Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(369,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 24x^{10} + 188x^{8} + 530x^{6} + 508x^{4} + 80x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.11 | ||
Root | \(1.65047i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 460.369 |
Dual form | 460.2.c.a.369.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.80150i | 1.61745i | 0.588187 | + | 0.808725i | \(0.299842\pi\) | ||||
−0.588187 | + | 0.808725i | \(0.700158\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.17393 | − | 0.523461i | −0.972213 | − | 0.234099i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.50896i | − | 1.70423i | −0.523357 | − | 0.852113i | \(-0.675321\pi\) | ||
0.523357 | − | 0.852113i | \(-0.324679\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.84843 | −1.61614 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.10479 | −1.23764 | −0.618820 | − | 0.785533i | \(-0.712389\pi\) | ||||
−0.618820 | + | 0.785533i | \(0.712389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.10245i | − | 1.13781i | −0.822402 | − | 0.568907i | \(-0.807366\pi\) | ||
0.822402 | − | 0.568907i | \(-0.192634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.46648 | − | 6.09029i | 0.378643 | − | 1.57250i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.26588i | 0.549556i | 0.961508 | + | 0.274778i | \(0.0886044\pi\) | ||||
−0.961508 | + | 0.274778i | \(0.911396\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.77484 | −1.55425 | −0.777127 | − | 0.629343i | \(-0.783324\pi\) | ||||
−0.777127 | + | 0.629343i | \(0.783324\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.6319 | 2.75650 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.45198 | + | 2.27594i | 0.890395 | + | 0.455188i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.17837i | − | 0.996579i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.13863 | −0.768525 | −0.384263 | − | 0.923224i | \(-0.625544\pi\) | ||||
−0.384263 | + | 0.923224i | \(0.625544\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.84124 | 0.330697 | 0.165349 | − | 0.986235i | \(-0.447125\pi\) | ||||
0.165349 | + | 0.986235i | \(0.447125\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 11.4996i | − | 2.00182i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.36026 | + | 9.80218i | −0.398958 | + | 1.65687i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11.1155i | − | 1.82738i | −0.406411 | − | 0.913690i | \(-0.633220\pi\) | ||
0.406411 | − | 0.913690i | \(-0.366780\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.4930 | 1.84036 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.36833 | 1.30691 | 0.653457 | − | 0.756964i | \(-0.273318\pi\) | ||||
0.653457 | + | 0.756964i | \(0.273318\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.43473i | 0.828789i | 0.910097 | + | 0.414395i | \(0.136007\pi\) | ||||
−0.910097 | + | 0.414395i | \(0.863993\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.5402 | + | 2.53796i | 1.57123 | + | 0.378337i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.593285i | 0.0865396i | 0.999063 | + | 0.0432698i | \(0.0137775\pi\) | ||||
−0.999063 | + | 0.0432698i | \(0.986222\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.3307 | −1.90439 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.34787 | −0.888879 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.70512i | 0.234216i | 0.993119 | + | 0.117108i | \(0.0373624\pi\) | ||||
−0.993119 | + | 0.117108i | \(0.962638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.92353 | + | 2.14870i | 1.20325 | + | 0.289730i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 18.9797i | − | 2.51393i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.19772 | −0.806874 | −0.403437 | − | 0.915007i | \(-0.632185\pi\) | ||||
−0.403437 | + | 0.915007i | \(0.632185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3814 | −1.45724 | −0.728620 | − | 0.684919i | \(-0.759838\pi\) | ||||
−0.728620 | + | 0.684919i | \(0.759838\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 21.8614i | 2.75427i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.14747 | + | 8.91846i | −0.266361 | + | 1.10620i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.78978i | 0.707335i | 0.935371 | + | 0.353667i | \(0.115066\pi\) | ||||
−0.935371 | + | 0.353667i | \(0.884934\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.80150 | −0.337261 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.9915 | −1.42312 | −0.711562 | − | 0.702623i | \(-0.752012\pi\) | ||||
−0.711562 | + | 0.702623i | \(0.752012\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.363592i | − | 0.0425552i | −0.999774 | − | 0.0212776i | \(-0.993227\pi\) | ||
0.999774 | − | 0.0212776i | \(-0.00677338\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.37605 | + | 12.4722i | −0.736243 | + | 1.44017i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.5083i | 2.10922i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.75692 | −0.197669 | −0.0988344 | − | 0.995104i | \(-0.531511\pi\) | ||||
−0.0988344 | + | 0.995104i | \(0.531511\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.0380417 | −0.00422685 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 9.72171i | − | 1.06710i | −0.845770 | − | 0.533548i | \(-0.820858\pi\) | ||
0.845770 | − | 0.533548i | \(-0.179142\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.18610 | − | 4.92587i | 0.128650 | − | 0.534286i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 11.5944i | − | 1.24305i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.2208 | 1.82540 | 0.912698 | − | 0.408634i | \(-0.133995\pi\) | ||||
0.912698 | + | 0.408634i | \(0.133995\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.4978 | −1.93909 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.15825i | 0.534886i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.7281 | + | 3.54636i | 1.51107 | + | 0.363849i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.38314i | − | 0.445040i | −0.974928 | − | 0.222520i | \(-0.928572\pi\) | ||
0.974928 | − | 0.222520i | \(-0.0714283\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.9018 | 2.00020 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.21428 | −0.319833 | −0.159917 | − | 0.987131i | \(-0.551123\pi\) | ||||
−0.159917 | + | 0.987131i | \(0.551123\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.09140i | − | 0.206072i | −0.994678 | − | 0.103036i | \(-0.967144\pi\) | ||
0.994678 | − | 0.103036i | \(-0.0328556\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −27.4609 | − | 6.61229i | −2.67990 | − | 0.645294i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.81411i | 0.175377i | 0.996148 | + | 0.0876885i | \(0.0279480\pi\) | ||||
−0.996148 | + | 0.0876885i | \(0.972052\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.16716 | −0.303359 | −0.151679 | − | 0.988430i | \(-0.548468\pi\) | ||||
