Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(169\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.31715 | −1.63848 | −0.819238 | − | 0.573454i | \(-0.805603\pi\) | ||||
−0.819238 | + | 0.573454i | \(0.805603\pi\) | |||||||
\(3\) | 2.98534 | 1.72359 | 0.861795 | − | 0.507257i | \(-0.169341\pi\) | ||||
0.861795 | + | 0.507257i | \(0.169341\pi\) | |||||||
\(4\) | 3.36921 | 1.68460 | ||||||||
\(5\) | 4.10060 | 1.83384 | 0.916922 | − | 0.399067i | \(-0.130666\pi\) | ||||
0.916922 | + | 0.399067i | \(0.130666\pi\) | |||||||
\(6\) | −6.91750 | −2.82406 | ||||||||
\(7\) | 4.34971 | 1.64404 | 0.822018 | − | 0.569462i | \(-0.192848\pi\) | ||||
0.822018 | + | 0.569462i | \(0.192848\pi\) | |||||||
\(8\) | −3.17266 | −1.12170 | ||||||||
\(9\) | 5.91228 | 1.97076 | ||||||||
\(10\) | −9.50172 | −3.00471 | ||||||||
\(11\) | −0.545613 | −0.164508 | −0.0822542 | − | 0.996611i | \(-0.526212\pi\) | ||||
−0.0822542 | + | 0.996611i | \(0.526212\pi\) | |||||||
\(12\) | 10.0582 | 2.90356 | ||||||||
\(13\) | −0.963474 | −0.267220 | −0.133610 | − | 0.991034i | \(-0.542657\pi\) | ||||
−0.133610 | + | 0.991034i | \(0.542657\pi\) | |||||||
\(14\) | −10.0789 | −2.69371 | ||||||||
\(15\) | 12.2417 | 3.16079 | ||||||||
\(16\) | 0.613135 | 0.153284 | ||||||||
\(17\) | 2.94781 | 0.714950 | 0.357475 | − | 0.933923i | \(-0.383638\pi\) | ||||
0.357475 | + | 0.933923i | \(0.383638\pi\) | |||||||
\(18\) | −13.6997 | −3.22904 | ||||||||
\(19\) | −6.11025 | −1.40179 | −0.700894 | − | 0.713265i | \(-0.747215\pi\) | ||||
−0.700894 | + | 0.713265i | \(0.747215\pi\) | |||||||
\(20\) | 13.8158 | 3.08930 | ||||||||
\(21\) | 12.9854 | 2.83364 | ||||||||
\(22\) | 1.26427 | 0.269543 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −9.47148 | −1.93336 | ||||||||
\(25\) | 11.8149 | 2.36298 | ||||||||
\(26\) | 2.23252 | 0.437833 | ||||||||
\(27\) | 8.69415 | 1.67319 | ||||||||
\(28\) | 14.6551 | 2.76955 | ||||||||
\(29\) | −0.866337 | −0.160875 | −0.0804374 | − | 0.996760i | \(-0.525632\pi\) | ||||
−0.0804374 | + | 0.996760i | \(0.525632\pi\) | |||||||
\(30\) | −28.3659 | −5.17888 | ||||||||
\(31\) | 3.20396 | 0.575447 | 0.287724 | − | 0.957713i | \(-0.407102\pi\) | ||||
0.287724 | + | 0.957713i | \(0.407102\pi\) | |||||||
\(32\) | 4.92459 | 0.870553 | ||||||||
\(33\) | −1.62884 | −0.283545 | ||||||||
\(34\) | −6.83054 | −1.17143 | ||||||||
\(35\) | 17.8364 | 3.01490 | ||||||||
\(36\) | 19.9197 | 3.31995 | ||||||||
\(37\) | 6.46531 | 1.06289 | 0.531445 | − | 0.847093i | \(-0.321649\pi\) | ||||
0.531445 | + | 0.847093i | \(0.321649\pi\) | |||||||
\(38\) | 14.1584 | 2.29680 | ||||||||
\(39\) | −2.87630 | −0.460577 | ||||||||
\(40\) | −13.0098 | −2.05703 | ||||||||
\(41\) | −8.92239 | −1.39344 | −0.696722 | − | 0.717342i | \(-0.745359\pi\) | ||||
−0.696722 | + | 0.717342i | \(0.745359\pi\) | |||||||
\(42\) | −30.0891 | −4.64285 | ||||||||
\(43\) | −0.710927 | −0.108415 | −0.0542077 | − | 0.998530i | \(-0.517263\pi\) | ||||
−0.0542077 | + | 0.998530i | \(0.517263\pi\) | |||||||
\(44\) | −1.83828 | −0.277131 | ||||||||
\(45\) | 24.2439 | 3.61407 | ||||||||
\(46\) | 2.31715 | 0.341646 | ||||||||
\(47\) | 10.6355 | 1.55135 | 0.775675 | − | 0.631132i | \(-0.217409\pi\) | ||||
0.775675 | + | 0.631132i | \(0.217409\pi\) | |||||||
\(48\) | 1.83042 | 0.264198 | ||||||||
\(49\) | 11.9200 | 1.70285 | ||||||||
\(50\) | −27.3770 | −3.87169 | ||||||||
\(51\) | 8.80024 | 1.23228 | ||||||||
\(52\) | −3.24614 | −0.450159 | ||||||||
\(53\) | −9.69067 | −1.33112 | −0.665558 | − | 0.746346i | \(-0.731806\pi\) | ||||
−0.665558 | + | 0.746346i | \(0.731806\pi\) | |||||||
\(54\) | −20.1457 | −2.74148 | ||||||||
\(55\) | −2.23734 | −0.301683 | ||||||||
\(56\) | −13.8001 | −1.84412 | ||||||||
\(57\) | −18.2412 | −2.41611 | ||||||||
\(58\) | 2.00744 | 0.263589 | ||||||||
\(59\) | −3.15331 | −0.410527 | −0.205263 | − | 0.978707i | \(-0.565805\pi\) | ||||
−0.205263 | + | 0.978707i | \(0.565805\pi\) | |||||||
\(60\) | 41.2448 | 5.32468 | ||||||||
\(61\) | −4.91744 | −0.629614 | −0.314807 | − | 0.949156i | \(-0.601940\pi\) | ||||
−0.314807 | + | 0.949156i | \(0.601940\pi\) | |||||||
\(62\) | −7.42406 | −0.942857 | ||||||||
\(63\) | 25.7167 | 3.24000 | ||||||||
\(64\) | −12.6373 | −1.57966 | ||||||||
\(65\) | −3.95082 | −0.490039 | ||||||||
\(66\) | 3.77428 | 0.464581 | ||||||||
\(67\) | 10.8742 | 1.32849 | 0.664247 | − | 0.747513i | \(-0.268752\pi\) | ||||
0.664247 | + | 0.747513i | \(0.268752\pi\) | |||||||
\(68\) | 9.93179 | 1.20441 | ||||||||
\(69\) | −2.98534 | −0.359393 | ||||||||
\(70\) | −41.3297 | −4.93985 | ||||||||
\(71\) | 0.572705 | 0.0679676 | 0.0339838 | − | 0.999422i | \(-0.489181\pi\) | ||||
0.0339838 | + | 0.999422i | \(0.489181\pi\) | |||||||
\(72\) | −18.7577 | −2.21061 | ||||||||
\(73\) | −10.5783 | −1.23809 | −0.619047 | − | 0.785354i | \(-0.712481\pi\) | ||||
−0.619047 | + | 0.785354i | \(0.712481\pi\) | |||||||
\(74\) | −14.9811 | −1.74152 | ||||||||
\(75\) | 35.2716 | 4.07281 | ||||||||
\(76\) | −20.5867 | −2.36146 | ||||||||
\(77\) | −2.37326 | −0.270458 | ||||||||
\(78\) | 6.66483 | 0.754644 | ||||||||
\(79\) | 3.84280 | 0.432348 | 0.216174 | − | 0.976355i | \(-0.430642\pi\) | ||||
0.216174 | + | 0.976355i | \(0.430642\pi\) | |||||||
\(80\) | 2.51422 | 0.281098 | ||||||||
\(81\) | 8.21820 | 0.913133 | ||||||||
\(82\) | 20.6746 | 2.28312 | ||||||||
\(83\) | −13.4059 | −1.47149 | −0.735743 | − | 0.677261i | \(-0.763167\pi\) | ||||
−0.735743 | + | 0.677261i | \(0.763167\pi\) | |||||||
\(84\) | 43.7504 | 4.77356 | ||||||||
\(85\) | 12.0878 | 1.31111 | ||||||||
\(86\) | 1.64733 | 0.177636 | ||||||||
\(87\) | −2.58631 | −0.277282 | ||||||||
\(88\) | 1.73104 | 0.184530 | ||||||||
\(89\) | 8.15308 | 0.864225 | 0.432112 | − | 0.901820i | \(-0.357768\pi\) | ||||
0.432112 | + | 0.901820i | \(0.357768\pi\) | |||||||
\(90\) | −56.1768 | −5.92156 | ||||||||
\(91\) | −4.19083 | −0.439318 | ||||||||
\(92\) | −3.36921 | −0.351264 | ||||||||
\(93\) | 9.56491 | 0.991835 | ||||||||
\(94\) | −24.6442 | −2.54185 | ||||||||
\(95\) | −25.0557 | −2.57066 | ||||||||
\(96\) | 14.7016 | 1.50048 | ||||||||
\(97\) | −5.38504 | −0.546768 | −0.273384 | − | 0.961905i | \(-0.588143\pi\) | ||||
−0.273384 | + | 0.961905i | \(0.588143\pi\) | |||||||
\(98\) | −27.6204 | −2.79008 | ||||||||
\(99\) | −3.22581 | −0.324207 | ||||||||
\(100\) | 39.8069 | 3.98069 | ||||||||
\(101\) | 1.33080 | 0.132419 | 0.0662097 | − | 0.997806i | \(-0.478909\pi\) | ||||
0.0662097 | + | 0.997806i | \(0.478909\pi\) | |||||||
\(102\) | −20.3915 | −2.01906 | ||||||||
\(103\) | −4.77051 | −0.470052 | −0.235026 | − | 0.971989i | \(-0.575518\pi\) | ||||
−0.235026 | + | 0.971989i | \(0.575518\pi\) | |||||||
\(104\) | 3.05678 | 0.299741 | ||||||||
\(105\) | 53.2478 | 5.19646 | ||||||||
\(106\) | 22.4548 | 2.18100 | ||||||||
\(107\) | 8.61297 | 0.832647 | 0.416324 | − | 0.909217i | \(-0.363318\pi\) | ||||
0.416324 | + | 0.909217i | \(0.363318\pi\) | |||||||
\(108\) | 29.2924 | 2.81866 | ||||||||
\(109\) | −10.6174 | −1.01696 | −0.508482 | − | 0.861073i | \(-0.669793\pi\) | ||||
−0.508482 | + | 0.861073i | \(0.669793\pi\) | |||||||
