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: | \(1\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.38443 | −1.68605 | −0.843023 | − | 0.537877i | \(-0.819226\pi\) | ||||
−0.843023 | + | 0.537877i | \(0.819226\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.68550 | 1.84275 | ||||||||
\(5\) | 2.70331 | 1.20896 | 0.604478 | − | 0.796622i | \(-0.293382\pi\) | ||||
0.604478 | + | 0.796622i | \(0.293382\pi\) | |||||||
\(6\) | 2.38443 | 0.973439 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −4.01897 | −1.42092 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −6.44585 | −2.03836 | ||||||||
\(11\) | 2.12042 | 0.639331 | 0.319665 | − | 0.947531i | \(-0.396430\pi\) | ||||
0.319665 | + | 0.947531i | \(0.396430\pi\) | |||||||
\(12\) | −3.68550 | −1.06391 | ||||||||
\(13\) | 0.628822 | 0.174404 | 0.0872019 | − | 0.996191i | \(-0.472207\pi\) | ||||
0.0872019 | + | 0.996191i | \(0.472207\pi\) | |||||||
\(14\) | −2.38443 | −0.637266 | ||||||||
\(15\) | −2.70331 | −0.697991 | ||||||||
\(16\) | 2.21194 | 0.552984 | ||||||||
\(17\) | −0.671193 | −0.162788 | −0.0813941 | − | 0.996682i | \(-0.525937\pi\) | ||||
−0.0813941 | + | 0.996682i | \(0.525937\pi\) | |||||||
\(18\) | −2.38443 | −0.562015 | ||||||||
\(19\) | −4.69479 | −1.07706 | −0.538530 | − | 0.842606i | \(-0.681020\pi\) | ||||
−0.538530 | + | 0.842606i | \(0.681020\pi\) | |||||||
\(20\) | 9.96306 | 2.22781 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −5.05599 | −1.07794 | ||||||||
\(23\) | −4.25009 | −0.886204 | −0.443102 | − | 0.896471i | \(-0.646122\pi\) | ||||
−0.443102 | + | 0.896471i | \(0.646122\pi\) | |||||||
\(24\) | 4.01897 | 0.820368 | ||||||||
\(25\) | 2.30788 | 0.461576 | ||||||||
\(26\) | −1.49938 | −0.294053 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.68550 | 0.696495 | ||||||||
\(29\) | −8.77796 | −1.63003 | −0.815013 | − | 0.579443i | \(-0.803270\pi\) | ||||
−0.815013 | + | 0.579443i | \(0.803270\pi\) | |||||||
\(30\) | 6.44585 | 1.17685 | ||||||||
\(31\) | 8.26491 | 1.48442 | 0.742211 | − | 0.670167i | \(-0.233777\pi\) | ||||
0.742211 | + | 0.670167i | \(0.233777\pi\) | |||||||
\(32\) | 2.76373 | 0.488563 | ||||||||
\(33\) | −2.12042 | −0.369118 | ||||||||
\(34\) | 1.60041 | 0.274468 | ||||||||
\(35\) | 2.70331 | 0.456943 | ||||||||
\(36\) | 3.68550 | 0.614251 | ||||||||
\(37\) | −2.88242 | −0.473866 | −0.236933 | − | 0.971526i | \(-0.576142\pi\) | ||||
−0.236933 | + | 0.971526i | \(0.576142\pi\) | |||||||
\(38\) | 11.1944 | 1.81597 | ||||||||
\(39\) | −0.628822 | −0.100692 | ||||||||
\(40\) | −10.8645 | −1.71783 | ||||||||
\(41\) | 0.950390 | 0.148426 | 0.0742130 | − | 0.997242i | \(-0.476356\pi\) | ||||
0.0742130 | + | 0.997242i | \(0.476356\pi\) | |||||||
\(42\) | 2.38443 | 0.367925 | ||||||||
\(43\) | −3.42276 | −0.521967 | −0.260983 | − | 0.965343i | \(-0.584047\pi\) | ||||
−0.260983 | + | 0.965343i | \(0.584047\pi\) | |||||||
\(44\) | 7.81482 | 1.17813 | ||||||||
\(45\) | 2.70331 | 0.402986 | ||||||||
\(46\) | 10.1340 | 1.49418 | ||||||||
\(47\) | 7.41532 | 1.08164 | 0.540818 | − | 0.841140i | \(-0.318115\pi\) | ||||
0.540818 | + | 0.841140i | \(0.318115\pi\) | |||||||
\(48\) | −2.21194 | −0.319265 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −5.50298 | −0.778239 | ||||||||
\(51\) | 0.671193 | 0.0939858 | ||||||||
\(52\) | 2.31753 | 0.321383 | ||||||||
\(53\) | 10.0416 | 1.37932 | 0.689659 | − | 0.724134i | \(-0.257760\pi\) | ||||
0.689659 | + | 0.724134i | \(0.257760\pi\) | |||||||
\(54\) | 2.38443 | 0.324480 | ||||||||
\(55\) | 5.73215 | 0.772923 | ||||||||
\(56\) | −4.01897 | −0.537057 | ||||||||
\(57\) | 4.69479 | 0.621841 | ||||||||
\(58\) | 20.9304 | 2.74830 | ||||||||
\(59\) | −8.47742 | −1.10367 | −0.551833 | − | 0.833955i | \(-0.686071\pi\) | ||||
−0.551833 | + | 0.833955i | \(0.686071\pi\) | |||||||
\(60\) | −9.96306 | −1.28623 | ||||||||
\(61\) | −8.41749 | −1.07775 | −0.538875 | − | 0.842386i | \(-0.681150\pi\) | ||||
−0.538875 | + | 0.842386i | \(0.681150\pi\) | |||||||
\(62\) | −19.7071 | −2.50280 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −11.0138 | −1.37672 | ||||||||
\(65\) | 1.69990 | 0.210847 | ||||||||
\(66\) | 5.05599 | 0.622350 | ||||||||
\(67\) | −0.248919 | −0.0304103 | −0.0152051 | − | 0.999884i | \(-0.504840\pi\) | ||||
−0.0152051 | + | 0.999884i | \(0.504840\pi\) | |||||||
\(68\) | −2.47368 | −0.299978 | ||||||||
\(69\) | 4.25009 | 0.511650 | ||||||||
\(70\) | −6.44585 | −0.770427 | ||||||||
\(71\) | −10.5508 | −1.25215 | −0.626073 | − | 0.779764i | \(-0.715339\pi\) | ||||
−0.626073 | + | 0.779764i | \(0.715339\pi\) | |||||||
\(72\) | −4.01897 | −0.473640 | ||||||||
\(73\) | −6.70043 | −0.784226 | −0.392113 | − | 0.919917i | \(-0.628256\pi\) | ||||
−0.392113 | + | 0.919917i | \(0.628256\pi\) | |||||||
\(74\) | 6.87292 | 0.798960 | ||||||||
\(75\) | −2.30788 | −0.266491 | ||||||||
\(76\) | −17.3027 | −1.98475 | ||||||||
\(77\) | 2.12042 | 0.241644 | ||||||||
\(78\) | 1.49938 | 0.169771 | ||||||||
\(79\) | 10.9350 | 1.23029 | 0.615143 | − | 0.788415i | \(-0.289098\pi\) | ||||
0.615143 | + | 0.788415i | \(0.289098\pi\) | |||||||
\(80\) | 5.97955 | 0.668534 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.26614 | −0.250253 | ||||||||
\(83\) | 1.52127 | 0.166981 | 0.0834907 | − | 0.996509i | \(-0.473393\pi\) | ||||
0.0834907 | + | 0.996509i | \(0.473393\pi\) | |||||||
\(84\) | −3.68550 | −0.402122 | ||||||||
\(85\) | −1.81444 | −0.196804 | ||||||||
\(86\) | 8.16134 | 0.880060 | ||||||||
\(87\) | 8.77796 | 0.941096 | ||||||||
\(88\) | −8.52190 | −0.908437 | ||||||||
\(89\) | 9.66286 | 1.02426 | 0.512130 | − | 0.858908i | \(-0.328856\pi\) | ||||
0.512130 | + | 0.858908i | \(0.328856\pi\) | |||||||
\(90\) | −6.44585 | −0.679452 | ||||||||
\(91\) | 0.628822 | 0.0659184 | ||||||||
\(92\) | −15.6637 | −1.63305 | ||||||||
\(93\) | −8.26491 | −0.857031 | ||||||||
\(94\) | −17.6813 | −1.82369 | ||||||||
\(95\) | −12.6915 | −1.30212 | ||||||||
\(96\) | −2.76373 | −0.282072 | ||||||||
\(97\) | −0.763992 | −0.0775716 | −0.0387858 | − | 0.999248i | \(-0.512349\pi\) | ||||
−0.0387858 | + | 0.999248i | \(0.512349\pi\) | |||||||
\(98\) | −2.38443 | −0.240864 | ||||||||
\(99\) | 2.12042 | 0.213110 | ||||||||
\(100\) | 8.50571 | 0.850571 | ||||||||
\(101\) | −1.38949 | −0.138259 | −0.0691295 | − | 0.997608i | \(-0.522022\pi\) | ||||
−0.0691295 | + | 0.997608i | \(0.522022\pi\) | |||||||
\(102\) | −1.60041 | −0.158464 | ||||||||
\(103\) | −17.9914 | −1.77274 | −0.886371 | − | 0.462975i | \(-0.846782\pi\) | ||||
−0.886371 | + | 0.462975i | \(0.846782\pi\) | |||||||
\(104\) | −2.52721 | −0.247814 | ||||||||
\(105\) | −2.70331 | −0.263816 | ||||||||
\(106\) | −23.9435 | −2.32559 | ||||||||
\(107\) | −5.00643 | −0.483990 | −0.241995 | − | 0.970277i | \(-0.577802\pi\) | ||||
−0.241995 | + | 0.970277i | \(0.577802\pi\) | |||||||
\(108\) | −3.68550 | −0.354638 | ||||||||
\(109\) | 3.95320 | 0.378648 | 0.189324 | − | 0.981915i | \(-0.439370\pi\) | ||||
0.189324 | + | 0.981915i | \(0.439370\pi\) | |||||||
\(110\) | −13.6679 | −1.30318 | ||||||||
\(111\) | 2.88242 | 0.273587 | ||||||||
\(112\) | 2.21194 | 0.209008 | ||||||||
