Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, 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("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(130.099211563\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1163891200.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2\cdot 7 \) |
Twist minimal: | no (minimal twist has level 245) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.04490\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.369315 | 0.130573 | 0.0652863 | − | 0.997867i | \(-0.479204\pi\) | ||||
0.0652863 | + | 0.997867i | \(0.479204\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.86361 | −0.982951 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −5.85867 | −0.258919 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.84657 | 0.0583938 | ||||||||
\(11\) | −30.6361 | −0.839739 | −0.419870 | − | 0.907584i | \(-0.637924\pi\) | ||||
−0.419870 | + | 0.907584i | \(0.637924\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −36.4622 | −0.777908 | −0.388954 | − | 0.921257i | \(-0.627164\pi\) | ||||
−0.388954 | + | 0.921257i | \(0.627164\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 60.7452 | 0.949143 | ||||||||
\(17\) | −79.7341 | −1.13755 | −0.568775 | − | 0.822493i | \(-0.692583\pi\) | ||||
−0.568775 | + | 0.822493i | \(0.692583\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 152.418 | 1.84038 | 0.920189 | − | 0.391474i | \(-0.128035\pi\) | ||||
0.920189 | + | 0.391474i | \(0.128035\pi\) | |||||||
\(20\) | −39.3180 | −0.439589 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.3144 | −0.109647 | ||||||||
\(23\) | −22.2207 | −0.201450 | −0.100725 | − | 0.994914i | \(-0.532116\pi\) | ||||
−0.100725 | + | 0.994914i | \(0.532116\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −13.4660 | −0.101573 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −101.285 | −0.648555 | −0.324278 | − | 0.945962i | \(-0.605121\pi\) | ||||
−0.324278 | + | 0.945962i | \(0.605121\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −249.956 | −1.44818 | −0.724089 | − | 0.689707i | \(-0.757739\pi\) | ||||
−0.724089 | + | 0.689707i | \(0.757739\pi\) | |||||||
\(32\) | 69.3034 | 0.382851 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −29.4470 | −0.148533 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.55765 | 0.0335803 | 0.0167901 | − | 0.999859i | \(-0.494655\pi\) | ||||
0.0167901 | + | 0.999859i | \(0.494655\pi\) | |||||||
\(38\) | 56.2904 | 0.240303 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −29.2933 | −0.115792 | ||||||||
\(41\) | 142.280 | 0.541960 | 0.270980 | − | 0.962585i | \(-0.412652\pi\) | ||||
0.270980 | + | 0.962585i | \(0.412652\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −237.530 | −0.842396 | −0.421198 | − | 0.906969i | \(-0.638390\pi\) | ||||
−0.421198 | + | 0.906969i | \(0.638390\pi\) | |||||||
\(44\) | 240.910 | 0.825422 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.20644 | −0.0263038 | ||||||||
\(47\) | −331.129 | −1.02766 | −0.513830 | − | 0.857892i | \(-0.671774\pi\) | ||||
−0.513830 | + | 0.857892i | \(0.671774\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.23287 | 0.0261145 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 286.725 | 0.764645 | ||||||||
\(53\) | 487.337 | 1.26303 | 0.631517 | − | 0.775362i | \(-0.282432\pi\) | ||||
0.631517 | + | 0.775362i | \(0.282432\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −153.180 | −0.375543 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −37.4059 | −0.0846835 | ||||||||
\(59\) | −717.355 | −1.58291 | −0.791454 | − | 0.611228i | \(-0.790676\pi\) | ||||
−0.791454 | + | 0.611228i | \(0.790676\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −354.592 | −0.744276 | −0.372138 | − | 0.928177i | \(-0.621375\pi\) | ||||
−0.372138 | + | 0.928177i | \(0.621375\pi\) | |||||||
\(62\) | −92.3126 | −0.189092 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −460.367 | −0.899153 | ||||||||
\(65\) | −182.311 | −0.347891 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 57.5883 | 0.105008 | 0.0525040 | − | 0.998621i | \(-0.483280\pi\) | ||||
0.0525040 | + | 0.998621i | \(0.483280\pi\) | |||||||
\(68\) | 626.997 | 1.11816 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 696.174 | 1.16367 | 0.581836 | − | 0.813306i | \(-0.302335\pi\) | ||||
0.581836 | + | 0.813306i | \(0.302335\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 261.035 | 0.418518 | 0.209259 | − | 0.977860i | \(-0.432895\pi\) | ||||
0.209259 | + | 0.977860i | \(0.432895\pi\) | |||||||
\(74\) | 2.79115 | 0.00438466 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1198.56 | −1.80900 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 271.344 | 0.386438 | 0.193219 | − | 0.981156i | \(-0.438107\pi\) | ||||
0.193219 | + | 0.981156i | \(0.438107\pi\) | |||||||
\(80\) | 303.726 | 0.424470 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 52.5460 | 0.0707651 | ||||||||
\(83\) | 681.441 | 0.901179 | 0.450590 | − | 0.892731i | \(-0.351214\pi\) | ||||
0.450590 | + | 0.892731i | \(0.351214\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −398.670 | −0.508728 | ||||||||
\(86\) | −87.7234 | −0.109994 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 179.487 | 0.217424 | ||||||||
\(89\) | 160.668 | 0.191357 | 0.0956784 | − | 0.995412i | \(-0.469498\pi\) | ||||
0.0956784 | + | 0.995412i | \(0.469498\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 174.735 | 0.198015 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −122.291 | −0.134184 | ||||||||
\(95\) | 762.092 | 0.823042 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 167.841 | 0.175687 | 0.0878436 | − | 0.996134i | \(-0.472002\pi\) | ||||
0.0878436 | + | 0.996134i | \(0.472002\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −196.590 | −0.196590 | ||||||||
\(101\) | −413.394 | −0.407270 | −0.203635 | − | 0.979047i | \(-0.565276\pi\) | ||||
−0.203635 | + | 0.979047i | \(0.565276\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1451.11 | 1.38817 | 0.694086 | − | 0.719892i | \(-0.255809\pi\) | ||||
0.694086 | + | 0.719892i | \(0.255809\pi\) | |||||||
\(104\) | 213.620 | 0.201415 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 179.981 | 0.164918 | ||||||||
\(107\) | 1780.63 | 1.60878 | 0.804391 | − | 0.594100i | \(-0.202492\pi\) | ||||
