Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.96258 | −1.38776 | −0.693878 | − | 0.720093i | \(-0.744099\pi\) | ||||
−0.693878 | + | 0.720093i | \(0.744099\pi\) | |||||||
\(3\) | −3.23511 | −1.86779 | −0.933895 | − | 0.357546i | \(-0.883614\pi\) | ||||
−0.933895 | + | 0.357546i | \(0.883614\pi\) | |||||||
\(4\) | 1.85173 | 0.925866 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.34917 | 2.59204 | ||||||||
\(7\) | 1.21428 | 0.458956 | 0.229478 | − | 0.973314i | \(-0.426298\pi\) | ||||
0.229478 | + | 0.973314i | \(0.426298\pi\) | |||||||
\(8\) | 0.290989 | 0.102880 | ||||||||
\(9\) | 7.46593 | 2.48864 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.74603 | 1.12947 | 0.564735 | − | 0.825272i | \(-0.308978\pi\) | ||||
0.564735 | + | 0.825272i | \(0.308978\pi\) | |||||||
\(12\) | −5.99055 | −1.72932 | ||||||||
\(13\) | 3.08267 | 0.854979 | 0.427490 | − | 0.904020i | \(-0.359398\pi\) | ||||
0.427490 | + | 0.904020i | \(0.359398\pi\) | |||||||
\(14\) | −2.38313 | −0.636919 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.27455 | −1.06864 | ||||||||
\(17\) | −7.01669 | −1.70180 | −0.850899 | − | 0.525330i | \(-0.823942\pi\) | ||||
−0.850899 | + | 0.525330i | \(0.823942\pi\) | |||||||
\(18\) | −14.6525 | −3.45363 | ||||||||
\(19\) | −2.30313 | −0.528374 | −0.264187 | − | 0.964471i | \(-0.585104\pi\) | ||||
−0.264187 | + | 0.964471i | \(0.585104\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.92834 | −0.857234 | ||||||||
\(22\) | −7.35189 | −1.56743 | ||||||||
\(23\) | −1.94524 | −0.405612 | −0.202806 | − | 0.979219i | \(-0.565006\pi\) | ||||
−0.202806 | + | 0.979219i | \(0.565006\pi\) | |||||||
\(24\) | −0.941382 | −0.192159 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.05000 | −1.18650 | ||||||||
\(27\) | −14.4478 | −2.78047 | ||||||||
\(28\) | 2.24853 | 0.424932 | ||||||||
\(29\) | 5.85578 | 1.08739 | 0.543696 | − | 0.839282i | \(-0.317025\pi\) | ||||
0.543696 | + | 0.839282i | \(0.317025\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.10334 | −0.736981 | −0.368491 | − | 0.929632i | \(-0.620125\pi\) | ||||
−0.368491 | + | 0.929632i | \(0.620125\pi\) | |||||||
\(32\) | 7.80719 | 1.38013 | ||||||||
\(33\) | −12.1188 | −2.10961 | ||||||||
\(34\) | 13.7708 | 2.36168 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 13.8249 | 2.30415 | ||||||||
\(37\) | 11.2364 | 1.84726 | 0.923628 | − | 0.383291i | \(-0.125209\pi\) | ||||
0.923628 | + | 0.383291i | \(0.125209\pi\) | |||||||
\(38\) | 4.52008 | 0.733254 | ||||||||
\(39\) | −9.97278 | −1.59692 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.17567 | −0.808304 | −0.404152 | − | 0.914692i | \(-0.632433\pi\) | ||||
−0.404152 | + | 0.914692i | \(0.632433\pi\) | |||||||
\(42\) | 7.70970 | 1.18963 | ||||||||
\(43\) | 2.18721 | 0.333547 | 0.166773 | − | 0.985995i | \(-0.446665\pi\) | ||||
0.166773 | + | 0.985995i | \(0.446665\pi\) | |||||||
\(44\) | 6.93664 | 1.04574 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.81770 | 0.562890 | ||||||||
\(47\) | 9.94112 | 1.45006 | 0.725031 | − | 0.688717i | \(-0.241826\pi\) | ||||
0.725031 | + | 0.688717i | \(0.241826\pi\) | |||||||
\(48\) | 13.8286 | 1.99599 | ||||||||
\(49\) | −5.52551 | −0.789359 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 22.6998 | 3.17860 | ||||||||
\(52\) | 5.70828 | 0.791596 | ||||||||
\(53\) | 0.642522 | 0.0882571 | 0.0441286 | − | 0.999026i | \(-0.485949\pi\) | ||||
0.0441286 | + | 0.999026i | \(0.485949\pi\) | |||||||
\(54\) | 28.3549 | 3.85862 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.353344 | 0.0472175 | ||||||||
\(57\) | 7.45087 | 0.986892 | ||||||||
\(58\) | −11.4925 | −1.50903 | ||||||||
\(59\) | 11.8585 | 1.54384 | 0.771920 | − | 0.635720i | \(-0.219297\pi\) | ||||
0.771920 | + | 0.635720i | \(0.219297\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.63058 | −0.976995 | −0.488498 | − | 0.872565i | \(-0.662455\pi\) | ||||
−0.488498 | + | 0.872565i | \(0.662455\pi\) | |||||||
\(62\) | 8.05314 | 1.02275 | ||||||||
\(63\) | 9.06576 | 1.14218 | ||||||||
\(64\) | −6.77314 | −0.846643 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 23.7842 | 2.92763 | ||||||||
\(67\) | 14.1894 | 1.73351 | 0.866753 | − | 0.498737i | \(-0.166203\pi\) | ||||
0.866753 | + | 0.498737i | \(0.166203\pi\) | |||||||
\(68\) | −12.9930 | −1.57564 | ||||||||
\(69\) | 6.29308 | 0.757598 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.64949 | 0.433115 | 0.216557 | − | 0.976270i | \(-0.430517\pi\) | ||||
0.216557 | + | 0.976270i | \(0.430517\pi\) | |||||||
\(72\) | 2.17251 | 0.256032 | ||||||||
\(73\) | −1.79732 | −0.210361 | −0.105180 | − | 0.994453i | \(-0.533542\pi\) | ||||
−0.105180 | + | 0.994453i | \(0.533542\pi\) | |||||||
\(74\) | −22.0524 | −2.56354 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.26478 | −0.489203 | ||||||||
\(77\) | 4.54874 | 0.518377 | ||||||||
\(78\) | 19.5724 | 2.21614 | ||||||||
\(79\) | −4.41542 | −0.496774 | −0.248387 | − | 0.968661i | \(-0.579900\pi\) | ||||
−0.248387 | + | 0.968661i | \(0.579900\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.3423 | 2.70470 | ||||||||
\(82\) | 10.1577 | 1.12173 | ||||||||
\(83\) | −8.23800 | −0.904238 | −0.452119 | − | 0.891958i | \(-0.649332\pi\) | ||||
−0.452119 | + | 0.891958i | \(0.649332\pi\) | |||||||
\(84\) | −7.27423 | −0.793684 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.29258 | −0.462881 | ||||||||
\(87\) | −18.9441 | −2.03102 | ||||||||
\(88\) | 1.09005 | 0.116200 | ||||||||
\(89\) | 6.52307 | 0.691444 | 0.345722 | − | 0.938337i | \(-0.387634\pi\) | ||||
0.345722 | + | 0.938337i | \(0.387634\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.74324 | 0.392398 | ||||||||
\(92\) | −3.60207 | −0.375542 | ||||||||
\(93\) | 13.2747 | 1.37653 | ||||||||
\(94\) | −19.5103 | −2.01233 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −25.2571 | −2.57779 | ||||||||
\(97\) | −1.16217 | −0.118000 | −0.0590000 | − | 0.998258i | \(-0.518791\pi\) | ||||
−0.0590000 | + | 0.998258i | \(0.518791\pi\) | |||||||
\(98\) | 10.8443 | 1.09544 | ||||||||
\(99\) | 27.9676 | 2.81085 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.3276 | −1.32615 | −0.663075 | − | 0.748553i | \(-0.730749\pi\) | ||||
−0.663075 | + | 0.748553i | \(0.730749\pi\) | |||||||
\(102\) | −44.5502 | −4.41112 | ||||||||
\(103\) | −5.20580 | −0.512943 | −0.256471 | − | 0.966552i | \(-0.582560\pi\) | ||||
−0.256471 | + | 0.966552i | \(0.582560\pi\) | |||||||
\(104\) | 0.897025 | 0.0879605 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.26100 | −0.122479 | ||||||||
\(107\) | 14.8141 | 1.43214 | 0.716069 | − | 0.698030i | \(-0.245940\pi\) | ||||
0.716069 | + | 0.698030i | \(0.245940\pi\) | |||||||
\(108\) | −26.7534 | −2.57435 | ||||||||
\(109\) | 3.47664 | 0.333001 | 0.166501 | − | 0.986041i | \(-0.446753\pi\) | ||||
