Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.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: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(158\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.74512 | −1.94109 | −0.970546 | − | 0.240914i | \(-0.922553\pi\) | ||||
−0.970546 | + | 0.240914i | \(0.922553\pi\) | |||||||
\(3\) | 2.49890 | 1.44274 | 0.721371 | − | 0.692549i | \(-0.243512\pi\) | ||||
0.721371 | + | 0.692549i | \(0.243512\pi\) | |||||||
\(4\) | 5.53568 | 2.76784 | ||||||||
\(5\) | 0.133996 | 0.0599250 | 0.0299625 | − | 0.999551i | \(-0.490461\pi\) | ||||
0.0299625 | + | 0.999551i | \(0.490461\pi\) | |||||||
\(6\) | −6.85979 | −2.80050 | ||||||||
\(7\) | 0.778013 | 0.294061 | 0.147031 | − | 0.989132i | \(-0.453028\pi\) | ||||
0.147031 | + | 0.989132i | \(0.453028\pi\) | |||||||
\(8\) | −9.70588 | −3.43155 | ||||||||
\(9\) | 3.24451 | 1.08150 | ||||||||
\(10\) | −0.367836 | −0.116320 | ||||||||
\(11\) | 5.21472 | 1.57230 | 0.786149 | − | 0.618037i | \(-0.212072\pi\) | ||||
0.786149 | + | 0.618037i | \(0.212072\pi\) | |||||||
\(12\) | 13.8331 | 3.99328 | ||||||||
\(13\) | −3.44123 | −0.954425 | −0.477213 | − | 0.878788i | \(-0.658353\pi\) | ||||
−0.477213 | + | 0.878788i | \(0.658353\pi\) | |||||||
\(14\) | −2.13574 | −0.570800 | ||||||||
\(15\) | 0.334844 | 0.0864563 | ||||||||
\(16\) | 15.5724 | 3.89311 | ||||||||
\(17\) | −3.95432 | −0.959063 | −0.479531 | − | 0.877525i | \(-0.659193\pi\) | ||||
−0.479531 | + | 0.877525i | \(0.659193\pi\) | |||||||
\(18\) | −8.90657 | −2.09930 | ||||||||
\(19\) | 2.36206 | 0.541894 | 0.270947 | − | 0.962594i | \(-0.412663\pi\) | ||||
0.270947 | + | 0.962594i | \(0.412663\pi\) | |||||||
\(20\) | 0.741761 | 0.165863 | ||||||||
\(21\) | 1.94418 | 0.424254 | ||||||||
\(22\) | −14.3150 | −3.05198 | ||||||||
\(23\) | −9.52848 | −1.98683 | −0.993413 | − | 0.114590i | \(-0.963445\pi\) | ||||
−0.993413 | + | 0.114590i | \(0.963445\pi\) | |||||||
\(24\) | −24.2540 | −4.95083 | ||||||||
\(25\) | −4.98204 | −0.996409 | ||||||||
\(26\) | 9.44659 | 1.85263 | ||||||||
\(27\) | 0.611007 | 0.117588 | ||||||||
\(28\) | 4.30683 | 0.813915 | ||||||||
\(29\) | 2.75153 | 0.510947 | 0.255473 | − | 0.966816i | \(-0.417769\pi\) | ||||
0.255473 | + | 0.966816i | \(0.417769\pi\) | |||||||
\(30\) | −0.919186 | −0.167820 | ||||||||
\(31\) | 5.63718 | 1.01247 | 0.506234 | − | 0.862396i | \(-0.331037\pi\) | ||||
0.506234 | + | 0.862396i | \(0.331037\pi\) | |||||||
\(32\) | −23.3364 | −4.12534 | ||||||||
\(33\) | 13.0311 | 2.26842 | ||||||||
\(34\) | 10.8551 | 1.86163 | ||||||||
\(35\) | 0.104251 | 0.0176216 | ||||||||
\(36\) | 17.9606 | 2.99343 | ||||||||
\(37\) | −0.680380 | −0.111854 | −0.0559269 | − | 0.998435i | \(-0.517811\pi\) | ||||
−0.0559269 | + | 0.998435i | \(0.517811\pi\) | |||||||
\(38\) | −6.48414 | −1.05187 | ||||||||
\(39\) | −8.59929 | −1.37699 | ||||||||
\(40\) | −1.30055 | −0.205635 | ||||||||
\(41\) | −11.8771 | −1.85490 | −0.927449 | − | 0.373951i | \(-0.878003\pi\) | ||||
−0.927449 | + | 0.373951i | \(0.878003\pi\) | |||||||
\(42\) | −5.33700 | −0.823517 | ||||||||
\(43\) | 1.80337 | 0.275012 | 0.137506 | − | 0.990501i | \(-0.456091\pi\) | ||||
0.137506 | + | 0.990501i | \(0.456091\pi\) | |||||||
\(44\) | 28.8671 | 4.35187 | ||||||||
\(45\) | 0.434752 | 0.0648091 | ||||||||
\(46\) | 26.1568 | 3.85661 | ||||||||
\(47\) | −6.64581 | −0.969392 | −0.484696 | − | 0.874683i | \(-0.661070\pi\) | ||||
−0.484696 | + | 0.874683i | \(0.661070\pi\) | |||||||
\(48\) | 38.9140 | 5.61675 | ||||||||
\(49\) | −6.39470 | −0.913528 | ||||||||
\(50\) | 13.6763 | 1.93412 | ||||||||
\(51\) | −9.88145 | −1.38368 | ||||||||
\(52\) | −19.0496 | −2.64170 | ||||||||
\(53\) | 7.46761 | 1.02576 | 0.512878 | − | 0.858462i | \(-0.328579\pi\) | ||||
0.512878 | + | 0.858462i | \(0.328579\pi\) | |||||||
\(54\) | −1.67729 | −0.228250 | ||||||||
\(55\) | 0.698754 | 0.0942199 | ||||||||
\(56\) | −7.55130 | −1.00908 | ||||||||
\(57\) | 5.90256 | 0.781813 | ||||||||
\(58\) | −7.55328 | −0.991795 | ||||||||
\(59\) | 8.15971 | 1.06230 | 0.531152 | − | 0.847277i | \(-0.321759\pi\) | ||||
0.531152 | + | 0.847277i | \(0.321759\pi\) | |||||||
\(60\) | 1.85359 | 0.239297 | ||||||||
\(61\) | −7.71717 | −0.988082 | −0.494041 | − | 0.869439i | \(-0.664481\pi\) | ||||
−0.494041 | + | 0.869439i | \(0.664481\pi\) | |||||||
\(62\) | −15.4747 | −1.96529 | ||||||||
\(63\) | 2.52427 | 0.318028 | ||||||||
\(64\) | 32.9165 | 4.11456 | ||||||||
\(65\) | −0.461112 | −0.0571939 | ||||||||
\(66\) | −35.7719 | −4.40322 | ||||||||
\(67\) | 11.0607 | 1.35128 | 0.675641 | − | 0.737230i | \(-0.263867\pi\) | ||||
0.675641 | + | 0.737230i | \(0.263867\pi\) | |||||||
\(68\) | −21.8898 | −2.65453 | ||||||||
\(69\) | −23.8107 | −2.86648 | ||||||||
\(70\) | −0.286181 | −0.0342052 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | −31.4908 | −3.71123 | ||||||||
\(73\) | −10.1689 | −1.19018 | −0.595091 | − | 0.803658i | \(-0.702884\pi\) | ||||
−0.595091 | + | 0.803658i | \(0.702884\pi\) | |||||||
\(74\) | 1.86773 | 0.217119 | ||||||||
\(75\) | −12.4496 | −1.43756 | ||||||||
\(76\) | 13.0756 | 1.49988 | ||||||||
\(77\) | 4.05712 | 0.462352 | ||||||||
\(78\) | 23.6061 | 2.67286 | ||||||||
\(79\) | −14.8433 | −1.67000 | −0.834999 | − | 0.550252i | \(-0.814532\pi\) | ||||
−0.834999 | + | 0.550252i | \(0.814532\pi\) | |||||||
\(80\) | 2.08665 | 0.233294 | ||||||||
\(81\) | −8.20668 | −0.911854 | ||||||||
\(82\) | 32.6042 | 3.60053 | ||||||||
\(83\) | −3.41548 | −0.374898 | −0.187449 | − | 0.982274i | \(-0.560022\pi\) | ||||
−0.187449 | + | 0.982274i | \(0.560022\pi\) | |||||||
\(84\) | 10.7624 | 1.17427 | ||||||||
\(85\) | −0.529864 | −0.0574718 | ||||||||
\(86\) | −4.95048 | −0.533823 | ||||||||
\(87\) | 6.87581 | 0.737164 | ||||||||
\(88\) | −50.6135 | −5.39541 | ||||||||
\(89\) | −7.86279 | −0.833454 | −0.416727 | − | 0.909032i | \(-0.636823\pi\) | ||||
−0.416727 | + | 0.909032i | \(0.636823\pi\) | |||||||
\(90\) | −1.19345 | −0.125800 | ||||||||
\(91\) | −2.67732 | −0.280659 | ||||||||
\(92\) | −52.7467 | −5.49922 | ||||||||
\(93\) | 14.0868 | 1.46073 | ||||||||
\(94\) | 18.2436 | 1.88168 | ||||||||
\(95\) | 0.316507 | 0.0324730 | ||||||||
\(96\) | −58.3155 | −5.95180 | ||||||||
\(97\) | −1.61476 | −0.163954 | −0.0819772 | − | 0.996634i | \(-0.526123\pi\) | ||||
−0.0819772 | + | 0.996634i | \(0.526123\pi\) | |||||||
\(98\) | 17.5542 | 1.77324 | ||||||||
\(99\) | 16.9192 | 1.70045 | ||||||||
\(100\) | −27.5790 | −2.75790 | ||||||||
\(101\) | −5.57692 | −0.554924 | −0.277462 | − | 0.960737i | \(-0.589493\pi\) | ||||
−0.277462 | + | 0.960737i | \(0.589493\pi\) | |||||||
\(102\) | 27.1258 | 2.68585 | ||||||||
\(103\) | −6.98037 | −0.687796 | −0.343898 | − | 0.939007i | \(-0.611747\pi\) | ||||
−0.343898 | + | 0.939007i | \(0.611747\pi\) | |||||||
\(104\) | 33.4001 | 3.27515 | ||||||||
\(105\) | 0.260513 | 0.0254234 | ||||||||
\(106\) | −20.4995 | −1.99109 | ||||||||
\(107\) | −11.9078 | −1.15117 | −0.575586 | − | 0.817741i | \(-0.695226\pi\) | ||||
−0.575586 | + | 0.817741i | \(0.695226\pi\) | |||||||
\(108\) | 3.38234 | 0.325466 | ||||||||
\(109\) | 14.4032 | 1.37958 | 0.689789 | − | 0.724010i | \(-0.257703\pi\) | ||||
