Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(673,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.673");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 722x^{3} + 11881x^{2} + 54936x + 127008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 673.3 | ||
Root | \(8.80977 - 8.80977i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.673 |
Dual form | 1344.4.c.a.673.4 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.6195i | 1.39705i | 0.715584 | + | 0.698527i | \(0.246161\pi\) | ||||
−0.715584 | + | 0.698527i | \(0.753839\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 13.3667i | − 0.366382i | −0.983077 | − | 0.183191i | \(-0.941357\pi\) | ||||
0.983077 | − | 0.183191i | \(-0.0586427\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.74714i | 0.165282i | 0.996579 | + | 0.0826411i | \(0.0263355\pi\) | ||||
−0.996579 | + | 0.0826411i | \(0.973664\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 46.8586 | 0.806590 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −25.3667 | −0.361901 | −0.180951 | − | 0.983492i | \(-0.557917\pi\) | ||||
−0.180951 | + | 0.983492i | \(0.557917\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 71.9701i | − 0.869004i | −0.900671 | − | 0.434502i | \(-0.856924\pi\) | ||||
0.900671 | − | 0.434502i | \(-0.143076\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000i | 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.6172 | −0.214110 | −0.107055 | − | 0.994253i | \(-0.534142\pi\) | ||||
−0.107055 | + | 0.994253i | \(0.534142\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −118.970 | −0.951761 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 9.49195i | − 0.0607797i | −0.999538 | − | 0.0303898i | \(-0.990325\pi\) | ||||
0.999538 | − | 0.0303898i | \(-0.00967487\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 74.7586 | 0.433130 | 0.216565 | − | 0.976268i | \(-0.430515\pi\) | ||||
0.216565 | + | 0.976268i | \(0.430515\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −40.1000 | −0.211531 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 109.337i | − 0.528037i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.2529i | 0.152193i | 0.997100 | + | 0.0760964i | \(0.0242457\pi\) | ||||
−0.997100 | + | 0.0760964i | \(0.975754\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 23.2414 | 0.0954258 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −406.514 | −1.54846 | −0.774229 | − | 0.632905i | \(-0.781862\pi\) | ||||
−0.774229 | + | 0.632905i | \(0.781862\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 141.940i | − 0.503388i | −0.967807 | − | 0.251694i | \(-0.919012\pi\) | ||||
0.967807 | − | 0.251694i | \(-0.0809876\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 140.576i | − 0.465685i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 127.044 | 0.394281 | 0.197141 | − | 0.980375i | \(-0.436834\pi\) | ||||
0.197141 | + | 0.980375i | \(0.436834\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 76.1000i | 0.208944i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 106.499i | 0.276014i | 0.990431 | + | 0.138007i | \(0.0440696\pi\) | ||||
−0.990431 | + | 0.138007i | \(0.955930\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 208.781 | 0.511856 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −215.910 | −0.501720 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 65.5265i | − 0.144590i | −0.997383 | − | 0.0722951i | \(-0.976968\pi\) | ||||
0.997383 | − | 0.0722951i | \(-0.0230323\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 35.5470i | − 0.0746120i | −0.999304 | − | 0.0373060i | \(-0.988122\pi\) | ||||
0.999304 | − | 0.0373060i | \(-0.0118776\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −121.007 | −0.230908 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 606.021i | − 1.10503i | −0.833502 | − | 0.552517i | \(-0.813668\pi\) | ||||
0.833502 | − | 0.552517i | \(-0.186332\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 70.8516i | 0.123616i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 921.470 | 1.54026 | 0.770129 | − | 0.637888i | \(-0.220192\pi\) | ||||
0.770129 | + | 0.637888i | \(0.220192\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 705.561 | 1.13123 | 0.565614 | − | 0.824670i | \(-0.308639\pi\) | ||||
0.565614 | + | 0.824670i | \(0.308639\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 356.910i | 0.549499i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 93.5668i | 0.138480i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 294.343 | 0.419191 | 0.209596 | − | 0.977788i | \(-0.432785\pi\) | ||||
0.209596 | + | 0.977788i | \(0.432785\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 291.740i | − 0.385815i | −0.981217 | − | 0.192907i | \(-0.938208\pi\) | ||||
0.981217 | − | 0.192907i | \(-0.0617917\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 396.216i | − 0.505596i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −28.4758 | −0.0350912 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.646871 | 0.000770429 0 | 0.000385214 | − | 1.00000i | \(-0.499877\pi\) | ||||
0.000385214 | 1.00000i | \(0.499877\pi\) | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 54.2300i | − 0.0624708i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 224.276i | − 0.250068i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1124.14 | 1.21405 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1353.90 | 1.41719 | 0.708597 | − | 0.705613i | \(-0.249328\pi\) | ||||
0.708597 | + | 0.705613i | \(0.249328\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 120.300i | 0.122127i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1146.50i | − 1.12952i | −0.825255 | − | 0.564760i | \(-0.808969\pi\) | ||||
0.825255 | − | 0.564760i | \(-0.191031\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −305.554 | −0.292302 | −0.146151 | − | 0.989262i | \(-0.546689\pi\) | ||||
−0.146151 | + | 0.989262i | \(0.546689\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −328.010 | −0.304862 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1528.22i | 1.38074i | 0.723458 | + | 0.690368i | \(0.242552\pi\) | ||||
−0.723458 | + | 0.690368i | \(0.757448\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 293.191i | − 0.257638i | −0.991668 | − | 0.128819i | \(-0.958881\pi\) | ||||
0.991668 | − | 0.128819i | \(-0.0411187\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 102.759 | 0.0878686 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 212.793 | 0.177150 | 0.0885748 | − | 0.996070i | \(-0.471769\pi\) | ||||