\(113\) | 5.42209 | 0.510067 | 0.255034 | − | 0.966932i | \(-0.417913\pi\) | ||||
0.255034 | + | 0.966932i | \(0.417913\pi\) | |||||||
\(114\) | −11.1944 | −1.04845 | ||||||||
\(115\) | −11.4893 | −1.07138 | ||||||||
\(116\) | −32.3512 | −3.00373 | ||||||||
\(117\) | 0.628822 | 0.0581346 | ||||||||
\(118\) | 20.2138 | 1.86083 | ||||||||
\(119\) | −0.671193 | −0.0615282 | ||||||||
\(120\) | 10.8645 | 0.991790 | ||||||||
\(121\) | −6.50382 | −0.591256 | ||||||||
\(122\) | 20.0709 | 1.81714 | ||||||||
\(123\) | −0.950390 | −0.0856938 | ||||||||
\(124\) | 30.4604 | 2.73542 | ||||||||
\(125\) | −7.27763 | −0.650931 | ||||||||
\(126\) | −2.38443 | −0.212422 | ||||||||
\(127\) | −4.21917 | −0.374391 | −0.187196 | − | 0.982323i | \(-0.559940\pi\) | ||||
−0.187196 | + | 0.982323i | \(0.559940\pi\) | |||||||
\(128\) | 20.7341 | 1.83266 | ||||||||
\(129\) | 3.42276 | 0.301358 | ||||||||
\(130\) | −4.05329 | −0.355497 | ||||||||
\(131\) | 8.52713 | 0.745018 | 0.372509 | − | 0.928028i | \(-0.378497\pi\) | ||||
0.372509 | + | 0.928028i | \(0.378497\pi\) | |||||||
\(132\) | −7.81482 | −0.680193 | ||||||||
\(133\) | −4.69479 | −0.407090 | ||||||||
\(134\) | 0.593529 | 0.0512731 | ||||||||
\(135\) | −2.70331 | −0.232664 | ||||||||
\(136\) | 2.69750 | 0.231309 | ||||||||
\(137\) | −7.13079 | −0.609225 | −0.304612 | − | 0.952476i | \(-0.598527\pi\) | ||||
−0.304612 | + | 0.952476i | \(0.598527\pi\) | |||||||
\(138\) | −10.1340 | −0.862666 | ||||||||
\(139\) | 4.66223 | 0.395445 | 0.197722 | − | 0.980258i | \(-0.436646\pi\) | ||||
0.197722 | + | 0.980258i | \(0.436646\pi\) | |||||||
\(140\) | 9.96306 | 0.842032 | ||||||||
\(141\) | −7.41532 | −0.624483 | ||||||||
\(142\) | 25.1576 | 2.11118 | ||||||||
\(143\) | 1.33337 | 0.111502 | ||||||||
\(144\) | 2.21194 | 0.184328 | ||||||||
\(145\) | −23.7295 | −1.97063 | ||||||||
\(146\) | 15.9767 | 1.32224 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −10.6232 | −0.873218 | ||||||||
\(149\) | 15.9461 | 1.30635 | 0.653177 | − | 0.757206i | \(-0.273436\pi\) | ||||
0.653177 | + | 0.757206i | \(0.273436\pi\) | |||||||
\(150\) | 5.50298 | 0.449317 | ||||||||
\(151\) | 19.9621 | 1.62449 | 0.812247 | − | 0.583314i | \(-0.198244\pi\) | ||||
0.812247 | + | 0.583314i | \(0.198244\pi\) | |||||||
\(152\) | 18.8682 | 1.53042 | ||||||||
\(153\) | −0.671193 | −0.0542627 | ||||||||
\(154\) | −5.05599 | −0.407423 | ||||||||
\(155\) | 22.3426 | 1.79460 | ||||||||
\(156\) | −2.31753 | −0.185551 | ||||||||
\(157\) | −15.4079 | −1.22968 | −0.614841 | − | 0.788651i | \(-0.710780\pi\) | ||||
−0.614841 | + | 0.788651i | \(0.710780\pi\) | |||||||
\(158\) | −26.0738 | −2.07432 | ||||||||
\(159\) | −10.0416 | −0.796350 | ||||||||
\(160\) | 7.47122 | 0.590652 | ||||||||
\(161\) | −4.25009 | −0.334954 | ||||||||
\(162\) | −2.38443 | −0.187338 | ||||||||
\(163\) | −23.8685 | −1.86952 | −0.934761 | − | 0.355276i | \(-0.884387\pi\) | ||||
−0.934761 | + | 0.355276i | \(0.884387\pi\) | |||||||
\(164\) | 3.50267 | 0.273512 | ||||||||
\(165\) | −5.73215 | −0.446247 | ||||||||
\(166\) | −3.62737 | −0.281538 | ||||||||
\(167\) | 11.1535 | 0.863080 | 0.431540 | − | 0.902094i | \(-0.357970\pi\) | ||||
0.431540 | + | 0.902094i | \(0.357970\pi\) | |||||||
\(168\) | 4.01897 | 0.310070 | ||||||||
\(169\) | −12.6046 | −0.969583 | ||||||||
\(170\) | 4.32641 | 0.331820 | ||||||||
\(171\) | −4.69479 | −0.359020 | ||||||||
\(172\) | −12.6146 | −0.961855 | ||||||||
\(173\) | −22.9710 | −1.74645 | −0.873227 | − | 0.487314i | \(-0.837977\pi\) | ||||
−0.873227 | + | 0.487314i | \(0.837977\pi\) | |||||||
\(174\) | −20.9304 | −1.58673 | ||||||||
\(175\) | 2.30788 | 0.174459 | ||||||||
\(176\) | 4.69023 | 0.353540 | ||||||||
\(177\) | 8.47742 | 0.637202 | ||||||||
\(178\) | −23.0404 | −1.72695 | ||||||||
\(179\) | −26.0779 | −1.94916 | −0.974578 | − | 0.224049i | \(-0.928072\pi\) | ||||
−0.974578 | + | 0.224049i | \(0.928072\pi\) | |||||||
\(180\) | 9.96306 | 0.742603 | ||||||||
\(181\) | −22.8074 | −1.69526 | −0.847631 | − | 0.530586i | \(-0.821972\pi\) | ||||
−0.847631 | + | 0.530586i | \(0.821972\pi\) | |||||||
\(182\) | −1.49938 | −0.111142 | ||||||||
\(183\) | 8.41749 | 0.622239 | ||||||||
\(184\) | 17.0810 | 1.25922 | ||||||||
\(185\) | −7.79206 | −0.572884 | ||||||||
\(186\) | 19.7071 | 1.44499 | ||||||||
\(187\) | −1.42321 | −0.104075 | ||||||||
\(188\) | 27.3292 | 1.99319 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 30.2619 | 2.19543 | ||||||||
\(191\) | 6.76855 | 0.489755 | 0.244877 | − | 0.969554i | \(-0.421252\pi\) | ||||
0.244877 | + | 0.969554i | \(0.421252\pi\) | |||||||
\(192\) | 11.0138 | 0.794852 | ||||||||
\(193\) | −21.9063 | −1.57685 | −0.788424 | − | 0.615133i | \(-0.789102\pi\) | ||||
−0.788424 | + | 0.615133i | \(0.789102\pi\) | |||||||
\(194\) | 1.82169 | 0.130789 | ||||||||
\(195\) | −1.69990 | −0.121732 | ||||||||
\(196\) | 3.68550 | 0.263250 | ||||||||
\(197\) | −4.14688 | −0.295453 | −0.147726 | − | 0.989028i | \(-0.547195\pi\) | ||||
−0.147726 | + | 0.989028i | \(0.547195\pi\) | |||||||
\(198\) | −5.05599 | −0.359314 | ||||||||
\(199\) | −14.8300 | −1.05127 | −0.525635 | − | 0.850710i | \(-0.676172\pi\) | ||||
−0.525635 | + | 0.850710i | \(0.676172\pi\) | |||||||
\(200\) | −9.27530 | −0.655863 | ||||||||
\(201\) | 0.248919 | 0.0175574 | ||||||||
\(202\) | 3.31313 | 0.233111 | ||||||||
\(203\) | −8.77796 | −0.616092 | ||||||||
\(204\) | 2.47368 | 0.173193 | ||||||||
\(205\) | 2.56920 | 0.179441 | ||||||||
\(206\) | 42.8992 | 2.98893 | ||||||||
\(207\) | −4.25009 | −0.295401 | ||||||||
\(208\) | 1.39091 | 0.0964425 | ||||||||
\(209\) | −9.95494 | −0.688597 | ||||||||
\(210\) | 6.44585 | 0.444806 | ||||||||
\(211\) | 19.0732 | 1.31306 | 0.656528 | − | 0.754302i | \(-0.272025\pi\) | ||||
0.656528 | + | 0.754302i | \(0.272025\pi\) | |||||||
\(212\) | 37.0083 | 2.54174 | ||||||||
\(213\) | 10.5508 | 0.722927 | ||||||||
\(214\) | 11.9375 | 0.816030 | ||||||||
\(215\) | −9.25279 | −0.631035 | ||||||||
\(216\) | 4.01897 | 0.273456 | ||||||||
\(217\) | 8.26491 | 0.561058 | ||||||||
\(218\) | −9.42613 | −0.638418 | ||||||||
\(219\) | 6.70043 | 0.452773 | ||||||||
\(220\) | 21.1259 | 1.42431 | ||||||||
\(221\) | −0.422061 | −0.0283909 | ||||||||
\(222\) | −6.87292 | −0.461280 | ||||||||
\(223\) | −13.9926 | −0.937014 | −0.468507 | − | 0.883460i | \(-0.655208\pi\) | ||||
−0.468507 | + | 0.883460i | \(0.655208\pi\) | |||||||
\(224\) | 2.76373 | 0.184659 | ||||||||
\(225\) | 2.30788 | 0.153859 | ||||||||
\(226\) | −12.9286 | −0.859997 | ||||||||
\(227\) | −26.7515 | −1.77556 | −0.887780 | − | 0.460268i | \(-0.847753\pi\) | ||||
−0.887780 | + | 0.460268i | \(0.847753\pi\) | |||||||
\(228\) | 17.3027 | 1.14590 | ||||||||
\(229\) | −20.5408 | −1.35737 | −0.678686 | − | 0.734428i | \(-0.737450\pi\) | ||||
−0.678686 | + | 0.734428i | \(0.737450\pi\) | |||||||
\(230\) | 27.3954 | 1.80640 | ||||||||
\(231\) | −2.12042 | −0.139513 | ||||||||
\(232\) | 35.2783 | 2.31614 | ||||||||
\(233\) | 28.9276 | 1.89511 | 0.947556 | − | 0.319589i | \(-0.103545\pi\) | ||||
0.947556 | + | 0.319589i | \(0.103545\pi\) | |||||||
\(234\) | −1.49938 | −0.0980176 | ||||||||