\(110\) | 5.18426 | 0.494300 | ||||||||
\(111\) | 19.3012 | 1.83199 | ||||||||
\(112\) | 2.66696 | 0.252004 | ||||||||
\(113\) | −6.70297 | −0.630562 | −0.315281 | − | 0.948998i | \(-0.602099\pi\) | ||||
−0.315281 | + | 0.948998i | \(0.602099\pi\) | |||||||
\(114\) | 42.2677 | 3.95873 | ||||||||
\(115\) | −4.10060 | −0.382383 | ||||||||
\(116\) | −2.91887 | −0.271010 | ||||||||
\(117\) | −5.69632 | −0.526625 | ||||||||
\(118\) | 7.30672 | 0.672638 | ||||||||
\(119\) | 12.8221 | 1.17540 | ||||||||
\(120\) | −38.8388 | −3.54548 | ||||||||
\(121\) | −10.7023 | −0.972937 | ||||||||
\(122\) | 11.3945 | 1.03161 | ||||||||
\(123\) | −26.6364 | −2.40172 | ||||||||
\(124\) | 10.7948 | 0.969400 | ||||||||
\(125\) | 27.9452 | 2.49950 | ||||||||
\(126\) | −59.5895 | −5.30866 | ||||||||
\(127\) | −5.31105 | −0.471279 | −0.235640 | − | 0.971841i | \(-0.575718\pi\) | ||||
−0.235640 | + | 0.971841i | \(0.575718\pi\) | |||||||
\(128\) | 19.4334 | 1.71769 | ||||||||
\(129\) | −2.12236 | −0.186864 | ||||||||
\(130\) | 9.15466 | 0.802917 | ||||||||
\(131\) | 4.17631 | 0.364886 | 0.182443 | − | 0.983216i | \(-0.441600\pi\) | ||||
0.182443 | + | 0.983216i | \(0.441600\pi\) | |||||||
\(132\) | −5.48790 | −0.477661 | ||||||||
\(133\) | −26.5778 | −2.30459 | ||||||||
\(134\) | −25.1972 | −2.17671 | ||||||||
\(135\) | 35.6512 | 3.06837 | ||||||||
\(136\) | −9.35241 | −0.801963 | ||||||||
\(137\) | 5.28181 | 0.451256 | 0.225628 | − | 0.974214i | \(-0.427557\pi\) | ||||
0.225628 | + | 0.974214i | \(0.427557\pi\) | |||||||
\(138\) | 6.91750 | 0.588857 | ||||||||
\(139\) | 7.86611 | 0.667195 | 0.333597 | − | 0.942716i | \(-0.391737\pi\) | ||||
0.333597 | + | 0.942716i | \(0.391737\pi\) | |||||||
\(140\) | 60.0945 | 5.07892 | ||||||||
\(141\) | 31.7507 | 2.67389 | ||||||||
\(142\) | −1.32705 | −0.111363 | ||||||||
\(143\) | 0.525683 | 0.0439599 | ||||||||
\(144\) | 3.62502 | 0.302085 | ||||||||
\(145\) | −3.55250 | −0.295019 | ||||||||
\(146\) | 24.5115 | 2.02859 | ||||||||
\(147\) | 35.5852 | 2.93502 | ||||||||
\(148\) | 21.7830 | 1.79055 | ||||||||
\(149\) | −9.19901 | −0.753613 | −0.376806 | − | 0.926292i | \(-0.622978\pi\) | ||||
−0.376806 | + | 0.926292i | \(0.622978\pi\) | |||||||
\(150\) | −81.7297 | −6.67320 | ||||||||
\(151\) | 12.6149 | 1.02658 | 0.513292 | − | 0.858214i | \(-0.328426\pi\) | ||||
0.513292 | + | 0.858214i | \(0.328426\pi\) | |||||||
\(152\) | 19.3858 | 1.57239 | ||||||||
\(153\) | 17.4283 | 1.40899 | ||||||||
\(154\) | 5.49920 | 0.443138 | ||||||||
\(155\) | 13.1381 | 1.05528 | ||||||||
\(156\) | −9.69085 | −0.775889 | ||||||||
\(157\) | −10.3294 | −0.824374 | −0.412187 | − | 0.911099i | \(-0.635235\pi\) | ||||
−0.412187 | + | 0.911099i | \(0.635235\pi\) | |||||||
\(158\) | −8.90436 | −0.708392 | ||||||||
\(159\) | −28.9300 | −2.29430 | ||||||||
\(160\) | 20.1938 | 1.59646 | ||||||||
\(161\) | −4.34971 | −0.342805 | ||||||||
\(162\) | −19.0428 | −1.49615 | ||||||||
\(163\) | −8.88713 | −0.696094 | −0.348047 | − | 0.937477i | \(-0.613155\pi\) | ||||
−0.348047 | + | 0.937477i | \(0.613155\pi\) | |||||||
\(164\) | −30.0614 | −2.34740 | ||||||||
\(165\) | −6.67923 | −0.519977 | ||||||||
\(166\) | 31.0635 | 2.41099 | ||||||||
\(167\) | −9.66583 | −0.747964 | −0.373982 | − | 0.927436i | \(-0.622008\pi\) | ||||
−0.373982 | + | 0.927436i | \(0.622008\pi\) | |||||||
\(168\) | −41.1982 | −3.17851 | ||||||||
\(169\) | −12.0717 | −0.928594 | ||||||||
\(170\) | −28.0093 | −2.14822 | ||||||||
\(171\) | −36.1255 | −2.76259 | ||||||||
\(172\) | −2.39526 | −0.182637 | ||||||||
\(173\) | 15.9808 | 1.21500 | 0.607500 | − | 0.794320i | \(-0.292172\pi\) | ||||
0.607500 | + | 0.794320i | \(0.292172\pi\) | |||||||
\(174\) | 5.99289 | 0.454320 | ||||||||
\(175\) | 51.3914 | 3.88483 | ||||||||
\(176\) | −0.334534 | −0.0252165 | ||||||||
\(177\) | −9.41373 | −0.707579 | ||||||||
\(178\) | −18.8920 | −1.41601 | ||||||||
\(179\) | 9.42663 | 0.704579 | 0.352290 | − | 0.935891i | \(-0.385403\pi\) | ||||
0.352290 | + | 0.935891i | \(0.385403\pi\) | |||||||
\(180\) | 81.6826 | 6.08826 | ||||||||
\(181\) | 2.94049 | 0.218565 | 0.109282 | − | 0.994011i | \(-0.465145\pi\) | ||||
0.109282 | + | 0.994011i | \(0.465145\pi\) | |||||||
\(182\) | 9.71080 | 0.719812 | ||||||||
\(183\) | −14.6803 | −1.08520 | ||||||||
\(184\) | 3.17266 | 0.233892 | ||||||||
\(185\) | 26.5116 | 1.94917 | ||||||||
\(186\) | −22.1634 | −1.62510 | ||||||||
\(187\) | −1.60836 | −0.117615 | ||||||||
\(188\) | 35.8333 | 2.61341 | ||||||||
\(189\) | 37.8170 | 2.75078 | ||||||||
\(190\) | 58.0579 | 4.21197 | ||||||||
\(191\) | 13.0312 | 0.942906 | 0.471453 | − | 0.881891i | \(-0.343730\pi\) | ||||
0.471453 | + | 0.881891i | \(0.343730\pi\) | |||||||
\(192\) | −37.7267 | −2.72269 | ||||||||
\(193\) | 3.51969 | 0.253353 | 0.126676 | − | 0.991944i | \(-0.459569\pi\) | ||||
0.126676 | + | 0.991944i | \(0.459569\pi\) | |||||||
\(194\) | 12.4780 | 0.895866 | ||||||||
\(195\) | −11.7946 | −0.844626 | ||||||||
\(196\) | 40.1608 | 2.86863 | ||||||||
\(197\) | −24.0936 | −1.71660 | −0.858298 | − | 0.513152i | \(-0.828478\pi\) | ||||
−0.858298 | + | 0.513152i | \(0.828478\pi\) | |||||||
\(198\) | 7.47471 | 0.531205 | ||||||||
\(199\) | 3.34319 | 0.236993 | 0.118496 | − | 0.992954i | \(-0.462193\pi\) | ||||
0.118496 | + | 0.992954i | \(0.462193\pi\) | |||||||
\(200\) | −37.4847 | −2.65057 | ||||||||
\(201\) | 32.4632 | 2.28978 | ||||||||
\(202\) | −3.08366 | −0.216966 | ||||||||
\(203\) | −3.76831 | −0.264484 | ||||||||
\(204\) | 29.6498 | 2.07590 | ||||||||
\(205\) | −36.5872 | −2.55536 | ||||||||
\(206\) | 11.0540 | 0.770169 | ||||||||
\(207\) | −5.91228 | −0.410932 | ||||||||
\(208\) | −0.590739 | −0.0409604 | ||||||||
\(209\) | 3.33383 | 0.230606 | ||||||||
\(210\) | −123.383 | −8.51427 | ||||||||
\(211\) | 25.8886 | 1.78224 | 0.891122 | − | 0.453764i | \(-0.149919\pi\) | ||||
0.891122 | + | 0.453764i | \(0.149919\pi\) | |||||||
\(212\) | −32.6498 | −2.24240 | ||||||||
\(213\) | 1.70972 | 0.117148 | ||||||||
\(214\) | −19.9576 | −1.36427 | ||||||||
\(215\) | −2.91523 | −0.198817 | ||||||||
\(216\) | −27.5836 | −1.87683 | ||||||||
\(217\) | 13.9363 | 0.946056 | ||||||||
\(218\) | 24.6022 | 1.66627 | ||||||||
\(219\) | −31.5798 | −2.13396 | ||||||||
\(220\) | −7.53805 | −0.508216 | ||||||||
\(221\) | −2.84014 | −0.191049 | ||||||||
\(222\) | −44.7238 | −3.00166 | ||||||||
\(223\) | −15.2530 | −1.02142 | −0.510710 | − | 0.859753i | \(-0.670617\pi\) | ||||
−0.510710 | + | 0.859753i | \(0.670617\pi\) | |||||||
\(224\) | 21.4205 | 1.43122 | ||||||||
\(225\) | 69.8531 | 4.65687 | ||||||||
\(226\) | 15.5318 | 1.03316 | ||||||||
\(227\) | 7.86731 | 0.522172 | 0.261086 | − | 0.965316i | \(-0.415919\pi\) | ||||
0.261086 | + | 0.965316i | \(0.415919\pi\) | |||||||
\(228\) | −61.4584 | −4.07018 | ||||||||
\(229\) | 6.65203 | 0.439578 | 0.219789 | − | 0.975547i | \(-0.429463\pi\) | ||||
0.219789 | + | 0.975547i | \(0.429463\pi\) | |||||||
\(230\) | 9.50172 | 0.626525 | ||||||||
\(231\) | −7.08499 | −0.466158 | ||||||||
\(232\) | 2.74859 | 0.180454 | ||||||||
\(233\) | −22.3251 | −1.46256 | −0.731282 | − | 0.682075i | \(-0.761078\pi\) | ||||
