Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6031,2,Mod(1,6031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6031, 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("6031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6031 = 37 \cdot 163 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6031.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: | \(48.1577774590\) |
Analytic rank: | \(1\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.18825 | −1.54733 | −0.773665 | − | 0.633595i | \(-0.781579\pi\) | ||||
−0.773665 | + | 0.633595i | \(0.781579\pi\) | |||||||
\(3\) | 1.71398 | 0.989569 | 0.494784 | − | 0.869016i | \(-0.335247\pi\) | ||||
0.494784 | + | 0.869016i | \(0.335247\pi\) | |||||||
\(4\) | 2.78846 | 1.39423 | ||||||||
\(5\) | 0.914186 | 0.408837 | 0.204418 | − | 0.978884i | \(-0.434470\pi\) | ||||
0.204418 | + | 0.978884i | \(0.434470\pi\) | |||||||
\(6\) | −3.75063 | −1.53119 | ||||||||
\(7\) | 0.835020 | 0.315608 | 0.157804 | − | 0.987470i | \(-0.449559\pi\) | ||||
0.157804 | + | 0.987470i | \(0.449559\pi\) | |||||||
\(8\) | −1.72535 | −0.610003 | ||||||||
\(9\) | −0.0622604 | −0.0207535 | ||||||||
\(10\) | −2.00047 | −0.632605 | ||||||||
\(11\) | 2.33428 | 0.703812 | 0.351906 | − | 0.936035i | \(-0.385534\pi\) | ||||
0.351906 | + | 0.936035i | \(0.385534\pi\) | |||||||
\(12\) | 4.77937 | 1.37969 | ||||||||
\(13\) | 3.32438 | 0.922018 | 0.461009 | − | 0.887395i | \(-0.347488\pi\) | ||||
0.461009 | + | 0.887395i | \(0.347488\pi\) | |||||||
\(14\) | −1.82724 | −0.488349 | ||||||||
\(15\) | 1.56690 | 0.404572 | ||||||||
\(16\) | −1.80142 | −0.450354 | ||||||||
\(17\) | −7.84946 | −1.90377 | −0.951887 | − | 0.306450i | \(-0.900859\pi\) | ||||
−0.951887 | + | 0.306450i | \(0.900859\pi\) | |||||||
\(18\) | 0.136242 | 0.0321125 | ||||||||
\(19\) | −5.24808 | −1.20399 | −0.601996 | − | 0.798499i | \(-0.705628\pi\) | ||||
−0.601996 | + | 0.798499i | \(0.705628\pi\) | |||||||
\(20\) | 2.54917 | 0.570012 | ||||||||
\(21\) | 1.43121 | 0.312316 | ||||||||
\(22\) | −5.10800 | −1.08903 | ||||||||
\(23\) | −2.29348 | −0.478224 | −0.239112 | − | 0.970992i | \(-0.576856\pi\) | ||||
−0.239112 | + | 0.970992i | \(0.576856\pi\) | |||||||
\(24\) | −2.95722 | −0.603640 | ||||||||
\(25\) | −4.16426 | −0.832853 | ||||||||
\(26\) | −7.27460 | −1.42667 | ||||||||
\(27\) | −5.24866 | −1.01011 | ||||||||
\(28\) | 2.32842 | 0.440030 | ||||||||
\(29\) | 5.13859 | 0.954212 | 0.477106 | − | 0.878846i | \(-0.341686\pi\) | ||||
0.477106 | + | 0.878846i | \(0.341686\pi\) | |||||||
\(30\) | −3.42878 | −0.626006 | ||||||||
\(31\) | 3.95083 | 0.709590 | 0.354795 | − | 0.934944i | \(-0.384551\pi\) | ||||
0.354795 | + | 0.934944i | \(0.384551\pi\) | |||||||
\(32\) | 7.39265 | 1.30685 | ||||||||
\(33\) | 4.00092 | 0.696471 | ||||||||
\(34\) | 17.1766 | 2.94577 | ||||||||
\(35\) | 0.763364 | 0.129032 | ||||||||
\(36\) | −0.173611 | −0.0289351 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 11.4841 | 1.86297 | ||||||||
\(39\) | 5.69794 | 0.912400 | ||||||||
\(40\) | −1.57729 | −0.249391 | ||||||||
\(41\) | 6.86656 | 1.07238 | 0.536189 | − | 0.844098i | \(-0.319864\pi\) | ||||
0.536189 | + | 0.844098i | \(0.319864\pi\) | |||||||
\(42\) | −3.13185 | −0.483255 | ||||||||
\(43\) | 3.74030 | 0.570391 | 0.285195 | − | 0.958469i | \(-0.407942\pi\) | ||||
0.285195 | + | 0.958469i | \(0.407942\pi\) | |||||||
\(44\) | 6.50905 | 0.981276 | ||||||||
\(45\) | −0.0569176 | −0.00848478 | ||||||||
\(46\) | 5.01872 | 0.739970 | ||||||||
\(47\) | −10.9703 | −1.60018 | −0.800091 | − | 0.599879i | \(-0.795216\pi\) | ||||
−0.800091 | + | 0.599879i | \(0.795216\pi\) | |||||||
\(48\) | −3.08760 | −0.445656 | ||||||||
\(49\) | −6.30274 | −0.900392 | ||||||||
\(50\) | 9.11247 | 1.28870 | ||||||||
\(51\) | −13.4538 | −1.88392 | ||||||||
\(52\) | 9.26990 | 1.28550 | ||||||||
\(53\) | 6.38689 | 0.877307 | 0.438653 | − | 0.898656i | \(-0.355456\pi\) | ||||
0.438653 | + | 0.898656i | \(0.355456\pi\) | |||||||
\(54\) | 11.4854 | 1.56297 | ||||||||
\(55\) | 2.13397 | 0.287744 | ||||||||
\(56\) | −1.44070 | −0.192522 | ||||||||
\(57\) | −8.99512 | −1.19143 | ||||||||
\(58\) | −11.2445 | −1.47648 | ||||||||
\(59\) | −8.21573 | −1.06960 | −0.534798 | − | 0.844980i | \(-0.679612\pi\) | ||||
−0.534798 | + | 0.844980i | \(0.679612\pi\) | |||||||
\(60\) | 4.36924 | 0.564066 | ||||||||
\(61\) | −4.46938 | −0.572246 | −0.286123 | − | 0.958193i | \(-0.592367\pi\) | ||||
−0.286123 | + | 0.958193i | \(0.592367\pi\) | |||||||
\(62\) | −8.64542 | −1.09797 | ||||||||
\(63\) | −0.0519887 | −0.00654995 | ||||||||
\(64\) | −12.5742 | −1.57177 | ||||||||
\(65\) | 3.03911 | 0.376955 | ||||||||
\(66\) | −8.75503 | −1.07767 | ||||||||
\(67\) | 4.37459 | 0.534441 | 0.267220 | − | 0.963635i | \(-0.413895\pi\) | ||||
0.267220 | + | 0.963635i | \(0.413895\pi\) | |||||||
\(68\) | −21.8879 | −2.65430 | ||||||||
\(69\) | −3.93099 | −0.473236 | ||||||||
\(70\) | −1.67043 | −0.199655 | ||||||||
\(71\) | −6.40629 | −0.760287 | −0.380143 | − | 0.924928i | \(-0.624125\pi\) | ||||
−0.380143 | + | 0.924928i | \(0.624125\pi\) | |||||||
\(72\) | 0.107421 | 0.0126597 | ||||||||
\(73\) | −4.99899 | −0.585087 | −0.292544 | − | 0.956252i | \(-0.594502\pi\) | ||||
−0.292544 | + | 0.956252i | \(0.594502\pi\) | |||||||
\(74\) | −2.18825 | −0.254379 | ||||||||
\(75\) | −7.13748 | −0.824165 | ||||||||
\(76\) | −14.6340 | −1.67864 | ||||||||
\(77\) | 1.94917 | 0.222129 | ||||||||
\(78\) | −12.4685 | −1.41178 | ||||||||
\(79\) | −4.86798 | −0.547691 | −0.273845 | − | 0.961774i | \(-0.588296\pi\) | ||||
−0.273845 | + | 0.961774i | \(0.588296\pi\) | |||||||
\(80\) | −1.64683 | −0.184121 | ||||||||
\(81\) | −8.80934 | −0.978816 | ||||||||
\(82\) | −15.0258 | −1.65932 | ||||||||
\(83\) | 4.72671 | 0.518823 | 0.259412 | − | 0.965767i | \(-0.416471\pi\) | ||||
0.259412 | + | 0.965767i | \(0.416471\pi\) | |||||||
\(84\) | 3.99087 | 0.435440 | ||||||||
\(85\) | −7.17587 | −0.778332 | ||||||||
\(86\) | −8.18473 | −0.882582 | ||||||||
\(87\) | 8.80746 | 0.944259 | ||||||||
\(88\) | −4.02745 | −0.429327 | ||||||||
\(89\) | −13.5605 | −1.43741 | −0.718704 | − | 0.695317i | \(-0.755264\pi\) | ||||
−0.718704 | + | 0.695317i | \(0.755264\pi\) | |||||||
\(90\) | 0.124550 | 0.0131287 | ||||||||
\(91\) | 2.77592 | 0.290996 | ||||||||
\(92\) | −6.39528 | −0.666754 | ||||||||
\(93\) | 6.77166 | 0.702188 | ||||||||
\(94\) | 24.0058 | 2.47601 | ||||||||
\(95\) | −4.79772 | −0.492236 | ||||||||
\(96\) | 12.6709 | 1.29322 | ||||||||
\(97\) | −3.59979 | −0.365503 | −0.182752 | − | 0.983159i | \(-0.558500\pi\) | ||||
−0.182752 | + | 0.983159i | \(0.558500\pi\) | |||||||
\(98\) | 13.7920 | 1.39320 | ||||||||
\(99\) | −0.145333 | −0.0146065 | ||||||||
\(100\) | −11.6119 | −1.16119 | ||||||||
\(101\) | −6.65567 | −0.662264 | −0.331132 | − | 0.943585i | \(-0.607430\pi\) | ||||
−0.331132 | + | 0.943585i | \(0.607430\pi\) | |||||||
\(102\) | 29.4404 | 2.91504 | ||||||||
\(103\) | 1.12889 | 0.111232 | 0.0556162 | − | 0.998452i | \(-0.482288\pi\) | ||||
0.0556162 | + | 0.998452i | \(0.482288\pi\) | |||||||
\(104\) | −5.73572 | −0.562433 | ||||||||
\(105\) | 1.30839 | 0.127686 | ||||||||
\(106\) | −13.9761 | −1.35748 | ||||||||
