Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50636 | −1.06516 | −0.532580 | − | 0.846380i | \(-0.678777\pi\) | ||||
−0.532580 | + | 0.846380i | \(0.678777\pi\) | |||||||
\(3\) | −0.544988 | −0.314649 | −0.157324 | − | 0.987547i | \(-0.550287\pi\) | ||||
−0.157324 | + | 0.987547i | \(0.550287\pi\) | |||||||
\(4\) | 0.269129 | 0.134564 | ||||||||
\(5\) | 3.40659 | 1.52347 | 0.761736 | − | 0.647887i | \(-0.224347\pi\) | ||||
0.761736 | + | 0.647887i | \(0.224347\pi\) | |||||||
\(6\) | 0.820949 | 0.335151 | ||||||||
\(7\) | −0.714897 | −0.270206 | −0.135103 | − | 0.990832i | \(-0.543137\pi\) | ||||
−0.135103 | + | 0.990832i | \(0.543137\pi\) | |||||||
\(8\) | 2.60732 | 0.921827 | ||||||||
\(9\) | −2.70299 | −0.900996 | ||||||||
\(10\) | −5.13156 | −1.62274 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.146672 | −0.0423405 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.07689 | 0.287812 | ||||||||
\(15\) | −1.85655 | −0.479359 | ||||||||
\(16\) | −4.46583 | −1.11646 | ||||||||
\(17\) | 5.08876 | 1.23420 | 0.617102 | − | 0.786883i | \(-0.288306\pi\) | ||||
0.617102 | + | 0.786883i | \(0.288306\pi\) | |||||||
\(18\) | 4.07168 | 0.959704 | ||||||||
\(19\) | −2.56104 | −0.587543 | −0.293772 | − | 0.955876i | \(-0.594910\pi\) | ||||
−0.293772 | + | 0.955876i | \(0.594910\pi\) | |||||||
\(20\) | 0.916811 | 0.205005 | ||||||||
\(21\) | 0.389610 | 0.0850199 | ||||||||
\(22\) | −1.50636 | −0.321158 | ||||||||
\(23\) | 0.472206 | 0.0984617 | 0.0492309 | − | 0.998787i | \(-0.484323\pi\) | ||||
0.0492309 | + | 0.998787i | \(0.484323\pi\) | |||||||
\(24\) | −1.42096 | −0.290052 | ||||||||
\(25\) | 6.60485 | 1.32097 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.10806 | 0.598146 | ||||||||
\(28\) | −0.192399 | −0.0363601 | ||||||||
\(29\) | 7.13941 | 1.32576 | 0.662878 | − | 0.748728i | \(-0.269335\pi\) | ||||
0.662878 | + | 0.748728i | \(0.269335\pi\) | |||||||
\(30\) | 2.79664 | 0.510594 | ||||||||
\(31\) | −7.93075 | −1.42441 | −0.712203 | − | 0.701974i | \(-0.752302\pi\) | ||||
−0.712203 | + | 0.701974i | \(0.752302\pi\) | |||||||
\(32\) | 1.51252 | 0.267377 | ||||||||
\(33\) | −0.544988 | −0.0948702 | ||||||||
\(34\) | −7.66551 | −1.31462 | ||||||||
\(35\) | −2.43536 | −0.411651 | ||||||||
\(36\) | −0.727452 | −0.121242 | ||||||||
\(37\) | 1.68838 | 0.277568 | 0.138784 | − | 0.990323i | \(-0.455681\pi\) | ||||
0.138784 | + | 0.990323i | \(0.455681\pi\) | |||||||
\(38\) | 3.85786 | 0.625827 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.88207 | 1.40438 | ||||||||
\(41\) | 1.29725 | 0.202597 | 0.101299 | − | 0.994856i | \(-0.467700\pi\) | ||||
0.101299 | + | 0.994856i | \(0.467700\pi\) | |||||||
\(42\) | −0.586894 | −0.0905598 | ||||||||
\(43\) | 9.09702 | 1.38728 | 0.693642 | − | 0.720320i | \(-0.256005\pi\) | ||||
0.693642 | + | 0.720320i | \(0.256005\pi\) | |||||||
\(44\) | 0.269129 | 0.0405727 | ||||||||
\(45\) | −9.20797 | −1.37264 | ||||||||
\(46\) | −0.711313 | −0.104877 | ||||||||
\(47\) | 7.45791 | 1.08785 | 0.543924 | − | 0.839135i | \(-0.316938\pi\) | ||||
0.543924 | + | 0.839135i | \(0.316938\pi\) | |||||||
\(48\) | 2.43382 | 0.351292 | ||||||||
\(49\) | −6.48892 | −0.926989 | ||||||||
\(50\) | −9.94929 | −1.40704 | ||||||||
\(51\) | −2.77331 | −0.388341 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.78116 | 1.06882 | 0.534412 | − | 0.845224i | \(-0.320533\pi\) | ||||
0.534412 | + | 0.845224i | \(0.320533\pi\) | |||||||
\(54\) | −4.68186 | −0.637121 | ||||||||
\(55\) | 3.40659 | 0.459344 | ||||||||
\(56\) | −1.86397 | −0.249083 | ||||||||
\(57\) | 1.39574 | 0.184870 | ||||||||
\(58\) | −10.7545 | −1.41214 | ||||||||
\(59\) | 11.1900 | 1.45681 | 0.728406 | − | 0.685146i | \(-0.240262\pi\) | ||||
0.728406 | + | 0.685146i | \(0.240262\pi\) | |||||||
\(60\) | −0.499651 | −0.0645046 | ||||||||
\(61\) | −14.3882 | −1.84222 | −0.921110 | − | 0.389304i | \(-0.872716\pi\) | ||||
−0.921110 | + | 0.389304i | \(0.872716\pi\) | |||||||
\(62\) | 11.9466 | 1.51722 | ||||||||
\(63\) | 1.93236 | 0.243454 | ||||||||
\(64\) | 6.65326 | 0.831657 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.820949 | 0.101052 | ||||||||
\(67\) | −7.36614 | −0.899917 | −0.449958 | − | 0.893050i | \(-0.648561\pi\) | ||||
−0.449958 | + | 0.893050i | \(0.648561\pi\) | |||||||
\(68\) | 1.36953 | 0.166080 | ||||||||
\(69\) | −0.257346 | −0.0309809 | ||||||||
\(70\) | 3.66854 | 0.438474 | ||||||||
\(71\) | −1.70293 | −0.202101 | −0.101050 | − | 0.994881i | \(-0.532220\pi\) | ||||
−0.101050 | + | 0.994881i | \(0.532220\pi\) | |||||||
\(72\) | −7.04756 | −0.830562 | ||||||||
\(73\) | −6.44348 | −0.754152 | −0.377076 | − | 0.926182i | \(-0.623070\pi\) | ||||
−0.377076 | + | 0.926182i | \(0.623070\pi\) | |||||||
\(74\) | −2.54331 | −0.295654 | ||||||||
\(75\) | −3.59956 | −0.415641 | ||||||||
\(76\) | −0.689249 | −0.0790623 | ||||||||
\(77\) | −0.714897 | −0.0814701 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.05937 | −0.569223 | −0.284612 | − | 0.958643i | \(-0.591865\pi\) | ||||
−0.284612 | + | 0.958643i | \(0.591865\pi\) | |||||||
\(80\) | −15.2132 | −1.70089 | ||||||||
\(81\) | 6.41511 | 0.712790 | ||||||||
\(82\) | −1.95414 | −0.215798 | ||||||||
\(83\) | −13.8551 | −1.52079 | −0.760396 | − | 0.649460i | \(-0.774995\pi\) | ||||
−0.760396 | + | 0.649460i | \(0.774995\pi\) | |||||||
\(84\) | 0.104855 | 0.0114407 | ||||||||
\(85\) | 17.3353 | 1.88028 | ||||||||
\(86\) | −13.7034 | −1.47768 | ||||||||
\(87\) | −3.89089 | −0.417147 | ||||||||
\(88\) | 2.60732 | 0.277941 | ||||||||
\(89\) | 8.30538 | 0.880369 | 0.440184 | − | 0.897907i | \(-0.354913\pi\) | ||||
0.440184 | + | 0.897907i | \(0.354913\pi\) | |||||||
\(90\) | 13.8705 | 1.46208 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.127084 | 0.0132494 | ||||||||
\(93\) | 4.32216 | 0.448187 | ||||||||
\(94\) | −11.2343 | −1.15873 | ||||||||
\(95\) | −8.72441 | −0.895106 | ||||||||
\(96\) | −0.824302 | −0.0841300 | ||||||||
\(97\) | 9.02088 | 0.915932 | 0.457966 | − | 0.888970i | \(-0.348578\pi\) | ||||
0.457966 | + | 0.888970i | \(0.348578\pi\) | |||||||
\(98\) | 9.77467 | 0.987391 | ||||||||
\(99\) | −2.70299 | −0.271661 | ||||||||
\(100\) | 1.77755 | 0.177755 | ||||||||
\(101\) | 11.9441 | 1.18848 | 0.594240 | − | 0.804288i | \(-0.297453\pi\) | ||||
0.594240 | + | 0.804288i | \(0.297453\pi\) | |||||||
\(102\) | 4.17761 | 0.413645 | ||||||||
\(103\) | 11.4370 | 1.12692 | 0.563460 | − | 0.826144i | \(-0.309470\pi\) | ||||
0.563460 | + | 0.826144i | \(0.309470\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.32724 | 0.129526 | ||||||||
\(106\) | −11.7212 | −1.13847 | ||||||||
\(107\) | −15.1805 | −1.46755 | −0.733776 | − | 0.679392i | \(-0.762244\pi\) | ||||
−0.733776 | + | 0.679392i | \(0.762244\pi\) | |||||||
\(108\) | 0.836468 | 0.0804891 | ||||||||
\(109\) | −6.09887 | −0.584166 | −0.292083 | − | 0.956393i | \(-0.594348\pi\) | ||||
−0.292083 | + | 0.956393i | \(0.594348\pi\) | |||||||
\(110\) | −5.13156 | −0.489275 | ||||||||
\(111\) | −0.920145 | −0.0873363 | ||||||||
\(112\) | 3.19261 | 0.301673 | ||||||||
