Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51152 | −1.77591 | −0.887957 | − | 0.459927i | \(-0.847876\pi\) | ||||
−0.887957 | + | 0.459927i | \(0.847876\pi\) | |||||||
\(3\) | −1.72847 | −0.997932 | −0.498966 | − | 0.866621i | \(-0.666287\pi\) | ||||
−0.498966 | + | 0.866621i | \(0.666287\pi\) | |||||||
\(4\) | 4.30774 | 2.15387 | ||||||||
\(5\) | −3.07277 | −1.37419 | −0.687093 | − | 0.726569i | \(-0.741114\pi\) | ||||
−0.687093 | + | 0.726569i | \(0.741114\pi\) | |||||||
\(6\) | 4.34109 | 1.77224 | ||||||||
\(7\) | −4.07006 | −1.53834 | −0.769169 | − | 0.639046i | \(-0.779329\pi\) | ||||
−0.769169 | + | 0.639046i | \(0.779329\pi\) | |||||||
\(8\) | −5.79593 | −2.04917 | ||||||||
\(9\) | −0.0123937 | −0.00413125 | ||||||||
\(10\) | 7.71734 | 2.44044 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −7.44579 | −2.14941 | ||||||||
\(13\) | 0.957676 | 0.265612 | 0.132806 | − | 0.991142i | \(-0.457601\pi\) | ||||
0.132806 | + | 0.991142i | \(0.457601\pi\) | |||||||
\(14\) | 10.2220 | 2.73195 | ||||||||
\(15\) | 5.31120 | 1.37134 | ||||||||
\(16\) | 5.94112 | 1.48528 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0.0311271 | 0.00733674 | ||||||||
\(19\) | −5.04648 | −1.15774 | −0.578871 | − | 0.815419i | \(-0.696506\pi\) | ||||
−0.578871 | + | 0.815419i | \(0.696506\pi\) | |||||||
\(20\) | −13.2367 | −2.95982 | ||||||||
\(21\) | 7.03497 | 1.53516 | ||||||||
\(22\) | −2.51152 | −0.535458 | ||||||||
\(23\) | 1.39295 | 0.290450 | 0.145225 | − | 0.989399i | \(-0.453609\pi\) | ||||
0.145225 | + | 0.989399i | \(0.453609\pi\) | |||||||
\(24\) | 10.0181 | 2.04493 | ||||||||
\(25\) | 4.44194 | 0.888388 | ||||||||
\(26\) | −2.40522 | −0.471703 | ||||||||
\(27\) | 5.20683 | 1.00205 | ||||||||
\(28\) | −17.5327 | −3.31338 | ||||||||
\(29\) | −8.87402 | −1.64786 | −0.823932 | − | 0.566688i | \(-0.808225\pi\) | ||||
−0.823932 | + | 0.566688i | \(0.808225\pi\) | |||||||
\(30\) | −13.3392 | −2.43539 | ||||||||
\(31\) | −0.871366 | −0.156502 | −0.0782509 | − | 0.996934i | \(-0.524934\pi\) | ||||
−0.0782509 | + | 0.996934i | \(0.524934\pi\) | |||||||
\(32\) | −3.32939 | −0.588558 | ||||||||
\(33\) | −1.72847 | −0.300888 | ||||||||
\(34\) | −2.51152 | −0.430722 | ||||||||
\(35\) | 12.5064 | 2.11396 | ||||||||
\(36\) | −0.0533890 | −0.00889816 | ||||||||
\(37\) | −3.42882 | −0.563694 | −0.281847 | − | 0.959459i | \(-0.590947\pi\) | ||||
−0.281847 | + | 0.959459i | \(0.590947\pi\) | |||||||
\(38\) | 12.6743 | 2.05605 | ||||||||
\(39\) | −1.65531 | −0.265062 | ||||||||
\(40\) | 17.8096 | 2.81594 | ||||||||
\(41\) | −4.61354 | −0.720513 | −0.360257 | − | 0.932853i | \(-0.617311\pi\) | ||||
−0.360257 | + | 0.932853i | \(0.617311\pi\) | |||||||
\(42\) | −17.6685 | −2.72630 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 4.30774 | 0.649416 | ||||||||
\(45\) | 0.0380832 | 0.00567710 | ||||||||
\(46\) | −3.49842 | −0.515814 | ||||||||
\(47\) | −10.9923 | −1.60339 | −0.801695 | − | 0.597734i | \(-0.796068\pi\) | ||||
−0.801695 | + | 0.597734i | \(0.796068\pi\) | |||||||
\(48\) | −10.2690 | −1.48221 | ||||||||
\(49\) | 9.56537 | 1.36648 | ||||||||
\(50\) | −11.1560 | −1.57770 | ||||||||
\(51\) | −1.72847 | −0.242034 | ||||||||
\(52\) | 4.12542 | 0.572092 | ||||||||
\(53\) | 7.25851 | 0.997034 | 0.498517 | − | 0.866880i | \(-0.333878\pi\) | ||||
0.498517 | + | 0.866880i | \(0.333878\pi\) | |||||||
\(54\) | −13.0771 | −1.77956 | ||||||||
\(55\) | −3.07277 | −0.414333 | ||||||||
\(56\) | 23.5898 | 3.15231 | ||||||||
\(57\) | 8.72268 | 1.15535 | ||||||||
\(58\) | 22.2873 | 2.92647 | ||||||||
\(59\) | −9.48152 | −1.23439 | −0.617194 | − | 0.786811i | \(-0.711731\pi\) | ||||
−0.617194 | + | 0.786811i | \(0.711731\pi\) | |||||||
\(60\) | 22.8792 | 2.95370 | ||||||||
\(61\) | −6.63668 | −0.849740 | −0.424870 | − | 0.905254i | \(-0.639680\pi\) | ||||
−0.424870 | + | 0.905254i | \(0.639680\pi\) | |||||||
\(62\) | 2.18845 | 0.277934 | ||||||||
\(63\) | 0.0504433 | 0.00635525 | ||||||||
\(64\) | −3.52041 | −0.440052 | ||||||||
\(65\) | −2.94272 | −0.365000 | ||||||||
\(66\) | 4.34109 | 0.534351 | ||||||||
\(67\) | −7.78213 | −0.950738 | −0.475369 | − | 0.879786i | \(-0.657686\pi\) | ||||
−0.475369 | + | 0.879786i | \(0.657686\pi\) | |||||||
\(68\) | 4.30774 | 0.522390 | ||||||||
\(69\) | −2.40767 | −0.289849 | ||||||||
\(70\) | −31.4100 | −3.75421 | ||||||||
\(71\) | −14.6845 | −1.74273 | −0.871366 | − | 0.490634i | \(-0.836765\pi\) | ||||
−0.871366 | + | 0.490634i | \(0.836765\pi\) | |||||||
\(72\) | 0.0718332 | 0.00846563 | ||||||||
\(73\) | 15.3747 | 1.79947 | 0.899735 | − | 0.436436i | \(-0.143760\pi\) | ||||
0.899735 | + | 0.436436i | \(0.143760\pi\) | |||||||
\(74\) | 8.61155 | 1.00107 | ||||||||
\(75\) | −7.67776 | −0.886551 | ||||||||
\(76\) | −21.7389 | −2.49362 | ||||||||
\(77\) | −4.07006 | −0.463826 | ||||||||
\(78\) | 4.15735 | 0.470728 | ||||||||
\(79\) | 14.9013 | 1.67653 | 0.838264 | − | 0.545264i | \(-0.183571\pi\) | ||||
0.838264 | + | 0.545264i | \(0.183571\pi\) | |||||||
\(80\) | −18.2557 | −2.04105 | ||||||||
\(81\) | −8.96267 | −0.995852 | ||||||||
\(82\) | 11.5870 | 1.27957 | ||||||||
\(83\) | −7.35421 | −0.807229 | −0.403615 | − | 0.914929i | \(-0.632246\pi\) | ||||
−0.403615 | + | 0.914929i | \(0.632246\pi\) | |||||||
\(84\) | 30.3048 | 3.30652 | ||||||||
\(85\) | −3.07277 | −0.333289 | ||||||||
\(86\) | 2.51152 | 0.270824 | ||||||||
\(87\) | 15.3385 | 1.64446 | ||||||||
\(88\) | −5.79593 | −0.617848 | ||||||||
\(89\) | 6.13495 | 0.650303 | 0.325152 | − | 0.945662i | \(-0.394585\pi\) | ||||
0.325152 | + | 0.945662i | \(0.394585\pi\) | |||||||
\(90\) | −0.0956467 | −0.0100820 | ||||||||
\(91\) | −3.89780 | −0.408600 | ||||||||
\(92\) | 6.00046 | 0.625591 | ||||||||
\(93\) | 1.50613 | 0.156178 | ||||||||
\(94\) | 27.6073 | 2.84748 | ||||||||
\(95\) | 15.5067 | 1.59095 | ||||||||
\(96\) | 5.75474 | 0.587341 | ||||||||
\(97\) | −14.7119 | −1.49377 | −0.746884 | − | 0.664955i | \(-0.768451\pi\) | ||||
−0.746884 | + | 0.664955i | \(0.768451\pi\) | |||||||
\(98\) | −24.0236 | −2.42675 | ||||||||
\(99\) | −0.0123937 | −0.00124562 | ||||||||
\(100\) | 19.1347 | 1.91347 | ||||||||
\(101\) | 2.71656 | 0.270308 | 0.135154 | − | 0.990825i | \(-0.456847\pi\) | ||||
0.135154 | + | 0.990825i | \(0.456847\pi\) | |||||||
\(102\) | 4.34109 | 0.429832 | ||||||||
\(103\) | 12.2332 | 1.20538 | 0.602688 | − | 0.797977i | \(-0.294096\pi\) | ||||
0.602688 | + | 0.797977i | \(0.294096\pi\) | |||||||
\(104\) | −5.55062 | −0.544283 | ||||||||
\(105\) | −21.6169 | −2.10959 | ||||||||
\(106\) | −18.2299 | −1.77065 | ||||||||
\(107\) | 7.02095 | 0.678741 | 0.339370 | − | 0.940653i | \(-0.389786\pi\) | ||||
0.339370 | + | 0.940653i | \(0.389786\pi\) | |||||||
\(108\) | 22.4296 | 2.15829 | ||||||||
\(109\) | 18.5287 | 1.77473 | 0.887365 | − | 0.461068i | \(-0.152534\pi\) | ||||
0.887365 | + | 0.461068i | \(0.152534\pi\) | |||||||
\(110\) | 7.71734 | 0.735819 | ||||||||
\(111\) | 5.92661 | 0.562529 | ||||||||
\(112\) | −24.1807 | −2.28486 | ||||||||
\(113\) | 18.9369 | 1.78143 | 0.890717 | − | 0.454559i | \(-0.150203\pi\) | ||||
0.890717 | + | 0.454559i | \(0.150203\pi\) | |||||||