\(107\) | −7.70706 | −0.745070 | −0.372535 | − | 0.928018i | \(-0.621511\pi\) | ||||
−0.372535 | + | 0.928018i | \(0.621511\pi\) | |||||||
\(108\) | −14.6357 | −1.40832 | ||||||||
\(109\) | 13.2167 | 1.26593 | 0.632967 | − | 0.774178i | \(-0.281837\pi\) | ||||
0.632967 | + | 0.774178i | \(0.281837\pi\) | |||||||
\(110\) | −4.66967 | −0.445235 | ||||||||
\(111\) | 1.71398 | 0.162684 | ||||||||
\(112\) | −1.50422 | −0.142135 | ||||||||
\(113\) | −0.630461 | −0.0593088 | −0.0296544 | − | 0.999560i | \(-0.509441\pi\) | ||||
−0.0296544 | + | 0.999560i | \(0.509441\pi\) | |||||||
\(114\) | 19.6836 | 1.84354 | ||||||||
\(115\) | −2.09667 | −0.195516 | ||||||||
\(116\) | 14.3287 | 1.33039 | ||||||||
\(117\) | −0.206977 | −0.0191351 | ||||||||
\(118\) | 17.9781 | 1.65502 | ||||||||
\(119\) | −6.55445 | −0.600846 | ||||||||
\(120\) | −2.70345 | −0.246790 | ||||||||
\(121\) | −5.55113 | −0.504648 | ||||||||
\(122\) | 9.78015 | 0.885453 | ||||||||
\(123\) | 11.7692 | 1.06119 | ||||||||
\(124\) | 11.0167 | 0.989331 | ||||||||
\(125\) | −8.37785 | −0.749337 | ||||||||
\(126\) | 0.113764 | 0.0101349 | ||||||||
\(127\) | −3.79018 | −0.336324 | −0.168162 | − | 0.985759i | \(-0.553783\pi\) | ||||
−0.168162 | + | 0.985759i | \(0.553783\pi\) | |||||||
\(128\) | 12.7302 | 1.12520 | ||||||||
\(129\) | 6.41082 | 0.564441 | ||||||||
\(130\) | −6.65034 | −0.583273 | ||||||||
\(131\) | 14.2847 | 1.24806 | 0.624030 | − | 0.781400i | \(-0.285494\pi\) | ||||
0.624030 | + | 0.781400i | \(0.285494\pi\) | |||||||
\(132\) | 11.1564 | 0.971040 | ||||||||
\(133\) | −4.38225 | −0.379989 | ||||||||
\(134\) | −9.57271 | −0.826956 | ||||||||
\(135\) | −4.79826 | −0.412968 | ||||||||
\(136\) | 13.5430 | 1.16131 | ||||||||
\(137\) | −6.88594 | −0.588306 | −0.294153 | − | 0.955758i | \(-0.595037\pi\) | ||||
−0.294153 | + | 0.955758i | \(0.595037\pi\) | |||||||
\(138\) | 8.60201 | 0.732252 | ||||||||
\(139\) | 19.4321 | 1.64821 | 0.824106 | − | 0.566436i | \(-0.191678\pi\) | ||||
0.824106 | + | 0.566436i | \(0.191678\pi\) | |||||||
\(140\) | 2.12861 | 0.179900 | ||||||||
\(141\) | −18.8029 | −1.58349 | ||||||||
\(142\) | 14.0186 | 1.17641 | ||||||||
\(143\) | 7.76004 | 0.648927 | ||||||||
\(144\) | 0.112157 | 0.00934641 | ||||||||
\(145\) | 4.69763 | 0.390117 | ||||||||
\(146\) | 10.9391 | 0.905323 | ||||||||
\(147\) | −10.8028 | −0.891000 | ||||||||
\(148\) | 2.78846 | 0.229210 | ||||||||
\(149\) | −18.3192 | −1.50076 | −0.750382 | − | 0.661005i | \(-0.770130\pi\) | ||||
−0.750382 | + | 0.661005i | \(0.770130\pi\) | |||||||
\(150\) | 15.6186 | 1.27526 | ||||||||
\(151\) | 2.98919 | 0.243256 | 0.121628 | − | 0.992576i | \(-0.461188\pi\) | ||||
0.121628 | + | 0.992576i | \(0.461188\pi\) | |||||||
\(152\) | 9.05476 | 0.734438 | ||||||||
\(153\) | 0.488710 | 0.0395099 | ||||||||
\(154\) | −4.26528 | −0.343706 | ||||||||
\(155\) | 3.61180 | 0.290106 | ||||||||
\(156\) | 15.8885 | 1.27210 | ||||||||
\(157\) | −2.72784 | −0.217705 | −0.108853 | − | 0.994058i | \(-0.534718\pi\) | ||||
−0.108853 | + | 0.994058i | \(0.534718\pi\) | |||||||
\(158\) | 10.6524 | 0.847458 | ||||||||
\(159\) | 10.9470 | 0.868155 | ||||||||
\(160\) | 6.75826 | 0.534288 | ||||||||
\(161\) | −1.91510 | −0.150931 | ||||||||
\(162\) | 19.2771 | 1.51455 | ||||||||
\(163\) | 1.00000 | 0.0783260 | ||||||||
\(164\) | 19.1471 | 1.49514 | ||||||||
\(165\) | 3.65759 | 0.284743 | ||||||||
\(166\) | −10.3432 | −0.802791 | ||||||||
\(167\) | −20.8505 | −1.61346 | −0.806728 | − | 0.590922i | \(-0.798764\pi\) | ||||
−0.806728 | + | 0.590922i | \(0.798764\pi\) | |||||||
\(168\) | −2.46934 | −0.190513 | ||||||||
\(169\) | −1.94848 | −0.149883 | ||||||||
\(170\) | 15.7026 | 1.20434 | ||||||||
\(171\) | 0.326747 | 0.0249870 | ||||||||
\(172\) | 10.4297 | 0.795255 | ||||||||
\(173\) | 0.640619 | 0.0487054 | 0.0243527 | − | 0.999703i | \(-0.492248\pi\) | ||||
0.0243527 | + | 0.999703i | \(0.492248\pi\) | |||||||
\(174\) | −19.2730 | −1.46108 | ||||||||
\(175\) | −3.47724 | −0.262855 | ||||||||
\(176\) | −4.20501 | −0.316965 | ||||||||
\(177\) | −14.0816 | −1.05844 | ||||||||
\(178\) | 29.6738 | 2.22414 | ||||||||
\(179\) | −19.8446 | −1.48326 | −0.741628 | − | 0.670812i | \(-0.765946\pi\) | ||||
−0.741628 | + | 0.670812i | \(0.765946\pi\) | |||||||
\(180\) | −0.158712 | −0.0118297 | ||||||||
\(181\) | −9.96944 | −0.741023 | −0.370511 | − | 0.928828i | \(-0.620818\pi\) | ||||
−0.370511 | + | 0.928828i | \(0.620818\pi\) | |||||||
\(182\) | −6.07443 | −0.450267 | ||||||||
\(183\) | −7.66045 | −0.566277 | ||||||||
\(184\) | 3.95705 | 0.291718 | ||||||||
\(185\) | 0.914186 | 0.0672123 | ||||||||
\(186\) | −14.8181 | −1.08652 | ||||||||
\(187\) | −18.3228 | −1.33990 | ||||||||
\(188\) | −30.5902 | −2.23102 | ||||||||
\(189\) | −4.38274 | −0.318797 | ||||||||
\(190\) | 10.4986 | 0.761651 | ||||||||
\(191\) | −12.1566 | −0.879620 | −0.439810 | − | 0.898091i | \(-0.644954\pi\) | ||||
−0.439810 | + | 0.898091i | \(0.644954\pi\) | |||||||
\(192\) | −21.5519 | −1.55538 | ||||||||
\(193\) | 5.19084 | 0.373645 | 0.186823 | − | 0.982394i | \(-0.440181\pi\) | ||||
0.186823 | + | 0.982394i | \(0.440181\pi\) | |||||||
\(194\) | 7.87725 | 0.565554 | ||||||||
\(195\) | 5.20898 | 0.373023 | ||||||||
\(196\) | −17.5749 | −1.25535 | ||||||||
\(197\) | −22.8147 | −1.62548 | −0.812741 | − | 0.582625i | \(-0.802026\pi\) | ||||
−0.812741 | + | 0.582625i | \(0.802026\pi\) | |||||||
\(198\) | 0.318026 | 0.0226011 | ||||||||
\(199\) | 14.1877 | 1.00574 | 0.502871 | − | 0.864361i | \(-0.332277\pi\) | ||||
0.502871 | + | 0.864361i | \(0.332277\pi\) | |||||||
\(200\) | 7.18480 | 0.508042 | ||||||||
\(201\) | 7.49797 | 0.528866 | ||||||||
\(202\) | 14.5643 | 1.02474 | ||||||||
\(203\) | 4.29082 | 0.301157 | ||||||||
\(204\) | −37.5155 | −2.62661 | ||||||||
\(205\) | 6.27732 | 0.438427 | ||||||||
\(206\) | −2.47029 | −0.172113 | ||||||||
\(207\) | 0.142793 | 0.00992481 | ||||||||
\(208\) | −5.98860 | −0.415235 | ||||||||
\(209\) | −12.2505 | −0.847384 | ||||||||
\(210\) | −2.86310 | −0.197572 | ||||||||
\(211\) | 0.554700 | 0.0381871 | 0.0190936 | − | 0.999818i | \(-0.493922\pi\) | ||||
0.0190936 | + | 0.999818i | \(0.493922\pi\) | |||||||
\(212\) | 17.8096 | 1.22317 | ||||||||
\(213\) | −10.9803 | −0.752356 | ||||||||
\(214\) | 16.8650 | 1.15287 | ||||||||
\(215\) | 3.41933 | 0.233197 | ||||||||
\(216\) | 9.05577 | 0.616167 | ||||||||
\(217\) | 3.29902 | 0.223952 | ||||||||
\(218\) | −28.9216 | −1.95882 | ||||||||
\(219\) | −8.56819 | −0.578984 | ||||||||
\(220\) | 5.95048 | 0.401181 | ||||||||
\(221\) | −26.0946 | −1.75531 | ||||||||
\(222\) | −3.75063 | −0.251726 | ||||||||
\(223\) | 6.75719 | 0.452495 | 0.226247 | − | 0.974070i | \(-0.427354\pi\) | ||||
0.226247 | + | 0.974070i | \(0.427354\pi\) | |||||||
\(224\) | 6.17301 | 0.412452 | ||||||||
\(225\) | 0.259269 | 0.0172846 | ||||||||
\(226\) | 1.37961 | 0.0917703 | ||||||||
\(227\) | 11.4761 | 0.761696 | 0.380848 | − | 0.924638i | \(-0.375632\pi\) | ||||
0.380848 | + | 0.924638i | \(0.375632\pi\) | |||||||
\(228\) | −25.0825 | −1.66113 | ||||||||
\(229\) | 7.75773 | 0.512645 | 0.256323 | − | 0.966591i | \(-0.417489\pi\) | ||||
0.256323 | + | 0.966591i | \(0.417489\pi\) | |||||||
\(230\) | 4.58805 | 0.302527 | ||||||||
\(231\) | 3.34085 | 0.219812 | ||||||||
