Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(449,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.6 | ||
Root | \(-0.437016 + 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.449 |
Dual form | 1200.3.c.k.449.5 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.52896 | + | 2.58114i | 0.509654 | + | 0.860380i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.48683i | 1.06955i | 0.844995 | + | 0.534774i | \(0.179603\pi\) | ||||
−0.844995 | + | 0.534774i | \(0.820397\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.32456 | + | 7.89292i | −0.480506 | + | 0.876991i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.48528i | 0.771389i | 0.922627 | + | 0.385695i | \(0.126038\pi\) | ||||
−0.922627 | + | 0.385695i | \(0.873962\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.0000i | 0.769231i | 0.923077 | + | 0.384615i | \(0.125666\pi\) | ||||
−0.923077 | + | 0.384615i | \(0.874334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −30.3870 | −1.78747 | −0.893734 | − | 0.448596i | \(-0.851924\pi\) | ||||
−0.893734 | + | 0.448596i | \(0.851924\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | 9.17377 | 0.398859 | 0.199430 | − | 0.979912i | \(-0.436091\pi\) | ||||
0.199430 | + | 0.979912i | \(0.436091\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −26.9848 | + | 0.905694i | −0.999437 | + | 0.0335442i | ||||
\(28\) | 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 | ||||||||
\(33\) | −21.9017 | + | 12.9737i | −0.663688 | + | 0.393141i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 15.9473i | 0.431009i | 0.976503 | + | 0.215504i | \(0.0691396\pi\) | ||||
−0.976503 | + | 0.215504i | \(0.930860\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | − | 14.4605i | − | 0.336291i | −0.985762 | − | 0.168145i | \(-0.946222\pi\) | ||
0.985762 | − | 0.168145i | \(-0.0537778\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −45.8688 | −0.975933 | −0.487966 | − | 0.872862i | \(-0.662261\pi\) | ||||
−0.487966 | + | 0.872862i | \(0.662261\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.05267 | −0.143932 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −46.4605 | − | 78.4330i | −0.910990 | − | 1.53790i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 30.3870 | 0.573339 | 0.286670 | − | 0.958030i | \(-0.407452\pi\) | ||||
0.286670 | + | 0.958030i | \(0.407452\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 41.2417 | + | 69.6228i | 0.723538 | + | 1.22145i | ||||
\(58\) | 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 | \(-0.645799\pi\) | ||||
−0.442191 | + | 0.896921i | \(0.645799\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −59.0930 | − | 32.3772i | −0.937984 | − | 0.513924i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 110.460i | 1.64866i | 0.566107 | + | 0.824332i | \(0.308449\pi\) | ||||
−0.566107 | + | 0.824332i | \(0.691551\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | − | 87.9473i | − | 1.20476i | −0.798210 | − | 0.602379i | \(-0.794220\pi\) | ||
0.798210 | − | 0.602379i | \(-0.205780\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −63.5279 | −0.825037 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −46.9737 | −0.594603 | −0.297302 | − | 0.954784i | \(-0.596087\pi\) | ||||
−0.297302 | + | 0.954784i | \(0.596087\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −43.5964 | − | 68.2668i | −0.538228 | − | 0.842799i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 26.1443 | 0.314992 | 0.157496 | − | 0.987520i | \(-0.449658\pi\) | ||||
0.157496 | + | 0.987520i | \(0.449658\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 69.2592 | − | 41.0263i | 0.796083 | − | 0.471567i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 60.7739i | 0.682853i | 0.939908 | + | 0.341427i | \(0.110910\pi\) | ||||
−0.939908 | + | 0.341427i | \(0.889090\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −74.8683 | −0.822729 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.2317 | − | 20.6491i | −0.131524 | − | 0.222033i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 36.0527i | 0.371677i | 0.982580 | + | 0.185838i | \(0.0595001\pi\) | ||||
−0.982580 | + | 0.185838i | \(0.940500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −66.9737 | − | 36.6951i | −0.676502 | − | 0.370657i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 48.1577i | 0.476809i | 0.971166 | + | 0.238405i | \(0.0766245\pi\) | ||||
−0.971166 | + | 0.238405i | \(0.923376\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 140.408i | 1.36318i | 0.731733 | + | 0.681591i | \(0.238712\pi\) | ||||
−0.731733 | + | 0.681591i | \(0.761288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 43.1149 | 0.402943 | 0.201471 | − | 0.979494i | \(-0.435428\pi\) | ||||
0.201471 | + | 0.979494i | \(0.435428\pi\) | |||||||
\(108\) | 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 | ||||||||
\(113\) | −7.90852 | −0.0699869 | −0.0349935 | − | 0.999388i | \(-0.511141\pi\) | ||||
−0.0349935 | + | 0.999388i | \(0.511141\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −78.9292 | − | 43.2456i | −0.674609 | − | 0.369620i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 227.502i | − | 1.91178i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 49.0000 | 0.404959 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 122.236 | − | 72.4078i | 0.993792 | − | 0.588682i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 134.460i | 1.05874i | 0.848390 | + | 0.529372i | \(0.177572\pi\) | ||||
