Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1932,2,Mod(1609,1932)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1932, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1932.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1932.k (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: | \(15.4270976705\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.14 | ||
Character | \(\chi\) | \(=\) | 1932.1609 |
Dual form | 1932.2.k.a.1609.16 |
$q$-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 \(\left(\mathbb{Z}/1932\mathbb{Z}\right)^\times\).
\(n\) | \(829\) | \(925\) | \(967\) | \(1289\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 1.41621 | 0.633346 | 0.316673 | − | 0.948535i | \(-0.397434\pi\) | ||||
0.316673 | + | 0.948535i | \(0.397434\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.53101 | + | 0.770692i | 0.956633 | + | 0.291294i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.81567i | − | 1.15047i | −0.817989 | − | 0.575234i | \(-0.804911\pi\) | ||
0.817989 | − | 0.575234i | \(-0.195089\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.45743i | − | 1.79097i | −0.445093 | − | 0.895484i | \(-0.646829\pi\) | ||
0.445093 | − | 0.895484i | \(-0.353171\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.41621i | − | 0.365663i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.92234 | −0.951306 | −0.475653 | − | 0.879633i | \(-0.657788\pi\) | ||||
−0.475653 | + | 0.879633i | \(0.657788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.414030 | −0.0949849 | −0.0474925 | − | 0.998872i | \(-0.515123\pi\) | ||||
−0.0474925 | + | 0.998872i | \(0.515123\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.770692 | − | 2.53101i | 0.168179 | − | 0.552313i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.75626 | − | 0.614837i | −0.991748 | − | 0.128202i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.99436 | −0.598873 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.316832 | 0.0588342 | 0.0294171 | − | 0.999567i | \(-0.490635\pi\) | ||||
0.0294171 | + | 0.999567i | \(0.490635\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.348692i | − | 0.0626269i | −0.999510 | − | 0.0313134i | \(-0.990031\pi\) | ||
0.999510 | − | 0.0313134i | \(-0.00996901\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.81567 | −0.664223 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.58444 | + | 1.09146i | 0.605880 | + | 0.184490i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.720567i | − | 0.118460i | −0.998244 | − | 0.0592302i | \(-0.981135\pi\) | ||
0.998244 | − | 0.0592302i | \(-0.0188646\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.45743 | −1.03402 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.82254i | 0.284633i | 0.989821 | + | 0.142317i | \(0.0454551\pi\) | ||||
−0.989821 | + | 0.142317i | \(0.954545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.25316i | − | 1.25859i | −0.777165 | − | 0.629297i | \(-0.783343\pi\) | ||
0.777165 | − | 0.629297i | \(-0.216657\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.41621 | −0.211115 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.93692i | 0.574258i | 0.957892 | + | 0.287129i | \(0.0927009\pi\) | ||||
−0.957892 | + | 0.287129i | \(0.907299\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.81207 | + | 3.90127i | 0.830295 | + | 0.557324i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.92234i | 0.549237i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.37616i | − | 1.01319i | −0.862183 | − | 0.506597i | \(-0.830903\pi\) | ||
0.862183 | − | 0.506597i | \(-0.169097\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.40378i | − | 0.728645i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.414030i | 0.0548396i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.43153i | 0.707125i | 0.935411 | + | 0.353562i | \(0.115030\pi\) | ||||
−0.935411 | + | 0.353562i | \(0.884970\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2869 | 1.44514 | 0.722570 | − | 0.691297i | \(-0.242961\pi\) | ||||
0.722570 | + | 0.691297i | \(0.242961\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.53101 | − | 0.770692i | −0.318878 | − | 0.0970981i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 9.14504i | − | 1.13430i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.0521i | − | 1.22806i | −0.789281 | − | 0.614032i | \(-0.789546\pi\) | ||
0.789281 | − | 0.614032i | \(-0.210454\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.614837 | + | 4.75626i | −0.0740177 | + | 0.572586i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9485 | 1.29934 | 0.649671 | − | 0.760215i | \(-0.274907\pi\) | ||||
0.649671 | + | 0.760215i | \(0.274907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7376i | 1.72491i | 0.506137 | + | 0.862453i | \(0.331073\pi\) | ||||
−0.506137 | + | 0.862453i | \(0.668927\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.99436i | 0.345759i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.94071 | − | 9.65752i | 0.335125 | − | 1.10058i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.54134i | − | 0.510940i | −0.966817 | − | 0.255470i | \(-0.917770\pi\) | ||
0.966817 | − | 0.255470i | \(-0.0822302\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.2420 | −1.23397 | −0.616983 | − | 0.786976i | \(-0.711645\pi\) | ||||
−0.616983 | + | 0.786976i | \(0.711645\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.55483 | −0.602506 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 0.316832i | − | 0.0339679i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.10525 | 0.647155 | 0.323578 | − | 0.946202i | \(-0.395114\pi\) | ||||
0.323578 | + | 0.946202i | \(0.395114\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.97669 | − | 16.3438i | 0.521699 | − | 1.71330i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.348692 | −0.0361576 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.586351 | −0.0601583 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.25498 | 0.635097 | 0.317549 | − | 0.948242i | \(-0.397140\pi\) | ||||
0.317549 | + | 0.948242i | \(0.397140\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.81567i | 0.383490i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.90949i | − | 0.886527i | −0.896391 | − | 0.443264i | \(-0.853821\pi\) | ||
0.896391 | − | 0.443264i | \(-0.146179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.4353 | −1.32382 | −0.661908 | − | 0.749585i | \(-0.730253\pi\) | ||||
−0.661908 | + | 0.749585i | \(0.730253\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.09146 | − | 3.58444i | 0.106515 | − | 0.349805i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.502808i | − | 0.0486083i | −0.999705 | − | 0.0243042i | \(-0.992263\pi\) | ||
0.999705 | − | 0.0243042i | \(-0.00773702\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.88249i | − | 0.371875i | −0.982562 | − | 0.185938i | \(-0.940468\pi\) | ||