\(235\) | 20.0459 | 1.30765 | ||||||||
\(236\) | −31.2436 | −2.03378 | ||||||||
\(237\) | −10.9350 | −0.710306 | ||||||||
\(238\) | 1.60041 | 0.103739 | ||||||||
\(239\) | 11.0244 | 0.713108 | 0.356554 | − | 0.934275i | \(-0.383952\pi\) | ||||
0.356554 | + | 0.934275i | \(0.383952\pi\) | |||||||
\(240\) | −5.97955 | −0.385978 | ||||||||
\(241\) | −0.651087 | −0.0419402 | −0.0209701 | − | 0.999780i | \(-0.506675\pi\) | ||||
−0.0209701 | + | 0.999780i | \(0.506675\pi\) | |||||||
\(242\) | 15.5079 | 0.996885 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −31.0227 | −1.98602 | ||||||||
\(245\) | 2.70331 | 0.172708 | ||||||||
\(246\) | 2.26614 | 0.144484 | ||||||||
\(247\) | −2.95219 | −0.187843 | ||||||||
\(248\) | −33.2164 | −2.10924 | ||||||||
\(249\) | −1.52127 | −0.0964067 | ||||||||
\(250\) | 17.3530 | 1.09750 | ||||||||
\(251\) | 25.1078 | 1.58479 | 0.792396 | − | 0.610007i | \(-0.208833\pi\) | ||||
0.792396 | + | 0.610007i | \(0.208833\pi\) | |||||||
\(252\) | 3.68550 | 0.232165 | ||||||||
\(253\) | −9.01197 | −0.566577 | ||||||||
\(254\) | 10.0603 | 0.631241 | ||||||||
\(255\) | 1.81444 | 0.113625 | ||||||||
\(256\) | −27.4115 | −1.71322 | ||||||||
\(257\) | 21.4888 | 1.34044 | 0.670218 | − | 0.742164i | \(-0.266201\pi\) | ||||
0.670218 | + | 0.742164i | \(0.266201\pi\) | |||||||
\(258\) | −8.16134 | −0.508103 | ||||||||
\(259\) | −2.88242 | −0.179105 | ||||||||
\(260\) | 6.26499 | 0.388538 | ||||||||
\(261\) | −8.77796 | −0.543342 | ||||||||
\(262\) | −20.3323 | −1.25614 | ||||||||
\(263\) | −8.15338 | −0.502759 | −0.251380 | − | 0.967889i | \(-0.580884\pi\) | ||||
−0.251380 | + | 0.967889i | \(0.580884\pi\) | |||||||
\(264\) | 8.52190 | 0.524487 | ||||||||
\(265\) | 27.1455 | 1.66754 | ||||||||
\(266\) | 11.1944 | 0.686373 | ||||||||
\(267\) | −9.66286 | −0.591357 | ||||||||
\(268\) | −0.917391 | −0.0560386 | ||||||||
\(269\) | 4.11605 | 0.250960 | 0.125480 | − | 0.992096i | \(-0.459953\pi\) | ||||
0.125480 | + | 0.992096i | \(0.459953\pi\) | |||||||
\(270\) | 6.44585 | 0.392282 | ||||||||
\(271\) | 6.69170 | 0.406492 | 0.203246 | − | 0.979128i | \(-0.434851\pi\) | ||||
0.203246 | + | 0.979128i | \(0.434851\pi\) | |||||||
\(272\) | −1.48464 | −0.0900192 | ||||||||
\(273\) | −0.628822 | −0.0380580 | ||||||||
\(274\) | 17.0029 | 1.02718 | ||||||||
\(275\) | 4.89368 | 0.295100 | ||||||||
\(276\) | 15.6637 | 0.942844 | ||||||||
\(277\) | −3.57687 | −0.214913 | −0.107457 | − | 0.994210i | \(-0.534271\pi\) | ||||
−0.107457 | + | 0.994210i | \(0.534271\pi\) | |||||||
\(278\) | −11.1168 | −0.666739 | ||||||||
\(279\) | 8.26491 | 0.494807 | ||||||||
\(280\) | −10.8645 | −0.649279 | ||||||||
\(281\) | 19.9376 | 1.18938 | 0.594688 | − | 0.803957i | \(-0.297276\pi\) | ||||
0.594688 | + | 0.803957i | \(0.297276\pi\) | |||||||
\(282\) | 17.6813 | 1.05291 | ||||||||
\(283\) | 4.01533 | 0.238687 | 0.119343 | − | 0.992853i | \(-0.461921\pi\) | ||||
0.119343 | + | 0.992853i | \(0.461921\pi\) | |||||||
\(284\) | −38.8849 | −2.30740 | ||||||||
\(285\) | 12.6915 | 0.751779 | ||||||||
\(286\) | −3.17932 | −0.187997 | ||||||||
\(287\) | 0.950390 | 0.0560998 | ||||||||
\(288\) | 2.76373 | 0.162854 | ||||||||
\(289\) | −16.5495 | −0.973500 | ||||||||
\(290\) | 56.5814 | 3.32258 | ||||||||
\(291\) | 0.763992 | 0.0447860 | ||||||||
\(292\) | −24.6945 | −1.44513 | ||||||||
\(293\) | −26.9013 | −1.57159 | −0.785795 | − | 0.618487i | \(-0.787746\pi\) | ||||
−0.785795 | + | 0.618487i | \(0.787746\pi\) | |||||||
\(294\) | 2.38443 | 0.139063 | ||||||||
\(295\) | −22.9171 | −1.33428 | ||||||||
\(296\) | 11.5843 | 0.673326 | ||||||||
\(297\) | −2.12042 | −0.123039 | ||||||||
\(298\) | −38.0223 | −2.20257 | ||||||||
\(299\) | −2.67255 | −0.154557 | ||||||||
\(300\) | −8.50571 | −0.491077 | ||||||||
\(301\) | −3.42276 | −0.197285 | ||||||||
\(302\) | −47.5983 | −2.73897 | ||||||||
\(303\) | 1.38949 | 0.0798239 | ||||||||
\(304\) | −10.3846 | −0.595597 | ||||||||
\(305\) | −22.7551 | −1.30295 | ||||||||
\(306\) | 1.60041 | 0.0914895 | ||||||||
\(307\) | −24.9984 | −1.42673 | −0.713367 | − | 0.700791i | \(-0.752831\pi\) | ||||
−0.713367 | + | 0.700791i | \(0.752831\pi\) | |||||||
\(308\) | 7.81482 | 0.445291 | ||||||||
\(309\) | 17.9914 | 1.02349 | ||||||||
\(310\) | −53.2744 | −3.02578 | ||||||||
\(311\) | 7.01552 | 0.397814 | 0.198907 | − | 0.980018i | \(-0.436261\pi\) | ||||
0.198907 | + | 0.980018i | \(0.436261\pi\) | |||||||
\(312\) | 2.52721 | 0.143075 | ||||||||
\(313\) | −8.08016 | −0.456717 | −0.228359 | − | 0.973577i | \(-0.573336\pi\) | ||||
−0.228359 | + | 0.973577i | \(0.573336\pi\) | |||||||
\(314\) | 36.7390 | 2.07330 | ||||||||
\(315\) | 2.70331 | 0.152314 | ||||||||
\(316\) | 40.3011 | 2.26711 | ||||||||
\(317\) | −8.21015 | −0.461128 | −0.230564 | − | 0.973057i | \(-0.574057\pi\) | ||||
−0.230564 | + | 0.973057i | \(0.574057\pi\) | |||||||
\(318\) | 23.9435 | 1.34268 | ||||||||
\(319\) | −18.6130 | −1.04213 | ||||||||
\(320\) | −29.7737 | −1.66440 | ||||||||
\(321\) | 5.00643 | 0.279432 | ||||||||
\(322\) | 10.1340 | 0.564747 | ||||||||
\(323\) | 3.15111 | 0.175333 | ||||||||
\(324\) | 3.68550 | 0.204750 | ||||||||
\(325\) | 1.45125 | 0.0805006 | ||||||||
\(326\) | 56.9127 | 3.15210 | ||||||||
\(327\) | −3.95320 | −0.218613 | ||||||||
\(328\) | −3.81959 | −0.210901 | ||||||||
\(329\) | 7.41532 | 0.408820 | ||||||||
\(330\) | 13.6679 | 0.752394 | ||||||||
\(331\) | 33.0162 | 1.81474 | 0.907369 | − | 0.420336i | \(-0.138088\pi\) | ||||
0.907369 | + | 0.420336i | \(0.138088\pi\) | |||||||
\(332\) | 5.60666 | 0.307705 | ||||||||
\(333\) | −2.88242 | −0.157955 | ||||||||
\(334\) | −26.5946 | −1.45519 | ||||||||
\(335\) | −0.672904 | −0.0367647 | ||||||||
\(336\) | −2.21194 | −0.120671 | ||||||||
\(337\) | 6.59010 | 0.358986 | 0.179493 | − | 0.983759i | \(-0.442554\pi\) | ||||
0.179493 | + | 0.983759i | \(0.442554\pi\) | |||||||
\(338\) | 30.0547 | 1.63476 | ||||||||
\(339\) | −5.42209 | −0.294488 | ||||||||
\(340\) | −6.68714 | −0.362661 | ||||||||
\(341\) | 17.5251 | 0.949036 | ||||||||
\(342\) | 11.1944 | 0.605324 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 13.7560 | 0.741673 | ||||||||
\(345\) | 11.4893 | 0.618563 | ||||||||
\(346\) | 54.7727 | 2.94460 | ||||||||
\(347\) | −10.2143 | −0.548330 | −0.274165 | − | 0.961683i | \(-0.588401\pi\) | ||||
−0.274165 | + | 0.961683i | \(0.588401\pi\) | |||||||
\(348\) | 32.3512 | 1.73421 | ||||||||
\(349\) | 0.804067 | 0.0430407 | 0.0215204 | − | 0.999768i | \(-0.493149\pi\) | ||||
0.0215204 | + | 0.999768i | \(0.493149\pi\) | |||||||
\(350\) | −5.50298 | −0.294147 | ||||||||
\(351\) | −0.628822 | −0.0335640 | ||||||||
\(352\) | 5.86027 | 0.312353 | ||||||||
\(353\) | 8.50057 | 0.452440 | 0.226220 | − | 0.974076i | \(-0.427363\pi\) | ||||
0.226220 | + | 0.974076i | \(0.427363\pi\) | |||||||
\(354\) | −20.2138 | −1.07435 | ||||||||
\(355\) | −28.5220 | −1.51379 | ||||||||
\(356\) | 35.6125 | 1.88746 | ||||||||
\(357\) | 0.671193 | 0.0355233 | ||||||||
\(358\) | 62.1810 | 3.28637 | ||||||||
\(359\) | 19.1932 | 1.01298 | 0.506489 | − | 0.862247i | \(-0.330943\pi\) | ||||
0.506489 | + | 0.862247i | \(0.330943\pi\) | |||||||
