Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.03548 | 0.732195 | 0.366098 | − | 0.930576i | \(-0.380694\pi\) | ||||
0.366098 | + | 0.930576i | \(0.380694\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.927780 | −0.463890 | ||||||||
\(5\) | −1.23903 | −0.554110 | −0.277055 | − | 0.960854i | \(-0.589358\pi\) | ||||
−0.277055 | + | 0.960854i | \(0.589358\pi\) | |||||||
\(6\) | −1.03548 | −0.422733 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −3.03166 | −1.07185 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.28299 | −0.405717 | ||||||||
\(11\) | 3.83036 | 1.15490 | 0.577449 | − | 0.816427i | \(-0.304048\pi\) | ||||
0.577449 | + | 0.816427i | \(0.304048\pi\) | |||||||
\(12\) | 0.927780 | 0.267827 | ||||||||
\(13\) | −5.12270 | −1.42078 | −0.710391 | − | 0.703807i | \(-0.751482\pi\) | ||||
−0.710391 | + | 0.703807i | \(0.751482\pi\) | |||||||
\(14\) | 1.03548 | 0.276744 | ||||||||
\(15\) | 1.23903 | 0.319916 | ||||||||
\(16\) | −1.28367 | −0.320916 | ||||||||
\(17\) | 8.19673 | 1.98800 | 0.994000 | − | 0.109383i | \(-0.0348874\pi\) | ||||
0.994000 | + | 0.109383i | \(0.0348874\pi\) | |||||||
\(18\) | 1.03548 | 0.244065 | ||||||||
\(19\) | −5.60125 | −1.28502 | −0.642508 | − | 0.766279i | \(-0.722106\pi\) | ||||
−0.642508 | + | 0.766279i | \(0.722106\pi\) | |||||||
\(20\) | 1.14955 | 0.257046 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 3.96627 | 0.845611 | ||||||||
\(23\) | −6.61860 | −1.38007 | −0.690036 | − | 0.723775i | \(-0.742405\pi\) | ||||
−0.690036 | + | 0.723775i | \(0.742405\pi\) | |||||||
\(24\) | 3.03166 | 0.618835 | ||||||||
\(25\) | −3.46481 | −0.692962 | ||||||||
\(26\) | −5.30446 | −1.04029 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.927780 | −0.175334 | ||||||||
\(29\) | 2.48459 | 0.461377 | 0.230688 | − | 0.973028i | \(-0.425902\pi\) | ||||
0.230688 | + | 0.973028i | \(0.425902\pi\) | |||||||
\(30\) | 1.28299 | 0.234241 | ||||||||
\(31\) | −2.69886 | −0.484730 | −0.242365 | − | 0.970185i | \(-0.577923\pi\) | ||||
−0.242365 | + | 0.970185i | \(0.577923\pi\) | |||||||
\(32\) | 4.73411 | 0.836880 | ||||||||
\(33\) | −3.83036 | −0.666780 | ||||||||
\(34\) | 8.48756 | 1.45560 | ||||||||
\(35\) | −1.23903 | −0.209434 | ||||||||
\(36\) | −0.927780 | −0.154630 | ||||||||
\(37\) | −4.88041 | −0.802334 | −0.401167 | − | 0.916005i | \(-0.631395\pi\) | ||||
−0.401167 | + | 0.916005i | \(0.631395\pi\) | |||||||
\(38\) | −5.79999 | −0.940882 | ||||||||
\(39\) | 5.12270 | 0.820289 | ||||||||
\(40\) | 3.75631 | 0.593925 | ||||||||
\(41\) | 4.66419 | 0.728425 | 0.364212 | − | 0.931316i | \(-0.381338\pi\) | ||||
0.364212 | + | 0.931316i | \(0.381338\pi\) | |||||||
\(42\) | −1.03548 | −0.159778 | ||||||||
\(43\) | 0.832065 | 0.126889 | 0.0634444 | − | 0.997985i | \(-0.479791\pi\) | ||||
0.0634444 | + | 0.997985i | \(0.479791\pi\) | |||||||
\(44\) | −3.55373 | −0.535745 | ||||||||
\(45\) | −1.23903 | −0.184703 | ||||||||
\(46\) | −6.85343 | −1.01048 | ||||||||
\(47\) | 11.2552 | 1.64174 | 0.820868 | − | 0.571118i | \(-0.193490\pi\) | ||||
0.820868 | + | 0.571118i | \(0.193490\pi\) | |||||||
\(48\) | 1.28367 | 0.185281 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.58774 | −0.507383 | ||||||||
\(51\) | −8.19673 | −1.14777 | ||||||||
\(52\) | 4.75274 | 0.659086 | ||||||||
\(53\) | 8.81550 | 1.21090 | 0.605451 | − | 0.795882i | \(-0.292993\pi\) | ||||
0.605451 | + | 0.795882i | \(0.292993\pi\) | |||||||
\(54\) | −1.03548 | −0.140911 | ||||||||
\(55\) | −4.74593 | −0.639941 | ||||||||
\(56\) | −3.03166 | −0.405123 | ||||||||
\(57\) | 5.60125 | 0.741904 | ||||||||
\(58\) | 2.57274 | 0.337818 | ||||||||
\(59\) | 3.93054 | 0.511712 | 0.255856 | − | 0.966715i | \(-0.417643\pi\) | ||||
0.255856 | + | 0.966715i | \(0.417643\pi\) | |||||||
\(60\) | −1.14955 | −0.148406 | ||||||||
\(61\) | 10.4880 | 1.34285 | 0.671427 | − | 0.741071i | \(-0.265682\pi\) | ||||
0.671427 | + | 0.741071i | \(0.265682\pi\) | |||||||
\(62\) | −2.79462 | −0.354917 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 7.46941 | 0.933676 | ||||||||
\(65\) | 6.34717 | 0.787270 | ||||||||
\(66\) | −3.96627 | −0.488214 | ||||||||
\(67\) | −14.2487 | −1.74076 | −0.870380 | − | 0.492381i | \(-0.836127\pi\) | ||||
−0.870380 | + | 0.492381i | \(0.836127\pi\) | |||||||
\(68\) | −7.60476 | −0.922213 | ||||||||
\(69\) | 6.61860 | 0.796785 | ||||||||
\(70\) | −1.28299 | −0.153347 | ||||||||
\(71\) | −5.94230 | −0.705222 | −0.352611 | − | 0.935770i | \(-0.614706\pi\) | ||||
−0.352611 | + | 0.935770i | \(0.614706\pi\) | |||||||
\(72\) | −3.03166 | −0.357284 | ||||||||
\(73\) | −7.41430 | −0.867778 | −0.433889 | − | 0.900966i | \(-0.642859\pi\) | ||||
−0.433889 | + | 0.900966i | \(0.642859\pi\) | |||||||
\(74\) | −5.05357 | −0.587466 | ||||||||
\(75\) | 3.46481 | 0.400082 | ||||||||
\(76\) | 5.19673 | 0.596105 | ||||||||
\(77\) | 3.83036 | 0.436510 | ||||||||
\(78\) | 5.30446 | 0.600612 | ||||||||
\(79\) | −11.7057 | −1.31699 | −0.658494 | − | 0.752586i | \(-0.728806\pi\) | ||||
−0.658494 | + | 0.752586i | \(0.728806\pi\) | |||||||
\(80\) | 1.59050 | 0.177823 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.82968 | 0.533349 | ||||||||
\(83\) | 3.95863 | 0.434516 | 0.217258 | − | 0.976114i | \(-0.430289\pi\) | ||||
0.217258 | + | 0.976114i | \(0.430289\pi\) | |||||||
\(84\) | 0.927780 | 0.101229 | ||||||||
\(85\) | −10.1560 | −1.10157 | ||||||||
\(86\) | 0.861588 | 0.0929074 | ||||||||
\(87\) | −2.48459 | −0.266376 | ||||||||
\(88\) | −11.6124 | −1.23788 | ||||||||
\(89\) | −11.8742 | −1.25867 | −0.629334 | − | 0.777135i | \(-0.716672\pi\) | ||||
−0.629334 | + | 0.777135i | \(0.716672\pi\) | |||||||
\(90\) | −1.28299 | −0.135239 | ||||||||
\(91\) | −5.12270 | −0.537005 | ||||||||
\(92\) | 6.14060 | 0.640202 | ||||||||
\(93\) | 2.69886 | 0.279859 | ||||||||
\(94\) | 11.6545 | 1.20207 | ||||||||
\(95\) | 6.94011 | 0.712040 | ||||||||
\(96\) | −4.73411 | −0.483173 | ||||||||
\(97\) | 13.7072 | 1.39176 | 0.695880 | − | 0.718159i | \(-0.255015\pi\) | ||||
0.695880 | + | 0.718159i | \(0.255015\pi\) | |||||||
\(98\) | 1.03548 | 0.104599 | ||||||||
\(99\) | 3.83036 | 0.384966 | ||||||||
\(100\) | 3.21458 | 0.321458 | ||||||||
\(101\) | 6.10771 | 0.607740 | 0.303870 | − | 0.952714i | \(-0.401721\pi\) | ||||
0.303870 | + | 0.952714i | \(0.401721\pi\) | |||||||
\(102\) | −8.48756 | −0.840393 | ||||||||
\(103\) | 16.6172 | 1.63734 | 0.818670 | − | 0.574264i | \(-0.194712\pi\) | ||||
0.818670 | + | 0.574264i | \(0.194712\pi\) | |||||||
\(104\) | 15.5303 | 1.52287 | ||||||||
\(105\) | 1.23903 | 0.120917 | ||||||||
\(106\) | 9.12828 | 0.886617 | ||||||||
\(107\) | −8.58131 | −0.829587 | −0.414793 | − | 0.909916i | \(-0.636146\pi\) | ||||
−0.414793 | + | 0.909916i | \(0.636146\pi\) | |||||||
\(108\) | 0.927780 | 0.0892756 | ||||||||
\(109\) | 16.0391 | 1.53627 | 0.768136 | − | 0.640287i | \(-0.221185\pi\) | ||||
0.768136 | + | 0.640287i | \(0.221185\pi\) | |||||||
\(110\) | −4.91432 | −0.468562 | ||||||||
\(111\) | 4.88041 | 0.463228 | ||||||||
\(112\) | −1.28367 | −0.121295 | ||||||||
\(113\) | −11.8028 | −1.11031 | −0.555155 | − | 0.831747i | \(-0.687341\pi\) | ||||
