Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, 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("2240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1120) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1 |
$q$-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 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.56155 | −0.470826 | −0.235413 | − | 0.971895i | \(-0.575644\pi\) | ||||
−0.235413 | + | 0.971895i | \(0.575644\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.56155 | −0.987797 | −0.493899 | − | 0.869520i | \(-0.664429\pi\) | ||||
−0.493899 | + | 0.869520i | \(0.664429\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.56155 | 0.403191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.438447 | 0.106339 | 0.0531695 | − | 0.998586i | \(-0.483068\pi\) | ||||
0.0531695 | + | 0.998586i | \(0.483068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.56155 | −0.340759 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.68466 | −1.24131 | −0.620655 | − | 0.784084i | \(-0.713133\pi\) | ||||
−0.620655 | + | 0.784084i | \(0.713133\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.12311 | 0.560926 | 0.280463 | − | 0.959865i | \(-0.409512\pi\) | ||||
0.280463 | + | 0.959865i | \(0.409512\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.43845 | 0.424479 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.12311 | 0.184637 | 0.0923187 | − | 0.995730i | \(-0.470572\pi\) | ||||
0.0923187 | + | 0.995730i | \(0.470572\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.56155 | 0.890561 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.561553 | 0.0837114 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.684658 | −0.0998677 | −0.0499338 | − | 0.998753i | \(-0.515901\pi\) | ||||
−0.0499338 | + | 0.998753i | \(0.515901\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.684658 | −0.0958714 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.1231 | −1.80260 | −0.901299 | − | 0.433198i | \(-0.857385\pi\) | ||||
−0.901299 | + | 0.433198i | \(0.857385\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.56155 | 0.210560 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.24621 | 0.813187 | 0.406594 | − | 0.913609i | \(-0.366716\pi\) | ||||
0.406594 | + | 0.913609i | \(0.366716\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.561553 | −0.0707490 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.56155 | 0.441756 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.2462 | 1.25177 | 0.625887 | − | 0.779914i | \(-0.284737\pi\) | ||||
0.625887 | + | 0.779914i | \(0.284737\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.246211 | −0.0288168 | −0.0144084 | − | 0.999896i | \(-0.504587\pi\) | ||||
−0.0144084 | + | 0.999896i | \(0.504587\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.56155 | −0.180313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.56155 | −0.177955 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.80776 | −0.878442 | −0.439221 | − | 0.898379i | \(-0.644746\pi\) | ||||
−0.439221 | + | 0.898379i | \(0.644746\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.2462 | 1.12467 | 0.562334 | − | 0.826910i | \(-0.309904\pi\) | ||||
0.562334 | + | 0.826910i | \(0.309904\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.438447 | −0.0475563 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.4384 | 1.11912 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.24621 | −0.450097 | −0.225049 | − | 0.974348i | \(-0.572254\pi\) | ||||
−0.225049 | + | 0.974348i | \(0.572254\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.56155 | −0.373352 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.87689 | −0.505710 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.9309 | 1.31293 | 0.656465 | − | 0.754356i | \(-0.272051\pi\) | ||||
0.656465 | + | 0.754356i | \(0.272051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.876894 | 0.0881312 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.3693 | 1.13129 | 0.565645 | − | 0.824649i | \(-0.308627\pi\) | ||||
0.565645 | + | 0.824649i | \(0.308627\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.31534 | 0.720802 | 0.360401 | − | 0.932797i | \(-0.382640\pi\) | ||||
0.360401 | + | 0.932797i | \(0.382640\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.56155 | 0.152392 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.1231 | 1.46201 | 0.731003 | − | 0.682374i | \(-0.239053\pi\) | ||||
0.731003 | + | 0.682374i | \(0.239053\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.80776 | −0.939413 | −0.469707 | − | 0.882823i | \(-0.655640\pi\) | ||||
−0.469707 | + | 0.882823i | \(0.655640\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.75379 | −0.166462 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.3693 | 1.82211 | 0.911056 | − | 0.412283i | \(-0.135268\pi\) | ||||
0.911056 | + | 0.412283i | \(0.135268\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.438447 | 0.0401924 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.56155 | −0.778323 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.12311 | −0.281601 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.24621 | −0.554262 | −0.277131 | − | 0.960832i | \(-0.589384\pi\) | ||||
−0.277131 | + | 0.960832i | \(0.589384\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.24621 | −0.549948 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.2462 | −1.24470 | −0.622349 | − | 0.782740i | \(-0.713821\pi\) | ||||
−0.622349 | + | 0.782740i | \(0.713821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.56155 | −0.478662 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.246211 | 0.0210352 | 0.0105176 | − | 0.999945i | \(-0.496652\pi\) | ||||
