Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4021,2,Mod(1,4021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4021, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4021.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1078466528\) |
Analytic rank: | \(1\) |
Dimension: | \(151\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.43685 | −1.72312 | −0.861558 | − | 0.507659i | \(-0.830511\pi\) | ||||
−0.861558 | + | 0.507659i | \(0.830511\pi\) | |||||||
\(3\) | −1.07161 | −0.618696 | −0.309348 | − | 0.950949i | \(-0.600111\pi\) | ||||
−0.309348 | + | 0.950949i | \(0.600111\pi\) | |||||||
\(4\) | 3.93825 | 1.96913 | ||||||||
\(5\) | 2.02983 | 0.907769 | 0.453885 | − | 0.891060i | \(-0.350038\pi\) | ||||
0.453885 | + | 0.891060i | \(0.350038\pi\) | |||||||
\(6\) | 2.61136 | 1.06608 | ||||||||
\(7\) | 3.59143 | 1.35743 | 0.678716 | − | 0.734401i | \(-0.262537\pi\) | ||||
0.678716 | + | 0.734401i | \(0.262537\pi\) | |||||||
\(8\) | −4.72324 | −1.66992 | ||||||||
\(9\) | −1.85165 | −0.617216 | ||||||||
\(10\) | −4.94641 | −1.56419 | ||||||||
\(11\) | −0.699000 | −0.210757 | −0.105378 | − | 0.994432i | \(-0.533605\pi\) | ||||
−0.105378 | + | 0.994432i | \(0.533605\pi\) | |||||||
\(12\) | −4.22028 | −1.21829 | ||||||||
\(13\) | −5.57852 | −1.54720 | −0.773602 | − | 0.633672i | \(-0.781547\pi\) | ||||
−0.773602 | + | 0.633672i | \(0.781547\pi\) | |||||||
\(14\) | −8.75178 | −2.33901 | ||||||||
\(15\) | −2.17520 | −0.561633 | ||||||||
\(16\) | 3.63334 | 0.908335 | ||||||||
\(17\) | −0.0570413 | −0.0138345 | −0.00691727 | − | 0.999976i | \(-0.502202\pi\) | ||||
−0.00691727 | + | 0.999976i | \(0.502202\pi\) | |||||||
\(18\) | 4.51219 | 1.06353 | ||||||||
\(19\) | 1.27541 | 0.292599 | 0.146299 | − | 0.989240i | \(-0.453264\pi\) | ||||
0.146299 | + | 0.989240i | \(0.453264\pi\) | |||||||
\(20\) | 7.99400 | 1.78751 | ||||||||
\(21\) | −3.84862 | −0.839837 | ||||||||
\(22\) | 1.70336 | 0.363158 | ||||||||
\(23\) | 1.59342 | 0.332251 | 0.166126 | − | 0.986105i | \(-0.446874\pi\) | ||||
0.166126 | + | 0.986105i | \(0.446874\pi\) | |||||||
\(24\) | 5.06149 | 1.03317 | ||||||||
\(25\) | −0.879774 | −0.175955 | ||||||||
\(26\) | 13.5940 | 2.66601 | ||||||||
\(27\) | 5.19909 | 1.00056 | ||||||||
\(28\) | 14.1440 | 2.67296 | ||||||||
\(29\) | −9.25685 | −1.71895 | −0.859477 | − | 0.511175i | \(-0.829210\pi\) | ||||
−0.859477 | + | 0.511175i | \(0.829210\pi\) | |||||||
\(30\) | 5.30063 | 0.967759 | ||||||||
\(31\) | 10.2053 | 1.83293 | 0.916463 | − | 0.400120i | \(-0.131031\pi\) | ||||
0.916463 | + | 0.400120i | \(0.131031\pi\) | |||||||
\(32\) | 0.592565 | 0.104752 | ||||||||
\(33\) | 0.749057 | 0.130394 | ||||||||
\(34\) | 0.139001 | 0.0238385 | ||||||||
\(35\) | 7.29000 | 1.23223 | ||||||||
\(36\) | −7.29226 | −1.21538 | ||||||||
\(37\) | −3.73274 | −0.613659 | −0.306830 | − | 0.951764i | \(-0.599268\pi\) | ||||
−0.306830 | + | 0.951764i | \(0.599268\pi\) | |||||||
\(38\) | −3.10798 | −0.504181 | ||||||||
\(39\) | 5.97801 | 0.957248 | ||||||||
\(40\) | −9.58740 | −1.51590 | ||||||||
\(41\) | 7.29221 | 1.13885 | 0.569426 | − | 0.822043i | \(-0.307166\pi\) | ||||
0.569426 | + | 0.822043i | \(0.307166\pi\) | |||||||
\(42\) | 9.37852 | 1.44714 | ||||||||
\(43\) | 9.81419 | 1.49665 | 0.748325 | − | 0.663332i | \(-0.230858\pi\) | ||||
0.748325 | + | 0.663332i | \(0.230858\pi\) | |||||||
\(44\) | −2.75284 | −0.415006 | ||||||||
\(45\) | −3.75854 | −0.560289 | ||||||||
\(46\) | −3.88293 | −0.572507 | ||||||||
\(47\) | −12.3638 | −1.80345 | −0.901725 | − | 0.432311i | \(-0.857698\pi\) | ||||
−0.901725 | + | 0.432311i | \(0.857698\pi\) | |||||||
\(48\) | −3.89353 | −0.561983 | ||||||||
\(49\) | 5.89835 | 0.842621 | ||||||||
\(50\) | 2.14388 | 0.303191 | ||||||||
\(51\) | 0.0611261 | 0.00855937 | ||||||||
\(52\) | −21.9696 | −3.04664 | ||||||||
\(53\) | −5.71490 | −0.785002 | −0.392501 | − | 0.919752i | \(-0.628390\pi\) | ||||
−0.392501 | + | 0.919752i | \(0.628390\pi\) | |||||||
\(54\) | −12.6694 | −1.72409 | ||||||||
\(55\) | −1.41885 | −0.191318 | ||||||||
\(56\) | −16.9632 | −2.26680 | ||||||||
\(57\) | −1.36674 | −0.181030 | ||||||||
\(58\) | 22.5576 | 2.96195 | ||||||||
\(59\) | 7.29092 | 0.949197 | 0.474598 | − | 0.880203i | \(-0.342593\pi\) | ||||
0.474598 | + | 0.880203i | \(0.342593\pi\) | |||||||
\(60\) | −8.56647 | −1.10593 | ||||||||
\(61\) | −15.5050 | −1.98522 | −0.992608 | − | 0.121362i | \(-0.961274\pi\) | ||||
−0.992608 | + | 0.121362i | \(0.961274\pi\) | |||||||
\(62\) | −24.8688 | −3.15834 | ||||||||
\(63\) | −6.65005 | −0.837828 | ||||||||
\(64\) | −8.71068 | −1.08883 | ||||||||
\(65\) | −11.3235 | −1.40450 | ||||||||
\(66\) | −1.82534 | −0.224684 | ||||||||
\(67\) | 13.7342 | 1.67790 | 0.838952 | − | 0.544206i | \(-0.183169\pi\) | ||||
0.838952 | + | 0.544206i | \(0.183169\pi\) | |||||||
\(68\) | −0.224643 | −0.0272420 | ||||||||
\(69\) | −1.70753 | −0.205562 | ||||||||
\(70\) | −17.7647 | −2.12328 | ||||||||
\(71\) | −12.3668 | −1.46766 | −0.733832 | − | 0.679331i | \(-0.762270\pi\) | ||||
−0.733832 | + | 0.679331i | \(0.762270\pi\) | |||||||
\(72\) | 8.74578 | 1.03070 | ||||||||
\(73\) | −4.43873 | −0.519514 | −0.259757 | − | 0.965674i | \(-0.583642\pi\) | ||||
−0.259757 | + | 0.965674i | \(0.583642\pi\) | |||||||
\(74\) | 9.09615 | 1.05741 | ||||||||
\(75\) | 0.942777 | 0.108863 | ||||||||
\(76\) | 5.02288 | 0.576164 | ||||||||
\(77\) | −2.51041 | −0.286088 | ||||||||
\(78\) | −14.5675 | −1.64945 | ||||||||
\(79\) | 3.28843 | 0.369977 | 0.184989 | − | 0.982741i | \(-0.440775\pi\) | ||||
0.184989 | + | 0.982741i | \(0.440775\pi\) | |||||||
\(80\) | 7.37508 | 0.824559 | ||||||||
\(81\) | −0.0164646 | −0.00182941 | ||||||||
\(82\) | −17.7700 | −1.96237 | ||||||||
\(83\) | 3.69258 | 0.405313 | 0.202656 | − | 0.979250i | \(-0.435043\pi\) | ||||
0.202656 | + | 0.979250i | \(0.435043\pi\) | |||||||
\(84\) | −15.1568 | −1.65375 | ||||||||
\(85\) | −0.115784 | −0.0125586 | ||||||||
\(86\) | −23.9157 | −2.57890 | ||||||||
\(87\) | 9.91975 | 1.06351 | ||||||||
\(88\) | 3.30155 | 0.351946 | ||||||||
\(89\) | 5.62527 | 0.596277 | 0.298139 | − | 0.954523i | \(-0.403634\pi\) | ||||
0.298139 | + | 0.954523i | \(0.403634\pi\) | |||||||
\(90\) | 9.15900 | 0.965443 | ||||||||
\(91\) | −20.0349 | −2.10022 | ||||||||
\(92\) | 6.27530 | 0.654245 | ||||||||
\(93\) | −10.9361 | −1.13402 | ||||||||
\(94\) | 30.1288 | 3.10755 | ||||||||
\(95\) | 2.58887 | 0.265612 | ||||||||
\(96\) | −0.635000 | −0.0648094 | ||||||||
\(97\) | −10.5580 | −1.07200 | −0.535999 | − | 0.844219i | \(-0.680065\pi\) | ||||
−0.535999 | + | 0.844219i | \(0.680065\pi\) | |||||||
\(98\) | −14.3734 | −1.45193 | ||||||||
\(99\) | 1.29430 | 0.130082 | ||||||||
\(100\) | −3.46477 | −0.346477 | ||||||||
\(101\) | −3.15445 | −0.313879 | −0.156940 | − | 0.987608i | \(-0.550163\pi\) | ||||
−0.156940 | + | 0.987608i | \(0.550163\pi\) | |||||||
\(102\) | −0.148955 | −0.0147488 | ||||||||
\(103\) | −6.76343 | −0.666421 | −0.333210 | − | 0.942853i | \(-0.608132\pi\) | ||||
−0.333210 | + | 0.942853i | \(0.608132\pi\) | |||||||
\(104\) | 26.3487 | 2.58370 | ||||||||
\(105\) | −7.81206 | −0.762379 | ||||||||
\(106\) | 13.9264 | 1.35265 | ||||||||
\(107\) | −9.15365 | −0.884916 | −0.442458 | − | 0.896789i | \(-0.645893\pi\) | ||||
