Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6043,2,Mod(1,6043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6043, 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("6043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6043 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6043.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: | \(48.2535979415\) |
Analytic rank: | \(0\) |
Dimension: | \(259\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62452 | −1.85582 | −0.927908 | − | 0.372809i | \(-0.878395\pi\) | ||||
−0.927908 | + | 0.372809i | \(0.878395\pi\) | |||||||
\(3\) | −2.36333 | −1.36447 | −0.682233 | − | 0.731135i | \(-0.738991\pi\) | ||||
−0.682233 | + | 0.731135i | \(0.738991\pi\) | |||||||
\(4\) | 4.88811 | 2.44405 | ||||||||
\(5\) | 3.68491 | 1.64794 | 0.823972 | − | 0.566631i | \(-0.191753\pi\) | ||||
0.823972 | + | 0.566631i | \(0.191753\pi\) | |||||||
\(6\) | 6.20260 | 2.53220 | ||||||||
\(7\) | 1.44250 | 0.545212 | 0.272606 | − | 0.962126i | \(-0.412114\pi\) | ||||
0.272606 | + | 0.962126i | \(0.412114\pi\) | |||||||
\(8\) | −7.57990 | −2.67990 | ||||||||
\(9\) | 2.58531 | 0.861769 | ||||||||
\(10\) | −9.67113 | −3.05828 | ||||||||
\(11\) | −2.04225 | −0.615763 | −0.307881 | − | 0.951425i | \(-0.599620\pi\) | ||||
−0.307881 | + | 0.951425i | \(0.599620\pi\) | |||||||
\(12\) | −11.5522 | −3.33483 | ||||||||
\(13\) | 4.18689 | 1.16123 | 0.580617 | − | 0.814177i | \(-0.302811\pi\) | ||||
0.580617 | + | 0.814177i | \(0.302811\pi\) | |||||||
\(14\) | −3.78586 | −1.01181 | ||||||||
\(15\) | −8.70865 | −2.24856 | ||||||||
\(16\) | 10.1174 | 2.52934 | ||||||||
\(17\) | 6.70285 | 1.62568 | 0.812840 | − | 0.582487i | \(-0.197920\pi\) | ||||
0.812840 | + | 0.582487i | \(0.197920\pi\) | |||||||
\(18\) | −6.78519 | −1.59929 | ||||||||
\(19\) | 3.78984 | 0.869450 | 0.434725 | − | 0.900563i | \(-0.356846\pi\) | ||||
0.434725 | + | 0.900563i | \(0.356846\pi\) | |||||||
\(20\) | 18.0123 | 4.02766 | ||||||||
\(21\) | −3.40909 | −0.743924 | ||||||||
\(22\) | 5.35994 | 1.14274 | ||||||||
\(23\) | −1.61930 | −0.337648 | −0.168824 | − | 0.985646i | \(-0.553997\pi\) | ||||
−0.168824 | + | 0.985646i | \(0.553997\pi\) | |||||||
\(24\) | 17.9138 | 3.65663 | ||||||||
\(25\) | 8.57859 | 1.71572 | ||||||||
\(26\) | −10.9886 | −2.15504 | ||||||||
\(27\) | 0.980053 | 0.188611 | ||||||||
\(28\) | 7.05108 | 1.33253 | ||||||||
\(29\) | 2.83106 | 0.525715 | 0.262857 | − | 0.964835i | \(-0.415335\pi\) | ||||
0.262857 | + | 0.964835i | \(0.415335\pi\) | |||||||
\(30\) | 22.8560 | 4.17292 | ||||||||
\(31\) | 1.97280 | 0.354326 | 0.177163 | − | 0.984182i | \(-0.443308\pi\) | ||||
0.177163 | + | 0.984182i | \(0.443308\pi\) | |||||||
\(32\) | −11.3935 | −2.01410 | ||||||||
\(33\) | 4.82651 | 0.840188 | ||||||||
\(34\) | −17.5918 | −3.01696 | ||||||||
\(35\) | 5.31548 | 0.898479 | ||||||||
\(36\) | 12.6373 | 2.10621 | ||||||||
\(37\) | −3.63001 | −0.596770 | −0.298385 | − | 0.954446i | \(-0.596448\pi\) | ||||
−0.298385 | + | 0.954446i | \(0.596448\pi\) | |||||||
\(38\) | −9.94652 | −1.61354 | ||||||||
\(39\) | −9.89498 | −1.58446 | ||||||||
\(40\) | −27.9313 | −4.41632 | ||||||||
\(41\) | 10.1067 | 1.57841 | 0.789204 | − | 0.614131i | \(-0.210493\pi\) | ||||
0.789204 | + | 0.614131i | \(0.210493\pi\) | |||||||
\(42\) | 8.94722 | 1.38059 | ||||||||
\(43\) | −4.57801 | −0.698140 | −0.349070 | − | 0.937097i | \(-0.613502\pi\) | ||||
−0.349070 | + | 0.937097i | \(0.613502\pi\) | |||||||
\(44\) | −9.98275 | −1.50496 | ||||||||
\(45\) | 9.52664 | 1.42015 | ||||||||
\(46\) | 4.24990 | 0.626613 | ||||||||
\(47\) | 5.72661 | 0.835311 | 0.417656 | − | 0.908605i | \(-0.362852\pi\) | ||||
0.417656 | + | 0.908605i | \(0.362852\pi\) | |||||||
\(48\) | −23.9107 | −3.45121 | ||||||||
\(49\) | −4.91920 | −0.702743 | ||||||||
\(50\) | −22.5147 | −3.18406 | ||||||||
\(51\) | −15.8410 | −2.21819 | ||||||||
\(52\) | 20.4660 | 2.83812 | ||||||||
\(53\) | 0.958172 | 0.131615 | 0.0658075 | − | 0.997832i | \(-0.479038\pi\) | ||||
0.0658075 | + | 0.997832i | \(0.479038\pi\) | |||||||
\(54\) | −2.57217 | −0.350028 | ||||||||
\(55\) | −7.52553 | −1.01474 | ||||||||
\(56\) | −10.9340 | −1.46111 | ||||||||
\(57\) | −8.95664 | −1.18634 | ||||||||
\(58\) | −7.43017 | −0.975630 | ||||||||
\(59\) | 9.09821 | 1.18449 | 0.592243 | − | 0.805759i | \(-0.298242\pi\) | ||||
0.592243 | + | 0.805759i | \(0.298242\pi\) | |||||||
\(60\) | −42.5688 | −5.49561 | ||||||||
\(61\) | −6.37699 | −0.816490 | −0.408245 | − | 0.912872i | \(-0.633859\pi\) | ||||
−0.408245 | + | 0.912872i | \(0.633859\pi\) | |||||||
\(62\) | −5.17767 | −0.657564 | ||||||||
\(63\) | 3.72930 | 0.469847 | ||||||||
\(64\) | 9.66764 | 1.20846 | ||||||||
\(65\) | 15.4283 | 1.91365 | ||||||||
\(66\) | −12.6673 | −1.55923 | ||||||||
\(67\) | 4.49415 | 0.549048 | 0.274524 | − | 0.961580i | \(-0.411480\pi\) | ||||
0.274524 | + | 0.961580i | \(0.411480\pi\) | |||||||
\(68\) | 32.7642 | 3.97325 | ||||||||
\(69\) | 3.82694 | 0.460710 | ||||||||
\(70\) | −13.9506 | −1.66741 | ||||||||
\(71\) | −1.97391 | −0.234259 | −0.117130 | − | 0.993117i | \(-0.537369\pi\) | ||||
−0.117130 | + | 0.993117i | \(0.537369\pi\) | |||||||
\(72\) | −19.5964 | −2.30945 | ||||||||
\(73\) | 3.64190 | 0.426252 | 0.213126 | − | 0.977025i | \(-0.431635\pi\) | ||||
0.213126 | + | 0.977025i | \(0.431635\pi\) | |||||||
\(74\) | 9.52704 | 1.10750 | ||||||||
\(75\) | −20.2740 | −2.34104 | ||||||||
\(76\) | 18.5252 | 2.12498 | ||||||||
\(77\) | −2.94594 | −0.335721 | ||||||||
\(78\) | 25.9696 | 2.94047 | ||||||||
\(79\) | −3.02288 | −0.340100 | −0.170050 | − | 0.985435i | \(-0.554393\pi\) | ||||
−0.170050 | + | 0.985435i | \(0.554393\pi\) | |||||||
\(80\) | 37.2817 | 4.16822 | ||||||||
\(81\) | −10.0721 | −1.11912 | ||||||||
\(82\) | −26.5254 | −2.92924 | ||||||||
\(83\) | −3.50471 | −0.384691 | −0.192346 | − | 0.981327i | \(-0.561610\pi\) | ||||
−0.192346 | + | 0.981327i | \(0.561610\pi\) | |||||||
\(84\) | −16.6640 | −1.81819 | ||||||||
\(85\) | 24.6994 | 2.67903 | ||||||||
\(86\) | 12.0151 | 1.29562 | ||||||||
\(87\) | −6.69072 | −0.717320 | ||||||||
\(88\) | 15.4801 | 1.65018 | ||||||||
\(89\) | 11.6591 | 1.23586 | 0.617932 | − | 0.786231i | \(-0.287971\pi\) | ||||
0.617932 | + | 0.786231i | \(0.287971\pi\) | |||||||
\(90\) | −25.0029 | −2.63553 | ||||||||
\(91\) | 6.03957 | 0.633119 | ||||||||
\(92\) | −7.91533 | −0.825230 | ||||||||
\(93\) | −4.66238 | −0.483466 | ||||||||
\(94\) | −15.0296 | −1.55018 | ||||||||
\(95\) | 13.9653 | 1.43280 | ||||||||
\(96\) | 26.9265 | 2.74817 | ||||||||
\(97\) | 8.22875 | 0.835503 | 0.417752 | − | 0.908561i | \(-0.362818\pi\) | ||||
0.417752 | + | 0.908561i | \(0.362818\pi\) | |||||||
\(98\) | 12.9106 | 1.30416 | ||||||||
\(99\) | −5.27985 | −0.530645 | ||||||||
\(100\) | 41.9331 | 4.19331 | ||||||||
\(101\) | 12.3860 | 1.23245 | 0.616226 | − | 0.787569i | \(-0.288661\pi\) | ||||
0.616226 | + | 0.787569i | \(0.288661\pi\) | |||||||
\(102\) | 41.5751 | 4.11655 | ||||||||
\(103\) | 4.92656 | 0.485429 | 0.242714 | − | 0.970098i | \(-0.421962\pi\) | ||||
0.242714 | + | 0.970098i | \(0.421962\pi\) | |||||||
\(104\) | −31.7362 | −3.11199 | ||||||||
\(105\) | −12.5622 | −1.22595 | ||||||||