\(232\) | −8.86585 | −0.582072 | ||||||||
\(233\) | 30.3130 | 1.98587 | 0.992935 | − | 0.118661i | \(-0.0378602\pi\) | ||||
0.992935 | + | 0.118661i | \(0.0378602\pi\) | |||||||
\(234\) | 0.452919 | 0.0296083 | ||||||||
\(235\) | −10.0289 | −0.654213 | ||||||||
\(236\) | −22.9092 | −1.49126 | ||||||||
\(237\) | −8.34364 | −0.541977 | ||||||||
\(238\) | 14.3428 | 0.929706 | ||||||||
\(239\) | −18.1701 | −1.17532 | −0.587662 | − | 0.809106i | \(-0.699952\pi\) | ||||
−0.587662 | + | 0.809106i | \(0.699952\pi\) | |||||||
\(240\) | −2.82264 | −0.182201 | ||||||||
\(241\) | 17.4502 | 1.12407 | 0.562034 | − | 0.827114i | \(-0.310019\pi\) | ||||
0.562034 | + | 0.827114i | \(0.310019\pi\) | |||||||
\(242\) | 12.1473 | 0.780857 | ||||||||
\(243\) | 0.646924 | 0.0415002 | ||||||||
\(244\) | −12.4627 | −0.797842 | ||||||||
\(245\) | −5.76188 | −0.368113 | ||||||||
\(246\) | −25.7540 | −1.64201 | ||||||||
\(247\) | −17.4466 | −1.11010 | ||||||||
\(248\) | −6.81656 | −0.432852 | ||||||||
\(249\) | 8.10150 | 0.513412 | ||||||||
\(250\) | 18.3329 | 1.15947 | ||||||||
\(251\) | 29.2719 | 1.84763 | 0.923814 | − | 0.382841i | \(-0.125054\pi\) | ||||
0.923814 | + | 0.382841i | \(0.125054\pi\) | |||||||
\(252\) | −0.144968 | −0.00913214 | ||||||||
\(253\) | −5.35363 | −0.336580 | ||||||||
\(254\) | 8.29389 | 0.520405 | ||||||||
\(255\) | −12.2993 | −0.770213 | ||||||||
\(256\) | −2.70855 | −0.169284 | ||||||||
\(257\) | 11.2034 | 0.698846 | 0.349423 | − | 0.936965i | \(-0.386378\pi\) | ||||
0.349423 | + | 0.936965i | \(0.386378\pi\) | |||||||
\(258\) | −14.0285 | −0.873376 | ||||||||
\(259\) | 0.835020 | 0.0518856 | ||||||||
\(260\) | 8.47442 | 0.525561 | ||||||||
\(261\) | −0.319931 | −0.0198032 | ||||||||
\(262\) | −31.2586 | −1.93116 | ||||||||
\(263\) | 8.47911 | 0.522844 | 0.261422 | − | 0.965225i | \(-0.415809\pi\) | ||||
0.261422 | + | 0.965225i | \(0.415809\pi\) | |||||||
\(264\) | −6.90298 | −0.424849 | ||||||||
\(265\) | 5.83881 | 0.358675 | ||||||||
\(266\) | 9.58947 | 0.587968 | ||||||||
\(267\) | −23.2424 | −1.42241 | ||||||||
\(268\) | 12.1984 | 0.745133 | ||||||||
\(269\) | −17.3014 | −1.05488 | −0.527441 | − | 0.849591i | \(-0.676849\pi\) | ||||
−0.527441 | + | 0.849591i | \(0.676849\pi\) | |||||||
\(270\) | 10.4998 | 0.638998 | ||||||||
\(271\) | −30.9441 | −1.87972 | −0.939859 | − | 0.341562i | \(-0.889044\pi\) | ||||
−0.939859 | + | 0.341562i | \(0.889044\pi\) | |||||||
\(272\) | 14.1401 | 0.857372 | ||||||||
\(273\) | 4.75789 | 0.287961 | ||||||||
\(274\) | 15.0682 | 0.910303 | ||||||||
\(275\) | −9.72056 | −0.586172 | ||||||||
\(276\) | −10.9614 | −0.659799 | ||||||||
\(277\) | −30.9477 | −1.85947 | −0.929733 | − | 0.368235i | \(-0.879962\pi\) | ||||
−0.929733 | + | 0.368235i | \(0.879962\pi\) | |||||||
\(278\) | −42.5224 | −2.55033 | ||||||||
\(279\) | −0.245980 | −0.0147265 | ||||||||
\(280\) | −1.31707 | −0.0787099 | ||||||||
\(281\) | 3.89759 | 0.232511 | 0.116255 | − | 0.993219i | \(-0.462911\pi\) | ||||
0.116255 | + | 0.993219i | \(0.462911\pi\) | |||||||
\(282\) | 41.1455 | 2.45018 | ||||||||
\(283\) | −9.62865 | −0.572364 | −0.286182 | − | 0.958175i | \(-0.592386\pi\) | ||||
−0.286182 | + | 0.958175i | \(0.592386\pi\) | |||||||
\(284\) | −17.8637 | −1.06001 | ||||||||
\(285\) | −8.22322 | −0.487101 | ||||||||
\(286\) | −16.9810 | −1.00410 | ||||||||
\(287\) | 5.73372 | 0.338451 | ||||||||
\(288\) | −0.460270 | −0.0271216 | ||||||||
\(289\) | 44.6140 | 2.62435 | ||||||||
\(290\) | −10.2796 | −0.603639 | ||||||||
\(291\) | −6.16998 | −0.361691 | ||||||||
\(292\) | −13.9395 | −0.815746 | ||||||||
\(293\) | −25.3379 | −1.48026 | −0.740128 | − | 0.672466i | \(-0.765235\pi\) | ||||
−0.740128 | + | 0.672466i | \(0.765235\pi\) | |||||||
\(294\) | 23.6393 | 1.37867 | ||||||||
\(295\) | −7.51071 | −0.437290 | ||||||||
\(296\) | −1.72535 | −0.100284 | ||||||||
\(297\) | −12.2519 | −0.710925 | ||||||||
\(298\) | 40.0870 | 2.32218 | ||||||||
\(299\) | −7.62441 | −0.440931 | ||||||||
\(300\) | −19.9026 | −1.14907 | ||||||||
\(301\) | 3.12323 | 0.180020 | ||||||||
\(302\) | −6.54110 | −0.376398 | ||||||||
\(303\) | −11.4077 | −0.655355 | ||||||||
\(304\) | 9.45397 | 0.542223 | ||||||||
\(305\) | −4.08585 | −0.233955 | ||||||||
\(306\) | −1.06942 | −0.0611348 | ||||||||
\(307\) | −8.05311 | −0.459615 | −0.229808 | − | 0.973236i | \(-0.573810\pi\) | ||||
−0.229808 | + | 0.973236i | \(0.573810\pi\) | |||||||
\(308\) | 5.43518 | 0.309698 | ||||||||
\(309\) | 1.93489 | 0.110072 | ||||||||
\(310\) | −7.90353 | −0.448890 | ||||||||
\(311\) | 31.3906 | 1.78000 | 0.889998 | − | 0.455965i | \(-0.150706\pi\) | ||||
0.889998 | + | 0.455965i | \(0.150706\pi\) | |||||||
\(312\) | −9.83092 | −0.556567 | ||||||||
\(313\) | 12.9650 | 0.732828 | 0.366414 | − | 0.930452i | \(-0.380585\pi\) | ||||
0.366414 | + | 0.930452i | \(0.380585\pi\) | |||||||
\(314\) | 5.96920 | 0.336861 | ||||||||
\(315\) | −0.0475273 | −0.00267786 | ||||||||
\(316\) | −13.5742 | −0.763606 | ||||||||
\(317\) | 32.5314 | 1.82714 | 0.913572 | − | 0.406678i | \(-0.133313\pi\) | ||||
0.913572 | + | 0.406678i | \(0.133313\pi\) | |||||||
\(318\) | −23.9549 | −1.34332 | ||||||||
\(319\) | 11.9949 | 0.671586 | ||||||||
\(320\) | −11.4951 | −0.642598 | ||||||||
\(321\) | −13.2098 | −0.737298 | ||||||||
\(322\) | 4.19073 | 0.233540 | ||||||||
\(323\) | 41.1946 | 2.29213 | ||||||||
\(324\) | −24.5645 | −1.36469 | ||||||||
\(325\) | −13.8436 | −0.767905 | ||||||||
\(326\) | −2.18825 | −0.121196 | ||||||||
\(327\) | 22.6533 | 1.25273 | ||||||||
\(328\) | −11.8472 | −0.654153 | ||||||||
\(329\) | −9.16041 | −0.505030 | ||||||||
\(330\) | −8.00373 | −0.440591 | ||||||||
\(331\) | 7.71502 | 0.424056 | 0.212028 | − | 0.977264i | \(-0.431993\pi\) | ||||
0.212028 | + | 0.977264i | \(0.431993\pi\) | |||||||
\(332\) | 13.1802 | 0.723359 | ||||||||
\(333\) | −0.0622604 | −0.00341185 | ||||||||
\(334\) | 45.6261 | 2.49655 | ||||||||
\(335\) | 3.99919 | 0.218499 | ||||||||
\(336\) | −2.57820 | −0.140653 | ||||||||
\(337\) | 17.0021 | 0.926161 | 0.463080 | − | 0.886316i | \(-0.346744\pi\) | ||||
0.463080 | + | 0.886316i | \(0.346744\pi\) | |||||||
\(338\) | 4.26377 | 0.231918 | ||||||||
\(339\) | −1.08060 | −0.0586901 | ||||||||
\(340\) | −20.0096 | −1.08517 | ||||||||
\(341\) | 9.22235 | 0.499418 | ||||||||
\(342\) | −0.715007 | −0.0386631 | ||||||||
\(343\) | −11.1081 | −0.599778 | ||||||||
\(344\) | −6.45332 | −0.347940 | ||||||||
\(345\) | −3.59366 | −0.193476 | ||||||||
\(346\) | −1.40184 | −0.0753633 | ||||||||
\(347\) | 15.0066 | 0.805596 | 0.402798 | − | 0.915289i | \(-0.368038\pi\) | ||||
0.402798 | + | 0.915289i | \(0.368038\pi\) | |||||||
\(348\) | 24.5592 | 1.31651 | ||||||||
\(349\) | 12.4938 | 0.668778 | 0.334389 | − | 0.942435i | \(-0.391470\pi\) | ||||
0.334389 | + | 0.942435i | \(0.391470\pi\) | |||||||
\(350\) | 7.60909 | 0.406723 | ||||||||
\(351\) | −17.4486 | −0.931336 | ||||||||
\(352\) | 17.2565 | 0.919776 | ||||||||
\(353\) | −8.10322 | −0.431291 | −0.215645 | − | 0.976472i | \(-0.569186\pi\) | ||||
−0.215645 | + | 0.976472i | \(0.569186\pi\) | |||||||
\(354\) | 30.8142 | 1.63776 | ||||||||
\(355\) | −5.85654 | −0.310833 | ||||||||
\(356\) | −37.8128 | −2.00407 | ||||||||
