Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(1\) |
Dimension: | \(243\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71870 | −1.92241 | −0.961206 | − | 0.275833i | \(-0.911046\pi\) | ||||
−0.961206 | + | 0.275833i | \(0.911046\pi\) | |||||||
\(3\) | 0.776703 | 0.448430 | 0.224215 | − | 0.974540i | \(-0.428018\pi\) | ||||
0.224215 | + | 0.974540i | \(0.428018\pi\) | |||||||
\(4\) | 5.39133 | 2.69567 | ||||||||
\(5\) | 1.67497 | 0.749070 | 0.374535 | − | 0.927213i | \(-0.377802\pi\) | ||||
0.374535 | + | 0.927213i | \(0.377802\pi\) | |||||||
\(6\) | −2.11162 | −0.862067 | ||||||||
\(7\) | 0.286183 | 0.108167 | 0.0540835 | − | 0.998536i | \(-0.482776\pi\) | ||||
0.0540835 | + | 0.998536i | \(0.482776\pi\) | |||||||
\(8\) | −9.22001 | −3.25977 | ||||||||
\(9\) | −2.39673 | −0.798911 | ||||||||
\(10\) | −4.55375 | −1.44002 | ||||||||
\(11\) | −5.88809 | −1.77532 | −0.887662 | − | 0.460495i | \(-0.847672\pi\) | ||||
−0.887662 | + | 0.460495i | \(0.847672\pi\) | |||||||
\(12\) | 4.18746 | 1.20882 | ||||||||
\(13\) | 2.73763 | 0.759282 | 0.379641 | − | 0.925134i | \(-0.376048\pi\) | ||||
0.379641 | + | 0.925134i | \(0.376048\pi\) | |||||||
\(14\) | −0.778045 | −0.207941 | ||||||||
\(15\) | 1.30096 | 0.335905 | ||||||||
\(16\) | 14.2838 | 3.57095 | ||||||||
\(17\) | 1.59192 | 0.386097 | 0.193048 | − | 0.981189i | \(-0.438163\pi\) | ||||
0.193048 | + | 0.981189i | \(0.438163\pi\) | |||||||
\(18\) | 6.51600 | 1.53583 | ||||||||
\(19\) | −1.02964 | −0.236215 | −0.118108 | − | 0.993001i | \(-0.537683\pi\) | ||||
−0.118108 | + | 0.993001i | \(0.537683\pi\) | |||||||
\(20\) | 9.03033 | 2.01924 | ||||||||
\(21\) | 0.222279 | 0.0485053 | ||||||||
\(22\) | 16.0079 | 3.41290 | ||||||||
\(23\) | 4.22846 | 0.881694 | 0.440847 | − | 0.897582i | \(-0.354678\pi\) | ||||
0.440847 | + | 0.897582i | \(0.354678\pi\) | |||||||
\(24\) | −7.16121 | −1.46178 | ||||||||
\(25\) | −2.19447 | −0.438894 | ||||||||
\(26\) | −7.44279 | −1.45965 | ||||||||
\(27\) | −4.19166 | −0.806685 | ||||||||
\(28\) | 1.54291 | 0.291582 | ||||||||
\(29\) | 6.29312 | 1.16860 | 0.584301 | − | 0.811537i | \(-0.301369\pi\) | ||||
0.584301 | + | 0.811537i | \(0.301369\pi\) | |||||||
\(30\) | −3.53691 | −0.645748 | ||||||||
\(31\) | −10.0645 | −1.80763 | −0.903815 | − | 0.427923i | \(-0.859245\pi\) | ||||
−0.903815 | + | 0.427923i | \(0.859245\pi\) | |||||||
\(32\) | −20.3933 | −3.60506 | ||||||||
\(33\) | −4.57330 | −0.796109 | ||||||||
\(34\) | −4.32795 | −0.742237 | ||||||||
\(35\) | 0.479348 | 0.0810246 | ||||||||
\(36\) | −12.9216 | −2.15360 | ||||||||
\(37\) | 7.64888 | 1.25747 | 0.628734 | − | 0.777621i | \(-0.283573\pi\) | ||||
0.628734 | + | 0.777621i | \(0.283573\pi\) | |||||||
\(38\) | 2.79928 | 0.454103 | ||||||||
\(39\) | 2.12633 | 0.340485 | ||||||||
\(40\) | −15.4433 | −2.44179 | ||||||||
\(41\) | −9.64721 | −1.50664 | −0.753320 | − | 0.657654i | \(-0.771549\pi\) | ||||
−0.753320 | + | 0.657654i | \(0.771549\pi\) | |||||||
\(42\) | −0.604310 | −0.0932471 | ||||||||
\(43\) | 0.886321 | 0.135163 | 0.0675813 | − | 0.997714i | \(-0.478472\pi\) | ||||
0.0675813 | + | 0.997714i | \(0.478472\pi\) | |||||||
\(44\) | −31.7446 | −4.78568 | ||||||||
\(45\) | −4.01446 | −0.598440 | ||||||||
\(46\) | −11.4959 | −1.69498 | ||||||||
\(47\) | 11.4726 | 1.67345 | 0.836724 | − | 0.547625i | \(-0.184468\pi\) | ||||
0.836724 | + | 0.547625i | \(0.184468\pi\) | |||||||
\(48\) | 11.0943 | 1.60132 | ||||||||
\(49\) | −6.91810 | −0.988300 | ||||||||
\(50\) | 5.96611 | 0.843735 | ||||||||
\(51\) | 1.23645 | 0.173137 | ||||||||
\(52\) | 14.7595 | 2.04677 | ||||||||
\(53\) | 7.67727 | 1.05455 | 0.527277 | − | 0.849693i | \(-0.323213\pi\) | ||||
0.527277 | + | 0.849693i | \(0.323213\pi\) | |||||||
\(54\) | 11.3959 | 1.55078 | ||||||||
\(55\) | −9.86238 | −1.32984 | ||||||||
\(56\) | −2.63861 | −0.352599 | ||||||||
\(57\) | −0.799723 | −0.105926 | ||||||||
\(58\) | −17.1091 | −2.24653 | ||||||||
\(59\) | −1.79305 | −0.233436 | −0.116718 | − | 0.993165i | \(-0.537237\pi\) | ||||
−0.116718 | + | 0.993165i | \(0.537237\pi\) | |||||||
\(60\) | 7.01388 | 0.905488 | ||||||||
\(61\) | 11.1902 | 1.43276 | 0.716381 | − | 0.697709i | \(-0.245797\pi\) | ||||
0.716381 | + | 0.697709i | \(0.245797\pi\) | |||||||
\(62\) | 27.3623 | 3.47501 | ||||||||
\(63\) | −0.685903 | −0.0864157 | ||||||||
\(64\) | 26.8757 | 3.35946 | ||||||||
\(65\) | 4.58545 | 0.568755 | ||||||||
\(66\) | 12.4334 | 1.53045 | ||||||||
\(67\) | 11.9139 | 1.45551 | 0.727757 | − | 0.685835i | \(-0.240563\pi\) | ||||
0.727757 | + | 0.685835i | \(0.240563\pi\) | |||||||
\(68\) | 8.58256 | 1.04079 | ||||||||
\(69\) | 3.28426 | 0.395378 | ||||||||
\(70\) | −1.30320 | −0.155763 | ||||||||
\(71\) | −10.0144 | −1.18849 | −0.594245 | − | 0.804284i | \(-0.702549\pi\) | ||||
−0.594245 | + | 0.804284i | \(0.702549\pi\) | |||||||
\(72\) | 22.0979 | 2.60426 | ||||||||
\(73\) | 6.68326 | 0.782217 | 0.391108 | − | 0.920345i | \(-0.372092\pi\) | ||||
0.391108 | + | 0.920345i | \(0.372092\pi\) | |||||||
\(74\) | −20.7950 | −2.41737 | ||||||||
\(75\) | −1.70445 | −0.196813 | ||||||||
\(76\) | −5.55112 | −0.636757 | ||||||||
\(77\) | −1.68507 | −0.192031 | ||||||||
\(78\) | −5.78084 | −0.654551 | ||||||||
\(79\) | 12.5463 | 1.41156 | 0.705782 | − | 0.708429i | \(-0.250596\pi\) | ||||
0.705782 | + | 0.708429i | \(0.250596\pi\) | |||||||
\(80\) | 23.9249 | 2.67489 | ||||||||
\(81\) | 3.93452 | 0.437169 | ||||||||
\(82\) | 26.2279 | 2.89638 | ||||||||
\(83\) | −10.3837 | −1.13976 | −0.569882 | − | 0.821726i | \(-0.693011\pi\) | ||||
−0.569882 | + | 0.821726i | \(0.693011\pi\) | |||||||
\(84\) | 1.19838 | 0.130754 | ||||||||
\(85\) | 2.66642 | 0.289214 | ||||||||
\(86\) | −2.40964 | −0.259838 | ||||||||
\(87\) | 4.88788 | 0.524036 | ||||||||
\(88\) | 54.2882 | 5.78714 | ||||||||
\(89\) | −4.50334 | −0.477353 | −0.238676 | − | 0.971099i | \(-0.576714\pi\) | ||||
−0.238676 | + | 0.971099i | \(0.576714\pi\) | |||||||
\(90\) | 10.9141 | 1.15045 | ||||||||
\(91\) | 0.783462 | 0.0821292 | ||||||||
\(92\) | 22.7970 | 2.37675 | ||||||||
\(93\) | −7.81710 | −0.810595 | ||||||||
\(94\) | −31.1905 | −3.21705 | ||||||||
\(95\) | −1.72461 | −0.176942 | ||||||||
\(96\) | −15.8395 | −1.61662 | ||||||||
\(97\) | −5.79710 | −0.588606 | −0.294303 | − | 0.955712i | \(-0.595088\pi\) | ||||
−0.294303 | + | 0.955712i | \(0.595088\pi\) | |||||||
\(98\) | 18.8082 | 1.89992 | ||||||||
\(99\) | 14.1122 | 1.41833 | ||||||||
\(100\) | −11.8311 | −1.18311 | ||||||||
\(101\) | −12.2652 | −1.22044 | −0.610218 | − | 0.792233i | \(-0.708918\pi\) | ||||
−0.610218 | + | 0.792233i | \(0.708918\pi\) | |||||||
\(102\) | −3.36153 | −0.332841 | ||||||||
\(103\) | −13.4798 | −1.32820 | −0.664102 | − | 0.747642i | \(-0.731186\pi\) | ||||
−0.664102 | + | 0.747642i | \(0.731186\pi\) | |||||||
\(104\) | −25.2410 | −2.47508 | ||||||||
\(105\) | 0.372311 | 0.0363339 | ||||||||
\(106\) | −20.8722 | −2.02729 | ||||||||
\(107\) | −10.2415 | −0.990081 | −0.495040 | − | 0.868870i | \(-0.664847\pi\) | ||||
−0.495040 | + | 0.868870i | \(0.664847\pi\) | |||||||
\(108\) | −22.5986 | −2.17455 | ||||||||
\(109\) | 9.45074 | 0.905217 | 0.452609 | − | 0.891709i | \(-0.350494\pi\) | ||||
