Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.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: | \(31.6926245622\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.574857.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 9x^{2} + 3x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.38687\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.38687 | 1.68777 | 0.843886 | − | 0.536523i | \(-0.180263\pi\) | ||||
0.843886 | + | 0.536523i | \(0.180263\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.69714 | 1.84857 | ||||||||
\(5\) | −2.92087 | −1.30625 | −0.653125 | − | 0.757250i | \(-0.726543\pi\) | ||||
−0.653125 | + | 0.757250i | \(0.726543\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 4.05086 | 1.43219 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.97172 | −2.20465 | ||||||||
\(11\) | 1.35371 | 0.408160 | 0.204080 | − | 0.978954i | \(-0.434580\pi\) | ||||
0.204080 | + | 0.978954i | \(0.434580\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.46600 | −0.406596 | −0.203298 | − | 0.979117i | \(-0.565166\pi\) | ||||
−0.203298 | + | 0.979117i | \(0.565166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.27458 | 0.568645 | ||||||||
\(17\) | −3.31027 | −0.802859 | −0.401430 | − | 0.915890i | \(-0.631487\pi\) | ||||
−0.401430 | + | 0.915890i | \(0.631487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.20659 | −0.506226 | −0.253113 | − | 0.967437i | \(-0.581454\pi\) | ||||
−0.253113 | + | 0.967437i | \(0.581454\pi\) | |||||||
\(20\) | −10.7989 | −2.41470 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.23114 | 0.688881 | ||||||||
\(23\) | −2.62830 | −0.548038 | −0.274019 | − | 0.961724i | \(-0.588353\pi\) | ||||
−0.274019 | + | 0.961724i | \(0.588353\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.53146 | 0.706292 | ||||||||
\(26\) | −3.49916 | −0.686241 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.04344 | 0.193762 | 0.0968810 | − | 0.995296i | \(-0.469113\pi\) | ||||
0.0968810 | + | 0.995296i | \(0.469113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.27458 | −0.588132 | −0.294066 | − | 0.955785i | \(-0.595009\pi\) | ||||
−0.294066 | + | 0.955785i | \(0.595009\pi\) | |||||||
\(32\) | −2.67259 | −0.472452 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.90119 | −1.35504 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.8755 | −1.78791 | −0.893957 | − | 0.448153i | \(-0.852082\pi\) | ||||
−0.893957 | + | 0.448153i | \(0.852082\pi\) | |||||||
\(38\) | −5.26683 | −0.854393 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11.8320 | −1.87081 | ||||||||
\(41\) | 1.80858 | 0.282452 | 0.141226 | − | 0.989977i | \(-0.454896\pi\) | ||||
0.141226 | + | 0.989977i | \(0.454896\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.34257 | 0.662236 | 0.331118 | − | 0.943589i | \(-0.392574\pi\) | ||||
0.331118 | + | 0.943589i | \(0.392574\pi\) | |||||||
\(44\) | 5.00488 | 0.754514 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.27340 | −0.924962 | ||||||||
\(47\) | 3.97914 | 0.580417 | 0.290209 | − | 0.956963i | \(-0.406275\pi\) | ||||
0.290209 | + | 0.956963i | \(0.406275\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 8.42913 | 1.19206 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.42002 | −0.751622 | ||||||||
\(53\) | −6.45486 | −0.886644 | −0.443322 | − | 0.896363i | \(-0.646200\pi\) | ||||
−0.443322 | + | 0.896363i | \(0.646200\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.95402 | −0.533160 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.49056 | 0.327026 | ||||||||
\(59\) | −12.2140 | −1.59013 | −0.795064 | − | 0.606526i | \(-0.792563\pi\) | ||||
−0.795064 | + | 0.606526i | \(0.792563\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.559734 | −0.0716666 | −0.0358333 | − | 0.999358i | \(-0.511409\pi\) | ||||
−0.0358333 | + | 0.999358i | \(0.511409\pi\) | |||||||
\(62\) | −7.81600 | −0.992632 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.9283 | −1.36604 | ||||||||
\(65\) | 4.28200 | 0.531117 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.8118 | 1.56521 | 0.782603 | − | 0.622521i | \(-0.213891\pi\) | ||||
0.782603 | + | 0.622521i | \(0.213891\pi\) | |||||||
\(68\) | −12.2386 | −1.48414 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.9177 | −1.53305 | −0.766525 | − | 0.642214i | \(-0.778016\pi\) | ||||
−0.766525 | + | 0.642214i | \(0.778016\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4554 | 1.22372 | 0.611858 | − | 0.790968i | \(-0.290422\pi\) | ||||
0.611858 | + | 0.790968i | \(0.290422\pi\) | |||||||
\(74\) | −25.9583 | −3.01759 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.15807 | −0.935794 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.767677 | 0.0863704 | 0.0431852 | − | 0.999067i | \(-0.486249\pi\) | ||||
0.0431852 | + | 0.999067i | \(0.486249\pi\) | |||||||
\(80\) | −6.64375 | −0.742793 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.31684 | 0.476715 | ||||||||
\(83\) | 1.96741 | 0.215952 | 0.107976 | − | 0.994154i | \(-0.465563\pi\) | ||||
0.107976 | + | 0.994154i | \(0.465563\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.66887 | 1.04874 | ||||||||
\(86\) | 10.3652 | 1.11770 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.48371 | 0.584565 | ||||||||
\(89\) | −6.40711 | −0.679153 | −0.339576 | − | 0.940579i | \(-0.610284\pi\) | ||||
−0.339576 | + | 0.940579i | \(0.610284\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.71719 | −1.01309 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.49769 | 0.979612 | ||||||||
\(95\) | 6.44514 | 0.661258 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.28285 | −0.840996 | −0.420498 | − | 0.907293i | \(-0.638145\pi\) | ||||
−0.420498 | + | 0.907293i | \(0.638145\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 13.0563 | 1.30563 | ||||||||
\(101\) | −16.2266 | −1.61461 | −0.807305 | − | 0.590134i | \(-0.799075\pi\) | ||||
−0.807305 | + | 0.590134i | \(0.799075\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.22683 | 0.219416 | 0.109708 | − | 0.993964i | \(-0.465008\pi\) | ||||
0.109708 | + | 0.993964i | \(0.465008\pi\) | |||||||
\(104\) | −5.93857 | −0.582325 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.4069 | −1.49645 | ||||||||