\(106\) | −2.51474 | −0.244253 | ||||||||
\(107\) | −2.17911 | −0.210663 | −0.105331 | − | 0.994437i | \(-0.533590\pi\) | ||||
−0.105331 | + | 0.994437i | \(0.533590\pi\) | |||||||
\(108\) | 4.79060 | 0.460976 | ||||||||
\(109\) | −9.72180 | −0.931180 | −0.465590 | − | 0.885001i | \(-0.654158\pi\) | ||||
−0.465590 | + | 0.885001i | \(0.654158\pi\) | |||||||
\(110\) | 19.7509 | 1.88318 | ||||||||
\(111\) | 8.57890 | 0.814273 | ||||||||
\(112\) | 14.5943 | 1.37903 | ||||||||
\(113\) | 17.4592 | 1.64242 | 0.821211 | − | 0.570625i | \(-0.193299\pi\) | ||||
0.821211 | + | 0.570625i | \(0.193299\pi\) | |||||||
\(114\) | 23.5069 | 2.20162 | ||||||||
\(115\) | −5.96700 | −0.556425 | ||||||||
\(116\) | 13.8385 | 1.28487 | ||||||||
\(117\) | 10.8244 | 1.00072 | ||||||||
\(118\) | −23.8784 | −2.19819 | ||||||||
\(119\) | 9.66884 | 0.886341 | ||||||||
\(120\) | 66.0107 | 6.02592 | ||||||||
\(121\) | −6.82920 | −0.620836 | ||||||||
\(122\) | 16.7365 | 1.51526 | ||||||||
\(123\) | −23.8855 | −2.15369 | ||||||||
\(124\) | 9.64328 | 0.865992 | ||||||||
\(125\) | 13.1868 | 1.17946 | ||||||||
\(126\) | −9.78762 | −0.871950 | ||||||||
\(127\) | 6.48617 | 0.575555 | 0.287777 | − | 0.957697i | \(-0.407084\pi\) | ||||
0.287777 | + | 0.957697i | \(0.407084\pi\) | |||||||
\(128\) | −2.58598 | −0.228570 | ||||||||
\(129\) | 10.8193 | 0.952588 | ||||||||
\(130\) | −40.4919 | −3.55138 | ||||||||
\(131\) | −0.598287 | −0.0522726 | −0.0261363 | − | 0.999658i | \(-0.508320\pi\) | ||||
−0.0261363 | + | 0.999658i | \(0.508320\pi\) | |||||||
\(132\) | 23.5925 | 2.05346 | ||||||||
\(133\) | 5.46684 | 0.474035 | ||||||||
\(134\) | −11.7950 | −1.01893 | ||||||||
\(135\) | 3.61141 | 0.310821 | ||||||||
\(136\) | −50.8069 | −4.35666 | ||||||||
\(137\) | 3.79200 | 0.323972 | 0.161986 | − | 0.986793i | \(-0.448210\pi\) | ||||
0.161986 | + | 0.986793i | \(0.448210\pi\) | |||||||
\(138\) | −10.0439 | −0.854993 | ||||||||
\(139\) | 1.58937 | 0.134809 | 0.0674043 | − | 0.997726i | \(-0.478528\pi\) | ||||
0.0674043 | + | 0.997726i | \(0.478528\pi\) | |||||||
\(140\) | 25.9826 | 2.19593 | ||||||||
\(141\) | −13.5338 | −1.13975 | ||||||||
\(142\) | 5.18056 | 0.434743 | ||||||||
\(143\) | −8.55069 | −0.715044 | ||||||||
\(144\) | 26.1565 | 2.17971 | ||||||||
\(145\) | 10.4322 | 0.866348 | ||||||||
\(146\) | −9.55824 | −0.791046 | ||||||||
\(147\) | 11.6257 | 0.958870 | ||||||||
\(148\) | −17.7439 | −1.45854 | ||||||||
\(149\) | −6.76024 | −0.553820 | −0.276910 | − | 0.960896i | \(-0.589310\pi\) | ||||
−0.276910 | + | 0.960896i | \(0.589310\pi\) | |||||||
\(150\) | 53.2096 | 4.34454 | ||||||||
\(151\) | −19.3917 | −1.57807 | −0.789035 | − | 0.614348i | \(-0.789419\pi\) | ||||
−0.789035 | + | 0.614348i | \(0.789419\pi\) | |||||||
\(152\) | −28.7266 | −2.33004 | ||||||||
\(153\) | 17.3289 | 1.40096 | ||||||||
\(154\) | 7.73169 | 0.623037 | ||||||||
\(155\) | 7.26962 | 0.583910 | ||||||||
\(156\) | −48.3677 | −3.87252 | ||||||||
\(157\) | 14.9557 | 1.19359 | 0.596796 | − | 0.802393i | \(-0.296440\pi\) | ||||
0.596796 | + | 0.802393i | \(0.296440\pi\) | |||||||
\(158\) | 7.93360 | 0.631163 | ||||||||
\(159\) | −2.26447 | −0.179584 | ||||||||
\(160\) | −41.9840 | −3.31912 | ||||||||
\(161\) | −2.33584 | −0.184090 | ||||||||
\(162\) | 26.4345 | 2.07689 | ||||||||
\(163\) | 16.0042 | 1.25354 | 0.626772 | − | 0.779202i | \(-0.284376\pi\) | ||||
0.626772 | + | 0.779202i | \(0.284376\pi\) | |||||||
\(164\) | 49.4029 | 3.85772 | ||||||||
\(165\) | 17.7853 | 1.38458 | ||||||||
\(166\) | 9.19817 | 0.713917 | ||||||||
\(167\) | −6.75575 | −0.522776 | −0.261388 | − | 0.965234i | \(-0.584180\pi\) | ||||
−0.261388 | + | 0.965234i | \(0.584180\pi\) | |||||||
\(168\) | 25.8405 | 1.99364 | ||||||||
\(169\) | 4.53002 | 0.348463 | ||||||||
\(170\) | −64.8242 | −4.97179 | ||||||||
\(171\) | 9.79791 | 0.749265 | ||||||||
\(172\) | −22.3778 | −1.70629 | ||||||||
\(173\) | −7.07484 | −0.537890 | −0.268945 | − | 0.963156i | \(-0.586675\pi\) | ||||
−0.268945 | + | 0.963156i | \(0.586675\pi\) | |||||||
\(174\) | 17.5599 | 1.33121 | ||||||||
\(175\) | 12.3746 | 0.935431 | ||||||||
\(176\) | −20.6623 | −1.55748 | ||||||||
\(177\) | −21.5020 | −1.61619 | ||||||||
\(178\) | −30.5996 | −2.29354 | ||||||||
\(179\) | 5.34826 | 0.399748 | 0.199874 | − | 0.979822i | \(-0.435947\pi\) | ||||
0.199874 | + | 0.979822i | \(0.435947\pi\) | |||||||
\(180\) | 46.5672 | 3.47092 | ||||||||
\(181\) | 6.47765 | 0.481480 | 0.240740 | − | 0.970590i | \(-0.422610\pi\) | ||||
0.240740 | + | 0.970590i | \(0.422610\pi\) | |||||||
\(182\) | −15.8510 | −1.17495 | ||||||||
\(183\) | 15.0709 | 1.11407 | ||||||||
\(184\) | 12.2742 | 0.904863 | ||||||||
\(185\) | −13.3763 | −0.983444 | ||||||||
\(186\) | 12.2365 | 0.897224 | ||||||||
\(187\) | −13.6889 | −1.00103 | ||||||||
\(188\) | 27.9923 | 2.04155 | ||||||||
\(189\) | 1.41372 | 0.102833 | ||||||||
\(190\) | −36.6521 | −2.65902 | ||||||||
\(191\) | −18.6051 | −1.34621 | −0.673107 | − | 0.739545i | \(-0.735041\pi\) | ||||
−0.673107 | + | 0.739545i | \(0.735041\pi\) | |||||||
\(192\) | −22.8478 | −1.64890 | ||||||||
\(193\) | −1.49834 | −0.107853 | −0.0539264 | − | 0.998545i | \(-0.517174\pi\) | ||||
−0.0539264 | + | 0.998545i | \(0.517174\pi\) | |||||||
\(194\) | −21.5965 | −1.55054 | ||||||||
\(195\) | −36.4621 | −2.61111 | ||||||||
\(196\) | −24.0456 | −1.71754 | ||||||||
\(197\) | 10.5944 | 0.754821 | 0.377411 | − | 0.926046i | \(-0.376815\pi\) | ||||
0.377411 | + | 0.926046i | \(0.376815\pi\) | |||||||
\(198\) | 13.8571 | 0.984780 | ||||||||
\(199\) | −21.2696 | −1.50776 | −0.753882 | − | 0.657010i | \(-0.771821\pi\) | ||||
−0.753882 | + | 0.657010i | \(0.771821\pi\) | |||||||
\(200\) | −65.0248 | −4.59795 | ||||||||
\(201\) | −10.6212 | −0.749158 | ||||||||
\(202\) | −32.5073 | −2.28721 | ||||||||
\(203\) | 4.08379 | 0.286626 | ||||||||
\(204\) | −77.4326 | −5.42137 | ||||||||
\(205\) | 37.2425 | 2.60113 | ||||||||
\(206\) | −12.9299 | −0.900866 | ||||||||
\(207\) | −4.18640 | −0.290975 | ||||||||
\(208\) | 42.3603 | 2.93716 | ||||||||
\(209\) | −7.73982 | −0.535375 | ||||||||
\(210\) | 32.9697 | 2.27513 | ||||||||
\(211\) | 15.4221 | 1.06170 | 0.530851 | − | 0.847465i | \(-0.321872\pi\) | ||||
0.530851 | + | 0.847465i | \(0.321872\pi\) | |||||||
\(212\) | 4.68365 | 0.321674 | ||||||||
\(213\) | 4.66498 | 0.319639 | ||||||||
\(214\) | 5.71913 | 0.390952 | ||||||||
\(215\) | −16.8696 | −1.15049 | ||||||||
\(216\) | −7.42870 | −0.505459 | ||||||||
\(217\) | 2.84576 | 0.193183 | ||||||||
\(218\) | 25.5151 | 1.72810 | ||||||||
\(219\) | −8.60700 | −0.581607 | ||||||||
\(220\) | −36.7856 | −2.48008 | ||||||||
\(221\) | 28.0641 | 1.88779 | ||||||||
\(222\) | −22.5155 | −1.51114 | ||||||||
\(223\) | −24.0319 | −1.60929 | −0.804646 | − | 0.593755i | \(-0.797645\pi\) | ||||
−0.804646 | + | 0.593755i | \(0.797645\pi\) | |||||||
\(224\) | −16.4350 | −1.09811 | ||||||||
\(225\) | 22.1783 | 1.47855 | ||||||||
\(226\) | −45.8220 | −3.04803 | ||||||||
\(227\) | 20.0790 | 1.33269 | 0.666347 | − | 0.745642i | \(-0.267857\pi\) | ||||
0.666347 | + | 0.745642i | \(0.267857\pi\) | |||||||
\(228\) | −43.7810 | −2.89947 | ||||||||
