Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(109,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.m (of order \(4\), degree \(2\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 109.11 | ||
Character | \(\chi\) | \(=\) | 429.109 |
Dual form | 429.2.m.a.307.11 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.06339 | + | 1.06339i | 0.751930 | + | 0.751930i | 0.974839 | − | 0.222909i | \(-0.0715553\pi\) |
−0.222909 | + | 0.974839i | \(0.571555\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.261597i | 0.130799i | ||||||||
\(5\) | 0.340859 | − | 0.340859i | 0.152437 | − | 0.152437i | −0.626769 | − | 0.779205i | \(-0.715623\pi\) |
0.779205 | + | 0.626769i | \(0.215623\pi\) | |||||||
\(6\) | −1.06339 | − | 1.06339i | −0.434127 | − | 0.434127i | ||||
\(7\) | 0.593196 | − | 0.593196i | 0.224207 | − | 0.224207i | −0.586060 | − | 0.810267i | \(-0.699322\pi\) |
0.810267 | + | 0.586060i | \(0.199322\pi\) | |||||||
\(8\) | 1.84860 | − | 1.84860i | 0.653579 | − | 0.653579i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.724932 | 0.229244 | ||||||||
\(11\) | 2.67537 | − | 1.96021i | 0.806654 | − | 0.591024i | ||||
\(12\) | − | 0.261597i | − | 0.0755166i | ||||||
\(13\) | −2.47736 | − | 2.61967i | −0.687096 | − | 0.726566i | ||||
\(14\) | 1.26160 | 0.337176 | ||||||||
\(15\) | −0.340859 | + | 0.340859i | −0.0880094 | + | 0.0880094i | ||||
\(16\) | 4.45476 | 1.11369 | ||||||||
\(17\) | 0.904472 | 0.219367 | 0.109683 | − | 0.993967i | \(-0.465016\pi\) | ||||
0.109683 | + | 0.993967i | \(0.465016\pi\) | |||||||
\(18\) | 1.06339 | + | 1.06339i | 0.250643 | + | 0.250643i | ||||
\(19\) | 2.48574 | + | 2.48574i | 0.570269 | + | 0.570269i | 0.932203 | − | 0.361935i | \(-0.117884\pi\) |
−0.361935 | + | 0.932203i | \(0.617884\pi\) | |||||||
\(20\) | 0.0891677 | + | 0.0891677i | 0.0199385 | + | 0.0199385i | ||||
\(21\) | −0.593196 | + | 0.593196i | −0.129446 | + | 0.129446i | ||||
\(22\) | 4.92942 | + | 0.760497i | 1.05096 | + | 0.162138i | ||||
\(23\) | 4.23536i | 0.883133i | 0.897228 | + | 0.441567i | \(0.145577\pi\) | ||||
−0.897228 | + | 0.441567i | \(0.854423\pi\) | |||||||
\(24\) | −1.84860 | + | 1.84860i | −0.377344 | + | 0.377344i | ||||
\(25\) | 4.76763i | 0.953526i | ||||||||
\(26\) | 0.151333 | − | 5.42013i | 0.0296788 | − | 1.06298i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.155178 | + | 0.155178i | 0.0293259 | + | 0.0293259i | ||||
\(29\) | − | 3.83750i | − | 0.712605i | −0.934371 | − | 0.356303i | \(-0.884037\pi\) | ||
0.934371 | − | 0.356303i | \(-0.115963\pi\) | |||||||
\(30\) | −0.724932 | −0.132354 | ||||||||
\(31\) | 5.60966 | − | 5.60966i | 1.00752 | − | 1.00752i | 0.00755339 | − | 0.999971i | \(-0.497596\pi\) |
0.999971 | − | 0.00755339i | \(-0.00240434\pi\) | |||||||
\(32\) | 1.03995 | + | 1.03995i | 0.183839 | + | 0.183839i | ||||
\(33\) | −2.67537 | + | 1.96021i | −0.465722 | + | 0.341228i | ||||
\(34\) | 0.961806 | + | 0.961806i | 0.164948 | + | 0.164948i | ||||
\(35\) | − | 0.404392i | − | 0.0683547i | ||||||
\(36\) | 0.261597i | 0.0435995i | ||||||||
\(37\) | 5.73990 | + | 5.73990i | 0.943633 | + | 0.943633i | 0.998494 | − | 0.0548608i | \(-0.0174715\pi\) |
−0.0548608 | + | 0.998494i | \(0.517471\pi\) | |||||||
\(38\) | 5.28663i | 0.857605i | ||||||||
\(39\) | 2.47736 | + | 2.61967i | 0.396695 | + | 0.419483i | ||||
\(40\) | − | 1.26022i | − | 0.199259i | ||||||
\(41\) | −2.91199 | − | 2.91199i | −0.454777 | − | 0.454777i | 0.442160 | − | 0.896936i | \(-0.354212\pi\) |
−0.896936 | + | 0.442160i | \(0.854212\pi\) | |||||||
\(42\) | −1.26160 | −0.194669 | ||||||||
\(43\) | −11.0774 | −1.68929 | −0.844643 | − | 0.535330i | \(-0.820187\pi\) | ||||
−0.844643 | + | 0.535330i | \(0.820187\pi\) | |||||||
\(44\) | 0.512784 | + | 0.699868i | 0.0773051 | + | 0.105509i | ||||
\(45\) | 0.340859 | − | 0.340859i | 0.0508122 | − | 0.0508122i | ||||
\(46\) | −4.50384 | + | 4.50384i | −0.664055 | + | 0.664055i | ||||
\(47\) | −5.97825 | − | 5.97825i | −0.872018 | − | 0.872018i | 0.120674 | − | 0.992692i | \(-0.461494\pi\) |
−0.992692 | + | 0.120674i | \(0.961494\pi\) | |||||||
\(48\) | −4.45476 | −0.642989 | ||||||||
\(49\) | 6.29624i | 0.899462i | ||||||||
\(50\) | −5.06985 | + | 5.06985i | −0.716985 | + | 0.716985i | ||||
\(51\) | −0.904472 | −0.126651 | ||||||||
\(52\) | 0.685299 | − | 0.648070i | 0.0950338 | − | 0.0898712i | ||||
\(53\) | 3.19429 | 0.438769 | 0.219385 | − | 0.975638i | \(-0.429595\pi\) | ||||
0.219385 | + | 0.975638i | \(0.429595\pi\) | |||||||
\(54\) | −1.06339 | − | 1.06339i | −0.144709 | − | 0.144709i | ||||
\(55\) | 0.243769 | − | 1.58008i | 0.0328699 | − | 0.213057i | ||||
\(56\) | − | 2.19316i | − | 0.293074i | ||||||
\(57\) | −2.48574 | − | 2.48574i | −0.329245 | − | 0.329245i | ||||
\(58\) | 4.08076 | − | 4.08076i | 0.535829 | − | 0.535829i | ||||
\(59\) | −5.71636 | − | 5.71636i | −0.744206 | − | 0.744206i | 0.229178 | − | 0.973385i | \(-0.426396\pi\) |
−0.973385 | + | 0.229178i | \(0.926396\pi\) | |||||||
\(60\) | −0.0891677 | − | 0.0891677i | −0.0115115 | − | 0.0115115i | ||||
\(61\) | 3.56455i | 0.456393i | 0.973615 | + | 0.228197i | \(0.0732829\pi\) | ||||
−0.973615 | + | 0.228197i | \(0.926717\pi\) | |||||||
\(62\) | 11.9305 | 1.51518 | ||||||||
\(63\) | 0.593196 | − | 0.593196i | 0.0747356 | − | 0.0747356i | ||||
\(64\) | − | 6.69778i | − | 0.837223i | ||||||
\(65\) | −1.73737 | − | 0.0485081i | −0.215494 | − | 0.00601669i | ||||
\(66\) | −4.92942 | − | 0.760497i | −0.606770 | − | 0.0936107i | ||||
\(67\) | −10.0412 | + | 10.0412i | −1.22673 | + | 1.22673i | −0.261530 | + | 0.965195i | \(0.584227\pi\) |
−0.965195 | + | 0.261530i | \(0.915773\pi\) | |||||||
\(68\) | 0.236607i | 0.0286928i | ||||||||
\(69\) | − | 4.23536i | − | 0.509877i | ||||||
\(70\) | 0.430027 | − | 0.430027i | 0.0513980 | − | 0.0513980i | ||||
\(71\) | −10.7137 | + | 10.7137i | −1.27148 | + | 1.27148i | −0.326164 | + | 0.945313i | \(0.605756\pi\) |
−0.945313 | + | 0.326164i | \(0.894244\pi\) | |||||||
\(72\) | 1.84860 | − | 1.84860i | 0.217860 | − | 0.217860i | ||||
\(73\) | 10.3258 | − | 10.3258i | 1.20854 | − | 1.20854i | 0.237045 | − | 0.971499i | \(-0.423821\pi\) |
0.971499 | − | 0.237045i | \(-0.0761789\pi\) | |||||||
\(74\) | 12.2075i | 1.41909i | ||||||||
\(75\) | − | 4.76763i | − | 0.550519i | ||||||
\(76\) | −0.650263 | + | 0.650263i | −0.0745903 | + | 0.0745903i | ||||
\(77\) | 0.424231 | − | 2.74980i | 0.0483456 | − | 0.313369i | ||||
\(78\) | −0.151333 | + | 5.42013i | −0.0171350 | + | 0.613709i | ||||
\(79\) | 7.59368i | 0.854356i | 0.904168 | + | 0.427178i | \(0.140492\pi\) | ||||
−0.904168 | + | 0.427178i | \(0.859508\pi\) | |||||||
\(80\) | 1.51845 | − | 1.51845i | 0.169767 | − | 0.169767i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 6.19316i | − | 0.683921i | ||||||
\(83\) | −5.02820 | − | 5.02820i | −0.551916 | − | 0.551916i | 0.375077 | − | 0.926994i | \(-0.377616\pi\) |
−0.926994 | + | 0.375077i | \(0.877616\pi\) | |||||||
\(84\) | −0.155178 | − | 0.155178i | −0.0169313 | − | 0.0169313i | ||||
\(85\) | 0.308297 | − | 0.308297i | 0.0334395 | − | 0.0334395i | ||||
\(86\) | −11.7796 | − | 11.7796i | −1.27023 | − | 1.27023i | ||||
\(87\) | 3.83750i | 0.411423i | ||||||||
\(88\) | 1.32205 | − | 8.56932i | 0.140931 | − | 0.913493i | ||||
\(89\) | 3.53432 | + | 3.53432i | 0.374637 | + | 0.374637i | 0.869163 | − | 0.494526i | \(-0.164658\pi\) |
−0.494526 | + | 0.869163i | \(0.664658\pi\) | |||||||
\(90\) | 0.724932 | 0.0764145 | ||||||||
\(91\) | −3.02354 | − | 0.0844186i | −0.316953 | − | 0.00884947i | ||||
\(92\) | −1.10796 | −0.115513 | ||||||||
\(93\) | −5.60966 | + | 5.60966i | −0.581695 | + | 0.581695i | ||||
\(94\) | − | 12.7144i | − | 1.31139i | ||||||
\(95\) | 1.69458 | 0.173860 | ||||||||
\(96\) | −1.03995 | − | 1.03995i | −0.106139 | − | 0.106139i | ||||
\(97\) | 0.0569832 | − | 0.0569832i | 0.00578577 | − | 0.00578577i | −0.704208 | − | 0.709994i | \(-0.748698\pi\) |
0.709994 | + | 0.704208i | \(0.248698\pi\) | |||||||
\(98\) | −6.69536 | + | 6.69536i | −0.676333 | + | 0.676333i | ||||
\(99\) | 2.67537 | − | 1.96021i | 0.268885 | − | 0.197008i | ||||
\(100\) | −1.24720 | −0.124720 | ||||||||
\(101\) | −4.22512 | −0.420416 | −0.210208 | − | 0.977657i | \(-0.567414\pi\) | ||||
−0.210208 | + | 0.977657i | \(0.567414\pi\) | |||||||
\(102\) | −0.961806 | − | 0.961806i | −0.0952330 | − | 0.0952330i | ||||
\(103\) | 15.4692i | 1.52422i | 0.647446 | + | 0.762111i | \(0.275837\pi\) | ||||
−0.647446 | + | 0.762111i | \(0.724163\pi\) | |||||||
\(104\) | −9.42238 | − | 0.263077i | −0.923940 | − | 0.0257968i | ||||
\(105\) | 0.404392i | 0.0394646i | ||||||||
\(106\) | 3.39678 | + | 3.39678i | 0.329924 | + | 0.329924i | ||||
\(107\) | − | 1.72944i | − | 0.167192i | −0.996500 | − | 0.0835958i | \(-0.973360\pi\) | ||
0.996500 | − | 0.0835958i | \(-0.0266405\pi\) | |||||||
\(108\) | − | 0.261597i | − | 0.0251722i | ||||||
\(109\) | 10.9131 | + | 10.9131i | 1.04529 | + | 1.04529i | 0.998925 | + | 0.0463649i | \(0.0147637\pi\) |
0.0463649 | + | 0.998925i | \(0.485236\pi\) | |||||||
\(110\) | 1.93946 | − | 1.42102i | 0.184920 | − | 0.135489i | ||||
\(111\) | −5.73990 | − | 5.73990i | −0.544807 | − | 0.544807i | ||||
\(112\) | 2.64255 | − | 2.64255i | 0.249697 | − | 0.249697i | ||||
\(113\) | −2.42476 | −0.228102 | −0.114051 | − | 0.993475i | \(-0.536383\pi\) | ||||
−0.114051 | + | 0.993475i | \(0.536383\pi\) | |||||||
