0.413741i | 0.978368 | + | 0.206870i | \(0.0663278\pi\) | ||||
−0.978368 | + | 0.206870i | \(0.933672\pi\) | |||||||
\(368\) | 14.7116i | 0.766895i | ||||||||
\(369\) | − | 18.4668i | − | 0.961345i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 30.9148i | − | 1.60502i | ||||||
\(372\) | 13.4016 | 0.694842 | ||||||||
\(373\) | −32.2834 | −1.67157 | −0.835786 | − | 0.549055i | \(-0.814988\pi\) | ||||
−0.835786 | + | 0.549055i | \(0.814988\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5775 | −0.546219 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.2784i | 1.35340i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 13.4887i | − | 0.692868i | −0.938074 | − | 0.346434i | \(-0.887392\pi\) | ||
0.938074 | − | 0.346434i | \(-0.112608\pi\) | |||||||
\(380\) | 11.5218i | 0.591056i | ||||||||
\(381\) | 22.2437i | 1.13958i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.0856 | −0.873032 | −0.436516 | − | 0.899696i | \(-0.643788\pi\) | ||||
−0.436516 | + | 0.899696i | \(0.643788\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 34.0579i | 1.73575i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.64959 | −0.0838536 | ||||||||
\(388\) | − | 4.16601i | − | 0.211497i | ||||||
\(389\) | −26.7750 | −1.35755 | −0.678773 | − | 0.734348i | \(-0.737488\pi\) | ||||
−0.678773 | + | 0.734348i | \(0.737488\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.21597 | − | 15.0016i | 0.112066 | − | 0.758662i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.0723 | 1.11340 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.95118 | 0.148490 | ||||||||
\(396\) | − | 15.0307i | − | 0.755322i | ||||||
\(397\) | − | 15.4944i | − | 0.777640i | −0.921314 | − | 0.388820i | \(-0.872883\pi\) | ||
0.921314 | − | 0.388820i | \(-0.127117\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.1924 | −0.560320 | ||||||||
\(400\) | −13.1880 | −0.659401 | ||||||||
\(401\) | − | 16.4177i | − | 0.819862i | −0.912117 | − | 0.409931i | \(-0.865553\pi\) | ||
0.912117 | − | 0.409931i | \(-0.134447\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 14.1751i | − | 0.706114i | ||||||
\(404\) | −29.6476 | −1.47502 | ||||||||
\(405\) | 32.3406i | 1.60702i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.82381 | 0.288676 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.1604 | −0.749635 | −0.374817 | − | 0.927099i | \(-0.622295\pi\) | ||||
−0.374817 | + | 0.927099i | \(0.622295\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.2186i | 0.701352i | ||||||||
\(412\) | −35.8606 | −1.76672 | ||||||||
\(413\) | − | 0.770806i | − | 0.0379289i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 16.1735i | − | 0.793924i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.6840 | −0.768046 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 29.0735i | − | 1.42033i | −0.704034 | − | 0.710167i | \(-0.748620\pi\) | ||
0.704034 | − | 0.710167i | \(-0.251380\pi\) | |||||||
\(420\) | − | 32.2391i | − | 1.57311i | ||||||
\(421\) | 23.3690 | 1.13894 | 0.569468 | − | 0.822014i | \(-0.307149\pi\) | ||||
0.569468 | + | 0.822014i | \(0.307149\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.70463 | 0.180125 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.4480 | + | 1.98648i | 0.652322 | + | 0.0963584i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.7682 | −1.05344 | ||||||||
\(428\) | 19.9795i | 0.965746i | ||||||||
\(429\) | −44.8113 | −2.16351 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 21.8386i | − | 1.05193i | −0.850507 | − | 0.525964i | \(-0.823705\pi\) | ||
0.850507 | − | 0.525964i | \(-0.176295\pi\) | |||||||
\(432\) | − | 11.6475i | − | 0.560389i | ||||||
\(433\) | 16.1436 | 0.775810 | 0.387905 | − | 0.921699i | \(-0.373199\pi\) | ||||
0.387905 | + | 0.921699i | \(0.373199\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 35.7815i | − | 1.71559i | ||||||
\(436\) | 40.7805i | 1.95303i | ||||||||
\(437\) | 7.35579i | 0.351875i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.6089i | 1.65179i | 0.563823 | + | 0.825896i | \(0.309330\pi\) | ||||
−0.563823 | + | 0.825896i | \(0.690670\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.436314 | −0.0207769 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.2825 | −1.62881 | −0.814406 | − | 0.580295i | \(-0.802937\pi\) | ||||
