Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6044,2,Mod(1,6044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6044, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6044 = 2^{2} \cdot 1511 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6044.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: | \(48.2615829817\) |
Analytic rank: | \(0\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6044.1 |
$q$-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 | ||||||||
\(3\) | −2.12225 | −1.22528 | −0.612640 | − | 0.790362i | \(-0.709892\pi\) | ||||
−0.612640 | + | 0.790362i | \(0.709892\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.499336 | −0.223310 | −0.111655 | − | 0.993747i | \(-0.535615\pi\) | ||||
−0.111655 | + | 0.993747i | \(0.535615\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0909608 | −0.0343799 | −0.0171900 | − | 0.999852i | \(-0.505472\pi\) | ||||
−0.0171900 | + | 0.999852i | \(0.505472\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50393 | 0.501310 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.99078 | −1.80629 | −0.903144 | − | 0.429338i | \(-0.858747\pi\) | ||||
−0.903144 | + | 0.429338i | \(0.858747\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.72950 | −0.479677 | −0.239838 | − | 0.970813i | \(-0.577094\pi\) | ||||
−0.239838 | + | 0.970813i | \(0.577094\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.05971 | 0.273617 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.991439 | 0.240459 | 0.120230 | − | 0.992746i | \(-0.461637\pi\) | ||||
0.120230 | + | 0.992746i | \(0.461637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.171467 | −0.0393373 | −0.0196686 | − | 0.999807i | \(-0.506261\pi\) | ||||
−0.0196686 | + | 0.999807i | \(0.506261\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.193041 | 0.0421250 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.88287 | −1.85221 | −0.926103 | − | 0.377270i | \(-0.876863\pi\) | ||||
−0.926103 | + | 0.377270i | \(0.876863\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.75066 | −0.950133 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.17503 | 0.611035 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.101836 | −0.0189105 | −0.00945523 | − | 0.999955i | \(-0.503010\pi\) | ||||
−0.00945523 | + | 0.999955i | \(0.503010\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.95137 | 0.709688 | 0.354844 | − | 0.934926i | \(-0.384534\pi\) | ||||
0.354844 | + | 0.934926i | \(0.384534\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.7139 | 2.21321 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0454200 | 0.00767738 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2433 | −1.68399 | −0.841993 | − | 0.539489i | \(-0.818617\pi\) | ||||
−0.841993 | + | 0.539489i | \(0.818617\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.67042 | 0.587738 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.52563 | −1.33148 | −0.665740 | − | 0.746184i | \(-0.731884\pi\) | ||||
−0.665740 | + | 0.746184i | \(0.731884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.82550 | 0.278386 | 0.139193 | − | 0.990265i | \(-0.455549\pi\) | ||||
0.139193 | + | 0.990265i | \(0.455549\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.750966 | −0.111947 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.29537 | 0.626544 | 0.313272 | − | 0.949663i | \(-0.398575\pi\) | ||||
0.313272 | + | 0.949663i | \(0.398575\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99173 | −0.998818 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.10408 | −0.294630 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.1387 | −1.53002 | −0.765008 | − | 0.644020i | \(-0.777265\pi\) | ||||
−0.765008 | + | 0.644020i | \(0.777265\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.99141 | 0.403362 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.363896 | 0.0481991 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.94489 | 1.03434 | 0.517168 | − | 0.855884i | \(-0.326986\pi\) | ||||
0.517168 | + | 0.855884i | \(0.326986\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.282218 | −0.0361344 | −0.0180672 | − | 0.999837i | \(-0.505751\pi\) | ||||
−0.0180672 | + | 0.999837i | \(0.505751\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.136799 | −0.0172350 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.863601 | 0.107116 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.845161 | −0.103253 | −0.0516264 | − | 0.998666i | \(-0.516441\pi\) | ||||
−0.0516264 | + | 0.998666i | \(0.516441\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 18.8516 | 2.26947 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.472422 | −0.0560661 | −0.0280331 | − | 0.999607i | \(-0.508924\pi\) | ||||
−0.0280331 | + | 0.999607i | \(0.508924\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.28928 | −0.150899 | −0.0754495 | − | 0.997150i | \(-0.524039\pi\) | ||||
−0.0754495 | + | 0.997150i | \(0.524039\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.0821 | 1.16418 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.544926 | 0.0621001 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.72295 | −1.09392 | −0.546959 | − | 0.837160i | \(-0.684214\pi\) | ||||
−0.546959 | + | 0.837160i | \(0.684214\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2500 | −1.25000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.08035 | 0.996698 | 0.498349 | − | 0.866976i | \(-0.333940\pi\) | ||||
0.498349 | + | 0.866976i | \(0.333940\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.495061 | −0.0536969 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.216121 | 0.0231706 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.22911 | −0.660285 | −0.330142 | − | 0.943931i | \(-0.607097\pi\) | ||||
−0.330142 | + | 0.943931i | \(0.607097\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.157316 | 0.0164913 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.38579 | −0.869566 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0856197 | 0.00878440 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.05618 | −0.817981 | −0.408991 | − | 0.912539i | \(-0.634119\pi\) | ||||
−0.408991 | + | 0.912539i | \(0.634119\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.00971 | −0.905510 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.57036 | 0.852782 | 0.426391 | − | 0.904539i | \(-0.359785\pi\) | ||||
0.426391 | + | 0.904539i | \(0.359785\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.9163 | 1.07562 | 0.537808 | − | 0.843067i | \(-0.319252\pi\) | ||||
