Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,4,Mod(1,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.a (trivial) |
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: | yes |
Analytic conductor: | \(40.8883236340\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.509800.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 10x^{2} + 5x + 15 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.11082\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.65527 | 1.29233 | 0.646167 | − | 0.763196i | \(-0.276371\pi\) | ||||
0.646167 | + | 0.763196i | \(0.276371\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.36103 | 0.670129 | ||||||||
\(5\) | 10.0822 | 0.901782 | 0.450891 | − | 0.892579i | \(-0.351106\pi\) | ||||
0.450891 | + | 0.892579i | \(0.351106\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −9.64616 | −0.426304 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 36.8533 | 1.16540 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −84.5724 | −1.80432 | −0.902161 | − | 0.431400i | \(-0.858020\pi\) | ||||
−0.902161 | + | 0.431400i | \(0.858020\pi\) | |||||||
\(14\) | −25.5869 | −0.488457 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −78.1476 | −1.22106 | ||||||||
\(17\) | 38.2525 | 0.545741 | 0.272871 | − | 0.962051i | \(-0.412027\pi\) | ||||
0.272871 | + | 0.962051i | \(0.412027\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −127.283 | −1.53688 | −0.768442 | − | 0.639919i | \(-0.778968\pi\) | ||||
−0.768442 | + | 0.639919i | \(0.778968\pi\) | |||||||
\(20\) | 54.0511 | 0.604310 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −40.2080 | −0.389654 | ||||||||
\(23\) | −140.378 | −1.27265 | −0.636323 | − | 0.771423i | \(-0.719545\pi\) | ||||
−0.636323 | + | 0.771423i | \(0.719545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.3486 | −0.186789 | ||||||||
\(26\) | −309.135 | −2.33179 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −37.5272 | −0.253285 | ||||||||
\(29\) | 116.806 | 0.747943 | 0.373971 | − | 0.927440i | \(-0.377996\pi\) | ||||
0.373971 | + | 0.927440i | \(0.377996\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 338.709 | 1.96238 | 0.981192 | − | 0.193034i | \(-0.0618327\pi\) | ||||
0.981192 | + | 0.193034i | \(0.0618327\pi\) | |||||||
\(32\) | −208.482 | −1.15171 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 139.823 | 0.705280 | ||||||||
\(35\) | −70.5756 | −0.340842 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −75.3416 | −0.334759 | −0.167379 | − | 0.985893i | \(-0.553531\pi\) | ||||
−0.167379 | + | 0.985893i | \(0.553531\pi\) | |||||||
\(38\) | −465.256 | −1.98617 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −97.2548 | −0.384434 | ||||||||
\(41\) | 22.4446 | 0.0854941 | 0.0427471 | − | 0.999086i | \(-0.486389\pi\) | ||||
0.0427471 | + | 0.999086i | \(0.486389\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 181.844 | 0.644906 | 0.322453 | − | 0.946585i | \(-0.395492\pi\) | ||||
0.322453 | + | 0.946585i | \(0.395492\pi\) | |||||||
\(44\) | −58.9713 | −0.202051 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −513.121 | −1.64468 | ||||||||
\(47\) | −300.530 | −0.932698 | −0.466349 | − | 0.884601i | \(-0.654431\pi\) | ||||
−0.466349 | + | 0.884601i | \(0.654431\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −85.3455 | −0.241394 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −453.395 | −1.20913 | ||||||||
\(53\) | 31.8596 | 0.0825708 | 0.0412854 | − | 0.999147i | \(-0.486855\pi\) | ||||
0.0412854 | + | 0.999147i | \(0.486855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −110.905 | −0.271898 | ||||||||
\(56\) | 67.5231 | 0.161128 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 426.958 | 0.966593 | ||||||||
\(59\) | 68.3030 | 0.150717 | 0.0753584 | − | 0.997157i | \(-0.475990\pi\) | ||||
0.0753584 | + | 0.997157i | \(0.475990\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −145.315 | −0.305012 | −0.152506 | − | 0.988303i | \(-0.548734\pi\) | ||||
−0.152506 | + | 0.988303i | \(0.548734\pi\) | |||||||
\(62\) | 1238.07 | 2.53606 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −136.877 | −0.267337 | ||||||||
\(65\) | −852.679 | −1.62710 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −668.020 | −1.21808 | −0.609042 | − | 0.793138i | \(-0.708446\pi\) | ||||
−0.609042 | + | 0.793138i | \(0.708446\pi\) | |||||||
\(68\) | 205.073 | 0.365717 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −257.973 | −0.440481 | ||||||||
\(71\) | −727.608 | −1.21621 | −0.608107 | − | 0.793855i | \(-0.708071\pi\) | ||||
−0.608107 | + | 0.793855i | \(0.708071\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −416.982 | −0.668548 | −0.334274 | − | 0.942476i | \(-0.608491\pi\) | ||||
−0.334274 | + | 0.942476i | \(0.608491\pi\) | |||||||
\(74\) | −275.394 | −0.432621 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −682.370 | −1.02991 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 458.805 | 0.653413 | 0.326707 | − | 0.945126i | \(-0.394061\pi\) | ||||
0.326707 | + | 0.945126i | \(0.394061\pi\) | |||||||
\(80\) | −787.902 | −1.10113 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 82.0412 | 0.110487 | ||||||||
\(83\) | −355.737 | −0.470449 | −0.235224 | − | 0.971941i | \(-0.575582\pi\) | ||||
−0.235224 | + | 0.971941i | \(0.575582\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 385.671 | 0.492140 | ||||||||
\(86\) | 664.690 | 0.833435 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 106.108 | 0.128536 | ||||||||
\(89\) | 1245.97 | 1.48396 | 0.741980 | − | 0.670422i | \(-0.233887\pi\) | ||||
0.741980 | + | 0.670422i | \(0.233887\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 592.007 | 0.681969 | ||||||||
\(92\) | −752.571 | −0.852837 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1098.52 | −1.20536 | ||||||||
\(95\) | −1283.30 | −1.38594 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −935.338 | −0.979063 | −0.489532 | − | 0.871986i | \(-0.662832\pi\) | ||||
−0.489532 | + | 0.871986i | \(0.662832\pi\) | |||||||
\(98\) | 179.108 | 0.184619 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −125.173 | −0.125173 | ||||||||
\(101\) | 533.395 | 0.525493 | 0.262747 | − | 0.964865i | \(-0.415372\pi\) | ||||
0.262747 | + | 0.964865i | \(0.415372\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −738.096 | −0.706086 | −0.353043 | − | 0.935607i | \(-0.614853\pi\) | ||||
−0.353043 | + | 0.935607i | \(0.614853\pi\) | |||||||
\(104\) | 815.800 | 0.769190 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 116.456 | 0.106709 | ||||||||
\(107\) | 2039.07 | 1.84228 | 0.921141 | − | 0.389229i | \(-0.127259\pi\) | ||||
0.921141 | + | 0.389229i | \(0.127259\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1488.69 | 1.30817 | 0.654085 | − | 0.756421i | \(-0.273054\pi\) | ||||
