Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.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: | \(48.2376278611\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65744 | −1.87909 | −0.939545 | − | 0.342425i | \(-0.888752\pi\) | ||||
−0.939545 | + | 0.342425i | \(0.888752\pi\) | |||||||
\(3\) | 2.58260 | 1.49106 | 0.745531 | − | 0.666471i | \(-0.232196\pi\) | ||||
0.745531 | + | 0.666471i | \(0.232196\pi\) | |||||||
\(4\) | 5.06196 | 2.53098 | ||||||||
\(5\) | 1.09780 | 0.490949 | 0.245475 | − | 0.969403i | \(-0.421056\pi\) | ||||
0.245475 | + | 0.969403i | \(0.421056\pi\) | |||||||
\(6\) | −6.86308 | −2.80184 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −8.13696 | −2.87685 | ||||||||
\(9\) | 3.66980 | 1.22327 | ||||||||
\(10\) | −2.91732 | −0.922538 | ||||||||
\(11\) | −0.201709 | −0.0608176 | −0.0304088 | − | 0.999538i | \(-0.509681\pi\) | ||||
−0.0304088 | + | 0.999538i | \(0.509681\pi\) | |||||||
\(12\) | 13.0730 | 3.77385 | ||||||||
\(13\) | 6.89294 | 1.91176 | 0.955879 | − | 0.293761i | \(-0.0949070\pi\) | ||||
0.955879 | + | 0.293761i | \(0.0949070\pi\) | |||||||
\(14\) | −2.65744 | −0.710229 | ||||||||
\(15\) | 2.83516 | 0.732036 | ||||||||
\(16\) | 11.4995 | 2.87488 | ||||||||
\(17\) | −3.73459 | −0.905772 | −0.452886 | − | 0.891568i | \(-0.649606\pi\) | ||||
−0.452886 | + | 0.891568i | \(0.649606\pi\) | |||||||
\(18\) | −9.75226 | −2.29863 | ||||||||
\(19\) | −0.944972 | −0.216792 | −0.108396 | − | 0.994108i | \(-0.534571\pi\) | ||||
−0.108396 | + | 0.994108i | \(0.534571\pi\) | |||||||
\(20\) | 5.55700 | 1.24258 | ||||||||
\(21\) | 2.58260 | 0.563569 | ||||||||
\(22\) | 0.536029 | 0.114282 | ||||||||
\(23\) | 9.13542 | 1.90487 | 0.952433 | − | 0.304747i | \(-0.0985718\pi\) | ||||
0.952433 | + | 0.304747i | \(0.0985718\pi\) | |||||||
\(24\) | −21.0145 | −4.28956 | ||||||||
\(25\) | −3.79484 | −0.758969 | ||||||||
\(26\) | −18.3175 | −3.59237 | ||||||||
\(27\) | 1.72982 | 0.332905 | ||||||||
\(28\) | 5.06196 | 0.956621 | ||||||||
\(29\) | 1.11926 | 0.207842 | 0.103921 | − | 0.994586i | \(-0.466861\pi\) | ||||
0.103921 | + | 0.994586i | \(0.466861\pi\) | |||||||
\(30\) | −7.53426 | −1.37556 | ||||||||
\(31\) | −3.58061 | −0.643096 | −0.321548 | − | 0.946893i | \(-0.604203\pi\) | ||||
−0.321548 | + | 0.946893i | \(0.604203\pi\) | |||||||
\(32\) | −14.2853 | −2.52531 | ||||||||
\(33\) | −0.520934 | −0.0906829 | ||||||||
\(34\) | 9.92444 | 1.70203 | ||||||||
\(35\) | 1.09780 | 0.185561 | ||||||||
\(36\) | 18.5764 | 3.09606 | ||||||||
\(37\) | −0.763262 | −0.125479 | −0.0627397 | − | 0.998030i | \(-0.519984\pi\) | ||||
−0.0627397 | + | 0.998030i | \(0.519984\pi\) | |||||||
\(38\) | 2.51120 | 0.407371 | ||||||||
\(39\) | 17.8017 | 2.85055 | ||||||||
\(40\) | −8.93273 | −1.41239 | ||||||||
\(41\) | 2.89507 | 0.452134 | 0.226067 | − | 0.974112i | \(-0.427413\pi\) | ||||
0.226067 | + | 0.974112i | \(0.427413\pi\) | |||||||
\(42\) | −6.86308 | −1.05900 | ||||||||
\(43\) | 2.11050 | 0.321848 | 0.160924 | − | 0.986967i | \(-0.448553\pi\) | ||||
0.160924 | + | 0.986967i | \(0.448553\pi\) | |||||||
\(44\) | −1.02104 | −0.153928 | ||||||||
\(45\) | 4.02869 | 0.600562 | ||||||||
\(46\) | −24.2768 | −3.57942 | ||||||||
\(47\) | 1.83346 | 0.267438 | 0.133719 | − | 0.991019i | \(-0.457308\pi\) | ||||
0.133719 | + | 0.991019i | \(0.457308\pi\) | |||||||
\(48\) | 29.6986 | 4.28663 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 10.0845 | 1.42617 | ||||||||
\(51\) | −9.64495 | −1.35056 | ||||||||
\(52\) | 34.8918 | 4.83862 | ||||||||
\(53\) | −4.73158 | −0.649933 | −0.324966 | − | 0.945726i | \(-0.605353\pi\) | ||||
−0.324966 | + | 0.945726i | \(0.605353\pi\) | |||||||
\(54\) | −4.59689 | −0.625558 | ||||||||
\(55\) | −0.221436 | −0.0298584 | ||||||||
\(56\) | −8.13696 | −1.08735 | ||||||||
\(57\) | −2.44048 | −0.323250 | ||||||||
\(58\) | −2.97437 | −0.390554 | ||||||||
\(59\) | 12.8856 | 1.67756 | 0.838781 | − | 0.544468i | \(-0.183269\pi\) | ||||
0.838781 | + | 0.544468i | \(0.183269\pi\) | |||||||
\(60\) | 14.3515 | 1.85277 | ||||||||
\(61\) | 5.93740 | 0.760206 | 0.380103 | − | 0.924944i | \(-0.375889\pi\) | ||||
0.380103 | + | 0.924944i | \(0.375889\pi\) | |||||||
\(62\) | 9.51523 | 1.20844 | ||||||||
\(63\) | 3.66980 | 0.462351 | ||||||||
\(64\) | 14.9633 | 1.87041 | ||||||||
\(65\) | 7.56704 | 0.938576 | ||||||||
\(66\) | 1.38435 | 0.170401 | ||||||||
\(67\) | 12.7010 | 1.55167 | 0.775834 | − | 0.630937i | \(-0.217329\pi\) | ||||
0.775834 | + | 0.630937i | \(0.217329\pi\) | |||||||
\(68\) | −18.9044 | −2.29249 | ||||||||
\(69\) | 23.5931 | 2.84028 | ||||||||
\(70\) | −2.91732 | −0.348687 | ||||||||
\(71\) | −10.9366 | −1.29794 | −0.648969 | − | 0.760815i | \(-0.724800\pi\) | ||||
−0.648969 | + | 0.760815i | \(0.724800\pi\) | |||||||
\(72\) | −29.8610 | −3.51916 | ||||||||
\(73\) | 7.90022 | 0.924651 | 0.462326 | − | 0.886710i | \(-0.347015\pi\) | ||||
0.462326 | + | 0.886710i | \(0.347015\pi\) | |||||||
\(74\) | 2.02832 | 0.235787 | ||||||||
\(75\) | −9.80055 | −1.13167 | ||||||||
\(76\) | −4.78341 | −0.548695 | ||||||||
\(77\) | −0.201709 | −0.0229869 | ||||||||
\(78\) | −47.3068 | −5.35644 | ||||||||
\(79\) | 1.83529 | 0.206486 | 0.103243 | − | 0.994656i | \(-0.467078\pi\) | ||||
0.103243 | + | 0.994656i | \(0.467078\pi\) | |||||||
\(80\) | 12.6241 | 1.41142 | ||||||||
\(81\) | −6.54197 | −0.726885 | ||||||||
\(82\) | −7.69347 | −0.849601 | ||||||||
\(83\) | −15.4099 | −1.69145 | −0.845727 | − | 0.533615i | \(-0.820833\pi\) | ||||
−0.845727 | + | 0.533615i | \(0.820833\pi\) | |||||||
\(84\) | 13.0730 | 1.42638 | ||||||||
\(85\) | −4.09982 | −0.444688 | ||||||||
\(86\) | −5.60851 | −0.604781 | ||||||||
\(87\) | 2.89061 | 0.309906 | ||||||||
\(88\) | 1.64130 | 0.174963 | ||||||||
\(89\) | −4.53745 | −0.480969 | −0.240485 | − | 0.970653i | \(-0.577306\pi\) | ||||
−0.240485 | + | 0.970653i | \(0.577306\pi\) | |||||||
\(90\) | −10.7060 | −1.12851 | ||||||||
\(91\) | 6.89294 | 0.722576 | ||||||||
\(92\) | 46.2431 | 4.82118 | ||||||||
\(93\) | −9.24726 | −0.958896 | ||||||||
\(94\) | −4.87231 | −0.502540 | ||||||||
\(95\) | −1.03739 | −0.106434 | ||||||||
\(96\) | −36.8932 | −3.76540 | ||||||||
\(97\) | 3.12512 | 0.317308 | 0.158654 | − | 0.987334i | \(-0.449285\pi\) | ||||
0.158654 | + | 0.987334i | \(0.449285\pi\) | |||||||
\(98\) | −2.65744 | −0.268441 | ||||||||
\(99\) | −0.740233 | −0.0743962 | ||||||||
\(100\) | −19.2093 | −1.92093 | ||||||||
\(101\) | 6.23661 | 0.620566 | 0.310283 | − | 0.950644i | \(-0.399576\pi\) | ||||
0.310283 | + | 0.950644i | \(0.399576\pi\) | |||||||
\(102\) | 25.6308 | 2.53783 | ||||||||
\(103\) | 19.7729 | 1.94829 | 0.974143 | − | 0.225933i | \(-0.0725429\pi\) | ||||
0.974143 | + | 0.225933i | \(0.0725429\pi\) | |||||||
\(104\) | −56.0876 | −5.49984 | ||||||||
\(105\) | 2.83516 | 0.276684 | ||||||||
\(106\) | 12.5739 | 1.22128 | ||||||||
\(107\) | −15.1879 | −1.46827 | −0.734137 | − | 0.679002i | \(-0.762413\pi\) | ||||
−0.734137 | + | 0.679002i | \(0.762413\pi\) | |||||||
\(108\) | 8.75630 | 0.842575 | ||||||||
\(109\) | 2.73020 | 0.261506 | 0.130753 | − | 0.991415i | \(-0.458261\pi\) | ||||
