Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,2,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, 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("1441.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(11.5064429313\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.714474 | 0.505209 | 0.252605 | − | 0.967570i | \(-0.418713\pi\) | ||||
0.252605 | + | 0.967570i | \(0.418713\pi\) | |||||||
\(3\) | 2.60520 | 1.50411 | 0.752056 | − | 0.659099i | \(-0.229062\pi\) | ||||
0.752056 | + | 0.659099i | \(0.229062\pi\) | |||||||
\(4\) | −1.48953 | −0.744764 | ||||||||
\(5\) | −0.266226 | −0.119060 | −0.0595299 | − | 0.998227i | \(-0.518960\pi\) | ||||
−0.0595299 | + | 0.998227i | \(0.518960\pi\) | |||||||
\(6\) | 1.86135 | 0.759891 | ||||||||
\(7\) | −4.25119 | −1.60680 | −0.803400 | − | 0.595440i | \(-0.796978\pi\) | ||||
−0.803400 | + | 0.595440i | \(0.796978\pi\) | |||||||
\(8\) | −2.49318 | −0.881471 | ||||||||
\(9\) | 3.78706 | 1.26235 | ||||||||
\(10\) | −0.190211 | −0.0601501 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −3.88052 | −1.12021 | ||||||||
\(13\) | −1.98481 | −0.550486 | −0.275243 | − | 0.961375i | \(-0.588758\pi\) | ||||
−0.275243 | + | 0.961375i | \(0.588758\pi\) | |||||||
\(14\) | −3.03736 | −0.811770 | ||||||||
\(15\) | −0.693572 | −0.179079 | ||||||||
\(16\) | 1.19775 | 0.299437 | ||||||||
\(17\) | −2.40857 | −0.584163 | −0.292081 | − | 0.956393i | \(-0.594348\pi\) | ||||
−0.292081 | + | 0.956393i | \(0.594348\pi\) | |||||||
\(18\) | 2.70576 | 0.637753 | ||||||||
\(19\) | −3.84156 | −0.881314 | −0.440657 | − | 0.897676i | \(-0.645254\pi\) | ||||
−0.440657 | + | 0.897676i | \(0.645254\pi\) | |||||||
\(20\) | 0.396551 | 0.0886715 | ||||||||
\(21\) | −11.0752 | −2.41681 | ||||||||
\(22\) | 0.714474 | 0.152326 | ||||||||
\(23\) | −4.84360 | −1.00996 | −0.504981 | − | 0.863131i | \(-0.668500\pi\) | ||||
−0.504981 | + | 0.863131i | \(0.668500\pi\) | |||||||
\(24\) | −6.49522 | −1.32583 | ||||||||
\(25\) | −4.92912 | −0.985825 | ||||||||
\(26\) | −1.41809 | −0.278111 | ||||||||
\(27\) | 2.05045 | 0.394610 | ||||||||
\(28\) | 6.33227 | 1.19669 | ||||||||
\(29\) | 7.38740 | 1.37181 | 0.685903 | − | 0.727693i | \(-0.259407\pi\) | ||||
0.685903 | + | 0.727693i | \(0.259407\pi\) | |||||||
\(30\) | −0.495539 | −0.0904726 | ||||||||
\(31\) | −7.56343 | −1.35843 | −0.679216 | − | 0.733938i | \(-0.737680\pi\) | ||||
−0.679216 | + | 0.733938i | \(0.737680\pi\) | |||||||
\(32\) | 5.84211 | 1.03275 | ||||||||
\(33\) | 2.60520 | 0.453507 | ||||||||
\(34\) | −1.72086 | −0.295124 | ||||||||
\(35\) | 1.13178 | 0.191305 | ||||||||
\(36\) | −5.64093 | −0.940156 | ||||||||
\(37\) | 7.68404 | 1.26325 | 0.631624 | − | 0.775275i | \(-0.282389\pi\) | ||||
0.631624 | + | 0.775275i | \(0.282389\pi\) | |||||||
\(38\) | −2.74469 | −0.445248 | ||||||||
\(39\) | −5.17081 | −0.827993 | ||||||||
\(40\) | 0.663748 | 0.104948 | ||||||||
\(41\) | 3.36181 | 0.525026 | 0.262513 | − | 0.964928i | \(-0.415449\pi\) | ||||
0.262513 | + | 0.964928i | \(0.415449\pi\) | |||||||
\(42\) | −7.91294 | −1.22099 | ||||||||
\(43\) | −6.49093 | −0.989857 | −0.494928 | − | 0.868934i | \(-0.664806\pi\) | ||||
−0.494928 | + | 0.868934i | \(0.664806\pi\) | |||||||
\(44\) | −1.48953 | −0.224555 | ||||||||
\(45\) | −1.00821 | −0.150296 | ||||||||
\(46\) | −3.46063 | −0.510242 | ||||||||
\(47\) | −7.86384 | −1.14706 | −0.573529 | − | 0.819185i | \(-0.694426\pi\) | ||||
−0.573529 | + | 0.819185i | \(0.694426\pi\) | |||||||
\(48\) | 3.12037 | 0.450386 | ||||||||
\(49\) | 11.0726 | 1.58180 | ||||||||
\(50\) | −3.52173 | −0.498048 | ||||||||
\(51\) | −6.27479 | −0.878647 | ||||||||
\(52\) | 2.95642 | 0.409982 | ||||||||
\(53\) | 2.59581 | 0.356563 | 0.178281 | − | 0.983980i | \(-0.442946\pi\) | ||||
0.178281 | + | 0.983980i | \(0.442946\pi\) | |||||||
\(54\) | 1.46500 | 0.199361 | ||||||||
\(55\) | −0.266226 | −0.0358979 | ||||||||
\(56\) | 10.5990 | 1.41635 | ||||||||
\(57\) | −10.0080 | −1.32560 | ||||||||
\(58\) | 5.27810 | 0.693049 | ||||||||
\(59\) | 9.89990 | 1.28886 | 0.644428 | − | 0.764665i | \(-0.277095\pi\) | ||||
0.644428 | + | 0.764665i | \(0.277095\pi\) | |||||||
\(60\) | 1.03309 | 0.133372 | ||||||||
\(61\) | −13.9195 | −1.78221 | −0.891105 | − | 0.453798i | \(-0.850069\pi\) | ||||
−0.891105 | + | 0.453798i | \(0.850069\pi\) | |||||||
\(62\) | −5.40387 | −0.686293 | ||||||||
\(63\) | −16.0995 | −2.02835 | ||||||||
\(64\) | 1.77854 | 0.222317 | ||||||||
\(65\) | 0.528407 | 0.0655408 | ||||||||
\(66\) | 1.86135 | 0.229116 | ||||||||
\(67\) | 2.88224 | 0.352121 | 0.176061 | − | 0.984379i | \(-0.443665\pi\) | ||||
0.176061 | + | 0.984379i | \(0.443665\pi\) | |||||||
\(68\) | 3.58762 | 0.435063 | ||||||||
\(69\) | −12.6186 | −1.51910 | ||||||||
\(70\) | 0.808625 | 0.0966492 | ||||||||
\(71\) | −2.24673 | −0.266638 | −0.133319 | − | 0.991073i | \(-0.542563\pi\) | ||||
−0.133319 | + | 0.991073i | \(0.542563\pi\) | |||||||
\(72\) | −9.44181 | −1.11273 | ||||||||
\(73\) | −1.68777 | −0.197539 | −0.0987695 | − | 0.995110i | \(-0.531491\pi\) | ||||
−0.0987695 | + | 0.995110i | \(0.531491\pi\) | |||||||
\(74\) | 5.49005 | 0.638205 | ||||||||
\(75\) | −12.8413 | −1.48279 | ||||||||
\(76\) | 5.72211 | 0.656371 | ||||||||
\(77\) | −4.25119 | −0.484468 | ||||||||
\(78\) | −3.69441 | −0.418310 | ||||||||
\(79\) | −1.28914 | −0.145039 | −0.0725195 | − | 0.997367i | \(-0.523104\pi\) | ||||
−0.0725195 | + | 0.997367i | \(0.523104\pi\) | |||||||
\(80\) | −0.318871 | −0.0356509 | ||||||||
\(81\) | −6.01934 | −0.668816 | ||||||||
\(82\) | 2.40192 | 0.265248 | ||||||||
\(83\) | −8.11186 | −0.890392 | −0.445196 | − | 0.895433i | \(-0.646866\pi\) | ||||
−0.445196 | + | 0.895433i | \(0.646866\pi\) | |||||||
\(84\) | 16.4968 | 1.79995 | ||||||||
\(85\) | 0.641223 | 0.0695504 | ||||||||
\(86\) | −4.63760 | −0.500085 | ||||||||
\(87\) | 19.2457 | 2.06335 | ||||||||
\(88\) | −2.49318 | −0.265773 | ||||||||
\(89\) | 6.17174 | 0.654204 | 0.327102 | − | 0.944989i | \(-0.393928\pi\) | ||||
0.327102 | + | 0.944989i | \(0.393928\pi\) | |||||||
\(90\) | −0.720343 | −0.0759308 | ||||||||
\(91\) | 8.43779 | 0.884521 | ||||||||
\(92\) | 7.21468 | 0.752183 | ||||||||
\(93\) | −19.7043 | −2.04324 | ||||||||
\(94\) | −5.61850 | −0.579504 | ||||||||
\(95\) | 1.02272 | 0.104929 | ||||||||
\(96\) | 15.2199 | 1.55337 | ||||||||
\(97\) | 10.5173 | 1.06787 | 0.533934 | − | 0.845526i | \(-0.320713\pi\) | ||||
0.533934 | + | 0.845526i | \(0.320713\pi\) | |||||||
\(98\) | 7.91110 | 0.799142 | ||||||||
\(99\) | 3.78706 | 0.380614 | ||||||||
\(100\) | 7.34206 | 0.734206 | ||||||||
\(101\) | 13.7609 | 1.36926 | 0.684631 | − | 0.728889i | \(-0.259963\pi\) | ||||
0.684631 | + | 0.728889i | \(0.259963\pi\) | |||||||
\(102\) | −4.48317 | −0.443900 | ||||||||
\(103\) | 3.27857 | 0.323047 | 0.161524 | − | 0.986869i | \(-0.448359\pi\) | ||||
0.161524 | + | 0.986869i | \(0.448359\pi\) | |||||||
\(104\) | 4.94847 | 0.485237 | ||||||||
\(105\) | 2.94851 | 0.287745 | ||||||||
\(106\) | 1.85464 | 0.180139 | ||||||||
\(107\) | 2.86062 | 0.276547 | 0.138273 | − | 0.990394i | \(-0.455845\pi\) | ||||
0.138273 | + | 0.990394i | \(0.455845\pi\) | |||||||
\(108\) | −3.05421 | −0.293891 | ||||||||