0.452609 | + | 0.891709i | \(0.350494\pi\) | |||||||
\(110\) | 26.8128 | 2.55650 | ||||||||
\(111\) | 5.94091 | 0.563886 | ||||||||
\(112\) | 4.08777 | 0.386258 | ||||||||
\(113\) | −3.83279 | −0.360559 | −0.180279 | − | 0.983615i | \(-0.557700\pi\) | ||||
−0.180279 | + | 0.983615i | \(0.557700\pi\) | |||||||
\(114\) | 2.17421 | 0.203633 | ||||||||
\(115\) | 7.08254 | 0.660451 | ||||||||
\(116\) | 33.9283 | 3.15016 | ||||||||
\(117\) | −6.56136 | −0.606598 | ||||||||
\(118\) | 4.87477 | 0.448759 | ||||||||
\(119\) | 0.455580 | 0.0417629 | ||||||||
\(120\) | −11.9948 | −1.09497 | ||||||||
\(121\) | 23.6695 | 2.15178 | ||||||||
\(122\) | −30.4229 | −2.75436 | ||||||||
\(123\) | −7.49302 | −0.675623 | ||||||||
\(124\) | −54.2608 | −4.87277 | ||||||||
\(125\) | −12.0505 | −1.07783 | ||||||||
\(126\) | 1.86477 | 0.166127 | ||||||||
\(127\) | 4.90761 | 0.435480 | 0.217740 | − | 0.976007i | \(-0.430132\pi\) | ||||
0.217740 | + | 0.976007i | \(0.430132\pi\) | |||||||
\(128\) | −32.2804 | −2.85321 | ||||||||
\(129\) | 0.688408 | 0.0606110 | ||||||||
\(130\) | −12.4665 | −1.09338 | ||||||||
\(131\) | −21.4469 | −1.87382 | −0.936911 | − | 0.349568i | \(-0.886328\pi\) | ||||
−0.936911 | + | 0.349568i | \(0.886328\pi\) | |||||||
\(132\) | −24.6561 | −2.14604 | ||||||||
\(133\) | −0.294665 | −0.0255507 | ||||||||
\(134\) | −32.3903 | −2.79810 | ||||||||
\(135\) | −7.02091 | −0.604264 | ||||||||
\(136\) | −14.6775 | −1.25859 | ||||||||
\(137\) | −9.94801 | −0.849916 | −0.424958 | − | 0.905213i | \(-0.639711\pi\) | ||||
−0.424958 | + | 0.905213i | \(0.639711\pi\) | |||||||
\(138\) | −8.92891 | −0.760079 | ||||||||
\(139\) | −1.24228 | −0.105369 | −0.0526843 | − | 0.998611i | \(-0.516778\pi\) | ||||
−0.0526843 | + | 0.998611i | \(0.516778\pi\) | |||||||
\(140\) | 2.58432 | 0.218415 | ||||||||
\(141\) | 8.91079 | 0.750424 | ||||||||
\(142\) | 27.2261 | 2.28477 | ||||||||
\(143\) | −16.1194 | −1.34797 | ||||||||
\(144\) | −34.2344 | −2.85287 | ||||||||
\(145\) | 10.5408 | 0.875365 | ||||||||
\(146\) | −18.1698 | −1.50374 | ||||||||
\(147\) | −5.37331 | −0.443183 | ||||||||
\(148\) | 41.2376 | 3.38971 | ||||||||
\(149\) | 3.85257 | 0.315615 | 0.157808 | − | 0.987470i | \(-0.449557\pi\) | ||||
0.157808 | + | 0.987470i | \(0.449557\pi\) | |||||||
\(150\) | 4.63389 | 0.378356 | ||||||||
\(151\) | −11.5679 | −0.941383 | −0.470692 | − | 0.882298i | \(-0.655996\pi\) | ||||
−0.470692 | + | 0.882298i | \(0.655996\pi\) | |||||||
\(152\) | 9.49328 | 0.770006 | ||||||||
\(153\) | −3.81540 | −0.308457 | ||||||||
\(154\) | 4.58120 | 0.369163 | ||||||||
\(155\) | −16.8577 | −1.35404 | ||||||||
\(156\) | 11.4637 | 0.917832 | ||||||||
\(157\) | 16.4542 | 1.31319 | 0.656595 | − | 0.754244i | \(-0.271996\pi\) | ||||
0.656595 | + | 0.754244i | \(0.271996\pi\) | |||||||
\(158\) | −34.1095 | −2.71361 | ||||||||
\(159\) | 5.96296 | 0.472894 | ||||||||
\(160\) | −34.1582 | −2.70044 | ||||||||
\(161\) | 1.21011 | 0.0953701 | ||||||||
\(162\) | −10.6968 | −0.840418 | ||||||||
\(163\) | −2.69664 | −0.211217 | −0.105608 | − | 0.994408i | \(-0.533679\pi\) | ||||
−0.105608 | + | 0.994408i | \(0.533679\pi\) | |||||||
\(164\) | −52.0113 | −4.06140 | ||||||||
\(165\) | −7.66014 | −0.596341 | ||||||||
\(166\) | 28.2303 | 2.19110 | ||||||||
\(167\) | −6.07722 | −0.470269 | −0.235135 | − | 0.971963i | \(-0.575553\pi\) | ||||
−0.235135 | + | 0.971963i | \(0.575553\pi\) | |||||||
\(168\) | −2.04942 | −0.158116 | ||||||||
\(169\) | −5.50539 | −0.423491 | ||||||||
\(170\) | −7.24919 | −0.555988 | ||||||||
\(171\) | 2.46777 | 0.188715 | ||||||||
\(172\) | 4.77845 | 0.364353 | ||||||||
\(173\) | −14.3190 | −1.08865 | −0.544326 | − | 0.838874i | \(-0.683214\pi\) | ||||
−0.544326 | + | 0.838874i | \(0.683214\pi\) | |||||||
\(174\) | −13.2887 | −1.00741 | ||||||||
\(175\) | −0.628019 | −0.0474738 | ||||||||
\(176\) | −84.1041 | −6.33959 | ||||||||
\(177\) | −1.39267 | −0.104680 | ||||||||
\(178\) | 12.2432 | 0.917669 | ||||||||
\(179\) | 13.8595 | 1.03591 | 0.517955 | − | 0.855408i | \(-0.326694\pi\) | ||||
0.517955 | + | 0.855408i | \(0.326694\pi\) | |||||||
\(180\) | −21.6433 | −1.61319 | ||||||||
\(181\) | −16.5516 | −1.23027 | −0.615135 | − | 0.788422i | \(-0.710898\pi\) | ||||
−0.615135 | + | 0.788422i | \(0.710898\pi\) | |||||||
\(182\) | −2.13000 | −0.157886 | ||||||||
\(183\) | 8.69149 | 0.642493 | ||||||||
\(184\) | −38.9864 | −2.87412 | ||||||||
\(185\) | 12.8117 | 0.941932 | ||||||||
\(186\) | 21.2523 | 1.55830 | ||||||||
\(187\) | −9.37335 | −0.685447 | ||||||||
\(188\) | 61.8525 | 4.51105 | ||||||||
\(189\) | −1.19958 | −0.0872567 | ||||||||
\(190\) | 4.68871 | 0.340155 | ||||||||
\(191\) | −16.0048 | −1.15807 | −0.579034 | − | 0.815304i | \(-0.696570\pi\) | ||||
−0.579034 | + | 0.815304i | \(0.696570\pi\) | |||||||
\(192\) | 20.8744 | 1.50648 | ||||||||
\(193\) | −9.94868 | −0.716122 | −0.358061 | − | 0.933698i | \(-0.616562\pi\) | ||||
−0.358061 | + | 0.933698i | \(0.616562\pi\) | |||||||
\(194\) | 15.7606 | 1.13154 | ||||||||
\(195\) | 3.56153 | 0.255047 | ||||||||
\(196\) | −37.2978 | −2.66413 | ||||||||
\(197\) | −24.5433 | −1.74864 | −0.874318 | − | 0.485354i | \(-0.838691\pi\) | ||||
−0.874318 | + | 0.485354i | \(0.838691\pi\) | |||||||
\(198\) | −38.3667 | −2.72661 | ||||||||
\(199\) | −3.51865 | −0.249431 | −0.124715 | − | 0.992193i | \(-0.539802\pi\) | ||||
−0.124715 | + | 0.992193i | \(0.539802\pi\) | |||||||
\(200\) | 20.2330 | 1.43069 | ||||||||
\(201\) | 9.25356 | 0.652696 | ||||||||
\(202\) | 33.3455 | 2.34618 | ||||||||
\(203\) | 1.80098 | 0.126404 | ||||||||
\(204\) | 6.66610 | 0.466720 | ||||||||
\(205\) | −16.1588 | −1.12858 | ||||||||
\(206\) | 36.6475 | 2.55336 | ||||||||
\(207\) | −10.1345 | −0.704395 | ||||||||
\(208\) | 39.1037 | 2.71135 | ||||||||
\(209\) | 6.06260 | 0.419359 | ||||||||
\(210\) | −1.01220 | −0.0698486 | ||||||||
\(211\) | 28.3742 | 1.95336 | 0.976679 | − | 0.214703i | \(-0.0688784\pi\) | ||||
0.976679 | + | 0.214703i | \(0.0688784\pi\) | |||||||
\(212\) | 41.3907 | 2.84272 | ||||||||
\(213\) | −7.77821 | −0.532954 | ||||||||
\(214\) | 27.8435 | 1.90334 | ||||||||
\(215\) | 1.48456 | 0.101246 | ||||||||
\(216\) | 38.6471 | 2.62961 | ||||||||
\(217\) | −2.88028 | −0.195526 | ||||||||
\(218\) | −25.6937 | −1.74020 | ||||||||
\(219\) | 5.19091 | 0.350769 | ||||||||
\(220\) | −53.1713 | −3.58481 | ||||||||
\(221\) | 4.35808 | 0.293156 | ||||||||
\(222\) | −16.1515 | −1.08402 | ||||||||
\(223\) | −22.0999 | −1.47992 | −0.739958 | − | 0.672653i | \(-0.765155\pi\) | ||||
−0.739958 | + | 0.672653i | \(0.765155\pi\) | |||||||
\(224\) | −5.83621 | −0.389948 | ||||||||
\(225\) | 5.25956 | 0.350637 | ||||||||
\(226\) | 10.4202 | 0.693142 | ||||||||
\(227\) | −20.3885 | −1.35323 | −0.676616 | − | 0.736336i | \(-0.736554\pi\) | ||||
−0.676616 | + | 0.736336i | \(0.736554\pi\) | |||||||
\(228\) | −4.31157 | −0.285541 | ||||||||
\(229\) | 1.71480 | 0.113317 | 0.0566586 | − | 0.998394i | \(-0.481955\pi\) | ||||
0.0566586 | + | 0.998394i | \(0.481955\pi\) | |||||||
\(230\) | −19.2553 | −1.26966 | ||||||||
\(231\) | −1.30880 | −0.0861126 | ||||||||
\(232\) | −58.0226 | −3.80937 | ||||||||