0.537808 | + | 0.843067i | \(0.319252\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0963924 | −0.00940693 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.5855 | 1.21668 | 0.608341 | − | 0.793676i | \(-0.291835\pi\) | ||||
0.608341 | + | 0.793676i | \(0.291835\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.67943 | 0.735556 | 0.367778 | − | 0.929914i | \(-0.380119\pi\) | ||||
0.367778 | + | 0.929914i | \(0.380119\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.7388 | 2.06335 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.6116 | −1.93897 | −0.969487 | − | 0.245144i | \(-0.921165\pi\) | ||||
−0.969487 | + | 0.245144i | \(0.921165\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.43554 | 0.413616 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.60104 | −0.240467 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0901820 | −0.00826697 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.8894 | 2.26268 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.0935 | 1.63143 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.86886 | 0.435484 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.6852 | −1.65804 | −0.829020 | − | 0.559219i | \(-0.811101\pi\) | ||||
−0.829020 | + | 0.559219i | \(0.811101\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.87416 | −0.341101 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.7804 | −1.81559 | −0.907795 | − | 0.419415i | \(-0.862235\pi\) | ||||
−0.907795 | + | 0.419415i | \(0.862235\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0155968 | 0.00135241 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.58541 | −0.136450 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.9678 | −1.19335 | −0.596676 | − | 0.802482i | \(-0.703512\pi\) | ||||
−0.596676 | + | 0.802482i | \(0.703512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.82195 | 0.154536 | 0.0772680 | − | 0.997010i | \(-0.475380\pi\) | ||||
0.0772680 | + | 0.997010i | \(0.475380\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.11584 | −0.767692 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.3610 | 0.866434 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0508503 | 0.00422289 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.8382 | 1.22383 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.93768 | −0.568357 | −0.284179 | − | 0.958771i | \(-0.591721\pi\) | ||||
−0.284179 | + | 0.958771i | \(0.591721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.7458 | 1.44413 | 0.722066 | − | 0.691824i | \(-0.243193\pi\) | ||||
0.722066 | + | 0.691824i | \(0.243193\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.49105 | 0.120545 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.97306 | −0.158480 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.8906 | 1.26821 | 0.634104 | − | 0.773248i | \(-0.281369\pi\) | ||||
0.634104 | + | 0.773248i | \(0.281369\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.6390 | 1.87470 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.807993 | 0.0636787 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.8649 | 0.851006 | 0.425503 | − | 0.904957i | \(-0.360097\pi\) | ||||
0.425503 | + | 0.904957i | \(0.360097\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.34851 | −0.494231 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.4310 | −1.50361 | −0.751807 | − | 0.659383i | \(-0.770818\pi\) | ||||
−0.751807 | + | 0.659383i | \(0.770818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0088 | −0.769910 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.257875 | −0.0197202 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.46800 | 0.263667 | 0.131834 | − | 0.991272i | \(-0.457914\pi\) | ||||
0.131834 | + | 0.991272i | \(0.457914\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.432124 | 0.0326655 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.8610 | −1.26735 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.38527 | −0.626745 | −0.313372 | − | 0.949630i | \(-0.601459\pi\) | ||||
−0.313372 | + | 0.949630i | \(0.601459\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.3824 | −1.58934 | −0.794671 | − | 0.607041i | \(-0.792356\pi\) | ||||
−0.794671 | + | 0.607041i | \(0.792356\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.598937 | 0.0442747 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.11484 | 0.376050 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.93949 | −0.434339 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.288803 | −0.0210073 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.65612 | 0.626335 | 0.313168 | − | 0.949698i | \(-0.398610\pi\) | ||||
0.313168 | + | 0.949698i | \(0.398610\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.3099 | 1.38996 | 0.694980 | − | 0.719029i | \(-0.255413\pi\) | ||||
0.694980 | + | 0.719029i | \(0.255413\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.83277 | −0.131248 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.5205 | −1.10579 | −0.552895 | − | 0.833251i | \(-0.686477\pi\) | ||||
−0.552895 | + | 0.833251i | \(0.686477\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.72616 | −0.122364 | −0.0611819 | − | 0.998127i | \(-0.519487\pi\) | ||||
−0.0611819 | + | 0.998127i | \(0.519487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.79364 | 0.126514 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.00926307 | 0.000650140 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.25715 | 0.297332 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.3592 | −0.928529 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.02722 | 0.0710544 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5443 | 0.794744 | 0.397372 | − | 0.917658i | \(-0.369922\pi\) | ||||
0.397372 | + | 0.917658i | \(0.369922\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.00260 | 0.0686967 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.911537 | −0.0621663 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.359420 | −0.0243990 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.73617 | 0.184893 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.71469 | −0.115343 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.90655 | 0.261602 | 0.130801 | − | 0.991409i | \(-0.458245\pi\) | ||||
0.130801 | + | 0.991409i | \(0.458245\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.14466 | −0.476311 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.26878 | −0.416074 | −0.208037 | − | 0.978121i | \(-0.566707\pi\) | ||||
