Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.288385.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 7x^{3} - 2x^{2} + 10x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.58597\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.58597 | 1.12145 | 0.560723 | − | 0.828003i | \(-0.310523\pi\) | ||||
0.560723 | + | 0.828003i | \(0.310523\pi\) | |||||||
\(3\) | −3.01851 | −1.74274 | −0.871368 | − | 0.490631i | \(-0.836766\pi\) | ||||
−0.871368 | + | 0.490631i | \(0.836766\pi\) | |||||||
\(4\) | 0.515286 | 0.257643 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −4.78725 | −1.95438 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.35471 | −0.832514 | ||||||||
\(9\) | 6.11138 | 2.03713 | ||||||||
\(10\) | 1.58597 | 0.501526 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.55539 | −0.449003 | ||||||||
\(13\) | −3.17071 | −0.879396 | −0.439698 | − | 0.898146i | \(-0.644915\pi\) | ||||
−0.439698 | + | 0.898146i | \(0.644915\pi\) | |||||||
\(14\) | −1.58597 | −0.423867 | ||||||||
\(15\) | −3.01851 | −0.779375 | ||||||||
\(16\) | −4.76505 | −1.19126 | ||||||||
\(17\) | 6.29047 | 1.52566 | 0.762831 | − | 0.646598i | \(-0.223809\pi\) | ||||
0.762831 | + | 0.646598i | \(0.223809\pi\) | |||||||
\(18\) | 9.69244 | 2.28453 | ||||||||
\(19\) | −1.15342 | −0.264614 | −0.132307 | − | 0.991209i | \(-0.542238\pi\) | ||||
−0.132307 | + | 0.991209i | \(0.542238\pi\) | |||||||
\(20\) | 0.515286 | 0.115221 | ||||||||
\(21\) | 3.01851 | 0.658692 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.96633 | 1.24407 | 0.622033 | − | 0.782991i | \(-0.286307\pi\) | ||||
0.622033 | + | 0.782991i | \(0.286307\pi\) | |||||||
\(24\) | 7.10769 | 1.45085 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.02863 | −0.986196 | ||||||||
\(27\) | −9.39172 | −1.80744 | ||||||||
\(28\) | −0.515286 | −0.0973799 | ||||||||
\(29\) | −8.32104 | −1.54518 | −0.772589 | − | 0.634907i | \(-0.781039\pi\) | ||||
−0.772589 | + | 0.634907i | \(0.781039\pi\) | |||||||
\(30\) | −4.78725 | −0.874028 | ||||||||
\(31\) | 8.69244 | 1.56121 | 0.780604 | − | 0.625026i | \(-0.214912\pi\) | ||||
0.780604 | + | 0.625026i | \(0.214912\pi\) | |||||||
\(32\) | −2.84780 | −0.503424 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.97646 | 1.71095 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 3.14911 | 0.524851 | ||||||||
\(37\) | 3.37140 | 0.554254 | 0.277127 | − | 0.960833i | \(-0.410618\pi\) | ||||
0.277127 | + | 0.960833i | \(0.410618\pi\) | |||||||
\(38\) | −1.82929 | −0.296750 | ||||||||
\(39\) | 9.57080 | 1.53256 | ||||||||
\(40\) | −2.35471 | −0.372312 | ||||||||
\(41\) | −6.78009 | −1.05887 | −0.529436 | − | 0.848350i | \(-0.677596\pi\) | ||||
−0.529436 | + | 0.848350i | \(0.677596\pi\) | |||||||
\(42\) | 4.78725 | 0.738688 | ||||||||
\(43\) | −5.11794 | −0.780479 | −0.390240 | − | 0.920713i | \(-0.627608\pi\) | ||||
−0.390240 | + | 0.920713i | \(0.627608\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.11138 | 0.911031 | ||||||||
\(46\) | 9.46240 | 1.39515 | ||||||||
\(47\) | 10.3868 | 1.51507 | 0.757536 | − | 0.652794i | \(-0.226403\pi\) | ||||
0.757536 | + | 0.652794i | \(0.226403\pi\) | |||||||
\(48\) | 14.3833 | 2.07606 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.58597 | 0.224289 | ||||||||
\(51\) | −18.9878 | −2.65883 | ||||||||
\(52\) | −1.63382 | −0.226570 | ||||||||
\(53\) | −8.18922 | −1.12488 | −0.562438 | − | 0.826840i | \(-0.690136\pi\) | ||||
−0.562438 | + | 0.826840i | \(0.690136\pi\) | |||||||
\(54\) | −14.8949 | −2.02694 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.35471 | 0.314661 | ||||||||
\(57\) | 3.48162 | 0.461152 | ||||||||
\(58\) | −13.1969 | −1.73283 | ||||||||
\(59\) | 7.10422 | 0.924891 | 0.462446 | − | 0.886648i | \(-0.346972\pi\) | ||||
0.462446 | + | 0.886648i | \(0.346972\pi\) | |||||||
\(60\) | −1.55539 | −0.200800 | ||||||||
\(61\) | −7.27196 | −0.931079 | −0.465540 | − | 0.885027i | \(-0.654140\pi\) | ||||
−0.465540 | + | 0.885027i | \(0.654140\pi\) | |||||||
\(62\) | 13.7859 | 1.75081 | ||||||||
\(63\) | −6.11138 | −0.769961 | ||||||||
\(64\) | 5.01360 | 0.626700 | ||||||||
\(65\) | −3.17071 | −0.393278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.71238 | −1.06439 | −0.532193 | − | 0.846623i | \(-0.678632\pi\) | ||||
−0.532193 | + | 0.846623i | \(0.678632\pi\) | |||||||
\(68\) | 3.24139 | 0.393076 | ||||||||
\(69\) | −18.0094 | −2.16808 | ||||||||
\(70\) | −1.58597 | −0.189559 | ||||||||
\(71\) | −12.5319 | −1.48726 | −0.743629 | − | 0.668593i | \(-0.766897\pi\) | ||||
−0.743629 | + | 0.668593i | \(0.766897\pi\) | |||||||
\(72\) | −14.3905 | −1.69594 | ||||||||
\(73\) | −4.48594 | −0.525039 | −0.262520 | − | 0.964927i | \(-0.584553\pi\) | ||||
−0.262520 | + | 0.964927i | \(0.584553\pi\) | |||||||
\(74\) | 5.34692 | 0.621567 | ||||||||
\(75\) | −3.01851 | −0.348547 | ||||||||
\(76\) | −0.594343 | −0.0681759 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 15.1790 | 1.71868 | ||||||||
\(79\) | 3.30007 | 0.371286 | 0.185643 | − | 0.982617i | \(-0.440563\pi\) | ||||
0.185643 | + | 0.982617i | \(0.440563\pi\) | |||||||
\(80\) | −4.76505 | −0.532749 | ||||||||
\(81\) | 10.0148 | 1.11276 | ||||||||
\(82\) | −10.7530 | −1.18747 | ||||||||
\(83\) | 7.14492 | 0.784257 | 0.392129 | − | 0.919910i | \(-0.371739\pi\) | ||||
0.392129 | + | 0.919910i | \(0.371739\pi\) | |||||||
\(84\) | 1.55539 | 0.169707 | ||||||||
\(85\) | 6.29047 | 0.682297 | ||||||||
\(86\) | −8.11688 | −0.875266 | ||||||||
\(87\) | 25.1171 | 2.69284 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.654265 | 0.0693520 | 0.0346760 | − | 0.999399i | \(-0.488960\pi\) | ||||
0.0346760 | + | 0.999399i | \(0.488960\pi\) | |||||||
\(90\) | 9.69244 | 1.02167 | ||||||||
\(91\) | 3.17071 | 0.332381 | ||||||||
\(92\) | 3.07437 | 0.320525 | ||||||||
\(93\) | −26.2382 | −2.72077 | ||||||||
\(94\) | 16.4731 | 1.69907 | ||||||||
\(95\) | −1.15342 | −0.118339 | ||||||||
\(96\) | 8.59609 | 0.877335 | ||||||||
\(97\) | 8.73507 | 0.886912 | 0.443456 | − | 0.896296i | \(-0.353752\pi\) | ||||
0.443456 | + | 0.896296i | \(0.353752\pi\) | |||||||
\(98\) | 1.58597 | 0.160207 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.515286 | 0.0515286 | ||||||||
\(101\) | −4.93648 | −0.491198 | −0.245599 | − | 0.969372i | \(-0.578985\pi\) | ||||
−0.245599 | + | 0.969372i | \(0.578985\pi\) | |||||||
\(102\) | −30.1140 | −2.98173 | ||||||||
\(103\) | −11.5887 | −1.14187 | −0.570933 | − | 0.820996i | \(-0.693419\pi\) | ||||
−0.570933 | + | 0.820996i | \(0.693419\pi\) | |||||||
\(104\) | 7.46608 | 0.732110 | ||||||||
\(105\) | 3.01851 | 0.294576 | ||||||||
\(106\) | −12.9878 | −1.26149 | ||||||||
\(107\) | 15.4407 | 1.49271 | 0.746356 | − | 0.665547i | \(-0.231802\pi\) | ||||
0.746356 | + | 0.665547i | \(0.231802\pi\) | |||||||
\(108\) | −4.83942 | −0.465673 | ||||||||
\(109\) | −18.6914 | −1.79031 | −0.895156 | − | 0.445753i | \(-0.852936\pi\) | ||||
−0.895156 | + | 0.445753i | \(0.852936\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.1766 | −0.965919 | ||||||||