−0.731282 | + | 0.682075i | \(0.761078\pi\) | |||||||
\(234\) | 13.1993 | 0.862863 | ||||||||
\(235\) | 43.6120 | 2.84493 | ||||||||
\(236\) | −10.6242 | −0.691574 | ||||||||
\(237\) | 11.4721 | 0.745191 | ||||||||
\(238\) | −29.7109 | −1.92587 | ||||||||
\(239\) | −30.2276 | −1.95526 | −0.977632 | − | 0.210323i | \(-0.932548\pi\) | ||||
−0.977632 | + | 0.210323i | \(0.932548\pi\) | |||||||
\(240\) | 7.50581 | 0.484498 | ||||||||
\(241\) | 6.66082 | 0.429061 | 0.214531 | − | 0.976717i | \(-0.431178\pi\) | ||||
0.214531 | + | 0.976717i | \(0.431178\pi\) | |||||||
\(242\) | 24.7989 | 1.59413 | ||||||||
\(243\) | −1.54830 | −0.0993237 | ||||||||
\(244\) | −16.5679 | −1.06065 | ||||||||
\(245\) | 48.8790 | 3.12276 | ||||||||
\(246\) | 61.7207 | 3.93517 | ||||||||
\(247\) | 5.88707 | 0.374585 | ||||||||
\(248\) | −10.1651 | −0.645482 | ||||||||
\(249\) | −40.0211 | −2.53624 | ||||||||
\(250\) | −64.7534 | −4.09537 | ||||||||
\(251\) | 12.5191 | 0.790198 | 0.395099 | − | 0.918639i | \(-0.370710\pi\) | ||||
0.395099 | + | 0.918639i | \(0.370710\pi\) | |||||||
\(252\) | 86.6448 | 5.45811 | ||||||||
\(253\) | 0.545613 | 0.0343024 | ||||||||
\(254\) | 12.3065 | 0.772179 | ||||||||
\(255\) | 36.0863 | 2.25981 | ||||||||
\(256\) | −19.7556 | −1.23473 | ||||||||
\(257\) | −7.34261 | −0.458020 | −0.229010 | − | 0.973424i | \(-0.573549\pi\) | ||||
−0.229010 | + | 0.973424i | \(0.573549\pi\) | |||||||
\(258\) | 4.91784 | 0.306171 | ||||||||
\(259\) | 28.1222 | 1.74743 | ||||||||
\(260\) | −13.3111 | −0.825521 | ||||||||
\(261\) | −5.12203 | −0.317045 | ||||||||
\(262\) | −9.67715 | −0.597856 | ||||||||
\(263\) | −14.2145 | −0.876504 | −0.438252 | − | 0.898852i | \(-0.644402\pi\) | ||||
−0.438252 | + | 0.898852i | \(0.644402\pi\) | |||||||
\(264\) | 5.16776 | 0.318054 | ||||||||
\(265\) | −39.7375 | −2.44106 | ||||||||
\(266\) | 61.5849 | 3.77601 | ||||||||
\(267\) | 24.3398 | 1.48957 | ||||||||
\(268\) | 36.6374 | 2.23799 | ||||||||
\(269\) | 0.204183 | 0.0124493 | 0.00622464 | − | 0.999981i | \(-0.498019\pi\) | ||||
0.00622464 | + | 0.999981i | \(0.498019\pi\) | |||||||
\(270\) | −82.6094 | −5.02745 | ||||||||
\(271\) | 27.2338 | 1.65434 | 0.827169 | − | 0.561953i | \(-0.189950\pi\) | ||||
0.827169 | + | 0.561953i | \(0.189950\pi\) | |||||||
\(272\) | 1.80741 | 0.109590 | ||||||||
\(273\) | −12.5111 | −0.757204 | ||||||||
\(274\) | −12.2388 | −0.739371 | ||||||||
\(275\) | −6.44637 | −0.388731 | ||||||||
\(276\) | −10.0582 | −0.605435 | ||||||||
\(277\) | 14.5703 | 0.875442 | 0.437721 | − | 0.899111i | \(-0.355786\pi\) | ||||
0.437721 | + | 0.899111i | \(0.355786\pi\) | |||||||
\(278\) | −18.2270 | −1.09318 | ||||||||
\(279\) | 18.9427 | 1.13407 | ||||||||
\(280\) | −56.5889 | −3.38183 | ||||||||
\(281\) | −0.382369 | −0.0228102 | −0.0114051 | − | 0.999935i | \(-0.503630\pi\) | ||||
−0.0114051 | + | 0.999935i | \(0.503630\pi\) | |||||||
\(282\) | −73.5713 | −4.38111 | ||||||||
\(283\) | 20.5295 | 1.22035 | 0.610175 | − | 0.792267i | \(-0.291099\pi\) | ||||
0.610175 | + | 0.792267i | \(0.291099\pi\) | |||||||
\(284\) | 1.92956 | 0.114498 | ||||||||
\(285\) | −74.7999 | −4.43076 | ||||||||
\(286\) | −1.21809 | −0.0720272 | ||||||||
\(287\) | −38.8098 | −2.29087 | ||||||||
\(288\) | 29.1156 | 1.71565 | ||||||||
\(289\) | −8.31039 | −0.488847 | ||||||||
\(290\) | 8.23169 | 0.483382 | ||||||||
\(291\) | −16.0762 | −0.942404 | ||||||||
\(292\) | −35.6404 | −2.08570 | ||||||||
\(293\) | −3.41734 | −0.199643 | −0.0998217 | − | 0.995005i | \(-0.531827\pi\) | ||||
−0.0998217 | + | 0.995005i | \(0.531827\pi\) | |||||||
\(294\) | −82.4564 | −4.80895 | ||||||||
\(295\) | −12.9305 | −0.752842 | ||||||||
\(296\) | −20.5122 | −1.19225 | ||||||||
\(297\) | −4.74364 | −0.275254 | ||||||||
\(298\) | 21.3155 | 1.23478 | ||||||||
\(299\) | 0.963474 | 0.0557191 | ||||||||
\(300\) | 118.837 | 6.86107 | ||||||||
\(301\) | −3.09233 | −0.178239 | ||||||||
\(302\) | −29.2306 | −1.68203 | ||||||||
\(303\) | 3.97289 | 0.228236 | ||||||||
\(304\) | −3.74641 | −0.214871 | ||||||||
\(305\) | −20.1645 | −1.15461 | ||||||||
\(306\) | −40.3841 | −2.30860 | ||||||||
\(307\) | −2.68413 | −0.153191 | −0.0765956 | − | 0.997062i | \(-0.524405\pi\) | ||||
−0.0765956 | + | 0.997062i | \(0.524405\pi\) | |||||||
\(308\) | −7.99599 | −0.455614 | ||||||||
\(309\) | −14.2416 | −0.810177 | ||||||||
\(310\) | −30.4431 | −1.72905 | ||||||||
\(311\) | −20.9938 | −1.19045 | −0.595225 | − | 0.803559i | \(-0.702937\pi\) | ||||
−0.595225 | + | 0.803559i | \(0.702937\pi\) | |||||||
\(312\) | 9.12553 | 0.516631 | ||||||||
\(313\) | 19.4512 | 1.09945 | 0.549724 | − | 0.835346i | \(-0.314733\pi\) | ||||
0.549724 | + | 0.835346i | \(0.314733\pi\) | |||||||
\(314\) | 23.9348 | 1.35072 | ||||||||
\(315\) | 105.454 | 5.94165 | ||||||||
\(316\) | 12.9472 | 0.728335 | ||||||||
\(317\) | 32.8284 | 1.84382 | 0.921912 | − | 0.387399i | \(-0.126627\pi\) | ||||
0.921912 | + | 0.387399i | \(0.126627\pi\) | |||||||
\(318\) | 67.0352 | 3.75915 | ||||||||
\(319\) | 0.472684 | 0.0264652 | ||||||||
\(320\) | −51.8206 | −2.89686 | ||||||||
\(321\) | 25.7127 | 1.43514 | ||||||||
\(322\) | 10.0789 | 0.561678 | ||||||||
\(323\) | −18.0119 | −1.00221 | ||||||||
\(324\) | 27.6888 | 1.53827 | ||||||||
\(325\) | −11.3834 | −0.631435 | ||||||||
\(326\) | 20.5928 | 1.14053 | ||||||||
\(327\) | −31.6966 | −1.75283 | ||||||||
\(328\) | 28.3077 | 1.56303 | ||||||||
\(329\) | 46.2614 | 2.55048 | ||||||||
\(330\) | 15.4768 | 0.851970 | ||||||||
\(331\) | −15.1321 | −0.831733 | −0.415866 | − | 0.909426i | \(-0.636522\pi\) | ||||
−0.415866 | + | 0.909426i | \(0.636522\pi\) | |||||||
\(332\) | −45.1671 | −2.47887 | ||||||||
\(333\) | 38.2247 | 2.09470 | ||||||||
\(334\) | 22.3972 | 1.22552 | ||||||||
\(335\) | 44.5907 | 2.43625 | ||||||||
\(336\) | 7.96178 | 0.434351 | ||||||||
\(337\) | 27.0690 | 1.47454 | 0.737272 | − | 0.675596i | \(-0.236114\pi\) | ||||
0.737272 | + | 0.675596i | \(0.236114\pi\) | |||||||
\(338\) | 27.9720 | 1.52148 | ||||||||
\(339\) | −20.0107 | −1.08683 | ||||||||
\(340\) | 40.7263 | 2.20869 | ||||||||
\(341\) | −1.74812 | −0.0946659 | ||||||||
\(342\) | 83.7084 | 4.52643 | ||||||||
\(343\) | 21.4004 | 1.15551 | ||||||||
\(344\) | 2.25553 | 0.121610 | ||||||||
\(345\) | −12.2417 | −0.659071 | ||||||||
\(346\) | −37.0301 | −1.99075 | ||||||||
\(347\) | −8.19856 | −0.440122 | −0.220061 | − | 0.975486i | \(-0.570626\pi\) | ||||
−0.220061 | + | 0.975486i | \(0.570626\pi\) | |||||||
\(348\) | −8.71382 | −0.467110 | ||||||||
\(349\) | 1.00000 | 0.0535288 | ||||||||
\(350\) | −119.082 | −6.36520 | ||||||||
\(351\) | −8.37659 | −0.447109 | ||||||||
\(352\) | −2.68692 | −0.143213 | ||||||||
\(353\) | 29.2908 | 1.55899 | 0.779496 | − | 0.626407i | \(-0.215475\pi\) | ||||
0.779496 | + | 0.626407i | \(0.215475\pi\) | |||||||
\(354\) | 21.8131 | 1.15935 | ||||||||
\(355\) | 2.34844 | 0.124642 | ||||||||
\(356\) | 27.4694 | 1.45588 | ||||||||
\(357\) | 38.2785 | 2.02591 | ||||||||
\(358\) | −21.8429 | −1.15444 | ||||||||
\(359\) | 30.3730 | 1.60302 | 0.801512 | − | 0.597978i | \(-0.204029\pi\) | ||||
0.801512 | + | 0.597978i | \(0.204029\pi\) | |||||||
