Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.59580 | −1.12840 | −0.564201 | − | 0.825637i | \(-0.690816\pi\) | ||||
−0.564201 | + | 0.825637i | \(0.690816\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.546582 | 0.273291 | ||||||||
\(5\) | 1.23722 | 0.553303 | 0.276651 | − | 0.960970i | \(-0.410775\pi\) | ||||
0.276651 | + | 0.960970i | \(0.410775\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.46504 | 0.931698 | 0.465849 | − | 0.884864i | \(-0.345749\pi\) | ||||
0.465849 | + | 0.884864i | \(0.345749\pi\) | |||||||
\(8\) | 2.31937 | 0.820020 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.97436 | −0.624348 | ||||||||
\(11\) | 4.04090 | 1.21838 | 0.609189 | − | 0.793025i | \(-0.291495\pi\) | ||||
0.609189 | + | 0.793025i | \(0.291495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.08460 | 1.68756 | 0.843782 | − | 0.536686i | \(-0.180324\pi\) | ||||
0.843782 | + | 0.536686i | \(0.180324\pi\) | |||||||
\(14\) | −3.93372 | −1.05133 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.79441 | −1.19860 | ||||||||
\(17\) | −5.58185 | −1.35380 | −0.676899 | − | 0.736076i | \(-0.736676\pi\) | ||||
−0.676899 | + | 0.736076i | \(0.736676\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.469978 | −0.107820 | −0.0539102 | − | 0.998546i | \(-0.517168\pi\) | ||||
−0.0539102 | + | 0.998546i | \(0.517168\pi\) | |||||||
\(20\) | 0.676244 | 0.151213 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.44848 | −1.37482 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.46928 | −0.693856 | ||||||||
\(26\) | −9.70981 | −1.90425 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.34735 | 0.254625 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00112 | −0.359411 | −0.179706 | − | 0.983720i | \(-0.557514\pi\) | ||||
−0.179706 | + | 0.983720i | \(0.557514\pi\) | |||||||
\(32\) | 3.01220 | 0.532486 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.90752 | 1.52763 | ||||||||
\(35\) | 3.04981 | 0.515511 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.90581 | 0.970909 | 0.485455 | − | 0.874262i | \(-0.338654\pi\) | ||||
0.485455 | + | 0.874262i | \(0.338654\pi\) | |||||||
\(38\) | 0.749992 | 0.121665 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.86957 | 0.453719 | ||||||||
\(41\) | 8.01822 | 1.25224 | 0.626118 | − | 0.779728i | \(-0.284643\pi\) | ||||
0.626118 | + | 0.779728i | \(0.284643\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.87624 | 1.04862 | 0.524308 | − | 0.851529i | \(-0.324324\pi\) | ||||
0.524308 | + | 0.851529i | \(0.324324\pi\) | |||||||
\(44\) | 2.20869 | 0.332972 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.59580 | 0.235288 | ||||||||
\(47\) | −8.37297 | −1.22132 | −0.610662 | − | 0.791892i | \(-0.709096\pi\) | ||||
−0.610662 | + | 0.791892i | \(0.709096\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.923569 | −0.131938 | ||||||||
\(50\) | 5.53628 | 0.782948 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.32573 | 0.461196 | ||||||||
\(53\) | 2.29752 | 0.315589 | 0.157795 | − | 0.987472i | \(-0.449562\pi\) | ||||
0.157795 | + | 0.987472i | \(0.449562\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.99950 | 0.674132 | ||||||||
\(56\) | 5.71733 | 0.764011 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.59580 | −0.209539 | ||||||||
\(59\) | 6.71576 | 0.874318 | 0.437159 | − | 0.899384i | \(-0.355985\pi\) | ||||
0.437159 | + | 0.899384i | \(0.355985\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00054 | 1.02436 | 0.512182 | − | 0.858877i | \(-0.328837\pi\) | ||||
0.512182 | + | 0.858877i | \(0.328837\pi\) | |||||||
\(62\) | 3.19338 | 0.405560 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.78196 | 0.597744 | ||||||||
\(65\) | 7.52800 | 0.933734 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.11908 | 0.747565 | 0.373782 | − | 0.927516i | \(-0.378061\pi\) | ||||
0.373782 | + | 0.927516i | \(0.378061\pi\) | |||||||
\(68\) | −3.05094 | −0.369981 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.86688 | −0.581704 | ||||||||
\(71\) | 0.713918 | 0.0847265 | 0.0423633 | − | 0.999102i | \(-0.486511\pi\) | ||||
0.0423633 | + | 0.999102i | \(0.486511\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.9116 | 1.62822 | 0.814112 | − | 0.580708i | \(-0.197224\pi\) | ||||
0.814112 | + | 0.580708i | \(0.197224\pi\) | |||||||
\(74\) | −9.42450 | −1.09558 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.256882 | −0.0294664 | ||||||||
