Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.702784 | −0.496943 | −0.248472 | − | 0.968639i | \(-0.579928\pi\) | ||||
−0.248472 | + | 0.968639i | \(0.579928\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.50609 | −0.753047 | ||||||||
\(5\) | 2.41068 | 1.07809 | 0.539044 | − | 0.842278i | \(-0.318786\pi\) | ||||
0.539044 | + | 0.842278i | \(0.318786\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.380608 | 0.143856 | 0.0719282 | − | 0.997410i | \(-0.477085\pi\) | ||||
0.0719282 | + | 0.997410i | \(0.477085\pi\) | |||||||
\(8\) | 2.46403 | 0.871165 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.69419 | −0.535749 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.87344 | 0.796949 | 0.398474 | − | 0.917180i | \(-0.369540\pi\) | ||||
0.398474 | + | 0.917180i | \(0.369540\pi\) | |||||||
\(14\) | −0.267485 | −0.0714885 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.28051 | 0.320127 | ||||||||
\(17\) | −1.85240 | −0.449274 | −0.224637 | − | 0.974443i | \(-0.572120\pi\) | ||||
−0.224637 | + | 0.974443i | \(0.572120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.38794 | −0.547831 | −0.273915 | − | 0.961754i | \(-0.588319\pi\) | ||||
−0.273915 | + | 0.961754i | \(0.588319\pi\) | |||||||
\(20\) | −3.63071 | −0.811851 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.702784 | 0.149834 | ||||||||
\(23\) | 5.66757 | 1.18177 | 0.590885 | − | 0.806756i | \(-0.298779\pi\) | ||||
0.590885 | + | 0.806756i | \(0.298779\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.811370 | 0.162274 | ||||||||
\(26\) | −2.01941 | −0.396038 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.573232 | −0.108331 | ||||||||
\(29\) | −2.60447 | −0.483639 | −0.241819 | − | 0.970321i | \(-0.577744\pi\) | ||||
−0.241819 | + | 0.970321i | \(0.577744\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.67698 | −0.840011 | −0.420006 | − | 0.907522i | \(-0.637972\pi\) | ||||
−0.420006 | + | 0.907522i | \(0.637972\pi\) | |||||||
\(32\) | −5.82798 | −1.03025 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.30184 | 0.223264 | ||||||||
\(35\) | 0.917524 | 0.155090 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.7819 | −1.77253 | −0.886265 | − | 0.463178i | \(-0.846709\pi\) | ||||
−0.886265 | + | 0.463178i | \(0.846709\pi\) | |||||||
\(38\) | 1.67821 | 0.272241 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.93998 | 0.939193 | ||||||||
\(41\) | 0.412567 | 0.0644321 | 0.0322161 | − | 0.999481i | \(-0.489744\pi\) | ||||
0.0322161 | + | 0.999481i | \(0.489744\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.52589 | −0.385195 | −0.192598 | − | 0.981278i | \(-0.561691\pi\) | ||||
−0.192598 | + | 0.981278i | \(0.561691\pi\) | |||||||
\(44\) | 1.50609 | 0.227052 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.98308 | −0.587273 | ||||||||
\(47\) | −7.69707 | −1.12273 | −0.561367 | − | 0.827567i | \(-0.689724\pi\) | ||||
−0.561367 | + | 0.827567i | \(0.689724\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.85514 | −0.979305 | ||||||||
\(50\) | −0.570218 | −0.0806410 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.32767 | −0.600140 | ||||||||
\(53\) | −3.19883 | −0.439393 | −0.219697 | − | 0.975568i | \(-0.570507\pi\) | ||||
−0.219697 | + | 0.975568i | \(0.570507\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.41068 | −0.325056 | ||||||||
\(56\) | 0.937829 | 0.125323 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.83038 | 0.240341 | ||||||||
\(59\) | −2.95404 | −0.384584 | −0.192292 | − | 0.981338i | \(-0.561592\pi\) | ||||
−0.192292 | + | 0.981338i | \(0.561592\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 3.28691 | 0.417438 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.53479 | 0.191849 | ||||||||
\(65\) | 6.92694 | 0.859181 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.09053 | 0.988416 | 0.494208 | − | 0.869344i | \(-0.335458\pi\) | ||||
0.494208 | + | 0.869344i | \(0.335458\pi\) | |||||||
\(68\) | 2.78990 | 0.338324 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.644821 | −0.0770709 | ||||||||
\(71\) | 15.0776 | 1.78938 | 0.894692 | − | 0.446684i | \(-0.147395\pi\) | ||||
0.894692 | + | 0.446684i | \(0.147395\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.1332 | 1.42008 | 0.710041 | − | 0.704161i | \(-0.248677\pi\) | ||||
0.710041 | + | 0.704161i | \(0.248677\pi\) | |||||||
\(74\) | 7.57734 | 0.880847 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.59646 | 0.412542 | ||||||||
\(77\) | −0.380608 | −0.0433743 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3863 | −1.28106 | −0.640530 | − | 0.767933i | \(-0.721285\pi\) | ||||
−0.640530 | + | 0.767933i | \(0.721285\pi\) | |||||||
\(80\) | 3.08690 | 0.345125 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.289946 | −0.0320191 | ||||||||
\(83\) | −13.0055 | −1.42754 | −0.713770 | − | 0.700380i | \(-0.753014\pi\) | ||||
−0.713770 | + | 0.700380i | \(0.753014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.46555 | −0.484357 | ||||||||
\(86\) | 1.77516 | 0.191420 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.46403 | −0.262666 | ||||||||
\(89\) | −6.76539 | −0.717130 | −0.358565 | − | 0.933505i | \(-0.616734\pi\) | ||||
−0.358565 | + | 0.933505i | \(0.616734\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.09365 | 0.114646 | ||||||||
\(92\) | −8.53590 | −0.889929 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.40938 | 0.557935 | ||||||||
\(95\) | −5.75655 | −0.590610 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.74475 | 0.684826 | 0.342413 | − | 0.939550i | \(-0.388756\pi\) | ||||
0.342413 | + | 0.939550i | \(0.388756\pi\) | |||||||
\(98\) | 4.81768 | 0.486659 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.22200 | −0.122200 | ||||||||
\(101\) | 5.42967 | 0.540272 | 0.270136 | − | 0.962822i | \(-0.412931\pi\) | ||||
0.270136 | + | 0.962822i | \(0.412931\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.08542 | 0.501081 | 0.250541 | − | 0.968106i | \(-0.419392\pi\) | ||||
0.250541 | + | 0.968106i | \(0.419392\pi\) | |||||||
\(104\) | 7.08023 | 0.694274 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.24809 | 0.218354 | ||||||||
\(107\) | −6.74418 | −0.651984 | −0.325992 | − | 0.945373i | \(-0.605698\pi\) | ||||
−0.325992 | + | 0.945373i | \(0.605698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.1031 | −1.35083 | −0.675417 | − | 0.737436i | \(-0.736036\pi\) | ||||
−0.675417 | + | 0.737436i | \(0.736036\pi\) | |||||||
\(110\) | 1.69419 | 0.161534 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.487372 | 0.0460523 | ||||||||
\(113\) | −13.1051 | −1.23283 | −0.616413 | − | 0.787423i | \(-0.711415\pi\) | ||||
