Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,3,Mod(641,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.641");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.l (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: | \(26.1581053786\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.3 | ||
Root | \(-1.58114 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.641 |
Dual form | 960.3.l.f.641.4 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 2.58114 | − | 1.52896i | 0.860380 | − | 0.509654i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.48683 | 1.06955 | 0.534774 | − | 0.844995i | \(-0.320397\pi\) | ||||
0.534774 | + | 0.844995i | \(0.320397\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.32456 | − | 7.89292i | 0.480506 | − | 0.876991i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 8.48528i | − | 0.771389i | −0.922627 | − | 0.385695i | \(-0.873962\pi\) | ||
0.922627 | − | 0.385695i | \(-0.126038\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.0000 | 0.769231 | 0.384615 | − | 0.923077i | \(-0.374334\pi\) | ||||
0.384615 | + | 0.923077i | \(0.374334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.41886 | − | 5.77160i | −0.227924 | − | 0.384773i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 30.3870i | 1.78747i | 0.448596 | + | 0.893734i | \(0.351924\pi\) | ||||
−0.448596 | + | 0.893734i | \(0.648076\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.9737 | 1.41967 | 0.709833 | − | 0.704370i | \(-0.248770\pi\) | ||||
0.709833 | + | 0.704370i | \(0.248770\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 19.3246 | − | 11.4471i | 0.920217 | − | 0.545099i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.17377i | 0.398859i | 0.979912 | + | 0.199430i | \(0.0639090\pi\) | ||||
−0.979912 | + | 0.199430i | \(0.936091\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.905694 | − | 26.9848i | −0.0335442 | − | 0.999437i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 26.8328i | − | 0.925270i | −0.886549 | − | 0.462635i | \(-0.846904\pi\) | ||
0.886549 | − | 0.462635i | \(-0.153096\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −0.258065 | −0.129032 | − | 0.991640i | \(-0.541187\pi\) | ||||
−0.129032 | + | 0.991640i | \(0.541187\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.9737 | − | 21.9017i | −0.393141 | − | 0.663688i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 16.7411i | − | 0.478316i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −15.9473 | −0.431009 | −0.215504 | − | 0.976503i | \(-0.569140\pi\) | ||||
−0.215504 | + | 0.976503i | \(0.569140\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 25.8114 | − | 15.2896i | 0.661830 | − | 0.392041i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 47.3575i | − | 1.15506i | −0.816369 | − | 0.577531i | \(-0.804016\pi\) | ||
0.816369 | − | 0.577531i | \(-0.195984\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14.4605 | −0.336291 | −0.168145 | − | 0.985762i | \(-0.553778\pi\) | ||||
−0.168145 | + | 0.985762i | \(0.553778\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −17.6491 | − | 9.67000i | −0.392202 | − | 0.214889i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 45.8688i | 0.975933i | 0.872862 | + | 0.487966i | \(0.162261\pi\) | ||||
−0.872862 | + | 0.487966i | \(0.837739\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.05267 | 0.143932 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 46.4605 | + | 78.4330i | 0.910990 | + | 1.53790i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 30.3870i | − | 0.573339i | −0.958030 | − | 0.286670i | \(-0.907452\pi\) | ||
0.958030 | − | 0.286670i | \(-0.0925482\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.9737 | −0.344976 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 69.6228 | − | 41.2417i | 1.22145 | − | 0.723538i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 24.0789i | 0.408116i | 0.978959 | + | 0.204058i | \(0.0654132\pi\) | ||||
−0.978959 | + | 0.204058i | \(0.934587\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 53.9473 | 0.884382 | 0.442191 | − | 0.896921i | \(-0.354201\pi\) | ||||
0.442191 | + | 0.896921i | \(0.354201\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 32.3772 | − | 59.0930i | 0.513924 | − | 0.937984i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 22.3607i | − | 0.344010i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −110.460 | −1.64866 | −0.824332 | − | 0.566107i | \(-0.808449\pi\) | ||||
−0.824332 | + | 0.566107i | \(0.808449\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.0263 | + | 23.6788i | 0.203280 | + | 0.343171i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.5936i | 0.219628i | 0.993952 | + | 0.109814i | \(0.0350255\pi\) | ||||
−0.993952 | + | 0.109814i | \(0.964974\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 87.9473 | 1.20476 | 0.602379 | − | 0.798210i | \(-0.294220\pi\) | ||||
0.602379 | + | 0.798210i | \(0.294220\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.9057 | + | 7.64481i | −0.172076 | + | 0.101931i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 63.5279i | − | 0.825037i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 46.9737 | 0.594603 | 0.297302 | − | 0.954784i | \(-0.403913\pi\) | ||||
0.297302 | + | 0.954784i | \(0.403913\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −43.5964 | − | 68.2668i | −0.538228 | − | 0.842799i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 26.1443i | − | 0.314992i | −0.987520 | − | 0.157496i | \(-0.949658\pi\) | ||
0.987520 | − | 0.157496i | \(-0.0503421\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 67.9473 | 0.799380 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −41.0263 | − | 69.2592i | −0.471567 | − | 0.796083i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 60.7739i | − | 0.682853i | −0.939908 | − | 0.341427i | \(-0.889090\pi\) | ||
0.939908 | − | 0.341427i | \(-0.110910\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 74.8683 | 0.822729 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.6491 | + | 12.2317i | −0.222033 | + | 0.131524i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 60.3150i | − | 0.634894i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 36.0527 | 0.371677 | 0.185838 | − | 0.982580i | \(-0.440500\pi\) | ||||
0.185838 | + | 0.982580i | \(0.440500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −66.9737 | − | 36.6951i | −0.676502 | − | 0.370657i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 48.1577i | − | 0.476809i | −0.971166 | − | 0.238405i | \(-0.923376\pi\) | ||
0.971166 | − | 0.238405i | \(-0.0766245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −140.408 | −1.36318 | −0.681591 | − | 0.731733i | \(-0.738712\pi\) | ||||
−0.681591 | + | 0.731733i | \(0.738712\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −25.5964 | − | 43.2110i | −0.243776 | − | 0.411534i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 43.1149i | 0.402943i | 0.979494 | + | 0.201471i | \(0.0645723\pi\) | ||||
−0.979494 | + | 0.201471i | \(0.935428\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −133.842 | −1.22791 | −0.613954 | − | 0.789342i | \(-0.710422\pi\) | ||||
−0.613954 | + | 0.789342i | \(0.710422\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −41.1623 | + | 24.3829i | −0.370831 | + | 0.219665i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 7.90852i | − | 0.0699869i | −0.999388 | − | 0.0349935i | \(-0.988859\pi\) | ||
