Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(49,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.bv (of order \(6\), degree \(2\), not 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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.5 | ||
Root | \(5.04537i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.49 |
Dual form | 624.4.bv.h.433.1 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | + | 2.59808i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 20.1174i | 1.79935i | 0.436556 | + | 0.899677i | \(0.356198\pi\) | ||||
−0.436556 | + | 0.899677i | \(0.643802\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.3609 | + | 7.71395i | 0.721423 | + | 0.416514i | 0.815276 | − | 0.579072i | \(-0.196585\pi\) |
−0.0938530 | + | 0.995586i | \(0.529918\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −23.3283 | + | 13.4686i | −0.639432 | + | 0.369176i | −0.784396 | − | 0.620261i | \(-0.787027\pi\) |
0.144964 | + | 0.989437i | \(0.453693\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.96071 | + | 46.7045i | −0.0845002 | + | 0.996423i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −52.2665 | + | 30.1761i | −0.899677 | + | 0.519429i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.6167 | − | 20.1207i | 0.165733 | − | 0.287059i | −0.771182 | − | 0.636615i | \(-0.780334\pi\) |
0.936915 | + | 0.349556i | \(0.113668\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 39.0399 | + | 22.5397i | 0.471388 | + | 0.272156i | 0.716821 | − | 0.697258i | \(-0.245597\pi\) |
−0.245433 | + | 0.969414i | \(0.578930\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 46.2837i | 0.480949i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 71.0050 | + | 122.984i | 0.643720 | + | 1.11496i | 0.984595 | + | 0.174848i | \(0.0559434\pi\) |
−0.340875 | + | 0.940109i | \(0.610723\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −279.710 | −2.23768 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.14534 | − | 1.98379i | −0.00733394 | − | 0.0127028i | 0.862335 | − | 0.506338i | \(-0.169001\pi\) |
−0.869669 | + | 0.493635i | \(0.835668\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 37.7740i | − | 0.218852i | −0.993995 | − | 0.109426i | \(-0.965099\pi\) | ||
0.993995 | − | 0.109426i | \(-0.0349012\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −69.9849 | − | 40.4058i | −0.369176 | − | 0.213144i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −155.185 | + | 268.787i | −0.749456 | + | 1.29810i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 271.793 | − | 156.920i | 1.20764 | − | 0.697228i | 0.245393 | − | 0.969424i | \(-0.421083\pi\) |
0.962242 | + | 0.272195i | \(0.0877497\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −127.283 | + | 59.7666i | −0.522605 | + | 0.245393i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.08201 | − | 2.93410i | 0.0193580 | − | 0.0111763i | −0.490290 | − | 0.871559i | \(-0.663109\pi\) |
0.509648 | + | 0.860383i | \(0.329776\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 180.449 | − | 312.547i | 0.639958 | − | 1.10844i | −0.345483 | − | 0.938425i | \(-0.612285\pi\) |
0.985441 | − | 0.170015i | \(-0.0543817\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −156.800 | − | 90.5283i | −0.519429 | − | 0.299892i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 209.748i | 0.650956i | 0.945550 | + | 0.325478i | \(0.105525\pi\) | ||||
−0.945550 | + | 0.325478i | \(0.894475\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −52.4900 | − | 90.9154i | −0.153032 | − | 0.265060i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 69.7003 | 0.191372 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 276.886 | 0.717609 | 0.358804 | − | 0.933413i | \(-0.383185\pi\) | ||||
0.358804 | + | 0.933413i | \(0.383185\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −270.953 | − | 469.305i | −0.664278 | − | 1.15056i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 135.238i | 0.314259i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −470.415 | − | 271.594i | −1.03801 | − | 0.599298i | −0.118744 | − | 0.992925i | \(-0.537887\pi\) |
−0.919270 | + | 0.393627i | \(0.871220\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −102.894 | + | 178.218i | −0.215971 | + | 0.374073i | −0.953573 | − | 0.301163i | \(-0.902625\pi\) |
0.737601 | + | 0.675236i | \(0.235958\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −120.249 | + | 69.4255i | −0.240474 | + | 0.138838i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −939.573 | − | 79.6791i | −1.79292 | − | 0.152046i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 426.585 | − | 246.289i | 0.777846 | − | 0.449090i | −0.0578203 | − | 0.998327i | \(-0.518415\pi\) |
0.835666 | + | 0.549237i | \(0.185082\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −213.015 | + | 368.953i | −0.371652 | + | 0.643720i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −716.081 | − | 413.430i | −1.19695 | − | 0.691057i | −0.237073 | − | 0.971492i | \(-0.576188\pi\) |
−0.959873 | + | 0.280435i | \(0.909521\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 66.1205i | 0.106011i | 0.998594 | + | 0.0530056i | \(0.0168801\pi\) | ||||
−0.998594 | + | 0.0530056i | \(0.983120\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −419.564 | − | 726.707i | −0.645962 | − | 1.11884i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −415.584 | −0.615068 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −317.642 | −0.452374 | −0.226187 | − | 0.974084i | \(-0.572626\pi\) | ||||
−0.226187 | + | 0.974084i | \(0.572626\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 141.450i | 0.187063i | 0.995616 | + | 0.0935313i | \(0.0298155\pi\) | ||||
−0.995616 | + | 0.0935313i | \(0.970184\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 404.777 | + | 233.698i | 0.516520 | + | 0.298213i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.43602 | − | 5.95136i | 0.00423425 | − | 0.00733394i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 555.399 | − | 320.660i | 0.661486 | − | 0.381909i | −0.131357 | − | 0.991335i | \(-0.541933\pi\) |
0.792843 | + | 0.609426i | \(0.208600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −413.195 | + | 593.464i | −0.475985 | + | 0.683648i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 98.1396 | − | 56.6609i | 0.109426 | − | 0.0631771i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −453.440 | + | 785.381i | −0.489705 | + | 0.848194i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −965.551 | − | 557.461i | −1.01069 | − | 0.583522i | −0.0992962 | − | 0.995058i | \(-0.531659\pi\) |
−0.911394 | + | 0.411536i | \(0.864992\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 242.435i | − | 0.246117i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 794.953 | + | 1376.90i | 0.783177 | + | 1.35650i | 0.930082 | + | 0.367351i | \(0.119735\pi\) |
−0.146906 | + | 0.989150i | \(0.546931\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 527.502 | 0.504625 | 0.252312 | − | 0.967646i | \(-0.418809\pi\) | ||||
0.252312 | + | 0.967646i | \(0.418809\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −931.107 | −0.865398 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 875.982 | + | 1517.25i | 0.791443 | + | 1.37082i | 0.925073 | + | 0.379788i | \(0.124003\pi\) |
−0.133630 | + | 0.991031i | \(0.542663\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 967.122i | − | 0.849848i | −0.905229 | − | 0.424924i | \(-0.860301\pi\) | ||
0.905229 | − | 0.424924i | \(-0.139699\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 815.379 | + | 470.759i | 0.697228 | + | 0.402545i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −955.487 | + | 1654.95i | −0.795439 | + | 1.37774i | 0.127120 | + | 0.991887i | \(0.459427\pi\) |
