Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 31 x^{10} + 131 x^{9} + 309 x^{8} - 1453 x^{7} - 1072 x^{6} + 6350 x^{5} + 1411 x^{4} - 11022 x^{3} - 2450 x^{2} + 6960 x + 3008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(3.77676\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.77676 | 1.68902 | 0.844509 | − | 0.535542i | \(-0.179892\pi\) | ||||
0.844509 | + | 0.535542i | \(0.179892\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.75359 | −0.662796 | −0.331398 | − | 0.943491i | \(-0.607520\pi\) | ||||
−0.331398 | + | 0.943491i | \(0.607520\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41460 | 0.728030 | 0.364015 | − | 0.931393i | \(-0.381406\pi\) | ||||
0.364015 | + | 0.931393i | \(0.381406\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.58092 | −0.438469 | −0.219235 | − | 0.975672i | \(-0.570356\pi\) | ||||
−0.219235 | + | 0.975672i | \(0.570356\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.77676 | 0.975155 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.811189 | 0.196742 | 0.0983712 | − | 0.995150i | \(-0.468637\pi\) | ||||
0.0983712 | + | 0.995150i | \(0.468637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.41955 | 0.784498 | 0.392249 | − | 0.919859i | \(-0.371697\pi\) | ||||
0.392249 | + | 0.919859i | \(0.371697\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.75359 | −0.382665 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.93574 | 1.44620 | 0.723101 | − | 0.690742i | \(-0.242716\pi\) | ||||
0.723101 | + | 0.690742i | \(0.242716\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.26390 | 1.85278 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.520367 | −0.0966297 | −0.0483149 | − | 0.998832i | \(-0.515385\pi\) | ||||
−0.0483149 | + | 0.998832i | \(0.515385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.53773 | −0.635394 | −0.317697 | − | 0.948192i | \(-0.602910\pi\) | ||||
−0.317697 | + | 0.948192i | \(0.602910\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.41460 | 0.420328 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.62290 | −1.11947 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.20908 | −1.51396 | −0.756982 | − | 0.653436i | \(-0.773327\pi\) | ||||
−0.756982 | + | 0.653436i | \(0.773327\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.58092 | −0.253150 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.31600 | −0.517873 | −0.258936 | − | 0.965894i | \(-0.583372\pi\) | ||||
−0.258936 | + | 0.965894i | \(0.583372\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00002 | 0.914995 | 0.457498 | − | 0.889211i | \(-0.348746\pi\) | ||||
0.457498 | + | 0.889211i | \(0.348746\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.77676 | 0.563006 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.4567 | 1.81699 | 0.908496 | − | 0.417893i | \(-0.137231\pi\) | ||||
0.908496 | + | 0.417893i | \(0.137231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.92491 | −0.560701 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.811189 | 0.113589 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.1117 | 1.66368 | 0.831838 | − | 0.555019i | \(-0.187289\pi\) | ||||
0.831838 | + | 0.555019i | \(0.187289\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.11937 | 1.22966 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.41955 | 0.452930 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.0728 | −1.31137 | −0.655683 | − | 0.755036i | \(-0.727619\pi\) | ||||
−0.655683 | + | 0.755036i | \(0.727619\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.5319 | −1.73258 | −0.866289 | − | 0.499544i | \(-0.833501\pi\) | ||||
−0.866289 | + | 0.499544i | \(0.833501\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.75359 | −0.220932 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.97076 | −0.740582 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.1817 | −1.73257 | −0.866286 | − | 0.499548i | \(-0.833500\pi\) | ||||
−0.866286 | + | 0.499548i | \(0.833500\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.93574 | 0.834965 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.5259 | 1.36787 | 0.683934 | − | 0.729544i | \(-0.260268\pi\) | ||||
0.683934 | + | 0.729544i | \(0.260268\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.71440 | 0.434738 | 0.217369 | − | 0.976089i | \(-0.430252\pi\) | ||||
0.217369 | + | 0.976089i | \(0.430252\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.26390 | 1.06970 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.23423 | −0.482536 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9098 | 1.45246 | 0.726232 | − | 0.687450i | \(-0.241270\pi\) | ||||
0.726232 | + | 0.687450i | \(0.241270\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0558 | 1.43306 | 0.716532 | − | 0.697554i | \(-0.245728\pi\) | ||||
0.716532 | + | 0.697554i | \(0.245728\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.06367 | 0.332301 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.520367 | −0.0557892 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.129594 | 0.0137369 | 0.00686844 | − | 0.999976i | \(-0.497814\pi\) | ||||
0.00686844 | + | 0.999976i | \(0.497814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.77230 | 0.290616 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.53773 | −0.366845 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.9148 | 1.32503 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.6438 | −1.18225 | −0.591123 | − | 0.806582i | \(-0.701315\pi\) | ||||
−0.591123 | + | 0.806582i | \(0.701315\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.41460 | 0.242677 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.16093 | 0.911547 | 0.455773 | − | 0.890096i | \(-0.349363\pi\) | ||||
0.455773 | + | 0.890096i | \(0.349363\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.06620 | −0.203589 | −0.101794 | − | 0.994805i | \(-0.532458\pi\) | ||||
−0.101794 | + | 0.994805i | \(0.532458\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.62290 | −0.646329 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.49830 | 0.338194 | 0.169097 | − | 0.985599i | \(-0.445915\pi\) | ||||
0.169097 | + | 0.985599i | \(0.445915\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.78182 | 0.841146 | 0.420573 | − | 0.907259i | \(-0.361829\pi\) | ||||
