Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.99568 | −1.41116 | −0.705581 | − | 0.708629i | \(-0.749314\pi\) | ||||
−0.705581 | + | 0.708629i | \(0.749314\pi\) | |||||||
\(3\) | 2.01372 | 1.16262 | 0.581311 | − | 0.813682i | \(-0.302540\pi\) | ||||
0.581311 | + | 0.813682i | \(0.302540\pi\) | |||||||
\(4\) | 1.98276 | 0.991378 | ||||||||
\(5\) | 2.98897 | 1.33671 | 0.668354 | − | 0.743843i | \(-0.266999\pi\) | ||||
0.668354 | + | 0.743843i | \(0.266999\pi\) | |||||||
\(6\) | −4.01875 | −1.64065 | ||||||||
\(7\) | −3.65858 | −1.38281 | −0.691406 | − | 0.722466i | \(-0.743009\pi\) | ||||
−0.691406 | + | 0.722466i | \(0.743009\pi\) | |||||||
\(8\) | 0.0344145 | 0.0121674 | ||||||||
\(9\) | 1.05506 | 0.351688 | ||||||||
\(10\) | −5.96504 | −1.88631 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 3.99271 | 1.15260 | ||||||||
\(13\) | −6.84703 | −1.89902 | −0.949512 | − | 0.313729i | \(-0.898422\pi\) | ||||
−0.949512 | + | 0.313729i | \(0.898422\pi\) | |||||||
\(14\) | 7.30137 | 1.95137 | ||||||||
\(15\) | 6.01894 | 1.55408 | ||||||||
\(16\) | −4.03419 | −1.00855 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.10557 | −0.496288 | ||||||||
\(19\) | −3.07074 | −0.704477 | −0.352238 | − | 0.935910i | \(-0.614579\pi\) | ||||
−0.352238 | + | 0.935910i | \(0.614579\pi\) | |||||||
\(20\) | 5.92640 | 1.32518 | ||||||||
\(21\) | −7.36735 | −1.60769 | ||||||||
\(22\) | −1.99568 | −0.425481 | ||||||||
\(23\) | −5.38280 | −1.12239 | −0.561196 | − | 0.827683i | \(-0.689659\pi\) | ||||
−0.561196 | + | 0.827683i | \(0.689659\pi\) | |||||||
\(24\) | 0.0693010 | 0.0141460 | ||||||||
\(25\) | 3.93394 | 0.786788 | ||||||||
\(26\) | 13.6645 | 2.67983 | ||||||||
\(27\) | −3.91656 | −0.753742 | ||||||||
\(28\) | −7.25407 | −1.37089 | ||||||||
\(29\) | 1.49706 | 0.277997 | 0.138998 | − | 0.990293i | \(-0.455612\pi\) | ||||
0.138998 | + | 0.990293i | \(0.455612\pi\) | |||||||
\(30\) | −12.0119 | −2.19306 | ||||||||
\(31\) | 6.38953 | 1.14759 | 0.573797 | − | 0.818998i | \(-0.305470\pi\) | ||||
0.573797 | + | 0.818998i | \(0.305470\pi\) | |||||||
\(32\) | 7.98214 | 1.41106 | ||||||||
\(33\) | 2.01372 | 0.350543 | ||||||||
\(34\) | −1.99568 | −0.342257 | ||||||||
\(35\) | −10.9354 | −1.84842 | ||||||||
\(36\) | 2.09193 | 0.348655 | ||||||||
\(37\) | −0.850029 | −0.139744 | −0.0698720 | − | 0.997556i | \(-0.522259\pi\) | ||||
−0.0698720 | + | 0.997556i | \(0.522259\pi\) | |||||||
\(38\) | 6.12823 | 0.994130 | ||||||||
\(39\) | −13.7880 | −2.20785 | ||||||||
\(40\) | 0.102864 | 0.0162642 | ||||||||
\(41\) | −2.35309 | −0.367490 | −0.183745 | − | 0.982974i | \(-0.558822\pi\) | ||||
−0.183745 | + | 0.982974i | \(0.558822\pi\) | |||||||
\(42\) | 14.7029 | 2.26871 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 1.98276 | 0.298912 | ||||||||
\(45\) | 3.15355 | 0.470104 | ||||||||
\(46\) | 10.7424 | 1.58388 | ||||||||
\(47\) | 2.66712 | 0.389039 | 0.194520 | − | 0.980899i | \(-0.437685\pi\) | ||||
0.194520 | + | 0.980899i | \(0.437685\pi\) | |||||||
\(48\) | −8.12373 | −1.17256 | ||||||||
\(49\) | 6.38520 | 0.912171 | ||||||||
\(50\) | −7.85090 | −1.11028 | ||||||||
\(51\) | 2.01372 | 0.281977 | ||||||||
\(52\) | −13.5760 | −1.88265 | ||||||||
\(53\) | 0.780277 | 0.107179 | 0.0535896 | − | 0.998563i | \(-0.482934\pi\) | ||||
0.0535896 | + | 0.998563i | \(0.482934\pi\) | |||||||
\(54\) | 7.81621 | 1.06365 | ||||||||
\(55\) | 2.98897 | 0.403033 | ||||||||
\(56\) | −0.125908 | −0.0168252 | ||||||||
\(57\) | −6.18361 | −0.819039 | ||||||||
\(58\) | −2.98765 | −0.392298 | ||||||||
\(59\) | 8.77764 | 1.14275 | 0.571376 | − | 0.820689i | \(-0.306410\pi\) | ||||
0.571376 | + | 0.820689i | \(0.306410\pi\) | |||||||
\(60\) | 11.9341 | 1.54068 | ||||||||
\(61\) | 6.61552 | 0.847031 | 0.423515 | − | 0.905889i | \(-0.360796\pi\) | ||||
0.423515 | + | 0.905889i | \(0.360796\pi\) | |||||||
\(62\) | −12.7515 | −1.61944 | ||||||||
\(63\) | −3.86003 | −0.486318 | ||||||||
\(64\) | −7.86145 | −0.982682 | ||||||||
\(65\) | −20.4656 | −2.53844 | ||||||||
\(66\) | −4.01875 | −0.494674 | ||||||||
\(67\) | 5.23002 | 0.638948 | 0.319474 | − | 0.947595i | \(-0.396494\pi\) | ||||
0.319474 | + | 0.947595i | \(0.396494\pi\) | |||||||
\(68\) | 1.98276 | 0.240444 | ||||||||
\(69\) | −10.8395 | −1.30492 | ||||||||
\(70\) | 21.8236 | 2.60841 | ||||||||
\(71\) | −0.390257 | −0.0463150 | −0.0231575 | − | 0.999732i | \(-0.507372\pi\) | ||||
−0.0231575 | + | 0.999732i | \(0.507372\pi\) | |||||||
\(72\) | 0.0363094 | 0.00427911 | ||||||||
\(73\) | 4.83248 | 0.565599 | 0.282799 | − | 0.959179i | \(-0.408737\pi\) | ||||
0.282799 | + | 0.959179i | \(0.408737\pi\) | |||||||
\(74\) | 1.69639 | 0.197201 | ||||||||
\(75\) | 7.92184 | 0.914736 | ||||||||
\(76\) | −6.08853 | −0.698402 | ||||||||
\(77\) | −3.65858 | −0.416934 | ||||||||
\(78\) | 27.5165 | 3.11563 | ||||||||
\(79\) | 11.9195 | 1.34104 | 0.670522 | − | 0.741890i | \(-0.266070\pi\) | ||||
0.670522 | + | 0.741890i | \(0.266070\pi\) | |||||||
\(80\) | −12.0581 | −1.34813 | ||||||||
\(81\) | −11.0520 | −1.22800 | ||||||||
\(82\) | 4.69602 | 0.518588 | ||||||||
\(83\) | −1.62949 | −0.178860 | −0.0894300 | − | 0.995993i | \(-0.528505\pi\) | ||||
−0.0894300 | + | 0.995993i | \(0.528505\pi\) | |||||||
\(84\) | −14.6076 | −1.59383 | ||||||||
\(85\) | 2.98897 | 0.324199 | ||||||||
\(86\) | −1.99568 | −0.215200 | ||||||||
\(87\) | 3.01465 | 0.323205 | ||||||||
\(88\) | 0.0344145 | 0.00366859 | ||||||||
\(89\) | 5.39227 | 0.571579 | 0.285790 | − | 0.958292i | \(-0.407744\pi\) | ||||
0.285790 | + | 0.958292i | \(0.407744\pi\) | |||||||
\(90\) | −6.29349 | −0.663392 | ||||||||
\(91\) | 25.0504 | 2.62600 | ||||||||
\(92\) | −10.6728 | −1.11271 | ||||||||
\(93\) | 12.8667 | 1.33422 | ||||||||
\(94\) | −5.32273 | −0.548997 | ||||||||
\(95\) | −9.17835 | −0.941679 | ||||||||
\(96\) | 16.0738 | 1.64052 | ||||||||
\(97\) | 1.69533 | 0.172134 | 0.0860671 | − | 0.996289i | \(-0.472570\pi\) | ||||
0.0860671 | + | 0.996289i | \(0.472570\pi\) | |||||||
\(98\) | −12.7428 | −1.28722 | ||||||||
\(99\) | 1.05506 | 0.106038 | ||||||||
\(100\) | 7.80004 | 0.780004 | ||||||||
\(101\) | 12.2693 | 1.22084 | 0.610418 | − | 0.792079i | \(-0.291001\pi\) | ||||
0.610418 | + | 0.792079i | \(0.291001\pi\) | |||||||
\(102\) | −4.01875 | −0.397915 | ||||||||
\(103\) | 12.0081 | 1.18319 | 0.591597 | − | 0.806234i | \(-0.298498\pi\) | ||||
0.591597 | + | 0.806234i | \(0.298498\pi\) | |||||||
\(104\) | −0.235637 | −0.0231061 | ||||||||
\(105\) | −22.0208 | −2.14901 | ||||||||
\(106\) | −1.55719 | −0.151247 | ||||||||
\(107\) | −14.7131 | −1.42237 | −0.711183 | − | 0.703007i | \(-0.751840\pi\) | ||||
−0.711183 | + | 0.703007i | \(0.751840\pi\) | |||||||
\(108\) | −7.76557 | −0.747243 | ||||||||
\(109\) | 2.41804 | 0.231606 | 0.115803 | − | 0.993272i | \(-0.463056\pi\) | ||||
0.115803 | + | 0.993272i | \(0.463056\pi\) | |||||||
\(110\) | −5.96504 | −0.568744 | ||||||||
\(111\) | −1.71172 | −0.162469 | ||||||||
\(112\) | 14.7594 | 1.39463 | ||||||||
\(113\) | 17.9932 | 1.69265 | 0.846327 | − | 0.532663i | \(-0.178809\pi\) | ||||
0.846327 | + | 0.532663i | \(0.178809\pi\) | |||||||
\(114\) | 12.3405 | 1.15580 | ||||||||