\(229\) | −23.9178 | −1.58053 | −0.790267 | − | 0.612763i | \(-0.790058\pi\) | ||||
−0.790267 | + | 0.612763i | \(0.790058\pi\) | |||||||
\(230\) | 15.6605 | 1.03262 | ||||||||
\(231\) | 6.96222 | 0.458081 | ||||||||
\(232\) | −21.4591 | −1.40886 | ||||||||
\(233\) | −18.3749 | −1.20378 | −0.601890 | − | 0.798579i | \(-0.705585\pi\) | ||||
−0.601890 | + | 0.798579i | \(0.705585\pi\) | |||||||
\(234\) | −28.4088 | −1.85714 | ||||||||
\(235\) | 21.1021 | 1.37655 | ||||||||
\(236\) | 44.4730 | 2.89495 | ||||||||
\(237\) | 7.14404 | 0.464055 | ||||||||
\(238\) | −25.3761 | −1.64489 | ||||||||
\(239\) | −18.6664 | −1.20743 | −0.603716 | − | 0.797200i | \(-0.706314\pi\) | ||||
−0.603716 | + | 0.797200i | \(0.706314\pi\) | |||||||
\(240\) | −88.1087 | −5.68739 | ||||||||
\(241\) | −12.6233 | −0.813136 | −0.406568 | − | 0.913621i | \(-0.633275\pi\) | ||||
−0.406568 | + | 0.913621i | \(0.633275\pi\) | |||||||
\(242\) | 17.9234 | 1.15216 | ||||||||
\(243\) | 20.8635 | 1.33839 | ||||||||
\(244\) | −31.1714 | −1.99555 | ||||||||
\(245\) | −18.1268 | −1.15808 | ||||||||
\(246\) | 62.6881 | 3.99685 | ||||||||
\(247\) | 15.8676 | 1.00963 | ||||||||
\(248\) | −14.9537 | −0.949558 | ||||||||
\(249\) | 8.28276 | 0.524899 | ||||||||
\(250\) | −34.6091 | −2.18887 | ||||||||
\(251\) | −21.4104 | −1.35141 | −0.675705 | − | 0.737172i | \(-0.736161\pi\) | ||||
−0.675705 | + | 0.737172i | \(0.736161\pi\) | |||||||
\(252\) | 18.2292 | 1.14833 | ||||||||
\(253\) | 3.30703 | 0.207911 | ||||||||
\(254\) | −17.0231 | −1.06812 | ||||||||
\(255\) | −58.3728 | −3.65545 | ||||||||
\(256\) | −12.5483 | −0.784270 | ||||||||
\(257\) | 17.7172 | 1.10517 | 0.552585 | − | 0.833457i | \(-0.313641\pi\) | ||||
0.552585 | + | 0.833457i | \(0.313641\pi\) | |||||||
\(258\) | −28.3955 | −1.76783 | ||||||||
\(259\) | −5.23628 | −0.325367 | ||||||||
\(260\) | 75.4153 | 4.67706 | ||||||||
\(261\) | 7.31916 | 0.453045 | ||||||||
\(262\) | 1.57022 | 0.0970083 | ||||||||
\(263\) | −24.2460 | −1.49507 | −0.747537 | − | 0.664221i | \(-0.768764\pi\) | ||||
−0.747537 | + | 0.664221i | \(0.768764\pi\) | |||||||
\(264\) | −36.5844 | −2.25162 | ||||||||
\(265\) | 3.53078 | 0.216894 | ||||||||
\(266\) | −14.3478 | −0.879722 | ||||||||
\(267\) | −27.5543 | −1.68630 | ||||||||
\(268\) | 21.9679 | 1.34190 | ||||||||
\(269\) | 12.8653 | 0.784410 | 0.392205 | − | 0.919878i | \(-0.371712\pi\) | ||||
0.392205 | + | 0.919878i | \(0.371712\pi\) | |||||||
\(270\) | −9.47822 | −0.576826 | ||||||||
\(271\) | 5.28306 | 0.320923 | 0.160461 | − | 0.987042i | \(-0.448702\pi\) | ||||
0.160461 | + | 0.987042i | \(0.448702\pi\) | |||||||
\(272\) | 67.8153 | 4.11190 | ||||||||
\(273\) | −14.2735 | −0.863870 | ||||||||
\(274\) | −9.95218 | −0.601233 | ||||||||
\(275\) | −17.5197 | −1.05648 | ||||||||
\(276\) | 18.7065 | 1.12600 | ||||||||
\(277\) | 17.1917 | 1.03295 | 0.516474 | − | 0.856303i | \(-0.327244\pi\) | ||||
0.516474 | + | 0.856303i | \(0.327244\pi\) | |||||||
\(278\) | −4.17134 | −0.250180 | ||||||||
\(279\) | 5.10031 | 0.305347 | ||||||||
\(280\) | −40.2908 | −2.40783 | ||||||||
\(281\) | 13.4915 | 0.804835 | 0.402418 | − | 0.915456i | \(-0.368170\pi\) | ||||
0.402418 | + | 0.915456i | \(0.368170\pi\) | |||||||
\(282\) | 35.5198 | 2.11517 | ||||||||
\(283\) | 15.9173 | 0.946183 | 0.473092 | − | 0.881013i | \(-0.343138\pi\) | ||||
0.473092 | + | 0.881013i | \(0.343138\pi\) | |||||||
\(284\) | −9.64866 | −0.572543 | ||||||||
\(285\) | −33.0044 | −1.95501 | ||||||||
\(286\) | 22.4414 | 1.32699 | ||||||||
\(287\) | 14.5789 | 0.860568 | ||||||||
\(288\) | −29.4556 | −1.73569 | ||||||||
\(289\) | 27.9282 | 1.64284 | ||||||||
\(290\) | −27.3796 | −1.60778 | ||||||||
\(291\) | −19.4472 | −1.14002 | ||||||||
\(292\) | 17.8020 | 1.04178 | ||||||||
\(293\) | −30.4994 | −1.78179 | −0.890896 | − | 0.454207i | \(-0.849923\pi\) | ||||
−0.890896 | + | 0.454207i | \(0.849923\pi\) | |||||||
\(294\) | −30.5118 | −1.77949 | ||||||||
\(295\) | 33.5261 | 1.95197 | ||||||||
\(296\) | 27.5151 | 1.59928 | ||||||||
\(297\) | −2.00152 | −0.116140 | ||||||||
\(298\) | 17.7424 | 1.02779 | ||||||||
\(299\) | −6.77984 | −0.392088 | ||||||||
\(300\) | −99.1015 | −5.72163 | ||||||||
\(301\) | −6.60376 | −0.380634 | ||||||||
\(302\) | 50.8938 | 2.92861 | ||||||||
\(303\) | −29.2721 | −1.68164 | ||||||||
\(304\) | 38.3433 | 2.19914 | ||||||||
\(305\) | −23.4987 | −1.34553 | ||||||||
\(306\) | −45.4801 | −2.59993 | ||||||||
\(307\) | −25.1799 | −1.43710 | −0.718548 | − | 0.695478i | \(-0.755193\pi\) | ||||
−0.718548 | + | 0.695478i | \(0.755193\pi\) | |||||||
\(308\) | −14.4001 | −0.820521 | ||||||||
\(309\) | −11.6431 | −0.662351 | ||||||||
\(310\) | −19.0793 | −1.08363 | ||||||||
\(311\) | −24.8377 | −1.40841 | −0.704207 | − | 0.709994i | \(-0.748697\pi\) | ||||
−0.704207 | + | 0.709994i | \(0.748697\pi\) | |||||||
\(312\) | 75.0029 | 4.24620 | ||||||||
\(313\) | −17.2778 | −0.976599 | −0.488300 | − | 0.872676i | \(-0.662383\pi\) | ||||
−0.488300 | + | 0.872676i | \(0.662383\pi\) | |||||||
\(314\) | −39.2515 | −2.21509 | ||||||||
\(315\) | 13.7421 | 0.774282 | ||||||||
\(316\) | −14.7761 | −0.831223 | ||||||||
\(317\) | −4.17294 | −0.234376 | −0.117188 | − | 0.993110i | \(-0.537388\pi\) | ||||
−0.117188 | + | 0.993110i | \(0.537388\pi\) | |||||||
\(318\) | 5.94316 | 0.333276 | ||||||||
\(319\) | −5.78174 | −0.323715 | ||||||||
\(320\) | 35.6244 | 1.99147 | ||||||||
\(321\) | 5.14996 | 0.287443 | ||||||||
\(322\) | 6.13046 | 0.341637 | ||||||||
\(323\) | 25.4028 | 1.41345 | ||||||||
\(324\) | −49.2335 | −2.73520 | ||||||||
\(325\) | 35.9176 | 1.99235 | ||||||||
\(326\) | −42.0033 | −2.32635 | ||||||||
\(327\) | 22.9758 | 1.27056 | ||||||||
\(328\) | −76.6081 | −4.22997 | ||||||||
\(329\) | 8.26061 | 0.455422 | ||||||||
\(330\) | −46.6778 | −2.56953 | ||||||||
\(331\) | −14.8212 | −0.814647 | −0.407323 | − | 0.913284i | \(-0.633538\pi\) | ||||
−0.407323 | + | 0.913284i | \(0.633538\pi\) | |||||||
\(332\) | −17.1314 | −0.940207 | ||||||||
\(333\) | −9.38470 | −0.514278 | ||||||||
\(334\) | 17.7306 | 0.970175 | ||||||||
\(335\) | 16.5606 | 0.904801 | ||||||||
\(336\) | −34.4910 | −1.88164 | ||||||||
\(337\) | 3.36606 | 0.183361 | 0.0916805 | − | 0.995788i | \(-0.470776\pi\) | ||||
0.0916805 | + | 0.995788i | \(0.470776\pi\) | |||||||
\(338\) | −11.8891 | −0.646684 | ||||||||
\(339\) | −41.2617 | −2.24103 | ||||||||
\(340\) | 120.733 | 6.54769 | ||||||||
\(341\) | −4.02897 | −0.218181 | ||||||||
\(342\) | −25.7148 | −1.39050 | ||||||||
\(343\) | −17.1934 | −0.928357 | ||||||||
\(344\) | 34.7008 | 1.87094 | ||||||||
\(345\) | 14.1020 | 0.759224 | ||||||||
\(346\) | 18.5681 | 0.998225 | ||||||||
\(347\) | 8.88548 | 0.476997 | 0.238499 | − | 0.971143i | \(-0.423345\pi\) | ||||
0.238499 | + | 0.971143i | \(0.423345\pi\) | |||||||
\(348\) | −32.7049 | −1.75317 | ||||||||
\(349\) | −29.2784 | −1.56724 | −0.783619 | − | 0.621242i | \(-0.786628\pi\) | ||||
−0.783619 | + | 0.621242i | \(0.786628\pi\) | |||||||
\(350\) | −32.4774 | −1.73599 | ||||||||
\(351\) | 4.10337 | 0.219022 | ||||||||
\(352\) | 23.2684 | 1.24021 | ||||||||
\(353\) | −3.25932 | −0.173476 | −0.0867381 | − | 0.996231i | \(-0.527644\pi\) | ||||
−0.0867381 | + | 0.996231i | \(0.527644\pi\) | |||||||