\(109\) | −11.3437 | −1.08653 | −0.543264 | − | 0.839562i | \(-0.682812\pi\) | ||||
−0.543264 | + | 0.839562i | \(0.682812\pi\) | |||||||
\(110\) | −0.190211 | −0.0181360 | ||||||||
\(111\) | 20.0185 | 1.90007 | ||||||||
\(112\) | −5.09185 | −0.481135 | ||||||||
\(113\) | 2.47478 | 0.232807 | 0.116404 | − | 0.993202i | \(-0.462863\pi\) | ||||
0.116404 | + | 0.993202i | \(0.462863\pi\) | |||||||
\(114\) | −7.15047 | −0.669703 | ||||||||
\(115\) | 1.28949 | 0.120246 | ||||||||
\(116\) | −11.0037 | −1.02167 | ||||||||
\(117\) | −7.51658 | −0.694908 | ||||||||
\(118\) | 7.07322 | 0.651142 | ||||||||
\(119\) | 10.2393 | 0.938633 | ||||||||
\(120\) | 1.72920 | 0.157853 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −9.94512 | −0.900389 | ||||||||
\(123\) | 8.75817 | 0.789698 | ||||||||
\(124\) | 11.2659 | 1.01171 | ||||||||
\(125\) | 2.64339 | 0.236432 | ||||||||
\(126\) | −11.5027 | −1.02474 | ||||||||
\(127\) | −18.9979 | −1.68579 | −0.842895 | − | 0.538078i | \(-0.819151\pi\) | ||||
−0.842895 | + | 0.538078i | \(0.819151\pi\) | |||||||
\(128\) | −10.4135 | −0.920432 | ||||||||
\(129\) | −16.9102 | −1.48886 | ||||||||
\(130\) | 0.377533 | 0.0331118 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | −3.88052 | −0.337756 | ||||||||
\(133\) | 16.3312 | 1.41610 | ||||||||
\(134\) | 2.05928 | 0.177895 | ||||||||
\(135\) | −0.545884 | −0.0469822 | ||||||||
\(136\) | 6.00498 | 0.514922 | ||||||||
\(137\) | 21.4642 | 1.83381 | 0.916904 | − | 0.399107i | \(-0.130680\pi\) | ||||
0.916904 | + | 0.399107i | \(0.130680\pi\) | |||||||
\(138\) | −9.01562 | −0.767461 | ||||||||
\(139\) | 4.21451 | 0.357470 | 0.178735 | − | 0.983897i | \(-0.442800\pi\) | ||||
0.178735 | + | 0.983897i | \(0.442800\pi\) | |||||||
\(140\) | −1.68581 | −0.142477 | ||||||||
\(141\) | −20.4869 | −1.72530 | ||||||||
\(142\) | −1.60523 | −0.134708 | ||||||||
\(143\) | −1.98481 | −0.165978 | ||||||||
\(144\) | 4.53594 | 0.377995 | ||||||||
\(145\) | −1.96672 | −0.163327 | ||||||||
\(146\) | −1.20587 | −0.0997985 | ||||||||
\(147\) | 28.8464 | 2.37921 | ||||||||
\(148\) | −11.4456 | −0.940822 | ||||||||
\(149\) | −12.0843 | −0.989983 | −0.494991 | − | 0.868898i | \(-0.664829\pi\) | ||||
−0.494991 | + | 0.868898i | \(0.664829\pi\) | |||||||
\(150\) | −9.17481 | −0.749120 | ||||||||
\(151\) | −16.6533 | −1.35522 | −0.677612 | − | 0.735420i | \(-0.736985\pi\) | ||||
−0.677612 | + | 0.735420i | \(0.736985\pi\) | |||||||
\(152\) | 9.57768 | 0.776852 | ||||||||
\(153\) | −9.12139 | −0.737420 | ||||||||
\(154\) | −3.03736 | −0.244758 | ||||||||
\(155\) | 2.01358 | 0.161735 | ||||||||
\(156\) | 7.70207 | 0.616659 | ||||||||
\(157\) | 18.0718 | 1.44228 | 0.721142 | − | 0.692787i | \(-0.243617\pi\) | ||||
0.721142 | + | 0.692787i | \(0.243617\pi\) | |||||||
\(158\) | −0.921053 | −0.0732751 | ||||||||
\(159\) | 6.76261 | 0.536310 | ||||||||
\(160\) | −1.55532 | −0.122959 | ||||||||
\(161\) | 20.5911 | 1.62281 | ||||||||
\(162\) | −4.30066 | −0.337892 | ||||||||
\(163\) | 9.04640 | 0.708569 | 0.354284 | − | 0.935138i | \(-0.384725\pi\) | ||||
0.354284 | + | 0.935138i | \(0.384725\pi\) | |||||||
\(164\) | −5.00750 | −0.391020 | ||||||||
\(165\) | −0.693572 | −0.0539945 | ||||||||
\(166\) | −5.79571 | −0.449834 | ||||||||
\(167\) | 8.80777 | 0.681565 | 0.340783 | − | 0.940142i | \(-0.389308\pi\) | ||||
0.340783 | + | 0.940142i | \(0.389308\pi\) | |||||||
\(168\) | 27.6124 | 2.13034 | ||||||||
\(169\) | −9.06055 | −0.696965 | ||||||||
\(170\) | 0.458137 | 0.0351375 | ||||||||
\(171\) | −14.5482 | −1.11253 | ||||||||
\(172\) | 9.66841 | 0.737209 | ||||||||
\(173\) | −4.77384 | −0.362949 | −0.181474 | − | 0.983396i | \(-0.558087\pi\) | ||||
−0.181474 | + | 0.983396i | \(0.558087\pi\) | |||||||
\(174\) | 13.7505 | 1.04242 | ||||||||
\(175\) | 20.9547 | 1.58402 | ||||||||
\(176\) | 1.19775 | 0.0902835 | ||||||||
\(177\) | 25.7912 | 1.93859 | ||||||||
\(178\) | 4.40955 | 0.330510 | ||||||||
\(179\) | −9.33183 | −0.697493 | −0.348747 | − | 0.937217i | \(-0.613393\pi\) | ||||
−0.348747 | + | 0.937217i | \(0.613393\pi\) | |||||||
\(180\) | 1.50176 | 0.111935 | ||||||||
\(181\) | −9.65106 | −0.717358 | −0.358679 | − | 0.933461i | \(-0.616773\pi\) | ||||
−0.358679 | + | 0.933461i | \(0.616773\pi\) | |||||||
\(182\) | 6.02858 | 0.446868 | ||||||||
\(183\) | −36.2631 | −2.68064 | ||||||||
\(184\) | 12.0760 | 0.890251 | ||||||||
\(185\) | −2.04569 | −0.150402 | ||||||||
\(186\) | −14.0782 | −1.03226 | ||||||||
\(187\) | −2.40857 | −0.176132 | ||||||||
\(188\) | 11.7134 | 0.854287 | ||||||||
\(189\) | −8.71688 | −0.634059 | ||||||||
\(190\) | 0.730709 | 0.0530112 | ||||||||
\(191\) | 21.3649 | 1.54591 | 0.772956 | − | 0.634459i | \(-0.218777\pi\) | ||||
0.772956 | + | 0.634459i | \(0.218777\pi\) | |||||||
\(192\) | 4.63345 | 0.334391 | ||||||||
\(193\) | −1.97627 | −0.142255 | −0.0711275 | − | 0.997467i | \(-0.522660\pi\) | ||||
−0.0711275 | + | 0.997467i | \(0.522660\pi\) | |||||||
\(194\) | 7.51433 | 0.539497 | ||||||||
\(195\) | 1.37660 | 0.0985807 | ||||||||
\(196\) | −16.4930 | −1.17807 | ||||||||
\(197\) | 1.08589 | 0.0773661 | 0.0386831 | − | 0.999252i | \(-0.487684\pi\) | ||||
0.0386831 | + | 0.999252i | \(0.487684\pi\) | |||||||
\(198\) | 2.70576 | 0.192290 | ||||||||
\(199\) | −2.84707 | −0.201823 | −0.100912 | − | 0.994895i | \(-0.532176\pi\) | ||||
−0.100912 | + | 0.994895i | \(0.532176\pi\) | |||||||
\(200\) | 12.2892 | 0.868976 | ||||||||
\(201\) | 7.50880 | 0.529630 | ||||||||
\(202\) | 9.83182 | 0.691764 | ||||||||
\(203\) | −31.4053 | −2.20422 | ||||||||
\(204\) | 9.34648 | 0.654384 | ||||||||
\(205\) | −0.895000 | −0.0625095 | ||||||||
\(206\) | 2.34245 | 0.163206 | ||||||||
\(207\) | −18.3430 | −1.27493 | ||||||||
\(208\) | −2.37729 | −0.164836 | ||||||||
\(209\) | −3.84156 | −0.265726 | ||||||||
\(210\) | 2.10663 | 0.145371 | ||||||||
\(211\) | −12.4333 | −0.855945 | −0.427972 | − | 0.903792i | \(-0.640772\pi\) | ||||
−0.427972 | + | 0.903792i | \(0.640772\pi\) | |||||||
\(212\) | −3.86654 | −0.265555 | ||||||||
\(213\) | −5.85317 | −0.401053 | ||||||||
\(214\) | 2.04384 | 0.139714 | ||||||||
\(215\) | 1.72805 | 0.117852 | ||||||||
\(216\) | −5.11214 | −0.347837 | ||||||||
\(217\) | 32.1536 | 2.18273 | ||||||||
\(218\) | −8.10477 | −0.548924 | ||||||||
\(219\) | −4.39699 | −0.297121 | ||||||||
\(220\) | 0.396551 | 0.0267355 | ||||||||
\(221\) | 4.78053 | 0.321574 | ||||||||
\(222\) | 14.3027 | 0.959932 | ||||||||
\(223\) | −3.20148 | −0.214387 | −0.107194 | − | 0.994238i | \(-0.534186\pi\) | ||||
−0.107194 | + | 0.994238i | \(0.534186\pi\) | |||||||
\(224\) | −24.8359 | −1.65942 | ||||||||
\(225\) | −18.6669 | −1.24446 | ||||||||
\(226\) | 1.76816 | 0.117616 | ||||||||
\(227\) | 16.9260 | 1.12342 | 0.561708 | − | 0.827336i | \(-0.310144\pi\) | ||||
0.561708 | + | 0.827336i | \(0.310144\pi\) | |||||||
\(228\) | 14.9072 | 0.987255 | ||||||||
\(229\) | −11.5175 | −0.761101 | −0.380550 | − | 0.924760i | \(-0.624265\pi\) | ||||
−0.380550 | + | 0.924760i | \(0.624265\pi\) | |||||||
\(230\) | 0.921309 | 0.0607493 | ||||||||
\(231\) | −11.0752 | −0.728695 | ||||||||
\(232\) | −18.4181 | −1.20921 | ||||||||
\(233\) | 11.5699 | 0.757970 | 0.378985 | − | 0.925403i | \(-0.376273\pi\) | ||||
