Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.a (trivial) |
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: | yes |
Analytic conductor: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1002) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.460811 | −0.206081 | −0.103041 | − | 0.994677i | \(-0.532857\pi\) | ||||
−0.103041 | + | 0.994677i | \(0.532857\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.369102 | 0.139508 | 0.0697538 | − | 0.997564i | \(-0.477779\pi\) | ||||
0.0697538 | + | 0.997564i | \(0.477779\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.04945 | 1.82398 | 0.911989 | − | 0.410215i | \(-0.134546\pi\) | ||||
0.911989 | + | 0.410215i | \(0.134546\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.36910 | −0.379721 | −0.189860 | − | 0.981811i | \(-0.560804\pi\) | ||||
−0.189860 | + | 0.981811i | \(0.560804\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.460811 | −0.118981 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.70928 | −1.86977 | −0.934887 | − | 0.354946i | \(-0.884499\pi\) | ||||
−0.934887 | + | 0.354946i | \(0.884499\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.78765 | −0.639531 | −0.319766 | − | 0.947497i | \(-0.603604\pi\) | ||||
−0.319766 | + | 0.947497i | \(0.603604\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.369102 | 0.0805447 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.63090 | 0.548580 | 0.274290 | − | 0.961647i | \(-0.411557\pi\) | ||||
0.274290 | + | 0.961647i | \(0.411557\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.78765 | −0.957531 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.04945 | 1.12335 | 0.561677 | − | 0.827356i | \(-0.310156\pi\) | ||||
0.561677 | + | 0.827356i | \(0.310156\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.09890 | −1.63421 | −0.817105 | − | 0.576489i | \(-0.804422\pi\) | ||||
−0.817105 | + | 0.576489i | \(0.804422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.04945 | 1.05307 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.170086 | −0.0287499 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.95774 | −1.14385 | −0.571923 | − | 0.820308i | \(-0.693802\pi\) | ||||
−0.571923 | + | 0.820308i | \(0.693802\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.36910 | −0.219232 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.26180 | −1.13410 | −0.567051 | − | 0.823683i | \(-0.691916\pi\) | ||||
−0.567051 | + | 0.823683i | \(0.691916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.447480 | 0.0682401 | 0.0341200 | − | 0.999418i | \(-0.489137\pi\) | ||||
0.0341200 | + | 0.999418i | \(0.489137\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.460811 | −0.0686937 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.89269 | 0.713673 | 0.356836 | − | 0.934167i | \(-0.383855\pi\) | ||||
0.356836 | + | 0.934167i | \(0.383855\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.86376 | −0.980538 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.70928 | −1.07951 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.66701 | 0.366343 | 0.183171 | − | 0.983081i | \(-0.441364\pi\) | ||||
0.183171 | + | 0.983081i | \(0.441364\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.78765 | −0.375887 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.78765 | −0.369234 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.14116 | −0.669322 | −0.334661 | − | 0.942339i | \(-0.608622\pi\) | ||||
−0.334661 | + | 0.942339i | \(0.608622\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8371 | −1.38755 | −0.693774 | − | 0.720192i | \(-0.744053\pi\) | ||||
−0.693774 | + | 0.720192i | \(0.744053\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.369102 | 0.0465025 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.630898 | 0.0782532 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6381 | 1.42182 | 0.710909 | − | 0.703284i | \(-0.248284\pi\) | ||||
0.710909 | + | 0.703284i | \(0.248284\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.63090 | 0.316723 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.55252 | 0.184250 | 0.0921251 | − | 0.995747i | \(-0.470634\pi\) | ||||
0.0921251 | + | 0.995747i | \(0.470634\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.81432 | 0.563473 | 0.281736 | − | 0.959492i | \(-0.409090\pi\) | ||||
0.281736 | + | 0.959492i | \(0.409090\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.78765 | −0.552831 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.23287 | 0.254459 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.4186 | −1.73472 | −0.867361 | − | 0.497679i | \(-0.834186\pi\) | ||||
−0.867361 | + | 0.497679i | \(0.834186\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.51026 | 0.495065 | 0.247533 | − | 0.968880i | \(-0.420380\pi\) | ||||
0.247533 | + | 0.968880i | \(0.420380\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.55252 | 0.385325 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.04945 | 0.648569 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.2062 | −1.82385 | −0.911927 | − | 0.410353i | \(-0.865406\pi\) | ||||
−0.911927 | + | 0.410353i | \(0.865406\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.505339 | −0.0529739 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.09890 | −0.943512 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.28458 | 0.131795 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.44748 | 0.146969 | 0.0734847 | − | 0.997296i | \(-0.476588\pi\) | ||||
0.0734847 | + | 0.997296i | \(0.476588\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.04945 | 0.607992 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.27513 | 0.126880 | 0.0634399 | − | 0.997986i | \(-0.479793\pi\) | ||||
0.0634399 | + | 0.997986i | \(0.479793\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.9155 | −1.37113 | −0.685566 | − | 0.728010i | \(-0.740445\pi\) | ||||
−0.685566 | + | 0.728010i | \(0.740445\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.170086 | −0.0165987 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −20.4391 | −1.97592 | −0.987960 | − | 0.154711i | \(-0.950555\pi\) | ||||
−0.987960 | + | 0.154711i | \(0.950555\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.3112 | 1.84968 | 0.924841 | − | 0.380354i | \(-0.124198\pi\) | ||||
