Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.90172 | 1.09796 | 0.548981 | − | 0.835835i | \(-0.315016\pi\) | ||||
0.548981 | + | 0.835835i | \(0.315016\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.81206 | −1.70480 | −0.852402 | − | 0.522888i | \(-0.824855\pi\) | ||||
−0.852402 | + | 0.522888i | \(0.824855\pi\) | |||||||
\(6\) | 1.90172 | 0.776376 | ||||||||
\(7\) | 1.69979 | 0.642459 | 0.321230 | − | 0.947001i | \(-0.395904\pi\) | ||||
0.321230 | + | 0.947001i | \(0.395904\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.616557 | 0.205519 | ||||||||
\(10\) | −3.81206 | −1.20548 | ||||||||
\(11\) | 3.78817 | 1.14218 | 0.571088 | − | 0.820889i | \(-0.306521\pi\) | ||||
0.571088 | + | 0.820889i | \(0.306521\pi\) | |||||||
\(12\) | 1.90172 | 0.548981 | ||||||||
\(13\) | 0.0820802 | 0.0227650 | 0.0113825 | − | 0.999935i | \(-0.496377\pi\) | ||||
0.0113825 | + | 0.999935i | \(0.496377\pi\) | |||||||
\(14\) | 1.69979 | 0.454287 | ||||||||
\(15\) | −7.24948 | −1.87181 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.51688 | −1.33804 | −0.669019 | − | 0.743245i | \(-0.733286\pi\) | ||||
−0.669019 | + | 0.743245i | \(0.733286\pi\) | |||||||
\(18\) | 0.616557 | 0.145324 | ||||||||
\(19\) | −5.52339 | −1.26715 | −0.633577 | − | 0.773680i | \(-0.718414\pi\) | ||||
−0.633577 | + | 0.773680i | \(0.718414\pi\) | |||||||
\(20\) | −3.81206 | −0.852402 | ||||||||
\(21\) | 3.23253 | 0.705395 | ||||||||
\(22\) | 3.78817 | 0.807641 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.90172 | 0.388188 | ||||||||
\(25\) | 9.53177 | 1.90635 | ||||||||
\(26\) | 0.0820802 | 0.0160973 | ||||||||
\(27\) | −4.53265 | −0.872309 | ||||||||
\(28\) | 1.69979 | 0.321230 | ||||||||
\(29\) | −7.55480 | −1.40289 | −0.701445 | − | 0.712723i | \(-0.747461\pi\) | ||||
−0.701445 | + | 0.712723i | \(0.747461\pi\) | |||||||
\(30\) | −7.24948 | −1.32357 | ||||||||
\(31\) | −4.11848 | −0.739701 | −0.369851 | − | 0.929091i | \(-0.620591\pi\) | ||||
−0.369851 | + | 0.929091i | \(0.620591\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 7.20406 | 1.25407 | ||||||||
\(34\) | −5.51688 | −0.946136 | ||||||||
\(35\) | −6.47969 | −1.09527 | ||||||||
\(36\) | 0.616557 | 0.102759 | ||||||||
\(37\) | −7.13271 | −1.17261 | −0.586305 | − | 0.810090i | \(-0.699418\pi\) | ||||
−0.586305 | + | 0.810090i | \(0.699418\pi\) | |||||||
\(38\) | −5.52339 | −0.896013 | ||||||||
\(39\) | 0.156094 | 0.0249950 | ||||||||
\(40\) | −3.81206 | −0.602739 | ||||||||
\(41\) | −0.552467 | −0.0862808 | −0.0431404 | − | 0.999069i | \(-0.513736\pi\) | ||||
−0.0431404 | + | 0.999069i | \(0.513736\pi\) | |||||||
\(42\) | 3.23253 | 0.498790 | ||||||||
\(43\) | −2.03192 | −0.309865 | −0.154932 | − | 0.987925i | \(-0.549516\pi\) | ||||
−0.154932 | + | 0.987925i | \(0.549516\pi\) | |||||||
\(44\) | 3.78817 | 0.571088 | ||||||||
\(45\) | −2.35035 | −0.350369 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 10.9517 | 1.59747 | 0.798736 | − | 0.601682i | \(-0.205502\pi\) | ||||
0.798736 | + | 0.601682i | \(0.205502\pi\) | |||||||
\(48\) | 1.90172 | 0.274490 | ||||||||
\(49\) | −4.11072 | −0.587246 | ||||||||
\(50\) | 9.53177 | 1.34800 | ||||||||
\(51\) | −10.4916 | −1.46911 | ||||||||
\(52\) | 0.0820802 | 0.0113825 | ||||||||
\(53\) | −10.8669 | −1.49268 | −0.746341 | − | 0.665564i | \(-0.768191\pi\) | ||||
−0.746341 | + | 0.665564i | \(0.768191\pi\) | |||||||
\(54\) | −4.53265 | −0.616816 | ||||||||
\(55\) | −14.4407 | −1.94719 | ||||||||
\(56\) | 1.69979 | 0.227144 | ||||||||
\(57\) | −10.5040 | −1.39129 | ||||||||
\(58\) | −7.55480 | −0.991993 | ||||||||
\(59\) | 7.85858 | 1.02310 | 0.511550 | − | 0.859253i | \(-0.329071\pi\) | ||||
0.511550 | + | 0.859253i | \(0.329071\pi\) | |||||||
\(60\) | −7.24948 | −0.935904 | ||||||||
\(61\) | 8.75538 | 1.12101 | 0.560506 | − | 0.828150i | \(-0.310607\pi\) | ||||
0.560506 | + | 0.828150i | \(0.310607\pi\) | |||||||
\(62\) | −4.11848 | −0.523048 | ||||||||
\(63\) | 1.04802 | 0.132037 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.312894 | −0.0388098 | ||||||||
\(66\) | 7.20406 | 0.886758 | ||||||||
\(67\) | 8.48643 | 1.03678 | 0.518391 | − | 0.855144i | \(-0.326531\pi\) | ||||
0.518391 | + | 0.855144i | \(0.326531\pi\) | |||||||
\(68\) | −5.51688 | −0.669019 | ||||||||
\(69\) | −1.90172 | −0.228941 | ||||||||
\(70\) | −6.47969 | −0.774470 | ||||||||
\(71\) | 4.08933 | 0.485314 | 0.242657 | − | 0.970112i | \(-0.421981\pi\) | ||||
0.242657 | + | 0.970112i | \(0.421981\pi\) | |||||||
\(72\) | 0.616557 | 0.0726619 | ||||||||
\(73\) | −0.0747777 | −0.00875206 | −0.00437603 | − | 0.999990i | \(-0.501393\pi\) | ||||
−0.00437603 | + | 0.999990i | \(0.501393\pi\) | |||||||
\(74\) | −7.13271 | −0.829161 | ||||||||
\(75\) | 18.1268 | 2.09310 | ||||||||
\(76\) | −5.52339 | −0.633577 | ||||||||
\(77\) | 6.43908 | 0.733802 | ||||||||
\(78\) | 0.156094 | 0.0176742 | ||||||||
\(79\) | −13.0743 | −1.47098 | −0.735488 | − | 0.677538i | \(-0.763047\pi\) | ||||
−0.735488 | + | 0.677538i | \(0.763047\pi\) | |||||||
\(80\) | −3.81206 | −0.426201 | ||||||||
\(81\) | −10.4695 | −1.16328 | ||||||||
\(82\) | −0.552467 | −0.0610097 | ||||||||
\(83\) | 8.10379 | 0.889506 | 0.444753 | − | 0.895653i | \(-0.353291\pi\) | ||||
0.444753 | + | 0.895653i | \(0.353291\pi\) | |||||||
\(84\) | 3.23253 | 0.352698 | ||||||||
\(85\) | 21.0306 | 2.28109 | ||||||||
\(86\) | −2.03192 | −0.219107 | ||||||||
\(87\) | −14.3671 | −1.54032 | ||||||||
\(88\) | 3.78817 | 0.403820 | ||||||||
\(89\) | 8.42844 | 0.893412 | 0.446706 | − | 0.894681i | \(-0.352597\pi\) | ||||
0.446706 | + | 0.894681i | \(0.352597\pi\) | |||||||
\(90\) | −2.35035 | −0.247748 | ||||||||
\(91\) | 0.139519 | 0.0146256 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −7.83222 | −0.812163 | ||||||||
\(94\) | 10.9517 | 1.12958 | ||||||||
\(95\) | 21.0555 | 2.16025 | ||||||||
\(96\) | 1.90172 | 0.194094 | ||||||||
\(97\) | −8.84960 | −0.898541 | −0.449271 | − | 0.893396i | \(-0.648316\pi\) | ||||
−0.449271 | + | 0.893396i | \(0.648316\pi\) | |||||||
\(98\) | −4.11072 | −0.415246 | ||||||||
\(99\) | 2.33562 | 0.234739 | ||||||||
\(100\) | 9.53177 | 0.953177 | ||||||||
\(101\) | −11.1586 | −1.11032 | −0.555161 | − | 0.831743i | \(-0.687343\pi\) | ||||
−0.555161 | + | 0.831743i | \(0.687343\pi\) | |||||||
\(102\) | −10.4916 | −1.03882 | ||||||||
\(103\) | −5.58492 | −0.550298 | −0.275149 | − | 0.961402i | \(-0.588727\pi\) | ||||
−0.275149 | + | 0.961402i | \(0.588727\pi\) | |||||||
\(104\) | 0.0820802 | 0.00804863 | ||||||||
\(105\) | −12.3226 | −1.20256 | ||||||||
\(106\) | −10.8669 | −1.05549 | ||||||||
\(107\) | −5.15619 | −0.498468 | −0.249234 | − | 0.968443i | \(-0.580179\pi\) | ||||
−0.249234 | + | 0.968443i | \(0.580179\pi\) | |||||||
\(108\) | −4.53265 | −0.436155 | ||||||||
\(109\) | −3.75229 | −0.359404 | −0.179702 | − | 0.983721i | \(-0.557513\pi\) | ||||
−0.179702 | + | 0.983721i | \(0.557513\pi\) | |||||||
\(110\) | −14.4407 | −1.37687 | ||||||||
\(111\) | −13.5644 | −1.28748 | ||||||||
\(112\) | 1.69979 | 0.160615 | ||||||||
\(113\) | −17.4683 | −1.64328 | −0.821640 | − | 0.570007i | \(-0.806940\pi\) | ||||
