Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.246832.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 209) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.15351\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | −2.26452 | −1.30742 | −0.653711 | − | 0.756745i | \(-0.726789\pi\) | ||||
−0.653711 | + | 0.756745i | \(0.726789\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.637602 | 0.285144 | 0.142572 | − | 0.989784i | \(-0.454463\pi\) | ||||
0.142572 | + | 0.989784i | \(0.454463\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.66942 | −1.00894 | −0.504472 | − | 0.863428i | \(-0.668313\pi\) | ||||
−0.504472 | + | 0.863428i | \(0.668313\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.12805 | 0.709351 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.20725 | −0.334831 | −0.167415 | − | 0.985886i | \(-0.553542\pi\) | ||||
−0.167415 | + | 0.985886i | \(0.553542\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.44386 | −0.372804 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.222022 | 0.0538483 | 0.0269242 | − | 0.999637i | \(-0.491429\pi\) | ||||
0.0269242 | + | 0.999637i | \(0.491429\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.04495 | 1.31912 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.48717 | 1.97821 | 0.989106 | − | 0.147206i | \(-0.0470279\pi\) | ||||
0.989106 | + | 0.147206i | \(0.0470279\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.59346 | −0.918693 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.97454 | 0.380001 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.94518 | 0.918297 | 0.459148 | − | 0.888360i | \(-0.348155\pi\) | ||||
0.459148 | + | 0.888360i | \(0.348155\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.05563 | 0.548808 | 0.274404 | − | 0.961615i | \(-0.411520\pi\) | ||||
0.274404 | + | 0.961615i | \(0.411520\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.26452 | 0.394202 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.70203 | −0.287695 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.18015 | 1.18041 | 0.590205 | − | 0.807254i | \(-0.299047\pi\) | ||||
0.590205 | + | 0.807254i | \(0.299047\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.73384 | 0.437765 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.92650 | −1.08174 | −0.540869 | − | 0.841107i | \(-0.681904\pi\) | ||||
−0.540869 | + | 0.841107i | \(0.681904\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.53538 | −0.234144 | −0.117072 | − | 0.993123i | \(-0.537351\pi\) | ||||
−0.117072 | + | 0.993123i | \(0.537351\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.35685 | 0.202267 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.94581 | −0.867285 | −0.433642 | − | 0.901085i | \(-0.642772\pi\) | ||||
−0.433642 | + | 0.901085i | \(0.642772\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.125785 | 0.0179692 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.502774 | −0.0704024 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.63879 | −1.32399 | −0.661995 | − | 0.749509i | \(-0.730290\pi\) | ||||
−0.661995 | + | 0.749509i | \(0.730290\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.637602 | −0.0859742 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.26452 | −0.299943 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.65817 | −0.346065 | −0.173032 | − | 0.984916i | \(-0.555357\pi\) | ||||
−0.173032 | + | 0.984916i | \(0.555357\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.809792 | −0.103683 | −0.0518416 | − | 0.998655i | \(-0.516509\pi\) | ||||
−0.0518416 | + | 0.998655i | \(0.516509\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.68066 | −0.715696 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.769744 | −0.0954750 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.22447 | 0.271763 | 0.135881 | − | 0.990725i | \(-0.456613\pi\) | ||||
0.135881 | + | 0.990725i | \(0.456613\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −21.4839 | −2.58636 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.58912 | −0.307272 | −0.153636 | − | 0.988127i | \(-0.549098\pi\) | ||||
−0.153636 | + | 0.988127i | \(0.549098\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.6108 | 1.94414 | 0.972071 | − | 0.234687i | \(-0.0754065\pi\) | ||||
0.972071 | + | 0.234687i | \(0.0754065\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.4020 | 1.20112 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.66942 | 0.304208 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.69298 | −0.640510 | −0.320255 | − | 0.947331i | \(-0.603769\pi\) | ||||
−0.320255 | + | 0.947331i | \(0.603769\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.8556 | −1.20617 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.93784 | 0.322470 | 0.161235 | − | 0.986916i | \(-0.448452\pi\) | ||||
0.161235 | + | 0.986916i | \(0.448452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.141562 | 0.0153545 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.1985 | −1.20060 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.54136 | −0.587383 | −0.293692 | − | 0.955900i | \(-0.594884\pi\) | ||||
−0.293692 | + | 0.955900i | \(0.594884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.22265 | 0.337826 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.91954 | −0.717523 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.637602 | 0.0654166 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.7728 | 1.39842 | 0.699209 | − | 0.714917i | \(-0.253536\pi\) | ||||
0.699209 | + | 0.714917i | \(0.253536\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.12805 | −0.213877 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0308 | 1.19711 | 0.598555 | − | 0.801082i | \(-0.295742\pi\) | ||||
0.598555 | + | 0.801082i | \(0.295742\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.53068 | −0.840553 | −0.420276 | − | 0.907396i | \(-0.638067\pi\) | ||||
−0.420276 | + | 0.907396i | \(0.638067\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.85427 | 0.376138 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.64585 | −0.159110 | −0.0795552 | − | 0.996830i | \(-0.525350\pi\) | ||||
−0.0795552 | + | 0.996830i | \(0.525350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.8065 | 1.60977 | 0.804886 | − | 0.593430i | \(-0.202226\pi\) | ||||
0.804886 | + | 0.593430i | \(0.202226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.2596 | −1.54329 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.2947 | −1.06252 | −0.531258 | − | 0.847210i | \(-0.678280\pi\) | ||||
