Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 30 x^{18} + 128 x^{17} + 348 x^{16} - 1644 x^{15} - 1934 x^{14} + 10948 x^{13} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(1.06664\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | 1.06664 | 0.615822 | 0.307911 | − | 0.951415i | \(-0.400370\pi\) | ||||
0.307911 | + | 0.951415i | \(0.400370\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.715473 | −0.319969 | −0.159985 | − | 0.987120i | \(-0.551144\pi\) | ||||
−0.159985 | + | 0.987120i | \(0.551144\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.86229 | −0.620763 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.203291 | −0.0612944 | −0.0306472 | − | 0.999530i | \(-0.509757\pi\) | ||||
−0.0306472 | + | 0.999530i | \(0.509757\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.07678 | −1.13070 | −0.565348 | − | 0.824853i | \(-0.691258\pi\) | ||||
−0.565348 | + | 0.824853i | \(0.691258\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.763149 | −0.197044 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.49788 | 0.363289 | 0.181645 | − | 0.983364i | \(-0.441858\pi\) | ||||
0.181645 | + | 0.983364i | \(0.441858\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.74419 | −0.400145 | −0.200073 | − | 0.979781i | \(-0.564118\pi\) | ||||
−0.200073 | + | 0.979781i | \(0.564118\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.09950 | −0.854804 | −0.427402 | − | 0.904062i | \(-0.640571\pi\) | ||||
−0.427402 | + | 0.904062i | \(0.640571\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.48810 | −0.897620 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.18629 | −0.998102 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.13540 | −0.953620 | −0.476810 | − | 0.879006i | \(-0.658207\pi\) | ||||
−0.476810 | + | 0.879006i | \(0.658207\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.89553 | −0.699657 | −0.349829 | − | 0.936814i | \(-0.613760\pi\) | ||||
−0.349829 | + | 0.936814i | \(0.613760\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.216837 | −0.0377465 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.19415 | 1.51151 | 0.755754 | − | 0.654856i | \(-0.227271\pi\) | ||||
0.755754 | + | 0.654856i | \(0.227271\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.34844 | −0.696308 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.74486 | 0.266089 | 0.133044 | − | 0.991110i | \(-0.457525\pi\) | ||||
0.133044 | + | 0.991110i | \(0.457525\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.33242 | 0.198625 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.43307 | 0.938360 | 0.469180 | − | 0.883103i | \(-0.344550\pi\) | ||||
0.469180 | + | 0.883103i | \(0.344550\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.59769 | 0.223722 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.61543 | 0.908699 | 0.454349 | − | 0.890824i | \(-0.349872\pi\) | ||||
0.454349 | + | 0.890824i | \(0.349872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.145449 | 0.0196123 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.86042 | −0.246418 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.8894 | 1.67806 | 0.839030 | − | 0.544085i | \(-0.183123\pi\) | ||||
0.839030 | + | 0.544085i | \(0.183123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.5230 | 1.85947 | 0.929737 | − | 0.368224i | \(-0.120034\pi\) | ||||
0.929737 | + | 0.368224i | \(0.120034\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.91683 | 0.361788 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.105967 | −0.0129460 | −0.00647299 | − | 0.999979i | \(-0.502060\pi\) | ||||
−0.00647299 | + | 0.999979i | \(0.502060\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.37267 | −0.526407 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.3712 | 1.70555 | 0.852775 | − | 0.522278i | \(-0.174918\pi\) | ||||
0.852775 | + | 0.522278i | \(0.174918\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.2224 | 1.54756 | 0.773782 | − | 0.633452i | \(-0.218362\pi\) | ||||
0.773782 | + | 0.633452i | \(0.218362\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.78716 | −0.552774 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.88922 | 0.775098 | 0.387549 | − | 0.921849i | \(-0.373322\pi\) | ||||
0.387549 | + | 0.921849i | \(0.373322\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.0549876 | 0.00610973 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.43452 | −0.267223 | −0.133612 | − | 0.991034i | \(-0.542657\pi\) | ||||
−0.133612 | + | 0.991034i | \(0.542657\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.07169 | −0.116241 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.47760 | −0.587261 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.37395 | −0.463638 | −0.231819 | − | 0.972759i | \(-0.574468\pi\) | ||||
−0.231819 | + | 0.972759i | \(0.574468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.15511 | −0.430864 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.24792 | 0.128034 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.1054 | 1.12758 | 0.563789 | − | 0.825919i | \(-0.309343\pi\) | ||||
0.563789 | + | 0.825919i | \(0.309343\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.378586 | 0.0380493 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.5526 | −1.64705 | −0.823523 | − | 0.567283i | \(-0.807995\pi\) | ||||
−0.823523 | + | 0.567283i | \(0.807995\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9276 | 1.66793 | 0.833964 | − | 0.551819i | \(-0.186066\pi\) | ||||
0.833964 | + | 0.551819i | \(0.186066\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0473 | 1.16466 | 0.582329 | − | 0.812953i | \(-0.302142\pi\) | ||||
0.582329 | + | 0.812953i | \(0.302142\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.740391 | −0.0709166 | −0.0354583 | − | 0.999371i | \(-0.511289\pi\) | ||||
