Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.54628 | −1.80049 | −0.900244 | − | 0.435385i | \(-0.856612\pi\) | ||||
−0.900244 | + | 0.435385i | \(0.856612\pi\) | |||||||
\(3\) | 1.17861 | 0.680472 | 0.340236 | − | 0.940340i | \(-0.389493\pi\) | ||||
0.340236 | + | 0.940340i | \(0.389493\pi\) | |||||||
\(4\) | 4.48352 | 2.24176 | ||||||||
\(5\) | 1.63315 | 0.730367 | 0.365183 | − | 0.930936i | \(-0.381006\pi\) | ||||
0.365183 | + | 0.930936i | \(0.381006\pi\) | |||||||
\(6\) | −3.00107 | −1.22518 | ||||||||
\(7\) | −0.708864 | −0.267925 | −0.133963 | − | 0.990986i | \(-0.542770\pi\) | ||||
−0.133963 | + | 0.990986i | \(0.542770\pi\) | |||||||
\(8\) | −6.32373 | −2.23578 | ||||||||
\(9\) | −1.61088 | −0.536958 | ||||||||
\(10\) | −4.15845 | −1.31502 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 5.28433 | 1.52545 | ||||||||
\(13\) | −0.231092 | −0.0640934 | −0.0320467 | − | 0.999486i | \(-0.510203\pi\) | ||||
−0.0320467 | + | 0.999486i | \(0.510203\pi\) | |||||||
\(14\) | 1.80496 | 0.482396 | ||||||||
\(15\) | 1.92485 | 0.496994 | ||||||||
\(16\) | 7.13491 | 1.78373 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 4.10173 | 0.966788 | ||||||||
\(19\) | 2.82304 | 0.647649 | 0.323824 | − | 0.946117i | \(-0.395031\pi\) | ||||
0.323824 | + | 0.946117i | \(0.395031\pi\) | |||||||
\(20\) | 7.32226 | 1.63731 | ||||||||
\(21\) | −0.835475 | −0.182316 | ||||||||
\(22\) | −2.54628 | −0.542868 | ||||||||
\(23\) | −4.91189 | −1.02420 | −0.512100 | − | 0.858926i | \(-0.671132\pi\) | ||||
−0.512100 | + | 0.858926i | \(0.671132\pi\) | |||||||
\(24\) | −7.45322 | −1.52138 | ||||||||
\(25\) | −2.33282 | −0.466564 | ||||||||
\(26\) | 0.588424 | 0.115399 | ||||||||
\(27\) | −5.43443 | −1.04586 | ||||||||
\(28\) | −3.17820 | −0.600624 | ||||||||
\(29\) | 5.74697 | 1.06719 | 0.533593 | − | 0.845741i | \(-0.320841\pi\) | ||||
0.533593 | + | 0.845741i | \(0.320841\pi\) | |||||||
\(30\) | −4.90120 | −0.894832 | ||||||||
\(31\) | 10.6463 | 1.91213 | 0.956066 | − | 0.293152i | \(-0.0947041\pi\) | ||||
0.956066 | + | 0.293152i | \(0.0947041\pi\) | |||||||
\(32\) | −5.52000 | −0.975808 | ||||||||
\(33\) | 1.17861 | 0.205170 | ||||||||
\(34\) | −2.54628 | −0.436683 | ||||||||
\(35\) | −1.15768 | −0.195684 | ||||||||
\(36\) | −7.22239 | −1.20373 | ||||||||
\(37\) | −5.71901 | −0.940200 | −0.470100 | − | 0.882613i | \(-0.655782\pi\) | ||||
−0.470100 | + | 0.882613i | \(0.655782\pi\) | |||||||
\(38\) | −7.18823 | −1.16608 | ||||||||
\(39\) | −0.272368 | −0.0436137 | ||||||||
\(40\) | −10.3276 | −1.63294 | ||||||||
\(41\) | −3.74440 | −0.584777 | −0.292389 | − | 0.956300i | \(-0.594450\pi\) | ||||
−0.292389 | + | 0.956300i | \(0.594450\pi\) | |||||||
\(42\) | 2.12735 | 0.328257 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 4.48352 | 0.675916 | ||||||||
\(45\) | −2.63080 | −0.392177 | ||||||||
\(46\) | 12.5070 | 1.84406 | ||||||||
\(47\) | −8.08760 | −1.17970 | −0.589849 | − | 0.807513i | \(-0.700813\pi\) | ||||
−0.589849 | + | 0.807513i | \(0.700813\pi\) | |||||||
\(48\) | 8.40929 | 1.21378 | ||||||||
\(49\) | −6.49751 | −0.928216 | ||||||||
\(50\) | 5.94001 | 0.840044 | ||||||||
\(51\) | 1.17861 | 0.165039 | ||||||||
\(52\) | −1.03611 | −0.143682 | ||||||||
\(53\) | 13.1046 | 1.80005 | 0.900024 | − | 0.435840i | \(-0.143549\pi\) | ||||
0.900024 | + | 0.435840i | \(0.143549\pi\) | |||||||
\(54\) | 13.8376 | 1.88305 | ||||||||
\(55\) | 1.63315 | 0.220214 | ||||||||
\(56\) | 4.48266 | 0.599021 | ||||||||
\(57\) | 3.32726 | 0.440707 | ||||||||
\(58\) | −14.6334 | −1.92146 | ||||||||
\(59\) | −10.6936 | −1.39219 | −0.696097 | − | 0.717948i | \(-0.745082\pi\) | ||||
−0.696097 | + | 0.717948i | \(0.745082\pi\) | |||||||
\(60\) | 8.63010 | 1.11414 | ||||||||
\(61\) | −7.14368 | −0.914654 | −0.457327 | − | 0.889299i | \(-0.651193\pi\) | ||||
−0.457327 | + | 0.889299i | \(0.651193\pi\) | |||||||
\(62\) | −27.1084 | −3.44277 | ||||||||
\(63\) | 1.14189 | 0.143865 | ||||||||
\(64\) | −0.214376 | −0.0267970 | ||||||||
\(65\) | −0.377408 | −0.0468117 | ||||||||
\(66\) | −3.00107 | −0.369406 | ||||||||
\(67\) | 1.17446 | 0.143483 | 0.0717415 | − | 0.997423i | \(-0.477144\pi\) | ||||
0.0717415 | + | 0.997423i | \(0.477144\pi\) | |||||||
\(68\) | 4.48352 | 0.543707 | ||||||||
\(69\) | −5.78921 | −0.696939 | ||||||||
\(70\) | 2.94777 | 0.352326 | ||||||||
\(71\) | −16.1972 | −1.92226 | −0.961130 | − | 0.276097i | \(-0.910959\pi\) | ||||
−0.961130 | + | 0.276097i | \(0.910959\pi\) | |||||||
\(72\) | 10.1867 | 1.20052 | ||||||||
\(73\) | 4.11659 | 0.481811 | 0.240905 | − | 0.970549i | \(-0.422556\pi\) | ||||
0.240905 | + | 0.970549i | \(0.422556\pi\) | |||||||
\(74\) | 14.5622 | 1.69282 | ||||||||
\(75\) | −2.74949 | −0.317484 | ||||||||
\(76\) | 12.6571 | 1.45187 | ||||||||
\(77\) | −0.708864 | −0.0807825 | ||||||||
\(78\) | 0.693523 | 0.0785260 | ||||||||
\(79\) | −6.14710 | −0.691603 | −0.345801 | − | 0.938308i | \(-0.612393\pi\) | ||||
−0.345801 | + | 0.938308i | \(0.612393\pi\) | |||||||
\(80\) | 11.6524 | 1.30278 | ||||||||
\(81\) | −1.57246 | −0.174717 | ||||||||
\(82\) | 9.53427 | 1.05288 | ||||||||
\(83\) | 7.46155 | 0.819012 | 0.409506 | − | 0.912307i | \(-0.365701\pi\) | ||||
0.409506 | + | 0.912307i | \(0.365701\pi\) | |||||||
\(84\) | −3.74587 | −0.408708 | ||||||||
\(85\) | 1.63315 | 0.177140 | ||||||||
\(86\) | 2.54628 | 0.274572 | ||||||||
\(87\) | 6.77345 | 0.726190 | ||||||||
\(88\) | −6.32373 | −0.674112 | ||||||||
\(89\) | −9.20969 | −0.976225 | −0.488112 | − | 0.872781i | \(-0.662314\pi\) | ||||
−0.488112 | + | 0.872781i | \(0.662314\pi\) | |||||||
\(90\) | 6.69874 | 0.706110 | ||||||||
\(91\) | 0.163813 | 0.0171722 | ||||||||
\(92\) | −22.0226 | −2.29601 | ||||||||
\(93\) | 12.5478 | 1.30115 | ||||||||
\(94\) | 20.5933 | 2.12403 | ||||||||
\(95\) | 4.61044 | 0.473021 | ||||||||
\(96\) | −6.50594 | −0.664010 | ||||||||
\(97\) | 0.962798 | 0.0977573 | 0.0488786 | − | 0.998805i | \(-0.484435\pi\) | ||||
0.0488786 | + | 0.998805i | \(0.484435\pi\) | |||||||
\(98\) | 16.5445 | 1.67124 | ||||||||
\(99\) | −1.61088 | −0.161899 | ||||||||
\(100\) | −10.4593 | −1.04593 | ||||||||
\(101\) | −11.2770 | −1.12210 | −0.561052 | − | 0.827780i | \(-0.689603\pi\) | ||||
−0.561052 | + | 0.827780i | \(0.689603\pi\) | |||||||
\(102\) | −3.00107 | −0.297150 | ||||||||
\(103\) | 2.45797 | 0.242191 | 0.121096 | − | 0.992641i | \(-0.461359\pi\) | ||||
0.121096 | + | 0.992641i | \(0.461359\pi\) | |||||||
\(104\) | 1.46136 | 0.143298 | ||||||||
\(105\) | −1.36446 | −0.133157 | ||||||||
\(106\) | −33.3678 | −3.24097 | ||||||||
\(107\) | 11.7185 | 1.13287 | 0.566435 | − | 0.824107i | \(-0.308322\pi\) | ||||
0.566435 | + | 0.824107i | \(0.308322\pi\) | |||||||
\(108\) | −24.3654 | −2.34456 | ||||||||
\(109\) | 13.6569 | 1.30809 | 0.654044 | − | 0.756456i | \(-0.273071\pi\) | ||||
0.654044 | + | 0.756456i | \(0.273071\pi\) | |||||||
\(110\) | −4.15845 | −0.396493 | ||||||||
\(111\) | −6.74049 | −0.639779 | ||||||||
\(112\) | −5.05768 | −0.477906 | ||||||||
\(113\) | 6.22921 | 0.585994 | 0.292997 | − | 0.956113i | \(-0.405347\pi\) | ||||
0.292997 | + | 0.956113i | \(0.405347\pi\) | |||||||
