Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1352,4,Mod(1,1352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1352, 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("1352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1352 = 2^{3} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1352.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: | \(79.7705823278\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 123x^{4} + 243x^{3} + 3138x^{2} - 3264x - 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 104) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.753179\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1352.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.753179 | 0.144949 | 0.0724747 | − | 0.997370i | \(-0.476910\pi\) | ||||
0.0724747 | + | 0.997370i | \(0.476910\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.26675 | −0.649958 | −0.324979 | − | 0.945721i | \(-0.605357\pi\) | ||||
−0.324979 | + | 0.945721i | \(0.605357\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.85313 | −0.154054 | −0.0770271 | − | 0.997029i | \(-0.524543\pi\) | ||||
−0.0770271 | + | 0.997029i | \(0.524543\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.4327 | −0.978990 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 58.0893 | 1.59223 | 0.796117 | − | 0.605143i | \(-0.206884\pi\) | ||||
0.796117 | + | 0.605143i | \(0.206884\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.47317 | −0.0942110 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 73.0634 | 1.04238 | 0.521190 | − | 0.853440i | \(-0.325488\pi\) | ||||
0.521190 | + | 0.853440i | \(0.325488\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −142.815 | −1.72442 | −0.862212 | − | 0.506548i | \(-0.830921\pi\) | ||||
−0.862212 | + | 0.506548i | \(0.830921\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.14891 | −0.0223301 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 48.8276 | 0.442663 | 0.221332 | − | 0.975199i | \(-0.428960\pi\) | ||||
0.221332 | + | 0.975199i | \(0.428960\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −72.1943 | −0.577555 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −40.2444 | −0.286853 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 38.8864 | 0.249001 | 0.124500 | − | 0.992220i | \(-0.460267\pi\) | ||||
0.124500 | + | 0.992220i | \(0.460267\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 153.866 | 0.891459 | 0.445730 | − | 0.895168i | \(-0.352944\pi\) | ||||
0.445730 | + | 0.895168i | \(0.352944\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 43.7516 | 0.230793 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 20.7330 | 0.100129 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −356.246 | −1.58288 | −0.791439 | − | 0.611249i | \(-0.790668\pi\) | ||||
−0.791439 | + | 0.611249i | \(0.790668\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.88294 | 0.0147906 | 0.00739528 | − | 0.999973i | \(-0.497646\pi\) | ||||
0.00739528 | + | 0.999973i | \(0.497646\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.1821 | 0.0432034 | 0.0216017 | − | 0.999767i | \(-0.493123\pi\) | ||||
0.0216017 | + | 0.999767i | \(0.493123\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 192.080 | 0.636302 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 258.312 | 0.801675 | 0.400837 | − | 0.916149i | \(-0.368719\pi\) | ||||
0.400837 | + | 0.916149i | \(0.368719\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −334.860 | −0.976267 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 55.0298 | 0.151092 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −302.642 | −0.784361 | −0.392180 | − | 0.919888i | \(-0.628279\pi\) | ||||
−0.392180 | + | 0.919888i | \(0.628279\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −422.120 | −1.03489 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −107.565 | −0.249954 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 110.686 | 0.244238 | 0.122119 | − | 0.992515i | \(-0.461031\pi\) | ||||
0.122119 | + | 0.992515i | \(0.461031\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −415.136 | −0.871355 | −0.435678 | − | 0.900103i | \(-0.643491\pi\) | ||||
−0.435678 | + | 0.900103i | \(0.643491\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 75.4159 | 0.150818 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 933.920 | 1.70293 | 0.851466 | − | 0.524409i | \(-0.175714\pi\) | ||||
0.851466 | + | 0.524409i | \(0.175714\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 36.7759 | 0.0641638 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 661.899 | 1.10638 | 0.553190 | − | 0.833055i | \(-0.313410\pi\) | ||||
0.553190 | + | 0.833055i | \(0.313410\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 436.800 | 0.700323 | 0.350162 | − | 0.936689i | \(-0.386127\pi\) | ||||
0.350162 | + | 0.936689i | \(0.386127\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −54.3753 | −0.0837162 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −165.736 | −0.245290 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −318.158 | −0.453109 | −0.226554 | − | 0.973999i | \(-0.572746\pi\) | ||||
−0.226554 | + | 0.973999i | \(0.572746\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 683.372 | 0.937410 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 595.656 | 0.787732 | 0.393866 | − | 0.919168i | \(-0.371137\pi\) | ||||
0.393866 | + | 0.919168i | \(0.371137\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −530.934 | −0.677504 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 29.2884 | 0.0360925 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1146.68 | 1.36571 | 0.682853 | − | 0.730556i | \(-0.260739\pi\) | ||||
0.682853 | + | 0.730556i | \(0.260739\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 115.889 | 0.129216 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1037.80 | 1.12080 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −669.840 | −0.701154 | −0.350577 | − | 0.936534i | \(-0.614015\pi\) | ||||
−0.350577 | + | 0.936534i | \(0.614015\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1535.46 | −1.55878 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1433.86 | 1.41261 | 0.706307 | − | 0.707906i | \(-0.250360\pi\) | ||||
0.706307 | + | 0.707906i | \(0.250360\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 794.312 | 0.759863 | 0.379931 | − | 0.925015i | \(-0.375948\pi\) | ||||
