Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(1,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, 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("1728.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 216) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.4164 | 1.37889 | 0.689443 | − | 0.724340i | \(-0.257855\pi\) | ||||
0.689443 | + | 0.724340i | \(0.257855\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −23.8328 | −1.28685 | −0.643426 | − | 0.765509i | \(-0.722487\pi\) | ||||
−0.643426 | + | 0.765509i | \(0.722487\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.2492 | 0.390573 | 0.195286 | − | 0.980746i | \(-0.437436\pi\) | ||||
0.195286 | + | 0.980746i | \(0.437436\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.8328 | 0.295118 | 0.147559 | − | 0.989053i | \(-0.452858\pi\) | ||||
0.147559 | + | 0.989053i | \(0.452858\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −80.5836 | −1.14967 | −0.574835 | − | 0.818269i | \(-0.694934\pi\) | ||||
−0.574835 | + | 0.818269i | \(0.694934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −144.331 | −1.74273 | −0.871365 | − | 0.490636i | \(-0.836765\pi\) | ||||
−0.871365 | + | 0.490636i | \(0.836765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 141.082 | 1.27903 | 0.639514 | − | 0.768780i | \(-0.279136\pi\) | ||||
0.639514 | + | 0.768780i | \(0.279136\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 112.666 | 0.901325 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 251.331 | 1.60935 | 0.804673 | − | 0.593718i | \(-0.202341\pi\) | ||||
0.804673 | + | 0.593718i | \(0.202341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.6687 | 0.0965740 | 0.0482870 | − | 0.998834i | \(-0.484624\pi\) | ||||
0.0482870 | + | 0.998834i | \(0.484624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −367.416 | −1.77442 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −305.164 | −1.35591 | −0.677955 | − | 0.735103i | \(-0.737134\pi\) | ||||
−0.677955 | + | 0.735103i | \(0.737134\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 429.325 | 1.63535 | 0.817674 | − | 0.575681i | \(-0.195263\pi\) | ||||
0.817674 | + | 0.575681i | \(0.195263\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −181.666 | −0.644273 | −0.322137 | − | 0.946693i | \(-0.604401\pi\) | ||||
−0.322137 | + | 0.946693i | \(0.604401\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 79.4164 | 0.246470 | 0.123235 | − | 0.992378i | \(-0.460673\pi\) | ||||
0.123235 | + | 0.992378i | \(0.460673\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 225.003 | 0.655986 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 663.830 | 1.72045 | 0.860227 | − | 0.509912i | \(-0.170322\pi\) | ||||
0.860227 | + | 0.509912i | \(0.170322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 219.672 | 0.538555 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 220.255 | 0.486014 | 0.243007 | − | 0.970025i | \(-0.421866\pi\) | ||||
0.243007 | + | 0.970025i | \(0.421866\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 473.158 | 0.993142 | 0.496571 | − | 0.867996i | \(-0.334592\pi\) | ||||
0.496571 | + | 0.867996i | \(0.334592\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 213.252 | 0.406934 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −647.663 | −1.18096 | −0.590482 | − | 0.807051i | \(-0.701062\pi\) | ||||
−0.590482 | + | 0.807051i | \(0.701062\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.4922 | −0.0242241 | −0.0121121 | − | 0.999927i | \(-0.503855\pi\) | ||||
−0.0121121 | + | 0.999927i | \(0.503855\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 776.003 | 1.24417 | 0.622084 | − | 0.782950i | \(-0.286286\pi\) | ||||
0.622084 | + | 0.782950i | \(0.286286\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −339.599 | −0.502609 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 257.827 | 0.367187 | 0.183593 | − | 0.983002i | \(-0.441227\pi\) | ||||
0.183593 | + | 0.983002i | \(0.441227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1285.15 | 1.69957 | 0.849784 | − | 0.527132i | \(-0.176733\pi\) | ||||
0.849784 | + | 0.527132i | \(0.176733\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1242.31 | −1.58526 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −156.255 | −0.186102 | −0.0930508 | − | 0.995661i | \(-0.529662\pi\) | ||||
−0.0930508 | + | 0.995661i | \(0.529662\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −329.675 | −0.379773 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2225.07 | −2.40302 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1161.64 | 1.21595 | 0.607975 | − | 0.793956i | \(-0.291982\pi\) | ||||
0.607975 | + | 0.793956i | \(0.291982\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1685.98 | −1.66100 | −0.830502 | − | 0.557016i | \(-0.811946\pi\) | ||||
−0.830502 | + | 0.557016i | \(0.811946\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 765.820 | 0.732607 | 0.366304 | − | 0.930495i | \(-0.380623\pi\) | ||||
0.366304 | + | 0.930495i | \(0.380623\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1747.89 | −1.57920 | −0.789602 | − | 0.613619i | \(-0.789713\pi\) | ||||