\(107\) | −17.5081 | −1.69257 | −0.846284 | − | 0.532732i | \(-0.821165\pi\) | ||||
−0.846284 | + | 0.532732i | \(0.821165\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.5983 | 1.49405 | 0.747025 | − | 0.664796i | \(-0.231482\pi\) | ||||
0.747025 | + | 0.664796i | \(0.231482\pi\) | |||||||
\(110\) | −9.43773 | −0.899852 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.68911 | −0.158898 | −0.0794491 | − | 0.996839i | \(-0.525316\pi\) | ||||
−0.0794491 | + | 0.996839i | \(0.525316\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.67690 | 0.715875 | ||||||||
\(116\) | 3.85775 | 0.358183 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −29.1532 | −2.68377 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.16746 | −0.833405 | ||||||||
\(122\) | −1.33601 | −0.120957 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.1066 | −1.08720 | ||||||||
\(125\) | 4.28942 | 0.383657 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.96918 | −0.352208 | −0.176104 | − | 0.984372i | \(-0.556350\pi\) | ||||
−0.176104 | + | 0.984372i | \(0.556350\pi\) | |||||||
\(128\) | −20.7392 | −1.83310 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.2206 | 0.896403 | ||||||||
\(131\) | 5.32863 | 0.465565 | 0.232782 | − | 0.972529i | \(-0.425217\pi\) | ||||
0.232782 | + | 0.972529i | \(0.425217\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 30.5800 | 2.64171 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.4095 | −1.14985 | ||||||||
\(137\) | 7.49543 | 0.640378 | 0.320189 | − | 0.947354i | \(-0.396254\pi\) | ||||
0.320189 | + | 0.947354i | \(0.396254\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0657 | 1.19304 | 0.596518 | − | 0.802600i | \(-0.296550\pi\) | ||||
0.596518 | + | 0.802600i | \(0.296550\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −30.8329 | −2.58744 | ||||||||
\(143\) | −1.98455 | −0.165956 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.04775 | −0.253102 | ||||||||
\(146\) | 24.9557 | 2.06535 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −40.2081 | −3.30509 | ||||||||
\(149\) | −2.17971 | −0.178569 | −0.0892846 | − | 0.996006i | \(-0.528458\pi\) | ||||
−0.0892846 | + | 0.996006i | \(0.528458\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0277 | 1.14156 | 0.570781 | − | 0.821102i | \(-0.306641\pi\) | ||||
0.570781 | + | 0.821102i | \(0.306641\pi\) | |||||||
\(152\) | −8.93857 | −0.725014 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.56461 | 0.768248 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.96623 | −0.236731 | −0.118365 | − | 0.992970i | \(-0.537765\pi\) | ||||
−0.118365 | + | 0.992970i | \(0.537765\pi\) | |||||||
\(158\) | 1.83234 | 0.145773 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.80628 | 0.617140 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.388555 | 0.0304340 | 0.0152170 | − | 0.999884i | \(-0.495156\pi\) | ||||
0.0152170 | + | 0.999884i | \(0.495156\pi\) | |||||||
\(164\) | 6.68657 | 0.522133 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.69596 | 0.364477 | ||||||||
\(167\) | −7.29778 | −0.564719 | −0.282360 | − | 0.959309i | \(-0.591117\pi\) | ||||
−0.282360 | + | 0.959309i | \(0.591117\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8508 | −0.834680 | ||||||||
\(170\) | 23.0783 | 1.77003 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 16.0551 | 1.22419 | ||||||||
\(173\) | −4.05508 | −0.308302 | −0.154151 | − | 0.988047i | \(-0.549264\pi\) | ||||
−0.154151 | + | 0.988047i | \(0.549264\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.07913 | 0.232098 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.2929 | −1.14625 | ||||||||
\(179\) | 10.5849 | 0.791149 | 0.395575 | − | 0.918434i | \(-0.370545\pi\) | ||||
0.395575 | + | 0.918434i | \(0.370545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.6312 | 1.45917 | 0.729586 | − | 0.683889i | \(-0.239713\pi\) | ||||
0.729586 | + | 0.683889i | \(0.239713\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.6469 | −0.784896 | ||||||||
\(185\) | 31.7657 | 2.33546 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.48117 | −0.327695 | ||||||||
\(188\) | 14.7115 | 1.07294 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.3837 | 1.11605 | ||||||||
\(191\) | −8.28714 | −0.599637 | −0.299818 | − | 0.953996i | \(-0.596926\pi\) | ||||
−0.299818 | + | 0.953996i | \(0.596926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.7848 | −1.35216 | −0.676082 | − | 0.736827i | \(-0.736323\pi\) | ||||
−0.676082 | + | 0.736827i | \(0.736323\pi\) | |||||||
\(194\) | −19.7701 | −1.41941 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.99634 | −0.427222 | −0.213611 | − | 0.976919i | \(-0.568522\pi\) | ||||
−0.213611 | + | 0.976919i | \(0.568522\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.4087 | 1.02140 | 0.510702 | − | 0.859758i | \(-0.329385\pi\) | ||||
0.510702 | + | 0.859758i | \(0.329385\pi\) | |||||||
\(200\) | 14.3054 | 1.01155 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −38.7308 | −2.72509 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.28261 | −0.368954 | ||||||||
\(206\) | 5.31515 | 0.370324 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.33454 | −0.231209 | ||||||||
\(209\) | −2.98709 | −0.206621 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8484 | 0.953360 | 0.476680 | − | 0.879077i | \(-0.341840\pi\) | ||||
0.476680 | + | 0.879077i | \(0.341840\pi\) | |||||||
\(212\) | −23.8646 | −1.63902 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −41.7894 | −2.85667 | ||||||||
\(215\) | −12.6841 | −0.865047 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 37.2312 | 2.52161 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −14.6186 | −0.985584 | ||||||||
\(221\) | 4.85287 | 0.326439 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.67513 | 0.313070 | 0.156535 | − | 0.987672i | \(-0.449968\pi\) | ||||
0.156535 | + | 0.987672i | \(0.449968\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.03169 | −0.268184 | ||||||||
\(227\) | 19.7126 | 1.30837 | 0.654187 | − | 0.756333i | \(-0.273011\pi\) | ||||
0.654187 | + | 0.756333i | \(0.273011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.0728 | −1.85510 | −0.927552 | − | 0.373694i | \(-0.878091\pi\) | ||||