−0.531258 | + | 0.847210i | \(0.678280\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.04904 | 0.564076 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.56909 | −0.237512 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.592670 | −0.0543300 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.6852 | 1.41429 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.11681 | −0.547104 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.5894 | −1.64954 | −0.824771 | − | 0.565467i | \(-0.808696\pi\) | ||||
−0.824771 | + | 0.565467i | \(0.808696\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.47690 | 0.306124 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.09098 | 0.270060 | 0.135030 | − | 0.990842i | \(-0.456887\pi\) | ||||
0.135030 | + | 0.990842i | \(0.456887\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.66942 | −0.231468 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.25897 | 0.108355 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.67619 | −0.741257 | −0.370629 | − | 0.928781i | \(-0.620858\pi\) | ||||
−0.370629 | + | 0.928781i | \(0.620858\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.5426 | −1.23348 | −0.616742 | − | 0.787166i | \(-0.711548\pi\) | ||||
−0.616742 | + | 0.787166i | \(0.711548\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.4644 | 1.13391 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.20725 | 0.100955 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.15306 | 0.261847 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.284842 | −0.0234933 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.4716 | −1.51325 | −0.756625 | − | 0.653849i | \(-0.773153\pi\) | ||||
−0.756625 | + | 0.653849i | \(0.773153\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.913992 | 0.0743796 | 0.0371898 | − | 0.999308i | \(-0.488159\pi\) | ||||
0.0371898 | + | 0.999308i | \(0.488159\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.472475 | 0.0381973 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.94828 | 0.156489 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.39421 | −0.191079 | −0.0955395 | − | 0.995426i | \(-0.530458\pi\) | ||||
−0.0955395 | + | 0.995426i | \(0.530458\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.8272 | 1.73101 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.3252 | −1.99591 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.1986 | −1.11212 | −0.556061 | − | 0.831141i | \(-0.687688\pi\) | ||||
−0.556061 | + | 0.831141i | \(0.687688\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.44386 | 0.112405 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.25056 | −0.715830 | −0.357915 | − | 0.933754i | \(-0.616512\pi\) | ||||
−0.357915 | + | 0.933754i | \(0.616512\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5426 | −0.887888 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.12805 | 0.162736 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.39376 | 0.410080 | 0.205040 | − | 0.978754i | \(-0.434268\pi\) | ||||
0.205040 | + | 0.978754i | \(0.434268\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.2619 | 0.926910 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.01949 | 0.452453 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.30720 | −0.0977048 | −0.0488524 | − | 0.998806i | \(-0.515556\pi\) | ||||
−0.0488524 | + | 0.998806i | \(0.515556\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.7624 | −0.799961 | −0.399980 | − | 0.916524i | \(-0.630983\pi\) | ||||
−0.399980 | + | 0.916524i | \(0.630983\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.83379 | 0.135558 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.57808 | 0.336587 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.222022 | −0.0162359 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.27088 | −0.383400 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.3041 | −1.10737 | −0.553684 | − | 0.832727i | \(-0.686778\pi\) | ||||
−0.553684 | + | 0.832727i | \(0.686778\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.3032 | −1.31749 | −0.658747 | − | 0.752364i | \(-0.728913\pi\) | ||||
−0.658747 | + | 0.752364i | \(0.728913\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.74310 | 0.124826 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.576171 | −0.0410505 | −0.0205252 | − | 0.999789i | \(-0.506534\pi\) | ||||
−0.0205252 | + | 0.999789i | \(0.506534\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1678 | 0.720778 | 0.360389 | − | 0.932802i | \(-0.382644\pi\) | ||||
0.360389 | + | 0.932802i | \(0.382644\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.03736 | −0.355308 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.2007 | −0.926510 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.41635 | −0.308451 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.1892 | 1.40325 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.25837 | 0.499687 | 0.249843 | − | 0.968286i | \(-0.419621\pi\) | ||||
0.249843 | + | 0.968286i | \(0.419621\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.86312 | 0.401734 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.978963 | −0.0667647 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.15675 | −0.553716 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −37.6154 | −2.54181 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.268036 | −0.0180301 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.2772 | −1.09000 | −0.545000 | − | 0.838436i | \(-0.683471\pi\) | ||||
−0.545000 | + | 0.838436i | \(0.683471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.77513 | −0.651675 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.9260 | 1.38890 | 0.694452 | − | 0.719539i | \(-0.255647\pi\) | ||||
0.694452 | + | 0.719539i | \(0.255647\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.8083 | −0.714234 | −0.357117 | − | 0.934060i | \(-0.616240\pi\) | ||||
−0.357117 | + | 0.934060i | \(0.616240\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.04495 | −0.397728 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.4173 | −1.66514 | −0.832570 | − | 0.553919i | \(-0.813132\pi\) | ||||
−0.832570 | + | 0.553919i | \(0.813132\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.79106 | −0.247301 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.8919 | 0.837417 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.352238 | −0.0227844 | −0.0113922 | − | 0.999935i | \(-0.503626\pi\) | ||||
