Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(0\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | ||||||||
\(3\) | −0.713769 | −0.412095 | −0.206047 | − | 0.978542i | \(-0.566060\pi\) | ||||
−0.206047 | + | 0.978542i | \(0.566060\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.26919 | −0.479708 | −0.239854 | − | 0.970809i | \(-0.577100\pi\) | ||||
−0.239854 | + | 0.970809i | \(0.577100\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.49053 | −0.830178 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.29319 | 0.389912 | 0.194956 | − | 0.980812i | \(-0.437544\pi\) | ||||
0.194956 | + | 0.980812i | \(0.437544\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.04543 | −0.844651 | −0.422326 | − | 0.906444i | \(-0.638786\pi\) | ||||
−0.422326 | + | 0.906444i | \(0.638786\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.713769 | 0.184294 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.63853 | −0.639937 | −0.319969 | − | 0.947428i | \(-0.603672\pi\) | ||||
−0.319969 | + | 0.947428i | \(0.603672\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.73419 | −1.08610 | −0.543049 | − | 0.839701i | \(-0.682730\pi\) | ||||
−0.543049 | + | 0.839701i | \(0.682730\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.905907 | 0.197685 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.57988 | −1.37200 | −0.685999 | − | 0.727602i | \(-0.740635\pi\) | ||||
−0.685999 | + | 0.727602i | \(0.740635\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.91897 | 0.754207 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.77789 | −1.07293 | −0.536464 | − | 0.843923i | \(-0.680240\pi\) | ||||
−0.536464 | + | 0.843923i | \(0.680240\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.97788 | −1.25326 | −0.626632 | − | 0.779315i | \(-0.715567\pi\) | ||||
−0.626632 | + | 0.779315i | \(0.715567\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.923041 | −0.160681 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.26919 | 0.214532 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.93757 | 0.647332 | 0.323666 | − | 0.946171i | \(-0.395085\pi\) | ||||
0.323666 | + | 0.946171i | \(0.395085\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.17374 | 0.348076 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.22630 | −0.816210 | −0.408105 | − | 0.912935i | \(-0.633810\pi\) | ||||
−0.408105 | + | 0.912935i | \(0.633810\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.20178 | 0.335769 | 0.167884 | − | 0.985807i | \(-0.446306\pi\) | ||||
0.167884 | + | 0.985807i | \(0.446306\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.49053 | 0.371267 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.7358 | −1.71184 | −0.855918 | − | 0.517111i | \(-0.827008\pi\) | ||||
−0.855918 | + | 0.517111i | \(0.827008\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.38916 | −0.769880 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.88330 | 0.263715 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.06456 | 1.10775 | 0.553876 | − | 0.832599i | \(-0.313148\pi\) | ||||
0.553876 | + | 0.832599i | \(0.313148\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.29319 | −0.174374 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.37912 | 0.447576 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.5685 | 1.50609 | 0.753043 | − | 0.657971i | \(-0.228585\pi\) | ||||
0.753043 | + | 0.657971i | \(0.228585\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.63094 | −0.977042 | −0.488521 | − | 0.872552i | \(-0.662463\pi\) | ||||
−0.488521 | + | 0.872552i | \(0.662463\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.16095 | 0.398243 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.04543 | 0.377739 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0096 | 1.22287 | 0.611436 | − | 0.791294i | \(-0.290592\pi\) | ||||
0.611436 | + | 0.791294i | \(0.290592\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.69651 | 0.565394 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0339 | 1.90287 | 0.951435 | − | 0.307851i | \(-0.0996099\pi\) | ||||
0.951435 | + | 0.307851i | \(0.0996099\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0878 | 1.41477 | 0.707387 | − | 0.706826i | \(-0.249874\pi\) | ||||
0.707387 | + | 0.706826i | \(0.249874\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.713769 | −0.0824190 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.64130 | −0.187044 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.86668 | 0.210018 | 0.105009 | − | 0.994471i | \(-0.466513\pi\) | ||||
0.105009 | + | 0.994471i | \(0.466513\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.67436 | 0.519373 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.9310 | −1.85842 | −0.929209 | − | 0.369556i | \(-0.879510\pi\) | ||||
−0.929209 | + | 0.369556i | \(0.879510\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.63853 | 0.286189 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.12408 | 0.442148 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.3893 | −1.31326 | −0.656630 | − | 0.754212i | \(-0.728019\pi\) | ||||
−0.656630 | + | 0.754212i | \(0.728019\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.86523 | 0.405186 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.98060 | 0.516464 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.73419 | 0.485718 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1561 | −1.33580 | −0.667898 | − | 0.744253i | \(-0.732806\pi\) | ||||
−0.667898 | + | 0.744253i | \(0.732806\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.22074 | −0.323697 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.6448 | 1.45721 | 0.728605 | − | 0.684934i | \(-0.240169\pi\) | ||||
0.728605 | + | 0.684934i | \(0.240169\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.0490 | −1.87696 | −0.938478 | − | 0.345340i | \(-0.887763\pi\) | ||||
−0.938478 | + | 0.345340i | \(0.887763\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.905907 | −0.0884075 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.104128 | 0.0100664 | 0.00503320 | − | 0.999987i | \(-0.498398\pi\) | ||||
0.00503320 | + | 0.999987i | \(0.498398\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.07641 | −0.869362 | −0.434681 | − | 0.900584i | \(-0.643139\pi\) | ||||
