Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(0\) |
Dimension: | \(186\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.39579 | −1.69408 | −0.847039 | − | 0.531530i | \(-0.821617\pi\) | ||||
−0.847039 | + | 0.531530i | \(0.821617\pi\) | |||||||
\(3\) | 3.13150 | 1.80797 | 0.903987 | − | 0.427560i | \(-0.140627\pi\) | ||||
0.903987 | + | 0.427560i | \(0.140627\pi\) | |||||||
\(4\) | 3.73980 | 1.86990 | ||||||||
\(5\) | 0.529965 | 0.237008 | 0.118504 | − | 0.992954i | \(-0.462190\pi\) | ||||
0.118504 | + | 0.992954i | \(0.462190\pi\) | |||||||
\(6\) | −7.50242 | −3.06285 | ||||||||
\(7\) | −1.46029 | −0.551938 | −0.275969 | − | 0.961167i | \(-0.588999\pi\) | ||||
−0.275969 | + | 0.961167i | \(0.588999\pi\) | |||||||
\(8\) | −4.16820 | −1.47368 | ||||||||
\(9\) | 6.80631 | 2.26877 | ||||||||
\(10\) | −1.26968 | −0.401510 | ||||||||
\(11\) | 4.42489 | 1.33415 | 0.667077 | − | 0.744989i | \(-0.267545\pi\) | ||||
0.667077 | + | 0.744989i | \(0.267545\pi\) | |||||||
\(12\) | 11.7112 | 3.38073 | ||||||||
\(13\) | 6.46275 | 1.79244 | 0.896222 | − | 0.443606i | \(-0.146301\pi\) | ||||
0.896222 | + | 0.443606i | \(0.146301\pi\) | |||||||
\(14\) | 3.49855 | 0.935027 | ||||||||
\(15\) | 1.65959 | 0.428504 | ||||||||
\(16\) | 2.50652 | 0.626631 | ||||||||
\(17\) | 1.71135 | 0.415064 | 0.207532 | − | 0.978228i | \(-0.433457\pi\) | ||||
0.207532 | + | 0.978228i | \(0.433457\pi\) | |||||||
\(18\) | −16.3065 | −3.84348 | ||||||||
\(19\) | −1.59807 | −0.366622 | −0.183311 | − | 0.983055i | \(-0.558682\pi\) | ||||
−0.183311 | + | 0.983055i | \(0.558682\pi\) | |||||||
\(20\) | 1.98197 | 0.443181 | ||||||||
\(21\) | −4.57291 | −0.997890 | ||||||||
\(22\) | −10.6011 | −2.26016 | ||||||||
\(23\) | 5.85306 | 1.22045 | 0.610223 | − | 0.792229i | \(-0.291080\pi\) | ||||
0.610223 | + | 0.792229i | \(0.291080\pi\) | |||||||
\(24\) | −13.0527 | −2.66438 | ||||||||
\(25\) | −4.71914 | −0.943827 | ||||||||
\(26\) | −15.4834 | −3.03654 | ||||||||
\(27\) | 11.9195 | 2.29391 | ||||||||
\(28\) | −5.46120 | −1.03207 | ||||||||
\(29\) | −6.42396 | −1.19290 | −0.596450 | − | 0.802651i | \(-0.703422\pi\) | ||||
−0.596450 | + | 0.802651i | \(0.703422\pi\) | |||||||
\(30\) | −3.97602 | −0.725919 | ||||||||
\(31\) | −2.54140 | −0.456449 | −0.228225 | − | 0.973608i | \(-0.573292\pi\) | ||||
−0.228225 | + | 0.973608i | \(0.573292\pi\) | |||||||
\(32\) | 2.33130 | 0.412120 | ||||||||
\(33\) | 13.8565 | 2.41211 | ||||||||
\(34\) | −4.10004 | −0.703151 | ||||||||
\(35\) | −0.773904 | −0.130814 | ||||||||
\(36\) | 25.4543 | 4.24238 | ||||||||
\(37\) | 7.82017 | 1.28563 | 0.642814 | − | 0.766022i | \(-0.277767\pi\) | ||||
0.642814 | + | 0.766022i | \(0.277767\pi\) | |||||||
\(38\) | 3.82864 | 0.621087 | ||||||||
\(39\) | 20.2381 | 3.24069 | ||||||||
\(40\) | −2.20900 | −0.349274 | ||||||||
\(41\) | 12.2992 | 1.92081 | 0.960405 | − | 0.278607i | \(-0.0898728\pi\) | ||||
0.960405 | + | 0.278607i | \(0.0898728\pi\) | |||||||
\(42\) | 10.9557 | 1.69050 | ||||||||
\(43\) | −2.30731 | −0.351861 | −0.175931 | − | 0.984403i | \(-0.556293\pi\) | ||||
−0.175931 | + | 0.984403i | \(0.556293\pi\) | |||||||
\(44\) | 16.5482 | 2.49474 | ||||||||
\(45\) | 3.60711 | 0.537716 | ||||||||
\(46\) | −14.0227 | −2.06753 | ||||||||
\(47\) | −1.76939 | −0.258092 | −0.129046 | − | 0.991639i | \(-0.541192\pi\) | ||||
−0.129046 | + | 0.991639i | \(0.541192\pi\) | |||||||
\(48\) | 7.84919 | 1.13293 | ||||||||
\(49\) | −4.86755 | −0.695364 | ||||||||
\(50\) | 11.3061 | 1.59892 | ||||||||
\(51\) | 5.35911 | 0.750425 | ||||||||
\(52\) | 24.1694 | 3.35169 | ||||||||
\(53\) | −0.795921 | −0.109328 | −0.0546641 | − | 0.998505i | \(-0.517409\pi\) | ||||
−0.0546641 | + | 0.998505i | \(0.517409\pi\) | |||||||
\(54\) | −28.5566 | −3.88606 | ||||||||
\(55\) | 2.34504 | 0.316205 | ||||||||
\(56\) | 6.08679 | 0.813381 | ||||||||
\(57\) | −5.00436 | −0.662844 | ||||||||
\(58\) | 15.3904 | 2.02086 | ||||||||
\(59\) | −14.9641 | −1.94817 | −0.974083 | − | 0.226191i | \(-0.927373\pi\) | ||||
−0.974083 | + | 0.226191i | \(0.927373\pi\) | |||||||
\(60\) | 6.20653 | 0.801260 | ||||||||
\(61\) | 12.9958 | 1.66394 | 0.831968 | − | 0.554824i | \(-0.187214\pi\) | ||||
0.831968 | + | 0.554824i | \(0.187214\pi\) | |||||||
\(62\) | 6.08866 | 0.773261 | ||||||||
\(63\) | −9.93920 | −1.25222 | ||||||||
\(64\) | −10.5984 | −1.32479 | ||||||||
\(65\) | 3.42503 | 0.424823 | ||||||||
\(66\) | −33.1974 | −4.08631 | ||||||||
\(67\) | 12.9765 | 1.58534 | 0.792668 | − | 0.609653i | \(-0.208691\pi\) | ||||
0.792668 | + | 0.609653i | \(0.208691\pi\) | |||||||
\(68\) | 6.40012 | 0.776129 | ||||||||
\(69\) | 18.3289 | 2.20654 | ||||||||
\(70\) | 1.85411 | 0.221608 | ||||||||
\(71\) | −9.51351 | −1.12905 | −0.564523 | − | 0.825417i | \(-0.690940\pi\) | ||||
−0.564523 | + | 0.825417i | \(0.690940\pi\) | |||||||
\(72\) | −28.3701 | −3.34345 | ||||||||
\(73\) | −0.209957 | −0.0245737 | −0.0122868 | − | 0.999925i | \(-0.503911\pi\) | ||||
−0.0122868 | + | 0.999925i | \(0.503911\pi\) | |||||||
\(74\) | −18.7355 | −2.17795 | ||||||||
\(75\) | −14.7780 | −1.70642 | ||||||||
\(76\) | −5.97647 | −0.685548 | ||||||||
\(77\) | −6.46162 | −0.736370 | ||||||||
\(78\) | −48.4862 | −5.48999 | ||||||||
\(79\) | −5.60830 | −0.630983 | −0.315492 | − | 0.948928i | \(-0.602169\pi\) | ||||
−0.315492 | + | 0.948928i | \(0.602169\pi\) | |||||||
\(80\) | 1.32837 | 0.148516 | ||||||||
\(81\) | 16.9070 | 1.87855 | ||||||||
\(82\) | −29.4663 | −3.25400 | ||||||||
\(83\) | −6.61460 | −0.726047 | −0.363023 | − | 0.931780i | \(-0.618255\pi\) | ||||
−0.363023 | + | 0.931780i | \(0.618255\pi\) | |||||||
\(84\) | −17.1018 | −1.86596 | ||||||||
\(85\) | 0.906958 | 0.0983734 | ||||||||
\(86\) | 5.52782 | 0.596080 | ||||||||
\(87\) | −20.1166 | −2.15673 | ||||||||
\(88\) | −18.4438 | −1.96612 | ||||||||
\(89\) | −9.99098 | −1.05904 | −0.529521 | − | 0.848297i | \(-0.677628\pi\) | ||||
−0.529521 | + | 0.848297i | \(0.677628\pi\) | |||||||
\(90\) | −8.64187 | −0.910933 | ||||||||
\(91\) | −9.43749 | −0.989318 | ||||||||
\(92\) | 21.8893 | 2.28212 | ||||||||
\(93\) | −7.95841 | −0.825249 | ||||||||
\(94\) | 4.23909 | 0.437228 | ||||||||
\(95\) | −0.846921 | −0.0868923 | ||||||||
\(96\) | 7.30048 | 0.745102 | ||||||||
\(97\) | −5.09962 | −0.517788 | −0.258894 | − | 0.965906i | \(-0.583358\pi\) | ||||
−0.258894 | + | 0.965906i | \(0.583358\pi\) | |||||||
\(98\) | 11.6616 | 1.17800 | ||||||||
\(99\) | 30.1172 | 3.02689 | ||||||||
\(100\) | −17.6486 | −1.76486 | ||||||||
\(101\) | −6.38324 | −0.635156 | −0.317578 | − | 0.948232i | \(-0.602870\pi\) | ||||
−0.317578 | + | 0.948232i | \(0.602870\pi\) | |||||||
\(102\) | −12.8393 | −1.27128 | ||||||||
\(103\) | 1.54634 | 0.152365 | 0.0761826 | − | 0.997094i | \(-0.475727\pi\) | ||||
0.0761826 | + | 0.997094i | \(0.475727\pi\) | |||||||
\(104\) | −26.9380 | −2.64149 | ||||||||
\(105\) | −2.42348 | −0.236508 | ||||||||
\(106\) | 1.90686 | 0.185211 | ||||||||
\(107\) | 17.1517 | 1.65812 | 0.829060 | − | 0.559160i | \(-0.188876\pi\) | ||||
0.829060 | + | 0.559160i | \(0.188876\pi\) | |||||||
\(108\) | 44.5765 | 4.28938 | ||||||||
\(109\) | 15.1280 | 1.44900 | 0.724499 | − | 0.689276i | \(-0.242071\pi\) | ||||
