Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(3497,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4028.3497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(32.1637419342\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3497.7 | ||
Character | \(\chi\) | \(=\) | 4028.3497 |
Dual form | 4028.2.c.a.3497.76 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4028\mathbb{Z}\right)^\times\).
\(n\) | \(2015\) | \(2281\) | \(2757\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − | 2.92218i | − | 1.68712i | −0.537033 | − | 0.843561i | \(-0.680455\pi\) | ||
0.537033 | − | 0.843561i | \(-0.319545\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.97792i | 1.33177i | 0.746056 | + | 0.665883i | \(0.231945\pi\) | ||||
−0.746056 | + | 0.665883i | \(0.768055\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.58698 | 0.977788 | 0.488894 | − | 0.872343i | \(-0.337401\pi\) | ||||
0.488894 | + | 0.872343i | \(0.337401\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.53915 | −1.84638 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.66211 | −1.70719 | −0.853596 | − | 0.520936i | \(-0.825583\pi\) | ||||
−0.853596 | + | 0.520936i | \(0.825583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.873190 | −0.242179 | −0.121090 | − | 0.992642i | \(-0.538639\pi\) | ||||
−0.121090 | + | 0.992642i | \(0.538639\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.70203 | 2.24685 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.71791 | 0.659189 | 0.329594 | − | 0.944123i | \(-0.393088\pi\) | ||||
0.329594 | + | 0.944123i | \(0.393088\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 7.55964i | − | 1.64965i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.52478i | 0.734967i | 0.930030 | + | 0.367483i | \(0.119781\pi\) | ||||
−0.930030 | + | 0.367483i | \(0.880219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.86801 | −0.773602 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.41985i | 1.42795i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.84976 | 1.08627 | 0.543137 | − | 0.839644i | \(-0.317237\pi\) | ||||
0.543137 | + | 0.839644i | \(0.317237\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.81613i | − | 0.865003i | −0.901633 | − | 0.432501i | \(-0.857631\pi\) | ||
0.901633 | − | 0.432501i | \(-0.142369\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.5457i | 2.88024i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.70383i | 1.30219i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.31304 | −1.53105 | −0.765527 | − | 0.643404i | \(-0.777522\pi\) | ||||
−0.765527 | + | 0.643404i | \(0.777522\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.55162i | 0.408586i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.85910i | 1.38356i | 0.722109 | + | 0.691779i | \(0.243173\pi\) | ||||
−0.722109 | + | 0.691779i | \(0.756827\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.93035 | 1.51436 | 0.757182 | − | 0.653204i | \(-0.226575\pi\) | ||||
0.757182 | + | 0.653204i | \(0.226575\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 16.4951i | − | 2.45895i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.77941 | 1.13474 | 0.567372 | − | 0.823462i | \(-0.307960\pi\) | ||||
0.567372 | + | 0.823462i | \(0.307960\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.307519 | −0.0439312 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 7.94222i | − | 1.11213i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.46126 | − | 6.40466i | 0.475440 | − | 0.879748i | ||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 16.8613i | − | 2.27358i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.92218 | −0.387052 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.6525 | 1.38683 | 0.693417 | − | 0.720537i | \(-0.256105\pi\) | ||||
0.693417 | + | 0.720537i | \(0.256105\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.91344i | 0.629101i | 0.949241 | + | 0.314550i | \(0.101854\pi\) | ||||
−0.949241 | + | 0.314550i | \(0.898146\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −14.3297 | −1.80537 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.60029i | − | 0.322526i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.27118i | − | 0.521808i | −0.965365 | − | 0.260904i | \(-0.915979\pi\) | ||
0.965365 | − | 0.260904i | \(-0.0840205\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.3000 | 1.23998 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4279i | 1.47492i | 0.675391 | + | 0.737460i | \(0.263975\pi\) | ||||
−0.675391 | + | 0.737460i | \(0.736025\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.3702i | − | 1.79894i | −0.436979 | − | 0.899471i | \(-0.643952\pi\) | ||
0.436979 | − | 0.899471i | \(-0.356048\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.3030i | 1.30516i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.6478 | −1.66927 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.78273i | 0.988135i | 0.869424 | + | 0.494067i | \(0.164490\pi\) | ||||
−0.869424 | + | 0.494067i | \(0.835510\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.06472 | 0.562747 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.63091i | − | 0.947365i | −0.880696 | − | 0.473682i | \(-0.842924\pi\) | ||
0.880696 | − | 0.473682i | \(-0.157076\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.09371i | 0.877886i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 17.0941i | − | 1.83268i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.0026 | 1.48427 | 0.742135 | − | 0.670250i | \(-0.233813\pi\) | ||||
0.742135 | + | 0.670250i | \(0.233813\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.25893 | −0.236800 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.0736 | −1.45937 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.97792 | 0.305528 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.5439 | 1.78131 | 0.890657 | − | 0.454677i | \(-0.150245\pi\) | ||||
0.890657 | + | 0.454677i | \(0.150245\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 31.3633 | 3.15213 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.35146i | 0.532490i | 0.963905 | + | 0.266245i | \(0.0857830\pi\) | ||||
−0.963905 | + | 0.266245i | \(0.914217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.1784i | 1.79118i | 0.444885 | + | 0.895588i | \(0.353244\pi\) | ||||
−0.444885 | + | 0.895588i | \(0.646756\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 22.5120 | 2.19695 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.7482 | 1.42576 | 0.712880 | − | 0.701286i | \(-0.247390\pi\) | ||||
