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: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 637) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36389 | −1.67152 | −0.835761 | − | 0.549093i | \(-0.814973\pi\) | ||||
−0.835761 | + | 0.549093i | \(0.814973\pi\) | |||||||
\(3\) | 2.98693 | 1.72450 | 0.862252 | − | 0.506479i | \(-0.169053\pi\) | ||||
0.862252 | + | 0.506479i | \(0.169053\pi\) | |||||||
\(4\) | 3.58797 | 1.79399 | ||||||||
\(5\) | −3.20263 | −1.43226 | −0.716130 | − | 0.697967i | \(-0.754088\pi\) | ||||
−0.716130 | + | 0.697967i | \(0.754088\pi\) | |||||||
\(6\) | −7.06077 | −2.88255 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.75379 | −1.32716 | ||||||||
\(9\) | 5.92175 | 1.97392 | ||||||||
\(10\) | 7.57066 | 2.39405 | ||||||||
\(11\) | 3.69364 | 1.11367 | 0.556837 | − | 0.830622i | \(-0.312015\pi\) | ||||
0.556837 | + | 0.830622i | \(0.312015\pi\) | |||||||
\(12\) | 10.7170 | 3.09374 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.56603 | −2.46994 | ||||||||
\(16\) | 1.69759 | 0.424399 | ||||||||
\(17\) | −1.46681 | −0.355753 | −0.177876 | − | 0.984053i | \(-0.556923\pi\) | ||||
−0.177876 | + | 0.984053i | \(0.556923\pi\) | |||||||
\(18\) | −13.9984 | −3.29945 | ||||||||
\(19\) | −5.91159 | −1.35621 | −0.678105 | − | 0.734965i | \(-0.737199\pi\) | ||||
−0.678105 | + | 0.734965i | \(0.737199\pi\) | |||||||
\(20\) | −11.4909 | −2.56945 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.73134 | −1.86153 | ||||||||
\(23\) | −0.690405 | −0.143959 | −0.0719797 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719797 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(24\) | −11.2123 | −2.28870 | ||||||||
\(25\) | 5.25684 | 1.05137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.72707 | 1.67952 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.78478 | −0.888512 | −0.444256 | − | 0.895900i | \(-0.646532\pi\) | ||||
−0.444256 | + | 0.895900i | \(0.646532\pi\) | |||||||
\(30\) | 22.6130 | 4.12856 | ||||||||
\(31\) | −2.10879 | −0.378750 | −0.189375 | − | 0.981905i | \(-0.560646\pi\) | ||||
−0.189375 | + | 0.981905i | \(0.560646\pi\) | |||||||
\(32\) | 3.49465 | 0.617773 | ||||||||
\(33\) | 11.0326 | 1.92053 | ||||||||
\(34\) | 3.46737 | 0.594649 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 21.2471 | 3.54118 | ||||||||
\(37\) | −1.25893 | −0.206967 | −0.103483 | − | 0.994631i | \(-0.532999\pi\) | ||||
−0.103483 | + | 0.994631i | \(0.532999\pi\) | |||||||
\(38\) | 13.9743 | 2.26694 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.0220 | 1.90084 | ||||||||
\(41\) | −0.259466 | −0.0405217 | −0.0202609 | − | 0.999795i | \(-0.506450\pi\) | ||||
−0.0202609 | + | 0.999795i | \(0.506450\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.61216 | −0.855846 | −0.427923 | − | 0.903815i | \(-0.640755\pi\) | ||||
−0.427923 | + | 0.903815i | \(0.640755\pi\) | |||||||
\(44\) | 13.2527 | 1.99791 | ||||||||
\(45\) | −18.9652 | −2.82716 | ||||||||
\(46\) | 1.63204 | 0.240631 | ||||||||
\(47\) | 11.6216 | 1.69518 | 0.847589 | − | 0.530653i | \(-0.178053\pi\) | ||||
0.847589 | + | 0.530653i | \(0.178053\pi\) | |||||||
\(48\) | 5.07059 | 0.731877 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −12.4266 | −1.75738 | ||||||||
\(51\) | −4.38125 | −0.613497 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.485623 | 0.0667055 | 0.0333527 | − | 0.999444i | \(-0.489382\pi\) | ||||
0.0333527 | + | 0.999444i | \(0.489382\pi\) | |||||||
\(54\) | −20.6298 | −2.80736 | ||||||||
\(55\) | −11.8293 | −1.59507 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.6575 | −2.33879 | ||||||||
\(58\) | 11.3107 | 1.48517 | ||||||||
\(59\) | −8.72883 | −1.13640 | −0.568198 | − | 0.822892i | \(-0.692359\pi\) | ||||
−0.568198 | + | 0.822892i | \(0.692359\pi\) | |||||||
\(60\) | −34.3226 | −4.43103 | ||||||||
\(61\) | 11.4632 | 1.46772 | 0.733858 | − | 0.679303i | \(-0.237718\pi\) | ||||
0.733858 | + | 0.679303i | \(0.237718\pi\) | |||||||
\(62\) | 4.98495 | 0.633089 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.6562 | −1.45702 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −26.0799 | −3.21022 | ||||||||
\(67\) | 0.341900 | 0.0417697 | 0.0208849 | − | 0.999782i | \(-0.493352\pi\) | ||||
0.0208849 | + | 0.999782i | \(0.493352\pi\) | |||||||
\(68\) | −5.26286 | −0.638215 | ||||||||
\(69\) | −2.06219 | −0.248259 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.20574 | 0.973842 | 0.486921 | − | 0.873446i | \(-0.338120\pi\) | ||||
0.486921 | + | 0.873446i | \(0.338120\pi\) | |||||||
\(72\) | −22.2290 | −2.61971 | ||||||||
\(73\) | −0.259823 | −0.0304100 | −0.0152050 | − | 0.999884i | \(-0.504840\pi\) | ||||
−0.0152050 | + | 0.999884i | \(0.504840\pi\) | |||||||
\(74\) | 2.97597 | 0.345950 | ||||||||
\(75\) | 15.7018 | 1.81309 | ||||||||
\(76\) | −21.2106 | −2.43302 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1259 | 1.13925 | 0.569627 | − | 0.821903i | \(-0.307088\pi\) | ||||
0.569627 | + | 0.821903i | \(0.307088\pi\) | |||||||
\(80\) | −5.43677 | −0.607849 | ||||||||
\(81\) | 8.30188 | 0.922431 | ||||||||
\(82\) | 0.613348 | 0.0677329 | ||||||||
\(83\) | 10.0995 | 1.10857 | 0.554285 | − | 0.832327i | \(-0.312992\pi\) | ||||
0.554285 | + | 0.832327i | \(0.312992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.69764 | 0.509530 | ||||||||
\(86\) | 13.2665 | 1.43056 | ||||||||
\(87\) | −14.2918 | −1.53224 | ||||||||
\(88\) | −13.8651 | −1.47803 | ||||||||
\(89\) | 2.50249 | 0.265263 | 0.132632 | − | 0.991165i | \(-0.457657\pi\) | ||||
0.132632 | + | 0.991165i | \(0.457657\pi\) | |||||||
\(90\) | 44.8316 | 4.72566 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.47715 | −0.258261 | ||||||||
\(93\) | −6.29881 | −0.653156 | ||||||||
\(94\) | −27.4721 | −2.83353 | ||||||||
\(95\) | 18.9326 | 1.94245 | ||||||||
\(96\) | 10.4383 | 1.06535 | ||||||||
\(97\) | 5.29215 | 0.537336 | 0.268668 | − | 0.963233i | \(-0.413417\pi\) | ||||
0.268668 | + | 0.963233i | \(0.413417\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 21.8728 | 2.19830 | ||||||||
\(100\) | 18.8614 | 1.88614 | ||||||||
\(101\) | 12.0085 | 1.19489 | 0.597445 | − | 0.801910i | \(-0.296183\pi\) | ||||
0.597445 | + | 0.801910i | \(0.296183\pi\) | |||||||
\(102\) | 10.3568 | 1.02547 | ||||||||
\(103\) | −8.36022 | −0.823756 | −0.411878 | − | 0.911239i | \(-0.635127\pi\) | ||||
−0.411878 | + | 0.911239i | \(0.635127\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.14796 | −0.111500 | ||||||||
\(107\) | 10.2830 | 0.994095 | 0.497048 | − | 0.867723i | \(-0.334417\pi\) | ||||
0.497048 | + | 0.867723i | \(0.334417\pi\) | |||||||
\(108\) | 31.3125 | 3.01304 | ||||||||
\(109\) | 19.7427 | 1.89101 | 0.945506 | − | 0.325604i | \(-0.105568\pi\) | ||||
0.945506 | + | 0.325604i | \(0.105568\pi\) | |||||||
\(110\) | 27.9633 | 2.66619 | ||||||||
\(111\) | −3.76034 | −0.356915 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.07097 | 0.288893 | 0.144446 | − | 0.989513i | \(-0.453860\pi\) | ||||