\(112\) | 4.76505 | 0.450255 | ||||||||
\(113\) | 2.74889 | 0.258594 | 0.129297 | − | 0.991606i | \(-0.458728\pi\) | ||||
0.129297 | + | 0.991606i | \(0.458728\pi\) | |||||||
\(114\) | 5.52173 | 0.517157 | ||||||||
\(115\) | 5.96633 | 0.556363 | ||||||||
\(116\) | −4.28771 | −0.398104 | ||||||||
\(117\) | −19.3774 | −1.79144 | ||||||||
\(118\) | 11.2671 | 1.03722 | ||||||||
\(119\) | −6.29047 | −0.576646 | ||||||||
\(120\) | 7.10769 | 0.648841 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −11.5331 | −1.04416 | ||||||||
\(123\) | 20.4657 | 1.84533 | ||||||||
\(124\) | 4.47909 | 0.402234 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −9.69244 | −0.863471 | ||||||||
\(127\) | 0.801691 | 0.0711386 | 0.0355693 | − | 0.999367i | \(-0.488676\pi\) | ||||
0.0355693 | + | 0.999367i | \(0.488676\pi\) | |||||||
\(128\) | 13.6470 | 1.20623 | ||||||||
\(129\) | 15.4485 | 1.36017 | ||||||||
\(130\) | −5.02863 | −0.441040 | ||||||||
\(131\) | −12.4209 | −1.08522 | −0.542611 | − | 0.839984i | \(-0.682564\pi\) | ||||
−0.542611 | + | 0.839984i | \(0.682564\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.15342 | 0.100015 | ||||||||
\(134\) | −13.8175 | −1.19365 | ||||||||
\(135\) | −9.39172 | −0.808310 | ||||||||
\(136\) | −14.8122 | −1.27014 | ||||||||
\(137\) | −19.1100 | −1.63268 | −0.816339 | − | 0.577573i | \(-0.804000\pi\) | ||||
−0.816339 | + | 0.577573i | \(0.804000\pi\) | |||||||
\(138\) | −28.5623 | −2.43138 | ||||||||
\(139\) | 2.87837 | 0.244140 | 0.122070 | − | 0.992521i | \(-0.461047\pi\) | ||||
0.122070 | + | 0.992521i | \(0.461047\pi\) | |||||||
\(140\) | −0.515286 | −0.0435496 | ||||||||
\(141\) | −31.3526 | −2.64037 | ||||||||
\(142\) | −19.8751 | −1.66788 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −29.1210 | −2.42675 | ||||||||
\(145\) | −8.32104 | −0.691025 | ||||||||
\(146\) | −7.11454 | −0.588803 | ||||||||
\(147\) | −3.01851 | −0.248962 | ||||||||
\(148\) | 1.73723 | 0.142800 | ||||||||
\(149\) | −15.4427 | −1.26511 | −0.632556 | − | 0.774514i | \(-0.717994\pi\) | ||||
−0.632556 | + | 0.774514i | \(0.717994\pi\) | |||||||
\(150\) | −4.78725 | −0.390877 | ||||||||
\(151\) | 12.8668 | 1.04709 | 0.523544 | − | 0.851999i | \(-0.324610\pi\) | ||||
0.523544 | + | 0.851999i | \(0.324610\pi\) | |||||||
\(152\) | 2.71597 | 0.220295 | ||||||||
\(153\) | 38.4434 | 3.10797 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.69244 | 0.698193 | ||||||||
\(156\) | 4.93170 | 0.394852 | ||||||||
\(157\) | −2.64189 | −0.210846 | −0.105423 | − | 0.994427i | \(-0.533620\pi\) | ||||
−0.105423 | + | 0.994427i | \(0.533620\pi\) | |||||||
\(158\) | 5.23379 | 0.416378 | ||||||||
\(159\) | 24.7192 | 1.96036 | ||||||||
\(160\) | −2.84780 | −0.225138 | ||||||||
\(161\) | −5.96633 | −0.470213 | ||||||||
\(162\) | 15.8832 | 1.24790 | ||||||||
\(163\) | −13.5443 | −1.06087 | −0.530435 | − | 0.847725i | \(-0.677972\pi\) | ||||
−0.530435 | + | 0.847725i | \(0.677972\pi\) | |||||||
\(164\) | −3.49368 | −0.272811 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.3316 | 0.879503 | ||||||||
\(167\) | −20.4083 | −1.57924 | −0.789620 | − | 0.613596i | \(-0.789722\pi\) | ||||
−0.789620 | + | 0.613596i | \(0.789722\pi\) | |||||||
\(168\) | −7.10769 | −0.548370 | ||||||||
\(169\) | −2.94661 | −0.226662 | ||||||||
\(170\) | 9.97646 | 0.765160 | ||||||||
\(171\) | −7.04901 | −0.539052 | ||||||||
\(172\) | −2.63720 | −0.201085 | ||||||||
\(173\) | −12.5397 | −0.953378 | −0.476689 | − | 0.879072i | \(-0.658163\pi\) | ||||
−0.476689 | + | 0.879072i | \(0.658163\pi\) | |||||||
\(174\) | 39.8349 | 3.01987 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.4441 | −1.61184 | ||||||||
\(178\) | 1.03764 | 0.0777745 | ||||||||
\(179\) | −11.5313 | −0.861893 | −0.430947 | − | 0.902377i | \(-0.641820\pi\) | ||||
−0.430947 | + | 0.902377i | \(0.641820\pi\) | |||||||
\(180\) | 3.14911 | 0.234721 | ||||||||
\(181\) | −2.25692 | −0.167756 | −0.0838779 | − | 0.996476i | \(-0.526731\pi\) | ||||
−0.0838779 | + | 0.996476i | \(0.526731\pi\) | |||||||
\(182\) | 5.02863 | 0.372747 | ||||||||
\(183\) | 21.9505 | 1.62262 | ||||||||
\(184\) | −14.0490 | −1.03570 | ||||||||
\(185\) | 3.37140 | 0.247870 | ||||||||
\(186\) | −41.6128 | −3.05120 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.35218 | 0.390348 | ||||||||
\(189\) | 9.39172 | 0.683147 | ||||||||
\(190\) | −1.82929 | −0.132711 | ||||||||
\(191\) | −9.31441 | −0.673967 | −0.336984 | − | 0.941511i | \(-0.609407\pi\) | ||||
−0.336984 | + | 0.941511i | \(0.609407\pi\) | |||||||
\(192\) | −15.1336 | −1.09217 | ||||||||
\(193\) | −3.67986 | −0.264882 | −0.132441 | − | 0.991191i | \(-0.542282\pi\) | ||||
−0.132441 | + | 0.991191i | \(0.542282\pi\) | |||||||
\(194\) | 13.8535 | 0.994625 | ||||||||
\(195\) | 9.57080 | 0.685380 | ||||||||
\(196\) | 0.515286 | 0.0368061 | ||||||||
\(197\) | −8.44369 | −0.601588 | −0.300794 | − | 0.953689i | \(-0.597252\pi\) | ||||
−0.300794 | + | 0.953689i | \(0.597252\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.8381 | 1.54806 | 0.774029 | − | 0.633150i | \(-0.218238\pi\) | ||||
0.774029 | + | 0.633150i | \(0.218238\pi\) | |||||||
\(200\) | −2.35471 | −0.166503 | ||||||||
\(201\) | 26.2984 | 1.85494 | ||||||||
\(202\) | −7.82908 | −0.550852 | ||||||||
\(203\) | 8.32104 | 0.584022 | ||||||||
\(204\) | −9.78415 | −0.685028 | ||||||||
\(205\) | −6.78009 | −0.473542 | ||||||||
\(206\) | −18.3792 | −1.28054 | ||||||||
\(207\) | 36.4625 | 2.53432 | ||||||||
\(208\) | 15.1086 | 1.04759 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.78725 | 0.330351 | ||||||||
\(211\) | −11.1893 | −0.770302 | −0.385151 | − | 0.922854i | \(-0.625851\pi\) | ||||
−0.385151 | + | 0.922854i | \(0.625851\pi\) | |||||||
\(212\) | −4.21979 | −0.289816 | ||||||||
\(213\) | 37.8275 | 2.59190 | ||||||||
\(214\) | 24.4885 | 1.67400 | ||||||||
\(215\) | −5.11794 | −0.349041 | ||||||||
\(216\) | 22.1147 | 1.50472 | ||||||||
\(217\) | −8.69244 | −0.590081 | ||||||||
\(218\) | −29.6439 | −2.00774 | ||||||||
\(219\) | 13.5408 | 0.915004 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.9452 | −1.34166 | ||||||||
\(222\) | −16.1397 | −1.08323 | ||||||||
\(223\) | −9.08965 | −0.608688 | −0.304344 | − | 0.952562i | \(-0.598437\pi\) | ||||
−0.304344 | + | 0.952562i | \(0.598437\pi\) | |||||||
\(224\) | 2.84780 | 0.190276 | ||||||||
\(225\) | 6.11138 | 0.407425 | ||||||||
\(226\) | 4.35964 | 0.289999 | ||||||||
\(227\) | −0.378617 | −0.0251297 | −0.0125649 | − | 0.999921i | \(-0.504000\pi\) | ||||
−0.0125649 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(228\) | 1.79403 | 0.118812 | ||||||||
\(229\) | −3.92667 | −0.259481 | −0.129741 | − | 0.991548i | \(-0.541415\pi\) | ||||
−0.129741 | + | 0.991548i | \(0.541415\pi\) | |||||||
\(230\) | 9.46240 | 0.623932 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.5936 | 1.28638 | ||||||||
\(233\) | 20.1205 | 1.31814 | 0.659070 | − | 0.752082i | \(-0.270950\pi\) | ||||
0.659070 | + | 0.752082i | \(0.270950\pi\) | |||||||
\(234\) | −30.7319 | −2.00901 | ||||||||
\(235\) | 10.3868 | 0.677561 | ||||||||
