Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, 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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.688892 | −0.487120 | −0.243560 | − | 0.969886i | \(-0.578315\pi\) | ||||
−0.243560 | + | 0.969886i | \(0.578315\pi\) | |||||||
\(3\) | 2.21432 | 1.27844 | 0.639219 | − | 0.769025i | \(-0.279258\pi\) | ||||
0.639219 | + | 0.769025i | \(0.279258\pi\) | |||||||
\(4\) | −1.52543 | −0.762714 | ||||||||
\(5\) | 3.21432 | 1.43749 | 0.718744 | − | 0.695275i | \(-0.244717\pi\) | ||||
0.718744 | + | 0.695275i | \(0.244717\pi\) | |||||||
\(6\) | −1.52543 | −0.622753 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.42864 | 0.858654 | ||||||||
\(9\) | 1.90321 | 0.634404 | ||||||||
\(10\) | −2.21432 | −0.700229 | ||||||||
\(11\) | −2.68889 | −0.810731 | −0.405366 | − | 0.914155i | \(-0.632856\pi\) | ||||
−0.405366 | + | 0.914155i | \(0.632856\pi\) | |||||||
\(12\) | −3.37778 | −0.975082 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.11753 | 1.83774 | ||||||||
\(16\) | 1.37778 | 0.344446 | ||||||||
\(17\) | −3.59210 | −0.871213 | −0.435607 | − | 0.900137i | \(-0.643466\pi\) | ||||
−0.435607 | + | 0.900137i | \(0.643466\pi\) | |||||||
\(18\) | −1.31111 | −0.309031 | ||||||||
\(19\) | −8.54617 | −1.96063 | −0.980313 | − | 0.197449i | \(-0.936734\pi\) | ||||
−0.980313 | + | 0.197449i | \(0.936734\pi\) | |||||||
\(20\) | −4.90321 | −1.09639 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.85236 | 0.394924 | ||||||||
\(23\) | −3.28100 | −0.684135 | −0.342068 | − | 0.939675i | \(-0.611127\pi\) | ||||
−0.342068 | + | 0.939675i | \(0.611127\pi\) | |||||||
\(24\) | 5.37778 | 1.09774 | ||||||||
\(25\) | 5.33185 | 1.06637 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.42864 | −0.467392 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.05086 | 0.380834 | 0.190417 | − | 0.981703i | \(-0.439016\pi\) | ||||
0.190417 | + | 0.981703i | \(0.439016\pi\) | |||||||
\(30\) | −4.90321 | −0.895200 | ||||||||
\(31\) | 5.83654 | 1.04827 | 0.524136 | − | 0.851634i | \(-0.324388\pi\) | ||||
0.524136 | + | 0.851634i | \(0.324388\pi\) | |||||||
\(32\) | −5.80642 | −1.02644 | ||||||||
\(33\) | −5.95407 | −1.03647 | ||||||||
\(34\) | 2.47457 | 0.424386 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.90321 | −0.483869 | ||||||||
\(37\) | −3.93332 | −0.646634 | −0.323317 | − | 0.946291i | \(-0.604798\pi\) | ||||
−0.323317 | + | 0.946291i | \(0.604798\pi\) | |||||||
\(38\) | 5.88739 | 0.955061 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.80642 | 1.23430 | ||||||||
\(41\) | 0.755569 | 0.118000 | 0.0590000 | − | 0.998258i | \(-0.481209\pi\) | ||||
0.0590000 | + | 0.998258i | \(0.481209\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.80642 | 1.34297 | 0.671484 | − | 0.741019i | \(-0.265657\pi\) | ||||
0.671484 | + | 0.741019i | \(0.265657\pi\) | |||||||
\(44\) | 4.10171 | 0.618356 | ||||||||
\(45\) | 6.11753 | 0.911948 | ||||||||
\(46\) | 2.26025 | 0.333256 | ||||||||
\(47\) | 1.88247 | 0.274586 | 0.137293 | − | 0.990530i | \(-0.456160\pi\) | ||||
0.137293 | + | 0.990530i | \(0.456160\pi\) | |||||||
\(48\) | 3.05086 | 0.440353 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.67307 | −0.519451 | ||||||||
\(51\) | −7.95407 | −1.11379 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.52543 | 0.346894 | 0.173447 | − | 0.984843i | \(-0.444509\pi\) | ||||
0.173447 | + | 0.984843i | \(0.444509\pi\) | |||||||
\(54\) | 1.67307 | 0.227676 | ||||||||
\(55\) | −8.64296 | −1.16542 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.9240 | −2.50654 | ||||||||
\(58\) | −1.41282 | −0.185512 | ||||||||
\(59\) | 7.33185 | 0.954526 | 0.477263 | − | 0.878761i | \(-0.341629\pi\) | ||||
0.477263 | + | 0.878761i | \(0.341629\pi\) | |||||||
\(60\) | −10.8573 | −1.40167 | ||||||||
\(61\) | −9.05086 | −1.15884 | −0.579422 | − | 0.815028i | \(-0.696722\pi\) | ||||
−0.579422 | + | 0.815028i | \(0.696722\pi\) | |||||||
\(62\) | −4.02074 | −0.510635 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.24443 | 0.155554 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.10171 | 0.504886 | ||||||||
\(67\) | −0.428639 | −0.0523666 | −0.0261833 | − | 0.999657i | \(-0.508335\pi\) | ||||
−0.0261833 | + | 0.999657i | \(0.508335\pi\) | |||||||
\(68\) | 5.47949 | 0.664486 | ||||||||
\(69\) | −7.26517 | −0.874624 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.98418 | −1.06623 | −0.533113 | − | 0.846044i | \(-0.678978\pi\) | ||||
−0.533113 | + | 0.846044i | \(0.678978\pi\) | |||||||
\(72\) | 4.62222 | 0.544733 | ||||||||
\(73\) | 5.79060 | 0.677739 | 0.338869 | − | 0.940833i | \(-0.389956\pi\) | ||||
0.338869 | + | 0.940833i | \(0.389956\pi\) | |||||||
\(74\) | 2.70964 | 0.314989 | ||||||||
\(75\) | 11.8064 | 1.36329 | ||||||||
\(76\) | 13.0366 | 1.49540 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.47949 | −0.503983 | −0.251991 | − | 0.967730i | \(-0.581085\pi\) | ||||
−0.251991 | + | 0.967730i | \(0.581085\pi\) | |||||||
\(80\) | 4.42864 | 0.495137 | ||||||||
\(81\) | −11.0874 | −1.23194 | ||||||||
\(82\) | −0.520505 | −0.0574802 | ||||||||
\(83\) | −10.8272 | −1.18844 | −0.594218 | − | 0.804304i | \(-0.702538\pi\) | ||||
−0.594218 | + | 0.804304i | \(0.702538\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.5462 | −1.25236 | ||||||||
\(86\) | −6.06668 | −0.654187 | ||||||||
\(87\) | 4.54125 | 0.486873 | ||||||||
\(88\) | −6.53035 | −0.696138 | ||||||||
\(89\) | 5.36196 | 0.568367 | 0.284183 | − | 0.958770i | \(-0.408278\pi\) | ||||
0.284183 | + | 0.958770i | \(0.408278\pi\) | |||||||
\(90\) | −4.21432 | −0.444228 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.00492 | 0.521799 | ||||||||
\(93\) | 12.9240 | 1.34015 | ||||||||
\(94\) | −1.29682 | −0.133757 | ||||||||
\(95\) | −27.4701 | −2.81838 | ||||||||
\(96\) | −12.8573 | −1.31224 | ||||||||
\(97\) | 9.62867 | 0.977643 | 0.488822 | − | 0.872384i | \(-0.337427\pi\) | ||||
0.488822 | + | 0.872384i | \(0.337427\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.11753 | −0.514331 | ||||||||
\(100\) | −8.13335 | −0.813335 | ||||||||
\(101\) | −13.6938 | −1.36259 | −0.681293 | − | 0.732011i | \(-0.738582\pi\) | ||||
−0.681293 | + | 0.732011i | \(0.738582\pi\) | |||||||
\(102\) | 5.47949 | 0.542551 | ||||||||
\(103\) | −12.2953 | −1.21149 | −0.605745 | − | 0.795659i | \(-0.707125\pi\) | ||||
−0.605745 | + | 0.795659i | \(0.707125\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.73975 | −0.168979 | ||||||||
\(107\) | −18.1891 | −1.75841 | −0.879205 | − | 0.476444i | \(-0.841925\pi\) | ||||
−0.879205 | + | 0.476444i | \(0.841925\pi\) | |||||||
\(108\) | 3.70471 | 0.356486 | ||||||||
\(109\) | −8.36196 | −0.800931 | −0.400465 | − | 0.916312i | \(-0.631152\pi\) | ||||
−0.400465 | + | 0.916312i | \(0.631152\pi\) | |||||||
\(110\) | 5.95407 | 0.567698 | ||||||||
\(111\) | −8.70964 | −0.826682 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.46520 | −0.796339 | −0.398170 | − | 0.917312i | \(-0.630354\pi\) | ||||