−0.922560 | + | 0.385854i | \(0.873907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2474.12 | + | 1428.44i | −2.00620 | + | 1.15828i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −346.203 | − | 241.041i | −0.273559 | − | 0.190464i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 310.421 | − | 179.221i | 0.239128 | − | 0.138061i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −302.694 | + | 524.281i | −0.227418 | + | 0.393900i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.2460 | + | 8.80230i | 0.0111763 | + | 0.00645266i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 3112.35i | − | 2.22702i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −616.557 | − | 1067.91i | −0.430792 | − | 0.746154i | 0.566150 | − | 0.824302i | \(-0.308432\pi\) |
−0.996942 | + | 0.0781488i | \(0.975099\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1082.69 | 0.738960 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1274.90 | 0.850292 | 0.425146 | − | 0.905125i | \(-0.360223\pi\) | ||||
0.425146 | + | 0.905125i | \(0.360223\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 347.740 | + | 602.304i | 0.226713 | + | 0.392679i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 543.170i | − | 0.346286i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1759.18 | − | 1015.66i | −1.09706 | − | 0.633385i | −0.161609 | − | 0.986855i | \(-0.551668\pi\) |
−0.935446 | + | 0.353470i | \(0.885002\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −722.832 | + | 1251.98i | −0.441078 | + | 0.763969i | −0.997770 | − | 0.0667498i | \(-0.978737\pi\) |
0.556692 | + | 0.830719i | \(0.312070\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −544.942 | + | 314.623i | −0.325478 | + | 0.187915i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −536.648 | − | 1142.88i | −0.313824 | − | 0.668340i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 39.9086 | − | 23.0413i | 0.0228568 | − | 0.0131964i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 157.470 | − | 272.746i | 0.0883532 | − | 0.153032i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 836.856 | + | 483.159i | 0.460120 | + | 0.265650i | 0.712095 | − | 0.702083i | \(-0.247747\pi\) |
−0.251975 | + | 0.967734i | \(0.581080\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1463.09i | − | 0.788505i | −0.919002 | − | 0.394252i | \(-0.871004\pi\) | ||
0.919002 | − | 0.394252i | \(-0.128996\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 104.550 | + | 181.087i | 0.0552445 | + | 0.0956862i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 759.914 | 0.393792 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −66.0424 | −0.0335717 | −0.0167859 | − | 0.999859i | \(-0.505343\pi\) | ||||
−0.0167859 | + | 0.999859i | \(0.505343\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 415.330 | + | 719.372i | 0.207156 | + | 0.358804i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2190.92i | 1.07247i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3052.95 | + | 1762.62i | 1.46703 | + | 0.846988i | 0.999319 | − | 0.0368953i | \(-0.0117468\pi\) |
0.467707 | + | 0.883883i | \(0.345080\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 812.859 | − | 1407.91i | 0.383521 | − | 0.664278i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −225.731 | + | 130.326i | −0.104596 | + | 0.0603887i | −0.551386 | − | 0.834250i | \(-0.685901\pi\) |
0.446789 | + | 0.894639i | \(0.352567\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2165.63 | − | 369.966i | −0.985719 | − | 0.168396i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −351.359 | + | 202.857i | −0.157129 | + | 0.0907186i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 455.876 | − | 789.601i | 0.200345 | − | 0.347007i | −0.748295 | − | 0.663366i | \(-0.769127\pi\) |
0.948640 | + | 0.316359i | \(0.102460\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3737.18 | − | 2157.66i | −1.61431 | − | 0.932023i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1629.57i | − | 0.692009i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1345.24 | − | 2330.03i | −0.561721 | − | 0.972930i | −0.997346 | − | 0.0728016i | \(-0.976806\pi\) |
0.435625 | − | 0.900128i | \(-0.356527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4773.85 | −1.96043 | −0.980213 | − | 0.197944i | \(-0.936573\pi\) | ||||
−0.980213 | + | 0.197944i | \(0.936573\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −617.364 | −0.249382 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3156.82 | + | 5467.77i | 1.25456 | + | 2.17296i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 625.844i | 0.244739i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −360.746 | − | 208.277i | −0.138838 | − | 0.0801582i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1028.74 | + | 1781.82i | −0.389721 | + | 0.675017i | −0.992412 | − | 0.122958i | \(-0.960762\pi\) |
0.602691 | + | 0.797975i | \(0.294095\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 632.089 | − | 364.937i | 0.235745 | − | 0.136107i | −0.377475 | − | 0.926020i | \(-0.623207\pi\) |
0.613219 | + | 0.789913i | \(0.289874\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1202.35 | − | 2560.60i | −0.441548 | − | 0.940351i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1473.21 | − | 850.557i | 0.532801 | − | 0.307613i | −0.209355 | − | 0.977840i | \(-0.567137\pi\) |
0.742156 | + | 0.670227i | \(0.233803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 920.440 | − | 1594.25i | 0.327881 | − | 0.567906i | −0.654211 | − | 0.756312i | \(-0.726999\pi\) |
0.982091 | + | 0.188407i | \(0.0603323\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1279.76 | + | 738.867i | 0.449090 | + | 0.259282i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 35.3404i | − | 0.0122188i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 59.0265 | + | 102.237i | 0.0201102 | + | 0.0348319i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1278.09 | −0.429147 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1214.31 | −0.401894 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 71.4850 | + | 123.816i | 0.0233234 | + | 0.0403972i | 0.877452 | − | 0.479665i | \(-0.159242\pi\) |
−0.854128 | + | 0.520063i | \(0.825909\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 2480.58i | − | 0.797964i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6287.63 | + | 3630.16i | 1.99448 | + | 1.15151i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 291.386 | − | 504.696i | 0.0911548 | − | 0.157885i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −171.786 | + | 99.1807i | −0.0530056 | + | 0.0306028i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 893.719 | + | 622.246i | 0.272027 | + | 0.189397i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2025.39 | − | 1169.36i | 0.608205 | − | 0.351148i | −0.164057 | − | 0.986451i | \(-0.552458\pi\) |
0.772263 | + | 0.635303i | \(0.219125\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1258.69 | − | 2180.12i | 0.372946 | − | 0.645962i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2840.01 | + | 1639.68i | 0.830388 | + | 0.479425i | 0.853986 | − | 0.520297i | \(-0.174179\pi\) |
−0.0235973 | + | 0.999722i | \(0.507512\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1143.72i | − | 0.330041i | −0.986290 | − | 0.165021i | \(-0.947231\pi\) | ||
0.986290 | − | 0.165021i | \(-0.0527690\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −623.376 | − | 1079.72i | −0.177555 | − | 0.307534i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4238.17 | 1.19164 | 0.595819 | − | 0.803118i | \(-0.296827\pi\) | ||||
0.595819 | + | 0.803118i | \(0.296827\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4219.59 | −1.17130 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −476.464 | − | 825.259i | −0.130589 | − | 0.226187i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3310.03i | 0.895849i | 0.894072 | + | 0.447924i | \(0.147837\pi\) | ||||