0.804391 | + | 0.594100i | \(0.202492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 37.8920 | 0.0332972 | 0.0166486 | − | 0.999861i | \(-0.494700\pi\) | ||||
0.0166486 | + | 0.999861i | \(0.494700\pi\) | |||||||
\(110\) | −56.5718 | −0.0490356 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −457.320 | −0.380717 | −0.190359 | − | 0.981715i | \(-0.560965\pi\) | ||||
−0.190359 | + | 0.981715i | \(0.560965\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −111.104 | −0.0900910 | ||||||||
\(116\) | 796.463 | 0.637498 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −264.930 | −0.206684 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −392.430 | −0.294838 | ||||||||
\(122\) | −130.956 | −0.0971820 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1965.56 | 1.42349 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2545.41 | −1.77849 | −0.889246 | − | 0.457429i | \(-0.848771\pi\) | ||||
−0.889246 | + | 0.457429i | \(0.848771\pi\) | |||||||
\(128\) | −724.447 | −0.500256 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −67.3302 | −0.0454250 | ||||||||
\(131\) | 970.873 | 0.647523 | 0.323762 | − | 0.946139i | \(-0.395052\pi\) | ||||
0.323762 | + | 0.946139i | \(0.395052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 21.2682 | 0.0137112 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 467.135 | 0.294533 | ||||||||
\(137\) | −183.635 | −0.114518 | −0.0572592 | − | 0.998359i | \(-0.518236\pi\) | ||||
−0.0572592 | + | 0.998359i | \(0.518236\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1078.90 | −0.658356 | −0.329178 | − | 0.944268i | \(-0.606772\pi\) | ||||
−0.329178 | + | 0.944268i | \(0.606772\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 257.108 | 0.151944 | ||||||||
\(143\) | 1117.06 | 0.653240 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −506.424 | −0.290043 | ||||||||
\(146\) | 96.4040 | 0.0546469 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −59.4304 | −0.0330077 | ||||||||
\(149\) | −1211.24 | −0.665962 | −0.332981 | − | 0.942934i | \(-0.608054\pi\) | ||||
−0.332981 | + | 0.942934i | \(0.608054\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −602.244 | −0.324569 | −0.162285 | − | 0.986744i | \(-0.551886\pi\) | ||||
−0.162285 | + | 0.986744i | \(0.551886\pi\) | |||||||
\(152\) | −892.969 | −0.476509 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1249.78 | −0.647644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1602.07 | 0.814389 | 0.407195 | − | 0.913341i | \(-0.366507\pi\) | ||||
0.407195 | + | 0.913341i | \(0.366507\pi\) | |||||||
\(158\) | 100.212 | 0.0504582 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 346.517 | 0.171216 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3091.61 | −1.48561 | −0.742803 | − | 0.669510i | \(-0.766504\pi\) | ||||
−0.742803 | + | 0.669510i | \(0.766504\pi\) | |||||||
\(164\) | −1118.83 | −0.532720 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 251.666 | 0.117669 | ||||||||
\(167\) | 3251.19 | 1.50649 | 0.753247 | − | 0.657738i | \(-0.228487\pi\) | ||||
0.753247 | + | 0.657738i | \(0.228487\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −867.505 | −0.394859 | ||||||||
\(170\) | −147.235 | −0.0664259 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1867.84 | 0.828034 | ||||||||
\(173\) | −2254.55 | −0.990809 | −0.495405 | − | 0.868662i | \(-0.664980\pi\) | ||||
−0.495405 | + | 0.868662i | \(0.664980\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1860.99 | −0.797033 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 59.3370 | 0.0249859 | ||||||||
\(179\) | 2685.46 | 1.12135 | 0.560673 | − | 0.828038i | \(-0.310543\pi\) | ||||
0.560673 | + | 0.828038i | \(0.310543\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1293.25 | 0.531087 | 0.265543 | − | 0.964099i | \(-0.414449\pi\) | ||||
0.265543 | + | 0.964099i | \(0.414449\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 130.184 | 0.0521591 | ||||||||
\(185\) | 37.7882 | 0.0150175 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2442.74 | 0.955245 | ||||||||
\(188\) | 2603.86 | 1.01014 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 281.452 | 0.107467 | ||||||||
\(191\) | 139.878 | 0.0529905 | 0.0264953 | − | 0.999649i | \(-0.491565\pi\) | ||||
0.0264953 | + | 0.999649i | \(0.491565\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2384.81 | 0.889442 | 0.444721 | − | 0.895669i | \(-0.353303\pi\) | ||||
0.444721 | + | 0.895669i | \(0.353303\pi\) | |||||||
\(194\) | 61.9861 | 0.0229399 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1008.67 | 0.364797 | 0.182399 | − | 0.983225i | \(-0.441614\pi\) | ||||
0.182399 | + | 0.983225i | \(0.441614\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 995.036 | 0.354453 | 0.177227 | − | 0.984170i | \(-0.443287\pi\) | ||||
0.177227 | + | 0.984170i | \(0.443287\pi\) | |||||||
\(200\) | −146.467 | −0.0517838 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −152.672 | −0.0531782 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 711.399 | 0.242372 | ||||||||
\(206\) | 535.915 | 0.181257 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2214.90 | −0.738346 | ||||||||
\(209\) | −4669.51 | −1.54544 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2307.30 | 0.752802 | 0.376401 | − | 0.926457i | \(-0.377161\pi\) | ||||
0.376401 | + | 0.926457i | \(0.377161\pi\) | |||||||
\(212\) | −3832.22 | −1.24150 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 657.612 | 0.210063 | ||||||||
\(215\) | −1187.65 | −0.376731 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 13.9941 | 0.00434770 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1204.55 | 0.369140 | ||||||||
\(221\) | 2907.28 | 0.884910 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1629.00 | 0.489173 | 0.244587 | − | 0.969627i | \(-0.421348\pi\) | ||||
0.244587 | + | 0.969627i | \(0.421348\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −168.895 | −0.0497112 | ||||||||
\(227\) | 2410.92 | 0.704926 | 0.352463 | − | 0.935826i | \(-0.385344\pi\) | ||||
0.352463 | + | 0.935826i | \(0.385344\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3666.59 | 1.05806 | 0.529028 | − | 0.848604i | \(-0.322557\pi\) | ||||
0.529028 | + | 0.848604i | \(0.322557\pi\) | |||||||
\(230\) | −41.0322 | −0.0117634 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 593.393 | 0.167923 | ||||||||
\(233\) | 3018.33 | 0.848658 | 0.424329 | − | 0.905508i | \(-0.360510\pi\) | ||||