\(236\) | 3.66071 | 0.238292 | ||||||||
\(237\) | −9.96127 | −0.647054 | ||||||||
\(238\) | −9.97646 | −0.646678 | ||||||||
\(239\) | −23.1335 | −1.49638 | −0.748190 | − | 0.663484i | \(-0.769077\pi\) | ||||
−0.748190 | + | 0.663484i | \(0.769077\pi\) | |||||||
\(240\) | 14.3833 | 0.928441 | ||||||||
\(241\) | −21.8666 | −1.40855 | −0.704276 | − | 0.709926i | \(-0.748728\pi\) | ||||
−0.704276 | + | 0.709926i | \(0.748728\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.05464 | −0.131805 | ||||||||
\(244\) | −3.74714 | −0.239886 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 32.4580 | 2.06944 | ||||||||
\(247\) | 3.65717 | 0.232700 | ||||||||
\(248\) | −20.4681 | −1.29973 | ||||||||
\(249\) | −21.5670 | −1.36675 | ||||||||
\(250\) | 1.58597 | 0.100305 | ||||||||
\(251\) | −23.5940 | −1.48924 | −0.744620 | − | 0.667489i | \(-0.767369\pi\) | ||||
−0.744620 | + | 0.667489i | \(0.767369\pi\) | |||||||
\(252\) | −3.14911 | −0.198375 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.27145 | 0.0797781 | ||||||||
\(255\) | −18.9878 | −1.18906 | ||||||||
\(256\) | 11.6165 | 0.726028 | ||||||||
\(257\) | 3.74757 | 0.233767 | 0.116884 | − | 0.993146i | \(-0.462710\pi\) | ||||
0.116884 | + | 0.993146i | \(0.462710\pi\) | |||||||
\(258\) | 24.5009 | 1.52536 | ||||||||
\(259\) | −3.37140 | −0.209488 | ||||||||
\(260\) | −1.63382 | −0.101325 | ||||||||
\(261\) | −50.8530 | −3.14772 | ||||||||
\(262\) | −19.6992 | −1.21702 | ||||||||
\(263\) | 20.4872 | 1.26330 | 0.631648 | − | 0.775256i | \(-0.282379\pi\) | ||||
0.631648 | + | 0.775256i | \(0.282379\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.18922 | −0.503059 | ||||||||
\(266\) | 1.82929 | 0.112161 | ||||||||
\(267\) | −1.97490 | −0.120862 | ||||||||
\(268\) | −4.48937 | −0.274232 | ||||||||
\(269\) | −29.4456 | −1.79533 | −0.897665 | − | 0.440678i | \(-0.854738\pi\) | ||||
−0.897665 | + | 0.440678i | \(0.854738\pi\) | |||||||
\(270\) | −14.8949 | −0.906477 | ||||||||
\(271\) | 18.6959 | 1.13569 | 0.567847 | − | 0.823134i | \(-0.307777\pi\) | ||||
0.567847 | + | 0.823134i | \(0.307777\pi\) | |||||||
\(272\) | −29.9744 | −1.81746 | ||||||||
\(273\) | −9.57080 | −0.579251 | ||||||||
\(274\) | −30.3078 | −1.83096 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.28000 | −0.558590 | ||||||||
\(277\) | −19.1250 | −1.14911 | −0.574554 | − | 0.818467i | \(-0.694824\pi\) | ||||
−0.574554 | + | 0.818467i | \(0.694824\pi\) | |||||||
\(278\) | 4.56499 | 0.273790 | ||||||||
\(279\) | 53.1228 | 3.18038 | ||||||||
\(280\) | 2.35471 | 0.140721 | ||||||||
\(281\) | 3.09043 | 0.184360 | 0.0921798 | − | 0.995742i | \(-0.470617\pi\) | ||||
0.0921798 | + | 0.995742i | \(0.470617\pi\) | |||||||
\(282\) | −49.7242 | −2.96103 | ||||||||
\(283\) | 14.4606 | 0.859592 | 0.429796 | − | 0.902926i | \(-0.358585\pi\) | ||||
0.429796 | + | 0.902926i | \(0.358585\pi\) | |||||||
\(284\) | −6.45749 | −0.383181 | ||||||||
\(285\) | 3.48162 | 0.206233 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.78009 | 0.400216 | ||||||||
\(288\) | −17.4040 | −1.02554 | ||||||||
\(289\) | 22.5700 | 1.32764 | ||||||||
\(290\) | −13.1969 | −0.774947 | ||||||||
\(291\) | −26.3669 | −1.54565 | ||||||||
\(292\) | −2.31154 | −0.135273 | ||||||||
\(293\) | 15.8628 | 0.926713 | 0.463357 | − | 0.886172i | \(-0.346645\pi\) | ||||
0.463357 | + | 0.886172i | \(0.346645\pi\) | |||||||
\(294\) | −4.78725 | −0.279198 | ||||||||
\(295\) | 7.10422 | 0.413624 | ||||||||
\(296\) | −7.93865 | −0.461424 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.4915 | −1.41876 | ||||||||
\(299\) | −18.9175 | −1.09403 | ||||||||
\(300\) | −1.55539 | −0.0898007 | ||||||||
\(301\) | 5.11794 | 0.294993 | ||||||||
\(302\) | 20.4063 | 1.17425 | ||||||||
\(303\) | 14.9008 | 0.856028 | ||||||||
\(304\) | 5.49613 | 0.315225 | ||||||||
\(305\) | −7.27196 | −0.416391 | ||||||||
\(306\) | 60.9699 | 3.48542 | ||||||||
\(307\) | 31.9573 | 1.82390 | 0.911950 | − | 0.410301i | \(-0.134576\pi\) | ||||
0.911950 | + | 0.410301i | \(0.134576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 34.9805 | 1.98997 | ||||||||
\(310\) | 13.7859 | 0.782987 | ||||||||
\(311\) | −34.1773 | −1.93802 | −0.969009 | − | 0.247024i | \(-0.920547\pi\) | ||||
−0.969009 | + | 0.247024i | \(0.920547\pi\) | |||||||
\(312\) | −22.5364 | −1.27587 | ||||||||
\(313\) | 7.10835 | 0.401788 | 0.200894 | − | 0.979613i | \(-0.435615\pi\) | ||||
0.200894 | + | 0.979613i | \(0.435615\pi\) | |||||||
\(314\) | −4.18995 | −0.236452 | ||||||||
\(315\) | −6.11138 | −0.344337 | ||||||||
\(316\) | 1.70048 | 0.0956593 | ||||||||
\(317\) | −7.93860 | −0.445876 | −0.222938 | − | 0.974833i | \(-0.571565\pi\) | ||||
−0.222938 | + | 0.974833i | \(0.571565\pi\) | |||||||
\(318\) | 39.2038 | 2.19844 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 5.01360 | 0.280269 | ||||||||
\(321\) | −46.6079 | −2.60140 | ||||||||
\(322\) | −9.46240 | −0.527319 | ||||||||
\(323\) | −7.25558 | −0.403711 | ||||||||
\(324\) | 5.16049 | 0.286694 | ||||||||
\(325\) | −3.17071 | −0.175879 | ||||||||
\(326\) | −21.4808 | −1.18971 | ||||||||
\(327\) | 56.4201 | 3.12004 | ||||||||
\(328\) | 15.9651 | 0.881526 | ||||||||
\(329\) | −10.3868 | −0.572643 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.9984 | −1.48397 | −0.741984 | − | 0.670417i | \(-0.766115\pi\) | ||||
−0.741984 | + | 0.670417i | \(0.766115\pi\) | |||||||
\(332\) | 3.68168 | 0.202058 | ||||||||
\(333\) | 20.6039 | 1.12909 | ||||||||
\(334\) | −32.3668 | −1.77103 | ||||||||
\(335\) | −8.71238 | −0.476008 | ||||||||
\(336\) | −14.3833 | −0.784675 | ||||||||
\(337\) | −5.99694 | −0.326674 | −0.163337 | − | 0.986570i | \(-0.552226\pi\) | ||||
−0.163337 | + | 0.986570i | \(0.552226\pi\) | |||||||
\(338\) | −4.67321 | −0.254189 | ||||||||
\(339\) | −8.29754 | −0.450660 | ||||||||
\(340\) | 3.24139 | 0.175789 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −11.1795 | −0.604518 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 12.0512 | 0.649760 | ||||||||
\(345\) | −18.0094 | −0.969594 | ||||||||
\(346\) | −19.8876 | −1.06916 | ||||||||
\(347\) | 1.59687 | 0.0857246 | 0.0428623 | − | 0.999081i | \(-0.486352\pi\) | ||||
0.0428623 | + | 0.999081i | \(0.486352\pi\) | |||||||
\(348\) | 12.9425 | 0.693790 | ||||||||
\(349\) | 1.62486 | 0.0869768 | 0.0434884 | − | 0.999054i | \(-0.486153\pi\) | ||||
0.0434884 | + | 0.999054i | \(0.486153\pi\) | |||||||
\(350\) | −1.58597 | −0.0847734 | ||||||||
\(351\) | 29.7784 | 1.58945 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6170 | 0.565088 | 0.282544 | − | 0.959254i | \(-0.408822\pi\) | ||||
0.282544 | + | 0.959254i | \(0.408822\pi\) | |||||||
\(354\) | −34.0097 | −1.80759 | ||||||||
\(355\) | −12.5319 | −0.665122 | ||||||||
\(356\) | 0.337134 | 0.0178680 | ||||||||
\(357\) | 18.9878 | 1.00494 | ||||||||
\(358\) | −18.2883 | −0.966568 | ||||||||
\(359\) | −17.8274 | −0.940895 | −0.470447 | − | 0.882428i | \(-0.655907\pi\) | ||||
−0.470447 | + | 0.882428i | \(0.655907\pi\) | |||||||
\(360\) | −14.3905 | −0.758446 | ||||||||