\(113\) | 13.7747 | 1.29582 | 0.647909 | − | 0.761718i | \(-0.275644\pi\) | ||||
0.647909 | + | 0.761718i | \(0.275644\pi\) | |||||||
\(114\) | −2.10248 | −0.196916 | ||||||||
\(115\) | 1.60861 | 0.150004 | ||||||||
\(116\) | 1.92142 | 0.178399 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.8562 | −1.55174 | ||||||||
\(119\) | −3.63794 | −0.333489 | ||||||||
\(120\) | −4.84062 | −0.441886 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 21.6738 | 1.96226 | ||||||||
\(123\) | −0.706988 | −0.0637469 | ||||||||
\(124\) | −2.13439 | −0.191674 | ||||||||
\(125\) | 5.46705 | 0.488988 | ||||||||
\(126\) | −2.91083 | −0.259318 | ||||||||
\(127\) | 3.52528 | 0.312818 | 0.156409 | − | 0.987692i | \(-0.450008\pi\) | ||||
0.156409 | + | 0.987692i | \(0.450008\pi\) | |||||||
\(128\) | −13.0472 | −1.15322 | ||||||||
\(129\) | −4.95777 | −0.436507 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.18273 | 0.802299 | 0.401149 | − | 0.916013i | \(-0.368611\pi\) | ||||
0.401149 | + | 0.916013i | \(0.368611\pi\) | |||||||
\(132\) | −0.146672 | −0.0127661 | ||||||||
\(133\) | 1.83088 | 0.158758 | ||||||||
\(134\) | 11.0961 | 0.958555 | ||||||||
\(135\) | 10.5879 | 0.911259 | ||||||||
\(136\) | 13.2680 | 1.13772 | ||||||||
\(137\) | 16.9513 | 1.44825 | 0.724123 | − | 0.689670i | \(-0.242245\pi\) | ||||
0.724123 | + | 0.689670i | \(0.242245\pi\) | |||||||
\(138\) | 0.387657 | 0.0329996 | ||||||||
\(139\) | 12.0540 | 1.02241 | 0.511205 | − | 0.859459i | \(-0.329199\pi\) | ||||
0.511205 | + | 0.859459i | \(0.329199\pi\) | |||||||
\(140\) | −0.655426 | −0.0553936 | ||||||||
\(141\) | −4.06447 | −0.342290 | ||||||||
\(142\) | 2.56523 | 0.215270 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.0711 | 1.00592 | ||||||||
\(145\) | 24.3210 | 2.01975 | ||||||||
\(146\) | 9.70621 | 0.803292 | ||||||||
\(147\) | 3.53638 | 0.291676 | ||||||||
\(148\) | 0.454391 | 0.0373507 | ||||||||
\(149\) | 14.1650 | 1.16044 | 0.580219 | − | 0.814460i | \(-0.302967\pi\) | ||||
0.580219 | + | 0.814460i | \(0.302967\pi\) | |||||||
\(150\) | 5.42224 | 0.442724 | ||||||||
\(151\) | −5.00340 | −0.407171 | −0.203585 | − | 0.979057i | \(-0.565259\pi\) | ||||
−0.203585 | + | 0.979057i | \(0.565259\pi\) | |||||||
\(152\) | −6.67745 | −0.541613 | ||||||||
\(153\) | −13.7548 | −1.11201 | ||||||||
\(154\) | 1.07689 | 0.0867787 | ||||||||
\(155\) | −27.0168 | −2.17004 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.7018 | 1.17333 | 0.586665 | − | 0.809829i | \(-0.300440\pi\) | ||||
0.586665 | + | 0.809829i | \(0.300440\pi\) | |||||||
\(158\) | 7.62124 | 0.606313 | ||||||||
\(159\) | −4.24064 | −0.336304 | ||||||||
\(160\) | 5.15252 | 0.407342 | ||||||||
\(161\) | −0.337579 | −0.0266049 | ||||||||
\(162\) | −9.66348 | −0.759235 | ||||||||
\(163\) | −11.1352 | −0.872174 | −0.436087 | − | 0.899904i | \(-0.643636\pi\) | ||||
−0.436087 | + | 0.899904i | \(0.643636\pi\) | |||||||
\(164\) | 0.349128 | 0.0272623 | ||||||||
\(165\) | −1.85655 | −0.144532 | ||||||||
\(166\) | 20.8708 | 1.61988 | ||||||||
\(167\) | −1.28527 | −0.0994573 | −0.0497286 | − | 0.998763i | \(-0.515836\pi\) | ||||
−0.0497286 | + | 0.998763i | \(0.515836\pi\) | |||||||
\(168\) | 1.01584 | 0.0783737 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −26.1133 | −2.00279 | ||||||||
\(171\) | 6.92246 | 0.529374 | ||||||||
\(172\) | 2.44827 | 0.186679 | ||||||||
\(173\) | 12.4553 | 0.946962 | 0.473481 | − | 0.880804i | \(-0.342997\pi\) | ||||
0.473481 | + | 0.880804i | \(0.342997\pi\) | |||||||
\(174\) | 5.86109 | 0.444328 | ||||||||
\(175\) | −4.72179 | −0.356934 | ||||||||
\(176\) | −4.46583 | −0.336624 | ||||||||
\(177\) | −6.09840 | −0.458384 | ||||||||
\(178\) | −12.5109 | −0.937733 | ||||||||
\(179\) | 8.97864 | 0.671095 | 0.335548 | − | 0.942023i | \(-0.391079\pi\) | ||||
0.335548 | + | 0.942023i | \(0.391079\pi\) | |||||||
\(180\) | −2.47813 | −0.184709 | ||||||||
\(181\) | 24.2769 | 1.80449 | 0.902245 | − | 0.431224i | \(-0.141918\pi\) | ||||
0.902245 | + | 0.431224i | \(0.141918\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.84139 | 0.579652 | ||||||||
\(184\) | 1.23119 | 0.0907647 | ||||||||
\(185\) | 5.75161 | 0.422867 | ||||||||
\(186\) | −6.51074 | −0.477391 | ||||||||
\(187\) | 5.08876 | 0.372127 | ||||||||
\(188\) | 2.00714 | 0.146385 | ||||||||
\(189\) | −2.22194 | −0.161623 | ||||||||
\(190\) | 13.1421 | 0.953430 | ||||||||
\(191\) | 20.5574 | 1.48748 | 0.743741 | − | 0.668468i | \(-0.233050\pi\) | ||||
0.743741 | + | 0.668468i | \(0.233050\pi\) | |||||||
\(192\) | −3.62594 | −0.261680 | ||||||||
\(193\) | −5.62205 | −0.404684 | −0.202342 | − | 0.979315i | \(-0.564855\pi\) | ||||
−0.202342 | + | 0.979315i | \(0.564855\pi\) | |||||||
\(194\) | −13.5887 | −0.975614 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.74635 | −0.124740 | ||||||||
\(197\) | 21.1290 | 1.50538 | 0.752691 | − | 0.658374i | \(-0.228756\pi\) | ||||
0.752691 | + | 0.658374i | \(0.228756\pi\) | |||||||
\(198\) | 4.07168 | 0.289362 | ||||||||
\(199\) | 17.2175 | 1.22052 | 0.610259 | − | 0.792202i | \(-0.291065\pi\) | ||||
0.610259 | + | 0.792202i | \(0.291065\pi\) | |||||||
\(200\) | 17.2209 | 1.21770 | ||||||||
\(201\) | 4.01445 | 0.283158 | ||||||||
\(202\) | −17.9921 | −1.26592 | ||||||||
\(203\) | −5.10395 | −0.358227 | ||||||||
\(204\) | −0.746377 | −0.0522569 | ||||||||
\(205\) | 4.41921 | 0.308651 | ||||||||
\(206\) | −17.2282 | −1.20035 | ||||||||
\(207\) | −1.27637 | −0.0887136 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.56104 | −0.177151 | ||||||||
\(210\) | −1.99931 | −0.137965 | ||||||||
\(211\) | −1.36491 | −0.0939642 | −0.0469821 | − | 0.998896i | \(-0.514960\pi\) | ||||
−0.0469821 | + | 0.998896i | \(0.514960\pi\) | |||||||
\(212\) | 2.09413 | 0.143826 | ||||||||
\(213\) | 0.928077 | 0.0635908 | ||||||||
\(214\) | 22.8673 | 1.56318 | ||||||||
\(215\) | 30.9898 | 2.11349 | ||||||||
\(216\) | 8.10370 | 0.551387 | ||||||||
\(217\) | 5.66967 | 0.384883 | ||||||||
\(218\) | 9.18712 | 0.622230 | ||||||||
\(219\) | 3.51161 | 0.237293 | ||||||||
\(220\) | 0.916811 | 0.0618114 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.38607 | 0.0930271 | ||||||||
\(223\) | 2.73109 | 0.182887 | 0.0914436 | − | 0.995810i | \(-0.470852\pi\) | ||||
0.0914436 | + | 0.995810i | \(0.470852\pi\) | |||||||
\(224\) | −1.08129 | −0.0722469 | ||||||||
\(225\) | −17.8528 | −1.19019 | ||||||||
\(226\) | −20.7497 | −1.38025 | ||||||||
\(227\) | 11.5837 | 0.768834 | 0.384417 | − | 0.923160i | \(-0.374402\pi\) | ||||
0.384417 | + | 0.923160i | \(0.374402\pi\) | |||||||
\(228\) | 0.375632 | 0.0248769 | ||||||||
\(229\) | 8.05000 | 0.531959 | 0.265979 | − | 0.963979i | \(-0.414305\pi\) | ||||
0.265979 | + | 0.963979i | \(0.414305\pi\) | |||||||
\(230\) | −2.42315 | −0.159778 | ||||||||
\(231\) | 0.389610 | 0.0256345 | ||||||||
\(232\) | 18.6147 | 1.22212 | ||||||||
\(233\) | −14.1199 | −0.925023 | −0.462511 | − | 0.886613i | \(-0.653052\pi\) | ||||
−0.462511 | + | 0.886613i | \(0.653052\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.4060 | 1.65731 | ||||||||
\(236\) | 3.01154 | 0.196035 | ||||||||
