Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.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: | \(48.2376278611\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.57785 | −1.82281 | −0.911406 | − | 0.411508i | \(-0.865002\pi\) | ||||
−0.911406 | + | 0.411508i | \(0.865002\pi\) | |||||||
\(3\) | −0.937633 | −0.541343 | −0.270671 | − | 0.962672i | \(-0.587246\pi\) | ||||
−0.270671 | + | 0.962672i | \(0.587246\pi\) | |||||||
\(4\) | 4.64529 | 2.32265 | ||||||||
\(5\) | −3.87896 | −1.73472 | −0.867362 | − | 0.497678i | \(-0.834186\pi\) | ||||
−0.867362 | + | 0.497678i | \(0.834186\pi\) | |||||||
\(6\) | 2.41707 | 0.986766 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −6.81916 | −2.41094 | ||||||||
\(9\) | −2.12084 | −0.706948 | ||||||||
\(10\) | 9.99936 | 3.16208 | ||||||||
\(11\) | 4.77034 | 1.43831 | 0.719156 | − | 0.694848i | \(-0.244529\pi\) | ||||
0.719156 | + | 0.694848i | \(0.244529\pi\) | |||||||
\(12\) | −4.35558 | −1.25735 | ||||||||
\(13\) | −5.45549 | −1.51308 | −0.756541 | − | 0.653947i | \(-0.773112\pi\) | ||||
−0.756541 | + | 0.653947i | \(0.773112\pi\) | |||||||
\(14\) | −2.57785 | −0.688958 | ||||||||
\(15\) | 3.63704 | 0.939080 | ||||||||
\(16\) | 8.28816 | 2.07204 | ||||||||
\(17\) | −2.70243 | −0.655435 | −0.327718 | − | 0.944776i | \(-0.606279\pi\) | ||||
−0.327718 | + | 0.944776i | \(0.606279\pi\) | |||||||
\(18\) | 5.46721 | 1.28863 | ||||||||
\(19\) | −0.0387091 | −0.00888047 | −0.00444023 | − | 0.999990i | \(-0.501413\pi\) | ||||
−0.00444023 | + | 0.999990i | \(0.501413\pi\) | |||||||
\(20\) | −18.0189 | −4.02915 | ||||||||
\(21\) | −0.937633 | −0.204608 | ||||||||
\(22\) | −12.2972 | −2.62177 | ||||||||
\(23\) | 8.78005 | 1.83077 | 0.915383 | − | 0.402583i | \(-0.131888\pi\) | ||||
0.915383 | + | 0.402583i | \(0.131888\pi\) | |||||||
\(24\) | 6.39387 | 1.30514 | ||||||||
\(25\) | 10.0463 | 2.00926 | ||||||||
\(26\) | 14.0634 | 2.75806 | ||||||||
\(27\) | 4.80147 | 0.924044 | ||||||||
\(28\) | 4.64529 | 0.877878 | ||||||||
\(29\) | −5.81159 | −1.07919 | −0.539593 | − | 0.841926i | \(-0.681422\pi\) | ||||
−0.539593 | + | 0.841926i | \(0.681422\pi\) | |||||||
\(30\) | −9.37573 | −1.71177 | ||||||||
\(31\) | 7.97829 | 1.43294 | 0.716471 | − | 0.697617i | \(-0.245756\pi\) | ||||
0.716471 | + | 0.697617i | \(0.245756\pi\) | |||||||
\(32\) | −7.72728 | −1.36600 | ||||||||
\(33\) | −4.47283 | −0.778620 | ||||||||
\(34\) | 6.96645 | 1.19474 | ||||||||
\(35\) | −3.87896 | −0.655664 | ||||||||
\(36\) | −9.85194 | −1.64199 | ||||||||
\(37\) | −10.0655 | −1.65475 | −0.827377 | − | 0.561646i | \(-0.810168\pi\) | ||||
−0.827377 | + | 0.561646i | \(0.810168\pi\) | |||||||
\(38\) | 0.0997860 | 0.0161874 | ||||||||
\(39\) | 5.11525 | 0.819095 | ||||||||
\(40\) | 26.4512 | 4.18231 | ||||||||
\(41\) | −1.45641 | −0.227453 | −0.113726 | − | 0.993512i | \(-0.536279\pi\) | ||||
−0.113726 | + | 0.993512i | \(0.536279\pi\) | |||||||
\(42\) | 2.41707 | 0.372963 | ||||||||
\(43\) | 6.85876 | 1.04595 | 0.522976 | − | 0.852347i | \(-0.324822\pi\) | ||||
0.522976 | + | 0.852347i | \(0.324822\pi\) | |||||||
\(44\) | 22.1596 | 3.34069 | ||||||||
\(45\) | 8.22667 | 1.22636 | ||||||||
\(46\) | −22.6336 | −3.33714 | ||||||||
\(47\) | −7.22348 | −1.05365 | −0.526826 | − | 0.849973i | \(-0.676618\pi\) | ||||
−0.526826 | + | 0.849973i | \(0.676618\pi\) | |||||||
\(48\) | −7.77125 | −1.12168 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −25.8979 | −3.66251 | ||||||||
\(51\) | 2.53389 | 0.354815 | ||||||||
\(52\) | −25.3424 | −3.51435 | ||||||||
\(53\) | −8.65850 | −1.18934 | −0.594668 | − | 0.803971i | \(-0.702717\pi\) | ||||
−0.594668 | + | 0.803971i | \(0.702717\pi\) | |||||||
\(54\) | −12.3775 | −1.68436 | ||||||||
\(55\) | −18.5040 | −2.49507 | ||||||||
\(56\) | −6.81916 | −0.911248 | ||||||||
\(57\) | 0.0362949 | 0.00480738 | ||||||||
\(58\) | 14.9814 | 1.96715 | ||||||||
\(59\) | −9.38313 | −1.22158 | −0.610790 | − | 0.791793i | \(-0.709148\pi\) | ||||
−0.610790 | + | 0.791793i | \(0.709148\pi\) | |||||||
\(60\) | 16.8951 | 2.18115 | ||||||||
\(61\) | 13.2500 | 1.69649 | 0.848243 | − | 0.529607i | \(-0.177660\pi\) | ||||
0.848243 | + | 0.529607i | \(0.177660\pi\) | |||||||
\(62\) | −20.5668 | −2.61199 | ||||||||
\(63\) | −2.12084 | −0.267201 | ||||||||
\(64\) | 3.34343 | 0.417929 | ||||||||
\(65\) | 21.1616 | 2.62478 | ||||||||
\(66\) | 11.5303 | 1.41928 | ||||||||
\(67\) | −0.538668 | −0.0658088 | −0.0329044 | − | 0.999459i | \(-0.510476\pi\) | ||||
−0.0329044 | + | 0.999459i | \(0.510476\pi\) | |||||||
\(68\) | −12.5536 | −1.52234 | ||||||||
\(69\) | −8.23246 | −0.991072 | ||||||||
\(70\) | 9.99936 | 1.19515 | ||||||||
\(71\) | 4.14396 | 0.491797 | 0.245899 | − | 0.969296i | \(-0.420917\pi\) | ||||
0.245899 | + | 0.969296i | \(0.420917\pi\) | |||||||
\(72\) | 14.4624 | 1.70441 | ||||||||
\(73\) | 0.785295 | 0.0919118 | 0.0459559 | − | 0.998943i | \(-0.485367\pi\) | ||||
0.0459559 | + | 0.998943i | \(0.485367\pi\) | |||||||
\(74\) | 25.9473 | 3.01631 | ||||||||
\(75\) | −9.41976 | −1.08770 | ||||||||
\(76\) | −0.179815 | −0.0206262 | ||||||||
\(77\) | 4.77034 | 0.543631 | ||||||||
\(78\) | −13.1863 | −1.49306 | ||||||||
\(79\) | 6.77643 | 0.762408 | 0.381204 | − | 0.924491i | \(-0.375510\pi\) | ||||
0.381204 | + | 0.924491i | \(0.375510\pi\) | |||||||
\(80\) | −32.1494 | −3.59441 | ||||||||
\(81\) | 1.86051 | 0.206724 | ||||||||
\(82\) | 3.75439 | 0.414603 | ||||||||
\(83\) | −10.7413 | −1.17901 | −0.589505 | − | 0.807765i | \(-0.700677\pi\) | ||||
−0.589505 | + | 0.807765i | \(0.700677\pi\) | |||||||
\(84\) | −4.35558 | −0.475233 | ||||||||
\(85\) | 10.4826 | 1.13700 | ||||||||
\(86\) | −17.6808 | −1.90657 | ||||||||
\(87\) | 5.44914 | 0.584209 | ||||||||
\(88\) | −32.5297 | −3.46768 | ||||||||
\(89\) | −12.2160 | −1.29489 | −0.647445 | − | 0.762113i | \(-0.724162\pi\) | ||||
−0.647445 | + | 0.762113i | \(0.724162\pi\) | |||||||
\(90\) | −21.2071 | −2.23542 | ||||||||
\(91\) | −5.45549 | −0.571891 | ||||||||
\(92\) | 40.7859 | 4.25222 | ||||||||
\(93\) | −7.48070 | −0.775713 | ||||||||
\(94\) | 18.6210 | 1.92061 | ||||||||
\(95\) | 0.150151 | 0.0154052 | ||||||||
\(96\) | 7.24535 | 0.739476 | ||||||||
\(97\) | 10.1833 | 1.03396 | 0.516979 | − | 0.855998i | \(-0.327056\pi\) | ||||
0.516979 | + | 0.855998i | \(0.327056\pi\) | |||||||
\(98\) | −2.57785 | −0.260402 | ||||||||
\(99\) | −10.1172 | −1.01681 | ||||||||
\(100\) | 46.6681 | 4.66681 | ||||||||
\(101\) | 7.67758 | 0.763947 | 0.381974 | − | 0.924173i | \(-0.375244\pi\) | ||||
0.381974 | + | 0.924173i | \(0.375244\pi\) | |||||||
\(102\) | −6.53197 | −0.646761 | ||||||||
\(103\) | −0.915048 | −0.0901623 | −0.0450812 | − | 0.998983i | \(-0.514355\pi\) | ||||
−0.0450812 | + | 0.998983i | \(0.514355\pi\) | |||||||
\(104\) | 37.2019 | 3.64794 | ||||||||
\(105\) | 3.63704 | 0.354939 | ||||||||
\(106\) | 22.3203 | 2.16794 | ||||||||
\(107\) | 0.196388 | 0.0189856 | 0.00949278 | − | 0.999955i | \(-0.496978\pi\) | ||||
0.00949278 | + | 0.999955i | \(0.496978\pi\) | |||||||
\(108\) | 22.3042 | 2.14623 | ||||||||
\(109\) | −3.09764 | −0.296700 | −0.148350 | − | 0.988935i | \(-0.547396\pi\) | ||||