0.130753 | + | 0.991415i | \(0.458261\pi\) | |||||||
\(110\) | 0.588451 | 0.0561066 | ||||||||
\(111\) | −1.97120 | −0.187098 | ||||||||
\(112\) | 11.4995 | 1.08660 | ||||||||
\(113\) | 7.22884 | 0.680032 | 0.340016 | − | 0.940420i | \(-0.389568\pi\) | ||||
0.340016 | + | 0.940420i | \(0.389568\pi\) | |||||||
\(114\) | 6.48542 | 0.607415 | ||||||||
\(115\) | 10.0288 | 0.935193 | ||||||||
\(116\) | 5.66567 | 0.526044 | ||||||||
\(117\) | 25.2957 | 2.33859 | ||||||||
\(118\) | −34.2427 | −3.15229 | ||||||||
\(119\) | −3.73459 | −0.342350 | ||||||||
\(120\) | −23.0696 | −2.10596 | ||||||||
\(121\) | −10.9593 | −0.996301 | ||||||||
\(122\) | −15.7782 | −1.42850 | ||||||||
\(123\) | 7.47680 | 0.674160 | ||||||||
\(124\) | −18.1249 | −1.62766 | ||||||||
\(125\) | −9.65495 | −0.863565 | ||||||||
\(126\) | −9.75226 | −0.868800 | ||||||||
\(127\) | 9.33001 | 0.827904 | 0.413952 | − | 0.910299i | \(-0.364148\pi\) | ||||
0.413952 | + | 0.910299i | \(0.364148\pi\) | |||||||
\(128\) | −11.1932 | −0.989352 | ||||||||
\(129\) | 5.45056 | 0.479895 | ||||||||
\(130\) | −20.1089 | −1.76367 | ||||||||
\(131\) | −12.8113 | −1.11933 | −0.559663 | − | 0.828720i | \(-0.689070\pi\) | ||||
−0.559663 | + | 0.828720i | \(0.689070\pi\) | |||||||
\(132\) | −2.63695 | −0.229517 | ||||||||
\(133\) | −0.944972 | −0.0819395 | ||||||||
\(134\) | −33.7520 | −2.91573 | ||||||||
\(135\) | 1.89899 | 0.163439 | ||||||||
\(136\) | 30.3882 | 2.60577 | ||||||||
\(137\) | 9.59042 | 0.819365 | 0.409682 | − | 0.912228i | \(-0.365640\pi\) | ||||
0.409682 | + | 0.912228i | \(0.365640\pi\) | |||||||
\(138\) | −62.6971 | −5.33713 | ||||||||
\(139\) | 7.32695 | 0.621464 | 0.310732 | − | 0.950498i | \(-0.399426\pi\) | ||||
0.310732 | + | 0.950498i | \(0.399426\pi\) | |||||||
\(140\) | 5.55700 | 0.469652 | ||||||||
\(141\) | 4.73509 | 0.398767 | ||||||||
\(142\) | 29.0634 | 2.43894 | ||||||||
\(143\) | −1.39037 | −0.116269 | ||||||||
\(144\) | 42.2010 | 3.51675 | ||||||||
\(145\) | 1.22872 | 0.102040 | ||||||||
\(146\) | −20.9943 | −1.73750 | ||||||||
\(147\) | 2.58260 | 0.213009 | ||||||||
\(148\) | −3.86360 | −0.317586 | ||||||||
\(149\) | −16.1427 | −1.32246 | −0.661232 | − | 0.750181i | \(-0.729966\pi\) | ||||
−0.661232 | + | 0.750181i | \(0.729966\pi\) | |||||||
\(150\) | 26.0443 | 2.12651 | ||||||||
\(151\) | −8.66249 | −0.704943 | −0.352472 | − | 0.935823i | \(-0.614659\pi\) | ||||
−0.352472 | + | 0.935823i | \(0.614659\pi\) | |||||||
\(152\) | 7.68920 | 0.623677 | ||||||||
\(153\) | −13.7052 | −1.10800 | ||||||||
\(154\) | 0.536029 | 0.0431945 | ||||||||
\(155\) | −3.93078 | −0.315728 | ||||||||
\(156\) | 90.1114 | 7.21469 | ||||||||
\(157\) | −13.9430 | −1.11278 | −0.556388 | − | 0.830923i | \(-0.687813\pi\) | ||||
−0.556388 | + | 0.830923i | \(0.687813\pi\) | |||||||
\(158\) | −4.87717 | −0.388007 | ||||||||
\(159\) | −12.2198 | −0.969090 | ||||||||
\(160\) | −15.6824 | −1.23980 | ||||||||
\(161\) | 9.13542 | 0.719972 | ||||||||
\(162\) | 17.3848 | 1.36588 | ||||||||
\(163\) | 19.8922 | 1.55808 | 0.779038 | − | 0.626977i | \(-0.215708\pi\) | ||||
0.779038 | + | 0.626977i | \(0.215708\pi\) | |||||||
\(164\) | 14.6547 | 1.14434 | ||||||||
\(165\) | −0.571879 | −0.0445207 | ||||||||
\(166\) | 40.9508 | 3.17840 | ||||||||
\(167\) | −19.3471 | −1.49713 | −0.748563 | − | 0.663063i | \(-0.769256\pi\) | ||||
−0.748563 | + | 0.663063i | \(0.769256\pi\) | |||||||
\(168\) | −21.0145 | −1.62130 | ||||||||
\(169\) | 34.5126 | 2.65482 | ||||||||
\(170\) | 10.8950 | 0.835610 | ||||||||
\(171\) | −3.46786 | −0.265194 | ||||||||
\(172\) | 10.6833 | 0.814591 | ||||||||
\(173\) | 11.9286 | 0.906917 | 0.453459 | − | 0.891277i | \(-0.350190\pi\) | ||||
0.453459 | + | 0.891277i | \(0.350190\pi\) | |||||||
\(174\) | −7.68160 | −0.582340 | ||||||||
\(175\) | −3.79484 | −0.286863 | ||||||||
\(176\) | −2.31956 | −0.174844 | ||||||||
\(177\) | 33.2783 | 2.50135 | ||||||||
\(178\) | 12.0580 | 0.903785 | ||||||||
\(179\) | 24.0119 | 1.79473 | 0.897366 | − | 0.441287i | \(-0.145478\pi\) | ||||
0.897366 | + | 0.441287i | \(0.145478\pi\) | |||||||
\(180\) | 20.3931 | 1.52001 | ||||||||
\(181\) | 19.0889 | 1.41887 | 0.709433 | − | 0.704773i | \(-0.248951\pi\) | ||||
0.709433 | + | 0.704773i | \(0.248951\pi\) | |||||||
\(182\) | −18.3175 | −1.35779 | ||||||||
\(183\) | 15.3339 | 1.13351 | ||||||||
\(184\) | −74.3346 | −5.48002 | ||||||||
\(185\) | −0.837906 | −0.0616041 | ||||||||
\(186\) | 24.5740 | 1.80185 | ||||||||
\(187\) | 0.753302 | 0.0550869 | ||||||||
\(188\) | 9.28092 | 0.676881 | ||||||||
\(189\) | 1.72982 | 0.125826 | ||||||||
\(190\) | 2.75679 | 0.199998 | ||||||||
\(191\) | −4.94147 | −0.357552 | −0.178776 | − | 0.983890i | \(-0.557214\pi\) | ||||
−0.178776 | + | 0.983890i | \(0.557214\pi\) | |||||||
\(192\) | 38.6440 | 2.78889 | ||||||||
\(193\) | 16.7400 | 1.20497 | 0.602487 | − | 0.798129i | \(-0.294176\pi\) | ||||
0.602487 | + | 0.798129i | \(0.294176\pi\) | |||||||
\(194\) | −8.30480 | −0.596250 | ||||||||
\(195\) | 19.5426 | 1.39948 | ||||||||
\(196\) | 5.06196 | 0.361569 | ||||||||
\(197\) | −15.2947 | −1.08970 | −0.544851 | − | 0.838533i | \(-0.683414\pi\) | ||||
−0.544851 | + | 0.838533i | \(0.683414\pi\) | |||||||
\(198\) | 1.96712 | 0.139797 | ||||||||
\(199\) | 3.44503 | 0.244212 | 0.122106 | − | 0.992517i | \(-0.461035\pi\) | ||||
0.122106 | + | 0.992517i | \(0.461035\pi\) | |||||||
\(200\) | 30.8785 | 2.18344 | ||||||||
\(201\) | 32.8014 | 2.31364 | ||||||||
\(202\) | −16.5734 | −1.16610 | ||||||||
\(203\) | 1.11926 | 0.0785569 | ||||||||
\(204\) | −48.8223 | −3.41825 | ||||||||
\(205\) | 3.17820 | 0.221975 | ||||||||
\(206\) | −52.5453 | −3.66101 | ||||||||
\(207\) | 33.5252 | 2.33016 | ||||||||
\(208\) | 79.2655 | 5.49608 | ||||||||
\(209\) | 0.190610 | 0.0131847 | ||||||||
\(210\) | −7.53426 | −0.519914 | ||||||||
\(211\) | 3.02911 | 0.208532 | 0.104266 | − | 0.994549i | \(-0.466751\pi\) | ||||
0.104266 | + | 0.994549i | \(0.466751\pi\) | |||||||
\(212\) | −23.9511 | −1.64497 | ||||||||
\(213\) | −28.2449 | −1.93531 | ||||||||
\(214\) | 40.3610 | 2.75902 | ||||||||
\(215\) | 2.31690 | 0.158011 | ||||||||
\(216\) | −14.0755 | −0.957717 | ||||||||
\(217\) | −3.58061 | −0.243067 | ||||||||
\(218\) | −7.25533 | −0.491393 | ||||||||
\(219\) | 20.4031 | 1.37871 | ||||||||
\(220\) | −1.12090 | −0.0755710 | ||||||||
\(221\) | −25.7423 | −1.73162 | ||||||||
\(222\) | 5.23833 | 0.351573 | ||||||||
\(223\) | −23.7583 | −1.59097 | −0.795487 | − | 0.605971i | \(-0.792785\pi\) | ||||
−0.795487 | + | 0.605971i | \(0.792785\pi\) | |||||||
\(224\) | −14.2853 | −0.954478 | ||||||||
\(225\) | −13.9263 | −0.928421 | ||||||||
\(226\) | −19.2102 | −1.27784 | ||||||||
\(227\) | 3.07064 | 0.203805 | 0.101903 | − | 0.994794i | \(-0.467507\pi\) | ||||
0.101903 | + | 0.994794i | \(0.467507\pi\) | |||||||
\(228\) | −12.3536 | −0.818139 | ||||||||
\(229\) | 10.3733 | 0.685484 | 0.342742 | − | 0.939430i | \(-0.388644\pi\) | ||||
0.342742 | + | 0.939430i | \(0.388644\pi\) | |||||||
\(230\) | −26.6510 | −1.75731 | ||||||||
\(231\) | −0.520934 | −0.0342749 | ||||||||
\(232\) | −9.10741 | −0.597931 | ||||||||
\(233\) | 26.6664 | 1.74697 | 0.873486 | − | 0.486849i | \(-0.161854\pi\) | ||||