0.999388 | − | 0.0349935i | \(-0.0111410\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.5132 | 0.178375 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 43.2456 | − | 78.9292i | 0.369620 | − | 0.674609i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 227.502i | 1.91178i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 49.0000 | 0.404959 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −72.4078 | − | 122.236i | −0.588682 | − | 0.993792i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 134.460 | 1.05874 | 0.529372 | − | 0.848390i | \(-0.322428\pi\) | ||||
0.529372 | + | 0.848390i | \(0.322428\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −37.3246 | + | 22.1095i | −0.289338 | + | 0.171392i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 220.394i | 1.68240i | 0.540727 | + | 0.841198i | \(0.318149\pi\) | ||||
−0.540727 | + | 0.841198i | \(0.681851\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 201.947 | 1.51840 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −60.3399 | + | 2.02519i | −0.446962 | + | 0.0150014i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 95.5153i | − | 0.697192i | −0.937273 | − | 0.348596i | \(-0.886659\pi\) | ||
0.937273 | − | 0.348596i | \(-0.113341\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −76.8157 | −0.552631 | −0.276315 | − | 0.961067i | \(-0.589113\pi\) | ||||
−0.276315 | + | 0.961067i | \(0.589113\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 70.1317 | + | 118.394i | 0.497388 | + | 0.839673i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 84.8528i | − | 0.593376i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −60.0000 | −0.413793 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 18.2039 | − | 10.7833i | 0.123836 | − | 0.0733555i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 276.237i | − | 1.85394i | −0.375139 | − | 0.926969i | \(-0.622405\pi\) | ||
0.375139 | − | 0.926969i | \(-0.377595\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.0527 | −0.119554 | −0.0597770 | − | 0.998212i | \(-0.519039\pi\) | ||||
−0.0597770 | + | 0.998212i | \(0.519039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 239.842 | + | 131.410i | 1.56759 | + | 0.858890i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.8885i | 0.115410i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −103.842 | −0.661414 | −0.330707 | − | 0.943733i | \(-0.607287\pi\) | ||||
−0.330707 | + | 0.943733i | \(0.607287\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −46.4605 | − | 78.4330i | −0.292204 | − | 0.493289i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 68.6825i | 0.426599i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3815 | −0.0698251 | −0.0349126 | − | 0.999390i | \(-0.511115\pi\) | ||||
−0.0349126 | + | 0.999390i | \(0.511115\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −48.9737 | + | 29.0100i | −0.296810 | + | 0.175818i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 252.270i | 1.51060i | 0.655382 | + | 0.755298i | \(0.272508\pi\) | ||||
−0.655382 | + | 0.755298i | \(0.727492\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −69.0000 | −0.408284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 116.649 | − | 212.901i | 0.682159 | − | 1.24504i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.8160i | 0.0683005i | 0.999417 | + | 0.0341502i | \(0.0108725\pi\) | ||||
−0.999417 | + | 0.0341502i | \(0.989128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −37.4342 | −0.213910 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 36.8157 | + | 62.1509i | 0.207998 | + | 0.351135i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 69.0358i | 0.385675i | 0.981231 | + | 0.192837i | \(0.0617690\pi\) | ||||
−0.981231 | + | 0.192837i | \(0.938231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 189.684 | 1.04798 | 0.523989 | − | 0.851725i | \(-0.324443\pi\) | ||||
0.523989 | + | 0.851725i | \(0.324443\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 139.246 | − | 82.4834i | 0.760905 | − | 0.450729i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 35.6593i | 0.192753i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 257.842 | 1.37883 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.78078 | − | 202.031i | −0.0358771 | − | 1.06895i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 108.708i | 0.569153i | 0.958653 | + | 0.284577i | \(0.0918530\pi\) | ||||
−0.958653 | + | 0.284577i | \(0.908147\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −167.947 | −0.870193 | −0.435097 | − | 0.900384i | \(-0.643286\pi\) | ||||
−0.435097 | + | 0.900384i | \(0.643286\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −34.1886 | − | 57.7160i | −0.175326 | − | 0.295980i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 171.659i | 0.871367i | 0.900100 | + | 0.435684i | \(0.143493\pi\) | ||||
−0.900100 | + | 0.435684i | \(0.856507\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −35.0790 | −0.176276 | −0.0881382 | − | 0.996108i | \(-0.528092\pi\) | ||||
−0.0881382 | + | 0.996108i | \(0.528092\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −285.114 | + | 168.890i | −1.41848 | + | 0.840248i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 200.893i | − | 0.989620i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −105.895 | −0.516559 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 72.4078 | + | 39.6725i | 0.349796 | + | 0.191654i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 228.879i | − | 1.09512i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −58.1580 | −0.275630 | −0.137815 | − | 0.990458i | \(-0.544008\pi\) | ||||
−0.137815 | + | 0.990458i | \(0.544008\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 23.8420 | + | 40.2492i | 0.111934 | + | 0.188963i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 32.3347i | 0.150394i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −59.8947 | −0.276012 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 227.004 | − | 134.468i | 1.03655 | − | 0.614009i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 303.870i | 1.37498i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −99.3815 | −0.445657 | −0.222828 | − | 0.974858i | \(-0.571529\pi\) | ||||
−0.222828 | + | 0.974858i | \(0.571529\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.6228 | + | 39.4646i | −0.0961012 | + | 0.175398i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 216.951i | 0.955733i | 0.878432 | + | 0.477867i | \(0.158590\pi\) | ||||
−0.878432 | + | 0.477867i | \(0.841410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −325.684 | −1.42220 | −0.711100 | − | 0.703090i | \(-0.751803\pi\) | ||||
−0.711100 | + | 0.703090i | \(0.751803\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −97.1317 | − | 163.974i | −0.420483 | − | 0.709845i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 51.7119i | 0.221939i | 0.993824 | + | 0.110970i | \(0.0353957\pi\) | ||||
−0.993824 | + | 0.110970i | \(0.964604\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 102.566 | 0.436450 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 121.246 | − | 71.8209i | 0.511585 | − | 0.303042i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 410.047i | − | 1.71568i | −0.513917 | − | 0.857840i | \(-0.671806\pi\) | ||
0.513917 | − | 0.857840i | \(-0.328194\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 445.526 | 1.84866 | 0.924328 | − | 0.381599i | \(-0.124627\pi\) | ||||