\(233\) | −12.6315 | −0.827516 | −0.413758 | − | 0.910387i | \(-0.635784\pi\) | ||||
−0.413758 | + | 0.910387i | \(0.635784\pi\) | |||||||
\(234\) | 17.8384 | 1.16613 | ||||||||
\(235\) | 19.2162 | 1.25353 | ||||||||
\(236\) | −9.66694 | −0.629264 | ||||||||
\(237\) | 9.74472 | 0.632988 | ||||||||
\(238\) | −1.23858 | −0.0802855 | ||||||||
\(239\) | −12.7421 | −0.824216 | −0.412108 | − | 0.911135i | \(-0.635207\pi\) | ||||
−0.412108 | + | 0.911135i | \(0.635207\pi\) | |||||||
\(240\) | 18.5826 | 1.19950 | ||||||||
\(241\) | 12.0466 | 0.775991 | 0.387996 | − | 0.921661i | \(-0.373168\pi\) | ||||
0.387996 | + | 0.921661i | \(0.373168\pi\) | |||||||
\(242\) | −64.3504 | −4.13660 | ||||||||
\(243\) | 15.6309 | 1.00272 | ||||||||
\(244\) | 60.3302 | 3.86225 | ||||||||
\(245\) | −11.5876 | −0.740306 | ||||||||
\(246\) | 20.3713 | 1.29882 | ||||||||
\(247\) | −2.81877 | −0.179354 | ||||||||
\(248\) | 92.7944 | 5.89245 | ||||||||
\(249\) | −8.06509 | −0.511104 | ||||||||
\(250\) | 32.7618 | 2.07204 | ||||||||
\(251\) | 17.5459 | 1.10749 | 0.553743 | − | 0.832688i | \(-0.313199\pi\) | ||||
0.553743 | + | 0.832688i | \(0.313199\pi\) | |||||||
\(252\) | −3.69793 | −0.232948 | ||||||||
\(253\) | −24.8975 | −1.56529 | ||||||||
\(254\) | −13.3423 | −0.837171 | ||||||||
\(255\) | 2.07102 | 0.129692 | ||||||||
\(256\) | 34.0093 | 2.12558 | ||||||||
\(257\) | 6.89542 | 0.430124 | 0.215062 | − | 0.976600i | \(-0.431005\pi\) | ||||
0.215062 | + | 0.976600i | \(0.431005\pi\) | |||||||
\(258\) | −1.87158 | −0.116519 | ||||||||
\(259\) | 2.18898 | 0.136016 | ||||||||
\(260\) | 24.7217 | 1.53317 | ||||||||
\(261\) | −15.0829 | −0.933609 | ||||||||
\(262\) | 58.3076 | 3.60226 | ||||||||
\(263\) | −28.7719 | −1.77415 | −0.887076 | − | 0.461623i | \(-0.847267\pi\) | ||||
−0.887076 | + | 0.461623i | \(0.847267\pi\) | |||||||
\(264\) | 42.1658 | 2.59513 | ||||||||
\(265\) | 12.8592 | 0.789935 | ||||||||
\(266\) | 0.801105 | 0.0491189 | ||||||||
\(267\) | −3.49776 | −0.214059 | ||||||||
\(268\) | 64.2317 | 3.92358 | ||||||||
\(269\) | 3.22591 | 0.196687 | 0.0983437 | − | 0.995153i | \(-0.468646\pi\) | ||||
0.0983437 | + | 0.995153i | \(0.468646\pi\) | |||||||
\(270\) | 19.0878 | 1.16164 | ||||||||
\(271\) | −2.89841 | −0.176066 | −0.0880328 | − | 0.996118i | \(-0.528058\pi\) | ||||
−0.0880328 | + | 0.996118i | \(0.528058\pi\) | |||||||
\(272\) | 22.7386 | 1.37873 | ||||||||
\(273\) | 0.608518 | 0.0368292 | ||||||||
\(274\) | 27.0457 | 1.63389 | ||||||||
\(275\) | 12.9212 | 0.779179 | ||||||||
\(276\) | 17.7065 | 1.06581 | ||||||||
\(277\) | 4.37992 | 0.263164 | 0.131582 | − | 0.991305i | \(-0.457994\pi\) | ||||
0.131582 | + | 0.991305i | \(0.457994\pi\) | |||||||
\(278\) | 3.37738 | 0.202562 | ||||||||
\(279\) | 24.1218 | 1.44414 | ||||||||
\(280\) | −4.41959 | −0.264121 | ||||||||
\(281\) | −23.5271 | −1.40351 | −0.701756 | − | 0.712418i | \(-0.747600\pi\) | ||||
−0.701756 | + | 0.712418i | \(0.747600\pi\) | |||||||
\(282\) | −24.2258 | −1.44262 | ||||||||
\(283\) | −19.6959 | −1.17080 | −0.585400 | − | 0.810744i | \(-0.699063\pi\) | ||||
−0.585400 | + | 0.810744i | \(0.699063\pi\) | |||||||
\(284\) | −53.9909 | −3.20377 | ||||||||
\(285\) | −1.33951 | −0.0793460 | ||||||||
\(286\) | 43.8238 | 2.59136 | ||||||||
\(287\) | −2.76086 | −0.162969 | ||||||||
\(288\) | 48.8773 | 2.88012 | ||||||||
\(289\) | −14.4658 | −0.850929 | ||||||||
\(290\) | −28.6573 | −1.68281 | ||||||||
\(291\) | −4.50263 | −0.263949 | ||||||||
\(292\) | 36.0317 | 2.10859 | ||||||||
\(293\) | −1.03319 | −0.0603598 | −0.0301799 | − | 0.999544i | \(-0.509608\pi\) | ||||
−0.0301799 | + | 0.999544i | \(0.509608\pi\) | |||||||
\(294\) | 14.6084 | 0.851980 | ||||||||
\(295\) | −3.00331 | −0.174860 | ||||||||
\(296\) | −70.5227 | −4.09905 | ||||||||
\(297\) | 24.6808 | 1.43213 | ||||||||
\(298\) | −10.4740 | −0.606742 | ||||||||
\(299\) | 11.5759 | 0.669454 | ||||||||
\(300\) | −9.18926 | −0.530542 | ||||||||
\(301\) | 0.253650 | 0.0146201 | ||||||||
\(302\) | 31.4497 | 1.80973 | ||||||||
\(303\) | −9.52645 | −0.547280 | ||||||||
\(304\) | −14.7071 | −0.843512 | ||||||||
\(305\) | 18.7433 | 1.07324 | ||||||||
\(306\) | 10.3729 | 0.592981 | ||||||||
\(307\) | −16.4083 | −0.936470 | −0.468235 | − | 0.883604i | \(-0.655110\pi\) | ||||
−0.468235 | + | 0.883604i | \(0.655110\pi\) | |||||||
\(308\) | −9.08476 | −0.517652 | ||||||||
\(309\) | −10.4698 | −0.595607 | ||||||||
\(310\) | 45.8310 | 2.60303 | ||||||||
\(311\) | −18.6475 | −1.05740 | −0.528702 | − | 0.848807i | \(-0.677321\pi\) | ||||
−0.528702 | + | 0.848807i | \(0.677321\pi\) | |||||||
\(312\) | −19.6047 | −1.10990 | ||||||||
\(313\) | 14.4425 | 0.816337 | 0.408169 | − | 0.912907i | \(-0.366168\pi\) | ||||
0.408169 | + | 0.912907i | \(0.366168\pi\) | |||||||
\(314\) | −44.7341 | −2.52449 | ||||||||
\(315\) | −1.14887 | −0.0647314 | ||||||||
\(316\) | 67.6410 | 3.80511 | ||||||||
\(317\) | 8.64657 | 0.485640 | 0.242820 | − | 0.970071i | \(-0.421928\pi\) | ||||
0.242820 | + | 0.970071i | \(0.421928\pi\) | |||||||
\(318\) | −16.2115 | −0.909096 | ||||||||
\(319\) | −37.0544 | −2.07465 | ||||||||
\(320\) | 45.0160 | 2.51647 | ||||||||
\(321\) | −7.95459 | −0.443982 | ||||||||
\(322\) | −3.28993 | −0.183341 | ||||||||
\(323\) | −1.63910 | −0.0912020 | ||||||||
\(324\) | 21.2123 | 1.17846 | ||||||||
\(325\) | −6.00764 | −0.333244 | ||||||||
\(326\) | 7.33134 | 0.406046 | ||||||||
\(327\) | 7.34042 | 0.405926 | ||||||||
\(328\) | 88.9473 | 4.91129 | ||||||||
\(329\) | 3.28325 | 0.181012 | ||||||||
\(330\) | 20.8256 | 1.14641 | ||||||||
\(331\) | −26.5530 | −1.45948 | −0.729742 | − | 0.683723i | \(-0.760360\pi\) | ||||
−0.729742 | + | 0.683723i | \(0.760360\pi\) | |||||||
\(332\) | −55.9822 | −3.07242 | ||||||||
\(333\) | −18.3323 | −1.00460 | ||||||||
\(334\) | 16.5221 | 0.904051 | ||||||||
\(335\) | 19.9554 | 1.09028 | ||||||||
\(336\) | 3.17499 | 0.173210 | ||||||||
\(337\) | −24.6658 | −1.34363 | −0.671816 | − | 0.740718i | \(-0.734485\pi\) | ||||
−0.671816 | + | 0.740718i | \(0.734485\pi\) | |||||||
\(338\) | 14.9675 | 0.814125 | ||||||||
\(339\) | −2.97694 | −0.161685 | ||||||||
\(340\) | 14.3755 | 0.779623 | ||||||||
\(341\) | 59.2604 | 3.20913 | ||||||||
\(342\) | −6.70912 | −0.362788 | ||||||||
\(343\) | −3.98312 | −0.215068 | ||||||||
\(344\) | −8.17189 | −0.440599 | ||||||||
\(345\) | 5.50103 | 0.296166 | ||||||||
\(346\) | 38.9290 | 2.09284 | ||||||||
\(347\) | 7.75477 | 0.416298 | 0.208149 | − | 0.978097i | \(-0.433256\pi\) | ||||
0.208149 | + | 0.978097i | \(0.433256\pi\) | |||||||
\(348\) | 26.3522 | 1.41263 | ||||||||
\(349\) | −27.4501 | −1.46937 | −0.734684 | − | 0.678409i | \(-0.762670\pi\) | ||||
−0.734684 | + | 0.678409i | \(0.762670\pi\) | |||||||
\(350\) | 1.70740 | 0.0912642 | ||||||||
\(351\) | −11.4752 | −0.612501 | ||||||||
\(352\) | 120.077 | 6.40015 | ||||||||
\(353\) | 22.5188 | 1.19855 | 0.599277 | − | 0.800542i | \(-0.295455\pi\) | ||||
0.599277 | + | 0.800542i | \(0.295455\pi\) | |||||||
\(354\) | 3.78625 | 0.201237 | ||||||||
\(355\) | −16.7738 | −0.890262 | ||||||||
\(356\) | −24.2790 | −1.28678 | ||||||||
\(357\) | 0.353850 | 0.0187277 | ||||||||
\(358\) | −37.6799 | −1.99144 | ||||||||