\(354\) | 56.4325 | 2.99936 | ||||||||
\(355\) | −7.27367 | −0.386046 | ||||||||
\(356\) | 56.9910 | 3.02052 | ||||||||
\(357\) | −22.8506 | −1.20938 | ||||||||
\(358\) | −14.0366 | −0.741859 | ||||||||
\(359\) | 18.9364 | 0.999427 | 0.499713 | − | 0.866191i | \(-0.333439\pi\) | ||||
0.499713 | + | 0.866191i | \(0.333439\pi\) | |||||||
\(360\) | −72.2109 | −3.80585 | ||||||||
\(361\) | −4.63708 | −0.244057 | ||||||||
\(362\) | −17.0007 | −0.893538 | ||||||||
\(363\) | 16.1396 | 0.847111 | ||||||||
\(364\) | 29.5221 | 1.54738 | ||||||||
\(365\) | 13.4201 | 0.702440 | ||||||||
\(366\) | −39.5539 | −2.06752 | ||||||||
\(367\) | 16.0713 | 0.838914 | 0.419457 | − | 0.907775i | \(-0.362220\pi\) | ||||
0.419457 | + | 0.907775i | \(0.362220\pi\) | |||||||
\(368\) | −16.3831 | −0.854029 | ||||||||
\(369\) | 26.1291 | 1.36022 | ||||||||
\(370\) | 35.1063 | 1.82509 | ||||||||
\(371\) | 1.38216 | 0.0717582 | ||||||||
\(372\) | −22.7902 | −1.18162 | ||||||||
\(373\) | 30.3065 | 1.56921 | 0.784605 | − | 0.619996i | \(-0.212866\pi\) | ||||
0.784605 | + | 0.619996i | \(0.212866\pi\) | |||||||
\(374\) | 35.9269 | 1.85773 | ||||||||
\(375\) | −31.1647 | −1.60934 | ||||||||
\(376\) | −43.4071 | −2.23855 | ||||||||
\(377\) | 11.8533 | 0.610477 | ||||||||
\(378\) | −3.71034 | −0.190840 | ||||||||
\(379\) | −21.7825 | −1.11889 | −0.559445 | − | 0.828867i | \(-0.688986\pi\) | ||||
−0.559445 | + | 0.828867i | \(0.688986\pi\) | |||||||
\(380\) | 68.2636 | 3.50185 | ||||||||
\(381\) | −15.3289 | −0.785325 | ||||||||
\(382\) | 48.8293 | 2.49833 | ||||||||
\(383\) | 22.1758 | 1.13313 | 0.566565 | − | 0.824017i | \(-0.308272\pi\) | ||||
0.566565 | + | 0.824017i | \(0.308272\pi\) | |||||||
\(384\) | 6.11151 | 0.311877 | ||||||||
\(385\) | −10.8555 | −0.553250 | ||||||||
\(386\) | 3.93242 | 0.200155 | ||||||||
\(387\) | −11.8356 | −0.601635 | ||||||||
\(388\) | 40.2230 | 2.04201 | ||||||||
\(389\) | 10.6234 | 0.538627 | 0.269314 | − | 0.963053i | \(-0.413203\pi\) | ||||
0.269314 | + | 0.963053i | \(0.413203\pi\) | |||||||
\(390\) | 95.6956 | 4.84574 | ||||||||
\(391\) | −10.8540 | −0.548908 | ||||||||
\(392\) | 37.2871 | 1.88328 | ||||||||
\(393\) | 1.41395 | 0.0713242 | ||||||||
\(394\) | −27.8053 | −1.40081 | ||||||||
\(395\) | −11.1390 | −0.560466 | ||||||||
\(396\) | −25.8085 | −1.29693 | ||||||||
\(397\) | 23.8991 | 1.19946 | 0.599730 | − | 0.800203i | \(-0.295275\pi\) | ||||
0.599730 | + | 0.800203i | \(0.295275\pi\) | |||||||
\(398\) | 55.8226 | 2.79813 | ||||||||
\(399\) | −12.9199 | −0.646805 | ||||||||
\(400\) | 86.7929 | 4.33964 | ||||||||
\(401\) | −6.67423 | −0.333295 | −0.166648 | − | 0.986017i | \(-0.553294\pi\) | ||||
−0.166648 | + | 0.986017i | \(0.553294\pi\) | |||||||
\(402\) | 27.8754 | 1.39030 | ||||||||
\(403\) | 8.25991 | 0.411455 | ||||||||
\(404\) | 60.5441 | 3.01218 | ||||||||
\(405\) | −37.1149 | −1.84425 | ||||||||
\(406\) | −10.7180 | −0.531925 | ||||||||
\(407\) | 7.41341 | 0.367469 | ||||||||
\(408\) | 120.073 | 5.94451 | ||||||||
\(409\) | −1.66836 | −0.0824952 | −0.0412476 | − | 0.999149i | \(-0.513133\pi\) | ||||
−0.0412476 | + | 0.999149i | \(0.513133\pi\) | |||||||
\(410\) | −97.7437 | −4.82722 | ||||||||
\(411\) | −8.96173 | −0.442049 | ||||||||
\(412\) | 24.0816 | 1.18641 | ||||||||
\(413\) | 13.1241 | 0.645797 | ||||||||
\(414\) | 10.9873 | 0.539996 | ||||||||
\(415\) | −12.9145 | −0.633950 | ||||||||
\(416\) | −47.7032 | −2.33884 | ||||||||
\(417\) | −3.75620 | −0.183942 | ||||||||
\(418\) | 20.3133 | 0.993557 | ||||||||
\(419\) | 30.0850 | 1.46975 | 0.734875 | − | 0.678202i | \(-0.237241\pi\) | ||||
0.734875 | + | 0.678202i | \(0.237241\pi\) | |||||||
\(420\) | −61.4054 | −2.99628 | ||||||||
\(421\) | 4.66050 | 0.227139 | 0.113569 | − | 0.993530i | \(-0.463772\pi\) | ||||
0.113569 | + | 0.993530i | \(0.463772\pi\) | |||||||
\(422\) | −40.4757 | −1.97032 | ||||||||
\(423\) | 14.8050 | 0.719846 | ||||||||
\(424\) | −7.26285 | −0.352715 | ||||||||
\(425\) | 57.5010 | 2.78921 | ||||||||
\(426\) | −12.2433 | −0.593192 | ||||||||
\(427\) | −9.19879 | −0.445161 | ||||||||
\(428\) | −10.6517 | −0.514871 | ||||||||
\(429\) | 20.2081 | 0.975654 | ||||||||
\(430\) | 44.2745 | 2.13511 | ||||||||
\(431\) | 17.1602 | 0.826578 | 0.413289 | − | 0.910600i | \(-0.364380\pi\) | ||||
0.413289 | + | 0.910600i | \(0.364380\pi\) | |||||||
\(432\) | 9.91556 | 0.477063 | ||||||||
\(433\) | −6.26900 | −0.301269 | −0.150634 | − | 0.988590i | \(-0.548132\pi\) | ||||
−0.150634 | + | 0.988590i | \(0.548132\pi\) | |||||||
\(434\) | −7.46876 | −0.358512 | ||||||||
\(435\) | −24.6547 | −1.18210 | ||||||||
\(436\) | −47.5212 | −2.27585 | ||||||||
\(437\) | −6.13691 | −0.293568 | ||||||||
\(438\) | 22.5892 | 1.07936 | ||||||||
\(439\) | −18.8050 | −0.897515 | −0.448757 | − | 0.893654i | \(-0.648133\pi\) | ||||
−0.448757 | + | 0.893654i | \(0.648133\pi\) | |||||||
\(440\) | 57.0427 | 2.71941 | ||||||||
\(441\) | −12.7177 | −0.605603 | ||||||||
\(442\) | −73.6547 | −3.50340 | ||||||||
\(443\) | −33.3164 | −1.58291 | −0.791456 | − | 0.611227i | \(-0.790676\pi\) | ||||
−0.791456 | + | 0.611227i | \(0.790676\pi\) | |||||||
\(444\) | 41.9346 | 1.99013 | ||||||||
\(445\) | 42.9629 | 2.03664 | ||||||||
\(446\) | 63.0721 | 2.98655 | ||||||||
\(447\) | 15.9766 | 0.755669 | ||||||||
\(448\) | 13.9455 | 0.658865 | ||||||||
\(449\) | −36.1979 | −1.70828 | −0.854141 | − | 0.520041i | \(-0.825917\pi\) | ||||
−0.854141 | + | 0.520041i | \(0.825917\pi\) | |||||||
\(450\) | −58.2074 | −2.74392 | ||||||||
\(451\) | −20.6405 | −0.971925 | ||||||||
\(452\) | 85.3423 | 4.01417 | ||||||||
\(453\) | 45.8288 | 2.15322 | ||||||||
\(454\) | −52.6979 | −2.47323 | ||||||||
\(455\) | 22.2553 | 1.04334 | ||||||||
\(456\) | 67.8904 | 3.17926 | ||||||||
\(457\) | −21.0418 | −0.984295 | −0.492147 | − | 0.870512i | \(-0.663788\pi\) | ||||
−0.492147 | + | 0.870512i | \(0.663788\pi\) | |||||||
\(458\) | 62.7728 | 2.93318 | ||||||||
\(459\) | 6.56915 | 0.306622 | ||||||||
\(460\) | −29.1673 | −1.35993 | ||||||||
\(461\) | −27.4626 | −1.27906 | −0.639531 | − | 0.768766i | \(-0.720871\pi\) | ||||
−0.639531 | + | 0.768766i | \(0.720871\pi\) | |||||||
\(462\) | −18.2725 | −0.850114 | ||||||||
\(463\) | 0.965338 | 0.0448630 | 0.0224315 | − | 0.999748i | \(-0.492859\pi\) | ||||
0.0224315 | + | 0.999748i | \(0.492859\pi\) | |||||||
\(464\) | 28.6429 | 1.32971 | ||||||||
\(465\) | −17.1805 | −0.796725 | ||||||||
\(466\) | 48.2253 | 2.23399 | ||||||||
\(467\) | −39.0325 | −1.80621 | −0.903104 | − | 0.429423i | \(-0.858717\pi\) | ||||
−0.903104 | + | 0.429423i | \(0.858717\pi\) | |||||||
\(468\) | 52.9108 | 2.44580 | ||||||||
\(469\) | 6.48280 | 0.299348 | ||||||||
\(470\) | −55.3828 | −2.55462 | ||||||||
\(471\) | −35.3451 | −1.62862 | ||||||||
\(472\) | −68.9635 | −3.17430 | ||||||||
\(473\) | 9.34945 | 0.429888 | ||||||||
\(474\) | −18.7497 | −0.861201 | ||||||||
\(475\) | 32.5115 | 1.49173 | ||||||||
\(476\) | 47.2623 | 2.16626 | ||||||||
\(477\) | 2.47717 | 0.113422 | ||||||||
\(478\) | 48.9904 | 2.24077 | ||||||||
\(479\) | 10.4600 | 0.477930 | 0.238965 | − | 0.971028i | \(-0.423192\pi\) | ||||
0.238965 | + | 0.971028i | \(0.423192\pi\) | |||||||