\(114\) | −21.9072 | −2.05180 | ||||||||
\(115\) | −4.28022 | −0.399132 | ||||||||
\(116\) | −38.2270 | −3.54928 | ||||||||
\(117\) | −0.0118692 | −0.00109731 | ||||||||
\(118\) | 23.8130 | 2.19217 | ||||||||
\(119\) | −4.07006 | −0.373102 | ||||||||
\(120\) | −30.7833 | −2.81012 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 16.6682 | 1.50906 | ||||||||
\(123\) | 7.97435 | 0.719023 | ||||||||
\(124\) | −3.75361 | −0.337084 | ||||||||
\(125\) | 1.71479 | 0.153376 | ||||||||
\(126\) | −0.126689 | −0.0112864 | ||||||||
\(127\) | 3.76221 | 0.333843 | 0.166921 | − | 0.985970i | \(-0.446617\pi\) | ||||
0.166921 | + | 0.985970i | \(0.446617\pi\) | |||||||
\(128\) | 15.5004 | 1.37005 | ||||||||
\(129\) | 1.72847 | 0.152183 | ||||||||
\(130\) | 7.39071 | 0.648208 | ||||||||
\(131\) | 11.3225 | 0.989255 | 0.494628 | − | 0.869105i | \(-0.335304\pi\) | ||||
0.494628 | + | 0.869105i | \(0.335304\pi\) | |||||||
\(132\) | −7.44579 | −0.648073 | ||||||||
\(133\) | 20.5395 | 1.78100 | ||||||||
\(134\) | 19.5450 | 1.68843 | ||||||||
\(135\) | −15.9994 | −1.37701 | ||||||||
\(136\) | −5.79593 | −0.496997 | ||||||||
\(137\) | −18.1406 | −1.54986 | −0.774928 | − | 0.632049i | \(-0.782214\pi\) | ||||
−0.774928 | + | 0.632049i | \(0.782214\pi\) | |||||||
\(138\) | 6.04691 | 0.514747 | ||||||||
\(139\) | 9.66277 | 0.819585 | 0.409793 | − | 0.912179i | \(-0.365601\pi\) | ||||
0.409793 | + | 0.912179i | \(0.365601\pi\) | |||||||
\(140\) | 53.8741 | 4.55320 | ||||||||
\(141\) | 18.9998 | 1.60007 | ||||||||
\(142\) | 36.8805 | 3.09494 | ||||||||
\(143\) | 0.957676 | 0.0800849 | ||||||||
\(144\) | −0.0736327 | −0.00613606 | ||||||||
\(145\) | 27.2679 | 2.26447 | ||||||||
\(146\) | −38.6138 | −3.19570 | ||||||||
\(147\) | −16.5334 | −1.36366 | ||||||||
\(148\) | −14.7704 | −1.21412 | ||||||||
\(149\) | 2.68124 | 0.219656 | 0.109828 | − | 0.993951i | \(-0.464970\pi\) | ||||
0.109828 | + | 0.993951i | \(0.464970\pi\) | |||||||
\(150\) | 19.2828 | 1.57444 | ||||||||
\(151\) | −12.9334 | −1.05250 | −0.526252 | − | 0.850329i | \(-0.676403\pi\) | ||||
−0.526252 | + | 0.850329i | \(0.676403\pi\) | |||||||
\(152\) | 29.2490 | 2.37241 | ||||||||
\(153\) | −0.0123937 | −0.00100197 | ||||||||
\(154\) | 10.2220 | 0.823715 | ||||||||
\(155\) | 2.67751 | 0.215063 | ||||||||
\(156\) | −7.13065 | −0.570909 | ||||||||
\(157\) | 16.1200 | 1.28652 | 0.643258 | − | 0.765649i | \(-0.277582\pi\) | ||||
0.643258 | + | 0.765649i | \(0.277582\pi\) | |||||||
\(158\) | −37.4249 | −2.97737 | ||||||||
\(159\) | −12.5461 | −0.994972 | ||||||||
\(160\) | 10.2304 | 0.808788 | ||||||||
\(161\) | −5.66938 | −0.446810 | ||||||||
\(162\) | 22.5099 | 1.76855 | ||||||||
\(163\) | 19.1671 | 1.50128 | 0.750640 | − | 0.660711i | \(-0.229745\pi\) | ||||
0.750640 | + | 0.660711i | \(0.229745\pi\) | |||||||
\(164\) | −19.8739 | −1.55189 | ||||||||
\(165\) | 5.31120 | 0.413476 | ||||||||
\(166\) | 18.4703 | 1.43357 | ||||||||
\(167\) | 3.03783 | 0.235074 | 0.117537 | − | 0.993068i | \(-0.462500\pi\) | ||||
0.117537 | + | 0.993068i | \(0.462500\pi\) | |||||||
\(168\) | −40.7742 | −3.14580 | ||||||||
\(169\) | −12.0829 | −0.929450 | ||||||||
\(170\) | 7.71734 | 0.591893 | ||||||||
\(171\) | 0.0625447 | 0.00478292 | ||||||||
\(172\) | −4.30774 | −0.328462 | ||||||||
\(173\) | 15.2981 | 1.16310 | 0.581548 | − | 0.813512i | \(-0.302447\pi\) | ||||
0.581548 | + | 0.813512i | \(0.302447\pi\) | |||||||
\(174\) | −38.5229 | −2.92041 | ||||||||
\(175\) | −18.0790 | −1.36664 | ||||||||
\(176\) | 5.94112 | 0.447829 | ||||||||
\(177\) | 16.3885 | 1.23184 | ||||||||
\(178\) | −15.4080 | −1.15488 | ||||||||
\(179\) | −10.3322 | −0.772262 | −0.386131 | − | 0.922444i | \(-0.626189\pi\) | ||||
−0.386131 | + | 0.922444i | \(0.626189\pi\) | |||||||
\(180\) | 0.164052 | 0.0122277 | ||||||||
\(181\) | −11.6949 | −0.869273 | −0.434636 | − | 0.900606i | \(-0.643123\pi\) | ||||
−0.434636 | + | 0.900606i | \(0.643123\pi\) | |||||||
\(182\) | 9.78940 | 0.725638 | ||||||||
\(183\) | 11.4713 | 0.847983 | ||||||||
\(184\) | −8.07343 | −0.595181 | ||||||||
\(185\) | 10.5360 | 0.774621 | ||||||||
\(186\) | −3.78267 | −0.277359 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −47.3519 | −3.45349 | ||||||||
\(189\) | −21.1921 | −1.54150 | ||||||||
\(190\) | −38.9454 | −2.82539 | ||||||||
\(191\) | −6.45239 | −0.466879 | −0.233439 | − | 0.972371i | \(-0.574998\pi\) | ||||
−0.233439 | + | 0.972371i | \(0.574998\pi\) | |||||||
\(192\) | 6.08493 | 0.439142 | ||||||||
\(193\) | 1.10464 | 0.0795134 | 0.0397567 | − | 0.999209i | \(-0.487342\pi\) | ||||
0.0397567 | + | 0.999209i | \(0.487342\pi\) | |||||||
\(194\) | 36.9493 | 2.65280 | ||||||||
\(195\) | 5.08641 | 0.364245 | ||||||||
\(196\) | 41.2051 | 2.94322 | ||||||||
\(197\) | −12.0890 | −0.861303 | −0.430652 | − | 0.902518i | \(-0.641716\pi\) | ||||
−0.430652 | + | 0.902518i | \(0.641716\pi\) | |||||||
\(198\) | 0.0311271 | 0.00221211 | ||||||||
\(199\) | 22.8358 | 1.61878 | 0.809392 | − | 0.587269i | \(-0.199797\pi\) | ||||
0.809392 | + | 0.587269i | \(0.199797\pi\) | |||||||
\(200\) | −25.7452 | −1.82046 | ||||||||
\(201\) | 13.4512 | 0.948772 | ||||||||
\(202\) | −6.82269 | −0.480043 | ||||||||
\(203\) | 36.1178 | 2.53497 | ||||||||
\(204\) | −7.44579 | −0.521310 | ||||||||
\(205\) | 14.1764 | 0.990119 | ||||||||
\(206\) | −30.7240 | −2.14064 | ||||||||
\(207\) | −0.0172639 | −0.00119992 | ||||||||
\(208\) | 5.68967 | 0.394507 | ||||||||
\(209\) | −5.04648 | −0.349072 | ||||||||
\(210\) | 54.2912 | 3.74645 | ||||||||
\(211\) | 0.490257 | 0.0337507 | 0.0168753 | − | 0.999858i | \(-0.494628\pi\) | ||||
0.0168753 | + | 0.999858i | \(0.494628\pi\) | |||||||
\(212\) | 31.2678 | 2.14748 | ||||||||
\(213\) | 25.3817 | 1.73913 | ||||||||
\(214\) | −17.6333 | −1.20538 | ||||||||
\(215\) | 3.07277 | 0.209561 | ||||||||
\(216\) | −30.1784 | −2.05338 | ||||||||
\(217\) | 3.54651 | 0.240753 | ||||||||
\(218\) | −46.5353 | −3.15177 | ||||||||
\(219\) | −26.5747 | −1.79575 | ||||||||
\(220\) | −13.2367 | −0.892418 | ||||||||
\(221\) | 0.957676 | 0.0644203 | ||||||||
\(222\) | −14.8848 | −0.999002 | ||||||||
\(223\) | 12.0925 | 0.809774 | 0.404887 | − | 0.914367i | \(-0.367311\pi\) | ||||
0.404887 | + | 0.914367i | \(0.367311\pi\) | |||||||
\(224\) | 13.5508 | 0.905400 | ||||||||
\(225\) | −0.0550523 | −0.00367015 | ||||||||
\(226\) | −47.5604 | −3.16367 | ||||||||
\(227\) | 0.839075 | 0.0556914 | 0.0278457 | − | 0.999612i | \(-0.491135\pi\) | ||||
0.0278457 | + | 0.999612i | \(0.491135\pi\) | |||||||
\(228\) | 37.5750 | 2.48847 | ||||||||
\(229\) | 16.7714 | 1.10828 | 0.554142 | − | 0.832422i | \(-0.313047\pi\) | ||||
0.554142 | + | 0.832422i | \(0.313047\pi\) | |||||||
\(230\) | 10.7499 | 0.708824 | ||||||||
\(231\) | 7.03497 | 0.462867 | ||||||||
\(232\) | 51.4332 | 3.37675 | ||||||||
\(233\) | −0.502200 | −0.0329002 | −0.0164501 | − | 0.999865i | \(-0.505236\pi\) | ||||
−0.0164501 | + | 0.999865i | \(0.505236\pi\) | |||||||
\(234\) | 0.0298097 | 0.00194872 | ||||||||
\(235\) | 33.7768 | 2.20336 | ||||||||
\(236\) | −40.8439 | −2.65871 | ||||||||
\(237\) | −25.7565 | −1.67306 | ||||||||
\(238\) | 10.2220 | 0.662596 | ||||||||