0.0885748 | + | 0.996070i | \(0.471769\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 368.890i | − 0.299123i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 69.7243i | − 0.0550941i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 177.567 | 0.136786 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1152.33 | 0.865764 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1219.54i | 0.894003i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 94.1840i | 0.0673926i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1886.23 | 1.31792 | 0.658961 | − | 0.752177i | \(-0.270996\pi\) | ||||
0.658961 | + | 0.752177i | \(0.270996\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −425.821 | −0.290631 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1107.68i | 0.738767i | 0.929277 | + | 0.369384i | \(0.120431\pi\) | ||||
−0.929277 | + | 0.369384i | \(0.879569\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 503.791i | 0.328453i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −421.728 | −0.268863 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −770.260 | −0.480348 | −0.240174 | − | 0.970730i | \(-0.577205\pi\) | ||||
−0.240174 | + | 0.970730i | \(0.577205\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 833.201i | 0.508426i | 0.967148 | + | 0.254213i | \(0.0818163\pi\) | ||||
−0.967148 | + | 0.254213i | \(0.918184\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 381.131i | − 0.227638i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 103.554 | 0.0605565 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 148.260 | 0.0849125 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 147.000i | − 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1247.39i | − 0.685838i | −0.939365 | − | 0.342919i | \(-0.888584\pi\) | ||||
0.939365 | − | 0.342919i | \(-0.111416\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1887.55 | 1.01726 | 0.508632 | − | 0.860984i | \(-0.330151\pi\) | ||||
0.508632 | + | 0.860984i | \(0.330151\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 228.300 | 0.120634 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1167.69i | 0.605107i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3920.85i | − 1.99311i | −0.0829520 | − | 0.996554i | \(-0.526435\pi\) | ||||
0.0829520 | − | 0.996554i | \(-0.473565\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 319.496 | 0.159357 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 165.320 | 0.0809260 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2552.50i | − 1.22655i | −0.789870 | − | 0.613274i | \(-0.789852\pi\) | ||||
0.789870 | − | 0.613274i | \(-0.210148\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 626.344i | − 0.295520i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1623.67 | 0.752354 | 0.376177 | − | 0.926548i | \(-0.377239\pi\) | ||||
0.376177 | + | 0.926548i | \(0.377239\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2136.98 | 0.972682 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 647.731i | 0.289668i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1973.48i | − 0.867289i | −0.901084 | − | 0.433645i | \(-0.857227\pi\) | ||||
0.901084 | − | 0.433645i | \(-0.142773\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 832.791 | 0.359732 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −196.579 | −0.0834792 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 814.995i | − 0.340310i | −0.985417 | − | 0.170155i | \(-0.945573\pi\) | ||||
0.985417 | − | 0.170155i | \(-0.0544269\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1335.83i | − 0.548574i | −0.961648 | − | 0.274287i | \(-0.911558\pi\) | ||||
0.961648 | − | 0.274287i | \(-0.0884418\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −106.641 | −0.0430773 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −535.014 | −0.212622 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 339.068i | 0.132594i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 189.000i | − 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 111.893 | 0.0423890 | 0.0211945 | − | 0.999775i | \(-0.493253\pi\) | ||||
0.0211945 | + | 0.999775i | \(0.493253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1515.23 | −0.565123 | −0.282561 | − | 0.959249i | \(-0.591184\pi\) | ||||
−0.282561 | + | 0.959249i | \(0.591184\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 363.020i | 0.133315i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2099.84i | 0.759428i | 0.925104 | + | 0.379714i | \(0.123978\pi\) | ||||
−0.925104 | + | 0.379714i | \(0.876022\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4567.75 | −1.62713 | −0.813566 | − | 0.581472i | \(-0.802477\pi\) | ||||
−0.813566 | + | 0.581472i | \(0.802477\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1818.06 | −0.637991 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 66.4436i | 0.0229726i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 6349.56i | − 2.16328i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 212.555 | 0.0713700 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −962.002 | −0.318388 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3093.08i | − 1.00918i | −0.863360 | − | 0.504589i | \(-0.831644\pi\) | ||||
0.863360 | − | 0.504589i | \(-0.168356\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 2764.41i | − 0.889269i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2217.04 | 0.703260 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −523.310 | −0.163708 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 2116.68i | − 0.653115i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 196.519i | − 0.0598159i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4006.78 | 1.20320 | 0.601601 | − | 0.798797i | \(-0.294530\pi\) | ||||
0.601601 | + | 0.798797i | \(0.294530\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1070.73 | 0.317254 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 4194.83i | − 1.22652i | −0.789881 | − | 0.613261i | \(-0.789858\pi\) | ||||
0.789881 | − | 0.613261i | \(-0.210142\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 4438.14i | − 1.28070i | −0.768083 | − | 0.640351i | \(-0.778789\pi\) | ||||
0.768083 | − | 0.640351i | \(-0.221211\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 280.700 | 0.0799512 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3390.24 | −0.953229 | −0.476614 | − | 0.879112i | \(-0.658136\pi\) | ||||
−0.476614 | + | 0.879112i | \(0.658136\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1984.36i | 0.550832i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 883.028i | − 0.242020i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5283.23 | 1.42989 | 0.714945 | − | 0.699181i | \(-0.246452\pi\) | ||||
