Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2200,2,Mod(1,2200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2200, 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("2200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2200.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: | \(17.5670884447\) |
Analytic rank: | \(1\) |
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 440) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2200.1 |
$q$-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 | \(-0.351145\pi\) | ||||
0.450781 | + | 0.892634i | \(0.351145\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.438447 | −0.165717 | −0.0828587 | − | 0.996561i | \(-0.526405\pi\) | ||||
−0.0828587 | + | 0.996561i | \(0.526405\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.12311 | −1.97559 | −0.987797 | − | 0.155747i | \(-0.950222\pi\) | ||||
−0.987797 | + | 0.155747i | \(0.950222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.68466 | −1.13620 | −0.568098 | − | 0.822961i | \(-0.692321\pi\) | ||||
−0.568098 | + | 0.822961i | \(0.692321\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.56155 | 1.27591 | 0.637954 | − | 0.770075i | \(-0.279781\pi\) | ||||
0.637954 | + | 0.770075i | \(0.279781\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.684658 | −0.149405 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.12311 | 1.48527 | 0.742635 | − | 0.669696i | \(-0.233576\pi\) | ||||
0.742635 | + | 0.669696i | \(0.233576\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.56155 | −1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.43845 | 0.824199 | 0.412099 | − | 0.911139i | \(-0.364796\pi\) | ||||
0.412099 | + | 0.911139i | \(0.364796\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.56155 | −0.998884 | −0.499442 | − | 0.866347i | \(-0.666462\pi\) | ||||
−0.499442 | + | 0.866347i | \(0.666462\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.56155 | −0.271831 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.5616 | −1.90071 | −0.950354 | − | 0.311171i | \(-0.899279\pi\) | ||||
−0.950354 | + | 0.311171i | \(0.899279\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.1231 | −1.78112 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24621 | 0.663147 | 0.331573 | − | 0.943429i | \(-0.392421\pi\) | ||||
0.331573 | + | 0.943429i | \(0.392421\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.12311 | −0.781266 | −0.390633 | − | 0.920546i | \(-0.627744\pi\) | ||||
−0.390633 | + | 0.920546i | \(0.627744\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.3693 | −1.95012 | −0.975058 | − | 0.221952i | \(-0.928757\pi\) | ||||
−0.975058 | + | 0.221952i | \(0.928757\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.80776 | −0.972538 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.31534 | −1.02435 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.68466 | 0.368766 | 0.184383 | − | 0.982854i | \(-0.440971\pi\) | ||||
0.184383 | + | 0.982854i | \(0.440971\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.68466 | 1.15031 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.12311 | −0.927349 | −0.463675 | − | 0.886006i | \(-0.653469\pi\) | ||||
−0.463675 | + | 0.886006i | \(0.653469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.43845 | −1.08043 | −0.540216 | − | 0.841526i | \(-0.681658\pi\) | ||||
−0.540216 | + | 0.841526i | \(0.681658\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.246211 | 0.0310197 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.1231 | 1.33906 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.68466 | −1.03068 | −0.515340 | − | 0.856986i | \(-0.672334\pi\) | ||||
−0.515340 | + | 0.856986i | \(0.672334\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.12311 | 0.833696 | 0.416848 | − | 0.908976i | \(-0.363135\pi\) | ||||
0.416848 | + | 0.908976i | \(0.363135\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.438447 | 0.0499657 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.3693 | 1.50417 | 0.752083 | − | 0.659069i | \(-0.229049\pi\) | ||||
0.752083 | + | 0.659069i | \(0.229049\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.93087 | 0.743067 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.68466 | −0.284573 | −0.142287 | − | 0.989825i | \(-0.545445\pi\) | ||||
−0.142287 | + | 0.989825i | \(0.545445\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.12311 | 0.327390 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.68466 | −0.900557 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1231 | 1.33245 | 0.666225 | − | 0.745751i | \(-0.267909\pi\) | ||||
0.666225 | + | 0.745751i | \(0.267909\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.561553 | 0.0564382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.00000 | −0.199007 | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995037 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.12311 | 0.108575 | 0.0542874 | − | 0.998525i | \(-0.482711\pi\) | ||||
0.0542874 | + | 0.998525i | \(0.482711\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2462 | 1.17297 | 0.586487 | − | 0.809959i | \(-0.300510\pi\) | ||||
0.586487 | + | 0.809959i | \(0.300510\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.0540 | −1.71361 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.12311 | −0.858230 | −0.429115 | − | 0.903250i | \(-0.641174\pi\) | ||||
