Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(369,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.c (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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 19x^{8} + 103x^{6} + 210x^{4} + 140x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.3 | ||
Root | \(-1.76216i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.369 |
Dual form | 370.2.c.a.369.8 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | − | 1.76216i | − | 1.01738i | −0.860949 | − | 0.508692i | \(-0.830129\pi\) | ||
0.860949 | − | 0.508692i | \(-0.169871\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.62868 | + | 1.53213i | −0.728367 | + | 0.685188i | ||||
\(6\) | 1.76216i | 0.719399i | ||||||||
\(7\) | 1.22131i | 0.461612i | 0.973000 | + | 0.230806i | \(0.0741363\pi\) | ||||
−0.973000 | + | 0.230806i | \(0.925864\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.105209 | −0.0350696 | ||||||||
\(10\) | 1.62868 | − | 1.53213i | 0.515033 | − | 0.484501i | ||||
\(11\) | 1.87120 | 0.564189 | 0.282094 | − | 0.959387i | \(-0.408971\pi\) | ||||
0.282094 | + | 0.959387i | \(0.408971\pi\) | |||||||
\(12\) | − | 1.76216i | − | 0.508692i | ||||||
\(13\) | 6.50491 | 1.80414 | 0.902069 | − | 0.431592i | \(-0.142048\pi\) | ||||
0.902069 | + | 0.431592i | \(0.142048\pi\) | |||||||
\(14\) | − | 1.22131i | − | 0.326409i | ||||||
\(15\) | 2.69985 | + | 2.86999i | 0.697099 | + | 0.741028i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.765994 | −0.185781 | −0.0928904 | − | 0.995676i | \(-0.529611\pi\) | ||||
−0.0928904 | + | 0.995676i | \(0.529611\pi\) | |||||||
\(18\) | 0.105209 | 0.0247979 | ||||||||
\(19\) | − | 3.34507i | − | 0.767412i | −0.923455 | − | 0.383706i | \(-0.874648\pi\) | ||
0.923455 | − | 0.383706i | \(-0.125352\pi\) | |||||||
\(20\) | −1.62868 | + | 1.53213i | −0.364183 | + | 0.342594i | ||||
\(21\) | 2.15215 | 0.469637 | ||||||||
\(22\) | −1.87120 | −0.398942 | ||||||||
\(23\) | 1.38964 | 0.289760 | 0.144880 | − | 0.989449i | \(-0.453720\pi\) | ||||
0.144880 | + | 0.989449i | \(0.453720\pi\) | |||||||
\(24\) | 1.76216i | 0.359699i | ||||||||
\(25\) | 0.305180 | − | 4.99068i | 0.0610360 | − | 0.998136i | ||||
\(26\) | −6.50491 | −1.27572 | ||||||||
\(27\) | − | 5.10109i | − | 0.981704i | ||||||
\(28\) | 1.22131i | 0.230806i | ||||||||
\(29\) | 1.72909i | 0.321084i | 0.987029 | + | 0.160542i | \(0.0513243\pi\) | ||||
−0.987029 | + | 0.160542i | \(0.948676\pi\) | |||||||
\(30\) | −2.69985 | − | 2.86999i | −0.492923 | − | 0.523986i | ||||
\(31\) | − | 4.11288i | − | 0.738695i | −0.929291 | − | 0.369348i | \(-0.879581\pi\) | ||
0.929291 | − | 0.369348i | \(-0.120419\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | − | 3.29736i | − | 0.573996i | ||||||
\(34\) | 0.765994 | 0.131367 | ||||||||
\(35\) | −1.87120 | − | 1.98912i | −0.316291 | − | 0.336223i | ||||
\(36\) | −0.105209 | −0.0175348 | ||||||||
\(37\) | 1.76599 | + | 5.82076i | 0.290328 | + | 0.956927i | ||||
\(38\) | 3.34507i | 0.542642i | ||||||||
\(39\) | − | 11.4627i | − | 1.83550i | ||||||
\(40\) | 1.62868 | − | 1.53213i | 0.257517 | − | 0.242250i | ||||
\(41\) | 3.73892 | 0.583921 | 0.291960 | − | 0.956430i | \(-0.405692\pi\) | ||||
0.291960 | + | 0.956430i | \(0.405692\pi\) | |||||||
\(42\) | −2.15215 | −0.332083 | ||||||||
\(43\) | 4.91814 | 0.750009 | 0.375005 | − | 0.927023i | \(-0.377641\pi\) | ||||
0.375005 | + | 0.927023i | \(0.377641\pi\) | |||||||
\(44\) | 1.87120 | 0.282094 | ||||||||
\(45\) | 0.171351 | − | 0.161193i | 0.0255435 | − | 0.0240292i | ||||
\(46\) | −1.38964 | −0.204891 | ||||||||
\(47\) | 6.30775i | 0.920080i | 0.887898 | + | 0.460040i | \(0.152165\pi\) | ||||
−0.887898 | + | 0.460040i | \(0.847835\pi\) | |||||||
\(48\) | − | 1.76216i | − | 0.254346i | ||||||
\(49\) | 5.50840 | 0.786914 | ||||||||
\(50\) | −0.305180 | + | 4.99068i | −0.0431590 | + | 0.705788i | ||||
\(51\) | 1.34980i | 0.189010i | ||||||||
\(52\) | 6.50491 | 0.902069 | ||||||||
\(53\) | 2.57768i | 0.354072i | 0.984204 | + | 0.177036i | \(0.0566509\pi\) | ||||
−0.984204 | + | 0.177036i | \(0.943349\pi\) | |||||||
\(54\) | 5.10109i | 0.694170i | ||||||||
\(55\) | −3.04759 | + | 2.86692i | −0.410936 | + | 0.386575i | ||||
\(56\) | − | 1.22131i | − | 0.163205i | ||||||
\(57\) | −5.89455 | −0.780752 | ||||||||
\(58\) | − | 1.72909i | − | 0.227041i | ||||||
\(59\) | − | 10.5664i | − | 1.37563i | −0.725887 | − | 0.687814i | \(-0.758571\pi\) | ||
0.725887 | − | 0.687814i | \(-0.241429\pi\) | |||||||
\(60\) | 2.69985 | + | 2.86999i | 0.348549 | + | 0.370514i | ||||
\(61\) | 11.1550i | 1.42825i | 0.700020 | + | 0.714123i | \(0.253174\pi\) | ||||
−0.700020 | + | 0.714123i | \(0.746826\pi\) | |||||||
\(62\) | 4.11288i | 0.522337i | ||||||||
\(63\) | − | 0.128493i | − | 0.0161886i | ||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.5944 | + | 9.96634i | −1.31407 | + | 1.23617i | ||||
\(66\) | 3.29736i | 0.405877i | ||||||||
\(67\) | 11.1219i | 1.35875i | 0.733789 | + | 0.679377i | \(0.237750\pi\) | ||||
−0.733789 | + | 0.679377i | \(0.762250\pi\) | |||||||
\(68\) | −0.765994 | −0.0928904 | ||||||||
\(69\) | − | 2.44877i | − | 0.294797i | ||||||
\(70\) | 1.87120 | + | 1.98912i | 0.223651 | + | 0.237746i | ||||
\(71\) | 0.963126 | 0.114302 | 0.0571510 | − | 0.998366i | \(-0.481798\pi\) | ||||
0.0571510 | + | 0.998366i | \(0.481798\pi\) | |||||||
\(72\) | 0.105209 | 0.0123990 | ||||||||
\(73\) | − | 9.03119i | − | 1.05702i | −0.848927 | − | 0.528511i | \(-0.822751\pi\) | ||
0.848927 | − | 0.528511i | \(-0.177249\pi\) | |||||||
\(74\) | −1.76599 | − | 5.82076i | −0.205293 | − | 0.676650i | ||||
\(75\) | −8.79437 | − | 0.537776i | −1.01549 | − | 0.0620971i | ||||
\(76\) | − | 3.34507i | − | 0.383706i | ||||||
\(77\) | 2.28532i | 0.260436i | ||||||||
\(78\) | 11.4627i | 1.29789i | ||||||||
\(79\) | − | 10.3333i | − | 1.16259i | −0.813694 | − | 0.581293i | \(-0.802547\pi\) | ||
0.813694 | − | 0.581293i | \(-0.197453\pi\) | |||||||
\(80\) | −1.62868 | + | 1.53213i | −0.182092 | + | 0.171297i | ||||
\(81\) | −9.30456 | −1.03384 | ||||||||
\(82\) | −3.73892 | −0.412894 | ||||||||
\(83\) | 0.00656819i | 0.000720953i | 1.00000 | 0.000360477i | \(0.000114743\pi\) | |||||
−1.00000 | 0.000360477i | \(0.999885\pi\) | ||||||||
\(84\) | 2.15215 | 0.234818 | ||||||||
\(85\) | 1.24756 | − | 1.17360i | 0.135317 | − | 0.127295i | ||||
\(86\) | −4.91814 | −0.530337 | ||||||||
\(87\) | 3.04694 | 0.326666 | ||||||||
\(88\) | −1.87120 | −0.199471 | ||||||||
\(89\) | 4.70144i | 0.498352i | 0.968458 | + | 0.249176i | \(0.0801598\pi\) | ||||
−0.968458 | + | 0.249176i | \(0.919840\pi\) | |||||||
\(90\) | −0.171351 | + | 0.161193i | −0.0180620 | + | 0.0169912i | ||||
\(91\) | 7.94452i | 0.832812i | ||||||||
\(92\) | 1.38964 | 0.144880 | ||||||||
\(93\) | −7.24756 | −0.751537 | ||||||||
\(94\) | − | 6.30775i | − | 0.650595i | ||||||
\(95\) | 5.12507 | + | 5.44804i | 0.525821 | + | 0.558957i | ||||
\(96\) | 1.76216i | 0.179850i | ||||||||
\(97\) | −0.403430 | −0.0409621 | −0.0204811 | − | 0.999790i | \(-0.506520\pi\) | ||||
−0.0204811 | + | 0.999790i | \(0.506520\pi\) | |||||||
\(98\) | −5.50840 | −0.556432 | ||||||||
\(99\) | −0.196867 | −0.0197859 | ||||||||
\(100\) | 0.305180 | − | 4.99068i | 0.0305180 | − | 0.499068i | ||||
\(101\) | −19.3724 | −1.92762 | −0.963812 | − | 0.266582i | \(-0.914106\pi\) | ||||
−0.963812 | + | 0.266582i | \(0.914106\pi\) | |||||||
\(102\) | − | 1.34980i | − | 0.133650i | ||||||
\(103\) | −5.56165 | −0.548005 | −0.274003 | − | 0.961729i | \(-0.588348\pi\) | ||||
−0.274003 | + | 0.961729i | \(0.588348\pi\) | |||||||
\(104\) | −6.50491 | −0.637859 | ||||||||
\(105\) | −3.50515 | + | 3.29736i | −0.342068 | + | 0.321789i | ||||
\(106\) | − | 2.57768i | − | 0.250367i | ||||||
\(107\) | − | 1.93484i | − | 0.187048i | −0.995617 | − | 0.0935241i | \(-0.970187\pi\) | ||
0.995617 | − | 0.0935241i | \(-0.0298132\pi\) | |||||||
\(108\) | − | 5.10109i | − | 0.490852i | ||||||
\(109\) | 8.70619i | 0.833901i | 0.908929 | + | 0.416951i | \(0.136901\pi\) | ||||
−0.908929 | + | 0.416951i | \(0.863099\pi\) | |||||||
\(110\) | 3.04759 | − | 2.86692i | 0.290576 | − | 0.273350i | ||||
\(111\) | 10.2571 | − | 3.11196i | 0.973562 | − | 0.295375i | ||||
\(112\) | 1.22131i | 0.115403i | ||||||||
