Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(66\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.46 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.56669 | 1.10781 | 0.553907 | − | 0.832578i | \(-0.313136\pi\) | ||||
0.553907 | + | 0.832578i | \(0.313136\pi\) | |||||||
\(3\) | 0.629934 | 0.363692 | 0.181846 | − | 0.983327i | \(-0.441793\pi\) | ||||
0.181846 | + | 0.983327i | \(0.441793\pi\) | |||||||
\(4\) | 0.454508 | 0.227254 | ||||||||
\(5\) | −2.16451 | −0.967997 | −0.483998 | − | 0.875069i | \(-0.660816\pi\) | ||||
−0.483998 | + | 0.875069i | \(0.660816\pi\) | |||||||
\(6\) | 0.986909 | 0.402904 | ||||||||
\(7\) | −5.08174 | −1.92072 | −0.960358 | − | 0.278770i | \(-0.910073\pi\) | ||||
−0.960358 | + | 0.278770i | \(0.910073\pi\) | |||||||
\(8\) | −2.42130 | −0.856060 | ||||||||
\(9\) | −2.60318 | −0.867728 | ||||||||
\(10\) | −3.39110 | −1.07236 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.286310 | 0.0826506 | ||||||||
\(13\) | −2.97614 | −0.825433 | −0.412717 | − | 0.910859i | \(-0.635420\pi\) | ||||
−0.412717 | + | 0.910859i | \(0.635420\pi\) | |||||||
\(14\) | −7.96149 | −2.12780 | ||||||||
\(15\) | −1.36350 | −0.352053 | ||||||||
\(16\) | −4.70244 | −1.17561 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −4.07837 | −0.961282 | ||||||||
\(19\) | −6.04783 | −1.38747 | −0.693733 | − | 0.720232i | \(-0.744035\pi\) | ||||
−0.693733 | + | 0.720232i | \(0.744035\pi\) | |||||||
\(20\) | −0.983785 | −0.219981 | ||||||||
\(21\) | −3.20116 | −0.698550 | ||||||||
\(22\) | −1.56669 | −0.334019 | ||||||||
\(23\) | 2.54252 | 0.530151 | 0.265076 | − | 0.964228i | \(-0.414603\pi\) | ||||
0.265076 | + | 0.964228i | \(0.414603\pi\) | |||||||
\(24\) | −1.52526 | −0.311342 | ||||||||
\(25\) | −0.314913 | −0.0629825 | ||||||||
\(26\) | −4.66268 | −0.914428 | ||||||||
\(27\) | −3.52963 | −0.679279 | ||||||||
\(28\) | −2.30969 | −0.436490 | ||||||||
\(29\) | 1.74304 | 0.323675 | 0.161838 | − | 0.986817i | \(-0.448258\pi\) | ||||
0.161838 | + | 0.986817i | \(0.448258\pi\) | |||||||
\(30\) | −2.13617 | −0.390010 | ||||||||
\(31\) | −4.76506 | −0.855829 | −0.427915 | − | 0.903819i | \(-0.640752\pi\) | ||||
−0.427915 | + | 0.903819i | \(0.640752\pi\) | |||||||
\(32\) | −2.52464 | −0.446298 | ||||||||
\(33\) | −0.629934 | −0.109657 | ||||||||
\(34\) | 1.56669 | 0.268685 | ||||||||
\(35\) | 10.9994 | 1.85925 | ||||||||
\(36\) | −1.18317 | −0.197195 | ||||||||
\(37\) | −11.5443 | −1.89786 | −0.948932 | − | 0.315481i | \(-0.897834\pi\) | ||||
−0.948932 | + | 0.315481i | \(0.897834\pi\) | |||||||
\(38\) | −9.47505 | −1.53706 | ||||||||
\(39\) | −1.87477 | −0.300204 | ||||||||
\(40\) | 5.24092 | 0.828663 | ||||||||
\(41\) | 1.39116 | 0.217263 | 0.108631 | − | 0.994082i | \(-0.465353\pi\) | ||||
0.108631 | + | 0.994082i | \(0.465353\pi\) | |||||||
\(42\) | −5.01521 | −0.773864 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −0.454508 | −0.0685196 | ||||||||
\(45\) | 5.63461 | 0.839958 | ||||||||
\(46\) | 3.98333 | 0.587310 | ||||||||
\(47\) | −3.18740 | −0.464930 | −0.232465 | − | 0.972605i | \(-0.574679\pi\) | ||||
−0.232465 | + | 0.972605i | \(0.574679\pi\) | |||||||
\(48\) | −2.96223 | −0.427560 | ||||||||
\(49\) | 18.8240 | 2.68915 | ||||||||
\(50\) | −0.493369 | −0.0697730 | ||||||||
\(51\) | 0.629934 | 0.0882084 | ||||||||
\(52\) | −1.35268 | −0.187583 | ||||||||
\(53\) | −6.48181 | −0.890345 | −0.445173 | − | 0.895445i | \(-0.646858\pi\) | ||||
−0.445173 | + | 0.895445i | \(0.646858\pi\) | |||||||
\(54\) | −5.52983 | −0.752515 | ||||||||
\(55\) | 2.16451 | 0.291862 | ||||||||
\(56\) | 12.3044 | 1.64425 | ||||||||
\(57\) | −3.80973 | −0.504611 | ||||||||
\(58\) | 2.73080 | 0.358572 | ||||||||
\(59\) | −2.15708 | −0.280828 | −0.140414 | − | 0.990093i | \(-0.544843\pi\) | ||||
−0.140414 | + | 0.990093i | \(0.544843\pi\) | |||||||
\(60\) | −0.619720 | −0.0800055 | ||||||||
\(61\) | −3.33319 | −0.426771 | −0.213385 | − | 0.976968i | \(-0.568449\pi\) | ||||
−0.213385 | + | 0.976968i | \(0.568449\pi\) | |||||||
\(62\) | −7.46535 | −0.948101 | ||||||||
\(63\) | 13.2287 | 1.66666 | ||||||||
\(64\) | 5.44955 | 0.681194 | ||||||||
\(65\) | 6.44188 | 0.799017 | ||||||||
\(66\) | −0.986909 | −0.121480 | ||||||||
\(67\) | 5.09482 | 0.622431 | 0.311216 | − | 0.950339i | \(-0.399264\pi\) | ||||
0.311216 | + | 0.950339i | \(0.399264\pi\) | |||||||
\(68\) | 0.454508 | 0.0551172 | ||||||||
\(69\) | 1.60162 | 0.192812 | ||||||||
\(70\) | 17.2327 | 2.05970 | ||||||||
\(71\) | 13.6817 | 1.62372 | 0.811858 | − | 0.583855i | \(-0.198456\pi\) | ||||
0.811858 | + | 0.583855i | \(0.198456\pi\) | |||||||
\(72\) | 6.30309 | 0.742827 | ||||||||
\(73\) | 10.0295 | 1.17387 | 0.586933 | − | 0.809636i | \(-0.300335\pi\) | ||||
0.586933 | + | 0.809636i | \(0.300335\pi\) | |||||||
\(74\) | −18.0862 | −2.10248 | ||||||||
\(75\) | −0.198374 | −0.0229063 | ||||||||
\(76\) | −2.74879 | −0.315307 | ||||||||
\(77\) | 5.08174 | 0.579118 | ||||||||
\(78\) | −2.93718 | −0.332570 | ||||||||
\(79\) | 9.72008 | 1.09359 | 0.546797 | − | 0.837265i | \(-0.315847\pi\) | ||||
0.546797 | + | 0.837265i | \(0.315847\pi\) | |||||||
\(80\) | 10.1785 | 1.13799 | ||||||||
\(81\) | 5.58611 | 0.620679 | ||||||||
\(82\) | 2.17951 | 0.240687 | ||||||||
\(83\) | −3.17833 | −0.348868 | −0.174434 | − | 0.984669i | \(-0.555809\pi\) | ||||
−0.174434 | + | 0.984669i | \(0.555809\pi\) | |||||||
\(84\) | −1.45495 | −0.158748 | ||||||||
\(85\) | −2.16451 | −0.234774 | ||||||||
\(86\) | −1.56669 | −0.168940 | ||||||||
\(87\) | 1.09800 | 0.117718 | ||||||||
\(88\) | 2.42130 | 0.258112 | ||||||||
\(89\) | −1.09226 | −0.115780 | −0.0578898 | − | 0.998323i | \(-0.518437\pi\) | ||||
−0.0578898 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(90\) | 8.82766 | 0.930518 | ||||||||
\(91\) | 15.1240 | 1.58542 | ||||||||
\(92\) | 1.15559 | 0.120479 | ||||||||
\(93\) | −3.00167 | −0.311259 | ||||||||
\(94\) | −4.99366 | −0.515056 | ||||||||
\(95\) | 13.0906 | 1.34306 | ||||||||
\(96\) | −1.59036 | −0.162315 | ||||||||
\(97\) | −10.8851 | −1.10521 | −0.552605 | − | 0.833443i | \(-0.686366\pi\) | ||||
−0.552605 | + | 0.833443i | \(0.686366\pi\) | |||||||
\(98\) | 29.4914 | 2.97908 | ||||||||
\(99\) | 2.60318 | 0.261630 | ||||||||
\(100\) | −0.143130 | −0.0143130 | ||||||||
\(101\) | −15.7641 | −1.56859 | −0.784294 | − | 0.620390i | \(-0.786974\pi\) | ||||
−0.784294 | + | 0.620390i | \(0.786974\pi\) | |||||||
\(102\) | 0.986909 | 0.0977186 | ||||||||
\(103\) | −17.8022 | −1.75411 | −0.877053 | − | 0.480393i | \(-0.840494\pi\) | ||||
−0.877053 | + | 0.480393i | \(0.840494\pi\) | |||||||
\(104\) | 7.20614 | 0.706620 | ||||||||
\(105\) | 6.92892 | 0.676194 | ||||||||
\(106\) | −10.1550 | −0.986338 | ||||||||
\(107\) | −9.99279 | −0.966039 | −0.483019 | − | 0.875610i | \(-0.660460\pi\) | ||||
−0.483019 | + | 0.875610i | \(0.660460\pi\) | |||||||
\(108\) | −1.60425 | −0.154369 | ||||||||
\(109\) | −0.914502 | −0.0875934 | −0.0437967 | − | 0.999040i | \(-0.513945\pi\) | ||||
−0.0437967 | + | 0.999040i | \(0.513945\pi\) | |||||||
\(110\) | 3.39110 | 0.323329 | ||||||||
\(111\) | −7.27212 | −0.690239 | ||||||||
\(112\) | 23.8965 | 2.25801 | ||||||||