0.924841 | + | 0.380354i | \(0.124198\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.95774 | −0.660399 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.7854 | −1.10868 | −0.554338 | − | 0.832292i | \(-0.687028\pi\) | ||||
−0.554338 | + | 0.832292i | \(0.687028\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.21235 | −0.113052 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.36910 | −0.126574 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.84551 | −0.260848 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.5958 | 2.32689 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.26180 | −0.654774 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.51026 | 0.403410 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7587 | 1.13215 | 0.566077 | − | 0.824352i | \(-0.308461\pi\) | ||||
0.566077 | + | 0.824352i | \(0.308461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.447480 | 0.0393984 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.5525 | −1.00935 | −0.504674 | − | 0.863310i | \(-0.668387\pi\) | ||||
−0.504674 | + | 0.863310i | \(0.668387\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.02893 | −0.0892195 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.460811 | −0.0396603 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.552520 | 0.0472050 | 0.0236025 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236025 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.55971 | 0.556387 | 0.278194 | − | 0.960525i | \(-0.410264\pi\) | ||||
0.278194 | + | 0.960525i | \(0.410264\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.89269 | 0.412039 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.28231 | −0.692602 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.78765 | −0.231502 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.86376 | −0.566114 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.4836 | 0.858850 | 0.429425 | − | 0.903103i | \(-0.358716\pi\) | ||||
0.429425 | + | 0.903103i | \(0.358716\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.97334 | 0.160588 | 0.0802940 | − | 0.996771i | \(-0.474414\pi\) | ||||
0.0802940 | + | 0.996771i | \(0.474414\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.70928 | −0.623258 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.19287 | 0.336780 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.76487 | −0.220660 | −0.110330 | − | 0.993895i | \(-0.535191\pi\) | ||||
−0.110330 | + | 0.993895i | \(0.535191\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.66701 | 0.211508 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.971071 | 0.0765311 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.40522 | −0.736674 | −0.368337 | − | 0.929692i | \(-0.620073\pi\) | ||||
−0.368337 | + | 0.929692i | \(0.620073\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.78765 | −0.217018 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1256 | −0.855812 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.78765 | −0.213177 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.3340 | −1.77405 | −0.887027 | − | 0.461718i | \(-0.847233\pi\) | ||||
−0.887027 | + | 0.461718i | \(0.847233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.76713 | −0.133583 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.14116 | −0.386433 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.1483 | 1.35647 | 0.678235 | − | 0.734845i | \(-0.262745\pi\) | ||||
0.678235 | + | 0.734845i | \(0.262745\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.54638 | 0.635247 | 0.317624 | − | 0.948217i | \(-0.397115\pi\) | ||||
0.317624 | + | 0.948217i | \(0.397115\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.8371 | −0.801102 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.20620 | 0.235725 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −46.6369 | −3.41043 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.369102 | 0.0268482 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.5753 | −0.909917 | −0.454959 | − | 0.890513i | \(-0.650346\pi\) | ||||
−0.454959 | + | 0.890513i | \(0.650346\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.7031 | 1.20232 | 0.601159 | − | 0.799130i | \(-0.294706\pi\) | ||||
0.601159 | + | 0.799130i | \(0.294706\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.630898 | 0.0451795 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.9854 | 1.49515 | 0.747576 | − | 0.664177i | \(-0.231218\pi\) | ||||
0.747576 | + | 0.664177i | \(0.231218\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.17727 | 0.650560 | 0.325280 | − | 0.945618i | \(-0.394541\pi\) | ||||
0.325280 | + | 0.945618i | \(0.394541\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.6381 | 0.820887 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.23287 | 0.156716 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.34632 | 0.233717 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.63090 | 0.182860 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.8638 | −1.16649 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.99386 | 0.206106 | 0.103053 | − | 0.994676i | \(-0.467139\pi\) | ||||
0.103053 | + | 0.994676i | \(0.467139\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.55252 | 0.106377 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.206204 | −0.0140630 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.35842 | −0.227985 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.81432 | 0.325321 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.5548 | 0.709992 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.8660 | 1.26336 | 0.631681 | − | 0.775228i | \(-0.282365\pi\) | ||||
0.631681 | + | 0.775228i | \(0.282365\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.78765 | −0.319177 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.7948 | 0.782851 | 0.391426 | − | 0.920210i | \(-0.371982\pi\) | ||||
0.391426 | + | 0.920210i | \(0.371982\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.0410 | 1.72084 | 0.860420 | − | 0.509585i | \(-0.170201\pi\) | ||||
0.860420 | + | 0.509585i | \(0.170201\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.23287 | 0.146912 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.97948 | −0.260704 | −0.130352 | − | 0.991468i | \(-0.541611\pi\) | ||||
−0.130352 | + | 0.991468i | \(0.541611\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.25461 | −0.147074 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.4186 | −1.00154 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.6537 | 0.947868 | 0.473934 | − | 0.880560i | \(-0.342834\pi\) | ||||