\(77\) | 9.96100 | 1.13516 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.01641 | 0.226864 | 0.113432 | − | 0.993546i | \(-0.463816\pi\) | ||||
0.113432 | + | 0.993546i | \(0.463816\pi\) | |||||||
\(80\) | −5.93176 | −0.663190 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.7955 | −1.41303 | ||||||||
\(83\) | −7.66901 | −0.841783 | −0.420891 | − | 0.907111i | \(-0.638283\pi\) | ||||
−0.420891 | + | 0.907111i | \(0.638283\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.90599 | −0.749060 | ||||||||
\(86\) | −10.9731 | −1.18326 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.37233 | 0.999094 | ||||||||
\(89\) | 0.733342 | 0.0777340 | 0.0388670 | − | 0.999244i | \(-0.487625\pi\) | ||||
0.0388670 | + | 0.999244i | \(0.487625\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.9988 | 1.57230 | ||||||||
\(92\) | −0.546582 | −0.0569851 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.3616 | 1.37814 | ||||||||
\(95\) | −0.581468 | −0.0596573 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.7405 | −1.29360 | −0.646801 | − | 0.762659i | \(-0.723894\pi\) | ||||
−0.646801 | + | 0.762659i | \(0.723894\pi\) | |||||||
\(98\) | 1.47383 | 0.148880 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.89625 | −0.189625 | ||||||||
\(101\) | −5.49886 | −0.547157 | −0.273579 | − | 0.961850i | \(-0.588207\pi\) | ||||
−0.273579 | + | 0.961850i | \(0.588207\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.6277 | 1.73691 | 0.868456 | − | 0.495766i | \(-0.165113\pi\) | ||||
0.868456 | + | 0.495766i | \(0.165113\pi\) | |||||||
\(104\) | 14.1124 | 1.38384 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.66639 | −0.356111 | ||||||||
\(107\) | −1.85338 | −0.179173 | −0.0895864 | − | 0.995979i | \(-0.528555\pi\) | ||||
−0.0895864 | + | 0.995979i | \(0.528555\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.48112 | −0.141866 | −0.0709330 | − | 0.997481i | \(-0.522598\pi\) | ||||
−0.0709330 | + | 0.997481i | \(0.522598\pi\) | |||||||
\(110\) | −7.97821 | −0.760692 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.8184 | −1.11674 | ||||||||
\(113\) | −10.0892 | −0.949111 | −0.474556 | − | 0.880225i | \(-0.657391\pi\) | ||||
−0.474556 | + | 0.880225i | \(0.657391\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.23722 | −0.115372 | ||||||||
\(116\) | 0.546582 | 0.0507489 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.7170 | −0.986582 | ||||||||
\(119\) | −13.7595 | −1.26133 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.32890 | 0.484445 | ||||||||
\(122\) | −12.7673 | −1.15589 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.09377 | −0.0982238 | ||||||||
\(125\) | −10.4784 | −0.937215 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.74706 | 0.776176 | 0.388088 | − | 0.921622i | \(-0.373136\pi\) | ||||
0.388088 | + | 0.921622i | \(0.373136\pi\) | |||||||
\(128\) | −13.6554 | −1.20698 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.0132 | −1.05363 | ||||||||
\(131\) | −1.66085 | −0.145109 | −0.0725546 | − | 0.997364i | \(-0.523115\pi\) | ||||
−0.0725546 | + | 0.997364i | \(0.523115\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.15852 | −0.100456 | ||||||||
\(134\) | −9.76484 | −0.843554 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.9464 | −1.11014 | ||||||||
\(137\) | −1.05944 | −0.0905145 | −0.0452572 | − | 0.998975i | \(-0.514411\pi\) | ||||
−0.0452572 | + | 0.998975i | \(0.514411\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.42956 | −0.290892 | −0.145446 | − | 0.989366i | \(-0.546462\pi\) | ||||
−0.145446 | + | 0.989366i | \(0.546462\pi\) | |||||||
\(140\) | 1.66697 | 0.140885 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.13927 | −0.0956056 | ||||||||
\(143\) | 24.5873 | 2.05609 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.23722 | 0.102746 | ||||||||
\(146\) | −22.2001 | −1.83729 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.22801 | 0.265341 | ||||||||
\(149\) | −16.0167 | −1.31214 | −0.656071 | − | 0.754699i | \(-0.727783\pi\) | ||||
−0.656071 | + | 0.754699i | \(0.727783\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.43031 | −0.686049 | −0.343024 | − | 0.939326i | \(-0.611451\pi\) | ||||
−0.343024 | + | 0.939326i | \(0.611451\pi\) | |||||||
\(152\) | −1.09005 | −0.0884149 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −15.8958 | −1.28092 | ||||||||
\(155\) | −2.47583 | −0.198863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.27432 | −0.261319 | −0.130659 | − | 0.991427i | \(-0.541709\pi\) | ||||
