Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, 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("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(1\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.39986 | −1.38556 | −0.692780 | − | 0.721149i | \(-0.743614\pi\) | ||||
−0.692780 | + | 0.721149i | \(0.743614\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.11547 | −0.498852 | −0.249426 | − | 0.968394i | \(-0.580242\pi\) | ||||
−0.249426 | + | 0.968394i | \(0.580242\pi\) | |||||||
\(6\) | 2.39986 | 0.979739 | ||||||||
\(7\) | 2.17590 | 0.822414 | 0.411207 | − | 0.911542i | \(-0.365107\pi\) | ||||
0.411207 | + | 0.911542i | \(0.365107\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.75933 | 0.919778 | ||||||||
\(10\) | 1.11547 | 0.352742 | ||||||||
\(11\) | −3.08509 | −0.930191 | −0.465095 | − | 0.885261i | \(-0.653980\pi\) | ||||
−0.465095 | + | 0.885261i | \(0.653980\pi\) | |||||||
\(12\) | −2.39986 | −0.692780 | ||||||||
\(13\) | 2.44024 | 0.676801 | 0.338400 | − | 0.941002i | \(-0.390114\pi\) | ||||
0.338400 | + | 0.941002i | \(0.390114\pi\) | |||||||
\(14\) | −2.17590 | −0.581535 | ||||||||
\(15\) | 2.67697 | 0.691190 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.89451 | 1.18709 | 0.593547 | − | 0.804800i | \(-0.297727\pi\) | ||||
0.593547 | + | 0.804800i | \(0.297727\pi\) | |||||||
\(18\) | −2.75933 | −0.650381 | ||||||||
\(19\) | −4.74068 | −1.08759 | −0.543794 | − | 0.839219i | \(-0.683013\pi\) | ||||
−0.543794 | + | 0.839219i | \(0.683013\pi\) | |||||||
\(20\) | −1.11547 | −0.249426 | ||||||||
\(21\) | −5.22187 | −1.13950 | ||||||||
\(22\) | 3.08509 | 0.657744 | ||||||||
\(23\) | −3.76943 | −0.785980 | −0.392990 | − | 0.919543i | \(-0.628559\pi\) | ||||
−0.392990 | + | 0.919543i | \(0.628559\pi\) | |||||||
\(24\) | 2.39986 | 0.489870 | ||||||||
\(25\) | −3.75573 | −0.751146 | ||||||||
\(26\) | −2.44024 | −0.478570 | ||||||||
\(27\) | 0.577565 | 0.111152 | ||||||||
\(28\) | 2.17590 | 0.411207 | ||||||||
\(29\) | 10.2097 | 1.89590 | 0.947951 | − | 0.318415i | \(-0.103151\pi\) | ||||
0.947951 | + | 0.318415i | \(0.103151\pi\) | |||||||
\(30\) | −2.67697 | −0.488745 | ||||||||
\(31\) | −7.37186 | −1.32403 | −0.662013 | − | 0.749493i | \(-0.730297\pi\) | ||||
−0.662013 | + | 0.749493i | \(0.730297\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.40380 | 1.28884 | ||||||||
\(34\) | −4.89451 | −0.839402 | ||||||||
\(35\) | −2.42715 | −0.410263 | ||||||||
\(36\) | 2.75933 | 0.459889 | ||||||||
\(37\) | 3.03887 | 0.499588 | 0.249794 | − | 0.968299i | \(-0.419637\pi\) | ||||
0.249794 | + | 0.968299i | \(0.419637\pi\) | |||||||
\(38\) | 4.74068 | 0.769040 | ||||||||
\(39\) | −5.85624 | −0.937748 | ||||||||
\(40\) | 1.11547 | 0.176371 | ||||||||
\(41\) | 9.67954 | 1.51169 | 0.755845 | − | 0.654750i | \(-0.227226\pi\) | ||||
0.755845 | + | 0.654750i | \(0.227226\pi\) | |||||||
\(42\) | 5.22187 | 0.805752 | ||||||||
\(43\) | −6.41301 | −0.977975 | −0.488988 | − | 0.872291i | \(-0.662634\pi\) | ||||
−0.488988 | + | 0.872291i | \(0.662634\pi\) | |||||||
\(44\) | −3.08509 | −0.465095 | ||||||||
\(45\) | −3.07795 | −0.458834 | ||||||||
\(46\) | 3.76943 | 0.555772 | ||||||||
\(47\) | −12.2581 | −1.78803 | −0.894016 | − | 0.448035i | \(-0.852124\pi\) | ||||
−0.894016 | + | 0.448035i | \(0.852124\pi\) | |||||||
\(48\) | −2.39986 | −0.346390 | ||||||||
\(49\) | −2.26544 | −0.323635 | ||||||||
\(50\) | 3.75573 | 0.531141 | ||||||||
\(51\) | −11.7461 | −1.64479 | ||||||||
\(52\) | 2.44024 | 0.338400 | ||||||||
\(53\) | −9.19250 | −1.26269 | −0.631344 | − | 0.775503i | \(-0.717496\pi\) | ||||
−0.631344 | + | 0.775503i | \(0.717496\pi\) | |||||||
\(54\) | −0.577565 | −0.0785966 | ||||||||
\(55\) | 3.44132 | 0.464028 | ||||||||
\(56\) | −2.17590 | −0.290767 | ||||||||
\(57\) | 11.3770 | 1.50692 | ||||||||
\(58\) | −10.2097 | −1.34061 | ||||||||
\(59\) | 12.8419 | 1.67188 | 0.835939 | − | 0.548822i | \(-0.184924\pi\) | ||||
0.835939 | + | 0.548822i | \(0.184924\pi\) | |||||||
\(60\) | 2.67697 | 0.345595 | ||||||||
\(61\) | 12.2248 | 1.56523 | 0.782615 | − | 0.622506i | \(-0.213886\pi\) | ||||
0.782615 | + | 0.622506i | \(0.213886\pi\) | |||||||
\(62\) | 7.37186 | 0.936227 | ||||||||
\(63\) | 6.00405 | 0.756439 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.72201 | −0.337624 | ||||||||
\(66\) | −7.40380 | −0.911344 | ||||||||
\(67\) | 1.55009 | 0.189374 | 0.0946868 | − | 0.995507i | \(-0.469815\pi\) | ||||
0.0946868 | + | 0.995507i | \(0.469815\pi\) | |||||||
\(68\) | 4.89451 | 0.593547 | ||||||||
\(69\) | 9.04611 | 1.08902 | ||||||||
\(70\) | 2.42715 | 0.290100 | ||||||||
\(71\) | 7.01211 | 0.832184 | 0.416092 | − | 0.909323i | \(-0.363399\pi\) | ||||
0.416092 | + | 0.909323i | \(0.363399\pi\) | |||||||
\(72\) | −2.75933 | −0.325191 | ||||||||
\(73\) | −6.82879 | −0.799250 | −0.399625 | − | 0.916679i | \(-0.630860\pi\) | ||||
−0.399625 | + | 0.916679i | \(0.630860\pi\) | |||||||
\(74\) | −3.03887 | −0.353262 | ||||||||
\(75\) | 9.01323 | 1.04076 | ||||||||
\(76\) | −4.74068 | −0.543794 | ||||||||
\(77\) | −6.71287 | −0.765002 | ||||||||
\(78\) | 5.85624 | 0.663088 | ||||||||
\(79\) | −10.4918 | −1.18042 | −0.590211 | − | 0.807249i | \(-0.700956\pi\) | ||||
−0.590211 | + | 0.807249i | \(0.700956\pi\) | |||||||
\(80\) | −1.11547 | −0.124713 | ||||||||
\(81\) | −9.66408 | −1.07379 | ||||||||
\(82\) | −9.67954 | −1.06893 | ||||||||
\(83\) | 9.20979 | 1.01091 | 0.505453 | − | 0.862854i | \(-0.331326\pi\) | ||||
0.505453 | + | 0.862854i | \(0.331326\pi\) | |||||||
\(84\) | −5.22187 | −0.569752 | ||||||||
\(85\) | −5.45967 | −0.592185 | ||||||||
\(86\) | 6.41301 | 0.691533 | ||||||||
\(87\) | −24.5020 | −2.62689 | ||||||||
\(88\) | 3.08509 | 0.328872 | ||||||||
\(89\) | 5.85474 | 0.620601 | 0.310301 | − | 0.950638i | \(-0.399570\pi\) | ||||
0.310301 | + | 0.950638i | \(0.399570\pi\) | |||||||
\(90\) | 3.07795 | 0.324444 | ||||||||
\(91\) | 5.30973 | 0.556611 | ||||||||
\(92\) | −3.76943 | −0.392990 | ||||||||
\(93\) | 17.6914 | 1.83452 | ||||||||
\(94\) | 12.2581 | 1.26433 | ||||||||
\(95\) | 5.28808 | 0.542546 | ||||||||
\(96\) | 2.39986 | 0.244935 | ||||||||
\(97\) | 3.65649 | 0.371260 | 0.185630 | − | 0.982620i | \(-0.440567\pi\) | ||||
0.185630 | + | 0.982620i | \(0.440567\pi\) | |||||||
\(98\) | 2.26544 | 0.228844 | ||||||||
\(99\) | −8.51280 | −0.855569 | ||||||||
\(100\) | −3.75573 | −0.375573 | ||||||||
\(101\) | −0.191837 | −0.0190885 | −0.00954426 | − | 0.999954i | \(-0.503038\pi\) | ||||
−0.00954426 | + | 0.999954i | \(0.503038\pi\) | |||||||
\(102\) | 11.7461 | 1.16304 | ||||||||
\(103\) | 0.505272 | 0.0497859 | 0.0248929 | − | 0.999690i | \(-0.492076\pi\) | ||||
0.0248929 | + | 0.999690i | \(0.492076\pi\) | |||||||
\(104\) | −2.44024 | −0.239285 | ||||||||
\(105\) | 5.82483 | 0.568445 | ||||||||
\(106\) | 9.19250 | 0.892855 | ||||||||
\(107\) | 13.9912 | 1.35258 | 0.676291 | − | 0.736634i | \(-0.263586\pi\) | ||||
0.676291 | + | 0.736634i | \(0.263586\pi\) | |||||||
\(108\) | 0.577565 | 0.0555762 | ||||||||
\(109\) | 0.384757 | 0.0368531 | 0.0184265 | − | 0.999830i | \(-0.494134\pi\) | ||||
0.0184265 | + | 0.999830i | \(0.494134\pi\) | |||||||
\(110\) | −3.44132 | −0.328117 | ||||||||
