Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, 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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.521397.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 9x^{3} - 3x^{2} + 18x + 12 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4600) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.36629\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | −1.36629 | −0.788825 | −0.394413 | − | 0.918933i | \(-0.629052\pi\) | ||||
−0.394413 | + | 0.918933i | \(0.629052\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.28093 | 1.24008 | 0.620038 | − | 0.784572i | \(-0.287117\pi\) | ||||
0.620038 | + | 0.784572i | \(0.287117\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.13327 | −0.377755 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.49709 | −1.05441 | −0.527207 | − | 0.849737i | \(-0.676761\pi\) | ||||
−0.527207 | + | 0.849737i | \(0.676761\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.41420 | 0.946928 | 0.473464 | − | 0.880813i | \(-0.343003\pi\) | ||||
0.473464 | + | 0.880813i | \(0.343003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.46023 | −1.80937 | −0.904685 | − | 0.426080i | \(-0.859894\pi\) | ||||
−0.904685 | + | 0.426080i | \(0.859894\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.49709 | −0.802288 | −0.401144 | − | 0.916015i | \(-0.631387\pi\) | ||||
−0.401144 | + | 0.916015i | \(0.631387\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.48269 | −0.978203 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.64722 | 1.08681 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.46268 | −0.643004 | −0.321502 | − | 0.946909i | \(-0.604188\pi\) | ||||
−0.321502 | + | 0.946909i | \(0.604188\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.01105 | −0.361195 | −0.180597 | − | 0.983557i | \(-0.557803\pi\) | ||||
−0.180597 | + | 0.983557i | \(0.557803\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.77803 | 0.831748 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.511497 | 0.0840896 | 0.0420448 | − | 0.999116i | \(-0.486613\pi\) | ||||
0.0420448 | + | 0.999116i | \(0.486613\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.66477 | −0.746961 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.07954 | −1.10564 | −0.552819 | − | 0.833301i | \(-0.686448\pi\) | ||||
−0.552819 | + | 0.833301i | \(0.686448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.76452 | 0.421586 | 0.210793 | − | 0.977531i | \(-0.432395\pi\) | ||||
0.210793 | + | 0.977531i | \(0.432395\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.889198 | 0.129703 | 0.0648514 | − | 0.997895i | \(-0.479343\pi\) | ||||
0.0648514 | + | 0.997895i | \(0.479343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.76452 | 0.537789 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.1928 | 1.42728 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14.2383 | −1.95577 | −0.977887 | − | 0.209132i | \(-0.932936\pi\) | ||||
−0.977887 | + | 0.209132i | \(0.932936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.77803 | 0.632865 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.71325 | 0.613613 | 0.306807 | − | 0.951772i | \(-0.400739\pi\) | ||||
0.306807 | + | 0.951772i | \(0.400739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.4769 | 1.72554 | 0.862769 | − | 0.505599i | \(-0.168728\pi\) | ||||
0.862769 | + | 0.505599i | \(0.168728\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.71817 | −0.468445 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.30025 | 0.281020 | 0.140510 | − | 0.990079i | \(-0.455126\pi\) | ||||
0.140510 | + | 0.990079i | \(0.455126\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.36629 | 0.164481 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6214 | 1.26053 | 0.630264 | − | 0.776381i | \(-0.282947\pi\) | ||||
0.630264 | + | 0.776381i | \(0.282947\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.70765 | 0.433948 | 0.216974 | − | 0.976177i | \(-0.430381\pi\) | ||||
0.216974 | + | 0.976177i | \(0.430381\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.4737 | −1.30755 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.97978 | 0.897796 | 0.448898 | − | 0.893583i | \(-0.351817\pi\) | ||||
0.448898 | + | 0.893583i | \(0.351817\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.31592 | −0.479546 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.42336 | −1.03435 | −0.517174 | − | 0.855880i | \(-0.673016\pi\) | ||||
−0.517174 | + | 0.855880i | \(0.673016\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.73101 | 0.507218 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.801390 | 0.0849471 | 0.0424736 | − | 0.999098i | \(-0.486476\pi\) | ||||
0.0424736 | + | 0.999098i | \(0.486476\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.2018 | 1.17426 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.74766 | 0.284919 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.7722 | 1.19529 | 0.597644 | − | 0.801762i | \(-0.296104\pi\) | ||||
0.597644 | + | 0.801762i | \(0.296104\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.96313 | 0.398310 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.1559 | 1.11006 | 0.555028 | − | 0.831831i | \(-0.312707\pi\) | ||||
0.555028 | + | 0.831831i | \(0.312707\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.28585 | −0.126698 | −0.0633491 | − | 0.997991i | \(-0.520178\pi\) | ||||
−0.0633491 | + | 0.997991i | \(0.520178\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.8975 | 1.34352 | 0.671759 | − | 0.740770i | \(-0.265539\pi\) | ||||
