Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [503,2,Mod(1,503)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(503, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("503.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 503.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: | \(4.01647522167\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 503.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.462244 | −0.326856 | −0.163428 | − | 0.986555i | \(-0.552255\pi\) | ||||
−0.163428 | + | 0.986555i | \(0.552255\pi\) | |||||||
\(3\) | 3.26409 | 1.88453 | 0.942263 | − | 0.334875i | \(-0.108694\pi\) | ||||
0.942263 | + | 0.334875i | \(0.108694\pi\) | |||||||
\(4\) | −1.78633 | −0.893165 | ||||||||
\(5\) | 1.15565 | 0.516823 | 0.258412 | − | 0.966035i | \(-0.416801\pi\) | ||||
0.258412 | + | 0.966035i | \(0.416801\pi\) | |||||||
\(6\) | −1.50881 | −0.615968 | ||||||||
\(7\) | −1.19216 | −0.450596 | −0.225298 | − | 0.974290i | \(-0.572336\pi\) | ||||
−0.225298 | + | 0.974290i | \(0.572336\pi\) | |||||||
\(8\) | 1.75021 | 0.618792 | ||||||||
\(9\) | 7.65430 | 2.55143 | ||||||||
\(10\) | −0.534193 | −0.168927 | ||||||||
\(11\) | 4.40104 | 1.32696 | 0.663482 | − | 0.748192i | \(-0.269078\pi\) | ||||
0.663482 | + | 0.748192i | \(0.269078\pi\) | |||||||
\(12\) | −5.83075 | −1.68319 | ||||||||
\(13\) | −5.45043 | −1.51168 | −0.755839 | − | 0.654758i | \(-0.772771\pi\) | ||||
−0.755839 | + | 0.654758i | \(0.772771\pi\) | |||||||
\(14\) | 0.551071 | 0.147280 | ||||||||
\(15\) | 3.77216 | 0.973966 | ||||||||
\(16\) | 2.76364 | 0.690910 | ||||||||
\(17\) | 1.75483 | 0.425608 | 0.212804 | − | 0.977095i | \(-0.431740\pi\) | ||||
0.212804 | + | 0.977095i | \(0.431740\pi\) | |||||||
\(18\) | −3.53816 | −0.833951 | ||||||||
\(19\) | −0.615110 | −0.141116 | −0.0705580 | − | 0.997508i | \(-0.522478\pi\) | ||||
−0.0705580 | + | 0.997508i | \(0.522478\pi\) | |||||||
\(20\) | −2.06438 | −0.461609 | ||||||||
\(21\) | −3.89134 | −0.849159 | ||||||||
\(22\) | −2.03436 | −0.433726 | ||||||||
\(23\) | 3.56383 | 0.743111 | 0.371555 | − | 0.928411i | \(-0.378825\pi\) | ||||
0.371555 | + | 0.928411i | \(0.378825\pi\) | |||||||
\(24\) | 5.71284 | 1.16613 | ||||||||
\(25\) | −3.66447 | −0.732894 | ||||||||
\(26\) | 2.51943 | 0.494101 | ||||||||
\(27\) | 15.1921 | 2.92372 | ||||||||
\(28\) | 2.12960 | 0.402457 | ||||||||
\(29\) | 5.04421 | 0.936687 | 0.468344 | − | 0.883546i | \(-0.344851\pi\) | ||||
0.468344 | + | 0.883546i | \(0.344851\pi\) | |||||||
\(30\) | −1.74366 | −0.318347 | ||||||||
\(31\) | 3.23953 | 0.581837 | 0.290919 | − | 0.956748i | \(-0.406039\pi\) | ||||
0.290919 | + | 0.956748i | \(0.406039\pi\) | |||||||
\(32\) | −4.77789 | −0.844620 | ||||||||
\(33\) | 14.3654 | 2.50070 | ||||||||
\(34\) | −0.811158 | −0.139112 | ||||||||
\(35\) | −1.37773 | −0.232878 | ||||||||
\(36\) | −13.6731 | −2.27885 | ||||||||
\(37\) | −8.64230 | −1.42078 | −0.710392 | − | 0.703806i | \(-0.751482\pi\) | ||||
−0.710392 | + | 0.703806i | \(0.751482\pi\) | |||||||
\(38\) | 0.284331 | 0.0461246 | ||||||||
\(39\) | −17.7907 | −2.84879 | ||||||||
\(40\) | 2.02263 | 0.319806 | ||||||||
\(41\) | −6.82821 | −1.06639 | −0.533193 | − | 0.845993i | \(-0.679008\pi\) | ||||
−0.533193 | + | 0.845993i | \(0.679008\pi\) | |||||||
\(42\) | 1.79875 | 0.277553 | ||||||||
\(43\) | 4.42298 | 0.674498 | 0.337249 | − | 0.941415i | \(-0.390504\pi\) | ||||
0.337249 | + | 0.941415i | \(0.390504\pi\) | |||||||
\(44\) | −7.86172 | −1.18520 | ||||||||
\(45\) | 8.84571 | 1.31864 | ||||||||
\(46\) | −1.64736 | −0.242890 | ||||||||
\(47\) | −4.24654 | −0.619422 | −0.309711 | − | 0.950831i | \(-0.600232\pi\) | ||||
−0.309711 | + | 0.950831i | \(0.600232\pi\) | |||||||
\(48\) | 9.02077 | 1.30204 | ||||||||
\(49\) | −5.57874 | −0.796963 | ||||||||
\(50\) | 1.69388 | 0.239551 | ||||||||
\(51\) | 5.72792 | 0.802069 | ||||||||
\(52\) | 9.73627 | 1.35018 | ||||||||
\(53\) | 9.55743 | 1.31281 | 0.656407 | − | 0.754407i | \(-0.272075\pi\) | ||||
0.656407 | + | 0.754407i | \(0.272075\pi\) | |||||||
\(54\) | −7.02245 | −0.955634 | ||||||||
\(55\) | 5.08608 | 0.685806 | ||||||||
\(56\) | −2.08654 | −0.278825 | ||||||||
\(57\) | −2.00778 | −0.265937 | ||||||||
\(58\) | −2.33166 | −0.306162 | ||||||||
\(59\) | −7.62933 | −0.993254 | −0.496627 | − | 0.867964i | \(-0.665428\pi\) | ||||
−0.496627 | + | 0.867964i | \(0.665428\pi\) | |||||||
\(60\) | −6.73832 | −0.869913 | ||||||||
\(61\) | −11.7842 | −1.50881 | −0.754406 | − | 0.656408i | \(-0.772075\pi\) | ||||
−0.754406 | + | 0.656408i | \(0.772075\pi\) | |||||||
\(62\) | −1.49745 | −0.190177 | ||||||||
\(63\) | −9.12519 | −1.14967 | ||||||||
\(64\) | −3.31873 | −0.414841 | ||||||||
\(65\) | −6.29880 | −0.781270 | ||||||||
\(66\) | −6.64033 | −0.817368 | ||||||||
\(67\) | 1.28059 | 0.156449 | 0.0782246 | − | 0.996936i | \(-0.475075\pi\) | ||||
0.0782246 | + | 0.996936i | \(0.475075\pi\) | |||||||
\(68\) | −3.13470 | −0.380138 | ||||||||
\(69\) | 11.6327 | 1.40041 | ||||||||
\(70\) | 0.636846 | 0.0761177 | ||||||||
\(71\) | 2.48267 | 0.294639 | 0.147319 | − | 0.989089i | \(-0.452936\pi\) | ||||
0.147319 | + | 0.989089i | \(0.452936\pi\) | |||||||
\(72\) | 13.3966 | 1.57881 | ||||||||
\(73\) | 14.5670 | 1.70494 | 0.852471 | − | 0.522775i | \(-0.175103\pi\) | ||||
0.852471 | + | 0.522775i | \(0.175103\pi\) | |||||||
\(74\) | 3.99485 | 0.464392 | ||||||||
\(75\) | −11.9612 | −1.38116 | ||||||||
\(76\) | 1.09879 | 0.126040 | ||||||||
\(77\) | −5.24677 | −0.597925 | ||||||||
\(78\) | 8.22365 | 0.931145 | ||||||||
\(79\) | −7.25582 | −0.816343 | −0.408172 | − | 0.912905i | \(-0.633833\pi\) | ||||
−0.408172 | + | 0.912905i | \(0.633833\pi\) | |||||||
\(80\) | 3.19380 | 0.357078 | ||||||||
\(81\) | 26.6255 | 2.95838 | ||||||||
\(82\) | 3.15630 | 0.348555 | ||||||||
\(83\) | −16.6438 | −1.82690 | −0.913448 | − | 0.406955i | \(-0.866591\pi\) | ||||
−0.913448 | + | 0.406955i | \(0.866591\pi\) | |||||||
\(84\) | 6.95121 | 0.758440 | ||||||||
\(85\) | 2.02797 | 0.219964 | ||||||||
\(86\) | −2.04450 | −0.220464 | ||||||||
\(87\) | 16.4648 | 1.76521 | ||||||||
\(88\) | 7.70274 | 0.821115 | ||||||||
\(89\) | 1.65082 | 0.174987 | 0.0874934 | − | 0.996165i | \(-0.472114\pi\) | ||||
0.0874934 | + | 0.996165i | \(0.472114\pi\) | |||||||
\(90\) | −4.08888 | −0.431005 | ||||||||
\(91\) | 6.49781 | 0.681156 | ||||||||
\(92\) | −6.36618 | −0.663721 | ||||||||
\(93\) | 10.5741 | 1.09649 | ||||||||
\(94\) | 1.96294 | 0.202462 | ||||||||
\(95\) | −0.710854 | −0.0729320 | ||||||||
\(96\) | −15.5955 | −1.59171 | ||||||||
\(97\) | −5.02063 | −0.509768 | −0.254884 | − | 0.966972i | \(-0.582037\pi\) | ||||
−0.254884 | + | 0.966972i | \(0.582037\pi\) | |||||||
\(98\) | 2.57874 | 0.260492 | ||||||||
\(99\) | 33.6869 | 3.38566 | ||||||||
\(100\) | 6.54595 | 0.654595 | ||||||||
\(101\) | −8.44195 | −0.840005 | −0.420003 | − | 0.907523i | \(-0.637971\pi\) | ||||
−0.420003 | + | 0.907523i | \(0.637971\pi\) | |||||||
\(102\) | −2.64769 | −0.262161 | ||||||||
\(103\) | −1.87584 | −0.184832 | −0.0924160 | − | 0.995720i | \(-0.529459\pi\) | ||||
−0.0924160 | + | 0.995720i | \(0.529459\pi\) | |||||||
\(104\) | −9.53939 | −0.935414 | ||||||||
\(105\) | −4.49703 | −0.438865 | ||||||||