−0.398170 | + | 0.917312i | \(0.630354\pi\) | |||||||
\(114\) | 13.0366 | 1.22099 | ||||||||
\(115\) | −10.5462 | −0.983436 | ||||||||
\(116\) | −3.12843 | −0.290468 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.05086 | −0.464969 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 17.2859 | 1.57798 | ||||||||
\(121\) | −3.76986 | −0.342714 | ||||||||
\(122\) | 6.23506 | 0.564496 | ||||||||
\(123\) | 1.67307 | 0.150856 | ||||||||
\(124\) | −8.90321 | −0.799532 | ||||||||
\(125\) | 1.06668 | 0.0954065 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.08742 | 0.362700 | 0.181350 | − | 0.983419i | \(-0.441953\pi\) | ||||
0.181350 | + | 0.983419i | \(0.441953\pi\) | |||||||
\(128\) | 10.7556 | 0.950667 | ||||||||
\(129\) | 19.5002 | 1.71690 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.93978 | −0.518961 | −0.259480 | − | 0.965748i | \(-0.583551\pi\) | ||||
−0.259480 | + | 0.965748i | \(0.583551\pi\) | |||||||
\(132\) | 9.08250 | 0.790530 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.295286 | 0.0255089 | ||||||||
\(135\) | −7.80642 | −0.671870 | ||||||||
\(136\) | −8.72393 | −0.748070 | ||||||||
\(137\) | −16.3620 | −1.39790 | −0.698948 | − | 0.715172i | \(-0.746348\pi\) | ||||
−0.698948 | + | 0.715172i | \(0.746348\pi\) | |||||||
\(138\) | 5.00492 | 0.426047 | ||||||||
\(139\) | −3.03011 | −0.257011 | −0.128505 | − | 0.991709i | \(-0.541018\pi\) | ||||
−0.128505 | + | 0.991709i | \(0.541018\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.16839 | 0.351041 | ||||||||
\(142\) | 6.18913 | 0.519380 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.62222 | 0.218518 | ||||||||
\(145\) | 6.59210 | 0.547444 | ||||||||
\(146\) | −3.98910 | −0.330140 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | 0.493197 | ||||||||
\(149\) | 14.5368 | 1.19090 | 0.595451 | − | 0.803392i | \(-0.296974\pi\) | ||||
0.595451 | + | 0.803392i | \(0.296974\pi\) | |||||||
\(150\) | −8.13335 | −0.664085 | ||||||||
\(151\) | 19.9748 | 1.62553 | 0.812764 | − | 0.582594i | \(-0.197962\pi\) | ||||
0.812764 | + | 0.582594i | \(0.197962\pi\) | |||||||
\(152\) | −20.7556 | −1.68350 | ||||||||
\(153\) | −6.83654 | −0.552701 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.7605 | 1.50688 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.39853 | −0.590467 | −0.295233 | − | 0.955425i | \(-0.595397\pi\) | ||||
−0.295233 | + | 0.955425i | \(0.595397\pi\) | |||||||
\(158\) | 3.08589 | 0.245500 | ||||||||
\(159\) | 5.59210 | 0.443483 | ||||||||
\(160\) | −18.6637 | −1.47550 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.63804 | 0.600101 | ||||||||
\(163\) | −2.32693 | −0.182259 | −0.0911296 | − | 0.995839i | \(-0.529048\pi\) | ||||
−0.0911296 | + | 0.995839i | \(0.529048\pi\) | |||||||
\(164\) | −1.15257 | −0.0900002 | ||||||||
\(165\) | −19.1383 | −1.48991 | ||||||||
\(166\) | 7.45875 | 0.578911 | ||||||||
\(167\) | −3.42219 | −0.264817 | −0.132408 | − | 0.991195i | \(-0.542271\pi\) | ||||
−0.132408 | + | 0.991195i | \(0.542271\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 7.95407 | 0.610049 | ||||||||
\(171\) | −16.2652 | −1.24383 | ||||||||
\(172\) | −13.4336 | −1.02430 | ||||||||
\(173\) | −8.27454 | −0.629102 | −0.314551 | − | 0.949241i | \(-0.601854\pi\) | ||||
−0.314551 | + | 0.949241i | \(0.601854\pi\) | |||||||
\(174\) | −3.12843 | −0.237166 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.70471 | −0.279253 | ||||||||
\(177\) | 16.2351 | 1.22030 | ||||||||
\(178\) | −3.69381 | −0.276863 | ||||||||
\(179\) | −16.2257 | −1.21277 | −0.606383 | − | 0.795173i | \(-0.707380\pi\) | ||||
−0.606383 | + | 0.795173i | \(0.707380\pi\) | |||||||
\(180\) | −9.33185 | −0.695555 | ||||||||
\(181\) | 9.20495 | 0.684199 | 0.342099 | − | 0.939664i | \(-0.388862\pi\) | ||||
0.342099 | + | 0.939664i | \(0.388862\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.0415 | −1.48151 | ||||||||
\(184\) | −7.96836 | −0.587435 | ||||||||
\(185\) | −12.6430 | −0.929529 | ||||||||
\(186\) | −8.90321 | −0.652815 | ||||||||
\(187\) | 9.65878 | 0.706320 | ||||||||
\(188\) | −2.87157 | −0.209431 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.9240 | 1.37289 | ||||||||
\(191\) | −6.66815 | −0.482490 | −0.241245 | − | 0.970464i | \(-0.577556\pi\) | ||||
−0.241245 | + | 0.970464i | \(0.577556\pi\) | |||||||
\(192\) | 2.75557 | 0.198866 | ||||||||
\(193\) | −20.6035 | −1.48307 | −0.741535 | − | 0.670914i | \(-0.765902\pi\) | ||||
−0.741535 | + | 0.670914i | \(0.765902\pi\) | |||||||
\(194\) | −6.63311 | −0.476230 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.36842 | 0.596225 | 0.298112 | − | 0.954531i | \(-0.403643\pi\) | ||||
0.298112 | + | 0.954531i | \(0.403643\pi\) | |||||||
\(198\) | 3.52543 | 0.250541 | ||||||||
\(199\) | 0.601472 | 0.0426372 | 0.0213186 | − | 0.999773i | \(-0.493214\pi\) | ||||
0.0213186 | + | 0.999773i | \(0.493214\pi\) | |||||||
\(200\) | 12.9491 | 0.915643 | ||||||||
\(201\) | −0.949145 | −0.0669475 | ||||||||
\(202\) | 9.43356 | 0.663743 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 12.1334 | 0.849505 | ||||||||
\(205\) | 2.42864 | 0.169624 | ||||||||
\(206\) | 8.47013 | 0.590142 | ||||||||
\(207\) | −6.24443 | −0.434018 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.9797 | 1.58954 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.90321 | −0.131023 | −0.0655113 | − | 0.997852i | \(-0.520868\pi\) | ||||
−0.0655113 | + | 0.997852i | \(0.520868\pi\) | |||||||
\(212\) | −3.85236 | −0.264581 | ||||||||
\(213\) | −19.8938 | −1.36310 | ||||||||
\(214\) | 12.5303 | 0.856557 | ||||||||
\(215\) | 28.3067 | 1.93050 | ||||||||
\(216\) | −5.89829 | −0.401328 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.76049 | 0.390150 | ||||||||
\(219\) | 12.8222 | 0.866447 | ||||||||
\(220\) | 13.1842 | 0.888879 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 6.00000 | 0.402694 | ||||||||
\(223\) | 10.6336 | 0.712078 | 0.356039 | − | 0.934471i | \(-0.384127\pi\) | ||||
0.356039 | + | 0.934471i | \(0.384127\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.1476 | 0.676510 | ||||||||
\(226\) | 5.83161 | 0.387913 | ||||||||
\(227\) | 15.0509 | 0.998960 | 0.499480 | − | 0.866325i | \(-0.333524\pi\) | ||||
0.499480 | + | 0.866325i | \(0.333524\pi\) | |||||||
\(228\) | 28.8671 | 1.91177 | ||||||||
\(229\) | −6.53480 | −0.431831 | −0.215916 | − | 0.976412i | \(-0.569274\pi\) | ||||
−0.215916 | + | 0.976412i | \(0.569274\pi\) | |||||||
\(230\) | 7.26517 | 0.479051 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.98079 | 0.327005 | ||||||||
\(233\) | −27.9590 | −1.83165 | −0.915827 | − | 0.401573i | \(-0.868464\pi\) | ||||
−0.915827 | + | 0.401573i | \(0.868464\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.05086 | 0.394714 | ||||||||
\(236\) | −11.1842 | −0.728030 | ||||||||
\(237\) | −9.91903 | −0.644310 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.5812 | 1.26660 | 0.633301 | − | 0.773905i | \(-0.281699\pi\) | ||||
0.633301 | + | 0.773905i | \(0.281699\pi\) | |||||||
\(240\) | 9.80642 | 0.633002 | ||||||||