−0.442458 | + | 0.896789i | \(0.645893\pi\) | |||||||
\(108\) | 20.4753 | 1.97024 | ||||||||
\(109\) | −0.816517 | −0.0782082 | −0.0391041 | − | 0.999235i | \(-0.512450\pi\) | ||||
−0.0391041 | + | 0.999235i | \(0.512450\pi\) | |||||||
\(110\) | 3.45754 | 0.329664 | ||||||||
\(111\) | 4.00005 | 0.379668 | ||||||||
\(112\) | 13.0489 | 1.23300 | ||||||||
\(113\) | 4.55559 | 0.428554 | 0.214277 | − | 0.976773i | \(-0.431260\pi\) | ||||
0.214277 | + | 0.976773i | \(0.431260\pi\) | |||||||
\(114\) | 3.33055 | 0.311935 | ||||||||
\(115\) | 3.23438 | 0.301607 | ||||||||
\(116\) | −36.4558 | −3.38484 | ||||||||
\(117\) | 10.3295 | 0.954958 | ||||||||
\(118\) | −17.7669 | −1.63558 | ||||||||
\(119\) | −0.204860 | −0.0187794 | ||||||||
\(120\) | 10.2740 | 0.937881 | ||||||||
\(121\) | −10.5114 | −0.955582 | ||||||||
\(122\) | 37.7835 | 3.42076 | ||||||||
\(123\) | −7.81442 | −0.704603 | ||||||||
\(124\) | 40.1911 | 3.60926 | ||||||||
\(125\) | −11.9350 | −1.06750 | ||||||||
\(126\) | 16.2052 | 1.44367 | ||||||||
\(127\) | 20.3524 | 1.80598 | 0.902990 | − | 0.429661i | \(-0.141367\pi\) | ||||
0.902990 | + | 0.429661i | \(0.141367\pi\) | |||||||
\(128\) | 20.0415 | 1.77144 | ||||||||
\(129\) | −10.5170 | −0.925971 | ||||||||
\(130\) | 27.5937 | 2.42012 | ||||||||
\(131\) | 0.0553331 | 0.00483448 | 0.00241724 | − | 0.999997i | \(-0.499231\pi\) | ||||
0.00241724 | + | 0.999997i | \(0.499231\pi\) | |||||||
\(132\) | 2.94998 | 0.256763 | ||||||||
\(133\) | 4.58054 | 0.397183 | ||||||||
\(134\) | −33.4683 | −2.89122 | ||||||||
\(135\) | 10.5533 | 0.908282 | ||||||||
\(136\) | 0.269420 | 0.0231026 | ||||||||
\(137\) | −13.0531 | −1.11520 | −0.557601 | − | 0.830109i | \(-0.688278\pi\) | ||||
−0.557601 | + | 0.830109i | \(0.688278\pi\) | |||||||
\(138\) | 4.16100 | 0.354208 | ||||||||
\(139\) | −21.7655 | −1.84613 | −0.923064 | − | 0.384647i | \(-0.874323\pi\) | ||||
−0.923064 | + | 0.384647i | \(0.874323\pi\) | |||||||
\(140\) | 28.7099 | 2.42643 | ||||||||
\(141\) | 13.2492 | 1.11579 | ||||||||
\(142\) | 30.1360 | 2.52895 | ||||||||
\(143\) | 3.89939 | 0.326083 | ||||||||
\(144\) | −6.72767 | −0.560639 | ||||||||
\(145\) | −18.7899 | −1.56041 | ||||||||
\(146\) | 10.8165 | 0.895182 | ||||||||
\(147\) | −6.32074 | −0.521326 | ||||||||
\(148\) | −14.7005 | −1.20837 | ||||||||
\(149\) | −7.22958 | −0.592270 | −0.296135 | − | 0.955146i | \(-0.595698\pi\) | ||||
−0.296135 | + | 0.955146i | \(0.595698\pi\) | |||||||
\(150\) | −2.29741 | −0.187583 | ||||||||
\(151\) | 2.37832 | 0.193545 | 0.0967725 | − | 0.995307i | \(-0.469148\pi\) | ||||
0.0967725 | + | 0.995307i | \(0.469148\pi\) | |||||||
\(152\) | −6.02406 | −0.488616 | ||||||||
\(153\) | 0.105620 | 0.00853889 | ||||||||
\(154\) | 6.11750 | 0.492962 | ||||||||
\(155\) | 20.7151 | 1.66387 | ||||||||
\(156\) | 23.5429 | 1.88494 | ||||||||
\(157\) | 18.5647 | 1.48162 | 0.740812 | − | 0.671712i | \(-0.234441\pi\) | ||||
0.740812 | + | 0.671712i | \(0.234441\pi\) | |||||||
\(158\) | −8.01342 | −0.637513 | ||||||||
\(159\) | 6.12416 | 0.485678 | ||||||||
\(160\) | 1.20281 | 0.0950903 | ||||||||
\(161\) | 5.72265 | 0.451008 | ||||||||
\(162\) | 0.0401219 | 0.00315228 | ||||||||
\(163\) | −5.19637 | −0.407011 | −0.203506 | − | 0.979074i | \(-0.565234\pi\) | ||||
−0.203506 | + | 0.979074i | \(0.565234\pi\) | |||||||
\(164\) | 28.7186 | 2.24254 | ||||||||
\(165\) | 1.52046 | 0.118368 | ||||||||
\(166\) | −8.99827 | −0.698401 | ||||||||
\(167\) | 1.99829 | 0.154632 | 0.0773160 | − | 0.997007i | \(-0.475365\pi\) | ||||
0.0773160 | + | 0.997007i | \(0.475365\pi\) | |||||||
\(168\) | 18.1780 | 1.40246 | ||||||||
\(169\) | 18.1199 | 1.39384 | ||||||||
\(170\) | 0.282149 | 0.0216399 | ||||||||
\(171\) | −2.36161 | −0.180596 | ||||||||
\(172\) | 38.6508 | 2.94709 | ||||||||
\(173\) | 2.75559 | 0.209504 | 0.104752 | − | 0.994498i | \(-0.466595\pi\) | ||||
0.104752 | + | 0.994498i | \(0.466595\pi\) | |||||||
\(174\) | −24.1730 | −1.83255 | ||||||||
\(175\) | −3.15964 | −0.238847 | ||||||||
\(176\) | −2.53971 | −0.191438 | ||||||||
\(177\) | −7.81304 | −0.587264 | ||||||||
\(178\) | −13.7080 | −1.02745 | ||||||||
\(179\) | −22.6072 | −1.68974 | −0.844869 | − | 0.534973i | \(-0.820322\pi\) | ||||
−0.844869 | + | 0.534973i | \(0.820322\pi\) | |||||||
\(180\) | −14.8021 | −1.10328 | ||||||||
\(181\) | 14.0374 | 1.04339 | 0.521696 | − | 0.853131i | \(-0.325299\pi\) | ||||
0.521696 | + | 0.853131i | \(0.325299\pi\) | |||||||
\(182\) | 48.8220 | 3.61893 | ||||||||
\(183\) | 16.6154 | 1.22825 | ||||||||
\(184\) | −7.52611 | −0.554832 | ||||||||
\(185\) | −7.57685 | −0.557061 | ||||||||
\(186\) | 26.6497 | 1.95405 | ||||||||
\(187\) | 0.0398719 | 0.00291572 | ||||||||
\(188\) | −48.6919 | −3.55122 | ||||||||
\(189\) | 18.6721 | 1.35820 | ||||||||
\(190\) | −6.30869 | −0.457680 | ||||||||
\(191\) | −9.00097 | −0.651287 | −0.325644 | − | 0.945493i | \(-0.605581\pi\) | ||||
−0.325644 | + | 0.945493i | \(0.605581\pi\) | |||||||
\(192\) | 9.33447 | 0.673657 | ||||||||
\(193\) | −10.8034 | −0.777643 | −0.388822 | − | 0.921313i | \(-0.627118\pi\) | ||||
−0.388822 | + | 0.921313i | \(0.627118\pi\) | |||||||
\(194\) | 25.7282 | 1.84718 | ||||||||
\(195\) | 12.1344 | 0.868961 | ||||||||
\(196\) | 23.2292 | 1.65923 | ||||||||
\(197\) | −4.68851 | −0.334042 | −0.167021 | − | 0.985953i | \(-0.553415\pi\) | ||||
−0.167021 | + | 0.985953i | \(0.553415\pi\) | |||||||
\(198\) | −3.15402 | −0.224147 | ||||||||
\(199\) | 8.19977 | 0.581266 | 0.290633 | − | 0.956835i | \(-0.406134\pi\) | ||||
0.290633 | + | 0.956835i | \(0.406134\pi\) | |||||||
\(200\) | 4.15539 | 0.293830 | ||||||||
\(201\) | −14.7178 | −1.03811 | ||||||||
\(202\) | 7.68693 | 0.540850 | ||||||||
\(203\) | −33.2453 | −2.33336 | ||||||||
\(204\) | 0.240730 | 0.0168545 | ||||||||
\(205\) | 14.8020 | 1.03381 | ||||||||
\(206\) | 16.4815 | 1.14832 | ||||||||
\(207\) | −2.95045 | −0.205071 | ||||||||
\(208\) | −20.2687 | −1.40538 | ||||||||
\(209\) | −0.891511 | −0.0616671 | ||||||||
\(210\) | 19.0368 | 1.31367 | ||||||||
\(211\) | 13.9709 | 0.961798 | 0.480899 | − | 0.876776i | \(-0.340310\pi\) | ||||
0.480899 | + | 0.876776i | \(0.340310\pi\) | |||||||
\(212\) | −22.5067 | −1.54577 | ||||||||
\(213\) | 13.2524 | 0.908037 | ||||||||
\(214\) | 22.3061 | 1.52481 | ||||||||
\(215\) | 19.9212 | 1.35861 | ||||||||
\(216\) | −24.5565 | −1.67086 | ||||||||
\(217\) | 36.6516 | 2.48807 | ||||||||
\(218\) | 1.98973 | 0.134762 | ||||||||
\(219\) | 4.75659 | 0.321421 | ||||||||
\(220\) | −5.58781 | −0.376730 | ||||||||
\(221\) | 0.318206 | 0.0214049 | ||||||||
\(222\) | −9.74755 | −0.654213 | ||||||||
\(223\) | 3.31724 | 0.222139 | 0.111069 | − | 0.993813i | \(-0.464572\pi\) | ||||
0.111069 | + | 0.993813i | \(0.464572\pi\) | |||||||
\(224\) | 2.12815 | 0.142193 | ||||||||
\(225\) | 1.62903 | 0.108602 | ||||||||
\(226\) | −11.1013 | −0.738448 | ||||||||
\(227\) | −2.29259 | −0.152165 | −0.0760824 | − | 0.997102i | \(-0.524241\pi\) | ||||
−0.0760824 | + | 0.997102i | \(0.524241\pi\) | |||||||
\(228\) | −5.38258 | −0.356470 | ||||||||
\(229\) | −9.01852 | −0.595960 | −0.297980 | − | 0.954572i | \(-0.596313\pi\) | ||||
−0.297980 | + | 0.954572i | \(0.596313\pi\) | |||||||