−0.208037 | + | 0.978121i | \(0.566707\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.3543 | 0.684235 | 0.342117 | − | 0.939657i | \(-0.388856\pi\) | ||||
0.342117 | + | 0.939657i | \(0.388856\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.15647 | −0.0760899 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.63035 | −0.630905 | −0.315452 | − | 0.948941i | \(-0.602156\pi\) | ||||
−0.315452 | + | 0.948941i | \(0.602156\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.14483 | −0.139914 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.6345 | 1.34035 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.74469 | −0.630331 | −0.315166 | − | 0.949037i | \(-0.602060\pi\) | ||||
−0.315166 | + | 0.949037i | \(0.602060\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.117859 | −0.00759197 | −0.00379598 | − | 0.999993i | \(-0.501208\pi\) | ||||
−0.00379598 | + | 0.999993i | \(0.501208\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.3501 | 0.920562 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.49122 | 0.223046 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.296552 | 0.0188692 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.2707 | −1.22123 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.9295 | 0.879221 | 0.439611 | − | 0.898188i | \(-0.355116\pi\) | ||||
0.439611 | + | 0.898188i | \(0.355116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 53.2153 | 3.34562 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.05064 | 0.0657937 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.18250 | 0.136141 | 0.0680704 | − | 0.997681i | \(-0.478316\pi\) | ||||
0.0680704 | + | 0.997681i | \(0.478316\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.931737 | 0.0578953 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.153154 | −0.00948000 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.97555 | −0.553456 | −0.276728 | − | 0.960948i | \(-0.589250\pi\) | ||||
−0.276728 | + | 0.960948i | \(0.589250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.56195 | 0.341668 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.2197 | 0.809033 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.1278 | 1.10527 | 0.552636 | − | 0.833422i | \(-0.313622\pi\) | ||||
0.552636 | + | 0.833422i | \(0.313622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.706196 | −0.0428983 | −0.0214492 | − | 0.999770i | \(-0.506828\pi\) | ||||
−0.0214492 | + | 0.999770i | \(0.506828\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.333864 | −0.0202064 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 28.4602 | 1.71621 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.3095 | 1.16020 | 0.580099 | − | 0.814546i | \(-0.303014\pi\) | ||||
0.580099 | + | 0.814546i | \(0.303014\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.94259 | 0.355773 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.5129 | 1.82024 | 0.910122 | − | 0.414340i | \(-0.135987\pi\) | ||||
0.910122 | + | 0.414340i | \(0.135987\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.0618746 | 0.00367806 | 0.00183903 | − | 0.999998i | \(-0.499415\pi\) | ||||
0.00183903 | + | 0.999998i | \(0.499415\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.181706 | −0.0107633 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.775498 | 0.0457762 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0170 | −0.942179 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.0972 | 1.00226 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.9403 | 1.51545 | 0.757723 | − | 0.652576i | \(-0.226312\pi\) | ||||
0.757723 | + | 0.652576i | \(0.226312\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.96717 | −0.230978 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.0209 | −1.10370 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.3629 | 0.888460 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.166049 | −0.00957089 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.1884 | −1.04490 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.140922 | 0.00806916 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.1562 | 0.865010 | 0.432505 | − | 0.901631i | \(-0.357630\pi\) | ||||
0.432505 | + | 0.901631i | \(0.357630\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.1671 | −1.31793 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.4188 | 1.27125 | 0.635626 | − | 0.771997i | \(-0.280742\pi\) | ||||
0.635626 | + | 0.771997i | \(0.280742\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.1346 | 0.572839 | 0.286420 | − | 0.958104i | \(-0.407535\pi\) | ||||
0.286420 | + | 0.958104i | \(0.407535\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0683084 | 0.00384874 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.369448 | 0.0207503 | 0.0103751 | − | 0.999946i | \(-0.496697\pi\) | ||||
0.0103751 | + | 0.999946i | \(0.496697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.610077 | 0.0341577 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.7094 | −1.49078 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.169999 | −0.00945901 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.21627 | 0.455756 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.2976 | −0.901262 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.390710 | −0.0215406 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.7982 | −1.03324 | −0.516622 | − | 0.856214i | \(-0.672811\pi\) | ||||
−0.516622 | + | 0.856214i | \(0.672811\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.4052 | −0.844198 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.422019 | 0.0230574 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.65923 | −0.199331 | −0.0996656 | − | 0.995021i | \(-0.531777\pi\) | ||||
−0.0996656 | + | 0.995021i | \(0.531777\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 43.7428 | 2.37578 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.6718 | −1.28190 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.27270 | 0.0687192 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.41330 | −0.506795 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.2193 | −1.24648 | −0.623238 | − | 0.782032i | \(-0.714183\pi\) | ||||
−0.623238 | + | 0.782032i | \(0.714183\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6150 | 0.728795 | 0.364397 | − | 0.931244i | \(-0.381275\pi\) | ||||
0.364397 | + | 0.931244i | \(0.381275\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.49121 | −0.293099 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.0014 | 0.798442 | 0.399221 | − | 0.916855i | \(-0.369281\pi\) | ||||