−0.814406 | + | 0.580295i | \(0.802937\pi\) | |||||||
\(444\) | −5.51280 | −0.261626 | ||||||||
\(445\) | 32.3469i | 1.53339i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.2430i | 1.05206i | ||||||||
\(448\) | 20.7623i | 0.980925i | ||||||||
\(449\) | − | 12.2926i | − | 0.580124i | −0.957008 | − | 0.290062i | \(-0.906324\pi\) | ||
0.957008 | − | 0.290062i | \(-0.0936760\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 51.0021 | 2.40159 | ||||||||
\(452\) | − | 13.8786i | − | 0.652793i | ||||||
\(453\) | − | 5.59343i | − | 0.262802i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −34.0999 | −1.59863 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5084 | 0.725454 | 0.362727 | − | 0.931895i | \(-0.381846\pi\) | ||||
0.362727 | + | 0.931895i | \(0.381846\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.75443 | + | 11.8771i | −0.0818898 | + | 0.554374i | ||||
\(460\) | −21.1880 | −0.987896 | ||||||||
\(461\) | −35.1416 | −1.63671 | −0.818354 | − | 0.574715i | \(-0.805113\pi\) | ||||
−0.818354 | + | 0.574715i | \(0.805113\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.8606 | 1.85248 | 0.926239 | − | 0.376937i | \(-0.123023\pi\) | ||||
0.926239 | + | 0.376937i | \(0.123023\pi\) | |||||||
\(464\) | 23.0436i | 1.06977i | ||||||||
\(465\) | 19.3014i | 0.895079i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.4428 | 1.17735 | 0.588675 | − | 0.808370i | \(-0.299650\pi\) | ||||
0.588675 | + | 0.808370i | \(0.299650\pi\) | |||||||
\(468\) | 15.0492 | 0.695652 | ||||||||
\(469\) | − | 5.23913i | − | 0.241921i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.3910i | 0.847413i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4.55588i | − | 0.209480i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.59401 | −0.302554 | ||||||||
\(476\) | 3.12737 | − | 21.1715i | 0.143343 | − | 0.970396i | ||||
\(477\) | −19.6498 | −0.899703 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 25.7274i | − | 1.17552i | −0.809037 | − | 0.587758i | \(-0.800011\pi\) | ||
0.809037 | − | 0.587758i | \(-0.199989\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.83099i | 0.265870i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 20.5822i | − | 0.936523i | ||||||
\(484\) | 19.5121 | 0.886915 | ||||||||
\(485\) | 6.00000 | 0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14.5472i | − | 0.659194i | −0.944122 | − | 0.329597i | \(-0.893087\pi\) | ||
0.944122 | − | 0.329597i | \(-0.106913\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.5733 | 0.568585 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.3154 | 1.54863 | 0.774316 | − | 0.632799i | \(-0.218094\pi\) | ||||
0.774316 | + | 0.632799i | \(0.218094\pi\) | |||||||
\(492\) | −48.2784 | −2.17656 | ||||||||
\(493\) | 3.47100 | − | 23.4978i | 0.156326 | − | 1.05829i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21.6476 | 0.972988 | ||||||||
\(496\) | − | 12.4303i | − | 0.558135i | ||||||
\(497\) | 9.31298 | 0.417744 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.0094i | 1.52247i | 0.648477 | + | 0.761234i | \(0.275406\pi\) | ||||
−0.648477 | + | 0.761234i | \(0.724594\pi\) | |||||||
\(500\) | 9.81080i | 0.438752i | ||||||||
\(501\) | 7.93062 | 0.354314 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.1601i | 0.854308i | 0.904179 | + | 0.427154i | \(0.140484\pi\) | ||||
−0.904179 | + | 0.427154i | \(0.859516\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 42.6993i | − | 1.90009i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 16.8348i | − | 0.747659i | ||||||
\(508\) | 20.6314 | 0.915372 | ||||||||
\(509\) | 16.7333 | 0.741691 | 0.370846 | − | 0.928695i | \(-0.379068\pi\) | ||||
0.370846 | + | 0.928695i | \(0.379068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.29722 | 0.367047 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 5.82374i | − | 0.257124i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 51.6473i | − | 2.27585i | ||||||
\(516\) | 4.31258i | 0.189851i | ||||||||
\(517\) | 10.2315i | 0.449982i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 45.9993 | 2.01915 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3597i | 0.716730i | 0.933582 | + | 0.358365i | \(0.116666\pi\) | ||||
−0.933582 | + | 0.358365i | \(0.883334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.50843 | −0.240867 | −0.120433 | − | 0.992721i | \(-0.538428\pi\) | ||||