−0.789602 | + | 0.613619i | \(0.789713\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1211.64 | 1.06472 | 0.532358 | − | 0.846519i | \(-0.321306\pi\) | ||||
0.532358 | + | 0.846519i | \(0.321306\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 964.426 | 0.802881 | 0.401440 | − | 0.915885i | \(-0.368510\pi\) | ||||
0.401440 | + | 0.915885i | \(0.368510\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2174.98 | 1.76363 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1920.53 | 1.47945 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1127.96 | −0.847453 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −190.152 | −0.136061 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2238.31 | 1.56392 | 0.781960 | − | 0.623329i | \(-0.214220\pi\) | ||||
0.781960 | + | 0.623329i | \(0.214220\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1674.31 | 1.11668 | 0.558340 | − | 0.829612i | \(-0.311438\pi\) | ||||
0.558340 | + | 0.829612i | \(0.311438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3439.82 | 2.24263 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −95.0758 | −0.0592911 | −0.0296455 | − | 0.999560i | \(-0.509438\pi\) | ||||
−0.0296455 | + | 0.999560i | \(0.509438\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1170.64 | 0.714334 | 0.357167 | − | 0.934041i | \(-0.383743\pi\) | ||||
0.357167 | + | 0.934041i | \(0.383743\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 197.107 | 0.115265 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3874.63 | 2.21910 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −859.136 | −0.472370 | −0.236185 | − | 0.971708i | \(-0.575897\pi\) | ||||
−0.236185 | + | 0.971708i | \(0.575897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2898.83 | −1.56227 | −0.781137 | − | 0.624359i | \(-0.785360\pi\) | ||||
−0.781137 | + | 0.624359i | \(0.785360\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 256.972 | 0.133164 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1309.02 | 0.665419 | 0.332710 | − | 0.943029i | \(-0.392037\pi\) | ||||
0.332710 | + | 0.943029i | \(0.392037\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3362.38 | −1.64592 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −190.988 | −0.0917749 | −0.0458874 | − | 0.998947i | \(-0.514612\pi\) | ||||
−0.0458874 | + | 0.998947i | \(0.514612\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1440.73 | 0.667587 | 0.333793 | − | 0.942646i | \(-0.391671\pi\) | ||||
0.333793 | + | 0.942646i | \(0.391671\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2005.65 | −0.912905 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1581.33 | 0.694947 | 0.347474 | − | 0.937690i | \(-0.387040\pi\) | ||||
0.347474 | + | 0.937690i | \(0.387040\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2685.14 | −1.15987 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −741.836 | −0.309762 | −0.154881 | − | 0.987933i | \(-0.549499\pi\) | ||||
−0.154881 | + | 0.987933i | \(0.549499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −626.786 | −0.257396 | −0.128698 | − | 0.991684i | \(-0.541080\pi\) | ||||
−0.128698 | + | 0.991684i | \(0.541080\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4704.53 | −1.86964 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1148.25 | −0.449030 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 182.615 | 0.0691808 | 0.0345904 | − | 0.999402i | \(-0.488987\pi\) | ||||
0.0345904 | + | 0.999402i | \(0.488987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1718.66 | 0.640994 | 0.320497 | − | 0.947250i | \(-0.396150\pi\) | ||||
0.320497 | + | 0.947250i | \(0.396150\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −119.587 | −0.0432497 | −0.0216249 | − | 0.999766i | \(-0.506884\pi\) | ||||
−0.0216249 | + | 0.999766i | \(0.506884\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −707.467 | −0.252015 | −0.126008 | − | 0.992029i | \(-0.540216\pi\) | ||||
−0.126008 | + | 0.992029i | \(0.540216\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5989.93 | −2.07099 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6618.65 | 2.25496 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2056.61 | −0.680663 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2388.62 | −0.779332 | −0.389666 | − | 0.920956i | \(-0.627410\pi\) | ||||
−0.389666 | + | 0.920956i | \(0.627410\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2800.63 | −0.888379 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −397.263 | −0.124276 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1114.70 | −0.339288 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5622.60 | −1.68842 | −0.844209 | − | 0.536014i | \(-0.819929\pi\) | ||||
−0.844209 | + | 0.536014i | \(0.819929\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3464.46 | 1.01297 | 0.506485 | − | 0.862249i | \(-0.330944\pi\) | ||||
0.506485 | + | 0.862249i | \(0.330944\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6082.62 | 1.75524 | 0.877622 | − | 0.479354i | \(-0.159129\pi\) | ||||