0.399221 | + | 0.916855i | \(0.369281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.235897 | 0.0125201 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.191388 | 0.0101294 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.1671 | −0.747713 | −0.373856 | − | 0.927487i | \(-0.621965\pi\) | ||||
−0.373856 | + | 0.927487i | \(0.621965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9706 | −0.998453 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −52.8215 | −2.77241 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.643784 | 0.0336972 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.12351 | −0.0586470 | −0.0293235 | − | 0.999570i | \(-0.509335\pi\) | ||||
−0.0293235 | + | 0.999570i | \(0.509335\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.8219 | −0.667484 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.01318 | 0.0526019 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.19359 | 0.372470 | 0.186235 | − | 0.982505i | \(-0.440371\pi\) | ||||
0.186235 | + | 0.982505i | \(0.440371\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.3329 | −0.533589 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.176125 | 0.00907090 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.91948 | 0.304063 | 0.152032 | − | 0.988376i | \(-0.451418\pi\) | ||||
0.152032 | + | 0.988376i | \(0.451418\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 39.6545 | 2.03156 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.77174 | 0.499313 | 0.249656 | − | 0.968334i | \(-0.419682\pi\) | ||||
0.249656 | + | 0.968334i | \(0.419682\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.272101 | −0.0138676 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.74542 | 0.139558 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.2916 | −0.724614 | −0.362307 | − | 0.932059i | \(-0.618011\pi\) | ||||
−0.362307 | + | 0.932059i | \(0.618011\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.80682 | −0.445380 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 44.1011 | 2.22460 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.85502 | 0.244282 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.7973 | 1.19435 | 0.597175 | − | 0.802111i | \(-0.296290\pi\) | ||||
0.597175 | + | 0.802111i | \(0.296290\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0331002 | −0.00165708 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.5586 | −0.926771 | −0.463386 | − | 0.886157i | \(-0.653365\pi\) | ||||
−0.463386 | + | 0.886157i | \(0.653365\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.83390 | −0.340421 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.61752 | 0.279137 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 61.3652 | 3.04176 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.9219 | 1.92457 | 0.962283 | − | 0.272051i | \(-0.0877019\pi\) | ||||
0.962283 | + | 0.272051i | \(0.0877019\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.6432 | 1.46219 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.722673 | −0.0355604 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.53415 | −0.222572 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.86663 | −0.189350 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.0419 | 1.85847 | 0.929235 | − | 0.369489i | \(-0.120467\pi\) | ||||
0.929235 | + | 0.369489i | \(0.120467\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.38416 | 0.408619 | 0.204309 | − | 0.978906i | \(-0.434505\pi\) | ||||
0.204309 | + | 0.978906i | \(0.434505\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.45994 | 0.314093 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.70999 | −0.228468 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0256708 | 0.00124230 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.9887 | −1.06162 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.6362 | −1.13851 | −0.569257 | − | 0.822160i | \(-0.692769\pi\) | ||||
−0.569257 | + | 0.822160i | \(0.692769\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.6966 | 0.562105 | 0.281052 | − | 0.959692i | \(-0.409317\pi\) | ||||
0.281052 | + | 0.959692i | \(0.409317\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.107917 | −0.00517422 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.52312 | 0.0728607 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.8022 | −1.23147 | −0.615736 | − | 0.787952i | \(-0.711141\pi\) | ||||
−0.615736 | + | 0.787952i | \(0.711141\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.5151 | −0.500717 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.1598 | −1.33791 | −0.668957 | − | 0.743301i | \(-0.733259\pi\) | ||||
−0.668957 | + | 0.743301i | \(0.733259\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.11042 | 0.147448 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.7235 | 0.696396 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.4005 | 1.00995 | 0.504977 | − | 0.863133i | \(-0.331501\pi\) | ||||
0.504977 | + | 0.863133i | \(0.331501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 51.0751 | 2.40503 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −37.6610 | −1.76947 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0785538 | −0.00368266 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.2516 | −1.32155 | −0.660777 | − | 0.750582i | \(-0.729773\pi\) | ||||
−0.660777 | + | 0.750582i | \(0.729773\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.14785 | 0.146929 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.4176 | −1.55641 | −0.778206 | − | 0.628009i | \(-0.783870\pi\) | ||||
−0.778206 | + | 0.628009i | \(0.783870\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.2409 | 0.661831 | 0.330916 | − | 0.943660i | \(-0.392642\pi\) | ||||
0.330916 | + | 0.943660i | \(0.392642\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.18733 | 0.194183 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.6400 | 1.74177 | 0.870885 | − | 0.491487i | \(-0.163546\pi\) | ||||
0.870885 | + | 0.491487i | \(0.163546\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0768765 | 0.00354983 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −33.7238 | −1.55391 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.9362 | −0.502845 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.814583 | 0.0373756 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.7518 | −0.767012 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.5608 | 1.76189 | 0.880945 | − | 0.473219i | \(-0.156908\pi\) | ||||