\(113\) | −14.7585 | −1.38837 | −0.694183 | − | 0.719798i | \(-0.744234\pi\) | ||||
−0.694183 | + | 0.719798i | \(0.744234\pi\) | |||||||
\(114\) | 5.89455 | 0.552075 | ||||||||
\(115\) | −2.26327 | + | 2.12910i | −0.211051 | + | 0.198540i | ||||
\(116\) | 1.72909i | 0.160542i | ||||||||
\(117\) | −0.684374 | −0.0632704 | ||||||||
\(118\) | 10.5664i | 0.972715i | ||||||||
\(119\) | − | 0.935517i | − | 0.0857587i | ||||||
\(120\) | −2.69985 | − | 2.86999i | −0.246462 | − | 0.261993i | ||||
\(121\) | −7.49860 | −0.681691 | ||||||||
\(122\) | − | 11.1550i | − | 1.00992i | ||||||
\(123\) | − | 6.58857i | − | 0.594072i | ||||||
\(124\) | − | 4.11288i | − | 0.369348i | ||||||
\(125\) | 7.14931 | + | 8.59578i | 0.639453 | + | 0.768830i | ||||
\(126\) | 0.128493i | 0.0114470i | ||||||||
\(127\) | − | 11.1280i | − | 0.987453i | −0.869617 | − | 0.493727i | \(-0.835634\pi\) | ||
0.869617 | − | 0.493727i | \(-0.164366\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | − | 8.66655i | − | 0.763047i | ||||||
\(130\) | 10.5944 | − | 9.96634i | 0.929191 | − | 0.874106i | ||||
\(131\) | 12.8363i | 1.12152i | 0.827980 | + | 0.560758i | \(0.189490\pi\) | ||||
−0.827980 | + | 0.560758i | \(0.810510\pi\) | |||||||
\(132\) | − | 3.29736i | − | 0.286998i | ||||||
\(133\) | 4.08537 | 0.354247 | ||||||||
\(134\) | − | 11.1219i | − | 0.960785i | ||||||
\(135\) | 7.81551 | + | 8.30802i | 0.672652 | + | 0.715041i | ||||
\(136\) | 0.765994 | 0.0656834 | ||||||||
\(137\) | 12.0355i | 1.02826i | 0.857713 | + | 0.514129i | \(0.171885\pi\) | ||||
−0.857713 | + | 0.514129i | \(0.828115\pi\) | |||||||
\(138\) | 2.44877i | 0.208453i | ||||||||
\(139\) | −9.78562 | −0.830005 | −0.415003 | − | 0.909820i | \(-0.636219\pi\) | ||||
−0.415003 | + | 0.909820i | \(0.636219\pi\) | |||||||
\(140\) | −1.87120 | − | 1.98912i | −0.158145 | − | 0.168111i | ||||
\(141\) | 11.1153 | 0.936075 | ||||||||
\(142\) | −0.963126 | −0.0808237 | ||||||||
\(143\) | 12.1720 | 1.01787 | ||||||||
\(144\) | −0.105209 | −0.00876740 | ||||||||
\(145\) | −2.64919 | − | 2.81613i | −0.220003 | − | 0.233867i | ||||
\(146\) | 9.03119i | 0.747427i | ||||||||
\(147\) | − | 9.70668i | − | 0.800594i | ||||||
\(148\) | 1.76599 | + | 5.82076i | 0.145164 | + | 0.478464i | ||||
\(149\) | −11.8876 | −0.973868 | −0.486934 | − | 0.873439i | \(-0.661885\pi\) | ||||
−0.486934 | + | 0.873439i | \(0.661885\pi\) | |||||||
\(150\) | 8.79437 | + | 0.537776i | 0.718058 | + | 0.0439093i | ||||
\(151\) | 21.3141 | 1.73452 | 0.867259 | − | 0.497857i | \(-0.165880\pi\) | ||||
0.867259 | + | 0.497857i | \(0.165880\pi\) | |||||||
\(152\) | 3.34507i | 0.271321i | ||||||||
\(153\) | 0.0805893 | 0.00651526 | ||||||||
\(154\) | − | 2.28532i | − | 0.184156i | ||||||
\(155\) | 6.30145 | + | 6.69856i | 0.506145 | + | 0.538041i | ||||
\(156\) | − | 11.4627i | − | 0.917750i | ||||||
\(157\) | − | 15.3009i | − | 1.22115i | −0.791960 | − | 0.610573i | \(-0.790939\pi\) | ||
0.791960 | − | 0.610573i | \(-0.209061\pi\) | |||||||
\(158\) | 10.3333i | 0.822072i | ||||||||
\(159\) | 4.54229 | 0.360227 | ||||||||
\(160\) | 1.62868 | − | 1.53213i | 0.128758 | − | 0.121125i | ||||
\(161\) | 1.69718i | 0.133757i | ||||||||
\(162\) | 9.30456 | 0.731035 | ||||||||
\(163\) | −14.9177 | −1.16844 | −0.584221 | − | 0.811595i | \(-0.698600\pi\) | ||||
−0.584221 | + | 0.811595i | \(0.698600\pi\) | |||||||
\(164\) | 3.73892 | 0.291960 | ||||||||
\(165\) | 5.05197 | + | 5.37033i | 0.393295 | + | 0.418080i | ||||
\(166\) | − | 0.00656819i | − | 0.000509791i | ||||||
\(167\) | 17.3041 | 1.33903 | 0.669514 | − | 0.742800i | \(-0.266502\pi\) | ||||
0.669514 | + | 0.742800i | \(0.266502\pi\) | |||||||
\(168\) | −2.15215 | −0.166042 | ||||||||
\(169\) | 29.3139 | 2.25491 | ||||||||
\(170\) | −1.24756 | + | 1.17360i | −0.0956832 | + | 0.0900109i | ||||
\(171\) | 0.351931i | 0.0269128i | ||||||||
\(172\) | 4.91814 | 0.375005 | ||||||||
\(173\) | − | 19.7322i | − | 1.50021i | −0.661317 | − | 0.750107i | \(-0.730002\pi\) | ||
0.661317 | − | 0.750107i | \(-0.269998\pi\) | |||||||
\(174\) | −3.04694 | −0.230988 | ||||||||
\(175\) | 6.09517 | + | 0.372720i | 0.460752 | + | 0.0281750i | ||||
\(176\) | 1.87120 | 0.141047 | ||||||||
\(177\) | −18.6197 | −1.39954 | ||||||||
\(178\) | − | 4.70144i | − | 0.352388i | ||||||
\(179\) | 3.70357i | 0.276818i | 0.990375 | + | 0.138409i | \(0.0441988\pi\) | ||||
−0.990375 | + | 0.138409i | \(0.955801\pi\) | |||||||
\(180\) | 0.171351 | − | 0.161193i | 0.0127718 | − | 0.0120146i | ||||
\(181\) | −10.4093 | −0.773714 | −0.386857 | − | 0.922140i | \(-0.626439\pi\) | ||||
−0.386857 | + | 0.922140i | \(0.626439\pi\) | |||||||
\(182\) | − | 7.94452i | − | 0.588887i | ||||||
\(183\) | 19.6568 | 1.45307 | ||||||||
\(184\) | −1.38964 | −0.102446 | ||||||||
\(185\) | −11.7944 | − | 6.77442i | −0.867140 | − | 0.498065i | ||||
\(186\) | 7.24756 | 0.531417 | ||||||||
\(187\) | −1.43333 | −0.104815 | ||||||||
\(188\) | 6.30775i | 0.460040i | ||||||||
\(189\) | 6.23001 | 0.453167 | ||||||||
\(190\) | −5.12507 | − | 5.44804i | −0.371812 | − | 0.395242i | ||||
\(191\) | − | 23.0954i | − | 1.67113i | −0.549395 | − | 0.835563i | \(-0.685142\pi\) | ||
0.549395 | − | 0.835563i | \(-0.314858\pi\) | |||||||
\(192\) | − | 1.76216i | − | 0.127173i | ||||||
\(193\) | −12.4951 | −0.899418 | −0.449709 | − | 0.893175i | \(-0.648472\pi\) | ||||
−0.449709 | + | 0.893175i | \(0.648472\pi\) | |||||||
\(194\) | 0.403430 | 0.0289646 | ||||||||
\(195\) | 17.5623 | + | 18.6690i | 1.25766 | + | 1.33692i | ||||
\(196\) | 5.50840 | 0.393457 | ||||||||
\(197\) | 5.51302i | 0.392786i | 0.980525 | + | 0.196393i | \(0.0629229\pi\) | ||||
−0.980525 | + | 0.196393i | \(0.937077\pi\) | |||||||
\(198\) | 0.196867 | 0.0139907 | ||||||||
\(199\) | 18.8033i | 1.33293i | 0.745537 | + | 0.666464i | \(0.232193\pi\) | ||||
−0.745537 | + | 0.666464i | \(0.767807\pi\) | |||||||
\(200\) | −0.305180 | + | 4.99068i | −0.0215795 | + | 0.352894i | ||||
\(201\) | 19.5985 | 1.38237 | ||||||||
\(202\) | 19.3724 | 1.36304 | ||||||||
\(203\) | −2.11176 | −0.148216 | ||||||||
\(204\) | 1.34980i | 0.0945052i | ||||||||
\(205\) | −6.08949 | + | 5.72849i | −0.425309 | + | 0.400095i | ||||
\(206\) | 5.56165 | 0.387498 | ||||||||
\(207\) | −0.146202 | −0.0101618 | ||||||||
\(208\) | 6.50491 | 0.451034 | ||||||||
\(209\) | − | 6.25931i | − | 0.432965i | ||||||
\(210\) | 3.50515 | − | 3.29736i | 0.241878 | − | 0.227539i | ||||
\(211\) | −26.6632 | −1.83557 | −0.917784 | − | 0.397081i | \(-0.870023\pi\) | ||||
−0.917784 | + | 0.397081i | \(0.870023\pi\) | |||||||
\(212\) | 2.57768i | 0.177036i | ||||||||
\(213\) | − | 1.69718i | − | 0.116289i | ||||||
\(214\) | 1.93484i | 0.132263i | ||||||||
\(215\) | −8.01006 | + | 7.53521i | −0.546282 | + | 0.513897i | ||||
\(216\) | 5.10109i | 0.347085i | ||||||||
\(217\) | 5.02311 | 0.340991 | ||||||||
\(218\) | − | 8.70619i | − | 0.589657i | ||||||
\(219\) | −15.9144 | −1.07540 | ||||||||
\(220\) | −3.04759 | + | 2.86692i | −0.205468 | + | 0.193288i | ||||
\(221\) | −4.98272 | −0.335174 | ||||||||
\(222\) | −10.2571 | + | 3.11196i | −0.688412 | + | 0.208861i | ||||
\(223\) | − | 10.8630i | − | 0.727441i | −0.931508 | − | 0.363721i | \(-0.881506\pi\) | ||
0.931508 | − | 0.363721i | \(-0.118494\pi\) | |||||||
\(224\) | − | 1.22131i | − | 0.0816023i | ||||||
\(225\) | −0.0321076 | + | 0.525063i | −0.00214051 | + | 0.0350042i | ||||
\(226\) | 14.7585 | 0.981723 | ||||||||
\(227\) | 6.82427 | 0.452942 | 0.226471 | − | 0.974018i | \(-0.427281\pi\) | ||||
0.226471 | + | 0.974018i | \(0.427281\pi\) | |||||||
\(228\) | −5.89455 | −0.390376 | ||||||||
\(229\) | 2.56189 | 0.169294 | 0.0846471 | − | 0.996411i | \(-0.473024\pi\) | ||||
0.0846471 | + | 0.996411i | \(0.473024\pi\) | |||||||
\(230\) | 2.26327 | − | 2.12910i | 0.149236 | − | 0.140389i | ||||
\(231\) | 4.02710 | 0.264964 | ||||||||
\(232\) | − | 1.72909i | − | 0.113520i | ||||||
\(233\) | − | 23.3423i | − | 1.52921i | −0.644502 | − | 0.764603i | \(-0.722935\pi\) | ||
0.644502 | − | 0.764603i | \(-0.277065\pi\) | |||||||
\(234\) | 0.684374 | 0.0447389 | ||||||||
\(235\) | −9.66427 | − | 10.2733i | −0.630428 | − | 0.670156i | ||||
\(236\) | − | 10.5664i | − | 0.687814i | ||||||
\(237\) | −18.2089 | −1.18280 | ||||||||
\(238\) | 0.935517i | 0.0606405i | ||||||||
\(239\) | 5.19256i | 0.335879i | 0.985797 | + | 0.167940i | \(0.0537113\pi\) | ||||