0.873486 | + | 0.486849i | \(0.161854\pi\) | |||||||
\(234\) | −67.2217 | −4.39442 | ||||||||
\(235\) | 2.01277 | 0.131299 | ||||||||
\(236\) | 65.2264 | 4.24588 | ||||||||
\(237\) | 4.73981 | 0.307884 | ||||||||
\(238\) | 9.92444 | 0.643306 | ||||||||
\(239\) | 2.85091 | 0.184410 | 0.0922049 | − | 0.995740i | \(-0.470609\pi\) | ||||
0.0922049 | + | 0.995740i | \(0.470609\pi\) | |||||||
\(240\) | 32.6030 | 2.10452 | ||||||||
\(241\) | 16.6970 | 1.07555 | 0.537775 | − | 0.843088i | \(-0.319265\pi\) | ||||
0.537775 | + | 0.843088i | \(0.319265\pi\) | |||||||
\(242\) | 29.1237 | 1.87214 | ||||||||
\(243\) | −22.0847 | −1.41674 | ||||||||
\(244\) | 30.0549 | 1.92407 | ||||||||
\(245\) | 1.09780 | 0.0701356 | ||||||||
\(246\) | −19.8691 | −1.26681 | ||||||||
\(247\) | −6.51364 | −0.414453 | ||||||||
\(248\) | 29.1353 | 1.85009 | ||||||||
\(249\) | −39.7975 | −2.52206 | ||||||||
\(250\) | 25.6574 | 1.62272 | ||||||||
\(251\) | −12.2581 | −0.773723 | −0.386861 | − | 0.922138i | \(-0.626441\pi\) | ||||
−0.386861 | + | 0.922138i | \(0.626441\pi\) | |||||||
\(252\) | 18.5764 | 1.17020 | ||||||||
\(253\) | −1.84270 | −0.115850 | ||||||||
\(254\) | −24.7939 | −1.55571 | ||||||||
\(255\) | −10.5882 | −0.663058 | ||||||||
\(256\) | −0.181202 | −0.0113251 | ||||||||
\(257\) | 18.7470 | 1.16940 | 0.584702 | − | 0.811248i | \(-0.301211\pi\) | ||||
0.584702 | + | 0.811248i | \(0.301211\pi\) | |||||||
\(258\) | −14.4845 | −0.901766 | ||||||||
\(259\) | −0.763262 | −0.0474268 | ||||||||
\(260\) | 38.3041 | 2.37552 | ||||||||
\(261\) | 4.10748 | 0.254246 | ||||||||
\(262\) | 34.0451 | 2.10332 | ||||||||
\(263\) | −4.93348 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548605\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548605\pi\) | |||||||
\(264\) | 4.23882 | 0.260881 | ||||||||
\(265\) | −5.19431 | −0.319084 | ||||||||
\(266\) | 2.51120 | 0.153972 | ||||||||
\(267\) | −11.7184 | −0.717155 | ||||||||
\(268\) | 64.2918 | 3.92724 | ||||||||
\(269\) | −1.78068 | −0.108570 | −0.0542851 | − | 0.998525i | \(-0.517288\pi\) | ||||
−0.0542851 | + | 0.998525i | \(0.517288\pi\) | |||||||
\(270\) | −5.04645 | −0.307117 | ||||||||
\(271\) | −12.0063 | −0.729329 | −0.364665 | − | 0.931139i | \(-0.618816\pi\) | ||||
−0.364665 | + | 0.931139i | \(0.618816\pi\) | |||||||
\(272\) | −42.9461 | −2.60399 | ||||||||
\(273\) | 17.8017 | 1.07741 | ||||||||
\(274\) | −25.4859 | −1.53966 | ||||||||
\(275\) | 0.765455 | 0.0461587 | ||||||||
\(276\) | 119.427 | 7.18868 | ||||||||
\(277\) | −7.22540 | −0.434132 | −0.217066 | − | 0.976157i | \(-0.569649\pi\) | ||||
−0.217066 | + | 0.976157i | \(0.569649\pi\) | |||||||
\(278\) | −19.4709 | −1.16779 | ||||||||
\(279\) | −13.1401 | −0.786678 | ||||||||
\(280\) | −8.93273 | −0.533833 | ||||||||
\(281\) | −9.73464 | −0.580720 | −0.290360 | − | 0.956918i | \(-0.593775\pi\) | ||||
−0.290360 | + | 0.956918i | \(0.593775\pi\) | |||||||
\(282\) | −12.5832 | −0.749319 | ||||||||
\(283\) | −2.40515 | −0.142971 | −0.0714856 | − | 0.997442i | \(-0.522774\pi\) | ||||
−0.0714856 | + | 0.997442i | \(0.522774\pi\) | |||||||
\(284\) | −55.3608 | −3.28506 | ||||||||
\(285\) | −2.67915 | −0.158699 | ||||||||
\(286\) | 3.69482 | 0.218479 | ||||||||
\(287\) | 2.89507 | 0.170891 | ||||||||
\(288\) | −52.4243 | −3.08913 | ||||||||
\(289\) | −3.05281 | −0.179577 | ||||||||
\(290\) | −3.26525 | −0.191742 | ||||||||
\(291\) | 8.07092 | 0.473126 | ||||||||
\(292\) | 39.9906 | 2.34027 | ||||||||
\(293\) | −6.60931 | −0.386120 | −0.193060 | − | 0.981187i | \(-0.561841\pi\) | ||||
−0.193060 | + | 0.981187i | \(0.561841\pi\) | |||||||
\(294\) | −6.86308 | −0.400263 | ||||||||
\(295\) | 14.1458 | 0.823598 | ||||||||
\(296\) | 6.21063 | 0.360986 | ||||||||
\(297\) | −0.348922 | −0.0202465 | ||||||||
\(298\) | 42.8983 | 2.48503 | ||||||||
\(299\) | 62.9699 | 3.64164 | ||||||||
\(300\) | −49.6100 | −2.86423 | ||||||||
\(301\) | 2.11050 | 0.121647 | ||||||||
\(302\) | 23.0200 | 1.32465 | ||||||||
\(303\) | 16.1066 | 0.925302 | ||||||||
\(304\) | −10.8667 | −0.623250 | ||||||||
\(305\) | 6.51805 | 0.373223 | ||||||||
\(306\) | 36.4207 | 2.08203 | ||||||||
\(307\) | −30.6581 | −1.74975 | −0.874875 | − | 0.484349i | \(-0.839057\pi\) | ||||
−0.874875 | + | 0.484349i | \(0.839057\pi\) | |||||||
\(308\) | −1.02104 | −0.0581794 | ||||||||
\(309\) | 51.0655 | 2.90502 | ||||||||
\(310\) | 10.4458 | 0.593281 | ||||||||
\(311\) | −3.30973 | −0.187678 | −0.0938388 | − | 0.995587i | \(-0.529914\pi\) | ||||
−0.0938388 | + | 0.995587i | \(0.529914\pi\) | |||||||
\(312\) | −144.852 | −8.20061 | ||||||||
\(313\) | 7.35994 | 0.416009 | 0.208004 | − | 0.978128i | \(-0.433303\pi\) | ||||
0.208004 | + | 0.978128i | \(0.433303\pi\) | |||||||
\(314\) | 37.0527 | 2.09101 | ||||||||
\(315\) | 4.02869 | 0.226991 | ||||||||
\(316\) | 9.29017 | 0.522613 | ||||||||
\(317\) | −11.7650 | −0.660787 | −0.330393 | − | 0.943843i | \(-0.607181\pi\) | ||||
−0.330393 | + | 0.943843i | \(0.607181\pi\) | |||||||
\(318\) | 32.4732 | 1.82101 | ||||||||
\(319\) | −0.225766 | −0.0126405 | ||||||||
\(320\) | 16.4266 | 0.918275 | ||||||||
\(321\) | −39.2243 | −2.18929 | ||||||||
\(322\) | −24.2768 | −1.35289 | ||||||||
\(323\) | 3.52909 | 0.196364 | ||||||||
\(324\) | −33.1152 | −1.83973 | ||||||||
\(325\) | −26.1576 | −1.45096 | ||||||||
\(326\) | −52.8622 | −2.92777 | ||||||||
\(327\) | 7.05100 | 0.389921 | ||||||||
\(328\) | −23.5571 | −1.30072 | ||||||||
\(329\) | 1.83346 | 0.101082 | ||||||||
\(330\) | 1.51973 | 0.0836584 | ||||||||
\(331\) | 18.1959 | 1.00014 | 0.500068 | − | 0.865986i | \(-0.333308\pi\) | ||||
0.500068 | + | 0.865986i | \(0.333308\pi\) | |||||||
\(332\) | −78.0042 | −4.28104 | ||||||||
\(333\) | −2.80102 | −0.153495 | ||||||||
\(334\) | 51.4138 | 2.81324 | ||||||||
\(335\) | 13.9431 | 0.761791 | ||||||||
\(336\) | 29.6986 | 1.62019 | ||||||||
\(337\) | 16.9310 | 0.922290 | 0.461145 | − | 0.887325i | \(-0.347439\pi\) | ||||
0.461145 | + | 0.887325i | \(0.347439\pi\) | |||||||
\(338\) | −91.7151 | −4.98864 | ||||||||
\(339\) | 18.6692 | 1.01397 | ||||||||
\(340\) | −20.7531 | −1.12550 | ||||||||
\(341\) | 0.722242 | 0.0391116 | ||||||||
\(342\) | 9.21561 | 0.498323 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −17.1730 | −0.925908 | ||||||||
\(345\) | 25.9004 | 1.39443 | ||||||||
\(346\) | −31.6996 | −1.70418 | ||||||||
\(347\) | −2.89197 | −0.155249 | −0.0776246 | − | 0.996983i | \(-0.524734\pi\) | ||||
−0.0776246 | + | 0.996983i | \(0.524734\pi\) | |||||||
\(348\) | 14.6321 | 0.784365 | ||||||||
\(349\) | −6.48634 | −0.347206 | −0.173603 | − | 0.984816i | \(-0.555541\pi\) | ||||
−0.173603 | + | 0.984816i | \(0.555541\pi\) | |||||||
\(350\) | 10.0845 | 0.539042 | ||||||||
\(351\) | 11.9236 | 0.636433 | ||||||||
\(352\) | 2.88148 | 0.153583 | ||||||||
\(353\) | 2.63388 | 0.140187 | 0.0700936 | − | 0.997540i | \(-0.477670\pi\) | ||||
0.0700936 | + | 0.997540i | \(0.477670\pi\) | |||||||
\(354\) | −88.4349 | −4.70026 | ||||||||
\(355\) | −12.0062 | −0.637222 | ||||||||
\(356\) | −22.9684 | −1.21732 | ||||||||
\(357\) | −9.64495 | −0.510465 | ||||||||
\(358\) | −63.8100 | −3.37246 | ||||||||