0.654085 | + | 0.756421i | \(0.273054\pi\) | |||||||
\(110\) | −405.387 | −0.351383 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 547.033 | 0.461516 | ||||||||
\(113\) | 532.743 | 0.443507 | 0.221753 | − | 0.975103i | \(-0.428822\pi\) | ||||
0.221753 | + | 0.975103i | \(0.428822\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1415.32 | −1.14765 | ||||||||
\(116\) | 626.201 | 0.501218 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 249.666 | 0.194776 | ||||||||
\(119\) | −267.768 | −0.206271 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −531.167 | −0.394177 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1815.83 | 1.31505 | ||||||||
\(125\) | −1495.68 | −1.07023 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2257.44 | −1.57729 | −0.788645 | − | 0.614849i | \(-0.789217\pi\) | ||||
−0.788645 | + | 0.614849i | \(0.789217\pi\) | |||||||
\(128\) | 1167.53 | 0.806220 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3116.78 | −2.10276 | ||||||||
\(131\) | −1174.21 | −0.783142 | −0.391571 | − | 0.920148i | \(-0.628068\pi\) | ||||
−0.391571 | + | 0.920148i | \(0.628068\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 890.984 | 0.580888 | ||||||||
\(134\) | −2441.79 | −1.57417 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −368.990 | −0.232652 | ||||||||
\(137\) | −2690.08 | −1.67758 | −0.838792 | − | 0.544451i | \(-0.816738\pi\) | ||||
−0.838792 | + | 0.544451i | \(0.816738\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.7500 | 0.0108312 | 0.00541559 | − | 0.999985i | \(-0.498276\pi\) | ||||
0.00541559 | + | 0.999985i | \(0.498276\pi\) | |||||||
\(140\) | −378.358 | −0.228408 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2659.61 | −1.57175 | ||||||||
\(143\) | 930.297 | 0.544023 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1177.67 | 0.674482 | ||||||||
\(146\) | −1524.18 | −0.863988 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −403.908 | −0.224332 | ||||||||
\(149\) | −1517.86 | −0.834550 | −0.417275 | − | 0.908780i | \(-0.637015\pi\) | ||||
−0.417275 | + | 0.908780i | \(0.637015\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1948.86 | 1.05031 | 0.525153 | − | 0.851008i | \(-0.324008\pi\) | ||||
0.525153 | + | 0.851008i | \(0.324008\pi\) | |||||||
\(152\) | 1227.80 | 0.655180 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 281.456 | 0.147275 | ||||||||
\(155\) | 3414.94 | 1.76964 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1554.20 | −0.790055 | −0.395027 | − | 0.918669i | \(-0.629265\pi\) | ||||
−0.395027 | + | 0.918669i | \(0.629265\pi\) | |||||||
\(158\) | 1677.06 | 0.844428 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2101.96 | −1.03859 | ||||||||
\(161\) | 982.647 | 0.481015 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3472.71 | −1.66873 | −0.834367 | − | 0.551209i | \(-0.814167\pi\) | ||||
−0.834367 | + | 0.551209i | \(0.814167\pi\) | |||||||
\(164\) | 120.326 | 0.0572921 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1300.32 | −0.607977 | ||||||||
\(167\) | 2228.90 | 1.03280 | 0.516400 | − | 0.856347i | \(-0.327272\pi\) | ||||
0.516400 | + | 0.856347i | \(0.327272\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4955.50 | 2.25558 | ||||||||
\(170\) | 1409.73 | 0.636009 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 974.872 | 0.432170 | ||||||||
\(173\) | 1008.04 | 0.443005 | 0.221502 | − | 0.975160i | \(-0.428904\pi\) | ||||
0.221502 | + | 0.975160i | \(0.428904\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 163.440 | 0.0705995 | ||||||||
\(176\) | 859.624 | 0.368162 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4554.36 | 1.91777 | ||||||||
\(179\) | 746.246 | 0.311603 | 0.155802 | − | 0.987788i | \(-0.450204\pi\) | ||||
0.155802 | + | 0.987788i | \(0.450204\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2787.76 | −1.14482 | −0.572410 | − | 0.819968i | \(-0.693991\pi\) | ||||
−0.572410 | + | 0.819968i | \(0.693991\pi\) | |||||||
\(182\) | 2163.95 | 0.881333 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1354.11 | 0.542534 | ||||||||
\(185\) | −759.611 | −0.301880 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −420.778 | −0.164547 | ||||||||
\(188\) | −1611.15 | −0.625028 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4690.82 | −1.79109 | ||||||||
\(191\) | 911.917 | 0.345466 | 0.172733 | − | 0.984969i | \(-0.444740\pi\) | ||||
0.172733 | + | 0.984969i | \(0.444740\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4454.66 | 1.66142 | 0.830709 | − | 0.556707i | \(-0.187935\pi\) | ||||
0.830709 | + | 0.556707i | \(0.187935\pi\) | |||||||
\(194\) | −3418.92 | −1.26528 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 262.690 | 0.0957327 | ||||||||
\(197\) | 1377.46 | 0.498171 | 0.249086 | − | 0.968481i | \(-0.419870\pi\) | ||||
0.249086 | + | 0.968481i | \(0.419870\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −94.3572 | −0.0336121 | −0.0168060 | − | 0.999859i | \(-0.505350\pi\) | ||||
−0.0168060 | + | 0.999859i | \(0.505350\pi\) | |||||||
\(200\) | 225.224 | 0.0796288 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1949.71 | 0.679113 | ||||||||
\(203\) | −817.643 | −0.282696 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 226.292 | 0.0770971 | ||||||||
\(206\) | −2697.95 | −0.912499 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6609.13 | 2.20318 | ||||||||
\(209\) | 1400.12 | 0.463388 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1174.19 | 0.383101 | 0.191550 | − | 0.981483i | \(-0.438648\pi\) | ||||
0.191550 | + | 0.981483i | \(0.438648\pi\) | |||||||
\(212\) | 170.800 | 0.0553330 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7453.35 | 2.38084 | ||||||||
\(215\) | 1833.40 | 0.581565 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2370.96 | −0.741712 | ||||||||
\(218\) | 5441.56 | 1.69059 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −594.563 | −0.182206 | ||||||||
\(221\) | −3235.11 | −0.984692 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 88.5875 | 0.0266021 | 0.0133010 | − | 0.999912i | \(-0.495766\pi\) | ||||
0.0133010 | + | 0.999912i | \(0.495766\pi\) | |||||||
\(224\) | 1459.37 | 0.435305 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1947.32 | 0.573159 | ||||||||
\(227\) | −883.312 | −0.258271 | −0.129135 | − | 0.991627i | \(-0.541220\pi\) | ||||
−0.129135 | + | 0.991627i | \(0.541220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1240.26 | 0.357898 | 0.178949 | − | 0.983858i | \(-0.442730\pi\) | ||||
0.178949 | + | 0.983858i | \(0.442730\pi\) | |||||||
\(230\) | −5173.40 | −1.48315 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1126.73 | −0.318851 | ||||||||
\(233\) | 5479.93 | 1.54078 | 0.770392 | − | 0.637571i | \(-0.220061\pi\) | ||||