\(114\) | − | 5.28663i | − | 0.495138i | ||||||
\(115\) | 1.44366 | + | 1.44366i | 0.134622 | + | 0.134622i | ||||
\(116\) | 1.00388 | 0.0932077 | ||||||||
\(117\) | −2.47736 | − | 2.61967i | −0.229032 | − | 0.242189i | ||||
\(118\) | − | 12.1574i | − | 1.11918i | ||||||
\(119\) | 0.536529 | − | 0.536529i | 0.0491835 | − | 0.0491835i | ||||
\(120\) | 1.26022i | 0.115042i | ||||||||
\(121\) | 3.31519 | − | 10.4885i | 0.301381 | − | 0.953504i | ||||
\(122\) | −3.79050 | + | 3.79050i | −0.343176 | + | 0.343176i | ||||
\(123\) | 2.91199 | + | 2.91199i | 0.262565 | + | 0.262565i | ||||
\(124\) | 1.46747 | + | 1.46747i | 0.131783 | + | 0.131783i | ||||
\(125\) | 3.32938 | + | 3.32938i | 0.297789 | + | 0.297789i | ||||
\(126\) | 1.26160 | 0.112392 | ||||||||
\(127\) | 8.96709 | 0.795701 | 0.397850 | − | 0.917450i | \(-0.369756\pi\) | ||||
0.397850 | + | 0.917450i | \(0.369756\pi\) | |||||||
\(128\) | 9.20225 | − | 9.20225i | 0.813372 | − | 0.813372i | ||||
\(129\) | 11.0774 | 0.975310 | ||||||||
\(130\) | −1.79592 | − | 1.89908i | −0.157512 | − | 0.166561i | ||||
\(131\) | − | 7.91810i | − | 0.691808i | −0.938270 | − | 0.345904i | \(-0.887572\pi\) | ||
0.938270 | − | 0.345904i | \(-0.112428\pi\) | |||||||
\(132\) | −0.512784 | − | 0.699868i | −0.0446321 | − | 0.0609157i | ||||
\(133\) | 2.94906 | 0.255716 | ||||||||
\(134\) | −21.3554 | −1.84482 | ||||||||
\(135\) | −0.340859 | + | 0.340859i | −0.0293365 | + | 0.0293365i | ||||
\(136\) | 1.67201 | − | 1.67201i | 0.143373 | − | 0.143373i | ||||
\(137\) | 8.64502 | + | 8.64502i | 0.738594 | + | 0.738594i | 0.972306 | − | 0.233712i | \(-0.0750873\pi\) |
−0.233712 | + | 0.972306i | \(0.575087\pi\) | |||||||
\(138\) | 4.50384 | − | 4.50384i | 0.383392 | − | 0.383392i | ||||
\(139\) | 4.37603i | 0.371170i | 0.982628 | + | 0.185585i | \(0.0594180\pi\) | ||||
−0.982628 | + | 0.185585i | \(0.940582\pi\) | |||||||
\(140\) | 0.105788 | 0.00894070 | ||||||||
\(141\) | 5.97825 | + | 5.97825i | 0.503460 | + | 0.503460i | ||||
\(142\) | −22.7856 | −1.91212 | ||||||||
\(143\) | −11.7629 | − | 2.15245i | −0.983667 | − | 0.179997i | ||||
\(144\) | 4.45476 | 0.371230 | ||||||||
\(145\) | −1.30804 | − | 1.30804i | −0.108627 | − | 0.108627i | ||||
\(146\) | 21.9607 | 1.81748 | ||||||||
\(147\) | − | 6.29624i | − | 0.519305i | ||||||
\(148\) | −1.50154 | + | 1.50154i | −0.123426 | + | 0.123426i | ||||
\(149\) | 12.7872 | + | 12.7872i | 1.04757 | + | 1.04757i | 0.998811 | + | 0.0487563i | \(0.0155258\pi\) |
0.0487563 | + | 0.998811i | \(0.484474\pi\) | |||||||
\(150\) | 5.06985 | − | 5.06985i | 0.413952 | − | 0.413952i | ||||
\(151\) | 0.961423 | − | 0.961423i | 0.0782395 | − | 0.0782395i | −0.666904 | − | 0.745144i | \(-0.732381\pi\) |
0.745144 | + | 0.666904i | \(0.232381\pi\) | |||||||
\(152\) | 9.19029 | 0.745431 | ||||||||
\(153\) | 0.904472 | 0.0731222 | ||||||||
\(154\) | 3.37524 | − | 2.47299i | 0.271984 | − | 0.199279i | ||||
\(155\) | − | 3.82421i | − | 0.307168i | ||||||
\(156\) | −0.685299 | + | 0.648070i | −0.0548678 | + | 0.0518872i | ||||
\(157\) | −1.39512 | −0.111342 | −0.0556712 | − | 0.998449i | \(-0.517730\pi\) | ||||
−0.0556712 | + | 0.998449i | \(0.517730\pi\) | |||||||
\(158\) | −8.07504 | + | 8.07504i | −0.642416 | + | 0.642416i | ||||
\(159\) | −3.19429 | −0.253324 | ||||||||
\(160\) | 0.708951 | 0.0560475 | ||||||||
\(161\) | 2.51240 | + | 2.51240i | 0.198005 | + | 0.198005i | ||||
\(162\) | 1.06339 | + | 1.06339i | 0.0835478 | + | 0.0835478i | ||||
\(163\) | −6.57771 | − | 6.57771i | −0.515206 | − | 0.515206i | 0.400911 | − | 0.916117i | \(-0.368694\pi\) |
−0.916117 | + | 0.400911i | \(0.868694\pi\) | |||||||
\(164\) | 0.761768 | − | 0.761768i | 0.0594841 | − | 0.0594841i | ||||
\(165\) | −0.243769 | + | 1.58008i | −0.0189774 | + | 0.123009i | ||||
\(166\) | − | 10.6939i | − | 0.830005i | ||||||
\(167\) | −15.9976 | + | 15.9976i | −1.23793 | + | 1.23793i | −0.277085 | + | 0.960845i | \(0.589368\pi\) |
−0.960845 | + | 0.277085i | \(0.910632\pi\) | |||||||
\(168\) | 2.19316i | 0.169206i | ||||||||
\(169\) | −0.725366 | + | 12.9797i | −0.0557974 | + | 0.998442i | ||||
\(170\) | 0.655681 | 0.0502884 | ||||||||
\(171\) | 2.48574 | + | 2.48574i | 0.190090 | + | 0.190090i | ||||
\(172\) | − | 2.89781i | − | 0.220956i | ||||||
\(173\) | −20.7838 | −1.58017 | −0.790083 | − | 0.613000i | \(-0.789963\pi\) | ||||
−0.790083 | + | 0.613000i | \(0.789963\pi\) | |||||||
\(174\) | −4.08076 | + | 4.08076i | −0.309361 | + | 0.309361i | ||||
\(175\) | 2.82814 | + | 2.82814i | 0.213787 | + | 0.213787i | ||||
\(176\) | 11.9181 | − | 8.73225i | 0.898363 | − | 0.658218i | ||||
\(177\) | 5.71636 | + | 5.71636i | 0.429668 | + | 0.429668i | ||||
\(178\) | 7.51672i | 0.563402i | ||||||||
\(179\) | − | 9.07529i | − | 0.678319i | −0.940729 | − | 0.339160i | \(-0.889857\pi\) | ||
0.940729 | − | 0.339160i | \(-0.110143\pi\) | |||||||
\(180\) | 0.0891677 | + | 0.0891677i | 0.00664617 | + | 0.00664617i | ||||
\(181\) | − | 5.13239i | − | 0.381488i | −0.981640 | − | 0.190744i | \(-0.938910\pi\) | ||
0.981640 | − | 0.190744i | \(-0.0610900\pi\) | |||||||
\(182\) | −3.12543 | − | 3.30497i | −0.231672 | − | 0.244981i | ||||
\(183\) | − | 3.56455i | − | 0.263499i | ||||||
\(184\) | 7.82948 | + | 7.82948i | 0.577197 | + | 0.577197i | ||||
\(185\) | 3.91299 | 0.287689 | ||||||||
\(186\) | −11.9305 | −0.874788 | ||||||||
\(187\) | 2.41979 | − | 1.77295i | 0.176953 | − | 0.129651i | ||||
\(188\) | 1.56389 | − | 1.56389i | 0.114059 | − | 0.114059i | ||||
\(189\) | −0.593196 | + | 0.593196i | −0.0431486 | + | 0.0431486i | ||||
\(190\) | 1.80199 | + | 1.80199i | 0.130730 | + | 0.130730i | ||||
\(191\) | 15.2998 | 1.10706 | 0.553528 | − | 0.832830i | \(-0.313281\pi\) | ||||
0.553528 | + | 0.832830i | \(0.313281\pi\) | |||||||
\(192\) | 6.69778i | 0.483371i | ||||||||
\(193\) | −3.02269 | + | 3.02269i | −0.217578 | + | 0.217578i | −0.807477 | − | 0.589899i | \(-0.799168\pi\) |
0.589899 | + | 0.807477i | \(0.299168\pi\) | |||||||
\(194\) | 0.121191 | 0.00870099 | ||||||||
\(195\) | 1.73737 | + | 0.0485081i | 0.124416 | + | 0.00347374i | ||||
\(196\) | −1.64708 | −0.117648 | ||||||||
\(197\) | −2.43306 | − | 2.43306i | −0.173348 | − | 0.173348i | 0.615100 | − | 0.788449i | \(-0.289115\pi\) |
−0.788449 | + | 0.615100i | \(0.789115\pi\) | |||||||
\(198\) | 4.92942 | + | 0.760497i | 0.350319 | + | 0.0540461i | ||||
\(199\) | 12.0900i | 0.857037i | 0.903533 | + | 0.428519i | \(0.140964\pi\) | ||||
−0.903533 | + | 0.428519i | \(0.859036\pi\) | |||||||
\(200\) | 8.81344 | + | 8.81344i | 0.623205 | + | 0.623205i | ||||
\(201\) | 10.0412 | − | 10.0412i | 0.708250 | − | 0.708250i | ||||
\(202\) | −4.49295 | − | 4.49295i | −0.316123 | − | 0.316123i | ||||
\(203\) | −2.27639 | − | 2.27639i | −0.159771 | − | 0.159771i | ||||
\(204\) | − | 0.236607i | − | 0.0165658i | ||||||
\(205\) | −1.98516 | −0.138649 | ||||||||
\(206\) | −16.4498 | + | 16.4498i | −1.14611 | + | 1.14611i | ||||
\(207\) | 4.23536i | 0.294378i | ||||||||
\(208\) | −11.0361 | − | 11.6700i | −0.765212 | − | 0.809170i | ||||
\(209\) | 11.5228 | + | 1.77771i | 0.797052 | + | 0.122967i | ||||
\(210\) | −0.430027 | + | 0.430027i | −0.0296747 | + | 0.0296747i | ||||
\(211\) | − | 10.8700i | − | 0.748322i | −0.927364 | − | 0.374161i | \(-0.877931\pi\) | ||
0.927364 | − | 0.374161i | \(-0.122069\pi\) | |||||||
\(212\) | 0.835617i | 0.0573904i | ||||||||
\(213\) | 10.7137 | − | 10.7137i | 0.734088 | − | 0.734088i | ||||
\(214\) | 1.83907 | − | 1.83907i | 0.125716 | − | 0.125716i | ||||
\(215\) | −3.77583 | + | 3.77583i | −0.257509 | + | 0.257509i | ||||
\(216\) | −1.84860 | + | 1.84860i | −0.125781 | + | 0.125781i | ||||
\(217\) | − | 6.65525i | − | 0.451788i | ||||||
\(218\) | 23.2099i | 1.57197i | ||||||||
\(219\) | −10.3258 | + | 10.3258i | −0.697753 | + | 0.697753i | ||||
\(220\) | 0.413343 | + | 0.0637694i | 0.0278676 | + | 0.00429933i | ||||
\(221\) | −2.24070 | − | 2.36942i | −0.150726 | − | 0.159384i | ||||
\(222\) | − | 12.2075i | − | 0.819314i | ||||||
\(223\) | −11.0822 | + | 11.0822i | −0.742122 | + | 0.742122i | −0.972986 | − | 0.230864i | \(-0.925845\pi\) |
0.230864 | + | 0.972986i | \(0.425845\pi\) | |||||||
\(224\) | 1.23379 | 0.0824358 | ||||||||
\(225\) | 4.76763i | 0.317842i | ||||||||
\(226\) | −2.57847 | − | 2.57847i | −0.171517 | − | 0.171517i | ||||
\(227\) | 2.78480 | + | 2.78480i | 0.184834 | + | 0.184834i | 0.793458 | − | 0.608624i | \(-0.208278\pi\) |
−0.608624 | + | 0.793458i | \(0.708278\pi\) | |||||||
\(228\) | 0.650263 | − | 0.650263i | 0.0430647 | − | 0.0430647i | ||||
\(229\) | 7.16234 | + | 7.16234i | 0.473301 | + | 0.473301i | 0.902981 | − | 0.429680i | \(-0.141374\pi\) |
−0.429680 | + | 0.902981i | \(0.641374\pi\) | |||||||
\(230\) | 3.07035i | 0.202453i | ||||||||
\(231\) | −0.424231 | + | 2.74980i | −0.0279124 | + | 0.180924i | ||||
\(232\) | −7.09400 | − | 7.09400i | −0.465744 | − | 0.465744i | ||||
\(233\) | 6.23108 | 0.408211 | 0.204106 | − | 0.978949i | \(-0.434571\pi\) | ||||
0.204106 | + | 0.978949i | \(0.434571\pi\) | |||||||
\(234\) | 0.151333 | − | 5.42013i | 0.00989292 | − | 0.354325i | ||||
\(235\) | −4.07548 | −0.265855 | ||||||||
\(236\) | 1.49538 | − | 1.49538i | 0.0973411 | − | 0.0973411i | ||||
\(237\) | − | 7.59368i | − | 0.493263i | ||||||
\(238\) | 1.14108 | 0.0739652 | ||||||||