\(111\) | −7.29288 | −0.692209 | ||||||||
\(112\) | 2.17590 | 0.205604 | ||||||||
\(113\) | −4.57147 | −0.430047 | −0.215024 | − | 0.976609i | \(-0.568983\pi\) | ||||
−0.215024 | + | 0.976609i | \(0.568983\pi\) | |||||||
\(114\) | −11.3770 | −1.06555 | ||||||||
\(115\) | 4.20468 | 0.392088 | ||||||||
\(116\) | 10.2097 | 0.947951 | ||||||||
\(117\) | 6.73344 | 0.622507 | ||||||||
\(118\) | −12.8419 | −1.18220 | ||||||||
\(119\) | 10.6500 | 0.976283 | ||||||||
\(120\) | −2.67697 | −0.244373 | ||||||||
\(121\) | −1.48220 | −0.134745 | ||||||||
\(122\) | −12.2248 | −1.10678 | ||||||||
\(123\) | −23.2296 | −2.09454 | ||||||||
\(124\) | −7.37186 | −0.662013 | ||||||||
\(125\) | 9.76674 | 0.873564 | ||||||||
\(126\) | −6.00405 | −0.534883 | ||||||||
\(127\) | 15.9153 | 1.41225 | 0.706125 | − | 0.708087i | \(-0.250442\pi\) | ||||
0.706125 | + | 0.708087i | \(0.250442\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 15.3903 | 1.35504 | ||||||||
\(130\) | 2.72201 | 0.238736 | ||||||||
\(131\) | −6.61371 | −0.577842 | −0.288921 | − | 0.957353i | \(-0.593297\pi\) | ||||
−0.288921 | + | 0.957353i | \(0.593297\pi\) | |||||||
\(132\) | 7.40380 | 0.644418 | ||||||||
\(133\) | −10.3153 | −0.894447 | ||||||||
\(134\) | −1.55009 | −0.133907 | ||||||||
\(135\) | −0.644255 | −0.0554486 | ||||||||
\(136\) | −4.89451 | −0.419701 | ||||||||
\(137\) | 15.5118 | 1.32526 | 0.662629 | − | 0.748947i | \(-0.269440\pi\) | ||||
0.662629 | + | 0.748947i | \(0.269440\pi\) | |||||||
\(138\) | −9.04611 | −0.770056 | ||||||||
\(139\) | 11.7343 | 0.995289 | 0.497645 | − | 0.867381i | \(-0.334198\pi\) | ||||
0.497645 | + | 0.867381i | \(0.334198\pi\) | |||||||
\(140\) | −2.42715 | −0.205132 | ||||||||
\(141\) | 29.4178 | 2.47743 | ||||||||
\(142\) | −7.01211 | −0.588443 | ||||||||
\(143\) | −7.52837 | −0.629554 | ||||||||
\(144\) | 2.75933 | 0.229945 | ||||||||
\(145\) | −11.3886 | −0.945776 | ||||||||
\(146\) | 6.82879 | 0.565155 | ||||||||
\(147\) | 5.43675 | 0.448415 | ||||||||
\(148\) | 3.03887 | 0.249794 | ||||||||
\(149\) | −15.9762 | −1.30882 | −0.654409 | − | 0.756141i | \(-0.727082\pi\) | ||||
−0.654409 | + | 0.756141i | \(0.727082\pi\) | |||||||
\(150\) | −9.01323 | −0.735927 | ||||||||
\(151\) | −4.50899 | −0.366936 | −0.183468 | − | 0.983026i | \(-0.558732\pi\) | ||||
−0.183468 | + | 0.983026i | \(0.558732\pi\) | |||||||
\(152\) | 4.74068 | 0.384520 | ||||||||
\(153\) | 13.5056 | 1.09186 | ||||||||
\(154\) | 6.71287 | 0.540938 | ||||||||
\(155\) | 8.22307 | 0.660493 | ||||||||
\(156\) | −5.85624 | −0.468874 | ||||||||
\(157\) | −11.5156 | −0.919044 | −0.459522 | − | 0.888166i | \(-0.651979\pi\) | ||||
−0.459522 | + | 0.888166i | \(0.651979\pi\) | |||||||
\(158\) | 10.4918 | 0.834685 | ||||||||
\(159\) | 22.0607 | 1.74953 | ||||||||
\(160\) | 1.11547 | 0.0881855 | ||||||||
\(161\) | −8.20191 | −0.646401 | ||||||||
\(162\) | 9.66408 | 0.759282 | ||||||||
\(163\) | −13.5787 | −1.06357 | −0.531785 | − | 0.846880i | \(-0.678478\pi\) | ||||
−0.531785 | + | 0.846880i | \(0.678478\pi\) | |||||||
\(164\) | 9.67954 | 0.755845 | ||||||||
\(165\) | −8.25870 | −0.642939 | ||||||||
\(166\) | −9.20979 | −0.714818 | ||||||||
\(167\) | 12.5466 | 0.970886 | 0.485443 | − | 0.874268i | \(-0.338658\pi\) | ||||
0.485443 | + | 0.874268i | \(0.338658\pi\) | |||||||
\(168\) | 5.22187 | 0.402876 | ||||||||
\(169\) | −7.04523 | −0.541941 | ||||||||
\(170\) | 5.45967 | 0.418738 | ||||||||
\(171\) | −13.0811 | −1.00034 | ||||||||
\(172\) | −6.41301 | −0.488988 | ||||||||
\(173\) | 4.85331 | 0.368990 | 0.184495 | − | 0.982833i | \(-0.440935\pi\) | ||||
0.184495 | + | 0.982833i | \(0.440935\pi\) | |||||||
\(174\) | 24.5020 | 1.85749 | ||||||||
\(175\) | −8.17211 | −0.617753 | ||||||||
\(176\) | −3.08509 | −0.232548 | ||||||||
\(177\) | −30.8189 | −2.31649 | ||||||||
\(178\) | −5.85474 | −0.438831 | ||||||||
\(179\) | 0.0898258 | 0.00671390 | 0.00335695 | − | 0.999994i | \(-0.498931\pi\) | ||||
0.00335695 | + | 0.999994i | \(0.498931\pi\) | |||||||
\(180\) | −3.07795 | −0.229417 | ||||||||
\(181\) | −15.9809 | −1.18785 | −0.593926 | − | 0.804520i | \(-0.702423\pi\) | ||||
−0.593926 | + | 0.804520i | \(0.702423\pi\) | |||||||
\(182\) | −5.30973 | −0.393583 | ||||||||
\(183\) | −29.3379 | −2.16872 | ||||||||
\(184\) | 3.76943 | 0.277886 | ||||||||
\(185\) | −3.38977 | −0.249221 | ||||||||
\(186\) | −17.6914 | −1.29720 | ||||||||
\(187\) | −15.1000 | −1.10422 | ||||||||
\(188\) | −12.2581 | −0.894016 | ||||||||
\(189\) | 1.25673 | 0.0914133 | ||||||||
\(190\) | −5.28808 | −0.383638 | ||||||||
\(191\) | −19.7638 | −1.43006 | −0.715029 | − | 0.699095i | \(-0.753586\pi\) | ||||
−0.715029 | + | 0.699095i | \(0.753586\pi\) | |||||||
\(192\) | −2.39986 | −0.173195 | ||||||||
\(193\) | −1.80147 | −0.129673 | −0.0648364 | − | 0.997896i | \(-0.520653\pi\) | ||||
−0.0648364 | + | 0.997896i | \(0.520653\pi\) | |||||||
\(194\) | −3.65649 | −0.262521 | ||||||||
\(195\) | 6.53245 | 0.467798 | ||||||||
\(196\) | −2.26544 | −0.161817 | ||||||||
\(197\) | −7.23693 | −0.515610 | −0.257805 | − | 0.966197i | \(-0.582999\pi\) | ||||
−0.257805 | + | 0.966197i | \(0.582999\pi\) | |||||||
\(198\) | 8.51280 | 0.604979 | ||||||||
\(199\) | −11.1295 | −0.788948 | −0.394474 | − | 0.918907i | \(-0.629073\pi\) | ||||
−0.394474 | + | 0.918907i | \(0.629073\pi\) | |||||||
\(200\) | 3.75573 | 0.265570 | ||||||||
\(201\) | −3.72000 | −0.262389 | ||||||||
\(202\) | 0.191837 | 0.0134976 | ||||||||
\(203\) | 22.2154 | 1.55922 | ||||||||
\(204\) | −11.7461 | −0.822395 | ||||||||
\(205\) | −10.7972 | −0.754111 | ||||||||
\(206\) | −0.505272 | −0.0352039 | ||||||||
\(207\) | −10.4011 | −0.722927 | ||||||||
\(208\) | 2.44024 | 0.169200 | ||||||||
\(209\) | 14.6255 | 1.01166 | ||||||||
\(210\) | −5.82483 | −0.401951 | ||||||||
\(211\) | 4.40223 | 0.303062 | 0.151531 | − | 0.988452i | \(-0.451580\pi\) | ||||
0.151531 | + | 0.988452i | \(0.451580\pi\) | |||||||
\(212\) | −9.19250 | −0.631344 | ||||||||
\(213\) | −16.8281 | −1.15304 | ||||||||
\(214\) | −13.9912 | −0.956421 | ||||||||
\(215\) | 7.15351 | 0.487865 | ||||||||
\(216\) | −0.577565 | −0.0392983 | ||||||||
\(217\) | −16.0405 | −1.08890 | ||||||||
\(218\) | −0.384757 | −0.0260591 | ||||||||
\(219\) | 16.3882 | 1.10741 | ||||||||
\(220\) | 3.44132 | 0.232014 | ||||||||
\(221\) | 11.9438 | 0.803426 | ||||||||
\(222\) | 7.29288 | 0.489466 | ||||||||
\(223\) | 12.5357 | 0.839450 | 0.419725 | − | 0.907651i | \(-0.362126\pi\) | ||||
0.419725 | + | 0.907651i | \(0.362126\pi\) | |||||||
\(224\) | −2.17590 | −0.145384 | ||||||||
\(225\) | −10.3633 | −0.690888 | ||||||||
\(226\) | 4.57147 | 0.304089 | ||||||||
\(227\) | 1.05018 | 0.0697031 | 0.0348516 | − | 0.999392i | \(-0.488904\pi\) | ||||
0.0348516 | + | 0.999392i | \(0.488904\pi\) | |||||||
\(228\) | 11.3770 | 0.753459 | ||||||||
\(229\) | −21.6909 | −1.43337 | −0.716687 | − | 0.697395i | \(-0.754342\pi\) | ||||
−0.716687 | + | 0.697395i | \(0.754342\pi\) | |||||||
\(230\) | −4.20468 | −0.277248 | ||||||||
\(231\) | 16.1099 | 1.05996 | ||||||||
\(232\) | −10.2097 | −0.670303 | ||||||||
\(233\) | 8.60751 | 0.563897 | 0.281948 | − | 0.959430i | \(-0.409019\pi\) | ||||
