Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(151,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{18} + x^{16} - 9x^{14} + 20x^{12} - 24x^{10} + 80x^{8} - 144x^{6} + 64x^{4} - 256x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.18 | ||
Root | \(-1.31446 + 0.521712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.151 |
Dual form | 380.2.f.a.151.17 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.31446 | + | 0.521712i | 0.929467 | + | 0.368906i | ||||
\(3\) | 2.15859 | 1.24626 | 0.623131 | − | 0.782118i | \(-0.285860\pi\) | ||||
0.623131 | + | 0.782118i | \(0.285860\pi\) | |||||||
\(4\) | 1.45563 | + | 1.37154i | 0.727817 | + | 0.685771i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.83739 | + | 1.12616i | 1.15836 | + | 0.459753i | ||||
\(7\) | − | 1.66163i | − | 0.628037i | −0.949417 | − | 0.314018i | \(-0.898325\pi\) | ||
0.949417 | − | 0.314018i | \(-0.101675\pi\) | |||||||
\(8\) | 1.19783 | + | 2.56227i | 0.423497 | + | 0.905898i | ||||
\(9\) | 1.65950 | 0.553167 | ||||||||
\(10\) | −1.31446 | − | 0.521712i | −0.415670 | − | 0.164980i | ||||
\(11\) | − | 1.77595i | − | 0.535468i | −0.963493 | − | 0.267734i | \(-0.913725\pi\) | ||
0.963493 | − | 0.267734i | \(-0.0862748\pi\) | |||||||
\(12\) | 3.14211 | + | 2.96060i | 0.907050 | + | 0.854650i | ||||
\(13\) | − | 0.769776i | − | 0.213497i | −0.994286 | − | 0.106749i | \(-0.965956\pi\) | ||
0.994286 | − | 0.106749i | \(-0.0340440\pi\) | |||||||
\(14\) | 0.866891 | − | 2.18415i | 0.231686 | − | 0.583739i | ||||
\(15\) | −2.15859 | −0.557345 | ||||||||
\(16\) | 0.237741 | + | 3.99293i | 0.0594353 | + | 0.998232i | ||||
\(17\) | −3.23899 | −0.785570 | −0.392785 | − | 0.919630i | \(-0.628488\pi\) | ||||
−0.392785 | + | 0.919630i | \(0.628488\pi\) | |||||||
\(18\) | 2.18136 | + | 0.865781i | 0.514150 | + | 0.204067i | ||||
\(19\) | −1.23206 | + | 4.18115i | −0.282653 | + | 0.959222i | ||||
\(20\) | −1.45563 | − | 1.37154i | −0.325490 | − | 0.306686i | ||||
\(21\) | − | 3.58677i | − | 0.782698i | ||||||
\(22\) | 0.926532 | − | 2.33442i | 0.197537 | − | 0.497700i | ||||
\(23\) | 3.06150i | 0.638367i | 0.947693 | + | 0.319184i | \(0.103409\pi\) | ||||
−0.947693 | + | 0.319184i | \(0.896591\pi\) | |||||||
\(24\) | 2.58562 | + | 5.53087i | 0.527788 | + | 1.12899i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.401601 | − | 1.01184i | 0.0787605 | − | 0.198439i | ||||
\(27\) | −2.89358 | −0.556870 | ||||||||
\(28\) | 2.27900 | − | 2.41872i | 0.430690 | − | 0.457096i | ||||
\(29\) | − | 6.45515i | − | 1.19869i | −0.800490 | − | 0.599346i | \(-0.795427\pi\) | ||
0.800490 | − | 0.599346i | \(-0.204573\pi\) | |||||||
\(30\) | −2.83739 | − | 1.12616i | −0.518034 | − | 0.205608i | ||||
\(31\) | −4.09806 | −0.736033 | −0.368016 | − | 0.929819i | \(-0.619963\pi\) | ||||
−0.368016 | + | 0.929819i | \(0.619963\pi\) | |||||||
\(32\) | −1.77065 | + | 5.37260i | −0.313011 | + | 0.949750i | ||||
\(33\) | − | 3.83354i | − | 0.667333i | ||||||
\(34\) | −4.25754 | − | 1.68982i | −0.730161 | − | 0.289801i | ||||
\(35\) | 1.66163i | 0.280867i | ||||||||
\(36\) | 2.41563 | + | 2.27608i | 0.402604 | + | 0.379346i | ||||
\(37\) | − | 5.34522i | − | 0.878749i | −0.898304 | − | 0.439374i | \(-0.855200\pi\) | ||
0.898304 | − | 0.439374i | \(-0.144800\pi\) | |||||||
\(38\) | −3.80085 | + | 4.85320i | −0.616579 | + | 0.787293i | ||||
\(39\) | − | 1.66163i | − | 0.266074i | ||||||
\(40\) | −1.19783 | − | 2.56227i | −0.189393 | − | 0.405130i | ||||
\(41\) | − | 3.83354i | − | 0.598698i | −0.954144 | − | 0.299349i | \(-0.903231\pi\) | ||
0.954144 | − | 0.299349i | \(-0.0967694\pi\) | |||||||
\(42\) | 1.87126 | − | 4.71469i | 0.288742 | − | 0.727492i | ||||
\(43\) | 11.5381i | 1.75955i | 0.475393 | + | 0.879774i | \(0.342306\pi\) | ||||
−0.475393 | + | 0.879774i | \(0.657694\pi\) | |||||||
\(44\) | 2.43579 | − | 2.58513i | 0.367209 | − | 0.389723i | ||||
\(45\) | −1.65950 | −0.247384 | ||||||||
\(46\) | −1.59722 | + | 4.02424i | −0.235497 | + | 0.593341i | ||||
\(47\) | − | 6.81499i | − | 0.994069i | −0.867731 | − | 0.497034i | \(-0.834422\pi\) | ||
0.867731 | − | 0.497034i | \(-0.165578\pi\) | |||||||
\(48\) | 0.513185 | + | 8.61909i | 0.0740719 | + | 1.24406i | ||||
\(49\) | 4.23899 | 0.605570 | ||||||||
\(50\) | 1.31446 | + | 0.521712i | 0.185893 | + | 0.0737812i | ||||
\(51\) | −6.99164 | −0.979026 | ||||||||
\(52\) | 1.05578 | − | 1.12051i | 0.146410 | − | 0.155387i | ||||
\(53\) | − | 5.59198i | − | 0.768118i | −0.923309 | − | 0.384059i | \(-0.874526\pi\) | ||
0.923309 | − | 0.384059i | \(-0.125474\pi\) | |||||||
\(54\) | −3.80351 | − | 1.50962i | −0.517593 | − | 0.205433i | ||||
\(55\) | 1.77595i | 0.239469i | ||||||||
\(56\) | 4.25754 | − | 1.99035i | 0.568937 | − | 0.265972i | ||||
\(57\) | −2.65950 | + | 9.02539i | −0.352260 | + | 1.19544i | ||||
\(58\) | 3.36773 | − | 8.48507i | 0.442204 | − | 1.11414i | ||||
\(59\) | 5.35770 | 0.697513 | 0.348756 | − | 0.937213i | \(-0.386604\pi\) | ||||
0.348756 | + | 0.937213i | \(0.386604\pi\) | |||||||
\(60\) | −3.14211 | − | 2.96060i | −0.405645 | − | 0.382211i | ||||
\(61\) | −4.94753 | −0.633466 | −0.316733 | − | 0.948515i | \(-0.602586\pi\) | ||||
−0.316733 | + | 0.948515i | \(0.602586\pi\) | |||||||
\(62\) | −5.38675 | − | 2.13800i | −0.684118 | − | 0.271527i | ||||
\(63\) | − | 2.75748i | − | 0.347409i | ||||||
\(64\) | −5.13041 | + | 6.13831i | −0.641301 | + | 0.767289i | ||||
\(65\) | 0.769776i | 0.0954790i | ||||||||
\(66\) | 2.00000 | − | 5.03905i | 0.246183 | − | 0.620264i | ||||
\(67\) | 6.72318 | 0.821368 | 0.410684 | − | 0.911778i | \(-0.365290\pi\) | ||||
0.410684 | + | 0.911778i | \(0.365290\pi\) | |||||||
\(68\) | −4.71478 | − | 4.44241i | −0.571751 | − | 0.538721i | ||||
\(69\) | 6.60852i | 0.795572i | ||||||||
\(70\) | −0.866891 | + | 2.18415i | −0.103613 | + | 0.261056i | ||||
\(71\) | −1.83362 | −0.217611 | −0.108805 | − | 0.994063i | \(-0.534703\pi\) | ||||
−0.108805 | + | 0.994063i | \(0.534703\pi\) | |||||||
\(72\) | 1.98780 | + | 4.25208i | 0.234264 | + | 0.501113i | ||||
\(73\) | 11.9331 | 1.39666 | 0.698332 | − | 0.715774i | \(-0.253926\pi\) | ||||
0.698332 | + | 0.715774i | \(0.253926\pi\) | |||||||
\(74\) | 2.78866 | − | 7.02610i | 0.324175 | − | 0.816768i | ||||
\(75\) | 2.15859 | 0.249252 | ||||||||
\(76\) | −7.52805 | + | 4.39641i | −0.863527 | + | 0.504303i | ||||
\(77\) | −2.95096 | −0.336294 | ||||||||
\(78\) | 0.866891 | − | 2.18415i | 0.0981561 | − | 0.247307i | ||||
\(79\) | 9.41868 | 1.05968 | 0.529842 | − | 0.848096i | \(-0.322251\pi\) | ||||
0.529842 | + | 0.848096i | \(0.322251\pi\) | |||||||
\(80\) | −0.237741 | − | 3.99293i | −0.0265803 | − | 0.446423i | ||||
\(81\) | −11.2246 | −1.24717 | ||||||||
\(82\) | 2.00000 | − | 5.03905i | 0.220863 | − | 0.556470i | ||||
\(83\) | 7.48061i | 0.821103i | 0.911837 | + | 0.410552i | \(0.134664\pi\) | ||||
−0.911837 | + | 0.410552i | \(0.865336\pi\) | |||||||
\(84\) | 4.91941 | − | 5.22103i | 0.536752 | − | 0.569661i | ||||
\(85\) | 3.23899 | 0.351318 | ||||||||
\(86\) | −6.01957 | + | 15.1665i | −0.649107 | + | 1.63544i | ||||
\(87\) | − | 13.9340i | − | 1.49388i | ||||||
\(88\) | 4.55045 | − | 2.12728i | 0.485079 | − | 0.226769i | ||||
\(89\) | 16.0161i | 1.69770i | 0.528633 | + | 0.848850i | \(0.322705\pi\) | ||||
−0.528633 | + | 0.848850i | \(0.677295\pi\) | |||||||
\(90\) | −2.18136 | − | 0.865781i | −0.229935 | − | 0.0912613i | ||||
\(91\) | −1.27908 | −0.134084 | ||||||||
\(92\) | −4.19898 | + | 4.45643i | −0.437774 | + | 0.464615i | ||||
\(93\) | −8.84602 | −0.917289 | ||||||||
\(94\) | 3.55546 | − | 8.95807i | 0.366718 | − | 0.923954i | ||||
\(95\) | 1.23206 | − | 4.18115i | 0.126406 | − | 0.428977i | ||||
\(96\) | −3.82211 | + | 11.5972i | −0.390093 | + | 1.18364i | ||||
\(97\) | 0.676382i | 0.0686762i | 0.999410 | + | 0.0343381i | \(0.0109323\pi\) | ||||
−0.999410 | + | 0.0343381i | \(0.989068\pi\) | |||||||
\(98\) | 5.57200 | + | 2.21153i | 0.562857 | + | 0.223398i | ||||
\(99\) | − | 2.94719i | − | 0.296203i | ||||||
\(100\) | 1.45563 | + | 1.37154i | 0.145563 | + | 0.137154i | ||||
\(101\) | −2.57949 | −0.256669 | −0.128334 | − | 0.991731i | \(-0.540963\pi\) | ||||
−0.128334 | + | 0.991731i | \(0.540963\pi\) | |||||||
\(102\) | −9.19026 | − | 3.64762i | −0.909972 | − | 0.361168i | ||||
\(103\) | −7.51628 | −0.740601 | −0.370301 | − | 0.928912i | \(-0.620745\pi\) | ||||
−0.370301 | + | 0.928912i | \(0.620745\pi\) | |||||||
\(104\) | 1.97237 | − | 0.922061i | 0.193407 | − | 0.0904155i | ||||
\(105\) | 3.58677i | 0.350033i | ||||||||
\(106\) | 2.91740 | − | 7.35046i | 0.283363 | − | 0.713940i | ||||
\(107\) | −1.32842 | −0.128423 | −0.0642116 | − | 0.997936i | \(-0.520453\pi\) | ||||
−0.0642116 | + | 0.997936i | \(0.520453\pi\) | |||||||
\(108\) | −4.21200 | − | 3.96867i | −0.405300 | − | 0.381886i | ||||
\(109\) | 2.43483i | 0.233214i | 0.993178 | + | 0.116607i | \(0.0372018\pi\) | ||||
−0.993178 | + | 0.116607i | \(0.962798\pi\) | |||||||
\(110\) | −0.926532 | + | 2.33442i | −0.0883413 | + | 0.222578i | ||||
\(111\) | − | 11.5381i | − | 1.09515i | ||||||
\(112\) | 6.63477 | − | 0.395037i | 0.626927 | − | 0.0373275i | ||||