−0.555155 | + | 0.831747i | \(0.687341\pi\) | |||||||
\(114\) | 5.79999 | 0.543219 | ||||||||
\(115\) | 8.20063 | 0.764712 | ||||||||
\(116\) | −2.30515 | −0.214028 | ||||||||
\(117\) | −5.12270 | −0.473594 | ||||||||
\(118\) | 4.07000 | 0.374673 | ||||||||
\(119\) | 8.19673 | 0.751393 | ||||||||
\(120\) | −3.75631 | −0.342903 | ||||||||
\(121\) | 3.67167 | 0.333788 | ||||||||
\(122\) | 10.8601 | 0.983231 | ||||||||
\(123\) | −4.66419 | −0.420556 | ||||||||
\(124\) | 2.50395 | 0.224861 | ||||||||
\(125\) | 10.4881 | 0.938088 | ||||||||
\(126\) | 1.03548 | 0.0922480 | ||||||||
\(127\) | 14.4486 | 1.28211 | 0.641054 | − | 0.767495i | \(-0.278497\pi\) | ||||
0.641054 | + | 0.767495i | \(0.278497\pi\) | |||||||
\(128\) | −1.73379 | −0.153247 | ||||||||
\(129\) | −0.832065 | −0.0732593 | ||||||||
\(130\) | 6.57237 | 0.576435 | ||||||||
\(131\) | 18.5110 | 1.61732 | 0.808658 | − | 0.588279i | \(-0.200194\pi\) | ||||
0.808658 | + | 0.588279i | \(0.200194\pi\) | |||||||
\(132\) | 3.55373 | 0.309313 | ||||||||
\(133\) | −5.60125 | −0.485690 | ||||||||
\(134\) | −14.7543 | −1.27458 | ||||||||
\(135\) | 1.23903 | 0.106639 | ||||||||
\(136\) | −24.8497 | −2.13084 | ||||||||
\(137\) | 7.05472 | 0.602725 | 0.301363 | − | 0.953510i | \(-0.402559\pi\) | ||||
0.301363 | + | 0.953510i | \(0.402559\pi\) | |||||||
\(138\) | 6.85343 | 0.583403 | ||||||||
\(139\) | 6.10390 | 0.517726 | 0.258863 | − | 0.965914i | \(-0.416652\pi\) | ||||
0.258863 | + | 0.965914i | \(0.416652\pi\) | |||||||
\(140\) | 1.14955 | 0.0971543 | ||||||||
\(141\) | −11.2552 | −0.947857 | ||||||||
\(142\) | −6.15314 | −0.516360 | ||||||||
\(143\) | −19.6218 | −1.64086 | ||||||||
\(144\) | −1.28367 | −0.106972 | ||||||||
\(145\) | −3.07848 | −0.255654 | ||||||||
\(146\) | −7.67736 | −0.635383 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 4.52795 | 0.372195 | ||||||||
\(149\) | 21.0560 | 1.72497 | 0.862486 | − | 0.506080i | \(-0.168906\pi\) | ||||
0.862486 | + | 0.506080i | \(0.168906\pi\) | |||||||
\(150\) | 3.58774 | 0.292938 | ||||||||
\(151\) | 16.0552 | 1.30656 | 0.653279 | − | 0.757118i | \(-0.273393\pi\) | ||||
0.653279 | + | 0.757118i | \(0.273393\pi\) | |||||||
\(152\) | 16.9811 | 1.37735 | ||||||||
\(153\) | 8.19673 | 0.662666 | ||||||||
\(154\) | 3.96627 | 0.319611 | ||||||||
\(155\) | 3.34397 | 0.268594 | ||||||||
\(156\) | −4.75274 | −0.380524 | ||||||||
\(157\) | 20.4675 | 1.63348 | 0.816741 | − | 0.577005i | \(-0.195779\pi\) | ||||
0.816741 | + | 0.577005i | \(0.195779\pi\) | |||||||
\(158\) | −12.1210 | −0.964293 | ||||||||
\(159\) | −8.81550 | −0.699115 | ||||||||
\(160\) | −5.86569 | −0.463724 | ||||||||
\(161\) | −6.61860 | −0.521618 | ||||||||
\(162\) | 1.03548 | 0.0813551 | ||||||||
\(163\) | 21.7920 | 1.70688 | 0.853442 | − | 0.521188i | \(-0.174511\pi\) | ||||
0.853442 | + | 0.521188i | \(0.174511\pi\) | |||||||
\(164\) | −4.32734 | −0.337909 | ||||||||
\(165\) | 4.74593 | 0.369470 | ||||||||
\(166\) | 4.09909 | 0.318151 | ||||||||
\(167\) | 8.03636 | 0.621872 | 0.310936 | − | 0.950431i | \(-0.399357\pi\) | ||||
0.310936 | + | 0.950431i | \(0.399357\pi\) | |||||||
\(168\) | 3.03166 | 0.233898 | ||||||||
\(169\) | 13.2421 | 1.01862 | ||||||||
\(170\) | −10.5163 | −0.806565 | ||||||||
\(171\) | −5.60125 | −0.428338 | ||||||||
\(172\) | −0.771973 | −0.0588624 | ||||||||
\(173\) | −13.5462 | −1.02990 | −0.514951 | − | 0.857220i | \(-0.672190\pi\) | ||||
−0.514951 | + | 0.857220i | \(0.672190\pi\) | |||||||
\(174\) | −2.57274 | −0.195039 | ||||||||
\(175\) | −3.46481 | −0.261915 | ||||||||
\(176\) | −4.91690 | −0.370626 | ||||||||
\(177\) | −3.93054 | −0.295437 | ||||||||
\(178\) | −12.2956 | −0.921591 | ||||||||
\(179\) | 23.5248 | 1.75833 | 0.879164 | − | 0.476518i | \(-0.158101\pi\) | ||||
0.879164 | + | 0.476518i | \(0.158101\pi\) | |||||||
\(180\) | 1.14955 | 0.0856820 | ||||||||
\(181\) | 11.9287 | 0.886651 | 0.443325 | − | 0.896361i | \(-0.353799\pi\) | ||||
0.443325 | + | 0.896361i | \(0.353799\pi\) | |||||||
\(182\) | −5.30446 | −0.393193 | ||||||||
\(183\) | −10.4880 | −0.775297 | ||||||||
\(184\) | 20.0653 | 1.47924 | ||||||||
\(185\) | 6.04697 | 0.444582 | ||||||||
\(186\) | 2.79462 | 0.204911 | ||||||||
\(187\) | 31.3964 | 2.29594 | ||||||||
\(188\) | −10.4423 | −0.761585 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 7.18635 | 0.521353 | ||||||||
\(191\) | −1.00000 | −0.0723575 | ||||||||
\(192\) | −7.46941 | −0.539058 | ||||||||
\(193\) | 16.9232 | 1.21816 | 0.609079 | − | 0.793109i | \(-0.291539\pi\) | ||||
0.609079 | + | 0.793109i | \(0.291539\pi\) | |||||||
\(194\) | 14.1936 | 1.01904 | ||||||||
\(195\) | −6.34717 | −0.454530 | ||||||||
\(196\) | −0.927780 | −0.0662700 | ||||||||
\(197\) | −7.23547 | −0.515506 | −0.257753 | − | 0.966211i | \(-0.582982\pi\) | ||||
−0.257753 | + | 0.966211i | \(0.582982\pi\) | |||||||
\(198\) | 3.96627 | 0.281870 | ||||||||
\(199\) | −15.4495 | −1.09519 | −0.547593 | − | 0.836745i | \(-0.684456\pi\) | ||||
−0.547593 | + | 0.836745i | \(0.684456\pi\) | |||||||
\(200\) | 10.5041 | 0.742753 | ||||||||
\(201\) | 14.2487 | 1.00503 | ||||||||
\(202\) | 6.32442 | 0.444984 | ||||||||
\(203\) | 2.48459 | 0.174384 | ||||||||
\(204\) | 7.60476 | 0.532440 | ||||||||
\(205\) | −5.77907 | −0.403628 | ||||||||
\(206\) | 17.2068 | 1.19885 | ||||||||
\(207\) | −6.61860 | −0.460024 | ||||||||
\(208\) | 6.57584 | 0.455952 | ||||||||
\(209\) | −21.4548 | −1.48406 | ||||||||
\(210\) | 1.28299 | 0.0885347 | ||||||||
\(211\) | 7.83218 | 0.539189 | 0.269595 | − | 0.962974i | \(-0.413110\pi\) | ||||
0.269595 | + | 0.962974i | \(0.413110\pi\) | |||||||
\(212\) | −8.17884 | −0.561725 | ||||||||
\(213\) | 5.94230 | 0.407160 | ||||||||
\(214\) | −8.88578 | −0.607420 | ||||||||
\(215\) | −1.03095 | −0.0703104 | ||||||||
\(216\) | 3.03166 | 0.206278 | ||||||||
\(217\) | −2.69886 | −0.183211 | ||||||||
\(218\) | 16.6082 | 1.12485 | ||||||||
\(219\) | 7.41430 | 0.501012 | ||||||||
\(220\) | 4.40317 | 0.296862 | ||||||||
\(221\) | −41.9894 | −2.82451 | ||||||||
\(222\) | 5.05357 | 0.339173 | ||||||||
\(223\) | −0.887704 | −0.0594450 | −0.0297225 | − | 0.999558i | \(-0.509462\pi\) | ||||
−0.0297225 | + | 0.999558i | \(0.509462\pi\) | |||||||
\(224\) | 4.73411 | 0.316311 | ||||||||
\(225\) | −3.46481 | −0.230987 | ||||||||
\(226\) | −12.2215 | −0.812965 | ||||||||
\(227\) | 19.0891 | 1.26699 | 0.633493 | − | 0.773748i | \(-0.281621\pi\) | ||||
0.633493 | + | 0.773748i | \(0.281621\pi\) | |||||||
\(228\) | −5.19673 | −0.344162 | ||||||||
\(229\) | 7.15988 | 0.473138 | 0.236569 | − | 0.971615i | \(-0.423977\pi\) | ||||
0.236569 | + | 0.971615i | \(0.423977\pi\) | |||||||
\(230\) | 8.49159 | 0.559919 | ||||||||
\(231\) | −3.83036 | −0.252019 | ||||||||
\(232\) | −7.53243 | −0.494528 | ||||||||
\(233\) | −12.1478 | −0.795827 | −0.397913 | − | 0.917423i | \(-0.630266\pi\) | ||||
−0.397913 | + | 0.917423i | \(0.630266\pi\) | |||||||
\(234\) | −5.30446 | −0.346763 | ||||||||
\(235\) | −13.9455 | −0.909703 | ||||||||
\(236\) | −3.64667 | −0.237378 | ||||||||
\(237\) | 11.7057 | 0.760364 | ||||||||
\(238\) | 8.48756 | 0.550167 | ||||||||