\(113\) | −11.8753 | −1.11713 | −0.558566 | − | 0.829460i | \(-0.688648\pi\) | ||||
−0.558566 | + | 0.829460i | \(0.688648\pi\) | |||||||
\(114\) | −5.96866 | −0.559016 | ||||||||
\(115\) | −5.50329 | −0.513185 | ||||||||
\(116\) | 0.792227 | 0.0735564 | ||||||||
\(117\) | 7.74744 | 0.716252 | ||||||||
\(118\) | −3.37947 | −0.311106 | ||||||||
\(119\) | −5.08174 | −0.465842 | ||||||||
\(120\) | 3.30144 | 0.301378 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.22206 | −0.472783 | ||||||||
\(123\) | 0.876340 | 0.0790169 | ||||||||
\(124\) | −2.16576 | −0.194491 | ||||||||
\(125\) | 11.5042 | 1.02896 | ||||||||
\(126\) | 20.7252 | 1.84635 | ||||||||
\(127\) | −9.91578 | −0.879883 | −0.439942 | − | 0.898026i | \(-0.645001\pi\) | ||||
−0.439942 | + | 0.898026i | \(0.645001\pi\) | |||||||
\(128\) | 13.5870 | 1.20093 | ||||||||
\(129\) | −0.629934 | −0.0554626 | ||||||||
\(130\) | 10.0924 | 0.885163 | ||||||||
\(131\) | −21.0223 | −1.83673 | −0.918364 | − | 0.395736i | \(-0.870490\pi\) | ||||
−0.918364 | + | 0.395736i | \(0.870490\pi\) | |||||||
\(132\) | −0.286310 | −0.0249201 | ||||||||
\(133\) | 30.7335 | 2.66493 | ||||||||
\(134\) | 7.98199 | 0.689538 | ||||||||
\(135\) | 7.63992 | 0.657539 | ||||||||
\(136\) | −2.42130 | −0.207625 | ||||||||
\(137\) | −15.2610 | −1.30384 | −0.651919 | − | 0.758288i | \(-0.726036\pi\) | ||||
−0.651919 | + | 0.758288i | \(0.726036\pi\) | |||||||
\(138\) | 2.50923 | 0.213600 | ||||||||
\(139\) | −17.8581 | −1.51470 | −0.757351 | − | 0.653008i | \(-0.773507\pi\) | ||||
−0.757351 | + | 0.653008i | \(0.773507\pi\) | |||||||
\(140\) | 4.99934 | 0.422521 | ||||||||
\(141\) | −2.00785 | −0.169092 | ||||||||
\(142\) | 21.4349 | 1.79878 | ||||||||
\(143\) | 2.97614 | 0.248878 | ||||||||
\(144\) | 12.2413 | 1.02011 | ||||||||
\(145\) | −3.77283 | −0.313316 | ||||||||
\(146\) | 15.7131 | 1.30043 | ||||||||
\(147\) | 11.8579 | 0.978023 | ||||||||
\(148\) | −5.24696 | −0.431297 | ||||||||
\(149\) | 21.0180 | 1.72186 | 0.860931 | − | 0.508721i | \(-0.169882\pi\) | ||||
0.860931 | + | 0.508721i | \(0.169882\pi\) | |||||||
\(150\) | −0.310790 | −0.0253759 | ||||||||
\(151\) | 11.8119 | 0.961242 | 0.480621 | − | 0.876928i | \(-0.340411\pi\) | ||||
0.480621 | + | 0.876928i | \(0.340411\pi\) | |||||||
\(152\) | 14.6436 | 1.18775 | ||||||||
\(153\) | −2.60318 | −0.210455 | ||||||||
\(154\) | 7.96149 | 0.641555 | ||||||||
\(155\) | 10.3140 | 0.828440 | ||||||||
\(156\) | −0.852099 | −0.0682225 | ||||||||
\(157\) | 9.98732 | 0.797075 | 0.398538 | − | 0.917152i | \(-0.369518\pi\) | ||||
0.398538 | + | 0.917152i | \(0.369518\pi\) | |||||||
\(158\) | 15.2283 | 1.21150 | ||||||||
\(159\) | −4.08311 | −0.323812 | ||||||||
\(160\) | 5.46461 | 0.432015 | ||||||||
\(161\) | −12.9204 | −1.01827 | ||||||||
\(162\) | 8.75169 | 0.687598 | ||||||||
\(163\) | −15.2520 | −1.19463 | −0.597313 | − | 0.802008i | \(-0.703765\pi\) | ||||
−0.597313 | + | 0.802008i | \(0.703765\pi\) | |||||||
\(164\) | 0.632294 | 0.0493739 | ||||||||
\(165\) | 1.36350 | 0.106148 | ||||||||
\(166\) | −4.97946 | −0.386481 | ||||||||
\(167\) | 8.39677 | 0.649762 | 0.324881 | − | 0.945755i | \(-0.394676\pi\) | ||||
0.324881 | + | 0.945755i | \(0.394676\pi\) | |||||||
\(168\) | 7.75097 | 0.598000 | ||||||||
\(169\) | −4.14258 | −0.318660 | ||||||||
\(170\) | −3.39110 | −0.260086 | ||||||||
\(171\) | 15.7436 | 1.20394 | ||||||||
\(172\) | −0.454508 | −0.0346559 | ||||||||
\(173\) | −15.3916 | −1.17020 | −0.585101 | − | 0.810960i | \(-0.698945\pi\) | ||||
−0.585101 | + | 0.810960i | \(0.698945\pi\) | |||||||
\(174\) | 1.72023 | 0.130410 | ||||||||
\(175\) | 1.60030 | 0.120971 | ||||||||
\(176\) | 4.70244 | 0.354460 | ||||||||
\(177\) | −1.35882 | −0.102135 | ||||||||
\(178\) | −1.71123 | −0.128262 | ||||||||
\(179\) | −17.8419 | −1.33356 | −0.666781 | − | 0.745253i | \(-0.732329\pi\) | ||||
−0.666781 | + | 0.745253i | \(0.732329\pi\) | |||||||
\(180\) | 2.56097 | 0.190884 | ||||||||
\(181\) | −5.42245 | −0.403047 | −0.201524 | − | 0.979484i | \(-0.564589\pi\) | ||||
−0.201524 | + | 0.979484i | \(0.564589\pi\) | |||||||
\(182\) | 23.6945 | 1.75636 | ||||||||
\(183\) | −2.09969 | −0.155213 | ||||||||
\(184\) | −6.15620 | −0.453841 | ||||||||
\(185\) | 24.9876 | 1.83713 | ||||||||
\(186\) | −4.70268 | −0.344817 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | −1.44870 | −0.105657 | ||||||||
\(189\) | 17.9367 | 1.30470 | ||||||||
\(190\) | 20.5088 | 1.48787 | ||||||||
\(191\) | 22.3555 | 1.61759 | 0.808794 | − | 0.588092i | \(-0.200121\pi\) | ||||
0.808794 | + | 0.588092i | \(0.200121\pi\) | |||||||
\(192\) | 3.43286 | 0.247745 | ||||||||
\(193\) | 17.7094 | 1.27475 | 0.637376 | − | 0.770553i | \(-0.280020\pi\) | ||||
0.637376 | + | 0.770553i | \(0.280020\pi\) | |||||||
\(194\) | −17.0535 | −1.22437 | ||||||||
\(195\) | 4.05796 | 0.290596 | ||||||||
\(196\) | 8.55567 | 0.611120 | ||||||||
\(197\) | −15.5660 | −1.10903 | −0.554517 | − | 0.832173i | \(-0.687097\pi\) | ||||
−0.554517 | + | 0.832173i | \(0.687097\pi\) | |||||||
\(198\) | 4.07837 | 0.289837 | ||||||||
\(199\) | 11.6103 | 0.823031 | 0.411515 | − | 0.911403i | \(-0.365000\pi\) | ||||
0.411515 | + | 0.911403i | \(0.365000\pi\) | |||||||
\(200\) | 0.762498 | 0.0539168 | ||||||||
\(201\) | 3.20940 | 0.226374 | ||||||||
\(202\) | −24.6974 | −1.73770 | ||||||||
\(203\) | −8.85769 | −0.621688 | ||||||||
\(204\) | 0.286310 | 0.0200457 | ||||||||
\(205\) | −3.01118 | −0.210310 | ||||||||
\(206\) | −27.8905 | −1.94323 | ||||||||
\(207\) | −6.61864 | −0.460027 | ||||||||
\(208\) | 13.9951 | 0.970387 | ||||||||
\(209\) | 6.04783 | 0.418337 | ||||||||
\(210\) | 10.8555 | 0.749098 | ||||||||
\(211\) | 7.07451 | 0.487029 | 0.243515 | − | 0.969897i | \(-0.421700\pi\) | ||||
0.243515 | + | 0.969897i | \(0.421700\pi\) | |||||||
\(212\) | −2.94604 | −0.202335 | ||||||||
\(213\) | 8.61855 | 0.590533 | ||||||||
\(214\) | −15.6556 | −1.07019 | ||||||||
\(215\) | 2.16451 | 0.147618 | ||||||||
\(216\) | 8.54631 | 0.581503 | ||||||||
\(217\) | 24.2148 | 1.64380 | ||||||||
\(218\) | −1.43274 | −0.0970373 | ||||||||
\(219\) | 6.31793 | 0.426926 | ||||||||
\(220\) | 0.983785 | 0.0663268 | ||||||||
\(221\) | −2.97614 | −0.200197 | ||||||||
\(222\) | −11.3931 | −0.764657 | ||||||||
\(223\) | 10.9540 | 0.733531 | 0.366766 | − | 0.930313i | \(-0.380465\pi\) | ||||
0.366766 | + | 0.930313i | \(0.380465\pi\) | |||||||
\(224\) | 12.8296 | 0.857212 | ||||||||
\(225\) | 0.819775 | 0.0546517 | ||||||||
\(226\) | −18.6048 | −1.23757 | ||||||||
\(227\) | −28.4848 | −1.89060 | −0.945301 | − | 0.326198i | \(-0.894232\pi\) | ||||
−0.945301 | + | 0.326198i | \(0.894232\pi\) | |||||||
\(228\) | −1.73155 | −0.114675 | ||||||||
\(229\) | 19.3709 | 1.28007 | 0.640034 | − | 0.768347i | \(-0.278920\pi\) | ||||
0.640034 | + | 0.768347i | \(0.278920\pi\) | |||||||
\(230\) | −8.62194 | −0.568514 | ||||||||
\(231\) | 3.20116 | 0.210621 | ||||||||
\(232\) | −4.22044 | −0.277085 | ||||||||
\(233\) | −0.0784137 | −0.00513705 | −0.00256852 | − | 0.999997i | \(-0.500818\pi\) | ||||
−0.00256852 | + | 0.999997i | \(0.500818\pi\) | |||||||
\(234\) | 12.1378 | 0.793474 | ||||||||
\(235\) | 6.89915 | 0.450051 | ||||||||