−0.130659 | + | 0.991427i | \(0.541709\pi\) | |||||||
\(158\) | −3.21779 | −0.255994 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.72676 | 0.294626 | ||||||||
\(161\) | −2.46504 | −0.194273 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.83003 | −0.221665 | −0.110833 | − | 0.993839i | \(-0.535352\pi\) | ||||
−0.110833 | + | 0.993839i | \(0.535352\pi\) | |||||||
\(164\) | 4.38262 | 0.342225 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.2382 | 0.949869 | ||||||||
\(167\) | −5.23171 | −0.404842 | −0.202421 | − | 0.979299i | \(-0.564881\pi\) | ||||
−0.202421 | + | 0.979299i | \(0.564881\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.0223 | 1.84787 | ||||||||
\(170\) | 11.0206 | 0.845241 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.75843 | 0.286577 | ||||||||
\(173\) | 10.6333 | 0.808434 | 0.404217 | − | 0.914663i | \(-0.367544\pi\) | ||||
0.404217 | + | 0.914663i | \(0.367544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.55192 | −0.646464 | ||||||||
\(176\) | −19.3738 | −1.46035 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.17027 | −0.0877153 | ||||||||
\(179\) | −25.2446 | −1.88687 | −0.943437 | − | 0.331553i | \(-0.892427\pi\) | ||||
−0.943437 | + | 0.331553i | \(0.892427\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3550 | 1.28999 | 0.644993 | − | 0.764189i | \(-0.276860\pi\) | ||||
0.644993 | + | 0.764189i | \(0.276860\pi\) | |||||||
\(182\) | −23.9351 | −1.77419 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.31937 | −0.170986 | ||||||||
\(185\) | 7.30680 | 0.537207 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.5557 | −1.64944 | ||||||||
\(188\) | −4.57652 | −0.333777 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.927907 | 0.0673175 | ||||||||
\(191\) | 7.59838 | 0.549800 | 0.274900 | − | 0.961473i | \(-0.411355\pi\) | ||||
0.274900 | + | 0.961473i | \(0.411355\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.6252 | 1.98850 | 0.994251 | − | 0.107071i | \(-0.0341471\pi\) | ||||
0.994251 | + | 0.107071i | \(0.0341471\pi\) | |||||||
\(194\) | 20.3313 | 1.45970 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.504806 | −0.0360576 | ||||||||
\(197\) | 9.20732 | 0.655995 | 0.327997 | − | 0.944679i | \(-0.393626\pi\) | ||||
0.327997 | + | 0.944679i | \(0.393626\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.01668 | −0.568287 | −0.284144 | − | 0.958782i | \(-0.591709\pi\) | ||||
−0.284144 | + | 0.958782i | \(0.591709\pi\) | |||||||
\(200\) | −8.04653 | −0.568976 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.77509 | 0.617413 | ||||||||
\(203\) | 2.46504 | 0.173012 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.92033 | 0.692866 | ||||||||
\(206\) | −28.1304 | −1.95993 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −29.1721 | −2.02272 | ||||||||
\(209\) | −1.89914 | −0.131366 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3826 | 1.60972 | 0.804862 | − | 0.593462i | \(-0.202239\pi\) | ||||
0.804862 | + | 0.593462i | \(0.202239\pi\) | |||||||
\(212\) | 1.25579 | 0.0862477 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.95762 | 0.202179 | ||||||||
\(215\) | 8.50744 | 0.580202 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.93284 | −0.334863 | ||||||||
\(218\) | 2.36358 | 0.160082 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.73264 | 0.184234 | ||||||||
\(221\) | −33.9633 | −2.28462 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.51986 | −0.302672 | −0.151336 | − | 0.988482i | \(-0.548358\pi\) | ||||
−0.151336 | + | 0.988482i | \(0.548358\pi\) | |||||||
\(224\) | 7.42519 | 0.496117 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.1003 | 1.07098 | ||||||||
\(227\) | 16.0461 | 1.06501 | 0.532507 | − | 0.846425i | \(-0.321250\pi\) | ||||
0.532507 | + | 0.846425i | \(0.321250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.3783 | −0.817980 | −0.408990 | − | 0.912539i | \(-0.634119\pi\) | ||||
−0.408990 | + | 0.912539i | \(0.634119\pi\) | |||||||
\(230\) | 1.97436 | 0.130186 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.31937 | 0.152274 | ||||||||
\(233\) | −12.8643 | −0.842767 | −0.421384 | − | 0.906882i | \(-0.638455\pi\) | ||||
−0.421384 | + | 0.906882i | \(0.638455\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.3592 | −0.675762 | ||||||||
\(236\) | 3.67072 | 0.238943 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 21.9574 | 1.42329 | ||||||||