\(237\) | 2.75729 | 0.179105 | ||||||||
\(238\) | 5.48006 | 0.355219 | ||||||||
\(239\) | −14.9340 | −0.965999 | −0.482999 | − | 0.875621i | \(-0.660453\pi\) | ||||
−0.482999 | + | 0.875621i | \(0.660453\pi\) | |||||||
\(240\) | 8.29103 | 0.535183 | ||||||||
\(241\) | −10.1399 | −0.653170 | −0.326585 | − | 0.945168i | \(-0.605898\pi\) | ||||
−0.326585 | + | 0.945168i | \(0.605898\pi\) | |||||||
\(242\) | −1.50636 | −0.0968327 | ||||||||
\(243\) | −12.8203 | −0.822425 | ||||||||
\(244\) | −3.87227 | −0.247897 | ||||||||
\(245\) | −22.1051 | −1.41224 | ||||||||
\(246\) | 1.06498 | 0.0679006 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −20.6780 | −1.31305 | ||||||||
\(249\) | 7.55084 | 0.478515 | ||||||||
\(250\) | −8.23536 | −0.520850 | ||||||||
\(251\) | −12.0199 | −0.758692 | −0.379346 | − | 0.925255i | \(-0.623851\pi\) | ||||
−0.379346 | + | 0.925255i | \(0.623851\pi\) | |||||||
\(252\) | 0.520053 | 0.0327603 | ||||||||
\(253\) | 0.472206 | 0.0296873 | ||||||||
\(254\) | −5.31035 | −0.333201 | ||||||||
\(255\) | −9.44753 | −0.591627 | ||||||||
\(256\) | 6.34738 | 0.396711 | ||||||||
\(257\) | 10.6786 | 0.666111 | 0.333055 | − | 0.942907i | \(-0.391920\pi\) | ||||
0.333055 | + | 0.942907i | \(0.391920\pi\) | |||||||
\(258\) | 7.46820 | 0.464950 | ||||||||
\(259\) | −1.20702 | −0.0750004 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.2977 | −1.19450 | ||||||||
\(262\) | −13.8325 | −0.854576 | ||||||||
\(263\) | −26.7639 | −1.65033 | −0.825167 | − | 0.564889i | \(-0.808919\pi\) | ||||
−0.825167 | + | 0.564889i | \(0.808919\pi\) | |||||||
\(264\) | −1.42096 | −0.0874539 | ||||||||
\(265\) | 26.5072 | 1.62832 | ||||||||
\(266\) | −2.75797 | −0.169102 | ||||||||
\(267\) | −4.52633 | −0.277007 | ||||||||
\(268\) | −1.98244 | −0.121097 | ||||||||
\(269\) | −30.2655 | −1.84532 | −0.922659 | − | 0.385616i | \(-0.873989\pi\) | ||||
−0.922659 | + | 0.385616i | \(0.873989\pi\) | |||||||
\(270\) | −15.9492 | −0.970636 | ||||||||
\(271\) | 2.68145 | 0.162887 | 0.0814434 | − | 0.996678i | \(-0.474047\pi\) | ||||
0.0814434 | + | 0.996678i | \(0.474047\pi\) | |||||||
\(272\) | −22.7255 | −1.37794 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.5348 | −1.54261 | ||||||||
\(275\) | 6.60485 | 0.398287 | ||||||||
\(276\) | −0.0692593 | −0.00416892 | ||||||||
\(277\) | −12.7298 | −0.764858 | −0.382429 | − | 0.923985i | \(-0.624912\pi\) | ||||
−0.382429 | + | 0.923985i | \(0.624912\pi\) | |||||||
\(278\) | −18.1578 | −1.08903 | ||||||||
\(279\) | 21.4367 | 1.28338 | ||||||||
\(280\) | −6.34977 | −0.379471 | ||||||||
\(281\) | 20.0318 | 1.19500 | 0.597499 | − | 0.801869i | \(-0.296161\pi\) | ||||
0.597499 | + | 0.801869i | \(0.296161\pi\) | |||||||
\(282\) | 6.12256 | 0.364593 | ||||||||
\(283\) | 18.9846 | 1.12852 | 0.564259 | − | 0.825598i | \(-0.309162\pi\) | ||||
0.564259 | + | 0.825598i | \(0.309162\pi\) | |||||||
\(284\) | −0.458308 | −0.0271956 | ||||||||
\(285\) | 4.75470 | 0.281644 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.927404 | −0.0547429 | ||||||||
\(288\) | −4.08831 | −0.240906 | ||||||||
\(289\) | 8.89544 | 0.523261 | ||||||||
\(290\) | −36.6363 | −2.15136 | ||||||||
\(291\) | −4.91627 | −0.288197 | ||||||||
\(292\) | −1.73412 | −0.101482 | ||||||||
\(293\) | −24.9067 | −1.45507 | −0.727533 | − | 0.686073i | \(-0.759333\pi\) | ||||
−0.727533 | + | 0.686073i | \(0.759333\pi\) | |||||||
\(294\) | −5.32708 | −0.310681 | ||||||||
\(295\) | 38.1197 | 2.21941 | ||||||||
\(296\) | 4.40214 | 0.255869 | ||||||||
\(297\) | 3.10806 | 0.180348 | ||||||||
\(298\) | −21.3376 | −1.23605 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.968745 | −0.0559305 | ||||||||
\(301\) | −6.50344 | −0.374852 | ||||||||
\(302\) | 7.53693 | 0.433702 | ||||||||
\(303\) | −6.50937 | −0.373954 | ||||||||
\(304\) | 11.4372 | 0.655966 | ||||||||
\(305\) | −49.0146 | −2.80657 | ||||||||
\(306\) | 20.7198 | 1.18447 | ||||||||
\(307\) | −14.1232 | −0.806051 | −0.403026 | − | 0.915189i | \(-0.632041\pi\) | ||||
−0.403026 | + | 0.915189i | \(0.632041\pi\) | |||||||
\(308\) | −0.192399 | −0.0109630 | ||||||||
\(309\) | −6.23302 | −0.354584 | ||||||||
\(310\) | 40.6971 | 2.31144 | ||||||||
\(311\) | −23.0707 | −1.30822 | −0.654110 | − | 0.756400i | \(-0.726956\pi\) | ||||
−0.654110 | + | 0.756400i | \(0.726956\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.92342 | 0.108718 | 0.0543589 | − | 0.998521i | \(-0.482688\pi\) | ||||
0.0543589 | + | 0.998521i | \(0.482688\pi\) | |||||||
\(314\) | −22.1462 | −1.24978 | ||||||||
\(315\) | 6.58275 | 0.370896 | ||||||||
\(316\) | −1.36162 | −0.0765971 | ||||||||
\(317\) | −17.0099 | −0.955372 | −0.477686 | − | 0.878531i | \(-0.658524\pi\) | ||||
−0.477686 | + | 0.878531i | \(0.658524\pi\) | |||||||
\(318\) | 6.38793 | 0.358218 | ||||||||
\(319\) | 7.13941 | 0.399730 | ||||||||
\(320\) | 22.6649 | 1.26701 | ||||||||
\(321\) | 8.27317 | 0.461763 | ||||||||
\(322\) | 0.508516 | 0.0283385 | ||||||||
\(323\) | −13.0325 | −0.725148 | ||||||||
\(324\) | 1.72649 | 0.0959161 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.7736 | 0.929005 | ||||||||
\(327\) | 3.32381 | 0.183807 | ||||||||
\(328\) | 3.38236 | 0.186759 | ||||||||
\(329\) | −5.33164 | −0.293943 | ||||||||
\(330\) | 2.79664 | 0.153950 | ||||||||
\(331\) | −27.1478 | −1.49218 | −0.746088 | − | 0.665847i | \(-0.768070\pi\) | ||||
−0.746088 | + | 0.665847i | \(0.768070\pi\) | |||||||
\(332\) | −3.72880 | −0.204644 | ||||||||
\(333\) | −4.56367 | −0.250087 | ||||||||
\(334\) | 1.93608 | 0.105938 | ||||||||
\(335\) | −25.0934 | −1.37100 | ||||||||
\(336\) | −1.73993 | −0.0949211 | ||||||||
\(337\) | 6.64985 | 0.362240 | 0.181120 | − | 0.983461i | \(-0.442028\pi\) | ||||
0.181120 | + | 0.983461i | \(0.442028\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.50706 | −0.407727 | ||||||||
\(340\) | 4.66543 | 0.253018 | ||||||||
\(341\) | −7.93075 | −0.429474 | ||||||||
\(342\) | −10.4277 | −0.563868 | ||||||||
\(343\) | 9.64319 | 0.520684 | ||||||||
\(344\) | 23.7189 | 1.27883 | ||||||||
\(345\) | −0.876673 | −0.0471985 | ||||||||
\(346\) | −18.7623 | −1.00867 | ||||||||
\(347\) | 28.0264 | 1.50454 | 0.752268 | − | 0.658857i | \(-0.228960\pi\) | ||||
0.752268 | + | 0.658857i | \(0.228960\pi\) | |||||||
\(348\) | −1.04715 | −0.0561331 | ||||||||
\(349\) | 13.7845 | 0.737867 | 0.368933 | − | 0.929456i | \(-0.379723\pi\) | ||||
0.368933 | + | 0.929456i | \(0.379723\pi\) | |||||||
\(350\) | 7.11272 | 0.380191 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.51252 | 0.0806173 | ||||||||
\(353\) | 2.28197 | 0.121457 | 0.0607286 | − | 0.998154i | \(-0.480658\pi\) | ||||
0.0607286 | + | 0.998154i | \(0.480658\pi\) | |||||||
\(354\) | 9.18640 | 0.488252 | ||||||||
\(355\) | −5.80119 | −0.307895 | ||||||||
\(356\) | 2.23522 | 0.118466 | ||||||||
\(357\) | 1.98263 | 0.104932 | ||||||||
\(358\) | −13.5251 | −0.714823 | ||||||||
\(359\) | 25.1375 | 1.32671 | 0.663354 | − | 0.748306i | \(-0.269132\pi\) | ||||
0.663354 | + | 0.748306i | \(0.269132\pi\) | |||||||
\(360\) | −24.0081 | −1.26534 | ||||||||
\(361\) | −12.4411 | −0.654793 | ||||||||