0.378985 | + | 0.925403i | \(0.376273\pi\) | |||||||
\(234\) | −5.37040 | −0.351074 | ||||||||
\(235\) | 2.09356 | 0.136569 | ||||||||
\(236\) | −14.7462 | −0.959894 | ||||||||
\(237\) | −3.35845 | −0.218155 | ||||||||
\(238\) | 7.31569 | 0.474206 | ||||||||
\(239\) | −6.83651 | −0.442217 | −0.221109 | − | 0.975249i | \(-0.570968\pi\) | ||||
−0.221109 | + | 0.975249i | \(0.570968\pi\) | |||||||
\(240\) | −0.830723 | −0.0536229 | ||||||||
\(241\) | −23.7835 | −1.53203 | −0.766016 | − | 0.642822i | \(-0.777764\pi\) | ||||
−0.766016 | + | 0.642822i | \(0.777764\pi\) | |||||||
\(242\) | 0.714474 | 0.0459281 | ||||||||
\(243\) | −21.8330 | −1.40058 | ||||||||
\(244\) | 20.7335 | 1.32733 | ||||||||
\(245\) | −2.94782 | −0.188329 | ||||||||
\(246\) | 6.25748 | 0.398963 | ||||||||
\(247\) | 7.62475 | 0.485151 | ||||||||
\(248\) | 18.8570 | 1.19742 | ||||||||
\(249\) | −21.1330 | −1.33925 | ||||||||
\(250\) | 1.88863 | 0.119448 | ||||||||
\(251\) | −17.6289 | −1.11273 | −0.556363 | − | 0.830939i | \(-0.687804\pi\) | ||||
−0.556363 | + | 0.830939i | \(0.687804\pi\) | |||||||
\(252\) | 23.9807 | 1.51064 | ||||||||
\(253\) | −4.84360 | −0.304515 | ||||||||
\(254\) | −13.5735 | −0.851677 | ||||||||
\(255\) | 1.67051 | 0.104612 | ||||||||
\(256\) | −10.9973 | −0.687328 | ||||||||
\(257\) | 21.6333 | 1.34945 | 0.674723 | − | 0.738071i | \(-0.264263\pi\) | ||||
0.674723 | + | 0.738071i | \(0.264263\pi\) | |||||||
\(258\) | −12.0819 | −0.752184 | ||||||||
\(259\) | −32.6663 | −2.02979 | ||||||||
\(260\) | −0.787076 | −0.0488124 | ||||||||
\(261\) | 27.9766 | 1.73171 | ||||||||
\(262\) | 0.714474 | 0.0441403 | ||||||||
\(263\) | 2.30575 | 0.142179 | 0.0710893 | − | 0.997470i | \(-0.477352\pi\) | ||||
0.0710893 | + | 0.997470i | \(0.477352\pi\) | |||||||
\(264\) | −6.49522 | −0.399753 | ||||||||
\(265\) | −0.691073 | −0.0424523 | ||||||||
\(266\) | 11.6682 | 0.715424 | ||||||||
\(267\) | 16.0786 | 0.983996 | ||||||||
\(268\) | −4.29317 | −0.262247 | ||||||||
\(269\) | −8.27886 | −0.504771 | −0.252386 | − | 0.967627i | \(-0.581215\pi\) | ||||
−0.252386 | + | 0.967627i | \(0.581215\pi\) | |||||||
\(270\) | −0.390020 | −0.0237359 | ||||||||
\(271\) | −11.6606 | −0.708330 | −0.354165 | − | 0.935183i | \(-0.615235\pi\) | ||||
−0.354165 | + | 0.935183i | \(0.615235\pi\) | |||||||
\(272\) | −2.88485 | −0.174920 | ||||||||
\(273\) | 21.9821 | 1.33042 | ||||||||
\(274\) | 15.3356 | 0.926457 | ||||||||
\(275\) | −4.92912 | −0.297237 | ||||||||
\(276\) | 18.7957 | 1.13137 | ||||||||
\(277\) | −18.2078 | −1.09400 | −0.546999 | − | 0.837133i | \(-0.684230\pi\) | ||||
−0.546999 | + | 0.837133i | \(0.684230\pi\) | |||||||
\(278\) | 3.01116 | 0.180597 | ||||||||
\(279\) | −28.6432 | −1.71482 | ||||||||
\(280\) | −2.82172 | −0.168630 | ||||||||
\(281\) | −9.98596 | −0.595712 | −0.297856 | − | 0.954611i | \(-0.596272\pi\) | ||||
−0.297856 | + | 0.954611i | \(0.596272\pi\) | |||||||
\(282\) | −14.6373 | −0.871640 | ||||||||
\(283\) | 11.1669 | 0.663806 | 0.331903 | − | 0.943313i | \(-0.392309\pi\) | ||||
0.331903 | + | 0.943313i | \(0.392309\pi\) | |||||||
\(284\) | 3.34656 | 0.198582 | ||||||||
\(285\) | 2.66440 | 0.157825 | ||||||||
\(286\) | −1.41809 | −0.0838535 | ||||||||
\(287\) | −14.2917 | −0.843611 | ||||||||
\(288\) | 22.1244 | 1.30369 | ||||||||
\(289\) | −11.1988 | −0.658754 | ||||||||
\(290\) | −1.40517 | −0.0825143 | ||||||||
\(291\) | 27.3996 | 1.60619 | ||||||||
\(292\) | 2.51399 | 0.147120 | ||||||||
\(293\) | −19.6074 | −1.14548 | −0.572738 | − | 0.819738i | \(-0.694119\pi\) | ||||
−0.572738 | + | 0.819738i | \(0.694119\pi\) | |||||||
\(294\) | 20.6100 | 1.20200 | ||||||||
\(295\) | −2.63561 | −0.153451 | ||||||||
\(296\) | −19.1577 | −1.11352 | ||||||||
\(297\) | 2.05045 | 0.118979 | ||||||||
\(298\) | −8.63390 | −0.500148 | ||||||||
\(299\) | 9.61361 | 0.555970 | ||||||||
\(300\) | 19.1275 | 1.10433 | ||||||||
\(301\) | 27.5942 | 1.59050 | ||||||||
\(302\) | −11.8983 | −0.684672 | ||||||||
\(303\) | 35.8499 | 2.05953 | ||||||||
\(304\) | −4.60121 | −0.263898 | ||||||||
\(305\) | 3.70573 | 0.212190 | ||||||||
\(306\) | −6.51699 | −0.372552 | ||||||||
\(307\) | 23.8034 | 1.35853 | 0.679266 | − | 0.733893i | \(-0.262298\pi\) | ||||
0.679266 | + | 0.733893i | \(0.262298\pi\) | |||||||
\(308\) | 6.33227 | 0.360814 | ||||||||
\(309\) | 8.54133 | 0.485899 | ||||||||
\(310\) | 1.43865 | 0.0817099 | ||||||||
\(311\) | −24.9116 | −1.41261 | −0.706304 | − | 0.707909i | \(-0.749639\pi\) | ||||
−0.706304 | + | 0.707909i | \(0.749639\pi\) | |||||||
\(312\) | 12.8917 | 0.729851 | ||||||||
\(313\) | 21.1283 | 1.19424 | 0.597120 | − | 0.802152i | \(-0.296311\pi\) | ||||
0.597120 | + | 0.802152i | \(0.296311\pi\) | |||||||
\(314\) | 12.9118 | 0.728655 | ||||||||
\(315\) | 4.28611 | 0.241495 | ||||||||
\(316\) | 1.92020 | 0.108020 | ||||||||
\(317\) | −22.2781 | −1.25126 | −0.625631 | − | 0.780119i | \(-0.715158\pi\) | ||||
−0.625631 | + | 0.780119i | \(0.715158\pi\) | |||||||
\(318\) | 4.83171 | 0.270949 | ||||||||
\(319\) | 7.38740 | 0.413615 | ||||||||
\(320\) | −0.473494 | −0.0264691 | ||||||||
\(321\) | 7.45249 | 0.415958 | ||||||||
\(322\) | 14.7118 | 0.819856 | ||||||||
\(323\) | 9.25265 | 0.514831 | ||||||||
\(324\) | 8.96598 | 0.498110 | ||||||||
\(325\) | 9.78335 | 0.542683 | ||||||||
\(326\) | 6.46341 | 0.357975 | ||||||||
\(327\) | −29.5526 | −1.63426 | ||||||||
\(328\) | −8.38157 | −0.462795 | ||||||||
\(329\) | 33.4307 | 1.84309 | ||||||||
\(330\) | −0.495539 | −0.0272785 | ||||||||
\(331\) | −24.2164 | −1.33105 | −0.665527 | − | 0.746373i | \(-0.731793\pi\) | ||||
−0.665527 | + | 0.746373i | \(0.731793\pi\) | |||||||
\(332\) | 12.0828 | 0.663132 | ||||||||
\(333\) | 29.0999 | 1.59467 | ||||||||
\(334\) | 6.29292 | 0.344333 | ||||||||
\(335\) | −0.767326 | −0.0419235 | ||||||||
\(336\) | −13.2653 | −0.723681 | ||||||||
\(337\) | 20.2912 | 1.10533 | 0.552666 | − | 0.833403i | \(-0.313610\pi\) | ||||
0.552666 | + | 0.833403i | \(0.313610\pi\) | |||||||
\(338\) | −6.47352 | −0.352113 | ||||||||
\(339\) | 6.44729 | 0.350169 | ||||||||
\(340\) | −0.955119 | −0.0517986 | ||||||||
\(341\) | −7.56343 | −0.409583 | ||||||||
\(342\) | −10.3943 | −0.562061 | ||||||||
\(343\) | −17.3135 | −0.934844 | ||||||||
\(344\) | 16.1830 | 0.872530 | ||||||||
\(345\) | 3.35939 | 0.180863 | ||||||||
\(346\) | −3.41079 | −0.183365 | ||||||||
\(347\) | 1.03831 | 0.0557395 | 0.0278697 | − | 0.999612i | \(-0.491128\pi\) | ||||
0.0278697 | + | 0.999612i | \(0.491128\pi\) | |||||||
\(348\) | −28.6669 | −1.53671 | ||||||||
\(349\) | 11.6628 | 0.624297 | 0.312148 | − | 0.950033i | \(-0.398951\pi\) | ||||
0.312148 | + | 0.950033i | \(0.398951\pi\) | |||||||
\(350\) | 14.9715 | 0.800263 | ||||||||
\(351\) | −4.06975 | −0.217227 | ||||||||
\(352\) | 5.84211 | 0.311385 | ||||||||
\(353\) | 3.76830 | 0.200567 | 0.100283 | − | 0.994959i | \(-0.468025\pi\) | ||||
0.100283 | + | 0.994959i | \(0.468025\pi\) | |||||||
\(354\) | 18.4271 | 0.979391 | ||||||||
\(355\) | 0.598137 | 0.0317458 | ||||||||
\(356\) | −9.19298 | −0.487227 | ||||||||
\(357\) | 26.6753 | 1.41181 | ||||||||
\(358\) | −6.66734 | −0.352380 | ||||||||