\(239\) | 14.5687 | 0.942368 | 0.471184 | − | 0.882035i | \(-0.343827\pi\) | ||||
0.471184 | + | 0.882035i | \(0.343827\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.8161 | 1.85621 | 0.928104 | − | 0.372322i | \(-0.121438\pi\) | ||||
0.928104 | + | 0.372322i | \(0.121438\pi\) | |||||||
\(242\) | −8.50386 | −0.546649 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.37295 | 0.279949 | ||||||||
\(245\) | −1.14266 | −0.0730019 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.85963 | −0.181954 | ||||||||
\(248\) | −4.64132 | −0.294724 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.7214 | 1.05756 | ||||||||
\(251\) | −0.648897 | −0.0409580 | −0.0204790 | − | 0.999790i | \(-0.506519\pi\) | ||||
−0.0204790 | + | 0.999790i | \(0.506519\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.04090 | −0.254049 | ||||||||
\(254\) | −13.9586 | −0.875839 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.2275 | 0.764217 | ||||||||
\(257\) | −30.6508 | −1.91195 | −0.955973 | − | 0.293455i | \(-0.905195\pi\) | ||||
−0.955973 | + | 0.293455i | \(0.905195\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.5581 | 0.904595 | ||||||||
\(260\) | 4.11467 | 0.255181 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.65039 | 0.163741 | ||||||||
\(263\) | 12.1422 | 0.748721 | 0.374361 | − | 0.927283i | \(-0.377862\pi\) | ||||
0.374361 | + | 0.927283i | \(0.377862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.84255 | 0.174616 | ||||||||
\(266\) | 1.84876 | 0.113355 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.34458 | 0.204303 | ||||||||
\(269\) | 19.5584 | 1.19250 | 0.596249 | − | 0.802800i | \(-0.296657\pi\) | ||||
0.596249 | + | 0.802800i | \(0.296657\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2198 | 0.620809 | 0.310404 | − | 0.950605i | \(-0.399536\pi\) | ||||
0.310404 | + | 0.950605i | \(0.399536\pi\) | |||||||
\(272\) | 26.7617 | 1.62267 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.69066 | 0.102137 | ||||||||
\(275\) | −14.0190 | −0.845379 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.8559 | 1.55353 | 0.776765 | − | 0.629791i | \(-0.216859\pi\) | ||||
0.776765 | + | 0.629791i | \(0.216859\pi\) | |||||||
\(278\) | 5.47290 | 0.328243 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.07362 | 0.422729 | ||||||||
\(281\) | 28.1037 | 1.67653 | 0.838263 | − | 0.545266i | \(-0.183571\pi\) | ||||
0.838263 | + | 0.545266i | \(0.183571\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −32.1961 | −1.91386 | −0.956929 | − | 0.290321i | \(-0.906238\pi\) | ||||
−0.956929 | + | 0.290321i | \(0.906238\pi\) | |||||||
\(284\) | 0.390215 | 0.0231550 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −39.2364 | −2.32010 | ||||||||
\(287\) | 19.7653 | 1.16671 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.1570 | 0.832767 | ||||||||
\(290\) | −1.97436 | −0.115939 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.60381 | 0.444979 | ||||||||
\(293\) | 15.0459 | 0.878990 | 0.439495 | − | 0.898245i | \(-0.355158\pi\) | ||||
0.439495 | + | 0.898245i | \(0.355158\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.30889 | 0.483762 | ||||||||
\(296\) | 13.6977 | 0.796165 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 25.5595 | 1.48062 | ||||||||
\(299\) | −6.08460 | −0.351881 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.9502 | 0.976994 | ||||||||
\(302\) | 13.4531 | 0.774139 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.25327 | 0.129234 | ||||||||
\(305\) | 9.89844 | 0.566783 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.9566 | −0.910688 | −0.455344 | − | 0.890315i | \(-0.650484\pi\) | ||||
−0.455344 | + | 0.890315i | \(0.650484\pi\) | |||||||
\(308\) | 5.44450 | 0.310229 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.95093 | 0.224398 | ||||||||
\(311\) | 6.18486 | 0.350711 | 0.175356 | − | 0.984505i | \(-0.443892\pi\) | ||||
0.175356 | + | 0.984505i | \(0.443892\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.6715 | −0.603187 | −0.301594 | − | 0.953437i | \(-0.597519\pi\) | ||||
−0.301594 | + | 0.953437i | \(0.597519\pi\) | |||||||
\(314\) | 5.22516 | 0.294873 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.10214 | 0.0620000 | ||||||||
\(317\) | −19.7517 | −1.10937 | −0.554684 | − | 0.832061i | \(-0.687161\pi\) | ||||
−0.554684 | + | 0.832061i | \(0.687161\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.04090 | 0.226247 | ||||||||