−0.821640 | + | 0.570007i | \(0.806940\pi\) | |||||||
\(114\) | −10.5040 | −0.983787 | ||||||||
\(115\) | 3.81206 | 0.355476 | ||||||||
\(116\) | −7.55480 | −0.701445 | ||||||||
\(117\) | 0.0506071 | 0.00467863 | ||||||||
\(118\) | 7.85858 | 0.723441 | ||||||||
\(119\) | −9.37752 | −0.859635 | ||||||||
\(120\) | −7.24948 | −0.661784 | ||||||||
\(121\) | 3.35024 | 0.304567 | ||||||||
\(122\) | 8.75538 | 0.792675 | ||||||||
\(123\) | −1.05064 | −0.0947330 | ||||||||
\(124\) | −4.11848 | −0.369851 | ||||||||
\(125\) | −17.2754 | −1.54516 | ||||||||
\(126\) | 1.04802 | 0.0933646 | ||||||||
\(127\) | 7.83989 | 0.695678 | 0.347839 | − | 0.937554i | \(-0.386916\pi\) | ||||
0.347839 | + | 0.937554i | \(0.386916\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.86415 | −0.340220 | ||||||||
\(130\) | −0.312894 | −0.0274427 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 7.20406 | 0.627033 | ||||||||
\(133\) | −9.38860 | −0.814095 | ||||||||
\(134\) | 8.48643 | 0.733116 | ||||||||
\(135\) | 17.2787 | 1.48712 | ||||||||
\(136\) | −5.51688 | −0.473068 | ||||||||
\(137\) | 6.68048 | 0.570752 | 0.285376 | − | 0.958416i | \(-0.407882\pi\) | ||||
0.285376 | + | 0.958416i | \(0.407882\pi\) | |||||||
\(138\) | −1.90172 | −0.161886 | ||||||||
\(139\) | 4.62069 | 0.391922 | 0.195961 | − | 0.980612i | \(-0.437217\pi\) | ||||
0.195961 | + | 0.980612i | \(0.437217\pi\) | |||||||
\(140\) | −6.47969 | −0.547633 | ||||||||
\(141\) | 20.8271 | 1.75396 | ||||||||
\(142\) | 4.08933 | 0.343169 | ||||||||
\(143\) | 0.310934 | 0.0260016 | ||||||||
\(144\) | 0.616557 | 0.0513797 | ||||||||
\(145\) | 28.7993 | 2.39165 | ||||||||
\(146\) | −0.0747777 | −0.00618864 | ||||||||
\(147\) | −7.81746 | −0.644773 | ||||||||
\(148\) | −7.13271 | −0.586305 | ||||||||
\(149\) | 7.66899 | 0.628268 | 0.314134 | − | 0.949379i | \(-0.398286\pi\) | ||||
0.314134 | + | 0.949379i | \(0.398286\pi\) | |||||||
\(150\) | 18.1268 | 1.48005 | ||||||||
\(151\) | −15.1421 | −1.23225 | −0.616125 | − | 0.787648i | \(-0.711299\pi\) | ||||
−0.616125 | + | 0.787648i | \(0.711299\pi\) | |||||||
\(152\) | −5.52339 | −0.448006 | ||||||||
\(153\) | −3.40147 | −0.274992 | ||||||||
\(154\) | 6.43908 | 0.518876 | ||||||||
\(155\) | 15.6999 | 1.26104 | ||||||||
\(156\) | 0.156094 | 0.0124975 | ||||||||
\(157\) | −19.7962 | −1.57991 | −0.789956 | − | 0.613163i | \(-0.789897\pi\) | ||||
−0.789956 | + | 0.613163i | \(0.789897\pi\) | |||||||
\(158\) | −13.0743 | −1.04014 | ||||||||
\(159\) | −20.6658 | −1.63891 | ||||||||
\(160\) | −3.81206 | −0.301369 | ||||||||
\(161\) | −1.69979 | −0.133962 | ||||||||
\(162\) | −10.4695 | −0.822564 | ||||||||
\(163\) | −24.5017 | −1.91912 | −0.959561 | − | 0.281501i | \(-0.909168\pi\) | ||||
−0.959561 | + | 0.281501i | \(0.909168\pi\) | |||||||
\(164\) | −0.552467 | −0.0431404 | ||||||||
\(165\) | −27.4623 | −2.13793 | ||||||||
\(166\) | 8.10379 | 0.628976 | ||||||||
\(167\) | 20.5000 | 1.58633 | 0.793167 | − | 0.609004i | \(-0.208430\pi\) | ||||
0.793167 | + | 0.609004i | \(0.208430\pi\) | |||||||
\(168\) | 3.23253 | 0.249395 | ||||||||
\(169\) | −12.9933 | −0.999482 | ||||||||
\(170\) | 21.0306 | 1.61298 | ||||||||
\(171\) | −3.40549 | −0.260424 | ||||||||
\(172\) | −2.03192 | −0.154932 | ||||||||
\(173\) | 5.38601 | 0.409491 | 0.204745 | − | 0.978815i | \(-0.434363\pi\) | ||||
0.204745 | + | 0.978815i | \(0.434363\pi\) | |||||||
\(174\) | −14.3671 | −1.08917 | ||||||||
\(175\) | 16.2020 | 1.22475 | ||||||||
\(176\) | 3.78817 | 0.285544 | ||||||||
\(177\) | 14.9449 | 1.12332 | ||||||||
\(178\) | 8.42844 | 0.631738 | ||||||||
\(179\) | 1.59431 | 0.119165 | 0.0595823 | − | 0.998223i | \(-0.481023\pi\) | ||||
0.0595823 | + | 0.998223i | \(0.481023\pi\) | |||||||
\(180\) | −2.35035 | −0.175185 | ||||||||
\(181\) | 6.50617 | 0.483600 | 0.241800 | − | 0.970326i | \(-0.422262\pi\) | ||||
0.241800 | + | 0.970326i | \(0.422262\pi\) | |||||||
\(182\) | 0.139519 | 0.0103418 | ||||||||
\(183\) | 16.6503 | 1.23083 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 27.1903 | 1.99907 | ||||||||
\(186\) | −7.83222 | −0.574286 | ||||||||
\(187\) | −20.8989 | −1.52828 | ||||||||
\(188\) | 10.9517 | 0.798736 | ||||||||
\(189\) | −7.70455 | −0.560423 | ||||||||
\(190\) | 21.0555 | 1.52753 | ||||||||
\(191\) | −20.6033 | −1.49080 | −0.745402 | − | 0.666615i | \(-0.767743\pi\) | ||||
−0.745402 | + | 0.666615i | \(0.767743\pi\) | |||||||
\(192\) | 1.90172 | 0.137245 | ||||||||
\(193\) | 1.60684 | 0.115663 | 0.0578315 | − | 0.998326i | \(-0.481581\pi\) | ||||
0.0578315 | + | 0.998326i | \(0.481581\pi\) | |||||||
\(194\) | −8.84960 | −0.635365 | ||||||||
\(195\) | −0.595039 | −0.0426116 | ||||||||
\(196\) | −4.11072 | −0.293623 | ||||||||
\(197\) | 17.9324 | 1.27763 | 0.638815 | − | 0.769360i | \(-0.279425\pi\) | ||||
0.638815 | + | 0.769360i | \(0.279425\pi\) | |||||||
\(198\) | 2.33562 | 0.165985 | ||||||||
\(199\) | −11.7766 | −0.834820 | −0.417410 | − | 0.908718i | \(-0.637062\pi\) | ||||
−0.417410 | + | 0.908718i | \(0.637062\pi\) | |||||||
\(200\) | 9.53177 | 0.673998 | ||||||||
\(201\) | 16.1388 | 1.13835 | ||||||||
\(202\) | −11.1586 | −0.785116 | ||||||||
\(203\) | −12.8415 | −0.901300 | ||||||||
\(204\) | −10.4916 | −0.734557 | ||||||||
\(205\) | 2.10603 | 0.147092 | ||||||||
\(206\) | −5.58492 | −0.389120 | ||||||||
\(207\) | −0.616557 | −0.0428536 | ||||||||
\(208\) | 0.0820802 | 0.00569124 | ||||||||
\(209\) | −20.9236 | −1.44731 | ||||||||
\(210\) | −12.3226 | −0.850339 | ||||||||
\(211\) | 15.5611 | 1.07127 | 0.535635 | − | 0.844450i | \(-0.320072\pi\) | ||||
0.535635 | + | 0.844450i | \(0.320072\pi\) | |||||||
\(212\) | −10.8669 | −0.746341 | ||||||||
\(213\) | 7.77678 | 0.532856 | ||||||||
\(214\) | −5.15619 | −0.352470 | ||||||||
\(215\) | 7.74579 | 0.528259 | ||||||||
\(216\) | −4.53265 | −0.308408 | ||||||||
\(217\) | −7.00054 | −0.475228 | ||||||||
\(218\) | −3.75229 | −0.254137 | ||||||||
\(219\) | −0.142207 | −0.00960943 | ||||||||
\(220\) | −14.4407 | −0.973593 | ||||||||
\(221\) | −0.452826 | −0.0304604 | ||||||||
\(222\) | −13.5644 | −0.910386 | ||||||||
\(223\) | −3.02774 | −0.202753 | −0.101376 | − | 0.994848i | \(-0.532325\pi\) | ||||
−0.101376 | + | 0.994848i | \(0.532325\pi\) | |||||||
\(224\) | 1.69979 | 0.113572 | ||||||||
\(225\) | 5.87688 | 0.391792 | ||||||||
\(226\) | −17.4683 | −1.16197 | ||||||||
\(227\) | 7.21767 | 0.479054 | 0.239527 | − | 0.970890i | \(-0.423008\pi\) | ||||
0.239527 | + | 0.970890i | \(0.423008\pi\) | |||||||
\(228\) | −10.5040 | −0.695643 | ||||||||
\(229\) | −7.54120 | −0.498337 | −0.249168 | − | 0.968460i | \(-0.580157\pi\) | ||||
−0.249168 | + | 0.968460i | \(0.580157\pi\) | |||||||
\(230\) | 3.81206 | 0.251360 | ||||||||
\(231\) | 12.2454 | 0.805686 | ||||||||
\(232\) | −7.55480 | −0.495997 | ||||||||
\(233\) | −15.3177 | −1.00349 | −0.501747 | − | 0.865014i | \(-0.667309\pi\) | ||||
−0.501747 | + | 0.865014i | \(0.667309\pi\) | |||||||
\(234\) | 0.0506071 | 0.00330829 | ||||||||
\(235\) | −41.7486 | −2.72338 | ||||||||
\(236\) | 7.85858 | 0.511550 | ||||||||
\(237\) | −24.8638 | −1.61507 | ||||||||
\(238\) | −9.37752 | −0.607854 | ||||||||