\(359\) | −2.25963 | −0.119259 | −0.0596294 | − | 0.998221i | \(-0.518992\pi\) | ||||
−0.0596294 | + | 0.998221i | \(0.518992\pi\) | |||||||
\(360\) | 37.0133 | 1.95077 | ||||||||
\(361\) | −17.9398 | −0.944202 | ||||||||
\(362\) | 44.9988 | 2.36508 | ||||||||
\(363\) | 18.3842 | 0.964921 | ||||||||
\(364\) | 4.22390 | 0.221393 | ||||||||
\(365\) | 11.1943 | 0.585935 | ||||||||
\(366\) | −23.6295 | −1.23514 | ||||||||
\(367\) | −6.64138 | −0.346677 | −0.173339 | − | 0.984862i | \(-0.555456\pi\) | ||||
−0.173339 | + | 0.984862i | \(0.555456\pi\) | |||||||
\(368\) | 60.3983 | 3.14848 | ||||||||
\(369\) | 23.1218 | 1.20367 | ||||||||
\(370\) | −34.8310 | −1.81078 | ||||||||
\(371\) | 2.19710 | 0.114068 | ||||||||
\(372\) | −42.1446 | −2.18509 | ||||||||
\(373\) | 29.2392 | 1.51395 | 0.756973 | − | 0.653446i | \(-0.226677\pi\) | ||||
0.756973 | + | 0.653446i | \(0.226677\pi\) | |||||||
\(374\) | 25.4833 | 1.31771 | ||||||||
\(375\) | −9.35969 | −0.483332 | ||||||||
\(376\) | −105.777 | −5.45505 | ||||||||
\(377\) | 17.2282 | 0.887298 | ||||||||
\(378\) | 3.26130 | 0.167743 | ||||||||
\(379\) | 17.3138 | 0.889349 | 0.444675 | − | 0.895692i | \(-0.353319\pi\) | ||||
0.444675 | + | 0.895692i | \(0.353319\pi\) | |||||||
\(380\) | −9.29797 | −0.476976 | ||||||||
\(381\) | 3.81176 | 0.195282 | ||||||||
\(382\) | 43.5123 | 2.22628 | ||||||||
\(383\) | −1.59035 | −0.0812630 | −0.0406315 | − | 0.999174i | \(-0.512937\pi\) | ||||
−0.0406315 | + | 0.999174i | \(0.512937\pi\) | |||||||
\(384\) | −25.0723 | −1.27946 | ||||||||
\(385\) | −2.82244 | −0.143845 | ||||||||
\(386\) | 27.0475 | 1.37668 | ||||||||
\(387\) | −2.12427 | −0.107983 | ||||||||
\(388\) | −31.2541 | −1.58669 | ||||||||
\(389\) | 19.9732 | 1.01268 | 0.506342 | − | 0.862333i | \(-0.330997\pi\) | ||||
0.506342 | + | 0.862333i | \(0.330997\pi\) | |||||||
\(390\) | −9.68275 | −0.490305 | ||||||||
\(391\) | 6.73136 | 0.340419 | ||||||||
\(392\) | 63.7849 | 3.22163 | ||||||||
\(393\) | −16.6579 | −0.840278 | ||||||||
\(394\) | 66.7258 | 3.36160 | ||||||||
\(395\) | 21.0146 | 1.05736 | ||||||||
\(396\) | 76.0833 | 3.82333 | ||||||||
\(397\) | 2.80364 | 0.140711 | 0.0703554 | − | 0.997522i | \(-0.477587\pi\) | ||||
0.0703554 | + | 0.997522i | \(0.477587\pi\) | |||||||
\(398\) | 9.56616 | 0.479508 | ||||||||
\(399\) | −0.228867 | −0.0114577 | ||||||||
\(400\) | −31.3453 | −1.56727 | ||||||||
\(401\) | −15.9283 | −0.795421 | −0.397711 | − | 0.917511i | \(-0.630195\pi\) | ||||
−0.397711 | + | 0.917511i | \(0.630195\pi\) | |||||||
\(402\) | −25.1576 | −1.25475 | ||||||||
\(403\) | −27.5528 | −1.37250 | ||||||||
\(404\) | −66.1259 | −3.28989 | ||||||||
\(405\) | 6.59021 | 0.327470 | ||||||||
\(406\) | −4.89633 | −0.243001 | ||||||||
\(407\) | −45.0372 | −2.23241 | ||||||||
\(408\) | −11.4001 | −0.564387 | ||||||||
\(409\) | 17.1977 | 0.850370 | 0.425185 | − | 0.905106i | \(-0.360209\pi\) | ||||
0.425185 | + | 0.905106i | \(0.360209\pi\) | |||||||
\(410\) | 43.9309 | 2.16959 | ||||||||
\(411\) | −7.72666 | −0.381128 | ||||||||
\(412\) | −72.6741 | −3.58040 | ||||||||
\(413\) | −0.513141 | −0.0252500 | ||||||||
\(414\) | 27.5526 | 1.35414 | ||||||||
\(415\) | −17.3925 | −0.853763 | ||||||||
\(416\) | −55.8293 | −2.73726 | ||||||||
\(417\) | −0.964881 | −0.0472504 | ||||||||
\(418\) | −16.4824 | −0.806180 | ||||||||
\(419\) | 23.7083 | 1.15823 | 0.579113 | − | 0.815247i | \(-0.303399\pi\) | ||||
0.579113 | + | 0.815247i | \(0.303399\pi\) | |||||||
\(420\) | 2.00725 | 0.0979439 | ||||||||
\(421\) | 18.6876 | 0.910779 | 0.455390 | − | 0.890292i | \(-0.349500\pi\) | ||||
0.455390 | + | 0.890292i | \(0.349500\pi\) | |||||||
\(422\) | −77.1409 | −3.75516 | ||||||||
\(423\) | −27.4967 | −1.33694 | ||||||||
\(424\) | −70.7845 | −3.43760 | ||||||||
\(425\) | −3.49342 | −0.169456 | ||||||||
\(426\) | 21.1466 | 1.02456 | ||||||||
\(427\) | 3.20245 | 0.154977 | ||||||||
\(428\) | −55.2152 | −2.66893 | ||||||||
\(429\) | −12.5200 | −0.604471 | ||||||||
\(430\) | −4.03608 | −0.194637 | ||||||||
\(431\) | −35.8779 | −1.72818 | −0.864090 | − | 0.503338i | \(-0.832105\pi\) | ||||
−0.864090 | + | 0.503338i | \(0.832105\pi\) | |||||||
\(432\) | −59.8728 | −2.88063 | ||||||||
\(433\) | −20.8102 | −1.00007 | −0.500036 | − | 0.866004i | \(-0.666680\pi\) | ||||
−0.500036 | + | 0.866004i | \(0.666680\pi\) | |||||||
\(434\) | 7.83060 | 0.375881 | ||||||||
\(435\) | 8.18707 | 0.392540 | ||||||||
\(436\) | 50.9521 | 2.44016 | ||||||||
\(437\) | −4.35378 | −0.208270 | ||||||||
\(438\) | −14.1125 | −0.674323 | ||||||||
\(439\) | −20.6423 | −0.985205 | −0.492603 | − | 0.870254i | \(-0.663954\pi\) | ||||
−0.492603 | + | 0.870254i | \(0.663954\pi\) | |||||||
\(440\) | 90.9312 | 4.33498 | ||||||||
\(441\) | 16.5808 | 0.789563 | ||||||||
\(442\) | −11.8483 | −0.563567 | ||||||||
\(443\) | −3.45252 | −0.164034 | −0.0820170 | − | 0.996631i | \(-0.526136\pi\) | ||||
−0.0820170 | + | 0.996631i | \(0.526136\pi\) | |||||||
\(444\) | 32.0294 | 1.52005 | ||||||||
\(445\) | −7.54296 | −0.357571 | ||||||||
\(446\) | 60.0829 | 2.84501 | ||||||||
\(447\) | 2.99231 | 0.141531 | ||||||||
\(448\) | 7.69136 | 0.363383 | ||||||||
\(449\) | 32.1167 | 1.51568 | 0.757841 | − | 0.652439i | \(-0.226254\pi\) | ||||
0.757841 | + | 0.652439i | \(0.226254\pi\) | |||||||
\(450\) | −14.2992 | −0.674069 | ||||||||
\(451\) | 56.8036 | 2.67478 | ||||||||
\(452\) | −20.6638 | −0.971946 | ||||||||
\(453\) | −8.98483 | −0.422144 | ||||||||
\(454\) | 55.4302 | 2.60147 | ||||||||
\(455\) | 1.31228 | 0.0615205 | ||||||||
\(456\) | 7.37346 | 0.345294 | ||||||||
\(457\) | −8.15065 | −0.381271 | −0.190636 | − | 0.981661i | \(-0.561055\pi\) | ||||
−0.190636 | + | 0.981661i | \(0.561055\pi\) | |||||||
\(458\) | −4.66203 | −0.217842 | ||||||||
\(459\) | −6.67278 | −0.311459 | ||||||||
\(460\) | 38.1843 | 1.78035 | ||||||||
\(461\) | 28.5191 | 1.32827 | 0.664133 | − | 0.747615i | \(-0.268801\pi\) | ||||
0.664133 | + | 0.747615i | \(0.268801\pi\) | |||||||
\(462\) | 3.55823 | 0.165544 | ||||||||
\(463\) | 13.4653 | 0.625784 | 0.312892 | − | 0.949789i | \(-0.398702\pi\) | ||||
0.312892 | + | 0.949789i | \(0.398702\pi\) | |||||||
\(464\) | 89.8895 | 4.17302 | ||||||||
\(465\) | −13.0934 | −0.607193 | ||||||||
\(466\) | 34.3412 | 1.59083 | ||||||||
\(467\) | 1.84824 | 0.0855264 | 0.0427632 | − | 0.999085i | \(-0.486384\pi\) | ||||
0.0427632 | + | 0.999085i | \(0.486384\pi\) | |||||||
\(468\) | −35.3745 | −1.63519 | ||||||||
\(469\) | 3.40955 | 0.157438 | ||||||||
\(470\) | −52.2432 | −2.40980 | ||||||||
\(471\) | 12.7800 | 0.588873 | ||||||||
\(472\) | 16.5320 | 0.760946 | ||||||||
\(473\) | −5.21873 | −0.239958 | ||||||||
\(474\) | −26.4930 | −1.21686 | ||||||||
\(475\) | 2.25951 | 0.103673 | ||||||||
\(476\) | 2.45618 | 0.112579 | ||||||||
\(477\) | −18.4004 | −0.842495 | ||||||||
\(478\) | 34.6419 | 1.58448 | ||||||||
\(479\) | −7.82347 | −0.357464 | −0.178732 | − | 0.983898i | \(-0.557199\pi\) | ||||
−0.178732 | + | 0.983898i | \(0.557199\pi\) | |||||||
\(480\) | −26.5308 | −1.21096 | ||||||||
\(481\) | 20.9398 | 0.954772 | ||||||||
\(482\) | −32.7512 | −1.49177 | ||||||||
\(483\) | 0.939897 | 0.0427668 | ||||||||
\(484\) | 127.610 | 5.80047 | ||||||||