−0.151679 | + | 0.988430i | \(0.548468\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 31.1402 | 2.95570 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 13.0407i | − | 1.22677i | −0.789785 | − | 0.613384i | \(-0.789808\pi\) | ||
0.789785 | − | 0.613384i | \(-0.210192\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.523461 | − | 2.17393i | 0.0488130 | − | 0.202720i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 19.8904i | 1.83887i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.2168 | 0.936568 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.84927 | 0.531752 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 23.4439i | 2.11387i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.48694 | − | 7.27818i | −0.759095 | − | 0.650980i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0290i | 1.06740i | 0.845674 | + | 0.533700i | \(0.179199\pi\) | ||||
−0.845674 | + | 0.533700i | \(0.820801\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.2254 | −1.34052 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.33814 | 0.116914 | 0.0584571 | − | 0.998290i | \(-0.481382\pi\) | ||||
0.0584571 | + | 0.998290i | \(0.481382\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30.5475i | 2.64880i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.71068 | + | 11.2574i | −0.233298 | + | 0.968886i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.53176i | − | 0.728917i | −0.931220 | − | 0.364459i | \(-0.881254\pi\) | ||
0.931220 | − | 0.364459i | \(-0.118746\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.2021 | 1.62870 | 0.814352 | − | 0.580371i | \(-0.197092\pi\) | ||||
0.814352 | + | 0.580371i | \(0.197092\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.66209 | −0.139973 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.8397i | 1.40820i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.99712 | + | 2.16641i | 0.747170 | + | 0.179911i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 37.3461i | − | 3.08025i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.9657 | 1.14412 | 0.572058 | − | 0.820213i | \(-0.306145\pi\) | ||||
0.572058 | + | 0.820213i | \(0.306145\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.38572 | −0.763799 | −0.381900 | − | 0.924204i | \(-0.624730\pi\) | ||||
−0.381900 | + | 0.924204i | \(0.624730\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 10.9859i | − | 0.888161i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00274 | − | 0.963819i | −0.321508 | − | 0.0774158i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 22.3649i | − | 1.78491i | −0.451133 | − | 0.892457i | \(-0.648980\pi\) | ||
0.451133 | − | 0.892457i | \(-0.351020\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.77690 | −0.378833 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.50896 | 0.355356 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.91327i | − | 0.463163i | −0.972816 | − | 0.231581i | \(-0.925610\pi\) | ||
0.972816 | − | 0.231581i | \(-0.0743900\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.01958 | + | 24.9993i | −0.468624 | + | 1.94619i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.73957i | 0.676288i | 0.941094 | + | 0.338144i | \(0.109799\pi\) | ||||
−0.941094 | + | 0.338144i | \(0.890201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.83010 | −0.294623 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 32.8473 | 2.51190 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5284i | 0.800462i | 0.916414 | + | 0.400231i | \(0.131070\pi\) | ||||
−0.916414 | + | 0.400231i | \(0.868930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.2621 | − | 20.0738i | 0.775743 | − | 1.51744i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 17.3629i | − | 1.30508i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.29655 | 0.246396 | 0.123198 | − | 0.992382i | \(-0.460685\pi\) | ||||
0.123198 | + | 0.992382i | \(0.460685\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.7994 | 1.17436 | 0.587180 | − | 0.809456i | \(-0.300238\pi\) | ||||
0.587180 | + | 0.809456i | \(0.300238\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 31.8850i | − | 2.35701i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.81854 | + | 24.1644i | −0.427788 | + | 1.77660i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.30095i | − | 0.680153i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23.3491 | −1.69840 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.9965 | −1.44689 | −0.723447 | − | 0.690380i | \(-0.757443\pi\) | ||||
−0.723447 | + | 0.690380i | \(0.757443\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 0.613407i | − | 0.0441540i | −0.999756 | − | 0.0220770i | \(-0.992972\pi\) | ||
0.999756 | − | 0.0220770i | \(-0.00702790\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −24.9851 | − | 6.01615i | −1.78922 | − | 0.430826i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.63996i | − | 0.330584i | −0.986245 | − | 0.165292i | \(-0.947143\pi\) | ||
0.986245 | − | 0.165292i | \(-0.0528566\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.1446 | 0.931795 | 0.465898 | − | 0.884839i | \(-0.345731\pi\) | ||||
0.465898 | + | 0.884839i | \(0.345731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.2201 | −1.14408 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.6609i | 1.30974i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.1922 | − | 4.38049i | −1.27060 | − | 0.305947i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 4.84843i | − | 0.336989i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.8093 | 1.92361 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.76863 | −0.465972 | −0.232986 | − | 0.972480i | \(-0.574850\pi\) | ||||
−0.232986 | + | 0.972480i | \(0.574850\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 33.5941i | − | 2.30183i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.84487 | − | 11.8148i | 0.194019 | − | 0.805759i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.30209i | − | 0.563583i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.01860 | 0.0688308 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.29565 | 0.625293 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5.46851i | − | 0.366199i | −0.983094 | − | 0.183099i | \(-0.941387\pi\) | ||
0.983094 | − | 0.183099i | \(-0.0586130\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.5851 | − | 11.0347i | −1.43901 | − | 0.735648i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.55927i | 0.368981i | 0.982834 | + | 0.184491i | \(0.0590636\pi\) | ||||
−0.982834 | + | 0.184491i | \(0.940936\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.33693 | 0.418756 | 0.209378 | − | 0.977835i | \(-0.432856\pi\) | ||||
0.209378 | + | 0.977835i | \(0.432856\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −51.8511 | −3.41155 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.84557i | 0.645005i | 0.946569 | + | 0.322502i | \(0.104524\pi\) | ||||
