Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32723 | −1.64560 | −0.822802 | − | 0.568328i | \(-0.807590\pi\) | ||||
−0.822802 | + | 0.568328i | \(0.807590\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.41602 | 1.70801 | ||||||||
\(5\) | 1.82757 | 0.817314 | 0.408657 | − | 0.912688i | \(-0.365997\pi\) | ||||
0.408657 | + | 0.912688i | \(0.365997\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −3.29542 | −1.16511 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.25318 | −1.34497 | ||||||||
\(11\) | 3.25127 | 0.980293 | 0.490147 | − | 0.871640i | \(-0.336943\pi\) | ||||
0.490147 | + | 0.871640i | \(0.336943\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.459637 | 0.127480 | 0.0637402 | − | 0.997967i | \(-0.479697\pi\) | ||||
0.0637402 | + | 0.997967i | \(0.479697\pi\) | |||||||
\(14\) | −2.32723 | −0.621980 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.837162 | 0.209291 | ||||||||
\(17\) | 0.923651 | 0.224018 | 0.112009 | − | 0.993707i | \(-0.464271\pi\) | ||||
0.112009 | + | 0.993707i | \(0.464271\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.76737 | 0.405463 | 0.202731 | − | 0.979234i | \(-0.435018\pi\) | ||||
0.202731 | + | 0.979234i | \(0.435018\pi\) | |||||||
\(20\) | 6.24302 | 1.39598 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.56646 | −1.61317 | ||||||||
\(23\) | −8.20514 | −1.71089 | −0.855445 | − | 0.517894i | \(-0.826716\pi\) | ||||
−0.855445 | + | 0.517894i | \(0.826716\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.65999 | −0.331998 | ||||||||
\(26\) | −1.06968 | −0.209782 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.41602 | 0.645567 | ||||||||
\(29\) | 7.06378 | 1.31171 | 0.655855 | − | 0.754887i | \(-0.272308\pi\) | ||||
0.655855 | + | 0.754887i | \(0.272308\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.26211 | −1.48392 | −0.741959 | − | 0.670445i | \(-0.766103\pi\) | ||||
−0.741959 | + | 0.670445i | \(0.766103\pi\) | |||||||
\(32\) | 4.64256 | 0.820696 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.14955 | −0.368645 | ||||||||
\(35\) | 1.82757 | 0.308916 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.64461 | 0.434771 | 0.217386 | − | 0.976086i | \(-0.430247\pi\) | ||||
0.217386 | + | 0.976086i | \(0.430247\pi\) | |||||||
\(38\) | −4.11309 | −0.667231 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.02260 | −0.952257 | ||||||||
\(41\) | −5.05480 | −0.789428 | −0.394714 | − | 0.918804i | \(-0.629156\pi\) | ||||
−0.394714 | + | 0.918804i | \(0.629156\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.3966 | −1.58546 | −0.792732 | − | 0.609570i | \(-0.791342\pi\) | ||||
−0.792732 | + | 0.609570i | \(0.791342\pi\) | |||||||
\(44\) | 11.1064 | 1.67435 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 19.0953 | 2.81545 | ||||||||
\(47\) | 6.87722 | 1.00315 | 0.501573 | − | 0.865115i | \(-0.332755\pi\) | ||||
0.501573 | + | 0.865115i | \(0.332755\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.86318 | 0.546337 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.57013 | 0.217738 | ||||||||
\(53\) | 1.18575 | 0.162875 | 0.0814375 | − | 0.996678i | \(-0.474049\pi\) | ||||
0.0814375 | + | 0.996678i | \(0.474049\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.94191 | 0.801208 | ||||||||
\(56\) | −3.29542 | −0.440368 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −16.4391 | −2.15856 | ||||||||
\(59\) | −4.54879 | −0.592202 | −0.296101 | − | 0.955157i | \(-0.595686\pi\) | ||||
−0.296101 | + | 0.955157i | \(0.595686\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.89946 | −0.755349 | −0.377674 | − | 0.925939i | \(-0.623276\pi\) | ||||
−0.377674 | + | 0.925939i | \(0.623276\pi\) | |||||||
\(62\) | 19.2279 | 2.44194 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.4786 | −1.55983 | ||||||||
\(65\) | 0.840019 | 0.104192 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.38576 | −0.780144 | −0.390072 | − | 0.920784i | \(-0.627550\pi\) | ||||
−0.390072 | + | 0.920784i | \(0.627550\pi\) | |||||||
\(68\) | 3.15521 | 0.382626 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.25318 | −0.508353 | ||||||||
\(71\) | −4.59096 | −0.544847 | −0.272424 | − | 0.962177i | \(-0.587825\pi\) | ||||
−0.272424 | + | 0.962177i | \(0.587825\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.10778 | −0.597821 | −0.298910 | − | 0.954281i | \(-0.596623\pi\) | ||||
−0.298910 | + | 0.954281i | \(0.596623\pi\) | |||||||
\(74\) | −6.15463 | −0.715461 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.03738 | 0.692535 | ||||||||
\(77\) | 3.25127 | 0.370516 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.1766 | −1.82001 | −0.910007 | − | 0.414594i | \(-0.863924\pi\) | ||||
−0.910007 | + | 0.414594i | \(0.863924\pi\) | |||||||
\(80\) | 1.52997 | 0.171056 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.7637 | 1.29908 | ||||||||
\(83\) | −10.0510 | −1.10324 | −0.551620 | − | 0.834095i | \(-0.685990\pi\) | ||||
−0.551620 | + | 0.834095i | \(0.685990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.68804 | 0.183093 | ||||||||
\(86\) | 24.1953 | 2.60905 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.7143 | −1.14215 | ||||||||
\(89\) | −16.1446 | −1.71133 | −0.855663 | − | 0.517533i | \(-0.826850\pi\) | ||||
−0.855663 | + | 0.517533i | \(0.826850\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.459637 | 0.0481831 | ||||||||
\(92\) | −28.0289 | −2.92222 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −16.0049 | −1.65078 | ||||||||
\(95\) | 3.23000 | 0.331391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.8106 | 1.80839 | 0.904196 | − | 0.427118i | \(-0.140471\pi\) | ||||
0.904196 | + | 0.427118i | \(0.140471\pi\) | |||||||
\(98\) | −2.32723 | −0.235086 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.67056 | −0.567056 | ||||||||
\(101\) | 9.57625 | 0.952872 | 0.476436 | − | 0.879209i | \(-0.341928\pi\) | ||||
0.476436 | + | 0.879209i | \(0.341928\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.3872 | −1.61468 | −0.807342 | − | 0.590084i | \(-0.799094\pi\) | ||||
−0.807342 | + | 0.590084i | \(0.799094\pi\) | |||||||
\(104\) | −1.51470 | −0.148528 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.75951 | −0.268028 | ||||||||
\(107\) | 6.81709 | 0.659033 | 0.329516 | − | 0.944150i | \(-0.393114\pi\) | ||||
0.329516 | + | 0.944150i | \(0.393114\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.06318 | −0.197617 | −0.0988083 | − | 0.995106i | \(-0.531503\pi\) | ||||
−0.0988083 | + | 0.995106i | \(0.531503\pi\) | |||||||
\(110\) | −13.8282 | −1.31847 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.837162 | 0.0791044 | ||||||||
