Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.306328 | −0.216607 | −0.108303 | − | 0.994118i | \(-0.534542\pi\) | ||||
−0.108303 | + | 0.994118i | \(0.534542\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.90616 | −0.953081 | ||||||||
\(5\) | −2.43700 | −1.08986 | −0.544931 | − | 0.838481i | \(-0.683444\pi\) | ||||
−0.544931 | + | 0.838481i | \(0.683444\pi\) | |||||||
\(6\) | −0.306328 | −0.125058 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.19657 | 0.423051 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.746523 | 0.236071 | ||||||||
\(11\) | 2.36218 | 0.712224 | 0.356112 | − | 0.934443i | \(-0.384102\pi\) | ||||
0.356112 | + | 0.934443i | \(0.384102\pi\) | |||||||
\(12\) | −1.90616 | −0.550262 | ||||||||
\(13\) | 2.69040 | 0.746183 | 0.373091 | − | 0.927795i | \(-0.378298\pi\) | ||||
0.373091 | + | 0.927795i | \(0.378298\pi\) | |||||||
\(14\) | 0.306328 | 0.0818697 | ||||||||
\(15\) | −2.43700 | −0.629232 | ||||||||
\(16\) | 3.44578 | 0.861446 | ||||||||
\(17\) | 0.171352 | 0.0415590 | 0.0207795 | − | 0.999784i | \(-0.493385\pi\) | ||||
0.0207795 | + | 0.999784i | \(0.493385\pi\) | |||||||
\(18\) | −0.306328 | −0.0722023 | ||||||||
\(19\) | 2.51953 | 0.578019 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(20\) | 4.64533 | 1.03873 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −0.723603 | −0.154273 | ||||||||
\(23\) | 2.11753 | 0.441535 | 0.220767 | − | 0.975327i | \(-0.429144\pi\) | ||||
0.220767 | + | 0.975327i | \(0.429144\pi\) | |||||||
\(24\) | 1.19657 | 0.244248 | ||||||||
\(25\) | 0.938987 | 0.187797 | ||||||||
\(26\) | −0.824146 | −0.161628 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.90616 | 0.360231 | ||||||||
\(29\) | 7.92009 | 1.47072 | 0.735362 | − | 0.677674i | \(-0.237012\pi\) | ||||
0.735362 | + | 0.677674i | \(0.237012\pi\) | |||||||
\(30\) | 0.746523 | 0.136296 | ||||||||
\(31\) | 3.29881 | 0.592484 | 0.296242 | − | 0.955113i | \(-0.404266\pi\) | ||||
0.296242 | + | 0.955113i | \(0.404266\pi\) | |||||||
\(32\) | −3.44868 | −0.609646 | ||||||||
\(33\) | 2.36218 | 0.411203 | ||||||||
\(34\) | −0.0524900 | −0.00900195 | ||||||||
\(35\) | 2.43700 | 0.411929 | ||||||||
\(36\) | −1.90616 | −0.317694 | ||||||||
\(37\) | −2.37894 | −0.391096 | −0.195548 | − | 0.980694i | \(-0.562648\pi\) | ||||
−0.195548 | + | 0.980694i | \(0.562648\pi\) | |||||||
\(38\) | −0.771802 | −0.125203 | ||||||||
\(39\) | 2.69040 | 0.430809 | ||||||||
\(40\) | −2.91604 | −0.461067 | ||||||||
\(41\) | 3.38192 | 0.528167 | 0.264083 | − | 0.964500i | \(-0.414931\pi\) | ||||
0.264083 | + | 0.964500i | \(0.414931\pi\) | |||||||
\(42\) | 0.306328 | 0.0472675 | ||||||||
\(43\) | 2.22643 | 0.339528 | 0.169764 | − | 0.985485i | \(-0.445700\pi\) | ||||
0.169764 | + | 0.985485i | \(0.445700\pi\) | |||||||
\(44\) | −4.50270 | −0.678808 | ||||||||
\(45\) | −2.43700 | −0.363287 | ||||||||
\(46\) | −0.648658 | −0.0956394 | ||||||||
\(47\) | −0.738129 | −0.107667 | −0.0538336 | − | 0.998550i | \(-0.517144\pi\) | ||||
−0.0538336 | + | 0.998550i | \(0.517144\pi\) | |||||||
\(48\) | 3.44578 | 0.497356 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.287638 | −0.0406782 | ||||||||
\(51\) | 0.171352 | 0.0239941 | ||||||||
\(52\) | −5.12834 | −0.711173 | ||||||||
\(53\) | −9.97324 | −1.36993 | −0.684965 | − | 0.728576i | \(-0.740183\pi\) | ||||
−0.684965 | + | 0.728576i | \(0.740183\pi\) | |||||||
\(54\) | −0.306328 | −0.0416860 | ||||||||
\(55\) | −5.75664 | −0.776226 | ||||||||
\(56\) | −1.19657 | −0.159898 | ||||||||
\(57\) | 2.51953 | 0.333720 | ||||||||
\(58\) | −2.42615 | −0.318569 | ||||||||
\(59\) | −13.5075 | −1.75852 | −0.879261 | − | 0.476340i | \(-0.841963\pi\) | ||||
−0.879261 | + | 0.476340i | \(0.841963\pi\) | |||||||
\(60\) | 4.64533 | 0.599709 | ||||||||
\(61\) | −4.21286 | −0.539401 | −0.269700 | − | 0.962944i | \(-0.586925\pi\) | ||||
−0.269700 | + | 0.962944i | \(0.586925\pi\) | |||||||
\(62\) | −1.01052 | −0.128336 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −5.83514 | −0.729392 | ||||||||
\(65\) | −6.55652 | −0.813236 | ||||||||
\(66\) | −0.723603 | −0.0890693 | ||||||||
\(67\) | −10.6261 | −1.29819 | −0.649093 | − | 0.760709i | \(-0.724851\pi\) | ||||
−0.649093 | + | 0.760709i | \(0.724851\pi\) | |||||||
\(68\) | −0.326625 | −0.0396091 | ||||||||
\(69\) | 2.11753 | 0.254920 | ||||||||
\(70\) | −0.746523 | −0.0892266 | ||||||||
\(71\) | 0.960879 | 0.114035 | 0.0570177 | − | 0.998373i | \(-0.481841\pi\) | ||||
0.0570177 | + | 0.998373i | \(0.481841\pi\) | |||||||
\(72\) | 1.19657 | 0.141017 | ||||||||
\(73\) | −6.48583 | −0.759109 | −0.379554 | − | 0.925169i | \(-0.623923\pi\) | ||||
−0.379554 | + | 0.925169i | \(0.623923\pi\) | |||||||
\(74\) | 0.728737 | 0.0847140 | ||||||||
\(75\) | 0.938987 | 0.108425 | ||||||||
\(76\) | −4.80263 | −0.550899 | ||||||||
\(77\) | −2.36218 | −0.269195 | ||||||||
\(78\) | −0.824146 | −0.0933161 | ||||||||
\(79\) | −0.640875 | −0.0721041 | −0.0360520 | − | 0.999350i | \(-0.511478\pi\) | ||||
−0.0360520 | + | 0.999350i | \(0.511478\pi\) | |||||||
\(80\) | −8.39739 | −0.938856 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.03598 | −0.114405 | ||||||||
\(83\) | −2.87557 | −0.315634 | −0.157817 | − | 0.987468i | \(-0.550446\pi\) | ||||
−0.157817 | + | 0.987468i | \(0.550446\pi\) | |||||||
\(84\) | 1.90616 | 0.207979 | ||||||||
\(85\) | −0.417585 | −0.0452935 | ||||||||
\(86\) | −0.682019 | −0.0735440 | ||||||||
\(87\) | 7.92009 | 0.849123 | ||||||||
\(88\) | 2.82651 | 0.301307 | ||||||||
\(89\) | 6.58516 | 0.698026 | 0.349013 | − | 0.937118i | \(-0.386517\pi\) | ||||
0.349013 | + | 0.937118i | \(0.386517\pi\) | |||||||
\(90\) | 0.746523 | 0.0786905 | ||||||||
\(91\) | −2.69040 | −0.282031 | ||||||||
\(92\) | −4.03635 | −0.420818 | ||||||||
\(93\) | 3.29881 | 0.342071 | ||||||||
\(94\) | 0.226110 | 0.0233214 | ||||||||
\(95\) | −6.14010 | −0.629961 | ||||||||
\(96\) | −3.44868 | −0.351979 | ||||||||
\(97\) | 5.45203 | 0.553570 | 0.276785 | − | 0.960932i | \(-0.410731\pi\) | ||||
0.276785 | + | 0.960932i | \(0.410731\pi\) | |||||||
\(98\) | −0.306328 | −0.0309438 | ||||||||
\(99\) | 2.36218 | 0.237408 | ||||||||
\(100\) | −1.78986 | −0.178986 | ||||||||
\(101\) | −9.41257 | −0.936586 | −0.468293 | − | 0.883573i | \(-0.655131\pi\) | ||||
−0.468293 | + | 0.883573i | \(0.655131\pi\) | |||||||
\(102\) | −0.0524900 | −0.00519728 | ||||||||
\(103\) | 17.4495 | 1.71935 | 0.859673 | − | 0.510844i | \(-0.170667\pi\) | ||||
0.859673 | + | 0.510844i | \(0.170667\pi\) | |||||||
\(104\) | 3.21925 | 0.315673 | ||||||||
\(105\) | 2.43700 | 0.237827 | ||||||||
\(106\) | 3.05509 | 0.296736 | ||||||||
\(107\) | 13.7634 | 1.33056 | 0.665278 | − | 0.746596i | \(-0.268313\pi\) | ||||
0.665278 | + | 0.746596i | \(0.268313\pi\) | |||||||
\(108\) | −1.90616 | −0.183421 | ||||||||
\(109\) | 6.73939 | 0.645516 | 0.322758 | − | 0.946481i | \(-0.395390\pi\) | ||||
0.322758 | + | 0.946481i | \(0.395390\pi\) | |||||||
\(110\) | 1.76342 | 0.168136 | ||||||||
\(111\) | −2.37894 | −0.225799 | ||||||||
\(112\) | −3.44578 | −0.325596 | ||||||||
\(113\) | −9.37588 | −0.882009 | −0.441005 | − | 0.897505i | \(-0.645378\pi\) | ||||