0.166501 | + | 0.986041i | \(0.446753\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −36.3510 | −3.45029 | ||||||||
\(112\) | −5.19052 | −0.490458 | ||||||||
\(113\) | −16.7076 | −1.57172 | −0.785858 | − | 0.618407i | \(-0.787778\pi\) | ||||
−0.785858 | + | 0.618407i | \(0.787778\pi\) | |||||||
\(114\) | −14.6230 | −1.36957 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.8433 | 1.00678 | ||||||||
\(117\) | 23.0150 | 2.12774 | ||||||||
\(118\) | −23.2732 | −2.14247 | ||||||||
\(119\) | −8.52026 | −0.781051 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.03271 | 0.275701 | ||||||||
\(122\) | 14.9756 | 1.35583 | ||||||||
\(123\) | 16.7439 | 1.50974 | ||||||||
\(124\) | −7.59828 | −0.682345 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −17.7923 | −1.58506 | ||||||||
\(127\) | −10.9817 | −0.974468 | −0.487234 | − | 0.873272i | \(-0.661994\pi\) | ||||
−0.487234 | + | 0.873272i | \(0.661994\pi\) | |||||||
\(128\) | −2.32152 | −0.205195 | ||||||||
\(129\) | −7.07587 | −0.622995 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3267 | 0.989615 | 0.494807 | − | 0.869003i | \(-0.335239\pi\) | ||||
0.494807 | + | 0.869003i | \(0.335239\pi\) | |||||||
\(132\) | −22.4408 | −1.95322 | ||||||||
\(133\) | −2.79665 | −0.242501 | ||||||||
\(134\) | −27.8478 | −2.40568 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.04178 | −0.175081 | ||||||||
\(137\) | 17.8065 | 1.52132 | 0.760658 | − | 0.649153i | \(-0.224876\pi\) | ||||
0.760658 | + | 0.649153i | \(0.224876\pi\) | |||||||
\(138\) | −12.3507 | −1.05136 | ||||||||
\(139\) | −2.75800 | −0.233930 | −0.116965 | − | 0.993136i | \(-0.537317\pi\) | ||||
−0.116965 | + | 0.993136i | \(0.537317\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −32.1606 | −2.70841 | ||||||||
\(142\) | −7.16243 | −0.601058 | ||||||||
\(143\) | 11.5478 | 0.965673 | ||||||||
\(144\) | −31.9135 | −2.65946 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.52739 | 0.291929 | ||||||||
\(147\) | 17.8756 | 1.47436 | ||||||||
\(148\) | 20.8068 | 1.71031 | ||||||||
\(149\) | 14.2456 | 1.16705 | 0.583523 | − | 0.812096i | \(-0.301674\pi\) | ||||
0.583523 | + | 0.812096i | \(0.301674\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7800 | 0.877268 | 0.438634 | − | 0.898666i | \(-0.355462\pi\) | ||||
0.438634 | + | 0.898666i | \(0.355462\pi\) | |||||||
\(152\) | −0.670186 | −0.0543592 | ||||||||
\(153\) | −52.3861 | −4.23517 | ||||||||
\(154\) | −8.92728 | −0.719381 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −18.4669 | −1.47854 | ||||||||
\(157\) | −15.2762 | −1.21917 | −0.609585 | − | 0.792720i | \(-0.708664\pi\) | ||||
−0.609585 | + | 0.792720i | \(0.708664\pi\) | |||||||
\(158\) | 8.66564 | 0.689401 | ||||||||
\(159\) | −2.07863 | −0.164846 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.36208 | −0.186158 | ||||||||
\(162\) | −47.7738 | −3.75346 | ||||||||
\(163\) | −5.85982 | −0.458976 | −0.229488 | − | 0.973311i | \(-0.573705\pi\) | ||||
−0.229488 | + | 0.973311i | \(0.573705\pi\) | |||||||
\(164\) | −9.58396 | −0.748381 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.1678 | 1.25486 | ||||||||
\(167\) | −10.3799 | −0.803224 | −0.401612 | − | 0.915810i | \(-0.631550\pi\) | ||||
−0.401612 | + | 0.915810i | \(0.631550\pi\) | |||||||
\(168\) | −1.14311 | −0.0881925 | ||||||||
\(169\) | −3.49713 | −0.269010 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.1950 | −1.31493 | ||||||||
\(172\) | 4.05013 | 0.308819 | ||||||||
\(173\) | −9.47871 | −0.720653 | −0.360327 | − | 0.932826i | \(-0.617335\pi\) | ||||
−0.360327 | + | 0.932826i | \(0.617335\pi\) | |||||||
\(174\) | 37.1794 | 2.81856 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.0126 | −1.20699 | ||||||||
\(177\) | −38.3634 | −2.88357 | ||||||||
\(178\) | −12.8021 | −0.959555 | ||||||||
\(179\) | 1.41908 | 0.106067 | 0.0530336 | − | 0.998593i | \(-0.483111\pi\) | ||||
0.0530336 | + | 0.998593i | \(0.483111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.1630 | 1.72169 | 0.860844 | − | 0.508868i | \(-0.169936\pi\) | ||||
0.860844 | + | 0.508868i | \(0.169936\pi\) | |||||||
\(182\) | −7.34642 | −0.544553 | ||||||||
\(183\) | 24.6858 | 1.82482 | ||||||||
\(184\) | −0.566045 | −0.0417294 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −26.0528 | −1.91028 | ||||||||
\(187\) | −26.2847 | −1.92213 | ||||||||
\(188\) | 18.4083 | 1.34256 | ||||||||
\(189\) | −17.5437 | −1.27612 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.3255 | 1.32599 | 0.662995 | − | 0.748624i | \(-0.269285\pi\) | ||||
0.662995 | + | 0.748624i | \(0.269285\pi\) | |||||||
\(192\) | 21.9119 | 1.58135 | ||||||||
\(193\) | 13.0035 | 0.936011 | 0.468005 | − | 0.883726i | \(-0.344973\pi\) | ||||
0.468005 | + | 0.883726i | \(0.344973\pi\) | |||||||
\(194\) | 2.28085 | 0.163755 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.2318 | −0.730841 | ||||||||
\(197\) | 13.3246 | 0.949339 | 0.474669 | − | 0.880164i | \(-0.342568\pi\) | ||||
0.474669 | + | 0.880164i | \(0.342568\pi\) | |||||||
\(198\) | −54.8887 | −3.90077 | ||||||||
\(199\) | 19.9295 | 1.41276 | 0.706381 | − | 0.707832i | \(-0.250327\pi\) | ||||
0.706381 | + | 0.707832i | \(0.250327\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −45.9041 | −3.23783 | ||||||||
\(202\) | 26.1566 | 1.84037 | ||||||||
\(203\) | 7.11058 | 0.499065 | ||||||||
\(204\) | 42.0339 | 2.94296 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.2168 | 0.711839 | ||||||||
\(207\) | −14.5231 | −1.00942 | ||||||||
\(208\) | −13.1770 | −0.913664 | ||||||||
\(209\) | −8.62758 | −0.596782 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9483 | −1.09793 | −0.548963 | − | 0.835847i | \(-0.684977\pi\) | ||||
−0.548963 | + | 0.835847i | \(0.684977\pi\) | |||||||
\(212\) | 1.18978 | 0.0817143 | ||||||||
\(213\) | −11.8065 | −0.808968 | ||||||||
\(214\) | −29.0740 | −1.98746 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.20415 | −0.286056 | ||||||||
\(217\) | −4.98262 | −0.338242 | ||||||||
\(218\) | −6.82319 | −0.462124 | ||||||||
\(219\) | 5.81453 | 0.392909 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.6302 | −1.45500 | ||||||||
\(222\) | 71.3419 | 4.78816 | ||||||||
\(223\) | 13.0628 | 0.874749 | 0.437375 | − | 0.899279i | \(-0.355908\pi\) | ||||
0.437375 | + | 0.899279i | \(0.355908\pi\) | |||||||
\(224\) | 9.48014 | 0.633419 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 32.7900 | 2.18116 | ||||||||
\(227\) | −2.03254 | −0.134904 | −0.0674521 | − | 0.997723i | \(-0.521487\pi\) | ||||
−0.0674521 | + | 0.997723i | \(0.521487\pi\) | |||||||
\(228\) | 13.7970 | 0.913730 | ||||||||
\(229\) | 28.9057 | 1.91014 | 0.955071 | − | 0.296378i | \(-0.0957787\pi\) | ||||
0.955071 | + | 0.296378i | \(0.0957787\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.7157 | −0.968220 | ||||||||
\(232\) | 1.70397 | 0.111871 | ||||||||
\(233\) | −17.8688 | −1.17063 | −0.585313 | − | 0.810807i | \(-0.699028\pi\) | ||||