0.689789 | + | 0.724010i | \(0.257703\pi\) | |||||||
\(110\) | −1.91816 | −0.182890 | ||||||||
\(111\) | −1.70020 | −0.161376 | ||||||||
\(112\) | 12.1156 | 1.14481 | ||||||||
\(113\) | −1.00000 | −0.0940721 | ||||||||
\(114\) | −16.2032 | −1.51757 | ||||||||
\(115\) | −1.27678 | −0.119060 | ||||||||
\(116\) | 15.2316 | 1.41422 | ||||||||
\(117\) | −11.1651 | −1.03221 | ||||||||
\(118\) | −22.3994 | −2.06203 | ||||||||
\(119\) | −3.07651 | −0.282023 | ||||||||
\(120\) | −3.24995 | −0.296679 | ||||||||
\(121\) | 16.1934 | 1.47212 | ||||||||
\(122\) | 21.1846 | 1.91796 | ||||||||
\(123\) | −29.6798 | −2.67614 | ||||||||
\(124\) | 31.2057 | 2.80235 | ||||||||
\(125\) | −1.33756 | −0.119635 | ||||||||
\(126\) | −6.92943 | −0.617323 | ||||||||
\(127\) | −2.52082 | −0.223687 | −0.111843 | − | 0.993726i | \(-0.535676\pi\) | ||||
−0.111843 | + | 0.993726i | \(0.535676\pi\) | |||||||
\(128\) | −43.6867 | −3.86140 | ||||||||
\(129\) | 4.50645 | 0.396771 | ||||||||
\(130\) | 1.26581 | 0.111019 | ||||||||
\(131\) | 5.36752 | 0.468962 | 0.234481 | − | 0.972121i | \(-0.424661\pi\) | ||||
0.234481 | + | 0.972121i | \(0.424661\pi\) | |||||||
\(132\) | 72.1360 | 6.27863 | ||||||||
\(133\) | 1.83771 | 0.159350 | ||||||||
\(134\) | −30.3630 | −2.62297 | ||||||||
\(135\) | 0.0818727 | 0.00704648 | ||||||||
\(136\) | 38.3801 | 3.29107 | ||||||||
\(137\) | 1.56581 | 0.133776 | 0.0668882 | − | 0.997760i | \(-0.478693\pi\) | ||||
0.0668882 | + | 0.997760i | \(0.478693\pi\) | |||||||
\(138\) | 65.3633 | 5.56410 | ||||||||
\(139\) | 13.1312 | 1.11377 | 0.556886 | − | 0.830589i | \(-0.311996\pi\) | ||||
0.556886 | + | 0.830589i | \(0.311996\pi\) | |||||||
\(140\) | 0.577100 | 0.0487738 | ||||||||
\(141\) | −16.6072 | −1.39858 | ||||||||
\(142\) | 2.74512 | 0.230365 | ||||||||
\(143\) | −17.9451 | −1.50064 | ||||||||
\(144\) | 50.5249 | 4.21041 | ||||||||
\(145\) | 0.368695 | 0.0306185 | ||||||||
\(146\) | 27.9149 | 2.31025 | ||||||||
\(147\) | −15.9797 | −1.31798 | ||||||||
\(148\) | −3.76637 | −0.309594 | ||||||||
\(149\) | −9.21209 | −0.754684 | −0.377342 | − | 0.926074i | \(-0.623162\pi\) | ||||
−0.377342 | + | 0.926074i | \(0.623162\pi\) | |||||||
\(150\) | 34.1758 | 2.79044 | ||||||||
\(151\) | 20.8538 | 1.69706 | 0.848531 | − | 0.529146i | \(-0.177487\pi\) | ||||
0.848531 | + | 0.529146i | \(0.177487\pi\) | |||||||
\(152\) | −22.9259 | −1.85953 | ||||||||
\(153\) | −12.8298 | −1.03723 | ||||||||
\(154\) | −11.1373 | −0.897469 | ||||||||
\(155\) | 0.755362 | 0.0606721 | ||||||||
\(156\) | −47.6030 | −3.81129 | ||||||||
\(157\) | 16.1024 | 1.28511 | 0.642557 | − | 0.766238i | \(-0.277874\pi\) | ||||
0.642557 | + | 0.766238i | \(0.277874\pi\) | |||||||
\(158\) | 40.7465 | 3.24162 | ||||||||
\(159\) | 18.6608 | 1.47990 | ||||||||
\(160\) | −3.12700 | −0.247211 | ||||||||
\(161\) | −7.41328 | −0.584249 | ||||||||
\(162\) | 22.5283 | 1.76999 | ||||||||
\(163\) | −11.4096 | −0.893671 | −0.446836 | − | 0.894616i | \(-0.647449\pi\) | ||||
−0.446836 | + | 0.894616i | \(0.647449\pi\) | |||||||
\(164\) | −65.7481 | −5.13406 | ||||||||
\(165\) | 1.74612 | 0.135935 | ||||||||
\(166\) | 9.37591 | 0.727712 | ||||||||
\(167\) | −8.57532 | −0.663578 | −0.331789 | − | 0.943354i | \(-0.607652\pi\) | ||||
−0.331789 | + | 0.943354i | \(0.607652\pi\) | |||||||
\(168\) | −18.8700 | −1.45585 | ||||||||
\(169\) | −1.15795 | −0.0890728 | ||||||||
\(170\) | 1.45454 | 0.111558 | ||||||||
\(171\) | 7.66373 | 0.586060 | ||||||||
\(172\) | 9.98290 | 0.761189 | ||||||||
\(173\) | 0.451920 | 0.0343588 | 0.0171794 | − | 0.999852i | \(-0.494531\pi\) | ||||
0.0171794 | + | 0.999852i | \(0.494531\pi\) | |||||||
\(174\) | −18.8749 | −1.43090 | ||||||||
\(175\) | −3.87610 | −0.293005 | ||||||||
\(176\) | 81.2059 | 6.12113 | ||||||||
\(177\) | 20.3903 | 1.53263 | ||||||||
\(178\) | 21.5843 | 1.61781 | ||||||||
\(179\) | −15.9262 | −1.19038 | −0.595191 | − | 0.803584i | \(-0.702924\pi\) | ||||
−0.595191 | + | 0.803584i | \(0.702924\pi\) | |||||||
\(180\) | 2.40665 | 0.179381 | ||||||||
\(181\) | 17.9545 | 1.33455 | 0.667274 | − | 0.744812i | \(-0.267461\pi\) | ||||
0.667274 | + | 0.744812i | \(0.267461\pi\) | |||||||
\(182\) | 7.34957 | 0.544786 | ||||||||
\(183\) | −19.2844 | −1.42555 | ||||||||
\(184\) | 92.4823 | 6.81788 | ||||||||
\(185\) | −0.0911684 | −0.00670284 | ||||||||
\(186\) | −38.6699 | −2.83541 | ||||||||
\(187\) | −20.6207 | −1.50793 | ||||||||
\(188\) | −36.7891 | −2.68312 | ||||||||
\(189\) | 0.475372 | 0.0345782 | ||||||||
\(190\) | −0.868851 | −0.0630330 | ||||||||
\(191\) | −22.5692 | −1.63305 | −0.816525 | − | 0.577310i | \(-0.804102\pi\) | ||||
−0.816525 | + | 0.577310i | \(0.804102\pi\) | |||||||
\(192\) | 82.2550 | 5.93624 | ||||||||
\(193\) | −26.8265 | −1.93101 | −0.965506 | − | 0.260382i | \(-0.916152\pi\) | ||||
−0.965506 | + | 0.260382i | \(0.916152\pi\) | |||||||
\(194\) | 4.43272 | 0.318251 | ||||||||
\(195\) | −1.15227 | −0.0825160 | ||||||||
\(196\) | −35.3990 | −2.52850 | ||||||||
\(197\) | −8.07047 | −0.574998 | −0.287499 | − | 0.957781i | \(-0.592824\pi\) | ||||
−0.287499 | + | 0.957781i | \(0.592824\pi\) | |||||||
\(198\) | −46.4453 | −3.30072 | ||||||||
\(199\) | 10.8653 | 0.770223 | 0.385111 | − | 0.922870i | \(-0.374163\pi\) | ||||
0.385111 | + | 0.922870i | \(0.374163\pi\) | |||||||
\(200\) | 48.3551 | 3.41922 | ||||||||
\(201\) | 27.6397 | 1.94955 | ||||||||
\(202\) | 15.3093 | 1.07716 | ||||||||
\(203\) | 2.14073 | 0.150250 | ||||||||
\(204\) | −54.7006 | −3.82981 | ||||||||
\(205\) | −1.59149 | −0.111155 | ||||||||
\(206\) | 19.1620 | 1.33508 | ||||||||
\(207\) | −30.9153 | −2.14876 | ||||||||
\(208\) | −53.5883 | −3.71568 | ||||||||
\(209\) | 12.3175 | 0.852019 | ||||||||
\(210\) | −0.715139 | −0.0493493 | ||||||||
\(211\) | −0.168646 | −0.0116100 | −0.00580502 | − | 0.999983i | \(-0.501848\pi\) | ||||
−0.00580502 | + | 0.999983i | \(0.501848\pi\) | |||||||
\(212\) | 41.3383 | 2.83913 | ||||||||
\(213\) | −2.49890 | −0.171222 | ||||||||
\(214\) | 32.6884 | 2.23453 | ||||||||
\(215\) | 0.241645 | 0.0164801 | ||||||||
\(216\) | −5.93036 | −0.403510 | ||||||||
\(217\) | 4.38580 | 0.297728 | ||||||||
\(218\) | −39.5386 | −2.67789 | ||||||||
\(219\) | −25.4111 | −1.71713 | ||||||||
\(220\) | 3.86808 | 0.260786 | ||||||||
\(221\) | 13.6077 | 0.915353 | ||||||||
\(222\) | 4.66726 | 0.313246 | ||||||||
\(223\) | 26.7387 | 1.79056 | 0.895279 | − | 0.445505i | \(-0.146976\pi\) | ||||
0.895279 | + | 0.445505i | \(0.146976\pi\) | |||||||
\(224\) | −18.1561 | −1.21310 | ||||||||
\(225\) | −16.1643 | −1.07762 | ||||||||
\(226\) | 2.74512 | 0.182603 | ||||||||
\(227\) | 8.83141 | 0.586161 | 0.293081 | − | 0.956088i | \(-0.405320\pi\) | ||||
0.293081 | + | 0.956088i | \(0.405320\pi\) | |||||||
\(228\) | 32.6747 | 2.16393 | ||||||||
\(229\) | −23.2357 | −1.53546 | −0.767728 | − | 0.640776i | \(-0.778613\pi\) | ||||
−0.767728 | + | 0.640776i | \(0.778613\pi\) | |||||||
\(230\) | 3.50492 | 0.231107 | ||||||||
\(231\) | 10.1384 | 0.667055 | ||||||||
\(232\) | −26.7060 | −1.75334 | ||||||||
\(233\) | 4.59897 | 0.301289 | 0.150644 | − | 0.988588i | \(-0.451865\pi\) | ||||
0.150644 | + | 0.988588i | \(0.451865\pi\) | |||||||