0.924328 | + | 0.381599i | \(0.124627\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −216.906 | − | 109.549i | −0.892616 | − | 0.450818i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 15.7702i | − | 0.0643683i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 269.737 | 1.09205 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −39.9737 | − | 67.4821i | −0.160537 | − | 0.271013i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 237.364i | 0.945675i | 0.881150 | + | 0.472838i | \(0.156770\pi\) | ||||
−0.881150 | + | 0.472838i | \(0.843230\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 77.8420 | 0.307676 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 175.381 | − | 103.889i | 0.687771 | − | 0.407407i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 318.887i | 1.24080i | 0.784284 | + | 0.620402i | \(0.213030\pi\) | ||||
−0.784284 | + | 0.620402i | \(0.786970\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −119.395 | −0.460985 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −211.789 | − | 116.040i | −0.811453 | − | 0.444598i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 36.2300i | − | 0.137757i | −0.997625 | − | 0.0688784i | \(-0.978058\pi\) | ||
0.997625 | − | 0.0688784i | \(-0.0219420\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −67.9473 | −0.256405 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −92.9210 | − | 156.866i | −0.348019 | − | 0.587513i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 528.041i | 1.96298i | 0.191518 | + | 0.981489i | \(0.438659\pi\) | ||||
−0.191518 | + | 0.981489i | \(0.561341\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 475.895 | 1.75607 | 0.878034 | − | 0.478597i | \(-0.158855\pi\) | ||||
0.878034 | + | 0.478597i | \(0.158855\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 193.246 | − | 114.471i | 0.707859 | − | 0.419307i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 42.4264i | 0.154278i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −188.158 | −0.679271 | −0.339635 | − | 0.940557i | \(-0.610304\pi\) | ||||
−0.339635 | + | 0.940557i | \(0.610304\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −34.5964 | + | 63.1434i | −0.124002 | + | 0.226320i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.4322i | 0.0869473i | 0.999055 | + | 0.0434736i | \(0.0138424\pi\) | ||||
−0.999055 | + | 0.0434736i | \(0.986158\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 198.460 | 0.701274 | 0.350637 | − | 0.936511i | \(-0.385965\pi\) | ||||
0.350637 | + | 0.936511i | \(0.385965\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −92.2192 | − | 155.681i | −0.323576 | − | 0.546250i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 354.558i | − | 1.23539i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −634.368 | −2.19504 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 93.0569 | − | 55.1231i | 0.319783 | − | 0.189427i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 513.825i | 1.75367i | 0.480794 | + | 0.876834i | \(0.340349\pi\) | ||||
−0.480794 | + | 0.876834i | \(0.659651\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 53.8420 | 0.182515 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −228.974 | + | 7.68507i | −0.770955 | + | 0.0258757i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 91.7377i | 0.306815i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −108.263 | −0.359679 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −73.6313 | − | 124.302i | −0.243008 | − | 0.410237i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 120.630i | − | 0.395508i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.3815 | −0.0370733 | −0.0185366 | − | 0.999828i | \(-0.505901\pi\) | ||||
−0.0185366 | + | 0.999828i | \(0.505901\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −362.412 | + | 214.678i | −1.17285 | + | 0.694751i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 518.756i | 1.66802i | 0.551746 | + | 0.834012i | \(0.313962\pi\) | ||||
−0.551746 | + | 0.834012i | \(0.686038\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −46.3160 | −0.147974 | −0.0739872 | − | 0.997259i | \(-0.523572\pi\) | ||||
−0.0739872 | + | 0.997259i | \(0.523572\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −132.136 | − | 72.3977i | −0.419479 | − | 0.229834i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 39.0957i | − | 0.123330i | −0.998097 | − | 0.0616651i | \(-0.980359\pi\) | ||
0.998097 | − | 0.0616651i | \(-0.0196411\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −227.684 | −0.713743 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 65.9210 | + | 111.286i | 0.205361 | + | 0.346684i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 819.648i | 2.53761i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −50.0000 | −0.153846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −345.465 | + | 204.639i | −1.05647 | + | 0.625808i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 343.412i | 1.04381i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −445.421 | −1.34568 | −0.672841 | − | 0.739787i | \(-0.734926\pi\) | ||||
−0.672841 | + | 0.739787i | \(0.734926\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −68.9651 | + | 125.871i | −0.207102 | + | 0.377991i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 246.997i | 0.737305i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 325.684 | 0.966421 | 0.483211 | − | 0.875504i | \(-0.339471\pi\) | ||||
0.483211 | + | 0.875504i | \(0.339471\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.0918 | − | 20.4130i | −0.0356691 | − | 0.0602153i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 67.8823i | 0.199068i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −314.053 | −0.915605 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 52.9473 | − | 31.3638i | 0.153471 | − | 0.0909097i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 51.8236i | − | 0.149348i | −0.997208 | − | 0.0746738i | \(-0.976208\pi\) | ||
0.997208 | − | 0.0746738i | \(-0.0237916\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 97.5787 | 0.279595 | 0.139798 | − | 0.990180i | \(-0.455355\pi\) | ||||
0.139798 | + | 0.990180i | \(0.455355\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.05694 | − | 269.848i | −0.0258033 | − | 0.768798i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 569.797i | 1.61416i | 0.590445 | + | 0.807078i | \(0.298952\pi\) | ||||
−0.590445 | + | 0.807078i | \(0.701048\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 34.8683 | 0.0982206 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 347.842 | + | 587.215i | 0.974347 | + | 1.64486i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 274.283i | 0.764019i | 0.924158 | + | 0.382010i | \(0.124768\pi\) | ||||
−0.924158 | + | 0.382010i | \(0.875232\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 366.579 | 1.01545 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 126.476 | − | 74.9191i | 0.348418 | − | 0.206389i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 196.656i | − | 0.538784i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −461.828 | −1.25839 | −0.629194 | − | 0.777248i | \(-0.716615\pi\) | ||||
−0.629194 | + | 0.777248i | \(0.716615\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −373.789 | − | 204.800i | −1.01298 | − | 0.555014i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 227.502i | − | 0.613213i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 491.947 | 1.31889 | 0.659447 | − | 0.751751i | \(-0.270791\pi\) | ||||