0.473934 | + | 0.880560i | \(0.342834\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.1483 | −0.653712 | −0.326856 | − | 0.945074i | \(-0.605989\pi\) | ||||
−0.326856 | + | 0.945074i | \(0.605989\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.16290 | 0.202070 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.81658 | 0.242843 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.51026 | 0.285826 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.7503 | 1.24663 | 0.623314 | − | 0.781971i | \(-0.285786\pi\) | ||||
0.623314 | + | 0.781971i | \(0.285786\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.9155 | 1.00060 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.55252 | 0.222467 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.62475 | −0.350863 | −0.175431 | − | 0.984492i | \(-0.556132\pi\) | ||||
−0.175431 | + | 0.984492i | \(0.556132\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.56812 | −0.159575 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.04945 | 0.374451 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.56690 | −0.528257 | −0.264129 | − | 0.964487i | \(-0.585084\pi\) | ||||
−0.264129 | + | 0.964487i | \(0.585084\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.22899 | −0.0754963 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.2062 | −1.05300 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.2195 | −0.866980 | −0.433490 | − | 0.901158i | \(-0.642718\pi\) | ||||
−0.433490 | + | 0.901158i | \(0.642718\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.2267 | 0.803466 | 0.401733 | − | 0.915757i | \(-0.368408\pi\) | ||||
0.401733 | + | 0.915757i | \(0.368408\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.505339 | −0.0305845 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −28.9627 | −1.74651 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.6670 | −1.00142 | −0.500712 | − | 0.865614i | \(-0.666928\pi\) | ||||
−0.500712 | + | 0.865614i | \(0.666928\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.09890 | −0.544737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.4391 | −1.04033 | −0.520164 | − | 0.854066i | \(-0.674129\pi\) | ||||
−0.520164 | + | 0.854066i | \(0.674129\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.9565 | −1.54295 | −0.771477 | − | 0.636257i | \(-0.780482\pi\) | ||||
−0.771477 | + | 0.636257i | \(0.780482\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.28458 | 0.0760920 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.68035 | −0.158216 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 42.4329 | 2.49605 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.44748 | 0.0848528 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.6225 | −0.854255 | −0.427127 | − | 0.904191i | \(-0.640474\pi\) | ||||
−0.427127 | + | 0.904191i | \(0.640474\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.36910 | 0.137934 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.04945 | 0.351025 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.60197 | −0.208307 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.165166 | 0.00952001 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.27513 | 0.0732541 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.99386 | 0.285947 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.170086 | 0.00970735 | 0.00485367 | − | 0.999988i | \(-0.498455\pi\) | ||||
0.00485367 | + | 0.999988i | \(0.498455\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.9155 | −0.791624 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.60197 | −0.260954 | −0.130477 | − | 0.991451i | \(-0.541651\pi\) | ||||
−0.130477 | + | 0.991451i | \(0.541651\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.5525 | −0.879080 | −0.439540 | − | 0.898223i | \(-0.644859\pi\) | ||||
−0.439540 | + | 0.898223i | \(0.644859\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.170086 | −0.00958329 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.68261 | 0.543830 | 0.271915 | − | 0.962321i | \(-0.412343\pi\) | ||||
0.271915 | + | 0.962321i | \(0.412343\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.5958 | 2.04897 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.4391 | −1.14080 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.4908 | 1.19578 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.55479 | 0.363594 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.3112 | 1.06791 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.80590 | 0.0995627 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.4307 | −1.78255 | −0.891275 | − | 0.453463i | \(-0.850188\pi\) | ||||
−0.891275 | + | 0.453463i | \(0.850188\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.95774 | −0.381282 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.36296 | −0.293010 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.09890 | −0.168808 | −0.0844038 | − | 0.996432i | \(-0.526899\pi\) | ||||
−0.0844038 | + | 0.996432i | \(0.526899\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.7854 | −0.640094 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −55.0433 | −2.98076 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.11715 | −0.276300 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.21235 | −0.0652706 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −31.2979 | −1.68016 | −0.840080 | − | 0.542463i | \(-0.817492\pi\) | ||||
−0.840080 | + | 0.542463i | \(0.817492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.7226 | −0.948669 | −0.474335 | − | 0.880345i | \(-0.657311\pi\) | ||||
−0.474335 | + | 0.880345i | \(0.657311\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.36910 | −0.0730773 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.1568 | −0.913162 | −0.456581 | − | 0.889682i | \(-0.650926\pi\) | ||||
−0.456581 | + | 0.889682i | \(0.650926\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.715418 | −0.0379705 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.84551 | −0.150600 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.5441 | 1.55928 | 0.779639 | − | 0.626229i | \(-0.215402\pi\) | ||||