0.982562 | − | 0.185938i | \(-0.0595323\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.720567 | −0.0683932 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.9492i | 1.12409i | 0.827108 | + | 0.562043i | \(0.189984\pi\) | ||||
−0.827108 | + | 0.562043i | \(0.810016\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.73583 | − | 0.870735i | −0.628120 | − | 0.0811965i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.45743i | 0.596989i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.92749 | − | 3.02292i | −0.910052 | − | 0.277110i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.55936 | −0.323578 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.82254 | 0.164333 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.3217 | −1.01264 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.57622 | 0.228602 | 0.114301 | − | 0.993446i | \(-0.463537\pi\) | ||||
0.114301 | + | 0.993446i | \(0.463537\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.25316 | −0.726650 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.76384i | 0.241478i | 0.992684 | + | 0.120739i | \(0.0385264\pi\) | ||||
−0.992684 | + | 0.120739i | \(0.961474\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.04792 | − | 0.319090i | −0.0908658 | − | 0.0276686i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.41621i | 0.121888i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 0.0166810i | − | 0.00142515i | −1.00000 | 0.000712577i | \(-0.999773\pi\) | |||
1.00000 | 0.000712577i | \(-0.000226820\pi\) | ||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.74742i | − | 0.826765i | −0.910557 | − | 0.413383i | \(-0.864347\pi\) | ||
0.910557 | − | 0.413383i | \(-0.135653\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.93692 | 0.331548 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −24.6394 | −2.06045 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.448699 | 0.0372624 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.90127 | − | 5.81207i | 0.321771 | − | 0.479371i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.75818i | 0.225959i | 0.993597 | + | 0.112980i | \(0.0360395\pi\) | ||||
−0.993597 | + | 0.112980i | \(0.963961\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.6689 | −1.19373 | −0.596867 | − | 0.802340i | \(-0.703588\pi\) | ||||
−0.596867 | + | 0.802340i | \(0.703588\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.92234 | 0.317102 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 0.493819i | − | 0.0396645i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.3297 | 1.70230 | 0.851148 | − | 0.524926i | \(-0.175907\pi\) | ||||
0.851148 | + | 0.524926i | \(0.175907\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.37616 | −0.584968 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.5643 | − | 5.22177i | −0.911395 | − | 0.411533i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6971 | 1.38615 | 0.693073 | − | 0.720867i | \(-0.256256\pi\) | ||||
0.693073 | + | 0.720867i | \(0.256256\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.40378 | −0.420683 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.34633i | − | 0.258947i | −0.991583 | − | 0.129473i | \(-0.958671\pi\) | ||
0.991583 | − | 0.129473i | \(-0.0413287\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −28.6984 | −2.20757 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.414030 | 0.0316616 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.1048i | 0.844286i | 0.906529 | + | 0.422143i | \(0.138722\pi\) | ||||
−0.906529 | + | 0.422143i | \(0.861278\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.57878 | − | 2.30773i | −0.572902 | − | 0.174448i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.43153 | 0.408259 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.4752 | −1.30616 | −0.653078 | − | 0.757290i | \(-0.726523\pi\) | ||||
−0.653078 | + | 0.757290i | \(0.726523\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8079 | 0.952005 | 0.476002 | − | 0.879444i | \(-0.342085\pi\) | ||||
0.476002 | + | 0.879444i | \(0.342085\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 11.2869i | − | 0.834352i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.02047i | − | 0.0750265i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.9664i | 1.09445i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.770692 | + | 2.53101i | −0.0560596 | + | 0.184104i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 24.8388i | − | 1.79727i | −0.438697 | − | 0.898635i | \(-0.644560\pi\) | ||
0.438697 | − | 0.898635i | \(-0.355440\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.14938 | 0.658587 | 0.329294 | − | 0.944228i | \(-0.393189\pi\) | ||||
0.329294 | + | 0.944228i | \(0.393189\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.14504 | −0.654890 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.5979 | −0.826317 | −0.413158 | − | 0.910659i | \(-0.635574\pi\) | ||||
−0.413158 | + | 0.910659i | \(0.635574\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.5243 | 1.17138 | 0.585690 | − | 0.810535i | \(-0.300824\pi\) | ||||
0.585690 | + | 0.810535i | \(0.300824\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.0521 | −0.709023 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.801906 | + | 0.244180i | 0.0562828 | + | 0.0171381i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.58109i | 0.180271i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.75626 | + | 0.614837i | 0.330583 | + | 0.0427341i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.57980i | 0.109277i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.78310 | 0.398125 | 0.199063 | − | 0.979987i | \(-0.436210\pi\) | ||||
0.199063 | + | 0.979987i | \(0.436210\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 10.9485i | − | 0.750176i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 11.6882i | − | 0.797126i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.268734 | − | 0.882544i | 0.0182429 | − | 0.0599110i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.7376 | 0.995875 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.3282i | 1.70376i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 18.2037i | − | 1.21901i | −0.792781 | − | 0.609506i | \(-0.791368\pi\) | ||
0.792781 | − | 0.609506i | \(-0.208632\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.99436 | 0.199624 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.39741 | 0.490983 | 0.245492 | − | 0.969399i | \(-0.421051\pi\) | ||||
0.245492 | + | 0.969399i | \(0.421051\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.8540 | 0.915501 | 0.457751 | − | 0.889081i | \(-0.348655\pi\) | ||||
0.457751 | + | 0.889081i | \(0.348655\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.65752 | − | 2.94071i | −0.635418 | − | 0.193485i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 30.0698 | 1.96994 | 0.984968 | − | 0.172737i | \(-0.0552611\pi\) | ||||