−0.429115 | + | 0.903250i | \(0.641174\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.00000 | 0.369800 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.05398 | 0.188288 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.63068 | 0.597869 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.1231 | −1.16449 | −0.582244 | − | 0.813014i | \(-0.697825\pi\) | ||||
−0.582244 | + | 0.813014i | \(0.697825\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.80776 | 0.332686 | 0.166343 | − | 0.986068i | \(-0.446804\pi\) | ||||
0.166343 | + | 0.986068i | \(0.446804\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.43845 | −0.211440 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.12311 | −0.0959534 | −0.0479767 | − | 0.998848i | \(-0.515277\pi\) | ||||
−0.0479767 | + | 0.998848i | \(0.515277\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20.8769 | −1.75815 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.12311 | 0.595664 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.6307 | −0.876804 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.6847 | −0.875321 | −0.437661 | − | 0.899140i | \(-0.644193\pi\) | ||||
−0.437661 | + | 0.899140i | \(0.644193\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.1231 | 1.23070 | 0.615350 | − | 0.788254i | \(-0.289015\pi\) | ||||
0.615350 | + | 0.788254i | \(0.289015\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.63068 | 0.212678 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.31534 | −0.743445 | −0.371723 | − | 0.928344i | \(-0.621233\pi\) | ||||
−0.371723 | + | 0.928344i | \(0.621233\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.19224 | 0.332466 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.12311 | −0.246135 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.192236 | −0.0150571 | −0.00752854 | − | 0.999972i | \(-0.502396\pi\) | ||||
−0.00752854 | + | 0.999972i | \(0.502396\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.6847 | −0.826804 | −0.413402 | − | 0.910549i | \(-0.635660\pi\) | ||||
−0.413402 | + | 0.910549i | \(0.635660\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.7386 | 2.90297 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.12311 | −0.238830 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.1231 | −1.45390 | −0.726951 | − | 0.686689i | \(-0.759063\pi\) | ||||
−0.726951 | + | 0.686689i | \(0.759063\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.1231 | −0.836064 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.24621 | −0.167890 | −0.0839449 | − | 0.996470i | \(-0.526752\pi\) | ||||
−0.0839449 | + | 0.996470i | \(0.526752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.24621 | 0.612936 | 0.306468 | − | 0.951881i | \(-0.400853\pi\) | ||||
0.306468 | + | 0.951881i | \(0.400853\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.1771 | −0.974078 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.68466 | 0.342576 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.43845 | 0.177371 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.24621 | −0.451960 | −0.225980 | − | 0.974132i | \(-0.572558\pi\) | ||||
−0.225980 | + | 0.974132i | \(0.572558\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.5616 | 1.83996 | 0.919980 | − | 0.391964i | \(-0.128204\pi\) | ||||
0.919980 | + | 0.391964i | \(0.128204\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.7386 | 1.90505 | 0.952524 | − | 0.304462i | \(-0.0984768\pi\) | ||||
0.952524 | + | 0.304462i | \(0.0984768\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.6847 | −1.18274 | −0.591372 | − | 0.806399i | \(-0.701414\pi\) | ||||
−0.591372 | + | 0.806399i | \(0.701414\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.94602 | −0.136584 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.56155 | −0.384701 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.31534 | 0.503609 | 0.251804 | − | 0.967778i | \(-0.418976\pi\) | ||||
0.251804 | + | 0.967778i | \(0.418976\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.5616 | −0.929222 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.43845 | 0.165533 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.1231 | 0.751630 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.3693 | 2.24466 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.8769 | −1.13016 | −0.565080 | − | 0.825036i | \(-0.691155\pi\) | ||||
−0.565080 | + | 0.825036i | \(0.691155\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.24621 | 0.547320 | 0.273660 | − | 0.961826i | \(-0.411766\pi\) | ||||
0.273660 | + | 0.961826i | \(0.411766\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.246211 | −0.0162701 | −0.00813505 | − | 0.999967i | \(-0.502589\pi\) | ||||
−0.00813505 | + | 0.999967i | \(0.502589\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.684658 | 0.0450472 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0540 | 0.658658 | 0.329329 | − | 0.944215i | \(-0.393178\pi\) | ||||
0.329329 | + | 0.944215i | \(0.393178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.8769 | 1.35610 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.6155 | 1.26882 | 0.634412 | − | 0.772995i | \(-0.281242\pi\) | ||||
0.634412 | + | 0.772995i | \(0.281242\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.4924 | −0.933539 | −0.466769 | − | 0.884379i | \(-0.654582\pi\) | ||||