−0.894072 | + | 0.447924i | \(0.852163\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4938.82 | + | 2851.43i | 1.32007 | + | 0.762145i | 0.983740 | − | 0.179598i | \(-0.0574798\pi\) |
0.336333 | + | 0.941743i | \(0.390813\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | − | 210.444i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1828.98 | − | 1055.96i | 0.476936 | − | 0.275359i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1207.33 | + | 1734.07i | −0.311015 | + | 0.446705i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −367.499 | + | 212.175i | −0.0935313 | + | 0.0540003i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1955.12 | − | 3386.36i | 0.491657 | − | 0.851574i | −0.508297 | − | 0.861182i | \(-0.669725\pi\) |
0.999954 | + | 0.00960748i | \(0.00305820\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3312.85 | − | 1912.68i | −0.823230 | − | 0.475292i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1402.19i | 0.344347i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3486.40 | + | 6038.63i | 0.846209 | + | 1.46568i | 0.884567 | + | 0.466413i | \(0.154454\pi\) |
−0.0383576 | + | 0.999264i | \(0.512213\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4841.88 | 1.16162 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.6161 | 0.00488930 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 140.845 | + | 243.951i | 0.0330224 | + | 0.0571965i | 0.882064 | − | 0.471129i | \(-0.156153\pi\) |
−0.849042 | + | 0.528326i | \(0.822820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5570.23i | 1.29123i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1666.20 | + | 961.980i | 0.381909 | + | 0.220495i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2166.56 | + | 3752.60i | −0.491070 | + | 0.850558i | −0.999947 | − | 0.0102813i | \(-0.996727\pi\) |
0.508877 | + | 0.860839i | \(0.330061\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −371.175 | + | 214.298i | −0.0832003 | + | 0.0480357i | −0.541023 | − | 0.841008i | \(-0.681963\pi\) |
0.457823 | + | 0.889044i | \(0.348629\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2161.66 | − | 183.316i | −0.479229 | − | 0.0406403i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6525.15 | − | 3767.30i | 1.43084 | − | 0.826096i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4469.37 | − | 7741.18i | 0.969454 | − | 1.67914i | 0.272313 | − | 0.962209i | \(-0.412211\pi\) |
0.697140 | − | 0.716935i | \(-0.254455\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 294.419 | + | 169.983i | 0.0631771 | + | 0.0364753i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 775.819i | 0.164703i | 0.996603 | + | 0.0823514i | \(0.0262430\pi\) | ||||
−0.996603 | + | 0.0823514i | \(0.973757\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2007.27 | + | 3476.69i | 0.421624 | + | 0.730274i | 0.996098 | − | 0.0882484i | \(-0.0281269\pi\) |
−0.574475 | + | 0.818522i | \(0.694794\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2720.64 | −0.565463 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 90.5340 | 0.0186204 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2186.60 | + | 3787.31i | 0.445065 | + | 0.770875i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 3344.77i | − | 0.673793i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4292.21 | + | 2478.11i | 0.855814 | + | 0.494104i | 0.862608 | − | 0.505873i | \(-0.168829\pi\) |
−0.00679458 | + | 0.999977i | \(0.502163\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5463.77 | − | 9463.53i | 1.07835 | − | 1.86776i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 629.864 | − | 363.652i | 0.123059 | − | 0.0710480i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6025.15 | + | 2829.15i | −1.16536 | + | 0.547204i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4821.94 | − | 2783.95i | 0.923362 | − | 0.533103i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2384.86 | + | 4130.70i | −0.452167 | + | 0.783177i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3585.28 | − | 2069.96i | −0.673090 | − | 0.388608i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3894.90i | 0.724084i | 0.932162 | + | 0.362042i | \(0.117920\pi\) | ||||
−0.932162 | + | 0.362042i | \(0.882080\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 791.254 | + | 1370.49i | 0.145673 | + | 0.252312i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3097.44 | 0.564758 | 0.282379 | − | 0.959303i | \(-0.408876\pi\) | ||||
0.282379 | + | 0.959303i | \(0.408876\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4487.36 | 0.810353 | 0.405177 | − | 0.914238i | \(-0.367210\pi\) | ||||
0.405177 | + | 0.914238i | \(0.367210\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1396.66 | − | 2419.09i | −0.249819 | − | 0.432699i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 6820.62i | − | 1.20847i | −0.796807 | − | 0.604233i | \(-0.793479\pi\) | ||
0.796807 | − | 0.604233i | \(-0.206521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 53.4377 | + | 30.8523i | 0.00937911 | + | 0.00541503i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2627.95 | + | 4551.74i | −0.456940 | + | 0.791443i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 907.031 | − | 523.675i | 0.156249 | − | 0.0902106i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1107.85 | − | 13063.7i | 0.189084 | − | 2.22967i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2512.66 | − | 1450.68i | 0.424924 | − | 0.245330i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1617.99 | + | 2802.44i | −0.271132 | + | 0.469615i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4341.35 | − | 2506.48i | −0.720913 | − | 0.416219i | 0.0941759 | − | 0.995556i | \(-0.469978\pi\) |
−0.815088 | + | 0.579337i | \(0.803312\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2824.56i | 0.464819i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4954.70 | + | 8581.78i | 0.808071 | + | 1.39962i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3220.79 | −0.520616 | −0.260308 | − | 0.965526i | \(-0.583824\pi\) | ||||
−0.260308 | + | 0.965526i | \(0.583824\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5732.92 | −0.918494 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 508.762 | + | 881.202i | 0.0807948 | + | 0.139941i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6911.39i | − | 1.08799i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7422.37 | − | 4285.31i | −1.15828 | − | 0.668734i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1680.36 | + | 2910.46i | −0.259960 | + | 0.450265i | −0.966231 | − | 0.257677i | \(-0.917043\pi\) |
0.706271 | + | 0.707942i | \(0.250376\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3976.20 | − | 2295.66i | 0.609859 | − | 0.352102i | −0.163051 | − | 0.986618i | \(-0.552134\pi\) |
0.772910 | + | 0.634515i | \(0.218800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 106.939 | − | 1261.02i | 0.0162621 | − | 0.191762i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1506.96 | − | 870.044i | 0.227216 | − | 0.131183i | −0.382071 | − | 0.924133i | \(-0.624789\pi\) |
0.609287 | + | 0.792950i | \(0.291456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8317.12 | − | 14405.7i | 1.24346 | − | 2.15373i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 931.262 | + | 537.664i | 0.138061 | + | 0.0797093i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1425.49i | 0.209567i | 0.994495 | + | 0.104784i | \(0.0334150\pi\) | ||||
−0.994495 | + | 0.104784i | \(0.966585\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2413.42 | − | 4180.17i | −0.351862 | − | 0.609443i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1816.16 | −0.262600 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1330.17 | −0.190752 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5424.61 | + | 9395.69i | 0.771559 | + | 1.33638i | 0.936708 | + | 0.350111i | \(0.113856\pi\) |