−0.585313 | + | 0.810807i | \(0.699028\pi\) | |||||||
\(234\) | −45.1689 | −2.95278 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 21.9587 | 1.42939 | ||||||||
\(237\) | 14.2844 | 0.927870 | ||||||||
\(238\) | 16.7217 | 1.08391 | ||||||||
\(239\) | 7.36076 | 0.476128 | 0.238064 | − | 0.971249i | \(-0.423487\pi\) | ||||
0.238064 | + | 0.971249i | \(0.423487\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −5.95195 | −0.382606 | ||||||||
\(243\) | −35.4067 | −2.27134 | ||||||||
\(244\) | −14.1298 | −0.904567 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −32.8612 | −2.09516 | ||||||||
\(247\) | −7.09979 | −0.451749 | ||||||||
\(248\) | −1.19403 | −0.0758208 | ||||||||
\(249\) | 26.6508 | 1.68893 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.59780 | −0.227091 | −0.113545 | − | 0.993533i | \(-0.536221\pi\) | ||||
−0.113545 | + | 0.993533i | \(0.536221\pi\) | |||||||
\(252\) | 16.7874 | 1.05750 | ||||||||
\(253\) | −7.28694 | −0.458126 | ||||||||
\(254\) | 21.5525 | 1.35232 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.1025 | 1.13140 | ||||||||
\(257\) | 15.9228 | 0.993236 | 0.496618 | − | 0.867969i | \(-0.334575\pi\) | ||||
0.496618 | + | 0.867969i | \(0.334575\pi\) | |||||||
\(258\) | 13.8870 | 0.864565 | ||||||||
\(259\) | 13.6442 | 0.847810 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 43.7189 | 2.70613 | ||||||||
\(262\) | −22.2295 | −1.37334 | ||||||||
\(263\) | 23.4695 | 1.44719 | 0.723595 | − | 0.690224i | \(-0.242488\pi\) | ||||
0.723595 | + | 0.690224i | \(0.242488\pi\) | |||||||
\(264\) | −3.52644 | −0.217037 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.48866 | 0.336532 | ||||||||
\(267\) | −21.1028 | −1.29147 | ||||||||
\(268\) | 26.2749 | 1.60499 | ||||||||
\(269\) | 14.7420 | 0.898837 | 0.449419 | − | 0.893321i | \(-0.351631\pi\) | ||||
0.449419 | + | 0.893321i | \(0.351631\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3518 | −1.23628 | −0.618141 | − | 0.786067i | \(-0.712114\pi\) | ||||
−0.618141 | + | 0.786067i | \(0.712114\pi\) | |||||||
\(272\) | 29.9932 | 1.81861 | ||||||||
\(273\) | −12.1098 | −0.732918 | ||||||||
\(274\) | −34.9468 | −2.11121 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.6531 | 0.701434 | ||||||||
\(277\) | −23.6076 | −1.41845 | −0.709223 | − | 0.704984i | \(-0.750954\pi\) | ||||
−0.709223 | + | 0.704984i | \(0.750954\pi\) | |||||||
\(278\) | 5.41280 | 0.324638 | ||||||||
\(279\) | −30.6352 | −1.83408 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.8608 | −1.84100 | −0.920502 | − | 0.390739i | \(-0.872220\pi\) | ||||
−0.920502 | + | 0.390739i | \(0.872220\pi\) | |||||||
\(282\) | 63.1178 | 3.75861 | ||||||||
\(283\) | −5.04636 | −0.299975 | −0.149987 | − | 0.988688i | \(-0.547923\pi\) | ||||
−0.149987 | + | 0.988688i | \(0.547923\pi\) | |||||||
\(284\) | 6.75788 | 0.401006 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.6635 | −1.34012 | ||||||||
\(287\) | −6.28474 | −0.370976 | ||||||||
\(288\) | 58.2879 | 3.43465 | ||||||||
\(289\) | 32.2339 | 1.89611 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.75973 | 0.220399 | ||||||||
\(292\) | −3.32816 | −0.194766 | ||||||||
\(293\) | −20.3712 | −1.19010 | −0.595050 | − | 0.803689i | \(-0.702868\pi\) | ||||
−0.595050 | + | 0.803689i | \(0.702868\pi\) | |||||||
\(294\) | −35.0824 | −2.04605 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.26968 | 0.190046 | ||||||||
\(297\) | −54.1217 | −3.14046 | ||||||||
\(298\) | −27.9582 | −1.61958 | ||||||||
\(299\) | −5.99655 | −0.346790 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.65590 | 0.153083 | ||||||||
\(302\) | −21.1567 | −1.21743 | ||||||||
\(303\) | 43.1164 | 2.47697 | ||||||||
\(304\) | 9.84485 | 0.564641 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 102.812 | 5.87738 | ||||||||
\(307\) | −16.8145 | −0.959655 | −0.479827 | − | 0.877363i | \(-0.659301\pi\) | ||||
−0.479827 | + | 0.877363i | \(0.659301\pi\) | |||||||
\(308\) | 8.42305 | 0.479948 | ||||||||
\(309\) | 16.8413 | 0.958070 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.455317 | 0.0258186 | 0.0129093 | − | 0.999917i | \(-0.495891\pi\) | ||||
0.0129093 | + | 0.999917i | \(0.495891\pi\) | |||||||
\(312\) | −2.90197 | −0.164292 | ||||||||
\(313\) | 22.8759 | 1.29302 | 0.646511 | − | 0.762904i | \(-0.276227\pi\) | ||||
0.646511 | + | 0.762904i | \(0.276227\pi\) | |||||||
\(314\) | 29.9807 | 1.69191 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.17618 | −0.459946 | ||||||||
\(317\) | −13.4104 | −0.753206 | −0.376603 | − | 0.926375i | \(-0.622908\pi\) | ||||
−0.376603 | + | 0.926375i | \(0.622908\pi\) | |||||||
\(318\) | 4.07948 | 0.228766 | ||||||||
\(319\) | 21.9359 | 1.22818 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −47.9254 | −2.67493 | ||||||||
\(322\) | 4.63578 | 0.258342 | ||||||||
\(323\) | 16.1603 | 0.899186 | ||||||||
\(324\) | 45.0754 | 2.50419 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.5004 | 0.636947 | ||||||||
\(327\) | −11.2473 | −0.621977 | ||||||||
\(328\) | −1.50607 | −0.0831585 | ||||||||
\(329\) | 12.0713 | 0.665515 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.745486 | 0.0409756 | 0.0204878 | − | 0.999790i | \(-0.493478\pi\) | ||||
0.0204878 | + | 0.999790i | \(0.493478\pi\) | |||||||
\(332\) | −15.2546 | −0.837203 | ||||||||
\(333\) | 83.8903 | 4.59716 | ||||||||
\(334\) | 20.3715 | 1.11468 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 16.7919 | 0.916074 | ||||||||
\(337\) | 13.0103 | 0.708714 | 0.354357 | − | 0.935110i | \(-0.384700\pi\) | ||||
0.354357 | + | 0.935110i | \(0.384700\pi\) | |||||||
\(338\) | 6.86341 | 0.373320 | ||||||||
\(339\) | 54.0508 | 2.93564 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.3712 | −0.832398 | ||||||||
\(342\) | 33.7466 | 1.82481 | ||||||||
\(343\) | −15.2095 | −0.821238 | ||||||||
\(344\) | 0.636455 | 0.0343154 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.6028 | 1.00009 | ||||||||
\(347\) | 4.20211 | 0.225581 | 0.112791 | − | 0.993619i | \(-0.464021\pi\) | ||||
0.112791 | + | 0.993619i | \(0.464021\pi\) | |||||||
\(348\) | −35.0794 | −1.88045 | ||||||||
\(349\) | −30.6653 | −1.64147 | −0.820737 | − | 0.571306i | \(-0.806437\pi\) | ||||
−0.820737 | + | 0.571306i | \(0.806437\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −44.5377 | −2.37725 | ||||||||
\(352\) | 29.2459 | 1.55881 | ||||||||
\(353\) | −15.1231 | −0.804919 | −0.402460 | − | 0.915438i | \(-0.631845\pi\) | ||||
−0.402460 | + | 0.915438i | \(0.631845\pi\) | |||||||
\(354\) | 75.2913 | 4.00169 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.0790 | 0.640184 | ||||||||
\(357\) | 27.5640 | 1.45884 | ||||||||
\(358\) | −2.78507 | −0.147195 | ||||||||
\(359\) | 6.66336 | 0.351679 | 0.175839 | − | 0.984419i | \(-0.443736\pi\) | ||||
0.175839 | + | 0.984419i | \(0.443736\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.6956 | −0.720821 | ||||||||
