Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1749,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.1749");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.c (of order \(2\), degree \(1\), not 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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1749.3 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1749 |
Dual form | 1900.2.c.e.1749.2 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.732051i | 0.422650i | 0.977416 | + | 0.211325i | \(0.0677778\pi\) | ||||
−0.977416 | + | 0.211325i | \(0.932222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.46410 | 0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410 | 1.04447 | 0.522233 | − | 0.852803i | \(-0.325099\pi\) | ||||
0.522233 | + | 0.852803i | \(0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.732051i | − 0.203034i | −0.994834 | − | 0.101517i | \(-0.967630\pi\) | ||||
0.994834 | − | 0.101517i | \(-0.0323697\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410i | 0.840168i | 0.907485 | + | 0.420084i | \(0.137999\pi\) | ||||
−0.907485 | + | 0.420084i | \(0.862001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.46410 | −0.319493 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 3.46410i | − 0.722315i | −0.932505 | − | 0.361158i | \(-0.882382\pi\) | ||||
0.932505 | − | 0.361158i | \(-0.117618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.46410 | 0.643268 | 0.321634 | − | 0.946864i | \(-0.395768\pi\) | ||||
0.321634 | + | 0.946864i | \(0.395768\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46410 | 0.981382 | 0.490691 | − | 0.871334i | \(-0.336744\pi\) | ||||
0.490691 | + | 0.871334i | \(0.336744\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.53590i | 0.441443i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.26795i | 0.537248i | 0.963245 | + | 0.268624i | \(0.0865688\pi\) | ||||
−0.963245 | + | 0.268624i | \(0.913431\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.535898 | 0.0858124 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.92820i | − 1.36154i | −0.732498 | − | 0.680769i | \(-0.761646\pi\) | ||||
0.732498 | − | 0.680769i | \(-0.238354\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 0.928203i | − 0.135392i | −0.997706 | − | 0.0676962i | \(-0.978435\pi\) | ||||
0.997706 | − | 0.0676962i | \(-0.0215649\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.53590 | −0.355097 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.26795i | 0.998330i | 0.866507 | + | 0.499165i | \(0.166360\pi\) | ||||
−0.866507 | + | 0.499165i | \(0.833640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 0.732051i | − 0.0969625i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.92820 | 0.901975 | 0.450988 | − | 0.892530i | \(-0.351072\pi\) | ||||
0.450988 | + | 0.892530i | \(0.351072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.39230 | −1.07452 | −0.537262 | − | 0.843415i | \(-0.680541\pi\) | ||||
−0.537262 | + | 0.843415i | \(0.680541\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.92820i | 0.620895i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.26795i | 0.399244i | 0.979873 | + | 0.199622i | \(0.0639713\pi\) | ||||
−0.979873 | + | 0.199622i | \(0.936029\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.53590 | 0.305286 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.46410 | −1.12318 | −0.561591 | − | 0.827415i | \(-0.689811\pi\) | ||||
−0.561591 | + | 0.827415i | \(0.689811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.46410i | 0.873607i | 0.899557 | + | 0.436804i | \(0.143889\pi\) | ||||
−0.899557 | + | 0.436804i | \(0.856111\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.92820i | 0.789542i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9282 | 1.22952 | 0.614759 | − | 0.788715i | \(-0.289253\pi\) | ||||
0.614759 | + | 0.788715i | \(0.289253\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.46410i | 0.380235i | 0.981761 | + | 0.190117i | \(0.0608868\pi\) | ||||
−0.981761 | + | 0.190117i | \(0.939113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.53590i | 0.271877i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.53590 | 0.904803 | 0.452402 | − | 0.891814i | \(-0.350567\pi\) | ||||
0.452402 | + | 0.891814i | \(0.350567\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.46410 | 0.153480 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000i | 0.414781i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.5885i | 1.48123i | 0.671928 | + | 0.740617i | \(0.265467\pi\) | ||||
−0.671928 | + | 0.740617i | \(0.734533\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.53590 | 0.857890 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.39230 | 0.437051 | 0.218525 | − | 0.975831i | \(-0.429875\pi\) | ||||
0.218525 | + | 0.975831i | \(0.429875\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.66025i | 0.360656i | 0.983607 | + | 0.180328i | \(0.0577158\pi\) | ||||
−0.983607 | + | 0.180328i | \(0.942284\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.6603i | 1.12724i | 0.826034 | + | 0.563620i | \(0.190592\pi\) | ||||
−0.826034 | + | 0.563620i | \(0.809408\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.39230 | −0.612272 | −0.306136 | − | 0.951988i | \(-0.599036\pi\) | ||||
−0.306136 | + | 0.951988i | \(0.599036\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.39230 | −0.227068 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.5885i | 1.74865i | 0.485336 | + | 0.874327i | \(0.338697\pi\) | ||||