−0.985797 | + | 0.167940i | \(0.946289\pi\) | |||||||
\(240\) | 2.69985 | + | 2.86999i | 0.174275 | + | 0.185257i | ||||
\(241\) | 15.5243i | 1.00001i | 0.866022 | + | 0.500005i | \(0.166669\pi\) | ||||
−0.866022 | + | 0.500005i | \(0.833331\pi\) | |||||||
\(242\) | 7.49860 | 0.482028 | ||||||||
\(243\) | 1.09286i | 0.0701072i | ||||||||
\(244\) | 11.1550i | 0.714123i | ||||||||
\(245\) | −8.97140 | + | 8.43956i | −0.573162 | + | 0.539184i | ||||
\(246\) | 6.58857i | 0.420072i | ||||||||
\(247\) | − | 21.7594i | − | 1.38452i | ||||||
\(248\) | 4.11288i | 0.261168i | ||||||||
\(249\) | 0.0115742 | 0.000733486 | ||||||||
\(250\) | −7.14931 | − | 8.59578i | −0.452162 | − | 0.543645i | ||||
\(251\) | − | 3.85199i | − | 0.243136i | −0.992583 | − | 0.121568i | \(-0.961208\pi\) | ||
0.992583 | − | 0.121568i | \(-0.0387922\pi\) | |||||||
\(252\) | − | 0.128493i | − | 0.00809428i | ||||||
\(253\) | 2.60030 | 0.163479 | ||||||||
\(254\) | 11.1280i | 0.698235i | ||||||||
\(255\) | −2.06807 | − | 2.19840i | −0.129508 | − | 0.137669i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.34529 | 0.208673 | 0.104337 | − | 0.994542i | \(-0.466728\pi\) | ||||
0.104337 | + | 0.994542i | \(0.466728\pi\) | |||||||
\(258\) | 8.66655i | 0.539556i | ||||||||
\(259\) | −7.10896 | + | 2.15683i | −0.441729 | + | 0.134019i | ||||
\(260\) | −10.5944 | + | 9.96634i | −0.657037 | + | 0.618086i | ||||
\(261\) | − | 0.181916i | − | 0.0112603i | ||||||
\(262\) | − | 12.8363i | − | 0.793031i | ||||||
\(263\) | − | 1.14405i | − | 0.0705454i | −0.999378 | − | 0.0352727i | \(-0.988770\pi\) | ||
0.999378 | − | 0.0352727i | \(-0.0112300\pi\) | |||||||
\(264\) | 3.29736i | 0.202938i | ||||||||
\(265\) | −3.94934 | − | 4.19821i | −0.242606 | − | 0.257894i | ||||
\(266\) | −4.08537 | −0.250490 | ||||||||
\(267\) | 8.28470 | 0.507015 | ||||||||
\(268\) | 11.1219i | 0.679377i | ||||||||
\(269\) | 15.1344 | 0.922760 | 0.461380 | − | 0.887203i | \(-0.347355\pi\) | ||||
0.461380 | + | 0.887203i | \(0.347355\pi\) | |||||||
\(270\) | −7.81551 | − | 8.30802i | −0.475637 | − | 0.505610i | ||||
\(271\) | −18.2842 | −1.11069 | −0.555344 | − | 0.831621i | \(-0.687413\pi\) | ||||
−0.555344 | + | 0.831621i | \(0.687413\pi\) | |||||||
\(272\) | −0.765994 | −0.0464452 | ||||||||
\(273\) | 13.9995 | 0.847289 | ||||||||
\(274\) | − | 12.0355i | − | 0.727088i | ||||||
\(275\) | 0.571054 | − | 9.33857i | 0.0344359 | − | 0.563137i | ||||
\(276\) | − | 2.44877i | − | 0.147398i | ||||||
\(277\) | 2.58352 | 0.155229 | 0.0776145 | − | 0.996983i | \(-0.475270\pi\) | ||||
0.0776145 | + | 0.996983i | \(0.475270\pi\) | |||||||
\(278\) | 9.78562 | 0.586902 | ||||||||
\(279\) | 0.432711i | 0.0259057i | ||||||||
\(280\) | 1.87120 | + | 1.98912i | 0.111826 | + | 0.118873i | ||||
\(281\) | − | 19.3056i | − | 1.15168i | −0.817563 | − | 0.575839i | \(-0.804675\pi\) | ||
0.817563 | − | 0.575839i | \(-0.195325\pi\) | |||||||
\(282\) | −11.1153 | −0.661905 | ||||||||
\(283\) | 9.02942 | 0.536743 | 0.268372 | − | 0.963315i | \(-0.413514\pi\) | ||||
0.268372 | + | 0.963315i | \(0.413514\pi\) | |||||||
\(284\) | 0.963126 | 0.0571510 | ||||||||
\(285\) | 9.60032 | − | 9.03119i | 0.568674 | − | 0.534962i | ||||
\(286\) | −12.1720 | −0.719746 | ||||||||
\(287\) | 4.56638i | 0.269545i | ||||||||
\(288\) | 0.105209 | 0.00619949 | ||||||||
\(289\) | −16.4133 | −0.965485 | ||||||||
\(290\) | 2.64919 | + | 2.81613i | 0.155566 | + | 0.165369i | ||||
\(291\) | 0.710909i | 0.0416742i | ||||||||
\(292\) | − | 9.03119i | − | 0.528511i | ||||||
\(293\) | 13.0845i | 0.764405i | 0.924079 | + | 0.382203i | \(0.124834\pi\) | ||||
−0.924079 | + | 0.382203i | \(0.875166\pi\) | |||||||
\(294\) | 9.70668i | 0.566105i | ||||||||
\(295\) | 16.1890 | + | 17.2092i | 0.942563 | + | 1.00196i | ||||
\(296\) | −1.76599 | − | 5.82076i | −0.102646 | − | 0.338325i | ||||
\(297\) | − | 9.54517i | − | 0.553867i | ||||||
\(298\) | 11.8876 | 0.688629 | ||||||||
\(299\) | 9.03948 | 0.522767 | ||||||||
\(300\) | −8.79437 | − | 0.537776i | −0.507743 | − | 0.0310485i | ||||
\(301\) | 6.00658i | 0.346213i | ||||||||
\(302\) | −21.3141 | −1.22649 | ||||||||
\(303\) | 34.1373i | 1.96113i | ||||||||
\(304\) | − | 3.34507i | − | 0.191853i | ||||||
\(305\) | −17.0908 | − | 18.1678i | −0.978616 | − | 1.04029i | ||||
\(306\) | −0.0805893 | −0.00460698 | ||||||||
\(307\) | − | 7.60942i | − | 0.434293i | −0.976139 | − | 0.217146i | \(-0.930325\pi\) | ||
0.976139 | − | 0.217146i | \(-0.0696749\pi\) | |||||||
\(308\) | 2.28532i | 0.130218i | ||||||||
\(309\) | 9.80051i | 0.557532i | ||||||||
\(310\) | −6.30145 | − | 6.69856i | −0.357898 | − | 0.380453i | ||||
\(311\) | − | 15.2359i | − | 0.863950i | −0.901886 | − | 0.431975i | \(-0.857817\pi\) | ||
0.901886 | − | 0.431975i | \(-0.142183\pi\) | |||||||
\(312\) | 11.4627i | 0.648947i | ||||||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | 15.3009i | 0.863480i | ||||||||
\(315\) | 0.196867 | + | 0.209273i | 0.0110922 | + | 0.0117912i | ||||
\(316\) | − | 10.3333i | − | 0.581293i | ||||||
\(317\) | 34.1403i | 1.91751i | 0.284230 | + | 0.958756i | \(0.408262\pi\) | ||||
−0.284230 | + | 0.958756i | \(0.591738\pi\) | |||||||
\(318\) | −4.54229 | −0.254719 | ||||||||
\(319\) | 3.23548i | 0.181152i | ||||||||
\(320\) | −1.62868 | + | 1.53213i | −0.0910458 | + | 0.0856484i | ||||
\(321\) | −3.40950 | −0.190300 | ||||||||
\(322\) | − | 1.69718i | − | 0.0945803i | ||||||
\(323\) | 2.56230i | 0.142570i | ||||||||
\(324\) | −9.30456 | −0.516920 | ||||||||
\(325\) | 1.98517 | − | 32.4639i | 0.110117 | − | 1.80077i | ||||
\(326\) | 14.9177 | 0.826213 | ||||||||
\(327\) | 15.3417 | 0.848398 | ||||||||
\(328\) | −3.73892 | −0.206447 | ||||||||
\(329\) | −7.70373 | −0.424720 | ||||||||
\(330\) | −5.05197 | − | 5.37033i | −0.278102 | − | 0.295627i | ||||
\(331\) | 27.2567i | 1.49817i | 0.662476 | + | 0.749083i | \(0.269506\pi\) | ||||
−0.662476 | + | 0.749083i | \(0.730494\pi\) | |||||||
\(332\) | 0.00656819i | 0.000360477i | ||||||||
\(333\) | −0.185798 | − | 0.612395i | −0.0101817 | − | 0.0335590i | ||||
\(334\) | −17.3041 | −0.946836 | ||||||||
\(335\) | −17.0401 | − | 18.1140i | −0.931002 | − | 0.989672i | ||||
\(336\) | 2.15215 | 0.117409 | ||||||||
\(337\) | 22.5315i | 1.22737i | 0.789552 | + | 0.613683i | \(0.210313\pi\) | ||||
−0.789552 | + | 0.613683i | \(0.789687\pi\) | |||||||
\(338\) | −29.3139 | −1.59446 | ||||||||
\(339\) | 26.0069i | 1.41250i | ||||||||
\(340\) | 1.24756 | − | 1.17360i | 0.0676583 | − | 0.0636473i | ||||
\(341\) | − | 7.69603i | − | 0.416764i | ||||||
\(342\) | − | 0.351931i | − | 0.0190302i | ||||||
\(343\) | 15.2766i | 0.824861i | ||||||||
\(344\) | −4.91814 | −0.265168 | ||||||||
\(345\) | 3.75182 | + | 3.98825i | 0.201991 | + | 0.214720i | ||||
\(346\) | 19.7322i | 1.06081i | ||||||||
\(347\) | −34.7252 | −1.86415 | −0.932073 | − | 0.362272i | \(-0.882001\pi\) | ||||
−0.932073 | + | 0.362272i | \(0.882001\pi\) | |||||||
\(348\) | 3.04694 | 0.163333 | ||||||||
\(349\) | 15.9343 | 0.852942 | 0.426471 | − | 0.904501i | \(-0.359757\pi\) | ||||
0.426471 | + | 0.904501i | \(0.359757\pi\) | |||||||
\(350\) | −6.09517 | − | 0.372720i | −0.325801 | − | 0.0199227i | ||||
\(351\) | − | 33.1821i | − | 1.77113i | ||||||
\(352\) | −1.87120 | −0.0997354 | ||||||||
\(353\) | 20.1925 | 1.07474 | 0.537370 | − | 0.843347i | \(-0.319418\pi\) | ||||
0.537370 | + | 0.843347i | \(0.319418\pi\) | |||||||
\(354\) | 18.6197 | 0.989625 | ||||||||
\(355\) | −1.56862 | + | 1.47563i | −0.0832538 | + | 0.0783183i | ||||
\(356\) | 4.70144i | 0.249176i | ||||||||
\(357\) | −1.64853 | −0.0872495 | ||||||||
\(358\) | − | 3.70357i | − | 0.195740i | ||||||
\(359\) | −30.8657 | −1.62903 | −0.814515 | − | 0.580143i | \(-0.802997\pi\) | ||||
−0.814515 | + | 0.580143i | \(0.802997\pi\) | |||||||
\(360\) | −0.171351 | + | 0.161193i | −0.00903100 | + | 0.00849562i | ||||
\(361\) | 7.81050 | 0.411079 | ||||||||
\(362\) | 10.4093 | 0.547099 | ||||||||
\(363\) | 13.2137i | 0.693541i | ||||||||
\(364\) | 7.94452i | 0.416406i | ||||||||
\(365\) | 13.8369 | + | 14.7089i | 0.724258 | + | 0.769899i | ||||
\(366\) | −19.6568 | −1.02748 | ||||||||
\(367\) | − | 28.9254i | − | 1.50989i | −0.655786 | − | 0.754947i | \(-0.727663\pi\) | ||
0.655786 | − | 0.754947i | \(-0.272337\pi\) | |||||||