\(106\) | −4.41786 | −0.429101 | ||||||||
\(107\) | 13.8463 | 1.33857 | 0.669287 | − | 0.743004i | \(-0.266599\pi\) | ||||
0.669287 | + | 0.743004i | \(0.266599\pi\) | |||||||
\(108\) | −27.1381 | −2.61136 | ||||||||
\(109\) | −7.29763 | −0.698986 | −0.349493 | − | 0.936939i | \(-0.613646\pi\) | ||||
−0.349493 | + | 0.936939i | \(0.613646\pi\) | |||||||
\(110\) | −2.35101 | −0.224160 | ||||||||
\(111\) | −28.2093 | −2.67750 | ||||||||
\(112\) | −3.29471 | −0.311321 | ||||||||
\(113\) | 13.2195 | 1.24358 | 0.621791 | − | 0.783183i | \(-0.286405\pi\) | ||||
0.621791 | + | 0.783183i | \(0.286405\pi\) | |||||||
\(114\) | 0.928083 | 0.0869229 | ||||||||
\(115\) | 4.11855 | 0.384057 | ||||||||
\(116\) | −9.01063 | −0.836616 | ||||||||
\(117\) | −41.7193 | −3.85695 | ||||||||
\(118\) | 3.52661 | 0.324651 | ||||||||
\(119\) | −2.09204 | −0.191777 | ||||||||
\(120\) | 6.60206 | 0.602683 | ||||||||
\(121\) | 8.36920 | 0.760836 | ||||||||
\(122\) | 5.44718 | 0.493164 | ||||||||
\(123\) | −22.2879 | −2.00963 | ||||||||
\(124\) | −5.78688 | −0.519677 | ||||||||
\(125\) | −10.0131 | −0.895600 | ||||||||
\(126\) | 4.21806 | 0.375775 | ||||||||
\(127\) | −17.3283 | −1.53764 | −0.768821 | − | 0.639464i | \(-0.779156\pi\) | ||||
−0.768821 | + | 0.639464i | \(0.779156\pi\) | |||||||
\(128\) | 11.0898 | 0.980213 | ||||||||
\(129\) | 14.4370 | 1.27111 | ||||||||
\(130\) | 2.91158 | 0.255363 | ||||||||
\(131\) | −17.4706 | −1.52641 | −0.763207 | − | 0.646154i | \(-0.776376\pi\) | ||||
−0.763207 | + | 0.646154i | \(0.776376\pi\) | |||||||
\(132\) | −25.6614 | −2.23354 | ||||||||
\(133\) | 0.733313 | 0.0635863 | ||||||||
\(134\) | −0.591946 | −0.0511363 | ||||||||
\(135\) | 17.5568 | 1.51105 | ||||||||
\(136\) | 3.07131 | 0.263363 | ||||||||
\(137\) | −4.00113 | −0.341839 | −0.170920 | − | 0.985285i | \(-0.554674\pi\) | ||||
−0.170920 | + | 0.985285i | \(0.554674\pi\) | |||||||
\(138\) | −5.37714 | −0.457732 | ||||||||
\(139\) | 12.7881 | 1.08467 | 0.542336 | − | 0.840162i | \(-0.317540\pi\) | ||||
0.542336 | + | 0.840162i | \(0.317540\pi\) | |||||||
\(140\) | 2.46108 | 0.207999 | ||||||||
\(141\) | −13.8611 | −1.16732 | ||||||||
\(142\) | −1.14760 | −0.0963043 | ||||||||
\(143\) | −23.9876 | −2.00594 | ||||||||
\(144\) | 21.1537 | 1.76281 | ||||||||
\(145\) | 5.82936 | 0.484102 | ||||||||
\(146\) | −6.73352 | −0.557270 | ||||||||
\(147\) | −18.2095 | −1.50190 | ||||||||
\(148\) | 15.4380 | 1.26900 | ||||||||
\(149\) | −16.2641 | −1.33241 | −0.666205 | − | 0.745768i | \(-0.732083\pi\) | ||||
−0.666205 | + | 0.745768i | \(0.732083\pi\) | |||||||
\(150\) | 5.52898 | 0.451439 | ||||||||
\(151\) | 2.50898 | 0.204178 | 0.102089 | − | 0.994775i | \(-0.467447\pi\) | ||||
0.102089 | + | 0.994775i | \(0.467447\pi\) | |||||||
\(152\) | −1.07657 | −0.0873215 | ||||||||
\(153\) | 13.4320 | 1.08591 | ||||||||
\(154\) | 2.42529 | 0.195435 | ||||||||
\(155\) | 3.74377 | 0.300707 | ||||||||
\(156\) | 31.7801 | 2.54444 | ||||||||
\(157\) | −10.4154 | −0.831241 | −0.415620 | − | 0.909538i | \(-0.636435\pi\) | ||||
−0.415620 | + | 0.909538i | \(0.636435\pi\) | |||||||
\(158\) | 3.35396 | 0.266826 | ||||||||
\(159\) | 31.1964 | 2.47403 | ||||||||
\(160\) | −5.52158 | −0.436519 | ||||||||
\(161\) | −4.24868 | −0.334843 | ||||||||
\(162\) | −12.3075 | −0.966965 | ||||||||
\(163\) | 19.0086 | 1.48887 | 0.744433 | − | 0.667698i | \(-0.232720\pi\) | ||||
0.744433 | + | 0.667698i | \(0.232720\pi\) | |||||||
\(164\) | 12.1974 | 0.952459 | ||||||||
\(165\) | 16.6014 | 1.29242 | ||||||||
\(166\) | 7.69350 | 0.597132 | ||||||||
\(167\) | −14.7463 | −1.14110 | −0.570552 | − | 0.821261i | \(-0.693271\pi\) | ||||
−0.570552 | + | 0.821261i | \(0.693271\pi\) | |||||||
\(168\) | −6.81065 | −0.525453 | ||||||||
\(169\) | 16.7072 | 1.28517 | ||||||||
\(170\) | −0.937416 | −0.0718965 | ||||||||
\(171\) | −4.70824 | −0.360048 | ||||||||
\(172\) | −7.90091 | −0.602438 | ||||||||
\(173\) | −7.94156 | −0.603785 | −0.301893 | − | 0.953342i | \(-0.597618\pi\) | ||||
−0.301893 | + | 0.953342i | \(0.597618\pi\) | |||||||
\(174\) | −7.61075 | −0.576969 | ||||||||
\(175\) | 4.36865 | 0.330239 | ||||||||
\(176\) | 12.1629 | 0.916813 | ||||||||
\(177\) | −24.9028 | −1.87181 | ||||||||
\(178\) | −0.763082 | −0.0571954 | ||||||||
\(179\) | 10.0275 | 0.749489 | 0.374745 | − | 0.927128i | \(-0.377730\pi\) | ||||
0.374745 | + | 0.927128i | \(0.377730\pi\) | |||||||
\(180\) | −15.8014 | −1.17776 | ||||||||
\(181\) | −14.7816 | −1.09871 | −0.549355 | − | 0.835589i | \(-0.685126\pi\) | ||||
−0.549355 | + | 0.835589i | \(0.685126\pi\) | |||||||
\(182\) | −3.00357 | −0.222640 | ||||||||
\(183\) | −38.4647 | −2.84340 | ||||||||
\(184\) | 6.23745 | 0.459831 | ||||||||
\(185\) | −9.98749 | −0.734295 | ||||||||
\(186\) | −4.88783 | −0.358393 | ||||||||
\(187\) | 7.72307 | 0.564767 | ||||||||
\(188\) | 7.58572 | 0.553246 | ||||||||
\(189\) | −18.1115 | −1.31742 | ||||||||
\(190\) | 0.328588 | 0.0238383 | ||||||||
\(191\) | 16.9559 | 1.22689 | 0.613445 | − | 0.789738i | \(-0.289783\pi\) | ||||
0.613445 | + | 0.789738i | \(0.289783\pi\) | |||||||
\(192\) | −10.8326 | −0.781778 | ||||||||
\(193\) | 13.2472 | 0.953552 | 0.476776 | − | 0.879025i | \(-0.341805\pi\) | ||||
0.476776 | + | 0.879025i | \(0.341805\pi\) | |||||||
\(194\) | 2.32076 | 0.166621 | ||||||||
\(195\) | −20.5599 | −1.47232 | ||||||||
\(196\) | 9.96548 | 0.711820 | ||||||||
\(197\) | 20.2227 | 1.44081 | 0.720405 | − | 0.693554i | \(-0.243956\pi\) | ||||
0.720405 | + | 0.693554i | \(0.243956\pi\) | |||||||
\(198\) | −15.5716 | −1.10662 | ||||||||
\(199\) | 12.8865 | 0.913496 | 0.456748 | − | 0.889596i | \(-0.349014\pi\) | ||||
0.456748 | + | 0.889596i | \(0.349014\pi\) | |||||||
\(200\) | −6.41358 | −0.453509 | ||||||||
\(201\) | 4.17997 | 0.294832 | ||||||||
\(202\) | 3.90224 | 0.274561 | ||||||||
\(203\) | −6.01353 | −0.422067 | ||||||||
\(204\) | −10.2320 | −0.716380 | ||||||||
\(205\) | −7.89103 | −0.551133 | ||||||||
\(206\) | 0.867095 | 0.0604134 | ||||||||
\(207\) | 27.2787 | 1.89600 | ||||||||
\(208\) | −15.0630 | −1.04443 | ||||||||
\(209\) | −2.70713 | −0.187256 | ||||||||
\(210\) | 2.07872 | 0.143446 | ||||||||
\(211\) | −21.1548 | −1.45636 | −0.728178 | − | 0.685388i | \(-0.759633\pi\) | ||||
−0.728178 | + | 0.685388i | \(0.759633\pi\) | |||||||
\(212\) | −17.0727 | −1.17256 | ||||||||
\(213\) | 8.10366 | 0.555254 | ||||||||
\(214\) | −6.40038 | −0.437521 | ||||||||
\(215\) | 5.11143 | 0.348596 | ||||||||
\(216\) | 26.5893 | 1.80917 | ||||||||
\(217\) | −3.86206 | −0.262174 | ||||||||
\(218\) | 3.37329 | 0.228468 | ||||||||
\(219\) | 47.5481 | 3.21301 | ||||||||
\(220\) | −9.08541 | −0.612538 | ||||||||
\(221\) | −9.56456 | −0.643382 | ||||||||
\(222\) | 13.0396 | 0.875158 | ||||||||
\(223\) | 13.4569 | 0.901139 | 0.450570 | − | 0.892741i | \(-0.351221\pi\) | ||||
0.450570 | + | 0.892741i | \(0.351221\pi\) | |||||||
\(224\) | 5.69603 | 0.380582 | ||||||||
\(225\) | −28.0490 | −1.86993 | ||||||||
\(226\) | −6.11062 | −0.406472 | ||||||||
\(227\) | 7.40471 | 0.491468 | 0.245734 | − | 0.969337i | \(-0.420971\pi\) | ||||
0.245734 | + | 0.969337i | \(0.420971\pi\) | |||||||
\(228\) | 3.58655 | 0.237525 | ||||||||
\(229\) | 12.1885 | 0.805439 | 0.402719 | − | 0.915323i | \(-0.368065\pi\) | ||||