−0.0113922 | + | 0.999935i | \(0.503626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.6832 | −1.01024 | −0.505122 | − | 0.863048i | \(-0.668552\pi\) | ||||
−0.505122 | + | 0.863048i | \(0.668552\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.6590 | 1.19697 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0802004 | 0.00512382 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.20725 | −0.0768154 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.65281 | −0.421605 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.16332 | −0.0734282 | −0.0367141 | − | 0.999326i | \(-0.511689\pi\) | ||||
−0.0367141 | + | 0.999326i | \(0.511689\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.48717 | −0.596453 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.320570 | −0.0200748 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.0510 | −0.938857 | −0.469428 | − | 0.882971i | \(-0.655540\pi\) | ||||
−0.469428 | + | 0.882971i | \(0.655540\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.1668 | −1.19097 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.5236 | 0.651394 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.6609 | 1.27400 | 0.637002 | − | 0.770862i | \(-0.280174\pi\) | ||||
0.637002 | + | 0.770862i | \(0.280174\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.14571 | −0.377528 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.5485 | 0.767958 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.82662 | −0.172342 | −0.0861711 | − | 0.996280i | \(-0.527463\pi\) | ||||
−0.0861711 | + | 0.996280i | \(0.527463\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.5970 | −1.43341 | −0.716707 | − | 0.697375i | \(-0.754351\pi\) | ||||
−0.716707 | + | 0.697375i | \(0.754351\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.29776 | −0.441680 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.59346 | 0.276996 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7773 | −1.12822 | −0.564110 | − | 0.825700i | \(-0.690781\pi\) | ||||
−0.564110 | + | 0.825700i | \(0.690781\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.50254 | 0.389297 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.2632 | 1.62639 | 0.813194 | − | 0.581993i | \(-0.197727\pi\) | ||||
0.813194 | + | 0.581993i | \(0.197727\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.2601 | 1.62044 | 0.810221 | − | 0.586124i | \(-0.199347\pi\) | ||||
0.810221 | + | 0.586124i | \(0.199347\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.44386 | −0.0855270 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.4897 | 1.09141 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9507 | −0.997100 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −31.1888 | −1.82832 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.9996 | 1.81101 | 0.905507 | − | 0.424332i | \(-0.139491\pi\) | ||||
0.905507 | + | 0.424332i | \(0.139491\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.69486 | −0.0986784 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.97454 | −0.114575 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.4534 | −0.662366 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.09858 | 0.236238 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −27.2440 | −1.56513 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.516325 | −0.0295647 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.2495 | 1.04156 | 0.520778 | − | 0.853692i | \(-0.325642\pi\) | ||||
0.520778 | + | 0.853692i | \(0.325642\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.3179 | 1.09896 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.8931 | −1.75179 | −0.875894 | − | 0.482503i | \(-0.839728\pi\) | ||||
−0.875894 | + | 0.482503i | \(0.839728\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.7973 | 1.62772 | 0.813859 | − | 0.581062i | \(-0.197363\pi\) | ||||
0.813859 | + | 0.581062i | \(0.197363\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.62200 | −0.204076 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.96040 | 0.334769 | 0.167385 | − | 0.985892i | \(-0.446468\pi\) | ||||
0.167385 | + | 0.985892i | \(0.446468\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.94518 | −0.276877 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.72706 | 0.208024 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.222022 | 0.0123536 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.54545 | 0.307606 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −38.0587 | −2.10465 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.8718 | 0.875043 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.4010 | −1.83589 | −0.917944 | − | 0.396711i | \(-0.870151\pi\) | ||||
−0.917944 | + | 0.396711i | \(0.870151\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.2797 | 0.837325 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.41833 | 0.0774915 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.9988 | 1.36177 | 0.680885 | − | 0.732390i | \(-0.261595\pi\) | ||||
0.680885 | + | 0.732390i | \(0.261595\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 25.5771 | 1.38916 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.05563 | −0.165472 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3501 | 0.990815 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.6982 | −0.737485 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.35577 | 0.448561 | 0.224281 | − | 0.974525i | \(-0.427997\pi\) | ||||
0.224281 | + | 0.974525i | \(0.427997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.3911 | −1.51974 | −0.759871 | − | 0.650074i | \(-0.774738\pi\) | ||||
−0.759871 | + | 0.650074i | \(0.774738\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.38377 | −0.127236 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.4082 | −0.660423 | −0.330212 | − | 0.943907i | \(-0.607120\pi\) | ||||
−0.330212 | + | 0.943907i | \(0.607120\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.65083 | −0.0876169 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.34211 | 0.0710322 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.1134 | −0.639319 | −0.319659 | − | 0.947533i | \(-0.603568\pi\) | ||||
−0.319659 | + | 0.947533i | \(0.603568\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.26452 | −0.118856 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.5911 | 0.554361 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.06064 | 0.211964 | 0.105982 | − | 0.994368i | \(-0.466201\pi\) | ||||