\(357\) | −11.2342 | −0.594578 | ||||||||
\(358\) | 43.4251 | 2.29509 | ||||||||
\(359\) | −37.5566 | −1.98216 | −0.991080 | − | 0.133268i | \(-0.957453\pi\) | ||||
−0.991080 | + | 0.133268i | \(0.957453\pi\) | |||||||
\(360\) | 0.0982027 | 0.00517574 | ||||||||
\(361\) | 8.54232 | 0.449596 | ||||||||
\(362\) | 21.8157 | 1.14661 | ||||||||
\(363\) | −9.51455 | −0.499384 | ||||||||
\(364\) | 7.74055 | 0.405715 | ||||||||
\(365\) | −4.57001 | −0.239205 | ||||||||
\(366\) | 16.7630 | 0.876217 | ||||||||
\(367\) | 31.3048 | 1.63410 | 0.817050 | − | 0.576567i | \(-0.195608\pi\) | ||||
0.817050 | + | 0.576567i | \(0.195608\pi\) | |||||||
\(368\) | 4.13152 | 0.215370 | ||||||||
\(369\) | −0.427515 | −0.0222555 | ||||||||
\(370\) | −2.00047 | −0.104000 | ||||||||
\(371\) | 5.33318 | 0.276885 | ||||||||
\(372\) | 18.8825 | 0.979011 | ||||||||
\(373\) | −16.2770 | −0.842794 | −0.421397 | − | 0.906876i | \(-0.638460\pi\) | ||||
−0.421397 | + | 0.906876i | \(0.638460\pi\) | |||||||
\(374\) | 40.0951 | 2.07327 | ||||||||
\(375\) | −14.3595 | −0.741521 | ||||||||
\(376\) | 18.9276 | 0.976115 | ||||||||
\(377\) | 17.0826 | 0.879801 | ||||||||
\(378\) | 9.59055 | 0.493284 | ||||||||
\(379\) | −37.8965 | −1.94661 | −0.973306 | − | 0.229511i | \(-0.926287\pi\) | ||||
−0.973306 | + | 0.229511i | \(0.926287\pi\) | |||||||
\(380\) | −13.3782 | −0.686290 | ||||||||
\(381\) | −6.49631 | −0.332816 | ||||||||
\(382\) | 26.6017 | 1.36106 | ||||||||
\(383\) | −5.49565 | −0.280815 | −0.140407 | − | 0.990094i | \(-0.544841\pi\) | ||||
−0.140407 | + | 0.990094i | \(0.544841\pi\) | |||||||
\(384\) | 21.8193 | 1.11346 | ||||||||
\(385\) | 1.78191 | 0.0908143 | ||||||||
\(386\) | −11.3589 | −0.578152 | ||||||||
\(387\) | −0.232873 | −0.0118376 | ||||||||
\(388\) | −10.0379 | −0.509595 | ||||||||
\(389\) | 16.7181 | 0.847642 | 0.423821 | − | 0.905746i | \(-0.360689\pi\) | ||||
0.423821 | + | 0.905746i | \(0.360689\pi\) | |||||||
\(390\) | −11.3986 | −0.577189 | ||||||||
\(391\) | 18.0026 | 0.910430 | ||||||||
\(392\) | 10.8744 | 0.549241 | ||||||||
\(393\) | 24.4838 | 1.23504 | ||||||||
\(394\) | 49.9244 | 2.51516 | ||||||||
\(395\) | −4.45024 | −0.223916 | ||||||||
\(396\) | −0.405256 | −0.0203649 | ||||||||
\(397\) | −15.4876 | −0.777301 | −0.388651 | − | 0.921385i | \(-0.627059\pi\) | ||||
−0.388651 | + | 0.921385i | \(0.627059\pi\) | |||||||
\(398\) | −31.0464 | −1.55622 | ||||||||
\(399\) | −7.51110 | −0.376025 | ||||||||
\(400\) | 7.50157 | 0.375079 | ||||||||
\(401\) | 7.31460 | 0.365274 | 0.182637 | − | 0.983180i | \(-0.441537\pi\) | ||||
0.182637 | + | 0.983180i | \(0.441537\pi\) | |||||||
\(402\) | −16.4075 | −0.818330 | ||||||||
\(403\) | 13.1341 | 0.654255 | ||||||||
\(404\) | −18.5590 | −0.923347 | ||||||||
\(405\) | −8.05338 | −0.400176 | ||||||||
\(406\) | −9.38941 | −0.465989 | ||||||||
\(407\) | 2.33428 | 0.115706 | ||||||||
\(408\) | 23.2126 | 1.14919 | ||||||||
\(409\) | 8.50298 | 0.420445 | 0.210223 | − | 0.977654i | \(-0.432581\pi\) | ||||
0.210223 | + | 0.977654i | \(0.432581\pi\) | |||||||
\(410\) | −13.7364 | −0.678391 | ||||||||
\(411\) | −11.8024 | −0.582169 | ||||||||
\(412\) | 3.14785 | 0.155084 | ||||||||
\(413\) | −6.86029 | −0.337573 | ||||||||
\(414\) | −0.312468 | −0.0153569 | ||||||||
\(415\) | 4.32109 | 0.212114 | ||||||||
\(416\) | 24.5760 | 1.20494 | ||||||||
\(417\) | 33.3063 | 1.63102 | ||||||||
\(418\) | 26.8072 | 1.31118 | ||||||||
\(419\) | −13.8256 | −0.675426 | −0.337713 | − | 0.941249i | \(-0.609653\pi\) | ||||
−0.337713 | + | 0.941249i | \(0.609653\pi\) | |||||||
\(420\) | 3.64840 | 0.178024 | ||||||||
\(421\) | 39.1308 | 1.90712 | 0.953559 | − | 0.301207i | \(-0.0973894\pi\) | ||||
0.953559 | + | 0.301207i | \(0.0973894\pi\) | |||||||
\(422\) | −1.21382 | −0.0590880 | ||||||||
\(423\) | 0.683015 | 0.0332093 | ||||||||
\(424\) | −11.0196 | −0.535159 | ||||||||
\(425\) | 32.6872 | 1.58556 | ||||||||
\(426\) | 24.0276 | 1.16414 | ||||||||
\(427\) | −3.73202 | −0.180605 | ||||||||
\(428\) | −21.4908 | −1.03880 | ||||||||
\(429\) | 13.3006 | 0.642158 | ||||||||
\(430\) | −7.48237 | −0.360832 | ||||||||
\(431\) | −29.1228 | −1.40279 | −0.701397 | − | 0.712771i | \(-0.747440\pi\) | ||||
−0.701397 | + | 0.712771i | \(0.747440\pi\) | |||||||
\(432\) | 9.45503 | 0.454905 | ||||||||
\(433\) | −20.0747 | −0.964730 | −0.482365 | − | 0.875970i | \(-0.660222\pi\) | ||||
−0.482365 | + | 0.875970i | \(0.660222\pi\) | |||||||
\(434\) | −7.21910 | −0.346528 | ||||||||
\(435\) | 8.05166 | 0.386047 | ||||||||
\(436\) | 36.8544 | 1.76500 | ||||||||
\(437\) | 12.0364 | 0.575778 | ||||||||
\(438\) | 18.7494 | 0.895880 | ||||||||
\(439\) | −13.1680 | −0.628474 | −0.314237 | − | 0.949345i | \(-0.601749\pi\) | ||||
−0.314237 | + | 0.949345i | \(0.601749\pi\) | |||||||
\(440\) | −3.68184 | −0.175525 | ||||||||
\(441\) | 0.392411 | 0.0186862 | ||||||||
\(442\) | 57.1017 | 2.71605 | ||||||||
\(443\) | −12.9488 | −0.615216 | −0.307608 | − | 0.951513i | \(-0.599529\pi\) | ||||
−0.307608 | + | 0.951513i | \(0.599529\pi\) | |||||||
\(444\) | 4.77937 | 0.226819 | ||||||||
\(445\) | −12.3968 | −0.587665 | ||||||||
\(446\) | −14.7865 | −0.700159 | ||||||||
\(447\) | −31.3987 | −1.48511 | ||||||||
\(448\) | −10.4997 | −0.496063 | ||||||||
\(449\) | −10.9711 | −0.517757 | −0.258879 | − | 0.965910i | \(-0.583353\pi\) | ||||
−0.258879 | + | 0.965910i | \(0.583353\pi\) | |||||||
\(450\) | −0.567346 | −0.0267449 | ||||||||
\(451\) | 16.0285 | 0.754752 | ||||||||
\(452\) | −1.75801 | −0.0826900 | ||||||||
\(453\) | 5.12341 | 0.240719 | ||||||||
\(454\) | −25.1126 | −1.17860 | ||||||||
\(455\) | 2.53771 | 0.118970 | ||||||||
\(456\) | 15.5197 | 0.726777 | ||||||||
\(457\) | −6.38113 | −0.298497 | −0.149248 | − | 0.988800i | \(-0.547685\pi\) | ||||
−0.149248 | + | 0.988800i | \(0.547685\pi\) | |||||||
\(458\) | −16.9759 | −0.793231 | ||||||||
\(459\) | 41.1992 | 1.92301 | ||||||||
\(460\) | −5.84648 | −0.272593 | ||||||||
\(461\) | −0.467707 | −0.0217833 | −0.0108917 | − | 0.999941i | \(-0.503467\pi\) | ||||
−0.0108917 | + | 0.999941i | \(0.503467\pi\) | |||||||
\(462\) | −7.31062 | −0.340121 | ||||||||
\(463\) | 9.90941 | 0.460529 | 0.230265 | − | 0.973128i | \(-0.426041\pi\) | ||||
0.230265 | + | 0.973128i | \(0.426041\pi\) | |||||||
\(464\) | −9.25674 | −0.429733 | ||||||||
\(465\) | 6.19056 | 0.287080 | ||||||||
\(466\) | −66.3325 | −3.07280 | ||||||||
\(467\) | 0.794519 | 0.0367660 | 0.0183830 | − | 0.999831i | \(-0.494148\pi\) | ||||
0.0183830 | + | 0.999831i | \(0.494148\pi\) | |||||||
\(468\) | −0.577148 | −0.0266787 | ||||||||
\(469\) | 3.65287 | 0.168674 | ||||||||
\(470\) | 21.9458 | 1.01228 | ||||||||
\(471\) | −4.67547 | −0.215434 | ||||||||
\(472\) | 14.1750 | 0.652457 | ||||||||
\(473\) | 8.73092 | 0.401448 | ||||||||
\(474\) | 18.2580 | 0.838618 | ||||||||
\(475\) | 21.8544 | 1.00275 | ||||||||
\(476\) | −18.2768 | −0.837717 | ||||||||
\(477\) | −0.397650 | −0.0182072 | ||||||||
\(478\) | 39.7608 | 1.81861 | ||||||||
\(479\) | −8.51874 | −0.389231 | −0.194616 | − | 0.980880i | \(-0.562346\pi\) | ||||
−0.194616 | + | 0.980880i | \(0.562346\pi\) | |||||||
\(480\) | 11.5836 | 0.528714 | ||||||||
\(481\) | 3.32438 | 0.151579 | ||||||||
\(482\) | −38.1856 | −1.73930 | ||||||||