0.877622 | + | 0.479354i | \(0.159129\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5024.29 | 1.41267 | 0.706335 | − | 0.707877i | \(-0.250347\pi\) | ||||
0.706335 | + | 0.707877i | \(0.250347\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1224.32 | 0.339853 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2670.20 | 0.722682 | 0.361341 | − | 0.932434i | \(-0.382319\pi\) | ||||
0.361341 | + | 0.932434i | \(0.382319\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 754.653 | 0.201707 | 0.100854 | − | 0.994901i | \(-0.467843\pi\) | ||||
0.100854 | + | 0.994901i | \(0.467843\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3468.74 | 0.904529 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1996.51 | −0.514311 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1588.91 | −0.399566 | −0.199783 | − | 0.979840i | \(-0.564024\pi\) | ||||
−0.199783 | + | 0.979840i | \(0.564024\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2010.31 | 0.499554 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4911.76 | 1.19217 | 0.596083 | − | 0.802923i | \(-0.296723\pi\) | ||||
0.596083 | + | 0.802923i | \(0.296723\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7272.92 | 1.74485 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5400.41 | 1.26617 | 0.633087 | − | 0.774081i | \(-0.281788\pi\) | ||||
0.633087 | + | 0.774081i | \(0.281788\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10233.9 | 2.37231 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3234.09 | −0.733034 | −0.366517 | − | 0.930411i | \(-0.619450\pi\) | ||||
−0.366517 | + | 0.930411i | \(0.619450\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6205.83 | 1.39106 | 0.695530 | − | 0.718497i | \(-0.255170\pi\) | ||||
0.695530 | + | 0.718497i | \(0.255170\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1605.40 | 0.352033 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1030.91 | −0.223615 | −0.111808 | − | 0.993730i | \(-0.535664\pi\) | ||||
−0.111808 | + | 0.993730i | \(0.535664\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3821.33 | 0.811250 | 0.405625 | − | 0.914040i | \(-0.367054\pi\) | ||||
0.405625 | + | 0.914040i | \(0.367054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4402.33 | −0.924705 | −0.462353 | − | 0.886696i | \(-0.652995\pi\) | ||||
−0.462353 | + | 0.886696i | \(0.652995\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10232.0 | −2.10445 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1580.72 | 0.321741 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5973.54 | 1.19105 | 0.595526 | − | 0.803336i | \(-0.296944\pi\) | ||||
0.595526 | + | 0.803336i | \(0.296944\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3395.55 | 0.670157 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1951.56 | 0.377464 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4329.60 | 0.829084 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7294.39 | 1.36943 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −219.622 | −0.0408290 | −0.0204145 | − | 0.999792i | \(-0.506499\pi\) | ||||
−0.0204145 | + | 0.999792i | \(0.506499\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 957.227 | 0.174532 | 0.0872659 | − | 0.996185i | \(-0.472187\pi\) | ||||
0.0872659 | + | 0.996185i | \(0.472187\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1874.05 | 0.338427 | 0.169214 | − | 0.985579i | \(-0.445877\pi\) | ||||
0.169214 | + | 0.985579i | \(0.445877\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2919.78 | −0.517322 | −0.258661 | − | 0.965968i | \(-0.583281\pi\) | ||||
−0.258661 | + | 0.965968i | \(0.583281\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3581.28 | 0.628567 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11630.7 | 2.00356 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1558.48 | 0.265997 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1892.72 | −0.317170 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6648.67 | −1.10406 | −0.552030 | − | 0.833824i | \(-0.686147\pi\) | ||||
−0.552030 | + | 0.833824i | \(0.686147\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9984.63 | −1.62841 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3886.34 | 0.628197 | 0.314098 | − | 0.949390i | \(-0.398298\pi\) | ||||
0.314098 | + | 0.949390i | \(0.398298\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 237.517 | 0.0377192 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2812.20 | 0.442695 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4207.76 | 0.650963 | 0.325481 | − | 0.945548i | \(-0.394474\pi\) | ||||
0.325481 | + | 0.945548i | \(0.394474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3011.42 | −0.461885 | −0.230942 | − | 0.972967i | \(-0.574181\pi\) | ||||
−0.230942 | + | 0.972967i | \(0.574181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2499.79 | 0.376914 | 0.188457 | − | 0.982081i | \(-0.439651\pi\) | ||||
0.188457 | + | 0.982081i | \(0.439651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −223.418 | −0.0334023 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8319.17 | 1.22303 | 0.611517 | − | 0.791231i | \(-0.290560\pi\) | ||||
