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: | \(74\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.65992 | −1.17374 | −0.586869 | − | 0.809682i | \(-0.699639\pi\) | ||||
−0.586869 | + | 0.809682i | \(0.699639\pi\) | |||||||
\(3\) | 0.748300 | 0.432031 | 0.216016 | − | 0.976390i | \(-0.430694\pi\) | ||||
0.216016 | + | 0.976390i | \(0.430694\pi\) | |||||||
\(4\) | 0.755318 | 0.377659 | ||||||||
\(5\) | −4.19197 | −1.87470 | −0.937352 | − | 0.348384i | \(-0.886731\pi\) | ||||
−0.937352 | + | 0.348384i | \(0.886731\pi\) | |||||||
\(6\) | −1.24211 | −0.507091 | ||||||||
\(7\) | −4.84394 | −1.83084 | −0.915419 | − | 0.402503i | \(-0.868140\pi\) | ||||
−0.915419 | + | 0.402503i | \(0.868140\pi\) | |||||||
\(8\) | 2.06607 | 0.730465 | ||||||||
\(9\) | −2.44005 | −0.813349 | ||||||||
\(10\) | 6.95831 | 2.20041 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.565204 | 0.163160 | ||||||||
\(13\) | −6.28082 | −1.74199 | −0.870994 | − | 0.491294i | \(-0.836524\pi\) | ||||
−0.870994 | + | 0.491294i | \(0.836524\pi\) | |||||||
\(14\) | 8.04053 | 2.14892 | ||||||||
\(15\) | −3.13685 | −0.809930 | ||||||||
\(16\) | −4.94013 | −1.23503 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 4.05027 | 0.954658 | ||||||||
\(19\) | −2.93145 | −0.672521 | −0.336261 | − | 0.941769i | \(-0.609162\pi\) | ||||
−0.336261 | + | 0.941769i | \(0.609162\pi\) | |||||||
\(20\) | −3.16627 | −0.707999 | ||||||||
\(21\) | −3.62472 | −0.790979 | ||||||||
\(22\) | 1.65992 | 0.353895 | ||||||||
\(23\) | 1.05441 | 0.219859 | 0.109929 | − | 0.993939i | \(-0.464938\pi\) | ||||
0.109929 | + | 0.993939i | \(0.464938\pi\) | |||||||
\(24\) | 1.54604 | 0.315583 | ||||||||
\(25\) | 12.5726 | 2.51451 | ||||||||
\(26\) | 10.4256 | 2.04464 | ||||||||
\(27\) | −4.07079 | −0.783423 | ||||||||
\(28\) | −3.65871 | −0.691432 | ||||||||
\(29\) | −3.95333 | −0.734115 | −0.367057 | − | 0.930198i | \(-0.619635\pi\) | ||||
−0.367057 | + | 0.930198i | \(0.619635\pi\) | |||||||
\(30\) | 5.20690 | 0.950645 | ||||||||
\(31\) | 8.30927 | 1.49239 | 0.746194 | − | 0.665728i | \(-0.231879\pi\) | ||||
0.746194 | + | 0.665728i | \(0.231879\pi\) | |||||||
\(32\) | 4.06806 | 0.719139 | ||||||||
\(33\) | −0.748300 | −0.130262 | ||||||||
\(34\) | 1.65992 | 0.284673 | ||||||||
\(35\) | 20.3056 | 3.43228 | ||||||||
\(36\) | −1.84301 | −0.307169 | ||||||||
\(37\) | −6.24581 | −1.02680 | −0.513402 | − | 0.858148i | \(-0.671615\pi\) | ||||
−0.513402 | + | 0.858148i | \(0.671615\pi\) | |||||||
\(38\) | 4.86596 | 0.789363 | ||||||||
\(39\) | −4.69994 | −0.752593 | ||||||||
\(40\) | −8.66088 | −1.36941 | ||||||||
\(41\) | −1.26183 | −0.197065 | −0.0985326 | − | 0.995134i | \(-0.531415\pi\) | ||||
−0.0985326 | + | 0.995134i | \(0.531415\pi\) | |||||||
\(42\) | 6.01673 | 0.928401 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −0.755318 | −0.113868 | ||||||||
\(45\) | 10.2286 | 1.52479 | ||||||||
\(46\) | −1.75022 | −0.258056 | ||||||||
\(47\) | 0.558074 | 0.0814035 | 0.0407017 | − | 0.999171i | \(-0.487041\pi\) | ||||
0.0407017 | + | 0.999171i | \(0.487041\pi\) | |||||||
\(48\) | −3.69670 | −0.533573 | ||||||||
\(49\) | 16.4638 | 2.35196 | ||||||||
\(50\) | −20.8694 | −2.95138 | ||||||||
\(51\) | −0.748300 | −0.104783 | ||||||||
\(52\) | −4.74402 | −0.657877 | ||||||||
\(53\) | 14.0460 | 1.92937 | 0.964683 | − | 0.263413i | \(-0.0848483\pi\) | ||||
0.964683 | + | 0.263413i | \(0.0848483\pi\) | |||||||
\(54\) | 6.75716 | 0.919533 | ||||||||
\(55\) | 4.19197 | 0.565244 | ||||||||
\(56\) | −10.0079 | −1.33736 | ||||||||
\(57\) | −2.19360 | −0.290550 | ||||||||
\(58\) | 6.56219 | 0.861658 | ||||||||
\(59\) | 15.2740 | 1.98851 | 0.994255 | − | 0.107040i | \(-0.0341374\pi\) | ||||
0.994255 | + | 0.107040i | \(0.0341374\pi\) | |||||||
\(60\) | −2.36932 | −0.305877 | ||||||||
\(61\) | −5.01667 | −0.642319 | −0.321159 | − | 0.947025i | \(-0.604073\pi\) | ||||
−0.321159 | + | 0.947025i | \(0.604073\pi\) | |||||||
\(62\) | −13.7927 | −1.75167 | ||||||||
\(63\) | 11.8194 | 1.48911 | ||||||||
\(64\) | 3.12762 | 0.390952 | ||||||||
\(65\) | 26.3290 | 3.26571 | ||||||||
\(66\) | 1.24211 | 0.152894 | ||||||||
\(67\) | 1.59494 | 0.194853 | 0.0974267 | − | 0.995243i | \(-0.468939\pi\) | ||||
0.0974267 | + | 0.995243i | \(0.468939\pi\) | |||||||
\(68\) | −0.755318 | −0.0915958 | ||||||||
\(69\) | 0.789011 | 0.0949858 | ||||||||
\(70\) | −33.7056 | −4.02859 | ||||||||
\(71\) | −15.0010 | −1.78029 | −0.890147 | − | 0.455674i | \(-0.849398\pi\) | ||||
−0.890147 | + | 0.455674i | \(0.849398\pi\) | |||||||
\(72\) | −5.04130 | −0.594123 | ||||||||
\(73\) | −6.68215 | −0.782087 | −0.391044 | − | 0.920372i | \(-0.627886\pi\) | ||||
−0.391044 | + | 0.920372i | \(0.627886\pi\) | |||||||
\(74\) | 10.3675 | 1.20520 | ||||||||
\(75\) | 9.40805 | 1.08635 | ||||||||
\(76\) | −2.21418 | −0.253984 | ||||||||
\(77\) | 4.84394 | 0.552018 | ||||||||
\(78\) | 7.80150 | 0.883346 | ||||||||
\(79\) | −0.622145 | −0.0699967 | −0.0349984 | − | 0.999387i | \(-0.511143\pi\) | ||||
−0.0349984 | + | 0.999387i | \(0.511143\pi\) | |||||||
\(80\) | 20.7089 | 2.31532 | ||||||||
\(81\) | 4.27397 | 0.474886 | ||||||||
\(82\) | 2.09454 | 0.231303 | ||||||||
\(83\) | 4.32948 | 0.475222 | 0.237611 | − | 0.971360i | \(-0.423636\pi\) | ||||
0.237611 | + | 0.971360i | \(0.423636\pi\) | |||||||
\(84\) | −2.73782 | −0.298720 | ||||||||
\(85\) | 4.19197 | 0.454682 | ||||||||
\(86\) | 1.65992 | 0.178993 | ||||||||
\(87\) | −2.95828 | −0.317160 | ||||||||
\(88\) | −2.06607 | −0.220243 | ||||||||
\(89\) | −9.83661 | −1.04268 | −0.521339 | − | 0.853349i | \(-0.674567\pi\) | ||||
−0.521339 | + | 0.853349i | \(0.674567\pi\) | |||||||
\(90\) | −16.9786 | −1.78970 | ||||||||
\(91\) | 30.4239 | 3.18930 | ||||||||
\(92\) | 0.796411 | 0.0830316 | ||||||||
\(93\) | 6.21783 | 0.644758 | ||||||||
\(94\) | −0.926355 | −0.0955463 | ||||||||
\(95\) | 12.2885 | 1.26078 | ||||||||
\(96\) | 3.04413 | 0.310690 | ||||||||
\(97\) | −6.90135 | −0.700726 | −0.350363 | − | 0.936614i | \(-0.613942\pi\) | ||||
−0.350363 | + | 0.936614i | \(0.613942\pi\) | |||||||
\(98\) | −27.3284 | −2.76059 | ||||||||
\(99\) | 2.44005 | 0.245234 | ||||||||
\(100\) | 9.49629 | 0.949629 | ||||||||
\(101\) | 2.85983 | 0.284563 | 0.142282 | − | 0.989826i | \(-0.454556\pi\) | ||||
0.142282 | + | 0.989826i | \(0.454556\pi\) | |||||||
\(102\) | 1.24211 | 0.122988 | ||||||||
\(103\) | 7.49956 | 0.738954 | 0.369477 | − | 0.929240i | \(-0.379537\pi\) | ||||
0.369477 | + | 0.929240i | \(0.379537\pi\) | |||||||
\(104\) | −12.9766 | −1.27246 | ||||||||
\(105\) | 15.1947 | 1.48285 | ||||||||
\(106\) | −23.3152 | −2.26457 | ||||||||
\(107\) | 3.64837 | 0.352702 | 0.176351 | − | 0.984327i | \(-0.443571\pi\) | ||||
0.176351 | + | 0.984327i | \(0.443571\pi\) | |||||||
\(108\) | −3.07474 | −0.295867 | ||||||||
\(109\) | −10.4995 | −1.00567 | −0.502834 | − | 0.864383i | \(-0.667709\pi\) | ||||
−0.502834 | + | 0.864383i | \(0.667709\pi\) | |||||||
\(110\) | −6.95831 | −0.663448 | ||||||||
\(111\) | −4.67374 | −0.443611 | ||||||||
\(112\) | 23.9297 | 2.26114 | ||||||||
\(113\) | 7.60601 | 0.715513 | 0.357757 | − | 0.933815i | \(-0.383542\pi\) | ||||
