Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8033,2,Mod(1,8033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8033, 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("8033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8033 = 29 \cdot 277 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8033.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: | \(64.1438279437\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59993 | −1.83843 | −0.919213 | − | 0.393760i | \(-0.871174\pi\) | ||||
−0.919213 | + | 0.393760i | \(0.871174\pi\) | |||||||
\(3\) | −1.45421 | −0.839587 | −0.419793 | − | 0.907620i | \(-0.637897\pi\) | ||||
−0.419793 | + | 0.907620i | \(0.637897\pi\) | |||||||
\(4\) | 4.75963 | 2.37981 | ||||||||
\(5\) | −1.16680 | −0.521810 | −0.260905 | − | 0.965364i | \(-0.584021\pi\) | ||||
−0.260905 | + | 0.965364i | \(0.584021\pi\) | |||||||
\(6\) | 3.78083 | 1.54352 | ||||||||
\(7\) | 3.18169 | 1.20257 | 0.601283 | − | 0.799036i | \(-0.294657\pi\) | ||||
0.601283 | + | 0.799036i | \(0.294657\pi\) | |||||||
\(8\) | −7.17483 | −2.53668 | ||||||||
\(9\) | −0.885282 | −0.295094 | ||||||||
\(10\) | 3.03360 | 0.959310 | ||||||||
\(11\) | 3.09017 | 0.931722 | 0.465861 | − | 0.884858i | \(-0.345745\pi\) | ||||
0.465861 | + | 0.884858i | \(0.345745\pi\) | |||||||
\(12\) | −6.92148 | −1.99806 | ||||||||
\(13\) | 1.04576 | 0.290041 | 0.145020 | − | 0.989429i | \(-0.453675\pi\) | ||||
0.145020 | + | 0.989429i | \(0.453675\pi\) | |||||||
\(14\) | −8.27216 | −2.21083 | ||||||||
\(15\) | 1.69677 | 0.438105 | ||||||||
\(16\) | 9.13479 | 2.28370 | ||||||||
\(17\) | 4.29740 | 1.04227 | 0.521136 | − | 0.853474i | \(-0.325509\pi\) | ||||
0.521136 | + | 0.853474i | \(0.325509\pi\) | |||||||
\(18\) | 2.30167 | 0.542509 | ||||||||
\(19\) | −6.83368 | −1.56775 | −0.783877 | − | 0.620916i | \(-0.786761\pi\) | ||||
−0.783877 | + | 0.620916i | \(0.786761\pi\) | |||||||
\(20\) | −5.55355 | −1.24181 | ||||||||
\(21\) | −4.62683 | −1.00966 | ||||||||
\(22\) | −8.03422 | −1.71290 | ||||||||
\(23\) | 3.18164 | 0.663417 | 0.331709 | − | 0.943382i | \(-0.392375\pi\) | ||||
0.331709 | + | 0.943382i | \(0.392375\pi\) | |||||||
\(24\) | 10.4337 | 2.12977 | ||||||||
\(25\) | −3.63857 | −0.727714 | ||||||||
\(26\) | −2.71889 | −0.533218 | ||||||||
\(27\) | 5.65000 | 1.08734 | ||||||||
\(28\) | 15.1436 | 2.86188 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −4.41149 | −0.805424 | ||||||||
\(31\) | −2.55535 | −0.458955 | −0.229477 | − | 0.973314i | \(-0.573702\pi\) | ||||
−0.229477 | + | 0.973314i | \(0.573702\pi\) | |||||||
\(32\) | −9.40013 | −1.66172 | ||||||||
\(33\) | −4.49375 | −0.782261 | ||||||||
\(34\) | −11.1729 | −1.91614 | ||||||||
\(35\) | −3.71240 | −0.627511 | ||||||||
\(36\) | −4.21361 | −0.702269 | ||||||||
\(37\) | 4.84526 | 0.796555 | 0.398278 | − | 0.917265i | \(-0.369608\pi\) | ||||
0.398278 | + | 0.917265i | \(0.369608\pi\) | |||||||
\(38\) | 17.7671 | 2.88220 | ||||||||
\(39\) | −1.52075 | −0.243514 | ||||||||
\(40\) | 8.37161 | 1.32367 | ||||||||
\(41\) | 10.0079 | 1.56298 | 0.781489 | − | 0.623919i | \(-0.214460\pi\) | ||||
0.781489 | + | 0.623919i | \(0.214460\pi\) | |||||||
\(42\) | 12.0294 | 1.85618 | ||||||||
\(43\) | −2.22184 | −0.338828 | −0.169414 | − | 0.985545i | \(-0.554187\pi\) | ||||
−0.169414 | + | 0.985545i | \(0.554187\pi\) | |||||||
\(44\) | 14.7081 | 2.21732 | ||||||||
\(45\) | 1.03295 | 0.153983 | ||||||||
\(46\) | −8.27203 | −1.21964 | ||||||||
\(47\) | −3.69215 | −0.538555 | −0.269278 | − | 0.963063i | \(-0.586785\pi\) | ||||
−0.269278 | + | 0.963063i | \(0.586785\pi\) | |||||||
\(48\) | −13.2839 | −1.91736 | ||||||||
\(49\) | 3.12314 | 0.446163 | ||||||||
\(50\) | 9.46002 | 1.33785 | ||||||||
\(51\) | −6.24930 | −0.875077 | ||||||||
\(52\) | 4.97741 | 0.690242 | ||||||||
\(53\) | −11.8110 | −1.62237 | −0.811185 | − | 0.584789i | \(-0.801177\pi\) | ||||
−0.811185 | + | 0.584789i | \(0.801177\pi\) | |||||||
\(54\) | −14.6896 | −1.99900 | ||||||||
\(55\) | −3.60562 | −0.486182 | ||||||||
\(56\) | −22.8281 | −3.05053 | ||||||||
\(57\) | 9.93758 | 1.31627 | ||||||||
\(58\) | 2.59993 | 0.341387 | ||||||||
\(59\) | 7.12627 | 0.927762 | 0.463881 | − | 0.885898i | \(-0.346457\pi\) | ||||
0.463881 | + | 0.885898i | \(0.346457\pi\) | |||||||
\(60\) | 8.07600 | 1.04261 | ||||||||
\(61\) | 2.04583 | 0.261942 | 0.130971 | − | 0.991386i | \(-0.458190\pi\) | ||||
0.130971 | + | 0.991386i | \(0.458190\pi\) | |||||||
\(62\) | 6.64373 | 0.843754 | ||||||||
\(63\) | −2.81669 | −0.354870 | ||||||||
\(64\) | 6.17009 | 0.771261 | ||||||||
\(65\) | −1.22019 | −0.151346 | ||||||||
\(66\) | 11.6834 | 1.43813 | ||||||||
\(67\) | −9.49425 | −1.15991 | −0.579954 | − | 0.814650i | \(-0.696929\pi\) | ||||
−0.579954 | + | 0.814650i | \(0.696929\pi\) | |||||||
\(68\) | 20.4540 | 2.48041 | ||||||||
\(69\) | −4.62676 | −0.556996 | ||||||||
\(70\) | 9.65198 | 1.15363 | ||||||||
\(71\) | 0.524942 | 0.0622992 | 0.0311496 | − | 0.999515i | \(-0.490083\pi\) | ||||
0.0311496 | + | 0.999515i | \(0.490083\pi\) | |||||||
\(72\) | 6.35175 | 0.748561 | ||||||||
\(73\) | 13.5622 | 1.58734 | 0.793669 | − | 0.608349i | \(-0.208168\pi\) | ||||
0.793669 | + | 0.608349i | \(0.208168\pi\) | |||||||
\(74\) | −12.5973 | −1.46441 | ||||||||
\(75\) | 5.29124 | 0.610979 | ||||||||
\(76\) | −32.5258 | −3.73096 | ||||||||
\(77\) | 9.83196 | 1.12046 | ||||||||
\(78\) | 3.95383 | 0.447683 | ||||||||
\(79\) | −12.2384 | −1.37693 | −0.688466 | − | 0.725269i | \(-0.741715\pi\) | ||||
−0.688466 | + | 0.725269i | \(0.741715\pi\) | |||||||
\(80\) | −10.6585 | −1.19166 | ||||||||
\(81\) | −5.56043 | −0.617825 | ||||||||
\(82\) | −26.0199 | −2.87342 | ||||||||
\(83\) | −5.35933 | −0.588263 | −0.294131 | − | 0.955765i | \(-0.595030\pi\) | ||||
−0.294131 | + | 0.955765i | \(0.595030\pi\) | |||||||
\(84\) | −22.0220 | −2.40280 | ||||||||
\(85\) | −5.01421 | −0.543868 | ||||||||
\(86\) | 5.77663 | 0.622910 | ||||||||
\(87\) | 1.45421 | 0.155907 | ||||||||
\(88\) | −22.1714 | −2.36348 | ||||||||
\(89\) | −14.1569 | −1.50063 | −0.750313 | − | 0.661083i | \(-0.770097\pi\) | ||||
−0.750313 | + | 0.661083i | \(0.770097\pi\) | |||||||
\(90\) | −2.68559 | −0.283087 | ||||||||
\(91\) | 3.32727 | 0.348793 | ||||||||
\(92\) | 15.1434 | 1.57881 | ||||||||
\(93\) | 3.71601 | 0.385332 | ||||||||
\(94\) | 9.59932 | 0.990094 | ||||||||
\(95\) | 7.97356 | 0.818070 | ||||||||
\(96\) | 13.6697 | 1.39516 | ||||||||
\(97\) | −12.9697 | −1.31687 | −0.658436 | − | 0.752637i | \(-0.728782\pi\) | ||||
−0.658436 | + | 0.752637i | \(0.728782\pi\) | |||||||
\(98\) | −8.11994 | −0.820238 | ||||||||
\(99\) | −2.73567 | −0.274945 | ||||||||
\(100\) | −17.3182 | −1.73182 | ||||||||
\(101\) | −5.99376 | −0.596402 | −0.298201 | − | 0.954503i | \(-0.596386\pi\) | ||||
−0.298201 | + | 0.954503i | \(0.596386\pi\) | |||||||
\(102\) | 16.2477 | 1.60877 | ||||||||
\(103\) | −15.7675 | −1.55362 | −0.776809 | − | 0.629736i | \(-0.783163\pi\) | ||||
−0.776809 | + | 0.629736i | \(0.783163\pi\) | |||||||
\(104\) | −7.50312 | −0.735742 | ||||||||
\(105\) | 5.39860 | 0.526850 | ||||||||
\(106\) | 30.7079 | 2.98261 | ||||||||
\(107\) | 11.3386 | 1.09615 | 0.548073 | − | 0.836431i | \(-0.315362\pi\) | ||||