\(360\) | −76.9176 | −4.05391 | ||||||||
\(361\) | 18.3352 | 0.965011 | ||||||||
\(362\) | −6.81357 | −0.358113 | ||||||||
\(363\) | −31.9501 | −1.67694 | ||||||||
\(364\) | −14.1198 | −0.740077 | ||||||||
\(365\) | −43.3773 | −2.27047 | ||||||||
\(366\) | 34.0164 | 1.77807 | ||||||||
\(367\) | −33.1909 | −1.73255 | −0.866275 | − | 0.499568i | \(-0.833492\pi\) | ||||
−0.866275 | + | 0.499568i | \(0.833492\pi\) | |||||||
\(368\) | −0.613135 | −0.0319619 | ||||||||
\(369\) | −52.7517 | −2.74614 | ||||||||
\(370\) | −61.4316 | −3.19368 | ||||||||
\(371\) | −42.1516 | −2.18840 | ||||||||
\(372\) | 32.2261 | 1.67085 | ||||||||
\(373\) | −2.09594 | −0.108524 | −0.0542618 | − | 0.998527i | \(-0.517281\pi\) | ||||
−0.0542618 | + | 0.998527i | \(0.517281\pi\) | |||||||
\(374\) | 3.72683 | 0.192710 | ||||||||
\(375\) | 83.4261 | 4.30811 | ||||||||
\(376\) | −33.7429 | −1.74016 | ||||||||
\(377\) | 0.834693 | 0.0429889 | ||||||||
\(378\) | −87.6279 | −4.50709 | ||||||||
\(379\) | −32.4212 | −1.66537 | −0.832683 | − | 0.553750i | \(-0.813196\pi\) | ||||
−0.832683 | + | 0.553750i | \(0.813196\pi\) | |||||||
\(380\) | −84.4178 | −4.33054 | ||||||||
\(381\) | −15.8553 | −0.812291 | ||||||||
\(382\) | −30.1954 | −1.54493 | ||||||||
\(383\) | −10.0177 | −0.511879 | −0.255939 | − | 0.966693i | \(-0.582385\pi\) | ||||
−0.255939 | + | 0.966693i | \(0.582385\pi\) | |||||||
\(384\) | 58.0155 | 2.96059 | ||||||||
\(385\) | −9.73177 | −0.495977 | ||||||||
\(386\) | −8.15566 | −0.415112 | ||||||||
\(387\) | −4.20320 | −0.213661 | ||||||||
\(388\) | −18.1433 | −0.921087 | ||||||||
\(389\) | −26.3769 | −1.33736 | −0.668682 | − | 0.743548i | \(-0.733141\pi\) | ||||
−0.668682 | + | 0.743548i | \(0.733141\pi\) | |||||||
\(390\) | 27.3298 | 1.38390 | ||||||||
\(391\) | −2.94781 | −0.149077 | ||||||||
\(392\) | −37.8180 | −1.91010 | ||||||||
\(393\) | 12.4677 | 0.628913 | ||||||||
\(394\) | 55.8285 | 2.81260 | ||||||||
\(395\) | 15.7578 | 0.792860 | ||||||||
\(396\) | −10.8684 | −0.546159 | ||||||||
\(397\) | 28.2842 | 1.41954 | 0.709772 | − | 0.704431i | \(-0.248798\pi\) | ||||
0.709772 | + | 0.704431i | \(0.248798\pi\) | |||||||
\(398\) | −7.74670 | −0.388307 | ||||||||
\(399\) | −79.3439 | −3.97217 | ||||||||
\(400\) | 7.24413 | 0.362207 | ||||||||
\(401\) | 7.52393 | 0.375727 | 0.187864 | − | 0.982195i | \(-0.439844\pi\) | ||||
0.187864 | + | 0.982195i | \(0.439844\pi\) | |||||||
\(402\) | −75.2223 | −3.75175 | ||||||||
\(403\) | −3.08693 | −0.153771 | ||||||||
\(404\) | 4.48373 | 0.223074 | ||||||||
\(405\) | 33.6995 | 1.67454 | ||||||||
\(406\) | 8.73176 | 0.433350 | ||||||||
\(407\) | −3.52755 | −0.174854 | ||||||||
\(408\) | −27.9202 | −1.38225 | ||||||||
\(409\) | −13.3689 | −0.661049 | −0.330525 | − | 0.943797i | \(-0.607226\pi\) | ||||
−0.330525 | + | 0.943797i | \(0.607226\pi\) | |||||||
\(410\) | 84.7781 | 4.18689 | ||||||||
\(411\) | 15.7680 | 0.777779 | ||||||||
\(412\) | −16.0728 | −0.791851 | ||||||||
\(413\) | −13.7160 | −0.674920 | ||||||||
\(414\) | 13.6997 | 0.673302 | ||||||||
\(415\) | −54.9721 | −2.69847 | ||||||||
\(416\) | −4.74472 | −0.232629 | ||||||||
\(417\) | 23.4830 | 1.14997 | ||||||||
\(418\) | −7.72500 | −0.377842 | ||||||||
\(419\) | −34.6726 | −1.69387 | −0.846934 | − | 0.531698i | \(-0.821554\pi\) | ||||
−0.846934 | + | 0.531698i | \(0.821554\pi\) | |||||||
\(420\) | 179.403 | 8.75396 | ||||||||
\(421\) | 30.3224 | 1.47783 | 0.738913 | − | 0.673801i | \(-0.235340\pi\) | ||||
0.738913 | + | 0.673801i | \(0.235340\pi\) | |||||||
\(422\) | −59.9879 | −2.92016 | ||||||||
\(423\) | 62.8802 | 3.05734 | ||||||||
\(424\) | 30.7452 | 1.49312 | ||||||||
\(425\) | 34.8282 | 1.68941 | ||||||||
\(426\) | −3.96169 | −0.191945 | ||||||||
\(427\) | −21.3894 | −1.03511 | ||||||||
\(428\) | 29.0189 | 1.40268 | ||||||||
\(429\) | 1.56935 | 0.0757687 | ||||||||
\(430\) | 6.75503 | 0.325757 | ||||||||
\(431\) | 9.64067 | 0.464375 | 0.232187 | − | 0.972671i | \(-0.425412\pi\) | ||||
0.232187 | + | 0.972671i | \(0.425412\pi\) | |||||||
\(432\) | 5.33069 | 0.256473 | ||||||||
\(433\) | 5.60750 | 0.269479 | 0.134740 | − | 0.990881i | \(-0.456980\pi\) | ||||
0.134740 | + | 0.990881i | \(0.456980\pi\) | |||||||
\(434\) | −32.2925 | −1.55009 | ||||||||
\(435\) | −10.6054 | −0.508492 | ||||||||
\(436\) | −35.7722 | −1.71318 | ||||||||
\(437\) | 6.11025 | 0.292293 | ||||||||
\(438\) | 73.1753 | 3.49645 | ||||||||
\(439\) | 28.2288 | 1.34729 | 0.673644 | − | 0.739056i | \(-0.264728\pi\) | ||||
0.673644 | + | 0.739056i | \(0.264728\pi\) | |||||||
\(440\) | 7.09832 | 0.338399 | ||||||||
\(441\) | 70.4741 | 3.35591 | ||||||||
\(442\) | 6.58105 | 0.313028 | ||||||||
\(443\) | −40.8126 | −1.93906 | −0.969532 | − | 0.244965i | \(-0.921224\pi\) | ||||
−0.969532 | + | 0.244965i | \(0.921224\pi\) | |||||||
\(444\) | 65.0296 | 3.08617 | ||||||||
\(445\) | 33.4325 | 1.58485 | ||||||||
\(446\) | 35.3437 | 1.67357 | ||||||||
\(447\) | −27.4622 | −1.29892 | ||||||||
\(448\) | −54.9686 | −2.59702 | ||||||||
\(449\) | −6.57105 | −0.310107 | −0.155054 | − | 0.987906i | \(-0.549555\pi\) | ||||
−0.155054 | + | 0.987906i | \(0.549555\pi\) | |||||||
\(450\) | −161.860 | −7.63017 | ||||||||
\(451\) | 4.86817 | 0.229233 | ||||||||
\(452\) | −22.5837 | −1.06225 | ||||||||
\(453\) | 37.6597 | 1.76941 | ||||||||
\(454\) | −18.2298 | −0.855566 | ||||||||
\(455\) | −17.1849 | −0.805641 | ||||||||
\(456\) | 57.8732 | 2.71016 | ||||||||
\(457\) | −12.1378 | −0.567783 | −0.283891 | − | 0.958856i | \(-0.591626\pi\) | ||||
−0.283891 | + | 0.958856i | \(0.591626\pi\) | |||||||
\(458\) | −15.4138 | −0.720239 | ||||||||
\(459\) | 25.6287 | 1.19625 | ||||||||
\(460\) | −13.8158 | −0.644163 | ||||||||
\(461\) | 2.57942 | 0.120135 | 0.0600677 | − | 0.998194i | \(-0.480868\pi\) | ||||
0.0600677 | + | 0.998194i | \(0.480868\pi\) | |||||||
\(462\) | 16.4170 | 0.763788 | ||||||||
\(463\) | −4.77406 | −0.221870 | −0.110935 | − | 0.993828i | \(-0.535384\pi\) | ||||
−0.110935 | + | 0.993828i | \(0.535384\pi\) | |||||||
\(464\) | −0.531181 | −0.0246595 | ||||||||
\(465\) | 39.2219 | 1.81887 | ||||||||
\(466\) | 51.7307 | 2.39638 | ||||||||
\(467\) | −28.0521 | −1.29810 | −0.649048 | − | 0.760748i | \(-0.724832\pi\) | ||||
−0.649048 | + | 0.760748i | \(0.724832\pi\) | |||||||
\(468\) | −19.1921 | −0.887155 | ||||||||
\(469\) | 47.2996 | 2.18409 | ||||||||
\(470\) | −101.056 | −4.66136 | ||||||||
\(471\) | −30.8367 | −1.42088 | ||||||||
\(472\) | 10.0044 | 0.460490 | ||||||||
\(473\) | 0.387891 | 0.0178352 | ||||||||
\(474\) | −26.5826 | −1.22098 | ||||||||
\(475\) | −72.1921 | −3.31240 | ||||||||
\(476\) | 43.2004 | 1.98009 | ||||||||
\(477\) | −57.2939 | −2.62331 | ||||||||
\(478\) | 70.0421 | 3.20365 | ||||||||
\(479\) | −28.4886 | −1.30168 | −0.650840 | − | 0.759215i | \(-0.725583\pi\) | ||||
−0.650840 | + | 0.759215i | \(0.725583\pi\) | |||||||
\(480\) | 60.2854 | 2.75164 | ||||||||
\(481\) | −6.22916 | −0.284025 | ||||||||
\(482\) | −15.4341 | −0.703006 | ||||||||
\(483\) | −12.9854 | −0.590855 | ||||||||
\(484\) | −36.0583 | −1.63901 | ||||||||
\(485\) | −22.0819 | −1.00269 | ||||||||
\(486\) | 3.58766 | 0.162739 | ||||||||