−0.848390 | + | 0.529372i | \(0.822428\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 37.3246 | − | 22.1095i | 0.289338 | − | 0.171392i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 220.394i | − | 1.68240i | −0.540727 | − | 0.841198i | \(-0.681851\pi\) | ||
0.540727 | − | 0.841198i | \(-0.318149\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 201.947i | 1.51840i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 95.5153 | 0.697192 | 0.348596 | − | 0.937273i | \(-0.386659\pi\) | ||||
0.348596 | + | 0.937273i | \(0.386659\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | −84.8528 | −0.593376 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.7833 | − | 18.2039i | −0.0733555 | − | 0.123836i | ||||
\(148\) | 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 | ||||||||
\(153\) | 131.410 | − | 239.842i | 0.858890 | − | 1.56759i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 103.842i | 0.661414i | 0.943733 | + | 0.330707i | \(0.107287\pi\) | ||||
−0.943733 | + | 0.330707i | \(0.892713\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 46.4605 | + | 78.4330i | 0.292204 | + | 0.493289i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 68.6825i | 0.426599i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 11.3815i | − | 0.0698251i | −0.999390 | − | 0.0349126i | \(-0.988885\pi\) | ||
0.999390 | − | 0.0349126i | \(-0.0111153\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −252.270 | −1.51060 | −0.755298 | − | 0.655382i | \(-0.772508\pi\) | ||||
−0.755298 | + | 0.655382i | \(0.772508\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 69.0000 | 0.408284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −116.649 | + | 212.901i | −0.682159 | + | 1.24504i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.8160 | −0.0683005 | −0.0341502 | − | 0.999417i | \(-0.510872\pi\) | ||||
−0.0341502 | + | 0.999417i | \(0.510872\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −62.1509 | + | 36.8157i | −0.351135 | + | 0.207998i | ||||
\(178\) | 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 | \(-0.675557\pi\) | ||||
−0.523989 | + | 0.851725i | \(0.675557\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −82.4834 | − | 139.246i | −0.450729 | − | 0.760905i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 257.842i | − | 1.37883i | ||||||
\(188\) | 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 | ||||||||
\(193\) | 167.947i | 0.870193i | 0.900384 | + | 0.435097i | \(0.143286\pi\) | ||||
−0.900384 | + | 0.435097i | \(0.856714\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 171.659 | 0.871367 | 0.435684 | − | 0.900100i | \(-0.356507\pi\) | ||||
0.435684 | + | 0.900100i | \(0.356507\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 35.0790 | 0.176276 | 0.0881382 | − | 0.996108i | \(-0.471908\pi\) | ||||
0.0881382 | + | 0.996108i | \(0.471908\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −285.114 | + | 168.890i | −1.41848 | + | 0.840248i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 200.893 | 0.989620 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −39.6725 | + | 72.4078i | −0.191654 | + | 0.349796i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 228.879i | 1.09512i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 58.1580 | 0.275630 | 0.137815 | − | 0.990458i | \(-0.455992\pi\) | ||||
0.137815 | + | 0.990458i | \(0.455992\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −40.2492 | + | 23.8420i | −0.188963 | + | 0.111934i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 59.8947i | − | 0.276012i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 227.004 | − | 134.468i | 1.03655 | − | 0.614009i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 303.870i | − | 1.37498i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 99.3815i | 0.445657i | 0.974858 | + | 0.222828i | \(0.0715290\pi\) | ||||
−0.974858 | + | 0.222828i | \(0.928471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 216.951 | 0.955733 | 0.477867 | − | 0.878432i | \(-0.341410\pi\) | ||||
0.477867 | + | 0.878432i | \(0.341410\pi\) | |||||||
\(228\) | 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 | ||||||||
\(233\) | 51.7119 | 0.221939 | 0.110970 | − | 0.993824i | \(-0.464604\pi\) | ||||
0.110970 | + | 0.993824i | \(0.464604\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −71.8209 | − | 121.246i | −0.303042 | − | 0.511585i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 410.047i | 1.71568i | 0.513917 | + | 0.857840i | \(0.328194\pi\) | ||||
−0.513917 | + | 0.857840i | \(0.671806\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 445.526 | 1.84866 | 0.924328 | − | 0.381599i | \(-0.124627\pi\) | ||||
0.924328 | + | 0.381599i | \(0.124627\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 109.549 | − | 216.906i | 0.450818 | − | 0.892616i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 269.737i | 1.09205i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 39.9737 | + | 67.4821i | 0.160537 | + | 0.271013i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 237.364i | − | 0.945675i | −0.881150 | − | 0.472838i | \(-0.843230\pi\) | ||