\(368\) | 1.38964 | 0.0724400 | ||||||||
\(369\) | −0.393367 | −0.0204779 | ||||||||
\(370\) | 11.7944 | + | 6.77442i | 0.613160 | + | 0.352185i | ||||
\(371\) | −3.14815 | −0.163444 | ||||||||
\(372\) | −7.24756 | −0.375768 | ||||||||
\(373\) | 27.8899i | 1.44408i | 0.691849 | + | 0.722042i | \(0.256796\pi\) | ||||
−0.691849 | + | 0.722042i | \(0.743204\pi\) | |||||||
\(374\) | 1.43333 | 0.0741157 | ||||||||
\(375\) | 15.1471 | − | 12.5982i | 0.782195 | − | 0.650570i | ||||
\(376\) | − | 6.30775i | − | 0.325298i | ||||||
\(377\) | 11.2476i | 0.579280i | ||||||||
\(378\) | −6.23001 | −0.320437 | ||||||||
\(379\) | −5.73365 | −0.294518 | −0.147259 | − | 0.989098i | \(-0.547045\pi\) | ||||
−0.147259 | + | 0.989098i | \(0.547045\pi\) | |||||||
\(380\) | 5.12507 | + | 5.44804i | 0.262911 | + | 0.279479i | ||||
\(381\) | −19.6094 | −1.00462 | ||||||||
\(382\) | 23.0954i | 1.18166i | ||||||||
\(383\) | 17.8363 | 0.911391 | 0.455696 | − | 0.890136i | \(-0.349391\pi\) | ||||
0.455696 | + | 0.890136i | \(0.349391\pi\) | |||||||
\(384\) | 1.76216i | 0.0899249i | ||||||||
\(385\) | −3.50140 | − | 3.72205i | −0.178448 | − | 0.189693i | ||||
\(386\) | 12.4951 | 0.635985 | ||||||||
\(387\) | −0.517431 | −0.0263025 | ||||||||
\(388\) | −0.403430 | −0.0204811 | ||||||||
\(389\) | 29.8974i | 1.51586i | 0.652337 | + | 0.757929i | \(0.273789\pi\) | ||||
−0.652337 | + | 0.757929i | \(0.726211\pi\) | |||||||
\(390\) | −17.5623 | − | 18.6690i | −0.889301 | − | 0.945343i | ||||
\(391\) | −1.06446 | −0.0538318 | ||||||||
\(392\) | −5.50840 | −0.278216 | ||||||||
\(393\) | 22.6197 | 1.14101 | ||||||||
\(394\) | − | 5.51302i | − | 0.277742i | ||||||
\(395\) | 15.8319 | + | 16.8296i | 0.796589 | + | 0.846789i | ||||
\(396\) | −0.196867 | −0.00989293 | ||||||||
\(397\) | 13.2064i | 0.662812i | 0.943488 | + | 0.331406i | \(0.107523\pi\) | ||||
−0.943488 | + | 0.331406i | \(0.892477\pi\) | |||||||
\(398\) | − | 18.8033i | − | 0.942523i | ||||||
\(399\) | − | 7.19908i | − | 0.360405i | ||||||
\(400\) | 0.305180 | − | 4.99068i | 0.0152590 | − | 0.249534i | ||||
\(401\) | − | 23.0269i | − | 1.14991i | −0.818185 | − | 0.574954i | \(-0.805020\pi\) | ||
0.818185 | − | 0.574954i | \(-0.194980\pi\) | |||||||
\(402\) | −19.5985 | −0.977487 | ||||||||
\(403\) | − | 26.7539i | − | 1.33271i | ||||||
\(404\) | −19.3724 | −0.963812 | ||||||||
\(405\) | 15.1541 | − | 14.2558i | 0.753014 | − | 0.708374i | ||||
\(406\) | 2.11176 | 0.104805 | ||||||||
\(407\) | 3.30453 | + | 10.8918i | 0.163800 | + | 0.539888i | ||||
\(408\) | − | 1.34980i | − | 0.0668252i | ||||||
\(409\) | 9.77049i | 0.483120i | 0.970386 | + | 0.241560i | \(0.0776590\pi\) | ||||
−0.970386 | + | 0.241560i | \(0.922341\pi\) | |||||||
\(410\) | 6.08949 | − | 5.72849i | 0.300739 | − | 0.282910i | ||||
\(411\) | 21.2084 | 1.04613 | ||||||||
\(412\) | −5.56165 | −0.274003 | ||||||||
\(413\) | 12.9049 | 0.635006 | ||||||||
\(414\) | 0.146202 | 0.00718545 | ||||||||
\(415\) | −0.0100633 | − | 0.0106975i | −0.000493988 | − | 0.000525118i | ||||
\(416\) | −6.50491 | −0.318930 | ||||||||
\(417\) | 17.2438i | 0.844434i | ||||||||
\(418\) | 6.25931i | 0.306153i | ||||||||
\(419\) | 2.06109 | 0.100691 | 0.0503455 | − | 0.998732i | \(-0.483968\pi\) | ||||
0.0503455 | + | 0.998732i | \(0.483968\pi\) | |||||||
\(420\) | −3.50515 | + | 3.29736i | −0.171034 | + | 0.160895i | ||||
\(421\) | − | 12.8910i | − | 0.628271i | −0.949378 | − | 0.314135i | \(-0.898285\pi\) | ||
0.949378 | − | 0.314135i | \(-0.101715\pi\) | |||||||
\(422\) | 26.6632 | 1.29794 | ||||||||
\(423\) | − | 0.663631i | − | 0.0322668i | ||||||
\(424\) | − | 2.57768i | − | 0.125183i | ||||||
\(425\) | −0.233766 | + | 3.82283i | −0.0113393 | + | 0.185434i | ||||
\(426\) | 1.69718i | 0.0822288i | ||||||||
\(427\) | −13.6237 | −0.659296 | ||||||||
\(428\) | − | 1.93484i | − | 0.0935241i | ||||||
\(429\) | − | 21.4490i | − | 1.03557i | ||||||
\(430\) | 8.01006 | − | 7.53521i | 0.386280 | − | 0.363380i | ||||
\(431\) | 9.41662i | 0.453582i | 0.973943 | + | 0.226791i | \(0.0728235\pi\) | ||||
−0.973943 | + | 0.226791i | \(0.927176\pi\) | |||||||
\(432\) | − | 5.10109i | − | 0.245426i | ||||||
\(433\) | 3.07581i | 0.147814i | 0.997265 | + | 0.0739069i | \(0.0235468\pi\) | ||||
−0.997265 | + | 0.0739069i | \(0.976453\pi\) | |||||||
\(434\) | −5.02311 | −0.241117 | ||||||||
\(435\) | −4.96248 | + | 4.66829i | −0.237933 | + | 0.223827i | ||||
\(436\) | 8.70619i | 0.416951i | ||||||||
\(437\) | − | 4.64844i | − | 0.222365i | ||||||
\(438\) | 15.9144 | 0.760420 | ||||||||
\(439\) | − | 1.93763i | − | 0.0924780i | −0.998930 | − | 0.0462390i | \(-0.985276\pi\) | ||
0.998930 | − | 0.0462390i | \(-0.0147236\pi\) | |||||||
\(440\) | 3.04759 | − | 2.86692i | 0.145288 | − | 0.136675i | ||||
\(441\) | −0.579532 | −0.0275968 | ||||||||
\(442\) | 4.98272 | 0.237004 | ||||||||
\(443\) | − | 26.5690i | − | 1.26233i | −0.775649 | − | 0.631165i | \(-0.782577\pi\) | ||
0.775649 | − | 0.631165i | \(-0.217423\pi\) | |||||||
\(444\) | 10.2571 | − | 3.11196i | 0.486781 | − | 0.147687i | ||||
\(445\) | −7.20320 | − | 7.65713i | −0.341465 | − | 0.362983i | ||||
\(446\) | 10.8630i | 0.514379i | ||||||||
\(447\) | 20.9478i | 0.990798i | ||||||||
\(448\) | 1.22131i | 0.0577015i | ||||||||
\(449\) | 0.777045i | 0.0366710i | 0.999832 | + | 0.0183355i | \(0.00583670\pi\) | ||||
−0.999832 | + | 0.0183355i | \(0.994163\pi\) | |||||||
\(450\) | 0.0321076 | − | 0.525063i | 0.00151357 | − | 0.0247517i | ||||
\(451\) | 6.99627 | 0.329442 | ||||||||
\(452\) | −14.7585 | −0.694183 | ||||||||
\(453\) | − | 37.5589i | − | 1.76467i | ||||||
\(454\) | −6.82427 | −0.320279 | ||||||||
\(455\) | −12.1720 | − | 12.9391i | −0.570633 | − | 0.606593i | ||||
\(456\) | 5.89455 | 0.276038 | ||||||||
\(457\) | 21.1753 | 0.990537 | 0.495268 | − | 0.868740i | \(-0.335070\pi\) | ||||
0.495268 | + | 0.868740i | \(0.335070\pi\) | |||||||
\(458\) | −2.56189 | −0.119709 | ||||||||
\(459\) | 3.90740i | 0.182382i | ||||||||
\(460\) | −2.26327 | + | 2.12910i | −0.105526 | + | 0.0992699i | ||||
\(461\) | − | 23.9797i | − | 1.11685i | −0.829556 | − | 0.558424i | \(-0.811406\pi\) | ||
0.829556 | − | 0.558424i | \(-0.188594\pi\) | |||||||
\(462\) | −4.02710 | −0.187358 | ||||||||
\(463\) | −25.1591 | −1.16924 | −0.584622 | − | 0.811306i | \(-0.698757\pi\) | ||||
−0.584622 | + | 0.811306i | \(0.698757\pi\) | |||||||
\(464\) | 1.72909i | 0.0802711i | ||||||||
\(465\) | 11.8039 | − | 11.1042i | 0.547394 | − | 0.514944i | ||||
\(466\) | 23.3423i | 1.08131i | ||||||||
\(467\) | 15.6162 | 0.722632 | 0.361316 | − | 0.932443i | \(-0.382328\pi\) | ||||
0.361316 | + | 0.932443i | \(0.382328\pi\) | |||||||
\(468\) | −0.684374 | −0.0316352 | ||||||||
\(469\) | −13.5833 | −0.627218 | ||||||||
\(470\) | 9.66427 | + | 10.2733i | 0.445780 | + | 0.473872i | ||||
\(471\) | −26.9626 | −1.24237 | ||||||||
\(472\) | 10.5664i | 0.486358i | ||||||||
\(473\) | 9.20284 | 0.423147 | ||||||||
\(474\) | 18.2089 | 0.836363 | ||||||||
\(475\) | −16.6942 | − | 1.02085i | −0.765981 | − | 0.0468398i | ||||
\(476\) | − | 0.935517i | − | 0.0428793i | ||||||
\(477\) | − | 0.271195i | − | 0.0124172i | ||||||
\(478\) | − | 5.19256i | − | 0.237502i | ||||||
\(479\) | − | 31.4974i | − | 1.43915i | −0.694414 | − | 0.719576i | \(-0.744336\pi\) | ||
0.694414 | − | 0.719576i | \(-0.255664\pi\) | |||||||
\(480\) | −2.69985 | − | 2.86999i | −0.123231 | − | 0.130997i | ||||
\(481\) | 11.4876 | + | 37.8635i | 0.523791 | + | 1.72643i | ||||
\(482\) | − | 15.5243i | − | 0.707114i | ||||||
\(483\) | 2.99071 | 0.136082 | ||||||||
\(484\) | −7.49860 | −0.340845 | ||||||||
\(485\) | 0.657058 | − | 0.618106i | 0.0298355 | − | 0.0280667i | ||||
\(486\) | − | 1.09286i | − | 0.0495733i | ||||||
\(487\) | 24.2768 | 1.10009 | 0.550043 | − | 0.835137i | \(-0.314611\pi\) | ||||
0.550043 | + | 0.835137i | \(0.314611\pi\) | |||||||
\(488\) | − | 11.1550i | − | 0.504961i | ||||||
\(489\) | 26.2873i | 1.18875i | ||||||||
\(490\) | 8.97140 | − | 8.43956i | 0.405287 | − | 0.381260i | ||||
\(491\) | 16.5129 | 0.745218 | 0.372609 | − | 0.927988i | \(-0.378463\pi\) | ||||
0.372609 | + | 0.927988i | \(0.378463\pi\) | |||||||
\(492\) | − | 6.58857i | − | 0.297036i | ||||||
\(493\) | − | 1.32447i | − | 0.0596513i | ||||||
\(494\) | 21.7594i | 0.979001i | ||||||||