0.105982 | + | 0.994368i | \(0.466201\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.7399 | −0.767331 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.7299 | 1.33583 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.4898 | 1.83759 | 0.918796 | − | 0.394732i | \(-0.129163\pi\) | ||||
0.918796 | + | 0.394732i | \(0.129163\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.8516 | 0.715296 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.97006 | −0.307474 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.5584 | −0.696449 | −0.348224 | − | 0.937411i | \(-0.613215\pi\) | ||||
−0.348224 | + | 0.937411i | \(0.613215\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.0961 | 2.15665 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.8326 | 1.21779 | 0.608894 | − | 0.793251i | \(-0.291613\pi\) | ||||
0.608894 | + | 0.793251i | \(0.291613\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.70203 | 0.0867432 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.26737 | −0.166090 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.7567 | −0.646789 | −0.323395 | − | 0.946264i | \(-0.604824\pi\) | ||||
−0.323395 | + | 0.946264i | \(0.604824\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.10636 | 0.106523 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.99958 | −0.353082 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.62986 | −0.182638 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.3169 | −1.52156 | −0.760780 | − | 0.649009i | \(-0.775184\pi\) | ||||
−0.760780 | + | 0.649009i | \(0.775184\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.04495 | 0.302626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.6370 | 1.62982 | 0.814908 | − | 0.579591i | \(-0.196788\pi\) | ||||
0.814908 | + | 0.579591i | \(0.196788\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.68891 | −0.183758 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.92152 | −0.343933 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.18015 | −0.355907 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.1587 | −1.14512 | −0.572562 | − | 0.819862i | \(-0.694050\pi\) | ||||
−0.572562 | + | 0.819862i | \(0.694050\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.6474 | 0.969135 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.09578 | 0.349160 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.87318 | 0.0919506 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.9319 | 1.61268 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.2213 | 0.694755 | 0.347377 | − | 0.937725i | \(-0.387072\pi\) | ||||
0.347377 | + | 0.937725i | \(0.387072\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.9605 | 0.777866 | 0.388933 | − | 0.921266i | \(-0.372844\pi\) | ||||
0.388933 | + | 0.921266i | \(0.372844\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.6530 | −0.615209 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.01985 | −0.0494701 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.16167 | 0.104611 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.73384 | −0.131991 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.5100 | −1.18061 | −0.590304 | − | 0.807181i | \(-0.700992\pi\) | ||||
−0.590304 | + | 0.807181i | \(0.700992\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.1839 | −0.921921 | −0.460961 | − | 0.887421i | \(-0.652495\pi\) | ||||
−0.460961 | + | 0.887421i | \(0.652495\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.14016 | −0.342344 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.48717 | 0.453833 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.7961 | −0.658450 | −0.329225 | − | 0.944251i | \(-0.606788\pi\) | ||||
−0.329225 | + | 0.944251i | \(0.606788\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.267676 | 0.0127465 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.1259 | −0.671140 | −0.335570 | − | 0.942015i | \(-0.608929\pi\) | ||||
−0.335570 | + | 0.942015i | \(0.608929\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.53318 | −0.167489 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 41.8292 | 1.97846 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.0016 | −0.991129 | −0.495565 | − | 0.868571i | \(-0.665039\pi\) | ||||
−0.495565 | + | 0.868571i | \(0.665039\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.92650 | 0.326156 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.06975 | −0.0972455 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.05477 | 0.0963290 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.4621 | −1.05073 | −0.525367 | − | 0.850876i | \(-0.676072\pi\) | ||||
−0.525367 | + | 0.850876i | \(0.676072\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.438393 | 0.0204624 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.1213 | −1.44946 | −0.724732 | − | 0.689031i | \(-0.758036\pi\) | ||||
−0.724732 | + | 0.689031i | \(0.758036\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.6932 | −1.47291 | −0.736455 | − | 0.676487i | \(-0.763502\pi\) | ||||
−0.736455 | + | 0.676487i | \(0.763502\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.41191 | −0.204597 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.75474 | 0.0811995 | 0.0405997 | − | 0.999175i | \(-0.487073\pi\) | ||||
0.0405997 | + | 0.999175i | \(0.487073\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.93804 | −0.274193 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.42174 | 0.249821 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.53538 | 0.0705970 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.59346 | −0.210763 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.5118 | −0.939173 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.1294 | 0.508515 | 0.254257 | − | 0.967137i | \(-0.418169\pi\) | ||||
0.254257 | + | 0.967137i | \(0.418169\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.66823 | −0.395237 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 57.3495 | 2.60949 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.78158 | 0.398751 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.27007 | −0.148181 | −0.0740905 | − | 0.997252i | \(-0.523605\pi\) | ||||
−0.0740905 | + | 0.997252i | \(0.523605\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.1531 | 1.45401 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.2686 | −1.32087 | −0.660437 | − | 0.750882i | \(-0.729629\pi\) | ||||