0.424329 | + | 0.905508i | \(0.360510\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1655.64 | −0.459584 | ||||||||
\(236\) | 5640.99 | 1.55592 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 546.873 | 0.148010 | 0.0740048 | − | 0.997258i | \(-0.476422\pi\) | ||||
0.0740048 | + | 0.997258i | \(0.476422\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3135.27 | 0.838010 | 0.419005 | − | 0.907984i | \(-0.362379\pi\) | ||||
0.419005 | + | 0.907984i | \(0.362379\pi\) | |||||||
\(242\) | −144.930 | −0.0384978 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2788.37 | 0.731587 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5557.52 | −1.43165 | ||||||||
\(248\) | 1464.41 | 0.374960 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 46.1644 | 0.0116788 | ||||||||
\(251\) | 914.967 | 0.230088 | 0.115044 | − | 0.993360i | \(-0.463299\pi\) | ||||
0.115044 | + | 0.993360i | \(0.463299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 680.756 | 0.169165 | ||||||||
\(254\) | −940.058 | −0.232222 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3415.38 | 0.833834 | ||||||||
\(257\) | 6334.18 | 1.53741 | 0.768707 | − | 0.639602i | \(-0.220901\pi\) | ||||
0.768707 | + | 0.639602i | \(0.220901\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1433.62 | 0.341960 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 358.558 | 0.0845487 | ||||||||
\(263\) | −4126.75 | −0.967553 | −0.483777 | − | 0.875191i | \(-0.660735\pi\) | ||||
−0.483777 | + | 0.875191i | \(0.660735\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2436.68 | 0.564846 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −452.852 | −0.103218 | ||||||||
\(269\) | 5887.07 | 1.33435 | 0.667176 | − | 0.744900i | \(-0.267503\pi\) | ||||
0.667176 | + | 0.744900i | \(0.267503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7237.72 | 1.62236 | 0.811181 | − | 0.584795i | \(-0.198825\pi\) | ||||
0.811181 | + | 0.584795i | \(0.198825\pi\) | |||||||
\(272\) | −4843.46 | −1.07970 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −67.8192 | −0.0149530 | ||||||||
\(275\) | −765.902 | −0.167948 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5640.17 | 1.22341 | 0.611705 | − | 0.791086i | \(-0.290484\pi\) | ||||
0.611705 | + | 0.791086i | \(0.290484\pi\) | |||||||
\(278\) | −398.456 | −0.0859632 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2593.05 | 0.550492 | 0.275246 | − | 0.961374i | \(-0.411241\pi\) | ||||
0.275246 | + | 0.961374i | \(0.411241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2533.26 | 0.532109 | 0.266054 | − | 0.963958i | \(-0.414280\pi\) | ||||
0.266054 | + | 0.963958i | \(0.414280\pi\) | |||||||
\(284\) | −5474.44 | −1.14383 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 412.547 | 0.0852952 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1444.52 | 0.294021 | ||||||||
\(290\) | −187.030 | −0.0378716 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2052.67 | −0.411382 | ||||||||
\(293\) | 589.215 | 0.117482 | 0.0587411 | − | 0.998273i | \(-0.481291\pi\) | ||||
0.0587411 | + | 0.998273i | \(0.481291\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3586.77 | −0.707898 | ||||||||
\(296\) | −44.2777 | −0.00869456 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −447.327 | −0.0869563 | ||||||||
\(299\) | 810.217 | 0.156709 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −222.418 | −0.0423798 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9258.68 | 1.74678 | ||||||||
\(305\) | −1772.96 | −0.332851 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5273.75 | 0.980420 | 0.490210 | − | 0.871604i | \(-0.336920\pi\) | ||||
0.490210 | + | 0.871604i | \(0.336920\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −461.563 | −0.0845646 | ||||||||
\(311\) | 3295.08 | 0.600795 | 0.300397 | − | 0.953814i | \(-0.402881\pi\) | ||||
0.300397 | + | 0.953814i | \(0.402881\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1819.37 | −0.328553 | −0.164276 | − | 0.986414i | \(-0.552529\pi\) | ||||
−0.164276 | + | 0.986414i | \(0.552529\pi\) | |||||||
\(314\) | 591.668 | 0.106337 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2133.75 | −0.379850 | ||||||||
\(317\) | −1887.91 | −0.334496 | −0.167248 | − | 0.985915i | \(-0.553488\pi\) | ||||
−0.167248 | + | 0.985915i | \(0.553488\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3102.97 | 0.544617 | ||||||||
\(320\) | −2301.83 | −0.402114 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12152.9 | −2.09352 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −911.556 | −0.155582 | ||||||||
\(326\) | −1141.78 | −0.193979 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −833.569 | −0.140324 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −456.387 | −0.0757863 | −0.0378932 | − | 0.999282i | \(-0.512065\pi\) | ||||
−0.0378932 | + | 0.999282i | \(0.512065\pi\) | |||||||
\(332\) | −5358.58 | −0.885815 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1200.71 | 0.196707 | ||||||||
\(335\) | 287.942 | 0.0469610 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8174.42 | 1.32133 | 0.660666 | − | 0.750680i | \(-0.270274\pi\) | ||||
0.660666 | + | 0.750680i | \(0.270274\pi\) | |||||||
\(338\) | −320.383 | −0.0515577 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3134.99 | 0.500055 | ||||||||
\(341\) | 7657.69 | 1.21609 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1391.61 | 0.218112 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −832.637 | −0.129372 | ||||||||
\(347\) | 7935.70 | 1.22770 | 0.613849 | − | 0.789424i | \(-0.289621\pi\) | ||||
0.613849 | + | 0.789424i | \(0.289621\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8649.40 | 1.32662 | 0.663312 | − | 0.748343i | \(-0.269150\pi\) | ||||
0.663312 | + | 0.748343i | \(0.269150\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2123.19 | −0.321495 | ||||||||
\(353\) | 4931.06 | 0.743495 | 0.371747 | − | 0.928334i | \(-0.378759\pi\) | ||||
0.371747 | + | 0.928334i | \(0.378759\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3480.87 | 0.520410 | ||||||||
\(356\) | −1263.43 | −0.188094 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 991.781 | 0.146417 | ||||||||
\(359\) | −8243.64 | −1.21193 | −0.605965 | − | 0.795491i | \(-0.707213\pi\) | ||||
−0.605965 | + | 0.795491i | \(0.707213\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16372.4 | 2.38699 | ||||||||