\(495\) | 0.320633 | − | 0.301625i | 0.0144114 | − | 0.0135570i | ||||
\(496\) | − | 4.11288i | − | 0.184674i | ||||||
\(497\) | 1.17628i | 0.0527632i | ||||||||
\(498\) | −0.0115742 | −0.000518653 | ||||||||
\(499\) | 22.8436i | 1.02262i | 0.859397 | + | 0.511310i | \(0.170839\pi\) | ||||
−0.859397 | + | 0.511310i | \(0.829161\pi\) | |||||||
\(500\) | 7.14931 | + | 8.59578i | 0.319727 | + | 0.384415i | ||||
\(501\) | − | 30.4925i | − | 1.36231i | ||||||
\(502\) | 3.85199i | 0.171923i | ||||||||
\(503\) | −37.0666 | −1.65272 | −0.826359 | − | 0.563144i | \(-0.809592\pi\) | ||||
−0.826359 | + | 0.563144i | \(0.809592\pi\) | |||||||
\(504\) | 0.128493i | 0.00572352i | ||||||||
\(505\) | 31.5514 | − | 29.6809i | 1.40402 | − | 1.32078i | ||||
\(506\) | −2.60030 | −0.115597 | ||||||||
\(507\) | − | 51.6557i | − | 2.29411i | ||||||
\(508\) | − | 11.1280i | − | 0.493727i | ||||||
\(509\) | 20.0939 | 0.890645 | 0.445323 | − | 0.895370i | \(-0.353089\pi\) | ||||
0.445323 | + | 0.895370i | \(0.353089\pi\) | |||||||
\(510\) | 2.06807 | + | 2.19840i | 0.0915757 | + | 0.0973466i | ||||
\(511\) | 11.0299 | 0.487934 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −17.0635 | −0.753372 | ||||||||
\(514\) | −3.34529 | −0.147554 | ||||||||
\(515\) | 9.05813 | − | 8.52114i | 0.399149 | − | 0.375486i | ||||
\(516\) | − | 8.66655i | − | 0.381524i | ||||||
\(517\) | 11.8031i | 0.519099i | ||||||||
\(518\) | 7.10896 | − | 2.15683i | 0.312350 | − | 0.0947656i | ||||
\(519\) | −34.7713 | −1.52629 | ||||||||
\(520\) | 10.5944 | − | 9.96634i | 0.464595 | − | 0.437053i | ||||
\(521\) | 32.3101 | 1.41553 | 0.707766 | − | 0.706447i | \(-0.249703\pi\) | ||||
0.707766 | + | 0.706447i | \(0.249703\pi\) | |||||||
\(522\) | 0.181916i | 0.00796223i | ||||||||
\(523\) | −38.5348 | −1.68501 | −0.842505 | − | 0.538688i | \(-0.818920\pi\) | ||||
−0.842505 | + | 0.538688i | \(0.818920\pi\) | |||||||
\(524\) | 12.8363i | 0.560758i | ||||||||
\(525\) | 0.656792 | − | 10.7407i | 0.0286648 | − | 0.468761i | ||||
\(526\) | 1.14405i | 0.0498831i | ||||||||
\(527\) | 3.15044i | 0.137235i | ||||||||
\(528\) | − | 3.29736i | − | 0.143499i | ||||||
\(529\) | −21.0689 | −0.916039 | ||||||||
\(530\) | 3.94934 | + | 4.19821i | 0.171548 | + | 0.182359i | ||||
\(531\) | 1.11168i | 0.0482427i | ||||||||
\(532\) | 4.08537 | 0.177123 | ||||||||
\(533\) | 24.3213 | 1.05347 | ||||||||
\(534\) | −8.28470 | −0.358514 | ||||||||
\(535\) | 2.96442 | + | 3.15123i | 0.128163 | + | 0.136240i | ||||
\(536\) | − | 11.1219i | − | 0.480392i | ||||||
\(537\) | 6.52628 | 0.281630 | ||||||||
\(538\) | −15.1344 | −0.652490 | ||||||||
\(539\) | 10.3073 | 0.443968 | ||||||||
\(540\) | 7.81551 | + | 8.30802i | 0.336326 | + | 0.357520i | ||||
\(541\) | 40.6354i | 1.74705i | 0.486776 | + | 0.873527i | \(0.338173\pi\) | ||||
−0.486776 | + | 0.873527i | \(0.661827\pi\) | |||||||
\(542\) | 18.2842 | 0.785374 | ||||||||
\(543\) | 18.3428i | 0.787164i | ||||||||
\(544\) | 0.765994 | 0.0328417 | ||||||||
\(545\) | −13.3390 | − | 14.1796i | −0.571379 | − | 0.607386i | ||||
\(546\) | −13.9995 | −0.599124 | ||||||||
\(547\) | −26.6260 | −1.13845 | −0.569223 | − | 0.822183i | \(-0.692756\pi\) | ||||
−0.569223 | + | 0.822183i | \(0.692756\pi\) | |||||||
\(548\) | 12.0355i | 0.514129i | ||||||||
\(549\) | − | 1.17360i | − | 0.0500880i | ||||||
\(550\) | −0.571054 | + | 9.33857i | −0.0243498 | + | 0.398198i | ||||
\(551\) | 5.78394 | 0.246404 | ||||||||
\(552\) | 2.44877i | 0.104226i | ||||||||
\(553\) | 12.6202 | 0.536664 | ||||||||
\(554\) | −2.58352 | −0.109763 | ||||||||
\(555\) | −11.9376 | + | 20.7836i | −0.506723 | + | 0.882214i | ||||
\(556\) | −9.78562 | −0.415003 | ||||||||
\(557\) | −31.8613 | −1.35001 | −0.675004 | − | 0.737814i | \(-0.735858\pi\) | ||||
−0.675004 | + | 0.737814i | \(0.735858\pi\) | |||||||
\(558\) | − | 0.432711i | − | 0.0183181i | ||||||
\(559\) | 31.9921 | 1.35312 | ||||||||
\(560\) | −1.87120 | − | 1.98912i | −0.0790727 | − | 0.0840557i | ||||
\(561\) | 2.52576i | 0.106638i | ||||||||
\(562\) | 19.3056i | 0.814360i | ||||||||
\(563\) | −0.477178 | −0.0201107 | −0.0100553 | − | 0.999949i | \(-0.503201\pi\) | ||||
−0.0100553 | + | 0.999949i | \(0.503201\pi\) | |||||||
\(564\) | 11.1153 | 0.468037 | ||||||||
\(565\) | 24.0369 | − | 22.6119i | 1.01124 | − | 0.951291i | ||||
\(566\) | −9.02942 | −0.379535 | ||||||||
\(567\) | − | 11.3638i | − | 0.477233i | ||||||
\(568\) | −0.963126 | −0.0404119 | ||||||||
\(569\) | 10.3567i | 0.434175i | 0.976152 | + | 0.217087i | \(0.0696557\pi\) | ||||
−0.976152 | + | 0.217087i | \(0.930344\pi\) | |||||||
\(570\) | −9.60032 | + | 9.03119i | −0.402113 | + | 0.378275i | ||||
\(571\) | −1.56306 | −0.0654119 | −0.0327059 | − | 0.999465i | \(-0.510412\pi\) | ||||
−0.0327059 | + | 0.999465i | \(0.510412\pi\) | |||||||
\(572\) | 12.1720 | 0.508937 | ||||||||
\(573\) | −40.6978 | −1.70018 | ||||||||
\(574\) | − | 4.56638i | − | 0.190597i | ||||||
\(575\) | 0.424091 | − | 6.93524i | 0.0176858 | − | 0.289220i | ||||
\(576\) | −0.105209 | −0.00438370 | ||||||||
\(577\) | −19.1344 | −0.796575 | −0.398287 | − | 0.917261i | \(-0.630395\pi\) | ||||
−0.398287 | + | 0.917261i | \(0.630395\pi\) | |||||||
\(578\) | 16.4133 | 0.682701 | ||||||||
\(579\) | 22.0184i | 0.915053i | ||||||||
\(580\) | −2.64919 | − | 2.81613i | −0.110001 | − | 0.116934i | ||||
\(581\) | −0.00802181 | −0.000332801 | ||||||||
\(582\) | − | 0.710909i | − | 0.0294681i | ||||||
\(583\) | 4.82337i | 0.199763i | ||||||||
\(584\) | 9.03119i | 0.373713i | ||||||||
\(585\) | 1.11462 | − | 1.04855i | 0.0460840 | − | 0.0433521i | ||||
\(586\) | − | 13.0845i | − | 0.540516i | ||||||
\(587\) | 7.16828 | 0.295867 | 0.147933 | − | 0.988997i | \(-0.452738\pi\) | ||||
0.147933 | + | 0.988997i | \(0.452738\pi\) | |||||||
\(588\) | − | 9.70668i | − | 0.400297i | ||||||
\(589\) | −13.7579 | −0.566884 | ||||||||
\(590\) | −16.1890 | − | 17.2092i | −0.666492 | − | 0.708493i | ||||
\(591\) | 9.71482 | 0.399614 | ||||||||
\(592\) | 1.76599 | + | 5.82076i | 0.0725819 | + | 0.239232i | ||||
\(593\) | − | 36.6287i | − | 1.50416i | −0.659071 | − | 0.752081i | \(-0.729050\pi\) | ||
0.659071 | − | 0.752081i | \(-0.270950\pi\) | |||||||
\(594\) | 9.54517i | 0.391643i | ||||||||
\(595\) | 1.43333 | + | 1.52366i | 0.0587608 | + | 0.0624638i | ||||
\(596\) | −11.8876 | −0.486934 | ||||||||
\(597\) | 33.1344 | 1.35610 | ||||||||
\(598\) | −9.03948 | −0.369652 | ||||||||
\(599\) | 38.3505 | 1.56696 | 0.783480 | − | 0.621417i | \(-0.213443\pi\) | ||||
0.783480 | + | 0.621417i | \(0.213443\pi\) | |||||||
\(600\) | 8.79437 | + | 0.537776i | 0.359029 | + | 0.0219546i | ||||
\(601\) | −20.5311 | −0.837480 | −0.418740 | − | 0.908106i | \(-0.637528\pi\) | ||||
−0.418740 | + | 0.908106i | \(0.637528\pi\) | |||||||
\(602\) | − | 6.00658i | − | 0.244810i | ||||||
\(603\) | − | 1.17012i | − | 0.0476510i | ||||||
\(604\) | 21.3141 | 0.867259 | ||||||||
\(605\) | 12.2128 | − | 11.4888i | 0.496521 | − | 0.467086i | ||||
\(606\) | − | 34.1373i | − | 1.38673i | ||||||
\(607\) | −35.3953 | −1.43665 | −0.718326 | − | 0.695706i | \(-0.755091\pi\) | ||||
−0.718326 | + | 0.695706i | \(0.755091\pi\) | |||||||
\(608\) | 3.34507i | 0.135661i | ||||||||
\(609\) | 3.72126i | 0.150793i | ||||||||
\(610\) | 17.0908 | + | 18.1678i | 0.691986 | + | 0.735594i | ||||
\(611\) | 41.0314i | 1.65995i | ||||||||
\(612\) | 0.0805893 | 0.00325763 | ||||||||
\(613\) | 10.3293i | 0.417198i | 0.978001 | + | 0.208599i | \(0.0668904\pi\) | ||||
−0.978001 | + | 0.208599i | \(0.933110\pi\) | |||||||
\(614\) | 7.60942i | 0.307091i | ||||||||
\(615\) | 10.0945 | + | 10.7307i | 0.407050 | + | 0.432702i | ||||
\(616\) | − | 2.28532i | − | 0.0920782i | ||||||
\(617\) | 2.91338i | 0.117288i | 0.998279 | + | 0.0586441i | \(0.0186777\pi\) | ||||
−0.998279 | + | 0.0586441i | \(0.981322\pi\) | |||||||
\(618\) | − | 9.80051i | − | 0.394234i | ||||||
\(619\) | 30.7715 | 1.23681 | 0.618405 | − | 0.785860i | \(-0.287779\pi\) | ||||
0.618405 | + | 0.785860i | \(0.287779\pi\) | |||||||
\(620\) | 6.30145 | + | 6.69856i | 0.253072 | + | 0.269021i | ||||
\(621\) | − | 7.08867i | − | 0.284459i | ||||||
\(622\) | 15.2359i | 0.610905i | ||||||||
\(623\) | −5.74193 | −0.230045 | ||||||||
\(624\) | − | 11.4627i | − | 0.458875i | ||||||
\(625\) | −24.8137 | − | 3.04611i | −0.992549 | − | 0.121844i | ||||