−0.660437 | + | 0.750882i | \(0.729629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.09794 | 0.0494487 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.35685 | −0.0609859 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.91145 | 0.310021 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.04828 | 0.0469275 | 0.0234638 | − | 0.999725i | \(-0.492531\pi\) | ||||
0.0234638 | + | 0.999725i | \(0.492531\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.9481 | 0.935891 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.4724 | −1.26952 | −0.634761 | − | 0.772709i | \(-0.718901\pi\) | ||||
−0.634761 | + | 0.772709i | \(0.718901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.67086 | 0.341349 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 26.1383 | 1.16084 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 39.6801 | 1.75879 | 0.879396 | − | 0.476091i | \(-0.157947\pi\) | ||||
0.879396 | + | 0.476091i | \(0.157947\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44.3410 | −1.96153 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.97454 | 0.0871782 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.43918 | −0.239679 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.94581 | 0.261496 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.2143 | −0.536147 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.3168 | −0.671043 | −0.335522 | − | 0.942033i | \(-0.608913\pi\) | ||||
−0.335522 | + | 0.942033i | \(0.608913\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.17850 | 0.182713 | 0.0913566 | − | 0.995818i | \(-0.470880\pi\) | ||||
0.0913566 | + | 0.995818i | \(0.470880\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −27.7672 | −1.21186 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.678418 | 0.0295524 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 67.0064 | 2.91332 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.65674 | −0.245481 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.36201 | 0.362199 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.04940 | −0.0453694 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.96018 | 0.127741 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.125785 | −0.00541792 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.6201 | −0.628565 | −0.314283 | − | 0.949329i | \(-0.601764\pi\) | ||||
−0.314283 | + | 0.949329i | \(0.601764\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.3716 | 1.04589 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.7159 | 0.459017 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.7220 | 1.48461 | 0.742303 | − | 0.670064i | \(-0.233733\pi\) | ||||
0.742303 | + | 0.670064i | \(0.233733\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.72328 | −0.0735478 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.94518 | 0.210672 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.1969 | 0.646240 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.3672 | −0.440061 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.07603 | −0.299821 | −0.149910 | − | 0.988700i | \(-0.547899\pi\) | ||||
−0.149910 | + | 0.988700i | \(0.547899\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.85359 | 0.0783985 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.502774 | 0.0212271 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.5712 | 1.37271 | 0.686357 | − | 0.727265i | \(-0.259209\pi\) | ||||
0.686357 | + | 0.727265i | \(0.259209\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.20152 | −0.302970 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 28.9780 | 1.21696 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.6457 | 1.36858 | 0.684290 | − | 0.729210i | \(-0.260112\pi\) | ||||
0.684290 | + | 0.729210i | \(0.260112\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.8059 | 1.49843 | 0.749216 | − | 0.662326i | \(-0.230431\pi\) | ||||
0.749216 | + | 0.662326i | \(0.230431\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 34.6565 | 1.44780 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −43.5790 | −1.81737 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7218 | 0.654509 | 0.327254 | − | 0.944936i | \(-0.393877\pi\) | ||||
0.327254 | + | 0.944936i | \(0.393877\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 41.4480 | 1.72252 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.84233 | −0.325355 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.63879 | 0.399198 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.63806 | −0.0677253 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.4810 | −1.01044 | −0.505220 | − | 0.862991i | \(-0.668588\pi\) | ||||
−0.505220 | + | 0.862991i | \(0.668588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.05563 | 0.125905 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.30475 | 0.0536703 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.2995 | −0.874666 | −0.437333 | − | 0.899300i | \(-0.644077\pi\) | ||||
−0.437333 | + | 0.899300i | \(0.644077\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.377887 | −0.0154919 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.0253 | −0.942361 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.90839 | 0.363987 | 0.181994 | − | 0.983300i | \(-0.441745\pi\) | ||||
0.181994 | + | 0.983300i | \(0.441745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.36794 | −0.341335 | −0.170668 | − | 0.985329i | \(-0.554592\pi\) | ||||
−0.170668 | + | 0.985329i | \(0.554592\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.73379 | 0.192775 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.637602 | 0.0259222 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.2321 | −1.75474 | −0.877368 | − | 0.479819i | \(-0.840702\pi\) | ||||
−0.877368 | + | 0.479819i | \(0.840702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.8933 | 1.21134 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.17807 | 0.290394 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.4893 | −0.504438 | −0.252219 | − | 0.967670i | \(-0.581160\pi\) | ||||
−0.252219 | + | 0.967670i | \(0.581160\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.0009 | 0.403276 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.4079 | −0.741073 | −0.370536 | − | 0.928818i | \(-0.620826\pi\) | ||||
−0.370536 | + | 0.928818i | \(0.620826\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.30900 | 0.293773 | 0.146887 | − | 0.989153i | \(-0.453075\pi\) | ||||