0.357757 | + | 0.933815i | \(0.383542\pi\) | |||||||
\(114\) | 3.64120 | 0.341029 | ||||||||
\(115\) | −4.42003 | −0.412170 | ||||||||
\(116\) | −2.98602 | −0.277245 | ||||||||
\(117\) | 15.3255 | 1.41684 | ||||||||
\(118\) | −25.3536 | −2.33399 | ||||||||
\(119\) | 4.84394 | 0.444043 | ||||||||
\(120\) | −6.48093 | −0.591626 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.32725 | 0.753913 | ||||||||
\(123\) | −0.944229 | −0.0851383 | ||||||||
\(124\) | 6.27614 | 0.563614 | ||||||||
\(125\) | −31.7440 | −2.83927 | ||||||||
\(126\) | −19.6193 | −1.74782 | ||||||||
\(127\) | 10.9743 | 0.973811 | 0.486905 | − | 0.873455i | \(-0.338126\pi\) | ||||
0.486905 | + | 0.873455i | \(0.338126\pi\) | |||||||
\(128\) | −13.3277 | −1.17801 | ||||||||
\(129\) | −0.748300 | −0.0658841 | ||||||||
\(130\) | −43.7039 | −3.83309 | ||||||||
\(131\) | −1.24622 | −0.108883 | −0.0544413 | − | 0.998517i | \(-0.517338\pi\) | ||||
−0.0544413 | + | 0.998517i | \(0.517338\pi\) | |||||||
\(132\) | −0.565204 | −0.0491947 | ||||||||
\(133\) | 14.1998 | 1.23128 | ||||||||
\(134\) | −2.64747 | −0.228707 | ||||||||
\(135\) | 17.0646 | 1.46869 | ||||||||
\(136\) | −2.06607 | −0.177164 | ||||||||
\(137\) | −4.42236 | −0.377827 | −0.188914 | − | 0.981994i | \(-0.560497\pi\) | ||||
−0.188914 | + | 0.981994i | \(0.560497\pi\) | |||||||
\(138\) | −1.30969 | −0.111488 | ||||||||
\(139\) | −20.1310 | −1.70749 | −0.853745 | − | 0.520691i | \(-0.825674\pi\) | ||||
−0.853745 | + | 0.520691i | \(0.825674\pi\) | |||||||
\(140\) | 15.3372 | 1.29623 | ||||||||
\(141\) | 0.417607 | 0.0351688 | ||||||||
\(142\) | 24.9004 | 2.08960 | ||||||||
\(143\) | 6.28082 | 0.525229 | ||||||||
\(144\) | 12.0542 | 1.00451 | ||||||||
\(145\) | 16.5722 | 1.37625 | ||||||||
\(146\) | 11.0918 | 0.917965 | ||||||||
\(147\) | 12.3198 | 1.01612 | ||||||||
\(148\) | −4.71757 | −0.387782 | ||||||||
\(149\) | 14.0325 | 1.14959 | 0.574795 | − | 0.818297i | \(-0.305082\pi\) | ||||
0.574795 | + | 0.818297i | \(0.305082\pi\) | |||||||
\(150\) | −15.6166 | −1.27509 | ||||||||
\(151\) | −16.8362 | −1.37011 | −0.685054 | − | 0.728492i | \(-0.740222\pi\) | ||||
−0.685054 | + | 0.728492i | \(0.740222\pi\) | |||||||
\(152\) | −6.05657 | −0.491253 | ||||||||
\(153\) | 2.44005 | 0.197266 | ||||||||
\(154\) | −8.04053 | −0.647924 | ||||||||
\(155\) | −34.8322 | −2.79779 | ||||||||
\(156\) | −3.54995 | −0.284223 | ||||||||
\(157\) | −11.4215 | −0.911538 | −0.455769 | − | 0.890098i | \(-0.650636\pi\) | ||||
−0.455769 | + | 0.890098i | \(0.650636\pi\) | |||||||
\(158\) | 1.03271 | 0.0821578 | ||||||||
\(159\) | 10.5106 | 0.833546 | ||||||||
\(160\) | −17.0532 | −1.34817 | ||||||||
\(161\) | −5.10748 | −0.402526 | ||||||||
\(162\) | −7.09443 | −0.557391 | ||||||||
\(163\) | 14.3182 | 1.12149 | 0.560744 | − | 0.827989i | \(-0.310515\pi\) | ||||
0.560744 | + | 0.827989i | \(0.310515\pi\) | |||||||
\(164\) | −0.953085 | −0.0744234 | ||||||||
\(165\) | 3.13685 | 0.244203 | ||||||||
\(166\) | −7.18657 | −0.557786 | ||||||||
\(167\) | −1.32051 | −0.102184 | −0.0510920 | − | 0.998694i | \(-0.516270\pi\) | ||||
−0.0510920 | + | 0.998694i | \(0.516270\pi\) | |||||||
\(168\) | −7.48891 | −0.577782 | ||||||||
\(169\) | 26.4488 | 2.03452 | ||||||||
\(170\) | −6.95831 | −0.533678 | ||||||||
\(171\) | 7.15288 | 0.546994 | ||||||||
\(172\) | −0.755318 | −0.0575925 | ||||||||
\(173\) | 2.99821 | 0.227950 | 0.113975 | − | 0.993484i | \(-0.463642\pi\) | ||||
0.113975 | + | 0.993484i | \(0.463642\pi\) | |||||||
\(174\) | 4.91049 | 0.372263 | ||||||||
\(175\) | −60.9008 | −4.60367 | ||||||||
\(176\) | 4.94013 | 0.372376 | ||||||||
\(177\) | 11.4296 | 0.859098 | ||||||||
\(178\) | 16.3279 | 1.22383 | ||||||||
\(179\) | −4.35032 | −0.325158 | −0.162579 | − | 0.986696i | \(-0.551981\pi\) | ||||
−0.162579 | + | 0.986696i | \(0.551981\pi\) | |||||||
\(180\) | 7.72584 | 0.575850 | ||||||||
\(181\) | −8.25994 | −0.613956 | −0.306978 | − | 0.951717i | \(-0.599318\pi\) | ||||
−0.306978 | + | 0.951717i | \(0.599318\pi\) | |||||||
\(182\) | −50.5011 | −3.74339 | ||||||||
\(183\) | −3.75397 | −0.277502 | ||||||||
\(184\) | 2.17847 | 0.160599 | ||||||||
\(185\) | 26.1822 | 1.92495 | ||||||||
\(186\) | −10.3211 | −0.756777 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 0.421523 | 0.0307428 | ||||||||
\(189\) | 19.7186 | 1.43432 | ||||||||
\(190\) | −20.3979 | −1.47982 | ||||||||
\(191\) | 4.95836 | 0.358775 | 0.179387 | − | 0.983779i | \(-0.442588\pi\) | ||||
0.179387 | + | 0.983779i | \(0.442588\pi\) | |||||||
\(192\) | 2.34040 | 0.168904 | ||||||||
\(193\) | 12.4907 | 0.899100 | 0.449550 | − | 0.893255i | \(-0.351584\pi\) | ||||
0.449550 | + | 0.893255i | \(0.351584\pi\) | |||||||
\(194\) | 11.4557 | 0.822468 | ||||||||
\(195\) | 19.7020 | 1.41089 | ||||||||
\(196\) | 12.4354 | 0.888241 | ||||||||
\(197\) | −16.1404 | −1.14995 | −0.574977 | − | 0.818169i | \(-0.694989\pi\) | ||||
−0.574977 | + | 0.818169i | \(0.694989\pi\) | |||||||
\(198\) | −4.05027 | −0.287840 | ||||||||
\(199\) | 11.8332 | 0.838831 | 0.419415 | − | 0.907794i | \(-0.362235\pi\) | ||||
0.419415 | + | 0.907794i | \(0.362235\pi\) | |||||||
\(200\) | 25.9758 | 1.83676 | ||||||||
\(201\) | 1.19350 | 0.0841827 | ||||||||
\(202\) | −4.74707 | −0.334003 | ||||||||
\(203\) | 19.1497 | 1.34404 | ||||||||
\(204\) | −0.565204 | −0.0395722 | ||||||||
\(205\) | 5.28956 | 0.369439 | ||||||||
\(206\) | −12.4486 | −0.867337 | ||||||||
\(207\) | −2.57280 | −0.178822 | ||||||||
\(208\) | 31.0281 | 2.15141 | ||||||||
\(209\) | 2.93145 | 0.202773 | ||||||||
\(210\) | −25.2219 | −1.74048 | ||||||||
\(211\) | 11.7935 | 0.811901 | 0.405950 | − | 0.913895i | \(-0.366941\pi\) | ||||
0.405950 | + | 0.913895i | \(0.366941\pi\) | |||||||
\(212\) | 10.6092 | 0.728642 | ||||||||
\(213\) | −11.2253 | −0.769142 | ||||||||
\(214\) | −6.05599 | −0.413979 | ||||||||
\(215\) | 4.19197 | 0.285890 | ||||||||
\(216\) | −8.41052 | −0.572263 | ||||||||
\(217\) | −40.2496 | −2.73232 | ||||||||
\(218\) | 17.4282 | 1.18039 | ||||||||
\(219\) | −5.00026 | −0.337886 | ||||||||
\(220\) | 3.16627 | 0.213470 | ||||||||
\(221\) | 6.28082 | 0.422494 | ||||||||
\(222\) | 7.75801 | 0.520683 | ||||||||
\(223\) | 18.5900 | 1.24488 | 0.622441 | − | 0.782667i | \(-0.286141\pi\) | ||||
0.622441 | + | 0.782667i | \(0.286141\pi\) | |||||||
\(224\) | −19.7055 | −1.31663 | ||||||||
\(225\) | −30.6777 | −2.04518 | ||||||||
\(226\) | −12.6253 | −0.839825 | ||||||||
\(227\) | 23.1495 | 1.53649 | 0.768244 | − | 0.640157i | \(-0.221131\pi\) | ||||
0.768244 | + | 0.640157i | \(0.221131\pi\) | |||||||
\(228\) | −1.65687 | −0.109729 | ||||||||
\(229\) | −13.9404 | −0.921207 | −0.460603 | − | 0.887606i | \(-0.652367\pi\) | ||||
−0.460603 | + | 0.887606i | \(0.652367\pi\) | |||||||
\(230\) | 7.33688 | 0.483779 | ||||||||
\(231\) | 3.62472 | 0.238489 | ||||||||
\(232\) | −8.16784 | −0.536245 | ||||||||
\(233\) | −18.7536 | −1.22859 | −0.614295 | − | 0.789076i | \(-0.710560\pi\) | ||||
−0.614295 | + | 0.789076i | \(0.710560\pi\) | |||||||
\(234\) | −25.4390 | −1.66300 | ||||||||
\(235\) | −2.33943 | −0.152607 | ||||||||
\(236\) | 11.5367 | 0.750978 | ||||||||