0.548073 | + | 0.836431i | \(0.315362\pi\) | |||||||
\(108\) | 26.8919 | 2.58767 | ||||||||
\(109\) | 9.73391 | 0.932340 | 0.466170 | − | 0.884695i | \(-0.345634\pi\) | ||||
0.466170 | + | 0.884695i | \(0.345634\pi\) | |||||||
\(110\) | 9.37435 | 0.893809 | ||||||||
\(111\) | −7.04601 | −0.668777 | ||||||||
\(112\) | 29.0640 | 2.74629 | ||||||||
\(113\) | 18.2462 | 1.71646 | 0.858229 | − | 0.513266i | \(-0.171565\pi\) | ||||
0.858229 | + | 0.513266i | \(0.171565\pi\) | |||||||
\(114\) | −25.8370 | −2.41986 | ||||||||
\(115\) | −3.71234 | −0.346178 | ||||||||
\(116\) | −4.75963 | −0.441920 | ||||||||
\(117\) | −0.925789 | −0.0855893 | ||||||||
\(118\) | −18.5278 | −1.70562 | ||||||||
\(119\) | 13.6730 | 1.25340 | ||||||||
\(120\) | −12.1741 | −1.11133 | ||||||||
\(121\) | −1.45084 | −0.131895 | ||||||||
\(122\) | −5.31902 | −0.481561 | ||||||||
\(123\) | −14.5536 | −1.31226 | ||||||||
\(124\) | −12.1625 | −1.09223 | ||||||||
\(125\) | 10.0795 | 0.901539 | ||||||||
\(126\) | 7.32320 | 0.652402 | ||||||||
\(127\) | 5.97922 | 0.530570 | 0.265285 | − | 0.964170i | \(-0.414534\pi\) | ||||
0.265285 | + | 0.964170i | \(0.414534\pi\) | |||||||
\(128\) | 2.75847 | 0.243817 | ||||||||
\(129\) | 3.23102 | 0.284475 | ||||||||
\(130\) | 3.17241 | 0.278239 | ||||||||
\(131\) | 2.99339 | 0.261534 | 0.130767 | − | 0.991413i | \(-0.458256\pi\) | ||||
0.130767 | + | 0.991413i | \(0.458256\pi\) | |||||||
\(132\) | −21.3886 | −1.86164 | ||||||||
\(133\) | −21.7426 | −1.88533 | ||||||||
\(134\) | 24.6844 | 2.13240 | ||||||||
\(135\) | −6.59244 | −0.567387 | ||||||||
\(136\) | −30.8331 | −2.64391 | ||||||||
\(137\) | −21.1681 | −1.80851 | −0.904254 | − | 0.426994i | \(-0.859573\pi\) | ||||
−0.904254 | + | 0.426994i | \(0.859573\pi\) | |||||||
\(138\) | 12.0292 | 1.02400 | ||||||||
\(139\) | 0.825350 | 0.0700053 | 0.0350027 | − | 0.999387i | \(-0.488856\pi\) | ||||
0.0350027 | + | 0.999387i | \(0.488856\pi\) | |||||||
\(140\) | −17.6696 | −1.49336 | ||||||||
\(141\) | 5.36915 | 0.452164 | ||||||||
\(142\) | −1.36481 | −0.114532 | ||||||||
\(143\) | 3.23157 | 0.270237 | ||||||||
\(144\) | −8.08686 | −0.673905 | ||||||||
\(145\) | 1.16680 | 0.0968977 | ||||||||
\(146\) | −35.2608 | −2.91821 | ||||||||
\(147\) | −4.54169 | −0.374592 | ||||||||
\(148\) | 23.0616 | 1.89565 | ||||||||
\(149\) | −7.01371 | −0.574586 | −0.287293 | − | 0.957843i | \(-0.592755\pi\) | ||||
−0.287293 | + | 0.957843i | \(0.592755\pi\) | |||||||
\(150\) | −13.7568 | −1.12324 | ||||||||
\(151\) | 4.47562 | 0.364221 | 0.182110 | − | 0.983278i | \(-0.441707\pi\) | ||||
0.182110 | + | 0.983278i | \(0.441707\pi\) | |||||||
\(152\) | 49.0305 | 3.97690 | ||||||||
\(153\) | −3.80441 | −0.307568 | ||||||||
\(154\) | −25.5624 | −2.05988 | ||||||||
\(155\) | 2.98159 | 0.239487 | ||||||||
\(156\) | −7.23818 | −0.579518 | ||||||||
\(157\) | −14.5569 | −1.16177 | −0.580884 | − | 0.813986i | \(-0.697293\pi\) | ||||
−0.580884 | + | 0.813986i | \(0.697293\pi\) | |||||||
\(158\) | 31.8190 | 2.53139 | ||||||||
\(159\) | 17.1757 | 1.36212 | ||||||||
\(160\) | 10.9681 | 0.867104 | ||||||||
\(161\) | 10.1230 | 0.797803 | ||||||||
\(162\) | 14.4567 | 1.13583 | ||||||||
\(163\) | −12.7429 | −0.998099 | −0.499049 | − | 0.866574i | \(-0.666317\pi\) | ||||
−0.499049 | + | 0.866574i | \(0.666317\pi\) | |||||||
\(164\) | 47.6341 | 3.71960 | ||||||||
\(165\) | 5.24332 | 0.408192 | ||||||||
\(166\) | 13.9339 | 1.08148 | ||||||||
\(167\) | −11.6489 | −0.901418 | −0.450709 | − | 0.892671i | \(-0.648829\pi\) | ||||
−0.450709 | + | 0.892671i | \(0.648829\pi\) | |||||||
\(168\) | 33.1967 | 2.56118 | ||||||||
\(169\) | −11.9064 | −0.915876 | ||||||||
\(170\) | 13.0366 | 0.999861 | ||||||||
\(171\) | 6.04973 | 0.462635 | ||||||||
\(172\) | −10.5751 | −0.806346 | ||||||||
\(173\) | −2.66418 | −0.202554 | −0.101277 | − | 0.994858i | \(-0.532293\pi\) | ||||
−0.101277 | + | 0.994858i | \(0.532293\pi\) | |||||||
\(174\) | −3.78083 | −0.286624 | ||||||||
\(175\) | −11.5768 | −0.875124 | ||||||||
\(176\) | 28.2280 | 2.12777 | ||||||||
\(177\) | −10.3631 | −0.778936 | ||||||||
\(178\) | 36.8069 | 2.75879 | ||||||||
\(179\) | 5.69199 | 0.425439 | 0.212720 | − | 0.977113i | \(-0.431768\pi\) | ||||
0.212720 | + | 0.977113i | \(0.431768\pi\) | |||||||
\(180\) | 4.91645 | 0.366451 | ||||||||
\(181\) | −6.33227 | −0.470674 | −0.235337 | − | 0.971914i | \(-0.575619\pi\) | ||||
−0.235337 | + | 0.971914i | \(0.575619\pi\) | |||||||
\(182\) | −8.65066 | −0.641230 | ||||||||
\(183\) | −2.97507 | −0.219923 | ||||||||
\(184\) | −22.8277 | −1.68288 | ||||||||
\(185\) | −5.65346 | −0.415651 | ||||||||
\(186\) | −9.66136 | −0.708405 | ||||||||
\(187\) | 13.2797 | 0.971107 | ||||||||
\(188\) | −17.5732 | −1.28166 | ||||||||
\(189\) | 17.9766 | 1.30760 | ||||||||
\(190\) | −20.7307 | −1.50396 | ||||||||
\(191\) | −10.1032 | −0.731044 | −0.365522 | − | 0.930803i | \(-0.619110\pi\) | ||||
−0.365522 | + | 0.930803i | \(0.619110\pi\) | |||||||
\(192\) | −8.97259 | −0.647541 | ||||||||
\(193\) | 10.3090 | 0.742060 | 0.371030 | − | 0.928621i | \(-0.379005\pi\) | ||||
0.371030 | + | 0.928621i | \(0.379005\pi\) | |||||||
\(194\) | 33.7202 | 2.42097 | ||||||||
\(195\) | 1.77441 | 0.127068 | ||||||||
\(196\) | 14.8650 | 1.06178 | ||||||||
\(197\) | −5.85194 | −0.416934 | −0.208467 | − | 0.978029i | \(-0.566847\pi\) | ||||
−0.208467 | + | 0.978029i | \(0.566847\pi\) | |||||||
\(198\) | 7.11255 | 0.505467 | ||||||||
\(199\) | −1.27055 | −0.0900667 | −0.0450333 | − | 0.998985i | \(-0.514339\pi\) | ||||
−0.0450333 | + | 0.998985i | \(0.514339\pi\) | |||||||
\(200\) | 26.1061 | 1.84598 | ||||||||
\(201\) | 13.8066 | 0.973843 | ||||||||
\(202\) | 15.5833 | 1.09644 | ||||||||
\(203\) | −3.18169 | −0.223311 | ||||||||
\(204\) | −29.7443 | −2.08252 | ||||||||
\(205\) | −11.6773 | −0.815578 | ||||||||
\(206\) | 40.9944 | 2.85621 | ||||||||
\(207\) | −2.81665 | −0.195771 | ||||||||
\(208\) | 9.55276 | 0.662365 | ||||||||
\(209\) | −21.1172 | −1.46071 | ||||||||
\(210\) | −14.0360 | −0.968574 | ||||||||
\(211\) | 24.7393 | 1.70312 | 0.851561 | − | 0.524256i | \(-0.175656\pi\) | ||||
0.851561 | + | 0.524256i | \(0.175656\pi\) | |||||||
\(212\) | −56.2161 | −3.86094 | ||||||||
\(213\) | −0.763375 | −0.0523056 | ||||||||
\(214\) | −29.4796 | −2.01518 | ||||||||
\(215\) | 2.59245 | 0.176804 | ||||||||
\(216\) | −40.5378 | −2.75825 | ||||||||
\(217\) | −8.13033 | −0.551923 | ||||||||
\(218\) | −25.3075 | −1.71404 | ||||||||
\(219\) | −19.7223 | −1.33271 | ||||||||
\(220\) | −17.1614 | −1.15702 | ||||||||
\(221\) | 4.49403 | 0.302301 | ||||||||
\(222\) | 18.3191 | 1.22950 | ||||||||
\(223\) | −13.8366 | −0.926565 | −0.463283 | − | 0.886211i | \(-0.653328\pi\) | ||||
−0.463283 | + | 0.886211i | \(0.653328\pi\) | |||||||
\(224\) | −29.9083 | −1.99833 | ||||||||
\(225\) | 3.22116 | 0.214744 | ||||||||
\(226\) | −47.4388 | −3.15558 | ||||||||
\(227\) | −10.2707 | −0.681688 | −0.340844 | − | 0.940120i | \(-0.610713\pi\) | ||||
−0.340844 | + | 0.940120i | \(0.610713\pi\) | |||||||
\(228\) | 47.2992 | 3.13246 | ||||||||
\(229\) | −7.67566 | −0.507222 | −0.253611 | − | 0.967306i | \(-0.581618\pi\) | ||||