0.281948 | + | 0.959430i | \(0.409019\pi\) | |||||||
\(234\) | −6.73344 | −0.440179 | ||||||||
\(235\) | 13.6735 | 0.891964 | ||||||||
\(236\) | 12.8419 | 0.835939 | ||||||||
\(237\) | 25.1789 | 1.63555 | ||||||||
\(238\) | −10.6500 | −0.690336 | ||||||||
\(239\) | 6.55061 | 0.423724 | 0.211862 | − | 0.977300i | \(-0.432047\pi\) | ||||
0.211862 | + | 0.977300i | \(0.432047\pi\) | |||||||
\(240\) | 2.67697 | 0.172798 | ||||||||
\(241\) | −7.04481 | −0.453796 | −0.226898 | − | 0.973919i | \(-0.572858\pi\) | ||||
−0.226898 | + | 0.973919i | \(0.572858\pi\) | |||||||
\(242\) | 1.48220 | 0.0952792 | ||||||||
\(243\) | 21.4598 | 1.37664 | ||||||||
\(244\) | 12.2248 | 0.782615 | ||||||||
\(245\) | 2.52703 | 0.161446 | ||||||||
\(246\) | 23.2296 | 1.48106 | ||||||||
\(247\) | −11.5684 | −0.736080 | ||||||||
\(248\) | 7.37186 | 0.468114 | ||||||||
\(249\) | −22.1022 | −1.40067 | ||||||||
\(250\) | −9.76674 | −0.617703 | ||||||||
\(251\) | −13.9653 | −0.881481 | −0.440741 | − | 0.897634i | \(-0.645284\pi\) | ||||
−0.440741 | + | 0.897634i | \(0.645284\pi\) | |||||||
\(252\) | 6.00405 | 0.378219 | ||||||||
\(253\) | 11.6290 | 0.731112 | ||||||||
\(254\) | −15.9153 | −0.998612 | ||||||||
\(255\) | 13.1025 | 0.820508 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.31452 | −0.144376 | −0.0721878 | − | 0.997391i | \(-0.522998\pi\) | ||||
−0.0721878 | + | 0.997391i | \(0.522998\pi\) | |||||||
\(258\) | −15.3903 | −0.958161 | ||||||||
\(259\) | 6.61230 | 0.410868 | ||||||||
\(260\) | −2.72201 | −0.168812 | ||||||||
\(261\) | 28.1721 | 1.74381 | ||||||||
\(262\) | 6.61371 | 0.408596 | ||||||||
\(263\) | 0.895260 | 0.0552041 | 0.0276021 | − | 0.999619i | \(-0.491213\pi\) | ||||
0.0276021 | + | 0.999619i | \(0.491213\pi\) | |||||||
\(264\) | −7.40380 | −0.455672 | ||||||||
\(265\) | 10.2539 | 0.629895 | ||||||||
\(266\) | 10.3153 | 0.632470 | ||||||||
\(267\) | −14.0506 | −0.859881 | ||||||||
\(268\) | 1.55009 | 0.0946868 | ||||||||
\(269\) | −0.172089 | −0.0104925 | −0.00524624 | − | 0.999986i | \(-0.501670\pi\) | ||||
−0.00524624 | + | 0.999986i | \(0.501670\pi\) | |||||||
\(270\) | 0.644255 | 0.0392081 | ||||||||
\(271\) | −21.5467 | −1.30887 | −0.654433 | − | 0.756120i | \(-0.727093\pi\) | ||||
−0.654433 | + | 0.756120i | \(0.727093\pi\) | |||||||
\(272\) | 4.89451 | 0.296773 | ||||||||
\(273\) | −12.7426 | −0.771218 | ||||||||
\(274\) | −15.5118 | −0.937100 | ||||||||
\(275\) | 11.5868 | 0.698709 | ||||||||
\(276\) | 9.04611 | 0.544512 | ||||||||
\(277\) | 22.9593 | 1.37949 | 0.689744 | − | 0.724053i | \(-0.257723\pi\) | ||||
0.689744 | + | 0.724053i | \(0.257723\pi\) | |||||||
\(278\) | −11.7343 | −0.703776 | ||||||||
\(279\) | −20.3414 | −1.21781 | ||||||||
\(280\) | 2.42715 | 0.145050 | ||||||||
\(281\) | −29.2208 | −1.74317 | −0.871583 | − | 0.490249i | \(-0.836906\pi\) | ||||
−0.871583 | + | 0.490249i | \(0.836906\pi\) | |||||||
\(282\) | −29.4178 | −1.75180 | ||||||||
\(283\) | −26.7992 | −1.59304 | −0.796522 | − | 0.604609i | \(-0.793329\pi\) | ||||
−0.796522 | + | 0.604609i | \(0.793329\pi\) | |||||||
\(284\) | 7.01211 | 0.416092 | ||||||||
\(285\) | −12.6907 | −0.751730 | ||||||||
\(286\) | 7.52837 | 0.445162 | ||||||||
\(287\) | 21.0618 | 1.24324 | ||||||||
\(288\) | −2.75933 | −0.162595 | ||||||||
\(289\) | 6.95624 | 0.409191 | ||||||||
\(290\) | 11.3886 | 0.668765 | ||||||||
\(291\) | −8.77507 | −0.514403 | ||||||||
\(292\) | −6.82879 | −0.399625 | ||||||||
\(293\) | −24.4877 | −1.43059 | −0.715294 | − | 0.698824i | \(-0.753707\pi\) | ||||
−0.715294 | + | 0.698824i | \(0.753707\pi\) | |||||||
\(294\) | −5.43675 | −0.317078 | ||||||||
\(295\) | −14.3248 | −0.834021 | ||||||||
\(296\) | −3.03887 | −0.176631 | ||||||||
\(297\) | −1.78184 | −0.103393 | ||||||||
\(298\) | 15.9762 | 0.925474 | ||||||||
\(299\) | −9.19831 | −0.531952 | ||||||||
\(300\) | 9.01323 | 0.520379 | ||||||||
\(301\) | −13.9541 | −0.804301 | ||||||||
\(302\) | 4.50899 | 0.259463 | ||||||||
\(303\) | 0.460383 | 0.0264483 | ||||||||
\(304\) | −4.74068 | −0.271897 | ||||||||
\(305\) | −13.6364 | −0.780819 | ||||||||
\(306\) | −13.5056 | −0.772063 | ||||||||
\(307\) | −9.44215 | −0.538892 | −0.269446 | − | 0.963015i | \(-0.586841\pi\) | ||||
−0.269446 | + | 0.963015i | \(0.586841\pi\) | |||||||
\(308\) | −6.71287 | −0.382501 | ||||||||
\(309\) | −1.21258 | −0.0689814 | ||||||||
\(310\) | −8.22307 | −0.467039 | ||||||||
\(311\) | −13.8748 | −0.786770 | −0.393385 | − | 0.919374i | \(-0.628696\pi\) | ||||
−0.393385 | + | 0.919374i | \(0.628696\pi\) | |||||||
\(312\) | 5.85624 | 0.331544 | ||||||||
\(313\) | −0.0463070 | −0.00261743 | −0.00130871 | − | 0.999999i | \(-0.500417\pi\) | ||||
−0.00130871 | + | 0.999999i | \(0.500417\pi\) | |||||||
\(314\) | 11.5156 | 0.649862 | ||||||||
\(315\) | −6.69732 | −0.377351 | ||||||||
\(316\) | −10.4918 | −0.590211 | ||||||||
\(317\) | 21.6109 | 1.21379 | 0.606894 | − | 0.794783i | \(-0.292415\pi\) | ||||
0.606894 | + | 0.794783i | \(0.292415\pi\) | |||||||
\(318\) | −22.0607 | −1.23710 | ||||||||
\(319\) | −31.4980 | −1.76355 | ||||||||
\(320\) | −1.11547 | −0.0623566 | ||||||||
\(321\) | −33.5770 | −1.87409 | ||||||||
\(322\) | 8.20191 | 0.457075 | ||||||||
\(323\) | −23.2033 | −1.29107 | ||||||||
\(324\) | −9.66408 | −0.536893 | ||||||||
\(325\) | −9.16488 | −0.508376 | ||||||||
\(326\) | 13.5787 | 0.752057 | ||||||||
\(327\) | −0.923364 | −0.0510622 | ||||||||
\(328\) | −9.67954 | −0.534463 | ||||||||
\(329\) | −26.6725 | −1.47050 | ||||||||
\(330\) | 8.25870 | 0.454626 | ||||||||
\(331\) | 15.1368 | 0.831994 | 0.415997 | − | 0.909366i | \(-0.363433\pi\) | ||||
0.415997 | + | 0.909366i | \(0.363433\pi\) | |||||||
\(332\) | 9.20979 | 0.505453 | ||||||||
\(333\) | 8.38527 | 0.459510 | ||||||||
\(334\) | −12.5466 | −0.686520 | ||||||||
\(335\) | −1.72908 | −0.0944695 | ||||||||
\(336\) | −5.22187 | −0.284876 | ||||||||
\(337\) | −4.24745 | −0.231374 | −0.115687 | − | 0.993286i | \(-0.536907\pi\) | ||||
−0.115687 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(338\) | 7.04523 | 0.383210 | ||||||||
\(339\) | 10.9709 | 0.595857 | ||||||||
\(340\) | −5.45967 | −0.296092 | ||||||||
\(341\) | 22.7429 | 1.23160 | ||||||||
\(342\) | 13.0811 | 0.707346 | ||||||||
\(343\) | −20.1607 | −1.08858 | ||||||||
\(344\) | 6.41301 | 0.345767 | ||||||||
\(345\) | −10.0906 | −0.543262 | ||||||||
\(346\) | −4.85331 | −0.260915 | ||||||||
\(347\) | −2.41227 | −0.129497 | −0.0647487 | − | 0.997902i | \(-0.520625\pi\) | ||||
−0.0647487 | + | 0.997902i | \(0.520625\pi\) | |||||||
\(348\) | −24.5020 | −1.31344 | ||||||||
\(349\) | −15.3301 | −0.820601 | −0.410300 | − | 0.911950i | \(-0.634576\pi\) | ||||
−0.410300 | + | 0.911950i | \(0.634576\pi\) | |||||||
\(350\) | 8.17211 | 0.436818 | ||||||||
\(351\) | 1.40940 | 0.0752280 | ||||||||
\(352\) | 3.08509 | 0.164436 | ||||||||
\(353\) | −28.0894 | −1.49505 | −0.747524 | − | 0.664235i | \(-0.768758\pi\) | ||||
−0.747524 | + | 0.664235i | \(0.768758\pi\) | |||||||
\(354\) | 30.8189 | 1.63800 | ||||||||
\(355\) | −7.82178 | −0.415137 | ||||||||
\(356\) | 5.85474 | 0.310301 | ||||||||
\(357\) | −25.5585 | −1.35270 | ||||||||
\(358\) | −0.0898258 | −0.00474744 | ||||||||