0.770392 | + | 0.637571i | \(0.220061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3030.01 | −0.841090 | ||||||||
\(236\) | 366.174 | 0.101000 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −978.764 | −0.266571 | ||||||||
\(239\) | −594.006 | −0.160766 | −0.0803830 | − | 0.996764i | \(-0.525614\pi\) | ||||
−0.0803830 | + | 0.996764i | \(0.525614\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 308.785 | 0.0825336 | 0.0412668 | − | 0.999148i | \(-0.486861\pi\) | ||||
0.0412668 | + | 0.999148i | \(0.486861\pi\) | |||||||
\(242\) | 442.288 | 0.117485 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −779.039 | −0.204397 | ||||||||
\(245\) | 494.029 | 0.128826 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10764.7 | 2.77303 | ||||||||
\(248\) | −3267.24 | −0.836573 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5467.14 | −1.38309 | ||||||||
\(251\) | −3487.59 | −0.877031 | −0.438515 | − | 0.898724i | \(-0.644495\pi\) | ||||
−0.438515 | + | 0.898724i | \(0.644495\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1544.16 | 0.383717 | ||||||||
\(254\) | −8251.58 | −2.03839 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5362.66 | 1.30924 | ||||||||
\(257\) | −451.445 | −0.109574 | −0.0547868 | − | 0.998498i | \(-0.517448\pi\) | ||||
−0.0547868 | + | 0.998498i | \(0.517448\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 527.391 | 0.126527 | ||||||||
\(260\) | −4571.24 | −1.09037 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4292.08 | −1.01208 | ||||||||
\(263\) | 5878.61 | 1.37829 | 0.689146 | − | 0.724622i | \(-0.257986\pi\) | ||||
0.689146 | + | 0.724622i | \(0.257986\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 321.216 | 0.0744609 | ||||||||
\(266\) | 3256.79 | 0.750701 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3581.27 | −0.816272 | ||||||||
\(269\) | 52.8516 | 0.0119792 | 0.00598962 | − | 0.999982i | \(-0.498093\pi\) | ||||
0.00598962 | + | 0.999982i | \(0.498093\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6822.19 | −1.52922 | −0.764610 | − | 0.644493i | \(-0.777069\pi\) | ||||
−0.764610 | + | 0.644493i | \(0.777069\pi\) | |||||||
\(272\) | −2989.34 | −0.666381 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9832.98 | −2.16800 | ||||||||
\(275\) | 256.835 | 0.0563189 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 469.032 | 0.101738 | 0.0508689 | − | 0.998705i | \(-0.483801\pi\) | ||||
0.0508689 | + | 0.998705i | \(0.483801\pi\) | |||||||
\(278\) | 64.8810 | 0.0139975 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 680.784 | 0.145302 | ||||||||
\(281\) | 2305.05 | 0.489352 | 0.244676 | − | 0.969605i | \(-0.421318\pi\) | ||||
0.244676 | + | 0.969605i | \(0.421318\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7370.80 | −1.54823 | −0.774114 | − | 0.633046i | \(-0.781805\pi\) | ||||
−0.774114 | + | 0.633046i | \(0.781805\pi\) | |||||||
\(284\) | −3900.73 | −0.815020 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3400.49 | 0.703060 | ||||||||
\(287\) | −157.112 | −0.0323137 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3449.74 | −0.702167 | ||||||||
\(290\) | 4304.69 | 0.871656 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2235.45 | −0.448013 | ||||||||
\(293\) | −1758.90 | −0.350702 | −0.175351 | − | 0.984506i | \(-0.556106\pi\) | ||||
−0.175351 | + | 0.984506i | \(0.556106\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 688.646 | 0.135914 | ||||||||
\(296\) | 726.757 | 0.142709 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5548.20 | −1.07852 | ||||||||
\(299\) | 11872.1 | 2.29626 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1272.91 | −0.243752 | ||||||||
\(302\) | 7123.63 | 1.35735 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9946.89 | 1.87662 | ||||||||
\(305\) | −1465.10 | −0.275054 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3468.10 | 0.644739 | 0.322369 | − | 0.946614i | \(-0.395521\pi\) | ||||
0.322369 | + | 0.946614i | \(0.395521\pi\) | |||||||
\(308\) | 412.799 | 0.0763682 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12482.5 | 2.28697 | ||||||||
\(311\) | −1983.98 | −0.361741 | −0.180870 | − | 0.983507i | \(-0.557891\pi\) | ||||
−0.180870 | + | 0.983507i | \(0.557891\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10094.2 | −1.82287 | −0.911436 | − | 0.411443i | \(-0.865025\pi\) | ||||
−0.911436 | + | 0.411443i | \(0.865025\pi\) | |||||||
\(314\) | −5681.03 | −1.02102 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2459.67 | 0.437871 | ||||||||
\(317\) | 3051.34 | 0.540633 | 0.270316 | − | 0.962772i | \(-0.412872\pi\) | ||||
0.270316 | + | 0.962772i | \(0.412872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1284.87 | −0.225513 | ||||||||
\(320\) | −1380.02 | −0.241080 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3591.84 | 0.621632 | ||||||||
\(323\) | −4868.91 | −0.838741 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1974.65 | 0.337027 | ||||||||
\(326\) | −12693.7 | −2.15656 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −216.504 | −0.0364465 | ||||||||
\(329\) | 2103.71 | 0.352527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.9826 | −0.00448066 | −0.00224033 | − | 0.999997i | \(-0.500713\pi\) | ||||
−0.00224033 | + | 0.999997i | \(0.500713\pi\) | |||||||
\(332\) | −1907.12 | −0.315261 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8147.25 | 1.33472 | ||||||||
\(335\) | −6735.13 | −1.09845 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6818.62 | 1.10218 | 0.551089 | − | 0.834447i | \(-0.314213\pi\) | ||||
0.551089 | + | 0.834447i | \(0.314213\pi\) | |||||||
\(338\) | 18113.7 | 2.91496 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2067.59 | 0.329797 | ||||||||
\(341\) | −3725.80 | −0.591681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −1754.10 | −0.274926 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3684.66 | 0.572510 | ||||||||
\(347\) | −11907.0 | −1.84208 | −0.921038 | − | 0.389473i | \(-0.872657\pi\) | ||||
−0.921038 | + | 0.389473i | \(0.872657\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4352.72 | −0.667609 | −0.333805 | − | 0.942642i | \(-0.608333\pi\) | ||||
−0.333805 | + | 0.942642i | \(0.608333\pi\) | |||||||
\(350\) | 597.419 | 0.0912382 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2293.30 | 0.347253 | ||||||||
\(353\) | 1326.31 | 0.199978 | 0.0999891 | − | 0.994989i | \(-0.468119\pi\) | ||||
0.0999891 | + | 0.994989i | \(0.468119\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7335.91 | −1.09676 | ||||||||
\(356\) | 6679.68 | 0.994444 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2727.73 | 0.402696 | ||||||||
\(359\) | 8292.92 | 1.21917 | 0.609587 | − | 0.792719i | \(-0.291335\pi\) | ||||
0.609587 | + | 0.792719i | \(0.291335\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9342.06 | 1.36201 | ||||||||