−0.927552 | + | 0.373694i | \(0.878091\pi\) | |||||||
\(230\) | 18.3238 | 1.20823 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.22683 | 0.277505 | ||||||||
\(233\) | −13.8023 | −0.904216 | −0.452108 | − | 0.891963i | \(-0.649328\pi\) | ||||
−0.452108 | + | 0.891963i | \(0.649328\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.6225 | −0.758171 | ||||||||
\(236\) | −45.1569 | −2.93947 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.0614 | 0.715501 | 0.357751 | − | 0.933817i | \(-0.383544\pi\) | ||||
0.357751 | + | 0.933817i | \(0.383544\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.1697 | 1.49249 | 0.746247 | − | 0.665669i | \(-0.231854\pi\) | ||||
0.746247 | + | 0.665669i | \(0.231854\pi\) | |||||||
\(242\) | −21.8815 | −1.40660 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.06942 | −0.132481 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.23486 | 0.205829 | ||||||||
\(248\) | −13.2649 | −0.842320 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.2383 | 0.647525 | ||||||||
\(251\) | −7.78402 | −0.491323 | −0.245662 | − | 0.969356i | \(-0.579005\pi\) | ||||
−0.245662 | + | 0.969356i | \(0.579005\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.55796 | −0.223687 | ||||||||
\(254\) | −9.47392 | −0.594447 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27.6452 | −1.72782 | ||||||||
\(257\) | 10.3760 | 0.647235 | 0.323618 | − | 0.946188i | \(-0.395101\pi\) | ||||
0.323618 | + | 0.946188i | \(0.395101\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 15.8312 | 0.981807 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.7187 | 0.785767 | ||||||||
\(263\) | 19.1331 | 1.17980 | 0.589898 | − | 0.807478i | \(-0.299168\pi\) | ||||
0.589898 | + | 0.807478i | \(0.299168\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.8538 | 1.15818 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 47.3669 | 2.89340 | ||||||||
\(269\) | 8.83681 | 0.538790 | 0.269395 | − | 0.963030i | \(-0.413176\pi\) | ||||
0.269395 | + | 0.963030i | \(0.413176\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.3391 | −1.11402 | −0.557010 | − | 0.830506i | \(-0.688052\pi\) | ||||
−0.557010 | + | 0.830506i | \(0.688052\pi\) | |||||||
\(272\) | −7.52949 | −0.456542 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.8906 | 1.08081 | ||||||||
\(275\) | 4.78059 | 0.288280 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.10482 | 0.306719 | 0.153360 | − | 0.988170i | \(-0.450991\pi\) | ||||
0.153360 | + | 0.988170i | \(0.450991\pi\) | |||||||
\(278\) | 33.5730 | 2.01357 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.70636 | −0.101793 | −0.0508964 | − | 0.998704i | \(-0.516208\pi\) | ||||
−0.0508964 | + | 0.998704i | \(0.516208\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.4883 | 0.742352 | 0.371176 | − | 0.928562i | \(-0.378955\pi\) | ||||
0.371176 | + | 0.928562i | \(0.378955\pi\) | |||||||
\(284\) | −47.7586 | −2.83395 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.73686 | −0.280096 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.04208 | −0.355417 | ||||||||
\(290\) | −7.27458 | −0.427178 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 38.6552 | 2.26213 | ||||||||
\(293\) | 5.20405 | 0.304024 | 0.152012 | − | 0.988379i | \(-0.451425\pi\) | ||||
0.152012 | + | 0.988379i | \(0.451425\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 35.6755 | 2.07711 | ||||||||
\(296\) | −44.0549 | −2.56064 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.20269 | −0.301384 | ||||||||
\(299\) | 3.85309 | 0.222830 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 33.4824 | 1.92669 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.01906 | −0.287863 | ||||||||
\(305\) | 1.63491 | 0.0936145 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.00136 | −0.285442 | −0.142721 | − | 0.989763i | \(-0.545585\pi\) | ||||
−0.142721 | + | 0.989763i | \(0.545585\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 22.8295 | 1.29663 | ||||||||
\(311\) | −32.3968 | −1.83706 | −0.918528 | − | 0.395355i | \(-0.870621\pi\) | ||||
−0.918528 | + | 0.395355i | \(0.870621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.51907 | −0.0858629 | −0.0429315 | − | 0.999078i | \(-0.513670\pi\) | ||||
−0.0429315 | + | 0.999078i | \(0.513670\pi\) | |||||||
\(314\) | −7.08000 | −0.399548 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.83821 | 0.159662 | ||||||||
\(317\) | 21.5089 | 1.20806 | 0.604029 | − | 0.796962i | \(-0.293561\pi\) | ||||
0.604029 | + | 0.796962i | \(0.293561\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.41252 | 0.0790860 | ||||||||
\(320\) | 31.9200 | 1.78439 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.30441 | 0.406428 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.17713 | −0.287175 | ||||||||
\(326\) | 0.927430 | 0.0513656 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.32629 | 0.404527 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.4780 | 1.07061 | 0.535305 | − | 0.844659i | \(-0.320197\pi\) | ||||
0.535305 | + | 0.844659i | \(0.320197\pi\) | |||||||
\(332\) | 7.27381 | 0.399202 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.4188 | −0.953116 | ||||||||
\(335\) | −37.4215 | −2.04455 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.69484 | −0.528112 | −0.264056 | − | 0.964507i | \(-0.585060\pi\) | ||||
−0.264056 | + | 0.964507i | \(0.585060\pi\) | |||||||
\(338\) | −25.8995 | −1.40875 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 35.7472 | 1.93866 | ||||||||
\(341\) | −4.43285 | −0.240052 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 17.5912 | 0.948451 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.67895 | −0.520344 | ||||||||
\(347\) | −2.02604 | −0.108763 | −0.0543817 | − | 0.998520i | \(-0.517319\pi\) | ||||
−0.0543817 | + | 0.998520i | \(0.517319\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.2915 | 0.872066 | 0.436033 | − | 0.899931i | \(-0.356383\pi\) | ||||
0.436033 | + | 0.899931i | \(0.356383\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.61792 | −0.192836 | ||||||||
\(353\) | 17.0614 | 0.908089 | 0.454045 | − | 0.890979i | \(-0.349981\pi\) | ||||