−0.253611 | + | 0.967306i | \(0.581618\pi\) | |||||||
\(230\) | 9.65183 | 0.636423 | ||||||||
\(231\) | −14.2977 | −0.940720 | ||||||||
\(232\) | 7.17483 | 0.471051 | ||||||||
\(233\) | −0.0796221 | −0.00521622 | −0.00260811 | − | 0.999997i | \(-0.500830\pi\) | ||||
−0.00260811 | + | 0.999997i | \(0.500830\pi\) | |||||||
\(234\) | 2.40699 | 0.157350 | ||||||||
\(235\) | 4.30801 | 0.281024 | ||||||||
\(236\) | 33.9184 | 2.20790 | ||||||||
\(237\) | 17.7972 | 1.15605 | ||||||||
\(238\) | −35.5487 | −2.30428 | ||||||||
\(239\) | 2.28804 | 0.148001 | 0.0740004 | − | 0.997258i | \(-0.476423\pi\) | ||||
0.0740004 | + | 0.997258i | \(0.476423\pi\) | |||||||
\(240\) | 15.4997 | 1.00050 | ||||||||
\(241\) | 12.2878 | 0.791528 | 0.395764 | − | 0.918352i | \(-0.370480\pi\) | ||||
0.395764 | + | 0.918352i | \(0.370480\pi\) | |||||||
\(242\) | 3.77209 | 0.242479 | ||||||||
\(243\) | −8.86400 | −0.568626 | ||||||||
\(244\) | 9.73740 | 0.623373 | ||||||||
\(245\) | −3.64409 | −0.232812 | ||||||||
\(246\) | 37.8384 | 2.41249 | ||||||||
\(247\) | −7.14636 | −0.454712 | ||||||||
\(248\) | 18.3342 | 1.16422 | ||||||||
\(249\) | 7.79357 | 0.493898 | ||||||||
\(250\) | −26.2060 | −1.65741 | ||||||||
\(251\) | 27.4924 | 1.73530 | 0.867652 | − | 0.497171i | \(-0.165628\pi\) | ||||
0.867652 | + | 0.497171i | \(0.165628\pi\) | |||||||
\(252\) | −13.4064 | −0.844524 | ||||||||
\(253\) | 9.83180 | 0.618120 | ||||||||
\(254\) | −15.5455 | −0.975414 | ||||||||
\(255\) | 7.29170 | 0.456624 | ||||||||
\(256\) | −19.5120 | −1.21950 | ||||||||
\(257\) | −4.63962 | −0.289412 | −0.144706 | − | 0.989475i | \(-0.546224\pi\) | ||||
−0.144706 | + | 0.989475i | \(0.546224\pi\) | |||||||
\(258\) | −8.40041 | −0.522987 | ||||||||
\(259\) | 15.4161 | 0.957910 | ||||||||
\(260\) | −5.80765 | −0.360175 | ||||||||
\(261\) | 0.885282 | 0.0547976 | ||||||||
\(262\) | −7.78261 | −0.480811 | ||||||||
\(263\) | −27.9900 | −1.72594 | −0.862969 | − | 0.505257i | \(-0.831398\pi\) | ||||
−0.862969 | + | 0.505257i | \(0.831398\pi\) | |||||||
\(264\) | 32.2419 | 1.98435 | ||||||||
\(265\) | 13.7812 | 0.846570 | ||||||||
\(266\) | 56.5293 | 3.46603 | ||||||||
\(267\) | 20.5870 | 1.25991 | ||||||||
\(268\) | −45.1891 | −2.76036 | ||||||||
\(269\) | 21.8130 | 1.32996 | 0.664980 | − | 0.746861i | \(-0.268440\pi\) | ||||
0.664980 | + | 0.746861i | \(0.268440\pi\) | |||||||
\(270\) | 17.1399 | 1.04310 | ||||||||
\(271\) | −28.6765 | −1.74197 | −0.870987 | − | 0.491306i | \(-0.836520\pi\) | ||||
−0.870987 | + | 0.491306i | \(0.836520\pi\) | |||||||
\(272\) | 39.2558 | 2.38023 | ||||||||
\(273\) | −4.83854 | −0.292842 | ||||||||
\(274\) | 55.0354 | 3.32481 | ||||||||
\(275\) | −11.2438 | −0.678027 | ||||||||
\(276\) | −22.0216 | −1.32555 | ||||||||
\(277\) | −1.00000 | −0.0600842 | ||||||||
\(278\) | −2.14585 | −0.128700 | ||||||||
\(279\) | 2.26221 | 0.135435 | ||||||||
\(280\) | 26.6359 | 1.59180 | ||||||||
\(281\) | 10.3356 | 0.616572 | 0.308286 | − | 0.951294i | \(-0.400245\pi\) | ||||
0.308286 | + | 0.951294i | \(0.400245\pi\) | |||||||
\(282\) | −13.9594 | −0.831270 | ||||||||
\(283\) | −2.29188 | −0.136238 | −0.0681190 | − | 0.997677i | \(-0.521700\pi\) | ||||
−0.0681190 | + | 0.997677i | \(0.521700\pi\) | |||||||
\(284\) | 2.49853 | 0.148260 | ||||||||
\(285\) | −11.5952 | −0.686840 | ||||||||
\(286\) | −8.40184 | −0.496811 | ||||||||
\(287\) | 31.8422 | 1.87958 | ||||||||
\(288\) | 8.32177 | 0.490365 | ||||||||
\(289\) | 1.46760 | 0.0863297 | ||||||||
\(290\) | −3.03360 | −0.178139 | ||||||||
\(291\) | 18.8606 | 1.10563 | ||||||||
\(292\) | 64.5511 | 3.77757 | ||||||||
\(293\) | 16.9457 | 0.989977 | 0.494989 | − | 0.868899i | \(-0.335172\pi\) | ||||
0.494989 | + | 0.868899i | \(0.335172\pi\) | |||||||
\(294\) | 11.8081 | 0.688661 | ||||||||
\(295\) | −8.31496 | −0.484115 | ||||||||
\(296\) | −34.7639 | −2.02061 | ||||||||
\(297\) | 17.4595 | 1.01310 | ||||||||
\(298\) | 18.2351 | 1.05633 | ||||||||
\(299\) | 3.32722 | 0.192418 | ||||||||
\(300\) | 25.1843 | 1.45402 | ||||||||
\(301\) | −7.06921 | −0.407462 | ||||||||
\(302\) | −11.6363 | −0.669593 | ||||||||
\(303\) | 8.71617 | 0.500731 | ||||||||
\(304\) | −62.4242 | −3.58027 | ||||||||
\(305\) | −2.38708 | −0.136684 | ||||||||
\(306\) | 9.89118 | 0.565441 | ||||||||
\(307\) | 15.0569 | 0.859342 | 0.429671 | − | 0.902985i | \(-0.358629\pi\) | ||||
0.429671 | + | 0.902985i | \(0.358629\pi\) | |||||||
\(308\) | 46.7965 | 2.66648 | ||||||||
\(309\) | 22.9292 | 1.30440 | ||||||||
\(310\) | −7.75192 | −0.440280 | ||||||||
\(311\) | 10.4771 | 0.594101 | 0.297051 | − | 0.954862i | \(-0.403997\pi\) | ||||
0.297051 | + | 0.954862i | \(0.403997\pi\) | |||||||
\(312\) | 10.9111 | 0.617719 | ||||||||
\(313\) | 17.5449 | 0.991694 | 0.495847 | − | 0.868410i | \(-0.334858\pi\) | ||||
0.495847 | + | 0.868410i | \(0.334858\pi\) | |||||||
\(314\) | 37.8469 | 2.13582 | ||||||||
\(315\) | 3.28652 | 0.185175 | ||||||||
\(316\) | −58.2503 | −3.27684 | ||||||||
\(317\) | 24.4682 | 1.37427 | 0.687135 | − | 0.726530i | \(-0.258868\pi\) | ||||
0.687135 | + | 0.726530i | \(0.258868\pi\) | |||||||
\(318\) | −44.6556 | −2.50416 | ||||||||
\(319\) | −3.09017 | −0.173016 | ||||||||
\(320\) | −7.19928 | −0.402452 | ||||||||
\(321\) | −16.4887 | −0.920309 | ||||||||
\(322\) | −26.3190 | −1.46670 | ||||||||
\(323\) | −29.3670 | −1.63402 | ||||||||
\(324\) | −26.4656 | −1.47031 | ||||||||
\(325\) | −3.80506 | −0.211067 | ||||||||
\(326\) | 33.1305 | 1.83493 | ||||||||
\(327\) | −14.1551 | −0.782780 | ||||||||
\(328\) | −71.8053 | −3.96478 | ||||||||
\(329\) | −11.7473 | −0.647648 | ||||||||
\(330\) | −13.6322 | −0.750431 | ||||||||
\(331\) | 23.5168 | 1.29260 | 0.646300 | − | 0.763083i | \(-0.276315\pi\) | ||||
0.646300 | + | 0.763083i | \(0.276315\pi\) | |||||||
\(332\) | −25.5084 | −1.39996 | ||||||||
\(333\) | −4.28942 | −0.235059 | ||||||||
\(334\) | 30.2863 | 1.65719 | ||||||||
\(335\) | 11.0779 | 0.605251 | ||||||||
\(336\) | −42.2651 | −2.30575 | ||||||||
\(337\) | −8.71267 | −0.474609 | −0.237305 | − | 0.971435i | \(-0.576264\pi\) | ||||
−0.237305 | + | 0.971435i | \(0.576264\pi\) | |||||||
\(338\) | 30.9558 | 1.68377 | ||||||||
\(339\) | −26.5338 | −1.44112 | ||||||||
\(340\) | −23.8658 | −1.29430 | ||||||||
\(341\) | −7.89647 | −0.427618 | ||||||||
\(342\) | −15.7289 | −0.850520 | ||||||||
\(343\) | −12.3350 | −0.666025 | ||||||||
\(344\) | 15.9413 | 0.859499 | ||||||||
\(345\) | 5.39852 | 0.290646 | ||||||||
\(346\) | 6.92667 | 0.372380 | ||||||||
\(347\) | 16.2624 | 0.873013 | 0.436507 | − | 0.899701i | \(-0.356216\pi\) | ||||
0.436507 | + | 0.899701i | \(0.356216\pi\) | |||||||
\(348\) | 6.92148 | 0.371030 | ||||||||
\(349\) | −3.94679 | −0.211267 | −0.105633 | − | 0.994405i | \(-0.533687\pi\) | ||||
−0.105633 | + | 0.994405i | \(0.533687\pi\) | |||||||
\(350\) | 30.0988 | 1.60885 | ||||||||
\(351\) | 5.90853 | 0.315374 | ||||||||
\(352\) | −29.0480 | −1.54826 | ||||||||
\(353\) | −18.3963 | −0.979136 | −0.489568 | − | 0.871965i | \(-0.662845\pi\) | ||||
−0.489568 | + | 0.871965i | \(0.662845\pi\) | |||||||
\(354\) | 26.9433 | 1.43202 | ||||||||
\(355\) | −0.612504 | −0.0325083 | ||||||||
\(356\) | −67.3815 | −3.57121 | ||||||||