0.724499 | + | 0.689276i | \(0.242071\pi\) | |||||||
\(110\) | −5.61821 | −0.535675 | ||||||||
\(111\) | 24.4889 | 2.32438 | ||||||||
\(112\) | −3.66025 | −0.345862 | ||||||||
\(113\) | −6.23685 | −0.586714 | −0.293357 | − | 0.956003i | \(-0.594772\pi\) | ||||
−0.293357 | + | 0.956003i | \(0.594772\pi\) | |||||||
\(114\) | 11.9894 | 1.12291 | ||||||||
\(115\) | 3.10192 | 0.289255 | ||||||||
\(116\) | −24.0243 | −2.23060 | ||||||||
\(117\) | 43.9875 | 4.06664 | ||||||||
\(118\) | 35.8509 | 3.30035 | ||||||||
\(119\) | −2.49907 | −0.229090 | ||||||||
\(120\) | −6.91750 | −0.631478 | ||||||||
\(121\) | 8.57962 | 0.779965 | ||||||||
\(122\) | −31.1351 | −2.81884 | ||||||||
\(123\) | 38.5149 | 3.47278 | ||||||||
\(124\) | −9.50435 | −0.853515 | ||||||||
\(125\) | −5.15081 | −0.460702 | ||||||||
\(126\) | 23.8122 | 2.12136 | ||||||||
\(127\) | −6.93786 | −0.615635 | −0.307818 | − | 0.951445i | \(-0.599599\pi\) | ||||
−0.307818 | + | 0.951445i | \(0.599599\pi\) | |||||||
\(128\) | 20.7288 | 1.83219 | ||||||||
\(129\) | −7.22534 | −0.636156 | ||||||||
\(130\) | −8.20565 | −0.719683 | ||||||||
\(131\) | −12.7954 | −1.11794 | −0.558969 | − | 0.829188i | \(-0.688803\pi\) | ||||
−0.558969 | + | 0.829188i | \(0.688803\pi\) | |||||||
\(132\) | 51.8208 | 4.51042 | ||||||||
\(133\) | 2.33365 | 0.202353 | ||||||||
\(134\) | −31.0890 | −2.68568 | ||||||||
\(135\) | 6.31691 | 0.543673 | ||||||||
\(136\) | −7.13326 | −0.611672 | ||||||||
\(137\) | −5.68126 | −0.485383 | −0.242692 | − | 0.970104i | \(-0.578030\pi\) | ||||
−0.242692 | + | 0.970104i | \(0.578030\pi\) | |||||||
\(138\) | −43.9121 | −3.73805 | ||||||||
\(139\) | −5.61317 | −0.476103 | −0.238051 | − | 0.971253i | \(-0.576509\pi\) | ||||
−0.238051 | + | 0.971253i | \(0.576509\pi\) | |||||||
\(140\) | −2.89425 | −0.244609 | ||||||||
\(141\) | −5.54085 | −0.466624 | ||||||||
\(142\) | 22.7924 | 1.91269 | ||||||||
\(143\) | 28.5969 | 2.39139 | ||||||||
\(144\) | 17.0602 | 1.42168 | ||||||||
\(145\) | −3.40448 | −0.282726 | ||||||||
\(146\) | 0.503014 | 0.0416297 | ||||||||
\(147\) | −15.2427 | −1.25720 | ||||||||
\(148\) | 29.2459 | 2.40400 | ||||||||
\(149\) | −8.32032 | −0.681627 | −0.340814 | − | 0.940131i | \(-0.610703\pi\) | ||||
−0.340814 | + | 0.940131i | \(0.610703\pi\) | |||||||
\(150\) | 35.4049 | 2.89080 | ||||||||
\(151\) | −2.37678 | −0.193419 | −0.0967097 | − | 0.995313i | \(-0.530832\pi\) | ||||
−0.0967097 | + | 0.995313i | \(0.530832\pi\) | |||||||
\(152\) | 6.66108 | 0.540285 | ||||||||
\(153\) | 11.6480 | 0.941685 | ||||||||
\(154\) | 15.4807 | 1.24747 | ||||||||
\(155\) | −1.34686 | −0.108182 | ||||||||
\(156\) | 75.6866 | 6.05978 | ||||||||
\(157\) | −19.7733 | −1.57808 | −0.789042 | − | 0.614339i | \(-0.789423\pi\) | ||||
−0.789042 | + | 0.614339i | \(0.789423\pi\) | |||||||
\(158\) | 13.4363 | 1.06893 | ||||||||
\(159\) | −2.49243 | −0.197663 | ||||||||
\(160\) | 1.23551 | 0.0976756 | ||||||||
\(161\) | −8.54717 | −0.673611 | ||||||||
\(162\) | −40.5055 | −3.18241 | ||||||||
\(163\) | −15.5566 | −1.21848 | −0.609242 | − | 0.792984i | \(-0.708526\pi\) | ||||
−0.609242 | + | 0.792984i | \(0.708526\pi\) | |||||||
\(164\) | 45.9965 | 3.59173 | ||||||||
\(165\) | 7.34349 | 0.571690 | ||||||||
\(166\) | 15.8472 | 1.22998 | ||||||||
\(167\) | 6.56436 | 0.507965 | 0.253983 | − | 0.967209i | \(-0.418259\pi\) | ||||
0.253983 | + | 0.967209i | \(0.418259\pi\) | |||||||
\(168\) | 19.0608 | 1.47057 | ||||||||
\(169\) | 28.7671 | 2.21285 | ||||||||
\(170\) | −2.17288 | −0.166652 | ||||||||
\(171\) | −10.8770 | −0.831782 | ||||||||
\(172\) | −8.62888 | −0.657946 | ||||||||
\(173\) | −8.26455 | −0.628342 | −0.314171 | − | 0.949366i | \(-0.601727\pi\) | ||||
−0.314171 | + | 0.949366i | \(0.601727\pi\) | |||||||
\(174\) | 48.1952 | 3.65367 | ||||||||
\(175\) | 6.89131 | 0.520934 | ||||||||
\(176\) | 11.0911 | 0.836022 | ||||||||
\(177\) | −46.8603 | −3.52223 | ||||||||
\(178\) | 23.9363 | 1.79410 | ||||||||
\(179\) | −19.9138 | −1.48843 | −0.744214 | − | 0.667941i | \(-0.767176\pi\) | ||||
−0.744214 | + | 0.667941i | \(0.767176\pi\) | |||||||
\(180\) | 13.4899 | 1.00548 | ||||||||
\(181\) | 19.8840 | 1.47797 | 0.738985 | − | 0.673722i | \(-0.235306\pi\) | ||||
0.738985 | + | 0.673722i | \(0.235306\pi\) | |||||||
\(182\) | 22.6102 | 1.67598 | ||||||||
\(183\) | 40.6963 | 3.00835 | ||||||||
\(184\) | −24.3967 | −1.79855 | ||||||||
\(185\) | 4.14442 | 0.304704 | ||||||||
\(186\) | 19.0667 | 1.39804 | ||||||||
\(187\) | 7.57254 | 0.553759 | ||||||||
\(188\) | −6.61718 | −0.482607 | ||||||||
\(189\) | −17.4059 | −1.26609 | ||||||||
\(190\) | 2.02904 | 0.147202 | ||||||||
\(191\) | 5.33729 | 0.386193 | 0.193096 | − | 0.981180i | \(-0.438147\pi\) | ||||
0.193096 | + | 0.981180i | \(0.438147\pi\) | |||||||
\(192\) | −33.1888 | −2.39519 | ||||||||
\(193\) | 14.1630 | 1.01948 | 0.509738 | − | 0.860330i | \(-0.329742\pi\) | ||||
0.509738 | + | 0.860330i | \(0.329742\pi\) | |||||||
\(194\) | 12.2176 | 0.877174 | ||||||||
\(195\) | 10.7255 | 0.768069 | ||||||||
\(196\) | −18.2037 | −1.30026 | ||||||||
\(197\) | −8.88875 | −0.633297 | −0.316649 | − | 0.948543i | \(-0.602558\pi\) | ||||
−0.316649 | + | 0.948543i | \(0.602558\pi\) | |||||||
\(198\) | −72.1544 | −5.12779 | ||||||||
\(199\) | 19.0844 | 1.35286 | 0.676429 | − | 0.736508i | \(-0.263527\pi\) | ||||
0.676429 | + | 0.736508i | \(0.263527\pi\) | |||||||
\(200\) | 19.6703 | 1.39090 | ||||||||
\(201\) | 40.6361 | 2.86625 | ||||||||
\(202\) | 15.2929 | 1.07600 | ||||||||
\(203\) | 9.38085 | 0.658407 | ||||||||
\(204\) | 20.0420 | 1.40322 | ||||||||
\(205\) | 6.51814 | 0.455247 | ||||||||
\(206\) | −3.70470 | −0.258119 | ||||||||
\(207\) | 39.8377 | 2.76891 | ||||||||
\(208\) | 16.1990 | 1.12320 | ||||||||
\(209\) | −7.07128 | −0.489130 | ||||||||
\(210\) | 5.80615 | 0.400662 | ||||||||
\(211\) | 10.0373 | 0.690994 | 0.345497 | − | 0.938420i | \(-0.387710\pi\) | ||||
0.345497 | + | 0.938420i | \(0.387710\pi\) | |||||||
\(212\) | −2.97659 | −0.204433 | ||||||||
\(213\) | −29.7916 | −2.04129 | ||||||||
\(214\) | −41.0919 | −2.80899 | ||||||||
\(215\) | −1.22279 | −0.0833938 | ||||||||
\(216\) | −49.6828 | −3.38049 | ||||||||
\(217\) | 3.71119 | 0.251932 | ||||||||
\(218\) | −36.2434 | −2.45472 | ||||||||
\(219\) | −0.657482 | −0.0444285 | ||||||||
\(220\) | 8.76997 | 0.591272 | ||||||||
\(221\) | 11.0600 | 0.743979 | ||||||||
\(222\) | −58.6702 | −3.93769 | ||||||||
\(223\) | −1.53730 | −0.102945 | −0.0514725 | − | 0.998674i | \(-0.516391\pi\) | ||||
−0.0514725 | + | 0.998674i | \(0.516391\pi\) | |||||||
\(224\) | −3.40438 | −0.227465 | ||||||||
\(225\) | −32.1199 | −2.14133 | ||||||||
\(226\) | 14.9422 | 0.993939 | ||||||||
\(227\) | 25.0467 | 1.66240 | 0.831202 | − | 0.555970i | \(-0.187653\pi\) | ||||
0.831202 | + | 0.555970i | \(0.187653\pi\) | |||||||
\(228\) | −18.7153 | −1.23945 | ||||||||
\(229\) | −10.0343 | −0.663086 | −0.331543 | − | 0.943440i | \(-0.607569\pi\) | ||||
−0.331543 | + | 0.943440i | \(0.607569\pi\) | |||||||
\(230\) | −7.43154 | −0.490021 | ||||||||
\(231\) | −20.2346 | −1.33134 | ||||||||
\(232\) | 26.7764 | 1.75795 | ||||||||
