Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.599456 | −0.423880 | −0.211940 | − | 0.977283i | \(-0.567978\pi\) | ||||
−0.211940 | + | 0.977283i | \(0.567978\pi\) | |||||||
\(3\) | 2.83593 | 1.63733 | 0.818663 | − | 0.574274i | \(-0.194716\pi\) | ||||
0.818663 | + | 0.574274i | \(0.194716\pi\) | |||||||
\(4\) | −1.64065 | −0.820326 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.70002 | −0.694029 | ||||||||
\(7\) | 0.360434 | 0.136231 | 0.0681155 | − | 0.997677i | \(-0.478301\pi\) | ||||
0.0681155 | + | 0.997677i | \(0.478301\pi\) | |||||||
\(8\) | 2.18241 | 0.771599 | ||||||||
\(9\) | 5.04251 | 1.68084 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.625458 | −0.188583 | −0.0942913 | − | 0.995545i | \(-0.530059\pi\) | ||||
−0.0942913 | + | 0.995545i | \(0.530059\pi\) | |||||||
\(12\) | −4.65278 | −1.34314 | ||||||||
\(13\) | 4.68460 | 1.29927 | 0.649637 | − | 0.760245i | \(-0.274921\pi\) | ||||
0.649637 | + | 0.760245i | \(0.274921\pi\) | |||||||
\(14\) | −0.216064 | −0.0577456 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.97304 | 0.493261 | ||||||||
\(17\) | −8.17080 | −1.98171 | −0.990855 | − | 0.134929i | \(-0.956919\pi\) | ||||
−0.990855 | + | 0.134929i | \(0.956919\pi\) | |||||||
\(18\) | −3.02276 | −0.712472 | ||||||||
\(19\) | −4.27121 | −0.979882 | −0.489941 | − | 0.871756i | \(-0.662982\pi\) | ||||
−0.489941 | + | 0.871756i | \(0.662982\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.02216 | 0.223055 | ||||||||
\(22\) | 0.374934 | 0.0799363 | ||||||||
\(23\) | −2.92878 | −0.610693 | −0.305347 | − | 0.952241i | \(-0.598772\pi\) | ||||
−0.305347 | + | 0.952241i | \(0.598772\pi\) | |||||||
\(24\) | 6.18917 | 1.26336 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.80821 | −0.550736 | ||||||||
\(27\) | 5.79241 | 1.11475 | ||||||||
\(28\) | −0.591346 | −0.111754 | ||||||||
\(29\) | −9.18926 | −1.70640 | −0.853201 | − | 0.521582i | \(-0.825342\pi\) | ||||
−0.853201 | + | 0.521582i | \(0.825342\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.11268 | −0.379449 | −0.189724 | − | 0.981837i | \(-0.560759\pi\) | ||||
−0.189724 | + | 0.981837i | \(0.560759\pi\) | |||||||
\(32\) | −5.54758 | −0.980682 | ||||||||
\(33\) | −1.77376 | −0.308771 | ||||||||
\(34\) | 4.89804 | 0.840007 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.27300 | −1.37883 | ||||||||
\(37\) | 2.51815 | 0.413981 | 0.206990 | − | 0.978343i | \(-0.433633\pi\) | ||||
0.206990 | + | 0.978343i | \(0.433633\pi\) | |||||||
\(38\) | 2.56040 | 0.415352 | ||||||||
\(39\) | 13.2852 | 2.12733 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.70037 | −0.421727 | −0.210864 | − | 0.977516i | \(-0.567628\pi\) | ||||
−0.210864 | + | 0.977516i | \(0.567628\pi\) | |||||||
\(42\) | −0.612743 | −0.0945483 | ||||||||
\(43\) | 1.59843 | 0.243758 | 0.121879 | − | 0.992545i | \(-0.461108\pi\) | ||||
0.121879 | + | 0.992545i | \(0.461108\pi\) | |||||||
\(44\) | 1.02616 | 0.154699 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.75568 | 0.258860 | ||||||||
\(47\) | −5.73910 | −0.837134 | −0.418567 | − | 0.908186i | \(-0.637468\pi\) | ||||
−0.418567 | + | 0.908186i | \(0.637468\pi\) | |||||||
\(48\) | 5.59542 | 0.807629 | ||||||||
\(49\) | −6.87009 | −0.981441 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −23.1718 | −3.24471 | ||||||||
\(52\) | −7.68580 | −1.06583 | ||||||||
\(53\) | 9.95812 | 1.36785 | 0.683927 | − | 0.729551i | \(-0.260271\pi\) | ||||
0.683927 | + | 0.729551i | \(0.260271\pi\) | |||||||
\(54\) | −3.47230 | −0.472520 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.786614 | 0.105116 | ||||||||
\(57\) | −12.1128 | −1.60439 | ||||||||
\(58\) | 5.50856 | 0.723309 | ||||||||
\(59\) | −6.89519 | −0.897678 | −0.448839 | − | 0.893613i | \(-0.648162\pi\) | ||||
−0.448839 | + | 0.893613i | \(0.648162\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.62027 | 0.591564 | 0.295782 | − | 0.955255i | \(-0.404420\pi\) | ||||
0.295782 | + | 0.955255i | \(0.404420\pi\) | |||||||
\(62\) | 1.26646 | 0.160841 | ||||||||
\(63\) | 1.81749 | 0.228982 | ||||||||
\(64\) | −0.620559 | −0.0775699 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.06329 | 0.130882 | ||||||||
\(67\) | 6.13471 | 0.749474 | 0.374737 | − | 0.927131i | \(-0.377733\pi\) | ||||
0.374737 | + | 0.927131i | \(0.377733\pi\) | |||||||
\(68\) | 13.4054 | 1.62565 | ||||||||
\(69\) | −8.30582 | −0.999904 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.7519 | −1.51337 | −0.756687 | − | 0.653778i | \(-0.773183\pi\) | ||||
−0.756687 | + | 0.653778i | \(0.773183\pi\) | |||||||
\(72\) | 11.0048 | 1.29693 | ||||||||
\(73\) | −0.559355 | −0.0654675 | −0.0327338 | − | 0.999464i | \(-0.510421\pi\) | ||||
−0.0327338 | + | 0.999464i | \(0.510421\pi\) | |||||||
\(74\) | −1.50952 | −0.175478 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.00756 | 0.803823 | ||||||||
\(77\) | −0.225436 | −0.0256908 | ||||||||
\(78\) | −7.96390 | −0.901734 | ||||||||
\(79\) | 4.10565 | 0.461922 | 0.230961 | − | 0.972963i | \(-0.425813\pi\) | ||||
0.230961 | + | 0.972963i | \(0.425813\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.29937 | 0.144374 | ||||||||
\(82\) | 1.61875 | 0.178761 | ||||||||
\(83\) | −15.1584 | −1.66385 | −0.831923 | − | 0.554891i | \(-0.812760\pi\) | ||||
−0.831923 | + | 0.554891i | \(0.812760\pi\) | |||||||
\(84\) | −1.67702 | −0.182978 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.958189 | −0.103324 | ||||||||
\(87\) | −26.0601 | −2.79394 | ||||||||
\(88\) | −1.36501 | −0.145510 | ||||||||
\(89\) | −13.6969 | −1.45187 | −0.725934 | − | 0.687764i | \(-0.758592\pi\) | ||||
−0.725934 | + | 0.687764i | \(0.758592\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.68849 | 0.177002 | ||||||||
\(92\) | 4.80511 | 0.500968 | ||||||||
\(93\) | −5.99142 | −0.621281 | ||||||||
\(94\) | 3.44034 | 0.354844 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −15.7325 | −1.60570 | ||||||||
\(97\) | 13.5129 | 1.37203 | 0.686016 | − | 0.727586i | \(-0.259358\pi\) | ||||
0.686016 | + | 0.727586i | \(0.259358\pi\) | |||||||
\(98\) | 4.11832 | 0.416013 | ||||||||
\(99\) | −3.15388 | −0.316976 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.92525 | 0.589585 | 0.294792 | − | 0.955561i | \(-0.404750\pi\) | ||||
0.294792 | + | 0.955561i | \(0.404750\pi\) | |||||||
\(102\) | 13.8905 | 1.37536 | ||||||||
\(103\) | −6.48880 | −0.639360 | −0.319680 | − | 0.947526i | \(-0.603575\pi\) | ||||
−0.319680 | + | 0.947526i | \(0.603575\pi\) | |||||||
\(104\) | 10.2237 | 1.00252 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.96946 | −0.579805 | ||||||||
\(107\) | −8.70727 | −0.841764 | −0.420882 | − | 0.907115i | \(-0.638279\pi\) | ||||
−0.420882 | + | 0.907115i | \(0.638279\pi\) | |||||||
\(108\) | −9.50334 | −0.914459 | ||||||||
\(109\) | 6.50110 | 0.622693 | 0.311346 | − | 0.950297i | \(-0.399220\pi\) | ||||