\(357\) | −19.8833 | −1.05234 | ||||||||
\(358\) | −14.7988 | −0.782139 | ||||||||
\(359\) | 24.8085 | 1.30934 | 0.654672 | − | 0.755913i | \(-0.272807\pi\) | ||||
0.654672 | + | 0.755913i | \(0.272807\pi\) | |||||||
\(360\) | −7.41124 | −0.390606 | ||||||||
\(361\) | 27.6992 | 1.45785 | ||||||||
\(362\) | 16.4635 | 0.865300 | ||||||||
\(363\) | 2.10983 | 0.110737 | ||||||||
\(364\) | 15.8366 | 0.830061 | ||||||||
\(365\) | −15.8244 | −0.828289 | ||||||||
\(366\) | 7.73496 | 0.404313 | ||||||||
\(367\) | 26.6310 | 1.39012 | 0.695062 | − | 0.718950i | \(-0.255377\pi\) | ||||
0.695062 | + | 0.718950i | \(0.255377\pi\) | |||||||
\(368\) | 29.0636 | 1.51504 | ||||||||
\(369\) | −8.85985 | −0.461226 | ||||||||
\(370\) | 14.6986 | 0.764143 | ||||||||
\(371\) | −37.5790 | −1.95101 | ||||||||
\(372\) | 17.6868 | 0.917019 | ||||||||
\(373\) | 3.53801 | 0.183191 | 0.0915956 | − | 0.995796i | \(-0.470803\pi\) | ||||
0.0915956 | + | 0.995796i | \(0.470803\pi\) | |||||||
\(374\) | −34.5262 | −1.78531 | ||||||||
\(375\) | −14.6577 | −0.756920 | ||||||||
\(376\) | 26.4905 | 1.36615 | ||||||||
\(377\) | −1.04576 | −0.0538592 | ||||||||
\(378\) | −46.7377 | −2.40393 | ||||||||
\(379\) | −0.0570090 | −0.00292836 | −0.00146418 | − | 0.999999i | \(-0.500466\pi\) | ||||
−0.00146418 | + | 0.999999i | \(0.500466\pi\) | |||||||
\(380\) | 37.9511 | 1.94685 | ||||||||
\(381\) | −8.69502 | −0.445459 | ||||||||
\(382\) | 26.2677 | 1.34397 | ||||||||
\(383\) | 3.12056 | 0.159453 | 0.0797265 | − | 0.996817i | \(-0.474595\pi\) | ||||
0.0797265 | + | 0.996817i | \(0.474595\pi\) | |||||||
\(384\) | −4.01139 | −0.204705 | ||||||||
\(385\) | −11.4720 | −0.584665 | ||||||||
\(386\) | −26.8027 | −1.36422 | ||||||||
\(387\) | 1.96696 | 0.0999860 | ||||||||
\(388\) | −61.7308 | −3.13391 | ||||||||
\(389\) | −2.32042 | −0.117650 | −0.0588249 | − | 0.998268i | \(-0.518735\pi\) | ||||
−0.0588249 | + | 0.998268i | \(0.518735\pi\) | |||||||
\(390\) | −4.61334 | −0.233606 | ||||||||
\(391\) | 13.6728 | 0.691461 | ||||||||
\(392\) | −22.4080 | −1.13177 | ||||||||
\(393\) | −4.35301 | −0.219581 | ||||||||
\(394\) | 15.2146 | 0.766502 | ||||||||
\(395\) | 14.2798 | 0.718497 | ||||||||
\(396\) | −13.0208 | −0.654319 | ||||||||
\(397\) | −22.7613 | −1.14236 | −0.571178 | − | 0.820826i | \(-0.693513\pi\) | ||||
−0.571178 | + | 0.820826i | \(0.693513\pi\) | |||||||
\(398\) | 3.30333 | 0.165581 | ||||||||
\(399\) | 31.6183 | 1.58289 | ||||||||
\(400\) | −33.2376 | −1.66188 | ||||||||
\(401\) | 5.70620 | 0.284954 | 0.142477 | − | 0.989798i | \(-0.454493\pi\) | ||||
0.142477 | + | 0.989798i | \(0.454493\pi\) | |||||||
\(402\) | −35.8962 | −1.79034 | ||||||||
\(403\) | −2.67227 | −0.133115 | ||||||||
\(404\) | −28.5281 | −1.41932 | ||||||||
\(405\) | 6.48792 | 0.322388 | ||||||||
\(406\) | 8.27216 | 0.410540 | ||||||||
\(407\) | 14.9727 | 0.742168 | ||||||||
\(408\) | 44.8377 | 2.21980 | ||||||||
\(409\) | −6.29813 | −0.311423 | −0.155711 | − | 0.987803i | \(-0.549767\pi\) | ||||
−0.155711 | + | 0.987803i | \(0.549767\pi\) | |||||||
\(410\) | 30.3601 | 1.49938 | ||||||||
\(411\) | 30.7827 | 1.51840 | ||||||||
\(412\) | −75.0474 | −3.69732 | ||||||||
\(413\) | 22.6736 | 1.11569 | ||||||||
\(414\) | 7.32308 | 0.359910 | ||||||||
\(415\) | 6.25328 | 0.306962 | ||||||||
\(416\) | −9.83025 | −0.481967 | ||||||||
\(417\) | −1.20023 | −0.0587755 | ||||||||
\(418\) | 54.9033 | 2.68541 | ||||||||
\(419\) | −12.6515 | −0.618065 | −0.309032 | − | 0.951052i | \(-0.600005\pi\) | ||||
−0.309032 | + | 0.951052i | \(0.600005\pi\) | |||||||
\(420\) | 25.6953 | 1.25380 | ||||||||
\(421\) | −19.0787 | −0.929837 | −0.464919 | − | 0.885353i | \(-0.653916\pi\) | ||||
−0.464919 | + | 0.885353i | \(0.653916\pi\) | |||||||
\(422\) | −64.3203 | −3.13106 | ||||||||
\(423\) | 3.26859 | 0.158924 | ||||||||
\(424\) | 84.7422 | 4.11544 | ||||||||
\(425\) | −15.6364 | −0.758476 | ||||||||
\(426\) | 1.98472 | 0.0961599 | ||||||||
\(427\) | 6.50920 | 0.315002 | ||||||||
\(428\) | 53.9676 | 2.60862 | ||||||||
\(429\) | −4.69937 | −0.226887 | ||||||||
\(430\) | −6.74018 | −0.325041 | ||||||||
\(431\) | 27.9122 | 1.34448 | 0.672241 | − | 0.740332i | \(-0.265332\pi\) | ||||
0.672241 | + | 0.740332i | \(0.265332\pi\) | |||||||
\(432\) | 51.6116 | 2.48316 | ||||||||
\(433\) | −20.2979 | −0.975453 | −0.487727 | − | 0.872996i | \(-0.662174\pi\) | ||||
−0.487727 | + | 0.872996i | \(0.662174\pi\) | |||||||
\(434\) | 21.1383 | 1.01467 | ||||||||
\(435\) | −1.69677 | −0.0813540 | ||||||||
\(436\) | 46.3298 | 2.21879 | ||||||||
\(437\) | −21.7423 | −1.04007 | ||||||||
\(438\) | 51.2765 | 2.45009 | ||||||||
\(439\) | −6.96865 | −0.332596 | −0.166298 | − | 0.986076i | \(-0.553181\pi\) | ||||
−0.166298 | + | 0.986076i | \(0.553181\pi\) | |||||||
\(440\) | 25.8697 | 1.23329 | ||||||||
\(441\) | −2.76486 | −0.131660 | ||||||||
\(442\) | −11.6841 | −0.555758 | ||||||||
\(443\) | 30.3877 | 1.44376 | 0.721880 | − | 0.692018i | \(-0.243278\pi\) | ||||
0.721880 | + | 0.692018i | \(0.243278\pi\) | |||||||
\(444\) | −33.5364 | −1.59157 | ||||||||
\(445\) | 16.5183 | 0.783042 | ||||||||
\(446\) | 35.9741 | 1.70342 | ||||||||
\(447\) | 10.1994 | 0.482414 | ||||||||
\(448\) | 19.6313 | 0.927492 | ||||||||
\(449\) | 19.5846 | 0.924255 | 0.462127 | − | 0.886814i | \(-0.347086\pi\) | ||||
0.462127 | + | 0.886814i | \(0.347086\pi\) | |||||||
\(450\) | −8.37479 | −0.394791 | ||||||||
\(451\) | 30.9263 | 1.45626 | ||||||||
\(452\) | 86.8451 | 4.08485 | ||||||||
\(453\) | −6.50848 | −0.305795 | ||||||||
\(454\) | 26.7030 | 1.25323 | ||||||||
\(455\) | −3.88227 | −0.182004 | ||||||||
\(456\) | −71.3005 | −3.33895 | ||||||||
\(457\) | −10.7321 | −0.502027 | −0.251014 | − | 0.967984i | \(-0.580764\pi\) | ||||
−0.251014 | + | 0.967984i | \(0.580764\pi\) | |||||||
\(458\) | 19.9562 | 0.932491 | ||||||||
\(459\) | 24.2803 | 1.13331 | ||||||||
\(460\) | −17.6694 | −0.823839 | ||||||||
\(461\) | 39.7219 | 1.85003 | 0.925016 | − | 0.379928i | \(-0.124051\pi\) | ||||
0.925016 | + | 0.379928i | \(0.124051\pi\) | |||||||
\(462\) | 37.1730 | 1.72944 | ||||||||
\(463\) | 1.53215 | 0.0712050 | 0.0356025 | − | 0.999366i | \(-0.488665\pi\) | ||||
0.0356025 | + | 0.999366i | \(0.488665\pi\) | |||||||
\(464\) | −9.13479 | −0.424072 | ||||||||
\(465\) | −4.33585 | −0.201070 | ||||||||
\(466\) | 0.207012 | 0.00958963 | ||||||||
\(467\) | 27.7463 | 1.28394 | 0.641972 | − | 0.766728i | \(-0.278116\pi\) | ||||
0.641972 | + | 0.766728i | \(0.278116\pi\) | |||||||
\(468\) | −4.40641 | −0.203686 | ||||||||
\(469\) | −30.2077 | −1.39486 | ||||||||
\(470\) | −11.2005 | −0.516641 | ||||||||
\(471\) | 21.1688 | 0.975405 | ||||||||
\(472\) | −51.1298 | −2.35344 | ||||||||
\(473\) | −6.86587 | −0.315693 | ||||||||
\(474\) | −46.2715 | −2.12532 | ||||||||
\(475\) | 24.8648 | 1.14088 | ||||||||
\(476\) | 65.0782 | 2.98286 | ||||||||
\(477\) | 10.4561 | 0.478752 | ||||||||
\(478\) | −5.94874 | −0.272089 | ||||||||
\(479\) | −8.55476 | −0.390877 | −0.195438 | − | 0.980716i | \(-0.562613\pi\) | ||||
−0.195438 | + | 0.980716i | \(0.562613\pi\) | |||||||
\(480\) | −15.9499 | −0.728009 | ||||||||
\(481\) | 5.06696 | 0.231033 | ||||||||
\(482\) | −31.9475 | −1.45517 | ||||||||