\(239\) | −25.7944 | −1.66850 | −0.834252 | − | 0.551383i | \(-0.814100\pi\) | ||||
−0.834252 | + | 0.551383i | \(0.814100\pi\) | |||||||
\(240\) | −1.59050 | −0.102666 | ||||||||
\(241\) | −20.8634 | −1.34393 | −0.671966 | − | 0.740582i | \(-0.734550\pi\) | ||||
−0.671966 | + | 0.740582i | \(0.734550\pi\) | |||||||
\(242\) | 3.80194 | 0.244398 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.73057 | −0.622936 | ||||||||
\(245\) | −1.23903 | −0.0791586 | ||||||||
\(246\) | −4.82968 | −0.307929 | ||||||||
\(247\) | 28.6935 | 1.82573 | ||||||||
\(248\) | 8.18203 | 0.519559 | ||||||||
\(249\) | −3.95863 | −0.250868 | ||||||||
\(250\) | 10.8603 | 0.686863 | ||||||||
\(251\) | 1.81295 | 0.114432 | 0.0572162 | − | 0.998362i | \(-0.481778\pi\) | ||||
0.0572162 | + | 0.998362i | \(0.481778\pi\) | |||||||
\(252\) | −0.927780 | −0.0584446 | ||||||||
\(253\) | −25.3516 | −1.59384 | ||||||||
\(254\) | 14.9613 | 0.938754 | ||||||||
\(255\) | 10.1560 | 0.635992 | ||||||||
\(256\) | −16.7341 | −1.04588 | ||||||||
\(257\) | 8.52307 | 0.531654 | 0.265827 | − | 0.964021i | \(-0.414355\pi\) | ||||
0.265827 | + | 0.964021i | \(0.414355\pi\) | |||||||
\(258\) | −0.861588 | −0.0536401 | ||||||||
\(259\) | −4.88041 | −0.303254 | ||||||||
\(260\) | −5.88878 | −0.365206 | ||||||||
\(261\) | 2.48459 | 0.153792 | ||||||||
\(262\) | 19.1678 | 1.18419 | ||||||||
\(263\) | −4.24451 | −0.261728 | −0.130864 | − | 0.991400i | \(-0.541775\pi\) | ||||
−0.130864 | + | 0.991400i | \(0.541775\pi\) | |||||||
\(264\) | 11.6124 | 0.714691 | ||||||||
\(265\) | −10.9227 | −0.670973 | ||||||||
\(266\) | −5.79999 | −0.355620 | ||||||||
\(267\) | 11.8742 | 0.726692 | ||||||||
\(268\) | 13.2197 | 0.807521 | ||||||||
\(269\) | 8.97669 | 0.547318 | 0.273659 | − | 0.961827i | \(-0.411766\pi\) | ||||
0.273659 | + | 0.961827i | \(0.411766\pi\) | |||||||
\(270\) | 1.28299 | 0.0780803 | ||||||||
\(271\) | −18.0420 | −1.09597 | −0.547986 | − | 0.836488i | \(-0.684605\pi\) | ||||
−0.547986 | + | 0.836488i | \(0.684605\pi\) | |||||||
\(272\) | −10.5219 | −0.637982 | ||||||||
\(273\) | 5.12270 | 0.310040 | ||||||||
\(274\) | 7.30503 | 0.441313 | ||||||||
\(275\) | −13.2715 | −0.800300 | ||||||||
\(276\) | −6.14060 | −0.369621 | ||||||||
\(277\) | −27.1151 | −1.62919 | −0.814594 | − | 0.580032i | \(-0.803040\pi\) | ||||
−0.814594 | + | 0.580032i | \(0.803040\pi\) | |||||||
\(278\) | 6.32047 | 0.379077 | ||||||||
\(279\) | −2.69886 | −0.161577 | ||||||||
\(280\) | 3.75631 | 0.224483 | ||||||||
\(281\) | −9.15118 | −0.545914 | −0.272957 | − | 0.962026i | \(-0.588002\pi\) | ||||
−0.272957 | + | 0.962026i | \(0.588002\pi\) | |||||||
\(282\) | −11.6545 | −0.694017 | ||||||||
\(283\) | 5.37462 | 0.319488 | 0.159744 | − | 0.987158i | \(-0.448933\pi\) | ||||
0.159744 | + | 0.987158i | \(0.448933\pi\) | |||||||
\(284\) | 5.51315 | 0.327145 | ||||||||
\(285\) | −6.94011 | −0.411097 | ||||||||
\(286\) | −20.3180 | −1.20143 | ||||||||
\(287\) | 4.66419 | 0.275319 | ||||||||
\(288\) | 4.73411 | 0.278960 | ||||||||
\(289\) | 50.1864 | 2.95214 | ||||||||
\(290\) | −3.18770 | −0.187188 | ||||||||
\(291\) | −13.7072 | −0.803532 | ||||||||
\(292\) | 6.87883 | 0.402553 | ||||||||
\(293\) | −0.496635 | −0.0290137 | −0.0145069 | − | 0.999895i | \(-0.504618\pi\) | ||||
−0.0145069 | + | 0.999895i | \(0.504618\pi\) | |||||||
\(294\) | −1.03548 | −0.0603905 | ||||||||
\(295\) | −4.87005 | −0.283545 | ||||||||
\(296\) | 14.7957 | 0.859985 | ||||||||
\(297\) | −3.83036 | −0.222260 | ||||||||
\(298\) | 21.8031 | 1.26302 | ||||||||
\(299\) | 33.9051 | 1.96078 | ||||||||
\(300\) | −3.21458 | −0.185594 | ||||||||
\(301\) | 0.832065 | 0.0479595 | ||||||||
\(302\) | 16.6249 | 0.956655 | ||||||||
\(303\) | −6.10771 | −0.350879 | ||||||||
\(304\) | 7.19013 | 0.412382 | ||||||||
\(305\) | −12.9950 | −0.744089 | ||||||||
\(306\) | 8.48756 | 0.485201 | ||||||||
\(307\) | −20.3271 | −1.16013 | −0.580065 | − | 0.814570i | \(-0.696973\pi\) | ||||
−0.580065 | + | 0.814570i | \(0.696973\pi\) | |||||||
\(308\) | −3.55373 | −0.202493 | ||||||||
\(309\) | −16.6172 | −0.945319 | ||||||||
\(310\) | 3.46261 | 0.196663 | ||||||||
\(311\) | −15.9129 | −0.902339 | −0.451169 | − | 0.892438i | \(-0.648993\pi\) | ||||
−0.451169 | + | 0.892438i | \(0.648993\pi\) | |||||||
\(312\) | −15.5303 | −0.879229 | ||||||||
\(313\) | −6.32660 | −0.357601 | −0.178800 | − | 0.983885i | \(-0.557222\pi\) | ||||
−0.178800 | + | 0.983885i | \(0.557222\pi\) | |||||||
\(314\) | 21.1937 | 1.19603 | ||||||||
\(315\) | −1.23903 | −0.0698113 | ||||||||
\(316\) | 10.8603 | 0.610938 | ||||||||
\(317\) | 12.6494 | 0.710463 | 0.355232 | − | 0.934778i | \(-0.384402\pi\) | ||||
0.355232 | + | 0.934778i | \(0.384402\pi\) | |||||||
\(318\) | −9.12828 | −0.511889 | ||||||||
\(319\) | 9.51688 | 0.532843 | ||||||||
\(320\) | −9.25481 | −0.517360 | ||||||||
\(321\) | 8.58131 | 0.478962 | ||||||||
\(322\) | −6.85343 | −0.381927 | ||||||||
\(323\) | −45.9120 | −2.55461 | ||||||||
\(324\) | −0.927780 | −0.0515433 | ||||||||
\(325\) | 17.7492 | 0.984547 | ||||||||
\(326\) | 22.5652 | 1.24977 | ||||||||
\(327\) | −16.0391 | −0.886966 | ||||||||
\(328\) | −14.1402 | −0.780764 | ||||||||
\(329\) | 11.2552 | 0.620518 | ||||||||
\(330\) | 4.91432 | 0.270524 | ||||||||
\(331\) | −8.80956 | −0.484217 | −0.242109 | − | 0.970249i | \(-0.577839\pi\) | ||||
−0.242109 | + | 0.970249i | \(0.577839\pi\) | |||||||
\(332\) | −3.67274 | −0.201568 | ||||||||
\(333\) | −4.88041 | −0.267445 | ||||||||
\(334\) | 8.32150 | 0.455332 | ||||||||
\(335\) | 17.6546 | 0.964573 | ||||||||
\(336\) | 1.28367 | 0.0700297 | ||||||||
\(337\) | −13.9721 | −0.761107 | −0.380554 | − | 0.924759i | \(-0.624267\pi\) | ||||
−0.380554 | + | 0.924759i | \(0.624267\pi\) | |||||||
\(338\) | 13.7119 | 0.745829 | ||||||||
\(339\) | 11.8028 | 0.641038 | ||||||||
\(340\) | 9.42251 | 0.511008 | ||||||||
\(341\) | −10.3376 | −0.559813 | ||||||||
\(342\) | −5.79999 | −0.313627 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.52254 | −0.136006 | ||||||||
\(345\) | −8.20063 | −0.441507 | ||||||||
\(346\) | −14.0269 | −0.754089 | ||||||||
\(347\) | −10.6632 | −0.572428 | −0.286214 | − | 0.958166i | \(-0.592397\pi\) | ||||
−0.286214 | + | 0.958166i | \(0.592397\pi\) | |||||||
\(348\) | 2.30515 | 0.123569 | ||||||||
\(349\) | 15.5601 | 0.832915 | 0.416458 | − | 0.909155i | \(-0.363271\pi\) | ||||
0.416458 | + | 0.909155i | \(0.363271\pi\) | |||||||
\(350\) | −3.58774 | −0.191773 | ||||||||
\(351\) | 5.12270 | 0.273430 | ||||||||
\(352\) | 18.1333 | 0.966510 | ||||||||
\(353\) | −8.40425 | −0.447313 | −0.223657 | − | 0.974668i | \(-0.571799\pi\) | ||||
−0.223657 | + | 0.974668i | \(0.571799\pi\) | |||||||
\(354\) | −4.07000 | −0.216318 | ||||||||
\(355\) | 7.36268 | 0.390771 | ||||||||
\(356\) | 11.0167 | 0.583883 | ||||||||
\(357\) | −8.19673 | −0.433817 | ||||||||
\(358\) | 24.3595 | 1.28744 | ||||||||
\(359\) | −0.934350 | −0.0493131 | −0.0246566 | − | 0.999696i | \(-0.507849\pi\) | ||||
−0.0246566 | + | 0.999696i | \(0.507849\pi\) | |||||||
\(360\) | 3.75631 | 0.197975 | ||||||||
\(361\) | 12.3740 | 0.651264 | ||||||||
\(362\) | 12.3519 | 0.649202 | ||||||||
\(363\) | −3.67167 | −0.192713 | ||||||||
