Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2376278611\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.81389 | −1.98972 | −0.994861 | − | 0.101250i | \(-0.967716\pi\) | ||||
−0.994861 | + | 0.101250i | \(0.967716\pi\) | |||||||
\(3\) | 0.225620 | 0.130262 | 0.0651308 | − | 0.997877i | \(-0.479254\pi\) | ||||
0.0651308 | + | 0.997877i | \(0.479254\pi\) | |||||||
\(4\) | 5.91799 | 2.95899 | ||||||||
\(5\) | −1.24518 | −0.556860 | −0.278430 | − | 0.960456i | \(-0.589814\pi\) | ||||
−0.278430 | + | 0.960456i | \(0.589814\pi\) | |||||||
\(6\) | −0.634869 | −0.259184 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −11.0248 | −3.89785 | ||||||||
\(9\) | −2.94910 | −0.983032 | ||||||||
\(10\) | 3.50380 | 1.10800 | ||||||||
\(11\) | 4.12431 | 1.24353 | 0.621763 | − | 0.783206i | \(-0.286417\pi\) | ||||
0.621763 | + | 0.783206i | \(0.286417\pi\) | |||||||
\(12\) | 1.33521 | 0.385443 | ||||||||
\(13\) | 3.68405 | 1.02177 | 0.510886 | − | 0.859649i | \(-0.329317\pi\) | ||||
0.510886 | + | 0.859649i | \(0.329317\pi\) | |||||||
\(14\) | −2.81389 | −0.752044 | ||||||||
\(15\) | −0.280936 | −0.0725375 | ||||||||
\(16\) | 19.1866 | 4.79665 | ||||||||
\(17\) | −6.21890 | −1.50830 | −0.754152 | − | 0.656700i | \(-0.771952\pi\) | ||||
−0.754152 | + | 0.656700i | \(0.771952\pi\) | |||||||
\(18\) | 8.29844 | 1.95596 | ||||||||
\(19\) | −1.83276 | −0.420465 | −0.210232 | − | 0.977651i | \(-0.567422\pi\) | ||||
−0.210232 | + | 0.977651i | \(0.567422\pi\) | |||||||
\(20\) | −7.36895 | −1.64775 | ||||||||
\(21\) | 0.225620 | 0.0492342 | ||||||||
\(22\) | −11.6054 | −2.47427 | ||||||||
\(23\) | −7.83940 | −1.63463 | −0.817314 | − | 0.576193i | \(-0.804538\pi\) | ||||
−0.817314 | + | 0.576193i | \(0.804538\pi\) | |||||||
\(24\) | −2.48741 | −0.507740 | ||||||||
\(25\) | −3.44953 | −0.689907 | ||||||||
\(26\) | −10.3665 | −2.03304 | ||||||||
\(27\) | −1.34223 | −0.258313 | ||||||||
\(28\) | 5.91799 | 1.11839 | ||||||||
\(29\) | −9.64129 | −1.79034 | −0.895171 | − | 0.445723i | \(-0.852947\pi\) | ||||
−0.895171 | + | 0.445723i | \(0.852947\pi\) | |||||||
\(30\) | 0.790525 | 0.144329 | ||||||||
\(31\) | 6.68893 | 1.20137 | 0.600684 | − | 0.799487i | \(-0.294895\pi\) | ||||
0.600684 | + | 0.799487i | \(0.294895\pi\) | |||||||
\(32\) | −31.9394 | −5.64615 | ||||||||
\(33\) | 0.930525 | 0.161984 | ||||||||
\(34\) | 17.4993 | 3.00111 | ||||||||
\(35\) | −1.24518 | −0.210473 | ||||||||
\(36\) | −17.4527 | −2.90879 | ||||||||
\(37\) | 4.67182 | 0.768042 | 0.384021 | − | 0.923324i | \(-0.374539\pi\) | ||||
0.384021 | + | 0.923324i | \(0.374539\pi\) | |||||||
\(38\) | 5.15720 | 0.836608 | ||||||||
\(39\) | 0.831194 | 0.133098 | ||||||||
\(40\) | 13.7278 | 2.17056 | ||||||||
\(41\) | −5.34630 | −0.834952 | −0.417476 | − | 0.908688i | \(-0.637085\pi\) | ||||
−0.417476 | + | 0.908688i | \(0.637085\pi\) | |||||||
\(42\) | −0.634869 | −0.0979624 | ||||||||
\(43\) | −6.30101 | −0.960895 | −0.480447 | − | 0.877024i | \(-0.659526\pi\) | ||||
−0.480447 | + | 0.877024i | \(0.659526\pi\) | |||||||
\(44\) | 24.4076 | 3.67959 | ||||||||
\(45\) | 3.67215 | 0.547412 | ||||||||
\(46\) | 22.0592 | 3.25245 | ||||||||
\(47\) | −1.19976 | −0.175002 | −0.0875012 | − | 0.996164i | \(-0.527888\pi\) | ||||
−0.0875012 | + | 0.996164i | \(0.527888\pi\) | |||||||
\(48\) | 4.32887 | 0.624819 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 9.70661 | 1.37272 | ||||||||
\(51\) | −1.40311 | −0.196474 | ||||||||
\(52\) | 21.8022 | 3.02342 | ||||||||
\(53\) | 8.21793 | 1.12882 | 0.564410 | − | 0.825495i | \(-0.309104\pi\) | ||||
0.564410 | + | 0.825495i | \(0.309104\pi\) | |||||||
\(54\) | 3.77690 | 0.513971 | ||||||||
\(55\) | −5.13550 | −0.692470 | ||||||||
\(56\) | −11.0248 | −1.47325 | ||||||||
\(57\) | −0.413507 | −0.0547703 | ||||||||
\(58\) | 27.1295 | 3.56228 | ||||||||
\(59\) | 12.7741 | 1.66304 | 0.831522 | − | 0.555492i | \(-0.187470\pi\) | ||||
0.831522 | + | 0.555492i | \(0.187470\pi\) | |||||||
\(60\) | −1.66258 | −0.214638 | ||||||||
\(61\) | −13.8054 | −1.76760 | −0.883800 | − | 0.467864i | \(-0.845024\pi\) | ||||
−0.883800 | + | 0.467864i | \(0.845024\pi\) | |||||||
\(62\) | −18.8219 | −2.39039 | ||||||||
\(63\) | −2.94910 | −0.371551 | ||||||||
\(64\) | 51.5009 | 6.43762 | ||||||||
\(65\) | −4.58730 | −0.568984 | ||||||||
\(66\) | −2.61840 | −0.322302 | ||||||||
\(67\) | 3.40155 | 0.415566 | 0.207783 | − | 0.978175i | \(-0.433375\pi\) | ||||
0.207783 | + | 0.978175i | \(0.433375\pi\) | |||||||
\(68\) | −36.8034 | −4.46306 | ||||||||
\(69\) | −1.76872 | −0.212929 | ||||||||
\(70\) | 3.50380 | 0.418784 | ||||||||
\(71\) | 11.9660 | 1.42010 | 0.710049 | − | 0.704152i | \(-0.248673\pi\) | ||||
0.710049 | + | 0.704152i | \(0.248673\pi\) | |||||||
\(72\) | 32.5132 | 3.83171 | ||||||||
\(73\) | −0.0538456 | −0.00630215 | −0.00315108 | − | 0.999995i | \(-0.501003\pi\) | ||||
−0.00315108 | + | 0.999995i | \(0.501003\pi\) | |||||||
\(74\) | −13.1460 | −1.52819 | ||||||||
\(75\) | −0.778282 | −0.0898683 | ||||||||
\(76\) | −10.8463 | −1.24415 | ||||||||
\(77\) | 4.12431 | 0.470009 | ||||||||
\(78\) | −2.33889 | −0.264827 | ||||||||
\(79\) | −1.41362 | −0.159045 | −0.0795223 | − | 0.996833i | \(-0.525339\pi\) | ||||
−0.0795223 | + | 0.996833i | \(0.525339\pi\) | |||||||
\(80\) | −23.8907 | −2.67106 | ||||||||
\(81\) | 8.54445 | 0.949384 | ||||||||
\(82\) | 15.0439 | 1.66132 | ||||||||
\(83\) | −13.8220 | −1.51717 | −0.758583 | − | 0.651576i | \(-0.774108\pi\) | ||||
−0.758583 | + | 0.651576i | \(0.774108\pi\) | |||||||
\(84\) | 1.33521 | 0.145684 | ||||||||
\(85\) | 7.74363 | 0.839915 | ||||||||
\(86\) | 17.7304 | 1.91191 | ||||||||
\(87\) | −2.17526 | −0.233213 | ||||||||
\(88\) | −45.4697 | −4.84708 | ||||||||
\(89\) | 9.62877 | 1.02065 | 0.510324 | − | 0.859982i | \(-0.329525\pi\) | ||||
0.510324 | + | 0.859982i | \(0.329525\pi\) | |||||||
\(90\) | −10.3330 | −1.08920 | ||||||||
\(91\) | 3.68405 | 0.386193 | ||||||||
\(92\) | −46.3935 | −4.83685 | ||||||||
\(93\) | 1.50915 | 0.156492 | ||||||||
\(94\) | 3.37598 | 0.348206 | ||||||||
\(95\) | 2.28211 | 0.234140 | ||||||||
\(96\) | −7.20616 | −0.735476 | ||||||||
\(97\) | 13.6002 | 1.38089 | 0.690444 | − | 0.723385i | \(-0.257415\pi\) | ||||
0.690444 | + | 0.723385i | \(0.257415\pi\) | |||||||
\(98\) | −2.81389 | −0.284246 | ||||||||
\(99\) | −12.1630 | −1.22243 | ||||||||
\(100\) | −20.4143 | −2.04143 | ||||||||
\(101\) | 2.67785 | 0.266456 | 0.133228 | − | 0.991085i | \(-0.457466\pi\) | ||||
0.133228 | + | 0.991085i | \(0.457466\pi\) | |||||||
\(102\) | 3.94819 | 0.390929 | ||||||||
\(103\) | −15.8953 | −1.56621 | −0.783104 | − | 0.621891i | \(-0.786365\pi\) | ||||
−0.783104 | + | 0.621891i | \(0.786365\pi\) | |||||||
\(104\) | −40.6159 | −3.98272 | ||||||||
\(105\) | −0.280936 | −0.0274166 | ||||||||
\(106\) | −23.1244 | −2.24604 | ||||||||
\(107\) | 10.5862 | 1.02340 | 0.511702 | − | 0.859163i | \(-0.329015\pi\) | ||||
0.511702 | + | 0.859163i | \(0.329015\pi\) | |||||||
\(108\) | −7.94332 | −0.764346 | ||||||||
\(109\) | −4.53186 | −0.434074 | −0.217037 | − | 0.976163i | \(-0.569639\pi\) | ||||
−0.217037 | + | 0.976163i | \(0.569639\pi\) | |||||||