−0.165149 | + | 0.986269i | \(0.552811\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 52.8138i | 0.00745089i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3699.46 | + | 2135.89i | 0.517700 | + | 0.298894i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 247.374 | − | 428.465i | 0.0343393 | − | 0.0594774i | −0.848345 | − | 0.529444i | \(-0.822401\pi\) |
0.882684 | + | 0.469966i | \(0.155734\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8086.13 | − | 4668.53i | 1.11351 | − | 0.642885i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 97.1882 | − | 45.6354i | 0.0132770 | − | 0.00623433i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10949.4 | + | 6321.66i | −1.48400 | + | 0.856786i | −0.999835 | − | 0.0181912i | \(-0.994209\pi\) |
−0.484163 | + | 0.874978i | \(0.660876\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1849.67 | − | 3203.72i | 0.248718 | − | 0.430792i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2010.48 | − | 1160.75i | −0.268227 | − | 0.154861i | 0.359855 | − | 0.933008i | \(-0.382826\pi\) |
−0.628082 | + | 0.778147i | \(0.716160\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 8360.47i | − | 1.10673i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1624.04 | + | 2812.92i | 0.213319 | + | 0.369480i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10477.6 | 1.36564 | 0.682821 | − | 0.730586i | \(-0.260753\pi\) | ||||
0.682821 | + | 0.730586i | \(0.260753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3299.38 | 0.426744 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1912.35 | + | 3312.28i | 0.245458 | + | 0.425146i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 6390.14i | − | 0.813982i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1530.14 | + | 883.424i | 0.193439 | + | 0.111682i | 0.593592 | − | 0.804766i | \(-0.297709\pi\) |
−0.400152 | + | 0.916449i | \(0.631043\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1043.22 | + | 1806.91i | −0.130893 | + | 0.226713i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4331.55 | + | 2500.82i | −0.539420 | + | 0.311434i | −0.744844 | − | 0.667239i | \(-0.767476\pi\) |
0.205424 | + | 0.978673i | \(0.434143\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1764.21 | + | 149.612i | 0.218069 | + | 0.0184930i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1411.20 | − | 814.754i | 0.173143 | − | 0.0999641i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4226.98 | + | 7321.34i | −0.514800 | + | 0.891660i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9706.92 | − | 5604.29i | −1.17354 | − | 0.677541i | −0.219025 | − | 0.975719i | \(-0.570288\pi\) |
−0.954510 | + | 0.298178i | \(0.903621\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6093.96i | − | 0.731370i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4190.13 | − | 7257.51i | −0.499232 | − | 0.864695i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2845.61 | −0.336592 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4336.99 | −0.509313 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1642.59 | + | 2845.06i | 0.191518 | + | 0.331719i | 0.945753 | − | 0.324885i | \(-0.105326\pi\) |
−0.754236 | + | 0.656604i | \(0.771992\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13289.9i | 1.53850i | 0.638948 | + | 0.769250i | \(0.279370\pi\) | ||||
−0.638948 | + | 0.769250i | \(0.720630\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1634.83 | − | 943.868i | −0.187915 | − | 0.108493i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3249.31 | + | 5627.96i | −0.370858 | + | 0.642344i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2749.52 | + | 1587.44i | −0.311613 | + | 0.179910i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2164.32 | − | 3108.58i | 0.243577 | − | 0.349845i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11857.8 | + | 6846.13i | −1.32523 | + | 0.765119i | −0.984557 | − | 0.175064i | \(-0.943987\pi\) |
−0.340668 | + | 0.940184i | \(0.610653\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5001.26 | + | 8662.43i | −0.555070 | + | 0.961409i | 0.442829 | + | 0.896606i | \(0.353975\pi\) |
−0.997898 | + | 0.0648023i | \(0.979358\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 119.726 | + | 69.1238i | 0.0131964 | + | 0.00761892i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6401.73i | 0.700769i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2243.60 | − | 3886.04i | −0.243921 | − | 0.422484i | 0.717907 | − | 0.696139i | \(-0.245100\pi\) |
−0.961828 | + | 0.273656i | \(0.911767\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 944.821 | 0.102021 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2035.35 | −0.218290 | −0.109145 | − | 0.994026i | \(-0.534811\pi\) | ||||
−0.109145 | + | 0.994026i | \(0.534811\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6450.84 | + | 11173.2i | 0.687190 | + | 1.19025i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2898.95i | 0.306747i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3096.55 | − | 1787.79i | −0.325468 | − | 0.187909i | 0.328359 | − | 0.944553i | \(-0.393504\pi\) |
−0.653827 | + | 0.756644i | \(0.726838\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −79.0365 | + | 136.895i | −0.00825207 | + | 0.0142930i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3801.21 | − | 2194.63i | 0.394252 | − | 0.227622i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11939.0 | − | 8312.41i | −1.23012 | − | 0.856465i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6978.95 | + | 4029.30i | −0.714358 | + | 0.412435i | −0.812672 | − | 0.582721i | \(-0.801988\pi\) |
0.0983147 | + | 0.995155i | \(0.468655\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −313.651 | + | 543.260i | −0.0318954 | + | 0.0552445i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10125.7 | + | 5846.07i | 1.02300 | + | 0.590626i | 0.914970 | − | 0.403522i | \(-0.132214\pi\) |
0.108025 | + | 0.994148i | \(0.465547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1732.40i | − | 0.173891i | −0.996213 | − | 0.0869455i | \(-0.972289\pi\) | ||
0.996213 | − | 0.0869455i | \(-0.0277106\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1139.87 | + | 1974.31i | 0.113678 | + | 0.196896i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10769.9 | 1.06718 | 0.533588 | − | 0.845745i | \(-0.320843\pi\) | ||||
0.533588 | + | 0.845745i | \(0.320843\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7599.44 | 0.748208 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −99.0636 | − | 171.583i | −0.00969132 | − | 0.0167859i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9721.58i | 0.945029i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10919.8 | − | 6304.57i | −1.05481 | − | 0.608997i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1245.99 | + | 2158.12i | −0.119601 | + | 0.207156i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6851.68 | + | 3955.82i | −0.653572 | + | 0.377340i | −0.789824 | − | 0.613334i | \(-0.789828\pi\) |
0.136251 | + | 0.990674i | \(0.456495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6252.37 | + | 13315.5i | 0.592689 | + | 1.26223i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5692.17 | + | 3286.37i | −0.536237 | + | 0.309597i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11214.7 | − | 19424.4i | 1.04996 | − | 1.81859i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9495.78 | + | 5482.39i | 0.883562 | + | 0.510125i | 0.871831 | − | 0.489806i | \(-0.162933\pi\) |
0.0117307 | + | 0.999931i | \(0.496266\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10575.7i | 0.978018i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4569.69 | + | 7914.93i | 0.420014 | + | 0.727486i | 0.995940 | − | 0.0900157i | \(-0.0286917\pi\) |