0.671759 | + | 0.740770i | \(0.265539\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.77713 | −0.361783 | −0.180892 | − | 0.983503i | \(-0.557898\pi\) | ||||
−0.180892 | + | 0.983503i | \(0.557898\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.698851 | −0.0663320 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.3111 | −1.81663 | −0.908317 | − | 0.418282i | \(-0.862632\pi\) | ||||
−0.908317 | + | 0.418282i | \(0.862632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.86919 | −0.357707 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.4765 | −2.24376 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.22966 | 0.111788 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.67267 | 0.872155 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.7612 | 1.22111 | 0.610553 | − | 0.791975i | \(-0.290947\pi\) | ||||
0.610553 | + | 0.791975i | \(0.290947\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.77713 | −0.332558 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.41665 | 0.647996 | 0.323998 | − | 0.946058i | \(-0.394973\pi\) | ||||
0.323998 | + | 0.946058i | \(0.394973\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.4737 | −0.994899 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.5502 | 1.75573 | 0.877863 | − | 0.478912i | \(-0.158969\pi\) | ||||
0.877863 | + | 0.478912i | \(0.158969\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.49652 | 0.466209 | 0.233104 | − | 0.972452i | \(-0.425112\pi\) | ||||
0.233104 | + | 0.972452i | \(0.425112\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.21490 | −0.102313 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.9398 | −0.998454 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.14341 | −0.424221 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.80139 | 0.393345 | 0.196673 | − | 0.980469i | \(-0.436986\pi\) | ||||
0.196673 | + | 0.980469i | \(0.436986\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.26862 | 0.265997 | 0.132998 | − | 0.991116i | \(-0.457539\pi\) | ||||
0.132998 | + | 0.991116i | \(0.457539\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.45441 | 0.683499 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.8392 | −1.74296 | −0.871480 | − | 0.490430i | \(-0.836840\pi\) | ||||
−0.871480 | + | 0.490430i | \(0.836840\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.4535 | 1.54276 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.28093 | −0.258574 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.2435 | 1.82057 | 0.910285 | − | 0.413982i | \(-0.135862\pi\) | ||||
0.910285 | + | 0.413982i | \(0.135862\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.13179 | −0.319728 | −0.159864 | − | 0.987139i | \(-0.551106\pi\) | ||||
−0.159864 | + | 0.987139i | \(0.551106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.34325 | −0.103327 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.96313 | 0.303068 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.88548 | −0.447465 | −0.223732 | − | 0.974651i | \(-0.571824\pi\) | ||||
−0.223732 | + | 0.974651i | \(0.571824\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.43965 | −0.484034 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.85789 | 0.512583 | 0.256292 | − | 0.966600i | \(-0.417499\pi\) | ||||
0.256292 | + | 0.966600i | \(0.417499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.29042 | −0.170246 | −0.0851229 | − | 0.996370i | \(-0.527128\pi\) | ||||
−0.0851229 | + | 0.996370i | \(0.527128\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.4133 | −1.36115 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26.0891 | 1.90782 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.5281 | 1.34772 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.58748 | 0.693725 | 0.346863 | − | 0.937916i | \(-0.387247\pi\) | ||||
0.346863 | + | 0.937916i | \(0.387247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.9410 | −1.00350 | −0.501749 | − | 0.865013i | \(-0.667310\pi\) | ||||
−0.501749 | + | 0.865013i | \(0.667310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.1011 | −1.07591 | −0.537954 | − | 0.842974i | \(-0.680803\pi\) | ||||
−0.537954 | + | 0.842974i | \(0.680803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.5128 | −1.02879 | −0.514394 | − | 0.857554i | \(-0.671983\pi\) | ||||
−0.514394 | + | 0.857554i | \(0.671983\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.14280 | −0.221676 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.3608 | −0.797374 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.13327 | 0.0787674 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.2297 | 0.845944 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.4846 | 1.61674 | 0.808372 | − | 0.588672i | \(-0.200349\pi\) | ||||
0.808372 | + | 0.588672i | \(0.200349\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.5119 | −0.994336 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.59811 | −0.447909 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.06571 | −0.342309 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.4707 | −1.71334 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.20720 | −0.549595 | −0.274797 | − | 0.961502i | \(-0.588611\pi\) | ||||
−0.274797 | + | 0.961502i | \(0.588611\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9942 | 1.12794 | 0.563972 | − | 0.825794i | \(-0.309273\pi\) | ||||
0.563972 | + | 0.825794i | \(0.309273\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.6818 | 1.30061 | 0.650306 | − | 0.759672i | \(-0.274641\pi\) | ||||