−0.616413 | + | 0.787423i | \(0.711415\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.6627 | 1.27405 | ||||||||
\(116\) | 3.92258 | 0.364203 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.07606 | 0.191116 | ||||||||
\(119\) | −0.705040 | −0.0646309 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.702784 | 0.0636271 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.04398 | 0.632568 | ||||||||
\(125\) | −10.0974 | −0.903142 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.54380 | −0.314461 | −0.157231 | − | 0.987562i | \(-0.550257\pi\) | ||||
−0.157231 | + | 0.987562i | \(0.550257\pi\) | |||||||
\(128\) | 10.5773 | 0.934912 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.86814 | −0.426964 | ||||||||
\(131\) | −2.56353 | −0.223976 | −0.111988 | − | 0.993710i | \(-0.535722\pi\) | ||||
−0.111988 | + | 0.993710i | \(0.535722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.908869 | −0.0788090 | ||||||||
\(134\) | −5.68590 | −0.491187 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.56437 | −0.391392 | ||||||||
\(137\) | −10.1411 | −0.866413 | −0.433207 | − | 0.901295i | \(-0.642618\pi\) | ||||
−0.433207 | + | 0.901295i | \(0.642618\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.9387 | −0.927812 | −0.463906 | − | 0.885885i | \(-0.653552\pi\) | ||||
−0.463906 | + | 0.885885i | \(0.653552\pi\) | |||||||
\(140\) | −1.38188 | −0.116790 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.5963 | −0.889222 | ||||||||
\(143\) | −2.87344 | −0.240289 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.27855 | −0.521405 | ||||||||
\(146\) | −8.52701 | −0.705700 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16.2385 | 1.33480 | ||||||||
\(149\) | 0.534433 | 0.0437825 | 0.0218912 | − | 0.999760i | \(-0.493031\pi\) | ||||
0.0218912 | + | 0.999760i | \(0.493031\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1663 | 1.07146 | 0.535729 | − | 0.844390i | \(-0.320037\pi\) | ||||
0.535729 | + | 0.844390i | \(0.320037\pi\) | |||||||
\(152\) | −5.88395 | −0.477251 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.267485 | 0.0215546 | ||||||||
\(155\) | −11.2747 | −0.905606 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7696 | 1.25856 | 0.629278 | − | 0.777181i | \(-0.283351\pi\) | ||||
0.629278 | + | 0.777181i | \(0.283351\pi\) | |||||||
\(158\) | 8.00212 | 0.636615 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.0494 | −1.11070 | ||||||||
\(161\) | 2.15712 | 0.170005 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1338 | 0.793742 | 0.396871 | − | 0.917874i | \(-0.370096\pi\) | ||||
0.396871 | + | 0.917874i | \(0.370096\pi\) | |||||||
\(164\) | −0.621365 | −0.0485204 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.14006 | 0.709407 | ||||||||
\(167\) | −1.44995 | −0.112201 | −0.0561003 | − | 0.998425i | \(-0.517867\pi\) | ||||
−0.0561003 | + | 0.998425i | \(0.517867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.74335 | −0.364873 | ||||||||
\(170\) | 3.13832 | 0.240698 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.80423 | 0.290070 | ||||||||
\(173\) | −20.4074 | −1.55155 | −0.775774 | − | 0.631011i | \(-0.782640\pi\) | ||||
−0.775774 | + | 0.631011i | \(0.782640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.308814 | 0.0233441 | ||||||||
\(176\) | −1.28051 | −0.0965220 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.75461 | 0.356373 | ||||||||
\(179\) | −2.18942 | −0.163645 | −0.0818224 | − | 0.996647i | \(-0.526074\pi\) | ||||
−0.0818224 | + | 0.996647i | \(0.526074\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.63386 | 0.567420 | 0.283710 | − | 0.958910i | \(-0.408435\pi\) | ||||
0.283710 | + | 0.958910i | \(0.408435\pi\) | |||||||
\(182\) | −0.768603 | −0.0569726 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.9651 | 1.02952 | ||||||||
\(185\) | −25.9916 | −1.91094 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.85240 | 0.135461 | ||||||||
\(188\) | 11.5925 | 0.845471 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.04561 | 0.293500 | ||||||||
\(191\) | −3.15980 | −0.228635 | −0.114318 | − | 0.993444i | \(-0.536468\pi\) | ||||
−0.114318 | + | 0.993444i | \(0.536468\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.0169 | 1.51283 | 0.756414 | − | 0.654093i | \(-0.226949\pi\) | ||||
0.756414 | + | 0.654093i | \(0.226949\pi\) | |||||||
\(194\) | −4.74011 | −0.340320 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.3245 | 0.737463 | ||||||||
\(197\) | 26.6116 | 1.89600 | 0.948001 | − | 0.318269i | \(-0.103101\pi\) | ||||
0.948001 | + | 0.318269i | \(0.103101\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.39584 | −0.311613 | −0.155807 | − | 0.987788i | \(-0.549798\pi\) | ||||
−0.155807 | + | 0.987788i | \(0.549798\pi\) | |||||||
\(200\) | 1.99924 | 0.141367 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.81589 | −0.268485 | ||||||||
\(203\) | −0.991284 | −0.0695745 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.994566 | 0.0694635 | ||||||||
\(206\) | −3.57395 | −0.249009 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.67946 | 0.255125 | ||||||||
\(209\) | 2.38794 | 0.165177 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.6321 | 1.14500 | 0.572500 | − | 0.819904i | \(-0.305974\pi\) | ||||
0.572500 | + | 0.819904i | \(0.305974\pi\) | |||||||
\(212\) | 4.81774 | 0.330884 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.73970 | 0.323999 | ||||||||
\(215\) | −6.08912 | −0.415274 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.78010 | −0.120841 | ||||||||
\(218\) | 9.91145 | 0.671288 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.63071 | 0.244782 | ||||||||
\(221\) | −5.32277 | −0.358048 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.4938 | −1.70719 | −0.853595 | − | 0.520938i | \(-0.825582\pi\) | ||||
−0.853595 | + | 0.520938i | \(0.825582\pi\) | |||||||
\(224\) | −2.21818 | −0.148208 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.21007 | 0.612645 | ||||||||
\(227\) | −10.5081 | −0.697444 | −0.348722 | − | 0.937226i | \(-0.613384\pi\) | ||||
−0.348722 | + | 0.937226i | \(0.613384\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1178 | 1.13117 | 0.565587 | − | 0.824689i | \(-0.308650\pi\) | ||||
0.565587 | + | 0.824689i | \(0.308650\pi\) | |||||||
\(230\) | −9.60192 | −0.633132 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.41750 | −0.421329 | ||||||||
\(233\) | −27.7248 | −1.81631 | −0.908156 | − | 0.418633i | \(-0.862510\pi\) | ||||
−0.908156 | + | 0.418633i | \(0.862510\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.5552 | −1.21041 | ||||||||
\(236\) | 4.44907 | 0.289610 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.495491 | 0.0321179 | ||||||||