\(362\) | 477.617 | 0.0693453 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1305.17 | 0.187167 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8179.11 | −1.16334 | −0.581670 | − | 0.813425i | \(-0.697601\pi\) | ||||
−0.581670 | + | 0.813425i | \(0.697601\pi\) | |||||||
\(368\) | −1349.80 | −0.191204 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13.9558 | 0.00196088 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12795.5 | −1.77620 | −0.888102 | − | 0.459646i | \(-0.847976\pi\) | ||||
−0.888102 | + | 0.459646i | \(0.847976\pi\) | |||||||
\(374\) | 902.140 | 0.124729 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1939.97 | 0.266081 | ||||||||
\(377\) | 3693.07 | 0.504516 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5735.40 | −0.777329 | −0.388664 | − | 0.921379i | \(-0.627063\pi\) | ||||
−0.388664 | + | 0.921379i | \(0.627063\pi\) | |||||||
\(380\) | −5992.79 | −0.809010 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 51.6589 | 0.00691910 | ||||||||
\(383\) | −737.841 | −0.0984384 | −0.0492192 | − | 0.998788i | \(-0.515673\pi\) | ||||
−0.0492192 | + | 0.998788i | \(0.515673\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 880.745 | 0.116137 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1319.83 | −0.172692 | ||||||||
\(389\) | 13034.0 | 1.69884 | 0.849419 | − | 0.527718i | \(-0.176952\pi\) | ||||
0.849419 | + | 0.527718i | \(0.176952\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1771.75 | 0.229159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 372.518 | 0.0476325 | ||||||||
\(395\) | 1356.72 | 0.172821 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8313.64 | 1.05101 | 0.525503 | − | 0.850792i | \(-0.323877\pi\) | ||||
0.525503 | + | 0.850792i | \(0.323877\pi\) | |||||||
\(398\) | 367.481 | 0.0462819 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1518.63 | 0.189829 | ||||||||
\(401\) | 14341.4 | 1.78598 | 0.892988 | − | 0.450080i | \(-0.148604\pi\) | ||||
0.892988 | + | 0.450080i | \(0.148604\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9113.97 | 1.12655 | ||||||||
\(404\) | 3250.77 | 0.400326 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −231.537 | −0.0281987 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6282.35 | −0.759517 | −0.379758 | − | 0.925086i | \(-0.623993\pi\) | ||||
−0.379758 | + | 0.925086i | \(0.623993\pi\) | |||||||
\(410\) | 262.730 | 0.0316471 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11410.9 | −1.36450 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3407.21 | 0.403020 | ||||||||
\(416\) | −2526.96 | −0.297823 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1724.52 | −0.201792 | ||||||||
\(419\) | −15226.1 | −1.77528 | −0.887640 | − | 0.460538i | \(-0.847656\pi\) | ||||
−0.887640 | + | 0.460538i | \(0.847656\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2026.55 | −0.234603 | −0.117302 | − | 0.993096i | \(-0.537424\pi\) | ||||
−0.117302 | + | 0.993096i | \(0.537424\pi\) | |||||||
\(422\) | 852.121 | 0.0982953 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2855.14 | −0.327024 | ||||||||
\(425\) | −1993.35 | −0.227510 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14002.2 | −1.58135 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −438.617 | −0.0491907 | ||||||||
\(431\) | −8983.56 | −1.00400 | −0.501999 | − | 0.864868i | \(-0.667402\pi\) | ||||
−0.501999 | + | 0.864868i | \(0.667402\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6836.59 | −0.758766 | −0.379383 | − | 0.925240i | \(-0.623864\pi\) | ||||
−0.379383 | + | 0.925240i | \(0.623864\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −297.968 | −0.0327295 | ||||||||
\(437\) | −3386.85 | −0.370743 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7802.96 | 0.848325 | 0.424163 | − | 0.905586i | \(-0.360568\pi\) | ||||
0.424163 | + | 0.905586i | \(0.360568\pi\) | |||||||
\(440\) | 897.433 | 0.0972351 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1073.70 | 0.115545 | ||||||||
\(443\) | −5184.37 | −0.556020 | −0.278010 | − | 0.960578i | \(-0.589675\pi\) | ||||
−0.278010 | + | 0.960578i | \(0.589675\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 803.339 | 0.0855773 | ||||||||
\(446\) | 601.612 | 0.0638726 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 772.951 | 0.0812424 | 0.0406212 | − | 0.999175i | \(-0.487066\pi\) | ||||
0.0406212 | + | 0.999175i | \(0.487066\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4358.90 | −0.455105 | ||||||||
\(452\) | 3596.18 | 0.374226 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 890.387 | 0.0920439 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11532.7 | 1.18048 | 0.590239 | − | 0.807228i | \(-0.299033\pi\) | ||||
0.590239 | + | 0.807228i | \(0.299033\pi\) | |||||||
\(458\) | 1354.13 | 0.138153 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 873.675 | 0.0885550 | ||||||||
\(461\) | −10400.7 | −1.05078 | −0.525391 | − | 0.850861i | \(-0.676081\pi\) | ||||
−0.525391 | + | 0.850861i | \(0.676081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13855.4 | −1.39075 | −0.695374 | − | 0.718648i | \(-0.744761\pi\) | ||||
−0.695374 | + | 0.718648i | \(0.744761\pi\) | |||||||
\(464\) | −6152.56 | −0.615572 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1114.71 | 0.110811 | ||||||||
\(467\) | 14734.5 | 1.46002 | 0.730011 | − | 0.683435i | \(-0.239515\pi\) | ||||
0.730011 | + | 0.683435i | \(0.239515\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −611.453 | −0.0600090 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4202.74 | 0.409845 | ||||||||
\(473\) | 7277.00 | 0.707393 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3810.46 | 0.368076 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 201.968 | 0.0193260 | ||||||||
\(479\) | 1471.23 | 0.140338 | 0.0701691 | − | 0.997535i | \(-0.477646\pi\) | ||||
0.0701691 | + | 0.997535i | \(0.477646\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −275.569 | −0.0261224 | ||||||||
\(482\) | 1157.90 | 0.109421 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3085.91 | 0.289812 | ||||||||
\(485\) | 839.204 | 0.0785697 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5610.00 | 0.521998 | 0.260999 | − | 0.965339i | \(-0.415948\pi\) | ||||
0.260999 | + | 0.965339i | \(0.415948\pi\) | |||||||