−0.485336 | + | 0.874327i | \(0.661303\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1.80385i | − 0.166766i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.92820 | −0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 4.39230i | − 0.396041i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 10.5885i | − 0.939574i | −0.882780 | − | 0.469787i | \(-0.844331\pi\) | ||||
0.882780 | − | 0.469787i | \(-0.155669\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.53590 | 0.575454 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.07180 | −0.443125 | −0.221562 | − | 0.975146i | \(-0.571116\pi\) | ||||
−0.221562 | + | 0.975146i | \(0.571116\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.00000i | − 0.173422i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 17.3205i | − 1.47979i | −0.672722 | − | 0.739895i | \(-0.734875\pi\) | ||||
0.672722 | − | 0.739895i | \(-0.265125\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.53590 | −0.384730 | −0.192365 | − | 0.981323i | \(-0.561616\pi\) | ||||
−0.192365 | + | 0.981323i | \(0.561616\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.679492 | 0.0572235 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 2.53590i | − 0.212062i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.19615i | 0.181136i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.3923 | −1.34291 | −0.671455 | − | 0.741045i | \(-0.734330\pi\) | ||||
−0.671455 | + | 0.741045i | \(0.734330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3923 | 1.00847 | 0.504236 | − | 0.863566i | \(-0.331774\pi\) | ||||
0.504236 | + | 0.863566i | \(0.331774\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.53590i | 0.690086i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.5359i | 1.31971i | 0.751394 | + | 0.659854i | \(0.229382\pi\) | ||||
−0.751394 | + | 0.659854i | \(0.770618\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.32051 | −0.421944 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820 | 0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 20.9282i | − 1.63922i | −0.572919 | − | 0.819612i | \(-0.694189\pi\) | ||||
0.572919 | − | 0.819612i | \(-0.305811\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 7.26795i | − 0.562411i | −0.959648 | − | 0.281205i | \(-0.909266\pi\) | ||||
0.959648 | − | 0.281205i | \(-0.0907342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4641 | 0.958777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.46410 | −0.188435 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 14.1962i | − 1.07931i | −0.841885 | − | 0.539657i | \(-0.818554\pi\) | ||||
0.841885 | − | 0.539657i | \(-0.181446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.07180i | 0.381220i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.7846 | 1.55351 | 0.776757 | − | 0.629800i | \(-0.216863\pi\) | ||||
0.776757 | + | 0.629800i | \(0.216863\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 6.14359i | − 0.454148i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0000i | 0.877527i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.00000 | −0.581914 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.92820 | −0.501307 | −0.250654 | − | 0.968077i | \(-0.580646\pi\) | ||||
−0.250654 | + | 0.968077i | \(0.580646\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.1962i | 1.30979i | 0.755721 | + | 0.654894i | \(0.227287\pi\) | ||||
−0.755721 | + | 0.654894i | \(0.772713\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 12.9282i | − 0.921096i | −0.887635 | − | 0.460548i | \(-0.847653\pi\) | ||||
0.887635 | − | 0.460548i | \(-0.152347\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.0718 | −0.926635 | −0.463318 | − | 0.886192i | \(-0.653341\pi\) | ||||
−0.463318 | + | 0.886192i | \(0.653341\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.39230 | −0.168740 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.92820i | 0.486265i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 8.53590i | − 0.593286i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.46410 | −0.239617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.3205 | −1.05471 | −0.527354 | − | 0.849646i | \(-0.676816\pi\) | ||||
−0.527354 | + | 0.849646i | \(0.676816\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 6.92820i | − 0.474713i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.9282i | 0.741855i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.46410 | −0.369230 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.53590 | 0.170583 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 7.66025i | − 0.512969i | −0.966548 | − | 0.256484i | \(-0.917436\pi\) | ||||
0.966548 | − | 0.256484i | \(-0.0825642\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2.19615i | − 0.145764i | −0.997341 | − | 0.0728819i | \(-0.976780\pi\) | ||||
0.997341 | − | 0.0728819i | \(-0.0232196\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5359 | −0.696232 | −0.348116 | − | 0.937452i | \(-0.613178\pi\) | ||||
−0.348116 | + | 0.937452i | \(0.613178\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.07180 | −0.333700 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 12.9282i | − 0.846955i | −0.905907 | − | 0.423477i | \(-0.860809\pi\) | ||||
0.905907 | − | 0.423477i | \(-0.139191\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.00000i | 0.519656i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.8564 | −0.896296 | −0.448148 | − | 0.893959i | \(-0.647916\pi\) | ||||