\(236\) | −0.980411 | −0.0638193 | ||||||||
\(237\) | 6.12301 | 0.397732 | ||||||||
\(238\) | −7.96149 | −0.516067 | ||||||||
\(239\) | −29.6117 | −1.91542 | −0.957712 | − | 0.287727i | \(-0.907100\pi\) | ||||
−0.957712 | + | 0.287727i | \(0.907100\pi\) | |||||||
\(240\) | 6.41175 | 0.413877 | ||||||||
\(241\) | −10.9636 | −0.706230 | −0.353115 | − | 0.935580i | \(-0.614878\pi\) | ||||
−0.353115 | + | 0.935580i | \(0.614878\pi\) | |||||||
\(242\) | 1.56669 | 0.100710 | ||||||||
\(243\) | 14.1078 | 0.905015 | ||||||||
\(244\) | −1.51496 | −0.0969854 | ||||||||
\(245\) | −40.7447 | −2.60309 | ||||||||
\(246\) | 1.37295 | 0.0875361 | ||||||||
\(247\) | 17.9992 | 1.14526 | ||||||||
\(248\) | 11.5376 | 0.732641 | ||||||||
\(249\) | −2.00214 | −0.126881 | ||||||||
\(250\) | 18.0234 | 1.13990 | ||||||||
\(251\) | −8.71374 | −0.550007 | −0.275003 | − | 0.961443i | \(-0.588679\pi\) | ||||
−0.275003 | + | 0.961443i | \(0.588679\pi\) | |||||||
\(252\) | 6.01254 | 0.378755 | ||||||||
\(253\) | −2.54252 | −0.159847 | ||||||||
\(254\) | −15.5349 | −0.974748 | ||||||||
\(255\) | −1.36350 | −0.0853854 | ||||||||
\(256\) | 10.3875 | 0.649220 | ||||||||
\(257\) | −18.9474 | −1.18190 | −0.590952 | − | 0.806707i | \(-0.701248\pi\) | ||||
−0.590952 | + | 0.806707i | \(0.701248\pi\) | |||||||
\(258\) | −0.986909 | −0.0614423 | ||||||||
\(259\) | 58.6649 | 3.64526 | ||||||||
\(260\) | 2.92789 | 0.181580 | ||||||||
\(261\) | −4.53746 | −0.280862 | ||||||||
\(262\) | −32.9354 | −2.03476 | ||||||||
\(263\) | −8.58628 | −0.529453 | −0.264726 | − | 0.964324i | \(-0.585282\pi\) | ||||
−0.264726 | + | 0.964324i | \(0.585282\pi\) | |||||||
\(264\) | 1.52526 | 0.0938733 | ||||||||
\(265\) | 14.0299 | 0.861851 | ||||||||
\(266\) | 48.1497 | 2.95225 | ||||||||
\(267\) | −0.688054 | −0.0421082 | ||||||||
\(268\) | 2.31564 | 0.141450 | ||||||||
\(269\) | 13.1918 | 0.804319 | 0.402159 | − | 0.915570i | \(-0.368260\pi\) | ||||
0.402159 | + | 0.915570i | \(0.368260\pi\) | |||||||
\(270\) | 11.9694 | 0.728432 | ||||||||
\(271\) | 21.2422 | 1.29037 | 0.645187 | − | 0.764025i | \(-0.276779\pi\) | ||||
0.645187 | + | 0.764025i | \(0.276779\pi\) | |||||||
\(272\) | −4.70244 | −0.285127 | ||||||||
\(273\) | 9.52710 | 0.576606 | ||||||||
\(274\) | −23.9093 | −1.44441 | ||||||||
\(275\) | 0.314913 | 0.0189899 | ||||||||
\(276\) | 0.727948 | 0.0438173 | ||||||||
\(277\) | −21.0921 | −1.26730 | −0.633651 | − | 0.773619i | \(-0.718444\pi\) | ||||
−0.633651 | + | 0.773619i | \(0.718444\pi\) | |||||||
\(278\) | −27.9780 | −1.67801 | ||||||||
\(279\) | 12.4043 | 0.742627 | ||||||||
\(280\) | −26.6330 | −1.59163 | ||||||||
\(281\) | 15.6359 | 0.932757 | 0.466379 | − | 0.884585i | \(-0.345558\pi\) | ||||
0.466379 | + | 0.884585i | \(0.345558\pi\) | |||||||
\(282\) | −3.14567 | −0.187322 | ||||||||
\(283\) | 13.8618 | 0.823997 | 0.411999 | − | 0.911184i | \(-0.364831\pi\) | ||||
0.411999 | + | 0.911184i | \(0.364831\pi\) | |||||||
\(284\) | 6.21843 | 0.368996 | ||||||||
\(285\) | 8.24619 | 0.488462 | ||||||||
\(286\) | 4.66268 | 0.275710 | ||||||||
\(287\) | −7.06952 | −0.417300 | ||||||||
\(288\) | 6.57211 | 0.387265 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −5.91084 | −0.347097 | ||||||||
\(291\) | −6.85687 | −0.401957 | ||||||||
\(292\) | 4.55849 | 0.266766 | ||||||||
\(293\) | −26.8652 | −1.56948 | −0.784740 | − | 0.619825i | \(-0.787203\pi\) | ||||
−0.784740 | + | 0.619825i | \(0.787203\pi\) | |||||||
\(294\) | 18.5776 | 1.08347 | ||||||||
\(295\) | 4.66902 | 0.271841 | ||||||||
\(296\) | 27.9521 | 1.62468 | ||||||||
\(297\) | 3.52963 | 0.204810 | ||||||||
\(298\) | 32.9286 | 1.90751 | ||||||||
\(299\) | −7.56689 | −0.437605 | ||||||||
\(300\) | −0.0901626 | −0.00520554 | ||||||||
\(301\) | 5.08174 | 0.292906 | ||||||||
\(302\) | 18.5056 | 1.06488 | ||||||||
\(303\) | −9.93034 | −0.570483 | ||||||||
\(304\) | 28.4395 | 1.63112 | ||||||||
\(305\) | 7.21471 | 0.413113 | ||||||||
\(306\) | −4.07837 | −0.233145 | ||||||||
\(307\) | −2.71255 | −0.154813 | −0.0774067 | − | 0.997000i | \(-0.524664\pi\) | ||||
−0.0774067 | + | 0.997000i | \(0.524664\pi\) | |||||||
\(308\) | 2.30969 | 0.131607 | ||||||||
\(309\) | −11.2142 | −0.637955 | ||||||||
\(310\) | 16.1588 | 0.917758 | ||||||||
\(311\) | 3.03068 | 0.171854 | 0.0859270 | − | 0.996301i | \(-0.472615\pi\) | ||||
0.0859270 | + | 0.996301i | \(0.472615\pi\) | |||||||
\(312\) | 4.53939 | 0.256992 | ||||||||
\(313\) | −9.30409 | −0.525898 | −0.262949 | − | 0.964810i | \(-0.584695\pi\) | ||||
−0.262949 | + | 0.964810i | \(0.584695\pi\) | |||||||
\(314\) | 15.6470 | 0.883012 | ||||||||
\(315\) | −28.6336 | −1.61332 | ||||||||
\(316\) | 4.41786 | 0.248524 | ||||||||
\(317\) | 0.111814 | 0.00628009 | 0.00314004 | − | 0.999995i | \(-0.499000\pi\) | ||||
0.00314004 | + | 0.999995i | \(0.499000\pi\) | |||||||
\(318\) | −6.39696 | −0.358724 | ||||||||
\(319\) | −1.74304 | −0.0975917 | ||||||||
\(320\) | −11.7956 | −0.659393 | ||||||||
\(321\) | −6.29479 | −0.351341 | ||||||||
\(322\) | −20.2422 | −1.12805 | ||||||||
\(323\) | −6.04783 | −0.336510 | ||||||||
\(324\) | 2.53893 | 0.141052 | ||||||||
\(325\) | 0.937225 | 0.0519879 | ||||||||
\(326\) | −23.8950 | −1.32342 | ||||||||
\(327\) | −0.576076 | −0.0318571 | ||||||||
\(328\) | −3.36842 | −0.185990 | ||||||||
\(329\) | 16.1975 | 0.892998 | ||||||||
\(330\) | 2.13617 | 0.117592 | ||||||||
\(331\) | 10.3632 | 0.569612 | 0.284806 | − | 0.958585i | \(-0.408071\pi\) | ||||
0.284806 | + | 0.958585i | \(0.408071\pi\) | |||||||
\(332\) | −1.44458 | −0.0792815 | ||||||||
\(333\) | 30.0518 | 1.64683 | ||||||||
\(334\) | 13.1551 | 0.719816 | ||||||||
\(335\) | −11.0278 | −0.602511 | ||||||||
\(336\) | 15.0532 | 0.821222 | ||||||||
\(337\) | 8.39881 | 0.457513 | 0.228756 | − | 0.973484i | \(-0.426534\pi\) | ||||
0.228756 | + | 0.973484i | \(0.426534\pi\) | |||||||
\(338\) | −6.49012 | −0.353016 | ||||||||
\(339\) | −7.48063 | −0.406292 | ||||||||
\(340\) | −0.983785 | −0.0533532 | ||||||||
\(341\) | 4.76506 | 0.258042 | ||||||||
\(342\) | 24.6653 | 1.33375 | ||||||||
\(343\) | −60.0866 | −3.24437 | ||||||||
\(344\) | 2.42130 | 0.130548 | ||||||||
\(345\) | −3.46671 | −0.186641 | ||||||||
\(346\) | −24.1138 | −1.29637 | ||||||||
\(347\) | −18.6269 | −0.999945 | −0.499973 | − | 0.866041i | \(-0.666657\pi\) | ||||
−0.499973 | + | 0.866041i | \(0.666657\pi\) | |||||||
\(348\) | 0.499051 | 0.0267519 | ||||||||
\(349\) | −26.3264 | −1.40922 | −0.704611 | − | 0.709594i | \(-0.748879\pi\) | ||||
−0.704611 | + | 0.709594i | \(0.748879\pi\) | |||||||
\(350\) | 2.50717 | 0.134014 | ||||||||
\(351\) | 10.5047 | 0.560699 | ||||||||
\(352\) | 2.52464 | 0.134564 | ||||||||
\(353\) | 2.66815 | 0.142011 | 0.0710057 | − | 0.997476i | \(-0.477379\pi\) | ||||
0.0710057 | + | 0.997476i | \(0.477379\pi\) | |||||||
\(354\) | −2.12884 | −0.113147 | ||||||||
\(355\) | −29.6141 | −1.57175 | ||||||||
\(356\) | −0.496442 | −0.0263114 | ||||||||
\(357\) | −3.20116 | −0.169423 | ||||||||
\(358\) | −27.9526 | −1.47734 | ||||||||
\(359\) | 16.1491 | 0.852318 | 0.426159 | − | 0.904648i | \(-0.359866\pi\) | ||||
0.426159 | + | 0.904648i | \(0.359866\pi\) | |||||||