−0.575926 | + | 0.817502i | \(0.695358\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −53.2204 | −0.00486192 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4877.16 | 0.442852 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6378.35 | − | 11047.6i | −0.575670 | − | 0.997090i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 12577.5i | − | 1.12835i | −0.825655 | − | 0.564175i | \(-0.809194\pi\) | ||
0.825655 | − | 0.564175i | \(-0.190806\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −677.193 | − | 390.978i | −0.0603887 | − | 0.0348655i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6607.30 | − | 11444.2i | 0.585696 | − | 1.01446i | −0.409092 | − | 0.912493i | \(-0.634155\pi\) |
0.994788 | − | 0.101962i | \(-0.0325120\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27699.6 | + | 15992.4i | −2.44083 | + | 1.40921i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2287.24 | − | 6181.41i | −0.200355 | − | 0.541471i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18809.9 | + | 10859.9i | −1.63798 | + | 0.945689i | −0.656454 | + | 0.754366i | \(0.727945\pi\) |
−0.981527 | + | 0.191323i | \(0.938722\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −510.050 | + | 883.432i | −0.0441551 | + | 0.0764789i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1054.08 | − | 608.572i | −0.0907186 | − | 0.0523764i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10612.0i | 0.907999i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2825.02 | − | 4893.07i | −0.240317 | − | 0.416242i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2735.26 | 0.231338 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4627.05 | −0.389088 | −0.194544 | − | 0.980894i | \(-0.562323\pi\) | ||||
−0.194544 | + | 0.980894i | \(0.562323\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6891.98 | + | 11937.3i | 0.576224 | + | 0.998049i | 0.995907 | + | 0.0903788i | \(0.0288078\pi\) |
−0.419683 | + | 0.907671i | \(0.637859\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 12946.0i | − | 1.07621i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −760.040 | − | 438.809i | −0.0628233 | − | 0.0362710i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3999.93 | + | 6928.07i | −0.328752 | + | 0.569415i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4233.74 | − | 2444.35i | 0.346005 | − | 0.199766i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 116.907 | + | 248.974i | 0.00950061 | + | 0.0202331i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30523.0 | + | 17622.5i | −2.46659 | + | 1.42409i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4035.73 | − | 6990.08i | 0.324310 | − | 0.561721i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2449.01 | + | 1413.93i | 0.195707 | + | 0.112992i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 454.638i | 0.0361302i | 0.999837 | + | 0.0180651i | \(0.00575061\pi\) | ||||
−0.999837 | + | 0.0180651i | \(0.994249\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7160.77 | − | 12402.8i | −0.565926 | − | 0.980213i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19456.0 | 1.52918 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11611.4 | −0.907621 | −0.453810 | − | 0.891098i | \(-0.649936\pi\) | ||||
−0.453810 | + | 0.891098i | \(0.649936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −926.047 | − | 1603.96i | −0.0719904 | − | 0.124691i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 103.263i | − | 0.00798390i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4244.00 | − | 2450.28i | −0.326353 | − | 0.188420i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9470.45 | + | 16403.3i | −0.724321 | + | 1.25456i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4229.61 | − | 2441.97i | 0.321749 | − | 0.185762i | −0.330423 | − | 0.943833i | \(-0.607191\pi\) |
0.652172 | + | 0.758071i | \(0.273858\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13882.6 | + | 9665.69i | 1.05040 | + | 0.731333i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1625.99 | + | 938.766i | −0.122370 | + | 0.0706501i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9808.67 | + | 16989.1i | −0.734256 | + | 1.27177i | 0.220793 | + | 0.975321i | \(0.429136\pi\) |
−0.955049 | + | 0.296448i | \(0.904198\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33293.3 | − | 19221.9i | −2.47905 | − | 1.43128i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1249.66i | − | 0.0925587i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3737.59 | + | 6473.70i | 0.275374 | + | 0.476963i | 0.970230 | − | 0.242187i | \(-0.0778648\pi\) |
−0.694855 | + | 0.719150i | \(0.744531\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7799.56 | −0.571631 | −0.285816 | − | 0.958285i | \(-0.592265\pi\) | ||||
−0.285816 | + | 0.958285i | \(0.592265\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6172.42 | −0.450011 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19860.8 | − | 34399.9i | −1.44044 | − | 2.49491i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 13136.1i | − | 0.947771i | −0.880587 | − | 0.473885i | \(-0.842851\pi\) | ||
0.880587 | − | 0.473885i | \(-0.157149\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1896.27 | + | 1094.81i | 0.136107 | + | 0.0785816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1091.14 | + | 1889.91i | −0.0779142 | + | 0.134951i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6459.29 | + | 3729.27i | −0.458862 | + | 0.264924i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4849.12 | − | 6964.69i | 0.342712 | − | 0.492230i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19183.1 | − | 11075.3i | 1.34884 | − | 0.778754i | 0.360756 | − | 0.932660i | \(-0.382519\pi\) |
0.988085 | + | 0.153907i | \(0.0491855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 851.414 | − | 1474.69i | 0.0595618 | − | 0.103164i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4419.63 | + | 2551.67i | 0.307613 | + | 0.177600i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 22770.3i | − | 1.57684i | −0.615138 | − | 0.788419i | \(-0.710900\pi\) | ||
0.615138 | − | 0.788419i | \(-0.289100\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3605.47 | + | 6244.86i | 0.248420 | + | 0.430276i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5522.64 | 0.378604 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7214.11 | 0.492088 | 0.246044 | − | 0.969259i | \(-0.420869\pi\) | ||||
0.246044 | + | 0.969259i | \(0.420869\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13638.4 | − | 23622.4i | −0.925658 | − | 1.60329i | −0.790499 | − | 0.612464i | \(-0.790179\pi\) |
−0.135160 | − | 0.990824i | \(-0.543155\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4433.20i | 0.299393i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10547.2 | − | 6089.41i | −0.708765 | − | 0.409206i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5783.08 | − | 10016.6i | 0.386701 | − | 0.669787i | −0.605302 | − | 0.795996i | \(-0.706948\pi\) |
0.992004 | + | 0.126209i | \(0.0402810\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 91.8170 | − | 53.0106i | 0.00610938 | − | 0.00352725i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9796.20 | − | 830.752i | −0.648628 | − | 0.0550059i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21197.3 | + | 12238.3i | −1.39666 | + | 0.806362i | −0.994041 | − | 0.109006i | \(-0.965233\pi\) |
−0.402619 | + | 0.915368i | \(0.631900\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −177.079 | + | 306.711i | −0.0116106 | + | 0.0201102i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2098.62 | + | 1211.64i | 0.136933 | + | 0.0790581i | 0.566901 | − | 0.823786i | \(-0.308142\pi\) |
−0.429969 | + | 0.902844i | \(0.641475\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 17223.4i | − | 1.11836i | −0.829045 | − | 0.559182i | \(-0.811115\pi\) | ||