−0.448148 | + | 0.893959i | \(0.647916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.8564 | 1.02140 | 0.510700 | − | 0.859759i | \(-0.329386\pi\) | ||||
0.510700 | + | 0.859759i | \(0.329386\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2679i | 0.979439i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.732051i | 0.0465793i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.53590 | −0.160706 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 12.0000i | − 0.754434i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.12436i | 0.569162i | 0.958652 | + | 0.284581i | \(0.0918544\pi\) | ||||
−0.958652 | + | 0.284581i | \(0.908146\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.53590 | −0.406121 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.53590 | 0.528359 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 15.4641i | − 0.953557i | −0.879023 | − | 0.476779i | \(-0.841804\pi\) | ||||
0.879023 | − | 0.476779i | \(-0.158196\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.24871i | 0.382415i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.3923 | 0.633630 | 0.316815 | − | 0.948487i | \(-0.397387\pi\) | ||||
0.316815 | + | 0.948487i | \(0.397387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.3923 | 1.11725 | 0.558626 | − | 0.829419i | \(-0.311329\pi\) | ||||
0.558626 | + | 0.829419i | \(0.311329\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.07180i | 0.0648681i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.39230i | − 0.143740i | −0.997414 | − | 0.0718698i | \(-0.977103\pi\) | ||||
0.997414 | − | 0.0718698i | \(-0.0228966\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.4641 | 0.806075 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.9282 | −0.771232 | −0.385616 | − | 0.922659i | \(-0.626011\pi\) | ||||
−0.385616 | + | 0.922659i | \(0.626011\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.39230i | 0.142208i | 0.997469 | + | 0.0711039i | \(0.0226522\pi\) | ||||
−0.997469 | + | 0.0711039i | \(0.977348\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 12.0000i | − 0.708338i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.6795 | −0.626043 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 11.6603i | − 0.681199i | −0.940208 | − | 0.340600i | \(-0.889370\pi\) | ||||
0.940208 | − | 0.340600i | \(-0.110630\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.8564i | 0.804030i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.53590 | −0.146655 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.8564 | 1.02923 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.21539i | 0.184719i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 18.1962i | − 1.03851i | −0.854620 | − | 0.519255i | \(-0.826210\pi\) | ||||
0.854620 | − | 0.519255i | \(-0.173790\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.67949 | −0.152431 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.3923 | −1.26975 | −0.634876 | − | 0.772614i | \(-0.718949\pi\) | ||||
−0.634876 | + | 0.772614i | \(0.718949\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.7846i | 1.74005i | 0.493008 | + | 0.870025i | \(0.335897\pi\) | ||||
−0.493008 | + | 0.870025i | \(0.664103\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 21.1244i | − 1.18646i | −0.805032 | − | 0.593231i | \(-0.797852\pi\) | ||||
0.805032 | − | 0.593231i | \(-0.202148\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.53590 | −0.476427 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3.46410i | − 0.192748i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 4.67949i | − 0.258776i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.85641 | 0.102347 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.2487 | 1.44276 | 0.721380 | − | 0.692540i | \(-0.243508\pi\) | ||||
0.721380 | + | 0.692540i | \(0.243508\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.05256i | 0.441278i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 20.7321i | − 1.12935i | −0.825314 | − | 0.564673i | \(-0.809002\pi\) | ||||
0.825314 | − | 0.564673i | \(-0.190998\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.6077 | −0.739069 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.9282 | 1.02502 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 31.1769i | − 1.67366i | −0.547459 | − | 0.836832i | \(-0.684405\pi\) | ||||
0.547459 | − | 0.836832i | \(-0.315595\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.07180 | −0.378545 | −0.189272 | − | 0.981925i | \(-0.560613\pi\) | ||||
−0.189272 | + | 0.981925i | \(0.560613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.92820 | 0.156296 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 22.3923i | − 1.19182i | −0.803050 | − | 0.595911i | \(-0.796791\pi\) | ||||
0.803050 | − | 0.595911i | \(-0.203209\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 5.07180i | − 0.268428i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.4641 | 0.816164 | 0.408082 | − | 0.912945i | \(-0.366198\pi\) | ||||
0.408082 | + | 0.912945i | \(0.366198\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.732051i | 0.0384227i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 23.8564i | − 1.24529i | −0.782503 | − | 0.622647i | \(-0.786057\pi\) | ||||
0.782503 | − | 0.622647i | \(-0.213943\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.7846 | −0.769656 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.5359 | −0.754666 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 14.5885i | − 0.755362i | −0.925936 | − | 0.377681i | \(-0.876722\pi\) | ||||