\(362\) | −36.5699 | −1.92207 | ||||||||
\(363\) | −0.544988 | −0.0286044 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.9503 | −1.14893 | ||||||||
\(366\) | −11.8120 | −0.617422 | ||||||||
\(367\) | 33.0134 | 1.72328 | 0.861641 | − | 0.507518i | \(-0.169437\pi\) | ||||
0.861641 | + | 0.507518i | \(0.169437\pi\) | |||||||
\(368\) | −2.10879 | −0.109928 | ||||||||
\(369\) | −3.50646 | −0.182539 | ||||||||
\(370\) | −8.66401 | −0.450420 | ||||||||
\(371\) | −5.56273 | −0.288802 | ||||||||
\(372\) | 1.16322 | 0.0603100 | ||||||||
\(373\) | −2.61028 | −0.135155 | −0.0675775 | − | 0.997714i | \(-0.521527\pi\) | ||||
−0.0675775 | + | 0.997714i | \(0.521527\pi\) | |||||||
\(374\) | −7.66551 | −0.396374 | ||||||||
\(375\) | −2.97948 | −0.153859 | ||||||||
\(376\) | 19.4452 | 1.00281 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.34705 | 0.172154 | ||||||||
\(379\) | 26.7425 | 1.37367 | 0.686835 | − | 0.726813i | \(-0.258999\pi\) | ||||
0.686835 | + | 0.726813i | \(0.258999\pi\) | |||||||
\(380\) | −2.34799 | −0.120449 | ||||||||
\(381\) | −1.92123 | −0.0984278 | ||||||||
\(382\) | −30.9669 | −1.58440 | ||||||||
\(383\) | −30.9425 | −1.58109 | −0.790544 | − | 0.612405i | \(-0.790202\pi\) | ||||
−0.790544 | + | 0.612405i | \(0.790202\pi\) | |||||||
\(384\) | 7.11059 | 0.362861 | ||||||||
\(385\) | −2.43536 | −0.124118 | ||||||||
\(386\) | 8.46885 | 0.431053 | ||||||||
\(387\) | −24.5892 | −1.24994 | ||||||||
\(388\) | 2.42778 | 0.123252 | ||||||||
\(389\) | 33.8926 | 1.71842 | 0.859212 | − | 0.511620i | \(-0.170954\pi\) | ||||
0.859212 | + | 0.511620i | \(0.170954\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.40294 | 0.121522 | ||||||||
\(392\) | −16.9187 | −0.854523 | ||||||||
\(393\) | −5.00448 | −0.252442 | ||||||||
\(394\) | −31.8280 | −1.60347 | ||||||||
\(395\) | −17.2352 | −0.867196 | ||||||||
\(396\) | −0.727452 | −0.0365558 | ||||||||
\(397\) | −19.3612 | −0.971709 | −0.485855 | − | 0.874040i | \(-0.661492\pi\) | ||||
−0.485855 | + | 0.874040i | \(0.661492\pi\) | |||||||
\(398\) | −25.9359 | −1.30005 | ||||||||
\(399\) | −0.997808 | −0.0499529 | ||||||||
\(400\) | −29.4961 | −1.47481 | ||||||||
\(401\) | 25.4197 | 1.26940 | 0.634700 | − | 0.772758i | \(-0.281124\pi\) | ||||
0.634700 | + | 0.772758i | \(0.281124\pi\) | |||||||
\(402\) | −6.04722 | −0.301608 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.21449 | 0.159927 | ||||||||
\(405\) | 21.8536 | 1.08592 | ||||||||
\(406\) | 7.68839 | 0.381569 | ||||||||
\(407\) | 1.68838 | 0.0836898 | ||||||||
\(408\) | −7.23091 | −0.357983 | ||||||||
\(409\) | −6.74419 | −0.333479 | −0.166739 | − | 0.986001i | \(-0.553324\pi\) | ||||
−0.166739 | + | 0.986001i | \(0.553324\pi\) | |||||||
\(410\) | −6.65694 | −0.328763 | ||||||||
\(411\) | −9.23825 | −0.455689 | ||||||||
\(412\) | 3.07802 | 0.151643 | ||||||||
\(413\) | −7.99969 | −0.393639 | ||||||||
\(414\) | 1.92267 | 0.0944941 | ||||||||
\(415\) | −47.1985 | −2.31688 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.56930 | −0.321700 | ||||||||
\(418\) | 3.85786 | 0.188694 | ||||||||
\(419\) | 13.9379 | 0.680911 | 0.340455 | − | 0.940261i | \(-0.389419\pi\) | ||||
0.340455 | + | 0.940261i | \(0.389419\pi\) | |||||||
\(420\) | 0.357199 | 0.0174295 | ||||||||
\(421\) | −28.7165 | −1.39956 | −0.699778 | − | 0.714361i | \(-0.746718\pi\) | ||||
−0.699778 | + | 0.714361i | \(0.746718\pi\) | |||||||
\(422\) | 2.05605 | 0.100087 | ||||||||
\(423\) | −20.1586 | −0.980147 | ||||||||
\(424\) | 20.2880 | 0.985271 | ||||||||
\(425\) | 33.6105 | 1.63035 | ||||||||
\(426\) | −1.39802 | −0.0677343 | ||||||||
\(427\) | 10.2861 | 0.497778 | ||||||||
\(428\) | −4.08550 | −0.197480 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −46.6819 | −2.25120 | ||||||||
\(431\) | 25.7254 | 1.23915 | 0.619574 | − | 0.784938i | \(-0.287305\pi\) | ||||
0.619574 | + | 0.784938i | \(0.287305\pi\) | |||||||
\(432\) | −13.8801 | −0.667804 | ||||||||
\(433\) | 15.2106 | 0.730973 | 0.365486 | − | 0.930817i | \(-0.380903\pi\) | ||||
0.365486 | + | 0.930817i | \(0.380903\pi\) | |||||||
\(434\) | −8.54059 | −0.409961 | ||||||||
\(435\) | −13.2547 | −0.635513 | ||||||||
\(436\) | −1.64138 | −0.0786079 | ||||||||
\(437\) | −1.20934 | −0.0578505 | ||||||||
\(438\) | −5.28977 | −0.252755 | ||||||||
\(439\) | 5.67704 | 0.270951 | 0.135475 | − | 0.990781i | \(-0.456744\pi\) | ||||
0.135475 | + | 0.990781i | \(0.456744\pi\) | |||||||
\(440\) | 8.88207 | 0.423436 | ||||||||
\(441\) | 17.5395 | 0.835213 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.03014 | 0.286501 | 0.143250 | − | 0.989686i | \(-0.454245\pi\) | ||||
0.143250 | + | 0.989686i | \(0.454245\pi\) | |||||||
\(444\) | −0.247637 | −0.0117524 | ||||||||
\(445\) | 28.2930 | 1.34122 | ||||||||
\(446\) | −4.11401 | −0.194804 | ||||||||
\(447\) | −7.71973 | −0.365131 | ||||||||
\(448\) | −4.75640 | −0.224719 | ||||||||
\(449\) | −4.47151 | −0.211023 | −0.105512 | − | 0.994418i | \(-0.533648\pi\) | ||||
−0.105512 | + | 0.994418i | \(0.533648\pi\) | |||||||
\(450\) | 26.8928 | 1.26774 | ||||||||
\(451\) | 1.29725 | 0.0610853 | ||||||||
\(452\) | 3.70717 | 0.174371 | ||||||||
\(453\) | 2.72679 | 0.128116 | ||||||||
\(454\) | −17.4492 | −0.818931 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.63913 | 0.170418 | ||||||||
\(457\) | −7.92953 | −0.370928 | −0.185464 | − | 0.982651i | \(-0.559379\pi\) | ||||
−0.185464 | + | 0.982651i | \(0.559379\pi\) | |||||||
\(458\) | −12.1262 | −0.566621 | ||||||||
\(459\) | 15.8162 | 0.738235 | ||||||||
\(460\) | 0.432923 | 0.0201852 | ||||||||
\(461\) | 1.29048 | 0.0601035 | 0.0300517 | − | 0.999548i | \(-0.490433\pi\) | ||||
0.0300517 | + | 0.999548i | \(0.490433\pi\) | |||||||
\(462\) | −0.586894 | −0.0273048 | ||||||||
\(463\) | −23.9826 | −1.11457 | −0.557283 | − | 0.830322i | \(-0.688156\pi\) | ||||
−0.557283 | + | 0.830322i | \(0.688156\pi\) | |||||||
\(464\) | −31.8834 | −1.48015 | ||||||||
\(465\) | 14.7238 | 0.682801 | ||||||||
\(466\) | 21.2696 | 0.985296 | ||||||||
\(467\) | −1.89329 | −0.0876112 | −0.0438056 | − | 0.999040i | \(-0.513948\pi\) | ||||
−0.0438056 | + | 0.999040i | \(0.513948\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.26603 | 0.243163 | ||||||||
\(470\) | −38.2707 | −1.76530 | ||||||||
\(471\) | −8.01230 | −0.369187 | ||||||||
\(472\) | 29.1759 | 1.34293 | ||||||||
\(473\) | 9.09702 | 0.418282 | ||||||||
\(474\) | −4.15348 | −0.190776 | ||||||||
\(475\) | −16.9153 | −0.776126 | ||||||||
\(476\) | −0.979074 | −0.0448758 | ||||||||
\(477\) | −21.0324 | −0.963006 | ||||||||
\(478\) | 22.4960 | 1.02894 | ||||||||
\(479\) | −10.4681 | −0.478300 | −0.239150 | − | 0.970983i | \(-0.576869\pi\) | ||||
−0.239150 | + | 0.970983i | \(0.576869\pi\) | |||||||
\(480\) | −2.80806 | −0.128170 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 15.2744 | 0.695730 | ||||||||
\(483\) | 0.183976 | 0.00837121 | ||||||||
\(484\) | 0.269129 | 0.0122331 | ||||||||
\(485\) | 30.7304 | 1.39540 | ||||||||
\(486\) | 19.3121 | 0.876013 | ||||||||
\(487\) | 30.9874 | 1.40417 | 0.702087 | − | 0.712091i | \(-0.252252\pi\) | ||||