\(239\) | −10.9034 | − | 10.9034i | −0.705284 | − | 0.705284i | 0.260255 | − | 0.965540i | \(-0.416193\pi\) |
−0.965540 | + | 0.260255i | \(0.916193\pi\) | |||||||
\(240\) | −1.51845 | + | 1.51845i | −0.0980152 | + | 0.0980152i | ||||
\(241\) | −20.0666 | + | 20.0666i | −1.29260 | + | 1.29260i | −0.359433 | + | 0.933171i | \(0.617030\pi\) |
−0.933171 | + | 0.359433i | \(0.882970\pi\) | |||||||
\(242\) | 14.6788 | − | 7.62807i | 0.943586 | − | 0.490351i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.932475 | −0.0596956 | ||||||||
\(245\) | 2.14613 | + | 2.14613i | 0.137111 | + | 0.137111i | ||||
\(246\) | 6.19316i | 0.394862i | ||||||||
\(247\) | 0.353750 | − | 12.6699i | 0.0225086 | − | 0.806167i | ||||
\(248\) | − | 20.7400i | − | 1.31699i | ||||||
\(249\) | 5.02820 | + | 5.02820i | 0.318649 | + | 0.318649i | ||||
\(250\) | 7.08087i | 0.447833i | ||||||||
\(251\) | − | 10.5928i | − | 0.668611i | −0.942465 | − | 0.334305i | \(-0.891498\pi\) | ||
0.942465 | − | 0.334305i | \(-0.108502\pi\) | |||||||
\(252\) | 0.155178 | + | 0.155178i | 0.00977531 | + | 0.00977531i | ||||
\(253\) | 8.30217 | + | 11.3311i | 0.521953 | + | 0.712383i | ||||
\(254\) | 9.53552 | + | 9.53552i | 0.598312 | + | 0.598312i | ||||
\(255\) | −0.308297 | + | 0.308297i | −0.0193063 | + | 0.0193063i | ||||
\(256\) | 6.17560 | 0.385975 | ||||||||
\(257\) | − | 3.34272i | − | 0.208513i | −0.994550 | − | 0.104257i | \(-0.966754\pi\) | ||
0.994550 | − | 0.104257i | \(-0.0332463\pi\) | |||||||
\(258\) | 11.7796 | + | 11.7796i | 0.733365 | + | 0.733365i | ||||
\(259\) | 6.80977 | 0.423138 | ||||||||
\(260\) | 0.0126896 | − | 0.454491i | 0.000786975 | − | 0.0281863i | ||||
\(261\) | − | 3.83750i | − | 0.237535i | ||||||
\(262\) | 8.42003 | − | 8.42003i | 0.520191 | − | 0.520191i | ||||
\(263\) | 2.69990i | 0.166483i | 0.996529 | + | 0.0832416i | \(0.0265273\pi\) | ||||
−0.996529 | + | 0.0832416i | \(0.973473\pi\) | |||||||
\(264\) | −1.32205 | + | 8.56932i | −0.0813665 | + | 0.527405i | ||||
\(265\) | 1.08880 | − | 1.08880i | 0.0668846 | − | 0.0668846i | ||||
\(266\) | 3.13601 | + | 3.13601i | 0.192281 | + | 0.192281i | ||||
\(267\) | −3.53432 | − | 3.53432i | −0.216297 | − | 0.216297i | ||||
\(268\) | −2.62674 | − | 2.62674i | −0.160454 | − | 0.160454i | ||||
\(269\) | 24.0709 | 1.46763 | 0.733816 | − | 0.679349i | \(-0.237738\pi\) | ||||
0.733816 | + | 0.679349i | \(0.237738\pi\) | |||||||
\(270\) | −0.724932 | −0.0441180 | ||||||||
\(271\) | 14.5615 | − | 14.5615i | 0.884551 | − | 0.884551i | −0.109443 | − | 0.993993i | \(-0.534907\pi\) |
0.993993 | + | 0.109443i | \(0.0349066\pi\) | |||||||
\(272\) | 4.02921 | 0.244306 | ||||||||
\(273\) | 3.02354 | + | 0.0844186i | 0.182993 | + | 0.00510924i | ||||
\(274\) | 18.3861i | 1.11074i | ||||||||
\(275\) | 9.34554 | + | 12.7552i | 0.563557 | + | 0.769165i | ||||
\(276\) | 1.10796 | 0.0666912 | ||||||||
\(277\) | −14.0099 | −0.841776 | −0.420888 | − | 0.907113i | \(-0.638281\pi\) | ||||
−0.420888 | + | 0.907113i | \(0.638281\pi\) | |||||||
\(278\) | −4.65343 | + | 4.65343i | −0.279094 | + | 0.279094i | ||||
\(279\) | 5.60966 | − | 5.60966i | 0.335842 | − | 0.335842i | ||||
\(280\) | −0.747560 | − | 0.747560i | −0.0446752 | − | 0.0446752i | ||||
\(281\) | 10.0982 | − | 10.0982i | 0.602408 | − | 0.602408i | −0.338543 | − | 0.940951i | \(-0.609934\pi\) |
0.940951 | + | 0.338543i | \(0.109934\pi\) | |||||||
\(282\) | 12.7144i | 0.757133i | ||||||||
\(283\) | 1.31783 | 0.0783370 | 0.0391685 | − | 0.999233i | \(-0.487529\pi\) | ||||
0.0391685 | + | 0.999233i | \(0.487529\pi\) | |||||||
\(284\) | −2.80266 | − | 2.80266i | −0.166307 | − | 0.166307i | ||||
\(285\) | −1.69458 | −0.100378 | ||||||||
\(286\) | −10.2197 | − | 14.7975i | −0.604304 | − | 0.874994i | ||||
\(287\) | −3.45476 | −0.203928 | ||||||||
\(288\) | 1.03995 | + | 1.03995i | 0.0612795 | + | 0.0612795i | ||||
\(289\) | −16.1819 | −0.951878 | ||||||||
\(290\) | − | 2.78192i | − | 0.163360i | ||||||
\(291\) | −0.0569832 | + | 0.0569832i | −0.00334041 | + | 0.00334041i | ||||
\(292\) | 2.70120 | + | 2.70120i | 0.158076 | + | 0.158076i | ||||
\(293\) | 18.6057 | − | 18.6057i | 1.08696 | − | 1.08696i | 0.0911161 | − | 0.995840i | \(-0.470957\pi\) |
0.995840 | − | 0.0911161i | \(-0.0290434\pi\) | |||||||
\(294\) | 6.69536 | − | 6.69536i | 0.390481 | − | 0.390481i | ||||
\(295\) | −3.89694 | −0.226889 | ||||||||
\(296\) | 21.2216 | 1.23348 | ||||||||
\(297\) | −2.67537 | + | 1.96021i | −0.155241 | + | 0.113743i | ||||
\(298\) | 27.1955i | 1.57539i | ||||||||
\(299\) | 11.0952 | − | 10.4925i | 0.641655 | − | 0.606797i | ||||
\(300\) | 1.24720 | 0.0720070 | ||||||||
\(301\) | −6.57106 | + | 6.57106i | −0.378750 | + | 0.378750i | ||||
\(302\) | 2.04473 | 0.117661 | ||||||||
\(303\) | 4.22512 | 0.242727 | ||||||||
\(304\) | 11.0734 | + | 11.0734i | 0.635103 | + | 0.635103i | ||||
\(305\) | 1.21501 | + | 1.21501i | 0.0695711 | + | 0.0695711i | ||||
\(306\) | 0.961806 | + | 0.961806i | 0.0549828 | + | 0.0549828i | ||||
\(307\) | −4.32402 | + | 4.32402i | −0.246785 | + | 0.246785i | −0.819650 | − | 0.572865i | \(-0.805832\pi\) |
0.572865 | + | 0.819650i | \(0.305832\pi\) | |||||||
\(308\) | 0.719340 | + | 0.110978i | 0.0409882 | + | 0.00632354i | ||||
\(309\) | − | 15.4692i | − | 0.880010i | ||||||
\(310\) | 4.06662 | − | 4.06662i | 0.230969 | − | 0.230969i | ||||
\(311\) | − | 25.3397i | − | 1.43688i | −0.695589 | − | 0.718440i | \(-0.744856\pi\) | ||
0.695589 | − | 0.718440i | \(-0.255144\pi\) | |||||||
\(312\) | 9.42238 | + | 0.263077i | 0.533437 | + | 0.0148938i | ||||
\(313\) | −2.06572 | −0.116761 | −0.0583807 | − | 0.998294i | \(-0.518594\pi\) | ||||
−0.0583807 | + | 0.998294i | \(0.518594\pi\) | |||||||
\(314\) | −1.48355 | − | 1.48355i | −0.0837217 | − | 0.0837217i | ||||
\(315\) | − | 0.404392i | − | 0.0227849i | ||||||
\(316\) | −1.98648 | −0.111748 | ||||||||
\(317\) | 11.9778 | − | 11.9778i | 0.672740 | − | 0.672740i | −0.285607 | − | 0.958347i | \(-0.592195\pi\) |
0.958347 | + | 0.285607i | \(0.0921952\pi\) | |||||||
\(318\) | −3.39678 | − | 3.39678i | −0.190482 | − | 0.190482i | ||||
\(319\) | −7.52228 | − | 10.2667i | −0.421167 | − | 0.574826i | ||||
\(320\) | −2.28300 | − | 2.28300i | −0.127623 | − | 0.127623i | ||||
\(321\) | 1.72944i | 0.0965281i | ||||||||
\(322\) | 5.34331i | 0.297771i | ||||||||
\(323\) | 2.24828 | + | 2.24828i | 0.125098 | + | 0.125098i | ||||
\(324\) | 0.261597i | 0.0145332i | ||||||||
\(325\) | 12.4896 | − | 11.8111i | 0.692800 | − | 0.655164i | ||||
\(326\) | − | 13.9893i | − | 0.774798i | ||||||
\(327\) | −10.9131 | − | 10.9131i | −0.603498 | − | 0.603498i | ||||
\(328\) | −10.7662 | −0.594465 | ||||||||
\(329\) | −7.09255 | −0.391025 | ||||||||
\(330\) | −1.93946 | + | 1.42102i | −0.106764 | + | 0.0782243i | ||||
\(331\) | 16.0602 | − | 16.0602i | 0.882747 | − | 0.882747i | −0.111066 | − | 0.993813i | \(-0.535427\pi\) |
0.993813 | + | 0.111066i | \(0.0354266\pi\) | |||||||
\(332\) | 1.31536 | − | 1.31536i | 0.0721898 | − | 0.0721898i | ||||
\(333\) | 5.73990 | + | 5.73990i | 0.314544 | + | 0.314544i | ||||
\(334\) | −34.0233 | −1.86167 | ||||||||
\(335\) | 6.84525i | 0.373996i | ||||||||
\(336\) | −2.64255 | + | 2.64255i | −0.144163 | + | 0.144163i | ||||
\(337\) | −25.2824 | −1.37722 | −0.688611 | − | 0.725131i | \(-0.741779\pi\) | ||||
−0.688611 | + | 0.725131i | \(0.741779\pi\) | |||||||
\(338\) | −14.5739 | + | 13.0312i | −0.792715 | + | 0.708803i | ||||
\(339\) | 2.42476 | 0.131695 | ||||||||
\(340\) | 0.0806497 | + | 0.0806497i | 0.00437384 | + | 0.00437384i | ||||
\(341\) | 4.01182 | − | 26.0040i | 0.217252 | − | 1.40820i | ||||
\(342\) | 5.28663i | 0.285868i | ||||||||
\(343\) | 7.88727 | + | 7.88727i | 0.425873 | + | 0.425873i | ||||
\(344\) | −20.4777 | + | 20.4777i | −1.10408 | + | 1.10408i | ||||
\(345\) | −1.44366 | − | 1.44366i | −0.0777240 | − | 0.0777240i | ||||
\(346\) | −22.1013 | − | 22.1013i | −1.18817 | − | 1.18817i | ||||
\(347\) | 25.8728i | 1.38893i | 0.719528 | + | 0.694464i | \(0.244358\pi\) | ||||
−0.719528 | + | 0.694464i | \(0.755642\pi\) | |||||||
\(348\) | −1.00388 | −0.0538135 | ||||||||
\(349\) | −3.71099 | + | 3.71099i | −0.198645 | + | 0.198645i | −0.799419 | − | 0.600774i | \(-0.794859\pi\) |
0.600774 | + | 0.799419i | \(0.294859\pi\) | |||||||
\(350\) | 6.01483i | 0.321506i | ||||||||
\(351\) | 2.47736 | + | 2.61967i | 0.132232 | + | 0.139828i | ||||
\(352\) | 4.82076 | + | 0.743732i | 0.256947 | + | 0.0396410i | ||||
\(353\) | 12.5514 | − | 12.5514i | 0.668045 | − | 0.668045i | −0.289218 | − | 0.957263i | \(-0.593395\pi\) |
0.957263 | + | 0.289218i | \(0.0933952\pi\) | |||||||
\(354\) | 12.1574i | 0.646161i | ||||||||
\(355\) | 7.30369i | 0.387640i | ||||||||
\(356\) | −0.924568 | + | 0.924568i | −0.0490020 | + | 0.0490020i | ||||
\(357\) | −0.536529 | + | 0.536529i | −0.0283961 | + | 0.0283961i | ||||
\(358\) | 9.65057 | − | 9.65057i | 0.510049 | − | 0.510049i | ||||
\(359\) | 9.87601 | − | 9.87601i | 0.521236 | − | 0.521236i | −0.396709 | − | 0.917945i | \(-0.629848\pi\) |
0.917945 | + | 0.396709i | \(0.129848\pi\) | |||||||
\(360\) | − | 1.26022i | − | 0.0664196i | ||||||
\(361\) | − | 6.64216i | − | 0.349587i | ||||||
\(362\) | 5.45774 | − | 5.45774i | 0.286852 | − | 0.286852i | ||||
\(363\) | −3.31519 | + | 10.4885i | −0.174002 | + | 0.550506i | ||||
\(364\) | 0.0220837 | − | 0.790949i | 0.00115750 | − | 0.0414570i | ||||