\(114\) | −8.47213 | −0.793487 | ||||||||
\(115\) | −8.02185 | −0.748041 | ||||||||
\(116\) | 25.7667 | 2.39237 | ||||||||
\(117\) | 0.372260 | 0.0344155 | ||||||||
\(118\) | 27.2290 | 2.50663 | ||||||||
\(119\) | −0.708864 | −0.0649814 | ||||||||
\(120\) | −12.1722 | −1.11117 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 18.1898 | 1.64682 | ||||||||
\(123\) | −4.41319 | −0.397924 | ||||||||
\(124\) | 47.7329 | 4.28654 | ||||||||
\(125\) | −11.9756 | −1.07113 | ||||||||
\(126\) | −2.90757 | −0.259027 | ||||||||
\(127\) | 4.24032 | 0.376268 | 0.188134 | − | 0.982143i | \(-0.439756\pi\) | ||||
0.188134 | + | 0.982143i | \(0.439756\pi\) | |||||||
\(128\) | 11.5859 | 1.02406 | ||||||||
\(129\) | −1.17861 | −0.103771 | ||||||||
\(130\) | 0.960984 | 0.0842839 | ||||||||
\(131\) | 2.94489 | 0.257296 | 0.128648 | − | 0.991690i | \(-0.458936\pi\) | ||||
0.128648 | + | 0.991690i | \(0.458936\pi\) | |||||||
\(132\) | 5.28433 | 0.459942 | ||||||||
\(133\) | −2.00115 | −0.173521 | ||||||||
\(134\) | −2.99050 | −0.258339 | ||||||||
\(135\) | −8.87524 | −0.763859 | ||||||||
\(136\) | −6.32373 | −0.542255 | ||||||||
\(137\) | 17.1564 | 1.46577 | 0.732885 | − | 0.680352i | \(-0.238173\pi\) | ||||
0.732885 | + | 0.680352i | \(0.238173\pi\) | |||||||
\(138\) | 14.7409 | 1.25483 | ||||||||
\(139\) | −4.16976 | −0.353674 | −0.176837 | − | 0.984240i | \(-0.556587\pi\) | ||||
−0.176837 | + | 0.984240i | \(0.556587\pi\) | |||||||
\(140\) | −5.19048 | −0.438676 | ||||||||
\(141\) | −9.53214 | −0.802751 | ||||||||
\(142\) | 41.2427 | 3.46101 | ||||||||
\(143\) | −0.231092 | −0.0193249 | ||||||||
\(144\) | −11.4935 | −0.957788 | ||||||||
\(145\) | 9.38567 | 0.779437 | ||||||||
\(146\) | −10.4820 | −0.867495 | ||||||||
\(147\) | −7.65804 | −0.631625 | ||||||||
\(148\) | −25.6413 | −2.10770 | ||||||||
\(149\) | −7.36718 | −0.603543 | −0.301772 | − | 0.953380i | \(-0.597578\pi\) | ||||
−0.301772 | + | 0.953380i | \(0.597578\pi\) | |||||||
\(150\) | 7.00096 | 0.571626 | ||||||||
\(151\) | 6.73449 | 0.548045 | 0.274023 | − | 0.961723i | \(-0.411646\pi\) | ||||
0.274023 | + | 0.961723i | \(0.411646\pi\) | |||||||
\(152\) | −17.8521 | −1.44800 | ||||||||
\(153\) | −1.61088 | −0.130232 | ||||||||
\(154\) | 1.80496 | 0.145448 | ||||||||
\(155\) | 17.3870 | 1.39656 | ||||||||
\(156\) | −1.22117 | −0.0977715 | ||||||||
\(157\) | 1.06032 | 0.0846225 | 0.0423113 | − | 0.999104i | \(-0.486528\pi\) | ||||
0.0423113 | + | 0.999104i | \(0.486528\pi\) | |||||||
\(158\) | 15.6522 | 1.24522 | ||||||||
\(159\) | 15.4452 | 1.22488 | ||||||||
\(160\) | −9.01499 | −0.712698 | ||||||||
\(161\) | 3.48186 | 0.274409 | ||||||||
\(162\) | 4.00390 | 0.314576 | ||||||||
\(163\) | −2.77089 | −0.217033 | −0.108517 | − | 0.994095i | \(-0.534610\pi\) | ||||
−0.108517 | + | 0.994095i | \(0.534610\pi\) | |||||||
\(164\) | −16.7881 | −1.31093 | ||||||||
\(165\) | 1.92485 | 0.149849 | ||||||||
\(166\) | −18.9992 | −1.47462 | ||||||||
\(167\) | −22.1394 | −1.71320 | −0.856598 | − | 0.515985i | \(-0.827426\pi\) | ||||
−0.856598 | + | 0.515985i | \(0.827426\pi\) | |||||||
\(168\) | 5.28331 | 0.407617 | ||||||||
\(169\) | −12.9466 | −0.995892 | ||||||||
\(170\) | −4.15845 | −0.318939 | ||||||||
\(171\) | −4.54756 | −0.347761 | ||||||||
\(172\) | −4.48352 | −0.341865 | ||||||||
\(173\) | −5.09869 | −0.387646 | −0.193823 | − | 0.981036i | \(-0.562089\pi\) | ||||
−0.193823 | + | 0.981036i | \(0.562089\pi\) | |||||||
\(174\) | −17.2471 | −1.30750 | ||||||||
\(175\) | 1.65365 | 0.125004 | ||||||||
\(176\) | 7.13491 | 0.537814 | ||||||||
\(177\) | −12.6037 | −0.947349 | ||||||||
\(178\) | 23.4504 | 1.75768 | ||||||||
\(179\) | −14.5637 | −1.08854 | −0.544270 | − | 0.838910i | \(-0.683193\pi\) | ||||
−0.544270 | + | 0.838910i | \(0.683193\pi\) | |||||||
\(180\) | −11.7953 | −0.879166 | ||||||||
\(181\) | 3.07250 | 0.228377 | 0.114189 | − | 0.993459i | \(-0.463573\pi\) | ||||
0.114189 | + | 0.993459i | \(0.463573\pi\) | |||||||
\(182\) | −0.417112 | −0.0309184 | ||||||||
\(183\) | −8.41962 | −0.622396 | ||||||||
\(184\) | 31.0614 | 2.28988 | ||||||||
\(185\) | −9.34001 | −0.686691 | ||||||||
\(186\) | −31.9503 | −2.34271 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −36.2609 | −2.64460 | ||||||||
\(189\) | 3.85227 | 0.280211 | ||||||||
\(190\) | −11.7395 | −0.851670 | ||||||||
\(191\) | −16.2062 | −1.17264 | −0.586320 | − | 0.810079i | \(-0.699424\pi\) | ||||
−0.586320 | + | 0.810079i | \(0.699424\pi\) | |||||||
\(192\) | −0.252666 | −0.0182346 | ||||||||
\(193\) | −2.05024 | −0.147580 | −0.0737899 | − | 0.997274i | \(-0.523509\pi\) | ||||
−0.0737899 | + | 0.997274i | \(0.523509\pi\) | |||||||
\(194\) | −2.45155 | −0.176011 | ||||||||
\(195\) | −0.444817 | −0.0318540 | ||||||||
\(196\) | −29.1317 | −2.08084 | ||||||||
\(197\) | −0.0852862 | −0.00607639 | −0.00303819 | − | 0.999995i | \(-0.500967\pi\) | ||||
−0.00303819 | + | 0.999995i | \(0.500967\pi\) | |||||||
\(198\) | 4.10173 | 0.291497 | ||||||||
\(199\) | −13.7575 | −0.975240 | −0.487620 | − | 0.873056i | \(-0.662135\pi\) | ||||
−0.487620 | + | 0.873056i | \(0.662135\pi\) | |||||||
\(200\) | 14.7521 | 1.04313 | ||||||||
\(201\) | 1.38423 | 0.0976361 | ||||||||
\(202\) | 28.7144 | 2.02034 | ||||||||
\(203\) | −4.07382 | −0.285926 | ||||||||
\(204\) | 5.28433 | 0.369977 | ||||||||
\(205\) | −6.11517 | −0.427102 | ||||||||
\(206\) | −6.25867 | −0.436062 | ||||||||
\(207\) | 7.91244 | 0.549953 | ||||||||
\(208\) | −1.64882 | −0.114325 | ||||||||
\(209\) | 2.82304 | 0.195273 | ||||||||
\(210\) | 3.47428 | 0.239748 | ||||||||
\(211\) | −13.1591 | −0.905910 | −0.452955 | − | 0.891533i | \(-0.649630\pi\) | ||||
−0.452955 | + | 0.891533i | \(0.649630\pi\) | |||||||
\(212\) | 58.7545 | 4.03528 | ||||||||
\(213\) | −19.0903 | −1.30804 | ||||||||
\(214\) | −29.8385 | −2.03972 | ||||||||
\(215\) | −1.63315 | −0.111380 | ||||||||
\(216\) | 34.3659 | 2.33830 | ||||||||
\(217\) | −7.54677 | −0.512308 | ||||||||
\(218\) | −34.7741 | −2.35520 | ||||||||
\(219\) | 4.85186 | 0.327859 | ||||||||
\(220\) | 7.32226 | 0.493667 | ||||||||
\(221\) | −0.231092 | −0.0155449 | ||||||||
\(222\) | 17.1632 | 1.15192 | ||||||||
\(223\) | 11.6518 | 0.780260 | 0.390130 | − | 0.920760i | \(-0.372430\pi\) | ||||
0.390130 | + | 0.920760i | \(0.372430\pi\) | |||||||
\(224\) | 3.91293 | 0.261444 | ||||||||
\(225\) | 3.75788 | 0.250526 | ||||||||
\(226\) | −15.8613 | −1.05508 | ||||||||
\(227\) | 9.90372 | 0.657333 | 0.328666 | − | 0.944446i | \(-0.393401\pi\) | ||||
0.328666 | + | 0.944446i | \(0.393401\pi\) | |||||||
\(228\) | 14.9178 | 0.987959 | ||||||||
\(229\) | −28.0539 | −1.85385 | −0.926926 | − | 0.375243i | \(-0.877559\pi\) | ||||
−0.926926 | + | 0.375243i | \(0.877559\pi\) | |||||||
\(230\) | 20.4258 | 1.34684 | ||||||||
\(231\) | −0.835475 | −0.0549702 | ||||||||
\(232\) | −36.3423 | −2.38599 | ||||||||
\(233\) | −12.5694 | −0.823448 | −0.411724 | − | 0.911309i | \(-0.635073\pi\) | ||||
−0.411724 | + | 0.911309i | \(0.635073\pi\) | |||||||
\(234\) | −0.947877 | −0.0619647 | ||||||||
\(235\) | −13.2083 | −0.861613 | ||||||||
\(236\) | −47.9452 | −3.12097 | ||||||||
\(237\) | −7.24504 | −0.470616 | ||||||||