\(360\) | −13.6431 | −0.719054 | ||||||||
\(361\) | 17.5762 | 0.925064 | ||||||||
\(362\) | −8.49528 | −0.446502 | ||||||||
\(363\) | 0.629934 | 0.0330630 | ||||||||
\(364\) | 6.87396 | 0.360294 | ||||||||
\(365\) | −21.7089 | −1.13630 | ||||||||
\(366\) | −3.28955 | −0.171948 | ||||||||
\(367\) | 11.5868 | 0.604826 | 0.302413 | − | 0.953177i | \(-0.402208\pi\) | ||||
0.302413 | + | 0.953177i | \(0.402208\pi\) | |||||||
\(368\) | −11.9560 | −0.623251 | ||||||||
\(369\) | −3.62145 | −0.188525 | ||||||||
\(370\) | 39.1478 | 2.03520 | ||||||||
\(371\) | 32.9389 | 1.71010 | ||||||||
\(372\) | −1.36428 | −0.0707348 | ||||||||
\(373\) | −26.9663 | −1.39626 | −0.698132 | − | 0.715969i | \(-0.745985\pi\) | ||||
−0.698132 | + | 0.715969i | \(0.745985\pi\) | |||||||
\(374\) | −1.56669 | −0.0810115 | ||||||||
\(375\) | 7.24686 | 0.374226 | ||||||||
\(376\) | 7.71766 | 0.398008 | ||||||||
\(377\) | −5.18755 | −0.267172 | ||||||||
\(378\) | 28.1011 | 1.44537 | ||||||||
\(379\) | 18.6871 | 0.959889 | 0.479945 | − | 0.877299i | \(-0.340657\pi\) | ||||
0.479945 | + | 0.877299i | \(0.340657\pi\) | |||||||
\(380\) | 5.94976 | 0.305216 | ||||||||
\(381\) | −6.24629 | −0.320007 | ||||||||
\(382\) | 35.0241 | 1.79199 | ||||||||
\(383\) | 23.9666 | 1.22463 | 0.612317 | − | 0.790612i | \(-0.290238\pi\) | ||||
0.612317 | + | 0.790612i | \(0.290238\pi\) | |||||||
\(384\) | 8.55893 | 0.436771 | ||||||||
\(385\) | −10.9994 | −0.560584 | ||||||||
\(386\) | 27.7451 | 1.41219 | ||||||||
\(387\) | 2.60318 | 0.132327 | ||||||||
\(388\) | −4.94734 | −0.251163 | ||||||||
\(389\) | −18.6189 | −0.944014 | −0.472007 | − | 0.881595i | \(-0.656470\pi\) | ||||
−0.472007 | + | 0.881595i | \(0.656470\pi\) | |||||||
\(390\) | 6.35755 | 0.321927 | ||||||||
\(391\) | 2.54252 | 0.128581 | ||||||||
\(392\) | −45.5787 | −2.30207 | ||||||||
\(393\) | −13.2427 | −0.668004 | ||||||||
\(394\) | −24.3871 | −1.22860 | ||||||||
\(395\) | −21.0392 | −1.05860 | ||||||||
\(396\) | 1.18317 | 0.0594564 | ||||||||
\(397\) | −10.3442 | −0.519162 | −0.259581 | − | 0.965721i | \(-0.583584\pi\) | ||||
−0.259581 | + | 0.965721i | \(0.583584\pi\) | |||||||
\(398\) | 18.1897 | 0.911766 | ||||||||
\(399\) | 19.3600 | 0.969215 | ||||||||
\(400\) | 1.48086 | 0.0740428 | ||||||||
\(401\) | −30.8948 | −1.54281 | −0.771407 | − | 0.636342i | \(-0.780447\pi\) | ||||
−0.771407 | + | 0.636342i | \(0.780447\pi\) | |||||||
\(402\) | 5.02812 | 0.250780 | ||||||||
\(403\) | 14.1815 | 0.706430 | ||||||||
\(404\) | −7.16491 | −0.356468 | ||||||||
\(405\) | −12.0912 | −0.600815 | ||||||||
\(406\) | −13.8772 | −0.688715 | ||||||||
\(407\) | 11.5443 | 0.572227 | ||||||||
\(408\) | −1.52526 | −0.0755116 | ||||||||
\(409\) | 12.3358 | 0.609964 | 0.304982 | − | 0.952358i | \(-0.401350\pi\) | ||||
0.304982 | + | 0.952358i | \(0.401350\pi\) | |||||||
\(410\) | −4.71757 | −0.232984 | ||||||||
\(411\) | −9.61345 | −0.474196 | ||||||||
\(412\) | −8.09126 | −0.398628 | ||||||||
\(413\) | 10.9617 | 0.539391 | ||||||||
\(414\) | −10.3693 | −0.509625 | ||||||||
\(415\) | 6.87953 | 0.337703 | ||||||||
\(416\) | 7.51370 | 0.368390 | ||||||||
\(417\) | −11.2494 | −0.550886 | ||||||||
\(418\) | 9.47505 | 0.463440 | ||||||||
\(419\) | −17.5947 | −0.859558 | −0.429779 | − | 0.902934i | \(-0.641408\pi\) | ||||
−0.429779 | + | 0.902934i | \(0.641408\pi\) | |||||||
\(420\) | 3.14925 | 0.153668 | ||||||||
\(421\) | 13.2859 | 0.647513 | 0.323756 | − | 0.946140i | \(-0.395054\pi\) | ||||
0.323756 | + | 0.946140i | \(0.395054\pi\) | |||||||
\(422\) | 11.0835 | 0.539538 | ||||||||
\(423\) | 8.29739 | 0.403433 | ||||||||
\(424\) | 15.6944 | 0.762189 | ||||||||
\(425\) | −0.314913 | −0.0152755 | ||||||||
\(426\) | 13.5026 | 0.654202 | ||||||||
\(427\) | 16.9384 | 0.819706 | ||||||||
\(428\) | −4.54180 | −0.219536 | ||||||||
\(429\) | 1.87477 | 0.0905149 | ||||||||
\(430\) | 3.39110 | 0.163534 | ||||||||
\(431\) | −9.85066 | −0.474490 | −0.237245 | − | 0.971450i | \(-0.576244\pi\) | ||||
−0.237245 | + | 0.971450i | \(0.576244\pi\) | |||||||
\(432\) | 16.5979 | 0.798566 | ||||||||
\(433\) | −31.2540 | −1.50197 | −0.750985 | − | 0.660319i | \(-0.770421\pi\) | ||||
−0.750985 | + | 0.660319i | \(0.770421\pi\) | |||||||
\(434\) | 37.9369 | 1.82103 | ||||||||
\(435\) | −2.37663 | −0.113951 | ||||||||
\(436\) | −0.415648 | −0.0199059 | ||||||||
\(437\) | −15.3767 | −0.735567 | ||||||||
\(438\) | 9.89821 | 0.472955 | ||||||||
\(439\) | 31.5349 | 1.50508 | 0.752539 | − | 0.658547i | \(-0.228829\pi\) | ||||
0.752539 | + | 0.658547i | \(0.228829\pi\) | |||||||
\(440\) | −5.24092 | −0.249851 | ||||||||
\(441\) | −49.0024 | −2.33345 | ||||||||
\(442\) | −4.66268 | −0.221781 | ||||||||
\(443\) | 8.55422 | 0.406423 | 0.203212 | − | 0.979135i | \(-0.434862\pi\) | ||||
0.203212 | + | 0.979135i | \(0.434862\pi\) | |||||||
\(444\) | −3.30523 | −0.156859 | ||||||||
\(445\) | 2.36421 | 0.112074 | ||||||||
\(446\) | 17.1614 | 0.812617 | ||||||||
\(447\) | 13.2400 | 0.626228 | ||||||||
\(448\) | −27.6932 | −1.30838 | ||||||||
\(449\) | 12.0337 | 0.567903 | 0.283952 | − | 0.958839i | \(-0.408354\pi\) | ||||
0.283952 | + | 0.958839i | \(0.408354\pi\) | |||||||
\(450\) | 1.28433 | 0.0605439 | ||||||||
\(451\) | −1.39116 | −0.0655072 | ||||||||
\(452\) | −5.39740 | −0.253872 | ||||||||
\(453\) | 7.44074 | 0.349597 | ||||||||
\(454\) | −44.6268 | −2.09444 | ||||||||
\(455\) | −32.7359 | −1.53468 | ||||||||
\(456\) | 9.22451 | 0.431977 | ||||||||
\(457\) | 32.4115 | 1.51615 | 0.758074 | − | 0.652169i | \(-0.226141\pi\) | ||||
0.758074 | + | 0.652169i | \(0.226141\pi\) | |||||||
\(458\) | 30.3482 | 1.41808 | ||||||||
\(459\) | −3.52963 | −0.164749 | ||||||||
\(460\) | −2.50129 | −0.116623 | ||||||||
\(461\) | −6.70361 | −0.312218 | −0.156109 | − | 0.987740i | \(-0.549895\pi\) | ||||
−0.156109 | + | 0.987740i | \(0.549895\pi\) | |||||||
\(462\) | 5.01521 | 0.233329 | ||||||||
\(463\) | −8.38243 | −0.389565 | −0.194782 | − | 0.980846i | \(-0.562400\pi\) | ||||
−0.194782 | + | 0.980846i | \(0.562400\pi\) | |||||||
\(464\) | −8.19656 | −0.380516 | ||||||||
\(465\) | 6.49713 | 0.301297 | ||||||||
\(466\) | −0.122850 | −0.00569090 | ||||||||
\(467\) | 7.20317 | 0.333323 | 0.166661 | − | 0.986014i | \(-0.446701\pi\) | ||||
0.166661 | + | 0.986014i | \(0.446701\pi\) | |||||||
\(468\) | 3.52128 | 0.162771 | ||||||||
\(469\) | −25.8905 | −1.19551 | ||||||||
\(470\) | 10.8088 | 0.498573 | ||||||||
\(471\) | 6.29135 | 0.289890 | ||||||||
\(472\) | 5.22295 | 0.240406 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 9.59284 | 0.440614 | ||||||||
\(475\) | 1.90454 | 0.0873861 | ||||||||
\(476\) | −2.30969 | −0.105864 | ||||||||
\(477\) | 16.8733 | 0.772577 | ||||||||
\(478\) | −46.3923 | −2.12194 | ||||||||
\(479\) | 18.1635 | 0.829914 | 0.414957 | − | 0.909841i | \(-0.363797\pi\) | ||||
0.414957 | + | 0.909841i | \(0.363797\pi\) | |||||||
\(480\) | 3.44234 | 0.157121 | ||||||||
\(481\) | 34.3573 | 1.56656 | ||||||||
\(482\) | −17.1766 | −0.782372 | ||||||||
\(483\) | −8.13899 | −0.370337 | ||||||||
\(484\) | 0.454508 | 0.0206595 | ||||||||
\(485\) | 23.5608 | 1.06984 | ||||||||
\(486\) | 22.1025 | 1.00259 | ||||||||