\(365\) | − | 7.03928i | − | 0.368453i | ||||||
\(366\) | 3.79050 | − | 3.79050i | 0.198133 | − | 0.198133i | ||||
\(367\) | −11.1557 | −0.582320 | −0.291160 | − | 0.956674i | \(-0.594041\pi\) | ||||
−0.291160 | + | 0.956674i | \(0.594041\pi\) | |||||||
\(368\) | 18.8675i | 0.983537i | ||||||||
\(369\) | −2.91199 | − | 2.91199i | −0.151592 | − | 0.151592i | ||||
\(370\) | 4.16103 | + | 4.16103i | 0.216322 | + | 0.216322i | ||||
\(371\) | 1.89484 | − | 1.89484i | 0.0983751 | − | 0.0983751i | ||||
\(372\) | −1.46747 | − | 1.46747i | −0.0760848 | − | 0.0760848i | ||||
\(373\) | − | 16.1948i | − | 0.838533i | −0.907863 | − | 0.419266i | \(-0.862287\pi\) | ||
0.907863 | − | 0.419266i | \(-0.137713\pi\) | |||||||
\(374\) | 4.45852 | + | 0.687848i | 0.230545 | + | 0.0355678i | ||||
\(375\) | −3.32938 | − | 3.32938i | −0.171929 | − | 0.171929i | ||||
\(376\) | −22.1028 | −1.13987 | ||||||||
\(377\) | −10.0530 | + | 9.50686i | −0.517755 | + | 0.489628i | ||||
\(378\) | −1.26160 | −0.0648896 | ||||||||
\(379\) | 15.5419 | − | 15.5419i | 0.798332 | − | 0.798332i | −0.184501 | − | 0.982832i | \(-0.559067\pi\) |
0.982832 | + | 0.184501i | \(0.0590667\pi\) | |||||||
\(380\) | 0.443296i | 0.0227406i | ||||||||
\(381\) | −8.96709 | −0.459398 | ||||||||
\(382\) | 16.2697 | + | 16.2697i | 0.832429 | + | 0.832429i | ||||
\(383\) | −19.3045 | + | 19.3045i | −0.986415 | + | 0.986415i | −0.999909 | − | 0.0134936i | \(-0.995705\pi\) |
0.0134936 | + | 0.999909i | \(0.495705\pi\) | |||||||
\(384\) | −9.20225 | + | 9.20225i | −0.469600 | + | 0.469600i | ||||
\(385\) | −0.792692 | − | 1.08190i | −0.0403993 | − | 0.0551386i | ||||
\(386\) | −6.42860 | −0.327207 | ||||||||
\(387\) | −11.0774 | −0.563095 | ||||||||
\(388\) | 0.0149066 | + | 0.0149066i | 0.000756770 | + | 0.000756770i | ||||
\(389\) | − | 31.5524i | − | 1.59977i | −0.600152 | − | 0.799886i | \(-0.704893\pi\) | ||
0.600152 | − | 0.799886i | \(-0.295107\pi\) | |||||||
\(390\) | 1.79592 | + | 1.89908i | 0.0909399 | + | 0.0961639i | ||||
\(391\) | 3.83076i | 0.193730i | ||||||||
\(392\) | 11.6392 | + | 11.6392i | 0.587870 | + | 0.587870i | ||||
\(393\) | 7.91810i | 0.399415i | ||||||||
\(394\) | − | 5.17459i | − | 0.260692i | ||||||
\(395\) | 2.58837 | + | 2.58837i | 0.130235 | + | 0.130235i | ||||
\(396\) | 0.512784 | + | 0.699868i | 0.0257684 | + | 0.0351697i | ||||
\(397\) | −13.5145 | − | 13.5145i | −0.678273 | − | 0.678273i | 0.281337 | − | 0.959609i | \(-0.409222\pi\) |
−0.959609 | + | 0.281337i | \(0.909222\pi\) | |||||||
\(398\) | −12.8564 | + | 12.8564i | −0.644432 | + | 0.644432i | ||||
\(399\) | −2.94906 | −0.147638 | ||||||||
\(400\) | 21.2387i | 1.06193i | ||||||||
\(401\) | −23.2634 | − | 23.2634i | −1.16172 | − | 1.16172i | −0.984100 | − | 0.177617i | \(-0.943161\pi\) |
−0.177617 | − | 0.984100i | \(-0.556839\pi\) | |||||||
\(402\) | 21.3554 | 1.06511 | ||||||||
\(403\) | −28.5926 | − | 0.798319i | −1.42430 | − | 0.0397671i | ||||
\(404\) | − | 1.10528i | − | 0.0549897i | ||||||
\(405\) | 0.340859 | − | 0.340859i | 0.0169374 | − | 0.0169374i | ||||
\(406\) | − | 4.84137i | − | 0.240273i | ||||||
\(407\) | 26.6077 | + | 4.10496i | 1.31890 | + | 0.203475i | ||||
\(408\) | −1.67201 | + | 1.67201i | −0.0827767 | + | 0.0827767i | ||||
\(409\) | 14.9710 | + | 14.9710i | 0.740270 | + | 0.740270i | 0.972630 | − | 0.232360i | \(-0.0746447\pi\) |
−0.232360 | + | 0.972630i | \(0.574645\pi\) | |||||||
\(410\) | −2.11100 | − | 2.11100i | −0.104255 | − | 0.104255i | ||||
\(411\) | −8.64502 | − | 8.64502i | −0.426427 | − | 0.426427i | ||||
\(412\) | −4.04669 | −0.199366 | ||||||||
\(413\) | −6.78184 | −0.333712 | ||||||||
\(414\) | −4.50384 | + | 4.50384i | −0.221352 | + | 0.221352i | ||||
\(415\) | −3.42781 | −0.168265 | ||||||||
\(416\) | 0.147997 | − | 5.30065i | 0.00725613 | − | 0.259886i | ||||
\(417\) | − | 4.37603i | − | 0.214295i | ||||||
\(418\) | 10.3629 | + | 14.1437i | 0.506865 | + | 0.691790i | ||||
\(419\) | −32.0945 | −1.56792 | −0.783960 | − | 0.620811i | \(-0.786804\pi\) | ||||
−0.783960 | + | 0.620811i | \(0.786804\pi\) | |||||||
\(420\) | −0.105788 | −0.00516192 | ||||||||
\(421\) | −13.4184 | + | 13.4184i | −0.653971 | + | 0.653971i | −0.953947 | − | 0.299976i | \(-0.903021\pi\) |
0.299976 | + | 0.953947i | \(0.403021\pi\) | |||||||
\(422\) | 11.5591 | − | 11.5591i | 0.562686 | − | 0.562686i | ||||
\(423\) | −5.97825 | − | 5.97825i | −0.290673 | − | 0.290673i | ||||
\(424\) | 5.90496 | − | 5.90496i | 0.286770 | − | 0.286770i | ||||
\(425\) | 4.31219i | 0.209172i | ||||||||
\(426\) | 22.7856 | 1.10397 | ||||||||
\(427\) | 2.11447 | + | 2.11447i | 0.102327 | + | 0.102327i | ||||
\(428\) | 0.452418 | 0.0218684 | ||||||||
\(429\) | 11.7629 | + | 2.15245i | 0.567921 | + | 0.103921i | ||||
\(430\) | −8.03035 | −0.387258 | ||||||||
\(431\) | −10.1064 | − | 10.1064i | −0.486806 | − | 0.486806i | 0.420491 | − | 0.907297i | \(-0.361858\pi\) |
−0.907297 | + | 0.420491i | \(0.861858\pi\) | |||||||
\(432\) | −4.45476 | −0.214330 | ||||||||
\(433\) | 5.96793i | 0.286800i | 0.989665 | + | 0.143400i | \(0.0458036\pi\) | ||||
−0.989665 | + | 0.143400i | \(0.954196\pi\) | |||||||
\(434\) | 7.07713 | − | 7.07713i | 0.339713 | − | 0.339713i | ||||
\(435\) | 1.30804 | + | 1.30804i | 0.0627160 | + | 0.0627160i | ||||
\(436\) | −2.85485 | + | 2.85485i | −0.136722 | + | 0.136722i | ||||
\(437\) | −10.5280 | + | 10.5280i | −0.503623 | + | 0.503623i | ||||
\(438\) | −21.9607 | −1.04932 | ||||||||
\(439\) | −22.3499 | −1.06670 | −0.533351 | − | 0.845894i | \(-0.679067\pi\) | ||||
−0.533351 | + | 0.845894i | \(0.679067\pi\) | |||||||
\(440\) | −2.47030 | − | 3.37156i | −0.117767 | − | 0.160733i | ||||
\(441\) | 6.29624i | 0.299821i | ||||||||
\(442\) | 0.136876 | − | 4.90236i | 0.00651053 | − | 0.233181i | ||||
\(443\) | 8.50146 | 0.403916 | 0.201958 | − | 0.979394i | \(-0.435269\pi\) | ||||
0.201958 | + | 0.979394i | \(0.435269\pi\) | |||||||
\(444\) | 1.50154 | − | 1.50154i | 0.0712600 | − | 0.0712600i | ||||
\(445\) | 2.40941 | 0.114217 | ||||||||
\(446\) | −23.5695 | −1.11605 | ||||||||
\(447\) | −12.7872 | − | 12.7872i | −0.604813 | − | 0.604813i | ||||
\(448\) | −3.97310 | − | 3.97310i | −0.187711 | − | 0.187711i | ||||
\(449\) | 27.2084 | + | 27.2084i | 1.28405 | + | 1.28405i | 0.938345 | + | 0.345701i | \(0.112359\pi\) |
0.345701 | + | 0.938345i | \(0.387641\pi\) | |||||||
\(450\) | −5.06985 | + | 5.06985i | −0.238995 | + | 0.238995i | ||||
\(451\) | −13.4987 | − | 2.08255i | −0.635631 | − | 0.0980633i | ||||
\(452\) | − | 0.634311i | − | 0.0298355i | ||||||
\(453\) | −0.961423 | + | 0.961423i | −0.0451716 | + | 0.0451716i | ||||
\(454\) | 5.92267i | 0.277964i | ||||||||
\(455\) | −1.05937 | + | 1.00183i | −0.0496643 | + | 0.0469663i | ||||
\(456\) | −9.19029 | −0.430375 | ||||||||
\(457\) | 10.0923 | + | 10.0923i | 0.472100 | + | 0.472100i | 0.902594 | − | 0.430494i | \(-0.141661\pi\) |
−0.430494 | + | 0.902594i | \(0.641661\pi\) | |||||||
\(458\) | 15.2327i | 0.711778i | ||||||||
\(459\) | −0.904472 | −0.0422171 | ||||||||
\(460\) | −0.377657 | + | 0.377657i | −0.0176084 | + | 0.0176084i | ||||
\(461\) | 4.18937 | + | 4.18937i | 0.195118 | + | 0.195118i | 0.797904 | − | 0.602785i | \(-0.205942\pi\) |
−0.602785 | + | 0.797904i | \(0.705942\pi\) | |||||||
\(462\) | −3.37524 | + | 2.47299i | −0.157030 | + | 0.115054i | ||||
\(463\) | 11.1196 | + | 11.1196i | 0.516772 | + | 0.516772i | 0.916593 | − | 0.399821i | \(-0.130928\pi\) |
−0.399821 | + | 0.916593i | \(0.630928\pi\) | |||||||
\(464\) | − | 17.0951i | − | 0.793621i | ||||||
\(465\) | 3.82421i | 0.177343i | ||||||||
\(466\) | 6.62607 | + | 6.62607i | 0.306947 | + | 0.306947i | ||||
\(467\) | − | 31.9283i | − | 1.47747i | −0.673998 | − | 0.738733i | \(-0.735425\pi\) | ||
0.673998 | − | 0.738733i | \(-0.264575\pi\) | |||||||
\(468\) | 0.685299 | − | 0.648070i | 0.0316779 | − | 0.0299571i | ||||
\(469\) | 11.9128i | 0.550081i | ||||||||
\(470\) | −4.33383 | − | 4.33383i | −0.199905 | − | 0.199905i | ||||
\(471\) | 1.39512 | 0.0642836 | ||||||||
\(472\) | −21.1345 | −0.972795 | ||||||||
\(473\) | −29.6361 | + | 21.7140i | −1.36267 | + | 0.998409i | ||||
\(474\) | 8.07504 | − | 8.07504i | 0.370899 | − | 0.370899i | ||||
\(475\) | −11.8511 | + | 11.8511i | −0.543766 | + | 0.543766i | ||||
\(476\) | 0.140354 | + | 0.140354i | 0.00643313 | + | 0.00643313i | ||||
\(477\) | 3.19429 | 0.146256 | ||||||||
\(478\) | − | 23.1892i | − | 1.06065i | ||||||
\(479\) | −23.1088 | + | 23.1088i | −1.05587 | + | 1.05587i | −0.0575245 | + | 0.998344i | \(0.518321\pi\) |
−0.998344 | + | 0.0575245i | \(0.981679\pi\) | |||||||
\(480\) | −0.708951 | −0.0323590 | ||||||||
\(481\) | 0.816853 | − | 29.2564i | 0.0372453 | − | 1.33398i | ||||
\(482\) | −42.6773 | −1.94390 | ||||||||
\(483\) | −2.51240 | − | 2.51240i | −0.114318 | − | 0.114318i | ||||
\(484\) | 2.74377 | + | 0.867243i | 0.124717 | + | 0.0394202i | ||||
\(485\) | − | 0.0388465i | − | 0.00176393i | ||||||
\(486\) | −1.06339 | − | 1.06339i | −0.0482364 | − | 0.0482364i | ||||
\(487\) | −11.5087 | + | 11.5087i | −0.521510 | + | 0.521510i | −0.918027 | − | 0.396517i | \(-0.870219\pi\) |
0.396517 | + | 0.918027i | \(0.370219\pi\) | |||||||
\(488\) | 6.58942 | + | 6.58942i | 0.298289 | + | 0.298289i | ||||
\(489\) | 6.57771 | + | 6.57771i | 0.297454 | + | 0.297454i | ||||
\(490\) | 4.56434i | 0.206196i | ||||||||