0.611517 | + | 0.791231i | \(0.290560\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13972.5 | 2.03711 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11963.2 | 1.71557 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4459.85 | 0.634339 | 0.317169 | − | 0.948369i | \(-0.397268\pi\) | ||||
0.317169 | + | 0.948369i | \(0.397268\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15820.9 | −2.21397 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1179.41 | 0.163719 | 0.0818596 | − | 0.996644i | \(-0.473914\pi\) | ||||
0.0818596 | + | 0.996644i | \(0.473914\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3476.62 | 0.474947 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8413.88 | 1.14035 | 0.570174 | − | 0.821524i | \(-0.306876\pi\) | ||||
0.570174 | + | 0.821524i | \(0.306876\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1601.94 | 0.213722 | 0.106861 | − | 0.994274i | \(-0.465920\pi\) | ||||
0.106861 | + | 0.994274i | \(0.465920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5235.40 | −0.693041 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5202.43 | −0.678081 | −0.339041 | − | 0.940772i | \(-0.610102\pi\) | ||||
−0.339041 | + | 0.940772i | \(0.610102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11368.9 | −1.47046 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3974.76 | 0.506309 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4310.87 | −0.544979 | −0.272489 | − | 0.962159i | \(-0.587847\pi\) | ||||
−0.272489 | + | 0.962159i | \(0.587847\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6240.59 | −0.777157 | −0.388579 | − | 0.921416i | \(-0.627034\pi\) | ||||
−0.388579 | + | 0.921416i | \(0.627034\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 230.576 | 0.0285007 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4348.35 | −0.529582 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2047.66 | 0.247556 | 0.123778 | − | 0.992310i | \(-0.460499\pi\) | ||||
0.123778 | + | 0.992310i | \(0.460499\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5249.31 | −0.625427 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19812.5 | 2.34351 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5960.12 | −0.694919 | −0.347459 | − | 0.937695i | \(-0.612956\pi\) | ||||
−0.347459 | + | 0.937695i | \(0.612956\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −311.567 | −0.0360685 | −0.0180342 | − | 0.999837i | \(-0.505741\pi\) | ||||
−0.0180342 | + | 0.999837i | \(0.505741\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9079.00 | −1.03623 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11276.7 | −1.27803 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17105.0 | 1.91164 | 0.955821 | − | 0.293950i | \(-0.0949700\pi\) | ||||
0.955821 | + | 0.293950i | \(0.0949700\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2582.96 | 0.286672 | 0.143336 | − | 0.989674i | \(-0.454217\pi\) | ||||
0.143336 | + | 0.989674i | \(0.454217\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20362.5 | −2.22900 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6797.87 | 0.739054 | 0.369527 | − | 0.929220i | \(-0.379520\pi\) | ||||
0.369527 | + | 0.929220i | \(0.379520\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10454.1 | −1.12119 | −0.560596 | − | 0.828089i | \(-0.689428\pi\) | ||||
−0.560596 | + | 0.828089i | \(0.689428\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2408.90 | −0.256613 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17208.6 | −1.80873 | −0.904367 | − | 0.426755i | \(-0.859657\pi\) | ||||
−0.904367 | + | 0.426755i | \(0.859657\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6117.55 | 0.638723 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5082.40 | −0.523663 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15788.1 | 1.61605 | 0.808025 | − | 0.589148i | \(-0.200537\pi\) | ||||
0.808025 | + | 0.589148i | \(0.200537\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5183.17 | 0.523654 | 0.261827 | − | 0.965115i | \(-0.415675\pi\) | ||||
0.261827 | + | 0.965115i | \(0.415675\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5833.38 | 0.585530 | 0.292765 | − | 0.956184i | \(-0.405425\pi\) | ||||
0.292765 | + | 0.956184i | \(0.405425\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6315.33 | −0.625779 | −0.312889 | − | 0.949790i | \(-0.601297\pi\) | ||||
−0.312889 | + | 0.949790i | \(0.601297\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15435.6 | 1.51972 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2588.59 | −0.251636 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16261.2 | −1.57077 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9735.88 | 0.928692 | 0.464346 | − | 0.885654i | \(-0.346289\pi\) | ||||
0.464346 | + | 0.885654i | \(0.346289\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4221.28 | −0.400153 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17908.4 | 1.67665 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13447.9 | −1.25130 | −0.625649 | − | 0.780104i | \(-0.715166\pi\) | ||||