\(115\) | −16.0890 | −1.50031 | ||||||||
\(116\) | 2.96830 | 0.275600 | ||||||||
\(117\) | −7.22405 | −0.667864 | ||||||||
\(118\) | −17.5174 | −1.61261 | ||||||||
\(119\) | −3.65858 | −0.335381 | ||||||||
\(120\) | 0.207139 | 0.0189091 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −13.2025 | −1.19530 | ||||||||
\(123\) | −4.73845 | −0.427252 | ||||||||
\(124\) | 12.6689 | 1.13770 | ||||||||
\(125\) | −3.18643 | −0.285003 | ||||||||
\(126\) | 7.70340 | 0.686273 | ||||||||
\(127\) | 8.43518 | 0.748501 | 0.374251 | − | 0.927328i | \(-0.377900\pi\) | ||||
0.374251 | + | 0.927328i | \(0.377900\pi\) | |||||||
\(128\) | −0.275305 | −0.0243338 | ||||||||
\(129\) | 2.01372 | 0.177298 | ||||||||
\(130\) | 40.8428 | 3.58215 | ||||||||
\(131\) | −0.202841 | −0.0177223 | −0.00886117 | − | 0.999961i | \(-0.502821\pi\) | ||||
−0.00886117 | + | 0.999961i | \(0.502821\pi\) | |||||||
\(132\) | 3.99271 | 0.347521 | ||||||||
\(133\) | 11.2346 | 0.974159 | ||||||||
\(134\) | −10.4375 | −0.901659 | ||||||||
\(135\) | −11.7065 | −1.00753 | ||||||||
\(136\) | 0.0344145 | 0.00295102 | ||||||||
\(137\) | 4.28062 | 0.365718 | 0.182859 | − | 0.983139i | \(-0.441465\pi\) | ||||
0.182859 | + | 0.983139i | \(0.441465\pi\) | |||||||
\(138\) | 21.6321 | 1.84145 | ||||||||
\(139\) | 0.0540394 | 0.00458356 | 0.00229178 | − | 0.999997i | \(-0.499271\pi\) | ||||
0.00229178 | + | 0.999997i | \(0.499271\pi\) | |||||||
\(140\) | −21.6822 | −1.83248 | ||||||||
\(141\) | 5.37083 | 0.452305 | ||||||||
\(142\) | 0.778831 | 0.0653580 | ||||||||
\(143\) | −6.84703 | −0.572578 | ||||||||
\(144\) | −4.25633 | −0.354694 | ||||||||
\(145\) | 4.47466 | 0.371600 | ||||||||
\(146\) | −9.64410 | −0.798151 | ||||||||
\(147\) | 12.8580 | 1.06051 | ||||||||
\(148\) | −1.68540 | −0.138539 | ||||||||
\(149\) | −1.26485 | −0.103620 | −0.0518101 | − | 0.998657i | \(-0.516499\pi\) | ||||
−0.0518101 | + | 0.998657i | \(0.516499\pi\) | |||||||
\(150\) | −15.8095 | −1.29084 | ||||||||
\(151\) | −6.21522 | −0.505787 | −0.252894 | − | 0.967494i | \(-0.581382\pi\) | ||||
−0.252894 | + | 0.967494i | \(0.581382\pi\) | |||||||
\(152\) | −0.105678 | −0.00857161 | ||||||||
\(153\) | 1.05506 | 0.0852968 | ||||||||
\(154\) | 7.30137 | 0.588361 | ||||||||
\(155\) | 19.0981 | 1.53400 | ||||||||
\(156\) | −27.3382 | −2.18881 | ||||||||
\(157\) | −3.37072 | −0.269013 | −0.134507 | − | 0.990913i | \(-0.542945\pi\) | ||||
−0.134507 | + | 0.990913i | \(0.542945\pi\) | |||||||
\(158\) | −23.7875 | −1.89243 | ||||||||
\(159\) | 1.57126 | 0.124609 | ||||||||
\(160\) | 23.8584 | 1.88617 | ||||||||
\(161\) | 19.6934 | 1.55206 | ||||||||
\(162\) | 22.0564 | 1.73291 | ||||||||
\(163\) | 3.40983 | 0.267079 | 0.133539 | − | 0.991044i | \(-0.457366\pi\) | ||||
0.133539 | + | 0.991044i | \(0.457366\pi\) | |||||||
\(164\) | −4.66559 | −0.364322 | ||||||||
\(165\) | 6.01894 | 0.468574 | ||||||||
\(166\) | 3.25195 | 0.252400 | ||||||||
\(167\) | 9.66139 | 0.747621 | 0.373810 | − | 0.927505i | \(-0.378051\pi\) | ||||
0.373810 | + | 0.927505i | \(0.378051\pi\) | |||||||
\(168\) | −0.253543 | −0.0195613 | ||||||||
\(169\) | 33.8818 | 2.60630 | ||||||||
\(170\) | −5.96504 | −0.457498 | ||||||||
\(171\) | −3.23983 | −0.247756 | ||||||||
\(172\) | 1.98276 | 0.151184 | ||||||||
\(173\) | −16.1204 | −1.22561 | −0.612807 | − | 0.790233i | \(-0.709960\pi\) | ||||
−0.612807 | + | 0.790233i | \(0.709960\pi\) | |||||||
\(174\) | −6.01629 | −0.456094 | ||||||||
\(175\) | −14.3926 | −1.08798 | ||||||||
\(176\) | −4.03419 | −0.304089 | ||||||||
\(177\) | 17.6757 | 1.32859 | ||||||||
\(178\) | −10.7613 | −0.806591 | ||||||||
\(179\) | 24.4422 | 1.82690 | 0.913450 | − | 0.406952i | \(-0.133408\pi\) | ||||
0.913450 | + | 0.406952i | \(0.133408\pi\) | |||||||
\(180\) | 6.25272 | 0.466050 | ||||||||
\(181\) | 19.2481 | 1.43070 | 0.715351 | − | 0.698765i | \(-0.246267\pi\) | ||||
0.715351 | + | 0.698765i | \(0.246267\pi\) | |||||||
\(182\) | −49.9927 | −3.70570 | ||||||||
\(183\) | 13.3218 | 0.984776 | ||||||||
\(184\) | −0.185246 | −0.0136565 | ||||||||
\(185\) | −2.54071 | −0.186797 | ||||||||
\(186\) | −25.6779 | −1.88279 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 5.28824 | 0.385685 | ||||||||
\(189\) | 14.3290 | 1.04228 | ||||||||
\(190\) | 18.3171 | 1.32886 | ||||||||
\(191\) | −5.69075 | −0.411768 | −0.205884 | − | 0.978576i | \(-0.566007\pi\) | ||||
−0.205884 | + | 0.978576i | \(0.566007\pi\) | |||||||
\(192\) | −15.8308 | −1.14249 | ||||||||
\(193\) | −21.2835 | −1.53202 | −0.766011 | − | 0.642828i | \(-0.777761\pi\) | ||||
−0.766011 | + | 0.642828i | \(0.777761\pi\) | |||||||
\(194\) | −3.38334 | −0.242909 | ||||||||
\(195\) | −41.2119 | −2.95125 | ||||||||
\(196\) | 12.6603 | 0.904306 | ||||||||
\(197\) | 19.3181 | 1.37636 | 0.688180 | − | 0.725540i | \(-0.258410\pi\) | ||||
0.688180 | + | 0.725540i | \(0.258410\pi\) | |||||||
\(198\) | −2.10557 | −0.149636 | ||||||||
\(199\) | 2.36371 | 0.167559 | 0.0837795 | − | 0.996484i | \(-0.473301\pi\) | ||||
0.0837795 | + | 0.996484i | \(0.473301\pi\) | |||||||
\(200\) | 0.135384 | 0.00957312 | ||||||||
\(201\) | 10.5318 | 0.742855 | ||||||||
\(202\) | −24.4855 | −1.72280 | ||||||||
\(203\) | −5.47710 | −0.384417 | ||||||||
\(204\) | 3.99271 | 0.279546 | ||||||||
\(205\) | −7.03330 | −0.491227 | ||||||||
\(206\) | −23.9644 | −1.66968 | ||||||||
\(207\) | −5.67920 | −0.394731 | ||||||||
\(208\) | 27.6222 | 1.91526 | ||||||||
\(209\) | −3.07074 | −0.212408 | ||||||||
\(210\) | 43.9465 | 3.03260 | ||||||||
\(211\) | 21.7421 | 1.49679 | 0.748394 | − | 0.663254i | \(-0.230825\pi\) | ||||
0.748394 | + | 0.663254i | \(0.230825\pi\) | |||||||
\(212\) | 1.54710 | 0.106255 | ||||||||
\(213\) | −0.785869 | −0.0538468 | ||||||||
\(214\) | 29.3627 | 2.00719 | ||||||||
\(215\) | 2.98897 | 0.203846 | ||||||||
\(216\) | −0.134786 | −0.00917104 | ||||||||
\(217\) | −23.3766 | −1.58691 | ||||||||
\(218\) | −4.82564 | −0.326834 | ||||||||
\(219\) | 9.73125 | 0.657577 | ||||||||
\(220\) | 5.92640 | 0.399558 | ||||||||
\(221\) | −6.84703 | −0.460581 | ||||||||
\(222\) | 3.41605 | 0.229270 | ||||||||
\(223\) | 17.2298 | 1.15379 | 0.576896 | − | 0.816818i | \(-0.304264\pi\) | ||||
0.576896 | + | 0.816818i | \(0.304264\pi\) | |||||||
\(224\) | −29.2033 | −1.95123 | ||||||||
\(225\) | 4.15055 | 0.276703 | ||||||||
\(226\) | −35.9087 | −2.38861 | ||||||||
\(227\) | −20.7921 | −1.38002 | −0.690009 | − | 0.723800i | \(-0.742394\pi\) | ||||
−0.690009 | + | 0.723800i | \(0.742394\pi\) | |||||||
\(228\) | −12.2606 | −0.811977 | ||||||||
\(229\) | 18.1741 | 1.20098 | 0.600491 | − | 0.799632i | \(-0.294972\pi\) | ||||
0.600491 | + | 0.799632i | \(0.294972\pi\) | |||||||
\(230\) | 32.1086 | 2.11718 | ||||||||
\(231\) | −7.36735 | −0.484736 | ||||||||
\(232\) | 0.0515204 | 0.00338248 | ||||||||
\(233\) | 4.54643 | 0.297847 | 0.148923 | − | 0.988849i | \(-0.452419\pi\) | ||||
0.148923 | + | 0.988849i | \(0.452419\pi\) | |||||||
\(234\) | 14.4169 | 0.942463 | ||||||||
\(235\) | 7.97194 | 0.520032 | ||||||||
\(236\) | 17.4039 | 1.13290 | ||||||||
\(237\) | 24.0024 | 1.55913 | ||||||||
\(238\) | 7.30137 | 0.473277 | ||||||||