0.881150 | − | 0.472838i | \(-0.156770\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 77.8420i | 0.307676i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −318.887 | −1.24080 | −0.620402 | − | 0.784284i | \(-0.713030\pi\) | ||||
−0.620402 | + | 0.784284i | \(0.713030\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −119.395 | −0.460985 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 211.789 | + | 116.040i | 0.811453 | + | 0.444598i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −36.2300 | −0.137757 | −0.0688784 | − | 0.997625i | \(-0.521942\pi\) | ||||
−0.0688784 | + | 0.997625i | \(0.521942\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −156.866 | + | 92.9210i | −0.587513 | + | 0.348019i | ||||
\(268\) | 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 | ||||||||
\(273\) | −114.471 | − | 193.246i | −0.419307 | − | 0.707859i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 188.158i | 0.679271i | 0.940557 | + | 0.339635i | \(0.110304\pi\) | ||||
−0.940557 | + | 0.339635i | \(0.889696\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 198.460i | 0.701274i | 0.936511 | + | 0.350637i | \(0.114035\pi\) | ||||
−0.936511 | + | 0.350637i | \(0.885965\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 354.558 | 1.23539 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 634.368 | 2.19504 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −93.0569 | + | 55.1231i | −0.319783 | + | 0.189427i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −513.825 | −1.75367 | −0.876834 | − | 0.480794i | \(-0.840349\pi\) | ||||
−0.876834 | + | 0.480794i | \(0.840349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.68507 | − | 228.974i | −0.0258757 | − | 0.770955i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 91.7377i | 0.306815i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 108.263 | 0.359679 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −124.302 | + | 73.6313i | −0.410237 | + | 0.243008i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.3815i | 0.0370733i | 0.999828 | + | 0.0185366i | \(0.00590073\pi\) | ||||
−0.999828 | + | 0.0185366i | \(0.994099\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 46.3160i | 0.147974i | 0.997259 | + | 0.0739872i | \(0.0235724\pi\) | ||||
−0.997259 | + | 0.0739872i | \(0.976428\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −39.0957 | −0.123330 | −0.0616651 | − | 0.998097i | \(-0.519641\pi\) | ||||
−0.0616651 | + | 0.998097i | \(0.519641\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 227.684 | 0.713743 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 65.9210 | + | 111.286i | 0.205361 | + | 0.346684i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −819.648 | −2.53761 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −204.639 | − | 345.465i | −0.625808 | − | 1.05647i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 343.412i | − | 1.04381i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 445.421 | 1.34568 | 0.672841 | − | 0.739787i | \(-0.265074\pi\) | ||||
0.672841 | + | 0.739787i | \(0.265074\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −125.871 | − | 68.9651i | −0.377991 | − | 0.207102i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 325.684i | 0.966421i | 0.875504 | + | 0.483211i | \(0.160529\pi\) | ||||
−0.875504 | + | 0.483211i | \(0.839471\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.0918 | − | 20.4130i | −0.0356691 | − | 0.0602153i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 67.8823i | − | 0.199068i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 314.053i | 0.915605i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −51.8236 | −0.149348 | −0.0746738 | − | 0.997208i | \(-0.523792\pi\) | ||||
−0.0746738 | + | 0.997208i | \(0.523792\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | 569.797 | 1.61416 | 0.807078 | − | 0.590445i | \(-0.201048\pi\) | ||||
0.807078 | + | 0.590445i | \(0.201048\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 587.215 | − | 347.842i | 1.64486 | − | 0.974347i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 274.283i | − | 0.764019i | −0.924158 | − | 0.382010i | \(-0.875232\pi\) | ||
0.924158 | − | 0.382010i | \(-0.124768\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 366.579 | 1.01545 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 74.9191 | + | 126.476i | 0.206389 | + | 0.348418i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 461.828i | − | 1.25839i | −0.777248 | − | 0.629194i | \(-0.783385\pi\) | ||
0.777248 | − | 0.629194i | \(-0.216615\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 373.789 | + | 204.800i | 1.01298 | + | 0.555014i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 227.502i | 0.613213i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 491.947i | 1.31889i | 0.751751 | + | 0.659447i | \(0.229209\pi\) | ||||
−0.751751 | + | 0.659447i | \(0.770791\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 268.328 | 0.711746 | ||||||||
\(378\) | 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 | ||||||||
\(383\) | 522.422 | 1.36402 | 0.682012 | − | 0.731341i | \(-0.261105\pi\) | ||||
0.682012 | + | 0.731341i | \(0.261105\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 114.136 | + | 62.5352i | 0.294924 | + | 0.161590i | ||||
\(388\) | 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 | ||||||||