\(483\) | −14.7209 | −0.669825 | ||||||||
\(484\) | −6.90548 | −0.313885 | ||||||||
\(485\) | 15.1331 | 0.687157 | ||||||||
\(486\) | 23.0458 | 1.04538 | ||||||||
\(487\) | −37.0106 | −1.67711 | −0.838555 | − | 0.544817i | \(-0.816599\pi\) | ||||
−0.838555 | + | 0.544817i | \(0.816599\pi\) | |||||||
\(488\) | −14.6785 | −0.664465 | ||||||||
\(489\) | 18.5308 | 0.837990 | ||||||||
\(490\) | 9.47437 | 0.428008 | ||||||||
\(491\) | −0.724907 | −0.0327146 | −0.0163573 | − | 0.999866i | \(-0.505207\pi\) | ||||
−0.0163573 | + | 0.999866i | \(0.505207\pi\) | |||||||
\(492\) | −69.2698 | −3.12292 | ||||||||
\(493\) | −4.29740 | −0.193545 | ||||||||
\(494\) | 18.5800 | 0.835955 | ||||||||
\(495\) | 3.19199 | 0.143469 | ||||||||
\(496\) | −23.3426 | −1.04811 | ||||||||
\(497\) | 1.67020 | 0.0749188 | ||||||||
\(498\) | −20.2627 | −0.907995 | ||||||||
\(499\) | −37.2504 | −1.66756 | −0.833778 | − | 0.552099i | \(-0.813827\pi\) | ||||
−0.833778 | + | 0.552099i | \(0.813827\pi\) | |||||||
\(500\) | 47.9747 | 2.14549 | ||||||||
\(501\) | 16.9399 | 0.756819 | ||||||||
\(502\) | −71.4783 | −3.19023 | ||||||||
\(503\) | 13.9476 | 0.621893 | 0.310946 | − | 0.950427i | \(-0.399354\pi\) | ||||
0.310946 | + | 0.950427i | \(0.399354\pi\) | |||||||
\(504\) | 20.2093 | 0.900193 | ||||||||
\(505\) | 6.99354 | 0.311208 | ||||||||
\(506\) | −25.5620 | −1.13637 | ||||||||
\(507\) | 17.3144 | 0.768958 | ||||||||
\(508\) | 28.4588 | 1.26266 | ||||||||
\(509\) | −36.4195 | −1.61427 | −0.807134 | − | 0.590368i | \(-0.798983\pi\) | ||||
−0.807134 | + | 0.590368i | \(0.798983\pi\) | |||||||
\(510\) | −18.9579 | −0.839470 | ||||||||
\(511\) | 43.1508 | 1.90888 | ||||||||
\(512\) | 45.2129 | 1.99815 | ||||||||
\(513\) | −38.6103 | −1.70469 | ||||||||
\(514\) | 12.0627 | 0.532062 | ||||||||
\(515\) | 18.3976 | 0.810693 | ||||||||
\(516\) | 15.3784 | 0.676998 | ||||||||
\(517\) | −11.4094 | −0.501784 | ||||||||
\(518\) | −40.0808 | −1.76105 | ||||||||
\(519\) | 3.87427 | 0.170061 | ||||||||
\(520\) | 8.75466 | 0.383917 | ||||||||
\(521\) | 12.4780 | 0.546669 | 0.273335 | − | 0.961919i | \(-0.411873\pi\) | ||||
0.273335 | + | 0.961919i | \(0.411873\pi\) | |||||||
\(522\) | −2.30167 | −0.100741 | ||||||||
\(523\) | −18.2832 | −0.799468 | −0.399734 | − | 0.916631i | \(-0.630898\pi\) | ||||
−0.399734 | + | 0.916631i | \(0.630898\pi\) | |||||||
\(524\) | 14.2474 | 0.622402 | ||||||||
\(525\) | 16.8351 | 0.734742 | ||||||||
\(526\) | 72.7720 | 3.17301 | ||||||||
\(527\) | −10.9814 | −0.478355 | ||||||||
\(528\) | −41.0494 | −1.78645 | ||||||||
\(529\) | −12.8772 | −0.559877 | ||||||||
\(530\) | −35.8300 | −1.55636 | ||||||||
\(531\) | −6.30876 | −0.273777 | ||||||||
\(532\) | −103.487 | −4.48672 | ||||||||
\(533\) | 10.4659 | 0.453327 | ||||||||
\(534\) | −53.5248 | −2.31624 | ||||||||
\(535\) | −13.2299 | −0.571980 | ||||||||
\(536\) | 68.1196 | 2.94232 | ||||||||
\(537\) | −8.27733 | −0.357193 | ||||||||
\(538\) | −56.7122 | −2.44504 | ||||||||
\(539\) | 9.65104 | 0.415700 | ||||||||
\(540\) | −31.3776 | −1.35027 | ||||||||
\(541\) | 15.7038 | 0.675160 | 0.337580 | − | 0.941297i | \(-0.390392\pi\) | ||||
0.337580 | + | 0.941297i | \(0.390392\pi\) | |||||||
\(542\) | 74.5569 | 3.20249 | ||||||||
\(543\) | 9.20844 | 0.395172 | ||||||||
\(544\) | −40.3961 | −1.73197 | ||||||||
\(545\) | −11.3576 | −0.486504 | ||||||||
\(546\) | 12.5799 | 0.538368 | ||||||||
\(547\) | −4.80939 | −0.205635 | −0.102817 | − | 0.994700i | \(-0.532786\pi\) | ||||
−0.102817 | + | 0.994700i | \(0.532786\pi\) | |||||||
\(548\) | −100.752 | −4.30391 | ||||||||
\(549\) | −1.81114 | −0.0772976 | ||||||||
\(550\) | 29.2331 | 1.24650 | ||||||||
\(551\) | 6.83368 | 0.291125 | ||||||||
\(552\) | 33.1962 | 1.41292 | ||||||||
\(553\) | −38.9389 | −1.65585 | ||||||||
\(554\) | 2.59993 | 0.110460 | ||||||||
\(555\) | 8.22130 | 0.348975 | ||||||||
\(556\) | 3.92836 | 0.166600 | ||||||||
\(557\) | −22.3816 | −0.948340 | −0.474170 | − | 0.880433i | \(-0.657252\pi\) | ||||
−0.474170 | + | 0.880433i | \(0.657252\pi\) | |||||||
\(558\) | −5.88157 | −0.248987 | ||||||||
\(559\) | −2.32350 | −0.0982738 | ||||||||
\(560\) | −33.9120 | −1.43304 | ||||||||
\(561\) | −19.3114 | −0.815328 | ||||||||
\(562\) | −26.8719 | −1.13352 | ||||||||
\(563\) | 24.7258 | 1.04207 | 0.521035 | − | 0.853535i | \(-0.325546\pi\) | ||||
0.521035 | + | 0.853535i | \(0.325546\pi\) | |||||||
\(564\) | 25.5551 | 1.07607 | ||||||||
\(565\) | −21.2897 | −0.895666 | ||||||||
\(566\) | 5.95872 | 0.250464 | ||||||||
\(567\) | −17.6916 | −0.742975 | ||||||||
\(568\) | −3.76637 | −0.158033 | ||||||||
\(569\) | −23.1811 | −0.971801 | −0.485900 | − | 0.874014i | \(-0.661508\pi\) | ||||
−0.485900 | + | 0.874014i | \(0.661508\pi\) | |||||||
\(570\) | 30.1467 | 1.26271 | ||||||||
\(571\) | 14.8743 | 0.622472 | 0.311236 | − | 0.950333i | \(-0.399257\pi\) | ||||
0.311236 | + | 0.950333i | \(0.399257\pi\) | |||||||
\(572\) | 15.3810 | 0.643114 | ||||||||
\(573\) | 14.6922 | 0.613775 | ||||||||
\(574\) | −82.7873 | −3.45548 | ||||||||
\(575\) | −11.5766 | −0.482778 | ||||||||
\(576\) | −5.46227 | −0.227595 | ||||||||
\(577\) | 17.8376 | 0.742591 | 0.371295 | − | 0.928515i | \(-0.378914\pi\) | ||||
0.371295 | + | 0.928515i | \(0.378914\pi\) | |||||||
\(578\) | −3.81567 | −0.158711 | ||||||||
\(579\) | −14.9915 | −0.623024 | ||||||||
\(580\) | 5.55355 | 0.230598 | ||||||||
\(581\) | −17.0517 | −0.707424 | ||||||||
\(582\) | −49.0362 | −2.03262 | ||||||||
\(583\) | −36.4981 | −1.51160 | ||||||||
\(584\) | −97.3067 | −4.02658 | ||||||||
\(585\) | 1.08021 | 0.0446613 | ||||||||
\(586\) | −44.0575 | −1.82000 | ||||||||
\(587\) | −33.7389 | −1.39255 | −0.696276 | − | 0.717774i | \(-0.745161\pi\) | ||||
−0.696276 | + | 0.717774i | \(0.745161\pi\) | |||||||
\(588\) | −21.6168 | −0.891460 | ||||||||
\(589\) | 17.4625 | 0.719528 | ||||||||
\(590\) | 21.6183 | 0.890011 | ||||||||
\(591\) | 8.50993 | 0.350052 | ||||||||
\(592\) | 44.2604 | 1.81909 | ||||||||
\(593\) | −13.0912 | −0.537590 | −0.268795 | − | 0.963197i | \(-0.586625\pi\) | ||||
−0.268795 | + | 0.963197i | \(0.586625\pi\) | |||||||
\(594\) | −45.3934 | −1.86251 | ||||||||
\(595\) | −15.9537 | −0.654036 | ||||||||
\(596\) | −33.3826 | −1.36741 | ||||||||
\(597\) | 1.84764 | 0.0756188 | ||||||||
\(598\) | −8.65053 | −0.353746 | ||||||||
\(599\) | −2.02815 | −0.0828678 | −0.0414339 | − | 0.999141i | \(-0.513193\pi\) | ||||
−0.0414339 | + | 0.999141i | \(0.513193\pi\) | |||||||
\(600\) | −37.9637 | −1.54986 | ||||||||
\(601\) | 26.4789 | 1.08010 | 0.540048 | − | 0.841634i | \(-0.318406\pi\) | ||||
0.540048 | + | 0.841634i | \(0.318406\pi\) | |||||||
\(602\) | 18.3794 | 0.749089 | ||||||||
\(603\) | 8.40509 | 0.342282 | ||||||||
\(604\) | 21.3023 | 0.866778 | ||||||||
\(605\) | 1.69285 | 0.0688241 | ||||||||
\(606\) | −22.6614 | −0.920557 | ||||||||
\(607\) | −15.0367 | −0.610323 | −0.305161 | − | 0.952301i | \(-0.598710\pi\) | ||||
−0.305161 | + | 0.952301i | \(0.598710\pi\) | |||||||
\(608\) | 64.2375 | 2.60517 | ||||||||
\(609\) | 4.62683 | 0.187489 | ||||||||
\(610\) | 6.20625 | 0.251284 | ||||||||
\(611\) | −3.86109 | −0.156203 | ||||||||
\(612\) | −18.1076 | −0.731954 | ||||||||