−0.441005 | + | 0.897505i | \(0.645378\pi\) | |||||||
\(114\) | −0.771802 | −0.0722859 | ||||||||
\(115\) | −5.16042 | −0.481211 | ||||||||
\(116\) | −15.0970 | −1.40172 | ||||||||
\(117\) | 2.69040 | 0.248728 | ||||||||
\(118\) | 4.13772 | 0.380908 | ||||||||
\(119\) | −0.171352 | −0.0157078 | ||||||||
\(120\) | −2.91604 | −0.266197 | ||||||||
\(121\) | −5.42010 | −0.492737 | ||||||||
\(122\) | 1.29052 | 0.116838 | ||||||||
\(123\) | 3.38192 | 0.304937 | ||||||||
\(124\) | −6.28808 | −0.564686 | ||||||||
\(125\) | 9.89670 | 0.885188 | ||||||||
\(126\) | 0.306328 | 0.0272899 | ||||||||
\(127\) | −8.58514 | −0.761808 | −0.380904 | − | 0.924615i | \(-0.624387\pi\) | ||||
−0.380904 | + | 0.924615i | \(0.624387\pi\) | |||||||
\(128\) | 8.68482 | 0.767637 | ||||||||
\(129\) | 2.22643 | 0.196026 | ||||||||
\(130\) | 2.00845 | 0.176152 | ||||||||
\(131\) | 22.3408 | 1.95192 | 0.975962 | − | 0.217942i | \(-0.0699345\pi\) | ||||
0.975962 | + | 0.217942i | \(0.0699345\pi\) | |||||||
\(132\) | −4.50270 | −0.391910 | ||||||||
\(133\) | −2.51953 | −0.218471 | ||||||||
\(134\) | 3.25508 | 0.281196 | ||||||||
\(135\) | −2.43700 | −0.209744 | ||||||||
\(136\) | 0.205034 | 0.0175816 | ||||||||
\(137\) | 11.0019 | 0.939956 | 0.469978 | − | 0.882678i | \(-0.344262\pi\) | ||||
0.469978 | + | 0.882678i | \(0.344262\pi\) | |||||||
\(138\) | −0.648658 | −0.0552174 | ||||||||
\(139\) | −2.37063 | −0.201075 | −0.100537 | − | 0.994933i | \(-0.532056\pi\) | ||||
−0.100537 | + | 0.994933i | \(0.532056\pi\) | |||||||
\(140\) | −4.64533 | −0.392602 | ||||||||
\(141\) | −0.738129 | −0.0621617 | ||||||||
\(142\) | −0.294344 | −0.0247008 | ||||||||
\(143\) | 6.35521 | 0.531450 | ||||||||
\(144\) | 3.44578 | 0.287149 | ||||||||
\(145\) | −19.3013 | −1.60289 | ||||||||
\(146\) | 1.98679 | 0.164428 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 4.53465 | 0.372746 | ||||||||
\(149\) | 22.1546 | 1.81497 | 0.907487 | − | 0.420081i | \(-0.137998\pi\) | ||||
0.907487 | + | 0.420081i | \(0.137998\pi\) | |||||||
\(150\) | −0.287638 | −0.0234856 | ||||||||
\(151\) | 19.9741 | 1.62547 | 0.812734 | − | 0.582635i | \(-0.197978\pi\) | ||||
0.812734 | + | 0.582635i | \(0.197978\pi\) | |||||||
\(152\) | 3.01479 | 0.244531 | ||||||||
\(153\) | 0.171352 | 0.0138530 | ||||||||
\(154\) | 0.723603 | 0.0583096 | ||||||||
\(155\) | −8.03922 | −0.645726 | ||||||||
\(156\) | −5.12834 | −0.410596 | ||||||||
\(157\) | 2.43145 | 0.194050 | 0.0970252 | − | 0.995282i | \(-0.469067\pi\) | ||||
0.0970252 | + | 0.995282i | \(0.469067\pi\) | |||||||
\(158\) | 0.196318 | 0.0156182 | ||||||||
\(159\) | −9.97324 | −0.790929 | ||||||||
\(160\) | 8.40444 | 0.664429 | ||||||||
\(161\) | −2.11753 | −0.166884 | ||||||||
\(162\) | −0.306328 | −0.0240674 | ||||||||
\(163\) | 20.6882 | 1.62043 | 0.810214 | − | 0.586134i | \(-0.199351\pi\) | ||||
0.810214 | + | 0.586134i | \(0.199351\pi\) | |||||||
\(164\) | −6.44649 | −0.503386 | ||||||||
\(165\) | −5.75664 | −0.448154 | ||||||||
\(166\) | 0.880867 | 0.0683685 | ||||||||
\(167\) | −2.73919 | −0.211965 | −0.105982 | − | 0.994368i | \(-0.533799\pi\) | ||||
−0.105982 | + | 0.994368i | \(0.533799\pi\) | |||||||
\(168\) | −1.19657 | −0.0923172 | ||||||||
\(169\) | −5.76174 | −0.443211 | ||||||||
\(170\) | 0.127918 | 0.00981088 | ||||||||
\(171\) | 2.51953 | 0.192673 | ||||||||
\(172\) | −4.24394 | −0.323597 | ||||||||
\(173\) | 9.56588 | 0.727281 | 0.363640 | − | 0.931539i | \(-0.381534\pi\) | ||||
0.363640 | + | 0.931539i | \(0.381534\pi\) | |||||||
\(174\) | −2.42615 | −0.183926 | ||||||||
\(175\) | −0.938987 | −0.0709808 | ||||||||
\(176\) | 8.13956 | 0.613543 | ||||||||
\(177\) | −13.5075 | −1.01528 | ||||||||
\(178\) | −2.01722 | −0.151197 | ||||||||
\(179\) | 18.4310 | 1.37760 | 0.688800 | − | 0.724952i | \(-0.258138\pi\) | ||||
0.688800 | + | 0.724952i | \(0.258138\pi\) | |||||||
\(180\) | 4.64533 | 0.346242 | ||||||||
\(181\) | 15.9260 | 1.18377 | 0.591885 | − | 0.806023i | \(-0.298384\pi\) | ||||
0.591885 | + | 0.806023i | \(0.298384\pi\) | |||||||
\(182\) | 0.824146 | 0.0610898 | ||||||||
\(183\) | −4.21286 | −0.311423 | ||||||||
\(184\) | 2.53376 | 0.186792 | ||||||||
\(185\) | 5.79749 | 0.426240 | ||||||||
\(186\) | −1.01052 | −0.0740949 | ||||||||
\(187\) | 0.404764 | 0.0295993 | ||||||||
\(188\) | 1.40699 | 0.102616 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 1.88089 | 0.136454 | ||||||||
\(191\) | −18.5006 | −1.33866 | −0.669329 | − | 0.742966i | \(-0.733419\pi\) | ||||
−0.669329 | + | 0.742966i | \(0.733419\pi\) | |||||||
\(192\) | −5.83514 | −0.421115 | ||||||||
\(193\) | 5.00974 | 0.360609 | 0.180305 | − | 0.983611i | \(-0.442292\pi\) | ||||
0.180305 | + | 0.983611i | \(0.442292\pi\) | |||||||
\(194\) | −1.67011 | −0.119907 | ||||||||
\(195\) | −6.55652 | −0.469522 | ||||||||
\(196\) | −1.90616 | −0.136154 | ||||||||
\(197\) | −16.2211 | −1.15570 | −0.577852 | − | 0.816142i | \(-0.696109\pi\) | ||||
−0.577852 | + | 0.816142i | \(0.696109\pi\) | |||||||
\(198\) | −0.723603 | −0.0514242 | ||||||||
\(199\) | −20.7295 | −1.46948 | −0.734738 | − | 0.678352i | \(-0.762695\pi\) | ||||
−0.734738 | + | 0.678352i | \(0.762695\pi\) | |||||||
\(200\) | 1.12356 | 0.0794479 | ||||||||
\(201\) | −10.6261 | −0.749508 | ||||||||
\(202\) | 2.88334 | 0.202871 | ||||||||
\(203\) | −7.92009 | −0.555881 | ||||||||
\(204\) | −0.326625 | −0.0228683 | ||||||||
\(205\) | −8.24175 | −0.575629 | ||||||||
\(206\) | −5.34526 | −0.372422 | ||||||||
\(207\) | 2.11753 | 0.147178 | ||||||||
\(208\) | 9.27054 | 0.642796 | ||||||||
\(209\) | 5.95158 | 0.411679 | ||||||||
\(210\) | −0.746523 | −0.0515150 | ||||||||
\(211\) | −19.6700 | −1.35414 | −0.677068 | − | 0.735921i | \(-0.736750\pi\) | ||||
−0.677068 | + | 0.735921i | \(0.736750\pi\) | |||||||
\(212\) | 19.0106 | 1.30565 | ||||||||
\(213\) | 0.960879 | 0.0658383 | ||||||||
\(214\) | −4.21611 | −0.288207 | ||||||||
\(215\) | −5.42582 | −0.370038 | ||||||||
\(216\) | 1.19657 | 0.0814162 | ||||||||
\(217\) | −3.29881 | −0.223938 | ||||||||
\(218\) | −2.06447 | −0.139823 | ||||||||
\(219\) | −6.48583 | −0.438271 | ||||||||
\(220\) | 10.9731 | 0.739806 | ||||||||
\(221\) | 0.461006 | 0.0310106 | ||||||||
\(222\) | 0.728737 | 0.0489096 | ||||||||
\(223\) | 13.1389 | 0.879844 | 0.439922 | − | 0.898036i | \(-0.355006\pi\) | ||||
0.439922 | + | 0.898036i | \(0.355006\pi\) | |||||||
\(224\) | 3.44868 | 0.230424 | ||||||||
\(225\) | 0.938987 | 0.0625992 | ||||||||
\(226\) | 2.87210 | 0.191049 | ||||||||
\(227\) | 14.1801 | 0.941164 | 0.470582 | − | 0.882356i | \(-0.344044\pi\) | ||||
0.470582 | + | 0.882356i | \(0.344044\pi\) | |||||||
\(228\) | −4.80263 | −0.318062 | ||||||||
\(229\) | −1.32939 | −0.0878486 | −0.0439243 | − | 0.999035i | \(-0.513986\pi\) | ||||
−0.0439243 | + | 0.999035i | \(0.513986\pi\) | |||||||
\(230\) | 1.58078 | 0.104234 | ||||||||
\(231\) | −2.36218 | −0.155420 | ||||||||
\(232\) | 9.47693 | 0.622191 | ||||||||
\(233\) | 22.9228 | 1.50172 | 0.750860 | − | 0.660462i | \(-0.229639\pi\) | ||||
0.750860 | + | 0.660462i | \(0.229639\pi\) | |||||||
\(234\) | −0.824146 | −0.0538761 | ||||||||
\(235\) | 1.79882 | 0.117342 | ||||||||
\(236\) | 25.7474 | 1.67601 | ||||||||