\(113\) | − | 17.9154i | − | 1.68534i | −0.538434 | − | 0.842668i | \(-0.680984\pi\) | ||
0.538434 | − | 0.842668i | \(-0.319016\pi\) | |||||||
\(114\) | −8.20447 | + | 10.4761i | −0.768419 | + | 0.981173i | ||||
\(115\) | − | 3.06150i | − | 0.285487i | ||||||
\(116\) | 8.85352 | − | 9.39634i | 0.822028 | − | 0.872428i | ||||
\(117\) | − | 1.27744i | − | 0.118100i | ||||||
\(118\) | 7.04250 | + | 2.79517i | 0.648315 | + | 0.257316i | ||||
\(119\) | 5.38200i | 0.493367i | ||||||||
\(120\) | −2.58562 | − | 5.53087i | −0.236034 | − | 0.504897i | ||||
\(121\) | 7.84602 | 0.713274 | ||||||||
\(122\) | −6.50335 | − | 2.58118i | −0.588785 | − | 0.233689i | ||||
\(123\) | − | 8.27502i | − | 0.746134i | ||||||
\(124\) | −5.96527 | − | 5.62066i | −0.535697 | − | 0.504750i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.43861 | − | 3.62460i | 0.128161 | − | 0.322905i | ||||
\(127\) | −15.9315 | −1.41369 | −0.706847 | − | 0.707367i | \(-0.749883\pi\) | ||||
−0.706847 | + | 0.707367i | \(0.749883\pi\) | |||||||
\(128\) | −9.94617 | + | 5.39200i | −0.879126 | + | 0.476590i | ||||
\(129\) | 24.9061i | 2.19286i | ||||||||
\(130\) | −0.401601 | + | 1.01184i | −0.0352227 | + | 0.0887445i | ||||
\(131\) | − | 4.53342i | − | 0.396087i | −0.980193 | − | 0.198043i | \(-0.936541\pi\) | ||
0.980193 | − | 0.198043i | \(-0.0634587\pi\) | |||||||
\(132\) | 5.25786 | − | 5.58023i | 0.457638 | − | 0.485696i | ||||
\(133\) | 6.94753 | + | 2.04722i | 0.602427 | + | 0.177517i | ||||
\(134\) | 8.83739 | + | 3.50756i | 0.763434 | + | 0.303007i | ||||
\(135\) | 2.89358 | 0.249040 | ||||||||
\(136\) | −3.87976 | − | 8.29915i | −0.332686 | − | 0.711646i | ||||
\(137\) | −19.4601 | −1.66259 | −0.831295 | − | 0.555832i | \(-0.812400\pi\) | ||||
−0.831295 | + | 0.555832i | \(0.812400\pi\) | |||||||
\(138\) | −3.44774 | + | 8.68667i | −0.293491 | + | 0.739458i | ||||
\(139\) | 7.75685i | 0.657927i | 0.944343 | + | 0.328964i | \(0.106699\pi\) | ||||
−0.944343 | + | 0.328964i | \(0.893301\pi\) | |||||||
\(140\) | −2.27900 | + | 2.41872i | −0.192610 | + | 0.204419i | ||||
\(141\) | − | 14.7108i | − | 1.23887i | ||||||
\(142\) | −2.41023 | − | 0.956621i | −0.202262 | − | 0.0802779i | ||||
\(143\) | −1.36708 | −0.114321 | ||||||||
\(144\) | 0.394532 | + | 6.62627i | 0.0328776 | + | 0.552189i | ||||
\(145\) | 6.45515i | 0.536071i | ||||||||
\(146\) | 15.6856 | + | 6.22563i | 1.29815 | + | 0.515237i | ||||
\(147\) | 9.15023 | 0.754698 | ||||||||
\(148\) | 7.33120 | − | 7.78068i | 0.602621 | − | 0.639568i | ||||
\(149\) | 21.7516 | 1.78196 | 0.890979 | − | 0.454044i | \(-0.150019\pi\) | ||||
0.890979 | + | 0.454044i | \(0.150019\pi\) | |||||||
\(150\) | 2.83739 | + | 1.12616i | 0.231672 | + | 0.0919506i | ||||
\(151\) | 13.9550 | 1.13564 | 0.567820 | − | 0.823153i | \(-0.307787\pi\) | ||||
0.567820 | + | 0.823153i | \(0.307787\pi\) | |||||||
\(152\) | −12.1890 | + | 1.85145i | −0.988660 | + | 0.150173i | ||||
\(153\) | −5.37511 | −0.434552 | ||||||||
\(154\) | −3.87894 | − | 1.53955i | −0.312574 | − | 0.124061i | ||||
\(155\) | 4.09806 | 0.329164 | ||||||||
\(156\) | 2.27900 | − | 2.41872i | 0.182466 | − | 0.193653i | ||||
\(157\) | −10.6941 | −0.853483 | −0.426741 | − | 0.904374i | \(-0.640339\pi\) | ||||
−0.426741 | + | 0.904374i | \(0.640339\pi\) | |||||||
\(158\) | 12.3805 | + | 4.91384i | 0.984942 | + | 0.390924i | ||||
\(159\) | − | 12.0708i | − | 0.957275i | ||||||
\(160\) | 1.77065 | − | 5.37260i | 0.139983 | − | 0.424741i | ||||
\(161\) | 5.08708 | 0.400918 | ||||||||
\(162\) | −14.7543 | − | 5.85598i | −1.15921 | − | 0.460089i | ||||
\(163\) | 8.21487i | 0.643438i | 0.946835 | + | 0.321719i | \(0.104261\pi\) | ||||
−0.946835 | + | 0.321719i | \(0.895739\pi\) | |||||||
\(164\) | 5.25786 | − | 5.58023i | 0.410570 | − | 0.435742i | ||||
\(165\) | 3.83354i | 0.298440i | ||||||||
\(166\) | −3.90272 | + | 9.83299i | −0.302910 | + | 0.763188i | ||||
\(167\) | 2.34064 | 0.181124 | 0.0905620 | − | 0.995891i | \(-0.471134\pi\) | ||||
0.0905620 | + | 0.995891i | \(0.471134\pi\) | |||||||
\(168\) | 9.19026 | − | 4.29634i | 0.709044 | − | 0.331470i | ||||
\(169\) | 12.4074 | 0.954419 | ||||||||
\(170\) | 4.25754 | + | 1.68982i | 0.326538 | + | 0.129603i | ||||
\(171\) | −2.04460 | + | 6.93863i | −0.156354 | + | 0.530610i | ||||
\(172\) | −15.8250 | + | 16.7953i | −1.20665 | + | 1.28063i | ||||
\(173\) | − | 4.12231i | − | 0.313413i | −0.987645 | − | 0.156707i | \(-0.949912\pi\) | ||
0.987645 | − | 0.156707i | \(-0.0500877\pi\) | |||||||
\(174\) | 7.26954 | − | 18.3158i | 0.551102 | − | 1.38851i | ||||
\(175\) | − | 1.66163i | − | 0.125607i | ||||||
\(176\) | 7.09123 | − | 0.422215i | 0.534521 | − | 0.0318257i | ||||
\(177\) | 11.5651 | 0.869283 | ||||||||
\(178\) | −8.35577 | + | 21.0526i | −0.626292 | + | 1.57796i | ||||
\(179\) | 1.16740 | 0.0872559 | 0.0436280 | − | 0.999048i | \(-0.486108\pi\) | ||||
0.0436280 | + | 0.999048i | \(0.486108\pi\) | |||||||
\(180\) | −2.41563 | − | 2.27608i | −0.180050 | − | 0.169649i | ||||
\(181\) | 22.5328i | 1.67485i | 0.546551 | + | 0.837426i | \(0.315940\pi\) | ||||
−0.546551 | + | 0.837426i | \(0.684060\pi\) | |||||||
\(182\) | −1.68131 | − | 0.667312i | −0.124627 | − | 0.0494645i | ||||
\(183\) | −10.6797 | −0.789464 | ||||||||
\(184\) | −7.84438 | + | 3.66716i | −0.578295 | + | 0.270346i | ||||
\(185\) | 5.34522i | 0.392988i | ||||||||
\(186\) | −11.6278 | − | 4.61507i | −0.852590 | − | 0.338393i | ||||
\(187\) | 5.75227i | 0.420648i | ||||||||
\(188\) | 9.34705 | − | 9.92014i | 0.681704 | − | 0.723500i | ||||
\(189\) | 4.80806i | 0.349735i | ||||||||
\(190\) | 3.80085 | − | 4.85320i | 0.275743 | − | 0.352088i | ||||
\(191\) | 20.5329i | 1.48571i | 0.669452 | + | 0.742855i | \(0.266529\pi\) | ||||
−0.669452 | + | 0.742855i | \(0.733471\pi\) | |||||||
\(192\) | −11.0744 | + | 13.2501i | −0.799229 | + | 0.956243i | ||||
\(193\) | − | 8.03672i | − | 0.578495i | −0.957254 | − | 0.289248i | \(-0.906595\pi\) | ||
0.957254 | − | 0.289248i | \(-0.0934051\pi\) | |||||||
\(194\) | −0.352876 | + | 0.889081i | −0.0253351 | + | 0.0638323i | ||||
\(195\) | 1.66163i | 0.118992i | ||||||||
\(196\) | 6.17042 | + | 5.81395i | 0.440744 | + | 0.415282i | ||||
\(197\) | 9.52701 | 0.678772 | 0.339386 | − | 0.940647i | \(-0.389781\pi\) | ||||
0.339386 | + | 0.940647i | \(0.389781\pi\) | |||||||
\(198\) | 1.53758 | − | 3.87397i | 0.109271 | − | 0.275311i | ||||
\(199\) | 6.98947i | 0.495470i | 0.968828 | + | 0.247735i | \(0.0796863\pi\) | ||||
−0.968828 | + | 0.247735i | \(0.920314\pi\) | |||||||
\(200\) | 1.19783 | + | 2.56227i | 0.0846993 | + | 0.181180i | ||||
\(201\) | 14.5126 | 1.02364 | ||||||||
\(202\) | −3.39064 | − | 1.34575i | −0.238565 | − | 0.0946865i | ||||
\(203\) | −10.7261 | −0.752822 | ||||||||
\(204\) | −10.1773 | − | 9.58933i | −0.712551 | − | 0.671388i | ||||
\(205\) | 3.83354i | 0.267746i | ||||||||
\(206\) | −9.87989 | − | 3.92133i | −0.688364 | − | 0.273212i | ||||
\(207\) | 5.08057i | 0.353124i | ||||||||
\(208\) | 3.07366 | − | 0.183007i | 0.213120 | − | 0.0126893i | ||||
\(209\) | 7.42550 | + | 2.18807i | 0.513633 | + | 0.151352i | ||||
\(210\) | −1.87126 | + | 4.71469i | −0.129129 | + | 0.325344i | ||||
\(211\) | 17.9456 | 1.23543 | 0.617713 | − | 0.786404i | \(-0.288059\pi\) | ||||
0.617713 | + | 0.786404i | \(0.288059\pi\) | |||||||
\(212\) | 7.66964 | − | 8.13988i | 0.526753 | − | 0.559049i | ||||
\(213\) | −3.95803 | −0.271200 | ||||||||
\(214\) | −1.74616 | − | 0.693052i | −0.119365 | − | 0.0473761i | ||||
\(215\) | − | 11.5381i | − | 0.786894i | ||||||
\(216\) | −3.46602 | − | 7.41413i | −0.235833 | − | 0.504468i | ||||
\(217\) | 6.80945i | 0.462256i | ||||||||
\(218\) | −1.27028 | + | 3.20050i | −0.0860341 | + | 0.216765i | ||||
\(219\) | 25.7586 | 1.74061 | ||||||||
\(220\) | −2.43579 | + | 2.58513i | −0.164221 | + | 0.174289i | ||||
\(221\) | 2.49330i | 0.167717i | ||||||||
\(222\) | 6.01957 | − | 15.1665i | 0.404007 | − | 1.01791i | ||||
\(223\) | 25.1311 | 1.68290 | 0.841451 | − | 0.540334i | \(-0.181702\pi\) | ||||
0.841451 | + | 0.540334i | \(0.181702\pi\) | |||||||
\(224\) | 8.92726 | + | 2.94217i | 0.596478 | + | 0.196582i | ||||
\(225\) | 1.65950 | 0.110633 | ||||||||
\(226\) | 9.34665 | − | 23.5491i | 0.621730 | − | 1.56646i | ||||
\(227\) | −14.7465 | −0.978759 | −0.489379 | − | 0.872071i | \(-0.662777\pi\) | ||||
−0.489379 | + | 0.872071i | \(0.662777\pi\) | |||||||
\(228\) | −16.2500 | + | 9.49004i | −1.07618 | + | 0.628493i | ||||
\(229\) | −18.9606 | −1.25295 | −0.626477 | − | 0.779440i | \(-0.715504\pi\) | ||||
−0.626477 | + | 0.779440i | \(0.715504\pi\) | |||||||
\(230\) | 1.59722 | − | 4.02424i | 0.105318 | − | 0.265350i | ||||
\(231\) | −6.36992 | −0.419110 | ||||||||
\(232\) | 16.5398 | − | 7.73217i | 1.08589 | − | 0.507642i | ||||
\(233\) | −18.6430 | −1.22134 | −0.610672 | − | 0.791884i | \(-0.709100\pi\) | ||||
−0.610672 | + | 0.791884i | \(0.709100\pi\) | |||||||
\(234\) | 0.666458 | − | 1.67916i | 0.0435677 | − | 0.109770i | ||||
\(235\) | 6.81499i | 0.444561i | ||||||||
\(236\) | 7.79885 | + | 7.34831i | 0.507662 | + | 0.478334i | ||||
\(237\) | 20.3311 | 1.32064 | ||||||||