0.712880 | + | 0.701286i | \(0.247390\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.50694i | − | 0.814817i | −0.913246 | − | 0.407409i | \(-0.866433\pi\) | ||
0.913246 | − | 0.407409i | \(-0.133567\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 27.2144i | 2.58308i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.62454 | −0.529112 | −0.264556 | − | 0.964370i | \(-0.585225\pi\) | ||||
−0.264556 | + | 0.964370i | \(0.585225\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.4965 | −0.978804 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.83673 | 0.447156 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.03118 | 0.644547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.0595 | 1.91450 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 25.8879 | 2.33423 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.37097i | 0.301509i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.4678i | 1.90496i | 0.304606 | + | 0.952478i | \(0.401475\pi\) | ||||
−0.304606 | + | 0.952478i | \(0.598525\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 29.0183i | − | 2.55492i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.0130 | 1.74854 | 0.874271 | − | 0.485437i | \(-0.161340\pi\) | ||||
0.874271 | + | 0.485437i | \(0.161340\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 2.58698i | − | 0.224320i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −22.0957 | −1.90170 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.4502i | 1.14912i | 0.818461 | + | 0.574562i | \(0.194828\pi\) | ||||
−0.818461 | + | 0.574562i | \(0.805172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.59168i | 0.389461i | 0.980857 | + | 0.194730i | \(0.0623832\pi\) | ||||
−0.980857 | + | 0.194730i | \(0.937617\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 22.7329i | − | 1.91445i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.94410 | 0.413446 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.4201i | 1.44666i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.898626i | 0.0741174i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.87188 | 0.153350 | 0.0766751 | − | 0.997056i | \(-0.475570\pi\) | ||||
0.0766751 | + | 0.997056i | \(0.475570\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.10740i | 0.497013i | 0.968630 | + | 0.248507i | \(0.0799398\pi\) | ||||
−0.968630 | + | 0.248507i | \(0.920060\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.0549 | −1.21712 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.3421 | 1.15198 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.7536i | − | 1.41689i | −0.705767 | − | 0.708444i | \(-0.749397\pi\) | ||
0.705767 | − | 0.708444i | \(-0.250603\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.7156 | − | 10.1144i | −1.48424 | − | 0.802126i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.11854i | 0.718641i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.5344 | 1.84335 | 0.921677 | − | 0.387959i | \(-0.126820\pi\) | ||||
0.921677 | + | 0.387959i | \(0.126820\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −49.2719 | −3.83581 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.03964i | − | 0.235215i | −0.993060 | − | 0.117607i | \(-0.962478\pi\) | ||
0.993060 | − | 0.117607i | \(-0.0375224\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2375 | −0.941349 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.53915i | 0.423589i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 20.7816i | − | 1.58000i | −0.613108 | − | 0.789999i | \(-0.710081\pi\) | ||
0.613108 | − | 0.789999i | \(-0.289919\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0065 | −0.756419 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 31.1285i | − | 2.33976i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 9.41793i | − | 0.703930i | −0.936013 | − | 0.351965i | \(-0.885514\pi\) | ||
0.936013 | − | 0.351965i | \(-0.114486\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.29826i | 0.691134i | 0.938394 | + | 0.345567i | \(0.112313\pi\) | ||||
−0.938394 | + | 0.345567i | \(0.887687\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.3580 | 1.06137 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 27.7335i | − | 2.03901i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.3891 | −1.12536 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 19.1950i | 1.39623i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.4023i | − | 0.825040i | −0.910949 | − | 0.412520i | \(-0.864649\pi\) | ||
0.910949 | − | 0.412520i | \(-0.135351\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.7323i | 1.42036i | 0.704020 | + | 0.710181i | \(0.251387\pi\) | ||||
−0.704020 | + | 0.710181i | \(0.748613\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.59852 | −0.544141 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.38501 | 0.241172 | 0.120586 | − | 0.992703i | \(-0.461523\pi\) | ||||
0.120586 | + | 0.992703i | \(0.461523\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.6520 | −1.25132 | −0.625660 | − | 0.780096i | \(-0.715170\pi\) | ||||
−0.625660 | + | 0.780096i | \(0.715170\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.4812 | −0.880353 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.1332 | 1.06214 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.3817 | −1.84258 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 19.5243i | − | 1.35703i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.66211i | 0.391657i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0167637 | 0.00115406 | 0.000577030 | − | 1.00000i | \(-0.499816\pi\) | ||||
0.000577030 | 1.00000i | \(0.499816\pi\) | ||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 36.3166 | 2.48837 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.5718i | 2.01678i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 12.4592i | − | 0.845789i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −44.9145 | −3.03504 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.37325 | −0.159642 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.4857 | −0.970035 | −0.485018 | − | 0.874504i | \(-0.661187\pi\) | ||||
−0.485018 | + | 0.874504i | \(0.661187\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 21.4255 | 1.42837 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.7948 | 1.77843 | 0.889217 | − | 0.457485i | \(-0.151250\pi\) | ||||
0.889217 | + | 0.457485i | \(0.151250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.31143 | 0.417071 | 0.208536 | − | 0.978015i | \(-0.433130\pi\) | ||||
0.208536 | + | 0.978015i | \(0.433130\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 42.8035i | 2.81626i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 17.1969i | − | 1.12661i | −0.826250 | − | 0.563304i | \(-0.809530\pi\) | ||