0.311346 | + | 0.950297i | \(0.399220\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.14129 | 0.677822 | ||||||||
\(112\) | 0.711151 | 0.0671975 | ||||||||
\(113\) | −6.93590 | −0.652474 | −0.326237 | − | 0.945288i | \(-0.605781\pi\) | ||||
−0.326237 | + | 0.945288i | \(0.605781\pi\) | |||||||
\(114\) | 7.26112 | 0.680066 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.0764 | 1.39981 | ||||||||
\(117\) | 23.6221 | 2.18387 | ||||||||
\(118\) | 4.13337 | 0.380507 | ||||||||
\(119\) | −2.94503 | −0.269971 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6088 | −0.964437 | ||||||||
\(122\) | −2.76965 | −0.250752 | ||||||||
\(123\) | −7.65807 | −0.690505 | ||||||||
\(124\) | 3.46617 | 0.311272 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.08951 | −0.0970608 | ||||||||
\(127\) | 5.45809 | 0.484327 | 0.242164 | − | 0.970235i | \(-0.422143\pi\) | ||||
0.242164 | + | 0.970235i | \(0.422143\pi\) | |||||||
\(128\) | 11.4672 | 1.01356 | ||||||||
\(129\) | 4.53304 | 0.399112 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.5419 | −1.00842 | −0.504210 | − | 0.863581i | \(-0.668216\pi\) | ||||
−0.504210 | + | 0.863581i | \(0.668216\pi\) | |||||||
\(132\) | 2.91012 | 0.253293 | ||||||||
\(133\) | −1.53949 | −0.133490 | ||||||||
\(134\) | −3.67749 | −0.317687 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.8321 | −1.52909 | ||||||||
\(137\) | 14.6748 | 1.25375 | 0.626875 | − | 0.779120i | \(-0.284334\pi\) | ||||
0.626875 | + | 0.779120i | \(0.284334\pi\) | |||||||
\(138\) | 4.97898 | 0.423839 | ||||||||
\(139\) | 12.9136 | 1.09532 | 0.547659 | − | 0.836701i | \(-0.315519\pi\) | ||||
0.547659 | + | 0.836701i | \(0.315519\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.2757 | −1.37066 | ||||||||
\(142\) | 7.64421 | 0.641488 | ||||||||
\(143\) | −2.93002 | −0.245020 | ||||||||
\(144\) | 9.94909 | 0.829091 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.335309 | 0.0277503 | ||||||||
\(147\) | −19.4831 | −1.60694 | ||||||||
\(148\) | −4.13140 | −0.339599 | ||||||||
\(149\) | −7.82834 | −0.641323 | −0.320661 | − | 0.947194i | \(-0.603905\pi\) | ||||
−0.320661 | + | 0.947194i | \(0.603905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.54793 | 0.532863 | 0.266431 | − | 0.963854i | \(-0.414155\pi\) | ||||
0.266431 | + | 0.963854i | \(0.414155\pi\) | |||||||
\(152\) | −9.32153 | −0.756076 | ||||||||
\(153\) | −41.2013 | −3.33093 | ||||||||
\(154\) | 0.135139 | 0.0108898 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −21.7964 | −1.74511 | ||||||||
\(157\) | −10.2687 | −0.819532 | −0.409766 | − | 0.912191i | \(-0.634390\pi\) | ||||
−0.409766 | + | 0.912191i | \(0.634390\pi\) | |||||||
\(158\) | −2.46116 | −0.195799 | ||||||||
\(159\) | 28.2406 | 2.23962 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.05563 | −0.0831954 | ||||||||
\(162\) | −0.778914 | −0.0611972 | ||||||||
\(163\) | 14.8492 | 1.16308 | 0.581540 | − | 0.813518i | \(-0.302450\pi\) | ||||
0.581540 | + | 0.813518i | \(0.302450\pi\) | |||||||
\(164\) | 4.43037 | 0.345954 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.08678 | 0.705271 | ||||||||
\(167\) | 12.9361 | 1.00102 | 0.500511 | − | 0.865730i | \(-0.333145\pi\) | ||||
0.500511 | + | 0.865730i | \(0.333145\pi\) | |||||||
\(168\) | 2.23078 | 0.172109 | ||||||||
\(169\) | 8.94547 | 0.688113 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −21.5376 | −1.64702 | ||||||||
\(172\) | −2.62247 | −0.199961 | ||||||||
\(173\) | 23.4676 | 1.78421 | 0.892103 | − | 0.451833i | \(-0.149230\pi\) | ||||
0.892103 | + | 0.451833i | \(0.149230\pi\) | |||||||
\(174\) | 15.6219 | 1.18429 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.23406 | −0.0930204 | ||||||||
\(177\) | −19.5543 | −1.46979 | ||||||||
\(178\) | 8.21069 | 0.615418 | ||||||||
\(179\) | 13.1703 | 0.984392 | 0.492196 | − | 0.870484i | \(-0.336194\pi\) | ||||
0.492196 | + | 0.870484i | \(0.336194\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.77626 | 0.280687 | 0.140344 | − | 0.990103i | \(-0.455179\pi\) | ||||
0.140344 | + | 0.990103i | \(0.455179\pi\) | |||||||
\(182\) | −1.01217 | −0.0750273 | ||||||||
\(183\) | 13.1028 | 0.968584 | ||||||||
\(184\) | −6.39181 | −0.471210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.59159 | 0.263348 | ||||||||
\(187\) | 5.11049 | 0.373716 | ||||||||
\(188\) | 9.41587 | 0.686723 | ||||||||
\(189\) | 2.08778 | 0.151864 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.804301 | −0.0581972 | −0.0290986 | − | 0.999577i | \(-0.509264\pi\) | ||||
−0.0290986 | + | 0.999577i | \(0.509264\pi\) | |||||||
\(192\) | −1.75986 | −0.127007 | ||||||||
\(193\) | −22.5417 | −1.62259 | −0.811293 | − | 0.584640i | \(-0.801236\pi\) | ||||
−0.811293 | + | 0.584640i | \(0.801236\pi\) | |||||||
\(194\) | −8.10042 | −0.581576 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.2714 | 0.805102 | ||||||||
\(197\) | −5.11900 | −0.364714 | −0.182357 | − | 0.983232i | \(-0.558373\pi\) | ||||
−0.182357 | + | 0.983232i | \(0.558373\pi\) | |||||||
\(198\) | 1.89061 | 0.134360 | ||||||||
\(199\) | 7.35358 | 0.521281 | 0.260641 | − | 0.965436i | \(-0.416066\pi\) | ||||
0.260641 | + | 0.965436i | \(0.416066\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.3976 | 1.22713 | ||||||||
\(202\) | −3.55193 | −0.249913 | ||||||||
\(203\) | −3.31212 | −0.232465 | ||||||||
\(204\) | 38.0169 | 2.66172 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.88975 | 0.271012 | ||||||||
\(207\) | −14.7684 | −1.02648 | ||||||||
\(208\) | 9.24292 | 0.640881 | ||||||||
\(209\) | 2.67146 | 0.184789 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9013 | 1.16353 | 0.581767 | − | 0.813355i | \(-0.302362\pi\) | ||||
0.581767 | + | 0.813355i | \(0.302362\pi\) | |||||||
\(212\) | −16.3378 | −1.12209 | ||||||||
\(213\) | −36.1635 | −2.47789 | ||||||||
\(214\) | 5.21963 | 0.356807 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 12.6414 | 0.860141 | ||||||||
\(217\) | −0.761481 | −0.0516927 | ||||||||
\(218\) | −3.89713 | −0.263947 | ||||||||
\(219\) | −1.58629 | −0.107192 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −38.2769 | −2.57479 | ||||||||
\(222\) | −4.28089 | −0.287315 | ||||||||
\(223\) | −21.6084 | −1.44701 | −0.723503 | − | 0.690321i | \(-0.757469\pi\) | ||||
−0.723503 | + | 0.690321i | \(0.757469\pi\) | |||||||
\(224\) | −1.99953 | −0.133599 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.15777 | 0.276570 | ||||||||
\(227\) | −6.07474 | −0.403195 | −0.201597 | − | 0.979468i | \(-0.564613\pi\) | ||||
−0.201597 | + | 0.979468i | \(0.564613\pi\) | |||||||
\(228\) | 19.8730 | 1.31612 | ||||||||
\(229\) | 14.2052 | 0.938709 | 0.469354 | − | 0.883010i | \(-0.344487\pi\) | ||||
0.469354 | + | 0.883010i | \(0.344487\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.639321 | −0.0420642 | ||||||||
\(232\) | −20.0547 | −1.31666 | ||||||||
\(233\) | 10.4653 | 0.685604 | 0.342802 | − | 0.939408i | \(-0.388624\pi\) | ||||