−0.466769 | + | 0.884379i | \(0.654582\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.75379 | 0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −39.6155 | −2.52068 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.36932 | 0.593756 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.63068 | −0.166047 | −0.0830236 | − | 0.996548i | \(-0.526458\pi\) | ||||
−0.0830236 | + | 0.996548i | \(0.526458\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.12311 | −0.447826 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.4924 | 1.65255 | 0.826276 | − | 0.563266i | \(-0.190455\pi\) | ||||
0.826276 | + | 0.563266i | \(0.190455\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.06913 | 0.314980 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.49242 | −0.154277 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.05398 | −0.496629 | −0.248315 | − | 0.968679i | \(-0.579877\pi\) | ||||
−0.248315 | + | 0.968679i | \(0.579877\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.19224 | −0.256561 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.12311 | 0.556246 | 0.278123 | − | 0.960546i | \(-0.410288\pi\) | ||||
0.278123 | + | 0.960546i | \(0.410288\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | −0.242983 | −0.121491 | − | 0.992592i | \(-0.538768\pi\) | ||||
−0.121491 | + | 0.992592i | \(0.538768\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.87689 | 0.295163 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.75379 | 0.345712 | 0.172856 | − | 0.984947i | \(-0.444701\pi\) | ||||
0.172856 | + | 0.984947i | \(0.444701\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.12311 | 0.186975 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.24621 | −0.491928 | −0.245964 | − | 0.969279i | \(-0.579104\pi\) | ||||
−0.245964 | + | 0.969279i | \(0.579104\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.00000 | 0.356663 | 0.178331 | − | 0.983970i | \(-0.442930\pi\) | ||||
0.178331 | + | 0.983970i | \(0.442930\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.86174 | −0.109895 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.94602 | 0.290943 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.4924 | 1.20129 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.87689 | −0.518594 | −0.259297 | − | 0.965798i | \(-0.583491\pi\) | ||||
−0.259297 | + | 0.965798i | \(0.583491\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.56155 | 0.322714 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −50.7386 | −2.93429 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.24621 | 0.129469 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.12311 | −0.179418 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.0000 | −1.02731 | −0.513657 | − | 0.857996i | \(-0.671710\pi\) | ||||
−0.513657 | + | 0.857996i | \(0.671710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5616 | −0.769005 | −0.384503 | − | 0.923124i | \(-0.625627\pi\) | ||||
−0.384503 | + | 0.923124i | \(0.625627\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.7386 | 1.39831 | 0.699155 | − | 0.714970i | \(-0.253560\pi\) | ||||
0.699155 | + | 0.714970i | \(0.253560\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.6847 | −1.04943 | −0.524717 | − | 0.851276i | \(-0.675829\pi\) | ||||
−0.524717 | + | 0.851276i | \(0.675829\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.43845 | −0.248505 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.75379 | 0.0978869 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.0540 | −1.44968 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.1231 | 1.05751 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.86174 | 0.323168 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.7386 | 1.68955 | 0.844774 | − | 0.535123i | \(-0.179735\pi\) | ||||
0.844774 | + | 0.535123i | \(0.179735\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.49242 | 0.355783 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.8078 | −0.861104 | −0.430552 | − | 0.902566i | \(-0.641681\pi\) | ||||
−0.430552 | + | 0.902566i | \(0.641681\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.2462 | −0.773748 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.56155 | 0.301175 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.05398 | 0.326884 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.0000 | 0.751559 | 0.375780 | − | 0.926709i | \(-0.377375\pi\) | ||||
0.375780 | + | 0.926709i | \(0.377375\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.4924 | −0.989877 | −0.494938 | − | 0.868928i | \(-0.664809\pi\) | ||||
−0.494938 | + | 0.868928i | \(0.664809\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 39.6155 | 2.11452 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.0000 | −0.532246 | −0.266123 | − | 0.963939i | \(-0.585743\pi\) | ||||
−0.266123 | + | 0.963939i | \(0.585743\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.20739 | 0.169753 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.7386 | −1.62232 | −0.811162 | − | 0.584822i | \(-0.801164\pi\) | ||||
−0.811162 | + | 0.584822i | \(0.801164\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.9309 | 0.627941 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.56155 | 0.0819603 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4924 | 0.860897 | 0.430449 | − | 0.902615i | \(-0.358355\pi\) | ||||
0.430449 | + | 0.902615i | \(0.358355\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.38447 | −0.124131 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.17708 | −0.0611110 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.36932 | 0.0709005 | 0.0354503 | − | 0.999371i | \(-0.488713\pi\) | ||||