0.714945 | + | 0.699181i | \(0.246452\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4582.43 | −1.22481 | −0.612407 | − | 0.790543i | \(-0.709798\pi\) | ||||
−0.612407 | + | 0.790543i | \(0.709798\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 765.358i | 0.199579i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 557.563 | 0.143631 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −875.220 | −0.222750 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 687.240i | − 0.172822i | −0.996260 | − | 0.0864108i | \(-0.972460\pi\) | ||||
0.996260 | − | 0.0864108i | \(-0.0275398\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 315.684i | 0.0784461i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1188.65 | −0.291906 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3107.94 | 0.754350 | 0.377175 | − | 0.926142i | \(-0.376895\pi\) | ||||
0.377175 | + | 0.926142i | \(0.376895\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 239.770i | − 0.0575235i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 85.4275i | 0.0202599i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6499.44 | 1.52385 | 0.761925 | − | 0.647665i | \(-0.224254\pi\) | ||||
0.761925 | + | 0.647665i | \(0.224254\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1663.46 | −0.385606 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.94061i | 0 0.000444807i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 5787.54i | − 1.31179i | −0.754851 | − | 0.655897i | \(-0.772291\pi\) | ||||
0.754851 | − | 0.655897i | \(-0.227709\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1272.04 | −0.285133 | −0.142567 | − | 0.989785i | \(-0.545535\pi\) | ||||
−0.142567 | + | 0.989785i | \(0.545535\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −162.690 | −0.0360676 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1590.24i | 0.348708i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4286.24i | 0.929730i | 0.885382 | + | 0.464865i | \(0.153897\pi\) | ||||
−0.885382 | + | 0.464865i | \(0.846103\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −672.827 | −0.144377 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4276.87 | 0.907960 | 0.453980 | − | 0.891012i | \(-0.350004\pi\) | ||||
0.453980 | + | 0.891012i | \(0.350004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2544.93i | − 0.534560i | −0.963619 | − | 0.267280i | \(-0.913875\pi\) | ||||
0.963619 | − | 0.267280i | \(-0.0861248\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 3372.42i | − 0.700930i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2845.60 | 0.585262 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4269.53 | −0.869027 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 4061.70i | − 0.818218i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3696.67i | 0.737071i | 0.929614 | + | 0.368536i | \(0.120141\pi\) | ||||
−0.929614 | + | 0.368536i | \(0.879859\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1023.49 | 0.202000 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 360.900 | 0.0705103 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 182.966i | − 0.0353886i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 993.582i | 0.190263i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3439.51 | −0.652128 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 555.229 | 0.104237 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2853.13i | 0.530413i | 0.964192 | + | 0.265206i | \(0.0854401\pi\) | ||||
−0.964192 | + | 0.265206i | \(0.914560\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 916.662i | 0.168761i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4295.78 | −0.783252 | −0.391626 | − | 0.920124i | \(-0.628087\pi\) | ||||
−0.391626 | + | 0.920124i | \(0.628087\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3462.76 | 0.625325 | 0.312663 | − | 0.949864i | \(-0.398779\pi\) | ||||
0.312663 | + | 0.949864i | \(0.398779\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 984.031i | 0.176012i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.6028i | 0.00223295i | 0.999999 | + | 0.00111648i | \(0.000355385\pi\) | ||||
−0.999999 | + | 0.00111648i | \(0.999645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −126.876 | −0.0222686 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4584.67 | 0.797169 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1825.64i | 0.314494i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 921.678i | − 0.157309i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −879.572 | −0.148748 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −889.306 | −0.149024 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4298.31i | 0.713765i | 0.934149 | + | 0.356883i | \(0.116160\pi\) | ||||
−0.934149 | + | 0.356883i | \(0.883840\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 308.276i | − 0.0507310i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9465.77 | 1.54379 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2888.55 | −0.466912 | −0.233456 | − | 0.972367i | \(-0.575003\pi\) | ||||
−0.233456 | + | 0.972367i | \(0.575003\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 638.379i | − 0.102277i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 999.274i | − 0.158691i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1106.67 | −0.172699 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 6581.98i | − 1.01827i | −0.860687 | − | 0.509134i | \(-0.829966\pi\) | ||||
0.860687 | − | 0.509134i | \(-0.170034\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 3708.89i | − 0.568861i | −0.958697 | − | 0.284430i | \(-0.908196\pi\) | ||||
0.958697 | − | 0.284430i | \(-0.0918045\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −209.173 | −0.0318086 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11185.6 | 1.68655 | 0.843274 | − | 0.537484i | \(-0.180625\pi\) | ||||
0.843274 | + | 0.537484i | \(0.180625\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14392.9i | 2.15183i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 532.700i | − 0.0789734i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1248.88 | −0.183603 | −0.0918015 | − | 0.995777i | \(-0.529263\pi\) | ||||
−0.0918015 | + | 0.995777i | \(0.529263\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1679.30 | 0.244832 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3457.00i | − 0.499849i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11020.5i | 1.58039i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5872.81 | −0.835309 | −0.417654 | − | 0.908606i | \(-0.637148\pi\) | ||||