\(238\) | 1.80496 | 0.116998 | ||||||||
\(239\) | 23.7323 | 1.53511 | 0.767556 | − | 0.640982i | \(-0.221473\pi\) | ||||
0.767556 | + | 0.640982i | \(0.221473\pi\) | |||||||
\(240\) | 13.7336 | 0.886502 | ||||||||
\(241\) | 23.0797 | 1.48670 | 0.743348 | − | 0.668905i | \(-0.233237\pi\) | ||||
0.743348 | + | 0.668905i | \(0.233237\pi\) | |||||||
\(242\) | −2.54628 | −0.163681 | ||||||||
\(243\) | 14.4500 | 0.926966 | ||||||||
\(244\) | −32.0288 | −2.05044 | ||||||||
\(245\) | −10.6114 | −0.677938 | ||||||||
\(246\) | 11.2372 | 0.716458 | ||||||||
\(247\) | −0.652381 | −0.0415100 | ||||||||
\(248\) | −67.3243 | −4.27510 | ||||||||
\(249\) | 8.79427 | 0.557314 | ||||||||
\(250\) | 30.4932 | 1.92856 | ||||||||
\(251\) | 1.14001 | 0.0719571 | 0.0359785 | − | 0.999353i | \(-0.488545\pi\) | ||||
0.0359785 | + | 0.999353i | \(0.488545\pi\) | |||||||
\(252\) | 5.11969 | 0.322510 | ||||||||
\(253\) | −4.91189 | −0.308808 | ||||||||
\(254\) | −10.7970 | −0.677466 | ||||||||
\(255\) | 1.92485 | 0.120539 | ||||||||
\(256\) | −29.0721 | −1.81700 | ||||||||
\(257\) | −5.65618 | −0.352823 | −0.176412 | − | 0.984316i | \(-0.556449\pi\) | ||||
−0.176412 | + | 0.984316i | \(0.556449\pi\) | |||||||
\(258\) | 3.00107 | 0.186838 | ||||||||
\(259\) | 4.05400 | 0.251903 | ||||||||
\(260\) | −1.69212 | −0.104941 | ||||||||
\(261\) | −9.25765 | −0.573034 | ||||||||
\(262\) | −7.49850 | −0.463259 | ||||||||
\(263\) | −20.9695 | −1.29304 | −0.646518 | − | 0.762898i | \(-0.723776\pi\) | ||||
−0.646518 | + | 0.762898i | \(0.723776\pi\) | |||||||
\(264\) | −7.45322 | −0.458714 | ||||||||
\(265\) | 21.4017 | 1.31470 | ||||||||
\(266\) | 5.09547 | 0.312424 | ||||||||
\(267\) | −10.8546 | −0.664293 | ||||||||
\(268\) | 5.26571 | 0.321654 | ||||||||
\(269\) | −7.89417 | −0.481316 | −0.240658 | − | 0.970610i | \(-0.577363\pi\) | ||||
−0.240658 | + | 0.970610i | \(0.577363\pi\) | |||||||
\(270\) | 22.5988 | 1.37532 | ||||||||
\(271\) | −21.2402 | −1.29025 | −0.645124 | − | 0.764078i | \(-0.723194\pi\) | ||||
−0.645124 | + | 0.764078i | \(0.723194\pi\) | |||||||
\(272\) | 7.13491 | 0.432618 | ||||||||
\(273\) | 0.193071 | 0.0116852 | ||||||||
\(274\) | −43.6849 | −2.63910 | ||||||||
\(275\) | −2.33282 | −0.140674 | ||||||||
\(276\) | −25.9560 | −1.56237 | ||||||||
\(277\) | 9.98539 | 0.599964 | 0.299982 | − | 0.953945i | \(-0.403019\pi\) | ||||
0.299982 | + | 0.953945i | \(0.403019\pi\) | |||||||
\(278\) | 10.6174 | 0.636787 | ||||||||
\(279\) | −17.1499 | −1.02674 | ||||||||
\(280\) | 7.32086 | 0.437505 | ||||||||
\(281\) | −28.8502 | −1.72106 | −0.860528 | − | 0.509403i | \(-0.829866\pi\) | ||||
−0.860528 | + | 0.509403i | \(0.829866\pi\) | |||||||
\(282\) | 24.2715 | 1.44534 | ||||||||
\(283\) | 2.25801 | 0.134225 | 0.0671125 | − | 0.997745i | \(-0.478621\pi\) | ||||
0.0671125 | + | 0.997745i | \(0.478621\pi\) | |||||||
\(284\) | −72.6207 | −4.30924 | ||||||||
\(285\) | 5.43392 | 0.321878 | ||||||||
\(286\) | 0.588424 | 0.0347942 | ||||||||
\(287\) | 2.65427 | 0.156677 | ||||||||
\(288\) | 8.89204 | 0.523968 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −23.8985 | −1.40337 | ||||||||
\(291\) | 1.13476 | 0.0665211 | ||||||||
\(292\) | 18.4568 | 1.08010 | ||||||||
\(293\) | −6.53576 | −0.381823 | −0.190912 | − | 0.981607i | \(-0.561144\pi\) | ||||
−0.190912 | + | 0.981607i | \(0.561144\pi\) | |||||||
\(294\) | 19.4995 | 1.13723 | ||||||||
\(295\) | −17.4643 | −1.01681 | ||||||||
\(296\) | 36.1655 | 2.10208 | ||||||||
\(297\) | −5.43443 | −0.315338 | ||||||||
\(298\) | 18.7589 | 1.08667 | ||||||||
\(299\) | 1.13510 | 0.0656444 | ||||||||
\(300\) | −12.3274 | −0.711722 | ||||||||
\(301\) | 0.708864 | 0.0408582 | ||||||||
\(302\) | −17.1479 | −0.986749 | ||||||||
\(303\) | −13.2912 | −0.763560 | ||||||||
\(304\) | 20.1421 | 1.15523 | ||||||||
\(305\) | −11.6667 | −0.668033 | ||||||||
\(306\) | 4.10173 | 0.234480 | ||||||||
\(307\) | 14.8500 | 0.847533 | 0.423767 | − | 0.905771i | \(-0.360708\pi\) | ||||
0.423767 | + | 0.905771i | \(0.360708\pi\) | |||||||
\(308\) | −3.17820 | −0.181095 | ||||||||
\(309\) | 2.89699 | 0.164804 | ||||||||
\(310\) | −44.2721 | −2.51449 | ||||||||
\(311\) | −0.386557 | −0.0219196 | −0.0109598 | − | 0.999940i | \(-0.503489\pi\) | ||||
−0.0109598 | + | 0.999940i | \(0.503489\pi\) | |||||||
\(312\) | 1.72238 | 0.0975105 | ||||||||
\(313\) | −6.02934 | −0.340799 | −0.170399 | − | 0.985375i | \(-0.554506\pi\) | ||||
−0.170399 | + | 0.985375i | \(0.554506\pi\) | |||||||
\(314\) | −2.69986 | −0.152362 | ||||||||
\(315\) | 1.86488 | 0.105074 | ||||||||
\(316\) | −27.5606 | −1.55041 | ||||||||
\(317\) | −15.2913 | −0.858846 | −0.429423 | − | 0.903104i | \(-0.641283\pi\) | ||||
−0.429423 | + | 0.903104i | \(0.641283\pi\) | |||||||
\(318\) | −39.3277 | −2.20539 | ||||||||
\(319\) | 5.74697 | 0.321769 | ||||||||
\(320\) | −0.350108 | −0.0195717 | ||||||||
\(321\) | 13.8115 | 0.770885 | ||||||||
\(322\) | −8.86577 | −0.494070 | ||||||||
\(323\) | 2.82304 | 0.157078 | ||||||||
\(324\) | −7.05013 | −0.391674 | ||||||||
\(325\) | 0.539096 | 0.0299037 | ||||||||
\(326\) | 7.05546 | 0.390766 | ||||||||
\(327\) | 16.0961 | 0.890117 | ||||||||
\(328\) | 23.6786 | 1.30743 | ||||||||
\(329\) | 5.73301 | 0.316071 | ||||||||
\(330\) | −4.90120 | −0.269802 | ||||||||
\(331\) | 25.0003 | 1.37414 | 0.687070 | − | 0.726591i | \(-0.258896\pi\) | ||||
0.687070 | + | 0.726591i | \(0.258896\pi\) | |||||||
\(332\) | 33.4540 | 1.83603 | ||||||||
\(333\) | 9.21262 | 0.504848 | ||||||||
\(334\) | 56.3729 | 3.08459 | ||||||||
\(335\) | 1.91807 | 0.104795 | ||||||||
\(336\) | −5.96104 | −0.325201 | ||||||||
\(337\) | −9.13469 | −0.497598 | −0.248799 | − | 0.968555i | \(-0.580036\pi\) | ||||
−0.248799 | + | 0.968555i | \(0.580036\pi\) | |||||||
\(338\) | 32.9656 | 1.79309 | ||||||||
\(339\) | 7.34181 | 0.398753 | ||||||||
\(340\) | 7.32226 | 0.397105 | ||||||||
\(341\) | 10.6463 | 0.576529 | ||||||||
\(342\) | 11.5793 | 0.626139 | ||||||||
\(343\) | 9.56790 | 0.516618 | ||||||||
\(344\) | 6.32373 | 0.340953 | ||||||||
\(345\) | −9.45464 | −0.509021 | ||||||||
\(346\) | 12.9827 | 0.697953 | ||||||||
\(347\) | −13.3251 | −0.715331 | −0.357666 | − | 0.933850i | \(-0.616427\pi\) | ||||
−0.357666 | + | 0.933850i | \(0.616427\pi\) | |||||||
\(348\) | 30.3689 | 1.62794 | ||||||||
\(349\) | 7.86651 | 0.421085 | 0.210542 | − | 0.977585i | \(-0.432477\pi\) | ||||
0.210542 | + | 0.977585i | \(0.432477\pi\) | |||||||
\(350\) | −4.21065 | −0.225069 | ||||||||
\(351\) | 1.25585 | 0.0670325 | ||||||||
\(352\) | −5.52000 | −0.294217 | ||||||||
\(353\) | −18.9598 | −1.00913 | −0.504564 | − | 0.863374i | \(-0.668347\pi\) | ||||
−0.504564 | + | 0.863374i | \(0.668347\pi\) | |||||||
\(354\) | 32.0924 | 1.70569 | ||||||||
\(355\) | −26.4525 | −1.40395 | ||||||||
\(356\) | −41.2918 | −2.18846 | ||||||||
\(357\) | −0.835475 | −0.0442180 | ||||||||
\(358\) | 37.0831 | 1.95990 | ||||||||
\(359\) | −6.01951 | −0.317697 | −0.158849 | − | 0.987303i | \(-0.550778\pi\) | ||||
−0.158849 | + | 0.987303i | \(0.550778\pi\) | |||||||
\(360\) | 16.6365 | 0.876819 | ||||||||
\(361\) | −11.0305 | −0.580551 | ||||||||
\(362\) | −7.82344 | −0.411191 | ||||||||