0.659447 | + | 0.751751i | \(0.270791\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.0943 | + | 28.8580i | 0.0455848 | + | 0.0769547i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 268.328i | − | 0.711746i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −258.763 | −0.682752 | −0.341376 | − | 0.939927i | \(-0.610893\pi\) | ||||
−0.341376 | + | 0.939927i | \(0.610893\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 347.061 | − | 205.585i | 0.910922 | − | 0.539593i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 522.422i | 1.36402i | 0.731341 | + | 0.682012i | \(0.238895\pi\) | ||||
−0.731341 | + | 0.682012i | \(0.761105\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −142.053 | −0.368968 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −62.5352 | + | 114.136i | −0.161590 | + | 0.294924i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 610.847i | − | 1.57030i | −0.619306 | − | 0.785150i | \(-0.712586\pi\) | ||
0.619306 | − | 0.785150i | \(-0.287414\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −278.763 | −0.712949 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 336.974 | + | 568.867i | 0.857439 | + | 1.44750i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 105.036i | − | 0.265915i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 214.000 | 0.539043 | 0.269521 | − | 0.962994i | \(-0.413135\pi\) | ||||
0.269521 | + | 0.962994i | \(0.413135\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 521.254 | − | 308.770i | 1.30640 | − | 0.773859i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 454.557i | 1.13356i | 0.823869 | + | 0.566780i | \(0.191811\pi\) | ||||
−0.823869 | + | 0.566780i | \(0.808189\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −80.0000 | −0.198511 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −152.649 | + | 97.4846i | −0.376911 | + | 0.240703i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 135.318i | 0.332476i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −573.842 | −1.40304 | −0.701518 | − | 0.712651i | \(-0.747494\pi\) | ||||
−0.701518 | + | 0.712651i | \(0.747494\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −146.039 | − | 246.538i | −0.355326 | − | 0.599850i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 180.274i | 0.436500i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −58.4605 | −0.140869 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −198.272 | + | 117.448i | −0.475472 | + | 0.281650i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 97.9159i | 0.233690i | 0.993150 | + | 0.116845i | \(0.0372780\pi\) | ||||
−0.993150 | + | 0.116845i | \(0.962722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −717.315 | −1.70384 | −0.851918 | − | 0.523675i | \(-0.824561\pi\) | ||||
−0.851918 | + | 0.523675i | \(0.824561\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 362.039 | + | 198.362i | 0.855885 | + | 0.468942i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 151.935i | − | 0.357494i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 403.895 | 0.945889 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −129.737 | − | 219.017i | −0.302416 | − | 0.510529i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 293.077i | − | 0.679994i | −0.940427 | − | 0.339997i | \(-0.889574\pi\) | ||
0.940427 | − | 0.339997i | \(-0.110426\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 487.526 | 1.12593 | 0.562963 | − | 0.826482i | \(-0.309661\pi\) | ||||
0.562963 | + | 0.826482i | \(0.309661\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −154.868 | + | 91.7377i | −0.356019 | + | 0.210891i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 247.450i | 0.566247i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −257.237 | −0.585961 | −0.292981 | − | 0.956118i | \(-0.594647\pi\) | ||||
−0.292981 | + | 0.956118i | \(0.594647\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 30.4997 | − | 55.6662i | 0.0691602 | − | 0.126227i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 293.096i | − | 0.661615i | −0.943698 | − | 0.330808i | \(-0.892679\pi\) | ||
0.943698 | − | 0.330808i | \(-0.107321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −135.895 | −0.305381 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −422.355 | − | 713.005i | −0.944866 | − | 1.59509i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 585.614i | − | 1.30426i | −0.758106 | − | 0.652132i | \(-0.773875\pi\) | ||
0.758106 | − | 0.652132i | \(-0.226125\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −401.842 | −0.891002 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −46.5964 | + | 27.6018i | −0.102862 | + | 0.0609312i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 167.411i | − | 0.367936i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −813.052 | −1.77911 | −0.889554 | − | 0.456831i | \(-0.848984\pi\) | ||||
−0.889554 | + | 0.456831i | \(0.848984\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 819.986 | − | 27.5213i | 1.78646 | − | 0.0599593i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 554.074i | − | 1.20190i | −0.799288 | − | 0.600948i | \(-0.794790\pi\) | ||
0.799288 | − | 0.600948i | \(-0.205210\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 449.723 | 0.971324 | 0.485662 | − | 0.874147i | \(-0.338579\pi\) | ||||
0.485662 | + | 0.874147i | \(0.338579\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 27.3509 | + | 46.1728i | 0.0588191 | + | 0.0992964i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 30.7221i | − | 0.0657862i | −0.999459 | − | 0.0328931i | \(-0.989528\pi\) | ||
0.999459 | − | 0.0328931i | \(-0.0104721\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −826.999 | −1.76332 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −268.031 | + | 158.770i | −0.569067 | + | 0.337092i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 122.701i | 0.259411i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −134.868 | −0.283933 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −239.842 | − | 131.410i | −0.502813 | − | 0.275493i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 735.242i | 1.53495i | 0.641078 | + | 0.767476i | \(0.278488\pi\) | ||||
−0.641078 | + | 0.767476i | \(0.721512\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −159.473 | −0.331545 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 105.013 | + | 177.279i | 0.217418 | + | 0.367037i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 80.6162i | − | 0.166219i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 92.6185 | 0.190182 | 0.0950909 | − | 0.995469i | \(-0.469686\pi\) | ||||
0.0950909 | + | 0.995469i | \(0.469686\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.3772 | + | 17.4019i | −0.0600761 | + | 0.0355866i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 898.323i | − | 1.82958i | −0.403933 | − | 0.914789i | \(-0.632357\pi\) | ||
0.403933 | − | 0.914789i | \(-0.367643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 815.368 | 1.65389 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −82.0527 | + | 149.758i | −0.165763 | + | 0.302541i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 116.747i | 0.234903i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 136.921 | 0.274391 | 0.137195 | − | 0.990544i | \(-0.456191\pi\) | ||||
0.137195 | + | 0.990544i | \(0.456191\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 385.710 | + | 651.143i | 0.769881 | + | 1.29969i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 443.077i | 0.880868i | 0.897785 | + | 0.440434i | \(0.145175\pi\) | ||||