\(360\) | −10.8645 | −0.572610 | ||||||||
\(361\) | 3.04109 | 0.160058 | ||||||||
\(362\) | 54.3827 | 2.85829 | ||||||||
\(363\) | 6.50382 | 0.341362 | ||||||||
\(364\) | 2.31753 | 0.121471 | ||||||||
\(365\) | −18.1133 | −0.948095 | ||||||||
\(366\) | −20.0709 | −1.04912 | ||||||||
\(367\) | 28.5258 | 1.48903 | 0.744516 | − | 0.667604i | \(-0.232680\pi\) | ||||
0.744516 | + | 0.667604i | \(0.232680\pi\) | |||||||
\(368\) | −9.40091 | −0.490057 | ||||||||
\(369\) | 0.950390 | 0.0494753 | ||||||||
\(370\) | 18.5796 | 0.965909 | ||||||||
\(371\) | 10.0416 | 0.521333 | ||||||||
\(372\) | −30.4604 | −1.57930 | ||||||||
\(373\) | 29.2428 | 1.51414 | 0.757068 | − | 0.653336i | \(-0.226631\pi\) | ||||
0.757068 | + | 0.653336i | \(0.226631\pi\) | |||||||
\(374\) | 3.39355 | 0.175476 | ||||||||
\(375\) | 7.27763 | 0.375815 | ||||||||
\(376\) | −29.8019 | −1.53692 | ||||||||
\(377\) | −5.51977 | −0.284283 | ||||||||
\(378\) | 2.38443 | 0.122642 | ||||||||
\(379\) | −12.7962 | −0.657297 | −0.328649 | − | 0.944452i | \(-0.606593\pi\) | ||||
−0.328649 | + | 0.944452i | \(0.606593\pi\) | |||||||
\(380\) | −46.7745 | −2.39948 | ||||||||
\(381\) | 4.21917 | 0.216155 | ||||||||
\(382\) | −16.1391 | −0.825749 | ||||||||
\(383\) | 1.00000 | 0.0510976 | ||||||||
\(384\) | −20.7341 | −1.05809 | ||||||||
\(385\) | 5.73215 | 0.292137 | ||||||||
\(386\) | 52.2339 | 2.65864 | ||||||||
\(387\) | −3.42276 | −0.173989 | ||||||||
\(388\) | −2.81570 | −0.142945 | ||||||||
\(389\) | 33.3570 | 1.69127 | 0.845634 | − | 0.533763i | \(-0.179222\pi\) | ||||
0.845634 | + | 0.533763i | \(0.179222\pi\) | |||||||
\(390\) | 4.05329 | 0.205246 | ||||||||
\(391\) | 2.85263 | 0.144264 | ||||||||
\(392\) | −4.01897 | −0.202989 | ||||||||
\(393\) | −8.52713 | −0.430137 | ||||||||
\(394\) | 9.88794 | 0.498147 | ||||||||
\(395\) | 29.5608 | 1.48736 | ||||||||
\(396\) | 7.81482 | 0.392709 | ||||||||
\(397\) | 27.3629 | 1.37330 | 0.686651 | − | 0.726987i | \(-0.259080\pi\) | ||||
0.686651 | + | 0.726987i | \(0.259080\pi\) | |||||||
\(398\) | 35.3611 | 1.77249 | ||||||||
\(399\) | 4.69479 | 0.235034 | ||||||||
\(400\) | 5.10489 | 0.255244 | ||||||||
\(401\) | −8.80353 | −0.439627 | −0.219814 | − | 0.975542i | \(-0.570545\pi\) | ||||
−0.219814 | + | 0.975542i | \(0.570545\pi\) | |||||||
\(402\) | −0.593529 | −0.0296025 | ||||||||
\(403\) | 5.19715 | 0.258889 | ||||||||
\(404\) | −5.12096 | −0.254777 | ||||||||
\(405\) | 2.70331 | 0.134329 | ||||||||
\(406\) | 20.9304 | 1.03876 | ||||||||
\(407\) | −6.11193 | −0.302957 | ||||||||
\(408\) | −2.69750 | −0.133546 | ||||||||
\(409\) | −1.53212 | −0.0757586 | −0.0378793 | − | 0.999282i | \(-0.512060\pi\) | ||||
−0.0378793 | + | 0.999282i | \(0.512060\pi\) | |||||||
\(410\) | −6.12607 | −0.302545 | ||||||||
\(411\) | 7.13079 | 0.351736 | ||||||||
\(412\) | −66.3073 | −3.26672 | ||||||||
\(413\) | −8.47742 | −0.417147 | ||||||||
\(414\) | 10.1340 | 0.498060 | ||||||||
\(415\) | 4.11247 | 0.201873 | ||||||||
\(416\) | 1.73789 | 0.0852072 | ||||||||
\(417\) | −4.66223 | −0.228310 | ||||||||
\(418\) | 23.7368 | 1.16101 | ||||||||
\(419\) | −13.4647 | −0.657796 | −0.328898 | − | 0.944365i | \(-0.606677\pi\) | ||||
−0.328898 | + | 0.944365i | \(0.606677\pi\) | |||||||
\(420\) | −9.96306 | −0.486148 | ||||||||
\(421\) | −29.2953 | −1.42777 | −0.713883 | − | 0.700265i | \(-0.753065\pi\) | ||||
−0.713883 | + | 0.700265i | \(0.753065\pi\) | |||||||
\(422\) | −45.4788 | −2.21387 | ||||||||
\(423\) | 7.41532 | 0.360545 | ||||||||
\(424\) | −40.3568 | −1.95990 | ||||||||
\(425\) | −1.54903 | −0.0751392 | ||||||||
\(426\) | −25.1576 | −1.21889 | ||||||||
\(427\) | −8.41749 | −0.407351 | ||||||||
\(428\) | −18.4512 | −0.891874 | ||||||||
\(429\) | −1.33337 | −0.0643755 | ||||||||
\(430\) | 22.0626 | 1.06395 | ||||||||
\(431\) | −23.9157 | −1.15198 | −0.575990 | − | 0.817457i | \(-0.695383\pi\) | ||||
−0.575990 | + | 0.817457i | \(0.695383\pi\) | |||||||
\(432\) | −2.21194 | −0.106422 | ||||||||
\(433\) | −32.7290 | −1.57286 | −0.786429 | − | 0.617681i | \(-0.788072\pi\) | ||||
−0.786429 | + | 0.617681i | \(0.788072\pi\) | |||||||
\(434\) | −19.7071 | −0.945971 | ||||||||
\(435\) | 23.7295 | 1.13774 | ||||||||
\(436\) | 14.5695 | 0.697755 | ||||||||
\(437\) | 19.9533 | 0.954495 | ||||||||
\(438\) | −15.9767 | −0.763396 | ||||||||
\(439\) | 33.1445 | 1.58190 | 0.790951 | − | 0.611879i | \(-0.209586\pi\) | ||||
0.790951 | + | 0.611879i | \(0.209586\pi\) | |||||||
\(440\) | −23.0373 | −1.09826 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 1.00637 | 0.0478683 | ||||||||
\(443\) | −29.5375 | −1.40337 | −0.701685 | − | 0.712487i | \(-0.747569\pi\) | ||||
−0.701685 | + | 0.712487i | \(0.747569\pi\) | |||||||
\(444\) | 10.6232 | 0.504153 | ||||||||
\(445\) | 26.1217 | 1.23829 | ||||||||
\(446\) | 33.3644 | 1.57985 | ||||||||
\(447\) | −15.9461 | −0.754223 | ||||||||
\(448\) | −11.0138 | −0.520353 | ||||||||
\(449\) | 8.53233 | 0.402666 | 0.201333 | − | 0.979523i | \(-0.435473\pi\) | ||||
0.201333 | + | 0.979523i | \(0.435473\pi\) | |||||||
\(450\) | −5.50298 | −0.259413 | ||||||||
\(451\) | 2.01523 | 0.0948933 | ||||||||
\(452\) | 19.9831 | 0.939928 | ||||||||
\(453\) | −19.9621 | −0.937902 | ||||||||
\(454\) | 63.7871 | 2.99368 | ||||||||
\(455\) | 1.69990 | 0.0796925 | ||||||||
\(456\) | −18.8682 | −0.883586 | ||||||||
\(457\) | −2.88815 | −0.135102 | −0.0675510 | − | 0.997716i | \(-0.521519\pi\) | ||||
−0.0675510 | + | 0.997716i | \(0.521519\pi\) | |||||||
\(458\) | 48.9780 | 2.28859 | ||||||||
\(459\) | 0.671193 | 0.0313286 | ||||||||
\(460\) | −42.3439 | −1.97429 | ||||||||
\(461\) | 16.8996 | 0.787095 | 0.393547 | − | 0.919304i | \(-0.371248\pi\) | ||||
0.393547 | + | 0.919304i | \(0.371248\pi\) | |||||||
\(462\) | 5.05599 | 0.235226 | ||||||||
\(463\) | 13.0716 | 0.607490 | 0.303745 | − | 0.952753i | \(-0.401763\pi\) | ||||
0.303745 | + | 0.952753i | \(0.401763\pi\) | |||||||
\(464\) | −19.4163 | −0.901378 | ||||||||
\(465\) | −22.3426 | −1.03611 | ||||||||
\(466\) | −68.9759 | −3.19525 | ||||||||
\(467\) | −3.86656 | −0.178923 | −0.0894616 | − | 0.995990i | \(-0.528515\pi\) | ||||
−0.0894616 | + | 0.995990i | \(0.528515\pi\) | |||||||
\(468\) | 2.31753 | 0.107128 | ||||||||
\(469\) | −0.248919 | −0.0114940 | ||||||||
\(470\) | −47.7981 | −2.20476 | ||||||||
\(471\) | 15.4079 | 0.709957 | ||||||||
\(472\) | 34.0705 | 1.56822 | ||||||||
\(473\) | −7.25770 | −0.333709 | ||||||||
\(474\) | 26.0738 | 1.19761 | ||||||||
\(475\) | −10.8350 | −0.497145 | ||||||||
\(476\) | −2.47368 | −0.113381 | ||||||||
\(477\) | 10.0416 | 0.459773 | ||||||||
\(478\) | −26.2869 | −1.20233 | ||||||||
\(479\) | 34.4647 | 1.57473 | 0.787367 | − | 0.616485i | \(-0.211444\pi\) | ||||
0.787367 | + | 0.616485i | \(0.211444\pi\) | |||||||
\(480\) | −7.47122 | −0.341013 | ||||||||
\(481\) | −1.81253 | −0.0826440 | ||||||||
\(482\) | 1.55247 | 0.0707132 | ||||||||
\(483\) | 4.25009 | 0.193386 | ||||||||
\(484\) | −23.9699 | −1.08954 | ||||||||
\(485\) | −2.06531 | −0.0937808 | ||||||||
\(486\) | 2.38443 | 0.108160 | ||||||||
\(487\) | 10.0622 | 0.455964 | 0.227982 | − | 0.973665i | \(-0.426787\pi\) | ||||