0.379931 | + | 0.925015i | \(0.375948\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 15.6156 | 0.0145136 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1564.54 | 1.41355 | 0.706776 | − | 0.707438i | \(-0.250149\pi\) | ||||
0.706776 | + | 0.707438i | \(0.250149\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2083.84 | 1.83115 | 0.915575 | − | 0.402147i | \(-0.131736\pi\) | ||||
0.915575 | + | 0.402147i | \(0.131736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −268.317 | −0.229437 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 198.368 | 0.165140 | 0.0825701 | − | 0.996585i | \(-0.473687\pi\) | ||||
0.0825701 | + | 0.996585i | \(0.473687\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −354.818 | −0.287712 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −208.459 | −0.160583 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2043.36 | 1.53521 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.92455 | 0.00214388 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1432.96 | 1.02534 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2167.88 | −1.51471 | −0.757356 | − | 0.653003i | \(-0.773509\pi\) | ||||
−0.757356 | + | 0.653003i | \(0.773509\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.17527 | 0.00626231 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −800.420 | −0.533840 | −0.266920 | − | 0.963719i | \(-0.586006\pi\) | ||||
−0.266920 | + | 0.963719i | \(0.586006\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 407.470 | 0.265655 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 292.446 | 0.186443 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1135.55 | −0.708149 | −0.354074 | − | 0.935217i | \(-0.615204\pi\) | ||||
−0.354074 | + | 0.935217i | \(0.615204\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2006.92 | −1.22464 | −0.612318 | − | 0.790611i | \(-0.709763\pi\) | ||||
−0.612318 | + | 0.790611i | \(0.709763\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 194.555 | 0.116202 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −282.578 | −0.161840 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −252.209 | −0.141509 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2587.13 | 1.42246 | 0.711229 | − | 0.702960i | \(-0.248139\pi\) | ||||
0.711229 | + | 0.702960i | \(0.248139\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1582.79 | 0.853016 | 0.426508 | − | 0.904484i | \(-0.359744\pi\) | ||||
0.426508 | + | 0.904484i | \(0.359744\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1931.26 | −1.02048 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1118.11 | −0.579411 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −270.338 | −0.137423 | −0.0687113 | − | 0.997637i | \(-0.521889\pi\) | ||||
−0.0687113 | + | 0.997637i | \(0.521889\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −227.944 | −0.113693 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −139.311 | −0.0681942 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −142.203 | −0.0683325 | −0.0341662 | − | 0.999416i | \(-0.510878\pi\) | ||||
−0.0341662 | + | 0.999416i | \(0.510878\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −317.932 | −0.150006 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 242.913 | 0.112558 | 0.0562789 | − | 0.998415i | \(-0.482076\pi\) | ||||
0.0562789 | + | 0.998415i | \(0.482076\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3774.99 | 1.68819 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3472.16 | 1.52592 | 0.762958 | − | 0.646448i | \(-0.223746\pi\) | ||||
0.762958 | + | 0.646448i | \(0.223746\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 205.979 | 0.0889748 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 83.3661 | 0.0354022 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −834.865 | −0.348607 | −0.174304 | − | 0.984692i | \(-0.555767\pi\) | ||||
−0.174304 | + | 0.984692i | \(0.555767\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 269.143 | 0.110526 | 0.0552632 | − | 0.998472i | \(-0.482400\pi\) | ||||
0.0552632 | + | 0.998472i | \(0.482400\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −312.671 | −0.126302 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2588.75 | 1.02880 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4244.20 | 1.65971 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 114.822 | 0.0441910 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1320.03 | −0.500072 | −0.250036 | − | 0.968237i | \(-0.580442\pi\) | ||||
−0.250036 | + | 0.968237i | \(0.580442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1299.38 | −0.484617 | −0.242309 | − | 0.970199i | \(-0.577905\pi\) | ||||
−0.242309 | + | 0.970199i | \(0.577905\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2470.61 | 0.893521 | 0.446761 | − | 0.894653i | \(-0.352578\pi\) | ||||
0.446761 | + | 0.894653i | \(0.352578\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1401.88 | −0.499380 | −0.249690 | − | 0.968326i | \(-0.580329\pi\) | ||||
−0.249690 | + | 0.968326i | \(0.580329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 703.409 | 0.246839 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −110.948 | −0.0383596 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −28.2163 | −0.00961325 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1290.65 | −0.433363 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8296.03 | −2.74569 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2691.00 | 0.877991 | 0.438996 | − | 0.898489i | \(-0.355334\pi\) | ||||
0.438996 | + | 0.898489i | \(0.355334\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 498.528 | 0.160369 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −88.5240 | −0.0280804 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −439.000 | −0.137333 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 328.989 | 0.101511 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5439.78 | 1.63352 | 0.816759 | − | 0.576979i | \(-0.195769\pi\) | ||||
0.816759 | + | 0.576979i | \(0.195769\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1908.29 | 0.565420 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4040.78 | −1.18148 | −0.590740 | − | 0.806862i | \(-0.701164\pi\) | ||||