0.420573 | + | 0.907259i | \(0.361829\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.20908 | −0.874087 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.230019 | −0.0216384 | −0.0108192 | − | 0.999941i | \(-0.503444\pi\) | ||||
−0.0108192 | + | 0.999941i | \(0.503444\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.1946 | 2.44266 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.58092 | −0.146156 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.42250 | −0.130400 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.16969 | −0.469972 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.31600 | −0.298994 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 16.1037 | 1.44036 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.4655 | −1.01740 | −0.508698 | − | 0.860945i | \(-0.669873\pi\) | ||||
−0.508698 | + | 0.860945i | \(0.669873\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00002 | 0.528273 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.3513 | 1.60336 | 0.801680 | − | 0.597754i | \(-0.203940\pi\) | ||||
0.801680 | + | 0.597754i | \(0.203940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.99650 | −0.519962 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.77676 | 0.325052 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.8506 | −1.43964 | −0.719822 | − | 0.694159i | \(-0.755776\pi\) | ||||
−0.719822 | + | 0.694159i | \(0.755776\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.9744 | 1.01566 | 0.507830 | − | 0.861458i | \(-0.330448\pi\) | ||||
0.507830 | + | 0.861458i | \(0.330448\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.4567 | 1.04904 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.81730 | −0.319219 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.96530 | −0.163209 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.92491 | −0.323721 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.00922 | 0.656141 | 0.328071 | − | 0.944653i | \(-0.393602\pi\) | ||||
0.328071 | + | 0.944653i | \(0.393602\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3118 | 0.920545 | 0.460272 | − | 0.887778i | \(-0.347752\pi\) | ||||
0.460272 | + | 0.887778i | \(0.347752\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.811189 | 0.0655808 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.3611 | −1.07319 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.7028 | −1.33303 | −0.666514 | − | 0.745492i | \(-0.732215\pi\) | ||||
−0.666514 | + | 0.745492i | \(0.732215\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.1117 | 0.960523 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.1625 | −0.958537 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.1384 | −1.18573 | −0.592864 | − | 0.805302i | \(-0.702003\pi\) | ||||
−0.592864 | + | 0.805302i | \(0.702003\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.11937 | 0.709942 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5007 | −0.807745 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.41955 | 0.261499 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.6112 | −1.49101 | −0.745507 | − | 0.666498i | \(-0.767792\pi\) | ||||
−0.745507 | + | 0.666498i | \(0.767792\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.2451 | −1.22802 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.0728 | −0.757117 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.58562 | −0.716463 | −0.358231 | − | 0.933633i | \(-0.616620\pi\) | ||||
−0.358231 | + | 0.933633i | \(0.616620\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6532 | 0.866176 | 0.433088 | − | 0.901352i | \(-0.357424\pi\) | ||||
0.433088 | + | 0.901352i | \(0.357424\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.5319 | −1.00030 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −34.7805 | −2.55711 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.95870 | 0.143234 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.75359 | −0.127555 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.42341 | −0.320067 | −0.160034 | − | 0.987112i | \(-0.551160\pi\) | ||||
−0.160034 | + | 0.987112i | \(0.551160\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.6988 | 1.34597 | 0.672983 | − | 0.739658i | \(-0.265013\pi\) | ||||
0.672983 | + | 0.739658i | \(0.265013\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.97076 | −0.427575 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.0189 | 0.927557 | 0.463778 | − | 0.885951i | \(-0.346493\pi\) | ||||
0.463778 | + | 0.885951i | \(0.346493\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.19991 | 0.0850596 | 0.0425298 | − | 0.999095i | \(-0.486458\pi\) | ||||
0.0425298 | + | 0.999095i | \(0.486458\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.1817 | −1.00030 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.912512 | 0.0640458 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.5237 | −0.874696 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.93574 | 0.482067 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.25685 | 0.571139 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.264859 | −0.0182336 | −0.00911681 | − | 0.999958i | \(-0.502902\pi\) | ||||
−0.00911681 | + | 0.999958i | \(0.502902\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.5259 | 0.789739 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.6606 | 1.54544 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.20373 | 0.421137 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.71440 | 0.250996 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.28243 | −0.0862654 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.3649 | −0.694086 | −0.347043 | − | 0.937849i | \(-0.612814\pi\) | ||||
−0.347043 | + | 0.937849i | \(0.612814\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.26390 | 0.617594 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.46824 | −0.562057 | −0.281028 | − | 0.959699i | \(-0.590676\pi\) | ||||
−0.281028 | + | 0.959699i | \(0.590676\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.0378672 | 0.00250233 | 0.00125117 | − | 0.999999i | \(-0.499602\pi\) | ||||
0.00125117 | + | 0.999999i | \(0.499602\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.23423 | −0.278592 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.89120 | 0.123896 | 0.0619482 | − | 0.998079i | \(-0.480269\pi\) | ||||