0.144446 | + | 0.989513i | \(0.453860\pi\) | |||||||
\(114\) | 41.7403 | 3.90934 | ||||||||
\(115\) | 2.21111 | 0.206187 | ||||||||
\(116\) | −17.1677 | −1.59398 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.6340 | 1.89951 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 35.9088 | 3.27801 | ||||||||
\(121\) | 2.64294 | 0.240268 | ||||||||
\(122\) | −27.0978 | −2.45332 | ||||||||
\(123\) | −0.775006 | −0.0698799 | ||||||||
\(124\) | −7.56628 | −0.679472 | ||||||||
\(125\) | −0.822557 | −0.0735717 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.4729 | 1.63921 | 0.819604 | − | 0.572930i | \(-0.194193\pi\) | ||||
0.819604 | + | 0.572930i | \(0.194193\pi\) | |||||||
\(128\) | 20.5646 | 1.81767 | ||||||||
\(129\) | −16.7631 | −1.47591 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.5565 | −1.09707 | −0.548535 | − | 0.836128i | \(-0.684814\pi\) | ||||
−0.548535 | + | 0.836128i | \(0.684814\pi\) | |||||||
\(132\) | 39.5848 | 3.44541 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.808214 | −0.0698190 | ||||||||
\(135\) | −27.9496 | −2.40552 | ||||||||
\(136\) | 5.50608 | 0.472142 | ||||||||
\(137\) | 17.7115 | 1.51320 | 0.756600 | − | 0.653878i | \(-0.226859\pi\) | ||||
0.756600 | + | 0.653878i | \(0.226859\pi\) | |||||||
\(138\) | 4.87479 | 0.414970 | ||||||||
\(139\) | −7.47516 | −0.634034 | −0.317017 | − | 0.948420i | \(-0.602681\pi\) | ||||
−0.317017 | + | 0.948420i | \(0.602681\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 34.7128 | 2.92334 | ||||||||
\(142\) | −19.3974 | −1.62780 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.0527 | 0.837727 | ||||||||
\(145\) | 15.3239 | 1.27258 | ||||||||
\(146\) | 0.614192 | 0.0508309 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.51700 | −0.371295 | ||||||||
\(149\) | −7.41588 | −0.607533 | −0.303766 | − | 0.952747i | \(-0.598244\pi\) | ||||
−0.303766 | + | 0.952747i | \(0.598244\pi\) | |||||||
\(150\) | −37.1173 | −3.03062 | ||||||||
\(151\) | 6.07902 | 0.494703 | 0.247352 | − | 0.968926i | \(-0.420440\pi\) | ||||
0.247352 | + | 0.968926i | \(0.420440\pi\) | |||||||
\(152\) | 22.1908 | 1.79991 | ||||||||
\(153\) | −8.68606 | −0.702226 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.75368 | 0.542468 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.38366 | −0.748897 | −0.374449 | − | 0.927248i | \(-0.622168\pi\) | ||||
−0.374449 | + | 0.927248i | \(0.622168\pi\) | |||||||
\(158\) | −23.9365 | −1.90429 | ||||||||
\(159\) | 1.45052 | 0.115034 | ||||||||
\(160\) | −11.1921 | −0.884811 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −19.6247 | −1.54186 | ||||||||
\(163\) | −24.6724 | −1.93249 | −0.966244 | − | 0.257629i | \(-0.917059\pi\) | ||||
−0.966244 | + | 0.257629i | \(0.917059\pi\) | |||||||
\(164\) | −0.930955 | −0.0726954 | ||||||||
\(165\) | −35.3334 | −2.75070 | ||||||||
\(166\) | −23.8742 | −1.85300 | ||||||||
\(167\) | −1.70532 | −0.131962 | −0.0659809 | − | 0.997821i | \(-0.521018\pi\) | ||||
−0.0659809 | + | 0.997821i | \(0.521018\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −11.1047 | −0.851691 | ||||||||
\(171\) | −35.0069 | −2.67705 | ||||||||
\(172\) | −20.1363 | −1.53537 | ||||||||
\(173\) | 2.89707 | 0.220260 | 0.110130 | − | 0.993917i | \(-0.464873\pi\) | ||||
0.110130 | + | 0.993917i | \(0.464873\pi\) | |||||||
\(174\) | 33.7842 | 2.56118 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.27029 | 0.472641 | ||||||||
\(177\) | −26.0724 | −1.95972 | ||||||||
\(178\) | −5.91561 | −0.443394 | ||||||||
\(179\) | 15.5118 | 1.15940 | 0.579702 | − | 0.814828i | \(-0.303169\pi\) | ||||
0.579702 | + | 0.814828i | \(0.303169\pi\) | |||||||
\(180\) | −68.0465 | −5.07189 | ||||||||
\(181\) | −19.4473 | −1.44551 | −0.722754 | − | 0.691105i | \(-0.757124\pi\) | ||||
−0.722754 | + | 0.691105i | \(0.757124\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 34.2398 | 2.53108 | ||||||||
\(184\) | 2.59163 | 0.191058 | ||||||||
\(185\) | 4.03189 | 0.296430 | ||||||||
\(186\) | 14.8897 | 1.09177 | ||||||||
\(187\) | −5.41785 | −0.396192 | ||||||||
\(188\) | 41.6978 | 3.04113 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −44.7546 | −3.24684 | ||||||||
\(191\) | 17.3793 | 1.25753 | 0.628763 | − | 0.777597i | \(-0.283562\pi\) | ||||
0.628763 | + | 0.777597i | \(0.283562\pi\) | |||||||
\(192\) | −34.8161 | −2.51264 | ||||||||
\(193\) | 11.6587 | 0.839211 | 0.419605 | − | 0.907707i | \(-0.362168\pi\) | ||||
0.419605 | + | 0.907707i | \(0.362168\pi\) | |||||||
\(194\) | −12.5101 | −0.898169 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.19575 | −0.441429 | −0.220714 | − | 0.975338i | \(-0.570839\pi\) | ||||
−0.220714 | + | 0.975338i | \(0.570839\pi\) | |||||||
\(198\) | −51.7048 | −3.67450 | ||||||||
\(199\) | 9.48200 | 0.672161 | 0.336081 | − | 0.941833i | \(-0.390899\pi\) | ||||
0.336081 | + | 0.941833i | \(0.390899\pi\) | |||||||
\(200\) | −19.7331 | −1.39534 | ||||||||
\(201\) | 1.02123 | 0.0720321 | ||||||||
\(202\) | −28.3867 | −1.99728 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −15.7198 | −1.10061 | ||||||||
\(205\) | 0.830972 | 0.0580376 | ||||||||
\(206\) | 19.7626 | 1.37693 | ||||||||
\(207\) | −4.08841 | −0.284164 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.8352 | −1.51038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.38187 | −0.163975 | −0.0819874 | − | 0.996633i | \(-0.526127\pi\) | ||||
−0.0819874 | + | 0.996633i | \(0.526127\pi\) | |||||||
\(212\) | 1.74240 | 0.119669 | ||||||||
\(213\) | 24.5100 | 1.67939 | ||||||||
\(214\) | −24.3079 | −1.66165 | ||||||||
\(215\) | 17.9737 | 1.22579 | ||||||||
\(216\) | −32.7595 | −2.22900 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −46.6697 | −3.16087 | ||||||||
\(219\) | −0.776073 | −0.0524421 | ||||||||
\(220\) | −42.4434 | −2.86153 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 8.88901 | 0.596592 | ||||||||
\(223\) | 2.30723 | 0.154504 | 0.0772518 | − | 0.997012i | \(-0.475385\pi\) | ||||
0.0772518 | + | 0.997012i | \(0.475385\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 31.1297 | 2.07531 | ||||||||
\(226\) | −7.25944 | −0.482891 | ||||||||
\(227\) | −5.22044 | −0.346493 | −0.173246 | − | 0.984879i | \(-0.555426\pi\) | ||||
−0.173246 | + | 0.984879i | \(0.555426\pi\) | |||||||
\(228\) | −63.3546 | −4.19576 | ||||||||
\(229\) | −15.9037 | −1.05095 | −0.525473 | − | 0.850810i | \(-0.676112\pi\) | ||||
−0.525473 | + | 0.850810i | \(0.676112\pi\) | |||||||
\(230\) | −5.22682 | −0.344647 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.9610 | 1.17920 | ||||||||
\(233\) | 18.5787 | 1.21713 | 0.608564 | − | 0.793505i | \(-0.291746\pi\) | ||||
0.608564 | + | 0.793505i | \(0.291746\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −37.2196 | −2.42794 | ||||||||
\(236\) | −31.3188 | −2.03868 | ||||||||
\(237\) | 30.2454 | 1.96465 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.30548 | −0.213814 | −0.106907 | − | 0.994269i | \(-0.534095\pi\) | ||||