−0.417654 | + | 0.908606i | \(0.637148\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3658.62 | 0.516153 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 745.491i | − 0.104323i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 7954.92i | − 1.10426i | −0.833757 | − | 0.552131i | \(-0.813815\pi\) | ||||
0.833757 | − | 0.552131i | \(-0.186185\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 282.552 | 0.0389091 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 73.5354 | 0.0100458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1706.16i | 0.231239i | 0.993294 | + | 0.115620i | \(0.0368853\pi\) | ||||
−0.993294 | + | 0.115620i | \(0.963115\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 5658.70i | − 0.760903i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6696.81 | 0.893449 | 0.446724 | − | 0.894672i | \(-0.352590\pi\) | ||||
0.446724 | + | 0.894672i | \(0.352590\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1461.47 | −0.193463 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1277.46i | 0.167796i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10007.1i | 1.30432i | 0.758081 | + | 0.652160i | \(0.226137\pi\) | ||||
−0.758081 | + | 0.652160i | \(0.773863\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 599.090 | 0.0774867 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3323.04 | 0.426527 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4597.50i | 0.585633i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7583.54i | 0.958707i | 0.877622 | + | 0.479354i | \(0.159129\pi\) | ||||
−0.877622 | + | 0.479354i | \(0.840871\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1511.37 | 0.189632 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4654.03 | −0.579579 | −0.289790 | − | 0.957090i | \(-0.593585\pi\) | ||||
−0.289790 | + | 0.957090i | \(0.593585\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 579.165i | 0.0715888i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1265.18i | 0.155228i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 457.847 | 0.0557608 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 631.125 | 0.0763011 | 0.0381505 | − | 0.999272i | \(-0.487853\pi\) | ||||
0.0381505 | + | 0.999272i | \(0.487853\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2310.78i | 0.277329i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 458.685i | 0.0546500i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4556.85 | 0.539004 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2499.60 | 0.293540 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10883.6i | 1.26897i | 0.772934 | + | 0.634486i | \(0.218788\pi\) | ||||
−0.772934 | + | 0.634486i | \(0.781212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 446.347i | 0.0516713i | 0.999666 | + | 0.0258356i | \(0.00822465\pi\) | ||||
−0.999666 | + | 0.0258356i | \(0.991775\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1143.39 | −0.131427 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3017.88 | 0.344444 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 248.829i | 0.0282007i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 310.661i | − 0.0349623i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10094.7 | 1.12817 | 0.564087 | − | 0.825715i | \(-0.309228\pi\) | ||||
0.564087 | + | 0.825715i | \(0.309228\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13157.6 | −1.46031 | −0.730154 | − | 0.683282i | \(-0.760552\pi\) | ||||
−0.730154 | + | 0.683282i | \(0.760552\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 444.780i | − 0.0490242i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1699.73i | 0.186062i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12868.8 | −1.39908 | −0.699538 | − | 0.714595i | \(-0.746611\pi\) | ||||
−0.699538 | + | 0.714595i | \(0.746611\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −441.000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 9934.79i | − 1.06550i | −0.846273 | − | 0.532750i | \(-0.821159\pi\) | ||||
0.846273 | − | 0.532750i | \(-0.178841\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.1038i | 0.00107633i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3742.16 | −0.395969 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4998.49 | 0.525375 | 0.262687 | − | 0.964881i | \(-0.415391\pi\) | ||||
0.262687 | + | 0.964881i | \(0.415391\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5433.74i | 0.567328i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 5662.66i | − 0.587318i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 847.047 | 0.0872752 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1960.32 | 0.200657 | 0.100328 | − | 0.994954i | \(-0.468011\pi\) | ||||
0.100328 | + | 0.994954i | \(0.468011\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 684.900i | − 0.0696480i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18568.0i | 1.87591i | 0.346752 | + | 0.937957i | \(0.387284\pi\) | ||||
−0.346752 | + | 0.937957i | \(0.612716\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7696.28 | 0.772520 | 0.386260 | − | 0.922390i | \(-0.373767\pi\) | ||||
0.386260 | + | 0.922390i | \(0.373767\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3503.08 | 0.349358 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10624.0i | 1.05272i | 0.850262 | + | 0.526359i | \(0.176443\pi\) | ||||
−0.850262 | + | 0.526359i | \(0.823557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4242.15i | 0.417663i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11762.5 | −1.15072 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1897.27 | −0.184432 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8562.29i | 0.827084i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 958.489i | − 0.0920046i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11097.2 | 1.05855 | 0.529274 | − | 0.848451i | \(-0.322464\pi\) | ||||
0.529274 | + | 0.848451i | \(0.322464\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −265.362 | −0.0251548 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 495.961i | − 0.0467226i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21147.3i | 1.97990i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12174.8 | −1.13284 | −0.566422 | − | 0.824116i | \(-0.691673\pi\) | ||||
−0.566422 | + | 0.824116i | \(0.691673\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7657.51 | −0.708148 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 17789.7i | − 1.63511i | −0.575854 | − | 0.817553i | \(-0.695330\pi\) | ||||