\(234\) | 30.6495 | 2.00362 | ||||||||
\(235\) | −0.890515 | −0.0580908 | ||||||||
\(236\) | 45.1695 | 2.94029 | ||||||||
\(237\) | −37.0919 | −2.40938 | ||||||||
\(238\) | 8.44539 | 0.547433 | ||||||||
\(239\) | −8.11859 | −0.525148 | −0.262574 | − | 0.964912i | \(-0.584571\pi\) | ||||
−0.262574 | + | 0.964912i | \(0.584571\pi\) | |||||||
\(240\) | 5.21433 | 0.336583 | ||||||||
\(241\) | −5.93005 | −0.381988 | −0.190994 | − | 0.981591i | \(-0.561171\pi\) | ||||
−0.190994 | + | 0.981591i | \(0.561171\pi\) | |||||||
\(242\) | −44.4527 | −2.85753 | ||||||||
\(243\) | −22.3407 | −1.43316 | ||||||||
\(244\) | −42.7198 | −2.73486 | ||||||||
\(245\) | −0.856866 | −0.0547431 | ||||||||
\(246\) | 81.4746 | 5.19463 | ||||||||
\(247\) | −8.12839 | −0.517197 | ||||||||
\(248\) | −54.7138 | −3.47433 | ||||||||
\(249\) | −8.53496 | −0.540881 | ||||||||
\(250\) | 3.67176 | 0.232222 | ||||||||
\(251\) | 0.929672 | 0.0586804 | 0.0293402 | − | 0.999569i | \(-0.490659\pi\) | ||||
0.0293402 | + | 0.999569i | \(0.490659\pi\) | |||||||
\(252\) | 13.9736 | 0.880252 | ||||||||
\(253\) | −49.6884 | −3.12388 | ||||||||
\(254\) | 6.91996 | 0.434197 | ||||||||
\(255\) | −1.32408 | −0.0829170 | ||||||||
\(256\) | 54.0925 | 3.38078 | ||||||||
\(257\) | 9.60806 | 0.599334 | 0.299667 | − | 0.954044i | \(-0.403124\pi\) | ||||
0.299667 | + | 0.954044i | \(0.403124\pi\) | |||||||
\(258\) | −12.3708 | −0.770169 | ||||||||
\(259\) | −0.529345 | −0.0328919 | ||||||||
\(260\) | −2.55257 | −0.158304 | ||||||||
\(261\) | 8.92737 | 0.552590 | ||||||||
\(262\) | −14.7345 | −0.910299 | ||||||||
\(263\) | −10.7085 | −0.660317 | −0.330159 | − | 0.943925i | \(-0.607102\pi\) | ||||
−0.330159 | + | 0.943925i | \(0.607102\pi\) | |||||||
\(264\) | −126.478 | −7.78419 | ||||||||
\(265\) | 1.00063 | 0.0614684 | ||||||||
\(266\) | −5.04474 | −0.309313 | ||||||||
\(267\) | −19.6483 | −1.20246 | ||||||||
\(268\) | 61.2287 | 3.74014 | ||||||||
\(269\) | 9.96734 | 0.607719 | 0.303860 | − | 0.952717i | \(-0.401725\pi\) | ||||
0.303860 | + | 0.952717i | \(0.401725\pi\) | |||||||
\(270\) | −0.224750 | −0.0136779 | ||||||||
\(271\) | 16.3909 | 0.995674 | 0.497837 | − | 0.867271i | \(-0.334128\pi\) | ||||
0.497837 | + | 0.867271i | \(0.334128\pi\) | |||||||
\(272\) | −61.5783 | −3.73373 | ||||||||
\(273\) | −6.69036 | −0.404919 | ||||||||
\(274\) | −4.29834 | −0.259672 | ||||||||
\(275\) | −25.9800 | −1.56665 | ||||||||
\(276\) | −131.809 | −7.93395 | ||||||||
\(277\) | 18.6461 | 1.12033 | 0.560167 | − | 0.828379i | \(-0.310737\pi\) | ||||
0.560167 | + | 0.828379i | \(0.310737\pi\) | |||||||
\(278\) | −36.0467 | −2.16194 | ||||||||
\(279\) | 18.2899 | 1.09499 | ||||||||
\(280\) | −1.01185 | −0.0604694 | ||||||||
\(281\) | −5.47560 | −0.326647 | −0.163324 | − | 0.986573i | \(-0.552221\pi\) | ||||
−0.163324 | + | 0.986573i | \(0.552221\pi\) | |||||||
\(282\) | 45.5889 | 2.71478 | ||||||||
\(283\) | −24.9385 | −1.48244 | −0.741221 | − | 0.671262i | \(-0.765753\pi\) | ||||
−0.741221 | + | 0.671262i | \(0.765753\pi\) | |||||||
\(284\) | −5.53568 | −0.328482 | ||||||||
\(285\) | 0.790921 | 0.0468501 | ||||||||
\(286\) | 49.2613 | 2.91288 | ||||||||
\(287\) | −9.24057 | −0.545453 | ||||||||
\(288\) | −75.7153 | −4.46157 | ||||||||
\(289\) | −1.36338 | −0.0801990 | ||||||||
\(290\) | −1.01211 | −0.0594333 | ||||||||
\(291\) | −4.03513 | −0.236544 | ||||||||
\(292\) | −56.2919 | −3.29424 | ||||||||
\(293\) | 1.27120 | 0.0742640 | 0.0371320 | − | 0.999310i | \(-0.488178\pi\) | ||||
0.0371320 | + | 0.999310i | \(0.488178\pi\) | |||||||
\(294\) | 43.8662 | 2.55833 | ||||||||
\(295\) | 1.09337 | 0.0636585 | ||||||||
\(296\) | 6.60369 | 0.383832 | ||||||||
\(297\) | 3.18623 | 0.184884 | ||||||||
\(298\) | 25.2883 | 1.46491 | ||||||||
\(299\) | 32.7897 | 1.89628 | ||||||||
\(300\) | −68.9173 | −3.97894 | ||||||||
\(301\) | 1.40305 | 0.0808703 | ||||||||
\(302\) | −57.2463 | −3.29416 | ||||||||
\(303\) | −13.9362 | −0.800612 | ||||||||
\(304\) | 36.7830 | 2.10965 | ||||||||
\(305\) | −1.03407 | −0.0592108 | ||||||||
\(306\) | 35.2194 | 2.01336 | ||||||||
\(307\) | −22.7215 | −1.29678 | −0.648392 | − | 0.761307i | \(-0.724558\pi\) | ||||
−0.648392 | + | 0.761307i | \(0.724558\pi\) | |||||||
\(308\) | 22.4590 | 1.27972 | ||||||||
\(309\) | −17.4433 | −0.992312 | ||||||||
\(310\) | −2.07356 | −0.117770 | ||||||||
\(311\) | 2.12491 | 0.120493 | 0.0602463 | − | 0.998184i | \(-0.480811\pi\) | ||||
0.0602463 | + | 0.998184i | \(0.480811\pi\) | |||||||
\(312\) | 83.4637 | 4.72520 | ||||||||
\(313\) | 5.69184 | 0.321722 | 0.160861 | − | 0.986977i | \(-0.448573\pi\) | ||||
0.160861 | + | 0.986977i | \(0.448573\pi\) | |||||||
\(314\) | −44.2031 | −2.49453 | ||||||||
\(315\) | 0.338243 | 0.0190578 | ||||||||
\(316\) | −82.1676 | −4.62229 | ||||||||
\(317\) | −25.3083 | −1.42146 | −0.710729 | − | 0.703466i | \(-0.751635\pi\) | ||||
−0.710729 | + | 0.703466i | \(0.751635\pi\) | |||||||
\(318\) | −51.2262 | −2.87262 | ||||||||
\(319\) | 14.3485 | 0.803361 | ||||||||
\(320\) | 4.41068 | 0.246565 | ||||||||
\(321\) | −29.7565 | −1.66084 | ||||||||
\(322\) | 20.3504 | 1.13408 | ||||||||
\(323\) | −9.34033 | −0.519710 | ||||||||
\(324\) | −45.4296 | −2.52387 | ||||||||
\(325\) | 17.1444 | 0.950998 | ||||||||
\(326\) | 31.3208 | 1.73470 | ||||||||
\(327\) | 35.9922 | 1.99038 | ||||||||
\(328\) | 115.278 | 6.36516 | ||||||||
\(329\) | −5.17053 | −0.285061 | ||||||||
\(330\) | −4.79330 | −0.263863 | ||||||||
\(331\) | 3.90131 | 0.214435 | 0.107218 | − | 0.994236i | \(-0.465806\pi\) | ||||
0.107218 | + | 0.994236i | \(0.465806\pi\) | |||||||
\(332\) | −18.9070 | −1.03766 | ||||||||
\(333\) | −2.20750 | −0.120970 | ||||||||
\(334\) | 23.5403 | 1.28807 | ||||||||
\(335\) | 1.48210 | 0.0809756 | ||||||||
\(336\) | 30.2756 | 1.65167 | ||||||||
\(337\) | −9.17818 | −0.499968 | −0.249984 | − | 0.968250i | \(-0.580425\pi\) | ||||
−0.249984 | + | 0.968250i | \(0.580425\pi\) | |||||||
\(338\) | 3.17870 | 0.172899 | ||||||||
\(339\) | −2.49890 | −0.135722 | ||||||||
\(340\) | −2.93316 | −0.159073 | ||||||||
\(341\) | 29.3964 | 1.59190 | ||||||||
\(342\) | −21.0379 | −1.13760 | ||||||||
\(343\) | −10.4212 | −0.562695 | ||||||||
\(344\) | −17.5033 | −0.943716 | ||||||||
\(345\) | −3.19055 | −0.171774 | ||||||||
\(346\) | −1.24057 | −0.0666937 | ||||||||
\(347\) | −11.6563 | −0.625746 | −0.312873 | − | 0.949795i | \(-0.601291\pi\) | ||||
−0.312873 | + | 0.949795i | \(0.601291\pi\) | |||||||
\(348\) | 38.0623 | 2.04035 | ||||||||
\(349\) | −4.27529 | −0.228851 | −0.114425 | − | 0.993432i | \(-0.536503\pi\) | ||||
−0.114425 | + | 0.993432i | \(0.536503\pi\) | |||||||
\(350\) | 10.6403 | 0.568751 | ||||||||
\(351\) | −2.10262 | −0.112229 | ||||||||
\(352\) | −121.693 | −6.48626 | ||||||||
\(353\) | −15.1145 | −0.804464 | −0.402232 | − | 0.915538i | \(-0.631765\pi\) | ||||
−0.402232 | + | 0.915538i | \(0.631765\pi\) | |||||||
\(354\) | −55.9738 | −2.97498 | ||||||||
\(355\) | −0.133996 | −0.00711179 | ||||||||
\(356\) | −43.5259 | −2.30687 | ||||||||
\(357\) | −7.68790 | −0.406887 | ||||||||
\(358\) | 43.7194 | 2.31064 | ||||||||
\(359\) | −25.0019 | −1.31955 | −0.659774 | − | 0.751464i | \(-0.729348\pi\) | ||||