\(239\) | 4.33818 | 0.280614 | 0.140307 | − | 0.990108i | \(-0.455191\pi\) | ||||
0.140307 | + | 0.990108i | \(0.455191\pi\) | |||||||
\(240\) | −7.24948 | −0.467952 | ||||||||
\(241\) | 7.00632 | 0.451316 | 0.225658 | − | 0.974207i | \(-0.427547\pi\) | ||||
0.225658 | + | 0.974207i | \(0.427547\pi\) | |||||||
\(242\) | 3.35024 | 0.215361 | ||||||||
\(243\) | −6.31220 | −0.404928 | ||||||||
\(244\) | 8.75538 | 0.560506 | ||||||||
\(245\) | 15.6703 | 1.00114 | ||||||||
\(246\) | −1.05064 | −0.0669863 | ||||||||
\(247\) | −0.453361 | −0.0288467 | ||||||||
\(248\) | −4.11848 | −0.261524 | ||||||||
\(249\) | 15.4112 | 0.976643 | ||||||||
\(250\) | −17.2754 | −1.09259 | ||||||||
\(251\) | −1.97249 | −0.124503 | −0.0622513 | − | 0.998061i | \(-0.519828\pi\) | ||||
−0.0622513 | + | 0.998061i | \(0.519828\pi\) | |||||||
\(252\) | 1.04802 | 0.0660187 | ||||||||
\(253\) | −3.78817 | −0.238160 | ||||||||
\(254\) | 7.83989 | 0.491918 | ||||||||
\(255\) | 39.9945 | 2.50455 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.3693 | 1.58249 | 0.791245 | − | 0.611499i | \(-0.209433\pi\) | ||||
0.791245 | + | 0.611499i | \(0.209433\pi\) | |||||||
\(258\) | −3.86415 | −0.240572 | ||||||||
\(259\) | −12.1241 | −0.753354 | ||||||||
\(260\) | −0.312894 | −0.0194049 | ||||||||
\(261\) | −4.65796 | −0.288320 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | −7.48012 | −0.461244 | −0.230622 | − | 0.973043i | \(-0.574076\pi\) | ||||
−0.230622 | + | 0.973043i | \(0.574076\pi\) | |||||||
\(264\) | 7.20406 | 0.443379 | ||||||||
\(265\) | 41.4252 | 2.54473 | ||||||||
\(266\) | −9.38860 | −0.575652 | ||||||||
\(267\) | 16.0286 | 0.980932 | ||||||||
\(268\) | 8.48643 | 0.518391 | ||||||||
\(269\) | 17.7556 | 1.08258 | 0.541290 | − | 0.840836i | \(-0.317936\pi\) | ||||
0.541290 | + | 0.840836i | \(0.317936\pi\) | |||||||
\(270\) | 17.2787 | 1.05155 | ||||||||
\(271\) | −17.8908 | −1.08679 | −0.543394 | − | 0.839478i | \(-0.682861\pi\) | ||||
−0.543394 | + | 0.839478i | \(0.682861\pi\) | |||||||
\(272\) | −5.51688 | −0.334510 | ||||||||
\(273\) | 0.265327 | 0.0160583 | ||||||||
\(274\) | 6.68048 | 0.403582 | ||||||||
\(275\) | 36.1080 | 2.17739 | ||||||||
\(276\) | −1.90172 | −0.114470 | ||||||||
\(277\) | −8.98310 | −0.539742 | −0.269871 | − | 0.962896i | \(-0.586981\pi\) | ||||
−0.269871 | + | 0.962896i | \(0.586981\pi\) | |||||||
\(278\) | 4.62069 | 0.277131 | ||||||||
\(279\) | −2.53928 | −0.152023 | ||||||||
\(280\) | −6.47969 | −0.387235 | ||||||||
\(281\) | 26.4602 | 1.57848 | 0.789241 | − | 0.614084i | \(-0.210474\pi\) | ||||
0.789241 | + | 0.614084i | \(0.210474\pi\) | |||||||
\(282\) | 20.8271 | 1.24024 | ||||||||
\(283\) | −12.7482 | −0.757803 | −0.378902 | − | 0.925437i | \(-0.623698\pi\) | ||||
−0.378902 | + | 0.925437i | \(0.623698\pi\) | |||||||
\(284\) | 4.08933 | 0.242657 | ||||||||
\(285\) | 40.0417 | 2.37187 | ||||||||
\(286\) | 0.310934 | 0.0183859 | ||||||||
\(287\) | −0.939076 | −0.0554319 | ||||||||
\(288\) | 0.616557 | 0.0363309 | ||||||||
\(289\) | 13.4359 | 0.790348 | ||||||||
\(290\) | 28.7993 | 1.69115 | ||||||||
\(291\) | −16.8295 | −0.986563 | ||||||||
\(292\) | −0.0747777 | −0.00437603 | ||||||||
\(293\) | −20.2959 | −1.18570 | −0.592850 | − | 0.805313i | \(-0.701997\pi\) | ||||
−0.592850 | + | 0.805313i | \(0.701997\pi\) | |||||||
\(294\) | −7.81746 | −0.455924 | ||||||||
\(295\) | −29.9574 | −1.74419 | ||||||||
\(296\) | −7.13271 | −0.414580 | ||||||||
\(297\) | −17.1705 | −0.996331 | ||||||||
\(298\) | 7.66899 | 0.444253 | ||||||||
\(299\) | −0.0820802 | −0.00474682 | ||||||||
\(300\) | 18.1268 | 1.04655 | ||||||||
\(301\) | −3.45383 | −0.199076 | ||||||||
\(302\) | −15.1421 | −0.871333 | ||||||||
\(303\) | −21.2206 | −1.21909 | ||||||||
\(304\) | −5.52339 | −0.316788 | ||||||||
\(305\) | −33.3760 | −1.91111 | ||||||||
\(306\) | −3.40147 | −0.194449 | ||||||||
\(307\) | 18.9836 | 1.08345 | 0.541725 | − | 0.840556i | \(-0.317771\pi\) | ||||
0.541725 | + | 0.840556i | \(0.317771\pi\) | |||||||
\(308\) | 6.43908 | 0.366901 | ||||||||
\(309\) | −10.6210 | −0.604206 | ||||||||
\(310\) | 15.6999 | 0.891693 | ||||||||
\(311\) | −12.9589 | −0.734834 | −0.367417 | − | 0.930056i | \(-0.619758\pi\) | ||||
−0.367417 | + | 0.930056i | \(0.619758\pi\) | |||||||
\(312\) | 0.156094 | 0.00883708 | ||||||||
\(313\) | −16.8440 | −0.952076 | −0.476038 | − | 0.879425i | \(-0.657928\pi\) | ||||
−0.476038 | + | 0.879425i | \(0.657928\pi\) | |||||||
\(314\) | −19.7962 | −1.11717 | ||||||||
\(315\) | −3.99509 | −0.225098 | ||||||||
\(316\) | −13.0743 | −0.735488 | ||||||||
\(317\) | −9.34656 | −0.524955 | −0.262478 | − | 0.964938i | \(-0.584540\pi\) | ||||
−0.262478 | + | 0.964938i | \(0.584540\pi\) | |||||||
\(318\) | −20.6658 | −1.15888 | ||||||||
\(319\) | −28.6189 | −1.60235 | ||||||||
\(320\) | −3.81206 | −0.213100 | ||||||||
\(321\) | −9.80566 | −0.547298 | ||||||||
\(322\) | −1.69979 | −0.0947255 | ||||||||
\(323\) | 30.4719 | 1.69550 | ||||||||
\(324\) | −10.4695 | −0.581640 | ||||||||
\(325\) | 0.782370 | 0.0433981 | ||||||||
\(326\) | −24.5017 | −1.35702 | ||||||||
\(327\) | −7.13582 | −0.394612 | ||||||||
\(328\) | −0.552467 | −0.0305049 | ||||||||
\(329\) | 18.6156 | 1.02631 | ||||||||
\(330\) | −27.4623 | −1.51175 | ||||||||
\(331\) | −16.0184 | −0.880454 | −0.440227 | − | 0.897887i | \(-0.645102\pi\) | ||||
−0.440227 | + | 0.897887i | \(0.645102\pi\) | |||||||
\(332\) | 8.10379 | 0.444753 | ||||||||
\(333\) | −4.39772 | −0.240994 | ||||||||
\(334\) | 20.5000 | 1.12171 | ||||||||
\(335\) | −32.3507 | −1.76751 | ||||||||
\(336\) | 3.23253 | 0.176349 | ||||||||
\(337\) | 33.5475 | 1.82745 | 0.913724 | − | 0.406336i | \(-0.133194\pi\) | ||||
0.913724 | + | 0.406336i | \(0.133194\pi\) | |||||||
\(338\) | −12.9933 | −0.706740 | ||||||||
\(339\) | −33.2199 | −1.80426 | ||||||||
\(340\) | 21.0306 | 1.14055 | ||||||||
\(341\) | −15.6015 | −0.844869 | ||||||||
\(342\) | −3.40549 | −0.184148 | ||||||||
\(343\) | −18.8859 | −1.01974 | ||||||||
\(344\) | −2.03192 | −0.109554 | ||||||||
\(345\) | 7.24948 | 0.390299 | ||||||||
\(346\) | 5.38601 | 0.289554 | ||||||||
\(347\) | −7.08623 | −0.380409 | −0.190204 | − | 0.981745i | \(-0.560915\pi\) | ||||
−0.190204 | + | 0.981745i | \(0.560915\pi\) | |||||||
\(348\) | −14.3671 | −0.770160 | ||||||||
\(349\) | 22.0543 | 1.18054 | 0.590269 | − | 0.807207i | \(-0.299022\pi\) | ||||
0.590269 | + | 0.807207i | \(0.299022\pi\) | |||||||
\(350\) | 16.2020 | 0.866033 | ||||||||
\(351\) | −0.372041 | −0.0198581 | ||||||||
\(352\) | 3.78817 | 0.201910 | ||||||||
\(353\) | −8.76815 | −0.466681 | −0.233341 | − | 0.972395i | \(-0.574966\pi\) | ||||
−0.233341 | + | 0.972395i | \(0.574966\pi\) | |||||||
\(354\) | 14.9449 | 0.794311 | ||||||||
\(355\) | −15.5888 | −0.827366 | ||||||||
\(356\) | 8.42844 | 0.446706 | ||||||||
\(357\) | −17.8335 | −0.943846 | ||||||||
\(358\) | 1.59431 | 0.0842621 | ||||||||
\(359\) | −11.0981 | −0.585735 | −0.292867 | − | 0.956153i | \(-0.594609\pi\) | ||||
−0.292867 | + | 0.956153i | \(0.594609\pi\) | |||||||
\(360\) | −2.35035 | −0.123874 | ||||||||
\(361\) | 11.5079 | 0.605678 | ||||||||
\(362\) | 6.50617 | 0.341957 | ||||||||
\(363\) | 6.37123 | 0.334403 | ||||||||