\(239\) | −6.12210 | −0.396006 | −0.198003 | − | 0.980201i | \(-0.563446\pi\) | ||||
−0.198003 | + | 0.980201i | \(0.563446\pi\) | |||||||
\(240\) | −24.2816 | −1.56737 | ||||||||
\(241\) | −29.8222 | −1.92102 | −0.960509 | − | 0.278249i | \(-0.910246\pi\) | ||||
−0.960509 | + | 0.278249i | \(0.910246\pi\) | |||||||
\(242\) | −1.99568 | −0.128287 | ||||||||
\(243\) | −10.5060 | −0.673961 | ||||||||
\(244\) | 13.1170 | 0.839727 | ||||||||
\(245\) | 19.0852 | 1.21931 | ||||||||
\(246\) | 9.45646 | 0.602922 | ||||||||
\(247\) | 21.0255 | 1.33782 | ||||||||
\(248\) | 0.219892 | 0.0139632 | ||||||||
\(249\) | −3.28134 | −0.207946 | ||||||||
\(250\) | 6.35910 | 0.402185 | ||||||||
\(251\) | 15.4748 | 0.976759 | 0.488380 | − | 0.872631i | \(-0.337588\pi\) | ||||
0.488380 | + | 0.872631i | \(0.337588\pi\) | |||||||
\(252\) | −7.65350 | −0.482125 | ||||||||
\(253\) | −5.38280 | −0.338414 | ||||||||
\(254\) | −16.8340 | −1.05626 | ||||||||
\(255\) | 6.01894 | 0.376921 | ||||||||
\(256\) | 16.2723 | 1.01702 | ||||||||
\(257\) | 0.895769 | 0.0558766 | 0.0279383 | − | 0.999610i | \(-0.491106\pi\) | ||||
0.0279383 | + | 0.999610i | \(0.491106\pi\) | |||||||
\(258\) | −4.01875 | −0.250196 | ||||||||
\(259\) | 3.10990 | 0.193240 | ||||||||
\(260\) | −40.5782 | −2.51655 | ||||||||
\(261\) | 1.57949 | 0.0977680 | ||||||||
\(262\) | 0.404807 | 0.0250091 | ||||||||
\(263\) | 16.3127 | 1.00589 | 0.502944 | − | 0.864319i | \(-0.332250\pi\) | ||||
0.502944 | + | 0.864319i | \(0.332250\pi\) | |||||||
\(264\) | 0.0693010 | 0.00426518 | ||||||||
\(265\) | 2.33222 | 0.143267 | ||||||||
\(266\) | −22.4206 | −1.37470 | ||||||||
\(267\) | 10.8585 | 0.664530 | ||||||||
\(268\) | 10.3698 | 0.633439 | ||||||||
\(269\) | −2.44411 | −0.149020 | −0.0745101 | − | 0.997220i | \(-0.523739\pi\) | ||||
−0.0745101 | + | 0.997220i | \(0.523739\pi\) | |||||||
\(270\) | 23.3624 | 1.42179 | ||||||||
\(271\) | −6.60008 | −0.400926 | −0.200463 | − | 0.979701i | \(-0.564245\pi\) | ||||
−0.200463 | + | 0.979701i | \(0.564245\pi\) | |||||||
\(272\) | −4.03419 | −0.244609 | ||||||||
\(273\) | 50.4445 | 3.05304 | ||||||||
\(274\) | −8.54277 | −0.516088 | ||||||||
\(275\) | 3.93394 | 0.237225 | ||||||||
\(276\) | −21.4920 | −1.29367 | ||||||||
\(277\) | 14.3396 | 0.861582 | 0.430791 | − | 0.902452i | \(-0.358235\pi\) | ||||
0.430791 | + | 0.902452i | \(0.358235\pi\) | |||||||
\(278\) | −0.107846 | −0.00646815 | ||||||||
\(279\) | 6.74135 | 0.403594 | ||||||||
\(280\) | −0.376335 | −0.0224903 | ||||||||
\(281\) | 5.10183 | 0.304350 | 0.152175 | − | 0.988354i | \(-0.451372\pi\) | ||||
0.152175 | + | 0.988354i | \(0.451372\pi\) | |||||||
\(282\) | −10.7185 | −0.638276 | ||||||||
\(283\) | 8.14402 | 0.484112 | 0.242056 | − | 0.970262i | \(-0.422178\pi\) | ||||
0.242056 | + | 0.970262i | \(0.422178\pi\) | |||||||
\(284\) | −0.773785 | −0.0459157 | ||||||||
\(285\) | −18.4826 | −1.09482 | ||||||||
\(286\) | 13.6645 | 0.808000 | ||||||||
\(287\) | 8.60895 | 0.508170 | ||||||||
\(288\) | 8.42166 | 0.496251 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −8.93001 | −0.524388 | ||||||||
\(291\) | 3.41391 | 0.200127 | ||||||||
\(292\) | 9.58162 | 0.560722 | ||||||||
\(293\) | −5.66645 | −0.331037 | −0.165519 | − | 0.986207i | \(-0.552930\pi\) | ||||
−0.165519 | + | 0.986207i | \(0.552930\pi\) | |||||||
\(294\) | −25.6605 | −1.49655 | ||||||||
\(295\) | 26.2361 | 1.52752 | ||||||||
\(296\) | −0.0292533 | −0.00170031 | ||||||||
\(297\) | −3.91656 | −0.227262 | ||||||||
\(298\) | 2.52423 | 0.146225 | ||||||||
\(299\) | 36.8562 | 2.13145 | ||||||||
\(300\) | 15.7071 | 0.906849 | ||||||||
\(301\) | −3.65858 | −0.210877 | ||||||||
\(302\) | 12.4036 | 0.713748 | ||||||||
\(303\) | 24.7068 | 1.41937 | ||||||||
\(304\) | 12.3880 | 0.710498 | ||||||||
\(305\) | 19.7736 | 1.13223 | ||||||||
\(306\) | −2.10557 | −0.120368 | ||||||||
\(307\) | 18.1046 | 1.03329 | 0.516643 | − | 0.856201i | \(-0.327182\pi\) | ||||
0.516643 | + | 0.856201i | \(0.327182\pi\) | |||||||
\(308\) | −7.25407 | −0.413339 | ||||||||
\(309\) | 24.1810 | 1.37561 | ||||||||
\(310\) | −38.1138 | −2.16472 | ||||||||
\(311\) | −26.3232 | −1.49265 | −0.746326 | − | 0.665580i | \(-0.768184\pi\) | ||||
−0.746326 | + | 0.665580i | \(0.768184\pi\) | |||||||
\(312\) | −0.474506 | −0.0268636 | ||||||||
\(313\) | −8.08672 | −0.457088 | −0.228544 | − | 0.973534i | \(-0.573397\pi\) | ||||
−0.228544 | + | 0.973534i | \(0.573397\pi\) | |||||||
\(314\) | 6.72690 | 0.379621 | ||||||||
\(315\) | −11.5375 | −0.650065 | ||||||||
\(316\) | 23.6334 | 1.32948 | ||||||||
\(317\) | 19.6879 | 1.10578 | 0.552890 | − | 0.833254i | \(-0.313525\pi\) | ||||
0.552890 | + | 0.833254i | \(0.313525\pi\) | |||||||
\(318\) | −3.13573 | −0.175843 | ||||||||
\(319\) | 1.49706 | 0.0838191 | ||||||||
\(320\) | −23.4976 | −1.31356 | ||||||||
\(321\) | −29.6280 | −1.65367 | ||||||||
\(322\) | −39.3018 | −2.19020 | ||||||||
\(323\) | −3.07074 | −0.170861 | ||||||||
\(324\) | −21.9135 | −1.21742 | ||||||||
\(325\) | −26.9358 | −1.49413 | ||||||||
\(326\) | −6.80495 | −0.376891 | ||||||||
\(327\) | 4.86925 | 0.269270 | ||||||||
\(328\) | −0.0809802 | −0.00447138 | ||||||||
\(329\) | −9.75786 | −0.537968 | ||||||||
\(330\) | −12.0119 | −0.661234 | ||||||||
\(331\) | 31.8317 | 1.74963 | 0.874813 | − | 0.484460i | \(-0.160984\pi\) | ||||
0.874813 | + | 0.484460i | \(0.160984\pi\) | |||||||
\(332\) | −3.23088 | −0.177318 | ||||||||
\(333\) | −0.896834 | −0.0491462 | ||||||||
\(334\) | −19.2811 | −1.05501 | ||||||||
\(335\) | 15.6324 | 0.854087 | ||||||||
\(336\) | 29.7213 | 1.62143 | ||||||||
\(337\) | −10.4485 | −0.569165 | −0.284583 | − | 0.958652i | \(-0.591855\pi\) | ||||
−0.284583 | + | 0.958652i | \(0.591855\pi\) | |||||||
\(338\) | −67.6175 | −3.67790 | ||||||||
\(339\) | 36.2332 | 1.96792 | ||||||||
\(340\) | 5.92640 | 0.321404 | ||||||||
\(341\) | 6.38953 | 0.346012 | ||||||||
\(342\) | 6.46567 | 0.349623 | ||||||||
\(343\) | 2.24931 | 0.121451 | ||||||||
\(344\) | 0.0344145 | 0.00185550 | ||||||||
\(345\) | −32.3988 | −1.74429 | ||||||||
\(346\) | 32.1713 | 1.72954 | ||||||||
\(347\) | −9.04774 | −0.485708 | −0.242854 | − | 0.970063i | \(-0.578084\pi\) | ||||
−0.242854 | + | 0.970063i | \(0.578084\pi\) | |||||||
\(348\) | 5.97732 | 0.320418 | ||||||||
\(349\) | 14.9812 | 0.801925 | 0.400962 | − | 0.916095i | \(-0.368676\pi\) | ||||
0.400962 | + | 0.916095i | \(0.368676\pi\) | |||||||
\(350\) | 28.7231 | 1.53532 | ||||||||
\(351\) | 26.8168 | 1.43137 | ||||||||
\(352\) | 7.98214 | 0.425450 | ||||||||
\(353\) | −1.94042 | −0.103278 | −0.0516391 | − | 0.998666i | \(-0.516445\pi\) | ||||
−0.0516391 | + | 0.998666i | \(0.516445\pi\) | |||||||
\(354\) | −35.2751 | −1.87485 | ||||||||
\(355\) | −1.16647 | −0.0619097 | ||||||||
\(356\) | 10.6916 | 0.566651 | ||||||||
\(357\) | −7.36735 | −0.389921 | ||||||||
\(358\) | −48.7790 | −2.57805 | ||||||||
\(359\) | 0.545541 | 0.0287926 | 0.0143963 | − | 0.999896i | \(-0.495417\pi\) | ||||
0.0143963 | + | 0.999896i | \(0.495417\pi\) | |||||||
\(360\) | 0.108528 | 0.00571991 | ||||||||
\(361\) | −9.57054 | −0.503713 | ||||||||
\(362\) | −38.4132 | −2.01895 | ||||||||