0.779639 | + | 0.626229i | \(0.215402\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.2290 | −0.590999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.5958 | 1.34343 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.21849 | −0.116121 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.6537 | 0.764916 | 0.382458 | − | 0.923973i | \(-0.375078\pi\) | ||||
0.382458 | + | 0.923973i | \(0.375078\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.26180 | −0.378034 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.984402 | 0.0511076 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.6030 | −1.73990 | −0.869949 | − | 0.493142i | \(-0.835848\pi\) | ||||
−0.869949 | + | 0.493142i | \(0.835848\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.51026 | 0.232909 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.28231 | −0.426561 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.2218 | −0.679158 | −0.339579 | − | 0.940577i | \(-0.610285\pi\) | ||||
−0.339579 | + | 0.940577i | \(0.610285\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.7587 | 0.653649 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.92162 | −0.149288 | −0.0746440 | − | 0.997210i | \(-0.523782\pi\) | ||||
−0.0746440 | + | 0.997210i | \(0.523782\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.02893 | −0.0524391 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.447480 | 0.0227467 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.0060 | 1.21715 | 0.608575 | − | 0.793496i | \(-0.291741\pi\) | ||||
0.608575 | + | 0.793496i | \(0.291741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.2823 | −1.02572 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.5525 | −0.582748 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.10504 | 0.357493 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.7031 | 0.838306 | 0.419153 | − | 0.907916i | \(-0.362327\pi\) | ||||
0.419153 | + | 0.907916i | \(0.362327\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.02893 | −0.0515109 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.5897 | −1.87714 | −0.938570 | − | 0.345090i | \(-0.887848\pi\) | ||||
−0.938570 | + | 0.345090i | \(0.887848\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.4573 | 0.620543 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.460811 | −0.0228979 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −42.0905 | −2.08635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.47027 | −0.221040 | −0.110520 | − | 0.993874i | \(-0.535252\pi\) | ||||
−0.110520 | + | 0.993874i | \(0.535252\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.552520 | 0.0272538 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.89761 | −0.0933754 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.07838 | −0.102024 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.55971 | 0.321230 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.9939 | 1.02562 | 0.512809 | − | 0.858503i | \(-0.328605\pi\) | ||||
0.512809 | + | 0.858503i | \(0.328605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.2907 | −0.988909 | −0.494455 | − | 0.869203i | \(-0.664632\pi\) | ||||
−0.494455 | + | 0.869203i | \(0.664632\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.89269 | 0.237891 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 36.9093 | 1.79037 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | −0.193574 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.28231 | −0.399874 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.789921 | 0.0380491 | 0.0190246 | − | 0.999819i | \(-0.493944\pi\) | ||||
0.0190246 | + | 0.999819i | \(0.493944\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.1362 | −0.487116 | −0.243558 | − | 0.969886i | \(-0.578315\pi\) | ||||
−0.243558 | + | 0.969886i | \(0.578315\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.78765 | −0.133658 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.33403 | −0.350834 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.17727 | −0.438007 | −0.219004 | − | 0.975724i | \(-0.570281\pi\) | ||||
−0.219004 | + | 0.975724i | \(0.570281\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.86376 | −0.326846 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.7431 | −0.890513 | −0.445256 | − | 0.895403i | \(-0.646887\pi\) | ||||
−0.445256 | + | 0.895403i | \(0.646887\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.92881 | 0.375862 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.4836 | 0.495857 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.2641 | −0.531584 | −0.265792 | − | 0.964030i | \(-0.585633\pi\) | ||||
−0.265792 | + | 0.964030i | \(0.585633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.9299 | −2.06858 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.97334 | 0.0927155 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.232866 | 0.0109169 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.0989 | 0.846631 | 0.423315 | − | 0.905982i | \(-0.360866\pi\) | ||||
0.423315 | + | 0.905982i | \(0.360866\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.70928 | −0.359838 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.76713 | −0.454901 | −0.227450 | − | 0.973790i | \(-0.573039\pi\) | ||||
−0.227450 | + | 0.973790i | \(0.573039\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.3545 | −1.13185 | −0.565926 | − | 0.824456i | \(-0.691481\pi\) | ||||
−0.565926 | + | 0.824456i | \(0.691481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.19287 | 0.194440 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.00000 | 0.277647 | 0.138823 | − | 0.990317i | \(-0.455668\pi\) | ||||
0.138823 | + | 0.990317i | \(0.455668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.29565 | 0.198354 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.76487 | −0.127398 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.70701 | 0.124468 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.3463 | 0.612371 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.66701 | 0.122114 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.7480 | −1.49630 | −0.748148 | − | 0.663532i | \(-0.769057\pi\) | ||||
−0.748148 | + | 0.663532i | \(0.769057\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.52586 | 0.434342 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.971071 | 0.0441852 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.667015 | −0.0302876 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.4619 | 1.56162 | 0.780808 | − | 0.624771i | \(-0.214808\pi\) | ||||