\(359\) | −12.7545 | −0.673156 | −0.336578 | − | 0.941656i | \(-0.609270\pi\) | ||||
−0.336578 | + | 0.941656i | \(0.609270\pi\) | |||||||
\(360\) | −32.7813 | −1.72773 | ||||||||
\(361\) | −18.1070 | −0.953001 | ||||||||
\(362\) | −50.7275 | −2.66618 | ||||||||
\(363\) | −28.3035 | −1.48555 | ||||||||
\(364\) | 34.8918 | 1.82883 | ||||||||
\(365\) | 8.67284 | 0.453957 | ||||||||
\(366\) | −40.7488 | −2.12998 | ||||||||
\(367\) | −10.0193 | −0.523001 | −0.261501 | − | 0.965203i | \(-0.584217\pi\) | ||||
−0.261501 | + | 0.965203i | \(0.584217\pi\) | |||||||
\(368\) | 105.053 | 5.47627 | ||||||||
\(369\) | 10.6243 | 0.553081 | ||||||||
\(370\) | 2.22668 | 0.115760 | ||||||||
\(371\) | −4.73158 | −0.245652 | ||||||||
\(372\) | −46.8093 | −2.42695 | ||||||||
\(373\) | −5.03488 | −0.260696 | −0.130348 | − | 0.991468i | \(-0.541610\pi\) | ||||
−0.130348 | + | 0.991468i | \(0.541610\pi\) | |||||||
\(374\) | −2.00185 | −0.103513 | ||||||||
\(375\) | −24.9348 | −1.28763 | ||||||||
\(376\) | −14.9188 | −0.769379 | ||||||||
\(377\) | 7.71502 | 0.397344 | ||||||||
\(378\) | −4.59689 | −0.236439 | ||||||||
\(379\) | −14.4989 | −0.744758 | −0.372379 | − | 0.928081i | \(-0.621458\pi\) | ||||
−0.372379 | + | 0.928081i | \(0.621458\pi\) | |||||||
\(380\) | −5.25121 | −0.269382 | ||||||||
\(381\) | 24.0956 | 1.23446 | ||||||||
\(382\) | 13.1316 | 0.671873 | ||||||||
\(383\) | 17.0756 | 0.872522 | 0.436261 | − | 0.899820i | \(-0.356302\pi\) | ||||
0.436261 | + | 0.899820i | \(0.356302\pi\) | |||||||
\(384\) | −28.9076 | −1.47519 | ||||||||
\(385\) | −0.221436 | −0.0112854 | ||||||||
\(386\) | −44.4856 | −2.26426 | ||||||||
\(387\) | 7.74510 | 0.393706 | ||||||||
\(388\) | 15.8192 | 0.803100 | ||||||||
\(389\) | −15.1910 | −0.770215 | −0.385107 | − | 0.922872i | \(-0.625836\pi\) | ||||
−0.385107 | + | 0.922872i | \(0.625836\pi\) | |||||||
\(390\) | −51.9332 | −2.62974 | ||||||||
\(391\) | −34.1171 | −1.72538 | ||||||||
\(392\) | −8.13696 | −0.410979 | ||||||||
\(393\) | −33.0864 | −1.66899 | ||||||||
\(394\) | 40.6447 | 2.04765 | ||||||||
\(395\) | 2.01478 | 0.101374 | ||||||||
\(396\) | −3.74703 | −0.188295 | ||||||||
\(397\) | 28.4481 | 1.42777 | 0.713885 | − | 0.700263i | \(-0.246934\pi\) | ||||
0.713885 | + | 0.700263i | \(0.246934\pi\) | |||||||
\(398\) | −9.15495 | −0.458896 | ||||||||
\(399\) | −2.44048 | −0.122177 | ||||||||
\(400\) | −43.6389 | −2.18194 | ||||||||
\(401\) | −33.4919 | −1.67251 | −0.836254 | − | 0.548343i | \(-0.815259\pi\) | ||||
−0.836254 | + | 0.548343i | \(0.815259\pi\) | |||||||
\(402\) | −87.1677 | −4.34753 | ||||||||
\(403\) | −24.6809 | −1.22944 | ||||||||
\(404\) | 31.5695 | 1.57064 | ||||||||
\(405\) | −7.18175 | −0.356864 | ||||||||
\(406\) | −2.97437 | −0.147616 | ||||||||
\(407\) | 0.153957 | 0.00763136 | ||||||||
\(408\) | 78.4806 | 3.88537 | ||||||||
\(409\) | −35.5569 | −1.75818 | −0.879088 | − | 0.476659i | \(-0.841848\pi\) | ||||
−0.879088 | + | 0.476659i | \(0.841848\pi\) | |||||||
\(410\) | −8.44586 | −0.417111 | ||||||||
\(411\) | 24.7682 | 1.22172 | ||||||||
\(412\) | 100.090 | 4.93107 | ||||||||
\(413\) | 12.8856 | 0.634059 | ||||||||
\(414\) | −89.0910 | −4.37858 | ||||||||
\(415\) | −16.9169 | −0.830419 | ||||||||
\(416\) | −98.4679 | −4.82778 | ||||||||
\(417\) | 18.9225 | 0.926641 | ||||||||
\(418\) | −0.506533 | −0.0247753 | ||||||||
\(419\) | 22.1475 | 1.08198 | 0.540989 | − | 0.841030i | \(-0.318050\pi\) | ||||
0.540989 | + | 0.841030i | \(0.318050\pi\) | |||||||
\(420\) | 14.3515 | 0.700281 | ||||||||
\(421\) | 14.6863 | 0.715764 | 0.357882 | − | 0.933767i | \(-0.383499\pi\) | ||||
0.357882 | + | 0.933767i | \(0.383499\pi\) | |||||||
\(422\) | −8.04965 | −0.391851 | ||||||||
\(423\) | 6.72844 | 0.327148 | ||||||||
\(424\) | 38.5007 | 1.86976 | ||||||||
\(425\) | 14.1722 | 0.687453 | ||||||||
\(426\) | 75.0589 | 3.63662 | ||||||||
\(427\) | 5.93740 | 0.287331 | ||||||||
\(428\) | −76.8808 | −3.71617 | ||||||||
\(429\) | −3.59076 | −0.173364 | ||||||||
\(430\) | −6.15700 | −0.296917 | ||||||||
\(431\) | 12.5056 | 0.602372 | 0.301186 | − | 0.953565i | \(-0.402618\pi\) | ||||
0.301186 | + | 0.953565i | \(0.402618\pi\) | |||||||
\(432\) | 19.8922 | 0.957062 | ||||||||
\(433\) | −22.4937 | −1.08098 | −0.540489 | − | 0.841351i | \(-0.681761\pi\) | ||||
−0.540489 | + | 0.841351i | \(0.681761\pi\) | |||||||
\(434\) | 9.51523 | 0.456746 | ||||||||
\(435\) | 3.17330 | 0.152148 | ||||||||
\(436\) | 13.8202 | 0.661866 | ||||||||
\(437\) | −8.63272 | −0.412959 | ||||||||
\(438\) | −54.2199 | −2.59073 | ||||||||
\(439\) | −28.8453 | −1.37671 | −0.688355 | − | 0.725374i | \(-0.741667\pi\) | ||||
−0.688355 | + | 0.725374i | \(0.741667\pi\) | |||||||
\(440\) | 1.80181 | 0.0858981 | ||||||||
\(441\) | 3.66980 | 0.174752 | ||||||||
\(442\) | 68.4086 | 3.25386 | ||||||||
\(443\) | 14.5488 | 0.691236 | 0.345618 | − | 0.938375i | \(-0.387669\pi\) | ||||
0.345618 | + | 0.938375i | \(0.387669\pi\) | |||||||
\(444\) | −9.97812 | −0.473540 | ||||||||
\(445\) | −4.98120 | −0.236132 | ||||||||
\(446\) | 63.1361 | 2.98958 | ||||||||
\(447\) | −41.6902 | −1.97188 | ||||||||
\(448\) | 14.9633 | 0.706947 | ||||||||
\(449\) | −37.5508 | −1.77213 | −0.886066 | − | 0.463558i | \(-0.846573\pi\) | ||||
−0.886066 | + | 0.463558i | \(0.846573\pi\) | |||||||
\(450\) | 37.0083 | 1.74459 | ||||||||
\(451\) | −0.583963 | −0.0274977 | ||||||||
\(452\) | 36.5921 | 1.72115 | ||||||||
\(453\) | −22.3717 | −1.05111 | ||||||||
\(454\) | −8.16002 | −0.382969 | ||||||||
\(455\) | 7.56704 | 0.354749 | ||||||||
\(456\) | 19.8581 | 0.929941 | ||||||||
\(457\) | −9.27077 | −0.433668 | −0.216834 | − | 0.976208i | \(-0.569573\pi\) | ||||
−0.216834 | + | 0.976208i | \(0.569573\pi\) | |||||||
\(458\) | −27.5663 | −1.28809 | ||||||||
\(459\) | −6.46019 | −0.301536 | ||||||||
\(460\) | 50.7655 | 2.36696 | ||||||||
\(461\) | 6.04166 | 0.281388 | 0.140694 | − | 0.990053i | \(-0.455067\pi\) | ||||
0.140694 | + | 0.990053i | \(0.455067\pi\) | |||||||
\(462\) | 1.38435 | 0.0644057 | ||||||||
\(463\) | 29.4709 | 1.36963 | 0.684814 | − | 0.728718i | \(-0.259884\pi\) | ||||
0.684814 | + | 0.728718i | \(0.259884\pi\) | |||||||
\(464\) | 12.8710 | 0.597521 | ||||||||
\(465\) | −10.1516 | −0.470770 | ||||||||
\(466\) | −70.8642 | −3.28272 | ||||||||
\(467\) | 5.00460 | 0.231585 | 0.115793 | − | 0.993273i | \(-0.463059\pi\) | ||||
0.115793 | + | 0.993273i | \(0.463059\pi\) | |||||||
\(468\) | 128.046 | 5.91893 | ||||||||
\(469\) | 12.7010 | 0.586476 | ||||||||
\(470\) | −5.34880 | −0.246722 | ||||||||
\(471\) | −36.0092 | −1.65922 | ||||||||
\(472\) | −104.850 | −4.82610 | ||||||||
\(473\) | −0.425707 | −0.0195740 | ||||||||
\(474\) | −12.5957 | −0.578542 | ||||||||
\(475\) | 3.58602 | 0.164538 | ||||||||
\(476\) | −18.9044 | −0.866480 | ||||||||
\(477\) | −17.3640 | −0.795041 | ||||||||
\(478\) | −7.57610 | −0.346523 | ||||||||
\(479\) | 14.1068 | 0.644554 | 0.322277 | − | 0.946645i | \(-0.395552\pi\) | ||||
0.322277 | + | 0.946645i | \(0.395552\pi\) | |||||||
\(480\) | −40.5012 | −1.84862 | ||||||||
\(481\) | −5.26112 | −0.239886 | ||||||||
\(482\) | −44.3713 | −2.02106 | ||||||||