\(241\) | −13.3575 | −0.860433 | −0.430217 | − | 0.902726i | \(-0.641563\pi\) | ||||
−0.430217 | + | 0.902726i | \(0.641563\pi\) | |||||||
\(242\) | 2.59703 | 0.166943 | ||||||||
\(243\) | −17.2652 | −1.10756 | ||||||||
\(244\) | 13.8064 | 0.883866 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.15257 | −0.0734849 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 14.1748 | 0.900103 | ||||||||
\(249\) | −23.9748 | −1.51934 | ||||||||
\(250\) | −0.734825 | −0.0464744 | ||||||||
\(251\) | −3.29682 | −0.208093 | −0.104047 | − | 0.994572i | \(-0.533179\pi\) | ||||
−0.104047 | + | 0.994572i | \(0.533179\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.82225 | 0.554650 | ||||||||
\(254\) | −2.81579 | −0.176678 | ||||||||
\(255\) | −25.5669 | −1.60106 | ||||||||
\(256\) | −9.89829 | −0.618643 | ||||||||
\(257\) | 23.6938 | 1.47798 | 0.738990 | − | 0.673717i | \(-0.235303\pi\) | ||||
0.738990 | + | 0.673717i | \(0.235303\pi\) | |||||||
\(258\) | −13.4336 | −0.836337 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.90321 | 0.241603 | ||||||||
\(262\) | 4.09187 | 0.252796 | ||||||||
\(263\) | 9.99063 | 0.616049 | 0.308024 | − | 0.951378i | \(-0.400332\pi\) | ||||
0.308024 | + | 0.951378i | \(0.400332\pi\) | |||||||
\(264\) | −14.4603 | −0.889969 | ||||||||
\(265\) | 8.11753 | 0.498656 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.8731 | 0.726622 | ||||||||
\(268\) | 0.653858 | 0.0399408 | ||||||||
\(269\) | 18.2034 | 1.10988 | 0.554941 | − | 0.831890i | \(-0.312741\pi\) | ||||
0.554941 | + | 0.831890i | \(0.312741\pi\) | |||||||
\(270\) | 5.37778 | 0.327282 | ||||||||
\(271\) | −24.1748 | −1.46852 | −0.734258 | − | 0.678870i | \(-0.762470\pi\) | ||||
−0.734258 | + | 0.678870i | \(0.762470\pi\) | |||||||
\(272\) | −4.94914 | −0.300086 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.2716 | 0.680944 | ||||||||
\(275\) | −14.3368 | −0.864540 | ||||||||
\(276\) | 11.0825 | 0.667088 | ||||||||
\(277\) | 1.69535 | 0.101863 | 0.0509317 | − | 0.998702i | \(-0.483781\pi\) | ||||
0.0509317 | + | 0.998702i | \(0.483781\pi\) | |||||||
\(278\) | 2.08742 | 0.125195 | ||||||||
\(279\) | 11.1082 | 0.665028 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.6479 | −0.694854 | −0.347427 | − | 0.937707i | \(-0.612945\pi\) | ||||
−0.347427 | + | 0.937707i | \(0.612945\pi\) | |||||||
\(282\) | −2.87157 | −0.170999 | ||||||||
\(283\) | −12.1334 | −0.721253 | −0.360626 | − | 0.932710i | \(-0.617437\pi\) | ||||
−0.360626 | + | 0.932710i | \(0.617437\pi\) | |||||||
\(284\) | 13.7047 | 0.813225 | ||||||||
\(285\) | −60.8276 | −3.60312 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −11.0509 | −0.651178 | ||||||||
\(289\) | −4.09679 | −0.240988 | ||||||||
\(290\) | −4.54125 | −0.266671 | ||||||||
\(291\) | 21.3210 | 1.24986 | ||||||||
\(292\) | −8.83314 | −0.516921 | ||||||||
\(293\) | 11.4538 | 0.669140 | 0.334570 | − | 0.942371i | \(-0.391409\pi\) | ||||
0.334570 | + | 0.942371i | \(0.391409\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.5669 | 1.37212 | ||||||||
\(296\) | −9.55262 | −0.555235 | ||||||||
\(297\) | 6.53035 | 0.378929 | ||||||||
\(298\) | −10.0143 | −0.580112 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −18.0098 | −1.03980 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.7605 | −0.791827 | ||||||||
\(303\) | −30.3225 | −1.74198 | ||||||||
\(304\) | −11.7748 | −0.675330 | ||||||||
\(305\) | −29.0923 | −1.66582 | ||||||||
\(306\) | 4.70964 | 0.269232 | ||||||||
\(307\) | 3.96989 | 0.226574 | 0.113287 | − | 0.993562i | \(-0.463862\pi\) | ||||
0.113287 | + | 0.993562i | \(0.463862\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.2257 | −1.54882 | ||||||||
\(310\) | −12.9240 | −0.734031 | ||||||||
\(311\) | −27.3481 | −1.55077 | −0.775386 | − | 0.631488i | \(-0.782444\pi\) | ||||
−0.775386 | + | 0.631488i | \(0.782444\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.1032 | 1.07978 | 0.539890 | − | 0.841736i | \(-0.318466\pi\) | ||||
0.539890 | + | 0.841736i | \(0.318466\pi\) | |||||||
\(314\) | 5.09679 | 0.287628 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.83314 | 0.384394 | ||||||||
\(317\) | −9.90813 | −0.556496 | −0.278248 | − | 0.960509i | \(-0.589754\pi\) | ||||
−0.278248 | + | 0.960509i | \(0.589754\pi\) | |||||||
\(318\) | −3.85236 | −0.216029 | ||||||||
\(319\) | −5.51453 | −0.308754 | ||||||||
\(320\) | 4.00000 | 0.223607 | ||||||||
\(321\) | −40.2766 | −2.24802 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.6987 | 1.70812 | ||||||||
\(324\) | 16.9131 | 0.939614 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.60300 | 0.0887821 | ||||||||
\(327\) | −18.5161 | −1.02394 | ||||||||
\(328\) | 1.83500 | 0.101321 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 13.1842 | 0.725767 | ||||||||
\(331\) | −23.4193 | −1.28724 | −0.643620 | − | 0.765345i | \(-0.722568\pi\) | ||||
−0.643620 | + | 0.765345i | \(0.722568\pi\) | |||||||
\(332\) | 16.5161 | 0.906437 | ||||||||
\(333\) | −7.48595 | −0.410227 | ||||||||
\(334\) | 2.35752 | 0.128998 | ||||||||
\(335\) | −1.37778 | −0.0752764 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.51606 | −0.409426 | −0.204713 | − | 0.978822i | \(-0.565626\pi\) | ||||
−0.204713 | + | 0.978822i | \(0.565626\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.7447 | −1.01807 | ||||||||
\(340\) | 17.6128 | 0.955191 | ||||||||
\(341\) | −15.6938 | −0.849868 | ||||||||
\(342\) | 11.2050 | 0.605894 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 21.3876 | 1.15314 | ||||||||
\(345\) | −23.3526 | −1.25726 | ||||||||
\(346\) | 5.70027 | 0.306448 | ||||||||
\(347\) | 5.64449 | 0.303012 | 0.151506 | − | 0.988456i | \(-0.451588\pi\) | ||||
0.151506 | + | 0.988456i | \(0.451588\pi\) | |||||||
\(348\) | −6.92735 | −0.371345 | ||||||||
\(349\) | 24.1590 | 1.29320 | 0.646601 | − | 0.762828i | \(-0.276190\pi\) | ||||
0.646601 | + | 0.762828i | \(0.276190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.6128 | 0.832168 | ||||||||
\(353\) | 36.1289 | 1.92295 | 0.961474 | − | 0.274896i | \(-0.0886436\pi\) | ||||
0.961474 | + | 0.274896i | \(0.0886436\pi\) | |||||||
\(354\) | −11.1842 | −0.594434 | ||||||||
\(355\) | −28.8780 | −1.53269 | ||||||||
\(356\) | −8.17929 | −0.433501 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.1778 | 0.590763 | ||||||||
\(359\) | −17.4128 | −0.919013 | −0.459507 | − | 0.888174i | \(-0.651974\pi\) | ||||
−0.459507 | + | 0.888174i | \(0.651974\pi\) | |||||||
\(360\) | 14.8573 | 0.783047 | ||||||||
\(361\) | 54.0370 | 2.84405 | ||||||||
\(362\) | −6.34122 | −0.333287 | ||||||||
\(363\) | −8.34767 | −0.438139 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.6128 | 0.974241 | ||||||||
\(366\) | 13.8064 | 0.721673 | ||||||||
\(367\) | −2.93825 | −0.153375 | −0.0766876 | − | 0.997055i | \(-0.524434\pi\) | ||||
−0.0766876 | + | 0.997055i | \(0.524434\pi\) | |||||||
\(368\) | −4.52051 | −0.235648 | ||||||||
\(369\) | 1.43801 | 0.0748597 | ||||||||