\(359\) | −19.5949 | −1.03418 | −0.517090 | − | 0.855931i | \(-0.672985\pi\) | ||||
−0.517090 | + | 0.855931i | \(0.672985\pi\) | |||||||
\(360\) | 2.51366 | 0.132481 | ||||||||
\(361\) | −4.24242 | −0.223286 | ||||||||
\(362\) | −6.89543 | −0.362416 | ||||||||
\(363\) | 2.60520 | 0.136737 | ||||||||
\(364\) | −12.5683 | −0.658759 | ||||||||
\(365\) | 0.449329 | 0.0235190 | ||||||||
\(366\) | −25.9090 | −1.35429 | ||||||||
\(367\) | 29.8625 | 1.55881 | 0.779405 | − | 0.626521i | \(-0.215522\pi\) | ||||
0.779405 | + | 0.626521i | \(0.215522\pi\) | |||||||
\(368\) | −5.80141 | −0.302419 | ||||||||
\(369\) | 12.7314 | 0.662769 | ||||||||
\(370\) | −1.46159 | −0.0759846 | ||||||||
\(371\) | −11.0353 | −0.572925 | ||||||||
\(372\) | 29.3500 | 1.52173 | ||||||||
\(373\) | −24.5808 | −1.27275 | −0.636373 | − | 0.771381i | \(-0.719566\pi\) | ||||
−0.636373 | + | 0.771381i | \(0.719566\pi\) | |||||||
\(374\) | −1.72086 | −0.0889834 | ||||||||
\(375\) | 6.88656 | 0.355620 | ||||||||
\(376\) | 19.6059 | 1.01110 | ||||||||
\(377\) | −14.6626 | −0.755160 | ||||||||
\(378\) | −6.22798 | −0.320333 | ||||||||
\(379\) | −27.5041 | −1.41279 | −0.706395 | − | 0.707818i | \(-0.749680\pi\) | ||||
−0.706395 | + | 0.707818i | \(0.749680\pi\) | |||||||
\(380\) | −1.52337 | −0.0781474 | ||||||||
\(381\) | −49.4933 | −2.53562 | ||||||||
\(382\) | 15.2647 | 0.781009 | ||||||||
\(383\) | −12.8012 | −0.654113 | −0.327057 | − | 0.945005i | \(-0.606057\pi\) | ||||
−0.327057 | + | 0.945005i | \(0.606057\pi\) | |||||||
\(384\) | −27.1292 | −1.38443 | ||||||||
\(385\) | 1.13178 | 0.0576807 | ||||||||
\(386\) | −1.41199 | −0.0718685 | ||||||||
\(387\) | −24.5815 | −1.24955 | ||||||||
\(388\) | −15.6658 | −0.795310 | ||||||||
\(389\) | 26.4465 | 1.34089 | 0.670445 | − | 0.741959i | \(-0.266103\pi\) | ||||
0.670445 | + | 0.741959i | \(0.266103\pi\) | |||||||
\(390\) | 0.983548 | 0.0498039 | ||||||||
\(391\) | 11.6661 | 0.589982 | ||||||||
\(392\) | −27.6060 | −1.39431 | ||||||||
\(393\) | 2.60520 | 0.131415 | ||||||||
\(394\) | 0.775836 | 0.0390861 | ||||||||
\(395\) | 0.343201 | 0.0172683 | ||||||||
\(396\) | −5.64093 | −0.283468 | ||||||||
\(397\) | −9.72895 | −0.488282 | −0.244141 | − | 0.969740i | \(-0.578506\pi\) | ||||
−0.244141 | + | 0.969740i | \(0.578506\pi\) | |||||||
\(398\) | −2.03416 | −0.101963 | ||||||||
\(399\) | 42.5460 | 2.12997 | ||||||||
\(400\) | −5.90384 | −0.295192 | ||||||||
\(401\) | −20.1705 | −1.00727 | −0.503634 | − | 0.863917i | \(-0.668004\pi\) | ||||
−0.503634 | + | 0.863917i | \(0.668004\pi\) | |||||||
\(402\) | 5.36484 | 0.267574 | ||||||||
\(403\) | 15.0119 | 0.747798 | ||||||||
\(404\) | −20.4973 | −1.01978 | ||||||||
\(405\) | 1.60251 | 0.0796292 | ||||||||
\(406\) | −22.4382 | −1.11359 | ||||||||
\(407\) | 7.68404 | 0.380884 | ||||||||
\(408\) | 15.6442 | 0.774501 | ||||||||
\(409\) | −36.3003 | −1.79493 | −0.897467 | − | 0.441081i | \(-0.854595\pi\) | ||||
−0.897467 | + | 0.441081i | \(0.854595\pi\) | |||||||
\(410\) | −0.639454 | −0.0315804 | ||||||||
\(411\) | 55.9185 | 2.75825 | ||||||||
\(412\) | −4.88352 | −0.240594 | ||||||||
\(413\) | −42.0864 | −2.07093 | ||||||||
\(414\) | −13.1056 | −0.644106 | ||||||||
\(415\) | 2.15959 | 0.106010 | ||||||||
\(416\) | −11.5955 | −0.568514 | ||||||||
\(417\) | 10.9796 | 0.537675 | ||||||||
\(418\) | −2.74469 | −0.134247 | ||||||||
\(419\) | 33.8065 | 1.65156 | 0.825779 | − | 0.563994i | \(-0.190736\pi\) | ||||
0.825779 | + | 0.563994i | \(0.190736\pi\) | |||||||
\(420\) | −4.39188 | −0.214302 | ||||||||
\(421\) | 18.2031 | 0.887164 | 0.443582 | − | 0.896234i | \(-0.353707\pi\) | ||||
0.443582 | + | 0.896234i | \(0.353707\pi\) | |||||||
\(422\) | −8.88327 | −0.432431 | ||||||||
\(423\) | −29.7808 | −1.44799 | ||||||||
\(424\) | −6.47182 | −0.314299 | ||||||||
\(425\) | 11.8721 | 0.575882 | ||||||||
\(426\) | −4.18194 | −0.202616 | ||||||||
\(427\) | 59.1745 | 2.86365 | ||||||||
\(428\) | −4.26098 | −0.205962 | ||||||||
\(429\) | −5.17081 | −0.249649 | ||||||||
\(430\) | 1.23465 | 0.0595400 | ||||||||
\(431\) | −22.8935 | −1.10274 | −0.551371 | − | 0.834260i | \(-0.685895\pi\) | ||||
−0.551371 | + | 0.834260i | \(0.685895\pi\) | |||||||
\(432\) | 2.45593 | 0.118161 | ||||||||
\(433\) | 10.7709 | 0.517619 | 0.258809 | − | 0.965928i | \(-0.416670\pi\) | ||||
0.258809 | + | 0.965928i | \(0.416670\pi\) | |||||||
\(434\) | 22.9729 | 1.10273 | ||||||||
\(435\) | −5.12369 | −0.245662 | ||||||||
\(436\) | 16.8967 | 0.809207 | ||||||||
\(437\) | 18.6070 | 0.890093 | ||||||||
\(438\) | −3.14153 | −0.150108 | ||||||||
\(439\) | 36.5458 | 1.74424 | 0.872119 | − | 0.489294i | \(-0.162745\pi\) | ||||
0.872119 | + | 0.489294i | \(0.162745\pi\) | |||||||
\(440\) | 0.663748 | 0.0316429 | ||||||||
\(441\) | 41.9328 | 1.99680 | ||||||||
\(442\) | 3.41557 | 0.162462 | ||||||||
\(443\) | −22.2850 | −1.05879 | −0.529395 | − | 0.848375i | \(-0.677581\pi\) | ||||
−0.529395 | + | 0.848375i | \(0.677581\pi\) | |||||||
\(444\) | −29.8180 | −1.41510 | ||||||||
\(445\) | −1.64308 | −0.0778894 | ||||||||
\(446\) | −2.28738 | −0.108310 | ||||||||
\(447\) | −31.4820 | −1.48905 | ||||||||
\(448\) | −7.56091 | −0.357220 | ||||||||
\(449\) | −28.5134 | −1.34563 | −0.672815 | − | 0.739810i | \(-0.734915\pi\) | ||||
−0.672815 | + | 0.739810i | \(0.734915\pi\) | |||||||
\(450\) | −13.3370 | −0.628713 | ||||||||
\(451\) | 3.36181 | 0.158301 | ||||||||
\(452\) | −3.68625 | −0.173387 | ||||||||
\(453\) | −43.3851 | −2.03841 | ||||||||
\(454\) | 12.0932 | 0.567560 | ||||||||
\(455\) | −2.24636 | −0.105311 | ||||||||
\(456\) | 24.9518 | 1.16847 | ||||||||
\(457\) | 41.2473 | 1.92947 | 0.964733 | − | 0.263229i | \(-0.0847874\pi\) | ||||
0.964733 | + | 0.263229i | \(0.0847874\pi\) | |||||||
\(458\) | −8.22898 | −0.384515 | ||||||||
\(459\) | −4.93865 | −0.230517 | ||||||||
\(460\) | −1.92074 | −0.0895548 | ||||||||
\(461\) | 2.54139 | 0.118364 | 0.0591822 | − | 0.998247i | \(-0.481151\pi\) | ||||
0.0591822 | + | 0.998247i | \(0.481151\pi\) | |||||||
\(462\) | −7.91294 | −0.368143 | ||||||||
\(463\) | 4.86610 | 0.226147 | 0.113074 | − | 0.993587i | \(-0.463930\pi\) | ||||
0.113074 | + | 0.993587i | \(0.463930\pi\) | |||||||
\(464\) | 8.84824 | 0.410769 | ||||||||
\(465\) | 5.24578 | 0.243267 | ||||||||
\(466\) | 8.26640 | 0.382934 | ||||||||
\(467\) | −23.3242 | −1.07932 | −0.539659 | − | 0.841884i | \(-0.681447\pi\) | ||||
−0.539659 | + | 0.841884i | \(0.681447\pi\) | |||||||
\(468\) | 11.1962 | 0.517542 | ||||||||
\(469\) | −12.2529 | −0.565788 | ||||||||
\(470\) | 1.49579 | 0.0689957 | ||||||||
\(471\) | 47.0806 | 2.16936 | ||||||||
\(472\) | −24.6822 | −1.13609 | ||||||||
\(473\) | −6.49093 | −0.298453 | ||||||||
\(474\) | −2.39953 | −0.110214 | ||||||||
\(475\) | 18.9355 | 0.868821 | ||||||||
\(476\) | −15.2517 | −0.699060 | ||||||||
\(477\) | 9.83051 | 0.450108 | ||||||||
\(478\) | −4.88451 | −0.223412 | ||||||||
\(479\) | −14.5582 | −0.665183 | −0.332591 | − | 0.943071i | \(-0.607923\pi\) | ||||
−0.332591 | + | 0.943071i | \(0.607923\pi\) | |||||||
\(480\) | −4.05192 | −0.184944 | ||||||||
\(481\) | −15.2513 | −0.695401 | ||||||||
\(482\) | −16.9927 | −0.773996 | ||||||||
\(483\) | 53.6439 | 2.44088 | ||||||||
\(484\) | −1.48953 | −0.0677058 | ||||||||