0.342802 | + | 0.939408i | \(0.388624\pi\) | |||||||
\(234\) | −14.1604 | −0.925696 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.3126 | 0.736389 | ||||||||
\(237\) | 11.6434 | 0.756317 | ||||||||
\(238\) | 1.76542 | 0.114435 | ||||||||
\(239\) | 19.5952 | 1.26751 | 0.633755 | − | 0.773534i | \(-0.281513\pi\) | ||||
0.633755 | + | 0.773534i | \(0.281513\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 6.35951 | 0.408805 | ||||||||
\(243\) | −13.6923 | −0.878363 | ||||||||
\(244\) | −7.58025 | −0.485276 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.59068 | 0.292691 | ||||||||
\(247\) | −20.0089 | −1.27314 | ||||||||
\(248\) | −4.61074 | −0.292782 | ||||||||
\(249\) | −42.9881 | −2.72426 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.43169 | −0.595323 | −0.297661 | − | 0.954672i | \(-0.596207\pi\) | ||||
−0.297661 | + | 0.954672i | \(0.596207\pi\) | |||||||
\(252\) | −2.98187 | −0.187840 | ||||||||
\(253\) | 1.83183 | 0.115166 | ||||||||
\(254\) | −3.27189 | −0.205296 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.63294 | −0.352059 | ||||||||
\(257\) | 18.5042 | 1.15426 | 0.577131 | − | 0.816652i | \(-0.304172\pi\) | ||||
0.577131 | + | 0.816652i | \(0.304172\pi\) | |||||||
\(258\) | −2.71736 | −0.169175 | ||||||||
\(259\) | 0.907625 | 0.0563971 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −46.3369 | −2.86818 | ||||||||
\(262\) | 6.91886 | 0.427449 | ||||||||
\(263\) | −23.9444 | −1.47647 | −0.738237 | − | 0.674541i | \(-0.764341\pi\) | ||||
−0.738237 | + | 0.674541i | \(0.764341\pi\) | |||||||
\(264\) | −3.87106 | −0.238247 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.922855 | 0.0565838 | ||||||||
\(267\) | −38.8435 | −2.37718 | ||||||||
\(268\) | −10.0649 | −0.614813 | ||||||||
\(269\) | −22.0724 | −1.34578 | −0.672890 | − | 0.739743i | \(-0.734947\pi\) | ||||
−0.672890 | + | 0.739743i | \(0.734947\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.04970 | −0.488984 | −0.244492 | − | 0.969651i | \(-0.578621\pi\) | ||||
−0.244492 | + | 0.969651i | \(0.578621\pi\) | |||||||
\(272\) | −16.1214 | −0.977501 | ||||||||
\(273\) | 4.78843 | 0.289809 | ||||||||
\(274\) | −8.79688 | −0.531439 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.6270 | 0.820247 | ||||||||
\(277\) | −16.6952 | −1.00312 | −0.501558 | − | 0.865124i | \(-0.667240\pi\) | ||||
−0.501558 | + | 0.865124i | \(0.667240\pi\) | |||||||
\(278\) | −7.74115 | −0.464283 | ||||||||
\(279\) | −10.6532 | −0.637791 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.81800 | 0.347073 | 0.173536 | − | 0.984827i | \(-0.444481\pi\) | ||||
0.173536 | + | 0.984827i | \(0.444481\pi\) | |||||||
\(282\) | 9.75657 | 0.580995 | ||||||||
\(283\) | −12.2054 | −0.725536 | −0.362768 | − | 0.931880i | \(-0.618168\pi\) | ||||
−0.362768 | + | 0.931880i | \(0.618168\pi\) | |||||||
\(284\) | 20.9214 | 1.24146 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.75642 | 0.103859 | ||||||||
\(287\) | −0.973304 | −0.0574523 | ||||||||
\(288\) | −27.9737 | −1.64837 | ||||||||
\(289\) | 49.7620 | 2.92718 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 38.3218 | 2.24646 | ||||||||
\(292\) | 0.917706 | 0.0537047 | ||||||||
\(293\) | −0.0653701 | −0.00381896 | −0.00190948 | − | 0.999998i | \(-0.500608\pi\) | ||||
−0.00190948 | + | 0.999998i | \(0.500608\pi\) | |||||||
\(294\) | 11.6793 | 0.681149 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.49563 | 0.319427 | ||||||||
\(297\) | −3.62291 | −0.210223 | ||||||||
\(298\) | 4.69275 | 0.271844 | ||||||||
\(299\) | −13.7202 | −0.793458 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.576128 | 0.0332075 | ||||||||
\(302\) | −3.92520 | −0.225870 | ||||||||
\(303\) | 16.8036 | 0.965342 | ||||||||
\(304\) | −8.42728 | −0.483338 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 24.6984 | 1.41191 | ||||||||
\(307\) | −8.55277 | −0.488133 | −0.244066 | − | 0.969759i | \(-0.578481\pi\) | ||||
−0.244066 | + | 0.969759i | \(0.578481\pi\) | |||||||
\(308\) | 0.369862 | 0.0210748 | ||||||||
\(309\) | −18.4018 | −1.04684 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.65202 | 0.490611 | 0.245306 | − | 0.969446i | \(-0.421112\pi\) | ||||
0.245306 | + | 0.969446i | \(0.421112\pi\) | |||||||
\(312\) | 28.9938 | 1.64145 | ||||||||
\(313\) | −1.44232 | −0.0815247 | −0.0407623 | − | 0.999169i | \(-0.512979\pi\) | ||||
−0.0407623 | + | 0.999169i | \(0.512979\pi\) | |||||||
\(314\) | 6.15564 | 0.347383 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.73595 | −0.378927 | ||||||||
\(317\) | −9.49802 | −0.533462 | −0.266731 | − | 0.963771i | \(-0.585943\pi\) | ||||
−0.266731 | + | 0.963771i | \(0.585943\pi\) | |||||||
\(318\) | −16.9290 | −0.949330 | ||||||||
\(319\) | 5.74749 | 0.321798 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.6932 | −1.37824 | ||||||||
\(322\) | 0.632805 | 0.0352648 | ||||||||
\(323\) | 34.8992 | 1.94184 | ||||||||
\(324\) | −2.13181 | −0.118434 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.90145 | −0.493006 | ||||||||
\(327\) | 18.4367 | 1.01955 | ||||||||
\(328\) | −5.89332 | −0.325404 | ||||||||
\(329\) | −2.06857 | −0.114044 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0047 | −0.879696 | −0.439848 | − | 0.898072i | \(-0.644968\pi\) | ||||
−0.439848 | + | 0.898072i | \(0.644968\pi\) | |||||||
\(332\) | 24.8696 | 1.36490 | ||||||||
\(333\) | 12.6978 | 0.695834 | ||||||||
\(334\) | −7.75460 | −0.424313 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.01678 | 0.110024 | ||||||||
\(337\) | −3.38373 | −0.184323 | −0.0921616 | − | 0.995744i | \(-0.529378\pi\) | ||||
−0.0921616 | + | 0.995744i | \(0.529378\pi\) | |||||||
\(338\) | −5.36242 | −0.291677 | ||||||||
\(339\) | −19.6697 | −1.06831 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.32139 | 0.0715574 | ||||||||
\(342\) | 12.9108 | 0.698139 | ||||||||
\(343\) | −4.99925 | −0.269934 | ||||||||
\(344\) | 3.48843 | 0.188084 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.0678 | −0.756288 | ||||||||
\(347\) | −34.0410 | −1.82742 | −0.913709 | − | 0.406369i | \(-0.866795\pi\) | ||||
−0.913709 | + | 0.406369i | \(0.866795\pi\) | |||||||
\(348\) | 42.7556 | 2.29194 | ||||||||
\(349\) | 5.88943 | 0.315254 | 0.157627 | − | 0.987499i | \(-0.449616\pi\) | ||||
0.157627 | + | 0.987499i | \(0.449616\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.1351 | 1.44837 | ||||||||
\(352\) | 3.46977 | 0.184940 | ||||||||
\(353\) | −33.8088 | −1.79946 | −0.899731 | − | 0.436444i | \(-0.856238\pi\) | ||||
−0.899731 | + | 0.436444i | \(0.856238\pi\) | |||||||
\(354\) | 11.7219 | 0.623015 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 22.4719 | 1.19101 | ||||||||
\(357\) | −8.35191 | −0.442030 | ||||||||
\(358\) | −7.89500 | −0.417264 | ||||||||
\(359\) | 12.9670 | 0.684371 | 0.342186 | − | 0.939632i | \(-0.388833\pi\) | ||||