0.984968 | + | 0.172737i | \(0.0552611\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.57548i | 0.363704i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.54134 | −0.294991 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.45467 | −0.417518 | −0.208759 | − | 0.977967i | \(-0.566942\pi\) | ||||
−0.208759 | + | 0.977967i | \(0.566942\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.1500 | 1.23356 | 0.616779 | − | 0.787137i | \(-0.288437\pi\) | ||||
0.616779 | + | 0.787137i | \(0.288437\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.23108 | + | 5.52499i | 0.525864 | + | 0.352979i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.67357i | 0.170115i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.2420i | 0.712431i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.3278 | 1.28308 | 0.641540 | − | 0.767090i | \(-0.278296\pi\) | ||||
0.641540 | + | 0.767090i | \(0.278296\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.34602 | + | 18.1483i | −0.147493 | + | 1.14098i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.55483i | 0.347857i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.5661i | 1.15812i | 0.815285 | + | 0.579060i | \(0.196580\pi\) | ||||
−0.815285 | + | 0.579060i | \(0.803420\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.555335 | − | 1.82376i | 0.0345069 | − | 0.113323i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.316832 | −0.0196114 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 24.8672i | − | 1.53338i | −0.642020 | − | 0.766688i | \(-0.721903\pi\) | ||
0.642020 | − | 0.766688i | \(-0.278097\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10.4462i | − | 0.641702i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.10525i | − | 0.373635i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 11.8372i | − | 0.721726i | −0.932619 | − | 0.360863i | \(-0.882482\pi\) | ||
0.932619 | − | 0.360863i | \(-0.117518\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.9783i | 1.03136i | 0.856782 | + | 0.515678i | \(0.172460\pi\) | ||||
−0.856782 | + | 0.515678i | \(0.827540\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.3438 | − | 4.97669i | −0.989174 | − | 0.301203i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.4255i | 0.688984i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.2648 | 1.27768 | 0.638838 | − | 0.769341i | \(-0.279415\pi\) | ||||
0.638838 | + | 0.769341i | \(0.279415\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.348692i | 0.0208756i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.40757i | 0.203278i | 0.994821 | + | 0.101639i | \(0.0324087\pi\) | ||||
−0.994821 | + | 0.101639i | \(0.967591\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.95787 | 0.532490 | 0.266245 | − | 0.963905i | \(-0.414217\pi\) | ||||
0.266245 | + | 0.963905i | \(0.414217\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.586351i | 0.0347324i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.40462 | + | 4.61288i | −0.0829121 | + | 0.272290i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.61527 | −0.0950162 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 6.25498i | − | 0.366674i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.8886 | −1.51243 | −0.756215 | − | 0.654324i | \(-0.772953\pi\) | ||||
−0.756215 | + | 0.654324i | \(0.772953\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.69216i | 0.447855i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.81567 | 0.221408 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.97027 | + | 30.7132i | −0.229606 | + | 1.77619i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.36064 | − | 20.8889i | 0.366621 | − | 1.20401i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.90949 | −0.511837 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.9846 | 0.915274 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.4476i | − | 0.596275i | −0.954523 | − | 0.298138i | \(-0.903635\pi\) | ||
0.954523 | − | 0.298138i | \(-0.0963654\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.4353i | 0.764306i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.2923i | 1.83113i | 0.402169 | + | 0.915565i | \(0.368256\pi\) | ||||
−0.402169 | + | 0.915565i | \(0.631744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.9154 | 0.786543 | 0.393271 | − | 0.919422i | \(-0.371343\pi\) | ||||
0.393271 | + | 0.919422i | \(0.371343\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.58444 | − | 1.09146i | −0.201960 | − | 0.0614967i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.23595 | 0.350246 | 0.175123 | − | 0.984547i | \(-0.443968\pi\) | ||||
0.175123 | + | 0.984547i | \(0.443968\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.20893i | − | 0.0676869i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.502808 | −0.0280640 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.62396 | 0.0903598 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.3359i | 1.07256i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.88249 | −0.214702 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.03415 | + | 9.96439i | −0.167278 | + | 0.549355i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.22381 | 0.122232 | 0.0611158 | − | 0.998131i | \(-0.480534\pi\) | ||||
0.0611158 | + | 0.998131i | \(0.480534\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.720567i | 0.0394868i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 14.2359i | − | 0.777790i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.25545i | 0.0683886i | 0.999415 | + | 0.0341943i | \(0.0108865\pi\) | ||||
−0.999415 | + | 0.0341943i | \(0.989113\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.9492 | 0.648991 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.33049 | −0.0720503 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.7037 | + | 14.3535i | 0.631943 | + | 0.775015i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.870735 | + | 6.73583i | −0.0468788 | + | 0.362645i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.4606 | −1.52784 | −0.763922 | − | 0.645309i | \(-0.776729\pi\) | ||||
−0.763922 | + | 0.645309i | \(0.776729\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.65625i | − | 0.142186i | −0.997470 | − | 0.0710928i | \(-0.977351\pi\) | ||
0.997470 | − | 0.0710928i | \(-0.0226487\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.45743 | 0.344672 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.69144i | 0.409374i | 0.978827 | + | 0.204687i | \(0.0656176\pi\) | ||||
−0.978827 | + | 0.204687i | \(0.934382\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.5053 | 0.822934 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.02292 | + | 9.92749i | −0.159990 | + | 0.525418i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.8134i | 1.62627i | 0.582077 | + | 0.813134i | \(0.302240\pi\) | ||||
−0.582077 | + | 0.813134i | \(0.697760\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8286 | −0.990978 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.55936i | 0.186818i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.8715i | 1.09246i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.2628 | −0.640111 | −0.320056 | − | 0.947399i | \(-0.603702\pi\) | ||||