\(483\) | 23.5931 | 1.07352 | ||||||||
\(484\) | −55.4756 | −2.52162 | ||||||||
\(485\) | 3.43074 | 0.155782 | ||||||||
\(486\) | 58.6887 | 2.66217 | ||||||||
\(487\) | −3.48237 | −0.157801 | −0.0789005 | − | 0.996882i | \(-0.525141\pi\) | ||||
−0.0789005 | + | 0.996882i | \(0.525141\pi\) | |||||||
\(488\) | −48.3124 | −2.18700 | ||||||||
\(489\) | 51.3735 | 2.32319 | ||||||||
\(490\) | −2.91732 | −0.131791 | ||||||||
\(491\) | −25.2607 | −1.14000 | −0.570001 | − | 0.821644i | \(-0.693057\pi\) | ||||
−0.570001 | + | 0.821644i | \(0.693057\pi\) | |||||||
\(492\) | 37.8473 | 1.70629 | ||||||||
\(493\) | −4.18000 | −0.188258 | ||||||||
\(494\) | 17.3096 | 0.778794 | ||||||||
\(495\) | −0.812625 | −0.0365248 | ||||||||
\(496\) | −41.1753 | −1.84883 | ||||||||
\(497\) | −10.9366 | −0.490575 | ||||||||
\(498\) | 105.759 | 4.73919 | ||||||||
\(499\) | 23.5572 | 1.05457 | 0.527283 | − | 0.849690i | \(-0.323211\pi\) | ||||
0.527283 | + | 0.849690i | \(0.323211\pi\) | |||||||
\(500\) | −48.8730 | −2.18567 | ||||||||
\(501\) | −49.9658 | −2.23231 | ||||||||
\(502\) | 32.5750 | 1.45390 | ||||||||
\(503\) | −11.5947 | −0.516984 | −0.258492 | − | 0.966013i | \(-0.583226\pi\) | ||||
−0.258492 | + | 0.966013i | \(0.583226\pi\) | |||||||
\(504\) | −29.8610 | −1.33012 | ||||||||
\(505\) | 6.84653 | 0.304666 | ||||||||
\(506\) | 4.89685 | 0.217692 | ||||||||
\(507\) | 89.1322 | 3.95850 | ||||||||
\(508\) | 47.2281 | 2.09541 | ||||||||
\(509\) | −23.2492 | −1.03050 | −0.515251 | − | 0.857039i | \(-0.672301\pi\) | ||||
−0.515251 | + | 0.857039i | \(0.672301\pi\) | |||||||
\(510\) | 28.1374 | 1.24595 | ||||||||
\(511\) | 7.90022 | 0.349485 | ||||||||
\(512\) | 22.8680 | 1.01063 | ||||||||
\(513\) | −1.63464 | −0.0721709 | ||||||||
\(514\) | −49.8189 | −2.19742 | ||||||||
\(515\) | 21.7067 | 0.956510 | ||||||||
\(516\) | 27.5905 | 1.21461 | ||||||||
\(517\) | −0.369827 | −0.0162650 | ||||||||
\(518\) | 2.02832 | 0.0891192 | ||||||||
\(519\) | 30.8068 | 1.35227 | ||||||||
\(520\) | −61.5728 | −2.70014 | ||||||||
\(521\) | 28.3399 | 1.24159 | 0.620797 | − | 0.783972i | \(-0.286809\pi\) | ||||
0.620797 | + | 0.783972i | \(0.286809\pi\) | |||||||
\(522\) | −10.9153 | −0.477752 | ||||||||
\(523\) | 26.8051 | 1.17210 | 0.586052 | − | 0.810273i | \(-0.300681\pi\) | ||||
0.586052 | + | 0.810273i | \(0.300681\pi\) | |||||||
\(524\) | −64.8502 | −2.83299 | ||||||||
\(525\) | −9.80055 | −0.427731 | ||||||||
\(526\) | 13.1104 | 0.571641 | ||||||||
\(527\) | 13.3721 | 0.582498 | ||||||||
\(528\) | −5.99049 | −0.260703 | ||||||||
\(529\) | 60.4559 | 2.62852 | ||||||||
\(530\) | 13.8036 | 0.599588 | ||||||||
\(531\) | 47.2876 | 2.05211 | ||||||||
\(532\) | −4.78341 | −0.207387 | ||||||||
\(533\) | 19.9556 | 0.864371 | ||||||||
\(534\) | 31.1409 | 1.34760 | ||||||||
\(535\) | −16.6733 | −0.720848 | ||||||||
\(536\) | −103.347 | −4.46392 | ||||||||
\(537\) | 62.0130 | 2.67606 | ||||||||
\(538\) | 4.73205 | 0.204013 | ||||||||
\(539\) | −0.201709 | −0.00868823 | ||||||||
\(540\) | 9.61264 | 0.413662 | ||||||||
\(541\) | −35.3368 | −1.51925 | −0.759624 | − | 0.650362i | \(-0.774617\pi\) | ||||
−0.759624 | + | 0.650362i | \(0.774617\pi\) | |||||||
\(542\) | 31.9059 | 1.37048 | ||||||||
\(543\) | 49.2989 | 2.11562 | ||||||||
\(544\) | 53.3499 | 2.28736 | ||||||||
\(545\) | 2.99720 | 0.128386 | ||||||||
\(546\) | −47.3068 | −2.02454 | ||||||||
\(547\) | −18.4131 | −0.787288 | −0.393644 | − | 0.919263i | \(-0.628786\pi\) | ||||
−0.393644 | + | 0.919263i | \(0.628786\pi\) | |||||||
\(548\) | 48.5463 | 2.07380 | ||||||||
\(549\) | 21.7891 | 0.929935 | ||||||||
\(550\) | −2.03415 | −0.0867363 | ||||||||
\(551\) | −1.05767 | −0.0450584 | ||||||||
\(552\) | −191.976 | −8.17105 | ||||||||
\(553\) | 1.83529 | 0.0780445 | ||||||||
\(554\) | 19.2010 | 0.815773 | ||||||||
\(555\) | −2.16397 | −0.0918555 | ||||||||
\(556\) | 37.0887 | 1.57291 | ||||||||
\(557\) | −5.77220 | −0.244576 | −0.122288 | − | 0.992495i | \(-0.539023\pi\) | ||||
−0.122288 | + | 0.992495i | \(0.539023\pi\) | |||||||
\(558\) | 34.9190 | 1.47824 | ||||||||
\(559\) | 14.5475 | 0.615295 | ||||||||
\(560\) | 12.6241 | 0.533467 | ||||||||
\(561\) | 1.94548 | 0.0821380 | ||||||||
\(562\) | 25.8692 | 1.09123 | ||||||||
\(563\) | −34.1916 | −1.44100 | −0.720502 | − | 0.693453i | \(-0.756089\pi\) | ||||
−0.720502 | + | 0.693453i | \(0.756089\pi\) | |||||||
\(564\) | 23.9689 | 1.00927 | ||||||||
\(565\) | 7.93579 | 0.333861 | ||||||||
\(566\) | 6.39153 | 0.268656 | ||||||||
\(567\) | −6.54197 | −0.274737 | ||||||||
\(568\) | 88.9909 | 3.73398 | ||||||||
\(569\) | 31.9694 | 1.34023 | 0.670114 | − | 0.742258i | \(-0.266245\pi\) | ||||
0.670114 | + | 0.742258i | \(0.266245\pi\) | |||||||
\(570\) | 7.11967 | 0.298210 | ||||||||
\(571\) | −15.5859 | −0.652251 | −0.326125 | − | 0.945326i | \(-0.605743\pi\) | ||||
−0.326125 | + | 0.945326i | \(0.605743\pi\) | |||||||
\(572\) | −7.03800 | −0.294274 | ||||||||
\(573\) | −12.7618 | −0.533132 | ||||||||
\(574\) | −7.69347 | −0.321119 | ||||||||
\(575\) | −34.6675 | −1.44573 | ||||||||
\(576\) | 54.9122 | 2.28801 | ||||||||
\(577\) | −24.3062 | −1.01188 | −0.505939 | − | 0.862569i | \(-0.668854\pi\) | ||||
−0.505939 | + | 0.862569i | \(0.668854\pi\) | |||||||
\(578\) | 8.11264 | 0.337441 | ||||||||
\(579\) | 43.2328 | 1.79669 | ||||||||
\(580\) | 6.21975 | 0.258261 | ||||||||
\(581\) | −15.4099 | −0.639310 | ||||||||
\(582\) | −21.4479 | −0.889046 | ||||||||
\(583\) | 0.954404 | 0.0395274 | ||||||||
\(584\) | −64.2838 | −2.66008 | ||||||||
\(585\) | 27.7695 | 1.14813 | ||||||||
\(586\) | 17.5638 | 0.725554 | ||||||||
\(587\) | −9.05280 | −0.373649 | −0.186824 | − | 0.982393i | \(-0.559820\pi\) | ||||
−0.186824 | + | 0.982393i | \(0.559820\pi\) | |||||||
\(588\) | 13.0730 | 0.539121 | ||||||||
\(589\) | 3.38358 | 0.139418 | ||||||||
\(590\) | −37.5915 | −1.54762 | ||||||||
\(591\) | −39.5000 | −1.62481 | ||||||||
\(592\) | −8.77715 | −0.360738 | ||||||||
\(593\) | 6.99060 | 0.287069 | 0.143535 | − | 0.989645i | \(-0.454153\pi\) | ||||
0.143535 | + | 0.989645i | \(0.454153\pi\) | |||||||
\(594\) | 0.927236 | 0.0380450 | ||||||||
\(595\) | −4.09982 | −0.168076 | ||||||||
\(596\) | −81.7139 | −3.34713 | ||||||||
\(597\) | 8.89712 | 0.364135 | ||||||||
\(598\) | −167.338 | −6.84298 | ||||||||
\(599\) | 39.1328 | 1.59892 | 0.799461 | − | 0.600718i | \(-0.205118\pi\) | ||||
0.799461 | + | 0.600718i | \(0.205118\pi\) | |||||||
\(600\) | 79.7467 | 3.25564 | ||||||||
\(601\) | 15.3010 | 0.624140 | 0.312070 | − | 0.950059i | \(-0.398978\pi\) | ||||
0.312070 | + | 0.950059i | \(0.398978\pi\) | |||||||
\(602\) | −5.60851 | −0.228586 | ||||||||
\(603\) | 46.6100 | 1.89811 | ||||||||
\(604\) | −43.8492 | −1.78420 | ||||||||
\(605\) | −12.0311 | −0.489134 | ||||||||
\(606\) | −42.8024 | −1.73873 | ||||||||
\(607\) | −24.1083 | −0.978524 | −0.489262 | − | 0.872137i | \(-0.662734\pi\) | ||||
−0.489262 | + | 0.872137i | \(0.662734\pi\) | |||||||
\(608\) | 13.4992 | 0.547466 | ||||||||
\(609\) | 2.89061 | 0.117133 | ||||||||
\(610\) | −17.3213 | −0.701319 | ||||||||
\(611\) | 12.6380 | 0.511277 | ||||||||
\(612\) | −69.3753 | −2.80433 | ||||||||