0.925936 | − | 0.377681i | \(-0.123278\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2.53590i | − 0.130605i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.07180 | −0.0550545 | −0.0275273 | − | 0.999621i | \(-0.508763\pi\) | ||||
−0.0275273 | + | 0.999621i | \(0.508763\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.75129 | 0.397111 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 23.6603i | − 1.20898i | −0.796612 | − | 0.604491i | \(-0.793376\pi\) | ||||
0.796612 | − | 0.604491i | \(-0.206624\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 22.0000i | − 1.11832i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 3.71281i | − 0.187287i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 12.5359i | − 0.629159i | −0.949231 | − | 0.314579i | \(-0.898137\pi\) | ||||
0.949231 | − | 0.314579i | \(-0.101863\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.46410 | 0.0732968 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.78461 | −0.139057 | −0.0695284 | − | 0.997580i | \(-0.522149\pi\) | ||||
−0.0695284 | + | 0.997580i | \(0.522149\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 4.00000i | − 0.199254i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.3205i | 0.561137i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.39230 | −0.316079 | −0.158040 | − | 0.987433i | \(-0.550517\pi\) | ||||
−0.158040 | + | 0.987433i | \(0.550517\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.6795 | 0.625433 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.8564i | 0.681829i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 3.32051i | − 0.162606i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0000 | −1.65706 | −0.828529 | − | 0.559946i | \(-0.810822\pi\) | ||||
−0.828529 | + | 0.559946i | \(0.810822\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 2.28719i | − 0.111207i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 16.7846i | − 0.812264i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.85641 | 0.0896281 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.5359 | −1.27819 | −0.639095 | − | 0.769128i | \(-0.720691\pi\) | ||||
−0.639095 | + | 0.769128i | \(0.720691\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.6603i | 1.90595i | 0.303049 | + | 0.952975i | \(0.401996\pi\) | ||||
−0.303049 | + | 0.952975i | \(0.598004\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.46410i | 0.165710i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.7128 | −1.13175 | −0.565875 | − | 0.824491i | \(-0.691462\pi\) | ||||
−0.565875 | + | 0.824491i | \(0.691462\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.39230 | 0.352015 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 34.3923i | − 1.63403i | −0.576618 | − | 0.817014i | \(-0.695628\pi\) | ||||
0.576618 | − | 0.817014i | \(-0.304372\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 12.0000i | − 0.567581i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.46410 | −0.163481 | −0.0817405 | − | 0.996654i | \(-0.526048\pi\) | ||||
−0.0817405 | + | 0.996654i | \(0.526048\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.7846 | −0.978709 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.07180i | 0.426230i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 6.78461i | − 0.317371i | −0.987329 | − | 0.158685i | \(-0.949274\pi\) | ||||
0.987329 | − | 0.158685i | \(-0.0507255\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.8564 | −0.646762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.7128 | 1.57016 | 0.785081 | − | 0.619393i | \(-0.212621\pi\) | ||||
0.785081 | + | 0.619393i | \(0.212621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 11.4641i | − 0.532782i | −0.963865 | − | 0.266391i | \(-0.914169\pi\) | ||||
0.963865 | − | 0.266391i | \(-0.0858312\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.32051i | 0.246204i | 0.992394 | + | 0.123102i | \(0.0392842\pi\) | ||||
−0.992394 | + | 0.123102i | \(0.960716\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.53590 | −0.301800 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.1051 | −0.557774 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 30.9282i | − 1.42208i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.9090i | 0.819995i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.60770 | 0.0734575 | 0.0367287 | − | 0.999325i | \(-0.488306\pi\) | ||||
0.0367287 | + | 0.999325i | \(0.488306\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.39230 | 0.109080 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.07180i | 0.230775i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1.80385i | − 0.0817401i | −0.999164 | − | 0.0408701i | \(-0.986987\pi\) | ||||
0.999164 | − | 0.0408701i | \(-0.0130130\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.3205 | 0.692817 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.07180 | 0.228887 | 0.114443 | − | 0.993430i | \(-0.463492\pi\) | ||||
0.114443 | + | 0.993430i | \(0.463492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0000i | 0.540453i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 18.9282i | − 0.849046i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.5359 | −0.740248 | −0.370124 | − | 0.928982i | \(-0.620685\pi\) | ||||
−0.370124 | + | 0.928982i | \(0.620685\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.32051 | 0.237703 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 8.53590i | − 0.380597i | −0.981726 | − | 0.190298i | \(-0.939054\pi\) | ||||