\(362\) | −10190.0 | −1.47949 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3173.77 | 0.457007 | ||||||||
\(365\) | −4204.10 | −0.602885 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11027.5 | −1.56848 | −0.784241 | − | 0.620457i | \(-0.786947\pi\) | ||||
−0.784241 | + | 0.620457i | \(0.786947\pi\) | |||||||
\(368\) | 10970.2 | 1.55397 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2776.59 | −0.390130 | ||||||||
\(371\) | −223.017 | −0.0312088 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8245.72 | 1.14463 | 0.572316 | − | 0.820034i | \(-0.306045\pi\) | ||||
0.572316 | + | 0.820034i | \(0.306045\pi\) | |||||||
\(374\) | −1538.06 | −0.212650 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2898.96 | 0.397613 | ||||||||
\(377\) | −9878.58 | −1.34953 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10163.4 | 1.37747 | 0.688734 | − | 0.725014i | \(-0.258167\pi\) | ||||
0.688734 | + | 0.725014i | \(0.258167\pi\) | |||||||
\(380\) | −6879.81 | −0.928755 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3333.31 | 0.446458 | ||||||||
\(383\) | −14338.9 | −1.91301 | −0.956506 | − | 0.291714i | \(-0.905774\pi\) | ||||
−0.956506 | + | 0.291714i | \(0.905774\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 776.332 | 0.102768 | ||||||||
\(386\) | 16283.0 | 2.14711 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5014.37 | −0.656098 | ||||||||
\(389\) | 2382.91 | 0.310587 | 0.155294 | − | 0.987868i | \(-0.450368\pi\) | ||||
0.155294 | + | 0.987868i | \(0.450368\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5369.82 | −0.694535 | ||||||||
\(392\) | −472.662 | −0.0609006 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5034.98 | 0.643804 | ||||||||
\(395\) | 4625.78 | 0.589236 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9868.22 | −1.24754 | −0.623768 | − | 0.781609i | \(-0.714399\pi\) | ||||
−0.623768 | + | 0.781609i | \(0.714399\pi\) | |||||||
\(398\) | −344.901 | −0.0434380 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1824.64 | 0.228080 | ||||||||
\(401\) | 5879.12 | 0.732143 | 0.366072 | − | 0.930587i | \(-0.380702\pi\) | ||||
0.366072 | + | 0.930587i | \(0.380702\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28645.4 | −3.54077 | ||||||||
\(404\) | 2859.55 | 0.352148 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2988.71 | −0.365338 | ||||||||
\(407\) | 828.758 | 0.100934 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5680.84 | 0.686796 | 0.343398 | − | 0.939190i | \(-0.388422\pi\) | ||||
0.343398 | + | 0.939190i | \(0.388422\pi\) | |||||||
\(410\) | 827.158 | 0.0996352 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3956.96 | −0.473168 | ||||||||
\(413\) | −478.121 | −0.0569656 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3586.62 | −0.424242 | ||||||||
\(416\) | 17631.8 | 2.07805 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5117.81 | 0.598853 | ||||||||
\(419\) | 1098.50 | 0.128079 | 0.0640395 | − | 0.997947i | \(-0.479602\pi\) | ||||
0.0640395 | + | 0.997947i | \(0.479602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5265.06 | −0.609509 | −0.304754 | − | 0.952431i | \(-0.598574\pi\) | ||||
−0.304754 | + | 0.952431i | \(0.598574\pi\) | |||||||
\(422\) | 4291.97 | 0.495095 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −307.323 | −0.0352003 | ||||||||
\(425\) | −893.143 | −0.101938 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1017.21 | 0.115284 | ||||||||
\(428\) | 10931.5 | 1.23457 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6701.56 | 0.751577 | ||||||||
\(431\) | −4273.45 | −0.477598 | −0.238799 | − | 0.971069i | \(-0.576754\pi\) | ||||
−0.238799 | + | 0.971069i | \(0.576754\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8560.19 | −0.950061 | −0.475031 | − | 0.879969i | \(-0.657563\pi\) | ||||
−0.475031 | + | 0.879969i | \(0.657563\pi\) | |||||||
\(434\) | −8666.52 | −0.958539 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7980.90 | 0.876642 | ||||||||
\(437\) | 17867.8 | 1.95591 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12664.2 | 1.37684 | 0.688419 | − | 0.725314i | \(-0.258305\pi\) | ||||
0.688419 | + | 0.725314i | \(0.258305\pi\) | |||||||
\(440\) | 1069.80 | 0.115911 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11825.2 | −1.27255 | ||||||||
\(443\) | −12368.9 | −1.32656 | −0.663279 | − | 0.748372i | \(-0.730836\pi\) | ||||
−0.663279 | + | 0.748372i | \(0.730836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12562.2 | 1.33821 | ||||||||
\(446\) | 323.812 | 0.0343788 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 958.136 | 0.101044 | ||||||||
\(449\) | 2092.69 | 0.219956 | 0.109978 | − | 0.993934i | \(-0.464922\pi\) | ||||
0.109978 | + | 0.993934i | \(0.464922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −246.891 | −0.0257775 | ||||||||
\(452\) | 2856.05 | 0.297207 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3228.75 | −0.333772 | ||||||||
\(455\) | 5968.75 | 0.614988 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7825.71 | 0.801031 | 0.400515 | − | 0.916290i | \(-0.368831\pi\) | ||||
0.400515 | + | 0.916290i | \(0.368831\pi\) | |||||||
\(458\) | 4533.49 | 0.462525 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7587.60 | −0.769073 | ||||||||
\(461\) | −4775.60 | −0.482477 | −0.241238 | − | 0.970466i | \(-0.577554\pi\) | ||||
−0.241238 | + | 0.970466i | \(0.577554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11518.3 | 1.15615 | 0.578077 | − | 0.815982i | \(-0.303803\pi\) | ||||
0.578077 | + | 0.815982i | \(0.303803\pi\) | |||||||
\(464\) | −9128.12 | −0.913280 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20030.7 | 1.99121 | ||||||||
\(467\) | 7420.17 | 0.735256 | 0.367628 | − | 0.929973i | \(-0.380170\pi\) | ||||
0.367628 | + | 0.929973i | \(0.380170\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4676.14 | 0.460392 | ||||||||
\(470\) | −11075.5 | −1.08697 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −658.861 | −0.0642512 | ||||||||
\(473\) | −2000.29 | −0.194447 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2971.89 | 0.287073 | ||||||||
\(476\) | −1435.51 | −0.138228 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2171.26 | −0.207764 | ||||||||
\(479\) | −10159.2 | −0.969076 | −0.484538 | − | 0.874770i | \(-0.661012\pi\) | ||||
−0.484538 | + | 0.874770i | \(0.661012\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6371.82 | 0.604013 | ||||||||
\(482\) | 1128.69 | 0.106661 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 648.685 | 0.0609208 | ||||||||
\(485\) | −9430.29 | −0.882902 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12344.9 | −1.14866 | −0.574331 | − | 0.818623i | \(-0.694738\pi\) | ||||
−0.574331 | + | 0.818623i | \(0.694738\pi\) | |||||||