\(230\) | −7.88171 | −0.519704 | ||||||||
\(231\) | 2.69019 | 0.177001 | ||||||||
\(232\) | 43.7223 | 2.87051 | ||||||||
\(233\) | −7.80223 | −0.511141 | −0.255571 | − | 0.966790i | \(-0.582263\pi\) | ||||
−0.255571 | + | 0.966790i | \(0.582263\pi\) | |||||||
\(234\) | −25.1714 | −1.64550 | ||||||||
\(235\) | −25.0965 | −1.63712 | ||||||||
\(236\) | 28.7135 | 1.86909 | ||||||||
\(237\) | −3.52392 | −0.228903 | ||||||||
\(238\) | 0.499213 | 0.0323592 | ||||||||
\(239\) | 19.7301 | 1.27624 | 0.638119 | − | 0.769938i | \(-0.279713\pi\) | ||||
0.638119 | + | 0.769938i | \(0.279713\pi\) | |||||||
\(240\) | −7.90323 | −0.510151 | ||||||||
\(241\) | −14.0580 | −0.905557 | −0.452779 | − | 0.891623i | \(-0.649567\pi\) | ||||
−0.452779 | + | 0.891623i | \(0.649567\pi\) | |||||||
\(242\) | 25.6147 | 1.64658 | ||||||||
\(243\) | −15.5796 | −0.999433 | ||||||||
\(244\) | −61.0628 | −3.90914 | ||||||||
\(245\) | 11.9727 | 0.764906 | ||||||||
\(246\) | 19.0426 | 1.21411 | ||||||||
\(247\) | −7.11489 | −0.452710 | ||||||||
\(248\) | −48.2021 | −3.06084 | ||||||||
\(249\) | −3.95701 | −0.250765 | ||||||||
\(250\) | 29.0838 | 1.83942 | ||||||||
\(251\) | −15.1627 | −0.957063 | −0.478532 | − | 0.878070i | \(-0.658831\pi\) | ||||
−0.478532 | + | 0.878070i | \(0.658831\pi\) | |||||||
\(252\) | −26.1896 | −1.64979 | ||||||||
\(253\) | −1.11380 | −0.0700241 | ||||||||
\(254\) | −49.5957 | −3.11191 | ||||||||
\(255\) | 0.124076 | 0.00776994 | ||||||||
\(256\) | −31.4169 | −1.96355 | ||||||||
\(257\) | 8.80216 | 0.549063 | 0.274532 | − | 0.961578i | \(-0.411477\pi\) | ||||
0.274532 | + | 0.961578i | \(0.411477\pi\) | |||||||
\(258\) | 25.6284 | 1.59556 | ||||||||
\(259\) | −13.4059 | −0.833001 | ||||||||
\(260\) | −44.5947 | −2.76565 | ||||||||
\(261\) | 17.1404 | 1.06096 | ||||||||
\(262\) | −0.134839 | −0.00833036 | ||||||||
\(263\) | −17.7323 | −1.09342 | −0.546710 | − | 0.837322i | \(-0.684120\pi\) | ||||
−0.546710 | + | 0.837322i | \(0.684120\pi\) | |||||||
\(264\) | −3.53798 | −0.217748 | ||||||||
\(265\) | −11.6003 | −0.712601 | ||||||||
\(266\) | −11.1621 | −0.684392 | ||||||||
\(267\) | −6.02811 | −0.368914 | ||||||||
\(268\) | 54.0889 | 3.30401 | ||||||||
\(269\) | −27.1110 | −1.65299 | −0.826493 | − | 0.562948i | \(-0.809667\pi\) | ||||
−0.826493 | + | 0.562948i | \(0.809667\pi\) | |||||||
\(270\) | −25.7168 | −1.56507 | ||||||||
\(271\) | 15.9858 | 0.971065 | 0.485533 | − | 0.874219i | \(-0.338626\pi\) | ||||
0.485533 | + | 0.874219i | \(0.338626\pi\) | |||||||
\(272\) | −0.207250 | −0.0125664 | ||||||||
\(273\) | 21.4696 | 1.29940 | ||||||||
\(274\) | 31.8085 | 1.92162 | ||||||||
\(275\) | 0.614962 | 0.0370836 | ||||||||
\(276\) | −6.72468 | −0.404778 | ||||||||
\(277\) | −12.1369 | −0.729237 | −0.364619 | − | 0.931157i | \(-0.618801\pi\) | ||||
−0.364619 | + | 0.931157i | \(0.618801\pi\) | |||||||
\(278\) | 53.0394 | 3.18109 | ||||||||
\(279\) | −18.8966 | −1.13131 | ||||||||
\(280\) | −34.4324 | −2.05773 | ||||||||
\(281\) | −23.6536 | −1.41106 | −0.705529 | − | 0.708681i | \(-0.749291\pi\) | ||||
−0.705529 | + | 0.708681i | \(0.749291\pi\) | |||||||
\(282\) | −32.2864 | −1.92263 | ||||||||
\(283\) | −2.95925 | −0.175909 | −0.0879546 | − | 0.996124i | \(-0.528033\pi\) | ||||
−0.0879546 | + | 0.996124i | \(0.528033\pi\) | |||||||
\(284\) | −48.7034 | −2.89002 | ||||||||
\(285\) | −2.77426 | −0.164333 | ||||||||
\(286\) | −9.50224 | −0.561879 | ||||||||
\(287\) | 26.1894 | 1.54591 | ||||||||
\(288\) | −1.09722 | −0.0646543 | ||||||||
\(289\) | −16.9967 | −0.999809 | ||||||||
\(290\) | 45.7881 | 2.68877 | ||||||||
\(291\) | 11.3140 | 0.663240 | ||||||||
\(292\) | −17.4808 | −1.02299 | ||||||||
\(293\) | −16.6100 | −0.970366 | −0.485183 | − | 0.874413i | \(-0.661247\pi\) | ||||
−0.485183 | + | 0.874413i | \(0.661247\pi\) | |||||||
\(294\) | 15.4027 | 0.898305 | ||||||||
\(295\) | 14.7994 | 0.861651 | ||||||||
\(296\) | 17.6307 | 1.02476 | ||||||||
\(297\) | −3.63416 | −0.210875 | ||||||||
\(298\) | 17.6174 | 1.02055 | ||||||||
\(299\) | −8.88893 | −0.514060 | ||||||||
\(300\) | 3.71290 | 0.214364 | ||||||||
\(301\) | 35.2469 | 2.03160 | ||||||||
\(302\) | −5.79562 | −0.333500 | ||||||||
\(303\) | 3.38035 | 0.194196 | ||||||||
\(304\) | 4.63399 | 0.265778 | ||||||||
\(305\) | −31.4727 | −1.80212 | ||||||||
\(306\) | −0.257381 | −0.0147135 | ||||||||
\(307\) | −4.42029 | −0.252279 | −0.126140 | − | 0.992012i | \(-0.540259\pi\) | ||||
−0.126140 | + | 0.992012i | \(0.540259\pi\) | |||||||
\(308\) | −9.88663 | −0.563343 | ||||||||
\(309\) | 7.24778 | 0.412312 | ||||||||
\(310\) | −50.4796 | −2.86705 | ||||||||
\(311\) | −21.9982 | −1.24740 | −0.623701 | − | 0.781663i | \(-0.714372\pi\) | ||||
−0.623701 | + | 0.781663i | \(0.714372\pi\) | |||||||
\(312\) | −28.2356 | −1.59853 | ||||||||
\(313\) | 3.60533 | 0.203785 | 0.101893 | − | 0.994795i | \(-0.467510\pi\) | ||||
0.101893 | + | 0.994795i | \(0.467510\pi\) | |||||||
\(314\) | −45.2395 | −2.55301 | ||||||||
\(315\) | −13.4985 | −0.760555 | ||||||||
\(316\) | 12.9507 | 0.728532 | ||||||||
\(317\) | 0.623785 | 0.0350352 | 0.0175176 | − | 0.999847i | \(-0.494424\pi\) | ||||
0.0175176 | + | 0.999847i | \(0.494424\pi\) | |||||||
\(318\) | −14.9237 | −0.836879 | ||||||||
\(319\) | 6.47054 | 0.362281 | ||||||||
\(320\) | −17.6812 | −0.988411 | ||||||||
\(321\) | 9.80916 | 0.547494 | ||||||||
\(322\) | −13.9453 | −0.777139 | ||||||||
\(323\) | −0.0727509 | −0.00404797 | ||||||||
\(324\) | −0.0648420 | −0.00360233 | ||||||||
\(325\) | 4.90784 | 0.272238 | ||||||||
\(326\) | 12.6628 | 0.701327 | ||||||||
\(327\) | 0.874990 | 0.0483871 | ||||||||
\(328\) | −34.4429 | −1.90179 | ||||||||
\(329\) | −44.4038 | −2.44806 | ||||||||
\(330\) | −3.70514 | −0.203961 | ||||||||
\(331\) | 11.3026 | 0.621247 | 0.310623 | − | 0.950533i | \(-0.399462\pi\) | ||||
0.310623 | + | 0.950533i | \(0.399462\pi\) | |||||||
\(332\) | 14.5423 | 0.798113 | ||||||||
\(333\) | 6.91172 | 0.378760 | ||||||||
\(334\) | −4.86953 | −0.266449 | ||||||||
\(335\) | 27.8782 | 1.52315 | ||||||||
\(336\) | −13.9833 | −0.762854 | ||||||||
\(337\) | 21.3269 | 1.16175 | 0.580876 | − | 0.813992i | \(-0.302710\pi\) | ||||
0.580876 | + | 0.813992i | \(0.302710\pi\) | |||||||
\(338\) | −44.1556 | −2.40175 | ||||||||
\(339\) | −4.88183 | −0.265145 | ||||||||
\(340\) | −0.455988 | −0.0247294 | ||||||||
\(341\) | −7.13351 | −0.386301 | ||||||||
\(342\) | 5.75489 | 0.311189 | ||||||||
\(343\) | −3.95650 | −0.213631 | ||||||||
\(344\) | −46.3548 | −2.49928 | ||||||||
\(345\) | −3.46600 | −0.186603 | ||||||||
\(346\) | −6.71498 | −0.360999 | ||||||||
\(347\) | 26.6198 | 1.42902 | 0.714512 | − | 0.699623i | \(-0.246649\pi\) | ||||
0.714512 | + | 0.699623i | \(0.246649\pi\) | |||||||
\(348\) | 39.0665 | 2.09418 | ||||||||
\(349\) | 10.1568 | 0.543683 | 0.271841 | − | 0.962342i | \(-0.412367\pi\) | ||||
0.271841 | + | 0.962342i | \(0.412367\pi\) | |||||||
\(350\) | 7.69959 | 0.411560 | ||||||||
\(351\) | −29.0032 | −1.54808 | ||||||||
\(352\) | −0.414203 | −0.0220771 | ||||||||
\(353\) | −2.09661 | −0.111591 | −0.0557955 | − | 0.998442i | \(-0.517770\pi\) | ||||
−0.0557955 | + | 0.998442i | \(0.517770\pi\) | |||||||
\(354\) | 19.0392 | 1.01192 | ||||||||