0.650306 | + | 0.759672i | \(0.274641\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.6764 | 1.03143 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.8799 | −1.62993 | −0.814967 | − | 0.579507i | \(-0.803245\pi\) | ||||
−0.814967 | + | 0.579507i | \(0.803245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.9027 | −0.708204 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.0718483 | 0.00464748 | 0.00232374 | − | 0.999997i | \(-0.499260\pi\) | ||||
0.00232374 | + | 0.999997i | \(0.499260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50658 | −0.547957 | −0.273979 | − | 0.961736i | \(-0.588340\pi\) | ||||
−0.273979 | + | 0.961736i | \(0.588340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0449 | −0.708530 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.9398 | −0.759709 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.8750 | 0.815920 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.8858 | 1.25518 | 0.627591 | − | 0.778543i | \(-0.284041\pi\) | ||||
0.627591 | + | 0.778543i | \(0.284041\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.49709 | 0.219860 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.4062 | 0.711498 | 0.355749 | − | 0.934582i | \(-0.384226\pi\) | ||||
0.355749 | + | 0.934582i | \(0.384226\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.67819 | 0.104277 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.92414 | 0.242898 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.3903 | −0.825679 | −0.412840 | − | 0.910804i | \(-0.635463\pi\) | ||||
−0.412840 | + | 0.910804i | \(0.635463\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.09493 | −0.0670084 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.8103 | 0.842027 | 0.421014 | − | 0.907054i | \(-0.361674\pi\) | ||||
0.421014 | + | 0.907054i | \(0.361674\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.7574 | −1.62540 | −0.812699 | − | 0.582683i | \(-0.802003\pi\) | ||||
−0.812699 | + | 0.582683i | \(0.802003\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.3048 | −0.926288 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.80667 | 0.108552 | 0.0542760 | − | 0.998526i | \(-0.482715\pi\) | ||||
0.0542760 | + | 0.998526i | \(0.482715\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.27905 | 0.136443 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.1348 | 1.61873 | 0.809364 | − | 0.587308i | \(-0.199812\pi\) | ||||
0.809364 | + | 0.587308i | \(0.199812\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.9875 | 1.24758 | 0.623788 | − | 0.781594i | \(-0.285593\pi\) | ||||
0.623788 | + | 0.781594i | \(0.285593\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.2275 | −1.37108 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.6550 | 2.27382 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.0842 | −0.942873 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.00671252 | −0.000392149 0 | −0.000196075 | − | 1.00000i | \(-0.500062\pi\) | ||||
−0.000196075 | 1.00000i | \(0.500062\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.7489 | −1.14594 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.41420 | −0.197448 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.07022 | 0.522799 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.2422 | −0.875641 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.9767 | −1.14013 | −0.570067 | − | 0.821598i | \(-0.693083\pi\) | ||||
−0.570067 | + | 0.821598i | \(0.693083\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.75683 | 0.0999427 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.8601 | −1.35298 | −0.676491 | − | 0.736451i | \(-0.736500\pi\) | ||||
−0.676491 | + | 0.736451i | \(0.736500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.4406 | 0.985803 | 0.492901 | − | 0.870085i | \(-0.335936\pi\) | ||||
0.492901 | + | 0.870085i | \(0.335936\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.35581 | −0.0761499 | −0.0380750 | − | 0.999275i | \(-0.512123\pi\) | ||||
−0.0380750 | + | 0.999275i | \(0.512123\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.1093 | 0.677992 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.9879 | −1.05980 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.0891 | 1.45164 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.16063 | 0.285384 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.91740 | 0.160841 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.4050 | −0.956667 | −0.478333 | − | 0.878178i | \(-0.658759\pi\) | ||||
−0.478333 | + | 0.878178i | \(0.658759\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.579662 | −0.0317653 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.4648 | −1.22373 | −0.611867 | − | 0.790961i | \(-0.709581\pi\) | ||||
−0.611867 | + | 0.790961i | \(0.709581\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.3845 | 1.43301 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.03282 | 0.380849 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.6154 | −0.573177 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.97296 | 0.159597 | 0.0797984 | − | 0.996811i | \(-0.474572\pi\) | ||||
0.0797984 | + | 0.996811i | \(0.474572\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.36975 | −0.233908 | −0.116954 | − | 0.993137i | \(-0.537313\pi\) | ||||
−0.116954 | + | 0.993137i | \(0.537313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.2807 | 1.02913 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.4419 | −1.67348 | −0.836742 | − | 0.547598i | \(-0.815542\pi\) | ||||