\(480\) | 99.2218 | 4.52883 | ||||||||
\(481\) | −15.1985 | −0.692990 | ||||||||
\(482\) | 33.1300 | 1.50903 | ||||||||
\(483\) | 5.52035 | 0.251185 | ||||||||
\(484\) | −33.3819 | −1.51736 | ||||||||
\(485\) | 30.3222 | 1.37686 | ||||||||
\(486\) | −54.7567 | −2.48381 | ||||||||
\(487\) | 9.88739 | 0.448040 | 0.224020 | − | 0.974584i | \(-0.428082\pi\) | ||||
0.224020 | + | 0.974584i | \(0.428082\pi\) | |||||||
\(488\) | 48.3369 | 2.18811 | ||||||||
\(489\) | −37.8231 | −1.71042 | ||||||||
\(490\) | 47.5743 | 2.14919 | ||||||||
\(491\) | 31.7982 | 1.43503 | 0.717516 | − | 0.696542i | \(-0.245279\pi\) | ||||
0.717516 | + | 0.696542i | \(0.245279\pi\) | |||||||
\(492\) | −116.755 | −5.26372 | ||||||||
\(493\) | 18.9762 | 0.854644 | ||||||||
\(494\) | −41.6450 | −1.87370 | ||||||||
\(495\) | −19.4558 | −0.874474 | ||||||||
\(496\) | 19.9596 | 0.896213 | ||||||||
\(497\) | −2.84735 | −0.127721 | ||||||||
\(498\) | −21.7383 | −0.974115 | ||||||||
\(499\) | 1.93556 | 0.0866474 | 0.0433237 | − | 0.999061i | \(-0.486205\pi\) | ||||
0.0433237 | + | 0.999061i | \(0.486205\pi\) | |||||||
\(500\) | 64.4585 | 2.88267 | ||||||||
\(501\) | 15.9660 | 0.713310 | ||||||||
\(502\) | 56.1919 | 2.50797 | ||||||||
\(503\) | −14.0918 | −0.628323 | −0.314162 | − | 0.949369i | \(-0.601723\pi\) | ||||
−0.314162 | + | 0.949369i | \(0.601723\pi\) | |||||||
\(504\) | −28.2677 | −1.25914 | ||||||||
\(505\) | 45.6413 | 2.03101 | ||||||||
\(506\) | −8.67937 | −0.385845 | ||||||||
\(507\) | −10.7059 | −0.475466 | ||||||||
\(508\) | 31.7051 | 1.40669 | ||||||||
\(509\) | 22.8242 | 1.01167 | 0.505833 | − | 0.862631i | \(-0.331185\pi\) | ||||
0.505833 | + | 0.862631i | \(0.331185\pi\) | |||||||
\(510\) | 153.201 | 6.78384 | ||||||||
\(511\) | 5.25343 | 0.232398 | ||||||||
\(512\) | 38.1053 | 1.68403 | ||||||||
\(513\) | 3.71425 | 0.163988 | ||||||||
\(514\) | −46.4992 | −2.05099 | ||||||||
\(515\) | 18.1540 | 0.799959 | ||||||||
\(516\) | 52.8860 | 2.32818 | ||||||||
\(517\) | −11.6952 | −0.514354 | ||||||||
\(518\) | 13.7427 | 0.603821 | ||||||||
\(519\) | 16.7201 | 0.733933 | ||||||||
\(520\) | −116.945 | −5.12838 | ||||||||
\(521\) | −19.0370 | −0.834024 | −0.417012 | − | 0.908901i | \(-0.636923\pi\) | ||||
−0.417012 | + | 0.908901i | \(0.636923\pi\) | |||||||
\(522\) | −19.2093 | −0.840768 | ||||||||
\(523\) | −34.8911 | −1.52568 | −0.762841 | − | 0.646587i | \(-0.776196\pi\) | ||||
−0.762841 | + | 0.646587i | \(0.776196\pi\) | |||||||
\(524\) | −2.92449 | −0.127757 | ||||||||
\(525\) | −29.2452 | −1.27636 | ||||||||
\(526\) | 63.6342 | 2.77458 | ||||||||
\(527\) | 13.2234 | 0.576021 | ||||||||
\(528\) | 48.8316 | 2.12512 | ||||||||
\(529\) | −20.3779 | −0.885994 | ||||||||
\(530\) | −9.26661 | −0.402516 | ||||||||
\(531\) | 23.5217 | 1.02075 | ||||||||
\(532\) | 26.7225 | 1.15857 | ||||||||
\(533\) | 42.3158 | 1.83290 | ||||||||
\(534\) | 72.3168 | 3.12946 | ||||||||
\(535\) | −8.02985 | −0.347161 | ||||||||
\(536\) | −34.0652 | −1.47139 | ||||||||
\(537\) | −12.6397 | −0.545443 | ||||||||
\(538\) | −33.7652 | −1.45572 | ||||||||
\(539\) | 10.0463 | 0.432723 | ||||||||
\(540\) | 17.6530 | 0.759663 | ||||||||
\(541\) | 10.1093 | 0.434634 | 0.217317 | − | 0.976101i | \(-0.430269\pi\) | ||||
0.217317 | + | 0.976101i | \(0.430269\pi\) | |||||||
\(542\) | −13.8655 | −0.595574 | ||||||||
\(543\) | −15.3088 | −0.656963 | ||||||||
\(544\) | −76.3687 | −3.27428 | ||||||||
\(545\) | −35.8240 | −1.53453 | ||||||||
\(546\) | 37.4610 | 1.60318 | ||||||||
\(547\) | 4.39700 | 0.188002 | 0.0940010 | − | 0.995572i | \(-0.470034\pi\) | ||||
0.0940010 | + | 0.995572i | \(0.470034\pi\) | |||||||
\(548\) | 18.5357 | 0.791806 | ||||||||
\(549\) | −16.4865 | −0.703626 | ||||||||
\(550\) | 45.9807 | 1.96062 | ||||||||
\(551\) | 10.7293 | 0.457082 | ||||||||
\(552\) | −29.0078 | −1.23466 | ||||||||
\(553\) | −4.36049 | −0.185427 | ||||||||
\(554\) | −45.1199 | −1.91696 | ||||||||
\(555\) | 31.6125 | 1.34188 | ||||||||
\(556\) | 7.76901 | 0.329480 | ||||||||
\(557\) | −12.8064 | −0.542625 | −0.271312 | − | 0.962491i | \(-0.587458\pi\) | ||||
−0.271312 | + | 0.962491i | \(0.587458\pi\) | |||||||
\(558\) | −13.3859 | −0.566669 | ||||||||
\(559\) | −19.1676 | −0.810703 | ||||||||
\(560\) | 53.7787 | 2.27256 | ||||||||
\(561\) | 32.3514 | 1.36588 | ||||||||
\(562\) | −35.4087 | −1.49363 | ||||||||
\(563\) | −6.63051 | −0.279443 | −0.139721 | − | 0.990191i | \(-0.544621\pi\) | ||||
−0.139721 | + | 0.990191i | \(0.544621\pi\) | |||||||
\(564\) | −66.1548 | −2.78562 | ||||||||
\(565\) | 64.3356 | 2.70662 | ||||||||
\(566\) | −41.7752 | −1.75594 | ||||||||
\(567\) | −14.5290 | −0.610160 | ||||||||
\(568\) | 14.9620 | 0.627791 | ||||||||
\(569\) | 41.1452 | 1.72490 | 0.862448 | − | 0.506146i | \(-0.168930\pi\) | ||||
0.862448 | + | 0.506146i | \(0.168930\pi\) | |||||||
\(570\) | 86.6208 | 3.62815 | ||||||||
\(571\) | 16.2718 | 0.680952 | 0.340476 | − | 0.940253i | \(-0.389412\pi\) | ||||
0.340476 | + | 0.940253i | \(0.389412\pi\) | |||||||
\(572\) | −41.7967 | −1.74761 | ||||||||
\(573\) | 43.9698 | 1.83686 | ||||||||
\(574\) | −38.2627 | −1.59706 | ||||||||
\(575\) | −13.8914 | −0.579309 | ||||||||
\(576\) | 24.9938 | 1.04141 | ||||||||
\(577\) | 4.69143 | 0.195307 | 0.0976535 | − | 0.995220i | \(-0.468866\pi\) | ||||
0.0976535 | + | 0.995220i | \(0.468866\pi\) | |||||||
\(578\) | −73.2981 | −3.04880 | ||||||||
\(579\) | 3.54106 | 0.147162 | ||||||||
\(580\) | 50.9938 | 2.11740 | ||||||||
\(581\) | −5.05553 | −0.209739 | ||||||||
\(582\) | 51.0396 | 2.11566 | ||||||||
\(583\) | −1.95683 | −0.0810436 | ||||||||
\(584\) | −27.6052 | −1.14231 | ||||||||
\(585\) | 39.8870 | 1.64912 | ||||||||
\(586\) | 80.0462 | 3.30668 | ||||||||
\(587\) | −10.8228 | −0.446704 | −0.223352 | − | 0.974738i | \(-0.571700\pi\) | ||||
−0.223352 | + | 0.974738i | \(0.571700\pi\) | |||||||
\(588\) | 56.8276 | 2.34353 | ||||||||
\(589\) | 7.47662 | 0.308069 | ||||||||
\(590\) | −87.9900 | −3.62249 | ||||||||
\(591\) | −25.0381 | −1.02993 | ||||||||
\(592\) | −36.7262 | −1.50944 | ||||||||
\(593\) | 44.7931 | 1.83943 | 0.919717 | − | 0.392582i | \(-0.128418\pi\) | ||||
0.919717 | + | 0.392582i | \(0.128418\pi\) | |||||||
\(594\) | 5.25302 | 0.215534 | ||||||||
\(595\) | 35.6288 | 1.46064 | ||||||||
\(596\) | −33.0448 | −1.35357 | ||||||||
\(597\) | 50.2670 | 2.05729 | ||||||||
\(598\) | 17.7938 | 0.727644 | ||||||||
\(599\) | 7.30926 | 0.298648 | 0.149324 | − | 0.988788i | \(-0.452290\pi\) | ||||
0.149324 | + | 0.988788i | \(0.452290\pi\) | |||||||
\(600\) | 153.675 | 6.27375 | ||||||||
\(601\) | 4.12192 | 0.168137 | 0.0840684 | − | 0.996460i | \(-0.473209\pi\) | ||||
0.0840684 | + | 0.996460i | \(0.473209\pi\) | |||||||
\(602\) | 17.3317 | 0.706387 | ||||||||
\(603\) | 11.6188 | 0.473153 | ||||||||
\(604\) | −94.7885 | −3.85689 | ||||||||
\(605\) | −25.1650 | −1.02310 | ||||||||
\(606\) | 76.8253 | 3.12082 | ||||||||
\(607\) | 47.8930 | 1.94392 | 0.971958 | − | 0.235154i | \(-0.0755595\pi\) | ||||
0.971958 | + | 0.235154i | \(0.0755595\pi\) | |||||||
\(608\) | −43.1795 | −1.75116 | ||||||||
\(609\) | −9.65133 | −0.391092 | ||||||||
\(610\) | 61.6727 | 2.49706 | ||||||||