\(113\) | 1.12170 | 0.105520 | 0.0527601 | − | 0.998607i | \(-0.483198\pi\) | ||||
0.0527601 | + | 0.998607i | \(0.483198\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.9955 | −1.39833 | ||||||||
\(116\) | 24.1300 | 2.24042 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.5861 | 0.974529 | ||||||||
\(119\) | 0.923651 | 0.0846709 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.429271 | −0.0390247 | ||||||||
\(122\) | 13.7294 | 1.24300 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −28.2235 | −2.53455 | ||||||||
\(125\) | −12.1716 | −1.08866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 19.7556 | 1.74617 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.95492 | −0.171458 | ||||||||
\(131\) | 7.11191 | 0.621371 | 0.310685 | − | 0.950513i | \(-0.399441\pi\) | ||||
0.310685 | + | 0.950513i | \(0.399441\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.76737 | 0.153251 | ||||||||
\(134\) | 14.8612 | 1.28381 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.04381 | −0.261005 | ||||||||
\(137\) | 11.6913 | 0.998858 | 0.499429 | − | 0.866355i | \(-0.333543\pi\) | ||||
0.499429 | + | 0.866355i | \(0.333543\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.50691 | −0.297452 | −0.148726 | − | 0.988878i | \(-0.547517\pi\) | ||||
−0.148726 | + | 0.988878i | \(0.547517\pi\) | |||||||
\(140\) | 6.24302 | 0.527631 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.6843 | 0.896603 | ||||||||
\(143\) | 1.49440 | 0.124968 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.9095 | 1.07208 | ||||||||
\(146\) | 11.8870 | 0.983776 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.03404 | 0.742594 | ||||||||
\(149\) | −6.88506 | −0.564046 | −0.282023 | − | 0.959408i | \(-0.591005\pi\) | ||||
−0.282023 | + | 0.959408i | \(0.591005\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.92974 | −0.726692 | −0.363346 | − | 0.931654i | \(-0.618366\pi\) | ||||
−0.363346 | + | 0.931654i | \(0.618366\pi\) | |||||||
\(152\) | −5.82422 | −0.472407 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.56646 | −0.609723 | ||||||||
\(155\) | −15.0996 | −1.21283 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.65410 | −0.531055 | −0.265527 | − | 0.964103i | \(-0.585546\pi\) | ||||
−0.265527 | + | 0.964103i | \(0.585546\pi\) | |||||||
\(158\) | 37.6468 | 2.99502 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.48460 | 0.670766 | ||||||||
\(161\) | −8.20514 | −0.646655 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.0373 | −1.72609 | −0.863046 | − | 0.505126i | \(-0.831446\pi\) | ||||
−0.863046 | + | 0.505126i | \(0.831446\pi\) | |||||||
\(164\) | −17.2673 | −1.34835 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.3910 | 1.81550 | ||||||||
\(167\) | −7.66316 | −0.592993 | −0.296497 | − | 0.955034i | \(-0.595818\pi\) | ||||
−0.296497 | + | 0.955034i | \(0.595818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7887 | −0.983749 | ||||||||
\(170\) | −3.92846 | −0.301299 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −35.5150 | −2.70799 | ||||||||
\(173\) | 4.68199 | 0.355965 | 0.177982 | − | 0.984034i | \(-0.443043\pi\) | ||||
0.177982 | + | 0.984034i | \(0.443043\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.65999 | −0.125483 | ||||||||
\(176\) | 2.72184 | 0.205166 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 37.5723 | 2.81616 | ||||||||
\(179\) | −12.8826 | −0.962894 | −0.481447 | − | 0.876475i | \(-0.659889\pi\) | ||||
−0.481447 | + | 0.876475i | \(0.659889\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.8820 | −0.883182 | −0.441591 | − | 0.897216i | \(-0.645586\pi\) | ||||
−0.441591 | + | 0.897216i | \(0.645586\pi\) | |||||||
\(182\) | −1.06968 | −0.0792903 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 27.0393 | 1.99337 | ||||||||
\(185\) | 4.83321 | 0.355345 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00303 | 0.219604 | ||||||||
\(188\) | 23.4927 | 1.71338 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.51696 | −0.545337 | ||||||||
\(191\) | −7.32022 | −0.529672 | −0.264836 | − | 0.964293i | \(-0.585318\pi\) | ||||
−0.264836 | + | 0.964293i | \(0.585318\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.18335 | −0.373106 | −0.186553 | − | 0.982445i | \(-0.559732\pi\) | ||||
−0.186553 | + | 0.982445i | \(0.559732\pi\) | |||||||
\(194\) | −41.4494 | −2.97590 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.41602 | 0.244002 | ||||||||
\(197\) | −4.87691 | −0.347465 | −0.173733 | − | 0.984793i | \(-0.555583\pi\) | ||||
−0.173733 | + | 0.984793i | \(0.555583\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1824 | −0.721808 | −0.360904 | − | 0.932603i | \(-0.617532\pi\) | ||||
−0.360904 | + | 0.932603i | \(0.617532\pi\) | |||||||
\(200\) | 5.47035 | 0.386812 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −22.2862 | −1.56805 | ||||||||
\(203\) | 7.06378 | 0.495780 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.23800 | −0.645210 | ||||||||
\(206\) | 38.1370 | 2.65713 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.384791 | 0.0266805 | ||||||||
\(209\) | 5.74620 | 0.397473 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.1853 | 1.18308 | 0.591542 | − | 0.806274i | \(-0.298519\pi\) | ||||
0.591542 | + | 0.806274i | \(0.298519\pi\) | |||||||
\(212\) | 4.05054 | 0.278192 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.8650 | −1.08451 | ||||||||
\(215\) | −19.0005 | −1.29582 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.26211 | −0.560868 | ||||||||
\(218\) | 4.80150 | 0.325199 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.2977 | 1.36847 | ||||||||
\(221\) | 0.424544 | 0.0285580 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7429 | 1.45602 | 0.728008 | − | 0.685569i | \(-0.240447\pi\) | ||||
0.728008 | + | 0.685569i | \(0.240447\pi\) | |||||||
\(224\) | 4.64256 | 0.310194 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.61045 | −0.173645 | ||||||||
\(227\) | −20.9089 | −1.38777 | −0.693885 | − | 0.720086i | \(-0.744102\pi\) | ||||
−0.693885 | + | 0.720086i | \(0.744102\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.612842 | −0.0404978 | −0.0202489 | − | 0.999795i | \(-0.506446\pi\) | ||||
−0.0202489 | + | 0.999795i | \(0.506446\pi\) | |||||||
\(230\) | 34.8980 | 2.30110 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −23.2781 | −1.52828 | ||||||||
\(233\) | −0.167173 | −0.0109519 | −0.00547593 | − | 0.999985i | \(-0.501743\pi\) | ||||
−0.00547593 | + | 0.999985i | \(0.501743\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.5686 | 0.819885 | ||||||||
\(236\) | −15.5388 | −1.01149 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.14955 | −0.139335 | ||||||||