0.780808 | + | 0.624771i | \(0.214808\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.40522 | −0.425319 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.7731 | −1.34364 | −0.671821 | − | 0.740714i | \(-0.734487\pi\) | ||||
−0.671821 | + | 0.740714i | \(0.734487\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −46.6369 | −2.10042 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.78765 | −0.125296 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.573039 | 0.0257043 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.4413 | −0.959846 | −0.479923 | − | 0.877311i | \(-0.659335\pi\) | ||||
−0.479923 | + | 0.877311i | \(0.659335\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.2823 | 1.43940 | 0.719699 | − | 0.694287i | \(-0.244280\pi\) | ||||
0.719699 | + | 0.694287i | \(0.244280\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.587592 | −0.0261475 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.1256 | −0.494103 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.08452 | 0.181043 | 0.0905216 | − | 0.995894i | \(-0.471147\pi\) | ||||
0.0905216 | + | 0.995894i | \(0.471147\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.77698 | 0.0786088 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.78765 | −0.123078 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.41241 | 0.282564 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.5981 | 1.30172 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.3340 | −1.02425 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.6719 | −0.993276 | −0.496638 | − | 0.867958i | \(-0.665432\pi\) | ||||
−0.496638 | + | 0.867958i | \(0.665432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.8660 | 0.956135 | 0.478067 | − | 0.878323i | \(-0.341337\pi\) | ||||
0.478067 | + | 0.878323i | \(0.341337\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.76713 | −0.0771241 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 70.1459 | 3.05560 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.0784 | −0.699060 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.14116 | −0.223107 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.94214 | 0.430642 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.41855 | 0.407199 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.1483 | 0.783159 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −41.5220 | −1.78848 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.3474 | 0.917795 | 0.458897 | − | 0.888489i | \(-0.348245\pi\) | ||||
0.458897 | + | 0.888489i | \(0.348245\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.54638 | 0.366760 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.89884 | −0.381184 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.9783 | 1.19626 | 0.598132 | − | 0.801398i | \(-0.295910\pi\) | ||||
0.598132 | + | 0.801398i | \(0.295910\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.8371 | −0.462516 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.8638 | −0.718420 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.69102 | −0.242007 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.20620 | 0.136096 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.8554 | −0.883670 | −0.441835 | − | 0.897096i | \(-0.645672\pi\) | ||||
−0.441835 | + | 0.897096i | \(0.645672\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.612646 | −0.0259122 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −46.6369 | −1.96901 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.3630 | 0.858196 | 0.429098 | − | 0.903258i | \(-0.358831\pi\) | ||||
0.429098 | + | 0.903258i | \(0.358831\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.43084 | 0.228477 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.369102 | 0.0155008 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.7093 | −0.658567 | −0.329284 | − | 0.944231i | \(-0.606807\pi\) | ||||
−0.329284 | + | 0.944231i | \(0.606807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.3991 | 1.02107 | 0.510535 | − | 0.859857i | \(-0.329447\pi\) | ||||
0.510535 | + | 0.859857i | \(0.329447\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.5753 | −0.525341 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.5958 | −0.525282 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.9276 | −1.66221 | −0.831104 | − | 0.556118i | \(-0.812290\pi\) | ||||
−0.831104 | + | 0.556118i | \(0.812290\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.7031 | 0.694158 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.66475 | 0.0690654 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.1340 | 0.668201 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.630898 | 0.0260844 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.0133 | −1.32133 | −0.660666 | − | 0.750680i | \(-0.729726\pi\) | ||||
−0.660666 | + | 0.750680i | \(0.729726\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.3646 | 1.04513 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.9854 | 0.863226 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.4163 | −0.674136 | −0.337068 | − | 0.941480i | \(-0.609435\pi\) | ||||
−0.337068 | + | 0.941480i | \(0.609435\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.31124 | 0.0537557 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.17727 | 0.375601 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.9526 | −1.91843 | −0.959216 | − | 0.282673i | \(-0.908779\pi\) | ||||
−0.959216 | + | 0.282673i | \(0.908779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.5136 | 1.48942 | 0.744710 | − | 0.667388i | \(-0.232588\pi\) | ||||
0.744710 | + | 0.667388i | \(0.232588\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.6381 | 0.473939 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.7948 | −0.479528 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.1727 | 1.50879 | 0.754397 | − | 0.656418i | \(-0.227929\pi\) | ||||
0.754397 | + | 0.656418i | \(0.227929\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.23287 | 0.0904803 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.69860 | −0.270996 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.3896 | −1.71210 | −0.856050 | − | 0.516892i | \(-0.827089\pi\) | ||||
−0.856050 | + | 0.516892i | \(0.827089\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.34632 | 0.134936 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.8059 | 1.15968 | 0.579841 | − | 0.814730i | \(-0.303115\pi\) | ||||