\(355\) | −25.1025 | −1.33230 | ||||||||
\(356\) | 22.1537 | 1.17415 | ||||||||
\(357\) | 0.219530 | 0.0116188 | ||||||||
\(358\) | 55.0903 | 2.91162 | ||||||||
\(359\) | 7.28312 | 0.384388 | 0.192194 | − | 0.981357i | \(-0.438440\pi\) | ||||
0.192194 | + | 0.981357i | \(0.438440\pi\) | |||||||
\(360\) | 17.7525 | 0.935638 | ||||||||
\(361\) | −17.3733 | −0.914386 | ||||||||
\(362\) | −34.2071 | −1.79789 | ||||||||
\(363\) | 11.2641 | 0.591214 | ||||||||
\(364\) | −78.9024 | −4.13561 | ||||||||
\(365\) | −9.00988 | −0.471598 | ||||||||
\(366\) | −40.4893 | −2.11641 | ||||||||
\(367\) | 26.9252 | 1.40549 | 0.702743 | − | 0.711444i | \(-0.251958\pi\) | ||||
0.702743 | + | 0.711444i | \(0.251958\pi\) | |||||||
\(368\) | 5.78944 | 0.301795 | ||||||||
\(369\) | −13.5026 | −0.702917 | ||||||||
\(370\) | 18.4637 | 0.959881 | ||||||||
\(371\) | −20.5247 | −1.06559 | ||||||||
\(372\) | −43.0693 | −2.23304 | ||||||||
\(373\) | 30.5207 | 1.58030 | 0.790152 | − | 0.612911i | \(-0.210002\pi\) | ||||
0.790152 | + | 0.612911i | \(0.210002\pi\) | |||||||
\(374\) | −0.0971619 | −0.00502412 | ||||||||
\(375\) | 12.7897 | 0.660455 | ||||||||
\(376\) | 58.3974 | 3.01161 | ||||||||
\(377\) | 51.6395 | 2.65957 | ||||||||
\(378\) | −45.5013 | −2.34033 | ||||||||
\(379\) | −25.8030 | −1.32541 | −0.662706 | − | 0.748880i | \(-0.730592\pi\) | ||||
−0.662706 | + | 0.748880i | \(0.730592\pi\) | |||||||
\(380\) | 10.1956 | 0.523024 | ||||||||
\(381\) | −21.8099 | −1.11735 | ||||||||
\(382\) | 21.9340 | 1.12224 | ||||||||
\(383\) | −35.7225 | −1.82533 | −0.912667 | − | 0.408705i | \(-0.865981\pi\) | ||||
−0.912667 | + | 0.408705i | \(0.865981\pi\) | |||||||
\(384\) | −21.4767 | −1.09598 | ||||||||
\(385\) | −5.09571 | −0.259702 | ||||||||
\(386\) | 26.3262 | 1.33997 | ||||||||
\(387\) | −18.1724 | −0.923756 | ||||||||
\(388\) | −41.5799 | −2.11090 | ||||||||
\(389\) | −13.9922 | −0.709434 | −0.354717 | − | 0.934974i | \(-0.615423\pi\) | ||||
−0.354717 | + | 0.934974i | \(0.615423\pi\) | |||||||
\(390\) | −29.5697 | −1.49732 | ||||||||
\(391\) | −0.0908907 | −0.00459654 | ||||||||
\(392\) | −27.8593 | −1.40711 | ||||||||
\(393\) | −0.0592956 | −0.00299107 | ||||||||
\(394\) | 11.4252 | 0.575594 | ||||||||
\(395\) | 6.67496 | 0.335854 | ||||||||
\(396\) | 5.09729 | 0.256148 | ||||||||
\(397\) | 10.3643 | 0.520171 | 0.260086 | − | 0.965586i | \(-0.416249\pi\) | ||||
0.260086 | + | 0.965586i | \(0.416249\pi\) | |||||||
\(398\) | −19.9816 | −1.00159 | ||||||||
\(399\) | −4.90856 | −0.245735 | ||||||||
\(400\) | −3.19652 | −0.159826 | ||||||||
\(401\) | 3.61257 | 0.180403 | 0.0902015 | − | 0.995924i | \(-0.471249\pi\) | ||||
0.0902015 | + | 0.995924i | \(0.471249\pi\) | |||||||
\(402\) | 35.8651 | 1.78879 | ||||||||
\(403\) | −56.9305 | −2.83591 | ||||||||
\(404\) | −12.4230 | −0.618068 | ||||||||
\(405\) | −0.0334205 | −0.00166068 | ||||||||
\(406\) | 81.0139 | 4.02065 | ||||||||
\(407\) | 2.60919 | 0.129333 | ||||||||
\(408\) | −0.288714 | −0.0142935 | ||||||||
\(409\) | 5.25608 | 0.259896 | 0.129948 | − | 0.991521i | \(-0.458519\pi\) | ||||
0.129948 | + | 0.991521i | \(0.458519\pi\) | |||||||
\(410\) | −36.0702 | −1.78138 | ||||||||
\(411\) | 13.9879 | 0.689971 | ||||||||
\(412\) | −26.6361 | −1.31227 | ||||||||
\(413\) | 26.1848 | 1.28847 | ||||||||
\(414\) | 7.18982 | 0.353360 | ||||||||
\(415\) | 7.49532 | 0.367931 | ||||||||
\(416\) | −3.30564 | −0.162072 | ||||||||
\(417\) | 23.3242 | 1.14219 | ||||||||
\(418\) | 2.17248 | 0.106260 | ||||||||
\(419\) | 5.70977 | 0.278940 | 0.139470 | − | 0.990226i | \(-0.455460\pi\) | ||||
0.139470 | + | 0.990226i | \(0.455460\pi\) | |||||||
\(420\) | −30.7659 | −1.50122 | ||||||||
\(421\) | 5.04277 | 0.245770 | 0.122885 | − | 0.992421i | \(-0.460785\pi\) | ||||
0.122885 | + | 0.992421i | \(0.460785\pi\) | |||||||
\(422\) | −34.0451 | −1.65729 | ||||||||
\(423\) | 22.8934 | 1.11312 | ||||||||
\(424\) | 26.9929 | 1.31089 | ||||||||
\(425\) | 0.0501834 | 0.00243425 | ||||||||
\(426\) | −32.2941 | −1.56465 | ||||||||
\(427\) | −55.6852 | −2.69480 | ||||||||
\(428\) | −36.0494 | −1.74251 | ||||||||
\(429\) | −4.17863 | −0.201746 | ||||||||
\(430\) | −48.5450 | −2.34105 | ||||||||
\(431\) | −10.4867 | −0.505126 | −0.252563 | − | 0.967581i | \(-0.581273\pi\) | ||||
−0.252563 | + | 0.967581i | \(0.581273\pi\) | |||||||
\(432\) | 18.8901 | 0.908848 | ||||||||
\(433\) | 27.0552 | 1.30019 | 0.650096 | − | 0.759852i | \(-0.274729\pi\) | ||||
0.650096 | + | 0.759852i | \(0.274729\pi\) | |||||||
\(434\) | −89.3145 | −4.28724 | ||||||||
\(435\) | 20.1354 | 0.965421 | ||||||||
\(436\) | −3.21565 | −0.154002 | ||||||||
\(437\) | 2.03226 | 0.0972162 | ||||||||
\(438\) | −11.5911 | −0.553845 | ||||||||
\(439\) | −3.14513 | −0.150109 | −0.0750545 | − | 0.997179i | \(-0.523913\pi\) | ||||
−0.0750545 | + | 0.997179i | \(0.523913\pi\) | |||||||
\(440\) | 6.70160 | 0.319486 | ||||||||
\(441\) | −10.9217 | −0.520079 | ||||||||
\(442\) | −0.775422 | −0.0368830 | ||||||||
\(443\) | −3.13688 | −0.149038 | −0.0745188 | − | 0.997220i | \(-0.523742\pi\) | ||||
−0.0745188 | + | 0.997220i | \(0.523742\pi\) | |||||||
\(444\) | 15.7532 | 0.747615 | ||||||||
\(445\) | 11.4184 | 0.541282 | ||||||||
\(446\) | −8.08362 | −0.382770 | ||||||||
\(447\) | 7.74731 | 0.366435 | ||||||||
\(448\) | −31.2838 | −1.47802 | ||||||||
\(449\) | 5.70852 | 0.269402 | 0.134701 | − | 0.990886i | \(-0.456993\pi\) | ||||
0.134701 | + | 0.990886i | \(0.456993\pi\) | |||||||
\(450\) | −3.96971 | −0.187134 | ||||||||
\(451\) | −5.09726 | −0.240020 | ||||||||
\(452\) | 17.9411 | 0.843878 | ||||||||
\(453\) | −2.54864 | −0.119745 | ||||||||
\(454\) | 5.58671 | 0.262197 | ||||||||
\(455\) | −40.6674 | −1.90652 | ||||||||
\(456\) | 6.45546 | 0.302305 | ||||||||
\(457\) | −10.3278 | −0.483114 | −0.241557 | − | 0.970387i | \(-0.577658\pi\) | ||||
−0.241557 | + | 0.970387i | \(0.577658\pi\) | |||||||
\(458\) | 21.9768 | 1.02691 | ||||||||
\(459\) | −0.296562 | −0.0138424 | ||||||||
\(460\) | 12.7378 | 0.593903 | ||||||||
\(461\) | −22.5154 | −1.04865 | −0.524324 | − | 0.851519i | \(-0.675682\pi\) | ||||
−0.524324 | + | 0.851519i | \(0.675682\pi\) | |||||||
\(462\) | −6.55559 | −0.304994 | ||||||||
\(463\) | 15.8379 | 0.736050 | 0.368025 | − | 0.929816i | \(-0.380034\pi\) | ||||
0.368025 | + | 0.929816i | \(0.380034\pi\) | |||||||
\(464\) | −33.6333 | −1.56139 | ||||||||
\(465\) | −22.1985 | −1.02943 | ||||||||
\(466\) | 19.0129 | 0.880756 | ||||||||
\(467\) | −37.2193 | −1.72230 | −0.861151 | − | 0.508349i | \(-0.830256\pi\) | ||||
−0.861151 | + | 0.508349i | \(0.830256\pi\) | |||||||
\(468\) | 40.6800 | 1.88043 | ||||||||
\(469\) | 49.3255 | 2.27764 | ||||||||
\(470\) | 61.1565 | 2.82094 | ||||||||
\(471\) | −19.8942 | −0.916675 | ||||||||
\(472\) | −34.4368 | −1.58508 | ||||||||
\(473\) | −6.86012 | −0.315429 | ||||||||
\(474\) | 8.58728 | 0.394427 | ||||||||
\(475\) | −1.12207 | −0.0514842 | ||||||||
\(476\) | −0.806789 | −0.0369791 | ||||||||
\(477\) | 10.5820 | 0.484516 | ||||||||
\(478\) | −48.0795 | −2.19910 | ||||||||
\(479\) | 27.6531 | 1.26350 | 0.631751 | − | 0.775171i | \(-0.282336\pi\) | ||||
0.631751 | + | 0.775171i | \(0.282336\pi\) | |||||||
\(480\) | −1.28894 | −0.0588320 | ||||||||