\(239\) | 14.2809 | 0.923752 | 0.461876 | − | 0.886945i | \(-0.347177\pi\) | ||||
0.461876 | + | 0.886945i | \(0.347177\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.6063 | −1.77828 | −0.889138 | − | 0.457640i | \(-0.848695\pi\) | ||||
−0.889138 | + | 0.457640i | \(0.848695\pi\) | |||||||
\(242\) | 0.999015 | 0.0642191 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −20.1527 | −1.29014 | ||||||||
\(245\) | 1.82757 | 0.116759 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.812350 | 0.0516886 | ||||||||
\(248\) | 27.2271 | 1.72892 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 28.3262 | 1.79150 | ||||||||
\(251\) | −9.82264 | −0.620000 | −0.310000 | − | 0.950737i | \(-0.600329\pi\) | ||||
−0.310000 | + | 0.950737i | \(0.600329\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.6771 | −1.67717 | ||||||||
\(254\) | −2.32723 | −0.146024 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −21.0187 | −1.31367 | ||||||||
\(257\) | 23.6795 | 1.47709 | 0.738544 | − | 0.674205i | \(-0.235514\pi\) | ||||
0.738544 | + | 0.674205i | \(0.235514\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.64461 | 0.164328 | ||||||||
\(260\) | 2.86952 | 0.177960 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.5511 | −1.02253 | ||||||||
\(263\) | 30.3269 | 1.87003 | 0.935017 | − | 0.354603i | \(-0.115384\pi\) | ||||
0.935017 | + | 0.354603i | \(0.115384\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.16704 | 0.133120 | ||||||||
\(266\) | −4.11309 | −0.252190 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −21.8139 | −1.33249 | ||||||||
\(269\) | −20.2768 | −1.23630 | −0.618148 | − | 0.786062i | \(-0.712117\pi\) | ||||
−0.618148 | + | 0.786062i | \(0.712117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.68123 | 0.527347 | 0.263674 | − | 0.964612i | \(-0.415066\pi\) | ||||
0.263674 | + | 0.964612i | \(0.415066\pi\) | |||||||
\(272\) | 0.773246 | 0.0468849 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −27.2085 | −1.64372 | ||||||||
\(275\) | −5.39706 | −0.325455 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.4172 | 1.70742 | 0.853711 | − | 0.520747i | \(-0.174347\pi\) | ||||
0.853711 | + | 0.520747i | \(0.174347\pi\) | |||||||
\(278\) | 8.16141 | 0.489489 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.02260 | −0.359919 | ||||||||
\(281\) | 6.58726 | 0.392963 | 0.196481 | − | 0.980508i | \(-0.437048\pi\) | ||||
0.196481 | + | 0.980508i | \(0.437048\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.9138 | 0.708202 | 0.354101 | − | 0.935207i | \(-0.384787\pi\) | ||||
0.354101 | + | 0.935207i | \(0.384787\pi\) | |||||||
\(284\) | −15.6828 | −0.930605 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.47783 | −0.205648 | ||||||||
\(287\) | −5.05480 | −0.298376 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1469 | −0.949816 | ||||||||
\(290\) | −30.0435 | −1.76422 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −17.4483 | −1.02108 | ||||||||
\(293\) | 16.9125 | 0.988037 | 0.494018 | − | 0.869451i | \(-0.335528\pi\) | ||||
0.494018 | + | 0.869451i | \(0.335528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.31323 | −0.484015 | ||||||||
\(296\) | −8.71509 | −0.506554 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.0231 | 0.928196 | ||||||||
\(299\) | −3.77139 | −0.218105 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.3966 | −0.599249 | ||||||||
\(302\) | 20.7816 | 1.19585 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.47958 | 0.0848595 | ||||||||
\(305\) | −10.7817 | −0.617357 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.0202 | 1.42798 | 0.713989 | − | 0.700157i | \(-0.246887\pi\) | ||||
0.713989 | + | 0.700157i | \(0.246887\pi\) | |||||||
\(308\) | 11.1064 | 0.632846 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 35.1403 | 1.99583 | ||||||||
\(311\) | 11.7577 | 0.666718 | 0.333359 | − | 0.942800i | \(-0.391818\pi\) | ||||
0.333359 | + | 0.942800i | \(0.391818\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0636 | −0.625351 | −0.312675 | − | 0.949860i | \(-0.601225\pi\) | ||||
−0.312675 | + | 0.949860i | \(0.601225\pi\) | |||||||
\(314\) | 15.4856 | 0.873906 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −55.2597 | −3.10860 | ||||||||
\(317\) | −23.5641 | −1.32349 | −0.661746 | − | 0.749728i | \(-0.730184\pi\) | ||||
−0.661746 | + | 0.749728i | \(0.730184\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.9662 | 1.28586 | ||||||||
\(320\) | −22.8056 | −1.27487 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 19.0953 | 1.06414 | ||||||||
\(323\) | 1.63243 | 0.0908311 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.762993 | −0.0423232 | ||||||||
\(326\) | 51.2859 | 2.84046 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16.6577 | 0.919766 | ||||||||
\(329\) | 6.87722 | 0.379153 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.4687 | 1.45485 | 0.727427 | − | 0.686185i | \(-0.240716\pi\) | ||||
0.727427 | + | 0.686185i | \(0.240716\pi\) | |||||||
\(332\) | −34.3344 | −1.88435 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.8340 | 0.975832 | ||||||||
\(335\) | −11.6704 | −0.637623 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.94742 | −0.378450 | −0.189225 | − | 0.981934i | \(-0.560598\pi\) | ||||
−0.189225 | + | 0.981934i | \(0.560598\pi\) | |||||||
\(338\) | 29.7624 | 1.61886 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.76637 | 0.312725 | ||||||||
\(341\) | −26.8623 | −1.45468 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 34.2611 | 1.84723 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.8961 | −0.585777 | ||||||||
\(347\) | −8.93641 | −0.479732 | −0.239866 | − | 0.970806i | \(-0.577103\pi\) | ||||
−0.239866 | + | 0.970806i | \(0.577103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.0502 | 1.23385 | 0.616925 | − | 0.787022i | \(-0.288378\pi\) | ||||
0.616925 | + | 0.787022i | \(0.288378\pi\) | |||||||
\(350\) | 3.86318 | 0.206496 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.0942 | 0.804523 | ||||||||
\(353\) | 6.27976 | 0.334238 | 0.167119 | − | 0.985937i | \(-0.446554\pi\) | ||||
0.167119 | + | 0.985937i | \(0.446554\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.39031 | −0.445311 | ||||||||
\(356\) | −55.1504 | −2.92296 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 29.9809 | 1.58454 | ||||||||
\(359\) | 1.98015 | 0.104508 | 0.0522541 | − | 0.998634i | \(-0.483359\pi\) | ||||
0.0522541 | + | 0.998634i | \(0.483359\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8764 | −0.835600 | ||||||||
\(362\) | 27.6522 | 1.45337 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.57013 | 0.0822972 | ||||||||