0.981726 | − | 0.190298i | \(-0.0609456\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.12436i | 0.405227i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.3205 | −1.29961 | −0.649804 | − | 0.760102i | \(-0.725149\pi\) | ||||
−0.649804 | + | 0.760102i | \(0.725149\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.9282 | −0.660385 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 4.00000i | − 0.176604i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 3.21539i | − 0.141413i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.3923 | 0.456172 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.7846 | 1.17346 | 0.586728 | − | 0.809784i | \(-0.300416\pi\) | ||||
0.586728 | + | 0.809784i | \(0.300416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 35.3731i | − 1.54676i | −0.633945 | − | 0.773378i | \(-0.718565\pi\) | ||||
0.633945 | − | 0.773378i | \(-0.281435\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.9282i | 0.824525i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.0718 | 0.740853 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.39230i | 0.190252i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.2154i | 0.656593i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.3923 | 0.447628 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.1769 | 1.42639 | 0.713193 | − | 0.700967i | \(-0.247248\pi\) | ||||
0.713193 | + | 0.700967i | \(0.247248\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.2487i | 0.439814i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.26795i | 0.139727i | 0.997557 | + | 0.0698637i | \(0.0222564\pi\) | ||||
−0.997557 | + | 0.0698637i | \(0.977744\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.6795 | −0.882579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.46410 | −0.147576 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.8564i | 0.929429i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 29.3205i | − 1.24235i | −0.783672 | − | 0.621175i | \(-0.786656\pi\) | ||||
0.783672 | − | 0.621175i | \(-0.213344\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.53590 | −0.276439 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.78461 | −0.370887 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 33.8038i | − 1.42466i | −0.701844 | − | 0.712331i | \(-0.747639\pi\) | ||||
0.701844 | − | 0.712331i | \(-0.252361\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.92820i | 0.374949i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.32051 | −0.223047 | −0.111524 | − | 0.993762i | \(-0.535573\pi\) | ||||
−0.111524 | + | 0.993762i | \(0.535573\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.39230 | −0.100115 | −0.0500574 | − | 0.998746i | \(-0.515940\pi\) | ||||
−0.0500574 | + | 0.998746i | \(0.515940\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 5.07180i | − 0.211877i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.7846i | 1.44810i | 0.689746 | + | 0.724051i | \(0.257722\pi\) | ||||
−0.689746 | + | 0.724051i | \(0.742278\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.3205 | −0.553581 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.92820 | −0.287430 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.1769i | 1.04272i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 19.1769i | − 0.791516i | −0.918355 | − | 0.395758i | \(-0.870482\pi\) | ||||
0.918355 | − | 0.395758i | \(-0.129518\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.46410 | −0.225144 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.46410 | 0.389301 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 4.14359i | − 0.170157i | −0.996374 | − | 0.0850785i | \(-0.972886\pi\) | ||||
0.996374 | − | 0.0850785i | \(-0.0271141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 9.56922i | − 0.391642i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.7846 | −0.849236 | −0.424618 | − | 0.905373i | \(-0.639592\pi\) | ||||
−0.424618 | + | 0.905373i | \(0.639592\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.6410 | −1.82095 | −0.910473 | − | 0.413570i | \(-0.864282\pi\) | ||||
−0.910473 | + | 0.413570i | \(0.864282\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.05256i | 0.327926i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.9090i | 1.05161i | 0.850604 | + | 0.525806i | \(0.176236\pi\) | ||||
−0.850604 | + | 0.525806i | \(0.823764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.07180 | −0.205520 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.679492 | −0.0274893 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.3923i | 0.581300i | 0.956829 | + | 0.290650i | \(0.0938715\pi\) | ||||
−0.956829 | + | 0.290650i | \(0.906129\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.3923i | 0.901480i | 0.892655 | + | 0.450740i | \(0.148840\pi\) | ||||
−0.892655 | + | 0.450740i | \(0.851160\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.3923 | −0.739249 | −0.369625 | − | 0.929181i | \(-0.620514\pi\) | ||||
−0.369625 | + | 0.929181i | \(0.620514\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.8564 | 0.556038 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.0718i | 0.683967i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2.53590i | − 0.101274i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.3205 | −0.451378 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.53590 | 0.180571 | 0.0902856 | − | 0.995916i | \(-0.471222\pi\) | ||||