\(233\) | −7.48980 | −0.490673 | −0.245337 | − | 0.969438i | \(-0.578898\pi\) | ||||
−0.245337 | + | 0.969438i | \(0.578898\pi\) | |||||||
\(234\) | −105.385 | −6.88921 | ||||||||
\(235\) | −0.937716 | −0.0611698 | ||||||||
\(236\) | −55.9630 | −3.64288 | ||||||||
\(237\) | −17.5624 | −1.14080 | ||||||||
\(238\) | 5.98725 | 0.388096 | ||||||||
\(239\) | −18.1515 | −1.17412 | −0.587062 | − | 0.809542i | \(-0.699716\pi\) | ||||
−0.587062 | + | 0.809542i | \(0.699716\pi\) | |||||||
\(240\) | 4.15980 | 0.268514 | ||||||||
\(241\) | 22.0854 | 1.42265 | 0.711323 | − | 0.702866i | \(-0.248097\pi\) | ||||
0.711323 | + | 0.702866i | \(0.248097\pi\) | |||||||
\(242\) | −20.5550 | −1.32132 | ||||||||
\(243\) | 17.1857 | 1.10247 | ||||||||
\(244\) | 48.6016 | 3.11140 | ||||||||
\(245\) | −2.57963 | −0.164807 | ||||||||
\(246\) | −92.2737 | −5.88315 | ||||||||
\(247\) | −10.3279 | −0.657150 | ||||||||
\(248\) | 10.5931 | 0.672661 | ||||||||
\(249\) | −20.7136 | −1.31267 | ||||||||
\(250\) | 12.3402 | 0.780465 | ||||||||
\(251\) | 6.25714 | 0.394947 | 0.197473 | − | 0.980308i | \(-0.436726\pi\) | ||||
0.197473 | + | 0.980308i | \(0.436726\pi\) | |||||||
\(252\) | −37.1706 | −2.34153 | ||||||||
\(253\) | 25.8991 | 1.62826 | ||||||||
\(254\) | 16.6216 | 1.04293 | ||||||||
\(255\) | 2.84014 | 0.177857 | ||||||||
\(256\) | −28.4652 | −1.77907 | ||||||||
\(257\) | 2.16060 | 0.134775 | 0.0673874 | − | 0.997727i | \(-0.478534\pi\) | ||||
0.0673874 | + | 0.997727i | \(0.478534\pi\) | |||||||
\(258\) | 17.3104 | 1.07770 | ||||||||
\(259\) | −11.4197 | −0.709587 | ||||||||
\(260\) | 12.8089 | 0.794377 | ||||||||
\(261\) | −43.7235 | −2.70642 | ||||||||
\(262\) | 30.6551 | 1.89388 | ||||||||
\(263\) | −0.965852 | −0.0595570 | −0.0297785 | − | 0.999557i | \(-0.509480\pi\) | ||||
−0.0297785 | + | 0.999557i | \(0.509480\pi\) | |||||||
\(264\) | −57.7569 | −3.55469 | ||||||||
\(265\) | −0.421811 | −0.0259116 | ||||||||
\(266\) | −5.59093 | −0.342802 | ||||||||
\(267\) | −31.2868 | −1.91472 | ||||||||
\(268\) | 48.5297 | 2.96442 | ||||||||
\(269\) | −14.7866 | −0.901552 | −0.450776 | − | 0.892637i | \(-0.648853\pi\) | ||||
−0.450776 | + | 0.892637i | \(0.648853\pi\) | |||||||
\(270\) | −15.1340 | −0.921025 | ||||||||
\(271\) | 14.8258 | 0.900602 | 0.450301 | − | 0.892877i | \(-0.351317\pi\) | ||||
0.450301 | + | 0.892877i | \(0.351317\pi\) | |||||||
\(272\) | 4.28955 | 0.260092 | ||||||||
\(273\) | −29.5535 | −1.78866 | ||||||||
\(274\) | 13.6111 | 0.822277 | ||||||||
\(275\) | −20.8816 | −1.25921 | ||||||||
\(276\) | 68.5464 | 4.12601 | ||||||||
\(277\) | 12.8112 | 0.769748 | 0.384874 | − | 0.922969i | \(-0.374245\pi\) | ||||
0.384874 | + | 0.922969i | \(0.374245\pi\) | |||||||
\(278\) | 13.4480 | 0.806555 | ||||||||
\(279\) | −17.2976 | −1.03558 | ||||||||
\(280\) | 3.22579 | 0.192778 | ||||||||
\(281\) | 20.9247 | 1.24826 | 0.624131 | − | 0.781320i | \(-0.285453\pi\) | ||||
0.624131 | + | 0.781320i | \(0.285453\pi\) | |||||||
\(282\) | 13.2747 | 0.790498 | ||||||||
\(283\) | −20.7712 | −1.23472 | −0.617360 | − | 0.786680i | \(-0.711798\pi\) | ||||
−0.617360 | + | 0.786680i | \(0.711798\pi\) | |||||||
\(284\) | −35.5787 | −2.11121 | ||||||||
\(285\) | −2.65214 | −0.157099 | ||||||||
\(286\) | −68.5122 | −4.05121 | ||||||||
\(287\) | −17.9604 | −1.06017 | ||||||||
\(288\) | 15.8676 | 0.935006 | ||||||||
\(289\) | −14.0713 | −0.827722 | ||||||||
\(290\) | 8.15640 | 0.478960 | ||||||||
\(291\) | −15.9695 | −0.936148 | ||||||||
\(292\) | −0.785200 | −0.0459503 | ||||||||
\(293\) | 20.2046 | 1.18036 | 0.590182 | − | 0.807270i | \(-0.299056\pi\) | ||||
0.590182 | + | 0.807270i | \(0.299056\pi\) | |||||||
\(294\) | 36.5184 | 2.12980 | ||||||||
\(295\) | −7.93048 | −0.461730 | ||||||||
\(296\) | −32.5961 | −1.89461 | ||||||||
\(297\) | 52.7423 | 3.06042 | ||||||||
\(298\) | 19.9337 | 1.15473 | ||||||||
\(299\) | 37.8268 | 2.18758 | ||||||||
\(300\) | −55.2668 | −3.19083 | ||||||||
\(301\) | 3.36934 | 0.194206 | ||||||||
\(302\) | 5.69426 | 0.327668 | ||||||||
\(303\) | −19.9891 | −1.14835 | ||||||||
\(304\) | −4.00560 | −0.229737 | ||||||||
\(305\) | 6.88730 | 0.394366 | ||||||||
\(306\) | −27.9062 | −1.59529 | ||||||||
\(307\) | −32.6732 | −1.86476 | −0.932379 | − | 0.361483i | \(-0.882270\pi\) | ||||
−0.932379 | + | 0.361483i | \(0.882270\pi\) | |||||||
\(308\) | −24.1652 | −1.37694 | ||||||||
\(309\) | 4.84237 | 0.275473 | ||||||||
\(310\) | 3.22678 | 0.183269 | ||||||||
\(311\) | −16.3018 | −0.924393 | −0.462197 | − | 0.886778i | \(-0.652939\pi\) | ||||
−0.462197 | + | 0.886778i | \(0.652939\pi\) | |||||||
\(312\) | −84.3566 | −4.77575 | ||||||||
\(313\) | −17.3529 | −0.980843 | −0.490422 | − | 0.871485i | \(-0.663157\pi\) | ||||
−0.490422 | + | 0.871485i | \(0.663157\pi\) | |||||||
\(314\) | 47.3727 | 2.67340 | ||||||||
\(315\) | −5.26743 | −0.296786 | ||||||||
\(316\) | −20.9739 | −1.17988 | ||||||||
\(317\) | −14.9627 | −0.840390 | −0.420195 | − | 0.907434i | \(-0.638038\pi\) | ||||
−0.420195 | + | 0.907434i | \(0.638038\pi\) | |||||||
\(318\) | 5.97134 | 0.334856 | ||||||||
\(319\) | −28.4253 | −1.59151 | ||||||||
\(320\) | −5.61676 | −0.313986 | ||||||||
\(321\) | 53.7107 | 2.99784 | ||||||||
\(322\) | 20.4772 | 1.14115 | ||||||||
\(323\) | −2.73486 | −0.152172 | ||||||||
\(324\) | 63.2287 | 3.51271 | ||||||||
\(325\) | −30.4986 | −1.69176 | ||||||||
\(326\) | 37.2702 | 2.06421 | ||||||||
\(327\) | 47.3733 | 2.61975 | ||||||||
\(328\) | −51.2655 | −2.83066 | ||||||||
\(329\) | 2.58383 | 0.142451 | ||||||||
\(330\) | −17.5934 | −0.968487 | ||||||||
\(331\) | 25.2940 | 1.39028 | 0.695141 | − | 0.718874i | \(-0.255342\pi\) | ||||
0.695141 | + | 0.718874i | \(0.255342\pi\) | |||||||
\(332\) | −24.7373 | −1.35764 | ||||||||
\(333\) | 53.2265 | 2.91680 | ||||||||
\(334\) | −15.7268 | −0.860533 | ||||||||
\(335\) | 6.87711 | 0.375737 | ||||||||
\(336\) | −11.4621 | −0.625309 | ||||||||
\(337\) | 22.1697 | 1.20766 | 0.603831 | − | 0.797112i | \(-0.293640\pi\) | ||||
0.603831 | + | 0.797112i | \(0.293640\pi\) | |||||||
\(338\) | −68.9199 | −3.74875 | ||||||||
\(339\) | −19.5307 | −1.06076 | ||||||||
\(340\) | 3.39184 | 0.183949 | ||||||||
\(341\) | −11.2454 | −0.608973 | ||||||||
\(342\) | 26.0589 | 1.40910 | ||||||||
\(343\) | 17.3301 | 0.935736 | ||||||||
\(344\) | 9.61733 | 0.518531 | ||||||||
\(345\) | 9.71366 | 0.522966 | ||||||||
\(346\) | 19.8001 | 1.06446 | ||||||||
\(347\) | −25.0865 | −1.34671 | −0.673357 | − | 0.739318i | \(-0.735148\pi\) | ||||
−0.673357 | + | 0.739318i | \(0.735148\pi\) | |||||||
\(348\) | −75.2323 | −4.03288 | ||||||||
\(349\) | 19.9923 | 1.07017 | 0.535083 | − | 0.844800i | \(-0.320281\pi\) | ||||
0.535083 | + | 0.844800i | \(0.320281\pi\) | |||||||
\(350\) | −16.5101 | −0.882504 | ||||||||
\(351\) | 77.0326 | 4.11170 | ||||||||
\(352\) | 10.3157 | 0.549831 | ||||||||
\(353\) | −2.44246 | −0.129999 | −0.0649995 | − | 0.997885i | \(-0.520705\pi\) | ||||
−0.0649995 | + | 0.997885i | \(0.520705\pi\) | |||||||
\(354\) | 112.267 | 5.96694 | ||||||||
\(355\) | −5.04183 | −0.267593 | ||||||||
\(356\) | −37.3643 | −1.98030 | ||||||||
\(357\) | −7.82586 | −0.414188 | ||||||||
\(358\) | 47.7093 | 2.52151 | ||||||||