−0.434681 | + | 0.900584i | \(0.643139\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.81052 | −0.266762 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.2232 | −1.52615 | −0.763073 | − | 0.646312i | \(-0.776310\pi\) | ||||
−0.763073 | + | 0.646312i | \(0.776310\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.57988 | 0.613577 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.58475 | 0.701210 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.34879 | 0.306983 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.32765 | −0.847968 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.73037 | 0.336356 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.425408 | 0.0377489 | 0.0188744 | − | 0.999822i | \(-0.493992\pi\) | ||||
0.0188744 | + | 0.999822i | \(0.493992\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.57157 | −0.138369 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.5119 | −1.35528 | −0.677639 | − | 0.735395i | \(-0.736997\pi\) | ||||
−0.677639 | + | 0.735395i | \(0.736997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00858 | 0.521010 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.91897 | −0.337292 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.6285 | 1.84784 | 0.923922 | − | 0.382581i | \(-0.124965\pi\) | ||||
0.923922 | + | 0.382581i | \(0.124965\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.58707 | −0.558708 | −0.279354 | − | 0.960188i | \(-0.590120\pi\) | ||||
−0.279354 | + | 0.960188i | \(0.590120\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.37663 | 0.705439 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.93833 | −0.329340 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.77789 | 0.479828 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.84662 | 0.317264 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.5561 | 0.946712 | 0.473356 | − | 0.880871i | \(-0.343042\pi\) | ||||
0.473356 | + | 0.880871i | \(0.343042\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.1816 | 1.47960 | 0.739800 | − | 0.672827i | \(-0.234920\pi\) | ||||
0.739800 | + | 0.672827i | \(0.234920\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.57134 | 0.531262 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.97788 | 0.560477 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.37146 | −0.348880 | −0.174440 | − | 0.984668i | \(-0.555812\pi\) | ||||
−0.174440 | + | 0.984668i | \(0.555812\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.75623 | −0.456499 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.35110 | 0.658159 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.46160 | −0.192807 | −0.0964035 | − | 0.995342i | \(-0.530734\pi\) | ||||
−0.0964035 | + | 0.995342i | \(0.530734\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.923041 | 0.0718587 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.932627 | 0.0721688 | 0.0360844 | − | 0.999349i | \(-0.488511\pi\) | ||||
0.0360844 | + | 0.999349i | \(0.488511\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.72534 | −0.286565 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.7907 | 0.901654 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.70436 | −0.129580 | −0.0647899 | − | 0.997899i | \(-0.520638\pi\) | ||||
−0.0647899 | + | 0.997899i | \(0.520638\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.26919 | −0.0959416 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.25722 | −0.620651 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.97102 | 0.595782 | 0.297891 | − | 0.954600i | \(-0.403717\pi\) | ||||
0.297891 | + | 0.954600i | \(0.403717\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0841 | 1.04686 | 0.523432 | − | 0.852067i | \(-0.324651\pi\) | ||||
0.523432 | + | 0.852067i | \(0.324651\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.44673 | 0.402634 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.93757 | −0.289496 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.41213 | −0.249519 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.97391 | −0.361799 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.9750 | 1.44534 | 0.722669 | − | 0.691195i | \(-0.242915\pi\) | ||||
0.722669 | + | 0.691195i | \(0.242915\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.00907017 | −0.000652885 0 | −0.000326443 | − | 1.00000i | \(-0.500104\pi\) | ||||
−0.000326443 | 1.00000i | \(0.500104\pi\) | ||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.17374 | −0.155665 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.828902 | 0.0590568 | 0.0295284 | − | 0.999564i | \(-0.490599\pi\) | ||||
0.0295284 | + | 0.999564i | \(0.490599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.85467 | 0.415027 | 0.207513 | − | 0.978232i | \(-0.433463\pi\) | ||||
0.207513 | + | 0.978232i | \(0.433463\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.14458 | −0.503940 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.33323 | 0.514692 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.22630 | 0.365020 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.3874 | 1.13900 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.12222 | −0.423483 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.55210 | 0.657594 | 0.328797 | − | 0.944401i | \(-0.393357\pi\) | ||||
0.328797 | + | 0.944401i | \(0.393357\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.4445 | −0.784163 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.20178 | −0.150160 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.85624 | 0.601201 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.62793 | −0.583021 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.03546 | 0.540524 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.31204 | −0.221791 | −0.110895 | − | 0.993832i | \(-0.535372\pi\) | ||||
−0.110895 | + | 0.993832i | \(0.535372\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.49053 | −0.166036 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −28.0737 | −1.86332 | −0.931659 | − | 0.363334i | \(-0.881638\pi\) | ||||
−0.931659 | + | 0.363334i | \(0.881638\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.37671 | 0.157058 | 0.0785288 | − | 0.996912i | \(-0.474978\pi\) | ||||
0.0785288 | + | 0.996912i | \(0.474978\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.17151 | 0.0770799 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.3565 | −1.53014 | −0.765068 | − | 0.643949i | \(-0.777295\pi\) | ||||