\(363\) | 1.17861 | 0.0618611 | ||||||||
\(364\) | 0.734457 | 0.0384960 | ||||||||
\(365\) | 6.72302 | 0.351899 | ||||||||
\(366\) | 21.4387 | 1.12062 | ||||||||
\(367\) | 11.3785 | 0.593950 | 0.296975 | − | 0.954885i | \(-0.404022\pi\) | ||||
0.296975 | + | 0.954885i | \(0.404022\pi\) | |||||||
\(368\) | −35.0459 | −1.82689 | ||||||||
\(369\) | 6.03176 | 0.314001 | ||||||||
\(370\) | 23.7822 | 1.23638 | ||||||||
\(371\) | −9.28934 | −0.482278 | ||||||||
\(372\) | 56.2585 | 2.91687 | ||||||||
\(373\) | 16.1380 | 0.835596 | 0.417798 | − | 0.908540i | \(-0.362802\pi\) | ||||
0.417798 | + | 0.908540i | \(0.362802\pi\) | |||||||
\(374\) | −2.54628 | −0.131665 | ||||||||
\(375\) | −14.1146 | −0.728873 | ||||||||
\(376\) | 51.1438 | 2.63754 | ||||||||
\(377\) | −1.32808 | −0.0683995 | ||||||||
\(378\) | −9.80894 | −0.504517 | ||||||||
\(379\) | −11.0914 | −0.569729 | −0.284864 | − | 0.958568i | \(-0.591949\pi\) | ||||
−0.284864 | + | 0.958568i | \(0.591949\pi\) | |||||||
\(380\) | 20.6710 | 1.06040 | ||||||||
\(381\) | 4.99769 | 0.256040 | ||||||||
\(382\) | 41.2655 | 2.11133 | ||||||||
\(383\) | 36.6621 | 1.87335 | 0.936674 | − | 0.350202i | \(-0.113887\pi\) | ||||
0.936674 | + | 0.350202i | \(0.113887\pi\) | |||||||
\(384\) | 13.6552 | 0.696841 | ||||||||
\(385\) | −1.15768 | −0.0590009 | ||||||||
\(386\) | 5.22049 | 0.265716 | ||||||||
\(387\) | 1.61088 | 0.0818854 | ||||||||
\(388\) | 4.31672 | 0.219148 | ||||||||
\(389\) | 10.8004 | 0.547600 | 0.273800 | − | 0.961787i | \(-0.411719\pi\) | ||||
0.273800 | + | 0.961787i | \(0.411719\pi\) | |||||||
\(390\) | 1.13263 | 0.0573528 | ||||||||
\(391\) | −4.91189 | −0.248405 | ||||||||
\(392\) | 41.0885 | 2.07528 | ||||||||
\(393\) | 3.47088 | 0.175083 | ||||||||
\(394\) | 0.217162 | 0.0109405 | ||||||||
\(395\) | −10.0391 | −0.505124 | ||||||||
\(396\) | −7.22239 | −0.362939 | ||||||||
\(397\) | −0.957048 | −0.0480329 | −0.0240164 | − | 0.999712i | \(-0.507645\pi\) | ||||
−0.0240164 | + | 0.999712i | \(0.507645\pi\) | |||||||
\(398\) | 35.0303 | 1.75591 | ||||||||
\(399\) | −2.35858 | −0.118076 | ||||||||
\(400\) | −16.6445 | −0.832224 | ||||||||
\(401\) | −21.9974 | −1.09850 | −0.549249 | − | 0.835659i | \(-0.685086\pi\) | ||||
−0.549249 | + | 0.835659i | \(0.685086\pi\) | |||||||
\(402\) | −3.52463 | −0.175793 | ||||||||
\(403\) | −2.46027 | −0.122555 | ||||||||
\(404\) | −50.5607 | −2.51549 | ||||||||
\(405\) | −2.56806 | −0.127608 | ||||||||
\(406\) | 10.3731 | 0.514807 | ||||||||
\(407\) | −5.71901 | −0.283481 | ||||||||
\(408\) | −7.45322 | −0.368989 | ||||||||
\(409\) | 1.59262 | 0.0787498 | 0.0393749 | − | 0.999225i | \(-0.487463\pi\) | ||||
0.0393749 | + | 0.999225i | \(0.487463\pi\) | |||||||
\(410\) | 15.5709 | 0.768992 | ||||||||
\(411\) | 20.2207 | 0.997415 | ||||||||
\(412\) | 11.0204 | 0.542934 | ||||||||
\(413\) | 7.58034 | 0.373004 | ||||||||
\(414\) | −20.1473 | −0.990183 | ||||||||
\(415\) | 12.1858 | 0.598179 | ||||||||
\(416\) | 1.27563 | 0.0625428 | ||||||||
\(417\) | −4.91453 | −0.240665 | ||||||||
\(418\) | −7.18823 | −0.351588 | ||||||||
\(419\) | −9.17654 | −0.448303 | −0.224152 | − | 0.974554i | \(-0.571961\pi\) | ||||
−0.224152 | + | 0.974554i | \(0.571961\pi\) | |||||||
\(420\) | −6.11756 | −0.298507 | ||||||||
\(421\) | 19.1887 | 0.935202 | 0.467601 | − | 0.883940i | \(-0.345118\pi\) | ||||
0.467601 | + | 0.883940i | \(0.345118\pi\) | |||||||
\(422\) | 33.5067 | 1.63108 | ||||||||
\(423\) | 13.0281 | 0.633449 | ||||||||
\(424\) | −82.8696 | −4.02450 | ||||||||
\(425\) | −2.33282 | −0.113158 | ||||||||
\(426\) | 48.6091 | 2.35512 | ||||||||
\(427\) | 5.06389 | 0.245059 | ||||||||
\(428\) | 52.5401 | 2.53962 | ||||||||
\(429\) | −0.272368 | −0.0131500 | ||||||||
\(430\) | 4.15845 | 0.200538 | ||||||||
\(431\) | 30.5385 | 1.47099 | 0.735493 | − | 0.677532i | \(-0.236951\pi\) | ||||
0.735493 | + | 0.677532i | \(0.236951\pi\) | |||||||
\(432\) | −38.7742 | −1.86552 | ||||||||
\(433\) | 40.2091 | 1.93233 | 0.966163 | − | 0.257933i | \(-0.0830413\pi\) | ||||
0.966163 | + | 0.257933i | \(0.0830413\pi\) | |||||||
\(434\) | 19.2162 | 0.922406 | ||||||||
\(435\) | 11.0621 | 0.530385 | ||||||||
\(436\) | 61.2308 | 2.93242 | ||||||||
\(437\) | −13.8664 | −0.663322 | ||||||||
\(438\) | −12.3542 | −0.590306 | ||||||||
\(439\) | 21.5005 | 1.02616 | 0.513081 | − | 0.858340i | \(-0.328504\pi\) | ||||
0.513081 | + | 0.858340i | \(0.328504\pi\) | |||||||
\(440\) | −10.3276 | −0.492349 | ||||||||
\(441\) | 10.4667 | 0.498413 | ||||||||
\(442\) | 0.588424 | 0.0279885 | ||||||||
\(443\) | −30.2540 | −1.43741 | −0.718707 | − | 0.695313i | \(-0.755266\pi\) | ||||
−0.718707 | + | 0.695313i | \(0.755266\pi\) | |||||||
\(444\) | −30.2211 | −1.43423 | ||||||||
\(445\) | −15.0408 | −0.713002 | ||||||||
\(446\) | −29.6686 | −1.40485 | ||||||||
\(447\) | −8.68304 | −0.410694 | ||||||||
\(448\) | 0.151963 | 0.00717960 | ||||||||
\(449\) | −10.8353 | −0.511348 | −0.255674 | − | 0.966763i | \(-0.582297\pi\) | ||||
−0.255674 | + | 0.966763i | \(0.582297\pi\) | |||||||
\(450\) | −9.56861 | −0.451068 | ||||||||
\(451\) | −3.74440 | −0.176317 | ||||||||
\(452\) | 27.9288 | 1.31366 | ||||||||
\(453\) | 7.93735 | 0.372929 | ||||||||
\(454\) | −25.2176 | −1.18352 | ||||||||
\(455\) | 0.267531 | 0.0125420 | ||||||||
\(456\) | −21.0407 | −0.985321 | ||||||||
\(457\) | −27.6430 | −1.29309 | −0.646543 | − | 0.762877i | \(-0.723786\pi\) | ||||
−0.646543 | + | 0.762877i | \(0.723786\pi\) | |||||||
\(458\) | 71.4329 | 3.33784 | ||||||||
\(459\) | −5.43443 | −0.253657 | ||||||||
\(460\) | −35.9661 | −1.67693 | ||||||||
\(461\) | 4.65593 | 0.216848 | 0.108424 | − | 0.994105i | \(-0.465420\pi\) | ||||
0.108424 | + | 0.994105i | \(0.465420\pi\) | |||||||
\(462\) | 2.12735 | 0.0989732 | ||||||||
\(463\) | 2.87153 | 0.133451 | 0.0667257 | − | 0.997771i | \(-0.478745\pi\) | ||||
0.0667257 | + | 0.997771i | \(0.478745\pi\) | |||||||
\(464\) | 41.0041 | 1.90357 | ||||||||
\(465\) | 20.4925 | 0.950318 | ||||||||
\(466\) | 32.0051 | 1.48261 | ||||||||
\(467\) | −18.4667 | −0.854537 | −0.427269 | − | 0.904125i | \(-0.640524\pi\) | ||||
−0.427269 | + | 0.904125i | \(0.640524\pi\) | |||||||
\(468\) | 1.66904 | 0.0771512 | ||||||||
\(469\) | −0.832531 | −0.0384427 | ||||||||
\(470\) | 33.6319 | 1.55132 | ||||||||
\(471\) | 1.24970 | 0.0575832 | ||||||||
\(472\) | 67.6237 | 3.11263 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 18.4479 | 0.847339 | ||||||||
\(475\) | −6.58564 | −0.302170 | ||||||||
\(476\) | −3.17820 | −0.145673 | ||||||||
\(477\) | −21.1098 | −0.966551 | ||||||||
\(478\) | −60.4289 | −2.76395 | ||||||||
\(479\) | −8.36694 | −0.382295 | −0.191148 | − | 0.981561i | \(-0.561221\pi\) | ||||
−0.191148 | + | 0.981561i | \(0.561221\pi\) | |||||||
\(480\) | −10.6252 | −0.484971 | ||||||||
\(481\) | 1.32162 | 0.0602606 | ||||||||
\(482\) | −58.7674 | −2.67678 | ||||||||
\(483\) | 4.10376 | 0.186727 | ||||||||
\(484\) | 4.48352 | 0.203796 | ||||||||
\(485\) | 1.57239 | 0.0713987 | ||||||||
\(486\) | −36.7936 | −1.66899 | ||||||||
\(487\) | −6.74347 | −0.305576 | −0.152788 | − | 0.988259i | \(-0.548825\pi\) | ||||
−0.152788 | + | 0.988259i | \(0.548825\pi\) | |||||||