\(320\) | 5.91634 | 0.330734 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.93372 | 0.219217 | ||||||||
\(323\) | 2.62335 | 0.145967 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.1092 | −1.17093 | ||||||||
\(326\) | 4.51617 | 0.250127 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 18.5972 | 1.02686 | ||||||||
\(329\) | −20.6397 | −1.13790 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.5464 | 0.634649 | 0.317325 | − | 0.948317i | \(-0.397216\pi\) | ||||
0.317325 | + | 0.948317i | \(0.397216\pi\) | |||||||
\(332\) | −4.19174 | −0.230052 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.34877 | 0.456824 | ||||||||
\(335\) | 7.57067 | 0.413630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.3595 | −0.618791 | −0.309395 | − | 0.950934i | \(-0.600127\pi\) | ||||
−0.309395 | + | 0.950934i | \(0.600127\pi\) | |||||||
\(338\) | −38.3349 | −2.08514 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.77469 | −0.204711 | ||||||||
\(341\) | −8.08632 | −0.437899 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.5319 | −1.05463 | ||||||||
\(344\) | 15.9485 | 0.859886 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.9686 | −0.912239 | ||||||||
\(347\) | 0.330557 | 0.0177452 | 0.00887262 | − | 0.999961i | \(-0.497176\pi\) | ||||
0.00887262 | + | 0.999961i | \(0.497176\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.3266 | −0.713358 | −0.356679 | − | 0.934227i | \(-0.616091\pi\) | ||||
−0.356679 | + | 0.934227i | \(0.616091\pi\) | |||||||
\(350\) | 13.6472 | 0.729472 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.1720 | 0.648770 | ||||||||
\(353\) | −14.4688 | −0.770094 | −0.385047 | − | 0.922897i | \(-0.625815\pi\) | ||||
−0.385047 | + | 0.922897i | \(0.625815\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.883276 | 0.0468794 | ||||||||
\(356\) | 0.400831 | 0.0212440 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 40.2854 | 2.12915 | ||||||||
\(359\) | −10.3405 | −0.545752 | −0.272876 | − | 0.962049i | \(-0.587975\pi\) | ||||
−0.272876 | + | 0.962049i | \(0.587975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7791 | −0.988375 | ||||||||
\(362\) | −27.6951 | −1.45562 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.19807 | 0.429696 | ||||||||
\(365\) | 17.2117 | 0.900901 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.70969 | −0.245844 | −0.122922 | − | 0.992416i | \(-0.539226\pi\) | ||||
−0.122922 | + | 0.992416i | \(0.539226\pi\) | |||||||
\(368\) | 4.79441 | 0.249926 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.6602 | −0.606185 | ||||||||
\(371\) | 5.66349 | 0.294034 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.70376 | −0.295329 | −0.147665 | − | 0.989037i | \(-0.547176\pi\) | ||||
−0.147665 | + | 0.989037i | \(0.547176\pi\) | |||||||
\(374\) | 35.9944 | 1.86123 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.4200 | −1.00151 | ||||||||
\(377\) | 6.08460 | 0.313373 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.98605 | −0.358849 | −0.179425 | − | 0.983772i | \(-0.557424\pi\) | ||||
−0.179425 | + | 0.983772i | \(0.557424\pi\) | |||||||
\(380\) | −0.317820 | −0.0163038 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.1255 | −0.620395 | ||||||||
\(383\) | 27.4430 | 1.40227 | 0.701136 | − | 0.713028i | \(-0.252677\pi\) | ||||
0.701136 | + | 0.713028i | \(0.252677\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.3240 | 0.628088 | ||||||||
\(386\) | −44.0843 | −2.24383 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.96373 | −0.353530 | ||||||||
\(389\) | −30.4907 | −1.54594 | −0.772969 | − | 0.634444i | \(-0.781229\pi\) | ||||
−0.772969 | + | 0.634444i | \(0.781229\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.58185 | 0.282286 | ||||||||
\(392\) | −2.14209 | −0.108192 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.6931 | −0.740226 | ||||||||
\(395\) | 2.49475 | 0.125525 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.9935 | −1.20420 | −0.602099 | − | 0.798422i | \(-0.705669\pi\) | ||||
−0.602099 | + | 0.798422i | \(0.705669\pi\) | |||||||
\(398\) | 12.7930 | 0.641257 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.6332 | 0.831658 | ||||||||
\(401\) | −21.0309 | −1.05023 | −0.525116 | − | 0.851031i | \(-0.675978\pi\) | ||||
−0.525116 | + | 0.851031i | \(0.675978\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.1760 | −0.606529 | ||||||||
\(404\) | −3.00558 | −0.149533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.93372 | −0.195227 | ||||||||