−0.765068 | + | 0.643949i | \(0.777295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.7358 | 0.765557 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.33238 | −0.0865474 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.80252 | 0.634072 | 0.317036 | − | 0.948413i | \(-0.397312\pi\) | ||||
0.317036 | + | 0.948413i | \(0.397312\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.60175 | −0.618503 | −0.309251 | − | 0.950980i | \(-0.600078\pi\) | ||||
−0.309251 | + | 0.950980i | \(0.600078\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.0933 | −0.968238 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.38916 | 0.344301 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.4177 | 0.917374 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0848 | 0.765844 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.87191 | 0.623109 | 0.311555 | − | 0.950228i | \(-0.399150\pi\) | ||||
0.311555 | + | 0.950228i | \(0.399150\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.50905 | −0.534959 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.88330 | −0.117937 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.1640 | −1.32017 | −0.660086 | − | 0.751190i | \(-0.729480\pi\) | ||||
−0.660086 | + | 0.751190i | \(0.729480\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.99751 | −0.310530 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.3900 | 0.890721 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.10690 | −0.376567 | −0.188284 | − | 0.982115i | \(-0.560292\pi\) | ||||
−0.188284 | + | 0.982115i | \(0.560292\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.06456 | −0.495402 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.84309 | 0.541188 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.13634 | 0.496081 | 0.248041 | − | 0.968750i | \(-0.420213\pi\) | ||||
0.248041 | + | 0.968750i | \(0.420213\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.98229 | 0.120415 | 0.0602077 | − | 0.998186i | \(-0.480824\pi\) | ||||
0.0602077 | + | 0.998186i | \(0.480824\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.75888 | −0.166975 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.29319 | 0.0779825 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.8515 | 1.19276 | 0.596379 | − | 0.802703i | \(-0.296606\pi\) | ||||
0.596379 | + | 0.802703i | \(0.296606\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.3786 | 1.04043 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.2799 | 1.03083 | 0.515417 | − | 0.856939i | \(-0.327637\pi\) | ||||
0.515417 | + | 0.856939i | \(0.327637\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.7464 | −1.41158 | −0.705789 | − | 0.708422i | \(-0.749407\pi\) | ||||
−0.705789 | + | 0.708422i | \(0.749407\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.37912 | −0.200162 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.63315 | 0.391543 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0382 | −0.590481 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.39039 | 0.550474 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.0950 | 0.998698 | 0.499349 | − | 0.866401i | \(-0.333572\pi\) | ||||
0.499349 | + | 0.866401i | \(0.333572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.5685 | −0.673542 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.06799 | 0.294075 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.0386 | 1.15886 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.79448 | −0.161071 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.4530 | −0.600509 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.63094 | 0.436947 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.2256 | 1.26848 | 0.634240 | − | 0.773136i | \(-0.281313\pi\) | ||||
0.634240 | + | 0.773136i | \(0.281313\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.5966 | 0.773484 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.0600 | −1.08079 | −0.540396 | − | 0.841411i | \(-0.681725\pi\) | ||||
−0.540396 | + | 0.841411i | \(0.681725\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.6001 | 0.768726 | 0.384363 | − | 0.923182i | \(-0.374421\pi\) | ||||
0.384363 | + | 0.923182i | \(0.374421\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.16095 | −0.178100 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.74631 | −0.322745 | −0.161372 | − | 0.986894i | \(-0.551592\pi\) | ||||
−0.161372 | + | 0.986894i | \(0.551592\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.47193 | −0.418348 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.0743231 | −0.00414831 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.4913 | 0.695034 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.04543 | −0.168930 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.47846 | 0.358260 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.8949 | 0.821182 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.2249 | 0.836838 | 0.418419 | − | 0.908254i | \(-0.362584\pi\) | ||||
0.418419 | + | 0.908254i | \(0.362584\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.80665 | −0.537401 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.0096 | −0.546885 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.0754 | 1.03910 | 0.519551 | − | 0.854440i | \(-0.326099\pi\) | ||||
0.519551 | + | 0.854440i | \(0.326099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.5796 | 0.628917 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.02374 | −0.488663 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7242 | 0.849025 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.69651 | −0.252852 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.6976 | −0.627962 | −0.313981 | − | 0.949429i | \(-0.601663\pi\) | ||||
−0.313981 | + | 0.949429i | \(0.601663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.9057 | 1.70787 | 0.853937 | − | 0.520377i | \(-0.174209\pi\) | ||||
0.853937 | + | 0.520377i | \(0.174209\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.9350 | −0.637042 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.0249 | 1.43839 | 0.719195 | − | 0.694808i | \(-0.244511\pi\) | ||||
0.719195 | + | 0.694808i | \(0.244511\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.0339 | −0.850989 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.39026 | −0.126506 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.56540 | 0.452064 | 0.226032 | − | 0.974120i | \(-0.427425\pi\) | ||||