−0.659774 | + | 0.751464i | \(0.729348\pi\) | |||||||
\(360\) | −4.21965 | −0.222395 | ||||||||
\(361\) | −13.4207 | −0.706351 | ||||||||
\(362\) | −49.2873 | −2.59048 | ||||||||
\(363\) | 40.4656 | 2.12389 | ||||||||
\(364\) | −14.8208 | −0.776821 | ||||||||
\(365\) | −1.36260 | −0.0713216 | ||||||||
\(366\) | 52.9381 | 2.76712 | ||||||||
\(367\) | 36.5969 | 1.91035 | 0.955173 | − | 0.296050i | \(-0.0956694\pi\) | ||||
0.955173 | + | 0.296050i | \(0.0956694\pi\) | |||||||
\(368\) | −148.382 | −7.73493 | ||||||||
\(369\) | −38.5355 | −2.00608 | ||||||||
\(370\) | 0.250268 | 0.0130108 | ||||||||
\(371\) | 5.80990 | 0.301635 | ||||||||
\(372\) | 77.9799 | 4.04307 | ||||||||
\(373\) | 30.2192 | 1.56469 | 0.782345 | − | 0.622845i | \(-0.214023\pi\) | ||||
0.782345 | + | 0.622845i | \(0.214023\pi\) | |||||||
\(374\) | 56.6062 | 2.92704 | ||||||||
\(375\) | −3.34242 | −0.172602 | ||||||||
\(376\) | 64.5035 | 3.32651 | ||||||||
\(377\) | −9.46865 | −0.487660 | ||||||||
\(378\) | −1.30495 | −0.0671195 | ||||||||
\(379\) | −3.47290 | −0.178391 | −0.0891955 | − | 0.996014i | \(-0.528430\pi\) | ||||
−0.0891955 | + | 0.996014i | \(0.528430\pi\) | |||||||
\(380\) | 1.75208 | 0.0898800 | ||||||||
\(381\) | −6.29929 | −0.322722 | ||||||||
\(382\) | 61.9552 | 3.16990 | ||||||||
\(383\) | 29.8244 | 1.52396 | 0.761978 | − | 0.647603i | \(-0.224228\pi\) | ||||
0.761978 | + | 0.647603i | \(0.224228\pi\) | |||||||
\(384\) | −109.169 | −5.57100 | ||||||||
\(385\) | 0.543640 | 0.0277064 | ||||||||
\(386\) | 73.6419 | 3.74827 | ||||||||
\(387\) | 5.85106 | 0.297426 | ||||||||
\(388\) | −8.93882 | −0.453800 | ||||||||
\(389\) | 24.5717 | 1.24584 | 0.622918 | − | 0.782287i | \(-0.285947\pi\) | ||||
0.622918 | + | 0.782287i | \(0.285947\pi\) | |||||||
\(390\) | 3.16313 | 0.160171 | ||||||||
\(391\) | 37.6786 | 1.90549 | ||||||||
\(392\) | 62.0661 | 3.13481 | ||||||||
\(393\) | 13.4129 | 0.676591 | ||||||||
\(394\) | 22.1544 | 1.11612 | ||||||||
\(395\) | −1.98894 | −0.100075 | ||||||||
\(396\) | 93.6595 | 4.70657 | ||||||||
\(397\) | 11.6193 | 0.583154 | 0.291577 | − | 0.956547i | \(-0.405820\pi\) | ||||
0.291577 | + | 0.956547i | \(0.405820\pi\) | |||||||
\(398\) | −29.8266 | −1.49507 | ||||||||
\(399\) | 4.59227 | 0.229901 | ||||||||
\(400\) | −77.5825 | −3.87913 | ||||||||
\(401\) | 14.4123 | 0.719716 | 0.359858 | − | 0.933007i | \(-0.382825\pi\) | ||||
0.359858 | + | 0.933007i | \(0.382825\pi\) | |||||||
\(402\) | −75.8742 | −3.78426 | ||||||||
\(403\) | −19.3988 | −0.966325 | ||||||||
\(404\) | −30.8721 | −1.53594 | ||||||||
\(405\) | −1.09967 | −0.0546428 | ||||||||
\(406\) | −5.87655 | −0.291648 | ||||||||
\(407\) | −3.54800 | −0.175868 | ||||||||
\(408\) | 95.9081 | 4.74816 | ||||||||
\(409\) | 22.3649 | 1.10587 | 0.552936 | − | 0.833224i | \(-0.313508\pi\) | ||||
0.552936 | + | 0.833224i | \(0.313508\pi\) | |||||||
\(410\) | 4.36884 | 0.215762 | ||||||||
\(411\) | 3.91281 | 0.193005 | ||||||||
\(412\) | −38.6411 | −1.90371 | ||||||||
\(413\) | 6.34836 | 0.312382 | ||||||||
\(414\) | 84.8661 | 4.17094 | ||||||||
\(415\) | −0.457662 | −0.0224658 | ||||||||
\(416\) | 80.3060 | 3.93733 | ||||||||
\(417\) | 32.8135 | 1.60689 | ||||||||
\(418\) | −33.8130 | −1.65385 | ||||||||
\(419\) | 17.0073 | 0.830863 | 0.415431 | − | 0.909624i | \(-0.363631\pi\) | ||||
0.415431 | + | 0.909624i | \(0.363631\pi\) | |||||||
\(420\) | 1.44212 | 0.0703681 | ||||||||
\(421\) | −14.5662 | −0.709913 | −0.354957 | − | 0.934883i | \(-0.615504\pi\) | ||||
−0.354957 | + | 0.934883i | \(0.615504\pi\) | |||||||
\(422\) | 0.462952 | 0.0225362 | ||||||||
\(423\) | −21.5624 | −1.04840 | ||||||||
\(424\) | −72.4797 | −3.51993 | ||||||||
\(425\) | 19.7006 | 0.955619 | ||||||||
\(426\) | 6.85979 | 0.332358 | ||||||||
\(427\) | −6.00406 | −0.290557 | ||||||||
\(428\) | −65.9179 | −3.18626 | ||||||||
\(429\) | −44.8429 | −2.16504 | ||||||||
\(430\) | −0.663345 | −0.0319894 | ||||||||
\(431\) | −16.9661 | −0.817226 | −0.408613 | − | 0.912708i | \(-0.633987\pi\) | ||||
−0.408613 | + | 0.912708i | \(0.633987\pi\) | |||||||
\(432\) | 9.51487 | 0.457784 | ||||||||
\(433\) | 5.11657 | 0.245886 | 0.122943 | − | 0.992414i | \(-0.460767\pi\) | ||||
0.122943 | + | 0.992414i | \(0.460767\pi\) | |||||||
\(434\) | −12.0396 | −0.577917 | ||||||||
\(435\) | 0.921333 | 0.0441745 | ||||||||
\(436\) | 79.7317 | 3.81846 | ||||||||
\(437\) | −22.5068 | −1.07665 | ||||||||
\(438\) | 69.7566 | 3.33310 | ||||||||
\(439\) | 18.6871 | 0.891886 | 0.445943 | − | 0.895061i | \(-0.352868\pi\) | ||||
0.445943 | + | 0.895061i | \(0.352868\pi\) | |||||||
\(440\) | −6.78202 | −0.323320 | ||||||||
\(441\) | −20.7477 | −0.987984 | ||||||||
\(442\) | −37.3548 | −1.77679 | ||||||||
\(443\) | −12.0757 | −0.573733 | −0.286866 | − | 0.957971i | \(-0.592614\pi\) | ||||
−0.286866 | + | 0.957971i | \(0.592614\pi\) | |||||||
\(444\) | −9.41179 | −0.446664 | ||||||||
\(445\) | −1.05358 | −0.0499447 | ||||||||
\(446\) | −73.4011 | −3.47564 | ||||||||
\(447\) | −23.0201 | −1.08881 | ||||||||
\(448\) | 25.6094 | 1.20993 | ||||||||
\(449\) | −17.6418 | −0.832569 | −0.416285 | − | 0.909234i | \(-0.636668\pi\) | ||||
−0.416285 | + | 0.909234i | \(0.636668\pi\) | |||||||
\(450\) | 44.3729 | 2.09176 | ||||||||
\(451\) | −61.9360 | −2.91645 | ||||||||
\(452\) | −5.53568 | −0.260377 | ||||||||
\(453\) | 52.1117 | 2.44842 | ||||||||
\(454\) | −24.2433 | −1.13779 | ||||||||
\(455\) | −0.358751 | −0.0168185 | ||||||||
\(456\) | −57.2895 | −2.68283 | ||||||||
\(457\) | 22.1992 | 1.03844 | 0.519218 | − | 0.854642i | \(-0.326223\pi\) | ||||
0.519218 | + | 0.854642i | \(0.326223\pi\) | |||||||
\(458\) | 63.7847 | 2.98046 | ||||||||
\(459\) | −2.41612 | −0.112775 | ||||||||
\(460\) | −7.06786 | −0.329541 | ||||||||
\(461\) | −25.5060 | −1.18793 | −0.593966 | − | 0.804490i | \(-0.702439\pi\) | ||||
−0.593966 | + | 0.804490i | \(0.702439\pi\) | |||||||
\(462\) | −27.8310 | −1.29482 | ||||||||
\(463\) | −18.3410 | −0.852377 | −0.426188 | − | 0.904634i | \(-0.640144\pi\) | ||||
−0.426188 | + | 0.904634i | \(0.640144\pi\) | |||||||
\(464\) | 42.8480 | 1.98917 | ||||||||
\(465\) | 1.88757 | 0.0875342 | ||||||||
\(466\) | −12.6247 | −0.584830 | ||||||||
\(467\) | −4.95595 | −0.229334 | −0.114667 | − | 0.993404i | \(-0.536580\pi\) | ||||
−0.114667 | + | 0.993404i | \(0.536580\pi\) | |||||||
\(468\) | −61.8065 | −2.85701 | ||||||||
\(469\) | 8.60539 | 0.397360 | ||||||||
\(470\) | 2.44457 | 0.112760 | ||||||||
\(471\) | 40.2384 | 1.85409 | ||||||||
\(472\) | −79.1971 | −3.64534 | ||||||||
\(473\) | 9.40409 | 0.432401 | ||||||||
\(474\) | 101.822 | 4.67682 | ||||||||
\(475\) | −11.7679 | −0.539948 | ||||||||
\(476\) | −17.0306 | −0.780596 | ||||||||
\(477\) | 24.2287 | 1.10936 | ||||||||
\(478\) | 22.2865 | 1.01936 | ||||||||
\(479\) | 17.1674 | 0.784399 | 0.392199 | − | 0.919880i | \(-0.371714\pi\) | ||||
0.392199 | + | 0.919880i | \(0.371714\pi\) | |||||||
\(480\) | −7.81406 | −0.356661 | ||||||||
\(481\) | 2.34134 | 0.106756 | ||||||||
\(482\) | 16.2787 | 0.741475 | ||||||||
\(483\) | −18.5251 | −0.842920 | ||||||||
\(484\) | 89.6413 | 4.07460 | ||||||||
\(485\) | −0.216372 | −0.00982496 | ||||||||