\(488\) | 1401.73 | 0.130028 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1805.81 | 0.166486 | ||||||||
\(491\) | −15344.9 | −1.41040 | −0.705200 | − | 0.709009i | \(-0.749143\pi\) | ||||
−0.705200 | + | 0.709009i | \(0.749143\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4468.13 | 0.408183 | ||||||||
\(494\) | 39347.8 | 3.58369 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −26469.3 | −2.39618 | ||||||||
\(497\) | 5093.26 | 0.459686 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5022.76 | −0.450601 | −0.225300 | − | 0.974289i | \(-0.572336\pi\) | ||||
−0.225300 | + | 0.974289i | \(0.572336\pi\) | |||||||
\(500\) | −8018.41 | −0.717188 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12748.1 | −1.13342 | ||||||||
\(503\) | −8735.90 | −0.774383 | −0.387191 | − | 0.921999i | \(-0.626555\pi\) | ||||
−0.387191 | + | 0.921999i | \(0.626555\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5377.82 | 0.473881 | ||||||||
\(506\) | 5644.33 | 0.495891 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12102.2 | −1.05699 | ||||||||
\(509\) | 21805.5 | 1.89884 | 0.949420 | − | 0.314008i | \(-0.101672\pi\) | ||||
0.949420 | + | 0.314008i | \(0.101672\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2918.87 | 0.252687 | ||||||||
\(512\) | 10261.7 | 0.885760 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1650.16 | −0.141606 | ||||||||
\(515\) | −7441.66 | −0.636735 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3305.83 | 0.281219 | ||||||||
\(518\) | 1927.76 | 0.163515 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8225.08 | 0.693642 | ||||||||
\(521\) | 4732.28 | 0.397936 | 0.198968 | − | 0.980006i | \(-0.436241\pi\) | ||||
0.198968 | + | 0.980006i | \(0.436241\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7511.23 | −0.627998 | −0.313999 | − | 0.949423i | \(-0.601669\pi\) | ||||
−0.313999 | + | 0.949423i | \(0.601669\pi\) | |||||||
\(524\) | −6295.00 | −0.524806 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21487.9 | 1.78121 | ||||||||
\(527\) | 12956.5 | 1.07095 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7539.02 | 0.619629 | ||||||||
\(530\) | 1174.13 | 0.0962283 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4776.59 | 0.389270 | ||||||||
\(533\) | −1898.20 | −0.154259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20558.4 | 1.66134 | ||||||||
\(536\) | 6443.82 | 0.519274 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 193.187 | 0.0154812 | ||||||||
\(539\) | −539.000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −598.410 | −0.0475557 | −0.0237779 | − | 0.999717i | \(-0.507569\pi\) | ||||
−0.0237779 | + | 0.999717i | \(0.507569\pi\) | |||||||
\(542\) | −24937.0 | −1.97626 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7974.95 | −0.628535 | ||||||||
\(545\) | 15009.3 | 1.17968 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14042.3 | −1.09763 | −0.548816 | − | 0.835943i | \(-0.684921\pi\) | ||||
−0.548816 | + | 0.835943i | \(0.684921\pi\) | |||||||
\(548\) | −14421.6 | −1.12420 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 938.801 | 0.0727829 | ||||||||
\(551\) | −14867.5 | −1.14950 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3211.64 | −0.246967 | ||||||||
\(554\) | 1714.44 | 0.131479 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 95.1581 | 0.00725828 | ||||||||
\(557\) | −4965.87 | −0.377757 | −0.188878 | − | 0.982000i | \(-0.560485\pi\) | ||||
−0.188878 | + | 0.982000i | \(0.560485\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15379.0 | −1.16362 | ||||||||
\(560\) | 5515.32 | 0.416187 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8425.60 | 0.632406 | ||||||||
\(563\) | 15362.4 | 1.14999 | 0.574997 | − | 0.818155i | \(-0.305003\pi\) | ||||
0.574997 | + | 0.818155i | \(0.305003\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5371.24 | 0.399947 | ||||||||
\(566\) | −26942.3 | −2.00083 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7018.62 | 0.518477 | ||||||||
\(569\) | −17735.3 | −1.30668 | −0.653341 | − | 0.757064i | \(-0.726633\pi\) | ||||
−0.653341 | + | 0.757064i | \(0.726633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19818.8 | −1.45252 | −0.726262 | − | 0.687418i | \(-0.758744\pi\) | ||||
−0.726262 | + | 0.687418i | \(0.758744\pi\) | |||||||
\(572\) | 4987.35 | 0.364566 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −574.288 | −0.0417602 | ||||||||
\(575\) | 3277.63 | 0.237716 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6579.03 | 0.474677 | 0.237339 | − | 0.971427i | \(-0.423725\pi\) | ||||
0.237339 | + | 0.971427i | \(0.423725\pi\) | |||||||
\(578\) | −12609.8 | −0.907434 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6313.50 | 0.451989 | ||||||||
\(581\) | 2490.16 | 0.177813 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −350.455 | −0.0248960 | ||||||||
\(584\) | 4022.27 | 0.285005 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6429.25 | −0.453225 | ||||||||
\(587\) | −13901.5 | −0.977470 | −0.488735 | − | 0.872432i | \(-0.662541\pi\) | ||||
−0.488735 | + | 0.872432i | \(0.662541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −43112.0 | −3.01596 | ||||||||
\(590\) | 2517.19 | 0.175646 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5887.76 | 0.408760 | ||||||||
\(593\) | −23928.0 | −1.65700 | −0.828502 | − | 0.559986i | \(-0.810807\pi\) | ||||
−0.828502 | + | 0.559986i | \(0.810807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2699.70 | −0.186011 | ||||||||
\(596\) | −8137.30 | −0.559256 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 43395.9 | 2.96754 | ||||||||
\(599\) | −24078.9 | −1.64247 | −0.821233 | − | 0.570594i | \(-0.806713\pi\) | ||||
−0.821233 | + | 0.570594i | \(0.806713\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11806.6 | −0.801336 | −0.400668 | − | 0.916223i | \(-0.631222\pi\) | ||||
−0.400668 | + | 0.916223i | \(0.631222\pi\) | |||||||
\(602\) | −4652.83 | −0.315009 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10447.9 | 0.703840 | ||||||||
\(605\) | 1219.95 | 0.0819802 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1957.71 | 0.130908 | 0.0654539 | − | 0.997856i | \(-0.479150\pi\) | ||||
0.0654539 | + | 0.997856i | \(0.479150\pi\) | |||||||
\(608\) | 26536.2 | 1.77004 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5355.35 | −0.355462 | ||||||||
\(611\) | 25416.6 | 1.68289 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16029.2 | −1.05614 | −0.528069 | − | 0.849201i | \(-0.677084\pi\) | ||||
−0.528069 | + | 0.849201i | \(0.677084\pi\) | |||||||
\(614\) | 12676.9 | 0.833218 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −742.754 | −0.0485819 | ||||||||
\(617\) | 7153.99 | 0.466789 | 0.233394 | − | 0.972382i | \(-0.425017\pi\) | ||||