\(487\) | −5.11109 | −0.231606 | −0.115803 | − | 0.993272i | \(-0.536944\pi\) | ||||
−0.115803 | + | 0.993272i | \(0.536944\pi\) | |||||||
\(488\) | 8.07065 | 0.365341 | ||||||||
\(489\) | −9.60773 | −0.434476 | ||||||||
\(490\) | −63.8343 | −2.88374 | ||||||||
\(491\) | −11.2012 | −0.505504 | −0.252752 | − | 0.967531i | \(-0.581336\pi\) | ||||
−0.252752 | + | 0.967531i | \(0.581336\pi\) | |||||||
\(492\) | 0.398303 | 0.0179569 | ||||||||
\(493\) | 1.74304 | 0.0785027 | ||||||||
\(494\) | 28.1991 | 1.26874 | ||||||||
\(495\) | −5.63461 | −0.253257 | ||||||||
\(496\) | 22.4074 | 1.00612 | ||||||||
\(497\) | −69.5267 | −3.11870 | ||||||||
\(498\) | −3.13673 | −0.140560 | ||||||||
\(499\) | −18.0883 | −0.809744 | −0.404872 | − | 0.914373i | \(-0.632684\pi\) | ||||
−0.404872 | + | 0.914373i | \(0.632684\pi\) | |||||||
\(500\) | 5.22873 | 0.233836 | ||||||||
\(501\) | 5.28941 | 0.236314 | ||||||||
\(502\) | −13.6517 | −0.609306 | ||||||||
\(503\) | 15.7378 | 0.701712 | 0.350856 | − | 0.936429i | \(-0.385891\pi\) | ||||
0.350856 | + | 0.936429i | \(0.385891\pi\) | |||||||
\(504\) | −32.0307 | −1.42676 | ||||||||
\(505\) | 34.1215 | 1.51839 | ||||||||
\(506\) | −3.98333 | −0.177080 | ||||||||
\(507\) | −2.60955 | −0.115894 | ||||||||
\(508\) | −4.50680 | −0.199957 | ||||||||
\(509\) | 22.5955 | 1.00153 | 0.500763 | − | 0.865584i | \(-0.333053\pi\) | ||||
0.500763 | + | 0.865584i | \(0.333053\pi\) | |||||||
\(510\) | −2.13617 | −0.0945912 | ||||||||
\(511\) | −50.9673 | −2.25466 | ||||||||
\(512\) | −10.9001 | −0.481719 | ||||||||
\(513\) | 21.3466 | 0.942476 | ||||||||
\(514\) | −29.6846 | −1.30933 | ||||||||
\(515\) | 38.5331 | 1.69797 | ||||||||
\(516\) | −0.286310 | −0.0126041 | ||||||||
\(517\) | 3.18740 | 0.140182 | ||||||||
\(518\) | 91.9095 | 4.03827 | ||||||||
\(519\) | −9.69570 | −0.425594 | ||||||||
\(520\) | −15.5977 | −0.684006 | ||||||||
\(521\) | −37.7269 | −1.65284 | −0.826422 | − | 0.563051i | \(-0.809628\pi\) | ||||
−0.826422 | + | 0.563051i | \(0.809628\pi\) | |||||||
\(522\) | −7.10878 | −0.311143 | ||||||||
\(523\) | −21.6502 | −0.946697 | −0.473348 | − | 0.880875i | \(-0.656955\pi\) | ||||
−0.473348 | + | 0.880875i | \(0.656955\pi\) | |||||||
\(524\) | −9.55481 | −0.417404 | ||||||||
\(525\) | 1.00808 | 0.0439964 | ||||||||
\(526\) | −13.4520 | −0.586536 | ||||||||
\(527\) | −4.76506 | −0.207569 | ||||||||
\(528\) | 2.96223 | 0.128914 | ||||||||
\(529\) | −16.5356 | −0.718940 | ||||||||
\(530\) | 21.9805 | 0.954772 | ||||||||
\(531\) | 5.61528 | 0.243682 | ||||||||
\(532\) | 13.9686 | 0.605616 | ||||||||
\(533\) | −4.14030 | −0.179336 | ||||||||
\(534\) | −1.07796 | −0.0466481 | ||||||||
\(535\) | 21.6294 | 0.935123 | ||||||||
\(536\) | −12.3361 | −0.532838 | ||||||||
\(537\) | −11.2392 | −0.485007 | ||||||||
\(538\) | 20.6674 | 0.891036 | ||||||||
\(539\) | −18.8240 | −0.810809 | ||||||||
\(540\) | 3.47240 | 0.149428 | ||||||||
\(541\) | 12.1670 | 0.523102 | 0.261551 | − | 0.965190i | \(-0.415766\pi\) | ||||
0.261551 | + | 0.965190i | \(0.415766\pi\) | |||||||
\(542\) | 33.2799 | 1.42950 | ||||||||
\(543\) | −3.41578 | −0.146585 | ||||||||
\(544\) | −2.52464 | −0.108243 | ||||||||
\(545\) | 1.97944 | 0.0847901 | ||||||||
\(546\) | 14.9260 | 0.638773 | ||||||||
\(547\) | −6.39262 | −0.273329 | −0.136664 | − | 0.990617i | \(-0.543638\pi\) | ||||
−0.136664 | + | 0.990617i | \(0.543638\pi\) | |||||||
\(548\) | −6.93626 | −0.296303 | ||||||||
\(549\) | 8.67690 | 0.370321 | ||||||||
\(550\) | 0.493369 | 0.0210373 | ||||||||
\(551\) | −10.5416 | −0.449088 | ||||||||
\(552\) | −3.87800 | −0.165059 | ||||||||
\(553\) | −49.3949 | −2.10048 | ||||||||
\(554\) | −33.0447 | −1.40394 | ||||||||
\(555\) | 15.7405 | 0.668149 | ||||||||
\(556\) | −8.11663 | −0.344222 | ||||||||
\(557\) | 12.1065 | 0.512968 | 0.256484 | − | 0.966548i | \(-0.417436\pi\) | ||||
0.256484 | + | 0.966548i | \(0.417436\pi\) | |||||||
\(558\) | 19.4337 | 0.822693 | ||||||||
\(559\) | 2.97614 | 0.125877 | ||||||||
\(560\) | −51.7242 | −2.18575 | ||||||||
\(561\) | −0.629934 | −0.0265958 | ||||||||
\(562\) | 24.4965 | 1.03332 | ||||||||
\(563\) | 38.5236 | 1.62357 | 0.811787 | − | 0.583953i | \(-0.198495\pi\) | ||||
0.811787 | + | 0.583953i | \(0.198495\pi\) | |||||||
\(564\) | −0.912584 | −0.0384267 | ||||||||
\(565\) | 25.7041 | 1.08138 | ||||||||
\(566\) | 21.7171 | 0.912837 | ||||||||
\(567\) | −28.3872 | −1.19215 | ||||||||
\(568\) | −33.1275 | −1.39000 | ||||||||
\(569\) | 13.7109 | 0.574792 | 0.287396 | − | 0.957812i | \(-0.407210\pi\) | ||||
0.287396 | + | 0.957812i | \(0.407210\pi\) | |||||||
\(570\) | 12.9192 | 0.541125 | ||||||||
\(571\) | −31.7878 | −1.33028 | −0.665138 | − | 0.746720i | \(-0.731627\pi\) | ||||
−0.665138 | + | 0.746720i | \(0.731627\pi\) | |||||||
\(572\) | 1.35268 | 0.0565584 | ||||||||
\(573\) | 14.0825 | 0.588305 | ||||||||
\(574\) | −11.0757 | −0.462292 | ||||||||
\(575\) | −0.800670 | −0.0333903 | ||||||||
\(576\) | −14.1862 | −0.591091 | ||||||||
\(577\) | 17.9768 | 0.748383 | 0.374192 | − | 0.927351i | \(-0.377920\pi\) | ||||
0.374192 | + | 0.927351i | \(0.377920\pi\) | |||||||
\(578\) | 1.56669 | 0.0651656 | ||||||||
\(579\) | 11.1558 | 0.463617 | ||||||||
\(580\) | −1.71478 | −0.0712024 | ||||||||
\(581\) | 16.1515 | 0.670075 | ||||||||
\(582\) | −10.7426 | −0.445293 | ||||||||
\(583\) | 6.48181 | 0.268449 | ||||||||
\(584\) | −24.2845 | −1.00490 | ||||||||
\(585\) | −16.7694 | −0.693329 | ||||||||
\(586\) | −42.0893 | −1.73869 | ||||||||
\(587\) | −12.2140 | −0.504127 | −0.252063 | − | 0.967711i | \(-0.581109\pi\) | ||||
−0.252063 | + | 0.967711i | \(0.581109\pi\) | |||||||
\(588\) | 5.38951 | 0.222260 | ||||||||
\(589\) | 28.8182 | 1.18743 | ||||||||
\(590\) | 7.31489 | 0.301149 | ||||||||
\(591\) | −9.80556 | −0.403347 | ||||||||
\(592\) | 54.2861 | 2.23115 | ||||||||
\(593\) | 18.4969 | 0.759577 | 0.379788 | − | 0.925073i | \(-0.375997\pi\) | ||||
0.379788 | + | 0.925073i | \(0.375997\pi\) | |||||||
\(594\) | 5.52983 | 0.226892 | ||||||||
\(595\) | 10.9994 | 0.450933 | ||||||||
\(596\) | 9.55285 | 0.391300 | ||||||||
\(597\) | 7.31371 | 0.299330 | ||||||||
\(598\) | −11.8549 | −0.484785 | ||||||||
\(599\) | 14.1644 | 0.578744 | 0.289372 | − | 0.957217i | \(-0.406554\pi\) | ||||
0.289372 | + | 0.957217i | \(0.406554\pi\) | |||||||
\(600\) | 0.480324 | 0.0196091 | ||||||||
\(601\) | 1.71394 | 0.0699132 | 0.0349566 | − | 0.999389i | \(-0.488871\pi\) | ||||
0.0349566 | + | 0.999389i | \(0.488871\pi\) | |||||||
\(602\) | 7.96149 | 0.324486 | ||||||||
\(603\) | −13.2627 | −0.540101 | ||||||||
\(604\) | 5.36862 | 0.218446 | ||||||||
\(605\) | −2.16451 | −0.0879997 | ||||||||
\(606\) | −15.5577 | −0.631990 | ||||||||
\(607\) | 5.75555 | 0.233610 | 0.116805 | − | 0.993155i | \(-0.462735\pi\) | ||||
0.116805 | + | 0.993155i | \(0.462735\pi\) | |||||||
\(608\) | 15.2686 | 0.619224 | ||||||||
\(609\) | −5.57976 | −0.226103 | ||||||||
\(610\) | 11.3032 | 0.457653 | ||||||||
\(611\) | 9.48616 | 0.383769 | ||||||||
\(612\) | −1.18317 | −0.0478267 | ||||||||
\(613\) | 42.8158 | 1.72931 | 0.864656 | − | 0.502364i | \(-0.167536\pi\) | ||||
0.864656 | + | 0.502364i | \(0.167536\pi\) | |||||||
\(614\) | −4.24971 | −0.171505 | ||||||||