−0.106907 | + | 0.994269i | \(0.534095\pi\) | |||||||
\(240\) | −16.2392 | −1.04824 | ||||||||
\(241\) | −13.1629 | −0.847895 | −0.423947 | − | 0.905687i | \(-0.639356\pi\) | ||||
−0.423947 | + | 0.905687i | \(0.639356\pi\) | |||||||
\(242\) | −6.24763 | −0.401613 | ||||||||
\(243\) | −1.38406 | −0.0887873 | ||||||||
\(244\) | 41.1297 | 2.63306 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.83203 | 0.116806 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 7.91595 | 0.502664 | ||||||||
\(249\) | 30.1666 | 1.91173 | ||||||||
\(250\) | 1.94443 | 0.122977 | ||||||||
\(251\) | −3.72428 | −0.235074 | −0.117537 | − | 0.993068i | \(-0.537500\pi\) | ||||
−0.117537 | + | 0.993068i | \(0.537500\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.55011 | −0.160324 | ||||||||
\(254\) | −43.6680 | −2.73997 | ||||||||
\(255\) | 14.0315 | 0.878688 | ||||||||
\(256\) | −25.3000 | −1.58125 | ||||||||
\(257\) | 17.0327 | 1.06247 | 0.531236 | − | 0.847224i | \(-0.321728\pi\) | ||||
0.531236 | + | 0.847224i | \(0.321728\pi\) | |||||||
\(258\) | 39.6261 | 2.46702 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.3343 | −1.75385 | ||||||||
\(262\) | 29.6823 | 1.83378 | ||||||||
\(263\) | 9.28371 | 0.572458 | 0.286229 | − | 0.958161i | \(-0.407598\pi\) | ||||
0.286229 | + | 0.958161i | \(0.407598\pi\) | |||||||
\(264\) | −41.4142 | −2.54886 | ||||||||
\(265\) | −1.55527 | −0.0955396 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.47476 | 0.457448 | ||||||||
\(268\) | 1.22673 | 0.0749343 | ||||||||
\(269\) | 22.1360 | 1.34966 | 0.674829 | − | 0.737975i | \(-0.264218\pi\) | ||||
0.674829 | + | 0.737975i | \(0.264218\pi\) | |||||||
\(270\) | 66.0697 | 4.02087 | ||||||||
\(271\) | 26.6209 | 1.61711 | 0.808553 | − | 0.588423i | \(-0.200251\pi\) | ||||
0.808553 | + | 0.588423i | \(0.200251\pi\) | |||||||
\(272\) | −2.49004 | −0.150981 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −41.8681 | −2.52935 | ||||||||
\(275\) | 19.4168 | 1.17088 | ||||||||
\(276\) | −7.39908 | −0.445373 | ||||||||
\(277\) | −1.68124 | −0.101016 | −0.0505079 | − | 0.998724i | \(-0.516084\pi\) | ||||
−0.0505079 | + | 0.998724i | \(0.516084\pi\) | |||||||
\(278\) | 17.6704 | 1.05980 | ||||||||
\(279\) | −12.4877 | −0.747621 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.6730 | −1.71049 | −0.855243 | − | 0.518227i | \(-0.826592\pi\) | ||||
−0.855243 | + | 0.518227i | \(0.826592\pi\) | |||||||
\(282\) | −82.0572 | −4.88643 | ||||||||
\(283\) | −3.58312 | −0.212994 | −0.106497 | − | 0.994313i | \(-0.533963\pi\) | ||||
−0.106497 | + | 0.994313i | \(0.533963\pi\) | |||||||
\(284\) | 29.4419 | 1.74706 | ||||||||
\(285\) | 56.5504 | 3.34976 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 20.6945 | 1.21943 | ||||||||
\(289\) | −14.8485 | −0.873440 | ||||||||
\(290\) | −36.2240 | −2.12714 | ||||||||
\(291\) | 15.8073 | 0.926639 | ||||||||
\(292\) | −0.932237 | −0.0545550 | ||||||||
\(293\) | 16.4408 | 0.960483 | 0.480242 | − | 0.877136i | \(-0.340549\pi\) | ||||
0.480242 | + | 0.877136i | \(0.340549\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.9552 | 1.62761 | ||||||||
\(296\) | 4.72575 | 0.274679 | ||||||||
\(297\) | 32.2346 | 1.87044 | ||||||||
\(298\) | 17.5303 | 1.01550 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 56.3376 | 3.25265 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −14.3701 | −0.826908 | ||||||||
\(303\) | 35.8685 | 2.06059 | ||||||||
\(304\) | −10.0355 | −0.575574 | ||||||||
\(305\) | −36.7125 | −2.10215 | ||||||||
\(306\) | 20.5329 | 1.17379 | ||||||||
\(307\) | 3.52583 | 0.201230 | 0.100615 | − | 0.994925i | \(-0.467919\pi\) | ||||
0.100615 | + | 0.994925i | \(0.467919\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.9714 | −1.42057 | ||||||||
\(310\) | −15.9649 | −0.906748 | ||||||||
\(311\) | −14.3241 | −0.812245 | −0.406123 | − | 0.913819i | \(-0.633119\pi\) | ||||
−0.406123 | + | 0.913819i | \(0.633119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.71897 | −0.379779 | −0.189889 | − | 0.981805i | \(-0.560813\pi\) | ||||
−0.189889 | + | 0.981805i | \(0.560813\pi\) | |||||||
\(314\) | 22.1819 | 1.25180 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 36.3315 | 2.04380 | ||||||||
\(317\) | 3.95457 | 0.222111 | 0.111055 | − | 0.993814i | \(-0.464577\pi\) | ||||
0.111055 | + | 0.993814i | \(0.464577\pi\) | |||||||
\(318\) | −3.42888 | −0.192282 | ||||||||
\(319\) | −17.6732 | −0.989511 | ||||||||
\(320\) | 37.3303 | 2.08683 | ||||||||
\(321\) | 30.7146 | 1.71432 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.67115 | 0.482476 | ||||||||
\(324\) | 29.7869 | 1.65483 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 58.3227 | 3.23020 | ||||||||
\(327\) | 58.9702 | 3.26106 | ||||||||
\(328\) | 0.973979 | 0.0537790 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 83.5243 | 4.59786 | ||||||||
\(331\) | −11.7998 | −0.648575 | −0.324287 | − | 0.945959i | \(-0.605125\pi\) | ||||
−0.324287 | + | 0.945959i | \(0.605125\pi\) | |||||||
\(332\) | 36.2369 | 1.98876 | ||||||||
\(333\) | −7.45507 | −0.408535 | ||||||||
\(334\) | 4.03119 | 0.220577 | ||||||||
\(335\) | −1.09498 | −0.0598251 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.7135 | −1.50965 | −0.754824 | − | 0.655927i | \(-0.772278\pi\) | ||||
−0.754824 | + | 0.655927i | \(0.772278\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.17278 | 0.498197 | ||||||||
\(340\) | 16.8550 | 0.914090 | ||||||||
\(341\) | −7.78911 | −0.421804 | ||||||||
\(342\) | 82.7525 | 4.47474 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 21.0668 | 1.13585 | ||||||||
\(345\) | 6.60444 | 0.355571 | ||||||||
\(346\) | −6.84834 | −0.368169 | ||||||||
\(347\) | 29.3788 | 1.57714 | 0.788569 | − | 0.614947i | \(-0.210822\pi\) | ||||
0.788569 | + | 0.614947i | \(0.210822\pi\) | |||||||
\(348\) | −51.2786 | −2.74882 | ||||||||
\(349\) | 20.5460 | 1.09980 | 0.549902 | − | 0.835229i | \(-0.314665\pi\) | ||||
0.549902 | + | 0.835229i | \(0.314665\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.9080 | 0.687997 | ||||||||
\(353\) | −3.49173 | −0.185846 | −0.0929229 | − | 0.995673i | \(-0.529621\pi\) | ||||
−0.0929229 | + | 0.995673i | \(0.529621\pi\) | |||||||
\(354\) | 61.6323 | 3.27572 | ||||||||
\(355\) | −26.2799 | −1.39479 | ||||||||
\(356\) | 8.97886 | 0.475879 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −36.6681 | −1.93797 | ||||||||
\(359\) | 24.4864 | 1.29234 | 0.646170 | − | 0.763193i | \(-0.276370\pi\) | ||||
0.646170 | + | 0.763193i | \(0.276370\pi\) | |||||||
\(360\) | 71.1912 | 3.75211 | ||||||||
\(361\) | 15.9468 | 0.839307 | ||||||||
\(362\) | 45.9713 | 2.41620 | ||||||||
\(363\) | 7.89429 | 0.414343 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.832116 | 0.0435550 | ||||||||
\(366\) | −80.9392 | −4.23076 | ||||||||
\(367\) | 1.50036 | 0.0783183 | 0.0391591 | − | 0.999233i | \(-0.487532\pi\) | ||||
0.0391591 | + | 0.999233i | \(0.487532\pi\) | |||||||
\(368\) | −1.17203 | −0.0610962 | ||||||||