\(370\) | 8.70964 | 0.452792 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −19.7146 | −1.02215 | ||||||||
\(373\) | −18.7699 | −0.971866 | −0.485933 | − | 0.873996i | \(-0.661520\pi\) | ||||
−0.485933 | + | 0.873996i | \(0.661520\pi\) | |||||||
\(374\) | −6.65386 | −0.344063 | ||||||||
\(375\) | 2.36196 | 0.121971 | ||||||||
\(376\) | 4.57184 | 0.235774 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.6894 | −1.21684 | −0.608421 | − | 0.793615i | \(-0.708197\pi\) | ||||
−0.608421 | + | 0.793615i | \(0.708197\pi\) | |||||||
\(380\) | 41.9037 | 2.14961 | ||||||||
\(381\) | 9.05086 | 0.463689 | ||||||||
\(382\) | 4.59364 | 0.235031 | ||||||||
\(383\) | 31.6128 | 1.61534 | 0.807671 | − | 0.589634i | \(-0.200728\pi\) | ||||
0.807671 | + | 0.589634i | \(0.200728\pi\) | |||||||
\(384\) | 23.8163 | 1.21537 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.1936 | 0.722434 | ||||||||
\(387\) | 16.7605 | 0.851984 | ||||||||
\(388\) | −14.6878 | −0.745662 | ||||||||
\(389\) | −20.0558 | −1.01687 | −0.508434 | − | 0.861101i | \(-0.669775\pi\) | ||||
−0.508434 | + | 0.861101i | \(0.669775\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.7857 | 0.596027 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.1526 | −0.663459 | ||||||||
\(394\) | −5.76494 | −0.290433 | ||||||||
\(395\) | −14.3985 | −0.724469 | ||||||||
\(396\) | 7.80642 | 0.392288 | ||||||||
\(397\) | 22.8731 | 1.14797 | 0.573984 | − | 0.818867i | \(-0.305397\pi\) | ||||
0.573984 | + | 0.818867i | \(0.305397\pi\) | |||||||
\(398\) | −0.414349 | −0.0207695 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.34614 | 0.367307 | ||||||||
\(401\) | 5.61285 | 0.280292 | 0.140146 | − | 0.990131i | \(-0.455243\pi\) | ||||
0.140146 | + | 0.990131i | \(0.455243\pi\) | |||||||
\(402\) | 0.653858 | 0.0326115 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 20.8889 | 1.03926 | ||||||||
\(405\) | −35.6385 | −1.77089 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.5763 | 0.524247 | ||||||||
\(408\) | −19.3176 | −0.956362 | ||||||||
\(409\) | −26.1175 | −1.29143 | −0.645714 | − | 0.763579i | \(-0.723440\pi\) | ||||
−0.645714 | + | 0.763579i | \(0.723440\pi\) | |||||||
\(410\) | −1.67307 | −0.0826271 | ||||||||
\(411\) | −36.2306 | −1.78712 | ||||||||
\(412\) | 18.7556 | 0.924021 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.30174 | 0.211419 | ||||||||
\(415\) | −34.8020 | −1.70836 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.70964 | −0.328572 | ||||||||
\(418\) | −15.8306 | −0.774298 | ||||||||
\(419\) | 25.2464 | 1.23337 | 0.616685 | − | 0.787210i | \(-0.288475\pi\) | ||||
0.616685 | + | 0.787210i | \(0.288475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.22861 | 0.401038 | 0.200519 | − | 0.979690i | \(-0.435737\pi\) | ||||
0.200519 | + | 0.979690i | \(0.435737\pi\) | |||||||
\(422\) | 1.31111 | 0.0638237 | ||||||||
\(423\) | 3.58274 | 0.174199 | ||||||||
\(424\) | 6.13335 | 0.297862 | ||||||||
\(425\) | −19.1526 | −0.929036 | ||||||||
\(426\) | 13.7047 | 0.663996 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 27.7462 | 1.34116 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −19.5002 | −0.940385 | ||||||||
\(431\) | 1.43801 | 0.0692664 | 0.0346332 | − | 0.999400i | \(-0.488974\pi\) | ||||
0.0346332 | + | 0.999400i | \(0.488974\pi\) | |||||||
\(432\) | −3.34614 | −0.160991 | ||||||||
\(433\) | 16.5018 | 0.793024 | 0.396512 | − | 0.918029i | \(-0.370220\pi\) | ||||
0.396512 | + | 0.918029i | \(0.370220\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.5970 | 0.699874 | ||||||||
\(436\) | 12.7556 | 0.610881 | ||||||||
\(437\) | 28.0400 | 1.34133 | ||||||||
\(438\) | −8.83314 | −0.422064 | ||||||||
\(439\) | 10.1619 | 0.485003 | 0.242501 | − | 0.970151i | \(-0.422032\pi\) | ||||
0.242501 | + | 0.970151i | \(0.422032\pi\) | |||||||
\(440\) | −20.9906 | −1.00069 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.20787 | 0.152410 | 0.0762052 | − | 0.997092i | \(-0.475720\pi\) | ||||
0.0762052 | + | 0.997092i | \(0.475720\pi\) | |||||||
\(444\) | 13.2859 | 0.630522 | ||||||||
\(445\) | 17.2351 | 0.817020 | ||||||||
\(446\) | −7.32540 | −0.346868 | ||||||||
\(447\) | 32.1891 | 1.52249 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.4099 | 0.868817 | 0.434409 | − | 0.900716i | \(-0.356957\pi\) | ||||
0.434409 | + | 0.900716i | \(0.356957\pi\) | |||||||
\(450\) | −6.99063 | −0.329542 | ||||||||
\(451\) | −2.03164 | −0.0956663 | ||||||||
\(452\) | 12.9131 | 0.607379 | ||||||||
\(453\) | 44.2306 | 2.07814 | ||||||||
\(454\) | −10.3684 | −0.486614 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −45.9595 | −2.15225 | ||||||||
\(457\) | −3.40297 | −0.159184 | −0.0795922 | − | 0.996828i | \(-0.525362\pi\) | ||||
−0.0795922 | + | 0.996828i | \(0.525362\pi\) | |||||||
\(458\) | 4.50177 | 0.210354 | ||||||||
\(459\) | 8.72393 | 0.407198 | ||||||||
\(460\) | 16.0874 | 0.750080 | ||||||||
\(461\) | 17.5714 | 0.818380 | 0.409190 | − | 0.912449i | \(-0.365811\pi\) | ||||
0.409190 | + | 0.912449i | \(0.365811\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.7714 | −0.732959 | −0.366479 | − | 0.930426i | \(-0.619437\pi\) | ||||
−0.366479 | + | 0.930426i | \(0.619437\pi\) | |||||||
\(464\) | 2.82564 | 0.131177 | ||||||||
\(465\) | 41.5417 | 1.92645 | ||||||||
\(466\) | 19.2607 | 0.892236 | ||||||||
\(467\) | 3.76694 | 0.174313 | 0.0871567 | − | 0.996195i | \(-0.472222\pi\) | ||||
0.0871567 | + | 0.996195i | \(0.472222\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.16839 | −0.192273 | ||||||||
\(471\) | −16.3827 | −0.754875 | ||||||||
\(472\) | 17.8064 | 0.819607 | ||||||||
\(473\) | −23.6795 | −1.08879 | ||||||||
\(474\) | 6.83314 | 0.313857 | ||||||||
\(475\) | −45.5669 | −2.09075 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.80642 | 0.220071 | ||||||||
\(478\) | −13.4893 | −0.616988 | ||||||||
\(479\) | −12.1032 | −0.553011 | −0.276506 | − | 0.961012i | \(-0.589176\pi\) | ||||
−0.276506 | + | 0.961012i | \(0.589176\pi\) | |||||||
\(480\) | −41.3274 | −1.88633 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 9.20189 | 0.419135 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.75065 | 0.261393 | ||||||||
\(485\) | 30.9496 | 1.40535 | ||||||||
\(486\) | 11.8938 | 0.539516 | ||||||||
\(487\) | 17.3778 | 0.787463 | 0.393731 | − | 0.919226i | \(-0.371184\pi\) | ||||
0.393731 | + | 0.919226i | \(0.371184\pi\) | |||||||
\(488\) | −21.9813 | −0.995045 | ||||||||
\(489\) | −5.15257 | −0.233007 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.3921 | −0.875152 | −0.437576 | − | 0.899181i | \(-0.644163\pi\) | ||||
−0.437576 | + | 0.899181i | \(0.644163\pi\) | |||||||
\(492\) | −2.55215 | −0.115060 | ||||||||
\(493\) | −7.36689 | −0.331788 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.4494 | −0.739345 | ||||||||
\(496\) | 8.04149 | 0.361073 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 16.5161 | 0.740102 | ||||||||
\(499\) | 10.6702 | 0.477662 | 0.238831 | − | 0.971061i | \(-0.423236\pi\) | ||||
0.238831 | + | 0.971061i | \(0.423236\pi\) | |||||||