−0.320056 | + | 0.947399i | \(0.603702\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.82254i | − | 0.0948777i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.68475 | − | 18.6692i | 0.295138 | − | 0.969255i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.25466i | 0.272076i | 0.990704 | + | 0.136038i | \(0.0434369\pi\) | ||||
−0.990704 | + | 0.136038i | \(0.956563\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.3217i | 0.584648i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.04592i | − | 0.105370i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 27.3170i | − | 1.40318i | −0.712582 | − | 0.701589i | \(-0.752474\pi\) | ||
0.712582 | − | 0.701589i | \(-0.247526\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 2.57622i | − | 0.131984i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.25226 | 0.268378 | 0.134189 | − | 0.990956i | \(-0.457157\pi\) | ||||
0.134189 | + | 0.990956i | \(0.457157\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.16465 | − | 13.6770i | 0.212250 | − | 0.697046i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.25316i | 0.419531i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.6799i | 1.65694i | 0.560036 | + | 0.828469i | \(0.310787\pi\) | ||||
−0.560036 | + | 0.828469i | \(0.689213\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.6556 | + | 2.41160i | 0.943456 | + | 0.121960i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.76384 | 0.139417 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 6.43146i | − | 0.323602i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.6473i | 0.835502i | 0.908561 | + | 0.417751i | \(0.137182\pi\) | ||||
−0.908561 | + | 0.417751i | \(0.862818\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.319090 | + | 1.04792i | −0.0159745 | + | 0.0524614i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10.6081i | − | 0.529743i | −0.964284 | − | 0.264871i | \(-0.914670\pi\) | ||
0.964284 | − | 0.264871i | \(-0.0853295\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.25165 | −0.112163 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.41621 | 0.0703718 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.74945 | −0.136285 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 27.2050i | − | 1.34520i | −0.740006 | − | 0.672600i | \(-0.765177\pi\) | ||
0.740006 | − | 0.672600i | \(-0.234823\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0166810 | −0.000822814 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.18604 | + | 13.7473i | −0.205982 | + | 0.676459i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.9209 | −0.781528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.74742 | −0.477333 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.3426 | 1.09151 | 0.545753 | − | 0.837946i | \(-0.316244\pi\) | ||||
0.545753 | + | 0.837946i | \(0.316244\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.38171i | − | 0.116078i | −0.998314 | − | 0.0580388i | \(-0.981515\pi\) | ||
0.998314 | − | 0.0580388i | \(-0.0184847\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.93692i | − | 0.191419i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.7449 | 0.569711 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.5673 | + | 8.69874i | 1.38247 | + | 0.420961i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.6394i | 1.18960i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 7.36006i | − | 0.354521i | −0.984164 | − | 0.177261i | \(-0.943276\pi\) | ||
0.984164 | − | 0.177261i | \(-0.0567236\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3355 | 0.929207 | 0.464604 | − | 0.885519i | \(-0.346197\pi\) | ||||
0.464604 | + | 0.885519i | \(0.346197\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 0.448699i | − | 0.0215135i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.96923 | + | 0.254561i | 0.0942011 | + | 0.0121773i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.31909i | − | 0.110684i | −0.998467 | − | 0.0553420i | \(-0.982375\pi\) | ||
0.998467 | − | 0.0553420i | \(-0.0176249\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.81207 | − | 3.90127i | −0.276765 | − | 0.185775i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.4269 | −1.30309 | −0.651545 | − | 0.758610i | \(-0.725879\pi\) | ||||
−0.651545 | + | 0.758610i | \(0.725879\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.64629 | 0.409873 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.75818 | 0.130458 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.19492 | 0.433935 | 0.216968 | − | 0.976179i | \(-0.430383\pi\) | ||||
0.216968 | + | 0.976179i | \(0.430383\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.95422 | 0.327462 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.6689i | 0.689203i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.04802 | − | 23.1462i | 0.330416 | − | 1.08511i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.93551i | 0.371207i | 0.982625 | + | 0.185604i | \(0.0594241\pi\) | ||||
−0.982625 | + | 0.185604i | \(0.940576\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 3.92234i | − | 0.183079i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 25.2115i | − | 1.17422i | −0.809508 | − | 0.587108i | \(-0.800266\pi\) | ||
0.809508 | − | 0.587108i | \(-0.199734\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.9267 | −0.507807 | −0.253904 | − | 0.967230i | \(-0.581715\pi\) | ||||
−0.253904 | + | 0.967230i | \(0.581715\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.493819 | −0.0229003 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.7340 | −1.28337 | −0.641687 | − | 0.766966i | \(-0.721765\pi\) | ||||
−0.641687 | + | 0.766966i | \(0.721765\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.74711 | − | 25.4421i | 0.357728 | − | 1.17481i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 21.3297i | − | 0.982821i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.4913 | −1.44797 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.23976 | 0.0568839 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.37616i | 0.337731i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.79293 | 0.310377 | 0.155188 | − | 0.987885i | \(-0.450402\pi\) | ||||
0.155188 | + | 0.987885i | \(0.450402\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.65301 | −0.212159 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.22177 | + | 11.5643i | −0.237599 | + | 0.526194i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.85834 | 0.402237 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.7910 | 1.89373 | 0.946866 | − | 0.321628i | \(-0.104230\pi\) | ||||
0.946866 | + | 0.321628i | \(0.104230\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 17.6971i | − | 0.800292i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.3317 | 1.36885 | 0.684426 | − | 0.729082i | \(-0.260053\pi\) | ||||