0.402719 | + | 0.915323i | \(0.368065\pi\) | |||||||
\(230\) | −1.90377 | −0.125531 | ||||||||
\(231\) | −17.1259 | −1.12680 | ||||||||
\(232\) | 8.82842 | 0.579614 | ||||||||
\(233\) | −1.43524 | −0.0940258 | −0.0470129 | − | 0.998894i | \(-0.514970\pi\) | ||||
−0.0470129 | + | 0.998894i | \(0.514970\pi\) | |||||||
\(234\) | 19.2845 | 1.26067 | ||||||||
\(235\) | −4.90752 | −0.320131 | ||||||||
\(236\) | 13.6285 | 0.887140 | ||||||||
\(237\) | −23.6837 | −1.53842 | ||||||||
\(238\) | 0.967034 | 0.0626835 | ||||||||
\(239\) | 2.26001 | 0.146188 | 0.0730938 | − | 0.997325i | \(-0.476713\pi\) | ||||
0.0730938 | + | 0.997325i | \(0.476713\pi\) | |||||||
\(240\) | 10.4249 | 0.672923 | ||||||||
\(241\) | 8.56718 | 0.551861 | 0.275930 | − | 0.961178i | \(-0.411014\pi\) | ||||
0.275930 | + | 0.961178i | \(0.411014\pi\) | |||||||
\(242\) | −3.86861 | −0.248684 | ||||||||
\(243\) | 41.3317 | 2.65143 | ||||||||
\(244\) | 21.0505 | 1.34762 | ||||||||
\(245\) | −6.44709 | −0.411889 | ||||||||
\(246\) | 10.3024 | 0.656860 | ||||||||
\(247\) | 3.35262 | 0.213322 | ||||||||
\(248\) | 5.66986 | 0.360036 | ||||||||
\(249\) | −54.3270 | −3.44283 | ||||||||
\(250\) | 4.62850 | 0.292732 | ||||||||
\(251\) | 17.3286 | 1.09377 | 0.546886 | − | 0.837207i | \(-0.315813\pi\) | ||||
0.546886 | + | 0.837207i | \(0.315813\pi\) | |||||||
\(252\) | 16.3006 | 1.02684 | ||||||||
\(253\) | 15.6846 | 0.986082 | ||||||||
\(254\) | 8.00992 | 0.502587 | ||||||||
\(255\) | 6.61948 | 0.414528 | ||||||||
\(256\) | 1.51124 | 0.0944524 | ||||||||
\(257\) | −10.2141 | −0.637141 | −0.318571 | − | 0.947899i | \(-0.603203\pi\) | ||||
−0.318571 | + | 0.947899i | \(0.603203\pi\) | |||||||
\(258\) | −6.67343 | −0.415469 | ||||||||
\(259\) | 10.3030 | 0.640200 | ||||||||
\(260\) | 11.2517 | 0.697803 | ||||||||
\(261\) | 38.6099 | 2.38990 | ||||||||
\(262\) | 8.07568 | 0.498917 | ||||||||
\(263\) | 13.5678 | 0.836624 | 0.418312 | − | 0.908303i | \(-0.362622\pi\) | ||||
0.418312 | + | 0.908303i | \(0.362622\pi\) | |||||||
\(264\) | 25.1425 | 1.54741 | ||||||||
\(265\) | 11.0451 | 0.678493 | ||||||||
\(266\) | −0.338969 | −0.0207835 | ||||||||
\(267\) | 5.38844 | 0.329767 | ||||||||
\(268\) | −2.28756 | −0.139735 | ||||||||
\(269\) | 15.6280 | 0.952854 | 0.476427 | − | 0.879214i | \(-0.341932\pi\) | ||||
0.476427 | + | 0.879214i | \(0.341932\pi\) | |||||||
\(270\) | −8.11551 | −0.493894 | ||||||||
\(271\) | −16.9869 | −1.03188 | −0.515941 | − | 0.856624i | \(-0.672558\pi\) | ||||
−0.515941 | + | 0.856624i | \(0.672558\pi\) | |||||||
\(272\) | 4.84971 | 0.294057 | ||||||||
\(273\) | 21.2095 | 1.28366 | ||||||||
\(274\) | 1.84950 | 0.111732 | ||||||||
\(275\) | −16.1275 | −0.972524 | ||||||||
\(276\) | −20.7798 | −1.25080 | ||||||||
\(277\) | 30.4548 | 1.82985 | 0.914926 | − | 0.403622i | \(-0.132249\pi\) | ||||
0.914926 | + | 0.403622i | \(0.132249\pi\) | |||||||
\(278\) | −5.91122 | −0.354531 | ||||||||
\(279\) | 24.7964 | 1.48452 | ||||||||
\(280\) | −2.41131 | −0.144103 | ||||||||
\(281\) | 17.6683 | 1.05400 | 0.527001 | − | 0.849864i | \(-0.323316\pi\) | ||||
0.527001 | + | 0.849864i | \(0.323316\pi\) | |||||||
\(282\) | 6.40721 | 0.381544 | ||||||||
\(283\) | −18.5963 | −1.10543 | −0.552717 | − | 0.833369i | \(-0.686409\pi\) | ||||
−0.552717 | + | 0.833369i | \(0.686409\pi\) | |||||||
\(284\) | −4.43487 | −0.263161 | ||||||||
\(285\) | −2.32029 | −0.137442 | ||||||||
\(286\) | 11.0881 | 0.655654 | ||||||||
\(287\) | 8.14034 | 0.480509 | ||||||||
\(288\) | −36.5714 | −2.15499 | ||||||||
\(289\) | −13.9206 | −0.818858 | ||||||||
\(290\) | −2.69458 | −0.158231 | ||||||||
\(291\) | −16.3878 | −0.960670 | ||||||||
\(292\) | −26.0215 | −1.52279 | ||||||||
\(293\) | −0.267742 | −0.0156416 | −0.00782082 | − | 0.999969i | \(-0.502489\pi\) | ||||
−0.00782082 | + | 0.999969i | \(0.502489\pi\) | |||||||
\(294\) | 8.41725 | 0.490904 | ||||||||
\(295\) | −8.81685 | −0.513337 | ||||||||
\(296\) | −15.1258 | −0.879170 | ||||||||
\(297\) | 66.8610 | 3.87967 | ||||||||
\(298\) | 7.51800 | 0.435506 | ||||||||
\(299\) | −19.4244 | −1.12334 | ||||||||
\(300\) | 21.3666 | 1.23360 | ||||||||
\(301\) | −5.27292 | −0.303926 | ||||||||
\(302\) | −1.15976 | −0.0667366 | ||||||||
\(303\) | −27.5553 | −1.58301 | ||||||||
\(304\) | −1.69994 | −0.0974984 | ||||||||
\(305\) | −13.6184 | −0.779790 | ||||||||
\(306\) | −6.20885 | −0.354936 | ||||||||
\(307\) | 2.39292 | 0.136571 | 0.0682856 | − | 0.997666i | \(-0.478247\pi\) | ||||
0.0682856 | + | 0.997666i | \(0.478247\pi\) | |||||||
\(308\) | 9.37247 | 0.534046 | ||||||||
\(309\) | −6.12292 | −0.348320 | ||||||||
\(310\) | −1.73054 | −0.0982879 | ||||||||
\(311\) | −1.74135 | −0.0987430 | −0.0493715 | − | 0.998780i | \(-0.515722\pi\) | ||||
−0.0493715 | + | 0.998780i | \(0.515722\pi\) | |||||||
\(312\) | −31.1375 | −1.76281 | ||||||||
\(313\) | 30.2027 | 1.70716 | 0.853578 | − | 0.520965i | \(-0.174428\pi\) | ||||
0.853578 | + | 0.520965i | \(0.174428\pi\) | |||||||
\(314\) | 4.81446 | 0.271696 | ||||||||
\(315\) | −10.5455 | −0.594174 | ||||||||
\(316\) | 12.9613 | 0.729129 | ||||||||
\(317\) | 28.0579 | 1.57589 | 0.787943 | − | 0.615748i | \(-0.211146\pi\) | ||||
0.787943 | + | 0.615748i | \(0.211146\pi\) | |||||||
\(318\) | −14.4203 | −0.808652 | ||||||||
\(319\) | 22.1998 | 1.24295 | ||||||||
\(320\) | −3.83529 | −0.214399 | ||||||||
\(321\) | 45.1957 | 2.52258 | ||||||||
\(322\) | 1.96392 | 0.109445 | ||||||||
\(323\) | −1.07941 | −0.0600601 | ||||||||
\(324\) | −47.5619 | −2.64233 | ||||||||
\(325\) | 19.9729 | 1.10790 | ||||||||
\(326\) | −8.78659 | −0.486644 | ||||||||
\(327\) | −23.8201 | −1.31726 | ||||||||
\(328\) | −11.9508 | −0.659871 | ||||||||
\(329\) | 5.06257 | 0.279109 | ||||||||
\(330\) | −7.67391 | −0.422435 | ||||||||
\(331\) | 18.1592 | 0.998122 | 0.499061 | − | 0.866567i | \(-0.333678\pi\) | ||||
0.499061 | + | 0.866567i | \(0.333678\pi\) | |||||||
\(332\) | 29.7314 | 1.63172 | ||||||||
\(333\) | −66.1508 | −3.62504 | ||||||||
\(334\) | 6.81640 | 0.372977 | ||||||||
\(335\) | 1.47992 | 0.0808566 | ||||||||
\(336\) | −10.7542 | −0.586692 | ||||||||
\(337\) | 19.4108 | 1.05737 | 0.528686 | − | 0.848818i | \(-0.322685\pi\) | ||||
0.528686 | + | 0.848818i | \(0.322685\pi\) | |||||||
\(338\) | −7.72280 | −0.420065 | ||||||||
\(339\) | 43.1496 | 2.34356 | ||||||||
\(340\) | −3.62262 | −0.196464 | ||||||||
\(341\) | 14.2573 | 0.772078 | ||||||||
\(342\) | 2.17636 | 0.117684 | ||||||||
\(343\) | 14.9959 | 0.809704 | ||||||||
\(344\) | 7.74114 | 0.417374 | ||||||||
\(345\) | 13.4433 | 0.723765 | ||||||||
\(346\) | 3.67094 | 0.197351 | ||||||||
\(347\) | −21.9756 | −1.17971 | −0.589856 | − | 0.807508i | \(-0.700816\pi\) | ||||
−0.589856 | + | 0.807508i | \(0.700816\pi\) | |||||||
\(348\) | −29.4115 | −1.57662 | ||||||||
\(349\) | −10.5591 | −0.565216 | −0.282608 | − | 0.959235i | \(-0.591200\pi\) | ||||
−0.282608 | + | 0.959235i | \(0.591200\pi\) | |||||||
\(350\) | −2.01938 | −0.107940 | ||||||||
\(351\) | −82.8034 | −4.41972 | ||||||||
\(352\) | −21.0277 | −1.12078 | ||||||||
\(353\) | −30.9628 | −1.64799 | −0.823993 | − | 0.566600i | \(-0.808258\pi\) | ||||
−0.823993 | + | 0.566600i | \(0.808258\pi\) | |||||||
\(354\) | 11.5112 | 0.611813 | ||||||||