\(363\) | 2.01372 | 0.105693 | ||||||||
\(364\) | 49.6688 | 2.60335 | ||||||||
\(365\) | 14.4441 | 0.756040 | ||||||||
\(366\) | −26.5861 | −1.38968 | ||||||||
\(367\) | −10.0219 | −0.523138 | −0.261569 | − | 0.965185i | \(-0.584240\pi\) | ||||
−0.261569 | + | 0.965185i | \(0.584240\pi\) | |||||||
\(368\) | 21.7153 | 1.13199 | ||||||||
\(369\) | −2.48265 | −0.129242 | ||||||||
\(370\) | 5.07046 | 0.263601 | ||||||||
\(371\) | −2.85470 | −0.148209 | ||||||||
\(372\) | 25.5115 | 1.32271 | ||||||||
\(373\) | −28.9043 | −1.49661 | −0.748303 | − | 0.663357i | \(-0.769131\pi\) | ||||
−0.748303 | + | 0.663357i | \(0.769131\pi\) | |||||||
\(374\) | −1.99568 | −0.103194 | ||||||||
\(375\) | −6.41657 | −0.331350 | ||||||||
\(376\) | 0.0917875 | 0.00473358 | ||||||||
\(377\) | −10.2504 | −0.527922 | ||||||||
\(378\) | −28.5962 | −1.47083 | ||||||||
\(379\) | −30.3828 | −1.56066 | −0.780330 | − | 0.625367i | \(-0.784949\pi\) | ||||
−0.780330 | + | 0.625367i | \(0.784949\pi\) | |||||||
\(380\) | −18.1984 | −0.933560 | ||||||||
\(381\) | 16.9861 | 0.870223 | ||||||||
\(382\) | 11.3569 | 0.581072 | ||||||||
\(383\) | −11.9180 | −0.608984 | −0.304492 | − | 0.952515i | \(-0.598487\pi\) | ||||
−0.304492 | + | 0.952515i | \(0.598487\pi\) | |||||||
\(384\) | −0.554388 | −0.0282910 | ||||||||
\(385\) | −10.9354 | −0.557318 | ||||||||
\(386\) | 42.4752 | 2.16193 | ||||||||
\(387\) | 1.05506 | 0.0536319 | ||||||||
\(388\) | 3.36142 | 0.170650 | ||||||||
\(389\) | −14.1172 | −0.715771 | −0.357885 | − | 0.933766i | \(-0.616502\pi\) | ||||
−0.357885 | + | 0.933766i | \(0.616502\pi\) | |||||||
\(390\) | 82.2459 | 4.16468 | ||||||||
\(391\) | −5.38280 | −0.272220 | ||||||||
\(392\) | 0.219743 | 0.0110987 | ||||||||
\(393\) | −0.408466 | −0.0206044 | ||||||||
\(394\) | −38.5529 | −1.94227 | ||||||||
\(395\) | 35.6269 | 1.79258 | ||||||||
\(396\) | 2.09193 | 0.105124 | ||||||||
\(397\) | −9.14910 | −0.459180 | −0.229590 | − | 0.973287i | \(-0.573739\pi\) | ||||
−0.229590 | + | 0.973287i | \(0.573739\pi\) | |||||||
\(398\) | −4.71722 | −0.236453 | ||||||||
\(399\) | 22.6232 | 1.13258 | ||||||||
\(400\) | −15.8703 | −0.793513 | ||||||||
\(401\) | 7.86101 | 0.392560 | 0.196280 | − | 0.980548i | \(-0.437114\pi\) | ||||
0.196280 | + | 0.980548i | \(0.437114\pi\) | |||||||
\(402\) | −21.0181 | −1.04829 | ||||||||
\(403\) | −43.7493 | −2.17931 | ||||||||
\(404\) | 24.3269 | 1.21031 | ||||||||
\(405\) | −33.0342 | −1.64148 | ||||||||
\(406\) | 10.9306 | 0.542475 | ||||||||
\(407\) | −0.850029 | −0.0421344 | ||||||||
\(408\) | 0.0693010 | 0.00343091 | ||||||||
\(409\) | 25.1811 | 1.24512 | 0.622562 | − | 0.782570i | \(-0.286092\pi\) | ||||
0.622562 | + | 0.782570i | \(0.286092\pi\) | |||||||
\(410\) | 14.0363 | 0.693201 | ||||||||
\(411\) | 8.61997 | 0.425192 | ||||||||
\(412\) | 23.8092 | 1.17299 | ||||||||
\(413\) | −32.1137 | −1.58021 | ||||||||
\(414\) | 11.3339 | 0.557030 | ||||||||
\(415\) | −4.87050 | −0.239084 | ||||||||
\(416\) | −54.6540 | −2.67963 | ||||||||
\(417\) | 0.108820 | 0.00532895 | ||||||||
\(418\) | 6.12823 | 0.299742 | ||||||||
\(419\) | −13.6261 | −0.665676 | −0.332838 | − | 0.942984i | \(-0.608006\pi\) | ||||
−0.332838 | + | 0.942984i | \(0.608006\pi\) | |||||||
\(420\) | −43.6618 | −2.13048 | ||||||||
\(421\) | −15.0241 | −0.732228 | −0.366114 | − | 0.930570i | \(-0.619312\pi\) | ||||
−0.366114 | + | 0.930570i | \(0.619312\pi\) | |||||||
\(422\) | −43.3904 | −2.11221 | ||||||||
\(423\) | 2.81398 | 0.136820 | ||||||||
\(424\) | 0.0268528 | 0.00130409 | ||||||||
\(425\) | 3.93394 | 0.190824 | ||||||||
\(426\) | 1.56835 | 0.0759866 | ||||||||
\(427\) | −24.2034 | −1.17128 | ||||||||
\(428\) | −29.1724 | −1.41010 | ||||||||
\(429\) | −13.7880 | −0.665691 | ||||||||
\(430\) | −5.96504 | −0.287660 | ||||||||
\(431\) | −16.1547 | −0.778145 | −0.389072 | − | 0.921207i | \(-0.627204\pi\) | ||||
−0.389072 | + | 0.921207i | \(0.627204\pi\) | |||||||
\(432\) | 15.8001 | 0.760185 | ||||||||
\(433\) | −14.0979 | −0.677503 | −0.338752 | − | 0.940876i | \(-0.610005\pi\) | ||||
−0.338752 | + | 0.940876i | \(0.610005\pi\) | |||||||
\(434\) | 46.6523 | 2.23938 | ||||||||
\(435\) | 9.01070 | 0.432030 | ||||||||
\(436\) | 4.79438 | 0.229609 | ||||||||
\(437\) | 16.5292 | 0.790699 | ||||||||
\(438\) | −19.4205 | −0.927948 | ||||||||
\(439\) | −13.9030 | −0.663556 | −0.331778 | − | 0.943357i | \(-0.607649\pi\) | ||||
−0.331778 | + | 0.943357i | \(0.607649\pi\) | |||||||
\(440\) | 0.102864 | 0.00490384 | ||||||||
\(441\) | 6.73678 | 0.320799 | ||||||||
\(442\) | 13.6645 | 0.649955 | ||||||||
\(443\) | −24.4830 | −1.16322 | −0.581611 | − | 0.813467i | \(-0.697577\pi\) | ||||
−0.581611 | + | 0.813467i | \(0.697577\pi\) | |||||||
\(444\) | −3.39392 | −0.161068 | ||||||||
\(445\) | 16.1173 | 0.764035 | ||||||||
\(446\) | −34.3852 | −1.62819 | ||||||||
\(447\) | −2.54704 | −0.120471 | ||||||||
\(448\) | 28.7617 | 1.35886 | ||||||||
\(449\) | −25.4448 | −1.20082 | −0.600408 | − | 0.799694i | \(-0.704995\pi\) | ||||
−0.600408 | + | 0.799694i | \(0.704995\pi\) | |||||||
\(450\) | −8.28319 | −0.390473 | ||||||||
\(451\) | −2.35309 | −0.110802 | ||||||||
\(452\) | 35.6761 | 1.67806 | ||||||||
\(453\) | −12.5157 | −0.588039 | ||||||||
\(454\) | 41.4944 | 1.94743 | ||||||||
\(455\) | 74.8749 | 3.51019 | ||||||||
\(456\) | −0.212806 | −0.00996554 | ||||||||
\(457\) | −22.7696 | −1.06512 | −0.532558 | − | 0.846394i | \(-0.678769\pi\) | ||||
−0.532558 | + | 0.846394i | \(0.678769\pi\) | |||||||
\(458\) | −36.2699 | −1.69478 | ||||||||
\(459\) | −3.91656 | −0.182809 | ||||||||
\(460\) | −31.9006 | −1.48737 | ||||||||
\(461\) | 31.7509 | 1.47879 | 0.739393 | − | 0.673274i | \(-0.235112\pi\) | ||||
0.739393 | + | 0.673274i | \(0.235112\pi\) | |||||||
\(462\) | 14.7029 | 0.684041 | ||||||||
\(463\) | 0.103811 | 0.00482449 | 0.00241224 | − | 0.999997i | \(-0.499232\pi\) | ||||
0.00241224 | + | 0.999997i | \(0.499232\pi\) | |||||||
\(464\) | −6.03942 | −0.280373 | ||||||||
\(465\) | 38.4582 | 1.78346 | ||||||||
\(466\) | −9.07324 | −0.420310 | ||||||||
\(467\) | −34.7660 | −1.60878 | −0.804388 | − | 0.594104i | \(-0.797507\pi\) | ||||
−0.804388 | + | 0.594104i | \(0.797507\pi\) | |||||||
\(468\) | −14.3235 | −0.662105 | ||||||||
\(469\) | −19.1344 | −0.883546 | ||||||||
\(470\) | −15.9095 | −0.733849 | ||||||||
\(471\) | −6.78769 | −0.312760 | ||||||||
\(472\) | 0.302078 | 0.0139043 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −47.9013 | −2.20018 | ||||||||
\(475\) | −12.0801 | −0.554273 | ||||||||
\(476\) | −7.25407 | −0.332490 | ||||||||
\(477\) | 0.823241 | 0.0376936 | ||||||||
\(478\) | 12.2178 | 0.558828 | ||||||||
\(479\) | 43.0851 | 1.96861 | 0.984305 | − | 0.176476i | \(-0.0564697\pi\) | ||||
0.984305 | + | 0.176476i | \(0.0564697\pi\) | |||||||
\(480\) | 48.0441 | 2.19290 | ||||||||
\(481\) | 5.82018 | 0.265377 | ||||||||
\(482\) | 59.5157 | 2.71087 | ||||||||
\(483\) | 39.6570 | 1.80446 | ||||||||
\(484\) | 1.98276 | 0.0901253 | ||||||||
\(485\) | 5.06728 | 0.230093 | ||||||||
\(486\) | 20.9667 | 0.951068 | ||||||||
\(487\) | −8.71484 | −0.394907 | −0.197453 | − | 0.980312i | \(-0.563267\pi\) | ||||