\(393\) | 568.867 | − | 336.974i | 1.44750 | − | 0.857439i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 214.000i | − | 0.539043i | −0.962994 | − | 0.269521i | \(-0.913135\pi\) | ||
0.962994 | − | 0.269521i | \(-0.0868655\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − | 80.0000i | − | 0.198511i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −135.318 | −0.332476 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 573.842 | 1.40304 | 0.701518 | − | 0.712651i | \(-0.252506\pi\) | ||||
0.701518 | + | 0.712651i | \(0.252506\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 146.039 | + | 246.538i | 0.355326 | + | 0.599850i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −180.274 | −0.436500 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −117.448 | − | 198.272i | −0.281650 | − | 0.475472i | ||||
\(418\) | 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 | \(-0.175439\pi\) | ||||
0.851918 | + | 0.523675i | \(0.175439\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 198.362 | − | 362.039i | 0.468942 | − | 0.855885i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 403.895i | − | 0.945889i | ||||||
\(428\) | 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 | ||||||||
\(433\) | − | 487.526i | − | 1.12593i | −0.826482 | − | 0.562963i | \(-0.809661\pi\) | ||
0.826482 | − | 0.562963i | \(-0.190339\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 247.450 | 0.566247 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 257.237 | 0.585961 | 0.292981 | − | 0.956118i | \(-0.405353\pi\) | ||||
0.292981 | + | 0.956118i | \(0.405353\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 30.4997 | − | 55.6662i | 0.0691602 | − | 0.126227i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 293.096 | 0.661615 | 0.330808 | − | 0.943698i | \(-0.392679\pi\) | ||||
0.330808 | + | 0.943698i | \(0.392679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 713.005 | − | 422.355i | 1.59509 | − | 0.944866i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 585.614i | 1.30426i | 0.758106 | + | 0.652132i | \(0.226125\pi\) | ||||
−0.758106 | + | 0.652132i | \(0.773875\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 401.842 | 0.891002 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −27.6018 | − | 46.5964i | −0.0609312 | − | 0.102862i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 813.052i | − | 1.77911i | −0.456831 | − | 0.889554i | \(-0.651016\pi\) | ||
0.456831 | − | 0.889554i | \(-0.348984\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 819.986 | − | 27.5213i | 1.78646 | − | 0.0599593i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 554.074i | 1.20190i | 0.799288 | + | 0.600948i | \(0.205210\pi\) | ||||
−0.799288 | + | 0.600948i | \(0.794790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 449.723i | − | 0.971324i | −0.874147 | − | 0.485662i | \(-0.838579\pi\) | ||
0.874147 | − | 0.485662i | \(-0.161421\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.7221 | −0.0657862 | −0.0328931 | − | 0.999459i | \(-0.510472\pi\) | ||||
−0.0328931 | + | 0.999459i | \(0.510472\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −826.999 | −1.76332 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −268.031 | + | 158.770i | −0.569067 | + | 0.337092i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 122.701 | 0.259411 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −131.410 | + | 239.842i | −0.275493 | + | 0.502813i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 735.242i | − | 1.53495i | −0.641078 | − | 0.767476i | \(-0.721512\pi\) | ||
0.641078 | − | 0.767476i | \(-0.278488\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −159.473 | −0.331545 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −177.279 | + | 105.013i | −0.367037 | + | 0.217418i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 92.6185i | 0.190182i | 0.995469 | + | 0.0950909i | \(0.0303142\pi\) | ||||
−0.995469 | + | 0.0950909i | \(0.969686\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.3772 | − | 17.4019i | 0.0600761 | − | 0.0355866i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 898.323i | 1.82958i | 0.403933 | + | 0.914789i | \(0.367643\pi\) | ||||
−0.403933 | + | 0.914789i | \(0.632357\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 815.368i | 1.65389i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −116.747 | −0.234903 | ||||||||
\(498\) | 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 | ||||||||
\(503\) | 443.077 | 0.880868 | 0.440434 | − | 0.897785i | \(-0.354825\pi\) | ||||
0.440434 | + | 0.897785i | \(0.354825\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 105.498 | + | 178.099i | 0.208083 | + | 0.351279i | ||||
\(508\) | 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 | ||||||||
\(513\) | −727.879 | + | 24.4299i | −1.41887 | + | 0.0476216i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 389.210i | − | 0.752824i | ||||||
\(518\) | 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 | ||||||||
\(523\) | 966.644i | 1.84827i | 0.382069 | + | 0.924134i | \(0.375212\pi\) | ||||