\(488\) | 45.1747 | 2.04496 | ||||||||
\(489\) | −3.26580 | −0.147685 | ||||||||
\(490\) | 27.0196 | 1.22062 | ||||||||
\(491\) | −10.1207 | −0.456740 | −0.228370 | − | 0.973574i | \(-0.573340\pi\) | ||||
−0.228370 | + | 0.973574i | \(0.573340\pi\) | |||||||
\(492\) | −19.7866 | −0.892050 | ||||||||
\(493\) | 5.74697 | 0.258831 | ||||||||
\(494\) | 1.66114 | 0.0747383 | ||||||||
\(495\) | −2.63080 | −0.118246 | ||||||||
\(496\) | 75.9604 | 3.41072 | ||||||||
\(497\) | 11.4816 | 0.515022 | ||||||||
\(498\) | −22.3926 | −1.00344 | ||||||||
\(499\) | 12.1933 | 0.545845 | 0.272923 | − | 0.962036i | \(-0.412010\pi\) | ||||
0.272923 | + | 0.962036i | \(0.412010\pi\) | |||||||
\(500\) | −53.6928 | −2.40122 | ||||||||
\(501\) | −26.0937 | −1.16578 | ||||||||
\(502\) | −2.90279 | −0.129558 | ||||||||
\(503\) | −23.1526 | −1.03232 | −0.516161 | − | 0.856491i | \(-0.672639\pi\) | ||||
−0.516161 | + | 0.856491i | \(0.672639\pi\) | |||||||
\(504\) | −7.22101 | −0.321649 | ||||||||
\(505\) | −18.4171 | −0.819548 | ||||||||
\(506\) | 12.5070 | 0.556005 | ||||||||
\(507\) | −15.2590 | −0.677676 | ||||||||
\(508\) | 19.0116 | 0.843502 | ||||||||
\(509\) | −21.1603 | −0.937916 | −0.468958 | − | 0.883221i | \(-0.655370\pi\) | ||||
−0.468958 | + | 0.883221i | \(0.655370\pi\) | |||||||
\(510\) | −4.90120 | −0.217029 | ||||||||
\(511\) | −2.91810 | −0.129089 | ||||||||
\(512\) | 50.8538 | 2.24744 | ||||||||
\(513\) | −15.3416 | −0.677348 | ||||||||
\(514\) | 14.4022 | 0.635254 | ||||||||
\(515\) | 4.01424 | 0.176888 | ||||||||
\(516\) | −5.28433 | −0.232630 | ||||||||
\(517\) | −8.08760 | −0.355692 | ||||||||
\(518\) | −10.3226 | −0.453549 | ||||||||
\(519\) | −6.00937 | −0.263782 | ||||||||
\(520\) | 2.38662 | 0.104660 | ||||||||
\(521\) | −16.4659 | −0.721384 | −0.360692 | − | 0.932685i | \(-0.617459\pi\) | ||||
−0.360692 | + | 0.932685i | \(0.617459\pi\) | |||||||
\(522\) | 23.5725 | 1.03174 | ||||||||
\(523\) | −30.3934 | −1.32901 | −0.664505 | − | 0.747284i | \(-0.731357\pi\) | ||||
−0.664505 | + | 0.747284i | \(0.731357\pi\) | |||||||
\(524\) | 13.2035 | 0.576796 | ||||||||
\(525\) | 1.94901 | 0.0850619 | ||||||||
\(526\) | 53.3942 | 2.32810 | ||||||||
\(527\) | 10.6463 | 0.463760 | ||||||||
\(528\) | 8.40929 | 0.365967 | ||||||||
\(529\) | 1.12665 | 0.0489847 | ||||||||
\(530\) | −54.4946 | −2.36710 | ||||||||
\(531\) | 17.2261 | 0.747551 | ||||||||
\(532\) | −8.97219 | −0.388994 | ||||||||
\(533\) | 0.865301 | 0.0374803 | ||||||||
\(534\) | 27.6389 | 1.19605 | ||||||||
\(535\) | 19.1381 | 0.827410 | ||||||||
\(536\) | −7.42696 | −0.320796 | ||||||||
\(537\) | −17.1649 | −0.740720 | ||||||||
\(538\) | 20.1007 | 0.866604 | ||||||||
\(539\) | −6.49751 | −0.279868 | ||||||||
\(540\) | −39.7923 | −1.71239 | ||||||||
\(541\) | −10.3622 | −0.445507 | −0.222753 | − | 0.974875i | \(-0.571504\pi\) | ||||
−0.222753 | + | 0.974875i | \(0.571504\pi\) | |||||||
\(542\) | 54.0833 | 2.32308 | ||||||||
\(543\) | 3.62129 | 0.155404 | ||||||||
\(544\) | −5.52000 | −0.236668 | ||||||||
\(545\) | 22.3037 | 0.955385 | ||||||||
\(546\) | −0.491613 | −0.0210391 | ||||||||
\(547\) | −26.6802 | −1.14076 | −0.570382 | − | 0.821379i | \(-0.693205\pi\) | ||||
−0.570382 | + | 0.821379i | \(0.693205\pi\) | |||||||
\(548\) | 76.9211 | 3.28591 | ||||||||
\(549\) | 11.5076 | 0.491131 | ||||||||
\(550\) | 5.94001 | 0.253283 | ||||||||
\(551\) | 16.2239 | 0.691162 | ||||||||
\(552\) | 36.6094 | 1.55820 | ||||||||
\(553\) | 4.35746 | 0.185298 | ||||||||
\(554\) | −25.4256 | −1.08023 | ||||||||
\(555\) | −11.0082 | −0.467274 | ||||||||
\(556\) | −18.6952 | −0.792853 | ||||||||
\(557\) | 18.5243 | 0.784901 | 0.392451 | − | 0.919773i | \(-0.371627\pi\) | ||||
0.392451 | + | 0.919773i | \(0.371627\pi\) | |||||||
\(558\) | 43.6683 | 1.84863 | ||||||||
\(559\) | 0.231092 | 0.00977415 | ||||||||
\(560\) | −8.25995 | −0.349047 | ||||||||
\(561\) | 1.17861 | 0.0497610 | ||||||||
\(562\) | 73.4605 | 3.09874 | ||||||||
\(563\) | 31.0547 | 1.30880 | 0.654399 | − | 0.756149i | \(-0.272921\pi\) | ||||
0.654399 | + | 0.756149i | \(0.272921\pi\) | |||||||
\(564\) | −42.7376 | −1.79958 | ||||||||
\(565\) | 10.1732 | 0.427991 | ||||||||
\(566\) | −5.74952 | −0.241670 | ||||||||
\(567\) | 1.11466 | 0.0468112 | ||||||||
\(568\) | 102.427 | 4.29774 | ||||||||
\(569\) | −17.2048 | −0.721262 | −0.360631 | − | 0.932709i | \(-0.617439\pi\) | ||||
−0.360631 | + | 0.932709i | \(0.617439\pi\) | |||||||
\(570\) | −13.8363 | −0.579537 | ||||||||
\(571\) | −24.1044 | −1.00874 | −0.504369 | − | 0.863488i | \(-0.668275\pi\) | ||||
−0.504369 | + | 0.863488i | \(0.668275\pi\) | |||||||
\(572\) | −1.03611 | −0.0433217 | ||||||||
\(573\) | −19.1008 | −0.797948 | ||||||||
\(574\) | −6.75850 | −0.282094 | ||||||||
\(575\) | 11.4586 | 0.477855 | ||||||||
\(576\) | 0.345333 | 0.0143889 | ||||||||
\(577\) | 15.9565 | 0.664280 | 0.332140 | − | 0.943230i | \(-0.392229\pi\) | ||||
0.332140 | + | 0.943230i | \(0.392229\pi\) | |||||||
\(578\) | −2.54628 | −0.105911 | ||||||||
\(579\) | −2.41644 | −0.100424 | ||||||||
\(580\) | 42.0808 | 1.74731 | ||||||||
\(581\) | −5.28922 | −0.219434 | ||||||||
\(582\) | −2.88942 | −0.119770 | ||||||||
\(583\) | 13.1046 | 0.542735 | ||||||||
\(584\) | −26.0322 | −1.07722 | ||||||||
\(585\) | 0.607957 | 0.0251359 | ||||||||
\(586\) | 16.6418 | 0.687468 | ||||||||
\(587\) | −30.1529 | −1.24455 | −0.622273 | − | 0.782801i | \(-0.713790\pi\) | ||||
−0.622273 | + | 0.782801i | \(0.713790\pi\) | |||||||
\(588\) | −34.3350 | −1.41595 | ||||||||
\(589\) | 30.0549 | 1.23839 | ||||||||
\(590\) | 44.4690 | 1.83076 | ||||||||
\(591\) | −0.100519 | −0.00413481 | ||||||||
\(592\) | −40.8047 | −1.67706 | ||||||||
\(593\) | −23.1415 | −0.950307 | −0.475154 | − | 0.879903i | \(-0.657608\pi\) | ||||
−0.475154 | + | 0.879903i | \(0.657608\pi\) | |||||||
\(594\) | 13.8376 | 0.567762 | ||||||||
\(595\) | −1.15768 | −0.0474603 | ||||||||
\(596\) | −33.0309 | −1.35300 | ||||||||
\(597\) | −16.2147 | −0.663623 | ||||||||
\(598\) | −2.89027 | −0.118192 | ||||||||
\(599\) | 37.6241 | 1.53728 | 0.768640 | − | 0.639681i | \(-0.220934\pi\) | ||||
0.768640 | + | 0.639681i | \(0.220934\pi\) | |||||||
\(600\) | 17.3870 | 0.709822 | ||||||||
\(601\) | 35.6946 | 1.45601 | 0.728007 | − | 0.685570i | \(-0.240447\pi\) | ||||
0.728007 | + | 0.685570i | \(0.240447\pi\) | |||||||
\(602\) | −1.80496 | −0.0735648 | ||||||||
\(603\) | −1.89191 | −0.0770444 | ||||||||
\(604\) | 30.1942 | 1.22859 | ||||||||
\(605\) | 1.63315 | 0.0663970 | ||||||||
\(606\) | 33.8431 | 1.37478 | ||||||||
\(607\) | −16.2869 | −0.661063 | −0.330532 | − | 0.943795i | \(-0.607228\pi\) | ||||
−0.330532 | + | 0.943795i | \(0.607228\pi\) | |||||||
\(608\) | −15.5832 | −0.631981 | ||||||||
\(609\) | −4.80145 | −0.194565 | ||||||||
\(610\) | 29.7066 | 1.20279 | ||||||||
\(611\) | 1.86898 | 0.0756108 | ||||||||
\(612\) | −7.22239 | −0.291948 | ||||||||
\(613\) | 44.0803 | 1.78039 | 0.890193 | − | 0.455584i | \(-0.150569\pi\) | ||||
0.890193 | + | 0.455584i | \(0.150569\pi\) | |||||||
\(614\) | −37.8122 | −1.52597 | ||||||||
\(615\) | −7.20741 | −0.290631 | ||||||||