−0.197453 | + | 0.980312i | \(0.563267\pi\) | |||||||
\(488\) | 0.227670 | 0.0103061 | ||||||||
\(489\) | 6.86645 | 0.310511 | ||||||||
\(490\) | −38.0879 | −1.72064 | ||||||||
\(491\) | 31.0375 | 1.40070 | 0.700352 | − | 0.713797i | \(-0.253026\pi\) | ||||
0.700352 | + | 0.713797i | \(0.253026\pi\) | |||||||
\(492\) | −9.39519 | −0.423568 | ||||||||
\(493\) | 1.49706 | 0.0674241 | ||||||||
\(494\) | −41.9602 | −1.88788 | ||||||||
\(495\) | 3.15355 | 0.141742 | ||||||||
\(496\) | −25.7766 | −1.15740 | ||||||||
\(497\) | 1.42779 | 0.0640450 | ||||||||
\(498\) | 6.54851 | 0.293446 | ||||||||
\(499\) | −10.2855 | −0.460440 | −0.230220 | − | 0.973139i | \(-0.573945\pi\) | ||||
−0.230220 | + | 0.973139i | \(0.573945\pi\) | |||||||
\(500\) | −6.31791 | −0.282545 | ||||||||
\(501\) | 19.4553 | 0.869199 | ||||||||
\(502\) | −30.8828 | −1.37837 | ||||||||
\(503\) | 5.63461 | 0.251235 | 0.125617 | − | 0.992079i | \(-0.459909\pi\) | ||||
0.125617 | + | 0.992079i | \(0.459909\pi\) | |||||||
\(504\) | −0.132841 | −0.00591720 | ||||||||
\(505\) | 36.6724 | 1.63190 | ||||||||
\(506\) | 10.7424 | 0.477557 | ||||||||
\(507\) | 68.2285 | 3.03013 | ||||||||
\(508\) | 16.7249 | 0.742048 | ||||||||
\(509\) | −40.8634 | −1.81124 | −0.905620 | − | 0.424090i | \(-0.860594\pi\) | ||||
−0.905620 | + | 0.424090i | \(0.860594\pi\) | |||||||
\(510\) | −12.0119 | −0.531896 | ||||||||
\(511\) | −17.6800 | −0.782117 | ||||||||
\(512\) | −31.9238 | −1.41085 | ||||||||
\(513\) | 12.0267 | 0.530993 | ||||||||
\(514\) | −1.78767 | −0.0788509 | ||||||||
\(515\) | 35.8919 | 1.58159 | ||||||||
\(516\) | 3.99271 | 0.175769 | ||||||||
\(517\) | 2.66712 | 0.117300 | ||||||||
\(518\) | −6.20638 | −0.272693 | ||||||||
\(519\) | −32.4620 | −1.42492 | ||||||||
\(520\) | −0.704312 | −0.0308861 | ||||||||
\(521\) | −26.8073 | −1.17445 | −0.587225 | − | 0.809424i | \(-0.699780\pi\) | ||||
−0.587225 | + | 0.809424i | \(0.699780\pi\) | |||||||
\(522\) | −3.15216 | −0.137966 | ||||||||
\(523\) | −29.3492 | −1.28335 | −0.641675 | − | 0.766976i | \(-0.721760\pi\) | ||||
−0.641675 | + | 0.766976i | \(0.721760\pi\) | |||||||
\(524\) | −0.402185 | −0.0175695 | ||||||||
\(525\) | −28.9827 | −1.26491 | ||||||||
\(526\) | −32.5551 | −1.41947 | ||||||||
\(527\) | 6.38953 | 0.278332 | ||||||||
\(528\) | −8.12373 | −0.353540 | ||||||||
\(529\) | 5.97457 | 0.259764 | ||||||||
\(530\) | −4.65438 | −0.202173 | ||||||||
\(531\) | 9.26096 | 0.401892 | ||||||||
\(532\) | 22.2754 | 0.965760 | ||||||||
\(533\) | 16.1117 | 0.697873 | ||||||||
\(534\) | −21.6702 | −0.937760 | ||||||||
\(535\) | −43.9769 | −1.90129 | ||||||||
\(536\) | 0.179988 | 0.00777431 | ||||||||
\(537\) | 49.2198 | 2.12399 | ||||||||
\(538\) | 4.87768 | 0.210292 | ||||||||
\(539\) | 6.38520 | 0.275030 | ||||||||
\(540\) | −23.2111 | −0.998845 | ||||||||
\(541\) | −30.7335 | −1.32133 | −0.660667 | − | 0.750679i | \(-0.729727\pi\) | ||||
−0.660667 | + | 0.750679i | \(0.729727\pi\) | |||||||
\(542\) | 13.1717 | 0.565772 | ||||||||
\(543\) | 38.7603 | 1.66336 | ||||||||
\(544\) | 7.98214 | 0.342232 | ||||||||
\(545\) | 7.22745 | 0.309590 | ||||||||
\(546\) | −100.671 | −4.30833 | ||||||||
\(547\) | 35.4321 | 1.51497 | 0.757483 | − | 0.652855i | \(-0.226429\pi\) | ||||
0.757483 | + | 0.652855i | \(0.226429\pi\) | |||||||
\(548\) | 8.48743 | 0.362565 | ||||||||
\(549\) | 6.97979 | 0.297890 | ||||||||
\(550\) | −7.85090 | −0.334763 | ||||||||
\(551\) | −4.59708 | −0.195842 | ||||||||
\(552\) | −0.373034 | −0.0158774 | ||||||||
\(553\) | −43.6083 | −1.85441 | ||||||||
\(554\) | −28.6173 | −1.21583 | ||||||||
\(555\) | −5.11628 | −0.217174 | ||||||||
\(556\) | 0.107147 | 0.00454404 | ||||||||
\(557\) | −30.6062 | −1.29683 | −0.648414 | − | 0.761288i | \(-0.724567\pi\) | ||||
−0.648414 | + | 0.761288i | \(0.724567\pi\) | |||||||
\(558\) | −13.4536 | −0.569537 | ||||||||
\(559\) | −6.84703 | −0.289599 | ||||||||
\(560\) | 44.1154 | 1.86422 | ||||||||
\(561\) | 2.01372 | 0.0850193 | ||||||||
\(562\) | −10.1816 | −0.429487 | ||||||||
\(563\) | −24.1511 | −1.01785 | −0.508925 | − | 0.860811i | \(-0.669957\pi\) | ||||
−0.508925 | + | 0.860811i | \(0.669957\pi\) | |||||||
\(564\) | 10.6490 | 0.448405 | ||||||||
\(565\) | 53.7810 | 2.26258 | ||||||||
\(566\) | −16.2529 | −0.683160 | ||||||||
\(567\) | 40.4347 | 1.69810 | ||||||||
\(568\) | −0.0134305 | −0.000563531 0 | ||||||||
\(569\) | 43.2255 | 1.81211 | 0.906054 | − | 0.423162i | \(-0.139080\pi\) | ||||
0.906054 | + | 0.423162i | \(0.139080\pi\) | |||||||
\(570\) | 36.8855 | 1.54496 | ||||||||
\(571\) | −15.6365 | −0.654366 | −0.327183 | − | 0.944961i | \(-0.606099\pi\) | ||||
−0.327183 | + | 0.944961i | \(0.606099\pi\) | |||||||
\(572\) | −13.5760 | −0.567641 | ||||||||
\(573\) | −11.4596 | −0.478731 | ||||||||
\(574\) | −17.1807 | −0.717110 | ||||||||
\(575\) | −21.1756 | −0.883084 | ||||||||
\(576\) | −8.29433 | −0.345597 | ||||||||
\(577\) | 18.1121 | 0.754018 | 0.377009 | − | 0.926210i | \(-0.376953\pi\) | ||||
0.377009 | + | 0.926210i | \(0.376953\pi\) | |||||||
\(578\) | −1.99568 | −0.0830095 | ||||||||
\(579\) | −42.8590 | −1.78116 | ||||||||
\(580\) | 8.87215 | 0.368396 | ||||||||
\(581\) | 5.96162 | 0.247330 | ||||||||
\(582\) | −6.81309 | −0.282412 | ||||||||
\(583\) | 0.780277 | 0.0323158 | ||||||||
\(584\) | 0.166307 | 0.00688184 | ||||||||
\(585\) | −21.5925 | −0.892738 | ||||||||
\(586\) | 11.3084 | 0.467147 | ||||||||
\(587\) | −13.8227 | −0.570526 | −0.285263 | − | 0.958449i | \(-0.592081\pi\) | ||||
−0.285263 | + | 0.958449i | \(0.592081\pi\) | |||||||
\(588\) | 25.4942 | 1.05136 | ||||||||
\(589\) | −19.6206 | −0.808453 | ||||||||
\(590\) | −52.3590 | −2.15558 | ||||||||
\(591\) | 38.9013 | 1.60018 | ||||||||
\(592\) | 3.42918 | 0.140938 | ||||||||
\(593\) | −1.32481 | −0.0544034 | −0.0272017 | − | 0.999630i | \(-0.508660\pi\) | ||||
−0.0272017 | + | 0.999630i | \(0.508660\pi\) | |||||||
\(594\) | 7.81621 | 0.320703 | ||||||||
\(595\) | −10.9354 | −0.448307 | ||||||||
\(596\) | −2.50788 | −0.102727 | ||||||||
\(597\) | 4.75985 | 0.194808 | ||||||||
\(598\) | −73.5534 | −3.00782 | ||||||||
\(599\) | 10.0144 | 0.409179 | 0.204589 | − | 0.978848i | \(-0.434414\pi\) | ||||
0.204589 | + | 0.978848i | \(0.434414\pi\) | |||||||
\(600\) | 0.272626 | 0.0111299 | ||||||||
\(601\) | 21.0792 | 0.859839 | 0.429919 | − | 0.902867i | \(-0.358542\pi\) | ||||
0.429919 | + | 0.902867i | \(0.358542\pi\) | |||||||
\(602\) | 7.30137 | 0.297582 | ||||||||
\(603\) | 5.51800 | 0.224710 | ||||||||
\(604\) | −12.3233 | −0.501426 | ||||||||
\(605\) | 2.98897 | 0.121519 | ||||||||
\(606\) | −49.3070 | −2.00296 | ||||||||
\(607\) | 21.0044 | 0.852541 | 0.426270 | − | 0.904596i | \(-0.359827\pi\) | ||||
0.426270 | + | 0.904596i | \(0.359827\pi\) | |||||||
\(608\) | −24.5111 | −0.994057 | ||||||||
\(609\) | −11.0293 | −0.446932 | ||||||||
\(610\) | −39.4618 | −1.59776 | ||||||||
\(611\) | −18.2618 | −0.738795 | ||||||||
\(612\) | 2.09193 | 0.0845613 | ||||||||
\(613\) | −19.2691 | −0.778272 | −0.389136 | − | 0.921180i | \(-0.627226\pi\) | ||||
−0.389136 | + | 0.921180i | \(0.627226\pi\) | |||||||
\(614\) | −36.1311 | −1.45813 | ||||||||