\(364\) | 0.139519 | 0.00731278 | ||||||||
\(365\) | 0.285057 | 0.0149205 | ||||||||
\(366\) | 16.6503 | 0.870327 | ||||||||
\(367\) | 11.0724 | 0.577972 | 0.288986 | − | 0.957333i | \(-0.406682\pi\) | ||||
0.288986 | + | 0.957333i | \(0.406682\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −0.340627 | −0.0177323 | ||||||||
\(370\) | 27.1903 | 1.41356 | ||||||||
\(371\) | −18.4714 | −0.958988 | ||||||||
\(372\) | −7.83222 | −0.406082 | ||||||||
\(373\) | −8.10125 | −0.419467 | −0.209733 | − | 0.977759i | \(-0.567260\pi\) | ||||
−0.209733 | + | 0.977759i | \(0.567260\pi\) | |||||||
\(374\) | −20.8989 | −1.08065 | ||||||||
\(375\) | −32.8530 | −1.69652 | ||||||||
\(376\) | 10.9517 | 0.564792 | ||||||||
\(377\) | −0.620099 | −0.0319367 | ||||||||
\(378\) | −7.70455 | −0.396279 | ||||||||
\(379\) | 2.20636 | 0.113333 | 0.0566666 | − | 0.998393i | \(-0.481953\pi\) | ||||
0.0566666 | + | 0.998393i | \(0.481953\pi\) | |||||||
\(380\) | 21.0555 | 1.08012 | ||||||||
\(381\) | 14.9093 | 0.763827 | ||||||||
\(382\) | −20.6033 | −1.05416 | ||||||||
\(383\) | −23.0649 | −1.17856 | −0.589281 | − | 0.807928i | \(-0.700589\pi\) | ||||
−0.589281 | + | 0.807928i | \(0.700589\pi\) | |||||||
\(384\) | 1.90172 | 0.0970470 | ||||||||
\(385\) | −24.5462 | −1.25099 | ||||||||
\(386\) | 1.60684 | 0.0817861 | ||||||||
\(387\) | −1.25279 | −0.0636831 | ||||||||
\(388\) | −8.84960 | −0.449271 | ||||||||
\(389\) | 3.60124 | 0.182590 | 0.0912951 | − | 0.995824i | \(-0.470899\pi\) | ||||
0.0912951 | + | 0.995824i | \(0.470899\pi\) | |||||||
\(390\) | −0.595039 | −0.0301310 | ||||||||
\(391\) | 5.51688 | 0.279000 | ||||||||
\(392\) | −4.11072 | −0.207623 | ||||||||
\(393\) | 1.90172 | 0.0959293 | ||||||||
\(394\) | 17.9324 | 0.903422 | ||||||||
\(395\) | 49.8400 | 2.50772 | ||||||||
\(396\) | 2.33562 | 0.117369 | ||||||||
\(397\) | 24.0232 | 1.20569 | 0.602844 | − | 0.797859i | \(-0.294034\pi\) | ||||
0.602844 | + | 0.797859i | \(0.294034\pi\) | |||||||
\(398\) | −11.7766 | −0.590307 | ||||||||
\(399\) | −17.8545 | −0.893844 | ||||||||
\(400\) | 9.53177 | 0.476589 | ||||||||
\(401\) | −12.1290 | −0.605694 | −0.302847 | − | 0.953039i | \(-0.597937\pi\) | ||||
−0.302847 | + | 0.953039i | \(0.597937\pi\) | |||||||
\(402\) | 16.1388 | 0.804932 | ||||||||
\(403\) | −0.338046 | −0.0168393 | ||||||||
\(404\) | −11.1586 | −0.555161 | ||||||||
\(405\) | 39.9104 | 1.98317 | ||||||||
\(406\) | −12.8415 | −0.637315 | ||||||||
\(407\) | −27.0199 | −1.33933 | ||||||||
\(408\) | −10.4916 | −0.519411 | ||||||||
\(409\) | −18.2638 | −0.903085 | −0.451542 | − | 0.892250i | \(-0.649126\pi\) | ||||
−0.451542 | + | 0.892250i | \(0.649126\pi\) | |||||||
\(410\) | 2.10603 | 0.104010 | ||||||||
\(411\) | 12.7044 | 0.626663 | ||||||||
\(412\) | −5.58492 | −0.275149 | ||||||||
\(413\) | 13.3579 | 0.657300 | ||||||||
\(414\) | −0.616557 | −0.0303021 | ||||||||
\(415\) | −30.8921 | −1.51643 | ||||||||
\(416\) | 0.0820802 | 0.00402431 | ||||||||
\(417\) | 8.78728 | 0.430315 | ||||||||
\(418\) | −20.9236 | −1.02340 | ||||||||
\(419\) | 33.0384 | 1.61403 | 0.807016 | − | 0.590529i | \(-0.201081\pi\) | ||||
0.807016 | + | 0.590529i | \(0.201081\pi\) | |||||||
\(420\) | −12.3226 | −0.601280 | ||||||||
\(421\) | 33.6532 | 1.64016 | 0.820079 | − | 0.572250i | \(-0.193929\pi\) | ||||
0.820079 | + | 0.572250i | \(0.193929\pi\) | |||||||
\(422\) | 15.5611 | 0.757502 | ||||||||
\(423\) | 6.75235 | 0.328311 | ||||||||
\(424\) | −10.8669 | −0.527743 | ||||||||
\(425\) | −52.5856 | −2.55078 | ||||||||
\(426\) | 7.77678 | 0.376786 | ||||||||
\(427\) | 14.8823 | 0.720205 | ||||||||
\(428\) | −5.15619 | −0.249234 | ||||||||
\(429\) | 0.591311 | 0.0285487 | ||||||||
\(430\) | 7.74579 | 0.373535 | ||||||||
\(431\) | −11.5779 | −0.557690 | −0.278845 | − | 0.960336i | \(-0.589951\pi\) | ||||
−0.278845 | + | 0.960336i | \(0.589951\pi\) | |||||||
\(432\) | −4.53265 | −0.218077 | ||||||||
\(433\) | 2.98800 | 0.143594 | 0.0717970 | − | 0.997419i | \(-0.477127\pi\) | ||||
0.0717970 | + | 0.997419i | \(0.477127\pi\) | |||||||
\(434\) | −7.00054 | −0.336037 | ||||||||
\(435\) | 54.7683 | 2.62594 | ||||||||
\(436\) | −3.75229 | −0.179702 | ||||||||
\(437\) | 5.52339 | 0.264220 | ||||||||
\(438\) | −0.142207 | −0.00679489 | ||||||||
\(439\) | −23.7476 | −1.13341 | −0.566706 | − | 0.823920i | \(-0.691783\pi\) | ||||
−0.566706 | + | 0.823920i | \(0.691783\pi\) | |||||||
\(440\) | −14.4407 | −0.688434 | ||||||||
\(441\) | −2.53449 | −0.120690 | ||||||||
\(442\) | −0.452826 | −0.0215388 | ||||||||
\(443\) | −18.6889 | −0.887935 | −0.443967 | − | 0.896043i | \(-0.646429\pi\) | ||||
−0.443967 | + | 0.896043i | \(0.646429\pi\) | |||||||
\(444\) | −13.5644 | −0.643740 | ||||||||
\(445\) | −32.1297 | −1.52309 | ||||||||
\(446\) | −3.02774 | −0.143368 | ||||||||
\(447\) | 14.5843 | 0.689814 | ||||||||
\(448\) | 1.69979 | 0.0803074 | ||||||||
\(449\) | 0.368707 | 0.0174004 | 0.00870018 | − | 0.999962i | \(-0.497231\pi\) | ||||
0.00870018 | + | 0.999962i | \(0.497231\pi\) | |||||||
\(450\) | 5.87688 | 0.277039 | ||||||||
\(451\) | −2.09284 | −0.0985479 | ||||||||
\(452\) | −17.4683 | −0.821640 | ||||||||
\(453\) | −28.7962 | −1.35296 | ||||||||
\(454\) | 7.21767 | 0.338742 | ||||||||
\(455\) | −0.531854 | −0.0249337 | ||||||||
\(456\) | −10.5040 | −0.491894 | ||||||||
\(457\) | 10.4175 | 0.487311 | 0.243656 | − | 0.969862i | \(-0.421653\pi\) | ||||
0.243656 | + | 0.969862i | \(0.421653\pi\) | |||||||
\(458\) | −7.54120 | −0.352377 | ||||||||
\(459\) | 25.0061 | 1.16718 | ||||||||
\(460\) | 3.81206 | 0.177738 | ||||||||
\(461\) | 16.8127 | 0.783044 | 0.391522 | − | 0.920169i | \(-0.371949\pi\) | ||||
0.391522 | + | 0.920169i | \(0.371949\pi\) | |||||||
\(462\) | 12.2454 | 0.569706 | ||||||||
\(463\) | 26.7192 | 1.24175 | 0.620874 | − | 0.783911i | \(-0.286778\pi\) | ||||
0.620874 | + | 0.783911i | \(0.286778\pi\) | |||||||
\(464\) | −7.55480 | −0.350723 | ||||||||
\(465\) | 29.8569 | 1.38458 | ||||||||
\(466\) | −15.3177 | −0.709578 | ||||||||
\(467\) | 40.8350 | 1.88962 | 0.944809 | − | 0.327622i | \(-0.106247\pi\) | ||||
0.944809 | + | 0.327622i | \(0.106247\pi\) | |||||||
\(468\) | 0.0506071 | 0.00233931 | ||||||||
\(469\) | 14.4251 | 0.666090 | ||||||||
\(470\) | −41.7486 | −1.92572 | ||||||||
\(471\) | −37.6470 | −1.73468 | ||||||||
\(472\) | 7.85858 | 0.361721 | ||||||||
\(473\) | −7.69726 | −0.353920 | ||||||||
\(474\) | −24.8638 | −1.14203 | ||||||||
\(475\) | −52.6477 | −2.41564 | ||||||||
\(476\) | −9.37752 | −0.429818 | ||||||||
\(477\) | −6.70005 | −0.306774 | ||||||||
\(478\) | 4.33818 | 0.198424 | ||||||||
\(479\) | 21.7109 | 0.991998 | 0.495999 | − | 0.868323i | \(-0.334802\pi\) | ||||
0.495999 | + | 0.868323i | \(0.334802\pi\) | |||||||
\(480\) | −7.24948 | −0.330892 | ||||||||
\(481\) | −0.585454 | −0.0266944 | ||||||||
\(482\) | 7.00632 | 0.319129 | ||||||||
\(483\) | −3.23253 | −0.147085 | ||||||||
\(484\) | 3.35024 | 0.152283 | ||||||||
\(485\) | 33.7352 | 1.53184 | ||||||||
\(486\) | −6.31220 | −0.286327 | ||||||||
\(487\) | 11.7332 | 0.531684 | 0.265842 | − | 0.964017i | \(-0.414350\pi\) | ||||
0.265842 | + | 0.964017i | \(0.414350\pi\) | |||||||