\(615\) | −1.89684 | −0.0764881 | ||||||||
\(616\) | −12.3044 | −0.495759 | ||||||||
\(617\) | 4.80588 | 0.193478 | 0.0967388 | − | 0.995310i | \(-0.469159\pi\) | ||||
0.0967388 | + | 0.995310i | \(0.469159\pi\) | |||||||
\(618\) | −17.5692 | −0.706736 | ||||||||
\(619\) | −21.8256 | −0.877246 | −0.438623 | − | 0.898671i | \(-0.644534\pi\) | ||||
−0.438623 | + | 0.898671i | \(0.644534\pi\) | |||||||
\(620\) | 4.68779 | 0.188266 | ||||||||
\(621\) | −8.97415 | −0.360120 | ||||||||
\(622\) | 4.74812 | 0.190382 | ||||||||
\(623\) | 5.55059 | 0.222380 | ||||||||
\(624\) | 8.81600 | 0.352923 | ||||||||
\(625\) | −23.3263 | −0.933051 | ||||||||
\(626\) | −14.5766 | −0.582598 | ||||||||
\(627\) | 3.80973 | 0.152146 | ||||||||
\(628\) | 4.53932 | 0.181139 | ||||||||
\(629\) | −11.5443 | −0.460300 | ||||||||
\(630\) | −44.8599 | −1.78726 | ||||||||
\(631\) | 13.3284 | 0.530597 | 0.265298 | − | 0.964166i | \(-0.414530\pi\) | ||||
0.265298 | + | 0.964166i | \(0.414530\pi\) | |||||||
\(632\) | −23.5353 | −0.936182 | ||||||||
\(633\) | 4.45647 | 0.177129 | ||||||||
\(634\) | 0.175177 | 0.00695718 | ||||||||
\(635\) | 21.4628 | 0.851724 | ||||||||
\(636\) | −1.85581 | −0.0735875 | ||||||||
\(637\) | −56.0230 | −2.21971 | ||||||||
\(638\) | −2.73080 | −0.108114 | ||||||||
\(639\) | −35.6159 | −1.40894 | ||||||||
\(640\) | −29.4092 | −1.16250 | ||||||||
\(641\) | −38.8411 | −1.53413 | −0.767065 | − | 0.641569i | \(-0.778284\pi\) | ||||
−0.767065 | + | 0.641569i | \(0.778284\pi\) | |||||||
\(642\) | −9.86197 | −0.389221 | ||||||||
\(643\) | −47.1691 | −1.86017 | −0.930084 | − | 0.367347i | \(-0.880266\pi\) | ||||
−0.930084 | + | 0.367347i | \(0.880266\pi\) | |||||||
\(644\) | −5.87242 | −0.231406 | ||||||||
\(645\) | 1.36350 | 0.0536876 | ||||||||
\(646\) | −9.47505 | −0.372791 | ||||||||
\(647\) | 33.0048 | 1.29755 | 0.648775 | − | 0.760980i | \(-0.275281\pi\) | ||||
0.648775 | + | 0.760980i | \(0.275281\pi\) | |||||||
\(648\) | −13.5257 | −0.531338 | ||||||||
\(649\) | 2.15708 | 0.0846729 | ||||||||
\(650\) | 1.46834 | 0.0575929 | ||||||||
\(651\) | 15.2537 | 0.597839 | ||||||||
\(652\) | −6.93214 | −0.271483 | ||||||||
\(653\) | 23.4943 | 0.919404 | 0.459702 | − | 0.888073i | \(-0.347956\pi\) | ||||
0.459702 | + | 0.888073i | \(0.347956\pi\) | |||||||
\(654\) | −0.902530 | −0.0352917 | ||||||||
\(655\) | 45.5029 | 1.77795 | ||||||||
\(656\) | −6.54185 | −0.255416 | ||||||||
\(657\) | −26.1087 | −1.01860 | ||||||||
\(658\) | 25.3764 | 0.989277 | ||||||||
\(659\) | −43.4618 | −1.69303 | −0.846517 | − | 0.532362i | \(-0.821304\pi\) | ||||
−0.846517 | + | 0.532362i | \(0.821304\pi\) | |||||||
\(660\) | 0.619720 | 0.0241226 | ||||||||
\(661\) | −47.8325 | −1.86047 | −0.930234 | − | 0.366968i | \(-0.880396\pi\) | ||||
−0.930234 | + | 0.366968i | \(0.880396\pi\) | |||||||
\(662\) | 16.2359 | 0.631025 | ||||||||
\(663\) | −1.87477 | −0.0728101 | ||||||||
\(664\) | 7.69571 | 0.298651 | ||||||||
\(665\) | −66.5228 | −2.57964 | ||||||||
\(666\) | 47.0818 | 1.82438 | ||||||||
\(667\) | 4.43172 | 0.171597 | ||||||||
\(668\) | 3.81640 | 0.147661 | ||||||||
\(669\) | 6.90027 | 0.266780 | ||||||||
\(670\) | −17.2771 | −0.667471 | ||||||||
\(671\) | 3.33319 | 0.128676 | ||||||||
\(672\) | 8.08178 | 0.311762 | ||||||||
\(673\) | 29.5896 | 1.14060 | 0.570298 | − | 0.821438i | \(-0.306828\pi\) | ||||
0.570298 | + | 0.821438i | \(0.306828\pi\) | |||||||
\(674\) | 13.1583 | 0.506839 | ||||||||
\(675\) | 1.11153 | 0.0427827 | ||||||||
\(676\) | −1.88283 | −0.0724167 | ||||||||
\(677\) | 2.28690 | 0.0878926 | 0.0439463 | − | 0.999034i | \(-0.486007\pi\) | ||||
0.0439463 | + | 0.999034i | \(0.486007\pi\) | |||||||
\(678\) | −11.7198 | −0.450097 | ||||||||
\(679\) | 55.3150 | 2.12279 | ||||||||
\(680\) | 5.24092 | 0.200980 | ||||||||
\(681\) | −17.9435 | −0.687598 | ||||||||
\(682\) | 7.46535 | 0.285863 | ||||||||
\(683\) | −32.2247 | −1.23304 | −0.616522 | − | 0.787338i | \(-0.711459\pi\) | ||||
−0.616522 | + | 0.787338i | \(0.711459\pi\) | |||||||
\(684\) | 7.15559 | 0.273601 | ||||||||
\(685\) | 33.0326 | 1.26211 | ||||||||
\(686\) | −94.1369 | −3.59416 | ||||||||
\(687\) | 12.2024 | 0.465551 | ||||||||
\(688\) | 4.70244 | 0.179279 | ||||||||
\(689\) | 19.2908 | 0.734921 | ||||||||
\(690\) | −5.43125 | −0.206764 | ||||||||
\(691\) | −36.0679 | −1.37209 | −0.686044 | − | 0.727560i | \(-0.740654\pi\) | ||||
−0.686044 | + | 0.727560i | \(0.740654\pi\) | |||||||
\(692\) | −6.99561 | −0.265933 | ||||||||
\(693\) | −13.2287 | −0.502516 | ||||||||
\(694\) | −29.1825 | −1.10775 | ||||||||
\(695\) | 38.6539 | 1.46623 | ||||||||
\(696\) | −2.65860 | −0.100774 | ||||||||
\(697\) | 1.39116 | 0.0526940 | ||||||||
\(698\) | −41.2453 | −1.56116 | ||||||||
\(699\) | −0.0493954 | −0.00186831 | ||||||||
\(700\) | 0.727350 | 0.0274913 | ||||||||
\(701\) | −27.6313 | −1.04362 | −0.521810 | − | 0.853062i | \(-0.674743\pi\) | ||||
−0.521810 | + | 0.853062i | \(0.674743\pi\) | |||||||
\(702\) | 16.4576 | 0.621151 | ||||||||
\(703\) | 69.8177 | 2.63322 | ||||||||
\(704\) | −5.44955 | −0.205388 | ||||||||
\(705\) | 4.34601 | 0.163680 | ||||||||
\(706\) | 4.18016 | 0.157322 | ||||||||
\(707\) | 80.1090 | 3.01281 | ||||||||
\(708\) | −0.617594 | −0.0232106 | ||||||||
\(709\) | −31.9970 | −1.20167 | −0.600836 | − | 0.799373i | \(-0.705165\pi\) | ||||
−0.600836 | + | 0.799373i | \(0.705165\pi\) | |||||||
\(710\) | −46.3960 | −1.74121 | ||||||||
\(711\) | −25.3032 | −0.948943 | ||||||||
\(712\) | 2.64470 | 0.0991143 | ||||||||
\(713\) | −12.1152 | −0.453719 | ||||||||
\(714\) | −5.01521 | −0.187690 | ||||||||
\(715\) | −6.44188 | −0.240913 | ||||||||
\(716\) | −8.10926 | −0.303057 | ||||||||
\(717\) | −18.6534 | −0.696626 | ||||||||
\(718\) | 25.3006 | 0.944211 | ||||||||
\(719\) | 28.1625 | 1.05028 | 0.525142 | − | 0.851015i | \(-0.324012\pi\) | ||||
0.525142 | + | 0.851015i | \(0.324012\pi\) | |||||||
\(720\) | −26.4964 | −0.987462 | ||||||||
\(721\) | 90.4663 | 3.36914 | ||||||||
\(722\) | 27.5364 | 1.02480 | ||||||||
\(723\) | −6.90637 | −0.256851 | ||||||||
\(724\) | −2.46455 | −0.0915941 | ||||||||
\(725\) | −0.548906 | −0.0203859 | ||||||||
\(726\) | 0.986909 | 0.0366276 | ||||||||
\(727\) | −17.0335 | −0.631737 | −0.315868 | − | 0.948803i | \(-0.602296\pi\) | ||||
−0.315868 | + | 0.948803i | \(0.602296\pi\) | |||||||
\(728\) | −36.6197 | −1.35722 | ||||||||
\(729\) | −7.87137 | −0.291532 | ||||||||
\(730\) | −34.0111 | −1.25881 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | −0.954325 | −0.0352729 | ||||||||
\(733\) | −12.9720 | −0.479133 | −0.239567 | − | 0.970880i | \(-0.577005\pi\) | ||||
−0.239567 | + | 0.970880i | \(0.577005\pi\) | |||||||
\(734\) | 18.1529 | 0.670035 | ||||||||
\(735\) | −25.6665 | −0.946723 | ||||||||
\(736\) | −6.41895 | −0.236606 | ||||||||
\(737\) | −5.09482 | −0.187670 | ||||||||
\(738\) | −5.67368 | −0.208851 | ||||||||
\(739\) | −27.5274 | −1.01261 | −0.506307 | − | 0.862353i | \(-0.668990\pi\) | ||||
−0.506307 | + | 0.862353i | \(0.668990\pi\) | |||||||
\(740\) | 11.3571 | 0.417494 | ||||||||
\(741\) | 11.3383 | 0.416523 | ||||||||
\(742\) | 51.6049 | 1.89447 | ||||||||