\(359\) | −13.4527 | −0.710007 | −0.355003 | − | 0.934865i | \(-0.615520\pi\) | ||||
−0.355003 | + | 0.934865i | \(0.615520\pi\) | |||||||
\(360\) | −15.0352 | −0.792423 | ||||||||
\(361\) | −16.4462 | −0.865588 | ||||||||
\(362\) | −47.6380 | −2.50380 | ||||||||
\(363\) | 26.8671 | 1.41016 | ||||||||
\(364\) | −35.2944 | −1.84993 | ||||||||
\(365\) | −0.111270 | −0.00582415 | ||||||||
\(366\) | −97.4996 | −5.09639 | ||||||||
\(367\) | 7.25487 | 0.378701 | 0.189351 | − | 0.981910i | \(-0.439362\pi\) | ||||
0.189351 | + | 0.981910i | \(0.439362\pi\) | |||||||
\(368\) | 14.6708 | 0.764770 | ||||||||
\(369\) | 83.7121 | 4.35788 | ||||||||
\(370\) | −9.92915 | −0.516192 | ||||||||
\(371\) | 1.16228 | 0.0603424 | ||||||||
\(372\) | −29.7629 | −1.54313 | ||||||||
\(373\) | 1.38444 | 0.0716837 | 0.0358419 | − | 0.999357i | \(-0.488589\pi\) | ||||
0.0358419 | + | 0.999357i | \(0.488589\pi\) | |||||||
\(374\) | −18.1422 | −0.938111 | ||||||||
\(375\) | −16.1298 | −0.832937 | ||||||||
\(376\) | 7.37518 | 0.380346 | ||||||||
\(377\) | −41.5164 | −2.13820 | ||||||||
\(378\) | 41.7009 | 2.14486 | ||||||||
\(379\) | 26.1572 | 1.34360 | 0.671802 | − | 0.740730i | \(-0.265520\pi\) | ||||
0.671802 | + | 0.740730i | \(0.265520\pi\) | |||||||
\(380\) | −3.16732 | −0.162480 | ||||||||
\(381\) | −21.7259 | −1.11305 | ||||||||
\(382\) | −12.7870 | −0.654241 | ||||||||
\(383\) | −10.8836 | −0.556125 | −0.278063 | − | 0.960563i | \(-0.589692\pi\) | ||||
−0.278063 | + | 0.960563i | \(0.589692\pi\) | |||||||
\(384\) | 64.9124 | 3.31254 | ||||||||
\(385\) | −3.42444 | −0.174525 | ||||||||
\(386\) | −33.9316 | −1.72707 | ||||||||
\(387\) | −15.7043 | −0.798292 | ||||||||
\(388\) | −19.0716 | −0.968213 | ||||||||
\(389\) | 34.1828 | 1.73314 | 0.866569 | − | 0.499057i | \(-0.166320\pi\) | ||||
0.866569 | + | 0.499057i | \(0.166320\pi\) | |||||||
\(390\) | −25.6960 | −1.30117 | ||||||||
\(391\) | 10.0166 | 0.506564 | ||||||||
\(392\) | 20.2889 | 1.02475 | ||||||||
\(393\) | −40.0688 | −2.02120 | ||||||||
\(394\) | 21.2956 | 1.07286 | ||||||||
\(395\) | −2.97220 | −0.149548 | ||||||||
\(396\) | 112.632 | 5.65998 | ||||||||
\(397\) | 24.3851 | 1.22386 | 0.611928 | − | 0.790914i | \(-0.290394\pi\) | ||||
0.611928 | + | 0.790914i | \(0.290394\pi\) | |||||||
\(398\) | −45.7222 | −2.29185 | ||||||||
\(399\) | 7.30782 | 0.365849 | ||||||||
\(400\) | −11.8286 | −0.591431 | ||||||||
\(401\) | 10.9896 | 0.548796 | 0.274398 | − | 0.961616i | \(-0.411521\pi\) | ||||
0.274398 | + | 0.961616i | \(0.411521\pi\) | |||||||
\(402\) | −97.3554 | −4.85565 | ||||||||
\(403\) | −16.4244 | −0.818160 | ||||||||
\(404\) | −23.8721 | −1.18768 | ||||||||
\(405\) | 8.96010 | 0.445231 | ||||||||
\(406\) | −22.4745 | −1.11539 | ||||||||
\(407\) | 34.6034 | 1.71523 | ||||||||
\(408\) | −22.3378 | −1.10589 | ||||||||
\(409\) | 10.3479 | 0.511670 | 0.255835 | − | 0.966720i | \(-0.417650\pi\) | ||||
0.255835 | + | 0.966720i | \(0.417650\pi\) | |||||||
\(410\) | −15.6161 | −0.771224 | ||||||||
\(411\) | −17.7909 | −0.877560 | ||||||||
\(412\) | 5.78300 | 0.284908 | ||||||||
\(413\) | 21.8520 | 1.07527 | ||||||||
\(414\) | −95.4428 | −4.69076 | ||||||||
\(415\) | −3.50551 | −0.172079 | ||||||||
\(416\) | 15.0666 | 0.738702 | ||||||||
\(417\) | −17.5776 | −0.860781 | ||||||||
\(418\) | 16.9413 | 0.828625 | ||||||||
\(419\) | 20.5506 | 1.00396 | 0.501982 | − | 0.864878i | \(-0.332604\pi\) | ||||
0.501982 | + | 0.864878i | \(0.332604\pi\) | |||||||
\(420\) | −9.06335 | −0.442246 | ||||||||
\(421\) | 30.2571 | 1.47464 | 0.737320 | − | 0.675544i | \(-0.236091\pi\) | ||||
0.737320 | + | 0.675544i | \(0.236091\pi\) | |||||||
\(422\) | −24.0472 | −1.17060 | ||||||||
\(423\) | −12.0430 | −0.585552 | ||||||||
\(424\) | 3.31756 | 0.161115 | ||||||||
\(425\) | −8.07611 | −0.391749 | ||||||||
\(426\) | 71.3744 | 3.45810 | ||||||||
\(427\) | −18.9776 | −0.918390 | ||||||||
\(428\) | 64.1441 | 3.10052 | ||||||||
\(429\) | 89.5514 | 4.32358 | ||||||||
\(430\) | 2.92955 | 0.141276 | ||||||||
\(431\) | −31.5229 | −1.51841 | −0.759203 | − | 0.650854i | \(-0.774411\pi\) | ||||
−0.759203 | + | 0.650854i | \(0.774411\pi\) | |||||||
\(432\) | 29.8765 | 1.43743 | ||||||||
\(433\) | −10.6414 | −0.511393 | −0.255696 | − | 0.966757i | \(-0.582305\pi\) | ||||
−0.255696 | + | 0.966757i | \(0.582305\pi\) | |||||||
\(434\) | −8.89122 | −0.426792 | ||||||||
\(435\) | −10.6611 | −0.511162 | ||||||||
\(436\) | 56.5757 | 2.70948 | ||||||||
\(437\) | −9.35359 | −0.447443 | ||||||||
\(438\) | 1.57519 | 0.0752654 | ||||||||
\(439\) | 3.21336 | 0.153365 | 0.0766827 | − | 0.997056i | \(-0.475567\pi\) | ||||
0.0766827 | + | 0.997056i | \(0.475567\pi\) | |||||||
\(440\) | −9.77458 | −0.465985 | ||||||||
\(441\) | −33.1301 | −1.57762 | ||||||||
\(442\) | −26.4975 | −1.26036 | ||||||||
\(443\) | −9.92140 | −0.471380 | −0.235690 | − | 0.971828i | \(-0.575735\pi\) | ||||
−0.235690 | + | 0.971828i | \(0.575735\pi\) | |||||||
\(444\) | 91.5836 | 4.34637 | ||||||||
\(445\) | −5.29487 | −0.251001 | ||||||||
\(446\) | 3.68304 | 0.174397 | ||||||||
\(447\) | −26.0551 | −1.23236 | ||||||||
\(448\) | 15.4767 | 0.731205 | ||||||||
\(449\) | −17.5137 | −0.826525 | −0.413262 | − | 0.910612i | \(-0.635611\pi\) | ||||
−0.413262 | + | 0.910612i | \(0.635611\pi\) | |||||||
\(450\) | 76.9525 | 3.62758 | ||||||||
\(451\) | 54.4225 | 2.56266 | ||||||||
\(452\) | −23.3246 | −1.09710 | ||||||||
\(453\) | −7.44289 | −0.349697 | ||||||||
\(454\) | −60.0065 | −2.81624 | ||||||||
\(455\) | −5.00154 | −0.234476 | ||||||||
\(456\) | 20.8592 | 0.976821 | ||||||||
\(457\) | −12.7970 | −0.598618 | −0.299309 | − | 0.954156i | \(-0.596756\pi\) | ||||
−0.299309 | + | 0.954156i | \(0.596756\pi\) | |||||||
\(458\) | 24.0401 | 1.12332 | ||||||||
\(459\) | 20.3984 | 0.952117 | ||||||||
\(460\) | 11.6006 | 0.540879 | ||||||||
\(461\) | 36.4427 | 1.69731 | 0.848653 | − | 0.528951i | \(-0.177414\pi\) | ||||
0.848653 | + | 0.528951i | \(0.177414\pi\) | |||||||
\(462\) | 48.4778 | 2.25539 | ||||||||
\(463\) | 3.63225 | 0.168805 | 0.0844025 | − | 0.996432i | \(-0.473102\pi\) | ||||
0.0844025 | + | 0.996432i | \(0.473102\pi\) | |||||||
\(464\) | −16.1018 | −0.747508 | ||||||||
\(465\) | −4.21768 | −0.195590 | ||||||||
\(466\) | 17.9440 | 0.831239 | ||||||||
\(467\) | −28.4290 | −1.31554 | −0.657768 | − | 0.753221i | \(-0.728499\pi\) | ||||
−0.657768 | + | 0.753221i | \(0.728499\pi\) | |||||||
\(468\) | 164.505 | 7.60423 | ||||||||
\(469\) | −18.9495 | −0.875008 | ||||||||
\(470\) | 2.24657 | 0.103627 | ||||||||
\(471\) | −61.9203 | −2.85313 | ||||||||
\(472\) | 62.3736 | 2.87098 | ||||||||
\(473\) | −10.2096 | −0.469437 | ||||||||
\(474\) | 42.0758 | 1.93261 | ||||||||
\(475\) | 7.54151 | 0.346028 | ||||||||
\(476\) | −9.34604 | −0.428375 | ||||||||
\(477\) | −5.41729 | −0.248041 | ||||||||
\(478\) | 43.4872 | 1.98906 | ||||||||
\(479\) | 13.5961 | 0.621219 | 0.310610 | − | 0.950538i | \(-0.399467\pi\) | ||||
0.310610 | + | 0.950538i | \(0.399467\pi\) | |||||||
\(480\) | 3.86900 | 0.176595 | ||||||||
\(481\) | 50.5398 | 2.30442 | ||||||||
\(482\) | −52.9119 | −2.41007 | ||||||||
\(483\) | −26.7655 | −1.21787 | ||||||||