0.233394 | + | 0.972382i | \(0.425017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11035.9 | −0.716590 | −0.358295 | − | 0.933608i | \(-0.616642\pi\) | ||||
−0.358295 | + | 0.933608i | \(0.616642\pi\) | |||||||
\(620\) | 18307.6 | 1.18589 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7252.00 | −0.467490 | ||||||||
\(623\) | −8721.78 | −0.560884 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12161.3 | −0.778321 | ||||||||
\(626\) | −36897.1 | −2.35576 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8332.11 | −0.529438 | ||||||||
\(629\) | −2882.01 | −0.182692 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4311.46 | −0.272007 | −0.136004 | − | 0.990708i | \(-0.543426\pi\) | ||||
−0.136004 | + | 0.990708i | \(0.543426\pi\) | |||||||
\(632\) | −4425.71 | −0.278553 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11153.5 | 0.698678 | ||||||||
\(635\) | −22760.1 | −1.42237 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4144.05 | −0.257760 | ||||||||
\(638\) | −4696.54 | −0.291439 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11771.3 | 0.727035 | ||||||||
\(641\) | −2692.13 | −0.165886 | −0.0829429 | − | 0.996554i | \(-0.526432\pi\) | ||||
−0.0829429 | + | 0.996554i | \(0.526432\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19694.3 | 1.20788 | 0.603941 | − | 0.797029i | \(-0.293596\pi\) | ||||
0.603941 | + | 0.797029i | \(0.293596\pi\) | |||||||
\(644\) | 5268.00 | 0.322342 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17797.2 | −1.08393 | ||||||||
\(647\) | 21225.5 | 1.28974 | 0.644870 | − | 0.764292i | \(-0.276911\pi\) | ||||
0.644870 | + | 0.764292i | \(0.276911\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −751.333 | −0.0454428 | ||||||||
\(650\) | 7217.88 | 0.435552 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18617.3 | −1.11827 | ||||||||
\(653\) | 12929.7 | 0.774850 | 0.387425 | − | 0.921901i | \(-0.373365\pi\) | ||||
0.387425 | + | 0.921901i | \(0.373365\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11838.7 | −0.706224 | ||||||||
\(656\) | −1753.99 | −0.104393 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7689.64 | 0.455582 | ||||||||
\(659\) | 20835.3 | 1.23161 | 0.615803 | − | 0.787900i | \(-0.288832\pi\) | ||||
0.615803 | + | 0.787900i | \(0.288832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1451.06 | −0.0853850 | −0.0426925 | − | 0.999088i | \(-0.513594\pi\) | ||||
−0.0426925 | + | 0.999088i | \(0.513594\pi\) | |||||||
\(662\) | −98.6288 | −0.00579051 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3431.50 | 0.200554 | ||||||||
\(665\) | 8983.10 | 0.523834 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16397.0 | −0.951867 | ||||||||
\(668\) | 11949.2 | 0.692109 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −24618.7 | −1.41956 | ||||||||
\(671\) | 1598.47 | 0.0919645 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28986.0 | −1.66022 | −0.830111 | − | 0.557598i | \(-0.811723\pi\) | ||||
−0.830111 | + | 0.557598i | \(0.811723\pi\) | |||||||
\(674\) | 24923.9 | 1.42438 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26566.6 | 1.51153 | ||||||||
\(677\) | −24818.6 | −1.40895 | −0.704474 | − | 0.709730i | \(-0.748817\pi\) | ||||
−0.704474 | + | 0.709730i | \(0.748817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6547.36 | 0.370051 | ||||||||
\(680\) | −3720.24 | −0.209801 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13618.8 | −0.764650 | ||||||||
\(683\) | 7450.70 | 0.417413 | 0.208706 | − | 0.977978i | \(-0.433075\pi\) | ||||
0.208706 | + | 0.977978i | \(0.433075\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27122.0 | −1.51282 | ||||||||
\(686\) | −1253.76 | −0.0697795 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14210.7 | −0.787467 | ||||||||
\(689\) | −2694.44 | −0.148984 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28469.1 | −1.56731 | −0.783657 | − | 0.621193i | \(-0.786648\pi\) | ||||
−0.783657 | + | 0.621193i | \(0.786648\pi\) | |||||||
\(692\) | 5404.13 | 0.296870 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −43523.3 | −2.38058 | ||||||||
\(695\) | 178.959 | 0.00976736 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 858.563 | 0.0466577 | ||||||||
\(698\) | −15910.4 | −0.862775 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 876.208 | 0.0473108 | ||||||||
\(701\) | −20045.7 | −1.08005 | −0.540027 | − | 0.841648i | \(-0.681586\pi\) | ||||
−0.540027 | + | 0.841648i | \(0.681586\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9589.73 | 0.514486 | ||||||||
\(704\) | 1505.64 | 0.0806052 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4848.02 | 0.258439 | ||||||||
\(707\) | −3733.77 | −0.198618 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15326.9 | 0.811868 | 0.405934 | − | 0.913902i | \(-0.366946\pi\) | ||||
0.405934 | + | 0.913902i | \(0.366946\pi\) | |||||||
\(710\) | −26814.8 | −1.41738 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12018.8 | −0.632618 | ||||||||
\(713\) | −47547.3 | −2.49742 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9379.47 | 0.490591 | ||||||||
\(716\) | 4000.64 | 0.208814 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 30312.9 | 1.57558 | ||||||||
\(719\) | 11023.4 | 0.571770 | 0.285885 | − | 0.958264i | \(-0.407712\pi\) | ||||
0.285885 | + | 0.958264i | \(0.407712\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5166.68 | 0.266875 | ||||||||
\(722\) | 34147.8 | 1.76018 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14945.3 | −0.767177 | ||||||||
\(725\) | −2727.26 | −0.139707 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28755.9 | 1.46698 | 0.733492 | − | 0.679699i | \(-0.237889\pi\) | ||||
0.733492 | + | 0.679699i | \(0.237889\pi\) | |||||||
\(728\) | −5710.60 | −0.290726 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15367.2 | −0.779129 | ||||||||
\(731\) | 6956.00 | 0.351952 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21500.9 | 1.08343 | 0.541714 | − | 0.840563i | \(-0.317775\pi\) | ||||
0.541714 | + | 0.840563i | \(0.317775\pi\) | |||||||
\(734\) | −40308.7 | −2.02700 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29266.3 | 1.46572 | ||||||||
\(737\) | 7348.21 | 0.367266 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2598.63 | −0.129353 | −0.0646767 | − | 0.997906i | \(-0.520602\pi\) | ||||
−0.0646767 | + | 0.997906i | \(0.520602\pi\) | |||||||
\(740\) | −4072.30 | −0.202298 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −815.189 | −0.0403322 | ||||||||
\(743\) | −29920.5 | −1.47736 | −0.738678 | − | 0.674058i | \(-0.764550\pi\) | ||||
−0.738678 | + | 0.674058i | \(0.764550\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15303.4 | −0.752583 | ||||||||
\(746\) | 30140.4 | 1.47925 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2255.80 | −0.110268 | ||||||||