\(616\) | 4.48266 | 0.180612 | ||||||||
\(617\) | 13.5115 | 0.543952 | 0.271976 | − | 0.962304i | \(-0.412323\pi\) | ||||
0.271976 | + | 0.962304i | \(0.412323\pi\) | |||||||
\(618\) | −7.37654 | −0.296728 | ||||||||
\(619\) | 16.6828 | 0.670536 | 0.335268 | − | 0.942123i | \(-0.391173\pi\) | ||||
0.335268 | + | 0.942123i | \(0.391173\pi\) | |||||||
\(620\) | 77.9550 | 3.13075 | ||||||||
\(621\) | 26.6933 | 1.07117 | ||||||||
\(622\) | 0.984281 | 0.0394661 | ||||||||
\(623\) | 6.52841 | 0.261555 | ||||||||
\(624\) | −1.94332 | −0.0777950 | ||||||||
\(625\) | −7.89384 | −0.315754 | ||||||||
\(626\) | 15.3524 | 0.613604 | ||||||||
\(627\) | 3.32726 | 0.132878 | ||||||||
\(628\) | 4.75395 | 0.189703 | ||||||||
\(629\) | −5.71901 | −0.228032 | ||||||||
\(630\) | −4.74850 | −0.189185 | ||||||||
\(631\) | −27.8685 | −1.10943 | −0.554714 | − | 0.832041i | \(-0.687172\pi\) | ||||
−0.554714 | + | 0.832041i | \(0.687172\pi\) | |||||||
\(632\) | 38.8726 | 1.54627 | ||||||||
\(633\) | −15.5095 | −0.616446 | ||||||||
\(634\) | 38.9359 | 1.54634 | ||||||||
\(635\) | 6.92509 | 0.274814 | ||||||||
\(636\) | 69.2487 | 2.74589 | ||||||||
\(637\) | 1.50152 | 0.0594925 | ||||||||
\(638\) | −14.6334 | −0.579341 | ||||||||
\(639\) | 26.0917 | 1.03217 | ||||||||
\(640\) | 18.9215 | 0.747936 | ||||||||
\(641\) | −17.8423 | −0.704728 | −0.352364 | − | 0.935863i | \(-0.614622\pi\) | ||||
−0.352364 | + | 0.935863i | \(0.614622\pi\) | |||||||
\(642\) | −35.1680 | −1.38797 | ||||||||
\(643\) | 19.8841 | 0.784151 | 0.392076 | − | 0.919933i | \(-0.371757\pi\) | ||||
0.392076 | + | 0.919933i | \(0.371757\pi\) | |||||||
\(644\) | 15.6110 | 0.615159 | ||||||||
\(645\) | −1.92485 | −0.0757909 | ||||||||
\(646\) | −7.18823 | −0.282817 | ||||||||
\(647\) | 9.45606 | 0.371756 | 0.185878 | − | 0.982573i | \(-0.440487\pi\) | ||||
0.185878 | + | 0.982573i | \(0.440487\pi\) | |||||||
\(648\) | 9.94378 | 0.390629 | ||||||||
\(649\) | −10.6936 | −0.419762 | ||||||||
\(650\) | −1.37269 | −0.0538412 | ||||||||
\(651\) | −8.89471 | −0.348611 | ||||||||
\(652\) | −12.4234 | −0.486536 | ||||||||
\(653\) | −28.9421 | −1.13259 | −0.566296 | − | 0.824202i | \(-0.691624\pi\) | ||||
−0.566296 | + | 0.824202i | \(0.691624\pi\) | |||||||
\(654\) | −40.9852 | −1.60265 | ||||||||
\(655\) | 4.80945 | 0.187921 | ||||||||
\(656\) | −26.7160 | −1.04308 | ||||||||
\(657\) | −6.63132 | −0.258712 | ||||||||
\(658\) | −14.5978 | −0.569082 | ||||||||
\(659\) | −33.0650 | −1.28803 | −0.644015 | − | 0.765013i | \(-0.722733\pi\) | ||||
−0.644015 | + | 0.765013i | \(0.722733\pi\) | |||||||
\(660\) | 8.63010 | 0.335926 | ||||||||
\(661\) | 6.93782 | 0.269850 | 0.134925 | − | 0.990856i | \(-0.456921\pi\) | ||||
0.134925 | + | 0.990856i | \(0.456921\pi\) | |||||||
\(662\) | −63.6576 | −2.47412 | ||||||||
\(663\) | −0.272368 | −0.0105779 | ||||||||
\(664\) | −47.1848 | −1.83113 | ||||||||
\(665\) | −3.26817 | −0.126734 | ||||||||
\(666\) | −23.4579 | −0.908974 | ||||||||
\(667\) | −28.2285 | −1.09301 | ||||||||
\(668\) | −99.2623 | −3.84057 | ||||||||
\(669\) | 13.7329 | 0.530945 | ||||||||
\(670\) | −4.88393 | −0.188683 | ||||||||
\(671\) | −7.14368 | −0.275779 | ||||||||
\(672\) | 4.61182 | 0.177905 | ||||||||
\(673\) | −17.0941 | −0.658930 | −0.329465 | − | 0.944168i | \(-0.606868\pi\) | ||||
−0.329465 | + | 0.944168i | \(0.606868\pi\) | |||||||
\(674\) | 23.2594 | 0.895920 | ||||||||
\(675\) | 12.6776 | 0.487959 | ||||||||
\(676\) | −58.0463 | −2.23255 | ||||||||
\(677\) | 15.7718 | 0.606158 | 0.303079 | − | 0.952965i | \(-0.401985\pi\) | ||||
0.303079 | + | 0.952965i | \(0.401985\pi\) | |||||||
\(678\) | −18.6943 | −0.717950 | ||||||||
\(679\) | −0.682492 | −0.0261916 | ||||||||
\(680\) | −10.3276 | −0.396045 | ||||||||
\(681\) | 11.6726 | 0.447296 | ||||||||
\(682\) | −27.1084 | −1.03803 | ||||||||
\(683\) | −41.0020 | −1.56890 | −0.784449 | − | 0.620193i | \(-0.787054\pi\) | ||||
−0.784449 | + | 0.620193i | \(0.787054\pi\) | |||||||
\(684\) | −20.3891 | −0.779596 | ||||||||
\(685\) | 28.0190 | 1.07055 | ||||||||
\(686\) | −24.3625 | −0.930165 | ||||||||
\(687\) | −33.0646 | −1.26149 | ||||||||
\(688\) | −7.13491 | −0.272016 | ||||||||
\(689\) | −3.02836 | −0.115371 | ||||||||
\(690\) | 24.0741 | 0.916487 | ||||||||
\(691\) | −0.482298 | −0.0183475 | −0.00917375 | − | 0.999958i | \(-0.502920\pi\) | ||||
−0.00917375 | + | 0.999958i | \(0.502920\pi\) | |||||||
\(692\) | −22.8601 | −0.869010 | ||||||||
\(693\) | 1.14189 | 0.0433768 | ||||||||
\(694\) | 33.9295 | 1.28795 | ||||||||
\(695\) | −6.80984 | −0.258312 | ||||||||
\(696\) | −42.8334 | −1.62360 | ||||||||
\(697\) | −3.74440 | −0.141829 | ||||||||
\(698\) | −20.0303 | −0.758158 | ||||||||
\(699\) | −14.8144 | −0.560333 | ||||||||
\(700\) | 7.41418 | 0.280230 | ||||||||
\(701\) | −0.593044 | −0.0223990 | −0.0111995 | − | 0.999937i | \(-0.503565\pi\) | ||||
−0.0111995 | + | 0.999937i | \(0.503565\pi\) | |||||||
\(702\) | −3.19775 | −0.120691 | ||||||||
\(703\) | −16.1450 | −0.608920 | ||||||||
\(704\) | −0.214376 | −0.00807960 | ||||||||
\(705\) | −15.5674 | −0.586303 | ||||||||
\(706\) | 48.2769 | 1.81692 | ||||||||
\(707\) | 7.99386 | 0.300640 | ||||||||
\(708\) | −56.5087 | −2.12373 | ||||||||
\(709\) | −16.9986 | −0.638397 | −0.319199 | − | 0.947688i | \(-0.603414\pi\) | ||||
−0.319199 | + | 0.947688i | \(0.603414\pi\) | |||||||
\(710\) | 67.3554 | 2.52780 | ||||||||
\(711\) | 9.90221 | 0.371362 | ||||||||
\(712\) | 58.2396 | 2.18262 | ||||||||
\(713\) | −52.2934 | −1.95840 | ||||||||
\(714\) | 2.12735 | 0.0796140 | ||||||||
\(715\) | −0.377408 | −0.0141143 | ||||||||
\(716\) | −65.2965 | −2.44024 | ||||||||
\(717\) | 27.9711 | 1.04460 | ||||||||
\(718\) | 15.3273 | 0.572011 | ||||||||
\(719\) | 24.5830 | 0.916790 | 0.458395 | − | 0.888748i | \(-0.348424\pi\) | ||||
0.458395 | + | 0.888748i | \(0.348424\pi\) | |||||||
\(720\) | −18.7705 | −0.699537 | ||||||||
\(721\) | −1.74237 | −0.0648891 | ||||||||
\(722\) | 28.0866 | 1.04528 | ||||||||
\(723\) | 27.2020 | 1.01165 | ||||||||
\(724\) | 13.7756 | 0.511967 | ||||||||
\(725\) | −13.4067 | −0.497911 | ||||||||
\(726\) | −3.00107 | −0.111380 | ||||||||
\(727\) | 21.0699 | 0.781440 | 0.390720 | − | 0.920510i | \(-0.372226\pi\) | ||||
0.390720 | + | 0.920510i | \(0.372226\pi\) | |||||||
\(728\) | −1.03591 | −0.0383933 | ||||||||
\(729\) | 21.7483 | 0.805492 | ||||||||
\(730\) | −17.1187 | −0.633590 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | −37.7495 | −1.39526 | ||||||||
\(733\) | 5.60797 | 0.207135 | 0.103567 | − | 0.994622i | \(-0.466974\pi\) | ||||
0.103567 | + | 0.994622i | \(0.466974\pi\) | |||||||
\(734\) | −28.9727 | −1.06940 | ||||||||
\(735\) | −12.5067 | −0.461318 | ||||||||
\(736\) | 27.1136 | 0.999422 | ||||||||
\(737\) | 1.17446 | 0.0432617 | ||||||||
\(738\) | −15.3585 | −0.565355 | ||||||||
\(739\) | 0.450844 | 0.0165846 | 0.00829229 | − | 0.999966i | \(-0.497360\pi\) | ||||
0.00829229 | + | 0.999966i | \(0.497360\pi\) | |||||||
\(740\) | −41.8761 | −1.53940 | ||||||||
\(741\) | −0.768903 | −0.0282464 | ||||||||
\(742\) | 23.6532 | 0.868337 | ||||||||
\(743\) | −17.6038 | −0.645819 | −0.322910 | − | 0.946430i | \(-0.604661\pi\) | ||||