−0.897785 | + | 0.440434i | \(0.854825\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −107.684 | −0.213236 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −178.099 | + | 105.498i | −0.351279 | + | 0.208083i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 213.062i | − | 0.418590i | −0.977853 | − | 0.209295i | \(-0.932883\pi\) | ||
0.977853 | − | 0.209295i | \(-0.0671168\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 658.447 | 1.28855 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.4299 | − | 727.879i | −0.0476216 | − | 1.41887i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 313.961i | 0.609634i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 389.210 | 0.752824 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.0662 | + | 30.4987i | 0.0348096 | + | 0.0587643i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.20085i | 0.00614366i | 0.999995 | + | 0.00307183i | \(0.000977795\pi\) | ||||
−0.999995 | + | 0.00307183i | \(0.999022\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 966.644 | 1.84827 | 0.924134 | − | 0.382069i | \(-0.124788\pi\) | ||||
0.924134 | + | 0.382069i | \(0.124788\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −96.6228 | + | 57.2354i | −0.184043 | + | 0.109020i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 243.096i | − | 0.461282i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 444.842 | 0.840911 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 190.053 | + | 104.130i | 0.357915 | + | 0.196102i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 473.575i | − | 0.888509i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 96.4078 | 0.180202 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 105.553 | + | 178.191i | 0.196561 | + | 0.331827i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 59.8439i | − | 0.111028i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 186.105 | 0.344002 | 0.172001 | − | 0.985097i | \(-0.444977\pi\) | ||||
0.172001 | + | 0.985097i | \(0.444977\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 489.601 | − | 290.019i | 0.901659 | − | 0.534106i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 299.280i | 0.549137i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −309.434 | −0.565693 | −0.282847 | − | 0.959165i | \(-0.591279\pi\) | ||||
−0.282847 | + | 0.959165i | \(0.591279\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 233.298 | − | 425.802i | 0.424951 | − | 0.775596i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 723.779i | − | 1.31357i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 351.684 | 0.635957 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 54.5217 | + | 92.0417i | 0.0982373 | + | 0.165841i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 4.00106i | − | 0.00718323i | −0.999994 | − | 0.00359161i | \(-0.998857\pi\) | ||
0.999994 | − | 0.00359161i | \(-0.00114325\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −144.605 | −0.258685 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 665.526 | − | 394.230i | 1.18632 | − | 0.702728i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 166.970i | − | 0.296572i | −0.988945 | − | 0.148286i | \(-0.952624\pi\) | ||
0.988945 | − | 0.148286i | \(-0.0473756\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.6840 | −0.0312991 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −326.399 | − | 511.102i | −0.575660 | − | 0.901414i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 156.289i | − | 0.274673i | −0.990524 | − | 0.137337i | \(-0.956146\pi\) | ||
0.990524 | − | 0.137337i | \(-0.0438542\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −144.105 | −0.252374 | −0.126187 | − | 0.992006i | \(-0.540274\pi\) | ||||
−0.126187 | + | 0.992006i | \(0.540274\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 166.211 | + | 280.591i | 0.290071 | + | 0.489688i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 45.8688i | − | 0.0797719i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 532.947 | 0.923651 | 0.461826 | − | 0.886971i | \(-0.347195\pi\) | ||||
0.461826 | + | 0.886971i | \(0.347195\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −433.495 | + | 256.785i | −0.748697 | + | 0.443497i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 195.738i | − | 0.336899i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −257.842 | −0.442268 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −176.491 | − | 96.7000i | −0.301694 | − | 0.165299i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 190.342i | − | 0.324262i | −0.986769 | − | 0.162131i | \(-0.948163\pi\) | ||
0.986769 | − | 0.162131i | \(-0.0518368\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −215.789 | −0.366366 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 262.460 | + | 443.077i | 0.444096 | + | 0.749707i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 345.719i | − | 0.583001i | −0.956571 | − | 0.291500i | \(-0.905846\pi\) | ||
0.956571 | − | 0.291500i | \(-0.0941544\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 508.710 | 0.854975 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −90.5438 | + | 53.6344i | −0.151665 | + | 0.0898399i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 704.055i | − | 1.17538i | −0.809085 | − | 0.587692i | \(-0.800037\pi\) | ||
0.809085 | − | 0.587692i | \(-0.199963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 338.474 | 0.563185 | 0.281592 | − | 0.959534i | \(-0.409137\pi\) | ||||
0.281592 | + | 0.959534i | \(0.409137\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −477.693 | + | 871.856i | −0.792193 | + | 1.44586i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 109.567i | − | 0.181103i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 816.513 | 1.34516 | 0.672581 | − | 0.740024i | \(-0.265186\pi\) | ||||
0.672581 | + | 0.740024i | \(0.265186\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −307.157 | − | 518.532i | −0.504363 | − | 0.851449i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 458.688i | 0.750717i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 229.263 | 0.374001 | 0.187001 | − | 0.982360i | \(-0.440123\pi\) | ||||
0.187001 | + | 0.982360i | \(0.440123\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −273.329 | + | 161.909i | −0.444437 | + | 0.263266i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1072.25i | − | 1.73785i | −0.494945 | − | 0.868924i | \(-0.664812\pi\) | ||
0.494945 | − | 0.868924i | \(-0.335188\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −80.7103 | −0.130388 | −0.0651941 | − | 0.997873i | \(-0.520767\pi\) | ||||
−0.0651941 | + | 0.997873i | \(0.520767\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 247.552 | − | 8.30863i | 0.398635 | − | 0.0133794i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 455.004i | − | 0.730344i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −349.947 | − | 590.769i | −0.558130 | − | 0.942215i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 484.591i | − | 0.770415i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −492.894 | −0.781131 | −0.390566 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390566 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −150.114 | + | 88.9213i | −0.237147 | + | 0.140476i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 300.663i | − | 0.473485i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 70.5267 | 0.110717 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 123.079 | + | 67.4353i | 0.192612 | + | 0.105533i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 65.4816i | 0.102155i | 0.998695 | + | 0.0510777i | \(0.0162656\pi\) | ||||