\(355\) | 2.86910 | 0.152276 | ||||||||
\(356\) | −2.94891 | −0.156292 | ||||||||
\(357\) | −6.82862 | −0.361409 | ||||||||
\(358\) | −4.63514 | −0.244975 | ||||||||
\(359\) | −23.8149 | −1.25690 | −0.628450 | − | 0.777850i | \(-0.716310\pi\) | ||||
−0.628450 | + | 0.777850i | \(0.716310\pi\) | |||||||
\(360\) | 15.4818 | 0.815964 | ||||||||
\(361\) | −18.6216 | −0.980086 | ||||||||
\(362\) | 6.83272 | 0.359120 | ||||||||
\(363\) | 27.3178 | 1.43381 | ||||||||
\(364\) | −11.6072 | −0.608385 | ||||||||
\(365\) | 16.8344 | 0.881154 | ||||||||
\(366\) | 17.7801 | 0.929380 | ||||||||
\(367\) | −7.44635 | −0.388696 | −0.194348 | − | 0.980933i | \(-0.562259\pi\) | ||||
−0.194348 | + | 0.980933i | \(0.562259\pi\) | |||||||
\(368\) | 9.84915 | 0.513422 | ||||||||
\(369\) | −52.2652 | −2.72082 | ||||||||
\(370\) | 4.61665 | 0.240008 | ||||||||
\(371\) | −11.3940 | −0.591549 | ||||||||
\(372\) | −18.8889 | −0.979344 | ||||||||
\(373\) | 33.4650 | 1.73275 | 0.866375 | − | 0.499394i | \(-0.166444\pi\) | ||||
0.866375 | + | 0.499394i | \(0.166444\pi\) | |||||||
\(374\) | −3.56994 | −0.184597 | ||||||||
\(375\) | −32.6837 | −1.68778 | ||||||||
\(376\) | −7.43233 | −0.383293 | ||||||||
\(377\) | −27.4931 | −1.41597 | ||||||||
\(378\) | 8.37191 | 0.430605 | ||||||||
\(379\) | −19.1182 | −0.982036 | −0.491018 | − | 0.871149i | \(-0.663375\pi\) | ||||
−0.491018 | + | 0.871149i | \(0.663375\pi\) | |||||||
\(380\) | 1.26982 | 0.0651404 | ||||||||
\(381\) | −56.5613 | −2.89773 | ||||||||
\(382\) | −7.83778 | −0.401016 | ||||||||
\(383\) | 13.8538 | 0.707897 | 0.353949 | − | 0.935265i | \(-0.384839\pi\) | ||||
0.353949 | + | 0.935265i | \(0.384839\pi\) | |||||||
\(384\) | 36.1983 | 1.84724 | ||||||||
\(385\) | −6.06344 | −0.309021 | ||||||||
\(386\) | −6.12342 | −0.311674 | ||||||||
\(387\) | 33.8548 | 1.72094 | ||||||||
\(388\) | 8.96851 | 0.455307 | ||||||||
\(389\) | 27.5211 | 1.39538 | 0.697688 | − | 0.716402i | \(-0.254212\pi\) | ||||
0.697688 | + | 0.716402i | \(0.254212\pi\) | |||||||
\(390\) | 9.50368 | 0.481237 | ||||||||
\(391\) | 6.25391 | 0.316274 | ||||||||
\(392\) | −9.76396 | −0.493155 | ||||||||
\(393\) | −57.0257 | −2.87657 | ||||||||
\(394\) | −9.34783 | −0.470937 | ||||||||
\(395\) | −8.38520 | −0.421905 | ||||||||
\(396\) | −60.1760 | −3.02396 | ||||||||
\(397\) | 20.6312 | 1.03545 | 0.517725 | − | 0.855547i | \(-0.326779\pi\) | ||||
0.517725 | + | 0.855547i | \(0.326779\pi\) | |||||||
\(398\) | −5.95668 | −0.298582 | ||||||||
\(399\) | 2.39360 | 0.119830 | ||||||||
\(400\) | −10.1273 | −0.506363 | ||||||||
\(401\) | −29.9855 | −1.49741 | −0.748703 | − | 0.662906i | \(-0.769323\pi\) | ||||
−0.748703 | + | 0.662906i | \(0.769323\pi\) | |||||||
\(402\) | −1.93217 | −0.0963677 | ||||||||
\(403\) | −17.6569 | −0.879551 | ||||||||
\(404\) | 15.0801 | 0.750264 | ||||||||
\(405\) | 30.7698 | 1.52896 | ||||||||
\(406\) | 2.77972 | 0.137955 | ||||||||
\(407\) | −38.0351 | −1.88533 | ||||||||
\(408\) | 10.0250 | 0.496314 | ||||||||
\(409\) | 6.08729 | 0.300997 | 0.150498 | − | 0.988610i | \(-0.451912\pi\) | ||||
0.150498 | + | 0.988610i | \(0.451912\pi\) | |||||||
\(410\) | 3.64758 | 0.180141 | ||||||||
\(411\) | −13.0600 | −0.644205 | ||||||||
\(412\) | 3.35087 | 0.165086 | ||||||||
\(413\) | 9.09542 | 0.447556 | ||||||||
\(414\) | −12.6094 | −0.619718 | ||||||||
\(415\) | −19.2345 | −0.944183 | ||||||||
\(416\) | 26.0416 | 1.27679 | ||||||||
\(417\) | 41.7415 | 2.04409 | ||||||||
\(418\) | 1.25135 | 0.0612057 | ||||||||
\(419\) | 30.5039 | 1.49021 | 0.745107 | − | 0.666945i | \(-0.232398\pi\) | ||||
0.745107 | + | 0.666945i | \(0.232398\pi\) | |||||||
\(420\) | 8.03318 | 0.391979 | ||||||||
\(421\) | 5.63147 | 0.274461 | 0.137231 | − | 0.990539i | \(-0.456180\pi\) | ||||
0.137231 | + | 0.990539i | \(0.456180\pi\) | |||||||
\(422\) | 9.77868 | 0.476019 | ||||||||
\(423\) | −32.5043 | −1.58041 | ||||||||
\(424\) | 16.7275 | 0.812359 | ||||||||
\(425\) | −6.43051 | −0.311925 | ||||||||
\(426\) | −3.74587 | −0.181488 | ||||||||
\(427\) | 14.0487 | 0.679865 | ||||||||
\(428\) | −24.7341 | −1.19557 | ||||||||
\(429\) | −78.2977 | −3.78025 | ||||||||
\(430\) | −2.36273 | −0.113941 | ||||||||
\(431\) | 22.6727 | 1.09211 | 0.546053 | − | 0.837751i | \(-0.316130\pi\) | ||||
0.546053 | + | 0.837751i | \(0.316130\pi\) | |||||||
\(432\) | 41.9854 | 2.02002 | ||||||||
\(433\) | 28.4524 | 1.36733 | 0.683667 | − | 0.729794i | \(-0.260384\pi\) | ||||
0.683667 | + | 0.729794i | \(0.260384\pi\) | |||||||
\(434\) | 1.78521 | 0.0856929 | ||||||||
\(435\) | 19.0276 | 0.912302 | ||||||||
\(436\) | 13.0360 | 0.624310 | ||||||||
\(437\) | −2.19215 | −0.104865 | ||||||||
\(438\) | −21.9788 | −1.05019 | ||||||||
\(439\) | −26.2203 | −1.25143 | −0.625713 | − | 0.780053i | \(-0.715192\pi\) | ||||
−0.625713 | + | 0.780053i | \(0.715192\pi\) | |||||||
\(440\) | 8.90169 | 0.424371 | ||||||||
\(441\) | −42.7014 | −2.03340 | ||||||||
\(442\) | 4.42116 | 0.210293 | ||||||||
\(443\) | 19.3673 | 0.920167 | 0.460083 | − | 0.887876i | \(-0.347820\pi\) | ||||
0.460083 | + | 0.887876i | \(0.347820\pi\) | |||||||
\(444\) | 50.3911 | 2.39145 | ||||||||
\(445\) | 1.90778 | 0.0904372 | ||||||||
\(446\) | −6.22036 | −0.294543 | ||||||||
\(447\) | −53.0877 | −2.51096 | ||||||||
\(448\) | 3.95647 | 0.186925 | ||||||||
\(449\) | −20.2189 | −0.954191 | −0.477095 | − | 0.878852i | \(-0.658310\pi\) | ||||
−0.477095 | + | 0.878852i | \(0.658310\pi\) | |||||||
\(450\) | 12.9655 | 0.611198 | ||||||||
\(451\) | −30.0512 | −1.41506 | ||||||||
\(452\) | −23.6143 | −1.11072 | ||||||||
\(453\) | 8.18953 | 0.384778 | ||||||||
\(454\) | −3.42278 | −0.160639 | ||||||||
\(455\) | 7.50921 | 0.352037 | ||||||||
\(456\) | −3.51403 | −0.164559 | ||||||||
\(457\) | 17.8331 | 0.834199 | 0.417100 | − | 0.908861i | \(-0.363047\pi\) | ||||
0.417100 | + | 0.908861i | \(0.363047\pi\) | |||||||
\(458\) | −5.63406 | −0.263262 | ||||||||
\(459\) | 26.6595 | 1.24436 | ||||||||
\(460\) | −7.35709 | −0.343026 | ||||||||
\(461\) | −1.01528 | −0.0472865 | −0.0236432 | − | 0.999720i | \(-0.507527\pi\) | ||||
−0.0236432 | + | 0.999720i | \(0.507527\pi\) | |||||||
\(462\) | 7.91636 | 0.368303 | ||||||||
\(463\) | −28.4914 | −1.32411 | −0.662054 | − | 0.749456i | \(-0.730315\pi\) | ||||
−0.662054 | + | 0.749456i | \(0.730315\pi\) | |||||||
\(464\) | 13.9404 | 0.647166 | ||||||||
\(465\) | 12.2200 | 0.566690 | ||||||||
\(466\) | 0.663432 | 0.0307329 | ||||||||
\(467\) | 24.1389 | 1.11701 | 0.558507 | − | 0.829500i | \(-0.311374\pi\) | ||||
0.558507 | + | 0.829500i | \(0.311374\pi\) | |||||||
\(468\) | 74.5244 | 3.44489 | ||||||||
\(469\) | −1.52668 | −0.0704953 | ||||||||
\(470\) | 2.26847 | 0.104637 | ||||||||
\(471\) | −33.9969 | −1.56649 | ||||||||
\(472\) | −13.3529 | −0.614618 | ||||||||
\(473\) | 19.4657 | 0.895036 | ||||||||
\(474\) | 10.9476 | 0.502841 | ||||||||
\(475\) | 2.25405 | 0.103423 | ||||||||
\(476\) | 3.73708 | 0.171289 | ||||||||
\(477\) | 73.1555 | 3.34956 | ||||||||
\(478\) | −1.04467 | −0.0477823 | ||||||||
\(479\) | 5.78476 | 0.264313 | 0.132156 | − | 0.991229i | \(-0.457810\pi\) | ||||
0.132156 | + | 0.991229i | \(0.457810\pi\) | |||||||
\(480\) | −18.0229 | −0.822631 | ||||||||
\(481\) | 47.1042 | 2.14777 | ||||||||