\(500\) | −1.62714 | −0.0727678 | ||||||||
\(501\) | −7.57781 | −0.338552 | ||||||||
\(502\) | 2.27115 | 0.101366 | ||||||||
\(503\) | 4.27655 | 0.190682 | 0.0953410 | − | 0.995445i | \(-0.469606\pi\) | ||||
0.0953410 | + | 0.995445i | \(0.469606\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −44.0163 | −1.95870 | ||||||||
\(506\) | −6.07758 | −0.270181 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.23506 | −0.276636 | ||||||||
\(509\) | 33.0765 | 1.46609 | 0.733046 | − | 0.680180i | \(-0.238098\pi\) | ||||
0.733046 | + | 0.680180i | \(0.238098\pi\) | |||||||
\(510\) | 17.6128 | 0.779910 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −14.6923 | −0.649313 | ||||||||
\(513\) | 20.7556 | 0.916381 | ||||||||
\(514\) | −16.3225 | −0.719954 | ||||||||
\(515\) | −39.5210 | −1.74150 | ||||||||
\(516\) | −29.7462 | −1.30950 | ||||||||
\(517\) | −5.06175 | −0.222616 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.3225 | −0.804268 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.3783 | −1.06803 | −0.534015 | − | 0.845475i | \(-0.679318\pi\) | ||||
−0.534015 | + | 0.845475i | \(0.679318\pi\) | |||||||
\(522\) | −2.68889 | −0.117690 | ||||||||
\(523\) | −34.9403 | −1.52783 | −0.763915 | − | 0.645317i | \(-0.776725\pi\) | ||||
−0.763915 | + | 0.645317i | \(0.776725\pi\) | |||||||
\(524\) | 9.06070 | 0.395818 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.88247 | −0.300090 | ||||||||
\(527\) | −20.9654 | −0.913269 | ||||||||
\(528\) | −8.20342 | −0.357008 | ||||||||
\(529\) | −12.2351 | −0.531959 | ||||||||
\(530\) | −5.59210 | −0.242905 | ||||||||
\(531\) | 13.9541 | 0.605555 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8.17929 | −0.353952 | ||||||||
\(535\) | −58.4657 | −2.52769 | ||||||||
\(536\) | −1.04101 | −0.0449648 | ||||||||
\(537\) | −35.9289 | −1.55045 | ||||||||
\(538\) | −12.5402 | −0.540646 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 11.9081 | 0.512445 | ||||||||
\(541\) | 30.4953 | 1.31110 | 0.655548 | − | 0.755153i | \(-0.272438\pi\) | ||||
0.655548 | + | 0.755153i | \(0.272438\pi\) | |||||||
\(542\) | 16.6539 | 0.715344 | ||||||||
\(543\) | 20.3827 | 0.874706 | ||||||||
\(544\) | 20.8573 | 0.894248 | ||||||||
\(545\) | −26.8780 | −1.15133 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.0049 | −0.427780 | −0.213890 | − | 0.976858i | \(-0.568613\pi\) | ||||
−0.213890 | + | 0.976858i | \(0.568613\pi\) | |||||||
\(548\) | 24.9590 | 1.06620 | ||||||||
\(549\) | −17.2257 | −0.735175 | ||||||||
\(550\) | 9.87649 | 0.421135 | ||||||||
\(551\) | −17.5270 | −0.746674 | ||||||||
\(552\) | −17.6445 | −0.750999 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.16791 | −0.0496198 | ||||||||
\(555\) | −27.9956 | −1.18835 | ||||||||
\(556\) | 4.62222 | 0.196026 | ||||||||
\(557\) | −14.1936 | −0.601401 | −0.300701 | − | 0.953719i | \(-0.597220\pi\) | ||||
−0.300701 | + | 0.953719i | \(0.597220\pi\) | |||||||
\(558\) | −7.65233 | −0.323949 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.3876 | 0.902986 | ||||||||
\(562\) | 8.02413 | 0.338478 | ||||||||
\(563\) | 21.3590 | 0.900177 | 0.450088 | − | 0.892984i | \(-0.351393\pi\) | ||||
0.450088 | + | 0.892984i | \(0.351393\pi\) | |||||||
\(564\) | −6.35857 | −0.267744 | ||||||||
\(565\) | −27.2099 | −1.14473 | ||||||||
\(566\) | 8.35857 | 0.351337 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.8193 | −0.915519 | ||||||||
\(569\) | 34.2672 | 1.43656 | 0.718278 | − | 0.695757i | \(-0.244931\pi\) | ||||
0.718278 | + | 0.695757i | \(0.244931\pi\) | |||||||
\(570\) | 41.9037 | 1.75515 | ||||||||
\(571\) | −37.6494 | −1.57558 | −0.787789 | − | 0.615945i | \(-0.788774\pi\) | ||||
−0.787789 | + | 0.615945i | \(0.788774\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.7654 | −0.616834 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.4938 | −0.729541 | ||||||||
\(576\) | 2.36842 | 0.0986840 | ||||||||
\(577\) | 28.3970 | 1.18218 | 0.591091 | − | 0.806605i | \(-0.298697\pi\) | ||||
0.591091 | + | 0.806605i | \(0.298697\pi\) | |||||||
\(578\) | 2.82225 | 0.117390 | ||||||||
\(579\) | −45.6227 | −1.89601 | ||||||||
\(580\) | −10.0558 | −0.417543 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −14.6878 | −0.608830 | ||||||||
\(583\) | −6.79060 | −0.281238 | ||||||||
\(584\) | 14.0633 | 0.581943 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.89045 | −0.325952 | ||||||||
\(587\) | −6.23659 | −0.257412 | −0.128706 | − | 0.991683i | \(-0.541082\pi\) | ||||
−0.128706 | + | 0.991683i | \(0.541082\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.8800 | −2.05527 | ||||||||
\(590\) | −16.2351 | −0.668387 | ||||||||
\(591\) | 18.5303 | 0.762237 | ||||||||
\(592\) | −5.41927 | −0.222731 | ||||||||
\(593\) | 17.5698 | 0.721506 | 0.360753 | − | 0.932661i | \(-0.382520\pi\) | ||||
0.360753 | + | 0.932661i | \(0.382520\pi\) | |||||||
\(594\) | −4.49871 | −0.184584 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.1748 | −0.908317 | ||||||||
\(597\) | 1.33185 | 0.0545090 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.9813 | 0.693836 | 0.346918 | − | 0.937896i | \(-0.387228\pi\) | ||||
0.346918 | + | 0.937896i | \(0.387228\pi\) | |||||||
\(600\) | 28.6735 | 1.17059 | ||||||||
\(601\) | 18.7052 | 0.763001 | 0.381500 | − | 0.924369i | \(-0.375408\pi\) | ||||
0.381500 | + | 0.924369i | \(0.375408\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.815792 | −0.0332216 | ||||||||
\(604\) | −30.4701 | −1.23981 | ||||||||
\(605\) | −12.1175 | −0.492648 | ||||||||
\(606\) | 20.8889 | 0.848554 | ||||||||
\(607\) | 10.3575 | 0.420399 | 0.210199 | − | 0.977659i | \(-0.432589\pi\) | ||||
0.210199 | + | 0.977659i | \(0.432589\pi\) | |||||||
\(608\) | 49.6227 | 2.01247 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.0415 | 0.811456 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 10.4286 | 0.421553 | ||||||||
\(613\) | 7.02227 | 0.283627 | 0.141814 | − | 0.989893i | \(-0.454707\pi\) | ||||
0.141814 | + | 0.989893i | \(0.454707\pi\) | |||||||
\(614\) | −2.73483 | −0.110369 | ||||||||
\(615\) | 5.37778 | 0.216853 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.9813 | −1.20700 | −0.603500 | − | 0.797363i | \(-0.706228\pi\) | ||||
−0.603500 | + | 0.797363i | \(0.706228\pi\) | |||||||
\(618\) | 18.7556 | 0.754460 | ||||||||
\(619\) | 0.0285802 | 0.00114874 | 0.000574368 | − | 1.00000i | \(-0.499817\pi\) | ||||
0.000574368 | 1.00000i | \(0.499817\pi\) | ||||||||
\(620\) | −28.6178 | −1.14932 | ||||||||
\(621\) | 7.96836 | 0.319759 | ||||||||
\(622\) | 18.8399 | 0.755412 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.2306 | −0.929225 | ||||||||
\(626\) | −13.1601 | −0.525982 | ||||||||
\(627\) | 50.8845 | 2.03213 | ||||||||
\(628\) | 11.2859 | 0.450357 | ||||||||
\(629\) | 14.1289 | 0.563356 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.1936 | 0.485419 | 0.242709 | − | 0.970099i | \(-0.421964\pi\) | ||||
0.242709 | + | 0.970099i | \(0.421964\pi\) | |||||||
\(632\) | −10.8791 | −0.432746 | ||||||||