\(484\) | 32.0861 | 1.45846 | ||||||||
\(485\) | −2.70262 | −0.122720 | ||||||||
\(486\) | −41.1734 | −1.86766 | ||||||||
\(487\) | −19.2412 | −0.871904 | −0.435952 | − | 0.899970i | \(-0.643588\pi\) | ||||
−0.435952 | + | 0.899970i | \(0.643588\pi\) | |||||||
\(488\) | −54.1689 | −2.45211 | ||||||||
\(489\) | −48.7154 | −2.20299 | ||||||||
\(490\) | 6.18025 | 0.279195 | ||||||||
\(491\) | 36.7971 | 1.66063 | 0.830315 | − | 0.557295i | \(-0.188161\pi\) | ||||
0.830315 | + | 0.557295i | \(0.188161\pi\) | |||||||
\(492\) | 144.038 | 6.49375 | ||||||||
\(493\) | −10.9937 | −0.495130 | ||||||||
\(494\) | 24.7435 | 1.11326 | ||||||||
\(495\) | 15.9610 | 0.717396 | ||||||||
\(496\) | −6.37009 | −0.286025 | ||||||||
\(497\) | 13.8925 | 0.623164 | ||||||||
\(498\) | 49.6255 | 2.22377 | ||||||||
\(499\) | −22.3439 | −1.00025 | −0.500125 | − | 0.865953i | \(-0.666713\pi\) | ||||
−0.500125 | + | 0.865953i | \(0.666713\pi\) | |||||||
\(500\) | −19.2630 | −0.861468 | ||||||||
\(501\) | 20.5563 | 0.918388 | ||||||||
\(502\) | −14.9908 | −0.669071 | ||||||||
\(503\) | 28.7700 | 1.28279 | 0.641394 | − | 0.767211i | \(-0.278356\pi\) | ||||
0.641394 | + | 0.767211i | \(0.278356\pi\) | |||||||
\(504\) | 41.4286 | 1.84538 | ||||||||
\(505\) | −3.38290 | −0.150537 | ||||||||
\(506\) | −62.0488 | −2.75841 | ||||||||
\(507\) | 90.0843 | 4.00078 | ||||||||
\(508\) | −25.9462 | −1.15118 | ||||||||
\(509\) | 29.8458 | 1.32289 | 0.661446 | − | 0.749993i | \(-0.269943\pi\) | ||||
0.661446 | + | 0.749993i | \(0.269943\pi\) | |||||||
\(510\) | −6.80438 | −0.301303 | ||||||||
\(511\) | 0.306599 | 0.0135631 | ||||||||
\(512\) | 26.7389 | 1.18170 | ||||||||
\(513\) | −19.0482 | −0.840997 | ||||||||
\(514\) | −5.17635 | −0.228319 | ||||||||
\(515\) | 0.819506 | 0.0361117 | ||||||||
\(516\) | −27.0214 | −1.18955 | ||||||||
\(517\) | −7.82935 | −0.344335 | ||||||||
\(518\) | 27.3593 | 1.20210 | ||||||||
\(519\) | −25.8805 | −1.13603 | ||||||||
\(520\) | −14.2762 | −0.626054 | ||||||||
\(521\) | −31.4999 | −1.38004 | −0.690019 | − | 0.723792i | \(-0.742398\pi\) | ||||
−0.690019 | + | 0.723792i | \(0.742398\pi\) | |||||||
\(522\) | 104.752 | 4.58488 | ||||||||
\(523\) | 4.27785 | 0.187057 | 0.0935286 | − | 0.995617i | \(-0.470185\pi\) | ||||
0.0935286 | + | 0.995617i | \(0.470185\pi\) | |||||||
\(524\) | −47.8523 | −2.09044 | ||||||||
\(525\) | 21.5802 | 0.941836 | ||||||||
\(526\) | 2.31398 | 0.100894 | ||||||||
\(527\) | −4.34924 | −0.189456 | ||||||||
\(528\) | 34.7318 | 1.51151 | ||||||||
\(529\) | 11.2583 | 0.489490 | ||||||||
\(530\) | 1.01057 | 0.0438963 | ||||||||
\(531\) | −101.851 | −4.41994 | ||||||||
\(532\) | 8.72738 | 0.378380 | ||||||||
\(533\) | 79.4865 | 3.44294 | ||||||||
\(534\) | 74.9565 | 3.24369 | ||||||||
\(535\) | 9.08982 | 0.392987 | ||||||||
\(536\) | −54.0888 | −2.33628 | ||||||||
\(537\) | −62.3602 | −2.69104 | ||||||||
\(538\) | 35.4255 | 1.52730 | ||||||||
\(539\) | −21.5384 | −0.927723 | ||||||||
\(540\) | 23.6240 | 1.01662 | ||||||||
\(541\) | −6.94259 | −0.298485 | −0.149243 | − | 0.988801i | \(-0.547684\pi\) | ||||
−0.149243 | + | 0.988801i | \(0.547684\pi\) | |||||||
\(542\) | −35.5194 | −1.52569 | ||||||||
\(543\) | 62.2670 | 2.67213 | ||||||||
\(544\) | 3.98968 | 0.171056 | ||||||||
\(545\) | 8.01730 | 0.343424 | ||||||||
\(546\) | 70.8040 | 3.03013 | ||||||||
\(547\) | −7.97016 | −0.340779 | −0.170390 | − | 0.985377i | \(-0.554503\pi\) | ||||
−0.170390 | + | 0.985377i | \(0.554503\pi\) | |||||||
\(548\) | −21.2468 | −0.907619 | ||||||||
\(549\) | 88.4532 | 3.77509 | ||||||||
\(550\) | 50.0280 | 2.13320 | ||||||||
\(551\) | 10.2659 | 0.437343 | ||||||||
\(552\) | −76.3984 | −3.25173 | ||||||||
\(553\) | 8.18975 | 0.348264 | ||||||||
\(554\) | −30.6928 | −1.30401 | ||||||||
\(555\) | 12.9783 | 0.550897 | ||||||||
\(556\) | −20.9921 | −0.890265 | ||||||||
\(557\) | 39.7466 | 1.68412 | 0.842060 | − | 0.539385i | \(-0.181343\pi\) | ||||
0.842060 | + | 0.539385i | \(0.181343\pi\) | |||||||
\(558\) | 41.4413 | 1.75435 | ||||||||
\(559\) | −14.9115 | −0.630691 | ||||||||
\(560\) | −1.93981 | −0.0819718 | ||||||||
\(561\) | 23.7134 | 1.00118 | ||||||||
\(562\) | −50.1311 | −2.11465 | ||||||||
\(563\) | 16.2836 | 0.686272 | 0.343136 | − | 0.939286i | \(-0.388511\pi\) | ||||
0.343136 | + | 0.939286i | \(0.388511\pi\) | |||||||
\(564\) | −20.7217 | −0.872541 | ||||||||
\(565\) | −3.30531 | −0.139056 | ||||||||
\(566\) | 49.7635 | 2.09171 | ||||||||
\(567\) | −24.6891 | −1.03684 | ||||||||
\(568\) | 39.6542 | 1.66385 | ||||||||
\(569\) | −15.1540 | −0.635287 | −0.317644 | − | 0.948210i | \(-0.602892\pi\) | ||||
−0.317644 | + | 0.948210i | \(0.602892\pi\) | |||||||
\(570\) | 6.35396 | 0.266138 | ||||||||
\(571\) | −40.6365 | −1.70058 | −0.850292 | − | 0.526312i | \(-0.823575\pi\) | ||||
−0.850292 | + | 0.526312i | \(0.823575\pi\) | |||||||
\(572\) | 106.947 | 4.47167 | ||||||||
\(573\) | 16.7137 | 0.698226 | ||||||||
\(574\) | 43.0293 | 1.79601 | ||||||||
\(575\) | −27.6214 | −1.15189 | ||||||||
\(576\) | −72.1357 | −3.00565 | ||||||||
\(577\) | −20.3499 | −0.847176 | −0.423588 | − | 0.905855i | \(-0.639230\pi\) | ||||
−0.423588 | + | 0.905855i | \(0.639230\pi\) | |||||||
\(578\) | 33.7118 | 1.40223 | ||||||||
\(579\) | 44.3515 | 1.84319 | ||||||||
\(580\) | −12.7321 | −0.528670 | ||||||||
\(581\) | 9.65924 | 0.400733 | ||||||||
\(582\) | 38.2595 | 1.58591 | ||||||||
\(583\) | −3.52186 | −0.145861 | ||||||||
\(584\) | 0.875145 | 0.0362138 | ||||||||
\(585\) | 23.3118 | 0.963826 | ||||||||
\(586\) | −48.4059 | −1.99963 | ||||||||
\(587\) | −34.2532 | −1.41378 | −0.706890 | − | 0.707324i | \(-0.749902\pi\) | ||||
−0.706890 | + | 0.707324i | \(0.749902\pi\) | |||||||
\(588\) | −57.0049 | −2.35084 | ||||||||
\(589\) | 4.06134 | 0.167345 | ||||||||
\(590\) | 18.9997 | 0.782207 | ||||||||
\(591\) | −27.8352 | −1.14499 | ||||||||
\(592\) | 19.6014 | 0.805614 | ||||||||
\(593\) | −15.4467 | −0.634319 | −0.317160 | − | 0.948372i | \(-0.602729\pi\) | ||||
−0.317160 | + | 0.948372i | \(0.602729\pi\) | |||||||
\(594\) | −126.360 | −5.18459 | ||||||||
\(595\) | −1.32442 | −0.0542960 | ||||||||
\(596\) | −31.1164 | −1.27458 | ||||||||
\(597\) | 59.7629 | 2.44593 | ||||||||
\(598\) | −90.6251 | −3.70594 | ||||||||
\(599\) | 12.2812 | 0.501796 | 0.250898 | − | 0.968013i | \(-0.419274\pi\) | ||||
0.250898 | + | 0.968013i | \(0.419274\pi\) | |||||||
\(600\) | 61.5977 | 2.51471 | ||||||||
\(601\) | 6.24490 | 0.254735 | 0.127367 | − | 0.991856i | \(-0.459347\pi\) | ||||
0.127367 | + | 0.991856i | \(0.459347\pi\) | |||||||
\(602\) | −8.07223 | −0.329000 | ||||||||
\(603\) | 88.3224 | 3.59677 | ||||||||
\(604\) | −8.88868 | −0.361675 | ||||||||
\(605\) | 4.54690 | 0.184858 | ||||||||
\(606\) | 47.8898 | 1.94539 | ||||||||
\(607\) | −34.3688 | −1.39499 | −0.697493 | − | 0.716592i | \(-0.745701\pi\) | ||||
−0.697493 | + | 0.716592i | \(0.745701\pi\) | |||||||
\(608\) | −3.72558 | −0.151092 | ||||||||
\(609\) | 29.3762 | 1.19038 | ||||||||
\(610\) | −16.5005 | −0.668086 | ||||||||
\(611\) | −11.4351 | −0.462616 | ||||||||
\(612\) | 43.5612 | 1.76086 | ||||||||
\(613\) | −42.5856 | −1.72002 | −0.860009 | − | 0.510279i | \(-0.829542\pi\) | ||||