\(485\) | −9.70997 | −0.440907 | ||||||||
\(486\) | −42.4958 | −1.92765 | ||||||||
\(487\) | −13.7905 | −0.624905 | −0.312453 | − | 0.949933i | \(-0.601151\pi\) | ||||
−0.312453 | + | 0.949933i | \(0.601151\pi\) | |||||||
\(488\) | −103.174 | −4.67047 | ||||||||
\(489\) | −2.09449 | −0.0947159 | ||||||||
\(490\) | 31.5033 | 1.42317 | ||||||||
\(491\) | −13.5499 | −0.611500 | −0.305750 | − | 0.952112i | \(-0.598907\pi\) | ||||
−0.305750 | + | 0.952112i | \(0.598907\pi\) | |||||||
\(492\) | −40.3973 | −1.82125 | ||||||||
\(493\) | 10.0181 | 0.451194 | ||||||||
\(494\) | 7.66338 | 0.344792 | ||||||||
\(495\) | 23.6375 | 1.06243 | ||||||||
\(496\) | −143.759 | −6.45495 | ||||||||
\(497\) | −2.86595 | −0.128555 | ||||||||
\(498\) | 21.9266 | 0.982553 | ||||||||
\(499\) | 0.794090 | 0.0355483 | 0.0177742 | − | 0.999842i | \(-0.494342\pi\) | ||||
0.0177742 | + | 0.999842i | \(0.494342\pi\) | |||||||
\(500\) | −64.9684 | −2.90548 | ||||||||
\(501\) | −4.72019 | −0.210883 | ||||||||
\(502\) | −47.7020 | −2.12904 | ||||||||
\(503\) | −11.0715 | −0.493654 | −0.246827 | − | 0.969060i | \(-0.579388\pi\) | ||||
−0.246827 | + | 0.969060i | \(0.579388\pi\) | |||||||
\(504\) | 6.32404 | 0.281695 | ||||||||
\(505\) | −20.5439 | −0.914192 | ||||||||
\(506\) | 67.6889 | 3.00914 | ||||||||
\(507\) | −4.27605 | −0.189906 | ||||||||
\(508\) | 26.4585 | 1.17391 | ||||||||
\(509\) | 11.4240 | 0.506360 | 0.253180 | − | 0.967419i | \(-0.418524\pi\) | ||||
0.253180 | + | 0.967419i | \(0.418524\pi\) | |||||||
\(510\) | −5.63047 | −0.249321 | ||||||||
\(511\) | 1.91263 | 0.0846100 | ||||||||
\(512\) | −27.9002 | −1.23303 | ||||||||
\(513\) | 4.31589 | 0.190551 | ||||||||
\(514\) | −18.7466 | −0.826876 | ||||||||
\(515\) | −22.5783 | −0.994918 | ||||||||
\(516\) | 3.71144 | 0.163387 | ||||||||
\(517\) | −67.5515 | −2.97091 | ||||||||
\(518\) | −5.95117 | −0.261479 | ||||||||
\(519\) | −11.1216 | −0.488184 | ||||||||
\(520\) | −42.2779 | −1.85401 | ||||||||
\(521\) | −21.0594 | −0.922628 | −0.461314 | − | 0.887237i | \(-0.652622\pi\) | ||||
−0.461314 | + | 0.887237i | \(0.652622\pi\) | |||||||
\(522\) | 41.0059 | 1.79478 | ||||||||
\(523\) | −22.4926 | −0.983535 | −0.491767 | − | 0.870727i | \(-0.663649\pi\) | ||||
−0.491767 | + | 0.870727i | \(0.663649\pi\) | |||||||
\(524\) | −115.627 | −5.05120 | ||||||||
\(525\) | −0.487785 | −0.0212887 | ||||||||
\(526\) | 78.2222 | 3.41065 | ||||||||
\(527\) | −16.0218 | −0.697921 | ||||||||
\(528\) | −65.3240 | −2.84286 | ||||||||
\(529\) | −5.12016 | −0.222616 | ||||||||
\(530\) | −34.9603 | −1.51858 | ||||||||
\(531\) | 4.29747 | 0.186494 | ||||||||
\(532\) | −1.58863 | −0.0688761 | ||||||||
\(533\) | −26.4105 | −1.14396 | ||||||||
\(534\) | 9.50935 | 0.411510 | ||||||||
\(535\) | −17.1542 | −0.741640 | ||||||||
\(536\) | −109.846 | −4.74463 | ||||||||
\(537\) | 10.7647 | 0.464533 | ||||||||
\(538\) | −8.77029 | −0.378114 | ||||||||
\(539\) | 40.7344 | 1.75455 | ||||||||
\(540\) | −37.8521 | −1.62889 | ||||||||
\(541\) | 6.35885 | 0.273388 | 0.136694 | − | 0.990613i | \(-0.456352\pi\) | ||||
0.136694 | + | 0.990613i | \(0.456352\pi\) | |||||||
\(542\) | 7.87989 | 0.338470 | ||||||||
\(543\) | −12.8557 | −0.551690 | ||||||||
\(544\) | −32.4645 | −1.39190 | ||||||||
\(545\) | 15.8297 | 0.678071 | ||||||||
\(546\) | −1.65438 | −0.0708008 | ||||||||
\(547\) | 35.4903 | 1.51746 | 0.758728 | − | 0.651408i | \(-0.225821\pi\) | ||||
0.758728 | + | 0.651408i | \(0.225821\pi\) | |||||||
\(548\) | −53.6330 | −2.29109 | ||||||||
\(549\) | −26.8200 | −1.14465 | ||||||||
\(550\) | −35.1289 | −1.49790 | ||||||||
\(551\) | −6.47963 | −0.276042 | ||||||||
\(552\) | −30.2809 | −1.28884 | ||||||||
\(553\) | 3.59052 | 0.152685 | ||||||||
\(554\) | −11.9077 | −0.505910 | ||||||||
\(555\) | 9.95085 | 0.422390 | ||||||||
\(556\) | −6.69753 | −0.284038 | ||||||||
\(557\) | 0.413168 | 0.0175065 | 0.00875326 | − | 0.999962i | \(-0.497214\pi\) | ||||
0.00875326 | + | 0.999962i | \(0.497214\pi\) | |||||||
\(558\) | −65.5800 | −2.77622 | ||||||||
\(559\) | 2.42642 | 0.102627 | ||||||||
\(560\) | 6.84690 | 0.289334 | ||||||||
\(561\) | −7.28031 | −0.307375 | ||||||||
\(562\) | 63.9632 | 2.69813 | ||||||||
\(563\) | 6.68044 | 0.281547 | 0.140774 | − | 0.990042i | \(-0.455041\pi\) | ||||
0.140774 | + | 0.990042i | \(0.455041\pi\) | |||||||
\(564\) | 48.0410 | 2.02289 | ||||||||
\(565\) | −6.41982 | −0.270084 | ||||||||
\(566\) | 53.5473 | 2.25076 | ||||||||
\(567\) | 1.12599 | 0.0472872 | ||||||||
\(568\) | 92.3328 | 3.87420 | ||||||||
\(569\) | 13.3154 | 0.558212 | 0.279106 | − | 0.960260i | \(-0.409962\pi\) | ||||
0.279106 | + | 0.960260i | \(0.409962\pi\) | |||||||
\(570\) | 3.64174 | 0.152536 | ||||||||
\(571\) | −27.5362 | −1.15236 | −0.576178 | − | 0.817324i | \(-0.695456\pi\) | ||||
−0.576178 | + | 0.817324i | \(0.695456\pi\) | |||||||
\(572\) | −86.9050 | −3.63368 | ||||||||
\(573\) | −12.4310 | −0.519312 | ||||||||
\(574\) | 7.50596 | 0.313293 | ||||||||
\(575\) | −9.27922 | −0.386970 | ||||||||
\(576\) | −64.4139 | −2.68391 | ||||||||
\(577\) | 34.6159 | 1.44108 | 0.720540 | − | 0.693413i | \(-0.243894\pi\) | ||||
0.720540 | + | 0.693413i | \(0.243894\pi\) | |||||||
\(578\) | 39.3282 | 1.63584 | ||||||||
\(579\) | −7.72718 | −0.321130 | ||||||||
\(580\) | 56.8289 | 2.35969 | ||||||||
\(581\) | −2.97165 | −0.123285 | ||||||||
\(582\) | 12.2413 | 0.507418 | ||||||||
\(583\) | −45.2044 | −1.87218 | ||||||||
\(584\) | −61.6198 | −2.54984 | ||||||||
\(585\) | −10.9901 | −0.454385 | ||||||||
\(586\) | 2.80895 | 0.116036 | ||||||||
\(587\) | 37.7832 | 1.55948 | 0.779740 | − | 0.626103i | \(-0.215351\pi\) | ||||
0.779740 | + | 0.626103i | \(0.215351\pi\) | |||||||
\(588\) | −28.9693 | −1.19467 | ||||||||
\(589\) | 10.3628 | 0.426990 | ||||||||
\(590\) | 8.16511 | 0.336152 | ||||||||
\(591\) | −19.0628 | −0.784140 | ||||||||
\(592\) | 109.255 | 4.49035 | ||||||||
\(593\) | −41.5243 | −1.70520 | −0.852599 | − | 0.522566i | \(-0.824975\pi\) | ||||
−0.852599 | + | 0.522566i | \(0.824975\pi\) | |||||||
\(594\) | −67.0998 | −2.75314 | ||||||||
\(595\) | 0.763083 | 0.0312834 | ||||||||
\(596\) | 20.7705 | 0.850793 | ||||||||
\(597\) | −2.73295 | −0.111852 | ||||||||
\(598\) | −31.4715 | −1.28697 | ||||||||
\(599\) | 9.55500 | 0.390407 | 0.195203 | − | 0.980763i | \(-0.437463\pi\) | ||||
0.195203 | + | 0.980763i | \(0.437463\pi\) | |||||||
\(600\) | 15.7151 | 0.641565 | ||||||||
\(601\) | −3.44598 | −0.140565 | −0.0702823 | − | 0.997527i | \(-0.522390\pi\) | ||||
−0.0702823 | + | 0.997527i | \(0.522390\pi\) | |||||||
\(602\) | −0.689597 | −0.0281059 | ||||||||
\(603\) | −28.5544 | −1.16283 | ||||||||
\(604\) | −62.3664 | −2.53765 | ||||||||
\(605\) | 39.6458 | 1.61183 | ||||||||
\(606\) | 25.8996 | 1.05210 | ||||||||
\(607\) | 39.5196 | 1.60405 | 0.802026 | − | 0.597290i | \(-0.203756\pi\) | ||||
0.802026 | + | 0.597290i | \(0.203756\pi\) | |||||||
\(608\) | 20.9977 | 0.851570 | ||||||||
\(609\) | 1.39883 | 0.0566834 | ||||||||
\(610\) | −50.9574 | −2.06321 | ||||||||
\(611\) | 31.4077 | 1.27062 | ||||||||
\(612\) | −20.5701 | −0.831497 | ||||||||
\(613\) | −14.2359 | −0.574982 | −0.287491 | − | 0.957783i | \(-0.592821\pi\) | ||||