\(613\) | 36.8835 | 1.48971 | 0.744856 | − | 0.667225i | \(-0.232518\pi\) | ||||
0.744856 | + | 0.667225i | \(0.232518\pi\) | |||||||
\(614\) | −39.1468 | −1.57984 | ||||||||
\(615\) | 16.9812 | 0.684748 | ||||||||
\(616\) | −70.5426 | −2.84224 | ||||||||
\(617\) | −44.6051 | −1.79573 | −0.897866 | − | 0.440268i | \(-0.854883\pi\) | ||||
−0.897866 | + | 0.440268i | \(0.854883\pi\) | |||||||
\(618\) | −59.6143 | −2.39804 | ||||||||
\(619\) | −9.59984 | −0.385850 | −0.192925 | − | 0.981213i | \(-0.561797\pi\) | ||||
−0.192925 | + | 0.981213i | \(0.561797\pi\) | |||||||
\(620\) | 14.1913 | 0.569935 | ||||||||
\(621\) | 17.9763 | 0.721363 | ||||||||
\(622\) | −27.2397 | −1.09221 | ||||||||
\(623\) | −45.0428 | −1.80460 | ||||||||
\(624\) | −13.8917 | −0.556113 | ||||||||
\(625\) | 6.43205 | 0.257282 | ||||||||
\(626\) | −45.6154 | −1.82316 | ||||||||
\(627\) | 30.7088 | 1.22639 | ||||||||
\(628\) | −69.2854 | −2.76479 | ||||||||
\(629\) | 20.8220 | 0.830227 | ||||||||
\(630\) | −8.54473 | −0.340430 | ||||||||
\(631\) | −32.9749 | −1.31271 | −0.656355 | − | 0.754452i | \(-0.727903\pi\) | ||||
−0.656355 | + | 0.754452i | \(0.727903\pi\) | |||||||
\(632\) | 87.8086 | 3.49284 | ||||||||
\(633\) | −35.9760 | −1.42992 | ||||||||
\(634\) | −63.6155 | −2.52649 | ||||||||
\(635\) | −6.97657 | −0.276857 | ||||||||
\(636\) | 81.7499 | 3.24159 | ||||||||
\(637\) | 3.26604 | 0.129405 | ||||||||
\(638\) | 8.03422 | 0.318078 | ||||||||
\(639\) | −0.464722 | −0.0183841 | ||||||||
\(640\) | −3.21859 | −0.127226 | ||||||||
\(641\) | −2.81895 | −0.111342 | −0.0556709 | − | 0.998449i | \(-0.517730\pi\) | ||||
−0.0556709 | + | 0.998449i | \(0.517730\pi\) | |||||||
\(642\) | 42.8694 | 1.69192 | ||||||||
\(643\) | −18.3449 | −0.723454 | −0.361727 | − | 0.932284i | \(-0.617813\pi\) | ||||
−0.361727 | + | 0.932284i | \(0.617813\pi\) | |||||||
\(644\) | 48.1816 | 1.89862 | ||||||||
\(645\) | −3.76996 | −0.148442 | ||||||||
\(646\) | 76.3521 | 3.00403 | ||||||||
\(647\) | −15.3799 | −0.604647 | −0.302323 | − | 0.953205i | \(-0.597762\pi\) | ||||
−0.302323 | + | 0.953205i | \(0.597762\pi\) | |||||||
\(648\) | 39.8951 | 1.56723 | ||||||||
\(649\) | 22.0214 | 0.864416 | ||||||||
\(650\) | 9.89288 | 0.388031 | ||||||||
\(651\) | 11.8232 | 0.463387 | ||||||||
\(652\) | −60.6513 | −2.37529 | ||||||||
\(653\) | −40.2577 | −1.57540 | −0.787702 | − | 0.616057i | \(-0.788729\pi\) | ||||
−0.787702 | + | 0.616057i | \(0.788729\pi\) | |||||||
\(654\) | 36.8023 | 1.43908 | ||||||||
\(655\) | −3.49270 | −0.136471 | ||||||||
\(656\) | 91.4204 | 3.56937 | ||||||||
\(657\) | −12.0064 | −0.468414 | ||||||||
\(658\) | 30.5420 | 1.19065 | ||||||||
\(659\) | 39.0552 | 1.52138 | 0.760688 | − | 0.649118i | \(-0.224862\pi\) | ||||
0.760688 | + | 0.649118i | \(0.224862\pi\) | |||||||
\(660\) | 24.9562 | 0.971420 | ||||||||
\(661\) | 40.8793 | 1.59002 | 0.795010 | − | 0.606596i | \(-0.207465\pi\) | ||||
0.795010 | + | 0.606596i | \(0.207465\pi\) | |||||||
\(662\) | −61.1420 | −2.37635 | ||||||||
\(663\) | −6.53525 | −0.253808 | ||||||||
\(664\) | 38.4523 | 1.49224 | ||||||||
\(665\) | 25.3694 | 0.983782 | ||||||||
\(666\) | 11.1522 | 0.432138 | ||||||||
\(667\) | −3.18164 | −0.123194 | ||||||||
\(668\) | −55.4443 | −2.14521 | ||||||||
\(669\) | 20.1212 | 0.777932 | ||||||||
\(670\) | −28.8018 | −1.11271 | ||||||||
\(671\) | 6.32197 | 0.244057 | ||||||||
\(672\) | 43.4928 | 1.67777 | ||||||||
\(673\) | −36.2824 | −1.39858 | −0.699292 | − | 0.714836i | \(-0.746501\pi\) | ||||
−0.699292 | + | 0.714836i | \(0.746501\pi\) | |||||||
\(674\) | 22.6523 | 0.872534 | ||||||||
\(675\) | −20.5579 | −0.791276 | ||||||||
\(676\) | −56.6700 | −2.17961 | ||||||||
\(677\) | 13.7005 | 0.526553 | 0.263277 | − | 0.964720i | \(-0.415197\pi\) | ||||
0.263277 | + | 0.964720i | \(0.415197\pi\) | |||||||
\(678\) | 68.9859 | 2.64939 | ||||||||
\(679\) | −41.2655 | −1.58362 | ||||||||
\(680\) | 35.9761 | 1.37962 | ||||||||
\(681\) | 14.9357 | 0.572337 | ||||||||
\(682\) | 20.5303 | 0.786144 | ||||||||
\(683\) | 11.0145 | 0.421459 | 0.210730 | − | 0.977544i | \(-0.432416\pi\) | ||||
0.210730 | + | 0.977544i | \(0.432416\pi\) | |||||||
\(684\) | 28.7945 | 1.10098 | ||||||||
\(685\) | 24.6989 | 0.943698 | ||||||||
\(686\) | 32.0700 | 1.22444 | ||||||||
\(687\) | 11.1620 | 0.425857 | ||||||||
\(688\) | −20.2960 | −0.773779 | ||||||||
\(689\) | −12.3515 | −0.470553 | ||||||||
\(690\) | −14.0358 | −0.534332 | ||||||||
\(691\) | −8.43574 | −0.320911 | −0.160455 | − | 0.987043i | \(-0.551296\pi\) | ||||
−0.160455 | + | 0.987043i | \(0.551296\pi\) | |||||||
\(692\) | −12.6805 | −0.482040 | ||||||||
\(693\) | −8.70406 | −0.330640 | ||||||||
\(694\) | −42.2812 | −1.60497 | ||||||||
\(695\) | −0.963021 | −0.0365295 | ||||||||
\(696\) | −10.4337 | −0.395488 | ||||||||
\(697\) | 43.0081 | 1.62905 | ||||||||
\(698\) | 10.2614 | 0.388399 | ||||||||
\(699\) | 0.115787 | 0.00437947 | ||||||||
\(700\) | −55.1012 | −2.08263 | ||||||||
\(701\) | −38.9674 | −1.47178 | −0.735889 | − | 0.677102i | \(-0.763236\pi\) | ||||
−0.735889 | + | 0.677102i | \(0.763236\pi\) | |||||||
\(702\) | −15.3617 | −0.579792 | ||||||||
\(703\) | −33.1109 | −1.24880 | ||||||||
\(704\) | 19.0666 | 0.718601 | ||||||||
\(705\) | −6.26474 | −0.235944 | ||||||||
\(706\) | 47.8290 | 1.80007 | ||||||||
\(707\) | −19.0703 | −0.717212 | ||||||||
\(708\) | −49.3244 | −1.85372 | ||||||||
\(709\) | −11.3186 | −0.425079 | −0.212539 | − | 0.977152i | \(-0.568173\pi\) | ||||
−0.212539 | + | 0.977152i | \(0.568173\pi\) | |||||||
\(710\) | 1.59247 | 0.0597642 | ||||||||
\(711\) | 10.8345 | 0.406324 | ||||||||
\(712\) | 101.573 | 3.80662 | ||||||||
\(713\) | −8.13020 | −0.304478 | ||||||||
\(714\) | 51.6952 | 1.93465 | ||||||||
\(715\) | −3.77060 | −0.141012 | ||||||||
\(716\) | 27.0917 | 1.01247 | ||||||||
\(717\) | −3.32728 | −0.124260 | ||||||||
\(718\) | −64.5004 | −2.40713 | ||||||||
\(719\) | 5.63486 | 0.210145 | 0.105072 | − | 0.994465i | \(-0.466493\pi\) | ||||
0.105072 | + | 0.994465i | \(0.466493\pi\) | |||||||
\(720\) | 9.43577 | 0.351651 | ||||||||
\(721\) | −50.1673 | −1.86833 | ||||||||
\(722\) | −72.0159 | −2.68015 | ||||||||
\(723\) | −17.8690 | −0.664557 | ||||||||
\(724\) | −30.1393 | −1.12012 | ||||||||
\(725\) | 3.63857 | 0.135133 | ||||||||
\(726\) | −5.48540 | −0.203582 | ||||||||
\(727\) | −3.75437 | −0.139242 | −0.0696210 | − | 0.997574i | \(-0.522179\pi\) | ||||
−0.0696210 | + | 0.997574i | \(0.522179\pi\) | |||||||
\(728\) | −23.8726 | −0.884777 | ||||||||
\(729\) | 29.5714 | 1.09524 | ||||||||
\(730\) | 41.1424 | 1.52275 | ||||||||
\(731\) | −9.54813 | −0.353150 | ||||||||
\(732\) | −14.1602 | −0.523376 | ||||||||
\(733\) | −21.2979 | −0.786655 | −0.393327 | − | 0.919399i | \(-0.628676\pi\) | ||||
−0.393327 | + | 0.919399i | \(0.628676\pi\) | |||||||
\(734\) | −69.2386 | −2.55564 | ||||||||
\(735\) | 5.29926 | 0.195466 | ||||||||
\(736\) | −29.9078 | −1.10242 | ||||||||
\(737\) | −29.3389 | −1.08071 | ||||||||
\(738\) | 23.0350 | 0.847929 | ||||||||
\(739\) | −10.8813 | −0.400274 | −0.200137 | − | 0.979768i | \(-0.564139\pi\) | ||||
−0.200137 | + | 0.979768i | \(0.564139\pi\) | |||||||
\(740\) | −26.9084 | −0.989171 | ||||||||