\(361\) | −17.6696 | −0.929980 | ||||||||
\(362\) | −3.57940 | −0.188129 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.63382 | 0.0856355 | ||||||||
\(365\) | −4.48594 | −0.234805 | ||||||||
\(366\) | 34.8127 | 1.81969 | ||||||||
\(367\) | 24.9036 | 1.29996 | 0.649978 | − | 0.759953i | \(-0.274778\pi\) | ||||
0.649978 | + | 0.759953i | \(0.274778\pi\) | |||||||
\(368\) | −28.4299 | −1.48201 | ||||||||
\(369\) | −41.4357 | −2.15706 | ||||||||
\(370\) | 5.34692 | 0.277973 | ||||||||
\(371\) | 8.18922 | 0.425163 | ||||||||
\(372\) | −13.5202 | −0.700988 | ||||||||
\(373\) | −2.62079 | −0.135700 | −0.0678498 | − | 0.997696i | \(-0.521614\pi\) | ||||
−0.0678498 | + | 0.997696i | \(0.521614\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.01851 | −0.155875 | ||||||||
\(376\) | −24.4579 | −1.26132 | ||||||||
\(377\) | 26.3836 | 1.35882 | ||||||||
\(378\) | 14.8949 | 0.766113 | ||||||||
\(379\) | −1.16480 | −0.0598316 | −0.0299158 | − | 0.999552i | \(-0.509524\pi\) | ||||
−0.0299158 | + | 0.999552i | \(0.509524\pi\) | |||||||
\(380\) | −0.594343 | −0.0304892 | ||||||||
\(381\) | −2.41991 | −0.123976 | ||||||||
\(382\) | −14.7723 | −0.755818 | ||||||||
\(383\) | −12.6727 | −0.647545 | −0.323773 | − | 0.946135i | \(-0.604951\pi\) | ||||
−0.323773 | + | 0.946135i | \(0.604951\pi\) | |||||||
\(384\) | −41.1935 | −2.10215 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.83614 | −0.297052 | ||||||||
\(387\) | −31.2777 | −1.58993 | ||||||||
\(388\) | 4.50106 | 0.228507 | ||||||||
\(389\) | 26.0879 | 1.32271 | 0.661355 | − | 0.750073i | \(-0.269982\pi\) | ||||
0.661355 | + | 0.750073i | \(0.269982\pi\) | |||||||
\(390\) | 15.1790 | 0.768617 | ||||||||
\(391\) | 37.5310 | 1.89803 | ||||||||
\(392\) | −2.35471 | −0.118931 | ||||||||
\(393\) | 37.4927 | 1.89126 | ||||||||
\(394\) | −13.3914 | −0.674649 | ||||||||
\(395\) | 3.30007 | 0.166044 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.8879 | 1.24909 | 0.624543 | − | 0.780990i | \(-0.285285\pi\) | ||||
0.624543 | + | 0.780990i | \(0.285285\pi\) | |||||||
\(398\) | 34.6344 | 1.73607 | ||||||||
\(399\) | −3.48162 | −0.174299 | ||||||||
\(400\) | −4.76505 | −0.238253 | ||||||||
\(401\) | 29.2391 | 1.46013 | 0.730066 | − | 0.683376i | \(-0.239489\pi\) | ||||
0.730066 | + | 0.683376i | \(0.239489\pi\) | |||||||
\(402\) | 41.7083 | 2.08022 | ||||||||
\(403\) | −27.5612 | −1.37292 | ||||||||
\(404\) | −2.54370 | −0.126554 | ||||||||
\(405\) | 10.0148 | 0.497640 | ||||||||
\(406\) | 13.1969 | 0.654950 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 44.7107 | 2.21351 | ||||||||
\(409\) | −2.22494 | −0.110016 | −0.0550082 | − | 0.998486i | \(-0.517518\pi\) | ||||
−0.0550082 | + | 0.998486i | \(0.517518\pi\) | |||||||
\(410\) | −10.7530 | −0.531052 | ||||||||
\(411\) | 57.6837 | 2.84533 | ||||||||
\(412\) | −5.97148 | −0.294194 | ||||||||
\(413\) | −7.10422 | −0.349576 | ||||||||
\(414\) | 57.8283 | 2.84211 | ||||||||
\(415\) | 7.14492 | 0.350730 | ||||||||
\(416\) | 9.02954 | 0.442709 | ||||||||
\(417\) | −8.68837 | −0.425472 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.8546 | 1.31193 | 0.655966 | − | 0.754791i | \(-0.272262\pi\) | ||||
0.655966 | + | 0.754791i | \(0.272262\pi\) | |||||||
\(420\) | 1.55539 | 0.0758954 | ||||||||
\(421\) | 34.3522 | 1.67422 | 0.837112 | − | 0.547031i | \(-0.184242\pi\) | ||||
0.837112 | + | 0.547031i | \(0.184242\pi\) | |||||||
\(422\) | −17.7458 | −0.863852 | ||||||||
\(423\) | 63.4777 | 3.08639 | ||||||||
\(424\) | 19.2832 | 0.936474 | ||||||||
\(425\) | 6.29047 | 0.305132 | ||||||||
\(426\) | 59.9931 | 2.90667 | ||||||||
\(427\) | 7.27196 | 0.351915 | ||||||||
\(428\) | 7.95639 | 0.384587 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.11688 | −0.391431 | ||||||||
\(431\) | 26.6494 | 1.28366 | 0.641829 | − | 0.766848i | \(-0.278176\pi\) | ||||
0.641829 | + | 0.766848i | \(0.278176\pi\) | |||||||
\(432\) | 44.7520 | 2.15313 | ||||||||
\(433\) | −0.137853 | −0.00662478 | −0.00331239 | − | 0.999995i | \(-0.501054\pi\) | ||||
−0.00331239 | + | 0.999995i | \(0.501054\pi\) | |||||||
\(434\) | −13.7859 | −0.661744 | ||||||||
\(435\) | 25.1171 | 1.20427 | ||||||||
\(436\) | −9.63142 | −0.461261 | ||||||||
\(437\) | −6.88171 | −0.329197 | ||||||||
\(438\) | 21.4753 | 1.02613 | ||||||||
\(439\) | −3.30273 | −0.157631 | −0.0788153 | − | 0.996889i | \(-0.525114\pi\) | ||||
−0.0788153 | + | 0.996889i | \(0.525114\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.11138 | 0.291018 | ||||||||
\(442\) | −31.6325 | −1.50460 | ||||||||
\(443\) | −4.46330 | −0.212058 | −0.106029 | − | 0.994363i | \(-0.533814\pi\) | ||||
−0.106029 | + | 0.994363i | \(0.533814\pi\) | |||||||
\(444\) | −5.24385 | −0.248862 | ||||||||
\(445\) | 0.654265 | 0.0310151 | ||||||||
\(446\) | −14.4159 | −0.682611 | ||||||||
\(447\) | 46.6138 | 2.20476 | ||||||||
\(448\) | −5.01360 | −0.236870 | ||||||||
\(449\) | −18.8425 | −0.889230 | −0.444615 | − | 0.895722i | \(-0.646660\pi\) | ||||
−0.444615 | + | 0.895722i | \(0.646660\pi\) | |||||||
\(450\) | 9.69244 | 0.456906 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.41646 | 0.0666248 | ||||||||
\(453\) | −38.8386 | −1.82480 | ||||||||
\(454\) | −0.600474 | −0.0281817 | ||||||||
\(455\) | 3.17071 | 0.148645 | ||||||||
\(456\) | −8.19819 | −0.383915 | ||||||||
\(457\) | 4.41629 | 0.206585 | 0.103293 | − | 0.994651i | \(-0.467062\pi\) | ||||
0.103293 | + | 0.994651i | \(0.467062\pi\) | |||||||
\(458\) | −6.22756 | −0.290995 | ||||||||
\(459\) | −59.0783 | −2.75754 | ||||||||
\(460\) | 3.07437 | 0.143343 | ||||||||
\(461\) | 15.0090 | 0.699040 | 0.349520 | − | 0.936929i | \(-0.386345\pi\) | ||||
0.349520 | + | 0.936929i | \(0.386345\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.25808 | 0.244364 | 0.122182 | − | 0.992508i | \(-0.461011\pi\) | ||||
0.122182 | + | 0.992508i | \(0.461011\pi\) | |||||||
\(464\) | 39.6502 | 1.84071 | ||||||||
\(465\) | −26.2382 | −1.21677 | ||||||||
\(466\) | 31.9105 | 1.47822 | ||||||||
\(467\) | 9.86973 | 0.456717 | 0.228358 | − | 0.973577i | \(-0.426664\pi\) | ||||
0.228358 | + | 0.973577i | \(0.426664\pi\) | |||||||
\(468\) | −9.98490 | −0.461552 | ||||||||
\(469\) | 8.71238 | 0.402300 | ||||||||
\(470\) | 16.4731 | 0.759848 | ||||||||
\(471\) | 7.97456 | 0.367448 | ||||||||
\(472\) | −16.7283 | −0.769985 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −15.7982 | −0.725637 | ||||||||
\(475\) | −1.15342 | −0.0529227 | ||||||||
\(476\) | −3.24139 | −0.148569 | ||||||||
\(477\) | −50.0474 | −2.29151 | ||||||||
\(478\) | −36.6889 | −1.67811 | ||||||||
\(479\) | −18.1109 | −0.827508 | −0.413754 | − | 0.910389i | \(-0.635783\pi\) | ||||
−0.413754 | + | 0.910389i | \(0.635783\pi\) | |||||||
\(480\) | 8.59609 | 0.392356 | ||||||||
\(481\) | −10.6897 | −0.487409 | ||||||||
\(482\) | −34.6797 | −1.57962 | ||||||||
\(483\) | 18.0094 | 0.819457 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.73507 | 0.396639 | ||||||||
\(486\) | −3.25859 | −0.147812 | ||||||||
\(487\) | 20.8870 | 0.946479 | 0.473240 | − | 0.880934i | \(-0.343084\pi\) | ||||