−0.860009 | + | 0.510279i | \(0.829542\pi\) | |||||||
\(614\) | 78.2781 | 3.15905 | ||||||||
\(615\) | 20.4116 | 0.823074 | ||||||||
\(616\) | 26.9333 | 1.08518 | ||||||||
\(617\) | 30.2193 | 1.21658 | 0.608292 | − | 0.793713i | \(-0.291855\pi\) | ||||
0.608292 | + | 0.793713i | \(0.291855\pi\) | |||||||
\(618\) | −11.6013 | −0.466672 | ||||||||
\(619\) | 39.6495 | 1.59365 | 0.796824 | − | 0.604211i | \(-0.206512\pi\) | ||||
0.796824 | + | 0.604211i | \(0.206512\pi\) | |||||||
\(620\) | −5.03697 | −0.202290 | ||||||||
\(621\) | 69.7654 | 2.79959 | ||||||||
\(622\) | 39.0558 | 1.56599 | ||||||||
\(623\) | 14.5897 | 0.584526 | ||||||||
\(624\) | 50.7273 | 2.03072 | ||||||||
\(625\) | 20.8659 | 0.834637 | ||||||||
\(626\) | 41.5739 | 1.66163 | ||||||||
\(627\) | −22.1437 | −0.884335 | ||||||||
\(628\) | −73.9484 | −2.95086 | ||||||||
\(629\) | 13.3831 | 0.533618 | ||||||||
\(630\) | 12.6196 | 0.502779 | ||||||||
\(631\) | −26.1083 | −1.03935 | −0.519677 | − | 0.854363i | \(-0.673948\pi\) | ||||
−0.519677 | + | 0.854363i | \(0.673948\pi\) | |||||||
\(632\) | 23.3765 | 0.929868 | ||||||||
\(633\) | 31.4317 | 1.24930 | ||||||||
\(634\) | 35.8475 | 1.42369 | ||||||||
\(635\) | −3.67682 | −0.145910 | ||||||||
\(636\) | −9.32120 | −0.369610 | ||||||||
\(637\) | −31.4577 | −1.24640 | ||||||||
\(638\) | 68.1010 | 2.69614 | ||||||||
\(639\) | −64.7519 | −2.56155 | ||||||||
\(640\) | 10.9856 | 0.434242 | ||||||||
\(641\) | −49.0900 | −1.93894 | −0.969470 | − | 0.245210i | \(-0.921143\pi\) | ||||
−0.969470 | + | 0.245210i | \(0.921143\pi\) | |||||||
\(642\) | −128.679 | −5.07857 | ||||||||
\(643\) | −6.00524 | −0.236824 | −0.118412 | − | 0.992965i | \(-0.537780\pi\) | ||||
−0.118412 | + | 0.992965i | \(0.537780\pi\) | |||||||
\(644\) | −31.9647 | −1.25959 | ||||||||
\(645\) | −3.82918 | −0.150774 | ||||||||
\(646\) | 6.55215 | 0.257791 | ||||||||
\(647\) | 33.1462 | 1.30311 | 0.651555 | − | 0.758601i | \(-0.274117\pi\) | ||||
0.651555 | + | 0.758601i | \(0.274117\pi\) | |||||||
\(648\) | −70.4716 | −2.76839 | ||||||||
\(649\) | −66.2146 | −2.59915 | ||||||||
\(650\) | 73.0682 | 2.86597 | ||||||||
\(651\) | 11.6216 | 0.455486 | ||||||||
\(652\) | −58.1785 | −2.27845 | ||||||||
\(653\) | −2.85218 | −0.111614 | −0.0558071 | − | 0.998442i | \(-0.517773\pi\) | ||||
−0.0558071 | + | 0.998442i | \(0.517773\pi\) | |||||||
\(654\) | −113.496 | −4.43806 | ||||||||
\(655\) | −6.78111 | −0.264960 | ||||||||
\(656\) | 30.8282 | 1.20364 | ||||||||
\(657\) | −1.42904 | −0.0557520 | ||||||||
\(658\) | −6.19030 | −0.241323 | ||||||||
\(659\) | −30.2362 | −1.17784 | −0.588918 | − | 0.808193i | \(-0.700446\pi\) | ||||
−0.588918 | + | 0.808193i | \(0.700446\pi\) | |||||||
\(660\) | 27.4632 | 1.06900 | ||||||||
\(661\) | 45.7913 | 1.78107 | 0.890537 | − | 0.454910i | \(-0.150329\pi\) | ||||
0.890537 | + | 0.454910i | \(0.150329\pi\) | |||||||
\(662\) | −60.5990 | −2.35525 | ||||||||
\(663\) | 34.6346 | 1.34509 | ||||||||
\(664\) | 27.5710 | 1.06996 | ||||||||
\(665\) | 1.23675 | 0.0479592 | ||||||||
\(666\) | −127.520 | −4.94128 | ||||||||
\(667\) | −37.5998 | −1.45587 | ||||||||
\(668\) | 24.5494 | 0.949845 | ||||||||
\(669\) | −4.81405 | −0.186122 | ||||||||
\(670\) | −16.4761 | −0.636528 | ||||||||
\(671\) | 57.5047 | 2.21995 | ||||||||
\(672\) | −10.6608 | −0.411250 | ||||||||
\(673\) | 14.6444 | 0.564502 | 0.282251 | − | 0.959341i | \(-0.408919\pi\) | ||||
0.282251 | + | 0.959341i | \(0.408919\pi\) | |||||||
\(674\) | −53.1140 | −2.04587 | ||||||||
\(675\) | −56.2497 | −2.16505 | ||||||||
\(676\) | 107.583 | 4.13782 | ||||||||
\(677\) | −41.9309 | −1.61154 | −0.805768 | − | 0.592232i | \(-0.798247\pi\) | ||||
−0.805768 | + | 0.592232i | \(0.798247\pi\) | |||||||
\(678\) | 46.7915 | 1.79702 | ||||||||
\(679\) | 7.44693 | 0.285787 | ||||||||
\(680\) | −3.78038 | −0.144971 | ||||||||
\(681\) | 78.4337 | 3.00559 | ||||||||
\(682\) | 26.9416 | 1.03165 | ||||||||
\(683\) | 16.6061 | 0.635414 | 0.317707 | − | 0.948189i | \(-0.397087\pi\) | ||||
0.317707 | + | 0.948189i | \(0.397087\pi\) | |||||||
\(684\) | −40.6777 | −1.55535 | ||||||||
\(685\) | −3.01087 | −0.115040 | ||||||||
\(686\) | −41.5192 | −1.58521 | ||||||||
\(687\) | −31.4225 | −1.19884 | ||||||||
\(688\) | −5.78332 | −0.220487 | ||||||||
\(689\) | −5.14384 | −0.195965 | ||||||||
\(690\) | −23.2719 | −0.885946 | ||||||||
\(691\) | 13.1873 | 0.501669 | 0.250834 | − | 0.968030i | \(-0.419295\pi\) | ||||
0.250834 | + | 0.968030i | \(0.419295\pi\) | |||||||
\(692\) | −30.9078 | −1.17494 | ||||||||
\(693\) | −43.9798 | −1.67066 | ||||||||
\(694\) | 60.1019 | 2.28144 | ||||||||
\(695\) | −2.97478 | −0.112840 | ||||||||
\(696\) | 83.8503 | 3.17834 | ||||||||
\(697\) | 21.0482 | 0.797259 | ||||||||
\(698\) | −47.8974 | −1.81294 | ||||||||
\(699\) | −23.4543 | −0.887124 | ||||||||
\(700\) | 25.7722 | 0.974096 | ||||||||
\(701\) | −18.5417 | −0.700311 | −0.350155 | − | 0.936692i | \(-0.613871\pi\) | ||||
−0.350155 | + | 0.936692i | \(0.613871\pi\) | |||||||
\(702\) | −184.554 | −6.96554 | ||||||||
\(703\) | −12.4972 | −0.471340 | ||||||||
\(704\) | −46.8965 | −1.76748 | ||||||||
\(705\) | −2.93646 | −0.110593 | ||||||||
\(706\) | 5.85162 | 0.220229 | ||||||||
\(707\) | 9.32139 | 0.350567 | ||||||||
\(708\) | −175.248 | −6.58623 | ||||||||
\(709\) | 21.4816 | 0.806757 | 0.403378 | − | 0.915033i | \(-0.367836\pi\) | ||||
0.403378 | + | 0.915033i | \(0.367836\pi\) | |||||||
\(710\) | 12.0792 | 0.453323 | ||||||||
\(711\) | −38.1719 | −1.43156 | ||||||||
\(712\) | 41.6444 | 1.56069 | ||||||||
\(713\) | −14.8750 | −0.557072 | ||||||||
\(714\) | 18.7491 | 0.701667 | ||||||||
\(715\) | 15.1554 | 0.566779 | ||||||||
\(716\) | −74.4737 | −2.78321 | ||||||||
\(717\) | −56.8415 | −2.12279 | ||||||||
\(718\) | 32.2298 | 1.20281 | ||||||||
\(719\) | 25.9331 | 0.967140 | 0.483570 | − | 0.875306i | \(-0.339340\pi\) | ||||
0.483570 | + | 0.875306i | \(0.339340\pi\) | |||||||
\(720\) | 9.04131 | 0.336950 | ||||||||
\(721\) | −2.25810 | −0.0840962 | ||||||||
\(722\) | 39.4016 | 1.46637 | ||||||||
\(723\) | 69.1605 | 2.57211 | ||||||||
\(724\) | 74.3624 | 2.76366 | ||||||||
\(725\) | 30.3155 | 1.12589 | ||||||||
\(726\) | −64.3679 | −2.38892 | ||||||||
\(727\) | 17.4509 | 0.647217 | 0.323608 | − | 0.946191i | \(-0.395104\pi\) | ||||
0.323608 | + | 0.946191i | \(0.395104\pi\) | |||||||
\(728\) | 39.3374 | 1.45794 | ||||||||
\(729\) | 3.09635 | 0.114680 | ||||||||
\(730\) | 0.266580 | 0.00986656 | ||||||||
\(731\) | −3.94862 | −0.146045 | ||||||||
\(732\) | 152.196 | 5.62533 | ||||||||
\(733\) | −33.3952 | −1.23348 | −0.616740 | − | 0.787167i | \(-0.711547\pi\) | ||||
−0.616740 | + | 0.787167i | \(0.711547\pi\) | |||||||
\(734\) | −17.3811 | −0.641550 | ||||||||
\(735\) | −8.07813 | −0.297966 | ||||||||
\(736\) | 13.6452 | 0.502970 | ||||||||
\(737\) | 57.4197 | 2.11508 | ||||||||
\(738\) | −200.557 | −7.38259 | ||||||||
\(739\) | 50.8204 | 1.86946 | 0.934730 | − | 0.355359i | \(-0.115641\pi\) | ||||
0.934730 | + | 0.355359i | \(0.115641\pi\) | |||||||
\(740\) | 15.4993 | 0.569766 | ||||||||
\(741\) | −32.3419 | −1.18811 | ||||||||
\(742\) | −2.78457 | −0.102225 | ||||||||