\(359\) | −25.9313 | −1.36860 | −0.684302 | − | 0.729199i | \(-0.739893\pi\) | ||||
−0.684302 | + | 0.729199i | \(0.739893\pi\) | |||||||
\(360\) | 3.07795 | 0.162222 | ||||||||
\(361\) | 3.47408 | 0.182846 | ||||||||
\(362\) | 15.9809 | 0.839938 | ||||||||
\(363\) | 3.55707 | 0.186698 | ||||||||
\(364\) | 5.30973 | 0.278305 | ||||||||
\(365\) | 7.61730 | 0.398708 | ||||||||
\(366\) | 29.3379 | 1.53352 | ||||||||
\(367\) | −11.4260 | −0.596430 | −0.298215 | − | 0.954499i | \(-0.596391\pi\) | ||||
−0.298215 | + | 0.954499i | \(0.596391\pi\) | |||||||
\(368\) | −3.76943 | −0.196495 | ||||||||
\(369\) | 26.7091 | 1.39042 | ||||||||
\(370\) | 3.38977 | 0.176226 | ||||||||
\(371\) | −20.0020 | −1.03845 | ||||||||
\(372\) | 17.6914 | 0.917259 | ||||||||
\(373\) | −9.88851 | −0.512008 | −0.256004 | − | 0.966676i | \(-0.582406\pi\) | ||||
−0.256004 | + | 0.966676i | \(0.582406\pi\) | |||||||
\(374\) | 15.1000 | 0.780804 | ||||||||
\(375\) | −23.4388 | −1.21038 | ||||||||
\(376\) | 12.2581 | 0.632165 | ||||||||
\(377\) | 24.9142 | 1.28315 | ||||||||
\(378\) | −1.25673 | −0.0646390 | ||||||||
\(379\) | −14.1178 | −0.725183 | −0.362591 | − | 0.931948i | \(-0.618108\pi\) | ||||
−0.362591 | + | 0.931948i | \(0.618108\pi\) | |||||||
\(380\) | 5.28808 | 0.271273 | ||||||||
\(381\) | −38.1944 | −1.95676 | ||||||||
\(382\) | 19.7638 | 1.01120 | ||||||||
\(383\) | −5.02639 | −0.256836 | −0.128418 | − | 0.991720i | \(-0.540990\pi\) | ||||
−0.128418 | + | 0.991720i | \(0.540990\pi\) | |||||||
\(384\) | 2.39986 | 0.122467 | ||||||||
\(385\) | 7.48799 | 0.381623 | ||||||||
\(386\) | 1.80147 | 0.0916925 | ||||||||
\(387\) | −17.6956 | −0.899520 | ||||||||
\(388\) | 3.65649 | 0.185630 | ||||||||
\(389\) | 23.9220 | 1.21290 | 0.606448 | − | 0.795124i | \(-0.292594\pi\) | ||||
0.606448 | + | 0.795124i | \(0.292594\pi\) | |||||||
\(390\) | −6.53245 | −0.330783 | ||||||||
\(391\) | −18.4495 | −0.933032 | ||||||||
\(392\) | 2.26544 | 0.114422 | ||||||||
\(393\) | 15.8720 | 0.800636 | ||||||||
\(394\) | 7.23693 | 0.364591 | ||||||||
\(395\) | 11.7033 | 0.588857 | ||||||||
\(396\) | −8.51280 | −0.427785 | ||||||||
\(397\) | 28.6601 | 1.43841 | 0.719204 | − | 0.694799i | \(-0.244507\pi\) | ||||
0.719204 | + | 0.694799i | \(0.244507\pi\) | |||||||
\(398\) | 11.1295 | 0.557870 | ||||||||
\(399\) | 24.7552 | 1.23931 | ||||||||
\(400\) | −3.75573 | −0.187787 | ||||||||
\(401\) | 4.87950 | 0.243671 | 0.121835 | − | 0.992550i | \(-0.461122\pi\) | ||||
0.121835 | + | 0.992550i | \(0.461122\pi\) | |||||||
\(402\) | 3.72000 | 0.185537 | ||||||||
\(403\) | −17.9891 | −0.896101 | ||||||||
\(404\) | −0.191837 | −0.00954426 | ||||||||
\(405\) | 10.7800 | 0.535661 | ||||||||
\(406\) | −22.2154 | −1.10253 | ||||||||
\(407\) | −9.37521 | −0.464712 | ||||||||
\(408\) | 11.7461 | 0.581521 | ||||||||
\(409\) | 3.25415 | 0.160907 | 0.0804536 | − | 0.996758i | \(-0.474363\pi\) | ||||
0.0804536 | + | 0.996758i | \(0.474363\pi\) | |||||||
\(410\) | 10.7972 | 0.533237 | ||||||||
\(411\) | −37.2261 | −1.83623 | ||||||||
\(412\) | 0.505272 | 0.0248929 | ||||||||
\(413\) | 27.9428 | 1.37498 | ||||||||
\(414\) | 10.4011 | 0.511187 | ||||||||
\(415\) | −10.2732 | −0.504293 | ||||||||
\(416\) | −2.44024 | −0.119643 | ||||||||
\(417\) | −28.1607 | −1.37903 | ||||||||
\(418\) | −14.6255 | −0.715354 | ||||||||
\(419\) | −39.6891 | −1.93894 | −0.969470 | − | 0.245211i | \(-0.921143\pi\) | ||||
−0.969470 | + | 0.245211i | \(0.921143\pi\) | |||||||
\(420\) | 5.82483 | 0.284222 | ||||||||
\(421\) | −8.27486 | −0.403292 | −0.201646 | − | 0.979458i | \(-0.564629\pi\) | ||||
−0.201646 | + | 0.979458i | \(0.564629\pi\) | |||||||
\(422\) | −4.40223 | −0.214297 | ||||||||
\(423\) | −33.8243 | −1.64459 | ||||||||
\(424\) | 9.19250 | 0.446427 | ||||||||
\(425\) | −18.3825 | −0.891681 | ||||||||
\(426\) | 16.8281 | 0.815323 | ||||||||
\(427\) | 26.6001 | 1.28727 | ||||||||
\(428\) | 13.9912 | 0.676291 | ||||||||
\(429\) | 18.0670 | 0.872285 | ||||||||
\(430\) | −7.15351 | −0.344973 | ||||||||
\(431\) | −38.3167 | −1.84565 | −0.922824 | − | 0.385221i | \(-0.874125\pi\) | ||||
−0.922824 | + | 0.385221i | \(0.874125\pi\) | |||||||
\(432\) | 0.577565 | 0.0277881 | ||||||||
\(433\) | −6.51220 | −0.312957 | −0.156478 | − | 0.987681i | \(-0.550014\pi\) | ||||
−0.156478 | + | 0.987681i | \(0.550014\pi\) | |||||||
\(434\) | 16.0405 | 0.769967 | ||||||||
\(435\) | 27.3312 | 1.31043 | ||||||||
\(436\) | 0.384757 | 0.0184265 | ||||||||
\(437\) | 17.8697 | 0.854822 | ||||||||
\(438\) | −16.3882 | −0.783056 | ||||||||
\(439\) | −15.2546 | −0.728061 | −0.364030 | − | 0.931387i | \(-0.618600\pi\) | ||||
−0.364030 | + | 0.931387i | \(0.618600\pi\) | |||||||
\(440\) | −3.44132 | −0.164059 | ||||||||
\(441\) | −6.25111 | −0.297672 | ||||||||
\(442\) | −11.9438 | −0.568108 | ||||||||
\(443\) | −16.6014 | −0.788755 | −0.394378 | − | 0.918948i | \(-0.629040\pi\) | ||||
−0.394378 | + | 0.918948i | \(0.629040\pi\) | |||||||
\(444\) | −7.29288 | −0.346105 | ||||||||
\(445\) | −6.53078 | −0.309589 | ||||||||
\(446\) | −12.5357 | −0.593581 | ||||||||
\(447\) | 38.3406 | 1.81345 | ||||||||
\(448\) | 2.17590 | 0.102802 | ||||||||
\(449\) | −12.8123 | −0.604650 | −0.302325 | − | 0.953205i | \(-0.597763\pi\) | ||||
−0.302325 | + | 0.953205i | \(0.597763\pi\) | |||||||
\(450\) | 10.3633 | 0.488531 | ||||||||
\(451\) | −29.8623 | −1.40616 | ||||||||
\(452\) | −4.57147 | −0.215024 | ||||||||
\(453\) | 10.8209 | 0.508413 | ||||||||
\(454\) | −1.05018 | −0.0492876 | ||||||||
\(455\) | −5.92283 | −0.277667 | ||||||||
\(456\) | −11.3770 | −0.532776 | ||||||||
\(457\) | −9.26228 | −0.433271 | −0.216636 | − | 0.976253i | \(-0.569508\pi\) | ||||
−0.216636 | + | 0.976253i | \(0.569508\pi\) | |||||||
\(458\) | 21.6909 | 1.01355 | ||||||||
\(459\) | 2.82690 | 0.131948 | ||||||||
\(460\) | 4.20468 | 0.196044 | ||||||||
\(461\) | 11.5580 | 0.538310 | 0.269155 | − | 0.963097i | \(-0.413256\pi\) | ||||
0.269155 | + | 0.963097i | \(0.413256\pi\) | |||||||
\(462\) | −16.1099 | −0.749503 | ||||||||
\(463\) | −26.6963 | −1.24068 | −0.620340 | − | 0.784333i | \(-0.713006\pi\) | ||||
−0.620340 | + | 0.784333i | \(0.713006\pi\) | |||||||
\(464\) | 10.2097 | 0.473976 | ||||||||
\(465\) | −19.7342 | −0.915153 | ||||||||
\(466\) | −8.60751 | −0.398735 | ||||||||
\(467\) | 16.7744 | 0.776228 | 0.388114 | − | 0.921611i | \(-0.373127\pi\) | ||||
0.388114 | + | 0.921611i | \(0.373127\pi\) | |||||||
\(468\) | 6.73344 | 0.311253 | ||||||||
\(469\) | 3.37285 | 0.155744 | ||||||||
\(470\) | −13.6735 | −0.630714 | ||||||||
\(471\) | 27.6358 | 1.27339 | ||||||||
\(472\) | −12.8419 | −0.591098 | ||||||||
\(473\) | 19.7847 | 0.909704 | ||||||||
\(474\) | −25.1789 | −1.15651 | ||||||||
\(475\) | 17.8047 | 0.816937 | ||||||||
\(476\) | 10.6500 | 0.488141 | ||||||||
\(477\) | −25.3652 | −1.16139 | ||||||||
\(478\) | −6.55061 | −0.299618 | ||||||||
\(479\) | 15.8014 | 0.721987 | 0.360993 | − | 0.932568i | \(-0.382438\pi\) | ||||
0.360993 | + | 0.932568i | \(0.382438\pi\) | |||||||
\(480\) | −2.67697 | −0.122186 | ||||||||
\(481\) | 7.41558 | 0.338122 | ||||||||
\(482\) | 7.04481 | 0.320882 | ||||||||
\(483\) | 19.6835 | 0.895628 | ||||||||
\(484\) | −1.48220 | −0.0673726 | ||||||||