0.829045 | − | 0.559182i | \(-0.188885\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1917.14 | − | 3320.58i | −0.123884 | − | 0.214573i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9894.22 | 0.636282 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27648.7 | 1.76952 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1821.47 | − | 3154.88i | −0.116017 | − | 0.200947i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 7291.57i | − | 0.462216i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8004.31 | + | 4621.29i | 0.504987 | + | 0.291554i | 0.730771 | − | 0.682623i | \(-0.239161\pi\) |
−0.225784 | + | 0.974177i | \(0.572494\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −214.455 | + | 371.447i | −0.0134657 | + | 0.0233234i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21483.5 | − | 12403.5i | 1.34259 | − | 0.775147i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4454.06 | − | 2091.43i | 0.277043 | − | 0.130087i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6444.73 | − | 3720.87i | 0.398982 | − | 0.230352i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5799.42 | + | 10044.9i | −0.357353 | + | 0.618953i | −0.987518 | − | 0.157508i | \(-0.949654\pi\) |
0.630165 | + | 0.776461i | \(0.282987\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21965.8 | − | 12682.0i | −1.34720 | − | 0.777804i | −0.359345 | − | 0.933205i | \(-0.617000\pi\) |
−0.987852 | + | 0.155401i | \(0.950333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21781.0i | 1.32965i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3295.05 | + | 5707.19i | 0.200219 | + | 0.346789i | 0.948599 | − | 0.316481i | \(-0.102501\pi\) |
−0.748380 | + | 0.663270i | \(0.769168\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14632.0 | 0.884985 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1748.32 | 0.105257 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7849.12 | − | 13595.1i | −0.470382 | − | 0.814726i | 0.529044 | − | 0.848594i | \(-0.322551\pi\) |
−0.999426 | + | 0.0338683i | \(0.989217\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25647.6i | 1.52998i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −515.358 | − | 297.542i | −0.0306028 | − | 0.0176685i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1420.41 | − | 2460.22i | 0.0839624 | − | 0.145427i | −0.820986 | − | 0.570948i | \(-0.806576\pi\) |
0.904949 | + | 0.425521i | \(0.139909\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18029.9 | − | 10409.5i | 1.06094 | − | 0.612533i | 0.135247 | − | 0.990812i | \(-0.456817\pi\) |
0.925692 | + | 0.378279i | \(0.123484\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −276.063 | + | 3255.32i | −0.0161710 | + | 0.190688i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12116.8 | + | 6995.63i | −0.706569 | + | 0.407938i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 162.650 | − | 281.718i | 0.00944202 | − | 0.0163541i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6076.16 | + | 3508.07i | 0.351148 | + | 0.202735i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5543.36i | − | 0.318925i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15632.3 | + | 27075.9i | 0.895364 | + | 1.55082i | 0.833354 | + | 0.552740i | \(0.186418\pi\) |
0.0620102 | + | 0.998076i | \(0.480249\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7552.16 | 0.430641 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27953.2 | −1.58689 | −0.793447 | − | 0.608639i | \(-0.791716\pi\) | ||||
−0.793447 | + | 0.608639i | \(0.791716\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8600.46 | − | 14896.4i | −0.486090 | − | 0.841933i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9838.09i | 0.553592i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30059.7 | − | 17354.9i | −1.68404 | − | 0.972282i | −0.958926 | − | 0.283655i | \(-0.908453\pi\) |
−0.725116 | − | 0.688627i | \(-0.758214\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20432.4 | − | 35390.0i | 1.13968 | − | 1.97399i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2971.48 | − | 1715.59i | 0.165021 | − | 0.0952747i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1096.67 | + | 12931.8i | −0.0606381 | + | 0.715042i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10271.7 | + | 5930.39i | −0.565492 | + | 0.326487i | −0.755347 | − | 0.655325i | \(-0.772532\pi\) |
0.189855 | + | 0.981812i | \(0.439198\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1870.13 | − | 3239.16i | 0.102511 | − | 0.177555i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25186.6 | − | 14541.5i | −1.37465 | − | 0.793655i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 136.338i | − | 0.00740916i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6357.26 | + | 11011.1i | 0.343996 | + | 0.595819i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16100.5 | −0.867486 | −0.433743 | − | 0.901037i | \(-0.642807\pi\) | ||||
−0.433743 | + | 0.901037i | \(0.642807\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14147.7 | 0.759019 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6329.39 | − | 10962.8i | −0.338125 | − | 0.585650i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24528.9i | 1.30482i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24651.8 | + | 14232.7i | 1.30581 | + | 0.753910i | 0.981394 | − | 0.192005i | \(-0.0614990\pi\) |
0.324416 | + | 0.945915i | \(0.394832\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1429.39 | − | 2475.78i | 0.0753957 | − | 0.130589i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4645.60 | − | 2682.14i | 0.244010 | − | 0.140879i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22991.8 | − | 10796.0i | 1.20258 | − | 0.564680i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8599.70 | + | 4965.04i | −0.447924 | + | 0.258609i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13911.0 | − | 24094.6i | 0.721550 | − | 1.24976i | −0.238829 | − | 0.971062i | \(-0.576763\pi\) |
0.960378 | − | 0.278699i | \(-0.0899033\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7047.93 | + | 4069.13i | 0.364048 | + | 0.210183i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17108.6i | 0.880049i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 320.363 | + | 554.884i | 0.0164110 | + | 0.0284247i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 866.153 | 0.0441869 | 0.0220934 | − | 0.999756i | \(-0.492967\pi\) | ||||
0.0220934 | + | 0.999756i | \(0.492967\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4192.45 | − | 7261.53i | −0.212125 | − | 0.367411i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23120.1i | 1.16502i | 0.812823 | + | 0.582511i | \(0.197930\pi\) | ||||
−0.812823 | + | 0.582511i | \(0.802070\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5486.94 | + | 3167.89i | 0.275359 | + | 0.158979i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6634.34 | + | 11491.0i | −0.331586 | + | 0.574324i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17983.1 | + | 10382.6i | −0.895156 | + | 0.516819i | −0.875626 | − | 0.482990i | \(-0.839551\pi\) |
−0.0195308 | + | 0.999809i | \(0.506217\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6316.24 | − | 535.639i | −0.313135 | − | 0.0265549i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32039.3 | + | 18497.9i | −1.58198 | + | 0.913354i | −0.587405 | + | 0.809293i | \(0.699850\pi\) |
−0.994571 | + | 0.104061i | \(0.966816\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9719.90 | + | 16835.4i | −0.477999 | + | 0.827919i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1102.50 | − | 636.526i | −0.0540003 | − | 0.0311771i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27029.1i | 1.31859i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17214.6 | + | 29816.5i | 0.836443 | + | 1.44876i | 0.892851 | + | 0.450353i | \(0.148702\pi\) |
−0.0564080 | + | 0.998408i | \(0.517965\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11730.7 | 0.567716 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29433.5 | 1.41880 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2134.44 | − | 3696.96i | −0.102480 | − | 0.177501i | 0.810226 | − | 0.586118i | \(-0.199345\pi\) |