\(486\) | 61.3280 | 2.78189 | ||||||||
\(487\) | 36.1274 | 1.63709 | 0.818544 | − | 0.574444i | \(-0.194782\pi\) | ||||
0.818544 | + | 0.574444i | \(0.194782\pi\) | |||||||
\(488\) | 74.9019 | 3.39065 | ||||||||
\(489\) | −28.5115 | −1.28934 | ||||||||
\(490\) | 2.35220 | 0.106262 | ||||||||
\(491\) | 21.1017 | 0.952304 | 0.476152 | − | 0.879363i | \(-0.342031\pi\) | ||||
0.476152 | + | 0.879363i | \(0.342031\pi\) | |||||||
\(492\) | −164.298 | −7.40713 | ||||||||
\(493\) | −10.8804 | −0.490030 | ||||||||
\(494\) | 22.3134 | 1.00393 | ||||||||
\(495\) | 2.26711 | 0.101899 | ||||||||
\(496\) | 87.7846 | 3.94165 | ||||||||
\(497\) | −0.778013 | −0.0348987 | ||||||||
\(498\) | 23.4295 | 1.04990 | ||||||||
\(499\) | 6.20555 | 0.277798 | 0.138899 | − | 0.990307i | \(-0.455644\pi\) | ||||
0.138899 | + | 0.990307i | \(0.455644\pi\) | |||||||
\(500\) | −7.40429 | −0.331130 | ||||||||
\(501\) | −21.4289 | −0.957372 | ||||||||
\(502\) | −2.55206 | −0.113904 | ||||||||
\(503\) | 5.41034 | 0.241235 | 0.120618 | − | 0.992699i | \(-0.461513\pi\) | ||||
0.120618 | + | 0.992699i | \(0.461513\pi\) | |||||||
\(504\) | −24.5003 | −1.09133 | ||||||||
\(505\) | −0.747287 | −0.0332538 | ||||||||
\(506\) | 136.401 | 6.06375 | ||||||||
\(507\) | −2.89359 | −0.128509 | ||||||||
\(508\) | −13.9545 | −0.619130 | ||||||||
\(509\) | 34.8140 | 1.54310 | 0.771551 | − | 0.636168i | \(-0.219481\pi\) | ||||
0.771551 | + | 0.636168i | \(0.219481\pi\) | |||||||
\(510\) | 3.63475 | 0.160950 | ||||||||
\(511\) | −7.91155 | −0.349986 | ||||||||
\(512\) | −61.1168 | −2.70101 | ||||||||
\(513\) | 1.44324 | 0.0637204 | ||||||||
\(514\) | −26.3753 | −1.16336 | ||||||||
\(515\) | −0.935344 | −0.0412162 | ||||||||
\(516\) | 24.9463 | 1.09820 | ||||||||
\(517\) | −34.6561 | −1.52417 | ||||||||
\(518\) | 1.45311 | 0.0638462 | ||||||||
\(519\) | 1.12930 | 0.0495709 | ||||||||
\(520\) | 4.47550 | 0.196263 | ||||||||
\(521\) | 37.9754 | 1.66373 | 0.831867 | − | 0.554975i | \(-0.187272\pi\) | ||||
0.831867 | + | 0.554975i | \(0.187272\pi\) | |||||||
\(522\) | −24.5067 | −1.07263 | ||||||||
\(523\) | −18.6861 | −0.817087 | −0.408543 | − | 0.912739i | \(-0.633963\pi\) | ||||
−0.408543 | + | 0.912739i | \(0.633963\pi\) | |||||||
\(524\) | 29.7129 | 1.29801 | ||||||||
\(525\) | −9.68598 | −0.422731 | ||||||||
\(526\) | 29.3962 | 1.28174 | ||||||||
\(527\) | −22.2912 | −0.971020 | ||||||||
\(528\) | 202.926 | 8.83120 | ||||||||
\(529\) | 67.7920 | 2.94748 | ||||||||
\(530\) | −2.74686 | −0.119316 | ||||||||
\(531\) | 26.4742 | 1.14888 | ||||||||
\(532\) | 10.1730 | 0.441056 | ||||||||
\(533\) | 40.8719 | 1.77036 | ||||||||
\(534\) | 53.9370 | 2.33408 | ||||||||
\(535\) | −1.59560 | −0.0689840 | ||||||||
\(536\) | −107.354 | −4.63699 | ||||||||
\(537\) | −39.7981 | −1.71741 | ||||||||
\(538\) | −27.3615 | −1.17964 | ||||||||
\(539\) | −33.3466 | −1.43634 | ||||||||
\(540\) | 0.453221 | 0.0195035 | ||||||||
\(541\) | −23.4288 | −1.00728 | −0.503642 | − | 0.863912i | \(-0.668007\pi\) | ||||
−0.503642 | + | 0.863912i | \(0.668007\pi\) | |||||||
\(542\) | −44.9949 | −1.93270 | ||||||||
\(543\) | 44.8666 | 1.92541 | ||||||||
\(544\) | 92.2796 | 3.95646 | ||||||||
\(545\) | 1.92998 | 0.0826712 | ||||||||
\(546\) | 18.3658 | 0.785986 | ||||||||
\(547\) | −24.9088 | −1.06502 | −0.532512 | − | 0.846422i | \(-0.678752\pi\) | ||||
−0.532512 | + | 0.846422i | \(0.678752\pi\) | |||||||
\(548\) | 8.66784 | 0.370272 | ||||||||
\(549\) | −25.0384 | −1.06861 | ||||||||
\(550\) | 71.3182 | 3.04102 | ||||||||
\(551\) | 6.49928 | 0.276879 | ||||||||
\(552\) | 231.104 | 9.83644 | ||||||||
\(553\) | −11.5483 | −0.491082 | ||||||||
\(554\) | −51.1857 | −2.17467 | ||||||||
\(555\) | −0.227821 | −0.00967046 | ||||||||
\(556\) | 72.6901 | 3.08275 | ||||||||
\(557\) | 1.19087 | 0.0504587 | 0.0252294 | − | 0.999682i | \(-0.491968\pi\) | ||||
0.0252294 | + | 0.999682i | \(0.491968\pi\) | |||||||
\(558\) | −50.2080 | −2.12547 | ||||||||
\(559\) | −6.20582 | −0.262478 | ||||||||
\(560\) | 1.62344 | 0.0686028 | ||||||||
\(561\) | −51.5290 | −2.17556 | ||||||||
\(562\) | 15.0312 | 0.634052 | ||||||||
\(563\) | 5.68885 | 0.239756 | 0.119878 | − | 0.992789i | \(-0.461750\pi\) | ||||
0.119878 | + | 0.992789i | \(0.461750\pi\) | |||||||
\(564\) | −91.9324 | −3.87105 | ||||||||
\(565\) | −0.133996 | −0.00563727 | ||||||||
\(566\) | 68.4592 | 2.87756 | ||||||||
\(567\) | −6.38491 | −0.268141 | ||||||||
\(568\) | 9.70588 | 0.407250 | ||||||||
\(569\) | −4.84561 | −0.203138 | −0.101569 | − | 0.994828i | \(-0.532386\pi\) | ||||
−0.101569 | + | 0.994828i | \(0.532386\pi\) | |||||||
\(570\) | −2.17117 | −0.0909404 | ||||||||
\(571\) | −30.1348 | −1.26110 | −0.630551 | − | 0.776148i | \(-0.717171\pi\) | ||||
−0.630551 | + | 0.776148i | \(0.717171\pi\) | |||||||
\(572\) | −99.3382 | −4.15354 | ||||||||
\(573\) | −56.3982 | −2.35607 | ||||||||
\(574\) | 25.3665 | 1.05878 | ||||||||
\(575\) | 47.4713 | 1.97969 | ||||||||
\(576\) | 106.798 | 4.44991 | ||||||||
\(577\) | −22.3183 | −0.929123 | −0.464561 | − | 0.885541i | \(-0.653788\pi\) | ||||
−0.464561 | + | 0.885541i | \(0.653788\pi\) | |||||||
\(578\) | 3.74265 | 0.155674 | ||||||||
\(579\) | −67.0367 | −2.78595 | ||||||||
\(580\) | 2.04098 | 0.0847471 | ||||||||
\(581\) | −2.65729 | −0.110243 | ||||||||
\(582\) | 11.0769 | 0.459154 | ||||||||
\(583\) | 38.9415 | 1.61279 | ||||||||
\(584\) | 98.6983 | 4.08416 | ||||||||
\(585\) | −1.49608 | −0.0618554 | ||||||||
\(586\) | −3.48958 | −0.144153 | ||||||||
\(587\) | −18.6554 | −0.769993 | −0.384996 | − | 0.922918i | \(-0.625797\pi\) | ||||
−0.384996 | + | 0.922918i | \(0.625797\pi\) | |||||||
\(588\) | −88.4587 | −3.64797 | ||||||||
\(589\) | 13.3154 | 0.548650 | ||||||||
\(590\) | −3.00143 | −0.123567 | ||||||||
\(591\) | −20.1673 | −0.829573 | ||||||||
\(592\) | −10.5952 | −0.435459 | ||||||||
\(593\) | 47.5299 | 1.95182 | 0.975909 | − | 0.218179i | \(-0.0700118\pi\) | ||||
0.975909 | + | 0.218179i | \(0.0700118\pi\) | |||||||
\(594\) | −8.74660 | −0.358877 | ||||||||
\(595\) | −0.412241 | −0.0169002 | ||||||||
\(596\) | −50.9952 | −2.08885 | ||||||||
\(597\) | 27.1514 | 1.11123 | ||||||||
\(598\) | −90.0116 | −3.68085 | ||||||||
\(599\) | −24.6595 | −1.00756 | −0.503781 | − | 0.863832i | \(-0.668058\pi\) | ||||
−0.503781 | + | 0.863832i | \(0.668058\pi\) | |||||||
\(600\) | 120.835 | 4.93306 | ||||||||
\(601\) | −17.5527 | −0.715989 | −0.357995 | − | 0.933724i | \(-0.616539\pi\) | ||||
−0.357995 | + | 0.933724i | \(0.616539\pi\) | |||||||
\(602\) | −3.85153 | −0.156977 | ||||||||
\(603\) | 35.8866 | 1.46142 | ||||||||
\(604\) | 115.440 | 4.69720 | ||||||||
\(605\) | 2.16985 | 0.0882169 | ||||||||
\(606\) | 38.2565 | 1.55406 | ||||||||
\(607\) | −5.15250 | −0.209133 | −0.104567 | − | 0.994518i | \(-0.533346\pi\) | ||||
−0.104567 | + | 0.994518i | \(0.533346\pi\) | |||||||
\(608\) | −55.1221 | −2.23549 | ||||||||
\(609\) | 5.34947 | 0.216771 | ||||||||
\(610\) | 2.83865 | 0.114934 | ||||||||
\(611\) | 22.8698 | 0.925212 | ||||||||
\(612\) | −71.0218 | −2.87089 | ||||||||
\(613\) | 31.1573 | 1.25843 | 0.629216 | − | 0.777231i | \(-0.283376\pi\) | ||||