\(364\) | 4.75274 | 0.249111 | ||||||||
\(365\) | 9.18652 | 0.480845 | ||||||||
\(366\) | −10.8601 | −0.567669 | ||||||||
\(367\) | 32.1892 | 1.68026 | 0.840130 | − | 0.542385i | \(-0.182478\pi\) | ||||
0.840130 | + | 0.542385i | \(0.182478\pi\) | |||||||
\(368\) | 8.49606 | 0.442888 | ||||||||
\(369\) | 4.66419 | 0.242808 | ||||||||
\(370\) | 6.26152 | 0.325521 | ||||||||
\(371\) | 8.81550 | 0.457678 | ||||||||
\(372\) | −2.50395 | −0.129824 | ||||||||
\(373\) | −12.6410 | −0.654526 | −0.327263 | − | 0.944933i | \(-0.606126\pi\) | ||||
−0.327263 | + | 0.944933i | \(0.606126\pi\) | |||||||
\(374\) | 32.5104 | 1.68107 | ||||||||
\(375\) | −10.4881 | −0.541605 | ||||||||
\(376\) | −34.1219 | −1.75970 | ||||||||
\(377\) | −12.7278 | −0.655515 | ||||||||
\(378\) | −1.03548 | −0.0532594 | ||||||||
\(379\) | −31.1978 | −1.60252 | −0.801262 | − | 0.598314i | \(-0.795837\pi\) | ||||
−0.801262 | + | 0.598314i | \(0.795837\pi\) | |||||||
\(380\) | −6.43889 | −0.330308 | ||||||||
\(381\) | −14.4486 | −0.740226 | ||||||||
\(382\) | −1.03548 | −0.0529798 | ||||||||
\(383\) | 15.3609 | 0.784905 | 0.392453 | − | 0.919772i | \(-0.371627\pi\) | ||||
0.392453 | + | 0.919772i | \(0.371627\pi\) | |||||||
\(384\) | 1.73379 | 0.0884769 | ||||||||
\(385\) | −4.74593 | −0.241875 | ||||||||
\(386\) | 17.5236 | 0.891930 | ||||||||
\(387\) | 0.832065 | 0.0422963 | ||||||||
\(388\) | −12.7173 | −0.645623 | ||||||||
\(389\) | 25.6288 | 1.29943 | 0.649716 | − | 0.760177i | \(-0.274888\pi\) | ||||
0.649716 | + | 0.760177i | \(0.274888\pi\) | |||||||
\(390\) | −6.57237 | −0.332805 | ||||||||
\(391\) | −54.2509 | −2.74358 | ||||||||
\(392\) | −3.03166 | −0.153122 | ||||||||
\(393\) | −18.5110 | −0.933758 | ||||||||
\(394\) | −7.49219 | −0.377451 | ||||||||
\(395\) | 14.5036 | 0.729757 | ||||||||
\(396\) | −3.55373 | −0.178582 | ||||||||
\(397\) | −18.3487 | −0.920896 | −0.460448 | − | 0.887687i | \(-0.652311\pi\) | ||||
−0.460448 | + | 0.887687i | \(0.652311\pi\) | |||||||
\(398\) | −15.9977 | −0.801890 | ||||||||
\(399\) | 5.60125 | 0.280413 | ||||||||
\(400\) | 4.44766 | 0.222383 | ||||||||
\(401\) | −5.97823 | −0.298539 | −0.149269 | − | 0.988797i | \(-0.547692\pi\) | ||||
−0.149269 | + | 0.988797i | \(0.547692\pi\) | |||||||
\(402\) | 14.7543 | 0.735877 | ||||||||
\(403\) | 13.8255 | 0.688695 | ||||||||
\(404\) | −5.66661 | −0.281924 | ||||||||
\(405\) | −1.23903 | −0.0615678 | ||||||||
\(406\) | 2.57274 | 0.127683 | ||||||||
\(407\) | −18.6937 | −0.926614 | ||||||||
\(408\) | 24.8497 | 1.23024 | ||||||||
\(409\) | −3.60182 | −0.178099 | −0.0890494 | − | 0.996027i | \(-0.528383\pi\) | ||||
−0.0890494 | + | 0.996027i | \(0.528383\pi\) | |||||||
\(410\) | −5.98411 | −0.295534 | ||||||||
\(411\) | −7.05472 | −0.347984 | ||||||||
\(412\) | −15.4171 | −0.759545 | ||||||||
\(413\) | 3.93054 | 0.193409 | ||||||||
\(414\) | −6.85343 | −0.336828 | ||||||||
\(415\) | −4.90486 | −0.240770 | ||||||||
\(416\) | −24.2514 | −1.18902 | ||||||||
\(417\) | −6.10390 | −0.298909 | ||||||||
\(418\) | −22.2160 | −1.08662 | ||||||||
\(419\) | 15.2335 | 0.744203 | 0.372102 | − | 0.928192i | \(-0.378637\pi\) | ||||
0.372102 | + | 0.928192i | \(0.378637\pi\) | |||||||
\(420\) | −1.14955 | −0.0560921 | ||||||||
\(421\) | 26.7843 | 1.30539 | 0.652693 | − | 0.757623i | \(-0.273639\pi\) | ||||
0.652693 | + | 0.757623i | \(0.273639\pi\) | |||||||
\(422\) | 8.11007 | 0.394792 | ||||||||
\(423\) | 11.2552 | 0.547245 | ||||||||
\(424\) | −26.7256 | −1.29791 | ||||||||
\(425\) | −28.4001 | −1.37761 | ||||||||
\(426\) | 6.15314 | 0.298121 | ||||||||
\(427\) | 10.4880 | 0.507551 | ||||||||
\(428\) | 7.96157 | 0.384837 | ||||||||
\(429\) | 19.6218 | 0.947349 | ||||||||
\(430\) | −1.06753 | −0.0514809 | ||||||||
\(431\) | 33.5761 | 1.61731 | 0.808653 | − | 0.588286i | \(-0.200197\pi\) | ||||
0.808653 | + | 0.588286i | \(0.200197\pi\) | |||||||
\(432\) | 1.28367 | 0.0617604 | ||||||||
\(433\) | −35.8077 | −1.72081 | −0.860405 | − | 0.509611i | \(-0.829789\pi\) | ||||
−0.860405 | + | 0.509611i | \(0.829789\pi\) | |||||||
\(434\) | −2.79462 | −0.134146 | ||||||||
\(435\) | 3.07848 | 0.147602 | ||||||||
\(436\) | −14.8808 | −0.712660 | ||||||||
\(437\) | 37.0724 | 1.77341 | ||||||||
\(438\) | 7.67736 | 0.366838 | ||||||||
\(439\) | −2.42248 | −0.115619 | −0.0578093 | − | 0.998328i | \(-0.518412\pi\) | ||||
−0.0578093 | + | 0.998328i | \(0.518412\pi\) | |||||||
\(440\) | 14.3880 | 0.685923 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −43.4792 | −2.06810 | ||||||||
\(443\) | 1.00578 | 0.0477863 | 0.0238931 | − | 0.999715i | \(-0.492394\pi\) | ||||
0.0238931 | + | 0.999715i | \(0.492394\pi\) | |||||||
\(444\) | −4.52795 | −0.214887 | ||||||||
\(445\) | 14.7125 | 0.697441 | ||||||||
\(446\) | −0.919200 | −0.0435254 | ||||||||
\(447\) | −21.0560 | −0.995914 | ||||||||
\(448\) | 7.46941 | 0.352896 | ||||||||
\(449\) | −33.4083 | −1.57664 | −0.788318 | − | 0.615268i | \(-0.789048\pi\) | ||||
−0.788318 | + | 0.615268i | \(0.789048\pi\) | |||||||
\(450\) | −3.58774 | −0.169128 | ||||||||
\(451\) | 17.8655 | 0.841256 | ||||||||
\(452\) | 10.9504 | 0.515062 | ||||||||
\(453\) | −16.0552 | −0.754341 | ||||||||
\(454\) | 19.7664 | 0.927681 | ||||||||
\(455\) | 6.34717 | 0.297560 | ||||||||
\(456\) | −16.9811 | −0.795212 | ||||||||
\(457\) | −11.3183 | −0.529448 | −0.264724 | − | 0.964324i | \(-0.585281\pi\) | ||||
−0.264724 | + | 0.964324i | \(0.585281\pi\) | |||||||
\(458\) | 7.41391 | 0.346429 | ||||||||
\(459\) | −8.19673 | −0.382591 | ||||||||
\(460\) | −7.60837 | −0.354742 | ||||||||
\(461\) | 24.0057 | 1.11806 | 0.559028 | − | 0.829149i | \(-0.311174\pi\) | ||||
0.559028 | + | 0.829149i | \(0.311174\pi\) | |||||||
\(462\) | −3.96627 | −0.184527 | ||||||||
\(463\) | −24.4560 | −1.13657 | −0.568284 | − | 0.822832i | \(-0.692393\pi\) | ||||
−0.568284 | + | 0.822832i | \(0.692393\pi\) | |||||||
\(464\) | −3.18938 | −0.148063 | ||||||||
\(465\) | −3.34397 | −0.155073 | ||||||||
\(466\) | −12.5788 | −0.582701 | ||||||||
\(467\) | 36.4231 | 1.68546 | 0.842730 | − | 0.538337i | \(-0.180947\pi\) | ||||
0.842730 | + | 0.538337i | \(0.180947\pi\) | |||||||
\(468\) | 4.75274 | 0.219695 | ||||||||
\(469\) | −14.2487 | −0.657945 | ||||||||
\(470\) | −14.4403 | −0.666080 | ||||||||
\(471\) | −20.4675 | −0.943091 | ||||||||
\(472\) | −11.9161 | −0.548481 | ||||||||
\(473\) | 3.18711 | 0.146544 | ||||||||
\(474\) | 12.1210 | 0.556735 | ||||||||
\(475\) | 19.4073 | 0.890466 | ||||||||
\(476\) | −7.60476 | −0.348564 | ||||||||
\(477\) | 8.81550 | 0.403634 | ||||||||
\(478\) | −26.7097 | −1.22167 | ||||||||
\(479\) | −2.84767 | −0.130113 | −0.0650566 | − | 0.997882i | \(-0.520723\pi\) | ||||
−0.0650566 | + | 0.997882i | \(0.520723\pi\) | |||||||
\(480\) | 5.86569 | 0.267731 | ||||||||
\(481\) | 25.0009 | 1.13994 | ||||||||
\(482\) | −21.6037 | −0.984021 | ||||||||
\(483\) | 6.61860 | 0.301157 | ||||||||
\(484\) | −3.40650 | −0.154841 | ||||||||
\(485\) | −16.9837 | −0.771188 | ||||||||
\(486\) | −1.03548 | −0.0469704 | ||||||||
\(487\) | −23.1098 | −1.04721 | −0.523603 | − | 0.851962i | \(-0.675413\pi\) | ||||