−0.590740 | + | 0.806862i | \(0.701164\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1072.07 | 0.309365 | 0.154682 | − | 0.987964i | \(-0.450565\pi\) | ||||
0.154682 | + | 0.987964i | \(0.450565\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −124.829 | −0.0355547 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4062.66 | 1.14229 | 0.571145 | − | 0.820849i | \(-0.306499\pi\) | ||||
0.571145 | + | 0.820849i | \(0.306499\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1877.09 | −0.521055 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −239.630 | −0.0656778 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4371.13 | 1.18303 | 0.591516 | − | 0.806293i | \(-0.298530\pi\) | ||||
0.591516 | + | 0.806293i | \(0.298530\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3447.22 | −0.921390 | −0.460695 | − | 0.887558i | \(-0.652400\pi\) | ||||
−0.460695 | + | 0.887558i | \(0.652400\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1601.30 | 0.422730 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2433.34 | 0.634533 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 448.636 | 0.114181 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6733.95 | 1.69340 | 0.846700 | − | 0.532071i | \(-0.178586\pi\) | ||||
0.846700 | + | 0.532071i | \(0.178586\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2836.36 | 0.704823 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −399.888 | −0.0982038 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3000.95 | 0.728381 | 0.364190 | − | 0.931325i | \(-0.381346\pi\) | ||||
0.364190 | + | 0.931325i | \(0.381346\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1016.41 | 0.243849 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1027.87 | −0.243769 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3161.43 | −0.741224 | −0.370612 | − | 0.928788i | \(-0.620852\pi\) | ||||
−0.370612 | + | 0.928788i | \(0.620852\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2199.23 | 0.509802 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 863.656 | 0.197958 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4342.67 | −0.984303 | −0.492151 | − | 0.870510i | \(-0.663789\pi\) | ||||
−0.492151 | + | 0.870510i | \(0.663789\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5871.90 | 1.31621 | 0.658104 | − | 0.752927i | \(-0.271359\pi\) | ||||
0.658104 | + | 0.752927i | \(0.271359\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4193.72 | −0.919602 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5414.31 | 1.17442 | 0.587210 | − | 0.809435i | \(-0.300226\pi\) | ||||
0.587210 | + | 0.809435i | \(0.300226\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4067.11 | −0.872729 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6679.68 | 1.41806 | 0.709032 | − | 0.705176i | \(-0.249132\pi\) | ||||
0.709032 | + | 0.705176i | \(0.249132\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8244.76 | −1.73180 | −0.865901 | − | 0.500215i | \(-0.833254\pi\) | ||||
−0.865901 | + | 0.500215i | \(0.833254\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 781.651 | 0.162460 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.0785 | −0.00227855 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 425.259 | 0.0865579 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −504.510 | −0.101632 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −539.918 | −0.107653 | −0.0538265 | − | 0.998550i | \(-0.517142\pi\) | ||||
−0.0538265 | + | 0.998550i | \(0.517142\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −804.325 | −0.158744 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2337.77 | −0.456738 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.7569 | −0.00665567 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1079.95 | 0.204758 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3016.69 | 0.566344 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4032.04 | −0.749578 | −0.374789 | − | 0.927110i | \(-0.622285\pi\) | ||||
−0.374789 | + | 0.927110i | \(0.622285\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 598.259 | 0.110142 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4146.61 | −0.756054 | −0.378027 | − | 0.925794i | \(-0.623397\pi\) | ||||
−0.378027 | + | 0.925794i | \(0.623397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4998.17 | 0.902597 | 0.451299 | − | 0.892373i | \(-0.350961\pi\) | ||||
0.451299 | + | 0.892373i | \(0.350961\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −548.028 | −0.0980251 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 65.9112 | 0.0116780 | 0.00583902 | − | 0.999983i | \(-0.498141\pi\) | ||||
0.00583902 | + | 0.999983i | \(0.498141\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2258.88 | 0.396467 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1178.38 | 0.204893 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10434.6 | −1.79751 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1569.50 | 0.265424 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −736.997 | −0.123501 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4073.09 | 0.676367 | 0.338184 | − | 0.941080i | \(-0.390188\pi\) | ||||
0.338184 | + | 0.941080i | \(0.390188\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9416.55 | 1.54962 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6786.57 | −1.10683 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6440.94 | −1.04113 | −0.520564 | − | 0.853822i | \(-0.674278\pi\) | ||||
−0.520564 | + | 0.853822i | \(0.674278\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 149.406 | 0.0239370 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8937.99 | 1.41941 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1934.02 | 0.304452 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −267.241 | −0.0417037 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8303.40 | −1.28458 | −0.642291 | − | 0.766461i | \(-0.722016\pi\) | ||||
−0.642291 | + | 0.766461i | \(0.722016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −650.474 | −0.0997681 | −0.0498841 | − | 0.998755i | \(-0.515885\pi\) | ||||
−0.0498841 | + | 0.998755i | \(0.515885\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3042.67 | −0.458768 | −0.229384 | − | 0.973336i | \(-0.573671\pi\) | ||||