0.227982 | + | 0.973665i | \(0.426787\pi\) | |||||||
\(488\) | 33.8296 | 1.53139 | ||||||||
\(489\) | 23.8685 | 1.07937 | ||||||||
\(490\) | −6.44585 | −0.291194 | ||||||||
\(491\) | 28.8117 | 1.30026 | 0.650128 | − | 0.759825i | \(-0.274715\pi\) | ||||
0.650128 | + | 0.759825i | \(0.274715\pi\) | |||||||
\(492\) | −3.50267 | −0.157912 | ||||||||
\(493\) | 5.89170 | 0.265349 | ||||||||
\(494\) | 7.03929 | 0.316712 | ||||||||
\(495\) | 5.73215 | 0.257641 | ||||||||
\(496\) | 18.2814 | 0.820861 | ||||||||
\(497\) | −10.5508 | −0.473267 | ||||||||
\(498\) | 3.62737 | 0.162546 | ||||||||
\(499\) | −34.4603 | −1.54265 | −0.771327 | − | 0.636439i | \(-0.780407\pi\) | ||||
−0.771327 | + | 0.636439i | \(0.780407\pi\) | |||||||
\(500\) | −26.8217 | −1.19950 | ||||||||
\(501\) | −11.1535 | −0.498300 | ||||||||
\(502\) | −59.8678 | −2.67203 | ||||||||
\(503\) | −11.2997 | −0.503831 | −0.251915 | − | 0.967749i | \(-0.581060\pi\) | ||||
−0.251915 | + | 0.967749i | \(0.581060\pi\) | |||||||
\(504\) | −4.01897 | −0.179019 | ||||||||
\(505\) | −3.75621 | −0.167149 | ||||||||
\(506\) | 21.4884 | 0.955276 | ||||||||
\(507\) | 12.6046 | 0.559789 | ||||||||
\(508\) | −15.5498 | −0.689910 | ||||||||
\(509\) | −23.9688 | −1.06240 | −0.531200 | − | 0.847247i | \(-0.678259\pi\) | ||||
−0.531200 | + | 0.847247i | \(0.678259\pi\) | |||||||
\(510\) | −4.32641 | −0.191577 | ||||||||
\(511\) | −6.70043 | −0.296410 | ||||||||
\(512\) | 23.8926 | 1.05591 | ||||||||
\(513\) | 4.69479 | 0.207280 | ||||||||
\(514\) | −51.2386 | −2.26004 | ||||||||
\(515\) | −48.6362 | −2.14317 | ||||||||
\(516\) | 12.6146 | 0.555327 | ||||||||
\(517\) | 15.7236 | 0.691523 | ||||||||
\(518\) | 6.87292 | 0.301979 | ||||||||
\(519\) | 22.9710 | 1.00832 | ||||||||
\(520\) | −6.83184 | −0.299596 | ||||||||
\(521\) | 13.4663 | 0.589968 | 0.294984 | − | 0.955502i | \(-0.404686\pi\) | ||||
0.294984 | + | 0.955502i | \(0.404686\pi\) | |||||||
\(522\) | 20.9304 | 0.916100 | ||||||||
\(523\) | −29.1859 | −1.27621 | −0.638106 | − | 0.769949i | \(-0.720282\pi\) | ||||
−0.638106 | + | 0.769949i | \(0.720282\pi\) | |||||||
\(524\) | 31.4268 | 1.37288 | ||||||||
\(525\) | −2.30788 | −0.100724 | ||||||||
\(526\) | 19.4412 | 0.847675 | ||||||||
\(527\) | −5.54735 | −0.241646 | ||||||||
\(528\) | −4.69023 | −0.204116 | ||||||||
\(529\) | −4.93678 | −0.214642 | ||||||||
\(530\) | −64.7266 | −2.81154 | ||||||||
\(531\) | −8.47742 | −0.367889 | ||||||||
\(532\) | −17.3027 | −0.750167 | ||||||||
\(533\) | 0.597626 | 0.0258861 | ||||||||
\(534\) | 23.0404 | 0.997056 | ||||||||
\(535\) | −13.5339 | −0.585123 | ||||||||
\(536\) | 1.00040 | 0.0432105 | ||||||||
\(537\) | 26.0779 | 1.12535 | ||||||||
\(538\) | −9.81443 | −0.423130 | ||||||||
\(539\) | 2.12042 | 0.0913330 | ||||||||
\(540\) | −9.96306 | −0.428742 | ||||||||
\(541\) | 41.4908 | 1.78383 | 0.891914 | − | 0.452205i | \(-0.149362\pi\) | ||||
0.891914 | + | 0.452205i | \(0.149362\pi\) | |||||||
\(542\) | −15.9559 | −0.685364 | ||||||||
\(543\) | 22.8074 | 0.978760 | ||||||||
\(544\) | −1.85500 | −0.0795323 | ||||||||
\(545\) | 10.6867 | 0.457769 | ||||||||
\(546\) | 1.49938 | 0.0641676 | ||||||||
\(547\) | −41.8908 | −1.79112 | −0.895561 | − | 0.444939i | \(-0.853225\pi\) | ||||
−0.895561 | + | 0.444939i | \(0.853225\pi\) | |||||||
\(548\) | −26.2806 | −1.12265 | ||||||||
\(549\) | −8.41749 | −0.359250 | ||||||||
\(550\) | −11.6686 | −0.497552 | ||||||||
\(551\) | 41.2107 | 1.75564 | ||||||||
\(552\) | −17.0810 | −0.727014 | ||||||||
\(553\) | 10.9350 | 0.465005 | ||||||||
\(554\) | 8.52880 | 0.362354 | ||||||||
\(555\) | 7.79206 | 0.330755 | ||||||||
\(556\) | 17.1827 | 0.728707 | ||||||||
\(557\) | −19.9302 | −0.844470 | −0.422235 | − | 0.906486i | \(-0.638754\pi\) | ||||
−0.422235 | + | 0.906486i | \(0.638754\pi\) | |||||||
\(558\) | −19.7071 | −0.834268 | ||||||||
\(559\) | −2.15231 | −0.0910329 | ||||||||
\(560\) | 5.97955 | 0.252682 | ||||||||
\(561\) | 1.42321 | 0.0600880 | ||||||||
\(562\) | −47.5397 | −2.00534 | ||||||||
\(563\) | 22.5664 | 0.951062 | 0.475531 | − | 0.879699i | \(-0.342256\pi\) | ||||
0.475531 | + | 0.879699i | \(0.342256\pi\) | |||||||
\(564\) | −27.3292 | −1.15077 | ||||||||
\(565\) | 14.6576 | 0.616649 | ||||||||
\(566\) | −9.57427 | −0.402437 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 42.4032 | 1.77920 | ||||||||
\(569\) | 4.21106 | 0.176537 | 0.0882685 | − | 0.996097i | \(-0.471867\pi\) | ||||
0.0882685 | + | 0.996097i | \(0.471867\pi\) | |||||||
\(570\) | −30.2619 | −1.26753 | ||||||||
\(571\) | 1.55138 | 0.0649231 | 0.0324615 | − | 0.999473i | \(-0.489665\pi\) | ||||
0.0324615 | + | 0.999473i | \(0.489665\pi\) | |||||||
\(572\) | 4.91413 | 0.205470 | ||||||||
\(573\) | −6.76855 | −0.282760 | ||||||||
\(574\) | −2.26614 | −0.0945868 | ||||||||
\(575\) | −9.80869 | −0.409051 | ||||||||
\(576\) | −11.0138 | −0.458908 | ||||||||
\(577\) | −32.8411 | −1.36719 | −0.683597 | − | 0.729859i | \(-0.739586\pi\) | ||||
−0.683597 | + | 0.729859i | \(0.739586\pi\) | |||||||
\(578\) | 39.4611 | 1.64137 | ||||||||
\(579\) | 21.9063 | 0.910393 | ||||||||
\(580\) | −87.4553 | −3.63139 | ||||||||
\(581\) | 1.52127 | 0.0631130 | ||||||||
\(582\) | −1.82169 | −0.0755113 | ||||||||
\(583\) | 21.2924 | 0.881840 | ||||||||
\(584\) | 26.9288 | 1.11432 | ||||||||
\(585\) | 1.69990 | 0.0702822 | ||||||||
\(586\) | 64.1443 | 2.64977 | ||||||||
\(587\) | 38.4391 | 1.58655 | 0.793277 | − | 0.608861i | \(-0.208373\pi\) | ||||
0.793277 | + | 0.608861i | \(0.208373\pi\) | |||||||
\(588\) | −3.68550 | −0.151988 | ||||||||
\(589\) | −38.8020 | −1.59881 | ||||||||
\(590\) | 54.6442 | 2.24967 | ||||||||
\(591\) | 4.14688 | 0.170580 | ||||||||
\(592\) | −6.37572 | −0.262040 | ||||||||
\(593\) | 15.7194 | 0.645520 | 0.322760 | − | 0.946481i | \(-0.395389\pi\) | ||||
0.322760 | + | 0.946481i | \(0.395389\pi\) | |||||||
\(594\) | 5.05599 | 0.207450 | ||||||||
\(595\) | −1.81444 | −0.0743849 | ||||||||
\(596\) | 58.7693 | 2.40729 | ||||||||
\(597\) | 14.8300 | 0.606952 | ||||||||
\(598\) | 6.37250 | 0.260591 | ||||||||
\(599\) | −25.2442 | −1.03145 | −0.515724 | − | 0.856755i | \(-0.672477\pi\) | ||||
−0.515724 | + | 0.856755i | \(0.672477\pi\) | |||||||
\(600\) | 9.27530 | 0.378663 | ||||||||
\(601\) | −40.7117 | −1.66066 | −0.830332 | − | 0.557269i | \(-0.811849\pi\) | ||||
−0.830332 | + | 0.557269i | \(0.811849\pi\) | |||||||
\(602\) | 8.16134 | 0.332631 | ||||||||
\(603\) | −0.248919 | −0.0101368 | ||||||||
\(604\) | 73.5705 | 2.99354 | ||||||||
\(605\) | −17.5818 | −0.714803 | ||||||||
\(606\) | −3.31313 | −0.134587 | ||||||||
\(607\) | −39.9451 | −1.62132 | −0.810661 | − | 0.585516i | \(-0.800892\pi\) | ||||
−0.810661 | + | 0.585516i | \(0.800892\pi\) | |||||||
\(608\) | −12.9751 | −0.526212 | ||||||||
\(609\) | 8.77796 | 0.355701 | ||||||||
\(610\) | 54.2579 | 2.19684 | ||||||||
\(611\) | 4.66292 | 0.188641 | ||||||||
\(612\) | −2.47368 | −0.0999928 | ||||||||
\(613\) | −5.38078 | −0.217328 | −0.108664 | − | 0.994079i | \(-0.534657\pi\) | ||||
−0.108664 | + | 0.994079i | \(0.534657\pi\) | |||||||
\(614\) | 59.6069 | 2.40554 | ||||||||
\(615\) | −2.56920 | −0.103600 | ||||||||