\(110\) | 14.4507 | 1.37782 | ||||||||
\(111\) | 1.05405 | 0.100046 | ||||||||
\(112\) | 19.1866 | 1.81296 | ||||||||
\(113\) | 7.19175 | 0.676543 | 0.338271 | − | 0.941049i | \(-0.390158\pi\) | ||||
0.338271 | + | 0.941049i | \(0.390158\pi\) | |||||||
\(114\) | 1.16356 | 0.108978 | ||||||||
\(115\) | 9.76144 | 0.910259 | ||||||||
\(116\) | −57.0570 | −5.29761 | ||||||||
\(117\) | −10.8646 | −1.00443 | ||||||||
\(118\) | −35.9449 | −3.30899 | ||||||||
\(119\) | −6.21890 | −0.570086 | ||||||||
\(120\) | 3.09727 | 0.282740 | ||||||||
\(121\) | 6.00992 | 0.546356 | ||||||||
\(122\) | 38.8469 | 3.51703 | ||||||||
\(123\) | −1.20623 | −0.108762 | ||||||||
\(124\) | 39.5850 | 3.55484 | ||||||||
\(125\) | 10.5212 | 0.941042 | ||||||||
\(126\) | 8.29844 | 0.739284 | ||||||||
\(127\) | −5.07599 | −0.450421 | −0.225211 | − | 0.974310i | \(-0.572307\pi\) | ||||
−0.225211 | + | 0.974310i | \(0.572307\pi\) | |||||||
\(128\) | −81.0392 | −7.16292 | ||||||||
\(129\) | −1.42163 | −0.125168 | ||||||||
\(130\) | 12.9082 | 1.13212 | ||||||||
\(131\) | 7.09883 | 0.620227 | 0.310114 | − | 0.950699i | \(-0.399633\pi\) | ||||
0.310114 | + | 0.950699i | \(0.399633\pi\) | |||||||
\(132\) | 5.50683 | 0.479308 | ||||||||
\(133\) | −1.83276 | −0.158921 | ||||||||
\(134\) | −9.57161 | −0.826861 | ||||||||
\(135\) | 1.67132 | 0.143844 | ||||||||
\(136\) | 68.5621 | 5.87915 | ||||||||
\(137\) | 1.13495 | 0.0969653 | 0.0484826 | − | 0.998824i | \(-0.484561\pi\) | ||||
0.0484826 | + | 0.998824i | \(0.484561\pi\) | |||||||
\(138\) | 4.97699 | 0.423670 | ||||||||
\(139\) | 3.72237 | 0.315728 | 0.157864 | − | 0.987461i | \(-0.449539\pi\) | ||||
0.157864 | + | 0.987461i | \(0.449539\pi\) | |||||||
\(140\) | −7.36895 | −0.622790 | ||||||||
\(141\) | −0.270688 | −0.0227961 | ||||||||
\(142\) | −33.6709 | −2.82560 | ||||||||
\(143\) | 15.1942 | 1.27060 | ||||||||
\(144\) | −56.5831 | −4.71526 | ||||||||
\(145\) | 12.0051 | 0.996971 | ||||||||
\(146\) | 0.151516 | 0.0125395 | ||||||||
\(147\) | 0.225620 | 0.0186088 | ||||||||
\(148\) | 27.6478 | 2.27263 | ||||||||
\(149\) | 18.1708 | 1.48861 | 0.744306 | − | 0.667839i | \(-0.232780\pi\) | ||||
0.744306 | + | 0.667839i | \(0.232780\pi\) | |||||||
\(150\) | 2.19000 | 0.178813 | ||||||||
\(151\) | 15.8005 | 1.28582 | 0.642912 | − | 0.765940i | \(-0.277726\pi\) | ||||
0.642912 | + | 0.765940i | \(0.277726\pi\) | |||||||
\(152\) | 20.2058 | 1.63891 | ||||||||
\(153\) | 18.3401 | 1.48271 | ||||||||
\(154\) | −11.6054 | −0.935186 | ||||||||
\(155\) | −8.32891 | −0.668994 | ||||||||
\(156\) | 4.91900 | 0.393835 | ||||||||
\(157\) | −11.3490 | −0.905749 | −0.452875 | − | 0.891574i | \(-0.649601\pi\) | ||||
−0.452875 | + | 0.891574i | \(0.649601\pi\) | |||||||
\(158\) | 3.97777 | 0.316454 | ||||||||
\(159\) | 1.85413 | 0.147042 | ||||||||
\(160\) | 39.7703 | 3.14412 | ||||||||
\(161\) | −7.83940 | −0.617831 | ||||||||
\(162\) | −24.0432 | −1.88901 | ||||||||
\(163\) | 4.94342 | 0.387198 | 0.193599 | − | 0.981081i | \(-0.437984\pi\) | ||||
0.193599 | + | 0.981081i | \(0.437984\pi\) | |||||||
\(164\) | −31.6393 | −2.47062 | ||||||||
\(165\) | −1.15867 | −0.0902022 | ||||||||
\(166\) | 38.8937 | 3.01874 | ||||||||
\(167\) | −4.51158 | −0.349117 | −0.174558 | − | 0.984647i | \(-0.555850\pi\) | ||||
−0.174558 | + | 0.984647i | \(0.555850\pi\) | |||||||
\(168\) | −2.48741 | −0.191908 | ||||||||
\(169\) | 0.572227 | 0.0440175 | ||||||||
\(170\) | −21.7897 | −1.67120 | ||||||||
\(171\) | 5.40499 | 0.413330 | ||||||||
\(172\) | −37.2893 | −2.84328 | ||||||||
\(173\) | 18.7126 | 1.42269 | 0.711344 | − | 0.702844i | \(-0.248087\pi\) | ||||
0.711344 | + | 0.702844i | \(0.248087\pi\) | |||||||
\(174\) | 6.12096 | 0.464028 | ||||||||
\(175\) | −3.44953 | −0.260760 | ||||||||
\(176\) | 79.1315 | 5.96476 | ||||||||
\(177\) | 2.88208 | 0.216631 | ||||||||
\(178\) | −27.0943 | −2.03081 | ||||||||
\(179\) | −1.65198 | −0.123475 | −0.0617376 | − | 0.998092i | \(-0.519664\pi\) | ||||
−0.0617376 | + | 0.998092i | \(0.519664\pi\) | |||||||
\(180\) | 21.7317 | 1.61979 | ||||||||
\(181\) | 13.8706 | 1.03099 | 0.515497 | − | 0.856891i | \(-0.327607\pi\) | ||||
0.515497 | + | 0.856891i | \(0.327607\pi\) | |||||||
\(182\) | −10.3665 | −0.768418 | ||||||||
\(183\) | −3.11477 | −0.230250 | ||||||||
\(184\) | 86.4277 | 6.37154 | ||||||||
\(185\) | −5.81724 | −0.427692 | ||||||||
\(186\) | −4.24660 | −0.311376 | ||||||||
\(187\) | −25.6487 | −1.87562 | ||||||||
\(188\) | −7.10014 | −0.517831 | ||||||||
\(189\) | −1.34223 | −0.0976330 | ||||||||
\(190\) | −6.42162 | −0.465874 | ||||||||
\(191\) | −25.6765 | −1.85789 | −0.928945 | − | 0.370219i | \(-0.879283\pi\) | ||||
−0.928945 | + | 0.370219i | \(0.879283\pi\) | |||||||
\(192\) | 11.6196 | 0.838574 | ||||||||
\(193\) | −14.0195 | −1.00914 | −0.504572 | − | 0.863370i | \(-0.668350\pi\) | ||||
−0.504572 | + | 0.863370i | \(0.668350\pi\) | |||||||
\(194\) | −38.2694 | −2.74758 | ||||||||
\(195\) | −1.03498 | −0.0741167 | ||||||||
\(196\) | 5.91799 | 0.422713 | ||||||||
\(197\) | 10.7051 | 0.762705 | 0.381353 | − | 0.924430i | \(-0.375458\pi\) | ||||
0.381353 | + | 0.924430i | \(0.375458\pi\) | |||||||
\(198\) | 34.2253 | 2.43229 | ||||||||
\(199\) | 19.7333 | 1.39885 | 0.699427 | − | 0.714704i | \(-0.253438\pi\) | ||||
0.699427 | + | 0.714704i | \(0.253438\pi\) | |||||||
\(200\) | 38.0304 | 2.68915 | ||||||||
\(201\) | 0.767457 | 0.0541323 | ||||||||
\(202\) | −7.53517 | −0.530172 | ||||||||
\(203\) | −9.64129 | −0.676686 | ||||||||
\(204\) | −8.30356 | −0.581365 | ||||||||
\(205\) | 6.65709 | 0.464952 | ||||||||
\(206\) | 44.7276 | 3.11632 | ||||||||
\(207\) | 23.1191 | 1.60689 | ||||||||
\(208\) | 70.6844 | 4.90108 | ||||||||
\(209\) | −7.55888 | −0.522858 | ||||||||
\(210\) | 0.790525 | 0.0545514 | ||||||||
\(211\) | −15.9611 | −1.09881 | −0.549403 | − | 0.835558i | \(-0.685145\pi\) | ||||
−0.549403 | + | 0.835558i | \(0.685145\pi\) | |||||||
\(212\) | 48.6336 | 3.34017 | ||||||||
\(213\) | 2.69976 | 0.184984 | ||||||||
\(214\) | −29.7884 | −2.03629 | ||||||||
\(215\) | 7.84588 | 0.535084 | ||||||||
\(216\) | 14.7978 | 1.00687 | ||||||||
\(217\) | 6.68893 | 0.454074 | ||||||||
\(218\) | 12.7522 | 0.863686 | ||||||||
\(219\) | −0.0121486 | −0.000820928 0 | ||||||||
\(220\) | −30.3918 | −2.04902 | ||||||||
\(221\) | −22.9107 | −1.54114 | ||||||||
\(222\) | −2.96599 | −0.199064 | ||||||||
\(223\) | −10.0023 | −0.669807 | −0.334903 | − | 0.942253i | \(-0.608704\pi\) | ||||
−0.334903 | + | 0.942253i | \(0.608704\pi\) | |||||||
\(224\) | −31.9394 | −2.13404 | ||||||||
\(225\) | 10.1730 | 0.678200 | ||||||||
\(226\) | −20.2368 | −1.34613 | ||||||||
\(227\) | 28.5169 | 1.89273 | 0.946367 | − | 0.323094i | \(-0.104723\pi\) | ||||
0.946367 | + | 0.323094i | \(0.104723\pi\) | |||||||
\(228\) | −2.44713 | −0.162065 | ||||||||
\(229\) | 8.51405 | 0.562624 | 0.281312 | − | 0.959616i | \(-0.409230\pi\) | ||||
0.281312 | + | 0.959616i | \(0.409230\pi\) | |||||||
\(230\) | −27.4676 | −1.81116 | ||||||||
\(231\) | 0.930525 | 0.0612240 | ||||||||
\(232\) | 106.293 | 6.97849 | ||||||||
\(233\) | 6.71699 | 0.440045 | 0.220022 | − | 0.975495i | \(-0.429387\pi\) | ||||