0.0105176 | + | 0.999945i | \(0.496652\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.1231 | 1.62200 | 0.811000 | − | 0.585046i | \(-0.198923\pi\) | ||||
0.811000 | + | 0.585046i | \(0.198923\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.06913 | 0.0900370 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.56155 | 0.465080 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.68466 | 0.555131 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.56155 | −0.128795 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.24621 | 0.675556 | 0.337778 | − | 0.941226i | \(-0.390325\pi\) | ||||
0.337778 | + | 0.941226i | \(0.390325\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.6847 | 1.03226 | 0.516131 | − | 0.856509i | \(-0.327372\pi\) | ||||
0.516131 | + | 0.856509i | \(0.327372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.246211 | −0.0199050 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.12311 | −0.250854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.4924 | 1.79509 | 0.897545 | − | 0.440922i | \(-0.145349\pi\) | ||||
0.897545 | + | 0.440922i | \(0.145349\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 20.4924 | 1.62515 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.87689 | 0.695292 | 0.347646 | − | 0.937626i | \(-0.386981\pi\) | ||||
0.347646 | + | 0.937626i | \(0.386981\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.43845 | −0.189833 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.8078 | 0.913712 | 0.456856 | − | 0.889541i | \(-0.348975\pi\) | ||||
0.456856 | + | 0.889541i | \(0.348975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.315342 | −0.0242570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.43845 | −0.641563 | −0.320782 | − | 0.947153i | \(-0.603946\pi\) | ||||
−0.320782 | + | 0.947153i | \(0.603946\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.75379 | −0.733140 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.24621 | 0.167890 | 0.0839449 | − | 0.996470i | \(-0.473248\pi\) | ||||
0.0839449 | + | 0.996470i | \(0.473248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.1231 | 1.57007 | 0.785034 | − | 0.619453i | \(-0.212645\pi\) | ||||
0.785034 | + | 0.619453i | \(0.212645\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.12311 | −0.230867 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.12311 | −0.0825724 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.684658 | −0.0500672 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.56155 | 0.404543 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.4384 | −1.62359 | −0.811795 | − | 0.583943i | \(-0.801509\pi\) | ||||
−0.811795 | + | 0.583943i | \(0.801509\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.246211 | 0.0177227 | 0.00886134 | − | 0.999961i | \(-0.497179\pi\) | ||||
0.00886134 | + | 0.999961i | \(0.497179\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.56155 | −0.398271 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.7386 | 1.76255 | 0.881277 | − | 0.472599i | \(-0.156684\pi\) | ||||
0.881277 | + | 0.472599i | \(0.156684\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.0000 | −1.12855 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.68466 | −0.469171 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.43845 | −0.443241 | −0.221620 | − | 0.975133i | \(-0.571135\pi\) | ||||
−0.221620 | + | 0.975133i | \(0.571135\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.24621 | −0.427983 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.12311 | 0.212010 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.384472 | 0.0259802 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.56155 | −0.105041 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.80776 | 0.254987 | 0.127493 | − | 0.991839i | \(-0.459307\pi\) | ||||
0.127493 | + | 0.991839i | \(0.459307\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.5616 | −1.16560 | −0.582801 | − | 0.812615i | \(-0.698043\pi\) | ||||
−0.582801 | + | 0.812615i | \(0.698043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.2462 | 1.07358 | 0.536790 | − | 0.843716i | \(-0.319637\pi\) | ||||
0.536790 | + | 0.843716i | \(0.319637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.43845 | 0.160438 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.630683 | 0.0413174 | 0.0206587 | − | 0.999787i | \(-0.493424\pi\) | ||||
0.0206587 | + | 0.999787i | \(0.493424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.684658 | 0.0446622 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.1922 | 0.791971 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.8078 | −1.02252 | −0.511260 | − | 0.859426i | \(-0.670821\pi\) | ||||
−0.511260 | + | 0.859426i | \(0.670821\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8769 | −0.700642 | −0.350321 | − | 0.936630i | \(-0.613928\pi\) | ||||
−0.350321 | + | 0.936630i | \(0.613928\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.0000 | −1.01396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.36932 | 0.0864305 | 0.0432153 | − | 0.999066i | \(-0.486240\pi\) | ||||
0.0432153 | + | 0.999066i | \(0.486240\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.684658 | 0.0428750 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.49242 | 0.155473 | 0.0777365 | − | 0.996974i | \(-0.475231\pi\) | ||||
0.0777365 | + | 0.996974i | \(0.475231\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.12311 | 0.0697864 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.75379 | 0.232354 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.3693 | 1.07104 | 0.535519 | − | 0.844523i | \(-0.320116\pi\) | ||||