0.342186 | + | 0.939632i | \(0.388833\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.756797 | −0.0398314 | ||||||||
\(362\) | −2.26370 | −0.118978 | ||||||||
\(363\) | −30.0858 | −1.57910 | ||||||||
\(364\) | −2.77022 | −0.145199 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.85453 | −0.410563 | ||||||||
\(367\) | 9.73813 | 0.508326 | 0.254163 | − | 0.967161i | \(-0.418200\pi\) | ||||
0.254163 | + | 0.967161i | \(0.418200\pi\) | |||||||
\(368\) | −5.77862 | −0.301231 | ||||||||
\(369\) | −13.6166 | −0.708854 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.58924 | 0.186344 | ||||||||
\(372\) | 9.82983 | 0.509653 | ||||||||
\(373\) | 10.8997 | 0.564367 | 0.282184 | − | 0.959360i | \(-0.408941\pi\) | ||||
0.282184 | + | 0.959360i | \(0.408941\pi\) | |||||||
\(374\) | −3.06352 | −0.158411 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.5251 | −0.645932 | ||||||||
\(377\) | −43.0480 | −2.21708 | ||||||||
\(378\) | −1.25153 | −0.0643719 | ||||||||
\(379\) | −32.8409 | −1.68692 | −0.843462 | − | 0.537189i | \(-0.819486\pi\) | ||||
−0.843462 | + | 0.537189i | \(0.819486\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.4788 | 0.793002 | ||||||||
\(382\) | 0.482143 | 0.0246686 | ||||||||
\(383\) | −15.9330 | −0.814138 | −0.407069 | − | 0.913397i | \(-0.633449\pi\) | ||||
−0.407069 | + | 0.913397i | \(0.633449\pi\) | |||||||
\(384\) | 32.5201 | 1.65953 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.5127 | 0.687781 | ||||||||
\(387\) | 8.06010 | 0.409718 | ||||||||
\(388\) | −22.1700 | −1.12551 | ||||||||
\(389\) | −35.3117 | −1.79037 | −0.895186 | − | 0.445692i | \(-0.852958\pi\) | ||||
−0.895186 | + | 0.445692i | \(0.852958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.9305 | 1.21022 | ||||||||
\(392\) | −14.9934 | −0.757279 | ||||||||
\(393\) | −32.7320 | −1.65111 | ||||||||
\(394\) | 3.06862 | 0.154595 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.17441 | 0.260024 | ||||||||
\(397\) | 22.1785 | 1.11310 | 0.556552 | − | 0.830812i | \(-0.312124\pi\) | ||||
0.556552 | + | 0.830812i | \(0.312124\pi\) | |||||||
\(398\) | −4.40815 | −0.220961 | ||||||||
\(399\) | −4.36588 | −0.218567 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.6544 | 1.43093 | 0.715466 | − | 0.698647i | \(-0.246214\pi\) | ||||
0.715466 | + | 0.698647i | \(0.246214\pi\) | |||||||
\(402\) | −10.4291 | −0.520157 | ||||||||
\(403\) | −9.89706 | −0.493008 | ||||||||
\(404\) | −9.72128 | −0.483652 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.98547 | 0.0985372 | ||||||||
\(407\) | −1.57499 | −0.0780696 | ||||||||
\(408\) | −50.5705 | −2.50361 | ||||||||
\(409\) | 19.8415 | 0.981098 | 0.490549 | − | 0.871414i | \(-0.336796\pi\) | ||||
0.490549 | + | 0.871414i | \(0.336796\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 41.6167 | 2.05280 | ||||||||
\(412\) | 10.6459 | 0.524484 | ||||||||
\(413\) | −2.48526 | −0.122292 | ||||||||
\(414\) | 8.85301 | 0.435102 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −25.9882 | −1.27418 | ||||||||
\(417\) | 36.6221 | 1.79339 | ||||||||
\(418\) | −1.60142 | −0.0783281 | ||||||||
\(419\) | −34.1544 | −1.66855 | −0.834277 | − | 0.551346i | \(-0.814115\pi\) | ||||
−0.834277 | + | 0.551346i | \(0.814115\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.6854 | −1.05688 | −0.528440 | − | 0.848971i | \(-0.677223\pi\) | ||||
−0.528440 | + | 0.848971i | \(0.677223\pi\) | |||||||
\(422\) | −10.1316 | −0.493198 | ||||||||
\(423\) | −28.9395 | −1.40709 | ||||||||
\(424\) | 21.7327 | 1.05543 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 21.6785 | 1.05032 | ||||||||
\(427\) | 1.66530 | 0.0805895 | ||||||||
\(428\) | 14.2856 | 0.690521 | ||||||||
\(429\) | −8.30933 | −0.401178 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.0237 | 1.63886 | 0.819431 | − | 0.573177i | \(-0.194289\pi\) | ||||
0.819431 | + | 0.573177i | \(0.194289\pi\) | |||||||
\(432\) | 11.4287 | 0.549863 | ||||||||
\(433\) | −18.2413 | −0.876620 | −0.438310 | − | 0.898824i | \(-0.644423\pi\) | ||||
−0.438310 | + | 0.898824i | \(0.644423\pi\) | |||||||
\(434\) | 0.456475 | 0.0219115 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.6660 | −0.510811 | ||||||||
\(437\) | 12.5094 | 0.598407 | ||||||||
\(438\) | 0.950912 | 0.0454363 | ||||||||
\(439\) | −33.1350 | −1.58145 | −0.790723 | − | 0.612174i | \(-0.790295\pi\) | ||||
−0.790723 | + | 0.612174i | \(0.790295\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −34.6425 | −1.64964 | ||||||||
\(442\) | 22.9453 | 1.09140 | ||||||||
\(443\) | 17.0218 | 0.808731 | 0.404366 | − | 0.914597i | \(-0.367492\pi\) | ||||
0.404366 | + | 0.914597i | \(0.367492\pi\) | |||||||
\(444\) | −11.7164 | −0.556035 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.9533 | 0.613357 | ||||||||
\(447\) | −22.2006 | −1.05005 | ||||||||
\(448\) | −0.223670 | −0.0105674 | ||||||||
\(449\) | 11.7660 | 0.555273 | 0.277636 | − | 0.960686i | \(-0.410449\pi\) | ||||
0.277636 | + | 0.960686i | \(0.410449\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.68897 | 0.0795304 | ||||||||
\(452\) | 11.3794 | 0.535242 | ||||||||
\(453\) | 18.5695 | 0.872470 | ||||||||
\(454\) | 3.64154 | 0.170906 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −26.4352 | −1.23794 | ||||||||
\(457\) | −38.1291 | −1.78360 | −0.891801 | − | 0.452428i | \(-0.850558\pi\) | ||||
−0.891801 | + | 0.452428i | \(0.850558\pi\) | |||||||
\(458\) | −8.51542 | −0.397899 | ||||||||
\(459\) | −47.3287 | −2.20911 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.15125 | 0.193343 | 0.0966715 | − | 0.995316i | \(-0.469180\pi\) | ||||
0.0966715 | + | 0.995316i | \(0.469180\pi\) | |||||||
\(462\) | 0.383245 | 0.0178302 | ||||||||
\(463\) | −32.8714 | −1.52766 | −0.763831 | − | 0.645416i | \(-0.776684\pi\) | ||||
−0.763831 | + | 0.645416i | \(0.776684\pi\) | |||||||
\(464\) | −18.1308 | −0.841702 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.27348 | −0.290614 | ||||||||
\(467\) | −27.9382 | −1.29283 | −0.646413 | − | 0.762988i | \(-0.723732\pi\) | ||||
−0.646413 | + | 0.762988i | \(0.723732\pi\) | |||||||
\(468\) | −38.7557 | −1.79148 | ||||||||
\(469\) | 2.21116 | 0.102102 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −29.1214 | −1.34184 | ||||||||
\(472\) | −15.0482 | −0.692647 | ||||||||
\(473\) | −0.999750 | −0.0459686 | ||||||||
\(474\) | −6.97968 | −0.320587 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.83177 | 0.221464 | ||||||||
\(477\) | 50.2139 | 2.29914 | ||||||||
\(478\) | −11.7465 | −0.537272 | ||||||||
\(479\) | 12.5295 | 0.572487 | 0.286244 | − | 0.958157i | \(-0.407593\pi\) | ||||
0.286244 | + | 0.958157i | \(0.407593\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.7965 | 0.537875 | ||||||||
\(482\) | 0.599456 | 0.0273045 | ||||||||
\(483\) | −2.99370 | −0.136218 | ||||||||
\(484\) | 17.4054 | 0.791153 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.20795 | 0.372320 | ||||||||