0.575854 | − | 0.817553i | \(-0.304670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 240.779i | 0.0219962i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1879.03 | −0.170619 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6450.29 | −0.582163 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 8148.36i | − 0.731004i | −0.930811 | − | 0.365502i | \(-0.880897\pi\) | ||||
0.930811 | − | 0.365502i | \(-0.119103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 4871.00i | − 0.434372i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13339.1 | −1.18243 | −0.591216 | − | 0.806513i | \(-0.701352\pi\) | ||||
−0.591216 | + | 0.806513i | \(0.701352\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17907.9 | 1.57800 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 6410.95i | − 0.561578i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17169.3i | 1.49512i | 0.664192 | + | 0.747562i | \(0.268776\pi\) | ||||
−0.664192 | + | 0.747562i | \(0.731224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4938.93 | −0.427564 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1943.19 | 0.167240 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4772.61i | − 0.408362i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1698.15i | − 0.144458i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5920.45 | −0.500730 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12337.0 | −1.03742 | −0.518708 | − | 0.854952i | \(-0.673587\pi\) | ||||
−0.518708 | + | 0.854952i | \(0.673587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2797.74i | − 0.233913i | −0.993137 | − | 0.116956i | \(-0.962686\pi\) | ||||
0.993137 | − | 0.116956i | \(-0.0373138\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 2498.37i | − 0.207691i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1896.38 | −0.156750 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11609.2 | −0.954157 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 589.738i | 0.0481967i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3149.32i | − 0.255933i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23870.1 | −1.92896 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2444.98 | −0.196478 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 654.967i | − 0.0523403i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 13646.6i | − 1.08450i | −0.840217 | − | 0.542250i | \(-0.817573\pi\) | ||||
0.840217 | − | 0.542250i | \(-0.182427\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4007.50 | −0.316719 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4579.51 | 0.359935 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 7329.24i | − 0.572899i | −0.958095 | − | 0.286450i | \(-0.907525\pi\) | ||||
0.958095 | − | 0.286450i | \(-0.0924751\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 319.923i | 0.0248707i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −683.136 | −0.0528178 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2060.40 | −0.158439 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1605.04i | 0.122757i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 825.578i | 0.0628023i | 0.999507 | + | 0.0314011i | \(0.00999693\pi\) | ||||
−0.999507 | + | 0.0314011i | \(0.990003\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1099.63 | 0.0832011 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1017.21 | 0.0765534 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7496.18i | − 0.561148i | −0.959832 | − | 0.280574i | \(-0.909475\pi\) | ||||
0.959832 | − | 0.280574i | \(-0.0905248\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3323.73i | 0.247487i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 905.513 | 0.0667154 | 0.0333577 | − | 0.999443i | \(-0.489380\pi\) | ||||
0.0333577 | + | 0.999443i | \(0.489380\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 24158.1i | − 1.77055i | −0.465065 | − | 0.885277i | \(-0.653969\pi\) | ||||
0.465065 | − | 0.885277i | \(-0.346031\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 335.679i | − 0.0244733i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2809.74 | 0.203781 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5227.62 | 0.377173 | 0.188586 | − | 0.982057i | \(-0.439609\pi\) | ||||
0.188586 | + | 0.982057i | \(0.439609\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4545.69i | 0.326274i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2042.18i | 0.145824i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1423.53 | 0.101127 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1089.06 | 0.0769695 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 11007.8i | − 0.774002i | −0.922079 | − | 0.387001i | \(-0.873511\pi\) | ||||
0.922079 | − | 0.387001i | \(-0.126489\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 5380.38i | − 0.376392i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6299.52 | 0.438456 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15552.3 | −1.07699 | −0.538496 | − | 0.842628i | \(-0.681007\pi\) | ||||
−0.538496 | + | 0.842628i | \(0.681007\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2773.51i | 0.191097i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13703.3i | 0.939425i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5854.56 | −0.399350 | −0.199675 | − | 0.979862i | \(-0.563989\pi\) | ||||
−0.199675 | + | 0.979862i | \(0.563989\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4846.77 | 0.328958 | 0.164479 | − | 0.986381i | \(-0.447406\pi\) | ||||
0.164479 | + | 0.986381i | \(0.447406\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5454.19i | 0.368344i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17998.9i | 1.20952i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17579.6 | −1.17551 | −0.587754 | − | 0.809040i | \(-0.699988\pi\) | ||||
−0.587754 | + | 0.809040i | \(0.699988\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 199.331 | 0.0132632 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 984.225i | 0.0651677i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8251.78i | 0.543697i | 0.962340 | + | 0.271848i | \(0.0876350\pi\) | ||||
−0.962340 | + | 0.271848i | \(0.912365\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −19048.7 | −1.24897 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9569.90 | −0.624424 | −0.312212 | − | 0.950012i | \(-0.601070\pi\) | ||||