\(483\) | −3.28245 | −0.149357 | ||||||||
\(484\) | −15.4791 | −0.703595 | ||||||||
\(485\) | −3.29088 | −0.149431 | ||||||||
\(486\) | −1.41563 | −0.0642145 | ||||||||
\(487\) | 9.02113 | 0.408786 | 0.204393 | − | 0.978889i | \(-0.434478\pi\) | ||||
0.204393 | + | 0.978889i | \(0.434478\pi\) | |||||||
\(488\) | 7.71124 | 0.349072 | ||||||||
\(489\) | 1.71398 | 0.0775090 | ||||||||
\(490\) | 12.6085 | 0.569592 | ||||||||
\(491\) | −35.6555 | −1.60911 | −0.804556 | − | 0.593877i | \(-0.797596\pi\) | ||||
−0.804556 | + | 0.593877i | \(0.797596\pi\) | |||||||
\(492\) | 32.8179 | 1.47954 | ||||||||
\(493\) | −40.3352 | −1.81660 | ||||||||
\(494\) | 38.1776 | 1.71769 | ||||||||
\(495\) | −0.132862 | −0.00597169 | ||||||||
\(496\) | −7.11709 | −0.319567 | ||||||||
\(497\) | −5.34938 | −0.239952 | ||||||||
\(498\) | −17.7281 | −0.794417 | ||||||||
\(499\) | 28.8981 | 1.29365 | 0.646827 | − | 0.762636i | \(-0.276095\pi\) | ||||
0.646827 | + | 0.762636i | \(0.276095\pi\) | |||||||
\(500\) | −23.3613 | −1.04475 | ||||||||
\(501\) | −35.7373 | −1.59663 | ||||||||
\(502\) | −64.0545 | −2.85889 | ||||||||
\(503\) | −41.8313 | −1.86516 | −0.932582 | − | 0.360958i | \(-0.882450\pi\) | ||||
−0.932582 | + | 0.360958i | \(0.882450\pi\) | |||||||
\(504\) | 0.0896985 | 0.00399549 | ||||||||
\(505\) | −6.08452 | −0.270758 | ||||||||
\(506\) | 11.7151 | 0.520800 | ||||||||
\(507\) | −3.33966 | −0.148320 | ||||||||
\(508\) | −10.5688 | −0.468913 | ||||||||
\(509\) | −19.2245 | −0.852109 | −0.426055 | − | 0.904697i | \(-0.640097\pi\) | ||||
−0.426055 | + | 0.904697i | \(0.640097\pi\) | |||||||
\(510\) | 26.9141 | 1.19177 | ||||||||
\(511\) | −4.17425 | −0.184658 | ||||||||
\(512\) | −19.5334 | −0.863262 | ||||||||
\(513\) | 27.5454 | 1.21616 | ||||||||
\(514\) | −24.5158 | −1.08135 | ||||||||
\(515\) | 1.03201 | 0.0454759 | ||||||||
\(516\) | 17.8763 | 0.786960 | ||||||||
\(517\) | −25.6078 | −1.12623 | ||||||||
\(518\) | −1.82724 | −0.0802841 | ||||||||
\(519\) | 1.09801 | 0.0481973 | ||||||||
\(520\) | −5.24351 | −0.229943 | ||||||||
\(521\) | 6.54734 | 0.286844 | 0.143422 | − | 0.989662i | \(-0.454189\pi\) | ||||
0.143422 | + | 0.989662i | \(0.454189\pi\) | |||||||
\(522\) | 0.700090 | 0.0306421 | ||||||||
\(523\) | −45.0246 | −1.96879 | −0.984395 | − | 0.175972i | \(-0.943693\pi\) | ||||
−0.984395 | + | 0.175972i | \(0.943693\pi\) | |||||||
\(524\) | 39.8323 | 1.74008 | ||||||||
\(525\) | −5.95993 | −0.260113 | ||||||||
\(526\) | −18.5545 | −0.809013 | ||||||||
\(527\) | −31.0119 | −1.35090 | ||||||||
\(528\) | −7.20732 | −0.313658 | ||||||||
\(529\) | −17.7399 | −0.771302 | ||||||||
\(530\) | −12.7768 | −0.554989 | ||||||||
\(531\) | 0.511515 | 0.0221978 | ||||||||
\(532\) | −12.2197 | −0.529792 | ||||||||
\(533\) | 22.8271 | 0.988751 | ||||||||
\(534\) | 50.8603 | 2.20094 | ||||||||
\(535\) | −7.04569 | −0.304612 | ||||||||
\(536\) | −7.54769 | −0.326010 | ||||||||
\(537\) | −34.0133 | −1.46778 | ||||||||
\(538\) | 37.8598 | 1.63225 | ||||||||
\(539\) | −14.7124 | −0.633707 | ||||||||
\(540\) | −13.3797 | −0.575772 | ||||||||
\(541\) | −0.681663 | −0.0293070 | −0.0146535 | − | 0.999893i | \(-0.504665\pi\) | ||||
−0.0146535 | + | 0.999893i | \(0.504665\pi\) | |||||||
\(542\) | 67.7135 | 2.90854 | ||||||||
\(543\) | −17.0875 | −0.733293 | ||||||||
\(544\) | −58.0283 | −2.48794 | ||||||||
\(545\) | 12.0826 | 0.517561 | ||||||||
\(546\) | −10.4115 | −0.445570 | ||||||||
\(547\) | −20.8613 | −0.891963 | −0.445981 | − | 0.895042i | \(-0.647145\pi\) | ||||
−0.445981 | + | 0.895042i | \(0.647145\pi\) | |||||||
\(548\) | −19.2012 | −0.820233 | ||||||||
\(549\) | 0.278266 | 0.0118761 | ||||||||
\(550\) | 21.2711 | 0.907001 | ||||||||
\(551\) | −26.9677 | −1.14886 | ||||||||
\(552\) | 6.78233 | 0.288675 | ||||||||
\(553\) | −4.06486 | −0.172855 | ||||||||
\(554\) | 67.7214 | 2.87721 | ||||||||
\(555\) | 1.56690 | 0.0665112 | ||||||||
\(556\) | 54.1857 | 2.29798 | ||||||||
\(557\) | 16.9391 | 0.717731 | 0.358866 | − | 0.933389i | \(-0.383164\pi\) | ||||
0.358866 | + | 0.933389i | \(0.383164\pi\) | |||||||
\(558\) | 0.538267 | 0.0227867 | ||||||||
\(559\) | 12.4342 | 0.525910 | ||||||||
\(560\) | −1.37514 | −0.0581101 | ||||||||
\(561\) | −31.4051 | −1.32592 | ||||||||
\(562\) | −8.52893 | −0.359771 | ||||||||
\(563\) | −4.76445 | −0.200797 | −0.100399 | − | 0.994947i | \(-0.532012\pi\) | ||||
−0.100399 | + | 0.994947i | \(0.532012\pi\) | |||||||
\(564\) | −52.4311 | −2.20775 | ||||||||
\(565\) | −0.576359 | −0.0242476 | ||||||||
\(566\) | 21.0699 | 0.885635 | ||||||||
\(567\) | −7.35597 | −0.308922 | ||||||||
\(568\) | 11.0531 | 0.463777 | ||||||||
\(569\) | −18.6340 | −0.781176 | −0.390588 | − | 0.920566i | \(-0.627728\pi\) | ||||
−0.390588 | + | 0.920566i | \(0.627728\pi\) | |||||||
\(570\) | 17.9945 | 0.753706 | ||||||||
\(571\) | −1.46100 | −0.0611410 | −0.0305705 | − | 0.999533i | \(-0.509732\pi\) | ||||
−0.0305705 | + | 0.999533i | \(0.509732\pi\) | |||||||
\(572\) | 21.6386 | 0.904754 | ||||||||
\(573\) | −20.8362 | −0.870445 | ||||||||
\(574\) | −12.5468 | −0.523695 | ||||||||
\(575\) | 9.55066 | 0.398290 | ||||||||
\(576\) | 0.782873 | 0.0326197 | ||||||||
\(577\) | −13.0993 | −0.545330 | −0.272665 | − | 0.962109i | \(-0.587905\pi\) | ||||
−0.272665 | + | 0.962109i | \(0.587905\pi\) | |||||||
\(578\) | −97.6268 | −4.06074 | ||||||||
\(579\) | 8.89702 | 0.369748 | ||||||||
\(580\) | 13.0991 | 0.543912 | ||||||||
\(581\) | 3.94689 | 0.163745 | ||||||||
\(582\) | 13.5015 | 0.559655 | ||||||||
\(583\) | 14.9088 | 0.617459 | ||||||||
\(584\) | 8.62500 | 0.356905 | ||||||||
\(585\) | −0.189216 | −0.00782312 | ||||||||
\(586\) | 55.4458 | 2.29044 | ||||||||
\(587\) | 27.2257 | 1.12372 | 0.561862 | − | 0.827231i | \(-0.310085\pi\) | ||||
0.561862 | + | 0.827231i | \(0.310085\pi\) | |||||||
\(588\) | −30.1231 | −1.24226 | ||||||||
\(589\) | −20.7343 | −0.854341 | ||||||||
\(590\) | 16.4353 | 0.676632 | ||||||||
\(591\) | −39.1041 | −1.60853 | ||||||||
\(592\) | −1.80142 | −0.0740378 | ||||||||
\(593\) | 21.8241 | 0.896210 | 0.448105 | − | 0.893981i | \(-0.352099\pi\) | ||||
0.448105 | + | 0.893981i | \(0.352099\pi\) | |||||||
\(594\) | 26.8102 | 1.10004 | ||||||||
\(595\) | −5.99199 | −0.245648 | ||||||||
\(596\) | −51.0822 | −2.09241 | ||||||||
\(597\) | 24.3176 | 0.995252 | ||||||||
\(598\) | 16.6842 | 0.682266 | ||||||||
\(599\) | 3.63381 | 0.148473 | 0.0742367 | − | 0.997241i | \(-0.476348\pi\) | ||||
0.0742367 | + | 0.997241i | \(0.476348\pi\) | |||||||
\(600\) | 12.3146 | 0.502743 | ||||||||
\(601\) | 44.5867 | 1.81873 | 0.909365 | − | 0.415999i | \(-0.136568\pi\) | ||||
0.909365 | + | 0.415999i | \(0.136568\pi\) | |||||||
\(602\) | −6.83441 | −0.278550 | ||||||||
\(603\) | −0.272364 | −0.0110915 | ||||||||
\(604\) | 8.33522 | 0.339155 | ||||||||
\(605\) | −5.07477 | −0.206319 | ||||||||
\(606\) | 24.9630 | 1.01405 | ||||||||
\(607\) | 42.8481 | 1.73915 | 0.869575 | − | 0.493801i | \(-0.164393\pi\) | ||||
0.869575 | + | 0.493801i | \(0.164393\pi\) | |||||||
\(608\) | −38.7972 | −1.57344 | ||||||||
\(609\) | 7.35440 | 0.298015 | ||||||||
\(610\) | 8.94088 | 0.362006 | ||||||||
\(611\) | −36.4695 | −1.47540 | ||||||||
\(612\) | 1.36275 | 0.0550859 | ||||||||