\(488\) | 2077.44 | 0.192707 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3193.98 | 0.293569 | 0.146784 | − | 0.989169i | \(-0.453108\pi\) | ||||
0.146784 | + | 0.989169i | \(0.453108\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8075.85 | 0.737764 | ||||||||
\(494\) | −2052.47 | −0.186933 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15183.6 | −1.37453 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8724.32 | 0.782673 | 0.391337 | − | 0.920248i | \(-0.372013\pi\) | ||||
0.391337 | + | 0.920248i | \(0.372013\pi\) | |||||||
\(500\) | −982.951 | −0.0879178 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 337.911 | 0.0300432 | ||||||||
\(503\) | 14636.7 | 1.29745 | 0.648726 | − | 0.761022i | \(-0.275302\pi\) | ||||
0.648726 | + | 0.761022i | \(0.275302\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2066.97 | −0.182136 | ||||||||
\(506\) | 251.413 | 0.0220883 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20016.1 | 1.74817 | ||||||||
\(509\) | −8530.56 | −0.742850 | −0.371425 | − | 0.928463i | \(-0.621131\pi\) | ||||
−0.371425 | + | 0.928463i | \(0.621131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7056.93 | 0.609131 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2339.31 | 0.200744 | ||||||||
\(515\) | 7255.53 | 0.620809 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10144.5 | 0.862967 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1068.10 | 0.0900756 | ||||||||
\(521\) | −13743.0 | −1.15564 | −0.577822 | − | 0.816163i | \(-0.696097\pi\) | ||||
−0.577822 | + | 0.816163i | \(0.696097\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2236.17 | −0.186961 | −0.0934806 | − | 0.995621i | \(-0.529799\pi\) | ||||
−0.0934806 | + | 0.995621i | \(0.529799\pi\) | |||||||
\(524\) | −7634.56 | −0.636483 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1524.07 | −0.126336 | ||||||||
\(527\) | 19930.0 | 1.64737 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11673.2 | −0.959418 | ||||||||
\(530\) | 899.903 | 0.0737534 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5187.84 | −0.421595 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8903.14 | 0.719470 | ||||||||
\(536\) | −337.391 | −0.0271885 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2174.18 | 0.174230 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19487.9 | −1.54870 | −0.774352 | − | 0.632755i | \(-0.781924\pi\) | ||||
−0.774352 | + | 0.632755i | \(0.781924\pi\) | |||||||
\(542\) | 2673.00 | 0.211836 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5525.84 | −0.435512 | ||||||||
\(545\) | 189.460 | 0.0148910 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15949.3 | −1.24670 | −0.623349 | − | 0.781944i | \(-0.714228\pi\) | ||||
−0.623349 | + | 0.781944i | \(0.714228\pi\) | |||||||
\(548\) | 1444.04 | 0.112566 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −282.859 | −0.0219294 | ||||||||
\(551\) | −15437.7 | −1.19359 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2083.00 | 0.159744 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8484.08 | 0.647132 | ||||||||
\(557\) | 6349.74 | 0.483029 | 0.241514 | − | 0.970397i | \(-0.422356\pi\) | ||||
0.241514 | + | 0.970397i | \(0.422356\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8660.88 | 0.655306 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 957.651 | 0.0718791 | ||||||||
\(563\) | 14805.0 | 1.10827 | 0.554135 | − | 0.832427i | \(-0.313049\pi\) | ||||
0.554135 | + | 0.832427i | \(0.313049\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2286.60 | −0.170262 | ||||||||
\(566\) | 935.571 | 0.0694788 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4078.65 | −0.301297 | ||||||||
\(569\) | −24578.7 | −1.81088 | −0.905442 | − | 0.424469i | \(-0.860461\pi\) | ||||
−0.905442 | + | 0.424469i | \(0.860461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15609.9 | −1.14405 | −0.572027 | − | 0.820235i | \(-0.693843\pi\) | ||||
−0.572027 | + | 0.820235i | \(0.693843\pi\) | |||||||
\(572\) | −8784.12 | −0.642103 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −555.518 | −0.0402899 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15111.3 | −1.09028 | −0.545141 | − | 0.838344i | \(-0.683524\pi\) | ||||
−0.545141 | + | 0.838344i | \(0.683524\pi\) | |||||||
\(578\) | 533.484 | 0.0383910 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3982.32 | 0.285098 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14930.1 | −1.06062 | ||||||||
\(584\) | −1529.31 | −0.108362 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 217.606 | 0.0153399 | ||||||||
\(587\) | 14983.2 | 1.05353 | 0.526766 | − | 0.850010i | \(-0.323404\pi\) | ||||
0.526766 | + | 0.850010i | \(0.323404\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38098.0 | −2.66519 | ||||||||
\(590\) | −1324.65 | −0.0924320 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 459.090 | 0.0318725 | ||||||||
\(593\) | 6931.01 | 0.479971 | 0.239985 | − | 0.970777i | \(-0.422857\pi\) | ||||
0.239985 | + | 0.970777i | \(0.422857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9524.68 | 0.654608 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 299.225 | 0.0204619 | ||||||||
\(599\) | −12309.2 | −0.839632 | −0.419816 | − | 0.907609i | \(-0.637905\pi\) | ||||
−0.419816 | + | 0.907609i | \(0.637905\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15293.6 | −1.03800 | −0.519001 | − | 0.854774i | \(-0.673696\pi\) | ||||
−0.519001 | + | 0.854774i | \(0.673696\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4735.81 | 0.319036 | ||||||||
\(605\) | −1962.15 | −0.131856 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5338.80 | 0.356994 | 0.178497 | − | 0.983940i | \(-0.442877\pi\) | ||||
0.178497 | + | 0.983940i | \(0.442877\pi\) | |||||||
\(608\) | 10563.1 | 0.704590 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −654.780 | −0.0434611 | ||||||||
\(611\) | 12073.7 | 0.799426 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28848.6 | −1.90079 | −0.950396 | − | 0.311043i | \(-0.899322\pi\) | ||||
−0.950396 | + | 0.311043i | \(0.899322\pi\) | |||||||
\(614\) | 1947.68 | 0.128016 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12346.6 | 0.805602 | 0.402801 | − | 0.915287i | \(-0.368037\pi\) | ||||
0.402801 | + | 0.915287i | \(0.368037\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6383.16 | 0.414477 | 0.207238 | − | 0.978290i | \(-0.433552\pi\) | ||||