−0.912706 | + | 0.408617i | \(0.866011\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 11476.1i | − | 0.548820i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6358.45 | + | 3671.05i | 0.302883 | + | 0.174869i | 0.643737 | − | 0.765247i | \(-0.277383\pi\) |
−0.340854 | + | 0.940116i | \(0.610716\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7460.33 | − | 12921.7i | 0.353974 | − | 0.613100i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3642.99 | + | 2103.28i | −0.172173 | + | 0.0994044i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14547.9 | − | 20894.8i | 0.684867 | − | 0.983661i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12755.2 | − | 7364.23i | 0.598134 | − | 0.345333i | −0.170173 | − | 0.985414i | \(-0.554433\pi\) |
0.768307 | + | 0.640081i | \(0.221099\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10459.2 | + | 18115.9i | −0.488559 | + | 0.846209i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8606.05 | + | 4968.71i | 0.400437 | + | 0.231193i | 0.686673 | − | 0.726967i | \(-0.259071\pi\) |
−0.286235 | + | 0.958159i | \(0.592404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10565.7i | 0.489719i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7262.83 | + | 12579.6i | 0.335331 | + | 0.580811i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 264.535 | 0.0121668 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22273.3 | 1.02049 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.9242 | + | 53.5623i | 0.00141142 | + | 0.00244465i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1328.60i | − | 0.0604074i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31441.1 | + | 18152.5i | 1.42408 | + | 0.822194i | 0.996645 | − | 0.0818508i | \(-0.0260831\pi\) |
0.427437 | + | 0.904045i | \(0.359416\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −422.536 | + | 731.854i | −0.0190655 | + | 0.0330224i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25532.4 | + | 14741.2i | −1.14770 | + | 0.662623i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7916.04 | − | 5511.49i | −0.354485 | − | 0.246808i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14471.9 | + | 8355.35i | −0.645616 | + | 0.372747i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4575.37 | + | 7924.77i | −0.203347 | + | 0.352208i | −0.949605 | − | 0.313449i | \(-0.898515\pi\) |
0.746258 | + | 0.665657i | \(0.231849\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4220.29 | + | 2436.59i | 0.186863 | + | 0.107885i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5771.88i | 0.254606i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −890.550 | − | 1542.48i | −0.0391368 | − | 0.0677869i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −44075.5 | −1.92976 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12999.4 | −0.567038 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15174.9 | − | 26283.8i | −0.659484 | − | 1.14226i | −0.980749 | − | 0.195271i | \(-0.937441\pi\) |
0.321265 | − | 0.946989i | \(-0.395892\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4238.72i | − | 0.183529i | −0.995781 | − | 0.0917643i | \(-0.970749\pi\) | ||
0.995781 | − | 0.0917643i | \(-0.0292506\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1113.53 | − | 642.894i | −0.0480357 | − | 0.0277334i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35459.3 | + | 61417.3i | −1.52403 | + | 2.63970i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14089.4 | − | 8134.53i | 0.603337 | − | 0.348337i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2766.22 | − | 5891.13i | −0.118021 | − | 0.251346i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5139.41 | + | 2967.24i | −0.218473 | + | 0.126136i | −0.605243 | − | 0.796041i | \(-0.706924\pi\) |
0.386770 | + | 0.922176i | \(0.373591\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11229.8 | − | 19450.6i | 0.475633 | − | 0.823820i | −0.523978 | − | 0.851732i | \(-0.675552\pi\) |
0.999610 | + | 0.0279120i | \(0.00888582\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 19575.4 | + | 11301.9i | 0.826096 | + | 0.476947i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 20138.4i | − | 0.846772i | −0.905949 | − | 0.423386i | \(-0.860841\pi\) | ||
0.905949 | − | 0.423386i | \(-0.139159\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2922.85 | + | 5062.53i | 0.122455 | + | 0.212098i | 0.920735 | − | 0.390188i | \(-0.127590\pi\) |
−0.798281 | + | 0.602286i | \(0.794257\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26816.2 | 1.11943 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2439.05 | −0.101450 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2621.82 | − | 4541.12i | −0.108661 | − | 0.188206i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1019.90i | 0.0421180i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24058.1 | − | 13889.9i | −0.989961 | − | 0.571554i | −0.0846986 | − | 0.996407i | \(-0.526993\pi\) |
−0.905263 | + | 0.424852i | \(0.860326\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12191.9 | − | 21116.9i | 0.499892 | − | 0.865839i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2015.64 | + | 1163.73i | −0.0823514 | + | 0.0475456i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7442.75 | − | 43566.7i | 0.303004 | − | 1.77366i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8088.55 | + | 4669.92i | −0.328130 | + | 0.189446i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6021.80 | + | 10430.1i | −0.243425 | + | 0.421624i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38597.3 | + | 22284.2i | 1.55476 | + | 0.897640i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16480.5i | 0.661526i | 0.943714 | + | 0.330763i | \(0.107306\pi\) | ||||
−0.943714 | + | 0.330763i | \(0.892694\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4080.96 | − | 7068.43i | −0.163235 | − | 0.282731i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45445.2 | 1.81141 | 0.905704 | − | 0.423910i | \(-0.139343\pi\) | ||||
0.905704 | + | 0.423910i | \(0.139343\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28243.1 | 1.12182 | 0.560909 | − | 0.827877i | \(-0.310452\pi\) | ||||
0.560909 | + | 0.827877i | \(0.310452\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 135.801 | + | 235.214i | 0.00537524 | + | 0.00931020i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 328.319i | − | 0.0129503i | −0.999979 | − | 0.00647514i | \(-0.997939\pi\) | ||
0.999979 | − | 0.00647514i | \(-0.00206112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15884.7 | + | 9171.05i | 0.624389 | + | 0.360491i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6559.81 | + | 11361.9i | −0.256958 | + | 0.445065i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7410.06 | − | 4278.20i | 0.289262 | − | 0.167006i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9813.24 | + | 20898.9i | 0.381755 | + | 0.813012i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8689.96 | − | 5017.15i | 0.336897 | − | 0.194507i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24008.5 | − | 41584.0i | 0.927584 | − | 1.60662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36788.7 | + | 21240.0i | 1.41650 | + | 0.817815i | 0.995989 | − | 0.0894746i | \(-0.0285188\pi\) |
0.420507 | + | 0.907289i | \(0.361852\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14868.6i | 0.570542i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2610.47 | − | 4521.47i | −0.0998287 | − | 0.172908i | 0.811785 | − | 0.583956i | \(-0.198496\pi\) |
−0.911614 | + | 0.411048i | \(0.865163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11790.3 | 0.449349 | 0.224674 | − | 0.974434i | \(-0.427868\pi\) | ||||
0.224674 | + | 0.974434i | \(0.427868\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32782.6 | 1.24517 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24676.2 | − | 42740.4i | −0.934097 | − | 1.61790i | −0.776236 | − | 0.630443i | \(-0.782873\pi\) |