−0.148350 | + | 0.988935i | \(0.547396\pi\) | |||||||
\(110\) | 47.7004 | 4.54805 | ||||||||
\(111\) | 9.43773 | 0.895789 | ||||||||
\(112\) | 8.28816 | 0.783157 | ||||||||
\(113\) | −15.3283 | −1.44196 | −0.720982 | − | 0.692954i | \(-0.756309\pi\) | ||||
−0.720982 | + | 0.692954i | \(0.756309\pi\) | |||||||
\(114\) | −0.0935627 | −0.00876295 | ||||||||
\(115\) | −34.0574 | −3.17587 | ||||||||
\(116\) | −26.9966 | −2.50657 | ||||||||
\(117\) | 11.5703 | 1.06967 | ||||||||
\(118\) | 24.1883 | 2.22671 | ||||||||
\(119\) | −2.70243 | −0.247731 | ||||||||
\(120\) | −24.8015 | −2.26406 | ||||||||
\(121\) | 11.7562 | 1.06874 | ||||||||
\(122\) | −34.1564 | −3.09238 | ||||||||
\(123\) | 1.36557 | 0.123130 | ||||||||
\(124\) | 37.0615 | 3.32822 | ||||||||
\(125\) | −19.5745 | −1.75079 | ||||||||
\(126\) | 5.46721 | 0.487058 | ||||||||
\(127\) | −17.2937 | −1.53457 | −0.767284 | − | 0.641308i | \(-0.778392\pi\) | ||||
−0.767284 | + | 0.641308i | \(0.778392\pi\) | |||||||
\(128\) | 6.83571 | 0.604198 | ||||||||
\(129\) | −6.43100 | −0.566218 | ||||||||
\(130\) | −54.5514 | −4.78448 | ||||||||
\(131\) | −17.5230 | −1.53099 | −0.765494 | − | 0.643443i | \(-0.777505\pi\) | ||||
−0.765494 | + | 0.643443i | \(0.777505\pi\) | |||||||
\(132\) | −20.7776 | −1.80846 | ||||||||
\(133\) | −0.0387091 | −0.00335650 | ||||||||
\(134\) | 1.38860 | 0.119957 | ||||||||
\(135\) | −18.6247 | −1.60296 | ||||||||
\(136\) | 18.4283 | 1.58021 | ||||||||
\(137\) | −4.12588 | −0.352498 | −0.176249 | − | 0.984346i | \(-0.556396\pi\) | ||||
−0.176249 | + | 0.984346i | \(0.556396\pi\) | |||||||
\(138\) | 21.2220 | 1.80654 | ||||||||
\(139\) | −0.708986 | −0.0601354 | −0.0300677 | − | 0.999548i | \(-0.509572\pi\) | ||||
−0.0300677 | + | 0.999548i | \(0.509572\pi\) | |||||||
\(140\) | −18.0189 | −1.52287 | ||||||||
\(141\) | 6.77297 | 0.570387 | ||||||||
\(142\) | −10.6825 | −0.896454 | ||||||||
\(143\) | −26.0246 | −2.17628 | ||||||||
\(144\) | −17.5779 | −1.46482 | ||||||||
\(145\) | 22.5429 | 1.87209 | ||||||||
\(146\) | −2.02437 | −0.167538 | ||||||||
\(147\) | −0.937633 | −0.0773347 | ||||||||
\(148\) | −46.7571 | −3.84341 | ||||||||
\(149\) | −10.9216 | −0.894736 | −0.447368 | − | 0.894350i | \(-0.647639\pi\) | ||||
−0.447368 | + | 0.894350i | \(0.647639\pi\) | |||||||
\(150\) | 24.2827 | 1.98267 | ||||||||
\(151\) | 14.3897 | 1.17101 | 0.585507 | − | 0.810667i | \(-0.300895\pi\) | ||||
0.585507 | + | 0.810667i | \(0.300895\pi\) | |||||||
\(152\) | 0.263963 | 0.0214102 | ||||||||
\(153\) | 5.73143 | 0.463359 | ||||||||
\(154\) | −12.2972 | −0.990937 | ||||||||
\(155\) | −30.9474 | −2.48576 | ||||||||
\(156\) | 23.7618 | 1.90247 | ||||||||
\(157\) | 5.89056 | 0.470117 | 0.235059 | − | 0.971981i | \(-0.424472\pi\) | ||||
0.235059 | + | 0.971981i | \(0.424472\pi\) | |||||||
\(158\) | −17.4686 | −1.38973 | ||||||||
\(159\) | 8.11849 | 0.643838 | ||||||||
\(160\) | 29.9738 | 2.36964 | ||||||||
\(161\) | 8.78005 | 0.691965 | ||||||||
\(162\) | −4.79612 | −0.376819 | ||||||||
\(163\) | 1.22587 | 0.0960175 | 0.0480087 | − | 0.998847i | \(-0.484712\pi\) | ||||
0.0480087 | + | 0.998847i | \(0.484712\pi\) | |||||||
\(164\) | −6.76543 | −0.528292 | ||||||||
\(165\) | 17.3499 | 1.35069 | ||||||||
\(166\) | 27.6894 | 2.14911 | ||||||||
\(167\) | −10.8973 | −0.843261 | −0.421630 | − | 0.906768i | \(-0.638542\pi\) | ||||
−0.421630 | + | 0.906768i | \(0.638542\pi\) | |||||||
\(168\) | 6.39387 | 0.493298 | ||||||||
\(169\) | 16.7624 | 1.28942 | ||||||||
\(170\) | −27.0226 | −2.07254 | ||||||||
\(171\) | 0.0820959 | 0.00627803 | ||||||||
\(172\) | 31.8610 | 2.42938 | ||||||||
\(173\) | 14.7965 | 1.12496 | 0.562479 | − | 0.826812i | \(-0.309848\pi\) | ||||
0.562479 | + | 0.826812i | \(0.309848\pi\) | |||||||
\(174\) | −14.0471 | −1.06490 | ||||||||
\(175\) | 10.0463 | 0.759431 | ||||||||
\(176\) | 39.5373 | 2.98024 | ||||||||
\(177\) | 8.79794 | 0.661293 | ||||||||
\(178\) | 31.4909 | 2.36034 | ||||||||
\(179\) | −2.18905 | −0.163617 | −0.0818087 | − | 0.996648i | \(-0.526070\pi\) | ||||
−0.0818087 | + | 0.996648i | \(0.526070\pi\) | |||||||
\(180\) | 38.2153 | 2.84840 | ||||||||
\(181\) | −14.1496 | −1.05173 | −0.525864 | − | 0.850568i | \(-0.676258\pi\) | ||||
−0.525864 | + | 0.850568i | \(0.676258\pi\) | |||||||
\(182\) | 14.0634 | 1.04245 | ||||||||
\(183\) | −12.4236 | −0.918381 | ||||||||
\(184\) | −59.8725 | −4.41386 | ||||||||
\(185\) | 39.0436 | 2.87054 | ||||||||
\(186\) | 19.2841 | 1.41398 | ||||||||
\(187\) | −12.8915 | −0.942721 | ||||||||
\(188\) | −33.5552 | −2.44726 | ||||||||
\(189\) | 4.80147 | 0.349256 | ||||||||
\(190\) | −0.387066 | −0.0280807 | ||||||||
\(191\) | 19.3731 | 1.40179 | 0.700893 | − | 0.713266i | \(-0.252785\pi\) | ||||
0.700893 | + | 0.713266i | \(0.252785\pi\) | |||||||
\(192\) | −3.13491 | −0.226243 | ||||||||
\(193\) | −21.6103 | −1.55554 | −0.777772 | − | 0.628547i | \(-0.783650\pi\) | ||||
−0.777772 | + | 0.628547i | \(0.783650\pi\) | |||||||
\(194\) | −26.2510 | −1.88471 | ||||||||
\(195\) | −19.8418 | −1.42090 | ||||||||
\(196\) | 4.64529 | 0.331807 | ||||||||
\(197\) | 14.1065 | 1.00505 | 0.502523 | − | 0.864564i | \(-0.332405\pi\) | ||||
0.502523 | + | 0.864564i | \(0.332405\pi\) | |||||||
\(198\) | 26.0805 | 1.85346 | ||||||||
\(199\) | −9.32295 | −0.660886 | −0.330443 | − | 0.943826i | \(-0.607198\pi\) | ||||
−0.330443 | + | 0.943826i | \(0.607198\pi\) | |||||||
\(200\) | −68.5075 | −4.84421 | ||||||||
\(201\) | 0.505073 | 0.0356251 | ||||||||
\(202\) | −19.7916 | −1.39253 | ||||||||
\(203\) | −5.81159 | −0.407894 | ||||||||
\(204\) | 11.7706 | 0.824110 | ||||||||
\(205\) | 5.64934 | 0.394567 | ||||||||
\(206\) | 2.35885 | 0.164349 | ||||||||
\(207\) | −18.6211 | −1.29426 | ||||||||
\(208\) | −45.2160 | −3.13516 | ||||||||
\(209\) | −0.184656 | −0.0127729 | ||||||||
\(210\) | −9.37573 | −0.646987 | ||||||||
\(211\) | 4.50025 | 0.309810 | 0.154905 | − | 0.987929i | \(-0.450493\pi\) | ||||
0.154905 | + | 0.987929i | \(0.450493\pi\) | |||||||
\(212\) | −40.2213 | −2.76241 | ||||||||
\(213\) | −3.88551 | −0.266231 | ||||||||
\(214\) | −0.506259 | −0.0346071 | ||||||||
\(215\) | −26.6049 | −1.81444 | ||||||||
\(216\) | −32.7420 | −2.22781 | ||||||||
\(217\) | 7.97829 | 0.541601 | ||||||||
\(218\) | 7.98524 | 0.540829 | ||||||||
\(219\) | −0.736319 | −0.0497558 | ||||||||
\(220\) | −85.9563 | −5.79517 | ||||||||
\(221\) | 14.7431 | 0.991727 | ||||||||
\(222\) | −24.3290 | −1.63286 | ||||||||
\(223\) | 16.5907 | 1.11100 | 0.555498 | − | 0.831518i | \(-0.312528\pi\) | ||||
0.555498 | + | 0.831518i | \(0.312528\pi\) | |||||||
\(224\) | −7.72728 | −0.516301 | ||||||||
\(225\) | −21.3067 | −1.42045 | ||||||||
\(226\) | 39.5140 | 2.62843 | ||||||||
\(227\) | −7.84887 | −0.520948 | −0.260474 | − | 0.965481i | \(-0.583879\pi\) | ||||
−0.260474 | + | 0.965481i | \(0.583879\pi\) | |||||||
\(228\) | 0.168600 | 0.0111658 | ||||||||
\(229\) | −20.8885 | −1.38035 | −0.690177 | − | 0.723641i | \(-0.742467\pi\) | ||||
−0.690177 | + | 0.723641i | \(0.742467\pi\) | |||||||
\(230\) | 87.7949 | 5.78902 | ||||||||
\(231\) | −4.47283 | −0.294291 | ||||||||
\(232\) | 39.6302 | 2.60185 | ||||||||