\(239\) | 6.31082 | 0.408213 | 0.204106 | − | 0.978949i | \(-0.434571\pi\) | ||||
0.204106 | + | 0.978949i | \(0.434571\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.6422 | 0.878774 | 0.439387 | − | 0.898298i | \(-0.355196\pi\) | ||||
0.439387 | + | 0.898298i | \(0.355196\pi\) | |||||||
\(242\) | −0.702784 | −0.0451767 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.50609 | 0.0964178 | ||||||||
\(245\) | −16.5255 | −1.05578 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.86160 | −0.436593 | ||||||||
\(248\) | −11.5242 | −0.731789 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.09632 | 0.448811 | ||||||||
\(251\) | 14.8480 | 0.937200 | 0.468600 | − | 0.883410i | \(-0.344759\pi\) | ||||
0.468600 | + | 0.883410i | \(0.344759\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.66757 | −0.356317 | ||||||||
\(254\) | 2.49053 | 0.156270 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.5032 | −0.656448 | ||||||||
\(257\) | −28.5319 | −1.77977 | −0.889887 | − | 0.456181i | \(-0.849217\pi\) | ||||
−0.889887 | + | 0.456181i | \(0.849217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.10367 | −0.254990 | ||||||||
\(260\) | −10.4326 | −0.647004 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.80161 | 0.111304 | ||||||||
\(263\) | 7.41082 | 0.456971 | 0.228485 | − | 0.973547i | \(-0.426623\pi\) | ||||
0.228485 | + | 0.973547i | \(0.426623\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.71136 | −0.473705 | ||||||||
\(266\) | 0.638739 | 0.0391636 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.1851 | −0.744324 | ||||||||
\(269\) | −20.8269 | −1.26984 | −0.634919 | − | 0.772578i | \(-0.718967\pi\) | ||||
−0.634919 | + | 0.772578i | \(0.718967\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.8005 | 1.08131 | 0.540653 | − | 0.841246i | \(-0.318177\pi\) | ||||
0.540653 | + | 0.841246i | \(0.318177\pi\) | |||||||
\(272\) | −2.37202 | −0.143825 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.12701 | 0.430558 | ||||||||
\(275\) | −0.811370 | −0.0489274 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.6366 | 0.699176 | 0.349588 | − | 0.936904i | \(-0.386322\pi\) | ||||
0.349588 | + | 0.936904i | \(0.386322\pi\) | |||||||
\(278\) | 7.68757 | 0.461070 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.26080 | 0.135109 | ||||||||
\(281\) | −2.80094 | −0.167090 | −0.0835452 | − | 0.996504i | \(-0.526624\pi\) | ||||
−0.0835452 | + | 0.996504i | \(0.526624\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.27012 | 0.432164 | 0.216082 | − | 0.976375i | \(-0.430672\pi\) | ||||
0.216082 | + | 0.976375i | \(0.430672\pi\) | |||||||
\(284\) | −22.7083 | −1.34749 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.01941 | 0.119410 | ||||||||
\(287\) | 0.157026 | 0.00926897 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5686 | −0.798153 | ||||||||
\(290\) | 4.41247 | 0.259109 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −18.2737 | −1.06939 | ||||||||
\(293\) | 13.6581 | 0.797914 | 0.398957 | − | 0.916970i | \(-0.369372\pi\) | ||||
0.398957 | + | 0.916970i | \(0.369372\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.12125 | −0.414615 | ||||||||
\(296\) | −26.5669 | −1.54417 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.375591 | −0.0217574 | ||||||||
\(299\) | 16.2854 | 0.941810 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.961375 | −0.0554128 | ||||||||
\(302\) | −9.25307 | −0.532454 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.05778 | −0.175376 | ||||||||
\(305\) | −2.41068 | −0.138035 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.32393 | 0.189707 | 0.0948533 | − | 0.995491i | \(-0.469762\pi\) | ||||
0.0948533 | + | 0.995491i | \(0.469762\pi\) | |||||||
\(308\) | 0.573232 | 0.0326629 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.92368 | 0.450035 | ||||||||
\(311\) | −21.8525 | −1.23914 | −0.619572 | − | 0.784940i | \(-0.712694\pi\) | ||||
−0.619572 | + | 0.784940i | \(0.712694\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.51873 | 0.481507 | 0.240754 | − | 0.970586i | \(-0.422605\pi\) | ||||
0.240754 | + | 0.970586i | \(0.422605\pi\) | |||||||
\(314\) | −11.0827 | −0.625431 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.1489 | 0.964699 | ||||||||
\(317\) | 4.34206 | 0.243874 | 0.121937 | − | 0.992538i | \(-0.461089\pi\) | ||||
0.121937 | + | 0.992538i | \(0.461089\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.60447 | 0.145823 | ||||||||
\(320\) | 3.69989 | 0.206830 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.51599 | −0.0844830 | ||||||||
\(323\) | 4.42343 | 0.246126 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.33142 | 0.129324 | ||||||||
\(326\) | −7.12189 | −0.394445 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.01658 | 0.0561311 | ||||||||
\(329\) | −2.92957 | −0.161512 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.9444 | 0.821419 | 0.410709 | − | 0.911766i | \(-0.365281\pi\) | ||||
0.410709 | + | 0.911766i | \(0.365281\pi\) | |||||||
\(332\) | 19.5875 | 1.07500 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.01900 | 0.0557573 | ||||||||
\(335\) | 19.5037 | 1.06560 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.2822 | −1.32273 | −0.661367 | − | 0.750063i | \(-0.730023\pi\) | ||||
−0.661367 | + | 0.750063i | \(0.730023\pi\) | |||||||
\(338\) | 3.33355 | 0.181321 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.72554 | 0.364744 | ||||||||
\(341\) | 4.67698 | 0.253273 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.27338 | −0.284736 | ||||||||
\(344\) | −6.22387 | −0.335569 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.3420 | 0.771032 | ||||||||
\(347\) | 2.45547 | 0.131816 | 0.0659082 | − | 0.997826i | \(-0.479006\pi\) | ||||
0.0659082 | + | 0.997826i | \(0.479006\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.87144 | 0.421349 | 0.210674 | − | 0.977556i | \(-0.432434\pi\) | ||||
0.210674 | + | 0.977556i | \(0.432434\pi\) | |||||||
\(350\) | −0.217030 | −0.0116007 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.82798 | 0.310632 | ||||||||
\(353\) | 1.93527 | 0.103004 | 0.0515019 | − | 0.998673i | \(-0.483599\pi\) | ||||
0.0515019 | + | 0.998673i | \(0.483599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.3473 | 1.92911 | ||||||||
\(356\) | 10.1893 | 0.540033 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.53869 | 0.0813223 | ||||||||
\(359\) | −27.2464 | −1.43801 | −0.719004 | − | 0.695006i | \(-0.755402\pi\) | ||||
−0.719004 | + | 0.695006i | \(0.755402\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.2977 | −0.699881 | ||||||||