0.226032 | + | 0.974120i | \(0.427425\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.41257 | 0.179609 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.65779 | 0.349444 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.0878 | −0.632706 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.0909754 | 0.00474888 | 0.00237444 | − | 0.999997i | \(-0.499244\pi\) | ||||
0.00237444 | + | 0.999997i | \(0.499244\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.0163 | 0.677600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.2354 | −0.531397 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4955 | −0.854104 | −0.427052 | − | 0.904227i | \(-0.640448\pi\) | ||||
−0.427052 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.713769 | 0.0368589 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.5962 | 0.906250 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.1710 | 0.779280 | 0.389640 | − | 0.920967i | \(-0.372599\pi\) | ||||
0.389640 | + | 0.920967i | \(0.372599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.303643 | −0.0155561 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.9960 | −0.868454 | −0.434227 | − | 0.900804i | \(-0.642978\pi\) | ||||
−0.434227 | + | 0.900804i | \(0.642978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.64130 | 0.0836486 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.48362 | −0.278748 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.6580 | 1.60513 | 0.802563 | − | 0.596568i | \(-0.203469\pi\) | ||||
0.802563 | + | 0.596568i | \(0.203469\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.3612 | 0.877993 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.0719 | 0.558503 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.86668 | −0.0939229 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.98075 | −0.199788 | −0.0998941 | − | 0.994998i | \(-0.531850\pi\) | ||||
−0.0998941 | + | 0.994998i | \(0.531850\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.28874 | −0.214705 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.2507 | 1.05857 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.67436 | −0.232271 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.09204 | 0.252403 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.9846 | 1.08707 | 0.543534 | − | 0.839387i | \(-0.317086\pi\) | ||||
0.543534 | + | 0.839387i | \(0.317086\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.4377 | −0.761487 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.6826 | −0.722481 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.9310 | 0.831109 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.70165 | 0.230241 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.6768 | −1.15669 | −0.578344 | − | 0.815793i | \(-0.696301\pi\) | ||||
−0.578344 | + | 0.815793i | \(0.696301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.3551 | −1.08952 | −0.544761 | − | 0.838591i | \(-0.683380\pi\) | ||||
−0.544761 | + | 0.838591i | \(0.683380\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.2283 | 1.42113 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.63853 | −0.127987 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.68510 | 0.468695 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.81106 | 0.135719 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.77421 | 0.0854606 | 0.0427303 | − | 0.999087i | \(-0.486394\pi\) | ||||
0.0427303 | + | 0.999087i | \(0.486394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.0472 | 0.771178 | 0.385589 | − | 0.922671i | \(-0.373998\pi\) | ||||
0.385589 | + | 0.922671i | \(0.373998\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.12408 | −0.197735 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.1504 | 1.49013 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.8644 | −1.09126 | −0.545630 | − | 0.838026i | \(-0.683709\pi\) | ||||
−0.545630 | + | 0.838026i | \(0.683709\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.4219 | 0.639138 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3451 | −0.491510 | −0.245755 | − | 0.969332i | \(-0.579036\pi\) | ||||
−0.245755 | + | 0.969332i | \(0.579036\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.3893 | 0.587308 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.24838 | −0.390135 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.3356 | −1.43163 | −0.715813 | − | 0.698292i | \(-0.753944\pi\) | ||||
−0.715813 | + | 0.698292i | \(0.753944\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.75861 | −0.318250 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.9775 | −0.609735 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.86523 | −0.181205 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.34804 | −0.203393 | −0.101696 | − | 0.994815i | \(-0.532427\pi\) | ||||
−0.101696 | + | 0.994815i | \(0.532427\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.3403 | −0.482645 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.81743 | 0.457243 | 0.228622 | − | 0.973515i | \(-0.426578\pi\) | ||||
0.228622 | + | 0.973515i | \(0.426578\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.39883 | 0.436801 | 0.218400 | − | 0.975859i | \(-0.429916\pi\) | ||||
0.218400 | + | 0.975859i | \(0.429916\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.98060 | −0.230970 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.11104 | −0.190236 | −0.0951182 | − | 0.995466i | \(-0.530323\pi\) | ||||
−0.0951182 | + | 0.995466i | \(0.530323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7041 | −0.586622 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.12021 | 0.143772 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.84733 | 0.130920 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.73419 | −0.217220 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.0850 | −0.919631 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.7238 | 0.489981 | 0.244990 | − | 0.969525i | \(-0.421215\pi\) | ||||
0.244990 | + | 0.969525i | \(0.421215\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.9916 | −0.546770 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.96076 | −0.271224 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.1561 | 0.597386 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.4659 | −1.15397 | −0.576985 | − | 0.816755i | \(-0.695771\pi\) | ||||