\(482\) | −3.96013 | −0.180379 | ||||||||
\(483\) | −13.8681 | −0.631019 | ||||||||
\(484\) | −14.9501 | −0.679552 | ||||||||
\(485\) | −5.80210 | −0.263460 | ||||||||
\(486\) | −19.1053 | −0.866636 | ||||||||
\(487\) | −11.7021 | −0.530272 | −0.265136 | − | 0.964211i | \(-0.585417\pi\) | ||||
−0.265136 | + | 0.964211i | \(0.585417\pi\) | |||||||
\(488\) | −20.6248 | −0.933641 | ||||||||
\(489\) | 62.0457 | 2.80580 | ||||||||
\(490\) | 2.98013 | 0.134628 | ||||||||
\(491\) | −8.18439 | −0.369356 | −0.184678 | − | 0.982799i | \(-0.559124\pi\) | ||||
−0.184678 | + | 0.982799i | \(0.559124\pi\) | |||||||
\(492\) | 39.8136 | 1.79493 | ||||||||
\(493\) | 8.85172 | 0.398661 | ||||||||
\(494\) | −1.54973 | −0.0697255 | ||||||||
\(495\) | 38.9304 | 1.74979 | ||||||||
\(496\) | 8.95290 | 0.401997 | ||||||||
\(497\) | −2.95975 | −0.132763 | ||||||||
\(498\) | 25.1123 | 1.12531 | ||||||||
\(499\) | −33.1230 | −1.48279 | −0.741396 | − | 0.671068i | \(-0.765836\pi\) | ||||
−0.741396 | + | 0.671068i | \(0.765836\pi\) | |||||||
\(500\) | 17.8867 | 0.799919 | ||||||||
\(501\) | −48.1334 | −2.15044 | ||||||||
\(502\) | −8.01004 | −0.357506 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | −15.9710 | −0.711404 | ||||||||
\(505\) | −9.75595 | −0.434134 | ||||||||
\(506\) | −7.25011 | −0.322306 | ||||||||
\(507\) | 54.5339 | 2.42193 | ||||||||
\(508\) | 30.9542 | 1.37337 | ||||||||
\(509\) | 23.0768 | 1.02286 | 0.511432 | − | 0.859324i | \(-0.329115\pi\) | ||||
0.511432 | + | 0.859324i | \(0.329115\pi\) | |||||||
\(510\) | −3.05981 | −0.135491 | ||||||||
\(511\) | −17.3663 | −0.768240 | ||||||||
\(512\) | −22.8782 | −1.01109 | ||||||||
\(513\) | −9.34481 | −0.412583 | ||||||||
\(514\) | 4.72143 | 0.208253 | ||||||||
\(515\) | −2.16782 | −0.0955255 | ||||||||
\(516\) | −25.7893 | −1.13531 | ||||||||
\(517\) | −18.6892 | −0.821951 | ||||||||
\(518\) | −4.76252 | −0.209253 | ||||||||
\(519\) | −25.9220 | −1.13785 | ||||||||
\(520\) | −11.0242 | −0.483444 | ||||||||
\(521\) | 20.0541 | 0.878587 | 0.439294 | − | 0.898344i | \(-0.355229\pi\) | ||||
0.439294 | + | 0.898344i | \(0.355229\pi\) | |||||||
\(522\) | −17.8472 | −0.781151 | ||||||||
\(523\) | −16.3241 | −0.713803 | −0.356902 | − | 0.934142i | \(-0.616167\pi\) | ||||
−0.356902 | + | 0.934142i | \(0.616167\pi\) | |||||||
\(524\) | 31.2083 | 1.36334 | ||||||||
\(525\) | 14.2597 | 0.622343 | ||||||||
\(526\) | −6.27162 | −0.273455 | ||||||||
\(527\) | 5.68482 | 0.247635 | ||||||||
\(528\) | 39.7008 | 1.72776 | ||||||||
\(529\) | −10.2991 | −0.447787 | ||||||||
\(530\) | −5.10551 | −0.221769 | ||||||||
\(531\) | −58.3972 | −2.53422 | ||||||||
\(532\) | −1.30994 | −0.0567931 | ||||||||
\(533\) | 37.2167 | 1.61203 | ||||||||
\(534\) | −2.49077 | −0.107786 | ||||||||
\(535\) | 16.0015 | 0.691807 | ||||||||
\(536\) | 2.24130 | 0.0968095 | ||||||||
\(537\) | 32.7306 | 1.41243 | ||||||||
\(538\) | −7.22393 | −0.311446 | ||||||||
\(539\) | −24.5523 | −1.05754 | ||||||||
\(540\) | −31.3622 | −1.34961 | ||||||||
\(541\) | 23.6199 | 1.01550 | 0.507748 | − | 0.861505i | \(-0.330478\pi\) | ||||
0.507748 | + | 0.861505i | \(0.330478\pi\) | |||||||
\(542\) | 7.85210 | 0.337277 | ||||||||
\(543\) | −48.2486 | −2.07055 | ||||||||
\(544\) | −8.38437 | −0.359477 | ||||||||
\(545\) | −8.43352 | −0.361252 | ||||||||
\(546\) | −9.80394 | −0.419570 | ||||||||
\(547\) | 16.8526 | 0.720565 | 0.360283 | − | 0.932843i | \(-0.382680\pi\) | ||||
0.360283 | + | 0.932843i | \(0.382680\pi\) | |||||||
\(548\) | 7.14733 | 0.305319 | ||||||||
\(549\) | −90.1999 | −3.84964 | ||||||||
\(550\) | 7.45483 | 0.317875 | ||||||||
\(551\) | −3.10275 | −0.132182 | ||||||||
\(552\) | 20.3596 | 0.866563 | ||||||||
\(553\) | 8.65013 | 0.367841 | ||||||||
\(554\) | −14.0775 | −0.598097 | ||||||||
\(555\) | −32.6001 | −1.38380 | ||||||||
\(556\) | −22.8438 | −0.968791 | ||||||||
\(557\) | −5.57574 | −0.236252 | −0.118126 | − | 0.992999i | \(-0.537689\pi\) | ||||
−0.118126 | + | 0.992999i | \(0.537689\pi\) | |||||||
\(558\) | −11.4620 | −0.485224 | ||||||||
\(559\) | −24.1072 | −1.01962 | ||||||||
\(560\) | −3.80754 | −0.160898 | ||||||||
\(561\) | 25.2088 | 1.06432 | ||||||||
\(562\) | −8.16707 | −0.344507 | ||||||||
\(563\) | 10.4567 | 0.440697 | 0.220348 | − | 0.975421i | \(-0.429281\pi\) | ||||
0.220348 | + | 0.975421i | \(0.429281\pi\) | |||||||
\(564\) | 24.7605 | 1.04261 | ||||||||
\(565\) | 15.2771 | 0.642712 | ||||||||
\(566\) | 8.59602 | 0.361318 | ||||||||
\(567\) | −31.7419 | −1.33304 | ||||||||
\(568\) | 4.34519 | 0.182320 | ||||||||
\(569\) | 13.4131 | 0.562308 | 0.281154 | − | 0.959663i | \(-0.409283\pi\) | ||||
0.281154 | + | 0.959663i | \(0.409283\pi\) | |||||||
\(570\) | 1.07254 | 0.0449238 | ||||||||
\(571\) | −24.1279 | −1.00972 | −0.504861 | − | 0.863201i | \(-0.668456\pi\) | ||||
−0.504861 | + | 0.863201i | \(0.668456\pi\) | |||||||
\(572\) | 42.8498 | 1.79164 | ||||||||
\(573\) | 55.3458 | 2.31210 | ||||||||
\(574\) | −3.76282 | −0.157057 | ||||||||
\(575\) | −13.0596 | −0.544621 | ||||||||
\(576\) | −25.4025 | −1.05844 | ||||||||
\(577\) | −45.6091 | −1.89873 | −0.949367 | − | 0.314170i | \(-0.898274\pi\) | ||||
−0.949367 | + | 0.314170i | \(0.898274\pi\) | |||||||
\(578\) | 6.43470 | 0.267648 | ||||||||
\(579\) | 43.2400 | 1.79699 | ||||||||
\(580\) | −10.4132 | −0.432383 | ||||||||
\(581\) | 19.8422 | 0.823192 | ||||||||
\(582\) | 7.57517 | 0.314001 | ||||||||
\(583\) | 42.0627 | 1.74206 | ||||||||
\(584\) | 25.4953 | 1.05500 | ||||||||
\(585\) | −48.2129 | −1.99336 | ||||||||
\(586\) | 0.123762 | 0.00511256 | ||||||||
\(587\) | −24.7383 | −1.02106 | −0.510530 | − | 0.859860i | \(-0.670551\pi\) | ||||
−0.510530 | + | 0.859860i | \(0.670551\pi\) | |||||||
\(588\) | 32.5283 | 1.34144 | ||||||||
\(589\) | −1.99267 | −0.0821066 | ||||||||
\(590\) | 4.07554 | 0.167787 | ||||||||
\(591\) | 66.0089 | 2.71524 | ||||||||
\(592\) | −23.8842 | −0.981634 | ||||||||
\(593\) | 11.6796 | 0.479625 | 0.239813 | − | 0.970819i | \(-0.422914\pi\) | ||||
0.239813 | + | 0.970819i | \(0.422914\pi\) | |||||||
\(594\) | −30.9061 | −1.26809 | ||||||||
\(595\) | −2.41767 | −0.0991149 | ||||||||
\(596\) | 29.0531 | 1.19006 | ||||||||
\(597\) | 42.0626 | 1.72151 | ||||||||
\(598\) | 8.97882 | 0.367171 | ||||||||
\(599\) | −27.7786 | −1.13500 | −0.567502 | − | 0.823372i | \(-0.692090\pi\) | ||||
−0.567502 | + | 0.823372i | \(0.692090\pi\) | |||||||
\(600\) | −20.9345 | −0.854649 | ||||||||
\(601\) | 7.88461 | 0.321620 | 0.160810 | − | 0.986985i | \(-0.448589\pi\) | ||||
0.160810 | + | 0.986985i | \(0.448589\pi\) | |||||||
\(602\) | 2.43738 | 0.0993400 | ||||||||
\(603\) | 9.80204 | 0.399170 | ||||||||
\(604\) | −4.48186 | −0.182364 | ||||||||
\(605\) | 9.67188 | 0.393218 | ||||||||
\(606\) | 12.7373 | 0.517416 | ||||||||
\(607\) | 14.3700 | 0.583260 | 0.291630 | − | 0.956531i | \(-0.405802\pi\) | ||||
0.291630 | + | 0.956531i | \(0.405802\pi\) | |||||||
\(608\) | 2.93893 | 0.119189 | ||||||||
\(609\) | −19.6287 | −0.795396 | ||||||||
\(610\) | 6.29504 | 0.254879 | ||||||||
\(611\) | 23.1455 | 0.936366 | ||||||||
\(612\) | −23.9940 | −0.969898 | ||||||||
\(613\) | −41.7791 | −1.68744 | −0.843722 | − | 0.536781i | \(-0.819640\pi\) | ||||