\(488\) | 8.75538 | 0.396338 | ||||||||
\(489\) | −46.5955 | −2.10712 | ||||||||
\(490\) | 15.6703 | 0.707912 | ||||||||
\(491\) | 6.44619 | 0.290912 | 0.145456 | − | 0.989365i | \(-0.453535\pi\) | ||||
0.145456 | + | 0.989365i | \(0.453535\pi\) | |||||||
\(492\) | −1.05064 | −0.0473665 | ||||||||
\(493\) | 41.6789 | 1.87712 | ||||||||
\(494\) | −0.453361 | −0.0203977 | ||||||||
\(495\) | −8.90352 | −0.400183 | ||||||||
\(496\) | −4.11848 | −0.184925 | ||||||||
\(497\) | 6.95099 | 0.311795 | ||||||||
\(498\) | 15.4112 | 0.690591 | ||||||||
\(499\) | 12.0858 | 0.541033 | 0.270516 | − | 0.962715i | \(-0.412806\pi\) | ||||
0.270516 | + | 0.962715i | \(0.412806\pi\) | |||||||
\(500\) | −17.2754 | −0.772578 | ||||||||
\(501\) | 38.9853 | 1.74173 | ||||||||
\(502\) | −1.97249 | −0.0880366 | ||||||||
\(503\) | −25.2036 | −1.12377 | −0.561887 | − | 0.827214i | \(-0.689924\pi\) | ||||
−0.561887 | + | 0.827214i | \(0.689924\pi\) | |||||||
\(504\) | 1.04802 | 0.0466823 | ||||||||
\(505\) | 42.5372 | 1.89288 | ||||||||
\(506\) | −3.78817 | −0.168405 | ||||||||
\(507\) | −24.7096 | −1.09739 | ||||||||
\(508\) | 7.83989 | 0.347839 | ||||||||
\(509\) | 22.6801 | 1.00528 | 0.502639 | − | 0.864496i | \(-0.332362\pi\) | ||||
0.502639 | + | 0.864496i | \(0.332362\pi\) | |||||||
\(510\) | 39.9945 | 1.77099 | ||||||||
\(511\) | −0.127106 | −0.00562284 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 25.0356 | 1.10535 | ||||||||
\(514\) | 25.3693 | 1.11899 | ||||||||
\(515\) | 21.2900 | 0.938150 | ||||||||
\(516\) | −3.86415 | −0.170110 | ||||||||
\(517\) | 41.4870 | 1.82459 | ||||||||
\(518\) | −12.1241 | −0.532702 | ||||||||
\(519\) | 10.2427 | 0.449605 | ||||||||
\(520\) | −0.312894 | −0.0137213 | ||||||||
\(521\) | 41.6078 | 1.82287 | 0.911434 | − | 0.411445i | \(-0.134976\pi\) | ||||
0.911434 | + | 0.411445i | \(0.134976\pi\) | |||||||
\(522\) | −4.65796 | −0.203873 | ||||||||
\(523\) | −18.1236 | −0.792489 | −0.396244 | − | 0.918145i | \(-0.629687\pi\) | ||||
−0.396244 | + | 0.918145i | \(0.629687\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | 30.8117 | 1.34473 | ||||||||
\(526\) | −7.48012 | −0.326149 | ||||||||
\(527\) | 22.7212 | 0.989749 | ||||||||
\(528\) | 7.20406 | 0.313516 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 41.4252 | 1.79940 | ||||||||
\(531\) | 4.84526 | 0.210266 | ||||||||
\(532\) | −9.38860 | −0.407047 | ||||||||
\(533\) | −0.0453466 | −0.00196418 | ||||||||
\(534\) | 16.0286 | 0.693624 | ||||||||
\(535\) | 19.6557 | 0.849790 | ||||||||
\(536\) | 8.48643 | 0.366558 | ||||||||
\(537\) | 3.03195 | 0.130838 | ||||||||
\(538\) | 17.7556 | 0.765499 | ||||||||
\(539\) | −15.5721 | −0.670739 | ||||||||
\(540\) | 17.2787 | 0.743558 | ||||||||
\(541\) | 39.1108 | 1.68150 | 0.840752 | − | 0.541421i | \(-0.182113\pi\) | ||||
0.840752 | + | 0.541421i | \(0.182113\pi\) | |||||||
\(542\) | −17.8908 | −0.768476 | ||||||||
\(543\) | 12.3730 | 0.530974 | ||||||||
\(544\) | −5.51688 | −0.236534 | ||||||||
\(545\) | 14.3039 | 0.612714 | ||||||||
\(546\) | 0.265327 | 0.0113549 | ||||||||
\(547\) | −26.1251 | −1.11703 | −0.558515 | − | 0.829495i | \(-0.688629\pi\) | ||||
−0.558515 | + | 0.829495i | \(0.688629\pi\) | |||||||
\(548\) | 6.68048 | 0.285376 | ||||||||
\(549\) | 5.39819 | 0.230389 | ||||||||
\(550\) | 36.1080 | 1.53965 | ||||||||
\(551\) | 41.7281 | 1.77768 | ||||||||
\(552\) | −1.90172 | −0.0809428 | ||||||||
\(553\) | −22.2236 | −0.945042 | ||||||||
\(554\) | −8.98310 | −0.381655 | ||||||||
\(555\) | 51.7084 | 2.19490 | ||||||||
\(556\) | 4.62069 | 0.195961 | ||||||||
\(557\) | 16.4895 | 0.698683 | 0.349342 | − | 0.936995i | \(-0.386405\pi\) | ||||
0.349342 | + | 0.936995i | \(0.386405\pi\) | |||||||
\(558\) | −2.53928 | −0.107496 | ||||||||
\(559\) | −0.166780 | −0.00705406 | ||||||||
\(560\) | −6.47969 | −0.273817 | ||||||||
\(561\) | −39.7439 | −1.67799 | ||||||||
\(562\) | 26.4602 | 1.11615 | ||||||||
\(563\) | −18.2186 | −0.767821 | −0.383910 | − | 0.923370i | \(-0.625423\pi\) | ||||
−0.383910 | + | 0.923370i | \(0.625423\pi\) | |||||||
\(564\) | 20.8271 | 0.876981 | ||||||||
\(565\) | 66.5901 | 2.80147 | ||||||||
\(566\) | −12.7482 | −0.535848 | ||||||||
\(567\) | −17.7960 | −0.747361 | ||||||||
\(568\) | 4.08933 | 0.171585 | ||||||||
\(569\) | −13.2476 | −0.555368 | −0.277684 | − | 0.960672i | \(-0.589567\pi\) | ||||
−0.277684 | + | 0.960672i | \(0.589567\pi\) | |||||||
\(570\) | 40.0417 | 1.67716 | ||||||||
\(571\) | 16.5933 | 0.694408 | 0.347204 | − | 0.937790i | \(-0.387131\pi\) | ||||
0.347204 | + | 0.937790i | \(0.387131\pi\) | |||||||
\(572\) | 0.310934 | 0.0130008 | ||||||||
\(573\) | −39.1819 | −1.63685 | ||||||||
\(574\) | −0.939076 | −0.0391963 | ||||||||
\(575\) | −9.53177 | −0.397502 | ||||||||
\(576\) | 0.616557 | 0.0256899 | ||||||||
\(577\) | 12.2119 | 0.508390 | 0.254195 | − | 0.967153i | \(-0.418189\pi\) | ||||
0.254195 | + | 0.967153i | \(0.418189\pi\) | |||||||
\(578\) | 13.4359 | 0.558860 | ||||||||
\(579\) | 3.05577 | 0.126994 | ||||||||
\(580\) | 28.7993 | 1.19583 | ||||||||
\(581\) | 13.7747 | 0.571472 | ||||||||
\(582\) | −16.8295 | −0.697606 | ||||||||
\(583\) | −41.1656 | −1.70491 | ||||||||
\(584\) | −0.0747777 | −0.00309432 | ||||||||
\(585\) | −0.192917 | −0.00797614 | ||||||||
\(586\) | −20.2959 | −0.838416 | ||||||||
\(587\) | 20.2571 | 0.836101 | 0.418050 | − | 0.908424i | \(-0.362714\pi\) | ||||
0.418050 | + | 0.908424i | \(0.362714\pi\) | |||||||
\(588\) | −7.81746 | −0.322387 | ||||||||
\(589\) | 22.7480 | 0.937315 | ||||||||
\(590\) | −29.9574 | −1.23333 | ||||||||
\(591\) | 34.1025 | 1.40279 | ||||||||
\(592\) | −7.13271 | −0.293153 | ||||||||
\(593\) | 1.22700 | 0.0503870 | 0.0251935 | − | 0.999683i | \(-0.491980\pi\) | ||||
0.0251935 | + | 0.999683i | \(0.491980\pi\) | |||||||
\(594\) | −17.1705 | −0.704513 | ||||||||
\(595\) | 35.7476 | 1.46551 | ||||||||
\(596\) | 7.66899 | 0.314134 | ||||||||
\(597\) | −22.3958 | −0.916599 | ||||||||
\(598\) | −0.0820802 | −0.00335651 | ||||||||
\(599\) | −30.1500 | −1.23189 | −0.615947 | − | 0.787787i | \(-0.711227\pi\) | ||||
−0.615947 | + | 0.787787i | \(0.711227\pi\) | |||||||
\(600\) | 18.1268 | 0.740024 | ||||||||
\(601\) | 33.6219 | 1.37146 | 0.685732 | − | 0.727854i | \(-0.259482\pi\) | ||||
0.685732 | + | 0.727854i | \(0.259482\pi\) | |||||||
\(602\) | −3.45383 | −0.140768 | ||||||||
\(603\) | 5.23236 | 0.213078 | ||||||||
\(604\) | −15.1421 | −0.616125 | ||||||||
\(605\) | −12.7713 | −0.519227 | ||||||||
\(606\) | −21.2206 | −0.862027 | ||||||||
\(607\) | 14.6986 | 0.596596 | 0.298298 | − | 0.954473i | \(-0.403581\pi\) | ||||
0.298298 | + | 0.954473i | \(0.403581\pi\) | |||||||
\(608\) | −5.52339 | −0.224003 | ||||||||
\(609\) | −24.4211 | −0.989592 | ||||||||
\(610\) | −33.3760 | −1.35136 | ||||||||
\(611\) | 0.898919 | 0.0363664 | ||||||||
\(612\) | −3.40147 | −0.137496 | ||||||||
\(613\) | −45.8172 | −1.85054 | −0.925270 | − | 0.379309i | \(-0.876162\pi\) | ||||
−0.925270 | + | 0.379309i | \(0.876162\pi\) | |||||||
\(614\) | 18.9836 | 0.766115 | ||||||||
\(615\) | 4.00510 | 0.161501 | ||||||||
\(616\) | 6.43908 | 0.259438 | ||||||||