\(485\) | −2.79998 | −0.127140 | ||||||||
\(486\) | −15.5991 | −0.707588 | ||||||||
\(487\) | 11.8275 | 0.535954 | 0.267977 | − | 0.963425i | \(-0.413645\pi\) | ||||
0.267977 | + | 0.963425i | \(0.413645\pi\) | |||||||
\(488\) | 34.7038 | 1.57097 | ||||||||
\(489\) | 23.5677 | 1.06577 | ||||||||
\(490\) | −2.10614 | −0.0951458 | ||||||||
\(491\) | −14.3248 | −0.646468 | −0.323234 | − | 0.946319i | \(-0.604770\pi\) | ||||
−0.323234 | + | 0.946319i | \(0.604770\pi\) | |||||||
\(492\) | −13.0455 | −0.588138 | ||||||||
\(493\) | −17.7930 | −0.801358 | ||||||||
\(494\) | 5.44768 | 0.245103 | ||||||||
\(495\) | −1.00821 | −0.0453159 | ||||||||
\(496\) | −9.05908 | −0.406765 | ||||||||
\(497\) | 9.55127 | 0.428433 | ||||||||
\(498\) | −15.0990 | −0.676601 | ||||||||
\(499\) | −1.55205 | −0.0694791 | −0.0347396 | − | 0.999396i | \(-0.511060\pi\) | ||||
−0.0347396 | + | 0.999396i | \(0.511060\pi\) | |||||||
\(500\) | −3.93740 | −0.176086 | ||||||||
\(501\) | 22.9460 | 1.02515 | ||||||||
\(502\) | −12.5954 | −0.562160 | ||||||||
\(503\) | 18.8718 | 0.841451 | 0.420726 | − | 0.907188i | \(-0.361775\pi\) | ||||
0.420726 | + | 0.907188i | \(0.361775\pi\) | |||||||
\(504\) | 40.1390 | 1.78793 | ||||||||
\(505\) | −3.66352 | −0.163024 | ||||||||
\(506\) | −3.46063 | −0.153844 | ||||||||
\(507\) | −23.6045 | −1.04831 | ||||||||
\(508\) | 28.2979 | 1.25552 | ||||||||
\(509\) | 26.1357 | 1.15844 | 0.579222 | − | 0.815170i | \(-0.303356\pi\) | ||||
0.579222 | + | 0.815170i | \(0.303356\pi\) | |||||||
\(510\) | 1.19354 | 0.0528507 | ||||||||
\(511\) | 7.17505 | 0.317406 | ||||||||
\(512\) | 12.9698 | 0.573187 | ||||||||
\(513\) | −7.87694 | −0.347776 | ||||||||
\(514\) | 15.4564 | 0.681752 | ||||||||
\(515\) | −0.872841 | −0.0384619 | ||||||||
\(516\) | 25.1881 | 1.10885 | ||||||||
\(517\) | −7.86384 | −0.345851 | ||||||||
\(518\) | −23.3392 | −1.02547 | ||||||||
\(519\) | −12.4368 | −0.545916 | ||||||||
\(520\) | −1.31741 | −0.0577723 | ||||||||
\(521\) | −19.2406 | −0.842946 | −0.421473 | − | 0.906841i | \(-0.638487\pi\) | ||||
−0.421473 | + | 0.906841i | \(0.638487\pi\) | |||||||
\(522\) | 19.9885 | 0.874873 | ||||||||
\(523\) | 42.4943 | 1.85815 | 0.929073 | − | 0.369897i | \(-0.120607\pi\) | ||||
0.929073 | + | 0.369897i | \(0.120607\pi\) | |||||||
\(524\) | −1.48953 | −0.0650703 | ||||||||
\(525\) | 54.5910 | 2.38255 | ||||||||
\(526\) | 1.64740 | 0.0718300 | ||||||||
\(527\) | 18.2170 | 0.793546 | ||||||||
\(528\) | 3.12037 | 0.135797 | ||||||||
\(529\) | 0.460505 | 0.0200220 | ||||||||
\(530\) | −0.493754 | −0.0214473 | ||||||||
\(531\) | 37.4915 | 1.62699 | ||||||||
\(532\) | −24.3258 | −1.05466 | ||||||||
\(533\) | −6.67253 | −0.289019 | ||||||||
\(534\) | 11.4878 | 0.497124 | ||||||||
\(535\) | −0.761572 | −0.0329256 | ||||||||
\(536\) | −7.18592 | −0.310385 | ||||||||
\(537\) | −24.3113 | −1.04911 | ||||||||
\(538\) | −5.91503 | −0.255015 | ||||||||
\(539\) | 11.0726 | 0.476932 | ||||||||
\(540\) | 0.813110 | 0.0349907 | ||||||||
\(541\) | −17.9628 | −0.772280 | −0.386140 | − | 0.922440i | \(-0.626192\pi\) | ||||
−0.386140 | + | 0.922440i | \(0.626192\pi\) | |||||||
\(542\) | −8.33118 | −0.357855 | ||||||||
\(543\) | −25.1429 | −1.07899 | ||||||||
\(544\) | −14.0711 | −0.603294 | ||||||||
\(545\) | 3.01999 | 0.129362 | ||||||||
\(546\) | 15.7056 | 0.672140 | ||||||||
\(547\) | 12.4288 | 0.531419 | 0.265709 | − | 0.964053i | \(-0.414394\pi\) | ||||
0.265709 | + | 0.964053i | \(0.414394\pi\) | |||||||
\(548\) | −31.9715 | −1.36575 | ||||||||
\(549\) | −52.7140 | −2.24978 | ||||||||
\(550\) | −3.52173 | −0.150167 | ||||||||
\(551\) | −28.3791 | −1.20899 | ||||||||
\(552\) | 31.4603 | 1.33904 | ||||||||
\(553\) | 5.48036 | 0.233049 | ||||||||
\(554\) | −13.0090 | −0.552698 | ||||||||
\(555\) | −5.32943 | −0.226222 | ||||||||
\(556\) | −6.27763 | −0.266231 | ||||||||
\(557\) | −22.8075 | −0.966386 | −0.483193 | − | 0.875514i | \(-0.660523\pi\) | ||||
−0.483193 | + | 0.875514i | \(0.660523\pi\) | |||||||
\(558\) | −20.4648 | −0.866344 | ||||||||
\(559\) | 12.8832 | 0.544902 | ||||||||
\(560\) | 1.35558 | 0.0572838 | ||||||||
\(561\) | −6.27479 | −0.264922 | ||||||||
\(562\) | −7.13470 | −0.300959 | ||||||||
\(563\) | 28.9191 | 1.21879 | 0.609397 | − | 0.792865i | \(-0.291412\pi\) | ||||
0.609397 | + | 0.792865i | \(0.291412\pi\) | |||||||
\(564\) | 30.5157 | 1.28494 | ||||||||
\(565\) | −0.658850 | −0.0277180 | ||||||||
\(566\) | 7.97849 | 0.335361 | ||||||||
\(567\) | 25.5894 | 1.07465 | ||||||||
\(568\) | 5.60149 | 0.235033 | ||||||||
\(569\) | −33.0466 | −1.38539 | −0.692693 | − | 0.721232i | \(-0.743576\pi\) | ||||
−0.692693 | + | 0.721232i | \(0.743576\pi\) | |||||||
\(570\) | 1.90364 | 0.0797348 | ||||||||
\(571\) | −7.45509 | −0.311986 | −0.155993 | − | 0.987758i | \(-0.549858\pi\) | ||||
−0.155993 | + | 0.987758i | \(0.549858\pi\) | |||||||
\(572\) | 2.95642 | 0.123614 | ||||||||
\(573\) | 55.6599 | 2.32523 | ||||||||
\(574\) | −10.2110 | −0.426200 | ||||||||
\(575\) | 23.8747 | 0.995645 | ||||||||
\(576\) | 6.73544 | 0.280643 | ||||||||
\(577\) | −30.8478 | −1.28421 | −0.642105 | − | 0.766617i | \(-0.721939\pi\) | ||||
−0.642105 | + | 0.766617i | \(0.721939\pi\) | |||||||
\(578\) | −8.00126 | −0.332808 | ||||||||
\(579\) | −5.14857 | −0.213967 | ||||||||
\(580\) | 2.92948 | 0.121640 | ||||||||
\(581\) | 34.4851 | 1.43068 | ||||||||
\(582\) | 19.5763 | 0.811464 | ||||||||
\(583\) | 2.59581 | 0.107508 | ||||||||
\(584\) | 4.20792 | 0.174125 | ||||||||
\(585\) | 2.00111 | 0.0827357 | ||||||||
\(586\) | −14.0090 | −0.578705 | ||||||||
\(587\) | 18.9140 | 0.780663 | 0.390332 | − | 0.920674i | \(-0.372360\pi\) | ||||
0.390332 | + | 0.920674i | \(0.372360\pi\) | |||||||
\(588\) | −42.9675 | −1.77195 | ||||||||
\(589\) | 29.0554 | 1.19721 | ||||||||
\(590\) | −1.88307 | −0.0775249 | ||||||||
\(591\) | 2.82895 | 0.116367 | ||||||||
\(592\) | 9.20354 | 0.378263 | ||||||||
\(593\) | 3.62157 | 0.148720 | 0.0743600 | − | 0.997231i | \(-0.476309\pi\) | ||||
0.0743600 | + | 0.997231i | \(0.476309\pi\) | |||||||
\(594\) | 1.46500 | 0.0601095 | ||||||||
\(595\) | −2.72596 | −0.111753 | ||||||||
\(596\) | 17.9999 | 0.737303 | ||||||||
\(597\) | −7.41718 | −0.303565 | ||||||||
\(598\) | 6.86867 | 0.280881 | ||||||||
\(599\) | 23.1218 | 0.944731 | 0.472366 | − | 0.881403i | \(-0.343400\pi\) | ||||
0.472366 | + | 0.881403i | \(0.343400\pi\) | |||||||
\(600\) | 32.0157 | 1.30704 | ||||||||
\(601\) | 31.8636 | 1.29974 | 0.649872 | − | 0.760044i | \(-0.274823\pi\) | ||||
0.649872 | + | 0.760044i | \(0.274823\pi\) | |||||||
\(602\) | 19.7153 | 0.803536 | ||||||||
\(603\) | 10.9152 | 0.444502 | ||||||||
\(604\) | 24.8055 | 1.00932 | ||||||||
\(605\) | −0.266226 | −0.0108236 | ||||||||
\(606\) | 25.6138 | 1.04049 | ||||||||
\(607\) | 1.26037 | 0.0511567 | 0.0255784 | − | 0.999673i | \(-0.491857\pi\) | ||||
0.0255784 | + | 0.999673i | \(0.491857\pi\) | |||||||
\(608\) | −22.4428 | −0.910176 | ||||||||
\(609\) | −81.8170 | −3.31539 | ||||||||
\(610\) | 2.64765 | 0.107200 | ||||||||
\(611\) | 15.6082 | 0.631440 | ||||||||
\(612\) | 13.5866 | 0.549204 | ||||||||
\(613\) | −46.8958 | −1.89410 | −0.947052 | − | 0.321081i | \(-0.895954\pi\) | ||||