−0.120433 | + | 0.992721i | \(0.538428\pi\) | |||||||
\(524\) | − | 20.4725i | − | 0.894345i | ||||||
\(525\) | 18.4507 | 0.805253 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.87234 | + | 12.6753i | −0.0815604 | + | 0.552143i | ||||
\(528\) | −39.2952 | −1.71011 | ||||||||
\(529\) | 9.47307 | 0.411873 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.489934 | −0.0212613 | ||||||||
\(532\) | 10.3811i | 0.450079i | ||||||||
\(533\) | 51.0650i | 2.21187i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.7750 | −1.24405 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 25.4956i | − | 1.10022i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.20502i | − | 0.0519039i | ||||||
\(540\) | 16.7750 | 0.721881 | ||||||||
\(541\) | 20.3903i | 0.876646i | 0.898817 | + | 0.438323i | \(0.144427\pi\) | ||||
−0.898817 | + | 0.438323i | \(0.855573\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.5614 | 0.882373 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −58.7332 | −2.51585 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.2148i | 1.20638i | 0.797598 | + | 0.603189i | \(0.206103\pi\) | ||||
−0.797598 | + | 0.603189i | \(0.793897\pi\) | |||||||
\(548\) | 13.1880 | 0.563364 | ||||||||
\(549\) | 13.8361i | 0.590512i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.5218i | 0.490845i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.65901 | 0.113073 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 7.93968i | − | 0.337021i | ||||||
\(556\) | 14.5472i | 0.616937i | ||||||||
\(557\) | −27.6333 | −1.17086 | −0.585430 | − | 0.810723i | \(-0.699074\pi\) | ||||
−0.585430 | + | 0.810723i | \(0.699074\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.56150 | 0.192931 | ||||||||
\(560\) | −29.9024 | −1.26361 | ||||||||
\(561\) | 40.0698 | + | 5.91895i | 1.69175 | + | 0.249898i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.7750 | 1.25487 | 0.627433 | − | 0.778670i | \(-0.284106\pi\) | ||||
0.627433 | + | 0.778670i | \(0.284106\pi\) | |||||||
\(564\) | − | 9.68514i | − | 0.407818i | ||||||
\(565\) | 19.9883 | 0.840913 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 29.1389i | 1.22372i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.9655 | −0.962765 | −0.481382 | − | 0.876511i | \(-0.659865\pi\) | ||||
−0.481382 | + | 0.876511i | \(0.659865\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.9517i | 0.960497i | 0.877132 | + | 0.480249i | \(0.159454\pi\) | ||||
−0.877132 | + | 0.480249i | \(0.840546\pi\) | |||||||
\(572\) | 41.5633i | 1.73785i | ||||||||
\(573\) | 49.3993i | 2.06369i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 12.1260i | − | 0.505691i | ||||||
\(576\) | 13.1968 | 0.549865 | ||||||||
\(577\) | 28.7376 | 1.19636 | 0.598180 | − | 0.801361i | \(-0.295891\pi\) | ||||
0.598180 | + | 0.801361i | \(0.295891\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.79513 | −0.323955 | ||||||||
\(580\) | −33.1880 | −1.37806 | ||||||||
\(581\) | − | 14.5723i | − | 0.604560i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 54.2692i | − | 2.24760i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 21.6743i | 0.896123i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.4178 | 1.00783 | 0.503916 | − | 0.863753i | \(-0.331892\pi\) | ||||
0.503916 | + | 0.863753i | \(0.331892\pi\) | |||||||
\(588\) | 1.14067i | 0.0470404i | ||||||||
\(589\) | − | 6.21513i | − | 0.256090i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 39.1598 | 1.61082 | ||||||||
\(592\) | 5.11322i | 0.210152i | ||||||||
\(593\) | 40.3154 | 1.65555 | 0.827777 | − | 0.561057i | \(-0.189605\pi\) | ||||
0.827777 | + | 0.561057i | \(0.189605\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.4918 | + | 4.50412i | 1.25004 | + | 0.184651i | ||||
\(596\) | 20.6308 | 0.845069 | ||||||||
\(597\) | −47.9118 | −1.96090 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.0487 | 1.10518 | 0.552590 | − | 0.833453i | \(-0.313640\pi\) | ||||
0.552590 | + | 0.833453i | \(0.313640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.47534i | 0.182553i | 0.995826 | + | 0.0912765i | \(0.0290947\pi\) | ||||
−0.995826 | + | 0.0912765i | \(0.970905\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.33006 | −0.135610 | ||||||||