\(743\) | −28.4767 | −1.04471 | −0.522354 | − | 0.852728i | \(-0.674946\pi\) | ||||
−0.522354 | + | 0.852728i | \(0.674946\pi\) | |||||||
\(744\) | 7.26795 | 0.266456 | ||||||||
\(745\) | −45.4936 | −1.66676 | ||||||||
\(746\) | −42.2478 | −1.54680 | ||||||||
\(747\) | 8.27379 | 0.302722 | ||||||||
\(748\) | −0.454508 | −0.0166185 | ||||||||
\(749\) | 50.7807 | 1.85549 | ||||||||
\(750\) | 11.3536 | 0.414573 | ||||||||
\(751\) | −47.3137 | −1.72650 | −0.863250 | − | 0.504776i | \(-0.831575\pi\) | ||||
−0.863250 | + | 0.504776i | \(0.831575\pi\) | |||||||
\(752\) | 14.9886 | 0.546576 | ||||||||
\(753\) | −5.48908 | −0.200033 | ||||||||
\(754\) | −8.12726 | −0.295977 | ||||||||
\(755\) | −25.5670 | −0.930479 | ||||||||
\(756\) | 8.15236 | 0.296498 | ||||||||
\(757\) | −27.7097 | −1.00712 | −0.503562 | − | 0.863959i | \(-0.667978\pi\) | ||||
−0.503562 | + | 0.863959i | \(0.667978\pi\) | |||||||
\(758\) | 29.2768 | 1.06338 | ||||||||
\(759\) | −1.60162 | −0.0581350 | ||||||||
\(760\) | −31.6962 | −1.14974 | ||||||||
\(761\) | 15.2571 | 0.553068 | 0.276534 | − | 0.961004i | \(-0.410814\pi\) | ||||
0.276534 | + | 0.961004i | \(0.410814\pi\) | |||||||
\(762\) | −9.78598 | −0.354509 | ||||||||
\(763\) | 4.64726 | 0.168242 | ||||||||
\(764\) | 10.1608 | 0.367603 | ||||||||
\(765\) | 5.63461 | 0.203720 | ||||||||
\(766\) | 37.5481 | 1.35667 | ||||||||
\(767\) | 6.41978 | 0.231805 | ||||||||
\(768\) | 6.54345 | 0.236116 | ||||||||
\(769\) | 25.5780 | 0.922366 | 0.461183 | − | 0.887305i | \(-0.347425\pi\) | ||||
0.461183 | + | 0.887305i | \(0.347425\pi\) | |||||||
\(770\) | −17.2327 | −0.621023 | ||||||||
\(771\) | −11.9356 | −0.429850 | ||||||||
\(772\) | 8.04907 | 0.289692 | ||||||||
\(773\) | −26.5470 | −0.954829 | −0.477415 | − | 0.878678i | \(-0.658426\pi\) | ||||
−0.477415 | + | 0.878678i | \(0.658426\pi\) | |||||||
\(774\) | 4.07837 | 0.146594 | ||||||||
\(775\) | 1.50058 | 0.0539023 | ||||||||
\(776\) | 26.3560 | 0.946126 | ||||||||
\(777\) | 36.9550 | 1.32575 | ||||||||
\(778\) | −29.1699 | −1.04579 | ||||||||
\(779\) | −8.41351 | −0.301445 | ||||||||
\(780\) | 1.84437 | 0.0660392 | ||||||||
\(781\) | −13.6817 | −0.489569 | ||||||||
\(782\) | 3.98333 | 0.142443 | ||||||||
\(783\) | −6.15231 | −0.219866 | ||||||||
\(784\) | −88.5189 | −3.16139 | ||||||||
\(785\) | −21.6176 | −0.771566 | ||||||||
\(786\) | −20.7471 | −0.740025 | ||||||||
\(787\) | −6.66587 | −0.237613 | −0.118806 | − | 0.992917i | \(-0.537907\pi\) | ||||
−0.118806 | + | 0.992917i | \(0.537907\pi\) | |||||||
\(788\) | −7.07488 | −0.252032 | ||||||||
\(789\) | −5.40879 | −0.192558 | ||||||||
\(790\) | −32.9618 | −1.17273 | ||||||||
\(791\) | 60.3470 | 2.14569 | ||||||||
\(792\) | −6.30309 | −0.223971 | ||||||||
\(793\) | 9.92004 | 0.352271 | ||||||||
\(794\) | −16.2062 | −0.575135 | ||||||||
\(795\) | 8.83792 | 0.313449 | ||||||||
\(796\) | 5.27696 | 0.187037 | ||||||||
\(797\) | −33.7256 | −1.19462 | −0.597311 | − | 0.802010i | \(-0.703764\pi\) | ||||
−0.597311 | + | 0.802010i | \(0.703764\pi\) | |||||||
\(798\) | 30.3311 | 1.07371 | ||||||||
\(799\) | −3.18740 | −0.112762 | ||||||||
\(800\) | 0.795042 | 0.0281090 | ||||||||
\(801\) | 2.84336 | 0.100465 | ||||||||
\(802\) | −48.4025 | −1.70915 | ||||||||
\(803\) | −10.0295 | −0.353934 | ||||||||
\(804\) | 1.45870 | 0.0514443 | ||||||||
\(805\) | 27.9663 | 0.985682 | ||||||||
\(806\) | 22.2180 | 0.782594 | ||||||||
\(807\) | 8.30996 | 0.292525 | ||||||||
\(808\) | 38.1697 | 1.34280 | ||||||||
\(809\) | 48.1316 | 1.69222 | 0.846108 | − | 0.533012i | \(-0.178940\pi\) | ||||
0.846108 | + | 0.533012i | \(0.178940\pi\) | |||||||
\(810\) | −18.9431 | −0.665592 | ||||||||
\(811\) | −22.6159 | −0.794151 | −0.397076 | − | 0.917786i | \(-0.629975\pi\) | ||||
−0.397076 | + | 0.917786i | \(0.629975\pi\) | |||||||
\(812\) | −4.02589 | −0.141281 | ||||||||
\(813\) | 13.3812 | 0.469299 | ||||||||
\(814\) | 18.0862 | 0.633922 | ||||||||
\(815\) | 33.0130 | 1.15639 | ||||||||
\(816\) | −2.96223 | −0.103699 | ||||||||
\(817\) | 6.04783 | 0.211587 | ||||||||
\(818\) | 19.3263 | 0.675727 | ||||||||
\(819\) | −39.3705 | −1.37572 | ||||||||
\(820\) | −1.36860 | −0.0477937 | ||||||||
\(821\) | 38.9210 | 1.35835 | 0.679177 | − | 0.733975i | \(-0.262337\pi\) | ||||
0.679177 | + | 0.733975i | \(0.262337\pi\) | |||||||
\(822\) | −15.0613 | −0.525322 | ||||||||
\(823\) | −33.9889 | −1.18478 | −0.592389 | − | 0.805652i | \(-0.701815\pi\) | ||||
−0.592389 | + | 0.805652i | \(0.701815\pi\) | |||||||
\(824\) | 43.1046 | 1.50162 | ||||||||
\(825\) | 0.198374 | 0.00690650 | ||||||||
\(826\) | 17.1736 | 0.597546 | ||||||||
\(827\) | 25.1509 | 0.874582 | 0.437291 | − | 0.899320i | \(-0.355938\pi\) | ||||
0.437291 | + | 0.899320i | \(0.355938\pi\) | |||||||
\(828\) | −3.00822 | −0.104543 | ||||||||
\(829\) | 3.29669 | 0.114499 | 0.0572495 | − | 0.998360i | \(-0.481767\pi\) | ||||
0.0572495 | + | 0.998360i | \(0.481767\pi\) | |||||||
\(830\) | 10.7781 | 0.374112 | ||||||||
\(831\) | −13.2866 | −0.460908 | ||||||||
\(832\) | −16.2186 | −0.562280 | ||||||||
\(833\) | 18.8240 | 0.652214 | ||||||||
\(834\) | −17.6243 | −0.610279 | ||||||||
\(835\) | −18.1749 | −0.628967 | ||||||||
\(836\) | 2.74879 | 0.0950687 | ||||||||
\(837\) | 16.8189 | 0.581347 | ||||||||
\(838\) | −27.5654 | −0.952231 | ||||||||
\(839\) | 5.04326 | 0.174113 | 0.0870564 | − | 0.996203i | \(-0.472254\pi\) | ||||
0.0870564 | + | 0.996203i | \(0.472254\pi\) | |||||||
\(840\) | −16.7770 | −0.578862 | ||||||||
\(841\) | −25.9618 | −0.895234 | ||||||||
\(842\) | 20.8148 | 0.717324 | ||||||||
\(843\) | 9.84956 | 0.339237 | ||||||||
\(844\) | 3.21542 | 0.110679 | ||||||||
\(845\) | 8.96663 | 0.308461 | ||||||||
\(846\) | 12.9994 | 0.446929 | ||||||||
\(847\) | −5.08174 | −0.174611 | ||||||||
\(848\) | 30.4803 | 1.04670 | ||||||||
\(849\) | 8.73200 | 0.299682 | ||||||||
\(850\) | −0.493369 | −0.0169224 | ||||||||
\(851\) | −29.3515 | −1.00615 | ||||||||
\(852\) | 3.91720 | 0.134201 | ||||||||
\(853\) | 6.25291 | 0.214095 | 0.107048 | − | 0.994254i | \(-0.465860\pi\) | ||||
0.107048 | + | 0.994254i | \(0.465860\pi\) | |||||||
\(854\) | 26.5371 | 0.908082 | ||||||||
\(855\) | −34.0771 | −1.16541 | ||||||||
\(856\) | 24.1956 | 0.826987 | ||||||||
\(857\) | −43.8554 | −1.49807 | −0.749037 | − | 0.662529i | \(-0.769483\pi\) | ||||
−0.749037 | + | 0.662529i | \(0.769483\pi\) | |||||||
\(858\) | 2.93718 | 0.100274 | ||||||||
\(859\) | 23.5808 | 0.804567 | 0.402283 | − | 0.915515i | \(-0.368217\pi\) | ||||
0.402283 | + | 0.915515i | \(0.368217\pi\) | |||||||
\(860\) | 0.983785 | 0.0335468 | ||||||||
\(861\) | −4.45333 | −0.151769 | ||||||||
\(862\) | −15.4329 | −0.525647 | ||||||||
\(863\) | 31.7604 | 1.08114 | 0.540568 | − | 0.841301i | \(-0.318210\pi\) | ||||
0.540568 | + | 0.841301i | \(0.318210\pi\) | |||||||
\(864\) | 8.91107 | 0.303161 | ||||||||
\(865\) | 33.3152 | 1.13275 | ||||||||
\(866\) | −48.9652 | −1.66390 | ||||||||
\(867\) | 0.629934 | 0.0213937 | ||||||||
\(868\) | 11.0058 | 0.373561 | ||||||||
\(869\) | −9.72008 | −0.329731 | ||||||||
\(870\) | −3.72344 | −0.126236 | ||||||||
\(871\) | −15.1629 | −0.513775 | ||||||||
\(872\) | 2.21428 | 0.0749852 | ||||||||