\(613\) | −2.78503 | −0.112486 | −0.0562431 | − | 0.998417i | \(-0.517912\pi\) | ||||
−0.0562431 | + | 0.998417i | \(0.517912\pi\) | |||||||
\(614\) | 81.4719 | 3.28794 | ||||||||
\(615\) | 8.20800 | 0.330979 | ||||||||
\(616\) | 1.64130 | 0.0661299 | ||||||||
\(617\) | −3.63539 | −0.146355 | −0.0731777 | − | 0.997319i | \(-0.523314\pi\) | ||||
−0.0731777 | + | 0.997319i | \(0.523314\pi\) | |||||||
\(618\) | −135.703 | −5.45879 | ||||||||
\(619\) | 26.9666 | 1.08388 | 0.541939 | − | 0.840418i | \(-0.317690\pi\) | ||||
0.541939 | + | 0.840418i | \(0.317690\pi\) | |||||||
\(620\) | −19.8974 | −0.799101 | ||||||||
\(621\) | 15.8027 | 0.634139 | ||||||||
\(622\) | 8.79539 | 0.352663 | ||||||||
\(623\) | −4.53745 | −0.181789 | ||||||||
\(624\) | 204.711 | 8.19499 | ||||||||
\(625\) | 8.37505 | 0.335002 | ||||||||
\(626\) | −19.5586 | −0.781718 | ||||||||
\(627\) | 0.492268 | 0.0196593 | ||||||||
\(628\) | −70.5791 | −2.81641 | ||||||||
\(629\) | 2.85047 | 0.113656 | ||||||||
\(630\) | −10.7060 | −0.426537 | ||||||||
\(631\) | 12.3049 | 0.489850 | 0.244925 | − | 0.969542i | \(-0.421237\pi\) | ||||
0.244925 | + | 0.969542i | \(0.421237\pi\) | |||||||
\(632\) | −14.9337 | −0.594030 | ||||||||
\(633\) | 7.82295 | 0.310935 | ||||||||
\(634\) | 31.2647 | 1.24168 | ||||||||
\(635\) | 10.2425 | 0.406459 | ||||||||
\(636\) | −61.8560 | −2.45275 | ||||||||
\(637\) | 6.89294 | 0.273108 | ||||||||
\(638\) | 0.599958 | 0.0237526 | ||||||||
\(639\) | −40.1352 | −1.58773 | ||||||||
\(640\) | −12.2879 | −0.485722 | ||||||||
\(641\) | 14.2533 | 0.562973 | 0.281487 | − | 0.959565i | \(-0.409173\pi\) | ||||
0.281487 | + | 0.959565i | \(0.409173\pi\) | |||||||
\(642\) | 104.236 | 4.11387 | ||||||||
\(643\) | −3.20817 | −0.126518 | −0.0632590 | − | 0.997997i | \(-0.520149\pi\) | ||||
−0.0632590 | + | 0.997997i | \(0.520149\pi\) | |||||||
\(644\) | 46.2431 | 1.82223 | ||||||||
\(645\) | 5.98361 | 0.235604 | ||||||||
\(646\) | −9.37832 | −0.368985 | ||||||||
\(647\) | 21.8809 | 0.860228 | 0.430114 | − | 0.902775i | \(-0.358473\pi\) | ||||
0.430114 | + | 0.902775i | \(0.358473\pi\) | |||||||
\(648\) | 53.2317 | 2.09114 | ||||||||
\(649\) | −2.59915 | −0.102025 | ||||||||
\(650\) | 69.5122 | 2.72649 | ||||||||
\(651\) | −9.24726 | −0.362429 | ||||||||
\(652\) | 100.693 | 3.94346 | ||||||||
\(653\) | −39.1116 | −1.53056 | −0.765278 | − | 0.643699i | \(-0.777399\pi\) | ||||
−0.765278 | + | 0.643699i | \(0.777399\pi\) | |||||||
\(654\) | −18.7376 | −0.732697 | ||||||||
\(655\) | −14.0642 | −0.549533 | ||||||||
\(656\) | 33.2920 | 1.29983 | ||||||||
\(657\) | 28.9922 | 1.13110 | ||||||||
\(658\) | −4.87231 | −0.189942 | ||||||||
\(659\) | 28.9293 | 1.12693 | 0.563463 | − | 0.826142i | \(-0.309469\pi\) | ||||
0.563463 | + | 0.826142i | \(0.309469\pi\) | |||||||
\(660\) | −2.89483 | −0.112681 | ||||||||
\(661\) | 20.3113 | 0.790017 | 0.395009 | − | 0.918677i | \(-0.370742\pi\) | ||||
0.395009 | + | 0.918677i | \(0.370742\pi\) | |||||||
\(662\) | −48.3543 | −1.87934 | ||||||||
\(663\) | −66.4820 | −2.58195 | ||||||||
\(664\) | 125.390 | 4.86606 | ||||||||
\(665\) | −1.03739 | −0.0402282 | ||||||||
\(666\) | 7.44352 | 0.288431 | ||||||||
\(667\) | 10.2249 | 0.395912 | ||||||||
\(668\) | −97.9345 | −3.78920 | ||||||||
\(669\) | −61.3581 | −2.37224 | ||||||||
\(670\) | −37.0528 | −1.43147 | ||||||||
\(671\) | −1.19763 | −0.0462339 | ||||||||
\(672\) | −36.8932 | −1.42319 | ||||||||
\(673\) | −26.7623 | −1.03161 | −0.515805 | − | 0.856706i | \(-0.672507\pi\) | ||||
−0.515805 | + | 0.856706i | \(0.672507\pi\) | |||||||
\(674\) | −44.9930 | −1.73307 | ||||||||
\(675\) | −6.56441 | −0.252664 | ||||||||
\(676\) | 174.702 | 6.71929 | ||||||||
\(677\) | 36.4205 | 1.39975 | 0.699876 | − | 0.714264i | \(-0.253239\pi\) | ||||
0.699876 | + | 0.714264i | \(0.253239\pi\) | |||||||
\(678\) | −49.6121 | −1.90534 | ||||||||
\(679\) | 3.12512 | 0.119931 | ||||||||
\(680\) | 33.3601 | 1.27930 | ||||||||
\(681\) | 7.93022 | 0.303887 | ||||||||
\(682\) | −1.91931 | −0.0734942 | ||||||||
\(683\) | −37.7085 | −1.44288 | −0.721438 | − | 0.692479i | \(-0.756519\pi\) | ||||
−0.721438 | + | 0.692479i | \(0.756519\pi\) | |||||||
\(684\) | −17.5542 | −0.671201 | ||||||||
\(685\) | 10.5283 | 0.402267 | ||||||||
\(686\) | −2.65744 | −0.101461 | ||||||||
\(687\) | 26.7899 | 1.02210 | ||||||||
\(688\) | 24.2697 | 0.925274 | ||||||||
\(689\) | −32.6145 | −1.24251 | ||||||||
\(690\) | −68.8287 | −2.62026 | ||||||||
\(691\) | −19.1993 | −0.730377 | −0.365188 | − | 0.930934i | \(-0.618995\pi\) | ||||
−0.365188 | + | 0.930934i | \(0.618995\pi\) | |||||||
\(692\) | 60.3823 | 2.29539 | ||||||||
\(693\) | −0.740233 | −0.0281191 | ||||||||
\(694\) | 7.68522 | 0.291727 | ||||||||
\(695\) | 8.04350 | 0.305107 | ||||||||
\(696\) | −23.5208 | −0.891552 | ||||||||
\(697\) | −10.8119 | −0.409531 | ||||||||
\(698\) | 17.2370 | 0.652431 | ||||||||
\(699\) | 68.8685 | 2.60485 | ||||||||
\(700\) | −19.2093 | −0.726045 | ||||||||
\(701\) | 18.1163 | 0.684241 | 0.342121 | − | 0.939656i | \(-0.388855\pi\) | ||||
0.342121 | + | 0.939656i | \(0.388855\pi\) | |||||||
\(702\) | −31.6861 | −1.19592 | ||||||||
\(703\) | 0.721261 | 0.0272029 | ||||||||
\(704\) | −3.01823 | −0.113754 | ||||||||
\(705\) | 5.19817 | 0.195774 | ||||||||
\(706\) | −6.99936 | −0.263424 | ||||||||
\(707\) | 6.23661 | 0.234552 | ||||||||
\(708\) | 168.453 | 6.33087 | ||||||||
\(709\) | −6.09378 | −0.228857 | −0.114428 | − | 0.993432i | \(-0.536504\pi\) | ||||
−0.114428 | + | 0.993432i | \(0.536504\pi\) | |||||||
\(710\) | 31.9057 | 1.19740 | ||||||||
\(711\) | 6.73515 | 0.252588 | ||||||||
\(712\) | 36.9211 | 1.38368 | ||||||||
\(713\) | −32.7104 | −1.22501 | ||||||||
\(714\) | 25.6308 | 0.959209 | ||||||||
\(715\) | −1.52634 | −0.0570820 | ||||||||
\(716\) | 121.547 | 4.54243 | ||||||||
\(717\) | 7.36274 | 0.274967 | ||||||||
\(718\) | 33.8942 | 1.26492 | ||||||||
\(719\) | 20.5232 | 0.765387 | 0.382693 | − | 0.923875i | \(-0.374997\pi\) | ||||
0.382693 | + | 0.923875i | \(0.374997\pi\) | |||||||
\(720\) | 46.3281 | 1.72655 | ||||||||
\(721\) | 19.7729 | 0.736383 | ||||||||
\(722\) | 48.1182 | 1.79078 | ||||||||
\(723\) | 43.1217 | 1.60371 | ||||||||
\(724\) | 96.6272 | 3.59112 | ||||||||
\(725\) | −4.24743 | −0.157746 | ||||||||
\(726\) | 75.2146 | 2.79148 | ||||||||
\(727\) | −45.4401 | −1.68528 | −0.842639 | − | 0.538479i | \(-0.818999\pi\) | ||||
−0.842639 | + | 0.538479i | \(0.818999\pi\) | |||||||
\(728\) | −56.0876 | −2.07874 | ||||||||
\(729\) | −37.4100 | −1.38556 | ||||||||
\(730\) | −23.0475 | −0.853026 | ||||||||
\(731\) | −7.88185 | −0.291521 | ||||||||
\(732\) | 77.6196 | 2.86890 | ||||||||
\(733\) | −16.7882 | −0.620088 | −0.310044 | − | 0.950722i | \(-0.600344\pi\) | ||||
−0.310044 | + | 0.950722i | \(0.600344\pi\) | |||||||
\(734\) | 26.6255 | 0.982767 | ||||||||
\(735\) | 2.83516 | 0.104577 | ||||||||
\(736\) | −130.502 | −4.81038 | ||||||||
\(737\) | −2.56190 | −0.0943688 | ||||||||
\(738\) | −28.2335 | −1.03929 | ||||||||
\(739\) | 38.1328 | 1.40274 | 0.701369 | − | 0.712799i | \(-0.252573\pi\) | ||||
0.701369 | + | 0.712799i | \(0.252573\pi\) | |||||||