\(369\) | −1.53649 | −0.0799865 | ||||||||
\(370\) | −9.53093 | −0.495490 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −22.6000 | −1.17175 | ||||||||
\(373\) | 9.07024 | 0.469639 | 0.234820 | − | 0.972039i | \(-0.424550\pi\) | ||||
0.234820 | + | 0.972039i | \(0.424550\pi\) | |||||||
\(374\) | 12.8072 | 0.662244 | ||||||||
\(375\) | −2.45692 | −0.126875 | ||||||||
\(376\) | −43.6249 | −2.24978 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.5801 | 1.26259 | 0.631297 | − | 0.775541i | \(-0.282523\pi\) | ||||
0.631297 | + | 0.775541i | \(0.282523\pi\) | |||||||
\(380\) | 67.9297 | 3.48472 | ||||||||
\(381\) | 55.1774 | 2.82682 | ||||||||
\(382\) | −41.0828 | −2.10198 | ||||||||
\(383\) | 5.39785 | 0.275817 | 0.137909 | − | 0.990445i | \(-0.455962\pi\) | ||||
0.137909 | + | 0.990445i | \(0.455962\pi\) | |||||||
\(384\) | 61.4249 | 3.13458 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −27.5598 | −1.40276 | ||||||||
\(387\) | −33.2338 | −1.68937 | ||||||||
\(388\) | 18.9881 | 0.963974 | ||||||||
\(389\) | 21.2762 | 1.07875 | 0.539373 | − | 0.842067i | \(-0.318661\pi\) | ||||
0.539373 | + | 0.842067i | \(0.318661\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.01269 | 0.0512140 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −37.5055 | −1.89190 | ||||||||
\(394\) | 14.6461 | 0.737858 | ||||||||
\(395\) | −32.4295 | −1.63171 | ||||||||
\(396\) | 78.4789 | 3.94372 | ||||||||
\(397\) | −18.8879 | −0.947957 | −0.473979 | − | 0.880536i | \(-0.657183\pi\) | ||||
−0.473979 | + | 0.880536i | \(0.657183\pi\) | |||||||
\(398\) | −22.4144 | −1.12353 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.92398 | 0.446199 | ||||||||
\(401\) | −10.5399 | −0.526335 | −0.263168 | − | 0.964750i | \(-0.584767\pi\) | ||||
−0.263168 | + | 0.964750i | \(0.584767\pi\) | |||||||
\(402\) | −2.41408 | −0.120403 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 43.0861 | 2.14361 | ||||||||
\(405\) | −26.5879 | −1.32116 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.65003 | −0.230493 | ||||||||
\(408\) | 16.4463 | 0.814212 | ||||||||
\(409\) | 32.6547 | 1.61467 | 0.807337 | − | 0.590091i | \(-0.200908\pi\) | ||||
0.807337 | + | 0.590091i | \(0.200908\pi\) | |||||||
\(410\) | −1.96433 | −0.0970112 | ||||||||
\(411\) | 52.9031 | 2.60952 | ||||||||
\(412\) | −29.9962 | −1.47781 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.66454 | 0.474986 | ||||||||
\(415\) | −32.3451 | −1.58776 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.3278 | −1.09340 | ||||||||
\(418\) | 51.6161 | 2.52463 | ||||||||
\(419\) | 36.1365 | 1.76539 | 0.882693 | − | 0.469951i | \(-0.155728\pi\) | ||||
0.882693 | + | 0.469951i | \(0.155728\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.6781 | −1.78758 | −0.893791 | − | 0.448485i | \(-0.851964\pi\) | ||||
−0.893791 | + | 0.448485i | \(0.851964\pi\) | |||||||
\(422\) | 5.63048 | 0.274087 | ||||||||
\(423\) | 68.8200 | 3.34614 | ||||||||
\(424\) | −1.82293 | −0.0885291 | ||||||||
\(425\) | −7.71076 | −0.374027 | ||||||||
\(426\) | −57.9388 | −2.80714 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 36.8951 | 1.78339 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −42.4877 | −2.04894 | ||||||||
\(431\) | 10.2938 | 0.495835 | 0.247917 | − | 0.968781i | \(-0.420254\pi\) | ||||
0.247917 | + | 0.968781i | \(0.420254\pi\) | |||||||
\(432\) | 14.8150 | 0.712788 | ||||||||
\(433\) | −27.9646 | −1.34389 | −0.671946 | − | 0.740600i | \(-0.734541\pi\) | ||||
−0.671946 | + | 0.740600i | \(0.734541\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 45.7714 | 2.19457 | ||||||||
\(436\) | 70.8364 | 3.39245 | ||||||||
\(437\) | 4.08139 | 0.195239 | ||||||||
\(438\) | 1.83455 | 0.0876582 | ||||||||
\(439\) | −16.7521 | −0.799534 | −0.399767 | − | 0.916617i | \(-0.630909\pi\) | ||||
−0.399767 | + | 0.916617i | \(0.630909\pi\) | |||||||
\(440\) | 44.4049 | 2.11692 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.02660 | 0.286332 | 0.143166 | − | 0.989699i | \(-0.454272\pi\) | ||||
0.143166 | + | 0.989699i | \(0.454272\pi\) | |||||||
\(444\) | −13.4920 | −0.640301 | ||||||||
\(445\) | −8.01455 | −0.379926 | ||||||||
\(446\) | −5.45404 | −0.258256 | ||||||||
\(447\) | −22.1507 | −1.04769 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.9836 | 1.41501 | 0.707506 | − | 0.706708i | \(-0.249820\pi\) | ||||
0.707506 | + | 0.706708i | \(0.249820\pi\) | |||||||
\(450\) | −73.5871 | −3.46893 | ||||||||
\(451\) | −0.958371 | −0.0451279 | ||||||||
\(452\) | 11.0186 | 0.518270 | ||||||||
\(453\) | 18.1576 | 0.853118 | ||||||||
\(454\) | 12.3405 | 0.579170 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 66.2825 | 3.10396 | ||||||||
\(457\) | 29.3206 | 1.37156 | 0.685779 | − | 0.727810i | \(-0.259462\pi\) | ||||
0.685779 | + | 0.727810i | \(0.259462\pi\) | |||||||
\(458\) | 37.5946 | 1.75668 | ||||||||
\(459\) | −12.8009 | −0.597496 | ||||||||
\(460\) | 7.93341 | 0.369897 | ||||||||
\(461\) | −8.44267 | −0.393214 | −0.196607 | − | 0.980482i | \(-0.562992\pi\) | ||||
−0.196607 | + | 0.980482i | \(0.562992\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.17390 | 0.240452 | 0.120226 | − | 0.992747i | \(-0.461638\pi\) | ||||
0.120226 | + | 0.992747i | \(0.461638\pi\) | |||||||
\(464\) | −8.12262 | −0.377083 | ||||||||
\(465\) | 20.1728 | 0.935489 | ||||||||
\(466\) | −43.9179 | −2.03446 | ||||||||
\(467\) | −40.3608 | −1.86768 | −0.933839 | − | 0.357694i | \(-0.883563\pi\) | ||||
−0.933839 | + | 0.357694i | \(0.883563\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 87.9829 | 4.05835 | ||||||||
\(471\) | −28.0283 | −1.29148 | ||||||||
\(472\) | 32.7662 | 1.50818 | ||||||||
\(473\) | −20.7293 | −0.953132 | ||||||||
\(474\) | −71.4967 | −3.28395 | ||||||||
\(475\) | −31.0762 | −1.42588 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.87574 | 0.131671 | ||||||||
\(478\) | 7.81378 | 0.357394 | ||||||||
\(479\) | −7.50735 | −0.343020 | −0.171510 | − | 0.985182i | \(-0.554865\pi\) | ||||
−0.171510 | + | 0.985182i | \(0.554865\pi\) | |||||||
\(480\) | −33.4299 | −1.52586 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 31.1156 | 1.41727 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.48281 | 0.431037 | ||||||||
\(485\) | −16.9488 | −0.769605 | ||||||||
\(486\) | 3.27176 | 0.148410 | ||||||||
\(487\) | 4.62597 | 0.209623 | 0.104811 | − | 0.994492i | \(-0.466576\pi\) | ||||
0.104811 | + | 0.994492i | \(0.466576\pi\) | |||||||
\(488\) | −43.0305 | −1.94790 | ||||||||
\(489\) | −73.6946 | −3.33258 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.1724 | 1.49705 | 0.748525 | − | 0.663106i | \(-0.230762\pi\) | ||||
0.748525 | + | 0.663106i | \(0.230762\pi\) | |||||||
\(492\) | −2.78070 | −0.125364 | ||||||||
\(493\) | 7.01835 | 0.316090 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −70.0505 | −3.14853 | ||||||||
\(496\) | −3.57987 | −0.160741 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −71.3106 | −3.19550 | ||||||||