0.579841 | + | 0.814730i | \(0.303115\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.0372 | 1.68962 | 0.844808 | − | 0.535069i | \(-0.179715\pi\) | ||||
0.844808 | + | 0.535069i | \(0.179715\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.63090 | 0.105574 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.35085 | −0.254441 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.8599 | 0.874396 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.8638 | −0.673474 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 53.6391 | 2.13873 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.1711 | 1.55938 | 0.779689 | − | 0.626167i | \(-0.215377\pi\) | ||||
0.779689 | + | 0.626167i | \(0.215377\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.99386 | 0.118995 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.87936 | −0.233315 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.39719 | 0.372330 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.55252 | 0.0614167 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.8310 | 1.81021 | 0.905107 | − | 0.425184i | \(-0.139791\pi\) | ||||
0.905107 | + | 0.425184i | \(0.139791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.55252 | 0.297842 | 0.148921 | − | 0.988849i | \(-0.452420\pi\) | ||||
0.148921 | + | 0.988849i | \(0.452420\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.206204 | −0.00811927 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.764867 | 0.0300700 | 0.0150350 | − | 0.999887i | \(-0.495214\pi\) | ||||
0.0150350 | + | 0.999887i | \(0.495214\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.1012 | −1.22083 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.35842 | −0.131627 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.0866 | 1.49044 | 0.745222 | − | 0.666816i | \(-0.232343\pi\) | ||||
0.745222 | + | 0.666816i | \(0.232343\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.32353 | 0.208008 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.81432 | 0.187824 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.38470 | −0.170804 | −0.0854018 | − | 0.996347i | \(-0.527217\pi\) | ||||
−0.0854018 | + | 0.996347i | \(0.527217\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.99612 | 0.233222 | 0.116611 | − | 0.993178i | \(-0.462797\pi\) | ||||
0.116611 | + | 0.993178i | \(0.462797\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.5548 | 0.409914 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.474142 | 0.0183864 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.9155 | 0.616250 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.8660 | 0.729403 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −65.5585 | −2.53086 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.6719 | −0.488467 | −0.244234 | − | 0.969716i | \(-0.578536\pi\) | ||||
−0.244234 | + | 0.969716i | \(0.578536\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.78765 | −0.184277 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.39576 | 0.130510 | 0.0652549 | − | 0.997869i | \(-0.479214\pi\) | ||||
0.0652549 | + | 0.997869i | \(0.479214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.534268 | 0.0205033 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.7948 | 0.451979 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 45.7237 | 1.74957 | 0.874783 | − | 0.484514i | \(-0.161004\pi\) | ||||
0.874783 | + | 0.484514i | \(0.161004\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.254607 | −0.00972805 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.0410 | 0.993528 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.65142 | −0.139108 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.80817 | −0.373120 | −0.186560 | − | 0.982444i | \(-0.559734\pi\) | ||||
−0.186560 | + | 0.982444i | \(0.559734\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.23287 | 0.0848196 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.02279 | −0.114661 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 55.9832 | 2.12051 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.97948 | −0.150518 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.0349 | −1.32325 | −0.661625 | − | 0.749835i | \(-0.730133\pi\) | ||||
−0.661625 | + | 0.749835i | \(0.730133\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.3958 | 0.731525 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.25461 | −0.0849134 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.470652 | 0.0177007 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.7392 | −1.30466 | −0.652330 | − | 0.757935i | \(-0.726208\pi\) | ||||
−0.652330 | + | 0.757935i | \(0.726208\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.4186 | −0.578241 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23.9383 | −0.896495 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.81658 | 0.142732 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.6537 | 0.547252 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.48255 | −0.167171 | −0.0835855 | − | 0.996501i | \(-0.526637\pi\) | ||||
−0.0835855 | + | 0.996501i | \(0.526637\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.13624 | −0.191283 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.1483 | −0.377421 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.9627 | −1.07565 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.7154 | 0.694116 | 0.347058 | − | 0.937844i | \(-0.387181\pi\) | ||||
0.347058 | + | 0.937844i | \(0.387181\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.44975 | −0.127594 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.971071 | 0.0358673 | 0.0179337 | − | 0.999839i | \(-0.494291\pi\) | ||||
0.0179337 | + | 0.999839i | \(0.494291\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.16290 | 0.116665 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 70.4040 | 2.59336 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.12291 | 0.188449 | 0.0942246 | − | 0.995551i | \(-0.469963\pi\) | ||||
0.0942246 | + | 0.995551i | \(0.469963\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.81658 | 0.140206 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.3523 | 1.04014 | 0.520072 | − | 0.854122i | \(-0.325905\pi\) | ||||