0.146887 | + | 0.989153i | \(0.453075\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.7328 | 0.751722 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.7922 | 0.592637 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.0672 | 0.762689 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.26452 | 0.0904362 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.59415 | 0.0635631 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.8397 | 0.471329 | 0.235665 | − | 0.971834i | \(-0.424273\pi\) | ||||
0.235665 | + | 0.971834i | \(0.424273\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.4367 | −0.653301 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.8526 | −0.470357 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.151853 | −0.00601664 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.50979 | −0.217964 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.5974 | −1.44551 | −0.722756 | − | 0.691104i | \(-0.757125\pi\) | ||||
−0.722756 | + | 0.691104i | \(0.757125\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.0452 | 0.553888 | 0.276944 | − | 0.960886i | \(-0.410678\pi\) | ||||
0.276944 | + | 0.960886i | \(0.410678\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.21688 | 0.0872896 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.5266 | 1.71121 | 0.855604 | − | 0.517631i | \(-0.173186\pi\) | ||||
0.855604 | + | 0.517631i | \(0.173186\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.65817 | 0.104342 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.4711 | 0.723941 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.0328 | 1.72314 | 0.861568 | − | 0.507642i | \(-0.169483\pi\) | ||||
0.861568 | + | 0.507642i | \(0.169483\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.97081 | 0.0770060 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 35.3486 | 1.37908 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.86784 | 0.150670 | 0.0753349 | − | 0.997158i | \(-0.475997\pi\) | ||||
0.0753349 | + | 0.997158i | \(0.475997\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.96999 | 0.309997 | 0.154998 | − | 0.987915i | \(-0.450463\pi\) | ||||
0.154998 | + | 0.987915i | \(0.450463\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.606973 | 0.0235729 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.70203 | −0.0660017 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 46.9158 | 1.81659 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 36.8600 | 1.42509 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.809792 | 0.0312617 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.7872 | 0.839835 | 0.419917 | − | 0.907562i | \(-0.362059\pi\) | ||||
0.419917 | + | 0.907562i | \(0.362059\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.06999 | −0.349104 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.2004 | 1.27599 | 0.637997 | − | 0.770039i | \(-0.279763\pi\) | ||||
0.637997 | + | 0.770039i | \(0.279763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.7654 | −1.41093 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −47.3873 | −1.81588 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.9595 | 1.33769 | 0.668843 | − | 0.743403i | \(-0.266790\pi\) | ||||
0.668843 | + | 0.743403i | \(0.266790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.53196 | −0.211365 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.4757 | 0.933805 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.6364 | 0.443312 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.4626 | 1.15885 | 0.579426 | − | 0.815025i | \(-0.303277\pi\) | ||||
0.579426 | + | 0.815025i | \(0.303277\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.68066 | 0.215790 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.27236 | −0.351721 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.53784 | −0.0582497 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 57.5579 | 2.17704 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.3329 | 0.390269 | 0.195135 | − | 0.980776i | \(-0.437486\pi\) | ||||
0.195135 | + | 0.980776i | \(0.437486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.18015 | 0.270805 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.58493 | 0.323327 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −32.1152 | −1.20782 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.4499 | −1.70691 | −0.853454 | − | 0.521169i | \(-0.825496\pi\) | ||||
−0.853454 | + | 0.521169i | \(0.825496\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.1150 | −0.454347 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.9893 | 1.08566 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.769744 | 0.0287868 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.797651 | 0.0297888 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.51239 | 0.280165 | 0.140082 | − | 0.990140i | \(-0.455263\pi\) | ||||
0.140082 | + | 0.990140i | \(0.455263\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.7719 | 0.848071 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 35.5149 | 1.32081 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.7155 | −0.843632 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.79898 | −0.177984 | −0.0889922 | − | 0.996032i | \(-0.528365\pi\) | ||||
−0.0889922 | + | 0.996032i | \(0.528365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.68700 | −0.358778 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.340889 | −0.0126082 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.55077 | −0.315830 | −0.157915 | − | 0.987453i | \(-0.550477\pi\) | ||||
−0.157915 | + | 0.987453i | \(0.550477\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.181616 | −0.00669899 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.22447 | −0.0819395 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.8820 | −1.43030 | −0.715149 | − | 0.698972i | \(-0.753641\pi\) | ||||
−0.715149 | + | 0.698972i | \(0.753641\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.73384 | 0.100430 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.4350 | −1.04318 | −0.521589 | − | 0.853197i | \(-0.674660\pi\) | ||||
−0.521589 | + | 0.853197i | \(0.674660\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.7775 | −0.431494 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.25189 | 0.228745 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.39346 | 0.160534 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.2732 | −0.666799 | −0.333400 | − | 0.942786i | \(-0.608196\pi\) | ||||