\(407\) | 23.8648 | 1.18293 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.0923 | 1.14184 | 0.570920 | − | 0.821006i | \(-0.306587\pi\) | ||||
0.570920 | + | 0.821006i | \(0.306587\pi\) | |||||||
\(410\) | −15.8309 | −0.781831 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.63500 | 0.474682 | ||||||||
\(413\) | 16.5546 | 0.814600 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.48827 | −0.465761 | ||||||||
\(416\) | 18.3280 | 0.898605 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.03064 | 0.148234 | ||||||||
\(419\) | 40.4641 | 1.97680 | 0.988401 | − | 0.151867i | \(-0.0485287\pi\) | ||||
0.988401 | + | 0.151867i | \(0.0485287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.9778 | −0.778709 | −0.389354 | − | 0.921088i | \(-0.627302\pi\) | ||||
−0.389354 | + | 0.921088i | \(0.627302\pi\) | |||||||
\(422\) | −37.3140 | −1.81642 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.32880 | 0.258789 | ||||||||
\(425\) | 19.3650 | 0.939340 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.7217 | 0.954398 | ||||||||
\(428\) | −1.01302 | −0.0489663 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.5762 | −0.654702 | ||||||||
\(431\) | −8.02554 | −0.386576 | −0.193288 | − | 0.981142i | \(-0.561915\pi\) | ||||
−0.193288 | + | 0.981142i | \(0.561915\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.3653 | −0.738408 | −0.369204 | − | 0.929348i | \(-0.620370\pi\) | ||||
−0.369204 | + | 0.929348i | \(0.620370\pi\) | |||||||
\(434\) | 7.87183 | 0.377860 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.809556 | −0.0387707 | ||||||||
\(437\) | 0.469978 | 0.0224821 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.13940 | 0.102108 | 0.0510541 | − | 0.998696i | \(-0.483742\pi\) | ||||
0.0510541 | + | 0.998696i | \(0.483742\pi\) | |||||||
\(440\) | 11.5957 | 0.552802 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 54.1987 | 2.57797 | ||||||||
\(443\) | 23.7135 | 1.12666 | 0.563331 | − | 0.826232i | \(-0.309520\pi\) | ||||
0.563331 | + | 0.826232i | \(0.309520\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.907307 | 0.0430105 | ||||||||
\(446\) | 7.21280 | 0.341536 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11.7877 | 0.556917 | ||||||||
\(449\) | 32.8609 | 1.55080 | 0.775400 | − | 0.631470i | \(-0.217548\pi\) | ||||
0.775400 | + | 0.631470i | \(0.217548\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.4009 | 1.52570 | ||||||||
\(452\) | −5.51457 | −0.259384 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −25.6063 | −1.20176 | ||||||||
\(455\) | 18.5568 | 0.869958 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.6100 | −0.823760 | −0.411880 | − | 0.911238i | \(-0.635128\pi\) | ||||
−0.411880 | + | 0.911238i | \(0.635128\pi\) | |||||||
\(458\) | 19.7533 | 0.923011 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.676244 | −0.0315300 | ||||||||
\(461\) | 15.0249 | 0.699778 | 0.349889 | − | 0.936791i | \(-0.386219\pi\) | ||||
0.349889 | + | 0.936791i | \(0.386219\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.01242 | −0.0470510 | −0.0235255 | − | 0.999723i | \(-0.507489\pi\) | ||||
−0.0235255 | + | 0.999723i | \(0.507489\pi\) | |||||||
\(464\) | −4.79441 | −0.222575 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.5288 | 0.950980 | ||||||||
\(467\) | −31.8850 | −1.47546 | −0.737731 | − | 0.675095i | \(-0.764103\pi\) | ||||
−0.737731 | + | 0.675095i | \(0.764103\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.0838 | 0.696505 | ||||||||
\(470\) | 16.5313 | 0.762531 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.5763 | 0.716958 | ||||||||
\(473\) | 27.7862 | 1.27761 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.63049 | 0.0748118 | ||||||||
\(476\) | −7.52069 | −0.344710 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −23.2487 | −1.06337 | ||||||||
\(479\) | 35.2220 | 1.60934 | 0.804668 | − | 0.593726i | \(-0.202343\pi\) | ||||
0.804668 | + | 0.593726i | \(0.202343\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.9345 | 1.63847 | ||||||||
\(482\) | −45.9847 | −2.09455 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.91268 | 0.132395 | ||||||||
\(485\) | −15.7628 | −0.715754 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.49271 | −0.339527 | −0.169763 | − | 0.985485i | \(-0.554300\pi\) | ||||
−0.169763 | + | 0.985485i | \(0.554300\pi\) | |||||||
\(488\) | 18.5562 | 0.839998 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.82346 | 0.0823755 | ||||||||