\(233\) | 27.4101 | 1.79569 | 0.897847 | − | 0.440308i | \(-0.145131\pi\) | ||||
0.897847 | + | 0.440308i | \(0.145131\pi\) | |||||||
\(234\) | −29.8263 | −1.94981 | ||||||||
\(235\) | 28.0196 | 1.82780 | ||||||||
\(236\) | −43.5874 | −2.83730 | ||||||||
\(237\) | −6.35380 | −0.412724 | ||||||||
\(238\) | 6.96645 | 0.451568 | ||||||||
\(239\) | −4.12394 | −0.266756 | −0.133378 | − | 0.991065i | \(-0.542582\pi\) | ||||
−0.133378 | + | 0.991065i | \(0.542582\pi\) | |||||||
\(240\) | 30.1444 | 1.94581 | ||||||||
\(241\) | 25.6840 | 1.65445 | 0.827227 | − | 0.561867i | \(-0.189917\pi\) | ||||
0.827227 | + | 0.561867i | \(0.189917\pi\) | |||||||
\(242\) | −30.3056 | −1.94812 | ||||||||
\(243\) | −16.1489 | −1.03595 | ||||||||
\(244\) | 61.5501 | 3.94034 | ||||||||
\(245\) | −3.87896 | −0.247818 | ||||||||
\(246\) | −3.52024 | −0.224442 | ||||||||
\(247\) | 0.211177 | 0.0134369 | ||||||||
\(248\) | −54.4052 | −3.45473 | ||||||||
\(249\) | 10.0714 | 0.638248 | ||||||||
\(250\) | 50.4600 | 3.19137 | ||||||||
\(251\) | −16.1249 | −1.01779 | −0.508897 | − | 0.860827i | \(-0.669947\pi\) | ||||
−0.508897 | + | 0.860827i | \(0.669947\pi\) | |||||||
\(252\) | −9.85194 | −0.620614 | ||||||||
\(253\) | 41.8838 | 2.63321 | ||||||||
\(254\) | 44.5805 | 2.79723 | ||||||||
\(255\) | −9.82884 | −0.615506 | ||||||||
\(256\) | −24.3083 | −1.51927 | ||||||||
\(257\) | −11.3156 | −0.705847 | −0.352924 | − | 0.935652i | \(-0.614812\pi\) | ||||
−0.352924 | + | 0.935652i | \(0.614812\pi\) | |||||||
\(258\) | 16.5781 | 1.03211 | ||||||||
\(259\) | −10.0655 | −0.625439 | ||||||||
\(260\) | 98.3020 | 6.09643 | ||||||||
\(261\) | 12.3255 | 0.762928 | ||||||||
\(262\) | 45.1715 | 2.79070 | ||||||||
\(263\) | 13.2993 | 0.820072 | 0.410036 | − | 0.912069i | \(-0.365516\pi\) | ||||
0.410036 | + | 0.912069i | \(0.365516\pi\) | |||||||
\(264\) | 30.5009 | 1.87720 | ||||||||
\(265\) | 33.5860 | 2.06317 | ||||||||
\(266\) | 0.0997860 | 0.00611827 | ||||||||
\(267\) | 11.4541 | 0.700979 | ||||||||
\(268\) | −2.50227 | −0.152850 | ||||||||
\(269\) | −2.87459 | −0.175267 | −0.0876336 | − | 0.996153i | \(-0.527930\pi\) | ||||
−0.0876336 | + | 0.996153i | \(0.527930\pi\) | |||||||
\(270\) | 48.0117 | 2.92190 | ||||||||
\(271\) | −7.82431 | −0.475293 | −0.237646 | − | 0.971352i | \(-0.576376\pi\) | ||||
−0.237646 | + | 0.971352i | \(0.576376\pi\) | |||||||
\(272\) | −22.3982 | −1.35809 | ||||||||
\(273\) | 5.11525 | 0.309589 | ||||||||
\(274\) | 10.6359 | 0.642537 | ||||||||
\(275\) | 47.9244 | 2.88995 | ||||||||
\(276\) | −38.2422 | −2.30191 | ||||||||
\(277\) | −30.3783 | −1.82525 | −0.912627 | − | 0.408793i | \(-0.865950\pi\) | ||||
−0.912627 | + | 0.408793i | \(0.865950\pi\) | |||||||
\(278\) | 1.82766 | 0.109616 | ||||||||
\(279\) | −16.9207 | −1.01302 | ||||||||
\(280\) | 26.4512 | 1.58076 | ||||||||
\(281\) | −11.1304 | −0.663982 | −0.331991 | − | 0.943282i | \(-0.607720\pi\) | ||||
−0.331991 | + | 0.943282i | \(0.607720\pi\) | |||||||
\(282\) | −17.4597 | −1.03971 | ||||||||
\(283\) | −12.1409 | −0.721699 | −0.360849 | − | 0.932624i | \(-0.617513\pi\) | ||||
−0.360849 | + | 0.932624i | \(0.617513\pi\) | |||||||
\(284\) | 19.2499 | 1.14227 | ||||||||
\(285\) | −0.140786 | −0.00833947 | ||||||||
\(286\) | 67.0873 | 3.96696 | ||||||||
\(287\) | −1.45641 | −0.0859690 | ||||||||
\(288\) | 16.3884 | 0.965693 | ||||||||
\(289\) | −9.69688 | −0.570405 | ||||||||
\(290\) | −58.1122 | −3.41247 | ||||||||
\(291\) | −9.54821 | −0.559726 | ||||||||
\(292\) | 3.64793 | 0.213479 | ||||||||
\(293\) | −18.9809 | −1.10888 | −0.554438 | − | 0.832225i | \(-0.687067\pi\) | ||||
−0.554438 | + | 0.832225i | \(0.687067\pi\) | |||||||
\(294\) | 2.41707 | 0.140967 | ||||||||
\(295\) | 36.3968 | 2.11910 | ||||||||
\(296\) | 68.6381 | 3.98951 | ||||||||
\(297\) | 22.9047 | 1.32906 | ||||||||
\(298\) | 28.1543 | 1.63094 | ||||||||
\(299\) | −47.8995 | −2.77010 | ||||||||
\(300\) | −43.7576 | −2.52634 | ||||||||
\(301\) | 6.85876 | 0.395333 | ||||||||
\(302\) | −37.0943 | −2.13454 | ||||||||
\(303\) | −7.19875 | −0.413557 | ||||||||
\(304\) | −0.320827 | −0.0184007 | ||||||||
\(305\) | −51.3962 | −2.94293 | ||||||||
\(306\) | −14.7747 | −0.844616 | ||||||||
\(307\) | −11.4907 | −0.655808 | −0.327904 | − | 0.944711i | \(-0.606342\pi\) | ||||
−0.327904 | + | 0.944711i | \(0.606342\pi\) | |||||||
\(308\) | 22.1596 | 1.26266 | ||||||||
\(309\) | 0.857979 | 0.0488087 | ||||||||
\(310\) | 79.7778 | 4.53107 | ||||||||
\(311\) | 16.1891 | 0.918000 | 0.459000 | − | 0.888436i | \(-0.348208\pi\) | ||||
0.459000 | + | 0.888436i | \(0.348208\pi\) | |||||||
\(312\) | −34.8817 | −1.97479 | ||||||||
\(313\) | −30.0000 | −1.69570 | −0.847850 | − | 0.530237i | \(-0.822103\pi\) | ||||
−0.847850 | + | 0.530237i | \(0.822103\pi\) | |||||||
\(314\) | −15.1849 | −0.856936 | ||||||||
\(315\) | 8.22667 | 0.463520 | ||||||||
\(316\) | 31.4785 | 1.77080 | ||||||||
\(317\) | −34.7882 | −1.95390 | −0.976951 | − | 0.213464i | \(-0.931525\pi\) | ||||
−0.976951 | + | 0.213464i | \(0.931525\pi\) | |||||||
\(318\) | −20.9282 | −1.17360 | ||||||||
\(319\) | −27.7233 | −1.55221 | ||||||||
\(320\) | −12.9690 | −0.724990 | ||||||||
\(321\) | −0.184140 | −0.0102777 | ||||||||
\(322\) | −22.6336 | −1.26132 | ||||||||
\(323\) | 0.104608 | 0.00582057 | ||||||||
\(324\) | 8.64263 | 0.480146 | ||||||||
\(325\) | −54.8076 | −3.04018 | ||||||||
\(326\) | −3.16010 | −0.175022 | ||||||||
\(327\) | 2.90445 | 0.160616 | ||||||||
\(328\) | 9.93147 | 0.548374 | ||||||||
\(329\) | −7.22348 | −0.398243 | ||||||||
\(330\) | −44.7254 | −2.46205 | ||||||||
\(331\) | 19.3672 | 1.06452 | 0.532258 | − | 0.846582i | \(-0.321344\pi\) | ||||
0.532258 | + | 0.846582i | \(0.321344\pi\) | |||||||
\(332\) | −49.8964 | −2.73842 | ||||||||
\(333\) | 21.3473 | 1.16983 | ||||||||
\(334\) | 28.0916 | 1.53711 | ||||||||
\(335\) | 2.08947 | 0.114160 | ||||||||
\(336\) | −7.77125 | −0.423956 | ||||||||
\(337\) | 24.3052 | 1.32399 | 0.661995 | − | 0.749508i | \(-0.269710\pi\) | ||||
0.661995 | + | 0.749508i | \(0.269710\pi\) | |||||||
\(338\) | −43.2109 | −2.35036 | ||||||||
\(339\) | 14.3723 | 0.780596 | ||||||||
\(340\) | 48.6948 | 2.64085 | ||||||||
\(341\) | 38.0592 | 2.06102 | ||||||||
\(342\) | −0.211631 | −0.0114437 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −46.7710 | −2.52172 | ||||||||
\(345\) | 31.9334 | 1.71924 | ||||||||
\(346\) | −38.1431 | −2.05059 | ||||||||
\(347\) | 16.5127 | 0.886451 | 0.443225 | − | 0.896410i | \(-0.353834\pi\) | ||||
0.443225 | + | 0.896410i | \(0.353834\pi\) | |||||||
\(348\) | 25.3129 | 1.35691 | ||||||||
\(349\) | −5.48655 | −0.293688 | −0.146844 | − | 0.989160i | \(-0.546912\pi\) | ||||
−0.146844 | + | 0.989160i | \(0.546912\pi\) | |||||||
\(350\) | −25.8979 | −1.38430 | ||||||||
\(351\) | −26.1944 | −1.39815 | ||||||||
\(352\) | −36.8618 | −1.96474 | ||||||||
\(353\) | 5.20186 | 0.276867 | 0.138433 | − | 0.990372i | \(-0.455793\pi\) | ||||
0.138433 | + | 0.990372i | \(0.455793\pi\) | |||||||
\(354\) | −22.6797 | −1.20541 | ||||||||
\(355\) | −16.0742 | −0.853132 | ||||||||
\(356\) | −56.7467 | −3.00757 | ||||||||
\(357\) | 2.53389 | 0.134107 | ||||||||