\(604\) | −5.18801 | −0.211097 | ||||||||
\(605\) | 28.1019i | 1.14250i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.7942i | 1.12813i | 0.825729 | + | 0.564067i | \(0.190764\pi\) | ||||
−0.825729 | + | 0.564067i | \(0.809236\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 32.2391i | − | 1.30639i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.2441 | −0.414434 | ||||||||
\(612\) | −13.4569 | − | 1.98780i | −0.543962 | − | 0.0803519i | ||||
\(613\) | 29.5105 | 1.19192 | 0.595959 | − | 0.803015i | \(-0.296772\pi\) | ||||
0.595959 | + | 0.803015i | \(0.296772\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 69.5318i | − | 2.80379i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.1889i | 0.490705i | 0.969434 | + | 0.245353i | \(0.0789038\pi\) | ||||
−0.969434 | + | 0.245353i | \(0.921096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.64528i | − | 0.267096i | −0.991042 | − | 0.133548i | \(-0.957363\pi\) | ||
0.991042 | − | 0.133548i | \(-0.0426371\pi\) | |||||||
\(620\) | 17.9024 | 0.718976 | ||||||||
\(621\) | 10.7096 | 0.429760 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.1445i | 1.16765i | ||||||||
\(624\) | − | 39.3437i | − | 1.57501i | ||||||
\(625\) | −30.6148 | −1.22459 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.6476 | −0.784651 | ||||||||
\(628\) | 17.0580 | 0.680688 | ||||||||
\(629\) | 0.770193 | − | 5.21401i | 0.0307096 | − | 0.207896i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7750 | 0.906658 | 0.453329 | − | 0.891343i | \(-0.350236\pi\) | ||||
0.453329 | + | 0.891343i | \(0.350236\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −46.5308 | −1.84944 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 29.7139i | 1.17916i | ||||||||
\(636\) | 51.3711i | 2.03700i | ||||||||
\(637\) | 1.20651 | 0.0478035 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 5.91944i | − | 0.234170i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.7984i | − | 0.505508i | −0.967531 | − | 0.252754i | \(-0.918664\pi\) | ||
0.967531 | − | 0.252754i | \(-0.0813363\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.41863i | − | 0.292562i | −0.989243 | − | 0.146281i | \(-0.953270\pi\) | ||
0.989243 | − | 0.146281i | \(-0.0467304\pi\) | |||||||
\(644\) | −19.0904 | −0.752266 | ||||||||
\(645\) | −6.21109 | −0.244562 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.5570 | 1.83035 | 0.915173 | − | 0.403062i | \(-0.132054\pi\) | ||||
0.915173 | + | 0.403062i | \(0.132054\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.35311i | − | 0.0531142i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.3905i | 0.681588i | ||||||||
\(652\) | − | 11.6620i | − | 0.456719i | ||||||
\(653\) | 23.8506i | 0.933344i | 0.884430 | + | 0.466672i | \(0.154547\pi\) | ||||
−0.884430 | + | 0.466672i | \(0.845453\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.4850 | 1.15207 | ||||||||
\(656\) | 44.7791i | 1.74833i | ||||||||
\(657\) | − | 5.27381i | − | 0.205751i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.8053 | 0.537779 | 0.268889 | − | 0.963171i | \(-0.413343\pi\) | ||||
0.268889 | + | 0.963171i | \(0.413343\pi\) | |||||||
\(660\) | − | 56.5940i | − | 2.20292i | ||||||
\(661\) | 35.0533 | 1.36341 | 0.681707 | − | 0.731625i | \(-0.261238\pi\) | ||||
0.681707 | + | 0.731625i | \(0.261238\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.92625 | + | 40.1192i | −0.230156 | + | 1.55810i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.9512 | −0.579782 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.1880 | −0.820403 | ||||||||
\(668\) | − | 7.35579i | − | 0.284604i | ||||||
\(669\) | − | 37.9822i | − | 1.46847i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.2129 | −1.47519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 32.1392i | − | 1.23887i | −0.785046 | − | 0.619437i | \(-0.787361\pi\) | ||
0.785046 | − | 0.619437i | \(-0.212639\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.60044i | 0.369521i | ||||||||
\(676\) | −15.6146 | −0.600560 | ||||||||
\(677\) | − | 1.48699i | − | 0.0571498i | −0.999592 | − | 0.0285749i | \(-0.990903\pi\) | ||
0.999592 | − | 0.0285749i | \(-0.00909691\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.40599 | 0.207463 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.2622 | 0.431568 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 36.8723i | − | 1.41088i | −0.708769 | − | 0.705441i | \(-0.750749\pi\) | ||