\(365\) | −9.33483 | −0.488607 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.94879 | −0.362724 | −0.181362 | − | 0.983416i | \(-0.558051\pi\) | ||||
−0.181362 | + | 0.983416i | \(0.558051\pi\) | |||||||
\(368\) | −6.86903 | −0.358073 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.2480 | −0.584756 | ||||||||
\(371\) | 1.18575 | 0.0615609 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.2338 | 1.20300 | 0.601500 | − | 0.798873i | \(-0.294570\pi\) | ||||
0.601500 | + | 0.798873i | \(0.294570\pi\) | |||||||
\(374\) | −6.98877 | −0.361381 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.6633 | −1.16877 | ||||||||
\(377\) | 3.24678 | 0.167217 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.06351 | 0.414195 | 0.207097 | − | 0.978320i | \(-0.433598\pi\) | ||||
0.207097 | + | 0.978320i | \(0.433598\pi\) | |||||||
\(380\) | 11.0337 | 0.566019 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.0359 | 0.871631 | ||||||||
\(383\) | −11.1000 | −0.567182 | −0.283591 | − | 0.958945i | \(-0.591526\pi\) | ||||
−0.283591 | + | 0.958945i | \(0.591526\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.94191 | 0.302828 | ||||||||
\(386\) | 12.0629 | 0.613984 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 60.8414 | 3.08875 | ||||||||
\(389\) | 30.6647 | 1.55476 | 0.777381 | − | 0.629030i | \(-0.216548\pi\) | ||||
0.777381 | + | 0.629030i | \(0.216548\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.57868 | −0.383270 | ||||||||
\(392\) | −3.29542 | −0.166444 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.3497 | 0.571790 | ||||||||
\(395\) | −29.5639 | −1.48752 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.05032 | 0.454222 | 0.227111 | − | 0.973869i | \(-0.427072\pi\) | ||||
0.227111 | + | 0.973869i | \(0.427072\pi\) | |||||||
\(398\) | 23.6967 | 1.18781 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.38968 | −0.0694840 | ||||||||
\(401\) | 32.6261 | 1.62927 | 0.814635 | − | 0.579974i | \(-0.196937\pi\) | ||||
0.814635 | + | 0.579974i | \(0.196937\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.79757 | −0.189171 | ||||||||
\(404\) | 32.7127 | 1.62752 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.4391 | −0.815857 | ||||||||
\(407\) | 8.59833 | 0.426203 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.4178 | 1.85019 | 0.925095 | − | 0.379735i | \(-0.123985\pi\) | ||||
0.925095 | + | 0.379735i | \(0.123985\pi\) | |||||||
\(410\) | 21.4990 | 1.06176 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −55.9792 | −2.75790 | ||||||||
\(413\) | −4.54879 | −0.223831 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.3689 | −0.901694 | ||||||||
\(416\) | 2.13389 | 0.104623 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.3727 | −0.654082 | ||||||||
\(419\) | −36.3659 | −1.77659 | −0.888295 | − | 0.459274i | \(-0.848110\pi\) | ||||
−0.888295 | + | 0.459274i | \(0.848110\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.7154 | 1.83814 | 0.919069 | − | 0.394096i | \(-0.128942\pi\) | ||||
0.919069 | + | 0.394096i | \(0.128942\pi\) | |||||||
\(422\) | −39.9942 | −1.94689 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.90753 | −0.189766 | ||||||||
\(425\) | −1.53325 | −0.0743736 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.89946 | −0.285495 | ||||||||
\(428\) | 23.2873 | 1.12564 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 44.2186 | 2.13241 | ||||||||
\(431\) | 2.24289 | 0.108036 | 0.0540181 | − | 0.998540i | \(-0.482797\pi\) | ||||
0.0540181 | + | 0.998540i | \(0.482797\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.95449 | 0.334211 | 0.167106 | − | 0.985939i | \(-0.446558\pi\) | ||||
0.167106 | + | 0.985939i | \(0.446558\pi\) | |||||||
\(434\) | 19.2279 | 0.922967 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.04786 | −0.337531 | ||||||||
\(437\) | −14.5015 | −0.693702 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.6892 | −0.605621 | −0.302810 | − | 0.953051i | \(-0.597925\pi\) | ||||
−0.302810 | + | 0.953051i | \(0.597925\pi\) | |||||||
\(440\) | −19.5811 | −0.933491 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.988015 | −0.0469951 | ||||||||
\(443\) | −15.1946 | −0.721918 | −0.360959 | − | 0.932582i | \(-0.617551\pi\) | ||||
−0.360959 | + | 0.932582i | \(0.617551\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.5054 | −1.39869 | ||||||||
\(446\) | −50.6009 | −2.39602 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.4786 | −0.589561 | ||||||||
\(449\) | −9.95655 | −0.469879 | −0.234939 | − | 0.972010i | \(-0.575489\pi\) | ||||
−0.234939 | + | 0.972010i | \(0.575489\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.4345 | −0.773871 | ||||||||
\(452\) | 3.83174 | 0.180230 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 48.6598 | 2.28372 | ||||||||
\(455\) | 0.840019 | 0.0393807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.7339 | 1.01667 | 0.508334 | − | 0.861160i | \(-0.330261\pi\) | ||||
0.508334 | + | 0.861160i | \(0.330261\pi\) | |||||||
\(458\) | 1.42623 | 0.0666433 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −51.2248 | −2.38837 | ||||||||
\(461\) | 30.8514 | 1.43690 | 0.718448 | − | 0.695581i | \(-0.244853\pi\) | ||||
0.718448 | + | 0.695581i | \(0.244853\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.6055 | −0.678773 | −0.339386 | − | 0.940647i | \(-0.610219\pi\) | ||||
−0.339386 | + | 0.940647i | \(0.610219\pi\) | |||||||
\(464\) | 5.91353 | 0.274529 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.389051 | 0.0180224 | ||||||||
\(467\) | 4.61228 | 0.213431 | 0.106715 | − | 0.994290i | \(-0.465967\pi\) | ||||
0.106715 | + | 0.994290i | \(0.465967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.38576 | −0.294867 | ||||||||
\(470\) | −29.2501 | −1.34921 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14.9901 | 0.689978 | ||||||||
\(473\) | −33.8021 | −1.55422 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.93382 | −0.134613 | ||||||||
\(476\) | 3.15521 | 0.144619 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −33.2349 | −1.52013 | ||||||||
\(479\) | 35.3743 | 1.61629 | 0.808147 | − | 0.588981i | \(-0.200471\pi\) | ||||
0.808147 | + | 0.588981i | \(0.200471\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.21556 | 0.0554248 | ||||||||
\(482\) | 64.2462 | 2.92634 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.46640 | −0.0666545 | ||||||||
\(485\) | 32.5501 | 1.47802 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.3071 | 0.784259 | 0.392129 | − | 0.919910i | \(-0.371739\pi\) | ||||
0.392129 | + | 0.919910i | \(0.371739\pi\) | |||||||