0.684426 | + | 0.729082i | \(0.260053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.24272 | −0.0559693 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.40378i | 0.242882i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.7107 | + | 8.43789i | 1.24299 | + | 0.378491i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.93356 | −0.176091 | −0.0880453 | − | 0.996116i | \(-0.528062\pi\) | ||||
−0.0880453 | + | 0.996116i | \(0.528062\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.34633 | −0.149503 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.9395 | −0.576945 | −0.288472 | − | 0.957488i | \(-0.593147\pi\) | ||||
−0.288472 | + | 0.957488i | \(0.593147\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 12.6177i | − | 0.561478i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.6984i | 1.27454i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.5446i | 1.04360i | 0.853068 | + | 0.521799i | \(0.174739\pi\) | ||||
−0.853068 | + | 0.521799i | \(0.825261\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3582 | + | 37.3011i | −0.502456 | + | 1.65010i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 0.414030i | − | 0.0182799i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.0271 | −0.838434 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.0220 | 0.660666 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.1048 | 0.487449 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.0306 | −0.877555 | −0.438778 | − | 0.898596i | \(-0.644588\pi\) | ||||
−0.438778 | + | 0.898596i | \(0.644588\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.82214 | 0.298311 | 0.149156 | − | 0.988814i | \(-0.452344\pi\) | ||||
0.149156 | + | 0.988814i | \(0.452344\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.30773 | + | 7.57878i | −0.100718 | + | 0.330765i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.36769i | 0.0595773i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.2440 | + | 5.84865i | 0.967128 | + | 0.254289i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 5.43153i | − | 0.235708i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.7689 | 0.509769 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 0.712080i | − | 0.0307859i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.4752i | 0.754110i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.8860 | − | 22.1769i | 0.641184 | − | 0.955229i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.9600 | −0.686174 | −0.343087 | − | 0.939304i | \(-0.611473\pi\) | ||||
−0.343087 | + | 0.939304i | \(0.611473\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 12.8079i | − | 0.549640i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 5.49841i | − | 0.235526i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.8572 | −0.849033 | −0.424517 | − | 0.905420i | \(-0.639556\pi\) | ||||
−0.424517 | + | 0.905420i | \(0.639556\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.2869 | −0.481714 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.131178 | −0.00558836 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.49997 | − | 11.4942i | 0.148834 | − | 0.488782i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.02047 | −0.0433166 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.8239i | 1.26368i | 0.775100 | + | 0.631839i | \(0.217699\pi\) | ||||
−0.775100 | + | 0.631839i | \(0.782301\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −53.2942 | −2.25410 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.9664 | 0.631880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.5948 | −1.16298 | −0.581492 | − | 0.813552i | \(-0.697531\pi\) | ||||
−0.581492 | + | 0.813552i | \(0.697531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.9225i | 0.711935i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.53101 | + | 0.770692i | 0.106293 | + | 0.0323660i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.8982i | 1.33724i | 0.743603 | + | 0.668622i | \(0.233116\pi\) | ||||
−0.743603 | + | 0.668622i | \(0.766884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.17986i | 0.0493757i | 0.999695 | + | 0.0246878i | \(0.00785918\pi\) | ||||
−0.999695 | + | 0.0246878i | \(0.992141\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.8388 | −1.03765 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.2420 | + | 1.84105i | 0.593931 | + | 0.0767769i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 17.7282i | − | 0.738033i | −0.929423 | − | 0.369017i | \(-0.879695\pi\) | ||
0.929423 | − | 0.369017i | \(-0.120305\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 9.14938i | − | 0.380235i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.4536 | − | 8.66410i | −1.18045 | − | 0.359448i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.1450 | −1.16565 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.14504i | 0.378101i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 14.3682i | − | 0.593039i | −0.955027 | − | 0.296520i | \(-0.904174\pi\) | ||
0.955027 | − | 0.296520i | \(-0.0958260\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.144369i | 0.00594861i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.5979i | 0.477074i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.6218i | 0.682574i | 0.939959 | + | 0.341287i | \(0.110863\pi\) | ||||
−0.939959 | + | 0.341287i | \(0.889137\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.0594 | − | 4.28107i | −0.576378 | − | 0.175507i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 16.5243i | − | 0.676296i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.9563 | 1.71429 | 0.857144 | − | 0.515077i | \(-0.172237\pi\) | ||||
0.857144 | + | 0.515077i | \(0.172237\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.5323i | 1.81651i | 0.418418 | + | 0.908255i | \(0.362585\pi\) | ||||
−0.418418 | + | 0.908255i | \(0.637415\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.0521i | 0.409355i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.04079 | −0.204937 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.6908i | 1.52982i | 0.644135 | + | 0.764912i | \(0.277218\pi\) | ||||
−0.644135 | + | 0.764912i | \(0.722782\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.244180 | − | 0.801906i | 0.00989467 | − | 0.0324949i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.4224 | 1.02848 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.4554i | 1.79554i | 0.440466 | + | 0.897769i | \(0.354813\pi\) | ||||
−0.440466 | + | 0.897769i | \(0.645187\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.58109 | 0.104080 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 42.6756i | − | 1.71805i | −0.511930 | − | 0.859027i | \(-0.671069\pi\) | ||
0.511930 | − | 0.859027i | \(-0.328931\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.2695 | 0.613734 | 0.306867 | − | 0.951752i | \(-0.400719\pi\) | ||||