0.535519 | + | 0.844523i | \(0.320116\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.1231 | 0.806146 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.63068 | 0.405791 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.4924 | −0.639734 | −0.319867 | − | 0.947462i | \(-0.603638\pi\) | ||||
−0.319867 | + | 0.947462i | \(0.603638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.3693 | −1.05511 | −0.527555 | − | 0.849521i | \(-0.676891\pi\) | ||||
−0.527555 | + | 0.849521i | \(0.676891\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.56155 | 0.336600 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.56155 | −0.0941652 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.24621 | 0.255130 | 0.127565 | − | 0.991830i | \(-0.459284\pi\) | ||||
0.127565 | + | 0.991830i | \(0.459284\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.75379 | −0.104997 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.68466 | 0.160153 | 0.0800766 | − | 0.996789i | \(-0.474483\pi\) | ||||
0.0800766 | + | 0.996789i | \(0.474483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.43845 | −0.382726 | −0.191363 | − | 0.981519i | \(-0.561291\pi\) | ||||
−0.191363 | + | 0.981519i | \(0.561291\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8078 | −0.988692 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.1922 | −1.18369 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.6847 | −0.857887 | −0.428943 | − | 0.903331i | \(-0.641114\pi\) | ||||
−0.428943 | + | 0.903331i | \(0.641114\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.24621 | −0.363668 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.68466 | −0.503935 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.7538 | −1.01993 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00000 | −0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.8078 | 1.35878 | 0.679390 | − | 0.733777i | \(-0.262244\pi\) | ||||
0.679390 | + | 0.733777i | \(0.262244\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.4233 | −0.649848 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.4924 | −1.61566 | −0.807829 | − | 0.589418i | \(-0.799357\pi\) | ||||
−0.807829 | + | 0.589418i | \(0.799357\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.9309 | −0.956989 | −0.478495 | − | 0.878090i | \(-0.658817\pi\) | ||||
−0.478495 | + | 0.878090i | \(0.658817\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.561553 | 0.0316399 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.0000 | −0.561656 | −0.280828 | − | 0.959758i | \(-0.590609\pi\) | ||||
−0.280828 | + | 0.959758i | \(0.590609\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.4384 | 0.584441 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.6155 | −1.31809 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.56155 | −0.197559 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.3153 | 0.846940 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.684658 | −0.0377464 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.4924 | 1.34623 | 0.673113 | − | 0.739540i | \(-0.264957\pi\) | ||||
0.673113 | + | 0.739540i | \(0.264957\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.630683 | −0.0345612 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.2462 | −0.559810 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.9848 | −1.68785 | −0.843926 | − | 0.536460i | \(-0.819761\pi\) | ||||
−0.843926 | + | 0.536460i | \(0.819761\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −30.2462 | −1.64275 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.87689 | −0.264099 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.75379 | 0.308880 | 0.154440 | − | 0.988002i | \(-0.450643\pi\) | ||||
0.154440 | + | 0.988002i | \(0.450643\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.3693 | 1.03682 | 0.518408 | − | 0.855133i | \(-0.326525\pi\) | ||||
0.518408 | + | 0.855133i | \(0.326525\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.8078 | −1.05726 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.6847 | 1.63318 | 0.816590 | − | 0.577218i | \(-0.195862\pi\) | ||||
0.816590 | + | 0.577218i | \(0.195862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | −0.212298 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.684658 | −0.0362360 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.7386 | −1.62232 | −0.811162 | − | 0.584822i | \(-0.801164\pi\) | ||||
−0.811162 | + | 0.584822i | \(0.801164\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.3693 | 0.701707 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.246211 | 0.0128873 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.0540 | 1.77760 | 0.888802 | − | 0.458292i | \(-0.151539\pi\) | ||||
0.888802 | + | 0.458292i | \(0.151539\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.12311 | −0.0584665 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.1231 | −0.681318 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.49242 | −0.336165 | −0.168082 | − | 0.985773i | \(-0.553757\pi\) | ||||
−0.168082 | + | 0.985773i | \(0.553757\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.56155 | 0.0806382 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.8078 | 1.22616 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.7538 | 0.706485 | 0.353242 | − | 0.935532i | \(-0.385079\pi\) | ||||
0.353242 | + | 0.935532i | \(0.385079\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.75379 | 0.499702 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.2462 | −0.727947 | −0.363974 | − | 0.931409i | \(-0.618580\pi\) | ||||
−0.363974 | + | 0.931409i | \(0.618580\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.56155 | 0.0795841 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.24621 | −0.114181 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.5616 | −1.39743 | −0.698713 | − | 0.715402i | \(-0.746244\pi\) | ||||