0.207238 | + | 0.978290i | \(0.433552\pi\) | |||||||
\(620\) | 9827.79 | 0.636603 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1216.92 | 0.0784473 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −671.921 | −0.0429000 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12598.1 | −0.800505 | ||||||||
\(629\) | −602.602 | −0.0381992 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25708.6 | 1.62194 | 0.810969 | − | 0.585090i | \(-0.198941\pi\) | ||||
0.810969 | + | 0.585090i | \(0.198941\pi\) | |||||||
\(632\) | −1589.72 | −0.100056 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −697.232 | −0.0436760 | ||||||||
\(635\) | −12727.0 | −0.795366 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1145.97 | 0.0711120 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3622.24 | −0.223721 | ||||||||
\(641\) | 18617.5 | 1.14719 | 0.573594 | − | 0.819139i | \(-0.305549\pi\) | ||||
0.573594 | + | 0.819139i | \(0.305549\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21168.8 | −1.29832 | −0.649158 | − | 0.760654i | \(-0.724879\pi\) | ||||
−0.649158 | + | 0.760654i | \(0.724879\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4488.26 | −0.273357 | ||||||||
\(647\) | 5952.47 | 0.361693 | 0.180847 | − | 0.983511i | \(-0.442116\pi\) | ||||
0.180847 | + | 0.983511i | \(0.442116\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21976.9 | 1.32923 | ||||||||
\(650\) | −336.651 | −0.0203147 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24311.2 | 1.46028 | ||||||||
\(653\) | 3040.63 | 0.182219 | 0.0911096 | − | 0.995841i | \(-0.470959\pi\) | ||||
0.0911096 | + | 0.995841i | \(0.470959\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4854.36 | 0.289581 | ||||||||
\(656\) | 8642.81 | 0.514398 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3335.95 | 0.197193 | 0.0985966 | − | 0.995127i | \(-0.468565\pi\) | ||||
0.0985966 | + | 0.995127i | \(0.468565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1547.90 | −0.0910838 | −0.0455419 | − | 0.998962i | \(-0.514501\pi\) | ||||
−0.0455419 | + | 0.998962i | \(0.514501\pi\) | |||||||
\(662\) | −168.550 | −0.00989561 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3992.34 | −0.233332 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2250.62 | 0.130651 | ||||||||
\(668\) | −25566.0 | −1.48081 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 106.341 | 0.00613181 | ||||||||
\(671\) | 10863.3 | 0.624998 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19632.4 | 1.12448 | 0.562239 | − | 0.826975i | \(-0.309940\pi\) | ||||
0.562239 | + | 0.826975i | \(0.309940\pi\) | |||||||
\(674\) | 3018.94 | 0.172530 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6821.72 | 0.388127 | ||||||||
\(677\) | −30318.2 | −1.72116 | −0.860579 | − | 0.509317i | \(-0.829898\pi\) | ||||
−0.860579 | + | 0.509317i | \(0.829898\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2335.68 | 0.131719 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2828.10 | 0.158788 | ||||||||
\(683\) | −28970.8 | −1.62304 | −0.811520 | − | 0.584325i | \(-0.801359\pi\) | ||||
−0.811520 | + | 0.584325i | \(0.801359\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −918.176 | −0.0512142 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14428.8 | −0.799554 | ||||||||
\(689\) | −17769.4 | −0.982525 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3434.91 | −0.189103 | −0.0945514 | − | 0.995520i | \(-0.530142\pi\) | ||||
−0.0945514 | + | 0.995520i | \(0.530142\pi\) | |||||||
\(692\) | 17728.9 | 0.973917 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2930.77 | 0.160304 | ||||||||
\(695\) | −5394.52 | −0.294426 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11344.5 | −0.616507 | ||||||||
\(698\) | 3194.35 | 0.173221 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16304.4 | −0.878471 | −0.439235 | − | 0.898372i | \(-0.644751\pi\) | ||||
−0.439235 | + | 0.898372i | \(0.644751\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1151.92 | 0.0618004 | ||||||||
\(704\) | 14103.8 | 0.755054 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1821.11 | 0.0970800 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16094.4 | 0.852519 | 0.426260 | − | 0.904601i | \(-0.359831\pi\) | ||||
0.426260 | + | 0.904601i | \(0.359831\pi\) | |||||||
\(710\) | 1285.54 | 0.0679512 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −941.299 | −0.0495459 | ||||||||
\(713\) | 5554.21 | 0.291735 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5585.30 | 0.292138 | ||||||||
\(716\) | −21117.4 | −1.10223 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3044.50 | −0.158245 | ||||||||
\(719\) | −8651.93 | −0.448766 | −0.224383 | − | 0.974501i | \(-0.572037\pi\) | ||||
−0.224383 | + | 0.974501i | \(0.572037\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6046.56 | 0.311676 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10169.6 | −0.522032 | ||||||||
\(725\) | −2532.12 | −0.129711 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6999.43 | −0.357076 | −0.178538 | − | 0.983933i | \(-0.557137\pi\) | ||||
−0.178538 | + | 0.983933i | \(0.557137\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 482.020 | 0.0244388 | ||||||||
\(731\) | 18939.3 | 0.958268 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5167.74 | 0.260402 | 0.130201 | − | 0.991488i | \(-0.458438\pi\) | ||||
0.130201 | + | 0.991488i | \(0.458438\pi\) | |||||||
\(734\) | −3020.67 | −0.151900 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1539.97 | −0.0771251 | ||||||||
\(737\) | −1764.28 | −0.0881793 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12319.1 | −0.613214 | −0.306607 | − | 0.951836i | \(-0.599194\pi\) | ||||
−0.306607 | + | 0.951836i | \(0.599194\pi\) | |||||||
\(740\) | −297.152 | −0.0147615 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16942.4 | −0.836548 | −0.418274 | − | 0.908321i | \(-0.637365\pi\) | ||||
−0.418274 | + | 0.908321i | \(0.637365\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6056.18 | −0.297827 | ||||||||
\(746\) | −4725.56 | −0.231923 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −19208.8 | −0.938959 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32917.9 | 1.59946 | 0.799728 | − | 0.600363i | \(-0.204977\pi\) | ||||
0.799728 | + | 0.600363i | \(0.204977\pi\) | |||||||