\(487\) | −11.4957 | −0.520922 | −0.260461 | − | 0.965484i | \(-0.583874\pi\) | ||||
−0.260461 | + | 0.965484i | \(0.583874\pi\) | |||||||
\(488\) | 15.6014 | 0.706241 | ||||||||
\(489\) | −26.5311 | −1.19978 | ||||||||
\(490\) | −113.260 | −5.11657 | ||||||||
\(491\) | −12.1437 | −0.548039 | −0.274020 | − | 0.961724i | \(-0.588353\pi\) | ||||
−0.274020 | + | 0.961724i | \(0.588353\pi\) | |||||||
\(492\) | −89.7435 | −4.04595 | ||||||||
\(493\) | −2.55380 | −0.115017 | ||||||||
\(494\) | −13.6412 | −0.613749 | ||||||||
\(495\) | −13.2278 | −0.594544 | ||||||||
\(496\) | 1.96446 | 0.0882067 | ||||||||
\(497\) | 2.49110 | 0.111741 | ||||||||
\(498\) | 92.7351 | 4.15556 | ||||||||
\(499\) | 19.5588 | 0.875573 | 0.437786 | − | 0.899079i | \(-0.355763\pi\) | ||||
0.437786 | + | 0.899079i | \(0.355763\pi\) | |||||||
\(500\) | 94.1532 | 4.21066 | ||||||||
\(501\) | −28.8558 | −1.28918 | ||||||||
\(502\) | −29.0087 | −1.29472 | ||||||||
\(503\) | −25.8214 | −1.15132 | −0.575660 | − | 0.817689i | \(-0.695255\pi\) | ||||
−0.575660 | + | 0.817689i | \(0.695255\pi\) | |||||||
\(504\) | −81.5903 | −3.63432 | ||||||||
\(505\) | 5.45707 | 0.242836 | ||||||||
\(506\) | −1.26427 | −0.0562036 | ||||||||
\(507\) | −36.0382 | −1.60051 | ||||||||
\(508\) | −17.8940 | −0.793918 | ||||||||
\(509\) | −31.0418 | −1.37590 | −0.687952 | − | 0.725757i | \(-0.741490\pi\) | ||||
−0.687952 | + | 0.725757i | \(0.741490\pi\) | |||||||
\(510\) | −83.6174 | −3.70264 | ||||||||
\(511\) | −46.0124 | −2.03547 | ||||||||
\(512\) | 6.90998 | 0.305381 | ||||||||
\(513\) | −53.1235 | −2.34546 | ||||||||
\(514\) | 17.0140 | 0.750454 | ||||||||
\(515\) | −19.5619 | −0.862002 | ||||||||
\(516\) | −7.15067 | −0.314791 | ||||||||
\(517\) | −5.80288 | −0.255210 | ||||||||
\(518\) | −65.1635 | −2.86312 | ||||||||
\(519\) | 47.7083 | 2.09416 | ||||||||
\(520\) | 12.5346 | 0.549679 | ||||||||
\(521\) | 25.6623 | 1.12428 | 0.562142 | − | 0.827041i | \(-0.309977\pi\) | ||||
0.562142 | + | 0.827041i | \(0.309977\pi\) | |||||||
\(522\) | 11.8685 | 0.519471 | ||||||||
\(523\) | 39.9316 | 1.74608 | 0.873042 | − | 0.487644i | \(-0.162144\pi\) | ||||
0.873042 | + | 0.487644i | \(0.162144\pi\) | |||||||
\(524\) | 14.0708 | 0.614687 | ||||||||
\(525\) | 153.421 | 6.69585 | ||||||||
\(526\) | 32.9372 | 1.43613 | ||||||||
\(527\) | 9.44467 | 0.411416 | ||||||||
\(528\) | −0.998699 | −0.0434628 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 92.0780 | 3.99961 | ||||||||
\(531\) | −18.6433 | −0.809049 | ||||||||
\(532\) | −89.5461 | −3.88232 | ||||||||
\(533\) | 8.59649 | 0.372355 | ||||||||
\(534\) | −56.3990 | −2.44062 | ||||||||
\(535\) | 35.3183 | 1.52694 | ||||||||
\(536\) | −34.5001 | −1.49018 | ||||||||
\(537\) | 28.1417 | 1.21440 | ||||||||
\(538\) | −0.473125 | −0.0203979 | ||||||||
\(539\) | −6.50368 | −0.280133 | ||||||||
\(540\) | 120.116 | 5.16898 | ||||||||
\(541\) | −27.1680 | −1.16804 | −0.584022 | − | 0.811738i | \(-0.698522\pi\) | ||||
−0.584022 | + | 0.811738i | \(0.698522\pi\) | |||||||
\(542\) | −63.1050 | −2.71059 | ||||||||
\(543\) | 8.77837 | 0.376716 | ||||||||
\(544\) | 14.5168 | 0.622402 | ||||||||
\(545\) | −43.5377 | −1.86495 | ||||||||
\(546\) | 28.9901 | 1.24066 | ||||||||
\(547\) | 38.6187 | 1.65122 | 0.825608 | − | 0.564244i | \(-0.190832\pi\) | ||||
0.825608 | + | 0.564244i | \(0.190832\pi\) | |||||||
\(548\) | 17.7955 | 0.760187 | ||||||||
\(549\) | −29.0733 | −1.24082 | ||||||||
\(550\) | 14.9372 | 0.636926 | ||||||||
\(551\) | 5.29354 | 0.225512 | ||||||||
\(552\) | 9.47148 | 0.403133 | ||||||||
\(553\) | 16.7150 | 0.710796 | ||||||||
\(554\) | −33.7615 | −1.43439 | ||||||||
\(555\) | 79.1464 | 3.35958 | ||||||||
\(556\) | 26.5025 | 1.12396 | ||||||||
\(557\) | −19.2525 | −0.815755 | −0.407877 | − | 0.913037i | \(-0.633731\pi\) | ||||
−0.407877 | + | 0.913037i | \(0.633731\pi\) | |||||||
\(558\) | −43.8931 | −1.85814 | ||||||||
\(559\) | 0.684959 | 0.0289707 | ||||||||
\(560\) | 10.9361 | 0.462136 | ||||||||
\(561\) | −4.80152 | −0.202720 | ||||||||
\(562\) | 0.886008 | 0.0373740 | ||||||||
\(563\) | −2.27043 | −0.0956873 | −0.0478437 | − | 0.998855i | \(-0.515235\pi\) | ||||
−0.0478437 | + | 0.998855i | \(0.515235\pi\) | |||||||
\(564\) | 106.975 | 4.50444 | ||||||||
\(565\) | −27.4862 | −1.15635 | ||||||||
\(566\) | −47.5699 | −1.99951 | ||||||||
\(567\) | 35.7468 | 1.50122 | ||||||||
\(568\) | −1.81700 | −0.0762396 | ||||||||
\(569\) | −37.2414 | −1.56124 | −0.780621 | − | 0.625005i | \(-0.785097\pi\) | ||||
−0.780621 | + | 0.625005i | \(0.785097\pi\) | |||||||
\(570\) | 173.323 | 7.25970 | ||||||||
\(571\) | −29.3935 | −1.23008 | −0.615040 | − | 0.788496i | \(-0.710860\pi\) | ||||
−0.615040 | + | 0.788496i | \(0.710860\pi\) | |||||||
\(572\) | 1.77114 | 0.0740549 | ||||||||
\(573\) | 38.9027 | 1.62518 | ||||||||
\(574\) | 89.9283 | 3.75354 | ||||||||
\(575\) | −11.8149 | −0.492716 | ||||||||
\(576\) | −74.7153 | −3.11314 | ||||||||
\(577\) | 44.6680 | 1.85955 | 0.929776 | − | 0.368126i | \(-0.120000\pi\) | ||||
0.929776 | + | 0.368126i | \(0.120000\pi\) | |||||||
\(578\) | 19.2565 | 0.800963 | ||||||||
\(579\) | 10.5075 | 0.436676 | ||||||||
\(580\) | −11.9691 | −0.496990 | ||||||||
\(581\) | −58.3116 | −2.41917 | ||||||||
\(582\) | 37.2510 | 1.54411 | ||||||||
\(583\) | 5.28735 | 0.218980 | ||||||||
\(584\) | 33.5613 | 1.38878 | ||||||||
\(585\) | −23.3583 | −0.965749 | ||||||||
\(586\) | 7.91851 | 0.327111 | ||||||||
\(587\) | −36.6454 | −1.51252 | −0.756258 | − | 0.654274i | \(-0.772974\pi\) | ||||
−0.756258 | + | 0.654274i | \(0.772974\pi\) | |||||||
\(588\) | 119.894 | 4.94434 | ||||||||
\(589\) | −19.5770 | −0.806655 | ||||||||
\(590\) | 29.9619 | 1.23351 | ||||||||
\(591\) | −71.9276 | −2.95871 | ||||||||
\(592\) | 3.96411 | 0.162924 | ||||||||
\(593\) | 13.4696 | 0.553132 | 0.276566 | − | 0.960995i | \(-0.410804\pi\) | ||||
0.276566 | + | 0.960995i | \(0.410804\pi\) | |||||||
\(594\) | 10.9917 | 0.450997 | ||||||||
\(595\) | 52.5784 | 2.15551 | ||||||||
\(596\) | −30.9934 | −1.26954 | ||||||||
\(597\) | 9.98058 | 0.408478 | ||||||||
\(598\) | −2.23252 | −0.0912944 | ||||||||
\(599\) | −8.07908 | −0.330102 | −0.165051 | − | 0.986285i | \(-0.552779\pi\) | ||||
−0.165051 | + | 0.986285i | \(0.552779\pi\) | |||||||
\(600\) | −111.905 | −4.56849 | ||||||||
\(601\) | 27.9642 | 1.14068 | 0.570342 | − | 0.821407i | \(-0.306811\pi\) | ||||
0.570342 | + | 0.821407i | \(0.306811\pi\) | |||||||
\(602\) | 7.16540 | 0.292040 | ||||||||
\(603\) | 64.2913 | 2.61814 | ||||||||
\(604\) | 42.5021 | 1.72939 | ||||||||
\(605\) | −43.8859 | −1.78421 | ||||||||
\(606\) | −9.20580 | −0.373960 | ||||||||
\(607\) | −13.6400 | −0.553629 | −0.276815 | − | 0.960923i | \(-0.589279\pi\) | ||||
−0.276815 | + | 0.960923i | \(0.589279\pi\) | |||||||
\(608\) | −30.0905 | −1.22033 | ||||||||
\(609\) | −11.2497 | −0.455861 | ||||||||
\(610\) | 46.7242 | 1.89181 | ||||||||
\(611\) | −10.2470 | −0.414551 | ||||||||
\(612\) | 58.7195 | 2.37360 | ||||||||
\(613\) | −29.5266 | −1.19257 | −0.596285 | − | 0.802773i | \(-0.703357\pi\) | ||||
−0.596285 | + | 0.802773i | \(0.703357\pi\) | |||||||