\(238\) | −2.80785 | + | 7.07445i | −0.182006 | + | 0.458568i | ||||
\(239\) | 7.49509i | 0.484817i | 0.970174 | + | 0.242409i | \(0.0779375\pi\) | ||||
−0.970174 | + | 0.242409i | \(0.922063\pi\) | |||||||
\(240\) | −0.513185 | − | 8.61909i | −0.0331259 | − | 0.556360i | ||||
\(241\) | 4.87794i | 0.314216i | 0.987581 | + | 0.157108i | \(0.0502171\pi\) | ||||
−0.987581 | + | 0.157108i | \(0.949783\pi\) | |||||||
\(242\) | 10.3133 | + | 4.09336i | 0.662965 | + | 0.263131i | ||||
\(243\) | −15.5484 | −0.997433 | ||||||||
\(244\) | −7.20179 | − | 6.78574i | −0.461047 | − | 0.434413i | ||||
\(245\) | −4.23899 | −0.270819 | ||||||||
\(246\) | 4.31718 | − | 10.8772i | 0.275253 | − | 0.693507i | ||||
\(247\) | 3.21855 | + | 0.948407i | 0.204792 | + | 0.0603457i | ||||
\(248\) | −4.90877 | − | 10.5003i | −0.311707 | − | 0.666770i | ||||
\(249\) | 16.1475i | 1.02331i | ||||||||
\(250\) | −1.31446 | − | 0.521712i | −0.0831340 | − | 0.0329959i | ||||
\(251\) | 17.3716i | 1.09648i | 0.836319 | + | 0.548242i | \(0.184703\pi\) | ||||
−0.836319 | + | 0.548242i | \(0.815297\pi\) | |||||||
\(252\) | 3.78200 | − | 4.01388i | 0.238243 | − | 0.252850i | ||||
\(253\) | 5.43706 | 0.341825 | ||||||||
\(254\) | −20.9414 | − | 8.31166i | −1.31398 | − | 0.521520i | ||||
\(255\) | 6.99164 | 0.437834 | ||||||||
\(256\) | −15.8870 | + | 1.89857i | −0.992935 | + | 0.118660i | ||||
\(257\) | − | 24.5463i | − | 1.53116i | −0.643342 | − | 0.765579i | \(-0.722453\pi\) | ||
0.643342 | − | 0.765579i | \(-0.277547\pi\) | |||||||
\(258\) | −12.9938 | + | 32.7381i | −0.808957 | + | 2.03819i | ||||
\(259\) | −8.88177 | −0.551886 | ||||||||
\(260\) | −1.05578 | + | 1.12051i | −0.0654767 | + | 0.0694912i | ||||
\(261\) | − | 10.7123i | − | 0.663077i | ||||||
\(262\) | 2.36514 | − | 5.95902i | 0.146119 | − | 0.368150i | ||||
\(263\) | − | 28.7200i | − | 1.77095i | −0.464686 | − | 0.885476i | \(-0.653833\pi\) | ||
0.464686 | − | 0.885476i | \(-0.346167\pi\) | |||||||
\(264\) | 9.82254 | − | 4.59192i | 0.604535 | − | 0.282613i | ||||
\(265\) | 5.59198i | 0.343513i | ||||||||
\(266\) | 8.06422 | + | 6.31560i | 0.494449 | + | 0.387234i | ||||
\(267\) | 34.5721i | 2.11578i | ||||||||
\(268\) | 9.78650 | + | 9.22113i | 0.597805 | + | 0.563270i | ||||
\(269\) | − | 20.1815i | − | 1.23049i | −0.788337 | − | 0.615243i | \(-0.789058\pi\) | ||
0.788337 | − | 0.615243i | \(-0.210942\pi\) | |||||||
\(270\) | 3.80351 | + | 1.50962i | 0.231474 | + | 0.0918723i | ||||
\(271\) | 0.948407i | 0.0576116i | 0.999585 | + | 0.0288058i | \(0.00917045\pi\) | ||||
−0.999585 | + | 0.0288058i | \(0.990830\pi\) | |||||||
\(272\) | −0.770040 | − | 12.9330i | −0.0466906 | − | 0.784181i | ||||
\(273\) | −2.76101 | −0.167104 | ||||||||
\(274\) | −25.5796 | − | 10.1526i | −1.54532 | − | 0.613339i | ||||
\(275\) | − | 1.77595i | − | 0.107094i | ||||||
\(276\) | −9.06387 | + | 9.61959i | −0.545581 | + | 0.579031i | ||||
\(277\) | 17.3321 | 1.04139 | 0.520693 | − | 0.853744i | \(-0.325674\pi\) | ||||
0.520693 | + | 0.853744i | \(0.325674\pi\) | |||||||
\(278\) | −4.04684 | + | 10.1961i | −0.242713 | + | 0.611522i | ||||
\(279\) | −6.80073 | −0.407149 | ||||||||
\(280\) | −4.25754 | + | 1.99035i | −0.254436 | + | 0.118946i | ||||
\(281\) | − | 13.5353i | − | 0.807449i | −0.914881 | − | 0.403724i | \(-0.867716\pi\) | ||
0.914881 | − | 0.403724i | \(-0.132284\pi\) | |||||||
\(282\) | 7.67477 | − | 19.3368i | 0.457026 | − | 1.15149i | ||||
\(283\) | − | 7.04363i | − | 0.418700i | −0.977841 | − | 0.209350i | \(-0.932865\pi\) | ||
0.977841 | − | 0.209350i | \(-0.0671348\pi\) | |||||||
\(284\) | −2.66908 | − | 2.51489i | −0.158381 | − | 0.149231i | ||||
\(285\) | 2.65950 | − | 9.02539i | 0.157535 | − | 0.534618i | ||||
\(286\) | −1.79698 | − | 0.713222i | −0.106258 | − | 0.0421737i | ||||
\(287\) | −6.36992 | −0.376004 | ||||||||
\(288\) | −2.93840 | + | 8.91583i | −0.173147 | + | 0.525370i | ||||
\(289\) | −6.50896 | −0.382880 | ||||||||
\(290\) | −3.36773 | + | 8.48507i | −0.197760 | + | 0.498260i | ||||
\(291\) | 1.46003i | 0.0855885i | ||||||||
\(292\) | 17.3702 | + | 16.3668i | 1.01652 | + | 0.957792i | ||||
\(293\) | 9.35302i | 0.546409i | 0.961956 | + | 0.273205i | \(0.0880836\pi\) | ||||
−0.961956 | + | 0.273205i | \(0.911916\pi\) | |||||||
\(294\) | 12.0277 | + | 4.77378i | 0.701467 | + | 0.278413i | ||||
\(295\) | −5.35770 | −0.311937 | ||||||||
\(296\) | 13.6959 | − | 6.40266i | 0.796056 | − | 0.372147i | ||||
\(297\) | 5.13885i | 0.298186i | ||||||||
\(298\) | 28.5917 | + | 11.3480i | 1.65627 | + | 0.657375i | ||||
\(299\) | 2.35667 | 0.136290 | ||||||||
\(300\) | 3.14211 | + | 2.96060i | 0.181410 | + | 0.170930i | ||||
\(301\) | 19.1721 | 1.10506 | ||||||||
\(302\) | 18.3433 | + | 7.28047i | 1.05554 | + | 0.418944i | ||||
\(303\) | −5.56805 | −0.319876 | ||||||||
\(304\) | −16.9880 | − | 3.92548i | −0.974326 | − | 0.225142i | ||||
\(305\) | 4.94753 | 0.283294 | ||||||||
\(306\) | −7.06539 | − | 2.80425i | −0.403901 | − | 0.160309i | ||||
\(307\) | 5.63492 | 0.321602 | 0.160801 | − | 0.986987i | \(-0.448592\pi\) | ||||
0.160801 | + | 0.986987i | \(0.448592\pi\) | |||||||
\(308\) | −4.29552 | − | 4.04737i | −0.244760 | − | 0.230621i | ||||
\(309\) | −16.2246 | −0.922983 | ||||||||
\(310\) | 5.38675 | + | 2.13800i | 0.305947 | + | 0.121430i | ||||
\(311\) | − | 13.8045i | − | 0.782779i | −0.920225 | − | 0.391390i | \(-0.871994\pi\) | ||
0.920225 | − | 0.391390i | \(-0.128006\pi\) | |||||||
\(312\) | 4.25754 | − | 1.99035i | 0.241035 | − | 0.112681i | ||||
\(313\) | −17.3620 | −0.981360 | −0.490680 | − | 0.871340i | \(-0.663252\pi\) | ||||
−0.490680 | + | 0.871340i | \(0.663252\pi\) | |||||||
\(314\) | −14.0570 | − | 5.57924i | −0.793284 | − | 0.314855i | ||||
\(315\) | 2.75748i | 0.155366i | ||||||||
\(316\) | 13.7102 | + | 12.9181i | 0.771257 | + | 0.726702i | ||||
\(317\) | 8.07275i | 0.453411i | 0.973963 | + | 0.226705i | \(0.0727955\pi\) | ||||
−0.973963 | + | 0.226705i | \(0.927205\pi\) | |||||||
\(318\) | 6.29747 | − | 15.8666i | 0.353144 | − | 0.889756i | ||||
\(319\) | −11.4640 | −0.641861 | ||||||||
\(320\) | 5.13041 | − | 6.13831i | 0.286799 | − | 0.343142i | ||||
\(321\) | −2.86751 | −0.160049 | ||||||||
\(322\) | 6.68679 | + | 2.65399i | 0.372640 | + | 0.147901i | ||||
\(323\) | 3.99062 | − | 13.5427i | 0.222044 | − | 0.753536i | ||||
\(324\) | −16.3389 | − | 15.3950i | −0.907714 | − | 0.855276i | ||||
\(325\) | − | 0.769776i | − | 0.0426995i | ||||||
\(326\) | −4.28579 | + | 10.7981i | −0.237368 | + | 0.598054i | ||||
\(327\) | 5.25579i | 0.290646i | ||||||||
\(328\) | 9.82254 | − | 4.59192i | 0.542359 | − | 0.253547i | ||||
\(329\) | −11.3240 | −0.624312 | ||||||||
\(330\) | −2.00000 | + | 5.03905i | −0.110096 | + | 0.277390i | ||||
\(331\) | 35.8536 | 1.97069 | 0.985347 | − | 0.170560i | \(-0.0545575\pi\) | ||||
0.985347 | + | 0.170560i | \(0.0545575\pi\) | |||||||
\(332\) | −10.2600 | + | 10.8890i | −0.563089 | + | 0.597613i | ||||
\(333\) | − | 8.87040i | − | 0.486095i | ||||||
\(334\) | 3.07669 | + | 1.22114i | 0.168349 | + | 0.0668177i | ||||
\(335\) | −6.72318 | −0.367327 | ||||||||
\(336\) | 14.3217 | − | 0.852723i | 0.781314 | − | 0.0465199i | ||||
\(337\) | − | 33.9314i | − | 1.84836i | −0.381953 | − | 0.924182i | \(-0.624748\pi\) | ||
0.381953 | − | 0.924182i | \(-0.375252\pi\) | |||||||
\(338\) | 16.3091 | + | 6.47311i | 0.887101 | + | 0.352091i | ||||
\(339\) | − | 38.6719i | − | 2.10037i | ||||||
\(340\) | 4.71478 | + | 4.44241i | 0.255695 | + | 0.240924i | ||||
\(341\) | 7.27793i | 0.394122i | ||||||||
\(342\) | −6.30752 | + | 8.05389i | −0.341071 | + | 0.435505i | ||||
\(343\) | − | 18.6750i | − | 1.00836i | ||||||
\(344\) | −29.5637 | + | 13.8207i | −1.59397 | + | 0.745163i | ||||
\(345\) | − | 6.60852i | − | 0.355791i | ||||||
\(346\) | 2.15066 | − | 5.41863i | 0.115620 | − | 0.291307i | ||||
\(347\) | 18.7299i | 1.00548i | 0.864439 | + | 0.502738i | \(0.167674\pi\) | ||||
−0.864439 | + | 0.502738i | \(0.832326\pi\) | |||||||
\(348\) | 19.1111 | − | 20.2828i | 1.02446 | − | 1.08727i | ||||
\(349\) | 4.20801 | 0.225250 | 0.112625 | − | 0.993638i | \(-0.464074\pi\) | ||||
0.112625 | + | 0.993638i | \(0.464074\pi\) | |||||||
\(350\) | 0.866891 | − | 2.18415i | 0.0463373 | − | 0.116748i | ||||
\(351\) | 2.22741i | 0.118890i | ||||||||
\(352\) | 9.54144 | + | 3.14459i | 0.508560 | + | 0.167607i | ||||
\(353\) | −21.5221 | −1.14550 | −0.572752 | − | 0.819729i | \(-0.694124\pi\) | ||||
−0.572752 | + | 0.819729i | \(0.694124\pi\) | |||||||
\(354\) | 15.2019 | + | 6.03362i | 0.807970 | + | 0.320684i | ||||
\(355\) | 1.83362 | 0.0973185 | ||||||||
\(356\) | −21.9667 | + | 23.3135i | −1.16423 | + | 1.23562i | ||||
\(357\) | 11.6175i | 0.614864i | ||||||||
\(358\) | 1.53451 | + | 0.609049i | 0.0811015 | + | 0.0321892i | ||||
\(359\) | − | 17.2360i | − | 0.909683i | −0.890572 | − | 0.454842i | \(-0.849696\pi\) | ||
0.890572 | − | 0.454842i | \(-0.150304\pi\) | |||||||
\(360\) | −1.98780 | − | 4.25208i | −0.104766 | − | 0.224104i | ||||
\(361\) | −15.9641 | − | 10.3028i | −0.840214 | − | 0.542254i | ||||
\(362\) | −11.7556 | + | 29.6186i | −0.617862 | + | 1.55672i | ||||
\(363\) | 16.9363 | 0.888926 | ||||||||