\(239\) | −18.0172 | −1.16543 | −0.582717 | − | 0.812675i | \(-0.698010\pi\) | ||||
−0.582717 | + | 0.812675i | \(0.698010\pi\) | |||||||
\(240\) | 31.5544 | 2.03683 | ||||||||
\(241\) | −29.2086 | −1.88149 | −0.940747 | − | 0.339110i | \(-0.889874\pi\) | ||||
−0.940747 | + | 0.339110i | \(0.889874\pi\) | |||||||
\(242\) | −2.51152 | −0.161447 | ||||||||
\(243\) | −0.128799 | −0.00826244 | ||||||||
\(244\) | −28.5891 | −1.83023 | ||||||||
\(245\) | −29.3922 | −1.87780 | ||||||||
\(246\) | −20.0278 | −1.27692 | ||||||||
\(247\) | −4.83289 | −0.307509 | ||||||||
\(248\) | 5.05037 | 0.320699 | ||||||||
\(249\) | 12.7115 | 0.805560 | ||||||||
\(250\) | −4.30674 | −0.272382 | ||||||||
\(251\) | 11.2257 | 0.708563 | 0.354281 | − | 0.935139i | \(-0.384726\pi\) | ||||
0.354281 | + | 0.935139i | \(0.384726\pi\) | |||||||
\(252\) | 0.217296 | 0.0136884 | ||||||||
\(253\) | 1.39295 | 0.0875740 | ||||||||
\(254\) | −9.44888 | −0.592875 | ||||||||
\(255\) | 5.31120 | 0.332600 | ||||||||
\(256\) | −31.8887 | −1.99304 | ||||||||
\(257\) | −9.25154 | −0.577095 | −0.288548 | − | 0.957466i | \(-0.593172\pi\) | ||||
−0.288548 | + | 0.957466i | \(0.593172\pi\) | |||||||
\(258\) | −4.34109 | −0.270264 | ||||||||
\(259\) | 13.9555 | 0.867152 | ||||||||
\(260\) | −12.6765 | −0.786161 | ||||||||
\(261\) | 0.109982 | 0.00680774 | ||||||||
\(262\) | −28.4368 | −1.75683 | ||||||||
\(263\) | −15.0524 | −0.928169 | −0.464084 | − | 0.885791i | \(-0.653617\pi\) | ||||
−0.464084 | + | 0.885791i | \(0.653617\pi\) | |||||||
\(264\) | 10.0181 | 0.616570 | ||||||||
\(265\) | −22.3038 | −1.37011 | ||||||||
\(266\) | −51.5853 | −3.16290 | ||||||||
\(267\) | −10.6041 | −0.648959 | ||||||||
\(268\) | −33.5234 | −2.04776 | ||||||||
\(269\) | −11.6076 | −0.707726 | −0.353863 | − | 0.935297i | \(-0.615132\pi\) | ||||
−0.353863 | + | 0.935297i | \(0.615132\pi\) | |||||||
\(270\) | 40.1829 | 2.44545 | ||||||||
\(271\) | −4.93739 | −0.299925 | −0.149962 | − | 0.988692i | \(-0.547915\pi\) | ||||
−0.149962 | + | 0.988692i | \(0.547915\pi\) | |||||||
\(272\) | 5.94112 | 0.360233 | ||||||||
\(273\) | 6.73722 | 0.407755 | ||||||||
\(274\) | 45.5605 | 2.75241 | ||||||||
\(275\) | 4.44194 | 0.267859 | ||||||||
\(276\) | −10.3716 | −0.624297 | ||||||||
\(277\) | 22.6927 | 1.36347 | 0.681736 | − | 0.731598i | \(-0.261225\pi\) | ||||
0.681736 | + | 0.731598i | \(0.261225\pi\) | |||||||
\(278\) | −24.2682 | −1.45551 | ||||||||
\(279\) | 0.0107995 | 0.000646548 0 | ||||||||
\(280\) | −72.4860 | −4.33187 | ||||||||
\(281\) | 19.8526 | 1.18431 | 0.592154 | − | 0.805825i | \(-0.298278\pi\) | ||||
0.592154 | + | 0.805825i | \(0.298278\pi\) | |||||||
\(282\) | −47.7184 | −2.84159 | ||||||||
\(283\) | 0.844338 | 0.0501907 | 0.0250953 | − | 0.999685i | \(-0.492011\pi\) | ||||
0.0250953 | + | 0.999685i | \(0.492011\pi\) | |||||||
\(284\) | −63.2570 | −3.75361 | ||||||||
\(285\) | −26.8028 | −1.58766 | ||||||||
\(286\) | −2.40522 | −0.142224 | ||||||||
\(287\) | 18.7774 | 1.10839 | ||||||||
\(288\) | 0.0412635 | 0.00243148 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −68.4838 | −4.02151 | ||||||||
\(291\) | 25.4291 | 1.49068 | ||||||||
\(292\) | 66.2301 | 3.87582 | ||||||||
\(293\) | −4.64842 | −0.271563 | −0.135782 | − | 0.990739i | \(-0.543355\pi\) | ||||
−0.135782 | + | 0.990739i | \(0.543355\pi\) | |||||||
\(294\) | 41.5241 | 2.42173 | ||||||||
\(295\) | 29.1346 | 1.69628 | ||||||||
\(296\) | 19.8732 | 1.15511 | ||||||||
\(297\) | 5.20683 | 0.302131 | ||||||||
\(298\) | −6.73400 | −0.390090 | ||||||||
\(299\) | 1.33399 | 0.0771469 | ||||||||
\(300\) | −33.0738 | −1.90951 | ||||||||
\(301\) | 4.07006 | 0.234594 | ||||||||
\(302\) | 32.4825 | 1.86916 | ||||||||
\(303\) | −4.69549 | −0.269749 | ||||||||
\(304\) | −29.9817 | −1.71957 | ||||||||
\(305\) | 20.3930 | 1.16770 | ||||||||
\(306\) | 0.0311271 | 0.00177942 | ||||||||
\(307\) | 30.7201 | 1.75329 | 0.876643 | − | 0.481141i | \(-0.159777\pi\) | ||||
0.876643 | + | 0.481141i | \(0.159777\pi\) | |||||||
\(308\) | −17.5327 | −0.999020 | ||||||||
\(309\) | −21.1448 | −1.20288 | ||||||||
\(310\) | −6.72462 | −0.381933 | ||||||||
\(311\) | 33.5002 | 1.89962 | 0.949811 | − | 0.312824i | \(-0.101275\pi\) | ||||
0.949811 | + | 0.312824i | \(0.101275\pi\) | |||||||
\(312\) | 9.59408 | 0.543158 | ||||||||
\(313\) | −20.1237 | −1.13746 | −0.568728 | − | 0.822525i | \(-0.692564\pi\) | ||||
−0.568728 | + | 0.822525i | \(0.692564\pi\) | |||||||
\(314\) | −40.4857 | −2.28474 | ||||||||
\(315\) | −0.155001 | −0.00873330 | ||||||||
\(316\) | 64.1909 | 3.61102 | ||||||||
\(317\) | 27.0592 | 1.51979 | 0.759897 | − | 0.650044i | \(-0.225249\pi\) | ||||
0.759897 | + | 0.650044i | \(0.225249\pi\) | |||||||
\(318\) | 31.5098 | 1.76698 | ||||||||
\(319\) | −8.87402 | −0.496850 | ||||||||
\(320\) | 10.8174 | 0.604713 | ||||||||
\(321\) | −12.1355 | −0.677337 | ||||||||
\(322\) | 14.2388 | 0.793496 | ||||||||
\(323\) | −5.04648 | −0.280793 | ||||||||
\(324\) | −38.6088 | −2.14493 | ||||||||
\(325\) | 4.25394 | 0.235966 | ||||||||
\(326\) | −48.1385 | −2.66614 | ||||||||
\(327\) | −32.0263 | −1.77106 | ||||||||
\(328\) | 26.7397 | 1.47645 | ||||||||
\(329\) | 44.7392 | 2.46655 | ||||||||
\(330\) | −13.3392 | −0.734298 | ||||||||
\(331\) | 10.6370 | 0.584661 | 0.292331 | − | 0.956317i | \(-0.405569\pi\) | ||||
0.292331 | + | 0.956317i | \(0.405569\pi\) | |||||||
\(332\) | −31.6800 | −1.73867 | ||||||||
\(333\) | 0.0424959 | 0.00232876 | ||||||||
\(334\) | −7.62956 | −0.417471 | ||||||||
\(335\) | 23.9127 | 1.30649 | ||||||||
\(336\) | 41.7956 | 2.28014 | ||||||||
\(337\) | 16.9782 | 0.924862 | 0.462431 | − | 0.886655i | \(-0.346977\pi\) | ||||
0.462431 | + | 0.886655i | \(0.346977\pi\) | |||||||
\(338\) | 30.3463 | 1.65062 | ||||||||
\(339\) | −32.7318 | −1.77775 | ||||||||
\(340\) | −13.2367 | −0.717861 | ||||||||
\(341\) | −0.871366 | −0.0471871 | ||||||||
\(342\) | −0.157082 | −0.00849404 | ||||||||
\(343\) | −10.4412 | −0.563772 | ||||||||
\(344\) | 5.79593 | 0.312495 | ||||||||
\(345\) | 7.39822 | 0.398307 | ||||||||
\(346\) | −38.4216 | −2.06556 | ||||||||
\(347\) | −27.1297 | −1.45640 | −0.728200 | − | 0.685365i | \(-0.759643\pi\) | ||||
−0.728200 | + | 0.685365i | \(0.759643\pi\) | |||||||
\(348\) | 66.0741 | 3.54194 | ||||||||
\(349\) | 20.6834 | 1.10715 | 0.553577 | − | 0.832798i | \(-0.313262\pi\) | ||||
0.553577 | + | 0.832798i | \(0.313262\pi\) | |||||||
\(350\) | 45.4057 | 2.42703 | ||||||||
\(351\) | 4.98646 | 0.266157 | ||||||||
\(352\) | −3.32939 | −0.177457 | ||||||||
\(353\) | 7.45407 | 0.396740 | 0.198370 | − | 0.980127i | \(-0.436435\pi\) | ||||
0.198370 | + | 0.980127i | \(0.436435\pi\) | |||||||
\(354\) | −41.1601 | −2.18763 | ||||||||
\(355\) | 45.1222 | 2.39484 | ||||||||
\(356\) | 26.4277 | 1.40067 | ||||||||
\(357\) | 7.03497 | 0.372330 | ||||||||
\(358\) | 25.9494 | 1.37147 | ||||||||
\(359\) | 33.0111 | 1.74226 | 0.871129 | − | 0.491054i | \(-0.163388\pi\) | ||||
0.871129 | + | 0.491054i | \(0.163388\pi\) | |||||||
\(360\) | −0.220727 | −0.0116333 | ||||||||
\(361\) | 6.46693 | 0.340365 | ||||||||
\(362\) | 29.3719 | 1.54375 | ||||||||