\(615\) | −14.1631 | −0.571111 | ||||||||
\(616\) | −0.125908 | −0.00507298 | ||||||||
\(617\) | 18.3306 | 0.737964 | 0.368982 | − | 0.929437i | \(-0.379706\pi\) | ||||
0.368982 | + | 0.929437i | \(0.379706\pi\) | |||||||
\(618\) | −48.2576 | −1.94120 | ||||||||
\(619\) | −14.5335 | −0.584152 | −0.292076 | − | 0.956395i | \(-0.594346\pi\) | ||||
−0.292076 | + | 0.956395i | \(0.594346\pi\) | |||||||
\(620\) | 37.8669 | 1.52077 | ||||||||
\(621\) | 21.0821 | 0.845994 | ||||||||
\(622\) | 52.5328 | 2.10637 | ||||||||
\(623\) | −19.7280 | −0.790387 | ||||||||
\(624\) | 55.6234 | 2.22672 | ||||||||
\(625\) | −29.1938 | −1.16775 | ||||||||
\(626\) | 16.1385 | 0.645025 | ||||||||
\(627\) | −6.18361 | −0.246950 | ||||||||
\(628\) | −6.68332 | −0.266694 | ||||||||
\(629\) | −0.850029 | −0.0338929 | ||||||||
\(630\) | 23.0252 | 0.917347 | ||||||||
\(631\) | 17.5475 | 0.698557 | 0.349278 | − | 0.937019i | \(-0.386427\pi\) | ||||
0.349278 | + | 0.937019i | \(0.386427\pi\) | |||||||
\(632\) | 0.410202 | 0.0163169 | ||||||||
\(633\) | 43.7825 | 1.74020 | ||||||||
\(634\) | −39.2907 | −1.56043 | ||||||||
\(635\) | 25.2125 | 1.00053 | ||||||||
\(636\) | 3.11542 | 0.123534 | ||||||||
\(637\) | −43.7196 | −1.73223 | ||||||||
\(638\) | −2.98765 | −0.118282 | ||||||||
\(639\) | −0.411746 | −0.0162884 | ||||||||
\(640\) | −0.822880 | −0.0325272 | ||||||||
\(641\) | 6.52429 | 0.257694 | 0.128847 | − | 0.991664i | \(-0.458872\pi\) | ||||
0.128847 | + | 0.991664i | \(0.458872\pi\) | |||||||
\(642\) | 59.1281 | 2.33360 | ||||||||
\(643\) | −19.1891 | −0.756743 | −0.378371 | − | 0.925654i | \(-0.623516\pi\) | ||||
−0.378371 | + | 0.925654i | \(0.623516\pi\) | |||||||
\(644\) | 39.0472 | 1.53868 | ||||||||
\(645\) | 6.01894 | 0.236996 | ||||||||
\(646\) | 6.12823 | 0.241112 | ||||||||
\(647\) | 40.3419 | 1.58600 | 0.793002 | − | 0.609219i | \(-0.208517\pi\) | ||||
0.793002 | + | 0.609219i | \(0.208517\pi\) | |||||||
\(648\) | −0.380350 | −0.0149415 | ||||||||
\(649\) | 8.77764 | 0.344553 | ||||||||
\(650\) | 53.7553 | 2.10846 | ||||||||
\(651\) | −47.0739 | −1.84497 | ||||||||
\(652\) | 6.76087 | 0.264776 | ||||||||
\(653\) | 25.4098 | 0.994361 | 0.497180 | − | 0.867647i | \(-0.334369\pi\) | ||||
0.497180 | + | 0.867647i | \(0.334369\pi\) | |||||||
\(654\) | −9.71749 | −0.379984 | ||||||||
\(655\) | −0.606287 | −0.0236896 | ||||||||
\(656\) | 9.49280 | 0.370632 | ||||||||
\(657\) | 5.09857 | 0.198914 | ||||||||
\(658\) | 19.4736 | 0.759160 | ||||||||
\(659\) | −7.05669 | −0.274890 | −0.137445 | − | 0.990509i | \(-0.543889\pi\) | ||||
−0.137445 | + | 0.990509i | \(0.543889\pi\) | |||||||
\(660\) | 11.9341 | 0.464534 | ||||||||
\(661\) | −35.1252 | −1.36621 | −0.683105 | − | 0.730320i | \(-0.739371\pi\) | ||||
−0.683105 | + | 0.730320i | \(0.739371\pi\) | |||||||
\(662\) | −63.5260 | −2.46901 | ||||||||
\(663\) | −13.7880 | −0.535481 | ||||||||
\(664\) | −0.0560781 | −0.00217625 | ||||||||
\(665\) | 33.5797 | 1.30217 | ||||||||
\(666\) | 1.78980 | 0.0693533 | ||||||||
\(667\) | −8.05837 | −0.312021 | ||||||||
\(668\) | 19.1562 | 0.741175 | ||||||||
\(669\) | 34.6959 | 1.34142 | ||||||||
\(670\) | −31.1973 | −1.20526 | ||||||||
\(671\) | 6.61552 | 0.255389 | ||||||||
\(672\) | −58.8072 | −2.26854 | ||||||||
\(673\) | 5.37573 | 0.207219 | 0.103609 | − | 0.994618i | \(-0.466961\pi\) | ||||
0.103609 | + | 0.994618i | \(0.466961\pi\) | |||||||
\(674\) | 20.8519 | 0.803184 | ||||||||
\(675\) | −15.4075 | −0.593035 | ||||||||
\(676\) | 67.1794 | 2.58382 | ||||||||
\(677\) | 35.6241 | 1.36915 | 0.684573 | − | 0.728944i | \(-0.259989\pi\) | ||||
0.684573 | + | 0.728944i | \(0.259989\pi\) | |||||||
\(678\) | −72.3100 | −2.77705 | ||||||||
\(679\) | −6.20248 | −0.238029 | ||||||||
\(680\) | 0.102864 | 0.00394465 | ||||||||
\(681\) | −41.8694 | −1.60444 | ||||||||
\(682\) | −12.7515 | −0.488280 | ||||||||
\(683\) | −46.5915 | −1.78278 | −0.891388 | − | 0.453242i | \(-0.850267\pi\) | ||||
−0.891388 | + | 0.453242i | \(0.850267\pi\) | |||||||
\(684\) | −6.42378 | −0.245619 | ||||||||
\(685\) | 12.7947 | 0.488858 | ||||||||
\(686\) | −4.48891 | −0.171388 | ||||||||
\(687\) | 36.5976 | 1.39629 | ||||||||
\(688\) | −4.03419 | −0.153802 | ||||||||
\(689\) | −5.34258 | −0.203536 | ||||||||
\(690\) | 64.6577 | 2.46148 | ||||||||
\(691\) | 11.8262 | 0.449890 | 0.224945 | − | 0.974371i | \(-0.427780\pi\) | ||||
0.224945 | + | 0.974371i | \(0.427780\pi\) | |||||||
\(692\) | −31.9629 | −1.21505 | ||||||||
\(693\) | −3.86003 | −0.146630 | ||||||||
\(694\) | 18.0564 | 0.685413 | ||||||||
\(695\) | 0.161522 | 0.00612689 | ||||||||
\(696\) | 0.103748 | 0.00393254 | ||||||||
\(697\) | −2.35309 | −0.0891295 | ||||||||
\(698\) | −29.8977 | −1.13165 | ||||||||
\(699\) | 9.15523 | 0.346283 | ||||||||
\(700\) | −28.5370 | −1.07860 | ||||||||
\(701\) | 22.6647 | 0.856034 | 0.428017 | − | 0.903771i | \(-0.359212\pi\) | ||||
0.428017 | + | 0.903771i | \(0.359212\pi\) | |||||||
\(702\) | −53.5178 | −2.01990 | ||||||||
\(703\) | 2.61022 | 0.0984464 | ||||||||
\(704\) | −7.86145 | −0.296290 | ||||||||
\(705\) | 16.0532 | 0.604600 | ||||||||
\(706\) | 3.87247 | 0.145742 | ||||||||
\(707\) | −44.8880 | −1.68819 | ||||||||
\(708\) | 35.0466 | 1.31713 | ||||||||
\(709\) | −13.2822 | −0.498822 | −0.249411 | − | 0.968398i | \(-0.580237\pi\) | ||||
−0.249411 | + | 0.968398i | \(0.580237\pi\) | |||||||
\(710\) | 2.32790 | 0.0873646 | ||||||||
\(711\) | 12.5758 | 0.471628 | ||||||||
\(712\) | 0.185572 | 0.00695461 | ||||||||
\(713\) | −34.3936 | −1.28805 | ||||||||
\(714\) | 14.7029 | 0.550242 | ||||||||
\(715\) | −20.4656 | −0.765369 | ||||||||
\(716\) | 48.4630 | 1.81115 | ||||||||
\(717\) | −12.3282 | −0.460405 | ||||||||
\(718\) | −1.08873 | −0.0406309 | ||||||||
\(719\) | 13.6866 | 0.510424 | 0.255212 | − | 0.966885i | \(-0.417855\pi\) | ||||
0.255212 | + | 0.966885i | \(0.417855\pi\) | |||||||
\(720\) | −12.7220 | −0.474122 | ||||||||
\(721\) | −43.9326 | −1.63614 | ||||||||
\(722\) | 19.0998 | 0.710820 | ||||||||
\(723\) | −60.0536 | −2.23342 | ||||||||
\(724\) | 38.1643 | 1.41837 | ||||||||
\(725\) | 5.88933 | 0.218724 | ||||||||
\(726\) | −4.01875 | −0.149150 | ||||||||
\(727\) | 1.26731 | 0.0470018 | 0.0235009 | − | 0.999724i | \(-0.492519\pi\) | ||||
0.0235009 | + | 0.999724i | \(0.492519\pi\) | |||||||
\(728\) | 0.862096 | 0.0319514 | ||||||||
\(729\) | 11.9999 | 0.444442 | ||||||||
\(730\) | −28.8259 | −1.06690 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 26.4139 | 0.976285 | ||||||||
\(733\) | −3.58895 | −0.132561 | −0.0662805 | − | 0.997801i | \(-0.521113\pi\) | ||||
−0.0662805 | + | 0.997801i | \(0.521113\pi\) | |||||||
\(734\) | 20.0005 | 0.738233 | ||||||||
\(735\) | 38.4321 | 1.41759 | ||||||||
\(736\) | −42.9663 | −1.58376 | ||||||||
\(737\) | 5.23002 | 0.192650 | ||||||||
\(738\) | 4.95459 | 0.182381 | ||||||||
\(739\) | −9.47879 | −0.348683 | −0.174342 | − | 0.984685i | \(-0.555780\pi\) | ||||
−0.174342 | + | 0.984685i | \(0.555780\pi\) | |||||||
\(740\) | −5.03761 | −0.185186 | ||||||||
\(741\) | 42.3394 | 1.55538 | ||||||||
\(742\) | 5.69709 | 0.209147 | ||||||||