\(362\) | −5.36496 | −0.281976 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.64715 | −0.0863339 | ||||||||
\(365\) | 29.2492 | 1.53097 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.1551 | 0.686691 | 0.343345 | − | 0.939209i | \(-0.388440\pi\) | ||||
0.343345 | + | 0.939209i | \(0.388440\pi\) | |||||||
\(368\) | 7.25738 | 0.378317 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18.2665 | 0.949631 | ||||||||
\(371\) | −1.21750 | −0.0632095 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5086 | −0.854785 | −0.427392 | − | 0.904066i | \(-0.640568\pi\) | ||||
−0.427392 | + | 0.904066i | \(0.640568\pi\) | |||||||
\(374\) | −1.30184 | −0.0673165 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.9658 | −0.978086 | ||||||||
\(377\) | −7.48380 | −0.385435 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.4445 | −0.793332 | −0.396666 | − | 0.917963i | \(-0.629833\pi\) | ||||
−0.396666 | + | 0.917963i | \(0.629833\pi\) | |||||||
\(380\) | 8.66991 | 0.444757 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.22066 | 0.113619 | ||||||||
\(383\) | −19.1481 | −0.978420 | −0.489210 | − | 0.872166i | \(-0.662715\pi\) | ||||
−0.489210 | + | 0.872166i | \(0.662715\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.917524 | −0.0467613 | ||||||||
\(386\) | −14.7703 | −0.751790 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.1582 | −0.515706 | ||||||||
\(389\) | −2.37394 | −0.120364 | −0.0601819 | − | 0.998187i | \(-0.519168\pi\) | ||||
−0.0601819 | + | 0.998187i | \(0.519168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.4986 | −0.530939 | ||||||||
\(392\) | −16.8912 | −0.853137 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.7022 | −0.942205 | ||||||||
\(395\) | −27.4487 | −1.38110 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −38.1843 | −1.91641 | −0.958207 | − | 0.286076i | \(-0.907649\pi\) | ||||
−0.958207 | + | 0.286076i | \(0.907649\pi\) | |||||||
\(398\) | 3.08933 | 0.154854 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.03897 | 0.0519483 | ||||||||
\(401\) | 4.91341 | 0.245364 | 0.122682 | − | 0.992446i | \(-0.460850\pi\) | ||||
0.122682 | + | 0.992446i | \(0.460850\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.4390 | −0.669446 | ||||||||
\(404\) | −8.17760 | −0.406851 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.696659 | 0.0345746 | ||||||||
\(407\) | 10.7819 | 0.534438 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.7395 | −0.827713 | −0.413857 | − | 0.910342i | \(-0.635818\pi\) | ||||
−0.413857 | + | 0.910342i | \(0.635818\pi\) | |||||||
\(410\) | −0.698966 | −0.0345194 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.65912 | −0.377338 | ||||||||
\(413\) | −1.12433 | −0.0553248 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −31.3521 | −1.53901 | ||||||||
\(416\) | −16.7463 | −0.821057 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.67821 | −0.0820837 | ||||||||
\(419\) | 26.2978 | 1.28473 | 0.642365 | − | 0.766399i | \(-0.277953\pi\) | ||||
0.642365 | + | 0.766399i | \(0.277953\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.6961 | 1.49604 | 0.748019 | − | 0.663678i | \(-0.231005\pi\) | ||||
0.748019 | + | 0.663678i | \(0.231005\pi\) | |||||||
\(422\) | −11.6888 | −0.569001 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.88201 | −0.382784 | ||||||||
\(425\) | −1.50298 | −0.0729054 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.380608 | −0.0184189 | ||||||||
\(428\) | 10.1574 | 0.490975 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.27933 | 0.206368 | ||||||||
\(431\) | −5.76571 | −0.277724 | −0.138862 | − | 0.990312i | \(-0.544345\pi\) | ||||
−0.138862 | + | 0.990312i | \(0.544345\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.7117 | −1.62008 | −0.810040 | − | 0.586375i | \(-0.800554\pi\) | ||||
−0.810040 | + | 0.586375i | \(0.800554\pi\) | |||||||
\(434\) | 1.25103 | 0.0600511 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.2406 | 1.01724 | ||||||||
\(437\) | −13.5338 | −0.647410 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.5662 | −1.26793 | −0.633967 | − | 0.773360i | \(-0.718574\pi\) | ||||
−0.633967 | + | 0.773360i | \(0.718574\pi\) | |||||||
\(440\) | −5.93998 | −0.283177 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.74076 | 0.177930 | ||||||||
\(443\) | −29.8314 | −1.41733 | −0.708667 | − | 0.705543i | \(-0.750703\pi\) | ||||
−0.708667 | + | 0.705543i | \(0.750703\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.3092 | −0.773130 | ||||||||
\(446\) | 17.9166 | 0.848376 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.584154 | 0.0275987 | ||||||||
\(449\) | −22.1043 | −1.04316 | −0.521582 | − | 0.853201i | \(-0.674658\pi\) | ||||
−0.521582 | + | 0.853201i | \(0.674658\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.412567 | −0.0194270 | ||||||||
\(452\) | 19.7376 | 0.928376 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.38489 | 0.346590 | ||||||||
\(455\) | 2.63645 | 0.123599 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.08398 | −0.0507063 | −0.0253531 | − | 0.999679i | \(-0.508071\pi\) | ||||
−0.0253531 | + | 0.999679i | \(0.508071\pi\) | |||||||
\(458\) | −12.0301 | −0.562129 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −20.5773 | −0.959422 | ||||||||
\(461\) | −1.55423 | −0.0723878 | −0.0361939 | − | 0.999345i | \(-0.511523\pi\) | ||||
−0.0361939 | + | 0.999345i | \(0.511523\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.51024 | −0.209609 | −0.104804 | − | 0.994493i | \(-0.533422\pi\) | ||||
−0.104804 | + | 0.994493i | \(0.533422\pi\) | |||||||
\(464\) | −3.33505 | −0.154826 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.4845 | 0.902604 | ||||||||
\(467\) | −33.8119 | −1.56463 | −0.782315 | − | 0.622883i | \(-0.785961\pi\) | ||||
−0.782315 | + | 0.622883i | \(0.785961\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.07932 | 0.142190 | ||||||||
\(470\) | 13.0403 | 0.601503 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.27885 | −0.335036 | ||||||||
\(473\) | 2.52589 | 0.116141 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.93750 | −0.0888987 | ||||||||
\(476\) | 1.06186 | 0.0486701 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.43514 | −0.202859 | ||||||||
\(479\) | 34.9203 | 1.59555 | 0.797775 | − | 0.602955i | \(-0.206010\pi\) | ||||
0.797775 | + | 0.602955i | \(0.206010\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.9811 | −1.41262 | ||||||||
\(482\) | −9.58755 | −0.436701 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.50609 | −0.0684588 | ||||||||
\(485\) | 16.2594 | 0.738303 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.76879 | 0.261409 | 0.130704 | − | 0.991421i | \(-0.458276\pi\) | ||||