\(363\) | −1.72847 | −0.0907211 | ||||||||
\(364\) | −16.7907 | −0.880071 | ||||||||
\(365\) | −47.2429 | −2.47281 | ||||||||
\(366\) | −28.8104 | −1.50594 | ||||||||
\(367\) | 24.3527 | 1.27120 | 0.635601 | − | 0.772017i | \(-0.280752\pi\) | ||||
0.635601 | + | 0.772017i | \(0.280752\pi\) | |||||||
\(368\) | 8.27567 | 0.431399 | ||||||||
\(369\) | 0.0571790 | 0.00297662 | ||||||||
\(370\) | −26.4613 | −1.37566 | ||||||||
\(371\) | −29.5426 | −1.53377 | ||||||||
\(372\) | 6.48800 | 0.336387 | ||||||||
\(373\) | −32.0815 | −1.66112 | −0.830559 | − | 0.556931i | \(-0.811979\pi\) | ||||
−0.830559 | + | 0.556931i | \(0.811979\pi\) | |||||||
\(374\) | −2.51152 | −0.129868 | ||||||||
\(375\) | −2.96397 | −0.153058 | ||||||||
\(376\) | 63.7105 | 3.28562 | ||||||||
\(377\) | −8.49844 | −0.437692 | ||||||||
\(378\) | 53.2244 | 2.73757 | ||||||||
\(379\) | −28.9196 | −1.48550 | −0.742751 | − | 0.669568i | \(-0.766479\pi\) | ||||
−0.742751 | + | 0.669568i | \(0.766479\pi\) | |||||||
\(380\) | 66.7987 | 3.42670 | ||||||||
\(381\) | −6.50287 | −0.333152 | ||||||||
\(382\) | 16.2053 | 0.829136 | ||||||||
\(383\) | −27.2853 | −1.39421 | −0.697107 | − | 0.716967i | \(-0.745530\pi\) | ||||
−0.697107 | + | 0.716967i | \(0.745530\pi\) | |||||||
\(384\) | −26.7919 | −1.36722 | ||||||||
\(385\) | 12.5064 | 0.637384 | ||||||||
\(386\) | −2.77432 | −0.141209 | ||||||||
\(387\) | 0.0123937 | 0.000630009 0 | ||||||||
\(388\) | −63.3750 | −3.21738 | ||||||||
\(389\) | −18.4624 | −0.936082 | −0.468041 | − | 0.883707i | \(-0.655040\pi\) | ||||
−0.468041 | + | 0.883707i | \(0.655040\pi\) | |||||||
\(390\) | −12.7746 | −0.646868 | ||||||||
\(391\) | 1.39295 | 0.0704445 | ||||||||
\(392\) | −55.4402 | −2.80015 | ||||||||
\(393\) | −19.5707 | −0.987210 | ||||||||
\(394\) | 30.3617 | 1.52960 | ||||||||
\(395\) | −45.7884 | −2.30386 | ||||||||
\(396\) | −0.0533890 | −0.00268290 | ||||||||
\(397\) | 30.3957 | 1.52551 | 0.762757 | − | 0.646685i | \(-0.223845\pi\) | ||||
0.762757 | + | 0.646685i | \(0.223845\pi\) | |||||||
\(398\) | −57.3525 | −2.87482 | ||||||||
\(399\) | −35.5018 | −1.77731 | ||||||||
\(400\) | 26.3901 | 1.31950 | ||||||||
\(401\) | −6.42102 | −0.320650 | −0.160325 | − | 0.987064i | \(-0.551254\pi\) | ||||
−0.160325 | + | 0.987064i | \(0.551254\pi\) | |||||||
\(402\) | −33.7829 | −1.68494 | ||||||||
\(403\) | −0.834486 | −0.0415687 | ||||||||
\(404\) | 11.7022 | 0.582207 | ||||||||
\(405\) | 27.5402 | 1.36849 | ||||||||
\(406\) | −90.7106 | −4.50189 | ||||||||
\(407\) | −3.42882 | −0.169960 | ||||||||
\(408\) | 10.0181 | 0.495969 | ||||||||
\(409\) | 5.19743 | 0.256996 | 0.128498 | − | 0.991710i | \(-0.458984\pi\) | ||||
0.128498 | + | 0.991710i | \(0.458984\pi\) | |||||||
\(410\) | −35.6042 | −1.75837 | ||||||||
\(411\) | 31.3555 | 1.54665 | ||||||||
\(412\) | 52.6975 | 2.59622 | ||||||||
\(413\) | 38.5903 | 1.89891 | ||||||||
\(414\) | 0.0433585 | 0.00213096 | ||||||||
\(415\) | 22.5978 | 1.10928 | ||||||||
\(416\) | −3.18847 | −0.156328 | ||||||||
\(417\) | −16.7018 | −0.817890 | ||||||||
\(418\) | 12.6743 | 0.619922 | ||||||||
\(419\) | −10.3251 | −0.504412 | −0.252206 | − | 0.967674i | \(-0.581156\pi\) | ||||
−0.252206 | + | 0.967674i | \(0.581156\pi\) | |||||||
\(420\) | −93.1198 | −4.54378 | ||||||||
\(421\) | 7.72873 | 0.376675 | 0.188338 | − | 0.982104i | \(-0.439690\pi\) | ||||
0.188338 | + | 0.982104i | \(0.439690\pi\) | |||||||
\(422\) | −1.23129 | −0.0599382 | ||||||||
\(423\) | 0.136236 | 0.00662400 | ||||||||
\(424\) | −42.0698 | −2.04309 | ||||||||
\(425\) | 4.44194 | 0.215466 | ||||||||
\(426\) | −63.7468 | −3.08854 | ||||||||
\(427\) | 27.0117 | 1.30719 | ||||||||
\(428\) | 30.2444 | 1.46192 | ||||||||
\(429\) | −1.65531 | −0.0799193 | ||||||||
\(430\) | −7.71734 | −0.372163 | ||||||||
\(431\) | −5.61361 | −0.270398 | −0.135199 | − | 0.990818i | \(-0.543167\pi\) | ||||
−0.135199 | + | 0.990818i | \(0.543167\pi\) | |||||||
\(432\) | 30.9344 | 1.48833 | ||||||||
\(433\) | 13.4380 | 0.645789 | 0.322894 | − | 0.946435i | \(-0.395344\pi\) | ||||
0.322894 | + | 0.946435i | \(0.395344\pi\) | |||||||
\(434\) | −8.90713 | −0.427556 | ||||||||
\(435\) | −47.1317 | −2.25979 | ||||||||
\(436\) | 79.8168 | 3.82253 | ||||||||
\(437\) | −7.02948 | −0.336266 | ||||||||
\(438\) | 66.7428 | 3.18910 | ||||||||
\(439\) | −19.8752 | −0.948591 | −0.474295 | − | 0.880366i | \(-0.657297\pi\) | ||||
−0.474295 | + | 0.880366i | \(0.657297\pi\) | |||||||
\(440\) | 17.8096 | 0.849038 | ||||||||
\(441\) | −0.118551 | −0.00564527 | ||||||||
\(442\) | −2.40522 | −0.114405 | ||||||||
\(443\) | −6.44799 | −0.306353 | −0.153177 | − | 0.988199i | \(-0.548950\pi\) | ||||
−0.153177 | + | 0.988199i | \(0.548950\pi\) | |||||||
\(444\) | 25.5303 | 1.21161 | ||||||||
\(445\) | −18.8513 | −0.893638 | ||||||||
\(446\) | −30.3706 | −1.43809 | ||||||||
\(447\) | −4.63445 | −0.219202 | ||||||||
\(448\) | 14.3283 | 0.676948 | ||||||||
\(449\) | 9.15718 | 0.432154 | 0.216077 | − | 0.976376i | \(-0.430674\pi\) | ||||
0.216077 | + | 0.976376i | \(0.430674\pi\) | |||||||
\(450\) | 0.138265 | 0.00651787 | ||||||||
\(451\) | −4.61354 | −0.217243 | ||||||||
\(452\) | 81.5751 | 3.83697 | ||||||||
\(453\) | 22.3550 | 1.05033 | ||||||||
\(454\) | −2.10736 | −0.0989031 | ||||||||
\(455\) | 11.9770 | 0.561493 | ||||||||
\(456\) | −50.5560 | −2.36750 | ||||||||
\(457\) | 29.6428 | 1.38663 | 0.693316 | − | 0.720633i | \(-0.256149\pi\) | ||||
0.693316 | + | 0.720633i | \(0.256149\pi\) | |||||||
\(458\) | −42.1217 | −1.96822 | ||||||||
\(459\) | 5.20683 | 0.243034 | ||||||||
\(460\) | −18.4380 | −0.859678 | ||||||||
\(461\) | 1.73615 | 0.0808604 | 0.0404302 | − | 0.999182i | \(-0.487127\pi\) | ||||
0.0404302 | + | 0.999182i | \(0.487127\pi\) | |||||||
\(462\) | −17.6685 | −0.822012 | ||||||||
\(463\) | 10.4156 | 0.484054 | 0.242027 | − | 0.970269i | \(-0.422188\pi\) | ||||
0.242027 | + | 0.970269i | \(0.422188\pi\) | |||||||
\(464\) | −52.7216 | −2.44754 | ||||||||
\(465\) | −4.62799 | −0.214618 | ||||||||
\(466\) | 1.26129 | 0.0584279 | ||||||||
\(467\) | −11.6323 | −0.538277 | −0.269139 | − | 0.963101i | \(-0.586739\pi\) | ||||
−0.269139 | + | 0.963101i | \(0.586739\pi\) | |||||||
\(468\) | −0.0511293 | −0.00236345 | ||||||||
\(469\) | 31.6737 | 1.46256 | ||||||||
\(470\) | −84.8311 | −3.91297 | ||||||||
\(471\) | −27.8629 | −1.28386 | ||||||||
\(472\) | 54.9542 | 2.52947 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 64.6879 | 2.97121 | ||||||||
\(475\) | −22.4161 | −1.02852 | ||||||||
\(476\) | −17.5327 | −0.803612 | ||||||||
\(477\) | −0.0899602 | −0.00411899 | ||||||||
\(478\) | 45.2505 | 2.06971 | ||||||||
\(479\) | −36.0123 | −1.64544 | −0.822722 | − | 0.568444i | \(-0.807545\pi\) | ||||
−0.822722 | + | 0.568444i | \(0.807545\pi\) | |||||||
\(480\) | −17.6830 | −0.807116 | ||||||||
\(481\) | −3.28370 | −0.149724 | ||||||||
\(482\) | 73.3581 | 3.34137 | ||||||||
\(483\) | 9.79935 | 0.445886 | ||||||||
\(484\) | 4.30774 | 0.195806 | ||||||||
\(485\) | 45.2064 | 2.05271 | ||||||||
\(486\) | 0.323481 | 0.0146734 | ||||||||
\(487\) | 4.95570 | 0.224564 | 0.112282 | − | 0.993676i | \(-0.464184\pi\) | ||||
0.112282 | + | 0.993676i | \(0.464184\pi\) | |||||||