0.629216 | + | 0.777231i | \(0.283376\pi\) | |||||||
\(614\) | 62.3732 | 2.51718 | ||||||||
\(615\) | −3.97698 | −0.160367 | ||||||||
\(616\) | −39.3779 | −1.58658 | ||||||||
\(617\) | 35.9892 | 1.44887 | 0.724435 | − | 0.689343i | \(-0.242101\pi\) | ||||
0.724435 | + | 0.689343i | \(0.242101\pi\) | |||||||
\(618\) | 47.8838 | 1.92617 | ||||||||
\(619\) | 14.7207 | 0.591676 | 0.295838 | − | 0.955238i | \(-0.404401\pi\) | ||||
0.295838 | + | 0.955238i | \(0.404401\pi\) | |||||||
\(620\) | 4.18144 | 0.167931 | ||||||||
\(621\) | −5.82197 | −0.233628 | ||||||||
\(622\) | −5.83313 | −0.233887 | ||||||||
\(623\) | −6.11735 | −0.245087 | ||||||||
\(624\) | −133.912 | −5.36077 | ||||||||
\(625\) | 24.7310 | 0.989240 | ||||||||
\(626\) | −15.6248 | −0.624491 | ||||||||
\(627\) | 30.7802 | 1.22924 | ||||||||
\(628\) | 89.1380 | 3.55699 | ||||||||
\(629\) | 2.69044 | 0.107275 | ||||||||
\(630\) | −0.928518 | −0.0369930 | ||||||||
\(631\) | 35.7762 | 1.42423 | 0.712114 | − | 0.702063i | \(-0.247738\pi\) | ||||
0.712114 | + | 0.702063i | \(0.247738\pi\) | |||||||
\(632\) | 144.067 | 5.73067 | ||||||||
\(633\) | −0.421429 | −0.0167503 | ||||||||
\(634\) | 69.4744 | 2.75918 | ||||||||
\(635\) | −0.337781 | −0.0134044 | ||||||||
\(636\) | 103.300 | 4.09613 | ||||||||
\(637\) | 22.0056 | 0.871894 | ||||||||
\(638\) | −39.3883 | −1.55940 | ||||||||
\(639\) | −3.24451 | −0.128351 | ||||||||
\(640\) | −5.85386 | −0.231394 | ||||||||
\(641\) | 33.2094 | 1.31169 | 0.655847 | − | 0.754894i | \(-0.272312\pi\) | ||||
0.655847 | + | 0.754894i | \(0.272312\pi\) | |||||||
\(642\) | 81.6851 | 3.22385 | ||||||||
\(643\) | −38.0963 | −1.50237 | −0.751186 | − | 0.660090i | \(-0.770518\pi\) | ||||
−0.751186 | + | 0.660090i | \(0.770518\pi\) | |||||||
\(644\) | −41.0376 | −1.61711 | ||||||||
\(645\) | 0.603848 | 0.0237765 | ||||||||
\(646\) | 25.6403 | 1.00881 | ||||||||
\(647\) | −21.3540 | −0.839511 | −0.419756 | − | 0.907637i | \(-0.637884\pi\) | ||||
−0.419756 | + | 0.907637i | \(0.637884\pi\) | |||||||
\(648\) | 79.6531 | 3.12907 | ||||||||
\(649\) | 42.5506 | 1.67026 | ||||||||
\(650\) | −47.0633 | −1.84598 | ||||||||
\(651\) | 10.9597 | 0.429544 | ||||||||
\(652\) | −63.1601 | −2.47354 | ||||||||
\(653\) | 37.7905 | 1.47886 | 0.739428 | − | 0.673236i | \(-0.235096\pi\) | ||||
0.739428 | + | 0.673236i | \(0.235096\pi\) | |||||||
\(654\) | −98.8030 | −3.86350 | ||||||||
\(655\) | 0.719227 | 0.0281025 | ||||||||
\(656\) | −184.956 | −7.22131 | ||||||||
\(657\) | −32.9932 | −1.28719 | ||||||||
\(658\) | 14.1937 | 0.553329 | ||||||||
\(659\) | 11.4690 | 0.446768 | 0.223384 | − | 0.974731i | \(-0.428290\pi\) | ||||
0.223384 | + | 0.974731i | \(0.428290\pi\) | |||||||
\(660\) | 9.66595 | 0.376247 | ||||||||
\(661\) | −16.4583 | −0.640155 | −0.320078 | − | 0.947391i | \(-0.603709\pi\) | ||||
−0.320078 | + | 0.947391i | \(0.603709\pi\) | |||||||
\(662\) | −10.7096 | −0.416239 | ||||||||
\(663\) | 34.0043 | 1.32062 | ||||||||
\(664\) | 33.1503 | 1.28648 | ||||||||
\(665\) | 0.246247 | 0.00954904 | ||||||||
\(666\) | 6.05985 | 0.234815 | ||||||||
\(667\) | −26.2179 | −1.01516 | ||||||||
\(668\) | −47.4703 | −1.83668 | ||||||||
\(669\) | 66.8175 | 2.58331 | ||||||||
\(670\) | −4.06853 | −0.157181 | ||||||||
\(671\) | −40.2429 | −1.55356 | ||||||||
\(672\) | −45.3702 | −1.75019 | ||||||||
\(673\) | −10.1133 | −0.389840 | −0.194920 | − | 0.980819i | \(-0.562445\pi\) | ||||
−0.194920 | + | 0.980819i | \(0.562445\pi\) | |||||||
\(674\) | 25.1952 | 0.970483 | ||||||||
\(675\) | −3.04407 | −0.117166 | ||||||||
\(676\) | −6.41002 | −0.246539 | ||||||||
\(677\) | −40.7602 | −1.56654 | −0.783270 | − | 0.621681i | \(-0.786450\pi\) | ||||
−0.783270 | + | 0.621681i | \(0.786450\pi\) | |||||||
\(678\) | 6.85979 | 0.263448 | ||||||||
\(679\) | −1.25631 | −0.0482126 | ||||||||
\(680\) | 5.14279 | 0.197217 | ||||||||
\(681\) | 22.0688 | 0.845679 | ||||||||
\(682\) | −80.6965 | −3.09003 | ||||||||
\(683\) | −15.9445 | −0.610101 | −0.305051 | − | 0.952336i | \(-0.598673\pi\) | ||||
−0.305051 | + | 0.952336i | \(0.598673\pi\) | |||||||
\(684\) | 42.4240 | 1.62212 | ||||||||
\(685\) | 0.209813 | 0.00801655 | ||||||||
\(686\) | 28.6076 | 1.09224 | ||||||||
\(687\) | −58.0636 | −2.21527 | ||||||||
\(688\) | 28.0829 | 1.07065 | ||||||||
\(689\) | −25.6978 | −0.979007 | ||||||||
\(690\) | 8.75845 | 0.333428 | ||||||||
\(691\) | 50.1087 | 1.90623 | 0.953113 | − | 0.302614i | \(-0.0978594\pi\) | ||||
0.953113 | + | 0.302614i | \(0.0978594\pi\) | |||||||
\(692\) | 2.50169 | 0.0950998 | ||||||||
\(693\) | 13.1634 | 0.500035 | ||||||||
\(694\) | 31.9981 | 1.21463 | ||||||||
\(695\) | 1.75953 | 0.0667428 | ||||||||
\(696\) | −66.7357 | −2.52961 | ||||||||
\(697\) | 46.9660 | 1.77896 | ||||||||
\(698\) | 11.7362 | 0.444221 | ||||||||
\(699\) | 11.4924 | 0.434682 | ||||||||
\(700\) | −21.4568 | −0.810992 | ||||||||
\(701\) | −3.38467 | −0.127837 | −0.0639185 | − | 0.997955i | \(-0.520360\pi\) | ||||
−0.0639185 | + | 0.997955i | \(0.520360\pi\) | |||||||
\(702\) | 5.77193 | 0.217848 | ||||||||
\(703\) | −1.60710 | −0.0606129 | ||||||||
\(704\) | 171.650 | 6.46931 | ||||||||
\(705\) | −2.22531 | −0.0838100 | ||||||||
\(706\) | 41.4911 | 1.56154 | ||||||||
\(707\) | −4.33892 | −0.163182 | ||||||||
\(708\) | 112.874 | 4.24207 | ||||||||
\(709\) | −4.55041 | −0.170894 | −0.0854471 | − | 0.996343i | \(-0.527232\pi\) | ||||
−0.0854471 | + | 0.996343i | \(0.527232\pi\) | |||||||
\(710\) | 0.367836 | 0.0138046 | ||||||||
\(711\) | −48.1591 | −1.80611 | ||||||||
\(712\) | 76.3152 | 2.86003 | ||||||||
\(713\) | −53.7138 | −2.01160 | ||||||||
\(714\) | 21.1042 | 0.789805 | ||||||||
\(715\) | −2.40457 | −0.0899259 | ||||||||
\(716\) | −88.1625 | −3.29479 | ||||||||
\(717\) | −20.2875 | −0.757652 | ||||||||
\(718\) | 68.6331 | 2.56136 | ||||||||
\(719\) | 5.05785 | 0.188626 | 0.0943129 | − | 0.995543i | \(-0.469935\pi\) | ||||
0.0943129 | + | 0.995543i | \(0.469935\pi\) | |||||||
\(720\) | 6.77015 | 0.252309 | ||||||||
\(721\) | −5.43082 | −0.202254 | ||||||||
\(722\) | 36.8414 | 1.37109 | ||||||||
\(723\) | −14.8186 | −0.551111 | ||||||||
\(724\) | 99.3905 | 3.69382 | ||||||||
\(725\) | −13.7083 | −0.509112 | ||||||||
\(726\) | −111.083 | −4.12267 | ||||||||
\(727\) | −12.1437 | −0.450384 | −0.225192 | − | 0.974314i | \(-0.572301\pi\) | ||||
−0.225192 | + | 0.974314i | \(0.572301\pi\) | |||||||
\(728\) | 25.9857 | 0.963096 | ||||||||
\(729\) | −31.2072 | −1.15582 | ||||||||
\(730\) | 3.74049 | 0.138442 | ||||||||
\(731\) | −7.13111 | −0.263754 | ||||||||
\(732\) | −106.753 | −3.94569 | ||||||||
\(733\) | −32.0282 | −1.18299 | −0.591493 | − | 0.806310i | \(-0.701461\pi\) | ||||
−0.591493 | + | 0.806310i | \(0.701461\pi\) | |||||||
\(734\) | −100.463 | −3.70816 | ||||||||
\(735\) | −2.14122 | −0.0789802 | ||||||||
\(736\) | 222.361 | 8.19633 | ||||||||
\(737\) | 57.6786 | 2.12462 | ||||||||
\(738\) | 105.785 | 3.89398 | ||||||||
\(739\) | −8.47985 | −0.311936 | −0.155968 | − | 0.987762i | \(-0.549850\pi\) | ||||
−0.155968 | + | 0.987762i | \(0.549850\pi\) | |||||||
\(740\) | −0.504680 | −0.0185524 | ||||||||
\(741\) | −20.3120 | −0.746182 | ||||||||
\(742\) | −15.9489 | −0.585502 | ||||||||