−0.382069 | + | 0.924134i | \(0.624788\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 243.096 | 0.461282 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −444.842 | −0.840911 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −190.053 | − | 104.130i | −0.357915 | − | 0.196102i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 473.575 | 0.888509 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −178.191 | + | 105.553i | −0.331827 | + | 0.196561i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 59.8439i | − | 0.111028i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −186.105 | −0.344002 | −0.172001 | − | 0.985097i | \(-0.555023\pi\) | ||||
−0.172001 | + | 0.985097i | \(0.555023\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −290.019 | − | 489.601i | −0.534106 | − | 0.901659i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 309.434i | 0.565693i | 0.959165 | + | 0.282847i | \(0.0912787\pi\) | ||||
−0.959165 | + | 0.282847i | \(0.908721\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 233.298 | − | 425.802i | 0.424951 | − | 0.775596i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 723.779i | − | 1.31357i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 351.684i | − | 0.635957i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.00106 | −0.00718323 | −0.00359161 | − | 0.999994i | \(-0.501143\pi\) | ||||
−0.00359161 | + | 0.999994i | \(0.501143\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 144.605 | 0.258685 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 665.526 | − | 394.230i | 1.18632 | − | 0.702728i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 166.970 | 0.296572 | 0.148286 | − | 0.988945i | \(-0.452624\pi\) | ||||
0.148286 | + | 0.988945i | \(0.452624\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 511.102 | − | 326.399i | 0.901414 | − | 0.575660i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 156.289i | 0.274673i | 0.990524 | + | 0.137337i | \(0.0438542\pi\) | ||||
−0.990524 | + | 0.137337i | \(0.956146\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 144.105 | 0.252374 | 0.126187 | − | 0.992006i | \(-0.459726\pi\) | ||||
0.126187 | + | 0.992006i | \(0.459726\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −280.591 | + | 166.211i | −0.489688 | + | 0.290071i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 532.947i | 0.923651i | 0.886971 | + | 0.461826i | \(0.152805\pi\) | ||||
−0.886971 | + | 0.461826i | \(0.847195\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −433.495 | + | 256.785i | −0.748697 | + | 0.443497i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 195.738i | 0.336899i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 257.842i | 0.442268i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −190.342 | −0.324262 | −0.162131 | − | 0.986769i | \(-0.551837\pi\) | ||||
−0.162131 | + | 0.986769i | \(0.551837\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −215.789 | −0.366366 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 262.460 | + | 443.077i | 0.444096 | + | 0.749707i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −345.719 | −0.583001 | −0.291500 | − | 0.956571i | \(-0.594154\pi\) | ||||
−0.291500 | + | 0.956571i | \(0.594154\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 53.6344 | + | 90.5438i | 0.0898399 | + | 0.151665i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 704.055i | 1.17538i | 0.809085 | + | 0.587692i | \(0.199963\pi\) | ||||
−0.809085 | + | 0.587692i | \(0.800037\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 338.474 | 0.563185 | 0.281592 | − | 0.959534i | \(-0.409137\pi\) | ||||
0.281592 | + | 0.959534i | \(0.409137\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −871.856 | − | 477.693i | −1.44586 | − | 0.792193i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 816.513i | 1.34516i | 0.740024 | + | 0.672581i | \(0.234814\pi\) | ||||
−0.740024 | + | 0.672581i | \(0.765186\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 307.157 | + | 518.532i | 0.504363 | + | 0.851449i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 458.688i | − | 0.750717i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 229.263i | 0.374001i | 0.982360 | + | 0.187001i | \(0.0598766\pi\) | ||||
−0.982360 | + | 0.187001i | \(0.940123\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1072.25 | 1.73785 | 0.868924 | − | 0.494945i | \(-0.164812\pi\) | ||||
0.868924 | + | 0.494945i | \(0.164812\pi\) | |||||||
\(618\) | 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 | ||||||||
\(623\) | −455.004 | −0.730344 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −590.769 | + | 349.947i | −0.942215 | + | 0.558130i | ||||
\(628\) | 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 | ||||||||
\(633\) | 88.9213 | + | 150.114i | 0.140476 | + | 0.237147i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 70.5267i | − | 0.110717i | ||||||
\(638\) | 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 | ||||||||
\(643\) | − | 428.619i | − | 0.666592i | −0.942822 | − | 0.333296i | \(-0.891839\pi\) | ||
0.942822 | − | 0.333296i | \(-0.108161\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −462.801 | −0.715303 | −0.357652 | − | 0.933855i | \(-0.616422\pi\) | ||||
−0.357652 | + | 0.933855i | \(0.616422\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −204.316 | −0.314817 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 154.596 | − | 91.5766i | 0.237475 | − | 0.140671i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −425.064 | −0.650941 | −0.325470 | − | 0.945552i | \(-0.605523\pi\) | ||||