−0.312212 | + | 0.950012i | \(0.601070\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 19931.9i | − 1.29423i | −0.762391 | − | 0.647117i | \(-0.775975\pi\) | ||||
0.762391 | − | 0.647117i | \(-0.224025\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 637.665i | − 0.0412055i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.52810 | −0.000291195 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16342.4 | −1.04591 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2886.01i | 0.183821i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 868.881i | − 0.0550788i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20939.7 | −1.32107 | −0.660537 | − | 0.750794i | \(-0.729671\pi\) | ||||
−0.660537 | + | 0.750794i | \(0.729671\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9279.25 | −0.582649 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 29462.1i | 1.84121i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 379.610i | 0.0236118i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8293.23 | −0.513420 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11964.1 | 0.737214 | 0.368607 | − | 0.929585i | \(-0.379835\pi\) | ||||
0.368607 | + | 0.929585i | \(0.379835\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8277.59i | 0.507677i | 0.967247 | + | 0.253838i | \(0.0816932\pi\) | ||||
−0.967247 | + | 0.253838i | \(0.918307\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 6651.12i | − 0.406028i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12733.4 | 0.773725 | 0.386862 | − | 0.922137i | \(-0.373559\pi\) | ||||
0.386862 | + | 0.922137i | \(0.373559\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −875.872 | −0.0529753 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1569.93i | 0.0945168i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22687.1i | 1.35959i | 0.733400 | + | 0.679797i | \(0.237932\pi\) | ||||
−0.733400 | + | 0.679797i | \(0.762068\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17301.5 | −1.03210 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6350.05 | −0.377076 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 11843.4i | − 0.700083i | −0.936734 | − | 0.350041i | \(-0.886168\pi\) | ||||
0.936734 | − | 0.350041i | \(-0.113832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27322.4i | 1.60774i | 0.594805 | + | 0.803870i | \(0.297229\pi\) | ||||
−0.594805 | + | 0.803870i | \(0.702771\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −589.558 | −0.0345347 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7868.98 | −0.458866 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 224.173i | 0.0130135i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 12020.3i | − 0.694669i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −475.146 | −0.0273365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31900.7 | 1.82717 | 0.913583 | − | 0.406653i | \(-0.133304\pi\) | ||||
0.913583 | + | 0.406653i | \(0.133304\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 3212.19i | − 0.183166i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 11279.2i | − 0.640320i | −0.947364 | − | 0.320160i | \(-0.896263\pi\) | ||||
0.947364 | − | 0.320160i | \(-0.103737\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9477.31 | −0.535649 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12584.5 | −0.708132 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4906.49i | 0.274878i | 0.990510 | + | 0.137439i | \(0.0438871\pi\) | ||||
−0.990510 | + | 0.137439i | \(0.956113\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 12031.1i | − 0.671073i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13314.4 | −0.739413 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −825.060 | −0.0456202 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 450.536i | − 0.0248035i | −0.999923 | − | 0.0124017i | \(-0.996052\pi\) | ||||
0.999923 | − | 0.0124017i | \(-0.00394770\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 842.101i | − 0.0461598i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13014.2 | −0.710298 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10311.9 | 0.560389 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10170.7i | 0.550347i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22019.5i | 1.18640i | 0.805057 | + | 0.593198i | \(0.202135\pi\) | ||||
−0.805057 | + | 0.593198i | \(0.797865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2465.18 | 0.132256 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5953.09 | 0.318023 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8025.53i | 0.426918i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 10311.6i | − 0.546206i | −0.961985 | − | 0.273103i | \(-0.911950\pi\) | ||||
0.961985 | − | 0.273103i | \(-0.0880499\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2649.08 | −0.139730 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1765.59 | −0.0927375 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1617.46i | 0.0846008i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 15849.7i | − 0.825547i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20881.3 | 1.08309 | 0.541544 | − | 0.840672i | \(-0.317840\pi\) | ||||
0.541544 | + | 0.840672i | \(0.317840\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2138.88 | 0.110480 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13747.3i | 0.707146i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1129.26i | 0.0578477i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17648.4 | −0.900334 | −0.450167 | − | 0.892944i | \(-0.648636\pi\) | ||||
−0.450167 | + | 0.892944i | \(0.648636\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3600.55i | 0.182177i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30985.8i | 1.56137i | 0.624923 | + | 0.780687i | \(0.285130\pi\) | ||||
−0.624923 | + | 0.780687i | \(0.714870\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2296.07 | 0.115227 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8100.49 | −0.404865 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1896.07i | − 0.0943815i | −0.998886 | − | 0.0471908i | \(-0.984973\pi\) | ||||
0.998886 | − | 0.0471908i | \(-0.0150269\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1672.69i | − 0.0829254i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9997.93 | −0.493659 | −0.246829 | − | 0.969059i | \(-0.579389\pi\) | ||||
−0.246829 | + | 0.969059i | \(0.579389\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19483.6 | 0.958153 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2625.66i | 0.128605i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 10697.6i | − 0.521869i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35412.2 | 1.72065 | 0.860326 | − | 0.509744i | \(-0.170260\pi\) | ||||