\(743\) | −4.00185 | −0.146814 | −0.0734068 | − | 0.997302i | \(-0.523387\pi\) | ||||
−0.0734068 | + | 0.997302i | \(0.523387\pi\) | |||||||
\(744\) | 33.1723 | 1.21615 | ||||||||
\(745\) | −4.40948 | −0.161551 | ||||||||
\(746\) | −3.31683 | −0.121438 | ||||||||
\(747\) | −45.0210 | −1.64723 | ||||||||
\(748\) | 28.3198 | 1.03548 | ||||||||
\(749\) | −25.0465 | −0.915180 | ||||||||
\(750\) | 38.6435 | 1.41106 | ||||||||
\(751\) | 49.9720 | 1.82350 | 0.911752 | − | 0.410742i | \(-0.134730\pi\) | ||||
0.911752 | + | 0.410742i | \(0.134730\pi\) | |||||||
\(752\) | −4.43502 | −0.161729 | ||||||||
\(753\) | 19.5942 | 0.714054 | ||||||||
\(754\) | 99.4646 | 3.62229 | ||||||||
\(755\) | −1.25961 | −0.0458419 | ||||||||
\(756\) | −65.0947 | −2.36747 | ||||||||
\(757\) | −52.0610 | −1.89219 | −0.946094 | − | 0.323891i | \(-0.895009\pi\) | ||||
−0.946094 | + | 0.323891i | \(0.895009\pi\) | |||||||
\(758\) | −62.6671 | −2.27617 | ||||||||
\(759\) | 81.1032 | 2.94386 | ||||||||
\(760\) | 3.53014 | 0.128052 | ||||||||
\(761\) | −13.7063 | −0.496855 | −0.248427 | − | 0.968651i | \(-0.579914\pi\) | ||||
−0.248427 | + | 0.968651i | \(0.579914\pi\) | |||||||
\(762\) | 52.0507 | 1.88560 | ||||||||
\(763\) | −22.0913 | −0.799757 | ||||||||
\(764\) | 19.9604 | 0.722142 | ||||||||
\(765\) | 6.17304 | 0.223187 | ||||||||
\(766\) | 26.0748 | 0.942120 | ||||||||
\(767\) | −96.7095 | −3.49198 | ||||||||
\(768\) | −89.1387 | −3.21652 | ||||||||
\(769\) | 4.44679 | 0.160355 | 0.0801777 | − | 0.996781i | \(-0.474451\pi\) | ||||
0.0801777 | + | 0.996781i | \(0.474451\pi\) | |||||||
\(770\) | 8.20422 | 0.295660 | ||||||||
\(771\) | 6.76594 | 0.243669 | ||||||||
\(772\) | 52.9669 | 1.90632 | ||||||||
\(773\) | 11.0974 | 0.399144 | 0.199572 | − | 0.979883i | \(-0.436045\pi\) | ||||
0.199572 | + | 0.979883i | \(0.436045\pi\) | |||||||
\(774\) | 37.6241 | 1.35237 | ||||||||
\(775\) | 11.9932 | 0.430809 | ||||||||
\(776\) | 21.2563 | 0.763055 | ||||||||
\(777\) | −35.7609 | −1.28292 | ||||||||
\(778\) | −81.8948 | −2.93607 | ||||||||
\(779\) | −19.6550 | −0.704212 | ||||||||
\(780\) | 40.1113 | 1.43621 | ||||||||
\(781\) | −42.0962 | −1.50632 | ||||||||
\(782\) | −23.9978 | −0.858158 | ||||||||
\(783\) | −76.5703 | −2.73640 | ||||||||
\(784\) | −12.2006 | −0.435737 | ||||||||
\(785\) | −10.4792 | −0.374018 | ||||||||
\(786\) | 95.9964 | 3.42408 | ||||||||
\(787\) | −1.88559 | −0.0672139 | −0.0336069 | − | 0.999435i | \(-0.510699\pi\) | ||||
−0.0336069 | + | 0.999435i | \(0.510699\pi\) | |||||||
\(788\) | −33.2422 | −1.18420 | ||||||||
\(789\) | −3.02457 | −0.107678 | ||||||||
\(790\) | 7.12077 | 0.253346 | ||||||||
\(791\) | 9.10762 | 0.323830 | ||||||||
\(792\) | −125.534 | −4.46067 | ||||||||
\(793\) | 83.9883 | 2.98251 | ||||||||
\(794\) | −58.4217 | −2.07331 | ||||||||
\(795\) | −1.32090 | −0.0468475 | ||||||||
\(796\) | 71.3719 | 2.52971 | ||||||||
\(797\) | 5.85623 | 0.207438 | 0.103719 | − | 0.994607i | \(-0.466926\pi\) | ||||
0.103719 | + | 0.994607i | \(0.466926\pi\) | |||||||
\(798\) | −17.5080 | −0.619776 | ||||||||
\(799\) | −3.02805 | −0.107125 | ||||||||
\(800\) | −11.0017 | −0.388970 | ||||||||
\(801\) | −68.0017 | −2.40272 | ||||||||
\(802\) | −26.3288 | −0.929704 | ||||||||
\(803\) | −0.929038 | −0.0327850 | ||||||||
\(804\) | 151.971 | 5.35960 | ||||||||
\(805\) | −4.52970 | −0.159651 | ||||||||
\(806\) | 39.3495 | 1.38603 | ||||||||
\(807\) | −46.3041 | −1.62998 | ||||||||
\(808\) | 26.6066 | 0.936019 | ||||||||
\(809\) | −7.49863 | −0.263638 | −0.131819 | − | 0.991274i | \(-0.542082\pi\) | ||||
−0.131819 | + | 0.991274i | \(0.542082\pi\) | |||||||
\(810\) | −21.4665 | −0.754256 | ||||||||
\(811\) | −31.3364 | −1.10037 | −0.550185 | − | 0.835043i | \(-0.685443\pi\) | ||||
−0.550185 | + | 0.835043i | \(0.685443\pi\) | |||||||
\(812\) | 35.0825 | 1.23116 | ||||||||
\(813\) | 46.4270 | 1.62826 | ||||||||
\(814\) | −82.9024 | −2.90573 | ||||||||
\(815\) | −8.24444 | −0.288790 | ||||||||
\(816\) | 13.4327 | 0.470240 | ||||||||
\(817\) | 3.68724 | 0.129000 | ||||||||
\(818\) | −24.7914 | −0.866810 | ||||||||
\(819\) | −64.2345 | −2.24454 | ||||||||
\(820\) | 24.3766 | 0.851267 | ||||||||
\(821\) | −44.4557 | −1.55152 | −0.775758 | − | 0.631031i | \(-0.782632\pi\) | ||||
−0.775758 | + | 0.631031i | \(0.782632\pi\) | |||||||
\(822\) | 42.6232 | 1.48666 | ||||||||
\(823\) | 48.7892 | 1.70068 | 0.850342 | − | 0.526231i | \(-0.176395\pi\) | ||||
0.850342 | + | 0.526231i | \(0.176395\pi\) | |||||||
\(824\) | −6.44545 | −0.224538 | ||||||||
\(825\) | −65.3909 | −2.27662 | ||||||||
\(826\) | −52.3528 | −1.82159 | ||||||||
\(827\) | −7.85896 | −0.273283 | −0.136641 | − | 0.990621i | \(-0.543631\pi\) | ||||
−0.136641 | + | 0.990621i | \(0.543631\pi\) | |||||||
\(828\) | 148.985 | 5.17760 | ||||||||
\(829\) | −12.8270 | −0.445500 | −0.222750 | − | 0.974876i | \(-0.571503\pi\) | ||||
−0.222750 | + | 0.974876i | \(0.571503\pi\) | |||||||
\(830\) | 8.39846 | 0.291515 | ||||||||
\(831\) | 40.1182 | 1.39168 | ||||||||
\(832\) | −68.4945 | −2.37462 | ||||||||
\(833\) | −8.33009 | −0.288621 | ||||||||
\(834\) | 42.1123 | 1.45823 | ||||||||
\(835\) | 3.47888 | 0.120392 | ||||||||
\(836\) | −26.4452 | −0.914626 | ||||||||
\(837\) | −30.2922 | −1.04705 | ||||||||
\(838\) | −49.2350 | −1.70079 | ||||||||
\(839\) | 19.3220 | 0.667070 | 0.333535 | − | 0.942738i | \(-0.391758\pi\) | ||||
0.333535 | + | 0.942738i | \(0.391758\pi\) | |||||||
\(840\) | 10.1016 | 0.348537 | ||||||||
\(841\) | 12.2672 | 0.423009 | ||||||||
\(842\) | −72.4896 | −2.49816 | ||||||||
\(843\) | 65.5257 | 2.25683 | ||||||||
\(844\) | 37.5374 | 1.29209 | ||||||||
\(845\) | 15.2456 | 0.524464 | ||||||||
\(846\) | 28.8526 | 0.991971 | ||||||||
\(847\) | −12.5287 | −0.430493 | ||||||||
\(848\) | −1.99500 | −0.0685084 | ||||||||
\(849\) | −65.0451 | −2.23234 | ||||||||
\(850\) | 19.3486 | 0.663653 | ||||||||
\(851\) | 45.7719 | 1.56904 | ||||||||
\(852\) | −111.415 | −3.81700 | ||||||||
\(853\) | 44.8801 | 1.53667 | 0.768333 | − | 0.640050i | \(-0.221086\pi\) | ||||
0.768333 | + | 0.640050i | \(0.221086\pi\) | |||||||
\(854\) | 45.4663 | 1.55582 | ||||||||
\(855\) | −5.76441 | −0.197139 | ||||||||
\(856\) | −71.4919 | −2.44354 | ||||||||
\(857\) | −11.4945 | −0.392645 | −0.196323 | − | 0.980539i | \(-0.562900\pi\) | ||||
−0.196323 | + | 0.980539i | \(0.562900\pi\) | |||||||
\(858\) | −214.546 | −7.32448 | ||||||||
\(859\) | −12.2624 | −0.418388 | −0.209194 | − | 0.977874i | \(-0.567084\pi\) | ||||
−0.209194 | + | 0.977874i | \(0.567084\pi\) | |||||||
\(860\) | −4.57301 | −0.155938 | ||||||||
\(861\) | −56.2430 | −1.91676 | ||||||||
\(862\) | 75.5223 | 2.57230 | ||||||||
\(863\) | 14.4831 | 0.493010 | 0.246505 | − | 0.969142i | \(-0.420718\pi\) | ||||
0.246505 | + | 0.969142i | \(0.420718\pi\) | |||||||
\(864\) | 27.7879 | 0.945364 | ||||||||
\(865\) | −4.37992 | −0.148922 | ||||||||
\(866\) | 25.4945 | 0.866339 | ||||||||
\(867\) | −44.0642 | −1.49650 | ||||||||
\(868\) | 13.8791 | 0.471088 | ||||||||
\(869\) | −24.8161 | −0.841828 | ||||||||
\(870\) | 25.5418 | 0.865948 | ||||||||
\(871\) | 83.8641 | 2.84163 | ||||||||