−0.946569 | + | 0.322502i | \(0.895476\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.310562 | − | 1.28976i | 0.0202588 | − | 0.0841349i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 4.92201i | − | 0.319719i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.9526 | −1.67873 | −0.839366 | − | 0.543567i | \(-0.817074\pi\) | ||||
−0.839366 | + | 0.543567i | \(0.817074\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3220 | −0.793729 | −0.396865 | − | 0.917877i | \(-0.629902\pi\) | ||||
−0.396865 | + | 0.917877i | \(0.629902\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.6417i | − | 1.00342i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 28.9801 | + | 6.97811i | 1.85147 | + | 0.445815i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.7934i | 1.76845i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 27.2354 | 1.72597 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.68797 | −0.485261 | −0.242630 | − | 0.970119i | \(-0.578010\pi\) | ||||
−0.242630 | + | 0.970119i | \(0.578010\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.10479i | − | 0.258066i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.7998 | + | 3.32286i | 0.864180 | + | 0.208086i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.7126i | 1.22964i | 0.788669 | + | 0.614818i | \(0.210771\pi\) | ||||
−0.788669 | + | 0.614818i | \(0.789229\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −50.1195 | −3.11427 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.0659 | 1.24205 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2.96836i | − | 0.183037i | −0.995803 | − | 0.0915183i | \(-0.970828\pi\) | ||
0.995803 | − | 0.0915183i | \(-0.0291720\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.892564 | − | 3.70682i | 0.0548297 | − | 0.227708i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 48.2440i | 2.95249i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.417916 | −0.0254808 | −0.0127404 | − | 0.999919i | \(-0.504056\pi\) | ||||
−0.0127404 | + | 0.999919i | \(0.504056\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1776 | 0.618245 | 0.309122 | − | 0.951022i | \(-0.399965\pi\) | ||||
0.309122 | + | 0.951022i | \(0.399965\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 51.8216i | − | 3.13639i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.2744 | − | 9.34224i | −1.10199 | − | 0.563358i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 18.8176i | − | 1.13064i | −0.824871 | − | 0.565321i | \(-0.808752\pi\) | ||
0.824871 | − | 0.565321i | \(-0.191248\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.92713 | −0.534454 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.9609 | −1.54870 | −0.774350 | − | 0.632757i | \(-0.781923\pi\) | ||||
−0.774350 | + | 0.632757i | \(0.781923\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.2612i | 1.32329i | 0.749817 | + | 0.661646i | \(0.230142\pi\) | ||||
−0.749817 | + | 0.661646i | \(0.769858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.93515 | + | 41.2607i | −0.588508 | + | 2.44407i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 37.7325i | − | 2.22728i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.8658 | 0.697988 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.2794 | 0.719830 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.21032i | 0.129128i | 0.997914 | + | 0.0645641i | \(0.0205657\pi\) | ||||
−0.997914 | + | 0.0645641i | \(0.979434\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.4734 | + | 3.24426i | 0.784453 | + | 0.188888i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.2561i | 1.23341i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.10245 | 0.237251 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.5050 | 1.41244 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 9.00483i | − | 0.517314i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.7424 | + | 5.95772i | 1.41675 | + | 0.341138i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 19.7730i | − | 1.12851i | −0.825602 | − | 0.564253i | \(-0.809164\pi\) | ||
0.825602 | − | 0.564253i | \(-0.190836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.85906 | 0.333310 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.1593 | 0.689490 | 0.344745 | − | 0.938696i | \(-0.387965\pi\) | ||||
0.344745 | + | 0.938696i | \(0.387965\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 34.0793i | − | 1.92628i | −0.269003 | − | 0.963139i | \(-0.586694\pi\) | ||
0.269003 | − | 0.963139i | \(-0.413306\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.4436 | − | 47.5252i | 0.644772 | − | 2.67774i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.66161i | − | 0.205657i | −0.994699 | − | 0.102828i | \(-0.967211\pi\) | ||
0.994699 | − | 0.102828i | \(-0.0327892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.9882 | 0.951157 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.08225 | −0.283663 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 15.3510i | − | 0.854150i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.33693 | − | 18.2640i | 0.517920 | − | 1.01311i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 8.87281i | − | 0.490667i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.67510 | 0.147483 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.50062 | 0.192412 | 0.0962058 | − | 0.995361i | \(-0.469329\pi\) | ||||
0.0962058 | + | 0.995361i | \(0.469329\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 53.8928i | 2.95331i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.03073 | − | 12.5866i | 0.165586 | − | 0.687680i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.3643i | 1.81747i | 0.417373 | + | 0.908735i | \(0.362951\pi\) | ||||
−0.417373 | + | 0.908735i | \(0.637049\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.5336 | 1.98423 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.55791 | −0.409284 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 28.5450i | 1.54128i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.09029 | + | 1.46648i | 0.327890 | + | 0.0789525i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 5.80416i | − | 0.311584i | −0.987790 | − | 0.155792i | \(-0.950207\pi\) | ||
0.987790 | − | 0.155792i | \(-0.0497929\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.496058 | 0.0265534 | 0.0132767 | − | 0.999912i | \(-0.495774\pi\) | ||||
0.0132767 | + | 0.999912i | \(0.495774\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.2440 | −1.13392 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 5.80547i | − | 0.308994i | −0.987993 | − | 0.154497i | \(-0.950624\pi\) | ||
0.987993 | − | 0.154497i | \(-0.0493757\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.0686 | + | 6.27706i | 1.38358 | + | 0.333152i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 28.6223i | 1.51485i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.3473 | −1.49611 | −0.748057 | − | 0.663635i | \(-0.769013\pi\) | ||||