\(613\) | 22.1752 | 0.895647 | 0.447824 | − | 0.894122i | \(-0.352199\pi\) | ||||
0.447824 | + | 0.894122i | \(0.352199\pi\) | |||||||
\(614\) | 17.6223 | 0.711176 | ||||||||
\(615\) | 10.7592 | 0.433854 | ||||||||
\(616\) | −3.36300 | −0.135499 | ||||||||
\(617\) | −37.0742 | −1.49255 | −0.746275 | − | 0.665638i | \(-0.768160\pi\) | ||||
−0.746275 | + | 0.665638i | \(0.768160\pi\) | |||||||
\(618\) | −4.23404 | −0.170318 | ||||||||
\(619\) | 22.9627 | 0.922947 | 0.461474 | − | 0.887154i | \(-0.347321\pi\) | ||||
0.461474 | + | 0.887154i | \(0.347321\pi\) | |||||||
\(620\) | 10.0713 | 0.404475 | ||||||||
\(621\) | 12.0377 | 0.483057 | ||||||||
\(622\) | −68.6906 | −2.75424 | ||||||||
\(623\) | −11.3233 | −0.453657 | ||||||||
\(624\) | −10.2644 | −0.410903 | ||||||||
\(625\) | 13.1624 | 0.526496 | ||||||||
\(626\) | −28.3708 | −1.13393 | ||||||||
\(627\) | −20.9971 | −0.838545 | ||||||||
\(628\) | −7.60646 | −0.303531 | ||||||||
\(629\) | −7.84946 | −0.312978 | ||||||||
\(630\) | 0.104002 | 0.00414353 | ||||||||
\(631\) | 44.4583 | 1.76986 | 0.884928 | − | 0.465727i | \(-0.154207\pi\) | ||||
0.884928 | + | 0.465727i | \(0.154207\pi\) | |||||||
\(632\) | 8.39896 | 0.334093 | ||||||||
\(633\) | 0.950746 | 0.0377888 | ||||||||
\(634\) | −71.1869 | −2.82719 | ||||||||
\(635\) | −3.46493 | −0.137502 | ||||||||
\(636\) | 30.5253 | 1.21041 | ||||||||
\(637\) | −20.9527 | −0.830177 | ||||||||
\(638\) | −26.2479 | −1.03917 | ||||||||
\(639\) | 0.398858 | 0.0157786 | ||||||||
\(640\) | 11.6378 | 0.460023 | ||||||||
\(641\) | 6.44954 | 0.254741 | 0.127371 | − | 0.991855i | \(-0.459346\pi\) | ||||
0.127371 | + | 0.991855i | \(0.459346\pi\) | |||||||
\(642\) | 28.9064 | 1.14084 | ||||||||
\(643\) | 22.6561 | 0.893468 | 0.446734 | − | 0.894667i | \(-0.352587\pi\) | ||||
0.446734 | + | 0.894667i | \(0.352587\pi\) | |||||||
\(644\) | −5.34018 | −0.210433 | ||||||||
\(645\) | 5.86068 | 0.230764 | ||||||||
\(646\) | −90.1442 | −3.54668 | ||||||||
\(647\) | −18.2558 | −0.717709 | −0.358855 | − | 0.933393i | \(-0.616833\pi\) | ||||
−0.358855 | + | 0.933393i | \(0.616833\pi\) | |||||||
\(648\) | 15.1992 | 0.597080 | ||||||||
\(649\) | −19.1778 | −0.752795 | ||||||||
\(650\) | 30.2933 | 1.18820 | ||||||||
\(651\) | 5.65447 | 0.221616 | ||||||||
\(652\) | 2.78846 | 0.109204 | ||||||||
\(653\) | −4.17584 | −0.163413 | −0.0817067 | − | 0.996656i | \(-0.526037\pi\) | ||||
−0.0817067 | + | 0.996656i | \(0.526037\pi\) | |||||||
\(654\) | −49.5712 | −1.93839 | ||||||||
\(655\) | 13.0589 | 0.510253 | ||||||||
\(656\) | −12.3695 | −0.482949 | ||||||||
\(657\) | 0.311239 | 0.0121426 | ||||||||
\(658\) | 20.0453 | 0.781448 | ||||||||
\(659\) | −5.16924 | −0.201365 | −0.100683 | − | 0.994919i | \(-0.532103\pi\) | ||||
−0.100683 | + | 0.994919i | \(0.532103\pi\) | |||||||
\(660\) | 10.1990 | 0.396997 | ||||||||
\(661\) | −13.8351 | −0.538123 | −0.269061 | − | 0.963123i | \(-0.586713\pi\) | ||||
−0.269061 | + | 0.963123i | \(0.586713\pi\) | |||||||
\(662\) | −16.8824 | −0.656155 | ||||||||
\(663\) | −44.7257 | −1.73700 | ||||||||
\(664\) | −8.15521 | −0.316484 | ||||||||
\(665\) | −4.00619 | −0.155353 | ||||||||
\(666\) | 0.136242 | 0.00527925 | ||||||||
\(667\) | −11.7853 | −0.456327 | ||||||||
\(668\) | −58.1406 | −2.24953 | ||||||||
\(669\) | 11.5817 | 0.447775 | ||||||||
\(670\) | −8.75124 | −0.338090 | ||||||||
\(671\) | −10.4328 | −0.402754 | ||||||||
\(672\) | 10.5804 | 0.408149 | ||||||||
\(673\) | 16.8321 | 0.648829 | 0.324414 | − | 0.945915i | \(-0.394833\pi\) | ||||
0.324414 | + | 0.945915i | \(0.394833\pi\) | |||||||
\(674\) | −37.2048 | −1.43308 | ||||||||
\(675\) | 21.8568 | 0.841269 | ||||||||
\(676\) | −5.43325 | −0.208971 | ||||||||
\(677\) | −20.0077 | −0.768957 | −0.384478 | − | 0.923134i | \(-0.625619\pi\) | ||||
−0.384478 | + | 0.923134i | \(0.625619\pi\) | |||||||
\(678\) | 2.36463 | 0.0908130 | ||||||||
\(679\) | −3.00589 | −0.115356 | ||||||||
\(680\) | 12.3809 | 0.474785 | ||||||||
\(681\) | 19.6699 | 0.753751 | ||||||||
\(682\) | −20.1808 | −0.772765 | ||||||||
\(683\) | 5.50311 | 0.210571 | 0.105285 | − | 0.994442i | \(-0.466424\pi\) | ||||
0.105285 | + | 0.994442i | \(0.466424\pi\) | |||||||
\(684\) | 0.911122 | 0.0348376 | ||||||||
\(685\) | −6.29503 | −0.240521 | ||||||||
\(686\) | 24.3072 | 0.928055 | ||||||||
\(687\) | 13.2966 | 0.507298 | ||||||||
\(688\) | −6.73784 | −0.256878 | ||||||||
\(689\) | 21.2325 | 0.808893 | ||||||||
\(690\) | 7.86384 | 0.299371 | ||||||||
\(691\) | 21.2934 | 0.810040 | 0.405020 | − | 0.914308i | \(-0.367265\pi\) | ||||
0.405020 | + | 0.914308i | \(0.367265\pi\) | |||||||
\(692\) | 1.78634 | 0.0679065 | ||||||||
\(693\) | −0.121356 | −0.00460994 | ||||||||
\(694\) | −32.8382 | −1.24652 | ||||||||
\(695\) | 17.7646 | 0.673849 | ||||||||
\(696\) | −15.1959 | −0.576000 | ||||||||
\(697\) | −53.8988 | −2.04156 | ||||||||
\(698\) | −27.3396 | −1.03482 | ||||||||
\(699\) | 51.9560 | 1.96515 | ||||||||
\(700\) | −9.69614 | −0.366480 | ||||||||
\(701\) | 23.2634 | 0.878648 | 0.439324 | − | 0.898329i | \(-0.355218\pi\) | ||||
0.439324 | + | 0.898329i | \(0.355218\pi\) | |||||||
\(702\) | 38.1819 | 1.44108 | ||||||||
\(703\) | −5.24808 | −0.197935 | ||||||||
\(704\) | −29.3517 | −1.10623 | ||||||||
\(705\) | −17.1894 | −0.647389 | ||||||||
\(706\) | 17.7319 | 0.667349 | ||||||||
\(707\) | −5.55761 | −0.209015 | ||||||||
\(708\) | −39.2660 | −1.47571 | ||||||||
\(709\) | 46.7812 | 1.75690 | 0.878452 | − | 0.477831i | \(-0.158577\pi\) | ||||
0.878452 | + | 0.477831i | \(0.158577\pi\) | |||||||
\(710\) | 12.8156 | 0.480961 | ||||||||
\(711\) | 0.303082 | 0.0113665 | ||||||||
\(712\) | 23.3965 | 0.876822 | ||||||||
\(713\) | −9.06116 | −0.339343 | ||||||||
\(714\) | 24.5833 | 0.920009 | ||||||||
\(715\) | 7.09413 | 0.265305 | ||||||||
\(716\) | −55.3359 | −2.06800 | ||||||||
\(717\) | −31.1432 | −1.16306 | ||||||||
\(718\) | 82.1833 | 3.06706 | ||||||||
\(719\) | 25.0578 | 0.934498 | 0.467249 | − | 0.884126i | \(-0.345245\pi\) | ||||
0.467249 | + | 0.884126i | \(0.345245\pi\) | |||||||
\(720\) | 0.102532 | 0.00382115 | ||||||||
\(721\) | 0.942642 | 0.0351058 | ||||||||
\(722\) | −18.6928 | −0.695673 | ||||||||
\(723\) | 29.9094 | 1.11234 | ||||||||
\(724\) | −27.7994 | −1.03316 | ||||||||
\(725\) | −21.3984 | −0.794718 | ||||||||
\(726\) | 20.8203 | 0.772712 | ||||||||
\(727\) | 9.48198 | 0.351667 | 0.175833 | − | 0.984420i | \(-0.443738\pi\) | ||||
0.175833 | + | 0.984420i | \(0.443738\pi\) | |||||||
\(728\) | −4.78944 | −0.177508 | ||||||||
\(729\) | 27.5368 | 1.01988 | ||||||||
\(730\) | 10.0003 | 0.370129 | ||||||||
\(731\) | −29.3593 | −1.08589 | ||||||||
\(732\) | −21.3608 | −0.789520 | ||||||||
\(733\) | 25.3630 | 0.936803 | 0.468401 | − | 0.883516i | \(-0.344830\pi\) | ||||
0.468401 | + | 0.883516i | \(0.344830\pi\) | |||||||
\(734\) | −68.5030 | −2.52849 | ||||||||
\(735\) | −9.87577 | −0.364273 | ||||||||
\(736\) | −16.9549 | −0.624967 | ||||||||
\(737\) | 10.2115 | 0.376146 | ||||||||
\(738\) | 0.935512 | 0.0344367 | ||||||||
\(739\) | −29.0231 | −1.06763 | −0.533816 | − | 0.845600i | \(-0.679243\pi\) | ||||
−0.533816 | + | 0.845600i | \(0.679243\pi\) | |||||||
\(740\) | 2.54917 | 0.0937094 | ||||||||
\(741\) | −29.9032 | −1.09852 | ||||||||