0.0619482 | + | 0.998079i | \(0.480269\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 47.0458 | 3.06893 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.9098 | 0.838580 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.5619 | −1.20067 | −0.600334 | − | 0.799749i | \(-0.704966\pi\) | ||||
−0.600334 | + | 0.799749i | \(0.704966\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.3402 | 1.82555 | 0.912776 | − | 0.408462i | \(-0.133935\pi\) | ||||
0.912776 | + | 0.408462i | \(0.133935\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.8234 | −0.947035 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.40604 | −0.343978 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.0558 | 0.827380 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.7155 | −0.865717 | −0.432858 | − | 0.901462i | \(-0.642495\pi\) | ||||
−0.432858 | + | 0.901462i | \(0.642495\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.7471 | 1.05288 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.06367 | 0.191854 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.7495 | 1.54383 | 0.771917 | − | 0.635724i | \(-0.219298\pi\) | ||||
0.771917 | + | 0.635724i | \(0.219298\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.1490 | 1.00345 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.520367 | −0.0322099 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.68918 | −0.412472 | −0.206236 | − | 0.978502i | \(-0.566121\pi\) | ||||
−0.206236 | + | 0.978502i | \(0.566121\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 45.7431 | 2.80998 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.129594 | 0.00793099 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4921 | −0.822628 | −0.411314 | − | 0.911494i | \(-0.634930\pi\) | ||||
−0.411314 | + | 0.911494i | \(0.634930\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.0913 | −1.40270 | −0.701349 | − | 0.712818i | \(-0.747418\pi\) | ||||
−0.701349 | + | 0.712818i | \(0.747418\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.77230 | 0.167787 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.3687 | 1.34888 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.5004 | 0.630906 | 0.315453 | − | 0.948941i | \(-0.397843\pi\) | ||||
0.315453 | + | 0.948941i | \(0.397843\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.53773 | −0.211798 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.39023 | 0.440864 | 0.220432 | − | 0.975402i | \(-0.429253\pi\) | ||||
0.220432 | + | 0.975402i | \(0.429253\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.2756 | −0.610819 | −0.305410 | − | 0.952221i | \(-0.598793\pi\) | ||||
−0.305410 | + | 0.952221i | \(0.598793\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.9148 | 0.765007 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.81492 | 0.343244 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3420 | −0.961292 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.6438 | −0.682570 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.5362 | −0.673950 | −0.336975 | − | 0.941514i | \(-0.609404\pi\) | ||||
−0.336975 | + | 0.941514i | \(0.609404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.0425 | −2.21492 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.41460 | 0.140109 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.9649 | −0.634115 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.5216 | −0.606455 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.16093 | 0.526282 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −51.1066 | −2.92635 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.0628 | −1.71577 | −0.857887 | − | 0.513839i | \(-0.828223\pi\) | ||||
−0.857887 | + | 0.513839i | \(0.828223\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.06620 | −0.117542 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.22673 | 0.182971 | 0.0914856 | − | 0.995806i | \(-0.470838\pi\) | ||||
0.0914856 | + | 0.995806i | \(0.470838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.2220 | 0.973448 | 0.486724 | − | 0.873556i | \(-0.338192\pi\) | ||||
0.486724 | + | 0.873556i | \(0.338192\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.62290 | −0.373158 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.51767 | 0.478400 | 0.239200 | − | 0.970970i | \(-0.423115\pi\) | ||||
0.239200 | + | 0.970970i | \(0.423115\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.25648 | −0.0703494 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.49830 | 0.195256 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.77390 | 0.154344 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.6455 | −0.812387 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.78182 | 0.485636 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.8439 | −1.20430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5876 | 0.856770 | 0.428385 | − | 0.903596i | \(-0.359083\pi\) | ||||
0.428385 | + | 0.903596i | \(0.359083\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.20908 | −0.504655 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −53.5609 | −2.92635 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.7917 | −1.35049 | −0.675246 | − | 0.737593i | \(-0.735962\pi\) | ||||
−0.675246 | + | 0.737593i | \(0.735962\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.230019 | −0.0124929 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.54220 | −0.462586 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1579 | 1.03443 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 26.1946 | 1.41027 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.0028 | 1.07380 | 0.536902 | − | 0.843645i | \(-0.319594\pi\) | ||||
0.536902 | + | 0.843645i | \(0.319594\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.8599 | 0.688374 | 0.344187 | − | 0.938901i | \(-0.388155\pi\) | ||||
0.344187 | + | 0.938901i | \(0.388155\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.58092 | −0.0843834 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.4529 | −0.928922 | −0.464461 | − | 0.885594i | \(-0.653752\pi\) | ||||
−0.464461 | + | 0.885594i | \(0.653752\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 43.5304 | 2.31035 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.42250 | −0.0752865 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.6090 | −1.56270 | −0.781352 | − | 0.624091i | \(-0.785469\pi\) | ||||