0.826250 | − | 0.563304i | \(-0.190470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.1665i | 1.51121i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.6648 | 1.66710 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.3930i | 1.06038i | 0.847880 | + | 0.530188i | \(0.177879\pi\) | ||||
−0.847880 | + | 0.530188i | \(0.822121\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.43061 | −0.0921535 | −0.0460768 | − | 0.998938i | \(-0.514672\pi\) | ||||
−0.0460768 | + | 0.998938i | \(0.514672\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.45953i | 0.478529i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 0.915766i | − | 0.0585062i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.873190i | 0.0555597i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.2211 | −1.59832 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.8073i | 1.37647i | 0.725489 | + | 0.688233i | \(0.241614\pi\) | ||||
−0.725489 | + | 0.688233i | \(0.758386\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 19.9577i | − | 1.25473i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 23.6513 | 1.48110 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 19.4605i | − | 1.21392i | −0.794734 | − | 0.606958i | \(-0.792390\pi\) | ||
0.794734 | − | 0.606958i | \(-0.207610\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.0927 | −1.49705 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −32.4027 | −2.00568 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 29.3106i | − | 1.80737i | −0.428201 | − | 0.903683i | \(-0.640853\pi\) | ||
0.428201 | − | 0.903683i | \(-0.359147\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.0726 | + | 10.3074i | 1.17162 | + | 0.633176i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 40.9181i | − | 2.50415i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.5932 | −1.37753 | −0.688767 | − | 0.724983i | \(-0.741848\pi\) | ||||
−0.688767 | + | 0.724983i | \(0.741848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.78178 | 0.472709 | 0.236355 | − | 0.971667i | \(-0.424047\pi\) | ||||
0.236355 | + | 0.971667i | \(0.424047\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.60100i | 0.399510i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.9011 | 1.32069 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.46870i | 0.508835i | 0.967095 | + | 0.254417i | \(0.0818837\pi\) | ||||
−0.967095 | + | 0.254417i | \(0.918116\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26.6773i | 1.59713i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.1573 | −0.963861 | −0.481930 | − | 0.876209i | \(-0.660064\pi\) | ||||
−0.481930 | + | 0.876209i | \(0.660064\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.1725i | − | 0.783023i | −0.920173 | − | 0.391512i | \(-0.871952\pi\) | ||
0.920173 | − | 0.391512i | \(-0.128048\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 8.70203i | − | 0.515464i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.9183i | 1.35283i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.61299 | −0.565470 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 51.2665i | − | 3.00529i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.19643 | 0.128317 | 0.0641584 | − | 0.997940i | \(-0.479564\pi\) | ||||
0.0641584 | + | 0.997940i | \(0.479564\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.7222i | 1.84694i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 42.0121i | − | 2.43779i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 3.07780i | − | 0.177994i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.6897 | 1.48073 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.6379 | 0.898376 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.6318 | −0.837816 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.24976 | 0.128400 | 0.0642002 | − | 0.997937i | \(-0.479550\pi\) | ||||
0.0642002 | + | 0.997937i | \(0.479550\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 53.1207 | 3.02193 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.02059 | −0.341397 | −0.170698 | − | 0.985323i | \(-0.554602\pi\) | ||||
−0.170698 | + | 0.985323i | \(0.554602\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 25.8826i | − | 1.46297i | −0.681857 | − | 0.731486i | \(-0.738827\pi\) | ||
0.681857 | − | 0.731486i | \(-0.261173\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 42.6727i | − | 2.40433i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.1795 | −1.07723 | −0.538613 | − | 0.842553i | \(-0.681052\pi\) | ||||
−0.538613 | + | 0.842553i | \(0.681052\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −33.1220 | −1.85448 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 43.0969i | − | 2.40543i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.71791i | − | 0.151228i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.37751 | 0.187350 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.8588 | −1.37470 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.1252 | 1.10954 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.77508 | −0.482322 | −0.241161 | − | 0.970485i | \(-0.577528\pi\) | ||||
−0.241161 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 51.5863 | 2.82691 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.7192 | 0.694926 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.2465i | 0.993952i | 0.867764 | + | 0.496976i | \(0.165556\pi\) | ||||
−0.867764 | + | 0.496976i | \(0.834444\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.4359i | 0.892677i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.2695i | 1.47673i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.9044 | −1.02074 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 30.6727i | 1.65136i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.9575 | 0.802961 | 0.401480 | − | 0.915868i | \(-0.368496\pi\) | ||||
0.401480 | + | 0.915868i | \(0.368496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 0.432682i | − | 0.0231609i | −0.999933 | − | 0.0115805i | \(-0.996314\pi\) | ||
0.999933 | − | 0.0115805i | \(-0.00368626\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 6.47894i | − | 0.345820i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 7.26390i | − | 0.386618i | −0.981138 | − | 0.193309i | \(-0.938078\pi\) | ||
0.981138 | − | 0.193309i | \(-0.0619220\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.0093 | −1.96425 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 20.5464i | − | 1.08743i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.6505i | 0.984333i | 0.870501 | + | 0.492167i | \(0.163795\pi\) | ||||