−0.947052 | + | 0.321081i | \(0.895954\pi\) | |||||||
\(614\) | 17.0069 | 0.686342 | ||||||||
\(615\) | −2.33165 | −0.0940213 | ||||||||
\(616\) | 10.5990 | 0.427045 | ||||||||
\(617\) | 3.67254 | 0.147851 | 0.0739253 | − | 0.997264i | \(-0.476447\pi\) | ||||
0.0739253 | + | 0.997264i | \(0.476447\pi\) | |||||||
\(618\) | 6.10255 | 0.245481 | ||||||||
\(619\) | 0.370412 | 0.0148881 | 0.00744405 | − | 0.999972i | \(-0.497630\pi\) | ||||
0.00744405 | + | 0.999972i | \(0.497630\pi\) | |||||||
\(620\) | −2.99929 | −0.120454 | ||||||||
\(621\) | −9.93159 | −0.398541 | ||||||||
\(622\) | −17.7987 | −0.713662 | ||||||||
\(623\) | −26.2373 | −1.05117 | ||||||||
\(624\) | −6.19332 | −0.247931 | ||||||||
\(625\) | 23.9419 | 0.957675 | ||||||||
\(626\) | 15.0956 | 0.603341 | ||||||||
\(627\) | −10.0080 | −0.399682 | ||||||||
\(628\) | −26.9184 | −1.07416 | ||||||||
\(629\) | −18.5075 | −0.737943 | ||||||||
\(630\) | 3.06231 | 0.122006 | ||||||||
\(631\) | 4.35362 | 0.173315 | 0.0866574 | − | 0.996238i | \(-0.472381\pi\) | ||||
0.0866574 | + | 0.996238i | \(0.472381\pi\) | |||||||
\(632\) | 3.21404 | 0.127848 | ||||||||
\(633\) | −32.3913 | −1.28744 | ||||||||
\(634\) | −15.9171 | −0.632149 | ||||||||
\(635\) | 5.05773 | 0.200710 | ||||||||
\(636\) | −10.0731 | −0.399424 | ||||||||
\(637\) | −21.9770 | −0.870761 | ||||||||
\(638\) | 5.27810 | 0.208962 | ||||||||
\(639\) | −8.50850 | −0.336591 | ||||||||
\(640\) | 2.77234 | 0.109587 | ||||||||
\(641\) | 39.9828 | 1.57922 | 0.789612 | − | 0.613606i | \(-0.210282\pi\) | ||||
0.789612 | + | 0.613606i | \(0.210282\pi\) | |||||||
\(642\) | 5.32461 | 0.210146 | ||||||||
\(643\) | −3.38648 | −0.133550 | −0.0667749 | − | 0.997768i | \(-0.521271\pi\) | ||||
−0.0667749 | + | 0.997768i | \(0.521271\pi\) | |||||||
\(644\) | −30.6710 | −1.20861 | ||||||||
\(645\) | 4.50192 | 0.177263 | ||||||||
\(646\) | 6.61077 | 0.260097 | ||||||||
\(647\) | −28.0366 | −1.10223 | −0.551116 | − | 0.834429i | \(-0.685798\pi\) | ||||
−0.551116 | + | 0.834429i | \(0.685798\pi\) | |||||||
\(648\) | 15.0073 | 0.589542 | ||||||||
\(649\) | 9.89990 | 0.388605 | ||||||||
\(650\) | 6.98995 | 0.274168 | ||||||||
\(651\) | 83.7666 | 3.28307 | ||||||||
\(652\) | −13.4749 | −0.527716 | ||||||||
\(653\) | −39.0063 | −1.52644 | −0.763218 | − | 0.646141i | \(-0.776382\pi\) | ||||
−0.763218 | + | 0.646141i | \(0.776382\pi\) | |||||||
\(654\) | −21.1145 | −0.825644 | ||||||||
\(655\) | −0.266226 | −0.0104023 | ||||||||
\(656\) | 4.02659 | 0.157212 | ||||||||
\(657\) | −6.39170 | −0.249364 | ||||||||
\(658\) | 23.8853 | 0.931147 | ||||||||
\(659\) | −4.52931 | −0.176437 | −0.0882184 | − | 0.996101i | \(-0.528117\pi\) | ||||
−0.0882184 | + | 0.996101i | \(0.528117\pi\) | |||||||
\(660\) | 1.03309 | 0.0402131 | ||||||||
\(661\) | −0.350350 | −0.0136270 | −0.00681351 | − | 0.999977i | \(-0.502169\pi\) | ||||
−0.00681351 | + | 0.999977i | \(0.502169\pi\) | |||||||
\(662\) | −17.3020 | −0.672461 | ||||||||
\(663\) | 12.4542 | 0.483683 | ||||||||
\(664\) | 20.2243 | 0.784855 | ||||||||
\(665\) | −4.34779 | −0.168600 | ||||||||
\(666\) | 20.7911 | 0.805641 | ||||||||
\(667\) | −35.7817 | −1.38547 | ||||||||
\(668\) | −13.1194 | −0.507605 | ||||||||
\(669\) | −8.34050 | −0.322462 | ||||||||
\(670\) | −0.548235 | −0.0211801 | ||||||||
\(671\) | −13.9195 | −0.537356 | ||||||||
\(672\) | −64.7025 | −2.49595 | ||||||||
\(673\) | −51.6049 | −1.98922 | −0.994611 | − | 0.103681i | \(-0.966938\pi\) | ||||
−0.994611 | + | 0.103681i | \(0.966938\pi\) | |||||||
\(674\) | 14.4975 | 0.558424 | ||||||||
\(675\) | −10.1069 | −0.389016 | ||||||||
\(676\) | 13.4959 | 0.519074 | ||||||||
\(677\) | −29.7237 | −1.14238 | −0.571188 | − | 0.820820i | \(-0.693517\pi\) | ||||
−0.571188 | + | 0.820820i | \(0.693517\pi\) | |||||||
\(678\) | 4.60642 | 0.176908 | ||||||||
\(679\) | −44.7110 | −1.71585 | ||||||||
\(680\) | −1.59868 | −0.0613066 | ||||||||
\(681\) | 44.0955 | 1.68974 | ||||||||
\(682\) | −5.40387 | −0.206925 | ||||||||
\(683\) | 31.8490 | 1.21867 | 0.609335 | − | 0.792913i | \(-0.291437\pi\) | ||||
0.609335 | + | 0.792913i | \(0.291437\pi\) | |||||||
\(684\) | 21.6700 | 0.828572 | ||||||||
\(685\) | −5.71432 | −0.218333 | ||||||||
\(686\) | −12.3701 | −0.472292 | ||||||||
\(687\) | −30.0055 | −1.14478 | ||||||||
\(688\) | −7.77448 | −0.296399 | ||||||||
\(689\) | −5.15219 | −0.196283 | ||||||||
\(690\) | 2.40019 | 0.0913738 | ||||||||
\(691\) | −48.1853 | −1.83306 | −0.916528 | − | 0.399971i | \(-0.869020\pi\) | ||||
−0.916528 | + | 0.399971i | \(0.869020\pi\) | |||||||
\(692\) | 7.11077 | 0.270311 | ||||||||
\(693\) | −16.0995 | −0.611571 | ||||||||
\(694\) | 0.741846 | 0.0281601 | ||||||||
\(695\) | −1.12201 | −0.0425603 | ||||||||
\(696\) | −47.9828 | −1.81878 | ||||||||
\(697\) | −8.09713 | −0.306701 | ||||||||
\(698\) | 8.33278 | 0.315400 | ||||||||
\(699\) | 30.1419 | 1.14007 | ||||||||
\(700\) | −31.2125 | −1.17972 | ||||||||
\(701\) | 18.3989 | 0.694918 | 0.347459 | − | 0.937695i | \(-0.387045\pi\) | ||||
0.347459 | + | 0.937695i | \(0.387045\pi\) | |||||||
\(702\) | −2.90773 | −0.109745 | ||||||||
\(703\) | −29.5187 | −1.11332 | ||||||||
\(704\) | 1.77854 | 0.0670312 | ||||||||
\(705\) | 5.45413 | 0.205415 | ||||||||
\(706\) | 2.69235 | 0.101328 | ||||||||
\(707\) | −58.5003 | −2.20013 | ||||||||
\(708\) | −38.4167 | −1.44379 | ||||||||
\(709\) | 4.91804 | 0.184701 | 0.0923505 | − | 0.995727i | \(-0.470562\pi\) | ||||
0.0923505 | + | 0.995727i | \(0.470562\pi\) | |||||||
\(710\) | 0.427353 | 0.0160383 | ||||||||
\(711\) | −4.88204 | −0.183091 | ||||||||
\(712\) | −15.3872 | −0.576661 | ||||||||
\(713\) | 36.6343 | 1.37196 | ||||||||
\(714\) | 19.0588 | 0.713259 | ||||||||
\(715\) | 0.528407 | 0.0197613 | ||||||||
\(716\) | 13.9000 | 0.519468 | ||||||||
\(717\) | −17.8105 | −0.665144 | ||||||||
\(718\) | −14.0000 | −0.522477 | ||||||||
\(719\) | −30.6686 | −1.14375 | −0.571873 | − | 0.820342i | \(-0.693783\pi\) | ||||
−0.571873 | + | 0.820342i | \(0.693783\pi\) | |||||||
\(720\) | −1.20759 | −0.0450041 | ||||||||
\(721\) | −13.9378 | −0.519072 | ||||||||
\(722\) | −3.03110 | −0.112806 | ||||||||
\(723\) | −61.9608 | −2.30435 | ||||||||
\(724\) | 14.3755 | 0.534262 | ||||||||
\(725\) | −36.4134 | −1.35236 | ||||||||
\(726\) | 1.86135 | 0.0690810 | ||||||||
\(727\) | −25.9818 | −0.963610 | −0.481805 | − | 0.876278i | \(-0.660019\pi\) | ||||
−0.481805 | + | 0.876278i | \(0.660019\pi\) | |||||||
\(728\) | −21.0369 | −0.779679 | ||||||||
\(729\) | −38.8212 | −1.43782 | ||||||||
\(730\) | 0.321034 | 0.0118820 | ||||||||
\(731\) | 15.6338 | 0.578238 | ||||||||
\(732\) | 54.0148 | 1.99645 | ||||||||
\(733\) | 12.5535 | 0.463676 | 0.231838 | − | 0.972754i | \(-0.425526\pi\) | ||||
0.231838 | + | 0.972754i | \(0.425526\pi\) | |||||||
\(734\) | 21.3360 | 0.787525 | ||||||||
\(735\) | −7.67966 | −0.283269 | ||||||||
\(736\) | −28.2969 | −1.04304 | ||||||||
\(737\) | 2.88224 | 0.106169 | ||||||||
\(738\) | 9.09623 | 0.334837 | ||||||||
\(739\) | 34.5797 | 1.27203 | 0.636017 | − | 0.771675i | \(-0.280581\pi\) | ||||
0.636017 | + | 0.771675i | \(0.280581\pi\) | |||||||
\(740\) | 3.04711 | 0.112014 | ||||||||
\(741\) | 19.8640 | 0.729722 | ||||||||