0.0902856 | + | 0.995916i | \(0.471222\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 11.2154i | − 0.445772i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.19615i | − 0.0870147i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.3205 | −0.922545 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.0718 | −0.437310 | −0.218655 | − | 0.975802i | \(-0.570167\pi\) | ||||
−0.218655 | + | 0.975802i | \(0.570167\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6.39230i | − 0.252088i | −0.992025 | − | 0.126044i | \(-0.959772\pi\) | ||||
0.992025 | − | 0.126044i | \(-0.0402280\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.53590i | 0.335581i | 0.985823 | + | 0.167790i | \(0.0536632\pi\) | ||||
−0.985823 | + | 0.167790i | \(0.946337\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | 0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | −0.313545 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 20.5359i | − 0.803632i | −0.915720 | − | 0.401816i | \(-0.868379\pi\) | ||||
0.915720 | − | 0.401816i | \(-0.131621\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.3923i | 0.717552i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.7846 | 1.27711 | 0.638554 | − | 0.769577i | \(-0.279533\pi\) | ||||
0.638554 | + | 0.769577i | \(0.279533\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.7846 | 1.81971 | 0.909855 | − | 0.414926i | \(-0.136193\pi\) | ||||
0.909855 | + | 0.414926i | \(0.136193\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.85641i | 0.0720969i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 12.0000i | − 0.464642i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.60770 | 0.216806 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.0718 | −1.12230 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.2679i | 1.82205i | 0.412356 | + | 0.911023i | \(0.364706\pi\) | ||||
−0.412356 | + | 0.911023i | \(0.635294\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 34.9808i | − 1.34442i | −0.740361 | − | 0.672210i | \(-0.765345\pi\) | ||||
0.740361 | − | 0.672210i | \(-0.234655\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.1769 | −1.11971 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.60770 | 0.0616070 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.339746i | 0.0130000i | 0.999979 | + | 0.00650001i | \(0.00206903\pi\) | ||||
−0.999979 | + | 0.00650001i | \(0.997931\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 7.71281i | − 0.294262i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.32051 | 0.202695 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.1769 | −0.425190 | −0.212595 | − | 0.977140i | \(-0.568191\pi\) | ||||
−0.212595 | + | 0.977140i | \(0.568191\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.0718i | 0.648504i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 20.7846i | − 0.787273i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.46410 | 0.357965 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.4641 | −1.26392 | −0.631961 | − | 0.775000i | \(-0.717750\pi\) | ||||
−0.631961 | + | 0.775000i | \(0.717750\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 3.26795i | − 0.123253i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.78461i | 0.330379i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.7846 | −0.405025 | −0.202512 | − | 0.979280i | \(-0.564911\pi\) | ||||
−0.202512 | + | 0.979280i | \(0.564911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.9282 | 1.00989 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 18.9282i | − 0.708867i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 10.1436i | − 0.378819i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.3205 | 0.645946 | 0.322973 | − | 0.946408i | \(-0.395318\pi\) | ||||
0.322973 | + | 0.946408i | \(0.395318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.32051 | −0.272630 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.6077i | 0.431695i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.8564i | 1.03314i | 0.856246 | + | 0.516568i | \(0.172791\pi\) | ||||
−0.856246 | + | 0.516568i | \(0.827209\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.21539 | 0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.9282 | 1.14392 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.7846i | 1.13706i | 0.822664 | + | 0.568528i | \(0.192487\pi\) | ||||
−0.822664 | + | 0.568528i | \(0.807513\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.3205i | 0.416996i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.0000 | 1.03000 | 0.514998 | − | 0.857191i | \(-0.327793\pi\) | ||||
0.514998 | + | 0.857191i | \(0.327793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.535898 | −0.0196867 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 45.1244i | − 1.65545i | −0.561132 | − | 0.827726i | \(-0.689634\pi\) | ||||
0.561132 | − | 0.827726i | \(-0.310366\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.53590i | 0.312312i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.3205 | −0.852113 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.5359 | −0.676385 | −0.338192 | − | 0.941077i | \(-0.609815\pi\) | ||||
−0.338192 | + | 0.941077i | \(0.609815\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 17.5692i | − 0.640258i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 10.0000i | − 0.363456i | −0.983349 | − | 0.181728i | \(-0.941831\pi\) | ||||
0.983349 | − | 0.181728i | \(-0.0581691\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.78461 | 0.318861 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.3923 | 1.46422 | 0.732110 | − | 0.681186i | \(-0.238536\pi\) | ||||