0.454045 | + | 0.890979i | \(0.349981\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.7309 | 2.00255 | ||||||||
\(356\) | −23.6880 | −1.25546 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.2647 | 1.33528 | ||||||||
\(359\) | 2.96726 | 0.156606 | 0.0783030 | − | 0.996930i | \(-0.475050\pi\) | ||||
0.0783030 | + | 0.996930i | \(0.475050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.1310 | −0.743736 | ||||||||
\(362\) | 46.8570 | 2.46275 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.5389 | −1.59848 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.1575 | 0.530216 | 0.265108 | − | 0.964219i | \(-0.414592\pi\) | ||||
0.265108 | + | 0.964219i | \(0.414592\pi\) | |||||||
\(368\) | −5.97827 | −0.311639 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 75.8207 | 3.94173 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.4846 | −1.31954 | −0.659771 | − | 0.751467i | \(-0.729347\pi\) | ||||
−0.659771 | + | 0.751467i | \(0.729347\pi\) | |||||||
\(374\) | −10.6960 | −0.553075 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.1189 | 0.831271 | ||||||||
\(377\) | −1.52969 | −0.0787829 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.85497 | 0.506216 | 0.253108 | − | 0.967438i | \(-0.418547\pi\) | ||||
0.253108 | + | 0.967438i | \(0.418547\pi\) | |||||||
\(380\) | 23.8286 | 1.22238 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −19.7803 | −1.01205 | ||||||||
\(383\) | −27.3127 | −1.39561 | −0.697806 | − | 0.716286i | \(-0.745840\pi\) | ||||
−0.697806 | + | 0.716286i | \(0.745840\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −44.8370 | −2.28214 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −30.6229 | −1.55464 | ||||||||
\(389\) | −4.18446 | −0.212161 | −0.106080 | − | 0.994358i | \(-0.533830\pi\) | ||||
−0.106080 | + | 0.994358i | \(0.533830\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.70038 | 0.439997 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.3125 | −0.721053 | ||||||||
\(395\) | −2.24228 | −0.112821 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.6709 | 1.53933 | 0.769664 | − | 0.638450i | \(-0.220424\pi\) | ||||
0.769664 | + | 0.638450i | \(0.220424\pi\) | |||||||
\(398\) | 34.3916 | 1.72390 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.03259 | 0.401629 | ||||||||
\(401\) | 6.84803 | 0.341974 | 0.170987 | − | 0.985273i | \(-0.445304\pi\) | ||||
0.170987 | + | 0.985273i | \(0.445304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.80055 | 0.239132 | ||||||||
\(404\) | −59.9922 | −2.98472 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.7223 | −0.729756 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.2698 | 0.903384 | 0.451692 | − | 0.892174i | \(-0.350821\pi\) | ||||
0.451692 | + | 0.892174i | \(0.350821\pi\) | |||||||
\(410\) | −12.6089 | −0.622709 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.23291 | 0.405606 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.74655 | −0.282087 | ||||||||
\(416\) | 3.91802 | 0.192097 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.12979 | −0.348729 | ||||||||
\(419\) | −22.4619 | −1.09734 | −0.548669 | − | 0.836040i | \(-0.684865\pi\) | ||||
−0.548669 | + | 0.836040i | \(0.684865\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.8354 | −1.01546 | −0.507728 | − | 0.861517i | \(-0.669515\pi\) | ||||
−0.507728 | + | 0.861517i | \(0.669515\pi\) | |||||||
\(422\) | 33.0542 | 1.60905 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −26.1477 | −1.26985 | ||||||||
\(425\) | −11.6901 | −0.567053 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −64.7298 | −3.12883 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −30.2752 | −1.46000 | ||||||||
\(431\) | −20.2427 | −0.975055 | −0.487527 | − | 0.873108i | \(-0.662101\pi\) | ||||
−0.487527 | + | 0.873108i | \(0.662101\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.6764 | 1.04170 | 0.520851 | − | 0.853648i | \(-0.325615\pi\) | ||||
0.520851 | + | 0.853648i | \(0.325615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 57.6693 | 2.76186 | ||||||||
\(437\) | 5.79956 | 0.277431 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.4781 | 1.69328 | 0.846639 | − | 0.532168i | \(-0.178623\pi\) | ||||
0.846639 | + | 0.532168i | \(0.178623\pi\) | |||||||
\(440\) | −16.0172 | −0.763589 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.5832 | 0.550955 | ||||||||
\(443\) | 19.2063 | 0.912517 | 0.456258 | − | 0.889847i | \(-0.349189\pi\) | ||||
0.456258 | + | 0.889847i | \(0.349189\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.7143 | 0.887144 | ||||||||
\(446\) | 11.1589 | 0.528390 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.6082 | 1.39730 | 0.698648 | − | 0.715465i | \(-0.253785\pi\) | ||||
0.698648 | + | 0.715465i | \(0.253785\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.44830 | 0.115286 | ||||||||
\(452\) | −6.24488 | −0.293735 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 47.0515 | 2.20823 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.56196 | −0.447290 | −0.223645 | − | 0.974671i | \(-0.571796\pi\) | ||||
−0.223645 | + | 0.974671i | \(0.571796\pi\) | |||||||
\(458\) | −67.0062 | −3.13099 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 28.3826 | 1.32335 | ||||||||
\(461\) | −21.8374 | −1.01707 | −0.508536 | − | 0.861041i | \(-0.669813\pi\) | ||||
−0.508536 | + | 0.861041i | \(0.669813\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.1489 | −1.21524 | −0.607621 | − | 0.794227i | \(-0.707876\pi\) | ||||
−0.607621 | + | 0.794227i | \(0.707876\pi\) | |||||||
\(464\) | 2.37339 | 0.110182 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −32.9442 | −1.52611 | ||||||||
\(467\) | 34.9527 | 1.61742 | 0.808709 | − | 0.588209i | \(-0.200167\pi\) | ||||
0.808709 | + | 0.588209i | \(0.200167\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −27.7415 | −1.27962 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −49.4772 | −2.27737 | ||||||||
\(473\) | 5.87861 | 0.270299 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.79247 | −0.357543 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 26.4021 | 1.20760 | ||||||||
\(479\) | −29.8109 | −1.36209 | −0.681047 | − | 0.732240i | \(-0.738475\pi\) | ||||