\(488\) | 38.4657 | 1.74126 | ||||||||
\(489\) | −33.1297 | −1.49818 | ||||||||
\(490\) | 73.8192 | 3.33481 | ||||||||
\(491\) | −27.7067 | −1.25039 | −0.625193 | − | 0.780470i | \(-0.714980\pi\) | ||||
−0.625193 | + | 0.780470i | \(0.714980\pi\) | |||||||
\(492\) | 34.3514 | 1.54868 | ||||||||
\(493\) | −8.87402 | −0.399666 | ||||||||
\(494\) | 12.1379 | 0.546110 | ||||||||
\(495\) | 0.0380832 | 0.00171171 | ||||||||
\(496\) | −5.17689 | −0.232449 | ||||||||
\(497\) | 59.7668 | 2.68091 | ||||||||
\(498\) | −31.9253 | −1.43061 | ||||||||
\(499\) | 19.4068 | 0.868767 | 0.434384 | − | 0.900728i | \(-0.356966\pi\) | ||||
0.434384 | + | 0.900728i | \(0.356966\pi\) | |||||||
\(500\) | 7.38687 | 0.330351 | ||||||||
\(501\) | −5.25079 | −0.234588 | ||||||||
\(502\) | −28.1937 | −1.25835 | ||||||||
\(503\) | 40.7164 | 1.81545 | 0.907727 | − | 0.419560i | \(-0.137816\pi\) | ||||
0.907727 | + | 0.419560i | \(0.137816\pi\) | |||||||
\(504\) | −0.292365 | −0.0130230 | ||||||||
\(505\) | −8.34737 | −0.371453 | ||||||||
\(506\) | −3.49842 | −0.155524 | ||||||||
\(507\) | 20.8848 | 0.927529 | ||||||||
\(508\) | 16.2066 | 0.719053 | ||||||||
\(509\) | −14.7463 | −0.653617 | −0.326809 | − | 0.945091i | \(-0.605973\pi\) | ||||
−0.326809 | + | 0.945091i | \(0.605973\pi\) | |||||||
\(510\) | −13.3392 | −0.590669 | ||||||||
\(511\) | −62.5758 | −2.76819 | ||||||||
\(512\) | 49.0883 | 2.16942 | ||||||||
\(513\) | −26.2761 | −1.16012 | ||||||||
\(514\) | 23.2354 | 1.02487 | ||||||||
\(515\) | −37.5900 | −1.65641 | ||||||||
\(516\) | 7.44579 | 0.327783 | ||||||||
\(517\) | −10.9923 | −0.483440 | ||||||||
\(518\) | −35.0495 | −1.53999 | ||||||||
\(519\) | −26.4424 | −1.16069 | ||||||||
\(520\) | 17.0558 | 0.747946 | ||||||||
\(521\) | 36.4465 | 1.59675 | 0.798374 | − | 0.602161i | \(-0.205694\pi\) | ||||
0.798374 | + | 0.602161i | \(0.205694\pi\) | |||||||
\(522\) | −0.276223 | −0.0120900 | ||||||||
\(523\) | 40.0022 | 1.74917 | 0.874587 | − | 0.484868i | \(-0.161132\pi\) | ||||
0.874587 | + | 0.484868i | \(0.161132\pi\) | |||||||
\(524\) | 48.7745 | 2.13073 | ||||||||
\(525\) | 31.2489 | 1.36381 | ||||||||
\(526\) | 37.8043 | 1.64835 | ||||||||
\(527\) | −0.871366 | −0.0379573 | ||||||||
\(528\) | −10.2690 | −0.446903 | ||||||||
\(529\) | −21.0597 | −0.915639 | ||||||||
\(530\) | 56.0164 | 2.43320 | ||||||||
\(531\) | 0.117512 | 0.00509957 | ||||||||
\(532\) | 88.4785 | 3.83603 | ||||||||
\(533\) | −4.41827 | −0.191377 | ||||||||
\(534\) | 26.6323 | 1.15249 | ||||||||
\(535\) | −21.5738 | −0.932716 | ||||||||
\(536\) | 45.1046 | 1.94822 | ||||||||
\(537\) | 17.8588 | 0.770665 | ||||||||
\(538\) | 29.1526 | 1.25686 | ||||||||
\(539\) | 9.56537 | 0.412010 | ||||||||
\(540\) | −68.9212 | −2.96590 | ||||||||
\(541\) | 16.1137 | 0.692780 | 0.346390 | − | 0.938091i | \(-0.387407\pi\) | ||||
0.346390 | + | 0.938091i | \(0.387407\pi\) | |||||||
\(542\) | 12.4003 | 0.532641 | ||||||||
\(543\) | 20.2142 | 0.867476 | ||||||||
\(544\) | −3.32939 | −0.142746 | ||||||||
\(545\) | −56.9346 | −2.43881 | ||||||||
\(546\) | −16.9207 | −0.724138 | ||||||||
\(547\) | 15.6845 | 0.670620 | 0.335310 | − | 0.942108i | \(-0.391159\pi\) | ||||
0.335310 | + | 0.942108i | \(0.391159\pi\) | |||||||
\(548\) | −78.1450 | −3.33819 | ||||||||
\(549\) | 0.0822533 | 0.00351049 | ||||||||
\(550\) | −11.1560 | −0.475694 | ||||||||
\(551\) | 44.7826 | 1.90780 | ||||||||
\(552\) | 13.9547 | 0.593950 | ||||||||
\(553\) | −60.6492 | −2.57907 | ||||||||
\(554\) | −56.9932 | −2.42141 | ||||||||
\(555\) | −18.2111 | −0.773019 | ||||||||
\(556\) | 41.6246 | 1.76528 | ||||||||
\(557\) | −11.5455 | −0.489198 | −0.244599 | − | 0.969624i | \(-0.578656\pi\) | ||||
−0.244599 | + | 0.969624i | \(0.578656\pi\) | |||||||
\(558\) | −0.0271231 | −0.00114821 | ||||||||
\(559\) | −0.957676 | −0.0405054 | ||||||||
\(560\) | 74.3018 | 3.13982 | ||||||||
\(561\) | −1.72847 | −0.0729760 | ||||||||
\(562\) | −49.8603 | −2.10323 | ||||||||
\(563\) | −26.3085 | −1.10877 | −0.554385 | − | 0.832260i | \(-0.687047\pi\) | ||||
−0.554385 | + | 0.832260i | \(0.687047\pi\) | |||||||
\(564\) | 81.8462 | 3.44635 | ||||||||
\(565\) | −58.1888 | −2.44802 | ||||||||
\(566\) | −2.12057 | −0.0891343 | ||||||||
\(567\) | 36.4786 | 1.53196 | ||||||||
\(568\) | 85.1104 | 3.57115 | ||||||||
\(569\) | −20.0636 | −0.841109 | −0.420554 | − | 0.907267i | \(-0.638164\pi\) | ||||
−0.420554 | + | 0.907267i | \(0.638164\pi\) | |||||||
\(570\) | 67.3158 | 2.81955 | ||||||||
\(571\) | 13.2226 | 0.553351 | 0.276675 | − | 0.960963i | \(-0.410767\pi\) | ||||
0.276675 | + | 0.960963i | \(0.410767\pi\) | |||||||
\(572\) | 4.12542 | 0.172492 | ||||||||
\(573\) | 11.1528 | 0.465913 | ||||||||
\(574\) | −47.1597 | −1.96841 | ||||||||
\(575\) | 6.18740 | 0.258032 | ||||||||
\(576\) | 0.0436311 | 0.00181796 | ||||||||
\(577\) | −4.43110 | −0.184469 | −0.0922345 | − | 0.995737i | \(-0.529401\pi\) | ||||
−0.0922345 | + | 0.995737i | \(0.529401\pi\) | |||||||
\(578\) | −2.51152 | −0.104465 | ||||||||
\(579\) | −1.90933 | −0.0793490 | ||||||||
\(580\) | 117.463 | 4.87738 | ||||||||
\(581\) | 29.9321 | 1.24179 | ||||||||
\(582\) | −63.8656 | −2.64732 | ||||||||
\(583\) | 7.25851 | 0.300617 | ||||||||
\(584\) | −89.1105 | −3.68742 | ||||||||
\(585\) | 0.0364713 | 0.00150790 | ||||||||
\(586\) | 11.6746 | 0.482273 | ||||||||
\(587\) | −30.1011 | −1.24241 | −0.621203 | − | 0.783650i | \(-0.713356\pi\) | ||||
−0.621203 | + | 0.783650i | \(0.713356\pi\) | |||||||
\(588\) | −71.2217 | −2.93713 | ||||||||
\(589\) | 4.39733 | 0.181189 | ||||||||
\(590\) | −73.1721 | −3.01245 | ||||||||
\(591\) | 20.8954 | 0.859522 | ||||||||
\(592\) | −20.3710 | −0.837244 | ||||||||
\(593\) | 34.6151 | 1.42147 | 0.710736 | − | 0.703459i | \(-0.248362\pi\) | ||||
0.710736 | + | 0.703459i | \(0.248362\pi\) | |||||||
\(594\) | −13.0771 | −0.536558 | ||||||||
\(595\) | 12.5064 | 0.512711 | ||||||||
\(596\) | 11.5501 | 0.473110 | ||||||||
\(597\) | −39.4709 | −1.61544 | ||||||||
\(598\) | −3.35035 | −0.137006 | ||||||||
\(599\) | −9.78730 | −0.399898 | −0.199949 | − | 0.979806i | \(-0.564078\pi\) | ||||
−0.199949 | + | 0.979806i | \(0.564078\pi\) | |||||||
\(600\) | 44.4997 | 1.81669 | ||||||||
\(601\) | −8.32684 | −0.339659 | −0.169829 | − | 0.985473i | \(-0.554322\pi\) | ||||
−0.169829 | + | 0.985473i | \(0.554322\pi\) | |||||||
\(602\) | −10.2220 | −0.416619 | ||||||||
\(603\) | 0.0964497 | 0.00392774 | ||||||||
\(604\) | −55.7136 | −2.26696 | ||||||||
\(605\) | −3.07277 | −0.124926 | ||||||||
\(606\) | 11.7928 | 0.479050 | ||||||||
\(607\) | 14.8722 | 0.603644 | 0.301822 | − | 0.953364i | \(-0.402405\pi\) | ||||
0.301822 | + | 0.953364i | \(0.402405\pi\) | |||||||
\(608\) | 16.8017 | 0.681398 | ||||||||
\(609\) | −62.4285 | −2.52973 | ||||||||
\(610\) | −51.2175 | −2.07374 | ||||||||
\(611\) | −10.5270 | −0.425879 | ||||||||
\(612\) | −0.0533890 | −0.00215812 | ||||||||
\(613\) | −18.1248 | −0.732054 | −0.366027 | − | 0.930604i | \(-0.619282\pi\) | ||||
−0.366027 | + | 0.930604i | \(0.619282\pi\) | |||||||
\(614\) | −77.1541 | −3.11369 | ||||||||
\(615\) | −24.5034 | −0.988072 | ||||||||