\(237\) | −0.640875 | −0.0416293 | ||||||||
\(238\) | 0.0524900 | 0.00340242 | ||||||||
\(239\) | −10.9920 | −0.711016 | −0.355508 | − | 0.934673i | \(-0.615692\pi\) | ||||
−0.355508 | + | 0.934673i | \(0.615692\pi\) | |||||||
\(240\) | −8.39739 | −0.542049 | ||||||||
\(241\) | 19.7582 | 1.27274 | 0.636370 | − | 0.771384i | \(-0.280435\pi\) | ||||
0.636370 | + | 0.771384i | \(0.280435\pi\) | |||||||
\(242\) | 1.66033 | 0.106730 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 8.03039 | 0.514093 | ||||||||
\(245\) | −2.43700 | −0.155694 | ||||||||
\(246\) | −1.03598 | −0.0660515 | ||||||||
\(247\) | 6.77854 | 0.431308 | ||||||||
\(248\) | 3.94725 | 0.250651 | ||||||||
\(249\) | −2.87557 | −0.182232 | ||||||||
\(250\) | −3.03164 | −0.191738 | ||||||||
\(251\) | −20.1895 | −1.27435 | −0.637176 | − | 0.770718i | \(-0.719898\pi\) | ||||
−0.637176 | + | 0.770718i | \(0.719898\pi\) | |||||||
\(252\) | 1.90616 | 0.120077 | ||||||||
\(253\) | 5.00198 | 0.314472 | ||||||||
\(254\) | 2.62987 | 0.165013 | ||||||||
\(255\) | −0.417585 | −0.0261502 | ||||||||
\(256\) | 9.00987 | 0.563117 | ||||||||
\(257\) | 14.1397 | 0.882013 | 0.441007 | − | 0.897504i | \(-0.354622\pi\) | ||||
0.441007 | + | 0.897504i | \(0.354622\pi\) | |||||||
\(258\) | −0.682019 | −0.0424606 | ||||||||
\(259\) | 2.37894 | 0.147820 | ||||||||
\(260\) | 12.4978 | 0.775080 | ||||||||
\(261\) | 7.92009 | 0.490241 | ||||||||
\(262\) | −6.84361 | −0.422800 | ||||||||
\(263\) | 18.6300 | 1.14878 | 0.574388 | − | 0.818583i | \(-0.305240\pi\) | ||||
0.574388 | + | 0.818583i | \(0.305240\pi\) | |||||||
\(264\) | 2.82651 | 0.173960 | ||||||||
\(265\) | 24.3048 | 1.49303 | ||||||||
\(266\) | 0.771802 | 0.0473222 | ||||||||
\(267\) | 6.58516 | 0.403005 | ||||||||
\(268\) | 20.2551 | 1.23728 | ||||||||
\(269\) | −13.2895 | −0.810275 | −0.405138 | − | 0.914256i | \(-0.632776\pi\) | ||||
−0.405138 | + | 0.914256i | \(0.632776\pi\) | |||||||
\(270\) | 0.746523 | 0.0454320 | ||||||||
\(271\) | −5.23080 | −0.317749 | −0.158874 | − | 0.987299i | \(-0.550786\pi\) | ||||
−0.158874 | + | 0.987299i | \(0.550786\pi\) | |||||||
\(272\) | 0.590442 | 0.0358008 | ||||||||
\(273\) | −2.69040 | −0.162830 | ||||||||
\(274\) | −3.37020 | −0.203601 | ||||||||
\(275\) | 2.21806 | 0.133754 | ||||||||
\(276\) | −4.03635 | −0.242960 | ||||||||
\(277\) | 2.73078 | 0.164077 | 0.0820385 | − | 0.996629i | \(-0.473857\pi\) | ||||
0.0820385 | + | 0.996629i | \(0.473857\pi\) | |||||||
\(278\) | 0.726192 | 0.0435541 | ||||||||
\(279\) | 3.29881 | 0.197495 | ||||||||
\(280\) | 2.91604 | 0.174267 | ||||||||
\(281\) | −16.1088 | −0.960968 | −0.480484 | − | 0.877003i | \(-0.659539\pi\) | ||||
−0.480484 | + | 0.877003i | \(0.659539\pi\) | |||||||
\(282\) | 0.226110 | 0.0134646 | ||||||||
\(283\) | −19.9453 | −1.18562 | −0.592812 | − | 0.805341i | \(-0.701982\pi\) | ||||
−0.592812 | + | 0.805341i | \(0.701982\pi\) | |||||||
\(284\) | −1.83159 | −0.108685 | ||||||||
\(285\) | −6.14010 | −0.363708 | ||||||||
\(286\) | −1.94678 | −0.115116 | ||||||||
\(287\) | −3.38192 | −0.199628 | ||||||||
\(288\) | −3.44868 | −0.203215 | ||||||||
\(289\) | −16.9706 | −0.998273 | ||||||||
\(290\) | 5.91253 | 0.347196 | ||||||||
\(291\) | 5.45203 | 0.319604 | ||||||||
\(292\) | 12.3630 | 0.723492 | ||||||||
\(293\) | −2.08843 | −0.122007 | −0.0610037 | − | 0.998138i | \(-0.519430\pi\) | ||||
−0.0610037 | + | 0.998138i | \(0.519430\pi\) | |||||||
\(294\) | −0.306328 | −0.0178654 | ||||||||
\(295\) | 32.9177 | 1.91654 | ||||||||
\(296\) | −2.84657 | −0.165453 | ||||||||
\(297\) | 2.36218 | 0.137068 | ||||||||
\(298\) | −6.78657 | −0.393136 | ||||||||
\(299\) | 5.69699 | 0.329466 | ||||||||
\(300\) | −1.78986 | −0.103338 | ||||||||
\(301\) | −2.22643 | −0.128329 | ||||||||
\(302\) | −6.11863 | −0.352088 | ||||||||
\(303\) | −9.41257 | −0.540738 | ||||||||
\(304\) | 8.68174 | 0.497932 | ||||||||
\(305\) | 10.2667 | 0.587872 | ||||||||
\(306\) | −0.0524900 | −0.00300065 | ||||||||
\(307\) | −23.3529 | −1.33282 | −0.666409 | − | 0.745586i | \(-0.732170\pi\) | ||||
−0.666409 | + | 0.745586i | \(0.732170\pi\) | |||||||
\(308\) | 4.50270 | 0.256565 | ||||||||
\(309\) | 17.4495 | 0.992665 | ||||||||
\(310\) | 2.46264 | 0.139869 | ||||||||
\(311\) | 7.02184 | 0.398172 | 0.199086 | − | 0.979982i | \(-0.436203\pi\) | ||||
0.199086 | + | 0.979982i | \(0.436203\pi\) | |||||||
\(312\) | 3.21925 | 0.182254 | ||||||||
\(313\) | −8.12440 | −0.459218 | −0.229609 | − | 0.973283i | \(-0.573745\pi\) | ||||
−0.229609 | + | 0.973283i | \(0.573745\pi\) | |||||||
\(314\) | −0.744821 | −0.0420327 | ||||||||
\(315\) | 2.43700 | 0.137310 | ||||||||
\(316\) | 1.22161 | 0.0687210 | ||||||||
\(317\) | −8.49255 | −0.476989 | −0.238495 | − | 0.971144i | \(-0.576654\pi\) | ||||
−0.238495 | + | 0.971144i | \(0.576654\pi\) | |||||||
\(318\) | 3.05509 | 0.171321 | ||||||||
\(319\) | 18.7087 | 1.04749 | ||||||||
\(320\) | 14.2203 | 0.794936 | ||||||||
\(321\) | 13.7634 | 0.768196 | ||||||||
\(322\) | 0.648658 | 0.0361483 | ||||||||
\(323\) | 0.431726 | 0.0240219 | ||||||||
\(324\) | −1.90616 | −0.105898 | ||||||||
\(325\) | 2.52625 | 0.140131 | ||||||||
\(326\) | −6.33739 | −0.350996 | ||||||||
\(327\) | 6.73939 | 0.372689 | ||||||||
\(328\) | 4.04670 | 0.223441 | ||||||||
\(329\) | 0.738129 | 0.0406944 | ||||||||
\(330\) | 1.76342 | 0.0970732 | ||||||||
\(331\) | −18.5559 | −1.01992 | −0.509962 | − | 0.860197i | \(-0.670340\pi\) | ||||
−0.509962 | + | 0.860197i | \(0.670340\pi\) | |||||||
\(332\) | 5.48130 | 0.300825 | ||||||||
\(333\) | −2.37894 | −0.130365 | ||||||||
\(334\) | 0.839091 | 0.0459130 | ||||||||
\(335\) | 25.8959 | 1.41484 | ||||||||
\(336\) | −3.44578 | −0.187983 | ||||||||
\(337\) | −7.71312 | −0.420161 | −0.210080 | − | 0.977684i | \(-0.567373\pi\) | ||||
−0.210080 | + | 0.977684i | \(0.567373\pi\) | |||||||
\(338\) | 1.76498 | 0.0960025 | ||||||||
\(339\) | −9.37588 | −0.509228 | ||||||||
\(340\) | 0.795986 | 0.0431684 | ||||||||
\(341\) | 7.79239 | 0.421982 | ||||||||
\(342\) | −0.771802 | −0.0417343 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.66408 | 0.143637 | ||||||||
\(345\) | −5.16042 | −0.277828 | ||||||||
\(346\) | −2.93030 | −0.157534 | ||||||||
\(347\) | 14.0342 | 0.753397 | 0.376699 | − | 0.926336i | \(-0.377059\pi\) | ||||
0.376699 | + | 0.926336i | \(0.377059\pi\) | |||||||
\(348\) | −15.0970 | −0.809283 | ||||||||
\(349\) | 25.5369 | 1.36696 | 0.683479 | − | 0.729971i | \(-0.260466\pi\) | ||||
0.683479 | + | 0.729971i | \(0.260466\pi\) | |||||||
\(350\) | 0.287638 | 0.0153749 | ||||||||
\(351\) | 2.69040 | 0.143603 | ||||||||
\(352\) | −8.14640 | −0.434205 | ||||||||
\(353\) | 22.3356 | 1.18881 | 0.594403 | − | 0.804167i | \(-0.297388\pi\) | ||||
0.594403 | + | 0.804167i | \(0.297388\pi\) | |||||||
\(354\) | 4.13772 | 0.219917 | ||||||||
\(355\) | −2.34167 | −0.124283 | ||||||||
\(356\) | −12.5524 | −0.665275 | ||||||||
\(357\) | −0.171352 | −0.00906891 | ||||||||
\(358\) | −5.64594 | −0.298397 | ||||||||
\(359\) | −11.3514 | −0.599106 | −0.299553 | − | 0.954080i | \(-0.596837\pi\) | ||||
−0.299553 | + | 0.954080i | \(0.596837\pi\) | |||||||
\(360\) | −2.91604 | −0.153689 | ||||||||