−0.870501 | + | 0.492167i | \(0.836205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 61.5398i | − | 3.23000i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 45.7712 | 2.39577 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.60750 | −0.0839110 | −0.0419555 | − | 0.999119i | \(-0.513359\pi\) | ||||
−0.0419555 | + | 0.999119i | \(0.513359\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 49.0719i | − | 2.55458i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.95422 | − | 16.5688i | 0.464880 | − | 0.860207i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.52528i | 0.0789761i | 0.999220 | + | 0.0394881i | \(0.0125727\pi\) | ||||
−0.999220 | + | 0.0394881i | \(0.987427\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.85059 | 0.508682 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.10795 | −0.263073 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.62205i | 0.0833194i | 0.999132 | + | 0.0416597i | \(0.0132645\pi\) | ||||
−0.999132 | + | 0.0416597i | \(0.986735\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 62.7327 | 3.21390 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 14.6255i | − | 0.747327i | −0.927564 | − | 0.373663i | \(-0.878102\pi\) | ||
0.927564 | − | 0.373663i | \(-0.121898\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 43.6200i | − | 2.22308i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −55.0057 | −2.79610 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 8.86911i | − | 0.449682i | −0.974396 | − | 0.224841i | \(-0.927814\pi\) | ||
0.974396 | − | 0.224841i | \(-0.0721862\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.58001i | 0.484482i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 58.4816i | − | 2.95001i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.1543 | −1.31597 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.58643i | − | 0.179998i | −0.995942 | − | 0.0899988i | \(-0.971314\pi\) | ||
0.995942 | − | 0.0899988i | \(-0.0286863\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.55964 | −0.378455 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.9600i | 1.74582i | 0.487881 | + | 0.872910i | \(0.337770\pi\) | ||||
−0.487881 | + | 0.872910i | \(0.662230\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.20540i | 0.209486i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.0823i | 0.749447i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 52.7315 | 2.61380 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.1962 | 1.24587 | 0.622935 | − | 0.782273i | \(-0.285940\pi\) | ||||
0.622935 | + | 0.782273i | \(0.285940\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 39.3038 | 1.93871 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.5578 | 1.35603 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.7022 | 1.26167 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.4177 | 0.657068 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 18.9135i | − | 0.923984i | −0.886884 | − | 0.461992i | \(-0.847135\pi\) | ||
0.886884 | − | 0.461992i | \(-0.152865\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.46033i | 0.266120i | 0.991108 | + | 0.133060i | \(0.0424803\pi\) | ||||
−0.991108 | + | 0.133060i | \(0.957520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −43.0913 | −2.09517 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.5129 | −0.509950 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.7110i | 0.615127i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 14.4476i | − | 0.697535i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.82835 | −0.232573 | −0.116287 | − | 0.993216i | \(-0.537099\pi\) | ||||
−0.116287 | + | 0.993216i | \(0.537099\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.2901 | −1.40759 | −0.703796 | − | 0.710402i | \(-0.748513\pi\) | ||||
−0.703796 | + | 0.710402i | \(0.748513\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 50.9048 | 2.44070 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.52478 | 0.168613 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.47016 | −0.404259 | −0.202129 | − | 0.979359i | \(-0.564786\pi\) | ||||
−0.202129 | + | 0.979359i | \(0.564786\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.70339 | 0.0811139 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 3.83398i | − | 0.182158i | −0.995844 | − | 0.0910789i | \(-0.970968\pi\) | ||
0.995844 | − | 0.0910789i | \(-0.0290316\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 41.6986i | 1.97670i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 5.46997i | − | 0.258721i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.02046 | 0.142544 | 0.0712721 | − | 0.997457i | \(-0.477294\pi\) | ||||
0.0712721 | + | 0.997457i | \(0.477294\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 50.1612i | − | 2.36200i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.8469 | 0.838522 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 6.72691i | − | 0.315362i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.32553i | − | 0.202340i | −0.994869 | − | 0.101170i | \(-0.967741\pi\) | ||
0.994869 | − | 0.101170i | \(-0.0322586\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.1665i | 0.941290i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.4438 | −1.04531 | −0.522657 | − | 0.852543i | \(-0.675059\pi\) | ||||
−0.522657 | + | 0.852543i | \(0.675059\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.2974i | − | 1.17567i | −0.808981 | − | 0.587835i | \(-0.799981\pi\) | ||
0.808981 | − | 0.587835i | \(-0.200019\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 41.9101i | − | 1.94353i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.6679 | 0.586199 | 0.293099 | − | 0.956082i | \(-0.405313\pi\) | ||||
0.293099 | + | 0.956082i | \(0.405313\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 11.0495i | − | 0.510217i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −51.8792 | −2.39047 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −56.2268 | −2.58531 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.86801i | 0.177477i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.1724 | + | 35.4764i | −0.877845 | + | 1.62435i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 2.71881i | − | 0.124225i | −0.998069 | − | 0.0621127i | \(-0.980216\pi\) | ||
0.998069 | − | 0.0621127i | \(-0.0197838\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.13205 | 0.370790 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 26.6460 | 1.21244 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 52.2443i | 2.37229i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.5719 | −0.841571 | −0.420786 | − | 0.907160i | \(-0.638246\pi\) | ||||