−0.576985 | + | 0.816755i | \(0.695771\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.75701 | 0.0794548 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.5251 | −0.520121 | −0.260061 | − | 0.965592i | \(-0.583743\pi\) | ||||
−0.260061 | + | 0.965592i | \(0.583743\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.2451 | 0.686606 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.22074 | 0.144761 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.3500 | −0.912821 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.7293 | −1.01750 | −0.508752 | − | 0.860913i | \(-0.669893\pi\) | ||||
−0.508752 | + | 0.860913i | \(0.669893\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.665680 | −0.0297404 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.1058 | 0.896472 | 0.448236 | − | 0.893915i | \(-0.352052\pi\) | ||||
0.448236 | + | 0.893915i | \(0.352052\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.6448 | −0.651684 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.65903 | 0.118092 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.2914 | 1.25399 | 0.626997 | − | 0.779022i | \(-0.284284\pi\) | ||||
0.626997 | + | 0.779022i | \(0.284284\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.3417 | −0.678678 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.5532 | −0.819143 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.0490 | 0.839400 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.1766 | −0.667466 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.21652 | 0.0533992 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.3444 | 1.19798 | 0.598990 | − | 0.800756i | \(-0.295569\pi\) | ||||
0.598990 | + | 0.800756i | \(0.295569\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.1402 | 1.27421 | 0.637106 | − | 0.770776i | \(-0.280131\pi\) | ||||
0.637106 | + | 0.770776i | \(0.280131\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.905907 | 0.0395370 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.4113 | 0.802010 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.2948 | 0.882381 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.8117 | −1.25032 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.9163 | 0.689413 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.104128 | −0.00450183 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.68947 | −0.245519 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.96923 | −0.300186 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.8977 | 0.597508 | 0.298754 | − | 0.954330i | \(-0.403429\pi\) | ||||
0.298754 | + | 0.954330i | \(0.403429\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.0528 | −0.431408 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.07641 | 0.388791 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.92237 | −0.167708 | −0.0838541 | − | 0.996478i | \(-0.526723\pi\) | ||||
−0.0838541 | + | 0.996478i | \(0.526723\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.0051 | 0.811119 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.3537 | 1.16530 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.36917 | −0.100747 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.81052 | 0.119300 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.8072 | −0.839258 | −0.419629 | − | 0.907696i | \(-0.637840\pi\) | ||||
−0.419629 | + | 0.907696i | \(0.637840\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.70539 | −0.283608 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.43547 | 0.102826 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.3190 | −1.10921 | −0.554606 | − | 0.832113i | \(-0.687131\pi\) | ||||
−0.554606 | + | 0.832113i | \(0.687131\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.2232 | 0.682513 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.93263 | −0.249147 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.41511 | −0.101247 | −0.0506234 | − | 0.998718i | \(-0.516121\pi\) | ||||
−0.0506234 | + | 0.998718i | \(0.516121\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.47436 | 0.270943 | 0.135472 | − | 0.990781i | \(-0.456745\pi\) | ||||
0.135472 | + | 0.990781i | \(0.456745\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.2575 | −0.595616 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.57988 | −0.274400 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.4985 | 1.47782 | 0.738911 | − | 0.673803i | \(-0.235340\pi\) | ||||
0.738911 | + | 0.673803i | \(0.235340\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.00647401 | 0.000269051 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.4886 | 0.891497 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.4290 | 0.431926 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.58475 | −0.313591 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.2013 | −0.462327 | −0.231164 | − | 0.972915i | \(-0.574253\pi\) | ||||
−0.231164 | + | 0.972915i | \(0.574253\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.0346 | 1.36117 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.591645 | −0.0243370 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.8629 | 1.02100 | 0.510498 | − | 0.859879i | \(-0.329461\pi\) | ||||
0.510498 | + | 0.859879i | \(0.329461\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.34879 | −0.137287 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.17889 | −0.171030 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.5793 | −0.554836 | −0.277418 | − | 0.960749i | \(-0.589479\pi\) | ||||
−0.277418 | + | 0.960749i | \(0.589479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.1672 | −0.659475 | −0.329737 | − | 0.944073i | \(-0.606960\pi\) | ||||
−0.329737 | + | 0.944073i | \(0.606960\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.9294 | −1.01520 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.32765 | 0.379223 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.5503 | 1.44294 | 0.721470 | − | 0.692445i | \(-0.243467\pi\) | ||||
0.721470 | + | 0.692445i | \(0.243467\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.23424 | −0.212102 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.7405 | 1.44590 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.80038 | −0.315054 | −0.157527 | − | 0.987515i | \(-0.550352\pi\) | ||||