−0.325470 | + | 0.945552i | \(0.605523\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 694.161 | + | 380.333i | 1.05656 | + | 0.578894i | ||||
\(658\) | 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 | \(-0.618808\pi\) | ||||
−0.364639 | + | 0.931149i | \(0.618808\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 784.330 | − | 464.605i | 1.18300 | − | 0.700762i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 246.158i | − | 0.369052i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −256.517 | + | 151.950i | −0.383434 | + | 0.227131i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 457.758i | − | 0.682203i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 184.579i | − | 0.274264i | −0.990553 | − | 0.137132i | \(-0.956212\pi\) | ||
0.990553 | − | 0.137132i | \(-0.0437884\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1065.85 | −1.57437 | −0.787187 | − | 0.616715i | \(-0.788463\pi\) | ||||
−0.787187 | + | 0.616715i | \(0.788463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −269.920 | −0.397526 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 331.710 | + | 559.982i | 0.487093 | + | 0.822293i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −788.926 | −1.15509 | −0.577545 | − | 0.816359i | \(-0.695989\pi\) | ||||
−0.577545 | + | 0.816359i | \(0.695989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −497.958 | − | 840.636i | −0.724830 | − | 1.22363i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 303.870i | 0.441030i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −932.000 | −1.34877 | −0.674385 | − | 0.738380i | \(-0.735591\pi\) | ||||
−0.674385 | + | 0.738380i | \(0.735591\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 274.730 | − | 501.421i | 0.396436 | − | 0.723551i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1439.05i | 2.06464i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 79.0655 | + | 133.476i | 0.113112 | + | 0.190952i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1352.75i | − | 1.92974i | −0.262721 | − | 0.964872i | \(-0.584620\pi\) | ||
0.262721 | − | 0.964872i | \(-0.415380\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 430.158i | 0.611889i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −360.549 | −0.509970 | ||||||||
\(708\) | 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 | ||||||||
\(713\) | −73.3901 | −0.102931 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1058.39 | + | 626.947i | −1.47614 | + | 0.874403i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 537.103i | 0.747014i | 0.927627 | + | 0.373507i | \(0.121845\pi\) | ||||
−0.927627 | + | 0.373507i | \(0.878155\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1051.21 | −1.45799 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 681.192 | + | 1149.96i | 0.942174 | + | 1.59055i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1117.83i | 1.53759i | 0.639495 | + | 0.768795i | \(0.279144\pi\) | ||||
−0.639495 | + | 0.768795i | \(0.720856\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 727.359 | − | 48.8800i | 0.997750 | − | 0.0670507i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 439.411i | 0.601109i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 7.52599i | − | 0.0102674i | −0.999987 | − | 0.00513369i | \(-0.998366\pi\) | ||
0.999987 | − | 0.00513369i | \(-0.00163411\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −937.288 | −1.27176 | ||||||||
\(738\) | 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 | ||||||||
\(743\) | −3.21898 | −0.00433241 | −0.00216620 | − | 0.999998i | \(-0.500690\pi\) | ||||
−0.00216620 | + | 0.999998i | \(0.500690\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −113.063 | + | 206.355i | −0.151356 | + | 0.276245i | ||||
\(748\) | 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 | ||||||||
\(753\) | 612.671 | − | 362.921i | 0.813639 | − | 0.481967i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 863.315i | − | 1.14044i | −0.821491 | − | 0.570221i | \(-0.806857\pi\) | ||
0.821491 | − | 0.570221i | \(-0.193143\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | − | 1002.05i | − | 1.31331i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −240.789 | −0.313936 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 741.684 | 0.964479 | 0.482239 | − | 0.876040i | \(-0.339824\pi\) | ||||
0.482239 | + | 0.876040i | \(0.339824\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −487.565 | − | 823.090i | −0.632380 | − | 1.06756i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 623.203 | 0.806214 | 0.403107 | − | 0.915153i | \(-0.367930\pi\) | ||||
0.403107 | + | 0.915153i | \(0.367930\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −182.550 | − | 308.175i | −0.234943 | − | 0.396622i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1277.41i | − | 1.63980i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −132.316 | −0.169419 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.3023 | + | 724.078i | 0.0310375 | + | 0.924749i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 335.303i | − | 0.426052i | −0.977046 | − | 0.213026i | \(-0.931668\pi\) | ||
0.977046 | − | 0.213026i | \(-0.0683320\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −55.3943 | − | 93.5147i | −0.0702083 | − | 0.118523i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 59.2098i | − | 0.0748543i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 539.473i | − | 0.680294i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −550.520 | −0.690740 | −0.345370 | − | 0.938467i | \(-0.612247\pi\) | ||||