−0.420786 | + | 0.907160i | \(0.638246\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 68.7717i | − | 3.10996i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.989061i | 0.0446357i | 0.999751 | + | 0.0223178i | \(0.00710458\pi\) | ||||
−0.999751 | + | 0.0223178i | \(0.992895\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.8991 | 0.716059 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 93.3974i | 4.19790i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.1508i | 1.44216i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.66523i | 0.119312i | 0.998219 | + | 0.0596560i | \(0.0190004\pi\) | ||||
−0.998219 | + | 0.0596560i | \(0.981000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.88239 | −0.396836 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 0.147697i | − | 0.00658547i | −0.999995 | − | 0.00329273i | \(-0.998952\pi\) | ||
0.999995 | − | 0.00329273i | \(-0.00104811\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.9362 | −0.709152 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.7603i | 1.58817i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.9681i | 1.46129i | 0.682760 | + | 0.730643i | \(0.260780\pi\) | ||||
−0.682760 | + | 0.730643i | \(0.739220\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 39.7624i | − | 1.75898i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.41985 | 0.327595 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −54.1340 | −2.38543 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −44.0479 | −1.93723 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −60.7277 | −2.66565 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.1515 | −1.18953 | −0.594764 | − | 0.803900i | \(-0.702755\pi\) | ||||
−0.594764 | + | 0.803900i | \(0.702755\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.3372 | 1.50146 | 0.750730 | − | 0.660609i | \(-0.229702\pi\) | ||||
0.750730 | + | 0.660609i | \(0.229702\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 29.2408i | 1.27617i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 13.0898i | − | 0.570200i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.5759 | 0.459824 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −59.0056 | −2.56063 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 7.73567i | − | 0.335069i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.9189i | 1.89878i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.5209 | −1.18762 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.74121 | 0.0749990 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.2077 | −1.25574 | −0.627869 | − | 0.778319i | \(-0.716073\pi\) | ||||
−0.627869 | + | 0.778319i | \(0.716073\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.1712 | 1.16603 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.3330 | 1.08515 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.0988080 | −0.00422472 | −0.00211236 | − | 0.999998i | \(-0.500672\pi\) | ||||
−0.00211236 | + | 0.999998i | \(0.500672\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 27.2162i | − | 1.16156i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 5.84976i | − | 0.249208i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.7208i | 0.966186i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −81.0423 | −3.44006 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.3316i | 0.564878i | 0.959285 | + | 0.282439i | \(0.0911434\pi\) | ||||
−0.959285 | + | 0.282439i | \(0.908857\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.67108 | −0.366748 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.9697i | 1.89862i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.76092i | 0.158504i | 0.996855 | + | 0.0792518i | \(0.0252531\pi\) | ||||
−0.996855 | + | 0.0792518i | \(0.974747\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 16.7494i | − | 0.704654i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.1023 | 0.550247 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.80431i | 0.201407i | 0.994916 | + | 0.100704i | \(0.0321094\pi\) | ||||
−0.994916 | + | 0.100704i | \(0.967891\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.1843i | 1.05393i | 0.849887 | + | 0.526966i | \(0.176670\pi\) | ||||
−0.849887 | + | 0.526966i | \(0.823330\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −33.3195 | −1.39194 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 13.6339i | − | 0.568572i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.2955 | 1.63589 | 0.817946 | − | 0.575294i | \(-0.195112\pi\) | ||||
0.817946 | + | 0.575294i | \(0.195112\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 57.6613 | 2.39632 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 22.3280i | − | 0.926322i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.5980 | + | 36.2639i | −0.811668 | + | 1.50190i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.4034i | 0.595507i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.4168 | −1.09034 | −0.545169 | − | 0.838326i | \(-0.683535\pi\) | ||||
−0.545169 | + | 0.838326i | \(0.683535\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.81613 | −0.198445 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 9.89162i | − | 0.406887i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.0602 | 1.39868 | 0.699342 | − | 0.714787i | \(-0.253476\pi\) | ||||
0.699342 | + | 0.714787i | \(0.253476\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.9383i | 0.858386i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 51.5824i | 2.11113i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.59920 | 0.351354 | 0.175677 | − | 0.984448i | \(-0.443789\pi\) | ||||
0.175677 | + | 0.984448i | \(0.443789\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.8138i | 1.17534i | 0.809101 | + | 0.587670i | \(0.199955\pi\) | ||||
−0.809101 | + | 0.587670i | \(0.800045\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.6587i | 0.963457i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 62.7136i | 2.54967i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.0936573 | 0.00380143 | 0.00190072 | − | 0.999998i | \(-0.499395\pi\) | ||||
0.00190072 | + | 0.999998i | \(0.499395\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 44.2221i | − | 1.79197i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.79290 | −0.274812 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 39.7266i | − | 1.60454i | −0.596959 | − | 0.802272i | \(-0.703625\pi\) | ||