−0.748057 | + | 0.663635i | \(0.769013\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.8984 | 1.41571 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.3868i | 0.860081i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.190326 | + | 0.790424i | −0.00996212 | + | 0.0413727i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 24.2615i | − | 1.26644i | −0.773972 | − | 0.633219i | \(-0.781733\pi\) | ||
0.773972 | − | 0.633219i | \(-0.218267\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −40.5732 | −2.11216 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.68832 | 0.399158 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6261i | 1.17153i | 0.810479 | + | 0.585767i | \(0.199207\pi\) | ||||
−0.810479 | + | 0.585767i | \(0.800793\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.3898 | − | 23.7762i | 1.05293 | − | 1.22780i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.9785i | 0.874439i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.43791 | −0.330693 | −0.165347 | − | 0.986236i | \(-0.552874\pi\) | ||||
−0.165347 | + | 0.986236i | \(0.552874\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −33.6993 | −1.72647 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.5145i | 0.741657i | 0.928701 | + | 0.370829i | \(0.120926\pi\) | ||||
−0.928701 | + | 0.370829i | \(0.879074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.68838 | − | 40.2359i | 0.493766 | − | 2.05061i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 26.3499i | − | 1.33944i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.1850 | 1.32763 | 0.663815 | − | 0.747897i | \(-0.268936\pi\) | ||||
0.663815 | + | 0.747897i | \(0.268936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.26588 | −0.114590 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.74882i | 0.189103i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.81942 | + | 0.919678i | 0.192176 | + | 0.0462740i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 20.6074i | − | 1.03426i | −0.855908 | − | 0.517129i | \(-0.827001\pi\) | ||
0.855908 | − | 0.517129i | \(-0.172999\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −85.5789 | −4.28430 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.4900 | 0.623719 | 0.311859 | − | 0.950128i | \(-0.399048\pi\) | ||||
0.311859 | + | 0.950128i | \(0.399048\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.55361i | − | 0.376272i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.0827001 | + | 0.0199133i | 0.00410940 | + | 0.000989501i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 45.6268i | 2.26164i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.11740 | −0.450826 | −0.225413 | − | 0.974263i | \(-0.572373\pi\) | ||||
−0.225413 | + | 0.974263i | \(0.572373\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.9018 | 1.17899 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.9453i | 1.37510i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.08894 | + | 21.1344i | −0.249806 | + | 1.03744i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 53.7949i | 2.63435i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.12358 | 0.348010 | 0.174005 | − | 0.984745i | \(-0.444329\pi\) | ||||
0.174005 | + | 0.984745i | \(0.444329\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.13707 | 0.347840 | 0.173920 | − | 0.984760i | \(-0.444357\pi\) | ||||
0.173920 | + | 0.984760i | \(0.444357\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.87650i | − | 0.139860i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.15700 | + | 10.0876i | −0.250151 | + | 0.489322i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 51.3183i | 2.48347i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −47.1764 | −2.27770 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.2840 | −0.688036 | −0.344018 | − | 0.938963i | \(-0.611788\pi\) | ||||
−0.344018 | + | 0.938963i | \(0.611788\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 17.5102i | − | 0.841485i | −0.907180 | − | 0.420743i | \(-0.861770\pi\) | ||
0.907180 | − | 0.420743i | \(-0.138230\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.06922 | + | 25.2055i | −0.290997 | + | 1.20851i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.77484i | − | 0.324084i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.991828 | −0.0473374 | −0.0236687 | − | 0.999720i | \(-0.507535\pi\) | ||||
−0.0236687 | + | 0.999720i | \(0.507535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 64.6330 | 3.07776 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.99095i | 0.142105i | 0.997473 | + | 0.0710523i | \(0.0226357\pi\) | ||||
−0.997473 | + | 0.0710523i | \(0.977364\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −37.4368 | − | 9.01440i | −1.77467 | − | 0.427323i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 39.1250i | 1.85055i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.8981 | −0.986244 | −0.493122 | − | 0.869960i | \(-0.664144\pi\) | ||||
−0.493122 | + | 0.869960i | \(0.664144\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −34.3502 | −1.61749 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 26.2941i | − | 1.23541i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 40.2130 | + | 9.68287i | 1.88521 | + | 0.453940i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.4482i | 1.56464i | 0.622877 | + | 0.782320i | \(0.285964\pi\) | ||||
−0.622877 | + | 0.782320i | \(0.714036\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.7336 | 0.547676 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.53331 | 0.397436 | 0.198718 | − | 0.980057i | \(-0.436322\pi\) | ||||
0.198718 | + | 0.980057i | \(0.436322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.5937i | 0.631751i | 0.948801 | + | 0.315876i | \(0.102298\pi\) | ||||
−0.948801 | + | 0.315876i | \(0.897702\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.70014 | − | 11.2137i | 0.125216 | − | 0.520023i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 31.3442i | − | 1.45044i | −0.688518 | − | 0.725219i | \(-0.741738\pi\) | ||
0.688518 | − | 0.725219i | \(-0.258262\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.1059 | 1.20546 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 62.6554 | 2.88701 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 22.3084i | − | 1.02574i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −30.1614 | − | 15.4191i | −1.38390 | − | 0.707478i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 8.26715i | − | 0.378527i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.0701 | −0.917027 | −0.458513 | − | 0.888687i | \(-0.651618\pi\) | ||||
−0.458513 | + | 0.888687i | \(0.651618\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −45.6009 | −2.07922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.6319i | 0.574770i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.29440 | + | 9.52866i | −0.104183 | + | 0.432674i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 26.8679i | − | 1.21750i | −0.793362 | − | 0.608750i | \(-0.791671\pi\) | ||
0.793362 | − | 0.608750i | \(-0.208329\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.5660 | 0.749143 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.2592 | 1.50097 | 0.750483 | − | 0.660890i | \(-0.229821\pi\) | ||||