\(741\) | 10.3923 | 0.381770 | ||||||||
\(742\) | 97.7028 | 3.58678 | ||||||||
\(743\) | 25.5938 | 0.938945 | 0.469472 | − | 0.882947i | \(-0.344444\pi\) | ||||
0.469472 | + | 0.882947i | \(0.344444\pi\) | |||||||
\(744\) | −26.6617 | −0.977467 | ||||||||
\(745\) | 8.18362 | 0.299825 | ||||||||
\(746\) | −9.19857 | −0.336783 | ||||||||
\(747\) | 4.74452 | 0.173593 | ||||||||
\(748\) | 63.2063 | 2.31105 | ||||||||
\(749\) | 36.0760 | 1.31819 | ||||||||
\(750\) | 38.1089 | 1.39154 | ||||||||
\(751\) | −8.97244 | −0.327409 | −0.163705 | − | 0.986509i | \(-0.552344\pi\) | ||||
−0.163705 | + | 0.986509i | \(0.552344\pi\) | |||||||
\(752\) | −33.7270 | −1.22990 | ||||||||
\(753\) | −39.9796 | −1.45694 | ||||||||
\(754\) | 2.71889 | 0.0990162 | ||||||||
\(755\) | −5.22217 | −0.190054 | ||||||||
\(756\) | 85.5617 | 3.11185 | ||||||||
\(757\) | −42.7727 | −1.55460 | −0.777301 | − | 0.629129i | \(-0.783412\pi\) | ||||
−0.777301 | + | 0.629129i | \(0.783412\pi\) | |||||||
\(758\) | 0.148219 | 0.00538357 | ||||||||
\(759\) | −14.2975 | −0.518966 | ||||||||
\(760\) | −57.2089 | −2.07518 | ||||||||
\(761\) | 29.8120 | 1.08068 | 0.540342 | − | 0.841446i | \(-0.318295\pi\) | ||||
0.540342 | + | 0.841446i | \(0.318295\pi\) | |||||||
\(762\) | 22.6064 | 0.818944 | ||||||||
\(763\) | 30.9703 | 1.12120 | ||||||||
\(764\) | −48.0876 | −1.73975 | ||||||||
\(765\) | 4.43899 | 0.160492 | ||||||||
\(766\) | −8.11322 | −0.293143 | ||||||||
\(767\) | 7.45234 | 0.269089 | ||||||||
\(768\) | 28.3745 | 1.02388 | ||||||||
\(769\) | 14.5679 | 0.525333 | 0.262666 | − | 0.964887i | \(-0.415398\pi\) | ||||
0.262666 | + | 0.964887i | \(0.415398\pi\) | |||||||
\(770\) | 29.8263 | 1.07486 | ||||||||
\(771\) | 6.74697 | 0.242986 | ||||||||
\(772\) | 49.0671 | 1.76597 | ||||||||
\(773\) | −25.5344 | −0.918409 | −0.459204 | − | 0.888331i | \(-0.651865\pi\) | ||||
−0.459204 | + | 0.888331i | \(0.651865\pi\) | |||||||
\(774\) | −5.11394 | −0.183817 | ||||||||
\(775\) | 9.29783 | 0.333988 | ||||||||
\(776\) | 93.0552 | 3.34049 | ||||||||
\(777\) | −22.4182 | −0.804248 | ||||||||
\(778\) | 6.03292 | 0.216290 | ||||||||
\(779\) | −68.3911 | −2.45036 | ||||||||
\(780\) | 8.44553 | 0.302399 | ||||||||
\(781\) | 1.62216 | 0.0580455 | ||||||||
\(782\) | −35.5482 | −1.27120 | ||||||||
\(783\) | −5.65000 | −0.201915 | ||||||||
\(784\) | 28.5292 | 1.01890 | ||||||||
\(785\) | 16.9850 | 0.606222 | ||||||||
\(786\) | 11.3175 | 0.403683 | ||||||||
\(787\) | 17.7630 | 0.633182 | 0.316591 | − | 0.948562i | \(-0.397462\pi\) | ||||
0.316591 | + | 0.948562i | \(0.397462\pi\) | |||||||
\(788\) | −27.8531 | −0.992224 | ||||||||
\(789\) | 40.7033 | 1.44907 | ||||||||
\(790\) | −37.1265 | −1.32090 | ||||||||
\(791\) | 58.0537 | 2.06415 | ||||||||
\(792\) | 19.6280 | 0.697450 | ||||||||
\(793\) | 2.13944 | 0.0759739 | ||||||||
\(794\) | 59.1777 | 2.10014 | ||||||||
\(795\) | −20.0407 | −0.710769 | ||||||||
\(796\) | −6.04733 | −0.214342 | ||||||||
\(797\) | −16.4074 | −0.581179 | −0.290589 | − | 0.956848i | \(-0.593851\pi\) | ||||
−0.290589 | + | 0.956848i | \(0.593851\pi\) | |||||||
\(798\) | −82.2053 | −2.91004 | ||||||||
\(799\) | −15.8666 | −0.561321 | ||||||||
\(800\) | 34.2030 | 1.20926 | ||||||||
\(801\) | 12.5328 | 0.442826 | ||||||||
\(802\) | −14.8357 | −0.523867 | ||||||||
\(803\) | 41.9096 | 1.47896 | ||||||||
\(804\) | 65.7143 | 2.31756 | ||||||||
\(805\) | −11.8115 | −0.416301 | ||||||||
\(806\) | 6.94772 | 0.244723 | ||||||||
\(807\) | −31.7206 | −1.11662 | ||||||||
\(808\) | 43.0042 | 1.51288 | ||||||||
\(809\) | −51.6436 | −1.81569 | −0.907846 | − | 0.419303i | \(-0.862274\pi\) | ||||
−0.907846 | + | 0.419303i | \(0.862274\pi\) | |||||||
\(810\) | −16.8681 | −0.592686 | ||||||||
\(811\) | −15.4385 | −0.542119 | −0.271060 | − | 0.962563i | \(-0.587374\pi\) | ||||
−0.271060 | + | 0.962563i | \(0.587374\pi\) | |||||||
\(812\) | −15.1436 | −0.531438 | ||||||||
\(813\) | 41.7016 | 1.46254 | ||||||||
\(814\) | −38.9279 | −1.36442 | ||||||||
\(815\) | 14.8684 | 0.520818 | ||||||||
\(816\) | −57.0860 | −1.99841 | ||||||||
\(817\) | 15.1833 | 0.531198 | ||||||||
\(818\) | 16.3747 | 0.572528 | ||||||||
\(819\) | −2.94557 | −0.102927 | ||||||||
\(820\) | −55.5796 | −1.94092 | ||||||||
\(821\) | −27.7562 | −0.968697 | −0.484349 | − | 0.874875i | \(-0.660943\pi\) | ||||
−0.484349 | + | 0.874875i | \(0.660943\pi\) | |||||||
\(822\) | −80.0329 | −2.79147 | ||||||||
\(823\) | −13.2744 | −0.462717 | −0.231358 | − | 0.972869i | \(-0.574317\pi\) | ||||
−0.231358 | + | 0.972869i | \(0.574317\pi\) | |||||||
\(824\) | 113.129 | 3.94104 | ||||||||
\(825\) | 16.3508 | 0.569263 | ||||||||
\(826\) | −58.9497 | −2.05112 | ||||||||
\(827\) | 18.7618 | 0.652411 | 0.326206 | − | 0.945299i | \(-0.394230\pi\) | ||||
0.326206 | + | 0.945299i | \(0.394230\pi\) | |||||||
\(828\) | −13.4062 | −0.465897 | ||||||||
\(829\) | −25.3072 | −0.878955 | −0.439477 | − | 0.898254i | \(-0.644836\pi\) | ||||
−0.439477 | + | 0.898254i | \(0.644836\pi\) | |||||||
\(830\) | −16.2581 | −0.564326 | ||||||||
\(831\) | 1.45421 | 0.0504459 | ||||||||
\(832\) | 6.45241 | 0.223697 | ||||||||
\(833\) | 13.4214 | 0.465023 | ||||||||
\(834\) | 3.12051 | 0.108054 | ||||||||
\(835\) | 13.5920 | 0.470369 | ||||||||
\(836\) | −100.510 | −3.47622 | ||||||||
\(837\) | −14.4377 | −0.499041 | ||||||||
\(838\) | 32.8929 | 1.13627 | ||||||||
\(839\) | −32.6367 | −1.12674 | −0.563371 | − | 0.826204i | \(-0.690496\pi\) | ||||
−0.563371 | + | 0.826204i | \(0.690496\pi\) | |||||||
\(840\) | −38.7340 | −1.33645 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 49.6032 | 1.70944 | ||||||||
\(843\) | −15.0302 | −0.517666 | ||||||||
\(844\) | 117.750 | 4.05311 | ||||||||
\(845\) | 13.8924 | 0.477914 | ||||||||
\(846\) | −8.49811 | −0.292171 | ||||||||
\(847\) | −4.61614 | −0.158612 | ||||||||
\(848\) | −107.891 | −3.70500 | ||||||||
\(849\) | 3.33286 | 0.114384 | ||||||||
\(850\) | 40.6535 | 1.39440 | ||||||||
\(851\) | 15.4159 | 0.528449 | ||||||||
\(852\) | −3.63338 | −0.124477 | ||||||||
\(853\) | −14.3527 | −0.491427 | −0.245713 | − | 0.969343i | \(-0.579022\pi\) | ||||
−0.245713 | + | 0.969343i | \(0.579022\pi\) | |||||||
\(854\) | −16.9235 | −0.579109 | ||||||||
\(855\) | −7.05885 | −0.241407 | ||||||||
\(856\) | −81.3527 | −2.78058 | ||||||||
\(857\) | −58.2887 | −1.99111 | −0.995553 | − | 0.0942080i | \(-0.969968\pi\) | ||||
−0.995553 | + | 0.0942080i | \(0.969968\pi\) | |||||||
\(858\) | 12.2180 | 0.417116 | ||||||||
\(859\) | −37.0161 | −1.26297 | −0.631486 | − | 0.775387i | \(-0.717555\pi\) | ||||
−0.631486 | + | 0.775387i | \(0.717555\pi\) | |||||||
\(860\) | 12.3391 | 0.420760 | ||||||||
\(861\) | −46.3051 | −1.57807 | ||||||||
\(862\) | −72.5696 | −2.47173 | ||||||||
\(863\) | −52.5341 | −1.78828 | −0.894141 | − | 0.447786i | \(-0.852213\pi\) | ||||
−0.894141 | + | 0.447786i | \(0.852213\pi\) | |||||||
\(864\) | −53.1108 | −1.80687 | ||||||||
\(865\) | 3.10857 | 0.105695 | ||||||||
\(866\) | 52.7730 | 1.79330 | ||||||||
\(867\) | −2.13420 | −0.0724813 | ||||||||
\(868\) | −38.6973 | −1.31347 | ||||||||
\(869\) | −37.8188 | −1.28292 | ||||||||
\(870\) | 4.41149 | 0.149563 | ||||||||