\(611\) | 23.9767 | 0.969992 | ||||||||
\(612\) | 84.7057 | 3.42402 | ||||||||
\(613\) | −36.4591 | −1.47257 | −0.736284 | − | 0.676673i | \(-0.763421\pi\) | ||||
−0.736284 | + | 0.676673i | \(0.763421\pi\) | |||||||
\(614\) | 66.0853 | 2.66699 | ||||||||
\(615\) | −88.0162 | −3.54915 | ||||||||
\(616\) | 22.3299 | 0.899699 | ||||||||
\(617\) | 11.3157 | 0.455552 | 0.227776 | − | 0.973714i | \(-0.426855\pi\) | ||||
0.227776 | + | 0.973714i | \(0.426855\pi\) | |||||||
\(618\) | 30.5575 | 1.22920 | ||||||||
\(619\) | −19.2107 | −0.772145 | −0.386073 | − | 0.922468i | \(-0.626169\pi\) | ||||
−0.386073 | + | 0.922468i | \(0.626169\pi\) | |||||||
\(620\) | 35.5347 | 1.42711 | ||||||||
\(621\) | −1.58700 | −0.0636843 | ||||||||
\(622\) | 65.1870 | 2.61376 | ||||||||
\(623\) | 16.8182 | 0.673809 | ||||||||
\(624\) | −100.111 | −4.00766 | ||||||||
\(625\) | 5.69930 | 0.227972 | ||||||||
\(626\) | 45.3460 | 1.81239 | ||||||||
\(627\) | 18.2917 | 0.730501 | ||||||||
\(628\) | 73.1049 | 2.91720 | ||||||||
\(629\) | −24.3314 | −0.970158 | ||||||||
\(630\) | −36.0665 | −1.43692 | ||||||||
\(631\) | −40.2222 | −1.60122 | −0.800609 | − | 0.599187i | \(-0.795491\pi\) | ||||
−0.800609 | + | 0.599187i | \(0.795491\pi\) | |||||||
\(632\) | 22.9131 | 0.911434 | ||||||||
\(633\) | −36.4475 | −1.44866 | ||||||||
\(634\) | 10.9520 | 0.434958 | ||||||||
\(635\) | 23.9010 | 0.948482 | ||||||||
\(636\) | −11.0690 | −0.438914 | ||||||||
\(637\) | −20.5962 | −0.816049 | ||||||||
\(638\) | 15.1743 | 0.600756 | ||||||||
\(639\) | −5.10315 | −0.201878 | ||||||||
\(640\) | −9.52911 | −0.376671 | ||||||||
\(641\) | 2.68531 | 0.106063 | 0.0530316 | − | 0.998593i | \(-0.483112\pi\) | ||||
0.0530316 | + | 0.998593i | \(0.483112\pi\) | |||||||
\(642\) | −13.5162 | −0.533440 | ||||||||
\(643\) | −42.3765 | −1.67117 | −0.835583 | − | 0.549364i | \(-0.814870\pi\) | ||||
−0.835583 | + | 0.549364i | \(0.814870\pi\) | |||||||
\(644\) | −11.4178 | −0.449926 | ||||||||
\(645\) | 39.8683 | 1.56981 | ||||||||
\(646\) | −66.6701 | −2.62310 | ||||||||
\(647\) | 10.8181 | 0.425304 | 0.212652 | − | 0.977128i | \(-0.431790\pi\) | ||||
0.212652 | + | 0.977128i | \(0.431790\pi\) | |||||||
\(648\) | 76.3455 | 2.99914 | ||||||||
\(649\) | −18.5809 | −0.729363 | ||||||||
\(650\) | −94.2665 | −3.69744 | ||||||||
\(651\) | −6.72547 | −0.263592 | ||||||||
\(652\) | 78.2302 | 3.06373 | ||||||||
\(653\) | 15.3427 | 0.600407 | 0.300203 | − | 0.953875i | \(-0.402945\pi\) | ||||
0.300203 | + | 0.953875i | \(0.402945\pi\) | |||||||
\(654\) | −60.3004 | −2.35793 | ||||||||
\(655\) | −2.20464 | −0.0861422 | ||||||||
\(656\) | 102.254 | 3.99234 | ||||||||
\(657\) | 9.41544 | 0.367331 | ||||||||
\(658\) | −21.6801 | −0.845180 | ||||||||
\(659\) | −22.6007 | −0.880397 | −0.440199 | − | 0.897900i | \(-0.645092\pi\) | ||||
−0.440199 | + | 0.897900i | \(0.645092\pi\) | |||||||
\(660\) | 86.9363 | 3.38399 | ||||||||
\(661\) | 6.82214 | 0.265350 | 0.132675 | − | 0.991160i | \(-0.457643\pi\) | ||||
0.132675 | + | 0.991160i | \(0.457643\pi\) | |||||||
\(662\) | 38.8985 | 1.51183 | ||||||||
\(663\) | −66.3245 | −2.57583 | ||||||||
\(664\) | 26.5653 | 1.03093 | ||||||||
\(665\) | 20.1448 | 0.781183 | ||||||||
\(666\) | 24.6303 | 0.954406 | ||||||||
\(667\) | −4.58435 | −0.177507 | ||||||||
\(668\) | −33.0228 | −1.27769 | ||||||||
\(669\) | 56.7951 | 2.19583 | ||||||||
\(670\) | −43.4636 | −1.67914 | ||||||||
\(671\) | 13.0234 | 0.502764 | ||||||||
\(672\) | 38.8413 | 1.49834 | ||||||||
\(673\) | −32.1276 | −1.23843 | −0.619213 | − | 0.785223i | \(-0.712548\pi\) | ||||
−0.619213 | + | 0.785223i | \(0.712548\pi\) | |||||||
\(674\) | −8.83429 | −0.340284 | ||||||||
\(675\) | 8.40748 | 0.323604 | ||||||||
\(676\) | 22.1432 | 0.851663 | ||||||||
\(677\) | −17.3343 | −0.666210 | −0.333105 | − | 0.942890i | \(-0.608096\pi\) | ||||
−0.333105 | + | 0.942890i | \(0.608096\pi\) | |||||||
\(678\) | 108.292 | 4.15894 | ||||||||
\(679\) | 11.8699 | 0.455527 | ||||||||
\(680\) | −187.219 | −7.17952 | ||||||||
\(681\) | −47.4533 | −1.81842 | ||||||||
\(682\) | 10.5741 | 0.404903 | ||||||||
\(683\) | −5.50702 | −0.210720 | −0.105360 | − | 0.994434i | \(-0.533600\pi\) | ||||
−0.105360 | + | 0.994434i | \(0.533600\pi\) | |||||||
\(684\) | 47.8932 | 1.83124 | ||||||||
\(685\) | 13.9732 | 0.533888 | ||||||||
\(686\) | 45.1245 | 1.72286 | ||||||||
\(687\) | 56.5256 | 2.15658 | ||||||||
\(688\) | −46.3174 | −1.76584 | ||||||||
\(689\) | 4.01176 | 0.152836 | ||||||||
\(690\) | −37.0109 | −1.40898 | ||||||||
\(691\) | −18.6106 | −0.707981 | −0.353990 | − | 0.935249i | \(-0.615175\pi\) | ||||
−0.353990 | + | 0.935249i | \(0.615175\pi\) | |||||||
\(692\) | −34.5826 | −1.31463 | ||||||||
\(693\) | −7.61617 | −0.289314 | ||||||||
\(694\) | −23.3201 | −0.885219 | ||||||||
\(695\) | 5.85670 | 0.222157 | ||||||||
\(696\) | 50.7149 | 1.92234 | ||||||||
\(697\) | 67.7440 | 2.56599 | ||||||||
\(698\) | 76.8418 | 2.90851 | ||||||||
\(699\) | 43.4259 | 1.64252 | ||||||||
\(700\) | 60.4883 | 2.28624 | ||||||||
\(701\) | −15.5127 | −0.585907 | −0.292954 | − | 0.956127i | \(-0.594638\pi\) | ||||
−0.292954 | + | 0.956127i | \(0.594638\pi\) | |||||||
\(702\) | −10.7694 | −0.406464 | ||||||||
\(703\) | −13.7572 | −0.518862 | ||||||||
\(704\) | −19.7438 | −0.744121 | ||||||||
\(705\) | −49.8710 | −1.87825 | ||||||||
\(706\) | 8.55416 | 0.321940 | ||||||||
\(707\) | 17.8668 | 0.671949 | ||||||||
\(708\) | −105.104 | −3.95006 | ||||||||
\(709\) | 21.7783 | 0.817900 | 0.408950 | − | 0.912557i | \(-0.365895\pi\) | ||||
0.408950 | + | 0.912557i | \(0.365895\pi\) | |||||||
\(710\) | 19.0899 | 0.716431 | ||||||||
\(711\) | −7.81507 | −0.293088 | ||||||||
\(712\) | −88.3749 | −3.31199 | ||||||||
\(713\) | −3.19457 | −0.119638 | ||||||||
\(714\) | 59.9719 | 2.24439 | ||||||||
\(715\) | −31.5085 | −1.17835 | ||||||||
\(716\) | 26.1429 | 0.977006 | ||||||||
\(717\) | 44.1149 | 1.64750 | ||||||||
\(718\) | −49.6990 | −1.85475 | ||||||||
\(719\) | −10.3831 | −0.387226 | −0.193613 | − | 0.981078i | \(-0.562021\pi\) | ||||
−0.193613 | + | 0.981078i | \(0.562021\pi\) | |||||||
\(720\) | 96.3846 | 3.59204 | ||||||||
\(721\) | 7.10655 | 0.264662 | ||||||||
\(722\) | 12.1701 | 0.452925 | ||||||||
\(723\) | 29.8329 | 1.10950 | ||||||||
\(724\) | 31.6634 | 1.17676 | ||||||||
\(725\) | 24.2865 | 0.901978 | ||||||||
\(726\) | −42.3588 | −1.57208 | ||||||||
\(727\) | −8.27682 | −0.306970 | −0.153485 | − | 0.988151i | \(-0.549050\pi\) | ||||
−0.153485 | + | 0.988151i | \(0.549050\pi\) | |||||||
\(728\) | −45.7793 | −1.69669 | ||||||||
\(729\) | −19.0909 | −0.707072 | ||||||||
\(730\) | −35.2213 | −1.30360 | ||||||||
\(731\) | −30.6857 | −1.13495 | ||||||||
\(732\) | 73.6682 | 2.72286 | ||||||||
\(733\) | −33.6508 | −1.24292 | −0.621461 | − | 0.783445i | \(-0.713460\pi\) | ||||
−0.621461 | + | 0.783445i | \(0.713460\pi\) | |||||||
\(734\) | −42.1794 | −1.55687 | ||||||||
\(735\) | 42.8396 | 1.58016 | ||||||||
\(736\) | 18.4495 | 0.680057 | ||||||||
\(737\) | −9.17820 | −0.338084 | ||||||||
\(738\) | −68.5762 | −2.52433 | ||||||||
\(739\) | −16.8784 | −0.620882 | −0.310441 | − | 0.950593i | \(-0.600477\pi\) | ||||
−0.310441 | + | 0.950593i | \(0.600477\pi\) | |||||||