0.750483 | + | 0.660890i | \(0.229821\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 9.37764i | − | 0.422348i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −43.2651 | − | 10.4178i | −1.94462 | − | 0.468245i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 54.0690i | 2.42533i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.4726 | 1.09554 | 0.547772 | − | 0.836627i | \(-0.315476\pi\) | ||||
0.547772 | + | 0.836627i | \(0.315476\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.4839 | −1.09386 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 39.8607i | − | 1.77730i | −0.458585 | − | 0.888650i | \(-0.651644\pi\) | ||
0.458585 | − | 0.888650i | \(-0.348356\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.98764 | + | 1.68255i | 0.310946 | + | 0.0748726i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 10.7300i | − | 0.476537i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.4456 | −0.906237 | −0.453119 | − | 0.891450i | \(-0.649689\pi\) | ||||
−0.453119 | + | 0.891450i | \(0.649689\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.63942 | −0.0725237 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 35.0826i | 1.54894i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.09477 | + | 4.54656i | −0.0482411 | + | 0.200345i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.43531i | − | 0.107105i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.4955 | −1.29471 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.3985 | −1.33178 | −0.665892 | − | 0.746048i | \(-0.731949\pi\) | ||||
−0.665892 | + | 0.746048i | \(0.731949\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.27912i | − | 0.187113i | −0.995614 | − | 0.0935564i | \(-0.970176\pi\) | ||
0.995614 | − | 0.0935564i | \(-0.0298235\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 56.2368 | + | 28.7494i | 2.45438 | + | 1.25473i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.17203i | 0.181737i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.0492 | 1.30402 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 34.3306i | − | 1.48703i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.949618 | − | 3.94376i | 0.0410556 | − | 0.170504i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.23529i | 0.398532i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 54.7198 | 2.35695 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.60876 | −0.155153 | −0.0775764 | − | 0.996986i | \(-0.524718\pi\) | ||||
−0.0775764 | + | 0.996986i | \(0.524718\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 44.2621i | 1.89947i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.88519 | + | 1.65788i | 0.294929 | + | 0.0710159i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 30.6519i | − | 1.31058i | −0.755377 | − | 0.655290i | \(-0.772546\pi\) | ||
0.755377 | − | 0.655290i | \(-0.227454\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 55.1819 | 2.35511 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.0386 | 1.19448 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.92187i | 0.336872i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −67.6967 | − | 16.3007i | −2.87357 | − | 0.691925i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 45.9504i | 1.94698i | 0.228725 | + | 0.973491i | \(0.426544\pi\) | ||||
−0.228725 | + | 0.973491i | \(0.573456\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.2957 | 0.943009 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.0566 | 1.10011 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.30591i | 0.181472i | 0.995875 | + | 0.0907362i | \(0.0289220\pi\) | ||||
−0.995875 | + | 0.0907362i | \(0.971078\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.82631 | + | 28.3497i | −0.287185 | + | 1.19268i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.171528i | 0.00720351i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.4627 | −1.23514 | −0.617571 | − | 0.786515i | \(-0.711883\pi\) | ||||
−0.617571 | + | 0.786515i | \(0.711883\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.7317 | −1.32793 | −0.663966 | − | 0.747763i | \(-0.731128\pi\) | ||||
−0.663966 | + | 0.747763i | \(0.731128\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 56.0202i | − | 2.34028i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.27594 | + | 4.45198i | −0.0949132 | + | 0.185660i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 24.1386i | − | 1.00490i | −0.864606 | − | 0.502451i | \(-0.832432\pi\) | ||
0.864606 | − | 0.502451i | \(-0.167568\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.71846 | 0.0714169 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.8348 | −1.81857 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.99915i | − | 0.289875i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.4119 | − | 43.2405i | 0.430478 | − | 1.78777i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 33.9551i | − | 1.40148i | −0.713419 | − | 0.700738i | \(-0.752854\pi\) | ||
0.713419 | − | 0.700738i | \(-0.247146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.4741 | −0.513988 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.9989 | 0.534702 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6.84201i | − | 0.280968i | −0.990083 | − | 0.140484i | \(-0.955134\pi\) | ||
0.990083 | − | 0.140484i | \(-0.0448658\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.2105 | − | 5.34807i | −0.910544 | − | 0.219250i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 36.8246i | 1.50713i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.6172 | −1.08755 | −0.543775 | − | 0.839231i | \(-0.683005\pi\) | ||||
−0.543775 | + | 0.839231i | \(0.683005\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0702 | 0.614728 | 0.307364 | − | 0.951592i | \(-0.400553\pi\) | ||||
0.307364 | + | 0.951592i | \(0.400553\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 28.0713i | − | 1.14315i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.7159 | − | 3.06186i | −0.516976 | − | 0.124482i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 43.4205i | − | 1.76238i | −0.472761 | − | 0.881191i | \(-0.656742\pi\) | ||
0.472761 | − | 0.881191i | \(-0.343258\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −52.2787 | −2.11844 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.43392 | 0.0984660 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.59633i | 0.185644i | 0.995683 | + | 0.0928220i | \(0.0295888\pi\) | ||||
−0.995683 | + | 0.0928220i | \(0.970411\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.2720 | − | 50.9655i | 0.494854 | − | 2.05513i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 30.4809i | − | 1.22712i | −0.789650 | − | 0.613558i | \(-0.789738\pi\) | ||
0.789650 | − | 0.613558i | \(-0.210262\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.0511 | 1.48921 | 0.744605 | − | 0.667506i | \(-0.232638\pi\) | ||||