\(491\) | −14.9382 | −0.674153 | −0.337076 | − | 0.941477i | \(-0.609438\pi\) | ||||
−0.337076 | + | 0.941477i | \(0.609438\pi\) | |||||||
\(492\) | −0.761768 | + | 0.761768i | −0.0343432 | + | 0.0343432i | ||||
\(493\) | − | 3.47091i | − | 0.156322i | ||||||
\(494\) | 13.8492 | − | 13.0969i | 0.623107 | − | 0.589257i | ||||
\(495\) | 0.243769 | − | 1.58008i | 0.0109566 | − | 0.0710192i | ||||
\(496\) | 24.9897 | − | 24.9897i | 1.12207 | − | 1.12207i | ||||
\(497\) | 12.7106i | 0.570148i | ||||||||
\(498\) | 10.6939i | 0.479204i | ||||||||
\(499\) | 9.54732 | − | 9.54732i | 0.427397 | − | 0.427397i | −0.460344 | − | 0.887741i | \(-0.652274\pi\) |
0.887741 | + | 0.460344i | \(0.152274\pi\) | |||||||
\(500\) | −0.870957 | + | 0.870957i | −0.0389504 | + | 0.0389504i | ||||
\(501\) | 15.9976 | − | 15.9976i | 0.714719 | − | 0.714719i | ||||
\(502\) | 11.2643 | − | 11.2643i | 0.502749 | − | 0.502749i | ||||
\(503\) | 9.79846i | 0.436892i | 0.975849 | + | 0.218446i | \(0.0700987\pi\) | ||||
−0.975849 | + | 0.218446i | \(0.929901\pi\) | |||||||
\(504\) | − | 2.19316i | − | 0.0976913i | ||||||
\(505\) | −1.44017 | + | 1.44017i | −0.0640868 | + | 0.0640868i | ||||
\(506\) | −3.22098 | + | 20.8779i | −0.143190 | + | 0.928135i | ||||
\(507\) | 0.725366 | − | 12.9797i | 0.0322147 | − | 0.576451i | ||||
\(508\) | 2.34577i | 0.104077i | ||||||||
\(509\) | 16.9617 | − | 16.9617i | 0.751816 | − | 0.751816i | −0.223002 | − | 0.974818i | \(-0.571586\pi\) |
0.974818 | + | 0.223002i | \(0.0715857\pi\) | |||||||
\(510\) | −0.655681 | −0.0290340 | ||||||||
\(511\) | − | 12.2504i | − | 0.541928i | ||||||
\(512\) | −11.8374 | − | 11.8374i | −0.523145 | − | 0.523145i | ||||
\(513\) | −2.48574 | − | 2.48574i | −0.109748 | − | 0.109748i | ||||
\(514\) | 3.55461 | − | 3.55461i | 0.156787 | − | 0.156787i | ||||
\(515\) | 5.27280 | + | 5.27280i | 0.232348 | + | 0.232348i | ||||
\(516\) | 2.89781i | 0.127569i | ||||||||
\(517\) | −27.7126 | − | 4.27542i | −1.21880 | − | 0.188033i | ||||
\(518\) | 7.24144 | + | 7.24144i | 0.318170 | + | 0.318170i | ||||
\(519\) | 20.7838 | 0.912309 | ||||||||
\(520\) | −3.30137 | + | 3.12203i | −0.144775 | + | 0.136910i | ||||
\(521\) | 15.1733 | 0.664755 | 0.332377 | − | 0.943146i | \(-0.392149\pi\) | ||||
0.332377 | + | 0.943146i | \(0.392149\pi\) | |||||||
\(522\) | 4.08076 | − | 4.08076i | 0.178610 | − | 0.178610i | ||||
\(523\) | − | 9.34555i | − | 0.408653i | −0.978903 | − | 0.204326i | \(-0.934500\pi\) | ||
0.978903 | − | 0.204326i | \(-0.0655003\pi\) | |||||||
\(524\) | 2.07135 | 0.0904874 | ||||||||
\(525\) | −2.82814 | − | 2.82814i | −0.123430 | − | 0.123430i | ||||
\(526\) | −2.87105 | + | 2.87105i | −0.125184 | + | 0.125184i | ||||
\(527\) | 5.07378 | − | 5.07378i | 0.221017 | − | 0.221017i | ||||
\(528\) | −11.9181 | + | 8.73225i | −0.518670 | + | 0.380022i | ||||
\(529\) | 5.06175 | 0.220076 | ||||||||
\(530\) | 2.31564 | 0.100585 | ||||||||
\(531\) | −5.71636 | − | 5.71636i | −0.248069 | − | 0.248069i | ||||
\(532\) | 0.771467i | 0.0334473i | ||||||||
\(533\) | −0.414410 | + | 14.8425i | −0.0179501 | + | 0.642901i | ||||
\(534\) | − | 7.51672i | − | 0.325280i | ||||||
\(535\) | −0.589496 | − | 0.589496i | −0.0254862 | − | 0.0254862i | ||||
\(536\) | 37.1243i | 1.60352i | ||||||||
\(537\) | 9.07529i | 0.391628i | ||||||||
\(538\) | 25.5968 | + | 25.5968i | 1.10356 | + | 1.10356i | ||||
\(539\) | 12.3419 | + | 16.8448i | 0.531604 | + | 0.725555i | ||||
\(540\) | −0.0891677 | − | 0.0891677i | −0.00383717 | − | 0.00383717i | ||||
\(541\) | 0.419846 | − | 0.419846i | 0.0180506 | − | 0.0180506i | −0.698024 | − | 0.716074i | \(-0.745937\pi\) |
0.716074 | + | 0.698024i | \(0.245937\pi\) | |||||||
\(542\) | 30.9692 | 1.33024 | ||||||||
\(543\) | 5.13239i | 0.220252i | ||||||||
\(544\) | 0.940604 | + | 0.940604i | 0.0403280 | + | 0.0403280i | ||||
\(545\) | 7.43968 | 0.318681 | ||||||||
\(546\) | 3.12543 | + | 3.30497i | 0.133756 | + | 0.141440i | ||||
\(547\) | − | 27.8941i | − | 1.19266i | −0.802738 | − | 0.596332i | \(-0.796624\pi\) | ||
0.802738 | − | 0.596332i | \(-0.203376\pi\) | |||||||
\(548\) | −2.26151 | + | 2.26151i | −0.0966070 | + | 0.0966070i | ||||
\(549\) | 3.56455i | 0.152131i | ||||||||
\(550\) | −3.62577 | + | 23.5017i | −0.154603 | + | 1.00211i | ||||
\(551\) | 9.53903 | − | 9.53903i | 0.406376 | − | 0.406376i | ||||
\(552\) | −7.82948 | − | 7.82948i | −0.333245 | − | 0.333245i | ||||
\(553\) | 4.50454 | + | 4.50454i | 0.191552 | + | 0.191552i | ||||
\(554\) | −14.8980 | − | 14.8980i | −0.632957 | − | 0.632957i | ||||
\(555\) | −3.91299 | −0.166097 | ||||||||
\(556\) | −1.14476 | −0.0485485 | ||||||||
\(557\) | −4.62070 | + | 4.62070i | −0.195785 | + | 0.195785i | −0.798190 | − | 0.602405i | \(-0.794209\pi\) |
0.602405 | + | 0.798190i | \(0.294209\pi\) | |||||||
\(558\) | 11.9305 | 0.505059 | ||||||||
\(559\) | 27.4427 | + | 29.0191i | 1.16070 | + | 1.22738i | ||||
\(560\) | − | 1.80147i | − | 0.0761260i | ||||||
\(561\) | −2.41979 | + | 1.77295i | −0.102164 | + | 0.0748540i | ||||
\(562\) | 21.4767 | 0.905938 | ||||||||
\(563\) | −10.6608 | −0.449298 | −0.224649 | − | 0.974440i | \(-0.572124\pi\) | ||||
−0.224649 | + | 0.974440i | \(0.572124\pi\) | |||||||
\(564\) | −1.56389 | + | 1.56389i | −0.0658518 | + | 0.0658518i | ||||
\(565\) | −0.826502 | + | 0.826502i | −0.0347712 | + | 0.0347712i | ||||
\(566\) | 1.40137 | + | 1.40137i | 0.0589040 | + | 0.0589040i | ||||
\(567\) | 0.593196 | − | 0.593196i | 0.0249119 | − | 0.0249119i | ||||
\(568\) | 39.6105i | 1.66202i | ||||||||
\(569\) | −18.7238 | −0.784942 | −0.392471 | − | 0.919764i | \(-0.628380\pi\) | ||||
−0.392471 | + | 0.919764i | \(0.628380\pi\) | |||||||
\(570\) | −1.80199 | − | 1.80199i | −0.0754773 | − | 0.0754773i | ||||
\(571\) | 30.4275 | 1.27335 | 0.636676 | − | 0.771131i | \(-0.280309\pi\) | ||||
0.636676 | + | 0.771131i | \(0.280309\pi\) | |||||||
\(572\) | 0.563075 | − | 3.07715i | 0.0235433 | − | 0.128662i | ||||
\(573\) | −15.2998 | −0.639159 | ||||||||
\(574\) | −3.67376 | − | 3.67376i | −0.153340 | − | 0.153340i | ||||
\(575\) | −20.1926 | −0.842090 | ||||||||
\(576\) | − | 6.69778i | − | 0.279074i | ||||||
\(577\) | 19.8858 | − | 19.8858i | 0.827856 | − | 0.827856i | −0.159364 | − | 0.987220i | \(-0.550944\pi\) |
0.987220 | + | 0.159364i | \(0.0509444\pi\) | |||||||
\(578\) | −17.2077 | − | 17.2077i | −0.715746 | − | 0.715746i | ||||
\(579\) | 3.02269 | − | 3.02269i | 0.125619 | − | 0.125619i | ||||
\(580\) | 0.342181 | − | 0.342181i | 0.0142083 | − | 0.0142083i | ||||
\(581\) | −5.96541 | −0.247487 | ||||||||
\(582\) | −0.121191 | −0.00502352 | ||||||||
\(583\) | 8.54590 | − | 6.26146i | 0.353935 | − | 0.259323i | ||||
\(584\) | − | 38.1766i | − | 1.57976i | ||||||
\(585\) | −1.73737 | − | 0.0485081i | −0.0718314 | − | 0.00200556i | ||||
\(586\) | 39.5702 | 1.63463 | ||||||||
\(587\) | 8.71948 | − | 8.71948i | 0.359891 | − | 0.359891i | −0.503881 | − | 0.863773i | \(-0.668095\pi\) |
0.863773 | + | 0.503881i | \(0.168095\pi\) | |||||||
\(588\) | 1.64708 | 0.0679243 | ||||||||
\(589\) | 27.8884 | 1.14912 | ||||||||
\(590\) | −4.14397 | − | 4.14397i | −0.170605 | − | 0.170605i | ||||
\(591\) | 2.43306 | + | 2.43306i | 0.100083 | + | 0.100083i | ||||
\(592\) | 25.5699 | + | 25.5699i | 1.05092 | + | 1.05092i | ||||
\(593\) | 10.4881 | − | 10.4881i | 0.430693 | − | 0.430693i | −0.458171 | − | 0.888864i | \(-0.651495\pi\) |
0.888864 | + | 0.458171i | \(0.151495\pi\) | |||||||
\(594\) | −4.92942 | − | 0.760497i | −0.202257 | − | 0.0312036i | ||||
\(595\) | − | 0.365761i | − | 0.0149948i | ||||||
\(596\) | −3.34509 | + | 3.34509i | −0.137020 | + | 0.137020i | ||||
\(597\) | − | 12.0900i | − | 0.494811i | ||||||
\(598\) | 22.9562 | + | 0.640948i | 0.938749 | + | 0.0262103i | ||||
\(599\) | −1.39995 | −0.0572002 | −0.0286001 | − | 0.999591i | \(-0.509105\pi\) | ||||
−0.0286001 | + | 0.999591i | \(0.509105\pi\) | |||||||
\(600\) | −8.81344 | − | 8.81344i | −0.359807 | − | 0.359807i | ||||
\(601\) | − | 39.0742i | − | 1.59387i | −0.604066 | − | 0.796934i | \(-0.706454\pi\) | ||
0.604066 | − | 0.796934i | \(-0.293546\pi\) | |||||||
\(602\) | −13.9752 | −0.569587 | ||||||||
\(603\) | −10.0412 | + | 10.0412i | −0.408909 | + | 0.408909i | ||||
\(604\) | 0.251505 | + | 0.251505i | 0.0102336 | + | 0.0102336i | ||||
\(605\) | −2.44510 | − | 4.70512i | −0.0994075 | − | 0.191291i | ||||
\(606\) | 4.49295 | + | 4.49295i | 0.182514 | + | 0.182514i | ||||
\(607\) | − | 34.0152i | − | 1.38063i | −0.723507 | − | 0.690317i | \(-0.757471\pi\) | ||
0.723507 | − | 0.690317i | \(-0.242529\pi\) | |||||||
\(608\) | 5.17009i | 0.209675i | ||||||||
\(609\) | 2.27639 | + | 2.27639i | 0.0922438 | + | 0.0922438i | ||||
\(610\) | 2.58405i | 0.104625i | ||||||||
\(611\) | −0.850774 | + | 30.4714i | −0.0344186 | + | 1.23274i | ||||
\(612\) | 0.236607i | 0.00956428i | ||||||||
\(613\) | 13.4425 | + | 13.4425i | 0.542939 | + | 0.542939i | 0.924389 | − | 0.381450i | \(-0.124575\pi\) |
−0.381450 | + | 0.924389i | \(0.624575\pi\) | |||||||
\(614\) | −9.19624 | −0.371130 | ||||||||
\(615\) | 1.98516 | 0.0800492 | ||||||||
\(616\) | −4.29905 | − | 5.86752i | −0.173214 | − | 0.236409i | ||||
\(617\) | −2.49119 | + | 2.49119i | −0.100292 | + | 0.100292i | −0.755472 | − | 0.655181i | \(-0.772592\pi\) |
0.655181 | + | 0.755472i | \(0.272592\pi\) | |||||||
\(618\) | 16.4498 | − | 16.4498i | 0.661707 | − | 0.661707i | ||||