\(362\) | −45.4592 | −2.38928 | ||||||||
\(363\) | −9.81116 | −0.514952 | ||||||||
\(364\) | 6.93148 | 0.363308 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −48.4478 | −2.53241 | ||||||||
\(367\) | 23.4363 | 1.22337 | 0.611684 | − | 0.791102i | \(-0.290493\pi\) | ||||
0.611684 | + | 0.791102i | \(0.290493\pi\) | |||||||
\(368\) | 8.31505 | 0.433452 | ||||||||
\(369\) | −38.6412 | −2.01158 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.780204 | 0.0405062 | ||||||||
\(372\) | 24.5813 | 1.27448 | ||||||||
\(373\) | −3.50768 | −0.181621 | −0.0908104 | − | 0.995868i | \(-0.528946\pi\) | ||||
−0.0908104 | + | 0.995868i | \(0.528946\pi\) | |||||||
\(374\) | 51.5859 | 2.66744 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.89276 | 0.149183 | ||||||||
\(377\) | 18.0515 | 0.929698 | ||||||||
\(378\) | 34.4310 | 1.77094 | ||||||||
\(379\) | −27.5949 | −1.41745 | −0.708727 | − | 0.705482i | \(-0.750730\pi\) | ||||
−0.708727 | + | 0.705482i | \(0.750730\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.5270 | 1.82010 | ||||||||
\(382\) | −35.9654 | −1.84015 | ||||||||
\(383\) | 12.1641 | 0.621556 | 0.310778 | − | 0.950483i | \(-0.399410\pi\) | ||||
0.310778 | + | 0.950483i | \(0.399410\pi\) | |||||||
\(384\) | 7.51036 | 0.383261 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.5204 | −1.29895 | ||||||||
\(387\) | 16.3296 | 0.830078 | ||||||||
\(388\) | −2.15202 | −0.109252 | ||||||||
\(389\) | −4.54451 | −0.230416 | −0.115208 | − | 0.993341i | \(-0.536753\pi\) | ||||
−0.115208 | + | 0.993341i | \(0.536753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.6492 | 0.690269 | ||||||||
\(392\) | −1.60787 | −0.0812095 | ||||||||
\(393\) | −36.6430 | −1.84839 | ||||||||
\(394\) | −26.1506 | −1.31745 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 51.7884 | 2.60247 | ||||||||
\(397\) | −21.6534 | −1.08675 | −0.543377 | − | 0.839489i | \(-0.682855\pi\) | ||||
−0.543377 | + | 0.839489i | \(0.682855\pi\) | |||||||
\(398\) | −39.1132 | −1.96057 | ||||||||
\(399\) | 9.04748 | 0.452940 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.9808 | 0.947857 | 0.473928 | − | 0.880563i | \(-0.342836\pi\) | ||||
0.473928 | + | 0.880563i | \(0.342836\pi\) | |||||||
\(402\) | 90.0907 | 4.49331 | ||||||||
\(403\) | −12.6492 | −0.630104 | ||||||||
\(404\) | −24.6792 | −1.22784 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.9551 | −0.692581 | ||||||||
\(407\) | 42.0919 | 2.08642 | ||||||||
\(408\) | 6.60538 | 0.327015 | ||||||||
\(409\) | −36.0879 | −1.78443 | −0.892216 | − | 0.451609i | \(-0.850850\pi\) | ||||
−0.892216 | + | 0.451609i | \(0.850850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −57.6061 | −2.84150 | ||||||||
\(412\) | −9.63975 | −0.474916 | ||||||||
\(413\) | 14.3995 | 0.708555 | ||||||||
\(414\) | 28.5027 | 1.40083 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 24.0670 | 1.17998 | ||||||||
\(417\) | 8.92242 | 0.436933 | ||||||||
\(418\) | 16.9323 | 0.828188 | ||||||||
\(419\) | 3.42426 | 0.167286 | 0.0836431 | − | 0.996496i | \(-0.473344\pi\) | ||||
0.0836431 | + | 0.996496i | \(0.473344\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.8400 | −1.45431 | −0.727156 | − | 0.686473i | \(-0.759158\pi\) | ||||
−0.727156 | + | 0.686473i | \(0.759158\pi\) | |||||||
\(422\) | 31.2998 | 1.52365 | ||||||||
\(423\) | 74.2197 | 3.60868 | ||||||||
\(424\) | 0.186967 | 0.00907992 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 23.1712 | 1.12265 | ||||||||
\(427\) | −9.26569 | −0.448398 | ||||||||
\(428\) | 27.4318 | 1.32597 | ||||||||
\(429\) | −37.3583 | −1.80368 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.8468 | −0.859650 | −0.429825 | − | 0.902912i | \(-0.641425\pi\) | ||||
−0.429825 | + | 0.902912i | \(0.641425\pi\) | |||||||
\(432\) | 61.7578 | 2.97132 | ||||||||
\(433\) | −25.4504 | −1.22307 | −0.611533 | − | 0.791219i | \(-0.709447\pi\) | ||||
−0.611533 | + | 0.791219i | \(0.709447\pi\) | |||||||
\(434\) | 9.77880 | 0.469397 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.43780 | 0.308315 | ||||||||
\(437\) | 4.48015 | 0.214315 | ||||||||
\(438\) | −11.4115 | −0.545262 | ||||||||
\(439\) | −35.8325 | −1.71019 | −0.855096 | − | 0.518469i | \(-0.826502\pi\) | ||||
−0.855096 | + | 0.518469i | \(0.826502\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −41.2531 | −1.96443 | ||||||||
\(442\) | 42.4510 | 2.01919 | ||||||||
\(443\) | 25.3602 | 1.20490 | 0.602450 | − | 0.798157i | \(-0.294191\pi\) | ||||
0.602450 | + | 0.798157i | \(0.294191\pi\) | |||||||
\(444\) | −67.3124 | −3.19450 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −25.6368 | −1.21394 | ||||||||
\(447\) | −46.0861 | −2.17980 | ||||||||
\(448\) | −8.22452 | −0.388572 | ||||||||
\(449\) | 9.57805 | 0.452016 | 0.226008 | − | 0.974125i | \(-0.427432\pi\) | ||||
0.226008 | + | 0.974125i | \(0.427432\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.3882 | −0.912955 | ||||||||
\(452\) | −30.9379 | −1.45520 | ||||||||
\(453\) | −34.8746 | −1.63855 | ||||||||
\(454\) | 3.98902 | 0.187214 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.16812 | 0.101532 | ||||||||
\(457\) | −19.4654 | −0.910554 | −0.455277 | − | 0.890350i | \(-0.650460\pi\) | ||||
−0.455277 | + | 0.890350i | \(0.650460\pi\) | |||||||
\(458\) | −56.7298 | −2.65081 | ||||||||
\(459\) | 101.376 | 4.73180 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.2477 | 0.523859 | 0.261930 | − | 0.965087i | \(-0.415641\pi\) | ||||
0.261930 | + | 0.965087i | \(0.415641\pi\) | |||||||
\(462\) | 28.8807 | 1.34365 | ||||||||
\(463\) | −11.8561 | −0.550999 | −0.275499 | − | 0.961301i | \(-0.588843\pi\) | ||||
−0.275499 | + | 0.961301i | \(0.588843\pi\) | |||||||
\(464\) | −25.0309 | −1.16203 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 35.0691 | 1.62454 | ||||||||
\(467\) | −22.5284 | −1.04249 | −0.521244 | − | 0.853408i | \(-0.674532\pi\) | ||||
−0.521244 | + | 0.853408i | \(0.674532\pi\) | |||||||
\(468\) | 42.6176 | 1.97000 | ||||||||
\(469\) | 17.2299 | 0.795604 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 49.4201 | 2.27716 | ||||||||
\(472\) | 3.45068 | 0.158831 | ||||||||
\(473\) | 8.19335 | 0.376731 | ||||||||
\(474\) | −28.0343 | −1.28766 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15.7772 | −0.723148 | ||||||||
\(477\) | 4.79702 | 0.219641 | ||||||||
\(478\) | −14.4461 | −0.660749 | ||||||||
\(479\) | 15.4805 | 0.707323 | 0.353662 | − | 0.935373i | \(-0.384936\pi\) | ||||
0.353662 | + | 0.935373i | \(0.384936\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.6382 | 1.57937 | ||||||||
\(482\) | −1.96258 | −0.0893932 | ||||||||
\(483\) | 7.64159 | 0.347704 | ||||||||
\(484\) | 5.61577 | 0.255262 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 69.4886 | 3.15207 | ||||||||
\(487\) | 32.2226 | 1.46015 | 0.730073 | − | 0.683370i | \(-0.239486\pi\) | ||||