−0.523603 | + | 0.851962i | \(0.675413\pi\) | |||||||
\(488\) | −31.7961 | −1.43934 | ||||||||
\(489\) | −21.7920 | −0.985470 | ||||||||
\(490\) | −1.28299 | −0.0579596 | ||||||||
\(491\) | −25.6490 | −1.15752 | −0.578761 | − | 0.815497i | \(-0.696464\pi\) | ||||
−0.578761 | + | 0.815497i | \(0.696464\pi\) | |||||||
\(492\) | 4.32734 | 0.195092 | ||||||||
\(493\) | 20.3655 | 0.917217 | ||||||||
\(494\) | 29.7116 | 1.33679 | ||||||||
\(495\) | −4.74593 | −0.213314 | ||||||||
\(496\) | 3.46444 | 0.155558 | ||||||||
\(497\) | −5.94230 | −0.266549 | ||||||||
\(498\) | −4.09909 | −0.183685 | ||||||||
\(499\) | −7.56274 | −0.338555 | −0.169277 | − | 0.985568i | \(-0.554143\pi\) | ||||
−0.169277 | + | 0.985568i | \(0.554143\pi\) | |||||||
\(500\) | −9.73068 | −0.435169 | ||||||||
\(501\) | −8.03636 | −0.359038 | ||||||||
\(502\) | 1.87727 | 0.0837868 | ||||||||
\(503\) | 9.87745 | 0.440414 | 0.220207 | − | 0.975453i | \(-0.429327\pi\) | ||||
0.220207 | + | 0.975453i | \(0.429327\pi\) | |||||||
\(504\) | −3.03166 | −0.135041 | ||||||||
\(505\) | −7.56762 | −0.336755 | ||||||||
\(506\) | −26.2511 | −1.16700 | ||||||||
\(507\) | −13.2421 | −0.588101 | ||||||||
\(508\) | −13.4051 | −0.594757 | ||||||||
\(509\) | 33.4259 | 1.48158 | 0.740789 | − | 0.671738i | \(-0.234452\pi\) | ||||
0.740789 | + | 0.671738i | \(0.234452\pi\) | |||||||
\(510\) | 10.5163 | 0.465671 | ||||||||
\(511\) | −7.41430 | −0.327989 | ||||||||
\(512\) | −13.8603 | −0.612544 | ||||||||
\(513\) | 5.60125 | 0.247301 | ||||||||
\(514\) | 8.82547 | 0.389275 | ||||||||
\(515\) | −20.5892 | −0.907267 | ||||||||
\(516\) | 0.771973 | 0.0339842 | ||||||||
\(517\) | 43.1114 | 1.89604 | ||||||||
\(518\) | −5.05357 | −0.222041 | ||||||||
\(519\) | 13.5462 | 0.594614 | ||||||||
\(520\) | −19.2425 | −0.843838 | ||||||||
\(521\) | 0.866290 | 0.0379529 | 0.0189764 | − | 0.999820i | \(-0.493959\pi\) | ||||
0.0189764 | + | 0.999820i | \(0.493959\pi\) | |||||||
\(522\) | 2.57274 | 0.112606 | ||||||||
\(523\) | −2.25721 | −0.0987010 | −0.0493505 | − | 0.998782i | \(-0.515715\pi\) | ||||
−0.0493505 | + | 0.998782i | \(0.515715\pi\) | |||||||
\(524\) | −17.1742 | −0.750256 | ||||||||
\(525\) | 3.46481 | 0.151217 | ||||||||
\(526\) | −4.39511 | −0.191636 | ||||||||
\(527\) | −22.1218 | −0.963642 | ||||||||
\(528\) | 4.91690 | 0.213981 | ||||||||
\(529\) | 20.8058 | 0.904600 | ||||||||
\(530\) | −11.3102 | −0.491284 | ||||||||
\(531\) | 3.93054 | 0.170571 | ||||||||
\(532\) | 5.19673 | 0.225307 | ||||||||
\(533\) | −23.8933 | −1.03493 | ||||||||
\(534\) | 12.2956 | 0.532081 | ||||||||
\(535\) | 10.6325 | 0.459682 | ||||||||
\(536\) | 43.1973 | 1.86584 | ||||||||
\(537\) | −23.5248 | −1.01517 | ||||||||
\(538\) | 9.29518 | 0.400744 | ||||||||
\(539\) | 3.83036 | 0.164985 | ||||||||
\(540\) | −1.14955 | −0.0494686 | ||||||||
\(541\) | 26.7012 | 1.14797 | 0.573986 | − | 0.818865i | \(-0.305396\pi\) | ||||
0.573986 | + | 0.818865i | \(0.305396\pi\) | |||||||
\(542\) | −18.6821 | −0.802466 | ||||||||
\(543\) | −11.9287 | −0.511908 | ||||||||
\(544\) | 38.8042 | 1.66372 | ||||||||
\(545\) | −19.8729 | −0.851264 | ||||||||
\(546\) | 5.30446 | 0.227010 | ||||||||
\(547\) | −14.9914 | −0.640985 | −0.320493 | − | 0.947251i | \(-0.603848\pi\) | ||||
−0.320493 | + | 0.947251i | \(0.603848\pi\) | |||||||
\(548\) | −6.54522 | −0.279598 | ||||||||
\(549\) | 10.4880 | 0.447618 | ||||||||
\(550\) | −13.7424 | −0.585976 | ||||||||
\(551\) | −13.9168 | −0.592876 | ||||||||
\(552\) | −20.0653 | −0.854037 | ||||||||
\(553\) | −11.7057 | −0.497775 | ||||||||
\(554\) | −28.0772 | −1.19288 | ||||||||
\(555\) | −6.04697 | −0.256679 | ||||||||
\(556\) | −5.66307 | −0.240168 | ||||||||
\(557\) | 35.3420 | 1.49749 | 0.748743 | − | 0.662860i | \(-0.230658\pi\) | ||||
0.748743 | + | 0.662860i | \(0.230658\pi\) | |||||||
\(558\) | −2.79462 | −0.118306 | ||||||||
\(559\) | −4.26242 | −0.180281 | ||||||||
\(560\) | 1.59050 | 0.0672108 | ||||||||
\(561\) | −31.3964 | −1.32556 | ||||||||
\(562\) | −9.47587 | −0.399716 | ||||||||
\(563\) | −12.8090 | −0.539836 | −0.269918 | − | 0.962883i | \(-0.586997\pi\) | ||||
−0.269918 | + | 0.962883i | \(0.586997\pi\) | |||||||
\(564\) | 10.4423 | 0.439701 | ||||||||
\(565\) | 14.6240 | 0.615235 | ||||||||
\(566\) | 5.56531 | 0.233928 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 18.0150 | 0.755894 | ||||||||
\(569\) | −14.9950 | −0.628624 | −0.314312 | − | 0.949320i | \(-0.601774\pi\) | ||||
−0.314312 | + | 0.949320i | \(0.601774\pi\) | |||||||
\(570\) | −7.18635 | −0.301003 | ||||||||
\(571\) | 17.8079 | 0.745237 | 0.372618 | − | 0.927985i | \(-0.378460\pi\) | ||||
0.372618 | + | 0.927985i | \(0.378460\pi\) | |||||||
\(572\) | 18.2047 | 0.761177 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | 4.82968 | 0.201587 | ||||||||
\(575\) | 22.9322 | 0.956338 | ||||||||
\(576\) | 7.46941 | 0.311225 | ||||||||
\(577\) | −17.7604 | −0.739376 | −0.369688 | − | 0.929156i | \(-0.620535\pi\) | ||||
−0.369688 | + | 0.929156i | \(0.620535\pi\) | |||||||
\(578\) | 51.9671 | 2.16154 | ||||||||
\(579\) | −16.9232 | −0.703304 | ||||||||
\(580\) | 2.85615 | 0.118595 | ||||||||
\(581\) | 3.95863 | 0.164232 | ||||||||
\(582\) | −14.1936 | −0.588343 | ||||||||
\(583\) | 33.7666 | 1.39847 | ||||||||
\(584\) | 22.4776 | 0.930131 | ||||||||
\(585\) | 6.34717 | 0.262423 | ||||||||
\(586\) | −0.514256 | −0.0212437 | ||||||||
\(587\) | −43.8320 | −1.80914 | −0.904570 | − | 0.426325i | \(-0.859808\pi\) | ||||
−0.904570 | + | 0.426325i | \(0.859808\pi\) | |||||||
\(588\) | 0.927780 | 0.0382610 | ||||||||
\(589\) | 15.1170 | 0.622885 | ||||||||
\(590\) | −5.04284 | −0.207610 | ||||||||
\(591\) | 7.23547 | 0.297628 | ||||||||
\(592\) | 6.26481 | 0.257482 | ||||||||
\(593\) | 28.9429 | 1.18854 | 0.594271 | − | 0.804265i | \(-0.297441\pi\) | ||||
0.594271 | + | 0.804265i | \(0.297441\pi\) | |||||||
\(594\) | −3.96627 | −0.162738 | ||||||||
\(595\) | −10.1560 | −0.416355 | ||||||||
\(596\) | −19.5353 | −0.800197 | ||||||||
\(597\) | 15.4495 | 0.632306 | ||||||||
\(598\) | 35.1081 | 1.43568 | ||||||||
\(599\) | 5.84676 | 0.238892 | 0.119446 | − | 0.992841i | \(-0.461888\pi\) | ||||
0.119446 | + | 0.992841i | \(0.461888\pi\) | |||||||
\(600\) | −10.5041 | −0.428829 | ||||||||
\(601\) | 13.8434 | 0.564685 | 0.282342 | − | 0.959314i | \(-0.408889\pi\) | ||||
0.282342 | + | 0.959314i | \(0.408889\pi\) | |||||||
\(602\) | 0.861588 | 0.0351157 | ||||||||
\(603\) | −14.2487 | −0.580253 | ||||||||
\(604\) | −14.8957 | −0.606099 | ||||||||
\(605\) | −4.54930 | −0.184955 | ||||||||
\(606\) | −6.32442 | −0.256912 | ||||||||
\(607\) | −8.80332 | −0.357316 | −0.178658 | − | 0.983911i | \(-0.557176\pi\) | ||||
−0.178658 | + | 0.983911i | \(0.557176\pi\) | |||||||
\(608\) | −26.5169 | −1.07540 | ||||||||
\(609\) | −2.48459 | −0.100681 | ||||||||
\(610\) | −13.4560 | −0.544818 | ||||||||
\(611\) | −57.6569 | −2.33255 | ||||||||
\(612\) | −7.60476 | −0.307404 | ||||||||
\(613\) | 3.82811 | 0.154616 | 0.0773080 | − | 0.997007i | \(-0.475368\pi\) | ||||
0.0773080 | + | 0.997007i | \(0.475368\pi\) | |||||||
\(614\) | −21.0483 | −0.849442 | ||||||||
\(615\) | 5.77907 | 0.233034 | ||||||||