0.596959 | − | 0.802272i | \(-0.296375\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 77.0921i | 3.10865i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.5087i | 0.664614i | 0.943171 | + | 0.332307i | \(0.107827\pi\) | ||||
−0.943171 | + | 0.332307i | \(0.892173\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.6618 | −0.508920 | −0.254460 | − | 0.967083i | \(-0.581898\pi\) | ||||
−0.254460 | + | 0.967083i | \(0.581898\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.1533 | −1.04950 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.2244 | 1.45130 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.3785 | −1.17514 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.5457 | 0.660773 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.3120 | −1.00925 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.0876i | 1.31720i | 0.752495 | + | 0.658598i | \(0.228850\pi\) | ||||
−0.752495 | + | 0.658598i | \(0.771150\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 0.0489865i | − | 0.00194704i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −63.9293 | −2.53696 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.268522 | 0.0106392 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 68.8400i | − | 2.72327i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.8134i | 0.664091i | 0.943263 | + | 0.332046i | \(0.107739\pi\) | ||||
−0.943263 | + | 0.332046i | \(0.892261\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.2951 | 0.603179 | 0.301589 | − | 0.953438i | \(-0.402483\pi\) | ||||
0.301589 | + | 0.953438i | \(0.402483\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 86.4142 | 3.40256 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.9648 | 1.25667 | 0.628333 | − | 0.777944i | \(-0.283737\pi\) | ||||
0.628333 | + | 0.777944i | \(0.283737\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −60.3155 | −2.36759 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.4082 | −1.42695 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.95730 | 0.389659 | 0.194830 | − | 0.980837i | \(-0.437585\pi\) | ||||
0.194830 | + | 0.980837i | \(0.437585\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 59.5971i | 2.32865i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 85.1377i | 3.32154i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.5258i | 1.15016i | 0.818097 | + | 0.575081i | \(0.195029\pi\) | ||||
−0.818097 | + | 0.575081i | \(0.804971\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.51958 | −0.0591048 | −0.0295524 | − | 0.999563i | \(-0.509408\pi\) | ||||
−0.0295524 | + | 0.999563i | \(0.509408\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.93506i | 0.269335i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.70383 | 0.298742 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.6191i | 0.798375i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 42.3299i | 1.63657i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 27.8204i | − | 1.07400i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.2225 | 0.933710 | 0.466855 | − | 0.884334i | \(-0.345387\pi\) | ||||
0.466855 | + | 0.884334i | \(0.345387\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 28.7001i | − | 1.10467i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.79160i | 0.299455i | 0.988727 | + | 0.149728i | \(0.0478397\pi\) | ||||
−0.988727 | + | 0.149728i | \(0.952160\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45.3858 | 1.74175 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 78.2993i | − | 3.00044i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.3274 | −1.04565 | −0.522827 | − | 0.852439i | \(-0.675123\pi\) | ||||
−0.522827 | + | 0.852439i | \(0.675123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −40.0535 | −1.53037 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 18.4432i | − | 0.703650i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.02234 | + | 5.59248i | −0.115142 | + | 0.213057i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 44.6616i | − | 1.69901i | −0.527582 | − | 0.849504i | \(-0.676901\pi\) | ||
0.527582 | − | 0.849504i | \(-0.323099\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 81.1363 | 3.08211 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.6736 | −0.518671 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0782i | 0.912027i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −50.2526 | −1.90073 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.84731i | 0.334158i | 0.985943 | + | 0.167079i | \(0.0534336\pi\) | ||||
−0.985943 | + | 0.167079i | \(0.946566\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.31304i | 0.351248i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 67.6967 | 2.54960 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.8441i | 0.520662i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 5.15654i | − | 0.193658i | −0.995301 | − | 0.0968289i | \(-0.969130\pi\) | ||
0.995301 | − | 0.0968289i | \(-0.0308700\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 48.6489i | − | 1.82448i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.9758 | 0.635748 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.7231i | 0.550614i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 47.9034 | 1.78898 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 19.0114i | − | 0.709004i | −0.935055 | − | 0.354502i | \(-0.884650\pi\) | ||
0.935055 | − | 0.354502i | \(-0.115350\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.0273i | 1.75139i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.18050i | 0.155474i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.6269 | −0.840344 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.9647 | 0.666274 | 0.333137 | − | 0.942879i | \(-0.391893\pi\) | ||||
0.333137 | + | 0.942879i | \(0.391893\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 36.9923 | 1.37008 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.9898 | 0.998252 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.1881 | −1.37358 | −0.686788 | − | 0.726858i | \(-0.740980\pi\) | ||||
−0.686788 | + | 0.726858i | \(0.740980\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.67604 | −0.0987071 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.1839i | 0.890825i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 27.4155i | − | 1.00850i | −0.863559 | − | 0.504248i | \(-0.831770\pi\) | ||
0.863559 | − | 0.504248i | \(-0.168230\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.55162 | 0.0937361 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.06951 | −0.0759230 | −0.0379615 | − | 0.999279i | \(-0.512086\pi\) | ||||