\(237\) | −0.465551 | −0.0302408 | ||||||||
\(238\) | −8.04053 | −0.521190 | ||||||||
\(239\) | −16.0295 | −1.03686 | −0.518430 | − | 0.855120i | \(-0.673483\pi\) | ||||
−0.518430 | + | 0.855120i | \(0.673483\pi\) | |||||||
\(240\) | 15.4964 | 1.00029 | ||||||||
\(241\) | 29.2477 | 1.88401 | 0.942004 | − | 0.335601i | \(-0.108939\pi\) | ||||
0.942004 | + | 0.335601i | \(0.108939\pi\) | |||||||
\(242\) | −1.65992 | −0.106703 | ||||||||
\(243\) | 15.4106 | 0.988589 | ||||||||
\(244\) | −3.78918 | −0.242577 | ||||||||
\(245\) | −69.0155 | −4.40924 | ||||||||
\(246\) | 1.56734 | 0.0999300 | ||||||||
\(247\) | 18.4119 | 1.17152 | ||||||||
\(248\) | 17.1675 | 1.09014 | ||||||||
\(249\) | 3.23975 | 0.205311 | ||||||||
\(250\) | 52.6923 | 3.33255 | ||||||||
\(251\) | 4.61912 | 0.291556 | 0.145778 | − | 0.989317i | \(-0.453431\pi\) | ||||
0.145778 | + | 0.989317i | \(0.453431\pi\) | |||||||
\(252\) | 8.92744 | 0.562376 | ||||||||
\(253\) | −1.05441 | −0.0662899 | ||||||||
\(254\) | −18.2164 | −1.14300 | ||||||||
\(255\) | 3.13685 | 0.196437 | ||||||||
\(256\) | 15.8676 | 0.991727 | ||||||||
\(257\) | −9.98817 | −0.623045 | −0.311522 | − | 0.950239i | \(-0.600839\pi\) | ||||
−0.311522 | + | 0.950239i | \(0.600839\pi\) | |||||||
\(258\) | 1.24211 | 0.0773306 | ||||||||
\(259\) | 30.2543 | 1.87991 | ||||||||
\(260\) | 19.8868 | 1.23332 | ||||||||
\(261\) | 9.64631 | 0.597092 | ||||||||
\(262\) | 2.06862 | 0.127799 | ||||||||
\(263\) | 16.3803 | 1.01005 | 0.505026 | − | 0.863104i | \(-0.331483\pi\) | ||||
0.505026 | + | 0.863104i | \(0.331483\pi\) | |||||||
\(264\) | −1.54604 | −0.0951520 | ||||||||
\(265\) | −58.8803 | −3.61699 | ||||||||
\(266\) | −23.5704 | −1.44520 | ||||||||
\(267\) | −7.36073 | −0.450470 | ||||||||
\(268\) | 1.20469 | 0.0735881 | ||||||||
\(269\) | 3.69553 | 0.225321 | 0.112660 | − | 0.993634i | \(-0.464063\pi\) | ||||
0.112660 | + | 0.993634i | \(0.464063\pi\) | |||||||
\(270\) | −28.3258 | −1.72385 | ||||||||
\(271\) | −1.96926 | −0.119624 | −0.0598121 | − | 0.998210i | \(-0.519050\pi\) | ||||
−0.0598121 | + | 0.998210i | \(0.519050\pi\) | |||||||
\(272\) | 4.94013 | 0.299539 | ||||||||
\(273\) | 22.7662 | 1.37787 | ||||||||
\(274\) | 7.34074 | 0.443470 | ||||||||
\(275\) | −12.5726 | −0.758155 | ||||||||
\(276\) | 0.595955 | 0.0358722 | ||||||||
\(277\) | −12.2466 | −0.735825 | −0.367912 | − | 0.929860i | \(-0.619927\pi\) | ||||
−0.367912 | + | 0.929860i | \(0.619927\pi\) | |||||||
\(278\) | 33.4158 | 2.00415 | ||||||||
\(279\) | −20.2750 | −1.21383 | ||||||||
\(280\) | 41.9528 | 2.50716 | ||||||||
\(281\) | −16.1496 | −0.963406 | −0.481703 | − | 0.876334i | \(-0.659982\pi\) | ||||
−0.481703 | + | 0.876334i | \(0.659982\pi\) | |||||||
\(282\) | −0.693192 | −0.0412790 | ||||||||
\(283\) | −11.3884 | −0.676973 | −0.338486 | − | 0.940971i | \(-0.609915\pi\) | ||||
−0.338486 | + | 0.940971i | \(0.609915\pi\) | |||||||
\(284\) | −11.3305 | −0.672344 | ||||||||
\(285\) | 9.19551 | 0.544695 | ||||||||
\(286\) | −10.4256 | −0.616481 | ||||||||
\(287\) | 6.11224 | 0.360794 | ||||||||
\(288\) | −9.92627 | −0.584911 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −27.5085 | −1.61535 | ||||||||
\(291\) | −5.16428 | −0.302735 | ||||||||
\(292\) | −5.04715 | −0.295362 | ||||||||
\(293\) | 21.4206 | 1.25140 | 0.625701 | − | 0.780063i | \(-0.284813\pi\) | ||||
0.625701 | + | 0.780063i | \(0.284813\pi\) | |||||||
\(294\) | −20.4499 | −1.19266 | ||||||||
\(295\) | −64.0282 | −3.72787 | ||||||||
\(296\) | −12.9043 | −0.750044 | ||||||||
\(297\) | 4.07079 | 0.236211 | ||||||||
\(298\) | −23.2928 | −1.34932 | ||||||||
\(299\) | −6.62254 | −0.382991 | ||||||||
\(300\) | 7.10607 | 0.410269 | ||||||||
\(301\) | 4.84394 | 0.279200 | ||||||||
\(302\) | 27.9466 | 1.60815 | ||||||||
\(303\) | 2.14001 | 0.122940 | ||||||||
\(304\) | 14.4818 | 0.830586 | ||||||||
\(305\) | 21.0297 | 1.20416 | ||||||||
\(306\) | −4.05027 | −0.231539 | ||||||||
\(307\) | 13.5387 | 0.772692 | 0.386346 | − | 0.922354i | \(-0.373737\pi\) | ||||
0.386346 | + | 0.922354i | \(0.373737\pi\) | |||||||
\(308\) | 3.65871 | 0.208475 | ||||||||
\(309\) | 5.61192 | 0.319251 | ||||||||
\(310\) | 57.8184 | 3.28387 | ||||||||
\(311\) | −14.3700 | −0.814846 | −0.407423 | − | 0.913240i | \(-0.633573\pi\) | ||||
−0.407423 | + | 0.913240i | \(0.633573\pi\) | |||||||
\(312\) | −9.71039 | −0.549742 | ||||||||
\(313\) | 26.5219 | 1.49911 | 0.749553 | − | 0.661944i | \(-0.230268\pi\) | ||||
0.749553 | + | 0.661944i | \(0.230268\pi\) | |||||||
\(314\) | 18.9588 | 1.06991 | ||||||||
\(315\) | −49.5467 | −2.79164 | ||||||||
\(316\) | −0.469917 | −0.0264349 | ||||||||
\(317\) | −6.68822 | −0.375648 | −0.187824 | − | 0.982203i | \(-0.560143\pi\) | ||||
−0.187824 | + | 0.982203i | \(0.560143\pi\) | |||||||
\(318\) | −17.4467 | −0.978364 | ||||||||
\(319\) | 3.95333 | 0.221344 | ||||||||
\(320\) | −13.1109 | −0.732920 | ||||||||
\(321\) | 2.73008 | 0.152378 | ||||||||
\(322\) | 8.47798 | 0.472459 | ||||||||
\(323\) | 2.93145 | 0.163110 | ||||||||
\(324\) | 3.22821 | 0.179345 | ||||||||
\(325\) | −78.9661 | −4.38025 | ||||||||
\(326\) | −23.7670 | −1.31633 | ||||||||
\(327\) | −7.85676 | −0.434480 | ||||||||
\(328\) | −2.60703 | −0.143949 | ||||||||
\(329\) | −2.70328 | −0.149036 | ||||||||
\(330\) | −5.20690 | −0.286630 | ||||||||
\(331\) | 5.75600 | 0.316379 | 0.158189 | − | 0.987409i | \(-0.449434\pi\) | ||||
0.158189 | + | 0.987409i | \(0.449434\pi\) | |||||||
\(332\) | 3.27013 | 0.179472 | ||||||||
\(333\) | 15.2401 | 0.835150 | ||||||||
\(334\) | 2.19193 | 0.119937 | ||||||||
\(335\) | −6.68595 | −0.365292 | ||||||||
\(336\) | 17.9066 | 0.976884 | ||||||||
\(337\) | 5.51727 | 0.300545 | 0.150273 | − | 0.988645i | \(-0.451985\pi\) | ||||
0.150273 | + | 0.988645i | \(0.451985\pi\) | |||||||
\(338\) | −43.9027 | −2.38799 | ||||||||
\(339\) | 5.69158 | 0.309124 | ||||||||
\(340\) | 3.16627 | 0.171715 | ||||||||
\(341\) | −8.30927 | −0.449972 | ||||||||
\(342\) | −11.8732 | −0.642028 | ||||||||
\(343\) | −45.8419 | −2.47523 | ||||||||
\(344\) | −2.06607 | −0.111395 | ||||||||
\(345\) | −3.30751 | −0.178070 | ||||||||
\(346\) | −4.97677 | −0.267553 | ||||||||
\(347\) | 5.45601 | 0.292894 | 0.146447 | − | 0.989219i | \(-0.453216\pi\) | ||||
0.146447 | + | 0.989219i | \(0.453216\pi\) | |||||||
\(348\) | −2.23444 | −0.119778 | ||||||||
\(349\) | 28.9211 | 1.54811 | 0.774054 | − | 0.633119i | \(-0.218226\pi\) | ||||
0.774054 | + | 0.633119i | \(0.218226\pi\) | |||||||
\(350\) | 101.090 | 5.40349 | ||||||||
\(351\) | 25.5679 | 1.36471 | ||||||||
\(352\) | −4.06806 | −0.216829 | ||||||||
\(353\) | −25.1437 | −1.33826 | −0.669132 | − | 0.743143i | \(-0.733334\pi\) | ||||
−0.669132 | + | 0.743143i | \(0.733334\pi\) | |||||||
\(354\) | −18.9721 | −1.00836 | ||||||||
\(355\) | 62.8837 | 3.33752 | ||||||||
\(356\) | −7.42977 | −0.393777 | ||||||||
\(357\) | 3.62472 | 0.191840 | ||||||||
\(358\) | 7.22116 | 0.381650 | ||||||||
\(359\) | −30.6370 | −1.61696 | −0.808479 | − | 0.588525i | \(-0.799709\pi\) | ||||
−0.808479 | + | 0.588525i | \(0.799709\pi\) | |||||||
\(360\) | 21.1330 | 1.11380 | ||||||||
\(361\) | −10.4066 | −0.547715 | ||||||||