−0.0354583 | + | 0.999371i | \(0.511289\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.80680 | 0.930820 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.3332 | 1.44242 | 0.721212 | − | 0.692714i | \(-0.243585\pi\) | ||||
0.721212 | + | 0.692714i | \(0.243585\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.93308 | 0.273511 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.59215 | 0.701894 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9587 | −0.996243 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.06664 | −0.0961753 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.78848 | 0.607180 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.9159 | −1.58978 | −0.794889 | − | 0.606756i | \(-0.792471\pi\) | ||||
−0.794889 | + | 0.606756i | \(0.792471\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.86113 | 0.163863 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.85953 | −0.337208 | −0.168604 | − | 0.985684i | \(-0.553926\pi\) | ||||
−0.168604 | + | 0.985684i | \(0.553926\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.71065 | 0.319362 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.19838 | −0.785871 | −0.392935 | − | 0.919566i | \(-0.628540\pi\) | ||||
−0.392935 | + | 0.919566i | \(0.628540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.85466 | −0.496586 | −0.248293 | − | 0.968685i | \(-0.579870\pi\) | ||||
−0.248293 | + | 0.968685i | \(0.579870\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.86174 | 0.577863 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.828772 | 0.0693054 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.67424 | 0.305129 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.8299 | −1.54260 | −0.771301 | − | 0.636470i | \(-0.780394\pi\) | ||||
−0.771301 | + | 0.636470i | \(0.780394\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.8901 | −1.78139 | −0.890696 | − | 0.454599i | \(-0.849783\pi\) | ||||
−0.890696 | + | 0.454599i | \(0.849783\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.78949 | −0.225517 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.78714 | 0.223869 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.114806 | −0.00916251 | −0.00458125 | − | 0.999990i | \(-0.501458\pi\) | ||||
−0.00458125 | + | 0.999990i | \(0.501458\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.05625 | 0.559597 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.14673 | 0.638101 | 0.319051 | − | 0.947738i | \(-0.396636\pi\) | ||||
0.319051 | + | 0.947738i | \(0.396636\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.155141 | 0.0120777 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.1119 | −1.40154 | −0.700769 | − | 0.713389i | \(-0.747160\pi\) | ||||
−0.700769 | + | 0.713389i | \(0.747160\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.62015 | 0.278473 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.24819 | 0.248395 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.7255 | 1.34765 | 0.673824 | − | 0.738892i | \(-0.264651\pi\) | ||||
0.673824 | + | 0.738892i | \(0.264651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.7483 | 1.03339 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.3759 | 1.74720 | 0.873598 | − | 0.486648i | \(-0.161781\pi\) | ||||
0.873598 | + | 0.486648i | \(0.161781\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.2576 | −1.35707 | −0.678537 | − | 0.734566i | \(-0.737386\pi\) | ||||
−0.678537 | + | 0.734566i | \(0.737386\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.4907 | 1.14511 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.57816 | −0.483636 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.304505 | −0.0222676 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.7507 | 0.994967 | 0.497484 | − | 0.867473i | \(-0.334257\pi\) | ||||
0.497484 | + | 0.867473i | \(0.334257\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.6068 | −0.907458 | −0.453729 | − | 0.891140i | \(-0.649907\pi\) | ||||
−0.453729 | + | 0.891140i | \(0.649907\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.11119 | 0.222797 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.817144 | 0.0582191 | 0.0291095 | − | 0.999576i | \(-0.490733\pi\) | ||||
0.0291095 | + | 0.999576i | \(0.490733\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.7193 | 1.82320 | 0.911598 | − | 0.411083i | \(-0.134849\pi\) | ||||
0.911598 | + | 0.411083i | \(0.134849\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.113029 | −0.00797243 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.715473 | 0.0499708 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.63445 | 0.530631 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.354578 | 0.0245267 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0150 | −0.758306 | −0.379153 | − | 0.925334i | \(-0.623785\pi\) | ||||
−0.379153 | + | 0.925334i | \(0.623785\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.3289 | 1.05032 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.24840 | −0.0851401 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.1035 | 0.953025 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.10653 | −0.410770 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.4981 | 1.70748 | 0.853740 | − | 0.520700i | \(-0.174329\pi\) | ||||
0.853740 | + | 0.520700i | \(0.174329\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.35814 | 0.557209 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.861316 | −0.0571676 | −0.0285838 | − | 0.999591i | \(-0.509100\pi\) | ||||
−0.0285838 | + | 0.999591i | \(0.509100\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.01082 | −0.397206 | −0.198603 | − | 0.980080i | \(-0.563640\pi\) | ||||
−0.198603 | + | 0.980080i | \(0.563640\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.80151 | −0.183533 | −0.0917664 | − | 0.995781i | \(-0.529251\pi\) | ||||