−0.681047 | + | 0.732240i | \(0.738475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.9434 | 0.726959 | ||||||||
\(482\) | 55.3031 | 2.51899 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −33.8934 | −1.54061 | ||||||||
\(485\) | 24.1931 | 1.09855 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.4506 | 1.01733 | 0.508667 | − | 0.860964i | \(-0.330139\pi\) | ||||
0.508667 | + | 0.860964i | \(0.330139\pi\) | |||||||
\(488\) | −2.26740 | −0.102640 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.0444 | 1.58153 | 0.790767 | − | 0.612118i | \(-0.209682\pi\) | ||||
0.790767 | + | 0.612118i | \(0.209682\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.45407 | −0.155564 | ||||||||
\(494\) | 7.72119 | 0.347393 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.44830 | −0.334438 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.93520 | −0.399994 | −0.199997 | − | 0.979796i | \(-0.564093\pi\) | ||||
−0.199997 | + | 0.979796i | \(0.564093\pi\) | |||||||
\(500\) | 15.8586 | 0.709217 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.5794 | −0.829241 | ||||||||
\(503\) | −12.6403 | −0.563603 | −0.281802 | − | 0.959473i | \(-0.590932\pi\) | ||||
−0.281802 | + | 0.959473i | \(0.590932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 47.3958 | 2.10909 | ||||||||
\(506\) | −8.49239 | −0.377533 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.6746 | −0.651082 | ||||||||
\(509\) | −28.1110 | −1.24600 | −0.623000 | − | 0.782222i | \(-0.714086\pi\) | ||||
−0.623000 | + | 0.782222i | \(0.714086\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −24.5070 | −1.08307 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.7661 | 1.09238 | ||||||||
\(515\) | −6.50427 | −0.286613 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.38662 | 0.236903 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.3458 | 0.760662 | ||||||||
\(521\) | −8.47536 | −0.371312 | −0.185656 | − | 0.982615i | \(-0.559441\pi\) | ||||
−0.185656 | + | 0.982615i | \(0.559441\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.4473 | 1.46255 | 0.731273 | − | 0.682085i | \(-0.238926\pi\) | ||||
0.731273 | + | 0.682085i | \(0.238926\pi\) | |||||||
\(524\) | 19.7007 | 0.860630 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 45.6681 | 1.99123 | ||||||||
\(527\) | 10.8398 | 0.472187 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.0921 | −0.699655 | ||||||||
\(530\) | 45.0015 | 1.95474 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.65138 | −0.114844 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 51.1387 | 2.21092 | ||||||||
\(536\) | 51.8987 | 2.24168 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.0923 | 0.909354 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.2586 | 0.784998 | 0.392499 | − | 0.919752i | \(-0.371611\pi\) | ||||
0.392499 | + | 0.919752i | \(0.371611\pi\) | |||||||
\(542\) | −43.7730 | −1.88021 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.84701 | 0.379312 | ||||||||
\(545\) | −45.5606 | −1.95160 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.77199 | 0.246792 | 0.123396 | − | 0.992357i | \(-0.460621\pi\) | ||||
0.123396 | + | 0.992357i | \(0.460621\pi\) | |||||||
\(548\) | 27.7117 | 1.18378 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.4106 | 0.486551 | ||||||||
\(551\) | −2.30244 | −0.0980874 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.1845 | 0.517672 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 52.0029 | 2.20541 | ||||||||
\(557\) | 33.3821 | 1.41445 | 0.707223 | − | 0.706991i | \(-0.249948\pi\) | ||||
0.707223 | + | 0.706991i | \(0.249948\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.36623 | −0.269263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.07286 | −0.171803 | ||||||||
\(563\) | 2.19131 | 0.0923528 | 0.0461764 | − | 0.998933i | \(-0.485296\pi\) | ||||
0.0461764 | + | 0.998933i | \(0.485296\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.93367 | 0.207561 | ||||||||
\(566\) | 29.8079 | 1.25292 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −52.3278 | −2.19563 | ||||||||
\(569\) | −18.9860 | −0.795936 | −0.397968 | − | 0.917399i | \(-0.630284\pi\) | ||||
−0.397968 | + | 0.917399i | \(0.630284\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.7380 | −0.909709 | −0.454854 | − | 0.890566i | \(-0.650309\pi\) | ||||
−0.454854 | + | 0.890566i | \(0.650309\pi\) | |||||||
\(572\) | −7.33717 | −0.306782 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.28172 | −0.387074 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.9032 | −1.28652 | −0.643258 | − | 0.765649i | \(-0.722418\pi\) | ||||
−0.643258 | + | 0.765649i | \(0.722418\pi\) | |||||||
\(578\) | −14.4217 | −0.599862 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.2680 | −0.467877 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.73804 | −0.361893 | ||||||||
\(584\) | 42.3535 | 1.75260 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.4214 | 0.513122 | ||||||||
\(587\) | 18.3666 | 0.758072 | 0.379036 | − | 0.925382i | \(-0.376256\pi\) | ||||
0.379036 | + | 0.925382i | \(0.376256\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.22565 | 0.297728 | ||||||||
\(590\) | 85.1527 | 3.50568 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.7371 | −1.01669 | ||||||||
\(593\) | −27.7550 | −1.13976 | −0.569880 | − | 0.821728i | \(-0.693010\pi\) | ||||
−0.569880 | + | 0.821728i | \(0.693010\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.05871 | −0.330098 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.19682 | 0.376086 | ||||||||
\(599\) | −0.402823 | −0.0164589 | −0.00822945 | − | 0.999966i | \(-0.502620\pi\) | ||||
−0.00822945 | + | 0.999966i | \(0.502620\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.7466 | 1.00943 | 0.504717 | − | 0.863285i | \(-0.331597\pi\) | ||||
0.504717 | + | 0.863285i | \(0.331597\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 51.8626 | 2.11026 | ||||||||
\(605\) | 26.7769 | 1.08864 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0697 | −0.976957 | −0.488479 | − | 0.872576i | \(-0.662448\pi\) | ||||
−0.488479 | + | 0.872576i | \(0.662448\pi\) | |||||||