\(626\) | 10.0000 | 0.399680 | ||||||||
\(627\) | −11.0299 | −0.440492 | ||||||||
\(628\) | − | 15.3009i | − | 0.610573i | ||||||
\(629\) | −1.35274 | − | 4.45867i | −0.0539373 | − | 0.177779i | ||||
\(630\) | −0.196867 | − | 0.209273i | −0.00784337 | − | 0.00833764i | ||||
\(631\) | 12.8167i | 0.510225i | 0.966911 | + | 0.255113i | \(0.0821126\pi\) | ||||
−0.966911 | + | 0.255113i | \(0.917887\pi\) | |||||||
\(632\) | 10.3333i | 0.411036i | ||||||||
\(633\) | 46.9847i | 1.86748i | ||||||||
\(634\) | − | 34.1403i | − | 1.35589i | ||||||
\(635\) | 17.0495 | + | 18.1240i | 0.676591 | + | 0.719228i | ||||
\(636\) | 4.54229 | 0.180114 | ||||||||
\(637\) | 35.8316 | 1.41970 | ||||||||
\(638\) | − | 3.23548i | − | 0.128094i | ||||||
\(639\) | −0.101329 | −0.00400853 | ||||||||
\(640\) | 1.62868 | − | 1.53213i | 0.0643791 | − | 0.0605626i | ||||
\(641\) | 39.8277 | 1.57310 | 0.786550 | − | 0.617527i | \(-0.211865\pi\) | ||||
0.786550 | + | 0.617527i | \(0.211865\pi\) | |||||||
\(642\) | 3.40950 | 0.134562 | ||||||||
\(643\) | −15.9821 | −0.630273 | −0.315137 | − | 0.949046i | \(-0.602050\pi\) | ||||
−0.315137 | + | 0.949046i | \(0.602050\pi\) | |||||||
\(644\) | 1.69718i | 0.0668784i | ||||||||
\(645\) | 13.2782 | + | 14.1150i | 0.522830 | + | 0.555778i | ||||
\(646\) | − | 2.56230i | − | 0.100812i | ||||||
\(647\) | 37.8647 | 1.48861 | 0.744307 | − | 0.667838i | \(-0.232780\pi\) | ||||
0.744307 | + | 0.667838i | \(0.232780\pi\) | |||||||
\(648\) | 9.30456 | 0.365518 | ||||||||
\(649\) | − | 19.7719i | − | 0.776113i | ||||||
\(650\) | −1.98517 | + | 32.4639i | −0.0778648 | + | 1.27334i | ||||
\(651\) | − | 8.85152i | − | 0.346919i | ||||||
\(652\) | −14.9177 | −0.584221 | ||||||||
\(653\) | −9.60006 | −0.375679 | −0.187840 | − | 0.982200i | \(-0.560149\pi\) | ||||
−0.187840 | + | 0.982200i | \(0.560149\pi\) | |||||||
\(654\) | −15.3417 | −0.599908 | ||||||||
\(655\) | −19.6669 | − | 20.9062i | −0.768449 | − | 0.816875i | ||||
\(656\) | 3.73892 | 0.145980 | ||||||||
\(657\) | 0.950161i | 0.0370693i | ||||||||
\(658\) | 7.70373 | 0.300323 | ||||||||
\(659\) | 30.3448 | 1.18207 | 0.591033 | − | 0.806647i | \(-0.298720\pi\) | ||||
0.591033 | + | 0.806647i | \(0.298720\pi\) | |||||||
\(660\) | 5.05197 | + | 5.37033i | 0.196648 | + | 0.209040i | ||||
\(661\) | − | 28.0304i | − | 1.09026i | −0.838353 | − | 0.545128i | \(-0.816481\pi\) | ||
0.838353 | − | 0.545128i | \(-0.183519\pi\) | |||||||
\(662\) | − | 27.2567i | − | 1.05936i | ||||||
\(663\) | 8.78035i | 0.341001i | ||||||||
\(664\) | − | 0.00656819i | − | 0.000254895i | ||||||
\(665\) | −6.65375 | + | 6.25931i | −0.258022 | + | 0.242725i | ||||
\(666\) | 0.185798 | + | 0.612395i | 0.00719953 | + | 0.0237298i | ||||
\(667\) | 2.40281i | 0.0930374i | ||||||||
\(668\) | 17.3041 | 0.669514 | ||||||||
\(669\) | −19.1424 | −0.740087 | ||||||||
\(670\) | 17.0401 | + | 18.1140i | 0.658318 | + | 0.699804i | ||||
\(671\) | 20.8732i | 0.805800i | ||||||||
\(672\) | −2.15215 | −0.0830208 | ||||||||
\(673\) | − | 1.70175i | − | 0.0655975i | −0.999462 | − | 0.0327987i | \(-0.989558\pi\) | ||
0.999462 | − | 0.0327987i | \(-0.0104420\pi\) | |||||||
\(674\) | − | 22.5315i | − | 0.867879i | ||||||
\(675\) | −25.4579 | − | 1.55675i | −0.979874 | − | 0.0599194i | ||||
\(676\) | 29.3139 | 1.12746 | ||||||||
\(677\) | 3.49272i | 0.134236i | 0.997745 | + | 0.0671180i | \(0.0213804\pi\) | ||||
−0.997745 | + | 0.0671180i | \(0.978620\pi\) | |||||||
\(678\) | − | 26.0069i | − | 0.998789i | ||||||
\(679\) | − | 0.492714i | − | 0.0189086i | ||||||
\(680\) | −1.24756 | + | 1.17360i | −0.0478416 | + | 0.0450055i | ||||
\(681\) | − | 12.0254i | − | 0.460816i | ||||||
\(682\) | 7.69603i | 0.294696i | ||||||||
\(683\) | −18.9186 | −0.723901 | −0.361950 | − | 0.932197i | \(-0.617889\pi\) | ||||
−0.361950 | + | 0.932197i | \(0.617889\pi\) | |||||||
\(684\) | 0.351931i | 0.0134564i | ||||||||
\(685\) | −18.4398 | − | 19.6019i | −0.704550 | − | 0.748949i | ||||
\(686\) | − | 15.2766i | − | 0.583265i | ||||||
\(687\) | − | 4.51446i | − | 0.172237i | ||||||
\(688\) | 4.91814 | 0.187502 | ||||||||
\(689\) | 16.7676i | 0.638795i | ||||||||
\(690\) | −3.75182 | − | 3.98825i | −0.142829 | − | 0.151830i | ||||
\(691\) | 4.56018 | 0.173477 | 0.0867386 | − | 0.996231i | \(-0.472355\pi\) | ||||
0.0867386 | + | 0.996231i | \(0.472355\pi\) | |||||||
\(692\) | − | 19.7322i | − | 0.750107i | ||||||
\(693\) | − | 0.240436i | − | 0.00913340i | ||||||
\(694\) | 34.7252 | 1.31815 | ||||||||
\(695\) | 15.9376 | − | 14.9928i | 0.604548 | − | 0.568709i | ||||
\(696\) | −3.04694 | −0.115494 | ||||||||
\(697\) | −2.86399 | −0.108481 | ||||||||
\(698\) | −15.9343 | −0.603121 | ||||||||
\(699\) | −41.1329 | −1.55579 | ||||||||
\(700\) | 6.09517 | + | 0.372720i | 0.230376 | + | 0.0140875i | ||||
\(701\) | 18.9895i | 0.717224i | 0.933487 | + | 0.358612i | \(0.116750\pi\) | ||||
−0.933487 | + | 0.358612i | \(0.883250\pi\) | |||||||
\(702\) | 33.1821i | 1.25238i | ||||||||
\(703\) | 19.4709 | − | 5.90737i | 0.734357 | − | 0.222801i | ||||
\(704\) | 1.87120 | 0.0705236 | ||||||||
\(705\) | −18.1032 | + | 17.0300i | −0.681806 | + | 0.641387i | ||||
\(706\) | −20.1925 | −0.759956 | ||||||||
\(707\) | − | 23.6597i | − | 0.889815i | ||||||
\(708\) | −18.6197 | −0.699770 | ||||||||
\(709\) | 10.8195i | 0.406336i | 0.979144 | + | 0.203168i | \(0.0651238\pi\) | ||||
−0.979144 | + | 0.203168i | \(0.934876\pi\) | |||||||
\(710\) | 1.56862 | − | 1.47563i | 0.0588693 | − | 0.0553794i | ||||
\(711\) | 1.08715i | 0.0407714i | ||||||||
\(712\) | − | 4.70144i | − | 0.176194i | ||||||
\(713\) | − | 5.71542i | − | 0.214044i | ||||||
\(714\) | 1.64853 | 0.0616947 | ||||||||
\(715\) | −19.8243 | + | 18.6490i | −0.741386 | + | 0.697435i | ||||
\(716\) | 3.70357i | 0.138409i | ||||||||
\(717\) | 9.15013 | 0.341718 | ||||||||
\(718\) | 30.8657 | 1.15190 | ||||||||
\(719\) | −8.43399 | −0.314535 | −0.157267 | − | 0.987556i | \(-0.550268\pi\) | ||||
−0.157267 | + | 0.987556i | \(0.550268\pi\) | |||||||
\(720\) | 0.171351 | − | 0.161193i | 0.00638588 | − | 0.00600731i | ||||
\(721\) | − | 6.79250i | − | 0.252966i | ||||||
\(722\) | −7.81050 | −0.290677 | ||||||||
\(723\) | 27.3564 | 1.01739 | ||||||||
\(724\) | −10.4093 | −0.386857 | ||||||||
\(725\) | 8.62934 | + | 0.527685i | 0.320486 | + | 0.0195977i | ||||
\(726\) | − | 13.2137i | − | 0.490408i | ||||||
\(727\) | −16.7156 | −0.619947 | −0.309974 | − | 0.950745i | \(-0.600320\pi\) | ||||
−0.309974 | + | 0.950745i | \(0.600320\pi\) | |||||||
\(728\) | − | 7.94452i | − | 0.294444i | ||||||
\(729\) | −25.9879 | −0.962514 | ||||||||
\(730\) | −13.8369 | − | 14.7089i | −0.512128 | − | 0.544401i | ||||
\(731\) | −3.76726 | −0.139337 | ||||||||
\(732\) | 19.6568 | 0.726537 | ||||||||
\(733\) | 10.4157i | 0.384711i | 0.981325 | + | 0.192356i | \(0.0616127\pi\) | ||||
−0.981325 | + | 0.192356i | \(0.938387\pi\) | |||||||
\(734\) | 28.9254i | 1.06766i | ||||||||
\(735\) | 14.8719 | + | 15.8091i | 0.548557 | + | 0.583126i | ||||
\(736\) | −1.38964 | −0.0512228 | ||||||||
\(737\) | 20.8113i | 0.766594i | ||||||||
\(738\) | 0.393367 | 0.0144800 | ||||||||
\(739\) | −19.7975 | −0.728261 | −0.364131 | − | 0.931348i | \(-0.618634\pi\) | ||||
−0.364131 | + | 0.931348i | \(0.618634\pi\) | |||||||
\(740\) | −11.7944 | − | 6.77442i | −0.433570 | − | 0.249033i | ||||
\(741\) | −38.3435 | −1.40858 | ||||||||
\(742\) | 3.14815 | 0.115572 | ||||||||
\(743\) | 34.4142i | 1.26253i | 0.775566 | + | 0.631267i | \(0.217465\pi\) | ||||
−0.775566 | + | 0.631267i | \(0.782535\pi\) | |||||||
\(744\) | 7.24756 | 0.265708 | ||||||||
\(745\) | 19.3610 | − | 18.2133i | 0.709333 | − | 0.667282i | ||||
\(746\) | − | 27.8899i | − | 1.02112i | ||||||
\(747\) | 0 | 0.000691032i | 0 | 2.52835e-5i | ||||||
\(748\) | −1.43333 | −0.0524077 | ||||||||
\(749\) | 2.36304 | 0.0863437 | ||||||||
\(750\) | −15.1471 | + | 12.5982i | −0.553095 | + | 0.460022i | ||||
\(751\) | −40.7020 | −1.48524 | −0.742618 | − | 0.669715i | \(-0.766416\pi\) | ||||
−0.742618 | + | 0.669715i | \(0.766416\pi\) | |||||||
\(752\) | 6.30775i | 0.230020i | ||||||||
\(753\) | −6.78783 | −0.247362 | ||||||||
\(754\) | − | 11.2476i | − | 0.409613i | ||||||
\(755\) | −34.7138 | + | 32.6559i | −1.26337 | + | 1.18847i | ||||
\(756\) | 6.23001 | 0.226583 | ||||||||