\(358\) | 5.64304 | 0.298244 | ||||||||
\(359\) | −1.03219 | −0.0544768 | −0.0272384 | − | 0.999629i | \(-0.508671\pi\) | ||||
−0.0272384 | + | 0.999629i | \(0.508671\pi\) | |||||||
\(360\) | −56.0989 | −2.95667 | ||||||||
\(361\) | −18.9985 | −0.999921 | ||||||||
\(362\) | 36.4754 | 1.91710 | ||||||||
\(363\) | −11.0230 | −0.578556 | ||||||||
\(364\) | −25.3424 | −1.32830 | ||||||||
\(365\) | −3.04613 | −0.159442 | ||||||||
\(366\) | 32.0262 | 1.67404 | ||||||||
\(367\) | 2.04562 | 0.106780 | 0.0533901 | − | 0.998574i | \(-0.482997\pi\) | ||||
0.0533901 | + | 0.998574i | \(0.482997\pi\) | |||||||
\(368\) | 72.7704 | 3.79342 | ||||||||
\(369\) | 3.08881 | 0.160797 | ||||||||
\(370\) | −100.648 | −5.23246 | ||||||||
\(371\) | −8.65850 | −0.449527 | ||||||||
\(372\) | −34.7501 | −1.80171 | ||||||||
\(373\) | −6.42788 | −0.332823 | −0.166412 | − | 0.986056i | \(-0.553218\pi\) | ||||
−0.166412 | + | 0.986056i | \(0.553218\pi\) | |||||||
\(374\) | 33.2323 | 1.71840 | ||||||||
\(375\) | 18.3537 | 0.947780 | ||||||||
\(376\) | 49.2581 | 2.54029 | ||||||||
\(377\) | 31.7051 | 1.63290 | ||||||||
\(378\) | −12.3775 | −0.636628 | ||||||||
\(379\) | 22.2017 | 1.14042 | 0.570212 | − | 0.821497i | \(-0.306861\pi\) | ||||
0.570212 | + | 0.821497i | \(0.306861\pi\) | |||||||
\(380\) | 0.697495 | 0.0357807 | ||||||||
\(381\) | 16.2151 | 0.830727 | ||||||||
\(382\) | −49.9408 | −2.55519 | ||||||||
\(383\) | 4.66101 | 0.238167 | 0.119083 | − | 0.992884i | \(-0.462004\pi\) | ||||
0.119083 | + | 0.992884i | \(0.462004\pi\) | |||||||
\(384\) | −6.40939 | −0.327078 | ||||||||
\(385\) | −18.5040 | −0.943049 | ||||||||
\(386\) | 55.7081 | 2.83547 | ||||||||
\(387\) | −14.5464 | −0.739434 | ||||||||
\(388\) | 47.3045 | 2.40152 | ||||||||
\(389\) | 28.6584 | 1.45304 | 0.726520 | − | 0.687145i | \(-0.241136\pi\) | ||||
0.726520 | + | 0.687145i | \(0.241136\pi\) | |||||||
\(390\) | 51.1492 | 2.59004 | ||||||||
\(391\) | −23.7275 | −1.19995 | ||||||||
\(392\) | −6.81916 | −0.344419 | ||||||||
\(393\) | 16.4301 | 0.828789 | ||||||||
\(394\) | −36.3643 | −1.83201 | ||||||||
\(395\) | −26.2855 | −1.32257 | ||||||||
\(396\) | −46.9971 | −2.36170 | ||||||||
\(397\) | 3.57455 | 0.179402 | 0.0897008 | − | 0.995969i | \(-0.471409\pi\) | ||||
0.0897008 | + | 0.995969i | \(0.471409\pi\) | |||||||
\(398\) | 24.0331 | 1.20467 | ||||||||
\(399\) | 0.0362949 | 0.00181702 | ||||||||
\(400\) | 83.2655 | 4.16327 | ||||||||
\(401\) | 26.5531 | 1.32600 | 0.662998 | − | 0.748621i | \(-0.269284\pi\) | ||||
0.662998 | + | 0.748621i | \(0.269284\pi\) | |||||||
\(402\) | −1.30200 | −0.0649379 | ||||||||
\(403\) | −43.5255 | −2.16816 | ||||||||
\(404\) | 35.6646 | 1.77438 | ||||||||
\(405\) | −7.21686 | −0.358609 | ||||||||
\(406\) | 14.9814 | 0.743514 | ||||||||
\(407\) | −48.0158 | −2.38005 | ||||||||
\(408\) | −17.2790 | −0.855437 | ||||||||
\(409\) | −14.7280 | −0.728252 | −0.364126 | − | 0.931350i | \(-0.618632\pi\) | ||||
−0.364126 | + | 0.931350i | \(0.618632\pi\) | |||||||
\(410\) | −14.5631 | −0.719222 | ||||||||
\(411\) | 3.86856 | 0.190822 | ||||||||
\(412\) | −4.25066 | −0.209415 | ||||||||
\(413\) | −9.38313 | −0.461714 | ||||||||
\(414\) | 48.0024 | 2.35919 | ||||||||
\(415\) | 41.6650 | 2.04526 | ||||||||
\(416\) | 42.1561 | 2.06687 | ||||||||
\(417\) | 0.664769 | 0.0325539 | ||||||||
\(418\) | 0.476014 | 0.0232826 | ||||||||
\(419\) | 2.03396 | 0.0993655 | 0.0496827 | − | 0.998765i | \(-0.484179\pi\) | ||||
0.0496827 | + | 0.998765i | \(0.484179\pi\) | |||||||
\(420\) | 16.8951 | 0.824397 | ||||||||
\(421\) | 17.9581 | 0.875224 | 0.437612 | − | 0.899164i | \(-0.355824\pi\) | ||||
0.437612 | + | 0.899164i | \(0.355824\pi\) | |||||||
\(422\) | −11.6010 | −0.564726 | ||||||||
\(423\) | 15.3199 | 0.744878 | ||||||||
\(424\) | 59.0437 | 2.86741 | ||||||||
\(425\) | −27.1495 | −1.31694 | ||||||||
\(426\) | 10.0162 | 0.485289 | ||||||||
\(427\) | 13.2500 | 0.641212 | ||||||||
\(428\) | 0.912280 | 0.0440967 | ||||||||
\(429\) | 24.4015 | 1.17812 | ||||||||
\(430\) | 68.5833 | 3.30738 | ||||||||
\(431\) | −26.1554 | −1.25986 | −0.629931 | − | 0.776651i | \(-0.716917\pi\) | ||||
−0.629931 | + | 0.776651i | \(0.716917\pi\) | |||||||
\(432\) | 39.7954 | 1.91466 | ||||||||
\(433\) | −14.0060 | −0.673086 | −0.336543 | − | 0.941668i | \(-0.609258\pi\) | ||||
−0.336543 | + | 0.941668i | \(0.609258\pi\) | |||||||
\(434\) | −20.5668 | −0.987238 | ||||||||
\(435\) | −21.1370 | −1.01344 | ||||||||
\(436\) | −14.3894 | −0.689130 | ||||||||
\(437\) | −0.339868 | −0.0162581 | ||||||||
\(438\) | 1.89812 | 0.0906955 | ||||||||
\(439\) | 40.1642 | 1.91693 | 0.958466 | − | 0.285207i | \(-0.0920623\pi\) | ||||
0.958466 | + | 0.285207i | \(0.0920623\pi\) | |||||||
\(440\) | 126.181 | 6.01546 | ||||||||
\(441\) | −2.12084 | −0.100993 | ||||||||
\(442\) | −38.0054 | −1.80773 | ||||||||
\(443\) | 26.4561 | 1.25697 | 0.628483 | − | 0.777823i | \(-0.283676\pi\) | ||||
0.628483 | + | 0.777823i | \(0.283676\pi\) | |||||||
\(444\) | 43.8410 | 2.08060 | ||||||||
\(445\) | 47.3852 | 2.24627 | ||||||||
\(446\) | −42.7683 | −2.02514 | ||||||||
\(447\) | 10.2405 | 0.484359 | ||||||||
\(448\) | 3.34343 | 0.157962 | ||||||||
\(449\) | 22.8507 | 1.07839 | 0.539195 | − | 0.842181i | \(-0.318729\pi\) | ||||
0.539195 | + | 0.842181i | \(0.318729\pi\) | |||||||
\(450\) | 54.9254 | 2.58921 | ||||||||
\(451\) | −6.94756 | −0.327148 | ||||||||
\(452\) | −71.2044 | −3.34917 | ||||||||
\(453\) | −13.4922 | −0.633920 | ||||||||
\(454\) | 20.2332 | 0.949590 | ||||||||
\(455\) | 21.1616 | 0.992073 | ||||||||
\(456\) | −0.247501 | −0.0115903 | ||||||||
\(457\) | −5.47242 | −0.255989 | −0.127995 | − | 0.991775i | \(-0.540854\pi\) | ||||
−0.127995 | + | 0.991775i | \(0.540854\pi\) | |||||||
\(458\) | 53.8475 | 2.51613 | ||||||||
\(459\) | −12.9756 | −0.605651 | ||||||||
\(460\) | −158.207 | −7.37643 | ||||||||
\(461\) | 37.7325 | 1.75738 | 0.878688 | − | 0.477396i | \(-0.158419\pi\) | ||||
0.878688 | + | 0.477396i | \(0.158419\pi\) | |||||||
\(462\) | 11.5303 | 0.536437 | ||||||||
\(463\) | 41.5515 | 1.93106 | 0.965532 | − | 0.260286i | \(-0.0838169\pi\) | ||||
0.965532 | + | 0.260286i | \(0.0838169\pi\) | |||||||
\(464\) | −48.1674 | −2.23612 | ||||||||
\(465\) | 29.0173 | 1.34565 | ||||||||
\(466\) | −70.6590 | −3.27321 | ||||||||
\(467\) | −22.8757 | −1.05856 | −0.529280 | − | 0.848447i | \(-0.677538\pi\) | ||||
−0.529280 | + | 0.848447i | \(0.677538\pi\) | |||||||
\(468\) | 53.7472 | 2.48447 | ||||||||
\(469\) | −0.538668 | −0.0248734 | ||||||||
\(470\) | −72.2302 | −3.33173 | ||||||||
\(471\) | −5.52318 | −0.254495 | ||||||||
\(472\) | 63.9851 | 2.94515 | ||||||||
\(473\) | 32.7187 | 1.50441 | ||||||||
\(474\) | 16.3791 | 0.752318 | ||||||||
\(475\) | −0.388884 | −0.0178432 | ||||||||
\(476\) | −12.5536 | −0.575392 | ||||||||
\(477\) | 18.3633 | 0.840799 | ||||||||
\(478\) | 10.6309 | 0.486246 | ||||||||
\(479\) | −13.5084 | −0.617214 | −0.308607 | − | 0.951190i | \(-0.599863\pi\) | ||||
−0.308607 | + | 0.951190i | \(0.599863\pi\) | |||||||
\(480\) | −28.1044 | −1.28279 | ||||||||
\(481\) | 54.9122 | 2.50378 | ||||||||
\(482\) | −66.2095 | −3.01576 | ||||||||