−0.836742 | + | 0.547598i | \(0.815542\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 33.4419 | 1.76993 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.7912 | −1.46676 | −0.733381 | − | 0.679818i | \(-0.762059\pi\) | ||||
−0.733381 | + | 0.679818i | \(0.762059\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.77034 | −0.356333 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.68007 | −0.0881809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.9061 | 0.725890 | 0.362945 | − | 0.931811i | \(-0.381771\pi\) | ||||
0.362945 | + | 0.931811i | \(0.381771\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.02299 | 0.417660 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −46.7148 | −2.42531 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.2799 | 1.36072 | 0.680362 | − | 0.732876i | \(-0.261823\pi\) | ||||
0.680362 | + | 0.732876i | \(0.261823\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.8223 | −0.608879 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.06792 | 0.157588 | 0.0787942 | − | 0.996891i | \(-0.474893\pi\) | ||||
0.0787942 | + | 0.996891i | \(0.474893\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.8017 | −0.963239 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.8872 | 1.47607 | 0.738034 | − | 0.674763i | \(-0.235754\pi\) | ||||
0.738034 | + | 0.674763i | \(0.235754\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.13294 | −0.159256 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.4697 | 1.24066 | 0.620331 | − | 0.784340i | \(-0.286998\pi\) | ||||
0.620331 | + | 0.784340i | \(0.286998\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.46023 | 0.377280 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.1333 | −0.511156 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.44828 | 0.424007 | 0.212004 | − | 0.977269i | \(-0.432001\pi\) | ||||
0.212004 | + | 0.977269i | \(0.432001\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.6764 | 0.784801 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.3352 | 1.01549 | 0.507746 | − | 0.861507i | \(-0.330479\pi\) | ||||
0.507746 | + | 0.861507i | \(0.330479\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.86611 | −0.342025 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.78875 | −0.0886652 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.05655 | 0.299477 | 0.149738 | − | 0.988726i | \(-0.452157\pi\) | ||||
0.149738 | + | 0.988726i | \(0.452157\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −28.0775 | −1.38496 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.4639 | 0.760927 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.50982 | −0.367757 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.02434 | −0.343162 | −0.171581 | − | 0.985170i | \(-0.554887\pi\) | ||||
−0.171581 | + | 0.985170i | \(0.554887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.17652 | 0.349762 | 0.174881 | − | 0.984590i | \(-0.444046\pi\) | ||||
0.174881 | + | 0.984590i | \(0.444046\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.00770 | −0.0489959 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 44.2167 | 2.13980 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.3131 | 0.787605 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.2944 | −0.544034 | −0.272017 | − | 0.962292i | \(-0.587691\pi\) | ||||
−0.272017 | + | 0.962292i | \(0.587691\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.2266 | 1.06814 | 0.534072 | − | 0.845439i | \(-0.320661\pi\) | ||||
0.534072 | + | 0.845439i | \(0.320661\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.49709 | 0.167289 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.2573 | 1.44410 | 0.722052 | − | 0.691839i | \(-0.243199\pi\) | ||||
0.722052 | + | 0.691839i | \(0.243199\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.26620 | −0.203153 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.0307 | 0.666620 | 0.333310 | − | 0.942817i | \(-0.391834\pi\) | ||||
0.333310 | + | 0.942817i | \(0.391834\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.56007 | −0.310281 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.70110 | 0.410630 | 0.205315 | − | 0.978696i | \(-0.434178\pi\) | ||||
0.205315 | + | 0.978696i | \(0.434178\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.7578 | 1.16580 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.46587 | −0.209825 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.8379 | 1.58287 | 0.791434 | − | 0.611255i | \(-0.209335\pi\) | ||||
0.791434 | + | 0.611255i | \(0.209335\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −42.1295 | −1.96644 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.6512 | 1.84674 | 0.923370 | − | 0.383912i | \(-0.125423\pi\) | ||||
0.923370 | + | 0.383912i | \(0.125423\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.8490 | −1.61957 | −0.809784 | − | 0.586727i | \(-0.800416\pi\) | ||||
−0.809784 | + | 0.586727i | \(0.800416\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.9442 | 0.645258 | 0.322629 | − | 0.946525i | \(-0.395433\pi\) | ||||
0.322629 | + | 0.946525i | \(0.395433\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.54697 | 0.348486 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.8386 | 1.37489 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.66780 | −0.444526 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.1357 | 0.738804 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.4103 | 1.48086 | 0.740432 | − | 0.672131i | \(-0.234621\pi\) | ||||
0.740432 | + | 0.672131i | \(0.234621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.74635 | 0.0796268 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.48269 | 0.203969 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.1999 | 1.14192 | 0.570959 | − | 0.820979i | \(-0.306572\pi\) | ||||