−0.843722 | + | 0.536781i | \(0.819640\pi\) | |||||||
\(614\) | −1.10611 | −0.0446391 | ||||||||
\(615\) | −25.7571 | −1.03862 | ||||||||
\(616\) | −9.18294 | −0.369991 | ||||||||
\(617\) | 28.8196 | 1.16023 | 0.580117 | − | 0.814533i | \(-0.303007\pi\) | ||||
0.580117 | + | 0.814533i | \(0.303007\pi\) | |||||||
\(618\) | 2.83028 | 0.113851 | ||||||||
\(619\) | −39.3446 | −1.58139 | −0.790697 | − | 0.612208i | \(-0.790282\pi\) | ||||
−0.790697 | + | 0.612208i | \(0.790282\pi\) | |||||||
\(620\) | −6.68762 | −0.268581 | ||||||||
\(621\) | 54.1420 | 2.17265 | ||||||||
\(622\) | 0.804929 | 0.0322747 | ||||||||
\(623\) | −1.96805 | −0.0788483 | ||||||||
\(624\) | −49.1671 | −1.96826 | ||||||||
\(625\) | 6.75067 | 0.270027 | ||||||||
\(626\) | −13.9610 | −0.557994 | ||||||||
\(627\) | −8.83632 | −0.352889 | ||||||||
\(628\) | 18.6054 | 0.742435 | ||||||||
\(629\) | −15.1657 | −0.604697 | ||||||||
\(630\) | 4.87461 | 0.194209 | ||||||||
\(631\) | 7.57350 | 0.301496 | 0.150748 | − | 0.988572i | \(-0.451832\pi\) | ||||
0.150748 | + | 0.988572i | \(0.451832\pi\) | |||||||
\(632\) | −12.6992 | −0.505147 | ||||||||
\(633\) | −69.0513 | −2.74454 | ||||||||
\(634\) | −12.9696 | −0.515088 | ||||||||
\(635\) | −20.0255 | −0.794689 | ||||||||
\(636\) | −55.7270 | −2.20972 | ||||||||
\(637\) | 30.4066 | 1.20475 | ||||||||
\(638\) | −10.2617 | −0.406266 | ||||||||
\(639\) | 19.0031 | 0.751751 | ||||||||
\(640\) | 12.8160 | 0.506597 | ||||||||
\(641\) | 22.7719 | 0.899435 | 0.449717 | − | 0.893171i | \(-0.351525\pi\) | ||||
0.449717 | + | 0.893171i | \(0.351525\pi\) | |||||||
\(642\) | −20.8914 | −0.824519 | ||||||||
\(643\) | −34.1940 | −1.34848 | −0.674240 | − | 0.738512i | \(-0.735529\pi\) | ||||
−0.674240 | + | 0.738512i | \(0.735529\pi\) | |||||||
\(644\) | 7.58954 | 0.299070 | ||||||||
\(645\) | 16.6842 | 0.656939 | ||||||||
\(646\) | 0.498952 | 0.0196310 | ||||||||
\(647\) | 15.5363 | 0.610797 | 0.305398 | − | 0.952225i | \(-0.401210\pi\) | ||||
0.305398 | + | 0.952225i | \(0.401210\pi\) | |||||||
\(648\) | 46.6001 | 1.83062 | ||||||||
\(649\) | −33.5770 | −1.31801 | ||||||||
\(650\) | −9.23237 | −0.362123 | ||||||||
\(651\) | −12.6061 | −0.494073 | ||||||||
\(652\) | −33.9556 | −1.32980 | ||||||||
\(653\) | 23.1091 | 0.904328 | 0.452164 | − | 0.891935i | \(-0.350652\pi\) | ||||
0.452164 | + | 0.891935i | \(0.350652\pi\) | |||||||
\(654\) | 11.0107 | 0.430553 | ||||||||
\(655\) | −20.1899 | −0.788886 | ||||||||
\(656\) | −18.8707 | −0.736777 | ||||||||
\(657\) | 111.500 | 4.35005 | ||||||||
\(658\) | −2.34014 | −0.0912283 | ||||||||
\(659\) | −20.3856 | −0.794111 | −0.397056 | − | 0.917795i | \(-0.629968\pi\) | ||||
−0.397056 | + | 0.917795i | \(0.629968\pi\) | |||||||
\(660\) | −29.6556 | −1.15434 | ||||||||
\(661\) | −40.4678 | −1.57401 | −0.787007 | − | 0.616944i | \(-0.788370\pi\) | ||||
−0.787007 | + | 0.616944i | \(0.788370\pi\) | |||||||
\(662\) | −8.39400 | −0.326242 | ||||||||
\(663\) | −31.2196 | −1.21247 | ||||||||
\(664\) | −29.1302 | −1.13047 | ||||||||
\(665\) | 0.847454 | 0.0328629 | ||||||||
\(666\) | 30.5778 | 1.18487 | ||||||||
\(667\) | 17.9767 | 0.696062 | ||||||||
\(668\) | 26.3418 | 1.01920 | ||||||||
\(669\) | 43.9245 | 1.69822 | ||||||||
\(670\) | −0.684083 | −0.0264284 | ||||||||
\(671\) | −51.8628 | −2.00214 | ||||||||
\(672\) | 18.5924 | 0.717217 | ||||||||
\(673\) | 28.4442 | 1.09644 | 0.548221 | − | 0.836333i | \(-0.315305\pi\) | ||||
0.548221 | + | 0.836333i | \(0.315305\pi\) | |||||||
\(674\) | −8.97250 | −0.345608 | ||||||||
\(675\) | −55.6709 | −2.14277 | ||||||||
\(676\) | −29.8446 | −1.14787 | ||||||||
\(677\) | −19.4502 | −0.747532 | −0.373766 | − | 0.927523i | \(-0.621934\pi\) | ||||
−0.373766 | + | 0.927523i | \(0.621934\pi\) | |||||||
\(678\) | −19.9456 | −0.766007 | ||||||||
\(679\) | 5.98542 | 0.229699 | ||||||||
\(680\) | 3.54937 | 0.136112 | ||||||||
\(681\) | 24.1697 | 0.926184 | ||||||||
\(682\) | −6.59037 | −0.252358 | ||||||||
\(683\) | −5.80487 | −0.222117 | −0.111059 | − | 0.993814i | \(-0.535424\pi\) | ||||
−0.111059 | + | 0.993814i | \(0.535424\pi\) | |||||||
\(684\) | 8.41048 | 0.321583 | ||||||||
\(685\) | −4.62391 | −0.176670 | ||||||||
\(686\) | −6.93178 | −0.264657 | ||||||||
\(687\) | 39.7844 | 1.51787 | ||||||||
\(688\) | 12.2235 | 0.466017 | ||||||||
\(689\) | −52.0921 | −1.98455 | ||||||||
\(690\) | −6.21410 | −0.236567 | ||||||||
\(691\) | 25.7605 | 0.979974 | 0.489987 | − | 0.871730i | \(-0.337001\pi\) | ||||
0.489987 | + | 0.871730i | \(0.337001\pi\) | |||||||
\(692\) | 14.1862 | 0.539280 | ||||||||
\(693\) | −40.1604 | −1.52557 | ||||||||
\(694\) | 10.1581 | 0.385596 | ||||||||
\(695\) | 14.7786 | 0.560584 | ||||||||
\(696\) | 28.8168 | 1.09230 | ||||||||
\(697\) | −11.9823 | −0.453863 | ||||||||
\(698\) | 4.88088 | 0.184744 | ||||||||
\(699\) | −4.68476 | −0.177194 | ||||||||
\(700\) | −7.80385 | −0.294958 | ||||||||
\(701\) | 0.176178 | 0.00665414 | 0.00332707 | − | 0.999994i | \(-0.498941\pi\) | ||||
0.00332707 | + | 0.999994i | \(0.498941\pi\) | |||||||
\(702\) | 38.2754 | 1.44461 | ||||||||
\(703\) | 5.31597 | 0.200495 | ||||||||
\(704\) | −14.6059 | −0.550479 | ||||||||
\(705\) | −16.0186 | −0.603296 | ||||||||
\(706\) | 14.3124 | 0.538654 | ||||||||
\(707\) | 10.0642 | 0.378503 | ||||||||
\(708\) | 44.4847 | 1.67184 | ||||||||
\(709\) | 10.4585 | 0.392778 | 0.196389 | − | 0.980526i | \(-0.437078\pi\) | ||||
0.196389 | + | 0.980526i | \(0.437078\pi\) | |||||||
\(710\) | −1.32622 | −0.0497723 | ||||||||
\(711\) | −55.5382 | −2.08285 | ||||||||
\(712\) | 2.88928 | 0.108280 | ||||||||
\(713\) | 11.5452 | 0.432370 | ||||||||
\(714\) | 3.15649 | 0.118129 | ||||||||
\(715\) | −27.7213 | −1.03672 | ||||||||
\(716\) | −17.9124 | −0.669418 | ||||||||
\(717\) | 7.37687 | 0.275494 | ||||||||
\(718\) | 11.0083 | 0.410825 | ||||||||
\(719\) | −37.8811 | −1.41273 | −0.706364 | − | 0.707849i | \(-0.749666\pi\) | ||||
−0.706364 | + | 0.707849i | \(0.749666\pi\) | |||||||
\(720\) | 24.4463 | 0.911062 | ||||||||
\(721\) | 2.23631 | 0.0832845 | ||||||||
\(722\) | 8.60774 | 0.320347 | ||||||||
\(723\) | 27.9641 | 1.04000 | ||||||||
\(724\) | 26.4049 | 0.981329 | ||||||||
\(725\) | −18.4844 | −0.686492 | ||||||||
\(726\) | −12.6275 | −0.468651 | ||||||||
\(727\) | −0.827571 | −0.0306929 | −0.0153465 | − | 0.999882i | \(-0.504885\pi\) | ||||
−0.0153465 | + | 0.999882i | \(0.504885\pi\) | |||||||
\(728\) | 11.3725 | 0.421494 | ||||||||
\(729\) | 55.0343 | 2.03831 | ||||||||
\(730\) | −7.78161 | −0.288010 | ||||||||
\(731\) | 7.76156 | 0.287072 | ||||||||
\(732\) | 68.7107 | 2.53962 | ||||||||
\(733\) | −1.87867 | −0.0693902 | −0.0346951 | − | 0.999398i | \(-0.511046\pi\) | ||||
−0.0346951 | + | 0.999398i | \(0.511046\pi\) | |||||||
\(734\) | 3.44203 | 0.127048 | ||||||||
\(735\) | −21.0439 | −0.776216 | ||||||||
\(736\) | −17.0276 | −0.627646 | ||||||||
\(737\) | 5.63594 | 0.207603 | ||||||||
\(738\) | 24.1593 | 0.889314 | ||||||||
\(739\) | −7.51194 | −0.276331 | −0.138166 | − | 0.990409i | \(-0.544121\pi\) | ||||
−0.138166 | + | 0.990409i | \(0.544121\pi\) | |||||||
\(740\) | 17.8410 | 0.655846 | ||||||||
\(741\) | 10.9433 | 0.402011 | ||||||||
\(742\) | 5.26682 | 0.193351 | ||||||||
\(743\) | −27.5006 | −1.00890 | −0.504450 | − | 0.863441i | \(-0.668305\pi\) | ||||