\(364\) | −1.86188 | − | 1.75432i | −0.0975888 | − | 0.0919512i | ||||
\(365\) | −11.9331 | −0.624607 | ||||||||
\(366\) | −14.0380 | − | 5.57171i | −0.733780 | − | 0.291238i | ||||
\(367\) | − | 38.0242i | − | 1.98485i | −0.122871 | − | 0.992423i | \(-0.539210\pi\) | ||
0.122871 | − | 0.992423i | \(-0.460790\pi\) | |||||||
\(368\) | −12.2244 | + | 0.727845i | −0.637239 | + | 0.0379415i | ||||
\(369\) | − | 6.36176i | − | 0.331180i | ||||||
\(370\) | −2.78866 | + | 7.02610i | −0.144976 | + | 0.365270i | ||||
\(371\) | −9.29180 | −0.482406 | ||||||||
\(372\) | −12.8766 | − | 12.1327i | −0.667619 | − | 0.629051i | ||||
\(373\) | 28.9684i | 1.49993i | 0.661480 | + | 0.749963i | \(0.269929\pi\) | ||||
−0.661480 | + | 0.749963i | \(0.730071\pi\) | |||||||
\(374\) | −3.00103 | + | 7.56115i | −0.155179 | + | 0.390978i | ||||
\(375\) | −2.15859 | −0.111469 | ||||||||
\(376\) | 17.4618 | − | 8.16320i | 0.900525 | − | 0.420985i | ||||
\(377\) | −4.96902 | −0.255918 | ||||||||
\(378\) | −2.50842 | + | 6.32003i | −0.129019 | + | 0.325067i | ||||
\(379\) | −36.2461 | −1.86183 | −0.930917 | − | 0.365230i | \(-0.880990\pi\) | ||||
−0.930917 | + | 0.365230i | \(0.880990\pi\) | |||||||
\(380\) | 7.52805 | − | 4.39641i | 0.386181 | − | 0.225531i | ||||
\(381\) | −34.3896 | −1.76183 | ||||||||
\(382\) | −10.7123 | + | 26.9898i | −0.548087 | + | 1.38092i | ||||
\(383\) | −28.6181 | −1.46232 | −0.731158 | − | 0.682208i | \(-0.761020\pi\) | ||||
−0.731158 | + | 0.682208i | \(0.761020\pi\) | |||||||
\(384\) | −21.4697 | + | 11.6391i | −1.09562 | + | 0.593956i | ||||
\(385\) | 2.95096 | 0.150395 | ||||||||
\(386\) | 4.19285 | − | 10.5640i | 0.213410 | − | 0.537692i | ||||
\(387\) | 19.1475i | 0.973324i | ||||||||
\(388\) | −0.927687 | + | 0.984565i | −0.0470962 | + | 0.0499837i | ||||
\(389\) | −14.6860 | −0.744609 | −0.372305 | − | 0.928111i | \(-0.621432\pi\) | ||||
−0.372305 | + | 0.928111i | \(0.621432\pi\) | |||||||
\(390\) | −0.866891 | + | 2.18415i | −0.0438967 | + | 0.110599i | ||||
\(391\) | − | 9.91617i | − | 0.501482i | ||||||
\(392\) | 5.07759 | + | 10.8614i | 0.256457 | + | 0.548584i | ||||
\(393\) | − | 9.78579i | − | 0.493628i | ||||||
\(394\) | 12.5229 | + | 4.97035i | 0.630896 | + | 0.250403i | ||||
\(395\) | −9.41868 | −0.473905 | ||||||||
\(396\) | 4.04219 | − | 4.29002i | 0.203128 | − | 0.215582i | ||||
\(397\) | −10.9560 | −0.549864 | −0.274932 | − | 0.961464i | \(-0.588655\pi\) | ||||
−0.274932 | + | 0.961464i | \(0.588655\pi\) | |||||||
\(398\) | −3.64649 | + | 9.18741i | −0.182782 | + | 0.460523i | ||||
\(399\) | 14.9968 | + | 4.41911i | 0.750781 | + | 0.221232i | ||||
\(400\) | 0.237741 | + | 3.99293i | 0.0118871 | + | 0.199646i | ||||
\(401\) | − | 34.9245i | − | 1.74404i | −0.489466 | − | 0.872022i | \(-0.662808\pi\) | ||
0.489466 | − | 0.872022i | \(-0.337192\pi\) | |||||||
\(402\) | 19.0763 | + | 7.57138i | 0.951438 | + | 0.377626i | ||||
\(403\) | 3.15459i | 0.157141i | ||||||||
\(404\) | −3.75479 | − | 3.53788i | −0.186808 | − | 0.176016i | ||||
\(405\) | 11.2246 | 0.557753 | ||||||||
\(406\) | −14.0990 | − | 5.59591i | −0.699723 | − | 0.277721i | ||||
\(407\) | −9.49282 | −0.470542 | ||||||||
\(408\) | −8.37479 | − | 17.9144i | −0.414614 | − | 0.886897i | ||||
\(409\) | 2.26893i | 0.112192i | 0.998425 | + | 0.0560958i | \(0.0178652\pi\) | ||||
−0.998425 | + | 0.0560958i | \(0.982135\pi\) | |||||||
\(410\) | −2.00000 | + | 5.03905i | −0.0987730 | + | 0.248861i | ||||
\(411\) | −42.0064 | −2.07202 | ||||||||
\(412\) | −10.9410 | − | 10.3089i | −0.539022 | − | 0.507883i | ||||
\(413\) | − | 8.90250i | − | 0.438064i | ||||||
\(414\) | −2.65059 | + | 6.67823i | −0.130269 | + | 0.328217i | ||||
\(415\) | − | 7.48061i | − | 0.367209i | ||||||
\(416\) | 4.13570 | + | 1.36301i | 0.202769 | + | 0.0668270i | ||||
\(417\) | 16.7438i | 0.819949i | ||||||||
\(418\) | 8.61902 | + | 6.75010i | 0.421570 | + | 0.330158i | ||||
\(419\) | 4.00991i | 0.195897i | 0.995191 | + | 0.0979484i | \(0.0312280\pi\) | ||||
−0.995191 | + | 0.0979484i | \(0.968772\pi\) | |||||||
\(420\) | −4.91941 | + | 5.22103i | −0.240043 | + | 0.254760i | ||||
\(421\) | 27.1083i | 1.32118i | 0.750749 | + | 0.660588i | \(0.229693\pi\) | ||||
−0.750749 | + | 0.660588i | \(0.770307\pi\) | |||||||
\(422\) | 23.5888 | + | 9.36242i | 1.14829 | + | 0.455756i | ||||
\(423\) | − | 11.3095i | − | 0.549886i | ||||||
\(424\) | 14.3281 | − | 6.69824i | 0.695836 | − | 0.325295i | ||||
\(425\) | −3.23899 | −0.157114 | ||||||||
\(426\) | −5.20269 | − | 2.06495i | −0.252071 | − | 0.100047i | ||||
\(427\) | 8.22095i | 0.397840i | ||||||||
\(428\) | −1.93369 | − | 1.82198i | −0.0934686 | − | 0.0880690i | ||||
\(429\) | −2.95096 | −0.142474 | ||||||||
\(430\) | 6.01957 | − | 15.1665i | 0.290290 | − | 0.731391i | ||||
\(431\) | −27.6130 | −1.33007 | −0.665037 | − | 0.746811i | \(-0.731584\pi\) | ||||
−0.665037 | + | 0.746811i | \(0.731584\pi\) | |||||||
\(432\) | −0.687924 | − | 11.5539i | −0.0330977 | − | 0.555886i | ||||
\(433\) | − | 26.0792i | − | 1.25329i | −0.779306 | − | 0.626643i | \(-0.784428\pi\) | ||
0.779306 | − | 0.626643i | \(-0.215572\pi\) | |||||||
\(434\) | −3.55257 | + | 8.95078i | −0.170529 | + | 0.429651i | ||||
\(435\) | 13.9340i | 0.668085i | ||||||||
\(436\) | −3.33947 | + | 3.54422i | −0.159932 | + | 0.169737i | ||||
\(437\) | −12.8006 | − | 3.77194i | −0.612336 | − | 0.180436i | ||||
\(438\) | 33.8588 | + | 13.4386i | 1.61784 | + | 0.642120i | ||||
\(439\) | −5.65595 | −0.269944 | −0.134972 | − | 0.990849i | \(-0.543094\pi\) | ||||
−0.134972 | + | 0.990849i | \(0.543094\pi\) | |||||||
\(440\) | −4.55045 | + | 2.12728i | −0.216934 | + | 0.101414i | ||||
\(441\) | 7.03461 | 0.334981 | ||||||||
\(442\) | −1.30078 | + | 3.27735i | −0.0618719 | + | 0.155888i | ||||
\(443\) | − | 3.53141i | − | 0.167782i | −0.996475 | − | 0.0838911i | \(-0.973265\pi\) | ||
0.996475 | − | 0.0838911i | \(-0.0267348\pi\) | |||||||
\(444\) | 15.8250 | − | 16.7953i | 0.751023 | − | 0.797069i | ||||
\(445\) | − | 16.0161i | − | 0.759235i | ||||||
\(446\) | 33.0339 | + | 13.1112i | 1.56420 | + | 0.620832i | ||||
\(447\) | 46.9527 | 2.22079 | ||||||||
\(448\) | 10.1996 | + | 8.52484i | 0.481886 | + | 0.402761i | ||||
\(449\) | − | 21.1466i | − | 0.997971i | −0.866610 | − | 0.498986i | \(-0.833706\pi\) | ||
0.866610 | − | 0.498986i | \(-0.166294\pi\) | |||||||
\(450\) | 2.18136 | + | 0.865781i | 0.102830 | + | 0.0408133i | ||||
\(451\) | −6.80815 | −0.320583 | ||||||||
\(452\) | 24.5717 | − | 26.0782i | 1.15576 | − | 1.22662i | ||||
\(453\) | 30.1230 | 1.41530 | ||||||||
\(454\) | −19.3837 | − | 7.69341i | −0.909724 | − | 0.361070i | ||||
\(455\) | 1.27908 | 0.0599643 | ||||||||
\(456\) | −26.3111 | + | 3.99653i | −1.23213 | + | 0.187154i | ||||
\(457\) | 30.9871 | 1.44952 | 0.724758 | − | 0.689003i | \(-0.241951\pi\) | ||||
0.724758 | + | 0.689003i | \(0.241951\pi\) | |||||||
\(458\) | −24.9231 | − | 9.89198i | −1.16458 | − | 0.462222i | ||||
\(459\) | 9.37228 | 0.437461 | ||||||||
\(460\) | 4.19898 | − | 4.45643i | 0.195778 | − | 0.207782i | ||||
\(461\) | −1.84809 | −0.0860743 | −0.0430371 | − | 0.999073i | \(-0.513703\pi\) | ||||
−0.0430371 | + | 0.999073i | \(0.513703\pi\) | |||||||
\(462\) | −8.37303 | − | 3.32326i | −0.389548 | − | 0.154612i | ||||
\(463\) | 22.5105i | 1.04615i | 0.852287 | + | 0.523075i | \(0.175215\pi\) | ||||
−0.852287 | + | 0.523075i | \(0.824785\pi\) | |||||||
\(464\) | 25.7750 | − | 1.53465i | 1.19657 | − | 0.0712445i | ||||
\(465\) | 8.84602 | 0.410224 | ||||||||
\(466\) | −24.5056 | − | 9.72627i | −1.13520 | − | 0.450561i | ||||
\(467\) | − | 21.9652i | − | 1.01643i | −0.861231 | − | 0.508213i | \(-0.830306\pi\) | ||
0.861231 | − | 0.508213i | \(-0.169694\pi\) | |||||||
\(468\) | 1.75207 | − | 1.85949i | 0.0809894 | − | 0.0859550i | ||||
\(469\) | − | 11.1714i | − | 0.515849i | ||||||
\(470\) | −3.55546 | + | 8.95807i | −0.164001 | + | 0.413205i | ||||
\(471\) | −23.0842 | −1.06366 | ||||||||
\(472\) | 6.41761 | + | 13.7278i | 0.295394 | + | 0.631875i | ||||
\(473\) | 20.4911 | 0.942181 | ||||||||
\(474\) | 26.7245 | + | 10.6069i | 1.22749 | + | 0.487193i | ||||
\(475\) | −1.23206 | + | 4.18115i | −0.0565306 | + | 0.191844i | ||||
\(476\) | −7.38164 | + | 7.83422i | −0.338337 | + | 0.359081i | ||||
\(477\) | − | 9.27990i | − | 0.424898i | ||||||
\(478\) | −3.91028 | + | 9.85203i | −0.178852 | + | 0.450622i | ||||
\(479\) | 18.2719i | 0.834865i | 0.908708 | + | 0.417433i | \(0.137070\pi\) | ||||
−0.908708 | + | 0.417433i | \(0.862930\pi\) | |||||||
\(480\) | 3.82211 | − | 11.5972i | 0.174455 | − | 0.529338i | ||||
\(481\) | −4.11462 | −0.187611 | ||||||||
\(482\) | −2.54488 | + | 6.41188i | −0.115916 | + | 0.292053i | ||||
\(483\) | 10.9809 | 0.499649 | ||||||||
\(484\) | 11.4209 | + | 10.7611i | 0.519133 | + | 0.489143i | ||||
\(485\) | − | 0.676382i | − | 0.0307129i | ||||||
\(486\) | −20.4379 | − | 8.11180i | −0.927081 | − | 0.367959i | ||||
\(487\) | −8.12733 | −0.368285 | −0.184142 | − | 0.982900i | \(-0.558951\pi\) | ||||
−0.184142 | + | 0.982900i | \(0.558951\pi\) | |||||||
\(488\) | −5.92629 | − | 12.6769i | −0.268271 | − | 0.573855i | ||||