0.473240 | + | 0.880934i | \(0.343084\pi\) | |||||||
\(488\) | 17.1233 | 0.775136 | ||||||||
\(489\) | 40.8835 | 1.84882 | ||||||||
\(490\) | 1.58597 | 0.0716466 | ||||||||
\(491\) | 28.0947 | 1.26790 | 0.633948 | − | 0.773376i | \(-0.281433\pi\) | ||||
0.633948 | + | 0.773376i | \(0.281433\pi\) | |||||||
\(492\) | 10.5457 | 0.475437 | ||||||||
\(493\) | −52.3432 | −2.35742 | ||||||||
\(494\) | 5.80015 | 0.260961 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −41.4199 | −1.85981 | ||||||||
\(497\) | 12.5319 | 0.562130 | ||||||||
\(498\) | −34.2045 | −1.53274 | ||||||||
\(499\) | 1.87174 | 0.0837906 | 0.0418953 | − | 0.999122i | \(-0.486660\pi\) | ||||
0.0418953 | + | 0.999122i | \(0.486660\pi\) | |||||||
\(500\) | 0.515286 | 0.0230443 | ||||||||
\(501\) | 61.6025 | 2.75220 | ||||||||
\(502\) | −37.4193 | −1.67010 | ||||||||
\(503\) | 10.7887 | 0.481044 | 0.240522 | − | 0.970644i | \(-0.422681\pi\) | ||||
0.240522 | + | 0.970644i | \(0.422681\pi\) | |||||||
\(504\) | 14.3905 | 0.641004 | ||||||||
\(505\) | −4.93648 | −0.219670 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.89435 | 0.395012 | ||||||||
\(508\) | 0.413100 | 0.0183284 | ||||||||
\(509\) | 40.7394 | 1.80574 | 0.902870 | − | 0.429913i | \(-0.141456\pi\) | ||||
0.902870 | + | 0.429913i | \(0.141456\pi\) | |||||||
\(510\) | −30.1140 | −1.33347 | ||||||||
\(511\) | 4.48594 | 0.198446 | ||||||||
\(512\) | −8.87068 | −0.392032 | ||||||||
\(513\) | 10.8326 | 0.478273 | ||||||||
\(514\) | 5.94352 | 0.262157 | ||||||||
\(515\) | −11.5887 | −0.510658 | ||||||||
\(516\) | 7.96042 | 0.350438 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −5.34692 | −0.234930 | ||||||||
\(519\) | 37.8513 | 1.66149 | ||||||||
\(520\) | 7.46608 | 0.327409 | ||||||||
\(521\) | −23.2302 | −1.01773 | −0.508867 | − | 0.860845i | \(-0.669935\pi\) | ||||
−0.508867 | + | 0.860845i | \(0.669935\pi\) | |||||||
\(522\) | −80.6511 | −3.53000 | ||||||||
\(523\) | 6.91423 | 0.302338 | 0.151169 | − | 0.988508i | \(-0.451696\pi\) | ||||
0.151169 | + | 0.988508i | \(0.451696\pi\) | |||||||
\(524\) | −6.40034 | −0.279600 | ||||||||
\(525\) | 3.01851 | 0.131738 | ||||||||
\(526\) | 32.4920 | 1.41672 | ||||||||
\(527\) | 54.6795 | 2.38188 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.5971 | 0.547701 | ||||||||
\(530\) | −12.9878 | −0.564154 | ||||||||
\(531\) | 43.4166 | 1.88412 | ||||||||
\(532\) | 0.594343 | 0.0257681 | ||||||||
\(533\) | 21.4977 | 0.931168 | ||||||||
\(534\) | −3.13213 | −0.135540 | ||||||||
\(535\) | 15.4407 | 0.667561 | ||||||||
\(536\) | 20.5151 | 0.886117 | ||||||||
\(537\) | 34.8074 | 1.50205 | ||||||||
\(538\) | −46.6997 | −2.01337 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.83942 | −0.208255 | ||||||||
\(541\) | −38.9010 | −1.67249 | −0.836243 | − | 0.548359i | \(-0.815253\pi\) | ||||
−0.836243 | + | 0.548359i | \(0.815253\pi\) | |||||||
\(542\) | 29.6510 | 1.27362 | ||||||||
\(543\) | 6.81254 | 0.292354 | ||||||||
\(544\) | −17.9140 | −0.768055 | ||||||||
\(545\) | −18.6914 | −0.800652 | ||||||||
\(546\) | −15.1790 | −0.649600 | ||||||||
\(547\) | −13.4121 | −0.573458 | −0.286729 | − | 0.958012i | \(-0.592568\pi\) | ||||
−0.286729 | + | 0.958012i | \(0.592568\pi\) | |||||||
\(548\) | −9.84712 | −0.420648 | ||||||||
\(549\) | −44.4417 | −1.89673 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.59769 | 0.408875 | ||||||||
\(552\) | 42.4069 | 1.80496 | ||||||||
\(553\) | −3.30007 | −0.140333 | ||||||||
\(554\) | −30.3315 | −1.28866 | ||||||||
\(555\) | −10.1766 | −0.431972 | ||||||||
\(556\) | 1.48318 | 0.0629010 | ||||||||
\(557\) | −17.5394 | −0.743167 | −0.371583 | − | 0.928400i | \(-0.621185\pi\) | ||||
−0.371583 | + | 0.928400i | \(0.621185\pi\) | |||||||
\(558\) | 84.2509 | 3.56662 | ||||||||
\(559\) | 16.2275 | 0.686350 | ||||||||
\(560\) | 4.76505 | 0.201360 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.90131 | 0.206749 | ||||||||
\(563\) | −32.5660 | −1.37249 | −0.686246 | − | 0.727369i | \(-0.740743\pi\) | ||||
−0.686246 | + | 0.727369i | \(0.740743\pi\) | |||||||
\(564\) | −16.1556 | −0.680272 | ||||||||
\(565\) | 2.74889 | 0.115647 | ||||||||
\(566\) | 22.9340 | 0.963987 | ||||||||
\(567\) | −10.0148 | −0.420583 | ||||||||
\(568\) | 29.5088 | 1.23816 | ||||||||
\(569\) | −23.3009 | −0.976825 | −0.488413 | − | 0.872613i | \(-0.662424\pi\) | ||||
−0.488413 | + | 0.872613i | \(0.662424\pi\) | |||||||
\(570\) | 5.52173 | 0.231280 | ||||||||
\(571\) | −40.6108 | −1.69951 | −0.849754 | − | 0.527179i | \(-0.823250\pi\) | ||||
−0.849754 | + | 0.527179i | \(0.823250\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28.1156 | 1.17455 | ||||||||
\(574\) | 10.7530 | 0.448821 | ||||||||
\(575\) | 5.96633 | 0.248813 | ||||||||
\(576\) | 30.6400 | 1.27667 | ||||||||
\(577\) | −13.8348 | −0.575949 | −0.287974 | − | 0.957638i | \(-0.592982\pi\) | ||||
−0.287974 | + | 0.957638i | \(0.592982\pi\) | |||||||
\(578\) | 35.7952 | 1.48888 | ||||||||
\(579\) | 11.1077 | 0.461620 | ||||||||
\(580\) | −4.28771 | −0.178038 | ||||||||
\(581\) | −7.14492 | −0.296421 | ||||||||
\(582\) | −41.8169 | −1.73337 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 10.5631 | 0.437102 | ||||||||
\(585\) | −19.3774 | −0.801157 | ||||||||
\(586\) | 25.1578 | 1.03926 | ||||||||
\(587\) | 4.36970 | 0.180357 | 0.0901784 | − | 0.995926i | \(-0.471256\pi\) | ||||
0.0901784 | + | 0.995926i | \(0.471256\pi\) | |||||||
\(588\) | −1.55539 | −0.0641433 | ||||||||
\(589\) | −10.0261 | −0.413117 | ||||||||
\(590\) | 11.2671 | 0.463857 | ||||||||
\(591\) | 25.4873 | 1.04841 | ||||||||
\(592\) | −16.0649 | −0.660263 | ||||||||
\(593\) | −31.5379 | −1.29511 | −0.647553 | − | 0.762020i | \(-0.724208\pi\) | ||||
−0.647553 | + | 0.762020i | \(0.724208\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.29047 | −0.257884 | ||||||||
\(596\) | −7.95739 | −0.325947 | ||||||||
\(597\) | −65.9183 | −2.69786 | ||||||||
\(598\) | −30.0025 | −1.22689 | ||||||||
\(599\) | −8.49529 | −0.347108 | −0.173554 | − | 0.984824i | \(-0.555525\pi\) | ||||
−0.173554 | + | 0.984824i | \(0.555525\pi\) | |||||||
\(600\) | 7.10769 | 0.290170 | ||||||||
\(601\) | −33.3257 | −1.35938 | −0.679692 | − | 0.733497i | \(-0.737887\pi\) | ||||
−0.679692 | + | 0.733497i | \(0.737887\pi\) | |||||||
\(602\) | 8.11688 | 0.330819 | ||||||||
\(603\) | −53.2447 | −2.16829 | ||||||||
\(604\) | 6.63010 | 0.269775 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 23.6321 | 0.959990 | ||||||||
\(607\) | 5.85092 | 0.237481 | 0.118741 | − | 0.992925i | \(-0.462114\pi\) | ||||
0.118741 | + | 0.992925i | \(0.462114\pi\) | |||||||
\(608\) | 3.28472 | 0.133213 | ||||||||
\(609\) | −25.1171 | −1.01780 | ||||||||
\(610\) | −11.5331 | −0.466961 | ||||||||
\(611\) | −32.9335 | −1.33235 | ||||||||
\(612\) | 19.8094 | 0.800746 | ||||||||
\(613\) | −15.9665 | −0.644879 | −0.322440 | − | 0.946590i | \(-0.604503\pi\) | ||||
−0.322440 | + | 0.946590i | \(0.604503\pi\) | |||||||
\(614\) | 50.6832 | 2.04541 | ||||||||