\(616\) | −8.52190 | −0.343357 | ||||||||
\(617\) | −37.4738 | −1.50864 | −0.754320 | − | 0.656507i | \(-0.772033\pi\) | ||||
−0.754320 | + | 0.656507i | \(0.772033\pi\) | |||||||
\(618\) | −42.8992 | −1.72566 | ||||||||
\(619\) | −6.64696 | −0.267164 | −0.133582 | − | 0.991038i | \(-0.542648\pi\) | ||||
−0.133582 | + | 0.991038i | \(0.542648\pi\) | |||||||
\(620\) | 82.3438 | 3.30701 | ||||||||
\(621\) | 4.25009 | 0.170550 | ||||||||
\(622\) | −16.7280 | −0.670732 | ||||||||
\(623\) | 9.66286 | 0.387134 | ||||||||
\(624\) | −1.39091 | −0.0556811 | ||||||||
\(625\) | −31.2131 | −1.24852 | ||||||||
\(626\) | 19.2666 | 0.770047 | ||||||||
\(627\) | 9.95494 | 0.397562 | ||||||||
\(628\) | −56.7858 | −2.26600 | ||||||||
\(629\) | 1.93466 | 0.0771398 | ||||||||
\(630\) | −6.44585 | −0.256809 | ||||||||
\(631\) | −35.4223 | −1.41014 | −0.705070 | − | 0.709137i | \(-0.749085\pi\) | ||||
−0.705070 | + | 0.709137i | \(0.749085\pi\) | |||||||
\(632\) | −43.9475 | −1.74814 | ||||||||
\(633\) | −19.0732 | −0.758093 | ||||||||
\(634\) | 19.5765 | 0.777483 | ||||||||
\(635\) | −11.4057 | −0.452623 | ||||||||
\(636\) | −37.0083 | −1.46748 | ||||||||
\(637\) | 0.628822 | 0.0249148 | ||||||||
\(638\) | 44.3813 | 1.75707 | ||||||||
\(639\) | −10.5508 | −0.417382 | ||||||||
\(640\) | 56.0508 | 2.21560 | ||||||||
\(641\) | −35.4173 | −1.39890 | −0.699450 | − | 0.714682i | \(-0.746572\pi\) | ||||
−0.699450 | + | 0.714682i | \(0.746572\pi\) | |||||||
\(642\) | −11.9375 | −0.471135 | ||||||||
\(643\) | 0.0772237 | 0.00304541 | 0.00152270 | − | 0.999999i | \(-0.499515\pi\) | ||||
0.00152270 | + | 0.999999i | \(0.499515\pi\) | |||||||
\(644\) | −15.6637 | −0.617237 | ||||||||
\(645\) | 9.25279 | 0.364328 | ||||||||
\(646\) | −7.51361 | −0.295619 | ||||||||
\(647\) | 36.9595 | 1.45303 | 0.726513 | − | 0.687153i | \(-0.241140\pi\) | ||||
0.726513 | + | 0.687153i | \(0.241140\pi\) | |||||||
\(648\) | −4.01897 | −0.157880 | ||||||||
\(649\) | −17.9757 | −0.705608 | ||||||||
\(650\) | −3.46039 | −0.135728 | ||||||||
\(651\) | −8.26491 | −0.323927 | ||||||||
\(652\) | −87.9673 | −3.44507 | ||||||||
\(653\) | −21.2583 | −0.831900 | −0.415950 | − | 0.909388i | \(-0.636551\pi\) | ||||
−0.415950 | + | 0.909388i | \(0.636551\pi\) | |||||||
\(654\) | 9.42613 | 0.368591 | ||||||||
\(655\) | 23.0515 | 0.900695 | ||||||||
\(656\) | 2.10220 | 0.0820772 | ||||||||
\(657\) | −6.70043 | −0.261409 | ||||||||
\(658\) | −17.6813 | −0.689289 | ||||||||
\(659\) | −15.4509 | −0.601882 | −0.300941 | − | 0.953643i | \(-0.597301\pi\) | ||||
−0.300941 | + | 0.953643i | \(0.597301\pi\) | |||||||
\(660\) | −21.1259 | −0.822323 | ||||||||
\(661\) | −36.3074 | −1.41220 | −0.706098 | − | 0.708114i | \(-0.749546\pi\) | ||||
−0.706098 | + | 0.708114i | \(0.749546\pi\) | |||||||
\(662\) | −78.7249 | −3.05973 | ||||||||
\(663\) | 0.422061 | 0.0163915 | ||||||||
\(664\) | −6.11394 | −0.237267 | ||||||||
\(665\) | −12.6915 | −0.492155 | ||||||||
\(666\) | 6.87292 | 0.266320 | ||||||||
\(667\) | 37.3071 | 1.44454 | ||||||||
\(668\) | 41.1061 | 1.59044 | ||||||||
\(669\) | 13.9926 | 0.540985 | ||||||||
\(670\) | 1.60449 | 0.0619870 | ||||||||
\(671\) | −17.8486 | −0.689038 | ||||||||
\(672\) | −2.76373 | −0.106613 | ||||||||
\(673\) | 31.8991 | 1.22962 | 0.614810 | − | 0.788675i | \(-0.289233\pi\) | ||||
0.614810 | + | 0.788675i | \(0.289233\pi\) | |||||||
\(674\) | −15.7136 | −0.605267 | ||||||||
\(675\) | −2.30788 | −0.0888304 | ||||||||
\(676\) | −46.4543 | −1.78670 | ||||||||
\(677\) | −3.10925 | −0.119498 | −0.0597491 | − | 0.998213i | \(-0.519030\pi\) | ||||
−0.0597491 | + | 0.998213i | \(0.519030\pi\) | |||||||
\(678\) | 12.9286 | 0.496520 | ||||||||
\(679\) | −0.763992 | −0.0293193 | ||||||||
\(680\) | 7.29218 | 0.279642 | ||||||||
\(681\) | 26.7515 | 1.02512 | ||||||||
\(682\) | −41.7873 | −1.60012 | ||||||||
\(683\) | −20.2933 | −0.776502 | −0.388251 | − | 0.921554i | \(-0.626921\pi\) | ||||
−0.388251 | + | 0.921554i | \(0.626921\pi\) | |||||||
\(684\) | −17.3027 | −0.661585 | ||||||||
\(685\) | −19.2767 | −0.736526 | ||||||||
\(686\) | −2.38443 | −0.0910379 | ||||||||
\(687\) | 20.5408 | 0.783679 | ||||||||
\(688\) | −7.57093 | −0.288639 | ||||||||
\(689\) | 6.31437 | 0.240558 | ||||||||
\(690\) | −27.3954 | −1.04293 | ||||||||
\(691\) | 44.0194 | 1.67458 | 0.837288 | − | 0.546763i | \(-0.184140\pi\) | ||||
0.837288 | + | 0.546763i | \(0.184140\pi\) | |||||||
\(692\) | −84.6597 | −3.21828 | ||||||||
\(693\) | 2.12042 | 0.0805481 | ||||||||
\(694\) | 24.3552 | 0.924510 | ||||||||
\(695\) | 12.6034 | 0.478076 | ||||||||
\(696\) | −35.2783 | −1.33722 | ||||||||
\(697\) | −0.637895 | −0.0241620 | ||||||||
\(698\) | −1.91724 | −0.0725686 | ||||||||
\(699\) | −28.9276 | −1.09414 | ||||||||
\(700\) | 8.50571 | 0.321486 | ||||||||
\(701\) | 21.2660 | 0.803206 | 0.401603 | − | 0.915814i | \(-0.368453\pi\) | ||||
0.401603 | + | 0.915814i | \(0.368453\pi\) | |||||||
\(702\) | 1.49938 | 0.0565905 | ||||||||
\(703\) | 13.5323 | 0.510382 | ||||||||
\(704\) | −23.3539 | −0.880182 | ||||||||
\(705\) | −20.0459 | −0.754973 | ||||||||
\(706\) | −20.2690 | −0.762835 | ||||||||
\(707\) | −1.38949 | −0.0522570 | ||||||||
\(708\) | 31.2436 | 1.17421 | ||||||||
\(709\) | −20.4536 | −0.768150 | −0.384075 | − | 0.923302i | \(-0.625480\pi\) | ||||
−0.384075 | + | 0.923302i | \(0.625480\pi\) | |||||||
\(710\) | 68.0087 | 2.55232 | ||||||||
\(711\) | 10.9350 | 0.410095 | ||||||||
\(712\) | −38.8347 | −1.45539 | ||||||||
\(713\) | −35.1266 | −1.31550 | ||||||||
\(714\) | −1.60041 | −0.0598939 | ||||||||
\(715\) | 3.60450 | 0.134801 | ||||||||
\(716\) | −96.1103 | −3.59181 | ||||||||
\(717\) | −11.0244 | −0.411713 | ||||||||
\(718\) | −45.7648 | −1.70793 | ||||||||
\(719\) | 47.4720 | 1.77041 | 0.885203 | − | 0.465205i | \(-0.154020\pi\) | ||||
0.885203 | + | 0.465205i | \(0.154020\pi\) | |||||||
\(720\) | 5.97955 | 0.222845 | ||||||||
\(721\) | −17.9914 | −0.670034 | ||||||||
\(722\) | −7.25128 | −0.269865 | ||||||||
\(723\) | 0.651087 | 0.0242142 | ||||||||
\(724\) | −84.0568 | −3.12395 | ||||||||
\(725\) | −20.2585 | −0.752382 | ||||||||
\(726\) | −15.5079 | −0.575552 | ||||||||
\(727\) | 36.1902 | 1.34222 | 0.671110 | − | 0.741358i | \(-0.265818\pi\) | ||||
0.671110 | + | 0.741358i | \(0.265818\pi\) | |||||||
\(728\) | −2.52721 | −0.0936648 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 43.1900 | 1.59853 | ||||||||
\(731\) | 2.29734 | 0.0849700 | ||||||||
\(732\) | 31.0227 | 1.14663 | ||||||||
\(733\) | −22.8890 | −0.845424 | −0.422712 | − | 0.906264i | \(-0.638922\pi\) | ||||
−0.422712 | + | 0.906264i | \(0.638922\pi\) | |||||||
\(734\) | −68.0177 | −2.51058 | ||||||||
\(735\) | −2.70331 | −0.0997131 | ||||||||
\(736\) | −11.7461 | −0.432967 | ||||||||
\(737\) | −0.527812 | −0.0194422 | ||||||||
\(738\) | −2.26614 | −0.0834177 | ||||||||
\(739\) | 3.38323 | 0.124454 | 0.0622271 | − | 0.998062i | \(-0.480180\pi\) | ||||
0.0622271 | + | 0.998062i | \(0.480180\pi\) | |||||||
\(740\) | −28.7177 | −1.05568 | ||||||||
\(741\) | 2.95219 | 0.108451 | ||||||||
\(742\) | −23.9435 | −0.878992 | ||||||||
\(743\) | −47.2702 | −1.73418 | −0.867088 | − | 0.498156i | \(-0.834011\pi\) | ||||