\(633\) | −4.21432 | −0.167504 | ||||||||
\(634\) | 6.82564 | 0.271081 | ||||||||
\(635\) | 13.1383 | 0.521377 | ||||||||
\(636\) | −8.53035 | −0.338250 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.79892 | 0.150401 | ||||||||
\(639\) | −17.0988 | −0.676418 | ||||||||
\(640\) | 34.5718 | 1.36657 | ||||||||
\(641\) | −2.82516 | −0.111587 | −0.0557935 | − | 0.998442i | \(-0.517769\pi\) | ||||
−0.0557935 | + | 0.998442i | \(0.517769\pi\) | |||||||
\(642\) | 27.7462 | 1.09506 | ||||||||
\(643\) | −37.7275 | −1.48783 | −0.743913 | − | 0.668276i | \(-0.767032\pi\) | ||||
−0.743913 | + | 0.668276i | \(0.767032\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 62.6800 | 2.46802 | ||||||||
\(646\) | −21.1481 | −0.832062 | ||||||||
\(647\) | −12.3664 | −0.486174 | −0.243087 | − | 0.970005i | \(-0.578160\pi\) | ||||
−0.243087 | + | 0.970005i | \(0.578160\pi\) | |||||||
\(648\) | −26.9273 | −1.05781 | ||||||||
\(649\) | −19.7146 | −0.773864 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.54956 | 0.139012 | ||||||||
\(653\) | −33.0005 | −1.29141 | −0.645704 | − | 0.763588i | \(-0.723436\pi\) | ||||
−0.645704 | + | 0.763588i | \(0.723436\pi\) | |||||||
\(654\) | 12.7556 | 0.498782 | ||||||||
\(655\) | −19.0923 | −0.746000 | ||||||||
\(656\) | 1.04101 | 0.0406446 | ||||||||
\(657\) | 11.0207 | 0.429960 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.8118 | 1.27817 | 0.639084 | − | 0.769137i | \(-0.279314\pi\) | ||||
0.639084 | + | 0.769137i | \(0.279314\pi\) | |||||||
\(660\) | 29.1941 | 1.13638 | ||||||||
\(661\) | −14.7067 | −0.572025 | −0.286013 | − | 0.958226i | \(-0.592330\pi\) | ||||
−0.286013 | + | 0.958226i | \(0.592330\pi\) | |||||||
\(662\) | 16.1334 | 0.627041 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −26.2953 | −1.02046 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.15701 | 0.199830 | ||||||||
\(667\) | −6.72885 | −0.260542 | ||||||||
\(668\) | 5.22030 | 0.201979 | ||||||||
\(669\) | 23.5462 | 0.910348 | ||||||||
\(670\) | 0.949145 | 0.0366687 | ||||||||
\(671\) | 24.3368 | 0.939511 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.2908 | 0.820702 | 0.410351 | − | 0.911928i | \(-0.365406\pi\) | ||||
0.410351 | + | 0.911928i | \(0.365406\pi\) | |||||||
\(674\) | 5.17775 | 0.199440 | ||||||||
\(675\) | −12.9491 | −0.498413 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.07160 | 0.118051 | 0.0590256 | − | 0.998256i | \(-0.481201\pi\) | ||||
0.0590256 | + | 0.998256i | \(0.481201\pi\) | |||||||
\(678\) | 12.9131 | 0.495923 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −28.0415 | −1.07534 | ||||||||
\(681\) | 33.3274 | 1.27711 | ||||||||
\(682\) | 10.8113 | 0.413988 | ||||||||
\(683\) | 24.7971 | 0.948833 | 0.474416 | − | 0.880301i | \(-0.342659\pi\) | ||||
0.474416 | + | 0.880301i | \(0.342659\pi\) | |||||||
\(684\) | 24.8113 | 0.948686 | ||||||||
\(685\) | −52.5926 | −2.00946 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.4701 | −0.552070 | ||||||||
\(688\) | 12.1334 | 0.462580 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 16.0874 | 0.612438 | ||||||||
\(691\) | −27.0953 | −1.03075 | −0.515376 | − | 0.856964i | \(-0.672348\pi\) | ||||
−0.515376 | + | 0.856964i | \(0.672348\pi\) | |||||||
\(692\) | 12.6222 | 0.479825 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.88845 | −0.147603 | ||||||||
\(695\) | −9.73975 | −0.369450 | ||||||||
\(696\) | 11.0291 | 0.418055 | ||||||||
\(697\) | −2.71408 | −0.102803 | ||||||||
\(698\) | −16.6430 | −0.629945 | ||||||||
\(699\) | −61.9101 | −2.34166 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.5205 | 0.510662 | 0.255331 | − | 0.966854i | \(-0.417815\pi\) | ||||
0.255331 | + | 0.966854i | \(0.417815\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.6149 | 1.26781 | ||||||||
\(704\) | −3.34614 | −0.126112 | ||||||||
\(705\) | 13.3985 | 0.504618 | ||||||||
\(706\) | −24.8889 | −0.936707 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −24.7654 | −0.930741 | ||||||||
\(709\) | 50.9753 | 1.91442 | 0.957209 | − | 0.289399i | \(-0.0934554\pi\) | ||||
0.957209 | + | 0.289399i | \(0.0934554\pi\) | |||||||
\(710\) | 19.8938 | 0.746603 | ||||||||
\(711\) | −8.52543 | −0.319729 | ||||||||
\(712\) | 13.0223 | 0.488030 | ||||||||
\(713\) | −19.1497 | −0.717160 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.7511 | 0.924993 | ||||||||
\(717\) | 43.3590 | 1.61927 | ||||||||
\(718\) | 11.9956 | 0.447670 | ||||||||
\(719\) | −41.5417 | −1.54924 | −0.774622 | − | 0.632424i | \(-0.782060\pi\) | ||||
−0.774622 | + | 0.632424i | \(0.782060\pi\) | |||||||
\(720\) | 8.42864 | 0.314117 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −37.2257 | −1.38540 | ||||||||
\(723\) | −29.5778 | −1.10001 | ||||||||
\(724\) | −14.0415 | −0.521848 | ||||||||
\(725\) | 10.9349 | 0.406110 | ||||||||
\(726\) | 5.75065 | 0.213427 | ||||||||
\(727\) | 20.8988 | 0.775092 | 0.387546 | − | 0.921850i | \(-0.373323\pi\) | ||||
0.387546 | + | 0.921850i | \(0.373323\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.96836 | −0.184013 | ||||||||
\(730\) | −12.8222 | −0.474573 | ||||||||
\(731\) | −31.6336 | −1.17001 | ||||||||
\(732\) | 30.5718 | 1.12997 | ||||||||
\(733\) | 19.3575 | 0.714986 | 0.357493 | − | 0.933916i | \(-0.383632\pi\) | ||||
0.357493 | + | 0.933916i | \(0.383632\pi\) | |||||||
\(734\) | 2.02413 | 0.0747122 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.0509 | 0.702224 | ||||||||
\(737\) | 1.15257 | 0.0424553 | ||||||||
\(738\) | −0.990632 | −0.0364657 | ||||||||
\(739\) | 1.31111 | 0.0482299 | 0.0241149 | − | 0.999709i | \(-0.492323\pi\) | ||||
0.0241149 | + | 0.999709i | \(0.492323\pi\) | |||||||
\(740\) | 19.2859 | 0.708964 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.5210 | 0.789528 | 0.394764 | − | 0.918783i | \(-0.370826\pi\) | ||||
0.394764 | + | 0.918783i | \(0.370826\pi\) | |||||||
\(744\) | 31.3876 | 1.15073 | ||||||||
\(745\) | 46.7259 | 1.71191 | ||||||||
\(746\) | 12.9304 | 0.473416 | ||||||||
\(747\) | −20.6064 | −0.753949 | ||||||||
\(748\) | −14.7338 | −0.538720 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.62714 | −0.0594147 | ||||||||
\(751\) | −16.3176 | −0.595436 | −0.297718 | − | 0.954654i | \(-0.596226\pi\) | ||||
−0.297718 | + | 0.954654i | \(0.596226\pi\) | |||||||
\(752\) | 2.59364 | 0.0945802 | ||||||||
\(753\) | −7.30021 | −0.266034 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 64.2054 | 2.33667 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.7462 | −0.681342 | −0.340671 | − | 0.940183i | \(-0.610654\pi\) | ||||
−0.340671 | + | 0.940183i | \(0.610654\pi\) | |||||||
\(758\) | 16.3194 | 0.592748 | ||||||||
\(759\) | 19.5353 | 0.709085 | ||||||||
\(760\) | −66.7150 | −2.42001 | ||||||||
\(761\) | −10.2968 | −0.373259 | −0.186630 | − | 0.982430i | \(-0.559756\pi\) | ||||
−0.186630 | + | 0.982430i | \(0.559756\pi\) | |||||||
\(762\) | −6.23506 | −0.225873 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.1718 | 0.368002 | ||||||||
\(765\) | −21.9748 | −0.794501 | ||||||||