0.702087 | + | 0.712091i | \(0.252252\pi\) | |||||||
\(488\) | −37.5146 | −1.69821 | ||||||||
\(489\) | 6.06854 | 0.274429 | ||||||||
\(490\) | 33.2983 | 1.50426 | ||||||||
\(491\) | −38.2427 | −1.72587 | −0.862934 | − | 0.505317i | \(-0.831376\pi\) | ||||
−0.862934 | + | 0.505317i | \(0.831376\pi\) | |||||||
\(492\) | −0.190271 | −0.00857806 | ||||||||
\(493\) | 36.3307 | 1.63625 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.20797 | −0.413867 | ||||||||
\(496\) | 35.4174 | 1.59029 | ||||||||
\(497\) | 1.21742 | 0.0546088 | ||||||||
\(498\) | −11.3743 | −0.509695 | ||||||||
\(499\) | −28.2177 | −1.26320 | −0.631600 | − | 0.775295i | \(-0.717601\pi\) | ||||
−0.631600 | + | 0.775295i | \(0.717601\pi\) | |||||||
\(500\) | 1.47134 | 0.0658003 | ||||||||
\(501\) | 0.700457 | 0.0312941 | ||||||||
\(502\) | 18.1064 | 0.808128 | ||||||||
\(503\) | −22.0249 | −0.982040 | −0.491020 | − | 0.871148i | \(-0.663376\pi\) | ||||
−0.491020 | + | 0.871148i | \(0.663376\pi\) | |||||||
\(504\) | 5.03828 | 0.224423 | ||||||||
\(505\) | 40.6886 | 1.81062 | ||||||||
\(506\) | −0.711313 | −0.0316217 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.948754 | 0.0420941 | ||||||||
\(509\) | −12.0558 | −0.534364 | −0.267182 | − | 0.963646i | \(-0.586093\pi\) | ||||
−0.267182 | + | 0.963646i | \(0.586093\pi\) | |||||||
\(510\) | 14.2314 | 0.630177 | ||||||||
\(511\) | 4.60642 | 0.203776 | ||||||||
\(512\) | 16.5330 | 0.730664 | ||||||||
\(513\) | −7.95987 | −0.351437 | ||||||||
\(514\) | −16.0858 | −0.709514 | ||||||||
\(515\) | 38.9611 | 1.71683 | ||||||||
\(516\) | −1.33428 | −0.0587383 | ||||||||
\(517\) | 7.45791 | 0.327998 | ||||||||
\(518\) | 1.81821 | 0.0798874 | ||||||||
\(519\) | −6.78801 | −0.297961 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.1905 | 0.928374 | 0.464187 | − | 0.885737i | \(-0.346347\pi\) | ||||
0.464187 | + | 0.885737i | \(0.346347\pi\) | |||||||
\(522\) | 29.0694 | 1.27233 | ||||||||
\(523\) | −40.9438 | −1.79035 | −0.895173 | − | 0.445718i | \(-0.852948\pi\) | ||||
−0.895173 | + | 0.445718i | \(0.852948\pi\) | |||||||
\(524\) | 2.47134 | 0.107961 | ||||||||
\(525\) | 2.57332 | 0.112309 | ||||||||
\(526\) | 40.3162 | 1.75787 | ||||||||
\(527\) | −40.3577 | −1.75801 | ||||||||
\(528\) | 2.43382 | 0.105918 | ||||||||
\(529\) | −22.7770 | −0.990305 | ||||||||
\(530\) | −39.9295 | −1.73442 | ||||||||
\(531\) | −30.2464 | −1.31258 | ||||||||
\(532\) | 0.492743 | 0.0213631 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.81830 | 0.295056 | ||||||||
\(535\) | −51.7136 | −2.23577 | ||||||||
\(536\) | −19.2059 | −0.829567 | ||||||||
\(537\) | −4.89325 | −0.211159 | ||||||||
\(538\) | 45.5908 | 1.96556 | ||||||||
\(539\) | −6.48892 | −0.279498 | ||||||||
\(540\) | 2.84950 | 0.122623 | ||||||||
\(541\) | −3.10501 | −0.133495 | −0.0667475 | − | 0.997770i | \(-0.521262\pi\) | ||||
−0.0667475 | + | 0.997770i | \(0.521262\pi\) | |||||||
\(542\) | −4.03924 | −0.173500 | ||||||||
\(543\) | −13.2306 | −0.567781 | ||||||||
\(544\) | 7.69682 | 0.329999 | ||||||||
\(545\) | −20.7764 | −0.889961 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.19998 | −0.136821 | −0.0684105 | − | 0.997657i | \(-0.521793\pi\) | ||||
−0.0684105 | + | 0.997657i | \(0.521793\pi\) | |||||||
\(548\) | 4.56208 | 0.194882 | ||||||||
\(549\) | 38.8911 | 1.65983 | ||||||||
\(550\) | −9.94929 | −0.424239 | ||||||||
\(551\) | −18.2843 | −0.778938 | ||||||||
\(552\) | −0.670984 | −0.0285590 | ||||||||
\(553\) | 3.61693 | 0.153807 | ||||||||
\(554\) | 19.1757 | 0.814696 | ||||||||
\(555\) | −3.13456 | −0.133055 | ||||||||
\(556\) | 3.24409 | 0.137580 | ||||||||
\(557\) | −18.5061 | −0.784130 | −0.392065 | − | 0.919938i | \(-0.628239\pi\) | ||||
−0.392065 | + | 0.919938i | \(0.628239\pi\) | |||||||
\(558\) | −32.2915 | −1.36701 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 10.8759 | 0.459591 | ||||||||
\(561\) | −2.77331 | −0.117089 | ||||||||
\(562\) | −30.1752 | −1.27286 | ||||||||
\(563\) | −13.3004 | −0.560547 | −0.280273 | − | 0.959920i | \(-0.590425\pi\) | ||||
−0.280273 | + | 0.959920i | \(0.590425\pi\) | |||||||
\(564\) | −1.09386 | −0.0460600 | ||||||||
\(565\) | 46.9248 | 1.97414 | ||||||||
\(566\) | −28.5977 | −1.20205 | ||||||||
\(567\) | −4.58615 | −0.192600 | ||||||||
\(568\) | −4.44009 | −0.186302 | ||||||||
\(569\) | −6.15820 | −0.258165 | −0.129083 | − | 0.991634i | \(-0.541203\pi\) | ||||
−0.129083 | + | 0.991634i | \(0.541203\pi\) | |||||||
\(570\) | −7.16230 | −0.299996 | ||||||||
\(571\) | −27.3358 | −1.14397 | −0.571983 | − | 0.820265i | \(-0.693826\pi\) | ||||
−0.571983 | + | 0.820265i | \(0.693826\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.2035 | −0.468034 | ||||||||
\(574\) | 1.39701 | 0.0583099 | ||||||||
\(575\) | 3.11885 | 0.130065 | ||||||||
\(576\) | −17.9837 | −0.749320 | ||||||||
\(577\) | 42.8994 | 1.78592 | 0.892962 | − | 0.450132i | \(-0.148623\pi\) | ||||
0.892962 | + | 0.450132i | \(0.148623\pi\) | |||||||
\(578\) | −13.3998 | −0.557357 | ||||||||
\(579\) | 3.06395 | 0.127333 | ||||||||
\(580\) | 6.54549 | 0.271787 | ||||||||
\(581\) | 9.90495 | 0.410927 | ||||||||
\(582\) | 7.40569 | 0.306976 | ||||||||
\(583\) | 7.78116 | 0.322263 | ||||||||
\(584\) | −16.8002 | −0.695197 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 37.5185 | 1.54988 | ||||||||
\(587\) | −13.5755 | −0.560322 | −0.280161 | − | 0.959953i | \(-0.590388\pi\) | ||||
−0.280161 | + | 0.959953i | \(0.590388\pi\) | |||||||
\(588\) | 0.951742 | 0.0392492 | ||||||||
\(589\) | 20.3110 | 0.836899 | ||||||||
\(590\) | −57.4220 | −2.36403 | ||||||||
\(591\) | −11.5151 | −0.473667 | ||||||||
\(592\) | −7.54000 | −0.309892 | ||||||||
\(593\) | −2.93581 | −0.120559 | −0.0602796 | − | 0.998182i | \(-0.519199\pi\) | ||||
−0.0602796 | + | 0.998182i | \(0.519199\pi\) | |||||||
\(594\) | −4.68186 | −0.192099 | ||||||||
\(595\) | −12.3930 | −0.508062 | ||||||||
\(596\) | 3.81220 | 0.156154 | ||||||||
\(597\) | −9.38335 | −0.384035 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.71523 | 0.396953 | 0.198477 | − | 0.980106i | \(-0.436401\pi\) | ||||
0.198477 | + | 0.980106i | \(0.436401\pi\) | |||||||
\(600\) | −9.38521 | −0.383149 | ||||||||
\(601\) | 0.492629 | 0.0200948 | 0.0100474 | − | 0.999950i | \(-0.496802\pi\) | ||||
0.0100474 | + | 0.999950i | \(0.496802\pi\) | |||||||
\(602\) | 9.79654 | 0.399277 | ||||||||
\(603\) | 19.9106 | 0.810821 | ||||||||
\(604\) | −1.34656 | −0.0547907 | ||||||||
\(605\) | 3.40659 | 0.138498 | ||||||||
\(606\) | 9.80548 | 0.398320 | ||||||||
\(607\) | −17.0589 | −0.692398 | −0.346199 | − | 0.938161i | \(-0.612528\pi\) | ||||
−0.346199 | + | 0.938161i | \(0.612528\pi\) | |||||||
\(608\) | −3.87361 | −0.157096 | ||||||||
\(609\) | 2.78159 | 0.112716 | ||||||||
\(610\) | 73.8338 | 2.98944 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.70182 | −0.149637 | ||||||||
\(613\) | 6.67577 | 0.269632 | 0.134816 | − | 0.990871i | \(-0.456956\pi\) | ||||
0.134816 | + | 0.990871i | \(0.456956\pi\) | |||||||
\(614\) | 21.2746 | 0.858573 | ||||||||