\(499\) | 28.3940 | 1.27109 | 0.635546 | − | 0.772063i | \(-0.280775\pi\) | ||||
0.635546 | + | 0.772063i | \(0.280775\pi\) | |||||||
\(500\) | −2.95131 | −0.131987 | ||||||||
\(501\) | −5.09368 | −0.227569 | ||||||||
\(502\) | 8.80378 | 0.392932 | ||||||||
\(503\) | 30.4910 | 1.35952 | 0.679762 | − | 0.733433i | \(-0.262083\pi\) | ||||
0.679762 | + | 0.733433i | \(0.262083\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.4588 | −1.71139 | ||||||||
\(506\) | 6.02817 | 0.267985 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 66.2804 | 2.94072 | ||||||||
\(509\) | −17.7496 | −0.786739 | −0.393370 | − | 0.919380i | \(-0.628691\pi\) | ||||
−0.393370 | + | 0.919380i | \(0.628691\pi\) | |||||||
\(510\) | −33.1689 | −1.46875 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.6773 | 0.825428 | ||||||||
\(513\) | −51.5908 | −2.27779 | ||||||||
\(514\) | −40.2635 | −1.77595 | ||||||||
\(515\) | 26.7747 | 1.17983 | ||||||||
\(516\) | −60.1456 | −2.64776 | ||||||||
\(517\) | 42.9258 | 1.88787 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.65333 | 0.379839 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.82051 | 0.167380 | 0.0836898 | − | 0.996492i | \(-0.473330\pi\) | ||||
0.0836898 | + | 0.996492i | \(0.473330\pi\) | |||||||
\(522\) | 66.9791 | 2.93160 | ||||||||
\(523\) | 19.9754 | 0.873462 | 0.436731 | − | 0.899592i | \(-0.356136\pi\) | ||||
0.436731 | + | 0.899592i | \(0.356136\pi\) | |||||||
\(524\) | −45.0525 | −1.96813 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.9457 | −0.956876 | ||||||||
\(527\) | 3.09319 | 0.134741 | ||||||||
\(528\) | 18.7289 | 0.815072 | ||||||||
\(529\) | −22.5233 | −0.979276 | ||||||||
\(530\) | 3.67649 | 0.159697 | ||||||||
\(531\) | −51.6899 | −2.24315 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −17.6695 | −0.764634 | ||||||||
\(535\) | −32.9326 | −1.42380 | ||||||||
\(536\) | −1.28342 | −0.0554353 | ||||||||
\(537\) | 46.3326 | 1.99940 | ||||||||
\(538\) | −52.3271 | −2.25598 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −100.282 | −4.31546 | ||||||||
\(541\) | 35.0586 | 1.50729 | 0.753643 | − | 0.657284i | \(-0.228295\pi\) | ||||
0.753643 | + | 0.657284i | \(0.228295\pi\) | |||||||
\(542\) | −62.9289 | −2.70303 | ||||||||
\(543\) | −58.0878 | −2.49279 | ||||||||
\(544\) | −5.12598 | −0.219774 | ||||||||
\(545\) | −63.2287 | −2.70842 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.0737 | −1.62792 | −0.813958 | − | 0.580924i | \(-0.802691\pi\) | ||||
−0.813958 | + | 0.580924i | \(0.802691\pi\) | |||||||
\(548\) | 63.5485 | 2.71466 | ||||||||
\(549\) | 67.8823 | 2.89715 | ||||||||
\(550\) | −45.8993 | −1.95715 | ||||||||
\(551\) | 28.2856 | 1.20501 | ||||||||
\(552\) | 7.74103 | 0.329480 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.97426 | 0.168850 | ||||||||
\(555\) | 12.0430 | 0.511195 | ||||||||
\(556\) | −26.8206 | −1.13745 | ||||||||
\(557\) | 22.4449 | 0.951023 | 0.475511 | − | 0.879710i | \(-0.342263\pi\) | ||||
0.475511 | + | 0.879710i | \(0.342263\pi\) | |||||||
\(558\) | 29.5196 | 1.24967 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.1827 | −0.683236 | ||||||||
\(562\) | 67.7797 | 2.85912 | ||||||||
\(563\) | −30.2185 | −1.27356 | −0.636779 | − | 0.771047i | \(-0.719734\pi\) | ||||
−0.636779 | + | 0.771047i | \(0.719734\pi\) | |||||||
\(564\) | 124.548 | 5.24444 | ||||||||
\(565\) | −9.83519 | −0.413770 | ||||||||
\(566\) | 8.47009 | 0.356024 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −30.8026 | −1.29245 | ||||||||
\(569\) | −15.0151 | −0.629466 | −0.314733 | − | 0.949180i | \(-0.601915\pi\) | ||||
−0.314733 | + | 0.949180i | \(0.601915\pi\) | |||||||
\(570\) | −133.679 | −5.59919 | ||||||||
\(571\) | 24.1365 | 1.01008 | 0.505041 | − | 0.863096i | \(-0.331477\pi\) | ||||
0.505041 | + | 0.863096i | \(0.331477\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 51.9109 | 2.16861 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.62935 | −0.151354 | ||||||||
\(576\) | −69.0248 | −2.87604 | ||||||||
\(577\) | 45.4117 | 1.89051 | 0.945257 | − | 0.326326i | \(-0.105811\pi\) | ||||
0.945257 | + | 0.326326i | \(0.105811\pi\) | |||||||
\(578\) | 35.1002 | 1.45997 | ||||||||
\(579\) | 34.8237 | 1.44722 | ||||||||
\(580\) | 54.9816 | 2.28299 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −37.3666 | −1.54890 | ||||||||
\(583\) | 1.79372 | 0.0742881 | ||||||||
\(584\) | 0.975320 | 0.0403590 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.8643 | −1.60547 | ||||||||
\(587\) | −30.2745 | −1.24956 | −0.624781 | − | 0.780800i | \(-0.714812\pi\) | ||||
−0.624781 | + | 0.780800i | \(0.714812\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.4663 | 0.513665 | ||||||||
\(590\) | −66.0830 | −2.72059 | ||||||||
\(591\) | −18.5063 | −0.761246 | ||||||||
\(592\) | −2.13715 | −0.0878364 | ||||||||
\(593\) | −29.8218 | −1.22463 | −0.612317 | − | 0.790612i | \(-0.709762\pi\) | ||||
−0.612317 | + | 0.790612i | \(0.709762\pi\) | |||||||
\(594\) | −76.1990 | −3.12648 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −26.6080 | −1.08990 | ||||||||
\(597\) | 28.3221 | 1.15915 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.6191 | 0.924191 | 0.462096 | − | 0.886830i | \(-0.347098\pi\) | ||||
0.462096 | + | 0.886830i | \(0.347098\pi\) | |||||||
\(600\) | −58.9412 | −2.40627 | ||||||||
\(601\) | 44.7823 | 1.82671 | 0.913355 | − | 0.407165i | \(-0.133483\pi\) | ||||
0.913355 | + | 0.407165i | \(0.133483\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.02465 | 0.0824500 | ||||||||
\(604\) | 21.8113 | 0.887491 | ||||||||
\(605\) | −8.46437 | −0.344126 | ||||||||
\(606\) | −84.7892 | −3.44433 | ||||||||
\(607\) | 4.30028 | 0.174543 | 0.0872715 | − | 0.996185i | \(-0.472185\pi\) | ||||
0.0872715 | + | 0.996185i | \(0.472185\pi\) | |||||||
\(608\) | −20.6589 | −0.837830 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 86.7842 | 3.51379 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −31.1653 | −1.25978 | ||||||||
\(613\) | −23.7060 | −0.957478 | −0.478739 | − | 0.877957i | \(-0.658906\pi\) | ||||
−0.478739 | + | 0.877957i | \(0.658906\pi\) | |||||||
\(614\) | −8.33468 | −0.336360 | ||||||||
\(615\) | 2.48206 | 0.100086 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.8712 | −0.477916 | −0.238958 | − | 0.971030i | \(-0.576806\pi\) | ||||
−0.238958 | + | 0.971030i | \(0.576806\pi\) | |||||||
\(618\) | 59.0296 | 2.37452 | ||||||||
\(619\) | 6.30946 | 0.253599 | 0.126799 | − | 0.991928i | \(-0.459530\pi\) | ||||
0.126799 | + | 0.991928i | \(0.459530\pi\) | |||||||
\(620\) | 24.2320 | 0.973180 | ||||||||
\(621\) | −6.02521 | −0.241783 | ||||||||
\(622\) | 33.8606 | 1.35769 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.6498 | −0.945994 | ||||||||
\(626\) | 15.8829 | 0.634808 | ||||||||
\(627\) | −65.2203 | −2.60465 | ||||||||
\(628\) | −33.6683 | −1.34351 | ||||||||
\(629\) | 1.84661 | 0.0736290 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.9665 | −0.516188 | −0.258094 | − | 0.966120i | \(-0.583094\pi\) | ||||