\(487\) | −20.2102 | −0.915812 | −0.457906 | − | 0.889001i | \(-0.651400\pi\) | ||||
−0.457906 | + | 0.889001i | \(0.651400\pi\) | |||||||
\(488\) | 10.0833 | 0.456451 | ||||||||
\(489\) | 42.1113 | 1.90434 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.0790 | 1.76361 | 0.881805 | − | 0.471614i | \(-0.156329\pi\) | ||||
0.881805 | + | 0.471614i | \(0.156329\pi\) | |||||||
\(492\) | 12.5642 | 0.566439 | ||||||||
\(493\) | 75.0836 | 3.38160 | ||||||||
\(494\) | 11.9945 | 0.539656 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.16841 | −0.187167 | ||||||||
\(497\) | −4.59622 | −0.206168 | ||||||||
\(498\) | 25.7695 | 1.15476 | ||||||||
\(499\) | −23.2259 | −1.03973 | −0.519867 | − | 0.854247i | \(-0.674018\pi\) | ||||
−0.519867 | + | 0.854247i | \(0.674018\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 36.6858 | 1.63900 | ||||||||
\(502\) | 5.65388 | 0.252345 | ||||||||
\(503\) | 20.7067 | 0.923267 | 0.461633 | − | 0.887071i | \(-0.347264\pi\) | ||||
0.461633 | + | 0.887071i | \(0.347264\pi\) | |||||||
\(504\) | 3.96651 | 0.176682 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.09810 | −0.0488165 | ||||||||
\(507\) | 25.3687 | 1.12667 | ||||||||
\(508\) | −8.95483 | −0.397306 | ||||||||
\(509\) | 13.4785 | 0.597425 | 0.298712 | − | 0.954343i | \(-0.403443\pi\) | ||||
0.298712 | + | 0.954343i | \(0.403443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.201610 | −0.00891871 | ||||||||
\(512\) | −19.5576 | −0.864332 | ||||||||
\(513\) | −24.7406 | −1.09232 | ||||||||
\(514\) | −11.0925 | −0.489268 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.43714 | −0.327402 | ||||||||
\(517\) | 3.58957 | 0.157869 | ||||||||
\(518\) | −0.544081 | −0.0239056 | ||||||||
\(519\) | 66.5524 | 2.92133 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.39561 | −0.104953 | −0.0524767 | − | 0.998622i | \(-0.516712\pi\) | ||||
−0.0524767 | + | 0.998622i | \(0.516712\pi\) | |||||||
\(522\) | 27.7770 | 1.21576 | ||||||||
\(523\) | −17.2203 | −0.752991 | −0.376496 | − | 0.926418i | \(-0.622871\pi\) | ||||
−0.376496 | + | 0.926418i | \(0.622871\pi\) | |||||||
\(524\) | 18.9362 | 0.827233 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.3536 | 0.625847 | ||||||||
\(527\) | 17.2623 | 0.751957 | ||||||||
\(528\) | −3.49970 | −0.152305 | ||||||||
\(529\) | −14.4222 | −0.627054 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −34.7691 | −1.50885 | ||||||||
\(532\) | 2.52576 | 0.109506 | ||||||||
\(533\) | −12.6502 | −0.547939 | ||||||||
\(534\) | 23.2850 | 1.00764 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13.3885 | 0.578294 | ||||||||
\(537\) | 37.3500 | 1.61177 | ||||||||
\(538\) | 13.2315 | 0.570448 | ||||||||
\(539\) | 4.29695 | 0.185083 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.63512 | 0.414246 | 0.207123 | − | 0.978315i | \(-0.433590\pi\) | ||||
0.207123 | + | 0.978315i | \(0.433590\pi\) | |||||||
\(542\) | 4.82544 | 0.207270 | ||||||||
\(543\) | 10.7092 | 0.459577 | ||||||||
\(544\) | 45.3282 | 1.94343 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.87046 | −0.122844 | ||||||||
\(547\) | −10.4736 | −0.447818 | −0.223909 | − | 0.974610i | \(-0.571882\pi\) | ||||
−0.223909 | + | 0.974610i | \(0.571882\pi\) | |||||||
\(548\) | −24.0762 | −1.02848 | ||||||||
\(549\) | 23.2977 | 0.994323 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 39.2492 | 1.67207 | ||||||||
\(552\) | −18.1267 | −0.771525 | ||||||||
\(553\) | 1.47982 | 0.0629281 | ||||||||
\(554\) | 10.0080 | 0.425200 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.1867 | −0.898518 | ||||||||
\(557\) | −12.5042 | −0.529821 | −0.264910 | − | 0.964273i | \(-0.585342\pi\) | ||||
−0.264910 | + | 0.964273i | \(0.585342\pi\) | |||||||
\(558\) | 6.38613 | 0.270347 | ||||||||
\(559\) | 7.48800 | 0.316709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.4930 | 0.611895 | ||||||||
\(562\) | −3.48764 | −0.147117 | ||||||||
\(563\) | 24.8151 | 1.04583 | 0.522915 | − | 0.852385i | \(-0.324844\pi\) | ||||
0.522915 | + | 0.852385i | \(0.324844\pi\) | |||||||
\(564\) | 26.7028 | 1.12439 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.31660 | 0.307540 | ||||||||
\(567\) | 0.468336 | 0.0196682 | ||||||||
\(568\) | −27.8299 | −1.16772 | ||||||||
\(569\) | 46.6025 | 1.95368 | 0.976838 | − | 0.213979i | \(-0.0686423\pi\) | ||||
0.976838 | + | 0.213979i | \(0.0686423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.5906 | −0.694295 | −0.347147 | − | 0.937811i | \(-0.612850\pi\) | ||||
−0.347147 | + | 0.937811i | \(0.612850\pi\) | |||||||
\(572\) | 4.80714 | 0.200997 | ||||||||
\(573\) | −2.28094 | −0.0952878 | ||||||||
\(574\) | 0.583453 | 0.0243529 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.12917 | −0.130382 | ||||||||
\(577\) | 38.4798 | 1.60194 | 0.800968 | − | 0.598707i | \(-0.204319\pi\) | ||||
0.800968 | + | 0.598707i | \(0.204319\pi\) | |||||||
\(578\) | −29.8301 | −1.24077 | ||||||||
\(579\) | −63.9266 | −2.65670 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.46358 | −0.226668 | ||||||||
\(582\) | −22.9722 | −0.952230 | ||||||||
\(583\) | −6.22838 | −0.257953 | ||||||||
\(584\) | −1.22074 | −0.0505147 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.0391865 | 0.00161878 | ||||||||
\(587\) | 35.9523 | 1.48391 | 0.741956 | − | 0.670449i | \(-0.233898\pi\) | ||||
0.741956 | + | 0.670449i | \(0.233898\pi\) | |||||||
\(588\) | 31.9650 | 1.31821 | ||||||||
\(589\) | 9.02370 | 0.371815 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.5171 | −0.597155 | ||||||||
\(592\) | 4.96842 | 0.204201 | ||||||||
\(593\) | 42.5918 | 1.74903 | 0.874517 | − | 0.484994i | \(-0.161178\pi\) | ||||
0.874517 | + | 0.484994i | \(0.161178\pi\) | |||||||
\(594\) | 2.17178 | 0.0891090 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.8436 | 0.526094 | ||||||||
\(597\) | 20.8542 | 0.853508 | ||||||||
\(598\) | 8.22464 | 0.336330 | ||||||||
\(599\) | −21.1344 | −0.863529 | −0.431765 | − | 0.901986i | \(-0.642109\pi\) | ||||
−0.431765 | + | 0.901986i | \(0.642109\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.3494 | 0.422161 | 0.211081 | − | 0.977469i | \(-0.432302\pi\) | ||||
0.211081 | + | 0.977469i | \(0.432302\pi\) | |||||||
\(602\) | −0.345363 | −0.0140760 | ||||||||
\(603\) | 30.9343 | 1.25974 | ||||||||
\(604\) | −10.7429 | −0.437121 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.0730 | −0.409189 | ||||||||
\(607\) | 8.32484 | 0.337895 | 0.168948 | − | 0.985625i | \(-0.445963\pi\) | ||||
0.168948 | + | 0.985625i | \(0.445963\pi\) | |||||||
\(608\) | 23.6948 | 0.960953 | ||||||||
\(609\) | −9.39294 | −0.380621 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.8854 | −1.08767 | ||||||||
\(612\) | 67.5971 | 2.73245 | ||||||||
\(613\) | 19.5004 | 0.787613 | 0.393806 | − | 0.919193i | \(-0.371158\pi\) | ||||
0.393806 | + | 0.919193i | \(0.371158\pi\) | |||||||