−0.998695 | + | 0.0510777i | \(0.983734\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −428.619 | −0.666592 | −0.333296 | − | 0.942822i | \(-0.608161\pi\) | ||||
−0.333296 | + | 0.942822i | \(0.608161\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.4384 | + | 83.4602i | 0.0766487 | + | 0.129396i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 462.801i | 0.715303i | 0.933855 | + | 0.357652i | \(0.116422\pi\) | ||||
−0.933855 | + | 0.357652i | \(0.883578\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 204.316 | 0.314817 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −154.596 | + | 91.5766i | −0.237475 | + | 0.140671i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 425.064i | 0.650941i | 0.945552 | + | 0.325470i | \(0.105523\pi\) | ||||
−0.945552 | + | 0.325470i | \(0.894477\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 492.816 | 0.752390 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 380.333 | − | 694.161i | 0.578894 | − | 1.05656i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 182.769i | 0.277343i | 0.990338 | + | 0.138671i | \(0.0442831\pi\) | ||||
−0.990338 | + | 0.138671i | \(0.955717\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 482.053 | 0.729278 | 0.364639 | − | 0.931149i | \(-0.381192\pi\) | ||||
0.364639 | + | 0.931149i | \(0.381192\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 464.605 | + | 784.330i | 0.700762 | + | 1.18300i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 451.568i | − | 0.679050i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 246.158 | 0.369052 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −256.517 | + | 151.950i | −0.383434 | + | 0.227131i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 457.758i | − | 0.682203i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 184.579 | 0.274264 | 0.137132 | − | 0.990553i | \(-0.456212\pi\) | ||||
0.137132 | + | 0.990553i | \(0.456212\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.52847 | + | 134.924i | 0.00670885 | + | 0.199887i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1065.85i | − | 1.57437i | −0.616715 | − | 0.787187i | \(-0.711537\pi\) | ||
0.616715 | − | 0.787187i | \(-0.288463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 269.920 | 0.397526 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 331.710 | + | 559.982i | 0.487093 | + | 0.822293i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 788.926i | 1.15509i | 0.816359 | + | 0.577545i | \(0.195989\pi\) | ||||
−0.816359 | + | 0.577545i | \(0.804011\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −213.579 | −0.311794 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −840.636 | + | 497.958i | −1.22363 | + | 0.724830i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 303.870i | − | 0.441030i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 932.000 | 1.34877 | 0.674385 | − | 0.738380i | \(-0.264409\pi\) | ||||
0.674385 | + | 0.738380i | \(0.264409\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −501.421 | − | 274.730i | −0.723551 | − | 0.396436i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 171.765i | 0.247144i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1439.05 | 2.06464 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 79.0655 | + | 133.476i | 0.113112 | + | 0.190952i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1352.75i | 1.92974i | 0.262721 | + | 0.964872i | \(0.415380\pi\) | ||||
−0.262721 | + | 0.964872i | \(0.584620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −430.158 | −0.611889 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 264.737 | − | 156.819i | 0.375513 | − | 0.222439i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 360.549i | − | 0.509970i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 269.473 | 0.380075 | 0.190038 | − | 0.981777i | \(-0.439139\pi\) | ||||
0.190038 | + | 0.981777i | \(0.439139\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 203.140 | − | 370.759i | 0.285711 | − | 0.521462i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 73.3901i | − | 0.102931i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −189.737 | −0.265366 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −626.947 | − | 1058.39i | −0.874403 | − | 1.47614i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 537.103i | − | 0.747014i | −0.927627 | − | 0.373507i | \(-0.878155\pi\) | ||
0.927627 | − | 0.373507i | \(-0.121845\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1051.21 | −1.45799 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1149.96 | − | 681.192i | 1.59055 | − | 0.942174i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 134.164i | 0.185054i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1117.83 | 1.53759 | 0.768795 | − | 0.639495i | \(-0.220856\pi\) | ||||
0.768795 | + | 0.639495i | \(0.220856\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −727.359 | + | 48.8800i | −0.997750 | + | 0.0670507i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 439.411i | − | 0.601109i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.52599 | −0.0102674 | −0.00513369 | − | 0.999987i | \(-0.501634\pi\) | ||||
−0.00513369 | + | 0.999987i | \(0.501634\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −24.1121 | − | 40.7052i | −0.0328056 | − | 0.0553812i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 937.288i | 1.27176i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −823.079 | −1.11377 | −0.556887 | − | 0.830588i | \(-0.688004\pi\) | ||||
−0.556887 | + | 0.830588i | \(0.688004\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 696.228 | − | 412.417i | 0.939579 | − | 0.556568i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.21898i | − | 0.00433241i | −0.999998 | − | 0.00216620i | \(-0.999310\pi\) | ||
0.999998 | − | 0.00216620i | \(-0.000689524\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −617.684 | −0.829106 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −206.355 | − | 113.063i | −0.276245 | − | 0.151356i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 322.794i | 0.430967i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1185.63 | −1.57874 | −0.789368 | − | 0.613920i | \(-0.789592\pi\) | ||||
−0.789368 | + | 0.613920i | \(0.789592\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 362.921 | + | 612.671i | 0.481967 | + | 0.813639i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40.3670i | 0.0534662i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 863.315 | 1.14044 | 0.570221 | − | 0.821491i | \(-0.306857\pi\) | ||||
0.570221 | + | 0.821491i | \(0.306857\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 200.921 | − | 119.017i | 0.264718 | − | 0.156808i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 570.597i | − | 0.749800i | −0.927065 | − | 0.374900i | \(-0.877677\pi\) | ||
0.927065 | − | 0.374900i | \(-0.122323\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1002.05 | −1.31331 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 293.842 | − | 536.303i | 0.384107 | − | 0.701050i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 240.789i | 0.313936i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −741.684 | −0.964479 | −0.482239 | − | 0.876040i | \(-0.660176\pi\) | ||||