−0.625649 | + | 0.780104i | \(0.715166\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7028.09 | 0.645974 | 0.322987 | − | 0.946403i | \(-0.395313\pi\) | ||||
0.322987 | + | 0.946403i | \(0.395313\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20253.2 | −1.85022 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 345.391 | 0.0311728 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1655.44 | 0.148513 | 0.0742563 | − | 0.997239i | \(-0.476342\pi\) | ||||
0.0742563 | + | 0.997239i | \(0.476342\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1909.16 | 0.169235 | 0.0846174 | − | 0.996414i | \(-0.473033\pi\) | ||||
0.0846174 | + | 0.996414i | \(0.473033\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25991.8 | −2.29033 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8865.70 | 0.772034 | 0.386017 | − | 0.922492i | \(-0.373851\pi\) | ||||
0.386017 | + | 0.922492i | \(0.373851\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18494.3 | −1.60106 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11806.2 | 1.01018 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1131.62 | 0.0962644 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9256.80 | −0.778403 | −0.389201 | − | 0.921153i | \(-0.627249\pi\) | ||||
−0.389201 | + | 0.921153i | \(0.627249\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13607.5 | 1.13770 | 0.568849 | − | 0.822442i | \(-0.307389\pi\) | ||||
0.568849 | + | 0.822442i | \(0.307389\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1343.23 | −0.111028 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7737.14 | 0.635912 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5938.77 | 0.482621 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26946.2 | −2.17754 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3206.12 | 0.256210 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 483.548 | 0.0384276 | 0.0192138 | − | 0.999815i | \(-0.493884\pi\) | ||||
0.0192138 | + | 0.999815i | \(0.493884\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18679.1 | 1.46812 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4711.28 | −0.368263 | −0.184131 | − | 0.982902i | \(-0.558947\pi\) | ||||
−0.184131 | + | 0.982902i | \(0.558947\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −36275.0 | −2.80466 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6144.73 | −0.472515 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21650.7 | −1.64698 | −0.823492 | − | 0.567327i | \(-0.807977\pi\) | ||||
−0.823492 | + | 0.567327i | \(0.807977\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2512.95 | −0.190137 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14023.0 | −1.04973 | −0.524866 | − | 0.851185i | \(-0.675884\pi\) | ||||
−0.524866 | + | 0.851185i | \(0.675884\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14868.0 | 1.10708 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4875.33 | −0.359200 | −0.179600 | − | 0.983740i | \(-0.557480\pi\) | ||||
−0.179600 | + | 0.983740i | \(0.557480\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25969.1 | −1.90328 | −0.951640 | − | 0.307215i | \(-0.900603\pi\) | ||||
−0.951640 | + | 0.307215i | \(0.900603\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15895.1 | 1.15282 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23113.1 | −1.66761 | −0.833806 | − | 0.552058i | \(-0.813843\pi\) | ||||
−0.833806 | + | 0.552058i | \(0.813843\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30628.9 | −2.18709 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9459.06 | 0.671963 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5471.66 | 0.384735 | 0.192368 | − | 0.981323i | \(-0.438383\pi\) | ||||
0.192368 | + | 0.981323i | \(0.438383\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2405.82 | −0.168302 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22609.2 | −1.56568 | −0.782841 | − | 0.622222i | \(-0.786230\pi\) | ||||
−0.782841 | + | 0.622222i | \(0.786230\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29607.7 | 2.04000 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3708.89 | −0.252990 | −0.126495 | − | 0.991967i | \(-0.540373\pi\) | ||||
−0.126495 | + | 0.991967i | \(0.540373\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10478.2 | −0.711170 | −0.355585 | − | 0.934644i | \(-0.615718\pi\) | ||||
−0.355585 | + | 0.934644i | \(0.615718\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17389.1 | −1.16854 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10713.6 | −0.716392 | −0.358196 | − | 0.933646i | \(-0.616608\pi\) | ||||
−0.358196 | + | 0.933646i | \(0.616608\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1098.55 | 0.0727376 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7860.62 | −0.517924 | −0.258962 | − | 0.965887i | \(-0.583381\pi\) | ||||
−0.258962 | + | 0.965887i | \(0.583381\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8528.00 | 0.556442 | 0.278221 | − | 0.960517i | \(-0.410255\pi\) | ||||
0.278221 | + | 0.960517i | \(0.410255\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8022.89 | −0.520949 | −0.260474 | − | 0.965481i | \(-0.583879\pi\) | ||||