\(489\) | 17.7325i | 0.801892i | ||||||||
\(490\) | −5.57200 | − | 2.21153i | −0.251717 | − | 0.0999067i | ||||
\(491\) | 28.5523i | 1.28855i | 0.764796 | + | 0.644273i | \(0.222840\pi\) | ||||
−0.764796 | + | 0.644273i | \(0.777160\pi\) | |||||||
\(492\) | 11.3495 | − | 12.0454i | 0.511677 | − | 0.543049i | ||||
\(493\) | 20.9082i | 0.941656i | ||||||||
\(494\) | 3.73588 | + | 2.92580i | 0.168085 | + | 0.131638i | ||||
\(495\) | 2.94719i | 0.132466i | ||||||||
\(496\) | −0.974276 | − | 16.3632i | −0.0437463 | − | 0.734732i | ||||
\(497\) | 3.04680i | 0.136668i | ||||||||
\(498\) | −8.42436 | + | 21.2254i | −0.377505 | + | 0.951132i | ||||
\(499\) | 11.8878i | 0.532172i | 0.963949 | + | 0.266086i | \(0.0857305\pi\) | ||||
−0.963949 | + | 0.266086i | \(0.914269\pi\) | |||||||
\(500\) | −1.45563 | − | 1.37154i | −0.0650979 | − | 0.0613373i | ||||
\(501\) | 5.05247 | 0.225728 | ||||||||
\(502\) | −9.06296 | + | 22.8343i | −0.404500 | + | 1.01915i | ||||
\(503\) | 13.7172i | 0.611619i | 0.952093 | + | 0.305809i | \(0.0989270\pi\) | ||||
−0.952093 | + | 0.305809i | \(0.901073\pi\) | |||||||
\(504\) | 7.06539 | − | 3.30299i | 0.314717 | − | 0.147127i | ||||
\(505\) | 2.57949 | 0.114786 | ||||||||
\(506\) | 7.14683 | + | 2.83658i | 0.317715 | + | 0.126101i | ||||
\(507\) | 26.7826 | 1.18946 | ||||||||
\(508\) | −23.1905 | − | 21.8508i | −1.02891 | − | 0.969471i | ||||
\(509\) | − | 9.78264i | − | 0.433608i | −0.976215 | − | 0.216804i | \(-0.930437\pi\) | ||
0.976215 | − | 0.216804i | \(-0.0695632\pi\) | |||||||
\(510\) | 9.19026 | + | 3.64762i | 0.406952 | + | 0.161519i | ||||
\(511\) | − | 19.8284i | − | 0.877156i | ||||||
\(512\) | −21.8733 | − | 5.79281i | −0.966675 | − | 0.256009i | ||||
\(513\) | 3.56506 | − | 12.0985i | 0.157401 | − | 0.534163i | ||||
\(514\) | 12.8061 | − | 32.2653i | 0.564853 | − | 1.42316i | ||||
\(515\) | 7.51628 | 0.331207 | ||||||||
\(516\) | −34.1597 | + | 36.2541i | −1.50380 | + | 1.59600i | ||||
\(517\) | −12.1031 | −0.532292 | ||||||||
\(518\) | −11.6748 | − | 4.63372i | −0.512960 | − | 0.203594i | ||||
\(519\) | − | 8.89837i | − | 0.390595i | ||||||
\(520\) | −1.97237 | + | 0.922061i | −0.0864942 | + | 0.0404350i | ||||
\(521\) | − | 34.7472i | − | 1.52230i | −0.648575 | − | 0.761150i | \(-0.724635\pi\) | ||
0.648575 | − | 0.761150i | \(-0.275365\pi\) | |||||||
\(522\) | 5.58875 | − | 14.0810i | 0.244613 | − | 0.616308i | ||||
\(523\) | 15.1384 | 0.661957 | 0.330978 | − | 0.943638i | \(-0.392621\pi\) | ||||
0.330978 | + | 0.943638i | \(0.392621\pi\) | |||||||
\(524\) | 6.21778 | − | 6.59900i | 0.271625 | − | 0.288279i | ||||
\(525\) | − | 3.58677i | − | 0.156540i | ||||||
\(526\) | 14.9836 | − | 37.7514i | 0.653314 | − | 1.64604i | ||||
\(527\) | 13.2736 | 0.578205 | ||||||||
\(528\) | 15.3070 | − | 0.911389i | 0.666153 | − | 0.0396631i | ||||
\(529\) | 13.6272 | 0.592487 | ||||||||
\(530\) | −2.91740 | + | 7.35046i | −0.126724 | + | 0.319284i | ||||
\(531\) | 8.89110 | 0.385841 | ||||||||
\(532\) | 7.30520 | + | 12.5088i | 0.316721 | + | 0.542327i | ||||
\(533\) | −2.95096 | −0.127820 | ||||||||
\(534\) | −18.0367 | + | 45.4438i | −0.780523 | + | 1.96655i | ||||
\(535\) | 1.32842 | 0.0574326 | ||||||||
\(536\) | 8.05323 | + | 17.2266i | 0.347847 | + | 0.744075i | ||||
\(537\) | 2.51995 | 0.108744 | ||||||||
\(538\) | 10.5289 | − | 26.5278i | 0.453934 | − | 1.14370i | ||||
\(539\) | − | 7.52821i | − | 0.324263i | ||||||
\(540\) | 4.21200 | + | 3.96867i | 0.181256 | + | 0.170785i | ||||
\(541\) | −0.101510 | −0.00436427 | −0.00218214 | − | 0.999998i | \(-0.500695\pi\) | ||||
−0.00218214 | + | 0.999998i | \(0.500695\pi\) | |||||||
\(542\) | −0.494795 | + | 1.24665i | −0.0212533 | + | 0.0535481i | ||||
\(543\) | 48.6391i | 2.08730i | ||||||||
\(544\) | 5.73513 | − | 17.4018i | 0.245892 | − | 0.746095i | ||||
\(545\) | − | 2.43483i | − | 0.104297i | ||||||
\(546\) | −3.62925 | − | 1.44045i | −0.155318 | − | 0.0616456i | ||||
\(547\) | −4.87194 | −0.208309 | −0.104155 | − | 0.994561i | \(-0.533214\pi\) | ||||
−0.104155 | + | 0.994561i | \(0.533214\pi\) | |||||||
\(548\) | −28.3268 | − | 26.6904i | −1.21006 | − | 1.14016i | ||||
\(549\) | −8.21043 | −0.350412 | ||||||||
\(550\) | 0.926532 | − | 2.33442i | 0.0395074 | − | 0.0995399i | ||||
\(551\) | 26.9900 | + | 7.95311i | 1.14981 | + | 0.338814i | ||||
\(552\) | −16.9328 | + | 7.91588i | −0.720707 | + | 0.336922i | ||||
\(553\) | − | 15.6504i | − | 0.665521i | ||||||
\(554\) | 22.7824 | + | 9.04236i | 0.967934 | + | 0.384173i | ||||
\(555\) | 11.5381i | 0.489766i | ||||||||
\(556\) | −10.6388 | + | 11.2911i | −0.451188 | + | 0.478851i | ||||
\(557\) | 19.9620 | 0.845817 | 0.422908 | − | 0.906172i | \(-0.361009\pi\) | ||||
0.422908 | + | 0.906172i | \(0.361009\pi\) | |||||||
\(558\) | −8.93932 | − | 3.54802i | −0.378432 | − | 0.150200i | ||||
\(559\) | 8.88177 | 0.375659 | ||||||||
\(560\) | −6.63477 | + | 0.395037i | −0.280370 | + | 0.0166934i | ||||
\(561\) | 12.4168i | 0.524237i | ||||||||
\(562\) | 7.06152 | − | 17.7917i | 0.297872 | − | 0.750497i | ||||
\(563\) | −16.6366 | −0.701150 | −0.350575 | − | 0.936535i | \(-0.614014\pi\) | ||||
−0.350575 | + | 0.936535i | \(0.614014\pi\) | |||||||
\(564\) | 20.1764 | − | 21.4135i | 0.849581 | − | 0.901670i | ||||
\(565\) | 17.9154i | 0.753705i | ||||||||
\(566\) | 3.67474 | − | 9.25860i | 0.154461 | − | 0.389168i | ||||
\(567\) | 18.6511i | 0.783271i | ||||||||
\(568\) | −2.19636 | − | 4.69822i | −0.0921574 | − | 0.197133i | ||||
\(569\) | 20.8399i | 0.873654i | 0.899546 | + | 0.436827i | \(0.143898\pi\) | ||||
−0.899546 | + | 0.436827i | \(0.856102\pi\) | |||||||
\(570\) | 8.20447 | − | 10.4761i | 0.343647 | − | 0.438794i | ||||
\(571\) | − | 14.0220i | − | 0.586801i | −0.955990 | − | 0.293400i | \(-0.905213\pi\) | ||
0.955990 | − | 0.293400i | \(-0.0947869\pi\) | |||||||
\(572\) | −1.98997 | − | 1.87501i | −0.0832048 | − | 0.0783981i | ||||
\(573\) | 44.3221i | 1.85158i | ||||||||
\(574\) | −8.37303 | − | 3.32326i | −0.349483 | − | 0.138710i | ||||
\(575\) | 3.06150i | 0.127673i | ||||||||
\(576\) | −8.51392 | + | 10.1865i | −0.354747 | + | 0.424439i | ||||
\(577\) | −28.0430 | −1.16745 | −0.583723 | − | 0.811953i | \(-0.698405\pi\) | ||||
−0.583723 | + | 0.811953i | \(0.698405\pi\) | |||||||
\(578\) | −8.55579 | − | 3.39580i | −0.355874 | − | 0.141247i | ||||
\(579\) | − | 17.3480i | − | 0.720956i | ||||||
\(580\) | −8.85352 | + | 9.39634i | −0.367622 | + | 0.390162i | ||||
\(581\) | 12.4300 | 0.515683 | ||||||||
\(582\) | −0.761715 | + | 1.91916i | −0.0315741 | + | 0.0795517i | ||||
\(583\) | −9.93106 | −0.411302 | ||||||||
\(584\) | 14.2938 | + | 30.5758i | 0.591482 | + | 1.26523i | ||||
\(585\) | 1.27744i | 0.0528158i | ||||||||
\(586\) | −4.87958 | + | 12.2942i | −0.201573 | + | 0.507869i | ||||
\(587\) | 29.7491i | 1.22788i | 0.789353 | + | 0.613939i | \(0.210416\pi\) | ||||
−0.789353 | + | 0.613939i | \(0.789584\pi\) | |||||||
\(588\) | 13.3194 | + | 12.5499i | 0.549282 | + | 0.517550i | ||||
\(589\) | 5.04904 | − | 17.1346i | 0.208042 | − | 0.706019i | ||||
\(590\) | −7.04250 | − | 2.79517i | −0.289935 | − | 0.115075i | ||||
\(591\) | 20.5649 | 0.845927 | ||||||||
\(592\) | 21.3431 | − | 1.27078i | 0.877195 | − | 0.0522286i | ||||
\(593\) | −11.3271 | −0.465149 | −0.232575 | − | 0.972579i | \(-0.574715\pi\) | ||||
−0.232575 | + | 0.972579i | \(0.574715\pi\) | |||||||
\(594\) | −2.68100 | + | 6.75484i | −0.110003 | + | 0.277154i | ||||
\(595\) | − | 5.38200i | − | 0.220640i | ||||||
\(596\) | 31.6623 | + | 29.8332i | 1.29694 | + | 1.22202i | ||||
\(597\) | 15.0874i | 0.617485i | ||||||||
\(598\) | 3.09776 | + | 1.22950i | 0.126677 | + | 0.0502781i | ||||
\(599\) | 18.8758 | 0.771244 | 0.385622 | − | 0.922657i | \(-0.373987\pi\) | ||||
0.385622 | + | 0.922657i | \(0.373987\pi\) | |||||||
\(600\) | 2.58562 | + | 5.53087i | 0.105558 | + | 0.225797i | ||||
\(601\) | 37.4036i | 1.52573i | 0.646560 | + | 0.762863i | \(0.276207\pi\) | ||||
−0.646560 | + | 0.762863i | \(0.723793\pi\) | |||||||
\(602\) | 25.2010 | + | 10.0023i | 1.02712 | + | 0.407663i | ||||
\(603\) | 11.1571 | 0.454354 | ||||||||
\(604\) | 20.3133 | + | 19.1399i | 0.826538 | + | 0.778789i | ||||
\(605\) | −7.84602 | −0.318986 | ||||||||
\(606\) | −7.31900 | − | 2.90492i | −0.297314 | − | 0.118004i | ||||
\(607\) | −29.0143 | −1.17765 | −0.588826 | − | 0.808260i | \(-0.700410\pi\) | ||||
−0.588826 | + | 0.808260i | \(0.700410\pi\) | |||||||
\(608\) | −20.2821 | − | 14.0227i | −0.822548 | − | 0.568696i | ||||
\(609\) | −23.1532 | −0.938213 | ||||||||
\(610\) | 6.50335 | + | 2.58118i | 0.263313 | + | 0.104509i | ||||
\(611\) | −5.24602 | −0.212231 | ||||||||
\(612\) | −7.82419 | − | 7.37219i | −0.316274 | − | 0.298003i | ||||
\(613\) | 13.4421 | 0.542919 | 0.271460 | − | 0.962450i | \(-0.412494\pi\) | ||||
0.271460 | + | 0.962450i | \(0.412494\pi\) | |||||||
\(614\) | 7.40690 | + | 2.93980i | 0.298918 | + | 0.118641i | ||||
\(615\) | 8.27502i | 0.333681i | ||||||||
\(616\) | −3.53475 | − | 7.56115i | −0.142419 | − | 0.304648i | ||||
\(617\) | 46.9822 | 1.89143 | 0.945716 | − | 0.324995i | \(-0.105363\pi\) | ||||
0.945716 | + | 0.324995i | \(0.105363\pi\) | |||||||