\(608\) | 5.89730 | 0.239167 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.90231 | 0.158000 | ||||||||
\(611\) | −5.83343 | −0.235995 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.3815 | −0.823200 | −0.411600 | − | 0.911365i | \(-0.635030\pi\) | ||||
−0.411600 | + | 0.911365i | \(0.635030\pi\) | |||||||
\(614\) | −11.9376 | −0.481762 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.8629 | −1.68534 | −0.842669 | − | 0.538431i | \(-0.819017\pi\) | ||||
−0.842669 | + | 0.538431i | \(0.819017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.8219 | −0.595743 | −0.297871 | − | 0.954606i | \(-0.596277\pi\) | ||||
−0.297871 | + | 0.954606i | \(0.596277\pi\) | |||||||
\(620\) | 35.3617 | 1.42016 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −77.3270 | −3.10053 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.1861 | −1.20744 | ||||||||
\(626\) | −3.62582 | −0.144917 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.9666 | −0.437614 | ||||||||
\(629\) | 36.0007 | 1.43544 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.0294 | −0.837169 | −0.418585 | − | 0.908178i | \(-0.637474\pi\) | ||||
−0.418585 | + | 0.908178i | \(0.637474\pi\) | |||||||
\(632\) | 3.10975 | 0.123699 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 51.3388 | 2.03893 | ||||||||
\(635\) | 11.5935 | 0.460072 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.37150 | 0.133479 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 60.5764 | 2.39449 | ||||||||
\(641\) | −11.9318 | −0.471279 | −0.235640 | − | 0.971840i | \(-0.575719\pi\) | ||||
−0.235640 | + | 0.971840i | \(0.575719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.9355 | −1.57490 | −0.787452 | − | 0.616377i | \(-0.788600\pi\) | ||||
−0.787452 | + | 0.616377i | \(0.788600\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.4347 | 0.685958 | ||||||||
\(647\) | −0.988954 | −0.0388798 | −0.0194399 | − | 0.999811i | \(-0.506188\pi\) | ||||
−0.0194399 | + | 0.999811i | \(0.506188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.5343 | −0.649027 | ||||||||
\(650\) | −12.3571 | −0.484686 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.43654 | 0.0562594 | ||||||||
\(653\) | −22.7147 | −0.888894 | −0.444447 | − | 0.895805i | \(-0.646600\pi\) | ||||
−0.444447 | + | 0.895805i | \(0.646600\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.5642 | −0.608144 | ||||||||
\(656\) | 4.11376 | 0.160615 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.3885 | −1.49540 | −0.747702 | − | 0.664035i | \(-0.768843\pi\) | ||||
−0.747702 | + | 0.664035i | \(0.768843\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.9258 | −1.31956 | −0.659780 | − | 0.751459i | \(-0.729351\pi\) | ||||
−0.659780 | + | 0.751459i | \(0.729351\pi\) | |||||||
\(662\) | 46.4915 | 1.80694 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.96972 | 0.309285 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.74247 | −0.106189 | ||||||||
\(668\) | −26.9809 | −1.04392 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −89.3201 | −3.45074 | ||||||||
\(671\) | −0.757720 | −0.0292514 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.2060 | 1.24145 | 0.620725 | − | 0.784028i | \(-0.286838\pi\) | ||||
0.620725 | + | 0.784028i | \(0.286838\pi\) | |||||||
\(674\) | −23.1403 | −0.891332 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −40.1171 | −1.54297 | ||||||||
\(677\) | −37.9684 | −1.45924 | −0.729622 | − | 0.683850i | \(-0.760304\pi\) | ||||
−0.729622 | + | 0.683850i | \(0.760304\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 39.1672 | 1.50199 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.5806 | −0.405153 | ||||||||
\(683\) | 15.1871 | 0.581120 | 0.290560 | − | 0.956857i | \(-0.406158\pi\) | ||||
0.290560 | + | 0.956857i | \(0.406158\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.8932 | −0.836495 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.87754 | 0.376578 | ||||||||
\(689\) | 9.46285 | 0.360506 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.69148 | −0.102389 | −0.0511943 | − | 0.998689i | \(-0.516303\pi\) | ||||
−0.0511943 | + | 0.998689i | \(0.516303\pi\) | |||||||
\(692\) | −14.9922 | −0.569919 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.83589 | −0.183568 | ||||||||
\(695\) | −41.0840 | −1.55841 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.98689 | −0.226770 | ||||||||
\(698\) | 38.8858 | 1.47185 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.8515 | 0.447625 | 0.223813 | − | 0.974632i | \(-0.428150\pi\) | ||||
0.223813 | + | 0.974632i | \(0.428150\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.9976 | 0.905088 | ||||||||
\(704\) | −14.7938 | −0.557562 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 40.7234 | 1.53265 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.0333 | −1.54104 | −0.770520 | − | 0.637416i | \(-0.780003\pi\) | ||||
−0.770520 | + | 0.637416i | \(0.780003\pi\) | |||||||
\(710\) | 90.0587 | 3.37984 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −25.9543 | −0.972679 | ||||||||
\(713\) | 8.60657 | 0.322318 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.79660 | 0.216781 | ||||||||
\(716\) | 39.1337 | 1.46250 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.08246 | 0.264315 | ||||||||
\(719\) | −20.9109 | −0.779845 | −0.389923 | − | 0.920848i | \(-0.627498\pi\) | ||||
−0.389923 | + | 0.920848i | \(0.627498\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −33.7288 | −1.25526 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 72.5792 | 2.69738 | ||||||||
\(725\) | 3.68487 | 0.136853 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.64330 | 0.0980347 | 0.0490173 | − | 0.998798i | \(-0.484391\pi\) | ||||
0.0490173 | + | 0.998798i | \(0.484391\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −72.8924 | −2.69787 | ||||||||
\(731\) | −14.3751 | −0.531683 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.1489 | −0.522602 | −0.261301 | − | 0.965257i | \(-0.584152\pi\) | ||||
−0.261301 | + | 0.965257i | \(0.584152\pi\) | |||||||
\(734\) | 24.2446 | 0.894884 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.02436 | 0.258921 | ||||||||