0.306867 | + | 0.951752i | \(0.400719\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.614837 | − | 4.75626i | 0.0246726 | − | 0.190862i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.4525 | + | 4.70527i | 0.619090 | + | 0.188513i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.06197 | −0.0424790 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.57980 | 0.0630912 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.82631i | 0.112692i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0071i | 0.557614i | 0.960347 | + | 0.278807i | \(0.0899390\pi\) | ||||
−0.960347 | + | 0.278807i | \(0.910061\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 5.78310i | − | 0.229858i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.64845 | 0.144784 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.1922 | − | 37.5310i | 0.998149 | − | 1.48703i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.9485 | −0.433114 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.11878i | 0.0441890i | 0.999756 | + | 0.0220945i | \(0.00703347\pi\) | ||||
−0.999756 | + | 0.0220945i | \(0.992967\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.79011 | −0.228340 | −0.114170 | − | 0.993461i | \(-0.536421\pi\) | ||||
−0.114170 | + | 0.993461i | \(0.536421\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.6882 | −0.460221 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.1981i | 0.715442i | 0.933828 | + | 0.357721i | \(0.116446\pi\) | ||||
−0.933828 | + | 0.357721i | \(0.883554\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.7249 | 0.813525 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.882544 | − | 0.268734i | −0.0345896 | − | 0.0105325i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.9672 | −0.859642 | −0.429821 | − | 0.902914i | \(-0.641423\pi\) | ||||
−0.429821 | + | 0.902914i | \(0.641423\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.91416i | 0.152939i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 14.7376i | − | 0.574969i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.6452i | 0.960041i | 0.877257 | + | 0.480020i | \(0.159371\pi\) | ||||
−0.877257 | + | 0.480020i | \(0.840629\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.14516 | −0.122333 | −0.0611663 | − | 0.998128i | \(-0.519482\pi\) | ||||
−0.0611663 | + | 0.998128i | \(0.519482\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 25.3282 | 0.983666 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.48406 | − | 0.451896i | −0.0575495 | − | 0.0175238i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.50693 | − | 0.194800i | −0.0583487 | − | 0.00754268i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.2037 | −0.703797 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 43.0672i | − | 1.66259i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.0745018 | −0.00287183 | −0.00143592 | − | 0.999999i | \(-0.500457\pi\) | ||||
−0.00143592 | + | 0.999999i | \(0.500457\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 2.99436i | − | 0.115253i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.4091 | 0.938116 | 0.469058 | − | 0.883167i | \(-0.344593\pi\) | ||||
0.469058 | + | 0.883167i | \(0.344593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.8315 | + | 4.82067i | 0.607555 | + | 0.185000i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 7.39741i | − | 0.283469i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.37727 | 0.167492 | 0.0837458 | − | 0.996487i | \(-0.473312\pi\) | ||||
0.0837458 | + | 0.996487i | \(0.473312\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.0236237i | − | 0.000902616i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 13.8540i | − | 0.528565i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −47.6310 | −1.81460 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.7370i | 0.712788i | 0.934336 | + | 0.356394i | \(0.115994\pi\) | ||||
−0.934336 | + | 0.356394i | \(0.884006\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.94071 | + | 9.65752i | −0.111708 | + | 0.366859i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 13.8043i | − | 0.523629i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 7.14862i | − | 0.270773i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 30.0698i | − | 1.13734i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 30.5807i | − | 1.15502i | −0.816385 | − | 0.577508i | \(-0.804025\pi\) | ||
0.816385 | − | 0.577508i | \(-0.195975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.298336i | 0.0112520i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.57548 | 0.209985 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.86647 | − | 22.5500i | 0.258240 | − | 0.848081i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.1030i | 1.20565i | 0.797872 | + | 0.602826i | \(0.205959\pi\) | ||||
−0.797872 | + | 0.602826i | \(0.794041\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.54134i | 0.170313i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.214389 | + | 1.65847i | −0.00802892 | + | 0.0621101i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34.8945 | −1.30498 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.45467i | 0.241054i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 32.8318i | − | 1.22442i | −0.790696 | − | 0.612209i | \(-0.790281\pi\) | ||
0.790696 | − | 0.612209i | \(-0.209719\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.0049 | − | 10.3545i | −1.26641 | − | 0.385620i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 19.1500i | − | 0.712195i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.948709 | −0.0352342 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.8639 | −0.588361 | −0.294180 | − | 0.955750i | \(-0.595047\pi\) | ||||
−0.294180 | + | 0.955750i | \(0.595047\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.3717i | 1.19731i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.3132 | −0.898027 | −0.449014 | − | 0.893525i | \(-0.648224\pi\) | ||||
−0.449014 | + | 0.893525i | \(0.648224\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.52499 | − | 8.23108i | 0.203792 | − | 0.303608i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38.3557 | −1.41285 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.2514 | −1.55424 | −0.777122 | − | 0.629350i | \(-0.783321\pi\) | ||||
−0.777122 | + | 0.629350i | \(0.783321\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.67357 | 0.0982160 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 43.6045i | − | 1.59969i | −0.600205 | − | 0.799846i | \(-0.704914\pi\) | ||
0.600205 | − | 0.799846i | \(-0.295086\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.90616i | 0.143110i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.2420 | 0.411322 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.387511 | − | 1.27262i | 0.0141593 | − | 0.0465004i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 0.977002i | − | 0.0356513i | −0.999841 | − | 0.0178256i | \(-0.994326\pi\) | ||