\(743\) | −45.6023 | −1.67299 | −0.836493 | − | 0.547978i | \(-0.815398\pi\) | ||||
−0.836493 | + | 0.547978i | \(0.815398\pi\) | |||||||
\(744\) | 0.442801 | 0.0162339 | ||||||||
\(745\) | −3.78058 | −0.138510 | ||||||||
\(746\) | 57.6838 | 2.11195 | ||||||||
\(747\) | −1.71922 | −0.0629028 | ||||||||
\(748\) | 1.98276 | 0.0724967 | ||||||||
\(749\) | 53.8289 | 1.96687 | ||||||||
\(750\) | 12.8054 | 0.467589 | ||||||||
\(751\) | −11.0599 | −0.403581 | −0.201791 | − | 0.979429i | \(-0.564676\pi\) | ||||
−0.201791 | + | 0.979429i | \(0.564676\pi\) | |||||||
\(752\) | −10.7597 | −0.392365 | ||||||||
\(753\) | 31.1618 | 1.13560 | ||||||||
\(754\) | 20.4566 | 0.744984 | ||||||||
\(755\) | −18.5771 | −0.676090 | ||||||||
\(756\) | 28.4110 | 1.03330 | ||||||||
\(757\) | 19.9278 | 0.724288 | 0.362144 | − | 0.932122i | \(-0.382045\pi\) | ||||
0.362144 | + | 0.932122i | \(0.382045\pi\) | |||||||
\(758\) | 60.6345 | 2.20235 | ||||||||
\(759\) | −10.8395 | −0.393447 | ||||||||
\(760\) | −0.315868 | −0.0114577 | ||||||||
\(761\) | 7.74149 | 0.280629 | 0.140314 | − | 0.990107i | \(-0.455189\pi\) | ||||
0.140314 | + | 0.990107i | \(0.455189\pi\) | |||||||
\(762\) | −33.8989 | −1.22803 | ||||||||
\(763\) | −8.84659 | −0.320268 | ||||||||
\(764\) | −11.2834 | −0.408218 | ||||||||
\(765\) | 3.15355 | 0.114017 | ||||||||
\(766\) | 23.7847 | 0.859375 | ||||||||
\(767\) | −60.1008 | −2.17011 | ||||||||
\(768\) | 32.7679 | 1.18241 | ||||||||
\(769\) | −13.1274 | −0.473388 | −0.236694 | − | 0.971584i | \(-0.576064\pi\) | ||||
−0.236694 | + | 0.971584i | \(0.576064\pi\) | |||||||
\(770\) | 21.8236 | 0.786467 | ||||||||
\(771\) | 1.80383 | 0.0649633 | ||||||||
\(772\) | −42.2000 | −1.51881 | ||||||||
\(773\) | −24.3671 | −0.876423 | −0.438211 | − | 0.898872i | \(-0.644388\pi\) | ||||
−0.438211 | + | 0.898872i | \(0.644388\pi\) | |||||||
\(774\) | −2.10557 | −0.0756832 | ||||||||
\(775\) | 25.1360 | 0.902912 | ||||||||
\(776\) | 0.0583437 | 0.00209442 | ||||||||
\(777\) | 6.26246 | 0.224665 | ||||||||
\(778\) | 28.1735 | 1.01007 | ||||||||
\(779\) | 7.22572 | 0.258888 | ||||||||
\(780\) | −81.7131 | −2.92580 | ||||||||
\(781\) | −0.390257 | −0.0139645 | ||||||||
\(782\) | 10.7424 | 0.384147 | ||||||||
\(783\) | −5.86331 | −0.209538 | ||||||||
\(784\) | −25.7591 | −0.919968 | ||||||||
\(785\) | −10.0750 | −0.359592 | ||||||||
\(786\) | 0.815168 | 0.0290761 | ||||||||
\(787\) | 41.9572 | 1.49561 | 0.747807 | − | 0.663916i | \(-0.231107\pi\) | ||||
0.747807 | + | 0.663916i | \(0.231107\pi\) | |||||||
\(788\) | 38.3031 | 1.36449 | ||||||||
\(789\) | 32.8493 | 1.16947 | ||||||||
\(790\) | −71.1000 | −2.52963 | ||||||||
\(791\) | −65.8294 | −2.34062 | ||||||||
\(792\) | 0.0363094 | 0.00129020 | ||||||||
\(793\) | −45.2967 | −1.60853 | ||||||||
\(794\) | 18.2587 | 0.647978 | ||||||||
\(795\) | 4.69644 | 0.166566 | ||||||||
\(796\) | 4.68666 | 0.166114 | ||||||||
\(797\) | −22.7238 | −0.804917 | −0.402458 | − | 0.915438i | \(-0.631844\pi\) | ||||
−0.402458 | + | 0.915438i | \(0.631844\pi\) | |||||||
\(798\) | −45.1488 | −1.59825 | ||||||||
\(799\) | 2.66712 | 0.0943559 | ||||||||
\(800\) | 31.4013 | 1.11020 | ||||||||
\(801\) | 5.68918 | 0.201017 | ||||||||
\(802\) | −15.6881 | −0.553966 | ||||||||
\(803\) | 4.83248 | 0.170534 | ||||||||
\(804\) | 20.8819 | 0.736450 | ||||||||
\(805\) | 58.8630 | 2.07465 | ||||||||
\(806\) | 87.3098 | 3.07536 | ||||||||
\(807\) | −4.92176 | −0.173254 | ||||||||
\(808\) | 0.422240 | 0.0148543 | ||||||||
\(809\) | 8.80446 | 0.309548 | 0.154774 | − | 0.987950i | \(-0.450535\pi\) | ||||
0.154774 | + | 0.987950i | \(0.450535\pi\) | |||||||
\(810\) | 65.9258 | 2.31640 | ||||||||
\(811\) | 44.9326 | 1.57780 | 0.788898 | − | 0.614524i | \(-0.210652\pi\) | ||||
0.788898 | + | 0.614524i | \(0.210652\pi\) | |||||||
\(812\) | −10.8598 | −0.381103 | ||||||||
\(813\) | −13.2907 | −0.466125 | ||||||||
\(814\) | 1.69639 | 0.0594585 | ||||||||
\(815\) | 10.1919 | 0.357006 | ||||||||
\(816\) | −8.12373 | −0.284387 | ||||||||
\(817\) | −3.07074 | −0.107432 | ||||||||
\(818\) | −50.2535 | −1.75707 | ||||||||
\(819\) | 26.4297 | 0.923530 | ||||||||
\(820\) | −13.9453 | −0.486992 | ||||||||
\(821\) | 48.4134 | 1.68964 | 0.844820 | − | 0.535051i | \(-0.179708\pi\) | ||||
0.844820 | + | 0.535051i | \(0.179708\pi\) | |||||||
\(822\) | −17.2027 | −0.600014 | ||||||||
\(823\) | −42.2303 | −1.47206 | −0.736028 | − | 0.676951i | \(-0.763301\pi\) | ||||
−0.736028 | + | 0.676951i | \(0.763301\pi\) | |||||||
\(824\) | 0.413253 | 0.0143963 | ||||||||
\(825\) | 7.92184 | 0.275803 | ||||||||
\(826\) | 64.0888 | 2.22993 | ||||||||
\(827\) | 36.6138 | 1.27319 | 0.636594 | − | 0.771199i | \(-0.280343\pi\) | ||||
0.636594 | + | 0.771199i | \(0.280343\pi\) | |||||||
\(828\) | −11.2605 | −0.391328 | ||||||||
\(829\) | 26.5336 | 0.921549 | 0.460774 | − | 0.887517i | \(-0.347572\pi\) | ||||
0.460774 | + | 0.887517i | \(0.347572\pi\) | |||||||
\(830\) | 9.71998 | 0.337386 | ||||||||
\(831\) | 28.8759 | 1.00169 | ||||||||
\(832\) | 53.8276 | 1.86614 | ||||||||
\(833\) | 6.38520 | 0.221234 | ||||||||
\(834\) | −0.217171 | −0.00752001 | ||||||||
\(835\) | 28.8776 | 0.999350 | ||||||||
\(836\) | −6.08853 | −0.210576 | ||||||||
\(837\) | −25.0250 | −0.864989 | ||||||||
\(838\) | 27.1933 | 0.939377 | ||||||||
\(839\) | 5.64083 | 0.194743 | 0.0973715 | − | 0.995248i | \(-0.468956\pi\) | ||||
0.0973715 | + | 0.995248i | \(0.468956\pi\) | |||||||
\(840\) | −0.757833 | −0.0261477 | ||||||||
\(841\) | −26.7588 | −0.922718 | ||||||||
\(842\) | 29.9833 | 1.03329 | ||||||||
\(843\) | 10.2737 | 0.353844 | ||||||||
\(844\) | 43.1093 | 1.48388 | ||||||||
\(845\) | 101.272 | 3.48386 | ||||||||
\(846\) | −5.61581 | −0.193076 | ||||||||
\(847\) | −3.65858 | −0.125710 | ||||||||
\(848\) | −3.14779 | −0.108095 | ||||||||
\(849\) | 16.3998 | 0.562839 | ||||||||
\(850\) | −7.85090 | −0.269284 | ||||||||
\(851\) | 4.57554 | 0.156848 | ||||||||
\(852\) | −1.55819 | −0.0533826 | ||||||||
\(853\) | 11.6787 | 0.399871 | 0.199935 | − | 0.979809i | \(-0.435927\pi\) | ||||
0.199935 | + | 0.979809i | \(0.435927\pi\) | |||||||
\(854\) | 48.3023 | 1.65287 | ||||||||
\(855\) | −9.68374 | −0.331177 | ||||||||
\(856\) | −0.506343 | −0.0173064 | ||||||||
\(857\) | −34.2962 | −1.17154 | −0.585768 | − | 0.810479i | \(-0.699207\pi\) | ||||
−0.585768 | + | 0.810479i | \(0.699207\pi\) | |||||||
\(858\) | 27.5165 | 0.939397 | ||||||||
\(859\) | 54.2497 | 1.85098 | 0.925488 | − | 0.378778i | \(-0.123656\pi\) | ||||
0.925488 | + | 0.378778i | \(0.123656\pi\) | |||||||
\(860\) | 5.92640 | 0.202088 | ||||||||
\(861\) | 17.3360 | 0.590809 | ||||||||
\(862\) | 32.2397 | 1.09809 | ||||||||
\(863\) | 56.3274 | 1.91741 | 0.958704 | − | 0.284406i | \(-0.0917963\pi\) | ||||
0.958704 | + | 0.284406i | \(0.0917963\pi\) | |||||||
\(864\) | −31.2625 | −1.06357 | ||||||||
\(865\) | −48.1835 | −1.63829 | ||||||||
\(866\) | 28.1350 | 0.956067 | ||||||||
\(867\) | 2.01372 | 0.0683895 | ||||||||
\(868\) | −46.3501 | −1.57322 | ||||||||
\(869\) | 11.9195 | 0.404340 | ||||||||
\(870\) | −17.9825 | −0.609665 | ||||||||
\(871\) | −35.8101 | −1.21338 | ||||||||
\(872\) | 0.0832155 | 0.00281803 | ||||||||