\(871\) | −9.92867 | −0.336420 | ||||||||
\(872\) | −69.8392 | −2.36505 | ||||||||
\(873\) | 11.4818 | 0.388601 | ||||||||
\(874\) | 56.5284 | 1.91210 | ||||||||
\(875\) | 32.0699 | 1.08416 | ||||||||
\(876\) | −93.8707 | −3.17160 | ||||||||
\(877\) | −16.9002 | −0.570678 | −0.285339 | − | 0.958427i | \(-0.592106\pi\) | ||||
−0.285339 | + | 0.958427i | \(0.592106\pi\) | |||||||
\(878\) | 18.1180 | 0.611453 | ||||||||
\(879\) | −24.6425 | −0.831172 | ||||||||
\(880\) | −32.9366 | −1.11029 | ||||||||
\(881\) | 13.3438 | 0.449564 | 0.224782 | − | 0.974409i | \(-0.427833\pi\) | ||||
0.224782 | + | 0.974409i | \(0.427833\pi\) | |||||||
\(882\) | 7.18844 | 0.242047 | ||||||||
\(883\) | 17.8576 | 0.600957 | 0.300478 | − | 0.953789i | \(-0.402854\pi\) | ||||
0.300478 | + | 0.953789i | \(0.402854\pi\) | |||||||
\(884\) | 21.3899 | 0.719420 | ||||||||
\(885\) | 12.0917 | 0.406457 | ||||||||
\(886\) | −79.0057 | −2.65425 | ||||||||
\(887\) | −36.5187 | −1.22618 | −0.613088 | − | 0.790014i | \(-0.710073\pi\) | ||||
−0.613088 | + | 0.790014i | \(0.710073\pi\) | |||||||
\(888\) | 50.5539 | 1.69648 | ||||||||
\(889\) | 19.0240 | 0.638045 | ||||||||
\(890\) | −42.9464 | −1.43957 | ||||||||
\(891\) | −17.1827 | −0.575641 | ||||||||
\(892\) | −65.8569 | −2.20505 | ||||||||
\(893\) | 25.2310 | 0.844322 | ||||||||
\(894\) | −26.5177 | −0.886884 | ||||||||
\(895\) | −6.64143 | −0.221998 | ||||||||
\(896\) | 8.77660 | 0.293206 | ||||||||
\(897\) | −4.83846 | −0.161552 | ||||||||
\(898\) | −50.9186 | −1.69917 | ||||||||
\(899\) | 2.55535 | 0.0852257 | ||||||||
\(900\) | 15.3315 | 0.511051 | ||||||||
\(901\) | −50.7567 | −1.69095 | ||||||||
\(902\) | −80.4060 | −2.67723 | ||||||||
\(903\) | 10.2801 | 0.342100 | ||||||||
\(904\) | −130.913 | −4.35412 | ||||||||
\(905\) | 7.38852 | 0.245603 | ||||||||
\(906\) | 16.9216 | 0.562182 | ||||||||
\(907\) | −7.04560 | −0.233945 | −0.116973 | − | 0.993135i | \(-0.537319\pi\) | ||||
−0.116973 | + | 0.993135i | \(0.537319\pi\) | |||||||
\(908\) | −48.8846 | −1.62229 | ||||||||
\(909\) | 5.30617 | 0.175995 | ||||||||
\(910\) | 10.0936 | 0.334600 | ||||||||
\(911\) | −6.57859 | −0.217958 | −0.108979 | − | 0.994044i | \(-0.534758\pi\) | ||||
−0.108979 | + | 0.994044i | \(0.534758\pi\) | |||||||
\(912\) | 90.7777 | 3.00595 | ||||||||
\(913\) | −16.5612 | −0.548097 | ||||||||
\(914\) | 27.9027 | 0.922940 | ||||||||
\(915\) | 3.47131 | 0.114758 | ||||||||
\(916\) | −36.5333 | −1.20709 | ||||||||
\(917\) | 9.52405 | 0.314512 | ||||||||
\(918\) | −63.1270 | −2.08350 | ||||||||
\(919\) | −34.0885 | −1.12448 | −0.562239 | − | 0.826975i | \(-0.690060\pi\) | ||||
−0.562239 | + | 0.826975i | \(0.690060\pi\) | |||||||
\(920\) | 26.6354 | 0.878144 | ||||||||
\(921\) | −21.8958 | −0.721493 | ||||||||
\(922\) | −103.274 | −3.40115 | ||||||||
\(923\) | 0.548962 | 0.0180693 | ||||||||
\(924\) | −68.0517 | −2.23874 | ||||||||
\(925\) | −17.6298 | −0.579665 | ||||||||
\(926\) | −3.98348 | −0.130905 | ||||||||
\(927\) | 13.9587 | 0.458463 | ||||||||
\(928\) | 9.40013 | 0.308574 | ||||||||
\(929\) | 18.3288 | 0.601347 | 0.300674 | − | 0.953727i | \(-0.402789\pi\) | ||||
0.300674 | + | 0.953727i | \(0.402789\pi\) | |||||||
\(930\) | 11.2729 | 0.369653 | ||||||||
\(931\) | −21.3425 | −0.699473 | ||||||||
\(932\) | −0.378971 | −0.0124136 | ||||||||
\(933\) | −15.2359 | −0.498800 | ||||||||
\(934\) | −72.1383 | −2.36044 | ||||||||
\(935\) | −15.4948 | −0.506733 | ||||||||
\(936\) | 6.64238 | 0.217113 | ||||||||
\(937\) | −3.22158 | −0.105244 | −0.0526222 | − | 0.998614i | \(-0.516758\pi\) | ||||
−0.0526222 | + | 0.998614i | \(0.516758\pi\) | |||||||
\(938\) | 78.5380 | 2.56436 | ||||||||
\(939\) | −25.5139 | −0.832613 | ||||||||
\(940\) | 20.5045 | 0.668784 | ||||||||
\(941\) | 39.5939 | 1.29072 | 0.645362 | − | 0.763877i | \(-0.276707\pi\) | ||||
0.645362 | + | 0.763877i | \(0.276707\pi\) | |||||||
\(942\) | −55.0372 | −1.79321 | ||||||||
\(943\) | 31.8417 | 1.03691 | ||||||||
\(944\) | 65.0970 | 2.11873 | ||||||||
\(945\) | −20.9751 | −0.682320 | ||||||||
\(946\) | 17.8508 | 0.580378 | ||||||||
\(947\) | 14.8190 | 0.481552 | 0.240776 | − | 0.970581i | \(-0.422598\pi\) | ||||
0.240776 | + | 0.970581i | \(0.422598\pi\) | |||||||
\(948\) | 84.7081 | 2.75119 | ||||||||
\(949\) | 14.1828 | 0.460393 | ||||||||
\(950\) | −64.6468 | −2.09742 | ||||||||
\(951\) | −35.5818 | −1.15382 | ||||||||
\(952\) | −98.1012 | −3.17948 | ||||||||
\(953\) | −38.5610 | −1.24911 | −0.624556 | − | 0.780980i | \(-0.714720\pi\) | ||||
−0.624556 | + | 0.780980i | \(0.714720\pi\) | |||||||
\(954\) | −27.1851 | −0.880150 | ||||||||
\(955\) | 11.7885 | 0.381466 | ||||||||
\(956\) | 10.8902 | 0.352214 | ||||||||
\(957\) | 4.49375 | 0.145262 | ||||||||
\(958\) | 22.2417 | 0.718598 | ||||||||
\(959\) | −67.3501 | −2.17485 | ||||||||
\(960\) | 10.4692 | 0.337893 | ||||||||
\(961\) | −24.4702 | −0.789361 | ||||||||
\(962\) | −13.1737 | −0.424738 | ||||||||
\(963\) | −10.0379 | −0.323466 | ||||||||
\(964\) | 58.4854 | 1.88369 | ||||||||
\(965\) | −12.0286 | −0.387215 | ||||||||
\(966\) | 38.2733 | 1.23142 | ||||||||
\(967\) | −18.0298 | −0.579798 | −0.289899 | − | 0.957057i | \(-0.593622\pi\) | ||||
−0.289899 | + | 0.957057i | \(0.593622\pi\) | |||||||
\(968\) | 10.4096 | 0.334576 | ||||||||
\(969\) | 42.7057 | 1.37191 | ||||||||
\(970\) | −39.3449 | −1.26329 | ||||||||
\(971\) | 12.7974 | 0.410688 | 0.205344 | − | 0.978690i | \(-0.434169\pi\) | ||||
0.205344 | + | 0.978690i | \(0.434169\pi\) | |||||||
\(972\) | −42.1893 | −1.35322 | ||||||||
\(973\) | 2.62601 | 0.0841859 | ||||||||
\(974\) | 96.2249 | 3.08324 | ||||||||
\(975\) | 5.53334 | 0.177209 | ||||||||
\(976\) | 18.6883 | 0.598196 | ||||||||
\(977\) | −26.6219 | −0.851711 | −0.425855 | − | 0.904791i | \(-0.640027\pi\) | ||||
−0.425855 | + | 0.904791i | \(0.640027\pi\) | |||||||
\(978\) | −48.1787 | −1.54058 | ||||||||
\(979\) | −43.7472 | −1.39817 | ||||||||
\(980\) | −17.3445 | −0.554050 | ||||||||
\(981\) | −8.61726 | −0.275128 | ||||||||
\(982\) | 1.88471 | 0.0601434 | ||||||||
\(983\) | 6.85150 | 0.218529 | 0.109264 | − | 0.994013i | \(-0.465150\pi\) | ||||
0.109264 | + | 0.994013i | \(0.465150\pi\) | |||||||
\(984\) | 104.420 | 3.32878 | ||||||||
\(985\) | 6.82806 | 0.217560 | ||||||||
\(986\) | 11.1729 | 0.355818 | ||||||||
\(987\) | 17.0830 | 0.543757 | ||||||||
\(988\) | −34.0140 | −1.08213 | ||||||||
\(989\) | −7.06909 | −0.224784 | ||||||||
\(990\) | −8.29895 | −0.263758 | ||||||||
\(991\) | 56.5802 | 1.79733 | 0.898665 | − | 0.438636i | \(-0.144538\pi\) | ||||
0.898665 | + | 0.438636i | \(0.144538\pi\) | |||||||
\(992\) | 24.0206 | 0.762656 | ||||||||
\(993\) | −34.1983 | −1.08525 | ||||||||
\(994\) | −4.34241 | −0.137733 | ||||||||
\(995\) | 1.48248 | 0.0469977 | ||||||||
\(996\) | 37.0945 | 1.17538 | ||||||||
\(997\) | 45.0507 | 1.42677 | 0.713385 | − | 0.700773i | \(-0.247161\pi\) | ||||
0.713385 | + | 0.700773i | \(0.247161\pi\) | |||||||
\(998\) | 96.8483 | 3.06568 | ||||||||
\(999\) | 27.3757 | 0.866130 |
(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 | 8033.2.a.b.1.8 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8033.2.a.b.1.8 | ✓ | 153 | 1.1 | even | 1 | trivial |