\(873\) | 28.3358 | 0.959021 | ||||||||
\(874\) | −24.0905 | −0.814872 | ||||||||
\(875\) | −58.4611 | −1.97635 | ||||||||
\(876\) | 2.87155 | 0.0970206 | ||||||||
\(877\) | −27.9723 | −0.944558 | −0.472279 | − | 0.881449i | \(-0.656569\pi\) | ||||
−0.472279 | + | 0.881449i | \(0.656569\pi\) | |||||||
\(878\) | 49.4053 | 1.66735 | ||||||||
\(879\) | −16.9233 | −0.570808 | ||||||||
\(880\) | −10.1785 | −0.343116 | ||||||||
\(881\) | −31.4662 | −1.06012 | −0.530062 | − | 0.847959i | \(-0.677831\pi\) | ||||
−0.530062 | + | 0.847959i | \(0.677831\pi\) | |||||||
\(882\) | −76.7715 | −2.58503 | ||||||||
\(883\) | 27.7318 | 0.933249 | 0.466625 | − | 0.884455i | \(-0.345470\pi\) | ||||
0.466625 | + | 0.884455i | \(0.345470\pi\) | |||||||
\(884\) | −1.35268 | −0.0454956 | ||||||||
\(885\) | 2.94117 | 0.0988664 | ||||||||
\(886\) | 13.4018 | 0.450242 | ||||||||
\(887\) | 14.3566 | 0.482046 | 0.241023 | − | 0.970519i | \(-0.422517\pi\) | ||||
0.241023 | + | 0.970519i | \(0.422517\pi\) | |||||||
\(888\) | 17.6080 | 0.590886 | ||||||||
\(889\) | 50.3894 | 1.69001 | ||||||||
\(890\) | 3.70398 | 0.124158 | ||||||||
\(891\) | −5.58611 | −0.187142 | ||||||||
\(892\) | 4.97866 | 0.166698 | ||||||||
\(893\) | 19.2768 | 0.645075 | ||||||||
\(894\) | 20.7429 | 0.693745 | ||||||||
\(895\) | 38.6188 | 1.29088 | ||||||||
\(896\) | −69.0457 | −2.30665 | ||||||||
\(897\) | −4.76664 | −0.159153 | ||||||||
\(898\) | 18.8530 | 0.629132 | ||||||||
\(899\) | −8.30570 | −0.277011 | ||||||||
\(900\) | 0.372594 | 0.0124198 | ||||||||
\(901\) | −6.48181 | −0.215940 | ||||||||
\(902\) | −2.17951 | −0.0725699 | ||||||||
\(903\) | 3.20116 | 0.106528 | ||||||||
\(904\) | 28.7536 | 0.956331 | ||||||||
\(905\) | 11.7369 | 0.390148 | ||||||||
\(906\) | 11.6573 | 0.387288 | ||||||||
\(907\) | −1.95467 | −0.0649037 | −0.0324519 | − | 0.999473i | \(-0.510332\pi\) | ||||
−0.0324519 | + | 0.999473i | \(0.510332\pi\) | |||||||
\(908\) | −12.9466 | −0.429647 | ||||||||
\(909\) | 41.0369 | 1.36111 | ||||||||
\(910\) | −51.2869 | −1.70015 | ||||||||
\(911\) | −2.21168 | −0.0732764 | −0.0366382 | − | 0.999329i | \(-0.511665\pi\) | ||||
−0.0366382 | + | 0.999329i | \(0.511665\pi\) | |||||||
\(912\) | 17.9150 | 0.593226 | ||||||||
\(913\) | 3.17833 | 0.105188 | ||||||||
\(914\) | 50.7787 | 1.67961 | ||||||||
\(915\) | 4.54479 | 0.150246 | ||||||||
\(916\) | 8.80424 | 0.290900 | ||||||||
\(917\) | 106.830 | 3.52783 | ||||||||
\(918\) | −5.52983 | −0.182512 | ||||||||
\(919\) | −8.08206 | −0.266602 | −0.133301 | − | 0.991076i | \(-0.542558\pi\) | ||||
−0.133301 | + | 0.991076i | \(0.542558\pi\) | |||||||
\(920\) | 13.3251 | 0.439317 | ||||||||
\(921\) | −1.70873 | −0.0563044 | ||||||||
\(922\) | −10.5025 | −0.345880 | ||||||||
\(923\) | −40.7186 | −1.34027 | ||||||||
\(924\) | 1.45495 | 0.0478644 | ||||||||
\(925\) | 3.63543 | 0.119532 | ||||||||
\(926\) | −13.1327 | −0.431566 | ||||||||
\(927\) | 46.3425 | 1.52209 | ||||||||
\(928\) | −4.40057 | −0.144456 | ||||||||
\(929\) | 8.28327 | 0.271765 | 0.135883 | − | 0.990725i | \(-0.456613\pi\) | ||||
0.135883 | + | 0.990725i | \(0.456613\pi\) | |||||||
\(930\) | 10.1790 | 0.333782 | ||||||||
\(931\) | −113.845 | −3.73110 | ||||||||
\(932\) | −0.0356396 | −0.00116741 | ||||||||
\(933\) | 1.90913 | 0.0625020 | ||||||||
\(934\) | 11.2851 | 0.369260 | ||||||||
\(935\) | 2.16451 | 0.0707869 | ||||||||
\(936\) | −18.7589 | −0.613154 | ||||||||
\(937\) | 42.0003 | 1.37209 | 0.686045 | − | 0.727559i | \(-0.259345\pi\) | ||||
0.686045 | + | 0.727559i | \(0.259345\pi\) | |||||||
\(938\) | −40.5623 | −1.32441 | ||||||||
\(939\) | −5.86096 | −0.191265 | ||||||||
\(940\) | 3.13572 | 0.102276 | ||||||||
\(941\) | −21.1720 | −0.690186 | −0.345093 | − | 0.938568i | \(-0.612153\pi\) | ||||
−0.345093 | + | 0.938568i | \(0.612153\pi\) | |||||||
\(942\) | 9.85658 | 0.321145 | ||||||||
\(943\) | 3.53705 | 0.115182 | ||||||||
\(944\) | 10.1435 | 0.330144 | ||||||||
\(945\) | −38.8240 | −1.26295 | ||||||||
\(946\) | 1.56669 | 0.0509374 | ||||||||
\(947\) | −30.4354 | −0.989019 | −0.494509 | − | 0.869172i | \(-0.664652\pi\) | ||||
−0.494509 | + | 0.869172i | \(0.664652\pi\) | |||||||
\(948\) | 2.78296 | 0.0903862 | ||||||||
\(949\) | −29.8492 | −0.968948 | ||||||||
\(950\) | 2.98381 | 0.0968077 | ||||||||
\(951\) | 0.0704353 | 0.00228402 | ||||||||
\(952\) | 12.3044 | 0.398788 | ||||||||
\(953\) | −24.5406 | −0.794947 | −0.397473 | − | 0.917614i | \(-0.630113\pi\) | ||||
−0.397473 | + | 0.917614i | \(0.630113\pi\) | |||||||
\(954\) | 26.4353 | 0.855873 | ||||||||
\(955\) | −48.3887 | −1.56582 | ||||||||
\(956\) | −13.4588 | −0.435288 | ||||||||
\(957\) | −1.09800 | −0.0354934 | ||||||||
\(958\) | 28.4566 | 0.919391 | ||||||||
\(959\) | 77.5526 | 2.50430 | ||||||||
\(960\) | −7.43044 | −0.239816 | ||||||||
\(961\) | −8.29423 | −0.267556 | ||||||||
\(962\) | 53.8272 | 1.73546 | ||||||||
\(963\) | 26.0131 | 0.838259 | ||||||||
\(964\) | −4.98306 | −0.160494 | ||||||||
\(965\) | −38.3321 | −1.23396 | ||||||||
\(966\) | −12.7513 | −0.410265 | ||||||||
\(967\) | 1.11302 | 0.0357922 | 0.0178961 | − | 0.999840i | \(-0.494303\pi\) | ||||
0.0178961 | + | 0.999840i | \(0.494303\pi\) | |||||||
\(968\) | −2.42130 | −0.0778236 | ||||||||
\(969\) | −3.80973 | −0.122386 | ||||||||
\(970\) | 36.9124 | 1.18518 | ||||||||
\(971\) | 4.40124 | 0.141243 | 0.0706213 | − | 0.997503i | \(-0.477502\pi\) | ||||
0.0706213 | + | 0.997503i | \(0.477502\pi\) | |||||||
\(972\) | 6.41210 | 0.205668 | ||||||||
\(973\) | 90.7500 | 2.90931 | ||||||||
\(974\) | −8.00749 | −0.256576 | ||||||||
\(975\) | 0.590390 | 0.0189076 | ||||||||
\(976\) | 15.6741 | 0.501716 | ||||||||
\(977\) | −3.61620 | −0.115692 | −0.0578462 | − | 0.998326i | \(-0.518423\pi\) | ||||
−0.0578462 | + | 0.998326i | \(0.518423\pi\) | |||||||
\(978\) | −15.0523 | −0.481319 | ||||||||
\(979\) | 1.09226 | 0.0349089 | ||||||||
\(980\) | −18.5188 | −0.591562 | ||||||||
\(981\) | 2.38062 | 0.0760072 | ||||||||
\(982\) | −17.5488 | −0.560005 | ||||||||
\(983\) | −46.1466 | −1.47185 | −0.735925 | − | 0.677063i | \(-0.763252\pi\) | ||||
−0.735925 | + | 0.677063i | \(0.763252\pi\) | |||||||
\(984\) | −2.12188 | −0.0676432 | ||||||||
\(985\) | 33.6928 | 1.07354 | ||||||||
\(986\) | 2.73080 | 0.0869665 | ||||||||
\(987\) | 10.2034 | 0.324777 | ||||||||
\(988\) | 8.18078 | 0.260265 | ||||||||
\(989\) | −2.54252 | −0.0808473 | ||||||||
\(990\) | −8.82766 | −0.280562 | ||||||||
\(991\) | 11.3089 | 0.359240 | 0.179620 | − | 0.983736i | \(-0.442513\pi\) | ||||
0.179620 | + | 0.983736i | \(0.442513\pi\) | |||||||
\(992\) | 12.0301 | 0.381955 | ||||||||
\(993\) | 6.52812 | 0.207164 | ||||||||
\(994\) | −108.927 | −3.45494 | ||||||||
\(995\) | −25.1305 | −0.796691 | ||||||||
\(996\) | −0.909989 | −0.0288341 | ||||||||
\(997\) | 1.28073 | 0.0405611 | 0.0202806 | − | 0.999794i | \(-0.493544\pi\) | ||||
0.0202806 | + | 0.999794i | \(0.493544\pi\) | |||||||
\(998\) | −28.3387 | −0.897046 | ||||||||
\(999\) | 40.7470 | 1.28918 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8041.2.a.f.1.46 | ✓ | 66 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.f.1.46 | ✓ | 66 | 1.1 | even | 1 | trivial |