0.730073 | + | 0.683370i | \(0.239486\pi\) | |||||||
\(488\) | −2.22042 | −0.100514 | ||||||||
\(489\) | 18.9571 | 0.857272 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.45290 | −0.426603 | −0.213302 | − | 0.976986i | \(-0.568422\pi\) | ||||
−0.213302 | + | 0.976986i | \(0.568422\pi\) | |||||||
\(492\) | 31.0051 | 1.39782 | ||||||||
\(493\) | −41.0882 | −1.85052 | ||||||||
\(494\) | 13.9339 | 0.626917 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.5399 | 0.787566 | ||||||||
\(497\) | 4.43152 | 0.198781 | ||||||||
\(498\) | −52.3045 | −2.34382 | ||||||||
\(499\) | 11.4148 | 0.510997 | 0.255498 | − | 0.966810i | \(-0.417760\pi\) | ||||
0.255498 | + | 0.966810i | \(0.417760\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.5802 | 1.50025 | ||||||||
\(502\) | 7.06098 | 0.315147 | ||||||||
\(503\) | 7.49525 | 0.334197 | 0.167098 | − | 0.985940i | \(-0.446560\pi\) | ||||
0.167098 | + | 0.985940i | \(0.446560\pi\) | |||||||
\(504\) | 2.63804 | 0.117508 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 14.3012 | 0.635767 | ||||||||
\(507\) | 11.3136 | 0.502455 | ||||||||
\(508\) | −20.3351 | −0.902226 | ||||||||
\(509\) | −15.9234 | −0.705791 | −0.352896 | − | 0.935663i | \(-0.614803\pi\) | ||||
−0.352896 | + | 0.935663i | \(0.614803\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.18246 | −0.0965463 | ||||||||
\(512\) | −30.8845 | −1.36492 | ||||||||
\(513\) | 33.2751 | 1.46913 | ||||||||
\(514\) | −31.2498 | −1.37837 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −13.1026 | −0.576810 | ||||||||
\(517\) | 37.2397 | 1.63780 | ||||||||
\(518\) | −26.7779 | −1.17655 | ||||||||
\(519\) | 30.6647 | 1.34603 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.84451 | 0.387485 | 0.193743 | − | 0.981052i | \(-0.437937\pi\) | ||||
0.193743 | + | 0.981052i | \(0.437937\pi\) | |||||||
\(522\) | −85.8019 | −3.75545 | ||||||||
\(523\) | 11.5432 | 0.504748 | 0.252374 | − | 0.967630i | \(-0.418789\pi\) | ||||
0.252374 | + | 0.967630i | \(0.418789\pi\) | |||||||
\(524\) | 20.9739 | 0.916250 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −46.0608 | −2.00835 | ||||||||
\(527\) | 28.7918 | 1.25419 | ||||||||
\(528\) | 51.8025 | 2.25441 | ||||||||
\(529\) | −19.2160 | −0.835479 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 88.5344 | 3.84206 | ||||||||
\(532\) | −5.17865 | −0.224523 | ||||||||
\(533\) | −15.9549 | −0.691084 | ||||||||
\(534\) | 41.4161 | 1.79225 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.12895 | 0.178344 | ||||||||
\(537\) | −4.59089 | −0.198111 | ||||||||
\(538\) | −28.9325 | −1.24737 | ||||||||
\(539\) | −20.6987 | −0.891557 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.15787 | 0.307741 | 0.153871 | − | 0.988091i | \(-0.450826\pi\) | ||||
0.153871 | + | 0.988091i | \(0.450826\pi\) | |||||||
\(542\) | 39.9420 | 1.71566 | ||||||||
\(543\) | −74.9347 | −3.21575 | ||||||||
\(544\) | −54.7806 | −2.34870 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 23.7665 | 1.01711 | ||||||||
\(547\) | 14.4508 | 0.617871 | 0.308935 | − | 0.951083i | \(-0.400027\pi\) | ||||
0.308935 | + | 0.951083i | \(0.400027\pi\) | |||||||
\(548\) | 32.9729 | 1.40853 | ||||||||
\(549\) | −56.9694 | −2.43139 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.4866 | −0.574550 | ||||||||
\(552\) | 1.83122 | 0.0779418 | ||||||||
\(553\) | −5.36158 | −0.227998 | ||||||||
\(554\) | 46.3319 | 1.96846 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.10707 | −0.216588 | ||||||||
\(557\) | 24.3566 | 1.03202 | 0.516011 | − | 0.856582i | \(-0.327416\pi\) | ||||
0.516011 | + | 0.856582i | \(0.327416\pi\) | |||||||
\(558\) | 60.1242 | 2.54526 | ||||||||
\(559\) | 6.74246 | 0.285176 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 85.0339 | 3.59013 | ||||||||
\(562\) | 60.5670 | 2.55486 | ||||||||
\(563\) | 7.51196 | 0.316592 | 0.158296 | − | 0.987392i | \(-0.449400\pi\) | ||||
0.158296 | + | 0.987392i | \(0.449400\pi\) | |||||||
\(564\) | −59.5528 | −2.50762 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.90390 | 0.416292 | ||||||||
\(567\) | 29.5585 | 1.24134 | ||||||||
\(568\) | 1.06196 | 0.0445590 | ||||||||
\(569\) | 9.01349 | 0.377865 | 0.188933 | − | 0.981990i | \(-0.439497\pi\) | ||||
0.188933 | + | 0.981990i | \(0.439497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.8260 | 0.913388 | 0.456694 | − | 0.889624i | \(-0.349033\pi\) | ||||
0.456694 | + | 0.889624i | \(0.349033\pi\) | |||||||
\(572\) | 21.3834 | 0.894084 | ||||||||
\(573\) | −59.2851 | −2.47667 | ||||||||
\(574\) | 12.3343 | 0.514825 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −50.5678 | −2.10699 | ||||||||
\(577\) | 26.7528 | 1.11373 | 0.556866 | − | 0.830602i | \(-0.312004\pi\) | ||||
0.556866 | + | 0.830602i | \(0.312004\pi\) | |||||||
\(578\) | −63.2618 | −2.63134 | ||||||||
\(579\) | −42.0677 | −1.74827 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.0033 | −0.415006 | ||||||||
\(582\) | −7.37879 | −0.305861 | ||||||||
\(583\) | 2.40690 | 0.0996837 | ||||||||
\(584\) | −0.523001 | −0.0216419 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 39.9802 | 1.65157 | ||||||||
\(587\) | 39.1291 | 1.61503 | 0.807516 | − | 0.589846i | \(-0.200811\pi\) | ||||
0.807516 | + | 0.589846i | \(0.200811\pi\) | |||||||
\(588\) | 33.1009 | 1.36506 | ||||||||
\(589\) | 9.45051 | 0.389402 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −43.1065 | −1.77317 | ||||||||
\(592\) | −48.0307 | −1.97405 | ||||||||
\(593\) | 4.23212 | 0.173792 | 0.0868961 | − | 0.996217i | \(-0.472305\pi\) | ||||
0.0868961 | + | 0.996217i | \(0.472305\pi\) | |||||||
\(594\) | 106.218 | 4.35819 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 26.3791 | 1.08053 | ||||||||
\(597\) | −64.4740 | −2.63874 | ||||||||
\(598\) | 11.7687 | 0.481259 | ||||||||
\(599\) | 28.1905 | 1.15183 | 0.575916 | − | 0.817509i | \(-0.304645\pi\) | ||||
0.575916 | + | 0.817509i | \(0.304645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.8977 | −1.46430 | −0.732149 | − | 0.681144i | \(-0.761483\pi\) | ||||
−0.732149 | + | 0.681144i | \(0.761483\pi\) | |||||||
\(602\) | −5.21242 | −0.212442 | ||||||||
\(603\) | 105.937 | 4.31408 | ||||||||
\(604\) | 19.9618 | 0.812232 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −84.6195 | −3.43743 | ||||||||
\(607\) | −6.86493 | −0.278639 | −0.139319 | − | 0.990247i | \(-0.544491\pi\) | ||||
−0.139319 | + | 0.990247i | \(0.544491\pi\) | |||||||
\(608\) | −17.9810 | −0.729224 | ||||||||
\(609\) | −23.0035 | −0.932150 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.6452 | 1.23977 | ||||||||
\(612\) | −97.0050 | −3.92120 | ||||||||
\(613\) | −35.8712 | −1.44883 | −0.724413 | − | 0.689367i | \(-0.757889\pi\) | ||||
−0.724413 | + | 0.689367i | \(0.757889\pi\) | |||||||
\(614\) | 32.9999 | 1.33177 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.32363 | 0.0533308 | ||||||||