−0.781352 | + | 0.624091i | \(0.785469\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.30668 | −0.384562 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.16969 | −0.271338 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0284 | 0.734281 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.1359 | 1.57308 | 0.786540 | − | 0.617540i | \(-0.211871\pi\) | ||||
0.786540 | + | 0.617540i | \(0.211871\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.31600 | −0.172624 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.2391 | −1.10268 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0710 | 0.521458 | 0.260729 | − | 0.965412i | \(-0.416037\pi\) | ||||
0.260729 | + | 0.965412i | \(0.416037\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.1037 | 0.831593 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.822660 | 0.0423691 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7931 | −0.554407 | −0.277203 | − | 0.960811i | \(-0.589408\pi\) | ||||
−0.277203 | + | 0.960811i | \(0.589408\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.4655 | −0.587394 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 35.0045 | 1.78865 | 0.894323 | − | 0.447422i | \(-0.147658\pi\) | ||||
0.894323 | + | 0.447422i | \(0.147658\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.9917 | −0.815011 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.00002 | 0.304998 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.6554 | 0.641655 | 0.320828 | − | 0.947138i | \(-0.396039\pi\) | ||||
0.320828 | + | 0.947138i | \(0.396039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.62620 | 0.284529 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.3513 | 0.925700 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 48.7571 | 2.45324 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.1156 | 1.16014 | 0.580069 | − | 0.814567i | \(-0.303025\pi\) | ||||
0.580069 | + | 0.814567i | \(0.303025\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.99650 | −0.300200 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.3533 | −0.566956 | −0.283478 | − | 0.958979i | \(-0.591488\pi\) | ||||
−0.283478 | + | 0.958979i | \(0.591488\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.59287 | 0.278601 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.77676 | 0.187669 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.2363 | −1.10221 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.5045 | −1.65669 | −0.828346 | − | 0.560217i | \(-0.810718\pi\) | ||||
−0.828346 | + | 0.560217i | \(0.810718\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.8506 | −0.831178 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.6636 | 0.869168 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 49.3087 | 2.42047 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.9744 | 0.586391 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.2541 | 1.28260 | 0.641299 | − | 0.767291i | \(-0.278396\pi\) | ||||
0.641299 | + | 0.767291i | \(0.278396\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.5746 | −1.34390 | −0.671951 | − | 0.740596i | \(-0.734543\pi\) | ||||
−0.671951 | + | 0.740596i | \(0.734543\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.4567 | 0.605664 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.51478 | 0.364520 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.7294 | 1.14835 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.81730 | −0.184301 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.4575 | −1.17808 | −0.589039 | − | 0.808105i | \(-0.700493\pi\) | ||||
−0.589039 | + | 0.808105i | \(0.700493\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.62253 | −0.126031 | −0.0630153 | − | 0.998013i | \(-0.520072\pi\) | ||||
−0.0630153 | + | 0.998013i | \(0.520072\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.96530 | −0.0942289 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.7171 | 1.13454 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.1576 | 1.39161 | 0.695807 | − | 0.718228i | \(-0.255047\pi\) | ||||
0.695807 | + | 0.718228i | \(0.255047\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.92491 | −0.186900 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −40.5738 | −1.92772 | −0.963859 | − | 0.266411i | \(-0.914162\pi\) | ||||
−0.963859 | + | 0.266411i | \(0.914162\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.489443 | 0.0232018 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.00922 | 0.378823 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.1601 | −1.28176 | −0.640881 | − | 0.767640i | \(-0.721431\pi\) | ||||
−0.640881 | + | 0.767640i | \(0.721431\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.00683 | −0.377027 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.3118 | 0.531477 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.4703 | 0.490855 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −39.8219 | −1.86279 | −0.931396 | − | 0.364007i | \(-0.881408\pi\) | ||||
−0.931396 | + | 0.364007i | \(0.881408\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.811189 | 0.0378631 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.6135 | 1.37924 | 0.689618 | − | 0.724173i | \(-0.257778\pi\) | ||||
0.689618 | + | 0.724173i | \(0.257778\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.07428 | 0.0964001 | 0.0482000 | − | 0.998838i | \(-0.484652\pi\) | ||||
0.0482000 | + | 0.998838i | \(0.484652\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.3611 | −0.619608 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.02001 | 0.417396 | 0.208698 | − | 0.977980i | \(-0.433077\pi\) | ||||
0.208698 | + | 0.977980i | \(0.433077\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.8690 | 1.14834 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.7028 | −0.769625 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.4877 | 0.666144 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.6784 | 1.45350 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.1117 | 0.554558 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.6751 | −1.17312 | −0.586562 | − | 0.809904i | \(-0.699519\pi\) | ||||
−0.586562 | + | 0.809904i | \(0.699519\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.5588 | 0.663826 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.1625 | −0.553412 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −43.9757 | −1.99683 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.17918 | 0.0534337 | 0.0267169 | − | 0.999643i | \(-0.491495\pi\) | ||||