0.744605 | + | 0.667506i | \(0.232638\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.17837 | 0.207801 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 77.6477i | − | 3.11089i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.6402 | + | 20.2649i | 0.585608 | + | 0.810594i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 77.9078i | 3.11134i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.1864 | 1.00425 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.3035 | −1.16655 | −0.583276 | − | 0.812274i | \(-0.698230\pi\) | ||||
−0.583276 | + | 0.812274i | \(0.698230\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 18.9624i | − | 0.753686i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.29671 | − | 26.1502i | 0.249877 | − | 1.03774i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 54.6886i | 2.16684i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 58.1397 | 2.29997 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.3307 | −0.447536 | −0.223768 | − | 0.974642i | \(-0.571836\pi\) | ||||
−0.223768 | + | 0.974642i | \(0.571836\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.2340i | 1.11344i | 0.830700 | + | 0.556721i | \(0.187941\pi\) | ||||
−0.830700 | + | 0.556721i | \(0.812059\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33.0991 | + | 7.96992i | 1.30327 | + | 0.313815i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 30.0192i | − | 1.18018i | −0.807338 | − | 0.590089i | \(-0.799093\pi\) | ||
0.807338 | − | 0.590089i | \(-0.200907\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.4403 | 0.998619 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.2584 | 0.911567 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.7192i | 0.928204i | 0.885782 | + | 0.464102i | \(0.153623\pi\) | ||||
−0.885782 | + | 0.464102i | \(0.846377\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.90904 | − | 0.700467i | −0.113666 | − | 0.0273695i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.76285i | 0.0687752i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.8488 | 0.656336 | 0.328168 | − | 0.944619i | \(-0.393569\pi\) | ||||
0.328168 | + | 0.944619i | \(0.393569\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.4941 | −0.913816 | −0.456908 | − | 0.889514i | \(-0.651043\pi\) | ||||
−0.456908 | + | 0.889514i | \(0.651043\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.0418i | 1.01138i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.9904 | − | 66.4082i | 0.620082 | − | 2.57520i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4.13863i | − | 0.160249i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.3201 | 0.592308 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 46.7182 | 1.80354 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 19.9329i | − | 0.768358i | −0.923259 | − | 0.384179i | \(-0.874485\pi\) | ||
0.923259 | − | 0.384179i | \(-0.125515\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.7857 | − | 23.0540i | 0.453630 | − | 0.887349i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.9965i | 1.30659i | 0.757102 | + | 0.653296i | \(0.226614\pi\) | ||||
−0.757102 | + | 0.653296i | \(0.773386\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.7634 | −0.758450 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.5743 | −0.596809 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.8223i | 0.452367i | 0.974085 | + | 0.226183i | \(0.0726248\pi\) | ||||
−0.974085 | + | 0.226183i | \(0.927375\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.46604 | + | 18.5475i | −0.170639 | + | 0.708663i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.7529i | 0.677316i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.99517 | 0.266495 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.0765 | −1.48654 | −0.743271 | − | 0.668991i | \(-0.766727\pi\) | ||||
−0.743271 | + | 0.668991i | \(0.766727\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 89.7362i | − | 3.40880i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.7442 | − | 10.0516i | −1.58345 | − | 0.381278i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.9616i | 0.718222i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.5824 | −1.04326 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.3454 | −1.37275 | −0.686373 | − | 0.727250i | \(-0.740798\pi\) | ||||
−0.686373 | + | 0.727250i | \(0.740798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 75.3059i | 2.84021i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.61328 | + | 0.870040i | 0.136084 | + | 0.0327676i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.4931i | 0.545068i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.6781 | 0.626359 | 0.313179 | − | 0.949694i | \(-0.398606\pi\) | ||||
0.313179 | + | 0.949694i | \(0.398606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.51829 | 0.319461 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.84124i | 0.0689551i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.81492 | − | 36.6084i | 0.329659 | − | 1.36907i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 72.7062i | − | 2.71526i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.1134 | 0.899278 | 0.449639 | − | 0.893210i | \(-0.351553\pi\) | ||||
0.449639 | + | 0.893210i | \(0.351553\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.43003 | −0.351193 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 34.5201i | − | 1.28382i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.4251 | − | 9.41928i | −0.684291 | − | 0.349823i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.05594i | − | 0.113339i | −0.998393 | − | 0.0566693i | \(-0.981952\pi\) | ||
0.998393 | − | 0.0566693i | \(-0.0180481\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.7062 | 1.61875 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.3144 | −0.455466 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.2230i | 1.81809i | 0.416696 | + | 0.909046i | \(0.363188\pi\) | ||||
−0.416696 | + | 0.909046i | \(0.636812\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.5492 | + | 81.1879i | −0.721083 | + | 2.99466i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 23.7658i | − | 0.875425i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1179 | −0.482548 | −0.241274 | − | 0.970457i | \(-0.577565\pi\) | ||||
−0.241274 | + | 0.970457i | \(0.577565\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −77.8634 | −2.86038 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 14.9149i | − | 0.547173i | −0.961847 | − | 0.273587i | \(-0.911790\pi\) | ||
0.961847 | − | 0.273587i | \(-0.0882100\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.3605 | − | 7.31050i | −1.11232 | − | 0.267836i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 47.1350i | 1.72458i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.17977 | 0.298882 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.40642 | 0.270264 | 0.135132 | − | 0.990828i | \(-0.456854\pi\) | ||||