\(362\) | 13.7108 | 0.720623 | ||||||||
\(363\) | 0.748300 | 0.0392756 | ||||||||
\(364\) | 22.9797 | 1.20447 | ||||||||
\(365\) | 28.0114 | 1.46618 | ||||||||
\(366\) | 6.23128 | 0.325714 | ||||||||
\(367\) | −0.270533 | −0.0141217 | −0.00706084 | − | 0.999975i | \(-0.502248\pi\) | ||||
−0.00706084 | + | 0.999975i | \(0.502248\pi\) | |||||||
\(368\) | −5.20890 | −0.271533 | ||||||||
\(369\) | 3.07893 | 0.160283 | ||||||||
\(370\) | −43.4602 | −2.25939 | ||||||||
\(371\) | −68.0380 | −3.53236 | ||||||||
\(372\) | 4.69644 | 0.243499 | ||||||||
\(373\) | 16.5054 | 0.854619 | 0.427309 | − | 0.904105i | \(-0.359462\pi\) | ||||
0.427309 | + | 0.904105i | \(0.359462\pi\) | |||||||
\(374\) | −1.65992 | −0.0858322 | ||||||||
\(375\) | −23.7540 | −1.22665 | ||||||||
\(376\) | 1.15302 | 0.0594624 | ||||||||
\(377\) | 24.8302 | 1.27882 | ||||||||
\(378\) | −32.7313 | −1.68352 | ||||||||
\(379\) | 31.9969 | 1.64357 | 0.821785 | − | 0.569797i | \(-0.192978\pi\) | ||||
0.821785 | + | 0.569797i | \(0.192978\pi\) | |||||||
\(380\) | 9.28176 | 0.476144 | ||||||||
\(381\) | 8.21206 | 0.420717 | ||||||||
\(382\) | −8.23046 | −0.421107 | ||||||||
\(383\) | 15.6854 | 0.801487 | 0.400744 | − | 0.916190i | \(-0.368752\pi\) | ||||
0.400744 | + | 0.916190i | \(0.368752\pi\) | |||||||
\(384\) | −9.97312 | −0.508939 | ||||||||
\(385\) | −20.3056 | −1.03487 | ||||||||
\(386\) | −20.7335 | −1.05531 | ||||||||
\(387\) | 2.44005 | 0.124035 | ||||||||
\(388\) | −5.21272 | −0.264636 | ||||||||
\(389\) | −33.7230 | −1.70982 | −0.854912 | − | 0.518773i | \(-0.826389\pi\) | ||||
−0.854912 | + | 0.518773i | \(0.826389\pi\) | |||||||
\(390\) | −32.7036 | −1.65601 | ||||||||
\(391\) | −1.05441 | −0.0533236 | ||||||||
\(392\) | 34.0152 | 1.71803 | ||||||||
\(393\) | −0.932544 | −0.0470406 | ||||||||
\(394\) | 26.7917 | 1.34974 | ||||||||
\(395\) | 2.60801 | 0.131223 | ||||||||
\(396\) | 1.84301 | 0.0926148 | ||||||||
\(397\) | −3.36733 | −0.169002 | −0.0845008 | − | 0.996423i | \(-0.526930\pi\) | ||||
−0.0845008 | + | 0.996423i | \(0.526930\pi\) | |||||||
\(398\) | −19.6421 | −0.984567 | ||||||||
\(399\) | 10.6257 | 0.531950 | ||||||||
\(400\) | −62.1102 | −3.10551 | ||||||||
\(401\) | −24.3690 | −1.21693 | −0.608466 | − | 0.793580i | \(-0.708215\pi\) | ||||
−0.608466 | + | 0.793580i | \(0.708215\pi\) | |||||||
\(402\) | −1.98110 | −0.0988084 | ||||||||
\(403\) | −52.1891 | −2.59972 | ||||||||
\(404\) | 2.16008 | 0.107468 | ||||||||
\(405\) | −17.9163 | −0.890271 | ||||||||
\(406\) | −31.7869 | −1.57756 | ||||||||
\(407\) | 6.24581 | 0.309593 | ||||||||
\(408\) | −1.54604 | −0.0765402 | ||||||||
\(409\) | −13.9069 | −0.687653 | −0.343827 | − | 0.939033i | \(-0.611723\pi\) | ||||
−0.343827 | + | 0.939033i | \(0.611723\pi\) | |||||||
\(410\) | −8.78022 | −0.433624 | ||||||||
\(411\) | −3.30925 | −0.163233 | ||||||||
\(412\) | 5.66455 | 0.279072 | ||||||||
\(413\) | −73.9865 | −3.64064 | ||||||||
\(414\) | 4.27063 | 0.209890 | ||||||||
\(415\) | −18.1490 | −0.890900 | ||||||||
\(416\) | −25.5508 | −1.25273 | ||||||||
\(417\) | −15.0640 | −0.737689 | ||||||||
\(418\) | −4.86596 | −0.238002 | ||||||||
\(419\) | −14.3978 | −0.703378 | −0.351689 | − | 0.936117i | \(-0.614393\pi\) | ||||
−0.351689 | + | 0.936117i | \(0.614393\pi\) | |||||||
\(420\) | 11.4768 | 0.560012 | ||||||||
\(421\) | 10.9606 | 0.534188 | 0.267094 | − | 0.963671i | \(-0.413937\pi\) | ||||
0.267094 | + | 0.963671i | \(0.413937\pi\) | |||||||
\(422\) | −19.5763 | −0.952958 | ||||||||
\(423\) | −1.36173 | −0.0662094 | ||||||||
\(424\) | 29.0200 | 1.40933 | ||||||||
\(425\) | −12.5726 | −0.609859 | ||||||||
\(426\) | 18.6330 | 0.902771 | ||||||||
\(427\) | 24.3004 | 1.17598 | ||||||||
\(428\) | 2.75568 | 0.133201 | ||||||||
\(429\) | 4.69994 | 0.226915 | ||||||||
\(430\) | −6.95831 | −0.335559 | ||||||||
\(431\) | −29.3010 | −1.41138 | −0.705689 | − | 0.708522i | \(-0.749362\pi\) | ||||
−0.705689 | + | 0.708522i | \(0.749362\pi\) | |||||||
\(432\) | 20.1102 | 0.967553 | ||||||||
\(433\) | −29.3956 | −1.41266 | −0.706332 | − | 0.707881i | \(-0.749651\pi\) | ||||
−0.706332 | + | 0.707881i | \(0.749651\pi\) | |||||||
\(434\) | 66.8109 | 3.20703 | ||||||||
\(435\) | 12.4010 | 0.594582 | ||||||||
\(436\) | −7.93044 | −0.379799 | ||||||||
\(437\) | −3.09094 | −0.147860 | ||||||||
\(438\) | 8.30000 | 0.396589 | ||||||||
\(439\) | −3.26017 | −0.155599 | −0.0777997 | − | 0.996969i | \(-0.524789\pi\) | ||||
−0.0777997 | + | 0.996969i | \(0.524789\pi\) | |||||||
\(440\) | 8.66088 | 0.412891 | ||||||||
\(441\) | −40.1723 | −1.91297 | ||||||||
\(442\) | −10.4256 | −0.495897 | ||||||||
\(443\) | 0.721239 | 0.0342671 | 0.0171336 | − | 0.999853i | \(-0.494546\pi\) | ||||
0.0171336 | + | 0.999853i | \(0.494546\pi\) | |||||||
\(444\) | −3.53016 | −0.167534 | ||||||||
\(445\) | 41.2347 | 1.95471 | ||||||||
\(446\) | −30.8579 | −1.46116 | ||||||||
\(447\) | 10.5005 | 0.496659 | ||||||||
\(448\) | −15.1500 | −0.715770 | ||||||||
\(449\) | −36.3085 | −1.71350 | −0.856752 | − | 0.515729i | \(-0.827521\pi\) | ||||
−0.856752 | + | 0.515729i | \(0.827521\pi\) | |||||||
\(450\) | 50.9223 | 2.40050 | ||||||||
\(451\) | 1.26183 | 0.0594174 | ||||||||
\(452\) | 5.74496 | 0.270220 | ||||||||
\(453\) | −12.5985 | −0.591930 | ||||||||
\(454\) | −38.4263 | −1.80343 | ||||||||
\(455\) | −127.536 | −5.97898 | ||||||||
\(456\) | −4.53213 | −0.212237 | ||||||||
\(457\) | −8.69797 | −0.406874 | −0.203437 | − | 0.979088i | \(-0.565211\pi\) | ||||
−0.203437 | + | 0.979088i | \(0.565211\pi\) | |||||||
\(458\) | 23.1399 | 1.08125 | ||||||||
\(459\) | 4.07079 | 0.190008 | ||||||||
\(460\) | −3.33853 | −0.155660 | ||||||||
\(461\) | 22.3554 | 1.04119 | 0.520597 | − | 0.853803i | \(-0.325709\pi\) | ||||
0.520597 | + | 0.853803i | \(0.325709\pi\) | |||||||
\(462\) | −6.01673 | −0.279923 | ||||||||
\(463\) | 20.6109 | 0.957869 | 0.478935 | − | 0.877851i | \(-0.341023\pi\) | ||||
0.478935 | + | 0.877851i | \(0.341023\pi\) | |||||||
\(464\) | 19.5300 | 0.906656 | ||||||||
\(465\) | −26.0649 | −1.20873 | ||||||||
\(466\) | 31.1294 | 1.44204 | ||||||||
\(467\) | 15.9024 | 0.735875 | 0.367937 | − | 0.929851i | \(-0.380064\pi\) | ||||
0.367937 | + | 0.929851i | \(0.380064\pi\) | |||||||
\(468\) | 11.5756 | 0.535084 | ||||||||
\(469\) | −7.72581 | −0.356745 | ||||||||
\(470\) | 3.88325 | 0.179121 | ||||||||
\(471\) | −8.54673 | −0.393813 | ||||||||
\(472\) | 31.5572 | 1.45254 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 0.772775 | 0.0354947 | ||||||||
\(475\) | −36.8559 | −1.69106 | ||||||||
\(476\) | 3.65871 | 0.167697 | ||||||||
\(477\) | −34.2729 | −1.56925 | ||||||||
\(478\) | 26.6075 | 1.21700 | ||||||||
\(479\) | 32.9750 | 1.50667 | 0.753334 | − | 0.657638i | \(-0.228444\pi\) | ||||
0.753334 | + | 0.657638i | \(0.228444\pi\) | |||||||
\(480\) | −12.7609 | −0.582453 | ||||||||
\(481\) | 39.2288 | 1.78868 | ||||||||
\(482\) | −48.5487 | −2.21133 | ||||||||
\(483\) | −3.82192 | −0.173904 | ||||||||
\(484\) | 0.755318 | 0.0343326 | ||||||||
\(485\) | 28.9302 | 1.31365 | ||||||||
\(486\) | −25.5802 | −1.16034 | ||||||||
\(487\) | 0.659605 | 0.0298895 | 0.0149448 | − | 0.999888i | \(-0.495243\pi\) | ||||