\(483\) | −8.23246 | −0.374590 | ||||||||
\(484\) | 54.6108 | 2.48231 | ||||||||
\(485\) | −39.5006 | −1.79363 | ||||||||
\(486\) | 41.6294 | 1.88835 | ||||||||
\(487\) | −9.95708 | −0.451198 | −0.225599 | − | 0.974220i | \(-0.572434\pi\) | ||||
−0.225599 | + | 0.974220i | \(0.572434\pi\) | |||||||
\(488\) | −90.3537 | −4.09012 | ||||||||
\(489\) | −1.14942 | −0.0519784 | ||||||||
\(490\) | 9.99936 | 0.451725 | ||||||||
\(491\) | 18.7931 | 0.848122 | 0.424061 | − | 0.905634i | \(-0.360604\pi\) | ||||
0.424061 | + | 0.905634i | \(0.360604\pi\) | |||||||
\(492\) | 6.34349 | 0.285987 | ||||||||
\(493\) | 15.7054 | 0.707336 | ||||||||
\(494\) | −0.544382 | −0.0244929 | ||||||||
\(495\) | 39.2440 | 1.76389 | ||||||||
\(496\) | 66.1253 | 2.96911 | ||||||||
\(497\) | 4.14396 | 0.185882 | ||||||||
\(498\) | −25.9625 | −1.16341 | ||||||||
\(499\) | 5.44976 | 0.243965 | 0.121982 | − | 0.992532i | \(-0.461075\pi\) | ||||
0.121982 | + | 0.992532i | \(0.461075\pi\) | |||||||
\(500\) | −90.9292 | −4.06648 | ||||||||
\(501\) | 10.2177 | 0.456493 | ||||||||
\(502\) | 41.5675 | 1.85525 | ||||||||
\(503\) | 9.54365 | 0.425530 | 0.212765 | − | 0.977103i | \(-0.431753\pi\) | ||||
0.212765 | + | 0.977103i | \(0.431753\pi\) | |||||||
\(504\) | 14.4624 | 0.644205 | ||||||||
\(505\) | −29.7810 | −1.32524 | ||||||||
\(506\) | −107.970 | −4.79986 | ||||||||
\(507\) | −15.7170 | −0.698015 | ||||||||
\(508\) | −80.3343 | −3.56426 | ||||||||
\(509\) | 5.18384 | 0.229770 | 0.114885 | − | 0.993379i | \(-0.463350\pi\) | ||||
0.114885 | + | 0.993379i | \(0.463350\pi\) | |||||||
\(510\) | 25.3372 | 1.12195 | ||||||||
\(511\) | 0.785295 | 0.0347394 | ||||||||
\(512\) | 48.9916 | 2.16514 | ||||||||
\(513\) | −0.185861 | −0.00820594 | ||||||||
\(514\) | 29.1699 | 1.28663 | ||||||||
\(515\) | 3.54943 | 0.156407 | ||||||||
\(516\) | −29.8739 | −1.31512 | ||||||||
\(517\) | −34.4585 | −1.51548 | ||||||||
\(518\) | 25.9473 | 1.14006 | ||||||||
\(519\) | −13.8737 | −0.608987 | ||||||||
\(520\) | −144.304 | −6.32817 | ||||||||
\(521\) | 8.47754 | 0.371408 | 0.185704 | − | 0.982606i | \(-0.440543\pi\) | ||||
0.185704 | + | 0.982606i | \(0.440543\pi\) | |||||||
\(522\) | −31.7732 | −1.39068 | ||||||||
\(523\) | −29.0396 | −1.26981 | −0.634907 | − | 0.772589i | \(-0.718962\pi\) | ||||
−0.634907 | + | 0.772589i | \(0.718962\pi\) | |||||||
\(524\) | −81.3993 | −3.55594 | ||||||||
\(525\) | −9.41976 | −0.411112 | ||||||||
\(526\) | −34.2836 | −1.49484 | ||||||||
\(527\) | −21.5608 | −0.939201 | ||||||||
\(528\) | −37.0715 | −1.61333 | ||||||||
\(529\) | 54.0893 | 2.35171 | ||||||||
\(530\) | −86.5795 | −3.76077 | ||||||||
\(531\) | 19.9002 | 0.863594 | ||||||||
\(532\) | −0.179815 | −0.00779597 | ||||||||
\(533\) | 7.94542 | 0.344154 | ||||||||
\(534\) | −29.5269 | −1.27775 | ||||||||
\(535\) | −0.761782 | −0.0329347 | ||||||||
\(536\) | 3.67326 | 0.158661 | ||||||||
\(537\) | 2.05253 | 0.0885731 | ||||||||
\(538\) | 7.41026 | 0.319479 | ||||||||
\(539\) | 4.77034 | 0.205473 | ||||||||
\(540\) | −86.5172 | −3.72311 | ||||||||
\(541\) | −12.0274 | −0.517100 | −0.258550 | − | 0.965998i | \(-0.583245\pi\) | ||||
−0.258550 | + | 0.965998i | \(0.583245\pi\) | |||||||
\(542\) | 20.1699 | 0.866370 | ||||||||
\(543\) | 13.2671 | 0.569346 | ||||||||
\(544\) | 20.8824 | 0.895327 | ||||||||
\(545\) | 12.0156 | 0.514693 | ||||||||
\(546\) | −13.1863 | −0.564323 | ||||||||
\(547\) | 3.77765 | 0.161520 | 0.0807602 | − | 0.996734i | \(-0.474265\pi\) | ||||
0.0807602 | + | 0.996734i | \(0.474265\pi\) | |||||||
\(548\) | −19.1659 | −0.818728 | ||||||||
\(549\) | −28.1012 | −1.19933 | ||||||||
\(550\) | −123.542 | −5.26784 | ||||||||
\(551\) | 0.224961 | 0.00958368 | ||||||||
\(552\) | 56.1385 | 2.38941 | ||||||||
\(553\) | 6.77643 | 0.288163 | ||||||||
\(554\) | 78.3105 | 3.32710 | ||||||||
\(555\) | −36.6086 | −1.55395 | ||||||||
\(556\) | −3.29345 | −0.139673 | ||||||||
\(557\) | 24.3605 | 1.03219 | 0.516093 | − | 0.856532i | \(-0.327386\pi\) | ||||
0.516093 | + | 0.856532i | \(0.327386\pi\) | |||||||
\(558\) | 43.6190 | 1.84654 | ||||||||
\(559\) | −37.4179 | −1.58261 | ||||||||
\(560\) | −32.1494 | −1.35856 | ||||||||
\(561\) | 12.0875 | 0.510335 | ||||||||
\(562\) | 28.6924 | 1.21032 | ||||||||
\(563\) | −29.2307 | −1.23193 | −0.615963 | − | 0.787775i | \(-0.711233\pi\) | ||||
−0.615963 | + | 0.787775i | \(0.711233\pi\) | |||||||
\(564\) | 31.4624 | 1.32481 | ||||||||
\(565\) | 59.4578 | 2.50141 | ||||||||
\(566\) | 31.2973 | 1.31552 | ||||||||
\(567\) | 1.86051 | 0.0781343 | ||||||||
\(568\) | −28.2583 | −1.18569 | ||||||||
\(569\) | −36.8201 | −1.54358 | −0.771789 | − | 0.635879i | \(-0.780638\pi\) | ||||
−0.771789 | + | 0.635879i | \(0.780638\pi\) | |||||||
\(570\) | 0.362926 | 0.0152013 | ||||||||
\(571\) | 2.39605 | 0.100272 | 0.0501359 | − | 0.998742i | \(-0.484035\pi\) | ||||
0.0501359 | + | 0.998742i | \(0.484035\pi\) | |||||||
\(572\) | −120.892 | −5.05474 | ||||||||
\(573\) | −18.1648 | −0.758847 | ||||||||
\(574\) | 3.75439 | 0.156705 | ||||||||
\(575\) | 88.2072 | 3.67849 | ||||||||
\(576\) | −7.09089 | −0.295454 | ||||||||
\(577\) | 29.6014 | 1.23232 | 0.616161 | − | 0.787620i | \(-0.288687\pi\) | ||||
0.616161 | + | 0.787620i | \(0.288687\pi\) | |||||||
\(578\) | 24.9971 | 1.03974 | ||||||||
\(579\) | 20.2625 | 0.842082 | ||||||||
\(580\) | 104.719 | 4.34820 | ||||||||
\(581\) | −10.7413 | −0.445624 | ||||||||
\(582\) | 24.6138 | 1.02028 | ||||||||
\(583\) | −41.3040 | −1.71064 | ||||||||
\(584\) | −5.35505 | −0.221594 | ||||||||
\(585\) | −44.8805 | −1.85558 | ||||||||
\(586\) | 48.9298 | 2.02127 | ||||||||
\(587\) | −2.76761 | −0.114232 | −0.0571158 | − | 0.998368i | \(-0.518190\pi\) | ||||
−0.0571158 | + | 0.998368i | \(0.518190\pi\) | |||||||
\(588\) | −4.35558 | −0.179621 | ||||||||
\(589\) | −0.308832 | −0.0127252 | ||||||||
\(590\) | −93.8253 | −3.86273 | ||||||||
\(591\) | −13.2267 | −0.544074 | ||||||||
\(592\) | −83.4243 | −3.42872 | ||||||||
\(593\) | −16.7820 | −0.689155 | −0.344578 | − | 0.938758i | \(-0.611978\pi\) | ||||
−0.344578 | + | 0.938758i | \(0.611978\pi\) | |||||||
\(594\) | −59.0447 | −2.42263 | ||||||||
\(595\) | 10.4826 | 0.429745 | ||||||||
\(596\) | −50.7342 | −2.07815 | ||||||||
\(597\) | 8.74150 | 0.357766 | ||||||||
\(598\) | 123.478 | 5.04937 | ||||||||
\(599\) | 16.2580 | 0.664282 | 0.332141 | − | 0.943230i | \(-0.392229\pi\) | ||||
0.332141 | + | 0.943230i | \(0.392229\pi\) | |||||||
\(600\) | 64.2349 | 2.62238 | ||||||||
\(601\) | −10.5859 | −0.431810 | −0.215905 | − | 0.976414i | \(-0.569270\pi\) | ||||
−0.215905 | + | 0.976414i | \(0.569270\pi\) | |||||||
\(602\) | −17.6808 | −0.720617 | ||||||||
\(603\) | 1.14243 | 0.0465234 | ||||||||
\(604\) | 66.8442 | 2.71985 | ||||||||
\(605\) | −45.6017 | −1.85397 | ||||||||
\(606\) | 18.5573 | 0.753838 | ||||||||
\(607\) | 27.1411 | 1.10162 | 0.550811 | − | 0.834630i | \(-0.314318\pi\) | ||||
0.550811 | + | 0.834630i | \(0.314318\pi\) | |||||||
\(608\) | 0.299116 | 0.0121307 | ||||||||
\(609\) | 5.44914 | 0.220810 | ||||||||
\(610\) | 132.491 | 5.36442 | ||||||||
\(611\) | 39.4076 | 1.59426 | ||||||||