0.570959 | + | 0.820979i | \(0.306572\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −31.7572 | −1.43611 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.9247 | 1.48587 | 0.742936 | − | 0.669363i | \(-0.233433\pi\) | ||||
0.742936 | + | 0.669363i | \(0.233433\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.8324 | 1.16343 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.8481 | 1.56315 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4047 | −0.555309 | −0.277654 | − | 0.960681i | \(-0.589557\pi\) | ||||
−0.277654 | + | 0.960681i | \(0.589557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.64521 | 0.252209 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.74517 | −0.166989 | −0.0834945 | − | 0.996508i | \(-0.526608\pi\) | ||||
−0.0834945 | + | 0.996508i | \(0.526608\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.83526 | 0.0815069 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.84783 | −0.259201 | −0.129600 | − | 0.991566i | \(-0.541369\pi\) | ||||
−0.129600 | + | 0.991566i | \(0.541369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.1646 | 0.538128 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.7489 | −0.871933 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.10961 | −0.136760 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.04124 | 0.352971 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.3808 | 0.805278 | 0.402639 | − | 0.915359i | \(-0.368093\pi\) | ||||
0.402639 | + | 0.915359i | \(0.368093\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.4541 | 1.02558 | 0.512789 | − | 0.858515i | \(-0.328612\pi\) | ||||
0.512789 | + | 0.858515i | \(0.328612\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.0029 | 0.653535 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.34137 | −0.231796 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.1710 | −1.04696 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.36984 | −0.404338 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.1649 | −0.567052 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.03474 | 0.130474 | 0.0652368 | − | 0.997870i | \(-0.479220\pi\) | ||||
0.0652368 | + | 0.997870i | \(0.479220\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.12937 | 0.134294 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4383 | 0.702851 | 0.351426 | − | 0.936216i | \(-0.385697\pi\) | ||||
0.351426 | + | 0.936216i | \(0.385697\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.2729 | −0.651830 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.1093 | 0.515875 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.1811 | 1.11334 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.72395 | 0.284903 | 0.142451 | − | 0.989802i | \(-0.454502\pi\) | ||||
0.142451 | + | 0.989802i | \(0.454502\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.43863 | 0.399212 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −35.6452 | −1.50494 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −42.0044 | −1.77027 | −0.885137 | − | 0.465331i | \(-0.845935\pi\) | ||||
−0.885137 | + | 0.465331i | \(0.845935\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.1602 | −0.594674 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.1152 | −1.63980 | −0.819898 | − | 0.572510i | \(-0.805970\pi\) | ||||
−0.819898 | + | 0.572510i | \(0.805970\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.2607 | 0.554944 | 0.277472 | − | 0.960734i | \(-0.410503\pi\) | ||||
0.277472 | + | 0.960734i | \(0.410503\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.0992 | −0.547228 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.31588 | −0.387825 | −0.193913 | − | 0.981019i | \(-0.562118\pi\) | ||||
−0.193913 | + | 0.981019i | \(0.562118\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.0474 | 0.791584 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.9174 | −1.28267 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 49.7925 | 2.06220 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.80336 | 0.322079 | 0.161040 | − | 0.986948i | \(-0.448515\pi\) | ||||
0.161040 | + | 0.986948i | \(0.448515\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.03282 | 0.289782 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.6324 | 0.848704 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.8383 | −0.527204 | −0.263602 | − | 0.964632i | \(-0.584911\pi\) | ||||
−0.263602 | + | 0.964632i | \(0.584911\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.8287 | 0.811534 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.4957 | 0.428843 | 0.214422 | − | 0.976741i | \(-0.431213\pi\) | ||||
0.214422 | + | 0.976741i | \(0.431213\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.1978 | −1.15021 | −0.575106 | − | 0.818079i | \(-0.695039\pi\) | ||||
−0.575106 | + | 0.818079i | \(0.695039\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.60679 | −0.106157 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −46.5662 | −1.89007 | −0.945033 | − | 0.326976i | \(-0.893970\pi\) | ||||
−0.945033 | + | 0.326976i | \(0.893970\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.5221 | 0.628989 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.03590 | 0.122819 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.3120 | 1.22429 | 0.612145 | − | 0.790746i | \(-0.290307\pi\) | ||||
0.612145 | + | 0.790746i | \(0.290307\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.1879 | 0.973768 | 0.486884 | − | 0.873467i | \(-0.338134\pi\) | ||||