\(614\) | 6.21954 | 0.251000 | ||||||||
\(615\) | −109.225 | −4.40439 | ||||||||
\(616\) | 7.52954 | 0.303374 | ||||||||
\(617\) | −12.2401 | −0.492767 | −0.246384 | − | 0.969172i | \(-0.579242\pi\) | ||||
−0.246384 | + | 0.969172i | \(0.579242\pi\) | |||||||
\(618\) | 33.0000 | 1.32745 | ||||||||
\(619\) | 22.1410 | 0.889922 | 0.444961 | − | 0.895550i | \(-0.353218\pi\) | ||||
0.444961 | + | 0.895550i | \(0.353218\pi\) | |||||||
\(620\) | 44.2651 | 1.77773 | ||||||||
\(621\) | −8.69415 | −0.348884 | ||||||||
\(622\) | 48.6460 | 1.95052 | ||||||||
\(623\) | 35.4635 | 1.42082 | ||||||||
\(624\) | −1.76356 | −0.0705989 | ||||||||
\(625\) | 55.5176 | 2.22071 | ||||||||
\(626\) | −45.0715 | −1.80142 | ||||||||
\(627\) | 9.95264 | 0.397470 | ||||||||
\(628\) | −34.8018 | −1.38874 | ||||||||
\(629\) | 19.0585 | 0.759913 | ||||||||
\(630\) | −244.353 | −9.73525 | ||||||||
\(631\) | 21.9194 | 0.872597 | 0.436299 | − | 0.899802i | \(-0.356289\pi\) | ||||
0.436299 | + | 0.899802i | \(0.356289\pi\) | |||||||
\(632\) | −12.1919 | −0.484967 | ||||||||
\(633\) | 77.2864 | 3.07186 | ||||||||
\(634\) | −76.0684 | −3.02106 | ||||||||
\(635\) | −21.7785 | −0.864252 | ||||||||
\(636\) | −97.4710 | −3.86498 | ||||||||
\(637\) | −11.4846 | −0.455035 | ||||||||
\(638\) | −1.09528 | −0.0433627 | ||||||||
\(639\) | 3.38599 | 0.133948 | ||||||||
\(640\) | 79.6887 | 3.14997 | ||||||||
\(641\) | −1.55726 | −0.0615081 | −0.0307541 | − | 0.999527i | \(-0.509791\pi\) | ||||
−0.0307541 | + | 0.999527i | \(0.509791\pi\) | |||||||
\(642\) | −59.5802 | −2.35144 | ||||||||
\(643\) | 4.67478 | 0.184355 | 0.0921777 | − | 0.995743i | \(-0.470617\pi\) | ||||
0.0921777 | + | 0.995743i | \(0.470617\pi\) | |||||||
\(644\) | −14.6551 | −0.577490 | ||||||||
\(645\) | −8.70295 | −0.342678 | ||||||||
\(646\) | 41.7363 | 1.64209 | ||||||||
\(647\) | 1.38033 | 0.0542663 | 0.0271332 | − | 0.999632i | \(-0.491362\pi\) | ||||
0.0271332 | + | 0.999632i | \(0.491362\pi\) | |||||||
\(648\) | −26.0736 | −1.02427 | ||||||||
\(649\) | 1.72049 | 0.0675351 | ||||||||
\(650\) | 26.3770 | 1.03459 | ||||||||
\(651\) | 41.6046 | 1.63061 | ||||||||
\(652\) | −29.9426 | −1.17264 | ||||||||
\(653\) | −26.3890 | −1.03268 | −0.516340 | − | 0.856384i | \(-0.672706\pi\) | ||||
−0.516340 | + | 0.856384i | \(0.672706\pi\) | |||||||
\(654\) | 73.4460 | 2.87196 | ||||||||
\(655\) | 17.1254 | 0.669143 | ||||||||
\(656\) | −5.47063 | −0.213592 | ||||||||
\(657\) | −62.5417 | −2.43998 | ||||||||
\(658\) | −107.195 | −4.17889 | ||||||||
\(659\) | 17.3896 | 0.677404 | 0.338702 | − | 0.940894i | \(-0.390012\pi\) | ||||
0.338702 | + | 0.940894i | \(0.390012\pi\) | |||||||
\(660\) | −22.5037 | −0.875955 | ||||||||
\(661\) | 37.7006 | 1.46638 | 0.733192 | − | 0.680021i | \(-0.238029\pi\) | ||||
0.733192 | + | 0.680021i | \(0.238029\pi\) | |||||||
\(662\) | 35.0633 | 1.36277 | ||||||||
\(663\) | −8.47880 | −0.329289 | ||||||||
\(664\) | 42.5323 | 1.65057 | ||||||||
\(665\) | −108.985 | −4.22626 | ||||||||
\(666\) | −88.5726 | −3.43212 | ||||||||
\(667\) | 0.866337 | 0.0335447 | ||||||||
\(668\) | −32.5662 | −1.26002 | ||||||||
\(669\) | −45.5356 | −1.76051 | ||||||||
\(670\) | −103.324 | −3.99174 | ||||||||
\(671\) | 2.68302 | 0.103577 | ||||||||
\(672\) | 63.9477 | 2.46684 | ||||||||
\(673\) | −38.3121 | −1.47682 | −0.738411 | − | 0.674351i | \(-0.764423\pi\) | ||||
−0.738411 | + | 0.674351i | \(0.764423\pi\) | |||||||
\(674\) | −62.7231 | −2.41600 | ||||||||
\(675\) | 102.721 | 3.95372 | ||||||||
\(676\) | −40.6721 | −1.56431 | ||||||||
\(677\) | 48.7721 | 1.87446 | 0.937232 | − | 0.348706i | \(-0.113379\pi\) | ||||
0.937232 | + | 0.348706i | \(0.113379\pi\) | |||||||
\(678\) | 46.3678 | 1.78074 | ||||||||
\(679\) | −23.4234 | −0.898906 | ||||||||
\(680\) | −38.3505 | −1.47067 | ||||||||
\(681\) | 23.4866 | 0.900009 | ||||||||
\(682\) | 4.05066 | 0.155108 | ||||||||
\(683\) | 23.2976 | 0.891459 | 0.445730 | − | 0.895168i | \(-0.352944\pi\) | ||||
0.445730 | + | 0.895168i | \(0.352944\pi\) | |||||||
\(684\) | −121.714 | −4.65386 | ||||||||
\(685\) | 21.6586 | 0.827532 | ||||||||
\(686\) | −49.5881 | −1.89328 | ||||||||
\(687\) | 19.8586 | 0.757653 | ||||||||
\(688\) | −0.435894 | −0.0166183 | ||||||||
\(689\) | 9.33670 | 0.355700 | ||||||||
\(690\) | 28.3659 | 1.07987 | ||||||||
\(691\) | 34.5762 | 1.31534 | 0.657670 | − | 0.753306i | \(-0.271542\pi\) | ||||
0.657670 | + | 0.753306i | \(0.271542\pi\) | |||||||
\(692\) | 53.8427 | 2.04679 | ||||||||
\(693\) | −14.0314 | −0.533007 | ||||||||
\(694\) | 18.9973 | 0.721129 | ||||||||
\(695\) | 32.2558 | 1.22353 | ||||||||
\(696\) | 8.20550 | 0.311029 | ||||||||
\(697\) | −26.3016 | −0.996242 | ||||||||
\(698\) | −2.31715 | −0.0877056 | ||||||||
\(699\) | −66.6480 | −2.52086 | ||||||||
\(700\) | 173.148 | 6.54439 | ||||||||
\(701\) | −4.83133 | −0.182477 | −0.0912384 | − | 0.995829i | \(-0.529083\pi\) | ||||
−0.0912384 | + | 0.995829i | \(0.529083\pi\) | |||||||
\(702\) | 19.4098 | 0.732578 | ||||||||
\(703\) | −39.5047 | −1.48995 | ||||||||
\(704\) | 6.89508 | 0.259868 | ||||||||
\(705\) | 130.197 | 4.90350 | ||||||||
\(706\) | −67.8713 | −2.55437 | ||||||||
\(707\) | 5.78858 | 0.217702 | ||||||||
\(708\) | −31.7168 | −1.19199 | ||||||||
\(709\) | −0.742927 | −0.0279012 | −0.0139506 | − | 0.999903i | \(-0.504441\pi\) | ||||
−0.0139506 | + | 0.999903i | \(0.504441\pi\) | |||||||
\(710\) | −5.44169 | −0.204223 | ||||||||
\(711\) | 22.7197 | 0.852055 | ||||||||
\(712\) | −25.8670 | −0.969405 | ||||||||
\(713\) | −3.20396 | −0.119989 | ||||||||
\(714\) | −88.6971 | −3.31941 | ||||||||
\(715\) | 2.15562 | 0.0806155 | ||||||||
\(716\) | 31.7602 | 1.18694 | ||||||||
\(717\) | −90.2399 | −3.37007 | ||||||||
\(718\) | −70.3789 | −2.62652 | ||||||||
\(719\) | 35.8759 | 1.33794 | 0.668972 | − | 0.743288i | \(-0.266735\pi\) | ||||
0.668972 | + | 0.743288i | \(0.266735\pi\) | |||||||
\(720\) | 14.8648 | 0.553977 | ||||||||
\(721\) | −20.7503 | −0.772782 | ||||||||
\(722\) | −42.4855 | −1.58115 | ||||||||
\(723\) | 19.8848 | 0.739525 | ||||||||
\(724\) | 9.90711 | 0.368195 | ||||||||
\(725\) | −10.2357 | −0.380144 | ||||||||
\(726\) | 74.0332 | 2.74763 | ||||||||
\(727\) | −46.6303 | −1.72942 | −0.864712 | − | 0.502268i | \(-0.832499\pi\) | ||||
−0.864712 | + | 0.502268i | \(0.832499\pi\) | |||||||
\(728\) | 13.2961 | 0.492786 | ||||||||
\(729\) | −29.2768 | −1.08433 | ||||||||
\(730\) | 100.512 | 3.72011 | ||||||||
\(731\) | −2.09568 | −0.0775115 | ||||||||
\(732\) | −49.4608 | −1.82812 | ||||||||
\(733\) | −46.4369 | −1.71519 | −0.857593 | − | 0.514329i | \(-0.828041\pi\) | ||||
−0.857593 | + | 0.514329i | \(0.828041\pi\) | |||||||
\(734\) | 76.9084 | 2.83874 | ||||||||
\(735\) | 145.921 | 5.38236 | ||||||||
\(736\) | −4.92459 | −0.181523 | ||||||||
\(737\) | −5.93310 | −0.218549 | ||||||||
\(738\) | 122.234 | 4.49949 | ||||||||
\(739\) | −38.6135 | −1.42042 | −0.710211 | − | 0.703989i | \(-0.751400\pi\) | ||||
−0.710211 | + | 0.703989i | \(0.751400\pi\) | |||||||
\(740\) | 89.3232 | 3.28359 | ||||||||
\(741\) | 17.5749 | 0.645631 | ||||||||
\(742\) | 97.6717 | 3.58564 | ||||||||