\(743\) | −32.4699 | −1.19120 | −0.595602 | − | 0.803280i | \(-0.703086\pi\) | ||||
−0.595602 | + | 0.803280i | \(0.703086\pi\) | |||||||
\(744\) | −136.724 | −5.01256 | ||||||||
\(745\) | −1.23439 | −0.0452244 | ||||||||
\(746\) | −82.9553 | −3.03721 | ||||||||
\(747\) | −11.0816 | −0.405453 | ||||||||
\(748\) | −114.150 | −4.17372 | ||||||||
\(749\) | −9.26444 | −0.338515 | ||||||||
\(750\) | 9.17536 | 0.335037 | ||||||||
\(751\) | −51.0343 | −1.86227 | −0.931134 | − | 0.364676i | \(-0.881180\pi\) | ||||
−0.931134 | + | 0.364676i | \(0.881180\pi\) | |||||||
\(752\) | −103.491 | −3.77395 | ||||||||
\(753\) | 2.32316 | 0.0846606 | ||||||||
\(754\) | 25.9926 | 0.946594 | ||||||||
\(755\) | 2.79434 | 0.101696 | ||||||||
\(756\) | 2.63151 | 0.0957070 | ||||||||
\(757\) | −2.85432 | −0.103742 | −0.0518710 | − | 0.998654i | \(-0.516518\pi\) | ||||
−0.0518710 | + | 0.998654i | \(0.516518\pi\) | |||||||
\(758\) | 9.53353 | 0.346273 | ||||||||
\(759\) | −124.166 | −4.50696 | ||||||||
\(760\) | −3.07198 | −0.111432 | ||||||||
\(761\) | 37.3657 | 1.35450 | 0.677252 | − | 0.735751i | \(-0.263170\pi\) | ||||
0.677252 | + | 0.735751i | \(0.263170\pi\) | |||||||
\(762\) | 17.2923 | 0.626434 | ||||||||
\(763\) | 11.2059 | 0.405681 | ||||||||
\(764\) | −124.936 | −4.52003 | ||||||||
\(765\) | −1.71915 | −0.0621559 | ||||||||
\(766\) | −81.8716 | −2.95814 | ||||||||
\(767\) | −28.0794 | −1.01389 | ||||||||
\(768\) | 135.172 | 4.87759 | ||||||||
\(769\) | −6.13271 | −0.221151 | −0.110576 | − | 0.993868i | \(-0.535269\pi\) | ||||
−0.110576 | + | 0.993868i | \(0.535269\pi\) | |||||||
\(770\) | −1.49236 | −0.0537808 | ||||||||
\(771\) | 24.0096 | 0.864684 | ||||||||
\(772\) | −148.503 | −5.34473 | ||||||||
\(773\) | −28.4469 | −1.02316 | −0.511581 | − | 0.859235i | \(-0.670940\pi\) | ||||
−0.511581 | + | 0.859235i | \(0.670940\pi\) | |||||||
\(774\) | −16.0619 | −0.577332 | ||||||||
\(775\) | −28.0847 | −1.00883 | ||||||||
\(776\) | 15.6727 | 0.562617 | ||||||||
\(777\) | −1.32278 | −0.0474545 | ||||||||
\(778\) | −67.4523 | −2.41828 | ||||||||
\(779\) | −28.0545 | −1.00516 | ||||||||
\(780\) | −6.37862 | −0.228391 | ||||||||
\(781\) | −5.21472 | −0.186598 | ||||||||
\(782\) | −103.432 | −3.69873 | ||||||||
\(783\) | 1.68121 | 0.0600814 | ||||||||
\(784\) | −99.5809 | −3.55646 | ||||||||
\(785\) | 2.15767 | 0.0770104 | ||||||||
\(786\) | −36.8200 | −1.31333 | ||||||||
\(787\) | 3.62360 | 0.129167 | 0.0645836 | − | 0.997912i | \(-0.479428\pi\) | ||||
0.0645836 | + | 0.997912i | \(0.479428\pi\) | |||||||
\(788\) | −44.6756 | −1.59150 | ||||||||
\(789\) | −26.7596 | −0.952667 | ||||||||
\(790\) | 5.45989 | 0.194254 | ||||||||
\(791\) | −0.778013 | −0.0276630 | ||||||||
\(792\) | −164.216 | −5.83516 | ||||||||
\(793\) | 26.5565 | 0.943050 | ||||||||
\(794\) | −31.8963 | −1.13196 | ||||||||
\(795\) | 2.50048 | 0.0886830 | ||||||||
\(796\) | 60.1470 | 2.13185 | ||||||||
\(797\) | 37.8531 | 1.34082 | 0.670412 | − | 0.741989i | \(-0.266117\pi\) | ||||
0.670412 | + | 0.741989i | \(0.266117\pi\) | |||||||
\(798\) | −12.6063 | −0.446259 | ||||||||
\(799\) | 26.2797 | 0.929707 | ||||||||
\(800\) | 116.263 | 4.11052 | ||||||||
\(801\) | −25.5109 | −0.901383 | ||||||||
\(802\) | −39.5635 | −1.39704 | ||||||||
\(803\) | −53.0281 | −1.87132 | ||||||||
\(804\) | 153.004 | 5.39605 | ||||||||
\(805\) | −0.993353 | −0.0350111 | ||||||||
\(806\) | 53.2521 | 1.87573 | ||||||||
\(807\) | 24.9074 | 0.876782 | ||||||||
\(808\) | 54.1289 | 1.90425 | ||||||||
\(809\) | −37.6959 | −1.32532 | −0.662659 | − | 0.748921i | \(-0.730572\pi\) | ||||
−0.662659 | + | 0.748921i | \(0.730572\pi\) | |||||||
\(810\) | 3.01871 | 0.106067 | ||||||||
\(811\) | −46.3074 | −1.62607 | −0.813036 | − | 0.582213i | \(-0.802187\pi\) | ||||
−0.813036 | + | 0.582213i | \(0.802187\pi\) | |||||||
\(812\) | 11.8504 | 0.415867 | ||||||||
\(813\) | 40.9592 | 1.43650 | ||||||||
\(814\) | 9.73967 | 0.341375 | ||||||||
\(815\) | −1.52885 | −0.0535532 | ||||||||
\(816\) | −153.878 | −5.38681 | ||||||||
\(817\) | 4.25967 | 0.149027 | ||||||||
\(818\) | −61.3942 | −2.14660 | ||||||||
\(819\) | −8.68659 | −0.303534 | ||||||||
\(820\) | −8.81000 | −0.307659 | ||||||||
\(821\) | −17.4335 | −0.608432 | −0.304216 | − | 0.952603i | \(-0.598394\pi\) | ||||
−0.304216 | + | 0.952603i | \(0.598394\pi\) | |||||||
\(822\) | −10.7411 | −0.374640 | ||||||||
\(823\) | 41.3021 | 1.43970 | 0.719851 | − | 0.694129i | \(-0.244210\pi\) | ||||
0.719851 | + | 0.694129i | \(0.244210\pi\) | |||||||
\(824\) | 67.7506 | 2.36020 | ||||||||
\(825\) | −64.9214 | −2.26027 | ||||||||
\(826\) | −17.4270 | −0.606363 | ||||||||
\(827\) | −17.4628 | −0.607240 | −0.303620 | − | 0.952793i | \(-0.598195\pi\) | ||||
−0.303620 | + | 0.952793i | \(0.598195\pi\) | |||||||
\(828\) | −171.137 | −5.94743 | ||||||||
\(829\) | −38.6660 | −1.34293 | −0.671463 | − | 0.741038i | \(-0.734334\pi\) | ||||
−0.671463 | + | 0.741038i | \(0.734334\pi\) | |||||||
\(830\) | 1.25634 | 0.0436081 | ||||||||
\(831\) | 46.5947 | 1.61635 | ||||||||
\(832\) | −113.273 | −3.92704 | ||||||||
\(833\) | 25.2866 | 0.876130 | ||||||||
\(834\) | −90.0771 | −3.11912 | ||||||||
\(835\) | −1.14906 | −0.0397649 | ||||||||
\(836\) | 68.1857 | 2.35825 | ||||||||
\(837\) | 3.44436 | 0.119054 | ||||||||
\(838\) | −46.6872 | −1.61278 | ||||||||
\(839\) | −48.6760 | −1.68048 | −0.840240 | − | 0.542214i | \(-0.817586\pi\) | ||||
−0.840240 | + | 0.542214i | \(0.817586\pi\) | |||||||
\(840\) | −2.52850 | −0.0872417 | ||||||||
\(841\) | −21.4291 | −0.738934 | ||||||||
\(842\) | 39.9860 | 1.37801 | ||||||||
\(843\) | −13.6830 | −0.471267 | ||||||||
\(844\) | −0.933569 | −0.0321348 | ||||||||
\(845\) | −0.155161 | −0.00533768 | ||||||||
\(846\) | 59.1914 | 2.03504 | ||||||||
\(847\) | 12.5986 | 0.432894 | ||||||||
\(848\) | 116.289 | 3.99338 | ||||||||
\(849\) | −62.3189 | −2.13878 | ||||||||
\(850\) | −54.0805 | −1.85494 | ||||||||
\(851\) | 6.48299 | 0.222234 | ||||||||
\(852\) | −13.8331 | −0.473915 | ||||||||
\(853\) | 22.0058 | 0.753464 | 0.376732 | − | 0.926322i | \(-0.377048\pi\) | ||||
0.376732 | + | 0.926322i | \(0.377048\pi\) | |||||||
\(854\) | 16.4819 | 0.563998 | ||||||||
\(855\) | 1.02691 | 0.0351196 | ||||||||
\(856\) | 115.576 | 3.95030 | ||||||||
\(857\) | −20.6128 | −0.704119 | −0.352060 | − | 0.935978i | \(-0.614519\pi\) | ||||
−0.352060 | + | 0.935978i | \(0.614519\pi\) | |||||||
\(858\) | 123.099 | 4.20254 | ||||||||
\(859\) | 28.2277 | 0.963115 | 0.481558 | − | 0.876414i | \(-0.340071\pi\) | ||||
0.481558 | + | 0.876414i | \(0.340071\pi\) | |||||||
\(860\) | 1.33767 | 0.0456142 | ||||||||
\(861\) | −23.0913 | −0.786948 | ||||||||
\(862\) | 46.5739 | 1.58631 | ||||||||
\(863\) | 14.2756 | 0.485946 | 0.242973 | − | 0.970033i | \(-0.421877\pi\) | ||||
0.242973 | + | 0.970033i | \(0.421877\pi\) | |||||||
\(864\) | −14.2587 | −0.485092 | ||||||||
\(865\) | 0.0605556 | 0.00205895 | ||||||||
\(866\) | −14.0456 | −0.477289 | ||||||||
\(867\) | −3.40696 | −0.115706 | ||||||||
\(868\) | 24.2784 | 0.824063 | ||||||||
\(869\) | −77.4035 | −2.62573 | ||||||||
\(870\) | −2.52917 | −0.0857469 | ||||||||
\(871\) | −38.0625 | −1.28970 | ||||||||