\(481\) | 20.8232 | 0.949456 | ||||||||
\(482\) | 34.2574 | 1.56038 | ||||||||
\(483\) | −6.13247 | −0.279037 | ||||||||
\(484\) | −41.3966 | −1.88166 | ||||||||
\(485\) | −21.4309 | −0.973127 | ||||||||
\(486\) | 37.9652 | 1.72214 | ||||||||
\(487\) | −1.24369 | −0.0563568 | −0.0281784 | − | 0.999603i | \(-0.508971\pi\) | ||||
−0.0281784 | + | 0.999603i | \(0.508971\pi\) | |||||||
\(488\) | 73.2341 | 3.31515 | ||||||||
\(489\) | 5.56850 | 0.251816 | ||||||||
\(490\) | −29.1756 | −1.31802 | ||||||||
\(491\) | 3.45145 | 0.155762 | 0.0778810 | − | 0.996963i | \(-0.475185\pi\) | ||||
0.0778810 | + | 0.996963i | \(0.475185\pi\) | |||||||
\(492\) | −30.7752 | −1.38745 | ||||||||
\(493\) | 0.528022 | 0.0237809 | ||||||||
\(494\) | 17.3380 | 0.780071 | ||||||||
\(495\) | 2.62722 | 0.118085 | ||||||||
\(496\) | 37.0793 | 1.66491 | ||||||||
\(497\) | −44.4143 | −1.99225 | ||||||||
\(498\) | 9.64266 | 0.432098 | ||||||||
\(499\) | 30.5598 | 1.36805 | 0.684023 | − | 0.729460i | \(-0.260229\pi\) | ||||
0.684023 | + | 0.729460i | \(0.260229\pi\) | |||||||
\(500\) | −47.0029 | −2.10204 | ||||||||
\(501\) | −2.14139 | −0.0956702 | ||||||||
\(502\) | 36.9494 | 1.64913 | ||||||||
\(503\) | −5.09930 | −0.227366 | −0.113683 | − | 0.993517i | \(-0.536265\pi\) | ||||
−0.113683 | + | 0.993517i | \(0.536265\pi\) | |||||||
\(504\) | 31.4098 | 1.39910 | ||||||||
\(505\) | −6.40300 | −0.284930 | ||||||||
\(506\) | 2.71417 | 0.120660 | ||||||||
\(507\) | −19.4175 | −0.862363 | ||||||||
\(508\) | 80.1528 | 3.55621 | ||||||||
\(509\) | −20.3945 | −0.903969 | −0.451985 | − | 0.892026i | \(-0.649284\pi\) | ||||
−0.451985 | + | 0.892026i | \(0.649284\pi\) | |||||||
\(510\) | −0.302355 | −0.0133885 | ||||||||
\(511\) | −15.9414 | −0.705204 | ||||||||
\(512\) | 36.4753 | 1.61200 | ||||||||
\(513\) | 6.63096 | 0.292764 | ||||||||
\(514\) | −21.4496 | −0.946100 | ||||||||
\(515\) | −13.7286 | −0.604956 | ||||||||
\(516\) | −41.4187 | −1.82335 | ||||||||
\(517\) | 8.64232 | 0.380089 | ||||||||
\(518\) | 32.6682 | 1.43536 | ||||||||
\(519\) | −2.95293 | −0.129619 | ||||||||
\(520\) | 53.4835 | 2.34541 | ||||||||
\(521\) | 37.2724 | 1.63293 | 0.816467 | − | 0.577392i | \(-0.195929\pi\) | ||||
0.816467 | + | 0.577392i | \(0.195929\pi\) | |||||||
\(522\) | −41.7687 | −1.82816 | ||||||||
\(523\) | −35.1765 | −1.53816 | −0.769080 | − | 0.639152i | \(-0.779285\pi\) | ||||
−0.769080 | + | 0.639152i | \(0.779285\pi\) | |||||||
\(524\) | 0.217916 | 0.00951970 | ||||||||
\(525\) | 3.38591 | 0.147773 | ||||||||
\(526\) | 43.2110 | 1.88409 | ||||||||
\(527\) | −0.582123 | −0.0253577 | ||||||||
\(528\) | 2.72158 | 0.118442 | ||||||||
\(529\) | −20.4610 | −0.889609 | ||||||||
\(530\) | 28.2682 | 1.22789 | ||||||||
\(531\) | −13.5002 | −0.585859 | ||||||||
\(532\) | 18.0393 | 0.782104 | ||||||||
\(533\) | −40.6798 | −1.76204 | ||||||||
\(534\) | 14.6896 | 0.635682 | ||||||||
\(535\) | −18.5804 | −0.803300 | ||||||||
\(536\) | −64.8701 | −2.80196 | ||||||||
\(537\) | 24.2261 | 1.04543 | ||||||||
\(538\) | 66.0655 | 2.84828 | ||||||||
\(539\) | −4.12295 | −0.177588 | ||||||||
\(540\) | 41.5615 | 1.78852 | ||||||||
\(541\) | −42.1942 | −1.81407 | −0.907036 | − | 0.421053i | \(-0.861661\pi\) | ||||
−0.907036 | + | 0.421053i | \(0.861661\pi\) | |||||||
\(542\) | −38.9549 | −1.67326 | ||||||||
\(543\) | −15.0427 | −0.645543 | ||||||||
\(544\) | −0.0338006 | −0.00144919 | ||||||||
\(545\) | −1.65739 | −0.0709950 | ||||||||
\(546\) | −52.3183 | −2.23902 | ||||||||
\(547\) | 22.7832 | 0.974141 | 0.487070 | − | 0.873363i | \(-0.338066\pi\) | ||||
0.487070 | + | 0.873363i | \(0.338066\pi\) | |||||||
\(548\) | −51.4064 | −2.19597 | ||||||||
\(549\) | 28.7098 | 1.22531 | ||||||||
\(550\) | −1.49857 | −0.0638994 | ||||||||
\(551\) | −11.8063 | −0.502963 | ||||||||
\(552\) | 8.06508 | 0.343272 | ||||||||
\(553\) | 11.8102 | 0.502219 | ||||||||
\(554\) | 29.5759 | 1.25656 | ||||||||
\(555\) | 8.11945 | 0.344651 | ||||||||
\(556\) | −85.7182 | −3.63526 | ||||||||
\(557\) | 24.6271 | 1.04348 | 0.521741 | − | 0.853104i | \(-0.325283\pi\) | ||||
0.521741 | + | 0.853104i | \(0.325283\pi\) | |||||||
\(558\) | 46.0483 | 1.94938 | ||||||||
\(559\) | −54.7487 | −2.31562 | ||||||||
\(560\) | 26.4871 | 1.11928 | ||||||||
\(561\) | −0.0427272 | −0.00180394 | ||||||||
\(562\) | 57.6405 | 2.43142 | ||||||||
\(563\) | −21.2483 | −0.895509 | −0.447755 | − | 0.894156i | \(-0.647776\pi\) | ||||
−0.447755 | + | 0.894156i | \(0.647776\pi\) | |||||||
\(564\) | 52.1789 | 2.19713 | ||||||||
\(565\) | 9.24710 | 0.389028 | ||||||||
\(566\) | 7.21126 | 0.303112 | ||||||||
\(567\) | −0.0591316 | −0.00248329 | ||||||||
\(568\) | 58.4112 | 2.45088 | ||||||||
\(569\) | 13.6503 | 0.572251 | 0.286125 | − | 0.958192i | \(-0.407633\pi\) | ||||
0.286125 | + | 0.958192i | \(0.407633\pi\) | |||||||
\(570\) | 6.76047 | 0.283165 | ||||||||
\(571\) | −0.986146 | −0.0412689 | −0.0206345 | − | 0.999787i | \(-0.506569\pi\) | ||||
−0.0206345 | + | 0.999787i | \(0.506569\pi\) | |||||||
\(572\) | 15.3568 | 0.642100 | ||||||||
\(573\) | 9.64555 | 0.402949 | ||||||||
\(574\) | −63.8198 | −2.66379 | ||||||||
\(575\) | −1.40185 | −0.0584612 | ||||||||
\(576\) | 16.1291 | 0.672046 | ||||||||
\(577\) | −30.9051 | −1.28660 | −0.643298 | − | 0.765616i | \(-0.722434\pi\) | ||||
−0.643298 | + | 0.765616i | \(0.722434\pi\) | |||||||
\(578\) | 41.4186 | 1.72279 | ||||||||
\(579\) | 11.5770 | 0.481124 | ||||||||
\(580\) | −73.9993 | −3.07265 | ||||||||
\(581\) | 13.2616 | 0.550185 | ||||||||
\(582\) | −27.5706 | −1.14284 | ||||||||
\(583\) | 3.99472 | 0.165444 | ||||||||
\(584\) | 20.9652 | 0.867545 | ||||||||
\(585\) | 20.9671 | 0.866882 | ||||||||
\(586\) | 40.4761 | 1.67205 | ||||||||
\(587\) | −5.00514 | −0.206584 | −0.103292 | − | 0.994651i | \(-0.532938\pi\) | ||||
−0.103292 | + | 0.994651i | \(0.532938\pi\) | |||||||
\(588\) | −24.8927 | −1.02656 | ||||||||
\(589\) | 13.0159 | 0.536312 | ||||||||
\(590\) | −36.0638 | −1.48473 | ||||||||
\(591\) | 5.02426 | 0.206671 | ||||||||
\(592\) | −13.5623 | −0.557408 | ||||||||
\(593\) | 27.1705 | 1.11576 | 0.557880 | − | 0.829922i | \(-0.311615\pi\) | ||||
0.557880 | + | 0.829922i | \(0.311615\pi\) | |||||||
\(594\) | 8.85592 | 0.363363 | ||||||||
\(595\) | −0.415831 | −0.0170474 | ||||||||
\(596\) | −28.4719 | −1.16626 | ||||||||
\(597\) | −8.78698 | −0.359627 | ||||||||
\(598\) | 21.6610 | 0.885785 | ||||||||
\(599\) | −16.0618 | −0.656268 | −0.328134 | − | 0.944631i | \(-0.606420\pi\) | ||||
−0.328134 | + | 0.944631i | \(0.606420\pi\) | |||||||
\(600\) | −4.45297 | −0.181792 | ||||||||
\(601\) | −29.5441 | −1.20513 | −0.602564 | − | 0.798071i | \(-0.705854\pi\) | ||||
−0.602564 | + | 0.798071i | \(0.705854\pi\) | |||||||
\(602\) | −85.8916 | −3.50068 | ||||||||
\(603\) | −25.4309 | −1.03563 | ||||||||
\(604\) | 9.36643 | 0.381115 | ||||||||
\(605\) | −21.3364 | −0.867448 | ||||||||
\(606\) | −8.23741 | −0.334622 | ||||||||
\(607\) | 38.1337 | 1.54780 | 0.773900 | − | 0.633308i | \(-0.218303\pi\) | ||||
0.773900 | + | 0.633308i | \(0.218303\pi\) | |||||||
\(608\) | 0.755762 | 0.0306502 | ||||||||
\(609\) | 35.6261 | 1.44364 | ||||||||
\(610\) | 76.6942 | 3.10526 | ||||||||
\(611\) | 68.9719 | 2.79030 | ||||||||