\(488\) | 19.4412 | 0.880061 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.25318 | −0.192139 | ||||||||
\(491\) | −3.61049 | −0.162939 | −0.0814696 | − | 0.996676i | \(-0.525961\pi\) | ||||
−0.0814696 | + | 0.996676i | \(0.525961\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.52447 | 0.293847 | ||||||||
\(494\) | −1.89053 | −0.0850589 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.91672 | −0.310570 | ||||||||
\(497\) | −4.59096 | −0.205933 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.71652 | 0.390205 | 0.195103 | − | 0.980783i | \(-0.437496\pi\) | ||||
0.195103 | + | 0.980783i | \(0.437496\pi\) | |||||||
\(500\) | −41.5784 | −1.85944 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.8596 | 1.02027 | ||||||||
\(503\) | −17.0106 | −0.758463 | −0.379232 | − | 0.925302i | \(-0.623812\pi\) | ||||
−0.379232 | + | 0.925302i | \(0.623812\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.5013 | 0.778796 | ||||||||
\(506\) | 62.0838 | 2.75996 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.41602 | 0.151561 | ||||||||
\(509\) | −33.1772 | −1.47055 | −0.735276 | − | 0.677768i | \(-0.762947\pi\) | ||||
−0.735276 | + | 0.677768i | \(0.762947\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.10778 | −0.225955 | ||||||||
\(512\) | 9.40417 | 0.415609 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −55.1078 | −2.43070 | ||||||||
\(515\) | −29.9488 | −1.31970 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.3597 | 0.983377 | ||||||||
\(518\) | −6.15463 | −0.270419 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.76821 | −0.121394 | ||||||||
\(521\) | −3.54384 | −0.155259 | −0.0776293 | − | 0.996982i | \(-0.524735\pi\) | ||||
−0.0776293 | + | 0.996982i | \(0.524735\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.14095 | 0.0498901 | 0.0249450 | − | 0.999689i | \(-0.492059\pi\) | ||||
0.0249450 | + | 0.999689i | \(0.492059\pi\) | |||||||
\(524\) | 24.2945 | 1.06131 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −70.5777 | −3.07733 | ||||||||
\(527\) | −7.63130 | −0.332425 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.3243 | 1.92714 | ||||||||
\(530\) | −5.04320 | −0.219063 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.03738 | 0.261754 | ||||||||
\(533\) | −2.32338 | −0.100637 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.4587 | 0.538637 | ||||||||
\(536\) | 21.0437 | 0.908950 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 47.1888 | 2.03445 | ||||||||
\(539\) | 3.25127 | 0.140042 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.1946 | −1.16919 | −0.584594 | − | 0.811326i | \(-0.698746\pi\) | ||||
−0.584594 | + | 0.811326i | \(0.698746\pi\) | |||||||
\(542\) | −20.2033 | −0.867804 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.28810 | 0.183851 | ||||||||
\(545\) | −3.77060 | −0.161515 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.6059 | −0.667262 | −0.333631 | − | 0.942704i | \(-0.608274\pi\) | ||||
−0.333631 | + | 0.942704i | \(0.608274\pi\) | |||||||
\(548\) | 39.9378 | 1.70606 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.5602 | 0.535570 | ||||||||
\(551\) | 12.4843 | 0.531850 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.1766 | −0.687900 | ||||||||
\(554\) | −66.1334 | −2.80974 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.9797 | −0.508052 | ||||||||
\(557\) | −24.7064 | −1.04685 | −0.523423 | − | 0.852073i | \(-0.675345\pi\) | ||||
−0.523423 | + | 0.852073i | \(0.675345\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.77866 | −0.202116 | ||||||||
\(560\) | 1.52997 | 0.0646531 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.3301 | −0.646661 | ||||||||
\(563\) | −34.7837 | −1.46596 | −0.732979 | − | 0.680251i | \(-0.761871\pi\) | ||||
−0.732979 | + | 0.680251i | \(0.761871\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.04998 | 0.0862432 | ||||||||
\(566\) | −27.7262 | −1.16542 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.1291 | 0.634804 | ||||||||
\(569\) | −12.2389 | −0.513080 | −0.256540 | − | 0.966534i | \(-0.582582\pi\) | ||||
−0.256540 | + | 0.966534i | \(0.582582\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.51258 | 0.146997 | 0.0734985 | − | 0.997295i | \(-0.476584\pi\) | ||||
0.0734985 | + | 0.997295i | \(0.476584\pi\) | |||||||
\(572\) | 5.10491 | 0.213447 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.7637 | 0.491008 | ||||||||
\(575\) | 13.6204 | 0.568011 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.0474 | 1.45904 | 0.729521 | − | 0.683958i | \(-0.239743\pi\) | ||||
0.729521 | + | 0.683958i | \(0.239743\pi\) | |||||||
\(578\) | 37.5776 | 1.56302 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 44.0993 | 1.83112 | ||||||||
\(581\) | −10.0510 | −0.416986 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.85518 | 0.159665 | ||||||||
\(584\) | 16.8323 | 0.696524 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.3593 | −1.62592 | ||||||||
\(587\) | 27.3306 | 1.12805 | 0.564027 | − | 0.825756i | \(-0.309251\pi\) | ||||
0.564027 | + | 0.825756i | \(0.309251\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.6022 | −0.601674 | ||||||||
\(590\) | 19.3468 | 0.796497 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.21397 | 0.0909935 | ||||||||
\(593\) | −13.2955 | −0.545980 | −0.272990 | − | 0.962017i | \(-0.588013\pi\) | ||||
−0.272990 | + | 0.962017i | \(0.588013\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.68804 | 0.0692028 | ||||||||
\(596\) | −23.5195 | −0.963396 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.77690 | 0.358914 | ||||||||
\(599\) | 30.9629 | 1.26511 | 0.632556 | − | 0.774515i | \(-0.282006\pi\) | ||||
0.632556 | + | 0.774515i | \(0.282006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.39614 | −0.301695 | −0.150847 | − | 0.988557i | \(-0.548200\pi\) | ||||
−0.150847 | + | 0.988557i | \(0.548200\pi\) | |||||||
\(602\) | 24.1953 | 0.986127 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −30.5042 | −1.24120 | ||||||||
\(605\) | −0.784523 | −0.0318954 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.5650 | 0.509998 | 0.254999 | − | 0.966941i | \(-0.417925\pi\) | ||||
0.254999 | + | 0.966941i | \(0.417925\pi\) | |||||||
\(608\) | 8.20513 | 0.332762 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.0915 | 1.01592 | ||||||||
\(611\) | 3.16103 | 0.127881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.4801 | −0.706017 | −0.353008 | − | 0.935620i | \(-0.614841\pi\) | ||||
−0.353008 | + | 0.935620i | \(0.614841\pi\) | |||||||
\(614\) | −58.2278 | −2.34988 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.7143 | −0.431690 | ||||||||