0.220022 | + | 0.975495i | \(0.429387\pi\) | |||||||
\(234\) | 30.5719 | 1.99854 | ||||||||
\(235\) | 1.49391 | 0.0974519 | ||||||||
\(236\) | 75.5968 | 4.92093 | ||||||||
\(237\) | −0.318940 | −0.0207174 | ||||||||
\(238\) | 17.4993 | 1.13431 | ||||||||
\(239\) | −24.6058 | −1.59162 | −0.795808 | − | 0.605548i | \(-0.792954\pi\) | ||||
−0.795808 | + | 0.605548i | \(0.792954\pi\) | |||||||
\(240\) | −5.39022 | −0.347937 | ||||||||
\(241\) | 3.12431 | 0.201255 | 0.100627 | − | 0.994924i | \(-0.467915\pi\) | ||||
0.100627 | + | 0.994924i | \(0.467915\pi\) | |||||||
\(242\) | −16.9113 | −1.08710 | ||||||||
\(243\) | 5.95449 | 0.381981 | ||||||||
\(244\) | −81.7002 | −5.23032 | ||||||||
\(245\) | −1.24518 | −0.0795515 | ||||||||
\(246\) | 3.39420 | 0.216406 | ||||||||
\(247\) | −6.75199 | −0.429619 | ||||||||
\(248\) | −73.7441 | −4.68276 | ||||||||
\(249\) | −3.11852 | −0.197628 | ||||||||
\(250\) | −29.6054 | −1.87241 | ||||||||
\(251\) | 6.44258 | 0.406652 | 0.203326 | − | 0.979111i | \(-0.434825\pi\) | ||||
0.203326 | + | 0.979111i | \(0.434825\pi\) | |||||||
\(252\) | −17.4527 | −1.09942 | ||||||||
\(253\) | −32.3321 | −2.03270 | ||||||||
\(254\) | 14.2833 | 0.896213 | ||||||||
\(255\) | 1.74712 | 0.109409 | ||||||||
\(256\) | 125.034 | 7.81460 | ||||||||
\(257\) | −2.74640 | −0.171316 | −0.0856578 | − | 0.996325i | \(-0.527299\pi\) | ||||
−0.0856578 | + | 0.996325i | \(0.527299\pi\) | |||||||
\(258\) | 4.00032 | 0.249049 | ||||||||
\(259\) | 4.67182 | 0.290293 | ||||||||
\(260\) | −27.1476 | −1.68362 | ||||||||
\(261\) | 28.4331 | 1.75996 | ||||||||
\(262\) | −19.9753 | −1.23408 | ||||||||
\(263\) | 5.79836 | 0.357542 | 0.178771 | − | 0.983891i | \(-0.442788\pi\) | ||||
0.178771 | + | 0.983891i | \(0.442788\pi\) | |||||||
\(264\) | −10.2588 | −0.631388 | ||||||||
\(265\) | −10.2328 | −0.628595 | ||||||||
\(266\) | 5.15720 | 0.316208 | ||||||||
\(267\) | 2.17244 | 0.132951 | ||||||||
\(268\) | 20.1304 | 1.22966 | ||||||||
\(269\) | −20.1785 | −1.23031 | −0.615153 | − | 0.788408i | \(-0.710906\pi\) | ||||
−0.615153 | + | 0.788408i | \(0.710906\pi\) | |||||||
\(270\) | −4.70291 | −0.286210 | ||||||||
\(271\) | 29.9023 | 1.81644 | 0.908218 | − | 0.418498i | \(-0.137443\pi\) | ||||
0.908218 | + | 0.418498i | \(0.137443\pi\) | |||||||
\(272\) | −119.320 | −7.23481 | ||||||||
\(273\) | 0.831194 | 0.0503061 | ||||||||
\(274\) | −3.19363 | −0.192934 | ||||||||
\(275\) | −14.2269 | −0.857917 | ||||||||
\(276\) | −10.4673 | −0.630056 | ||||||||
\(277\) | 1.72153 | 0.103436 | 0.0517182 | − | 0.998662i | \(-0.483530\pi\) | ||||
0.0517182 | + | 0.998662i | \(0.483530\pi\) | |||||||
\(278\) | −10.4744 | −0.628210 | ||||||||
\(279\) | −19.7263 | −1.18098 | ||||||||
\(280\) | 13.7278 | 0.820395 | ||||||||
\(281\) | 10.2983 | 0.614344 | 0.307172 | − | 0.951654i | \(-0.400617\pi\) | ||||
0.307172 | + | 0.951654i | \(0.400617\pi\) | |||||||
\(282\) | 0.761688 | 0.0453579 | ||||||||
\(283\) | −12.0010 | −0.713388 | −0.356694 | − | 0.934221i | \(-0.616096\pi\) | ||||
−0.356694 | + | 0.934221i | \(0.616096\pi\) | |||||||
\(284\) | 70.8144 | 4.20206 | ||||||||
\(285\) | 0.514890 | 0.0304994 | ||||||||
\(286\) | −42.7547 | −2.52814 | ||||||||
\(287\) | −5.34630 | −0.315582 | ||||||||
\(288\) | 94.1925 | 5.55034 | ||||||||
\(289\) | 21.6747 | 1.27498 | ||||||||
\(290\) | −33.7811 | −1.98369 | ||||||||
\(291\) | 3.06847 | 0.179877 | ||||||||
\(292\) | −0.318658 | −0.0186480 | ||||||||
\(293\) | 29.8631 | 1.74462 | 0.872309 | − | 0.488954i | \(-0.162622\pi\) | ||||
0.872309 | + | 0.488954i | \(0.162622\pi\) | |||||||
\(294\) | −0.634869 | −0.0370263 | ||||||||
\(295\) | −15.9060 | −0.926083 | ||||||||
\(296\) | −51.5058 | −2.99372 | ||||||||
\(297\) | −5.53578 | −0.321219 | ||||||||
\(298\) | −51.1307 | −2.96192 | ||||||||
\(299\) | −28.8807 | −1.67022 | ||||||||
\(300\) | −4.60586 | −0.265920 | ||||||||
\(301\) | −6.30101 | −0.363184 | ||||||||
\(302\) | −44.4608 | −2.55843 | ||||||||
\(303\) | 0.604174 | 0.0347089 | ||||||||
\(304\) | −35.1645 | −2.01682 | ||||||||
\(305\) | 17.1902 | 0.984307 | ||||||||
\(306\) | −51.6071 | −2.95018 | ||||||||
\(307\) | −19.1930 | −1.09540 | −0.547702 | − | 0.836674i | \(-0.684497\pi\) | ||||
−0.547702 | + | 0.836674i | \(0.684497\pi\) | |||||||
\(308\) | 24.4076 | 1.39075 | ||||||||
\(309\) | −3.58629 | −0.204017 | ||||||||
\(310\) | 23.4367 | 1.33111 | ||||||||
\(311\) | 3.76320 | 0.213391 | 0.106696 | − | 0.994292i | \(-0.465973\pi\) | ||||
0.106696 | + | 0.994292i | \(0.465973\pi\) | |||||||
\(312\) | −9.16374 | −0.518795 | ||||||||
\(313\) | −29.9377 | −1.69218 | −0.846091 | − | 0.533039i | \(-0.821050\pi\) | ||||
−0.846091 | + | 0.533039i | \(0.821050\pi\) | |||||||
\(314\) | 31.9349 | 1.80219 | ||||||||
\(315\) | 3.67215 | 0.206902 | ||||||||
\(316\) | −8.36578 | −0.470612 | ||||||||
\(317\) | 19.0952 | 1.07249 | 0.536246 | − | 0.844062i | \(-0.319842\pi\) | ||||
0.536246 | + | 0.844062i | \(0.319842\pi\) | |||||||
\(318\) | −5.21731 | −0.292572 | ||||||||
\(319\) | −39.7636 | −2.22634 | ||||||||
\(320\) | −64.1278 | −3.58485 | ||||||||
\(321\) | 2.38845 | 0.133310 | ||||||||
\(322\) | 22.0592 | 1.22931 | ||||||||
\(323\) | 11.3978 | 0.634189 | ||||||||
\(324\) | 50.5660 | 2.80922 | ||||||||
\(325\) | −12.7083 | −0.704927 | ||||||||
\(326\) | −13.9102 | −0.770417 | ||||||||
\(327\) | −1.02248 | −0.0565431 | ||||||||
\(328\) | 58.9419 | 3.25452 | ||||||||
\(329\) | −1.19976 | −0.0661447 | ||||||||
\(330\) | 3.26037 | 0.179477 | ||||||||
\(331\) | 4.28947 | 0.235771 | 0.117885 | − | 0.993027i | \(-0.462388\pi\) | ||||
0.117885 | + | 0.993027i | \(0.462388\pi\) | |||||||
\(332\) | −81.7987 | −4.48929 | ||||||||
\(333\) | −13.7776 | −0.755010 | ||||||||
\(334\) | 12.6951 | 0.694645 | ||||||||
\(335\) | −4.23554 | −0.231412 | ||||||||
\(336\) | 4.32887 | 0.236159 | ||||||||
\(337\) | −6.64071 | −0.361743 | −0.180871 | − | 0.983507i | \(-0.557892\pi\) | ||||
−0.180871 | + | 0.983507i | \(0.557892\pi\) | |||||||
\(338\) | −1.61019 | −0.0875826 | ||||||||
\(339\) | 1.62260 | 0.0881275 | ||||||||
\(340\) | 45.8267 | 2.48530 | ||||||||
\(341\) | 27.5872 | 1.49393 | ||||||||
\(342\) | −15.2091 | −0.822412 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 69.4673 | 3.74543 | ||||||||
\(345\) | 2.20237 | 0.118572 | ||||||||
\(346\) | −52.6551 | −2.83076 | ||||||||
\(347\) | −18.8861 | −1.01386 | −0.506929 | − | 0.861988i | \(-0.669220\pi\) | ||||
−0.506929 | + | 0.861988i | \(0.669220\pi\) | |||||||
\(348\) | −12.8732 | −0.690075 | ||||||||
\(349\) | 15.3084 | 0.819439 | 0.409719 | − | 0.912212i | \(-0.365627\pi\) | ||||
0.409719 | + | 0.912212i | \(0.365627\pi\) | |||||||
\(350\) | 9.70661 | 0.518840 | ||||||||
\(351\) | −4.94485 | −0.263937 | ||||||||
\(352\) | −131.728 | −7.02113 | ||||||||
\(353\) | −23.1957 | −1.23458 | −0.617292 | − | 0.786734i | \(-0.711770\pi\) | ||||
−0.617292 | + | 0.786734i | \(0.711770\pi\) | |||||||
\(354\) | −8.10987 | −0.431035 | ||||||||
\(355\) | −14.8998 | −0.790797 | ||||||||
\(356\) | 56.9830 | 3.02009 | ||||||||
\(357\) | −1.40311 | −0.0742602 | ||||||||
\(358\) | 4.64851 | 0.245681 | ||||||||