\(485\) | −4.07870 | −0.185204 | ||||||||
\(486\) | −21.4598 | −0.973434 | ||||||||
\(487\) | −33.7514 | −1.52942 | −0.764712 | − | 0.644373i | \(-0.777119\pi\) | ||||
−0.764712 | + | 0.644373i | \(0.777119\pi\) | |||||||
\(488\) | −12.2248 | −0.553392 | ||||||||
\(489\) | 32.5871 | 1.47364 | ||||||||
\(490\) | −2.52703 | −0.114160 | ||||||||
\(491\) | 25.6541 | 1.15775 | 0.578876 | − | 0.815416i | \(-0.303492\pi\) | ||||
0.578876 | + | 0.815416i | \(0.303492\pi\) | |||||||
\(492\) | −23.2296 | −1.04727 | ||||||||
\(493\) | 49.9717 | 2.25061 | ||||||||
\(494\) | 11.5684 | 0.520487 | ||||||||
\(495\) | 9.49576 | 0.426803 | ||||||||
\(496\) | −7.37186 | −0.331006 | ||||||||
\(497\) | 15.2577 | 0.684400 | ||||||||
\(498\) | 22.1022 | 0.990424 | ||||||||
\(499\) | 31.0571 | 1.39031 | 0.695153 | − | 0.718862i | \(-0.255337\pi\) | ||||
0.695153 | + | 0.718862i | \(0.255337\pi\) | |||||||
\(500\) | 9.76674 | 0.436782 | ||||||||
\(501\) | −30.1101 | −1.34522 | ||||||||
\(502\) | 13.9653 | 0.623302 | ||||||||
\(503\) | 8.43562 | 0.376126 | 0.188063 | − | 0.982157i | \(-0.439779\pi\) | ||||
0.188063 | + | 0.982157i | \(0.439779\pi\) | |||||||
\(504\) | −6.00405 | −0.267441 | ||||||||
\(505\) | 0.213988 | 0.00952235 | ||||||||
\(506\) | −11.6290 | −0.516974 | ||||||||
\(507\) | 16.9076 | 0.750892 | ||||||||
\(508\) | 15.9153 | 0.706125 | ||||||||
\(509\) | 12.5957 | 0.558294 | 0.279147 | − | 0.960248i | \(-0.409948\pi\) | ||||
0.279147 | + | 0.960248i | \(0.409948\pi\) | |||||||
\(510\) | −13.1025 | −0.580186 | ||||||||
\(511\) | −14.8588 | −0.657314 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.73805 | −0.120888 | ||||||||
\(514\) | 2.31452 | 0.102089 | ||||||||
\(515\) | −0.563614 | −0.0248358 | ||||||||
\(516\) | 15.3903 | 0.677522 | ||||||||
\(517\) | 37.8175 | 1.66321 | ||||||||
\(518\) | −6.61230 | −0.290528 | ||||||||
\(519\) | −11.6473 | −0.511258 | ||||||||
\(520\) | 2.72201 | 0.119368 | ||||||||
\(521\) | −25.1364 | −1.10124 | −0.550622 | − | 0.834755i | \(-0.685609\pi\) | ||||
−0.550622 | + | 0.834755i | \(0.685609\pi\) | |||||||
\(522\) | −28.1721 | −1.23306 | ||||||||
\(523\) | 15.8137 | 0.691487 | 0.345743 | − | 0.938329i | \(-0.387627\pi\) | ||||
0.345743 | + | 0.938329i | \(0.387627\pi\) | |||||||
\(524\) | −6.61371 | −0.288921 | ||||||||
\(525\) | 19.6119 | 0.855935 | ||||||||
\(526\) | −0.895260 | −0.0390352 | ||||||||
\(527\) | −36.0817 | −1.57174 | ||||||||
\(528\) | 7.40380 | 0.322209 | ||||||||
\(529\) | −8.79141 | −0.382235 | ||||||||
\(530\) | −10.2539 | −0.445403 | ||||||||
\(531\) | 35.4352 | 1.53776 | ||||||||
\(532\) | −10.3153 | −0.447224 | ||||||||
\(533\) | 23.6204 | 1.02311 | ||||||||
\(534\) | 14.0506 | 0.608028 | ||||||||
\(535\) | −15.6068 | −0.674739 | ||||||||
\(536\) | −1.55009 | −0.0669537 | ||||||||
\(537\) | −0.215569 | −0.00930251 | ||||||||
\(538\) | 0.172089 | 0.00741930 | ||||||||
\(539\) | 6.98910 | 0.301042 | ||||||||
\(540\) | −0.644255 | −0.0277243 | ||||||||
\(541\) | −17.4454 | −0.750036 | −0.375018 | − | 0.927017i | \(-0.622364\pi\) | ||||
−0.375018 | + | 0.927017i | \(0.622364\pi\) | |||||||
\(542\) | 21.5467 | 0.925508 | ||||||||
\(543\) | 38.3520 | 1.64584 | ||||||||
\(544\) | −4.89451 | −0.209850 | ||||||||
\(545\) | −0.429185 | −0.0183843 | ||||||||
\(546\) | 12.7426 | 0.545333 | ||||||||
\(547\) | −5.98124 | −0.255740 | −0.127870 | − | 0.991791i | \(-0.540814\pi\) | ||||
−0.127870 | + | 0.991791i | \(0.540814\pi\) | |||||||
\(548\) | 15.5118 | 0.662629 | ||||||||
\(549\) | 33.7324 | 1.43966 | ||||||||
\(550\) | −11.5868 | −0.494062 | ||||||||
\(551\) | −48.4012 | −2.06196 | ||||||||
\(552\) | −9.04611 | −0.385028 | ||||||||
\(553\) | −22.8292 | −0.970796 | ||||||||
\(554\) | −22.9593 | −0.975446 | ||||||||
\(555\) | 8.13497 | 0.345310 | ||||||||
\(556\) | 11.7343 | 0.497645 | ||||||||
\(557\) | −6.42454 | −0.272216 | −0.136108 | − | 0.990694i | \(-0.543459\pi\) | ||||
−0.136108 | + | 0.990694i | \(0.543459\pi\) | |||||||
\(558\) | 20.3414 | 0.861121 | ||||||||
\(559\) | −15.6493 | −0.661895 | ||||||||
\(560\) | −2.42715 | −0.102566 | ||||||||
\(561\) | 36.2380 | 1.52997 | ||||||||
\(562\) | 29.2208 | 1.23260 | ||||||||
\(563\) | −34.3048 | −1.44577 | −0.722887 | − | 0.690966i | \(-0.757185\pi\) | ||||
−0.722887 | + | 0.690966i | \(0.757185\pi\) | |||||||
\(564\) | 29.4178 | 1.23871 | ||||||||
\(565\) | 5.09933 | 0.214530 | ||||||||
\(566\) | 26.7992 | 1.12645 | ||||||||
\(567\) | −21.0281 | −0.883097 | ||||||||
\(568\) | −7.01211 | −0.294221 | ||||||||
\(569\) | −22.1850 | −0.930044 | −0.465022 | − | 0.885299i | \(-0.653954\pi\) | ||||
−0.465022 | + | 0.885299i | \(0.653954\pi\) | |||||||
\(570\) | 12.6907 | 0.531553 | ||||||||
\(571\) | 31.0720 | 1.30032 | 0.650161 | − | 0.759797i | \(-0.274701\pi\) | ||||
0.650161 | + | 0.759797i | \(0.274701\pi\) | |||||||
\(572\) | −7.52837 | −0.314777 | ||||||||
\(573\) | 47.4303 | 1.98143 | ||||||||
\(574\) | −21.0618 | −0.879101 | ||||||||
\(575\) | 14.1570 | 0.590386 | ||||||||
\(576\) | 2.75933 | 0.114972 | ||||||||
\(577\) | 19.7780 | 0.823369 | 0.411685 | − | 0.911326i | \(-0.364941\pi\) | ||||
0.411685 | + | 0.911326i | \(0.364941\pi\) | |||||||
\(578\) | −6.95624 | −0.289342 | ||||||||
\(579\) | 4.32328 | 0.179669 | ||||||||
\(580\) | −11.3886 | −0.472888 | ||||||||
\(581\) | 20.0396 | 0.831383 | ||||||||
\(582\) | 8.77507 | 0.363738 | ||||||||
\(583\) | 28.3597 | 1.17454 | ||||||||
\(584\) | 6.82879 | 0.282577 | ||||||||
\(585\) | −7.51093 | −0.310539 | ||||||||
\(586\) | 24.4877 | 1.01158 | ||||||||
\(587\) | −26.3763 | −1.08867 | −0.544333 | − | 0.838869i | \(-0.683217\pi\) | ||||
−0.544333 | + | 0.838869i | \(0.683217\pi\) | |||||||
\(588\) | 5.43675 | 0.224208 | ||||||||
\(589\) | 34.9477 | 1.43999 | ||||||||
\(590\) | 14.3248 | 0.589742 | ||||||||
\(591\) | 17.3676 | 0.714409 | ||||||||
\(592\) | 3.03887 | 0.124897 | ||||||||
\(593\) | 11.2107 | 0.460370 | 0.230185 | − | 0.973147i | \(-0.426067\pi\) | ||||
0.230185 | + | 0.973147i | \(0.426067\pi\) | |||||||
\(594\) | 1.78184 | 0.0731098 | ||||||||
\(595\) | −11.8797 | −0.487021 | ||||||||
\(596\) | −15.9762 | −0.654409 | ||||||||
\(597\) | 26.7092 | 1.09314 | ||||||||
\(598\) | 9.19831 | 0.376147 | ||||||||
\(599\) | 39.8917 | 1.62993 | 0.814966 | − | 0.579509i | \(-0.196755\pi\) | ||||
0.814966 | + | 0.579509i | \(0.196755\pi\) | |||||||
\(600\) | −9.01323 | −0.367964 | ||||||||
\(601\) | 15.9475 | 0.650513 | 0.325256 | − | 0.945626i | \(-0.394549\pi\) | ||||
0.325256 | + | 0.945626i | \(0.394549\pi\) | |||||||
\(602\) | 13.9541 | 0.568727 | ||||||||
\(603\) | 4.27722 | 0.174182 | ||||||||
\(604\) | −4.50899 | −0.183468 | ||||||||
\(605\) | 1.65334 | 0.0672179 | ||||||||
\(606\) | −0.460383 | −0.0187018 | ||||||||
\(607\) | −4.43351 | −0.179950 | −0.0899752 | − | 0.995944i | \(-0.528679\pi\) | ||||
−0.0899752 | + | 0.995944i | \(0.528679\pi\) | |||||||
\(608\) | 4.74068 | 0.192260 | ||||||||
\(609\) | −53.3140 | −2.16039 | ||||||||
\(610\) | 13.6364 | 0.552122 | ||||||||
\(611\) | −29.9128 | −1.21014 | ||||||||
\(612\) | 13.5056 | 0.545931 | ||||||||
\(613\) | 36.7439 | 1.48407 | 0.742036 | − | 0.670360i | \(-0.233860\pi\) | ||||