\(742\) | −7.88444 | −0.289447 | ||||||||
\(743\) | −53.7937 | −1.97350 | −0.986749 | − | 0.162254i | \(-0.948124\pi\) | ||||
−0.986749 | + | 0.162254i | \(0.948124\pi\) | |||||||
\(744\) | 49.1262 | 1.80105 | ||||||||
\(745\) | 3.21715 | 0.117867 | ||||||||
\(746\) | −17.5623 | −0.643003 | ||||||||
\(747\) | −30.7201 | −1.12399 | ||||||||
\(748\) | 3.58762 | 0.131177 | ||||||||
\(749\) | −12.1611 | −0.444355 | ||||||||
\(750\) | 4.92027 | 0.179663 | ||||||||
\(751\) | 8.65830 | 0.315946 | 0.157973 | − | 0.987443i | \(-0.449504\pi\) | ||||
0.157973 | + | 0.987443i | \(0.449504\pi\) | |||||||
\(752\) | −9.41888 | −0.343471 | ||||||||
\(753\) | −45.9268 | −1.67367 | ||||||||
\(754\) | −10.4760 | −0.381514 | ||||||||
\(755\) | 4.43353 | 0.161353 | ||||||||
\(756\) | 12.9840 | 0.472224 | ||||||||
\(757\) | 38.9883 | 1.41705 | 0.708527 | − | 0.705684i | \(-0.249360\pi\) | ||||
0.708527 | + | 0.705684i | \(0.249360\pi\) | |||||||
\(758\) | −19.6509 | −0.713754 | ||||||||
\(759\) | −12.6186 | −0.458025 | ||||||||
\(760\) | −2.54983 | −0.0924920 | ||||||||
\(761\) | −11.7092 | −0.424458 | −0.212229 | − | 0.977220i | \(-0.568072\pi\) | ||||
−0.212229 | + | 0.977220i | \(0.568072\pi\) | |||||||
\(762\) | −35.3617 | −1.28102 | ||||||||
\(763\) | 48.2242 | 1.74583 | ||||||||
\(764\) | −31.8237 | −1.15134 | ||||||||
\(765\) | 2.42835 | 0.0877972 | ||||||||
\(766\) | −9.14615 | −0.330464 | ||||||||
\(767\) | −19.6494 | −0.709498 | ||||||||
\(768\) | −28.6500 | −1.03382 | ||||||||
\(769\) | 31.3179 | 1.12935 | 0.564676 | − | 0.825313i | \(-0.309001\pi\) | ||||
0.564676 | + | 0.825313i | \(0.309001\pi\) | |||||||
\(770\) | 0.808625 | 0.0291408 | ||||||||
\(771\) | 56.3589 | 2.02972 | ||||||||
\(772\) | 2.94371 | 0.105946 | ||||||||
\(773\) | −33.1955 | −1.19396 | −0.596980 | − | 0.802256i | \(-0.703633\pi\) | ||||
−0.596980 | + | 0.802256i | \(0.703633\pi\) | |||||||
\(774\) | −17.5629 | −0.631284 | ||||||||
\(775\) | 37.2811 | 1.33918 | ||||||||
\(776\) | −26.2214 | −0.941295 | ||||||||
\(777\) | −85.1023 | −3.05303 | ||||||||
\(778\) | 18.8953 | 0.677430 | ||||||||
\(779\) | −12.9146 | −0.462713 | ||||||||
\(780\) | −2.05049 | −0.0734193 | ||||||||
\(781\) | −2.24673 | −0.0803942 | ||||||||
\(782\) | 8.33515 | 0.298064 | ||||||||
\(783\) | 15.1475 | 0.541329 | ||||||||
\(784\) | 13.2622 | 0.473650 | ||||||||
\(785\) | −4.81118 | −0.171718 | ||||||||
\(786\) | 1.86135 | 0.0663920 | ||||||||
\(787\) | −22.0869 | −0.787311 | −0.393656 | − | 0.919258i | \(-0.628790\pi\) | ||||
−0.393656 | + | 0.919258i | \(0.628790\pi\) | |||||||
\(788\) | −1.61746 | −0.0576195 | ||||||||
\(789\) | 6.00694 | 0.213853 | ||||||||
\(790\) | 0.245208 | 0.00872412 | ||||||||
\(791\) | −10.5208 | −0.374075 | ||||||||
\(792\) | −9.44181 | −0.335500 | ||||||||
\(793\) | 27.6275 | 0.981081 | ||||||||
\(794\) | −6.95108 | −0.246685 | ||||||||
\(795\) | −1.80038 | −0.0638530 | ||||||||
\(796\) | 4.24079 | 0.150311 | ||||||||
\(797\) | −15.1330 | −0.536038 | −0.268019 | − | 0.963414i | \(-0.586369\pi\) | ||||
−0.268019 | + | 0.963414i | \(0.586369\pi\) | |||||||
\(798\) | 30.3980 | 1.07608 | ||||||||
\(799\) | 18.9406 | 0.670069 | ||||||||
\(800\) | −28.7965 | −1.01811 | ||||||||
\(801\) | 23.3728 | 0.825837 | ||||||||
\(802\) | −14.4113 | −0.508881 | ||||||||
\(803\) | −1.68777 | −0.0595602 | ||||||||
\(804\) | −11.1846 | −0.394449 | ||||||||
\(805\) | −5.48188 | −0.193211 | ||||||||
\(806\) | 10.7256 | 0.377795 | ||||||||
\(807\) | −21.5681 | −0.759233 | ||||||||
\(808\) | −34.3084 | −1.20697 | ||||||||
\(809\) | −1.66364 | −0.0584904 | −0.0292452 | − | 0.999572i | \(-0.509310\pi\) | ||||
−0.0292452 | + | 0.999572i | \(0.509310\pi\) | |||||||
\(810\) | 1.14495 | 0.0402294 | ||||||||
\(811\) | −29.3003 | −1.02887 | −0.514436 | − | 0.857529i | \(-0.671999\pi\) | ||||
−0.514436 | + | 0.857529i | \(0.671999\pi\) | |||||||
\(812\) | 46.7790 | 1.64162 | ||||||||
\(813\) | −30.3782 | −1.06541 | ||||||||
\(814\) | 5.49005 | 0.192426 | ||||||||
\(815\) | −2.40839 | −0.0843621 | ||||||||
\(816\) | −7.51561 | −0.263099 | ||||||||
\(817\) | 24.9353 | 0.872375 | ||||||||
\(818\) | −25.9356 | −0.906817 | ||||||||
\(819\) | 31.9544 | 1.11658 | ||||||||
\(820\) | 1.33313 | 0.0465548 | ||||||||
\(821\) | 7.42566 | 0.259157 | 0.129579 | − | 0.991569i | \(-0.458638\pi\) | ||||
0.129579 | + | 0.991569i | \(0.458638\pi\) | |||||||
\(822\) | 39.9523 | 1.39350 | ||||||||
\(823\) | 54.3346 | 1.89399 | 0.946993 | − | 0.321254i | \(-0.104104\pi\) | ||||
0.946993 | + | 0.321254i | \(0.104104\pi\) | |||||||
\(824\) | −8.17405 | −0.284757 | ||||||||
\(825\) | −12.8413 | −0.447078 | ||||||||
\(826\) | −30.0696 | −1.04626 | ||||||||
\(827\) | −24.3212 | −0.845730 | −0.422865 | − | 0.906193i | \(-0.638975\pi\) | ||||
−0.422865 | + | 0.906193i | \(0.638975\pi\) | |||||||
\(828\) | 27.3225 | 0.949521 | ||||||||
\(829\) | −14.6214 | −0.507821 | −0.253910 | − | 0.967228i | \(-0.581717\pi\) | ||||
−0.253910 | + | 0.967228i | \(0.581717\pi\) | |||||||
\(830\) | 1.54297 | 0.0535572 | ||||||||
\(831\) | −47.4349 | −1.64550 | ||||||||
\(832\) | −3.53006 | −0.122383 | ||||||||
\(833\) | −26.6692 | −0.924032 | ||||||||
\(834\) | 7.84466 | 0.271638 | ||||||||
\(835\) | −2.34486 | −0.0811471 | ||||||||
\(836\) | 5.72211 | 0.197903 | ||||||||
\(837\) | −15.5085 | −0.536051 | ||||||||
\(838\) | 24.1539 | 0.834382 | ||||||||
\(839\) | −32.5592 | −1.12407 | −0.562034 | − | 0.827114i | \(-0.689981\pi\) | ||||
−0.562034 | + | 0.827114i | \(0.689981\pi\) | |||||||
\(840\) | −7.35114 | −0.253639 | ||||||||
\(841\) | 25.5737 | 0.881852 | ||||||||
\(842\) | 13.0056 | 0.448204 | ||||||||
\(843\) | −26.0154 | −0.896018 | ||||||||
\(844\) | 18.5198 | 0.637476 | ||||||||
\(845\) | 2.41215 | 0.0829806 | ||||||||
\(846\) | −21.2776 | −0.731540 | ||||||||
\(847\) | −4.25119 | −0.146073 | ||||||||
\(848\) | 3.10913 | 0.106768 | ||||||||
\(849\) | 29.0921 | 0.998439 | ||||||||
\(850\) | 8.48231 | 0.290941 | ||||||||
\(851\) | −37.2185 | −1.27583 | ||||||||
\(852\) | 8.71846 | 0.298690 | ||||||||
\(853\) | −40.7002 | −1.39355 | −0.696773 | − | 0.717291i | \(-0.745382\pi\) | ||||
−0.696773 | + | 0.717291i | \(0.745382\pi\) | |||||||
\(854\) | 42.2786 | 1.44674 | ||||||||
\(855\) | 3.87312 | 0.132458 | ||||||||
\(856\) | −7.13203 | −0.243768 | ||||||||
\(857\) | 46.5073 | 1.58866 | 0.794330 | − | 0.607486i | \(-0.207822\pi\) | ||||
0.794330 | + | 0.607486i | \(0.207822\pi\) | |||||||
\(858\) | −3.69441 | −0.126125 | ||||||||
\(859\) | −2.91381 | −0.0994178 | −0.0497089 | − | 0.998764i | \(-0.515829\pi\) | ||||
−0.0497089 | + | 0.998764i | \(0.515829\pi\) | |||||||
\(860\) | −2.57398 | −0.0877721 | ||||||||
\(861\) | −37.2327 | −1.26889 | ||||||||
\(862\) | −16.3568 | −0.557115 | ||||||||
\(863\) | −2.91705 | −0.0992975 | −0.0496488 | − | 0.998767i | \(-0.515810\pi\) | ||||
−0.0496488 | + | 0.998767i | \(0.515810\pi\) | |||||||
\(864\) | 11.9790 | 0.407533 | ||||||||
\(865\) | 1.27092 | 0.0432126 | ||||||||
\(866\) | 7.69556 | 0.261506 | ||||||||
\(867\) | −29.1751 | −0.990840 | ||||||||
\(868\) | −47.8937 | −1.62562 | ||||||||
\(869\) | −1.28914 | −0.0437309 | ||||||||
\(870\) | −3.66074 | −0.124111 | ||||||||