\(616\) | −11.6124 | −0.467875 | ||||||||
\(617\) | −16.1738 | −0.651134 | −0.325567 | − | 0.945519i | \(-0.605555\pi\) | ||||
−0.325567 | + | 0.945519i | \(0.605555\pi\) | |||||||
\(618\) | −17.2068 | −0.692158 | ||||||||
\(619\) | 14.0786 | 0.565867 | 0.282933 | − | 0.959140i | \(-0.408692\pi\) | ||||
0.282933 | + | 0.959140i | \(0.408692\pi\) | |||||||
\(620\) | −3.10246 | −0.124598 | ||||||||
\(621\) | 6.61860 | 0.265595 | ||||||||
\(622\) | −16.4775 | −0.660688 | ||||||||
\(623\) | −11.8742 | −0.475732 | ||||||||
\(624\) | −6.57584 | −0.263244 | ||||||||
\(625\) | 4.32894 | 0.173158 | ||||||||
\(626\) | −6.55107 | −0.261833 | ||||||||
\(627\) | 21.4548 | 0.856823 | ||||||||
\(628\) | −18.9893 | −0.757755 | ||||||||
\(629\) | −40.0034 | −1.59504 | ||||||||
\(630\) | −1.28299 | −0.0511155 | ||||||||
\(631\) | 27.2900 | 1.08640 | 0.543198 | − | 0.839605i | \(-0.317213\pi\) | ||||
0.543198 | + | 0.839605i | \(0.317213\pi\) | |||||||
\(632\) | 35.4875 | 1.41162 | ||||||||
\(633\) | −7.83218 | −0.311301 | ||||||||
\(634\) | 13.0983 | 0.520198 | ||||||||
\(635\) | −17.9023 | −0.710430 | ||||||||
\(636\) | 8.17884 | 0.324312 | ||||||||
\(637\) | −5.12270 | −0.202969 | ||||||||
\(638\) | 9.85454 | 0.390145 | ||||||||
\(639\) | −5.94230 | −0.235074 | ||||||||
\(640\) | 2.14821 | 0.0849155 | ||||||||
\(641\) | −10.9172 | −0.431203 | −0.215602 | − | 0.976481i | \(-0.569171\pi\) | ||||
−0.215602 | + | 0.976481i | \(0.569171\pi\) | |||||||
\(642\) | 8.88578 | 0.350694 | ||||||||
\(643\) | −13.7672 | −0.542927 | −0.271463 | − | 0.962449i | \(-0.587508\pi\) | ||||
−0.271463 | + | 0.962449i | \(0.587508\pi\) | |||||||
\(644\) | 6.14060 | 0.241973 | ||||||||
\(645\) | 1.03095 | 0.0405937 | ||||||||
\(646\) | −47.5409 | −1.87047 | ||||||||
\(647\) | −17.3544 | −0.682273 | −0.341136 | − | 0.940014i | \(-0.610812\pi\) | ||||
−0.341136 | + | 0.940014i | \(0.610812\pi\) | |||||||
\(648\) | −3.03166 | −0.119095 | ||||||||
\(649\) | 15.0554 | 0.590975 | ||||||||
\(650\) | 18.3789 | 0.720881 | ||||||||
\(651\) | 2.69886 | 0.105777 | ||||||||
\(652\) | −20.2182 | −0.791806 | ||||||||
\(653\) | 3.04672 | 0.119228 | 0.0596138 | − | 0.998222i | \(-0.481013\pi\) | ||||
0.0596138 | + | 0.998222i | \(0.481013\pi\) | |||||||
\(654\) | −16.6082 | −0.649433 | ||||||||
\(655\) | −22.9357 | −0.896171 | ||||||||
\(656\) | −5.98726 | −0.233763 | ||||||||
\(657\) | −7.41430 | −0.289259 | ||||||||
\(658\) | 11.6545 | 0.454340 | ||||||||
\(659\) | −6.91247 | −0.269271 | −0.134636 | − | 0.990895i | \(-0.542986\pi\) | ||||
−0.134636 | + | 0.990895i | \(0.542986\pi\) | |||||||
\(660\) | −4.40317 | −0.171393 | ||||||||
\(661\) | 14.9233 | 0.580450 | 0.290225 | − | 0.956958i | \(-0.406270\pi\) | ||||
0.290225 | + | 0.956958i | \(0.406270\pi\) | |||||||
\(662\) | −9.12213 | −0.354542 | ||||||||
\(663\) | 41.9894 | 1.63073 | ||||||||
\(664\) | −12.0012 | −0.465738 | ||||||||
\(665\) | 6.94011 | 0.269126 | ||||||||
\(666\) | −5.05357 | −0.195822 | ||||||||
\(667\) | −16.4445 | −0.636733 | ||||||||
\(668\) | −7.45597 | −0.288480 | ||||||||
\(669\) | 0.887704 | 0.0343206 | ||||||||
\(670\) | 18.2810 | 0.706256 | ||||||||
\(671\) | 40.1729 | 1.55086 | ||||||||
\(672\) | −4.73411 | −0.182622 | ||||||||
\(673\) | 26.9290 | 1.03804 | 0.519019 | − | 0.854763i | \(-0.326297\pi\) | ||||
0.519019 | + | 0.854763i | \(0.326297\pi\) | |||||||
\(674\) | −14.4678 | −0.557279 | ||||||||
\(675\) | 3.46481 | 0.133361 | ||||||||
\(676\) | −12.2857 | −0.472528 | ||||||||
\(677\) | 6.28677 | 0.241620 | 0.120810 | − | 0.992676i | \(-0.461451\pi\) | ||||
0.120810 | + | 0.992676i | \(0.461451\pi\) | |||||||
\(678\) | 12.2215 | 0.469365 | ||||||||
\(679\) | 13.7072 | 0.526036 | ||||||||
\(680\) | 30.7895 | 1.18072 | ||||||||
\(681\) | −19.0891 | −0.731495 | ||||||||
\(682\) | −10.7044 | −0.409893 | ||||||||
\(683\) | 25.9587 | 0.993280 | 0.496640 | − | 0.867957i | \(-0.334567\pi\) | ||||
0.496640 | + | 0.867957i | \(0.334567\pi\) | |||||||
\(684\) | 5.19673 | 0.198702 | ||||||||
\(685\) | −8.74100 | −0.333976 | ||||||||
\(686\) | 1.03548 | 0.0395348 | ||||||||
\(687\) | −7.15988 | −0.273166 | ||||||||
\(688\) | −1.06809 | −0.0407207 | ||||||||
\(689\) | −45.1592 | −1.72043 | ||||||||
\(690\) | −8.49159 | −0.323269 | ||||||||
\(691\) | 5.97760 | 0.227399 | 0.113699 | − | 0.993515i | \(-0.463730\pi\) | ||||
0.113699 | + | 0.993515i | \(0.463730\pi\) | |||||||
\(692\) | 12.5679 | 0.477761 | ||||||||
\(693\) | 3.83036 | 0.145503 | ||||||||
\(694\) | −11.0415 | −0.419129 | ||||||||
\(695\) | −7.56291 | −0.286877 | ||||||||
\(696\) | 7.53243 | 0.285516 | ||||||||
\(697\) | 38.2311 | 1.44811 | ||||||||
\(698\) | 16.1122 | 0.609857 | ||||||||
\(699\) | 12.1478 | 0.459471 | ||||||||
\(700\) | 3.21458 | 0.121500 | ||||||||
\(701\) | 26.6366 | 1.00605 | 0.503025 | − | 0.864272i | \(-0.332220\pi\) | ||||
0.503025 | + | 0.864272i | \(0.332220\pi\) | |||||||
\(702\) | 5.30446 | 0.200204 | ||||||||
\(703\) | 27.3364 | 1.03101 | ||||||||
\(704\) | 28.6105 | 1.07830 | ||||||||
\(705\) | 13.9455 | 0.525217 | ||||||||
\(706\) | −8.70244 | −0.327521 | ||||||||
\(707\) | 6.10771 | 0.229704 | ||||||||
\(708\) | 3.64667 | 0.137050 | ||||||||
\(709\) | 16.8165 | 0.631558 | 0.315779 | − | 0.948833i | \(-0.397734\pi\) | ||||
0.315779 | + | 0.948833i | \(0.397734\pi\) | |||||||
\(710\) | 7.62392 | 0.286120 | ||||||||
\(711\) | −11.7057 | −0.438996 | ||||||||
\(712\) | 35.9987 | 1.34911 | ||||||||
\(713\) | 17.8627 | 0.668962 | ||||||||
\(714\) | −8.48756 | −0.317639 | ||||||||
\(715\) | 24.3120 | 0.909216 | ||||||||
\(716\) | −21.8259 | −0.815671 | ||||||||
\(717\) | 25.7944 | 0.963311 | ||||||||
\(718\) | −0.967502 | −0.0361068 | ||||||||
\(719\) | −8.74812 | −0.326250 | −0.163125 | − | 0.986605i | \(-0.552157\pi\) | ||||
−0.163125 | + | 0.986605i | \(0.552157\pi\) | |||||||
\(720\) | 1.59050 | 0.0592744 | ||||||||
\(721\) | 16.6172 | 0.618856 | ||||||||
\(722\) | 12.8131 | 0.476852 | ||||||||
\(723\) | 20.8634 | 0.775919 | ||||||||
\(724\) | −11.0672 | −0.411308 | ||||||||
\(725\) | −8.60863 | −0.319716 | ||||||||
\(726\) | −3.80194 | −0.141103 | ||||||||
\(727\) | −1.47591 | −0.0547384 | −0.0273692 | − | 0.999625i | \(-0.508713\pi\) | ||||
−0.0273692 | + | 0.999625i | \(0.508713\pi\) | |||||||
\(728\) | 15.5303 | 0.575591 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.51247 | 0.352072 | ||||||||
\(731\) | 6.82022 | 0.252255 | ||||||||
\(732\) | 9.73057 | 0.359652 | ||||||||
\(733\) | 49.1283 | 1.81460 | 0.907298 | − | 0.420489i | \(-0.138141\pi\) | ||||
0.907298 | + | 0.420489i | \(0.138141\pi\) | |||||||
\(734\) | 33.3313 | 1.23028 | ||||||||
\(735\) | 1.23903 | 0.0457022 | ||||||||
\(736\) | −31.3331 | −1.15496 | ||||||||
\(737\) | −54.5778 | −2.01040 | ||||||||
\(738\) | 4.82968 | 0.177783 | ||||||||
\(739\) | 3.95747 | 0.145578 | 0.0727889 | − | 0.997347i | \(-0.476810\pi\) | ||||
0.0727889 | + | 0.997347i | \(0.476810\pi\) | |||||||
\(740\) | −5.61025 | −0.206237 | ||||||||
\(741\) | −28.6935 | −1.05408 | ||||||||
\(742\) | 9.12828 | 0.335110 | ||||||||
\(743\) | −16.0435 | −0.588580 | −0.294290 | − | 0.955716i | \(-0.595083\pi\) | ||||