0.880945 | + | 0.473219i | \(0.156908\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.7157 | 0.807768 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.71476 | −0.0780243 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.02274 | 0.182663 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.9010 | −0.765857 | −0.382929 | − | 0.923778i | \(-0.625085\pi\) | ||||
−0.382929 | + | 0.923778i | \(0.625085\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.0580 | −1.04272 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.5936 | 1.42580 | 0.712899 | − | 0.701266i | \(-0.247382\pi\) | ||||
0.712899 | + | 0.701266i | \(0.247382\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.100964 | −0.00454719 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.49887 | 0.202209 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.0429718 | 0.00192755 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7837 | 0.661810 | 0.330905 | − | 0.943664i | \(-0.392646\pi\) | ||||
0.330905 | + | 0.943664i | \(0.392646\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 41.2373 | 1.84235 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.5093 | 0.557763 | 0.278881 | − | 0.960326i | \(-0.410036\pi\) | ||||
0.278881 | + | 0.960326i | \(0.410036\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.27949 | −0.190435 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.2412 | 0.943355 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −37.9373 | −1.68154 | −0.840772 | − | 0.541390i | \(-0.817898\pi\) | ||||
−0.840772 | + | 0.541390i | \(0.817898\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.117274 | 0.00518790 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.544413 | −0.0240364 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.45091 | −0.240196 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.7326 | −1.13172 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.35995 | −0.323066 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.7642 | 0.909695 | 0.454848 | − | 0.890569i | \(-0.349694\pi\) | ||||
0.454848 | + | 0.890569i | \(0.349694\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.8026 | 0.778455 | 0.389228 | − | 0.921142i | \(-0.372742\pi\) | ||||
0.389228 | + | 0.921142i | \(0.372742\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.917074 | −0.0400244 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.91755 | 0.170651 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 55.9054 | 2.43067 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.9486 | 0.518523 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.7451 | 0.638679 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.28437 | −0.271697 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.7956 | 0.767938 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41.8859 | 1.80415 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.2441 | 0.526413 | 0.263207 | − | 0.964739i | \(-0.415220\pi\) | ||||
0.263207 | + | 0.964739i | \(0.415220\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 45.3787 | 1.94739 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.83461 | −0.164257 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.6674 | −1.48227 | −0.741135 | − | 0.671357i | \(-0.765712\pi\) | ||||
−0.741135 | + | 0.671357i | \(0.765712\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.424436 | −0.0181145 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0174615 | 0.000743886 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.884407 | 0.0376088 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.8549 | −0.460767 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.70453 | 0.0722234 | 0.0361117 | − | 0.999348i | \(-0.488503\pi\) | ||||
0.0361117 | + | 0.999348i | \(0.488503\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.15720 | −0.133535 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.6051 | 0.532186 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.0501719 | −0.00211449 | −0.00105725 | − | 0.999999i | \(-0.500337\pi\) | ||||
−0.00105725 | + | 0.999999i | \(0.500337\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.2921 | 0.432992 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.02331 | 0.0429749 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.8035 | −0.746363 | −0.373182 | − | 0.927758i | \(-0.621733\pi\) | ||||
−0.373182 | + | 0.927758i | \(0.621733\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.8677 | 1.79396 | 0.896980 | − | 0.442072i | \(-0.145756\pi\) | ||||
0.896980 | + | 0.442072i | \(0.145756\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.3704 | −0.767436 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 42.1995 | 1.75984 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.8902 | 1.32761 | 0.663804 | − | 0.747907i | \(-0.268941\pi\) | ||||
0.663804 | + | 0.747907i | \(0.268941\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −40.9805 | −1.70309 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.825956 | −0.0342664 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 66.7294 | 2.76365 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.29879 | 0.0536985 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −35.4373 | −1.46265 | −0.731326 | − | 0.682028i | \(-0.761098\pi\) | ||||
−0.731326 | + | 0.682028i | \(0.761098\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.677531 | −0.0279172 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 32.9383 | 1.35490 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.8530 | 0.445680 | 0.222840 | − | 0.974855i | \(-0.428467\pi\) | ||||
0.222840 | + | 0.974855i | \(0.428467\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0450311 | 0.00184610 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.66333 | 0.149930 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.8873 | 0.730857 | 0.365428 | − | 0.930839i | \(-0.380923\pi\) | ||||
0.365428 | + | 0.930839i | \(0.380923\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.5916 | −0.432040 | −0.216020 | − | 0.976389i | \(-0.569308\pi\) | ||||
−0.216020 | + | 0.976389i | \(0.569308\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.27106 | −0.0517617 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.4282 | −0.505278 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.2267 | −1.22686 | −0.613431 | − | 0.789748i | \(-0.710211\pi\) | ||||