−0.229384 | + | 0.973336i | \(0.573671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4809.86 | −0.719100 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −157.007 | −0.0232764 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13014.1 | −1.91325 | −0.956627 | − | 0.291317i | \(-0.905907\pi\) | ||||
−0.956627 | + | 0.291317i | \(0.905907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13537.2 | 1.97364 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1539.02 | 0.222528 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3174.12 | −0.455181 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8850.83 | 1.25888 | 0.629441 | − | 0.777048i | \(-0.283284\pi\) | ||||
0.629441 | + | 0.777048i | \(0.283284\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −102.637 | −0.0144798 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 863.476 | 0.120834 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10671.7 | 1.48139 | 0.740694 | − | 0.671843i | \(-0.234497\pi\) | ||||
0.740694 | + | 0.671843i | \(0.234497\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1079.28 | 0.148623 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7451.00 | 1.00985 | 0.504923 | − | 0.863164i | \(-0.331521\pi\) | ||||
0.504923 | + | 0.863164i | \(0.331521\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1632.80 | −0.219556 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 641.269 | 0.0855543 | 0.0427772 | − | 0.999085i | \(-0.486379\pi\) | ||||
0.0427772 | + | 0.999085i | \(0.486379\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1204.36 | 0.159428 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −322.005 | −0.0422957 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4522.54 | 0.589465 | 0.294732 | − | 0.955580i | \(-0.404769\pi\) | ||||
0.294732 | + | 0.955580i | \(0.404769\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3567.51 | 0.461424 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −602.859 | −0.0773797 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2311.98 | 0.294502 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7380.01 | −0.932978 | −0.466489 | − | 0.884527i | \(-0.654481\pi\) | ||||
−0.466489 | + | 0.884527i | \(0.654481\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 306.898 | 0.0385065 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9770.19 | 1.21671 | 0.608354 | − | 0.793666i | \(-0.291830\pi\) | ||||
0.608354 | + | 0.793666i | \(0.291830\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4965.90 | −0.609277 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20694.1 | −2.52031 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7925.84 | 0.958209 | 0.479104 | − | 0.877758i | \(-0.340962\pi\) | ||||
0.479104 | + | 0.877758i | \(0.340962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −855.271 | −0.102646 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −315.800 | −0.0376259 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4328.48 | −0.511992 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1511.57 | −0.177510 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15583.2 | −1.81692 | −0.908462 | − | 0.417967i | \(-0.862743\pi\) | ||||
−0.908462 | + | 0.417967i | \(0.862743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15726.7 | −1.82060 | −0.910298 | − | 0.413954i | \(-0.864148\pi\) | ||||
−0.910298 | + | 0.413954i | \(0.864148\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6827.89 | −0.784831 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5274.76 | −0.602032 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1184.43 | 0.134236 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9844.23 | 1.10019 | 0.550093 | − | 0.835104i | \(-0.314592\pi\) | ||||
0.550093 | + | 0.835104i | \(0.314592\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12317.4 | 1.36706 | 0.683531 | − | 0.729921i | \(-0.260443\pi\) | ||||
0.683531 | + | 0.729921i | \(0.260443\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −212.832 | −0.0234586 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6973.32 | −0.763339 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9182.20 | 0.998274 | 0.499137 | − | 0.866523i | \(-0.333650\pi\) | ||||
0.499137 | + | 0.866523i | \(0.333650\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8851.25 | 0.955756 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8288.47 | 0.888933 | 0.444466 | − | 0.895795i | \(-0.353393\pi\) | ||||
0.444466 | + | 0.895795i | \(0.353393\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8332.64 | −0.887652 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1948.58 | 0.206184 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10295.4 | 1.08212 | 0.541058 | − | 0.840986i | \(-0.318024\pi\) | ||||
0.541058 | + | 0.840986i | \(0.318024\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 225.557 | 0.0235500 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1192.12 | 0.123644 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12210.5 | −1.24985 | −0.624924 | − | 0.780685i | \(-0.714870\pi\) | ||||
−0.624924 | + | 0.780685i | \(0.714870\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2940.39 | −0.299010 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9114.70 | −0.920854 | −0.460427 | − | 0.887697i | \(-0.652304\pi\) | ||||
−0.460427 | + | 0.887697i | \(0.652304\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.376664 | 3.78079e−5 0 | 1.89040e−5 | − | 1.00000i | \(-0.499994\pi\) | ||||
1.89040e−5 | 1.00000i | \(0.499994\pi\) | ||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −842.137 | −0.0839853 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5771.35 | 0.571877 | 0.285938 | − | 0.958248i | \(-0.407695\pi\) | ||||
0.285938 | + | 0.958248i | \(0.407695\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2664.59 | −0.262344 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −203.613 | −0.0199193 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 707.647 | 0.0687899 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10310.4 | 0.995949 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7999.66 | 0.767881 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8609.07 | 0.821207 | 0.410604 | − | 0.911814i | \(-0.365318\pi\) | ||||