−0.157527 | + | 0.987515i | \(0.550352\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.73037 | −0.150423 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.1170 | 1.49427 | 0.747137 | − | 0.664670i | \(-0.231428\pi\) | ||||
0.747137 | + | 0.664670i | \(0.231428\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.52549 | 0.101508 | 0.0507540 | − | 0.998711i | \(-0.483838\pi\) | ||||
0.0507540 | + | 0.998711i | \(0.483838\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.7864 | −1.03477 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.7243 | 0.629982 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.36986 | 0.174515 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.3894 | −0.414252 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.5770 | −0.978394 | −0.489197 | − | 0.872173i | \(-0.662710\pi\) | ||||
−0.489197 | + | 0.872173i | \(0.662710\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.81800 | −0.270991 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.425408 | −0.0168818 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.4123 | 0.650280 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −39.9329 | −1.57972 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.9876 | 1.57942 | 0.789708 | − | 0.613483i | \(-0.210232\pi\) | ||||
0.789708 | + | 0.613483i | \(0.210232\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.4864 | −1.28114 | −0.640568 | − | 0.767901i | \(-0.721301\pi\) | ||||
−0.640568 | + | 0.767901i | \(0.721301\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.57157 | 0.0618804 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.6263 | −1.12542 | −0.562708 | − | 0.826655i | \(-0.690241\pi\) | ||||
−0.562708 | + | 0.826655i | \(0.690241\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.9603 | 0.587242 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.32131 | −0.247752 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.94845 | −0.271914 | −0.135957 | − | 0.990715i | \(-0.543411\pi\) | ||||
−0.135957 | + | 0.990715i | \(0.543411\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.5119 | 0.606099 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.1052 | −1.17451 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.3012 | −1.60887 | −0.804433 | − | 0.594043i | \(-0.797531\pi\) | ||||
−0.804433 | + | 0.594043i | \(0.797531\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.83665 | 0.382601 | 0.191301 | − | 0.981531i | \(-0.438729\pi\) | ||||
0.191301 | + | 0.981531i | \(0.438729\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.73547 | −0.222747 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.00858 | −0.233003 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.0178 | 1.47206 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.36403 | 0.0913988 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.86828 | −0.380961 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.51047 | 0.250960 | 0.125480 | − | 0.992096i | \(-0.459953\pi\) | ||||
0.125480 | + | 0.992096i | \(0.459953\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.91897 | 0.150841 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.7856 | 0.529823 | 0.264911 | − | 0.964273i | \(-0.414657\pi\) | ||||
0.264911 | + | 0.964273i | \(0.414657\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.6975 | 0.640791 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.0382 | 0.767864 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.1093 | −0.731197 | −0.365599 | − | 0.930773i | \(-0.619136\pi\) | ||||
−0.365599 | + | 0.930773i | \(0.619136\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.6285 | −0.826381 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.69642 | −0.0647226 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.5601 | −0.935664 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2019 | 0.616348 | 0.308174 | − | 0.951330i | \(-0.400282\pi\) | ||||
0.308174 | + | 0.951330i | \(0.400282\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.08772 | 0.155280 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.58707 | 0.249862 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.7897 | 0.522323 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.6712 | 0.630561 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.1986 | 1.25389 | 0.626947 | − | 0.779062i | \(-0.284304\pi\) | ||||
0.626947 | + | 0.779062i | \(0.284304\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.6412 | −0.703066 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.37663 | −0.315482 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.5870 | −0.699035 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.03245 | −0.264109 | −0.132055 | − | 0.991242i | \(-0.542157\pi\) | ||||
−0.132055 | + | 0.991242i | \(0.542157\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.64903 | −0.174352 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.9136 | 1.71948 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.93833 | 0.147285 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.99674 | −0.261298 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.8501 | −1.03863 | −0.519316 | − | 0.854582i | \(-0.673813\pi\) | ||||
−0.519316 | + | 0.854582i | \(0.673813\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.1768 | 0.900390 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.85343 | 0.254882 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.77789 | −0.214586 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.5901 | −1.50540 | −0.752702 | − | 0.658362i | \(-0.771250\pi\) | ||||
−0.752702 | + | 0.658362i | \(0.771250\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.24991 | −0.120367 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.80947 | −0.214871 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.6563 | −1.53861 | −0.769305 | − | 0.638882i | \(-0.779397\pi\) | ||||
−0.769305 | + | 0.638882i | \(0.779397\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.84662 | −0.141885 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.9444 | 0.476813 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.66063 | −0.208230 | −0.104115 | − | 0.994565i | \(-0.533201\pi\) | ||||
−0.104115 | + | 0.994565i | \(0.533201\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.2909 | −0.378045 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.5400 | −1.56064 | −0.780320 | − | 0.625380i | \(-0.784944\pi\) | ||||