−0.260474 | + | 0.965481i | \(0.583879\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3724.01 | 0.239485 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17014.7 | −1.08894 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24591.2 | 1.55885 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3984.40 | 0.251373 | 0.125687 | − | 0.992070i | \(-0.459887\pi\) | ||||
0.125687 | + | 0.992070i | \(0.459887\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 34506.7 | 2.15647 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3112.43 | 0.193593 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14750.2 | 0.908892 | 0.454446 | − | 0.890774i | \(-0.349837\pi\) | ||||
0.454446 | + | 0.890774i | \(0.349837\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9810.74 | 0.601707 | 0.300854 | − | 0.953670i | \(-0.402728\pi\) | ||||
0.300854 | + | 0.953670i | \(0.402728\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5683.55 | −0.345353 | −0.172677 | − | 0.984979i | \(-0.555242\pi\) | ||||
−0.172677 | + | 0.984979i | \(0.555242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3138.47 | 0.189824 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3405.52 | −0.204086 | −0.102043 | − | 0.994780i | \(-0.532538\pi\) | ||||
−0.102043 | + | 0.994780i | \(0.532538\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25811.8 | 1.53977 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19049.1 | −1.12602 | −0.563011 | − | 0.826449i | \(-0.690357\pi\) | ||||
−0.563011 | + | 0.826449i | \(0.690357\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20422.5 | −1.20173 | −0.600864 | − | 0.799351i | \(-0.705177\pi\) | ||||
−0.600864 | + | 0.799351i | \(0.705177\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 53029.7 | 3.09233 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35458.3 | 2.05840 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6742.13 | 0.387894 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8613.45 | 0.493349 | 0.246675 | − | 0.969098i | \(-0.420662\pi\) | ||||
0.246675 | + | 0.969098i | \(0.420662\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10469.1 | −0.594329 | −0.297164 | − | 0.954826i | \(-0.596041\pi\) | ||||
−0.297164 | + | 0.954826i | \(0.596041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27685.2 | −1.56475 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9490.28 | −0.531677 | −0.265839 | − | 0.964018i | \(-0.585649\pi\) | ||||
−0.265839 | + | 0.964018i | \(0.585649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1465.73 | −0.0817556 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9182.63 | 0.507737 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15814.7 | 0.870652 | 0.435326 | − | 0.900273i | \(-0.356633\pi\) | ||||
0.435326 | + | 0.900273i | \(0.356633\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18047.1 | 0.984985 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34596.6 | −1.88011 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15790.6 | 0.850791 | 0.425395 | − | 0.905008i | \(-0.360135\pi\) | ||||
0.425395 | + | 0.905008i | \(0.360135\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44044.7 | 2.36298 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 40181.7 | 2.13746 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27542.9 | −1.45895 | −0.729474 | − | 0.684009i | \(-0.760235\pi\) | ||||
−0.729474 | + | 0.684009i | \(0.760235\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2351.66 | 0.123521 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3038.68 | 0.158937 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19578.6 | −1.01552 | −0.507761 | − | 0.861498i | \(-0.669527\pi\) | ||||
−0.507761 | + | 0.861498i | \(0.669527\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18251.7 | −0.942756 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28316.4 | 1.45054 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20948.0 | −1.06866 | −0.534330 | − | 0.845276i | \(-0.679436\pi\) | ||||
−0.534330 | + | 0.845276i | \(0.679436\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14639.3 | 0.740702 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 825.349 | 0.0415893 | 0.0207946 | − | 0.999784i | \(-0.493380\pi\) | ||||
0.0207946 | + | 0.999784i | \(0.493380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9228.69 | −0.461253 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22821.1 | 1.13598 | 0.567988 | − | 0.823037i | \(-0.307722\pi\) | ||||
0.567988 | + | 0.823037i | \(0.307722\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12056.5 | −0.595301 | −0.297650 | − | 0.954675i | \(-0.596203\pi\) | ||||
−0.297650 | + | 0.954675i | \(0.596203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13244.8 | −0.651345 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 41657.1 | 2.03220 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7722.32 | 0.375221 | 0.187611 | − | 0.982243i | \(-0.439926\pi\) | ||||
0.187611 | + | 0.982243i | \(0.439926\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −44689.5 | −2.15420 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1440.60 | 0.0691671 | 0.0345835 | − | 0.999402i | \(-0.488990\pi\) | ||||