−0.504450 | + | 0.863441i | \(0.668305\pi\) | |||||||
\(744\) | 18.5069 | 0.678498 | ||||||||
\(745\) | −18.7957 | −0.688621 | ||||||||
\(746\) | −15.4690 | −0.566359 | ||||||||
\(747\) | −127.397 | −4.66121 | ||||||||
\(748\) | −13.7960 | −0.504430 | ||||||||
\(749\) | −16.5071 | −0.603156 | ||||||||
\(750\) | 15.1079 | 0.551661 | ||||||||
\(751\) | 47.8281 | 1.74527 | 0.872636 | − | 0.488371i | \(-0.162409\pi\) | ||||
0.872636 | + | 0.488371i | \(0.162409\pi\) | |||||||
\(752\) | −11.7359 | −0.427964 | ||||||||
\(753\) | 56.5622 | 2.06124 | ||||||||
\(754\) | 12.7085 | 0.462818 | ||||||||
\(755\) | 2.89950 | 0.105524 | ||||||||
\(756\) | 32.3531 | 1.17667 | ||||||||
\(757\) | −20.2702 | −0.736732 | −0.368366 | − | 0.929681i | \(-0.620083\pi\) | ||||
−0.368366 | + | 0.929681i | \(0.620083\pi\) | |||||||
\(758\) | 8.83727 | 0.320984 | ||||||||
\(759\) | 51.1960 | 1.85830 | ||||||||
\(760\) | −1.24414 | −0.0451298 | ||||||||
\(761\) | 3.13530 | 0.113655 | 0.0568273 | − | 0.998384i | \(-0.481902\pi\) | ||||
0.0568273 | + | 0.998384i | \(0.481902\pi\) | |||||||
\(762\) | 26.1451 | 0.947138 | ||||||||
\(763\) | 8.69998 | 0.314960 | ||||||||
\(764\) | −30.2889 | −1.09581 | ||||||||
\(765\) | 15.5227 | 0.561224 | ||||||||
\(766\) | −6.40384 | −0.231380 | ||||||||
\(767\) | 41.5831 | 1.50148 | ||||||||
\(768\) | 4.93282 | 0.177998 | ||||||||
\(769\) | 4.09365 | 0.147621 | 0.0738104 | − | 0.997272i | \(-0.476484\pi\) | ||||
0.0738104 | + | 0.997272i | \(0.476484\pi\) | |||||||
\(770\) | 2.80279 | 0.101005 | ||||||||
\(771\) | −33.3399 | −1.20071 | ||||||||
\(772\) | −23.6638 | −0.851679 | ||||||||
\(773\) | −41.3716 | −1.48803 | −0.744017 | − | 0.668161i | \(-0.767082\pi\) | ||||
−0.744017 | + | 0.668161i | \(0.767082\pi\) | |||||||
\(774\) | −15.6492 | −0.562499 | ||||||||
\(775\) | −11.8712 | −0.426425 | ||||||||
\(776\) | −8.78715 | −0.315440 | ||||||||
\(777\) | 33.6301 | 1.20647 | ||||||||
\(778\) | −12.7215 | −0.456087 | ||||||||
\(779\) | 4.20010 | 0.150484 | ||||||||
\(780\) | 36.7267 | 1.31503 | ||||||||
\(781\) | 10.9263 | 0.390975 | ||||||||
\(782\) | −2.89083 | −0.103376 | ||||||||
\(783\) | 76.6321 | 2.73861 | ||||||||
\(784\) | −15.4176 | −0.550630 | ||||||||
\(785\) | −12.0366 | −0.429605 | ||||||||
\(786\) | 26.3598 | 0.940222 | ||||||||
\(787\) | −7.19226 | −0.256376 | −0.128188 | − | 0.991750i | \(-0.540916\pi\) | ||||
−0.128188 | + | 0.991750i | \(0.540916\pi\) | |||||||
\(788\) | −36.1245 | −1.28688 | ||||||||
\(789\) | 44.2864 | 1.57664 | ||||||||
\(790\) | 3.87601 | 0.137902 | ||||||||
\(791\) | −15.7598 | −0.560353 | ||||||||
\(792\) | 58.9592 | 2.09502 | ||||||||
\(793\) | 64.2290 | 2.28084 | ||||||||
\(794\) | −9.53664 | −0.338443 | ||||||||
\(795\) | 36.0521 | 1.27864 | ||||||||
\(796\) | −23.0195 | −0.815903 | ||||||||
\(797\) | 25.2489 | 0.894362 | 0.447181 | − | 0.894443i | \(-0.352428\pi\) | ||||
0.447181 | + | 0.894443i | \(0.352428\pi\) | |||||||
\(798\) | −1.10643 | −0.0391671 | ||||||||
\(799\) | −7.45194 | −0.263631 | ||||||||
\(800\) | 17.5084 | 0.619017 | ||||||||
\(801\) | 12.6359 | 0.446467 | ||||||||
\(802\) | 13.8606 | 0.489436 | ||||||||
\(803\) | 64.1102 | 2.26240 | ||||||||
\(804\) | −7.46681 | −0.263334 | ||||||||
\(805\) | −4.90999 | −0.173054 | ||||||||
\(806\) | 8.16177 | 0.287486 | ||||||||
\(807\) | 51.0111 | 1.79568 | ||||||||
\(808\) | −14.7752 | −0.519789 | ||||||||
\(809\) | −8.37431 | −0.294425 | −0.147212 | − | 0.989105i | \(-0.547030\pi\) | ||||
−0.147212 | + | 0.989105i | \(0.547030\pi\) | |||||||
\(810\) | −14.2231 | −0.499750 | ||||||||
\(811\) | 8.34874 | 0.293164 | 0.146582 | − | 0.989199i | \(-0.453173\pi\) | ||||
0.146582 | + | 0.989199i | \(0.453173\pi\) | |||||||
\(812\) | 10.7422 | 0.376976 | ||||||||
\(813\) | −55.4469 | −1.94461 | ||||||||
\(814\) | 17.5815 | 0.616231 | ||||||||
\(815\) | 21.9673 | 0.769480 | ||||||||
\(816\) | 15.8299 | 0.554157 | ||||||||
\(817\) | −2.72062 | −0.0951825 | ||||||||
\(818\) | −2.81381 | −0.0983826 | ||||||||
\(819\) | 49.7362 | 1.73792 | ||||||||
\(820\) | 14.0960 | 0.492253 | ||||||||
\(821\) | 22.5847 | 0.788210 | 0.394105 | − | 0.919065i | \(-0.371055\pi\) | ||||
0.394105 | + | 0.919065i | \(0.371055\pi\) | |||||||
\(822\) | 6.03693 | 0.210562 | ||||||||
\(823\) | −17.6855 | −0.616479 | −0.308239 | − | 0.951309i | \(-0.599740\pi\) | ||||
−0.308239 | + | 0.951309i | \(0.599740\pi\) | |||||||
\(824\) | −3.28311 | −0.114373 | ||||||||
\(825\) | −52.6416 | −1.83275 | ||||||||
\(826\) | −4.20430 | −0.146286 | ||||||||
\(827\) | 1.43859 | 0.0500246 | 0.0250123 | − | 0.999687i | \(-0.492038\pi\) | ||||
0.0250123 | + | 0.999687i | \(0.492038\pi\) | |||||||
\(828\) | −48.7287 | −1.69344 | ||||||||
\(829\) | −8.86981 | −0.308061 | −0.154031 | − | 0.988066i | \(-0.549225\pi\) | ||||
−0.154031 | + | 0.988066i | \(0.549225\pi\) | |||||||
\(830\) | 8.89101 | 0.308612 | ||||||||
\(831\) | 99.4073 | 3.44840 | ||||||||
\(832\) | 18.0885 | 0.627105 | ||||||||
\(833\) | −9.78973 | −0.339194 | ||||||||
\(834\) | −19.2948 | −0.668123 | ||||||||
\(835\) | −17.0416 | −0.589749 | ||||||||
\(836\) | 4.83583 | 0.167251 | ||||||||
\(837\) | 49.2153 | 1.70113 | ||||||||
\(838\) | −14.1003 | −0.487085 | ||||||||
\(839\) | −27.3712 | −0.944957 | −0.472479 | − | 0.881342i | \(-0.656641\pi\) | ||||
−0.472479 | + | 0.881342i | \(0.656641\pi\) | |||||||
\(840\) | −7.87074 | −0.271566 | ||||||||
\(841\) | −3.55591 | −0.122617 | ||||||||
\(842\) | −2.60311 | −0.0897092 | ||||||||
\(843\) | 57.6710 | 1.98629 | ||||||||
\(844\) | 37.7895 | 1.30077 | ||||||||
\(845\) | 19.3077 | 0.664206 | ||||||||
\(846\) | 15.0249 | 0.516567 | ||||||||
\(847\) | −9.97746 | −0.342830 | ||||||||
\(848\) | 26.4133 | 0.907036 | ||||||||
\(849\) | −60.7000 | −2.08322 | ||||||||
\(850\) | 2.97246 | 0.101955 | ||||||||
\(851\) | −30.7997 | −1.05580 | ||||||||
\(852\) | −14.4758 | −0.495934 | ||||||||
\(853\) | 7.83097 | 0.268127 | 0.134064 | − | 0.990973i | \(-0.457197\pi\) | ||||
0.134064 | + | 0.990973i | \(0.457197\pi\) | |||||||
\(854\) | −6.49393 | −0.222218 | ||||||||
\(855\) | −5.44109 | −0.186081 | ||||||||
\(856\) | 24.2340 | 0.828300 | ||||||||
\(857\) | 18.5978 | 0.635288 | 0.317644 | − | 0.948210i | \(-0.397108\pi\) | ||||
0.317644 | + | 0.948210i | \(0.397108\pi\) | |||||||
\(858\) | 36.1927 | 1.23560 | ||||||||
\(859\) | 53.3853 | 1.82148 | 0.910742 | − | 0.412975i | \(-0.135510\pi\) | ||||
0.910742 | + | 0.412975i | \(0.135510\pi\) | |||||||
\(860\) | −9.13070 | −0.311354 | ||||||||
\(861\) | 26.5708 | 0.905532 | ||||||||
\(862\) | −10.4803 | −0.356961 | ||||||||
\(863\) | −7.76573 | −0.264349 | −0.132174 | − | 0.991226i | \(-0.542196\pi\) | ||||
−0.132174 | + | 0.991226i | \(0.542196\pi\) | |||||||
\(864\) | −72.5861 | −2.46943 | ||||||||
\(865\) | −9.17768 | −0.312050 | ||||||||
\(866\) | −13.1519 | −0.446921 | ||||||||
\(867\) | −45.4381 | −1.54316 | ||||||||
\(868\) | 6.89891 | 0.234164 | ||||||||
\(869\) | −31.9332 | −1.08326 | ||||||||
\(870\) | −8.79537 | −0.298191 | ||||||||
\(871\) | −6.97978 | −0.236501 | ||||||||
\(872\) | −12.7724 | −0.432527 | ||||||||
\(873\) | −38.4294 | −1.30064 | ||||||||
\(874\) | 1.01331 | 0.0342757 | ||||||||