\(612\) | 0.415960 | 0.0168142 | ||||||||
\(613\) | −11.7360 | −0.474012 | −0.237006 | − | 0.971508i | \(-0.576166\pi\) | ||||
−0.237006 | + | 0.971508i | \(0.576166\pi\) | |||||||
\(614\) | 10.7716 | 0.434706 | ||||||||
\(615\) | −15.8620 | −0.639617 | ||||||||
\(616\) | 11.8573 | 0.477743 | ||||||||
\(617\) | −15.2634 | −0.614483 | −0.307242 | − | 0.951632i | \(-0.599406\pi\) | ||||
−0.307242 | + | 0.951632i | \(0.599406\pi\) | |||||||
\(618\) | −17.6618 | −0.710460 | ||||||||
\(619\) | −18.7830 | −0.754952 | −0.377476 | − | 0.926019i | \(-0.623208\pi\) | ||||
−0.377476 | + | 0.926019i | \(0.623208\pi\) | |||||||
\(620\) | 81.5812 | 3.27638 | ||||||||
\(621\) | 8.28433 | 0.332439 | ||||||||
\(622\) | 53.6063 | 2.14942 | ||||||||
\(623\) | 20.2027 | 0.809406 | ||||||||
\(624\) | 21.7202 | 0.869503 | ||||||||
\(625\) | −19.8271 | −0.793085 | ||||||||
\(626\) | −8.78567 | −0.351146 | ||||||||
\(627\) | 0.955354 | 0.0381532 | ||||||||
\(628\) | 73.1125 | 2.91751 | ||||||||
\(629\) | 0.212920 | 0.00848970 | ||||||||
\(630\) | 32.8939 | 1.31052 | ||||||||
\(631\) | −46.1200 | −1.83601 | −0.918005 | − | 0.396569i | \(-0.870201\pi\) | ||||
−0.918005 | + | 0.396569i | \(0.870201\pi\) | |||||||
\(632\) | −15.5321 | −0.617832 | ||||||||
\(633\) | −14.9714 | −0.595060 | ||||||||
\(634\) | −1.52007 | −0.0603698 | ||||||||
\(635\) | 41.3119 | 1.63941 | ||||||||
\(636\) | 24.1185 | 0.956361 | ||||||||
\(637\) | −32.9041 | −1.30371 | ||||||||
\(638\) | −15.7678 | −0.624251 | ||||||||
\(639\) | 22.8989 | 0.905865 | ||||||||
\(640\) | 40.6809 | 1.60806 | ||||||||
\(641\) | 9.91182 | 0.391493 | 0.195747 | − | 0.980654i | \(-0.437287\pi\) | ||||
0.195747 | + | 0.980654i | \(0.437287\pi\) | |||||||
\(642\) | −23.9035 | −0.943395 | ||||||||
\(643\) | −15.0888 | −0.595043 | −0.297522 | − | 0.954715i | \(-0.596160\pi\) | ||||
−0.297522 | + | 0.954715i | \(0.596160\pi\) | |||||||
\(644\) | 22.5373 | 0.888093 | ||||||||
\(645\) | −21.3478 | −0.840568 | ||||||||
\(646\) | 0.177283 | 0.00697512 | ||||||||
\(647\) | 33.4370 | 1.31454 | 0.657272 | − | 0.753654i | \(-0.271710\pi\) | ||||
0.657272 | + | 0.753654i | \(0.271710\pi\) | |||||||
\(648\) | 0.0777665 | 0.00305496 | ||||||||
\(649\) | −5.09635 | −0.200049 | ||||||||
\(650\) | −11.9597 | −0.469098 | ||||||||
\(651\) | −39.2763 | −1.53936 | ||||||||
\(652\) | −20.4646 | −0.801457 | ||||||||
\(653\) | −44.3877 | −1.73702 | −0.868512 | − | 0.495669i | \(-0.834923\pi\) | ||||
−0.868512 | + | 0.495669i | \(0.834923\pi\) | |||||||
\(654\) | −2.13222 | −0.0833765 | ||||||||
\(655\) | 0.112317 | 0.00438859 | ||||||||
\(656\) | 26.4951 | 1.03446 | ||||||||
\(657\) | 8.21895 | 0.320652 | ||||||||
\(658\) | 108.206 | 4.21829 | ||||||||
\(659\) | −45.5212 | −1.77325 | −0.886626 | − | 0.462486i | \(-0.846957\pi\) | ||||
−0.886626 | + | 0.462486i | \(0.846957\pi\) | |||||||
\(660\) | 5.98797 | 0.233081 | ||||||||
\(661\) | −7.82259 | −0.304264 | −0.152132 | − | 0.988360i | \(-0.548614\pi\) | ||||
−0.152132 | + | 0.988360i | \(0.548614\pi\) | |||||||
\(662\) | −27.5428 | −1.07048 | ||||||||
\(663\) | −0.340994 | −0.0132431 | ||||||||
\(664\) | −17.4409 | −0.676840 | ||||||||
\(665\) | 9.29773 | 0.360550 | ||||||||
\(666\) | −16.8429 | −0.652647 | ||||||||
\(667\) | −14.7500 | −0.571124 | ||||||||
\(668\) | 7.86976 | 0.304490 | ||||||||
\(669\) | −3.55479 | −0.137436 | ||||||||
\(670\) | −67.9351 | −2.62456 | ||||||||
\(671\) | 10.8380 | 0.418397 | ||||||||
\(672\) | −2.28056 | −0.0879743 | ||||||||
\(673\) | −11.7259 | −0.452000 | −0.226000 | − | 0.974127i | \(-0.572565\pi\) | ||||
−0.226000 | + | 0.974127i | \(0.572565\pi\) | |||||||
\(674\) | −51.9706 | −2.00183 | ||||||||
\(675\) | −4.57402 | −0.176054 | ||||||||
\(676\) | 71.3609 | 2.74465 | ||||||||
\(677\) | −24.5974 | −0.945355 | −0.472678 | − | 0.881235i | \(-0.656712\pi\) | ||||
−0.472678 | + | 0.881235i | \(0.656712\pi\) | |||||||
\(678\) | 11.8963 | 0.456875 | ||||||||
\(679\) | −37.9181 | −1.45516 | ||||||||
\(680\) | 0.546878 | 0.0209718 | ||||||||
\(681\) | 2.45677 | 0.0941437 | ||||||||
\(682\) | 17.3833 | 0.665641 | ||||||||
\(683\) | 28.9165 | 1.10646 | 0.553230 | − | 0.833028i | \(-0.313395\pi\) | ||||
0.553230 | + | 0.833028i | \(0.313395\pi\) | |||||||
\(684\) | −9.30060 | −0.355617 | ||||||||
\(685\) | −26.4956 | −1.01235 | ||||||||
\(686\) | 9.64142 | 0.368111 | ||||||||
\(687\) | 9.66435 | 0.368718 | ||||||||
\(688\) | 35.6583 | 1.35946 | ||||||||
\(689\) | 31.8807 | 1.21456 | ||||||||
\(690\) | 8.44614 | 0.321539 | ||||||||
\(691\) | −50.4019 | −1.91738 | −0.958689 | − | 0.284456i | \(-0.908187\pi\) | ||||
−0.958689 | + | 0.284456i | \(0.908187\pi\) | |||||||
\(692\) | 10.8522 | 0.412540 | ||||||||
\(693\) | 4.64839 | 0.176578 | ||||||||
\(694\) | −64.8685 | −2.46238 | ||||||||
\(695\) | −44.1804 | −1.67586 | ||||||||
\(696\) | −46.8534 | −1.77597 | ||||||||
\(697\) | −0.415957 | −0.0157555 | ||||||||
\(698\) | −24.7507 | −0.936828 | ||||||||
\(699\) | 8.36097 | 0.316241 | ||||||||
\(700\) | −12.4435 | −0.470320 | ||||||||
\(701\) | 2.12343 | 0.0802007 | 0.0401003 | − | 0.999196i | \(-0.487232\pi\) | ||||
0.0401003 | + | 0.999196i | \(0.487232\pi\) | |||||||
\(702\) | 70.6766 | 2.66752 | ||||||||
\(703\) | −4.76077 | −0.179556 | ||||||||
\(704\) | 6.08877 | 0.229479 | ||||||||
\(705\) | 26.8937 | 1.01288 | ||||||||
\(706\) | 5.10912 | 0.192284 | ||||||||
\(707\) | −11.3290 | −0.426070 | ||||||||
\(708\) | −30.7697 | −1.15640 | ||||||||
\(709\) | 22.9837 | 0.863170 | 0.431585 | − | 0.902072i | \(-0.357954\pi\) | ||||
0.431585 | + | 0.902072i | \(0.357954\pi\) | |||||||
\(710\) | 61.1710 | 2.29571 | ||||||||
\(711\) | −6.08901 | −0.228356 | ||||||||
\(712\) | −26.5695 | −0.995735 | ||||||||
\(713\) | 16.2613 | 0.608992 | ||||||||
\(714\) | −0.534963 | −0.0200205 | ||||||||
\(715\) | 7.91511 | 0.296008 | ||||||||
\(716\) | −89.0328 | −3.32731 | ||||||||
\(717\) | −21.1431 | −0.789602 | ||||||||
\(718\) | −17.7479 | −0.662345 | ||||||||
\(719\) | −19.1718 | −0.714987 | −0.357494 | − | 0.933916i | \(-0.616369\pi\) | ||||
−0.357494 | + | 0.933916i | \(0.616369\pi\) | |||||||
\(720\) | −13.6560 | −0.508931 | ||||||||
\(721\) | −24.2904 | −0.904620 | ||||||||
\(722\) | 42.3363 | 1.57559 | ||||||||
\(723\) | 15.0648 | 0.560264 | ||||||||
\(724\) | 55.2829 | 2.05457 | ||||||||
\(725\) | 8.14393 | 0.302458 | ||||||||
\(726\) | −27.4491 | −1.01873 | ||||||||
\(727\) | 10.2018 | 0.378366 | 0.189183 | − | 0.981942i | \(-0.439416\pi\) | ||||
0.189183 | + | 0.981942i | \(0.439416\pi\) | |||||||
\(728\) | 94.6295 | 3.50720 | ||||||||
\(729\) | 16.7447 | 0.620174 | ||||||||
\(730\) | 21.9557 | 0.812619 | ||||||||
\(731\) | −0.559814 | −0.0207055 | ||||||||
\(732\) | 65.4356 | 2.41857 | ||||||||
\(733\) | −33.7170 | −1.24536 | −0.622682 | − | 0.782475i | \(-0.713957\pi\) | ||||
−0.622682 | + | 0.782475i | \(0.713957\pi\) | |||||||
\(734\) | −65.6129 | −2.42182 | ||||||||
\(735\) | −12.8301 | −0.473244 | ||||||||
\(736\) | 0.944205 | 0.0348038 | ||||||||
\(737\) | −9.60023 | −0.353629 | ||||||||
\(738\) | 32.9038 | 1.21121 | ||||||||
\(739\) | −25.8951 | −0.952567 | −0.476283 | − | 0.879292i | \(-0.658016\pi\) | ||||
−0.476283 | + | 0.879292i | \(0.658016\pi\) | |||||||