\(359\) | −27.1701 | −1.43398 | −0.716991 | − | 0.697082i | \(-0.754481\pi\) | ||||
−0.716991 | + | 0.697082i | \(0.754481\pi\) | |||||||
\(360\) | −40.4847 | −2.13373 | ||||||||
\(361\) | −15.6410 | −0.823210 | ||||||||
\(362\) | −39.0304 | −2.05139 | ||||||||
\(363\) | 1.35596 | 0.0711692 | ||||||||
\(364\) | 21.8022 | 1.14274 | ||||||||
\(365\) | 0.0670474 | 0.00350942 | ||||||||
\(366\) | 8.76462 | 0.458134 | ||||||||
\(367\) | −10.8239 | −0.565005 | −0.282503 | − | 0.959267i | \(-0.591165\pi\) | ||||
−0.282503 | + | 0.959267i | \(0.591165\pi\) | |||||||
\(368\) | −150.411 | −7.84074 | ||||||||
\(369\) | 15.7668 | 0.820784 | ||||||||
\(370\) | 16.3691 | 0.850989 | ||||||||
\(371\) | 8.21793 | 0.426654 | ||||||||
\(372\) | 8.93116 | 0.463059 | ||||||||
\(373\) | 16.2909 | 0.843511 | 0.421755 | − | 0.906710i | \(-0.361414\pi\) | ||||
0.421755 | + | 0.906710i | \(0.361414\pi\) | |||||||
\(374\) | 72.1726 | 3.73195 | ||||||||
\(375\) | 2.37378 | 0.122582 | ||||||||
\(376\) | 13.2271 | 0.682134 | ||||||||
\(377\) | −35.5190 | −1.82932 | ||||||||
\(378\) | 3.77690 | 0.194263 | ||||||||
\(379\) | 5.44932 | 0.279913 | 0.139956 | − | 0.990158i | \(-0.455304\pi\) | ||||
0.139956 | + | 0.990158i | \(0.455304\pi\) | |||||||
\(380\) | 13.5055 | 0.692819 | ||||||||
\(381\) | −1.14524 | −0.0586726 | ||||||||
\(382\) | 72.2510 | 3.69668 | ||||||||
\(383\) | 7.33864 | 0.374987 | 0.187494 | − | 0.982266i | \(-0.439964\pi\) | ||||
0.187494 | + | 0.982266i | \(0.439964\pi\) | |||||||
\(384\) | −18.2840 | −0.933053 | ||||||||
\(385\) | −5.13550 | −0.261729 | ||||||||
\(386\) | 39.4493 | 2.00792 | ||||||||
\(387\) | 18.5823 | 0.944590 | ||||||||
\(388\) | 80.4857 | 4.08604 | ||||||||
\(389\) | 13.4449 | 0.681682 | 0.340841 | − | 0.940121i | \(-0.389288\pi\) | ||||
0.340841 | + | 0.940121i | \(0.389288\pi\) | |||||||
\(390\) | 2.91233 | 0.147472 | ||||||||
\(391\) | 48.7524 | 2.46552 | ||||||||
\(392\) | −11.0248 | −0.556836 | ||||||||
\(393\) | 1.60163 | 0.0807918 | ||||||||
\(394\) | −30.1229 | −1.51757 | ||||||||
\(395\) | 1.76021 | 0.0885656 | ||||||||
\(396\) | −71.9804 | −3.61715 | ||||||||
\(397\) | −10.6630 | −0.535160 | −0.267580 | − | 0.963536i | \(-0.586224\pi\) | ||||
−0.267580 | + | 0.963536i | \(0.586224\pi\) | |||||||
\(398\) | −55.5273 | −2.78333 | ||||||||
\(399\) | −0.413507 | −0.0207012 | ||||||||
\(400\) | −66.1848 | −3.30924 | ||||||||
\(401\) | 6.09173 | 0.304206 | 0.152103 | − | 0.988365i | \(-0.451395\pi\) | ||||
0.152103 | + | 0.988365i | \(0.451395\pi\) | |||||||
\(402\) | −2.15954 | −0.107708 | ||||||||
\(403\) | 24.6424 | 1.22752 | ||||||||
\(404\) | 15.8475 | 0.788440 | ||||||||
\(405\) | −10.6394 | −0.528674 | ||||||||
\(406\) | 27.1295 | 1.34642 | ||||||||
\(407\) | 19.2680 | 0.955080 | ||||||||
\(408\) | 15.4689 | 0.765827 | ||||||||
\(409\) | −11.0362 | −0.545705 | −0.272852 | − | 0.962056i | \(-0.587967\pi\) | ||||
−0.272852 | + | 0.962056i | \(0.587967\pi\) | |||||||
\(410\) | −18.7323 | −0.925124 | ||||||||
\(411\) | 0.256067 | 0.0126308 | ||||||||
\(412\) | −94.0681 | −4.63440 | ||||||||
\(413\) | 12.7741 | 0.628571 | ||||||||
\(414\) | −65.0547 | −3.19727 | ||||||||
\(415\) | 17.2109 | 0.844850 | ||||||||
\(416\) | −117.667 | −5.76908 | ||||||||
\(417\) | 0.839840 | 0.0411272 | ||||||||
\(418\) | 21.2699 | 1.04034 | ||||||||
\(419\) | 24.8513 | 1.21407 | 0.607034 | − | 0.794676i | \(-0.292359\pi\) | ||||
0.607034 | + | 0.794676i | \(0.292359\pi\) | |||||||
\(420\) | −1.66258 | −0.0811255 | ||||||||
\(421\) | 19.0847 | 0.930131 | 0.465066 | − | 0.885276i | \(-0.346031\pi\) | ||||
0.465066 | + | 0.885276i | \(0.346031\pi\) | |||||||
\(422\) | 44.9127 | 2.18632 | ||||||||
\(423\) | 3.53820 | 0.172033 | ||||||||
\(424\) | −90.6010 | −4.39998 | ||||||||
\(425\) | 21.4523 | 1.04059 | ||||||||
\(426\) | −7.59682 | −0.368067 | ||||||||
\(427\) | −13.8054 | −0.668090 | ||||||||
\(428\) | 62.6489 | 3.02825 | ||||||||
\(429\) | 3.42810 | 0.165510 | ||||||||
\(430\) | −22.0774 | −1.06467 | ||||||||
\(431\) | 9.14848 | 0.440667 | 0.220333 | − | 0.975425i | \(-0.429285\pi\) | ||||
0.220333 | + | 0.975425i | \(0.429285\pi\) | |||||||
\(432\) | −25.7529 | −1.23904 | ||||||||
\(433\) | 19.0731 | 0.916594 | 0.458297 | − | 0.888799i | \(-0.348460\pi\) | ||||
0.458297 | + | 0.888799i | \(0.348460\pi\) | |||||||
\(434\) | −18.8219 | −0.903482 | ||||||||
\(435\) | 2.70859 | 0.129867 | ||||||||
\(436\) | −26.8195 | −1.28442 | ||||||||
\(437\) | 14.3678 | 0.687303 | ||||||||
\(438\) | 0.0341849 | 0.00163342 | ||||||||
\(439\) | 16.6094 | 0.792723 | 0.396362 | − | 0.918094i | \(-0.370273\pi\) | ||||
0.396362 | + | 0.918094i | \(0.370273\pi\) | |||||||
\(440\) | 56.6178 | 2.69915 | ||||||||
\(441\) | −2.94910 | −0.140433 | ||||||||
\(442\) | 64.4683 | 3.06645 | ||||||||
\(443\) | 16.5280 | 0.785270 | 0.392635 | − | 0.919694i | \(-0.371564\pi\) | ||||
0.392635 | + | 0.919694i | \(0.371564\pi\) | |||||||
\(444\) | 6.23788 | 0.296036 | ||||||||
\(445\) | −11.9895 | −0.568358 | ||||||||
\(446\) | 28.1455 | 1.33273 | ||||||||
\(447\) | 4.09969 | 0.193909 | ||||||||
\(448\) | 51.5009 | 2.43319 | ||||||||
\(449\) | −0.869622 | −0.0410400 | −0.0205200 | − | 0.999789i | \(-0.506532\pi\) | ||||
−0.0205200 | + | 0.999789i | \(0.506532\pi\) | |||||||
\(450\) | −28.6257 | −1.34943 | ||||||||
\(451\) | −22.0498 | −1.03828 | ||||||||
\(452\) | 42.5607 | 2.00189 | ||||||||
\(453\) | 3.56489 | 0.167493 | ||||||||
\(454\) | −80.2435 | −3.76601 | ||||||||
\(455\) | −4.58730 | −0.215056 | ||||||||
\(456\) | 4.55883 | 0.213487 | ||||||||
\(457\) | 6.35781 | 0.297406 | 0.148703 | − | 0.988882i | \(-0.452490\pi\) | ||||
0.148703 | + | 0.988882i | \(0.452490\pi\) | |||||||
\(458\) | −23.9576 | −1.11947 | ||||||||
\(459\) | 8.34721 | 0.389614 | ||||||||
\(460\) | 57.7681 | 2.69345 | ||||||||
\(461\) | 3.94964 | 0.183953 | 0.0919765 | − | 0.995761i | \(-0.470682\pi\) | ||||
0.0919765 | + | 0.995761i | \(0.470682\pi\) | |||||||
\(462\) | −2.61840 | −0.121819 | ||||||||
\(463\) | 26.8026 | 1.24562 | 0.622810 | − | 0.782373i | \(-0.285991\pi\) | ||||
0.622810 | + | 0.782373i | \(0.285991\pi\) | |||||||
\(464\) | −184.984 | −8.58765 | ||||||||
\(465\) | −1.87917 | −0.0871442 | ||||||||
\(466\) | −18.9009 | −0.875567 | ||||||||
\(467\) | 34.4026 | 1.59196 | 0.795982 | − | 0.605320i | \(-0.206955\pi\) | ||||
0.795982 | + | 0.605320i | \(0.206955\pi\) | |||||||
\(468\) | −64.2967 | −2.97211 | ||||||||
\(469\) | 3.40155 | 0.157069 | ||||||||
\(470\) | −4.20370 | −0.193902 | ||||||||
\(471\) | −2.56056 | −0.117984 | ||||||||
\(472\) | −140.832 | −6.48230 | ||||||||
\(473\) | −25.9873 | −1.19490 | ||||||||
\(474\) | 0.897463 | 0.0412218 | ||||||||
\(475\) | 6.32217 | 0.290081 | ||||||||
\(476\) | −36.8034 | −1.68688 | ||||||||
\(477\) | −24.2355 | −1.10967 | ||||||||
\(478\) | 69.2381 | 3.16688 | ||||||||
\(479\) | −16.6804 | −0.762146 | −0.381073 | − | 0.924545i | \(-0.624445\pi\) | ||||
−0.381073 | + | 0.924545i | \(0.624445\pi\) | |||||||
\(480\) | 8.97295 | 0.409557 | ||||||||
\(481\) | 17.2112 | 0.784764 | ||||||||
\(482\) | −8.79147 | −0.400441 | ||||||||
\(483\) | −1.76872 | −0.0804796 | ||||||||
\(484\) | 35.5666 | 1.61667 | ||||||||