−0.698713 | + | 0.715402i | \(0.746244\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.2462 | 1.12217 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.80776 | 0.392851 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.1771 | −1.36398 | −0.681989 | − | 0.731362i | \(-0.738885\pi\) | ||||
−0.681989 | + | 0.731362i | \(0.738885\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.68466 | −0.333816 | −0.166908 | − | 0.985972i | \(-0.553378\pi\) | ||||
−0.166908 | + | 0.985972i | \(0.553378\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.1231 | −0.554081 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.00000 | 0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.75379 | −0.0869321 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.7386 | 0.629885 | 0.314942 | − | 0.949111i | \(-0.398015\pi\) | ||||
0.314942 | + | 0.949111i | \(0.398015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.384472 | −0.0189646 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.24621 | 0.307356 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.2462 | −0.502967 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.8617 | −1.46234 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.0000 | −0.781651 | −0.390826 | − | 0.920465i | \(-0.627810\pi\) | ||||
−0.390826 | + | 0.920465i | \(0.627810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9309 | 1.21506 | 0.607528 | − | 0.794298i | \(-0.292161\pi\) | ||||
0.607528 | + | 0.794298i | \(0.292161\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.384472 | 0.0186937 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.438447 | 0.0212678 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.00000 | 0.0967868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.68466 | −0.419299 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.6847 | −0.996345 | −0.498172 | − | 0.867078i | \(-0.665995\pi\) | ||||
−0.498172 | + | 0.867078i | \(0.665995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.2462 | 0.588515 | 0.294258 | − | 0.955726i | \(-0.404928\pi\) | ||||
0.294258 | + | 0.955726i | \(0.404928\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.4384 | −0.500485 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.1231 | 0.530877 | 0.265438 | − | 0.964128i | \(-0.414483\pi\) | ||||
0.265438 | + | 0.964128i | \(0.414483\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.561553 | −0.0267406 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.4924 | 1.16367 | 0.581835 | − | 0.813307i | \(-0.302335\pi\) | ||||
0.581835 | + | 0.813307i | \(0.302335\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.24621 | 0.201290 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.8769 | −0.609056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.6847 | 1.25933 | 0.629663 | − | 0.776868i | \(-0.283193\pi\) | ||||
0.629663 | + | 0.776868i | \(0.283193\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.12311 | −0.147061 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.8078 | −0.930650 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.56155 | 0.166968 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.4924 | 0.677927 | 0.338963 | − | 0.940800i | \(-0.389924\pi\) | ||||
0.338963 | + | 0.940800i | \(0.389924\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.43845 | 0.113817 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.3693 | −0.715820 | −0.357910 | − | 0.933756i | \(-0.616511\pi\) | ||||
−0.357910 | + | 0.933756i | \(0.616511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.8769 | −0.598440 | −0.299220 | − | 0.954184i | \(-0.596726\pi\) | ||||
−0.299220 | + | 0.954184i | \(0.596726\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.87689 | 0.226161 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.9309 | −1.24621 | −0.623106 | − | 0.782137i | \(-0.714129\pi\) | ||||
−0.623106 | + | 0.782137i | \(0.714129\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.2462 | 0.473126 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.1231 | −1.61839 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.24621 | −0.287201 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.36932 | 0.337418 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.7386 | 1.58725 | 0.793624 | − | 0.608408i | \(-0.208192\pi\) | ||||
0.793624 | + | 0.608408i | \(0.208192\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.9309 | −0.587161 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.6155 | 1.43264 | 0.716318 | − | 0.697774i | \(-0.245826\pi\) | ||||
0.716318 | + | 0.697774i | \(0.245826\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.8617 | −0.626850 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.9309 | −1.57641 | −0.788204 | − | 0.615414i | \(-0.788989\pi\) | ||||
−0.788204 | + | 0.615414i | \(0.788989\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.93087 | −0.132000 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.876894 | −0.0394135 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.00000 | 0.179425 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0540 | −0.629142 | −0.314571 | − | 0.949234i | \(-0.601861\pi\) | ||||
−0.314571 | + | 0.949234i | \(0.601861\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.4384 | −0.823769 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.1771 | 0.587537 | 0.293768 | − | 0.955877i | \(-0.405091\pi\) | ||||
0.293768 | + | 0.955877i | \(0.405091\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.3693 | −0.505928 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.492423 | 0.0218693 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.73863 | 0.210036 | 0.105018 | − | 0.994470i | \(-0.466510\pi\) | ||||