0.520072 | + | 0.854122i | \(0.325905\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.83096 | −0.176993 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.51026 | 0.165022 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.54411 | −0.275656 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.93827 | 0.289671 | 0.144836 | − | 0.989456i | \(-0.453735\pi\) | ||||
0.144836 | + | 0.989456i | \(0.453735\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.7503 | 0.719741 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.909336 | −0.0330941 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.93003 | 0.251876 | 0.125938 | − | 0.992038i | \(-0.459806\pi\) | ||||
0.125938 | + | 0.992038i | \(0.459806\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.9155 | 0.577695 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.7382 | −0.643009 | −0.321505 | − | 0.946908i | \(-0.604189\pi\) | ||||
−0.321505 | + | 0.946908i | \(0.604189\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.12783 | 0.258045 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.55252 | 0.128442 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.03877 | 0.254155 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.5090 | 1.06412 | 0.532062 | − | 0.846706i | \(-0.321417\pi\) | ||||
0.532062 | + | 0.846706i | \(0.321417\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.62475 | −0.202571 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.3207 | 0.407177 | 0.203589 | − | 0.979057i | \(-0.434739\pi\) | ||||
0.203589 | + | 0.979057i | \(0.434739\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.5624 | 1.56481 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.56812 | −0.0921307 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.2434 | 0.725294 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.39189 | 0.336068 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.04945 | 0.216190 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.27408 | 0.0454739 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.2784 | −1.29319 | −0.646593 | − | 0.762835i | \(-0.723807\pi\) | ||||
−0.646593 | + | 0.762835i | \(0.723807\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.56690 | −0.304990 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.35001 | −0.154669 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.8371 | 0.526881 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.22899 | −0.0435878 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.6264 | −0.588936 | −0.294468 | − | 0.955661i | \(-0.595142\pi\) | ||||
−0.294468 | + | 0.955661i | \(0.595142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.7191 | −1.33441 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.2062 | −0.607951 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.1240 | 1.02776 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.447480 | −0.0157716 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.2195 | −0.500551 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.35473 | 0.153104 | 0.0765520 | − | 0.997066i | \(-0.475609\pi\) | ||||
0.0765520 | + | 0.997066i | \(0.475609\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.5597 | 1.14333 | 0.571663 | − | 0.820489i | \(-0.306298\pi\) | ||||
0.571663 | + | 0.820489i | \(0.306298\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.2267 | 0.463881 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.33403 | 0.151814 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.24742 | −0.0436417 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.505339 | −0.0176580 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.7770 | 1.10902 | 0.554512 | − | 0.832176i | \(-0.312905\pi\) | ||||
0.554512 | + | 0.832176i | \(0.312905\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.40400 | 0.0837981 | 0.0418990 | − | 0.999122i | \(-0.486659\pi\) | ||||
0.0418990 | + | 0.999122i | \(0.486659\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −28.9627 | −1.00835 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.8036 | −1.38411 | −0.692054 | − | 0.721846i | \(-0.743294\pi\) | ||||
−0.692054 | + | 0.721846i | \(0.743294\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.1184 | 0.455620 | 0.227810 | − | 0.973706i | \(-0.426844\pi\) | ||||
0.227810 | + | 0.973706i | \(0.426844\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.6670 | −0.578172 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 52.9146 | 1.83338 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.460811 | 0.0159470 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.09890 | −0.314504 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.6574 | −1.67984 | −0.839920 | − | 0.542711i | \(-0.817398\pi\) | ||||
−0.839920 | + | 0.542711i | \(0.817398\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.59583 | 0.261925 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.4391 | −0.600633 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.12678 | 0.176367 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.44748 | 0.324619 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.9565 | −0.890825 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.3051 | −0.627491 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.8720 | −1.02280 | −0.511399 | − | 0.859343i | \(-0.670873\pi\) | ||||
−0.511399 | + | 0.859343i | \(0.670873\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.28458 | 0.0439318 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.633165 | 0.0216285 | 0.0108143 | − | 0.999942i | \(-0.496558\pi\) | ||||
0.0108143 | + | 0.999942i | \(0.496558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.5837 | −0.599949 | −0.299974 | − | 0.953947i | \(-0.596978\pi\) | ||||
−0.299974 | + | 0.953947i | \(0.596978\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.68035 | −0.0913459 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.3197 | 0.793810 | 0.396905 | − | 0.917860i | \(-0.370084\pi\) | ||||
0.396905 | + | 0.917860i | \(0.370084\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.7526 | 0.365599 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.4329 | 1.44110 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −93.2737 | −3.16409 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.9337 | −0.539894 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.44748 | 0.0489898 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.66475 | 0.0562787 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.2641 | 0.481663 | 0.240832 | − | 0.970567i | \(-0.422580\pi\) | ||||