−0.0379615 | + | 0.999279i | \(0.512086\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.57430i | 0.204227i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 47.8079i | 1.74920i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38.1533 | 1.39409 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.1874 | 1.90435 | 0.952173 | − | 0.305561i | \(-0.0988440\pi\) | ||||
0.952173 | + | 0.305561i | \(0.0988440\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 63.7250 | 2.32227 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.1874 | −0.661906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.9213 | −0.651360 | −0.325680 | − | 0.945480i | \(-0.605593\pi\) | ||||
−0.325680 | + | 0.945480i | \(0.605593\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −58.3200 | −2.11688 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.2321i | 0.515912i | 0.966157 | + | 0.257956i | \(0.0830489\pi\) | ||||
−0.966157 | + | 0.257956i | \(0.916951\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 22.0073i | − | 0.796718i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 44.8323i | − | 1.62091i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.30163 | −0.335862 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 38.0329i | − | 1.37150i | −0.727836 | − | 0.685751i | \(-0.759474\pi\) | ||
0.727836 | − | 0.685751i | \(-0.240526\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −56.8673 | −2.04802 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.06510i | 0.0742766i | 0.999310 | + | 0.0371383i | \(0.0118242\pi\) | ||||
−0.999310 | + | 0.0371383i | \(0.988176\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.6289i | 0.669168i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 70.4032i | 2.52570i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.85910 | 0.317410 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 70.3682i | − | 2.51797i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 43.4044i | 1.55115i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 52.8687 | 1.88697 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 0.607130i | − | 0.0216418i | −0.999941 | − | 0.0108209i | \(-0.996556\pi\) | ||
0.999941 | − | 0.0108209i | \(-0.00344447\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −85.6508 | −3.04925 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.5506 | −0.517359 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.29036i | − | 0.152355i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 30.1200 | − | 55.7335i | 1.06824 | − | 1.97666i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.6605i | 0.448457i | 0.974537 | + | 0.224228i | \(0.0719861\pi\) | ||||
−0.974537 | + | 0.224228i | \(0.928014\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.1437 | 0.748011 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −77.5624 | −2.74053 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 87.0277i | 3.07114i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.1543 | −0.957063 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 66.0215i | 2.32407i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.2797i | 0.853629i | 0.904339 | + | 0.426815i | \(0.140364\pi\) | ||||
−0.904339 | + | 0.426815i | \(0.859636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.0449 | 1.23059 | 0.615296 | − | 0.788296i | \(-0.289036\pi\) | ||||
0.615296 | + | 0.788296i | \(0.289036\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 22.7398i | − | 0.797519i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 70.0835i | 2.45492i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 9.93035i | − | 0.347419i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.5125 | 0.437223 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.54165i | 0.158505i | 0.996855 | + | 0.0792523i | \(0.0252533\pi\) | ||||
−0.996855 | + | 0.0792523i | \(0.974747\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.6886 | −0.860592 | −0.430296 | − | 0.902688i | \(-0.641591\pi\) | ||||
−0.430296 | + | 0.902688i | \(0.641591\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 63.9991i | − | 2.22816i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.2861i | − | 0.601096i | −0.953767 | − | 0.300548i | \(-0.902830\pi\) | ||
0.953767 | − | 0.300548i | \(-0.0971695\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.94233i | − | 0.310580i | −0.987869 | − | 0.155290i | \(-0.950369\pi\) | ||
0.987869 | − | 0.155290i | \(-0.0496312\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.7471 | 0.858467 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.835807 | −0.0289590 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.05182 | 0.313251 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 35.7350 | 1.23518 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.5160 | −1.15710 | −0.578550 | − | 0.815647i | \(-0.696381\pi\) | ||||
−0.578550 | + | 0.815647i | \(0.696381\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.21971 | 0.179990 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 47.2144i | 1.62615i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 36.4424i | − | 1.25366i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 54.4807 | 1.87198 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −38.4924 | −1.32106 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 32.8264i | − | 1.12527i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.2734i | 0.488713i | 0.969685 | + | 0.244356i | \(0.0785767\pi\) | ||||
−0.969685 | + | 0.244356i | \(0.921423\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.4951 | −0.564122 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.9870 | −0.375307 | −0.187654 | − | 0.982235i | \(-0.560088\pi\) | ||||
−0.187654 | + | 0.982235i | \(0.560088\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.00168 | −0.0682964 | −0.0341482 | − | 0.999417i | \(-0.510872\pi\) | ||||
−0.0341482 | + | 0.999417i | \(0.510872\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 66.9716 | 2.28238 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.1696 | 1.06102 | 0.530512 | − | 0.847677i | \(-0.322000\pi\) | ||||
0.530512 | + | 0.847677i | \(0.322000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 61.8860 | 2.10419 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.0909i | 0.954017i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 49.7288i | − | 1.68694i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.72955i | 0.126371i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −97.1783 | −3.28899 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.72065i | 0.294812i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.8240 | −0.500571 | −0.250285 | − | 0.968172i | \(-0.580524\pi\) | ||||