\(875\) | 11.9373 | 0.403554 | ||||||||
\(876\) | −84.9367 | −2.86975 | ||||||||
\(877\) | −10.5052 | −0.354735 | −0.177367 | − | 0.984145i | \(-0.556758\pi\) | ||||
−0.177367 | + | 0.984145i | \(0.556758\pi\) | |||||||
\(878\) | 12.1202 | 0.409036 | ||||||||
\(879\) | −0.873934 | −0.0294771 | ||||||||
\(880\) | 14.0561 | 0.473830 | ||||||||
\(881\) | −30.9478 | −1.04266 | −0.521329 | − | 0.853356i | \(-0.674563\pi\) | ||||
−0.521329 | + | 0.853356i | \(0.674563\pi\) | |||||||
\(882\) | 19.7385 | 0.664629 | ||||||||
\(883\) | −38.1189 | −1.28280 | −0.641402 | − | 0.767205i | \(-0.721647\pi\) | ||||
−0.641402 | + | 0.767205i | \(0.721647\pi\) | |||||||
\(884\) | 17.0855 | 0.574647 | ||||||||
\(885\) | −28.7790 | −0.967396 | ||||||||
\(886\) | −8.95240 | −0.300762 | ||||||||
\(887\) | 0.00758081 | 0.000254539 0 | 0.000127269 | − | 1.00000i | \(-0.499959\pi\) | ||||
0.000127269 | 1.00000i | \(0.499959\pi\) | ||||||||
\(888\) | −49.3721 | −1.65682 | ||||||||
\(889\) | 20.6582 | 0.692855 | ||||||||
\(890\) | −0.881857 | −0.0295599 | ||||||||
\(891\) | 117.180 | 3.92567 | ||||||||
\(892\) | −24.0384 | −0.804866 | ||||||||
\(893\) | 2.61209 | 0.0874103 | ||||||||
\(894\) | 24.5395 | 0.820722 | ||||||||
\(895\) | 11.5883 | 0.387354 | ||||||||
\(896\) | −13.2209 | −0.441680 | ||||||||
\(897\) | −63.4031 | −2.11697 | ||||||||
\(898\) | 9.34608 | 0.311883 | ||||||||
\(899\) | 16.3409 | 0.545000 | ||||||||
\(900\) | 50.1047 | 1.67016 | ||||||||
\(901\) | 16.7716 | 0.558744 | ||||||||
\(902\) | 13.8910 | 0.462520 | ||||||||
\(903\) | −17.2113 | −0.572756 | ||||||||
\(904\) | 23.1368 | 0.769519 | ||||||||
\(905\) | −17.0824 | −0.567839 | ||||||||
\(906\) | −3.78556 | −0.125767 | ||||||||
\(907\) | −50.7472 | −1.68503 | −0.842516 | − | 0.538671i | \(-0.818926\pi\) | ||||
−0.842516 | + | 0.538671i | \(0.818926\pi\) | |||||||
\(908\) | −13.2273 | −0.438962 | ||||||||
\(909\) | −64.6172 | −2.14322 | ||||||||
\(910\) | −3.47109 | −0.115065 | ||||||||
\(911\) | 22.5478 | 0.747042 | 0.373521 | − | 0.927622i | \(-0.378150\pi\) | ||||
0.373521 | + | 0.927622i | \(0.378150\pi\) | |||||||
\(912\) | −5.54877 | −0.183738 | ||||||||
\(913\) | −73.2502 | −2.42423 | ||||||||
\(914\) | −8.24326 | −0.272663 | ||||||||
\(915\) | −44.4519 | −1.46953 | ||||||||
\(916\) | −21.7727 | −0.719390 | ||||||||
\(917\) | 20.8278 | 0.687796 | ||||||||
\(918\) | −12.3232 | −0.406725 | ||||||||
\(919\) | −45.2864 | −1.49386 | −0.746930 | − | 0.664902i | \(-0.768473\pi\) | ||||
−0.746930 | + | 0.664902i | \(0.768473\pi\) | |||||||
\(920\) | 7.20832 | 0.237651 | ||||||||
\(921\) | 7.81072 | 0.257372 | ||||||||
\(922\) | 0.469309 | 0.0154559 | ||||||||
\(923\) | −13.5316 | −0.445399 | ||||||||
\(924\) | 30.5926 | 1.00642 | ||||||||
\(925\) | 31.6694 | 1.04128 | ||||||||
\(926\) | 13.1700 | 0.432792 | ||||||||
\(927\) | −14.3582 | −0.471587 | ||||||||
\(928\) | −24.1007 | −0.791144 | ||||||||
\(929\) | −21.8628 | −0.717297 | −0.358648 | − | 0.933473i | \(-0.616762\pi\) | ||||
−0.358648 | + | 0.933473i | \(0.616762\pi\) | |||||||
\(930\) | −5.64863 | −0.185226 | ||||||||
\(931\) | 3.43154 | 0.112464 | ||||||||
\(932\) | 2.56382 | 0.0839806 | ||||||||
\(933\) | −5.68394 | −0.186084 | ||||||||
\(934\) | −11.1581 | −0.365103 | ||||||||
\(935\) | 8.92518 | 0.291885 | ||||||||
\(936\) | −73.0174 | −2.38665 | ||||||||
\(937\) | −50.1531 | −1.63843 | −0.819216 | − | 0.573485i | \(-0.805591\pi\) | ||||
−0.819216 | + | 0.573485i | \(0.805591\pi\) | |||||||
\(938\) | 0.705697 | 0.0230418 | ||||||||
\(939\) | 98.5843 | 3.21718 | ||||||||
\(940\) | 8.76646 | 0.285930 | ||||||||
\(941\) | 20.1369 | 0.656445 | 0.328222 | − | 0.944600i | \(-0.393550\pi\) | ||||
0.328222 | + | 0.944600i | \(0.393550\pi\) | |||||||
\(942\) | 15.7149 | 0.512018 | ||||||||
\(943\) | −24.3346 | −0.792443 | ||||||||
\(944\) | −21.0847 | −0.686249 | ||||||||
\(945\) | −20.9305 | −0.680871 | ||||||||
\(946\) | −8.99792 | −0.292548 | ||||||||
\(947\) | −33.7774 | −1.09762 | −0.548809 | − | 0.835948i | \(-0.684919\pi\) | ||||
−0.548809 | + | 0.835948i | \(0.684919\pi\) | |||||||
\(948\) | 42.3069 | 1.37406 | ||||||||
\(949\) | −79.3966 | −2.57732 | ||||||||
\(950\) | −1.04192 | −0.0338044 | ||||||||
\(951\) | 91.5835 | 2.96980 | ||||||||
\(952\) | −3.66151 | −0.118670 | ||||||||
\(953\) | −15.4539 | −0.500600 | −0.250300 | − | 0.968168i | \(-0.580529\pi\) | ||||
−0.250300 | + | 0.968168i | \(0.580529\pi\) | |||||||
\(954\) | −33.8157 | −1.09482 | ||||||||
\(955\) | 19.5952 | 0.634085 | ||||||||
\(956\) | −4.03712 | −0.130570 | ||||||||
\(957\) | 72.4623 | 2.34237 | ||||||||
\(958\) | −2.67397 | −0.0863921 | ||||||||
\(959\) | 4.77000 | 0.154031 | ||||||||
\(960\) | −12.5187 | −0.404041 | ||||||||
\(961\) | −20.5054 | −0.661465 | ||||||||
\(962\) | −21.7736 | −0.702011 | ||||||||
\(963\) | 105.984 | 3.41529 | ||||||||
\(964\) | −15.3038 | −0.492903 | ||||||||
\(965\) | 15.3091 | 0.492818 | ||||||||
\(966\) | 6.41043 | 0.206252 | ||||||||
\(967\) | −4.78054 | −0.153732 | −0.0768659 | − | 0.997041i | \(-0.524491\pi\) | ||||
−0.0768659 | + | 0.997041i | \(0.524491\pi\) | |||||||
\(968\) | 14.6478 | 0.470799 | ||||||||
\(969\) | −3.52330 | −0.113185 | ||||||||
\(970\) | 2.68199 | 0.0861134 | ||||||||
\(971\) | 36.6685 | 1.17675 | 0.588374 | − | 0.808589i | \(-0.299768\pi\) | ||||
0.588374 | + | 0.808589i | \(0.299768\pi\) | |||||||
\(972\) | −73.8322 | −2.36817 | ||||||||
\(973\) | −15.2455 | −0.488749 | ||||||||
\(974\) | 5.40921 | 0.173322 | ||||||||
\(975\) | 65.1935 | 2.08786 | ||||||||
\(976\) | −32.5673 | −1.04245 | ||||||||
\(977\) | −39.0452 | −1.24917 | −0.624583 | − | 0.780958i | \(-0.714731\pi\) | ||||
−0.624583 | + | 0.780958i | \(0.714731\pi\) | |||||||
\(978\) | −28.6802 | −0.917093 | ||||||||
\(979\) | 7.26534 | 0.232201 | ||||||||
\(980\) | 11.5166 | 0.367885 | ||||||||
\(981\) | −55.8583 | −1.78342 | ||||||||
\(982\) | 3.78318 | 0.120726 | ||||||||
\(983\) | −51.2714 | −1.63530 | −0.817652 | − | 0.575712i | \(-0.804725\pi\) | ||||
−0.817652 | + | 0.575712i | \(0.804725\pi\) | |||||||
\(984\) | −39.0085 | −1.24354 | ||||||||
\(985\) | 23.3704 | 0.744644 | ||||||||
\(986\) | −4.09165 | −0.130305 | ||||||||
\(987\) | 16.5247 | 0.525987 | ||||||||
\(988\) | −5.98888 | −0.190532 | ||||||||
\(989\) | 15.7628 | 0.501227 | ||||||||
\(990\) | −17.9953 | −0.571929 | ||||||||
\(991\) | 41.3736 | 1.31428 | 0.657138 | − | 0.753770i | \(-0.271767\pi\) | ||||
0.657138 | + | 0.753770i | \(0.271767\pi\) | |||||||
\(992\) | −15.4781 | −0.491431 | ||||||||
\(993\) | 59.2734 | 1.88099 | ||||||||
\(994\) | 1.36813 | 0.0433943 | ||||||||
\(995\) | 14.8923 | 0.472116 | ||||||||
\(996\) | 97.0460 | 3.07502 | ||||||||
\(997\) | 20.3663 | 0.645008 | 0.322504 | − | 0.946568i | \(-0.395475\pi\) | ||||
0.322504 | + | 0.946568i | \(0.395475\pi\) | |||||||
\(998\) | 15.3109 | 0.484659 | ||||||||
\(999\) | −131.294 | −4.15397 |
(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 | 503.2.a.f.1.10 | ✓ | 26 | |
3.2 | odd | 2 | 4527.2.a.o.1.17 | 26 | |||
4.3 | odd | 2 | 8048.2.a.u.1.2 | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.f.1.10 | ✓ | 26 | 1.1 | even | 1 | trivial | |
4527.2.a.o.1.17 | 26 | 3.2 | odd | 2 | |||
8048.2.a.u.1.2 | 26 | 4.3 | odd | 2 |