\(743\) | −33.7719 | −1.23897 | −0.619486 | − | 0.785008i | \(-0.712659\pi\) | ||||
−0.619486 | + | 0.785008i | \(0.712659\pi\) | |||||||
\(744\) | −30.3462 | −1.11255 | ||||||||
\(745\) | −37.7215 | −1.38201 | ||||||||
\(746\) | 4.85661 | 0.177813 | ||||||||
\(747\) | −79.2592 | −2.89994 | ||||||||
\(748\) | −5.41891 | −0.198135 | ||||||||
\(749\) | 37.4639 | 1.36890 | ||||||||
\(750\) | −193.311 | −7.05873 | ||||||||
\(751\) | −12.6038 | −0.459920 | −0.229960 | − | 0.973200i | \(-0.573860\pi\) | ||||
−0.229960 | + | 0.973200i | \(0.573860\pi\) | |||||||
\(752\) | 6.52101 | 0.237797 | ||||||||
\(753\) | 37.3738 | 1.36198 | ||||||||
\(754\) | −1.93411 | −0.0704362 | ||||||||
\(755\) | 51.7286 | 1.88259 | ||||||||
\(756\) | 127.413 | 4.63398 | ||||||||
\(757\) | 32.1846 | 1.16977 | 0.584884 | − | 0.811117i | \(-0.301140\pi\) | ||||
0.584884 | + | 0.811117i | \(0.301140\pi\) | |||||||
\(758\) | 75.1250 | 2.72866 | ||||||||
\(759\) | 1.62884 | 0.0591232 | ||||||||
\(760\) | 79.4932 | 2.88352 | ||||||||
\(761\) | 1.28667 | 0.0466417 | 0.0233209 | − | 0.999728i | \(-0.492576\pi\) | ||||
0.0233209 | + | 0.999728i | \(0.492576\pi\) | |||||||
\(762\) | 36.7392 | 1.33092 | ||||||||
\(763\) | −46.1826 | −1.67192 | ||||||||
\(764\) | 43.9049 | 1.58842 | ||||||||
\(765\) | 71.4665 | 2.58388 | ||||||||
\(766\) | 23.2125 | 0.838701 | ||||||||
\(767\) | 3.03814 | 0.109701 | ||||||||
\(768\) | −58.9773 | −2.12816 | ||||||||
\(769\) | 35.5882 | 1.28334 | 0.641671 | − | 0.766980i | \(-0.278241\pi\) | ||||
0.641671 | + | 0.766980i | \(0.278241\pi\) | |||||||
\(770\) | 22.5500 | 0.812646 | ||||||||
\(771\) | −21.9202 | −0.789438 | ||||||||
\(772\) | 11.8586 | 0.426799 | ||||||||
\(773\) | 25.6472 | 0.922464 | 0.461232 | − | 0.887280i | \(-0.347408\pi\) | ||||
0.461232 | + | 0.887280i | \(0.347408\pi\) | |||||||
\(774\) | 9.73946 | 0.350078 | ||||||||
\(775\) | 37.8545 | 1.35977 | ||||||||
\(776\) | 17.0849 | 0.613313 | ||||||||
\(777\) | 83.9545 | 3.01185 | ||||||||
\(778\) | 61.1195 | 2.19124 | ||||||||
\(779\) | 54.5181 | 1.95331 | ||||||||
\(780\) | −39.7383 | −1.42286 | ||||||||
\(781\) | −0.312475 | −0.0111812 | ||||||||
\(782\) | 6.83054 | 0.244260 | ||||||||
\(783\) | −7.53207 | −0.269174 | ||||||||
\(784\) | 7.30854 | 0.261019 | ||||||||
\(785\) | −42.3566 | −1.51177 | ||||||||
\(786\) | −28.8896 | −1.03046 | ||||||||
\(787\) | −5.50017 | −0.196060 | −0.0980299 | − | 0.995183i | \(-0.531254\pi\) | ||||
−0.0980299 | + | 0.995183i | \(0.531254\pi\) | |||||||
\(788\) | −81.1762 | −2.89178 | ||||||||
\(789\) | −42.4352 | −1.51073 | ||||||||
\(790\) | −36.5132 | −1.29908 | ||||||||
\(791\) | −29.1560 | −1.03667 | ||||||||
\(792\) | 10.2344 | 0.363664 | ||||||||
\(793\) | 4.73783 | 0.168245 | ||||||||
\(794\) | −65.5389 | −2.32589 | ||||||||
\(795\) | −118.630 | −4.20738 | ||||||||
\(796\) | 11.2639 | 0.399239 | ||||||||
\(797\) | −9.98728 | −0.353767 | −0.176884 | − | 0.984232i | \(-0.556602\pi\) | ||||
−0.176884 | + | 0.984232i | \(0.556602\pi\) | |||||||
\(798\) | 183.852 | 6.50830 | ||||||||
\(799\) | 31.3515 | 1.10914 | ||||||||
\(800\) | 58.1837 | 2.05710 | ||||||||
\(801\) | 48.2033 | 1.70318 | ||||||||
\(802\) | −17.4341 | −0.615620 | ||||||||
\(803\) | 5.77164 | 0.203677 | ||||||||
\(804\) | 109.375 | 3.85737 | ||||||||
\(805\) | −17.8364 | −0.628651 | ||||||||
\(806\) | 7.15289 | 0.251950 | ||||||||
\(807\) | 0.609558 | 0.0214575 | ||||||||
\(808\) | −4.22217 | −0.148535 | ||||||||
\(809\) | 20.4557 | 0.719184 | 0.359592 | − | 0.933110i | \(-0.382916\pi\) | ||||
0.359592 | + | 0.933110i | \(0.382916\pi\) | |||||||
\(810\) | −78.0871 | −2.74370 | ||||||||
\(811\) | −29.6616 | −1.04156 | −0.520779 | − | 0.853691i | \(-0.674359\pi\) | ||||
−0.520779 | + | 0.853691i | \(0.674359\pi\) | |||||||
\(812\) | −12.6962 | −0.445550 | ||||||||
\(813\) | 81.3024 | 2.85140 | ||||||||
\(814\) | 8.17389 | 0.286495 | ||||||||
\(815\) | −36.4425 | −1.27653 | ||||||||
\(816\) | 5.39573 | 0.188888 | ||||||||
\(817\) | 4.34394 | 0.151975 | ||||||||
\(818\) | 30.9778 | 1.08311 | ||||||||
\(819\) | −24.7774 | −0.865791 | ||||||||
\(820\) | −123.270 | −4.30476 | ||||||||
\(821\) | −9.28615 | −0.324089 | −0.162044 | − | 0.986783i | \(-0.551809\pi\) | ||||
−0.162044 | + | 0.986783i | \(0.551809\pi\) | |||||||
\(822\) | −36.5370 | −1.27437 | ||||||||
\(823\) | 3.11075 | 0.108434 | 0.0542169 | − | 0.998529i | \(-0.482734\pi\) | ||||
0.0542169 | + | 0.998529i | \(0.482734\pi\) | |||||||
\(824\) | 15.1352 | 0.527260 | ||||||||
\(825\) | −19.2446 | −0.670012 | ||||||||
\(826\) | 31.7821 | 1.10584 | ||||||||
\(827\) | −43.0032 | −1.49537 | −0.747684 | − | 0.664055i | \(-0.768834\pi\) | ||||
−0.747684 | + | 0.664055i | \(0.768834\pi\) | |||||||
\(828\) | −19.9197 | −0.692257 | ||||||||
\(829\) | 36.2793 | 1.26003 | 0.630016 | − | 0.776582i | \(-0.283048\pi\) | ||||
0.630016 | + | 0.776582i | \(0.283048\pi\) | |||||||
\(830\) | 127.379 | 4.42138 | ||||||||
\(831\) | 43.4972 | 1.50890 | ||||||||
\(832\) | 12.1757 | 0.422117 | ||||||||
\(833\) | 35.1378 | 1.21745 | ||||||||
\(834\) | −54.4138 | −1.88420 | ||||||||
\(835\) | −39.6357 | −1.37165 | ||||||||
\(836\) | 11.2324 | 0.388479 | ||||||||
\(837\) | 27.8557 | 0.962833 | ||||||||
\(838\) | 80.3418 | 2.77536 | ||||||||
\(839\) | −7.09339 | −0.244891 | −0.122445 | − | 0.992475i | \(-0.539074\pi\) | ||||
−0.122445 | + | 0.992475i | \(0.539074\pi\) | |||||||
\(840\) | −168.937 | −5.82889 | ||||||||
\(841\) | −28.2495 | −0.974119 | ||||||||
\(842\) | −70.2618 | −2.42138 | ||||||||
\(843\) | −1.14150 | −0.0393155 | ||||||||
\(844\) | 87.2240 | 3.00237 | ||||||||
\(845\) | −49.5013 | −1.70290 | ||||||||
\(846\) | −145.703 | −5.00938 | ||||||||
\(847\) | −46.5519 | −1.59954 | ||||||||
\(848\) | −5.94168 | −0.204038 | ||||||||
\(849\) | 61.2875 | 2.10338 | ||||||||
\(850\) | −80.7023 | −2.76806 | ||||||||
\(851\) | −6.46531 | −0.221628 | ||||||||
\(852\) | 5.76041 | 0.197348 | ||||||||
\(853\) | −29.5462 | −1.01164 | −0.505821 | − | 0.862638i | \(-0.668810\pi\) | ||||
−0.505821 | + | 0.862638i | \(0.668810\pi\) | |||||||
\(854\) | 49.5626 | 1.69600 | ||||||||
\(855\) | −148.136 | −5.06615 | ||||||||
\(856\) | −27.3260 | −0.933984 | ||||||||
\(857\) | −19.0737 | −0.651544 | −0.325772 | − | 0.945448i | \(-0.605624\pi\) | ||||
−0.325772 | + | 0.945448i | \(0.605624\pi\) | |||||||
\(858\) | −3.63642 | −0.124145 | ||||||||
\(859\) | 21.9360 | 0.748447 | 0.374224 | − | 0.927339i | \(-0.377909\pi\) | ||||
0.374224 | + | 0.927339i | \(0.377909\pi\) | |||||||
\(860\) | −9.82200 | −0.334927 | ||||||||
\(861\) | −115.861 | −3.94852 | ||||||||
\(862\) | −22.3389 | −0.760867 | ||||||||
\(863\) | −48.8604 | −1.66323 | −0.831613 | − | 0.555356i | \(-0.812582\pi\) | ||||
−0.831613 | + | 0.555356i | \(0.812582\pi\) | |||||||
\(864\) | 42.8152 | 1.45660 | ||||||||
\(865\) | 65.5310 | 2.22812 | ||||||||
\(866\) | −12.9934 | −0.441535 | ||||||||
\(867\) | −24.8094 | −0.842571 | ||||||||
\(868\) | 46.9542 | 1.59373 | ||||||||
\(869\) | −2.09668 | −0.0711250 | ||||||||
\(870\) | 24.5744 | 0.833151 | ||||||||
\(871\) | −10.4770 | −0.355000 | ||||||||