−0.780320 | + | 0.625380i | \(0.784944\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.5561 | −0.423382 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.1672 | 1.54282 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.132158 | −0.00482893 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.2386 | 1.21289 | 0.606446 | − | 0.795125i | \(-0.292595\pi\) | ||||
0.606446 | + | 0.795125i | \(0.292595\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.04627 | −0.256780 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.1816 | −0.661697 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.15003 | 0.259872 | 0.129936 | − | 0.991522i | \(-0.458523\pi\) | ||||
0.129936 | + | 0.991522i | \(0.458523\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.07350 | 0.220454 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.4653 | 1.10437 | 0.552183 | − | 0.833723i | \(-0.313795\pi\) | ||||
0.552183 | + | 0.833723i | \(0.313795\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.5197 | 0.417040 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.57134 | −0.237587 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.2310 | −1.27212 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.6977 | −0.566072 | −0.283036 | − | 0.959109i | \(-0.591342\pi\) | ||||
−0.283036 | + | 0.959109i | \(0.591342\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.1062 | 0.544036 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.2779 | −0.693378 | −0.346689 | − | 0.937980i | \(-0.612694\pi\) | ||||
−0.346689 | + | 0.937980i | \(0.612694\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.97788 | −0.250653 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.56707 | 0.127968 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.7423 | 0.886485 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.7349 | 0.741952 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.6434 | −0.809210 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.37146 | 0.156024 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.271020 | −0.00966082 | −0.00483041 | − | 0.999988i | \(-0.501538\pi\) | ||||
−0.00483041 | + | 0.999988i | \(0.501538\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.35892 | 0.155181 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.5902 | 0.732104 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.2395 | 0.825260 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.75623 | 0.204153 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.4376 | −1.50322 | −0.751608 | − | 0.659610i | \(-0.770722\pi\) | ||||
−0.751608 | + | 0.659610i | \(0.770722\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.9651 | 1.09547 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30.8559 | 1.09024 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.6319 | 0.551638 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.35110 | −0.294337 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.80747 | −0.204433 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.0743 | −0.776091 | −0.388046 | − | 0.921640i | \(-0.626850\pi\) | ||||
−0.388046 | + | 0.921640i | \(0.626850\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.9990 | −1.75570 | −0.877851 | − | 0.478933i | \(-0.841024\pi\) | ||||
−0.877851 | + | 0.478933i | \(0.841024\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.41490 | −0.0496226 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.46160 | 0.0862259 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.4237 | −0.364678 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.62647 | −0.336376 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.3871 | −1.02562 | −0.512809 | − | 0.858503i | \(-0.671395\pi\) | ||||
−0.512809 | + | 0.858503i | \(0.671395\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.3806 | 0.361845 | 0.180922 | − | 0.983497i | \(-0.442092\pi\) | ||||
0.180922 | + | 0.983497i | \(0.442092\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.923041 | −0.0321362 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.0873 | 0.559411 | 0.279706 | − | 0.960086i | \(-0.409763\pi\) | ||||
0.279706 | + | 0.960086i | \(0.409763\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.89833 | 0.343783 | 0.171892 | − | 0.985116i | \(-0.445012\pi\) | ||||
0.171892 | + | 0.985116i | \(0.445012\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.1694 | −0.491530 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.2195 | 0.492675 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.932627 | −0.0322749 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.3461 | −0.945220 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.0686 | −0.451179 | −0.225589 | − | 0.974222i | \(-0.572431\pi\) | ||||
−0.225589 | + | 0.974222i | \(0.572431\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.38405 | 0.151174 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.3339 | −0.424802 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.72534 | 0.128156 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.8385 | 0.406777 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.9495 | 0.581704 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.9087 | −0.888139 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.49114 | 0.256492 | 0.128246 | − | 0.991742i | \(-0.459065\pi\) | ||||
0.128246 | + | 0.991742i | \(0.459065\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.7907 | −0.403232 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.2677 | 0.384897 | 0.192448 | − | 0.981307i | \(-0.438357\pi\) | ||||
0.192448 | + | 0.981307i | \(0.438357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.2435 | −0.588341 | −0.294171 | − | 0.955753i | \(-0.595043\pi\) | ||||
−0.294171 | + | 0.955753i | \(0.595043\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.73454 | −0.161353 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.2898 | 0.758754 | 0.379377 | − | 0.925242i | \(-0.376138\pi\) | ||||
0.379377 | + | 0.925242i | \(0.376138\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.70436 | 0.0579498 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.16494 | 0.243334 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.41398 | 0.0818886 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.4837 | −1.03290 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 32.7656 | 1.10895 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.26919 | 0.0429064 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.7198 | −1.13864 | −0.569318 | − | 0.822117i | \(-0.692793\pi\) | ||||