\(617\) | −10.4210 | −0.419534 | −0.209767 | − | 0.977751i | \(-0.567271\pi\) | ||||
−0.209767 | + | 0.977751i | \(0.567271\pi\) | |||||||
\(618\) | −33.0525 | −1.32957 | ||||||||
\(619\) | 34.6351 | 1.39210 | 0.696051 | − | 0.717993i | \(-0.254939\pi\) | ||||
0.696051 | + | 0.717993i | \(0.254939\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.1044 | 1.12779 | ||||||||
\(622\) | −0.893597 | −0.0358300 | ||||||||
\(623\) | 7.92086 | 0.317343 | ||||||||
\(624\) | 42.6292 | 1.70653 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −44.8959 | −1.79440 | ||||||||
\(627\) | 27.9112 | 1.11466 | ||||||||
\(628\) | −28.2874 | −1.12879 | ||||||||
\(629\) | −78.8425 | −3.14365 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.20201 | −0.326517 | −0.163258 | − | 0.986583i | \(-0.552200\pi\) | ||||
−0.163258 | + | 0.986583i | \(0.552200\pi\) | |||||||
\(632\) | −1.28484 | −0.0511082 | ||||||||
\(633\) | 51.5945 | 2.05070 | ||||||||
\(634\) | 26.3191 | 1.04527 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.84906 | −0.152625 | ||||||||
\(637\) | −17.0333 | −0.674886 | ||||||||
\(638\) | −43.0511 | −1.70441 | ||||||||
\(639\) | 27.2468 | 1.07787 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.5973 | 1.16902 | 0.584511 | − | 0.811386i | \(-0.301286\pi\) | ||||
0.584511 | + | 0.811386i | \(0.301286\pi\) | |||||||
\(642\) | 94.0575 | 3.71215 | ||||||||
\(643\) | 19.1406 | 0.754831 | 0.377416 | − | 0.926044i | \(-0.376813\pi\) | ||||
0.377416 | + | 0.926044i | \(0.376813\pi\) | |||||||
\(644\) | −4.37394 | −0.172357 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.7160 | −1.24785 | ||||||||
\(647\) | −11.2382 | −0.441819 | −0.220910 | − | 0.975294i | \(-0.570903\pi\) | ||||
−0.220910 | + | 0.975294i | \(0.570903\pi\) | |||||||
\(648\) | 7.08335 | 0.278260 | ||||||||
\(649\) | 44.4221 | 1.74372 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.1193 | 0.631765 | ||||||||
\(652\) | −10.8508 | −0.424950 | ||||||||
\(653\) | 9.74451 | 0.381332 | 0.190666 | − | 0.981655i | \(-0.438935\pi\) | ||||
0.190666 | + | 0.981655i | \(0.438935\pi\) | |||||||
\(654\) | 22.0738 | 0.863152 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 22.1237 | 0.863785 | ||||||||
\(657\) | −13.4187 | −0.523512 | ||||||||
\(658\) | −23.6910 | −0.923572 | ||||||||
\(659\) | 25.5113 | 0.993779 | 0.496890 | − | 0.867814i | \(-0.334475\pi\) | ||||
0.496890 | + | 0.867814i | \(0.334475\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.6125 | 0.646151 | 0.323076 | − | 0.946373i | \(-0.395283\pi\) | ||||
0.323076 | + | 0.946373i | \(0.395283\pi\) | |||||||
\(662\) | −1.46308 | −0.0568641 | ||||||||
\(663\) | 69.9759 | 2.71764 | ||||||||
\(664\) | −2.39717 | −0.0930282 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −164.642 | −6.37973 | ||||||||
\(667\) | −11.3909 | −0.441059 | ||||||||
\(668\) | −19.2209 | −0.743678 | ||||||||
\(669\) | −42.2596 | −1.63385 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.5843 | −1.10349 | ||||||||
\(672\) | −30.6693 | −1.18309 | ||||||||
\(673\) | 38.3964 | 1.48007 | 0.740035 | − | 0.672568i | \(-0.234809\pi\) | ||||
0.740035 | + | 0.672568i | \(0.234809\pi\) | |||||||
\(674\) | −25.5337 | −0.983522 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.47575 | −0.249067 | ||||||||
\(677\) | −16.2559 | −0.624766 | −0.312383 | − | 0.949956i | \(-0.601127\pi\) | ||||
−0.312383 | + | 0.949956i | \(0.601127\pi\) | |||||||
\(678\) | −106.079 | −4.07395 | ||||||||
\(679\) | −1.41120 | −0.0541569 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.57547 | 0.251973 | ||||||||
\(682\) | 30.1673 | 1.15516 | ||||||||
\(683\) | 1.61455 | 0.0617790 | 0.0308895 | − | 0.999523i | \(-0.490166\pi\) | ||||
0.0308895 | + | 0.999523i | \(0.490166\pi\) | |||||||
\(684\) | −31.8405 | −1.21745 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 29.8500 | 1.13968 | ||||||||
\(687\) | −93.5130 | −3.56775 | ||||||||
\(688\) | −9.34935 | −0.356441 | ||||||||
\(689\) | 1.98068 | 0.0754580 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.6842 | 1.73791 | 0.868954 | − | 0.494892i | \(-0.164792\pi\) | ||||
0.868954 | + | 0.494892i | \(0.164792\pi\) | |||||||
\(692\) | −17.5520 | −0.667228 | ||||||||
\(693\) | 33.9606 | 1.29006 | ||||||||
\(694\) | −8.24700 | −0.313052 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.51253 | −0.208952 | ||||||||
\(697\) | 36.3161 | 1.37557 | ||||||||
\(698\) | 60.1831 | 2.27797 | ||||||||
\(699\) | 57.8076 | 2.18648 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.16904 | −0.308540 | −0.154270 | − | 0.988029i | \(-0.549303\pi\) | ||||
−0.154270 | + | 0.988029i | \(0.549303\pi\) | |||||||
\(702\) | 87.4090 | 3.29904 | ||||||||
\(703\) | −25.8789 | −0.976042 | ||||||||
\(704\) | −25.3724 | −0.956257 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.6803 | 1.11703 | ||||||||
\(707\) | −16.1836 | −0.608645 | ||||||||
\(708\) | −71.0387 | −2.66980 | ||||||||
\(709\) | 26.7104 | 1.00313 | 0.501565 | − | 0.865120i | \(-0.332758\pi\) | ||||
0.501565 | + | 0.865120i | \(0.332758\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −32.9652 | −1.23629 | ||||||||
\(712\) | 1.89814 | 0.0711359 | ||||||||
\(713\) | 7.98199 | 0.298928 | ||||||||
\(714\) | −54.0965 | −2.02451 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.62776 | 0.0982040 | ||||||||
\(717\) | −23.8129 | −0.889307 | ||||||||
\(718\) | −13.0774 | −0.488044 | ||||||||
\(719\) | 33.8315 | 1.26170 | 0.630850 | − | 0.775905i | \(-0.282706\pi\) | ||||
0.630850 | + | 0.775905i | \(0.282706\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.32132 | −0.235418 | ||||||||
\(722\) | 26.8787 | 1.00032 | ||||||||
\(723\) | −3.23511 | −0.120315 | ||||||||
\(724\) | 42.8916 | 1.59405 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 19.2552 | 0.714628 | ||||||||
\(727\) | 17.2402 | 0.639402 | 0.319701 | − | 0.947518i | \(-0.396417\pi\) | ||||
0.319701 | + | 0.947518i | \(0.396417\pi\) | |||||||
\(728\) | 1.08924 | 0.0403700 | ||||||||
\(729\) | 41.5177 | 1.53769 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.3470 | −0.567629 | ||||||||
\(732\) | 45.7114 | 1.68954 | ||||||||
\(733\) | 21.9745 | 0.811647 | 0.405824 | − | 0.913951i | \(-0.366985\pi\) | ||||
0.405824 | + | 0.913951i | \(0.366985\pi\) | |||||||
\(734\) | −45.9958 | −1.69774 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.1869 | −0.559796 | ||||||||
\(737\) | 53.1537 | 1.95794 | ||||||||
\(738\) | 75.8366 | 2.79158 | ||||||||
\(739\) | −30.0201 | −1.10431 | −0.552154 | − | 0.833742i | \(-0.686194\pi\) | ||||
−0.552154 | + | 0.833742i | \(0.686194\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.9686 | 0.843773 | ||||||||
\(742\) | −1.53121 | −0.0562127 | ||||||||
\(743\) | −22.4069 | −0.822028 | −0.411014 | − | 0.911629i | \(-0.634825\pi\) | ||||