0.742036 | + | 0.670360i | \(0.233860\pi\) | |||||||
\(614\) | 9.44215 | 0.381054 | ||||||||
\(615\) | 25.9118 | 1.04487 | ||||||||
\(616\) | 6.71287 | 0.270469 | ||||||||
\(617\) | −6.32609 | −0.254679 | −0.127339 | − | 0.991859i | \(-0.540644\pi\) | ||||
−0.127339 | + | 0.991859i | \(0.540644\pi\) | |||||||
\(618\) | 1.21258 | 0.0487772 | ||||||||
\(619\) | −33.3567 | −1.34072 | −0.670359 | − | 0.742037i | \(-0.733860\pi\) | ||||
−0.670359 | + | 0.742037i | \(0.733860\pi\) | |||||||
\(620\) | 8.22307 | 0.330247 | ||||||||
\(621\) | −2.17709 | −0.0873636 | ||||||||
\(622\) | 13.8748 | 0.556331 | ||||||||
\(623\) | 12.7394 | 0.510392 | ||||||||
\(624\) | −5.85624 | −0.234437 | ||||||||
\(625\) | 7.88417 | 0.315367 | ||||||||
\(626\) | 0.0463070 | 0.00185080 | ||||||||
\(627\) | −35.0991 | −1.40172 | ||||||||
\(628\) | −11.5156 | −0.459522 | ||||||||
\(629\) | 14.8738 | 0.593058 | ||||||||
\(630\) | 6.69732 | 0.266828 | ||||||||
\(631\) | 48.2403 | 1.92042 | 0.960208 | − | 0.279287i | \(-0.0900981\pi\) | ||||
0.960208 | + | 0.279287i | \(0.0900981\pi\) | |||||||
\(632\) | 10.4918 | 0.417342 | ||||||||
\(633\) | −10.5647 | −0.419911 | ||||||||
\(634\) | −21.6109 | −0.858278 | ||||||||
\(635\) | −17.7530 | −0.704505 | ||||||||
\(636\) | 22.0607 | 0.874765 | ||||||||
\(637\) | −5.52822 | −0.219036 | ||||||||
\(638\) | 31.4980 | 1.24702 | ||||||||
\(639\) | 19.3487 | 0.765424 | ||||||||
\(640\) | 1.11547 | 0.0440927 | ||||||||
\(641\) | −37.7308 | −1.49028 | −0.745139 | − | 0.666909i | \(-0.767617\pi\) | ||||
−0.745139 | + | 0.666909i | \(0.767617\pi\) | |||||||
\(642\) | 33.5770 | 1.32518 | ||||||||
\(643\) | 4.13355 | 0.163011 | 0.0815057 | − | 0.996673i | \(-0.474027\pi\) | ||||
0.0815057 | + | 0.996673i | \(0.474027\pi\) | |||||||
\(644\) | −8.20191 | −0.323201 | ||||||||
\(645\) | −17.1674 | −0.675967 | ||||||||
\(646\) | 23.2033 | 0.912923 | ||||||||
\(647\) | 21.7095 | 0.853488 | 0.426744 | − | 0.904372i | \(-0.359661\pi\) | ||||
0.426744 | + | 0.904372i | \(0.359661\pi\) | |||||||
\(648\) | 9.66408 | 0.379641 | ||||||||
\(649\) | −39.6186 | −1.55517 | ||||||||
\(650\) | 9.16488 | 0.359476 | ||||||||
\(651\) | 38.4949 | 1.50873 | ||||||||
\(652\) | −13.5787 | −0.531785 | ||||||||
\(653\) | 18.9136 | 0.740146 | 0.370073 | − | 0.929003i | \(-0.379333\pi\) | ||||
0.370073 | + | 0.929003i | \(0.379333\pi\) | |||||||
\(654\) | 0.923364 | 0.0361064 | ||||||||
\(655\) | 7.37738 | 0.288258 | ||||||||
\(656\) | 9.67954 | 0.377923 | ||||||||
\(657\) | −18.8429 | −0.735132 | ||||||||
\(658\) | 26.6725 | 1.03980 | ||||||||
\(659\) | −2.75660 | −0.107382 | −0.0536910 | − | 0.998558i | \(-0.517099\pi\) | ||||
−0.0536910 | + | 0.998558i | \(0.517099\pi\) | |||||||
\(660\) | −8.25870 | −0.321469 | ||||||||
\(661\) | 4.40930 | 0.171502 | 0.0857510 | − | 0.996317i | \(-0.472671\pi\) | ||||
0.0857510 | + | 0.996317i | \(0.472671\pi\) | |||||||
\(662\) | −15.1368 | −0.588308 | ||||||||
\(663\) | −28.6634 | −1.11320 | ||||||||
\(664\) | −9.20979 | −0.357409 | ||||||||
\(665\) | 11.5064 | 0.446197 | ||||||||
\(666\) | −8.38527 | −0.324923 | ||||||||
\(667\) | −38.4849 | −1.49014 | ||||||||
\(668\) | 12.5466 | 0.485443 | ||||||||
\(669\) | −30.0839 | −1.16311 | ||||||||
\(670\) | 1.72908 | 0.0668000 | ||||||||
\(671\) | −37.7148 | −1.45596 | ||||||||
\(672\) | 5.22187 | 0.201438 | ||||||||
\(673\) | 11.0555 | 0.426158 | 0.213079 | − | 0.977035i | \(-0.431651\pi\) | ||||
0.213079 | + | 0.977035i | \(0.431651\pi\) | |||||||
\(674\) | 4.24745 | 0.163606 | ||||||||
\(675\) | −2.16918 | −0.0834917 | ||||||||
\(676\) | −7.04523 | −0.270970 | ||||||||
\(677\) | −41.9181 | −1.61104 | −0.805522 | − | 0.592566i | \(-0.798115\pi\) | ||||
−0.805522 | + | 0.592566i | \(0.798115\pi\) | |||||||
\(678\) | −10.9709 | −0.421334 | ||||||||
\(679\) | 7.95617 | 0.305330 | ||||||||
\(680\) | 5.45967 | 0.209369 | ||||||||
\(681\) | −2.52029 | −0.0965779 | ||||||||
\(682\) | −22.7429 | −0.870870 | ||||||||
\(683\) | 48.4854 | 1.85524 | 0.927620 | − | 0.373525i | \(-0.121851\pi\) | ||||
0.927620 | + | 0.373525i | \(0.121851\pi\) | |||||||
\(684\) | −13.0811 | −0.500170 | ||||||||
\(685\) | −17.3029 | −0.661109 | ||||||||
\(686\) | 20.1607 | 0.769740 | ||||||||
\(687\) | 52.0551 | 1.98603 | ||||||||
\(688\) | −6.41301 | −0.244494 | ||||||||
\(689\) | −22.4319 | −0.854588 | ||||||||
\(690\) | 10.0906 | 0.384144 | ||||||||
\(691\) | 7.97421 | 0.303353 | 0.151677 | − | 0.988430i | \(-0.451533\pi\) | ||||
0.151677 | + | 0.988430i | \(0.451533\pi\) | |||||||
\(692\) | 4.85331 | 0.184495 | ||||||||
\(693\) | −18.5230 | −0.703632 | ||||||||
\(694\) | 2.41227 | 0.0915685 | ||||||||
\(695\) | −13.0892 | −0.496503 | ||||||||
\(696\) | 24.5020 | 0.928745 | ||||||||
\(697\) | 47.3766 | 1.79452 | ||||||||
\(698\) | 15.3301 | 0.580252 | ||||||||
\(699\) | −20.6568 | −0.781313 | ||||||||
\(700\) | −8.17211 | −0.308877 | ||||||||
\(701\) | −49.7799 | −1.88016 | −0.940080 | − | 0.340954i | \(-0.889250\pi\) | ||||
−0.940080 | + | 0.340954i | \(0.889250\pi\) | |||||||
\(702\) | −1.40940 | −0.0531942 | ||||||||
\(703\) | −14.4063 | −0.543346 | ||||||||
\(704\) | −3.08509 | −0.116274 | ||||||||
\(705\) | −32.8146 | −1.23587 | ||||||||
\(706\) | 28.0894 | 1.05716 | ||||||||
\(707\) | −0.417419 | −0.0156987 | ||||||||
\(708\) | −30.8189 | −1.15824 | ||||||||
\(709\) | 24.3834 | 0.915738 | 0.457869 | − | 0.889020i | \(-0.348613\pi\) | ||||
0.457869 | + | 0.889020i | \(0.348613\pi\) | |||||||
\(710\) | 7.82178 | 0.293546 | ||||||||
\(711\) | −28.9504 | −1.08573 | ||||||||
\(712\) | −5.85474 | −0.219416 | ||||||||
\(713\) | 27.7877 | 1.04066 | ||||||||
\(714\) | 25.5585 | 0.956502 | ||||||||
\(715\) | 8.39766 | 0.314055 | ||||||||
\(716\) | 0.0898258 | 0.00335695 | ||||||||
\(717\) | −15.7206 | −0.587095 | ||||||||
\(718\) | 25.9313 | 0.967749 | ||||||||
\(719\) | 25.7291 | 0.959535 | 0.479768 | − | 0.877396i | \(-0.340721\pi\) | ||||
0.479768 | + | 0.877396i | \(0.340721\pi\) | |||||||
\(720\) | −3.07795 | −0.114708 | ||||||||
\(721\) | 1.09942 | 0.0409446 | ||||||||
\(722\) | −3.47408 | −0.129292 | ||||||||
\(723\) | 16.9066 | 0.628762 | ||||||||
\(724\) | −15.9809 | −0.593926 | ||||||||
\(725\) | −38.3451 | −1.42410 | ||||||||
\(726\) | −3.55707 | −0.132015 | ||||||||
\(727\) | 28.5151 | 1.05756 | 0.528782 | − | 0.848757i | \(-0.322649\pi\) | ||||
0.528782 | + | 0.848757i | \(0.322649\pi\) | |||||||
\(728\) | −5.30973 | −0.196792 | ||||||||
\(729\) | −22.5082 | −0.833637 | ||||||||
\(730\) | −7.61730 | −0.281929 | ||||||||
\(731\) | −31.3886 | −1.16095 | ||||||||
\(732\) | −29.3379 | −1.08436 | ||||||||
\(733\) | −24.5700 | −0.907515 | −0.453758 | − | 0.891125i | \(-0.649917\pi\) | ||||
−0.453758 | + | 0.891125i | \(0.649917\pi\) | |||||||
\(734\) | 11.4260 | 0.421740 | ||||||||
\(735\) | −6.06452 | −0.223693 | ||||||||
\(736\) | 3.76943 | 0.138943 | ||||||||
\(737\) | −4.78217 | −0.176154 | ||||||||
\(738\) | −26.7091 | −0.983175 | ||||||||
\(739\) | 33.8597 | 1.24555 | 0.622775 | − | 0.782401i | \(-0.286005\pi\) | ||||
0.622775 | + | 0.782401i | \(0.286005\pi\) | |||||||
\(740\) | −3.38977 | −0.124610 | ||||||||
\(741\) | 27.7626 | 1.01988 | ||||||||