0.732110 | + | 0.681186i | \(0.238536\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 12.7846i | − 0.462834i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 5.07180i | − 0.183132i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.4641 | 1.35099 | 0.675495 | − | 0.737365i | \(-0.263930\pi\) | ||||
0.675495 | + | 0.737365i | \(0.263930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.67949 | −0.240556 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.0526i | 0.577370i | 0.957424 | + | 0.288685i | \(0.0932181\pi\) | ||||
−0.957424 | + | 0.288685i | \(0.906782\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 4.78461i | − 0.171647i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | 0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.7846 | −1.17313 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.8564i | 0.495188i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.80385i | − 0.0643002i | −0.999483 | − | 0.0321501i | \(-0.989765\pi\) | ||||
0.999483 | − | 0.0321501i | \(-0.0102355\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.3205 | 0.403021 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −37.1769 | −1.32186 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.14359i | 0.218165i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.6603i | 0.413027i | 0.978444 | + | 0.206514i | \(0.0662118\pi\) | ||||
−0.978444 | + | 0.206514i | \(0.933788\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.21539 | 0.113752 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.0333 | 0.743176 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.8564i | 0.912453i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.60770i | 0.267804i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.7128 | 1.60718 | 0.803588 | − | 0.595185i | \(-0.202921\pi\) | ||||
0.803588 | + | 0.595185i | \(0.202921\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.3923 | 1.27791 | 0.638953 | − | 0.769246i | \(-0.279368\pi\) | ||||
0.638953 | + | 0.769246i | \(0.279368\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.4641i | 0.472207i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.92820i | 0.312358i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.60770 | 0.126063 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.8564 | −1.53060 | −0.765300 | − | 0.643674i | \(-0.777409\pi\) | ||||
−0.765300 | + | 0.643674i | \(0.777409\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 43.5692i | − 1.51873i | −0.650666 | − | 0.759364i | \(-0.725510\pi\) | ||||
0.650666 | − | 0.759364i | \(-0.274490\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 12.3397i | − 0.429095i | −0.976714 | − | 0.214548i | \(-0.931172\pi\) | ||||
0.976714 | − | 0.214548i | \(-0.0688277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.2487 | 1.39790 | 0.698948 | − | 0.715173i | \(-0.253652\pi\) | ||||
0.698948 | + | 0.715173i | \(0.253652\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.75129 | 0.0607515 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.3923i | 0.360072i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.8564i | 0.755468i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.07180 | −0.175098 | −0.0875489 | − | 0.996160i | \(-0.527903\pi\) | ||||
−0.0875489 | + | 0.996160i | \(0.527903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.0000 | −0.586207 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 9.46410i | − 0.325961i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000i | 0.0687208i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.75129 | −0.0601041 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3205 | 0.388062 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 24.6410i | − 0.843692i | −0.906667 | − | 0.421846i | \(-0.861382\pi\) | ||||
0.906667 | − | 0.421846i | \(-0.138618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.1962i | 0.484931i | 0.970160 | + | 0.242466i | \(0.0779562\pi\) | ||||
−0.970160 | + | 0.242466i | \(0.922044\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.71281 | 0.263158 | 0.131579 | − | 0.991306i | \(-0.457995\pi\) | ||||
0.131579 | + | 0.991306i | \(0.457995\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.78461 | 0.299379 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.7321i | 1.38654i | 0.720680 | + | 0.693268i | \(0.243830\pi\) | ||||
−0.720680 | + | 0.693268i | \(0.756170\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.66025i | 0.124309i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.8564 | 1.28419 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.39230 | 0.0810602 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.9474i | 1.21664i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 50.9808i | − 1.72150i | −0.509030 | − | 0.860749i | \(-0.669996\pi\) | ||||
0.509030 | − | 0.860749i | \(-0.330004\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.53590 | 0.287909 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.3205 | −1.18998 | −0.594989 | − | 0.803734i | \(-0.702844\pi\) | ||||
−0.594989 | + | 0.803734i | \(0.702844\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.0000i | 0.740359i | 0.928960 | + | 0.370179i | \(0.120704\pi\) | ||||
−0.928960 | + | 0.370179i | \(0.879296\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 54.5885i | 1.83290i | 0.400148 | + | 0.916451i | \(0.368959\pi\) | ||||