0.0354503 | + | 0.999371i | \(0.488713\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −31.6155 | −1.62828 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.1231 | −1.18775 | −0.593877 | − | 0.804556i | \(-0.702403\pi\) | ||||
−0.593877 | + | 0.804556i | \(0.702403\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.4924 | −1.04986 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.3693 | 1.29631 | 0.648156 | − | 0.761508i | \(-0.275541\pi\) | ||||
0.648156 | + | 0.761508i | \(0.275541\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.87689 | 0.146241 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.4924 | 0.937603 | 0.468802 | − | 0.883304i | \(-0.344686\pi\) | ||||
0.468802 | + | 0.883304i | \(0.344686\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.3693 | −1.68756 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.94602 | 0.299937 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0000 | 0.702640 | 0.351320 | − | 0.936255i | \(-0.385733\pi\) | ||||
0.351320 | + | 0.936255i | \(0.385733\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.80776 | −0.190627 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.1922 | 0.508976 | 0.254488 | − | 0.967076i | \(-0.418093\pi\) | ||||
0.254488 | + | 0.967076i | \(0.418093\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 39.6155 | 1.97339 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.5616 | 0.573085 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.36932 | −0.364389 | −0.182195 | − | 0.983262i | \(-0.558320\pi\) | ||||
−0.182195 | + | 0.983262i | \(0.558320\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.75379 | −0.0865080 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.12311 | 0.153678 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.24621 | −0.305878 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.4924 | −1.58736 | −0.793679 | − | 0.608336i | \(-0.791837\pi\) | ||||
−0.793679 | + | 0.608336i | \(0.791837\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.6155 | −0.663580 | −0.331790 | − | 0.943353i | \(-0.607653\pi\) | ||||
−0.331790 | + | 0.943353i | \(0.607653\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.50758 | 0.365031 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.69981 | 0.179047 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.1231 | 0.537029 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.00000 | 0.385346 | 0.192673 | − | 0.981263i | \(-0.438284\pi\) | ||||
0.192673 | + | 0.981263i | \(0.438284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.1231 | 0.630656 | 0.315328 | − | 0.948983i | \(-0.397885\pi\) | ||||
0.315328 | + | 0.948983i | \(0.397885\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 39.6155 | 1.89507 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.24621 | −0.298115 | −0.149058 | − | 0.988828i | \(-0.547624\pi\) | ||||
−0.149058 | + | 0.988828i | \(0.547624\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.82292 | 0.182044 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000 | 0.570137 | 0.285069 | − | 0.958507i | \(-0.407984\pi\) | ||||
0.285069 | + | 0.958507i | \(0.407984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.6847 | −0.789157 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.2462 | −0.766706 | −0.383353 | − | 0.923602i | \(-0.625231\pi\) | ||||
−0.383353 | + | 0.923602i | \(0.625231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.24621 | −0.199946 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.6155 | 1.10955 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.68466 | 0.406251 | 0.203126 | − | 0.979153i | \(-0.434890\pi\) | ||||
0.203126 | + | 0.979153i | \(0.434890\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.0540 | 1.21610 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.0540 | 0.747708 | 0.373854 | − | 0.927488i | \(-0.378036\pi\) | ||||
0.373854 | + | 0.927488i | \(0.378036\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.63068 | 0.122258 | 0.0611291 | − | 0.998130i | \(-0.480530\pi\) | ||||
0.0611291 | + | 0.998130i | \(0.480530\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.1922 | −0.564189 | −0.282095 | − | 0.959387i | \(-0.591029\pi\) | ||||
−0.282095 | + | 0.959387i | \(0.591029\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.5464 | −0.670263 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.12311 | 0.235561 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.50758 | −0.0690272 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.24621 | −0.102632 | −0.0513160 | − | 0.998682i | \(-0.516342\pi\) | ||||
−0.0513160 | + | 0.998682i | \(0.516342\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 82.3542 | 3.75503 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.87689 | −0.221906 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.7538 | 0.623244 | 0.311622 | − | 0.950206i | \(-0.399128\pi\) | ||||
0.311622 | + | 0.950206i | \(0.399128\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.300187 | −0.0135749 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.6847 | −1.29452 | −0.647260 | − | 0.762269i | \(-0.724085\pi\) | ||||
−0.647260 | + | 0.762269i | \(0.724085\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.7926 | −0.936452 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.80776 | 0.170802 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.7386 | 1.37605 | 0.688025 | − | 0.725687i | \(-0.258478\pi\) | ||||