\(742\) | 20.0020 | 0.734297 | ||||||||
\(743\) | −3.58016 | −0.131343 | −0.0656716 | − | 0.997841i | \(-0.520919\pi\) | ||||
−0.0656716 | + | 0.997841i | \(0.520919\pi\) | |||||||
\(744\) | −17.6914 | −0.648600 | ||||||||
\(745\) | 17.8209 | 0.652907 | ||||||||
\(746\) | 9.88851 | 0.362044 | ||||||||
\(747\) | 25.4129 | 0.929809 | ||||||||
\(748\) | −15.1000 | −0.552112 | ||||||||
\(749\) | 30.4436 | 1.11238 | ||||||||
\(750\) | 23.4388 | 0.855865 | ||||||||
\(751\) | −29.5711 | −1.07907 | −0.539533 | − | 0.841964i | \(-0.681399\pi\) | ||||
−0.539533 | + | 0.841964i | \(0.681399\pi\) | |||||||
\(752\) | −12.2581 | −0.447008 | ||||||||
\(753\) | 33.5148 | 1.22135 | ||||||||
\(754\) | −24.9142 | −0.907323 | ||||||||
\(755\) | 5.02963 | 0.183047 | ||||||||
\(756\) | 1.25673 | 0.0457066 | ||||||||
\(757\) | 40.8057 | 1.48311 | 0.741554 | − | 0.670893i | \(-0.234089\pi\) | ||||
0.741554 | + | 0.670893i | \(0.234089\pi\) | |||||||
\(758\) | 14.1178 | 0.512782 | ||||||||
\(759\) | −27.9081 | −1.01300 | ||||||||
\(760\) | −5.28808 | −0.191819 | ||||||||
\(761\) | −11.8362 | −0.429063 | −0.214532 | − | 0.976717i | \(-0.568822\pi\) | ||||
−0.214532 | + | 0.976717i | \(0.568822\pi\) | |||||||
\(762\) | 38.1944 | 1.38364 | ||||||||
\(763\) | 0.837195 | 0.0303085 | ||||||||
\(764\) | −19.7638 | −0.715029 | ||||||||
\(765\) | −15.0651 | −0.544678 | ||||||||
\(766\) | 5.02639 | 0.181611 | ||||||||
\(767\) | 31.3374 | 1.13153 | ||||||||
\(768\) | −2.39986 | −0.0865975 | ||||||||
\(769\) | −38.5674 | −1.39078 | −0.695388 | − | 0.718635i | \(-0.744767\pi\) | ||||
−0.695388 | + | 0.718635i | \(0.744767\pi\) | |||||||
\(770\) | −7.48799 | −0.269848 | ||||||||
\(771\) | 5.55452 | 0.200041 | ||||||||
\(772\) | −1.80147 | −0.0648364 | ||||||||
\(773\) | −50.8072 | −1.82741 | −0.913704 | − | 0.406379i | \(-0.866791\pi\) | ||||
−0.913704 | + | 0.406379i | \(0.866791\pi\) | |||||||
\(774\) | 17.6956 | 0.636057 | ||||||||
\(775\) | 27.6867 | 0.994536 | ||||||||
\(776\) | −3.65649 | −0.131260 | ||||||||
\(777\) | −15.8686 | −0.569283 | ||||||||
\(778\) | −23.9220 | −0.857646 | ||||||||
\(779\) | −45.8876 | −1.64410 | ||||||||
\(780\) | 6.53245 | 0.233899 | ||||||||
\(781\) | −21.6330 | −0.774090 | ||||||||
\(782\) | 18.4495 | 0.659753 | ||||||||
\(783\) | 5.89679 | 0.210734 | ||||||||
\(784\) | −2.26544 | −0.0809087 | ||||||||
\(785\) | 12.8453 | 0.458467 | ||||||||
\(786\) | −15.8720 | −0.566135 | ||||||||
\(787\) | −14.4544 | −0.515245 | −0.257622 | − | 0.966246i | \(-0.582939\pi\) | ||||
−0.257622 | + | 0.966246i | \(0.582939\pi\) | |||||||
\(788\) | −7.23693 | −0.257805 | ||||||||
\(789\) | −2.14850 | −0.0764887 | ||||||||
\(790\) | −11.7033 | −0.416385 | ||||||||
\(791\) | −9.94707 | −0.353677 | ||||||||
\(792\) | 8.51280 | 0.302489 | ||||||||
\(793\) | 29.8315 | 1.05935 | ||||||||
\(794\) | −28.6601 | −1.01711 | ||||||||
\(795\) | −24.6080 | −0.872757 | ||||||||
\(796\) | −11.1295 | −0.394474 | ||||||||
\(797\) | −25.1644 | −0.891369 | −0.445684 | − | 0.895190i | \(-0.647040\pi\) | ||||
−0.445684 | + | 0.895190i | \(0.647040\pi\) | |||||||
\(798\) | −24.7552 | −0.876325 | ||||||||
\(799\) | −59.9975 | −2.12256 | ||||||||
\(800\) | 3.75573 | 0.132785 | ||||||||
\(801\) | 16.1552 | 0.570816 | ||||||||
\(802\) | −4.87950 | −0.172301 | ||||||||
\(803\) | 21.0675 | 0.743455 | ||||||||
\(804\) | −3.72000 | −0.131194 | ||||||||
\(805\) | 9.14897 | 0.322459 | ||||||||
\(806\) | 17.9891 | 0.633639 | ||||||||
\(807\) | 0.412991 | 0.0145380 | ||||||||
\(808\) | 0.191837 | 0.00674881 | ||||||||
\(809\) | −26.9931 | −0.949027 | −0.474513 | − | 0.880248i | \(-0.657376\pi\) | ||||
−0.474513 | + | 0.880248i | \(0.657376\pi\) | |||||||
\(810\) | −10.7800 | −0.378770 | ||||||||
\(811\) | 29.0890 | 1.02145 | 0.510727 | − | 0.859743i | \(-0.329376\pi\) | ||||
0.510727 | + | 0.859743i | \(0.329376\pi\) | |||||||
\(812\) | 22.2154 | 0.779609 | ||||||||
\(813\) | 51.7090 | 1.81351 | ||||||||
\(814\) | 9.37521 | 0.328601 | ||||||||
\(815\) | 15.1467 | 0.530564 | ||||||||
\(816\) | −11.7461 | −0.411197 | ||||||||
\(817\) | 30.4021 | 1.06363 | ||||||||
\(818\) | −3.25415 | −0.113779 | ||||||||
\(819\) | 14.6513 | 0.511958 | ||||||||
\(820\) | −10.7972 | −0.377055 | ||||||||
\(821\) | 36.5009 | 1.27389 | 0.636945 | − | 0.770909i | \(-0.280198\pi\) | ||||
0.636945 | + | 0.770909i | \(0.280198\pi\) | |||||||
\(822\) | 37.2261 | 1.29841 | ||||||||
\(823\) | −3.11125 | −0.108451 | −0.0542256 | − | 0.998529i | \(-0.517269\pi\) | ||||
−0.0542256 | + | 0.998529i | \(0.517269\pi\) | |||||||
\(824\) | −0.505272 | −0.0176020 | ||||||||
\(825\) | −27.8067 | −0.968104 | ||||||||
\(826\) | −27.9428 | −0.972255 | ||||||||
\(827\) | −13.2201 | −0.459709 | −0.229854 | − | 0.973225i | \(-0.573825\pi\) | ||||
−0.229854 | + | 0.973225i | \(0.573825\pi\) | |||||||
\(828\) | −10.4011 | −0.361464 | ||||||||
\(829\) | 50.0567 | 1.73854 | 0.869271 | − | 0.494337i | \(-0.164589\pi\) | ||||
0.869271 | + | 0.494337i | \(0.164589\pi\) | |||||||
\(830\) | 10.2732 | 0.356589 | ||||||||
\(831\) | −55.0991 | −1.91137 | ||||||||
\(832\) | 2.44024 | 0.0846001 | ||||||||
\(833\) | −11.0882 | −0.384185 | ||||||||
\(834\) | 28.1607 | 0.975124 | ||||||||
\(835\) | −13.9953 | −0.484329 | ||||||||
\(836\) | 14.6255 | 0.505832 | ||||||||
\(837\) | −4.25773 | −0.147169 | ||||||||
\(838\) | 39.6891 | 1.37104 | ||||||||
\(839\) | −3.83504 | −0.132400 | −0.0662001 | − | 0.997806i | \(-0.521088\pi\) | ||||
−0.0662001 | + | 0.997806i | \(0.521088\pi\) | |||||||
\(840\) | −5.82483 | −0.200976 | ||||||||
\(841\) | 75.2390 | 2.59445 | ||||||||
\(842\) | 8.27486 | 0.285171 | ||||||||
\(843\) | 70.1258 | 2.41526 | ||||||||
\(844\) | 4.40223 | 0.151531 | ||||||||
\(845\) | 7.85873 | 0.270348 | ||||||||
\(846\) | 33.8243 | 1.16290 | ||||||||
\(847\) | −3.22512 | −0.110816 | ||||||||
\(848\) | −9.19250 | −0.315672 | ||||||||
\(849\) | 64.3143 | 2.20726 | ||||||||
\(850\) | 18.3825 | 0.630513 | ||||||||
\(851\) | −11.4548 | −0.392666 | ||||||||
\(852\) | −16.8281 | −0.576521 | ||||||||
\(853\) | −34.1418 | −1.16899 | −0.584496 | − | 0.811397i | \(-0.698708\pi\) | ||||
−0.584496 | + | 0.811397i | \(0.698708\pi\) | |||||||
\(854\) | −26.6001 | −0.910235 | ||||||||
\(855\) | 14.5916 | 0.499022 | ||||||||
\(856\) | −13.9912 | −0.478210 | ||||||||
\(857\) | 5.03986 | 0.172158 | 0.0860792 | − | 0.996288i | \(-0.472566\pi\) | ||||
0.0860792 | + | 0.996288i | \(0.472566\pi\) | |||||||
\(858\) | −18.0670 | −0.616799 | ||||||||
\(859\) | −47.8652 | −1.63314 | −0.816571 | − | 0.577246i | \(-0.804128\pi\) | ||||
−0.816571 | + | 0.577246i | \(0.804128\pi\) | |||||||
\(860\) | 7.15351 | 0.243933 | ||||||||
\(861\) | −50.5453 | −1.72258 | ||||||||
\(862\) | 38.3167 | 1.30507 | ||||||||
\(863\) | 30.9367 | 1.05310 | 0.526549 | − | 0.850145i | \(-0.323486\pi\) | ||||
0.526549 | + | 0.850145i | \(0.323486\pi\) | |||||||
\(864\) | −0.577565 | −0.0196491 | ||||||||
\(865\) | −5.41371 | −0.184072 | ||||||||
\(866\) | 6.51220 | 0.221294 | ||||||||
\(867\) | −16.6940 | −0.566959 | ||||||||
\(868\) | −16.0405 | −0.544449 | ||||||||
\(869\) | 32.3683 | 1.09802 | ||||||||
\(870\) | −27.3312 | −0.926614 | ||||||||
\(871\) | 3.78259 | 0.128168 | ||||||||