0.708769 | − | 0.705441i | \(-0.249251\pi\) | |||||||
\(684\) | 6.59838 | 0.252295 | ||||||||
\(685\) | 18.9937i | 0.725713i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 52.2411i | − | 1.99312i | ||||||
\(688\) | 4.00000 | 0.152499 | ||||||||
\(689\) | 54.3362 | 2.07004 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.4274i | 1.49989i | 0.661500 | + | 0.749945i | \(0.269920\pi\) | ||||
−0.661500 | + | 0.749945i | \(0.730080\pi\) | |||||||
\(692\) | − | 42.6652i | − | 1.62189i | ||||||
\(693\) | 19.5045 | 0.740914 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.9512 | −0.794724 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.74497 | − | 45.6617i | 0.255484 | − | 1.72956i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.21580 | −0.348574 | ||||||||
\(700\) | − | 17.1133i | − | 0.646823i | ||||||
\(701\) | 30.2642 | 1.14306 | 0.571531 | − | 0.820581i | \(-0.306350\pi\) | ||||
0.571531 | + | 0.820581i | \(0.306350\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.55661i | 0.0964245i | ||||||||
\(704\) | 36.4471i | 1.37365i | ||||||||
\(705\) | 13.9488 | 0.525342 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 38.4720i | − | 1.44689i | ||||||
\(708\) | 1.28085i | 0.0481372i | ||||||||
\(709\) | − | 22.4394i | − | 0.842729i | −0.906891 | − | 0.421364i | \(-0.861551\pi\) | ||
0.906891 | − | 0.421364i | \(-0.138449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1.69010i | − | 0.0633838i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.4293 | 0.428030 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −59.8606 | −2.23866 | ||||||||
\(716\) | −23.6476 | −0.883753 | ||||||||
\(717\) | 1.81626i | 0.0678296i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 9.98975i | − | 0.372555i | −0.982497 | − | 0.186277i | \(-0.940358\pi\) | ||
0.982497 | − | 0.186277i | \(-0.0596423\pi\) | |||||||
\(720\) | 19.0063i | 0.708323i | ||||||||
\(721\) | − | 46.5342i | − | 1.73302i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.6616 | −0.433701 | ||||||||
\(724\) | − | 19.0711i | − | 0.708770i | ||||||
\(725\) | − | 18.9937i | − | 0.705409i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.5496 | −1.09593 | −0.547966 | − | 0.836500i | \(-0.684598\pi\) | ||||
−0.547966 | + | 0.836500i | \(0.684598\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.315499 | −0.0116851 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.07885 | − | 0.602510i | −0.150862 | − | 0.0222847i | ||||
\(732\) | 36.1722 | 1.33696 | ||||||||
\(733\) | −19.6894 | −0.727245 | −0.363623 | − | 0.931546i | \(-0.618460\pi\) | ||||
−0.363623 | + | 0.931546i | \(0.618460\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.64282 | −0.0605964 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 9.19702i | − | 0.338777i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.8026 | 0.691664 | 0.345832 | − | 0.938296i | \(-0.387597\pi\) | ||||
0.345832 | + | 0.938296i | \(0.387597\pi\) | |||||||
\(740\) | −7.36420 | −0.270713 | ||||||||
\(741\) | − | 19.6719i | − | 0.722664i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.6918i | 0.428931i | 0.976732 | + | 0.214466i | \(0.0688010\pi\) | ||||
−0.976732 | + | 0.214466i | \(0.931199\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.7130i | 1.08860i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.26231 | −0.338890 | ||||||||
\(748\) | 5.48993 | − | 37.1655i | 0.200732 | − | 1.35890i | ||||
\(749\) | −25.9262 | −0.947324 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 39.4562i | − | 1.43978i | −0.694089 | − | 0.719889i | \(-0.744193\pi\) | ||
0.694089 | − | 0.719889i | \(-0.255807\pi\) | |||||||
\(752\) | −8.98314 | −0.327581 | ||||||||
\(753\) | − | 11.1559i | − | 0.406545i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 7.47191i | − | 0.271931i | ||||||
\(756\) | 15.1143 | 0.549700 | ||||||||
\(757\) | −34.3521 | −1.24855 | −0.624275 | − | 0.781205i | \(-0.714605\pi\) | ||||
−0.624275 | + | 0.781205i | \(0.714605\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 36.1310i | − | 1.31147i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.0536 | −0.400693 | −0.200347 | − | 0.979725i | \(-0.564207\pi\) | ||||