0.486884 | + | 0.873467i | \(0.338134\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.29534 | 0.172644 | 0.0863221 | − | 0.996267i | \(-0.472489\pi\) | ||||
0.0863221 | + | 0.996267i | \(0.472489\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.64722 | −0.226615 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.62931 | 0.105341 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.7092 | −0.667301 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.81588 | −0.152149 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.3857 | −0.493066 | −0.246533 | − | 0.969134i | \(-0.579291\pi\) | ||||
−0.246533 | + | 0.969134i | \(0.579291\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.0866 | −1.27533 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.8528 | 0.509248 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0369 | −0.476171 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.21653 | −0.206041 | −0.103020 | − | 0.994679i | \(-0.532851\pi\) | ||||
−0.103020 | + | 0.994679i | \(0.532851\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.5639 | −0.495471 | −0.247735 | − | 0.968828i | \(-0.579686\pi\) | ||||
−0.247735 | + | 0.968828i | \(0.579686\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.7423 | 0.894094 | 0.447047 | − | 0.894510i | \(-0.352476\pi\) | ||||
0.447047 | + | 0.894510i | \(0.352476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.4827 | −0.647002 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.01490 | 0.353322 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.36997 | 0.366675 | 0.183338 | − | 0.983050i | \(-0.441310\pi\) | ||||
0.183338 | + | 0.983050i | \(0.441310\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.20175 | −0.163926 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.4086 | 0.600235 | 0.300117 | − | 0.953902i | \(-0.402974\pi\) | ||||
0.300117 | + | 0.953902i | \(0.402974\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.1386 | 1.67790 | 0.838948 | − | 0.544211i | \(-0.183171\pi\) | ||||
0.838948 | + | 0.544211i | \(0.183171\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 34.8002 | 1.35153 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.46268 | 0.134076 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.2134 | 0.433534 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −47.1299 | −1.81943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.6356 | −0.487066 | −0.243533 | − | 0.969893i | \(-0.578306\pi\) | ||||
−0.243533 | + | 0.969893i | \(0.578306\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.9139 | 0.419454 | 0.209727 | − | 0.977760i | \(-0.432742\pi\) | ||||
0.209727 | + | 0.977760i | \(0.432742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.6238 | 1.48225 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.2189 | −0.889750 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.5334 | −0.670896 | −0.335448 | − | 0.942059i | \(-0.608888\pi\) | ||||
−0.335448 | + | 0.942059i | \(0.608888\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.8910 | −1.02596 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −48.6122 | −1.85198 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 52.2318 | 1.98699 | 0.993496 | − | 0.113871i | \(-0.0363250\pi\) | ||||
0.993496 | + | 0.113871i | \(0.0363250\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.0028 | 0.493935 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.8150 | 2.00051 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 33.9930 | 1.28573 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0270 | 0.983026 | 0.491513 | − | 0.870870i | \(-0.336444\pi\) | ||||
0.491513 | + | 0.870870i | \(0.336444\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.78875 | −0.0674641 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36.6019 | 1.37655 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.7971 | −1.30683 | −0.653415 | − | 0.757000i | \(-0.726664\pi\) | ||||
−0.653415 | + | 0.757000i | \(0.726664\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.04321 | −0.339147 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.01105 | 0.0753143 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.0981652 | −0.00366605 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.40110 | −0.164133 | −0.0820667 | − | 0.996627i | \(-0.526152\pi\) | ||||
−0.0820667 | + | 0.996627i | \(0.526152\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.21878 | −0.157115 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.6224 | 0.432242 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.744921 | 0.0276276 | 0.0138138 | − | 0.999905i | \(-0.495603\pi\) | ||||
0.0138138 | + | 0.999905i | \(0.495603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.0382 | 1.03845 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.6240 | −0.762805 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.35631 | 0.271711 | 0.135856 | − | 0.990729i | \(-0.456622\pi\) | ||||
0.135856 | + | 0.990729i | \(0.456622\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.04419 | −0.296311 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.2496 | −0.487394 | −0.243697 | − | 0.969851i | \(-0.578360\pi\) | ||||
−0.243697 | + | 0.969851i | \(0.578360\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.3131 | 0.599278 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.8314 | −1.05772 | −0.528861 | − | 0.848708i | \(-0.677381\pi\) | ||||