\(618\) | −21.3266 | − | 8.46454i | −0.857882 | − | 0.340494i | ||||
\(619\) | 13.2142i | 0.531125i | 0.964094 | + | 0.265563i | \(0.0855577\pi\) | ||||
−0.964094 | + | 0.265563i | \(0.914442\pi\) | |||||||
\(620\) | 5.96527 | + | 5.62066i | 0.239571 | + | 0.225731i | ||||
\(621\) | − | 8.85871i | − | 0.355488i | ||||||
\(622\) | 7.20195 | − | 18.1455i | 0.288772 | − | 0.727567i | ||||
\(623\) | 26.6128 | 1.06622 | ||||||||
\(624\) | 6.63477 | − | 0.395037i | 0.265603 | − | 0.0158142i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −22.8218 | − | 9.05798i | −0.912142 | − | 0.362030i | ||||
\(627\) | 16.0286 | + | 4.72313i | 0.640121 | + | 0.188624i | ||||
\(628\) | −15.5667 | − | 14.6674i | −0.621179 | − | 0.585294i | ||||
\(629\) | 17.3131i | 0.690319i | ||||||||
\(630\) | −1.43861 | + | 3.62460i | −0.0573155 | + | 0.144408i | ||||
\(631\) | − | 28.5124i | − | 1.13506i | −0.823352 | − | 0.567530i | \(-0.807899\pi\) | ||
0.823352 | − | 0.567530i | \(-0.192101\pi\) | |||||||
\(632\) | 11.2820 | + | 24.1332i | 0.448773 | + | 0.959966i | ||||
\(633\) | 38.7371 | 1.53966 | ||||||||
\(634\) | −4.21165 | + | 10.6113i | −0.167266 | + | 0.421430i | ||||
\(635\) | 15.9315 | 0.632223 | ||||||||
\(636\) | 16.5556 | − | 17.5706i | 0.656472 | − | 0.696721i | ||||
\(637\) | − | 3.26307i | − | 0.129288i | ||||||
\(638\) | −15.0690 | − | 5.98090i | −0.596588 | − | 0.236786i | ||||
\(639\) | −3.04290 | −0.120375 | ||||||||
\(640\) | 9.94617 | − | 5.39200i | 0.393157 | − | 0.213138i | ||||
\(641\) | 6.69678i | 0.264507i | 0.991216 | + | 0.132253i | \(0.0422213\pi\) | ||||
−0.991216 | + | 0.132253i | \(0.957779\pi\) | |||||||
\(642\) | −3.76924 | − | 1.49601i | −0.148760 | − | 0.0590430i | ||||
\(643\) | − | 6.10252i | − | 0.240660i | −0.992734 | − | 0.120330i | \(-0.961605\pi\) | ||
0.992734 | − | 0.120330i | \(-0.0383953\pi\) | |||||||
\(644\) | 7.40493 | + | 6.97715i | 0.291795 | + | 0.274938i | ||||
\(645\) | − | 24.9061i | − | 0.980675i | ||||||
\(646\) | 12.3109 | − | 15.7195i | 0.484366 | − | 0.618474i | ||||
\(647\) | − | 46.2880i | − | 1.81977i | −0.414860 | − | 0.909885i | \(-0.636169\pi\) | ||
0.414860 | − | 0.909885i | \(-0.363831\pi\) | |||||||
\(648\) | −13.4451 | − | 28.7603i | −0.528174 | − | 1.12981i | ||||
\(649\) | − | 9.51498i | − | 0.373496i | ||||||
\(650\) | 0.401601 | − | 1.01184i | 0.0157521 | − | 0.0396878i | ||||
\(651\) | 14.6988i | 0.576091i | ||||||||
\(652\) | −11.2670 | + | 11.9578i | −0.441251 | + | 0.468305i | ||||
\(653\) | −17.4421 | −0.682560 | −0.341280 | − | 0.939962i | \(-0.610860\pi\) | ||||
−0.341280 | + | 0.939962i | \(0.610860\pi\) | |||||||
\(654\) | −2.74201 | + | 6.90855i | −0.107221 | + | 0.270146i | ||||
\(655\) | 4.53342i | 0.177135i | ||||||||
\(656\) | 15.3070 | − | 0.911389i | 0.597639 | − | 0.0355838i | ||||
\(657\) | 19.8030 | 0.772588 | ||||||||
\(658\) | −14.8850 | − | 5.90786i | −0.580277 | − | 0.230312i | ||||
\(659\) | −3.47777 | −0.135475 | −0.0677373 | − | 0.997703i | \(-0.521578\pi\) | ||||
−0.0677373 | + | 0.997703i | \(0.521578\pi\) | |||||||
\(660\) | −5.25786 | + | 5.58023i | −0.204662 | + | 0.217210i | ||||
\(661\) | 32.9565i | 1.28186i | 0.767600 | + | 0.640930i | \(0.221451\pi\) | ||||
−0.767600 | + | 0.640930i | \(0.778549\pi\) | |||||||
\(662\) | 47.1283 | + | 18.7053i | 1.83170 | + | 0.727001i | ||||
\(663\) | 5.38200i | 0.209019i | ||||||||
\(664\) | −19.1673 | + | 8.96049i | −0.743836 | + | 0.347735i | ||||
\(665\) | −6.94753 | − | 2.04722i | −0.269413 | − | 0.0793878i | ||||
\(666\) | 4.62779 | − | 11.6598i | 0.179323 | − | 0.451809i | ||||
\(667\) | 19.7625 | 0.765206 | ||||||||
\(668\) | 3.40711 | + | 3.21029i | 0.131825 | + | 0.124210i | ||||
\(669\) | 54.2476 | 2.09734 | ||||||||
\(670\) | −8.83739 | − | 3.50756i | −0.341418 | − | 0.135509i | ||||
\(671\) | 8.78654i | 0.339201i | ||||||||
\(672\) | 19.2703 | + | 6.35094i | 0.743367 | + | 0.244993i | ||||
\(673\) | 30.4788i | 1.17487i | 0.809271 | + | 0.587435i | \(0.199862\pi\) | ||||
−0.809271 | + | 0.587435i | \(0.800138\pi\) | |||||||
\(674\) | 17.7024 | − | 44.6017i | 0.681872 | − | 1.71799i | ||||
\(675\) | −2.89358 | −0.111374 | ||||||||
\(676\) | 18.0607 | + | 17.0173i | 0.694642 | + | 0.654513i | ||||
\(677\) | − | 21.1145i | − | 0.811497i | −0.913985 | − | 0.405749i | \(-0.867011\pi\) | ||
0.913985 | − | 0.405749i | \(-0.132989\pi\) | |||||||
\(678\) | 20.1756 | − | 50.8328i | 0.774838 | − | 1.95222i | ||||
\(679\) | 1.12390 | 0.0431312 | ||||||||
\(680\) | 3.87976 | + | 8.29915i | 0.148782 | + | 0.318258i | ||||
\(681\) | −31.8316 | −1.21979 | ||||||||
\(682\) | −3.79698 | + | 9.56658i | −0.145394 | + | 0.366323i | ||||
\(683\) | −12.4356 | −0.475837 | −0.237918 | − | 0.971285i | \(-0.576465\pi\) | ||||
−0.237918 | + | 0.971285i | \(0.576465\pi\) | |||||||
\(684\) | −12.4928 | + | 7.29585i | −0.477675 | + | 0.278964i | ||||
\(685\) | 19.4601 | 0.743533 | ||||||||
\(686\) | 9.74298 | − | 24.5477i | 0.371989 | − | 0.937234i | ||||
\(687\) | −40.9282 | −1.56151 | ||||||||
\(688\) | −46.0709 | + | 2.74309i | −1.75644 | + | 0.104579i | ||||
\(689\) | −4.30457 | −0.163991 | ||||||||
\(690\) | 3.44774 | − | 8.68667i | 0.131253 | − | 0.330696i | ||||
\(691\) | − | 2.47203i | − | 0.0940404i | −0.998894 | − | 0.0470202i | \(-0.985027\pi\) | ||
0.998894 | − | 0.0470202i | \(-0.0149725\pi\) | |||||||
\(692\) | 5.65392 | − | 6.00058i | 0.214930 | − | 0.228108i | ||||
\(693\) | −4.89713 | −0.186027 | ||||||||
\(694\) | −9.77163 | + | 24.6198i | −0.370926 | + | 0.934556i | ||||
\(695\) | − | 7.75685i | − | 0.294234i | ||||||
\(696\) | 35.7026 | − | 16.6906i | 1.35330 | − | 0.632655i | ||||
\(697\) | 12.4168i | 0.470319i | ||||||||
\(698\) | 5.53128 | + | 2.19537i | 0.209362 | + | 0.0830959i | ||||
\(699\) | −40.2425 | −1.52211 | ||||||||
\(700\) | 2.27900 | − | 2.41872i | 0.0861379 | − | 0.0914192i | ||||
\(701\) | 20.4326 | 0.771727 | 0.385864 | − | 0.922556i | \(-0.373903\pi\) | ||||
0.385864 | + | 0.922556i | \(0.373903\pi\) | |||||||
\(702\) | −1.16207 | + | 2.92785i | −0.0438594 | + | 0.110505i | ||||
\(703\) | 22.3492 | + | 6.58561i | 0.842915 | + | 0.248381i | ||||
\(704\) | 10.9013 | + | 9.11133i | 0.410859 | + | 0.343396i | ||||
\(705\) | 14.7108i | 0.554039i | ||||||||
\(706\) | −28.2900 | − | 11.2283i | −1.06471 | − | 0.422583i | ||||
\(707\) | 4.28615i | 0.161197i | ||||||||
\(708\) | 16.8345 | + | 15.8620i | 0.632679 | + | 0.596129i | ||||
\(709\) | −29.1721 | −1.09558 | −0.547790 | − | 0.836616i | \(-0.684531\pi\) | ||||
−0.547790 | + | 0.836616i | \(0.684531\pi\) | |||||||
\(710\) | 2.41023 | + | 0.956621i | 0.0904543 | + | 0.0359013i | ||||
\(711\) | 15.6303 | 0.586183 | ||||||||
\(712\) | −41.0374 | + | 19.1845i | −1.53794 | + | 0.718971i | ||||
\(713\) | − | 12.5462i | − | 0.469859i | ||||||
\(714\) | −6.06099 | + | 15.2708i | −0.226827 | + | 0.571496i | ||||
\(715\) | 1.36708 | 0.0511259 | ||||||||
\(716\) | 1.69931 | + | 1.60115i | 0.0635063 | + | 0.0598376i | ||||
\(717\) | 16.1788i | 0.604209i | ||||||||
\(718\) | 8.99224 | − | 22.6562i | 0.335587 | − | 0.845520i | ||||
\(719\) | 17.2158i | 0.642039i | 0.947073 | + | 0.321020i | \(0.104026\pi\) | ||||
−0.947073 | + | 0.321020i | \(0.895974\pi\) | |||||||
\(720\) | −0.394532 | − | 6.62627i | −0.0147033 | − | 0.246947i | ||||
\(721\) | 12.4893i | 0.465125i | ||||||||
\(722\) | −15.6091 | − | 21.8713i | −0.580911 | − | 0.813967i | ||||
\(723\) | 10.5295i | 0.391595i | ||||||||
\(724\) | −30.9047 | + | 32.7995i | −1.14857 | + | 1.21899i | ||||
\(725\) | − | 6.45515i | − | 0.239738i | ||||||
\(726\) | 22.2622 | + | 8.83587i | 0.826227 | + | 0.327930i | ||||
\(727\) | − | 31.6614i | − | 1.17426i | −0.809494 | − | 0.587128i | \(-0.800259\pi\) | ||
0.809494 | − | 0.587128i | \(-0.199741\pi\) | |||||||
\(728\) | −1.53212 | − | 3.27735i | −0.0567842 | − | 0.121467i | ||||
\(729\) | 0.110993 | 0.00411086 | ||||||||
\(730\) | −15.6856 | − | 6.22563i | −0.580551 | − | 0.230421i | ||||
\(731\) | − | 37.3718i | − | 1.38225i | ||||||
\(732\) | −15.5457 | − | 14.6476i | −0.574585 | − | 0.541392i | ||||
\(733\) | −25.0202 | −0.924141 | −0.462071 | − | 0.886843i | \(-0.652893\pi\) | ||||
−0.462071 | + | 0.886843i | \(0.652893\pi\) | |||||||
\(734\) | 19.8376 | − | 49.9814i | 0.732221 | − | 1.84485i | ||||
\(735\) | −9.15023 | −0.337511 | ||||||||
\(736\) | −16.4482 | − | 5.42086i | −0.606289 | − | 0.199816i | ||||
\(737\) | − | 11.9400i | − | 0.439816i | ||||||
\(738\) | 3.31900 | − | 8.36231i | 0.122174 | − | 0.307821i | ||||
\(739\) | − | 46.5491i | − | 1.71233i | −0.516699 | − | 0.856167i | \(-0.672839\pi\) | ||
0.516699 | − | 0.856167i | \(-0.327161\pi\) | |||||||
\(740\) | −7.33120 | + | 7.78068i | −0.269500 | + | 0.286024i | ||||
\(741\) | 6.94753 | + | 2.04722i | 0.255224 | + | 0.0752065i | ||||
\(742\) | −12.2137 | − | 4.84764i | −0.448381 | − | 0.177962i | ||||
\(743\) | 6.64028 | 0.243608 | 0.121804 | − | 0.992554i | \(-0.461132\pi\) | ||||
0.121804 | + | 0.992554i | \(0.461132\pi\) | |||||||
\(744\) | −10.5960 | − | 22.6658i | −0.388469 | − | 0.830970i | ||||
\(745\) | −21.7516 | −0.796916 | ||||||||