−0.333400 | + | 0.942786i | \(0.608196\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.63436 | 0.0960015 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.582763 | 0.0212089 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.10637 | 0.0402117 | 0.0201058 | − | 0.999798i | \(-0.493600\pi\) | ||||
0.0201058 | + | 0.999798i | \(0.493600\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.4839 | 0.779816 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.10110 | 0.0399147 | 0.0199573 | − | 0.999801i | \(-0.493647\pi\) | ||||
0.0199573 | + | 0.999801i | \(0.493647\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44.8636 | −1.62417 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.301251 | 0.0108918 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.20908 | 0.115873 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.2914 | 1.09234 | 0.546169 | − | 0.837675i | \(-0.316086\pi\) | ||||
0.546169 | + | 0.837675i | \(0.316086\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.0833 | 1.22748 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.9677 | −1.58141 | −0.790704 | − | 0.612199i | \(-0.790285\pi\) | ||||
−0.790704 | + | 0.612199i | \(0.790285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.0359 | −0.504186 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 43.4036 | 1.55710 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.92650 | −0.248168 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.58912 | 0.0926461 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.76447 | 0.348954 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.52655 | −0.0544851 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.8350 | 1.34867 | 0.674337 | − | 0.738424i | \(-0.264430\pi\) | ||||
0.674337 | + | 0.738424i | \(0.264430\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −46.7870 | −1.66566 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.1502 | 1.07202 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.977621 | 0.0347163 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.9171 | 0.493588 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.2902 | 0.399918 | 0.199959 | − | 0.979804i | \(-0.435919\pi\) | ||||
0.199959 | + | 0.979804i | \(0.435919\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.32010 | −0.0467018 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.7923 | −0.416661 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.6108 | −0.586181 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.1474 | −0.569121 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.40095 | 0.225324 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.8104 | 0.626180 | 0.313090 | − | 0.949723i | \(-0.398636\pi\) | ||||
0.313090 | + | 0.949723i | \(0.398636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.1638 | −0.988965 | −0.494482 | − | 0.869188i | \(-0.664642\pi\) | ||||
−0.494482 | + | 0.869188i | \(0.664642\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 53.4358 | 1.87408 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.05307 | −0.317115 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.53538 | −0.0537162 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.85797 | 0.239637 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.2644 | −1.54484 | −0.772418 | − | 0.635114i | \(-0.780953\pi\) | ||||
−0.772418 | + | 0.635114i | \(0.780953\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.4258 | 0.781716 | 0.390858 | − | 0.920451i | \(-0.372178\pi\) | ||||
0.390858 | + | 0.920451i | \(0.372178\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.4020 | −0.362151 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.7303 | −0.686090 | −0.343045 | − | 0.939319i | \(-0.611458\pi\) | ||||
−0.343045 | + | 0.939319i | \(0.611458\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.70836 | 0.198259 | 0.0991297 | − | 0.995075i | \(-0.468394\pi\) | ||||
0.0991297 | + | 0.995075i | \(0.468394\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.5216 | 1.47506 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.0279270 | 0.000967612 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.89817 | −0.204115 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.03348 | 0.208547 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.0666011 | 0.00229932 | 0.00114966 | − | 0.999999i | \(-0.499634\pi\) | ||||
0.00114966 | + | 0.999999i | \(0.499634\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.54521 | −0.156731 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −61.7381 | −2.12637 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.35955 | −0.253176 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.66942 | −0.0917222 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −61.7310 | −2.11860 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 68.1193 | 2.33510 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.8615 | −0.508848 | −0.254424 | − | 0.967093i | \(-0.581886\pi\) | ||||
−0.254424 | + | 0.967093i | \(0.581886\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.35685 | 0.0464033 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.5169 | 0.427569 | 0.213785 | − | 0.976881i | \(-0.431421\pi\) | ||||
0.213785 | + | 0.976881i | \(0.431421\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.2738 | 0.725854 | 0.362927 | − | 0.931818i | \(-0.381777\pi\) | ||||
0.362927 | + | 0.931818i | \(0.381777\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −41.8703 | −1.42694 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.4402 | 1.17236 | 0.586179 | − | 0.810181i | \(-0.300631\pi\) | ||||
0.586179 | + | 0.810181i | \(0.300631\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.43907 | 0.116932 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.3852 | 1.30363 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.69298 | 0.193121 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.68549 | −0.0909944 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.3093 | 0.991969 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.3283 | 0.551998 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.910260 | −0.0307373 | −0.0153687 | − | 0.999882i | \(-0.504892\pi\) | ||||
−0.0153687 | + | 0.999882i | \(0.504892\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −70.1991 | −2.36776 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.7502 | 1.13707 | 0.568537 | − | 0.822658i | \(-0.307510\pi\) | ||||