\(737\) | 17.3435 | 0.638855 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7181 | 0.578200 | 0.289100 | − | 0.957299i | \(-0.406644\pi\) | ||||
0.289100 | + | 0.957299i | \(0.406644\pi\) | |||||||
\(740\) | 117.442 | 4.31727 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.0991 | 0.774051 | 0.387026 | − | 0.922069i | \(-0.373503\pi\) | ||||
0.387026 | + | 0.922069i | \(0.373503\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.36665 | 0.233256 | ||||||||
\(746\) | −60.8283 | −2.22708 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16.5675 | −0.605768 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0370 | 0.475725 | 0.237863 | − | 0.971299i | \(-0.423553\pi\) | ||||
0.237863 | + | 0.971299i | \(0.423553\pi\) | |||||||
\(752\) | 9.05088 | 0.330052 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.65116 | −0.132968 | ||||||||
\(755\) | −40.9732 | −1.49117 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.6856 | −0.461065 | −0.230532 | − | 0.973065i | \(-0.574047\pi\) | ||||
−0.230532 | + | 0.973065i | \(0.574047\pi\) | |||||||
\(758\) | 23.5225 | 0.854377 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 26.1084 | 0.947050 | ||||||||
\(761\) | −6.04077 | −0.218978 | −0.109489 | − | 0.993988i | \(-0.534921\pi\) | ||||
−0.109489 | + | 0.993988i | \(0.534921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −30.6388 | −1.10847 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −65.1918 | −2.35547 | ||||||||
\(767\) | 17.9058 | 0.646540 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.216258 | 0.00779848 | 0.00389924 | − | 0.999992i | \(-0.498759\pi\) | ||||
0.00389924 | + | 0.999992i | \(0.498759\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −69.4503 | −2.49957 | ||||||||
\(773\) | −37.6264 | −1.35333 | −0.676663 | − | 0.736293i | \(-0.736575\pi\) | ||||
−0.676663 | + | 0.736293i | \(0.736575\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.5640 | −0.415393 | ||||||||
\(776\) | −33.5527 | −1.20447 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.98776 | −0.358078 | ||||||||
\(779\) | −3.99078 | −0.142985 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.4869 | −0.625730 | ||||||||
\(782\) | 20.7667 | 0.742614 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.66396 | 0.309230 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.8135 | −1.09838 | −0.549191 | − | 0.835697i | \(-0.685064\pi\) | ||||
−0.549191 | + | 0.835697i | \(0.685064\pi\) | |||||||
\(788\) | −22.1693 | −0.789750 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.35203 | −0.190417 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.820571 | 0.0291393 | ||||||||
\(794\) | 73.2074 | 2.59803 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 53.2710 | 1.88814 | ||||||||
\(797\) | 35.9583 | 1.27371 | 0.636855 | − | 0.770984i | \(-0.280235\pi\) | ||||
0.636855 | + | 0.770984i | \(0.280235\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.1720 | −0.465994 | ||||||||
\(800\) | −9.43814 | −0.333689 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.3454 | 0.577174 | ||||||||
\(803\) | 14.1537 | 0.499472 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.4583 | 0.403600 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −65.7318 | −2.31244 | ||||||||
\(809\) | −38.9636 | −1.36989 | −0.684943 | − | 0.728596i | \(-0.740173\pi\) | ||||
−0.684943 | + | 0.728596i | \(0.740173\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.2811 | 0.993082 | 0.496541 | − | 0.868013i | \(-0.334603\pi\) | ||||
0.496541 | + | 0.868013i | \(0.334603\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −35.1401 | −1.23166 | ||||||||
\(815\) | −1.13492 | −0.0397544 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.58227 | −0.335241 | ||||||||
\(818\) | 43.6076 | 1.52471 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.5306 | −0.682037 | ||||||||
\(821\) | −41.5834 | −1.45127 | −0.725635 | − | 0.688080i | \(-0.758454\pi\) | ||||
−0.725635 | + | 0.688080i | \(0.758454\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.45998 | 0.294896 | 0.147448 | − | 0.989070i | \(-0.452894\pi\) | ||||
0.147448 | + | 0.989070i | \(0.452894\pi\) | |||||||
\(824\) | 9.02057 | 0.314247 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.2823 | −1.53985 | −0.769923 | − | 0.638137i | \(-0.779706\pi\) | ||||
−0.769923 | + | 0.638137i | \(0.779706\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.6327 | −0.577679 | −0.288839 | − | 0.957378i | \(-0.593269\pi\) | ||||
−0.288839 | + | 0.957378i | \(0.593269\pi\) | |||||||
\(830\) | −13.7163 | −0.476099 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16.0209 | 0.555425 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.3158 | 0.737665 | ||||||||
\(836\) | −11.0437 | −0.381954 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −53.6137 | −1.85205 | ||||||||
\(839\) | −29.6012 | −1.02195 | −0.510974 | − | 0.859596i | \(-0.670715\pi\) | ||||
−0.510974 | + | 0.859596i | \(0.670715\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9112 | −0.962456 | ||||||||
\(842\) | −49.7314 | −1.71386 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 51.1994 | 1.76236 | ||||||||
\(845\) | 31.6938 | 1.09030 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.6821 | −0.504186 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −27.9027 | −0.957055 | ||||||||
\(851\) | 28.5839 | 0.979844 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.1238 | −1.03142 | −0.515710 | − | 0.856763i | \(-0.672472\pi\) | ||||
−0.515710 | + | 0.856763i | \(0.672472\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −70.9227 | −2.42409 | ||||||||
\(857\) | 37.0894 | 1.26695 | 0.633475 | − | 0.773763i | \(-0.281628\pi\) | ||||
0.633475 | + | 0.773763i | \(0.281628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.78333 | 0.129085 | 0.0645427 | − | 0.997915i | \(-0.479441\pi\) | ||||
0.0645427 | + | 0.997915i | \(0.479441\pi\) | |||||||
\(860\) | −46.8949 | −1.59910 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −48.3166 | −1.64567 | ||||||||
\(863\) | 0.427118 | 0.0145393 | 0.00726963 | − | 0.999974i | \(-0.497686\pi\) | ||||
0.00726963 | + | 0.999974i | \(0.497686\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.8444 | 0.402720 | ||||||||