\(872\) | −139.796 | −4.73409 | ||||||||
\(873\) | −5.23912 | −0.177317 | ||||||||
\(874\) | 61.7840 | 2.08987 | ||||||||
\(875\) | −1.04064 | −0.0351800 | ||||||||
\(876\) | −140.668 | −4.75273 | ||||||||
\(877\) | 28.6359 | 0.966964 | 0.483482 | − | 0.875354i | \(-0.339372\pi\) | ||||
0.483482 | + | 0.875354i | \(0.339372\pi\) | |||||||
\(878\) | −51.2983 | −1.73123 | ||||||||
\(879\) | 3.17659 | 0.107144 | ||||||||
\(880\) | 10.8813 | 0.366808 | ||||||||
\(881\) | −50.8714 | −1.71390 | −0.856951 | − | 0.515399i | \(-0.827644\pi\) | ||||
−0.856951 | + | 0.515399i | \(0.827644\pi\) | |||||||
\(882\) | 56.9548 | 1.91777 | ||||||||
\(883\) | 12.0825 | 0.406608 | 0.203304 | − | 0.979116i | \(-0.434832\pi\) | ||||
0.203304 | + | 0.979116i | \(0.434832\pi\) | |||||||
\(884\) | 75.3280 | 2.53355 | ||||||||
\(885\) | 2.73223 | 0.0918427 | ||||||||
\(886\) | 33.1492 | 1.11367 | ||||||||
\(887\) | −5.86444 | −0.196909 | −0.0984543 | − | 0.995142i | \(-0.531390\pi\) | ||||
−0.0984543 | + | 0.995142i | \(0.531390\pi\) | |||||||
\(888\) | 16.5020 | 0.553770 | ||||||||
\(889\) | −1.96123 | −0.0657777 | ||||||||
\(890\) | 2.89222 | 0.0969473 | ||||||||
\(891\) | −42.7956 | −1.43371 | ||||||||
\(892\) | 148.017 | 4.95598 | ||||||||
\(893\) | −15.6978 | −0.525307 | ||||||||
\(894\) | 63.1930 | 2.11349 | ||||||||
\(895\) | −2.13405 | −0.0713336 | ||||||||
\(896\) | −33.9889 | −1.13549 | ||||||||
\(897\) | 81.9382 | 2.73584 | ||||||||
\(898\) | 48.4289 | 1.61609 | ||||||||
\(899\) | 15.5109 | 0.517317 | ||||||||
\(900\) | −89.4804 | −2.98268 | ||||||||
\(901\) | −29.5293 | −0.983764 | ||||||||
\(902\) | 170.022 | 5.66111 | ||||||||
\(903\) | 3.50608 | 0.116675 | ||||||||
\(904\) | 9.70588 | 0.322813 | ||||||||
\(905\) | 2.40584 | 0.0799728 | ||||||||
\(906\) | −143.053 | −4.75261 | ||||||||
\(907\) | −34.5248 | −1.14638 | −0.573188 | − | 0.819424i | \(-0.694293\pi\) | ||||
−0.573188 | + | 0.819424i | \(0.694293\pi\) | |||||||
\(908\) | 48.8879 | 1.62240 | ||||||||
\(909\) | −18.0944 | −0.600153 | ||||||||
\(910\) | 0.984815 | 0.0326463 | ||||||||
\(911\) | 12.7656 | 0.422944 | 0.211472 | − | 0.977384i | \(-0.432174\pi\) | ||||
0.211472 | + | 0.977384i | \(0.432174\pi\) | |||||||
\(912\) | 91.9171 | 3.04368 | ||||||||
\(913\) | −17.8108 | −0.589452 | ||||||||
\(914\) | −60.9396 | −2.01570 | ||||||||
\(915\) | −2.58404 | −0.0854259 | ||||||||
\(916\) | −128.625 | −4.24990 | ||||||||
\(917\) | 4.17600 | 0.137904 | ||||||||
\(918\) | 6.63253 | 0.218906 | ||||||||
\(919\) | 37.9051 | 1.25038 | 0.625188 | − | 0.780474i | \(-0.285022\pi\) | ||||
0.625188 | + | 0.780474i | \(0.285022\pi\) | |||||||
\(920\) | 12.3923 | 0.408561 | ||||||||
\(921\) | −56.7787 | −1.87092 | ||||||||
\(922\) | 70.0170 | 2.30589 | ||||||||
\(923\) | 3.44123 | 0.113269 | ||||||||
\(924\) | 56.1227 | 1.84630 | ||||||||
\(925\) | 3.38969 | 0.111452 | ||||||||
\(926\) | 50.3481 | 1.65454 | ||||||||
\(927\) | −22.6479 | −0.743854 | ||||||||
\(928\) | −64.2109 | −2.10783 | ||||||||
\(929\) | 54.5941 | 1.79118 | 0.895588 | − | 0.444884i | \(-0.146755\pi\) | ||||
0.895588 | + | 0.444884i | \(0.146755\pi\) | |||||||
\(930\) | −5.18162 | −0.169912 | ||||||||
\(931\) | −15.1047 | −0.495035 | ||||||||
\(932\) | 25.4585 | 0.833920 | ||||||||
\(933\) | 5.30994 | 0.173840 | ||||||||
\(934\) | 13.6047 | 0.445159 | ||||||||
\(935\) | −2.76309 | −0.0903628 | ||||||||
\(936\) | 108.367 | 3.54209 | ||||||||
\(937\) | 49.7854 | 1.62642 | 0.813209 | − | 0.581971i | \(-0.197718\pi\) | ||||
0.813209 | + | 0.581971i | \(0.197718\pi\) | |||||||
\(938\) | −23.6228 | −0.771313 | ||||||||
\(939\) | 14.2233 | 0.464161 | ||||||||
\(940\) | −4.92961 | −0.160786 | ||||||||
\(941\) | 1.53077 | 0.0499018 | 0.0249509 | − | 0.999689i | \(-0.492057\pi\) | ||||
0.0249509 | + | 0.999689i | \(0.492057\pi\) | |||||||
\(942\) | −110.459 | −3.59896 | ||||||||
\(943\) | 113.171 | 3.68536 | ||||||||
\(944\) | 127.066 | 4.13566 | ||||||||
\(945\) | 0.0636980 | 0.00207210 | ||||||||
\(946\) | −25.8154 | −0.839330 | ||||||||
\(947\) | −11.0910 | −0.360410 | −0.180205 | − | 0.983629i | \(-0.557676\pi\) | ||||
−0.180205 | + | 0.983629i | \(0.557676\pi\) | |||||||
\(948\) | −205.329 | −6.66877 | ||||||||
\(949\) | 34.9936 | 1.13594 | ||||||||
\(950\) | 32.3043 | 1.04809 | ||||||||
\(951\) | −63.2431 | −2.05080 | ||||||||
\(952\) | 29.8602 | 0.967775 | ||||||||
\(953\) | 19.6338 | 0.636001 | 0.318001 | − | 0.948090i | \(-0.396989\pi\) | ||||
0.318001 | + | 0.948090i | \(0.396989\pi\) | |||||||
\(954\) | −66.5108 | −2.15337 | ||||||||
\(955\) | −3.02419 | −0.0978605 | ||||||||
\(956\) | −44.9419 | −1.45353 | ||||||||
\(957\) | 35.8554 | 1.15904 | ||||||||
\(958\) | −47.1266 | −1.52259 | ||||||||
\(959\) | 1.21822 | 0.0393385 | ||||||||
\(960\) | 11.0219 | 0.355729 | ||||||||
\(961\) | 0.777834 | 0.0250914 | ||||||||
\(962\) | −6.42727 | −0.207224 | ||||||||
\(963\) | −38.6350 | −1.24500 | ||||||||
\(964\) | −32.8269 | −1.05728 | ||||||||
\(965\) | −3.59465 | −0.115716 | ||||||||
\(966\) | 50.8535 | 1.63619 | ||||||||
\(967\) | 9.40582 | 0.302471 | 0.151235 | − | 0.988498i | \(-0.451675\pi\) | ||||
0.151235 | + | 0.988498i | \(0.451675\pi\) | |||||||
\(968\) | −157.171 | −5.05166 | ||||||||
\(969\) | −23.3406 | −0.749807 | ||||||||
\(970\) | 0.593968 | 0.0190712 | ||||||||
\(971\) | −24.4561 | −0.784833 | −0.392417 | − | 0.919788i | \(-0.628361\pi\) | ||||
−0.392417 | + | 0.919788i | \(0.628361\pi\) | |||||||
\(972\) | −123.671 | −3.96675 | ||||||||
\(973\) | 10.2162 | 0.327517 | ||||||||
\(974\) | −99.1740 | −3.17774 | ||||||||
\(975\) | 42.8421 | 1.37204 | ||||||||
\(976\) | −120.175 | −3.84671 | ||||||||
\(977\) | −27.5757 | −0.882225 | −0.441112 | − | 0.897452i | \(-0.645416\pi\) | ||||
−0.441112 | + | 0.897452i | \(0.645416\pi\) | |||||||
\(978\) | 78.2676 | 2.50272 | ||||||||
\(979\) | −41.0023 | −1.31044 | ||||||||
\(980\) | −4.74334 | −0.151520 | ||||||||
\(981\) | 46.7314 | 1.49202 | ||||||||
\(982\) | −57.9266 | −1.84851 | ||||||||
\(983\) | −28.2464 | −0.900919 | −0.450460 | − | 0.892797i | \(-0.648740\pi\) | ||||
−0.450460 | + | 0.892797i | \(0.648740\pi\) | |||||||
\(984\) | 288.068 | 9.18329 | ||||||||
\(985\) | −1.08141 | −0.0344567 | ||||||||
\(986\) | 29.8681 | 0.951193 | ||||||||
\(987\) | −12.9206 | −0.411269 | ||||||||
\(988\) | −44.9962 | −1.43152 | ||||||||
\(989\) | −17.1834 | −0.546401 | ||||||||
\(990\) | −6.22350 | −0.197796 | ||||||||
\(991\) | −6.91095 | −0.219534 | −0.109767 | − | 0.993957i | \(-0.535010\pi\) | ||||
−0.109767 | + | 0.993957i | \(0.535010\pi\) | |||||||
\(992\) | −131.552 | −4.17677 | ||||||||
\(993\) | 9.74898 | 0.309375 | ||||||||
\(994\) | 2.13574 | 0.0677415 | ||||||||
\(995\) | 1.45591 | 0.0461556 | ||||||||
\(996\) | −47.2468 | −1.49707 | ||||||||
\(997\) | −17.7333 | −0.561620 | −0.280810 | − | 0.959763i | \(-0.590603\pi\) | ||||
−0.280810 | + | 0.959763i | \(0.590603\pi\) | |||||||
\(998\) | −17.0350 | −0.539233 | ||||||||
\(999\) | −0.415717 | −0.0131527 |
(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 | 8023.2.a.c.1.5 | ✓ | 158 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.c.1.5 | ✓ | 158 | 1.1 | even | 1 | trivial |