0.130704 | + | 0.991421i | \(0.458276\pi\) | |||||||
\(488\) | −2.46403 | −0.111541 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.6139 | 0.524662 | ||||||||
\(491\) | −17.1848 | −0.775538 | −0.387769 | − | 0.921757i | \(-0.626754\pi\) | ||||
−0.387769 | + | 0.921757i | \(0.626754\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.82454 | 0.217286 | ||||||||
\(494\) | 4.82222 | 0.216962 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.98892 | −0.268910 | ||||||||
\(497\) | 5.73866 | 0.257414 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.81898 | 0.260494 | 0.130247 | − | 0.991482i | \(-0.458423\pi\) | ||||
0.130247 | + | 0.991482i | \(0.458423\pi\) | |||||||
\(500\) | 15.2077 | 0.680109 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.4350 | −0.465735 | ||||||||
\(503\) | 8.74737 | 0.390026 | 0.195013 | − | 0.980801i | \(-0.437525\pi\) | ||||
0.195013 | + | 0.980801i | \(0.437525\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.0892 | 0.582461 | ||||||||
\(506\) | 3.98308 | 0.177069 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.33730 | 0.236804 | ||||||||
\(509\) | −38.5778 | −1.70993 | −0.854965 | − | 0.518685i | \(-0.826422\pi\) | ||||
−0.854965 | + | 0.518685i | \(0.826422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.61799 | 0.204288 | ||||||||
\(512\) | −13.7732 | −0.608695 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.0518 | 0.884447 | ||||||||
\(515\) | 12.2593 | 0.540210 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.69707 | 0.338517 | ||||||||
\(518\) | 2.88400 | 0.126715 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.0682 | 0.748488 | ||||||||
\(521\) | 10.0315 | 0.439488 | 0.219744 | − | 0.975558i | \(-0.429478\pi\) | ||||
0.219744 | + | 0.975558i | \(0.429478\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.98871 | −0.436776 | −0.218388 | − | 0.975862i | \(-0.570080\pi\) | ||||
−0.218388 | + | 0.975862i | \(0.570080\pi\) | |||||||
\(524\) | 3.86091 | 0.168665 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.20821 | −0.227089 | ||||||||
\(527\) | 8.66366 | 0.377395 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.12136 | 0.396581 | ||||||||
\(530\) | 5.41942 | 0.235405 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.36884 | 0.0593469 | ||||||||
\(533\) | 1.18549 | 0.0513491 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.2580 | −0.702896 | ||||||||
\(536\) | 19.9353 | 0.861074 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.6368 | 0.631038 | ||||||||
\(539\) | 6.85514 | 0.295272 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.2991 | −0.829733 | −0.414867 | − | 0.909882i | \(-0.636172\pi\) | ||||
−0.414867 | + | 0.909882i | \(0.636172\pi\) | |||||||
\(542\) | −12.5099 | −0.537348 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.7958 | 0.462865 | ||||||||
\(545\) | −33.9981 | −1.45632 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.6238 | −1.05284 | −0.526420 | − | 0.850225i | \(-0.676466\pi\) | ||||
−0.526420 | + | 0.850225i | \(0.676466\pi\) | |||||||
\(548\) | 15.2735 | 0.652450 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.570218 | 0.0243142 | ||||||||
\(551\) | 6.21933 | 0.264952 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.33373 | −0.184289 | ||||||||
\(554\) | −8.17802 | −0.347451 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.4748 | 0.698686 | ||||||||
\(557\) | −36.0247 | −1.52642 | −0.763209 | − | 0.646152i | \(-0.776377\pi\) | ||||
−0.763209 | + | 0.646152i | \(0.776377\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.25800 | −0.306981 | ||||||||
\(560\) | 1.17490 | 0.0496485 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.96846 | 0.0830345 | ||||||||
\(563\) | 9.03522 | 0.380789 | 0.190394 | − | 0.981708i | \(-0.439023\pi\) | ||||
0.190394 | + | 0.981708i | \(0.439023\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −31.5922 | −1.32910 | ||||||||
\(566\) | −5.10933 | −0.214761 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 37.1517 | 1.55885 | ||||||||
\(569\) | 20.1685 | 0.845506 | 0.422753 | − | 0.906245i | \(-0.361064\pi\) | ||||
0.422753 | + | 0.906245i | \(0.361064\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.5977 | 0.443502 | 0.221751 | − | 0.975103i | \(-0.428823\pi\) | ||||
0.221751 | + | 0.975103i | \(0.428823\pi\) | |||||||
\(572\) | 4.32767 | 0.180949 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.110356 | −0.00460616 | ||||||||
\(575\) | 4.59849 | 0.191770 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.2551 | 1.09302 | 0.546508 | − | 0.837454i | \(-0.315957\pi\) | ||||
0.546508 | + | 0.837454i | \(0.315957\pi\) | |||||||
\(578\) | 9.53580 | 0.396637 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.45609 | 0.392643 | ||||||||
\(581\) | −4.95000 | −0.205361 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.19883 | 0.132482 | ||||||||
\(584\) | 29.8965 | 1.23713 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.59869 | −0.396518 | ||||||||
\(587\) | 28.0666 | 1.15843 | 0.579216 | − | 0.815174i | \(-0.303359\pi\) | ||||
0.579216 | + | 0.815174i | \(0.303359\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.1684 | 0.460184 | ||||||||
\(590\) | 5.00470 | 0.206040 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13.8063 | −0.567435 | ||||||||
\(593\) | 1.25793 | 0.0516569 | 0.0258285 | − | 0.999666i | \(-0.491778\pi\) | ||||
0.0258285 | + | 0.999666i | \(0.491778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.69962 | −0.0696778 | ||||||||
\(596\) | −0.804907 | −0.0329703 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.4451 | −0.468026 | ||||||||
\(599\) | −1.05494 | −0.0431036 | −0.0215518 | − | 0.999768i | \(-0.506861\pi\) | ||||
−0.0215518 | + | 0.999768i | \(0.506861\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.9488 | 1.83350 | 0.916749 | − | 0.399464i | \(-0.130804\pi\) | ||||
0.916749 | + | 0.399464i | \(0.130804\pi\) | |||||||
\(602\) | 0.675639 | 0.0275370 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.8297 | −0.806859 | ||||||||
\(605\) | 2.41068 | 0.0980080 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.9112 | 0.605229 | 0.302614 | − | 0.953113i | \(-0.402141\pi\) | ||||
0.302614 | + | 0.953113i | \(0.402141\pi\) | |||||||
\(608\) | 13.9169 | 0.564403 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.69419 | 0.0685956 | ||||||||
\(611\) | −22.1171 | −0.894761 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −48.0971 | −1.94263 | −0.971313 | − | 0.237807i | \(-0.923572\pi\) | ||||
−0.971313 | + | 0.237807i | \(0.923572\pi\) | |||||||