−0.345370 | + | 0.938467i | \(0.612247\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1393.81 | 1.74445 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −479.684 | − | 262.820i | −0.598856 | − | 0.328115i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 746.258 | 0.929337 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1362.95 | + | 807.354i | −1.68891 | + | 1.00044i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 560.288i | 0.692569i | 0.938130 | + | 0.346284i | \(0.112557\pi\) | ||||
−0.938130 | + | 0.346284i | \(0.887443\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 237.842 | 0.293270 | 0.146635 | − | 0.989191i | \(-0.453156\pi\) | ||||
0.146635 | + | 0.989191i | \(0.453156\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 727.624 | + | 1228.35i | 0.894987 | + | 1.51089i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 390.053i | − | 0.477421i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 323.772 | − | 590.930i | 0.395326 | − | 0.721526i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 65.4816i | 0.0797584i | 0.999205 | + | 0.0398792i | \(0.0126973\pi\) | ||||
−0.999205 | + | 0.0398792i | \(0.987303\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 521.512i | 0.633673i | 0.948480 | + | 0.316836i | \(0.102621\pi\) | ||||
−0.948480 | + | 0.316836i | \(0.897379\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 987.512 | 1.19409 | 0.597045 | − | 0.802208i | \(-0.296342\pi\) | ||||
0.597045 | + | 0.802208i | \(0.296342\pi\) | |||||||
\(828\) | 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 | ||||||||
\(833\) | 214.309 | 0.257274 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 215.878 | − | 7.24555i | 0.257919 | − | 0.00865657i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 129.363i | − | 0.154187i | −0.997024 | − | 0.0770934i | \(-0.975436\pi\) | ||
0.997024 | − | 0.0770934i | \(-0.0245640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 121.000 | 0.143876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −63.0629 | + | 37.3559i | −0.0748077 | + | 0.0443130i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 366.855i | 0.433123i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −512.254 | + | 303.438i | −0.603362 | + | 0.357407i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 146.297i | 0.171912i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1080.42i | − | 1.26661i | −0.773902 | − | 0.633306i | \(-0.781697\pi\) | ||
0.773902 | − | 0.633306i | \(-0.218303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −702.548 | −0.819776 | −0.409888 | − | 0.912136i | \(-0.634432\pi\) | ||||
−0.409888 | + | 0.912136i | \(0.634432\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | −419.221 | −0.485772 | −0.242886 | − | 0.970055i | \(-0.578094\pi\) | ||||
−0.242886 | + | 0.970055i | \(0.578094\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 969.924 | + | 1637.39i | 1.11871 | + | 1.88857i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 398.585i | − | 0.458671i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1104.60 | −1.26820 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −284.561 | − | 155.912i | −0.325958 | − | 0.178593i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1079.42i | 1.23081i | 0.788211 | + | 0.615405i | \(0.211008\pi\) | ||||
−0.788211 | + | 0.615405i | \(0.788992\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − | 875.749i | − | 0.991788i | −0.868383 | − | 0.495894i | \(-0.834840\pi\) | ||
0.868383 | − | 0.495894i | \(-0.165160\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1015.05 | 1.14436 | 0.572182 | − | 0.820127i | \(-0.306097\pi\) | ||||
0.572182 | + | 0.820127i | \(0.306097\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1006.68 | −1.13238 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 579.263 | − | 369.928i | 0.650126 | − | 0.415183i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1237.25 | −1.38550 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −236.788 | + | 140.263i | −0.263977 | + | 0.156369i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 214.663i | 0.238779i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −923.368 | −1.02483 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 165.530 | + | 279.443i | 0.183312 | + | 0.309460i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1504.70i | − | 1.65898i | −0.558520 | − | 0.829491i | \(-0.688631\pi\) | ||
0.558520 | − | 0.829491i | \(-0.311369\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | 221.842i | 0.242981i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1650.05 | 1.79940 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −780.289 | −0.849063 | −0.424532 | − | 0.905413i | \(-0.639561\pi\) | ||||
−0.424532 | + | 0.905413i | \(0.639561\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.3772 | + | 17.4019i | −0.0318971 | + | 0.0188945i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −155.936 | −0.168945 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1108.23 | − | 607.201i | −1.19550 | − | 0.655018i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1093.84i | − | 1.17744i | −0.808339 | − | 0.588718i | \(-0.799633\pi\) | ||