0.0149448 | + | 0.999888i | \(0.495243\pi\) | |||||||
\(488\) | −10.3648 | −0.469191 | ||||||||
\(489\) | 10.7143 | 0.484517 | ||||||||
\(490\) | 114.560 | 5.17529 | ||||||||
\(491\) | 9.54344 | 0.430689 | 0.215345 | − | 0.976538i | \(-0.430912\pi\) | ||||
0.215345 | + | 0.976538i | \(0.430912\pi\) | |||||||
\(492\) | −0.713193 | −0.0321532 | ||||||||
\(493\) | 3.95333 | 0.178049 | ||||||||
\(494\) | −30.5622 | −1.37506 | ||||||||
\(495\) | −10.2286 | −0.459741 | ||||||||
\(496\) | −41.0489 | −1.84315 | ||||||||
\(497\) | 72.6640 | 3.25943 | ||||||||
\(498\) | −5.37771 | −0.240981 | ||||||||
\(499\) | −40.7447 | −1.82398 | −0.911991 | − | 0.410210i | \(-0.865455\pi\) | ||||
−0.911991 | + | 0.410210i | \(0.865455\pi\) | |||||||
\(500\) | −23.9768 | −1.07227 | ||||||||
\(501\) | −0.988136 | −0.0441467 | ||||||||
\(502\) | −7.66735 | −0.342211 | ||||||||
\(503\) | −11.5257 | −0.513904 | −0.256952 | − | 0.966424i | \(-0.582718\pi\) | ||||
−0.256952 | + | 0.966424i | \(0.582718\pi\) | |||||||
\(504\) | 24.4198 | 1.08774 | ||||||||
\(505\) | −11.9883 | −0.533472 | ||||||||
\(506\) | 1.75022 | 0.0778069 | ||||||||
\(507\) | 19.7916 | 0.878976 | ||||||||
\(508\) | 8.28908 | 0.367768 | ||||||||
\(509\) | 35.9366 | 1.59286 | 0.796432 | − | 0.604729i | \(-0.206718\pi\) | ||||
0.796432 | + | 0.604729i | \(0.206718\pi\) | |||||||
\(510\) | −5.20690 | −0.230565 | ||||||||
\(511\) | 32.3680 | 1.43187 | ||||||||
\(512\) | 0.316506 | 0.0139877 | ||||||||
\(513\) | 11.9333 | 0.526869 | ||||||||
\(514\) | 16.5795 | 0.731291 | ||||||||
\(515\) | −31.4379 | −1.38532 | ||||||||
\(516\) | −0.565204 | −0.0248817 | ||||||||
\(517\) | −0.558074 | −0.0245441 | ||||||||
\(518\) | −50.2196 | −2.20652 | ||||||||
\(519\) | 2.24356 | 0.0984813 | ||||||||
\(520\) | 54.3975 | 2.38549 | ||||||||
\(521\) | 24.1351 | 1.05738 | 0.528689 | − | 0.848815i | \(-0.322684\pi\) | ||||
0.528689 | + | 0.848815i | \(0.322684\pi\) | |||||||
\(522\) | −16.0121 | −0.700829 | ||||||||
\(523\) | 24.2416 | 1.06001 | 0.530006 | − | 0.847994i | \(-0.322190\pi\) | ||||
0.530006 | + | 0.847994i | \(0.322190\pi\) | |||||||
\(524\) | −0.941291 | −0.0411205 | ||||||||
\(525\) | −45.5720 | −1.98893 | ||||||||
\(526\) | −27.1899 | −1.18554 | ||||||||
\(527\) | −8.30927 | −0.361957 | ||||||||
\(528\) | 3.69670 | 0.160878 | ||||||||
\(529\) | −21.8882 | −0.951662 | ||||||||
\(530\) | 97.7364 | 4.24540 | ||||||||
\(531\) | −37.2694 | −1.61735 | ||||||||
\(532\) | 10.7253 | 0.465003 | ||||||||
\(533\) | 7.92535 | 0.343285 | ||||||||
\(534\) | 12.2182 | 0.528733 | ||||||||
\(535\) | −15.2939 | −0.661211 | ||||||||
\(536\) | 3.29526 | 0.142334 | ||||||||
\(537\) | −3.25534 | −0.140478 | ||||||||
\(538\) | −6.13427 | −0.264467 | ||||||||
\(539\) | −16.4638 | −0.709144 | ||||||||
\(540\) | 12.8892 | 0.554663 | ||||||||
\(541\) | 12.5408 | 0.539169 | 0.269585 | − | 0.962977i | \(-0.413114\pi\) | ||||
0.269585 | + | 0.962977i | \(0.413114\pi\) | |||||||
\(542\) | 3.26881 | 0.140407 | ||||||||
\(543\) | −6.18091 | −0.265248 | ||||||||
\(544\) | −4.06806 | −0.174417 | ||||||||
\(545\) | 44.0134 | 1.88533 | ||||||||
\(546\) | −37.7900 | −1.61726 | ||||||||
\(547\) | 23.2311 | 0.993291 | 0.496646 | − | 0.867953i | \(-0.334565\pi\) | ||||
0.496646 | + | 0.867953i | \(0.334565\pi\) | |||||||
\(548\) | −3.34029 | −0.142690 | ||||||||
\(549\) | 12.2409 | 0.522429 | ||||||||
\(550\) | 20.8694 | 0.889874 | ||||||||
\(551\) | 11.5890 | 0.493708 | ||||||||
\(552\) | 1.63015 | 0.0693838 | ||||||||
\(553\) | 3.01363 | 0.128153 | ||||||||
\(554\) | 20.3283 | 0.863665 | ||||||||
\(555\) | 19.5921 | 0.831640 | ||||||||
\(556\) | −15.2053 | −0.644849 | ||||||||
\(557\) | −14.2236 | −0.602673 | −0.301336 | − | 0.953518i | \(-0.597433\pi\) | ||||
−0.301336 | + | 0.953518i | \(0.597433\pi\) | |||||||
\(558\) | 33.6548 | 1.42472 | ||||||||
\(559\) | 6.28082 | 0.265651 | ||||||||
\(560\) | −100.312 | −4.23897 | ||||||||
\(561\) | 0.748300 | 0.0315932 | ||||||||
\(562\) | 26.8070 | 1.13079 | ||||||||
\(563\) | 32.8224 | 1.38330 | 0.691650 | − | 0.722233i | \(-0.256884\pi\) | ||||
0.691650 | + | 0.722233i | \(0.256884\pi\) | |||||||
\(564\) | 0.315426 | 0.0132818 | ||||||||
\(565\) | −31.8841 | −1.34138 | ||||||||
\(566\) | 18.9039 | 0.794588 | ||||||||
\(567\) | −20.7029 | −0.869439 | ||||||||
\(568\) | −30.9931 | −1.30044 | ||||||||
\(569\) | 31.7758 | 1.33211 | 0.666056 | − | 0.745902i | \(-0.267981\pi\) | ||||
0.666056 | + | 0.745902i | \(0.267981\pi\) | |||||||
\(570\) | −15.2638 | −0.639329 | ||||||||
\(571\) | 31.3723 | 1.31289 | 0.656445 | − | 0.754374i | \(-0.272059\pi\) | ||||
0.656445 | + | 0.754374i | \(0.272059\pi\) | |||||||
\(572\) | 4.74402 | 0.198357 | ||||||||
\(573\) | 3.71034 | 0.155002 | ||||||||
\(574\) | −10.1458 | −0.423478 | ||||||||
\(575\) | 13.2566 | 0.552838 | ||||||||
\(576\) | −7.63154 | −0.317981 | ||||||||
\(577\) | −31.3695 | −1.30593 | −0.652966 | − | 0.757388i | \(-0.726475\pi\) | ||||
−0.652966 | + | 0.757388i | \(0.726475\pi\) | |||||||
\(578\) | −1.65992 | −0.0690434 | ||||||||
\(579\) | 9.34678 | 0.388439 | ||||||||
\(580\) | 12.5173 | 0.519752 | ||||||||
\(581\) | −20.9717 | −0.870054 | ||||||||
\(582\) | 8.57227 | 0.355332 | ||||||||
\(583\) | −14.0460 | −0.581726 | ||||||||
\(584\) | −13.8058 | −0.571287 | ||||||||
\(585\) | −64.2440 | −2.65616 | ||||||||
\(586\) | −35.5563 | −1.46882 | ||||||||
\(587\) | 18.2496 | 0.753243 | 0.376622 | − | 0.926367i | \(-0.377086\pi\) | ||||
0.376622 | + | 0.926367i | \(0.377086\pi\) | |||||||
\(588\) | 9.30538 | 0.383748 | ||||||||
\(589\) | −24.3582 | −1.00366 | ||||||||
\(590\) | 106.281 | 4.37554 | ||||||||
\(591\) | −12.0778 | −0.496816 | ||||||||
\(592\) | 30.8551 | 1.26814 | ||||||||
\(593\) | −7.34187 | −0.301494 | −0.150747 | − | 0.988572i | \(-0.548168\pi\) | ||||
−0.150747 | + | 0.988572i | \(0.548168\pi\) | |||||||
\(594\) | −6.75716 | −0.277250 | ||||||||
\(595\) | −20.3056 | −0.832450 | ||||||||
\(596\) | 10.5990 | 0.434153 | ||||||||
\(597\) | 8.85476 | 0.362401 | ||||||||
\(598\) | 10.9928 | 0.449531 | ||||||||
\(599\) | −48.7027 | −1.98994 | −0.994969 | − | 0.100188i | \(-0.968056\pi\) | ||||
−0.994969 | + | 0.100188i | \(0.968056\pi\) | |||||||
\(600\) | 19.4377 | 0.793539 | ||||||||
\(601\) | 39.5910 | 1.61495 | 0.807476 | − | 0.589900i | \(-0.200833\pi\) | ||||
0.807476 | + | 0.589900i | \(0.200833\pi\) | |||||||
\(602\) | −8.04053 | −0.327707 | ||||||||
\(603\) | −3.89174 | −0.158484 | ||||||||
\(604\) | −12.7167 | −0.517434 | ||||||||
\(605\) | −4.19197 | −0.170428 | ||||||||
\(606\) | −3.55223 | −0.144299 | ||||||||
\(607\) | −4.78672 | −0.194287 | −0.0971434 | − | 0.995270i | \(-0.530971\pi\) | ||||
−0.0971434 | + | 0.995270i | \(0.530971\pi\) | |||||||
\(608\) | −11.9253 | −0.483636 | ||||||||
\(609\) | 14.3297 | 0.580669 | ||||||||
\(610\) | −34.9075 | −1.41336 | ||||||||
\(611\) | −3.50516 | −0.141804 | ||||||||
\(612\) | 1.84301 | 0.0744993 | ||||||||
\(613\) | 15.6460 | 0.631937 | 0.315969 | − | 0.948770i | \(-0.397671\pi\) | ||||
0.315969 | + | 0.948770i | \(0.397671\pi\) | |||||||
\(614\) | −22.4730 | −0.906938 | ||||||||