\(485\) | −16.9346 | −0.768962 | ||||||||
\(486\) | −16.7553 | −0.760036 | ||||||||
\(487\) | −26.9676 | −1.22202 | −0.611009 | − | 0.791623i | \(-0.709236\pi\) | ||||
−0.611009 | + | 0.791623i | \(0.709236\pi\) | |||||||
\(488\) | 152.202 | 6.88985 | ||||||||
\(489\) | 1.11533 | 0.0504370 | ||||||||
\(490\) | 3.50380 | 0.158285 | ||||||||
\(491\) | −26.2886 | −1.18639 | −0.593193 | − | 0.805060i | \(-0.702133\pi\) | ||||
−0.593193 | + | 0.805060i | \(0.702133\pi\) | |||||||
\(492\) | −7.13845 | −0.321826 | ||||||||
\(493\) | 59.9582 | 2.70038 | ||||||||
\(494\) | 18.9994 | 0.854822 | ||||||||
\(495\) | 15.1451 | 0.680720 | ||||||||
\(496\) | 128.338 | 5.76254 | ||||||||
\(497\) | 11.9660 | 0.536747 | ||||||||
\(498\) | 8.77519 | 0.393226 | ||||||||
\(499\) | 12.7873 | 0.572436 | 0.286218 | − | 0.958165i | \(-0.407602\pi\) | ||||
0.286218 | + | 0.958165i | \(0.407602\pi\) | |||||||
\(500\) | 62.2641 | 2.78454 | ||||||||
\(501\) | −1.01790 | −0.0454765 | ||||||||
\(502\) | −18.1287 | −0.809125 | ||||||||
\(503\) | −37.0549 | −1.65220 | −0.826098 | − | 0.563526i | \(-0.809444\pi\) | ||||
−0.826098 | + | 0.563526i | \(0.809444\pi\) | |||||||
\(504\) | 32.5132 | 1.44825 | ||||||||
\(505\) | −3.33439 | −0.148379 | ||||||||
\(506\) | 90.9790 | 4.04451 | ||||||||
\(507\) | 0.129106 | 0.00573378 | ||||||||
\(508\) | −30.0397 | −1.33279 | ||||||||
\(509\) | −5.13313 | −0.227522 | −0.113761 | − | 0.993508i | \(-0.536290\pi\) | ||||
−0.113761 | + | 0.993508i | \(0.536290\pi\) | |||||||
\(510\) | −4.91619 | −0.217693 | ||||||||
\(511\) | −0.0538456 | −0.00238199 | ||||||||
\(512\) | −189.753 | −8.38596 | ||||||||
\(513\) | 2.45999 | 0.108611 | ||||||||
\(514\) | 7.72807 | 0.340870 | ||||||||
\(515\) | 19.7924 | 0.872159 | ||||||||
\(516\) | −8.41319 | −0.370370 | ||||||||
\(517\) | −4.94816 | −0.217620 | ||||||||
\(518\) | −13.1460 | −0.577602 | ||||||||
\(519\) | 4.22192 | 0.185322 | ||||||||
\(520\) | 50.5740 | 2.21782 | ||||||||
\(521\) | 28.7925 | 1.26142 | 0.630712 | − | 0.776017i | \(-0.282763\pi\) | ||||
0.630712 | + | 0.776017i | \(0.282763\pi\) | |||||||
\(522\) | −80.0076 | −3.50184 | ||||||||
\(523\) | 17.7568 | 0.776450 | 0.388225 | − | 0.921565i | \(-0.373088\pi\) | ||||
0.388225 | + | 0.921565i | \(0.373088\pi\) | |||||||
\(524\) | 42.0108 | 1.83525 | ||||||||
\(525\) | −0.778282 | −0.0339670 | ||||||||
\(526\) | −16.3160 | −0.711410 | ||||||||
\(527\) | −41.5978 | −1.81203 | ||||||||
\(528\) | 17.8536 | 0.776979 | ||||||||
\(529\) | 38.4561 | 1.67201 | ||||||||
\(530\) | 28.7940 | 1.25073 | ||||||||
\(531\) | −37.6720 | −1.63482 | ||||||||
\(532\) | −10.8463 | −0.470245 | ||||||||
\(533\) | −19.6960 | −0.853130 | ||||||||
\(534\) | −6.11301 | −0.264536 | ||||||||
\(535\) | −13.1817 | −0.569893 | ||||||||
\(536\) | −37.5014 | −1.61982 | ||||||||
\(537\) | −0.372720 | −0.0160841 | ||||||||
\(538\) | 56.7802 | 2.44797 | ||||||||
\(539\) | 4.12431 | 0.177647 | ||||||||
\(540\) | 9.89084 | 0.425634 | ||||||||
\(541\) | −18.5554 | −0.797757 | −0.398878 | − | 0.917004i | \(-0.630600\pi\) | ||||
−0.398878 | + | 0.917004i | \(0.630600\pi\) | |||||||
\(542\) | −84.1419 | −3.61420 | ||||||||
\(543\) | 3.12948 | 0.134299 | ||||||||
\(544\) | 198.628 | 8.51611 | ||||||||
\(545\) | 5.64298 | 0.241718 | ||||||||
\(546\) | −2.33889 | −0.100095 | ||||||||
\(547\) | 29.9525 | 1.28067 | 0.640337 | − | 0.768094i | \(-0.278795\pi\) | ||||
0.640337 | + | 0.768094i | \(0.278795\pi\) | |||||||
\(548\) | 6.71662 | 0.286920 | ||||||||
\(549\) | 40.7135 | 1.73761 | ||||||||
\(550\) | 40.0331 | 1.70702 | ||||||||
\(551\) | 17.6702 | 0.752775 | ||||||||
\(552\) | 19.4998 | 0.829966 | ||||||||
\(553\) | −1.41362 | −0.0601132 | ||||||||
\(554\) | −4.84419 | −0.205810 | ||||||||
\(555\) | −1.31248 | −0.0557118 | ||||||||
\(556\) | 22.0290 | 0.934236 | ||||||||
\(557\) | −8.27286 | −0.350532 | −0.175266 | − | 0.984521i | \(-0.556079\pi\) | ||||
−0.175266 | + | 0.984521i | \(0.556079\pi\) | |||||||
\(558\) | 55.5077 | 2.34983 | ||||||||
\(559\) | −23.2132 | −0.981815 | ||||||||
\(560\) | −23.8907 | −1.00957 | ||||||||
\(561\) | −5.78684 | −0.244321 | ||||||||
\(562\) | −28.9783 | −1.22237 | ||||||||
\(563\) | 25.7075 | 1.08344 | 0.541721 | − | 0.840559i | \(-0.317773\pi\) | ||||
0.541721 | + | 0.840559i | \(0.317773\pi\) | |||||||
\(564\) | −1.60193 | −0.0674534 | ||||||||
\(565\) | −8.95500 | −0.376740 | ||||||||
\(566\) | 33.7696 | 1.41944 | ||||||||
\(567\) | 8.54445 | 0.358833 | ||||||||
\(568\) | −131.922 | −5.53534 | ||||||||
\(569\) | −28.1916 | −1.18185 | −0.590927 | − | 0.806725i | \(-0.701238\pi\) | ||||
−0.590927 | + | 0.806725i | \(0.701238\pi\) | |||||||
\(570\) | −1.44884 | −0.0606854 | ||||||||
\(571\) | 42.4672 | 1.77720 | 0.888599 | − | 0.458685i | \(-0.151679\pi\) | ||||
0.888599 | + | 0.458685i | \(0.151679\pi\) | |||||||
\(572\) | 89.9189 | 3.75970 | ||||||||
\(573\) | −5.79313 | −0.242011 | ||||||||
\(574\) | 15.0439 | 0.627921 | ||||||||
\(575\) | 27.0423 | 1.12774 | ||||||||
\(576\) | −151.881 | −6.32838 | ||||||||
\(577\) | 7.28929 | 0.303457 | 0.151729 | − | 0.988422i | \(-0.451516\pi\) | ||||
0.151729 | + | 0.988422i | \(0.451516\pi\) | |||||||
\(578\) | −60.9903 | −2.53686 | ||||||||
\(579\) | −3.16307 | −0.131453 | ||||||||
\(580\) | 71.0461 | 2.95003 | ||||||||
\(581\) | −13.8220 | −0.573435 | ||||||||
\(582\) | −8.63433 | −0.357905 | ||||||||
\(583\) | 33.8933 | 1.40372 | ||||||||
\(584\) | 0.593637 | 0.0245649 | ||||||||
\(585\) | 13.5284 | 0.559330 | ||||||||
\(586\) | −84.0314 | −3.47131 | ||||||||
\(587\) | 5.98008 | 0.246824 | 0.123412 | − | 0.992355i | \(-0.460616\pi\) | ||||
0.123412 | + | 0.992355i | \(0.460616\pi\) | |||||||
\(588\) | 1.33521 | 0.0550633 | ||||||||
\(589\) | −12.2592 | −0.505133 | ||||||||
\(590\) | 44.7578 | 1.84265 | ||||||||
\(591\) | 2.41528 | 0.0993512 | ||||||||
\(592\) | 89.6363 | 3.68403 | ||||||||
\(593\) | −6.64002 | −0.272673 | −0.136336 | − | 0.990663i | \(-0.543533\pi\) | ||||
−0.136336 | + | 0.990663i | \(0.543533\pi\) | |||||||
\(594\) | 15.5771 | 0.639136 | ||||||||
\(595\) | 7.74363 | 0.317458 | ||||||||
\(596\) | 107.535 | 4.40479 | ||||||||
\(597\) | 4.45221 | 0.182217 | ||||||||
\(598\) | 81.2673 | 3.32327 | ||||||||
\(599\) | −30.7495 | −1.25639 | −0.628195 | − | 0.778056i | \(-0.716206\pi\) | ||||
−0.628195 | + | 0.778056i | \(0.716206\pi\) | |||||||
\(600\) | 8.58040 | 0.350293 | ||||||||
\(601\) | 9.29276 | 0.379060 | 0.189530 | − | 0.981875i | \(-0.439304\pi\) | ||||
0.189530 | + | 0.981875i | \(0.439304\pi\) | |||||||
\(602\) | 17.7304 | 0.722635 | ||||||||
\(603\) | −10.0315 | −0.408515 | ||||||||
\(604\) | 93.5069 | 3.80474 | ||||||||
\(605\) | −7.48342 | −0.304244 | ||||||||
\(606\) | −1.70008 | −0.0690611 | ||||||||
\(607\) | −0.544087 | −0.0220838 | −0.0110419 | − | 0.999939i | \(-0.503515\pi\) | ||||
−0.0110419 | + | 0.999939i | \(0.503515\pi\) | |||||||
\(608\) | 58.5374 | 2.37401 | ||||||||
\(609\) | −2.17526 | −0.0881461 | ||||||||
\(610\) | −48.3713 | −1.95850 | ||||||||
\(611\) | −4.41996 | −0.178812 | ||||||||
\(612\) | 108.537 | 4.38733 | ||||||||