−0.200347 | + | 0.979725i | \(0.564207\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −52.9186 | −1.91578 | ||||||||
\(764\) | 45.8188 | 1.65767 | ||||||||
\(765\) | 2.86287 | − | 19.3809i | 0.103507 | − | 0.700720i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.35478 | 0.0489182 | ||||||||
\(768\) | − | 34.5007i | − | 1.24494i | ||||||
\(769\) | 33.1232 | 1.19445 | 0.597227 | − | 0.802072i | \(-0.296269\pi\) | ||||
0.597227 | + | 0.802072i | \(0.296269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 11.6569i | − | 0.419813i | ||||||
\(772\) | 7.23013i | 0.260218i | ||||||||
\(773\) | −9.89756 | −0.355991 | −0.177995 | − | 0.984031i | \(-0.556961\pi\) | ||||
−0.177995 | + | 0.984031i | \(0.556961\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.2456i | 0.368034i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 7.15364i | − | 0.256636i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.3895i | 0.802189i | ||||||||
\(780\) | 56.6638 | 2.02889 | ||||||||
\(781\) | 16.3484 | 0.584993 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.7750 | 0.599489 | ||||||||
\(784\) | 1.05799 | 0.0377854 | ||||||||
\(785\) | 24.5674i | 0.876847i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 32.4485i | − | 1.15666i | −0.815801 | − | 0.578332i | \(-0.803704\pi\) | ||
0.815801 | − | 0.578332i | \(-0.196296\pi\) | |||||||
\(788\) | − | 36.3214i | − | 1.29390i | ||||||
\(789\) | 59.7754i | 2.12806i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0094 | 0.640341 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 38.2601i | − | 1.35865i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −73.9860 | −2.62401 | ||||||||
\(796\) | 44.4391i | 1.57510i | ||||||||
\(797\) | −14.3666 | −0.508891 | −0.254446 | − | 0.967087i | \(-0.581893\pi\) | ||||
−0.254446 | + | 0.967087i | \(0.581893\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.16021 | + | 1.35311i | 0.324065 | + | 0.0478695i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.5246 | 0.654535 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.5653 | 0.513999 | ||||||||
\(804\) | 8.70587i | 0.307032i | ||||||||
\(805\) | − | 27.4945i | − | 0.969052i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.6102 | 0.479102 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.3848i | 1.73628i | 0.496322 | + | 0.868139i | \(0.334684\pi\) | ||||
−0.496322 | + | 0.868139i | \(0.665316\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.7120i | 0.551722i | 0.961197 | + | 0.275861i | \(0.0889630\pi\) | ||||
−0.961197 | + | 0.275861i | \(0.911037\pi\) | |||||||
\(812\) | −29.9024 | −1.04937 | ||||||||
\(813\) | 23.9143i | 0.838713i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.7959 | 0.588335 | ||||||||
\(816\) | −5.19675 | + | 35.1807i | −0.181923 | + | 1.23157i | ||||
\(817\) | 2.00000 | 0.0699711 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 19.5285i | 0.682382i | ||||||||
\(820\) | −64.4920 | −2.25216 | ||||||||
\(821\) | − | 33.2443i | − | 1.16023i | −0.814533 | − | 0.580117i | \(-0.803007\pi\) | ||
0.814533 | − | 0.580117i | \(-0.196993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.3444i | 1.30175i | 0.759187 | + | 0.650873i | \(0.225597\pi\) | ||||
−0.759187 | + | 0.650873i | \(0.774403\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 32.3891 | 1.12764 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.6157i | 0.716878i | 0.933553 | + | 0.358439i | \(0.116691\pi\) | ||||
−0.933553 | + | 0.358439i | \(0.883309\pi\) | |||||||
\(828\) | 12.1341i | 0.421688i | ||||||||
\(829\) | −38.5570 | −1.33914 | −0.669570 | − | 0.742749i | \(-0.733522\pi\) | ||||
−0.669570 | + | 0.742749i | \(0.733522\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.7194 | 1.27378 | ||||||||
\(832\) | −36.4920 | −1.26513 | ||||||||
\(833\) | −1.07885 | − | 0.159363i | −0.0373798 | − | 0.00552159i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5940 | 0.366621 | ||||||||
\(836\) | 18.2235i | 0.630274i | ||||||||
\(837\) | −9.04882 | −0.312773 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.8034i | 0.580117i | 0.957009 | + | 0.290058i | \(0.0936747\pi\) | ||||
−0.957009 | + | 0.290058i | \(0.906325\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.18801 | −0.144414 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.67295i | 0.195387i | ||||||||