\(740\) | −4.24145 | −0.155919 | ||||||||
\(741\) | −16.8221 | −0.617975 | ||||||||
\(742\) | 12.5739 | 0.461601 | ||||||||
\(743\) | −36.3387 | −1.33314 | −0.666569 | − | 0.745443i | \(-0.732238\pi\) | ||||
−0.666569 | + | 0.745443i | \(0.732238\pi\) | |||||||
\(744\) | 75.2446 | 2.75860 | ||||||||
\(745\) | −17.7214 | −0.649263 | ||||||||
\(746\) | 13.3799 | 0.489872 | ||||||||
\(747\) | −56.5512 | −2.06910 | ||||||||
\(748\) | 3.81319 | 0.139424 | ||||||||
\(749\) | −15.1879 | −0.554955 | ||||||||
\(750\) | 66.2627 | 2.41957 | ||||||||
\(751\) | 21.3400 | 0.778709 | 0.389354 | − | 0.921088i | \(-0.372698\pi\) | ||||
0.389354 | + | 0.921088i | \(0.372698\pi\) | |||||||
\(752\) | 21.0840 | 0.768853 | ||||||||
\(753\) | −31.6577 | −1.15367 | ||||||||
\(754\) | −20.5022 | −0.746645 | ||||||||
\(755\) | −9.50965 | −0.346091 | ||||||||
\(756\) | 8.75630 | 0.318464 | ||||||||
\(757\) | −21.3199 | −0.774884 | −0.387442 | − | 0.921894i | \(-0.626641\pi\) | ||||
−0.387442 | + | 0.921894i | \(0.626641\pi\) | |||||||
\(758\) | 38.5299 | 1.39947 | ||||||||
\(759\) | −4.75895 | −0.172739 | ||||||||
\(760\) | 8.44118 | 0.306194 | ||||||||
\(761\) | −28.4371 | −1.03084 | −0.515422 | − | 0.856937i | \(-0.672365\pi\) | ||||
−0.515422 | + | 0.856937i | \(0.672365\pi\) | |||||||
\(762\) | −64.0326 | −2.31966 | ||||||||
\(763\) | 2.73020 | 0.0988399 | ||||||||
\(764\) | −25.0135 | −0.904957 | ||||||||
\(765\) | −15.0455 | −0.543972 | ||||||||
\(766\) | −45.3773 | −1.63955 | ||||||||
\(767\) | 88.8197 | 3.20709 | ||||||||
\(768\) | −0.467972 | −0.0168865 | ||||||||
\(769\) | −38.5724 | −1.39096 | −0.695478 | − | 0.718548i | \(-0.744807\pi\) | ||||
−0.695478 | + | 0.718548i | \(0.744807\pi\) | |||||||
\(770\) | 0.588451 | 0.0212063 | ||||||||
\(771\) | 48.4159 | 1.74366 | ||||||||
\(772\) | 84.7374 | 3.04977 | ||||||||
\(773\) | 26.8384 | 0.965311 | 0.482655 | − | 0.875810i | \(-0.339672\pi\) | ||||
0.482655 | + | 0.875810i | \(0.339672\pi\) | |||||||
\(774\) | −20.5821 | −0.739809 | ||||||||
\(775\) | 13.5878 | 0.488090 | ||||||||
\(776\) | −25.4290 | −0.912847 | ||||||||
\(777\) | −1.97120 | −0.0707163 | ||||||||
\(778\) | 40.3691 | 1.44730 | ||||||||
\(779\) | −2.73576 | −0.0980189 | ||||||||
\(780\) | 98.9240 | 3.54205 | ||||||||
\(781\) | 2.20602 | 0.0789376 | ||||||||
\(782\) | 90.6639 | 3.24214 | ||||||||
\(783\) | 1.93613 | 0.0691916 | ||||||||
\(784\) | 11.4995 | 0.410697 | ||||||||
\(785\) | −15.3066 | −0.546316 | ||||||||
\(786\) | 87.9249 | 3.13618 | ||||||||
\(787\) | 45.1165 | 1.60823 | 0.804114 | − | 0.594475i | \(-0.202640\pi\) | ||||
0.804114 | + | 0.594475i | \(0.202640\pi\) | |||||||
\(788\) | −77.4212 | −2.75801 | ||||||||
\(789\) | −12.7412 | −0.453598 | ||||||||
\(790\) | −5.35414 | −0.190492 | ||||||||
\(791\) | 7.22884 | 0.257028 | ||||||||
\(792\) | 6.02325 | 0.214027 | ||||||||
\(793\) | 40.9261 | 1.45333 | ||||||||
\(794\) | −75.5990 | −2.68291 | ||||||||
\(795\) | −13.4148 | −0.475774 | ||||||||
\(796\) | 17.4386 | 0.618095 | ||||||||
\(797\) | −16.4931 | −0.584215 | −0.292108 | − | 0.956385i | \(-0.594357\pi\) | ||||
−0.292108 | + | 0.956385i | \(0.594357\pi\) | |||||||
\(798\) | 6.48542 | 0.229581 | ||||||||
\(799\) | −6.84724 | −0.242238 | ||||||||
\(800\) | 54.2105 | 1.91663 | ||||||||
\(801\) | −16.6516 | −0.588354 | ||||||||
\(802\) | 89.0026 | 3.14279 | ||||||||
\(803\) | −1.59355 | −0.0562351 | ||||||||
\(804\) | 166.040 | 5.85577 | ||||||||
\(805\) | 10.0288 | 0.353470 | ||||||||
\(806\) | 65.5879 | 2.31024 | ||||||||
\(807\) | −4.59878 | −0.161885 | ||||||||
\(808\) | −50.7471 | −1.78528 | ||||||||
\(809\) | 40.5318 | 1.42502 | 0.712511 | − | 0.701661i | \(-0.247558\pi\) | ||||
0.712511 | + | 0.701661i | \(0.247558\pi\) | |||||||
\(810\) | 19.0850 | 0.670579 | ||||||||
\(811\) | −47.1625 | −1.65610 | −0.828050 | − | 0.560654i | \(-0.810550\pi\) | ||||
−0.828050 | + | 0.560654i | \(0.810550\pi\) | |||||||
\(812\) | 5.66567 | 0.198826 | ||||||||
\(813\) | −31.0074 | −1.08748 | ||||||||
\(814\) | −0.409131 | −0.0143400 | ||||||||
\(815\) | 21.8376 | 0.764936 | ||||||||
\(816\) | −110.912 | −3.88271 | ||||||||
\(817\) | −1.99436 | −0.0697739 | ||||||||
\(818\) | 94.4902 | 3.30377 | ||||||||
\(819\) | 25.2957 | 0.883904 | ||||||||
\(820\) | 16.0879 | 0.561815 | ||||||||
\(821\) | 16.1751 | 0.564516 | 0.282258 | − | 0.959338i | \(-0.408917\pi\) | ||||
0.282258 | + | 0.959338i | \(0.408917\pi\) | |||||||
\(822\) | −65.8198 | −2.29573 | ||||||||
\(823\) | −8.17106 | −0.284825 | −0.142413 | − | 0.989807i | \(-0.545486\pi\) | ||||
−0.142413 | + | 0.989807i | \(0.545486\pi\) | |||||||
\(824\) | −160.892 | −5.60493 | ||||||||
\(825\) | 1.97686 | 0.0688255 | ||||||||
\(826\) | −34.2427 | −1.19145 | ||||||||
\(827\) | −38.1759 | −1.32751 | −0.663753 | − | 0.747952i | \(-0.731037\pi\) | ||||
−0.663753 | + | 0.747952i | \(0.731037\pi\) | |||||||
\(828\) | 169.703 | 5.89759 | ||||||||
\(829\) | −21.2420 | −0.737765 | −0.368883 | − | 0.929476i | \(-0.620260\pi\) | ||||
−0.368883 | + | 0.929476i | \(0.620260\pi\) | |||||||
\(830\) | 44.9556 | 1.56043 | ||||||||
\(831\) | −18.6603 | −0.647318 | ||||||||
\(832\) | 103.141 | 3.57576 | ||||||||
\(833\) | −3.73459 | −0.129396 | ||||||||
\(834\) | −50.2854 | −1.74124 | ||||||||
\(835\) | −21.2392 | −0.735014 | ||||||||
\(836\) | 0.964859 | 0.0333703 | ||||||||
\(837\) | −6.19382 | −0.214090 | ||||||||
\(838\) | −58.8556 | −2.03313 | ||||||||
\(839\) | 43.1075 | 1.48824 | 0.744118 | − | 0.668048i | \(-0.232870\pi\) | ||||
0.744118 | + | 0.668048i | \(0.232870\pi\) | |||||||
\(840\) | −23.0696 | −0.795978 | ||||||||
\(841\) | −27.7472 | −0.956802 | ||||||||
\(842\) | −39.0278 | −1.34499 | ||||||||
\(843\) | −25.1406 | −0.865889 | ||||||||
\(844\) | 15.3332 | 0.527791 | ||||||||
\(845\) | 37.8878 | 1.30338 | ||||||||
\(846\) | −17.8804 | −0.614741 | ||||||||
\(847\) | −10.9593 | −0.376566 | ||||||||
\(848\) | −54.4110 | −1.86848 | ||||||||
\(849\) | −6.21153 | −0.213179 | ||||||||
\(850\) | −37.6617 | −1.29179 | ||||||||
\(851\) | −6.97271 | −0.239022 | ||||||||
\(852\) | −142.974 | −4.89822 | ||||||||
\(853\) | −38.3179 | −1.31198 | −0.655990 | − | 0.754769i | \(-0.727749\pi\) | ||||
−0.655990 | + | 0.754769i | \(0.727749\pi\) | |||||||
\(854\) | −15.7782 | −0.539920 | ||||||||
\(855\) | −3.80700 | −0.130197 | ||||||||
\(856\) | 123.584 | 4.22400 | ||||||||
\(857\) | 6.33448 | 0.216382 | 0.108191 | − | 0.994130i | \(-0.465494\pi\) | ||||
0.108191 | + | 0.994130i | \(0.465494\pi\) | |||||||
\(858\) | 9.54222 | 0.325766 | ||||||||
\(859\) | −1.61931 | −0.0552501 | −0.0276250 | − | 0.999618i | \(-0.508794\pi\) | ||||
−0.0276250 | + | 0.999618i | \(0.508794\pi\) | |||||||
\(860\) | 11.7280 | 0.399923 | ||||||||
\(861\) | 7.47680 | 0.254809 | ||||||||
\(862\) | −33.2327 | −1.13191 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | −24.7111 | −0.840688 | ||||||||
\(865\) | 13.0952 | 0.445251 | ||||||||
\(866\) | 59.7755 | 2.03125 | ||||||||
\(867\) | −7.88417 | −0.267760 | ||||||||
\(868\) | −18.1249 | −0.615199 | ||||||||
\(869\) | −0.370195 | −0.0125580 | ||||||||
\(870\) | −8.43283 | −0.285900 | ||||||||
\(871\) | 87.5469 | 2.96642 | ||||||||