\(752\) | −20114.5 | −0.975397 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1363.90 | 0.0658760 | ||||||||
\(755\) | −3011.22 | −0.145152 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9433.45 | −0.452926 | −0.226463 | − | 0.974020i | \(-0.572716\pi\) | ||||
−0.226463 | + | 0.974020i | \(0.572716\pi\) | |||||||
\(758\) | −2118.17 | −0.101498 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4464.84 | −0.213101 | ||||||||
\(761\) | 34551.0 | 1.64582 | 0.822912 | − | 0.568170i | \(-0.192348\pi\) | ||||
0.822912 | + | 0.568170i | \(0.192348\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1099.94 | −0.0520871 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −272.495 | −0.0128533 | ||||||||
\(767\) | 26156.4 | 1.23136 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −348.011 | −0.0163194 | −0.00815970 | − | 0.999967i | \(-0.502597\pi\) | ||||
−0.00815970 | + | 0.999967i | \(0.502597\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18753.2 | −0.874277 | ||||||||
\(773\) | 30083.9 | 1.39979 | 0.699897 | − | 0.714243i | \(-0.253229\pi\) | ||||
0.699897 | + | 0.714243i | \(0.253229\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6248.91 | −0.289635 | ||||||||
\(776\) | −983.323 | −0.0454887 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4813.64 | 0.221822 | ||||||||
\(779\) | 21686.1 | 0.997412 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21328.1 | −0.977181 | ||||||||
\(782\) | 654.333 | 0.0299219 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8010.35 | 0.364206 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31958.4 | 1.44751 | 0.723757 | − | 0.690055i | \(-0.242413\pi\) | ||||
0.723757 | + | 0.690055i | \(0.242413\pi\) | |||||||
\(788\) | −7931.81 | −0.358578 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 501.058 | 0.0225656 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12929.2 | 0.578979 | ||||||||
\(794\) | 3070.35 | 0.137233 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7824.57 | −0.348410 | ||||||||
\(797\) | 364.165 | 0.0161849 | 0.00809247 | − | 0.999967i | \(-0.497424\pi\) | ||||
0.00809247 | + | 0.999967i | \(0.497424\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26402.2 | 1.16902 | ||||||||
\(800\) | 1732.59 | 0.0765702 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5296.50 | 0.233199 | ||||||||
\(803\) | −7997.08 | −0.351446 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3365.92 | 0.147096 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2421.94 | 0.105450 | ||||||||
\(809\) | −30714.8 | −1.33482 | −0.667412 | − | 0.744688i | \(-0.732598\pi\) | ||||
−0.667412 | + | 0.744688i | \(0.732598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18967.6 | 0.821260 | 0.410630 | − | 0.911802i | \(-0.365309\pi\) | ||||
0.410630 | + | 0.911802i | \(0.365309\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −85.5100 | −0.00368197 | ||||||||
\(815\) | −15458.1 | −0.664383 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36204.0 | −1.55033 | ||||||||
\(818\) | −2320.17 | −0.0991720 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5594.16 | −0.238240 | ||||||||
\(821\) | 14817.0 | 0.629860 | 0.314930 | − | 0.949115i | \(-0.398019\pi\) | ||||
0.314930 | + | 0.949115i | \(0.398019\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26588.1 | −1.12613 | −0.563063 | − | 0.826414i | \(-0.690377\pi\) | ||||
−0.563063 | + | 0.826414i | \(0.690377\pi\) | |||||||
\(824\) | −8501.54 | −0.359424 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11287.0 | 0.474592 | 0.237296 | − | 0.971437i | \(-0.423739\pi\) | ||||
0.237296 | + | 0.971437i | \(0.423739\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14448.6 | 0.605332 | 0.302666 | − | 0.953097i | \(-0.402123\pi\) | ||||
0.302666 | + | 0.953097i | \(0.402123\pi\) | |||||||
\(830\) | 1258.33 | 0.0526233 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16786.0 | 0.699459 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16255.9 | 0.673724 | ||||||||
\(836\) | 36719.2 | 1.51909 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5623.21 | −0.231803 | ||||||||
\(839\) | −40032.0 | −1.64727 | −0.823635 | − | 0.567120i | \(-0.808057\pi\) | ||||
−0.823635 | + | 0.567120i | \(0.808057\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14130.4 | −0.579376 | ||||||||
\(842\) | −748.434 | −0.0306327 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18143.7 | −0.739967 | ||||||||
\(845\) | −4337.53 | −0.176586 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 29603.3 | 1.19880 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −736.175 | −0.0297066 | ||||||||
\(851\) | −167.936 | −0.00676473 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10864.4 | 0.436098 | 0.218049 | − | 0.975938i | \(-0.430031\pi\) | ||||
0.218049 | + | 0.975938i | \(0.430031\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10432.1 | −0.416544 | ||||||||
\(857\) | −42013.7 | −1.67463 | −0.837316 | − | 0.546719i | \(-0.815877\pi\) | ||||
−0.837316 | + | 0.546719i | \(0.815877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16135.6 | 0.640908 | 0.320454 | − | 0.947264i | \(-0.396165\pi\) | ||||
0.320454 | + | 0.947264i | \(0.396165\pi\) | |||||||
\(860\) | 9339.22 | 0.370308 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3317.76 | −0.131094 | ||||||||
\(863\) | 46246.8 | 1.82417 | 0.912086 | − | 0.409998i | \(-0.134471\pi\) | ||||
0.912086 | + | 0.409998i | \(0.134471\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11272.7 | −0.443103 | ||||||||
\(866\) | −2524.85 | −0.0990739 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8312.93 | −0.324507 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2099.80 | −0.0816865 | ||||||||
\(872\) | −221.996 | −0.00862127 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1250.81 | −0.0484089 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25094.1 | −0.966212 | −0.483106 | − | 0.875562i | \(-0.660491\pi\) | ||||
−0.483106 | + | 0.875562i | \(0.660491\pi\) | |||||||
\(878\) | 2881.75 | 0.110768 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9304.97 | −0.356444 | ||||||||
\(881\) | 27546.6 | 1.05342 | 0.526712 | − | 0.850044i | \(-0.323424\pi\) | ||||
0.526712 | + | 0.850044i | \(0.323424\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5825.31 | 0.222013 | 0.111006 | − | 0.993820i | \(-0.464593\pi\) | ||||