\(844\) | 43.1582i | 1.48557i | ||||||||
\(845\) | − | 22.4885i | − | 0.773628i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.3198i | 0.869998i | ||||||||
\(848\) | 47.6476 | 1.63623 | ||||||||
\(849\) | 52.9505 | 1.81726 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.70148 | −0.161165 | ||||||||
\(852\) | −15.4754 | −0.530178 | ||||||||
\(853\) | − | 5.48523i | − | 0.187811i | −0.995581 | − | 0.0939053i | \(-0.970065\pi\) | ||
0.995581 | − | 0.0939053i | \(-0.0299351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.50315i | 0.325001i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 51.6338i | 1.76378i | 0.471459 | + | 0.881888i | \(0.343728\pi\) | ||||
−0.471459 | + | 0.881888i | \(0.656272\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.9836 | 1.94425 | 0.972127 | − | 0.234454i | \(-0.0753302\pi\) | ||||
0.972127 | + | 0.234454i | \(0.0753302\pi\) | |||||||
\(860\) | 5.76090i | 0.196445i | ||||||||
\(861\) | − | 62.6481i | − | 2.13504i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.1392 | 1.16211 | 0.581056 | − | 0.813864i | \(-0.302640\pi\) | ||||
0.581056 | + | 0.813864i | \(0.302640\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 61.4476 | 2.08928 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.5984 | − | 35.0914i | 0.359940 | − | 1.19177i | ||||
\(868\) | 16.1300 | 0.547489 | ||||||||
\(869\) | 4.66776 | 0.158343 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.20836 | 0.312013 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.43612i | − | 0.116295i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.7309 | −0.430383 | ||||||||
\(876\) | −13.7875 | −0.465836 | ||||||||
\(877\) | − | 2.60006i | − | 0.0877979i | −0.999036 | − | 0.0438989i | \(-0.986022\pi\) | ||
0.999036 | − | 0.0438989i | \(-0.0139780\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 59.2400i | 1.99811i | ||||||||
\(880\) | −52.4920 | −1.76951 | ||||||||
\(881\) | 44.6678i | 1.50490i | 0.658650 | + | 0.752449i | \(0.271128\pi\) | ||||
−0.658650 | + | 0.752449i | \(0.728872\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.98806 | −0.302472 | −0.151236 | − | 0.988498i | \(-0.548325\pi\) | ||||
−0.151236 | + | 0.988498i | \(0.548325\pi\) | |||||||
\(884\) | 37.2113 | + | 5.49670i | 1.25155 | + | 0.184874i | ||||
\(885\) | −1.84471 | −0.0620093 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 22.0946i | − | 0.741863i | −0.928660 | − | 0.370932i | \(-0.879038\pi\) | ||
0.928660 | − | 0.370932i | \(-0.120962\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.7722i | 0.897911i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 51.1517i | 1.71365i | ||||||||
\(892\) | −35.2291 | −1.17956 | ||||||||
\(893\) | −4.49157 | −0.150305 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 34.0579i | − | 1.13843i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 36.1755 | 1.20787 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.9024 | 0.597077 | ||||||||
\(900\) | −10.8774 | −0.362581 | ||||||||
\(901\) | −48.5868 | − | 7.17705i | −1.61866 | − | 0.239102i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.59619 | −0.186230 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.4666 | 0.913022 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 19.1868i | − | 0.637086i | −0.947908 | − | 0.318543i | \(-0.896806\pi\) | ||
0.947908 | − | 0.318543i | \(-0.103194\pi\) | |||||||
\(908\) | − | 10.4459i | − | 0.346659i | ||||||
\(909\) | −24.4533 | −0.811064 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 7.04646i | − | 0.233460i | −0.993164 | − | 0.116730i | \(-0.962759\pi\) | ||
0.993164 | − | 0.116730i | \(-0.0372412\pi\) | |||||||
\(912\) | − | 17.2503i | − | 0.571216i | ||||||
\(913\) | − | 25.5808i | − | 0.846602i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 52.0962i | 1.72225i | ||||||||
\(916\) | −48.4546 | −1.60098 | ||||||||
\(917\) | 26.5660 | 0.877286 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.4593 | 0.938785 | 0.469393 | − | 0.882990i | \(-0.344473\pi\) | ||||
0.469393 | + | 0.882990i | \(0.344473\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 7.52884i | − | 0.248084i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.3686i | 0.538779i | ||||||||
\(924\) | − | 50.9912i | − | 1.67749i | ||||||