\(617\) | 43.9764 | 1.77042 | 0.885212 | − | 0.465188i | \(-0.154013\pi\) | ||||
0.885212 | + | 0.465188i | \(0.154013\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.9321 | 0.921717 | 0.460858 | − | 0.887474i | \(-0.347542\pi\) | ||||
0.460858 | + | 0.887474i | \(0.347542\pi\) | |||||||
\(620\) | −51.5805 | −2.07152 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −27.3629 | −1.09715 | ||||||||
\(623\) | −16.1446 | −0.646821 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9445 | −0.557780 | ||||||||
\(626\) | 25.7476 | 1.02908 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.7305 | −0.907048 | ||||||||
\(629\) | 2.44270 | 0.0973967 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.27656 | 0.0508189 | 0.0254094 | − | 0.999677i | \(-0.491911\pi\) | ||||
0.0254094 | + | 0.999677i | \(0.491911\pi\) | |||||||
\(632\) | 53.3087 | 2.12051 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 54.8392 | 2.17794 | ||||||||
\(635\) | 1.82757 | 0.0725249 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.459637 | 0.0182115 | ||||||||
\(638\) | −53.4478 | −2.11602 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 36.1048 | 1.42717 | ||||||||
\(641\) | −19.4343 | −0.767610 | −0.383805 | − | 0.923414i | \(-0.625386\pi\) | ||||
−0.383805 | + | 0.923414i | \(0.625386\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.5251 | 1.12492 | 0.562459 | − | 0.826825i | \(-0.309855\pi\) | ||||
0.562459 | + | 0.826825i | \(0.309855\pi\) | |||||||
\(644\) | −28.0289 | −1.10449 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.79906 | −0.149472 | ||||||||
\(647\) | 49.8165 | 1.95849 | 0.979243 | − | 0.202688i | \(-0.0649676\pi\) | ||||
0.979243 | + | 0.202688i | \(0.0649676\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.7893 | −0.580532 | ||||||||
\(650\) | 1.77566 | 0.0696472 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −75.2798 | −2.94818 | ||||||||
\(653\) | −21.2095 | −0.829994 | −0.414997 | − | 0.909823i | \(-0.636217\pi\) | ||||
−0.414997 | + | 0.909823i | \(0.636217\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.9975 | 0.507855 | ||||||||
\(656\) | −4.23169 | −0.165220 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.0049 | −0.623936 | ||||||||
\(659\) | 17.4609 | 0.680179 | 0.340089 | − | 0.940393i | \(-0.389543\pi\) | ||||
0.340089 | + | 0.940393i | \(0.389543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.0081 | 1.55613 | 0.778067 | − | 0.628182i | \(-0.216200\pi\) | ||||
0.778067 | + | 0.628182i | \(0.216200\pi\) | |||||||
\(662\) | −61.5990 | −2.39411 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 33.1222 | 1.28539 | ||||||||
\(665\) | 3.23000 | 0.125254 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −57.9593 | −2.24419 | ||||||||
\(668\) | −26.1775 | −1.01284 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 27.1598 | 1.04927 | ||||||||
\(671\) | −19.1807 | −0.740463 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.7911 | −1.26400 | −0.632001 | − | 0.774967i | \(-0.717766\pi\) | ||||
−0.632001 | + | 0.774967i | \(0.717766\pi\) | |||||||
\(674\) | 16.1683 | 0.622779 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −43.6866 | −1.68025 | ||||||||
\(677\) | −11.8714 | −0.456254 | −0.228127 | − | 0.973631i | \(-0.573260\pi\) | ||||
−0.228127 | + | 0.973631i | \(0.573260\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.8106 | 0.683508 | ||||||||
\(680\) | −5.56278 | −0.213323 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 62.5149 | 2.39382 | ||||||||
\(683\) | 36.6310 | 1.40165 | 0.700824 | − | 0.713334i | \(-0.252816\pi\) | ||||
0.700824 | + | 0.713334i | \(0.252816\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.3667 | 0.816380 | ||||||||
\(686\) | −2.32723 | −0.0888542 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.70363 | −0.331823 | ||||||||
\(689\) | 0.545014 | 0.0207634 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.1927 | −0.616000 | −0.308000 | − | 0.951386i | \(-0.599660\pi\) | ||||
−0.308000 | + | 0.951386i | \(0.599660\pi\) | |||||||
\(692\) | 15.9938 | 0.607992 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.7971 | 0.789448 | ||||||||
\(695\) | −6.40913 | −0.243112 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.66887 | −0.176846 | ||||||||
\(698\) | −53.6432 | −2.03043 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.67056 | −0.214327 | ||||||||
\(701\) | −38.7730 | −1.46444 | −0.732218 | − | 0.681071i | \(-0.761515\pi\) | ||||
−0.732218 | + | 0.681071i | \(0.761515\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.67401 | 0.176284 | ||||||||
\(704\) | −40.5714 | −1.52909 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.6145 | −0.550023 | ||||||||
\(707\) | 9.57625 | 0.360152 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.5278 | −1.37183 | −0.685915 | − | 0.727682i | \(-0.740598\pi\) | ||||
−0.685915 | + | 0.727682i | \(0.740598\pi\) | |||||||
\(710\) | 19.5262 | 0.732806 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 53.2032 | 1.99388 | ||||||||
\(713\) | 67.7917 | 2.53882 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.73113 | 0.102138 | ||||||||
\(716\) | −44.0074 | −1.64463 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.60827 | −0.171979 | ||||||||
\(719\) | −41.7503 | −1.55702 | −0.778512 | − | 0.627630i | \(-0.784025\pi\) | ||||
−0.778512 | + | 0.627630i | \(0.784025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.3872 | −0.610293 | ||||||||
\(722\) | 36.9481 | 1.37507 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −40.5892 | −1.50848 | ||||||||
\(725\) | −11.7258 | −0.435485 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.1822 | −0.637251 | −0.318626 | − | 0.947881i | \(-0.603221\pi\) | ||||
−0.318626 | + | 0.947881i | \(0.603221\pi\) | |||||||
\(728\) | −1.51470 | −0.0561384 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21.7243 | 0.804054 | ||||||||
\(731\) | −9.60282 | −0.355173 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.994796 | −0.0367436 | −0.0183718 | − | 0.999831i | \(-0.505848\pi\) | ||||
−0.0183718 | + | 0.999831i | \(0.505848\pi\) | |||||||
\(734\) | 16.1715 | 0.596899 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.0928 | −1.40412 | ||||||||
\(737\) | −20.7618 | −0.764770 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.0471 | −0.406373 | −0.203187 | − | 0.979140i | \(-0.565130\pi\) | ||||
−0.203187 | + | 0.979140i | \(0.565130\pi\) | |||||||
\(740\) | 16.5103 | 0.606932 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.75951 | −0.101305 | ||||||||
\(743\) | 19.7759 | 0.725507 | 0.362753 | − | 0.931885i | \(-0.381837\pi\) | ||||