\(619\) | 19.9863 | + | 19.9863i | 0.803318 | + | 0.803318i | 0.983613 | − | 0.180295i | \(-0.0577051\pi\) |
−0.180295 | + | 0.983613i | \(0.557705\pi\) | |||||||
\(620\) | 1.00040 | 0.0401771 | ||||||||
\(621\) | − | 4.23536i | − | 0.169959i | ||||||
\(622\) | 26.9459 | − | 26.9459i | 1.08043 | − | 1.08043i | ||||
\(623\) | 4.19309 | 0.167993 | ||||||||
\(624\) | 11.0361 | + | 11.6700i | 0.441796 | + | 0.467174i | ||||
\(625\) | −21.5685 | −0.862738 | ||||||||
\(626\) | −2.19667 | − | 2.19667i | −0.0877965 | − | 0.0877965i | ||||
\(627\) | −11.5228 | − | 1.77771i | −0.460178 | − | 0.0709949i | ||||
\(628\) | − | 0.364958i | − | 0.0145634i | ||||||
\(629\) | 5.19157 | + | 5.19157i | 0.207002 | + | 0.207002i | ||||
\(630\) | 0.430027 | − | 0.430027i | 0.0171327 | − | 0.0171327i | ||||
\(631\) | 28.6905 | + | 28.6905i | 1.14215 | + | 1.14215i | 0.988056 | + | 0.154095i | \(0.0492462\pi\) |
0.154095 | + | 0.988056i | \(0.450754\pi\) | |||||||
\(632\) | 14.0377 | + | 14.0377i | 0.558389 | + | 0.558389i | ||||
\(633\) | 10.8700i | 0.432044i | ||||||||
\(634\) | 25.4741 | 1.01171 | ||||||||
\(635\) | 3.05651 | − | 3.05651i | 0.121294 | − | 0.121294i | ||||
\(636\) | − | 0.835617i | − | 0.0331344i | ||||||
\(637\) | 16.4941 | − | 15.5981i | 0.653519 | − | 0.618017i | ||||
\(638\) | 2.91840 | − | 18.9166i | 0.115541 | − | 0.748917i | ||||
\(639\) | −10.7137 | + | 10.7137i | −0.423826 | + | 0.423826i | ||||
\(640\) | − | 6.27334i | − | 0.247975i | ||||||
\(641\) | 24.7358i | 0.977007i | 0.872562 | + | 0.488503i | \(0.162457\pi\) | ||||
−0.872562 | + | 0.488503i | \(0.837543\pi\) | |||||||
\(642\) | −1.83907 | + | 1.83907i | −0.0725824 | + | 0.0725824i | ||||
\(643\) | 19.2632 | − | 19.2632i | 0.759668 | − | 0.759668i | −0.216594 | − | 0.976262i | \(-0.569495\pi\) |
0.976262 | + | 0.216594i | \(0.0694947\pi\) | |||||||
\(644\) | −0.657236 | + | 0.657236i | −0.0258987 | + | 0.0258987i | ||||
\(645\) | 3.77583 | − | 3.77583i | 0.148673 | − | 0.148673i | ||||
\(646\) | 4.78161i | 0.188130i | ||||||||
\(647\) | 21.1882i | 0.832995i | 0.909137 | + | 0.416497i | \(0.136742\pi\) | ||||
−0.909137 | + | 0.416497i | \(0.863258\pi\) | |||||||
\(648\) | 1.84860 | − | 1.84860i | 0.0726199 | − | 0.0726199i | ||||
\(649\) | −26.4986 | − | 4.08812i | −1.04016 | − | 0.160473i | ||||
\(650\) | 25.8412 | + | 0.721498i | 1.01358 | + | 0.0282995i | ||||
\(651\) | 6.65525i | 0.260840i | ||||||||
\(652\) | 1.72071 | − | 1.72071i | 0.0673882 | − | 0.0673882i | ||||
\(653\) | 5.78280 | 0.226298 | 0.113149 | − | 0.993578i | \(-0.463906\pi\) | ||||
0.113149 | + | 0.993578i | \(0.463906\pi\) | |||||||
\(654\) | − | 23.2099i | − | 0.907577i | ||||||
\(655\) | −2.69895 | − | 2.69895i | −0.105457 | − | 0.105457i | ||||
\(656\) | −12.9722 | − | 12.9722i | −0.506480 | − | 0.506480i | ||||
\(657\) | 10.3258 | − | 10.3258i | 0.402848 | − | 0.402848i | ||||
\(658\) | −7.54215 | − | 7.54215i | −0.294024 | − | 0.294024i | ||||
\(659\) | − | 49.6324i | − | 1.93340i | −0.255906 | − | 0.966702i | \(-0.582374\pi\) | ||
0.255906 | − | 0.966702i | \(-0.417626\pi\) | |||||||
\(660\) | −0.413343 | − | 0.0637694i | −0.0160894 | − | 0.00248222i | ||||
\(661\) | −7.29834 | − | 7.29834i | −0.283872 | − | 0.283872i | 0.550779 | − | 0.834651i | \(-0.314331\pi\) |
−0.834651 | + | 0.550779i | \(0.814331\pi\) | |||||||
\(662\) | 34.1564 | 1.32753 | ||||||||
\(663\) | 2.24070 | + | 2.36942i | 0.0870217 | + | 0.0920206i | ||||
\(664\) | −18.5902 | −0.721442 | ||||||||
\(665\) | 1.00522 | − | 1.00522i | 0.0389806 | − | 0.0389806i | ||||
\(666\) | 12.2075i | 0.473031i | ||||||||
\(667\) | 16.2532 | 0.629325 | ||||||||
\(668\) | −4.18492 | − | 4.18492i | −0.161919 | − | 0.161919i | ||||
\(669\) | 11.0822 | − | 11.0822i | 0.428465 | − | 0.428465i | ||||
\(670\) | −7.27917 | + | 7.27917i | −0.281219 | + | 0.281219i | ||||
\(671\) | 6.98724 | + | 9.53647i | 0.269739 | + | 0.368151i | ||||
\(672\) | −1.23379 | −0.0475943 | ||||||||
\(673\) | 28.5157 | 1.09920 | 0.549600 | − | 0.835428i | \(-0.314780\pi\) | ||||
0.549600 | + | 0.835428i | \(0.314780\pi\) | |||||||
\(674\) | −26.8851 | − | 26.8851i | −1.03557 | − | 1.03557i | ||||
\(675\) | − | 4.76763i | − | 0.183506i | ||||||
\(676\) | −3.39546 | − | 0.189754i | −0.130595 | − | 0.00729822i | ||||
\(677\) | 45.4172i | 1.74552i | 0.488146 | + | 0.872762i | \(0.337673\pi\) | ||||
−0.488146 | + | 0.872762i | \(0.662327\pi\) | |||||||
\(678\) | 2.57847 | + | 2.57847i | 0.0990255 | + | 0.0990255i | ||||
\(679\) | − | 0.0676044i | − | 0.00259442i | ||||||
\(680\) | − | 1.13984i | − | 0.0437108i | ||||||
\(681\) | −2.78480 | − | 2.78480i | −0.106714 | − | 0.106714i | ||||
\(682\) | 31.9185 | − | 23.3863i | 1.22222 | − | 0.895506i | ||||
\(683\) | −9.28933 | − | 9.28933i | −0.355446 | − | 0.355446i | 0.506685 | − | 0.862131i | \(-0.330871\pi\) |
−0.862131 | + | 0.506685i | \(0.830871\pi\) | |||||||
\(684\) | −0.650263 | + | 0.650263i | −0.0248634 | + | 0.0248634i | ||||
\(685\) | 5.89346 | 0.225178 | ||||||||
\(686\) | 16.7745i | 0.640453i | ||||||||
\(687\) | −7.16234 | − | 7.16234i | −0.273260 | − | 0.273260i | ||||
\(688\) | −49.3471 | −1.88134 | ||||||||
\(689\) | −7.91341 | − | 8.36799i | −0.301477 | − | 0.318795i | ||||
\(690\) | − | 3.07035i | − | 0.116886i | ||||||
\(691\) | 9.23750 | − | 9.23750i | 0.351411 | − | 0.351411i | −0.509223 | − | 0.860634i | \(-0.670067\pi\) |
0.860634 | + | 0.509223i | \(0.170067\pi\) | |||||||
\(692\) | − | 5.43699i | − | 0.206683i | ||||||
\(693\) | 0.424231 | − | 2.74980i | 0.0161152 | − | 0.104456i | ||||
\(694\) | −27.5129 | + | 27.5129i | −1.04438 | + | 1.04438i | ||||
\(695\) | 1.49161 | + | 1.49161i | 0.0565800 | + | 0.0565800i | ||||
\(696\) | 7.09400 | + | 7.09400i | 0.268897 | + | 0.268897i | ||||
\(697\) | −2.63381 | − | 2.63381i | −0.0997628 | − | 0.0997628i | ||||
\(698\) | −7.89245 | −0.298734 | ||||||||
\(699\) | −6.23108 | −0.235681 | ||||||||
\(700\) | −0.739833 | + | 0.739833i | −0.0279630 | + | 0.0279630i | ||||
\(701\) | −14.4108 | −0.544287 | −0.272144 | − | 0.962257i | \(-0.587733\pi\) | ||||
−0.272144 | + | 0.962257i | \(0.587733\pi\) | |||||||
\(702\) | −0.151333 | + | 5.42013i | −0.00571168 | + | 0.204570i | ||||
\(703\) | 28.5358i | 1.07625i | ||||||||
\(704\) | −13.1290 | − | 17.9190i | −0.494819 | − | 0.675349i | ||||
\(705\) | 4.07548 | 0.153492 | ||||||||
\(706\) | 26.6941 | 1.00465 | ||||||||
\(707\) | −2.50633 | + | 2.50633i | −0.0942601 | + | 0.0942601i | ||||
\(708\) | −1.49538 | + | 1.49538i | −0.0561999 | + | 0.0561999i | ||||
\(709\) | 10.7215 | + | 10.7215i | 0.402653 | + | 0.402653i | 0.879167 | − | 0.476514i | \(-0.158100\pi\) |
−0.476514 | + | 0.879167i | \(0.658100\pi\) | |||||||
\(710\) | −7.76667 | + | 7.76667i | −0.291478 | + | 0.291478i | ||||
\(711\) | 7.59368i | 0.284785i | ||||||||
\(712\) | 13.0671 | 0.489710 | ||||||||
\(713\) | 23.7589 | + | 23.7589i | 0.889779 | + | 0.889779i | ||||
\(714\) | −1.14108 | −0.0427038 | ||||||||
\(715\) | −4.74319 | + | 3.27582i | −0.177385 | + | 0.122509i | ||||
\(716\) | 2.37407 | 0.0887231 | ||||||||
\(717\) | 10.9034 | + | 10.9034i | 0.407196 | + | 0.407196i | ||||
\(718\) | 21.0041 | 0.783867 | ||||||||
\(719\) | 11.7786i | 0.439269i | 0.975582 | + | 0.219635i | \(0.0704865\pi\) | ||||
−0.975582 | + | 0.219635i | \(0.929513\pi\) | |||||||
\(720\) | 1.51845 | − | 1.51845i | 0.0565891 | − | 0.0565891i | ||||
\(721\) | 9.17625 | + | 9.17625i | 0.341741 | + | 0.341741i | ||||
\(722\) | 7.06321 | − | 7.06321i | 0.262865 | − | 0.262865i | ||||
\(723\) | 20.0666 | − | 20.0666i | 0.746285 | − | 0.746285i | ||||
\(724\) | 1.34262 | 0.0498981 | ||||||||
\(725\) | 18.2958 | 0.679488 | ||||||||
\(726\) | −14.6788 | + | 7.62807i | −0.544780 | + | 0.283104i | ||||
\(727\) | 4.53380i | 0.168149i | 0.996459 | + | 0.0840746i | \(0.0267934\pi\) | ||||
−0.996459 | + | 0.0840746i | \(0.973207\pi\) | |||||||
\(728\) | −5.74537 | + | 5.43326i | −0.212938 | + | 0.201370i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.48550 | − | 7.48550i | 0.277051 | − | 0.277051i | ||||
\(731\) | −10.0192 | −0.370573 | ||||||||
\(732\) | 0.932475 | 0.0344653 | ||||||||
\(733\) | −14.5897 | − | 14.5897i | −0.538883 | − | 0.538883i | 0.384318 | − | 0.923201i | \(-0.374437\pi\) |
−0.923201 | + | 0.384318i | \(0.874437\pi\) | |||||||
\(734\) | −11.8628 | − | 11.8628i | −0.437864 | − | 0.437864i | ||||
\(735\) | −2.14613 | − | 2.14613i | −0.0791611 | − | 0.0791611i | ||||
\(736\) | −4.40455 | + | 4.40455i | −0.162354 | + | 0.162354i | ||||
\(737\) | −7.18108 | + | 46.5466i | −0.264518 | + | 1.71457i | ||||
\(738\) | − | 6.19316i | − | 0.227974i | ||||||
\(739\) | −10.8534 | + | 10.8534i | −0.399248 | + | 0.399248i | −0.877968 | − | 0.478720i | \(-0.841101\pi\) |
0.478720 | + | 0.877968i | \(0.341101\pi\) | |||||||
\(740\) | 1.02363i | 0.0376293i | ||||||||
\(741\) | −0.353750 | + | 12.6699i | −0.0129953 | + | 0.465441i | ||||
\(742\) | 4.02991 | 0.147943 | ||||||||
\(743\) | −10.8987 | − | 10.8987i | −0.399836 | − | 0.399836i | 0.478339 | − | 0.878175i | \(-0.341239\pi\) |
−0.878175 | + | 0.478339i | \(0.841239\pi\) | |||||||
\(744\) | 20.7400i | 0.760367i | ||||||||
\(745\) | 8.71725 | 0.319375 | ||||||||
\(746\) | 17.2213 | − | 17.2213i | 0.630518 | − | 0.630518i | ||||
\(747\) | −5.02820 | − | 5.02820i | −0.183972 | − | 0.183972i | ||||