−0.0917664 | + | 0.995781i | \(0.529251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.60269 | −0.300246 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.34828 | 0.477322 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.6931 | 1.27384 | 0.636919 | − | 0.770930i | \(-0.280208\pi\) | ||||
0.636919 | + | 0.770930i | \(0.280208\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.80922 | 0.180958 | 0.0904789 | − | 0.995898i | \(-0.471160\pi\) | ||||
0.0904789 | + | 0.995898i | \(0.471160\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.6175 | 1.00186 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.11069 | 0.452443 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.59675 | −0.164562 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.62156 | −0.102352 | −0.0511760 | − | 0.998690i | \(-0.516297\pi\) | ||||
−0.0511760 | + | 0.998690i | \(0.516297\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.833389 | 0.0523947 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.14311 | −0.0715840 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.7893 | 0.797773 | 0.398887 | − | 0.917000i | \(-0.369397\pi\) | ||||
0.398887 | + | 0.917000i | \(0.369397\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.56361 | 0.591972 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.4563 | −1.50804 | −0.754020 | − | 0.656852i | \(-0.771888\pi\) | ||||
−0.754020 | + | 0.656852i | \(0.771888\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.73316 | −0.290756 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.66541 | −0.285518 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.5542 | 0.948358 | 0.474179 | − | 0.880429i | \(-0.342745\pi\) | ||||
0.474179 | + | 0.880429i | \(0.342745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.47684 | −0.393440 | −0.196720 | − | 0.980460i | \(-0.563029\pi\) | ||||
−0.196720 | + | 0.980460i | \(0.563029\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.912388 | 0.0550191 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.79599 | −0.408331 | −0.204166 | − | 0.978936i | \(-0.565448\pi\) | ||||
−0.204166 | + | 0.978936i | \(0.565448\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.25459 | 0.434321 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.02577 | −0.538432 | −0.269216 | − | 0.963080i | \(-0.586765\pi\) | ||||
−0.269216 | + | 0.963080i | \(0.586765\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.9495 | −1.24532 | −0.622661 | − | 0.782492i | \(-0.713948\pi\) | ||||
−0.622661 | + | 0.782492i | \(0.713948\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.33108 | 0.0788463 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.7564 | −0.868021 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.8454 | 0.694388 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.7143 | −1.15172 | −0.575861 | − | 0.817547i | \(-0.695333\pi\) | ||||
−0.575861 | + | 0.817547i | \(0.695333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.22203 | −0.536927 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.05432 | 0.0611781 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.7128 | 0.966524 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.6556 | −1.01429 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.3908 | −0.594974 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.69256 | 0.153672 | 0.0768361 | − | 0.997044i | \(-0.475518\pi\) | ||||
0.0768361 | + | 0.997044i | \(0.475518\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.0556 | 1.02715 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.2409 | 0.807527 | 0.403764 | − | 0.914863i | \(-0.367702\pi\) | ||||
0.403764 | + | 0.914863i | \(0.367702\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.4841 | 1.77959 | 0.889794 | − | 0.456363i | \(-0.150848\pi\) | ||||
0.889794 | + | 0.456363i | \(0.150848\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.8349 | −1.05787 | −0.528936 | − | 0.848662i | \(-0.677409\pi\) | ||||
−0.528936 | + | 0.848662i | \(0.677409\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.04398 | 0.0584516 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.8501 | 0.717222 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.61259 | −0.145368 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.2970 | 1.01493 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.789727 | −0.0436720 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.16405 | 0.448737 | 0.224368 | − | 0.974504i | \(-0.427968\pi\) | ||||
0.224368 | + | 0.974504i | \(0.427968\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.1222 | −0.938288 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.0758168 | 0.00414232 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.7590 | 1.56660 | 0.783300 | − | 0.621643i | \(-0.213535\pi\) | ||||
0.783300 | + | 0.621643i | \(0.213535\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.3549 | 0.888277 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.791924 | 0.0428851 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.12853 | 0.168434 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.3427 | −0.877320 | −0.438660 | − | 0.898653i | \(-0.644547\pi\) | ||||
−0.438660 | + | 0.898653i | \(0.644547\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.3702 | 1.83980 | 0.919898 | − | 0.392157i | \(-0.128271\pi\) | ||||
0.919898 | + | 0.392157i | \(0.128271\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.1434 | 1.12855 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.6237 | 1.78961 | 0.894806 | − | 0.446456i | \(-0.147314\pi\) | ||||
0.894806 | + | 0.446456i | \(0.147314\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.2822 | −0.545723 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.2344 | 1.49015 | 0.745076 | − | 0.666980i | \(-0.232413\pi\) | ||||