\(614\) | −2.33600 | −0.0942734 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.937829 | −0.0377862 | ||||||||
\(617\) | −29.3356 | −1.18100 | −0.590502 | − | 0.807036i | \(-0.701070\pi\) | ||||
−0.590502 | + | 0.807036i | \(0.701070\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.5047 | −1.30647 | −0.653236 | − | 0.757154i | \(-0.726589\pi\) | ||||
−0.653236 | + | 0.757154i | \(0.726589\pi\) | |||||||
\(620\) | 16.9808 | 0.681964 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.3576 | 0.615784 | ||||||||
\(623\) | −2.57496 | −0.103164 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.3985 | −1.13594 | ||||||||
\(626\) | −5.98683 | −0.239282 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −23.7506 | −0.947751 | ||||||||
\(629\) | 19.9724 | 0.796352 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.5348 | 1.05633 | 0.528167 | − | 0.849140i | \(-0.322879\pi\) | ||||
0.528167 | + | 0.849140i | \(0.322879\pi\) | |||||||
\(632\) | −28.0562 | −1.11602 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.05153 | −0.121192 | ||||||||
\(635\) | −8.54296 | −0.339017 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.6978 | −0.780456 | ||||||||
\(638\) | −1.83038 | −0.0724656 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 25.4985 | 1.00792 | ||||||||
\(641\) | 6.11121 | 0.241378 | 0.120689 | − | 0.992690i | \(-0.461490\pi\) | ||||
0.120689 | + | 0.992690i | \(0.461490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.1837 | 0.993146 | 0.496573 | − | 0.867995i | \(-0.334591\pi\) | ||||
0.496573 | + | 0.867995i | \(0.334591\pi\) | |||||||
\(644\) | −3.24883 | −0.128022 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.10872 | −0.122311 | ||||||||
\(647\) | −1.12978 | −0.0444163 | −0.0222081 | − | 0.999753i | \(-0.507070\pi\) | ||||
−0.0222081 | + | 0.999753i | \(0.507070\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.95404 | 0.115956 | ||||||||
\(650\) | −1.63849 | −0.0642667 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.2625 | −0.597725 | ||||||||
\(653\) | −31.7849 | −1.24384 | −0.621919 | − | 0.783081i | \(-0.713647\pi\) | ||||
−0.621919 | + | 0.783081i | \(0.713647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.17984 | −0.241466 | ||||||||
\(656\) | 0.528296 | 0.0206265 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.05885 | 0.0802625 | ||||||||
\(659\) | 10.6011 | 0.412962 | 0.206481 | − | 0.978451i | \(-0.433799\pi\) | ||||
0.206481 | + | 0.978451i | \(0.433799\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.22285 | −0.358727 | −0.179364 | − | 0.983783i | \(-0.557404\pi\) | ||||
−0.179364 | + | 0.983783i | \(0.557404\pi\) | |||||||
\(662\) | −10.5027 | −0.408199 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −32.0459 | −1.24362 | ||||||||
\(665\) | −2.19099 | −0.0849630 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.7610 | −0.571550 | ||||||||
\(668\) | 2.18376 | 0.0844923 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.7069 | −0.529543 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0076 | −1.54218 | −0.771090 | − | 0.636726i | \(-0.780288\pi\) | ||||
−0.771090 | + | 0.636726i | \(0.780288\pi\) | |||||||
\(674\) | 17.0651 | 0.657324 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.14393 | 0.274767 | ||||||||
\(677\) | −29.5650 | −1.13628 | −0.568138 | − | 0.822933i | \(-0.692336\pi\) | ||||
−0.568138 | + | 0.822933i | \(0.692336\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.56711 | 0.0985166 | ||||||||
\(680\) | −11.0032 | −0.421955 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.28691 | −0.125862 | ||||||||
\(683\) | 40.1267 | 1.53541 | 0.767703 | − | 0.640806i | \(-0.221400\pi\) | ||||
0.767703 | + | 0.640806i | \(0.221400\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.4469 | −0.934070 | ||||||||
\(686\) | 3.70605 | 0.141498 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.23443 | −0.123311 | ||||||||
\(689\) | −9.19165 | −0.350174 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.15715 | 0.234229 | 0.117114 | − | 0.993118i | \(-0.462636\pi\) | ||||
0.117114 | + | 0.993118i | \(0.462636\pi\) | |||||||
\(692\) | 30.7355 | 1.16839 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.72566 | −0.0655053 | ||||||||
\(695\) | −26.3698 | −1.00026 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.764241 | −0.0289477 | ||||||||
\(698\) | −5.53193 | −0.209387 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.465103 | −0.0175792 | ||||||||
\(701\) | −41.4955 | −1.56726 | −0.783631 | − | 0.621226i | \(-0.786635\pi\) | ||||
−0.783631 | + | 0.621226i | \(0.786635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.7465 | 0.971047 | ||||||||
\(704\) | −1.53479 | −0.0578446 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.36007 | −0.0511871 | ||||||||
\(707\) | 2.06658 | 0.0777216 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.1998 | 1.20929 | 0.604645 | − | 0.796495i | \(-0.293315\pi\) | ||||
0.604645 | + | 0.796495i | \(0.293315\pi\) | |||||||
\(710\) | −25.5443 | −0.958660 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.6701 | −0.624739 | ||||||||
\(713\) | −26.5071 | −0.992700 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.92694 | −0.259053 | ||||||||
\(716\) | 3.29747 | 0.123232 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.1483 | 0.714609 | ||||||||
\(719\) | −9.41955 | −0.351290 | −0.175645 | − | 0.984454i | \(-0.556201\pi\) | ||||
−0.175645 | + | 0.984454i | \(0.556201\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.93555 | 0.0720837 | ||||||||
\(722\) | 9.34545 | 0.347801 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.4973 | −0.427294 | ||||||||
\(725\) | −2.11319 | −0.0784820 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0232 | 1.18768 | 0.593838 | − | 0.804585i | \(-0.297612\pi\) | ||||
0.593838 | + | 0.804585i | \(0.297612\pi\) | |||||||
\(728\) | 2.69479 | 0.0998757 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −20.5559 | −0.760807 | ||||||||
\(731\) | 4.67897 | 0.173058 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.1215 | 0.669334 | 0.334667 | − | 0.942336i | \(-0.391376\pi\) | ||||
0.334667 | + | 0.942336i | \(0.391376\pi\) | |||||||
\(734\) | −9.24520 | −0.341246 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33.0305 | −1.21752 | ||||||||
\(737\) | −8.09053 | −0.298019 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.9867 | 1.39736 | 0.698681 | − | 0.715433i | \(-0.253771\pi\) | ||||
0.698681 | + | 0.715433i | \(0.253771\pi\) | |||||||
\(740\) | 39.1459 | 1.43903 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.855641 | 0.0314116 | ||||||||
\(743\) | 15.3100 | 0.561671 | 0.280835 | − | 0.959756i | \(-0.409389\pi\) | ||||