0.105018 | + | 0.994470i | \(0.466510\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.246211 | −0.0108917 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.31534 | −0.322352 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.06913 | 0.0470203 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.1771 | 0.578410 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.8617 | 1.74637 | 0.873187 | − | 0.487385i | \(-0.162049\pi\) | ||||
0.873187 | + | 0.487385i | \(0.162049\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.9848 | −1.26742 | −0.633709 | − | 0.773571i | \(-0.718468\pi\) | ||||
−0.633709 | + | 0.773571i | \(0.718468\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.56155 | −0.0681518 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.36932 | 0.0596484 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.50758 | −0.152216 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.12311 | −0.308536 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.1231 | −0.653829 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.50758 | −0.151363 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.56155 | −0.0672608 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.19224 | −0.0942516 | −0.0471258 | − | 0.998889i | \(-0.515006\pi\) | ||||
−0.0471258 | + | 0.998889i | \(0.515006\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.9848 | −1.41552 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.80776 | 0.420118 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.8769 | 1.06366 | 0.531830 | − | 0.846851i | \(-0.321505\pi\) | ||||
0.531830 | + | 0.846851i | \(0.321505\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.12311 | −0.0479330 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.80776 | −0.332020 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.75379 | 0.0744442 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.1231 | −0.556044 | −0.278022 | − | 0.960575i | \(-0.589679\pi\) | ||||
−0.278022 | + | 0.960575i | \(0.589679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.2462 | −0.602551 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.06913 | 0.0451387 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.9848 | −1.55873 | −0.779363 | − | 0.626573i | \(-0.784457\pi\) | ||||
−0.779363 | + | 0.626573i | \(0.784457\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.3693 | −0.814873 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.00000 | −0.293972 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.2462 | 1.35183 | 0.675916 | − | 0.736979i | \(-0.263748\pi\) | ||||
0.675916 | + | 0.736979i | \(0.263748\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.4924 | −1.69456 | −0.847278 | − | 0.531150i | \(-0.821760\pi\) | ||||
−0.847278 | + | 0.531150i | \(0.821760\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 35.0388 | 1.46377 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.8078 | 1.40744 | 0.703718 | − | 0.710480i | \(-0.251522\pi\) | ||||
0.703718 | + | 0.710480i | \(0.251522\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.384472 | −0.0159781 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.2462 | 0.425084 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.4924 | 0.848709 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.492423 | −0.0203245 | −0.0101622 | − | 0.999948i | \(-0.503235\pi\) | ||||
−0.0101622 | + | 0.999948i | \(0.503235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −38.6307 | −1.58905 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.31534 | 0.218275 | 0.109137 | − | 0.994027i | \(-0.465191\pi\) | ||||
0.109137 | + | 0.994027i | \(0.465191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.438447 | −0.0179746 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.9848 | −1.02256 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.1922 | −0.988468 | −0.494234 | − | 0.869329i | \(-0.664551\pi\) | ||||
−0.494234 | + | 0.869329i | \(0.664551\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.4924 | 1.24381 | 0.621906 | − | 0.783092i | \(-0.286359\pi\) | ||||
0.621906 | + | 0.783092i | \(0.286359\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.75379 | −0.234312 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.56155 | 0.348077 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.6847 | 0.677209 | 0.338605 | − | 0.940929i | \(-0.390045\pi\) | ||||
0.338605 | + | 0.940929i | \(0.390045\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.4384 | 0.422987 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.43845 | 0.0986490 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.0000 | −1.05013 | −0.525065 | − | 0.851062i | \(-0.675959\pi\) | ||||
−0.525065 | + | 0.851062i | \(0.675959\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.12311 | 0.125936 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.9848 | −0.925335 | −0.462668 | − | 0.886532i | \(-0.653108\pi\) | ||||
−0.462668 | + | 0.886532i | \(0.653108\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.9848 | 1.32577 | 0.662886 | − | 0.748720i | \(-0.269331\pi\) | ||||
0.662886 | + | 0.748720i | \(0.269331\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.24621 | −0.170121 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.492423 | 0.0196342 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.80776 | 0.310822 | 0.155411 | − | 0.987850i | \(-0.450330\pi\) | ||||