\(361\) | −12.6520 | −0.665894 | ||||||||
\(362\) | −4.87858 | −0.256412 | ||||||||
\(363\) | −5.42010 | −0.284482 | ||||||||
\(364\) | 5.12834 | 0.268798 | ||||||||
\(365\) | 15.8060 | 0.827323 | ||||||||
\(366\) | 1.29052 | 0.0674564 | ||||||||
\(367\) | 11.2450 | 0.586985 | 0.293492 | − | 0.955961i | \(-0.405183\pi\) | ||||
0.293492 | + | 0.955961i | \(0.405183\pi\) | |||||||
\(368\) | 7.29653 | 0.380358 | ||||||||
\(369\) | 3.38192 | 0.176056 | ||||||||
\(370\) | −1.77594 | −0.0923265 | ||||||||
\(371\) | 9.97324 | 0.517785 | ||||||||
\(372\) | −6.28808 | −0.326022 | ||||||||
\(373\) | 31.7766 | 1.64533 | 0.822665 | − | 0.568527i | \(-0.192486\pi\) | ||||
0.822665 | + | 0.568527i | \(0.192486\pi\) | |||||||
\(374\) | −0.123991 | −0.00641141 | ||||||||
\(375\) | 9.89670 | 0.511064 | ||||||||
\(376\) | −0.883222 | −0.0455487 | ||||||||
\(377\) | 21.3082 | 1.09743 | ||||||||
\(378\) | 0.306328 | 0.0157558 | ||||||||
\(379\) | 1.52851 | 0.0785143 | 0.0392572 | − | 0.999229i | \(-0.487501\pi\) | ||||
0.0392572 | + | 0.999229i | \(0.487501\pi\) | |||||||
\(380\) | 11.7040 | 0.600404 | ||||||||
\(381\) | −8.58514 | −0.439830 | ||||||||
\(382\) | 5.66727 | 0.289963 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 8.68482 | 0.443195 | ||||||||
\(385\) | 5.75664 | 0.293386 | ||||||||
\(386\) | −1.53463 | −0.0781104 | ||||||||
\(387\) | 2.22643 | 0.113176 | ||||||||
\(388\) | −10.3925 | −0.527597 | ||||||||
\(389\) | −28.0586 | −1.42263 | −0.711315 | − | 0.702874i | \(-0.751900\pi\) | ||||
−0.711315 | + | 0.702874i | \(0.751900\pi\) | |||||||
\(390\) | 2.00845 | 0.101702 | ||||||||
\(391\) | 0.362842 | 0.0183497 | ||||||||
\(392\) | 1.19657 | 0.0604358 | ||||||||
\(393\) | 22.3408 | 1.12694 | ||||||||
\(394\) | 4.96897 | 0.250333 | ||||||||
\(395\) | 1.56181 | 0.0785834 | ||||||||
\(396\) | −4.50270 | −0.226269 | ||||||||
\(397\) | −4.94249 | −0.248057 | −0.124028 | − | 0.992279i | \(-0.539581\pi\) | ||||
−0.124028 | + | 0.992279i | \(0.539581\pi\) | |||||||
\(398\) | 6.35003 | 0.318298 | ||||||||
\(399\) | −2.51953 | −0.126134 | ||||||||
\(400\) | 3.23555 | 0.161777 | ||||||||
\(401\) | −27.2911 | −1.36285 | −0.681425 | − | 0.731888i | \(-0.738639\pi\) | ||||
−0.681425 | + | 0.731888i | \(0.738639\pi\) | |||||||
\(402\) | 3.25508 | 0.162348 | ||||||||
\(403\) | 8.87513 | 0.442102 | ||||||||
\(404\) | 17.9419 | 0.892643 | ||||||||
\(405\) | −2.43700 | −0.121096 | ||||||||
\(406\) | 2.42615 | 0.120408 | ||||||||
\(407\) | −5.61949 | −0.278548 | ||||||||
\(408\) | 0.205034 | 0.0101507 | ||||||||
\(409\) | −23.3549 | −1.15483 | −0.577413 | − | 0.816452i | \(-0.695938\pi\) | ||||
−0.577413 | + | 0.816452i | \(0.695938\pi\) | |||||||
\(410\) | 2.52468 | 0.124685 | ||||||||
\(411\) | 11.0019 | 0.542684 | ||||||||
\(412\) | −33.2615 | −1.63868 | ||||||||
\(413\) | 13.5075 | 0.664659 | ||||||||
\(414\) | −0.648658 | −0.0318798 | ||||||||
\(415\) | 7.00776 | 0.343998 | ||||||||
\(416\) | −9.27832 | −0.454907 | ||||||||
\(417\) | −2.37063 | −0.116090 | ||||||||
\(418\) | −1.82314 | −0.0891725 | ||||||||
\(419\) | 33.3672 | 1.63009 | 0.815047 | − | 0.579394i | \(-0.196711\pi\) | ||||
0.815047 | + | 0.579394i | \(0.196711\pi\) | |||||||
\(420\) | −4.64533 | −0.226669 | ||||||||
\(421\) | 13.4422 | 0.655135 | 0.327568 | − | 0.944828i | \(-0.393771\pi\) | ||||
0.327568 | + | 0.944828i | \(0.393771\pi\) | |||||||
\(422\) | 6.02546 | 0.293315 | ||||||||
\(423\) | −0.738129 | −0.0358891 | ||||||||
\(424\) | −11.9337 | −0.579550 | ||||||||
\(425\) | 0.160897 | 0.00780467 | ||||||||
\(426\) | −0.294344 | −0.0142610 | ||||||||
\(427\) | 4.21286 | 0.203874 | ||||||||
\(428\) | −26.2352 | −1.26813 | ||||||||
\(429\) | 6.35521 | 0.306833 | ||||||||
\(430\) | 1.66208 | 0.0801527 | ||||||||
\(431\) | 25.4599 | 1.22636 | 0.613180 | − | 0.789943i | \(-0.289890\pi\) | ||||
0.613180 | + | 0.789943i | \(0.289890\pi\) | |||||||
\(432\) | 3.44578 | 0.165785 | ||||||||
\(433\) | −5.92183 | −0.284585 | −0.142293 | − | 0.989825i | \(-0.545447\pi\) | ||||
−0.142293 | + | 0.989825i | \(0.545447\pi\) | |||||||
\(434\) | 1.01052 | 0.0485065 | ||||||||
\(435\) | −19.3013 | −0.925426 | ||||||||
\(436\) | −12.8464 | −0.615230 | ||||||||
\(437\) | 5.33516 | 0.255215 | ||||||||
\(438\) | 1.98679 | 0.0949326 | ||||||||
\(439\) | 30.7000 | 1.46523 | 0.732615 | − | 0.680643i | \(-0.238300\pi\) | ||||
0.732615 | + | 0.680643i | \(0.238300\pi\) | |||||||
\(440\) | −6.88822 | −0.328383 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −0.141219 | −0.00671710 | ||||||||
\(443\) | 4.78673 | 0.227424 | 0.113712 | − | 0.993514i | \(-0.463726\pi\) | ||||
0.113712 | + | 0.993514i | \(0.463726\pi\) | |||||||
\(444\) | 4.53465 | 0.215205 | ||||||||
\(445\) | −16.0481 | −0.760751 | ||||||||
\(446\) | −4.02481 | −0.190580 | ||||||||
\(447\) | 22.1546 | 1.04788 | ||||||||
\(448\) | 5.83514 | 0.275684 | ||||||||
\(449\) | 3.21623 | 0.151783 | 0.0758917 | − | 0.997116i | \(-0.475820\pi\) | ||||
0.0758917 | + | 0.997116i | \(0.475820\pi\) | |||||||
\(450\) | −0.287638 | −0.0135594 | ||||||||
\(451\) | 7.98870 | 0.376173 | ||||||||
\(452\) | 17.8720 | 0.840626 | ||||||||
\(453\) | 19.9741 | 0.938465 | ||||||||
\(454\) | −4.34375 | −0.203863 | ||||||||
\(455\) | 6.55652 | 0.307374 | ||||||||
\(456\) | 3.01479 | 0.141180 | ||||||||
\(457\) | 24.4198 | 1.14231 | 0.571155 | − | 0.820843i | \(-0.306496\pi\) | ||||
0.571155 | + | 0.820843i | \(0.306496\pi\) | |||||||
\(458\) | 0.407230 | 0.0190286 | ||||||||
\(459\) | 0.171352 | 0.00799803 | ||||||||
\(460\) | 9.83660 | 0.458634 | ||||||||
\(461\) | −12.4350 | −0.579154 | −0.289577 | − | 0.957155i | \(-0.593515\pi\) | ||||
−0.289577 | + | 0.957155i | \(0.593515\pi\) | |||||||
\(462\) | 0.723603 | 0.0336650 | ||||||||
\(463\) | −5.14321 | −0.239025 | −0.119513 | − | 0.992833i | \(-0.538133\pi\) | ||||
−0.119513 | + | 0.992833i | \(0.538133\pi\) | |||||||
\(464\) | 27.2909 | 1.26695 | ||||||||
\(465\) | −8.03922 | −0.372810 | ||||||||
\(466\) | −7.02189 | −0.325283 | ||||||||
\(467\) | 4.02430 | 0.186222 | 0.0931111 | − | 0.995656i | \(-0.470319\pi\) | ||||
0.0931111 | + | 0.995656i | \(0.470319\pi\) | |||||||
\(468\) | −5.12834 | −0.237058 | ||||||||
\(469\) | 10.6261 | 0.490668 | ||||||||
\(470\) | −0.551030 | −0.0254171 | ||||||||
\(471\) | 2.43145 | 0.112035 | ||||||||
\(472\) | −16.1626 | −0.743944 | ||||||||
\(473\) | 5.25923 | 0.241820 | ||||||||
\(474\) | 0.196318 | 0.00901719 | ||||||||
\(475\) | 2.36580 | 0.108551 | ||||||||
\(476\) | 0.326625 | 0.0149708 | ||||||||
\(477\) | −9.97324 | −0.456643 | ||||||||
\(478\) | 3.36717 | 0.154011 | ||||||||
\(479\) | 31.8259 | 1.45416 | 0.727081 | − | 0.686552i | \(-0.240876\pi\) | ||||
0.727081 | + | 0.686552i | \(0.240876\pi\) | |||||||
\(480\) | 8.40444 | 0.383608 | ||||||||
\(481\) | −6.40031 | −0.291829 | ||||||||
\(482\) | −6.05251 | −0.275684 | ||||||||
\(483\) | −2.11753 | −0.0963507 | ||||||||
\(484\) | 10.3316 | 0.469618 | ||||||||
\(485\) | −13.2866 | −0.603315 | ||||||||
\(486\) | −0.306328 | −0.0138953 | ||||||||
\(487\) | −32.7544 | −1.48424 | −0.742122 | − | 0.670265i | \(-0.766180\pi\) | ||||
−0.742122 | + | 0.670265i | \(0.766180\pi\) | |||||||