−0.294290 | + | 0.955716i | \(0.595083\pi\) | |||||||
\(744\) | −8.18203 | −0.299968 | ||||||||
\(745\) | −26.0890 | −0.955825 | ||||||||
\(746\) | −13.0895 | −0.479241 | ||||||||
\(747\) | 3.95863 | 0.144839 | ||||||||
\(748\) | −29.1290 | −1.06506 | ||||||||
\(749\) | −8.58131 | −0.313554 | ||||||||
\(750\) | −10.8603 | −0.396561 | ||||||||
\(751\) | −17.6973 | −0.645783 | −0.322892 | − | 0.946436i | \(-0.604655\pi\) | ||||
−0.322892 | + | 0.946436i | \(0.604655\pi\) | |||||||
\(752\) | −14.4479 | −0.526860 | ||||||||
\(753\) | −1.81295 | −0.0660675 | ||||||||
\(754\) | −13.1794 | −0.479965 | ||||||||
\(755\) | −19.8929 | −0.723977 | ||||||||
\(756\) | 0.927780 | 0.0337430 | ||||||||
\(757\) | −32.6516 | −1.18674 | −0.593372 | − | 0.804929i | \(-0.702204\pi\) | ||||
−0.593372 | + | 0.804929i | \(0.702204\pi\) | |||||||
\(758\) | −32.3047 | −1.17336 | ||||||||
\(759\) | 25.3516 | 0.920205 | ||||||||
\(760\) | −21.0400 | −0.763203 | ||||||||
\(761\) | −0.230812 | −0.00836692 | −0.00418346 | − | 0.999991i | \(-0.501332\pi\) | ||||
−0.00418346 | + | 0.999991i | \(0.501332\pi\) | |||||||
\(762\) | −14.9613 | −0.541990 | ||||||||
\(763\) | 16.0391 | 0.580656 | ||||||||
\(764\) | 0.927780 | 0.0335659 | ||||||||
\(765\) | −10.1560 | −0.367190 | ||||||||
\(766\) | 15.9059 | 0.574704 | ||||||||
\(767\) | −20.1350 | −0.727032 | ||||||||
\(768\) | 16.7341 | 0.603841 | ||||||||
\(769\) | 32.6341 | 1.17682 | 0.588408 | − | 0.808564i | \(-0.299755\pi\) | ||||
0.588408 | + | 0.808564i | \(0.299755\pi\) | |||||||
\(770\) | −4.91432 | −0.177100 | ||||||||
\(771\) | −8.52307 | −0.306951 | ||||||||
\(772\) | −15.7010 | −0.565091 | ||||||||
\(773\) | −52.2980 | −1.88103 | −0.940515 | − | 0.339754i | \(-0.889656\pi\) | ||||
−0.940515 | + | 0.339754i | \(0.889656\pi\) | |||||||
\(774\) | 0.861588 | 0.0309691 | ||||||||
\(775\) | 9.35104 | 0.335899 | ||||||||
\(776\) | −41.5557 | −1.49176 | ||||||||
\(777\) | 4.88041 | 0.175084 | ||||||||
\(778\) | 26.5381 | 0.951438 | ||||||||
\(779\) | −26.1253 | −0.936037 | ||||||||
\(780\) | 5.88878 | 0.210852 | ||||||||
\(781\) | −22.7612 | −0.814459 | ||||||||
\(782\) | −56.1757 | −2.00884 | ||||||||
\(783\) | −2.48459 | −0.0887920 | ||||||||
\(784\) | −1.28367 | −0.0458452 | ||||||||
\(785\) | −25.3598 | −0.905129 | ||||||||
\(786\) | −19.1678 | −0.683693 | ||||||||
\(787\) | −6.56073 | −0.233865 | −0.116932 | − | 0.993140i | \(-0.537306\pi\) | ||||
−0.116932 | + | 0.993140i | \(0.537306\pi\) | |||||||
\(788\) | 6.71293 | 0.239138 | ||||||||
\(789\) | 4.24451 | 0.151109 | ||||||||
\(790\) | 15.0182 | 0.534325 | ||||||||
\(791\) | −11.8028 | −0.419658 | ||||||||
\(792\) | −11.6124 | −0.412627 | ||||||||
\(793\) | −53.7270 | −1.90790 | ||||||||
\(794\) | −18.9998 | −0.674276 | ||||||||
\(795\) | 10.9227 | 0.387387 | ||||||||
\(796\) | 14.3337 | 0.508045 | ||||||||
\(797\) | −1.35342 | −0.0479407 | −0.0239703 | − | 0.999713i | \(-0.507631\pi\) | ||||
−0.0239703 | + | 0.999713i | \(0.507631\pi\) | |||||||
\(798\) | 5.79999 | 0.205317 | ||||||||
\(799\) | 92.2557 | 3.26377 | ||||||||
\(800\) | −16.4028 | −0.579926 | ||||||||
\(801\) | −11.8742 | −0.419556 | ||||||||
\(802\) | −6.19035 | −0.218589 | ||||||||
\(803\) | −28.3994 | −1.00219 | ||||||||
\(804\) | −13.2197 | −0.466222 | ||||||||
\(805\) | 8.20063 | 0.289034 | ||||||||
\(806\) | 14.3160 | 0.504259 | ||||||||
\(807\) | −8.97669 | −0.315994 | ||||||||
\(808\) | −18.5165 | −0.651408 | ||||||||
\(809\) | 8.74726 | 0.307537 | 0.153769 | − | 0.988107i | \(-0.450859\pi\) | ||||
0.153769 | + | 0.988107i | \(0.450859\pi\) | |||||||
\(810\) | −1.28299 | −0.0450797 | ||||||||
\(811\) | −14.0354 | −0.492848 | −0.246424 | − | 0.969162i | \(-0.579256\pi\) | ||||
−0.246424 | + | 0.969162i | \(0.579256\pi\) | |||||||
\(812\) | −2.30515 | −0.0808950 | ||||||||
\(813\) | 18.0420 | 0.632760 | ||||||||
\(814\) | −19.3570 | −0.678463 | ||||||||
\(815\) | −27.0009 | −0.945802 | ||||||||
\(816\) | 10.5219 | 0.368339 | ||||||||
\(817\) | −4.66061 | −0.163054 | ||||||||
\(818\) | −3.72962 | −0.130403 | ||||||||
\(819\) | −5.12270 | −0.179002 | ||||||||
\(820\) | 5.36170 | 0.187239 | ||||||||
\(821\) | −25.5355 | −0.891196 | −0.445598 | − | 0.895233i | \(-0.647009\pi\) | ||||
−0.445598 | + | 0.895233i | \(0.647009\pi\) | |||||||
\(822\) | −7.30503 | −0.254792 | ||||||||
\(823\) | 47.0500 | 1.64006 | 0.820029 | − | 0.572322i | \(-0.193957\pi\) | ||||
0.820029 | + | 0.572322i | \(0.193957\pi\) | |||||||
\(824\) | −50.3777 | −1.75499 | ||||||||
\(825\) | 13.2715 | 0.462053 | ||||||||
\(826\) | 4.07000 | 0.141613 | ||||||||
\(827\) | 18.2998 | 0.636346 | 0.318173 | − | 0.948033i | \(-0.396931\pi\) | ||||
0.318173 | + | 0.948033i | \(0.396931\pi\) | |||||||
\(828\) | 6.14060 | 0.213401 | ||||||||
\(829\) | −36.4853 | −1.26719 | −0.633594 | − | 0.773665i | \(-0.718421\pi\) | ||||
−0.633594 | + | 0.773665i | \(0.718421\pi\) | |||||||
\(830\) | −5.07889 | −0.176291 | ||||||||
\(831\) | 27.1151 | 0.940612 | ||||||||
\(832\) | −38.2635 | −1.32655 | ||||||||
\(833\) | 8.19673 | 0.284000 | ||||||||
\(834\) | −6.32047 | −0.218860 | ||||||||
\(835\) | −9.95728 | −0.344586 | ||||||||
\(836\) | 19.9053 | 0.688441 | ||||||||
\(837\) | 2.69886 | 0.0932863 | ||||||||
\(838\) | 15.7740 | 0.544902 | ||||||||
\(839\) | 39.8482 | 1.37571 | 0.687857 | − | 0.725846i | \(-0.258552\pi\) | ||||
0.687857 | + | 0.725846i | \(0.258552\pi\) | |||||||
\(840\) | −3.75631 | −0.129605 | ||||||||
\(841\) | −22.8268 | −0.787132 | ||||||||
\(842\) | 27.7346 | 0.955797 | ||||||||
\(843\) | 9.15118 | 0.315184 | ||||||||
\(844\) | −7.26654 | −0.250124 | ||||||||
\(845\) | −16.4073 | −0.564428 | ||||||||
\(846\) | 11.6545 | 0.400691 | ||||||||
\(847\) | 3.67167 | 0.126160 | ||||||||
\(848\) | −11.3162 | −0.388598 | ||||||||
\(849\) | −5.37462 | −0.184456 | ||||||||
\(850\) | −29.4078 | −1.00868 | ||||||||
\(851\) | 32.3015 | 1.10728 | ||||||||
\(852\) | −5.51315 | −0.188877 | ||||||||
\(853\) | 12.8208 | 0.438975 | 0.219488 | − | 0.975615i | \(-0.429561\pi\) | ||||
0.219488 | + | 0.975615i | \(0.429561\pi\) | |||||||
\(854\) | 10.8601 | 0.371626 | ||||||||
\(855\) | 6.94011 | 0.237347 | ||||||||
\(856\) | 26.0156 | 0.889195 | ||||||||
\(857\) | −29.2405 | −0.998838 | −0.499419 | − | 0.866361i | \(-0.666453\pi\) | ||||
−0.499419 | + | 0.866361i | \(0.666453\pi\) | |||||||
\(858\) | 20.3180 | 0.693645 | ||||||||
\(859\) | −40.5745 | −1.38438 | −0.692192 | − | 0.721714i | \(-0.743355\pi\) | ||||
−0.692192 | + | 0.721714i | \(0.743355\pi\) | |||||||
\(860\) | 0.956497 | 0.0326163 | ||||||||
\(861\) | −4.66419 | −0.158955 | ||||||||
\(862\) | 34.7674 | 1.18418 | ||||||||
\(863\) | 20.9432 | 0.712915 | 0.356458 | − | 0.934311i | \(-0.383984\pi\) | ||||
0.356458 | + | 0.934311i | \(0.383984\pi\) | |||||||
\(864\) | −4.73411 | −0.161058 | ||||||||
\(865\) | 16.7842 | 0.570679 | ||||||||
\(866\) | −37.0782 | −1.25997 | ||||||||
\(867\) | −50.1864 | −1.70442 | ||||||||
\(868\) | 2.50395 | 0.0849895 | ||||||||
\(869\) | −44.8369 | −1.52099 | ||||||||
\(870\) | 3.18770 | 0.108073 | ||||||||
\(871\) | 72.9920 | 2.47324 | ||||||||
\(872\) | −48.6252 | −1.64666 | ||||||||