0.688025 | + | 0.725687i | \(0.258478\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.6847 | −0.745416 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.12311 | −0.228428 | −0.114214 | − | 0.993456i | \(-0.536435\pi\) | ||||
−0.114214 | + | 0.993456i | \(0.536435\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 58.9309 | 2.61721 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −41.6155 | −1.84458 | −0.922288 | − | 0.386504i | \(-0.873683\pi\) | ||||
−0.922288 | + | 0.386504i | \(0.873683\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.12311 | −0.138158 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −30.9309 | −1.36563 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3693 | 0.587982 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.8617 | −1.31078 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.49242 | 0.109195 | 0.0545975 | − | 0.998508i | \(-0.482612\pi\) | ||||
0.0545975 | + | 0.998508i | \(0.482612\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.1231 | −1.44837 | −0.724186 | − | 0.689605i | \(-0.757784\pi\) | ||||
−0.724186 | + | 0.689605i | \(0.757784\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.0540 | 1.13493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.7386 | 1.20603 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.2462 | −1.31011 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.50758 | −0.151363 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.80776 | 0.293231 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.9309 | 0.899888 | 0.449944 | − | 0.893057i | \(-0.351444\pi\) | ||||
0.449944 | + | 0.893057i | \(0.351444\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.8769 | 0.552600 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.3693 | 1.51228 | 0.756141 | − | 0.654408i | \(-0.227082\pi\) | ||||
0.756141 | + | 0.654408i | \(0.227082\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.73863 | 0.202240 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.6847 | 1.05160 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.86174 | −0.249267 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.3693 | −1.75287 | −0.876437 | − | 0.481516i | \(-0.840086\pi\) | ||||
−0.876437 | + | 0.481516i | \(0.840086\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.4924 | 1.54347 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.31534 | 0.308854 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.9848 | −0.968696 | −0.484348 | − | 0.874876i | \(-0.660943\pi\) | ||||
−0.484348 | + | 0.874876i | \(0.660943\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.06913 | 0.128891 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.6155 | −1.57692 | −0.788462 | − | 0.615083i | \(-0.789123\pi\) | ||||
−0.788462 | + | 0.615083i | \(0.789123\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.3002 | −1.18433 | −0.592163 | − | 0.805818i | \(-0.701726\pi\) | ||||
−0.592163 | + | 0.805818i | \(0.701726\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.75379 | −0.407470 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.2462 | 1.34243 | 0.671214 | − | 0.741264i | \(-0.265773\pi\) | ||||
0.671214 | + | 0.741264i | \(0.265773\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39.9157 | 1.65884 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.63068 | −0.109139 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.68466 | −0.111187 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.0540 | −1.40556 | −0.702779 | − | 0.711408i | \(-0.748058\pi\) | ||||
−0.702779 | + | 0.711408i | \(0.748058\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.9309 | −1.27448 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 41.7538 | 1.71752 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.6155 | 0.805513 | 0.402757 | − | 0.915307i | \(-0.368052\pi\) | ||||
0.402757 | + | 0.915307i | \(0.368052\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.0540 | −1.06632 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.06913 | −0.0436835 | −0.0218417 | − | 0.999761i | \(-0.506953\pi\) | ||||
−0.0218417 | + | 0.999761i | \(0.506953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.9848 | 1.59022 | 0.795112 | − | 0.606462i | \(-0.207412\pi\) | ||||
0.795112 | + | 0.606462i | \(0.207412\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.80776 | −0.235730 | −0.117865 | − | 0.993030i | \(-0.537605\pi\) | ||||
−0.117865 | + | 0.993030i | \(0.537605\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.03882 | −0.123139 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 95.2311 | 3.85264 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.1231 | 0.449258 | 0.224629 | − | 0.974444i | \(-0.427883\pi\) | ||||
0.224629 | + | 0.974444i | \(0.427883\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.6155 | −0.548141 | −0.274070 | − | 0.961710i | \(-0.588370\pi\) | ||||
−0.274070 | + | 0.961710i | \(0.588370\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.7386 | 0.592396 | 0.296198 | − | 0.955127i | \(-0.404281\pi\) | ||||
0.296198 | + | 0.955127i | \(0.404281\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −39.6155 | −1.58972 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.17708 | 0.0471588 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.68466 | −0.346832 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 54.1619 | 2.15958 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1922 | −0.485365 | −0.242683 | − | 0.970106i | \(-0.578027\pi\) | ||||