0.135132 | + | 0.990828i | \(0.456854\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 21.5379i | − | 0.784884i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.4039 | + | 4.91306i | 0.742575 | + | 0.178804i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.37246i | 0.0498831i | 0.999689 | + | 0.0249415i | \(0.00793996\pi\) | ||||
−0.999689 | + | 0.0249415i | \(0.992060\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.4996 | 0.417408 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.9083 | −1.22918 | −0.614588 | − | 0.788849i | \(-0.710678\pi\) | ||||
−0.614588 | + | 0.788849i | \(0.710678\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2806i | 0.516992i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.75071 | + | 23.8827i | −0.207917 | + | 0.863481i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.4258i | 0.918073i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.17267 | −0.258653 | −0.129327 | − | 0.991602i | \(-0.541282\pi\) | ||||
−0.129327 | + | 0.991602i | \(0.541282\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −55.2248 | −1.98887 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 3.13634i | − | 0.112806i | −0.998408 | − | 0.0564031i | \(-0.982037\pi\) | ||
0.998408 | − | 0.0564031i | \(-0.0179632\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.19718 | + | 4.19056i | 0.294451 | + | 0.150529i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 140.410i | − | 5.03718i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −56.6941 | −2.03128 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.2224 | 1.76131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.4314i | 0.765896i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.7072 | + | 48.6198i | −0.417846 | + | 1.73532i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 0.546252i | − | 0.0194718i | −0.999953 | − | 0.00973589i | \(-0.996901\pi\) | ||
0.999953 | − | 0.00973589i | \(-0.00309908\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.31586 | 0.296052 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −58.8001 | −2.09069 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.6916i | 1.65807i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.3847 | + | 2.50052i | 0.368306 | + | 0.0886843i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 45.0453i | − | 1.59559i | −0.602931 | − | 0.797794i | \(-0.706000\pi\) | ||
0.602931 | − | 0.797794i | \(-0.294000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.34431 | −0.0475584 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −83.4936 | −2.95010 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.49247i | 0.0526680i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.80218 | − | 2.36026i | −0.345481 | − | 0.0831884i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1.17079i | − | 0.0412139i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.0227 | −1.47744 | −0.738719 | − | 0.674013i | \(-0.764569\pi\) | ||||
−0.738719 | + | 0.674013i | \(0.764569\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.9218 | 0.523974 | 0.261987 | − | 0.965071i | \(-0.415622\pi\) | ||||
0.261987 | + | 0.965071i | \(0.415622\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.5126i | 0.999980i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.09537 | + | 12.8551i | −0.108426 | + | 0.450293i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 36.8194i | − | 1.28815i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 89.6851 | 3.13385 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.2317 | 1.12489 | 0.562447 | − | 0.826833i | \(-0.309860\pi\) | ||||
0.562447 | + | 0.826833i | \(0.309860\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.3609i | 1.09317i | 0.837403 | + | 0.546586i | \(0.184073\pi\) | ||||
−0.837403 | + | 0.546586i | \(0.815927\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26.1723 | − | 51.1958i | 0.911204 | − | 1.78241i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 29.6787i | − | 1.03203i | −0.856580 | − | 0.516015i | \(-0.827415\pi\) | ||
0.856580 | − | 0.516015i | \(-0.172585\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.4868 | −0.607342 | −0.303671 | − | 0.952777i | \(-0.598212\pi\) | ||||
−0.303671 | + | 0.952777i | \(0.598212\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 52.7177 | 1.82876 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 30.2058i | − | 1.04657i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.57482 | − | 18.9992i | 0.158318 | − | 0.657496i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 9.53465i | − | 0.329566i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.2177 | −0.767039 | −0.383520 | − | 0.923533i | \(-0.625288\pi\) | ||||
−0.383520 | + | 0.923533i | \(0.625288\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.8717 | −0.409369 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 72.7297i | − | 2.50494i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.32638 | + | 2.00491i | 0.286436 | + | 0.0689709i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 26.3741i | − | 0.906225i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −62.3649 | −2.14036 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.1155 | 0.381035 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.5885i | 0.910374i | 0.890396 | + | 0.455187i | \(0.150428\pi\) | ||||
−0.890396 | + | 0.455187i | \(0.849572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −71.4079 | − | 17.1943i | −2.44210 | − | 0.588032i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 21.0394i | − | 0.718692i | −0.933204 | − | 0.359346i | \(-0.883000\pi\) | ||
0.933204 | − | 0.359346i | \(-0.117000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.7924 | 1.46006 | 0.730028 | − | 0.683417i | \(-0.239507\pi\) | ||||
0.730028 | + | 0.683417i | \(0.239507\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 105.708 | 3.60251 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 44.5471i | − | 1.51640i | −0.652022 | − | 0.758200i | \(-0.726079\pi\) | ||
0.652022 | − | 0.758200i | \(-0.273921\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.51123 | − | 22.8881i | 0.187387 | − | 0.778220i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.2421i | 1.12896i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.21177 | 0.244643 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.7523 | 0.804816 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.2513i | 0.719249i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −32.8170 | + | 38.2673i | −1.10942 | + | 1.29367i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.1814i | 0.411336i | 0.978622 | + | 0.205668i | \(0.0659367\pi\) | ||||
−0.978622 | + | 0.205668i | \(0.934063\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.19222 | −0.208858 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.3075 | −0.515723 | −0.257862 | − | 0.966182i | \(-0.583018\pi\) | ||||
−0.257862 | + | 0.966182i | \(0.583018\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.1308i | 0.812065i | 0.913859 | + | 0.406033i | \(0.133088\pi\) | ||||