0.280835 | + | 0.959756i | \(0.409389\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.28835 | 0.0472014 | ||||||||
\(746\) | 11.6020 | 0.424780 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.78990 | −0.102009 | ||||||||
\(749\) | −2.56689 | −0.0937921 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.5527 | 1.07839 | 0.539197 | − | 0.842180i | \(-0.318728\pi\) | ||||
0.539197 | + | 0.842180i | \(0.318728\pi\) | |||||||
\(752\) | −9.85617 | −0.359418 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.25949 | 0.191539 | ||||||||
\(755\) | 31.7397 | 1.15513 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.2744 | −0.446122 | −0.223061 | − | 0.974805i | \(-0.571605\pi\) | ||||
−0.223061 | + | 0.974805i | \(0.571605\pi\) | |||||||
\(758\) | 10.8542 | 0.394241 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.1843 | −0.514519 | ||||||||
\(761\) | 43.1127 | 1.56283 | 0.781416 | − | 0.624010i | \(-0.214498\pi\) | ||||
0.781416 | + | 0.624010i | \(0.214498\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.36777 | −0.194326 | ||||||||
\(764\) | 4.75896 | 0.172173 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.4570 | 0.486220 | ||||||||
\(767\) | −8.48826 | −0.306493 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.1046 | −0.724992 | −0.362496 | − | 0.931985i | \(-0.618075\pi\) | ||||
−0.362496 | + | 0.931985i | \(0.618075\pi\) | |||||||
\(770\) | 0.644821 | 0.0232377 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −31.6534 | −1.13923 | ||||||||
\(773\) | 33.3091 | 1.19804 | 0.599022 | − | 0.800733i | \(-0.295556\pi\) | ||||
0.599022 | + | 0.800733i | \(0.295556\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.79476 | −0.136312 | ||||||||
\(776\) | 16.6193 | 0.596597 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.66837 | 0.0598140 | ||||||||
\(779\) | −0.985185 | −0.0352979 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.0776 | −0.539519 | ||||||||
\(782\) | 7.37827 | 0.263846 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.77807 | −0.313502 | ||||||||
\(785\) | 38.0156 | 1.35683 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.3276 | −0.831540 | −0.415770 | − | 0.909470i | \(-0.636488\pi\) | ||||
−0.415770 | + | 0.909470i | \(0.636488\pi\) | |||||||
\(788\) | −40.0796 | −1.42778 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 19.2905 | 0.686327 | ||||||||
\(791\) | −4.98792 | −0.177350 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.87344 | −0.102039 | ||||||||
\(794\) | 26.8353 | 0.952349 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.62056 | 0.234659 | ||||||||
\(797\) | −1.30429 | −0.0462002 | −0.0231001 | − | 0.999733i | \(-0.507354\pi\) | ||||
−0.0231001 | + | 0.999733i | \(0.507354\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.2581 | 0.504415 | ||||||||
\(800\) | −4.72864 | −0.167183 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.45307 | −0.121932 | ||||||||
\(803\) | −12.1332 | −0.428171 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.20013 | 0.183281 | ||||||||
\(806\) | 9.44474 | 0.332677 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.3789 | 0.470667 | ||||||||
\(809\) | 40.5654 | 1.42620 | 0.713102 | − | 0.701060i | \(-0.247290\pi\) | ||||
0.713102 | + | 0.701060i | \(0.247290\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.7975 | −0.800530 | −0.400265 | − | 0.916400i | \(-0.631082\pi\) | ||||
−0.400265 | + | 0.916400i | \(0.631082\pi\) | |||||||
\(812\) | 1.49297 | 0.0523929 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.57734 | −0.265585 | ||||||||
\(815\) | 24.4294 | 0.855724 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.03168 | 0.211022 | ||||||||
\(818\) | 11.7642 | 0.411327 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.49791 | −0.0523093 | ||||||||
\(821\) | −1.93050 | −0.0673750 | −0.0336875 | − | 0.999432i | \(-0.510725\pi\) | ||||
−0.0336875 | + | 0.999432i | \(0.510725\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.886777 | −0.0309111 | −0.0154556 | − | 0.999881i | \(-0.504920\pi\) | ||||
−0.0154556 | + | 0.999881i | \(0.504920\pi\) | |||||||
\(824\) | 12.5306 | 0.436525 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.790164 | 0.0274933 | ||||||||
\(827\) | 29.2678 | 1.01774 | 0.508871 | − | 0.860843i | \(-0.330063\pi\) | ||||
0.508871 | + | 0.860843i | \(0.330063\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.6952 | −1.58706 | −0.793529 | − | 0.608532i | \(-0.791759\pi\) | ||||
−0.793529 | + | 0.608532i | \(0.791759\pi\) | |||||||
\(830\) | 22.0338 | 0.764803 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.41013 | 0.152894 | ||||||||
\(833\) | 12.6985 | 0.439976 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.49536 | −0.120962 | ||||||||
\(836\) | −3.59646 | −0.124386 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.4817 | −0.638438 | ||||||||
\(839\) | 32.2318 | 1.11277 | 0.556383 | − | 0.830926i | \(-0.312189\pi\) | ||||
0.556383 | + | 0.830926i | \(0.312189\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2167 | −0.766094 | ||||||||
\(842\) | −21.5727 | −0.743446 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.0495 | −0.862240 | ||||||||
\(845\) | −11.4347 | −0.393365 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.380608 | 0.0130779 | ||||||||
\(848\) | −4.09613 | −0.140662 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.05627 | 0.0362299 | ||||||||
\(851\) | −61.1071 | −2.09472 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.70072 | −0.0924710 | −0.0462355 | − | 0.998931i | \(-0.514722\pi\) | ||||
−0.0462355 | + | 0.998931i | \(0.514722\pi\) | |||||||
\(854\) | 0.267485 | 0.00915316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.6178 | −0.567986 | ||||||||
\(857\) | 14.4998 | 0.495303 | 0.247652 | − | 0.968849i | \(-0.420341\pi\) | ||||
0.247652 | + | 0.968849i | \(0.420341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.3214 | 0.932195 | 0.466098 | − | 0.884733i | \(-0.345660\pi\) | ||||
0.466098 | + | 0.884733i | \(0.345660\pi\) | |||||||
\(860\) | 9.17078 | 0.312721 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.05205 | 0.138013 | ||||||||
\(863\) | −25.9733 | −0.884142 | −0.442071 | − | 0.896980i | \(-0.645756\pi\) | ||||
−0.442071 | + | 0.896980i | \(0.645756\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49.1957 | −1.67271 | ||||||||
\(866\) | 23.6920 | 0.805088 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.68100 | 0.0909989 | ||||||||
\(869\) | 11.3863 | 0.386254 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.2477 | 0.787717 | ||||||||
\(872\) | −34.7505 | −1.17680 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.51135 | 0.321726 | ||||||||