0.0267169 | + | 0.999643i | \(0.491495\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.1384 | −0.684581 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.20030 | 0.144428 | 0.0722138 | − | 0.997389i | \(-0.476994\pi\) | ||||
0.0722138 | + | 0.997389i | \(0.476994\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.422116 | −0.0190112 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.11937 | 0.409885 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.2117 | −0.906617 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.2627 | 1.35475 | 0.677373 | − | 0.735640i | \(-0.263118\pi\) | ||||
0.677373 | + | 0.735640i | \(0.263118\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.41219 | 0.375081 | 0.187540 | − | 0.982257i | \(-0.439948\pi\) | ||||
0.187540 | + | 0.982257i | \(0.439948\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.5986 | 1.53962 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.5007 | −0.466352 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.2162 | −1.38363 | −0.691816 | − | 0.722074i | \(-0.743189\pi\) | ||||
−0.691816 | + | 0.722074i | \(0.743189\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.51356 | −0.288143 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.41955 | 0.150977 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.80354 | −0.343865 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.0779 | 1.32283 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.6112 | −0.860837 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.42706 | 0.106331 | 0.0531656 | − | 0.998586i | \(-0.483069\pi\) | ||||
0.0531656 | + | 0.998586i | \(0.483069\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.6211 | 0.464429 | 0.232214 | − | 0.972665i | \(-0.425403\pi\) | ||||
0.232214 | + | 0.972665i | \(0.425403\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.2451 | −0.708995 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.86977 | −0.125009 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.1045 | 1.09150 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.0728 | −0.437122 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.24235 | 0.227071 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.2123 | 0.571215 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.58562 | −0.413650 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.47710 | −0.408208 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.6519 | −0.844902 | −0.422451 | − | 0.906386i | \(-0.638830\pi\) | ||||
−0.422451 | + | 0.906386i | \(0.638830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.6532 | 0.500087 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.1668 | 1.42071 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.2002 | 0.820941 | 0.410471 | − | 0.911874i | \(-0.365364\pi\) | ||||
0.410471 | + | 0.911874i | \(0.365364\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.5319 | −0.577526 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.77942 | −0.0758059 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.6385 | −0.962687 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −34.7805 | −1.47635 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.0785 | 0.681268 | 0.340634 | − | 0.940196i | \(-0.389358\pi\) | ||||
0.340634 | + | 0.940196i | \(0.389358\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.48558 | −0.401197 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.95870 | 0.0826964 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.0926 | 1.35254 | 0.676270 | − | 0.736654i | \(-0.263595\pi\) | ||||
0.676270 | + | 0.736654i | \(0.263595\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.868728 | −0.0365476 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.75359 | −0.0736440 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.5180 | 0.482861 | 0.241430 | − | 0.970418i | \(-0.422383\pi\) | ||||
0.241430 | + | 0.970418i | \(0.422383\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.7614 | −0.534050 | −0.267025 | − | 0.963690i | \(-0.586041\pi\) | ||||
−0.267025 | + | 0.963690i | \(0.586041\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.42341 | −0.184791 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 64.2521 | 2.67950 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.3828 | −0.848546 | −0.424273 | − | 0.905534i | \(-0.639470\pi\) | ||||
−0.424273 | + | 0.905534i | \(0.639470\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.6988 | 0.777094 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.8946 | −0.949829 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.2450 | 1.21121 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.97076 | −0.246861 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −41.5389 | −1.71450 | −0.857248 | − | 0.514904i | \(-0.827827\pi\) | ||||
−0.857248 | + | 0.514904i | \(0.827827\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0974 | −0.498466 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.0189 | 0.535525 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.55642 | 0.310305 | 0.155152 | − | 0.987891i | \(-0.450413\pi\) | ||||
0.155152 | + | 0.987891i | \(0.450413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.37242 | −0.220248 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.19991 | 0.0491092 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.56179 | 0.227249 | 0.113624 | − | 0.993524i | \(-0.463754\pi\) | ||||
0.113624 | + | 0.993524i | \(0.463754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.53324 | −0.144124 | −0.0720619 | − | 0.997400i | \(-0.522958\pi\) | ||||
−0.0720619 | + | 0.997400i | \(0.522958\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.1817 | −0.577524 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.5247 | −0.793791 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.0346 | 0.610236 | 0.305118 | − | 0.952314i | \(-0.401304\pi\) | ||||
0.305118 | + | 0.952314i | \(0.401304\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.912512 | 0.0369769 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.6930 | −0.796695 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.2450 | −1.54470 | −0.772350 | − | 0.635197i | \(-0.780919\pi\) | ||||
−0.772350 | + | 0.635197i | \(0.780919\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.5237 | −0.505006 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.92434 | 0.278764 | 0.139382 | − | 0.990239i | \(-0.455488\pi\) | ||||