−0.242683 | + | 0.970106i | \(0.578027\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.4233 | 0.454035 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 48.4924 | 1.92134 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.87689 | 0.192927 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.4384 | 0.649280 | 0.324640 | − | 0.945838i | \(-0.394757\pi\) | ||||
0.324640 | + | 0.945838i | \(0.394757\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.3002 | 1.11605 | 0.558025 | − | 0.829824i | \(-0.311559\pi\) | ||||
0.558025 | + | 0.829824i | \(0.311559\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.8769 | −1.44978 | −0.724890 | − | 0.688864i | \(-0.758110\pi\) | ||||
−0.724890 | + | 0.688864i | \(0.758110\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.12311 | 0.279606 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.80776 | 0.149238 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.4384 | −0.956350 | −0.478175 | − | 0.878264i | \(-0.658702\pi\) | ||||
−0.478175 | + | 0.878264i | \(0.658702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.06913 | −0.197465 | −0.0987326 | − | 0.995114i | \(-0.531479\pi\) | ||||
−0.0987326 | + | 0.995114i | \(0.531479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.4924 | −1.18602 | −0.593009 | − | 0.805196i | \(-0.702060\pi\) | ||||
−0.593009 | + | 0.805196i | \(0.702060\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 52.1080 | 2.02371 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.6155 | 1.22416 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.3542 | −1.01891 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.43845 | 0.325763 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.0691 | 0.503778 | 0.251889 | − | 0.967756i | \(-0.418948\pi\) | ||||
0.251889 | + | 0.967756i | \(0.418948\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.7538 | −1.14353 | −0.571765 | − | 0.820417i | \(-0.693741\pi\) | ||||
−0.571765 | + | 0.820417i | \(0.693741\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.75379 | −0.220810 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.8769 | 0.493444 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.17708 | 0.198095 | 0.0990477 | − | 0.995083i | \(-0.468420\pi\) | ||||
0.0990477 | + | 0.995083i | \(0.468420\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.384472 | −0.0146685 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.1231 | −0.728532 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.6155 | −1.35488 | −0.677439 | − | 0.735579i | \(-0.736910\pi\) | ||||
−0.677439 | + | 0.735579i | \(0.736910\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.246211 | −0.00935279 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.8920 | −0.753465 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.6998 | 0.593821 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.4384 | −0.620872 | −0.310436 | − | 0.950594i | \(-0.600475\pi\) | ||||
−0.310436 | + | 0.950594i | \(0.600475\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −64.3002 | −2.42513 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.876894 | 0.0329790 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.7538 | −0.591646 | −0.295823 | − | 0.955243i | \(-0.595594\pi\) | ||||
−0.295823 | + | 0.955243i | \(0.595594\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.50758 | −0.281556 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.6155 | −1.48361 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 30.6307 | 1.14392 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.82292 | −0.105277 | −0.0526386 | − | 0.998614i | \(-0.516763\pi\) | ||||
−0.0526386 | + | 0.998614i | \(0.516763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.6307 | −0.841644 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.1231 | 0.709237 | 0.354618 | − | 0.935011i | \(-0.384611\pi\) | ||||
0.354618 | + | 0.935011i | \(0.384611\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000 | 0.887672 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.2462 | 1.11717 | 0.558585 | − | 0.829448i | \(-0.311345\pi\) | ||||
0.558585 | + | 0.829448i | \(0.311345\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.75379 | 0.211657 | 0.105828 | − | 0.994384i | \(-0.466251\pi\) | ||||
0.105828 | + | 0.994384i | \(0.466251\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −61.8617 | −2.27255 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.4384 | −0.603068 | −0.301534 | − | 0.953455i | \(-0.597499\pi\) | ||||
−0.301534 | + | 0.953455i | \(0.597499\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.36932 | −0.123277 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.492423 | −0.0179927 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.8078 | −1.89049 | −0.945246 | − | 0.326358i | \(-0.894178\pi\) | ||||
−0.945246 | + | 0.326358i | \(0.894178\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.10795 | −0.149702 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.1231 | −0.403743 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.2462 | 0.878924 | 0.439462 | − | 0.898261i | \(-0.355169\pi\) | ||||