−0.411014 | + | 0.911629i | \(0.634825\pi\) | |||||||
\(744\) | 3.86281 | 0.141617 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.88411 | 0.252045 | ||||||||
\(747\) | −61.5043 | −2.25033 | ||||||||
\(748\) | −48.6722 | −1.77963 | ||||||||
\(749\) | 17.9886 | 0.657288 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.9661 | 1.56786 | 0.783928 | − | 0.620851i | \(-0.213213\pi\) | ||||
0.783928 | + | 0.620851i | \(0.213213\pi\) | |||||||
\(752\) | −42.4938 | −1.54959 | ||||||||
\(753\) | 11.6393 | 0.424158 | ||||||||
\(754\) | −35.4275 | −1.29019 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −32.4862 | −1.18151 | ||||||||
\(757\) | −8.52285 | −0.309768 | −0.154884 | − | 0.987933i | \(-0.549500\pi\) | ||||
−0.154884 | + | 0.987933i | \(0.549500\pi\) | |||||||
\(758\) | 54.1573 | 1.96708 | ||||||||
\(759\) | 23.5740 | 0.855683 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 53.7209 | 1.94738 | 0.973690 | − | 0.227875i | \(-0.0731779\pi\) | ||||
0.973690 | + | 0.227875i | \(0.0731779\pi\) | |||||||
\(762\) | −69.7246 | −2.52586 | ||||||||
\(763\) | 4.22162 | 0.152833 | ||||||||
\(764\) | 33.9340 | 1.22769 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.8730 | −0.862568 | ||||||||
\(767\) | 36.5557 | 1.31995 | ||||||||
\(768\) | −58.5634 | −2.11323 | ||||||||
\(769\) | 31.4243 | 1.13319 | 0.566595 | − | 0.823996i | \(-0.308260\pi\) | ||||
0.566595 | + | 0.823996i | \(0.308260\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −51.5120 | −1.85516 | ||||||||
\(772\) | 24.0789 | 0.866620 | ||||||||
\(773\) | 48.4159 | 1.74140 | 0.870699 | − | 0.491816i | \(-0.163667\pi\) | ||||
0.870699 | + | 0.491816i | \(0.163667\pi\) | |||||||
\(774\) | −32.0481 | −1.15195 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.338178 | −0.0121399 | ||||||||
\(777\) | −44.1405 | −1.58353 | ||||||||
\(778\) | 8.91899 | 0.319761 | ||||||||
\(779\) | 11.9202 | 0.427087 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.6711 | 0.489190 | ||||||||
\(782\) | −26.7876 | −0.957924 | ||||||||
\(783\) | −84.6030 | −3.02346 | ||||||||
\(784\) | 23.6191 | 0.843539 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 71.9149 | 2.56512 | ||||||||
\(787\) | −23.9666 | −0.854316 | −0.427158 | − | 0.904177i | \(-0.640485\pi\) | ||||
−0.427158 | + | 0.904177i | \(0.640485\pi\) | |||||||
\(788\) | 24.6736 | 0.878960 | ||||||||
\(789\) | −75.9263 | −2.70305 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.2877 | −0.721349 | ||||||||
\(792\) | 8.13826 | 0.289181 | ||||||||
\(793\) | −23.5226 | −0.835311 | ||||||||
\(794\) | 42.4967 | 1.50815 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 36.9040 | 1.30803 | ||||||||
\(797\) | 5.68070 | 0.201221 | 0.100610 | − | 0.994926i | \(-0.467920\pi\) | ||||
0.100610 | + | 0.994926i | \(0.467920\pi\) | |||||||
\(798\) | −17.7564 | −0.628571 | ||||||||
\(799\) | −69.7537 | −2.46771 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 48.7008 | 1.72076 | ||||||||
\(802\) | −37.2514 | −1.31539 | ||||||||
\(803\) | −6.73281 | −0.237596 | ||||||||
\(804\) | −85.0021 | −2.99779 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.8252 | 0.874430 | ||||||||
\(807\) | −47.6921 | −1.67884 | ||||||||
\(808\) | −3.87820 | −0.136435 | ||||||||
\(809\) | −3.08707 | −0.108535 | −0.0542677 | − | 0.998526i | \(-0.517282\pi\) | ||||
−0.0542677 | + | 0.998526i | \(0.517282\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.14545 | −0.250911 | −0.125455 | − | 0.992099i | \(-0.540039\pi\) | ||||
−0.125455 | + | 0.992099i | \(0.540039\pi\) | |||||||
\(812\) | 13.1669 | 0.462067 | ||||||||
\(813\) | 65.8402 | 2.30912 | ||||||||
\(814\) | −82.6089 | −2.89544 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −97.0313 | −3.39678 | ||||||||
\(817\) | −5.03743 | −0.176237 | ||||||||
\(818\) | 70.8255 | 2.47636 | ||||||||
\(819\) | 27.9468 | 0.976539 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.0857 | −0.945298 | −0.472649 | − | 0.881251i | \(-0.656702\pi\) | ||||
−0.472649 | + | 0.881251i | \(0.656702\pi\) | |||||||
\(822\) | 113.057 | 3.94331 | ||||||||
\(823\) | −20.4296 | −0.712130 | −0.356065 | − | 0.934461i | \(-0.615882\pi\) | ||||
−0.356065 | + | 0.934461i | \(0.615882\pi\) | |||||||
\(824\) | −1.51483 | −0.0527717 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.2603 | −0.983301 | ||||||||
\(827\) | −32.6171 | −1.13421 | −0.567103 | − | 0.823647i | \(-0.691936\pi\) | ||||
−0.567103 | + | 0.823647i | \(0.691936\pi\) | |||||||
\(828\) | −26.8928 | −0.934590 | ||||||||
\(829\) | −41.5411 | −1.44278 | −0.721390 | − | 0.692529i | \(-0.756497\pi\) | ||||
−0.721390 | + | 0.692529i | \(0.756497\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 76.3733 | 2.64936 | ||||||||
\(832\) | −20.8794 | −0.723862 | ||||||||
\(833\) | 38.7708 | 1.34333 | ||||||||
\(834\) | −17.5110 | −0.606356 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15.9760 | −0.552540 | ||||||||
\(837\) | 59.2841 | 2.04916 | ||||||||
\(838\) | −6.72040 | −0.232152 | ||||||||
\(839\) | 52.1241 | 1.79952 | 0.899762 | − | 0.436381i | \(-0.143740\pi\) | ||||
0.899762 | + | 0.436381i | \(0.143740\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.29019 | 0.182421 | ||||||||
\(842\) | 58.5634 | 2.01823 | ||||||||
\(843\) | 99.8382 | 3.43861 | ||||||||
\(844\) | −29.5319 | −1.01653 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −145.662 | −5.00797 | ||||||||
\(847\) | 3.68258 | 0.126535 | ||||||||
\(848\) | −2.74649 | −0.0943150 | ||||||||
\(849\) | 16.3255 | 0.560290 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.8576 | −0.749268 | ||||||||
\(852\) | −21.8625 | −0.748996 | ||||||||
\(853\) | 33.8361 | 1.15853 | 0.579263 | − | 0.815141i | \(-0.303341\pi\) | ||||
0.579263 | + | 0.815141i | \(0.303341\pi\) | |||||||
\(854\) | 18.1847 | 0.622267 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.31076 | 0.147339 | ||||||||
\(857\) | 34.4148 | 1.17559 | 0.587793 | − | 0.809011i | \(-0.299997\pi\) | ||||
0.587793 | + | 0.809011i | \(0.299997\pi\) | |||||||
\(858\) | 73.3188 | 2.50306 | ||||||||
\(859\) | 17.7350 | 0.605111 | 0.302555 | − | 0.953132i | \(-0.402160\pi\) | ||||
0.302555 | + | 0.953132i | \(0.402160\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.3318 | 0.692906 | ||||||||
\(862\) | 35.0258 | 1.19298 | ||||||||
\(863\) | −0.378077 | −0.0128699 | −0.00643495 | − | 0.999979i | \(-0.502048\pi\) | ||||
−0.00643495 | + | 0.999979i | \(0.502048\pi\) | |||||||
\(864\) | −112.796 | −3.83741 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 49.9485 | 1.69732 | ||||||||
\(867\) | −104.280 | −3.54154 | ||||||||
\(868\) | −9.22647 | −0.313167 | ||||||||
\(869\) | −16.5403 | −0.561091 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.7412 | 1.48211 | ||||||||
\(872\) | 1.01166 | 0.0342593 | ||||||||
\(873\) | −8.67665 | −0.293660 | ||||||||