\(748\) | 0.463799 | + | 0.633011i | 0.0169582 | + | 0.0231452i | ||||
\(749\) | −1.02590 | − | 1.02590i | −0.0374855 | − | 0.0374855i | ||||
\(750\) | − | 7.08087i | − | 0.258557i | ||||||
\(751\) | − | 14.3910i | − | 0.525136i | −0.964913 | − | 0.262568i | \(-0.915431\pi\) | ||
0.964913 | − | 0.262568i | \(-0.0845694\pi\) | |||||||
\(752\) | −26.6317 | − | 26.6317i | −0.971158 | − | 0.971158i | ||||
\(753\) | 10.5928i | 0.386023i | ||||||||
\(754\) | −20.7997 | − | 0.580738i | −0.757482 | − | 0.0211492i | ||||
\(755\) | − | 0.655419i | − | 0.0238531i | ||||||
\(756\) | −0.155178 | − | 0.155178i | −0.00564378 | − | 0.00564378i | ||||
\(757\) | −31.3586 | −1.13975 | −0.569874 | − | 0.821732i | \(-0.693008\pi\) | ||||
−0.569874 | + | 0.821732i | \(0.693008\pi\) | |||||||
\(758\) | 33.0541 | 1.20058 | ||||||||
\(759\) | −8.30217 | − | 11.3311i | −0.301350 | − | 0.411294i | ||||
\(760\) | 3.13259 | − | 3.13259i | 0.113631 | − | 0.113631i | ||||
\(761\) | −15.8784 | + | 15.8784i | −0.575591 | + | 0.575591i | −0.933685 | − | 0.358095i | \(-0.883426\pi\) |
0.358095 | + | 0.933685i | \(0.383426\pi\) | |||||||
\(762\) | −9.53552 | − | 9.53552i | −0.345435 | − | 0.345435i | ||||
\(763\) | 12.9473 | 0.468722 | ||||||||
\(764\) | 4.00239i | 0.144801i | ||||||||
\(765\) | 0.308297 | − | 0.308297i | 0.0111465 | − | 0.0111465i | ||||
\(766\) | −41.0565 | −1.48343 | ||||||||
\(767\) | −0.813503 | + | 29.1365i | −0.0293739 | + | 1.05206i | ||||
\(768\) | −6.17560 | −0.222843 | ||||||||
\(769\) | −29.6154 | − | 29.6154i | −1.06796 | − | 1.06796i | −0.997516 | − | 0.0704438i | \(-0.977558\pi\) |
−0.0704438 | − | 0.997516i | \(-0.522442\pi\) | |||||||
\(770\) | 0.307539 | − | 1.99342i | 0.0110829 | − | 0.0718379i | ||||
\(771\) | 3.34272i | 0.120385i | ||||||||
\(772\) | −0.790728 | − | 0.790728i | −0.0284589 | − | 0.0284589i | ||||
\(773\) | −6.78348 | + | 6.78348i | −0.243985 | + | 0.243985i | −0.818496 | − | 0.574512i | \(-0.805192\pi\) |
0.574512 | + | 0.818496i | \(0.305192\pi\) | |||||||
\(774\) | −11.7796 | − | 11.7796i | −0.423408 | − | 0.423408i | ||||
\(775\) | 26.7448 | + | 26.7448i | 0.960701 | + | 0.960701i | ||||
\(776\) | − | 0.210678i | − | 0.00756291i | ||||||
\(777\) | −6.80977 | −0.244299 | ||||||||
\(778\) | 33.5526 | − | 33.5526i | 1.20292 | − | 1.20292i | ||||
\(779\) | − | 14.4769i | − | 0.518690i | ||||||
\(780\) | −0.0126896 | + | 0.454491i | −0.000454360 | + | 0.0162734i | ||||
\(781\) | −7.66200 | + | 49.6639i | −0.274168 | + | 1.77712i | ||||
\(782\) | −4.07359 | + | 4.07359i | −0.145671 | + | 0.145671i | ||||
\(783\) | 3.83750i | 0.137141i | ||||||||
\(784\) | 28.0482i | 1.00172i | ||||||||
\(785\) | −0.475538 | + | 0.475538i | −0.0169727 | + | 0.0169727i | ||||
\(786\) | −8.42003 | + | 8.42003i | −0.300332 | + | 0.300332i | ||||
\(787\) | −32.1568 | + | 32.1568i | −1.14627 | + | 1.14627i | −0.158985 | + | 0.987281i | \(0.550822\pi\) |
−0.987281 | + | 0.158985i | \(0.949178\pi\) | |||||||
\(788\) | 0.636482 | − | 0.636482i | 0.0226737 | − | 0.0226737i | ||||
\(789\) | − | 2.69990i | − | 0.0961192i | ||||||
\(790\) | 5.50490i | 0.195856i | ||||||||
\(791\) | −1.43836 | + | 1.43836i | −0.0511421 | + | 0.0511421i | ||||
\(792\) | 1.32205 | − | 8.56932i | 0.0469770 | − | 0.304498i | ||||
\(793\) | 9.33794 | − | 8.83067i | 0.331600 | − | 0.313586i | ||||
\(794\) | − | 28.7423i | − | 1.02003i | ||||||
\(795\) | −1.08880 | + | 1.08880i | −0.0386158 | + | 0.0386158i | ||||
\(796\) | −3.16271 | −0.112099 | ||||||||
\(797\) | − | 11.2998i | − | 0.400260i | −0.979769 | − | 0.200130i | \(-0.935864\pi\) | ||
0.979769 | − | 0.200130i | \(-0.0641365\pi\) | |||||||
\(798\) | −3.13601 | − | 3.13601i | −0.111013 | − | 0.111013i | ||||
\(799\) | −5.40716 | − | 5.40716i | −0.191292 | − | 0.191292i | ||||
\(800\) | −4.95809 | + | 4.95809i | −0.175295 | + | 0.175295i | ||||
\(801\) | 3.53432 | + | 3.53432i | 0.124879 | + | 0.124879i | ||||
\(802\) | − | 49.4760i | − | 1.74706i | ||||||
\(803\) | 7.38463 | − | 47.8660i | 0.260598 | − | 1.68916i | ||||
\(804\) | 2.62674 | + | 2.62674i | 0.0926381 | + | 0.0926381i | ||||
\(805\) | 1.71275 | 0.0603663 | ||||||||
\(806\) | −29.5562 | − | 31.2540i | −1.04107 | − | 1.10088i | ||||
\(807\) | −24.0709 | −0.847337 | ||||||||
\(808\) | −7.81057 | + | 7.81057i | −0.274775 | + | 0.274775i | ||||
\(809\) | − | 11.2868i | − | 0.396822i | −0.980119 | − | 0.198411i | \(-0.936422\pi\) | ||
0.980119 | − | 0.198411i | \(-0.0635781\pi\) | |||||||
\(810\) | 0.724932 | 0.0254715 | ||||||||
\(811\) | 16.0782 | + | 16.0782i | 0.564583 | + | 0.564583i | 0.930606 | − | 0.366023i | \(-0.119281\pi\) |
−0.366023 | + | 0.930606i | \(0.619281\pi\) | |||||||
\(812\) | 0.595496 | − | 0.595496i | 0.0208978 | − | 0.0208978i | ||||
\(813\) | −14.5615 | + | 14.5615i | −0.510696 | + | 0.510696i | ||||
\(814\) | 23.9292 | + | 32.6596i | 0.838718 | + | 1.14472i | ||||
\(815\) | −4.48414 | −0.157073 | ||||||||
\(816\) | −4.02921 | −0.141050 | ||||||||
\(817\) | −27.5355 | − | 27.5355i | −0.963347 | − | 0.963347i | ||||
\(818\) | 31.8401i | 1.11326i | ||||||||
\(819\) | −3.02354 | − | 0.0844186i | −0.105651 | − | 0.00294982i | ||||
\(820\) | − | 0.519311i | − | 0.0181351i | ||||||
\(821\) | 13.3586 | + | 13.3586i | 0.466219 | + | 0.466219i | 0.900687 | − | 0.434468i | \(-0.143064\pi\) |
−0.434468 | + | 0.900687i | \(0.643064\pi\) | |||||||
\(822\) | − | 18.3861i | − | 0.641287i | ||||||
\(823\) | 1.49260i | 0.0520287i | 0.999662 | + | 0.0260144i | \(0.00828156\pi\) | ||||
−0.999662 | + | 0.0260144i | \(0.991718\pi\) | |||||||
\(824\) | 28.5963 | + | 28.5963i | 0.996200 | + | 0.996200i | ||||
\(825\) | −9.34554 | − | 12.7552i | −0.325370 | − | 0.444078i | ||||
\(826\) | −7.21174 | − | 7.21174i | −0.250929 | − | 0.250929i | ||||
\(827\) | −4.46825 | + | 4.46825i | −0.155376 | + | 0.155376i | −0.780514 | − | 0.625138i | \(-0.785043\pi\) |
0.625138 | + | 0.780514i | \(0.285043\pi\) | |||||||
\(828\) | −1.10796 | −0.0385042 | ||||||||
\(829\) | 6.17244i | 0.214378i | 0.994239 | + | 0.107189i | \(0.0341850\pi\) | ||||
−0.994239 | + | 0.107189i | \(0.965815\pi\) | |||||||
\(830\) | −3.64510 | − | 3.64510i | −0.126523 | − | 0.126523i | ||||
\(831\) | 14.0099 | 0.485999 | ||||||||
\(832\) | −17.5460 | + | 16.5928i | −0.608298 | + | 0.575253i | ||||
\(833\) | 5.69477i | 0.197312i | ||||||||
\(834\) | 4.65343 | − | 4.65343i | 0.161135 | − | 0.161135i | ||||
\(835\) | 10.9058i | 0.377412i | ||||||||
\(836\) | −0.465044 | + | 3.01434i | −0.0160839 | + | 0.104253i | ||||
\(837\) | −5.60966 | + | 5.60966i | −0.193898 | + | 0.193898i | ||||
\(838\) | −34.1290 | − | 34.1290i | −1.17897 | − | 1.17897i | ||||
\(839\) | 11.5079 | + | 11.5079i | 0.397297 | + | 0.397297i | 0.877279 | − | 0.479981i | \(-0.159357\pi\) |
−0.479981 | + | 0.877279i | \(0.659357\pi\) | |||||||
\(840\) | 0.747560 | + | 0.747560i | 0.0257933 | + | 0.0257933i | ||||
\(841\) | 14.2736 | 0.492194 | ||||||||
\(842\) | −28.5379 | −0.983481 | ||||||||
\(843\) | −10.0982 | + | 10.0982i | −0.347800 | + | 0.347800i | ||||
\(844\) | 2.84356 | 0.0978794 | ||||||||
\(845\) | 4.17702 | + | 4.67151i | 0.143694 | + | 0.160705i | ||||
\(846\) | − | 12.7144i | − | 0.437131i | ||||||
\(847\) | −4.25520 | − | 8.18831i | −0.146211 | − | 0.281354i | ||||
\(848\) | 14.2298 | 0.488653 | ||||||||
\(849\) | −1.31783 | −0.0452279 | ||||||||
\(850\) | −4.58554 | + | 4.58554i | −0.157283 | + | 0.157283i | ||||
\(851\) | −24.3105 | + | 24.3105i | −0.833354 | + | 0.833354i | ||||
\(852\) | 2.80266 | + | 2.80266i | 0.0960176 | + | 0.0960176i | ||||
\(853\) | −5.12828 | + | 5.12828i | −0.175589 | + | 0.175589i | −0.789430 | − | 0.613841i | \(-0.789624\pi\) |
0.613841 | + | 0.789430i | \(0.289624\pi\) | |||||||
\(854\) | 4.49702i | 0.153885i | ||||||||
\(855\) | 1.69458 | 0.0579533 | ||||||||
\(856\) | −3.19705 | − | 3.19705i | −0.109273 | − | 0.109273i | ||||
\(857\) | 35.7213 | 1.22022 | 0.610108 | − | 0.792318i | \(-0.291126\pi\) | ||||
0.610108 | + | 0.792318i | \(0.291126\pi\) | |||||||
\(858\) | 10.2197 | + | 14.7975i | 0.348895 | + | 0.505178i | ||||
\(859\) | 30.2899 | 1.03348 | 0.516739 | − | 0.856143i | \(-0.327146\pi\) | ||||
0.516739 | + | 0.856143i | \(0.327146\pi\) | |||||||
\(860\) | −0.987745 | − | 0.987745i | −0.0336818 | − | 0.0336818i | ||||
\(861\) | 3.45476 | 0.117738 | ||||||||
\(862\) | − | 21.4940i | − | 0.732088i | ||||||
\(863\) | −35.6355 | + | 35.6355i | −1.21305 | + | 1.21305i | −0.243026 | + | 0.970020i | \(0.578140\pi\) |
−0.970020 | + | 0.243026i | \(0.921860\pi\) | |||||||
\(864\) | −1.03995 | − | 1.03995i | −0.0353798 | − | 0.0353798i | ||||
\(865\) | −7.08436 | + | 7.08436i | −0.240875 | + | 0.240875i | ||||
\(866\) | −6.34624 | + | 6.34624i | −0.215654 | + | 0.215654i | ||||
\(867\) | 16.1819 | 0.549567 | ||||||||
\(868\) | 1.74100 | 0.0590932 | ||||||||
\(869\) | 14.8852 | + | 20.3159i | 0.504945 | + | 0.689169i | ||||
\(870\) | 2.78192i | 0.0943161i | ||||||||
\(871\) | 51.1802 | + | 1.42898i | 1.73418 | + | 0.0484190i | ||||
\(872\) | 40.3481 | 1.36636 | ||||||||
\(873\) | 0.0569832 | − | 0.0569832i | 0.00192859 | − | 0.00192859i | ||||
\(874\) | −22.3908 | −0.757379 | ||||||||
\(875\) | 3.94995 | 0.133533 | ||||||||
\(876\) | −2.70120 | − | 2.70120i | −0.0912651 | − | 0.0912651i | ||||
\(877\) | −11.0527 | − | 11.0527i | −0.373222 | − | 0.373222i | 0.495427 | − | 0.868649i | \(-0.335011\pi\) |