\(740\) | −65.3847 | −2.40359 | ||||||||
\(741\) | −37.5004 | −1.37761 | ||||||||
\(742\) | −3.62751 | −0.133170 | ||||||||
\(743\) | 20.7718 | 0.762044 | 0.381022 | − | 0.924566i | \(-0.375572\pi\) | ||||
0.381022 | + | 0.924566i | \(0.375572\pi\) | |||||||
\(744\) | 35.3404 | 1.29564 | ||||||||
\(745\) | −24.9109 | −0.912664 | ||||||||
\(746\) | −79.5400 | −2.91217 | ||||||||
\(747\) | −9.06074 | −0.331515 | ||||||||
\(748\) | −66.9129 | −2.44658 | ||||||||
\(749\) | −3.14336 | −0.114856 | ||||||||
\(750\) | 81.7925 | 2.98664 | ||||||||
\(751\) | 28.2718 | 1.03165 | 0.515826 | − | 0.856693i | \(-0.327485\pi\) | ||||
0.515826 | + | 0.856693i | \(0.327485\pi\) | |||||||
\(752\) | 57.9382 | 2.11279 | ||||||||
\(753\) | 50.5997 | 1.84395 | ||||||||
\(754\) | −31.1093 | −1.13293 | ||||||||
\(755\) | −71.4566 | −2.60057 | ||||||||
\(756\) | 6.91043 | 0.251330 | ||||||||
\(757\) | 43.2007 | 1.57016 | 0.785078 | − | 0.619397i | \(-0.212623\pi\) | ||||
0.785078 | + | 0.619397i | \(0.212623\pi\) | |||||||
\(758\) | 57.1686 | 2.07646 | ||||||||
\(759\) | −7.81559 | −0.283688 | ||||||||
\(760\) | −105.855 | −3.83977 | ||||||||
\(761\) | −1.39520 | −0.0505758 | −0.0252879 | − | 0.999680i | \(-0.508050\pi\) | ||||
−0.0252879 | + | 0.999680i | \(0.508050\pi\) | |||||||
\(762\) | 40.2311 | 1.45742 | ||||||||
\(763\) | −14.0237 | −0.507691 | ||||||||
\(764\) | −90.9435 | −3.29022 | ||||||||
\(765\) | 63.8556 | 2.30870 | ||||||||
\(766\) | −58.2008 | −2.10288 | ||||||||
\(767\) | 38.0932 | 1.37547 | ||||||||
\(768\) | 29.6558 | 1.07011 | ||||||||
\(769\) | 39.3227 | 1.41801 | 0.709006 | − | 0.705203i | \(-0.249144\pi\) | ||||
0.709006 | + | 0.705203i | \(0.249144\pi\) | |||||||
\(770\) | 28.4906 | 1.02673 | ||||||||
\(771\) | −41.8716 | −1.50797 | ||||||||
\(772\) | −7.32405 | −0.263598 | ||||||||
\(773\) | 45.8371 | 1.64864 | 0.824322 | − | 0.566121i | \(-0.191557\pi\) | ||||
0.824322 | + | 0.566121i | \(0.191557\pi\) | |||||||
\(774\) | 31.0627 | 1.11652 | ||||||||
\(775\) | 16.9239 | 0.607924 | ||||||||
\(776\) | −62.3731 | −2.23906 | ||||||||
\(777\) | 12.3750 | 0.443952 | ||||||||
\(778\) | −27.8813 | −0.999593 | ||||||||
\(779\) | 38.3030 | 1.37235 | ||||||||
\(780\) | −178.231 | −6.38169 | ||||||||
\(781\) | 4.03122 | 0.144248 | ||||||||
\(782\) | 28.4864 | 1.01867 | ||||||||
\(783\) | 2.77459 | 0.0991557 | ||||||||
\(784\) | −49.7694 | −1.77748 | ||||||||
\(785\) | 55.1104 | 1.96697 | ||||||||
\(786\) | −3.71093 | −0.132365 | ||||||||
\(787\) | 1.56296 | 0.0557134 | 0.0278567 | − | 0.999612i | \(-0.491132\pi\) | ||||
0.0278567 | + | 0.999612i | \(0.491132\pi\) | |||||||
\(788\) | 51.7867 | 1.84482 | ||||||||
\(789\) | 57.3012 | 2.03998 | ||||||||
\(790\) | 29.2346 | 1.04012 | ||||||||
\(791\) | 25.1848 | 0.895469 | ||||||||
\(792\) | 40.0207 | 1.42208 | ||||||||
\(793\) | −26.6997 | −0.948136 | ||||||||
\(794\) | −62.7236 | −2.22598 | ||||||||
\(795\) | −8.34439 | −0.295945 | ||||||||
\(796\) | −103.968 | −3.68505 | ||||||||
\(797\) | −25.7735 | −0.912945 | −0.456472 | − | 0.889738i | \(-0.650887\pi\) | ||||
−0.456472 | + | 0.889738i | \(0.650887\pi\) | |||||||
\(798\) | 33.9086 | 1.20035 | ||||||||
\(799\) | 38.3846 | 1.35795 | ||||||||
\(800\) | −97.7400 | −3.45563 | ||||||||
\(801\) | 30.1424 | 1.06503 | ||||||||
\(802\) | 17.5167 | 0.618535 | ||||||||
\(803\) | −7.43769 | −0.262470 | ||||||||
\(804\) | −51.9173 | −1.83098 | ||||||||
\(805\) | −8.60737 | −0.303370 | ||||||||
\(806\) | −21.6783 | −0.763586 | ||||||||
\(807\) | −30.4049 | −1.07030 | ||||||||
\(808\) | −93.8846 | −3.30285 | ||||||||
\(809\) | −39.1604 | −1.37681 | −0.688403 | − | 0.725329i | \(-0.741688\pi\) | ||||
−0.688403 | + | 0.725329i | \(0.741688\pi\) | |||||||
\(810\) | 97.4087 | 3.42259 | ||||||||
\(811\) | −36.4710 | −1.28067 | −0.640335 | − | 0.768095i | \(-0.721205\pi\) | ||||
−0.640335 | + | 0.768095i | \(0.721205\pi\) | |||||||
\(812\) | 19.9620 | 0.700530 | ||||||||
\(813\) | −12.4856 | −0.437889 | ||||||||
\(814\) | −19.4566 | −0.681955 | ||||||||
\(815\) | 58.9741 | 2.06577 | ||||||||
\(816\) | −160.270 | −5.61056 | ||||||||
\(817\) | −17.3499 | −0.606997 | ||||||||
\(818\) | 4.37865 | 0.153096 | ||||||||
\(819\) | 15.6141 | 0.545602 | ||||||||
\(820\) | 182.045 | 6.35730 | ||||||||
\(821\) | 10.7306 | 0.374501 | 0.187250 | − | 0.982312i | \(-0.440042\pi\) | ||||
0.187250 | + | 0.982312i | \(0.440042\pi\) | |||||||
\(822\) | 23.5202 | 0.820362 | ||||||||
\(823\) | 53.4014 | 1.86146 | 0.930728 | − | 0.365712i | \(-0.119174\pi\) | ||||
0.930728 | + | 0.365712i | \(0.119174\pi\) | |||||||
\(824\) | −37.3428 | −1.30090 | ||||||||
\(825\) | 41.4047 | 1.44153 | ||||||||
\(826\) | −34.4446 | −1.19848 | ||||||||
\(827\) | −43.0751 | −1.49787 | −0.748934 | − | 0.662645i | \(-0.769434\pi\) | ||||
−0.748934 | + | 0.662645i | \(0.769434\pi\) | |||||||
\(828\) | −20.4636 | −0.711158 | ||||||||
\(829\) | −56.2030 | −1.95201 | −0.976005 | − | 0.217747i | \(-0.930129\pi\) | ||||
−0.976005 | + | 0.217747i | \(0.930129\pi\) | |||||||
\(830\) | 33.8945 | 1.17649 | ||||||||
\(831\) | −40.6295 | −1.40942 | ||||||||
\(832\) | 40.4773 | 1.40330 | ||||||||
\(833\) | −32.9727 | −1.14244 | ||||||||
\(834\) | 9.85822 | 0.341362 | ||||||||
\(835\) | −24.8944 | −0.861505 | ||||||||
\(836\) | −37.8331 | −1.30848 | ||||||||
\(837\) | 1.93345 | 0.0668299 | ||||||||
\(838\) | −78.9588 | −2.72759 | ||||||||
\(839\) | 4.98207 | 0.172000 | 0.0860001 | − | 0.996295i | \(-0.472591\pi\) | ||||
0.0860001 | + | 0.996295i | \(0.472591\pi\) | |||||||
\(840\) | 95.2202 | 3.28541 | ||||||||
\(841\) | −20.9851 | −0.723624 | ||||||||
\(842\) | −12.2316 | −0.421528 | ||||||||
\(843\) | −31.8848 | −1.09817 | ||||||||
\(844\) | 75.3849 | 2.59486 | ||||||||
\(845\) | 16.6927 | 0.574248 | ||||||||
\(846\) | −38.8561 | −1.33590 | ||||||||
\(847\) | −9.85110 | −0.338488 | ||||||||
\(848\) | 9.69419 | 0.332900 | ||||||||
\(849\) | −37.6177 | −1.29104 | ||||||||
\(850\) | −150.913 | −5.17626 | ||||||||
\(851\) | 5.87809 | 0.201498 | ||||||||
\(852\) | 22.8029 | 0.781215 | ||||||||
\(853\) | −24.7630 | −0.847870 | −0.423935 | − | 0.905693i | \(-0.639351\pi\) | ||||
−0.423935 | + | 0.905693i | \(0.639351\pi\) | |||||||
\(854\) | 24.1424 | 0.826136 | ||||||||
\(855\) | 36.1045 | 1.23475 | ||||||||
\(856\) | 16.5175 | 0.564555 | ||||||||
\(857\) | −7.91151 | −0.270252 | −0.135126 | − | 0.990828i | \(-0.543144\pi\) | ||||
−0.135126 | + | 0.990828i | \(0.543144\pi\) | |||||||
\(858\) | −53.0364 | −1.81063 | ||||||||
\(859\) | 12.0684 | 0.411769 | 0.205884 | − | 0.978576i | \(-0.433993\pi\) | ||||
0.205884 | + | 0.978576i | \(0.433993\pi\) | |||||||
\(860\) | −82.4602 | −2.81187 | ||||||||
\(861\) | −34.4548 | −1.17422 | ||||||||
\(862\) | −45.0373 | −1.53398 | ||||||||
\(863\) | −37.3672 | −1.27199 | −0.635997 | − | 0.771691i | \(-0.719411\pi\) | ||||
−0.635997 | + | 0.771691i | \(0.719411\pi\) | |||||||
\(864\) | −11.1662 | −0.379882 | ||||||||
\(865\) | −26.0702 | −0.886412 | ||||||||
\(866\) | 16.4531 | 0.559100 | ||||||||
\(867\) | −66.0034 | −2.24159 | ||||||||
\(868\) | 13.9104 | 0.472150 | ||||||||
\(869\) | 6.17348 | 0.209421 | ||||||||
\(870\) | 64.7068 | 2.19377 | ||||||||