0.999841 | − | 0.0178256i | \(-0.00567438\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 20.3278i | − | 0.740786i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.7741 | −0.756047 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.8339i | 1.81125i | 0.424084 | + | 0.905623i | \(0.360596\pi\) | ||||
−0.424084 | + | 0.905623i | \(0.639404\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.1483 | + | 2.34602i | 0.658742 | + | 0.0851550i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.2166i | 0.986600i | 0.869859 | + | 0.493300i | \(0.164210\pi\) | ||||
−0.869859 | + | 0.493300i | \(0.835790\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.99221 | − | 9.82665i | 0.108325 | − | 0.355749i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.55483 | 0.200835 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35.0737 | 1.26644 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.9223 | 1.15115 | 0.575573 | − | 0.817750i | \(-0.304779\pi\) | ||||
0.575573 | + | 0.817750i | \(0.304779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.5661 | 0.668641 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.2617 | 0.980536 | 0.490268 | − | 0.871572i | \(-0.336899\pi\) | ||||
0.490268 | + | 0.871572i | \(0.336899\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.04411i | 0.0375055i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.82376 | − | 0.555335i | −0.0654272 | − | 0.0199225i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 0.754587i | − | 0.0270359i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 41.7757i | − | 1.49485i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.316832i | 0.0113226i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.2072 | 1.07814 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.0958 | −0.823277 | −0.411638 | − | 0.911347i | \(-0.635043\pi\) | ||||
−0.411638 | + | 0.911347i | \(0.635043\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.8672 | −0.885295 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.20916 | + | 30.2436i | −0.327440 | + | 1.07534i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 72.8844i | − | 2.58820i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.4462 | −0.370487 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.80488 | −0.134776 | −0.0673879 | − | 0.997727i | \(-0.521467\pi\) | ||||
−0.0673879 | + | 0.997727i | \(0.521467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15.4419i | − | 0.546295i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.10525 | −0.215718 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 56.2339 | 1.98445 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.3774 | − | 7.39510i | −0.577228 | − | 0.260643i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.8372 | −0.416688 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.70521 | 0.341217 | 0.170609 | − | 0.985339i | \(-0.445427\pi\) | ||||
0.170609 | + | 0.985339i | \(0.445427\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.10574i | − | 0.284631i | −0.989821 | − | 0.142316i | \(-0.954545\pi\) | ||
0.989821 | − | 0.142316i | \(-0.0454548\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.9783 | 0.595454 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.0628 | 0.877910 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.41705i | 0.119548i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.97669 | + | 16.3438i | −0.173900 | + | 0.571100i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 51.1589 | 1.78546 | 0.892729 | − | 0.450594i | \(-0.148788\pi\) | ||||
0.892729 | + | 0.450594i | \(0.148788\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.6472 | 1.31230 | 0.656149 | − | 0.754631i | \(-0.272184\pi\) | ||||
0.656149 | + | 0.754631i | \(0.272184\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.4255 | 0.397785 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.0680i | 0.663059i | 0.943445 | + | 0.331530i | \(0.107565\pi\) | ||||
−0.943445 | + | 0.331530i | \(0.892435\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.40163i | − | 0.0486805i | −0.999704 | − | 0.0243403i | \(-0.992251\pi\) | ||
0.999704 | − | 0.0243403i | \(-0.00774851\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 21.2648i | − | 0.737667i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.7969 | − | 15.3021i | −0.789865 | − | 0.530186i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 4.73909i | − | 0.164003i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.348692 | 0.0120525 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.0355 | 1.45123 | 0.725614 | − | 0.688102i | \(-0.241556\pi\) | ||||
0.725614 | + | 0.688102i | \(0.241556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8996 | −0.996539 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.40757 | 0.117363 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.6428 | −1.39815 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.00880 | − | 2.74317i | −0.309546 | − | 0.0942566i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 8.95787i | − | 0.307433i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.443031 | + | 3.42720i | −0.0151869 | + | 0.117483i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 25.0768i | − | 0.858614i | −0.903159 | − | 0.429307i | \(-0.858758\pi\) | ||
0.903159 | − | 0.429307i | \(-0.141242\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.586351 | 0.0200528 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.825211i | 0.0281887i | 0.999901 | + | 0.0140943i | \(0.00448652\pi\) | ||||
−0.999901 | + | 0.0140943i | \(0.995513\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.4033i | 0.934988i | 0.883996 | + | 0.467494i | \(0.154843\pi\) | ||||
−0.883996 | + | 0.467494i | \(0.845157\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.61288 | + | 1.40462i | 0.157207 | + | 0.0478693i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.6654 | −0.567295 | −0.283648 | − | 0.958929i | \(-0.591545\pi\) | ||||
−0.283648 | + | 0.958929i | \(0.591545\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.7267i | 0.534725i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.61527i | 0.0548576i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.3283 | −0.587821 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −64.9110 | −2.19942 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.25498 | −0.211699 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.6553 | − | 8.72552i | −0.968725 | − | 0.294976i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.1019 | 0.374883 | 0.187442 | − | 0.982276i | \(-0.439980\pi\) | ||||
0.187442 | + | 0.982276i | \(0.439980\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.8886i | 0.873201i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.1891 | −1.21924 | −0.609620 | − | 0.792694i | \(-0.708678\pi\) | ||||
−0.609620 | + | 0.792694i | \(0.708678\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.5853 | −1.46676 | −0.733380 | − | 0.679819i | \(-0.762059\pi\) | ||||