\(491\) | −16.3875 | −0.739557 | −0.369778 | − | 0.929120i | \(-0.620566\pi\) | ||||
−0.369778 | + | 0.929120i | \(0.620566\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.58185 | −0.251394 | ||||||||
\(494\) | 4.56340 | 0.205317 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.59418 | 0.430791 | ||||||||
\(497\) | 1.75984 | 0.0789396 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.5285 | −1.27711 | −0.638555 | − | 0.769576i | \(-0.720468\pi\) | ||||
−0.638555 | + | 0.769576i | \(0.720468\pi\) | |||||||
\(500\) | −5.72730 | −0.256133 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.03551 | 0.0462171 | ||||||||
\(503\) | −1.07113 | −0.0477591 | −0.0238796 | − | 0.999715i | \(-0.507602\pi\) | ||||
−0.0238796 | + | 0.999715i | \(0.507602\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.80332 | −0.302744 | ||||||||
\(506\) | 6.44848 | 0.286670 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.78099 | 0.212122 | ||||||||
\(509\) | −19.7132 | −0.873772 | −0.436886 | − | 0.899517i | \(-0.643919\pi\) | ||||
−0.436886 | + | 0.899517i | \(0.643919\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.2926 | 1.51701 | ||||||||
\(512\) | 7.79828 | 0.344639 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 48.9126 | 2.15744 | ||||||||
\(515\) | 21.8094 | 0.961038 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.8344 | −1.48803 | ||||||||
\(518\) | −23.2318 | −1.02075 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.4602 | 0.765680 | ||||||||
\(521\) | −11.5600 | −0.506453 | −0.253226 | − | 0.967407i | \(-0.581492\pi\) | ||||
−0.253226 | + | 0.967407i | \(0.581492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.9631 | 1.35392 | 0.676961 | − | 0.736019i | \(-0.263297\pi\) | ||||
0.676961 | + | 0.736019i | \(0.263297\pi\) | |||||||
\(524\) | −0.907791 | −0.0396570 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.3766 | −0.844859 | ||||||||
\(527\) | 11.1699 | 0.486570 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −4.53614 | −0.197037 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.633224 | −0.0274538 | ||||||||
\(533\) | 48.7877 | 2.11323 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.29304 | −0.0991368 | ||||||||
\(536\) | 14.1924 | 0.613018 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −31.2113 | −1.34562 | ||||||||
\(539\) | −3.73205 | −0.160751 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0458 | −0.861837 | −0.430918 | − | 0.902391i | \(-0.641810\pi\) | ||||
−0.430918 | + | 0.902391i | \(0.641810\pi\) | |||||||
\(542\) | −16.3088 | −0.700522 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16.8136 | −0.720878 | ||||||||
\(545\) | −1.83248 | −0.0784948 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.01462 | 0.171653 | 0.0858264 | − | 0.996310i | \(-0.472647\pi\) | ||||
0.0858264 | + | 0.996310i | \(0.472647\pi\) | |||||||
\(548\) | −0.579073 | −0.0247368 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 22.3716 | 0.953927 | ||||||||
\(551\) | −0.469978 | −0.0200217 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.97054 | 0.211369 | ||||||||
\(554\) | −41.2608 | −1.75301 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.87454 | −0.0794981 | ||||||||
\(557\) | 0.128470 | 0.00544345 | 0.00272172 | − | 0.999996i | \(-0.499134\pi\) | ||||
0.00272172 | + | 0.999996i | \(0.499134\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.8391 | 1.76961 | ||||||||
\(560\) | −14.6220 | −0.617893 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −44.8479 | −1.89180 | ||||||||
\(563\) | −31.2296 | −1.31617 | −0.658086 | − | 0.752943i | \(-0.728634\pi\) | ||||
−0.658086 | + | 0.752943i | \(0.728634\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.4826 | −0.525146 | ||||||||
\(566\) | 51.3786 | 2.15960 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.65584 | 0.0694774 | ||||||||
\(569\) | 18.6330 | 0.781138 | 0.390569 | − | 0.920574i | \(-0.372278\pi\) | ||||
0.390569 | + | 0.920574i | \(0.372278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.08799 | −0.171077 | −0.0855386 | − | 0.996335i | \(-0.527261\pi\) | ||||
−0.0855386 | + | 0.996335i | \(0.527261\pi\) | |||||||
\(572\) | 13.4390 | 0.561911 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −31.5414 | −1.31651 | ||||||||
\(575\) | 3.46928 | 0.144679 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.8197 | 1.69935 | 0.849674 | − | 0.527308i | \(-0.176799\pi\) | ||||