\(740\) | −29.8396 | −1.09692 | ||||||||
\(741\) | 7.62441 | 0.280090 | ||||||||
\(742\) | 50.0156 | 1.83613 | ||||||||
\(743\) | 47.8074 | 1.75388 | 0.876941 | − | 0.480598i | \(-0.159580\pi\) | ||||
0.876941 | + | 0.480598i | \(0.159580\pi\) | |||||||
\(744\) | 51.6540 | 1.89373 | ||||||||
\(745\) | −14.6748 | −0.537645 | ||||||||
\(746\) | −74.3746 | −2.72305 | ||||||||
\(747\) | −6.83735 | −0.250165 | ||||||||
\(748\) | 0.157026 | 0.00574142 | ||||||||
\(749\) | −32.8746 | −1.20121 | ||||||||
\(750\) | −31.1665 | −1.13804 | ||||||||
\(751\) | 18.9193 | 0.690376 | 0.345188 | − | 0.938534i | \(-0.387815\pi\) | ||||
0.345188 | + | 0.938534i | \(0.387815\pi\) | |||||||
\(752\) | −44.9220 | −1.63814 | ||||||||
\(753\) | 16.2486 | 0.592131 | ||||||||
\(754\) | −125.838 | −4.58275 | ||||||||
\(755\) | 4.82759 | 0.175694 | ||||||||
\(756\) | 73.5356 | 2.67446 | ||||||||
\(757\) | 43.6512 | 1.58653 | 0.793265 | − | 0.608876i | \(-0.208379\pi\) | ||||
0.793265 | + | 0.608876i | \(0.208379\pi\) | |||||||
\(758\) | 62.8781 | 2.28384 | ||||||||
\(759\) | 1.19356 | 0.0433236 | ||||||||
\(760\) | −12.2278 | −0.443551 | ||||||||
\(761\) | −20.7315 | −0.751516 | −0.375758 | − | 0.926718i | \(-0.622618\pi\) | ||||
−0.375758 | + | 0.926718i | \(0.622618\pi\) | |||||||
\(762\) | 53.1474 | 1.92533 | ||||||||
\(763\) | −2.93246 | −0.106162 | ||||||||
\(764\) | −35.4481 | −1.28247 | ||||||||
\(765\) | 0.214392 | 0.00775135 | ||||||||
\(766\) | 87.0504 | 3.14526 | ||||||||
\(767\) | −40.6725 | −1.46860 | ||||||||
\(768\) | 33.6667 | 1.21484 | ||||||||
\(769\) | −44.5445 | −1.60632 | −0.803158 | − | 0.595766i | \(-0.796849\pi\) | ||||
−0.803158 | + | 0.595766i | \(0.796849\pi\) | |||||||
\(770\) | 12.4175 | 0.447496 | ||||||||
\(771\) | −9.43250 | −0.339703 | ||||||||
\(772\) | −42.5464 | −1.53128 | ||||||||
\(773\) | 7.53079 | 0.270864 | 0.135432 | − | 0.990787i | \(-0.456758\pi\) | ||||
0.135432 | + | 0.990787i | \(0.456758\pi\) | |||||||
\(774\) | 44.2835 | 1.59174 | ||||||||
\(775\) | −8.97836 | −0.322512 | ||||||||
\(776\) | 49.8678 | 1.79015 | ||||||||
\(777\) | 14.3659 | 0.515374 | ||||||||
\(778\) | 34.0970 | 1.22244 | ||||||||
\(779\) | 9.30054 | 0.333227 | ||||||||
\(780\) | 47.7883 | 1.71109 | ||||||||
\(781\) | 8.64436 | 0.309320 | ||||||||
\(782\) | 0.221487 | 0.00792037 | ||||||||
\(783\) | −48.1271 | −1.71992 | ||||||||
\(784\) | 21.4307 | 0.765383 | ||||||||
\(785\) | 37.6833 | 1.34497 | ||||||||
\(786\) | 0.144495 | 0.00515396 | ||||||||
\(787\) | 38.8712 | 1.38561 | 0.692805 | − | 0.721125i | \(-0.256375\pi\) | ||||
0.692805 | + | 0.721125i | \(0.256375\pi\) | |||||||
\(788\) | −18.4645 | −0.657772 | ||||||||
\(789\) | 19.0021 | 0.676494 | ||||||||
\(790\) | −16.2659 | −0.578715 | ||||||||
\(791\) | 16.3611 | 0.581733 | ||||||||
\(792\) | −6.11330 | −0.217227 | ||||||||
\(793\) | 86.4952 | 3.07153 | ||||||||
\(794\) | −25.2564 | −0.896316 | ||||||||
\(795\) | 12.4310 | 0.440883 | ||||||||
\(796\) | 32.2928 | 1.14459 | ||||||||
\(797\) | −11.0465 | −0.391287 | −0.195644 | − | 0.980675i | \(-0.562680\pi\) | ||||
−0.195644 | + | 0.980675i | \(0.562680\pi\) | |||||||
\(798\) | 11.9614 | 0.423430 | ||||||||
\(799\) | 0.705249 | 0.0249499 | ||||||||
\(800\) | −0.521323 | −0.0184316 | ||||||||
\(801\) | −10.4160 | −0.368032 | ||||||||
\(802\) | −8.80330 | −0.310855 | ||||||||
\(803\) | 3.10267 | 0.109491 | ||||||||
\(804\) | −57.9624 | −2.04417 | ||||||||
\(805\) | 11.6160 | 0.409411 | ||||||||
\(806\) | 138.731 | 4.88660 | ||||||||
\(807\) | 29.0525 | 1.02269 | ||||||||
\(808\) | 14.8992 | 0.524153 | ||||||||
\(809\) | −2.35835 | −0.0829152 | −0.0414576 | − | 0.999140i | \(-0.513200\pi\) | ||||
−0.0414576 | + | 0.999140i | \(0.513200\pi\) | |||||||
\(810\) | 0.0814409 | 0.00286154 | ||||||||
\(811\) | −50.5944 | −1.77661 | −0.888305 | − | 0.459255i | \(-0.848116\pi\) | ||||
−0.888305 | + | 0.459255i | \(0.848116\pi\) | |||||||
\(812\) | −130.928 | −4.59469 | ||||||||
\(813\) | −17.1305 | −0.600794 | ||||||||
\(814\) | −6.35821 | −0.222855 | ||||||||
\(815\) | −10.5478 | −0.369472 | ||||||||
\(816\) | 0.222092 | 0.00777478 | ||||||||
\(817\) | 12.5171 | 0.437918 | ||||||||
\(818\) | −12.8083 | −0.447832 | ||||||||
\(819\) | 37.0975 | 1.29629 | ||||||||
\(820\) | 58.2939 | 2.03571 | ||||||||
\(821\) | 12.0978 | 0.422215 | 0.211108 | − | 0.977463i | \(-0.432293\pi\) | ||||
0.211108 | + | 0.977463i | \(0.432293\pi\) | |||||||
\(822\) | −34.0864 | −1.18890 | ||||||||
\(823\) | 46.0771 | 1.60615 | 0.803074 | − | 0.595880i | \(-0.203196\pi\) | ||||
0.803074 | + | 0.595880i | \(0.203196\pi\) | |||||||
\(824\) | 31.9453 | 1.11287 | ||||||||
\(825\) | −0.659001 | −0.0229435 | ||||||||
\(826\) | −63.8085 | −2.22018 | ||||||||
\(827\) | 18.6727 | 0.649312 | 0.324656 | − | 0.945832i | \(-0.394751\pi\) | ||||
0.324656 | + | 0.945832i | \(0.394751\pi\) | |||||||
\(828\) | −11.6196 | −0.403810 | ||||||||
\(829\) | −14.3860 | −0.499645 | −0.249823 | − | 0.968292i | \(-0.580372\pi\) | ||||
−0.249823 | + | 0.968292i | \(0.580372\pi\) | |||||||
\(830\) | −18.2650 | −0.633987 | ||||||||
\(831\) | 13.0061 | 0.451176 | ||||||||
\(832\) | 48.5927 | 1.68465 | ||||||||
\(833\) | −0.336449 | −0.0116573 | ||||||||
\(834\) | −56.8377 | −1.96813 | ||||||||
\(835\) | 4.05619 | 0.140370 | ||||||||
\(836\) | −3.51100 | −0.121430 | ||||||||
\(837\) | 53.0582 | 1.83396 | ||||||||
\(838\) | −13.9139 | −0.480646 | ||||||||
\(839\) | −25.7863 | −0.890244 | −0.445122 | − | 0.895470i | \(-0.646840\pi\) | ||||
−0.445122 | + | 0.895470i | \(0.646840\pi\) | |||||||
\(840\) | 36.8982 | 1.27311 | ||||||||
\(841\) | 56.6892 | 1.95480 | ||||||||
\(842\) | −12.2885 | −0.423490 | ||||||||
\(843\) | 25.3475 | 0.873016 | ||||||||
\(844\) | 55.0211 | 1.89390 | ||||||||
\(845\) | 36.7804 | 1.26529 | ||||||||
\(846\) | −55.7880 | −1.91803 | ||||||||
\(847\) | −37.7509 | −1.29714 | ||||||||
\(848\) | −20.7642 | −0.713045 | ||||||||
\(849\) | 3.17117 | 0.108834 | ||||||||
\(850\) | −0.122290 | −0.00419450 | ||||||||
\(851\) | −5.94783 | −0.203889 | ||||||||
\(852\) | 52.1912 | 1.78804 | ||||||||
\(853\) | 34.3691 | 1.17678 | 0.588388 | − | 0.808578i | \(-0.299763\pi\) | ||||
0.588388 | + | 0.808578i | \(0.299763\pi\) | |||||||
\(854\) | 135.697 | 4.64345 | ||||||||
\(855\) | −4.79367 | −0.163940 | ||||||||
\(856\) | 43.2349 | 1.47774 | ||||||||
\(857\) | 38.1880 | 1.30448 | 0.652238 | − | 0.758014i | \(-0.273830\pi\) | ||||
0.652238 | + | 0.758014i | \(0.273830\pi\) | |||||||
\(858\) | 10.1827 | 0.347632 | ||||||||
\(859\) | 55.7453 | 1.90200 | 0.951002 | − | 0.309184i | \(-0.100056\pi\) | ||||
0.951002 | + | 0.309184i | \(0.100056\pi\) | |||||||
\(860\) | 78.4547 | 2.67528 | ||||||||
\(861\) | −28.0649 | −0.956450 | ||||||||
\(862\) | 25.5545 | 0.870390 | ||||||||
\(863\) | 28.2678 | 0.962247 | 0.481124 | − | 0.876653i | \(-0.340229\pi\) | ||||
0.481124 | + | 0.876653i | \(0.340229\pi\) | |||||||
\(864\) | 3.08079 | 0.104811 | ||||||||
\(865\) | 5.59340 | 0.190181 | ||||||||
\(866\) | −65.9296 | −2.24038 | ||||||||
\(867\) | 18.2139 | 0.618577 | ||||||||
\(868\) | 144.343 | 4.89933 | ||||||||
\(869\) | −2.29861 | −0.0779751 | ||||||||
\(870\) | −49.0671 | −1.66353 | ||||||||