\(871\) | 18.8165 | 0.637573 | ||||||||
\(872\) | 73.6903 | 2.49547 | ||||||||
\(873\) | 21.2739 | 0.720011 | ||||||||
\(874\) | 16.1064 | 0.544809 | ||||||||
\(875\) | 19.0219 | 0.643059 | ||||||||
\(876\) | −42.0719 | −1.42148 | ||||||||
\(877\) | −6.53901 | −0.220807 | −0.110403 | − | 0.993887i | \(-0.535214\pi\) | ||||
−0.110403 | + | 0.993887i | \(0.535214\pi\) | |||||||
\(878\) | 49.3542 | 1.66562 | ||||||||
\(879\) | 72.0799 | 2.43120 | ||||||||
\(880\) | −76.1386 | −2.56663 | ||||||||
\(881\) | 18.1282 | 0.610756 | 0.305378 | − | 0.952231i | \(-0.401217\pi\) | ||||
0.305378 | + | 0.952231i | \(0.401217\pi\) | |||||||
\(882\) | 33.3777 | 1.12389 | ||||||||
\(883\) | 43.8052 | 1.47416 | 0.737081 | − | 0.675804i | \(-0.236204\pi\) | ||||
0.737081 | + | 0.675804i | \(0.236204\pi\) | |||||||
\(884\) | 137.180 | 4.61387 | ||||||||
\(885\) | −79.2332 | −2.66339 | ||||||||
\(886\) | 87.4396 | 2.93759 | ||||||||
\(887\) | 33.2280 | 1.11569 | 0.557844 | − | 0.829946i | \(-0.311629\pi\) | ||||
0.557844 | + | 0.829946i | \(0.311629\pi\) | |||||||
\(888\) | −65.0272 | −2.18217 | ||||||||
\(889\) | 9.35628 | 0.313800 | ||||||||
\(890\) | −112.757 | −3.77962 | ||||||||
\(891\) | 20.5698 | 0.689114 | ||||||||
\(892\) | −117.470 | −3.93320 | ||||||||
\(893\) | 21.7029 | 0.726261 | ||||||||
\(894\) | −41.9310 | −1.40238 | ||||||||
\(895\) | 19.7079 | 0.658762 | ||||||||
\(896\) | −3.73026 | −0.124619 | ||||||||
\(897\) | 16.0230 | 0.534992 | ||||||||
\(898\) | 95.0020 | 3.17026 | ||||||||
\(899\) | 5.58513 | 0.186274 | ||||||||
\(900\) | 108.410 | 3.61366 | ||||||||
\(901\) | 6.42248 | 0.213964 | ||||||||
\(902\) | 54.1715 | 1.80371 | ||||||||
\(903\) | 15.6068 | 0.519363 | ||||||||
\(904\) | −132.339 | −4.40152 | ||||||||
\(905\) | 23.8696 | 0.793452 | ||||||||
\(906\) | −120.279 | −3.99599 | ||||||||
\(907\) | 16.7223 | 0.555255 | 0.277628 | − | 0.960689i | \(-0.410452\pi\) | ||||
0.277628 | + | 0.960689i | \(0.410452\pi\) | |||||||
\(908\) | 98.1485 | 3.25717 | ||||||||
\(909\) | 32.0216 | 1.06209 | ||||||||
\(910\) | −58.4095 | −1.93626 | ||||||||
\(911\) | 0.157192 | 0.00520800 | 0.00260400 | − | 0.999997i | \(-0.499171\pi\) | ||||
0.00260400 | + | 0.999997i | \(0.499171\pi\) | |||||||
\(912\) | −90.6177 | −3.00065 | ||||||||
\(913\) | 7.15750 | 0.236879 | ||||||||
\(914\) | 55.2247 | 1.82667 | ||||||||
\(915\) | 55.5350 | 1.83593 | ||||||||
\(916\) | −116.913 | −3.86291 | ||||||||
\(917\) | −0.863027 | −0.0284997 | ||||||||
\(918\) | −17.2409 | −0.569033 | ||||||||
\(919\) | 21.1490 | 0.697642 | 0.348821 | − | 0.937189i | \(-0.386582\pi\) | ||||
0.348821 | + | 0.937189i | \(0.386582\pi\) | |||||||
\(920\) | 45.2292 | 1.49116 | ||||||||
\(921\) | 59.5084 | 1.96087 | ||||||||
\(922\) | 72.0762 | 2.37370 | ||||||||
\(923\) | −8.26452 | −0.272030 | ||||||||
\(924\) | 34.0321 | 1.11957 | ||||||||
\(925\) | −31.1404 | −1.02389 | ||||||||
\(926\) | −2.53355 | −0.0832576 | ||||||||
\(927\) | 12.7367 | 0.418328 | ||||||||
\(928\) | −32.2556 | −1.05884 | ||||||||
\(929\) | 35.0599 | 1.15028 | 0.575139 | − | 0.818056i | \(-0.304948\pi\) | ||||
0.575139 | + | 0.818056i | \(0.304948\pi\) | |||||||
\(930\) | 45.0905 | 1.47858 | ||||||||
\(931\) | −18.6430 | −0.611000 | ||||||||
\(932\) | −89.8185 | −2.94210 | ||||||||
\(933\) | 58.6995 | 1.92173 | ||||||||
\(934\) | 102.442 | 3.35199 | ||||||||
\(935\) | −50.4425 | −1.64965 | ||||||||
\(936\) | −82.0478 | −2.68181 | ||||||||
\(937\) | −17.9980 | −0.587969 | −0.293984 | − | 0.955810i | \(-0.594981\pi\) | ||||
−0.293984 | + | 0.955810i | \(0.594981\pi\) | |||||||
\(938\) | −17.0142 | −0.555535 | ||||||||
\(939\) | 40.8331 | 1.33254 | ||||||||
\(940\) | 103.149 | 3.36435 | ||||||||
\(941\) | 27.5627 | 0.898518 | 0.449259 | − | 0.893402i | \(-0.351688\pi\) | ||||
0.449259 | + | 0.893402i | \(0.351688\pi\) | |||||||
\(942\) | 92.7640 | 3.02241 | ||||||||
\(943\) | −16.3659 | −0.532947 | ||||||||
\(944\) | 92.0500 | 2.99597 | ||||||||
\(945\) | 5.20945 | 0.169463 | ||||||||
\(946\) | −24.5378 | −0.797794 | ||||||||
\(947\) | −21.2393 | −0.690183 | −0.345092 | − | 0.938569i | \(-0.612152\pi\) | ||||
−0.345092 | + | 0.938569i | \(0.612152\pi\) | |||||||
\(948\) | 34.9208 | 1.13418 | ||||||||
\(949\) | 15.2482 | 0.494978 | ||||||||
\(950\) | −85.3272 | −2.76838 | ||||||||
\(951\) | 9.86202 | 0.319798 | ||||||||
\(952\) | −73.2888 | −2.37530 | ||||||||
\(953\) | −28.5794 | −0.925779 | −0.462889 | − | 0.886416i | \(-0.653187\pi\) | ||||
−0.462889 | + | 0.886416i | \(0.653187\pi\) | |||||||
\(954\) | −6.50138 | −0.210490 | ||||||||
\(955\) | −68.5580 | −2.21849 | ||||||||
\(956\) | −91.2435 | −2.95103 | ||||||||
\(957\) | 13.6641 | 0.441699 | ||||||||
\(958\) | −27.4525 | −0.886951 | ||||||||
\(959\) | 5.46994 | 0.176634 | ||||||||
\(960\) | −84.1921 | −2.71729 | ||||||||
\(961\) | −27.1080 | −0.874453 | ||||||||
\(962\) | 39.8887 | 1.28606 | ||||||||
\(963\) | −5.63368 | −0.181543 | ||||||||
\(964\) | −61.7038 | −1.98735 | ||||||||
\(965\) | −5.52125 | −0.177735 | ||||||||
\(966\) | −14.4883 | −0.466153 | ||||||||
\(967\) | 45.1205 | 1.45098 | 0.725489 | − | 0.688234i | \(-0.241614\pi\) | ||||
0.725489 | + | 0.688234i | \(0.241614\pi\) | |||||||
\(968\) | 51.7646 | 1.66378 | ||||||||
\(969\) | −60.0350 | −1.92860 | ||||||||
\(970\) | −79.5813 | −2.55520 | ||||||||
\(971\) | 36.6463 | 1.17604 | 0.588018 | − | 0.808848i | \(-0.299909\pi\) | ||||
0.588018 | + | 0.808848i | \(0.299909\pi\) | |||||||
\(972\) | 101.983 | 3.27111 | ||||||||
\(973\) | 2.29266 | 0.0734994 | ||||||||
\(974\) | −25.9497 | −0.831481 | ||||||||
\(975\) | −84.8850 | −2.71850 | ||||||||
\(976\) | −64.5184 | −2.06518 | ||||||||
\(977\) | −31.8335 | −1.01844 | −0.509221 | − | 0.860636i | \(-0.670066\pi\) | ||||
−0.509221 | + | 0.860636i | \(0.670066\pi\) | |||||||
\(978\) | 99.2675 | 3.17423 | ||||||||
\(979\) | −23.8109 | −0.760999 | ||||||||
\(980\) | −88.6060 | −2.83041 | ||||||||
\(981\) | −25.1339 | −0.802462 | ||||||||
\(982\) | −83.4550 | −2.66316 | ||||||||
\(983\) | 12.9485 | 0.412992 | 0.206496 | − | 0.978447i | \(-0.433794\pi\) | ||||
0.206496 | + | 0.978447i | \(0.433794\pi\) | |||||||
\(984\) | 181.050 | 5.77166 | ||||||||
\(985\) | 39.0395 | 1.24390 | ||||||||
\(986\) | −49.8033 | −1.58606 | ||||||||
\(987\) | −19.5225 | −0.621408 | ||||||||
\(988\) | 77.5628 | 2.46760 | ||||||||
\(989\) | 7.41319 | 0.235726 | ||||||||
\(990\) | 51.0622 | 1.62286 | ||||||||
\(991\) | 25.2059 | 0.800692 | 0.400346 | − | 0.916364i | \(-0.368890\pi\) | ||||
0.400346 | + | 0.916364i | \(0.368890\pi\) | |||||||
\(992\) | −22.4771 | −0.713648 | ||||||||
\(993\) | 35.0273 | 1.11156 | ||||||||
\(994\) | 7.47293 | 0.237027 | ||||||||
\(995\) | −78.3767 | −2.48471 | ||||||||
\(996\) | 40.4870 | 1.28288 | ||||||||
\(997\) | 12.2848 | 0.389063 | 0.194532 | − | 0.980896i | \(-0.437681\pi\) | ||||
0.194532 | + | 0.980896i | \(0.437681\pi\) | |||||||
\(998\) | −5.07991 | −0.160802 | ||||||||
\(999\) | −3.55760 | −0.112558 |
(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 | 6043.2.a.c.1.8 | ✓ | 259 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6043.2.a.c.1.8 | ✓ | 259 | 1.1 | even | 1 | trivial |