−0.868649 | + | 0.495427i | \(0.835011\pi\) | |||||||
\(878\) | −23.7666 | − | 23.7666i | −0.802085 | − | 0.802085i | ||||
\(879\) | −18.6057 | + | 18.6057i | −0.627555 | + | 0.627555i | ||||
\(880\) | 1.08593 | − | 7.03886i | 0.0366069 | − | 0.237280i | ||||
\(881\) | 3.31294i | 0.111616i | 0.998442 | + | 0.0558078i | \(0.0177734\pi\) | ||||
−0.998442 | + | 0.0558078i | \(0.982227\pi\) | |||||||
\(882\) | −6.69536 | + | 6.69536i | −0.225444 | + | 0.225444i | ||||
\(883\) | − | 45.5406i | − | 1.53256i | −0.642504 | − | 0.766282i | \(-0.722105\pi\) | ||
0.642504 | − | 0.766282i | \(-0.277895\pi\) | |||||||
\(884\) | 0.619833 | − | 0.586161i | 0.0208472 | − | 0.0197147i | ||||
\(885\) | 3.89694 | 0.130994 | ||||||||
\(886\) | 9.04037 | + | 9.04037i | 0.303717 | + | 0.303717i | ||||
\(887\) | 4.15521i | 0.139518i | 0.997564 | + | 0.0697591i | \(0.0222231\pi\) | ||||
−0.997564 | + | 0.0697591i | \(0.977777\pi\) | |||||||
\(888\) | −21.2216 | −0.712149 | ||||||||
\(889\) | 5.31924 | − | 5.31924i | 0.178402 | − | 0.178402i | ||||
\(890\) | 2.56214 | + | 2.56214i | 0.0858832 | + | 0.0858832i | ||||
\(891\) | 2.67537 | − | 1.96021i | 0.0896282 | − | 0.0656694i | ||||
\(892\) | −2.89908 | − | 2.89908i | −0.0970685 | − | 0.0970685i | ||||
\(893\) | − | 29.7208i | − | 0.994569i | ||||||
\(894\) | − | 27.1955i | − | 0.909555i | ||||||
\(895\) | −3.09339 | − | 3.09339i | −0.103401 | − | 0.103401i | ||||
\(896\) | − | 10.9175i | − | 0.364727i | ||||||
\(897\) | −11.0952 | + | 10.4925i | −0.370460 | + | 0.350335i | ||||
\(898\) | 57.8664i | 1.93103i | ||||||||
\(899\) | −21.5271 | − | 21.5271i | −0.717967 | − | 0.717967i | ||||
\(900\) | −1.24720 | −0.0415733 | ||||||||
\(901\) | 2.88914 | 0.0962514 | ||||||||
\(902\) | −12.1399 | − | 16.5690i | −0.404214 | − | 0.551687i | ||||
\(903\) | 6.57106 | − | 6.57106i | 0.218671 | − | 0.218671i | ||||
\(904\) | −4.48242 | + | 4.48242i | −0.149083 | + | 0.149083i | ||||
\(905\) | −1.74942 | − | 1.74942i | −0.0581528 | − | 0.0581528i | ||||
\(906\) | −2.04473 | −0.0679318 | ||||||||
\(907\) | 27.8469i | 0.924642i | 0.886713 | + | 0.462321i | \(0.152983\pi\) | ||||
−0.886713 | + | 0.462321i | \(0.847017\pi\) | |||||||
\(908\) | −0.728497 | + | 0.728497i | −0.0241760 | + | 0.0241760i | ||||
\(909\) | −4.22512 | −0.140139 | ||||||||
\(910\) | −2.19186 | − | 0.0611977i | −0.0726594 | − | 0.00202868i | ||||
\(911\) | 0.853342 | 0.0282725 | 0.0141362 | − | 0.999900i | \(-0.495500\pi\) | ||||
0.0141362 | + | 0.999900i | \(0.495500\pi\) | |||||||
\(912\) | −11.0734 | − | 11.0734i | −0.366677 | − | 0.366677i | ||||
\(913\) | −23.3086 | − | 3.59598i | −0.771401 | − | 0.119009i | ||||
\(914\) | 21.4642i | 0.709972i | ||||||||
\(915\) | −1.21501 | − | 1.21501i | −0.0401669 | − | 0.0401669i | ||||
\(916\) | −1.87365 | + | 1.87365i | −0.0619070 | + | 0.0619070i | ||||
\(917\) | −4.69698 | − | 4.69698i | −0.155108 | − | 0.155108i | ||||
\(918\) | −0.961806 | − | 0.961806i | −0.0317443 | − | 0.0317443i | ||||
\(919\) | 9.14685i | 0.301727i | 0.988555 | + | 0.150863i | \(0.0482053\pi\) | ||||
−0.988555 | + | 0.150863i | \(0.951795\pi\) | |||||||
\(920\) | 5.33750 | 0.175972 | ||||||||
\(921\) | 4.32402 | − | 4.32402i | 0.142481 | − | 0.142481i | ||||
\(922\) | 8.90987i | 0.293431i | ||||||||
\(923\) | 54.6079 | + | 1.52468i | 1.79744 | + | 0.0501853i | ||||
\(924\) | −0.719340 | − | 0.110978i | −0.0236646 | − | 0.00365090i | ||||
\(925\) | −27.3657 | + | 27.3657i | −0.899779 | + | 0.899779i | ||||
\(926\) | 23.6490i | 0.777153i | ||||||||
\(927\) | 15.4692i | 0.508074i | ||||||||
\(928\) | 3.99080 | − | 3.99080i | 0.131004 | − | 0.131004i | ||||
\(929\) | 1.36910 | − | 1.36910i | 0.0449187 | − | 0.0449187i | −0.684291 | − | 0.729209i | \(-0.739888\pi\) |
0.729209 | + | 0.684291i | \(0.239888\pi\) | |||||||
\(930\) | −4.06662 | + | 4.06662i | −0.133350 | + | 0.133350i | ||||
\(931\) | −15.6508 | + | 15.6508i | −0.512935 | + | 0.512935i | ||||
\(932\) | 1.63003i | 0.0533935i | ||||||||
\(933\) | 25.3397i | 0.829583i | ||||||||
\(934\) | 33.9522 | − | 33.9522i | 1.11095 | − | 1.11095i | ||||
\(935\) | 0.220483 | − | 1.42913i | 0.00721055 | − | 0.0467377i | ||||
\(936\) | −9.42238 | − | 0.263077i | −0.307980 | − | 0.00859894i | ||||
\(937\) | 28.2759i | 0.923733i | 0.886950 | + | 0.461866i | \(0.152820\pi\) | ||||
−0.886950 | + | 0.461866i | \(0.847180\pi\) | |||||||
\(938\) | −12.6679 | + | 12.6679i | −0.413622 | + | 0.413622i | ||||
\(939\) | 2.06572 | 0.0674123 | ||||||||
\(940\) | − | 1.06613i | − | 0.0347735i | ||||||
\(941\) | −14.4692 | − | 14.4692i | −0.471682 | − | 0.471682i | 0.430777 | − | 0.902458i | \(-0.358240\pi\) |
−0.902458 | + | 0.430777i | \(0.858240\pi\) | |||||||
\(942\) | 1.48355 | + | 1.48355i | 0.0483368 | + | 0.0483368i | ||||
\(943\) | 12.3333 | − | 12.3333i | 0.401628 | − | 0.401628i | ||||
\(944\) | −25.4650 | − | 25.4650i | −0.828815 | − | 0.828815i | ||||
\(945\) | 0.404392i | 0.0131549i | ||||||||
\(946\) | −54.6051 | − | 8.42432i | −1.77537 | − | 0.273898i | ||||
\(947\) | −24.9844 | − | 24.9844i | −0.811883 | − | 0.811883i | 0.173033 | − | 0.984916i | \(-0.444643\pi\) |
−0.984916 | + | 0.173033i | \(0.944643\pi\) | |||||||
\(948\) | 1.98648 | 0.0645180 | ||||||||
\(949\) | −52.6310 | − | 1.46948i | −1.70847 | − | 0.0477013i | ||||
\(950\) | −25.2047 | −0.817748 | ||||||||
\(951\) | −11.9778 | + | 11.9778i | −0.388407 | + | 0.388407i | ||||
\(952\) | − | 1.98365i | − | 0.0642906i | ||||||
\(953\) | 33.6749 | 1.09084 | 0.545419 | − | 0.838164i | \(-0.316371\pi\) | ||||
0.545419 | + | 0.838164i | \(0.316371\pi\) | |||||||
\(954\) | 3.39678 | + | 3.39678i | 0.109975 | + | 0.109975i | ||||
\(955\) | 5.21508 | − | 5.21508i | 0.168756 | − | 0.168756i | ||||
\(956\) | 2.85231 | − | 2.85231i | 0.0922502 | − | 0.0922502i | ||||
\(957\) | 7.52228 | + | 10.2667i | 0.243161 | + | 0.331876i | ||||
\(958\) | −49.1474 | −1.58788 | ||||||||
\(959\) | 10.2564 | 0.331196 | ||||||||
\(960\) | 2.28300 | + | 2.28300i | 0.0736835 | + | 0.0736835i | ||||
\(961\) | − | 31.9366i | − | 1.03021i | ||||||
\(962\) | 31.9796 | − | 30.2424i | 1.03107 | − | 0.975053i | ||||
\(963\) | − | 1.72944i | − | 0.0557306i | ||||||
\(964\) | −5.24937 | − | 5.24937i | −0.169071 | − | 0.169071i | ||||
\(965\) | 2.06062i | 0.0663338i | ||||||||
\(966\) | − | 5.34331i | − | 0.171918i | ||||||
\(967\) | 4.46666 | + | 4.46666i | 0.143638 | + | 0.143638i | 0.775269 | − | 0.631631i | \(-0.217614\pi\) |
−0.631631 | + | 0.775269i | \(0.717614\pi\) | |||||||
\(968\) | −13.2607 | − | 25.5176i | −0.426214 | − | 0.820166i | ||||
\(969\) | −2.24828 | − | 2.24828i | −0.0722253 | − | 0.0722253i | ||||
\(970\) | 0.0413089 | − | 0.0413089i | 0.00132635 | − | 0.00132635i | ||||
\(971\) | 9.86851 | 0.316696 | 0.158348 | − | 0.987383i | \(-0.449383\pi\) | ||||
0.158348 | + | 0.987383i | \(0.449383\pi\) | |||||||
\(972\) | − | 0.261597i | − | 0.00839073i | ||||||
\(973\) | 2.59584 | + | 2.59584i | 0.0832189 | + | 0.0832189i | ||||
\(974\) | −24.4765 | −0.784278 | ||||||||
\(975\) | −12.4896 | + | 11.8111i | −0.399988 | + | 0.378259i | ||||
\(976\) | 15.8792i | 0.508281i | ||||||||
\(977\) | −3.67733 | + | 3.67733i | −0.117648 | + | 0.117648i | −0.763480 | − | 0.645832i | \(-0.776511\pi\) |
0.645832 | + | 0.763480i | \(0.276511\pi\) | |||||||
\(978\) | 13.9893i | 0.447330i | ||||||||
\(979\) | 16.3836 | + | 2.52761i | 0.523622 | + | 0.0807829i | ||||
\(980\) | −0.561421 | + | 0.561421i | −0.0179339 | + | 0.0179339i | ||||
\(981\) | 10.9131 | + | 10.9131i | 0.348430 | + | 0.348430i | ||||
\(982\) | −15.8852 | − | 15.8852i | −0.506916 | − | 0.506916i | ||||
\(983\) | −3.59212 | − | 3.59212i | −0.114571 | − | 0.114571i | 0.647497 | − | 0.762068i | \(-0.275816\pi\) |
−0.762068 | + | 0.647497i | \(0.775816\pi\) | |||||||
\(984\) | 10.7662 | 0.343214 | ||||||||
\(985\) | −1.65866 | −0.0528493 | ||||||||
\(986\) | 3.69093 | − | 3.69093i | 0.117543 | − | 0.117543i | ||||
\(987\) | 7.09255 | 0.225758 | ||||||||
\(988\) | 3.31441 | + | 0.0925399i | 0.105446 | + | 0.00294409i | ||||
\(989\) | − | 46.9167i | − | 1.49186i | ||||||
\(990\) | 1.93946 | − | 1.42102i | 0.0616401 | − | 0.0451628i | ||||
\(991\) | −19.1798 | −0.609266 | −0.304633 | − | 0.952470i | \(-0.598534\pi\) | ||||
−0.304633 | + | 0.952470i | \(0.598534\pi\) | |||||||
\(992\) | 11.6675 | 0.370444 | ||||||||
\(993\) | −16.0602 | + | 16.0602i | −0.509654 | + | 0.509654i | ||||
\(994\) | −13.5163 | + | 13.5163i | −0.428712 | + | 0.428712i | ||||
\(995\) | 4.12098 | + | 4.12098i | 0.130644 | + | 0.130644i | ||||
\(996\) | −1.31536 | + | 1.31536i | −0.0416788 | + | 0.0416788i | ||||
\(997\) | − | 18.5649i | − | 0.587957i | −0.955812 | − | 0.293978i | \(-0.905021\pi\) | ||
0.955812 | − | 0.293978i | \(-0.0949793\pi\) | |||||||
\(998\) | 20.3050 | 0.642745 | ||||||||
\(999\) | −5.73990 | − | 5.73990i | −0.181602 | − | 0.181602i |
(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 | 429.2.m.a.109.11 | yes | 28 | |
11.10 | odd | 2 | inner | 429.2.m.a.109.4 | ✓ | 28 | |
13.8 | odd | 4 | inner | 429.2.m.a.307.4 | yes | 28 | |
143.21 | even | 4 | inner | 429.2.m.a.307.11 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.m.a.109.4 | ✓ | 28 | 11.10 | odd | 2 | inner | |
429.2.m.a.109.11 | yes | 28 | 1.1 | even | 1 | trivial | |
429.2.m.a.307.4 | yes | 28 | 13.8 | odd | 4 | inner | |
429.2.m.a.307.11 | yes | 28 | 143.21 | even | 4 | inner |