\(872\) | −22.2155 | −0.752313 | ||||||||
\(873\) | 11.4686 | 0.388152 | ||||||||
\(874\) | 22.9409 | 0.775987 | ||||||||
\(875\) | −9.65495 | −0.326397 | ||||||||
\(876\) | 103.280 | 3.48950 | ||||||||
\(877\) | 3.21481 | 0.108556 | 0.0542782 | − | 0.998526i | \(-0.482714\pi\) | ||||
0.0542782 | + | 0.998526i | \(0.482714\pi\) | |||||||
\(878\) | 76.6545 | 2.58696 | ||||||||
\(879\) | −17.0692 | −0.575729 | ||||||||
\(880\) | −2.54641 | −0.0858393 | ||||||||
\(881\) | −12.7458 | −0.429415 | −0.214708 | − | 0.976678i | \(-0.568880\pi\) | ||||
−0.214708 | + | 0.976678i | \(0.568880\pi\) | |||||||
\(882\) | −9.75226 | −0.328376 | ||||||||
\(883\) | 52.0451 | 1.75146 | 0.875729 | − | 0.482803i | \(-0.160381\pi\) | ||||
0.875729 | + | 0.482803i | \(0.160381\pi\) | |||||||
\(884\) | −130.307 | −4.38269 | ||||||||
\(885\) | 36.5328 | 1.22804 | ||||||||
\(886\) | −38.6626 | −1.29889 | ||||||||
\(887\) | 27.0434 | 0.908027 | 0.454014 | − | 0.890995i | \(-0.349992\pi\) | ||||
0.454014 | + | 0.890995i | \(0.349992\pi\) | |||||||
\(888\) | 16.0395 | 0.538252 | ||||||||
\(889\) | 9.33001 | 0.312918 | ||||||||
\(890\) | 13.2372 | 0.443713 | ||||||||
\(891\) | 1.31958 | 0.0442074 | ||||||||
\(892\) | −120.264 | −4.02672 | ||||||||
\(893\) | −1.73257 | −0.0579783 | ||||||||
\(894\) | 110.789 | 3.70534 | ||||||||
\(895\) | 26.3602 | 0.881123 | ||||||||
\(896\) | −11.1932 | −0.373940 | ||||||||
\(897\) | 162.626 | 5.42992 | ||||||||
\(898\) | 99.7889 | 3.33000 | ||||||||
\(899\) | −4.00764 | −0.133662 | ||||||||
\(900\) | −70.4945 | −2.34982 | ||||||||
\(901\) | 17.6705 | 0.588691 | ||||||||
\(902\) | 1.55184 | 0.0516707 | ||||||||
\(903\) | 5.45056 | 0.181383 | ||||||||
\(904\) | −58.8208 | −1.95635 | ||||||||
\(905\) | 20.9557 | 0.696591 | ||||||||
\(906\) | 59.4513 | 1.97514 | ||||||||
\(907\) | −36.7548 | −1.22042 | −0.610212 | − | 0.792238i | \(-0.708916\pi\) | ||||
−0.610212 | + | 0.792238i | \(0.708916\pi\) | |||||||
\(908\) | 15.5435 | 0.515828 | ||||||||
\(909\) | 22.8871 | 0.759118 | ||||||||
\(910\) | −20.1089 | −0.666605 | ||||||||
\(911\) | 46.5940 | 1.54373 | 0.771864 | − | 0.635787i | \(-0.219324\pi\) | ||||
0.771864 | + | 0.635787i | \(0.219324\pi\) | |||||||
\(912\) | −28.0644 | −0.929305 | ||||||||
\(913\) | 3.10832 | 0.102870 | ||||||||
\(914\) | 24.6365 | 0.814902 | ||||||||
\(915\) | 16.8335 | 0.556498 | ||||||||
\(916\) | 52.5090 | 1.73495 | ||||||||
\(917\) | −12.8113 | −0.423066 | ||||||||
\(918\) | 17.1675 | 0.566613 | ||||||||
\(919\) | 16.6303 | 0.548582 | 0.274291 | − | 0.961647i | \(-0.411557\pi\) | ||||
0.274291 | + | 0.961647i | \(0.411557\pi\) | |||||||
\(920\) | −81.6042 | −2.69041 | ||||||||
\(921\) | −79.1775 | −2.60899 | ||||||||
\(922\) | −16.0553 | −0.528754 | ||||||||
\(923\) | −75.3855 | −2.48134 | ||||||||
\(924\) | −2.63695 | −0.0867491 | ||||||||
\(925\) | 2.89646 | 0.0952349 | ||||||||
\(926\) | −78.3169 | −2.57365 | ||||||||
\(927\) | 72.5628 | 2.38327 | ||||||||
\(928\) | −15.9890 | −0.524866 | ||||||||
\(929\) | −3.18717 | −0.104568 | −0.0522838 | − | 0.998632i | \(-0.516650\pi\) | ||||
−0.0522838 | + | 0.998632i | \(0.516650\pi\) | |||||||
\(930\) | 26.9772 | 0.884619 | ||||||||
\(931\) | −0.944972 | −0.0309702 | ||||||||
\(932\) | 134.984 | 4.42155 | ||||||||
\(933\) | −8.54770 | −0.279839 | ||||||||
\(934\) | −13.2994 | −0.435170 | ||||||||
\(935\) | 0.826973 | 0.0270449 | ||||||||
\(936\) | −205.830 | −6.72777 | ||||||||
\(937\) | 24.2766 | 0.793082 | 0.396541 | − | 0.918017i | \(-0.370210\pi\) | ||||
0.396541 | + | 0.918017i | \(0.370210\pi\) | |||||||
\(938\) | −33.7520 | −1.10204 | ||||||||
\(939\) | 19.0078 | 0.620295 | ||||||||
\(940\) | 10.1886 | 0.332314 | ||||||||
\(941\) | 43.0560 | 1.40358 | 0.701792 | − | 0.712382i | \(-0.252383\pi\) | ||||
0.701792 | + | 0.712382i | \(0.252383\pi\) | |||||||
\(942\) | 95.6922 | 3.11782 | ||||||||
\(943\) | 26.4477 | 0.861256 | ||||||||
\(944\) | 148.178 | 4.82279 | ||||||||
\(945\) | 1.89899 | 0.0617743 | ||||||||
\(946\) | 1.13129 | 0.0367814 | ||||||||
\(947\) | −15.6826 | −0.509615 | −0.254807 | − | 0.966992i | \(-0.582012\pi\) | ||||
−0.254807 | + | 0.966992i | \(0.582012\pi\) | |||||||
\(948\) | 23.9928 | 0.779248 | ||||||||
\(949\) | 54.4558 | 1.76771 | ||||||||
\(950\) | −9.52962 | −0.309182 | ||||||||
\(951\) | −30.3842 | −0.985274 | ||||||||
\(952\) | 30.3882 | 0.984889 | ||||||||
\(953\) | −33.6534 | −1.09014 | −0.545071 | − | 0.838390i | \(-0.683497\pi\) | ||||
−0.545071 | + | 0.838390i | \(0.683497\pi\) | |||||||
\(954\) | 46.1436 | 1.49395 | ||||||||
\(955\) | −5.42473 | −0.175540 | ||||||||
\(956\) | 14.4312 | 0.466738 | ||||||||
\(957\) | −0.583062 | −0.0188477 | ||||||||
\(958\) | −37.4878 | −1.21118 | ||||||||
\(959\) | 9.59042 | 0.309691 | ||||||||
\(960\) | 42.4233 | 1.36921 | ||||||||
\(961\) | −18.1793 | −0.586427 | ||||||||
\(962\) | 13.9811 | 0.450768 | ||||||||
\(963\) | −55.7367 | −1.79609 | ||||||||
\(964\) | 84.5198 | 2.72220 | ||||||||
\(965\) | 18.3772 | 0.591581 | ||||||||
\(966\) | −62.6971 | −2.01725 | ||||||||
\(967\) | 15.6080 | 0.501919 | 0.250959 | − | 0.967998i | \(-0.419254\pi\) | ||||
0.250959 | + | 0.967998i | \(0.419254\pi\) | |||||||
\(968\) | 89.1755 | 2.86621 | ||||||||
\(969\) | 9.11421 | 0.292791 | ||||||||
\(970\) | −9.11698 | −0.292729 | ||||||||
\(971\) | 29.5832 | 0.949370 | 0.474685 | − | 0.880156i | \(-0.342562\pi\) | ||||
0.474685 | + | 0.880156i | \(0.342562\pi\) | |||||||
\(972\) | −111.792 | −3.58573 | ||||||||
\(973\) | 7.32695 | 0.234891 | ||||||||
\(974\) | 9.25416 | 0.296522 | ||||||||
\(975\) | −67.5546 | −2.16348 | ||||||||
\(976\) | 68.2773 | 2.18550 | ||||||||
\(977\) | 50.5527 | 1.61733 | 0.808663 | − | 0.588273i | \(-0.200192\pi\) | ||||
0.808663 | + | 0.588273i | \(0.200192\pi\) | |||||||
\(978\) | −136.522 | −4.36548 | ||||||||
\(979\) | 0.915247 | 0.0292514 | ||||||||
\(980\) | 5.55700 | 0.177512 | ||||||||
\(981\) | 10.0193 | 0.319891 | ||||||||
\(982\) | 67.1288 | 2.14217 | ||||||||
\(983\) | 29.7400 | 0.948558 | 0.474279 | − | 0.880375i | \(-0.342709\pi\) | ||||
0.474279 | + | 0.880375i | \(0.342709\pi\) | |||||||
\(984\) | −60.8384 | −1.93946 | ||||||||
\(985\) | −16.7905 | −0.534989 | ||||||||
\(986\) | 11.1081 | 0.353753 | ||||||||
\(987\) | 4.73509 | 0.150720 | ||||||||
\(988\) | −32.9718 | −1.04897 | ||||||||
\(989\) | 19.2803 | 0.613077 | ||||||||
\(990\) | 2.15950 | 0.0686334 | ||||||||
\(991\) | −33.5539 | −1.06588 | −0.532938 | − | 0.846154i | \(-0.678912\pi\) | ||||
−0.532938 | + | 0.846154i | \(0.678912\pi\) | |||||||
\(992\) | 51.1501 | 1.62402 | ||||||||
\(993\) | 46.9926 | 1.49126 | ||||||||
\(994\) | 29.0634 | 0.921834 | ||||||||
\(995\) | 3.78194 | 0.119896 | ||||||||
\(996\) | −201.453 | −6.38330 | ||||||||
\(997\) | −3.59942 | −0.113995 | −0.0569974 | − | 0.998374i | \(-0.518153\pi\) | ||||
−0.0569974 | + | 0.998374i | \(0.518153\pi\) | |||||||
\(998\) | −62.6017 | −1.98162 | ||||||||
\(999\) | −1.32031 | −0.0417727 |
(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 | 6041.2.a.f.1.6 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.6 | ✓ | 132 | 1.1 | even | 1 | trivial |