−0.287491 | + | 0.957783i | \(0.592821\pi\) | |||||||
\(614\) | 44.6092 | 1.80028 | ||||||||
\(615\) | −12.5506 | −0.506089 | ||||||||
\(616\) | 15.5363 | 0.625977 | ||||||||
\(617\) | −1.34464 | −0.0541333 | −0.0270667 | − | 0.999634i | \(-0.508617\pi\) | ||||
−0.0270667 | + | 0.999634i | \(0.508617\pi\) | |||||||
\(618\) | 28.4643 | 1.14500 | ||||||||
\(619\) | −0.352190 | −0.0141557 | −0.00707786 | − | 0.999975i | \(-0.502253\pi\) | ||||
−0.00707786 | + | 0.999975i | \(0.502253\pi\) | |||||||
\(620\) | −90.8854 | −3.65004 | ||||||||
\(621\) | −17.7242 | −0.711249 | ||||||||
\(622\) | 50.6970 | 2.03277 | ||||||||
\(623\) | −1.28878 | −0.0516338 | ||||||||
\(624\) | 30.3720 | 1.21585 | ||||||||
\(625\) | −9.21195 | −0.368478 | ||||||||
\(626\) | −39.2648 | −1.56934 | ||||||||
\(627\) | 4.70884 | 0.188053 | ||||||||
\(628\) | 88.7101 | 3.53992 | ||||||||
\(629\) | 12.1764 | 0.485504 | ||||||||
\(630\) | 3.12343 | 0.124440 | ||||||||
\(631\) | 30.8908 | 1.22974 | 0.614872 | − | 0.788627i | \(-0.289208\pi\) | ||||
0.614872 | + | 0.788627i | \(0.289208\pi\) | |||||||
\(632\) | −115.677 | −4.60137 | ||||||||
\(633\) | 22.0383 | 0.875944 | ||||||||
\(634\) | −23.5074 | −0.933599 | ||||||||
\(635\) | 8.22011 | 0.326205 | ||||||||
\(636\) | 32.1483 | 1.27476 | ||||||||
\(637\) | −18.9392 | −0.750398 | ||||||||
\(638\) | 100.740 | 3.98833 | ||||||||
\(639\) | 24.0018 | 0.949497 | ||||||||
\(640\) | −54.0687 | −2.13725 | ||||||||
\(641\) | 45.2428 | 1.78698 | 0.893491 | − | 0.449081i | \(-0.148248\pi\) | ||||
0.893491 | + | 0.449081i | \(0.148248\pi\) | |||||||
\(642\) | 21.6261 | 0.853516 | ||||||||
\(643\) | 30.0501 | 1.18506 | 0.592531 | − | 0.805548i | \(-0.298129\pi\) | ||||
0.592531 | + | 0.805548i | \(0.298129\pi\) | |||||||
\(644\) | 6.52411 | 0.257086 | ||||||||
\(645\) | 1.15306 | 0.0454019 | ||||||||
\(646\) | 4.45622 | 0.175328 | ||||||||
\(647\) | 10.8704 | 0.427361 | 0.213681 | − | 0.976904i | \(-0.431455\pi\) | ||||
0.213681 | + | 0.976904i | \(0.431455\pi\) | |||||||
\(648\) | −36.2763 | −1.42507 | ||||||||
\(649\) | 10.5577 | 0.414424 | ||||||||
\(650\) | 16.3330 | 0.640632 | ||||||||
\(651\) | −2.23712 | −0.0876796 | ||||||||
\(652\) | −14.5385 | −0.569370 | ||||||||
\(653\) | 32.2029 | 1.26020 | 0.630098 | − | 0.776516i | \(-0.283015\pi\) | ||||
0.630098 | + | 0.776516i | \(0.283015\pi\) | |||||||
\(654\) | −19.9564 | −0.780357 | ||||||||
\(655\) | −35.9229 | −1.40362 | ||||||||
\(656\) | −137.799 | −5.38013 | ||||||||
\(657\) | −16.0180 | −0.624921 | ||||||||
\(658\) | −8.92618 | −0.347979 | ||||||||
\(659\) | 23.3307 | 0.908837 | 0.454418 | − | 0.890788i | \(-0.349847\pi\) | ||||
0.454418 | + | 0.890788i | \(0.349847\pi\) | |||||||
\(660\) | −41.2983 | −1.60754 | ||||||||
\(661\) | −4.99815 | −0.194405 | −0.0972027 | − | 0.995265i | \(-0.530990\pi\) | ||||
−0.0972027 | + | 0.995265i | \(0.530990\pi\) | |||||||
\(662\) | 72.1896 | 2.80573 | ||||||||
\(663\) | 3.38494 | 0.131460 | ||||||||
\(664\) | 95.7383 | 3.71536 | ||||||||
\(665\) | −0.493555 | −0.0191392 | ||||||||
\(666\) | 49.8401 | 1.93126 | ||||||||
\(667\) | 26.6102 | 1.03035 | ||||||||
\(668\) | −32.7643 | −1.26769 | ||||||||
\(669\) | −17.1650 | −0.663639 | ||||||||
\(670\) | −54.2528 | −2.09597 | ||||||||
\(671\) | −65.8890 | −2.54362 | ||||||||
\(672\) | −4.53300 | −0.174864 | ||||||||
\(673\) | −31.3777 | −1.20952 | −0.604761 | − | 0.796407i | \(-0.706731\pi\) | ||||
−0.604761 | + | 0.796407i | \(0.706731\pi\) | |||||||
\(674\) | 67.0589 | 2.58301 | ||||||||
\(675\) | 9.19847 | 0.354049 | ||||||||
\(676\) | −29.6814 | −1.14159 | ||||||||
\(677\) | 31.6084 | 1.21481 | 0.607405 | − | 0.794393i | \(-0.292211\pi\) | ||||
0.607405 | + | 0.794393i | \(0.292211\pi\) | |||||||
\(678\) | 8.09341 | 0.310826 | ||||||||
\(679\) | −1.65903 | −0.0636677 | ||||||||
\(680\) | −24.5844 | −0.942769 | ||||||||
\(681\) | −15.8358 | −0.606829 | ||||||||
\(682\) | −161.111 | −6.16927 | ||||||||
\(683\) | −12.1091 | −0.463342 | −0.231671 | − | 0.972794i | \(-0.574419\pi\) | ||||
−0.231671 | + | 0.972794i | \(0.574419\pi\) | |||||||
\(684\) | 13.3045 | 0.508712 | ||||||||
\(685\) | −16.6626 | −0.636647 | ||||||||
\(686\) | 10.8289 | 0.413450 | ||||||||
\(687\) | 1.33189 | 0.0508148 | ||||||||
\(688\) | 12.6600 | 0.482658 | ||||||||
\(689\) | 21.0175 | 0.800704 | ||||||||
\(690\) | −14.9557 | −0.569352 | ||||||||
\(691\) | 13.5973 | 0.517267 | 0.258634 | − | 0.965975i | \(-0.416728\pi\) | ||||
0.258634 | + | 0.965975i | \(0.416728\pi\) | |||||||
\(692\) | −77.1983 | −2.93464 | ||||||||
\(693\) | 4.03866 | 0.153416 | ||||||||
\(694\) | −21.0829 | −0.800296 | ||||||||
\(695\) | −2.08078 | −0.0789285 | ||||||||
\(696\) | −45.0663 | −1.70824 | ||||||||
\(697\) | −15.3576 | −0.581709 | ||||||||
\(698\) | 74.6285 | 2.82473 | ||||||||
\(699\) | −9.81091 | −0.371083 | ||||||||
\(700\) | −3.38586 | −0.127974 | ||||||||
\(701\) | −40.5949 | −1.53325 | −0.766624 | − | 0.642096i | \(-0.778065\pi\) | ||||
−0.766624 | + | 0.642096i | \(0.778065\pi\) | |||||||
\(702\) | 31.1977 | 1.17748 | ||||||||
\(703\) | −7.87558 | −0.297033 | ||||||||
\(704\) | −158.246 | −5.96414 | ||||||||
\(705\) | 14.9253 | 0.562120 | ||||||||
\(706\) | −61.2218 | −2.30411 | ||||||||
\(707\) | −3.51010 | −0.132011 | ||||||||
\(708\) | −7.50835 | −0.282181 | ||||||||
\(709\) | −35.4611 | −1.33177 | −0.665885 | − | 0.746054i | \(-0.731946\pi\) | ||||
−0.665885 | + | 0.746054i | \(0.731946\pi\) | |||||||
\(710\) | 45.6030 | 1.71145 | ||||||||
\(711\) | −30.0700 | −1.12771 | ||||||||
\(712\) | 41.5208 | 1.55606 | ||||||||
\(713\) | −42.5571 | −1.59378 | ||||||||
\(714\) | −0.962013 | −0.0360024 | ||||||||
\(715\) | −26.9995 | −1.00973 | ||||||||
\(716\) | 74.7213 | 2.79247 | ||||||||
\(717\) | −9.89681 | −0.369603 | ||||||||
\(718\) | 6.14326 | 0.229264 | ||||||||
\(719\) | 22.5770 | 0.841979 | 0.420990 | − | 0.907065i | \(-0.361683\pi\) | ||||
0.420990 | + | 0.907065i | \(0.361683\pi\) | |||||||
\(720\) | −57.3416 | −2.13700 | ||||||||
\(721\) | −3.85769 | −0.143668 | ||||||||
\(722\) | 48.7731 | 1.81515 | ||||||||
\(723\) | 9.35665 | 0.347978 | ||||||||
\(724\) | −89.2351 | −3.31639 | ||||||||
\(725\) | −13.8101 | −0.512893 | ||||||||
\(726\) | −49.9812 | −1.85498 | ||||||||
\(727\) | −33.2160 | −1.23191 | −0.615956 | − | 0.787781i | \(-0.711230\pi\) | ||||
−0.615956 | + | 0.787781i | \(0.711230\pi\) | |||||||
\(728\) | −7.22353 | −0.267722 | ||||||||
\(729\) | 0.337037 | 0.0124829 | ||||||||
\(730\) | −30.4339 | −1.12641 | ||||||||
\(731\) | 1.41095 | 0.0521859 | ||||||||
\(732\) | 46.8587 | 1.73195 | ||||||||
\(733\) | −3.92461 | −0.144959 | −0.0724794 | − | 0.997370i | \(-0.523091\pi\) | ||||
−0.0724794 | + | 0.997370i | \(0.523091\pi\) | |||||||
\(734\) | 18.0559 | 0.666456 | ||||||||
\(735\) | −9.00014 | −0.331975 | ||||||||
\(736\) | −86.2322 | −3.17856 | ||||||||
\(737\) | −70.1500 | −2.58401 | ||||||||
\(738\) | −62.8611 | −2.31395 | ||||||||
\(739\) | 5.48372 | 0.201722 | 0.100861 | − | 0.994901i | \(-0.467840\pi\) | ||||
0.100861 | + | 0.994901i | \(0.467840\pi\) | |||||||
\(740\) | 69.0719 | 2.53913 | ||||||||
\(741\) | −2.18935 | −0.0804276 | ||||||||