\(615\) | 20.4657 | 0.825258 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.3079 | −1.26041 | −0.630205 | − | 0.776429i | \(-0.717029\pi\) | ||||
−0.630205 | + | 0.776429i | \(0.717029\pi\) | |||||||
\(618\) | 55.4779 | 2.23165 | ||||||||
\(619\) | 19.9543 | 0.802032 | 0.401016 | − | 0.916071i | \(-0.368657\pi\) | ||||
0.401016 | + | 0.916071i | \(0.368657\pi\) | |||||||
\(620\) | 4.47909 | 0.179885 | ||||||||
\(621\) | −56.0341 | −2.24857 | ||||||||
\(622\) | −54.2041 | −2.17339 | ||||||||
\(623\) | −0.654265 | −0.0262126 | ||||||||
\(624\) | −45.6054 | −1.82568 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.2736 | 0.450583 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.36133 | −0.0543229 | ||||||||
\(629\) | 21.2077 | 0.845605 | ||||||||
\(630\) | −9.69244 | −0.386156 | ||||||||
\(631\) | −44.6493 | −1.77746 | −0.888730 | − | 0.458431i | \(-0.848412\pi\) | ||||
−0.888730 | + | 0.458431i | \(0.848412\pi\) | |||||||
\(632\) | −7.77068 | −0.309101 | ||||||||
\(633\) | 33.7749 | 1.34243 | ||||||||
\(634\) | −12.5903 | −0.500026 | ||||||||
\(635\) | 0.801691 | 0.0318141 | ||||||||
\(636\) | 12.7375 | 0.505073 | ||||||||
\(637\) | −3.17071 | −0.125628 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −76.5869 | −3.02973 | ||||||||
\(640\) | 13.6470 | 0.539444 | ||||||||
\(641\) | 30.5351 | 1.20607 | 0.603033 | − | 0.797716i | \(-0.293959\pi\) | ||||
0.603033 | + | 0.797716i | \(0.293959\pi\) | |||||||
\(642\) | −73.9186 | −2.91733 | ||||||||
\(643\) | 40.8926 | 1.61265 | 0.806324 | − | 0.591474i | \(-0.201454\pi\) | ||||
0.806324 | + | 0.591474i | \(0.201454\pi\) | |||||||
\(644\) | −3.07437 | −0.121147 | ||||||||
\(645\) | 15.4485 | 0.608286 | ||||||||
\(646\) | −11.5071 | −0.452741 | ||||||||
\(647\) | −16.6431 | −0.654307 | −0.327154 | − | 0.944971i | \(-0.606089\pi\) | ||||
−0.327154 | + | 0.944971i | \(0.606089\pi\) | |||||||
\(648\) | −23.5819 | −0.926386 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.02863 | −0.197239 | ||||||||
\(651\) | 26.2382 | 1.02835 | ||||||||
\(652\) | −6.97918 | −0.273326 | ||||||||
\(653\) | −4.44966 | −0.174129 | −0.0870644 | − | 0.996203i | \(-0.527749\pi\) | ||||
−0.0870644 | + | 0.996203i | \(0.527749\pi\) | |||||||
\(654\) | 89.4804 | 3.49896 | ||||||||
\(655\) | −12.4209 | −0.485326 | ||||||||
\(656\) | 32.3075 | 1.26140 | ||||||||
\(657\) | −27.4153 | −1.06957 | ||||||||
\(658\) | −16.4731 | −0.642189 | ||||||||
\(659\) | 35.0740 | 1.36629 | 0.683145 | − | 0.730283i | \(-0.260612\pi\) | ||||
0.683145 | + | 0.730283i | \(0.260612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.9685 | 1.20453 | 0.602267 | − | 0.798295i | \(-0.294264\pi\) | ||||
0.602267 | + | 0.798295i | \(0.294264\pi\) | |||||||
\(662\) | −42.8186 | −1.66419 | ||||||||
\(663\) | 60.2048 | 2.33816 | ||||||||
\(664\) | −16.8242 | −0.652905 | ||||||||
\(665\) | 1.15342 | 0.0447279 | ||||||||
\(666\) | 32.6771 | 1.26621 | ||||||||
\(667\) | −49.6461 | −1.92230 | ||||||||
\(668\) | −10.5161 | −0.406880 | ||||||||
\(669\) | 27.4372 | 1.06078 | ||||||||
\(670\) | −13.8175 | −0.533818 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −8.59609 | −0.331602 | ||||||||
\(673\) | 9.33892 | 0.359989 | 0.179995 | − | 0.983668i | \(-0.442392\pi\) | ||||
0.179995 | + | 0.983668i | \(0.442392\pi\) | |||||||
\(674\) | −9.51093 | −0.366347 | ||||||||
\(675\) | −9.39172 | −0.361487 | ||||||||
\(676\) | −1.51834 | −0.0583978 | ||||||||
\(677\) | −20.4271 | −0.785076 | −0.392538 | − | 0.919736i | \(-0.628403\pi\) | ||||
−0.392538 | + | 0.919736i | \(0.628403\pi\) | |||||||
\(678\) | −13.1596 | −0.505392 | ||||||||
\(679\) | −8.73507 | −0.335221 | ||||||||
\(680\) | −14.8122 | −0.568022 | ||||||||
\(681\) | 1.14286 | 0.0437945 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.7278 | 1.06098 | 0.530488 | − | 0.847693i | \(-0.322009\pi\) | ||||
0.530488 | + | 0.847693i | \(0.322009\pi\) | |||||||
\(684\) | −3.63226 | −0.138883 | ||||||||
\(685\) | −19.1100 | −0.730156 | ||||||||
\(686\) | −1.58597 | −0.0605524 | ||||||||
\(687\) | 11.8527 | 0.452208 | ||||||||
\(688\) | 24.3873 | 0.929756 | ||||||||
\(689\) | 25.9656 | 0.989211 | ||||||||
\(690\) | −28.5623 | −1.08735 | ||||||||
\(691\) | 36.1009 | 1.37334 | 0.686672 | − | 0.726967i | \(-0.259071\pi\) | ||||
0.686672 | + | 0.726967i | \(0.259071\pi\) | |||||||
\(692\) | −6.46155 | −0.245631 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.53259 | 0.0961356 | ||||||||
\(695\) | 2.87837 | 0.109183 | ||||||||
\(696\) | −59.1434 | −2.24182 | ||||||||
\(697\) | −42.6499 | −1.61548 | ||||||||
\(698\) | 2.57697 | 0.0975398 | ||||||||
\(699\) | −60.7340 | −2.29717 | ||||||||
\(700\) | −0.515286 | −0.0194760 | ||||||||
\(701\) | 42.8713 | 1.61923 | 0.809614 | − | 0.586963i | \(-0.199677\pi\) | ||||
0.809614 | + | 0.586963i | \(0.199677\pi\) | |||||||
\(702\) | 47.2275 | 1.78249 | ||||||||
\(703\) | −3.88865 | −0.146663 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.3526 | −1.18081 | ||||||||
\(706\) | 16.8383 | 0.633716 | ||||||||
\(707\) | 4.93648 | 0.185655 | ||||||||
\(708\) | −11.0499 | −0.415279 | ||||||||
\(709\) | −30.1475 | −1.13221 | −0.566106 | − | 0.824333i | \(-0.691551\pi\) | ||||
−0.566106 | + | 0.824333i | \(0.691551\pi\) | |||||||
\(710\) | −19.8751 | −0.745899 | ||||||||
\(711\) | 20.1680 | 0.756357 | ||||||||
\(712\) | −1.54060 | −0.0577365 | ||||||||
\(713\) | 51.8620 | 1.94225 | ||||||||
\(714\) | 30.1140 | 1.12699 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.94194 | −0.222061 | ||||||||
\(717\) | 69.8286 | 2.60780 | ||||||||
\(718\) | −28.2736 | −1.05516 | ||||||||
\(719\) | −45.5833 | −1.69997 | −0.849986 | − | 0.526805i | \(-0.823390\pi\) | ||||
−0.849986 | + | 0.526805i | \(0.823390\pi\) | |||||||
\(720\) | −29.1210 | −1.08528 | ||||||||
\(721\) | 11.5887 | 0.431585 | ||||||||
\(722\) | −28.0234 | −1.04292 | ||||||||
\(723\) | 66.0045 | 2.45473 | ||||||||
\(724\) | −1.16296 | −0.0432211 | ||||||||
\(725\) | −8.32104 | −0.309036 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.4698 | 0.610831 | 0.305416 | − | 0.952219i | \(-0.401205\pi\) | ||||
0.305416 | + | 0.952219i | \(0.401205\pi\) | |||||||
\(728\) | −7.46608 | −0.276711 | ||||||||
\(729\) | −23.8425 | −0.883056 | ||||||||
\(730\) | −7.11454 | −0.263321 | ||||||||
\(731\) | −32.1943 | −1.19075 | ||||||||
\(732\) | 11.3108 | 0.418058 | ||||||||
\(733\) | −19.9387 | −0.736453 | −0.368227 | − | 0.929736i | \(-0.620035\pi\) | ||||
−0.368227 | + | 0.929736i | \(0.620035\pi\) | |||||||
\(734\) | 39.4962 | 1.45783 | ||||||||
\(735\) | −3.01851 | −0.111339 | ||||||||
\(736\) | −16.9909 | −0.626293 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −65.7156 | −2.41902 | ||||||||
\(739\) | −7.42054 | −0.272969 | −0.136485 | − | 0.990642i | \(-0.543580\pi\) | ||||
−0.136485 | + | 0.990642i | \(0.543580\pi\) | |||||||
\(740\) | 1.73723 | 0.0638620 | ||||||||
\(741\) | −11.0392 | −0.405535 | ||||||||
\(742\) | 12.9878 | 0.476798 | ||||||||
\(743\) | −19.5947 | −0.718859 | −0.359429 | − | 0.933172i | \(-0.617029\pi\) | ||||