\(612\) | 26.6242 | 1.07622 | ||||||||
\(613\) | 26.1294 | 1.05536 | 0.527679 | − | 0.849444i | \(-0.323062\pi\) | ||||
0.527679 | + | 0.849444i | \(0.323062\pi\) | |||||||
\(614\) | 29.6212 | 1.19542 | ||||||||
\(615\) | −5.29701 | −0.213596 | ||||||||
\(616\) | −32.5297 | −1.31066 | ||||||||
\(617\) | −33.8120 | −1.36122 | −0.680610 | − | 0.732646i | \(-0.738285\pi\) | ||||
−0.680610 | + | 0.732646i | \(0.738285\pi\) | |||||||
\(618\) | −2.21174 | −0.0889691 | ||||||||
\(619\) | 27.2344 | 1.09464 | 0.547322 | − | 0.836922i | \(-0.315647\pi\) | ||||
0.547322 | + | 0.836922i | \(0.315647\pi\) | |||||||
\(620\) | −143.760 | −5.77354 | ||||||||
\(621\) | 42.1572 | 1.69171 | ||||||||
\(622\) | −41.7330 | −1.67334 | ||||||||
\(623\) | −12.2160 | −0.489422 | ||||||||
\(624\) | 42.3960 | 1.69720 | ||||||||
\(625\) | 25.6970 | 1.02788 | ||||||||
\(626\) | 77.3354 | 3.09094 | ||||||||
\(627\) | 0.173139 | 0.00691451 | ||||||||
\(628\) | 27.3634 | 1.09192 | ||||||||
\(629\) | 27.2012 | 1.08458 | ||||||||
\(630\) | −21.2071 | −0.844911 | ||||||||
\(631\) | 3.53009 | 0.140531 | 0.0702654 | − | 0.997528i | \(-0.477615\pi\) | ||||
0.0702654 | + | 0.997528i | \(0.477615\pi\) | |||||||
\(632\) | −46.2095 | −1.83812 | ||||||||
\(633\) | −4.21958 | −0.167713 | ||||||||
\(634\) | 89.6787 | 3.56160 | ||||||||
\(635\) | 67.0815 | 2.66205 | ||||||||
\(636\) | 37.7128 | 1.49541 | ||||||||
\(637\) | −5.45549 | −0.216154 | ||||||||
\(638\) | 71.4664 | 2.82938 | ||||||||
\(639\) | −8.78869 | −0.347675 | ||||||||
\(640\) | −26.5155 | −1.04812 | ||||||||
\(641\) | 19.6280 | 0.775258 | 0.387629 | − | 0.921815i | \(-0.373294\pi\) | ||||
0.387629 | + | 0.921815i | \(0.373294\pi\) | |||||||
\(642\) | 0.474685 | 0.0187343 | ||||||||
\(643\) | 18.8869 | 0.744825 | 0.372413 | − | 0.928067i | \(-0.378531\pi\) | ||||
0.372413 | + | 0.928067i | \(0.378531\pi\) | |||||||
\(644\) | 40.7859 | 1.60719 | ||||||||
\(645\) | 24.9456 | 0.982232 | ||||||||
\(646\) | −0.269665 | −0.0106098 | ||||||||
\(647\) | −0.274991 | −0.0108110 | −0.00540551 | − | 0.999985i | \(-0.501721\pi\) | ||||
−0.00540551 | + | 0.999985i | \(0.501721\pi\) | |||||||
\(648\) | −12.6871 | −0.498398 | ||||||||
\(649\) | −44.7608 | −1.75701 | ||||||||
\(650\) | 141.286 | 5.54168 | ||||||||
\(651\) | −7.48070 | −0.293192 | ||||||||
\(652\) | 5.69452 | 0.223015 | ||||||||
\(653\) | 28.3654 | 1.11002 | 0.555012 | − | 0.831842i | \(-0.312714\pi\) | ||||
0.555012 | + | 0.831842i | \(0.312714\pi\) | |||||||
\(654\) | −7.48723 | −0.292774 | ||||||||
\(655\) | 67.9708 | 2.65584 | ||||||||
\(656\) | −12.0709 | −0.471291 | ||||||||
\(657\) | −1.66549 | −0.0649769 | ||||||||
\(658\) | 18.6210 | 0.725923 | ||||||||
\(659\) | 29.1550 | 1.13572 | 0.567859 | − | 0.823126i | \(-0.307772\pi\) | ||||
0.567859 | + | 0.823126i | \(0.307772\pi\) | |||||||
\(660\) | 80.5955 | 3.13717 | ||||||||
\(661\) | −45.7238 | −1.77845 | −0.889224 | − | 0.457472i | \(-0.848755\pi\) | ||||
−0.889224 | + | 0.457472i | \(0.848755\pi\) | |||||||
\(662\) | −49.9256 | −1.94041 | ||||||||
\(663\) | −13.8236 | −0.536864 | ||||||||
\(664\) | 73.2465 | 2.84252 | ||||||||
\(665\) | 0.150151 | 0.00582260 | ||||||||
\(666\) | −55.0301 | −2.13237 | ||||||||
\(667\) | −51.0261 | −1.97574 | ||||||||
\(668\) | −50.6213 | −1.95860 | ||||||||
\(669\) | −15.5560 | −0.601430 | ||||||||
\(670\) | −5.38633 | −0.208092 | ||||||||
\(671\) | 63.2070 | 2.44008 | ||||||||
\(672\) | 7.24535 | 0.279496 | ||||||||
\(673\) | −32.1405 | −1.23892 | −0.619462 | − | 0.785026i | \(-0.712649\pi\) | ||||
−0.619462 | + | 0.785026i | \(0.712649\pi\) | |||||||
\(674\) | −62.6552 | −2.41339 | ||||||||
\(675\) | 48.2371 | 1.85665 | ||||||||
\(676\) | 77.8662 | 2.99486 | ||||||||
\(677\) | 12.2598 | 0.471182 | 0.235591 | − | 0.971852i | \(-0.424297\pi\) | ||||
0.235591 | + | 0.971852i | \(0.424297\pi\) | |||||||
\(678\) | −37.0496 | −1.42288 | ||||||||
\(679\) | 10.1833 | 0.390800 | ||||||||
\(680\) | −71.4826 | −2.74123 | ||||||||
\(681\) | 7.35936 | 0.282011 | ||||||||
\(682\) | −98.1107 | −3.75685 | ||||||||
\(683\) | 8.27120 | 0.316489 | 0.158244 | − | 0.987400i | \(-0.449417\pi\) | ||||
0.158244 | + | 0.987400i | \(0.449417\pi\) | |||||||
\(684\) | 0.381360 | 0.0145816 | ||||||||
\(685\) | 16.0041 | 0.611486 | ||||||||
\(686\) | −2.57785 | −0.0984226 | ||||||||
\(687\) | 19.5858 | 0.747244 | ||||||||
\(688\) | 56.8465 | 2.16725 | ||||||||
\(689\) | 47.2364 | 1.79956 | ||||||||
\(690\) | −82.3194 | −3.13384 | ||||||||
\(691\) | 6.83587 | 0.260049 | 0.130024 | − | 0.991511i | \(-0.458494\pi\) | ||||
0.130024 | + | 0.991511i | \(0.458494\pi\) | |||||||
\(692\) | 68.7341 | 2.61288 | ||||||||
\(693\) | −10.1172 | −0.384319 | ||||||||
\(694\) | −42.5673 | −1.61583 | ||||||||
\(695\) | 2.75013 | 0.104318 | ||||||||
\(696\) | −37.1586 | −1.40849 | ||||||||
\(697\) | 3.93584 | 0.149080 | ||||||||
\(698\) | 14.1435 | 0.535339 | ||||||||
\(699\) | −25.7006 | −0.972086 | ||||||||
\(700\) | 46.6681 | 1.76389 | ||||||||
\(701\) | 29.0289 | 1.09641 | 0.548204 | − | 0.836345i | \(-0.315312\pi\) | ||||
0.548204 | + | 0.836345i | \(0.315312\pi\) | |||||||
\(702\) | 67.5251 | 2.54857 | ||||||||
\(703\) | 0.389625 | 0.0146950 | ||||||||
\(704\) | 15.9493 | 0.601112 | ||||||||
\(705\) | −26.2721 | −0.989464 | ||||||||
\(706\) | −13.4096 | −0.504677 | ||||||||
\(707\) | 7.67758 | 0.288745 | ||||||||
\(708\) | 40.8690 | 1.53595 | ||||||||
\(709\) | 37.1815 | 1.39638 | 0.698190 | − | 0.715913i | \(-0.253989\pi\) | ||||
0.698190 | + | 0.715913i | \(0.253989\pi\) | |||||||
\(710\) | 41.4369 | 1.55510 | ||||||||
\(711\) | −14.3718 | −0.538983 | ||||||||
\(712\) | 83.3025 | 3.12190 | ||||||||
\(713\) | 70.0497 | 2.62338 | ||||||||
\(714\) | −6.53197 | −0.244453 | ||||||||
\(715\) | 100.948 | 3.77525 | ||||||||
\(716\) | −10.1688 | −0.380025 | ||||||||
\(717\) | 3.86674 | 0.144406 | ||||||||
\(718\) | 2.66082 | 0.0993010 | ||||||||
\(719\) | 32.2138 | 1.20137 | 0.600685 | − | 0.799485i | \(-0.294894\pi\) | ||||
0.600685 | + | 0.799485i | \(0.294894\pi\) | |||||||
\(720\) | 68.1839 | 2.54106 | ||||||||
\(721\) | −0.915048 | −0.0340781 | ||||||||
\(722\) | 48.9752 | 1.82267 | ||||||||
\(723\) | −24.0822 | −0.895627 | ||||||||
\(724\) | −65.7289 | −2.44279 | ||||||||
\(725\) | −58.3851 | −2.16837 | ||||||||
\(726\) | 28.4155 | 1.05460 | ||||||||
\(727\) | 29.9834 | 1.11202 | 0.556011 | − | 0.831175i | \(-0.312331\pi\) | ||||
0.556011 | + | 0.831175i | \(0.312331\pi\) | |||||||
\(728\) | 37.2019 | 1.37879 | ||||||||
\(729\) | 9.56020 | 0.354081 | ||||||||
\(730\) | 7.85245 | 0.290632 | ||||||||
\(731\) | −18.5353 | −0.685554 | ||||||||
\(732\) | −57.7114 | −2.13307 | ||||||||
\(733\) | 15.6602 | 0.578423 | 0.289212 | − | 0.957265i | \(-0.406607\pi\) | ||||
0.289212 | + | 0.957265i | \(0.406607\pi\) | |||||||
\(734\) | −5.27328 | −0.194640 | ||||||||
\(735\) | 3.63704 | 0.134154 | ||||||||
\(736\) | −67.8459 | −2.50083 | ||||||||
\(737\) | −2.56963 | −0.0946535 | ||||||||
\(738\) | −7.96248 | −0.293103 | ||||||||
\(739\) | 7.31965 | 0.269258 | 0.134629 | − | 0.990896i | \(-0.457016\pi\) | ||||
0.134629 | + | 0.990896i | \(0.457016\pi\) | |||||||