0.860326 | + | 0.509744i | \(0.170260\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2061.72 | −0.0997786 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29482.7i | 1.42117i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 29416.3i | − 1.41235i | −0.708035 | − | 0.706177i | \(-0.750418\pi\) | ||||
0.708035 | − | 0.706177i | \(-0.249582\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 947.051 | 0.0452909 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 848.266 | 0.0404069 | 0.0202034 | − | 0.999796i | \(-0.493569\pi\) | ||||
0.0202034 | + | 0.999796i | \(0.493569\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2052.34i | 0.0973781i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3565.94i | 0.168532i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 507.643 | 0.0238982 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3380.24 | 0.158510 | 0.0792552 | − | 0.996854i | \(-0.474746\pi\) | ||||
0.0792552 | + | 0.996854i | \(0.474746\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 9323.82i | − 0.435524i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20128.7i | 0.936582i | 0.883574 | + | 0.468291i | \(0.155130\pi\) | ||||
−0.883574 | + | 0.468291i | \(0.844870\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8894.04 | −0.412236 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −719.310 | −0.0332112 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29256.8i | 1.34562i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 12317.0i | − 0.564324i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 256.283 | 0.0116971 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 61241.9 | 2.78448 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 31312.6i | − 1.41826i | −0.705076 | − | 0.709131i | \(-0.749087\pi\) | ||||
0.705076 | − | 0.709131i | \(-0.250913\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 19498.3i | − 0.879795i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1489.55 | −0.0669562 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 275.388 | 0.0123320 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4990.38i | 0.222630i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19940.7i | 0.886244i | 0.896461 | + | 0.443122i | \(0.146129\pi\) | ||||
−0.896461 | + | 0.443122i | \(0.853871\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3222.68 | −0.142691 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.82184 | −0.000256810 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 9431.01i | − 0.414462i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2582.23i | 0.113058i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17362.6 | −0.757364 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24087.6 | −1.04681 | −0.523407 | − | 0.852083i | \(-0.675339\pi\) | ||||
−0.523407 | + | 0.852083i | \(0.675339\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5952.49i | 0.257731i | 0.991662 | + | 0.128866i | \(0.0411336\pi\) | ||||
−0.991662 | + | 0.128866i | \(0.958866\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3816.13i | 0.164622i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39868.9 | 1.71356 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10215.5 | −0.437446 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 488.070i | 0.0208236i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31555.8i | 1.34142i | 0.741720 | + | 0.670710i | \(0.234010\pi\) | ||||
−0.741720 | + | 0.670710i | \(0.765990\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39793.7 | −1.68544 | −0.842722 | − | 0.538349i | \(-0.819048\pi\) | ||||
−0.842722 | + | 0.538349i | \(0.819048\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4770.71 | 0.201327 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 775.434i | − 0.0326052i | −0.999867 | − | 0.0163026i | \(-0.994810\pi\) | ||||
0.999867 | − | 0.0163026i | \(-0.00518950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37882.7i | 1.58712i | 0.608495 | + | 0.793558i | \(0.291774\pi\) | ||||
−0.608495 | + | 0.793558i | \(0.708226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12858.7 | 0.536780 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1242.97 | −0.0517002 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25360.9i | 1.05108i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2018.48i | 0.0833560i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 455.725 | 0.0187525 | 0.00937627 | − | 0.999956i | \(-0.497015\pi\) | ||||
0.00937627 | + | 0.999956i | \(0.497015\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24298.9 | 0.996306 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 12830.6i | − 0.524211i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33378.7i | 1.35889i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8066.32 | −0.327228 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7634.79 | −0.308628 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 808.957i | − 0.0325860i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 33752.9i | − 1.35484i | −0.735597 | − | 0.677420i | \(-0.763098\pi\) | ||||
0.735597 | − | 0.677420i | \(-0.236902\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10117.3 | −0.404682 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29740.1 | 1.18542 | 0.592708 | − | 0.805417i | \(-0.298059\pi\) | ||||
0.592708 | + | 0.805417i | \(0.298059\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19320.9i | 0.767430i | 0.923452 | + | 0.383715i | \(0.125355\pi\) | ||||
−0.923452 | + | 0.383715i | \(0.874645\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 8536.79i | − 0.337901i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22903.7 | 0.903418 | 0.451709 | − | 0.892165i | \(-0.350815\pi\) | ||||
0.451709 | + | 0.892165i | \(0.350815\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30824.9 | 1.21165 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12808.6i | 0.501733i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 3934.38i | − 0.153584i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4694.93 | 0.182642 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12185.1 | −0.472398 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 659.288i | − 0.0254720i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 28372.3i | − 1.09243i | −0.837644 | − | 0.546217i | \(-0.816067\pi\) | ||||