\(488\) | −5.04097 | −0.228194 | ||||||||
\(489\) | 20.6882 | 0.935555 | ||||||||
\(490\) | 0.746523 | 0.0337245 | ||||||||
\(491\) | 8.80770 | 0.397486 | 0.198743 | − | 0.980052i | \(-0.436314\pi\) | ||||
0.198743 | + | 0.980052i | \(0.436314\pi\) | |||||||
\(492\) | −6.44649 | −0.290630 | ||||||||
\(493\) | 1.35712 | 0.0611218 | ||||||||
\(494\) | −2.07646 | −0.0934243 | ||||||||
\(495\) | −5.75664 | −0.258742 | ||||||||
\(496\) | 11.3670 | 0.510393 | ||||||||
\(497\) | −0.960879 | −0.0431013 | ||||||||
\(498\) | 0.880867 | 0.0394726 | ||||||||
\(499\) | 18.5080 | 0.828530 | 0.414265 | − | 0.910156i | \(-0.364039\pi\) | ||||
0.414265 | + | 0.910156i | \(0.364039\pi\) | |||||||
\(500\) | −18.8647 | −0.843656 | ||||||||
\(501\) | −2.73919 | −0.122378 | ||||||||
\(502\) | 6.18463 | 0.276033 | ||||||||
\(503\) | 4.74817 | 0.211711 | 0.105855 | − | 0.994382i | \(-0.466242\pi\) | ||||
0.105855 | + | 0.994382i | \(0.466242\pi\) | |||||||
\(504\) | −1.19657 | −0.0532994 | ||||||||
\(505\) | 22.9385 | 1.02075 | ||||||||
\(506\) | −1.53225 | −0.0681167 | ||||||||
\(507\) | −5.76174 | −0.255888 | ||||||||
\(508\) | 16.3647 | 0.726065 | ||||||||
\(509\) | 43.0093 | 1.90635 | 0.953177 | − | 0.302412i | \(-0.0977919\pi\) | ||||
0.953177 | + | 0.302412i | \(0.0977919\pi\) | |||||||
\(510\) | 0.127918 | 0.00566431 | ||||||||
\(511\) | 6.48583 | 0.286916 | ||||||||
\(512\) | −20.1296 | −0.889612 | ||||||||
\(513\) | 2.51953 | 0.111240 | ||||||||
\(514\) | −4.33140 | −0.191050 | ||||||||
\(515\) | −42.5244 | −1.87385 | ||||||||
\(516\) | −4.24394 | −0.186829 | ||||||||
\(517\) | −1.74359 | −0.0766832 | ||||||||
\(518\) | −0.728737 | −0.0320189 | ||||||||
\(519\) | 9.56588 | 0.419896 | ||||||||
\(520\) | −7.84532 | −0.344040 | ||||||||
\(521\) | −17.0535 | −0.747129 | −0.373564 | − | 0.927604i | \(-0.621864\pi\) | ||||
−0.373564 | + | 0.927604i | \(0.621864\pi\) | |||||||
\(522\) | −2.42615 | −0.106190 | ||||||||
\(523\) | 20.7197 | 0.906008 | 0.453004 | − | 0.891508i | \(-0.350352\pi\) | ||||
0.453004 | + | 0.891508i | \(0.350352\pi\) | |||||||
\(524\) | −42.5852 | −1.86034 | ||||||||
\(525\) | −0.938987 | −0.0409808 | ||||||||
\(526\) | −5.70690 | −0.248833 | ||||||||
\(527\) | 0.565258 | 0.0246230 | ||||||||
\(528\) | 8.13956 | 0.354229 | ||||||||
\(529\) | −18.5161 | −0.805047 | ||||||||
\(530\) | −7.44526 | −0.323401 | ||||||||
\(531\) | −13.5075 | −0.586174 | ||||||||
\(532\) | 4.80263 | 0.208220 | ||||||||
\(533\) | 9.09872 | 0.394109 | ||||||||
\(534\) | −2.01722 | −0.0872937 | ||||||||
\(535\) | −33.5414 | −1.45012 | ||||||||
\(536\) | −12.7149 | −0.549198 | ||||||||
\(537\) | 18.4310 | 0.795357 | ||||||||
\(538\) | 4.07095 | 0.175511 | ||||||||
\(539\) | 2.36218 | 0.101746 | ||||||||
\(540\) | 4.64533 | 0.199903 | ||||||||
\(541\) | 9.36879 | 0.402796 | 0.201398 | − | 0.979510i | \(-0.435452\pi\) | ||||
0.201398 | + | 0.979510i | \(0.435452\pi\) | |||||||
\(542\) | 1.60234 | 0.0688265 | ||||||||
\(543\) | 15.9260 | 0.683449 | ||||||||
\(544\) | −0.590938 | −0.0253362 | ||||||||
\(545\) | −16.4239 | −0.703523 | ||||||||
\(546\) | 0.824146 | 0.0352702 | ||||||||
\(547\) | 24.4702 | 1.04627 | 0.523135 | − | 0.852250i | \(-0.324762\pi\) | ||||
0.523135 | + | 0.852250i | \(0.324762\pi\) | |||||||
\(548\) | −20.9714 | −0.895855 | ||||||||
\(549\) | −4.21286 | −0.179800 | ||||||||
\(550\) | −0.679454 | −0.0289720 | ||||||||
\(551\) | 19.9549 | 0.850107 | ||||||||
\(552\) | 2.53376 | 0.107844 | ||||||||
\(553\) | 0.640875 | 0.0272528 | ||||||||
\(554\) | −0.836516 | −0.0355402 | ||||||||
\(555\) | 5.79749 | 0.246090 | ||||||||
\(556\) | 4.51882 | 0.191641 | ||||||||
\(557\) | −29.6662 | −1.25700 | −0.628499 | − | 0.777811i | \(-0.716330\pi\) | ||||
−0.628499 | + | 0.777811i | \(0.716330\pi\) | |||||||
\(558\) | −1.01052 | −0.0427787 | ||||||||
\(559\) | 5.98999 | 0.253350 | ||||||||
\(560\) | 8.39739 | 0.354854 | ||||||||
\(561\) | 0.404764 | 0.0170892 | ||||||||
\(562\) | 4.93457 | 0.208152 | ||||||||
\(563\) | 28.1376 | 1.18586 | 0.592929 | − | 0.805255i | \(-0.297972\pi\) | ||||
0.592929 | + | 0.805255i | \(0.297972\pi\) | |||||||
\(564\) | 1.40699 | 0.0592451 | ||||||||
\(565\) | 22.8491 | 0.961267 | ||||||||
\(566\) | 6.10980 | 0.256814 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 1.14976 | 0.0482427 | ||||||||
\(569\) | −1.12434 | −0.0471349 | −0.0235675 | − | 0.999722i | \(-0.507502\pi\) | ||||
−0.0235675 | + | 0.999722i | \(0.507502\pi\) | |||||||
\(570\) | 1.88089 | 0.0787816 | ||||||||
\(571\) | 2.47463 | 0.103560 | 0.0517800 | − | 0.998659i | \(-0.483511\pi\) | ||||
0.0517800 | + | 0.998659i | \(0.483511\pi\) | |||||||
\(572\) | −12.1141 | −0.506515 | ||||||||
\(573\) | −18.5006 | −0.772875 | ||||||||
\(574\) | 1.03598 | 0.0432409 | ||||||||
\(575\) | 1.98833 | 0.0829191 | ||||||||
\(576\) | −5.83514 | −0.243131 | ||||||||
\(577\) | −19.8352 | −0.825752 | −0.412876 | − | 0.910787i | \(-0.635476\pi\) | ||||
−0.412876 | + | 0.910787i | \(0.635476\pi\) | |||||||
\(578\) | 5.19859 | 0.216233 | ||||||||
\(579\) | 5.00974 | 0.208198 | ||||||||
\(580\) | 36.7914 | 1.52768 | ||||||||
\(581\) | 2.87557 | 0.119299 | ||||||||
\(582\) | −1.67011 | −0.0692284 | ||||||||
\(583\) | −23.5586 | −0.975697 | ||||||||
\(584\) | −7.76073 | −0.321141 | ||||||||
\(585\) | −6.55652 | −0.271079 | ||||||||
\(586\) | 0.639746 | 0.0264276 | ||||||||
\(587\) | 40.3637 | 1.66599 | 0.832994 | − | 0.553283i | \(-0.186625\pi\) | ||||
0.832994 | + | 0.553283i | \(0.186625\pi\) | |||||||
\(588\) | −1.90616 | −0.0786088 | ||||||||
\(589\) | 8.31145 | 0.342467 | ||||||||
\(590\) | −10.0836 | −0.415137 | ||||||||
\(591\) | −16.2211 | −0.667246 | ||||||||
\(592\) | −8.19732 | −0.336908 | ||||||||
\(593\) | 26.3896 | 1.08369 | 0.541845 | − | 0.840478i | \(-0.317726\pi\) | ||||
0.541845 | + | 0.840478i | \(0.317726\pi\) | |||||||
\(594\) | −0.723603 | −0.0296898 | ||||||||
\(595\) | 0.417585 | 0.0171193 | ||||||||
\(596\) | −42.2302 | −1.72982 | ||||||||
\(597\) | −20.7295 | −0.848402 | ||||||||
\(598\) | −1.74515 | −0.0713645 | ||||||||
\(599\) | 22.0752 | 0.901968 | 0.450984 | − | 0.892532i | \(-0.351073\pi\) | ||||
0.450984 | + | 0.892532i | \(0.351073\pi\) | |||||||
\(600\) | 1.12356 | 0.0458692 | ||||||||
\(601\) | 6.36684 | 0.259709 | 0.129854 | − | 0.991533i | \(-0.458549\pi\) | ||||
0.129854 | + | 0.991533i | \(0.458549\pi\) | |||||||
\(602\) | 0.682019 | 0.0277970 | ||||||||
\(603\) | −10.6261 | −0.432728 | ||||||||
\(604\) | −38.0739 | −1.54920 | ||||||||
\(605\) | 13.2088 | 0.537014 | ||||||||
\(606\) | 2.88334 | 0.117128 | ||||||||
\(607\) | 25.7019 | 1.04321 | 0.521603 | − | 0.853188i | \(-0.325334\pi\) | ||||
0.521603 | + | 0.853188i | \(0.325334\pi\) | |||||||
\(608\) | −8.68904 | −0.352387 | ||||||||
\(609\) | −7.92009 | −0.320938 | ||||||||
\(610\) | −3.14499 | −0.127337 | ||||||||
\(611\) | −1.98586 | −0.0803394 | ||||||||
\(612\) | −0.326625 | −0.0132030 | ||||||||
\(613\) | 28.5562 | 1.15337 | 0.576687 | − | 0.816965i | \(-0.304345\pi\) | ||||
0.576687 | + | 0.816965i | \(0.304345\pi\) | |||||||
\(614\) | 7.15364 | 0.288697 | ||||||||
\(615\) | −8.24175 | −0.332339 | ||||||||
\(616\) | −2.82651 | −0.113883 | ||||||||