0.0345835 | + | 0.999402i | \(0.488990\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30722.6 | −1.46346 | −0.731729 | − | 0.681595i | \(-0.761286\pi\) | ||||
−0.731729 | + | 0.681595i | \(0.761286\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28876.8 | −1.37013 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3046.75 | 0.143431 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40280.9 | −1.88890 | −0.944451 | − | 0.328652i | \(-0.893406\pi\) | ||||
−0.944451 | + | 0.328652i | \(0.893406\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4282.45 | 0.199261 | 0.0996306 | − | 0.995024i | \(-0.468234\pi\) | ||||
0.0996306 | + | 0.995024i | \(0.468234\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1877.99 | 0.0870446 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −61965.0 | −2.84997 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −206.503 | −0.00946128 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20180.3 | 0.917537 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12571.6 | −0.569416 | −0.284708 | − | 0.958614i | \(-0.591897\pi\) | ||||
−0.284708 | + | 0.958614i | \(0.591897\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22985.0 | −1.03319 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6545.11 | 0.293094 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28074.0 | 1.24772 | 0.623860 | − | 0.781536i | \(-0.285564\pi\) | ||||
0.623860 | + | 0.781536i | \(0.285564\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6399.66 | −0.283359 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11057.4 | 0.485939 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −51835.9 | −2.26953 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −293.254 | −0.0127445 | −0.00637223 | − | 0.999980i | \(-0.502028\pi\) | ||||
−0.00637223 | + | 0.999980i | \(0.502028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45634.2 | −1.97588 | −0.987938 | − | 0.154851i | \(-0.950510\pi\) | ||||
−0.987938 | + | 0.154851i | \(0.950510\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2944.34 | −0.126547 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26220.0 | 1.12279 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5406.68 | −0.229835 | −0.114917 | − | 0.993375i | \(-0.536660\pi\) | ||||
−0.114917 | + | 0.993375i | \(0.536660\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1228.88 | −0.0520487 | −0.0260243 | − | 0.999661i | \(-0.508285\pi\) | ||||
−0.0260243 | + | 0.999661i | \(0.508285\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45769.8 | 1.92451 | 0.962256 | − | 0.272147i | \(-0.0877337\pi\) | ||||
0.962256 | + | 0.272147i | \(0.0877337\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13630.9 | 0.571076 | 0.285538 | − | 0.958367i | \(-0.407828\pi\) | ||||
0.285538 | + | 0.958367i | \(0.407828\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18131.6 | −0.754167 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22210.9 | 0.920525 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44987.6 | 1.85119 | 0.925593 | − | 0.378520i | \(-0.123567\pi\) | ||||
0.925593 | + | 0.378520i | \(0.123567\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38778.4 | 1.59000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30920.0 | −1.25879 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26882.5 | 1.09055 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43053.2 | −1.73425 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26043.2 | −1.04537 | −0.522685 | − | 0.852526i | \(-0.675070\pi\) | ||||
−0.522685 | + | 0.852526i | \(0.675070\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13706.4 | −0.546327 | −0.273163 | − | 0.961968i | \(-0.588070\pi\) | ||||
−0.273163 | + | 0.961968i | \(0.588070\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45319.1 | −1.80008 | −0.900039 | − | 0.435810i | \(-0.856462\pi\) | ||||
−0.900039 | + | 0.435810i | \(0.856462\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28057.3 | 1.10670 | 0.553350 | − | 0.832949i | \(-0.313349\pi\) | ||||
0.553350 | + | 0.832949i | \(0.313349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24378.4 | 0.958253 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3673.83 | 0.143413 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8959.00 | −0.348524 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4531.85 | 0.175091 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3923.18 | −0.151056 | −0.0755282 | − | 0.997144i | \(-0.524064\pi\) | ||||
−0.0755282 | + | 0.997144i | \(0.524064\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2441.97 | 0.0933849 | 0.0466924 | − | 0.998909i | \(-0.485132\pi\) | ||||
0.0466924 | + | 0.998909i | \(0.485132\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44576.9 | 1.69890 | 0.849452 | − | 0.527667i | \(-0.176933\pi\) | ||||
0.849452 | + | 0.527667i | \(0.176933\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17095.5 | 0.647137 | 0.323568 | − | 0.946205i | \(-0.395117\pi\) | ||||