\(613\) | 11.7191 | 0.473331 | 0.236666 | − | 0.971591i | \(-0.423945\pi\) | ||||
0.236666 | + | 0.971591i | \(0.423945\pi\) | |||||||
\(614\) | 54.0071 | 2.17955 | ||||||||
\(615\) | 1.50197 | 0.0605653 | ||||||||
\(616\) | −45.4697 | −1.83202 | ||||||||
\(617\) | −2.03619 | −0.0819741 | −0.0409871 | − | 0.999160i | \(-0.513050\pi\) | ||||
−0.0409871 | + | 0.999160i | \(0.513050\pi\) | |||||||
\(618\) | 10.0914 | 0.405936 | ||||||||
\(619\) | 39.5680 | 1.59037 | 0.795186 | − | 0.606365i | \(-0.207373\pi\) | ||||
0.795186 | + | 0.606365i | \(0.207373\pi\) | |||||||
\(620\) | −49.2904 | −1.97955 | ||||||||
\(621\) | 10.5223 | 0.422245 | ||||||||
\(622\) | −10.5892 | −0.424589 | ||||||||
\(623\) | 9.62877 | 0.385769 | ||||||||
\(624\) | 15.9478 | 0.638422 | ||||||||
\(625\) | 4.14694 | 0.165878 | ||||||||
\(626\) | 84.2416 | 3.36697 | ||||||||
\(627\) | −1.70543 | −0.0681083 | ||||||||
\(628\) | −67.1633 | −2.68011 | ||||||||
\(629\) | −29.0536 | −1.15844 | ||||||||
\(630\) | −10.3330 | −0.411678 | ||||||||
\(631\) | 33.4087 | 1.32998 | 0.664990 | − | 0.746852i | \(-0.268436\pi\) | ||||
0.664990 | + | 0.746852i | \(0.268436\pi\) | |||||||
\(632\) | 15.5849 | 0.619932 | ||||||||
\(633\) | −3.60113 | −0.143132 | ||||||||
\(634\) | −53.7317 | −2.13396 | ||||||||
\(635\) | 6.32051 | 0.250822 | ||||||||
\(636\) | 10.9727 | 0.435096 | ||||||||
\(637\) | 3.68405 | 0.145967 | ||||||||
\(638\) | 111.891 | 4.42979 | ||||||||
\(639\) | −35.2888 | −1.39600 | ||||||||
\(640\) | 100.908 | 3.98874 | ||||||||
\(641\) | 14.5134 | 0.573243 | 0.286621 | − | 0.958044i | \(-0.407468\pi\) | ||||
0.286621 | + | 0.958044i | \(0.407468\pi\) | |||||||
\(642\) | −6.72084 | −0.265250 | ||||||||
\(643\) | −40.1988 | −1.58529 | −0.792643 | − | 0.609687i | \(-0.791295\pi\) | ||||
−0.792643 | + | 0.609687i | \(0.791295\pi\) | |||||||
\(644\) | −46.3935 | −1.82816 | ||||||||
\(645\) | 1.77018 | 0.0697009 | ||||||||
\(646\) | −32.0721 | −1.26186 | ||||||||
\(647\) | −31.5030 | −1.23851 | −0.619254 | − | 0.785190i | \(-0.712565\pi\) | ||||
−0.619254 | + | 0.785190i | \(0.712565\pi\) | |||||||
\(648\) | −94.2008 | −3.70056 | ||||||||
\(649\) | 52.6842 | 2.06804 | ||||||||
\(650\) | 35.7596 | 1.40261 | ||||||||
\(651\) | 1.50915 | 0.0591484 | ||||||||
\(652\) | 29.2551 | 1.14572 | ||||||||
\(653\) | 35.5305 | 1.39042 | 0.695208 | − | 0.718809i | \(-0.255312\pi\) | ||||
0.695208 | + | 0.718809i | \(0.255312\pi\) | |||||||
\(654\) | 2.87714 | 0.112505 | ||||||||
\(655\) | −8.83930 | −0.345380 | ||||||||
\(656\) | −102.577 | −4.00497 | ||||||||
\(657\) | 0.158796 | 0.00619522 | ||||||||
\(658\) | 3.37598 | 0.131610 | ||||||||
\(659\) | 23.1778 | 0.902881 | 0.451440 | − | 0.892301i | \(-0.350910\pi\) | ||||
0.451440 | + | 0.892301i | \(0.350910\pi\) | |||||||
\(660\) | −6.85699 | −0.266908 | ||||||||
\(661\) | −10.5632 | −0.410860 | −0.205430 | − | 0.978672i | \(-0.565859\pi\) | ||||
−0.205430 | + | 0.978672i | \(0.565859\pi\) | |||||||
\(662\) | −12.0701 | −0.469118 | ||||||||
\(663\) | −5.16911 | −0.200752 | ||||||||
\(664\) | 152.385 | 5.91369 | ||||||||
\(665\) | 2.28211 | 0.0884966 | ||||||||
\(666\) | 38.7688 | 1.50226 | ||||||||
\(667\) | 75.5819 | 2.92654 | ||||||||
\(668\) | −26.6995 | −1.03303 | ||||||||
\(669\) | −2.25672 | −0.0872500 | ||||||||
\(670\) | 11.9183 | 0.460446 | ||||||||
\(671\) | −56.9377 | −2.19806 | ||||||||
\(672\) | −7.20616 | −0.277984 | ||||||||
\(673\) | −11.2628 | −0.434150 | −0.217075 | − | 0.976155i | \(-0.569652\pi\) | ||||
−0.217075 | + | 0.976155i | \(0.569652\pi\) | |||||||
\(674\) | 18.6862 | 0.719767 | ||||||||
\(675\) | 4.63007 | 0.178212 | ||||||||
\(676\) | 3.38643 | 0.130247 | ||||||||
\(677\) | −0.608062 | −0.0233697 | −0.0116849 | − | 0.999932i | \(-0.503719\pi\) | ||||
−0.0116849 | + | 0.999932i | \(0.503719\pi\) | |||||||
\(678\) | −4.56582 | −0.175349 | ||||||||
\(679\) | 13.6002 | 0.521927 | ||||||||
\(680\) | −85.3720 | −3.27387 | ||||||||
\(681\) | 6.43397 | 0.246550 | ||||||||
\(682\) | −77.6275 | −2.97251 | ||||||||
\(683\) | −22.0405 | −0.843358 | −0.421679 | − | 0.906745i | \(-0.638559\pi\) | ||||
−0.421679 | + | 0.906745i | \(0.638559\pi\) | |||||||
\(684\) | 31.9867 | 1.22304 | ||||||||
\(685\) | −1.41321 | −0.0539961 | ||||||||
\(686\) | −2.81389 | −0.107435 | ||||||||
\(687\) | 1.92094 | 0.0732883 | ||||||||
\(688\) | −120.895 | −4.60908 | ||||||||
\(689\) | 30.2753 | 1.15340 | ||||||||
\(690\) | −6.19724 | −0.235925 | ||||||||
\(691\) | −21.1030 | −0.802797 | −0.401398 | − | 0.915904i | \(-0.631476\pi\) | ||||
−0.401398 | + | 0.915904i | \(0.631476\pi\) | |||||||
\(692\) | 110.741 | 4.20973 | ||||||||
\(693\) | −12.1630 | −0.462033 | ||||||||
\(694\) | 53.1434 | 2.01730 | ||||||||
\(695\) | −4.63502 | −0.175816 | ||||||||
\(696\) | 23.9818 | 0.909029 | ||||||||
\(697\) | 33.2481 | 1.25936 | ||||||||
\(698\) | −43.0761 | −1.63046 | ||||||||
\(699\) | 1.51548 | 0.0573209 | ||||||||
\(700\) | −20.4143 | −0.771588 | ||||||||
\(701\) | 27.6644 | 1.04487 | 0.522435 | − | 0.852679i | \(-0.325024\pi\) | ||||
0.522435 | + | 0.852679i | \(0.325024\pi\) | |||||||
\(702\) | 13.9143 | 0.525161 | ||||||||
\(703\) | −8.56233 | −0.322934 | ||||||||
\(704\) | 212.406 | 8.00534 | ||||||||
\(705\) | 0.337055 | 0.0126942 | ||||||||
\(706\) | 65.2703 | 2.45648 | ||||||||
\(707\) | 2.67785 | 0.100711 | ||||||||
\(708\) | 17.0561 | 0.641008 | ||||||||
\(709\) | 28.3531 | 1.06482 | 0.532412 | − | 0.846485i | \(-0.321286\pi\) | ||||
0.532412 | + | 0.846485i | \(0.321286\pi\) | |||||||
\(710\) | 41.9263 | 1.57347 | ||||||||
\(711\) | 4.16890 | 0.156346 | ||||||||
\(712\) | −106.155 | −3.97834 | ||||||||
\(713\) | −52.4372 | −1.96379 | ||||||||
\(714\) | 3.94819 | 0.147757 | ||||||||
\(715\) | −18.9194 | −0.707546 | ||||||||
\(716\) | −9.77643 | −0.365362 | ||||||||
\(717\) | −5.55155 | −0.207326 | ||||||||
\(718\) | 76.4537 | 2.85323 | ||||||||
\(719\) | −21.7253 | −0.810218 | −0.405109 | − | 0.914268i | \(-0.632766\pi\) | ||||
−0.405109 | + | 0.914268i | \(0.632766\pi\) | |||||||
\(720\) | 70.4560 | 2.62574 | ||||||||
\(721\) | −15.8953 | −0.591971 | ||||||||
\(722\) | 44.0120 | 1.63796 | ||||||||
\(723\) | 0.704906 | 0.0262157 | ||||||||
\(724\) | 82.0861 | 3.05071 | ||||||||
\(725\) | 33.2579 | 1.23517 | ||||||||
\(726\) | −3.81551 | −0.141607 | ||||||||
\(727\) | −5.78059 | −0.214390 | −0.107195 | − | 0.994238i | \(-0.534187\pi\) | ||||
−0.107195 | + | 0.994238i | \(0.534187\pi\) | |||||||
\(728\) | −40.6159 | −1.50533 | ||||||||
\(729\) | −24.2899 | −0.899626 | ||||||||
\(730\) | −0.188664 | −0.00698277 | ||||||||
\(731\) | 39.1853 | 1.44932 | ||||||||
\(732\) | −18.4332 | −0.681309 | ||||||||
\(733\) | −8.04894 | −0.297294 | −0.148647 | − | 0.988890i | \(-0.547492\pi\) | ||||
−0.148647 | + | 0.988890i | \(0.547492\pi\) | |||||||
\(734\) | 30.4574 | 1.12420 | ||||||||
\(735\) | −0.280936 | −0.0103625 | ||||||||
\(736\) | 250.386 | 9.22935 | ||||||||
\(737\) | 14.0291 | 0.516767 | ||||||||
\(738\) | −44.3659 | −1.63313 | ||||||||
\(739\) | −6.17166 | −0.227028 | −0.113514 | − | 0.993536i | \(-0.536211\pi\) | ||||
−0.113514 | + | 0.993536i | \(0.536211\pi\) | |||||||
\(740\) | −34.4264 | −1.26554 | ||||||||