0.808339 | − | 0.588718i | \(-0.200367\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −190.236 | −0.204335 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1338.98 | + | 793.157i | −1.43513 | + | 0.850115i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 407.947i | − | 0.435376i | −0.976018 | − | 0.217688i | \(-0.930148\pi\) | ||
0.976018 | − | 0.217688i | \(-0.0698515\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −119.548 | + | 70.8154i | −0.127314 | + | 0.0754157i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 671.008i | 0.713079i | 0.934280 | + | 0.356540i | \(0.116044\pi\) | ||||
−0.934280 | + | 0.356540i | \(0.883956\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 434.447i | − | 0.460707i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1608.13 | −1.69813 | −0.849064 | − | 0.528290i | \(-0.822833\pi\) | ||||
−0.849064 | + | 0.528290i | \(0.822833\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 879.473 | 0.926737 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −59.7758 | − | 100.911i | −0.0628557 | − | 0.106111i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −695.440 | −0.729737 | −0.364869 | − | 0.931059i | \(-0.618886\pi\) | ||||
−0.364869 | + | 0.931059i | \(0.618886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 348.120 | + | 587.684i | 0.363762 | + | 0.614090i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 715.107i | 0.745680i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −897.000 | −0.933403 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −186.453 | + | 340.302i | −0.193617 | + | 0.353377i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1030.07i | 1.06522i | 0.846361 | + | 0.532609i | \(0.178788\pi\) | ||||
−0.846361 | + | 0.532609i | \(0.821212\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1253.21 | − | 2115.63i | −1.29330 | − | 2.18331i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1165.24i | − | 1.20004i | −0.799986 | − | 0.600019i | \(-0.795160\pi\) | ||
0.799986 | − | 0.600019i | \(-0.204840\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 575.106i | − | 0.591065i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −726.440 | −0.743541 | −0.371771 | − | 0.928325i | \(-0.621249\pi\) | ||||
−0.371771 | + | 0.928325i | \(0.621249\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −515.684 | −0.526746 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 578.807 | − | 1056.40i | 0.590017 | − | 1.07686i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1024.21 | −1.04192 | −0.520960 | − | 0.853581i | \(-0.674426\pi\) | ||||
−0.520960 | + | 0.853581i | \(0.674426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 886.395 | − | 525.064i | 0.898070 | − | 0.531980i | ||||
\(988\) | 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 | ||||||||
\(993\) | 681.031 | + | 1149.69i | 0.685832 | + | 1.15780i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 901.368i | 0.904080i | 0.891998 | + | 0.452040i | \(0.149304\pi\) | ||||
−0.891998 | + | 0.452040i | \(0.850696\pi\) | |||||||
\(998\) | 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 | 1200.3.c.k.449.6 | 8 | ||
3.2 | odd | 2 | inner | 1200.3.c.k.449.4 | 8 | ||
4.3 | odd | 2 | 150.3.b.b.149.1 | 8 | |||
5.2 | odd | 4 | 1200.3.l.u.401.3 | 4 | |||
5.3 | odd | 4 | 240.3.l.c.161.2 | 4 | |||
5.4 | even | 2 | inner | 1200.3.c.k.449.3 | 8 | ||
12.11 | even | 2 | 150.3.b.b.149.7 | 8 | |||
15.2 | even | 4 | 1200.3.l.u.401.4 | 4 | |||
15.8 | even | 4 | 240.3.l.c.161.1 | 4 | |||
15.14 | odd | 2 | inner | 1200.3.c.k.449.5 | 8 | ||
20.3 | even | 4 | 30.3.d.a.11.4 | yes | 4 | ||
20.7 | even | 4 | 150.3.d.c.101.1 | 4 | |||
20.19 | odd | 2 | 150.3.b.b.149.8 | 8 | |||
40.3 | even | 4 | 960.3.l.e.641.2 | 4 | |||
40.13 | odd | 4 | 960.3.l.f.641.3 | 4 | |||
60.23 | odd | 4 | 30.3.d.a.11.2 | ✓ | 4 | ||
60.47 | odd | 4 | 150.3.d.c.101.3 | 4 | |||
60.59 | even | 2 | 150.3.b.b.149.2 | 8 | |||
120.53 | even | 4 | 960.3.l.f.641.4 | 4 | |||
120.83 | odd | 4 | 960.3.l.e.641.1 | 4 | |||
180.23 | odd | 12 | 810.3.h.a.431.3 | 8 | |||
180.43 | even | 12 | 810.3.h.a.701.3 | 8 | |||
180.83 | odd | 12 | 810.3.h.a.701.2 | 8 | |||
180.103 | even | 12 | 810.3.h.a.431.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.3.d.a.11.2 | ✓ | 4 | 60.23 | odd | 4 | ||
30.3.d.a.11.4 | yes | 4 | 20.3 | even | 4 | ||
150.3.b.b.149.1 | 8 | 4.3 | odd | 2 | |||
150.3.b.b.149.2 | 8 | 60.59 | even | 2 | |||
150.3.b.b.149.7 | 8 | 12.11 | even | 2 | |||
150.3.b.b.149.8 | 8 | 20.19 | odd | 2 | |||
150.3.d.c.101.1 | 4 | 20.7 | even | 4 | |||
150.3.d.c.101.3 | 4 | 60.47 | odd | 4 | |||
240.3.l.c.161.1 | 4 | 15.8 | even | 4 | |||
240.3.l.c.161.2 | 4 | 5.3 | odd | 4 | |||
810.3.h.a.431.2 | 8 | 180.103 | even | 12 | |||
810.3.h.a.431.3 | 8 | 180.23 | odd | 12 | |||
810.3.h.a.701.2 | 8 | 180.83 | odd | 12 | |||
810.3.h.a.701.3 | 8 | 180.43 | even | 12 | |||
960.3.l.e.641.1 | 4 | 120.83 | odd | 4 | |||
960.3.l.e.641.2 | 4 | 40.3 | even | 4 | |||
960.3.l.f.641.3 | 4 | 40.13 | odd | 4 | |||
960.3.l.f.641.4 | 4 | 120.53 | even | 4 | |||
1200.3.c.k.449.3 | 8 | 5.4 | even | 2 | inner | ||
1200.3.c.k.449.4 | 8 | 3.2 | odd | 2 | inner | ||
1200.3.c.k.449.5 | 8 | 15.14 | odd | 2 | inner | ||
1200.3.c.k.449.6 | 8 | 1.1 | even | 1 | trivial | ||
1200.3.l.u.401.3 | 4 | 5.2 | odd | 4 | |||
1200.3.l.u.401.4 | 4 | 15.2 | even | 4 |