−0.322910 | + | 0.946430i | \(0.604661\pi\) | |||||||
\(744\) | −79.3492 | −2.90908 | ||||||||
\(745\) | −12.0317 | −0.440808 | ||||||||
\(746\) | −41.0919 | −1.50448 | ||||||||
\(747\) | −12.0196 | −0.439775 | ||||||||
\(748\) | 4.48352 | 0.163934 | ||||||||
\(749\) | −8.30681 | −0.303524 | ||||||||
\(750\) | 35.9396 | 1.31233 | ||||||||
\(751\) | −16.4118 | −0.598874 | −0.299437 | − | 0.954116i | \(-0.596799\pi\) | ||||
−0.299437 | + | 0.954116i | \(0.596799\pi\) | |||||||
\(752\) | −57.7044 | −2.10426 | ||||||||
\(753\) | 1.34363 | 0.0489648 | ||||||||
\(754\) | 3.38165 | 0.123153 | ||||||||
\(755\) | 10.9984 | 0.400274 | ||||||||
\(756\) | 17.2717 | 0.628167 | ||||||||
\(757\) | −33.4257 | −1.21488 | −0.607438 | − | 0.794367i | \(-0.707803\pi\) | ||||
−0.607438 | + | 0.794367i | \(0.707803\pi\) | |||||||
\(758\) | 28.2419 | 1.02579 | ||||||||
\(759\) | −5.78921 | −0.210135 | ||||||||
\(760\) | −29.1552 | −1.05757 | ||||||||
\(761\) | −18.6102 | −0.674620 | −0.337310 | − | 0.941394i | \(-0.609517\pi\) | ||||
−0.337310 | + | 0.941394i | \(0.609517\pi\) | |||||||
\(762\) | −12.7255 | −0.460997 | ||||||||
\(763\) | −9.68084 | −0.350470 | ||||||||
\(764\) | −72.6609 | −2.62878 | ||||||||
\(765\) | −2.63080 | −0.0951168 | ||||||||
\(766\) | −93.3519 | −3.37294 | ||||||||
\(767\) | 2.47122 | 0.0892304 | ||||||||
\(768\) | −34.2647 | −1.23642 | ||||||||
\(769\) | −30.3092 | −1.09298 | −0.546489 | − | 0.837467i | \(-0.684036\pi\) | ||||
−0.546489 | + | 0.837467i | \(0.684036\pi\) | |||||||
\(770\) | 2.94777 | 0.106230 | ||||||||
\(771\) | −6.66644 | −0.240086 | ||||||||
\(772\) | −9.19231 | −0.330839 | ||||||||
\(773\) | 40.8955 | 1.47091 | 0.735455 | − | 0.677574i | \(-0.236969\pi\) | ||||
0.735455 | + | 0.677574i | \(0.236969\pi\) | |||||||
\(774\) | −4.10173 | −0.147434 | ||||||||
\(775\) | −24.8359 | −0.892132 | ||||||||
\(776\) | −6.08847 | −0.218563 | ||||||||
\(777\) | 4.77809 | 0.171413 | ||||||||
\(778\) | −27.5007 | −0.985949 | ||||||||
\(779\) | −10.5706 | −0.378730 | ||||||||
\(780\) | −1.99435 | −0.0714091 | ||||||||
\(781\) | −16.1972 | −0.579583 | ||||||||
\(782\) | 12.5070 | 0.447250 | ||||||||
\(783\) | −31.2315 | −1.11612 | ||||||||
\(784\) | −46.3592 | −1.65569 | ||||||||
\(785\) | 1.73166 | 0.0618055 | ||||||||
\(786\) | −8.83782 | −0.315235 | ||||||||
\(787\) | 23.7482 | 0.846532 | 0.423266 | − | 0.906005i | \(-0.360883\pi\) | ||||
0.423266 | + | 0.906005i | \(0.360883\pi\) | |||||||
\(788\) | −0.382382 | −0.0136218 | ||||||||
\(789\) | −24.7149 | −0.879875 | ||||||||
\(790\) | 25.5624 | 0.909470 | ||||||||
\(791\) | −4.41566 | −0.157003 | ||||||||
\(792\) | 10.1867 | 0.361970 | ||||||||
\(793\) | 1.65085 | 0.0586233 | ||||||||
\(794\) | 2.43691 | 0.0864827 | ||||||||
\(795\) | 25.2243 | 0.894613 | ||||||||
\(796\) | −61.6818 | −2.18625 | ||||||||
\(797\) | −30.4224 | −1.07762 | −0.538808 | − | 0.842428i | \(-0.681125\pi\) | ||||
−0.538808 | + | 0.842428i | \(0.681125\pi\) | |||||||
\(798\) | 6.00558 | 0.212595 | ||||||||
\(799\) | −8.08760 | −0.286119 | ||||||||
\(800\) | 12.8772 | 0.455277 | ||||||||
\(801\) | 14.8357 | 0.524192 | ||||||||
\(802\) | 56.0115 | 1.97783 | ||||||||
\(803\) | 4.11659 | 0.145271 | ||||||||
\(804\) | 6.20622 | 0.218877 | ||||||||
\(805\) | 5.68640 | 0.200419 | ||||||||
\(806\) | 6.26454 | 0.220659 | ||||||||
\(807\) | −9.30416 | −0.327522 | ||||||||
\(808\) | 71.3128 | 2.50877 | ||||||||
\(809\) | 4.74344 | 0.166770 | 0.0833852 | − | 0.996517i | \(-0.473427\pi\) | ||||
0.0833852 | + | 0.996517i | \(0.473427\pi\) | |||||||
\(810\) | 6.53898 | 0.229756 | ||||||||
\(811\) | 30.4007 | 1.06751 | 0.533756 | − | 0.845638i | \(-0.320780\pi\) | ||||
0.533756 | + | 0.845638i | \(0.320780\pi\) | |||||||
\(812\) | −18.2651 | −0.640978 | ||||||||
\(813\) | −25.0339 | −0.877977 | ||||||||
\(814\) | 14.5622 | 0.510404 | ||||||||
\(815\) | −4.52528 | −0.158514 | ||||||||
\(816\) | 8.40929 | 0.294384 | ||||||||
\(817\) | −2.82304 | −0.0987655 | ||||||||
\(818\) | −4.05524 | −0.141788 | ||||||||
\(819\) | −0.263882 | −0.00922077 | ||||||||
\(820\) | −27.4175 | −0.957460 | ||||||||
\(821\) | −9.40907 | −0.328379 | −0.164189 | − | 0.986429i | \(-0.552501\pi\) | ||||
−0.164189 | + | 0.986429i | \(0.552501\pi\) | |||||||
\(822\) | −51.4876 | −1.79583 | ||||||||
\(823\) | 42.3813 | 1.47732 | 0.738660 | − | 0.674078i | \(-0.235459\pi\) | ||||
0.738660 | + | 0.674078i | \(0.235459\pi\) | |||||||
\(824\) | −15.5435 | −0.541485 | ||||||||
\(825\) | −2.74949 | −0.0957249 | ||||||||
\(826\) | −19.3016 | −0.671590 | ||||||||
\(827\) | −46.3265 | −1.61093 | −0.805465 | − | 0.592643i | \(-0.798085\pi\) | ||||
−0.805465 | + | 0.592643i | \(0.798085\pi\) | |||||||
\(828\) | 35.4756 | 1.23286 | ||||||||
\(829\) | −34.6287 | −1.20271 | −0.601353 | − | 0.798983i | \(-0.705371\pi\) | ||||
−0.601353 | + | 0.798983i | \(0.705371\pi\) | |||||||
\(830\) | −31.0285 | −1.07701 | ||||||||
\(831\) | 11.7689 | 0.408258 | ||||||||
\(832\) | 0.0495406 | 0.00171751 | ||||||||
\(833\) | −6.49751 | −0.225125 | ||||||||
\(834\) | 12.5137 | 0.433315 | ||||||||
\(835\) | −36.1569 | −1.25126 | ||||||||
\(836\) | 12.6571 | 0.437756 | ||||||||
\(837\) | −57.8566 | −1.99982 | ||||||||
\(838\) | 23.3660 | 0.807165 | ||||||||
\(839\) | −8.22244 | −0.283870 | −0.141935 | − | 0.989876i | \(-0.545332\pi\) | ||||
−0.141935 | + | 0.989876i | \(0.545332\pi\) | |||||||
\(840\) | 8.62845 | 0.297710 | ||||||||
\(841\) | 4.02768 | 0.138885 | ||||||||
\(842\) | −48.8598 | −1.68382 | ||||||||
\(843\) | −34.0031 | −1.17113 | ||||||||
\(844\) | −58.9991 | −2.03083 | ||||||||
\(845\) | −21.1437 | −0.727367 | ||||||||
\(846\) | −33.1732 | −1.14052 | ||||||||
\(847\) | −0.708864 | −0.0243568 | ||||||||
\(848\) | 93.4998 | 3.21080 | ||||||||
\(849\) | 2.66132 | 0.0913362 | ||||||||
\(850\) | 5.94001 | 0.203741 | ||||||||
\(851\) | 28.0912 | 0.962952 | ||||||||
\(852\) | −85.5916 | −2.93232 | ||||||||
\(853\) | 45.5009 | 1.55792 | 0.778960 | − | 0.627074i | \(-0.215747\pi\) | ||||
0.778960 | + | 0.627074i | \(0.215747\pi\) | |||||||
\(854\) | −12.8941 | −0.441226 | ||||||||
\(855\) | −7.42685 | −0.253993 | ||||||||
\(856\) | −74.1046 | −2.53284 | ||||||||
\(857\) | 2.98251 | 0.101881 | 0.0509403 | − | 0.998702i | \(-0.483778\pi\) | ||||
0.0509403 | + | 0.998702i | \(0.483778\pi\) | |||||||
\(858\) | 0.693523 | 0.0236765 | ||||||||
\(859\) | −23.4095 | −0.798722 | −0.399361 | − | 0.916794i | \(-0.630768\pi\) | ||||
−0.399361 | + | 0.916794i | \(0.630768\pi\) | |||||||
\(860\) | −7.32226 | −0.249687 | ||||||||
\(861\) | 3.12835 | 0.106614 | ||||||||
\(862\) | −77.7593 | −2.64849 | ||||||||
\(863\) | −31.6326 | −1.07679 | −0.538393 | − | 0.842694i | \(-0.680968\pi\) | ||||
−0.538393 | + | 0.842694i | \(0.680968\pi\) | |||||||
\(864\) | 29.9981 | 1.02056 | ||||||||
\(865\) | −8.32693 | −0.283124 | ||||||||
\(866\) | −102.383 | −3.47913 | ||||||||
\(867\) | 1.17861 | 0.0400277 | ||||||||
\(868\) | −33.8361 | −1.14847 | ||||||||
\(869\) | −6.14710 | −0.208526 | ||||||||
\(870\) | −28.1670 | −0.954952 | ||||||||
\(871\) | −0.271408 | −0.00919631 | ||||||||
\(872\) | −86.3622 | −2.92459 | ||||||||