−0.569318 | + | 0.822117i | \(0.692793\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.2019 | −0.411559 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.9805 | 1.34698 | 0.673489 | − | 0.739197i | \(-0.264795\pi\) | ||||
0.673489 | + | 0.739197i | \(0.264795\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.78565 | −0.0600920 | −0.0300460 | − | 0.999549i | \(-0.509565\pi\) | ||||
−0.0300460 | + | 0.999549i | \(0.509565\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.25722 | 0.277563 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.5734 | 1.42948 | 0.714738 | − | 0.699392i | \(-0.246546\pi\) | ||||
0.714738 | + | 0.699392i | \(0.246546\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.539923 | −0.0181084 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.04484 | 0.202510 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 55.5594 | 1.85922 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.97102 | −0.266442 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.3029 | −0.477560 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40.3174 | 1.34466 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.2786 | −0.708892 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.99461 | 0.0663765 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.0841 | −0.468172 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.4336 | −0.711691 | −0.355845 | − | 0.934545i | \(-0.615807\pi\) | ||||
−0.355845 | + | 0.934545i | \(0.615807\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −36.4733 | −1.20974 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.3406 | 1.73412 | 0.867060 | − | 0.498203i | \(-0.166007\pi\) | ||||
0.867060 | + | 0.498203i | \(0.166007\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.8950 | −0.724620 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.44673 | −0.180063 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.6875 | 0.650137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.10491 | −0.201383 | −0.100691 | − | 0.994918i | \(-0.532105\pi\) | ||||
−0.100691 | + | 0.994918i | \(0.532105\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.8639 | −0.522735 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −48.8300 | −1.60726 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.93757 | 0.129466 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 47.4422 | 1.55821 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.75417 | −0.0575526 | −0.0287763 | − | 0.999586i | \(-0.509161\pi\) | ||||
−0.0287763 | + | 0.999586i | \(0.509161\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.5133 | 0.836166 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.6044 | 0.445389 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.41213 | 0.111588 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.16858 | −0.201519 | −0.100759 | − | 0.994911i | \(-0.532127\pi\) | ||||
−0.100759 | + | 0.994911i | \(0.532127\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.70737 | −0.316788 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.0330 | 0.946450 | 0.473225 | − | 0.880942i | \(-0.343090\pi\) | ||||
0.473225 | + | 0.880942i | \(0.343090\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.3884 | 1.11984 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.97391 | 0.161801 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.8720 | −0.808232 | −0.404116 | − | 0.914708i | \(-0.632421\pi\) | ||||
−0.404116 | + | 0.914708i | \(0.632421\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36.8127 | −1.19499 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.10154 | 0.133001 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.96771 | −0.193313 | −0.0966566 | − | 0.995318i | \(-0.530815\pi\) | ||||
−0.0966566 | + | 0.995318i | \(0.530815\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.9750 | −0.646374 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.33323 | 0.172399 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.4506 | −0.886425 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.6908 | 0.570671 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.259333 | −0.00835690 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.00907017 | 0.000291979 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.6316 | 1.14583 | 0.572917 | − | 0.819613i | \(-0.305812\pi\) | ||||
0.572917 | + | 0.819613i | \(0.305812\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.91591 | −0.286420 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.9878 | −0.833989 | −0.416994 | − | 0.908909i | \(-0.636917\pi\) | ||||
−0.416994 | + | 0.908909i | \(0.636917\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.36022 | 0.268016 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.17374 | 0.0696153 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.8423 | 0.922746 | 0.461373 | − | 0.887206i | \(-0.347357\pi\) | ||||
0.461373 | + | 0.887206i | \(0.347357\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.0217 | −0.512057 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.6051 | 0.721725 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.2422 | 0.581835 | 0.290918 | − | 0.956748i | \(-0.406039\pi\) | ||||
0.290918 | + | 0.956748i | \(0.406039\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.828902 | −0.0264110 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.6315 | −0.338405 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.4875 | −0.460675 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61.8319 | −1.96416 | −0.982078 | − | 0.188477i | \(-0.939645\pi\) | ||||
−0.982078 | + | 0.188477i | \(0.939645\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.8671 | −0.344857 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.85467 | −0.185606 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.7987 | −1.10209 | −0.551043 | − | 0.834477i | \(-0.685770\pi\) | ||||
−0.551043 | + | 0.834477i | \(0.685770\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.4312 | 0.488223 |
(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 | 8020.2.a.e.1.15 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.e.1.15 | ✓ | 35 | 1.1 | even | 1 | trivial |