\(740\) | 181.369 | 6.66725 | ||||||||
\(741\) | −0.198007 | −0.00727395 | ||||||||
\(742\) | 22.3203 | 0.819403 | ||||||||
\(743\) | 0.653864 | 0.0239880 | 0.0119940 | − | 0.999928i | \(-0.496182\pi\) | ||||
0.0119940 | + | 0.999928i | \(0.496182\pi\) | |||||||
\(744\) | 51.0121 | 1.87019 | ||||||||
\(745\) | 42.3646 | 1.55212 | ||||||||
\(746\) | 16.5701 | 0.606674 | ||||||||
\(747\) | 22.7806 | 0.833499 | ||||||||
\(748\) | −59.8848 | −2.18961 | ||||||||
\(749\) | 0.196388 | 0.00717587 | ||||||||
\(750\) | −47.3130 | −1.72763 | ||||||||
\(751\) | 41.9202 | 1.52969 | 0.764844 | − | 0.644215i | \(-0.222816\pi\) | ||||
0.764844 | + | 0.644215i | \(0.222816\pi\) | |||||||
\(752\) | −59.8693 | −2.18321 | ||||||||
\(753\) | 15.1192 | 0.550975 | ||||||||
\(754\) | −81.7309 | −2.97646 | ||||||||
\(755\) | −55.8169 | −2.03139 | ||||||||
\(756\) | 22.3042 | 0.811198 | ||||||||
\(757\) | 35.1913 | 1.27905 | 0.639524 | − | 0.768771i | \(-0.279132\pi\) | ||||
0.639524 | + | 0.768771i | \(0.279132\pi\) | |||||||
\(758\) | −57.2326 | −2.07878 | ||||||||
\(759\) | −39.2717 | −1.42547 | ||||||||
\(760\) | −1.02390 | −0.0371408 | ||||||||
\(761\) | 18.9471 | 0.686833 | 0.343417 | − | 0.939183i | \(-0.388416\pi\) | ||||
0.343417 | + | 0.939183i | \(0.388416\pi\) | |||||||
\(762\) | −41.8001 | −1.51426 | ||||||||
\(763\) | −3.09764 | −0.112142 | ||||||||
\(764\) | 89.9936 | 3.25585 | ||||||||
\(765\) | −22.2320 | −0.803799 | ||||||||
\(766\) | −12.0154 | −0.434133 | ||||||||
\(767\) | 51.1896 | 1.84835 | ||||||||
\(768\) | 22.7922 | 0.822444 | ||||||||
\(769\) | −34.3114 | −1.23730 | −0.618651 | − | 0.785666i | \(-0.712320\pi\) | ||||
−0.618651 | + | 0.785666i | \(0.712320\pi\) | |||||||
\(770\) | 47.7004 | 1.71900 | ||||||||
\(771\) | 10.6099 | 0.382105 | ||||||||
\(772\) | −100.386 | −3.61298 | ||||||||
\(773\) | 51.0131 | 1.83482 | 0.917408 | − | 0.397949i | \(-0.130278\pi\) | ||||
0.917408 | + | 0.397949i | \(0.130278\pi\) | |||||||
\(774\) | 37.4983 | 1.34785 | ||||||||
\(775\) | 80.1524 | 2.87916 | ||||||||
\(776\) | −69.4416 | −2.49281 | ||||||||
\(777\) | 9.43773 | 0.338577 | ||||||||
\(778\) | −73.8770 | −2.64862 | ||||||||
\(779\) | 0.0563761 | 0.00201989 | ||||||||
\(780\) | −92.1712 | −3.30026 | ||||||||
\(781\) | 19.7681 | 0.707358 | ||||||||
\(782\) | 61.1657 | 2.18728 | ||||||||
\(783\) | −27.9042 | −0.997215 | ||||||||
\(784\) | 8.28816 | 0.296006 | ||||||||
\(785\) | −22.8492 | −0.815524 | ||||||||
\(786\) | −42.3543 | −1.51073 | ||||||||
\(787\) | 40.7167 | 1.45139 | 0.725696 | − | 0.688015i | \(-0.241518\pi\) | ||||
0.725696 | + | 0.688015i | \(0.241518\pi\) | |||||||
\(788\) | 65.5287 | 2.33436 | ||||||||
\(789\) | −12.4699 | −0.443940 | ||||||||
\(790\) | 67.7600 | 2.41079 | ||||||||
\(791\) | −15.3283 | −0.545011 | ||||||||
\(792\) | 68.9905 | 2.45147 | ||||||||
\(793\) | −72.2852 | −2.56692 | ||||||||
\(794\) | −9.21465 | −0.327016 | ||||||||
\(795\) | −31.4913 | −1.11688 | ||||||||
\(796\) | −43.3078 | −1.53500 | ||||||||
\(797\) | −3.82027 | −0.135321 | −0.0676604 | − | 0.997708i | \(-0.521553\pi\) | ||||
−0.0676604 | + | 0.997708i | \(0.521553\pi\) | |||||||
\(798\) | −0.0935627 | −0.00331208 | ||||||||
\(799\) | 19.5209 | 0.690601 | ||||||||
\(800\) | −77.6308 | −2.74466 | ||||||||
\(801\) | 25.9081 | 0.915419 | ||||||||
\(802\) | −68.4497 | −2.41704 | ||||||||
\(803\) | 3.74613 | 0.132198 | ||||||||
\(804\) | 2.34621 | 0.0827445 | ||||||||
\(805\) | −34.0574 | −1.20037 | ||||||||
\(806\) | 112.202 | 3.95215 | ||||||||
\(807\) | 2.69532 | 0.0948796 | ||||||||
\(808\) | −52.3546 | −1.84183 | ||||||||
\(809\) | 37.8866 | 1.33202 | 0.666011 | − | 0.745942i | \(-0.268000\pi\) | ||||
0.666011 | + | 0.745942i | \(0.268000\pi\) | |||||||
\(810\) | 18.6040 | 0.653676 | ||||||||
\(811\) | −36.1885 | −1.27075 | −0.635375 | − | 0.772204i | \(-0.719154\pi\) | ||||
−0.635375 | + | 0.772204i | \(0.719154\pi\) | |||||||
\(812\) | −26.9966 | −0.947393 | ||||||||
\(813\) | 7.33633 | 0.257296 | ||||||||
\(814\) | 123.777 | 4.33839 | ||||||||
\(815\) | −4.75510 | −0.166564 | ||||||||
\(816\) | 21.0012 | 0.735191 | ||||||||
\(817\) | −0.265496 | −0.00928854 | ||||||||
\(818\) | 37.9665 | 1.32747 | ||||||||
\(819\) | 11.5703 | 0.404297 | ||||||||
\(820\) | 26.2428 | 0.916440 | ||||||||
\(821\) | −12.6712 | −0.442226 | −0.221113 | − | 0.975248i | \(-0.570969\pi\) | ||||
−0.221113 | + | 0.975248i | \(0.570969\pi\) | |||||||
\(822\) | −9.97256 | −0.347833 | ||||||||
\(823\) | 43.0404 | 1.50029 | 0.750146 | − | 0.661272i | \(-0.229983\pi\) | ||||
0.750146 | + | 0.661272i | \(0.229983\pi\) | |||||||
\(824\) | 6.23985 | 0.217376 | ||||||||
\(825\) | −44.9355 | −1.56445 | ||||||||
\(826\) | 24.1883 | 0.841618 | ||||||||
\(827\) | 23.5051 | 0.817352 | 0.408676 | − | 0.912680i | \(-0.365991\pi\) | ||||
0.408676 | + | 0.912680i | \(0.365991\pi\) | |||||||
\(828\) | −86.5005 | −3.00610 | ||||||||
\(829\) | 36.3196 | 1.26143 | 0.630716 | − | 0.776014i | \(-0.282761\pi\) | ||||
0.630716 | + | 0.776014i | \(0.282761\pi\) | |||||||
\(830\) | −107.406 | −3.72812 | ||||||||
\(831\) | 28.4837 | 0.988088 | ||||||||
\(832\) | −18.2400 | −0.632360 | ||||||||
\(833\) | −2.70243 | −0.0936336 | ||||||||
\(834\) | −1.71367 | −0.0593396 | ||||||||
\(835\) | 42.2703 | 1.46282 | ||||||||
\(836\) | −0.857779 | −0.0296669 | ||||||||
\(837\) | 38.3075 | 1.32410 | ||||||||
\(838\) | −5.24324 | −0.181125 | ||||||||
\(839\) | −8.78489 | −0.303288 | −0.151644 | − | 0.988435i | \(-0.548457\pi\) | ||||
−0.151644 | + | 0.988435i | \(0.548457\pi\) | |||||||
\(840\) | −24.8015 | −0.855735 | ||||||||
\(841\) | 4.77462 | 0.164642 | ||||||||
\(842\) | −46.2932 | −1.59537 | ||||||||
\(843\) | 10.4362 | 0.359442 | ||||||||
\(844\) | 20.9050 | 0.719579 | ||||||||
\(845\) | −65.0206 | −2.23678 | ||||||||
\(846\) | −39.4923 | −1.35777 | ||||||||
\(847\) | 11.7562 | 0.403947 | ||||||||
\(848\) | −71.7630 | −2.46435 | ||||||||
\(849\) | 11.3837 | 0.390686 | ||||||||
\(850\) | 69.9872 | 2.40054 | ||||||||
\(851\) | −88.3754 | −3.02947 | ||||||||
\(852\) | −18.0493 | −0.618360 | ||||||||
\(853\) | −43.7324 | −1.49737 | −0.748685 | − | 0.662926i | \(-0.769314\pi\) | ||||
−0.748685 | + | 0.662926i | \(0.769314\pi\) | |||||||
\(854\) | −34.1564 | −1.16881 | ||||||||
\(855\) | −0.318447 | −0.0108906 | ||||||||
\(856\) | −1.33920 | −0.0457730 | ||||||||
\(857\) | −53.4661 | −1.82637 | −0.913184 | − | 0.407547i | \(-0.866384\pi\) | ||||
−0.913184 | + | 0.407547i | \(0.866384\pi\) | |||||||
\(858\) | −62.9033 | −2.14748 | ||||||||
\(859\) | 35.8246 | 1.22232 | 0.611160 | − | 0.791507i | \(-0.290703\pi\) | ||||
0.611160 | + | 0.791507i | \(0.290703\pi\) | |||||||
\(860\) | −123.587 | −4.21429 | ||||||||
\(861\) | 1.36557 | 0.0465387 | ||||||||
\(862\) | 67.4247 | 2.29649 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | −37.1023 | −1.26225 | ||||||||
\(865\) | −57.3950 | −1.95149 | ||||||||
\(866\) | 36.1053 | 1.22691 | ||||||||
\(867\) | 9.09211 | 0.308784 | ||||||||
\(868\) | 37.0615 | 1.25795 | ||||||||
\(869\) | 32.3259 | 1.09658 | ||||||||
\(870\) | 54.4879 | 1.84731 | ||||||||
\(871\) | 2.93870 | 0.0995740 | ||||||||