\(873\) | −1.55095 | −0.0524916 | ||||||||
\(874\) | 35.3078 | 1.19430 | ||||||||
\(875\) | 8.48907 | 0.286983 | ||||||||
\(876\) | 21.7534 | 0.734980 | ||||||||
\(877\) | −6.18409 | −0.208822 | −0.104411 | − | 0.994534i | \(-0.533296\pi\) | ||||
−0.104411 | + | 0.994534i | \(0.533296\pi\) | |||||||
\(878\) | −54.7462 | −1.84759 | ||||||||
\(879\) | −7.70312 | −0.259820 | ||||||||
\(880\) | 11.6524 | 0.392802 | ||||||||
\(881\) | 52.8354 | 1.78007 | 0.890034 | − | 0.455894i | \(-0.150680\pi\) | ||||
0.890034 | + | 0.455894i | \(0.150680\pi\) | |||||||
\(882\) | −26.6511 | −0.897388 | ||||||||
\(883\) | −2.83578 | −0.0954316 | −0.0477158 | − | 0.998861i | \(-0.515194\pi\) | ||||
−0.0477158 | + | 0.998861i | \(0.515194\pi\) | |||||||
\(884\) | −1.03611 | −0.0348480 | ||||||||
\(885\) | −20.5837 | −0.691912 | ||||||||
\(886\) | 77.0352 | 2.58805 | ||||||||
\(887\) | 21.8491 | 0.733619 | 0.366810 | − | 0.930296i | \(-0.380450\pi\) | ||||
0.366810 | + | 0.930296i | \(0.380450\pi\) | |||||||
\(888\) | 42.6251 | 1.43040 | ||||||||
\(889\) | −3.00581 | −0.100812 | ||||||||
\(890\) | 38.2980 | 1.28375 | ||||||||
\(891\) | −1.57246 | −0.0526792 | ||||||||
\(892\) | 52.2410 | 1.74916 | ||||||||
\(893\) | −22.8316 | −0.764030 | ||||||||
\(894\) | 22.1094 | 0.739450 | ||||||||
\(895\) | −23.7847 | −0.795033 | ||||||||
\(896\) | −8.21280 | −0.274370 | ||||||||
\(897\) | 1.33784 | 0.0446691 | ||||||||
\(898\) | 27.5896 | 0.920677 | ||||||||
\(899\) | 61.1840 | 2.04060 | ||||||||
\(900\) | 16.8485 | 0.561618 | ||||||||
\(901\) | 13.1046 | 0.436576 | ||||||||
\(902\) | 9.53427 | 0.317457 | ||||||||
\(903\) | 0.835475 | 0.0278029 | ||||||||
\(904\) | −39.3918 | −1.31015 | ||||||||
\(905\) | 5.01786 | 0.166799 | ||||||||
\(906\) | −20.2107 | −0.671455 | ||||||||
\(907\) | −13.5528 | −0.450012 | −0.225006 | − | 0.974357i | \(-0.572240\pi\) | ||||
−0.225006 | + | 0.974357i | \(0.572240\pi\) | |||||||
\(908\) | 44.4035 | 1.47358 | ||||||||
\(909\) | 18.1659 | 0.602523 | ||||||||
\(910\) | −0.681207 | −0.0225818 | ||||||||
\(911\) | 30.7440 | 1.01860 | 0.509298 | − | 0.860590i | \(-0.329905\pi\) | ||||
0.509298 | + | 0.860590i | \(0.329905\pi\) | |||||||
\(912\) | 23.7397 | 0.786101 | ||||||||
\(913\) | 7.46155 | 0.246941 | ||||||||
\(914\) | 70.3868 | 2.32819 | ||||||||
\(915\) | −13.7505 | −0.454578 | ||||||||
\(916\) | −125.780 | −4.15589 | ||||||||
\(917\) | −2.08753 | −0.0689362 | ||||||||
\(918\) | 13.8376 | 0.456707 | ||||||||
\(919\) | −27.6083 | −0.910713 | −0.455356 | − | 0.890309i | \(-0.650488\pi\) | ||||
−0.455356 | + | 0.890309i | \(0.650488\pi\) | |||||||
\(920\) | 50.7280 | 1.67245 | ||||||||
\(921\) | 17.5024 | 0.576722 | ||||||||
\(922\) | −11.8553 | −0.390433 | ||||||||
\(923\) | 3.74305 | 0.123204 | ||||||||
\(924\) | −3.74587 | −0.123230 | ||||||||
\(925\) | 13.3414 | 0.438664 | ||||||||
\(926\) | −7.31171 | −0.240278 | ||||||||
\(927\) | −3.95948 | −0.130047 | ||||||||
\(928\) | −31.7233 | −1.04137 | ||||||||
\(929\) | −49.2689 | −1.61646 | −0.808230 | − | 0.588867i | \(-0.799574\pi\) | ||||
−0.808230 | + | 0.588867i | \(0.799574\pi\) | |||||||
\(930\) | −52.1796 | −1.71104 | ||||||||
\(931\) | −18.3427 | −0.601158 | ||||||||
\(932\) | −56.3551 | −1.84597 | ||||||||
\(933\) | −0.455600 | −0.0149157 | ||||||||
\(934\) | 47.0213 | 1.53859 | ||||||||
\(935\) | 1.63315 | 0.0534097 | ||||||||
\(936\) | −2.35407 | −0.0769453 | ||||||||
\(937\) | 7.84795 | 0.256381 | 0.128191 | − | 0.991750i | \(-0.459083\pi\) | ||||
0.128191 | + | 0.991750i | \(0.459083\pi\) | |||||||
\(938\) | 2.11985 | 0.0692157 | ||||||||
\(939\) | −7.10625 | −0.231904 | ||||||||
\(940\) | −59.2195 | −1.93153 | ||||||||
\(941\) | −25.5271 | −0.832159 | −0.416079 | − | 0.909328i | \(-0.636596\pi\) | ||||
−0.416079 | + | 0.909328i | \(0.636596\pi\) | |||||||
\(942\) | −3.18209 | −0.103678 | ||||||||
\(943\) | 18.3921 | 0.598928 | ||||||||
\(944\) | −76.2983 | −2.48330 | ||||||||
\(945\) | 6.29133 | 0.204657 | ||||||||
\(946\) | 2.54628 | 0.0827866 | ||||||||
\(947\) | −16.2764 | −0.528911 | −0.264456 | − | 0.964398i | \(-0.585192\pi\) | ||||
−0.264456 | + | 0.964398i | \(0.585192\pi\) | |||||||
\(948\) | −32.4833 | −1.05501 | ||||||||
\(949\) | −0.951312 | −0.0308809 | ||||||||
\(950\) | 16.7688 | 0.544053 | ||||||||
\(951\) | −18.0225 | −0.584420 | ||||||||
\(952\) | 4.48266 | 0.145284 | ||||||||
\(953\) | −14.8188 | −0.480029 | −0.240015 | − | 0.970769i | \(-0.577152\pi\) | ||||
−0.240015 | + | 0.970769i | \(0.577152\pi\) | |||||||
\(954\) | 53.7514 | 1.74026 | ||||||||
\(955\) | −26.4672 | −0.856458 | ||||||||
\(956\) | 106.404 | 3.44135 | ||||||||
\(957\) | 6.77345 | 0.218954 | ||||||||
\(958\) | 21.3045 | 0.688319 | ||||||||
\(959\) | −12.1616 | −0.392717 | ||||||||
\(960\) | −0.412642 | −0.0133180 | ||||||||
\(961\) | 82.3437 | 2.65625 | ||||||||
\(962\) | −3.36520 | −0.108499 | ||||||||
\(963\) | −18.8770 | −0.608304 | ||||||||
\(964\) | 103.478 | 3.33282 | ||||||||
\(965\) | −3.34836 | −0.107787 | ||||||||
\(966\) | −10.4493 | −0.336201 | ||||||||
\(967\) | −35.0273 | −1.12640 | −0.563200 | − | 0.826320i | \(-0.690430\pi\) | ||||
−0.563200 | + | 0.826320i | \(0.690430\pi\) | |||||||
\(968\) | −6.32373 | −0.203252 | ||||||||
\(969\) | 3.32726 | 0.106887 | ||||||||
\(970\) | −4.00375 | −0.128553 | ||||||||
\(971\) | 48.1082 | 1.54387 | 0.771933 | − | 0.635704i | \(-0.219290\pi\) | ||||
0.771933 | + | 0.635704i | \(0.219290\pi\) | |||||||
\(972\) | 64.7868 | 2.07804 | ||||||||
\(973\) | 2.95579 | 0.0947583 | ||||||||
\(974\) | 17.1707 | 0.550186 | ||||||||
\(975\) | 0.635385 | 0.0203486 | ||||||||
\(976\) | −50.9695 | −1.63149 | ||||||||
\(977\) | −3.92085 | −0.125439 | −0.0627195 | − | 0.998031i | \(-0.519977\pi\) | ||||
−0.0627195 | + | 0.998031i | \(0.519977\pi\) | |||||||
\(978\) | 8.31564 | 0.265905 | ||||||||
\(979\) | −9.20969 | −0.294343 | ||||||||
\(980\) | −47.5765 | −1.51978 | ||||||||
\(981\) | −21.9995 | −0.702389 | ||||||||
\(982\) | 25.7700 | 0.822355 | ||||||||
\(983\) | −53.9594 | −1.72104 | −0.860519 | − | 0.509419i | \(-0.829860\pi\) | ||||
−0.860519 | + | 0.509419i | \(0.829860\pi\) | |||||||
\(984\) | 27.9078 | 0.889669 | ||||||||
\(985\) | −0.139285 | −0.00443799 | ||||||||
\(986\) | −14.6334 | −0.466022 | ||||||||
\(987\) | 6.75699 | 0.215077 | ||||||||
\(988\) | −2.92496 | −0.0930555 | ||||||||
\(989\) | 4.91189 | 0.156189 | ||||||||
\(990\) | 6.69874 | 0.212900 | ||||||||
\(991\) | 29.8959 | 0.949673 | 0.474837 | − | 0.880074i | \(-0.342507\pi\) | ||||
0.474837 | + | 0.880074i | \(0.342507\pi\) | |||||||
\(992\) | −58.7676 | −1.86587 | ||||||||
\(993\) | 29.4656 | 0.935063 | ||||||||
\(994\) | −29.2354 | −0.927291 | ||||||||
\(995\) | −22.4680 | −0.712283 | ||||||||
\(996\) | 39.4293 | 1.24937 | ||||||||
\(997\) | 3.03654 | 0.0961682 | 0.0480841 | − | 0.998843i | \(-0.484688\pi\) | ||||
0.0480841 | + | 0.998843i | \(0.484688\pi\) | |||||||
\(998\) | −31.0474 | −0.982788 | ||||||||
\(999\) | 31.0796 | 0.983314 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8041.2.a.c.1.3 | ✓ | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.c.1.3 | ✓ | 60 | 1.1 | even | 1 | trivial |