−0.613431 | + | 0.789748i | \(0.710211\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0196585 | −0.000796604 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.42884 | −0.300539 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.2329 | −0.655642 | −0.327821 | − | 0.944740i | \(-0.606314\pi\) | ||||
−0.327821 | + | 0.944740i | \(0.606314\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.03473 | −0.364315 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.7233 | −0.834287 | −0.417144 | − | 0.908841i | \(-0.636969\pi\) | ||||
−0.417144 | + | 0.908841i | \(0.636969\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.1370 | −0.447636 | −0.223818 | − | 0.974631i | \(-0.571852\pi\) | ||||
−0.223818 | + | 0.974631i | \(0.571852\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.2034 | −1.13176 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.566605 | 0.0227005 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.3221 | 0.852885 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.18002 | −0.0870615 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.1556 | −0.404930 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.97550 | −0.397118 | −0.198559 | − | 0.980089i | \(-0.563626\pi\) | ||||
−0.198559 | + | 0.980089i | \(0.563626\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.4999 | −0.973783 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.33017 | 0.370256 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0922 | 0.479110 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.710489 | −0.0281065 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.4343 | −1.16259 | −0.581293 | − | 0.813694i | \(-0.697453\pi\) | ||||
−0.581293 | + | 0.813694i | \(0.697453\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.83020 | 0.151048 | 0.0755242 | − | 0.997144i | \(-0.475937\pi\) | ||||
0.0755242 | + | 0.997144i | \(0.475937\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.93451 | 0.0761711 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.31181 | −0.326771 | −0.163386 | − | 0.986562i | \(-0.552241\pi\) | ||||
−0.163386 | + | 0.986562i | \(0.552241\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −47.5961 | −1.86831 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.762778 | 0.0298956 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.4205 | 0.407785 | 0.203893 | − | 0.978993i | \(-0.434641\pi\) | ||||
0.203893 | + | 0.978993i | \(0.434641\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.3764 | 0.405439 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.93899 | −0.0756471 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.88523 | −0.385074 | −0.192537 | − | 0.981290i | \(-0.561672\pi\) | ||||
−0.192537 | + | 0.981290i | \(0.561672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.1127 | 1.32683 | 0.663415 | − | 0.748252i | \(-0.269106\pi\) | ||||
0.663415 | + | 0.748252i | \(0.269106\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.63900 | 0.141327 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.00778803 | −0.000302007 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.904595 | 0.0350261 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.29066 | −0.320535 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.69071 | 0.0652690 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.592944 | 0.0228563 | 0.0114282 | − | 0.999935i | \(-0.496362\pi\) | ||||
0.0114282 | + | 0.999935i | \(0.496362\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.0835 | −0.580564 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.2324 | 0.585429 | 0.292714 | − | 0.956200i | \(-0.405441\pi\) | ||||
0.292714 | + | 0.956200i | \(0.405441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.732796 | 0.0281221 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.3039 | 0.509806 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.9810 | −1.03240 | −0.516200 | − | 0.856468i | \(-0.672654\pi\) | ||||
−0.516200 | + | 0.856468i | \(0.672654\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.97463 | 0.266487 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.9745 | −0.838379 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.2643 | 0.733913 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.4958 | 1.50249 | 0.751246 | − | 0.660022i | \(-0.229453\pi\) | ||||
0.751246 | + | 0.660022i | \(0.229453\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.819530 | 0.0311314 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.909767 | −0.0345094 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.45264 | −0.320166 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.4380 | 0.773035 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.2447 | −1.55779 | −0.778895 | − | 0.627154i | \(-0.784219\pi\) | ||||
−0.778895 | + | 0.627154i | \(0.784219\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.75639 | 0.0662434 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.55187 | 0.171433 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.779566 | −0.0293186 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.93993 | −0.0728557 | −0.0364278 | − | 0.999336i | \(-0.511598\pi\) | ||||
−0.0364278 | + | 0.999336i | \(0.511598\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.6226 | −0.548391 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.0995 | −1.31449 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.17364 | −0.193483 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.6806 | 0.772332 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.6548 | −1.21782 | −0.608909 | − | 0.793240i | \(-0.708393\pi\) | ||||
−0.608909 | + | 0.793240i | \(0.708393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.992956 | −0.0369796 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.250126 | 0.00930228 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.483788 | 0.0179674 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.5702 | −1.13379 | −0.566893 | − | 0.823791i | \(-0.691855\pi\) | ||||
−0.566893 | + | 0.823791i | \(0.691855\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.29541 | 0.122052 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.80987 | 0.0669405 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.8563 | −1.32438 | −0.662192 | − | 0.749334i | \(-0.730374\pi\) | ||||
−0.662192 | + | 0.749334i | \(0.730374\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.40923 | −0.273294 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.06317 | 0.186504 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.80175 | −0.139850 | −0.0699249 | − | 0.997552i | \(-0.522276\pi\) | ||||