0.155411 | + | 0.987850i | \(0.450330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.0540 | 0.399610 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.24621 | 0.247873 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.56155 | −0.141114 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.24621 | −0.0888587 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.24621 | −0.167715 | −0.0838576 | − | 0.996478i | \(-0.526724\pi\) | ||||
−0.0838576 | + | 0.996478i | \(0.526724\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.43845 | 0.253908 | 0.126954 | − | 0.991909i | \(-0.459480\pi\) | ||||
0.126954 | + | 0.991909i | \(0.459480\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.24621 | 0.245944 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.7538 | 1.32700 | 0.663499 | − | 0.748177i | \(-0.269071\pi\) | ||||
0.663499 | + | 0.748177i | \(0.269071\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.75379 | −0.382870 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.87689 | −0.191141 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.8769 | −0.582178 | −0.291089 | − | 0.956696i | \(-0.594018\pi\) | ||||
−0.291089 | + | 0.956696i | \(0.594018\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.2462 | 0.556646 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.138261 | 0.00539406 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.3153 | −0.440783 | −0.220392 | − | 0.975411i | \(-0.570734\pi\) | ||||
−0.220392 | + | 0.975411i | \(0.570734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.1231 | −0.666012 | −0.333006 | − | 0.942925i | \(-0.608063\pi\) | ||||
−0.333006 | + | 0.942925i | \(0.608063\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.43845 | 0.0947014 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.94602 | −0.229887 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.12311 | −0.120566 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.75379 | −0.298887 | −0.149443 | − | 0.988770i | \(-0.547748\pi\) | ||||
−0.149443 | + | 0.988770i | \(0.547748\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.56155 | 0.214064 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.8078 | −1.29934 | −0.649669 | − | 0.760217i | \(-0.725092\pi\) | ||||
−0.649669 | + | 0.760217i | \(0.725092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.9309 | 0.496241 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.4233 | 1.05086 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.1231 | 0.578670 | 0.289335 | − | 0.957228i | \(-0.406566\pi\) | ||||
0.289335 | + | 0.957228i | \(0.406566\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.246211 | −0.00940725 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.3693 | −0.967900 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 46.7386 | 1.78060 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.49242 | −0.170900 | −0.0854499 | − | 0.996342i | \(-0.527233\pi\) | ||||
−0.0854499 | + | 0.996342i | \(0.527233\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.876894 | 0.0333105 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.1231 | −0.725381 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.876894 | 0.0332147 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.984845 | −0.0372503 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.1922 | −0.384955 | −0.192478 | − | 0.981301i | \(-0.561652\pi\) | ||||
−0.192478 | + | 0.981301i | \(0.561652\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.06913 | −0.0402658 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.3693 | 0.427587 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.3002 | 1.58862 | 0.794308 | − | 0.607515i | \(-0.207833\pi\) | ||||
0.794308 | + | 0.607515i | \(0.207833\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.38447 | 0.164431 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.56155 | −0.207990 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.6847 | 0.921865 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.31534 | 0.272438 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.9848 | 0.631673 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.68466 | −0.248262 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.9848 | −1.22334 | −0.611670 | − | 0.791113i | \(-0.709502\pi\) | ||||
−0.611670 | + | 0.791113i | \(0.709502\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.75379 | 0.0648662 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.1771 | 0.856065 | 0.428033 | − | 0.903763i | \(-0.359207\pi\) | ||||
0.428033 | + | 0.903763i | \(0.359207\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.56155 | 0.0575987 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0000 | −0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.9309 | 0.990668 | 0.495334 | − | 0.868703i | \(-0.335046\pi\) | ||||
0.495334 | + | 0.868703i | \(0.335046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.2462 | 1.10963 | 0.554813 | − | 0.831975i | \(-0.312790\pi\) | ||||
0.554813 | + | 0.831975i | \(0.312790\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.24621 | −0.302118 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.75379 | −0.210520 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.1231 | 0.552586 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.06913 | −0.184975 | −0.0924876 | − | 0.995714i | \(-0.529482\pi\) | ||||
−0.0924876 | + | 0.995714i | \(0.529482\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.13826 | −0.0779225 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.6847 | −0.461642 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.38447 | −0.0866651 | −0.0433326 | − | 0.999061i | \(-0.513797\pi\) | ||||
−0.0433326 | + | 0.999061i | \(0.513797\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.3693 | 0.412137 | 0.206069 | − | 0.978538i | \(-0.433933\pi\) | ||||