−0.482239 | + | 0.876040i | \(0.660176\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 487.565 | + | 823.090i | 0.632380 | + | 1.06756i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 623.203i | − | 0.806214i | −0.915153 | − | 0.403107i | \(-0.867930\pi\) | ||
0.915153 | − | 0.403107i | \(-0.132070\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.0000 | 0.0516129 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −308.175 | + | 182.550i | −0.396622 | + | 0.234943i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1277.41i | − | 1.63980i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 132.316 | 0.169419 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −724.078 | + | 24.3023i | −0.924749 | + | 0.0310375i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 232.198i | 0.295793i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 335.303 | 0.426052 | 0.213026 | − | 0.977046i | \(-0.431668\pi\) | ||||
0.213026 | + | 0.977046i | \(0.431668\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −55.3943 | − | 93.5147i | −0.0702083 | − | 0.118523i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 59.2098i | − | 0.0748543i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 539.473 | 0.680294 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −175.381 | + | 103.889i | −0.220606 | + | 0.130678i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 550.520i | − | 0.690740i | −0.938467 | − | 0.345370i | \(-0.887753\pi\) | ||
0.938467 | − | 0.345370i | \(-0.112247\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1393.81 | −1.74445 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −479.684 | − | 262.820i | −0.598856 | − | 0.328115i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 746.258i | − | 0.929337i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 153.579 | 0.190781 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 807.354 | + | 1362.95i | 1.00044 | + | 1.68891i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 560.288i | − | 0.692569i | −0.938130 | − | 0.346284i | \(-0.887443\pi\) | ||
0.938130 | − | 0.346284i | \(-0.112557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −237.842 | −0.293270 | −0.146635 | − | 0.989191i | \(-0.546844\pi\) | ||||
−0.146635 | + | 0.989191i | \(0.546844\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1228.35 | − | 727.624i | 1.51089 | − | 0.894987i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.4498i | 0.0312267i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −390.053 | −0.477421 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 323.772 | − | 590.930i | 0.395326 | − | 0.721526i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 65.4816i | − | 0.0797584i | −0.999205 | − | 0.0398792i | \(-0.987303\pi\) | ||
0.999205 | − | 0.0398792i | \(-0.0126973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −521.512 | −0.633673 | −0.316836 | − | 0.948480i | \(-0.602621\pi\) | ||||
−0.316836 | + | 0.948480i | \(0.602621\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 64.8683 | + | 109.508i | 0.0786283 | + | 0.132738i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 987.512i | 1.19409i | 0.802208 | + | 0.597045i | \(0.203658\pi\) | ||||
−0.802208 | + | 0.597045i | \(0.796342\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −333.631 | −0.402450 | −0.201225 | − | 0.979545i | \(-0.564492\pi\) | ||||
−0.201225 | + | 0.979545i | \(0.564492\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −485.662 | + | 287.686i | −0.584431 | + | 0.346193i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 214.309i | 0.257274i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 564.092 | 0.675559 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.24555 | + | 215.878i | 0.00865657 | + | 0.257919i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 129.363i | 0.154187i | 0.997024 | + | 0.0770934i | \(0.0245640\pi\) | ||||
−0.997024 | + | 0.0770934i | \(0.975436\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 121.000 | 0.143876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 37.3559 | + | 63.0629i | 0.0443130 | + | 0.0748077i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 154.289i | 0.182590i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 366.855 | 0.433123 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 512.254 | − | 303.438i | 0.603362 | − | 0.357407i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 146.297i | − | 0.171912i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1080.42 | −1.26661 | −0.633306 | − | 0.773902i | \(-0.718303\pi\) | ||||
−0.633306 | + | 0.773902i | \(0.718303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −476.061 | − | 260.835i | −0.556797 | − | 0.305071i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 702.548i | 0.819776i | 0.912136 | + | 0.409888i | \(0.134432\pi\) | ||||
−0.912136 | + | 0.409888i | \(0.865568\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −281.132 | −0.327278 | −0.163639 | − | 0.986520i | \(-0.552323\pi\) | ||||
−0.163639 | + | 0.986520i | \(0.552323\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −542.105 | − | 915.163i | −0.629623 | − | 1.06291i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 419.221i | − | 0.485772i | −0.970055 | − | 0.242886i | \(-0.921906\pi\) | ||
0.970055 | − | 0.242886i | \(-0.0780941\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.4213 | 0.0305449 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1637.39 | + | 969.924i | −1.88857 | + | 1.11871i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 398.585i | − | 0.458671i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1104.60 | −1.26820 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 155.912 | − | 284.561i | 0.178593 | − | 0.325958i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 83.7053i | 0.0956632i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1079.42 | −1.23081 | −0.615405 | − | 0.788211i | \(-0.711008\pi\) | ||||
−0.615405 | + | 0.788211i | \(0.711008\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 785.618 | + | 1326.25i | 0.893763 | + | 1.50882i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 748.212i | − | 0.849275i | −0.905363 | − | 0.424638i | \(-0.860401\pi\) | ||
0.905363 | − | 0.424638i | \(-0.139599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −875.749 | −0.991788 | −0.495894 | − | 0.868383i | \(-0.665160\pi\) | ||||
−0.495894 | + | 0.868383i | \(0.665160\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 138.974 | − | 82.3223i | 0.157032 | − | 0.0930196i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1015.05i | − | 1.14436i | −0.820127 | − | 0.572182i | \(-0.806097\pi\) | ||
0.820127 | − | 0.572182i | \(-0.193903\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1006.68 | 1.13238 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −579.263 | + | 369.928i | −0.650126 | + | 0.415183i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1237.25i | 1.38550i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 154.369 | 0.172479 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 140.263 | + | 236.788i | 0.156369 | + | 0.263977i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 214.663i | 0.238779i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 923.368 | 1.02483 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −279.443 | + | 165.530i | −0.309460 | + | 0.183312i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 424.146i | − | 0.468670i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1504.70 | 1.65898 | 0.829491 | − | 0.558520i | \(-0.188631\pi\) | ||||