\(766\) | −21.7778 | −0.786865 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −21.9180 | −0.790897 | ||||||||
\(769\) | 9.36641 | 0.337761 | 0.168881 | − | 0.985637i | \(-0.445985\pi\) | ||||
0.168881 | + | 0.985637i | \(0.445985\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 52.4657 | 1.88951 | ||||||||
\(772\) | 31.4291 | 1.13116 | ||||||||
\(773\) | −3.71456 | −0.133603 | −0.0668017 | − | 0.997766i | \(-0.521279\pi\) | ||||
−0.0668017 | + | 0.997766i | \(0.521279\pi\) | |||||||
\(774\) | −11.5462 | −0.415019 | ||||||||
\(775\) | 31.1195 | 1.11785 | ||||||||
\(776\) | 23.3846 | 0.839457 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.8163 | 0.495337 | ||||||||
\(779\) | −6.45722 | −0.231354 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.1575 | 0.864423 | ||||||||
\(782\) | −8.11906 | −0.290337 | ||||||||
\(783\) | −4.98079 | −0.177999 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.7812 | −0.848789 | ||||||||
\(786\) | 9.06070 | 0.323184 | ||||||||
\(787\) | 6.23659 | 0.222311 | 0.111155 | − | 0.993803i | \(-0.464545\pi\) | ||||
0.111155 | + | 0.993803i | \(0.464545\pi\) | |||||||
\(788\) | −12.7654 | −0.454749 | ||||||||
\(789\) | 22.1225 | 0.787580 | ||||||||
\(790\) | 9.91903 | 0.352903 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −12.4286 | −0.441632 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −15.7571 | −0.559199 | ||||||||
\(795\) | 17.9748 | 0.637501 | ||||||||
\(796\) | −0.917502 | −0.0325200 | ||||||||
\(797\) | 40.0701 | 1.41935 | 0.709677 | − | 0.704527i | \(-0.248841\pi\) | ||||
0.709677 | + | 0.704527i | \(0.248841\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.76202 | −0.239223 | ||||||||
\(800\) | −30.9590 | −1.09457 | ||||||||
\(801\) | 10.2050 | 0.360574 | ||||||||
\(802\) | −3.86665 | −0.136536 | ||||||||
\(803\) | −15.5703 | −0.549464 | ||||||||
\(804\) | 1.44785 | 0.0510618 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 40.3082 | 1.41892 | ||||||||
\(808\) | −33.2573 | −1.16999 | ||||||||
\(809\) | −2.57136 | −0.0904042 | −0.0452021 | − | 0.998978i | \(-0.514393\pi\) | ||||
−0.0452021 | + | 0.998978i | \(0.514393\pi\) | |||||||
\(810\) | 24.5511 | 0.862637 | ||||||||
\(811\) | −28.3654 | −0.996042 | −0.498021 | − | 0.867165i | \(-0.665940\pi\) | ||||
−0.498021 | + | 0.867165i | \(0.665940\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −53.5308 | −1.87741 | ||||||||
\(814\) | −7.28592 | −0.255371 | ||||||||
\(815\) | −7.47949 | −0.261995 | ||||||||
\(816\) | −10.9590 | −0.383641 | ||||||||
\(817\) | −75.2612 | −2.63306 | ||||||||
\(818\) | 17.9922 | 0.629081 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.70471 | −0.129374 | ||||||||
\(821\) | 31.7846 | 1.10929 | 0.554646 | − | 0.832087i | \(-0.312854\pi\) | ||||
0.554646 | + | 0.832087i | \(0.312854\pi\) | |||||||
\(822\) | 24.9590 | 0.870545 | ||||||||
\(823\) | 30.9131 | 1.07756 | 0.538781 | − | 0.842446i | \(-0.318885\pi\) | ||||
0.538781 | + | 0.842446i | \(0.318885\pi\) | |||||||
\(824\) | −29.8608 | −1.04025 | ||||||||
\(825\) | −31.7462 | −1.10526 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −49.7560 | −1.73019 | −0.865094 | − | 0.501610i | \(-0.832741\pi\) | ||||
−0.865094 | + | 0.501610i | \(0.832741\pi\) | |||||||
\(828\) | 9.52543 | 0.331031 | ||||||||
\(829\) | 19.9190 | 0.691817 | 0.345908 | − | 0.938268i | \(-0.387571\pi\) | ||||
0.345908 | + | 0.938268i | \(0.387571\pi\) | |||||||
\(830\) | 23.9748 | 0.832178 | ||||||||
\(831\) | 3.75404 | 0.130226 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.62222 | 0.160054 | ||||||||
\(835\) | −11.0000 | −0.380671 | ||||||||
\(836\) | −35.0539 | −1.21237 | ||||||||
\(837\) | −14.1748 | −0.489954 | ||||||||
\(838\) | −17.3921 | −0.600799 | ||||||||
\(839\) | 11.5625 | 0.399181 | 0.199590 | − | 0.979879i | \(-0.436039\pi\) | ||||
0.199590 | + | 0.979879i | \(0.436039\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.7940 | −0.854965 | ||||||||
\(842\) | −5.66862 | −0.195354 | ||||||||
\(843\) | −25.7921 | −0.888328 | ||||||||
\(844\) | 2.90321 | 0.0999327 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.46812 | −0.0848557 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.47949 | 0.119486 | ||||||||
\(849\) | −26.8671 | −0.922077 | ||||||||
\(850\) | 13.1941 | 0.452552 | ||||||||
\(851\) | 12.9052 | 0.442385 | ||||||||
\(852\) | 30.3466 | 1.03966 | ||||||||
\(853\) | 1.74467 | 0.0597363 | 0.0298682 | − | 0.999554i | \(-0.490491\pi\) | ||||
0.0298682 | + | 0.999554i | \(0.490491\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −52.2815 | −1.78799 | ||||||||
\(856\) | −44.1748 | −1.50986 | ||||||||
\(857\) | 42.3368 | 1.44620 | 0.723098 | − | 0.690745i | \(-0.242717\pi\) | ||||
0.723098 | + | 0.690745i | \(0.242717\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.37778 | 0.183488 | 0.0917438 | − | 0.995783i | \(-0.470756\pi\) | ||||
0.0917438 | + | 0.995783i | \(0.470756\pi\) | |||||||
\(860\) | −43.1798 | −1.47242 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.990632 | −0.0337411 | ||||||||
\(863\) | −15.4291 | −0.525213 | −0.262607 | − | 0.964903i | \(-0.584582\pi\) | ||||
−0.262607 | + | 0.964903i | \(0.584582\pi\) | |||||||
\(864\) | 14.1017 | 0.479750 | ||||||||
\(865\) | −26.5970 | −0.904326 | ||||||||
\(866\) | −11.3679 | −0.386298 | ||||||||
\(867\) | −9.07160 | −0.308088 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0449 | 0.408595 | ||||||||
\(870\) | −10.0558 | −0.340923 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −20.3082 | −0.687722 | ||||||||
\(873\) | 18.3254 | 0.620221 | ||||||||
\(874\) | −19.3165 | −0.653391 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −19.5594 | −0.660851 | ||||||||
\(877\) | −38.5181 | −1.30066 | −0.650331 | − | 0.759651i | \(-0.725370\pi\) | ||||
−0.650331 | + | 0.759651i | \(0.725370\pi\) | |||||||
\(878\) | −7.00048 | −0.236255 | ||||||||
\(879\) | 25.3624 | 0.855454 | ||||||||
\(880\) | −11.9081 | −0.401423 | ||||||||
\(881\) | 41.7373 | 1.40617 | 0.703083 | − | 0.711108i | \(-0.251806\pi\) | ||||
0.703083 | + | 0.711108i | \(0.251806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.8439 | 1.77834 | 0.889170 | − | 0.457577i | \(-0.151283\pi\) | ||||
0.889170 | + | 0.457577i | \(0.151283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 52.1847 | 1.75417 | ||||||||
\(886\) | −2.20987 | −0.0742422 | ||||||||
\(887\) | −8.99063 | −0.301876 | −0.150938 | − | 0.988543i | \(-0.548229\pi\) | ||||
−0.150938 | + | 0.988543i | \(0.548229\pi\) | |||||||
\(888\) | −21.1526 | −0.709834 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −11.8731 | −0.397987 | ||||||||
\(891\) | 29.8129 | 0.998769 | ||||||||
\(892\) | −16.2208 | −0.543112 | ||||||||
\(893\) | −16.0879 | −0.538361 | ||||||||
\(894\) | −22.1748 | −0.741638 | ||||||||
\(895\) | −52.1546 | −1.74334 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.6824 | −0.423218 | ||||||||
\(899\) | 11.9699 | 0.399218 | ||||||||
\(900\) | −15.4795 | −0.515983 | ||||||||
\(901\) | −9.07160 | −0.302219 | ||||||||