−0.528861 | + | 0.848708i | \(0.677381\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.6792 | 0.390730 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.5966 | 1.66607 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.3962 | 0.890228 | 0.445114 | − | 0.895474i | \(-0.353163\pi\) | ||||
0.445114 | + | 0.895474i | \(0.353163\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.1697 | −0.990120 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.49825 | 0.345220 | 0.172610 | − | 0.984990i | \(-0.444780\pi\) | ||||
0.172610 | + | 0.984990i | \(0.444780\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.77803 | −0.173431 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.43957 | −0.305934 | −0.152967 | − | 0.988231i | \(-0.548883\pi\) | ||||
−0.152967 | + | 0.988231i | \(0.548883\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.3925 | −0.448639 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.0920 | 0.581048 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.85911 | 0.319468 | 0.159734 | − | 0.987160i | \(-0.448936\pi\) | ||||
0.159734 | + | 0.987160i | \(0.448936\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.5841 | −0.561247 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.7351 | 1.17740 | 0.588699 | − | 0.808352i | \(-0.299640\pi\) | ||||
0.588699 | + | 0.808352i | \(0.299640\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.29288 | −0.0822567 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.7578 | 0.887041 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.1440 | −1.32912 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.5545 | −0.698822 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.736862 | −0.0262663 | −0.0131331 | − | 0.999914i | \(-0.504181\pi\) | ||||
−0.0131331 | + | 0.999914i | \(0.504181\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.2949 | 0.651316 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −63.3584 | −2.25276 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.0127 | 1.63396 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.7353 | −1.47834 | −0.739170 | − | 0.673519i | \(-0.764782\pi\) | ||||
−0.739170 | + | 0.673519i | \(0.764782\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.63362 | −0.234681 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.908187 | −0.0320892 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.9660 | −0.457560 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.8688 | −0.664212 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.3182 | 0.749506 | 0.374753 | − | 0.927125i | \(-0.377727\pi\) | ||||
0.374753 | + | 0.927125i | \(0.377727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.3126 | −0.853732 | −0.426866 | − | 0.904315i | \(-0.640382\pi\) | ||||
−0.426866 | + | 0.904315i | \(0.640382\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 36.5583 | 1.28216 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.66780 | −0.338233 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.6946 | −0.443584 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.3157 | 1.72113 | 0.860566 | − | 0.509340i | \(-0.170110\pi\) | ||||
0.860566 | + | 0.509340i | \(0.170110\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.5427 | −1.44809 | −0.724043 | − | 0.689755i | \(-0.757718\pi\) | ||||
−0.724043 | + | 0.689755i | \(0.757718\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.306510 | 0.0106584 | 0.00532919 | − | 0.999986i | \(-0.498304\pi\) | ||||
0.00532919 | + | 0.999986i | \(0.498304\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.5423 | 0.609268 | 0.304634 | − | 0.952469i | \(-0.401466\pi\) | ||||
0.304634 | + | 0.952469i | \(0.401466\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.46842 | −0.0856285 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.0842 | −0.973060 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.3568 | −0.392549 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.1480 | 1.52416 | 0.762078 | − | 0.647485i | \(-0.224179\pi\) | ||||
0.762078 | + | 0.647485i | \(0.224179\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.0098 | −0.586546 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −37.0739 | −1.27689 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.03445 | 0.138625 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.6749 | −0.984119 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.511497 | −0.0175339 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.2098 | −1.41100 | −0.705499 | − | 0.708711i | \(-0.749277\pi\) | ||||
−0.705499 | + | 0.708711i | \(0.749277\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.3245 | 0.660114 | 0.330057 | − | 0.943961i | \(-0.392932\pi\) | ||||
0.330057 | + | 0.943961i | \(0.392932\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.2174 | 0.553330 | 0.276665 | − | 0.960966i | \(-0.410771\pi\) | ||||
0.276665 | + | 0.960966i | \(0.410771\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.7354 | 1.08154 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 56.9036 | 1.93702 | 0.968510 | − | 0.248974i | \(-0.0800933\pi\) | ||||
0.968510 | + | 0.248974i | \(0.0800933\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −52.8137 | −1.79365 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.9061 | −0.946648 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.85351 | 0.266106 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.3410 | −0.451526 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.4569 | 1.12976 | 0.564880 | − | 0.825173i | \(-0.308923\pi\) | ||||
0.564880 | + | 0.825173i | \(0.308923\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.00917121 | 0.000309337 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.99700 | −0.202044 | −0.101022 | − | 0.994884i | \(-0.532211\pi\) | ||||