0.837644 | − | 0.546217i | \(-0.183933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11090.0 | 0.425548 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44790.3 | −1.71285 | −0.856427 | − | 0.516269i | \(-0.827321\pi\) | ||||
−0.856427 | + | 0.516269i | \(0.827321\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 50005.6i | − 1.90580i | −0.303281 | − | 0.952901i | \(-0.598082\pi\) | ||||
0.303281 | − | 0.952901i | \(-0.401918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 3070.48i | − 0.116625i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5305.70 | 0.200843 | 0.100422 | − | 0.994945i | \(-0.467981\pi\) | ||||
0.100422 | + | 0.994945i | \(0.467981\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13203.6 | −0.498128 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1082.70i | − 0.0407092i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 9143.35i | − 0.342632i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12729.8 | 0.475432 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −548.897 | −0.0204316 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 709.604i | − 0.0263255i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2701.52i | − 0.0998897i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2980.74 | 0.109848 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20865.1 | 0.766387 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18224.3i | 0.667175i | 0.942719 | + | 0.333587i | \(0.108259\pi\) | ||||
−0.942719 | + | 0.333587i | \(0.891741\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10318.5i | 0.376507i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7287.74 | −0.265042 | −0.132521 | − | 0.991180i | \(-0.542307\pi\) | ||||
−0.132521 | + | 0.991180i | \(0.542307\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3899.60 | −0.141356 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1665.69i | − 0.0601813i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 7753.76i | − 0.279228i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40520.1 | 1.45444 | 0.727222 | − | 0.686403i | \(-0.240811\pi\) | ||||
0.727222 | + | 0.686403i | \(0.240811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8559.39 | 0.306234 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7138.76i | 0.254578i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 4075.07i | − 0.144851i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2749.98 | 0.0974340 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13417.8 | −0.473869 | −0.236935 | − | 0.971526i | \(-0.576143\pi\) | ||||
−0.236935 | + | 0.971526i | \(0.576143\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 3526.54i | − 0.124143i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12887.3i | 0.452211i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5296.09 | −0.185241 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29216.3 | −1.01863 | −0.509314 | − | 0.860581i | \(-0.670101\pi\) | ||||
−0.509314 | + | 0.860581i | \(0.670101\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 10388.3i | − 0.361032i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9792.02i | 0.339225i | 0.985511 | + | 0.169612i | \(0.0542516\pi\) | ||||
−0.985511 | + | 0.169612i | \(0.945748\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9600.72 | 0.331540 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2952.09 | 0.101621 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 17608.5i | − 0.604222i | −0.953273 | − | 0.302111i | \(-0.902309\pi\) | ||||
0.953273 | − | 0.302111i | \(-0.0976913\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5466.08i | 0.186972i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37.8085 | 0.00128919 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2510.99 | 0.0853503 | 0.0426751 | − | 0.999089i | \(-0.486412\pi\) | ||||
0.0426751 | + | 0.999089i | \(0.486412\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1747.72i | 0.0592198i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 380.627i | 0.0128568i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5391.82 | 0.181555 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24202.2 | −0.812398 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 13754.0i | − 0.460246i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 23667.2i | − 0.789507i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29783.0 | −0.990442 | −0.495221 | − | 0.868767i | \(-0.664913\pi\) | ||||
−0.495221 | + | 0.868767i | \(0.664913\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5476.93 | 0.181573 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36466.0i | 1.20520i | 0.798043 | + | 0.602600i | \(0.205869\pi\) | ||||
−0.798043 | + | 0.602600i | \(0.794131\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 5832.40i | − 0.192167i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2765.03 | −0.0908225 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35245.9 | −1.15416 | −0.577082 | − | 0.816687i | \(-0.695809\pi\) | ||||
−0.577082 | + | 0.816687i | \(0.695809\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 8.64652i | 0 0.000282272i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2638.72i | 0.0858794i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35994.4 | 1.16790 | 0.583949 | − | 0.811790i | \(-0.301507\pi\) | ||||
0.583949 | + | 0.811790i | \(0.301507\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32798.5 | −1.06096 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2667.92i | 0.0860392i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3352.23i | 0.107780i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20472.2 | 0.656227 | 0.328114 | − | 0.944638i | \(-0.393587\pi\) | ||||
0.328114 | + | 0.944638i | \(0.393587\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12894.9 | 0.412092 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 71346.2i | − 2.27319i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45849.5i | 1.45644i | 0.685344 | + | 0.728219i | \(0.259652\pi\) | ||||
−0.685344 | + | 0.728219i | \(0.740348\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −924.827 | −0.0292895 |
(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 | 1344.4.c.a.673.3 | ✓ | 6 | |
4.3 | odd | 2 | 1344.4.c.d.673.6 | yes | 6 | ||
8.3 | odd | 2 | 1344.4.c.d.673.1 | yes | 6 | ||
8.5 | even | 2 | inner | 1344.4.c.a.673.4 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.c.a.673.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1344.4.c.a.673.4 | yes | 6 | 8.5 | even | 2 | inner | |
1344.4.c.d.673.1 | yes | 6 | 8.3 | odd | 2 | ||
1344.4.c.d.673.6 | yes | 6 | 4.3 | odd | 2 |