\(742\) | −11.6704 | −0.428432 | ||||||||
\(743\) | −13.1053 | −0.480787 | −0.240393 | − | 0.970676i | \(-0.577276\pi\) | ||||
−0.240393 | + | 0.970676i | \(0.577276\pi\) | |||||||
\(744\) | −11.6835 | −0.428337 | ||||||||
\(745\) | −16.7471 | −0.613567 | ||||||||
\(746\) | 35.6183 | 1.30408 | ||||||||
\(747\) | −0.294287 | −0.0107674 | ||||||||
\(748\) | −51.0925 | −1.86813 | ||||||||
\(749\) | −6.43555 | −0.235150 | ||||||||
\(750\) | 31.4222 | 1.14738 | ||||||||
\(751\) | 5.05435 | 0.184436 | 0.0922180 | − | 0.995739i | \(-0.470604\pi\) | ||||
0.0922180 | + | 0.995739i | \(0.470604\pi\) | |||||||
\(752\) | 19.7621 | 0.720648 | ||||||||
\(753\) | 50.1716 | 1.82836 | ||||||||
\(754\) | −37.3812 | −1.36134 | ||||||||
\(755\) | 2.73267 | 0.0994521 | ||||||||
\(756\) | −12.2211 | −0.444476 | ||||||||
\(757\) | 3.41290 | 0.124044 | 0.0620219 | − | 0.998075i | \(-0.480245\pi\) | ||||
0.0620219 | + | 0.998075i | \(0.480245\pi\) | |||||||
\(758\) | 82.9272 | 3.01205 | ||||||||
\(759\) | −9.17604 | −0.333069 | ||||||||
\(760\) | 8.27774 | 0.300265 | ||||||||
\(761\) | −6.65851 | −0.241371 | −0.120685 | − | 0.992691i | \(-0.538509\pi\) | ||||
−0.120685 | + | 0.992691i | \(0.538509\pi\) | |||||||
\(762\) | 14.2156 | 0.514976 | ||||||||
\(763\) | 11.0362 | 0.399539 | ||||||||
\(764\) | −33.8982 | −1.22639 | ||||||||
\(765\) | 0.446772 | 0.0161531 | ||||||||
\(766\) | 12.0259 | 0.434513 | ||||||||
\(767\) | −27.3122 | −0.986187 | ||||||||
\(768\) | −4.64241 | −0.167519 | ||||||||
\(769\) | −16.0066 | −0.577212 | −0.288606 | − | 0.957448i | \(-0.593192\pi\) | ||||
−0.288606 | + | 0.957448i | \(0.593192\pi\) | |||||||
\(770\) | −3.89926 | −0.140520 | ||||||||
\(771\) | 19.2024 | 0.691556 | ||||||||
\(772\) | 14.4745 | 0.520947 | ||||||||
\(773\) | 16.2364 | 0.583982 | 0.291991 | − | 0.956421i | \(-0.405682\pi\) | ||||
0.291991 | + | 0.956421i | \(0.405682\pi\) | |||||||
\(774\) | 0.509585 | 0.0183166 | ||||||||
\(775\) | −16.4523 | −0.590984 | ||||||||
\(776\) | 6.21089 | 0.222958 | ||||||||
\(777\) | 1.43121 | 0.0513444 | ||||||||
\(778\) | −36.5835 | −1.31158 | ||||||||
\(779\) | −36.0363 | −1.29113 | ||||||||
\(780\) | 14.5250 | 0.520079 | ||||||||
\(781\) | −14.9541 | −0.535099 | ||||||||
\(782\) | −39.3943 | −1.40874 | ||||||||
\(783\) | −26.9707 | −0.963855 | ||||||||
\(784\) | 11.3539 | 0.405495 | ||||||||
\(785\) | −2.49375 | −0.0890058 | ||||||||
\(786\) | −53.5767 | −1.91102 | ||||||||
\(787\) | −40.8762 | −1.45708 | −0.728539 | − | 0.685005i | \(-0.759800\pi\) | ||||
−0.728539 | + | 0.685005i | \(0.759800\pi\) | |||||||
\(788\) | −63.6179 | −2.26629 | ||||||||
\(789\) | 14.5331 | 0.517391 | ||||||||
\(790\) | 9.73826 | 0.346472 | ||||||||
\(791\) | −0.526447 | −0.0187183 | ||||||||
\(792\) | 0.250750 | 0.00891003 | ||||||||
\(793\) | −14.8579 | −0.527621 | ||||||||
\(794\) | 33.8908 | 1.20274 | ||||||||
\(795\) | 10.0076 | 0.354934 | ||||||||
\(796\) | 39.5619 | 1.40224 | ||||||||
\(797\) | 43.0186 | 1.52380 | 0.761898 | − | 0.647697i | \(-0.224268\pi\) | ||||
0.761898 | + | 0.647697i | \(0.224268\pi\) | |||||||
\(798\) | 16.4362 | 0.581835 | ||||||||
\(799\) | 86.1109 | 3.04638 | ||||||||
\(800\) | −30.7850 | −1.08841 | ||||||||
\(801\) | 0.844280 | 0.0298312 | ||||||||
\(802\) | −16.0062 | −0.565199 | ||||||||
\(803\) | −11.6690 | −0.411792 | ||||||||
\(804\) | 20.9078 | 0.737361 | ||||||||
\(805\) | −1.75076 | −0.0617062 | ||||||||
\(806\) | −28.7407 | −1.01235 | ||||||||
\(807\) | −29.6542 | −1.04388 | ||||||||
\(808\) | 11.4833 | 0.403982 | ||||||||
\(809\) | −12.2106 | −0.429303 | −0.214652 | − | 0.976691i | \(-0.568862\pi\) | ||||
−0.214652 | + | 0.976691i | \(0.568862\pi\) | |||||||
\(810\) | 17.6228 | 0.619204 | ||||||||
\(811\) | −27.6071 | −0.969417 | −0.484708 | − | 0.874676i | \(-0.661074\pi\) | ||||
−0.484708 | + | 0.874676i | \(0.661074\pi\) | |||||||
\(812\) | 11.9648 | 0.419882 | ||||||||
\(813\) | −53.0376 | −1.86011 | ||||||||
\(814\) | −5.10800 | −0.179035 | ||||||||
\(815\) | 0.914186 | 0.0320226 | ||||||||
\(816\) | 24.2360 | 0.848429 | ||||||||
\(817\) | −19.6294 | −0.686746 | ||||||||
\(818\) | −18.6067 | −0.650567 | ||||||||
\(819\) | −0.172830 | −0.00603918 | ||||||||
\(820\) | 17.5040 | 0.611268 | ||||||||
\(821\) | −20.4762 | −0.714624 | −0.357312 | − | 0.933985i | \(-0.616307\pi\) | ||||
−0.357312 | + | 0.933985i | \(0.616307\pi\) | |||||||
\(822\) | 25.8266 | 0.900807 | ||||||||
\(823\) | −0.0564176 | −0.00196660 | −0.000983298 | − | 1.00000i | \(-0.500313\pi\) | ||||
−0.000983298 | 1.00000i | \(0.500313\pi\) | ||||||||
\(824\) | −1.94772 | −0.0678521 | ||||||||
\(825\) | −16.6609 | −0.580057 | ||||||||
\(826\) | 15.0121 | 0.522337 | ||||||||
\(827\) | −33.2434 | −1.15599 | −0.577993 | − | 0.816042i | \(-0.696164\pi\) | ||||
−0.577993 | + | 0.816042i | \(0.696164\pi\) | |||||||
\(828\) | 0.398173 | 0.0138375 | ||||||||
\(829\) | −8.71472 | −0.302675 | −0.151337 | − | 0.988482i | \(-0.548358\pi\) | ||||
−0.151337 | + | 0.988482i | \(0.548358\pi\) | |||||||
\(830\) | −9.45565 | −0.328210 | ||||||||
\(831\) | −53.0438 | −1.84007 | ||||||||
\(832\) | −41.8014 | −1.44920 | ||||||||
\(833\) | 49.4731 | 1.71414 | ||||||||
\(834\) | −72.8828 | −2.52372 | ||||||||
\(835\) | −19.0612 | −0.659640 | ||||||||
\(836\) | −34.1600 | −1.18145 | ||||||||
\(837\) | −20.7366 | −0.716761 | ||||||||
\(838\) | 30.2540 | 1.04511 | ||||||||
\(839\) | 34.8972 | 1.20479 | 0.602393 | − | 0.798199i | \(-0.294214\pi\) | ||||
0.602393 | + | 0.798199i | \(0.294214\pi\) | |||||||
\(840\) | −2.25743 | −0.0778888 | ||||||||
\(841\) | −2.59490 | −0.0894793 | ||||||||
\(842\) | −85.6281 | −2.95094 | ||||||||
\(843\) | 6.68041 | 0.230086 | ||||||||
\(844\) | 1.54676 | 0.0532416 | ||||||||
\(845\) | −1.78127 | −0.0612776 | ||||||||
\(846\) | −1.49461 | −0.0513858 | ||||||||
\(847\) | −4.63530 | −0.159271 | ||||||||
\(848\) | −11.5054 | −0.395099 | ||||||||
\(849\) | −16.5033 | −0.566393 | ||||||||
\(850\) | −71.5280 | −2.45339 | ||||||||
\(851\) | −2.29348 | −0.0786196 | ||||||||
\(852\) | −30.6180 | −1.04896 | ||||||||
\(853\) | −0.236114 | −0.00808440 | −0.00404220 | − | 0.999992i | \(-0.501287\pi\) | ||||
−0.00404220 | + | 0.999992i | \(0.501287\pi\) | |||||||
\(854\) | 8.16662 | 0.279456 | ||||||||
\(855\) | 0.298708 | 0.0102156 | ||||||||
\(856\) | 13.2974 | 0.454495 | ||||||||
\(857\) | −50.1929 | −1.71456 | −0.857278 | − | 0.514854i | \(-0.827846\pi\) | ||||
−0.857278 | + | 0.514854i | \(0.827846\pi\) | |||||||
\(858\) | −29.1051 | −0.993631 | ||||||||
\(859\) | 10.9770 | 0.374529 | 0.187264 | − | 0.982310i | \(-0.440038\pi\) | ||||
0.187264 | + | 0.982310i | \(0.440038\pi\) | |||||||
\(860\) | 9.53467 | 0.325129 | ||||||||
\(861\) | 9.82749 | 0.334920 | ||||||||
\(862\) | 63.7280 | 2.17059 | ||||||||
\(863\) | −24.4521 | −0.832361 | −0.416180 | − | 0.909282i | \(-0.636632\pi\) | ||||
−0.416180 | + | 0.909282i | \(0.636632\pi\) | |||||||
\(864\) | −38.8016 | −1.32006 | ||||||||
\(865\) | 0.585645 | 0.0199125 | ||||||||
\(866\) | 43.9286 | 1.49275 | ||||||||
\(867\) | 76.4677 | 2.59698 | ||||||||
\(868\) | 9.19918 | 0.312241 | ||||||||
\(869\) | −11.3632 | −0.385471 | ||||||||
\(870\) | −17.6191 | −0.597343 | ||||||||
\(871\) | 14.5428 | 0.492764 | ||||||||