−0.867088 | + | 0.498156i | \(0.834011\pi\) | |||||||
\(744\) | 33.2164 | 1.21777 | ||||||||
\(745\) | 43.1072 | 1.57932 | ||||||||
\(746\) | −69.7275 | −2.55290 | ||||||||
\(747\) | 1.52127 | 0.0556604 | ||||||||
\(748\) | −5.24525 | −0.191785 | ||||||||
\(749\) | −5.00643 | −0.182931 | ||||||||
\(750\) | −17.3530 | −0.633642 | ||||||||
\(751\) | 23.3447 | 0.851860 | 0.425930 | − | 0.904756i | \(-0.359947\pi\) | ||||
0.425930 | + | 0.904756i | \(0.359947\pi\) | |||||||
\(752\) | 16.4022 | 0.598127 | ||||||||
\(753\) | −25.1078 | −0.914980 | ||||||||
\(754\) | 13.1615 | 0.479314 | ||||||||
\(755\) | 53.9638 | 1.96394 | ||||||||
\(756\) | −3.68550 | −0.134041 | ||||||||
\(757\) | −3.83114 | −0.139245 | −0.0696226 | − | 0.997573i | \(-0.522180\pi\) | ||||
−0.0696226 | + | 0.997573i | \(0.522180\pi\) | |||||||
\(758\) | 30.5117 | 1.10823 | ||||||||
\(759\) | 9.01197 | 0.327114 | ||||||||
\(760\) | 51.0067 | 1.85021 | ||||||||
\(761\) | 12.6167 | 0.457357 | 0.228678 | − | 0.973502i | \(-0.426560\pi\) | ||||
0.228678 | + | 0.973502i | \(0.426560\pi\) | |||||||
\(762\) | −10.0603 | −0.364447 | ||||||||
\(763\) | 3.95320 | 0.143116 | ||||||||
\(764\) | 24.9455 | 0.902497 | ||||||||
\(765\) | −1.81444 | −0.0656013 | ||||||||
\(766\) | −2.38443 | −0.0861529 | ||||||||
\(767\) | −5.33079 | −0.192484 | ||||||||
\(768\) | 27.4115 | 0.989129 | ||||||||
\(769\) | −14.4670 | −0.521695 | −0.260848 | − | 0.965380i | \(-0.584002\pi\) | ||||
−0.260848 | + | 0.965380i | \(0.584002\pi\) | |||||||
\(770\) | −13.6679 | −0.492557 | ||||||||
\(771\) | −21.4888 | −0.773901 | ||||||||
\(772\) | −80.7356 | −2.90574 | ||||||||
\(773\) | −49.7595 | −1.78972 | −0.894862 | − | 0.446344i | \(-0.852726\pi\) | ||||
−0.894862 | + | 0.446344i | \(0.852726\pi\) | |||||||
\(774\) | 8.16134 | 0.293353 | ||||||||
\(775\) | 19.0744 | 0.685174 | ||||||||
\(776\) | 3.07046 | 0.110223 | ||||||||
\(777\) | 2.88242 | 0.103406 | ||||||||
\(778\) | −79.5375 | −2.85156 | ||||||||
\(779\) | −4.46189 | −0.159864 | ||||||||
\(780\) | −6.26499 | −0.224323 | ||||||||
\(781\) | −22.3721 | −0.800536 | ||||||||
\(782\) | −6.80189 | −0.243235 | ||||||||
\(783\) | 8.77796 | 0.313699 | ||||||||
\(784\) | 2.21194 | 0.0789977 | ||||||||
\(785\) | −41.6522 | −1.48663 | ||||||||
\(786\) | 20.3323 | 0.725230 | ||||||||
\(787\) | 2.56648 | 0.0914851 | 0.0457425 | − | 0.998953i | \(-0.485435\pi\) | ||||
0.0457425 | + | 0.998953i | \(0.485435\pi\) | |||||||
\(788\) | −15.2833 | −0.544446 | ||||||||
\(789\) | 8.15338 | 0.290268 | ||||||||
\(790\) | −70.4855 | −2.50776 | ||||||||
\(791\) | 5.42209 | 0.192787 | ||||||||
\(792\) | −8.52190 | −0.302812 | ||||||||
\(793\) | −5.29310 | −0.187963 | ||||||||
\(794\) | −65.2448 | −2.31545 | ||||||||
\(795\) | −27.1455 | −0.962752 | ||||||||
\(796\) | −54.6560 | −1.93723 | ||||||||
\(797\) | −27.0618 | −0.958580 | −0.479290 | − | 0.877657i | \(-0.659106\pi\) | ||||
−0.479290 | + | 0.877657i | \(0.659106\pi\) | |||||||
\(798\) | −11.1944 | −0.396278 | ||||||||
\(799\) | −4.97711 | −0.176078 | ||||||||
\(800\) | 6.37836 | 0.225509 | ||||||||
\(801\) | 9.66286 | 0.341420 | ||||||||
\(802\) | 20.9914 | 0.741232 | ||||||||
\(803\) | −14.2077 | −0.501380 | ||||||||
\(804\) | 0.917391 | 0.0323539 | ||||||||
\(805\) | −11.4893 | −0.404944 | ||||||||
\(806\) | −12.3922 | −0.436498 | ||||||||
\(807\) | −4.11605 | −0.144892 | ||||||||
\(808\) | 5.58430 | 0.196455 | ||||||||
\(809\) | −26.4470 | −0.929826 | −0.464913 | − | 0.885356i | \(-0.653914\pi\) | ||||
−0.464913 | + | 0.885356i | \(0.653914\pi\) | |||||||
\(810\) | −6.44585 | −0.226484 | ||||||||
\(811\) | 32.7868 | 1.15130 | 0.575650 | − | 0.817696i | \(-0.304749\pi\) | ||||
0.575650 | + | 0.817696i | \(0.304749\pi\) | |||||||
\(812\) | −32.3512 | −1.13530 | ||||||||
\(813\) | −6.69170 | −0.234688 | ||||||||
\(814\) | 14.5735 | 0.510800 | ||||||||
\(815\) | −64.5238 | −2.26017 | ||||||||
\(816\) | 1.48464 | 0.0519726 | ||||||||
\(817\) | 16.0692 | 0.562189 | ||||||||
\(818\) | 3.65324 | 0.127733 | ||||||||
\(819\) | 0.628822 | 0.0219728 | ||||||||
\(820\) | 9.46880 | 0.330665 | ||||||||
\(821\) | −44.3537 | −1.54795 | −0.773977 | − | 0.633214i | \(-0.781735\pi\) | ||||
−0.773977 | + | 0.633214i | \(0.781735\pi\) | |||||||
\(822\) | −17.0029 | −0.593043 | ||||||||
\(823\) | −23.3414 | −0.813629 | −0.406815 | − | 0.913511i | \(-0.633360\pi\) | ||||
−0.406815 | + | 0.913511i | \(0.633360\pi\) | |||||||
\(824\) | 72.3067 | 2.51892 | ||||||||
\(825\) | −4.89368 | −0.170376 | ||||||||
\(826\) | 20.2138 | 0.703328 | ||||||||
\(827\) | −8.07449 | −0.280777 | −0.140389 | − | 0.990096i | \(-0.544835\pi\) | ||||
−0.140389 | + | 0.990096i | \(0.544835\pi\) | |||||||
\(828\) | −15.6637 | −0.544352 | ||||||||
\(829\) | −6.30212 | −0.218882 | −0.109441 | − | 0.993993i | \(-0.534906\pi\) | ||||
−0.109441 | + | 0.993993i | \(0.534906\pi\) | |||||||
\(830\) | −9.80589 | −0.340368 | ||||||||
\(831\) | 3.57687 | 0.124080 | ||||||||
\(832\) | −6.92571 | −0.240106 | ||||||||
\(833\) | −0.671193 | −0.0232555 | ||||||||
\(834\) | 11.1168 | 0.384942 | ||||||||
\(835\) | 30.1512 | 1.04343 | ||||||||
\(836\) | −36.6890 | −1.26891 | ||||||||
\(837\) | −8.26491 | −0.285677 | ||||||||
\(838\) | 32.1057 | 1.10907 | ||||||||
\(839\) | 29.0067 | 1.00142 | 0.500711 | − | 0.865615i | \(-0.333072\pi\) | ||||
0.500711 | + | 0.865615i | \(0.333072\pi\) | |||||||
\(840\) | 10.8645 | 0.374861 | ||||||||
\(841\) | 48.0526 | 1.65699 | ||||||||
\(842\) | 69.8526 | 2.40728 | ||||||||
\(843\) | −19.9376 | −0.686686 | ||||||||
\(844\) | 70.2945 | 2.41964 | ||||||||
\(845\) | −34.0741 | −1.17218 | ||||||||
\(846\) | −17.6813 | −0.607896 | ||||||||
\(847\) | −6.50382 | −0.223474 | ||||||||
\(848\) | 22.2113 | 0.762741 | ||||||||
\(849\) | −4.01533 | −0.137806 | ||||||||
\(850\) | 3.69356 | 0.126688 | ||||||||
\(851\) | 12.2505 | 0.419942 | ||||||||
\(852\) | 38.8849 | 1.33218 | ||||||||
\(853\) | 45.1348 | 1.54539 | 0.772693 | − | 0.634780i | \(-0.218909\pi\) | ||||
0.772693 | + | 0.634780i | \(0.218909\pi\) | |||||||
\(854\) | 20.0709 | 0.686813 | ||||||||
\(855\) | −12.6915 | −0.434040 | ||||||||
\(856\) | 20.1207 | 0.687711 | ||||||||
\(857\) | 40.1085 | 1.37008 | 0.685041 | − | 0.728505i | \(-0.259784\pi\) | ||||
0.685041 | + | 0.728505i | \(0.259784\pi\) | |||||||
\(858\) | 3.17932 | 0.108540 | ||||||||
\(859\) | 21.1098 | 0.720257 | 0.360129 | − | 0.932903i | \(-0.382733\pi\) | ||||
0.360129 | + | 0.932903i | \(0.382733\pi\) | |||||||
\(860\) | −34.1012 | −1.16284 | ||||||||
\(861\) | −0.950390 | −0.0323892 | ||||||||
\(862\) | 57.0254 | 1.94229 | ||||||||
\(863\) | 29.3890 | 1.00041 | 0.500207 | − | 0.865906i | \(-0.333257\pi\) | ||||
0.500207 | + | 0.865906i | \(0.333257\pi\) | |||||||
\(864\) | −2.76373 | −0.0940240 | ||||||||
\(865\) | −62.0977 | −2.11139 | ||||||||
\(866\) | 78.0401 | 2.65191 | ||||||||
\(867\) | 16.5495 | 0.562050 | ||||||||
\(868\) | 30.4604 | 1.03389 | ||||||||
\(869\) | 23.1868 | 0.786560 | ||||||||
\(870\) | −56.5814 | −1.91829 | ||||||||
\(871\) | −0.156525 | −0.00530366 | ||||||||
\(872\) | −15.8878 | −0.538028 | ||||||||