\(617\) | 44.2281 | 1.78056 | 0.890279 | − | 0.455416i | \(-0.150509\pi\) | ||||
0.890279 | + | 0.455416i | \(0.150509\pi\) | |||||||
\(618\) | −5.34526 | −0.215018 | ||||||||
\(619\) | 36.6561 | 1.47333 | 0.736667 | − | 0.676256i | \(-0.236399\pi\) | ||||
0.736667 | + | 0.676256i | \(0.236399\pi\) | |||||||
\(620\) | 15.3241 | 0.615429 | ||||||||
\(621\) | 2.11753 | 0.0849734 | ||||||||
\(622\) | −2.15099 | −0.0862467 | ||||||||
\(623\) | −6.58516 | −0.263829 | ||||||||
\(624\) | 9.27054 | 0.371119 | ||||||||
\(625\) | −28.8132 | −1.15253 | ||||||||
\(626\) | 2.48873 | 0.0994698 | ||||||||
\(627\) | 5.95158 | 0.237683 | ||||||||
\(628\) | −4.63473 | −0.184946 | ||||||||
\(629\) | −0.407637 | −0.0162535 | ||||||||
\(630\) | −0.746523 | −0.0297422 | ||||||||
\(631\) | −46.2267 | −1.84025 | −0.920127 | − | 0.391620i | \(-0.871915\pi\) | ||||
−0.920127 | + | 0.391620i | \(0.871915\pi\) | |||||||
\(632\) | −0.766851 | −0.0305037 | ||||||||
\(633\) | −19.6700 | −0.781811 | ||||||||
\(634\) | 2.60151 | 0.103319 | ||||||||
\(635\) | 20.9220 | 0.830265 | ||||||||
\(636\) | 19.0106 | 0.753820 | ||||||||
\(637\) | 2.69040 | 0.106598 | ||||||||
\(638\) | −5.73100 | −0.226892 | ||||||||
\(639\) | 0.960879 | 0.0380118 | ||||||||
\(640\) | −21.1649 | −0.836618 | ||||||||
\(641\) | −0.547650 | −0.0216309 | −0.0108154 | − | 0.999942i | \(-0.503443\pi\) | ||||
−0.0108154 | + | 0.999942i | \(0.503443\pi\) | |||||||
\(642\) | −4.21611 | −0.166397 | ||||||||
\(643\) | −2.70137 | −0.106532 | −0.0532659 | − | 0.998580i | \(-0.516963\pi\) | ||||
−0.0532659 | + | 0.998580i | \(0.516963\pi\) | |||||||
\(644\) | 4.03635 | 0.159054 | ||||||||
\(645\) | −5.42582 | −0.213641 | ||||||||
\(646\) | −0.132250 | −0.00520330 | ||||||||
\(647\) | −5.21463 | −0.205008 | −0.102504 | − | 0.994733i | \(-0.532686\pi\) | ||||
−0.102504 | + | 0.994733i | \(0.532686\pi\) | |||||||
\(648\) | 1.19657 | 0.0470056 | ||||||||
\(649\) | −31.9071 | −1.25246 | ||||||||
\(650\) | −0.773863 | −0.0303534 | ||||||||
\(651\) | −3.29881 | −0.129291 | ||||||||
\(652\) | −39.4352 | −1.54440 | ||||||||
\(653\) | 46.1150 | 1.80462 | 0.902309 | − | 0.431090i | \(-0.141871\pi\) | ||||
0.902309 | + | 0.431090i | \(0.141871\pi\) | |||||||
\(654\) | −2.06447 | −0.0807270 | ||||||||
\(655\) | −54.4446 | −2.12733 | ||||||||
\(656\) | 11.6534 | 0.454987 | ||||||||
\(657\) | −6.48583 | −0.253036 | ||||||||
\(658\) | −0.226110 | −0.00881468 | ||||||||
\(659\) | −12.6598 | −0.493156 | −0.246578 | − | 0.969123i | \(-0.579306\pi\) | ||||
−0.246578 | + | 0.969123i | \(0.579306\pi\) | |||||||
\(660\) | 10.9731 | 0.427127 | ||||||||
\(661\) | −7.95024 | −0.309229 | −0.154614 | − | 0.987975i | \(-0.549413\pi\) | ||||
−0.154614 | + | 0.987975i | \(0.549413\pi\) | |||||||
\(662\) | 5.68419 | 0.220922 | ||||||||
\(663\) | 0.461006 | 0.0179040 | ||||||||
\(664\) | −3.44081 | −0.133529 | ||||||||
\(665\) | 6.14010 | 0.238103 | ||||||||
\(666\) | 0.728737 | 0.0282380 | ||||||||
\(667\) | 16.7710 | 0.649376 | ||||||||
\(668\) | 5.22134 | 0.202020 | ||||||||
\(669\) | 13.1389 | 0.507978 | ||||||||
\(670\) | −7.93263 | −0.306464 | ||||||||
\(671\) | −9.95153 | −0.384174 | ||||||||
\(672\) | 3.44868 | 0.133036 | ||||||||
\(673\) | 7.93560 | 0.305895 | 0.152947 | − | 0.988234i | \(-0.451123\pi\) | ||||
0.152947 | + | 0.988234i | \(0.451123\pi\) | |||||||
\(674\) | 2.36275 | 0.0910096 | ||||||||
\(675\) | 0.938987 | 0.0361416 | ||||||||
\(676\) | 10.9828 | 0.422416 | ||||||||
\(677\) | −27.9758 | −1.07520 | −0.537599 | − | 0.843201i | \(-0.680668\pi\) | ||||
−0.537599 | + | 0.843201i | \(0.680668\pi\) | |||||||
\(678\) | 2.87210 | 0.110302 | ||||||||
\(679\) | −5.45203 | −0.209230 | ||||||||
\(680\) | −0.499669 | −0.0191614 | ||||||||
\(681\) | 14.1801 | 0.543381 | ||||||||
\(682\) | −2.38703 | −0.0914041 | ||||||||
\(683\) | 17.0364 | 0.651878 | 0.325939 | − | 0.945391i | \(-0.394320\pi\) | ||||
0.325939 | + | 0.945391i | \(0.394320\pi\) | |||||||
\(684\) | −4.80263 | −0.183633 | ||||||||
\(685\) | −26.8117 | −1.02442 | ||||||||
\(686\) | 0.306328 | 0.0116957 | ||||||||
\(687\) | −1.32939 | −0.0507194 | ||||||||
\(688\) | 7.67180 | 0.292485 | ||||||||
\(689\) | −26.8320 | −1.02222 | ||||||||
\(690\) | 1.58078 | 0.0601793 | ||||||||
\(691\) | −36.5982 | −1.39226 | −0.696131 | − | 0.717914i | \(-0.745097\pi\) | ||||
−0.696131 | + | 0.717914i | \(0.745097\pi\) | |||||||
\(692\) | −18.2341 | −0.693158 | ||||||||
\(693\) | −2.36218 | −0.0897318 | ||||||||
\(694\) | −4.29908 | −0.163191 | ||||||||
\(695\) | 5.77725 | 0.219143 | ||||||||
\(696\) | 9.47693 | 0.359222 | ||||||||
\(697\) | 0.579498 | 0.0219501 | ||||||||
\(698\) | −7.82266 | −0.296092 | ||||||||
\(699\) | 22.9228 | 0.867018 | ||||||||
\(700\) | 1.78986 | 0.0676505 | ||||||||
\(701\) | 21.2960 | 0.804338 | 0.402169 | − | 0.915565i | \(-0.368256\pi\) | ||||
0.402169 | + | 0.915565i | \(0.368256\pi\) | |||||||
\(702\) | −0.824146 | −0.0311054 | ||||||||
\(703\) | −5.99381 | −0.226061 | ||||||||
\(704\) | −13.7837 | −0.519491 | ||||||||
\(705\) | 1.79882 | 0.0677476 | ||||||||
\(706\) | −6.84204 | −0.257504 | ||||||||
\(707\) | 9.41257 | 0.353996 | ||||||||
\(708\) | 25.7474 | 0.967648 | ||||||||
\(709\) | −25.2962 | −0.950018 | −0.475009 | − | 0.879981i | \(-0.657555\pi\) | ||||
−0.475009 | + | 0.879981i | \(0.657555\pi\) | |||||||
\(710\) | 0.717318 | 0.0269205 | ||||||||
\(711\) | −0.640875 | −0.0240347 | ||||||||
\(712\) | 7.87959 | 0.295300 | ||||||||
\(713\) | 6.98532 | 0.261602 | ||||||||
\(714\) | 0.0524900 | 0.00196439 | ||||||||
\(715\) | −15.4877 | −0.579206 | ||||||||
\(716\) | −35.1325 | −1.31296 | ||||||||
\(717\) | −10.9920 | −0.410505 | ||||||||
\(718\) | 3.47726 | 0.129770 | ||||||||
\(719\) | 23.8157 | 0.888174 | 0.444087 | − | 0.895984i | \(-0.353528\pi\) | ||||
0.444087 | + | 0.895984i | \(0.353528\pi\) | |||||||
\(720\) | −8.39739 | −0.312952 | ||||||||
\(721\) | −17.4495 | −0.649852 | ||||||||
\(722\) | 3.87566 | 0.144237 | ||||||||
\(723\) | 19.7582 | 0.734817 | ||||||||
\(724\) | −30.3575 | −1.12823 | ||||||||
\(725\) | 7.43687 | 0.276198 | ||||||||
\(726\) | 1.66033 | 0.0616206 | ||||||||
\(727\) | −19.4656 | −0.721940 | −0.360970 | − | 0.932577i | \(-0.617554\pi\) | ||||
−0.360970 | + | 0.932577i | \(0.617554\pi\) | |||||||
\(728\) | −3.21925 | −0.119313 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.84182 | −0.179204 | ||||||||
\(731\) | 0.381503 | 0.0141104 | ||||||||
\(732\) | 8.03039 | 0.296812 | ||||||||
\(733\) | 6.14765 | 0.227068 | 0.113534 | − | 0.993534i | \(-0.463783\pi\) | ||||
0.113534 | + | 0.993534i | \(0.463783\pi\) | |||||||
\(734\) | −3.44466 | −0.127145 | ||||||||
\(735\) | −2.43700 | −0.0898902 | ||||||||
\(736\) | −7.30266 | −0.269180 | ||||||||
\(737\) | −25.1008 | −0.924599 | ||||||||
\(738\) | −1.03598 | −0.0381348 | ||||||||
\(739\) | −25.9676 | −0.955235 | −0.477617 | − | 0.878568i | \(-0.658500\pi\) | ||||
−0.477617 | + | 0.878568i | \(0.658500\pi\) | |||||||
\(740\) | −11.0510 | −0.406242 | ||||||||
\(741\) | 6.77854 | 0.249016 | ||||||||
\(742\) | −3.05509 | −0.112156 | ||||||||
\(743\) | 42.2560 | 1.55022 | 0.775111 | − | 0.631825i | \(-0.217694\pi\) | ||||