0.139382 | + | 0.990239i | \(0.455488\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.8045 | −1.35872 | −0.679359 | − | 0.733806i | \(-0.737742\pi\) | ||||
−0.679359 | + | 0.733806i | \(0.737742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.93574 | 0.278322 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.227254 | −0.00910475 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5004 | 0.580016 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.25685 | 0.329747 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.47031 | −0.297861 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.7676 | 0.826746 | 0.413373 | − | 0.910562i | \(-0.364351\pi\) | ||||
0.413373 | + | 0.910562i | \(0.364351\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.264859 | −0.0105272 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −43.3023 | −1.71840 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.20498 | 0.245850 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.5259 | 0.455956 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.4228 | −1.67560 | −0.837800 | − | 0.545977i | \(-0.816158\pi\) | ||||
−0.837800 | + | 0.545977i | \(0.816158\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.1884 | −0.677844 | −0.338922 | − | 0.940814i | \(-0.610062\pi\) | ||||
−0.338922 | + | 0.940814i | \(0.610062\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.6606 | 0.892262 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.9398 | −1.33431 | −0.667155 | − | 0.744919i | \(-0.732488\pi\) | ||||
−0.667155 | + | 0.744919i | \(0.732488\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.3218 | −0.954714 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.20373 | 0.243143 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.87635 | −0.151693 | −0.0758466 | − | 0.997119i | \(-0.524166\pi\) | ||||
−0.0758466 | + | 0.997119i | \(0.524166\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 69.3084 | 2.70810 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.71440 | 0.144913 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.8087 | 0.927457 | 0.463728 | − | 0.885977i | \(-0.346511\pi\) | ||||
0.463728 | + | 0.885977i | \(0.346511\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.05094 | 0.118668 | 0.0593340 | − | 0.998238i | \(-0.481102\pi\) | ||||
0.0593340 | + | 0.998238i | \(0.481102\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.28243 | −0.0498054 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.6473 | −0.878226 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.60913 | −0.139746 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.3649 | −0.400731 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.6741 | −1.26137 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.3106 | −0.590180 | −0.295090 | − | 0.955469i | \(-0.595350\pi\) | ||||
−0.295090 | + | 0.955469i | \(0.595350\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.26390 | 0.356568 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.9262 | 0.650526 | 0.325263 | − | 0.945624i | \(-0.394547\pi\) | ||||
0.325263 | + | 0.945624i | \(0.394547\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.4184 | 0.783588 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.46824 | −0.324504 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.54551 | −0.0591372 | −0.0295686 | − | 0.999563i | \(-0.509413\pi\) | ||||
−0.0295686 | + | 0.999563i | \(0.509413\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −63.6406 | −2.43158 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.0378672 | 0.00144472 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.1477 | −0.729470 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.5564 | −1.16242 | −0.581211 | − | 0.813753i | \(-0.697421\pi\) | ||||
−0.581211 | + | 0.813753i | \(0.697421\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.23423 | −0.160845 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 45.2246 | 1.71547 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.68991 | −0.101887 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.89120 | 0.0715316 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.5235 | −1.45501 | −0.727507 | − | 0.686100i | \(-0.759321\pi\) | ||||
−0.727507 | + | 0.686100i | \(0.759321\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.4909 | −1.18770 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 47.0458 | 1.77185 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.0646 | −0.604170 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.4274 | 0.729610 | 0.364805 | − | 0.931084i | \(-0.381136\pi\) | ||||
0.364805 | + | 0.931084i | \(0.381136\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.9098 | 0.484155 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.5368 | −0.918909 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.4170 | −0.539166 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.5619 | −0.693206 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.55899 | 0.0954341 | 0.0477170 | − | 0.998861i | \(-0.484805\pi\) | ||||
0.0477170 | + | 0.998861i | \(0.484805\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.62328 | 0.134938 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.3402 | 1.05398 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.82063 | −0.179034 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.2028 | 0.749282 | 0.374641 | − | 0.927170i | \(-0.377766\pi\) | ||||
0.374641 | + | 0.927170i | \(0.377766\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.86716 | 0.180018 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.2646 | 0.600745 | 0.300372 | − | 0.953822i | \(-0.402889\pi\) | ||||
0.300372 | + | 0.953822i | \(0.402889\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.8234 | −0.546771 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −34.2432 | −1.26137 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.8478 | −1.76011 | −0.880054 | − | 0.474873i | \(-0.842494\pi\) | ||||
−0.880054 | + | 0.474873i | \(0.842494\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.40604 | −0.198596 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.1597 | −1.21651 | −0.608256 | − | 0.793741i | \(-0.708130\pi\) | ||||