\(617\) | 41.5817 | 1.67402 | 0.837008 | − | 0.547191i | \(-0.184303\pi\) | ||||
0.837008 | + | 0.547191i | \(0.184303\pi\) | |||||||
\(618\) | −10.6210 | −0.427238 | ||||||||
\(619\) | 8.25007 | 0.331598 | 0.165799 | − | 0.986160i | \(-0.446980\pi\) | ||||
0.165799 | + | 0.986160i | \(0.446980\pi\) | |||||||
\(620\) | 15.6999 | 0.630522 | ||||||||
\(621\) | 4.53265 | 0.181889 | ||||||||
\(622\) | −12.9589 | −0.519606 | ||||||||
\(623\) | 14.3266 | 0.573981 | ||||||||
\(624\) | 0.156094 | 0.00624876 | ||||||||
\(625\) | 18.1958 | 0.727832 | ||||||||
\(626\) | −16.8440 | −0.673220 | ||||||||
\(627\) | −39.7908 | −1.58909 | ||||||||
\(628\) | −19.7962 | −0.789956 | ||||||||
\(629\) | 39.3503 | 1.56900 | ||||||||
\(630\) | −3.99509 | −0.159168 | ||||||||
\(631\) | −42.9920 | −1.71149 | −0.855743 | − | 0.517402i | \(-0.826899\pi\) | ||||
−0.855743 | + | 0.517402i | \(0.826899\pi\) | |||||||
\(632\) | −13.0743 | −0.520068 | ||||||||
\(633\) | 29.5929 | 1.17621 | ||||||||
\(634\) | −9.34656 | −0.371200 | ||||||||
\(635\) | −29.8861 | −1.18599 | ||||||||
\(636\) | −20.6658 | −0.819454 | ||||||||
\(637\) | −0.337409 | −0.0133686 | ||||||||
\(638\) | −28.6189 | −1.13303 | ||||||||
\(639\) | 2.52130 | 0.0997413 | ||||||||
\(640\) | −3.81206 | −0.150685 | ||||||||
\(641\) | −13.7923 | −0.544764 | −0.272382 | − | 0.962189i | \(-0.587811\pi\) | ||||
−0.272382 | + | 0.962189i | \(0.587811\pi\) | |||||||
\(642\) | −9.80566 | −0.386998 | ||||||||
\(643\) | 50.2295 | 1.98086 | 0.990429 | − | 0.138021i | \(-0.0440741\pi\) | ||||
0.990429 | + | 0.138021i | \(0.0440741\pi\) | |||||||
\(644\) | −1.69979 | −0.0669810 | ||||||||
\(645\) | 14.7304 | 0.580007 | ||||||||
\(646\) | 30.4719 | 1.19890 | ||||||||
\(647\) | 20.1171 | 0.790886 | 0.395443 | − | 0.918490i | \(-0.370591\pi\) | ||||
0.395443 | + | 0.918490i | \(0.370591\pi\) | |||||||
\(648\) | −10.4695 | −0.411282 | ||||||||
\(649\) | 29.7697 | 1.16856 | ||||||||
\(650\) | 0.782370 | 0.0306871 | ||||||||
\(651\) | −13.3131 | −0.521782 | ||||||||
\(652\) | −24.5017 | −0.959561 | ||||||||
\(653\) | −0.300068 | −0.0117426 | −0.00587128 | − | 0.999983i | \(-0.501869\pi\) | ||||
−0.00587128 | + | 0.999983i | \(0.501869\pi\) | |||||||
\(654\) | −7.13582 | −0.279033 | ||||||||
\(655\) | −3.81206 | −0.148949 | ||||||||
\(656\) | −0.552467 | −0.0215702 | ||||||||
\(657\) | −0.0461047 | −0.00179871 | ||||||||
\(658\) | 18.6156 | 0.725711 | ||||||||
\(659\) | −6.02316 | −0.234629 | −0.117314 | − | 0.993095i | \(-0.537429\pi\) | ||||
−0.117314 | + | 0.993095i | \(0.537429\pi\) | |||||||
\(660\) | −27.4623 | −1.06897 | ||||||||
\(661\) | −37.6291 | −1.46360 | −0.731802 | − | 0.681517i | \(-0.761320\pi\) | ||||
−0.731802 | + | 0.681517i | \(0.761320\pi\) | |||||||
\(662\) | −16.0184 | −0.622575 | ||||||||
\(663\) | −0.861151 | −0.0334443 | ||||||||
\(664\) | 8.10379 | 0.314488 | ||||||||
\(665\) | 35.7899 | 1.38787 | ||||||||
\(666\) | −4.39772 | −0.170408 | ||||||||
\(667\) | 7.55480 | 0.292523 | ||||||||
\(668\) | 20.5000 | 0.793167 | ||||||||
\(669\) | −5.75793 | −0.222614 | ||||||||
\(670\) | −32.3507 | −1.24982 | ||||||||
\(671\) | 33.1669 | 1.28039 | ||||||||
\(672\) | 3.23253 | 0.124697 | ||||||||
\(673\) | 41.8784 | 1.61429 | 0.807146 | − | 0.590352i | \(-0.201011\pi\) | ||||
0.807146 | + | 0.590352i | \(0.201011\pi\) | |||||||
\(674\) | 33.5475 | 1.29220 | ||||||||
\(675\) | −43.2042 | −1.66293 | ||||||||
\(676\) | −12.9933 | −0.499741 | ||||||||
\(677\) | −45.9654 | −1.76659 | −0.883296 | − | 0.468815i | \(-0.844681\pi\) | ||||
−0.883296 | + | 0.468815i | \(0.844681\pi\) | |||||||
\(678\) | −33.2199 | −1.27580 | ||||||||
\(679\) | −15.0424 | −0.577276 | ||||||||
\(680\) | 21.0306 | 0.806488 | ||||||||
\(681\) | 13.7260 | 0.525982 | ||||||||
\(682\) | −15.6015 | −0.597413 | ||||||||
\(683\) | 11.9940 | 0.458936 | 0.229468 | − | 0.973316i | \(-0.426301\pi\) | ||||
0.229468 | + | 0.973316i | \(0.426301\pi\) | |||||||
\(684\) | −3.40549 | −0.130212 | ||||||||
\(685\) | −25.4664 | −0.973019 | ||||||||
\(686\) | −18.8859 | −0.721066 | ||||||||
\(687\) | −14.3413 | −0.547155 | ||||||||
\(688\) | −2.03192 | −0.0774662 | ||||||||
\(689\) | −0.891957 | −0.0339808 | ||||||||
\(690\) | 7.24948 | 0.275983 | ||||||||
\(691\) | 0.814765 | 0.0309951 | 0.0154976 | − | 0.999880i | \(-0.495067\pi\) | ||||
0.0154976 | + | 0.999880i | \(0.495067\pi\) | |||||||
\(692\) | 5.38601 | 0.204745 | ||||||||
\(693\) | 3.97006 | 0.150810 | ||||||||
\(694\) | −7.08623 | −0.268990 | ||||||||
\(695\) | −17.6143 | −0.668150 | ||||||||
\(696\) | −14.3671 | −0.544585 | ||||||||
\(697\) | 3.04789 | 0.115447 | ||||||||
\(698\) | 22.0543 | 0.834767 | ||||||||
\(699\) | −29.1300 | −1.10180 | ||||||||
\(700\) | 16.2020 | 0.612377 | ||||||||
\(701\) | 1.72387 | 0.0651098 | 0.0325549 | − | 0.999470i | \(-0.489636\pi\) | ||||
0.0325549 | + | 0.999470i | \(0.489636\pi\) | |||||||
\(702\) | −0.372041 | −0.0140418 | ||||||||
\(703\) | 39.3968 | 1.48588 | ||||||||
\(704\) | 3.78817 | 0.142772 | ||||||||
\(705\) | −79.3943 | −2.99016 | ||||||||
\(706\) | −8.76815 | −0.329994 | ||||||||
\(707\) | −18.9672 | −0.713336 | ||||||||
\(708\) | 14.9449 | 0.561662 | ||||||||
\(709\) | −23.4873 | −0.882084 | −0.441042 | − | 0.897486i | \(-0.645391\pi\) | ||||
−0.441042 | + | 0.897486i | \(0.645391\pi\) | |||||||
\(710\) | −15.5888 | −0.585036 | ||||||||
\(711\) | −8.06106 | −0.302313 | ||||||||
\(712\) | 8.42844 | 0.315869 | ||||||||
\(713\) | 4.11848 | 0.154238 | ||||||||
\(714\) | −17.8335 | −0.667400 | ||||||||
\(715\) | −1.18530 | −0.0443276 | ||||||||
\(716\) | 1.59431 | 0.0595823 | ||||||||
\(717\) | 8.25003 | 0.308103 | ||||||||
\(718\) | −11.0981 | −0.414177 | ||||||||
\(719\) | 23.5350 | 0.877709 | 0.438855 | − | 0.898558i | \(-0.355384\pi\) | ||||
0.438855 | + | 0.898558i | \(0.355384\pi\) | |||||||
\(720\) | −2.35035 | −0.0875923 | ||||||||
\(721\) | −9.49317 | −0.353544 | ||||||||
\(722\) | 11.5079 | 0.428279 | ||||||||
\(723\) | 13.3241 | 0.495528 | ||||||||
\(724\) | 6.50617 | 0.241800 | ||||||||
\(725\) | −72.0106 | −2.67441 | ||||||||
\(726\) | 6.37123 | 0.236458 | ||||||||
\(727\) | −24.0772 | −0.892973 | −0.446486 | − | 0.894790i | \(-0.647325\pi\) | ||||
−0.446486 | + | 0.894790i | \(0.647325\pi\) | |||||||
\(728\) | 0.139519 | 0.00517092 | ||||||||
\(729\) | 19.4045 | 0.718686 | ||||||||
\(730\) | 0.285057 | 0.0105504 | ||||||||
\(731\) | 11.2098 | 0.414611 | ||||||||
\(732\) | 16.6503 | 0.615414 | ||||||||
\(733\) | 32.1388 | 1.18707 | 0.593536 | − | 0.804807i | \(-0.297731\pi\) | ||||
0.593536 | + | 0.804807i | \(0.297731\pi\) | |||||||
\(734\) | 11.0724 | 0.408688 | ||||||||
\(735\) | 29.8006 | 1.09921 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 32.1480 | 1.18419 | ||||||||
\(738\) | −0.340627 | −0.0125386 | ||||||||
\(739\) | 9.88353 | 0.363572 | 0.181786 | − | 0.983338i | \(-0.441812\pi\) | ||||
0.181786 | + | 0.983338i | \(0.441812\pi\) | |||||||
\(740\) | 27.1903 | 0.999535 | ||||||||
\(741\) | −0.862169 | −0.0316726 | ||||||||
\(742\) | −18.4714 | −0.678107 | ||||||||
\(743\) | 9.05882 | 0.332336 | 0.166168 | − | 0.986097i | \(-0.446861\pi\) | ||||