\(615\) | 3.95818 | 0.159609 | ||||||||
\(616\) | 10.0079 | 0.403230 | ||||||||
\(617\) | 42.6394 | 1.71660 | 0.858298 | − | 0.513152i | \(-0.171522\pi\) | ||||
0.858298 | + | 0.513152i | \(0.171522\pi\) | |||||||
\(618\) | −9.31531 | −0.374717 | ||||||||
\(619\) | 47.2806 | 1.90037 | 0.950184 | − | 0.311689i | \(-0.100895\pi\) | ||||
0.950184 | + | 0.311689i | \(0.100895\pi\) | |||||||
\(620\) | −26.3094 | −1.05661 | ||||||||
\(621\) | −4.29226 | −0.172242 | ||||||||
\(622\) | 23.8529 | 0.956415 | ||||||||
\(623\) | 47.6479 | 1.90897 | ||||||||
\(624\) | 23.2183 | 0.929477 | ||||||||
\(625\) | 70.2067 | 2.80827 | ||||||||
\(626\) | −44.0241 | −1.75956 | ||||||||
\(627\) | 2.19360 | 0.0876041 | ||||||||
\(628\) | −8.62689 | −0.344250 | ||||||||
\(629\) | 6.24581 | 0.249037 | ||||||||
\(630\) | 82.2433 | 3.27665 | ||||||||
\(631\) | −45.5649 | −1.81391 | −0.906955 | − | 0.421227i | \(-0.861600\pi\) | ||||
−0.906955 | + | 0.421227i | \(0.861600\pi\) | |||||||
\(632\) | −1.28539 | −0.0511301 | ||||||||
\(633\) | 8.82510 | 0.350766 | ||||||||
\(634\) | 11.1019 | 0.440912 | ||||||||
\(635\) | −46.0038 | −1.82561 | ||||||||
\(636\) | 7.93886 | 0.314796 | ||||||||
\(637\) | −103.406 | −4.09709 | ||||||||
\(638\) | −6.56219 | −0.259800 | ||||||||
\(639\) | 36.6032 | 1.44800 | ||||||||
\(640\) | 55.8693 | 2.20843 | ||||||||
\(641\) | 40.3077 | 1.59206 | 0.796029 | − | 0.605259i | \(-0.206930\pi\) | ||||
0.796029 | + | 0.605259i | \(0.206930\pi\) | |||||||
\(642\) | −4.53170 | −0.178852 | ||||||||
\(643\) | 47.0140 | 1.85405 | 0.927026 | − | 0.374998i | \(-0.122357\pi\) | ||||
0.927026 | + | 0.374998i | \(0.122357\pi\) | |||||||
\(644\) | −3.85777 | −0.152017 | ||||||||
\(645\) | 3.13685 | 0.123513 | ||||||||
\(646\) | −4.86596 | −0.191449 | ||||||||
\(647\) | 19.0359 | 0.748377 | 0.374189 | − | 0.927353i | \(-0.377921\pi\) | ||||
0.374189 | + | 0.927353i | \(0.377921\pi\) | |||||||
\(648\) | 8.83031 | 0.346887 | ||||||||
\(649\) | −15.2740 | −0.599558 | ||||||||
\(650\) | 131.077 | 5.14126 | ||||||||
\(651\) | −30.1188 | −1.18045 | ||||||||
\(652\) | 10.8148 | 0.423540 | ||||||||
\(653\) | −9.36412 | −0.366447 | −0.183223 | − | 0.983071i | \(-0.558653\pi\) | ||||
−0.183223 | + | 0.983071i | \(0.558653\pi\) | |||||||
\(654\) | 13.0415 | 0.509965 | ||||||||
\(655\) | 5.22410 | 0.204123 | ||||||||
\(656\) | 6.23362 | 0.243382 | ||||||||
\(657\) | 16.3048 | 0.636110 | ||||||||
\(658\) | 4.48721 | 0.174930 | ||||||||
\(659\) | 10.5023 | 0.409111 | 0.204555 | − | 0.978855i | \(-0.434425\pi\) | ||||
0.204555 | + | 0.978855i | \(0.434425\pi\) | |||||||
\(660\) | 2.36932 | 0.0922255 | ||||||||
\(661\) | 26.0634 | 1.01375 | 0.506874 | − | 0.862020i | \(-0.330801\pi\) | ||||
0.506874 | + | 0.862020i | \(0.330801\pi\) | |||||||
\(662\) | −9.55448 | −0.371345 | ||||||||
\(663\) | 4.69994 | 0.182531 | ||||||||
\(664\) | 8.94499 | 0.347133 | ||||||||
\(665\) | −59.5250 | −2.30828 | ||||||||
\(666\) | −25.2972 | −0.980247 | ||||||||
\(667\) | −4.16841 | −0.161402 | ||||||||
\(668\) | −0.997404 | −0.0385907 | ||||||||
\(669\) | 13.9109 | 0.537828 | ||||||||
\(670\) | 11.0981 | 0.428757 | ||||||||
\(671\) | 5.01667 | 0.193666 | ||||||||
\(672\) | −14.7456 | −0.568824 | ||||||||
\(673\) | 0.460715 | 0.0177593 | 0.00887963 | − | 0.999961i | \(-0.497173\pi\) | ||||
0.00887963 | + | 0.999961i | \(0.497173\pi\) | |||||||
\(674\) | −9.15821 | −0.352761 | ||||||||
\(675\) | −51.1803 | −1.96993 | ||||||||
\(676\) | 19.9772 | 0.768355 | ||||||||
\(677\) | −8.44152 | −0.324434 | −0.162217 | − | 0.986755i | \(-0.551864\pi\) | ||||
−0.162217 | + | 0.986755i | \(0.551864\pi\) | |||||||
\(678\) | −9.44753 | −0.362830 | ||||||||
\(679\) | 33.4297 | 1.28292 | ||||||||
\(680\) | 8.66088 | 0.332130 | ||||||||
\(681\) | 17.3228 | 0.663811 | ||||||||
\(682\) | 13.7927 | 0.528149 | ||||||||
\(683\) | 17.3761 | 0.664876 | 0.332438 | − | 0.943125i | \(-0.392129\pi\) | ||||
0.332438 | + | 0.943125i | \(0.392129\pi\) | |||||||
\(684\) | 5.40270 | 0.206577 | ||||||||
\(685\) | 18.5384 | 0.708315 | ||||||||
\(686\) | 76.0936 | 2.90527 | ||||||||
\(687\) | −10.4316 | −0.397990 | ||||||||
\(688\) | 4.94013 | 0.188341 | ||||||||
\(689\) | −88.2204 | −3.36093 | ||||||||
\(690\) | 5.49018 | 0.209008 | ||||||||
\(691\) | 23.9542 | 0.911259 | 0.455630 | − | 0.890169i | \(-0.349414\pi\) | ||||
0.455630 | + | 0.890169i | \(0.349414\pi\) | |||||||
\(692\) | 2.26460 | 0.0860872 | ||||||||
\(693\) | −11.8194 | −0.448984 | ||||||||
\(694\) | −9.05651 | −0.343781 | ||||||||
\(695\) | 84.3885 | 3.20104 | ||||||||
\(696\) | −6.11199 | −0.231675 | ||||||||
\(697\) | 1.26183 | 0.0477953 | ||||||||
\(698\) | −48.0065 | −1.81707 | ||||||||
\(699\) | −14.0333 | −0.530789 | ||||||||
\(700\) | −45.9995 | −1.73862 | ||||||||
\(701\) | 21.7328 | 0.820837 | 0.410419 | − | 0.911897i | \(-0.365383\pi\) | ||||
0.410419 | + | 0.911897i | \(0.365383\pi\) | |||||||
\(702\) | −42.4405 | −1.60181 | ||||||||
\(703\) | 18.3093 | 0.690548 | ||||||||
\(704\) | −3.12762 | −0.117877 | ||||||||
\(705\) | −1.75059 | −0.0659311 | ||||||||
\(706\) | 41.7364 | 1.57077 | ||||||||
\(707\) | −13.8528 | −0.520989 | ||||||||
\(708\) | 8.63295 | 0.324446 | ||||||||
\(709\) | −15.0549 | −0.565399 | −0.282700 | − | 0.959208i | \(-0.591230\pi\) | ||||
−0.282700 | + | 0.959208i | \(0.591230\pi\) | |||||||
\(710\) | −104.382 | −3.91737 | ||||||||
\(711\) | 1.51806 | 0.0569318 | ||||||||
\(712\) | −20.3231 | −0.761640 | ||||||||
\(713\) | 8.76134 | 0.328115 | ||||||||
\(714\) | −6.01673 | −0.225170 | ||||||||
\(715\) | −26.3290 | −0.984649 | ||||||||
\(716\) | −3.28588 | −0.122799 | ||||||||
\(717\) | −11.9948 | −0.447956 | ||||||||
\(718\) | 50.8548 | 1.89788 | ||||||||
\(719\) | −2.97089 | −0.110795 | −0.0553977 | − | 0.998464i | \(-0.517643\pi\) | ||||
−0.0553977 | + | 0.998464i | \(0.517643\pi\) | |||||||
\(720\) | −50.5306 | −1.88316 | ||||||||
\(721\) | −36.3274 | −1.35290 | ||||||||
\(722\) | 17.2741 | 0.642874 | ||||||||
\(723\) | 21.8860 | 0.813950 | ||||||||
\(724\) | −6.23888 | −0.231866 | ||||||||
\(725\) | −49.7035 | −1.84594 | ||||||||
\(726\) | −1.24211 | −0.0460992 | ||||||||
\(727\) | −10.1691 | −0.377151 | −0.188576 | − | 0.982059i | \(-0.560387\pi\) | ||||
−0.188576 | + | 0.982059i | \(0.560387\pi\) | |||||||
\(728\) | 62.8579 | 2.32967 | ||||||||
\(729\) | −1.29019 | −0.0477849 | ||||||||
\(730\) | −46.4965 | −1.72091 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −2.83544 | −0.104801 | ||||||||
\(733\) | −36.8645 | −1.36162 | −0.680810 | − | 0.732460i | \(-0.738372\pi\) | ||||
−0.680810 | + | 0.732460i | \(0.738372\pi\) | |||||||
\(734\) | 0.449061 | 0.0165752 | ||||||||
\(735\) | −51.6443 | −1.90493 | ||||||||
\(736\) | 4.28939 | 0.158109 | ||||||||
\(737\) | −1.59494 | −0.0587505 | ||||||||
\(738\) | −5.11076 | −0.188130 | ||||||||
\(739\) | −21.5423 | −0.792448 | −0.396224 | − | 0.918154i | \(-0.629680\pi\) | ||||
−0.396224 | + | 0.918154i | \(0.629680\pi\) | |||||||
\(740\) | 19.7759 | 0.726976 | ||||||||
\(741\) | 13.7776 | 0.506134 | ||||||||
\(742\) | 112.937 | 4.14606 | ||||||||
\(743\) | −13.9268 | −0.510924 | −0.255462 | − | 0.966819i | \(-0.582228\pi\) | ||||