−0.157861 | − | 0.987461i | \(-0.550460\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 19024.4i | − | 0.717724i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1889.59 | + | 1090.96i | 0.0710480 | + | 0.0410196i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4727.67 | + | 8188.56i | −0.177162 | + | 0.306853i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46874.1 | − | 27062.8i | 1.75065 | − | 1.01074i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16388.1 | − | 11410.1i | −0.610013 | − | 0.424717i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −74.9355 | + | 43.2640i | −0.00278002 | + | 0.00160505i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3216.51 | − | 5571.16i | 0.118932 | − | 0.205996i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14465.8 | + | 8351.84i | 0.533103 | + | 0.307787i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 96037.3i | − | 3.52750i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3044.47 | − | 5273.17i | −0.111455 | − | 0.193046i | 0.804902 | − | 0.593408i | \(-0.202218\pi\) |
−0.916357 | + | 0.400362i | \(0.868884\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14309.2 | −0.522118 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30301.7 | 1.10202 | 0.551010 | − | 0.834499i | \(-0.314243\pi\) | ||||
0.551010 | + | 0.834499i | \(0.314243\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1905.14 | − | 3299.80i | −0.0690590 | − | 0.119614i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 12419.8i | − | 0.448726i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17033.8 | + | 9834.49i | 0.613421 | + | 0.354159i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17347.9 | − | 30047.4i | 0.622692 | − | 1.07853i | −0.366290 | − | 0.930501i | \(-0.619372\pi\) |
0.988982 | − | 0.148034i | \(-0.0472945\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10119.3 | + | 5842.36i | −0.362042 | + | 0.209025i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22145.2 | − | 31806.7i | 0.789728 | − | 1.13427i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −76023.1 | + | 43892.0i | −2.70230 | + | 1.56017i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2373.76 | + | 4111.47i | −0.0841041 | + | 0.145673i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14714.5 | − | 8495.40i | −0.519662 | − | 0.300027i | 0.217134 | − | 0.976142i | \(-0.430329\pi\) |
−0.736796 | + | 0.676115i | \(0.763662\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4732.44i | − | 0.166594i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4646.16 | + | 8047.38i | 0.163032 | + | 0.282379i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12590.3 | −0.440372 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9307.86 | 0.324519 | 0.162260 | − | 0.986748i | \(-0.448122\pi\) | ||||
0.162260 | + | 0.986748i | \(0.448122\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6731.04 | + | 11658.5i | 0.233929 | + | 0.405177i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 52285.3i | − | 1.81132i | −0.424006 | − | 0.905659i | \(-0.639377\pi\) | ||
0.424006 | − | 0.905659i | \(-0.360623\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 721.697 | + | 416.672i | 0.0249222 | + | 0.0143889i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4189.98 | − | 7257.26i | 0.144233 | − | 0.249819i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10694.1 | + | 6174.26i | −0.366962 | + | 0.211865i | −0.672130 | − | 0.740433i | \(-0.734621\pi\) |
0.305169 | + | 0.952298i | \(0.401287\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3088.13 | − | 261.884i | −0.105632 | − | 0.00895797i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17720.5 | − | 10230.9i | 0.604233 | − | 0.348854i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12815.5 | + | 22197.1i | −0.435609 | + | 0.754497i | −0.997345 | − | 0.0728193i | \(-0.976800\pi\) |
0.561736 | + | 0.827317i | \(0.310134\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35845.7 | − | 20695.5i | −1.21459 | − | 0.701247i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 185.114i | 0.00625274i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15669.5 | − | 27140.4i | −0.527627 | − | 0.913878i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28364.1 | 0.952104 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15767.7 | −0.527629 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7341.57 | + | 12716.0i | 0.244905 | + | 0.424188i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 11185.6i | − | 0.371981i | −0.982552 | − | 0.185991i | \(-0.940451\pi\) | ||
0.982552 | − | 0.185991i | \(-0.0595494\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2721.09 | + | 1571.02i | 0.0902106 | + | 0.0520831i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11770.6 | + | 20387.3i | −0.389019 | + | 0.673801i | −0.992318 | − | 0.123714i | \(-0.960519\pi\) |
0.603299 | + | 0.797515i | \(0.293853\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19315.4 | + | 11151.8i | −0.636408 | + | 0.367430i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 35602.3 | − | 16717.3i | 1.16942 | − | 0.549109i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20956.8 | + | 12099.4i | −0.686251 | + | 0.396207i | −0.802206 | − | 0.597047i | \(-0.796341\pi\) |
0.115955 | + | 0.993254i | \(0.463007\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8637.68 | + | 14960.9i | −0.281983 | + | 0.488409i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7537.97 | + | 4352.05i | 0.245330 | + | 0.141641i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33757.4i | 1.09532i | 0.836702 | + | 0.547658i | \(0.184480\pi\) | ||||
−0.836702 | + | 0.547658i | \(0.815520\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17111.0 | + | 29637.1i | 0.553504 | + | 0.958697i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9707.93 | −0.313077 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51251.1 | 1.64782 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12649.3 | + | 21909.2i | 0.405466 | + | 0.702288i | 0.994376 | − | 0.105911i | \(-0.0337758\pi\) |
−0.588909 | + | 0.808199i | \(0.700442\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 15038.9i | − | 0.480608i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32072.1 | + | 18516.8i | 1.02186 | + | 0.589973i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14383.0 | − | 24912.2i | 0.456886 | − | 0.791350i | −0.541908 | − | 0.840438i | \(-0.682298\pi\) |
0.998794 | + | 0.0490874i | \(0.0156313\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7338.41 | + | 4236.83i | −0.232409 | + | 0.134182i |
(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 | 624.4.bv.h.49.5 | 10 | ||
4.3 | odd | 2 | 39.4.j.c.10.5 | yes | 10 | ||
12.11 | even | 2 | 117.4.q.e.10.1 | 10 | |||
13.4 | even | 6 | inner | 624.4.bv.h.433.1 | 10 | ||
52.3 | odd | 6 | 507.4.b.i.337.9 | 10 | |||
52.11 | even | 12 | 507.4.a.r.1.2 | 10 | |||
52.15 | even | 12 | 507.4.a.r.1.9 | 10 | |||
52.23 | odd | 6 | 507.4.b.i.337.2 | 10 | |||
52.43 | odd | 6 | 39.4.j.c.4.5 | ✓ | 10 | ||
156.11 | odd | 12 | 1521.4.a.bk.1.9 | 10 | |||
156.95 | even | 6 | 117.4.q.e.82.1 | 10 | |||
156.119 | odd | 12 | 1521.4.a.bk.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.5 | ✓ | 10 | 52.43 | odd | 6 | ||
39.4.j.c.10.5 | yes | 10 | 4.3 | odd | 2 | ||
117.4.q.e.10.1 | 10 | 12.11 | even | 2 | |||
117.4.q.e.82.1 | 10 | 156.95 | even | 6 | |||
507.4.a.r.1.2 | 10 | 52.11 | even | 12 | |||
507.4.a.r.1.9 | 10 | 52.15 | even | 12 | |||
507.4.b.i.337.2 | 10 | 52.23 | odd | 6 | |||
507.4.b.i.337.9 | 10 | 52.3 | odd | 6 | |||
624.4.bv.h.49.5 | 10 | 1.1 | even | 1 | trivial | ||
624.4.bv.h.433.1 | 10 | 13.4 | even | 6 | inner | ||
1521.4.a.bk.1.2 | 10 | 156.119 | odd | 12 | |||
1521.4.a.bk.1.9 | 10 | 156.11 | odd | 12 |