\(616\) | 23.5898 | 0.950458 | ||||||||
\(617\) | −9.31026 | −0.374817 | −0.187409 | − | 0.982282i | \(-0.560009\pi\) | ||||
−0.187409 | + | 0.982282i | \(0.560009\pi\) | |||||||
\(618\) | 53.1055 | 2.13622 | ||||||||
\(619\) | 20.6673 | 0.830687 | 0.415343 | − | 0.909665i | \(-0.363661\pi\) | ||||
0.415343 | + | 0.909665i | \(0.363661\pi\) | |||||||
\(620\) | 11.5340 | 0.463217 | ||||||||
\(621\) | 7.25285 | 0.291047 | ||||||||
\(622\) | −84.1365 | −3.37356 | ||||||||
\(623\) | −24.9696 | −1.00039 | ||||||||
\(624\) | −9.83441 | −0.393692 | ||||||||
\(625\) | −27.4789 | −1.09915 | ||||||||
\(626\) | 50.5410 | 2.02002 | ||||||||
\(627\) | 8.72268 | 0.348350 | ||||||||
\(628\) | 69.4408 | 2.77099 | ||||||||
\(629\) | −3.42882 | −0.136716 | ||||||||
\(630\) | 0.389287 | 0.0155096 | ||||||||
\(631\) | −30.7411 | −1.22379 | −0.611893 | − | 0.790941i | \(-0.709592\pi\) | ||||
−0.611893 | + | 0.790941i | \(0.709592\pi\) | |||||||
\(632\) | −86.3669 | −3.43549 | ||||||||
\(633\) | −0.847394 | −0.0336809 | ||||||||
\(634\) | −67.9596 | −2.69902 | ||||||||
\(635\) | −11.5604 | −0.458762 | ||||||||
\(636\) | −54.0454 | −2.14304 | ||||||||
\(637\) | 9.16053 | 0.362953 | ||||||||
\(638\) | 22.2873 | 0.882362 | ||||||||
\(639\) | 0.181996 | 0.00719966 | ||||||||
\(640\) | −47.6291 | −1.88271 | ||||||||
\(641\) | 25.0640 | 0.989968 | 0.494984 | − | 0.868902i | \(-0.335174\pi\) | ||||
0.494984 | + | 0.868902i | \(0.335174\pi\) | |||||||
\(642\) | 30.4785 | 1.20289 | ||||||||
\(643\) | 21.8511 | 0.861724 | 0.430862 | − | 0.902418i | \(-0.358210\pi\) | ||||
0.430862 | + | 0.902418i | \(0.358210\pi\) | |||||||
\(644\) | −24.4222 | −0.962370 | ||||||||
\(645\) | −5.31120 | −0.209128 | ||||||||
\(646\) | 12.6743 | 0.498665 | ||||||||
\(647\) | −39.4577 | −1.55124 | −0.775622 | − | 0.631198i | \(-0.782564\pi\) | ||||
−0.775622 | + | 0.631198i | \(0.782564\pi\) | |||||||
\(648\) | 51.9469 | 2.04067 | ||||||||
\(649\) | −9.48152 | −0.372182 | ||||||||
\(650\) | −10.6839 | −0.419055 | ||||||||
\(651\) | −6.13003 | −0.240255 | ||||||||
\(652\) | 82.5666 | 3.23356 | ||||||||
\(653\) | −29.8903 | −1.16970 | −0.584850 | − | 0.811142i | \(-0.698846\pi\) | ||||
−0.584850 | + | 0.811142i | \(0.698846\pi\) | |||||||
\(654\) | 80.4348 | 3.14525 | ||||||||
\(655\) | −34.7916 | −1.35942 | ||||||||
\(656\) | −27.4096 | −1.07016 | ||||||||
\(657\) | −0.190550 | −0.00743406 | ||||||||
\(658\) | −112.363 | −4.38038 | ||||||||
\(659\) | 38.9056 | 1.51555 | 0.757774 | − | 0.652517i | \(-0.226287\pi\) | ||||
0.757774 | + | 0.652517i | \(0.226287\pi\) | |||||||
\(660\) | 22.8792 | 0.890573 | ||||||||
\(661\) | 13.8252 | 0.537736 | 0.268868 | − | 0.963177i | \(-0.413350\pi\) | ||||
0.268868 | + | 0.963177i | \(0.413350\pi\) | |||||||
\(662\) | −26.7150 | −1.03831 | ||||||||
\(663\) | −1.65531 | −0.0642871 | ||||||||
\(664\) | 42.6245 | 1.65415 | ||||||||
\(665\) | −63.1131 | −2.44742 | ||||||||
\(666\) | −0.106729 | −0.00413568 | ||||||||
\(667\) | −12.3611 | −0.478622 | ||||||||
\(668\) | 13.0862 | 0.506319 | ||||||||
\(669\) | −20.9015 | −0.808099 | ||||||||
\(670\) | −60.0573 | −2.32022 | ||||||||
\(671\) | −6.63668 | −0.256206 | ||||||||
\(672\) | −23.4221 | −0.903528 | ||||||||
\(673\) | 51.0698 | 1.96860 | 0.984299 | − | 0.176511i | \(-0.0564813\pi\) | ||||
0.984299 | + | 0.176511i | \(0.0564813\pi\) | |||||||
\(674\) | −42.6411 | −1.64247 | ||||||||
\(675\) | 23.1284 | 0.890214 | ||||||||
\(676\) | −52.0498 | −2.00191 | ||||||||
\(677\) | 1.76712 | 0.0679161 | 0.0339580 | − | 0.999423i | \(-0.489189\pi\) | ||||
0.0339580 | + | 0.999423i | \(0.489189\pi\) | |||||||
\(678\) | 82.2067 | 3.15713 | ||||||||
\(679\) | 59.8783 | 2.29792 | ||||||||
\(680\) | 17.8096 | 0.682966 | ||||||||
\(681\) | −1.45032 | −0.0555762 | ||||||||
\(682\) | 2.18845 | 0.0838002 | ||||||||
\(683\) | 2.31279 | 0.0884966 | 0.0442483 | − | 0.999021i | \(-0.485911\pi\) | ||||
0.0442483 | + | 0.999021i | \(0.485911\pi\) | |||||||
\(684\) | 0.269426 | 0.0103018 | ||||||||
\(685\) | 55.7420 | 2.12979 | ||||||||
\(686\) | 26.2233 | 1.00121 | ||||||||
\(687\) | −28.9888 | −1.10599 | ||||||||
\(688\) | −5.94112 | −0.226503 | ||||||||
\(689\) | 6.95131 | 0.264824 | ||||||||
\(690\) | −18.5808 | −0.707359 | ||||||||
\(691\) | 2.51007 | 0.0954875 | 0.0477438 | − | 0.998860i | \(-0.484797\pi\) | ||||
0.0477438 | + | 0.998860i | \(0.484797\pi\) | |||||||
\(692\) | 65.9003 | 2.50515 | ||||||||
\(693\) | 0.0504433 | 0.00191618 | ||||||||
\(694\) | 68.1369 | 2.58644 | ||||||||
\(695\) | −29.6915 | −1.12626 | ||||||||
\(696\) | −88.9007 | −3.36977 | ||||||||
\(697\) | −4.61354 | −0.174750 | ||||||||
\(698\) | −51.9467 | −1.96621 | ||||||||
\(699\) | 0.868037 | 0.0328322 | ||||||||
\(700\) | −77.8794 | −2.94356 | ||||||||
\(701\) | 22.4762 | 0.848913 | 0.424457 | − | 0.905448i | \(-0.360465\pi\) | ||||
0.424457 | + | 0.905448i | \(0.360465\pi\) | |||||||
\(702\) | −12.5236 | −0.472672 | ||||||||
\(703\) | 17.3035 | 0.652612 | ||||||||
\(704\) | −3.52041 | −0.132681 | ||||||||
\(705\) | −58.3822 | −2.19880 | ||||||||
\(706\) | −18.7210 | −0.704576 | ||||||||
\(707\) | −11.0565 | −0.415824 | ||||||||
\(708\) | 70.5974 | 2.65321 | ||||||||
\(709\) | −35.5549 | −1.33529 | −0.667646 | − | 0.744479i | \(-0.732698\pi\) | ||||
−0.667646 | + | 0.744479i | \(0.732698\pi\) | |||||||
\(710\) | −113.325 | −4.25302 | ||||||||
\(711\) | −0.184683 | −0.00692615 | ||||||||
\(712\) | −35.5577 | −1.33258 | ||||||||
\(713\) | −1.21377 | −0.0454560 | ||||||||
\(714\) | −17.6685 | −0.661226 | ||||||||
\(715\) | −2.94272 | −0.110052 | ||||||||
\(716\) | −44.5082 | −1.66335 | ||||||||
\(717\) | 31.1421 | 1.16302 | ||||||||
\(718\) | −82.9080 | −3.09410 | ||||||||
\(719\) | −24.1014 | −0.898830 | −0.449415 | − | 0.893323i | \(-0.648368\pi\) | ||||
−0.449415 | + | 0.893323i | \(0.648368\pi\) | |||||||
\(720\) | 0.226257 | 0.00843209 | ||||||||
\(721\) | −49.7900 | −1.85428 | ||||||||
\(722\) | −16.2418 | −0.604458 | ||||||||
\(723\) | 50.4862 | 1.87760 | ||||||||
\(724\) | −50.3784 | −1.87230 | ||||||||
\(725\) | −39.4179 | −1.46394 | ||||||||
\(726\) | 4.34109 | 0.161113 | ||||||||
\(727\) | −31.0090 | −1.15006 | −0.575031 | − | 0.818132i | \(-0.695010\pi\) | ||||
−0.575031 | + | 0.818132i | \(0.695010\pi\) | |||||||
\(728\) | 22.5913 | 0.837291 | ||||||||
\(729\) | 27.1106 | 1.00410 | ||||||||
\(730\) | 118.652 | 4.39149 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | 49.4153 | 1.82644 | ||||||||
\(733\) | −53.2069 | −1.96524 | −0.982620 | − | 0.185628i | \(-0.940568\pi\) | ||||
−0.982620 | + | 0.185628i | \(0.940568\pi\) | |||||||
\(734\) | −61.1624 | −2.25755 | ||||||||
\(735\) | 50.8036 | 1.87392 | ||||||||
\(736\) | −4.63766 | −0.170947 | ||||||||
\(737\) | −7.78213 | −0.286658 | ||||||||
\(738\) | −0.143606 | −0.00528622 | ||||||||
\(739\) | 35.7246 | 1.31415 | 0.657076 | − | 0.753824i | \(-0.271793\pi\) | ||||
0.657076 | + | 0.753824i | \(0.271793\pi\) | |||||||
\(740\) | 45.3862 | 1.66843 | ||||||||
\(741\) | 8.35350 | 0.306874 | ||||||||
\(742\) | 74.1968 | 2.72385 | ||||||||
\(743\) | −44.3788 | −1.62810 | −0.814051 | − | 0.580794i | \(-0.802742\pi\) | ||||