\(615\) | −2.40842 | −0.0971167 | ||||||||
\(616\) | −1.86397 | −0.0751013 | ||||||||
\(617\) | −26.3268 | −1.05988 | −0.529938 | − | 0.848036i | \(-0.677785\pi\) | ||||
−0.529938 | + | 0.848036i | \(0.677785\pi\) | |||||||
\(618\) | 9.38918 | 0.377688 | ||||||||
\(619\) | −32.7137 | −1.31487 | −0.657437 | − | 0.753510i | \(-0.728359\pi\) | ||||
−0.657437 | + | 0.753510i | \(0.728359\pi\) | |||||||
\(620\) | −7.27100 | −0.292010 | ||||||||
\(621\) | 1.46764 | 0.0588945 | ||||||||
\(622\) | 34.7528 | 1.39346 | ||||||||
\(623\) | −5.93749 | −0.237881 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.4002 | −0.576010 | ||||||||
\(626\) | −2.89736 | −0.115802 | ||||||||
\(627\) | 1.39574 | 0.0557403 | ||||||||
\(628\) | 3.95667 | 0.157888 | ||||||||
\(629\) | 8.59175 | 0.342575 | ||||||||
\(630\) | −9.91601 | −0.395063 | ||||||||
\(631\) | 12.0666 | 0.480364 | 0.240182 | − | 0.970728i | \(-0.422793\pi\) | ||||
0.240182 | + | 0.970728i | \(0.422793\pi\) | |||||||
\(632\) | −13.1914 | −0.524725 | ||||||||
\(633\) | 0.743858 | 0.0295657 | ||||||||
\(634\) | 25.6231 | 1.01762 | ||||||||
\(635\) | 12.0092 | 0.476570 | ||||||||
\(636\) | −1.14128 | −0.0452546 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.7545 | −0.425776 | ||||||||
\(639\) | 4.60300 | 0.182092 | ||||||||
\(640\) | −44.4466 | −1.75691 | ||||||||
\(641\) | −11.7037 | −0.462267 | −0.231134 | − | 0.972922i | \(-0.574243\pi\) | ||||
−0.231134 | + | 0.972922i | \(0.574243\pi\) | |||||||
\(642\) | −12.4624 | −0.491851 | ||||||||
\(643\) | −16.5792 | −0.653820 | −0.326910 | − | 0.945055i | \(-0.606007\pi\) | ||||
−0.326910 | + | 0.945055i | \(0.606007\pi\) | |||||||
\(644\) | −0.0908521 | −0.00358007 | ||||||||
\(645\) | −16.8891 | −0.665007 | ||||||||
\(646\) | 19.6317 | 0.772399 | ||||||||
\(647\) | −24.6423 | −0.968789 | −0.484394 | − | 0.874850i | \(-0.660960\pi\) | ||||
−0.484394 | + | 0.874850i | \(0.660960\pi\) | |||||||
\(648\) | 16.7262 | 0.657069 | ||||||||
\(649\) | 11.1900 | 0.439245 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.08990 | −0.121103 | ||||||||
\(652\) | −2.99680 | −0.117364 | ||||||||
\(653\) | −19.6532 | −0.769090 | −0.384545 | − | 0.923106i | \(-0.625642\pi\) | ||||
−0.384545 | + | 0.923106i | \(0.625642\pi\) | |||||||
\(654\) | −5.00687 | −0.195784 | ||||||||
\(655\) | 31.2818 | 1.22228 | ||||||||
\(656\) | −5.79331 | −0.226191 | ||||||||
\(657\) | 17.4166 | 0.679488 | ||||||||
\(658\) | 8.03138 | 0.313096 | ||||||||
\(659\) | 26.2883 | 1.02405 | 0.512023 | − | 0.858971i | \(-0.328896\pi\) | ||||
0.512023 | + | 0.858971i | \(0.328896\pi\) | |||||||
\(660\) | −0.499651 | −0.0194489 | ||||||||
\(661\) | −31.9156 | −1.24137 | −0.620687 | − | 0.784059i | \(-0.713146\pi\) | ||||
−0.620687 | + | 0.784059i | \(0.713146\pi\) | |||||||
\(662\) | 40.8944 | 1.58941 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −36.1246 | −1.40191 | ||||||||
\(665\) | 6.23706 | 0.241863 | ||||||||
\(666\) | 6.87454 | 0.266383 | ||||||||
\(667\) | 3.37127 | 0.130536 | ||||||||
\(668\) | −0.345903 | −0.0133834 | ||||||||
\(669\) | −1.48841 | −0.0575452 | ||||||||
\(670\) | 37.7998 | 1.46033 | ||||||||
\(671\) | −14.3882 | −0.555450 | ||||||||
\(672\) | 0.589292 | 0.0227324 | ||||||||
\(673\) | 5.89178 | 0.227111 | 0.113556 | − | 0.993532i | \(-0.463776\pi\) | ||||
0.113556 | + | 0.993532i | \(0.463776\pi\) | |||||||
\(674\) | −10.0171 | −0.385844 | ||||||||
\(675\) | 20.5282 | 0.790133 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 47.2553 | 1.81617 | 0.908084 | − | 0.418787i | \(-0.137545\pi\) | ||||
0.908084 | + | 0.418787i | \(0.137545\pi\) | |||||||
\(678\) | 11.3084 | 0.434295 | ||||||||
\(679\) | −6.44901 | −0.247490 | ||||||||
\(680\) | 45.1987 | 1.73329 | ||||||||
\(681\) | −6.31295 | −0.241913 | ||||||||
\(682\) | 11.9466 | 0.457459 | ||||||||
\(683\) | 50.4460 | 1.93026 | 0.965132 | − | 0.261763i | \(-0.0843039\pi\) | ||||
0.965132 | + | 0.261763i | \(0.0843039\pi\) | |||||||
\(684\) | 1.86303 | 0.0712349 | ||||||||
\(685\) | 57.7461 | 2.20636 | ||||||||
\(686\) | −14.5261 | −0.554611 | ||||||||
\(687\) | −4.38715 | −0.167380 | ||||||||
\(688\) | −40.6257 | −1.54884 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.32059 | 0.0502739 | ||||||||
\(691\) | −17.4666 | −0.664462 | −0.332231 | − | 0.943198i | \(-0.607801\pi\) | ||||
−0.332231 | + | 0.943198i | \(0.607801\pi\) | |||||||
\(692\) | 3.35209 | 0.127427 | ||||||||
\(693\) | 1.93236 | 0.0734043 | ||||||||
\(694\) | −42.2179 | −1.60257 | ||||||||
\(695\) | 41.0631 | 1.55761 | ||||||||
\(696\) | −10.1448 | −0.384538 | ||||||||
\(697\) | 6.60141 | 0.250046 | ||||||||
\(698\) | −20.7644 | −0.785946 | ||||||||
\(699\) | 7.69515 | 0.291057 | ||||||||
\(700\) | −1.27077 | −0.0480305 | ||||||||
\(701\) | −32.8524 | −1.24082 | −0.620409 | − | 0.784278i | \(-0.713034\pi\) | ||||
−0.620409 | + | 0.784278i | \(0.713034\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.32401 | −0.163083 | ||||||||
\(704\) | 6.65326 | 0.250754 | ||||||||
\(705\) | −13.8460 | −0.521469 | ||||||||
\(706\) | −3.43748 | −0.129371 | ||||||||
\(707\) | −8.53879 | −0.321134 | ||||||||
\(708\) | −1.64125 | −0.0616821 | ||||||||
\(709\) | −11.9069 | −0.447171 | −0.223586 | − | 0.974684i | \(-0.571776\pi\) | ||||
−0.223586 | + | 0.974684i | \(0.571776\pi\) | |||||||
\(710\) | 8.73869 | 0.327957 | ||||||||
\(711\) | 13.6754 | 0.512868 | ||||||||
\(712\) | 21.6548 | 0.811547 | ||||||||
\(713\) | −3.74495 | −0.140249 | ||||||||
\(714\) | −2.98656 | −0.111769 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.41641 | 0.0903055 | ||||||||
\(717\) | 8.13883 | 0.303950 | ||||||||
\(718\) | −37.8663 | −1.41316 | ||||||||
\(719\) | 5.95330 | 0.222021 | 0.111010 | − | 0.993819i | \(-0.464591\pi\) | ||||
0.111010 | + | 0.993819i | \(0.464591\pi\) | |||||||
\(720\) | 41.1212 | 1.53250 | ||||||||
\(721\) | −8.17627 | −0.304500 | ||||||||
\(722\) | 18.7408 | 0.697459 | ||||||||
\(723\) | 5.52614 | 0.205519 | ||||||||
\(724\) | 6.53362 | 0.242820 | ||||||||
\(725\) | 47.1547 | 1.75128 | ||||||||
\(726\) | 0.820949 | 0.0304683 | ||||||||
\(727\) | 4.11309 | 0.152546 | 0.0762730 | − | 0.997087i | \(-0.475698\pi\) | ||||
0.0762730 | + | 0.997087i | \(0.475698\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.2584 | −0.454015 | ||||||||
\(730\) | 33.0651 | 1.22379 | ||||||||
\(731\) | 46.2925 | 1.71219 | ||||||||
\(732\) | 2.11034 | 0.0780005 | ||||||||
\(733\) | −47.3957 | −1.75060 | −0.875301 | − | 0.483579i | \(-0.839336\pi\) | ||||
−0.875301 | + | 0.483579i | \(0.839336\pi\) | |||||||
\(734\) | −49.7301 | −1.83557 | ||||||||
\(735\) | 12.0470 | 0.444360 | ||||||||
\(736\) | 0.714219 | 0.0263264 | ||||||||
\(737\) | −7.36614 | −0.271335 | ||||||||
\(738\) | 5.28201 | 0.194433 | ||||||||
\(739\) | 45.5262 | 1.67471 | 0.837354 | − | 0.546661i | \(-0.184102\pi\) | ||||
0.837354 | + | 0.546661i | \(0.184102\pi\) | |||||||
\(740\) | 1.54792 | 0.0569028 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.37949 | 0.307621 | ||||||||
\(743\) | −12.3917 | −0.454606 | −0.227303 | − | 0.973824i | \(-0.572991\pi\) | ||||