0.775111 | + | 0.631825i | \(0.217694\pi\) | |||||||
\(744\) | 3.94725 | 0.144713 | ||||||||
\(745\) | −53.9908 | −1.97807 | ||||||||
\(746\) | −9.73407 | −0.356390 | ||||||||
\(747\) | −2.87557 | −0.105211 | ||||||||
\(748\) | −0.771547 | −0.0282105 | ||||||||
\(749\) | −13.7634 | −0.502903 | ||||||||
\(750\) | −3.03164 | −0.110700 | ||||||||
\(751\) | −16.8502 | −0.614872 | −0.307436 | − | 0.951569i | \(-0.599471\pi\) | ||||
−0.307436 | + | 0.951569i | \(0.599471\pi\) | |||||||
\(752\) | −2.54343 | −0.0927494 | ||||||||
\(753\) | −20.1895 | −0.735748 | ||||||||
\(754\) | −6.52731 | −0.237711 | ||||||||
\(755\) | −48.6769 | −1.77154 | ||||||||
\(756\) | 1.90616 | 0.0693265 | ||||||||
\(757\) | 39.2076 | 1.42502 | 0.712511 | − | 0.701661i | \(-0.247558\pi\) | ||||
0.712511 | + | 0.701661i | \(0.247558\pi\) | |||||||
\(758\) | −0.468226 | −0.0170067 | ||||||||
\(759\) | 5.00198 | 0.181560 | ||||||||
\(760\) | −7.34704 | −0.266505 | ||||||||
\(761\) | 30.4699 | 1.10453 | 0.552267 | − | 0.833667i | \(-0.313763\pi\) | ||||
0.552267 | + | 0.833667i | \(0.313763\pi\) | |||||||
\(762\) | 2.62987 | 0.0952702 | ||||||||
\(763\) | −6.73939 | −0.243982 | ||||||||
\(764\) | 35.2652 | 1.27585 | ||||||||
\(765\) | −0.417585 | −0.0150978 | ||||||||
\(766\) | 0.306328 | 0.0110681 | ||||||||
\(767\) | −36.3405 | −1.31218 | ||||||||
\(768\) | 9.00987 | 0.325116 | ||||||||
\(769\) | −10.1240 | −0.365080 | −0.182540 | − | 0.983198i | \(-0.558432\pi\) | ||||
−0.182540 | + | 0.983198i | \(0.558432\pi\) | |||||||
\(770\) | −1.76342 | −0.0635493 | ||||||||
\(771\) | 14.1397 | 0.509231 | ||||||||
\(772\) | −9.54938 | −0.343690 | ||||||||
\(773\) | 8.48170 | 0.305066 | 0.152533 | − | 0.988298i | \(-0.451257\pi\) | ||||
0.152533 | + | 0.988298i | \(0.451257\pi\) | |||||||
\(774\) | −0.682019 | −0.0245147 | ||||||||
\(775\) | 3.09754 | 0.111267 | ||||||||
\(776\) | 6.52373 | 0.234188 | ||||||||
\(777\) | 2.37894 | 0.0853441 | ||||||||
\(778\) | 8.59515 | 0.308151 | ||||||||
\(779\) | 8.52083 | 0.305291 | ||||||||
\(780\) | 12.4978 | 0.447493 | ||||||||
\(781\) | 2.26977 | 0.0812187 | ||||||||
\(782\) | −0.111149 | −0.00397467 | ||||||||
\(783\) | 7.92009 | 0.283041 | ||||||||
\(784\) | 3.44578 | 0.123064 | ||||||||
\(785\) | −5.92544 | −0.211488 | ||||||||
\(786\) | −6.84361 | −0.244104 | ||||||||
\(787\) | −31.6332 | −1.12760 | −0.563801 | − | 0.825911i | \(-0.690662\pi\) | ||||
−0.563801 | + | 0.825911i | \(0.690662\pi\) | |||||||
\(788\) | 30.9200 | 1.10148 | ||||||||
\(789\) | 18.6300 | 0.663246 | ||||||||
\(790\) | −0.478428 | −0.0170217 | ||||||||
\(791\) | 9.37588 | 0.333368 | ||||||||
\(792\) | 2.82651 | 0.100436 | ||||||||
\(793\) | −11.3343 | −0.402492 | ||||||||
\(794\) | 1.51403 | 0.0537308 | ||||||||
\(795\) | 24.3048 | 0.862003 | ||||||||
\(796\) | 39.5138 | 1.40053 | ||||||||
\(797\) | 19.9684 | 0.707317 | 0.353659 | − | 0.935375i | \(-0.384937\pi\) | ||||
0.353659 | + | 0.935375i | \(0.384937\pi\) | |||||||
\(798\) | 0.771802 | 0.0273215 | ||||||||
\(799\) | −0.126480 | −0.00447454 | ||||||||
\(800\) | −3.23826 | −0.114490 | ||||||||
\(801\) | 6.58516 | 0.232675 | ||||||||
\(802\) | 8.36002 | 0.295203 | ||||||||
\(803\) | −15.3207 | −0.540656 | ||||||||
\(804\) | 20.2551 | 0.714342 | ||||||||
\(805\) | 5.16042 | 0.181881 | ||||||||
\(806\) | −2.71870 | −0.0957622 | ||||||||
\(807\) | −13.2895 | −0.467813 | ||||||||
\(808\) | −11.2628 | −0.396223 | ||||||||
\(809\) | −11.4147 | −0.401319 | −0.200660 | − | 0.979661i | \(-0.564309\pi\) | ||||
−0.200660 | + | 0.979661i | \(0.564309\pi\) | |||||||
\(810\) | 0.746523 | 0.0262302 | ||||||||
\(811\) | −39.4376 | −1.38484 | −0.692420 | − | 0.721495i | \(-0.743455\pi\) | ||||
−0.692420 | + | 0.721495i | \(0.743455\pi\) | |||||||
\(812\) | 15.0970 | 0.529800 | ||||||||
\(813\) | −5.23080 | −0.183452 | ||||||||
\(814\) | 1.72141 | 0.0603354 | ||||||||
\(815\) | −50.4173 | −1.76604 | ||||||||
\(816\) | 0.590442 | 0.0206696 | ||||||||
\(817\) | 5.60955 | 0.196253 | ||||||||
\(818\) | 7.15427 | 0.250143 | ||||||||
\(819\) | −2.69040 | −0.0940102 | ||||||||
\(820\) | 15.7101 | 0.548621 | ||||||||
\(821\) | 9.09700 | 0.317487 | 0.158744 | − | 0.987320i | \(-0.449256\pi\) | ||||
0.158744 | + | 0.987320i | \(0.449256\pi\) | |||||||
\(822\) | −3.37020 | −0.117549 | ||||||||
\(823\) | 35.0617 | 1.22217 | 0.611087 | − | 0.791564i | \(-0.290733\pi\) | ||||
0.611087 | + | 0.791564i | \(0.290733\pi\) | |||||||
\(824\) | 20.8795 | 0.727371 | ||||||||
\(825\) | 2.21806 | 0.0772229 | ||||||||
\(826\) | −4.13772 | −0.143970 | ||||||||
\(827\) | −10.5157 | −0.365668 | −0.182834 | − | 0.983144i | \(-0.558527\pi\) | ||||
−0.182834 | + | 0.983144i | \(0.558527\pi\) | |||||||
\(828\) | −4.03635 | −0.140273 | ||||||||
\(829\) | −25.7538 | −0.894467 | −0.447233 | − | 0.894417i | \(-0.647591\pi\) | ||||
−0.447233 | + | 0.894417i | \(0.647591\pi\) | |||||||
\(830\) | −2.14668 | −0.0745122 | ||||||||
\(831\) | 2.73078 | 0.0947299 | ||||||||
\(832\) | −15.6989 | −0.544260 | ||||||||
\(833\) | 0.171352 | 0.00593699 | ||||||||
\(834\) | 0.726192 | 0.0251460 | ||||||||
\(835\) | 6.67541 | 0.231012 | ||||||||
\(836\) | −11.3447 | −0.392364 | ||||||||
\(837\) | 3.29881 | 0.114024 | ||||||||
\(838\) | −10.2213 | −0.353090 | ||||||||
\(839\) | 38.3857 | 1.32522 | 0.662611 | − | 0.748963i | \(-0.269448\pi\) | ||||
0.662611 | + | 0.748963i | \(0.269448\pi\) | |||||||
\(840\) | 2.91604 | 0.100613 | ||||||||
\(841\) | 33.7279 | 1.16303 | ||||||||
\(842\) | −4.11774 | −0.141907 | ||||||||
\(843\) | −16.1088 | −0.554815 | ||||||||
\(844\) | 37.4941 | 1.29060 | ||||||||
\(845\) | 14.0414 | 0.483038 | ||||||||
\(846\) | 0.226110 | 0.00777381 | ||||||||
\(847\) | 5.42010 | 0.186237 | ||||||||
\(848\) | −34.3656 | −1.18012 | ||||||||
\(849\) | −19.9453 | −0.684520 | ||||||||
\(850\) | −0.0492874 | −0.00169054 | ||||||||
\(851\) | −5.03747 | −0.172682 | ||||||||
\(852\) | −1.83159 | −0.0627493 | ||||||||
\(853\) | −7.13436 | −0.244276 | −0.122138 | − | 0.992513i | \(-0.538975\pi\) | ||||
−0.122138 | + | 0.992513i | \(0.538975\pi\) | |||||||
\(854\) | −1.29052 | −0.0441606 | ||||||||
\(855\) | −6.14010 | −0.209987 | ||||||||
\(856\) | 16.4688 | 0.562892 | ||||||||
\(857\) | 29.6253 | 1.01198 | 0.505990 | − | 0.862539i | \(-0.331127\pi\) | ||||
0.505990 | + | 0.862539i | \(0.331127\pi\) | |||||||
\(858\) | −1.94678 | −0.0664620 | ||||||||
\(859\) | 31.0671 | 1.05999 | 0.529997 | − | 0.847999i | \(-0.322193\pi\) | ||||
0.529997 | + | 0.847999i | \(0.322193\pi\) | |||||||
\(860\) | 10.3425 | 0.352676 | ||||||||
\(861\) | −3.38192 | −0.115255 | ||||||||
\(862\) | −7.79909 | −0.265638 | ||||||||
\(863\) | −10.6748 | −0.363374 | −0.181687 | − | 0.983356i | \(-0.558156\pi\) | ||||
−0.181687 | + | 0.983356i | \(0.558156\pi\) | |||||||
\(864\) | −3.44868 | −0.117326 | ||||||||
\(865\) | −23.3121 | −0.792635 | ||||||||
\(866\) | 1.81402 | 0.0616431 | ||||||||
\(867\) | −16.9706 | −0.576353 | ||||||||
\(868\) | 6.28808 | 0.213431 | ||||||||
\(869\) | −1.51386 | −0.0513543 | ||||||||
\(870\) | 5.91253 | 0.200454 | ||||||||
\(871\) | −28.5885 | −0.968684 | ||||||||
\(872\) | 8.06414 | 0.273086 | ||||||||
\(873\) | 5.45203 | 0.184523 | ||||||||