0.323568 | + | 0.946205i | \(0.395117\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −53345.2 | −2.01253 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11462.3 | −0.429530 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11436.4 | −0.427126 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4189.37 | 0.155421 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53493.8 | −1.97795 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9662.79 | −0.354919 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33142.7 | −1.21332 | −0.606662 | − | 0.794960i | \(-0.707492\pi\) | ||||
−0.606662 | + | 0.794960i | \(0.707492\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32750.5 | 1.19108 | 0.595539 | − | 0.803326i | \(-0.296939\pi\) | ||||
0.595539 | + | 0.803326i | \(0.296939\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18312.5 | 0.663805 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −39903.5 | −1.43700 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6095.76 | −0.218804 | −0.109402 | − | 0.993998i | \(-0.534894\pi\) | ||||
−0.109402 | + | 0.993998i | \(0.534894\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −200.468 | −0.00714897 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34381.5 | −1.22212 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24708.0 | −0.872597 | −0.436298 | − | 0.899802i | \(-0.643711\pi\) | ||||
−0.436298 | + | 0.899802i | \(0.643711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32475.0 | −1.14321 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17701.9 | −0.619161 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44713.2 | −1.55893 | −0.779465 | − | 0.626446i | \(-0.784509\pi\) | ||||
−0.779465 | + | 0.626446i | \(0.784509\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10172.7 | −0.352414 | −0.176207 | − | 0.984353i | \(-0.556383\pi\) | ||||
−0.176207 | + | 0.984353i | \(0.556383\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 60570.1 | 2.09166 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13346.6 | 0.457978 | 0.228989 | − | 0.973429i | \(-0.426458\pi\) | ||||
0.228989 | + | 0.973429i | \(0.426458\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10734.3 | 0.367176 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36232.4 | −1.23157 | −0.615783 | − | 0.787916i | \(-0.711160\pi\) | ||||
−0.615783 | + | 0.787916i | \(0.711160\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2815.26 | 0.0953924 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2265.92 | 0.0762988 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29513.2 | −0.990673 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26495.6 | 0.883857 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5429.03 | −0.180544 | −0.0902718 | − | 0.995917i | \(-0.528774\pi\) | ||||
−0.0902718 | + | 0.995917i | \(0.528774\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5645.37 | 0.186579 | 0.0932897 | − | 0.995639i | \(-0.470262\pi\) | ||||
0.0932897 | + | 0.995639i | \(0.470262\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27899.7 | −0.919242 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 51103.6 | 1.67344 | 0.836719 | − | 0.547632i | \(-0.184471\pi\) | ||||
0.836719 | + | 0.547632i | \(0.184471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2226.52 | −0.0726863 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32082.5 | −1.04097 | −0.520485 | − | 0.853871i | \(-0.674249\pi\) | ||||
−0.520485 | + | 0.853871i | \(0.674249\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1843.60 | −0.0596364 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25629.8 | −0.824043 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27696.1 | 0.887785 | 0.443893 | − | 0.896080i | \(-0.353597\pi\) | ||||
0.443893 | + | 0.896080i | \(0.353597\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10906.6 | −0.347500 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41284.9 | 1.31144 | 0.655720 | − | 0.755004i | \(-0.272365\pi\) | ||||
0.655720 | + | 0.755004i | \(0.272365\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1728.4.a.br.1.2 | 2 | ||
3.2 | odd | 2 | 1728.4.a.bj.1.1 | 2 | |||
4.3 | odd | 2 | 1728.4.a.bq.1.2 | 2 | |||
8.3 | odd | 2 | 216.4.a.f.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 432.4.a.p.1.1 | 2 | |||
12.11 | even | 2 | 1728.4.a.bi.1.1 | 2 | |||
24.5 | odd | 2 | 432.4.a.r.1.2 | 2 | |||
24.11 | even | 2 | 216.4.a.g.1.2 | yes | 2 | ||
72.11 | even | 6 | 648.4.i.o.433.1 | 4 | |||
72.43 | odd | 6 | 648.4.i.r.433.2 | 4 | |||
72.59 | even | 6 | 648.4.i.o.217.1 | 4 | |||
72.67 | odd | 6 | 648.4.i.r.217.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.4.a.f.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
216.4.a.g.1.2 | yes | 2 | 24.11 | even | 2 | ||
432.4.a.p.1.1 | 2 | 8.5 | even | 2 | |||
432.4.a.r.1.2 | 2 | 24.5 | odd | 2 | |||
648.4.i.o.217.1 | 4 | 72.59 | even | 6 | |||
648.4.i.o.433.1 | 4 | 72.11 | even | 6 | |||
648.4.i.r.217.2 | 4 | 72.67 | odd | 6 | |||
648.4.i.r.433.2 | 4 | 72.43 | odd | 6 | |||
1728.4.a.bi.1.1 | 2 | 12.11 | even | 2 | |||
1728.4.a.bj.1.1 | 2 | 3.2 | odd | 2 | |||
1728.4.a.bq.1.2 | 2 | 4.3 | odd | 2 | |||
1728.4.a.br.1.2 | 2 | 1.1 | even | 1 | trivial |