0.206069 | + | 0.978538i | \(0.433933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.80776 | −0.355065 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.246211 | 0.00890179 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.2462 | −0.803264 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.89205 | −0.140169 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.19224 | 0.222719 | 0.111360 | − | 0.993780i | \(-0.464479\pi\) | ||||
0.111360 | + | 0.993780i | \(0.464479\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.12311 | 0.112185 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.75379 | −0.0629168 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.24621 | −0.223507 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −37.1771 | −1.32860 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.4924 | −0.802789 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.0540 | −0.786139 | −0.393070 | − | 0.919509i | \(-0.628587\pi\) | ||||
−0.393070 | + | 0.919509i | \(0.628587\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.1231 | −0.965608 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.3693 | 0.688694 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.12311 | −0.252949 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20.4924 | −0.726791 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.0691 | 0.392089 | 0.196044 | − | 0.980595i | \(-0.437190\pi\) | ||||
0.196044 | + | 0.980595i | \(0.437190\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.300187 | −0.0106198 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.38447 | 0.0842512 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.384472 | 0.0135677 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.3845 | 0.576761 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.05398 | 0.142530 | 0.0712651 | − | 0.997457i | \(-0.477296\pi\) | ||||
0.0712651 | + | 0.997457i | \(0.477296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.8617 | −1.04859 | −0.524294 | − | 0.851537i | \(-0.675671\pi\) | ||||
−0.524294 | + | 0.851537i | \(0.675671\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.1231 | 0.951249 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.87689 | −0.310944 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.00000 | 0.0698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.4233 | 0.747678 | 0.373839 | − | 0.927494i | \(-0.378041\pi\) | ||||
0.373839 | + | 0.927494i | \(0.378041\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.63068 | 0.231131 | 0.115566 | − | 0.993300i | \(-0.463132\pi\) | ||||
0.115566 | + | 0.993300i | \(0.463132\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.43845 | 0.0848958 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.1080 | 1.67288 | 0.836439 | − | 0.548061i | \(-0.184634\pi\) | ||||
0.836439 | + | 0.548061i | \(0.184634\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.7538 | 0.408226 | 0.204113 | − | 0.978947i | \(-0.434569\pi\) | ||||
0.204113 | + | 0.978947i | \(0.434569\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.63068 | −0.230016 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.438447 | 0.0151913 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.8078 | −0.408625 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.3693 | 0.600371 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.9848 | −0.586382 | −0.293191 | − | 0.956054i | \(-0.594717\pi\) | ||||
−0.293191 | + | 0.956054i | \(0.594717\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6847 | 0.540850 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.19224 | −0.144388 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.315342 | 0.0108481 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.56155 | −0.294178 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.0540 | 0.345052 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.7538 | 0.950272 | 0.475136 | − | 0.879912i | \(-0.342399\pi\) | ||||
0.475136 | + | 0.879912i | \(0.342399\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.7386 | −0.708418 | −0.354209 | − | 0.935166i | \(-0.615250\pi\) | ||||
−0.354209 | + | 0.935166i | \(0.615250\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.2311 | 1.33855 | 0.669273 | − | 0.743016i | \(-0.266606\pi\) | ||||
0.669273 | + | 0.743016i | \(0.266606\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.12311 | −0.106435 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.3542 | 1.44175 | 0.720876 | − | 0.693064i | \(-0.243740\pi\) | ||||
0.720876 | + | 0.693064i | \(0.243740\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.43845 | 0.286916 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.2462 | 0.891368 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.1922 | 0.413593 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.4924 | −1.23650 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.26137 | −0.245760 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.3693 | −1.46448 | −0.732239 | − | 0.681048i | \(-0.761525\pi\) | ||||
−0.732239 | + | 0.681048i | \(0.761525\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.9309 | 0.773439 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.12311 | 0.172602 | 0.0863009 | − | 0.996269i | \(-0.472495\pi\) | ||||
0.0863009 | + | 0.996269i | \(0.472495\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.8617 | 1.94720 | 0.973601 | − | 0.228255i | \(-0.0733021\pi\) | ||||
0.973601 | + | 0.228255i | \(0.0733021\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.75379 | 0.327870 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.4924 | −0.419454 | −0.209727 | − | 0.977760i | \(-0.567258\pi\) | ||||