\(757\) | 2.06470 | 0.0750426 | 0.0375213 | − | 0.999296i | \(-0.488054\pi\) | ||||
0.0375213 | + | 0.999296i | \(0.488054\pi\) | |||||||
\(758\) | 5.73365 | 0.208256 | ||||||||
\(759\) | − | 4.58214i | − | 0.166321i | ||||||
\(760\) | −5.12507 | − | 5.44804i | −0.185906 | − | 0.197621i | ||||
\(761\) | 9.07263 | 0.328883 | 0.164441 | − | 0.986387i | \(-0.447418\pi\) | ||||
0.164441 | + | 0.986387i | \(0.447418\pi\) | |||||||
\(762\) | 19.6094 | 0.710373 | ||||||||
\(763\) | −10.6330 | −0.384939 | ||||||||
\(764\) | − | 23.0954i | − | 0.835563i | ||||||
\(765\) | −0.131254 | + | 0.123473i | −0.00474550 | + | 0.00446417i | ||||
\(766\) | −17.8363 | −0.644451 | ||||||||
\(767\) | − | 68.7335i | − | 2.48182i | ||||||
\(768\) | − | 1.76216i | − | 0.0635865i | ||||||
\(769\) | − | 50.9991i | − | 1.83907i | −0.393002 | − | 0.919537i | \(-0.628564\pi\) | ||
0.393002 | − | 0.919537i | \(-0.371436\pi\) | |||||||
\(770\) | 3.50140 | + | 3.72205i | 0.126182 | + | 0.134133i | ||||
\(771\) | − | 5.89493i | − | 0.212301i | ||||||
\(772\) | −12.4951 | −0.449709 | ||||||||
\(773\) | − | 40.9981i | − | 1.47460i | −0.675565 | − | 0.737300i | \(-0.736100\pi\) | ||
0.675565 | − | 0.737300i | \(-0.263900\pi\) | |||||||
\(774\) | 0.517431 | 0.0185987 | ||||||||
\(775\) | −20.5261 | − | 1.25517i | −0.737318 | − | 0.0450870i | ||||
\(776\) | 0.403430 | 0.0144823 | ||||||||
\(777\) | 3.80068 | + | 12.5271i | 0.136349 | + | 0.449408i | ||||
\(778\) | − | 29.8974i | − | 1.07187i | ||||||
\(779\) | − | 12.5069i | − | 0.448108i | ||||||
\(780\) | 17.5623 | + | 18.6690i | 0.628831 | + | 0.668459i | ||||
\(781\) | 1.80220 | 0.0644879 | ||||||||
\(782\) | 1.06446 | 0.0380648 | ||||||||
\(783\) | 8.82025 | 0.315210 | ||||||||
\(784\) | 5.50840 | 0.196729 | ||||||||
\(785\) | 23.4429 | + | 24.9202i | 0.836713 | + | 0.889441i | ||||
\(786\) | −22.6197 | −0.806817 | ||||||||
\(787\) | 30.4357i | 1.08492i | 0.840083 | + | 0.542458i | \(0.182506\pi\) | ||||
−0.840083 | + | 0.542458i | \(0.817494\pi\) | |||||||
\(788\) | 5.51302i | 0.196393i | ||||||||
\(789\) | −2.01601 | −0.0717718 | ||||||||
\(790\) | −15.8319 | − | 16.8296i | −0.563274 | − | 0.598770i | ||||
\(791\) | − | 18.0248i | − | 0.640887i | ||||||
\(792\) | 0.196867 | 0.00699536 | ||||||||
\(793\) | 72.5620i | 2.57675i | ||||||||
\(794\) | − | 13.2064i | − | 0.468679i | ||||||
\(795\) | −7.39793 | + | 6.95936i | −0.262377 | + | 0.246823i | ||||
\(796\) | 18.8033i | 0.666464i | ||||||||
\(797\) | 0.999495 | 0.0354039 | 0.0177020 | − | 0.999843i | \(-0.494365\pi\) | ||||
0.0177020 | + | 0.999843i | \(0.494365\pi\) | |||||||
\(798\) | 7.19908i | 0.254845i | ||||||||
\(799\) | − | 4.83170i | − | 0.170933i | ||||||
\(800\) | −0.305180 | + | 4.99068i | −0.0107898 | + | 0.176447i | ||||
\(801\) | − | 0.494633i | − | 0.0174770i | ||||||
\(802\) | 23.0269i | 0.813108i | ||||||||
\(803\) | − | 16.8992i | − | 0.596360i | ||||||
\(804\) | 19.5985 | 0.691187 | ||||||||
\(805\) | −2.60030 | − | 2.76416i | −0.0916484 | − | 0.0974239i | ||||
\(806\) | 26.7539i | 0.942367i | ||||||||
\(807\) | − | 26.6692i | − | 0.938801i | ||||||
\(808\) | 19.3724 | 0.681518 | ||||||||
\(809\) | 21.8030i | 0.766552i | 0.923634 | + | 0.383276i | \(0.125204\pi\) | ||||
−0.923634 | + | 0.383276i | \(0.874796\pi\) | |||||||
\(810\) | −15.1541 | + | 14.2558i | −0.532462 | + | 0.500896i | ||||
\(811\) | −40.9653 | −1.43848 | −0.719242 | − | 0.694759i | \(-0.755511\pi\) | ||||
−0.719242 | + | 0.694759i | \(0.755511\pi\) | |||||||
\(812\) | −2.11176 | −0.0741082 | ||||||||
\(813\) | 32.2197i | 1.12999i | ||||||||
\(814\) | −3.30453 | − | 10.8918i | −0.115824 | − | 0.381758i | ||||
\(815\) | 24.2961 | − | 22.8557i | 0.851054 | − | 0.800601i | ||||
\(816\) | 1.34980i | 0.0472526i | ||||||||
\(817\) | − | 16.4515i | − | 0.575566i | ||||||
\(818\) | − | 9.77049i | − | 0.341617i | ||||||
\(819\) | − | 0.835833i | − | 0.0292064i | ||||||
\(820\) | −6.08949 | + | 5.72849i | −0.212654 | + | 0.200048i | ||||
\(821\) | 36.2693 | 1.26581 | 0.632904 | − | 0.774230i | \(-0.281863\pi\) | ||||
0.632904 | + | 0.774230i | \(0.281863\pi\) | |||||||
\(822\) | −21.2084 | −0.739728 | ||||||||
\(823\) | 48.5397i | 1.69199i | 0.533194 | + | 0.845993i | \(0.320992\pi\) | ||||
−0.533194 | + | 0.845993i | \(0.679008\pi\) | |||||||
\(824\) | 5.56165 | 0.193749 | ||||||||
\(825\) | −16.4561 | − | 1.00629i | −0.572926 | − | 0.0350345i | ||||
\(826\) | −12.9049 | −0.449017 | ||||||||
\(827\) | −39.6895 | −1.38014 | −0.690069 | − | 0.723743i | \(-0.742420\pi\) | ||||
−0.690069 | + | 0.723743i | \(0.742420\pi\) | |||||||
\(828\) | −0.146202 | −0.00508088 | ||||||||
\(829\) | − | 53.4506i | − | 1.85641i | −0.372064 | − | 0.928207i | \(-0.621350\pi\) | ||
0.372064 | − | 0.928207i | \(-0.378650\pi\) | |||||||
\(830\) | 0.0100633 | + | 0.0106975i | 0.000349302 | + | 0.000371315i | ||||
\(831\) | − | 4.55258i | − | 0.157927i | ||||||
\(832\) | 6.50491 | 0.225517 | ||||||||
\(833\) | −4.21940 | −0.146194 | ||||||||
\(834\) | − | 17.2438i | − | 0.597105i | ||||||
\(835\) | −28.1827 | + | 26.5120i | −0.975303 | + | 0.917485i | ||||
\(836\) | − | 6.25931i | − | 0.216483i | ||||||
\(837\) | −20.9802 | −0.725181 | ||||||||
\(838\) | −2.06109 | −0.0711993 | ||||||||
\(839\) | −33.5857 | −1.15951 | −0.579753 | − | 0.814792i | \(-0.696851\pi\) | ||||
−0.579753 | + | 0.814792i | \(0.696851\pi\) | |||||||
\(840\) | 3.50515 | − | 3.29736i | 0.120939 | − | 0.113770i | ||||
\(841\) | 26.0102 | 0.896905 | ||||||||
\(842\) | 12.8910i | 0.444255i | ||||||||
\(843\) | −34.0196 | −1.17170 | ||||||||
\(844\) | −26.6632 | −0.917784 | ||||||||
\(845\) | −47.7428 | + | 44.9125i | −1.64240 | + | 1.54504i | ||||
\(846\) | 0.663631i | 0.0228161i | ||||||||
\(847\) | − | 9.15813i | − | 0.314677i | ||||||
\(848\) | 2.57768i | 0.0885180i | ||||||||
\(849\) | − | 15.9113i | − | 0.546074i | ||||||
\(850\) | 0.233766 | − | 3.82283i | 0.00801811 | − | 0.131122i | ||||
\(851\) | 2.45409 | + | 8.08876i | 0.0841253 | + | 0.277279i | ||||
\(852\) | − | 1.69718i | − | 0.0581445i | ||||||
\(853\) | −0.641846 | −0.0219764 | −0.0109882 | − | 0.999940i | \(-0.503498\pi\) | ||||
−0.0109882 | + | 0.999940i | \(0.503498\pi\) | |||||||
\(854\) | 13.6237 | 0.466192 | ||||||||
\(855\) | −0.539202 | − | 0.573182i | −0.0184403 | − | 0.0196024i | ||||
\(856\) | 1.93484i | 0.0661315i | ||||||||
\(857\) | −20.5938 | −0.703470 | −0.351735 | − | 0.936100i | \(-0.614408\pi\) | ||||
−0.351735 | + | 0.936100i | \(0.614408\pi\) | |||||||
\(858\) | 21.4490i | 0.732258i | ||||||||
\(859\) | 6.18892i | 0.211163i | 0.994411 | + | 0.105582i | \(0.0336704\pi\) | ||||
−0.994411 | + | 0.105582i | \(0.966330\pi\) | |||||||
\(860\) | −8.01006 | + | 7.53521i | −0.273141 | + | 0.256949i | ||||
\(861\) | 8.04670 | 0.274231 | ||||||||
\(862\) | − | 9.41662i | − | 0.320731i | ||||||
\(863\) | 48.8873i | 1.66414i | 0.554669 | + | 0.832071i | \(0.312845\pi\) | ||||
−0.554669 | + | 0.832071i | \(0.687155\pi\) | |||||||
\(864\) | 5.10109i | 0.173542i | ||||||||
\(865\) | 30.2323 | + | 32.1374i | 1.02793 | + | 1.09271i | ||||
\(866\) | − | 3.07581i | − | 0.104520i | ||||||
\(867\) | 28.9228i | 0.982269i | ||||||||
\(868\) | 5.02311 | 0.170495 | ||||||||
\(869\) | − | 19.3357i | − | 0.655918i | ||||||
\(870\) | 4.96248 | − | 4.66829i | 0.168244 | − | 0.158270i | ||||
\(871\) | 72.3469i | 2.45138i | ||||||||
\(872\) | − | 8.70619i | − | 0.294829i | ||||||
\(873\) | 0.0424444 | 0.00143653 | ||||||||
\(874\) | 4.64844i | 0.157236i | ||||||||
\(875\) | −10.4981 | + | 8.73153i | −0.354901 | + | 0.295180i | ||||
\(876\) | −15.9144 | −0.537698 | ||||||||
\(877\) | 2.65696i | 0.0897190i | 0.998993 | + | 0.0448595i | \(0.0142840\pi\) | ||||
−0.998993 | + | 0.0448595i | \(0.985716\pi\) | |||||||
\(878\) | 1.93763i | 0.0653918i | ||||||||
\(879\) | 23.0570 | 0.777693 | ||||||||
\(880\) | −3.04759 | + | 2.86692i | −0.102734 | + | 0.0966438i | ||||
\(881\) | −1.97718 | −0.0666130 | −0.0333065 | − | 0.999445i | \(-0.510604\pi\) | ||||
−0.0333065 | + | 0.999445i | \(0.510604\pi\) | |||||||
\(882\) | 0.579532 | 0.0195139 | ||||||||
\(883\) | 35.6965 | 1.20128 | 0.600641 | − | 0.799519i | \(-0.294912\pi\) | ||||
0.600641 | + | 0.799519i | \(0.294912\pi\) | |||||||
\(884\) | −4.98272 | −0.167587 | ||||||||
\(885\) | 30.3254 | − | 28.5277i | 1.01938 | − | 0.958948i | ||||