\(746\) | −15.1131 | + | 38.0779i | −0.553332 | + | 1.39413i | ||||
\(747\) | 12.4141i | 0.454207i | ||||||||
\(748\) | −7.88948 | + | 8.37320i | −0.288468 | + | 0.306154i | ||||
\(749\) | 2.20734i | 0.0806545i | ||||||||
\(750\) | −2.83739 | − | 1.12616i | −0.103607 | − | 0.0411216i | ||||
\(751\) | −35.0039 | −1.27731 | −0.638656 | − | 0.769492i | \(-0.720509\pi\) | ||||
−0.638656 | + | 0.769492i | \(0.720509\pi\) | |||||||
\(752\) | 27.2118 | − | 1.62020i | 0.992312 | − | 0.0590827i | ||||
\(753\) | 37.4981i | 1.36651i | ||||||||
\(754\) | −6.53160 | − | 2.59240i | −0.237867 | − | 0.0944095i | ||||
\(755\) | −13.9550 | −0.507874 | ||||||||
\(756\) | −6.59446 | + | 6.99878i | −0.239838 | + | 0.254543i | ||||
\(757\) | −38.3062 | −1.39226 | −0.696131 | − | 0.717915i | \(-0.745097\pi\) | ||||
−0.696131 | + | 0.717915i | \(0.745097\pi\) | |||||||
\(758\) | −47.6441 | − | 18.9100i | −1.73051 | − | 0.686842i | ||||
\(759\) | 11.7364 | 0.426004 | ||||||||
\(760\) | 12.1890 | − | 1.85145i | 0.442142 | − | 0.0671593i | ||||
\(761\) | 13.7624 | 0.498886 | 0.249443 | − | 0.968390i | \(-0.419753\pi\) | ||||
0.249443 | + | 0.968390i | \(0.419753\pi\) | |||||||
\(762\) | −45.2039 | − | 17.9414i | −1.63756 | − | 0.649950i | ||||
\(763\) | 4.04578 | 0.146467 | ||||||||
\(764\) | −28.1618 | + | 29.8884i | −1.01886 | + | 1.08133i | ||||
\(765\) | 5.37511 | 0.194337 | ||||||||
\(766\) | −37.6175 | − | 14.9304i | −1.35917 | − | 0.539457i | ||||
\(767\) | − | 4.12423i | − | 0.148917i | ||||||
\(768\) | −34.2934 | + | 4.09822i | −1.23746 | + | 0.147882i | ||||
\(769\) | −15.8867 | −0.572888 | −0.286444 | − | 0.958097i | \(-0.592473\pi\) | ||||
−0.286444 | + | 0.958097i | \(0.592473\pi\) | |||||||
\(770\) | 3.87894 | + | 1.53955i | 0.139787 | + | 0.0554816i | ||||
\(771\) | − | 52.9854i | − | 1.90822i | ||||||
\(772\) | 11.0227 | − | 11.6985i | 0.396716 | − | 0.421039i | ||||
\(773\) | 48.1094i | 1.73037i | 0.501449 | + | 0.865187i | \(0.332801\pi\) | ||||
−0.501449 | + | 0.865187i | \(0.667199\pi\) | |||||||
\(774\) | −9.98949 | + | 25.1688i | −0.359065 | + | 0.904672i | ||||
\(775\) | −4.09806 | −0.147207 | ||||||||
\(776\) | −1.73307 | + | 0.810191i | −0.0622136 | + | 0.0290842i | ||||
\(777\) | −19.1721 | −0.687795 | ||||||||
\(778\) | −19.3042 | − | 7.66185i | −0.692089 | − | 0.274691i | ||||
\(779\) | 16.0286 | + | 4.72313i | 0.574284 | + | 0.169224i | ||||
\(780\) | −2.27900 | + | 2.41872i | −0.0816011 | + | 0.0866042i | ||||
\(781\) | 3.25641i | 0.116524i | ||||||||
\(782\) | 5.17338 | − | 13.0345i | 0.185000 | − | 0.466111i | ||||
\(783\) | 18.6785i | 0.667516i | ||||||||
\(784\) | 1.00778 | + | 16.9260i | 0.0359922 | + | 0.604499i | ||||
\(785\) | 10.6941 | 0.381689 | ||||||||
\(786\) | 5.10536 | − | 12.8631i | 0.182102 | − | 0.458811i | ||||
\(787\) | −42.6101 | −1.51889 | −0.759444 | − | 0.650573i | \(-0.774529\pi\) | ||||
−0.759444 | + | 0.650573i | \(0.774529\pi\) | |||||||
\(788\) | 13.8678 | + | 13.0667i | 0.494021 | + | 0.465482i | ||||
\(789\) | − | 61.9946i | − | 2.20707i | ||||||
\(790\) | −12.3805 | − | 4.91384i | −0.440479 | − | 0.174826i | ||||
\(791\) | −29.7687 | −1.05845 | ||||||||
\(792\) | 7.55147 | − | 3.53023i | 0.268330 | − | 0.125441i | ||||
\(793\) | 3.80849i | 0.135243i | ||||||||
\(794\) | −14.4012 | − | 5.71585i | −0.511080 | − | 0.202848i | ||||
\(795\) | 12.0708i | 0.428107i | ||||||||
\(796\) | −9.58635 | + | 10.1741i | −0.339779 | + | 0.360612i | ||||
\(797\) | 44.6109i | 1.58020i | 0.612979 | + | 0.790099i | \(0.289971\pi\) | ||||
−0.612979 | + | 0.790099i | \(0.710029\pi\) | |||||||
\(798\) | 17.4073 | + | 13.6328i | 0.616212 | + | 0.482595i | ||||
\(799\) | 22.0737i | 0.780911i | ||||||||
\(800\) | −1.77065 | + | 5.37260i | −0.0626021 | + | 0.189950i | ||||
\(801\) | 26.5787i | 0.939112i | ||||||||
\(802\) | 18.2205 | − | 45.9070i | 0.643388 | − | 1.62103i | ||||
\(803\) | − | 21.1925i | − | 0.747868i | ||||||
\(804\) | 21.1250 | + | 19.9046i | 0.745022 | + | 0.701982i | ||||
\(805\) | −5.08708 | −0.179296 | ||||||||
\(806\) | −1.64578 | + | 4.14659i | −0.0579703 | + | 0.146057i | ||||
\(807\) | − | 43.5635i | − | 1.53351i | ||||||
\(808\) | −3.08979 | − | 6.60933i | −0.108698 | − | 0.232515i | ||||
\(809\) | −31.0971 | −1.09331 | −0.546657 | − | 0.837357i | \(-0.684100\pi\) | ||||
−0.546657 | + | 0.837357i | \(0.684100\pi\) | |||||||
\(810\) | 14.7543 | + | 5.85598i | 0.518413 | + | 0.205758i | ||||
\(811\) | 8.88630 | 0.312040 | 0.156020 | − | 0.987754i | \(-0.450134\pi\) | ||||
0.156020 | + | 0.987754i | \(0.450134\pi\) | |||||||
\(812\) | −15.6132 | − | 14.7113i | −0.547917 | − | 0.516264i | ||||
\(813\) | 2.04722i | 0.0717992i | ||||||||
\(814\) | −12.4780 | − | 4.95251i | −0.437353 | − | 0.173586i | ||||
\(815\) | − | 8.21487i | − | 0.287754i | ||||||
\(816\) | −1.66220 | − | 27.9171i | −0.0581886 | − | 0.977295i | ||||
\(817\) | −48.2427 | − | 14.2156i | −1.68780 | − | 0.497341i | ||||
\(818\) | −1.18373 | + | 2.98243i | −0.0413881 | + | 0.104278i | ||||
\(819\) | −2.12264 | −0.0741710 | ||||||||
\(820\) | −5.25786 | + | 5.58023i | −0.183612 | + | 0.194870i | ||||
\(821\) | 38.8722 | 1.35665 | 0.678325 | − | 0.734762i | \(-0.262706\pi\) | ||||
0.678325 | + | 0.734762i | \(0.262706\pi\) | |||||||
\(822\) | −55.2159 | − | 21.9152i | −1.92587 | − | 0.764380i | ||||
\(823\) | − | 7.15869i | − | 0.249536i | −0.992186 | − | 0.124768i | \(-0.960181\pi\) | ||
0.992186 | − | 0.124768i | \(-0.0398187\pi\) | |||||||
\(824\) | −9.00323 | − | 19.2587i | −0.313642 | − | 0.670909i | ||||
\(825\) | − | 3.83354i | − | 0.133467i | ||||||
\(826\) | 4.64454 | − | 11.7020i | 0.161604 | − | 0.407166i | ||||
\(827\) | 44.3377 | 1.54177 | 0.770886 | − | 0.636973i | \(-0.219814\pi\) | ||||
0.770886 | + | 0.636973i | \(0.219814\pi\) | |||||||
\(828\) | −6.96821 | + | 7.39545i | −0.242162 | + | 0.257010i | ||||
\(829\) | − | 54.3640i | − | 1.88814i | −0.329744 | − | 0.944071i | \(-0.606962\pi\) | ||
0.329744 | − | 0.944071i | \(-0.393038\pi\) | |||||||
\(830\) | 3.90272 | − | 9.83299i | 0.135465 | − | 0.341308i | ||||
\(831\) | 37.4129 | 1.29784 | ||||||||
\(832\) | 4.72513 | + | 3.94927i | 0.163814 | + | 0.136916i | ||||
\(833\) | −13.7300 | −0.475717 | ||||||||
\(834\) | −8.73545 | + | 22.0092i | −0.302484 | + | 0.762116i | ||||
\(835\) | −2.34064 | −0.0810011 | ||||||||
\(836\) | 7.80779 | + | 13.3694i | 0.270038 | + | 0.462391i | ||||
\(837\) | 11.8581 | 0.409875 | ||||||||
\(838\) | −2.09202 | + | 5.27088i | −0.0722675 | + | 0.182080i | ||||
\(839\) | −27.8039 | −0.959896 | −0.479948 | − | 0.877297i | \(-0.659344\pi\) | ||||
−0.479948 | + | 0.877297i | \(0.659344\pi\) | |||||||
\(840\) | −9.19026 | + | 4.29634i | −0.317094 | + | 0.148238i | ||||
\(841\) | −12.6690 | −0.436862 | ||||||||
\(842\) | −14.1427 | + | 35.6328i | −0.487389 | + | 1.22799i | ||||
\(843\) | − | 29.2171i | − | 1.00629i | ||||||
\(844\) | 26.1222 | + | 24.6132i | 0.899164 | + | 0.847220i | ||||
\(845\) | −12.4074 | −0.426829 | ||||||||
\(846\) | 5.90029 | − | 14.8659i | 0.202856 | − | 0.511101i | ||||
\(847\) | − | 13.0372i | − | 0.447962i | ||||||
\(848\) | 22.3284 | − | 1.32944i | 0.766760 | − | 0.0456533i | ||||
\(849\) | − | 15.2043i | − | 0.521810i | ||||||
\(850\) | −4.25754 | − | 1.68982i | −0.146032 | − | 0.0579603i | ||||
\(851\) | 16.3644 | 0.560964 | ||||||||
\(852\) | −5.76144 | − | 5.42861i | −0.197384 | − | 0.185981i | ||||
\(853\) | 28.4880 | 0.975409 | 0.487704 | − | 0.873009i | \(-0.337834\pi\) | ||||
0.487704 | + | 0.873009i | \(0.337834\pi\) | |||||||
\(854\) | −4.28897 | + | 10.8062i | −0.146765 | + | 0.369779i | ||||
\(855\) | 2.04460 | − | 6.93863i | 0.0699238 | − | 0.237296i | ||||
\(856\) | −1.59122 | − | 3.40376i | −0.0543868 | − | 0.116338i | ||||
\(857\) | 40.9485i | 1.39877i | 0.714744 | + | 0.699386i | \(0.246543\pi\) | ||||
−0.714744 | + | 0.699386i | \(0.753457\pi\) | |||||||
\(858\) | −3.87894 | − | 1.53955i | −0.132425 | − | 0.0525594i | ||||
\(859\) | − | 35.8112i | − | 1.22186i | −0.791683 | − | 0.610932i | \(-0.790795\pi\) | ||
0.791683 | − | 0.610932i | \(-0.209205\pi\) | |||||||
\(860\) | 15.8250 | − | 16.7953i | 0.539629 | − | 0.572715i | ||||
\(861\) | −13.7500 | −0.468599 | ||||||||
\(862\) | −36.2964 | − | 14.4060i | −1.23626 | − | 0.490672i | ||||
\(863\) | 11.3664 | 0.386918 | 0.193459 | − | 0.981108i | \(-0.438029\pi\) | ||||
0.193459 | + | 0.981108i | \(0.438029\pi\) | |||||||
\(864\) | 5.12354 | − | 15.5461i | 0.174306 | − | 0.528888i | ||||
\(865\) | 4.12231i | 0.140163i | ||||||||
\(866\) | 13.6058 | − | 34.2802i | 0.462345 | − | 1.16489i | ||||
\(867\) | −14.0502 | −0.477168 | ||||||||
\(868\) | −9.33945 | + | 9.91207i | −0.317002 | + | 0.336438i | ||||
\(869\) | − | 16.7271i | − | 0.567427i | ||||||
\(870\) | −7.26954 | + | 18.3158i | −0.246460 | + | 0.620963i | ||||
\(871\) | − | 5.17535i | − | 0.175360i | ||||||
\(872\) | −6.23868 | + | 2.91651i | −0.211268 | + | 0.0987655i | ||||
\(873\) | 1.12246i | 0.0379894i | ||||||||
\(874\) | −14.8581 | − | 11.6363i | −0.502582 | − | 0.393604i | ||||
\(875\) | 1.66163i | 0.0561733i | ||||||||
\(876\) | 37.4951 | + | 35.3291i | 1.26684 | + | 1.19366i | ||||