−0.227303 | + | 0.973824i | \(0.572991\pi\) | |||||||
\(744\) | 11.2693 | 0.413151 | ||||||||
\(745\) | 48.2542 | 1.76790 | ||||||||
\(746\) | 3.93202 | 0.143962 | ||||||||
\(747\) | 37.4501 | 1.37023 | ||||||||
\(748\) | 1.36953 | 0.0500750 | ||||||||
\(749\) | 10.8525 | 0.396541 | ||||||||
\(750\) | 4.48817 | 0.163885 | ||||||||
\(751\) | 1.04500 | 0.0381326 | 0.0190663 | − | 0.999818i | \(-0.493931\pi\) | ||||
0.0190663 | + | 0.999818i | \(0.493931\pi\) | |||||||
\(752\) | −33.3057 | −1.21453 | ||||||||
\(753\) | 6.55072 | 0.238722 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.0445 | −0.620314 | ||||||||
\(756\) | −0.597989 | −0.0217486 | ||||||||
\(757\) | 25.6560 | 0.932483 | 0.466241 | − | 0.884658i | \(-0.345608\pi\) | ||||
0.466241 | + | 0.884658i | \(0.345608\pi\) | |||||||
\(758\) | −40.2839 | −1.46318 | ||||||||
\(759\) | −0.257346 | −0.00934108 | ||||||||
\(760\) | −22.7473 | −0.825133 | ||||||||
\(761\) | −0.152493 | −0.00552788 | −0.00276394 | − | 0.999996i | \(-0.500880\pi\) | ||||
−0.00276394 | + | 0.999996i | \(0.500880\pi\) | |||||||
\(762\) | 2.89408 | 0.104841 | ||||||||
\(763\) | 4.36007 | 0.157845 | ||||||||
\(764\) | 5.53259 | 0.200162 | ||||||||
\(765\) | −46.8571 | −1.69412 | ||||||||
\(766\) | 46.6106 | 1.68411 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.45924 | −0.124825 | ||||||||
\(769\) | −19.7792 | −0.713257 | −0.356629 | − | 0.934246i | \(-0.616074\pi\) | ||||
−0.356629 | + | 0.934246i | \(0.616074\pi\) | |||||||
\(770\) | 3.66854 | 0.132205 | ||||||||
\(771\) | −5.81969 | −0.209591 | ||||||||
\(772\) | −1.51305 | −0.0544560 | ||||||||
\(773\) | −20.9831 | −0.754708 | −0.377354 | − | 0.926069i | \(-0.623166\pi\) | ||||
−0.377354 | + | 0.926069i | \(0.623166\pi\) | |||||||
\(774\) | 37.0402 | 1.33138 | ||||||||
\(775\) | −52.3814 | −1.88160 | ||||||||
\(776\) | 23.5203 | 0.844331 | ||||||||
\(777\) | 0.657810 | 0.0235988 | ||||||||
\(778\) | −51.0546 | −1.83039 | ||||||||
\(779\) | −3.32232 | −0.119035 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.70293 | −0.0609357 | ||||||||
\(782\) | −3.61970 | −0.129440 | ||||||||
\(783\) | 22.1897 | 0.792995 | ||||||||
\(784\) | 28.9784 | 1.03494 | ||||||||
\(785\) | 50.0830 | 1.78754 | ||||||||
\(786\) | 7.53855 | 0.268891 | ||||||||
\(787\) | −7.93451 | −0.282835 | −0.141417 | − | 0.989950i | \(-0.545166\pi\) | ||||
−0.141417 | + | 0.989950i | \(0.545166\pi\) | |||||||
\(788\) | 5.68643 | 0.202571 | ||||||||
\(789\) | 14.5860 | 0.519276 | ||||||||
\(790\) | 25.9624 | 0.923702 | ||||||||
\(791\) | −9.84752 | −0.350137 | ||||||||
\(792\) | −7.04756 | −0.250424 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 29.1649 | 1.03503 | ||||||||
\(795\) | −14.4461 | −0.512350 | ||||||||
\(796\) | 4.63373 | 0.164238 | ||||||||
\(797\) | −26.1000 | −0.924510 | −0.462255 | − | 0.886747i | \(-0.652960\pi\) | ||||
−0.462255 | + | 0.886747i | \(0.652960\pi\) | |||||||
\(798\) | 1.50306 | 0.0532078 | ||||||||
\(799\) | 37.9515 | 1.34263 | ||||||||
\(800\) | 9.98993 | 0.353197 | ||||||||
\(801\) | −22.4493 | −0.793209 | ||||||||
\(802\) | −38.2913 | −1.35211 | ||||||||
\(803\) | −6.44348 | −0.227385 | ||||||||
\(804\) | 1.08040 | 0.0381029 | ||||||||
\(805\) | −1.14999 | −0.0405319 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.4943 | 0.580627 | ||||||||
\(808\) | 31.1420 | 1.09557 | ||||||||
\(809\) | 54.6289 | 1.92065 | 0.960325 | − | 0.278884i | \(-0.0899644\pi\) | ||||
0.960325 | + | 0.278884i | \(0.0899644\pi\) | |||||||
\(810\) | −32.9195 | −1.15667 | ||||||||
\(811\) | 28.1892 | 0.989858 | 0.494929 | − | 0.868934i | \(-0.335194\pi\) | ||||
0.494929 | + | 0.868934i | \(0.335194\pi\) | |||||||
\(812\) | −1.37362 | −0.0482045 | ||||||||
\(813\) | −1.46136 | −0.0512521 | ||||||||
\(814\) | −2.54331 | −0.0891430 | ||||||||
\(815\) | −37.9330 | −1.32873 | ||||||||
\(816\) | 12.3851 | 0.433566 | ||||||||
\(817\) | −23.2979 | −0.815089 | ||||||||
\(818\) | 10.1592 | 0.355208 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.18934 | 0.0415334 | ||||||||
\(821\) | 9.16089 | 0.319717 | 0.159859 | − | 0.987140i | \(-0.448896\pi\) | ||||
0.159859 | + | 0.987140i | \(0.448896\pi\) | |||||||
\(822\) | 13.9162 | 0.485382 | ||||||||
\(823\) | −30.9586 | −1.07915 | −0.539575 | − | 0.841938i | \(-0.681415\pi\) | ||||
−0.539575 | + | 0.841938i | \(0.681415\pi\) | |||||||
\(824\) | 29.8199 | 1.03882 | ||||||||
\(825\) | −3.59956 | −0.125321 | ||||||||
\(826\) | 12.0504 | 0.419288 | ||||||||
\(827\) | −23.2966 | −0.810102 | −0.405051 | − | 0.914294i | \(-0.632746\pi\) | ||||
−0.405051 | + | 0.914294i | \(0.632746\pi\) | |||||||
\(828\) | −0.343507 | −0.0119377 | ||||||||
\(829\) | 30.1486 | 1.04710 | 0.523552 | − | 0.851994i | \(-0.324607\pi\) | ||||
0.523552 | + | 0.851994i | \(0.324607\pi\) | |||||||
\(830\) | 71.0981 | 2.46785 | ||||||||
\(831\) | 6.93757 | 0.240662 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.0205 | −1.14409 | ||||||||
\(834\) | 9.89575 | 0.342662 | ||||||||
\(835\) | −4.37839 | −0.151520 | ||||||||
\(836\) | −0.689249 | −0.0238382 | ||||||||
\(837\) | −24.6492 | −0.852002 | ||||||||
\(838\) | −20.9955 | −0.725278 | ||||||||
\(839\) | 42.8447 | 1.47916 | 0.739581 | − | 0.673067i | \(-0.235024\pi\) | ||||
0.739581 | + | 0.673067i | \(0.235024\pi\) | |||||||
\(840\) | 3.46054 | 0.119400 | ||||||||
\(841\) | 21.9712 | 0.757627 | ||||||||
\(842\) | 43.2574 | 1.49075 | ||||||||
\(843\) | −10.9171 | −0.376005 | ||||||||
\(844\) | −0.367336 | −0.0126442 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 30.3662 | 1.04401 | ||||||||
\(847\) | −0.714897 | −0.0245642 | ||||||||
\(848\) | −34.7493 | −1.19330 | ||||||||
\(849\) | −10.3464 | −0.355087 | ||||||||
\(850\) | −50.6295 | −1.73658 | ||||||||
\(851\) | 0.797262 | 0.0273298 | ||||||||
\(852\) | 0.249772 | 0.00855705 | ||||||||
\(853\) | −27.6138 | −0.945478 | −0.472739 | − | 0.881203i | \(-0.656735\pi\) | ||||
−0.472739 | + | 0.881203i | \(0.656735\pi\) | |||||||
\(854\) | −15.4946 | −0.530213 | ||||||||
\(855\) | 23.5820 | 0.806487 | ||||||||
\(856\) | −39.5803 | −1.35283 | ||||||||
\(857\) | 19.6565 | 0.671453 | 0.335726 | − | 0.941960i | \(-0.391018\pi\) | ||||
0.335726 | + | 0.941960i | \(0.391018\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.1151 | −1.43695 | −0.718474 | − | 0.695553i | \(-0.755159\pi\) | ||||
−0.718474 | + | 0.695553i | \(0.755159\pi\) | |||||||
\(860\) | 8.34025 | 0.284400 | ||||||||
\(861\) | 0.505424 | 0.0172248 | ||||||||
\(862\) | −38.7518 | −1.31989 | ||||||||
\(863\) | 37.7215 | 1.28405 | 0.642027 | − | 0.766682i | \(-0.278094\pi\) | ||||
0.642027 | + | 0.766682i | \(0.278094\pi\) | |||||||
\(864\) | 4.70099 | 0.159931 | ||||||||
\(865\) | 42.4302 | 1.44267 | ||||||||
\(866\) | −22.9126 | −0.778602 | ||||||||
\(867\) | −4.84791 | −0.164644 | ||||||||
\(868\) | 1.52587 | 0.0517915 | ||||||||
\(869\) | −5.05937 | −0.171627 | ||||||||
\(870\) | 19.9663 | 0.676922 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −15.9017 | −0.538500 | ||||||||
\(873\) | −24.3833 | −0.825251 | ||||||||
\(874\) | 1.82170 | 0.0616200 | ||||||||