−0.0699249 | + | 0.997552i | \(0.522276\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.629357 | −0.0231200 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.8001 | −1.64356 | −0.821778 | − | 0.569808i | \(-0.807017\pi\) | ||||
−0.821778 | + | 0.569808i | \(0.807017\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.46423 | 0.126920 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.6562 | 0.499655 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.14478 | −0.0418294 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.92611 | −0.362209 | −0.181104 | − | 0.983464i | \(-0.557967\pi\) | ||||
−0.181104 | + | 0.983464i | \(0.557967\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.5618 | −1.07729 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.86111 | −0.322489 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.56108 | 0.274812 | 0.137406 | − | 0.990515i | \(-0.456123\pi\) | ||||
0.137406 | + | 0.990515i | \(0.456123\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −112.936 | −4.09932 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.3775 | 0.448685 | 0.224343 | − | 0.974510i | \(-0.427976\pi\) | ||||
0.224343 | + | 0.974510i | \(0.427976\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.698527 | −0.0252884 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.744537 | −0.0269188 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.7407 | −0.496147 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.7979 | 0.389383 | 0.194691 | − | 0.980865i | \(-0.437629\pi\) | ||||
0.194691 | + | 0.980865i | \(0.437629\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.63181 | −0.166811 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.0401 | −1.08047 | −0.540233 | − | 0.841515i | \(-0.681664\pi\) | ||||
−0.540233 | + | 0.841515i | \(0.681664\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.7716 | −0.674297 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.97737 | −0.0709379 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.46187 | 0.0523768 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.83017 | 0.101272 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.323332 | −0.0115550 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.93475 | −0.283203 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −48.0365 | −1.71232 | −0.856158 | − | 0.516713i | \(-0.827155\pi\) | ||||
−0.856158 | + | 0.516713i | \(0.827155\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.0483 | 0.678139 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.87484 | 0.0666618 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.488096 | 0.0173328 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.8038 | −0.418638 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.6947 | −1.01642 | −0.508210 | − | 0.861233i | \(-0.669693\pi\) | ||||
−0.508210 | + | 0.861233i | \(0.669693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.25860 | 0.150658 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.36815 | −0.331007 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.72380 | 0.272567 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.403460 | −0.0142201 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38.4717 | −1.35427 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.06849 | −0.283673 | −0.141836 | − | 0.989890i | \(-0.545301\pi\) | ||||
−0.141836 | + | 0.989890i | \(0.545301\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.74183 | 0.342082 | 0.171041 | − | 0.985264i | \(-0.445287\pi\) | ||||
0.171041 | + | 0.985264i | \(0.445287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.49872 | 0.0525625 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.42524 | −0.190038 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.313013 | −0.0109509 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.236593 | 0.00826723 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.8338 | −1.28551 | −0.642755 | − | 0.766072i | \(-0.722209\pi\) | ||||
−0.642755 | + | 0.766072i | \(0.722209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.14156 | 0.318655 | 0.159327 | − | 0.987226i | \(-0.449067\pi\) | ||||
0.159327 | + | 0.987226i | \(0.449067\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −60.3995 | −2.10284 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.3922 | 0.709105 | 0.354553 | − | 0.935036i | \(-0.384633\pi\) | ||||
0.354553 | + | 0.935036i | \(0.384633\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.4389 | 0.466754 | 0.233377 | − | 0.972386i | \(-0.425022\pi\) | ||||
0.233377 | + | 0.972386i | \(0.425022\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.9796 | −1.42157 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.93187 | −0.240175 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.70259 | 0.335772 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.5457 | 0.433644 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.0771 | −1.24552 | −0.622759 | − | 0.782414i | \(-0.713988\pi\) | ||||
−0.622759 | + | 0.782414i | \(0.713988\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9896 | −0.999642 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −64.7558 | −2.23031 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.99777 | 0.171929 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.26396 | −0.0777906 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.131313 | −0.00450665 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 90.9897 | 3.11909 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.6517 | −1.35765 | −0.678824 | − | 0.734301i | \(-0.737510\pi\) | ||||
−0.678824 | + | 0.734301i | \(0.737510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.128766 | 0.00440370 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.3706 | 1.34487 | 0.672437 | − | 0.740154i | \(-0.265248\pi\) | ||||
0.672437 | + | 0.740154i | \(0.265248\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.8736 | −1.56519 | −0.782593 | − | 0.622533i | \(-0.786104\pi\) | ||||
−0.782593 | + | 0.622533i | \(0.786104\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.64580 | −0.0560886 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 51.7247 | 1.76073 | 0.880365 | − | 0.474296i | \(-0.157297\pi\) | ||||