\(614\) | 5.12701 | 0.206909 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.491994 | −0.0198230 | ||||||||
\(617\) | 17.9240 | 0.721591 | 0.360796 | − | 0.932645i | \(-0.382505\pi\) | ||||
0.360796 | + | 0.932645i | \(0.382505\pi\) | |||||||
\(618\) | 11.0311 | 0.443734 | ||||||||
\(619\) | −34.3316 | −1.37991 | −0.689953 | − | 0.723855i | \(-0.742369\pi\) | ||||
−0.689953 | + | 0.723855i | \(0.742369\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.9647 | −0.680771 | ||||||||
\(622\) | −5.18651 | −0.207960 | ||||||||
\(623\) | −4.93682 | −0.197790 | ||||||||
\(624\) | 26.2123 | 1.04933 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.864607 | 0.0345566 | ||||||||
\(627\) | 7.57607 | 0.302559 | ||||||||
\(628\) | 16.8474 | 0.672284 | ||||||||
\(629\) | −20.5753 | −0.820390 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.90161 | −0.0757020 | −0.0378510 | − | 0.999283i | \(-0.512051\pi\) | ||||
−0.0378510 | + | 0.999283i | \(0.512051\pi\) | |||||||
\(632\) | 8.96023 | 0.356419 | ||||||||
\(633\) | 47.9310 | 1.90508 | ||||||||
\(634\) | 5.69364 | 0.226123 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −46.3329 | −1.83722 | ||||||||
\(637\) | −32.1836 | −1.27516 | ||||||||
\(638\) | −3.44537 | −0.136403 | ||||||||
\(639\) | −64.3016 | −2.54373 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.3867 | −0.568240 | −0.284120 | − | 0.958789i | \(-0.591701\pi\) | ||||
−0.284120 | + | 0.958789i | \(0.591701\pi\) | |||||||
\(642\) | 14.8025 | 0.584209 | ||||||||
\(643\) | 6.97932 | 0.275238 | 0.137619 | − | 0.990485i | \(-0.456055\pi\) | ||||
0.137619 | + | 0.990485i | \(0.456055\pi\) | |||||||
\(644\) | 1.73192 | 0.0682473 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.9205 | −0.823107 | ||||||||
\(647\) | 14.3296 | 0.563356 | 0.281678 | − | 0.959509i | \(-0.409109\pi\) | ||||
0.281678 | + | 0.959509i | \(0.409109\pi\) | |||||||
\(648\) | 2.83575 | 0.111399 | ||||||||
\(649\) | 4.31265 | 0.169286 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.15951 | −0.0846378 | ||||||||
\(652\) | −24.3624 | −0.954105 | ||||||||
\(653\) | 2.72501 | 0.106638 | 0.0533188 | − | 0.998578i | \(-0.483020\pi\) | ||||
0.0533188 | + | 0.998578i | \(0.483020\pi\) | |||||||
\(654\) | −11.0520 | −0.432167 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.32795 | −0.208022 | ||||||||
\(657\) | −2.82055 | −0.110040 | ||||||||
\(658\) | 1.24001 | 0.0483408 | ||||||||
\(659\) | 35.4962 | 1.38274 | 0.691368 | − | 0.722502i | \(-0.257008\pi\) | ||||
0.691368 | + | 0.722502i | \(0.257008\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.0204 | 0.739810 | 0.369905 | − | 0.929070i | \(-0.379390\pi\) | ||||
0.369905 | + | 0.929070i | \(0.379390\pi\) | |||||||
\(662\) | 9.59410 | 0.372885 | ||||||||
\(663\) | −108.551 | −4.21576 | ||||||||
\(664\) | −33.0818 | −1.28382 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.61176 | −0.294950 | ||||||||
\(667\) | 26.9133 | 1.04209 | ||||||||
\(668\) | −21.2236 | −0.821165 | ||||||||
\(669\) | −61.2800 | −2.36922 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.88978 | −0.111559 | ||||||||
\(672\) | −5.67054 | −0.218746 | ||||||||
\(673\) | −6.00845 | −0.231609 | −0.115804 | − | 0.993272i | \(-0.536945\pi\) | ||||
−0.115804 | + | 0.993272i | \(0.536945\pi\) | |||||||
\(674\) | 2.02840 | 0.0781309 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.6764 | −0.564477 | ||||||||
\(677\) | −3.66159 | −0.140726 | −0.0703632 | − | 0.997521i | \(-0.522416\pi\) | ||||
−0.0703632 | + | 0.997521i | \(0.522416\pi\) | |||||||
\(678\) | 11.7911 | 0.452836 | ||||||||
\(679\) | 4.87052 | 0.186913 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.2276 | −0.660161 | ||||||||
\(682\) | −0.792117 | −0.0303317 | ||||||||
\(683\) | 0.903303 | 0.0345639 | 0.0172820 | − | 0.999851i | \(-0.494499\pi\) | ||||
0.0172820 | + | 0.999851i | \(0.494499\pi\) | |||||||
\(684\) | 35.3357 | 1.35109 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.99683 | 0.114419 | ||||||||
\(687\) | 40.2851 | 1.53697 | ||||||||
\(688\) | 3.15377 | 0.120236 | ||||||||
\(689\) | 46.6498 | 1.77722 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.44227 | 0.283117 | 0.141559 | − | 0.989930i | \(-0.454789\pi\) | ||||
0.141559 | + | 0.989930i | \(0.454789\pi\) | |||||||
\(692\) | −38.5021 | −1.46363 | ||||||||
\(693\) | −1.13676 | −0.0431820 | ||||||||
\(694\) | 20.4061 | 0.774605 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −56.8739 | −2.15580 | ||||||||
\(697\) | 22.0642 | 0.835741 | ||||||||
\(698\) | −3.53046 | −0.133630 | ||||||||
\(699\) | 29.6789 | 1.12256 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.7088 | 0.631082 | 0.315541 | − | 0.948912i | \(-0.397814\pi\) | ||||
0.315541 | + | 0.948912i | \(0.397814\pi\) | |||||||
\(702\) | −16.2663 | −0.613933 | ||||||||
\(703\) | −10.7555 | −0.405652 | ||||||||
\(704\) | 0.388133 | 0.0146283 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.2669 | 0.762755 | ||||||||
\(707\) | 2.13566 | 0.0803197 | ||||||||
\(708\) | 32.0818 | 1.20571 | ||||||||
\(709\) | −6.73868 | −0.253076 | −0.126538 | − | 0.991962i | \(-0.540387\pi\) | ||||
−0.126538 | + | 0.991962i | \(0.540387\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.7028 | 0.776415 | ||||||||
\(712\) | −29.8923 | −1.12026 | ||||||||
\(713\) | 6.18758 | 0.231727 | ||||||||
\(714\) | 5.00660 | 0.187367 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.6078 | −0.807523 | ||||||||
\(717\) | 55.5708 | 2.07533 | ||||||||
\(718\) | −7.77314 | −0.290091 | ||||||||
\(719\) | −20.5983 | −0.768188 | −0.384094 | − | 0.923294i | \(-0.625486\pi\) | ||||
−0.384094 | + | 0.923294i | \(0.625486\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.33878 | −0.0871007 | ||||||||
\(722\) | 0.453667 | 0.0168837 | ||||||||
\(723\) | −2.83593 | −0.105469 | ||||||||
\(724\) | −6.19554 | −0.230255 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 18.0351 | 0.669347 | ||||||||
\(727\) | −6.45223 | −0.239300 | −0.119650 | − | 0.992816i | \(-0.538177\pi\) | ||||
−0.119650 | + | 0.992816i | \(0.538177\pi\) | |||||||
\(728\) | 3.68497 | 0.136574 | ||||||||
\(729\) | −42.7286 | −1.58254 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.0605 | −0.483058 | ||||||||
\(732\) | −21.4971 | −0.794555 | ||||||||
\(733\) | −41.0167 | −1.51499 | −0.757494 | − | 0.652842i | \(-0.773576\pi\) | ||||
−0.757494 | + | 0.652842i | \(0.773576\pi\) | |||||||
\(734\) | −5.83758 | −0.215469 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.2476 | 0.598896 | ||||||||
\(737\) | −3.83700 | −0.141338 | ||||||||
\(738\) | 8.16258 | 0.300469 | ||||||||
\(739\) | 52.6069 | 1.93518 | 0.967589 | − | 0.252531i | \(-0.0812631\pi\) | ||||
0.967589 | + | 0.252531i | \(0.0812631\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −56.7438 | −2.08454 | ||||||||
\(742\) | −2.15159 | −0.0789875 | ||||||||
\(743\) | 36.7709 | 1.34899 | 0.674497 | − | 0.738278i | \(-0.264361\pi\) | ||||