−0.359429 | + | 0.933172i | \(0.617029\pi\) | |||||||
\(744\) | 61.7831 | 2.26508 | ||||||||
\(745\) | −15.4427 | −0.565776 | ||||||||
\(746\) | −4.15649 | −0.152180 | ||||||||
\(747\) | 43.6653 | 1.59763 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.4407 | −0.564192 | ||||||||
\(750\) | −4.78725 | −0.174806 | ||||||||
\(751\) | −26.0399 | −0.950209 | −0.475105 | − | 0.879929i | \(-0.657590\pi\) | ||||
−0.475105 | + | 0.879929i | \(0.657590\pi\) | |||||||
\(752\) | −49.4937 | −1.80485 | ||||||||
\(753\) | 71.2186 | 2.59535 | ||||||||
\(754\) | 41.8435 | 1.52385 | ||||||||
\(755\) | 12.8668 | 0.468272 | ||||||||
\(756\) | 4.83942 | 0.176008 | ||||||||
\(757\) | 50.1682 | 1.82339 | 0.911697 | − | 0.410862i | \(-0.134772\pi\) | ||||
0.911697 | + | 0.410862i | \(0.134772\pi\) | |||||||
\(758\) | −1.84733 | −0.0670979 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.71597 | 0.0985187 | ||||||||
\(761\) | 49.1453 | 1.78152 | 0.890759 | − | 0.454477i | \(-0.150174\pi\) | ||||
0.890759 | + | 0.454477i | \(0.150174\pi\) | |||||||
\(762\) | −3.83789 | −0.139032 | ||||||||
\(763\) | 18.6914 | 0.676674 | ||||||||
\(764\) | −4.79958 | −0.173643 | ||||||||
\(765\) | 38.4434 | 1.38992 | ||||||||
\(766\) | −20.0985 | −0.726187 | ||||||||
\(767\) | −22.5254 | −0.813346 | ||||||||
\(768\) | −35.0643 | −1.26527 | ||||||||
\(769\) | −12.7595 | −0.460120 | −0.230060 | − | 0.973176i | \(-0.573892\pi\) | ||||
−0.230060 | + | 0.973176i | \(0.573892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.3121 | −0.407394 | ||||||||
\(772\) | −1.89618 | −0.0682451 | ||||||||
\(773\) | −15.4282 | −0.554915 | −0.277457 | − | 0.960738i | \(-0.589492\pi\) | ||||
−0.277457 | + | 0.960738i | \(0.589492\pi\) | |||||||
\(774\) | −49.6053 | −1.78303 | ||||||||
\(775\) | 8.69244 | 0.312241 | ||||||||
\(776\) | −20.5685 | −0.738367 | ||||||||
\(777\) | 10.1766 | 0.365083 | ||||||||
\(778\) | 41.3745 | 1.48335 | ||||||||
\(779\) | 7.82032 | 0.280192 | ||||||||
\(780\) | 4.93170 | 0.176583 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 59.5229 | 2.12853 | ||||||||
\(783\) | 78.1488 | 2.79281 | ||||||||
\(784\) | −4.76505 | −0.170180 | ||||||||
\(785\) | −2.64189 | −0.0942931 | ||||||||
\(786\) | 59.4621 | 2.12094 | ||||||||
\(787\) | −19.1854 | −0.683885 | −0.341942 | − | 0.939721i | \(-0.611085\pi\) | ||||
−0.341942 | + | 0.939721i | \(0.611085\pi\) | |||||||
\(788\) | −4.35092 | −0.154995 | ||||||||
\(789\) | −61.8408 | −2.20159 | ||||||||
\(790\) | 5.23379 | 0.186210 | ||||||||
\(791\) | −2.74889 | −0.0977392 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.0573 | 0.818788 | ||||||||
\(794\) | 39.4713 | 1.40078 | ||||||||
\(795\) | 24.7192 | 0.876700 | ||||||||
\(796\) | 11.2528 | 0.398846 | ||||||||
\(797\) | −35.4716 | −1.25647 | −0.628235 | − | 0.778024i | \(-0.716222\pi\) | ||||
−0.628235 | + | 0.778024i | \(0.716222\pi\) | |||||||
\(798\) | −5.52173 | −0.195467 | ||||||||
\(799\) | 65.3379 | 2.31149 | ||||||||
\(800\) | −2.84780 | −0.100685 | ||||||||
\(801\) | 3.99846 | 0.141279 | ||||||||
\(802\) | 46.3722 | 1.63746 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 13.5512 | 0.477913 | ||||||||
\(805\) | −5.96633 | −0.210286 | ||||||||
\(806\) | −43.7111 | −1.53966 | ||||||||
\(807\) | 88.8817 | 3.12879 | ||||||||
\(808\) | 11.6239 | 0.408929 | ||||||||
\(809\) | 22.3975 | 0.787453 | 0.393726 | − | 0.919228i | \(-0.371186\pi\) | ||||
0.393726 | + | 0.919228i | \(0.371186\pi\) | |||||||
\(810\) | 15.8832 | 0.558077 | ||||||||
\(811\) | −5.90988 | −0.207524 | −0.103762 | − | 0.994602i | \(-0.533088\pi\) | ||||
−0.103762 | + | 0.994602i | \(0.533088\pi\) | |||||||
\(812\) | 4.28771 | 0.150469 | ||||||||
\(813\) | −56.4336 | −1.97921 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.5443 | −0.474436 | ||||||||
\(816\) | 90.4779 | 3.16736 | ||||||||
\(817\) | 5.90316 | 0.206525 | ||||||||
\(818\) | −3.52868 | −0.123378 | ||||||||
\(819\) | 19.3774 | 0.677101 | ||||||||
\(820\) | −3.49368 | −0.122005 | ||||||||
\(821\) | 47.8343 | 1.66943 | 0.834715 | − | 0.550682i | \(-0.185632\pi\) | ||||
0.834715 | + | 0.550682i | \(0.185632\pi\) | |||||||
\(822\) | 91.4843 | 3.19088 | ||||||||
\(823\) | 9.18303 | 0.320100 | 0.160050 | − | 0.987109i | \(-0.448834\pi\) | ||||
0.160050 | + | 0.987109i | \(0.448834\pi\) | |||||||
\(824\) | 27.2879 | 0.950620 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.2671 | −0.392031 | ||||||||
\(827\) | −34.8116 | −1.21052 | −0.605259 | − | 0.796028i | \(-0.706931\pi\) | ||||
−0.605259 | + | 0.796028i | \(0.706931\pi\) | |||||||
\(828\) | 18.7886 | 0.652950 | ||||||||
\(829\) | 21.3407 | 0.741194 | 0.370597 | − | 0.928794i | \(-0.379153\pi\) | ||||
0.370597 | + | 0.928794i | \(0.379153\pi\) | |||||||
\(830\) | 11.3316 | 0.393326 | ||||||||
\(831\) | 57.7288 | 2.00259 | ||||||||
\(832\) | −15.8967 | −0.551117 | ||||||||
\(833\) | 6.29047 | 0.217952 | ||||||||
\(834\) | −13.7795 | −0.477144 | ||||||||
\(835\) | −20.4083 | −0.706258 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −81.6369 | −2.82178 | ||||||||
\(838\) | 42.5904 | 1.47126 | ||||||||
\(839\) | −24.9743 | −0.862209 | −0.431105 | − | 0.902302i | \(-0.641876\pi\) | ||||
−0.431105 | + | 0.902302i | \(0.641876\pi\) | |||||||
\(840\) | −7.10769 | −0.245239 | ||||||||
\(841\) | 40.2397 | 1.38757 | ||||||||
\(842\) | 54.4814 | 1.87755 | ||||||||
\(843\) | −9.32848 | −0.321290 | ||||||||
\(844\) | −5.76568 | −0.198463 | ||||||||
\(845\) | −2.94661 | −0.101366 | ||||||||
\(846\) | 100.673 | 3.46123 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 39.0220 | 1.34002 | ||||||||
\(849\) | −43.6494 | −1.49804 | ||||||||
\(850\) | 9.97646 | 0.342190 | ||||||||
\(851\) | 20.1149 | 0.689529 | ||||||||
\(852\) | 19.4920 | 0.667784 | ||||||||
\(853\) | 0.765445 | 0.0262083 | 0.0131042 | − | 0.999914i | \(-0.495829\pi\) | ||||
0.0131042 | + | 0.999914i | \(0.495829\pi\) | |||||||
\(854\) | 11.5331 | 0.394654 | ||||||||
\(855\) | −7.04901 | −0.241071 | ||||||||
\(856\) | −36.3584 | −1.24270 | ||||||||
\(857\) | 0.632460 | 0.0216044 | 0.0108022 | − | 0.999942i | \(-0.496561\pi\) | ||||
0.0108022 | + | 0.999942i | \(0.496561\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.43917 | 0.253821 | 0.126911 | − | 0.991914i | \(-0.459494\pi\) | ||||
0.126911 | + | 0.991914i | \(0.459494\pi\) | |||||||
\(860\) | −2.63720 | −0.0899279 | ||||||||
\(861\) | −20.4657 | −0.697471 | ||||||||
\(862\) | 42.2651 | 1.43955 | ||||||||
\(863\) | −58.4772 | −1.99059 | −0.995294 | − | 0.0968976i | \(-0.969108\pi\) | ||||
−0.995294 | + | 0.0968976i | \(0.969108\pi\) | |||||||
\(864\) | 26.7457 | 0.909907 | ||||||||
\(865\) | −12.5397 | −0.426364 | ||||||||
\(866\) | −0.218630 | −0.00742934 | ||||||||
\(867\) | −68.1276 | −2.31373 | ||||||||
\(868\) | −4.47909 | −0.152030 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 39.8349 | 1.35053 | ||||||||
\(871\) | 27.6244 | 0.936018 | ||||||||
\(872\) | 44.0128 | 1.49046 | ||||||||
\(873\) | 53.3833 | 1.80675 | ||||||||