\(874\) | −8.79267 | −0.297416 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.7669 | 0.363781 | ||||||||
\(877\) | 19.1653 | 0.647166 | 0.323583 | − | 0.946200i | \(-0.395113\pi\) | ||||
0.323583 | + | 0.946200i | \(0.395113\pi\) | |||||||
\(878\) | 70.3243 | 2.37333 | ||||||||
\(879\) | 65.9031 | 2.22286 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.0027 | 0.774981 | 0.387490 | − | 0.921874i | \(-0.373342\pi\) | ||||
0.387490 | + | 0.921874i | \(0.373342\pi\) | |||||||
\(882\) | 80.9626 | 2.72615 | ||||||||
\(883\) | −27.9811 | −0.941639 | −0.470819 | − | 0.882230i | \(-0.656042\pi\) | ||||
−0.470819 | + | 0.882230i | \(0.656042\pi\) | |||||||
\(884\) | −40.0532 | −1.34714 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −49.7715 | −1.67211 | ||||||||
\(887\) | −10.0014 | −0.335814 | −0.167907 | − | 0.985803i | \(-0.553701\pi\) | ||||
−0.167907 | + | 0.985803i | \(0.553701\pi\) | |||||||
\(888\) | −10.5778 | −0.354966 | ||||||||
\(889\) | −13.3349 | −0.447238 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 91.1870 | 3.05488 | ||||||||
\(892\) | 24.1888 | 0.809900 | ||||||||
\(893\) | −22.8957 | −0.766175 | ||||||||
\(894\) | 90.4478 | 3.02503 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.81898 | −0.0941756 | ||||||||
\(897\) | 19.3995 | 0.647730 | ||||||||
\(898\) | −18.7977 | −0.627288 | ||||||||
\(899\) | −24.0282 | −0.801387 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.50838 | −0.150196 | ||||||||
\(902\) | 38.0510 | 1.26696 | ||||||||
\(903\) | −8.59211 | −0.285928 | ||||||||
\(904\) | −4.86172 | −0.161699 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 68.4444 | 2.27391 | ||||||||
\(907\) | −45.3028 | −1.50425 | −0.752127 | − | 0.659018i | \(-0.770972\pi\) | ||||
−0.752127 | + | 0.659018i | \(0.770972\pi\) | |||||||
\(908\) | −3.76371 | −0.124903 | ||||||||
\(909\) | −99.5033 | −3.30032 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.64639 | 0.253336 | 0.126668 | − | 0.991945i | \(-0.459572\pi\) | ||||
0.126668 | + | 0.991945i | \(0.459572\pi\) | |||||||
\(912\) | −31.8492 | −1.05463 | ||||||||
\(913\) | −30.8598 | −1.02131 | ||||||||
\(914\) | 38.2025 | 1.26363 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 53.5256 | 1.76853 | ||||||||
\(917\) | 13.7538 | 0.454190 | ||||||||
\(918\) | −198.958 | −6.56659 | ||||||||
\(919\) | −2.02115 | −0.0666717 | −0.0333359 | − | 0.999444i | \(-0.510613\pi\) | ||||
−0.0333359 | + | 0.999444i | \(0.510613\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 54.3968 | 1.79243 | ||||||||
\(922\) | −22.0746 | −0.726989 | ||||||||
\(923\) | 11.2502 | 0.370304 | ||||||||
\(924\) | −27.2495 | −0.896442 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23.2685 | 0.764652 | ||||||||
\(927\) | −38.8662 | −1.27653 | ||||||||
\(928\) | 45.7172 | 1.50074 | ||||||||
\(929\) | 19.6792 | 0.645654 | 0.322827 | − | 0.946458i | \(-0.395367\pi\) | ||||
0.322827 | + | 0.946458i | \(0.395367\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.7260 | 0.417077 | ||||||||
\(932\) | −33.0883 | −1.08384 | ||||||||
\(933\) | −1.47300 | −0.0482238 | ||||||||
\(934\) | 44.2138 | 1.44672 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.69712 | 0.218902 | ||||||||
\(937\) | 45.8003 | 1.49623 | 0.748115 | − | 0.663569i | \(-0.230959\pi\) | ||||
0.748115 | + | 0.663569i | \(0.230959\pi\) | |||||||
\(938\) | −33.8151 | −1.10410 | ||||||||
\(939\) | −74.0061 | −2.41510 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.8116 | 1.75421 | 0.877104 | − | 0.480300i | \(-0.159472\pi\) | ||||
0.877104 | + | 0.480300i | \(0.159472\pi\) | |||||||
\(942\) | −96.9910 | −3.16014 | ||||||||
\(943\) | 10.0680 | 0.327858 | ||||||||
\(944\) | −50.6896 | −1.64981 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.0801 | −0.522810 | ||||||||
\(947\) | −12.2954 | −0.399548 | −0.199774 | − | 0.979842i | \(-0.564021\pi\) | ||||
−0.199774 | + | 0.979842i | \(0.564021\pi\) | |||||||
\(948\) | 26.4508 | 0.859083 | ||||||||
\(949\) | −5.54055 | −0.179854 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.3843 | 1.40683 | ||||||||
\(952\) | −2.47930 | −0.0803547 | ||||||||
\(953\) | −36.4439 | −1.18053 | −0.590266 | − | 0.807209i | \(-0.700977\pi\) | ||||
−0.590266 | + | 0.807209i | \(0.700977\pi\) | |||||||
\(954\) | −9.41455 | −0.304807 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.6301 | 0.440830 | ||||||||
\(957\) | −70.9651 | −2.29398 | ||||||||
\(958\) | −30.3818 | −0.981592 | ||||||||
\(959\) | 21.6222 | 0.698218 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.1626 | −0.456859 | ||||||||
\(962\) | −67.9803 | −2.19177 | ||||||||
\(963\) | 110.601 | 3.56408 | ||||||||
\(964\) | 1.85173 | 0.0596403 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14.9972 | −0.482528 | ||||||||
\(967\) | 28.2135 | 0.907285 | 0.453642 | − | 0.891184i | \(-0.350124\pi\) | ||||
0.453642 | + | 0.891184i | \(0.350124\pi\) | |||||||
\(968\) | 0.882487 | 0.0283642 | ||||||||
\(969\) | −52.2805 | −1.67949 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.67228 | −0.182032 | −0.0910160 | − | 0.995849i | \(-0.529011\pi\) | ||||
−0.0910160 | + | 0.995849i | \(0.529011\pi\) | |||||||
\(972\) | −65.5638 | −2.10296 | ||||||||
\(973\) | −3.34899 | −0.107364 | ||||||||
\(974\) | −63.2395 | −2.02632 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.6173 | 1.04405 | ||||||||
\(977\) | 19.6175 | 0.627618 | 0.313809 | − | 0.949486i | \(-0.398395\pi\) | ||||
0.313809 | + | 0.949486i | \(0.398395\pi\) | |||||||
\(978\) | −37.2050 | −1.18968 | ||||||||
\(979\) | 24.4356 | 0.780965 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.9563 | 0.828722 | ||||||||
\(982\) | 18.5521 | 0.592021 | ||||||||
\(983\) | 15.2911 | 0.487710 | 0.243855 | − | 0.969812i | \(-0.421588\pi\) | ||||
0.243855 | + | 0.969812i | \(0.421588\pi\) | |||||||
\(984\) | 4.87229 | 0.155323 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 80.6390 | 2.56807 | ||||||||
\(987\) | −39.0521 | −1.24304 | ||||||||
\(988\) | −13.1469 | −0.418259 | ||||||||
\(989\) | −4.25466 | −0.135290 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.6378 | 0.750879 | 0.375439 | − | 0.926847i | \(-0.377492\pi\) | ||||
0.375439 | + | 0.926847i | \(0.377492\pi\) | |||||||
\(992\) | −32.0355 | −1.01713 | ||||||||
\(993\) | −2.41173 | −0.0765339 | ||||||||
\(994\) | −8.69722 | −0.275859 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 49.3502 | 1.56372 | ||||||||
\(997\) | −21.7194 | −0.687860 | −0.343930 | − | 0.938995i | \(-0.611758\pi\) | ||||
−0.343930 | + | 0.938995i | \(0.611758\pi\) | |||||||
\(998\) | −22.4025 | −0.709138 | ||||||||
\(999\) | −162.341 | −5.13625 |
(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 | 6025.2.a.k.1.5 | 25 | ||
5.4 | even | 2 | 1205.2.a.d.1.21 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.a.d.1.21 | ✓ | 25 | 5.4 | even | 2 | ||
6025.2.a.k.1.5 | 25 | 1.1 | even | 1 | trivial |