0.362753 | + | 0.931885i | \(0.381837\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.5829 | −0.461003 | ||||||||
\(746\) | −54.0705 | −1.97966 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.2584 | 0.375085 | ||||||||
\(749\) | 6.81709 | 0.249091 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.4494 | −1.76794 | −0.883972 | − | 0.467540i | \(-0.845140\pi\) | ||||
−0.883972 | + | 0.467540i | \(0.845140\pi\) | |||||||
\(752\) | 5.75735 | 0.209949 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.55601 | −0.275174 | ||||||||
\(755\) | −16.3197 | −0.593935 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.1784 | −1.53300 | −0.766500 | − | 0.642244i | \(-0.778004\pi\) | ||||
−0.766500 | + | 0.642244i | \(0.778004\pi\) | |||||||
\(758\) | −18.7657 | −0.681600 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.6442 | −0.386105 | ||||||||
\(761\) | −26.8590 | −0.973639 | −0.486819 | − | 0.873503i | \(-0.661843\pi\) | ||||
−0.486819 | + | 0.873503i | \(0.661843\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.06318 | −0.0746921 | ||||||||
\(764\) | −25.0060 | −0.904686 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.8322 | 0.933357 | ||||||||
\(767\) | −2.09079 | −0.0754942 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.8390 | −1.43663 | −0.718316 | − | 0.695717i | \(-0.755087\pi\) | ||||
−0.718316 | + | 0.695717i | \(0.755087\pi\) | |||||||
\(770\) | −13.8282 | −0.498335 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.7064 | −0.637269 | ||||||||
\(773\) | 39.5219 | 1.42151 | 0.710753 | − | 0.703442i | \(-0.248355\pi\) | ||||
0.710753 | + | 0.703442i | \(0.248355\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.7150 | 0.492658 | ||||||||
\(776\) | −58.6933 | −2.10697 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −71.3639 | −2.55852 | ||||||||
\(779\) | −8.93372 | −0.320084 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.9264 | −0.534110 | ||||||||
\(782\) | 17.6374 | 0.630711 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.837162 | 0.0298986 | ||||||||
\(785\) | −12.1608 | −0.434039 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.8077 | −0.492191 | −0.246095 | − | 0.969246i | \(-0.579148\pi\) | ||||
−0.246095 | + | 0.969246i | \(0.579148\pi\) | |||||||
\(788\) | −16.6596 | −0.593474 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 68.8022 | 2.44787 | ||||||||
\(791\) | 1.12170 | 0.0398829 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.71161 | −0.0962922 | ||||||||
\(794\) | −21.0622 | −0.747470 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −34.7832 | −1.23286 | ||||||||
\(797\) | 0.963524 | 0.0341298 | 0.0170649 | − | 0.999854i | \(-0.494568\pi\) | ||||
0.0170649 | + | 0.999854i | \(0.494568\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.35215 | 0.224723 | ||||||||
\(800\) | −7.70659 | −0.272469 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −75.9286 | −2.68113 | ||||||||
\(803\) | −16.6068 | −0.586040 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.9955 | −0.528520 | ||||||||
\(806\) | 8.83784 | 0.311300 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −31.5577 | −1.11020 | ||||||||
\(809\) | 3.44050 | 0.120961 | 0.0604807 | − | 0.998169i | \(-0.480737\pi\) | ||||
0.0604807 | + | 0.998169i | \(0.480737\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.4147 | −1.80542 | −0.902708 | − | 0.430255i | \(-0.858424\pi\) | ||||
−0.902708 | + | 0.430255i | \(0.858424\pi\) | |||||||
\(812\) | 24.1300 | 0.846798 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.0103 | −0.701362 | ||||||||
\(815\) | −40.2746 | −1.41076 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.3746 | −0.642847 | ||||||||
\(818\) | −87.0800 | −3.04468 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −31.5572 | −1.10203 | ||||||||
\(821\) | −8.94184 | −0.312072 | −0.156036 | − | 0.987751i | \(-0.549872\pi\) | ||||
−0.156036 | + | 0.987751i | \(0.549872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.5739 | −0.856593 | −0.428296 | − | 0.903638i | \(-0.640886\pi\) | ||||
−0.428296 | + | 0.903638i | \(0.640886\pi\) | |||||||
\(824\) | 54.0028 | 1.88128 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.5861 | 0.368337 | ||||||||
\(827\) | −21.9314 | −0.762628 | −0.381314 | − | 0.924446i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924446i | \(0.624528\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.4559 | −0.536805 | −0.268402 | − | 0.963307i | \(-0.586496\pi\) | ||||
−0.268402 | + | 0.963307i | \(0.586496\pi\) | |||||||
\(830\) | 42.7487 | 1.48383 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.73565 | −0.198848 | ||||||||
\(833\) | 0.923651 | 0.0320026 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0050 | −0.484662 | ||||||||
\(836\) | 19.6291 | 0.678888 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 84.6319 | 2.92356 | ||||||||
\(839\) | 5.25125 | 0.181293 | 0.0906466 | − | 0.995883i | \(-0.471107\pi\) | ||||
0.0906466 | + | 0.995883i | \(0.471107\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.8970 | 0.720585 | ||||||||
\(842\) | −87.7727 | −3.02485 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 58.7054 | 2.02072 | ||||||||
\(845\) | −23.3723 | −0.804032 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.429271 | −0.0147499 | ||||||||
\(848\) | 0.992663 | 0.0340882 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.56823 | 0.122389 | ||||||||
\(851\) | −21.6994 | −0.743845 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.692697 | 0.0237175 | 0.0118588 | − | 0.999930i | \(-0.496225\pi\) | ||||
0.0118588 | + | 0.999930i | \(0.496225\pi\) | |||||||
\(854\) | 13.7294 | 0.469811 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22.4651 | −0.767843 | ||||||||
\(857\) | 29.2977 | 1.00079 | 0.500395 | − | 0.865797i | \(-0.333188\pi\) | ||||
0.500395 | + | 0.865797i | \(0.333188\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.3475 | 0.967206 | 0.483603 | − | 0.875288i | \(-0.339328\pi\) | ||||
0.483603 | + | 0.875288i | \(0.339328\pi\) | |||||||
\(860\) | −64.9061 | −2.21328 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.21974 | −0.177785 | ||||||||
\(863\) | 30.8219 | 1.04919 | 0.524595 | − | 0.851352i | \(-0.324217\pi\) | ||||
0.524595 | + | 0.851352i | \(0.324217\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.55666 | 0.290935 | ||||||||
\(866\) | −16.1847 | −0.549979 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −28.2235 | −0.957969 | ||||||||
\(869\) | −52.5945 | −1.78415 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.93513 | −0.0994531 | ||||||||
\(872\) | 6.79903 | 0.230244 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 33.7485 | 1.14156 | ||||||||