\(874\) | −10.9142 | −0.369177 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 6.97740 | 0.235744 | ||||||||
\(877\) | 29.1727 | 0.985093 | 0.492546 | − | 0.870286i | \(-0.336066\pi\) | ||||
0.492546 | + | 0.870286i | \(0.336066\pi\) | |||||||
\(878\) | −5.23801 | −0.176774 | ||||||||
\(879\) | −47.8819 | −1.61502 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.474047 | 0.0159711 | 0.00798553 | − | 0.999968i | \(-0.497458\pi\) | ||||
0.00798553 | + | 0.999968i | \(0.497458\pi\) | |||||||
\(882\) | 9.69244 | 0.326361 | ||||||||
\(883\) | 6.21786 | 0.209248 | 0.104624 | − | 0.994512i | \(-0.466636\pi\) | ||||
0.104624 | + | 0.994512i | \(0.466636\pi\) | |||||||
\(884\) | −10.2775 | −0.345670 | ||||||||
\(885\) | −21.4441 | −0.720837 | ||||||||
\(886\) | −7.07864 | −0.237811 | ||||||||
\(887\) | 5.89043 | 0.197781 | 0.0988906 | − | 0.995098i | \(-0.468471\pi\) | ||||
0.0988906 | + | 0.995098i | \(0.468471\pi\) | |||||||
\(888\) | 23.9629 | 0.804141 | ||||||||
\(889\) | −0.801691 | −0.0268879 | ||||||||
\(890\) | 1.03764 | 0.0347818 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.68377 | −0.156824 | ||||||||
\(893\) | −11.9804 | −0.400909 | ||||||||
\(894\) | 73.9279 | 2.47252 | ||||||||
\(895\) | −11.5313 | −0.385450 | ||||||||
\(896\) | −13.6470 | −0.455914 | ||||||||
\(897\) | 57.1026 | 1.90660 | ||||||||
\(898\) | −29.8835 | −0.997225 | ||||||||
\(899\) | −72.3301 | −2.41234 | ||||||||
\(900\) | 3.14911 | 0.104970 | ||||||||
\(901\) | −51.5140 | −1.71618 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.4485 | −0.514095 | ||||||||
\(904\) | −6.47282 | −0.215283 | ||||||||
\(905\) | −2.25692 | −0.0750226 | ||||||||
\(906\) | −61.5967 | −2.04641 | ||||||||
\(907\) | 6.97336 | 0.231547 | 0.115773 | − | 0.993276i | \(-0.463065\pi\) | ||||
0.115773 | + | 0.993276i | \(0.463065\pi\) | |||||||
\(908\) | −0.195096 | −0.00647450 | ||||||||
\(909\) | −30.1687 | −1.00063 | ||||||||
\(910\) | 5.02863 | 0.166698 | ||||||||
\(911\) | −25.4630 | −0.843626 | −0.421813 | − | 0.906683i | \(-0.638606\pi\) | ||||
−0.421813 | + | 0.906683i | \(0.638606\pi\) | |||||||
\(912\) | −16.5901 | −0.549353 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 7.00408 | 0.231674 | ||||||||
\(915\) | 21.9505 | 0.725660 | ||||||||
\(916\) | −2.02336 | −0.0668536 | ||||||||
\(917\) | 12.4209 | 0.410176 | ||||||||
\(918\) | −93.6961 | −3.09243 | ||||||||
\(919\) | −27.0003 | −0.890658 | −0.445329 | − | 0.895367i | \(-0.646913\pi\) | ||||
−0.445329 | + | 0.895367i | \(0.646913\pi\) | |||||||
\(920\) | −14.0490 | −0.463180 | ||||||||
\(921\) | −96.4633 | −3.17858 | ||||||||
\(922\) | 23.8038 | 0.783936 | ||||||||
\(923\) | 39.7349 | 1.30789 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.37140 | 0.110851 | ||||||||
\(926\) | 8.33914 | 0.274041 | ||||||||
\(927\) | −70.8228 | −2.32613 | ||||||||
\(928\) | 23.6966 | 0.777880 | ||||||||
\(929\) | 0.622063 | 0.0204092 | 0.0102046 | − | 0.999948i | \(-0.496752\pi\) | ||||
0.0102046 | + | 0.999948i | \(0.496752\pi\) | |||||||
\(930\) | −41.6128 | −1.36454 | ||||||||
\(931\) | −1.15342 | −0.0378020 | ||||||||
\(932\) | 10.3678 | 0.339609 | ||||||||
\(933\) | 103.164 | 3.37745 | ||||||||
\(934\) | 15.6531 | 0.512183 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 45.6281 | 1.49140 | ||||||||
\(937\) | −29.3023 | −0.957263 | −0.478631 | − | 0.878016i | \(-0.658867\pi\) | ||||
−0.478631 | + | 0.878016i | \(0.658867\pi\) | |||||||
\(938\) | 13.8175 | 0.451159 | ||||||||
\(939\) | −21.4566 | −0.700209 | ||||||||
\(940\) | 5.35218 | 0.174569 | ||||||||
\(941\) | −8.77735 | −0.286133 | −0.143067 | − | 0.989713i | \(-0.545696\pi\) | ||||
−0.143067 | + | 0.989713i | \(0.545696\pi\) | |||||||
\(942\) | 12.6474 | 0.412074 | ||||||||
\(943\) | −40.4523 | −1.31731 | ||||||||
\(944\) | −33.8520 | −1.10179 | ||||||||
\(945\) | 9.39172 | 0.305513 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.4838 | −1.38054 | −0.690269 | − | 0.723553i | \(-0.742508\pi\) | ||||
−0.690269 | + | 0.723553i | \(0.742508\pi\) | |||||||
\(948\) | −5.13290 | −0.166709 | ||||||||
\(949\) | 14.2236 | 0.461717 | ||||||||
\(950\) | −1.82929 | −0.0593500 | ||||||||
\(951\) | 23.9627 | 0.777044 | ||||||||
\(952\) | 14.8122 | 0.480066 | ||||||||
\(953\) | −29.1406 | −0.943958 | −0.471979 | − | 0.881610i | \(-0.656460\pi\) | ||||
−0.471979 | + | 0.881610i | \(0.656460\pi\) | |||||||
\(954\) | −79.3734 | −2.56981 | ||||||||
\(955\) | −9.31441 | −0.301407 | ||||||||
\(956\) | −11.9204 | −0.385532 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −28.7232 | −0.928006 | ||||||||
\(959\) | 19.1100 | 0.617094 | ||||||||
\(960\) | −15.1336 | −0.488434 | ||||||||
\(961\) | 44.5584 | 1.43737 | ||||||||
\(962\) | −16.9535 | −0.546604 | ||||||||
\(963\) | 94.3642 | 3.04084 | ||||||||
\(964\) | −11.2676 | −0.362904 | ||||||||
\(965\) | −3.67986 | −0.118459 | ||||||||
\(966\) | 28.5623 | 0.918977 | ||||||||
\(967\) | 4.05314 | 0.130340 | 0.0651701 | − | 0.997874i | \(-0.479241\pi\) | ||||
0.0651701 | + | 0.997874i | \(0.479241\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.9010 | 0.703562 | ||||||||
\(970\) | 13.8535 | 0.444810 | ||||||||
\(971\) | −5.05440 | −0.162203 | −0.0811016 | − | 0.996706i | \(-0.525844\pi\) | ||||
−0.0811016 | + | 0.996706i | \(0.525844\pi\) | |||||||
\(972\) | −1.05873 | −0.0339587 | ||||||||
\(973\) | −2.87837 | −0.0922763 | ||||||||
\(974\) | 33.1260 | 1.06143 | ||||||||
\(975\) | 9.57080 | 0.306511 | ||||||||
\(976\) | 34.6513 | 1.10916 | ||||||||
\(977\) | −10.3457 | −0.330987 | −0.165494 | − | 0.986211i | \(-0.552922\pi\) | ||||
−0.165494 | + | 0.986211i | \(0.552922\pi\) | |||||||
\(978\) | 64.8399 | 2.07335 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.515286 | 0.0164602 | ||||||||
\(981\) | −114.230 | −3.64709 | ||||||||
\(982\) | 44.5572 | 1.42188 | ||||||||
\(983\) | 35.5145 | 1.13274 | 0.566369 | − | 0.824152i | \(-0.308348\pi\) | ||||
0.566369 | + | 0.824152i | \(0.308348\pi\) | |||||||
\(984\) | −48.1908 | −1.53627 | ||||||||
\(985\) | −8.44369 | −0.269038 | ||||||||
\(986\) | −83.0145 | −2.64372 | ||||||||
\(987\) | 31.3526 | 0.997966 | ||||||||
\(988\) | 1.88449 | 0.0599536 | ||||||||
\(989\) | −30.5354 | −0.970968 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.9460 | 1.68188 | 0.840942 | − | 0.541126i | \(-0.182002\pi\) | ||||
0.840942 | + | 0.541126i | \(0.182002\pi\) | |||||||
\(992\) | −24.7543 | −0.785950 | ||||||||
\(993\) | 81.4949 | 2.58616 | ||||||||
\(994\) | 19.8751 | 0.630399 | ||||||||
\(995\) | 21.8381 | 0.692313 | ||||||||
\(996\) | −11.1132 | −0.352134 | ||||||||
\(997\) | 23.2468 | 0.736233 | 0.368117 | − | 0.929780i | \(-0.380003\pi\) | ||||
0.368117 | + | 0.929780i | \(0.380003\pi\) | |||||||
\(998\) | 2.96852 | 0.0939667 | ||||||||
\(999\) | −31.6632 | −1.00178 |
(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 | 4235.2.a.bc.1.4 | ✓ | 5 | |
11.10 | odd | 2 | 4235.2.a.bd.1.2 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4235.2.a.bc.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
4235.2.a.bd.1.2 | yes | 5 | 11.10 | odd | 2 |