0.410604 | + | 0.911814i | \(0.365318\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −104.926 | −0.00988470 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4867.56 | 0.455721 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3635.16 | −0.338244 | −0.169122 | − | 0.985595i | \(-0.554093\pi\) | ||||
−0.169122 | + | 0.985595i | \(0.554093\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −107.104 | −0.00990475 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17387.5 | −1.59814 | −0.799068 | − | 0.601241i | \(-0.794673\pi\) | ||||
−0.799068 | + | 0.601241i | \(0.794673\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2841.17 | 0.259554 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11157.8 | 1.01314 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1888.48 | −0.170443 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1174.90 | −0.105403 | −0.0527014 | − | 0.998610i | \(-0.516783\pi\) | ||||
−0.0527014 | + | 0.998610i | \(0.516783\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 182.957 | 0.0163152 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21573.0 | 1.91231 | 0.956155 | − | 0.292862i | \(-0.0946077\pi\) | ||||
0.956155 | + | 0.292862i | \(0.0946077\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10419.5 | −0.918140 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21860.2 | −1.90361 | −0.951804 | − | 0.306708i | \(-0.900773\pi\) | ||||
−0.951804 | + | 0.306708i | \(0.900773\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1246.25 | −0.107888 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5747.51 | 0.494657 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5772.07 | −0.493879 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15005.2 | 1.27645 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2615.16 | 0.221180 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18858.4 | 1.58580 | 0.792899 | − | 0.609353i | \(-0.208571\pi\) | ||||
0.792899 | + | 0.609353i | \(0.208571\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14433.7 | −1.20677 | −0.603386 | − | 0.797450i | \(-0.706182\pi\) | ||||
−0.603386 | + | 0.797450i | \(0.706182\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 155.139 | 0.0128968 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11242.0 | 0.929240 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9782.87 | −0.804049 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2925.72 | −0.239107 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11369.1 | −0.918749 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −628.803 | −0.0505304 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19451.8 | −1.55445 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9419.76 | 0.748590 | 0.374295 | − | 0.927310i | \(-0.377885\pi\) | ||||
0.374295 | + | 0.927310i | \(0.377885\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 202.713 | 0.0160207 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15142.7 | −1.19017 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12270.8 | −0.959162 | −0.479581 | − | 0.877498i | \(-0.659211\pi\) | ||||
−0.479581 | + | 0.877498i | \(0.659211\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10973.2 | 0.853048 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5553.57 | −0.429383 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 907.745 | 0.0698034 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1949.79 | 0.149124 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18279.2 | −1.39051 | −0.695254 | − | 0.718765i | \(-0.744708\pi\) | ||||
−0.695254 | + | 0.718765i | \(0.744708\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3196.64 | 0.240575 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23994.1 | −1.79615 | −0.898073 | − | 0.439847i | \(-0.855033\pi\) | ||||
−0.898073 | + | 0.439847i | \(0.855033\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1441.49 | −0.107334 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1949.75 | −0.144412 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10263.6 | 0.756191 | 0.378096 | − | 0.925767i | \(-0.376579\pi\) | ||||
0.378096 | + | 0.925767i | \(0.376579\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18173.6 | −1.33195 | −0.665974 | − | 0.745975i | \(-0.731984\pi\) | ||||
−0.665974 | + | 0.745975i | \(0.731984\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −994.216 | −0.0724851 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3525.07 | −0.255662 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21688.8 | −1.56484 | −0.782422 | − | 0.622748i | \(-0.786016\pi\) | ||||
−0.782422 | + | 0.622748i | \(0.786016\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −978.663 | −0.0702450 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1699.48 | −0.121353 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17580.3 | −1.24889 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −929.325 | −0.0653447 | −0.0326724 | − | 0.999466i | \(-0.510402\pi\) | ||||
−0.0326724 | + | 0.999466i | \(0.510402\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21974.5 | −1.53725 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1860.81 | 0.129515 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8355.69 | 0.578629 | 0.289315 | − | 0.957234i | \(-0.406573\pi\) | ||||
0.289315 | + | 0.957234i | \(0.406573\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1514.82 | 0.104372 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1055.87 | −0.0723848 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 241.352 | 0.0164631 | 0.00823154 | − | 0.999966i | \(-0.497380\pi\) | ||||
0.00823154 | + | 0.999966i | \(0.497380\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8607.03 | −0.584173 | −0.292087 | − | 0.956392i | \(-0.594350\pi\) | ||||
−0.292087 | + | 0.956392i | \(0.594350\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24686.1 | −1.66715 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14848.6 | −0.997821 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4892.10 | −0.327124 | −0.163562 | − | 0.986533i | \(-0.552298\pi\) | ||||
−0.163562 | + | 0.986533i | \(0.552298\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −83.5635 | −0.00556021 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3875.72 | 0.255365 | 0.127682 | − | 0.991815i | \(-0.459246\pi\) | ||||