−0.258094 | + | 0.966120i | \(0.583094\pi\) | |||||||
\(632\) | −38.0105 | −1.51198 | ||||||||
\(633\) | −7.11448 | −0.282775 | ||||||||
\(634\) | −9.34816 | −0.371263 | ||||||||
\(635\) | −59.1620 | −2.34777 | ||||||||
\(636\) | 5.20443 | 0.206369 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 41.7776 | 1.65399 | ||||||||
\(639\) | 48.5923 | 1.92228 | ||||||||
\(640\) | −65.8606 | −2.60337 | ||||||||
\(641\) | 33.4554 | 1.32141 | 0.660704 | − | 0.750647i | \(-0.270258\pi\) | ||||
0.660704 | + | 0.750647i | \(0.270258\pi\) | |||||||
\(642\) | −72.6059 | −2.86553 | ||||||||
\(643\) | −6.18209 | −0.243798 | −0.121899 | − | 0.992543i | \(-0.538898\pi\) | ||||
−0.121899 | + | 0.992543i | \(0.538898\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 53.6861 | 2.11389 | ||||||||
\(646\) | −20.4976 | −0.806469 | ||||||||
\(647\) | 36.4228 | 1.43193 | 0.715963 | − | 0.698138i | \(-0.245988\pi\) | ||||
0.715963 | + | 0.698138i | \(0.245988\pi\) | |||||||
\(648\) | −31.1635 | −1.22422 | ||||||||
\(649\) | −32.2411 | −1.26557 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −88.5237 | −3.46685 | ||||||||
\(653\) | −40.1127 | −1.56973 | −0.784867 | − | 0.619665i | \(-0.787269\pi\) | ||||
−0.784867 | + | 0.619665i | \(0.787269\pi\) | |||||||
\(654\) | −139.399 | −5.45093 | ||||||||
\(655\) | 40.2139 | 1.57129 | ||||||||
\(656\) | −0.440467 | −0.0171974 | ||||||||
\(657\) | −1.53861 | −0.0600267 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.1273 | 0.939866 | 0.469933 | − | 0.882702i | \(-0.344278\pi\) | ||||
0.469933 | + | 0.882702i | \(0.344278\pi\) | |||||||
\(660\) | −126.775 | −4.93472 | ||||||||
\(661\) | 8.07479 | 0.314073 | 0.157036 | − | 0.987593i | \(-0.449806\pi\) | ||||
0.157036 | + | 0.987593i | \(0.449806\pi\) | |||||||
\(662\) | 27.8934 | 1.08411 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −37.9115 | −1.47125 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.6230 | 0.682876 | ||||||||
\(667\) | 3.30344 | 0.127910 | ||||||||
\(668\) | −6.11864 | −0.236737 | ||||||||
\(669\) | 6.89154 | 0.266442 | ||||||||
\(670\) | 2.58841 | 0.0999990 | ||||||||
\(671\) | 42.3410 | 1.63455 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.261731 | 0.0100890 | 0.00504449 | − | 0.999987i | \(-0.498394\pi\) | ||||
0.00504449 | + | 0.999987i | \(0.498394\pi\) | |||||||
\(674\) | 65.5115 | 2.52341 | ||||||||
\(675\) | 45.8768 | 1.76580 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.8129 | −0.530874 | −0.265437 | − | 0.964128i | \(-0.585516\pi\) | ||||
−0.265437 | + | 0.964128i | \(0.585516\pi\) | |||||||
\(678\) | −21.6834 | −0.832748 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −17.6339 | −0.676230 | ||||||||
\(681\) | −15.5931 | −0.597528 | ||||||||
\(682\) | 18.4126 | 0.705054 | ||||||||
\(683\) | −17.5572 | −0.671809 | −0.335904 | − | 0.941896i | \(-0.609042\pi\) | ||||
−0.335904 | + | 0.941896i | \(0.609042\pi\) | |||||||
\(684\) | −125.604 | −4.80258 | ||||||||
\(685\) | −56.7235 | −2.16729 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −47.5032 | −1.81236 | ||||||||
\(688\) | −9.52716 | −0.363220 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −15.6122 | −0.594345 | ||||||||
\(691\) | −37.1774 | −1.41430 | −0.707148 | − | 0.707066i | \(-0.750018\pi\) | ||||
−0.707148 | + | 0.707066i | \(0.750018\pi\) | |||||||
\(692\) | 10.3946 | 0.395143 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −69.4483 | −2.63622 | ||||||||
\(695\) | 23.9402 | 0.908102 | ||||||||
\(696\) | 53.6484 | 2.03354 | ||||||||
\(697\) | 0.380586 | 0.0144157 | ||||||||
\(698\) | −48.5686 | −1.83835 | ||||||||
\(699\) | 55.4932 | 2.09894 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.8575 | 1.65647 | 0.828237 | − | 0.560378i | \(-0.189344\pi\) | ||||
0.828237 | + | 0.560378i | \(0.189344\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.44227 | 0.280691 | ||||||||
\(704\) | −43.0536 | −1.62264 | ||||||||
\(705\) | −111.172 | −4.18699 | ||||||||
\(706\) | 8.25405 | 0.310645 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −93.5470 | −3.51571 | ||||||||
\(709\) | 35.5668 | 1.33574 | 0.667870 | − | 0.744278i | \(-0.267206\pi\) | ||||
0.667870 | + | 0.744278i | \(0.267206\pi\) | |||||||
\(710\) | 62.1228 | 2.33143 | ||||||||
\(711\) | 59.9631 | 2.24879 | ||||||||
\(712\) | −9.39382 | −0.352048 | ||||||||
\(713\) | 1.45592 | 0.0545246 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 55.6558 | 2.07996 | ||||||||
\(717\) | −9.87323 | −0.368722 | ||||||||
\(718\) | −57.8830 | −2.16018 | ||||||||
\(719\) | 9.99656 | 0.372809 | 0.186404 | − | 0.982473i | \(-0.440317\pi\) | ||||
0.186404 | + | 0.982473i | \(0.440317\pi\) | |||||||
\(720\) | −32.1952 | −1.19984 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −37.6966 | −1.40292 | ||||||||
\(723\) | −39.3166 | −1.46220 | ||||||||
\(724\) | −69.7765 | −2.59322 | ||||||||
\(725\) | −25.1528 | −0.934152 | ||||||||
\(726\) | −18.6612 | −0.692583 | ||||||||
\(727\) | 39.8985 | 1.47975 | 0.739877 | − | 0.672742i | \(-0.234884\pi\) | ||||
0.739877 | + | 0.672742i | \(0.234884\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.0397 | −1.07555 | ||||||||
\(730\) | −1.96703 | −0.0728031 | ||||||||
\(731\) | 8.23195 | 0.304470 | ||||||||
\(732\) | 122.852 | 4.54072 | ||||||||
\(733\) | 6.81455 | 0.251701 | 0.125850 | − | 0.992049i | \(-0.459834\pi\) | ||||
0.125850 | + | 0.992049i | \(0.459834\pi\) | |||||||
\(734\) | −3.54669 | −0.130911 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.41272 | −0.0889342 | ||||||||
\(737\) | 1.26285 | 0.0465178 | ||||||||
\(738\) | 3.63209 | 0.133699 | ||||||||
\(739\) | −25.8854 | −0.952209 | −0.476105 | − | 0.879389i | \(-0.657952\pi\) | ||||
−0.476105 | + | 0.879389i | \(0.657952\pi\) | |||||||
\(740\) | 14.4663 | 0.531791 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.75671 | −0.101134 | −0.0505670 | − | 0.998721i | \(-0.516103\pi\) | ||||
−0.0505670 | + | 0.998721i | \(0.516103\pi\) | |||||||
\(744\) | 23.6444 | 0.866846 | ||||||||
\(745\) | 23.7503 | 0.870144 | ||||||||
\(746\) | −21.4410 | −0.785012 | ||||||||
\(747\) | 59.8070 | 2.18822 | ||||||||
\(748\) | −19.4391 | −0.710763 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.80789 | 0.212074 | ||||||||
\(751\) | 26.3749 | 0.962432 | 0.481216 | − | 0.876602i | \(-0.340195\pi\) | ||||
0.481216 | + | 0.876602i | \(0.340195\pi\) | |||||||
\(752\) | 19.7287 | 0.719431 | ||||||||
\(753\) | −11.1242 | −0.405387 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.4688 | −0.708544 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.7869 | 0.537439 | 0.268720 | − | 0.963218i | \(-0.413400\pi\) | ||||
0.268720 | + | 0.963218i | \(0.413400\pi\) | |||||||
\(758\) | −58.1046 | −2.11045 | ||||||||
\(759\) | −7.61699 | −0.276479 | ||||||||
\(760\) | −71.0690 | −2.57794 | ||||||||
\(761\) | −23.6210 | −0.856260 | −0.428130 | − | 0.903717i | \(-0.640827\pi\) | ||||