0.111006 | + | 0.993820i | \(0.464593\pi\) | |||||||
\(884\) | −22861.7 | −0.869823 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1914.67 | −0.0726010 | ||||||||
\(887\) | −6214.29 | −0.235237 | −0.117619 | − | 0.993059i | \(-0.537526\pi\) | ||||
−0.117619 | + | 0.993059i | \(0.537526\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 296.685 | 0.0111740 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12809.8 | −0.480833 | ||||||||
\(893\) | −50470.1 | −1.89128 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13427.3 | 0.501481 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 285.462 | 0.0106080 | ||||||||
\(899\) | 25316.8 | 0.939223 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38857.3 | −1.43677 | ||||||||
\(902\) | −1609.80 | −0.0594242 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2679.28 | 0.0985748 | ||||||||
\(905\) | 6466.26 | 0.237509 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24415.9 | 0.893845 | 0.446923 | − | 0.894573i | \(-0.352520\pi\) | ||||
0.446923 | + | 0.894573i | \(0.352520\pi\) | |||||||
\(908\) | −18958.5 | −0.692907 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3493.35 | 0.127047 | 0.0635236 | − | 0.997980i | \(-0.479766\pi\) | ||||
0.0635236 | + | 0.997980i | \(0.479766\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20876.7 | −0.756755 | ||||||||
\(914\) | 4259.21 | 0.154138 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28832.6 | −1.04002 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15656.7 | 0.561989 | 0.280995 | − | 0.959709i | \(-0.409336\pi\) | ||||
0.280995 | + | 0.959709i | \(0.409336\pi\) | |||||||
\(920\) | 650.919 | 0.0233263 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3841.14 | −0.137203 | ||||||||
\(923\) | −25384.1 | −0.905230 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 188.941 | 0.00671605 | ||||||||
\(926\) | −5117.02 | −0.181594 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7019.38 | −0.248300 | ||||||||
\(929\) | 30504.5 | 1.07731 | 0.538654 | − | 0.842527i | \(-0.318933\pi\) | ||||
0.538654 | + | 0.842527i | \(0.318933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −23735.0 | −0.834189 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5441.66 | 0.190639 | ||||||||
\(935\) | 12213.7 | 0.427199 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50290.7 | 1.75339 | 0.876694 | − | 0.481049i | \(-0.159744\pi\) | ||||
0.876694 | + | 0.481049i | \(0.159744\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13019.3 | 0.451748 | ||||||||
\(941\) | −18681.7 | −0.647189 | −0.323595 | − | 0.946196i | \(-0.604891\pi\) | ||||
−0.323595 | + | 0.946196i | \(0.604891\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3161.56 | −0.109178 | ||||||||
\(944\) | −43575.8 | −1.50241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2687.50 | 0.0923660 | ||||||||
\(947\) | −16332.6 | −0.560440 | −0.280220 | − | 0.959936i | \(-0.590407\pi\) | ||||
−0.280220 | + | 0.959936i | \(0.590407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9517.91 | −0.325568 | ||||||||
\(950\) | 1407.26 | 0.0480606 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34233.6 | 1.16362 | 0.581812 | − | 0.813323i | \(-0.302344\pi\) | ||||
0.581812 | + | 0.813323i | \(0.302344\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 699.388 | 0.0236981 | ||||||||
\(956\) | −4300.40 | −0.145486 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 543.345 | 0.0183243 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32687.2 | 1.09722 | ||||||||
\(962\) | −101.772 | −0.00341086 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24654.5 | −0.823723 | ||||||||
\(965\) | 11924.0 | 0.397770 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53792.0 | 1.78887 | 0.894434 | − | 0.447200i | \(-0.147579\pi\) | ||||
0.894434 | + | 0.447200i | \(0.147579\pi\) | |||||||
\(968\) | 2299.11 | 0.0763392 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 309.931 | 0.0102590 | ||||||||
\(971\) | −826.331 | −0.0273102 | −0.0136551 | − | 0.999907i | \(-0.504347\pi\) | ||||
−0.0136551 | + | 0.999907i | \(0.504347\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2071.85 | 0.0681586 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −21539.8 | −0.706425 | ||||||||
\(977\) | −8703.52 | −0.285005 | −0.142503 | − | 0.989794i | \(-0.545515\pi\) | ||||
−0.142503 | + | 0.989794i | \(0.545515\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4922.23 | −0.160690 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1179.58 | 0.0383320 | ||||||||
\(983\) | −41000.9 | −1.33034 | −0.665170 | − | 0.746692i | \(-0.731641\pi\) | ||||
−0.665170 | + | 0.746692i | \(0.731641\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5043.37 | 0.163142 | ||||||||
\(986\) | 2982.53 | 0.0963317 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 43702.1 | 1.40724 | ||||||||
\(989\) | 5278.09 | 0.169700 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18341.0 | −0.587912 | −0.293956 | − | 0.955819i | \(-0.594972\pi\) | ||||
−0.293956 | + | 0.955819i | \(0.594972\pi\) | |||||||
\(992\) | −17322.8 | −0.554436 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4975.18 | 0.158516 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57335.4 | −1.82129 | −0.910646 | − | 0.413187i | \(-0.864416\pi\) | ||||
−0.910646 | + | 0.413187i | \(0.864416\pi\) | |||||||
\(998\) | 3222.02 | 0.102196 | ||||||||
\(999\) | 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 | 2205.4.a.ca.1.4 | 6 | ||
3.2 | odd | 2 | 245.4.a.p.1.3 | yes | 6 | ||
7.6 | odd | 2 | 2205.4.a.bz.1.4 | 6 | |||
15.14 | odd | 2 | 1225.4.a.bi.1.4 | 6 | |||
21.2 | odd | 6 | 245.4.e.p.116.4 | 12 | |||
21.5 | even | 6 | 245.4.e.q.116.4 | 12 | |||
21.11 | odd | 6 | 245.4.e.p.226.4 | 12 | |||
21.17 | even | 6 | 245.4.e.q.226.4 | 12 | |||
21.20 | even | 2 | 245.4.a.o.1.3 | ✓ | 6 | ||
105.104 | even | 2 | 1225.4.a.bj.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.o.1.3 | ✓ | 6 | 21.20 | even | 2 | ||
245.4.a.p.1.3 | yes | 6 | 3.2 | odd | 2 | ||
245.4.e.p.116.4 | 12 | 21.2 | odd | 6 | |||
245.4.e.p.226.4 | 12 | 21.11 | odd | 6 | |||
245.4.e.q.116.4 | 12 | 21.5 | even | 6 | |||
245.4.e.q.226.4 | 12 | 21.17 | even | 6 | |||
1225.4.a.bi.1.4 | 6 | 15.14 | odd | 2 | |||
1225.4.a.bj.1.4 | 6 | 105.104 | even | 2 | |||
2205.4.a.bz.1.4 | 6 | 7.6 | odd | 2 | |||
2205.4.a.ca.1.4 | 6 | 1.1 | even | 1 | trivial |