\(872\) | 21.1233 | 0.715325 | ||||||||
\(873\) | −21.5972 | −0.730955 | ||||||||
\(874\) | 0.876126 | 0.0296354 | ||||||||
\(875\) | −19.5745 | −0.661738 | ||||||||
\(876\) | −3.42042 | −0.115565 | ||||||||
\(877\) | 26.8140 | 0.905446 | 0.452723 | − | 0.891651i | \(-0.350453\pi\) | ||||
0.452723 | + | 0.891651i | \(0.350453\pi\) | |||||||
\(878\) | −103.537 | −3.49421 | ||||||||
\(879\) | 17.7971 | 0.600282 | ||||||||
\(880\) | −153.364 | −5.16989 | ||||||||
\(881\) | −10.3868 | −0.349940 | −0.174970 | − | 0.984574i | \(-0.555983\pi\) | ||||
−0.174970 | + | 0.984574i | \(0.555983\pi\) | |||||||
\(882\) | 5.46721 | 0.184091 | ||||||||
\(883\) | −24.1229 | −0.811800 | −0.405900 | − | 0.913918i | \(-0.633042\pi\) | ||||
−0.405900 | + | 0.913918i | \(0.633042\pi\) | |||||||
\(884\) | 68.4859 | 2.30343 | ||||||||
\(885\) | −34.1268 | −1.14716 | ||||||||
\(886\) | −68.1997 | −2.29122 | ||||||||
\(887\) | 8.97630 | 0.301395 | 0.150697 | − | 0.988580i | \(-0.451848\pi\) | ||||
0.150697 | + | 0.988580i | \(0.451848\pi\) | |||||||
\(888\) | −64.3574 | −2.15969 | ||||||||
\(889\) | −17.2937 | −0.580012 | ||||||||
\(890\) | −122.152 | −4.09454 | ||||||||
\(891\) | 8.87529 | 0.297333 | ||||||||
\(892\) | 77.0687 | 2.58045 | ||||||||
\(893\) | 0.279614 | 0.00935693 | ||||||||
\(894\) | −26.3984 | −0.882895 | ||||||||
\(895\) | 8.49124 | 0.283831 | ||||||||
\(896\) | 6.83571 | 0.228365 | ||||||||
\(897\) | 44.9121 | 1.49957 | ||||||||
\(898\) | −58.9055 | −1.96570 | ||||||||
\(899\) | −46.3666 | −1.54641 | ||||||||
\(900\) | −98.9758 | −3.29919 | ||||||||
\(901\) | 23.3990 | 0.779533 | ||||||||
\(902\) | 17.9097 | 0.596329 | ||||||||
\(903\) | −6.43100 | −0.214010 | ||||||||
\(904\) | 104.526 | 3.47648 | ||||||||
\(905\) | 54.8856 | 1.82446 | ||||||||
\(906\) | 34.7809 | 1.15552 | ||||||||
\(907\) | 23.3138 | 0.774122 | 0.387061 | − | 0.922054i | \(-0.373490\pi\) | ||||
0.387061 | + | 0.922054i | \(0.373490\pi\) | |||||||
\(908\) | −36.4603 | −1.20998 | ||||||||
\(909\) | −16.2829 | −0.540071 | ||||||||
\(910\) | −54.5514 | −1.80836 | ||||||||
\(911\) | −48.2761 | −1.59946 | −0.799729 | − | 0.600361i | \(-0.795024\pi\) | ||||
−0.799729 | + | 0.600361i | \(0.795024\pi\) | |||||||
\(912\) | 0.300818 | 0.00996107 | ||||||||
\(913\) | −51.2396 | −1.69578 | ||||||||
\(914\) | 14.1071 | 0.466620 | ||||||||
\(915\) | 48.1907 | 1.59314 | ||||||||
\(916\) | −97.0334 | −3.20607 | ||||||||
\(917\) | −17.5230 | −0.578659 | ||||||||
\(918\) | 33.4492 | 1.10399 | ||||||||
\(919\) | −0.876920 | −0.0289269 | −0.0144635 | − | 0.999895i | \(-0.504604\pi\) | ||||
−0.0144635 | + | 0.999895i | \(0.504604\pi\) | |||||||
\(920\) | 232.243 | 7.65683 | ||||||||
\(921\) | 10.7741 | 0.355017 | ||||||||
\(922\) | −97.2685 | −3.20337 | ||||||||
\(923\) | −22.6073 | −0.744129 | ||||||||
\(924\) | −20.7776 | −0.683533 | ||||||||
\(925\) | −101.121 | −3.32484 | ||||||||
\(926\) | −107.113 | −3.51997 | ||||||||
\(927\) | 1.94067 | 0.0637401 | ||||||||
\(928\) | 44.9078 | 1.47417 | ||||||||
\(929\) | −9.86588 | −0.323689 | −0.161845 | − | 0.986816i | \(-0.551744\pi\) | ||||
−0.161845 | + | 0.986816i | \(0.551744\pi\) | |||||||
\(930\) | −74.8023 | −2.45286 | ||||||||
\(931\) | −0.0387091 | −0.00126864 | ||||||||
\(932\) | 127.328 | 4.17076 | ||||||||
\(933\) | −15.1794 | −0.496952 | ||||||||
\(934\) | 58.9700 | 1.92956 | ||||||||
\(935\) | 50.0056 | 1.63536 | ||||||||
\(936\) | −78.8994 | −2.57891 | ||||||||
\(937\) | 18.3261 | 0.598689 | 0.299344 | − | 0.954145i | \(-0.403232\pi\) | ||||
0.299344 | + | 0.954145i | \(0.403232\pi\) | |||||||
\(938\) | 1.38860 | 0.0453395 | ||||||||
\(939\) | 28.1290 | 0.917954 | ||||||||
\(940\) | 130.159 | 4.24532 | ||||||||
\(941\) | 18.2305 | 0.594297 | 0.297149 | − | 0.954831i | \(-0.403964\pi\) | ||||
0.297149 | + | 0.954831i | \(0.403964\pi\) | |||||||
\(942\) | 14.2379 | 0.463896 | ||||||||
\(943\) | −12.7873 | −0.416412 | ||||||||
\(944\) | −77.7689 | −2.53116 | ||||||||
\(945\) | −18.6247 | −0.605862 | ||||||||
\(946\) | −84.3437 | −2.74225 | ||||||||
\(947\) | −43.3043 | −1.40720 | −0.703601 | − | 0.710595i | \(-0.748426\pi\) | ||||
−0.703601 | + | 0.710595i | \(0.748426\pi\) | |||||||
\(948\) | −29.5153 | −0.958611 | ||||||||
\(949\) | −4.28417 | −0.139070 | ||||||||
\(950\) | 1.00248 | 0.0325248 | ||||||||
\(951\) | 32.6186 | 1.05773 | ||||||||
\(952\) | 18.4283 | 0.597264 | ||||||||
\(953\) | 4.98702 | 0.161545 | 0.0807727 | − | 0.996733i | \(-0.474261\pi\) | ||||
0.0807727 | + | 0.996733i | \(0.474261\pi\) | |||||||
\(954\) | −47.3378 | −1.53262 | ||||||||
\(955\) | −75.1473 | −2.43171 | ||||||||
\(956\) | −19.1569 | −0.619579 | ||||||||
\(957\) | 25.9943 | 0.840276 | ||||||||
\(958\) | 34.8225 | 1.12506 | ||||||||
\(959\) | −4.12588 | −0.133232 | ||||||||
\(960\) | 12.1602 | 0.392468 | ||||||||
\(961\) | 32.6531 | 1.05332 | ||||||||
\(962\) | −141.555 | −4.56392 | ||||||||
\(963\) | −0.416509 | −0.0134218 | ||||||||
\(964\) | 119.310 | 3.84271 | ||||||||
\(965\) | 83.8255 | 2.69844 | ||||||||
\(966\) | 21.2220 | 0.682808 | ||||||||
\(967\) | 6.61202 | 0.212628 | 0.106314 | − | 0.994333i | \(-0.466095\pi\) | ||||
0.106314 | + | 0.994333i | \(0.466095\pi\) | |||||||
\(968\) | −80.1671 | −2.57667 | ||||||||
\(969\) | −0.0980844 | −0.00315092 | ||||||||
\(970\) | 101.827 | 3.26945 | ||||||||
\(971\) | −35.4704 | −1.13830 | −0.569150 | − | 0.822234i | \(-0.692728\pi\) | ||||
−0.569150 | + | 0.822234i | \(0.692728\pi\) | |||||||
\(972\) | −75.0163 | −2.40615 | ||||||||
\(973\) | −0.708986 | −0.0227291 | ||||||||
\(974\) | 25.6678 | 0.822450 | ||||||||
\(975\) | 51.3894 | 1.64578 | ||||||||
\(976\) | 109.818 | 3.51519 | ||||||||
\(977\) | 0.708286 | 0.0226601 | 0.0113300 | − | 0.999936i | \(-0.496393\pi\) | ||||
0.0113300 | + | 0.999936i | \(0.496393\pi\) | |||||||
\(978\) | 2.96302 | 0.0947468 | ||||||||
\(979\) | −58.2743 | −1.86245 | ||||||||
\(980\) | −18.0189 | −0.575593 | ||||||||
\(981\) | 6.56962 | 0.209752 | ||||||||
\(982\) | −48.4458 | −1.54597 | ||||||||
\(983\) | 22.7953 | 0.727057 | 0.363528 | − | 0.931583i | \(-0.381572\pi\) | ||||
0.363528 | + | 0.931583i | \(0.381572\pi\) | |||||||
\(984\) | −9.31207 | −0.296858 | ||||||||
\(985\) | −54.7185 | −1.74347 | ||||||||
\(986\) | −40.4862 | −1.28934 | ||||||||
\(987\) | 6.77297 | 0.215586 | ||||||||
\(988\) | 0.980979 | 0.0312091 | ||||||||
\(989\) | 60.2203 | 1.91489 | ||||||||
\(990\) | −101.165 | −3.21524 | ||||||||
\(991\) | −51.4319 | −1.63379 | −0.816895 | − | 0.576787i | \(-0.804306\pi\) | ||||
−0.816895 | + | 0.576787i | \(0.804306\pi\) | |||||||
\(992\) | −61.6505 | −1.95740 | ||||||||
\(993\) | −18.1593 | −0.576268 | ||||||||
\(994\) | −10.6825 | −0.338828 | ||||||||
\(995\) | 36.1633 | 1.14645 | ||||||||
\(996\) | 46.7845 | 1.48242 | ||||||||
\(997\) | 10.0962 | 0.319751 | 0.159875 | − | 0.987137i | \(-0.448891\pi\) | ||||
0.159875 | + | 0.987137i | \(0.448891\pi\) | |||||||
\(998\) | −14.0487 | −0.444702 | ||||||||
\(999\) | −48.3291 | −1.52907 |
(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 | 6041.2.a.f.1.11 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.11 | ✓ | 132 | 1.1 | even | 1 | trivial |