0.745076 | + | 0.666980i | \(0.232413\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.9578 | −0.839884 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.6889 | −0.613509 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.46027 | −0.495173 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7369 | −0.664861 | −0.332431 | − | 0.943128i | \(-0.607869\pi\) | ||||
−0.332431 | + | 0.943128i | \(0.607869\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.86229 | 0.0969469 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.0901714 | 0.00466890 | 0.00233445 | − | 0.999997i | \(-0.499257\pi\) | ||||
0.00233445 | + | 0.999997i | \(0.499257\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.24083 | 0.373915 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.9359 | 1.07825 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.3658 | −0.635186 | −0.317593 | − | 0.948227i | \(-0.602875\pi\) | ||||
−0.317593 | + | 0.948227i | \(0.602875\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.1097 | −0.979020 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.1692 | −0.724013 | −0.362007 | − | 0.932175i | \(-0.617908\pi\) | ||||
−0.362007 | + | 0.932175i | \(0.617908\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.24943 | −0.165178 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6685 | −0.946530 | −0.473265 | − | 0.880920i | \(-0.656925\pi\) | ||||
−0.473265 | + | 0.880920i | \(0.656925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.14055 | −0.310541 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.11671 | −0.207660 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.92905 | −0.248007 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.9221 | −0.899485 | −0.449743 | − | 0.893158i | \(-0.648484\pi\) | ||||
−0.449743 | + | 0.893158i | \(0.648484\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.32147 | −0.115928 | −0.0579642 | − | 0.998319i | \(-0.518461\pi\) | ||||
−0.0579642 | + | 0.998319i | \(0.518461\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.8812 | 0.791099 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.0393421 | −0.00195493 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.86908 | −0.0926470 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.74754 | 0.135857 | 0.0679287 | − | 0.997690i | \(-0.478361\pi\) | ||||
0.0679287 | + | 0.997690i | \(0.478361\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.81132 | −0.483957 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.74183 | 0.0855033 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.24479 | −0.305809 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.3395 | −0.700532 | −0.350266 | − | 0.936650i | \(-0.613909\pi\) | ||||
−0.350266 | + | 0.936650i | \(0.613909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.5005 | 1.19408 | 0.597041 | − | 0.802211i | \(-0.296343\pi\) | ||||
0.597041 | + | 0.802211i | \(0.296343\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.9802 | −0.582499 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.72263 | −0.326096 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.883997 | 0.0426798 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.7836 | −1.62730 | −0.813648 | − | 0.581357i | \(-0.802522\pi\) | ||||
−0.813648 | + | 0.581357i | \(0.802522\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.9803 | 0.719907 | 0.359953 | − | 0.932970i | \(-0.382793\pi\) | ||||
0.359953 | + | 0.932970i | \(0.382793\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.91908 | 0.187905 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.15031 | 0.342046 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.9944 | 0.524733 | 0.262367 | − | 0.964968i | \(-0.415497\pi\) | ||||
0.262367 | + | 0.964968i | \(0.415497\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.5677 | 1.54734 | 0.773669 | − | 0.633590i | \(-0.218419\pi\) | ||||
0.773669 | + | 0.633590i | \(0.218419\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.12944 | 0.148350 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.0846 | −0.949969 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.8875 | −1.92960 | −0.964801 | − | 0.262982i | \(-0.915294\pi\) | ||||
−0.964801 | + | 0.262982i | \(0.915294\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.203291 | 0.00957258 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.3488 | −1.09702 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.66835 | −0.124820 | −0.0624101 | − | 0.998051i | \(-0.519879\pi\) | ||||
−0.0624101 | + | 0.998051i | \(0.519879\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.76844 | −0.362600 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.07360 | 0.236301 | 0.118151 | − | 0.992996i | \(-0.462303\pi\) | ||||
0.118151 | + | 0.992996i | \(0.462303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.9827 | −1.57931 | −0.789655 | − | 0.613551i | \(-0.789741\pi\) | ||||
−0.789655 | + | 0.613551i | \(0.789741\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.97287 | 0.137863 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.6133 | 0.953869 | 0.476935 | − | 0.878939i | \(-0.341748\pi\) | ||||
0.476935 | + | 0.878939i | \(0.341748\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.122456 | −0.00564248 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.354714 | −0.0163097 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.82811 | 0.359178 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.3198 | −0.564086 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.766787 | −0.0350354 | −0.0175177 | − | 0.999847i | \(-0.505576\pi\) | ||||