0.880365 | + | 0.474296i | \(0.157297\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.73170 | −0.0588795 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.9921 | 1.15443 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 58.2480 | 1.97593 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.46170 | 0.0495280 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.1159 | −0.410062 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.442875 | −0.0149719 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.1286 | 0.814766 | 0.407383 | − | 0.913257i | \(-0.366441\pi\) | ||||
0.407383 | + | 0.913257i | \(0.366441\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −55.0516 | −1.85685 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.6777 | −1.47154 | −0.735770 | − | 0.677232i | \(-0.763179\pi\) | ||||
−0.735770 | + | 0.677232i | \(0.763179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.7644 | 1.03531 | 0.517653 | − | 0.855591i | \(-0.326806\pi\) | ||||
0.517653 | + | 0.855591i | \(0.326806\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.41931 | 0.283012 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.32049 | 0.279375 | 0.139687 | − | 0.990196i | \(-0.455390\pi\) | ||||
0.139687 | + | 0.990196i | \(0.455390\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.69962 | 0.0570033 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 67.3962 | 2.25786 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.736515 | −0.0246465 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.18707 | 0.139958 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.6039 | −1.08861 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.402392 | −0.0134205 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.0433 | −0.367907 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.352396 | 0.0117270 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.6770 | 0.354915 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.8510 | −1.45605 | −0.728025 | − | 0.685551i | \(-0.759562\pi\) | ||||
−0.728025 | + | 0.685551i | \(0.759562\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.8892 | 0.427508 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.5806 | 0.714997 | 0.357498 | − | 0.933914i | \(-0.383630\pi\) | ||||
0.357498 | + | 0.933914i | \(0.383630\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.3984 | −1.80032 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.299071 | −0.00988697 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.89020 | 0.0624198 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.26334 | 0.173621 | 0.0868107 | − | 0.996225i | \(-0.472332\pi\) | ||||
0.0868107 | + | 0.996225i | \(0.472332\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.1652 | −1.05988 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.817053 | 0.0268936 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.6624 | 1.60001 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.4174 | 0.539217 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.4477 | 0.802103 | 0.401051 | − | 0.916056i | \(-0.368645\pi\) | ||||
0.401051 | + | 0.916056i | \(0.368645\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.19885 | 0.0392908 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −47.5781 | −1.55764 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.96580 | 0.0969920 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.4119 | −1.61422 | −0.807108 | − | 0.590404i | \(-0.798969\pi\) | ||||
−0.807108 | + | 0.590404i | \(0.798969\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.5080 | −0.701888 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.1962 | 1.04957 | 0.524784 | − | 0.851236i | \(-0.324146\pi\) | ||||
0.524784 | + | 0.851236i | \(0.324146\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 75.7320 | 2.46617 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.144210 | 0.00469114 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.1315 | −0.751672 | −0.375836 | − | 0.926686i | \(-0.622644\pi\) | ||||
−0.375836 | + | 0.926686i | \(0.622644\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.22981 | 0.0723827 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.784059 | −0.0254249 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.9741 | 1.16532 | 0.582658 | − | 0.812718i | \(-0.302013\pi\) | ||||
0.582658 | + | 0.812718i | \(0.302013\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.32231 | −0.139867 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.29473 | −0.0418528 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.27052 | 0.0410273 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.3866 | −0.496343 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.9276 | 0.609934 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.64215 | −0.310392 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.67208 | 0.150244 | 0.0751220 | − | 0.997174i | \(-0.476065\pi\) | ||||
0.0751220 | + | 0.997174i | \(0.476065\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.360780 | 0.0115899 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.7247 | 0.793454 | 0.396727 | − | 0.917937i | \(-0.370146\pi\) | ||||
0.396727 | + | 0.917937i | \(0.370146\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.165726 | −0.00531294 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.4369 | −0.558429 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56.7770 | −1.81646 | −0.908228 | − | 0.418476i | \(-0.862564\pi\) | ||||
−0.908228 | + | 0.418476i | \(0.862564\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.3172 | 1.19266 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.5493 | 0.368741 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.05308 | 0.193063 | 0.0965316 | − | 0.995330i | \(-0.469225\pi\) | ||||
0.0965316 | + | 0.995330i | \(0.469225\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.74994 | 0.246934 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.829184 | 0.0263932 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.2157 | −0.515628 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.3882 | 1.31474 | 0.657369 | − | 0.753569i | \(-0.271669\pi\) | ||||
0.657369 | + | 0.753569i | \(0.271669\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 39.8945 | 1.26601 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.861931 | 0.0273251 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.2892 | −1.18096 | −0.590480 | − | 0.807052i | \(-0.701062\pi\) | ||||
−0.590480 | + | 0.807052i | \(0.701062\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −32.5227 | −1.02897 |
(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 | 6044.2.a.b.1.14 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6044.2.a.b.1.14 | ✓ | 63 | 1.1 | even | 1 | trivial |