−0.400148 | + | 0.916451i | \(0.631041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.1769 | 0.710251 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.4641 | 0.518067 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.928203i | 0.0310611i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 1.85641i | − 0.0619836i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.9282 | 0.631291 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.1769 | −0.838765 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.0718i | 0.435002i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.5885i | 1.28131i | 0.767829 | + | 0.640654i | \(0.221337\pi\) | ||||
−0.767829 | + | 0.640654i | \(0.778663\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.8231 | 0.358979 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.4641 | 0.711137 | 0.355569 | − | 0.934650i | \(-0.384287\pi\) | ||||
0.355569 | + | 0.934650i | \(0.384287\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000i | 0.397142i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 10.1436i | − 0.334971i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.4974 | 1.73173 | 0.865865 | − | 0.500278i | \(-0.166769\pi\) | ||||
0.865865 | + | 0.500278i | \(0.166769\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.3205 | 0.438926 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.92820i | 0.228045i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.01924i | 0.296231i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.5692 | −1.16699 | −0.583494 | − | 0.812117i | \(-0.698315\pi\) | ||||
−0.583494 | + | 0.812117i | \(0.698315\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.00000 | −0.0983210 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 16.3923i | − 0.536660i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 11.1769i | − 0.365134i | −0.983193 | − | 0.182567i | \(-0.941559\pi\) | ||||
0.983193 | − | 0.182567i | \(-0.0584406\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.5359 | −0.735431 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.6410 | −0.542482 | −0.271241 | − | 0.962512i | \(-0.587434\pi\) | ||||
−0.271241 | + | 0.962512i | \(0.587434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.7846i | 0.676840i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.3205i | 1.34274i | 0.741124 | + | 0.671368i | \(0.234293\pi\) | ||||
−0.741124 | + | 0.671368i | \(0.765707\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.46410 | 0.177372 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.4641 | 0.501458 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 29.4115i | − 0.952733i | −0.879247 | − | 0.476367i | \(-0.841953\pi\) | ||||
0.879247 | − | 0.476367i | \(-0.158047\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.78461i | 0.283966i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34.6410 | 1.11862 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.14359 | −0.0368901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 28.7321i | 0.925877i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 10.6795i | − 0.343429i | −0.985147 | − | 0.171715i | \(-0.945069\pi\) | ||||
0.985147 | − | 0.171715i | \(-0.0549307\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.53590 | 0.0814648 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.4641 | −0.688816 | −0.344408 | − | 0.938820i | \(-0.611920\pi\) | ||||
−0.344408 | + | 0.938820i | \(0.611920\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9.07180i | − 0.290828i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.8038i | 0.697567i | 0.937203 | + | 0.348783i | \(0.113405\pi\) | ||||
−0.937203 | + | 0.348783i | \(0.886595\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.5692 | 0.945036 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.7513 | −0.502900 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 56.4449i | − 1.80031i | −0.435568 | − | 0.900156i | \(-0.643452\pi\) | ||||
0.435568 | − | 0.900156i | \(-0.356548\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.35898i | 0.0432569i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.9282 | −0.983460 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.3923 | 0.393655 | 0.196827 | − | 0.980438i | \(-0.436936\pi\) | ||||
0.196827 | + | 0.980438i | \(0.436936\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.2154i | 0.609782i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.60770i | 0.304279i | 0.988359 | + | 0.152139i | \(0.0486163\pi\) | ||||
−0.988359 | + | 0.152139i | \(0.951384\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.0718 | −0.413573 |
(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 | 1900.2.c.e.1749.3 | 4 | ||
5.2 | odd | 4 | 1900.2.a.d.1.2 | 2 | |||
5.3 | odd | 4 | 380.2.a.d.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 1900.2.c.e.1749.2 | 4 | ||
15.8 | even | 4 | 3420.2.a.h.1.1 | 2 | |||
20.3 | even | 4 | 1520.2.a.l.1.2 | 2 | |||
20.7 | even | 4 | 7600.2.a.bf.1.1 | 2 | |||
40.3 | even | 4 | 6080.2.a.bj.1.1 | 2 | |||
40.13 | odd | 4 | 6080.2.a.z.1.2 | 2 | |||
95.18 | even | 4 | 7220.2.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.a.d.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
1520.2.a.l.1.2 | 2 | 20.3 | even | 4 | |||
1900.2.a.d.1.2 | 2 | 5.2 | odd | 4 | |||
1900.2.c.e.1749.2 | 4 | 5.4 | even | 2 | inner | ||
1900.2.c.e.1749.3 | 4 | 1.1 | even | 1 | trivial | ||
3420.2.a.h.1.1 | 2 | 15.8 | even | 4 | |||
6080.2.a.z.1.2 | 2 | 40.13 | odd | 4 | |||
6080.2.a.bj.1.1 | 2 | 40.3 | even | 4 | |||
7220.2.a.h.1.2 | 2 | 95.18 | even | 4 | |||
7600.2.a.bf.1.1 | 2 | 20.7 | even | 4 |