0.240832 | + | 0.970567i | \(0.422580\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.6225 | −0.493204 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.8227 | −0.364627 | −0.182313 | − | 0.983240i | \(-0.558359\pi\) | ||||
−0.182313 | + | 0.983240i | \(0.558359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.8783 | 0.399737 | 0.199869 | − | 0.979823i | \(-0.435948\pi\) | ||||
0.199869 | + | 0.979823i | \(0.435948\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.36910 | 0.0796365 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.07223 | −0.136732 | −0.0683661 | − | 0.997660i | \(-0.521779\pi\) | ||||
−0.0683661 | + | 0.997660i | \(0.521779\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.70928 | 0.157944 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.04945 | 0.202664 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.6391 | −0.456416 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.36296 | −0.279543 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.60197 | −0.120266 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −55.0433 | −1.83580 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.5608 | −0.684978 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.165166 | 0.00549638 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.93827 | −0.130912 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.1422 | −0.369971 | −0.184985 | − | 0.982741i | \(-0.559224\pi\) | ||||
−0.184985 | + | 0.982741i | \(0.559224\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.27513 | 0.0422933 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.7670 | −0.853697 | −0.426849 | − | 0.904323i | \(-0.640376\pi\) | ||||
−0.426849 | + | 0.904323i | \(0.640376\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.2846 | 0.902988 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.99386 | 0.165092 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.26406 | −0.140812 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.01664 | −0.132497 | −0.0662484 | − | 0.997803i | \(-0.521103\pi\) | ||||
−0.0662484 | + | 0.997803i | \(0.521103\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.170086 | 0.00560454 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.12556 | −0.0699636 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.3112 | 1.09527 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.9155 | −0.457044 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.4924 | 1.29570 | 0.647852 | − | 0.761766i | \(-0.275668\pi\) | ||||
0.647852 | + | 0.761766i | \(0.275668\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.1338 | 0.627085 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.60197 | −0.150662 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.4908 | 0.702824 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.23126 | −0.105561 | −0.0527803 | − | 0.998606i | \(-0.516808\pi\) | ||||
−0.0527803 | + | 0.998606i | \(0.516808\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.5525 | −0.507537 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.0966 | −1.01372 | −0.506861 | − | 0.862028i | \(-0.669194\pi\) | ||||
−0.506861 | + | 0.862028i | \(0.669194\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.1050 | −0.622146 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.170086 | −0.00553291 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.8203 | 1.19650 | 0.598249 | − | 0.801310i | \(-0.295863\pi\) | ||||
0.598249 | + | 0.801310i | \(0.295863\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.59129 | −0.213962 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.68261 | 0.313980 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.13850 | −0.198846 | −0.0994228 | − | 0.995045i | \(-0.531700\pi\) | ||||
−0.0994228 | + | 0.995045i | \(0.531700\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.79484 | 0.187517 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 36.5958 | 1.18298 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.203936 | 0.00658545 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.7899 | 1.67064 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.4391 | −0.658640 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.69699 | −0.247775 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.6742 | 0.696995 | 0.348498 | − | 0.937310i | \(-0.386692\pi\) | ||||
0.348498 | + | 0.937310i | \(0.386692\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.4908 | 0.690383 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.8299 | −0.700555 | −0.350278 | − | 0.936646i | \(-0.613913\pi\) | ||||
−0.350278 | + | 0.936646i | \(0.613913\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.42120 | 0.0776202 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.55479 | 0.209921 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.4741 | 0.782997 | 0.391499 | − | 0.920179i | \(-0.371957\pi\) | ||||
0.391499 | + | 0.920179i | \(0.371957\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −104.088 | −3.32667 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.3112 | 0.616561 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.3402 | −1.09528 | −0.547641 | − | 0.836714i | \(-0.684474\pi\) | ||||
−0.547641 | + | 0.836714i | \(0.684474\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.67033 | −0.308122 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.80590 | 0.0574826 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.17727 | 0.0374351 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.1340 | −0.830173 | −0.415086 | − | 0.909782i | \(-0.636249\pi\) | ||||
−0.415086 | + | 0.909782i | \(0.636249\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.4307 | −1.02916 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.22899 | −0.134068 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.78765 | −0.0882859 | −0.0441429 | − | 0.999025i | \(-0.514056\pi\) | ||||
−0.0441429 | + | 0.999025i | \(0.514056\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.95774 | −0.220133 |
(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 | 8016.2.a.l.1.2 | 3 | ||
4.3 | odd | 2 | 1002.2.a.h.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 3006.2.a.o.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1002.2.a.h.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
3006.2.a.o.1.2 | 3 | 12.11 | even | 2 | |||
8016.2.a.l.1.2 | 3 | 1.1 | even | 1 | trivial |