\(866\) | 51.7388 | 1.75815 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.03922 | 0.0352530 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.7821 | −0.636407 | ||||||||
\(872\) | 63.1866 | 2.13977 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.8428 | 0.468240 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.2608 | 0.380249 | 0.190124 | − | 0.981760i | \(-0.439111\pi\) | ||||
0.190124 | + | 0.981760i | \(0.439111\pi\) | |||||||
\(878\) | 84.6816 | 2.85786 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.99374 | −0.303179 | ||||||||
\(881\) | −35.4810 | −1.19538 | −0.597692 | − | 0.801726i | \(-0.703916\pi\) | ||||
−0.597692 | + | 0.801726i | \(0.703916\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.30092 | −0.178390 | −0.0891952 | − | 0.996014i | \(-0.528429\pi\) | ||||
−0.0891952 | + | 0.996014i | \(0.528429\pi\) | |||||||
\(884\) | 17.9418 | 0.603447 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 45.8428 | 1.54012 | ||||||||
\(887\) | 57.5664 | 1.93289 | 0.966446 | − | 0.256870i | \(-0.0826913\pi\) | ||||
0.966446 | + | 0.256870i | \(0.0826913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 44.6686 | 1.49730 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.2846 | 0.578732 | ||||||||
\(893\) | −8.78032 | −0.293822 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.9169 | −1.03344 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 70.6708 | 2.35832 | ||||||||
\(899\) | −3.41683 | −0.113958 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.3674 | 0.711850 | ||||||||
\(902\) | 5.84377 | 0.194576 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.84235 | −0.227573 | ||||||||
\(905\) | −57.3400 | −1.90605 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.8972 | 0.693879 | 0.346939 | − | 0.937888i | \(-0.387221\pi\) | ||||
0.346939 | + | 0.937888i | \(0.387221\pi\) | |||||||
\(908\) | 72.8804 | 2.41862 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.7639 | 0.754201 | 0.377101 | − | 0.926172i | \(-0.376921\pi\) | ||||
0.377101 | + | 0.926172i | \(0.376921\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.66332 | 0.0881430 | ||||||||
\(914\) | −22.8231 | −0.754923 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −103.789 | −3.42929 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.3030 | −1.23051 | −0.615257 | − | 0.788327i | \(-0.710948\pi\) | ||||
−0.615257 | + | 0.788327i | \(0.710948\pi\) | |||||||
\(920\) | 31.0980 | 1.02527 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −52.1231 | −1.71658 | ||||||||
\(923\) | 18.9374 | 0.623332 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −38.4062 | −1.26279 | ||||||||
\(926\) | −62.4140 | −2.05105 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.78869 | −0.0915432 | ||||||||
\(929\) | 5.66725 | 0.185937 | 0.0929683 | − | 0.995669i | \(-0.470364\pi\) | ||||
0.0929683 | + | 0.995669i | \(0.470364\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −51.0289 | −1.67151 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 83.4275 | 2.72983 | ||||||||
\(935\) | 13.0889 | 0.428052 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.64754 | 0.249834 | 0.124917 | − | 0.992167i | \(-0.460134\pi\) | ||||
0.124917 | + | 0.992167i | \(0.460134\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −42.9702 | −1.40153 | ||||||||
\(941\) | 20.4552 | 0.666819 | 0.333410 | − | 0.942782i | \(-0.391801\pi\) | ||||
0.333410 | + | 0.942782i | \(0.391801\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.75348 | −0.154795 | ||||||||
\(944\) | −27.7817 | −0.904219 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.0315 | 0.456202 | ||||||||
\(947\) | 4.76687 | 0.154902 | 0.0774512 | − | 0.996996i | \(-0.475322\pi\) | ||||
0.0774512 | + | 0.996996i | \(0.475322\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.3277 | −0.497558 | ||||||||
\(950\) | −18.5996 | −0.603451 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.9412 | 1.58536 | 0.792680 | − | 0.609638i | \(-0.208685\pi\) | ||||
0.792680 | + | 0.609638i | \(0.208685\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.2056 | 0.783276 | ||||||||
\(956\) | 40.8955 | 1.32266 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −71.1546 | −2.29890 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.2771 | −0.654101 | ||||||||
\(962\) | 38.0549 | 1.22694 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 85.6619 | 2.75898 | ||||||||
\(965\) | 54.8680 | 1.76626 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.91712 | 0.190282 | 0.0951409 | − | 0.995464i | \(-0.469670\pi\) | ||||
0.0951409 | + | 0.995464i | \(0.469670\pi\) | |||||||
\(968\) | −37.1361 | −1.19360 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 57.7458 | 1.85410 | ||||||||
\(971\) | −28.9775 | −0.929933 | −0.464966 | − | 0.885328i | \(-0.653934\pi\) | ||||
−0.464966 | + | 0.885328i | \(0.653934\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 53.5866 | 1.71703 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.27316 | −0.0407528 | ||||||||
\(977\) | −22.8455 | −0.730893 | −0.365447 | − | 0.930832i | \(-0.619084\pi\) | ||||
−0.365447 | + | 0.930832i | \(0.619084\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.67340 | −0.277203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 83.6465 | 2.66927 | ||||||||
\(983\) | −31.2703 | −0.997367 | −0.498684 | − | 0.866784i | \(-0.666183\pi\) | ||||
−0.498684 | + | 0.866784i | \(0.666183\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.5145 | 0.558059 | ||||||||
\(986\) | −8.24442 | −0.262556 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.9598 | 0.380490 | ||||||||
\(989\) | −11.4136 | −0.362930 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.01463 | −0.222827 | −0.111414 | − | 0.993774i | \(-0.535538\pi\) | ||||
−0.111414 | + | 0.993774i | \(0.535538\pi\) | |||||||
\(992\) | 8.75161 | 0.277864 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42.0858 | −1.33421 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.2878 | 0.674191 | 0.337095 | − | 0.941470i | \(-0.390555\pi\) | ||||
0.337095 | + | 0.941470i | \(0.390555\pi\) | |||||||
\(998\) | −21.3271 | −0.675099 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))