\(877\) | − | 0.163580i | − | 0.00552371i | −0.999996 | − | 0.00276186i | \(-0.999121\pi\) | ||
0.999996 | − | 0.00276186i | \(-0.000879127\pi\) | |||||||
\(878\) | −7.43455 | − | 2.95078i | −0.250904 | − | 0.0995839i | ||||
\(879\) | 20.1893i | 0.680969i | ||||||||
\(880\) | −7.09123 | + | 0.422215i | −0.239045 | + | 0.0142329i | ||||
\(881\) | −9.30245 | −0.313408 | −0.156704 | − | 0.987646i | \(-0.550087\pi\) | ||||
−0.156704 | + | 0.987646i | \(0.550087\pi\) | |||||||
\(882\) | 9.24674 | + | 3.67004i | 0.311354 | + | 0.123577i | ||||
\(883\) | 31.0359i | 1.04444i | 0.852810 | + | 0.522221i | \(0.174896\pi\) | ||||
−0.852810 | + | 0.522221i | \(0.825104\pi\) | |||||||
\(884\) | −3.41966 | + | 3.62933i | −0.115016 | + | 0.122067i | ||||
\(885\) | −11.5651 | −0.388755 | ||||||||
\(886\) | 1.84238 | − | 4.64191i | 0.0618959 | − | 0.155948i | ||||
\(887\) | −42.0820 | −1.41297 | −0.706487 | − | 0.707726i | \(-0.749721\pi\) | ||||
−0.706487 | + | 0.707726i | \(0.749721\pi\) | |||||||
\(888\) | 29.5637 | − | 13.8207i | 0.992094 | − | 0.463793i | ||||
\(889\) | 26.4723i | 0.887852i | ||||||||
\(890\) | 8.35577 | − | 21.0526i | 0.280086 | − | 0.705683i | ||||
\(891\) | 19.9342i | 0.667821i | ||||||||
\(892\) | 36.5817 | + | 34.4684i | 1.22484 | + | 1.15409i | ||||
\(893\) | 28.4945 | + | 8.39645i | 0.953533 | + | 0.280977i | ||||
\(894\) | 61.7176 | + | 24.4958i | 2.06415 | + | 0.819261i | ||||
\(895\) | −1.16740 | −0.0390220 | ||||||||
\(896\) | 8.95951 | + | 16.5268i | 0.299316 | + | 0.552123i | ||||
\(897\) | 5.08708 | 0.169853 | ||||||||
\(898\) | 11.0324 | − | 27.7965i | 0.368157 | − | 0.927581i | ||||
\(899\) | 26.4536i | 0.882276i | ||||||||
\(900\) | 2.41563 | + | 2.27608i | 0.0805209 | + | 0.0758692i | ||||
\(901\) | 18.1124i | 0.603410i | ||||||||
\(902\) | −8.94908 | − | 3.55189i | −0.297972 | − | 0.118265i | ||||
\(903\) | 41.3846 | 1.37719 | ||||||||
\(904\) | 45.9039 | − | 21.4596i | 1.52674 | − | 0.713734i | ||||
\(905\) | − | 22.5328i | − | 0.749016i | ||||||
\(906\) | 39.5957 | + | 15.7155i | 1.31548 | + | 0.522114i | ||||
\(907\) | 3.59980 | 0.119530 | 0.0597648 | − | 0.998212i | \(-0.480965\pi\) | ||||
0.0597648 | + | 0.998212i | \(0.480965\pi\) | |||||||
\(908\) | −21.4655 | − | 20.2254i | −0.712357 | − | 0.671205i | ||||
\(909\) | −4.28066 | −0.141981 | ||||||||
\(910\) | 1.68131 | + | 0.667312i | 0.0557348 | + | 0.0221212i | ||||
\(911\) | 39.5505 | 1.31037 | 0.655184 | − | 0.755469i | \(-0.272591\pi\) | ||||
0.655184 | + | 0.755469i | \(0.272591\pi\) | |||||||
\(912\) | −36.6700 | − | 8.47350i | −1.21426 | − | 0.280585i | ||||
\(913\) | 13.2852 | 0.439674 | ||||||||
\(914\) | 40.7315 | + | 16.1663i | 1.34728 | + | 0.534735i | ||||
\(915\) | 10.6797 | 0.353059 | ||||||||
\(916\) | −27.5997 | − | 26.0053i | −0.911921 | − | 0.859240i | ||||
\(917\) | −7.53287 | −0.248757 | ||||||||
\(918\) | 12.3195 | + | 4.88963i | 0.406605 | + | 0.161382i | ||||
\(919\) | 39.0368i | 1.28771i | 0.765149 | + | 0.643853i | \(0.222665\pi\) | ||||
−0.765149 | + | 0.643853i | \(0.777335\pi\) | |||||||
\(920\) | 7.84438 | − | 3.66716i | 0.258622 | − | 0.120903i | ||||
\(921\) | 12.1635 | 0.400800 | ||||||||
\(922\) | −2.42925 | − | 0.964172i | −0.0800032 | − | 0.0317533i | ||||
\(923\) | 1.41148i | 0.0464593i | ||||||||
\(924\) | −9.27227 | − | 8.73661i | −0.305035 | − | 0.287413i | ||||
\(925\) | − | 5.34522i | − | 0.175750i | ||||||
\(926\) | −11.7440 | + | 29.5892i | −0.385931 | + | 0.972362i | ||||
\(927\) | −12.4733 | −0.409676 | ||||||||
\(928\) | 34.6809 | + | 11.4298i | 1.13846 | + | 0.375203i | ||||
\(929\) | 55.1653 | 1.80991 | 0.904957 | − | 0.425504i | \(-0.139903\pi\) | ||||
0.904957 | + | 0.425504i | \(0.139903\pi\) | |||||||
\(930\) | 11.6278 | + | 4.61507i | 0.381290 | + | 0.151334i | ||||
\(931\) | −5.22267 | + | 17.7239i | −0.171166 | + | 0.580876i | ||||
\(932\) | −27.1374 | − | 25.5697i | −0.888914 | − | 0.837562i | ||||
\(933\) | − | 29.7981i | − | 0.975547i | ||||||
\(934\) | 11.4595 | − | 28.8724i | 0.374966 | − | 0.944735i | ||||
\(935\) | − | 5.75227i | − | 0.188119i | ||||||
\(936\) | 3.27315 | − | 1.53016i | 0.106986 | − | 0.0500149i | ||||
\(937\) | 3.90000 | 0.127407 | 0.0637037 | − | 0.997969i | \(-0.479709\pi\) | ||||
0.0637037 | + | 0.997969i | \(0.479709\pi\) | |||||||
\(938\) | 5.82827 | − | 14.6845i | 0.190300 | − | 0.479465i | ||||
\(939\) | −37.4775 | −1.22303 | ||||||||
\(940\) | −9.34705 | + | 9.92014i | −0.304867 | + | 0.323559i | ||||
\(941\) | − | 12.3135i | − | 0.401408i | −0.979652 | − | 0.200704i | \(-0.935677\pi\) | ||
0.979652 | − | 0.200704i | \(-0.0643229\pi\) | |||||||
\(942\) | −30.3433 | − | 12.0433i | −0.988639 | − | 0.392391i | ||||
\(943\) | 11.7364 | 0.382189 | ||||||||
\(944\) | 1.27374 | + | 21.3929i | 0.0414568 | + | 0.696280i | ||||
\(945\) | − | 4.80806i | − | 0.156406i | ||||||
\(946\) | 26.9348 | + | 10.6904i | 0.875726 | + | 0.347576i | ||||
\(947\) | 8.23515i | 0.267607i | 0.991008 | + | 0.133803i | \(0.0427190\pi\) | ||||
−0.991008 | + | 0.133803i | \(0.957281\pi\) | |||||||
\(948\) | 29.5946 | + | 27.8849i | 0.961187 | + | 0.905660i | ||||
\(949\) | − | 9.18581i | − | 0.298184i | ||||||
\(950\) | −3.80085 | + | 4.85320i | −0.123316 | + | 0.157459i | ||||
\(951\) | 17.4257i | 0.565069i | ||||||||
\(952\) | −13.7901 | + | 6.44672i | −0.446940 | + | 0.208939i | ||||
\(953\) | 51.7464i | 1.67623i | 0.545494 | + | 0.838114i | \(0.316342\pi\) | ||||
−0.545494 | + | 0.838114i | \(0.683658\pi\) | |||||||
\(954\) | 4.84143 | − | 12.1981i | 0.156747 | − | 0.394928i | ||||
\(955\) | − | 20.5329i | − | 0.664430i | ||||||
\(956\) | −10.2798 | + | 10.9101i | −0.332474 | + | 0.352858i | ||||
\(957\) | −24.7461 | −0.799926 | ||||||||
\(958\) | −9.53267 | + | 24.0178i | −0.307987 | + | 0.775980i | ||||
\(959\) | 32.3355i | 1.04417i | ||||||||
\(960\) | 11.0744 | − | 13.2501i | 0.357426 | − | 0.427645i | ||||
\(961\) | −14.2059 | −0.458256 | ||||||||
\(962\) | −5.40852 | − | 2.14665i | −0.174378 | − | 0.0692106i | ||||
\(963\) | −2.20451 | −0.0710395 | ||||||||
\(964\) | −6.69031 | + | 7.10050i | −0.215480 | + | 0.228692i | ||||
\(965\) | 8.03672i | 0.258711i | ||||||||
\(966\) | 14.4340 | + | 5.72887i | 0.464407 | + | 0.184323i | ||||
\(967\) | 5.86800i | 0.188702i | 0.995539 | + | 0.0943510i | \(0.0300776\pi\) | ||||
−0.995539 | + | 0.0943510i | \(0.969922\pi\) | |||||||
\(968\) | 9.39819 | + | 20.1036i | 0.302069 | + | 0.646153i | ||||
\(969\) | 8.61409 | − | 29.2331i | 0.276725 | − | 0.939103i | ||||
\(970\) | 0.352876 | − | 0.889081i | 0.0113302 | − | 0.0285467i | ||||
\(971\) | 31.2042 | 1.00139 | 0.500696 | − | 0.865623i | \(-0.333078\pi\) | ||||
0.500696 | + | 0.865623i | \(0.333078\pi\) | |||||||
\(972\) | −22.6328 | − | 21.3254i | −0.725949 | − | 0.684011i | ||||
\(973\) | 12.8890 | 0.413203 | ||||||||
\(974\) | −10.6831 | − | 4.24012i | −0.342308 | − | 0.135862i | ||||
\(975\) | − | 1.66163i | − | 0.0532147i | ||||||
\(976\) | −1.17623 | − | 19.7551i | −0.0376502 | − | 0.632346i | ||||
\(977\) | 23.7345i | 0.759335i | 0.925123 | + | 0.379667i | \(0.123962\pi\) | ||||
−0.925123 | + | 0.379667i | \(0.876038\pi\) | |||||||
\(978\) | −9.25126 | + | 23.3088i | −0.295823 | + | 0.745332i | ||||
\(979\) | 28.4437 | 0.909064 | ||||||||
\(980\) | −6.17042 | − | 5.81395i | −0.197107 | − | 0.185720i | ||||
\(981\) | 4.04060i | 0.129006i | ||||||||
\(982\) | −14.8961 | + | 37.5310i | −0.475352 | + | 1.19766i | ||||
\(983\) | 8.16622 | 0.260462 | 0.130231 | − | 0.991484i | \(-0.458428\pi\) | ||||
0.130231 | + | 0.991484i | \(0.458428\pi\) | |||||||
\(984\) | 21.2028 | − | 9.91207i | 0.675921 | − | 0.315985i | ||||
\(985\) | −9.52701 | −0.303556 | ||||||||
\(986\) | −10.9080 | + | 27.4830i | −0.347382 | + | 0.875238i | ||||
\(987\) | −24.4438 | −0.778056 | ||||||||
\(988\) | 3.38425 | + | 5.79491i | 0.107667 | + | 0.184361i | ||||
\(989\) | −35.3240 | −1.12324 | ||||||||
\(990\) | −1.53758 | + | 3.87397i | −0.0488675 | + | 0.123123i | ||||
\(991\) | 40.4095 | 1.28365 | 0.641825 | − | 0.766851i | \(-0.278178\pi\) | ||||
0.641825 | + | 0.766851i | \(0.278178\pi\) | |||||||
\(992\) | 7.25624 | − | 22.0172i | 0.230386 | − | 0.699047i | ||||
\(993\) | 77.3932 | 2.45600 | ||||||||
\(994\) | −1.58955 | + | 4.00491i | −0.0504174 | + | 0.127028i | ||||
\(995\) | − | 6.98947i | − | 0.221581i | ||||||
\(996\) | −22.1471 | + | 23.5049i | −0.701756 | + | 0.744782i | ||||
\(997\) | −11.3678 | −0.360023 | −0.180012 | − | 0.983664i | \(-0.557614\pi\) | ||||
−0.180012 | + | 0.983664i | \(0.557614\pi\) | |||||||
\(998\) | −6.20202 | + | 15.6261i | −0.196321 | + | 0.494636i | ||||
\(999\) | 15.4668i | 0.489349i |
(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 | 380.2.f.a.151.18 | yes | 20 | |
4.3 | odd | 2 | inner | 380.2.f.a.151.4 | yes | 20 | |
19.18 | odd | 2 | inner | 380.2.f.a.151.3 | ✓ | 20 | |
76.75 | even | 2 | inner | 380.2.f.a.151.17 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.f.a.151.3 | ✓ | 20 | 19.18 | odd | 2 | inner | |
380.2.f.a.151.4 | yes | 20 | 4.3 | odd | 2 | inner | |
380.2.f.a.151.17 | yes | 20 | 76.75 | even | 2 | inner | |
380.2.f.a.151.18 | yes | 20 | 1.1 | even | 1 | trivial |