0.166168 | + | 0.986097i | \(0.446861\pi\) | |||||||
\(744\) | −7.83222 | −0.287143 | ||||||||
\(745\) | −29.2346 | −1.07107 | ||||||||
\(746\) | −8.10125 | −0.296608 | ||||||||
\(747\) | 4.99644 | 0.182810 | ||||||||
\(748\) | −20.8989 | −0.764138 | ||||||||
\(749\) | −8.76443 | −0.320245 | ||||||||
\(750\) | −32.8530 | −1.19962 | ||||||||
\(751\) | −44.0372 | −1.60694 | −0.803470 | − | 0.595345i | \(-0.797015\pi\) | ||||
−0.803470 | + | 0.595345i | \(0.797015\pi\) | |||||||
\(752\) | 10.9517 | 0.399368 | ||||||||
\(753\) | −3.75114 | −0.136699 | ||||||||
\(754\) | −0.620099 | −0.0225827 | ||||||||
\(755\) | 57.7227 | 2.10074 | ||||||||
\(756\) | −7.70455 | −0.280212 | ||||||||
\(757\) | −8.98333 | −0.326505 | −0.163252 | − | 0.986584i | \(-0.552198\pi\) | ||||
−0.163252 | + | 0.986584i | \(0.552198\pi\) | |||||||
\(758\) | 2.20636 | 0.0801387 | ||||||||
\(759\) | −7.20406 | −0.261491 | ||||||||
\(760\) | 21.0555 | 0.763763 | ||||||||
\(761\) | −48.8188 | −1.76968 | −0.884841 | − | 0.465893i | \(-0.845733\pi\) | ||||
−0.884841 | + | 0.465893i | \(0.845733\pi\) | |||||||
\(762\) | 14.9093 | 0.540107 | ||||||||
\(763\) | −6.37810 | −0.230903 | ||||||||
\(764\) | −20.6033 | −0.745402 | ||||||||
\(765\) | 12.9666 | 0.468808 | ||||||||
\(766\) | −23.0649 | −0.833369 | ||||||||
\(767\) | 0.645034 | 0.0232908 | ||||||||
\(768\) | 1.90172 | 0.0686226 | ||||||||
\(769\) | −13.4763 | −0.485967 | −0.242984 | − | 0.970030i | \(-0.578126\pi\) | ||||
−0.242984 | + | 0.970030i | \(0.578126\pi\) | |||||||
\(770\) | −24.5462 | −0.884582 | ||||||||
\(771\) | 48.2453 | 1.73751 | ||||||||
\(772\) | 1.60684 | 0.0578315 | ||||||||
\(773\) | −0.981471 | −0.0353011 | −0.0176505 | − | 0.999844i | \(-0.505619\pi\) | ||||
−0.0176505 | + | 0.999844i | \(0.505619\pi\) | |||||||
\(774\) | −1.25279 | −0.0450307 | ||||||||
\(775\) | −39.2564 | −1.41013 | ||||||||
\(776\) | −8.84960 | −0.317682 | ||||||||
\(777\) | −23.0567 | −0.827154 | ||||||||
\(778\) | 3.60124 | 0.129111 | ||||||||
\(779\) | 3.05149 | 0.109331 | ||||||||
\(780\) | −0.595039 | −0.0213058 | ||||||||
\(781\) | 15.4911 | 0.554315 | ||||||||
\(782\) | 5.51688 | 0.197283 | ||||||||
\(783\) | 34.2433 | 1.22375 | ||||||||
\(784\) | −4.11072 | −0.146812 | ||||||||
\(785\) | 75.4644 | 2.69344 | ||||||||
\(786\) | 1.90172 | 0.0678323 | ||||||||
\(787\) | −31.0430 | −1.10656 | −0.553281 | − | 0.832995i | \(-0.686624\pi\) | ||||
−0.553281 | + | 0.832995i | \(0.686624\pi\) | |||||||
\(788\) | 17.9324 | 0.638815 | ||||||||
\(789\) | −14.2251 | −0.506428 | ||||||||
\(790\) | 49.8400 | 1.77323 | ||||||||
\(791\) | −29.6924 | −1.05574 | ||||||||
\(792\) | 2.33562 | 0.0829927 | ||||||||
\(793\) | 0.718644 | 0.0255198 | ||||||||
\(794\) | 24.0232 | 0.852551 | ||||||||
\(795\) | 78.7793 | 2.79401 | ||||||||
\(796\) | −11.7766 | −0.417410 | ||||||||
\(797\) | −4.27674 | −0.151490 | −0.0757450 | − | 0.997127i | \(-0.524133\pi\) | ||||
−0.0757450 | + | 0.997127i | \(0.524133\pi\) | |||||||
\(798\) | −17.8545 | −0.632043 | ||||||||
\(799\) | −60.4193 | −2.13748 | ||||||||
\(800\) | 9.53177 | 0.336999 | ||||||||
\(801\) | 5.19661 | 0.183613 | ||||||||
\(802\) | −12.1290 | −0.428291 | ||||||||
\(803\) | −0.283271 | −0.00999640 | ||||||||
\(804\) | 16.1388 | 0.569173 | ||||||||
\(805\) | 6.47969 | 0.228379 | ||||||||
\(806\) | −0.338046 | −0.0119072 | ||||||||
\(807\) | 33.7663 | 1.18863 | ||||||||
\(808\) | −11.1586 | −0.392558 | ||||||||
\(809\) | 7.29946 | 0.256635 | 0.128318 | − | 0.991733i | \(-0.459042\pi\) | ||||
0.128318 | + | 0.991733i | \(0.459042\pi\) | |||||||
\(810\) | 39.9104 | 1.40231 | ||||||||
\(811\) | 18.9530 | 0.665530 | 0.332765 | − | 0.943010i | \(-0.392018\pi\) | ||||
0.332765 | + | 0.943010i | \(0.392018\pi\) | |||||||
\(812\) | −12.8415 | −0.450650 | ||||||||
\(813\) | −34.0234 | −1.19325 | ||||||||
\(814\) | −27.0199 | −0.947048 | ||||||||
\(815\) | 93.4019 | 3.27173 | ||||||||
\(816\) | −10.4916 | −0.367279 | ||||||||
\(817\) | 11.2231 | 0.392646 | ||||||||
\(818\) | −18.2638 | −0.638577 | ||||||||
\(819\) | 0.0860213 | 0.00300583 | ||||||||
\(820\) | 2.10603 | 0.0735459 | ||||||||
\(821\) | −6.97547 | −0.243446 | −0.121723 | − | 0.992564i | \(-0.538842\pi\) | ||||
−0.121723 | + | 0.992564i | \(0.538842\pi\) | |||||||
\(822\) | 12.7044 | 0.443118 | ||||||||
\(823\) | −13.0591 | −0.455211 | −0.227606 | − | 0.973753i | \(-0.573090\pi\) | ||||
−0.227606 | + | 0.973753i | \(0.573090\pi\) | |||||||
\(824\) | −5.58492 | −0.194560 | ||||||||
\(825\) | 68.6674 | 2.39069 | ||||||||
\(826\) | 13.3579 | 0.464782 | ||||||||
\(827\) | 24.1786 | 0.840771 | 0.420386 | − | 0.907346i | \(-0.361895\pi\) | ||||
0.420386 | + | 0.907346i | \(0.361895\pi\) | |||||||
\(828\) | −0.616557 | −0.0214268 | ||||||||
\(829\) | −47.8361 | −1.66142 | −0.830709 | − | 0.556707i | \(-0.812065\pi\) | ||||
−0.830709 | + | 0.556707i | \(0.812065\pi\) | |||||||
\(830\) | −30.8921 | −1.07228 | ||||||||
\(831\) | −17.0834 | −0.592616 | ||||||||
\(832\) | 0.0820802 | 0.00284562 | ||||||||
\(833\) | 22.6783 | 0.785758 | ||||||||
\(834\) | 8.78728 | 0.304279 | ||||||||
\(835\) | −78.1470 | −2.70439 | ||||||||
\(836\) | −20.9236 | −0.723656 | ||||||||
\(837\) | 18.6676 | 0.645248 | ||||||||
\(838\) | 33.0384 | 1.14129 | ||||||||
\(839\) | 26.9570 | 0.930659 | 0.465330 | − | 0.885137i | \(-0.345936\pi\) | ||||
0.465330 | + | 0.885137i | \(0.345936\pi\) | |||||||
\(840\) | −12.3226 | −0.425169 | ||||||||
\(841\) | 28.0749 | 0.968101 | ||||||||
\(842\) | 33.6532 | 1.15977 | ||||||||
\(843\) | 50.3200 | 1.73311 | ||||||||
\(844\) | 15.5611 | 0.535635 | ||||||||
\(845\) | 49.5310 | 1.70392 | ||||||||
\(846\) | 6.75235 | 0.232151 | ||||||||
\(847\) | 5.69469 | 0.195672 | ||||||||
\(848\) | −10.8669 | −0.373171 | ||||||||
\(849\) | −24.2436 | −0.832038 | ||||||||
\(850\) | −52.5856 | −1.80367 | ||||||||
\(851\) | 7.13271 | 0.244506 | ||||||||
\(852\) | 7.77678 | 0.266428 | ||||||||
\(853\) | 47.7188 | 1.63386 | 0.816931 | − | 0.576736i | \(-0.195674\pi\) | ||||
0.816931 | + | 0.576736i | \(0.195674\pi\) | |||||||
\(854\) | 14.8823 | 0.509262 | ||||||||
\(855\) | 12.9819 | 0.443972 | ||||||||
\(856\) | −5.15619 | −0.176235 | ||||||||
\(857\) | 25.3827 | 0.867057 | 0.433528 | − | 0.901140i | \(-0.357268\pi\) | ||||
0.433528 | + | 0.901140i | \(0.357268\pi\) | |||||||
\(858\) | 0.591311 | 0.0201870 | ||||||||
\(859\) | 32.2608 | 1.10072 | 0.550362 | − | 0.834926i | \(-0.314490\pi\) | ||||
0.550362 | + | 0.834926i | \(0.314490\pi\) | |||||||
\(860\) | 7.74579 | 0.264129 | ||||||||
\(861\) | −1.78586 | −0.0608621 | ||||||||
\(862\) | −11.5779 | −0.394346 | ||||||||
\(863\) | 3.87368 | 0.131862 | 0.0659308 | − | 0.997824i | \(-0.478998\pi\) | ||||
0.0659308 | + | 0.997824i | \(0.478998\pi\) | |||||||
\(864\) | −4.53265 | −0.154204 | ||||||||
\(865\) | −20.5318 | −0.698101 | ||||||||
\(866\) | 2.98800 | 0.101536 | ||||||||
\(867\) | 25.5514 | 0.867772 | ||||||||
\(868\) | −7.00054 | −0.237614 | ||||||||
\(869\) | −49.5277 | −1.68011 | ||||||||
\(870\) | 54.7683 | 1.85682 | ||||||||
\(871\) | 0.696568 | 0.0236023 | ||||||||
\(872\) | −3.75229 | −0.127069 | ||||||||
\(873\) | −5.45628 | −0.184667 | ||||||||