\(872\) | −63.0565 | −2.13536 | ||||||||
\(873\) | −34.7096 | −1.17474 | ||||||||
\(874\) | 22.4092 | 0.758004 | ||||||||
\(875\) | 7.52168 | 0.254279 | ||||||||
\(876\) | −2.45885 | −0.0830770 | ||||||||
\(877\) | −4.57721 | −0.154561 | −0.0772807 | − | 0.997009i | \(-0.524624\pi\) | ||||
−0.0772807 | + | 0.997009i | \(0.524624\pi\) | |||||||
\(878\) | −7.69854 | −0.259813 | ||||||||
\(879\) | 63.2707 | 2.13407 | ||||||||
\(880\) | 5.87789 | 0.198144 | ||||||||
\(881\) | −22.1840 | −0.747397 | −0.373698 | − | 0.927550i | \(-0.621910\pi\) | ||||
−0.373698 | + | 0.927550i | \(0.621910\pi\) | |||||||
\(882\) | 79.3726 | 2.67262 | ||||||||
\(883\) | 17.0892 | 0.575098 | 0.287549 | − | 0.957766i | \(-0.407160\pi\) | ||||
0.287549 | + | 0.957766i | \(0.407160\pi\) | |||||||
\(884\) | 41.3624 | 1.39117 | ||||||||
\(885\) | −24.8343 | −0.834796 | ||||||||
\(886\) | 23.7696 | 0.798555 | ||||||||
\(887\) | −5.99375 | −0.201250 | −0.100625 | − | 0.994924i | \(-0.532084\pi\) | ||||
−0.100625 | + | 0.994924i | \(0.532084\pi\) | |||||||
\(888\) | −102.075 | −3.42540 | ||||||||
\(889\) | 10.1313 | 0.339793 | ||||||||
\(890\) | 12.6854 | 0.425215 | ||||||||
\(891\) | 74.8114 | 2.50627 | ||||||||
\(892\) | −5.74918 | −0.192497 | ||||||||
\(893\) | 2.82761 | 0.0946224 | ||||||||
\(894\) | 62.4226 | 2.08772 | ||||||||
\(895\) | −10.5536 | −0.352769 | ||||||||
\(896\) | −30.2701 | −1.01125 | ||||||||
\(897\) | 118.455 | 3.95509 | ||||||||
\(898\) | 41.9592 | 1.40020 | ||||||||
\(899\) | 16.3259 | 0.544498 | ||||||||
\(900\) | −120.122 | −4.00407 | ||||||||
\(901\) | −1.36210 | −0.0453782 | ||||||||
\(902\) | −130.385 | −4.34134 | ||||||||
\(903\) | 10.5511 | 0.351119 | ||||||||
\(904\) | 25.9965 | 0.864629 | ||||||||
\(905\) | 10.5379 | 0.350290 | ||||||||
\(906\) | 17.8316 | 0.592415 | ||||||||
\(907\) | −22.8978 | −0.760307 | −0.380154 | − | 0.924923i | \(-0.624129\pi\) | ||||
−0.380154 | + | 0.924923i | \(0.624129\pi\) | |||||||
\(908\) | 93.6696 | 3.10853 | ||||||||
\(909\) | −43.4464 | −1.44102 | ||||||||
\(910\) | 11.9826 | 0.397221 | ||||||||
\(911\) | −42.6176 | −1.41199 | −0.705993 | − | 0.708219i | \(-0.749499\pi\) | ||||
−0.705993 | + | 0.708219i | \(0.749499\pi\) | |||||||
\(912\) | −12.5435 | −0.415358 | ||||||||
\(913\) | −29.2689 | −0.968658 | ||||||||
\(914\) | 30.6589 | 1.01411 | ||||||||
\(915\) | 21.5676 | 0.713003 | ||||||||
\(916\) | −37.5264 | −1.23991 | ||||||||
\(917\) | 18.6850 | 0.617033 | ||||||||
\(918\) | −48.8703 | −1.61296 | ||||||||
\(919\) | −1.50308 | −0.0495821 | −0.0247910 | − | 0.999693i | \(-0.507892\pi\) | ||||
−0.0247910 | + | 0.999693i | \(0.507892\pi\) | |||||||
\(920\) | −12.9294 | −0.426270 | ||||||||
\(921\) | −102.316 | −3.37143 | ||||||||
\(922\) | −87.3090 | −2.87537 | ||||||||
\(923\) | −61.4834 | −2.02375 | ||||||||
\(924\) | −75.6734 | −2.48947 | ||||||||
\(925\) | −36.9045 | −1.21341 | ||||||||
\(926\) | −8.70211 | −0.285969 | ||||||||
\(927\) | 10.5249 | 0.345682 | ||||||||
\(928\) | −14.9762 | −0.491617 | ||||||||
\(929\) | −28.0069 | −0.918878 | −0.459439 | − | 0.888209i | \(-0.651950\pi\) | ||||
−0.459439 | + | 0.888209i | \(0.651950\pi\) | |||||||
\(930\) | 10.1047 | 0.331345 | ||||||||
\(931\) | 7.77868 | 0.254936 | ||||||||
\(932\) | −28.0104 | −0.917511 | ||||||||
\(933\) | −51.0493 | −1.67128 | ||||||||
\(934\) | 68.1098 | 2.22862 | ||||||||
\(935\) | 4.01318 | 0.131245 | ||||||||
\(936\) | −183.349 | −5.99294 | ||||||||
\(937\) | −17.3071 | −0.565397 | −0.282699 | − | 0.959209i | \(-0.591230\pi\) | ||||
−0.282699 | + | 0.959209i | \(0.591230\pi\) | |||||||
\(938\) | 45.3991 | 1.48233 | ||||||||
\(939\) | −54.3406 | −1.77334 | ||||||||
\(940\) | −3.50687 | −0.114382 | ||||||||
\(941\) | 0.476801 | 0.0155433 | 0.00777163 | − | 0.999970i | \(-0.497526\pi\) | ||||
0.00777163 | + | 0.999970i | \(0.497526\pi\) | |||||||
\(942\) | 148.348 | 4.83343 | ||||||||
\(943\) | 71.9878 | 2.34425 | ||||||||
\(944\) | −37.5080 | −1.22078 | ||||||||
\(945\) | −9.22453 | −0.300074 | ||||||||
\(946\) | 24.4600 | 0.795263 | ||||||||
\(947\) | 23.5709 | 0.765950 | 0.382975 | − | 0.923759i | \(-0.374899\pi\) | ||||
0.382975 | + | 0.923759i | \(0.374899\pi\) | |||||||
\(948\) | −65.6800 | −2.13319 | ||||||||
\(949\) | −1.35690 | −0.0440469 | ||||||||
\(950\) | −18.0679 | −0.586199 | ||||||||
\(951\) | −46.8558 | −1.51940 | ||||||||
\(952\) | 10.4166 | 0.337605 | ||||||||
\(953\) | −0.209171 | −0.00677570 | −0.00338785 | − | 0.999994i | \(-0.501078\pi\) | ||||
−0.00338785 | + | 0.999994i | \(0.501078\pi\) | |||||||
\(954\) | 12.9787 | 0.420200 | ||||||||
\(955\) | 2.82858 | 0.0915306 | ||||||||
\(956\) | −67.8831 | −2.19550 | ||||||||
\(957\) | −89.0139 | −2.87741 | ||||||||
\(958\) | −32.5733 | −1.05239 | ||||||||
\(959\) | 8.29630 | 0.267901 | ||||||||
\(960\) | −17.5889 | −0.567679 | ||||||||
\(961\) | −24.5413 | −0.791654 | ||||||||
\(962\) | −121.083 | −3.90386 | ||||||||
\(963\) | 116.740 | 3.76189 | ||||||||
\(964\) | 82.5950 | 2.66021 | ||||||||
\(965\) | 7.50590 | 0.241623 | ||||||||
\(966\) | 64.1244 | 2.06317 | ||||||||
\(967\) | −40.5567 | −1.30421 | −0.652107 | − | 0.758127i | \(-0.726115\pi\) | ||||
−0.652107 | + | 0.758127i | \(0.726115\pi\) | |||||||
\(968\) | −35.7616 | −1.14942 | ||||||||
\(969\) | −8.56423 | −0.275123 | ||||||||
\(970\) | 6.47491 | 0.207897 | ||||||||
\(971\) | −26.1376 | −0.838795 | −0.419397 | − | 0.907803i | \(-0.637759\pi\) | ||||
−0.419397 | + | 0.907803i | \(0.637759\pi\) | |||||||
\(972\) | 64.2713 | 2.06150 | ||||||||
\(973\) | 8.19686 | 0.262779 | ||||||||
\(974\) | 46.0980 | 1.47707 | ||||||||
\(975\) | −95.5064 | −3.05865 | ||||||||
\(976\) | 32.5742 | 1.04267 | ||||||||
\(977\) | 26.7372 | 0.855400 | 0.427700 | − | 0.903921i | \(-0.359324\pi\) | ||||
0.427700 | + | 0.903921i | \(0.359324\pi\) | |||||||
\(978\) | 116.712 | 3.73203 | ||||||||
\(979\) | −44.2090 | −1.41292 | ||||||||
\(980\) | −9.64732 | −0.308172 | ||||||||
\(981\) | 102.966 | 3.28744 | ||||||||
\(982\) | −88.1580 | −2.81324 | ||||||||
\(983\) | −9.80023 | −0.312579 | −0.156289 | − | 0.987711i | \(-0.549953\pi\) | ||||
−0.156289 | + | 0.987711i | \(0.549953\pi\) | |||||||
\(984\) | −160.538 | −5.11777 | ||||||||
\(985\) | −4.71073 | −0.150096 | ||||||||
\(986\) | 26.3385 | 0.838788 | ||||||||
\(987\) | 8.09126 | 0.257548 | ||||||||
\(988\) | −38.6244 | −1.22881 | ||||||||
\(989\) | −13.5048 | −0.429428 | ||||||||
\(990\) | −38.2393 | −1.21532 | ||||||||
\(991\) | 29.8744 | 0.948991 | 0.474495 | − | 0.880258i | \(-0.342631\pi\) | ||||
0.474495 | + | 0.880258i | \(0.342631\pi\) | |||||||
\(992\) | −5.92478 | −0.188112 | ||||||||
\(993\) | 79.2081 | 2.51359 | ||||||||
\(994\) | −33.2835 | −1.05569 | ||||||||
\(995\) | 10.1141 | 0.320638 | ||||||||
\(996\) | −77.4650 | −2.45457 | ||||||||
\(997\) | 23.8507 | 0.755359 | 0.377680 | − | 0.925936i | \(-0.376722\pi\) | ||||
0.377680 | + | 0.925936i | \(0.376722\pi\) | |||||||
\(998\) | 53.5312 | 1.69450 | ||||||||
\(999\) | 93.2124 | 2.94911 |
(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 | 4019.2.a.b.1.19 | ✓ | 186 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.b.1.19 | ✓ | 186 | 1.1 | even | 1 | trivial |