−0.255462 | + | 0.966819i | \(0.582228\pi\) | |||||||
\(744\) | 12.8464 | 0.470973 | ||||||||
\(745\) | −58.8239 | −2.15514 | ||||||||
\(746\) | −27.3976 | −1.00310 | ||||||||
\(747\) | −10.5641 | −0.386521 | ||||||||
\(748\) | 0.755318 | 0.0276172 | ||||||||
\(749\) | −17.6725 | −0.645739 | ||||||||
\(750\) | 39.4296 | 1.43977 | ||||||||
\(751\) | 14.8201 | 0.540791 | 0.270396 | − | 0.962749i | \(-0.412845\pi\) | ||||
0.270396 | + | 0.962749i | \(0.412845\pi\) | |||||||
\(752\) | −2.75696 | −0.100536 | ||||||||
\(753\) | 3.45649 | 0.125961 | ||||||||
\(754\) | −41.2160 | −1.50100 | ||||||||
\(755\) | 70.5767 | 2.56855 | ||||||||
\(756\) | 14.8938 | 0.541684 | ||||||||
\(757\) | 2.76362 | 0.100445 | 0.0502227 | − | 0.998738i | \(-0.484007\pi\) | ||||
0.0502227 | + | 0.998738i | \(0.484007\pi\) | |||||||
\(758\) | −53.1121 | −1.92912 | ||||||||
\(759\) | −0.789011 | −0.0286393 | ||||||||
\(760\) | 25.3889 | 0.920954 | ||||||||
\(761\) | −42.9345 | −1.55637 | −0.778187 | − | 0.628033i | \(-0.783860\pi\) | ||||
−0.778187 | + | 0.628033i | \(0.783860\pi\) | |||||||
\(762\) | −13.6313 | −0.493811 | ||||||||
\(763\) | 50.8588 | 1.84121 | ||||||||
\(764\) | 3.74514 | 0.135494 | ||||||||
\(765\) | −10.2286 | −0.369816 | ||||||||
\(766\) | −26.0365 | −0.940736 | ||||||||
\(767\) | −95.9335 | −3.46396 | ||||||||
\(768\) | 11.8737 | 0.428457 | ||||||||
\(769\) | −9.49894 | −0.342540 | −0.171270 | − | 0.985224i | \(-0.554787\pi\) | ||||
−0.171270 | + | 0.985224i | \(0.554787\pi\) | |||||||
\(770\) | 33.7056 | 1.21467 | ||||||||
\(771\) | −7.47415 | −0.269175 | ||||||||
\(772\) | 9.43444 | 0.339553 | ||||||||
\(773\) | −17.9773 | −0.646600 | −0.323300 | − | 0.946297i | \(-0.604792\pi\) | ||||
−0.323300 | + | 0.946297i | \(0.604792\pi\) | |||||||
\(774\) | −4.05027 | −0.145584 | ||||||||
\(775\) | 104.469 | 3.75263 | ||||||||
\(776\) | −14.2587 | −0.511856 | ||||||||
\(777\) | 22.6393 | 0.812180 | ||||||||
\(778\) | 55.9773 | 2.00688 | ||||||||
\(779\) | 3.69900 | 0.132530 | ||||||||
\(780\) | 14.8813 | 0.532835 | ||||||||
\(781\) | 15.0010 | 0.536779 | ||||||||
\(782\) | 1.75022 | 0.0625879 | ||||||||
\(783\) | 16.0932 | 0.575123 | ||||||||
\(784\) | −81.3331 | −2.90475 | ||||||||
\(785\) | 47.8787 | 1.70886 | ||||||||
\(786\) | 1.54794 | 0.0552134 | ||||||||
\(787\) | −17.5727 | −0.626400 | −0.313200 | − | 0.949687i | \(-0.601401\pi\) | ||||
−0.313200 | + | 0.949687i | \(0.601401\pi\) | |||||||
\(788\) | −12.1911 | −0.434291 | ||||||||
\(789\) | 12.2574 | 0.436374 | ||||||||
\(790\) | −4.32907 | −0.154021 | ||||||||
\(791\) | −36.8431 | −1.30999 | ||||||||
\(792\) | 5.04130 | 0.179135 | ||||||||
\(793\) | 31.5088 | 1.11891 | ||||||||
\(794\) | 5.58949 | 0.198364 | ||||||||
\(795\) | −44.0601 | −1.56265 | ||||||||
\(796\) | 8.93780 | 0.316792 | ||||||||
\(797\) | −2.74406 | −0.0971995 | −0.0485997 | − | 0.998818i | \(-0.515476\pi\) | ||||
−0.0485997 | + | 0.998818i | \(0.515476\pi\) | |||||||
\(798\) | −17.6377 | −0.624369 | ||||||||
\(799\) | −0.558074 | −0.0197432 | ||||||||
\(800\) | 51.1460 | 1.80829 | ||||||||
\(801\) | 24.0018 | 0.848062 | ||||||||
\(802\) | 40.4506 | 1.42836 | ||||||||
\(803\) | 6.68215 | 0.235808 | ||||||||
\(804\) | 0.901469 | 0.0317924 | ||||||||
\(805\) | 21.4104 | 0.754616 | ||||||||
\(806\) | 86.6294 | 3.05139 | ||||||||
\(807\) | 2.76537 | 0.0973455 | ||||||||
\(808\) | 5.90859 | 0.207863 | ||||||||
\(809\) | 30.6731 | 1.07841 | 0.539204 | − | 0.842175i | \(-0.318725\pi\) | ||||
0.539204 | + | 0.842175i | \(0.318725\pi\) | |||||||
\(810\) | 29.7396 | 1.04494 | ||||||||
\(811\) | −4.37804 | −0.153734 | −0.0768668 | − | 0.997041i | \(-0.524492\pi\) | ||||
−0.0768668 | + | 0.997041i | \(0.524492\pi\) | |||||||
\(812\) | 14.4641 | 0.507591 | ||||||||
\(813\) | −1.47360 | −0.0516814 | ||||||||
\(814\) | −10.3675 | −0.363381 | ||||||||
\(815\) | −60.0214 | −2.10246 | ||||||||
\(816\) | 3.69670 | 0.129410 | ||||||||
\(817\) | 2.93145 | 0.102559 | ||||||||
\(818\) | 23.0843 | 0.807124 | ||||||||
\(819\) | −74.2358 | −2.59401 | ||||||||
\(820\) | 3.99530 | 0.139522 | ||||||||
\(821\) | −21.4480 | −0.748540 | −0.374270 | − | 0.927320i | \(-0.622107\pi\) | ||||
−0.374270 | + | 0.927320i | \(0.622107\pi\) | |||||||
\(822\) | 5.49307 | 0.191593 | ||||||||
\(823\) | 48.2740 | 1.68273 | 0.841364 | − | 0.540469i | \(-0.181753\pi\) | ||||
0.841364 | + | 0.540469i | \(0.181753\pi\) | |||||||
\(824\) | 15.4946 | 0.539780 | ||||||||
\(825\) | −9.40805 | −0.327546 | ||||||||
\(826\) | 122.811 | 4.27315 | ||||||||
\(827\) | −29.6162 | −1.02986 | −0.514928 | − | 0.857234i | \(-0.672181\pi\) | ||||
−0.514928 | + | 0.857234i | \(0.672181\pi\) | |||||||
\(828\) | −1.94328 | −0.0675337 | ||||||||
\(829\) | 20.9282 | 0.726865 | 0.363433 | − | 0.931620i | \(-0.381605\pi\) | ||||
0.363433 | + | 0.931620i | \(0.381605\pi\) | |||||||
\(830\) | 30.1258 | 1.04568 | ||||||||
\(831\) | −9.16410 | −0.317899 | ||||||||
\(832\) | −19.6440 | −0.681034 | ||||||||
\(833\) | −16.4638 | −0.570435 | ||||||||
\(834\) | 25.0050 | 0.865853 | ||||||||
\(835\) | 5.53553 | 0.191565 | ||||||||
\(836\) | 2.21418 | 0.0765790 | ||||||||
\(837\) | −33.8253 | −1.16917 | ||||||||
\(838\) | 23.8991 | 0.825581 | ||||||||
\(839\) | 24.2176 | 0.836083 | 0.418041 | − | 0.908428i | \(-0.362717\pi\) | ||||
0.418041 | + | 0.908428i | \(0.362717\pi\) | |||||||
\(840\) | 31.3933 | 1.08317 | ||||||||
\(841\) | −13.3712 | −0.461075 | ||||||||
\(842\) | −18.1937 | −0.626996 | ||||||||
\(843\) | −12.0848 | −0.416222 | ||||||||
\(844\) | 8.90787 | 0.306622 | ||||||||
\(845\) | −110.872 | −3.81412 | ||||||||
\(846\) | 2.26035 | 0.0777125 | ||||||||
\(847\) | −4.84394 | −0.166440 | ||||||||
\(848\) | −69.3891 | −2.38283 | ||||||||
\(849\) | −8.52197 | −0.292473 | ||||||||
\(850\) | 20.8694 | 0.715815 | ||||||||
\(851\) | −6.58561 | −0.225752 | ||||||||
\(852\) | −8.47864 | −0.290473 | ||||||||
\(853\) | −35.4526 | −1.21387 | −0.606937 | − | 0.794750i | \(-0.707602\pi\) | ||||
−0.606937 | + | 0.794750i | \(0.707602\pi\) | |||||||
\(854\) | −40.3367 | −1.38029 | ||||||||
\(855\) | −29.9846 | −1.02545 | ||||||||
\(856\) | 7.53778 | 0.257636 | ||||||||
\(857\) | −25.2119 | −0.861221 | −0.430611 | − | 0.902538i | \(-0.641702\pi\) | ||||
−0.430611 | + | 0.902538i | \(0.641702\pi\) | |||||||
\(858\) | −7.80150 | −0.266339 | ||||||||
\(859\) | 11.3017 | 0.385608 | 0.192804 | − | 0.981237i | \(-0.438242\pi\) | ||||
0.192804 | + | 0.981237i | \(0.438242\pi\) | |||||||
\(860\) | 3.16627 | 0.107969 | ||||||||
\(861\) | 4.57379 | 0.155874 | ||||||||
\(862\) | 48.6371 | 1.65659 | ||||||||
\(863\) | −19.7984 | −0.673946 | −0.336973 | − | 0.941514i | \(-0.609403\pi\) | ||||
−0.336973 | + | 0.941514i | \(0.609403\pi\) | |||||||
\(864\) | −16.5602 | −0.563390 | ||||||||
\(865\) | −12.5684 | −0.427338 | ||||||||
\(866\) | 48.7942 | 1.65810 | ||||||||
\(867\) | 0.748300 | 0.0254136 | ||||||||
\(868\) | −30.4013 | −1.03189 | ||||||||
\(869\) | 0.622145 | 0.0211048 | ||||||||
\(870\) | −20.5846 | −0.697883 | ||||||||
\(871\) | −10.0176 | −0.339432 | ||||||||
\(872\) | −21.6926 | −0.734605 | ||||||||