0.674497 | + | 0.738278i | \(0.264361\pi\) | |||||||
\(744\) | −13.0757 | −0.479380 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.53392 | −0.239224 | ||||||||
\(747\) | −76.4362 | −2.79665 | ||||||||
\(748\) | −8.38454 | −0.306569 | ||||||||
\(749\) | −3.13839 | −0.114674 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.6384 | 1.55590 | 0.777949 | − | 0.628327i | \(-0.216260\pi\) | ||||
0.777949 | + | 0.628327i | \(0.216260\pi\) | |||||||
\(752\) | −11.3235 | −0.412926 | ||||||||
\(753\) | −26.7476 | −0.974737 | ||||||||
\(754\) | 25.8054 | 0.939777 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.42532 | −0.124578 | ||||||||
\(757\) | 38.5991 | 1.40291 | 0.701453 | − | 0.712715i | \(-0.252535\pi\) | ||||
0.701453 | + | 0.712715i | \(0.252535\pi\) | |||||||
\(758\) | 19.6867 | 0.715052 | ||||||||
\(759\) | 5.19494 | 0.188564 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.8171 | 0.500868 | 0.250434 | − | 0.968134i | \(-0.419427\pi\) | ||||
0.250434 | + | 0.968134i | \(0.419427\pi\) | |||||||
\(762\) | −9.27885 | −0.336137 | ||||||||
\(763\) | 2.34322 | 0.0848301 | ||||||||
\(764\) | 1.31958 | 0.0477407 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.55113 | 0.345096 | ||||||||
\(767\) | −32.3012 | −1.16633 | ||||||||
\(768\) | −15.9746 | −0.576435 | ||||||||
\(769\) | −30.8304 | −1.11177 | −0.555886 | − | 0.831259i | \(-0.687621\pi\) | ||||
−0.555886 | + | 0.831259i | \(0.687621\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 52.4767 | 1.88990 | ||||||||
\(772\) | 36.9830 | 1.33105 | ||||||||
\(773\) | −2.27083 | −0.0816762 | −0.0408381 | − | 0.999166i | \(-0.513003\pi\) | ||||
−0.0408381 | + | 0.999166i | \(0.513003\pi\) | |||||||
\(774\) | −4.83168 | −0.173671 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 29.4908 | 1.05866 | ||||||||
\(777\) | 2.57396 | 0.0923404 | ||||||||
\(778\) | 21.1678 | 0.758902 | ||||||||
\(779\) | 11.5338 | 0.413243 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.97578 | 0.285396 | ||||||||
\(782\) | −14.3453 | −0.512986 | ||||||||
\(783\) | −53.2280 | −1.90221 | ||||||||
\(784\) | −13.5550 | −0.484107 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 19.6214 | 0.699873 | ||||||||
\(787\) | −5.81025 | −0.207113 | −0.103557 | − | 0.994624i | \(-0.533022\pi\) | ||||
−0.103557 | + | 0.994624i | \(0.533022\pi\) | |||||||
\(788\) | 8.39850 | 0.299184 | ||||||||
\(789\) | −67.9046 | −2.41747 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.49993 | −0.0888873 | ||||||||
\(792\) | −6.88305 | −0.244579 | ||||||||
\(793\) | 21.6441 | 0.768604 | ||||||||
\(794\) | −13.2950 | −0.471822 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.0647 | −0.427621 | ||||||||
\(797\) | 17.8987 | 0.634003 | 0.317002 | − | 0.948425i | \(-0.397324\pi\) | ||||
0.317002 | + | 0.948425i | \(0.397324\pi\) | |||||||
\(798\) | 2.61715 | 0.0926462 | ||||||||
\(799\) | 46.8931 | 1.65896 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −69.0668 | −2.44035 | ||||||||
\(802\) | −17.1771 | −0.606543 | ||||||||
\(803\) | 0.349853 | 0.0123460 | ||||||||
\(804\) | −28.5435 | −1.00665 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.93286 | 0.208976 | ||||||||
\(807\) | −62.5959 | −2.20348 | ||||||||
\(808\) | 12.9313 | 0.454923 | ||||||||
\(809\) | −30.9388 | −1.08775 | −0.543876 | − | 0.839166i | \(-0.683044\pi\) | ||||
−0.543876 | + | 0.839166i | \(0.683044\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.9632 | 0.525429 | 0.262714 | − | 0.964874i | \(-0.415382\pi\) | ||||
0.262714 | + | 0.964874i | \(0.415382\pi\) | |||||||
\(812\) | 5.43403 | 0.190697 | ||||||||
\(813\) | −22.8284 | −0.800627 | ||||||||
\(814\) | 0.944140 | 0.0330921 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −45.7191 | −1.60049 | ||||||||
\(817\) | −6.82722 | −0.238854 | ||||||||
\(818\) | −11.8941 | −0.415867 | ||||||||
\(819\) | 8.51421 | 0.297511 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.0601 | 1.04911 | 0.524553 | − | 0.851378i | \(-0.324232\pi\) | ||||
0.524553 | + | 0.851378i | \(0.324232\pi\) | |||||||
\(822\) | −24.9474 | −0.870139 | ||||||||
\(823\) | −29.1394 | −1.01573 | −0.507867 | − | 0.861435i | \(-0.669566\pi\) | ||||
−0.507867 | + | 0.861435i | \(0.669566\pi\) | |||||||
\(824\) | −14.1612 | −0.493330 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.48980 | 0.0518369 | ||||||||
\(827\) | −29.5419 | −1.02727 | −0.513637 | − | 0.858008i | \(-0.671702\pi\) | ||||
−0.513637 | + | 0.858008i | \(0.671702\pi\) | |||||||
\(828\) | 24.2298 | 0.842044 | ||||||||
\(829\) | −51.4599 | −1.78728 | −0.893638 | − | 0.448789i | \(-0.851855\pi\) | ||||
−0.893638 | + | 0.448789i | \(0.851855\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −47.3464 | −1.64243 | ||||||||
\(832\) | −2.90707 | −0.100785 | ||||||||
\(833\) | 56.1341 | 1.94493 | ||||||||
\(834\) | −21.9534 | −0.760183 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.38293 | −0.151587 | ||||||||
\(837\) | −12.2375 | −0.422991 | ||||||||
\(838\) | 20.4741 | 0.707266 | ||||||||
\(839\) | 10.3376 | 0.356893 | 0.178446 | − | 0.983950i | \(-0.442893\pi\) | ||||
0.178446 | + | 0.983950i | \(0.442893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55.4425 | 1.91181 | ||||||||
\(842\) | 12.9994 | 0.447990 | ||||||||
\(843\) | 16.4994 | 0.568271 | ||||||||
\(844\) | −27.7292 | −0.954478 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17.3479 | 0.596435 | ||||||||
\(847\) | −3.82377 | −0.131386 | ||||||||
\(848\) | 19.6478 | 0.674709 | ||||||||
\(849\) | −34.6137 | −1.18794 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.37510 | −0.252815 | ||||||||
\(852\) | 59.3318 | 2.03267 | ||||||||
\(853\) | 19.2879 | 0.660404 | 0.330202 | − | 0.943910i | \(-0.392883\pi\) | ||||
0.330202 | + | 0.943910i | \(0.392883\pi\) | |||||||
\(854\) | −0.998274 | −0.0341602 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.0029 | −0.649504 | ||||||||
\(857\) | −2.52022 | −0.0860889 | −0.0430445 | − | 0.999073i | \(-0.513706\pi\) | ||||
−0.0430445 | + | 0.999073i | \(0.513706\pi\) | |||||||
\(858\) | 4.98108 | 0.170051 | ||||||||
\(859\) | 41.4410 | 1.41395 | 0.706974 | − | 0.707240i | \(-0.250060\pi\) | ||||
0.706974 | + | 0.707240i | \(0.250060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.76022 | −0.0940682 | ||||||||
\(862\) | −20.3957 | −0.694680 | ||||||||
\(863\) | −53.8341 | −1.83253 | −0.916266 | − | 0.400570i | \(-0.868812\pi\) | ||||
−0.916266 | + | 0.400570i | \(0.868812\pi\) | |||||||
\(864\) | −32.1339 | −1.09322 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.9349 | 0.371581 | ||||||||
\(867\) | 141.122 | 4.79274 | ||||||||
\(868\) | 1.24933 | 0.0424049 | ||||||||
\(869\) | −2.56791 | −0.0871105 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.7387 | 0.973773 | ||||||||
\(872\) | 14.1881 | 0.480469 | ||||||||
\(873\) | 68.1392 | 2.30616 | ||||||||