0.439462 | + | 0.898261i | \(0.355169\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.36932 | −0.194382 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 50.7386 | 1.83207 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.2462 | 0.730097 | 0.365049 | − | 0.930988i | \(-0.381052\pi\) | ||||
0.365049 | + | 0.930988i | \(0.381052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.3693 | 1.48988 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.0691 | −0.541999 | −0.270999 | − | 0.962579i | \(-0.587354\pi\) | ||||
−0.270999 | + | 0.962579i | \(0.587354\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.91571 | 0.283975 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.6155 | 0.846114 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.68466 | 0.310762 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.6847 | −0.882158 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.8617 | −1.42092 | −0.710459 | − | 0.703739i | \(-0.751513\pi\) | ||||
−0.710459 | + | 0.703739i | \(0.751513\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.5767 | −0.447743 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.00000 | 0.142224 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 60.1080 | 2.13450 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.75379 | −0.132966 | −0.0664830 | − | 0.997788i | \(-0.521178\pi\) | ||||
−0.0664830 | + | 0.997788i | \(0.521178\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 62.6307 | 2.21571 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.50758 | 0.0532676 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.12311 | −0.251369 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.2462 | 0.501490 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.73863 | 0.307234 | 0.153617 | − | 0.988130i | \(-0.450908\pi\) | ||||
0.153617 | + | 0.988130i | \(0.450908\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.9309 | 0.945671 | 0.472835 | − | 0.881151i | \(-0.343231\pi\) | ||||
0.472835 | + | 0.881151i | \(0.343231\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.24621 | −0.219064 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.4924 | −0.996824 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.75379 | −0.0612823 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.4924 | −0.645390 | −0.322695 | − | 0.946503i | \(-0.604589\pi\) | ||||
−0.322695 | + | 0.946503i | \(0.604589\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.4924 | 0.714321 | 0.357160 | − | 0.934043i | \(-0.383745\pi\) | ||||
0.357160 | + | 0.934043i | \(0.383745\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.8617 | 0.968848 | 0.484424 | − | 0.874833i | \(-0.339029\pi\) | ||||
0.484424 | + | 0.874833i | \(0.339029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.1231 | −1.42826 | −0.714132 | − | 0.700011i | \(-0.753178\pi\) | ||||
−0.714132 | + | 0.700011i | \(0.753178\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.98485 | 0.311681 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.8920 | 1.10499 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.9309 | 1.06913 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.4924 | 1.81224 | 0.906120 | − | 0.423021i | \(-0.139030\pi\) | ||||
0.906120 | + | 0.423021i | \(0.139030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.30019 | −0.320696 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.8769 | −0.443504 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.438447 | −0.0150652 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.36932 | 0.321554 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −82.3542 | −2.82306 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.8769 | 0.988726 | 0.494363 | − | 0.869256i | \(-0.335401\pi\) | ||||
0.494363 | + | 0.869256i | \(0.335401\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.80776 | 0.266708 | 0.133354 | − | 0.991068i | \(-0.457425\pi\) | ||||
0.133354 | + | 0.991068i | \(0.457425\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.8617 | −1.15535 | −0.577674 | − | 0.816268i | \(-0.696039\pi\) | ||||
−0.577674 | + | 0.816268i | \(0.696039\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.90720 | −0.0990773 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.8769 | −0.710658 | −0.355329 | − | 0.934741i | \(-0.615631\pi\) | ||||
−0.355329 | + | 0.934741i | \(0.615631\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.72348 | 0.262303 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.3693 | −0.453523 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.36932 | −0.249414 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.6155 | −0.527299 | −0.263649 | − | 0.964619i | \(-0.584926\pi\) | ||||
−0.263649 | + | 0.964619i | \(0.584926\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.8617 | −0.467545 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.4924 | 1.29684 | 0.648421 | − | 0.761282i | \(-0.275430\pi\) | ||||
0.648421 | + | 0.761282i | \(0.275430\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.5464 | −1.43180 | −0.715900 | − | 0.698203i | \(-0.753983\pi\) | ||||
−0.715900 | + | 0.698203i | \(0.753983\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.8769 | 0.633824 | 0.316912 | − | 0.948455i | \(-0.397354\pi\) | ||||