0.568537 | + | 0.822658i | \(0.307510\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.8800 | −1.34207 | −0.671035 | − | 0.741426i | \(-0.734150\pi\) | ||||
−0.671035 | + | 0.741426i | \(0.734150\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.83804 | 0.129014 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.1868 | 0.543500 | 0.271750 | − | 0.962368i | \(-0.412398\pi\) | ||||
0.271750 | + | 0.962368i | \(0.412398\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 49.6228 | 1.66430 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.8556 | 0.363675 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.94581 | −0.198969 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.833474 | −0.0278599 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.9364 | 0.865991 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.1106 | 0.503968 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.14003 | −0.0712946 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.28131 | −0.308863 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.86211 | −0.228104 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.3005 | 0.474839 | 0.237419 | − | 0.971407i | \(-0.423698\pi\) | ||||
0.237419 | + | 0.971407i | \(0.423698\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25.6022 | 0.849171 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.50108 | 0.281653 | 0.140827 | − | 0.990034i | \(-0.455024\pi\) | ||||
0.140827 | + | 0.990034i | \(0.455024\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.93784 | −0.0972285 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.16923 | 0.0386535 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.25111 | −0.272476 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.0156 | 0.858177 | 0.429088 | − | 0.903263i | \(-0.358835\pi\) | ||||
0.429088 | + | 0.903263i | \(0.358835\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −41.3265 | −1.36175 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.12571 | 0.102884 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.9818 | −1.08443 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.1537 | −0.596247 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.99773 | 0.196779 | 0.0983896 | − | 0.995148i | \(-0.468631\pi\) | ||||
0.0983896 | + | 0.995148i | \(0.468631\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.125785 | 0.00412242 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 69.9581 | 2.29033 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.141562 | −0.00462957 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.5847 | −1.65253 | −0.826265 | − | 0.563282i | \(-0.809539\pi\) | ||||
−0.826265 | + | 0.563282i | \(0.809539\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −65.2120 | −2.12811 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.8640 | −0.712747 | −0.356373 | − | 0.934344i | \(-0.615987\pi\) | ||||
−0.356373 | + | 0.934344i | \(0.615987\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −65.7129 | −2.13991 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.36072 | −0.109324 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.1722 | 1.07795 | 0.538976 | − | 0.842321i | \(-0.318812\pi\) | ||||
0.538976 | + | 0.842321i | \(0.318812\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.0533 | −0.650958 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.4974 | −0.437685 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.4494 | 0.727209 | 0.363604 | − | 0.931553i | \(-0.381546\pi\) | ||||
0.363604 | + | 0.931553i | \(0.381546\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.75794 | −0.315760 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.1985 | 0.361995 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.1604 | 0.747887 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6631 | −0.698810 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.50246 | −0.112865 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.6702 | −0.375676 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.790013 | 0.0254051 | 0.0127026 | − | 0.999919i | \(-0.495957\pi\) | ||||
0.0127026 | + | 0.999919i | \(0.495957\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.502774 | −0.0161514 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.6970 | −1.65904 | −0.829518 | − | 0.558479i | \(-0.811385\pi\) | ||||
−0.829518 | + | 0.558479i | \(0.811385\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.8201 | 1.24452 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.5578 | −0.402171 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.4536 | 0.686360 | 0.343180 | − | 0.939270i | \(-0.388496\pi\) | ||||
0.343180 | + | 0.939270i | \(0.388496\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.54136 | 0.177103 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.7651 | 1.14189 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.9916 | 1.37122 | 0.685610 | − | 0.727969i | \(-0.259536\pi\) | ||||
0.685610 | + | 0.727969i | \(0.259536\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.367368 | −0.0117053 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −35.9421 | −1.14405 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.5664 | −0.463186 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.7319 | −1.83392 | −0.916958 | − | 0.398985i | \(-0.869363\pi\) | ||||
−0.916958 | + | 0.398985i | \(0.869363\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 75.6373 | 2.40028 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.48303 | 0.205526 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.3487 | −0.961152 | −0.480576 | − | 0.876953i | \(-0.659572\pi\) | ||||
−0.480576 | + | 0.876953i | \(0.659572\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.1775 | 0.448557 |
(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 | 3344.2.a.t.1.1 | 5 | ||
4.3 | odd | 2 | 209.2.a.c.1.3 | ✓ | 5 | ||
12.11 | even | 2 | 1881.2.a.k.1.3 | 5 | |||
20.19 | odd | 2 | 5225.2.a.h.1.3 | 5 | |||
44.43 | even | 2 | 2299.2.a.n.1.3 | 5 | |||
76.75 | even | 2 | 3971.2.a.h.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
209.2.a.c.1.3 | ✓ | 5 | 4.3 | odd | 2 | ||
1881.2.a.k.1.3 | 5 | 12.11 | even | 2 | |||
2299.2.a.n.1.3 | 5 | 44.43 | even | 2 | |||
3344.2.a.t.1.1 | 5 | 1.1 | even | 1 | trivial | ||
3971.2.a.h.1.3 | 5 | 76.75 | even | 2 | |||
5225.2.a.h.1.3 | 5 | 20.19 | odd | 2 |