\(875\) | −12.1716 | −0.411475 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.7468 | −1.03825 | −0.519123 | − | 0.854700i | \(-0.673741\pi\) | ||||
−0.519123 | + | 0.854700i | \(0.673741\pi\) | |||||||
\(878\) | 29.5307 | 0.996611 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.97435 | 0.167685 | ||||||||
\(881\) | −44.5343 | −1.50040 | −0.750200 | − | 0.661211i | \(-0.770043\pi\) | ||||
−0.750200 | + | 0.661211i | \(0.770043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.5101 | 0.757525 | 0.378763 | − | 0.925494i | \(-0.376350\pi\) | ||||
0.378763 | + | 0.925494i | \(0.376350\pi\) | |||||||
\(884\) | 1.45025 | 0.0487773 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.3614 | 1.18799 | ||||||||
\(887\) | −10.1771 | −0.341713 | −0.170857 | − | 0.985296i | \(-0.554653\pi\) | ||||
−0.170857 | + | 0.985296i | \(0.554653\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 68.6660 | 2.30169 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 74.2744 | 2.48689 | ||||||||
\(893\) | 12.1546 | 0.406738 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.5439 | −0.786987 | ||||||||
\(896\) | 19.7556 | 0.659989 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.1712 | 0.773234 | ||||||||
\(899\) | −58.3617 | −1.94647 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.09522 | 0.0364870 | ||||||||
\(902\) | 38.2470 | 1.27348 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.69645 | −0.122942 | ||||||||
\(905\) | −21.7152 | −0.721837 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.9867 | −1.52696 | −0.763482 | − | 0.645829i | \(-0.776512\pi\) | ||||
−0.763482 | + | 0.645829i | \(0.776512\pi\) | |||||||
\(908\) | −71.4251 | −2.37033 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.95492 | −0.0648050 | ||||||||
\(911\) | −19.6478 | −0.650961 | −0.325480 | − | 0.945549i | \(-0.605526\pi\) | ||||
−0.325480 | + | 0.945549i | \(0.605526\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.6785 | −1.08150 | ||||||||
\(914\) | −50.5799 | −1.67303 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.09348 | −0.0691706 | ||||||||
\(917\) | 7.11191 | 0.234856 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.5078 | 1.43519 | 0.717594 | − | 0.696461i | \(-0.245243\pi\) | ||||
0.717594 | + | 0.696461i | \(0.245243\pi\) | |||||||
\(920\) | 49.4163 | 1.62921 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −71.7986 | −2.36456 | ||||||||
\(923\) | −2.11018 | −0.0694574 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.39002 | −0.144343 | ||||||||
\(926\) | 33.9903 | 1.11699 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 32.7940 | 1.07652 | ||||||||
\(929\) | −24.1917 | −0.793706 | −0.396853 | − | 0.917882i | \(-0.629898\pi\) | ||||
−0.396853 | + | 0.917882i | \(0.629898\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.76737 | 0.0579233 | ||||||||
\(932\) | −0.571066 | −0.0187059 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.7339 | −0.351222 | ||||||||
\(935\) | 5.48826 | 0.179485 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.6803 | 1.10029 | 0.550144 | − | 0.835069i | \(-0.314573\pi\) | ||||
0.550144 | + | 0.835069i | \(0.314573\pi\) | |||||||
\(938\) | 14.8612 | 0.485234 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 42.9346 | 1.40037 | ||||||||
\(941\) | 36.5879 | 1.19273 | 0.596366 | − | 0.802712i | \(-0.296611\pi\) | ||||
0.596366 | + | 0.802712i | \(0.296611\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.4753 | 1.35062 | ||||||||
\(944\) | −3.80807 | −0.123942 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 78.6653 | 2.55763 | ||||||||
\(947\) | 0.972952 | 0.0316167 | 0.0158084 | − | 0.999875i | \(-0.494968\pi\) | ||||
0.0158084 | + | 0.999875i | \(0.494968\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.34773 | −0.0762105 | ||||||||
\(950\) | 6.82768 | 0.221519 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.04381 | −0.0986506 | ||||||||
\(953\) | −7.66231 | −0.248207 | −0.124103 | − | 0.992269i | \(-0.539605\pi\) | ||||
−0.124103 | + | 0.992269i | \(0.539605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.3782 | −0.432909 | ||||||||
\(956\) | 48.7837 | 1.57778 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −82.3243 | −2.65978 | ||||||||
\(959\) | 11.6913 | 0.377533 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.2624 | 1.20201 | ||||||||
\(962\) | −2.82890 | −0.0912073 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −94.3036 | −3.03731 | ||||||||
\(965\) | −9.47293 | −0.304945 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.37101 | −0.301351 | −0.150676 | − | 0.988583i | \(-0.548145\pi\) | ||||
−0.150676 | + | 0.988583i | \(0.548145\pi\) | |||||||
\(968\) | 1.41463 | 0.0454678 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −75.7517 | −2.43224 | ||||||||
\(971\) | 4.76122 | 0.152795 | 0.0763974 | − | 0.997077i | \(-0.475658\pi\) | ||||
0.0763974 | + | 0.997077i | \(0.475658\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.50691 | −0.112426 | ||||||||
\(974\) | −40.2776 | −1.29058 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.93880 | −0.158087 | ||||||||
\(977\) | 52.6338 | 1.68391 | 0.841953 | − | 0.539551i | \(-0.181406\pi\) | ||||
0.841953 | + | 0.539551i | \(0.181406\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −52.4904 | −1.67760 | ||||||||
\(980\) | 6.24302 | 0.199426 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.40246 | 0.268133 | ||||||||
\(983\) | −54.7160 | −1.74517 | −0.872585 | − | 0.488462i | \(-0.837558\pi\) | ||||
−0.872585 | + | 0.488462i | \(0.837558\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.91289 | −0.283988 | ||||||||
\(986\) | −15.1840 | −0.483556 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.77501 | 0.0882847 | ||||||||
\(989\) | 85.3054 | 2.71255 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.5606 | 1.41552 | 0.707758 | − | 0.706455i | \(-0.249707\pi\) | ||||
0.707758 | + | 0.706455i | \(0.249707\pi\) | |||||||
\(992\) | −38.3573 | −1.21785 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.6843 | 0.338884 | ||||||||
\(995\) | −18.6090 | −0.589944 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.0547 | 0.856830 | 0.428415 | − | 0.903582i | \(-0.359072\pi\) | ||||
0.428415 | + | 0.903582i | \(0.359072\pi\) | |||||||
\(998\) | −20.2854 | −0.642123 | ||||||||
\(999\) | 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 | 8001.2.a.x.1.2 | ✓ | 22 | |
3.2 | odd | 2 | inner | 8001.2.a.x.1.21 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.x.1.2 | ✓ | 22 | 1.1 | even | 1 | trivial | |
8001.2.a.x.1.21 | yes | 22 | 3.2 | odd | 2 | inner |