−0.733380 | + | 0.679819i | \(0.762059\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.69216 | 0.258569 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.1239i | 1.17934i | 0.807642 | + | 0.589672i | \(0.200743\pi\) | ||||
−0.807642 | + | 0.589672i | \(0.799257\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.52044 | + | 1.98547i | 0.218689 | + | 0.0665905i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 3.81567i | − | 0.127830i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.63000i | − | 0.0545459i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.7484 | −0.827249 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.7132 | + | 3.97027i | 1.02548 | + | 0.132563i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 0.110477i | − | 0.00368460i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.9318i | 0.963857i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.8889 | − | 6.36064i | −0.695138 | − | 0.211669i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.1386 | 0.602948 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 47.1105i | − | 1.56428i | −0.623103 | − | 0.782140i | \(-0.714128\pi\) | ||
0.623103 | − | 0.782140i | \(-0.285872\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.90949i | 0.295509i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45.0198i | − | 1.49157i | −0.666185 | − | 0.745786i | \(-0.732074\pi\) | ||
0.666185 | − | 0.745786i | \(-0.267926\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.8957i | 1.41964i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 15.9846i | − | 0.528434i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.13007 | + | 6.99532i | −0.0703411 | + | 0.231006i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 32.1007i | − | 1.05891i | −0.848339 | − | 0.529453i | \(-0.822397\pi\) | ||
0.848339 | − | 0.529453i | \(-0.177603\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.4476 | −0.344260 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 70.6989i | − | 2.32708i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.15764i | 0.0709427i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.4353 | 0.441272 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.0188i | 0.492751i | 0.969174 | + | 0.246376i | \(0.0792397\pi\) | ||||
−0.969174 | + | 0.246376i | \(0.920760\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.40637 | − | 1.61524i | −0.0788655 | − | 0.0529374i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.2923 | 1.05720 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.1954i | 0.693165i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.1357 | −0.951821 | −0.475910 | − | 0.879494i | \(-0.657881\pi\) | ||||
−0.475910 | + | 0.879494i | \(0.657881\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 13.9154i | − | 0.454111i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.6796 | 0.771934 | 0.385967 | − | 0.922513i | \(-0.373868\pi\) | ||||
0.385967 | + | 0.922513i | \(0.373868\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.12057 | − | 8.66848i | 0.0364907 | − | 0.282284i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.09146 | + | 3.58444i | −0.0355051 | + | 0.116602i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.6928 | −0.509948 | −0.254974 | − | 0.966948i | \(-0.582067\pi\) | ||||
−0.254974 | + | 0.966948i | \(0.582067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 95.1670 | 3.08925 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 6.23595i | − | 0.202215i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 52.8288i | − | 1.71129i | −0.517562 | − | 0.855646i | \(-0.673160\pi\) | ||
0.517562 | − | 0.855646i | \(-0.326840\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 35.1768i | − | 1.13829i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.20893 | −0.0390790 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.0128559 | − | 0.0422199i | 0.000415140 | − | 0.00136335i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.8784 | 0.996078 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.502808i | 0.0162028i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.9574 | 0.417114 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.0844 | −0.999607 | −0.499804 | − | 0.866139i | \(-0.666595\pi\) | ||||
−0.499804 | + | 0.866139i | \(0.666595\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.62396i | − | 0.0521692i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.31232 | −0.202572 | −0.101286 | − | 0.994857i | \(-0.532296\pi\) | ||||
−0.101286 | + | 0.994857i | \(0.532296\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.51226 | − | 24.6709i | 0.240832 | − | 0.790911i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.3359 | 0.619244 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 40.8629i | − | 1.30732i | −0.756788 | − | 0.653660i | \(-0.773233\pi\) | ||
0.756788 | − | 0.653660i | \(-0.226767\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 23.2956i | − | 0.744532i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.88249i | 0.123958i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.5720 | 1.13457 | 0.567285 | − | 0.823522i | \(-0.307994\pi\) | ||||
0.567285 | + | 0.823522i | \(0.307994\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.4250 | −0.523345 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.96439 | + | 3.03415i | 0.317170 | + | 0.0965781i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.07435 | + | 39.2541i | −0.161355 | + | 1.24821i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.81745 | 0.121265 | 0.0606327 | − | 0.998160i | \(-0.480688\pi\) | ||||
0.0606327 | + | 0.998160i | \(0.480688\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.22381i | − | 0.0705705i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.4019 | 0.741889 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0193i | 0.348985i | 0.984659 | + | 0.174492i | \(0.0558284\pi\) | ||||
−0.984659 | + | 0.174492i | \(0.944172\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.720567 | 0.0227977 |
(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 | 1932.2.k.a.1609.14 | yes | 32 | |
3.2 | odd | 2 | 5796.2.k.d.5473.12 | 32 | |||
7.6 | odd | 2 | inner | 1932.2.k.a.1609.15 | yes | 32 | |
21.20 | even | 2 | 5796.2.k.d.5473.22 | 32 | |||
23.22 | odd | 2 | inner | 1932.2.k.a.1609.13 | ✓ | 32 | |
69.68 | even | 2 | 5796.2.k.d.5473.21 | 32 | |||
161.160 | even | 2 | inner | 1932.2.k.a.1609.16 | yes | 32 | |
483.482 | odd | 2 | 5796.2.k.d.5473.11 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.2.k.a.1609.13 | ✓ | 32 | 23.22 | odd | 2 | inner | |
1932.2.k.a.1609.14 | yes | 32 | 1.1 | even | 1 | trivial | |
1932.2.k.a.1609.15 | yes | 32 | 7.6 | odd | 2 | inner | |
1932.2.k.a.1609.16 | yes | 32 | 161.160 | even | 2 | inner | |
5796.2.k.d.5473.11 | 32 | 483.482 | odd | 2 | |||
5796.2.k.d.5473.12 | 32 | 3.2 | odd | 2 | |||
5796.2.k.d.5473.21 | 32 | 69.68 | even | 2 | |||
5796.2.k.d.5473.22 | 32 | 21.20 | even | 2 |