0.127682 | + | 0.991815i | \(0.459246\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.2520 | −0.00139343 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8663.76 | −0.565300 | −0.282650 | − | 0.959223i | \(-0.591213\pi\) | ||||
−0.282650 | + | 0.959223i | \(0.591213\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3269.09 | −0.212271 | −0.106136 | − | 0.994352i | \(-0.533848\pi\) | ||||
−0.106136 | + | 0.994352i | \(0.533848\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1965.04 | −0.126979 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3271.62 | −0.210393 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1388.69 | −0.0888761 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6248.40 | −0.397985 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26028.5 | −1.64996 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11170.0 | 0.704710 | 0.352355 | − | 0.935866i | \(-0.385381\pi\) | ||||
0.352355 | + | 0.935866i | \(0.385381\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2026.81 | 0.127264 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15753.5 | 0.984499 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17495.8 | −1.08313 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20320.3 | −1.25211 | −0.626057 | − | 0.779778i | \(-0.715332\pi\) | ||||
−0.626057 | + | 0.779778i | \(0.715332\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10873.6 | −0.666892 | −0.333446 | − | 0.942769i | \(-0.608212\pi\) | ||||
−0.333446 | + | 0.942769i | \(0.608212\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −66.6744 | −0.00407024 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7533.72 | 0.457776 | 0.228888 | − | 0.973453i | \(-0.426491\pi\) | ||||
0.228888 | + | 0.973453i | \(0.426491\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6429.65 | 0.388884 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −330.646 | −0.0199063 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3839.50 | −0.230094 | −0.115047 | − | 0.993360i | \(-0.536702\pi\) | ||||
−0.115047 | + | 0.993360i | \(0.536702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5816.45 | 0.346973 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11545.8 | −0.685609 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5500.42 | −0.325138 | −0.162569 | − | 0.986697i | \(-0.551978\pi\) | ||||
−0.162569 | + | 0.986697i | \(0.551978\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13859.1 | 0.815517 | 0.407759 | − | 0.913090i | \(-0.366310\pi\) | ||||
0.407759 | + | 0.913090i | \(0.366310\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2960.98 | −0.172665 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1898.73 | 0.110223 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4097.13 | 0.236777 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24114.9 | −1.38740 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2069.86 | 0.118554 | 0.0592772 | − | 0.998242i | \(-0.481120\pi\) | ||||
0.0592772 | + | 0.998242i | \(0.481120\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2905.42 | 0.165673 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7030.18 | 0.399102 | 0.199551 | − | 0.979887i | \(-0.436052\pi\) | ||||
0.199551 | + | 0.979887i | \(0.436052\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1911.14 | 0.108016 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3043.43 | −0.171255 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3831.34 | 0.214644 | 0.107322 | − | 0.994224i | \(-0.465772\pi\) | ||||
0.107322 | + | 0.994224i | \(0.465772\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8251.74 | 0.460267 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 807.463 | 0.0448422 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8186.94 | 0.450718 | 0.225359 | − | 0.974276i | \(-0.427645\pi\) | ||||
0.225359 | + | 0.974276i | \(0.427645\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4380.85 | 0.240137 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14583.8 | 0.795962 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 283.701 | 0.0154174 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3059.91 | 0.165574 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2297.51 | −0.123789 | −0.0618943 | − | 0.998083i | \(-0.519714\pi\) | ||||
−0.0618943 | + | 0.998083i | \(0.519714\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50877.3 | 2.72955 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1413.79 | −0.0755266 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4090.97 | −0.217619 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28328.7 | 1.50057 | 0.750285 | − | 0.661114i | \(-0.229916\pi\) | ||||
0.750285 | + | 0.661114i | \(0.229916\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8409.79 | 0.443589 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7512.93 | 0.394616 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3292.24 | 0.171480 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1170.26 | 0.0607001 | 0.0303500 | − | 0.999539i | \(-0.490338\pi\) | ||||
0.0303500 | + | 0.999539i | \(0.490338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2266.27 | −0.117060 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2596.38 | −0.133555 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2807.38 | −0.143812 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30312.6 | 1.54640 | 0.773201 | − | 0.634162i | \(-0.218655\pi\) | ||||
0.773201 | + | 0.634162i | \(0.218655\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17245.0 | −0.876136 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 890.062 | 0.0450344 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27438.1 | 1.38260 | 0.691302 | − | 0.722565i | \(-0.257037\pi\) | ||||
0.691302 | + | 0.722565i | \(0.257037\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1832.74 | 0.0919751 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54250.7 | 2.71147 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17327.6 | −0.862526 | −0.431263 | − | 0.902226i | \(-0.641932\pi\) | ||||
−0.431263 | + | 0.902226i | \(0.641932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17296.0 | −0.854007 | −0.427004 | − | 0.904250i | \(-0.640431\pi\) | ||||