\(871\) | −76.6167 | −2.59606 | ||||||||
\(872\) | 3.85661 | 0.130601 | ||||||||
\(873\) | 19.5496 | 0.661654 | ||||||||
\(874\) | −4.95232 | −0.167515 | ||||||||
\(875\) | −42.8636 | −1.44905 | ||||||||
\(876\) | 18.7327 | 0.632919 | ||||||||
\(877\) | −39.4428 | −1.33189 | −0.665945 | − | 0.746001i | \(-0.731972\pi\) | ||||
−0.665945 | + | 0.746001i | \(0.731972\pi\) | |||||||
\(878\) | 7.66423 | 0.258655 | ||||||||
\(879\) | 17.7995 | 0.600361 | ||||||||
\(880\) | −5.15518 | −0.173781 | ||||||||
\(881\) | −51.9652 | −1.75075 | −0.875375 | − | 0.483444i | \(-0.839386\pi\) | ||||
−0.875375 | + | 0.483444i | \(0.839386\pi\) | |||||||
\(882\) | 26.6145 | 0.896156 | ||||||||
\(883\) | 38.4928 | 1.29538 | 0.647692 | − | 0.761902i | \(-0.275734\pi\) | ||||
0.647692 | + | 0.761902i | \(0.275734\pi\) | |||||||
\(884\) | 1.25318 | 0.0421489 | ||||||||
\(885\) | −15.8592 | −0.533100 | ||||||||
\(886\) | 7.64411 | 0.256809 | ||||||||
\(887\) | 54.7458 | 1.83819 | 0.919093 | − | 0.394041i | \(-0.128923\pi\) | ||||
0.919093 | + | 0.394041i | \(0.128923\pi\) | |||||||
\(888\) | −18.8932 | −0.634015 | ||||||||
\(889\) | 73.0940 | 2.45150 | ||||||||
\(890\) | −27.8249 | −0.932692 | ||||||||
\(891\) | 0.0115088 | 0.000385559 0 | ||||||||
\(892\) | 13.0641 | 0.437419 | ||||||||
\(893\) | −15.7689 | −0.527687 | ||||||||
\(894\) | −18.8791 | −0.631410 | ||||||||
\(895\) | −45.8888 | −1.53389 | ||||||||
\(896\) | 71.9776 | 2.40460 | ||||||||
\(897\) | 9.52549 | 0.318047 | ||||||||
\(898\) | −13.9108 | −0.464210 | ||||||||
\(899\) | −94.4689 | −3.15071 | ||||||||
\(900\) | 6.41554 | 0.213851 | ||||||||
\(901\) | 0.325985 | 0.0108601 | ||||||||
\(902\) | 12.4213 | 0.413583 | ||||||||
\(903\) | −37.7711 | −1.25694 | ||||||||
\(904\) | −21.5172 | −0.715651 | ||||||||
\(905\) | 28.4936 | 0.947160 | ||||||||
\(906\) | 6.21065 | 0.206335 | ||||||||
\(907\) | 8.22837 | 0.273219 | 0.136609 | − | 0.990625i | \(-0.456380\pi\) | ||||
0.136609 | + | 0.990625i | \(0.456380\pi\) | |||||||
\(908\) | −9.02882 | −0.299632 | ||||||||
\(909\) | 5.84092 | 0.193731 | ||||||||
\(910\) | 99.1006 | 3.28515 | ||||||||
\(911\) | −8.57553 | −0.284120 | −0.142060 | − | 0.989858i | \(-0.545373\pi\) | ||||
−0.142060 | + | 0.989858i | \(0.545373\pi\) | |||||||
\(912\) | −4.96585 | −0.164436 | ||||||||
\(913\) | −2.58111 | −0.0854223 | ||||||||
\(914\) | 25.1673 | 0.832461 | ||||||||
\(915\) | 33.7265 | 1.11496 | ||||||||
\(916\) | −35.5172 | −1.17352 | ||||||||
\(917\) | 0.198725 | 0.00656247 | ||||||||
\(918\) | 0.722679 | 0.0238520 | ||||||||
\(919\) | 19.2320 | 0.634404 | 0.317202 | − | 0.948358i | \(-0.397257\pi\) | ||||
0.317202 | + | 0.948358i | \(0.397257\pi\) | |||||||
\(920\) | −15.2768 | −0.503660 | ||||||||
\(921\) | 4.73684 | 0.156084 | ||||||||
\(922\) | 54.8668 | 1.80694 | ||||||||
\(923\) | 68.9882 | 2.27077 | ||||||||
\(924\) | 10.5946 | 0.348538 | ||||||||
\(925\) | 3.28397 | 0.107976 | ||||||||
\(926\) | −38.5947 | −1.26830 | ||||||||
\(927\) | 12.5235 | 0.411325 | ||||||||
\(928\) | −5.48528 | −0.180063 | ||||||||
\(929\) | −37.2500 | −1.22213 | −0.611067 | − | 0.791579i | \(-0.709259\pi\) | ||||
−0.611067 | + | 0.791579i | \(0.709259\pi\) | |||||||
\(930\) | 54.0945 | 1.77383 | ||||||||
\(931\) | 7.52280 | 0.246550 | ||||||||
\(932\) | −30.7272 | −1.00650 | ||||||||
\(933\) | 23.5735 | 0.771762 | ||||||||
\(934\) | 90.6979 | 2.96773 | ||||||||
\(935\) | 0.0809333 | 0.00264680 | ||||||||
\(936\) | −48.7885 | −1.59470 | ||||||||
\(937\) | 30.2830 | 0.989303 | 0.494652 | − | 0.869091i | \(-0.335296\pi\) | ||||
0.494652 | + | 0.869091i | \(0.335296\pi\) | |||||||
\(938\) | −120.199 | −3.92464 | ||||||||
\(939\) | −3.86352 | −0.126081 | ||||||||
\(940\) | −98.8365 | −3.22369 | ||||||||
\(941\) | 9.51868 | 0.310300 | 0.155150 | − | 0.987891i | \(-0.450414\pi\) | ||||
0.155150 | + | 0.987891i | \(0.450414\pi\) | |||||||
\(942\) | 48.4792 | 1.57954 | ||||||||
\(943\) | 11.6196 | 0.378385 | ||||||||
\(944\) | 26.4904 | 0.862189 | ||||||||
\(945\) | 37.9013 | 1.23293 | ||||||||
\(946\) | 16.7171 | 0.543520 | ||||||||
\(947\) | 9.06861 | 0.294690 | 0.147345 | − | 0.989085i | \(-0.452927\pi\) | ||||
0.147345 | + | 0.989085i | \(0.452927\pi\) | |||||||
\(948\) | −13.8781 | −0.450740 | ||||||||
\(949\) | 24.7615 | 0.803793 | ||||||||
\(950\) | 2.73432 | 0.0887132 | ||||||||
\(951\) | −0.668455 | −0.0216762 | ||||||||
\(952\) | 0.967602 | 0.0313602 | ||||||||
\(953\) | −23.6680 | −0.766680 | −0.383340 | − | 0.923607i | \(-0.625226\pi\) | ||||
−0.383340 | + | 0.923607i | \(0.625226\pi\) | |||||||
\(954\) | −25.7867 | −0.834876 | ||||||||
\(955\) | −18.2705 | −0.591219 | ||||||||
\(956\) | 77.7023 | 2.51307 | ||||||||
\(957\) | −6.93391 | −0.224141 | ||||||||
\(958\) | −67.3865 | −2.17716 | ||||||||
\(959\) | −46.8793 | −1.51381 | ||||||||
\(960\) | 18.9474 | 0.611525 | ||||||||
\(961\) | 73.1481 | 2.35962 | ||||||||
\(962\) | −50.7431 | −1.63602 | ||||||||
\(963\) | 16.9493 | 0.546184 | ||||||||
\(964\) | −55.3641 | −1.78316 | ||||||||
\(965\) | −21.9290 | −0.705920 | ||||||||
\(966\) | 14.9439 | 0.480813 | ||||||||
\(967\) | 12.1322 | 0.390147 | 0.195073 | − | 0.980789i | \(-0.437506\pi\) | ||||
0.195073 | + | 0.980789i | \(0.437506\pi\) | |||||||
\(968\) | 49.6479 | 1.59574 | ||||||||
\(969\) | 0.0779608 | 0.00250446 | ||||||||
\(970\) | 52.2239 | 1.67681 | ||||||||
\(971\) | 10.1344 | 0.325229 | 0.162615 | − | 0.986690i | \(-0.448007\pi\) | ||||
0.162615 | + | 0.986690i | \(0.448007\pi\) | |||||||
\(972\) | −61.3565 | −1.96801 | ||||||||
\(973\) | −78.1693 | −2.50599 | ||||||||
\(974\) | 3.03068 | 0.0971093 | ||||||||
\(975\) | −5.25930 | −0.168433 | ||||||||
\(976\) | −56.3351 | −1.80324 | ||||||||
\(977\) | −3.98483 | −0.127486 | −0.0637430 | − | 0.997966i | \(-0.520304\pi\) | ||||
−0.0637430 | + | 0.997966i | \(0.520304\pi\) | |||||||
\(978\) | −13.5696 | −0.433908 | ||||||||
\(979\) | −3.93207 | −0.125669 | ||||||||
\(980\) | 47.1514 | 1.50620 | ||||||||
\(981\) | 1.51190 | 0.0482713 | ||||||||
\(982\) | −8.41069 | −0.268396 | ||||||||
\(983\) | −24.2374 | −0.773053 | −0.386526 | − | 0.922278i | \(-0.626325\pi\) | ||||
−0.386526 | + | 0.922278i | \(0.626325\pi\) | |||||||
\(984\) | 36.9094 | 1.17663 | ||||||||
\(985\) | −9.51689 | −0.303233 | ||||||||
\(986\) | −1.28671 | −0.0409773 | ||||||||
\(987\) | 47.5836 | 1.51460 | ||||||||
\(988\) | −28.0203 | −0.891443 | ||||||||
\(989\) | 15.6381 | 0.497264 | ||||||||
\(990\) | −6.40214 | −0.203473 | ||||||||
\(991\) | 36.8311 | 1.16998 | 0.584990 | − | 0.811041i | \(-0.301098\pi\) | ||||
0.584990 | + | 0.811041i | \(0.301098\pi\) | |||||||
\(992\) | 6.04730 | 0.192002 | ||||||||
\(993\) | −12.1120 | −0.384363 | ||||||||
\(994\) | 108.231 | 3.43288 | ||||||||
\(995\) | 16.6442 | 0.527656 | ||||||||
\(996\) | −15.5837 | −0.493789 | ||||||||
\(997\) | −61.1628 | −1.93705 | −0.968523 | − | 0.248924i | \(-0.919923\pi\) | ||||
−0.968523 | + | 0.248924i | \(0.919923\pi\) | |||||||
\(998\) | −74.4699 | −2.35730 | ||||||||
\(999\) | −19.4069 | −0.614006 |
(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 | 4021.2.a.b.1.13 | ✓ | 151 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4021.2.a.b.1.13 | ✓ | 151 | 1.1 | even | 1 | trivial |