−0.0175177 | + | 0.999847i | \(0.505576\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.4825 | −1.70906 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.94558 | −0.360790 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.65740 | −0.256361 | −0.128181 | − | 0.991751i | \(-0.540914\pi\) | ||||
−0.128181 | + | 0.991751i | \(0.540914\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.68960 | 0.392957 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.55831 | 0.250843 | 0.125422 | − | 0.992104i | \(-0.459972\pi\) | ||||
0.125422 | + | 0.992104i | \(0.459972\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.69222 | −0.346440 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.270868 | −0.0121746 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.1207 | 1.57222 | 0.786108 | − | 0.618089i | \(-0.212093\pi\) | ||||
0.786108 | + | 0.618089i | \(0.212093\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.3187 | −0.863098 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.33640 | −0.371702 | −0.185851 | − | 0.982578i | \(-0.559504\pi\) | ||||
−0.185851 | + | 0.982578i | \(0.559504\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.8429 | 0.527004 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.86138 | 0.171490 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.4727 | 1.30635 | 0.653177 | − | 0.757205i | \(-0.273436\pi\) | ||||
0.653177 | + | 0.757205i | \(0.273436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.04589 | 0.399386 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.1112 | −0.533685 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.30778 | −0.0575163 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.9067 | 0.829911 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.8169 | 0.517707 | 0.258853 | − | 0.965917i | \(-0.416655\pi\) | ||||
0.258853 | + | 0.965917i | \(0.416655\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.4835 | 1.59531 | 0.797656 | − | 0.603113i | \(-0.206073\pi\) | ||||
0.797656 | + | 0.603113i | \(0.206073\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.83503 | −0.254178 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.19413 | −0.269310 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.0038 | −1.04168 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.07678 | 0.176585 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.61953 | −0.372655 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.9335 | 1.07596 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.4703 | 0.751107 | 0.375553 | − | 0.926801i | \(-0.377453\pi\) | ||||
0.375553 | + | 0.926801i | \(0.377453\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.4742 | −0.835717 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.529730 | 0.0226911 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.4215 | 0.958673 | 0.479337 | − | 0.877631i | \(-0.340877\pi\) | ||||
0.479337 | + | 0.877631i | \(0.340877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27.0459 | −1.15429 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.95713 | 0.381587 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.01650 | −0.297834 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.30562 | −0.224806 | −0.112403 | − | 0.993663i | \(-0.535855\pi\) | ||||
−0.112403 | + | 0.993663i | \(0.535855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.11341 | −0.300865 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.324796 | −0.0137129 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.36390 | −0.352496 | −0.176248 | − | 0.984346i | \(-0.556396\pi\) | ||||
−0.176248 | + | 0.984346i | \(0.556396\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.9705 | −0.461531 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.7650 | 1.28974 | 0.644868 | − | 0.764294i | \(-0.276912\pi\) | ||||
0.644868 | + | 0.764294i | \(0.276912\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.4697 | −0.438145 | −0.219072 | − | 0.975709i | \(-0.570303\pi\) | ||||
−0.219072 | + | 0.975709i | \(0.570303\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.6670 | 0.612723 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.3989 | 0.767289 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.1722 | 0.798150 | 0.399075 | − | 0.916918i | \(-0.369331\pi\) | ||||
0.399075 | + | 0.916918i | \(0.369331\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.4469 | −0.558833 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.34485 | −0.0556982 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.43197 | −0.224585 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.2967 | 0.961559 | 0.480779 | − | 0.876842i | \(-0.340354\pi\) | ||||
0.480779 | + | 0.876842i | \(0.340354\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.79455 | 0.279964 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.871595 | 0.0358526 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.59717 | −0.147718 | −0.0738590 | − | 0.997269i | \(-0.523531\pi\) | ||||
−0.0738590 | + | 0.997269i | \(0.523531\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.4332 | 1.12276 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.0452 | −1.71792 | −0.858961 | − | 0.512041i | \(-0.828889\pi\) | ||||
−0.858961 | + | 0.512041i | \(0.828889\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.9085 | 0.812084 | 0.406042 | − | 0.913854i | \(-0.366909\pi\) | ||||
0.406042 | + | 0.913854i | \(0.366909\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.197342 | 0.00803639 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.84063 | 0.318767 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.6134 | 1.52668 | 0.763341 | − | 0.645996i | \(-0.223558\pi\) | ||||
0.763341 | + | 0.645996i | \(0.223558\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.2262 | −1.06100 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.3767 | 0.661448 | 0.330724 | − | 0.943728i | \(-0.392707\pi\) | ||||