\(875\) | −3.84317 | −0.129923 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.74500 | −0.0926922 | −0.0463461 | − | 0.998925i | \(-0.514758\pi\) | ||||
−0.0463461 | + | 0.998925i | \(0.514758\pi\) | |||||||
\(878\) | 18.6703 | 0.630091 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.08690 | −0.104059 | ||||||||
\(881\) | −51.4362 | −1.73293 | −0.866465 | − | 0.499239i | \(-0.833613\pi\) | ||||
−0.866465 | + | 0.499239i | \(0.833613\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.4088 | 1.73004 | 0.865021 | − | 0.501735i | \(-0.167305\pi\) | ||||
0.865021 | + | 0.501735i | \(0.167305\pi\) | |||||||
\(884\) | 8.01659 | 0.269627 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.9651 | 0.704335 | ||||||||
\(887\) | −32.0556 | −1.07632 | −0.538160 | − | 0.842843i | \(-0.680880\pi\) | ||||
−0.538160 | + | 0.842843i | \(0.680880\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.34880 | −0.0452373 | ||||||||
\(890\) | 11.4618 | 0.384202 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 38.3960 | 1.28559 | ||||||||
\(893\) | 18.3801 | 0.615068 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.27799 | −0.176424 | ||||||||
\(896\) | 4.02582 | 0.134493 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.5345 | 0.518394 | ||||||||
\(899\) | 12.1811 | 0.406262 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.92553 | 0.197408 | ||||||||
\(902\) | 0.289946 | 0.00965413 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32.2914 | −1.07400 | ||||||||
\(905\) | 18.4028 | 0.611729 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.5518 | 1.57893 | 0.789466 | − | 0.613795i | \(-0.210358\pi\) | ||||
0.789466 | + | 0.613795i | \(0.210358\pi\) | |||||||
\(908\) | 15.8261 | 0.525208 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.85285 | −0.0614215 | ||||||||
\(911\) | −0.501609 | −0.0166191 | −0.00830953 | − | 0.999965i | \(-0.502645\pi\) | ||||
−0.00830953 | + | 0.999965i | \(0.502645\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.0055 | 0.430419 | ||||||||
\(914\) | 0.761802 | 0.0251982 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −25.7810 | −0.851827 | ||||||||
\(917\) | −0.975699 | −0.0322204 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.293282 | −0.00967447 | −0.00483724 | − | 0.999988i | \(-0.501540\pi\) | ||||
−0.00483724 | + | 0.999988i | \(0.501540\pi\) | |||||||
\(920\) | 33.6652 | 1.10991 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.09229 | 0.0359726 | ||||||||
\(923\) | 43.3246 | 1.42605 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.74809 | −0.287635 | ||||||||
\(926\) | 3.16973 | 0.104164 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.1788 | 0.498269 | ||||||||
\(929\) | 13.1097 | 0.430114 | 0.215057 | − | 0.976601i | \(-0.431006\pi\) | ||||
0.215057 | + | 0.976601i | \(0.431006\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.3697 | 0.536494 | ||||||||
\(932\) | 41.7562 | 1.36777 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.7625 | 0.777532 | ||||||||
\(935\) | 4.46555 | 0.146039 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.9120 | 0.911844 | 0.455922 | − | 0.890020i | \(-0.349310\pi\) | ||||
0.455922 | + | 0.890020i | \(0.349310\pi\) | |||||||
\(938\) | −2.16410 | −0.0706604 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 27.9458 | 0.911492 | ||||||||
\(941\) | 40.5741 | 1.32268 | 0.661340 | − | 0.750087i | \(-0.269988\pi\) | ||||
0.661340 | + | 0.750087i | \(0.269988\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.33825 | 0.0761440 | ||||||||
\(944\) | −3.78268 | −0.123116 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.77516 | −0.0577154 | ||||||||
\(947\) | 14.0369 | 0.456138 | 0.228069 | − | 0.973645i | \(-0.426759\pi\) | ||||
0.228069 | + | 0.973645i | \(0.426759\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.8639 | 1.13173 | ||||||||
\(950\) | 1.36165 | 0.0441776 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.73724 | −0.0563042 | ||||||||
\(953\) | −20.8014 | −0.673824 | −0.336912 | − | 0.941536i | \(-0.609383\pi\) | ||||
−0.336912 | + | 0.941536i | \(0.609383\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.61726 | −0.246489 | ||||||||
\(956\) | −9.50469 | −0.307404 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.5415 | −0.792899 | ||||||||
\(959\) | −3.85979 | −0.124639 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.12582 | −0.294381 | ||||||||
\(962\) | 21.7730 | 0.701990 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.5465 | −0.661758 | ||||||||
\(965\) | 50.6649 | 1.63096 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.9347 | 0.962636 | 0.481318 | − | 0.876546i | \(-0.340158\pi\) | ||||
0.481318 | + | 0.876546i | \(0.340158\pi\) | |||||||
\(968\) | 2.46403 | 0.0791968 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.4269 | −0.366895 | ||||||||
\(971\) | 34.0269 | 1.09198 | 0.545988 | − | 0.837793i | \(-0.316154\pi\) | ||||
0.545988 | + | 0.837793i | \(0.316154\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.16337 | −0.133472 | ||||||||
\(974\) | −4.05421 | −0.129905 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.28051 | −0.0409881 | ||||||||
\(977\) | −8.40382 | −0.268862 | −0.134431 | − | 0.990923i | \(-0.542921\pi\) | ||||
−0.134431 | + | 0.990923i | \(0.542921\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.76539 | 0.216223 | ||||||||
\(980\) | 24.8890 | 0.795050 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.0772 | 0.385399 | ||||||||
\(983\) | −3.76815 | −0.120185 | −0.0600926 | − | 0.998193i | \(-0.519140\pi\) | ||||
−0.0600926 | + | 0.998193i | \(0.519140\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 64.1521 | 2.04406 | ||||||||
\(986\) | −3.39061 | −0.107979 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.3342 | 0.328775 | ||||||||
\(989\) | −14.3157 | −0.455212 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.8258 | −0.947448 | −0.473724 | − | 0.880673i | \(-0.657091\pi\) | ||||
−0.473724 | + | 0.880673i | \(0.657091\pi\) | |||||||
\(992\) | 27.2574 | 0.865422 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.03304 | −0.127920 | ||||||||
\(995\) | −10.5970 | −0.335946 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.9003 | 0.345216 | 0.172608 | − | 0.984991i | \(-0.444781\pi\) | ||||
0.172608 | + | 0.984991i | \(0.444781\pi\) | |||||||
\(998\) | −4.08949 | −0.129451 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.n.1.11 | ✓ | 25 | |
3.2 | odd | 2 | 6039.2.a.o.1.15 | yes | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.n.1.11 | ✓ | 25 | 1.1 | even | 1 | trivial | |
6039.2.a.o.1.15 | yes | 25 | 3.2 | odd | 2 |