\(875\) | −3.90838 | −0.132127 | ||||||||
\(876\) | 0.945076 | 0.0319312 | ||||||||
\(877\) | 7.22842 | 0.244086 | 0.122043 | − | 0.992525i | \(-0.461055\pi\) | ||||
0.122043 | + | 0.992525i | \(0.461055\pi\) | |||||||
\(878\) | −8.55169 | −0.288605 | ||||||||
\(879\) | 13.5738 | 0.457834 | ||||||||
\(880\) | −15.2132 | −0.512838 | ||||||||
\(881\) | 12.4762 | 0.420333 | 0.210167 | − | 0.977666i | \(-0.432599\pi\) | ||||
0.210167 | + | 0.977666i | \(0.432599\pi\) | |||||||
\(882\) | −26.4208 | −0.889635 | ||||||||
\(883\) | 8.37451 | 0.281825 | 0.140912 | − | 0.990022i | \(-0.454996\pi\) | ||||
0.140912 | + | 0.990022i | \(0.454996\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.7747 | −0.698335 | ||||||||
\(886\) | −9.08358 | −0.305169 | ||||||||
\(887\) | −36.3121 | −1.21924 | −0.609620 | − | 0.792694i | \(-0.708678\pi\) | ||||
−0.609620 | + | 0.792694i | \(0.708678\pi\) | |||||||
\(888\) | −2.39911 | −0.0805090 | ||||||||
\(889\) | −2.52021 | −0.0845252 | ||||||||
\(890\) | −42.6195 | −1.42861 | ||||||||
\(891\) | 6.41511 | 0.214914 | ||||||||
\(892\) | 0.735014 | 0.0246101 | ||||||||
\(893\) | −19.1000 | −0.639157 | ||||||||
\(894\) | 11.6287 | 0.388922 | ||||||||
\(895\) | 30.5865 | 1.02240 | ||||||||
\(896\) | 9.32744 | 0.311608 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.73571 | 0.224774 | ||||||||
\(899\) | −56.6209 | −1.88841 | ||||||||
\(900\) | −4.80471 | −0.160157 | ||||||||
\(901\) | 39.5964 | 1.31915 | ||||||||
\(902\) | −1.95414 | −0.0650656 | ||||||||
\(903\) | 3.54429 | 0.117947 | ||||||||
\(904\) | 35.9151 | 1.19452 | ||||||||
\(905\) | 82.7015 | 2.74909 | ||||||||
\(906\) | −4.10754 | −0.136464 | ||||||||
\(907\) | −30.5852 | −1.01557 | −0.507783 | − | 0.861485i | \(-0.669535\pi\) | ||||
−0.507783 | + | 0.861485i | \(0.669535\pi\) | |||||||
\(908\) | 3.11749 | 0.103458 | ||||||||
\(909\) | −32.2847 | −1.07082 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.5722 | 0.482798 | 0.241399 | − | 0.970426i | \(-0.422394\pi\) | ||||
0.241399 | + | 0.970426i | \(0.422394\pi\) | |||||||
\(912\) | −6.23311 | −0.206399 | ||||||||
\(913\) | −13.8551 | −0.458536 | ||||||||
\(914\) | 11.9447 | 0.395097 | ||||||||
\(915\) | 26.7124 | 0.883084 | ||||||||
\(916\) | 2.16648 | 0.0715827 | ||||||||
\(917\) | −6.56471 | −0.216786 | ||||||||
\(918\) | −23.8249 | −0.786338 | ||||||||
\(919\) | −53.0844 | −1.75109 | −0.875547 | − | 0.483133i | \(-0.839499\pi\) | ||||
−0.875547 | + | 0.483133i | \(0.839499\pi\) | |||||||
\(920\) | 4.19416 | 0.138277 | ||||||||
\(921\) | 7.69695 | 0.253623 | ||||||||
\(922\) | −1.94393 | −0.0640198 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.104855 | 0.00344949 | ||||||||
\(925\) | 11.1515 | 0.366658 | ||||||||
\(926\) | 36.1265 | 1.18719 | ||||||||
\(927\) | −30.9140 | −1.01535 | ||||||||
\(928\) | 10.7985 | 0.354477 | ||||||||
\(929\) | 32.8684 | 1.07838 | 0.539189 | − | 0.842185i | \(-0.318731\pi\) | ||||
0.539189 | + | 0.842185i | \(0.318731\pi\) | |||||||
\(930\) | −22.1794 | −0.727292 | ||||||||
\(931\) | 16.6184 | 0.544646 | ||||||||
\(932\) | −3.80006 | −0.124475 | ||||||||
\(933\) | 12.5732 | 0.411630 | ||||||||
\(934\) | 2.85199 | 0.0933199 | ||||||||
\(935\) | 17.3353 | 0.566925 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.3227 | −1.41529 | −0.707646 | − | 0.706567i | \(-0.750243\pi\) | ||||
−0.707646 | + | 0.706567i | \(0.750243\pi\) | |||||||
\(938\) | −7.93255 | −0.259007 | ||||||||
\(939\) | −1.04824 | −0.0342079 | ||||||||
\(940\) | 6.83749 | 0.223014 | ||||||||
\(941\) | −39.7733 | −1.29657 | −0.648287 | − | 0.761396i | \(-0.724514\pi\) | ||||
−0.648287 | + | 0.761396i | \(0.724514\pi\) | |||||||
\(942\) | 12.0694 | 0.393243 | ||||||||
\(943\) | 0.612571 | 0.0199481 | ||||||||
\(944\) | −49.9725 | −1.62647 | ||||||||
\(945\) | −7.56925 | −0.246228 | ||||||||
\(946\) | −13.7034 | −0.445537 | ||||||||
\(947\) | −22.1817 | −0.720808 | −0.360404 | − | 0.932796i | \(-0.617361\pi\) | ||||
−0.360404 | + | 0.932796i | \(0.617361\pi\) | |||||||
\(948\) | 0.742066 | 0.0241012 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 25.4805 | 0.826698 | ||||||||
\(951\) | 9.27020 | 0.300607 | ||||||||
\(952\) | −9.48527 | −0.307419 | ||||||||
\(953\) | 47.1622 | 1.52773 | 0.763866 | − | 0.645375i | \(-0.223299\pi\) | ||||
0.763866 | + | 0.645375i | \(0.223299\pi\) | |||||||
\(954\) | 31.6824 | 1.02576 | ||||||||
\(955\) | 70.0306 | 2.26614 | ||||||||
\(956\) | −4.01916 | −0.129989 | ||||||||
\(957\) | −3.89089 | −0.125775 | ||||||||
\(958\) | 15.7688 | 0.509465 | ||||||||
\(959\) | −12.1184 | −0.391325 | ||||||||
\(960\) | −12.3521 | −0.398662 | ||||||||
\(961\) | 31.8968 | 1.02893 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.0326 | 1.32226 | ||||||||
\(964\) | −2.72895 | −0.0878934 | ||||||||
\(965\) | −19.1520 | −0.616525 | ||||||||
\(966\) | −0.277135 | −0.00891667 | ||||||||
\(967\) | −8.94456 | −0.287638 | −0.143819 | − | 0.989604i | \(-0.545938\pi\) | ||||
−0.143819 | + | 0.989604i | \(0.545938\pi\) | |||||||
\(968\) | 2.60732 | 0.0838024 | ||||||||
\(969\) | 7.10256 | 0.228167 | ||||||||
\(970\) | −46.2912 | −1.48632 | ||||||||
\(971\) | −24.8292 | −0.796806 | −0.398403 | − | 0.917210i | \(-0.630436\pi\) | ||||
−0.398403 | + | 0.917210i | \(0.630436\pi\) | |||||||
\(972\) | −3.45032 | −0.110669 | ||||||||
\(973\) | −8.61740 | −0.276261 | ||||||||
\(974\) | −46.6783 | −1.49567 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 64.2552 | 2.05676 | ||||||||
\(977\) | −9.23253 | −0.295375 | −0.147687 | − | 0.989034i | \(-0.547183\pi\) | ||||
−0.147687 | + | 0.989034i | \(0.547183\pi\) | |||||||
\(978\) | −9.14142 | −0.292310 | ||||||||
\(979\) | 8.30538 | 0.265441 | ||||||||
\(980\) | −5.94911 | −0.190037 | ||||||||
\(981\) | 16.4852 | 0.526331 | ||||||||
\(982\) | 57.6073 | 1.83832 | ||||||||
\(983\) | −56.3251 | −1.79649 | −0.898246 | − | 0.439494i | \(-0.855158\pi\) | ||||
−0.898246 | + | 0.439494i | \(0.855158\pi\) | |||||||
\(984\) | −1.84334 | −0.0587636 | ||||||||
\(985\) | 71.9779 | 2.29341 | ||||||||
\(986\) | −54.7272 | −1.74287 | ||||||||
\(987\) | 2.90568 | 0.0924887 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.29567 | 0.136594 | ||||||||
\(990\) | 13.8705 | 0.440835 | ||||||||
\(991\) | −17.4706 | −0.554972 | −0.277486 | − | 0.960730i | \(-0.589501\pi\) | ||||
−0.277486 | + | 0.960730i | \(0.589501\pi\) | |||||||
\(992\) | −11.9954 | −0.380854 | ||||||||
\(993\) | 14.7952 | 0.469511 | ||||||||
\(994\) | −1.83388 | −0.0581671 | ||||||||
\(995\) | 58.6531 | 1.85943 | ||||||||
\(996\) | 2.03215 | 0.0643911 | ||||||||
\(997\) | −10.5546 | −0.334268 | −0.167134 | − | 0.985934i | \(-0.553451\pi\) | ||||
−0.167134 | + | 0.985934i | \(0.553451\pi\) | |||||||
\(998\) | 42.5061 | 1.34551 | ||||||||
\(999\) | 5.24758 | 0.166026 |
(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 | 1859.2.a.t.1.7 | yes | 21 | |
13.12 | even | 2 | 1859.2.a.s.1.15 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.2.a.s.1.15 | ✓ | 21 | 13.12 | even | 2 | ||
1859.2.a.t.1.7 | yes | 21 | 1.1 | even | 1 | trivial |