\(874\) | −1.63431 | −0.0552814 | ||||||||
\(875\) | −9.89670 | −0.334570 | ||||||||
\(876\) | 12.3630 | 0.417708 | ||||||||
\(877\) | 22.7772 | 0.769130 | 0.384565 | − | 0.923098i | \(-0.374351\pi\) | ||||
0.384565 | + | 0.923098i | \(0.374351\pi\) | |||||||
\(878\) | −9.40427 | −0.317379 | ||||||||
\(879\) | −2.08843 | −0.0704410 | ||||||||
\(880\) | −19.8361 | −0.668676 | ||||||||
\(881\) | −26.4125 | −0.889860 | −0.444930 | − | 0.895565i | \(-0.646771\pi\) | ||||
−0.444930 | + | 0.895565i | \(0.646771\pi\) | |||||||
\(882\) | −0.306328 | −0.0103146 | ||||||||
\(883\) | −41.7787 | −1.40597 | −0.702983 | − | 0.711206i | \(-0.748149\pi\) | ||||
−0.702983 | + | 0.711206i | \(0.748149\pi\) | |||||||
\(884\) | −0.878752 | −0.0295556 | ||||||||
\(885\) | 32.9177 | 1.10652 | ||||||||
\(886\) | −1.46631 | −0.0492617 | ||||||||
\(887\) | −14.8523 | −0.498691 | −0.249346 | − | 0.968415i | \(-0.580216\pi\) | ||||
−0.249346 | + | 0.968415i | \(0.580216\pi\) | |||||||
\(888\) | −2.84657 | −0.0955245 | ||||||||
\(889\) | 8.58514 | 0.287936 | ||||||||
\(890\) | 4.91598 | 0.164784 | ||||||||
\(891\) | 2.36218 | 0.0791360 | ||||||||
\(892\) | −25.0448 | −0.838563 | ||||||||
\(893\) | −1.85974 | −0.0622337 | ||||||||
\(894\) | −6.78657 | −0.226977 | ||||||||
\(895\) | −44.9165 | −1.50139 | ||||||||
\(896\) | −8.68482 | −0.290140 | ||||||||
\(897\) | 5.69699 | 0.190217 | ||||||||
\(898\) | −0.985223 | −0.0328773 | ||||||||
\(899\) | 26.1269 | 0.871381 | ||||||||
\(900\) | −1.78986 | −0.0596621 | ||||||||
\(901\) | −1.70893 | −0.0569329 | ||||||||
\(902\) | −2.44717 | −0.0814817 | ||||||||
\(903\) | −2.22643 | −0.0740910 | ||||||||
\(904\) | −11.2189 | −0.373135 | ||||||||
\(905\) | −38.8117 | −1.29014 | ||||||||
\(906\) | −6.11863 | −0.203278 | ||||||||
\(907\) | −22.8304 | −0.758071 | −0.379035 | − | 0.925382i | \(-0.623744\pi\) | ||||
−0.379035 | + | 0.925382i | \(0.623744\pi\) | |||||||
\(908\) | −27.0295 | −0.897006 | ||||||||
\(909\) | −9.41257 | −0.312195 | ||||||||
\(910\) | −2.00845 | −0.0665794 | ||||||||
\(911\) | 0.990631 | 0.0328211 | 0.0164105 | − | 0.999865i | \(-0.494776\pi\) | ||||
0.0164105 | + | 0.999865i | \(0.494776\pi\) | |||||||
\(912\) | 8.68174 | 0.287481 | ||||||||
\(913\) | −6.79260 | −0.224802 | ||||||||
\(914\) | −7.48047 | −0.247432 | ||||||||
\(915\) | 10.2667 | 0.339408 | ||||||||
\(916\) | 2.53404 | 0.0837269 | ||||||||
\(917\) | −22.3408 | −0.737758 | ||||||||
\(918\) | −0.0524900 | −0.00173243 | ||||||||
\(919\) | 33.7570 | 1.11354 | 0.556771 | − | 0.830666i | \(-0.312040\pi\) | ||||
0.556771 | + | 0.830666i | \(0.312040\pi\) | |||||||
\(920\) | −6.17479 | −0.203577 | ||||||||
\(921\) | −23.3529 | −0.769503 | ||||||||
\(922\) | 3.80918 | 0.125449 | ||||||||
\(923\) | 2.58515 | 0.0850912 | ||||||||
\(924\) | 4.50270 | 0.148128 | ||||||||
\(925\) | −2.23380 | −0.0734468 | ||||||||
\(926\) | 1.57551 | 0.0517745 | ||||||||
\(927\) | 17.4495 | 0.573115 | ||||||||
\(928\) | −27.3138 | −0.896621 | ||||||||
\(929\) | −18.1225 | −0.594579 | −0.297289 | − | 0.954787i | \(-0.596083\pi\) | ||||
−0.297289 | + | 0.954787i | \(0.596083\pi\) | |||||||
\(930\) | 2.46264 | 0.0807532 | ||||||||
\(931\) | 2.51953 | 0.0825742 | ||||||||
\(932\) | −43.6945 | −1.43126 | ||||||||
\(933\) | 7.02184 | 0.229885 | ||||||||
\(934\) | −1.23276 | −0.0403370 | ||||||||
\(935\) | −0.986412 | −0.0322591 | ||||||||
\(936\) | 3.21925 | 0.105224 | ||||||||
\(937\) | 35.2334 | 1.15102 | 0.575512 | − | 0.817793i | \(-0.304803\pi\) | ||||
0.575512 | + | 0.817793i | \(0.304803\pi\) | |||||||
\(938\) | −3.25508 | −0.106282 | ||||||||
\(939\) | −8.12440 | −0.265130 | ||||||||
\(940\) | −3.42885 | −0.111837 | ||||||||
\(941\) | −31.3577 | −1.02223 | −0.511115 | − | 0.859512i | \(-0.670768\pi\) | ||||
−0.511115 | + | 0.859512i | \(0.670768\pi\) | |||||||
\(942\) | −0.744821 | −0.0242676 | ||||||||
\(943\) | 7.16130 | 0.233204 | ||||||||
\(944\) | −46.5438 | −1.51487 | ||||||||
\(945\) | 2.43700 | 0.0792757 | ||||||||
\(946\) | −1.61105 | −0.0523798 | ||||||||
\(947\) | −25.8681 | −0.840600 | −0.420300 | − | 0.907385i | \(-0.638075\pi\) | ||||
−0.420300 | + | 0.907385i | \(0.638075\pi\) | |||||||
\(948\) | 1.22161 | 0.0396761 | ||||||||
\(949\) | −17.4495 | −0.566434 | ||||||||
\(950\) | −0.724713 | −0.0235128 | ||||||||
\(951\) | −8.49255 | −0.275390 | ||||||||
\(952\) | −0.205034 | −0.00664520 | ||||||||
\(953\) | 48.1449 | 1.55957 | 0.779784 | − | 0.626049i | \(-0.215329\pi\) | ||||
0.779784 | + | 0.626049i | \(0.215329\pi\) | |||||||
\(954\) | 3.05509 | 0.0989121 | ||||||||
\(955\) | 45.0861 | 1.45895 | ||||||||
\(956\) | 20.9526 | 0.677656 | ||||||||
\(957\) | 18.7087 | 0.604766 | ||||||||
\(958\) | −9.74917 | −0.314981 | ||||||||
\(959\) | −11.0019 | −0.355270 | ||||||||
\(960\) | 14.2203 | 0.458957 | ||||||||
\(961\) | −20.1178 | −0.648962 | ||||||||
\(962\) | 1.96060 | 0.0632121 | ||||||||
\(963\) | 13.7634 | 0.443518 | ||||||||
\(964\) | −37.6624 | −1.21302 | ||||||||
\(965\) | −12.2088 | −0.393014 | ||||||||
\(966\) | 0.648658 | 0.0208702 | ||||||||
\(967\) | 40.9603 | 1.31719 | 0.658597 | − | 0.752495i | \(-0.271150\pi\) | ||||
0.658597 | + | 0.752495i | \(0.271150\pi\) | |||||||
\(968\) | −6.48552 | −0.208453 | ||||||||
\(969\) | 0.431726 | 0.0138690 | ||||||||
\(970\) | 4.07007 | 0.130682 | ||||||||
\(971\) | 44.3932 | 1.42464 | 0.712322 | − | 0.701852i | \(-0.247643\pi\) | ||||
0.712322 | + | 0.701852i | \(0.247643\pi\) | |||||||
\(972\) | −1.90616 | −0.0611402 | ||||||||
\(973\) | 2.37063 | 0.0759991 | ||||||||
\(974\) | 10.0336 | 0.321497 | ||||||||
\(975\) | 2.52625 | 0.0809048 | ||||||||
\(976\) | −14.5166 | −0.464665 | ||||||||
\(977\) | 29.3721 | 0.939697 | 0.469849 | − | 0.882747i | \(-0.344308\pi\) | ||||
0.469849 | + | 0.882747i | \(0.344308\pi\) | |||||||
\(978\) | −6.33739 | −0.202648 | ||||||||
\(979\) | 15.5553 | 0.497151 | ||||||||
\(980\) | 4.64533 | 0.148390 | ||||||||
\(981\) | 6.73939 | 0.215172 | ||||||||
\(982\) | −2.69805 | −0.0860982 | ||||||||
\(983\) | 13.0541 | 0.416362 | 0.208181 | − | 0.978090i | \(-0.433246\pi\) | ||||
0.208181 | + | 0.978090i | \(0.433246\pi\) | |||||||
\(984\) | 4.04670 | 0.129004 | ||||||||
\(985\) | 39.5308 | 1.25956 | ||||||||
\(986\) | −0.415725 | −0.0132394 | ||||||||
\(987\) | 0.738129 | 0.0234949 | ||||||||
\(988\) | −12.9210 | −0.411072 | ||||||||
\(989\) | 4.71452 | 0.149913 | ||||||||
\(990\) | 1.76342 | 0.0560453 | ||||||||
\(991\) | −51.3168 | −1.63013 | −0.815066 | − | 0.579369i | \(-0.803299\pi\) | ||||
−0.815066 | + | 0.579369i | \(0.803299\pi\) | |||||||
\(992\) | −11.3765 | −0.361206 | ||||||||
\(993\) | −18.5559 | −0.588853 | ||||||||
\(994\) | 0.294344 | 0.00933603 | ||||||||
\(995\) | 50.5179 | 1.60152 | ||||||||
\(996\) | 5.48130 | 0.173681 | ||||||||
\(997\) | −39.8128 | −1.26088 | −0.630442 | − | 0.776237i | \(-0.717126\pi\) | ||||
−0.630442 | + | 0.776237i | \(0.717126\pi\) | |||||||
\(998\) | −5.66951 | −0.179465 | ||||||||
\(999\) | −2.37894 | −0.0752664 |
(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 | 8043.2.a.p.1.17 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.p.1.17 | ✓ | 41 | 1.1 | even | 1 | trivial |