−0.427004 | + | 0.904250i | \(0.640431\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18800.1 | −0.924538 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15744.8 | −0.771181 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4463.83 | −0.217764 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11089.6 | −0.538835 | −0.269417 | − | 0.963024i | \(-0.586831\pi\) | ||||
−0.269417 | + | 0.963024i | \(0.586831\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5071.87 | 0.245457 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11501.7 | −0.554425 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23761.4 | −1.14085 | −0.570425 | − | 0.821350i | \(-0.693221\pi\) | ||||
−0.570425 | + | 0.821350i | \(0.693221\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2136.29 | 0.102164 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17689.7 | 0.842641 | 0.421321 | − | 0.906912i | \(-0.361567\pi\) | ||||
0.421321 | + | 0.906912i | \(0.361567\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5945.45 | −0.282097 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14034.0 | 0.663269 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28732.2 | −1.34735 | −0.673673 | − | 0.739029i | \(-0.735284\pi\) | ||||
−0.673673 | + | 0.739029i | \(0.735284\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2260.25 | 0.105578 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5188.28 | 0.241410 | 0.120705 | − | 0.992688i | \(-0.461485\pi\) | ||||
0.120705 | + | 0.992688i | \(0.461485\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11108.3 | −0.514866 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 765.542 | 0.0353458 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −554.543 | −0.0255052 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38449.2 | 1.76162 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1564.96 | −0.0714267 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1964.48 | 0.0893189 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15807.0 | −0.715956 | −0.357978 | − | 0.933730i | \(-0.616534\pi\) | ||||
−0.357978 | + | 0.933730i | \(0.616534\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2381.12 | −0.107440 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −565.967 | −0.0254406 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1656.41 | 0.0738954 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22603.4 | 1.00458 | 0.502292 | − | 0.864698i | \(-0.332490\pi\) | ||||
0.502292 | + | 0.864698i | \(0.332490\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18873.2 | 0.835650 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30309.9 | −1.33701 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25373.4 | 1.11508 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1012.34 | 0.0443233 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3270.81 | −0.142674 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9902.20 | −0.430337 | −0.215169 | − | 0.976577i | \(-0.569030\pi\) | ||||
−0.215169 | + | 0.976577i | \(0.569030\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3136.80 | 0.135818 | 0.0679088 | − | 0.997692i | \(-0.478367\pi\) | ||||
0.0679088 | + | 0.997692i | \(0.478367\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4422.59 | 0.190784 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1033.35 | 0.0444133 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1739.78 | −0.0745010 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 773.946 | 0.0329000 | 0.0164500 | − | 0.999865i | \(-0.494764\pi\) | ||||
0.0164500 | + | 0.999865i | \(0.494764\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12381.7 | −0.524423 | −0.262212 | − | 0.965010i | \(-0.584452\pi\) | ||||
−0.262212 | + | 0.965010i | \(0.584452\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3158.62 | −0.133296 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39362.3 | 1.65509 | 0.827545 | − | 0.561399i | \(-0.189737\pi\) | ||||
0.827545 | + | 0.561399i | \(0.189737\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11667.1 | 0.488800 | 0.244400 | − | 0.969674i | \(-0.421409\pi\) | ||||
0.244400 | + | 0.969674i | \(0.421409\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4077.94 | 0.170231 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24466.0 | −1.01764 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1765.19 | −0.0731578 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6192.26 | −0.255718 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46018.4 | −1.89360 | −0.946801 | − | 0.321821i | \(-0.895705\pi\) | ||||
−0.946801 | + | 0.321821i | \(0.895705\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22876.8 | −0.937999 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5030.99 | 0.205548 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5829.97 | −0.236505 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6209.78 | −0.251024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17394.6 | −0.700682 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6667.50 | −0.267633 | −0.133817 | − | 0.991006i | \(-0.542723\pi\) | ||||
−0.133817 | + | 0.991006i | \(0.542723\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27431.9 | −1.09725 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23981.7 | 0.955890 | 0.477945 | − | 0.878390i | \(-0.341382\pi\) | ||||
0.477945 | + | 0.878390i | \(0.341382\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4760.36 | 0.189082 | 0.0945409 | − | 0.995521i | \(-0.469862\pi\) | ||||
0.0945409 | + | 0.995521i | \(0.469862\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.34410 | −0.000330274 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49009.9 | −1.93316 | −0.966580 | − | 0.256363i | \(-0.917476\pi\) | ||||
−0.966580 | + | 0.256363i | \(0.917476\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25231.3 | −0.991781 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 320.296 | 0.0125465 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18481.6 | −0.721455 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17705.7 | 0.686423 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4088.42 | −0.157959 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48161.3 | 1.85438 | 0.927189 | − | 0.374593i | \(-0.122218\pi\) | ||||