\(872\) | 33.6854 | 1.14073 | ||||||||
\(873\) | −31.8379 | −1.07755 | ||||||||
\(874\) | −14.1584 | −0.478915 | ||||||||
\(875\) | 121.554 | 4.10926 | ||||||||
\(876\) | −106.399 | −3.59488 | ||||||||
\(877\) | 16.4276 | 0.554722 | 0.277361 | − | 0.960766i | \(-0.410540\pi\) | ||||
0.277361 | + | 0.960766i | \(0.410540\pi\) | |||||||
\(878\) | −65.4105 | −2.20750 | ||||||||
\(879\) | −10.2019 | −0.344103 | ||||||||
\(880\) | −1.37179 | −0.0462430 | ||||||||
\(881\) | 1.92067 | 0.0647090 | 0.0323545 | − | 0.999476i | \(-0.489699\pi\) | ||||
0.0323545 | + | 0.999476i | \(0.489699\pi\) | |||||||
\(882\) | −163.299 | −5.49858 | ||||||||
\(883\) | 11.5051 | 0.387179 | 0.193589 | − | 0.981083i | \(-0.437987\pi\) | ||||
0.193589 | + | 0.981083i | \(0.437987\pi\) | |||||||
\(884\) | −9.56902 | −0.321841 | ||||||||
\(885\) | −38.6019 | −1.29759 | ||||||||
\(886\) | 94.5691 | 3.17711 | ||||||||
\(887\) | 53.8440 | 1.80791 | 0.903953 | − | 0.427632i | \(-0.140652\pi\) | ||||
0.903953 | + | 0.427632i | \(0.140652\pi\) | |||||||
\(888\) | −61.2361 | −2.05495 | ||||||||
\(889\) | −23.1015 | −0.774799 | ||||||||
\(890\) | −77.4683 | −2.59674 | ||||||||
\(891\) | −4.48395 | −0.150218 | ||||||||
\(892\) | −51.3906 | −1.72069 | ||||||||
\(893\) | −64.9858 | −2.17467 | ||||||||
\(894\) | 63.6342 | 2.12825 | ||||||||
\(895\) | 38.6548 | 1.29209 | ||||||||
\(896\) | 84.5297 | 2.82394 | ||||||||
\(897\) | 2.87630 | 0.0960369 | ||||||||
\(898\) | 15.2261 | 0.508103 | ||||||||
\(899\) | −2.77571 | −0.0925749 | ||||||||
\(900\) | 235.349 | 7.84498 | ||||||||
\(901\) | −28.5663 | −0.951681 | ||||||||
\(902\) | −11.2803 | −0.375593 | ||||||||
\(903\) | −9.23165 | −0.307210 | ||||||||
\(904\) | 21.2662 | 0.707305 | ||||||||
\(905\) | 12.0578 | 0.400814 | ||||||||
\(906\) | −87.2635 | −2.89913 | ||||||||
\(907\) | −44.7141 | −1.48471 | −0.742353 | − | 0.670008i | \(-0.766290\pi\) | ||||
−0.742353 | + | 0.670008i | \(0.766290\pi\) | |||||||
\(908\) | 26.5066 | 0.879652 | ||||||||
\(909\) | 7.86805 | 0.260967 | ||||||||
\(910\) | 39.8201 | 1.32002 | ||||||||
\(911\) | −56.4648 | −1.87076 | −0.935381 | − | 0.353641i | \(-0.884943\pi\) | ||||
−0.935381 | + | 0.353641i | \(0.884943\pi\) | |||||||
\(912\) | −11.1843 | −0.370350 | ||||||||
\(913\) | 7.31441 | 0.242072 | ||||||||
\(914\) | 28.1252 | 0.930298 | ||||||||
\(915\) | −60.1979 | −1.99008 | ||||||||
\(916\) | 22.4121 | 0.740515 | ||||||||
\(917\) | 18.1657 | 0.599885 | ||||||||
\(918\) | −59.3858 | −1.96002 | ||||||||
\(919\) | 41.2827 | 1.36179 | 0.680894 | − | 0.732382i | \(-0.261591\pi\) | ||||
0.680894 | + | 0.732382i | \(0.261591\pi\) | |||||||
\(920\) | 13.0098 | 0.428921 | ||||||||
\(921\) | −8.01304 | −0.264039 | ||||||||
\(922\) | −5.97691 | −0.196839 | ||||||||
\(923\) | −0.551787 | −0.0181623 | ||||||||
\(924\) | −23.8708 | −0.785291 | ||||||||
\(925\) | 76.3871 | 2.51159 | ||||||||
\(926\) | 11.0622 | 0.363528 | ||||||||
\(927\) | −28.2046 | −0.926360 | ||||||||
\(928\) | −4.26636 | −0.140050 | ||||||||
\(929\) | 16.4305 | 0.539066 | 0.269533 | − | 0.962991i | \(-0.413131\pi\) | ||||
0.269533 | + | 0.962991i | \(0.413131\pi\) | |||||||
\(930\) | −90.8831 | −2.98017 | ||||||||
\(931\) | −72.8340 | −2.38704 | ||||||||
\(932\) | −75.2178 | −2.46384 | ||||||||
\(933\) | −62.6738 | −2.05185 | ||||||||
\(934\) | 65.0010 | 2.12690 | ||||||||
\(935\) | −6.59526 | −0.215688 | ||||||||
\(936\) | 18.0725 | 0.590718 | ||||||||
\(937\) | −42.2225 | −1.37935 | −0.689675 | − | 0.724119i | \(-0.742246\pi\) | ||||
−0.689675 | + | 0.724119i | \(0.742246\pi\) | |||||||
\(938\) | −109.600 | −3.57858 | ||||||||
\(939\) | 58.0686 | 1.89500 | ||||||||
\(940\) | 146.938 | 4.79259 | ||||||||
\(941\) | 15.7266 | 0.512672 | 0.256336 | − | 0.966588i | \(-0.417485\pi\) | ||||
0.256336 | + | 0.966588i | \(0.417485\pi\) | |||||||
\(942\) | 71.4535 | 2.32808 | ||||||||
\(943\) | 8.92239 | 0.290553 | ||||||||
\(944\) | −1.93341 | −0.0629270 | ||||||||
\(945\) | 155.072 | 5.04451 | ||||||||
\(946\) | −0.898803 | −0.0292226 | ||||||||
\(947\) | 8.32328 | 0.270470 | 0.135235 | − | 0.990814i | \(-0.456821\pi\) | ||||
0.135235 | + | 0.990814i | \(0.456821\pi\) | |||||||
\(948\) | 38.6518 | 1.25535 | ||||||||
\(949\) | 10.1919 | 0.330843 | ||||||||
\(950\) | 167.280 | 5.42729 | ||||||||
\(951\) | 98.0039 | 3.17800 | ||||||||
\(952\) | −40.6803 | −1.31846 | ||||||||
\(953\) | 8.24534 | 0.267093 | 0.133546 | − | 0.991043i | \(-0.457363\pi\) | ||||
0.133546 | + | 0.991043i | \(0.457363\pi\) | |||||||
\(954\) | 132.759 | 4.29823 | ||||||||
\(955\) | 53.4358 | 1.72914 | ||||||||
\(956\) | −101.843 | −3.29384 | ||||||||
\(957\) | 1.41113 | 0.0456152 | ||||||||
\(958\) | 66.0126 | 2.13277 | ||||||||
\(959\) | 22.9743 | 0.741880 | ||||||||
\(960\) | −154.702 | −4.99299 | ||||||||
\(961\) | −20.7347 | −0.668860 | ||||||||
\(962\) | 14.4339 | 0.465368 | ||||||||
\(963\) | 50.9223 | 1.64095 | ||||||||
\(964\) | 22.4417 | 0.722797 | ||||||||
\(965\) | 14.4328 | 0.464609 | ||||||||
\(966\) | 30.0891 | 0.968102 | ||||||||
\(967\) | 4.91301 | 0.157992 | 0.0789958 | − | 0.996875i | \(-0.474829\pi\) | ||||
0.0789958 | + | 0.996875i | \(0.474829\pi\) | |||||||
\(968\) | 33.9548 | 1.09135 | ||||||||
\(969\) | −53.7717 | −1.72740 | ||||||||
\(970\) | 51.1672 | 1.64288 | ||||||||
\(971\) | 58.3791 | 1.87347 | 0.936737 | − | 0.350035i | \(-0.113830\pi\) | ||||
0.936737 | + | 0.350035i | \(0.113830\pi\) | |||||||
\(972\) | −5.21655 | −0.167321 | ||||||||
\(973\) | 34.2153 | 1.09689 | ||||||||
\(974\) | 26.6374 | 0.853518 | ||||||||
\(975\) | −33.9832 | −1.08833 | ||||||||
\(976\) | −3.01505 | −0.0965096 | ||||||||
\(977\) | −29.7116 | −0.950559 | −0.475280 | − | 0.879835i | \(-0.657653\pi\) | ||||
−0.475280 | + | 0.879835i | \(0.657653\pi\) | |||||||
\(978\) | 61.4767 | 1.96581 | ||||||||
\(979\) | −4.44842 | −0.142172 | ||||||||
\(980\) | 164.683 | 5.26062 | ||||||||
\(981\) | −62.7731 | −2.00419 | ||||||||
\(982\) | 28.1389 | 0.897949 | ||||||||
\(983\) | 21.6379 | 0.690141 | 0.345071 | − | 0.938577i | \(-0.387855\pi\) | ||||
0.345071 | + | 0.938577i | \(0.387855\pi\) | |||||||
\(984\) | 84.5083 | 2.69403 | ||||||||
\(985\) | −98.7981 | −3.14797 | ||||||||
\(986\) | 5.91755 | 0.188453 | ||||||||
\(987\) | 138.106 | 4.39597 | ||||||||
\(988\) | 19.8347 | 0.631027 | ||||||||
\(989\) | 0.710927 | 0.0226062 | ||||||||
\(990\) | 30.6508 | 0.974146 | ||||||||
\(991\) | 8.25744 | 0.262306 | 0.131153 | − | 0.991362i | \(-0.458132\pi\) | ||||
0.131153 | + | 0.991362i | \(0.458132\pi\) | |||||||
\(992\) | 15.7782 | 0.500958 | ||||||||
\(993\) | −45.1744 | −1.43357 | ||||||||
\(994\) | −5.77227 | −0.183085 | ||||||||
\(995\) | 13.7091 | 0.434608 | ||||||||
\(996\) | −134.839 | −4.27255 | ||||||||
\(997\) | 29.6257 | 0.938254 | 0.469127 | − | 0.883131i | \(-0.344569\pi\) | ||||
0.469127 | + | 0.883131i | \(0.344569\pi\) | |||||||
\(998\) | −45.3208 | −1.43460 | ||||||||
\(999\) | 56.2104 | 1.77842 |
(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 | 8027.2.a.e.1.20 | ✓ | 169 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.e.1.20 | ✓ | 169 | 1.1 | even | 1 | trivial |