\(742\) | −5.97326 | −0.219285 | ||||||||
\(743\) | 41.9463 | 1.53886 | 0.769430 | − | 0.638731i | \(-0.220540\pi\) | ||||
0.769430 | + | 0.638731i | \(0.220540\pi\) | |||||||
\(744\) | 72.0737 | 2.64235 | ||||||||
\(745\) | 6.45295 | 0.236418 | ||||||||
\(746\) | −79.4925 | −2.91043 | ||||||||
\(747\) | 24.8871 | 0.910570 | ||||||||
\(748\) | −50.5348 | −1.84774 | ||||||||
\(749\) | −2.93093 | −0.107094 | ||||||||
\(750\) | 25.4462 | 0.929163 | ||||||||
\(751\) | 1.46744 | 0.0535475 | 0.0267738 | − | 0.999642i | \(-0.491477\pi\) | ||||
0.0267738 | + | 0.999642i | \(0.491477\pi\) | |||||||
\(752\) | 163.872 | 5.97579 | ||||||||
\(753\) | 13.6279 | 0.496630 | ||||||||
\(754\) | −46.8384 | −1.70575 | ||||||||
\(755\) | −19.3759 | −0.705162 | ||||||||
\(756\) | −6.46734 | −0.235215 | ||||||||
\(757\) | 24.5037 | 0.890601 | 0.445301 | − | 0.895381i | \(-0.353097\pi\) | ||||
0.445301 | + | 0.895381i | \(0.353097\pi\) | |||||||
\(758\) | −47.0710 | −1.70970 | ||||||||
\(759\) | −19.3380 | −0.701924 | ||||||||
\(760\) | 15.9010 | 0.576789 | ||||||||
\(761\) | 23.9544 | 0.868346 | 0.434173 | − | 0.900830i | \(-0.357041\pi\) | ||||
0.434173 | + | 0.900830i | \(0.357041\pi\) | |||||||
\(762\) | −10.3630 | −0.375413 | ||||||||
\(763\) | 2.70464 | 0.0979145 | ||||||||
\(764\) | −86.2872 | −3.12176 | ||||||||
\(765\) | −6.39069 | −0.231056 | ||||||||
\(766\) | 4.32368 | 0.156221 | ||||||||
\(767\) | −4.90871 | −0.177243 | ||||||||
\(768\) | 26.4151 | 0.953173 | ||||||||
\(769\) | −15.6888 | −0.565754 | −0.282877 | − | 0.959156i | \(-0.591289\pi\) | ||||
−0.282877 | + | 0.959156i | \(0.591289\pi\) | |||||||
\(770\) | 7.67337 | 0.276529 | ||||||||
\(771\) | 5.35569 | 0.192881 | ||||||||
\(772\) | −53.6366 | −1.93043 | ||||||||
\(773\) | 2.69024 | 0.0967612 | 0.0483806 | − | 0.998829i | \(-0.484594\pi\) | ||||
0.0483806 | + | 0.998829i | \(0.484594\pi\) | |||||||
\(774\) | 5.77526 | 0.207587 | ||||||||
\(775\) | 22.0862 | 0.793358 | ||||||||
\(776\) | 53.4493 | 1.91872 | ||||||||
\(777\) | 1.70019 | 0.0609938 | ||||||||
\(778\) | −54.3012 | −1.94679 | ||||||||
\(779\) | 9.93313 | 0.355891 | ||||||||
\(780\) | 19.2014 | 0.687521 | ||||||||
\(781\) | 58.9656 | 2.10995 | ||||||||
\(782\) | −18.3005 | −0.654426 | ||||||||
\(783\) | −26.3786 | −0.942694 | ||||||||
\(784\) | −98.8166 | −3.52917 | ||||||||
\(785\) | 27.5603 | 0.983671 | ||||||||
\(786\) | 45.2877 | 1.61536 | ||||||||
\(787\) | −14.6904 | −0.523655 | −0.261828 | − | 0.965115i | \(-0.584325\pi\) | ||||
−0.261828 | + | 0.965115i | \(0.584325\pi\) | |||||||
\(788\) | −132.321 | −4.71374 | ||||||||
\(789\) | −22.3472 | −0.795583 | ||||||||
\(790\) | −57.1325 | −2.03268 | ||||||||
\(791\) | −1.09688 | −0.0390005 | ||||||||
\(792\) | −130.114 | −4.62341 | ||||||||
\(793\) | 30.6347 | 1.08787 | ||||||||
\(794\) | −7.62226 | −0.270504 | ||||||||
\(795\) | 9.98779 | 0.354230 | ||||||||
\(796\) | −18.9702 | −0.672382 | ||||||||
\(797\) | 44.5164 | 1.57685 | 0.788426 | − | 0.615130i | \(-0.210896\pi\) | ||||
0.788426 | + | 0.615130i | \(0.210896\pi\) | |||||||
\(798\) | 0.622221 | 0.0220264 | ||||||||
\(799\) | 18.2634 | 0.646113 | ||||||||
\(800\) | 44.7525 | 1.58224 | ||||||||
\(801\) | 10.7933 | 0.381362 | ||||||||
\(802\) | 43.3043 | 1.52913 | ||||||||
\(803\) | −39.3516 | −1.38869 | ||||||||
\(804\) | 49.8890 | 1.75945 | ||||||||
\(805\) | 2.02690 | 0.0714389 | ||||||||
\(806\) | 74.9077 | 2.63851 | ||||||||
\(807\) | 2.50558 | 0.0882005 | ||||||||
\(808\) | 113.086 | 3.97834 | ||||||||
\(809\) | 0.884733 | 0.0311056 | 0.0155528 | − | 0.999879i | \(-0.495049\pi\) | ||||
0.0155528 | + | 0.999879i | \(0.495049\pi\) | |||||||
\(810\) | −17.9168 | −0.629532 | ||||||||
\(811\) | −22.0729 | −0.775085 | −0.387542 | − | 0.921852i | \(-0.626676\pi\) | ||||
−0.387542 | + | 0.921852i | \(0.626676\pi\) | |||||||
\(812\) | 9.70969 | 0.340743 | ||||||||
\(813\) | −2.25120 | −0.0789531 | ||||||||
\(814\) | 122.443 | 4.29162 | ||||||||
\(815\) | −4.51679 | −0.158216 | ||||||||
\(816\) | 17.6612 | 0.618264 | ||||||||
\(817\) | −0.912590 | −0.0319275 | ||||||||
\(818\) | −46.7553 | −1.63476 | ||||||||
\(819\) | −1.87775 | −0.0656139 | ||||||||
\(820\) | −87.1174 | −3.04227 | ||||||||
\(821\) | −16.1828 | −0.564783 | −0.282392 | − | 0.959299i | \(-0.591128\pi\) | ||||
−0.282392 | + | 0.959299i | \(0.591128\pi\) | |||||||
\(822\) | 21.0065 | 0.732684 | ||||||||
\(823\) | −19.9634 | −0.695879 | −0.347940 | − | 0.937517i | \(-0.613119\pi\) | ||||
−0.347940 | + | 0.937517i | \(0.613119\pi\) | |||||||
\(824\) | 124.284 | 4.32964 | ||||||||
\(825\) | 10.0360 | 0.349407 | ||||||||
\(826\) | 1.39508 | 0.0485409 | ||||||||
\(827\) | −20.2344 | −0.703620 | −0.351810 | − | 0.936072i | \(-0.614434\pi\) | ||||
−0.351810 | + | 0.936072i | \(0.614434\pi\) | |||||||
\(828\) | −54.6383 | −1.89881 | ||||||||
\(829\) | −27.7151 | −0.962586 | −0.481293 | − | 0.876560i | \(-0.659833\pi\) | ||||
−0.481293 | + | 0.876560i | \(0.659833\pi\) | |||||||
\(830\) | 47.2849 | 1.64128 | ||||||||
\(831\) | 3.40190 | 0.118011 | ||||||||
\(832\) | 73.5757 | 2.55078 | ||||||||
\(833\) | −11.0131 | −0.381580 | ||||||||
\(834\) | 2.62322 | 0.0908348 | ||||||||
\(835\) | −10.1792 | −0.352264 | ||||||||
\(836\) | 32.6855 | 1.13045 | ||||||||
\(837\) | 42.1868 | 1.45819 | ||||||||
\(838\) | −64.4557 | −2.22659 | ||||||||
\(839\) | −46.8928 | −1.61892 | −0.809459 | − | 0.587176i | \(-0.800239\pi\) | ||||
−0.809459 | + | 0.587176i | \(0.800239\pi\) | |||||||
\(840\) | −3.43271 | −0.118440 | ||||||||
\(841\) | 10.6033 | 0.365631 | ||||||||
\(842\) | −50.8060 | −1.75089 | ||||||||
\(843\) | −18.2736 | −0.629376 | ||||||||
\(844\) | 152.975 | 5.26560 | ||||||||
\(845\) | −9.22137 | −0.317225 | ||||||||
\(846\) | 74.7553 | 2.57014 | ||||||||
\(847\) | 6.77382 | 0.232751 | ||||||||
\(848\) | 109.660 | 3.76576 | ||||||||
\(849\) | −15.2979 | −0.525022 | ||||||||
\(850\) | 9.49755 | 0.325763 | ||||||||
\(851\) | 32.3429 | 1.10870 | ||||||||
\(852\) | −41.9349 | −1.43667 | ||||||||
\(853\) | 52.2677 | 1.78961 | 0.894805 | − | 0.446457i | \(-0.147314\pi\) | ||||
0.894805 | + | 0.446457i | \(0.147314\pi\) | |||||||
\(854\) | −8.70650 | −0.297930 | ||||||||
\(855\) | 4.13344 | 0.141361 | ||||||||
\(856\) | 94.4265 | 3.22743 | ||||||||
\(857\) | 24.0388 | 0.821151 | 0.410575 | − | 0.911827i | \(-0.365328\pi\) | ||||
0.410575 | + | 0.911827i | \(0.365328\pi\) | |||||||
\(858\) | 34.0381 | 1.16204 | ||||||||
\(859\) | −39.1147 | −1.33458 | −0.667289 | − | 0.744799i | \(-0.732545\pi\) | ||||
−0.667289 | + | 0.744799i | \(0.732545\pi\) | |||||||
\(860\) | 8.00376 | 0.272926 | ||||||||
\(861\) | −2.14437 | −0.0730800 | ||||||||
\(862\) | 97.5414 | 3.32227 | ||||||||
\(863\) | 5.96931 | 0.203198 | 0.101599 | − | 0.994825i | \(-0.467604\pi\) | ||||
0.101599 | + | 0.994825i | \(0.467604\pi\) | |||||||
\(864\) | 85.4818 | 2.90815 | ||||||||
\(865\) | −23.9839 | −0.815476 | ||||||||
\(866\) | 56.5766 | 1.92255 | ||||||||
\(867\) | −11.2356 | −0.381582 | ||||||||
\(868\) | −15.5285 | −0.527072 | ||||||||
\(869\) | −73.8734 | −2.50599 | ||||||||
\(870\) | −22.2582 | −0.754623 | ||||||||
\(871\) | 32.6158 | 1.10514 | ||||||||