0.927189 | + | 0.374593i | \(0.122218\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −406.655 | −0.0156042 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25752.2 | −0.984804 | −0.492402 | − | 0.870368i | \(-0.663881\pi\) | ||||
−0.492402 | + | 0.870368i | \(0.663881\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41104.6 | −1.56657 | −0.783285 | − | 0.621663i | \(-0.786457\pi\) | ||||
−0.783285 | + | 0.621663i | \(0.786457\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −605.801 | −0.0230099 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48960.9 | 1.85338 | 0.926689 | − | 0.375829i | \(-0.122642\pi\) | ||||
0.926689 | + | 0.375829i | \(0.122642\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6185.24 | 0.233348 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 39696.6 | 1.49258 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36890.9 | −1.38243 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6066.75 | 0.226580 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5983.31 | 0.221974 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22112.1 | −0.817603 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −26.1782 | −0.000964735 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1955.80 | −0.0718375 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42398.2 | 1.55216 | 0.776081 | − | 0.630634i | \(-0.217205\pi\) | ||||
0.776081 | + | 0.630634i | \(0.217205\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −37900.7 | −1.38293 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8150.26 | −0.296411 | −0.148205 | − | 0.988957i | \(-0.547350\pi\) | ||||
−0.148205 | + | 0.988957i | \(0.547350\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34601.2 | 1.25425 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2272.11 | 0.0820913 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2283.70 | 0.0822403 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27015.2 | −0.969693 | −0.484847 | − | 0.874599i | \(-0.661125\pi\) | ||||
−0.484847 | + | 0.874599i | \(0.661125\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3036.85 | −0.108651 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25718.9 | 0.914198 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20995.8 | −0.743898 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18722.9 | −0.661227 | −0.330613 | − | 0.943766i | \(-0.607256\pi\) | ||||
−0.330613 | + | 0.943766i | \(0.607256\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 47823.0 | 1.68350 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3123.14 | −0.109590 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −30841.5 | −1.07874 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15955.0 | 0.556274 | 0.278137 | − | 0.960541i | \(-0.410283\pi\) | ||||
0.278137 | + | 0.960541i | \(0.410283\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3764.51 | 0.130831 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9021.18 | 0.312521 | 0.156260 | − | 0.987716i | \(-0.450056\pi\) | ||||
0.156260 | + | 0.987716i | \(0.450056\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 189.594 | 0.00654724 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −834.385 | −0.0287223 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12497.9 | −0.428857 | −0.214428 | − | 0.976740i | \(-0.568789\pi\) | ||||
−0.214428 | + | 0.976740i | \(0.568789\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 49.6429 | 0.00169272 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36334.4 | 1.23503 | 0.617516 | − | 0.786558i | \(-0.288139\pi\) | ||||
0.617516 | + | 0.786558i | \(0.288139\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9592.30 | 0.325026 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1701.34 | 0.0574677 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3239.86 | 0.109093 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6116.11 | −0.205301 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −41355.1 | −1.38385 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9442.24 | 0.314981 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40930.2 | 1.36114 | 0.680572 | − | 0.732681i | \(-0.261731\pi\) | ||||
0.680572 | + | 0.732681i | \(0.261731\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7859.09 | −0.260547 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29443.0 | 0.973092 | 0.486546 | − | 0.873655i | \(-0.338257\pi\) | ||||
0.486546 | + | 0.873655i | \(0.338257\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5725.99 | 0.188661 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26831.2 | 0.878614 | 0.439307 | − | 0.898337i | \(-0.355224\pi\) | ||||
0.439307 | + | 0.898337i | \(0.355224\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 66609.8 | 2.17452 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −55081.5 | −1.79268 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3409.34 | 0.110622 | 0.0553108 | − | 0.998469i | \(-0.482385\pi\) | ||||
0.0553108 | + | 0.998469i | \(0.482385\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17953.3 | −0.580751 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −555.091 | −0.0179015 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 594.820 | 0.0191246 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23214.8 | −0.744138 | −0.372069 | − | 0.928205i | \(-0.621352\pi\) | ||||
−0.372069 | + | 0.928205i | \(0.621352\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3067.77 | 0.0980390 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10187.1 | 0.324576 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13047.0 | −0.414446 | −0.207223 | − | 0.978294i | \(-0.566443\pi\) | ||||
−0.207223 | + | 0.978294i | \(0.566443\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14336.9 | 0.454054 |
(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 | 1352.4.a.n.1.4 | 6 | ||
13.3 | even | 3 | 104.4.i.c.9.3 | ✓ | 12 | ||
13.9 | even | 3 | 104.4.i.c.81.3 | yes | 12 | ||
13.12 | even | 2 | 1352.4.a.m.1.4 | 6 | |||
52.3 | odd | 6 | 208.4.i.h.113.4 | 12 | |||
52.35 | odd | 6 | 208.4.i.h.81.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
104.4.i.c.9.3 | ✓ | 12 | 13.3 | even | 3 | ||
104.4.i.c.81.3 | yes | 12 | 13.9 | even | 3 | ||
208.4.i.h.81.4 | 12 | 52.35 | odd | 6 | |||
208.4.i.h.113.4 | 12 | 52.3 | odd | 6 | |||
1352.4.a.m.1.4 | 6 | 13.12 | even | 2 | |||
1352.4.a.n.1.4 | 6 | 1.1 | even | 1 | trivial |