\(741\) | −1.52338 | −0.0559628 | ||||||||
\(742\) | −23.1244 | −0.848923 | ||||||||
\(743\) | −21.1424 | −0.775640 | −0.387820 | − | 0.921735i | \(-0.626772\pi\) | ||||
−0.387820 | + | 0.921735i | \(0.626772\pi\) | |||||||
\(744\) | −16.6381 | −0.609983 | ||||||||
\(745\) | −22.6259 | −0.828949 | ||||||||
\(746\) | −45.8408 | −1.67835 | ||||||||
\(747\) | 40.7625 | 1.49142 | ||||||||
\(748\) | −151.788 | −5.54994 | ||||||||
\(749\) | 10.5862 | 0.386811 | ||||||||
\(750\) | −6.67956 | −0.243903 | ||||||||
\(751\) | 9.58269 | 0.349677 | 0.174839 | − | 0.984597i | \(-0.444060\pi\) | ||||
0.174839 | + | 0.984597i | \(0.444060\pi\) | |||||||
\(752\) | −23.0192 | −0.839425 | ||||||||
\(753\) | 1.45357 | 0.0529711 | ||||||||
\(754\) | 99.9466 | 3.63984 | ||||||||
\(755\) | −19.6744 | −0.716024 | ||||||||
\(756\) | −7.94332 | −0.288896 | ||||||||
\(757\) | −9.53376 | −0.346510 | −0.173255 | − | 0.984877i | \(-0.555429\pi\) | ||||
−0.173255 | + | 0.984877i | \(0.555429\pi\) | |||||||
\(758\) | −15.3338 | −0.556948 | ||||||||
\(759\) | −7.29475 | −0.264783 | ||||||||
\(760\) | −25.1598 | −0.912644 | ||||||||
\(761\) | 17.3227 | 0.627948 | 0.313974 | − | 0.949432i | \(-0.398339\pi\) | ||||
0.313974 | + | 0.949432i | \(0.398339\pi\) | |||||||
\(762\) | 3.22259 | 0.116742 | ||||||||
\(763\) | −4.53186 | −0.164064 | ||||||||
\(764\) | −151.953 | −5.49748 | ||||||||
\(765\) | −22.8367 | −0.825663 | ||||||||
\(766\) | −20.6501 | −0.746120 | ||||||||
\(767\) | 47.0603 | 1.69925 | ||||||||
\(768\) | 28.2100 | 1.01794 | ||||||||
\(769\) | 7.16435 | 0.258353 | 0.129177 | − | 0.991622i | \(-0.458767\pi\) | ||||
0.129177 | + | 0.991622i | \(0.458767\pi\) | |||||||
\(770\) | 14.4507 | 0.520768 | ||||||||
\(771\) | −0.619641 | −0.0223158 | ||||||||
\(772\) | −82.9671 | −2.98605 | ||||||||
\(773\) | 37.5855 | 1.35185 | 0.675927 | − | 0.736968i | \(-0.263743\pi\) | ||||
0.675927 | + | 0.736968i | \(0.263743\pi\) | |||||||
\(774\) | −52.2885 | −1.87947 | ||||||||
\(775\) | −23.0737 | −0.828832 | ||||||||
\(776\) | −149.939 | −5.38250 | ||||||||
\(777\) | 1.05405 | 0.0378140 | ||||||||
\(778\) | −37.8324 | −1.35636 | ||||||||
\(779\) | 9.79850 | 0.351068 | ||||||||
\(780\) | −6.12502 | −0.219311 | ||||||||
\(781\) | 49.3513 | 1.76593 | ||||||||
\(782\) | −137.184 | −4.90569 | ||||||||
\(783\) | 12.9408 | 0.462468 | ||||||||
\(784\) | 19.1866 | 0.685236 | ||||||||
\(785\) | 14.1315 | 0.504376 | ||||||||
\(786\) | −4.50683 | −0.160753 | ||||||||
\(787\) | −16.1960 | −0.577326 | −0.288663 | − | 0.957431i | \(-0.593211\pi\) | ||||
−0.288663 | + | 0.957431i | \(0.593211\pi\) | |||||||
\(788\) | 63.3525 | 2.25684 | ||||||||
\(789\) | 1.30822 | 0.0465740 | ||||||||
\(790\) | −4.95303 | −0.176221 | ||||||||
\(791\) | 7.19175 | 0.255709 | ||||||||
\(792\) | 134.094 | 4.76484 | ||||||||
\(793\) | −50.8598 | −1.80608 | ||||||||
\(794\) | 30.0045 | 1.06482 | ||||||||
\(795\) | −2.30872 | −0.0818818 | ||||||||
\(796\) | 116.781 | 4.13920 | ||||||||
\(797\) | −1.54570 | −0.0547515 | −0.0273758 | − | 0.999625i | \(-0.508715\pi\) | ||||
−0.0273758 | + | 0.999625i | \(0.508715\pi\) | |||||||
\(798\) | 1.16356 | 0.0411897 | ||||||||
\(799\) | 7.46116 | 0.263957 | ||||||||
\(800\) | 110.176 | 3.89532 | ||||||||
\(801\) | −28.3962 | −1.00333 | ||||||||
\(802\) | −17.1415 | −0.605286 | ||||||||
\(803\) | −0.222076 | −0.00783689 | ||||||||
\(804\) | 4.54180 | 0.160177 | ||||||||
\(805\) | 9.76144 | 0.344046 | ||||||||
\(806\) | −69.3410 | −2.44243 | ||||||||
\(807\) | −4.55267 | −0.160262 | ||||||||
\(808\) | −29.5227 | −1.03860 | ||||||||
\(809\) | 48.5618 | 1.70734 | 0.853670 | − | 0.520814i | \(-0.174372\pi\) | ||||
0.853670 | + | 0.520814i | \(0.174372\pi\) | |||||||
\(810\) | 29.9380 | 1.05191 | ||||||||
\(811\) | 11.8743 | 0.416964 | 0.208482 | − | 0.978026i | \(-0.433148\pi\) | ||||
0.208482 | + | 0.978026i | \(0.433148\pi\) | |||||||
\(812\) | −57.0570 | −2.00231 | ||||||||
\(813\) | 6.74655 | 0.236612 | ||||||||
\(814\) | −54.2181 | −1.90034 | ||||||||
\(815\) | −6.15543 | −0.215615 | ||||||||
\(816\) | −26.9208 | −0.942417 | ||||||||
\(817\) | 11.5483 | 0.404022 | ||||||||
\(818\) | 31.0547 | 1.08580 | ||||||||
\(819\) | −10.8646 | −0.379640 | ||||||||
\(820\) | 39.3966 | 1.37579 | ||||||||
\(821\) | 6.75381 | 0.235709 | 0.117855 | − | 0.993031i | \(-0.462398\pi\) | ||||
0.117855 | + | 0.993031i | \(0.462398\pi\) | |||||||
\(822\) | −0.720544 | −0.0251319 | ||||||||
\(823\) | −37.4394 | −1.30506 | −0.652528 | − | 0.757764i | \(-0.726292\pi\) | ||||
−0.652528 | + | 0.757764i | \(0.726292\pi\) | |||||||
\(824\) | 175.242 | 6.10485 | ||||||||
\(825\) | −3.20988 | −0.111754 | ||||||||
\(826\) | −35.9449 | −1.25068 | ||||||||
\(827\) | 31.0660 | 1.08027 | 0.540135 | − | 0.841578i | \(-0.318373\pi\) | ||||
0.540135 | + | 0.841578i | \(0.318373\pi\) | |||||||
\(828\) | 136.819 | 4.75478 | ||||||||
\(829\) | 29.7453 | 1.03310 | 0.516548 | − | 0.856258i | \(-0.327217\pi\) | ||||
0.516548 | + | 0.856258i | \(0.327217\pi\) | |||||||
\(830\) | −48.4296 | −1.68102 | ||||||||
\(831\) | 0.388410 | 0.0134738 | ||||||||
\(832\) | 189.732 | 6.57777 | ||||||||
\(833\) | −6.21890 | −0.215472 | ||||||||
\(834\) | −2.36322 | −0.0818316 | ||||||||
\(835\) | 5.61772 | 0.194409 | ||||||||
\(836\) | −44.7333 | −1.54714 | ||||||||
\(837\) | −8.97810 | −0.310329 | ||||||||
\(838\) | −69.9290 | −2.41566 | ||||||||
\(839\) | −23.8695 | −0.824067 | −0.412033 | − | 0.911169i | \(-0.635181\pi\) | ||||
−0.412033 | + | 0.911169i | \(0.635181\pi\) | |||||||
\(840\) | 3.09727 | 0.106866 | ||||||||
\(841\) | 63.9544 | 2.20533 | ||||||||
\(842\) | −53.7023 | −1.85070 | ||||||||
\(843\) | 2.32350 | 0.0800254 | ||||||||
\(844\) | −94.4575 | −3.25136 | ||||||||
\(845\) | −0.712525 | −0.0245116 | ||||||||
\(846\) | −9.95610 | −0.342298 | ||||||||
\(847\) | 6.00992 | 0.206503 | ||||||||
\(848\) | 157.674 | 5.41456 | ||||||||
\(849\) | −2.70767 | −0.0929270 | ||||||||
\(850\) | −60.3644 | −2.07048 | ||||||||
\(851\) | −36.6242 | −1.25546 | ||||||||
\(852\) | 15.9771 | 0.547367 | ||||||||
\(853\) | −22.5549 | −0.772266 | −0.386133 | − | 0.922443i | \(-0.626189\pi\) | ||||
−0.386133 | + | 0.922443i | \(0.626189\pi\) | |||||||
\(854\) | 38.8469 | 1.32931 | ||||||||
\(855\) | −6.73017 | −0.230167 | ||||||||
\(856\) | −116.710 | −3.98908 | ||||||||
\(857\) | 23.4946 | 0.802562 | 0.401281 | − | 0.915955i | \(-0.368565\pi\) | ||||
0.401281 | + | 0.915955i | \(0.368565\pi\) | |||||||
\(858\) | −9.64630 | −0.329319 | ||||||||
\(859\) | −20.5325 | −0.700560 | −0.350280 | − | 0.936645i | \(-0.613914\pi\) | ||||
−0.350280 | + | 0.936645i | \(0.613914\pi\) | |||||||
\(860\) | 46.4318 | 1.58331 | ||||||||
\(861\) | −1.20623 | −0.0411082 | ||||||||
\(862\) | −25.7428 | −0.876804 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | 42.8702 | 1.45847 | ||||||||
\(865\) | −23.3005 | −0.792239 | ||||||||
\(866\) | −53.6696 | −1.82377 | ||||||||
\(867\) | 4.89024 | 0.166081 | ||||||||
\(868\) | 39.5850 | 1.34360 | ||||||||
\(869\) | −5.83020 | −0.197776 | ||||||||
\(870\) | −7.62168 | −0.258399 | ||||||||
\(871\) | 12.5315 | 0.424614 | ||||||||