\(886\) | 26.5690i | 0.892602i | ||||||||
\(887\) | 0.181192i | 0.00608382i | 0.999995 | + | 0.00304191i | \(0.000968271\pi\) | ||||
−0.999995 | + | 0.00304191i | \(0.999032\pi\) | |||||||
\(888\) | −10.2571 | + | 3.11196i | −0.344206 | + | 0.104431i | ||||
\(889\) | 13.5908 | 0.455820 | ||||||||
\(890\) | 7.20320 | + | 7.65713i | 0.241452 | + | 0.256668i | ||||
\(891\) | −17.4107 | −0.583281 | ||||||||
\(892\) | − | 10.8630i | − | 0.363721i | ||||||
\(893\) | 21.0999 | 0.706081 | ||||||||
\(894\) | − | 20.9478i | − | 0.700600i | ||||||
\(895\) | −5.67434 | − | 6.03192i | −0.189672 | − | 0.201625i | ||||
\(896\) | − | 1.22131i | − | 0.0408011i | ||||||
\(897\) | − | 15.9290i | − | 0.531854i | ||||||
\(898\) | − | 0.777045i | − | 0.0259303i | ||||||
\(899\) | 7.11155 | 0.237184 | ||||||||
\(900\) | −0.0321076 | + | 0.525063i | −0.00107025 | + | 0.0175021i | ||||
\(901\) | − | 1.97449i | − | 0.0657798i | ||||||
\(902\) | −6.99627 | −0.232950 | ||||||||
\(903\) | 10.5846 | 0.352232 | ||||||||
\(904\) | 14.7585 | 0.490862 | ||||||||
\(905\) | 16.9533 | − | 15.9483i | 0.563548 | − | 0.530139i | ||||
\(906\) | 37.5589i | 1.24781i | ||||||||
\(907\) | 28.0542 | 0.931525 | 0.465762 | − | 0.884910i | \(-0.345780\pi\) | ||||
0.465762 | + | 0.884910i | \(0.345780\pi\) | |||||||
\(908\) | 6.82427 | 0.226471 | ||||||||
\(909\) | 2.03814 | 0.0676010 | ||||||||
\(910\) | 12.1720 | + | 12.9391i | 0.403498 | + | 0.428926i | ||||
\(911\) | − | 33.0379i | − | 1.09459i | −0.836939 | − | 0.547297i | \(-0.815657\pi\) | ||
0.836939 | − | 0.547297i | \(-0.184343\pi\) | |||||||
\(912\) | −5.89455 | −0.195188 | ||||||||
\(913\) | 0.0122904i | 0.000406754i | ||||||||
\(914\) | −21.1753 | −0.700415 | ||||||||
\(915\) | −32.0146 | + | 30.1167i | −1.05837 | + | 0.995628i | ||||
\(916\) | 2.56189 | 0.0846471 | ||||||||
\(917\) | −15.6772 | −0.517705 | ||||||||
\(918\) | − | 3.90740i | − | 0.128963i | ||||||
\(919\) | − | 24.1489i | − | 0.796600i | −0.917255 | − | 0.398300i | \(-0.869600\pi\) | ||
0.917255 | − | 0.398300i | \(-0.130400\pi\) | |||||||
\(920\) | 2.26327 | − | 2.12910i | 0.0746180 | − | 0.0701944i | ||||
\(921\) | −13.4090 | −0.441842 | ||||||||
\(922\) | 23.9797i | 0.789731i | ||||||||
\(923\) | 6.26505 | 0.206217 | ||||||||
\(924\) | 4.02710 | 0.132482 | ||||||||
\(925\) | 29.5885 | − | 7.03712i | 0.972864 | − | 0.231379i | ||||
\(926\) | 25.1591 | 0.826781 | ||||||||
\(927\) | 0.585134 | 0.0192183 | ||||||||
\(928\) | − | 1.72909i | − | 0.0567602i | ||||||
\(929\) | 30.9086 | 1.01408 | 0.507039 | − | 0.861923i | \(-0.330740\pi\) | ||||
0.507039 | + | 0.861923i | \(0.330740\pi\) | |||||||
\(930\) | −11.8039 | + | 11.1042i | −0.387066 | + | 0.364120i | ||||
\(931\) | − | 18.4260i | − | 0.603887i | ||||||
\(932\) | − | 23.3423i | − | 0.764603i | ||||||
\(933\) | −26.8481 | −0.878969 | ||||||||
\(934\) | −15.6162 | −0.510978 | ||||||||
\(935\) | 2.33443 | − | 2.19604i | 0.0763441 | − | 0.0718182i | ||||
\(936\) | 0.684374 | 0.0223695 | ||||||||
\(937\) | − | 33.6530i | − | 1.09940i | −0.835363 | − | 0.549698i | \(-0.814743\pi\) | ||
0.835363 | − | 0.549698i | \(-0.185257\pi\) | |||||||
\(938\) | 13.5833 | 0.443510 | ||||||||
\(939\) | 17.6216i | 0.575059i | ||||||||
\(940\) | −9.66427 | − | 10.2733i | −0.315214 | − | 0.335078i | ||||
\(941\) | −33.8242 | −1.10264 | −0.551319 | − | 0.834294i | \(-0.685875\pi\) | ||||
−0.551319 | + | 0.834294i | \(0.685875\pi\) | |||||||
\(942\) | 26.9626 | 0.878490 | ||||||||
\(943\) | 5.19575 | 0.169197 | ||||||||
\(944\) | − | 10.5664i | − | 0.343907i | ||||||
\(945\) | −10.1467 | + | 9.54517i | −0.330072 | + | 0.310504i | ||||
\(946\) | −9.20284 | −0.299210 | ||||||||
\(947\) | 17.3591 | 0.564095 | 0.282048 | − | 0.959400i | \(-0.408986\pi\) | ||||
0.282048 | + | 0.959400i | \(0.408986\pi\) | |||||||
\(948\) | −18.2089 | −0.591398 | ||||||||
\(949\) | − | 58.7471i | − | 1.90701i | ||||||
\(950\) | 16.6942 | + | 1.02085i | 0.541630 | + | 0.0331207i | ||||
\(951\) | 60.1607 | 1.95085 | ||||||||
\(952\) | 0.935517i | 0.0303203i | ||||||||
\(953\) | − | 15.0520i | − | 0.487582i | −0.969828 | − | 0.243791i | \(-0.921609\pi\) | ||
0.969828 | − | 0.243791i | \(-0.0783911\pi\) | |||||||
\(954\) | 0.271195i | 0.00878026i | ||||||||
\(955\) | 35.3851 | + | 37.6150i | 1.14503 | + | 1.21719i | ||||
\(956\) | 5.19256i | 0.167940i | ||||||||
\(957\) | 5.70144 | 0.184301 | ||||||||
\(958\) | 31.4974i | 1.01763i | ||||||||
\(959\) | −14.6990 | −0.474657 | ||||||||
\(960\) | 2.69985 | + | 2.86999i | 0.0871373 | + | 0.0926285i | ||||
\(961\) | 14.0842 | 0.454329 | ||||||||
\(962\) | −11.4876 | − | 37.8635i | −0.370376 | − | 1.22077i | ||||
\(963\) | 0.203562i | 0.00655970i | ||||||||
\(964\) | 15.5243i | 0.500005i | ||||||||
\(965\) | 20.3505 | − | 19.1441i | 0.655106 | − | 0.616270i | ||||
\(966\) | −2.99071 | −0.0962244 | ||||||||
\(967\) | 23.3045 | 0.749423 | 0.374712 | − | 0.927141i | \(-0.377742\pi\) | ||||
0.374712 | + | 0.927141i | \(0.377742\pi\) | |||||||
\(968\) | 7.49860 | 0.241014 | ||||||||
\(969\) | 4.51519 | 0.145049 | ||||||||
\(970\) | −0.657058 | + | 0.618106i | −0.0210969 | + | 0.0198462i | ||||
\(971\) | −40.7911 | −1.30905 | −0.654524 | − | 0.756041i | \(-0.727131\pi\) | ||||
−0.654524 | + | 0.756041i | \(0.727131\pi\) | |||||||
\(972\) | 1.09286i | 0.0350536i | ||||||||
\(973\) | − | 11.9513i | − | 0.383140i | ||||||
\(974\) | −24.2768 | −0.777878 | ||||||||
\(975\) | −57.2066 | − | 3.49819i | −1.83208 | − | 0.112032i | ||||
\(976\) | 11.1550i | 0.357061i | ||||||||
\(977\) | −2.64739 | −0.0846976 | −0.0423488 | − | 0.999103i | \(-0.513484\pi\) | ||||
−0.0423488 | + | 0.999103i | \(0.513484\pi\) | |||||||
\(978\) | − | 26.2873i | − | 0.840575i | ||||||
\(979\) | 8.79735i | 0.281165i | ||||||||
\(980\) | −8.97140 | + | 8.43956i | −0.286581 | + | 0.269592i | ||||
\(981\) | − | 0.915967i | − | 0.0292446i | ||||||
\(982\) | −16.5129 | −0.526949 | ||||||||
\(983\) | 27.8528i | 0.888367i | 0.895936 | + | 0.444183i | \(0.146506\pi\) | ||||
−0.895936 | + | 0.444183i | \(0.853494\pi\) | |||||||
\(984\) | 6.58857i | 0.210036i | ||||||||
\(985\) | −8.44664 | − | 8.97893i | −0.269132 | − | 0.286093i | ||||
\(986\) | 1.32447i | 0.0421798i | ||||||||
\(987\) | 13.5752i | 0.432104i | ||||||||
\(988\) | − | 21.7594i | − | 0.692258i | ||||||
\(989\) | 6.83444 | 0.217323 | ||||||||
\(990\) | −0.320633 | + | 0.301625i | −0.0101904 | + | 0.00958627i | ||||
\(991\) | 47.8484i | 1.51995i | 0.649950 | + | 0.759977i | \(0.274790\pi\) | ||||
−0.649950 | + | 0.759977i | \(0.725210\pi\) | |||||||
\(992\) | 4.11288i | 0.130584i | ||||||||
\(993\) | 48.0307 | 1.52421 | ||||||||
\(994\) | − | 1.17628i | − | 0.0373092i | ||||||
\(995\) | −28.8090 | − | 30.6245i | −0.913306 | − | 0.970861i | ||||
\(996\) | 0.0115742 | 0.000366743 | ||||||||
\(997\) | −3.95282 | −0.125187 | −0.0625936 | − | 0.998039i | \(-0.519937\pi\) | ||||
−0.0625936 | + | 0.998039i | \(0.519937\pi\) | |||||||
\(998\) | − | 22.8436i | − | 0.723101i | ||||||
\(999\) | 29.6922 | − | 9.00849i | 0.939420 | − | 0.285016i |
(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 | 370.2.c.a.369.3 | ✓ | 10 | |
3.2 | odd | 2 | 3330.2.e.d.739.7 | 10 | |||
5.2 | odd | 4 | 1850.2.d.i.1701.3 | 20 | |||
5.3 | odd | 4 | 1850.2.d.i.1701.18 | 20 | |||
5.4 | even | 2 | 370.2.c.b.369.8 | yes | 10 | ||
15.14 | odd | 2 | 3330.2.e.c.739.3 | 10 | |||
37.36 | even | 2 | 370.2.c.b.369.3 | yes | 10 | ||
111.110 | odd | 2 | 3330.2.e.c.739.4 | 10 | |||
185.73 | odd | 4 | 1850.2.d.i.1701.8 | 20 | |||
185.147 | odd | 4 | 1850.2.d.i.1701.13 | 20 | |||
185.184 | even | 2 | inner | 370.2.c.a.369.8 | yes | 10 | |
555.554 | odd | 2 | 3330.2.e.d.739.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.c.a.369.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
370.2.c.a.369.8 | yes | 10 | 185.184 | even | 2 | inner | |
370.2.c.b.369.3 | yes | 10 | 37.36 | even | 2 | ||
370.2.c.b.369.8 | yes | 10 | 5.4 | even | 2 | ||
1850.2.d.i.1701.3 | 20 | 5.2 | odd | 4 | |||
1850.2.d.i.1701.8 | 20 | 185.73 | odd | 4 | |||
1850.2.d.i.1701.13 | 20 | 185.147 | odd | 4 | |||
1850.2.d.i.1701.18 | 20 | 5.3 | odd | 4 | |||
3330.2.e.c.739.3 | 10 | 15.14 | odd | 2 | |||
3330.2.e.c.739.4 | 10 | 111.110 | odd | 2 | |||
3330.2.e.d.739.7 | 10 | 3.2 | odd | 2 | |||
3330.2.e.d.739.8 | 10 | 555.554 | odd | 2 |