\(873\) | 13.7072 | 0.463920 | ||||||||
\(874\) | 38.3878 | 1.29849 | ||||||||
\(875\) | 10.4881 | 0.354564 | ||||||||
\(876\) | −6.87883 | −0.232414 | ||||||||
\(877\) | 24.1235 | 0.814594 | 0.407297 | − | 0.913296i | \(-0.366471\pi\) | ||||
0.407297 | + | 0.913296i | \(0.366471\pi\) | |||||||
\(878\) | −2.50843 | −0.0846554 | ||||||||
\(879\) | 0.496635 | 0.0167511 | ||||||||
\(880\) | 6.09218 | 0.205367 | ||||||||
\(881\) | 50.0546 | 1.68638 | 0.843191 | − | 0.537615i | \(-0.180675\pi\) | ||||
0.843191 | + | 0.537615i | \(0.180675\pi\) | |||||||
\(882\) | 1.03548 | 0.0348665 | ||||||||
\(883\) | −43.1155 | −1.45095 | −0.725476 | − | 0.688248i | \(-0.758380\pi\) | ||||
−0.725476 | + | 0.688248i | \(0.758380\pi\) | |||||||
\(884\) | 38.9569 | 1.31026 | ||||||||
\(885\) | 4.87005 | 0.163705 | ||||||||
\(886\) | 1.04147 | 0.0349889 | ||||||||
\(887\) | 33.6337 | 1.12931 | 0.564655 | − | 0.825327i | \(-0.309009\pi\) | ||||
0.564655 | + | 0.825327i | \(0.309009\pi\) | |||||||
\(888\) | −14.7957 | −0.496513 | ||||||||
\(889\) | 14.4486 | 0.484592 | ||||||||
\(890\) | 15.2345 | 0.510663 | ||||||||
\(891\) | 3.83036 | 0.128322 | ||||||||
\(892\) | 0.823593 | 0.0275759 | ||||||||
\(893\) | −63.0431 | −2.10966 | ||||||||
\(894\) | −21.8031 | −0.729203 | ||||||||
\(895\) | −29.1479 | −0.974308 | ||||||||
\(896\) | −1.73379 | −0.0579217 | ||||||||
\(897\) | −33.9051 | −1.13206 | ||||||||
\(898\) | −34.5937 | −1.15441 | ||||||||
\(899\) | −6.70556 | −0.223643 | ||||||||
\(900\) | 3.21458 | 0.107153 | ||||||||
\(901\) | 72.2583 | 2.40727 | ||||||||
\(902\) | 18.4994 | 0.615964 | ||||||||
\(903\) | −0.832065 | −0.0276894 | ||||||||
\(904\) | 35.7820 | 1.19009 | ||||||||
\(905\) | −14.7800 | −0.491302 | ||||||||
\(906\) | −16.6249 | −0.552325 | ||||||||
\(907\) | 35.9648 | 1.19419 | 0.597095 | − | 0.802171i | \(-0.296322\pi\) | ||||
0.597095 | + | 0.802171i | \(0.296322\pi\) | |||||||
\(908\) | −17.7104 | −0.587742 | ||||||||
\(909\) | 6.10771 | 0.202580 | ||||||||
\(910\) | 6.57237 | 0.217872 | ||||||||
\(911\) | 2.30081 | 0.0762292 | 0.0381146 | − | 0.999273i | \(-0.487865\pi\) | ||||
0.0381146 | + | 0.999273i | \(0.487865\pi\) | |||||||
\(912\) | −7.19013 | −0.238089 | ||||||||
\(913\) | 15.1630 | 0.501822 | ||||||||
\(914\) | −11.7199 | −0.387659 | ||||||||
\(915\) | 12.9950 | 0.429600 | ||||||||
\(916\) | −6.64279 | −0.219484 | ||||||||
\(917\) | 18.5110 | 0.611288 | ||||||||
\(918\) | −8.48756 | −0.280131 | ||||||||
\(919\) | 0.384600 | 0.0126868 | 0.00634339 | − | 0.999980i | \(-0.497981\pi\) | ||||
0.00634339 | + | 0.999980i | \(0.497981\pi\) | |||||||
\(920\) | −24.8615 | −0.819660 | ||||||||
\(921\) | 20.3271 | 0.669801 | ||||||||
\(922\) | 24.8574 | 0.818636 | ||||||||
\(923\) | 30.4406 | 1.00197 | ||||||||
\(924\) | 3.55373 | 0.116909 | ||||||||
\(925\) | 16.9097 | 0.555987 | ||||||||
\(926\) | −25.3238 | −0.832190 | ||||||||
\(927\) | 16.6172 | 0.545780 | ||||||||
\(928\) | 11.7623 | 0.386117 | ||||||||
\(929\) | −11.2518 | −0.369161 | −0.184580 | − | 0.982817i | \(-0.559093\pi\) | ||||
−0.184580 | + | 0.982817i | \(0.559093\pi\) | |||||||
\(930\) | −3.46261 | −0.113544 | ||||||||
\(931\) | −5.60125 | −0.183574 | ||||||||
\(932\) | 11.2705 | 0.369176 | ||||||||
\(933\) | 15.9129 | 0.520965 | ||||||||
\(934\) | 37.7154 | 1.23409 | ||||||||
\(935\) | −38.9011 | −1.27220 | ||||||||
\(936\) | 15.5303 | 0.507623 | ||||||||
\(937\) | −39.3918 | −1.28687 | −0.643437 | − | 0.765499i | \(-0.722492\pi\) | ||||
−0.643437 | + | 0.765499i | \(0.722492\pi\) | |||||||
\(938\) | −14.7543 | −0.481745 | ||||||||
\(939\) | 6.32660 | 0.206461 | ||||||||
\(940\) | 12.9383 | 0.422002 | ||||||||
\(941\) | 8.20737 | 0.267553 | 0.133776 | − | 0.991012i | \(-0.457290\pi\) | ||||
0.133776 | + | 0.991012i | \(0.457290\pi\) | |||||||
\(942\) | −21.1937 | −0.690527 | ||||||||
\(943\) | −30.8704 | −1.00528 | ||||||||
\(944\) | −5.04550 | −0.164217 | ||||||||
\(945\) | 1.23903 | 0.0403056 | ||||||||
\(946\) | 3.30019 | 0.107299 | ||||||||
\(947\) | −28.7034 | −0.932734 | −0.466367 | − | 0.884591i | \(-0.654437\pi\) | ||||
−0.466367 | + | 0.884591i | \(0.654437\pi\) | |||||||
\(948\) | −10.8603 | −0.352725 | ||||||||
\(949\) | 37.9812 | 1.23292 | ||||||||
\(950\) | 20.0958 | 0.651995 | ||||||||
\(951\) | −12.6494 | −0.410186 | ||||||||
\(952\) | −24.8497 | −0.805383 | ||||||||
\(953\) | 30.1159 | 0.975549 | 0.487774 | − | 0.872970i | \(-0.337809\pi\) | ||||
0.487774 | + | 0.872970i | \(0.337809\pi\) | |||||||
\(954\) | 9.12828 | 0.295539 | ||||||||
\(955\) | 1.23903 | 0.0400940 | ||||||||
\(956\) | 23.9316 | 0.774002 | ||||||||
\(957\) | −9.51688 | −0.307637 | ||||||||
\(958\) | −2.94871 | −0.0952683 | ||||||||
\(959\) | 7.05472 | 0.227809 | ||||||||
\(960\) | 9.25481 | 0.298698 | ||||||||
\(961\) | −23.7161 | −0.765037 | ||||||||
\(962\) | 25.8879 | 0.834660 | ||||||||
\(963\) | −8.58131 | −0.276529 | ||||||||
\(964\) | 19.3567 | 0.623436 | ||||||||
\(965\) | −20.9683 | −0.674994 | ||||||||
\(966\) | 6.85343 | 0.220505 | ||||||||
\(967\) | 17.7704 | 0.571457 | 0.285729 | − | 0.958311i | \(-0.407764\pi\) | ||||
0.285729 | + | 0.958311i | \(0.407764\pi\) | |||||||
\(968\) | −11.1313 | −0.357772 | ||||||||
\(969\) | 45.9120 | 1.47490 | ||||||||
\(970\) | −17.5862 | −0.564660 | ||||||||
\(971\) | −8.46689 | −0.271716 | −0.135858 | − | 0.990728i | \(-0.543379\pi\) | ||||
−0.135858 | + | 0.990728i | \(0.543379\pi\) | |||||||
\(972\) | 0.927780 | 0.0297585 | ||||||||
\(973\) | 6.10390 | 0.195682 | ||||||||
\(974\) | −23.9298 | −0.766760 | ||||||||
\(975\) | −17.7492 | −0.568429 | ||||||||
\(976\) | −13.4631 | −0.430944 | ||||||||
\(977\) | 27.0824 | 0.866444 | 0.433222 | − | 0.901287i | \(-0.357377\pi\) | ||||
0.433222 | + | 0.901287i | \(0.357377\pi\) | |||||||
\(978\) | −22.5652 | −0.721556 | ||||||||
\(979\) | −45.4827 | −1.45363 | ||||||||
\(980\) | 1.14955 | 0.0367209 | ||||||||
\(981\) | 16.0391 | 0.512090 | ||||||||
\(982\) | −26.5590 | −0.847532 | ||||||||
\(983\) | −41.1798 | −1.31343 | −0.656716 | − | 0.754138i | \(-0.728055\pi\) | ||||
−0.656716 | + | 0.754138i | \(0.728055\pi\) | |||||||
\(984\) | 14.1402 | 0.450775 | ||||||||
\(985\) | 8.96496 | 0.285647 | ||||||||
\(986\) | 21.0881 | 0.671582 | ||||||||
\(987\) | −11.2552 | −0.358256 | ||||||||
\(988\) | −26.6213 | −0.846936 | ||||||||
\(989\) | −5.50710 | −0.175116 | ||||||||
\(990\) | −4.91432 | −0.156187 | ||||||||
\(991\) | −35.4471 | −1.12602 | −0.563008 | − | 0.826452i | \(-0.690356\pi\) | ||||
−0.563008 | + | 0.826452i | \(0.690356\pi\) | |||||||
\(992\) | −12.7767 | −0.405661 | ||||||||
\(993\) | 8.80956 | 0.279563 | ||||||||
\(994\) | −6.15314 | −0.195166 | ||||||||
\(995\) | 19.1424 | 0.606854 | ||||||||
\(996\) | 3.67274 | 0.116375 | ||||||||
\(997\) | 22.3218 | 0.706939 | 0.353469 | − | 0.935446i | \(-0.385002\pi\) | ||||
0.353469 | + | 0.935446i | \(0.385002\pi\) | |||||||
\(998\) | −7.83107 | −0.247888 | ||||||||
\(999\) | 4.88041 | 0.154409 |
(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 | 4011.2.a.l.1.20 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.l.1.20 | ✓ | 28 | 1.1 | even | 1 | trivial |