0.829491 | + | 0.558520i | \(0.188631\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −380.105 | − | 208.261i | −0.418158 | − | 0.229110i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1002.19i | 1.10010i | 0.835131 | + | 0.550051i | \(0.185392\pi\) | ||||
−0.835131 | + | 0.550051i | \(0.814608\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −221.842 | −0.242981 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −184.438 | − | 311.363i | −0.201572 | − | 0.340287i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1650.05i | 1.79940i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 780.289 | 0.849063 | 0.424532 | − | 0.905413i | \(-0.360439\pi\) | ||||
0.424532 | + | 0.905413i | \(0.360439\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.3772 | + | 17.4019i | −0.0318971 | + | 0.0188945i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 155.936i | 0.168945i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 79.7367 | 0.0862018 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −607.201 | + | 1108.23i | −0.655018 | + | 1.19550i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1093.84i | 1.17744i | 0.808339 | + | 0.588718i | \(0.200367\pi\) | ||||
−0.808339 | + | 0.588718i | \(0.799633\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 190.236 | 0.204335 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 793.157 | + | 1338.98i | 0.850115 | + | 1.43513i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 576.552i | − | 0.616633i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −407.947 | −0.435376 | −0.217688 | − | 0.976018i | \(-0.569852\pi\) | ||||
−0.217688 | + | 0.976018i | \(0.569852\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −119.548 | + | 70.8154i | −0.127314 | + | 0.0754157i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 671.008i | − | 0.713079i | −0.934280 | − | 0.356540i | \(-0.883956\pi\) | ||
0.934280 | − | 0.356540i | \(-0.116044\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 434.447 | 0.460707 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −451.754 | + | 15.1623i | −0.478047 | + | 0.0160447i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1608.13i | − | 1.69813i | −0.528290 | − | 0.849064i | \(-0.677167\pi\) | ||
0.528290 | − | 0.849064i | \(-0.322833\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 879.473 | 0.926737 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −59.7758 | − | 100.911i | −0.0628557 | − | 0.106111i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 695.440i | − | 0.729737i | −0.931059 | − | 0.364869i | \(-0.881114\pi\) | ||
0.931059 | − | 0.364869i | \(-0.118886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 243.079 | 0.254533 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −587.684 | + | 348.120i | −0.614090 | + | 0.363762i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 715.107i | − | 0.745680i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −897.000 | −0.933403 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 340.302 | + | 186.453i | 0.353377 | + | 0.193617i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 375.542i | 0.389162i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1030.07 | 1.06522 | 0.532609 | − | 0.846361i | \(-0.321212\pi\) | ||||
0.532609 | + | 0.846361i | \(0.321212\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1253.21 | + | 2115.63i | 1.29330 | + | 2.18331i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1165.24i | 1.20004i | 0.799986 | + | 0.600019i | \(0.204840\pi\) | ||||
−0.799986 | + | 0.600019i | \(0.795160\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −575.106 | −0.591065 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −129.057 | + | 76.4481i | −0.132366 | + | 0.0784083i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 726.440i | 0.743541i | 0.928325 | + | 0.371771i | \(0.121249\pi\) | ||||
−0.928325 | + | 0.371771i | \(0.878751\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −515.684 | −0.526746 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −578.807 | + | 1056.40i | −0.590017 | + | 1.07686i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1024.21i | − | 1.04192i | −0.853581 | − | 0.520960i | \(-0.825574\pi\) | ||
0.853581 | − | 0.520960i | \(-0.174426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 383.842 | 0.389687 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 525.064 | + | 886.395i | 0.531980 | + | 0.898070i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 132.657i | − | 0.134133i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1797.89 | 1.81422 | 0.907111 | − | 0.420892i | \(-0.138283\pi\) | ||||
0.907111 | + | 0.420892i | \(0.138283\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1149.69 | + | 681.031i | −1.15780 | + | 0.685832i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 78.4390i | 0.0788332i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −901.368 | −0.904080 | −0.452040 | − | 0.891998i | \(-0.649304\pi\) | ||||
−0.452040 | + | 0.891998i | \(0.649304\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.4434 | + | 430.336i | 0.0144579 | + | 0.430766i |
(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 | 960.3.l.f.641.3 | 4 | ||
3.2 | odd | 2 | inner | 960.3.l.f.641.4 | 4 | ||
4.3 | odd | 2 | 960.3.l.e.641.2 | 4 | |||
8.3 | odd | 2 | 30.3.d.a.11.4 | yes | 4 | ||
8.5 | even | 2 | 240.3.l.c.161.2 | 4 | |||
12.11 | even | 2 | 960.3.l.e.641.1 | 4 | |||
24.5 | odd | 2 | 240.3.l.c.161.1 | 4 | |||
24.11 | even | 2 | 30.3.d.a.11.2 | ✓ | 4 | ||
40.3 | even | 4 | 150.3.b.b.149.8 | 8 | |||
40.13 | odd | 4 | 1200.3.c.k.449.3 | 8 | |||
40.19 | odd | 2 | 150.3.d.c.101.1 | 4 | |||
40.27 | even | 4 | 150.3.b.b.149.1 | 8 | |||
40.29 | even | 2 | 1200.3.l.u.401.3 | 4 | |||
40.37 | odd | 4 | 1200.3.c.k.449.6 | 8 | |||
72.11 | even | 6 | 810.3.h.a.701.2 | 8 | |||
72.43 | odd | 6 | 810.3.h.a.701.3 | 8 | |||
72.59 | even | 6 | 810.3.h.a.431.3 | 8 | |||
72.67 | odd | 6 | 810.3.h.a.431.2 | 8 | |||
120.29 | odd | 2 | 1200.3.l.u.401.4 | 4 | |||
120.53 | even | 4 | 1200.3.c.k.449.5 | 8 | |||
120.59 | even | 2 | 150.3.d.c.101.3 | 4 | |||
120.77 | even | 4 | 1200.3.c.k.449.4 | 8 | |||
120.83 | odd | 4 | 150.3.b.b.149.2 | 8 | |||
120.107 | odd | 4 | 150.3.b.b.149.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.3.d.a.11.2 | ✓ | 4 | 24.11 | even | 2 | ||
30.3.d.a.11.4 | yes | 4 | 8.3 | odd | 2 | ||
150.3.b.b.149.1 | 8 | 40.27 | even | 4 | |||
150.3.b.b.149.2 | 8 | 120.83 | odd | 4 | |||
150.3.b.b.149.7 | 8 | 120.107 | odd | 4 | |||
150.3.b.b.149.8 | 8 | 40.3 | even | 4 | |||
150.3.d.c.101.1 | 4 | 40.19 | odd | 2 | |||
150.3.d.c.101.3 | 4 | 120.59 | even | 2 | |||
240.3.l.c.161.1 | 4 | 24.5 | odd | 2 | |||
240.3.l.c.161.2 | 4 | 8.5 | even | 2 | |||
810.3.h.a.431.2 | 8 | 72.67 | odd | 6 | |||
810.3.h.a.431.3 | 8 | 72.59 | even | 6 | |||
810.3.h.a.701.2 | 8 | 72.11 | even | 6 | |||
810.3.h.a.701.3 | 8 | 72.43 | odd | 6 | |||
960.3.l.e.641.1 | 4 | 12.11 | even | 2 | |||
960.3.l.e.641.2 | 4 | 4.3 | odd | 2 | |||
960.3.l.f.641.3 | 4 | 1.1 | even | 1 | trivial | ||
960.3.l.f.641.4 | 4 | 3.2 | odd | 2 | inner | ||
1200.3.c.k.449.3 | 8 | 40.13 | odd | 4 | |||
1200.3.c.k.449.4 | 8 | 120.77 | even | 4 | |||
1200.3.c.k.449.5 | 8 | 120.53 | even | 4 | |||
1200.3.c.k.449.6 | 8 | 40.37 | odd | 4 | |||
1200.3.l.u.401.3 | 4 | 40.29 | even | 2 | |||
1200.3.l.u.401.4 | 4 | 120.29 | odd | 2 |