\(749\) | −14273.5 | −0.696317 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17763.1 | 0.863096 | 0.431548 | − | 0.902090i | \(-0.357968\pi\) | ||||
0.431548 | + | 0.902090i | \(0.357968\pi\) | |||||||
\(752\) | 23485.7 | 1.13888 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −36108.9 | −1.74404 | ||||||||
\(755\) | 19648.9 | 0.947147 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6472.04 | 0.310740 | 0.155370 | − | 0.987856i | \(-0.450343\pi\) | ||||
0.155370 | + | 0.987856i | \(0.450343\pi\) | |||||||
\(758\) | 37150.1 | 1.78015 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12378.9 | 0.590830 | ||||||||
\(761\) | 33720.2 | 1.60625 | 0.803126 | − | 0.595809i | \(-0.203169\pi\) | ||||
0.803126 | + | 0.595809i | \(0.203169\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10420.8 | −0.494441 | ||||||||
\(764\) | 4888.81 | 0.231507 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −52412.6 | −2.47225 | ||||||||
\(767\) | −5776.55 | −0.271941 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9361.49 | −0.438991 | −0.219495 | − | 0.975614i | \(-0.570441\pi\) | ||||
−0.219495 | + | 0.975614i | \(0.570441\pi\) | |||||||
\(770\) | 2837.71 | 0.132810 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23881.6 | 1.11336 | ||||||||
\(773\) | −34886.0 | −1.62324 | −0.811618 | − | 0.584188i | \(-0.801413\pi\) | ||||
−0.811618 | + | 0.584188i | \(0.801413\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7908.38 | −0.366551 | ||||||||
\(776\) | 9022.42 | 0.417379 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8710.20 | 0.401383 | ||||||||
\(779\) | −2856.83 | −0.131395 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8003.69 | 0.366702 | ||||||||
\(782\) | −19628.2 | −0.897572 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3829.23 | −0.174437 | ||||||||
\(785\) | −15669.8 | −0.712458 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9526.64 | −0.431497 | −0.215748 | − | 0.976449i | \(-0.569219\pi\) | ||||
−0.215748 | + | 0.976449i | \(0.569219\pi\) | |||||||
\(788\) | 7384.58 | 0.333839 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16908.5 | 0.761490 | ||||||||
\(791\) | −3729.20 | −0.167630 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12289.7 | 0.550339 | ||||||||
\(794\) | −36071.1 | −1.61223 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −505.852 | −0.0225244 | ||||||||
\(797\) | 33267.9 | 1.47856 | 0.739278 | − | 0.673400i | \(-0.235167\pi\) | ||||
0.739278 | + | 0.673400i | \(0.235167\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11496.0 | −0.509012 | ||||||||
\(800\) | 4867.75 | 0.215126 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21489.8 | 0.946174 | ||||||||
\(803\) | 4586.80 | 0.201575 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9907.27 | 0.433771 | ||||||||
\(806\) | −104707. | −4.57586 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5145.22 | −0.224020 | ||||||||
\(809\) | −17949.6 | −0.780069 | −0.390035 | − | 0.920800i | \(-0.627537\pi\) | ||||
−0.390035 | + | 0.920800i | \(0.627537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10877.9 | 0.470991 | 0.235495 | − | 0.971875i | \(-0.424329\pi\) | ||||
0.235495 | + | 0.971875i | \(0.424329\pi\) | |||||||
\(812\) | −4383.41 | −0.189443 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3029.34 | 0.130440 | ||||||||
\(815\) | −35012.7 | −1.50484 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23145.7 | −0.991147 | ||||||||
\(818\) | 20765.0 | 0.887570 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1213.16 | 0.0516650 | ||||||||
\(821\) | 4519.04 | 0.192102 | 0.0960509 | − | 0.995376i | \(-0.469379\pi\) | ||||
0.0960509 | + | 0.995376i | \(0.469379\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36987.7 | 1.56660 | 0.783300 | − | 0.621644i | \(-0.213535\pi\) | ||||
0.783300 | + | 0.621644i | \(0.213535\pi\) | |||||||
\(824\) | 7119.80 | 0.301007 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1747.66 | −0.0736186 | ||||||||
\(827\) | −15325.3 | −0.644392 | −0.322196 | − | 0.946673i | \(-0.604421\pi\) | ||||
−0.322196 | + | 0.946673i | \(0.604421\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26546.3 | 1.11217 | 0.556087 | − | 0.831124i | \(-0.312302\pi\) | ||||
0.556087 | + | 0.831124i | \(0.312302\pi\) | |||||||
\(830\) | −13110.1 | −0.548263 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11576.0 | 0.482362 | ||||||||
\(833\) | 1874.37 | 0.0779630 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22472.3 | 0.931361 | ||||||||
\(836\) | 7506.07 | 0.310530 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4015.31 | 0.165521 | ||||||||
\(839\) | −11906.5 | −0.489938 | −0.244969 | − | 0.969531i | \(-0.578778\pi\) | ||||
−0.244969 | + | 0.969531i | \(0.578778\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10745.3 | −0.440581 | ||||||||
\(842\) | −19245.2 | −0.787689 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6294.85 | 0.256727 | ||||||||
\(845\) | 49962.5 | 2.03404 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −847.000 | −0.0343604 | ||||||||
\(848\) | −2489.75 | −0.100824 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3264.68 | −0.131738 | ||||||||
\(851\) | 10576.3 | 0.426030 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6859.53 | −0.275341 | −0.137670 | − | 0.990478i | \(-0.543961\pi\) | ||||
−0.137670 | + | 0.990478i | \(0.543961\pi\) | |||||||
\(854\) | 3718.17 | 0.148985 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19669.2 | −0.785372 | ||||||||
\(857\) | −5193.59 | −0.207013 | −0.103506 | − | 0.994629i | \(-0.533006\pi\) | ||||
−0.103506 | + | 0.994629i | \(0.533006\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5265.73 | 0.209155 | 0.104578 | − | 0.994517i | \(-0.466651\pi\) | ||||
0.104578 | + | 0.994517i | \(0.466651\pi\) | |||||||
\(860\) | 9828.89 | 0.389724 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15620.6 | −0.617216 | ||||||||
\(863\) | 16016.7 | 0.631767 | 0.315884 | − | 0.948798i | \(-0.397699\pi\) | ||||
0.315884 | + | 0.948798i | \(0.397699\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10163.3 | 0.399494 | ||||||||
\(866\) | −31289.8 | −1.22780 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12710.8 | −0.497042 | ||||||||
\(869\) | −5046.86 | −0.197011 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56496.0 | 2.19781 | ||||||||
\(872\) | −14360.1 | −0.557678 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 65311.7 | 2.52769 | ||||||||
\(875\) | 10469.8 | 0.404507 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11195.5 | −0.431065 | −0.215533 | − | 0.976497i | \(-0.569149\pi\) | ||||
−0.215533 | + | 0.976497i | \(0.569149\pi\) | |||||||