−0.428130 | + | 0.903717i | \(0.640827\pi\) | |||||||
\(762\) | −130.433 | −4.72510 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 62.3566 | 2.25598 | ||||||||
\(765\) | 27.8182 | 1.00577 | ||||||||
\(766\) | −12.7599 | −0.461034 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −75.5694 | −2.72687 | ||||||||
\(769\) | 1.14323 | 0.0412258 | 0.0206129 | − | 0.999788i | \(-0.493438\pi\) | ||||
0.0206129 | + | 0.999788i | \(0.493438\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50.8756 | 1.83224 | ||||||||
\(772\) | 41.8310 | 1.50553 | ||||||||
\(773\) | −17.3478 | −0.623956 | −0.311978 | − | 0.950089i | \(-0.600992\pi\) | ||||
−0.311978 | + | 0.950089i | \(0.600992\pi\) | |||||||
\(774\) | 78.5610 | 2.82382 | ||||||||
\(775\) | −11.0856 | −0.398206 | ||||||||
\(776\) | −19.8656 | −0.713133 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −50.2946 | −1.80315 | ||||||||
\(779\) | 1.53385 | 0.0549560 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.3090 | 1.08454 | ||||||||
\(782\) | −2.39389 | −0.0856053 | ||||||||
\(783\) | −41.7571 | −1.49228 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.0524 | 1.07262 | ||||||||
\(786\) | 88.6588 | 3.16235 | ||||||||
\(787\) | 1.10051 | 0.0392291 | 0.0196145 | − | 0.999808i | \(-0.493756\pi\) | ||||
0.0196145 | + | 0.999808i | \(0.493756\pi\) | |||||||
\(788\) | −22.2302 | −0.791917 | ||||||||
\(789\) | 27.7298 | 0.987207 | ||||||||
\(790\) | 76.6598 | 2.72743 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −82.1058 | −2.91750 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 44.6489 | 1.58453 | ||||||||
\(795\) | −4.64549 | −0.164758 | ||||||||
\(796\) | 34.0211 | 1.20585 | ||||||||
\(797\) | 12.6348 | 0.447546 | 0.223773 | − | 0.974641i | \(-0.428162\pi\) | ||||
0.223773 | + | 0.974641i | \(0.428162\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.0466 | −0.603065 | ||||||||
\(800\) | 18.3708 | 0.649506 | ||||||||
\(801\) | 14.8191 | 0.523608 | ||||||||
\(802\) | 24.9151 | 0.879781 | ||||||||
\(803\) | −0.959691 | −0.0338668 | ||||||||
\(804\) | 3.66415 | 0.129225 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 66.1188 | 2.32749 | ||||||||
\(808\) | −45.0773 | −1.58581 | ||||||||
\(809\) | 41.3610 | 1.45418 | 0.727088 | − | 0.686545i | \(-0.240873\pi\) | ||||
0.727088 | + | 0.686545i | \(0.240873\pi\) | |||||||
\(810\) | 62.8507 | 2.20835 | ||||||||
\(811\) | −15.3408 | −0.538687 | −0.269343 | − | 0.963044i | \(-0.586807\pi\) | ||||
−0.269343 | + | 0.963044i | \(0.586807\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 79.5148 | 2.78871 | ||||||||
\(814\) | 10.9921 | 0.385275 | ||||||||
\(815\) | 79.0164 | 2.76782 | ||||||||
\(816\) | −7.43758 | −0.260367 | ||||||||
\(817\) | 33.1767 | 1.16071 | ||||||||
\(818\) | −77.1922 | −2.69896 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.98150 | 0.104119 | ||||||||
\(821\) | −32.8479 | −1.14640 | −0.573200 | − | 0.819415i | \(-0.694298\pi\) | ||||
−0.573200 | + | 0.819415i | \(0.694298\pi\) | |||||||
\(822\) | −125.057 | −4.36187 | ||||||||
\(823\) | −32.5941 | −1.13616 | −0.568080 | − | 0.822973i | \(-0.692314\pi\) | ||||
−0.568080 | + | 0.822973i | \(0.692314\pi\) | |||||||
\(824\) | 31.3825 | 1.09326 | ||||||||
\(825\) | 57.9968 | 2.01919 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.24226 | 0.217065 | 0.108532 | − | 0.994093i | \(-0.465385\pi\) | ||||
0.108532 | + | 0.994093i | \(0.465385\pi\) | |||||||
\(828\) | −14.6691 | −0.509786 | ||||||||
\(829\) | −21.7031 | −0.753780 | −0.376890 | − | 0.926258i | \(-0.623006\pi\) | ||||
−0.376890 | + | 0.926258i | \(0.623006\pi\) | |||||||
\(830\) | 76.4602 | 2.65397 | ||||||||
\(831\) | −5.02174 | −0.174202 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 52.7804 | 1.82763 | ||||||||
\(835\) | 5.46151 | 0.189003 | ||||||||
\(836\) | −78.3442 | −2.70959 | ||||||||
\(837\) | −18.4036 | −0.636120 | ||||||||
\(838\) | −85.4228 | −2.95088 | ||||||||
\(839\) | −3.30632 | −0.114147 | −0.0570734 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570734 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.10587 | −0.210547 | ||||||||
\(842\) | 86.7030 | 2.98798 | ||||||||
\(843\) | −85.6442 | −2.94974 | ||||||||
\(844\) | −8.54608 | −0.294168 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −162.683 | −5.59315 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.824391 | 0.0283097 | ||||||||
\(849\) | −10.7025 | −0.367309 | ||||||||
\(850\) | 18.2274 | 0.625194 | ||||||||
\(851\) | 0.869172 | 0.0297948 | ||||||||
\(852\) | 87.9410 | 3.01281 | ||||||||
\(853\) | −1.65549 | −0.0566828 | −0.0283414 | − | 0.999598i | \(-0.509023\pi\) | ||||
−0.0283414 | + | 0.999598i | \(0.509023\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 112.114 | 3.83423 | ||||||||
\(856\) | −38.6002 | −1.31933 | ||||||||
\(857\) | 48.2809 | 1.64924 | 0.824622 | − | 0.565683i | \(-0.191388\pi\) | ||||
0.824622 | + | 0.565683i | \(0.191388\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.1342 | 0.550492 | 0.275246 | − | 0.961374i | \(-0.411241\pi\) | ||||
0.275246 | + | 0.961374i | \(0.411241\pi\) | |||||||
\(860\) | 64.4890 | 2.19906 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.3334 | −0.828798 | ||||||||
\(863\) | −1.89828 | −0.0646181 | −0.0323090 | − | 0.999478i | \(-0.510286\pi\) | ||||
−0.0323090 | + | 0.999478i | \(0.510286\pi\) | |||||||
\(864\) | 30.4980 | 1.03756 | ||||||||
\(865\) | −9.27823 | −0.315469 | ||||||||
\(866\) | 66.1052 | 2.24635 | ||||||||
\(867\) | −44.3514 | −1.50625 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.4014 | 1.26876 | ||||||||
\(870\) | −108.198 | −3.66827 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −74.1101 | −2.50968 | ||||||||
\(873\) | 31.3388 | 1.06066 | ||||||||
\(874\) | −9.64795 | −0.326347 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.78453 | −0.0940804 | ||||||||
\(877\) | 6.36015 | 0.214767 | 0.107383 | − | 0.994218i | \(-0.465753\pi\) | ||||
0.107383 | + | 0.994218i | \(0.465753\pi\) | |||||||
\(878\) | 39.6001 | 1.33644 | ||||||||
\(879\) | 49.1076 | 1.65636 | ||||||||
\(880\) | −20.0814 | −0.676945 | ||||||||
\(881\) | −21.6166 | −0.728280 | −0.364140 | − | 0.931344i | \(-0.618637\pi\) | ||||
−0.364140 | + | 0.931344i | \(0.618637\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.14172 | −0.206685 | −0.103343 | − | 0.994646i | \(-0.532954\pi\) | ||||
−0.103343 | + | 0.994646i | \(0.532954\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 83.5002 | 2.80683 | ||||||||
\(886\) | −14.2462 | −0.478611 | ||||||||
\(887\) | −33.8633 | −1.13702 | −0.568509 | − | 0.822677i | \(-0.692479\pi\) | ||||
−0.568509 | + | 0.822677i | \(0.692479\pi\) | |||||||
\(888\) | 14.1155 | 0.473685 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 18.9455 | 0.635055 | ||||||||
\(891\) | 30.6641 | 1.02729 | ||||||||
\(892\) | 8.27828 | 0.277177 | ||||||||
\(893\) | −68.7018 | −2.29902 | ||||||||
\(894\) | 52.3618 | 1.75124 | ||||||||