\(902\) | 1.39958 | 0.0466010 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.5589 | −0.683780 | ||||||||
\(905\) | 29.5877 | 0.983527 | ||||||||
\(906\) | −30.4701 | −1.01230 | ||||||||
\(907\) | −20.7003 | −0.687341 | −0.343671 | − | 0.939090i | \(-0.611670\pi\) | ||||
−0.343671 | + | 0.939090i | \(0.611670\pi\) | |||||||
\(908\) | −22.9590 | −0.761921 | ||||||||
\(909\) | −26.0622 | −0.864430 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.8988 | 0.990590 | 0.495295 | − | 0.868725i | \(-0.335060\pi\) | ||||
0.495295 | + | 0.868725i | \(0.335060\pi\) | |||||||
\(912\) | −26.0731 | −0.863368 | ||||||||
\(913\) | 29.1131 | 0.963503 | ||||||||
\(914\) | 2.34428 | 0.0775420 | ||||||||
\(915\) | −64.4197 | −2.12965 | ||||||||
\(916\) | 9.96836 | 0.329364 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.00984 | −0.198354 | ||||||||
\(919\) | 38.5847 | 1.27279 | 0.636397 | − | 0.771362i | \(-0.280424\pi\) | ||||
0.636397 | + | 0.771362i | \(0.280424\pi\) | |||||||
\(920\) | −25.6128 | −0.844431 | ||||||||
\(921\) | 8.79060 | 0.289660 | ||||||||
\(922\) | −12.1048 | −0.398649 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.9719 | −0.689552 | ||||||||
\(926\) | 10.8648 | 0.357039 | ||||||||
\(927\) | −23.4005 | −0.768574 | ||||||||
\(928\) | −11.9081 | −0.390904 | ||||||||
\(929\) | 3.25581 | 0.106820 | 0.0534098 | − | 0.998573i | \(-0.482991\pi\) | ||||
0.0534098 | + | 0.998573i | \(0.482991\pi\) | |||||||
\(930\) | −28.6178 | −0.938414 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 42.6494 | 1.39703 | ||||||||
\(933\) | −60.5575 | −1.98257 | ||||||||
\(934\) | −2.59502 | −0.0849116 | ||||||||
\(935\) | 31.0464 | 1.01533 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.6840 | 0.381699 | 0.190849 | − | 0.981619i | \(-0.438876\pi\) | ||||
0.190849 | + | 0.981619i | \(0.438876\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.3007 | 1.38043 | ||||||||
\(940\) | −9.23014 | −0.301054 | ||||||||
\(941\) | −41.9699 | −1.36818 | −0.684090 | − | 0.729398i | \(-0.739800\pi\) | ||||
−0.684090 | + | 0.729398i | \(0.739800\pi\) | |||||||
\(942\) | 11.2859 | 0.367715 | ||||||||
\(943\) | −2.47902 | −0.0807279 | ||||||||
\(944\) | 10.1017 | 0.328783 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.3126 | 0.530370 | ||||||||
\(947\) | 20.3555 | 0.661465 | 0.330733 | − | 0.943725i | \(-0.392704\pi\) | ||||
0.330733 | + | 0.943725i | \(0.392704\pi\) | |||||||
\(948\) | 15.1308 | 0.491424 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 31.3907 | 1.01845 | ||||||||
\(951\) | −21.9398 | −0.711446 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.5496 | −0.989597 | −0.494799 | − | 0.869008i | \(-0.664758\pi\) | ||||
−0.494799 | + | 0.869008i | \(0.664758\pi\) | |||||||
\(954\) | −3.31111 | −0.107201 | ||||||||
\(955\) | −21.4336 | −0.693574 | ||||||||
\(956\) | −29.8697 | −0.966055 | ||||||||
\(957\) | −12.2109 | −0.394723 | ||||||||
\(958\) | 8.33783 | 0.269383 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.85728 | 0.285867 | ||||||||
\(961\) | 3.06515 | 0.0988757 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.6178 | −1.11554 | ||||||||
\(964\) | 20.3759 | 0.656264 | ||||||||
\(965\) | −66.2262 | −2.13190 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.4548 | −1.75115 | −0.875574 | − | 0.483084i | \(-0.839516\pi\) | ||||
−0.875574 | + | 0.483084i | \(0.839516\pi\) | |||||||
\(968\) | −9.15563 | −0.294273 | ||||||||
\(969\) | 67.9768 | 2.18373 | ||||||||
\(970\) | −21.3210 | −0.684575 | ||||||||
\(971\) | 54.6035 | 1.75231 | 0.876155 | − | 0.482030i | \(-0.160101\pi\) | ||||
0.876155 | + | 0.482030i | \(0.160101\pi\) | |||||||
\(972\) | 26.3368 | 0.844752 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11.9714 | −0.383589 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.4701 | −0.399159 | ||||||||
\(977\) | −32.6474 | −1.04448 | −0.522242 | − | 0.852798i | \(-0.674904\pi\) | ||||
−0.522242 | + | 0.852798i | \(0.674904\pi\) | |||||||
\(978\) | 3.54956 | 0.113502 | ||||||||
\(979\) | −14.4177 | −0.460793 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.9146 | −0.508114 | ||||||||
\(982\) | 13.3590 | 0.426304 | ||||||||
\(983\) | −27.5052 | −0.877278 | −0.438639 | − | 0.898663i | \(-0.644539\pi\) | ||||
−0.438639 | + | 0.898663i | \(0.644539\pi\) | |||||||
\(984\) | 4.06329 | 0.129533 | ||||||||
\(985\) | 26.8988 | 0.857066 | ||||||||
\(986\) | 5.07499 | 0.161621 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.8938 | −0.918771 | ||||||||
\(990\) | 11.3319 | 0.360150 | ||||||||
\(991\) | −6.29390 | −0.199932 | −0.0999662 | − | 0.994991i | \(-0.531873\pi\) | ||||
−0.0999662 | + | 0.994991i | \(0.531873\pi\) | |||||||
\(992\) | −33.8894 | −1.07599 | ||||||||
\(993\) | −51.8578 | −1.64566 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.93332 | 0.0612905 | ||||||||
\(996\) | 36.5718 | 1.15882 | ||||||||
\(997\) | 20.8702 | 0.660965 | 0.330483 | − | 0.943812i | \(-0.392788\pi\) | ||||
0.330483 | + | 0.943812i | \(0.392788\pi\) | |||||||
\(998\) | −7.35059 | −0.232679 | ||||||||
\(999\) | 9.55262 | 0.302232 |
(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 | 8281.2.a.be.1.2 | 3 | ||
7.6 | odd | 2 | 1183.2.a.h.1.2 | 3 | |||
13.5 | odd | 4 | 637.2.c.d.246.4 | 6 | |||
13.8 | odd | 4 | 637.2.c.d.246.3 | 6 | |||
13.12 | even | 2 | 8281.2.a.bi.1.2 | 3 | |||
91.5 | even | 12 | 637.2.r.e.116.4 | 12 | |||
91.18 | odd | 12 | 637.2.r.d.324.3 | 12 | |||
91.31 | even | 12 | 637.2.r.e.324.3 | 12 | |||
91.34 | even | 4 | 91.2.c.a.64.3 | ✓ | 6 | ||
91.44 | odd | 12 | 637.2.r.d.116.4 | 12 | |||
91.47 | even | 12 | 637.2.r.e.116.3 | 12 | |||
91.60 | odd | 12 | 637.2.r.d.324.4 | 12 | |||
91.73 | even | 12 | 637.2.r.e.324.4 | 12 | |||
91.83 | even | 4 | 91.2.c.a.64.4 | yes | 6 | ||
91.86 | odd | 12 | 637.2.r.d.116.3 | 12 | |||
91.90 | odd | 2 | 1183.2.a.j.1.2 | 3 | |||
273.83 | odd | 4 | 819.2.c.b.64.3 | 6 | |||
273.125 | odd | 4 | 819.2.c.b.64.4 | 6 | |||
364.83 | odd | 4 | 1456.2.k.c.337.6 | 6 | |||
364.307 | odd | 4 | 1456.2.k.c.337.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.c.a.64.3 | ✓ | 6 | 91.34 | even | 4 | ||
91.2.c.a.64.4 | yes | 6 | 91.83 | even | 4 | ||
637.2.c.d.246.3 | 6 | 13.8 | odd | 4 | |||
637.2.c.d.246.4 | 6 | 13.5 | odd | 4 | |||
637.2.r.d.116.3 | 12 | 91.86 | odd | 12 | |||
637.2.r.d.116.4 | 12 | 91.44 | odd | 12 | |||
637.2.r.d.324.3 | 12 | 91.18 | odd | 12 | |||
637.2.r.d.324.4 | 12 | 91.60 | odd | 12 | |||
637.2.r.e.116.3 | 12 | 91.47 | even | 12 | |||
637.2.r.e.116.4 | 12 | 91.5 | even | 12 | |||
637.2.r.e.324.3 | 12 | 91.31 | even | 12 | |||
637.2.r.e.324.4 | 12 | 91.73 | even | 12 | |||
819.2.c.b.64.3 | 6 | 273.83 | odd | 4 | |||
819.2.c.b.64.4 | 6 | 273.125 | odd | 4 | |||
1183.2.a.h.1.2 | 3 | 7.6 | odd | 2 | |||
1183.2.a.j.1.2 | 3 | 91.90 | odd | 2 | |||
1456.2.k.c.337.5 | 6 | 364.307 | odd | 4 | |||
1456.2.k.c.337.6 | 6 | 364.83 | odd | 4 | |||
8281.2.a.be.1.2 | 3 | 1.1 | even | 1 | trivial | ||
8281.2.a.bi.1.2 | 3 | 13.12 | even | 2 |