\(871\) | −5.72068 | −0.193838 | ||||||||
\(872\) | 28.2818 | 0.957743 | ||||||||
\(873\) | 39.8296 | 1.34803 | ||||||||
\(874\) | 13.2942 | 0.449683 | ||||||||
\(875\) | −11.2376 | −0.379899 | ||||||||
\(876\) | 6.54943 | 0.221285 | ||||||||
\(877\) | 30.6741 | 1.03579 | 0.517896 | − | 0.855444i | \(-0.326715\pi\) | ||||
0.517896 | + | 0.855444i | \(0.326715\pi\) | |||||||
\(878\) | 26.1110 | 0.881205 | ||||||||
\(879\) | −51.0812 | −1.72293 | ||||||||
\(880\) | −0.318871 | −0.0107491 | ||||||||
\(881\) | 11.6939 | 0.393976 | 0.196988 | − | 0.980406i | \(-0.436884\pi\) | ||||
0.196988 | + | 0.980406i | \(0.436884\pi\) | |||||||
\(882\) | 29.9598 | 1.00880 | ||||||||
\(883\) | −26.5476 | −0.893399 | −0.446699 | − | 0.894684i | \(-0.647401\pi\) | ||||
−0.446699 | + | 0.894684i | \(0.647401\pi\) | |||||||
\(884\) | −7.12074 | −0.239496 | ||||||||
\(885\) | −6.86629 | −0.230808 | ||||||||
\(886\) | −15.9220 | −0.534910 | ||||||||
\(887\) | 17.0043 | 0.570947 | 0.285473 | − | 0.958387i | \(-0.407849\pi\) | ||||
0.285473 | + | 0.958387i | \(0.407849\pi\) | |||||||
\(888\) | −49.9095 | −1.67485 | ||||||||
\(889\) | 80.7637 | 2.70873 | ||||||||
\(890\) | −1.17394 | −0.0393504 | ||||||||
\(891\) | −6.01934 | −0.201656 | ||||||||
\(892\) | 4.76870 | 0.159668 | ||||||||
\(893\) | 30.2094 | 1.01092 | ||||||||
\(894\) | −22.4930 | −0.752279 | ||||||||
\(895\) | 2.48437 | 0.0830435 | ||||||||
\(896\) | 44.2698 | 1.47895 | ||||||||
\(897\) | 25.0454 | 0.836241 | ||||||||
\(898\) | −20.3721 | −0.679825 | ||||||||
\(899\) | −55.8741 | −1.86351 | ||||||||
\(900\) | 27.8049 | 0.926829 | ||||||||
\(901\) | −6.25219 | −0.208291 | ||||||||
\(902\) | 2.40192 | 0.0799752 | ||||||||
\(903\) | 71.8883 | 2.39229 | ||||||||
\(904\) | −6.17005 | −0.205213 | ||||||||
\(905\) | 2.56936 | 0.0854085 | ||||||||
\(906\) | −30.9975 | −1.02982 | ||||||||
\(907\) | 29.5835 | 0.982304 | 0.491152 | − | 0.871074i | \(-0.336576\pi\) | ||||
0.491152 | + | 0.871074i | \(0.336576\pi\) | |||||||
\(908\) | −25.2117 | −0.836680 | ||||||||
\(909\) | 52.1135 | 1.72849 | ||||||||
\(910\) | −1.60496 | −0.0532040 | ||||||||
\(911\) | −28.2406 | −0.935654 | −0.467827 | − | 0.883820i | \(-0.654963\pi\) | ||||
−0.467827 | + | 0.883820i | \(0.654963\pi\) | |||||||
\(912\) | −11.9871 | −0.396932 | ||||||||
\(913\) | −8.11186 | −0.268463 | ||||||||
\(914\) | 29.4701 | 0.974784 | ||||||||
\(915\) | 9.65417 | 0.319157 | ||||||||
\(916\) | 17.1557 | 0.566840 | ||||||||
\(917\) | −4.25119 | −0.140387 | ||||||||
\(918\) | −3.52854 | −0.116459 | ||||||||
\(919\) | 38.4904 | 1.26968 | 0.634841 | − | 0.772643i | \(-0.281066\pi\) | ||||
0.634841 | + | 0.772643i | \(0.281066\pi\) | |||||||
\(920\) | −3.21493 | −0.105993 | ||||||||
\(921\) | 62.0126 | 2.04338 | ||||||||
\(922\) | 1.81576 | 0.0597988 | ||||||||
\(923\) | 4.45932 | 0.146780 | ||||||||
\(924\) | 16.4968 | 0.542705 | ||||||||
\(925\) | −37.8756 | −1.24534 | ||||||||
\(926\) | 3.47670 | 0.114252 | ||||||||
\(927\) | 12.4162 | 0.407800 | ||||||||
\(928\) | 43.1580 | 1.41673 | ||||||||
\(929\) | −27.9687 | −0.917623 | −0.458812 | − | 0.888534i | \(-0.651725\pi\) | ||||
−0.458812 | + | 0.888534i | \(0.651725\pi\) | |||||||
\(930\) | 3.74797 | 0.122901 | ||||||||
\(931\) | −42.5362 | −1.39407 | ||||||||
\(932\) | −17.2337 | −0.564509 | ||||||||
\(933\) | −64.8997 | −2.12472 | ||||||||
\(934\) | −16.6646 | −0.545281 | ||||||||
\(935\) | 0.641223 | 0.0209702 | ||||||||
\(936\) | 18.7402 | 0.612541 | ||||||||
\(937\) | 19.5560 | 0.638867 | 0.319434 | − | 0.947609i | \(-0.396507\pi\) | ||||
0.319434 | + | 0.947609i | \(0.396507\pi\) | |||||||
\(938\) | −8.75441 | −0.285841 | ||||||||
\(939\) | 55.0434 | 1.79627 | ||||||||
\(940\) | −3.11841 | −0.101711 | ||||||||
\(941\) | 16.1475 | 0.526393 | 0.263196 | − | 0.964742i | \(-0.415223\pi\) | ||||
0.263196 | + | 0.964742i | \(0.415223\pi\) | |||||||
\(942\) | 33.6378 | 1.09598 | ||||||||
\(943\) | −16.2833 | −0.530256 | ||||||||
\(944\) | 11.8576 | 0.385931 | ||||||||
\(945\) | 2.32066 | 0.0754910 | ||||||||
\(946\) | −4.63760 | −0.150781 | ||||||||
\(947\) | −26.2944 | −0.854454 | −0.427227 | − | 0.904144i | \(-0.640509\pi\) | ||||
−0.427227 | + | 0.904144i | \(0.640509\pi\) | |||||||
\(948\) | 5.00251 | 0.162474 | ||||||||
\(949\) | 3.34990 | 0.108742 | ||||||||
\(950\) | 13.5289 | 0.438936 | ||||||||
\(951\) | −58.0388 | −1.88204 | ||||||||
\(952\) | −25.5283 | −0.827377 | ||||||||
\(953\) | 58.3380 | 1.88975 | 0.944876 | − | 0.327428i | \(-0.106182\pi\) | ||||
0.944876 | + | 0.327428i | \(0.106182\pi\) | |||||||
\(954\) | 7.02364 | 0.227399 | ||||||||
\(955\) | −5.68790 | −0.184056 | ||||||||
\(956\) | 10.1832 | 0.329347 | ||||||||
\(957\) | 19.2457 | 0.622124 | ||||||||
\(958\) | −10.4015 | −0.336056 | ||||||||
\(959\) | −91.2483 | −2.94656 | ||||||||
\(960\) | −1.23354 | −0.0398125 | ||||||||
\(961\) | 26.2055 | 0.845340 | ||||||||
\(962\) | −10.8967 | −0.351323 | ||||||||
\(963\) | 10.8334 | 0.349100 | ||||||||
\(964\) | 35.4262 | 1.14100 | ||||||||
\(965\) | 0.526134 | 0.0169369 | ||||||||
\(966\) | 38.3272 | 1.23316 | ||||||||
\(967\) | 25.0975 | 0.807083 | 0.403541 | − | 0.914961i | \(-0.367779\pi\) | ||||
0.403541 | + | 0.914961i | \(0.367779\pi\) | |||||||
\(968\) | −2.49318 | −0.0801337 | ||||||||
\(969\) | 24.1050 | 0.774364 | ||||||||
\(970\) | −2.00051 | −0.0642325 | ||||||||
\(971\) | −53.2720 | −1.70958 | −0.854790 | − | 0.518974i | \(-0.826314\pi\) | ||||
−0.854790 | + | 0.518974i | \(0.826314\pi\) | |||||||
\(972\) | 32.5208 | 1.04310 | ||||||||
\(973\) | −17.9167 | −0.574383 | ||||||||
\(974\) | 8.45042 | 0.270769 | ||||||||
\(975\) | 25.4876 | 0.816256 | ||||||||
\(976\) | −16.6720 | −0.533659 | ||||||||
\(977\) | 51.6324 | 1.65187 | 0.825933 | − | 0.563768i | \(-0.190649\pi\) | ||||
0.825933 | + | 0.563768i | \(0.190649\pi\) | |||||||
\(978\) | 16.8385 | 0.538435 | ||||||||
\(979\) | 6.17174 | 0.197250 | ||||||||
\(980\) | 4.39086 | 0.140261 | ||||||||
\(981\) | −42.9593 | −1.37158 | ||||||||
\(982\) | −10.2347 | −0.326602 | ||||||||
\(983\) | 19.9166 | 0.635242 | 0.317621 | − | 0.948218i | \(-0.397116\pi\) | ||||
0.317621 | + | 0.948218i | \(0.397116\pi\) | |||||||
\(984\) | −21.8357 | −0.696096 | ||||||||
\(985\) | −0.289091 | −0.00921120 | ||||||||
\(986\) | −12.7127 | −0.404854 | ||||||||
\(987\) | 87.0936 | 2.77222 | ||||||||
\(988\) | −11.3573 | −0.361323 | ||||||||
\(989\) | 31.4395 | 0.999717 | ||||||||
\(990\) | −0.720343 | −0.0228940 | ||||||||
\(991\) | −32.4303 | −1.03018 | −0.515092 | − | 0.857135i | \(-0.672242\pi\) | ||||
−0.515092 | + | 0.857135i | \(0.672242\pi\) | |||||||
\(992\) | −44.1864 | −1.40292 | ||||||||
\(993\) | −63.0886 | −2.00206 | ||||||||
\(994\) | 6.82413 | 0.216448 | ||||||||
\(995\) | 0.757964 | 0.0240291 | ||||||||
\(996\) | 31.4782 | 0.997425 | ||||||||
\(997\) | −13.8957 | −0.440082 | −0.220041 | − | 0.975491i | \(-0.570619\pi\) | ||||
−0.220041 | + | 0.975491i | \(0.570619\pi\) | |||||||
\(998\) | −1.10890 | −0.0351015 | ||||||||
\(999\) | 15.7558 | 0.498491 |
(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 | 1441.2.a.c.1.17 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.2.a.c.1.17 | ✓ | 23 | 1.1 | even | 1 | trivial |