\(895\) | −49.6785 | −1.66057 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −70.8778 | −2.36522 | ||||||||
\(899\) | 10.0901 | 0.336524 | ||||||||
\(900\) | 111.692 | 3.72308 | ||||||||
\(901\) | −0.712315 | −0.0237307 | ||||||||
\(902\) | 2.26548 | 0.0754323 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.5278 | −0.383408 | ||||||||
\(905\) | 62.2826 | 2.07034 | ||||||||
\(906\) | −42.9225 | −1.42601 | ||||||||
\(907\) | −12.3172 | −0.408985 | −0.204492 | − | 0.978868i | \(-0.565554\pi\) | ||||
−0.204492 | + | 0.978868i | \(0.565554\pi\) | |||||||
\(908\) | −18.7308 | −0.621603 | ||||||||
\(909\) | 71.1113 | 2.35861 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7667 | 0.588636 | 0.294318 | − | 0.955708i | \(-0.404908\pi\) | ||||
0.294318 | + | 0.955708i | \(0.404908\pi\) | |||||||
\(912\) | −29.9753 | −0.992580 | ||||||||
\(913\) | 37.3040 | 1.23458 | ||||||||
\(914\) | −69.3106 | −2.29259 | ||||||||
\(915\) | −109.658 | −3.62517 | ||||||||
\(916\) | −57.0620 | −1.88538 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 30.2599 | 0.998727 | ||||||||
\(919\) | −24.2474 | −0.799847 | −0.399924 | − | 0.916548i | \(-0.630963\pi\) | ||||
−0.399924 | + | 0.916548i | \(0.630963\pi\) | |||||||
\(920\) | −8.30004 | −0.273644 | ||||||||
\(921\) | 10.5314 | 0.347022 | ||||||||
\(922\) | 19.9575 | 0.657266 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.61799 | −0.217598 | ||||||||
\(926\) | −12.2305 | −0.401920 | ||||||||
\(927\) | −49.5071 | −1.62603 | ||||||||
\(928\) | −16.7211 | −0.548898 | ||||||||
\(929\) | 47.0817 | 1.54470 | 0.772351 | − | 0.635196i | \(-0.219081\pi\) | ||||
0.772351 | + | 0.635196i | \(0.219081\pi\) | |||||||
\(930\) | −47.6862 | −1.56369 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 66.6597 | 2.18351 | ||||||||
\(933\) | −42.7851 | −1.40072 | ||||||||
\(934\) | 95.4086 | 3.12186 | ||||||||
\(935\) | 17.3514 | 0.567450 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.4852 | −0.963240 | −0.481620 | − | 0.876380i | \(-0.659952\pi\) | ||||
−0.481620 | + | 0.876380i | \(0.659952\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.0691 | −0.654930 | ||||||||
\(940\) | −133.543 | −4.35568 | ||||||||
\(941\) | −48.3265 | −1.57540 | −0.787700 | − | 0.616059i | \(-0.788728\pi\) | ||||
−0.787700 | + | 0.616059i | \(0.788728\pi\) | |||||||
\(942\) | 66.2559 | 2.15873 | ||||||||
\(943\) | 0.179136 | 0.00583348 | ||||||||
\(944\) | −14.8180 | −0.482285 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 49.0017 | 1.59318 | ||||||||
\(947\) | 2.72235 | 0.0884645 | 0.0442322 | − | 0.999021i | \(-0.485916\pi\) | ||||
0.0442322 | + | 0.999021i | \(0.485916\pi\) | |||||||
\(948\) | 108.520 | 3.52455 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 73.4608 | 2.38338 | ||||||||
\(951\) | 11.8120 | 0.383031 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.6384 | 1.28402 | 0.642008 | − | 0.766698i | \(-0.278102\pi\) | ||||
0.642008 | + | 0.766698i | \(0.278102\pi\) | |||||||
\(954\) | −6.79793 | −0.220091 | ||||||||
\(955\) | −55.6596 | −1.80110 | ||||||||
\(956\) | −11.8600 | −0.383578 | ||||||||
\(957\) | −52.7887 | −1.70642 | ||||||||
\(958\) | 17.7465 | 0.573365 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 111.503 | 3.59875 | ||||||||
\(961\) | −26.5530 | −0.856548 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 60.8934 | 1.96226 | ||||||||
\(964\) | −47.2280 | −1.52111 | ||||||||
\(965\) | −37.3385 | −1.20197 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.7830 | 0.764810 | 0.382405 | − | 0.923995i | \(-0.375096\pi\) | ||||
0.382405 | + | 0.923995i | \(0.375096\pi\) | |||||||
\(968\) | −9.92105 | −0.318875 | ||||||||
\(969\) | 25.9001 | 0.832032 | ||||||||
\(970\) | 40.0651 | 1.28641 | ||||||||
\(971\) | 37.3407 | 1.19832 | 0.599160 | − | 0.800629i | \(-0.295501\pi\) | ||||
0.599160 | + | 0.800629i | \(0.295501\pi\) | |||||||
\(972\) | −4.96596 | −0.159283 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.9353 | −0.350389 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.4599 | 0.622896 | ||||||||
\(977\) | 50.4817 | 1.61505 | 0.807527 | − | 0.589831i | \(-0.200806\pi\) | ||||
0.807527 | + | 0.589831i | \(0.200806\pi\) | |||||||
\(978\) | 174.206 | 5.57049 | ||||||||
\(979\) | 9.24329 | 0.295417 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 116.912 | 3.73270 | ||||||||
\(982\) | −78.4159 | −2.50235 | ||||||||
\(983\) | −7.90270 | −0.252057 | −0.126028 | − | 0.992027i | \(-0.540223\pi\) | ||||
−0.126028 | + | 0.992027i | \(0.540223\pi\) | |||||||
\(984\) | 2.90921 | 0.0927421 | ||||||||
\(985\) | 19.8427 | 0.632241 | ||||||||
\(986\) | −16.5906 | −0.528352 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.87466 | 0.123207 | ||||||||
\(990\) | 165.591 | 5.26284 | ||||||||
\(991\) | 5.86521 | 0.186315 | 0.0931573 | − | 0.995651i | \(-0.470304\pi\) | ||||
0.0931573 | + | 0.995651i | \(0.470304\pi\) | |||||||
\(992\) | −7.36949 | −0.233981 | ||||||||
\(993\) | −35.2451 | −1.11847 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.3673 | −0.962709 | ||||||||
\(996\) | 108.237 | 3.42962 | ||||||||
\(997\) | 51.3199 | 1.62532 | 0.812659 | − | 0.582740i | \(-0.198019\pi\) | ||||
0.812659 | + | 0.582740i | \(0.198019\pi\) | |||||||
\(998\) | −67.1204 | −2.12466 | ||||||||
\(999\) | −10.9868 | −0.347606 |
(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.cx.1.6 | 32 | ||
7.6 | odd | 2 | inner | 8281.2.a.cx.1.5 | 32 | ||
13.2 | odd | 12 | 637.2.q.j.589.3 | yes | 32 | ||
13.7 | odd | 12 | 637.2.q.j.491.3 | ✓ | 32 | ||
13.12 | even | 2 | inner | 8281.2.a.cx.1.28 | 32 | ||
91.2 | odd | 12 | 637.2.k.j.459.13 | 32 | |||
91.20 | even | 12 | 637.2.q.j.491.4 | yes | 32 | ||
91.33 | even | 12 | 637.2.u.j.361.13 | 32 | |||
91.41 | even | 12 | 637.2.q.j.589.4 | yes | 32 | ||
91.46 | odd | 12 | 637.2.k.j.569.3 | 32 | |||
91.54 | even | 12 | 637.2.k.j.459.14 | 32 | |||
91.59 | even | 12 | 637.2.k.j.569.4 | 32 | |||
91.67 | odd | 12 | 637.2.u.j.30.14 | 32 | |||
91.72 | odd | 12 | 637.2.u.j.361.14 | 32 | |||
91.80 | even | 12 | 637.2.u.j.30.13 | 32 | |||
91.90 | odd | 2 | inner | 8281.2.a.cx.1.27 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.k.j.459.13 | 32 | 91.2 | odd | 12 | |||
637.2.k.j.459.14 | 32 | 91.54 | even | 12 | |||
637.2.k.j.569.3 | 32 | 91.46 | odd | 12 | |||
637.2.k.j.569.4 | 32 | 91.59 | even | 12 | |||
637.2.q.j.491.3 | ✓ | 32 | 13.7 | odd | 12 | ||
637.2.q.j.491.4 | yes | 32 | 91.20 | even | 12 | ||
637.2.q.j.589.3 | yes | 32 | 13.2 | odd | 12 | ||
637.2.q.j.589.4 | yes | 32 | 91.41 | even | 12 | ||
637.2.u.j.30.13 | 32 | 91.80 | even | 12 | |||
637.2.u.j.30.14 | 32 | 91.67 | odd | 12 | |||
637.2.u.j.361.13 | 32 | 91.33 | even | 12 | |||
637.2.u.j.361.14 | 32 | 91.72 | odd | 12 | |||
8281.2.a.cx.1.5 | 32 | 7.6 | odd | 2 | inner | ||
8281.2.a.cx.1.6 | 32 | 1.1 | even | 1 | trivial | ||
8281.2.a.cx.1.27 | 32 | 91.90 | odd | 2 | inner | ||
8281.2.a.cx.1.28 | 32 | 13.12 | even | 2 | inner |