−0.101022 | + | 0.994884i | \(0.532211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.3210 | −1.72709 | −0.863544 | − | 0.504273i | \(-0.831761\pi\) | ||||
−0.863544 | + | 0.504273i | \(0.831761\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.1121 | −0.910336 | −0.455168 | − | 0.890405i | \(-0.650421\pi\) | ||||
−0.455168 | + | 0.890405i | \(0.650421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.1495 | 1.51426 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.0932 | 0.505640 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.10961 | −0.104059 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.66477 | 0.155752 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.96362 | 0.232250 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 106.221 | 3.53872 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.3925 | −0.412397 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.6194 | −1.34875 | −0.674373 | − | 0.738391i | \(-0.735586\pi\) | ||||
−0.674373 | + | 0.738391i | \(0.735586\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.6426 | −0.419329 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.2475 | −1.06841 | −0.534203 | − | 0.845356i | \(-0.679388\pi\) | ||||
−0.534203 | + | 0.845356i | \(0.679388\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.9544 | 1.09063 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.3335 | 0.803565 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.4042 | 1.00294 | 0.501470 | − | 0.865175i | \(-0.332793\pi\) | ||||
0.501470 | + | 0.865175i | \(0.332793\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.2939 | 0.899366 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.2636 | 1.19363 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.45720 | 0.0478609 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.2834 | −0.829520 | −0.414760 | − | 0.909931i | \(-0.636134\pi\) | ||||
−0.414760 | + | 0.909931i | \(0.636134\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.1649 | −0.431462 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.5997 | 1.06727 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.1769 | 0.724487 | 0.362243 | − | 0.932084i | \(-0.382011\pi\) | ||||
0.362243 | + | 0.932084i | \(0.382011\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.8289 | −0.777626 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.23228 | 0.137968 | 0.0689842 | − | 0.997618i | \(-0.478024\pi\) | ||||
0.0689842 | + | 0.997618i | \(0.478024\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.07954 | 0.230542 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.2374 | 1.47002 | 0.735009 | − | 0.678058i | \(-0.237178\pi\) | ||||
0.735009 | + | 0.678058i | \(0.237178\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.6587 | 0.410917 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.85242 | 0.0600690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.7170 | 1.41613 | 0.708066 | − | 0.706146i | \(-0.249568\pi\) | ||||
0.708066 | + | 0.706146i | \(0.249568\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.5448 | −0.534817 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 67.4240 | 2.17723 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.9557 | −0.869538 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.7495 | −0.507521 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.58482 | −0.179596 | −0.0897979 | − | 0.995960i | \(-0.528622\pi\) | ||||
−0.0897979 | + | 0.995960i | \(0.528622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35.6452 | −1.14509 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.1206 | −1.25544 | −0.627720 | − | 0.778439i | \(-0.716012\pi\) | ||||
−0.627720 | + | 0.778439i | \(0.716012\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.0337 | 0.578135 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 52.3050 | 1.67339 | 0.836693 | − | 0.547672i | \(-0.184486\pi\) | ||||
0.836693 | + | 0.547672i | \(0.184486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.80253 | −0.0895694 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.28049 | 0.136665 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.4395 | 0.715710 | 0.357855 | − | 0.933777i | \(-0.383508\pi\) | ||||
0.357855 | + | 0.933777i | \(0.383508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.98600 | −0.126876 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.76452 | −0.0879067 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.851383 | 0.0270451 | 0.0135225 | − | 0.999909i | \(-0.495696\pi\) | ||||
0.0135225 | + | 0.999909i | \(0.495696\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.7802 | 0.754643 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.1784 | −0.385693 | −0.192846 | − | 0.981229i | \(-0.561772\pi\) | ||||
−0.192846 | + | 0.981229i | \(0.561772\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.88853 | 0.0913892 |
(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 | 9200.2.a.cv.1.2 | 5 | ||
4.3 | odd | 2 | 4600.2.a.bd.1.4 | ✓ | 5 | ||
5.4 | even | 2 | 9200.2.a.ct.1.4 | 5 | |||
20.3 | even | 4 | 4600.2.e.w.4049.7 | 10 | |||
20.7 | even | 4 | 4600.2.e.w.4049.4 | 10 | |||
20.19 | odd | 2 | 4600.2.a.bf.1.2 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bd.1.4 | ✓ | 5 | 4.3 | odd | 2 | ||
4600.2.a.bf.1.2 | yes | 5 | 20.19 | odd | 2 | ||
4600.2.e.w.4049.4 | 10 | 20.7 | even | 4 | |||
4600.2.e.w.4049.7 | 10 | 20.3 | even | 4 | |||
9200.2.a.ct.1.4 | 5 | 5.4 | even | 2 | |||
9200.2.a.cv.1.2 | 5 | 1.1 | even | 1 | trivial |