0.330724 | + | 0.943728i | \(0.392707\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.763149 | 0.0307731 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.8650 | 0.920509 | 0.460255 | − | 0.887787i | \(-0.347758\pi\) | ||||
0.460255 | + | 0.887787i | \(0.347758\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.3938 | −0.578536 | −0.289268 | − | 0.957248i | \(-0.593412\pi\) | ||||
−0.289268 | + | 0.957248i | \(0.593412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.2612 | 0.853182 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.5835 | 0.703341 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.378205 | 0.0151041 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.7717 | 0.549115 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.5118 | −1.37389 | −0.686946 | − | 0.726709i | \(-0.741049\pi\) | ||||
−0.686946 | + | 0.726709i | \(0.741049\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.7490 | −0.466981 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.8183 | 0.508680 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.7634 | −1.05874 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.1524 | 1.07245 | 0.536227 | − | 0.844074i | \(-0.319849\pi\) | ||||
0.536227 | + | 0.844074i | \(0.319849\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.5059 | 1.16360 | 0.581800 | − | 0.813332i | \(-0.302349\pi\) | ||||
0.581800 | + | 0.813332i | \(0.302349\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.33159 | −0.0524312 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.5174 | −0.885251 | −0.442625 | − | 0.896707i | \(-0.645953\pi\) | ||||
−0.442625 | + | 0.896707i | \(0.645953\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.62030 | −0.102856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.7254 | −0.576248 | −0.288124 | − | 0.957593i | \(-0.593032\pi\) | ||||
−0.288124 | + | 0.957593i | \(0.593032\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.76139 | 0.107896 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.6239 | −0.960671 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.4025 | −0.755816 | −0.377908 | − | 0.925843i | \(-0.623356\pi\) | ||||
−0.377908 | + | 0.925843i | \(0.623356\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.44756 | 0.172990 | 0.0864950 | − | 0.996252i | \(-0.472433\pi\) | ||||
0.0864950 | + | 0.996252i | \(0.472433\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.51344 | −0.252961 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.0526 | 0.815159 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27.1972 | 1.05150 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.95238 | −0.113975 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.2080 | −1.31862 | −0.659310 | − | 0.751871i | \(-0.729152\pi\) | ||||
−0.659310 | + | 0.751871i | \(0.729152\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 23.2766 | 0.895916 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.76820 | −0.298556 | −0.149278 | − | 0.988795i | \(-0.547695\pi\) | ||||
−0.149278 | + | 0.988795i | \(0.547695\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.918711 | −0.0352051 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.2431 | 1.42507 | 0.712534 | − | 0.701637i | \(-0.247547\pi\) | ||||
0.712534 | + | 0.701637i | \(0.247547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.58119 | 0.251454 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.41135 | −0.244608 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.9696 | −1.02746 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.92228 | −0.0731271 | −0.0365635 | − | 0.999331i | \(-0.511641\pi\) | ||||
−0.0365635 | + | 0.999331i | \(0.511641\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.18885 | 0.158892 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.49788 | −0.0567362 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.98818 | −0.113024 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.1648 | 1.89470 | 0.947350 | − | 0.320201i | \(-0.103750\pi\) | ||||
0.947350 | + | 0.320201i | \(0.103750\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.0364 | −0.604823 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.90939 | −0.184898 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.8140 | −1.57036 | −0.785180 | − | 0.619268i | \(-0.787429\pi\) | ||||
−0.785180 | + | 0.619268i | \(0.787429\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.8297 | −0.481152 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.9697 | 0.598070 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.592964 | −0.0221756 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.0053 | 0.784458 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.9341 | −0.855298 | −0.427649 | − | 0.903945i | \(-0.640658\pi\) | ||||
−0.427649 | + | 0.903945i | \(0.640658\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.99641 | 0.111438 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.0482 | 0.855989 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.6789 | −0.692762 | −0.346381 | − | 0.938094i | \(-0.612589\pi\) | ||||
−0.346381 | + | 0.938094i | \(0.612589\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.4932 | 0.610861 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.61359 | 0.0966671 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 52.7201 | 1.94726 | 0.973631 | − | 0.228127i | \(-0.0732600\pi\) | ||||
0.973631 | + | 0.228127i | \(0.0732600\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.0215422 | 0.000793517 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.8600 | −0.399490 | −0.199745 | − | 0.979848i | \(-0.564011\pi\) | ||||
−0.199745 | + | 0.979848i | \(0.564011\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.58452 | 0.278624 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.6159 | −1.19656 | −0.598281 | − | 0.801286i | \(-0.704149\pi\) | ||||