\(873\) | −0.763992 | −0.0258572 | ||||||||
\(874\) | −47.5772 | −1.60932 | ||||||||
\(875\) | −7.27763 | −0.246029 | ||||||||
\(876\) | 24.6945 | 0.834349 | ||||||||
\(877\) | 47.0360 | 1.58829 | 0.794146 | − | 0.607727i | \(-0.207918\pi\) | ||||
0.794146 | + | 0.607727i | \(0.207918\pi\) | |||||||
\(878\) | −79.0308 | −2.66716 | ||||||||
\(879\) | 26.9013 | 0.907358 | ||||||||
\(880\) | 12.6791 | 0.427414 | ||||||||
\(881\) | −48.3447 | −1.62877 | −0.814387 | − | 0.580321i | \(-0.802927\pi\) | ||||
−0.814387 | + | 0.580321i | \(0.802927\pi\) | |||||||
\(882\) | −2.38443 | −0.0802879 | ||||||||
\(883\) | 4.66484 | 0.156984 | 0.0784922 | − | 0.996915i | \(-0.474989\pi\) | ||||
0.0784922 | + | 0.996915i | \(0.474989\pi\) | |||||||
\(884\) | −1.55551 | −0.0523173 | ||||||||
\(885\) | 22.9171 | 0.770350 | ||||||||
\(886\) | 70.4302 | 2.36615 | ||||||||
\(887\) | −14.4277 | −0.484436 | −0.242218 | − | 0.970222i | \(-0.577875\pi\) | ||||
−0.242218 | + | 0.970222i | \(0.577875\pi\) | |||||||
\(888\) | −11.5843 | −0.388745 | ||||||||
\(889\) | −4.21917 | −0.141507 | ||||||||
\(890\) | −62.2853 | −2.08781 | ||||||||
\(891\) | 2.12042 | 0.0710367 | ||||||||
\(892\) | −51.5698 | −1.72668 | ||||||||
\(893\) | −34.8134 | −1.16499 | ||||||||
\(894\) | 38.0223 | 1.27166 | ||||||||
\(895\) | −70.4967 | −2.35644 | ||||||||
\(896\) | 20.7341 | 0.692679 | ||||||||
\(897\) | 2.67255 | 0.0892337 | ||||||||
\(898\) | −20.3448 | −0.678913 | ||||||||
\(899\) | −72.5490 | −2.41965 | ||||||||
\(900\) | 8.50571 | 0.283524 | ||||||||
\(901\) | −6.73984 | −0.224537 | ||||||||
\(902\) | −4.80517 | −0.159995 | ||||||||
\(903\) | 3.42276 | 0.113902 | ||||||||
\(904\) | −21.7912 | −0.724765 | ||||||||
\(905\) | −61.6555 | −2.04950 | ||||||||
\(906\) | 47.5983 | 1.58135 | ||||||||
\(907\) | −24.0267 | −0.797792 | −0.398896 | − | 0.916996i | \(-0.630607\pi\) | ||||
−0.398896 | + | 0.916996i | \(0.630607\pi\) | |||||||
\(908\) | −98.5928 | −3.27192 | ||||||||
\(909\) | −1.38949 | −0.0460863 | ||||||||
\(910\) | −4.05329 | −0.134365 | ||||||||
\(911\) | −24.2309 | −0.802804 | −0.401402 | − | 0.915902i | \(-0.631477\pi\) | ||||
−0.401402 | + | 0.915902i | \(0.631477\pi\) | |||||||
\(912\) | 10.3846 | 0.343868 | ||||||||
\(913\) | 3.22574 | 0.106756 | ||||||||
\(914\) | 6.88659 | 0.227788 | ||||||||
\(915\) | 22.7551 | 0.752260 | ||||||||
\(916\) | −75.7031 | −2.50130 | ||||||||
\(917\) | 8.52713 | 0.281591 | ||||||||
\(918\) | −1.60041 | −0.0528215 | ||||||||
\(919\) | −7.27817 | −0.240085 | −0.120042 | − | 0.992769i | \(-0.538303\pi\) | ||||
−0.120042 | + | 0.992769i | \(0.538303\pi\) | |||||||
\(920\) | 46.1751 | 1.52235 | ||||||||
\(921\) | 24.9984 | 0.823725 | ||||||||
\(922\) | −40.2960 | −1.32708 | ||||||||
\(923\) | −6.63455 | −0.218379 | ||||||||
\(924\) | −7.81482 | −0.257089 | ||||||||
\(925\) | −6.65227 | −0.218725 | ||||||||
\(926\) | −31.1684 | −1.02426 | ||||||||
\(927\) | −17.9914 | −0.590914 | ||||||||
\(928\) | −24.2599 | −0.796371 | ||||||||
\(929\) | 37.6980 | 1.23683 | 0.618415 | − | 0.785852i | \(-0.287775\pi\) | ||||
0.618415 | + | 0.785852i | \(0.287775\pi\) | |||||||
\(930\) | 53.2744 | 1.74694 | ||||||||
\(931\) | −4.69479 | −0.153866 | ||||||||
\(932\) | 106.613 | 3.49222 | ||||||||
\(933\) | −7.01552 | −0.229678 | ||||||||
\(934\) | 9.21954 | 0.301673 | ||||||||
\(935\) | −3.84738 | −0.125823 | ||||||||
\(936\) | −2.52721 | −0.0826046 | ||||||||
\(937\) | 21.5519 | 0.704070 | 0.352035 | − | 0.935987i | \(-0.385490\pi\) | ||||
0.352035 | + | 0.935987i | \(0.385490\pi\) | |||||||
\(938\) | 0.593529 | 0.0193794 | ||||||||
\(939\) | 8.08016 | 0.263686 | ||||||||
\(940\) | 73.8793 | 2.40968 | ||||||||
\(941\) | −31.4780 | −1.02615 | −0.513077 | − | 0.858343i | \(-0.671494\pi\) | ||||
−0.513077 | + | 0.858343i | \(0.671494\pi\) | |||||||
\(942\) | −36.7390 | −1.19702 | ||||||||
\(943\) | −4.03924 | −0.131536 | ||||||||
\(944\) | −18.7515 | −0.610310 | ||||||||
\(945\) | −2.70331 | −0.0879387 | ||||||||
\(946\) | 17.3055 | 0.562649 | ||||||||
\(947\) | 5.02412 | 0.163262 | 0.0816309 | − | 0.996663i | \(-0.473987\pi\) | ||||
0.0816309 | + | 0.996663i | \(0.473987\pi\) | |||||||
\(948\) | −40.3011 | −1.30892 | ||||||||
\(949\) | −4.21337 | −0.136772 | ||||||||
\(950\) | 25.8354 | 0.838210 | ||||||||
\(951\) | 8.21015 | 0.266232 | ||||||||
\(952\) | 2.69750 | 0.0874266 | ||||||||
\(953\) | −35.5182 | −1.15055 | −0.575273 | − | 0.817961i | \(-0.695104\pi\) | ||||
−0.575273 | + | 0.817961i | \(0.695104\pi\) | |||||||
\(954\) | −23.9435 | −0.775198 | ||||||||
\(955\) | 18.2975 | 0.592092 | ||||||||
\(956\) | 40.6304 | 1.31408 | ||||||||
\(957\) | 18.6130 | 0.601672 | ||||||||
\(958\) | −82.1787 | −2.65507 | ||||||||
\(959\) | −7.13079 | −0.230265 | ||||||||
\(960\) | 29.7737 | 0.960942 | ||||||||
\(961\) | 37.3087 | 1.20351 | ||||||||
\(962\) | 4.32184 | 0.139342 | ||||||||
\(963\) | −5.00643 | −0.161330 | ||||||||
\(964\) | −2.39959 | −0.0772855 | ||||||||
\(965\) | −59.2194 | −1.90634 | ||||||||
\(966\) | −10.1340 | −0.326057 | ||||||||
\(967\) | −36.8541 | −1.18515 | −0.592574 | − | 0.805516i | \(-0.701888\pi\) | ||||
−0.592574 | + | 0.805516i | \(0.701888\pi\) | |||||||
\(968\) | 26.1386 | 0.840128 | ||||||||
\(969\) | −3.15111 | −0.101228 | ||||||||
\(970\) | 4.92458 | 0.158119 | ||||||||
\(971\) | 33.7414 | 1.08281 | 0.541406 | − | 0.840761i | \(-0.317892\pi\) | ||||
0.541406 | + | 0.840761i | \(0.317892\pi\) | |||||||
\(972\) | −3.68550 | −0.118213 | ||||||||
\(973\) | 4.66223 | 0.149464 | ||||||||
\(974\) | −23.9927 | −0.768776 | ||||||||
\(975\) | −1.45125 | −0.0464771 | ||||||||
\(976\) | −18.6189 | −0.595978 | ||||||||
\(977\) | 29.8470 | 0.954891 | 0.477445 | − | 0.878661i | \(-0.341563\pi\) | ||||
0.477445 | + | 0.878661i | \(0.341563\pi\) | |||||||
\(978\) | −56.9127 | −1.81987 | ||||||||
\(979\) | 20.4893 | 0.654841 | ||||||||
\(980\) | 9.96306 | 0.318258 | ||||||||
\(981\) | 3.95320 | 0.126216 | ||||||||
\(982\) | −68.6995 | −2.19229 | ||||||||
\(983\) | −34.6141 | −1.10402 | −0.552010 | − | 0.833838i | \(-0.686139\pi\) | ||||
−0.552010 | + | 0.833838i | \(0.686139\pi\) | |||||||
\(984\) | 3.81959 | 0.121764 | ||||||||
\(985\) | −11.2103 | −0.357190 | ||||||||
\(986\) | −14.0484 | −0.447391 | ||||||||
\(987\) | −7.41532 | −0.236032 | ||||||||
\(988\) | −10.8803 | −0.346149 | ||||||||
\(989\) | 14.5470 | 0.462569 | ||||||||
\(990\) | −13.6679 | −0.434395 | ||||||||
\(991\) | 36.3178 | 1.15367 | 0.576836 | − | 0.816860i | \(-0.304287\pi\) | ||||
0.576836 | + | 0.816860i | \(0.304287\pi\) | |||||||
\(992\) | 22.8420 | 0.725233 | ||||||||
\(993\) | −33.0162 | −1.04774 | ||||||||
\(994\) | 25.1576 | 0.797950 | ||||||||
\(995\) | −40.0901 | −1.27094 | ||||||||
\(996\) | −5.60666 | −0.177654 | ||||||||
\(997\) | −32.5037 | −1.02940 | −0.514702 | − | 0.857369i | \(-0.672097\pi\) | ||||
−0.514702 | + | 0.857369i | \(0.672097\pi\) | |||||||
\(998\) | 82.1681 | 2.60099 | ||||||||
\(999\) | 2.88242 | 0.0911956 |
(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.o.1.5 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.o.1.5 | ✓ | 41 | 1.1 | even | 1 | trivial |