0.316912 | + | 0.948455i | \(0.397354\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.75379 | 0.192976 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.00000 | 0.234509 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −74.3542 | −2.48817 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −79.2311 | −2.64545 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.6847 | −0.823279 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.5767 | −0.418991 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.50758 | 0.116725 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.3153 | 1.03981 | 0.519904 | − | 0.854224i | \(-0.325968\pi\) | ||||
0.519904 | + | 0.854224i | \(0.325968\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.12311 | 0.0372511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.5616 | 1.50952 | 0.754761 | − | 0.656000i | \(-0.227753\pi\) | ||||
0.754761 | + | 0.656000i | \(0.227753\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.00000 | −0.198571 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.66950 | −0.0551319 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.2311 | 1.55801 | 0.779004 | − | 0.627018i | \(-0.215725\pi\) | ||||
0.779004 | + | 0.627018i | \(0.215725\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.1080 | −0.926188 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 61.8617 | 2.03620 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.5464 | −1.19905 | −0.599524 | − | 0.800357i | \(-0.704643\pi\) | ||||
−0.599524 | + | 0.800357i | \(0.704643\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.8617 | −1.24087 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.1771 | −0.693307 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.38447 | 0.273909 | 0.136954 | − | 0.990577i | \(-0.456269\pi\) | ||||
0.136954 | + | 0.990577i | \(0.456269\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.6307 | 1.26066 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.0540 | −0.914533 | −0.457267 | − | 0.889330i | \(-0.651172\pi\) | ||||
−0.457267 | + | 0.889330i | \(0.651172\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.2462 | 0.984952 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.0540 | −1.62654 | −0.813268 | − | 0.581890i | \(-0.802314\pi\) | ||||
−0.813268 | + | 0.581890i | \(0.802314\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50.7386 | −1.64705 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.1771 | −0.946132 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.43845 | 0.0789891 | 0.0394945 | − | 0.999220i | \(-0.487425\pi\) | ||||
0.0394945 | + | 0.999220i | \(0.487425\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.93087 | −0.224043 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.492423 | 0.0159012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.0691303 | −0.00223001 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.630683 | −0.0203235 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.43845 | 0.271362 | 0.135681 | − | 0.990753i | \(-0.456678\pi\) | ||||
0.135681 | + | 0.990753i | \(0.456678\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −40.6847 | −1.30698 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.0000 | −0.898563 | −0.449281 | − | 0.893390i | \(-0.648320\pi\) | ||||
−0.449281 | + | 0.893390i | \(0.648320\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.75379 | 0.0562239 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.8617 | −1.14732 | −0.573659 | − | 0.819094i | \(-0.694477\pi\) | ||||
−0.573659 | + | 0.819094i | \(0.694477\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.68466 | 0.0858021 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.87689 | −0.219562 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.3693 | 1.31948 | 0.659738 | − | 0.751496i | \(-0.270667\pi\) | ||||
0.659738 | + | 0.751496i | \(0.270667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.15342 | 0.291356 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.4924 | −1.16039 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 48.0000 | 1.52323 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.7386 | −1.60691 | −0.803454 | − | 0.595366i | \(-0.797007\pi\) | ||||
−0.803454 | + | 0.595366i | \(0.797007\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 64.3002 | 2.03437 |
(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 | 2200.2.a.l.1.2 | 2 | ||
4.3 | odd | 2 | 4400.2.a.bt.1.1 | 2 | |||
5.2 | odd | 4 | 2200.2.b.f.1849.2 | 4 | |||
5.3 | odd | 4 | 2200.2.b.f.1849.3 | 4 | |||
5.4 | even | 2 | 440.2.a.g.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 3960.2.a.bf.1.1 | 2 | |||
20.3 | even | 4 | 4400.2.b.w.4049.2 | 4 | |||
20.7 | even | 4 | 4400.2.b.w.4049.3 | 4 | |||
20.19 | odd | 2 | 880.2.a.k.1.2 | 2 | |||
40.19 | odd | 2 | 3520.2.a.br.1.1 | 2 | |||
40.29 | even | 2 | 3520.2.a.bm.1.2 | 2 | |||
55.54 | odd | 2 | 4840.2.a.m.1.1 | 2 | |||
60.59 | even | 2 | 7920.2.a.by.1.2 | 2 | |||
220.219 | even | 2 | 9680.2.a.bm.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.a.g.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
880.2.a.k.1.2 | 2 | 20.19 | odd | 2 | |||
2200.2.a.l.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2200.2.b.f.1849.2 | 4 | 5.2 | odd | 4 | |||
2200.2.b.f.1849.3 | 4 | 5.3 | odd | 4 | |||
3520.2.a.bm.1.2 | 2 | 40.29 | even | 2 | |||
3520.2.a.br.1.1 | 2 | 40.19 | odd | 2 | |||
3960.2.a.bf.1.1 | 2 | 15.14 | odd | 2 | |||
4400.2.a.bt.1.1 | 2 | 4.3 | odd | 2 | |||
4400.2.b.w.4049.2 | 4 | 20.3 | even | 4 | |||
4400.2.b.w.4049.3 | 4 | 20.7 | even | 4 | |||
4840.2.a.m.1.1 | 2 | 55.54 | odd | 2 | |||
7920.2.a.by.1.2 | 2 | 60.59 | even | 2 | |||
9680.2.a.bm.1.2 | 2 | 220.219 | even | 2 |