\(872\) | −0.384757 | −0.0130295 | ||||||||
\(873\) | 10.0895 | 0.341477 | ||||||||
\(874\) | −17.8697 | −0.604451 | ||||||||
\(875\) | 21.2515 | 0.718431 | ||||||||
\(876\) | 16.3882 | 0.553704 | ||||||||
\(877\) | 25.5362 | 0.862297 | 0.431149 | − | 0.902281i | \(-0.358108\pi\) | ||||
0.431149 | + | 0.902281i | \(0.358108\pi\) | |||||||
\(878\) | 15.2546 | 0.514817 | ||||||||
\(879\) | 58.7671 | 1.98217 | ||||||||
\(880\) | 3.44132 | 0.116007 | ||||||||
\(881\) | −27.2693 | −0.918725 | −0.459363 | − | 0.888249i | \(-0.651922\pi\) | ||||
−0.459363 | + | 0.888249i | \(0.651922\pi\) | |||||||
\(882\) | 6.25111 | 0.210486 | ||||||||
\(883\) | −1.68445 | −0.0566864 | −0.0283432 | − | 0.999598i | \(-0.509023\pi\) | ||||
−0.0283432 | + | 0.999598i | \(0.509023\pi\) | |||||||
\(884\) | 11.9438 | 0.401713 | ||||||||
\(885\) | 34.3775 | 1.15559 | ||||||||
\(886\) | 16.6014 | 0.557734 | ||||||||
\(887\) | 32.1257 | 1.07868 | 0.539338 | − | 0.842090i | \(-0.318675\pi\) | ||||
0.539338 | + | 0.842090i | \(0.318675\pi\) | |||||||
\(888\) | 7.29288 | 0.244733 | ||||||||
\(889\) | 34.6301 | 1.16146 | ||||||||
\(890\) | 6.53078 | 0.218912 | ||||||||
\(891\) | 29.8146 | 0.998826 | ||||||||
\(892\) | 12.5357 | 0.419725 | ||||||||
\(893\) | 58.1119 | 1.94464 | ||||||||
\(894\) | −38.3406 | −1.28230 | ||||||||
\(895\) | −0.100198 | −0.00334924 | ||||||||
\(896\) | −2.17590 | −0.0726918 | ||||||||
\(897\) | 22.0747 | 0.737052 | ||||||||
\(898\) | 12.8123 | 0.427552 | ||||||||
\(899\) | −75.2648 | −2.51022 | ||||||||
\(900\) | −10.3633 | −0.345444 | ||||||||
\(901\) | −44.9928 | −1.49893 | ||||||||
\(902\) | 29.8623 | 0.994306 | ||||||||
\(903\) | 33.4879 | 1.11441 | ||||||||
\(904\) | 4.57147 | 0.152045 | ||||||||
\(905\) | 17.8262 | 0.592563 | ||||||||
\(906\) | −10.8209 | −0.359502 | ||||||||
\(907\) | −17.8293 | −0.592011 | −0.296006 | − | 0.955186i | \(-0.595655\pi\) | ||||
−0.296006 | + | 0.955186i | \(0.595655\pi\) | |||||||
\(908\) | 1.05018 | 0.0348516 | ||||||||
\(909\) | −0.529343 | −0.0175572 | ||||||||
\(910\) | 5.92283 | 0.196340 | ||||||||
\(911\) | −36.2989 | −1.20264 | −0.601319 | − | 0.799009i | \(-0.705358\pi\) | ||||
−0.601319 | + | 0.799009i | \(0.705358\pi\) | |||||||
\(912\) | 11.3770 | 0.376730 | ||||||||
\(913\) | −28.4131 | −0.940335 | ||||||||
\(914\) | 9.26228 | 0.306369 | ||||||||
\(915\) | 32.7255 | 1.08187 | ||||||||
\(916\) | −21.6909 | −0.716687 | ||||||||
\(917\) | −14.3908 | −0.475226 | ||||||||
\(918\) | −2.82690 | −0.0933015 | ||||||||
\(919\) | −30.3322 | −1.00057 | −0.500284 | − | 0.865861i | \(-0.666771\pi\) | ||||
−0.500284 | + | 0.865861i | \(0.666771\pi\) | |||||||
\(920\) | −4.20468 | −0.138624 | ||||||||
\(921\) | 22.6599 | 0.746668 | ||||||||
\(922\) | −11.5580 | −0.380643 | ||||||||
\(923\) | 17.1112 | 0.563223 | ||||||||
\(924\) | 16.1099 | 0.529978 | ||||||||
\(925\) | −11.4132 | −0.375264 | ||||||||
\(926\) | 26.6963 | 0.877294 | ||||||||
\(927\) | 1.39421 | 0.0457920 | ||||||||
\(928\) | −10.2097 | −0.335151 | ||||||||
\(929\) | −7.14366 | −0.234376 | −0.117188 | − | 0.993110i | \(-0.537388\pi\) | ||||
−0.117188 | + | 0.993110i | \(0.537388\pi\) | |||||||
\(930\) | 19.7342 | 0.647111 | ||||||||
\(931\) | 10.7397 | 0.351981 | ||||||||
\(932\) | 8.60751 | 0.281948 | ||||||||
\(933\) | 33.2977 | 1.09012 | ||||||||
\(934\) | −16.7744 | −0.548876 | ||||||||
\(935\) | 16.8436 | 0.550845 | ||||||||
\(936\) | −6.73344 | −0.220089 | ||||||||
\(937\) | −31.2391 | −1.02054 | −0.510269 | − | 0.860015i | \(-0.670454\pi\) | ||||
−0.510269 | + | 0.860015i | \(0.670454\pi\) | |||||||
\(938\) | −3.37285 | −0.110127 | ||||||||
\(939\) | 0.111130 | 0.00362660 | ||||||||
\(940\) | 13.6735 | 0.445982 | ||||||||
\(941\) | −47.9745 | −1.56392 | −0.781962 | − | 0.623326i | \(-0.785781\pi\) | ||||
−0.781962 | + | 0.623326i | \(0.785781\pi\) | |||||||
\(942\) | −27.6358 | −0.900423 | ||||||||
\(943\) | −36.4863 | −1.18816 | ||||||||
\(944\) | 12.8419 | 0.417970 | ||||||||
\(945\) | −1.40184 | −0.0456018 | ||||||||
\(946\) | −19.7847 | −0.643258 | ||||||||
\(947\) | 39.0875 | 1.27017 | 0.635086 | − | 0.772442i | \(-0.280965\pi\) | ||||
0.635086 | + | 0.772442i | \(0.280965\pi\) | |||||||
\(948\) | 25.1789 | 0.817773 | ||||||||
\(949\) | −16.6639 | −0.540933 | ||||||||
\(950\) | −17.8047 | −0.577662 | ||||||||
\(951\) | −51.8631 | −1.68178 | ||||||||
\(952\) | −10.6500 | −0.345168 | ||||||||
\(953\) | −39.7808 | −1.28863 | −0.644313 | − | 0.764762i | \(-0.722857\pi\) | ||||
−0.644313 | + | 0.764762i | \(0.722857\pi\) | |||||||
\(954\) | 25.3652 | 0.821228 | ||||||||
\(955\) | 22.0459 | 0.713388 | ||||||||
\(956\) | 6.55061 | 0.211862 | ||||||||
\(957\) | 75.5909 | 2.44351 | ||||||||
\(958\) | −15.8014 | −0.510522 | ||||||||
\(959\) | 33.7521 | 1.08991 | ||||||||
\(960\) | 2.67697 | 0.0863988 | ||||||||
\(961\) | 23.3443 | 0.753043 | ||||||||
\(962\) | −7.41558 | −0.239088 | ||||||||
\(963\) | 38.6065 | 1.24408 | ||||||||
\(964\) | −7.04481 | −0.226898 | ||||||||
\(965\) | 2.00948 | 0.0646876 | ||||||||
\(966\) | −19.6835 | −0.633305 | ||||||||
\(967\) | −52.3995 | −1.68506 | −0.842528 | − | 0.538653i | \(-0.818933\pi\) | ||||
−0.842528 | + | 0.538653i | \(0.818933\pi\) | |||||||
\(968\) | 1.48220 | 0.0476396 | ||||||||
\(969\) | 55.6848 | 1.78885 | ||||||||
\(970\) | 4.07870 | 0.130959 | ||||||||
\(971\) | −24.2010 | −0.776648 | −0.388324 | − | 0.921523i | \(-0.626946\pi\) | ||||
−0.388324 | + | 0.921523i | \(0.626946\pi\) | |||||||
\(972\) | 21.4598 | 0.688322 | ||||||||
\(973\) | 25.5327 | 0.818540 | ||||||||
\(974\) | 33.7514 | 1.08147 | ||||||||
\(975\) | 21.9945 | 0.704386 | ||||||||
\(976\) | 12.2248 | 0.391307 | ||||||||
\(977\) | 34.5719 | 1.10605 | 0.553027 | − | 0.833163i | \(-0.313473\pi\) | ||||
0.553027 | + | 0.833163i | \(0.313473\pi\) | |||||||
\(978\) | −32.5871 | −1.04202 | ||||||||
\(979\) | −18.0624 | −0.577278 | ||||||||
\(980\) | 2.52703 | 0.0807230 | ||||||||
\(981\) | 1.06167 | 0.0338967 | ||||||||
\(982\) | −25.6541 | −0.818654 | ||||||||
\(983\) | −0.624849 | −0.0199296 | −0.00996479 | − | 0.999950i | \(-0.503172\pi\) | ||||
−0.00996479 | + | 0.999950i | \(0.503172\pi\) | |||||||
\(984\) | 23.2296 | 0.740531 | ||||||||
\(985\) | 8.07256 | 0.257213 | ||||||||
\(986\) | −49.9717 | −1.59142 | ||||||||
\(987\) | 64.0103 | 2.03747 | ||||||||
\(988\) | −11.5684 | −0.368040 | ||||||||
\(989\) | 24.1734 | 0.768669 | ||||||||
\(990\) | −9.49576 | −0.301795 | ||||||||
\(991\) | −18.3251 | −0.582115 | −0.291057 | − | 0.956706i | \(-0.594007\pi\) | ||||
−0.291057 | + | 0.956706i | \(0.594007\pi\) | |||||||
\(992\) | 7.37186 | 0.234057 | ||||||||
\(993\) | −36.3262 | −1.15278 | ||||||||
\(994\) | −15.2577 | −0.483944 | ||||||||
\(995\) | 12.4146 | 0.393569 | ||||||||
\(996\) | −22.1022 | −0.700335 | ||||||||
\(997\) | 12.8911 | 0.408264 | 0.204132 | − | 0.978943i | \(-0.434563\pi\) | ||||
0.204132 | + | 0.978943i | \(0.434563\pi\) | |||||||
\(998\) | −31.0571 | −0.983095 | ||||||||
\(999\) | 1.75515 | 0.0555304 |
(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 | 4034.2.a.b.1.5 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.b.1.5 | ✓ | 35 | 1.1 | even | 1 | trivial |