\(872\) | −87.1360 | −2.95080 | ||||||||
\(873\) | 13.8941 | 0.470244 | ||||||||
\(874\) | 11.8366 | 0.400380 | ||||||||
\(875\) | −3.44865 | −0.116586 | ||||||||
\(876\) | 27.9859 | 0.945557 | ||||||||
\(877\) | −55.6428 | −1.87892 | −0.939462 | − | 0.342654i | \(-0.888674\pi\) | ||||
−0.939462 | + | 0.342654i | \(0.888674\pi\) | |||||||
\(878\) | 56.1203 | 1.89397 | ||||||||
\(879\) | −0.802485 | −0.0270672 | ||||||||
\(880\) | −140.872 | −4.74880 | ||||||||
\(881\) | 1.64744 | 0.0555035 | 0.0277518 | − | 0.999615i | \(-0.491165\pi\) | ||||
0.0277518 | + | 0.999615i | \(0.491165\pi\) | |||||||
\(882\) | −45.0783 | −1.51787 | ||||||||
\(883\) | 32.1842 | 1.08308 | 0.541542 | − | 0.840674i | \(-0.317841\pi\) | ||||
0.541542 | + | 0.840674i | \(0.317841\pi\) | |||||||
\(884\) | 23.4959 | 0.790251 | ||||||||
\(885\) | −2.33268 | −0.0784123 | ||||||||
\(886\) | 9.38636 | 0.315341 | ||||||||
\(887\) | 23.8081 | 0.799397 | 0.399699 | − | 0.916647i | \(-0.369115\pi\) | ||||
0.399699 | + | 0.916647i | \(0.369115\pi\) | |||||||
\(888\) | −54.7752 | −1.83814 | ||||||||
\(889\) | 1.40447 | 0.0471045 | ||||||||
\(890\) | 20.5071 | 0.687398 | ||||||||
\(891\) | −23.1668 | −0.776117 | ||||||||
\(892\) | −119.148 | −3.98936 | ||||||||
\(893\) | −11.8126 | −0.395294 | ||||||||
\(894\) | −8.13519 | −0.272081 | ||||||||
\(895\) | 23.2143 | 0.775969 | ||||||||
\(896\) | −9.23809 | −0.308623 | ||||||||
\(897\) | 8.99107 | 0.300203 | ||||||||
\(898\) | −87.3157 | −2.91376 | ||||||||
\(899\) | −63.3368 | −2.11240 | ||||||||
\(900\) | 28.3560 | 0.945200 | ||||||||
\(901\) | 12.2216 | 0.407160 | ||||||||
\(902\) | −154.432 | −5.14202 | ||||||||
\(903\) | 0.197011 | 0.00655610 | ||||||||
\(904\) | 35.3384 | 1.17534 | ||||||||
\(905\) | −27.7234 | −0.921558 | ||||||||
\(906\) | 24.4271 | 0.811535 | ||||||||
\(907\) | −42.9573 | −1.42637 | −0.713187 | − | 0.700973i | \(-0.752749\pi\) | ||||
−0.713187 | + | 0.700973i | \(0.752749\pi\) | |||||||
\(908\) | −109.921 | −3.64786 | ||||||||
\(909\) | 29.3965 | 0.975020 | ||||||||
\(910\) | −3.56769 | −0.118268 | ||||||||
\(911\) | 1.20152 | 0.0398081 | 0.0199040 | − | 0.999802i | \(-0.493664\pi\) | ||||
0.0199040 | + | 0.999802i | \(0.493664\pi\) | |||||||
\(912\) | −11.4231 | −0.378256 | ||||||||
\(913\) | 61.1404 | 2.02345 | ||||||||
\(914\) | 22.1592 | 0.732960 | ||||||||
\(915\) | 14.5580 | 0.481272 | ||||||||
\(916\) | 9.24505 | 0.305465 | ||||||||
\(917\) | −6.13773 | −0.202686 | ||||||||
\(918\) | 18.1413 | 0.598752 | ||||||||
\(919\) | −27.8314 | −0.918073 | −0.459037 | − | 0.888417i | \(-0.651805\pi\) | ||||
−0.459037 | + | 0.888417i | \(0.651805\pi\) | |||||||
\(920\) | −65.3011 | −2.15291 | ||||||||
\(921\) | −12.7444 | −0.419941 | ||||||||
\(922\) | −77.5348 | −2.55347 | ||||||||
\(923\) | −27.4157 | −0.902398 | ||||||||
\(924\) | −7.05616 | −0.232131 | ||||||||
\(925\) | −16.7852 | −0.551895 | ||||||||
\(926\) | −36.6080 | −1.20301 | ||||||||
\(927\) | 32.3075 | 1.06112 | ||||||||
\(928\) | −128.337 | −4.21288 | ||||||||
\(929\) | −35.3260 | −1.15901 | −0.579505 | − | 0.814969i | \(-0.696754\pi\) | ||||
−0.579505 | + | 0.814969i | \(0.696754\pi\) | |||||||
\(930\) | 35.5971 | 1.16727 | ||||||||
\(931\) | 7.12314 | 0.233451 | ||||||||
\(932\) | −68.1005 | −2.23070 | ||||||||
\(933\) | −14.4836 | −0.474172 | ||||||||
\(934\) | −5.02481 | −0.164417 | ||||||||
\(935\) | −15.7001 | −0.513448 | ||||||||
\(936\) | 60.4958 | 1.97737 | ||||||||
\(937\) | −2.85338 | −0.0932157 | −0.0466079 | − | 0.998913i | \(-0.514841\pi\) | ||||
−0.0466079 | + | 0.998913i | \(0.514841\pi\) | |||||||
\(938\) | −9.26954 | −0.302661 | ||||||||
\(939\) | 11.2175 | 0.366070 | ||||||||
\(940\) | 103.601 | 3.37910 | ||||||||
\(941\) | 23.5288 | 0.767018 | 0.383509 | − | 0.923537i | \(-0.374716\pi\) | ||||
0.383509 | + | 0.923537i | \(0.374716\pi\) | |||||||
\(942\) | −34.7451 | −1.13206 | ||||||||
\(943\) | −40.7928 | −1.32840 | ||||||||
\(944\) | −25.6116 | −0.833586 | ||||||||
\(945\) | −2.00926 | −0.0653614 | ||||||||
\(946\) | 14.1882 | 0.461297 | ||||||||
\(947\) | 25.7916 | 0.838114 | 0.419057 | − | 0.907960i | \(-0.362361\pi\) | ||||
0.419057 | + | 0.907960i | \(0.362361\pi\) | |||||||
\(948\) | 52.5370 | 1.70632 | ||||||||
\(949\) | 18.2963 | 0.593923 | ||||||||
\(950\) | −6.14293 | −0.199303 | ||||||||
\(951\) | 6.71582 | 0.217775 | ||||||||
\(952\) | −4.20045 | −0.136137 | ||||||||
\(953\) | −14.1177 | −0.457319 | −0.228659 | − | 0.973507i | \(-0.573434\pi\) | ||||
−0.228659 | + | 0.973507i | \(0.573434\pi\) | |||||||
\(954\) | 50.0251 | 1.61962 | ||||||||
\(955\) | −26.8076 | −0.867474 | ||||||||
\(956\) | −68.6967 | −2.22181 | ||||||||
\(957\) | −28.7803 | −0.930334 | ||||||||
\(958\) | 21.2697 | 0.687192 | ||||||||
\(959\) | −2.84695 | −0.0919328 | ||||||||
\(960\) | 34.9641 | 1.12846 | ||||||||
\(961\) | 70.2934 | 2.26753 | ||||||||
\(962\) | −56.9290 | −1.83546 | ||||||||
\(963\) | 24.5461 | 0.790986 | ||||||||
\(964\) | 64.9473 | 2.09181 | ||||||||
\(965\) | −16.6638 | −0.536426 | ||||||||
\(966\) | −2.55530 | −0.0822154 | ||||||||
\(967\) | −32.3859 | −1.04146 | −0.520730 | − | 0.853722i | \(-0.674340\pi\) | ||||
−0.520730 | + | 0.853722i | \(0.674340\pi\) | |||||||
\(968\) | −218.233 | −7.01429 | ||||||||
\(969\) | −1.27309 | −0.0408977 | ||||||||
\(970\) | 26.3985 | 0.847605 | ||||||||
\(971\) | −55.7842 | −1.79020 | −0.895100 | − | 0.445865i | \(-0.852896\pi\) | ||||
−0.895100 | + | 0.445865i | \(0.852896\pi\) | |||||||
\(972\) | 84.2715 | 2.70301 | ||||||||
\(973\) | −0.355518 | −0.0113974 | ||||||||
\(974\) | 37.4921 | 1.20133 | ||||||||
\(975\) | −4.66616 | −0.149437 | ||||||||
\(976\) | 159.839 | 5.11631 | ||||||||
\(977\) | 7.25606 | 0.232142 | 0.116071 | − | 0.993241i | \(-0.462970\pi\) | ||||
0.116071 | + | 0.993241i | \(0.462970\pi\) | |||||||
\(978\) | 5.69428 | 0.182083 | ||||||||
\(979\) | 26.5160 | 0.847456 | ||||||||
\(980\) | −62.4727 | −1.99562 | ||||||||
\(981\) | −22.6509 | −0.723188 | ||||||||
\(982\) | 36.8382 | 1.17555 | ||||||||
\(983\) | 41.7273 | 1.33090 | 0.665448 | − | 0.746445i | \(-0.268241\pi\) | ||||
0.665448 | + | 0.746445i | \(0.268241\pi\) | |||||||
\(984\) | 69.0857 | 2.20237 | ||||||||
\(985\) | −41.1093 | −1.30985 | ||||||||
\(986\) | −27.2363 | −0.867380 | ||||||||
\(987\) | 2.55011 | 0.0811710 | ||||||||
\(988\) | −15.1969 | −0.483478 | ||||||||
\(989\) | 3.74777 | 0.119172 | ||||||||
\(990\) | −64.2632 | −2.04242 | ||||||||
\(991\) | −0.308961 | −0.00981447 | −0.00490723 | − | 0.999988i | \(-0.501562\pi\) | ||||
−0.00490723 | + | 0.999988i | \(0.501562\pi\) | |||||||
\(992\) | 205.248 | 6.51662 | ||||||||
\(993\) | −20.6238 | −0.654476 | ||||||||
\(994\) | 7.79165 | 0.247136 | ||||||||
\(995\) | −5.89364 | −0.186841 | ||||||||
\(996\) | −43.4816 | −1.37777 | ||||||||
\(997\) | 57.2366 | 1.81270 | 0.906350 | − | 0.422527i | \(-0.138857\pi\) | ||||
0.906350 | + | 0.422527i | \(0.138857\pi\) | |||||||
\(998\) | −2.15889 | −0.0683385 | ||||||||
\(999\) | −32.0615 | −1.01438 |
(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 | 6037.2.a.a.1.11 | ✓ | 243 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.a.1.11 | ✓ | 243 | 1.1 | even | 1 | trivial |