−0.598281 | + | 0.801286i | \(0.704149\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.4723 | 0.493585 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.53378 | 0.165882 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5099 | 0.456491 | 0.228246 | − | 0.973604i | \(-0.426701\pi\) | ||||
0.228246 | + | 0.973604i | \(0.426701\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.72961 | −0.0630307 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.6618 | 0.569991 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.9033 | −1.66838 | −0.834192 | − | 0.551474i | \(-0.814066\pi\) | ||||
−0.834192 | + | 0.551474i | \(0.814066\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.888922 | 0.0322658 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.5517 | 0.599998 | 0.299999 | − | 0.953940i | \(-0.403014\pi\) | ||||
0.299999 | + | 0.953940i | \(0.403014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.99580 | 0.0721583 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −52.5474 | −1.89738 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.3183 | 0.480269 | 0.240134 | − | 0.970740i | \(-0.422809\pi\) | ||||
0.240134 | + | 0.970740i | \(0.422809\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.6415 | 0.491286 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.1812 | 0.581998 | 0.290999 | − | 0.956723i | \(-0.406012\pi\) | ||||
0.290999 | + | 0.956723i | \(0.406012\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.4835 | 0.628026 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.74419 | 0.0624922 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.92153 | −0.104541 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.6337 | 0.951810 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0821405 | 0.00293172 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.8464 | −0.636156 | −0.318078 | − | 0.948065i | \(-0.603037\pi\) | ||||
−0.318078 | + | 0.948065i | \(0.603037\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.0859 | −0.928684 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −59.2069 | −2.10250 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.04855 | −0.179054 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.13372 | −0.252689 | −0.126345 | − | 0.991986i | \(-0.540325\pi\) | ||||
−0.126345 | + | 0.991986i | \(0.540325\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.63597 | 0.340896 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.14556 | 0.287809 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.68799 | −0.0948571 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.5907 | 0.584020 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.3449 | 0.891081 | 0.445540 | − | 0.895262i | \(-0.353012\pi\) | ||||
0.445540 | + | 0.895262i | \(0.353012\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.80874 | 0.0635136 | 0.0317568 | − | 0.999496i | \(-0.489890\pi\) | ||||
0.0317568 | + | 0.999496i | \(0.489890\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.90842 | −0.242289 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.82877 | −0.204173 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.04337 | −0.106474 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.5388 | −1.69402 | −0.847008 | − | 0.531581i | \(-0.821598\pi\) | ||||
−0.847008 | + | 0.531581i | \(0.821598\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.2821 | 1.02071 | 0.510355 | − | 0.859964i | \(-0.329514\pi\) | ||||
0.510355 | + | 0.859964i | \(0.329514\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.973186 | 0.0338820 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.6267 | −0.612940 | −0.306470 | − | 0.951880i | \(-0.599148\pi\) | ||||
−0.306470 | + | 0.951880i | \(0.599148\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.7256 | 1.58812 | 0.794058 | − | 0.607843i | \(-0.207965\pi\) | ||||
0.794058 | + | 0.607843i | \(0.207965\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.24884 | −0.251459 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.9585 | 0.448449 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.2033 | 0.698329 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.4240 | 0.843210 | 0.421605 | − | 0.906780i | \(-0.361467\pi\) | ||||
0.421605 | + | 0.906780i | \(0.361467\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.62763 | −0.0906081 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.62720 | −0.331578 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.59012 | −0.0891029 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.3455 | −0.766896 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.6914 | −1.29204 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.48129 | −0.0507185 | −0.0253592 | − | 0.999678i | \(-0.508073\pi\) | ||||
−0.0253592 | + | 0.999678i | \(0.508073\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.32399 | −0.0794789 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.323927 | 0.0110652 | 0.00553258 | − | 0.999985i | \(-0.498239\pi\) | ||||
0.00553258 | + | 0.999985i | \(0.498239\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.8939 | −0.985847 | −0.492924 | − | 0.870073i | \(-0.664072\pi\) | ||||
−0.492924 | + | 0.870073i | \(0.664072\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.8493 | 1.05012 | 0.525062 | − | 0.851064i | \(-0.324042\pi\) | ||||
0.525062 | + | 0.851064i | \(0.324042\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.6821 | −0.431206 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.7397 | −0.534547 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.40051 | −0.0475092 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.432006 | 0.0146380 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.6814 | −0.699959 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.8540 | −1.04187 | −0.520933 | − | 0.853597i | \(-0.674416\pi\) | ||||