\(874\) | −7.49885 | −0.253653 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.60255 | 0.0879321 | ||||||||
\(877\) | −36.8178 | −1.24325 | −0.621624 | − | 0.783316i | \(-0.713527\pi\) | ||||
−0.621624 | + | 0.783316i | \(0.713527\pi\) | |||||||
\(878\) | 19.8630 | 0.670343 | ||||||||
\(879\) | −0.185385 | −0.00625288 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.7279 | 1.37216 | 0.686080 | − | 0.727526i | \(-0.259330\pi\) | ||||
0.686080 | + | 0.727526i | \(0.259330\pi\) | |||||||
\(882\) | 20.7666 | 0.699249 | ||||||||
\(883\) | 28.6309 | 0.963507 | 0.481753 | − | 0.876307i | \(-0.340000\pi\) | ||||
0.481753 | + | 0.876307i | \(0.340000\pi\) | |||||||
\(884\) | 62.7991 | 2.11216 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.2038 | −0.342805 | ||||||||
\(887\) | −4.30342 | −0.144495 | −0.0722473 | − | 0.997387i | \(-0.523017\pi\) | ||||
−0.0722473 | + | 0.997387i | \(0.523017\pi\) | |||||||
\(888\) | 15.5852 | 0.523006 | ||||||||
\(889\) | 1.96728 | 0.0659804 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.812699 | −0.0272264 | ||||||||
\(892\) | 35.4519 | 1.18702 | ||||||||
\(893\) | 24.5129 | 0.820293 | ||||||||
\(894\) | 13.3083 | 0.445097 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.13315 | 0.138079 | ||||||||
\(897\) | −38.9095 | −1.29915 | ||||||||
\(898\) | −7.05321 | −0.235369 | ||||||||
\(899\) | 19.4140 | 0.647492 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −81.3659 | −2.71069 | ||||||||
\(902\) | −1.01246 | −0.0337113 | ||||||||
\(903\) | 1.63386 | 0.0543714 | ||||||||
\(904\) | −15.1370 | −0.503448 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11.1316 | −0.369822 | ||||||||
\(907\) | 45.3984 | 1.50743 | 0.753714 | − | 0.657202i | \(-0.228260\pi\) | ||||
0.753714 | + | 0.657202i | \(0.228260\pi\) | |||||||
\(908\) | 9.96654 | 0.330751 | ||||||||
\(909\) | 29.8781 | 0.990995 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.5189 | −0.481032 | −0.240516 | − | 0.970645i | \(-0.577317\pi\) | ||||
−0.240516 | + | 0.970645i | \(0.577317\pi\) | |||||||
\(912\) | −23.8992 | −0.791381 | ||||||||
\(913\) | 9.48091 | 0.313772 | ||||||||
\(914\) | 22.8567 | 0.756032 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.3059 | −0.770047 | ||||||||
\(917\) | −4.16009 | −0.137378 | ||||||||
\(918\) | 28.3715 | 0.936398 | ||||||||
\(919\) | 12.2387 | 0.403718 | 0.201859 | − | 0.979415i | \(-0.435302\pi\) | ||||
0.201859 | + | 0.979415i | \(0.435302\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.2551 | −0.799232 | ||||||||
\(922\) | −2.48849 | −0.0819542 | ||||||||
\(923\) | −59.7376 | −1.96629 | ||||||||
\(924\) | 1.04890 | 0.0345064 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 19.7050 | 0.647545 | ||||||||
\(927\) | −32.7198 | −1.07466 | ||||||||
\(928\) | 50.9781 | 1.67344 | ||||||||
\(929\) | −47.9762 | −1.57405 | −0.787024 | − | 0.616922i | \(-0.788379\pi\) | ||||
−0.787024 | + | 0.616922i | \(0.788379\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.3436 | 0.961696 | ||||||||
\(932\) | −17.1699 | −0.562419 | ||||||||
\(933\) | 24.5366 | 0.803291 | ||||||||
\(934\) | 16.7477 | 0.548002 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 51.5532 | 1.68507 | ||||||||
\(937\) | −20.7632 | −0.678306 | −0.339153 | − | 0.940731i | \(-0.610140\pi\) | ||||
−0.339153 | + | 0.940731i | \(0.610140\pi\) | |||||||
\(938\) | −1.32549 | −0.0432788 | ||||||||
\(939\) | −4.09032 | −0.133482 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.2342 | −1.24640 | −0.623199 | − | 0.782063i | \(-0.714167\pi\) | ||||
−0.623199 | + | 0.782063i | \(0.714167\pi\) | |||||||
\(942\) | 17.4570 | 0.568779 | ||||||||
\(943\) | 7.90879 | 0.257546 | ||||||||
\(944\) | −13.6045 | −0.442790 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.599306 | 0.0194851 | ||||||||
\(947\) | −17.4619 | −0.567437 | −0.283718 | − | 0.958908i | \(-0.591568\pi\) | ||||
−0.283718 | + | 0.958908i | \(0.591568\pi\) | |||||||
\(948\) | −19.1027 | −0.620427 | ||||||||
\(949\) | −2.62035 | −0.0850602 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.9357 | −0.873451 | ||||||||
\(952\) | −6.42727 | −0.208309 | ||||||||
\(953\) | 23.5351 | 0.762377 | 0.381188 | − | 0.924497i | \(-0.375515\pi\) | ||||
0.381188 | + | 0.924497i | \(0.375515\pi\) | |||||||
\(954\) | −30.1011 | −0.974558 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −32.1490 | −1.03977 | ||||||||
\(957\) | 16.2995 | 0.526888 | ||||||||
\(958\) | −7.51089 | −0.242666 | ||||||||
\(959\) | 5.28928 | 0.170800 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.5366 | −0.856019 | ||||||||
\(962\) | −7.07149 | −0.227994 | ||||||||
\(963\) | −43.9065 | −1.41487 | ||||||||
\(964\) | 1.64065 | 0.0528419 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.79459 | 0.0577400 | ||||||||
\(967\) | 56.8777 | 1.82906 | 0.914531 | − | 0.404515i | \(-0.132560\pi\) | ||||
0.914531 | + | 0.404515i | \(0.132560\pi\) | |||||||
\(968\) | −23.1528 | −0.744158 | ||||||||
\(969\) | 98.9717 | 3.17943 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.8532 | −1.02222 | −0.511108 | − | 0.859516i | \(-0.670765\pi\) | ||||
−0.511108 | + | 0.859516i | \(0.670765\pi\) | |||||||
\(972\) | 22.4643 | 0.720544 | ||||||||
\(973\) | 4.65450 | 0.149216 | ||||||||
\(974\) | 12.1151 | 0.388194 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.11599 | 0.291796 | ||||||||
\(977\) | −52.0439 | −1.66503 | −0.832516 | − | 0.554002i | \(-0.813100\pi\) | ||||
−0.832516 | + | 0.554002i | \(0.813100\pi\) | |||||||
\(978\) | −25.2439 | −0.807211 | ||||||||
\(979\) | 8.56683 | 0.273797 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32.7819 | 1.04664 | ||||||||
\(982\) | −23.4261 | −0.747558 | ||||||||
\(983\) | 9.89877 | 0.315722 | 0.157861 | − | 0.987461i | \(-0.449540\pi\) | ||||
0.157861 | + | 0.987461i | \(0.449540\pi\) | |||||||
\(984\) | −16.7131 | −0.532793 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −45.0093 | −1.43339 | ||||||||
\(987\) | −5.86631 | −0.186727 | ||||||||
\(988\) | 32.8276 | 1.04439 | ||||||||
\(989\) | −4.68145 | −0.148862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.2687 | 0.770921 | 0.385461 | − | 0.922724i | \(-0.374043\pi\) | ||||
0.385461 | + | 0.922724i | \(0.374043\pi\) | |||||||
\(992\) | 11.7203 | 0.372119 | ||||||||
\(993\) | −45.3882 | −1.44035 | ||||||||
\(994\) | 2.75523 | 0.0873906 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 70.5285 | 2.23478 | ||||||||
\(997\) | 21.7614 | 0.689191 | 0.344596 | − | 0.938751i | \(-0.388016\pi\) | ||||
0.344596 | + | 0.938751i | \(0.388016\pi\) | |||||||
\(998\) | 13.9229 | 0.440722 | ||||||||
\(999\) | 14.5862 | 0.461485 |
(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 | 6025.2.a.l.1.20 | ✓ | 40 | |
5.4 | even | 2 | 6025.2.a.o.1.21 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.l.1.20 | ✓ | 40 | 1.1 | even | 1 | trivial | |
6025.2.a.o.1.21 | yes | 40 | 5.4 | even | 2 |