−0.814051 | + | 0.580794i | \(0.802742\pi\) | |||||||
\(744\) | −8.72941 | −0.320036 | ||||||||
\(745\) | −8.23885 | −0.301848 | ||||||||
\(746\) | 80.5734 | 2.95000 | ||||||||
\(747\) | 0.0911462 | 0.00333486 | ||||||||
\(748\) | 4.30774 | 0.157506 | ||||||||
\(749\) | −28.5757 | −1.04413 | ||||||||
\(750\) | 7.44406 | 0.271819 | ||||||||
\(751\) | −53.7911 | −1.96287 | −0.981433 | − | 0.191806i | \(-0.938566\pi\) | ||||
−0.981433 | + | 0.191806i | \(0.938566\pi\) | |||||||
\(752\) | −65.3064 | −2.38148 | ||||||||
\(753\) | −19.4034 | −0.707098 | ||||||||
\(754\) | 21.3440 | 0.777303 | ||||||||
\(755\) | 39.7414 | 1.44634 | ||||||||
\(756\) | −91.2900 | −3.32018 | ||||||||
\(757\) | −13.5792 | −0.493544 | −0.246772 | − | 0.969074i | \(-0.579370\pi\) | ||||
−0.246772 | + | 0.969074i | \(0.579370\pi\) | |||||||
\(758\) | 72.6322 | 2.63812 | ||||||||
\(759\) | −2.40767 | −0.0873929 | ||||||||
\(760\) | −89.8756 | −3.26013 | ||||||||
\(761\) | 33.2124 | 1.20395 | 0.601975 | − | 0.798515i | \(-0.294381\pi\) | ||||
0.601975 | + | 0.798515i | \(0.294381\pi\) | |||||||
\(762\) | 16.3321 | 0.591649 | ||||||||
\(763\) | −75.4130 | −2.73013 | ||||||||
\(764\) | −27.7952 | −1.00559 | ||||||||
\(765\) | 0.0380832 | 0.00137690 | ||||||||
\(766\) | 68.5276 | 2.47600 | ||||||||
\(767\) | −9.08023 | −0.327868 | ||||||||
\(768\) | 55.1186 | 1.98892 | ||||||||
\(769\) | 5.48535 | 0.197807 | 0.0989035 | − | 0.995097i | \(-0.468466\pi\) | ||||
0.0989035 | + | 0.995097i | \(0.468466\pi\) | |||||||
\(770\) | −31.4100 | −1.13194 | ||||||||
\(771\) | 15.9910 | 0.575902 | ||||||||
\(772\) | 4.75848 | 0.171261 | ||||||||
\(773\) | 25.4863 | 0.916677 | 0.458338 | − | 0.888778i | \(-0.348445\pi\) | ||||
0.458338 | + | 0.888778i | \(0.348445\pi\) | |||||||
\(774\) | −0.0311271 | −0.00111884 | ||||||||
\(775\) | −3.87055 | −0.139034 | ||||||||
\(776\) | 85.2691 | 3.06098 | ||||||||
\(777\) | −24.1216 | −0.865359 | ||||||||
\(778\) | 46.3687 | 1.66240 | ||||||||
\(779\) | 23.2821 | 0.834168 | ||||||||
\(780\) | 21.9109 | 0.784536 | ||||||||
\(781\) | −14.6845 | −0.525453 | ||||||||
\(782\) | −3.49842 | −0.125103 | ||||||||
\(783\) | −46.2055 | −1.65125 | ||||||||
\(784\) | 56.8290 | 2.02961 | ||||||||
\(785\) | −49.5332 | −1.76791 | ||||||||
\(786\) | 49.1521 | 1.75320 | ||||||||
\(787\) | 36.7552 | 1.31018 | 0.655090 | − | 0.755551i | \(-0.272631\pi\) | ||||
0.655090 | + | 0.755551i | \(0.272631\pi\) | |||||||
\(788\) | −52.0761 | −1.85513 | ||||||||
\(789\) | 26.0176 | 0.926249 | ||||||||
\(790\) | 114.998 | 4.09146 | ||||||||
\(791\) | −77.0743 | −2.74044 | ||||||||
\(792\) | 0.0718332 | 0.00255248 | ||||||||
\(793\) | −6.35579 | −0.225701 | ||||||||
\(794\) | −76.3393 | −2.70918 | ||||||||
\(795\) | 38.5514 | 1.36728 | ||||||||
\(796\) | 98.3704 | 3.48665 | ||||||||
\(797\) | 8.07288 | 0.285956 | 0.142978 | − | 0.989726i | \(-0.454332\pi\) | ||||
0.142978 | + | 0.989726i | \(0.454332\pi\) | |||||||
\(798\) | 89.1635 | 3.15635 | ||||||||
\(799\) | −10.9923 | −0.388879 | ||||||||
\(800\) | −14.7889 | −0.522868 | ||||||||
\(801\) | −0.0760350 | −0.00268656 | ||||||||
\(802\) | 16.1265 | 0.569447 | ||||||||
\(803\) | 15.3747 | 0.542561 | ||||||||
\(804\) | 57.9441 | 2.04353 | ||||||||
\(805\) | 17.4207 | 0.614000 | ||||||||
\(806\) | 2.09583 | 0.0738224 | ||||||||
\(807\) | 20.0633 | 0.706262 | ||||||||
\(808\) | −15.7450 | −0.553906 | ||||||||
\(809\) | −29.7142 | −1.04469 | −0.522347 | − | 0.852733i | \(-0.674944\pi\) | ||||
−0.522347 | + | 0.852733i | \(0.674944\pi\) | |||||||
\(810\) | −69.1679 | −2.43031 | ||||||||
\(811\) | −18.7036 | −0.656771 | −0.328385 | − | 0.944544i | \(-0.606504\pi\) | ||||
−0.328385 | + | 0.944544i | \(0.606504\pi\) | |||||||
\(812\) | 155.586 | 5.46000 | ||||||||
\(813\) | 8.53412 | 0.299305 | ||||||||
\(814\) | 8.61155 | 0.301835 | ||||||||
\(815\) | −58.8961 | −2.06304 | ||||||||
\(816\) | −10.2690 | −0.359488 | ||||||||
\(817\) | 5.04648 | 0.176554 | ||||||||
\(818\) | −13.0535 | −0.456403 | ||||||||
\(819\) | 0.0483083 | 0.00168803 | ||||||||
\(820\) | 61.0680 | 2.13259 | ||||||||
\(821\) | −13.7431 | −0.479639 | −0.239819 | − | 0.970818i | \(-0.577088\pi\) | ||||
−0.239819 | + | 0.970818i | \(0.577088\pi\) | |||||||
\(822\) | −78.7500 | −2.74672 | ||||||||
\(823\) | −18.6551 | −0.650276 | −0.325138 | − | 0.945667i | \(-0.605411\pi\) | ||||
−0.325138 | + | 0.945667i | \(0.605411\pi\) | |||||||
\(824\) | −70.9029 | −2.47002 | ||||||||
\(825\) | −7.67776 | −0.267305 | ||||||||
\(826\) | −96.9204 | −3.37229 | ||||||||
\(827\) | 17.3331 | 0.602730 | 0.301365 | − | 0.953509i | \(-0.402558\pi\) | ||||
0.301365 | + | 0.953509i | \(0.402558\pi\) | |||||||
\(828\) | −0.0743681 | −0.00258447 | ||||||||
\(829\) | −9.87328 | −0.342913 | −0.171457 | − | 0.985192i | \(-0.554847\pi\) | ||||
−0.171457 | + | 0.985192i | \(0.554847\pi\) | |||||||
\(830\) | −56.7549 | −1.96999 | ||||||||
\(831\) | −39.2236 | −1.36065 | ||||||||
\(832\) | −3.37142 | −0.116883 | ||||||||
\(833\) | 9.56537 | 0.331420 | ||||||||
\(834\) | 41.9469 | 1.45250 | ||||||||
\(835\) | −9.33455 | −0.323036 | ||||||||
\(836\) | −21.7389 | −0.751855 | ||||||||
\(837\) | −4.53705 | −0.156823 | ||||||||
\(838\) | 25.9316 | 0.895792 | ||||||||
\(839\) | −10.8840 | −0.375757 | −0.187878 | − | 0.982192i | \(-0.560161\pi\) | ||||
−0.187878 | + | 0.982192i | \(0.560161\pi\) | |||||||
\(840\) | 125.290 | 4.32291 | ||||||||
\(841\) | 49.7483 | 1.71546 | ||||||||
\(842\) | −19.4109 | −0.668943 | ||||||||
\(843\) | −34.3147 | −1.18186 | ||||||||
\(844\) | 2.11190 | 0.0726945 | ||||||||
\(845\) | 37.1279 | 1.27724 | ||||||||
\(846\) | −0.342158 | −0.0117636 | ||||||||
\(847\) | −4.07006 | −0.139849 | ||||||||
\(848\) | 43.1237 | 1.48087 | ||||||||
\(849\) | −1.45941 | −0.0500869 | ||||||||
\(850\) | −11.1560 | −0.382648 | ||||||||
\(851\) | −4.77617 | −0.163725 | ||||||||
\(852\) | 109.338 | 3.74585 | ||||||||
\(853\) | −25.2059 | −0.863032 | −0.431516 | − | 0.902105i | \(-0.642021\pi\) | ||||
−0.431516 | + | 0.902105i | \(0.642021\pi\) | |||||||
\(854\) | −67.8404 | −2.32145 | ||||||||
\(855\) | −0.192186 | −0.00657262 | ||||||||
\(856\) | −40.6929 | −1.39085 | ||||||||
\(857\) | 5.71204 | 0.195119 | 0.0975597 | − | 0.995230i | \(-0.468896\pi\) | ||||
0.0975597 | + | 0.995230i | \(0.468896\pi\) | |||||||
\(858\) | 4.15735 | 0.141930 | ||||||||
\(859\) | 34.0504 | 1.16178 | 0.580892 | − | 0.813981i | \(-0.302704\pi\) | ||||
0.580892 | + | 0.813981i | \(0.302704\pi\) | |||||||
\(860\) | 13.2367 | 0.451368 | ||||||||
\(861\) | −32.4561 | −1.10610 | ||||||||
\(862\) | 14.0987 | 0.480203 | ||||||||
\(863\) | 0.247807 | 0.00843545 | 0.00421773 | − | 0.999991i | \(-0.498657\pi\) | ||||
0.00421773 | + | 0.999991i | \(0.498657\pi\) | |||||||
\(864\) | −17.3355 | −0.589767 | ||||||||
\(865\) | −47.0077 | −1.59831 | ||||||||
\(866\) | −33.7498 | −1.14686 | ||||||||
\(867\) | −1.72847 | −0.0587019 | ||||||||
\(868\) | 15.2774 | 0.518549 | ||||||||
\(869\) | 14.9013 | 0.505492 | ||||||||
\(870\) | 118.372 | 4.01319 | ||||||||
\(871\) | −7.45276 | −0.252527 | ||||||||
\(872\) | −107.391 | −3.63672 | ||||||||