\(873\) | 1.78868 | 0.0605375 | ||||||||
\(874\) | −32.9871 | −1.11580 | ||||||||
\(875\) | 11.6578 | 0.394105 | ||||||||
\(876\) | 19.2947 | 0.651907 | ||||||||
\(877\) | −34.3979 | −1.16153 | −0.580767 | − | 0.814070i | \(-0.697247\pi\) | ||||
−0.580767 | + | 0.814070i | \(0.697247\pi\) | |||||||
\(878\) | 27.7461 | 0.936385 | ||||||||
\(879\) | −11.4106 | −0.384871 | ||||||||
\(880\) | −12.0581 | −0.406478 | ||||||||
\(881\) | 6.57047 | 0.221365 | 0.110682 | − | 0.993856i | \(-0.464696\pi\) | ||||
0.110682 | + | 0.993856i | \(0.464696\pi\) | |||||||
\(882\) | −13.4445 | −0.452700 | ||||||||
\(883\) | 26.4466 | 0.889999 | 0.444999 | − | 0.895531i | \(-0.353204\pi\) | ||||
0.444999 | + | 0.895531i | \(0.353204\pi\) | |||||||
\(884\) | −13.5760 | −0.456610 | ||||||||
\(885\) | 52.8321 | 1.77593 | ||||||||
\(886\) | 48.8603 | 1.64149 | ||||||||
\(887\) | 16.9262 | 0.568326 | 0.284163 | − | 0.958776i | \(-0.408284\pi\) | ||||
0.284163 | + | 0.958776i | \(0.408284\pi\) | |||||||
\(888\) | −0.0589079 | −0.00197682 | ||||||||
\(889\) | −30.8608 | −1.03504 | ||||||||
\(890\) | −32.1651 | −1.07818 | ||||||||
\(891\) | −11.0520 | −0.370257 | ||||||||
\(892\) | 34.1625 | 1.14384 | ||||||||
\(893\) | −8.19003 | −0.274069 | ||||||||
\(894\) | 5.08309 | 0.170004 | ||||||||
\(895\) | 73.0571 | 2.44203 | ||||||||
\(896\) | 1.00723 | 0.0336491 | ||||||||
\(897\) | 74.2181 | 2.47807 | ||||||||
\(898\) | 50.7799 | 1.69455 | ||||||||
\(899\) | 9.56549 | 0.319027 | ||||||||
\(900\) | 8.22953 | 0.274318 | ||||||||
\(901\) | 0.780277 | 0.0259948 | ||||||||
\(902\) | 4.69602 | 0.156360 | ||||||||
\(903\) | −7.36735 | −0.245170 | ||||||||
\(904\) | 0.619225 | 0.0205951 | ||||||||
\(905\) | 57.5321 | 1.91243 | ||||||||
\(906\) | 24.9774 | 0.829818 | ||||||||
\(907\) | 21.7189 | 0.721163 | 0.360581 | − | 0.932728i | \(-0.382578\pi\) | ||||
0.360581 | + | 0.932728i | \(0.382578\pi\) | |||||||
\(908\) | −41.2256 | −1.36812 | ||||||||
\(909\) | 12.9448 | 0.429353 | ||||||||
\(910\) | −149.427 | −4.95344 | ||||||||
\(911\) | −7.92085 | −0.262430 | −0.131215 | − | 0.991354i | \(-0.541888\pi\) | ||||
−0.131215 | + | 0.991354i | \(0.541888\pi\) | |||||||
\(912\) | 24.9459 | 0.826040 | ||||||||
\(913\) | −1.62949 | −0.0539283 | ||||||||
\(914\) | 45.4408 | 1.50305 | ||||||||
\(915\) | 39.8184 | 1.31636 | ||||||||
\(916\) | 36.0349 | 1.19063 | ||||||||
\(917\) | 0.742111 | 0.0245067 | ||||||||
\(918\) | 7.81621 | 0.257973 | ||||||||
\(919\) | 14.8547 | 0.490011 | 0.245005 | − | 0.969522i | \(-0.421210\pi\) | ||||
0.245005 | + | 0.969522i | \(0.421210\pi\) | |||||||
\(920\) | −0.553695 | −0.0182548 | ||||||||
\(921\) | 36.4576 | 1.20132 | ||||||||
\(922\) | −63.3648 | −2.08681 | ||||||||
\(923\) | 2.67210 | 0.0879534 | ||||||||
\(924\) | −14.6076 | −0.480556 | ||||||||
\(925\) | −3.34396 | −0.109949 | ||||||||
\(926\) | −0.207173 | −0.00680813 | ||||||||
\(927\) | 12.6693 | 0.416115 | ||||||||
\(928\) | 11.9497 | 0.392269 | ||||||||
\(929\) | −35.7661 | −1.17345 | −0.586724 | − | 0.809787i | \(-0.699583\pi\) | ||||
−0.586724 | + | 0.809787i | \(0.699583\pi\) | |||||||
\(930\) | −76.7505 | −2.51675 | ||||||||
\(931\) | −19.6073 | −0.642603 | ||||||||
\(932\) | 9.01446 | 0.295278 | ||||||||
\(933\) | −53.0075 | −1.73539 | ||||||||
\(934\) | 69.3819 | 2.27024 | ||||||||
\(935\) | 2.98897 | 0.0977497 | ||||||||
\(936\) | −0.248612 | −0.00812613 | ||||||||
\(937\) | 49.5046 | 1.61725 | 0.808623 | − | 0.588328i | \(-0.200213\pi\) | ||||
0.808623 | + | 0.588328i | \(0.200213\pi\) | |||||||
\(938\) | 38.1863 | 1.24683 | ||||||||
\(939\) | −16.2844 | −0.531420 | ||||||||
\(940\) | 15.8064 | 0.515548 | ||||||||
\(941\) | −21.8253 | −0.711483 | −0.355742 | − | 0.934584i | \(-0.615772\pi\) | ||||
−0.355742 | + | 0.934584i | \(0.615772\pi\) | |||||||
\(942\) | 13.5461 | 0.441355 | ||||||||
\(943\) | 12.6662 | 0.412468 | ||||||||
\(944\) | −35.4107 | −1.15252 | ||||||||
\(945\) | 42.8290 | 1.39323 | ||||||||
\(946\) | −1.99568 | −0.0648853 | ||||||||
\(947\) | 42.9854 | 1.39684 | 0.698420 | − | 0.715688i | \(-0.253887\pi\) | ||||
0.698420 | + | 0.715688i | \(0.253887\pi\) | |||||||
\(948\) | 47.5910 | 1.54568 | ||||||||
\(949\) | −33.0881 | −1.07409 | ||||||||
\(950\) | 24.1081 | 0.782169 | ||||||||
\(951\) | 39.6458 | 1.28560 | ||||||||
\(952\) | −0.125908 | −0.00408070 | ||||||||
\(953\) | 18.3008 | 0.592821 | 0.296410 | − | 0.955061i | \(-0.404210\pi\) | ||||
0.296410 | + | 0.955061i | \(0.404210\pi\) | |||||||
\(954\) | −1.64293 | −0.0531918 | ||||||||
\(955\) | −17.0095 | −0.550414 | ||||||||
\(956\) | −12.1386 | −0.392591 | ||||||||
\(957\) | 3.01465 | 0.0974499 | ||||||||
\(958\) | −85.9843 | −2.77803 | ||||||||
\(959\) | −15.6610 | −0.505720 | ||||||||
\(960\) | −47.3177 | −1.52717 | ||||||||
\(961\) | 9.82608 | 0.316970 | ||||||||
\(962\) | −11.6152 | −0.374490 | ||||||||
\(963\) | −15.5232 | −0.500229 | ||||||||
\(964\) | −59.1302 | −1.90445 | ||||||||
\(965\) | −63.6158 | −2.04786 | ||||||||
\(966\) | −79.1428 | −2.54638 | ||||||||
\(967\) | 18.5193 | 0.595539 | 0.297770 | − | 0.954638i | \(-0.403757\pi\) | ||||
0.297770 | + | 0.954638i | \(0.403757\pi\) | |||||||
\(968\) | 0.0344145 | 0.00110612 | ||||||||
\(969\) | −6.18361 | −0.198646 | ||||||||
\(970\) | −10.1127 | −0.324699 | ||||||||
\(971\) | −12.4524 | −0.399618 | −0.199809 | − | 0.979835i | \(-0.564032\pi\) | ||||
−0.199809 | + | 0.979835i | \(0.564032\pi\) | |||||||
\(972\) | −20.8309 | −0.668150 | ||||||||
\(973\) | −0.197707 | −0.00633821 | ||||||||
\(974\) | 17.3921 | 0.557278 | ||||||||
\(975\) | −54.2411 | −1.73711 | ||||||||
\(976\) | −26.6883 | −0.854271 | ||||||||
\(977\) | 40.4508 | 1.29414 | 0.647069 | − | 0.762432i | \(-0.275995\pi\) | ||||
0.647069 | + | 0.762432i | \(0.275995\pi\) | |||||||
\(978\) | −13.7033 | −0.438182 | ||||||||
\(979\) | 5.39227 | 0.172338 | ||||||||
\(980\) | 37.8412 | 1.20879 | ||||||||
\(981\) | 2.55118 | 0.0814530 | ||||||||
\(982\) | −61.9411 | −1.97662 | ||||||||
\(983\) | −8.73218 | −0.278513 | −0.139257 | − | 0.990256i | \(-0.544471\pi\) | ||||
−0.139257 | + | 0.990256i | \(0.544471\pi\) | |||||||
\(984\) | −0.163071 | −0.00519852 | ||||||||
\(985\) | 57.7413 | 1.83979 | ||||||||
\(986\) | −2.98765 | −0.0951463 | ||||||||
\(987\) | −19.6496 | −0.625453 | ||||||||
\(988\) | 41.6884 | 1.32628 | ||||||||
\(989\) | −5.38280 | −0.171163 | ||||||||
\(990\) | −6.29349 | −0.200020 | ||||||||
\(991\) | 2.56381 | 0.0814422 | 0.0407211 | − | 0.999171i | \(-0.487034\pi\) | ||||
0.0407211 | + | 0.999171i | \(0.487034\pi\) | |||||||
\(992\) | 51.0021 | 1.61932 | ||||||||
\(993\) | 64.1000 | 2.03415 | ||||||||
\(994\) | −2.84941 | −0.0903779 | ||||||||
\(995\) | 7.06506 | 0.223977 | ||||||||
\(996\) | −6.50609 | −0.206153 | ||||||||
\(997\) | 4.72770 | 0.149728 | 0.0748640 | − | 0.997194i | \(-0.476148\pi\) | ||||
0.0748640 | + | 0.997194i | \(0.476148\pi\) | |||||||
\(998\) | 20.5265 | 0.649756 | ||||||||
\(999\) | 3.32919 | 0.105331 |
(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 | 8041.2.a.j.1.15 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.j.1.15 | ✓ | 82 | 1.1 | even | 1 | trivial |