−0.913859 | + | 0.406033i | \(0.866912\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.08882 | + | 37.7459i | −0.305517 | + | 1.26881i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.9353i | 0.602210i | 0.953591 | + | 0.301105i | \(0.0973555\pi\) | ||||
−0.953591 | + | 0.301105i | \(0.902645\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 54.2383 | 1.81909 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.156153 | 0.00523132 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 4.01941i | − | 0.134505i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.16648 | − | 1.72561i | −0.239549 | − | 0.0576809i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.4930i | 0.383741i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.62024 | −0.254149 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.86359 | −0.128715 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 68.6509i | 2.28456i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −34.3469 | − | 8.27037i | −1.14173 | − | 0.274916i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.7750i | 1.75236i | 0.481980 | + | 0.876182i | \(0.339918\pi\) | ||||
−0.481980 | + | 0.876182i | \(0.660082\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.5842 | 0.516896 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.2848 | 0.771461 | 0.385731 | − | 0.922611i | \(-0.373949\pi\) | ||||
0.385731 | + | 0.922611i | \(0.373949\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.9055i | 1.32068i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.6906 | + | 69.3160i | −0.551773 | + | 2.29152i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 6.03364i | − | 0.199248i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.79940 | 0.323253 | 0.161626 | − | 0.986852i | \(-0.448326\pi\) | ||||
0.161626 | + | 0.986852i | \(0.448326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 55.3942 | 1.82530 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 49.1944i | 1.61925i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.2983 | − | 49.4861i | 0.831802 | − | 1.62709i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.1400i | 0.333041i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.0707 | 1.08501 | 0.542507 | − | 0.840051i | \(-0.317475\pi\) | ||||
0.542507 | + | 0.840051i | \(0.317475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 90.3135 | 2.95990 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.0643i | 1.11521i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.86868 | + | 20.2196i | −0.159223 | + | 0.661253i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.0078i | 1.01298i | 0.862245 | + | 0.506491i | \(0.169058\pi\) | ||||
−0.862245 | + | 0.506491i | \(0.830942\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 95.4734 | 3.11566 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.6560 | 0.542971 | 0.271486 | − | 0.962442i | \(-0.412485\pi\) | ||||
0.271486 | + | 0.962442i | \(0.412485\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.36833i | 0.272510i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 50.7594 | + | 12.2223i | 1.65120 | + | 0.397593i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 16.3503i | − | 0.531312i | −0.964068 | − | 0.265656i | \(-0.914411\pi\) | ||
0.964068 | − | 0.265656i | \(-0.0855885\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.49162 | −0.0484199 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.2580 | 0.332639 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 14.2223i | − | 0.460704i | −0.973107 | − | 0.230352i | \(-0.926012\pi\) | ||
0.973107 | − | 0.230352i | \(-0.0739877\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.4710 | + | 10.4674i | 1.40669 | + | 0.338716i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 47.5925i | 1.53845i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −38.4693 | −1.24224 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6098 | −0.890639 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 8.79560i | − | 0.283434i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.321095 | + | 1.33351i | −0.0103364 | + | 0.0429271i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.2933i | 1.00632i | 0.864192 | + | 0.503162i | \(0.167830\pi\) | ||||
−0.864192 | + | 0.503162i | \(0.832170\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 43.0058 | 1.38154 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.4671 | −1.00983 | −0.504914 | − | 0.863170i | \(-0.668476\pi\) | ||||
−0.504914 | + | 0.863170i | \(0.668476\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 86.5817i | − | 2.77568i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 51.1667 | + | 26.1574i | 1.63865 | + | 0.837709i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 27.8139i | − | 0.889846i | −0.895569 | − | 0.444923i | \(-0.853231\pi\) | ||
0.895569 | − | 0.444923i | \(-0.146769\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −70.6875 | −2.25918 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.3557 | 0.490271 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 57.5702i | − | 1.83621i | −0.396343 | − | 0.918103i | \(-0.629721\pi\) | ||
0.396343 | − | 0.918103i | \(-0.370279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.42884 | + | 10.0870i | −0.0773893 | + | 0.321398i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.49431i | 0.238546i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.43473 | −0.172814 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.4772 | −1.53993 | −0.769964 | − | 0.638088i | \(-0.779726\pi\) | ||||
−0.769964 | + | 0.638088i | \(0.779726\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.80701i | 0.311216i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.5755 | − | 6.88068i | −0.905903 | − | 0.218132i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 20.6703i | − | 0.654634i | −0.944915 | − | 0.327317i | \(-0.893856\pi\) | ||
0.944915 | − | 0.327317i | \(-0.106144\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −57.5603 | −1.82113 |
(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 | 460.2.c.a.369.11 | yes | 12 | |
3.2 | odd | 2 | 4140.2.f.b.829.12 | 12 | |||
4.3 | odd | 2 | 1840.2.e.f.369.2 | 12 | |||
5.2 | odd | 4 | 2300.2.a.o.1.5 | 6 | |||
5.3 | odd | 4 | 2300.2.a.n.1.2 | 6 | |||
5.4 | even | 2 | inner | 460.2.c.a.369.2 | ✓ | 12 | |
15.14 | odd | 2 | 4140.2.f.b.829.11 | 12 | |||
20.3 | even | 4 | 9200.2.a.cy.1.5 | 6 | |||
20.7 | even | 4 | 9200.2.a.cx.1.2 | 6 | |||
20.19 | odd | 2 | 1840.2.e.f.369.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.c.a.369.2 | ✓ | 12 | 5.4 | even | 2 | inner | |
460.2.c.a.369.11 | yes | 12 | 1.1 | even | 1 | trivial | |
1840.2.e.f.369.2 | 12 | 4.3 | odd | 2 | |||
1840.2.e.f.369.11 | 12 | 20.19 | odd | 2 | |||
2300.2.a.n.1.2 | 6 | 5.3 | odd | 4 | |||
2300.2.a.o.1.5 | 6 | 5.2 | odd | 4 | |||
4140.2.f.b.829.11 | 12 | 15.14 | odd | 2 | |||
4140.2.f.b.829.12 | 12 | 3.2 | odd | 2 | |||
9200.2.a.cx.1.2 | 6 | 20.7 | even | 4 | |||
9200.2.a.cy.1.5 | 6 | 20.3 | even | 4 |