\(873\) | 16.8396 | 0.569935 | ||||||||
\(874\) | 5.13070 | 0.173548 | ||||||||
\(875\) | 153.766 | 5.19823 | ||||||||
\(876\) | −3.77678 | −0.127606 | ||||||||
\(877\) | 8.44053 | 0.285016 | 0.142508 | − | 0.989794i | \(-0.454483\pi\) | ||||
0.142508 | + | 0.989794i | \(0.454483\pi\) | |||||||
\(878\) | 5.41161 | 0.182633 | ||||||||
\(879\) | 16.0290 | 0.540645 | ||||||||
\(880\) | −20.7089 | −0.698095 | ||||||||
\(881\) | −25.3386 | −0.853679 | −0.426839 | − | 0.904327i | \(-0.640373\pi\) | ||||
−0.426839 | + | 0.904327i | \(0.640373\pi\) | |||||||
\(882\) | 66.6827 | 2.24532 | ||||||||
\(883\) | −11.2129 | −0.377345 | −0.188673 | − | 0.982040i | \(-0.560419\pi\) | ||||
−0.188673 | + | 0.982040i | \(0.560419\pi\) | |||||||
\(884\) | 4.74402 | 0.159559 | ||||||||
\(885\) | −47.9123 | −1.61055 | ||||||||
\(886\) | −1.19720 | −0.0402206 | ||||||||
\(887\) | −43.6585 | −1.46591 | −0.732954 | − | 0.680278i | \(-0.761859\pi\) | ||||
−0.732954 | + | 0.680278i | \(0.761859\pi\) | |||||||
\(888\) | −9.65625 | −0.324043 | ||||||||
\(889\) | −53.1588 | −1.78289 | ||||||||
\(890\) | −68.4461 | −2.29432 | ||||||||
\(891\) | −4.27397 | −0.143184 | ||||||||
\(892\) | 14.0414 | 0.470141 | ||||||||
\(893\) | −1.63597 | −0.0547456 | ||||||||
\(894\) | −17.4300 | −0.582947 | ||||||||
\(895\) | 18.2364 | 0.609575 | ||||||||
\(896\) | 64.5586 | 2.15675 | ||||||||
\(897\) | −4.95564 | −0.165464 | ||||||||
\(898\) | 60.2690 | 2.01120 | ||||||||
\(899\) | −32.8493 | −1.09558 | ||||||||
\(900\) | −23.1714 | −0.772380 | ||||||||
\(901\) | −14.0460 | −0.467940 | ||||||||
\(902\) | −2.09454 | −0.0697404 | ||||||||
\(903\) | 3.62472 | 0.120623 | ||||||||
\(904\) | 15.7145 | 0.522657 | ||||||||
\(905\) | 34.6254 | 1.15099 | ||||||||
\(906\) | 20.9125 | 0.694770 | ||||||||
\(907\) | −8.24484 | −0.273765 | −0.136883 | − | 0.990587i | \(-0.543708\pi\) | ||||
−0.136883 | + | 0.990587i | \(0.543708\pi\) | |||||||
\(908\) | 17.4853 | 0.580269 | ||||||||
\(909\) | −6.97811 | −0.231449 | ||||||||
\(910\) | 211.699 | 7.01776 | ||||||||
\(911\) | 5.28115 | 0.174972 | 0.0874861 | − | 0.996166i | \(-0.472117\pi\) | ||||
0.0874861 | + | 0.996166i | \(0.472117\pi\) | |||||||
\(912\) | 10.8367 | 0.358839 | ||||||||
\(913\) | −4.32948 | −0.143285 | ||||||||
\(914\) | 14.4379 | 0.477563 | ||||||||
\(915\) | 15.7365 | 0.520233 | ||||||||
\(916\) | −10.5294 | −0.347902 | ||||||||
\(917\) | 6.03660 | 0.199346 | ||||||||
\(918\) | −6.75716 | −0.223020 | ||||||||
\(919\) | 9.39302 | 0.309847 | 0.154924 | − | 0.987926i | \(-0.450487\pi\) | ||||
0.154924 | + | 0.987926i | \(0.450487\pi\) | |||||||
\(920\) | −9.13208 | −0.301076 | ||||||||
\(921\) | 10.1310 | 0.333827 | ||||||||
\(922\) | −37.1080 | −1.22209 | ||||||||
\(923\) | 94.2188 | 3.10125 | ||||||||
\(924\) | 2.73782 | 0.0900675 | ||||||||
\(925\) | −78.5259 | −2.58191 | ||||||||
\(926\) | −34.2123 | −1.12429 | ||||||||
\(927\) | −18.2993 | −0.601027 | ||||||||
\(928\) | −16.0824 | −0.527931 | ||||||||
\(929\) | 2.44089 | 0.0800830 | 0.0400415 | − | 0.999198i | \(-0.487251\pi\) | ||||
0.0400415 | + | 0.999198i | \(0.487251\pi\) | |||||||
\(930\) | 43.2655 | 1.41873 | ||||||||
\(931\) | −48.2627 | −1.58175 | ||||||||
\(932\) | −14.1650 | −0.463988 | ||||||||
\(933\) | −10.7530 | −0.352039 | ||||||||
\(934\) | −26.3966 | −0.863723 | ||||||||
\(935\) | −4.19197 | −0.137092 | ||||||||
\(936\) | 31.6635 | 1.03495 | ||||||||
\(937\) | −31.7626 | −1.03764 | −0.518819 | − | 0.854884i | \(-0.673628\pi\) | ||||
−0.518819 | + | 0.854884i | \(0.673628\pi\) | |||||||
\(938\) | 12.8242 | 0.418725 | ||||||||
\(939\) | 19.8463 | 0.647661 | ||||||||
\(940\) | −1.76701 | −0.0576336 | ||||||||
\(941\) | −44.8123 | −1.46084 | −0.730420 | − | 0.682998i | \(-0.760676\pi\) | ||||
−0.730420 | + | 0.682998i | \(0.760676\pi\) | |||||||
\(942\) | 14.1869 | 0.462233 | ||||||||
\(943\) | −1.33048 | −0.0433265 | ||||||||
\(944\) | −75.4557 | −2.45587 | ||||||||
\(945\) | −82.6599 | −2.68893 | ||||||||
\(946\) | −1.65992 | −0.0539685 | ||||||||
\(947\) | 43.3275 | 1.40795 | 0.703977 | − | 0.710223i | \(-0.251406\pi\) | ||||
0.703977 | + | 0.710223i | \(0.251406\pi\) | |||||||
\(948\) | −0.351639 | −0.0114207 | ||||||||
\(949\) | 41.9694 | 1.36239 | ||||||||
\(950\) | 61.1776 | 1.98486 | ||||||||
\(951\) | −5.00479 | −0.162292 | ||||||||
\(952\) | 10.0079 | 0.324358 | ||||||||
\(953\) | −30.6277 | −0.992129 | −0.496064 | − | 0.868286i | \(-0.665222\pi\) | ||||
−0.496064 | + | 0.868286i | \(0.665222\pi\) | |||||||
\(954\) | 56.8901 | 1.84189 | ||||||||
\(955\) | −20.7853 | −0.672596 | ||||||||
\(956\) | −12.1073 | −0.391579 | ||||||||
\(957\) | 2.95828 | 0.0956275 | ||||||||
\(958\) | −54.7357 | −1.76843 | ||||||||
\(959\) | 21.4216 | 0.691741 | ||||||||
\(960\) | −9.81086 | −0.316644 | ||||||||
\(961\) | 38.0440 | 1.22722 | ||||||||
\(962\) | −65.1165 | −2.09944 | ||||||||
\(963\) | −8.90220 | −0.286870 | ||||||||
\(964\) | 22.0913 | 0.711513 | ||||||||
\(965\) | −52.3605 | −1.68555 | ||||||||
\(966\) | 6.34407 | 0.204117 | ||||||||
\(967\) | 4.84734 | 0.155880 | 0.0779400 | − | 0.996958i | \(-0.475166\pi\) | ||||
0.0779400 | + | 0.996958i | \(0.475166\pi\) | |||||||
\(968\) | 2.06607 | 0.0664059 | ||||||||
\(969\) | 2.19360 | 0.0704687 | ||||||||
\(970\) | −48.0217 | −1.54188 | ||||||||
\(971\) | 5.16076 | 0.165617 | 0.0828083 | − | 0.996565i | \(-0.473611\pi\) | ||||
0.0828083 | + | 0.996565i | \(0.473611\pi\) | |||||||
\(972\) | 11.6399 | 0.373349 | ||||||||
\(973\) | 97.5134 | 3.12614 | ||||||||
\(974\) | −1.09489 | −0.0350825 | ||||||||
\(975\) | −59.0903 | −1.89241 | ||||||||
\(976\) | 24.7830 | 0.793285 | ||||||||
\(977\) | −52.1470 | −1.66833 | −0.834166 | − | 0.551514i | \(-0.814050\pi\) | ||||
−0.834166 | + | 0.551514i | \(0.814050\pi\) | |||||||
\(978\) | −17.7848 | −0.568696 | ||||||||
\(979\) | 9.83661 | 0.314379 | ||||||||
\(980\) | −52.1286 | −1.66519 | ||||||||
\(981\) | 25.6192 | 0.817959 | ||||||||
\(982\) | −15.8413 | −0.505516 | ||||||||
\(983\) | −47.8234 | −1.52533 | −0.762665 | − | 0.646794i | \(-0.776109\pi\) | ||||
−0.762665 | + | 0.646794i | \(0.776109\pi\) | |||||||
\(984\) | −1.95084 | −0.0621905 | ||||||||
\(985\) | 67.6599 | 2.15582 | ||||||||
\(986\) | −6.56219 | −0.208983 | ||||||||
\(987\) | −2.02286 | −0.0643884 | ||||||||
\(988\) | 13.9069 | 0.442436 | ||||||||
\(989\) | −1.05441 | −0.0335281 | ||||||||
\(990\) | 16.9786 | 0.539615 | ||||||||
\(991\) | −7.60793 | −0.241674 | −0.120837 | − | 0.992672i | \(-0.538558\pi\) | ||||
−0.120837 | + | 0.992672i | \(0.538558\pi\) | |||||||
\(992\) | 33.8026 | 1.07324 | ||||||||
\(993\) | 4.30722 | 0.136685 | ||||||||
\(994\) | −120.616 | −3.82571 | ||||||||
\(995\) | −49.6042 | −1.57256 | ||||||||
\(996\) | 2.44704 | 0.0775374 | ||||||||
\(997\) | 27.8752 | 0.882818 | 0.441409 | − | 0.897306i | \(-0.354479\pi\) | ||||
0.441409 | + | 0.897306i | \(0.354479\pi\) | |||||||
\(998\) | 67.6327 | 2.14088 | ||||||||
\(999\) | 25.4253 | 0.804422 |
(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.h.1.20 | ✓ | 74 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.h.1.20 | ✓ | 74 | 1.1 | even | 1 | trivial |