\(874\) | 5.52339 | 0.186832 | ||||||||
\(875\) | −29.3645 | −0.992700 | ||||||||
\(876\) | −0.142207 | −0.00480471 | ||||||||
\(877\) | −15.0557 | −0.508394 | −0.254197 | − | 0.967152i | \(-0.581811\pi\) | ||||
−0.254197 | + | 0.967152i | \(0.581811\pi\) | |||||||
\(878\) | −23.7476 | −0.801444 | ||||||||
\(879\) | −38.5972 | −1.30185 | ||||||||
\(880\) | −14.4407 | −0.486797 | ||||||||
\(881\) | 27.1079 | 0.913289 | 0.456645 | − | 0.889649i | \(-0.349051\pi\) | ||||
0.456645 | + | 0.889649i | \(0.349051\pi\) | |||||||
\(882\) | −2.53449 | −0.0853408 | ||||||||
\(883\) | −2.43104 | −0.0818111 | −0.0409056 | − | 0.999163i | \(-0.513024\pi\) | ||||
−0.0409056 | + | 0.999163i | \(0.513024\pi\) | |||||||
\(884\) | −0.452826 | −0.0152302 | ||||||||
\(885\) | −56.9707 | −1.91505 | ||||||||
\(886\) | −18.6889 | −0.627865 | ||||||||
\(887\) | 3.03543 | 0.101920 | 0.0509598 | − | 0.998701i | \(-0.483772\pi\) | ||||
0.0509598 | + | 0.998701i | \(0.483772\pi\) | |||||||
\(888\) | −13.5644 | −0.455193 | ||||||||
\(889\) | 13.3261 | 0.446945 | ||||||||
\(890\) | −32.1297 | −1.07699 | ||||||||
\(891\) | −39.6604 | −1.32867 | ||||||||
\(892\) | −3.02774 | −0.101376 | ||||||||
\(893\) | −60.4906 | −2.02424 | ||||||||
\(894\) | 14.5843 | 0.487772 | ||||||||
\(895\) | −6.07761 | −0.203152 | ||||||||
\(896\) | 1.69979 | 0.0567859 | ||||||||
\(897\) | −0.156094 | −0.00521183 | ||||||||
\(898\) | 0.368707 | 0.0123039 | ||||||||
\(899\) | 31.1143 | 1.03772 | ||||||||
\(900\) | 5.87688 | 0.195896 | ||||||||
\(901\) | 59.9513 | 1.99727 | ||||||||
\(902\) | −2.09284 | −0.0696839 | ||||||||
\(903\) | −6.56824 | −0.218577 | ||||||||
\(904\) | −17.4683 | −0.580987 | ||||||||
\(905\) | −24.8019 | −0.824443 | ||||||||
\(906\) | −28.7962 | −0.956690 | ||||||||
\(907\) | −24.0127 | −0.797330 | −0.398665 | − | 0.917097i | \(-0.630526\pi\) | ||||
−0.398665 | + | 0.917097i | \(0.630526\pi\) | |||||||
\(908\) | 7.21767 | 0.239527 | ||||||||
\(909\) | −6.87991 | −0.228192 | ||||||||
\(910\) | −0.531854 | −0.0176308 | ||||||||
\(911\) | −19.7543 | −0.654491 | −0.327245 | − | 0.944939i | \(-0.606120\pi\) | ||||
−0.327245 | + | 0.944939i | \(0.606120\pi\) | |||||||
\(912\) | −10.5040 | −0.347821 | ||||||||
\(913\) | 30.6985 | 1.01597 | ||||||||
\(914\) | 10.4175 | 0.344581 | ||||||||
\(915\) | −63.4720 | −2.09832 | ||||||||
\(916\) | −7.54120 | −0.249168 | ||||||||
\(917\) | 1.69979 | 0.0561319 | ||||||||
\(918\) | 25.0061 | 0.825324 | ||||||||
\(919\) | 50.2839 | 1.65871 | 0.829356 | − | 0.558720i | \(-0.188707\pi\) | ||||
0.829356 | + | 0.558720i | \(0.188707\pi\) | |||||||
\(920\) | 3.81206 | 0.125680 | ||||||||
\(921\) | 36.1016 | 1.18959 | ||||||||
\(922\) | 16.8127 | 0.553695 | ||||||||
\(923\) | 0.335653 | 0.0110482 | ||||||||
\(924\) | 12.2454 | 0.402843 | ||||||||
\(925\) | −67.9874 | −2.23541 | ||||||||
\(926\) | 26.7192 | 0.878048 | ||||||||
\(927\) | −3.44342 | −0.113097 | ||||||||
\(928\) | −7.55480 | −0.247998 | ||||||||
\(929\) | −49.4977 | −1.62397 | −0.811983 | − | 0.583681i | \(-0.801612\pi\) | ||||
−0.811983 | + | 0.583681i | \(0.801612\pi\) | |||||||
\(930\) | 29.8569 | 0.979045 | ||||||||
\(931\) | 22.7051 | 0.744131 | ||||||||
\(932\) | −15.3177 | −0.501747 | ||||||||
\(933\) | −24.6443 | −0.806819 | ||||||||
\(934\) | 40.8350 | 1.33616 | ||||||||
\(935\) | 79.6676 | 2.60541 | ||||||||
\(936\) | 0.0506071 | 0.00165414 | ||||||||
\(937\) | −34.1441 | −1.11544 | −0.557719 | − | 0.830030i | \(-0.688323\pi\) | ||||
−0.557719 | + | 0.830030i | \(0.688323\pi\) | |||||||
\(938\) | 14.4251 | 0.470997 | ||||||||
\(939\) | −32.0326 | −1.04534 | ||||||||
\(940\) | −41.7486 | −1.36169 | ||||||||
\(941\) | −39.0998 | −1.27462 | −0.637309 | − | 0.770609i | \(-0.719952\pi\) | ||||
−0.637309 | + | 0.770609i | \(0.719952\pi\) | |||||||
\(942\) | −37.6470 | −1.22661 | ||||||||
\(943\) | 0.552467 | 0.0179908 | ||||||||
\(944\) | 7.85858 | 0.255775 | ||||||||
\(945\) | 29.3702 | 0.955412 | ||||||||
\(946\) | −7.69726 | −0.250259 | ||||||||
\(947\) | 0.739702 | 0.0240371 | 0.0120185 | − | 0.999928i | \(-0.496174\pi\) | ||||
0.0120185 | + | 0.999928i | \(0.496174\pi\) | |||||||
\(948\) | −24.8638 | −0.807537 | ||||||||
\(949\) | −0.00613777 | −0.000199240 0 | ||||||||
\(950\) | −52.6477 | −1.70812 | ||||||||
\(951\) | −17.7746 | −0.576381 | ||||||||
\(952\) | −9.37752 | −0.303927 | ||||||||
\(953\) | 3.22958 | 0.104616 | 0.0523081 | − | 0.998631i | \(-0.483342\pi\) | ||||
0.0523081 | + | 0.998631i | \(0.483342\pi\) | |||||||
\(954\) | −6.70005 | −0.216922 | ||||||||
\(955\) | 78.5411 | 2.54153 | ||||||||
\(956\) | 4.33818 | 0.140307 | ||||||||
\(957\) | −54.4252 | −1.75932 | ||||||||
\(958\) | 21.7109 | 0.701448 | ||||||||
\(959\) | 11.3554 | 0.366685 | ||||||||
\(960\) | −7.24948 | −0.233976 | ||||||||
\(961\) | −14.0381 | −0.452842 | ||||||||
\(962\) | −0.585454 | −0.0188758 | ||||||||
\(963\) | −3.17908 | −0.102445 | ||||||||
\(964\) | 7.00632 | 0.225658 | ||||||||
\(965\) | −6.12537 | −0.197183 | ||||||||
\(966\) | −3.23253 | −0.104005 | ||||||||
\(967\) | −48.5822 | −1.56230 | −0.781150 | − | 0.624344i | \(-0.785366\pi\) | ||||
−0.781150 | + | 0.624344i | \(0.785366\pi\) | |||||||
\(968\) | 3.35024 | 0.107681 | ||||||||
\(969\) | 57.9491 | 1.86159 | ||||||||
\(970\) | 33.7352 | 1.08317 | ||||||||
\(971\) | −42.7600 | −1.37223 | −0.686117 | − | 0.727491i | \(-0.740686\pi\) | ||||
−0.686117 | + | 0.727491i | \(0.740686\pi\) | |||||||
\(972\) | −6.31220 | −0.202464 | ||||||||
\(973\) | 7.85419 | 0.251794 | ||||||||
\(974\) | 11.7332 | 0.375958 | ||||||||
\(975\) | 1.48785 | 0.0476494 | ||||||||
\(976\) | 8.75538 | 0.280253 | ||||||||
\(977\) | 24.6400 | 0.788302 | 0.394151 | − | 0.919046i | \(-0.371039\pi\) | ||||
0.394151 | + | 0.919046i | \(0.371039\pi\) | |||||||
\(978\) | −46.5955 | −1.48996 | ||||||||
\(979\) | 31.9284 | 1.02043 | ||||||||
\(980\) | 15.6703 | 0.500570 | ||||||||
\(981\) | −2.31350 | −0.0738644 | ||||||||
\(982\) | 6.44619 | 0.205706 | ||||||||
\(983\) | 12.9428 | 0.412811 | 0.206406 | − | 0.978467i | \(-0.433823\pi\) | ||||
0.206406 | + | 0.978467i | \(0.433823\pi\) | |||||||
\(984\) | −1.05064 | −0.0334932 | ||||||||
\(985\) | −68.3593 | −2.17811 | ||||||||
\(986\) | 41.6789 | 1.32733 | ||||||||
\(987\) | 35.4017 | 1.12685 | ||||||||
\(988\) | −0.453361 | −0.0144233 | ||||||||
\(989\) | 2.03192 | 0.0646113 | ||||||||
\(990\) | −8.90352 | −0.282972 | ||||||||
\(991\) | 43.3100 | 1.37579 | 0.687894 | − | 0.725811i | \(-0.258535\pi\) | ||||
0.687894 | + | 0.725811i | \(0.258535\pi\) | |||||||
\(992\) | −4.11848 | −0.130762 | ||||||||
\(993\) | −30.4627 | −0.966704 | ||||||||
\(994\) | 6.95099 | 0.220472 | ||||||||
\(995\) | 44.8930 | 1.42320 | ||||||||
\(996\) | 15.4112 | 0.488322 | ||||||||
\(997\) | −17.5067 | −0.554444 | −0.277222 | − | 0.960806i | \(-0.589414\pi\) | ||||
−0.277222 | + | 0.960806i | \(0.589414\pi\) | |||||||
\(998\) | 12.0858 | 0.382568 | ||||||||
\(999\) | 32.3301 | 1.02288 |
(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 | 6026.2.a.g.1.18 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.g.1.18 | ✓ | 21 | 1.1 | even | 1 | trivial |