−0.209727 | + | 0.977760i | \(0.567258\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.24621 | −0.209491 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.9309 | 0.366198 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.24621 | −0.0750826 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.8769 | −0.696283 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.75379 | −0.191686 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.24621 | −0.207861 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.1231 | −0.702156 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.2462 | 0.605856 | 0.302928 | − | 0.953014i | \(-0.402036\pi\) | ||||
0.302928 | + | 0.953014i | \(0.402036\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.38447 | −0.211760 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.7386 | 1.28347 | 0.641734 | − | 0.766927i | \(-0.278215\pi\) | ||||
0.641734 | + | 0.766927i | \(0.278215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.0000 | −0.529523 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.12311 | 0.103247 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.2462 | −0.470451 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.05398 | −0.199702 | −0.0998511 | − | 0.995002i | \(-0.531837\pi\) | ||||
−0.0998511 | + | 0.995002i | \(0.531837\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −37.1771 | −1.22503 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.2462 | −0.468920 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.12311 | 0.0369275 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.10795 | −0.134923 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.1080 | −1.11905 | −0.559523 | − | 0.828815i | \(-0.689016\pi\) | ||||
−0.559523 | + | 0.828815i | \(0.689016\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 44.4924 | 1.45662 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.684658 | 0.0223907 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.6847 | 1.78647 | 0.893235 | − | 0.449590i | \(-0.148430\pi\) | ||||
0.893235 | + | 0.449590i | \(0.148430\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.4384 | 0.862786 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.50758 | 0.179542 | 0.0897709 | − | 0.995962i | \(-0.471386\pi\) | ||||
0.0897709 | + | 0.995962i | \(0.471386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.56155 | −0.180917 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.63068 | −0.0854857 | −0.0427429 | − | 0.999086i | \(-0.513610\pi\) | ||||
−0.0427429 | + | 0.999086i | \(0.513610\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.876894 | 0.0284652 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.6155 | 0.506368 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.24621 | −0.137548 | −0.0687741 | − | 0.997632i | \(-0.521909\pi\) | ||||
−0.0687741 | + | 0.997632i | \(0.521909\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.4384 | 0.726091 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.3002 | −0.526910 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.246211 | 0.00795058 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.2462 | −0.685362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.49242 | −0.273664 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.246211 | −0.00792582 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.8617 | 0.960289 | 0.480144 | − | 0.877189i | \(-0.340584\pi\) | ||||
0.480144 | + | 0.877189i | \(0.340584\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.13826 | 0.0686200 | 0.0343100 | − | 0.999411i | \(-0.489077\pi\) | ||||
0.0343100 | + | 0.999411i | \(0.489077\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.1231 | 0.613059 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.56155 | 0.178112 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.8617 | −0.891376 | −0.445688 | − | 0.895188i | \(-0.647041\pi\) | ||||
−0.445688 | + | 0.895188i | \(0.647041\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.63068 | 0.211918 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.50758 | 0.175843 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.05398 | −0.0655116 | −0.0327558 | − | 0.999463i | \(-0.510428\pi\) | ||||
−0.0327558 | + | 0.999463i | \(0.510428\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.7386 | −0.788238 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.06913 | 0.0340308 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.2462 | 1.34200 | 0.670998 | − | 0.741460i | \(-0.265866\pi\) | ||||
0.670998 | + | 0.741460i | \(0.265866\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −38.2462 | −1.21371 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.0000 | −0.507234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.6847 | −0.465068 | −0.232534 | − | 0.972588i | \(-0.574702\pi\) | ||||
−0.232534 | + | 0.972588i | \(0.574702\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.24621 | 0.197621 |
(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 | 2240.2.a.bj.1.1 | 2 | ||
4.3 | odd | 2 | 2240.2.a.bc.1.2 | 2 | |||
8.3 | odd | 2 | 1120.2.a.t.1.1 | yes | 2 | ||
8.5 | even | 2 | 1120.2.a.r.1.2 | ✓ | 2 | ||
40.19 | odd | 2 | 5600.2.a.ba.1.2 | 2 | |||
40.29 | even | 2 | 5600.2.a.bh.1.1 | 2 | |||
56.13 | odd | 2 | 7840.2.a.bh.1.1 | 2 | |||
56.27 | even | 2 | 7840.2.a.bc.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.a.r.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
1120.2.a.t.1.1 | yes | 2 | 8.3 | odd | 2 | ||
2240.2.a.bc.1.2 | 2 | 4.3 | odd | 2 | |||
2240.2.a.bj.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5600.2.a.ba.1.2 | 2 | 40.19 | odd | 2 | |||
5600.2.a.bh.1.1 | 2 | 40.29 | even | 2 | |||
7840.2.a.bc.1.2 | 2 | 56.27 | even | 2 | |||
7840.2.a.bh.1.1 | 2 | 56.13 | odd | 2 |