\(872\) | −22.8035 | −0.772224 | ||||||||
\(873\) | 0.224124 | 0.00758546 | ||||||||
\(874\) | −26.3386 | −0.890918 | ||||||||
\(875\) | −6.99566 | −0.236497 | ||||||||
\(876\) | −23.8920 | −0.807237 | ||||||||
\(877\) | 13.8825 | 0.468779 | 0.234390 | − | 0.972143i | \(-0.424691\pi\) | ||||
0.234390 | + | 0.972143i | \(0.424691\pi\) | |||||||
\(878\) | 28.8149 | 0.972456 | ||||||||
\(879\) | −43.4287 | −1.46481 | ||||||||
\(880\) | −3.84416 | −0.129587 | ||||||||
\(881\) | −14.4570 | −0.487069 | −0.243535 | − | 0.969892i | \(-0.578307\pi\) | ||||
−0.243535 | + | 0.969892i | \(0.578307\pi\) | |||||||
\(882\) | −0.858696 | −0.0289138 | ||||||||
\(883\) | −16.1102 | −0.542150 | −0.271075 | − | 0.962558i | \(-0.587379\pi\) | ||||
−0.271075 | + | 0.962558i | \(0.587379\pi\) | |||||||
\(884\) | −72.7637 | −2.44731 | ||||||||
\(885\) | −12.8732 | −0.432729 | ||||||||
\(886\) | 28.3353 | 0.951942 | ||||||||
\(887\) | −55.6919 | −1.86995 | −0.934976 | − | 0.354711i | \(-0.884579\pi\) | ||||
−0.934976 | + | 0.354711i | \(0.884579\pi\) | |||||||
\(888\) | −2.95722 | −0.0992377 | ||||||||
\(889\) | −3.16488 | −0.106147 | ||||||||
\(890\) | 27.1274 | 0.909311 | ||||||||
\(891\) | −20.5635 | −0.688903 | ||||||||
\(892\) | 18.8421 | 0.630882 | ||||||||
\(893\) | 57.5730 | 1.92661 | ||||||||
\(894\) | 68.7084 | 2.29795 | ||||||||
\(895\) | −18.1417 | −0.606409 | ||||||||
\(896\) | 10.6300 | 0.355122 | ||||||||
\(897\) | −13.0681 | −0.436332 | ||||||||
\(898\) | 24.0075 | 0.801141 | ||||||||
\(899\) | 20.3017 | 0.677099 | ||||||||
\(900\) | 0.722960 | 0.0240987 | ||||||||
\(901\) | −50.1336 | −1.67019 | ||||||||
\(902\) | −35.0744 | −1.16785 | ||||||||
\(903\) | 5.35316 | 0.178142 | ||||||||
\(904\) | 1.08776 | 0.0361785 | ||||||||
\(905\) | −9.11393 | −0.302957 | ||||||||
\(906\) | −11.2113 | −0.372472 | ||||||||
\(907\) | 30.2278 | 1.00370 | 0.501849 | − | 0.864955i | \(-0.332653\pi\) | ||||
0.501849 | + | 0.864955i | \(0.332653\pi\) | |||||||
\(908\) | 32.0007 | 1.06198 | ||||||||
\(909\) | 0.414384 | 0.0137443 | ||||||||
\(910\) | −5.55316 | −0.184086 | ||||||||
\(911\) | −9.80346 | −0.324803 | −0.162401 | − | 0.986725i | \(-0.551924\pi\) | ||||
−0.162401 | + | 0.986725i | \(0.551924\pi\) | |||||||
\(912\) | 16.2040 | 0.536567 | ||||||||
\(913\) | 11.0335 | 0.365154 | ||||||||
\(914\) | 13.9635 | 0.461873 | ||||||||
\(915\) | −7.00308 | −0.231515 | ||||||||
\(916\) | 21.6321 | 0.714745 | ||||||||
\(917\) | 11.9280 | 0.393898 | ||||||||
\(918\) | −90.1543 | −2.97554 | ||||||||
\(919\) | −37.6404 | −1.24164 | −0.620821 | − | 0.783953i | \(-0.713200\pi\) | ||||
−0.620821 | + | 0.783953i | \(0.713200\pi\) | |||||||
\(920\) | 3.61749 | 0.119265 | ||||||||
\(921\) | −13.8029 | −0.454821 | ||||||||
\(922\) | 1.02346 | 0.0337060 | ||||||||
\(923\) | −21.2970 | −0.700998 | ||||||||
\(924\) | 9.31581 | 0.306468 | ||||||||
\(925\) | −4.16426 | −0.136920 | ||||||||
\(926\) | −21.6843 | −0.712591 | ||||||||
\(927\) | −0.0702849 | −0.00230846 | ||||||||
\(928\) | 37.9878 | 1.24701 | ||||||||
\(929\) | −21.5188 | −0.706010 | −0.353005 | − | 0.935621i | \(-0.614840\pi\) | ||||
−0.353005 | + | 0.935621i | \(0.614840\pi\) | |||||||
\(930\) | −13.5465 | −0.444208 | ||||||||
\(931\) | 33.0773 | 1.08406 | ||||||||
\(932\) | 84.5265 | 2.76876 | ||||||||
\(933\) | 53.8029 | 1.76143 | ||||||||
\(934\) | −1.73861 | −0.0568891 | ||||||||
\(935\) | −16.7505 | −0.547800 | ||||||||
\(936\) | 0.357108 | 0.0116724 | ||||||||
\(937\) | −45.8465 | −1.49774 | −0.748870 | − | 0.662717i | \(-0.769403\pi\) | ||||
−0.748870 | + | 0.662717i | \(0.769403\pi\) | |||||||
\(938\) | −7.99340 | −0.260994 | ||||||||
\(939\) | 22.2219 | 0.725183 | ||||||||
\(940\) | −27.9652 | −0.912123 | ||||||||
\(941\) | −3.70795 | −0.120876 | −0.0604378 | − | 0.998172i | \(-0.519250\pi\) | ||||
−0.0604378 | + | 0.998172i | \(0.519250\pi\) | |||||||
\(942\) | 10.2311 | 0.333348 | ||||||||
\(943\) | −15.7483 | −0.512837 | ||||||||
\(944\) | 14.7999 | 0.481697 | ||||||||
\(945\) | −4.00664 | −0.130336 | ||||||||
\(946\) | −19.1055 | −0.621172 | ||||||||
\(947\) | −37.7647 | −1.22719 | −0.613594 | − | 0.789622i | \(-0.710277\pi\) | ||||
−0.613594 | + | 0.789622i | \(0.710277\pi\) | |||||||
\(948\) | −23.2659 | −0.755641 | ||||||||
\(949\) | −16.6186 | −0.539461 | ||||||||
\(950\) | −47.8229 | −1.55158 | ||||||||
\(951\) | 55.7582 | 1.80808 | ||||||||
\(952\) | 11.3087 | 0.366517 | ||||||||
\(953\) | 28.4079 | 0.920221 | 0.460110 | − | 0.887862i | \(-0.347810\pi\) | ||||
0.460110 | + | 0.887862i | \(0.347810\pi\) | |||||||
\(954\) | 0.870160 | 0.0281725 | ||||||||
\(955\) | −11.1134 | −0.359621 | ||||||||
\(956\) | −50.6665 | −1.63867 | ||||||||
\(957\) | 20.5591 | 0.664581 | ||||||||
\(958\) | 18.6412 | 0.602269 | ||||||||
\(959\) | −5.74990 | −0.185674 | ||||||||
\(960\) | −19.7025 | −0.635895 | ||||||||
\(961\) | −15.3909 | −0.496482 | ||||||||
\(962\) | −7.27460 | −0.234542 | ||||||||
\(963\) | 0.479845 | 0.0154628 | ||||||||
\(964\) | 48.6593 | 1.56721 | ||||||||
\(965\) | 4.74540 | 0.152760 | ||||||||
\(966\) | 7.18285 | 0.231104 | ||||||||
\(967\) | 39.5934 | 1.27324 | 0.636619 | − | 0.771178i | \(-0.280332\pi\) | ||||
0.636619 | + | 0.771178i | \(0.280332\pi\) | |||||||
\(968\) | 9.57763 | 0.307837 | ||||||||
\(969\) | 70.6068 | 2.26822 | ||||||||
\(970\) | 7.20128 | 0.231219 | ||||||||
\(971\) | −16.2409 | −0.521197 | −0.260598 | − | 0.965447i | \(-0.583920\pi\) | ||||
−0.260598 | + | 0.965447i | \(0.583920\pi\) | |||||||
\(972\) | 1.80392 | 0.0578608 | ||||||||
\(973\) | 16.2262 | 0.520188 | ||||||||
\(974\) | −19.7405 | −0.632527 | ||||||||
\(975\) | −23.7277 | −0.759895 | ||||||||
\(976\) | 8.05122 | 0.257713 | ||||||||
\(977\) | −36.7740 | −1.17651 | −0.588253 | − | 0.808677i | \(-0.700184\pi\) | ||||
−0.588253 | + | 0.808677i | \(0.700184\pi\) | |||||||
\(978\) | −3.75063 | −0.119932 | ||||||||
\(979\) | −31.6540 | −1.01166 | ||||||||
\(980\) | −16.0668 | −0.513234 | ||||||||
\(981\) | −0.822880 | −0.0262725 | ||||||||
\(982\) | 78.0234 | 2.48983 | ||||||||
\(983\) | 11.9710 | 0.381816 | 0.190908 | − | 0.981608i | \(-0.438857\pi\) | ||||
0.190908 | + | 0.981608i | \(0.438857\pi\) | |||||||
\(984\) | −20.3059 | −0.647329 | ||||||||
\(985\) | −20.8569 | −0.664557 | ||||||||
\(986\) | 88.2636 | 2.81089 | ||||||||
\(987\) | −15.7008 | −0.499762 | ||||||||
\(988\) | −48.6492 | −1.54774 | ||||||||
\(989\) | −8.57832 | −0.272775 | ||||||||
\(990\) | 0.290735 | 0.00924017 | ||||||||
\(991\) | −39.6244 | −1.25871 | −0.629354 | − | 0.777118i | \(-0.716681\pi\) | ||||
−0.629354 | + | 0.777118i | \(0.716681\pi\) | |||||||
\(992\) | 29.2071 | 0.927327 | ||||||||
\(993\) | 13.2234 | 0.419633 | ||||||||
\(994\) | 11.7058 | 0.371286 | ||||||||
\(995\) | 12.9702 | 0.411184 | ||||||||
\(996\) | 22.5907 | 0.715813 | ||||||||
\(997\) | 34.2298 | 1.08407 | 0.542034 | − | 0.840356i | \(-0.317654\pi\) | ||||
0.542034 | + | 0.840356i | \(0.317654\pi\) | |||||||
\(998\) | −63.2363 | −2.00171 | ||||||||
\(999\) | −5.24866 | −0.166060 |
(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 | 6031.2.a.b.1.16 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6031.2.a.b.1.16 | ✓ | 109 | 1.1 | even | 1 | trivial |