−0.608256 | + | 0.793741i | \(0.708130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.2489 | 1.10823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.0558 | 0.477688 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.13460 | −0.224154 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.8667 | 1.60072 | 0.800359 | − | 0.599521i | \(-0.204642\pi\) | ||||
0.800359 | + | 0.599521i | \(0.204642\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.7155 | −0.499822 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 42.7221 | 1.55482 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.8859 | −1.74044 | −0.870221 | − | 0.492661i | \(-0.836024\pi\) | ||||
−0.870221 | + | 0.492661i | \(0.836024\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.7471 | 0.607880 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.3472 | 0.520084 | 0.260042 | − | 0.965597i | \(-0.416264\pi\) | ||||
0.260042 | + | 0.965597i | \(0.416264\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.3997 | −0.557508 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.06367 | 0.110767 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.9243 | 0.574993 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.42450 | 0.231673 | 0.115837 | − | 0.993268i | \(-0.463045\pi\) | ||||
0.115837 | + | 0.993268i | \(0.463045\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.7495 | 0.891332 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.35272 | 0.156556 | 0.0782782 | − | 0.996932i | \(-0.475058\pi\) | ||||
0.0782782 | + | 0.996932i | \(0.475058\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.7732 | −1.17725 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.1490 | 0.579342 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.3392 | −0.406270 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.8304 | 0.995849 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.520367 | −0.0185964 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −63.0825 | −2.25151 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.33561 | −0.154548 | −0.0772739 | − | 0.997010i | \(-0.524622\pi\) | ||||
−0.0772739 | + | 0.997010i | \(0.524622\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.68918 | −0.238141 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.403360 | 0.0143418 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.3928 | 0.759682 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 45.7431 | 1.62234 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.2783 | −0.612027 | −0.306014 | − | 0.952027i | \(-0.598995\pi\) | ||||
−0.306014 | + | 0.952027i | \(0.598995\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.1047 | 0.357479 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.129594 | 0.00457896 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.96881 | 0.316503 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −45.9347 | −1.61899 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.4921 | −0.474945 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.9662 | 0.561342 | 0.280671 | − | 0.959804i | \(-0.409443\pi\) | ||||
0.280671 | + | 0.959804i | \(0.409443\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.3014 | −1.73121 | −0.865603 | − | 0.500731i | \(-0.833065\pi\) | ||||
−0.865603 | + | 0.500731i | \(0.833065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.0913 | −0.809848 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −57.1740 | −2.00272 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.5174 | 0.717812 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.77230 | 0.0968719 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.2189 | 1.33385 | 0.666924 | − | 0.745126i | \(-0.267610\pi\) | ||||
0.666924 | + | 0.745126i | \(0.267610\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.4225 | −0.502736 | −0.251368 | − | 0.967892i | \(-0.580881\pi\) | ||||
−0.251368 | + | 0.967892i | \(0.580881\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 22.3687 | 0.778777 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.6869 | −1.20618 | −0.603090 | − | 0.797673i | \(-0.706064\pi\) | ||||
−0.603090 | + | 0.797673i | \(0.706064\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.5439 | −1.51234 | −0.756171 | − | 0.654375i | \(-0.772932\pi\) | ||||
−0.756171 | + | 0.654375i | \(0.772932\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.5004 | 0.364254 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.18385 | −0.110314 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.77676 | 0.130700 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.53773 | −0.122282 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.1785 | 0.454974 | 0.227487 | − | 0.973781i | \(-0.426949\pi\) | ||||
0.227487 | + | 0.973781i | \(0.426949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7292 | −0.990663 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.39023 | 0.254533 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −39.6585 | −1.36430 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.06554 | 0.311496 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.2756 | −0.352657 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −63.8718 | −2.18950 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.4897 | 0.461878 | 0.230939 | − | 0.972968i | \(-0.425820\pi\) | ||||
0.230939 | + | 0.972968i | \(0.425820\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.9148 | 0.441677 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.7955 | 0.915317 | 0.457659 | − | 0.889128i | \(-0.348688\pi\) | ||||
0.457659 | + | 0.889128i | \(0.348688\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.2866 | 1.57928 | 0.789640 | − | 0.613571i | \(-0.210268\pi\) | ||||
0.789640 | + | 0.613571i | \(0.210268\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.81492 | 0.198172 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.0943 | −0.377653 | −0.188827 | − | 0.982010i | \(-0.560468\pi\) | ||||
−0.188827 | + | 0.982010i | \(0.560468\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −74.0668 | −2.51835 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.3420 | −0.555002 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.1720 | 1.05744 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.4202 | 0.759680 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.6438 | −0.394082 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.2394 | −0.954666 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.85241 | 0.130087 | 0.0650433 | − | 0.997882i | \(-0.479281\pi\) | ||||