\(925\) | − | 4.21458i | − | 0.138574i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.5777 | −0.971459 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 14.8727i | − | 0.487956i | −0.969781 | − | 0.243978i | \(-0.921547\pi\) | ||
0.969781 | − | 0.243978i | \(-0.0784525\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.528996 | 0.0173371 | ||||||||
\(932\) | 8.54782i | 0.279993i | ||||||||
\(933\) | 50.2791 | 1.64606 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 53.5267 | + | 7.90674i | 1.75051 | + | 0.258578i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.51214 | −0.180074 | −0.0900368 | − | 0.995938i | \(-0.528698\pi\) | ||||
−0.0900368 | + | 0.995938i | \(0.528698\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.13734 | 0.135017 | ||||||||
\(940\) | − | 12.9378i | − | 0.421983i | ||||||
\(941\) | − | 5.45173i | − | 0.177721i | −0.996044 | − | 0.0888607i | \(-0.971677\pi\) | ||
0.996044 | − | 0.0888607i | \(-0.0283226\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.1732 | −1.34078 | ||||||||
\(944\) | 1.18801 | 0.0386664 | ||||||||
\(945\) | 21.7679i | 0.708111i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.42303i | 0.0787380i | 0.999225 | + | 0.0393690i | \(0.0125348\pi\) | ||||
−0.999225 | + | 0.0393690i | \(0.987465\pi\) | |||||||
\(948\) | −4.41848 | −0.143506 | ||||||||
\(949\) | 14.5833i | 0.473393i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34.8037 | −1.12859 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.41782 | 0.207894 | 0.103947 | − | 0.994583i | \(-0.466853\pi\) | ||||
0.103947 | + | 0.994583i | \(0.466853\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 65.9894i | 2.13537i | ||||||||
\(956\) | 1.68462 | 0.0544844 | ||||||||
\(957\) | − | 56.5940i | − | 1.82943i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.1133i | 0.552618i | ||||||||
\(960\) | 49.6888 | 1.60370 | ||||||||
\(961\) | 21.3431 | 0.688486 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.4790i | 0.531029i | ||||||||
\(964\) | 10.8164i | 0.348372i | ||||||||
\(965\) | −10.4130 | −0.335207 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.5294 | −1.27118 | −0.635590 | − | 0.772026i | \(-0.719243\pi\) | ||||
−0.635590 | + | 0.772026i | \(0.719243\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.59838 | + | 17.5904i | −0.0834719 | + | 0.565084i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.2761 | 0.426050 | 0.213025 | − | 0.977047i | \(-0.431668\pi\) | ||||
0.213025 | + | 0.977047i | \(0.431668\pi\) | |||||||
\(972\) | − | 30.9488i | − | 0.992685i | ||||||
\(973\) | −18.8770 | −0.605169 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 32.4291i | 1.03856i | ||||||||
\(976\) | − | 33.5504i | − | 1.07392i | ||||||
\(977\) | −46.4849 | −1.48718 | −0.743592 | − | 0.668634i | \(-0.766879\pi\) | ||||
−0.743592 | + | 0.668634i | \(0.766879\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 51.1617i | 1.63513i | ||||||||
\(980\) | 1.52375i | 0.0486743i | ||||||||
\(981\) | 33.6357i | 1.07390i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.51722i | − | 0.0802869i | −0.999194 | − | 0.0401434i | \(-0.987219\pi\) | ||
0.999194 | − | 0.0401434i | \(-0.0127815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.3110 | 1.66677 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.5678 | 0.400039 | ||||||||
\(988\) | −18.2460 | −0.580483 | ||||||||
\(989\) | 3.67790i | 0.116950i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 41.0343i | − | 1.30350i | −0.758435 | − | 0.651749i | \(-0.774036\pi\) | ||
0.758435 | − | 0.651749i | \(-0.225964\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42.2947i | 1.34218i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −64.0023 | −2.02901 | ||||||||
\(996\) | 24.2147i | 0.767273i | ||||||||
\(997\) | 15.0255i | 0.475863i | 0.971282 | + | 0.237932i | \(0.0764695\pi\) | ||||
−0.971282 | + | 0.237932i | \(0.923531\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.72226 | 0.117767 |
(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 | 731.2.d.b.560.2 | ✓ | 8 | |
17.16 | even | 2 | inner | 731.2.d.b.560.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.d.b.560.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
731.2.d.b.560.7 | yes | 8 | 17.16 | even | 2 | inner |