−0.250285 | + | 0.968172i | \(0.580524\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 6.41836i | − | 0.216486i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.61644i | − | 0.121841i | −0.998143 | − | 0.0609204i | \(-0.980596\pi\) | ||
0.998143 | − | 0.0609204i | \(-0.0194036\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 25.4476i | − | 0.856381i | −0.903689 | − | 0.428190i | \(-0.859151\pi\) | ||
0.903689 | − | 0.428190i | \(-0.140849\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 92.6981 | 3.11601 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.30599i | 0.0438507i | 0.999760 | + | 0.0219254i | \(0.00697962\pi\) | ||||
−0.999760 | + | 0.0219254i | \(0.993020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 55.5368i | 1.86264i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.6770 | −0.960717 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 7.77941i | − | 0.260328i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.0459 | 0.937470 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.99389 | −0.300297 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 28.1732i | − | 0.939629i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.40737 | − | 17.4073i | 0.313405 | − | 0.579920i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 75.0698i | − | 2.49817i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.6895 | −0.920429 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.9488 | −1.02764 | −0.513820 | − | 0.857898i | \(-0.671770\pi\) | ||||
−0.513820 | + | 0.857898i | \(0.671770\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 29.6425i | − | 0.983180i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.79189 | −0.0924995 | −0.0462497 | − | 0.998930i | \(-0.514727\pi\) | ||||
−0.0462497 | + | 0.998930i | \(0.514727\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.8692i | 1.61733i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 42.7568i | 1.41350i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 51.7733 | 1.70970 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.8280i | 1.04991i | 0.851130 | + | 0.524954i | \(0.175918\pi\) | ||||
−0.851130 | + | 0.524954i | \(0.824082\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 6.57420i | − | 0.216627i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 10.8519i | − | 0.357195i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.0229 | 1.18443 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 100.693i | − | 3.30720i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.3188 | 1.25720 | 0.628600 | − | 0.777729i | \(-0.283628\pi\) | ||||
0.628600 | + | 0.777729i | \(0.283628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.307519i | 0.0100785i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.5933i | 0.575978i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 45.8275i | − | 1.49872i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.1830 | 1.67208 | 0.836038 | − | 0.548672i | \(-0.184866\pi\) | ||||
0.836038 | + | 0.548672i | \(0.184866\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −75.6337 | −2.46821 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.87662 | 0.0611759 | 0.0305880 | − | 0.999532i | \(-0.490262\pi\) | ||||
0.0305880 | + | 0.999532i | \(0.490262\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.2264 | −1.01687 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −57.1613 | −1.85946 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.86890 | 0.158218 | 0.0791090 | − | 0.996866i | \(-0.474792\pi\) | ||||
0.0791090 | + | 0.996866i | \(0.474792\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.4211i | 0.435667i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 56.0459i | 1.81741i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.45162 | −0.306168 | −0.153084 | − | 0.988213i | \(-0.548920\pi\) | ||||
−0.153084 | + | 0.988213i | \(0.548920\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33.9551 | 1.09876 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 96.7886i | 3.12873i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34.7953i | 1.12360i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.80488 | 0.251770 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −81.6923 | −2.63250 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −58.7612 | −1.89159 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.39579 | −0.141359 | −0.0706796 | − | 0.997499i | \(-0.522517\pi\) | ||||
−0.0706796 | + | 0.997499i | \(0.522517\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.94222 | −0.255141 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.0827 | 1.83187 | 0.915935 | − | 0.401326i | \(-0.131450\pi\) | ||||
0.915935 | + | 0.401326i | \(0.131450\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.8786i | 0.380810i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 9.86969i | − | 0.316083i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.1020i | 1.21899i | 0.792790 | + | 0.609495i | \(0.208628\pi\) | ||||
−0.792790 | + | 0.609495i | \(0.791372\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −79.2842 | −2.53393 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.1212i | 1.50446i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −58.2692 | −1.85850 | −0.929250 | − | 0.369452i | \(-0.879546\pi\) | ||||
−0.929250 | + | 0.369452i | \(0.879546\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.0803i | 0.321185i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 58.8095i | − | 1.87193i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35.0023i | 1.11301i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.404629 | −0.0128535 | −0.00642673 | − | 0.999979i | \(-0.502046\pi\) | ||||
−0.00642673 | + | 0.999979i | \(0.502046\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.6424i | 0.813737i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 52.5663i | − | 1.66647i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.5759 | 1.06336 | 0.531679 | − | 0.846946i | \(-0.321561\pi\) | ||||
0.531679 | + | 0.846946i | \(0.321561\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 69.1014i | − | 2.18627i |
(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 | 4028.2.c.a.3497.7 | ✓ | 82 | |
53.52 | even | 2 | inner | 4028.2.c.a.3497.76 | yes | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.c.a.3497.7 | ✓ | 82 | 1.1 | even | 1 | trivial | |
4028.2.c.a.3497.76 | yes | 82 | 53.52 | even | 2 | inner |