\(878\) | 46291.3 | 1.77933 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8666.92 | 0.332002 | ||||||||
\(881\) | −45542.5 | −1.74162 | −0.870809 | − | 0.491621i | \(-0.836405\pi\) | ||||
−0.870809 | + | 0.491621i | \(0.836405\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10394.9 | 0.396167 | 0.198083 | − | 0.980185i | \(-0.436528\pi\) | ||||
0.198083 | + | 0.980185i | \(0.436528\pi\) | |||||||
\(884\) | −17343.5 | −0.659871 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −45211.8 | −1.71436 | ||||||||
\(887\) | 4020.51 | 0.152193 | 0.0760967 | − | 0.997100i | \(-0.475754\pi\) | ||||
0.0760967 | + | 0.997100i | \(0.475754\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15802.1 | 0.596159 | ||||||||
\(890\) | 45918.1 | 1.72941 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 474.920 | 0.0178268 | ||||||||
\(893\) | 38252.5 | 1.43345 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7523.82 | 0.280998 | ||||||||
\(896\) | −8172.72 | −0.304723 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7649.36 | 0.284257 | ||||||||
\(899\) | 39563.3 | 1.46775 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1218.71 | 0.0450623 | ||||||||
\(902\) | −902.453 | −0.0333131 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5138.93 | −0.189069 | ||||||||
\(905\) | −28106.8 | −1.03238 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23907.5 | −0.875231 | −0.437615 | − | 0.899162i | \(-0.644177\pi\) | ||||
−0.437615 | + | 0.899162i | \(0.644177\pi\) | |||||||
\(908\) | −4735.46 | −0.173075 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 21817.4 | 0.794770 | ||||||||
\(911\) | −40571.4 | −1.47551 | −0.737755 | − | 0.675069i | \(-0.764114\pi\) | ||||
−0.737755 | + | 0.675069i | \(0.764114\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3913.11 | 0.141846 | ||||||||
\(914\) | 28605.1 | 1.03520 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6649.07 | 0.239838 | ||||||||
\(917\) | 8219.50 | 0.296000 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20551.0 | 0.737667 | 0.368834 | − | 0.929495i | \(-0.379757\pi\) | ||||
0.368834 | + | 0.929495i | \(0.379757\pi\) | |||||||
\(920\) | 13652.5 | 0.489248 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17456.1 | −0.623521 | ||||||||
\(923\) | 61535.6 | 2.19444 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1759.12 | 0.0625292 | ||||||||
\(926\) | 42102.4 | 1.49414 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −24351.9 | −0.861413 | ||||||||
\(929\) | −34068.4 | −1.20317 | −0.601587 | − | 0.798807i | \(-0.705465\pi\) | ||||
−0.601587 | + | 0.798807i | \(0.705465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6236.89 | −0.219555 | ||||||||
\(932\) | 29378.1 | 1.03252 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27122.8 | 0.950197 | ||||||||
\(935\) | −4242.38 | −0.148386 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15597.9 | 0.543824 | 0.271912 | − | 0.962322i | \(-0.412344\pi\) | ||||
0.271912 | + | 0.962322i | \(0.412344\pi\) | |||||||
\(938\) | 17092.6 | 0.594981 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16244.0 | −0.563639 | ||||||||
\(941\) | 22855.3 | 0.791775 | 0.395887 | − | 0.918299i | \(-0.370437\pi\) | ||||
0.395887 | + | 0.918299i | \(0.370437\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3150.73 | −0.108804 | ||||||||
\(944\) | −5337.71 | −0.184034 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7311.59 | −0.251290 | ||||||||
\(947\) | −36670.7 | −1.25833 | −0.629164 | − | 0.777272i | \(-0.716603\pi\) | ||||
−0.629164 | + | 0.777272i | \(0.716603\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35265.1 | 1.20628 | ||||||||
\(950\) | 10863.1 | 0.370994 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2582.93 | 0.0879341 | ||||||||
\(953\) | 19922.8 | 0.677192 | 0.338596 | − | 0.940932i | \(-0.390048\pi\) | ||||
0.338596 | + | 0.940932i | \(0.390048\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9194.16 | 0.311535 | ||||||||
\(956\) | −3184.49 | −0.107734 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37134.8 | −1.25237 | ||||||||
\(959\) | 18830.6 | 0.634068 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 84932.7 | 2.85095 | ||||||||
\(962\) | 23290.8 | 0.780587 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1655.41 | 0.0553081 | ||||||||
\(965\) | 44913.0 | 1.49824 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24523.8 | 0.815545 | 0.407772 | − | 0.913084i | \(-0.366306\pi\) | ||||
0.407772 | + | 0.913084i | \(0.366306\pi\) | |||||||
\(968\) | −1167.19 | −0.0387549 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −34470.3 | −1.14100 | ||||||||
\(971\) | −4493.82 | −0.148520 | −0.0742602 | − | 0.997239i | \(-0.523660\pi\) | ||||
−0.0742602 | + | 0.997239i | \(0.523660\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −124.250 | −0.00409380 | ||||||||
\(974\) | −45123.8 | −1.48446 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11356.0 | 0.372436 | ||||||||
\(977\) | 18285.3 | 0.598771 | 0.299385 | − | 0.954132i | \(-0.403218\pi\) | ||||
0.299385 | + | 0.954132i | \(0.403218\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13705.7 | −0.447431 | ||||||||
\(980\) | 2648.51 | 0.0863300 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −56089.9 | −1.82271 | ||||||||
\(983\) | 25850.8 | 0.838772 | 0.419386 | − | 0.907808i | \(-0.362245\pi\) | ||||
0.419386 | + | 0.907808i | \(0.362245\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13887.8 | 0.449242 | ||||||||
\(986\) | 16332.2 | 0.527509 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 57709.7 | 1.85829 | ||||||||
\(989\) | −25526.9 | −0.820738 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26842.1 | −0.860412 | −0.430206 | − | 0.902731i | \(-0.641559\pi\) | ||||
−0.430206 | + | 0.902731i | \(0.641559\pi\) | |||||||
\(992\) | −70614.6 | −2.26010 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18617.2 | 0.594068 | ||||||||
\(995\) | −951.331 | −0.0303108 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10468.1 | −0.332526 | −0.166263 | − | 0.986081i | \(-0.553170\pi\) | ||||
−0.166263 | + | 0.986081i | \(0.553170\pi\) | |||||||
\(998\) | −18359.6 | −0.582327 | ||||||||
\(999\) | 0 | 0 |
(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 | 693.4.a.m.1.3 | 4 | ||
3.2 | odd | 2 | 77.4.a.c.1.2 | ✓ | 4 | ||
12.11 | even | 2 | 1232.4.a.w.1.1 | 4 | |||
15.14 | odd | 2 | 1925.4.a.q.1.3 | 4 | |||
21.20 | even | 2 | 539.4.a.f.1.2 | 4 | |||
33.32 | even | 2 | 847.4.a.e.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.4.a.c.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
539.4.a.f.1.2 | 4 | 21.20 | even | 2 | |||
693.4.a.m.1.3 | 4 | 1.1 | even | 1 | trivial | ||
847.4.a.e.1.3 | 4 | 33.32 | even | 2 | |||
1232.4.a.w.1.1 | 4 | 12.11 | even | 2 | |||
1925.4.a.q.1.3 | 4 | 15.14 | odd | 2 |