0.0650433 | + | 0.997882i | \(0.479281\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.5362 | −0.389105 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.4047 | −1.69818 | −0.849089 | − | 0.528250i | \(-0.822849\pi\) | ||||
−0.849089 | + | 0.528250i | \(0.822849\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.621522 | 0.0209159 | 0.0104579 | − | 0.999945i | \(-0.496671\pi\) | ||||
0.0104579 | + | 0.999945i | \(0.496671\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −38.0425 | −1.27878 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.37732 | 0.0462458 | 0.0231229 | − | 0.999733i | \(-0.492639\pi\) | ||||
0.0231229 | + | 0.999733i | \(0.492639\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.1058 | 0.674326 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.41460 | 0.0808923 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.5962 | 1.42543 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.2026 | −1.21012 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.9649 | −0.366106 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.84092 | 0.0613980 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.82491 | 0.327315 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.5216 | −0.350137 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 44.0113 | 1.46299 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.57385 | 0.185077 | 0.0925383 | − | 0.995709i | \(-0.470502\pi\) | ||||
0.0925383 | + | 0.995709i | \(0.470502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.16093 | 0.303849 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.4020 | −1.76929 | −0.884644 | − | 0.466267i | \(-0.845599\pi\) | ||||
−0.884644 | + | 0.466267i | \(0.845599\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.5247 | 1.04331 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −51.1066 | −1.68953 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.1807 | −1.06270 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.9803 | 1.81363 | 0.906816 | − | 0.421527i | \(-0.138506\pi\) | ||||
0.906816 | + | 0.421527i | \(0.138506\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.0628 | −0.990602 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.2215 | −0.599768 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −85.3121 | −2.80504 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.06620 | −0.0678630 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.7144 | −1.66389 | −0.831943 | − | 0.554861i | \(-0.812772\pi\) | ||||
−0.831943 | + | 0.554861i | \(0.812772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.4214 | −0.439869 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.22673 | 0.105638 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.39754 | 0.241925 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.1997 | 1.34594 | 0.672968 | − | 0.739672i | \(-0.265019\pi\) | ||||
0.672968 | + | 0.739672i | \(0.265019\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.2220 | 0.562020 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.2604 | 0.367078 | 0.183539 | − | 0.983012i | \(-0.441245\pi\) | ||||
0.183539 | + | 0.983012i | \(0.441245\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.9989 | −0.748949 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.62290 | −0.215443 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.2686 | 1.50353 | 0.751763 | − | 0.659433i | \(-0.229204\pi\) | ||||
0.751763 | + | 0.659433i | \(0.229204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.87219 | −0.190619 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.51767 | 0.276204 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.24795 | 0.202391 | 0.101196 | − | 0.994867i | \(-0.467733\pi\) | ||||
0.101196 | + | 0.994867i | \(0.467733\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.7062 | −0.540599 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.25648 | −0.0406162 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.5491 | 0.954190 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.4845 | −0.596274 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.49830 | 0.112731 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 70.6207 | 2.27336 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.48597 | −0.208575 | −0.104287 | − | 0.994547i | \(-0.533256\pi\) | ||||
−0.104287 | + | 0.994547i | \(0.533256\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.77390 | 0.0891106 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.0219 | −0.482077 | −0.241038 | − | 0.970516i | \(-0.577488\pi\) | ||||
−0.241038 | + | 0.970516i | \(0.577488\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.9983 | −0.673175 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.6455 | −0.469032 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.0541 | 0.833543 | 0.416772 | − | 0.909011i | \(-0.363161\pi\) | ||||
0.416772 | + | 0.909011i | \(0.363161\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.312917 | 0.0100009 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.78182 | 0.280382 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.46591 | 0.110545 | 0.0552727 | − | 0.998471i | \(-0.482397\pi\) | ||||
0.0552727 | + | 0.998471i | \(0.482397\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.1692 | 1.56666 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.8439 | −0.695300 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.6146 | 1.32327 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.3162 | −0.994791 | −0.497395 | − | 0.867524i | \(-0.665710\pi\) | ||||
−0.497395 | + | 0.867524i | \(0.665710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.5876 | 0.494656 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.53178 | 0.143667 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.0051 | 0.475215 | 0.237607 | − | 0.971361i | \(-0.423637\pi\) | ||||
0.237607 | + | 0.971361i | \(0.423637\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.20908 | −0.291362 |
(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 | 4008.2.a.l.1.12 | ✓ | 12 | |
4.3 | odd | 2 | 8016.2.a.bf.1.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.l.1.12 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8016.2.a.bf.1.12 | 12 | 4.3 | odd | 2 |