\(873\) | 0.182336 | 0.00617112 | ||||||||
\(874\) | 17.6547 | 0.597179 | ||||||||
\(875\) | −6.97930 | −0.235943 | ||||||||
\(876\) | −114.477 | −3.86781 | ||||||||
\(877\) | 12.9801 | 0.438306 | 0.219153 | − | 0.975690i | \(-0.429671\pi\) | ||||
0.219153 | + | 0.975690i | \(0.429671\pi\) | |||||||
\(878\) | 49.9169 | 1.68461 | ||||||||
\(879\) | 8.03465 | 0.271002 | ||||||||
\(880\) | −18.2557 | −0.615400 | ||||||||
\(881\) | −12.2860 | −0.413927 | −0.206963 | − | 0.978349i | \(-0.566358\pi\) | ||||
−0.206963 | + | 0.978349i | \(0.566358\pi\) | |||||||
\(882\) | 0.297743 | 0.0100255 | ||||||||
\(883\) | −17.6559 | −0.594169 | −0.297085 | − | 0.954851i | \(-0.596014\pi\) | ||||
−0.297085 | + | 0.954851i | \(0.596014\pi\) | |||||||
\(884\) | 4.12542 | 0.138753 | ||||||||
\(885\) | −50.3582 | −1.69277 | ||||||||
\(886\) | 16.1943 | 0.544057 | ||||||||
\(887\) | 2.88101 | 0.0967349 | 0.0483674 | − | 0.998830i | \(-0.484598\pi\) | ||||
0.0483674 | + | 0.998830i | \(0.484598\pi\) | |||||||
\(888\) | −34.3502 | −1.15272 | ||||||||
\(889\) | −15.3124 | −0.513562 | ||||||||
\(890\) | 47.3455 | 1.58702 | ||||||||
\(891\) | −8.96267 | −0.300261 | ||||||||
\(892\) | 52.0913 | 1.74415 | ||||||||
\(893\) | 55.4723 | 1.85631 | ||||||||
\(894\) | 11.6395 | 0.389283 | ||||||||
\(895\) | 31.7484 | 1.06123 | ||||||||
\(896\) | −63.0874 | −2.10760 | ||||||||
\(897\) | −2.30577 | −0.0769873 | ||||||||
\(898\) | −22.9984 | −0.767468 | ||||||||
\(899\) | 7.73252 | 0.257894 | ||||||||
\(900\) | −0.237151 | −0.00790502 | ||||||||
\(901\) | 7.25851 | 0.241816 | ||||||||
\(902\) | 11.5870 | 0.385805 | ||||||||
\(903\) | −7.03497 | −0.234109 | ||||||||
\(904\) | −109.757 | −3.65046 | ||||||||
\(905\) | 35.9357 | 1.19454 | ||||||||
\(906\) | −56.1450 | −1.86529 | ||||||||
\(907\) | −33.5907 | −1.11536 | −0.557681 | − | 0.830056i | \(-0.688309\pi\) | ||||
−0.557681 | + | 0.830056i | \(0.688309\pi\) | |||||||
\(908\) | 3.61452 | 0.119952 | ||||||||
\(909\) | −0.0336683 | −0.00111671 | ||||||||
\(910\) | −30.0806 | −0.997162 | ||||||||
\(911\) | −53.4280 | −1.77015 | −0.885075 | − | 0.465449i | \(-0.845893\pi\) | ||||
−0.885075 | + | 0.465449i | \(0.845893\pi\) | |||||||
\(912\) | 51.8225 | 1.71601 | ||||||||
\(913\) | −7.35421 | −0.243389 | ||||||||
\(914\) | −74.4486 | −2.46254 | ||||||||
\(915\) | −35.2487 | −1.16529 | ||||||||
\(916\) | 72.2466 | 2.38710 | ||||||||
\(917\) | −46.0834 | −1.52181 | ||||||||
\(918\) | −13.0771 | −0.431607 | ||||||||
\(919\) | −21.0869 | −0.695593 | −0.347796 | − | 0.937570i | \(-0.613070\pi\) | ||||
−0.347796 | + | 0.937570i | \(0.613070\pi\) | |||||||
\(920\) | 24.8078 | 0.817890 | ||||||||
\(921\) | −53.0987 | −1.74966 | ||||||||
\(922\) | −4.36037 | −0.143601 | ||||||||
\(923\) | −14.0630 | −0.462890 | ||||||||
\(924\) | 30.3048 | 0.996955 | ||||||||
\(925\) | −15.2306 | −0.500779 | ||||||||
\(926\) | −26.1590 | −0.859638 | ||||||||
\(927\) | −0.151616 | −0.00497971 | ||||||||
\(928\) | 29.5450 | 0.969864 | ||||||||
\(929\) | 54.5513 | 1.78977 | 0.894885 | − | 0.446297i | \(-0.147257\pi\) | ||||
0.894885 | + | 0.446297i | \(0.147257\pi\) | |||||||
\(930\) | 11.6233 | 0.381143 | ||||||||
\(931\) | −48.2714 | −1.58203 | ||||||||
\(932\) | −2.16334 | −0.0708627 | ||||||||
\(933\) | −57.9041 | −1.89569 | ||||||||
\(934\) | 29.2147 | 0.955934 | ||||||||
\(935\) | −3.07277 | −0.100490 | ||||||||
\(936\) | 0.0687930 | 0.00224857 | ||||||||
\(937\) | 42.6946 | 1.39477 | 0.697386 | − | 0.716696i | \(-0.254346\pi\) | ||||
0.697386 | + | 0.716696i | \(0.254346\pi\) | |||||||
\(938\) | −79.5492 | −2.59737 | ||||||||
\(939\) | 34.7831 | 1.13510 | ||||||||
\(940\) | 145.502 | 4.74574 | ||||||||
\(941\) | −40.4869 | −1.31984 | −0.659918 | − | 0.751338i | \(-0.729409\pi\) | ||||
−0.659918 | + | 0.751338i | \(0.729409\pi\) | |||||||
\(942\) | 69.9784 | 2.28002 | ||||||||
\(943\) | −6.42642 | −0.209273 | ||||||||
\(944\) | −56.3308 | −1.83341 | ||||||||
\(945\) | 65.1185 | 2.11831 | ||||||||
\(946\) | 2.51152 | 0.0816566 | ||||||||
\(947\) | 41.8258 | 1.35915 | 0.679577 | − | 0.733604i | \(-0.262163\pi\) | ||||
0.679577 | + | 0.733604i | \(0.262163\pi\) | |||||||
\(948\) | −110.952 | −3.60355 | ||||||||
\(949\) | 14.7240 | 0.477960 | ||||||||
\(950\) | 56.2986 | 1.82657 | ||||||||
\(951\) | −46.7709 | −1.51665 | ||||||||
\(952\) | 23.5898 | 0.764548 | ||||||||
\(953\) | 42.1410 | 1.36508 | 0.682541 | − | 0.730847i | \(-0.260875\pi\) | ||||
0.682541 | + | 0.730847i | \(0.260875\pi\) | |||||||
\(954\) | 0.225937 | 0.00731497 | ||||||||
\(955\) | 19.8267 | 0.641578 | ||||||||
\(956\) | −77.6132 | −2.51019 | ||||||||
\(957\) | 15.3385 | 0.495823 | ||||||||
\(958\) | 90.4456 | 2.92216 | ||||||||
\(959\) | 73.8333 | 2.38420 | ||||||||
\(960\) | −18.6976 | −0.603463 | ||||||||
\(961\) | −30.2407 | −0.975507 | ||||||||
\(962\) | 8.24707 | 0.265896 | ||||||||
\(963\) | −0.0870158 | −0.00280405 | ||||||||
\(964\) | −125.823 | −4.05249 | ||||||||
\(965\) | −3.39430 | −0.109266 | ||||||||
\(966\) | −24.6113 | −0.791855 | ||||||||
\(967\) | −40.4434 | −1.30057 | −0.650287 | − | 0.759689i | \(-0.725351\pi\) | ||||
−0.650287 | + | 0.759689i | \(0.725351\pi\) | |||||||
\(968\) | −5.79593 | −0.186288 | ||||||||
\(969\) | 8.72268 | 0.280213 | ||||||||
\(970\) | −113.537 | −3.64544 | ||||||||
\(971\) | −32.2416 | −1.03468 | −0.517341 | − | 0.855780i | \(-0.673078\pi\) | ||||
−0.517341 | + | 0.855780i | \(0.673078\pi\) | |||||||
\(972\) | −0.554831 | −0.0177962 | ||||||||
\(973\) | −39.3280 | −1.26080 | ||||||||
\(974\) | −12.4463 | −0.398806 | ||||||||
\(975\) | −7.35281 | −0.235478 | ||||||||
\(976\) | −39.4293 | −1.26210 | ||||||||
\(977\) | −47.1595 | −1.50876 | −0.754382 | − | 0.656435i | \(-0.772063\pi\) | ||||
−0.754382 | + | 0.656435i | \(0.772063\pi\) | |||||||
\(978\) | 83.2059 | 2.66063 | ||||||||
\(979\) | 6.13495 | 0.196074 | ||||||||
\(980\) | −126.614 | −4.04453 | ||||||||
\(981\) | −0.229640 | −0.00733185 | ||||||||
\(982\) | 69.5859 | 2.22058 | ||||||||
\(983\) | 21.0037 | 0.669914 | 0.334957 | − | 0.942233i | \(-0.391278\pi\) | ||||
0.334957 | + | 0.942233i | \(0.391278\pi\) | |||||||
\(984\) | −46.2188 | −1.47340 | ||||||||
\(985\) | 37.1467 | 1.18359 | ||||||||
\(986\) | 22.2873 | 0.709772 | ||||||||
\(987\) | −77.3304 | −2.46145 | ||||||||
\(988\) | −20.8188 | −0.662335 | ||||||||
\(989\) | −1.39295 | −0.0442932 | ||||||||
\(990\) | −0.0956467 | −0.00303985 | ||||||||
\(991\) | −24.0947 | −0.765392 | −0.382696 | − | 0.923874i | \(-0.625004\pi\) | ||||
−0.382696 | + | 0.923874i | \(0.625004\pi\) | |||||||
\(992\) | 2.90111 | 0.0921104 | ||||||||
\(993\) | −18.3857 | −0.583452 | ||||||||
\(994\) | −150.106 | −4.76106 | ||||||||
\(995\) | −70.1691 | −2.22451 | ||||||||
\(996\) | 54.7579 | 1.73507 | ||||||||
\(997\) | 42.9102 | 1.35898 | 0.679490 | − | 0.733685i | \(-0.262201\pi\) | ||||
0.679490 | + | 0.733685i | \(0.262201\pi\) | |||||||
\(998\) | −48.7406 | −1.54286 | ||||||||
\(999\) | −17.8533 | −0.564853 |
(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 | 8041.2.a.c.1.5 | ✓ | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.c.1.5 | ✓ | 60 | 1.1 | even | 1 | trivial |