\(872\) | 49.9629 | 1.69196 | ||||||||
\(873\) | −40.1082 | −1.35746 | ||||||||
\(874\) | −40.4293 | −1.36754 | ||||||||
\(875\) | 10.5212 | 0.355680 | ||||||||
\(876\) | −0.0718954 | −0.00242912 | ||||||||
\(877\) | −34.4856 | −1.16450 | −0.582248 | − | 0.813011i | \(-0.697827\pi\) | ||||
−0.582248 | + | 0.813011i | \(0.697827\pi\) | |||||||
\(878\) | −46.7371 | −1.57730 | ||||||||
\(879\) | 6.73769 | 0.227257 | ||||||||
\(880\) | −98.5327 | −3.32154 | ||||||||
\(881\) | 18.0702 | 0.608802 | 0.304401 | − | 0.952544i | \(-0.401544\pi\) | ||||
0.304401 | + | 0.952544i | \(0.401544\pi\) | |||||||
\(882\) | 8.29844 | 0.279423 | ||||||||
\(883\) | 15.1250 | 0.508998 | 0.254499 | − | 0.967073i | \(-0.418089\pi\) | ||||
0.254499 | + | 0.967073i | \(0.418089\pi\) | |||||||
\(884\) | −135.585 | −4.56023 | ||||||||
\(885\) | −3.58870 | −0.120633 | ||||||||
\(886\) | −46.5081 | −1.56247 | ||||||||
\(887\) | −26.2847 | −0.882555 | −0.441278 | − | 0.897371i | \(-0.645475\pi\) | ||||
−0.441278 | + | 0.897371i | \(0.645475\pi\) | |||||||
\(888\) | −11.6207 | −0.389966 | ||||||||
\(889\) | −5.07599 | −0.170243 | ||||||||
\(890\) | 33.7373 | 1.13088 | ||||||||
\(891\) | 35.2400 | 1.18058 | ||||||||
\(892\) | −59.1938 | −1.98195 | ||||||||
\(893\) | 2.19887 | 0.0735823 | ||||||||
\(894\) | −11.5361 | −0.385825 | ||||||||
\(895\) | 2.05701 | 0.0687584 | ||||||||
\(896\) | −81.0392 | −2.70733 | ||||||||
\(897\) | −6.51606 | −0.217565 | ||||||||
\(898\) | 2.44702 | 0.0816582 | ||||||||
\(899\) | −64.4899 | −2.15086 | ||||||||
\(900\) | 60.2037 | 2.00679 | ||||||||
\(901\) | −51.1065 | −1.70260 | ||||||||
\(902\) | 62.0457 | 2.06590 | ||||||||
\(903\) | −1.42163 | −0.0473089 | ||||||||
\(904\) | −79.2875 | −2.63706 | ||||||||
\(905\) | −17.2714 | −0.574120 | ||||||||
\(906\) | −10.0312 | −0.333265 | ||||||||
\(907\) | 50.2750 | 1.66935 | 0.834677 | − | 0.550739i | \(-0.185654\pi\) | ||||
0.834677 | + | 0.550739i | \(0.185654\pi\) | |||||||
\(908\) | 168.763 | 5.60059 | ||||||||
\(909\) | −7.89722 | −0.261934 | ||||||||
\(910\) | 12.9082 | 0.427901 | ||||||||
\(911\) | −0.484125 | −0.0160398 | −0.00801989 | − | 0.999968i | \(-0.502553\pi\) | ||||
−0.00801989 | + | 0.999968i | \(0.502553\pi\) | |||||||
\(912\) | −7.93380 | −0.262714 | ||||||||
\(913\) | −57.0064 | −1.88664 | ||||||||
\(914\) | −17.8902 | −0.591755 | ||||||||
\(915\) | 3.87844 | 0.128217 | ||||||||
\(916\) | 50.3860 | 1.66480 | ||||||||
\(917\) | 7.09883 | 0.234424 | ||||||||
\(918\) | −23.4881 | −0.775224 | ||||||||
\(919\) | −1.50492 | −0.0496426 | −0.0248213 | − | 0.999692i | \(-0.507902\pi\) | ||||
−0.0248213 | + | 0.999692i | \(0.507902\pi\) | |||||||
\(920\) | −107.618 | −3.54806 | ||||||||
\(921\) | −4.33032 | −0.142689 | ||||||||
\(922\) | −11.1139 | −0.366016 | ||||||||
\(923\) | 44.0832 | 1.45102 | ||||||||
\(924\) | 5.50683 | 0.181162 | ||||||||
\(925\) | −16.1156 | −0.529877 | ||||||||
\(926\) | −75.4195 | −2.47844 | ||||||||
\(927\) | 46.8767 | 1.53963 | ||||||||
\(928\) | 307.937 | 10.1085 | ||||||||
\(929\) | 4.47406 | 0.146789 | 0.0733945 | − | 0.997303i | \(-0.476617\pi\) | ||||
0.0733945 | + | 0.997303i | \(0.476617\pi\) | |||||||
\(930\) | 5.28777 | 0.173393 | ||||||||
\(931\) | −1.83276 | −0.0600664 | ||||||||
\(932\) | 39.7511 | 1.30209 | ||||||||
\(933\) | 0.849051 | 0.0277967 | ||||||||
\(934\) | −96.8053 | −3.16757 | ||||||||
\(935\) | 31.9371 | 1.04446 | ||||||||
\(936\) | 119.780 | 3.91514 | ||||||||
\(937\) | 13.8454 | 0.452310 | 0.226155 | − | 0.974091i | \(-0.427384\pi\) | ||||
0.226155 | + | 0.974091i | \(0.427384\pi\) | |||||||
\(938\) | −9.57161 | −0.312524 | ||||||||
\(939\) | −6.75454 | −0.220426 | ||||||||
\(940\) | 8.84094 | 0.288360 | ||||||||
\(941\) | −40.9664 | −1.33547 | −0.667734 | − | 0.744400i | \(-0.732735\pi\) | ||||
−0.667734 | + | 0.744400i | \(0.732735\pi\) | |||||||
\(942\) | 7.20513 | 0.234756 | ||||||||
\(943\) | 41.9118 | 1.36483 | ||||||||
\(944\) | 245.091 | 7.97704 | ||||||||
\(945\) | 1.67132 | 0.0543680 | ||||||||
\(946\) | 73.1255 | 2.37751 | ||||||||
\(947\) | −48.6265 | −1.58015 | −0.790075 | − | 0.613010i | \(-0.789958\pi\) | ||||
−0.790075 | + | 0.613010i | \(0.789958\pi\) | |||||||
\(948\) | −1.88748 | −0.0613026 | ||||||||
\(949\) | −0.198370 | −0.00643936 | ||||||||
\(950\) | −17.7899 | −0.577181 | ||||||||
\(951\) | 4.30824 | 0.139704 | ||||||||
\(952\) | 68.5621 | 2.22211 | ||||||||
\(953\) | 14.9688 | 0.484888 | 0.242444 | − | 0.970165i | \(-0.422051\pi\) | ||||
0.242444 | + | 0.970165i | \(0.422051\pi\) | |||||||
\(954\) | 68.1960 | 2.20793 | ||||||||
\(955\) | 31.9719 | 1.03458 | ||||||||
\(956\) | −145.617 | −4.70958 | ||||||||
\(957\) | −8.97146 | −0.290006 | ||||||||
\(958\) | 46.9368 | 1.51646 | ||||||||
\(959\) | 1.13495 | 0.0366494 | ||||||||
\(960\) | −14.4685 | −0.466968 | ||||||||
\(961\) | 13.7418 | 0.443285 | ||||||||
\(962\) | −48.4305 | −1.56146 | ||||||||
\(963\) | −31.2197 | −1.00604 | ||||||||
\(964\) | 18.4896 | 0.595511 | ||||||||
\(965\) | 17.4567 | 0.561952 | ||||||||
\(966\) | 4.97699 | 0.160132 | ||||||||
\(967\) | 13.1427 | 0.422641 | 0.211320 | − | 0.977417i | \(-0.432224\pi\) | ||||
0.211320 | + | 0.977417i | \(0.432224\pi\) | |||||||
\(968\) | −66.2581 | −2.12962 | ||||||||
\(969\) | 2.57156 | 0.0826104 | ||||||||
\(970\) | 47.6522 | 1.53002 | ||||||||
\(971\) | 22.4397 | 0.720126 | 0.360063 | − | 0.932928i | \(-0.382755\pi\) | ||||
0.360063 | + | 0.932928i | \(0.382755\pi\) | |||||||
\(972\) | 35.2386 | 1.13028 | ||||||||
\(973\) | 3.72237 | 0.119334 | ||||||||
\(974\) | 75.8839 | 2.43148 | ||||||||
\(975\) | −2.86723 | −0.0918249 | ||||||||
\(976\) | −264.879 | −8.47856 | ||||||||
\(977\) | 23.8032 | 0.761533 | 0.380766 | − | 0.924671i | \(-0.375660\pi\) | ||||
0.380766 | + | 0.924671i | \(0.375660\pi\) | |||||||
\(978\) | −3.13842 | −0.100356 | ||||||||
\(979\) | 39.7120 | 1.26920 | ||||||||
\(980\) | −7.36895 | −0.235392 | ||||||||
\(981\) | 13.3649 | 0.426708 | ||||||||
\(982\) | 73.9732 | 2.36058 | ||||||||
\(983\) | −5.39300 | −0.172010 | −0.0860050 | − | 0.996295i | \(-0.527410\pi\) | ||||
−0.0860050 | + | 0.996295i | \(0.527410\pi\) | |||||||
\(984\) | 13.2984 | 0.423939 | ||||||||
\(985\) | −13.3297 | −0.424720 | ||||||||
\(986\) | −168.716 | −5.37301 | ||||||||
\(987\) | −0.270688 | −0.00861611 | ||||||||
\(988\) | −39.9582 | −1.27124 | ||||||||
\(989\) | 49.3961 | 1.57070 | ||||||||
\(990\) | −42.6166 | −1.35444 | ||||||||
\(991\) | 39.3701 | 1.25063 | 0.625316 | − | 0.780371i | \(-0.284970\pi\) | ||||
0.625316 | + | 0.780371i | \(0.284970\pi\) | |||||||
\(992\) | −213.641 | −6.78310 | ||||||||
\(993\) | 0.967788 | 0.0307118 | ||||||||
\(994\) | −33.6709 | −1.06798 | ||||||||
\(995\) | −24.5714 | −0.778967 | ||||||||
\(996\) | −18.4554 | −0.584781 | ||||||||
\(997\) | −59.4927 | −1.88415 | −0.942076 | − | 0.335400i | \(-0.891128\pi\) | ||||
−0.942076 | + | 0.335400i | \(0.891128\pi\) | |||||||
\(998\) | −35.9819 | −1.13899 | ||||||||
\(999\) | −6.27067 | −0.198395 |
(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 | 6041.2.a.f.1.1 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.1 | ✓ | 132 | 1.1 | even | 1 | trivial |