−0.520933 | + | 0.853597i | \(0.674416\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.0280 | −0.709257 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53.8585 | −1.81454 | −0.907270 | − | 0.420550i | \(-0.861837\pi\) | ||||
−0.907270 | + | 0.420550i | \(0.861837\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.1687 | 0.476814 | 0.238407 | − | 0.971165i | \(-0.423375\pi\) | ||||
0.238407 | + | 0.971165i | \(0.423375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.83654 | −0.330652 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.6309 | −1.09564 | −0.547820 | − | 0.836596i | \(-0.684542\pi\) | ||||
−0.547820 | + | 0.836596i | \(0.684542\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.0111785 | −0.000374493 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.2205 | −0.375480 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.7248 | −0.559049 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.8264 | 0.595207 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.0051 | 0.667207 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.90911 | 0.330120 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.0628 | 0.434222 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.1270 | 1.59803 | 0.799016 | − | 0.601310i | \(-0.205354\pi\) | ||||
0.799016 | + | 0.601310i | \(0.205354\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.8257 | 1.02243 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.3867 | −0.675441 | −0.337720 | − | 0.941247i | \(-0.609656\pi\) | ||||
−0.337720 | + | 0.941247i | \(0.609656\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.494915 | 0.0163793 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.0832 | −0.366398 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.66405 | −0.0878789 | −0.0439395 | − | 0.999034i | \(-0.513991\pi\) | ||||
−0.0439395 | + | 0.999034i | \(0.513991\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.87198 | 0.0946348 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −58.5883 | −1.92846 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.2642 | −1.35676 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −31.5241 | −1.03539 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.5871 | −1.03634 | −0.518170 | − | 0.855278i | \(-0.673387\pi\) | ||||
−0.518170 | + | 0.855278i | \(0.673387\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.1898 | 0.497293 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.217865 | 0.00712495 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.30876 | −0.238767 | −0.119383 | − | 0.992848i | \(-0.538092\pi\) | ||||
−0.119383 | + | 0.992848i | \(0.538092\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.5821 | 1.09591 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.93375 | 0.0956374 | 0.0478187 | − | 0.998856i | \(-0.484773\pi\) | ||||
0.0478187 | + | 0.998856i | \(0.484773\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.09950 | 0.133498 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.7181 | −0.933212 | −0.466606 | − | 0.884465i | \(-0.654523\pi\) | ||||
−0.466606 | + | 0.884465i | \(0.654523\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −53.9048 | −1.74982 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.0899 | −0.651461 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.0891 | 1.26622 | 0.633110 | − | 0.774062i | \(-0.281778\pi\) | ||||
0.633110 | + | 0.774062i | \(0.281778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.83827 | −0.318359 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.11355 | 0.0359958 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.8249 | −0.510480 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.4356 | −0.722976 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.01983 | 0.290359 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.10133 | 0.131890 | 0.0659450 | − | 0.997823i | \(-0.478994\pi\) | ||||
0.0659450 | + | 0.997823i | \(0.478994\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.78668 | −0.0895211 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.9460 | 1.05729 | 0.528644 | − | 0.848844i | \(-0.322701\pi\) | ||||
0.528644 | + | 0.848844i | \(0.322701\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.5162 | 0.625019 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.9811 | −0.927186 | −0.463593 | − | 0.886048i | \(-0.653440\pi\) | ||||
−0.463593 | + | 0.886048i | \(0.653440\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.889183 | 0.0284184 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.37882 | 0.0440224 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.2495 | −1.12428 | −0.562142 | − | 0.827040i | \(-0.690023\pi\) | ||||
−0.562142 | + | 0.827040i | \(0.690023\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.584644 | −0.0186283 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.15305 | −0.227454 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.6066 | 1.54404 | 0.772021 | − | 0.635598i | \(-0.219246\pi\) | ||||
0.772021 | + | 0.635598i | \(0.219246\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.70807 | 0.276342 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.4015 | −0.583366 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.6793 | 1.00329 | 0.501647 | − | 0.865072i | \(-0.332728\pi\) | ||||
0.501647 | + | 0.865072i | \(0.332728\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −47.6835 | −1.50864 |
(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 | 8036.2.a.t.1.13 | yes | 20 | |
7.6 | odd | 2 | 8036.2.a.s.1.8 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.8 | ✓ | 20 | 7.6 | odd | 2 | ||
8036.2.a.t.1.13 | yes | 20 | 1.1 | even | 1 | trivial |