0.849674 | + | 0.527308i | \(0.176799\pi\) | |||||||
\(578\) | −22.5918 | −0.939696 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.676244 | 0.0280795 | ||||||||
\(581\) | −18.9044 | −0.784287 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.28407 | 0.384507 | ||||||||
\(584\) | 32.2660 | 1.33518 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.0102 | −0.991854 | ||||||||
\(587\) | 0.932895 | 0.0385047 | 0.0192524 | − | 0.999815i | \(-0.493871\pi\) | ||||
0.0192524 | + | 0.999815i | \(0.493871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.940481 | 0.0387519 | ||||||||
\(590\) | −13.2593 | −0.545879 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −28.3149 | −1.16374 | ||||||||
\(593\) | −6.06982 | −0.249257 | −0.124629 | − | 0.992203i | \(-0.539774\pi\) | ||||
−0.124629 | + | 0.992203i | \(0.539774\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.0236 | −0.697898 | ||||||||
\(596\) | −8.75446 | −0.358597 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.70981 | 0.397064 | ||||||||
\(599\) | 43.7176 | 1.78625 | 0.893126 | − | 0.449807i | \(-0.148507\pi\) | ||||
0.893126 | + | 0.449807i | \(0.148507\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.9621 | 0.528735 | 0.264367 | − | 0.964422i | \(-0.414837\pi\) | ||||
0.264367 | + | 0.964422i | \(0.414837\pi\) | |||||||
\(602\) | −27.0492 | −1.10244 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.60786 | −0.187491 | ||||||||
\(605\) | 6.59304 | 0.268045 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.54188 | 0.265527 | 0.132763 | − | 0.991148i | \(-0.457615\pi\) | ||||
0.132763 | + | 0.991148i | \(0.457615\pi\) | |||||||
\(608\) | −1.41567 | −0.0574129 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.7960 | −0.639559 | ||||||||
\(611\) | −50.9462 | −2.06106 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.99617 | −0.121014 | −0.0605072 | − | 0.998168i | \(-0.519272\pi\) | ||||
−0.0605072 | + | 0.998168i | \(0.519272\pi\) | |||||||
\(614\) | 25.4635 | 1.02762 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 23.1032 | 0.930854 | ||||||||
\(617\) | 11.7247 | 0.472017 | 0.236008 | − | 0.971751i | \(-0.424161\pi\) | ||||
0.236008 | + | 0.971751i | \(0.424161\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.9741 | 1.68708 | 0.843540 | − | 0.537066i | \(-0.180467\pi\) | ||||
0.843540 | + | 0.537066i | \(0.180467\pi\) | |||||||
\(620\) | −1.35324 | −0.0543475 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.86981 | −0.395743 | ||||||||
\(623\) | 1.80772 | 0.0724247 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.38230 | 0.175292 | ||||||||
\(626\) | 17.0296 | 0.680638 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.78968 | −0.0714161 | ||||||||
\(629\) | −32.9653 | −1.31441 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.6939 | 0.784000 | 0.392000 | − | 0.919965i | \(-0.371783\pi\) | ||||
0.392000 | + | 0.919965i | \(0.371783\pi\) | |||||||
\(632\) | 4.67680 | 0.186033 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.5198 | 1.25181 | ||||||||
\(635\) | 10.8221 | 0.429461 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.61955 | −0.222655 | ||||||||
\(638\) | −6.44848 | −0.255298 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.8948 | −0.667827 | ||||||||
\(641\) | −2.43221 | −0.0960667 | −0.0480333 | − | 0.998846i | \(-0.515295\pi\) | ||||
−0.0480333 | + | 0.998846i | \(0.515295\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.93996 | 0.0765047 | 0.0382524 | − | 0.999268i | \(-0.487821\pi\) | ||||
0.0382524 | + | 0.999268i | \(0.487821\pi\) | |||||||
\(644\) | −1.34735 | −0.0530929 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.18634 | −0.164709 | ||||||||
\(647\) | −26.6233 | −1.04667 | −0.523335 | − | 0.852127i | \(-0.675312\pi\) | ||||
−0.523335 | + | 0.852127i | \(0.675312\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.1377 | 1.06525 | ||||||||
\(650\) | 33.6861 | 1.32128 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.54684 | −0.0605791 | ||||||||
\(653\) | −33.9855 | −1.32995 | −0.664977 | − | 0.746864i | \(-0.731559\pi\) | ||||
−0.664977 | + | 0.746864i | \(0.731559\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.05484 | −0.0802893 | ||||||||
\(656\) | −38.4427 | −1.50093 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 32.9369 | 1.28401 | ||||||||
\(659\) | −0.545221 | −0.0212388 | −0.0106194 | − | 0.999944i | \(-0.503380\pi\) | ||||
−0.0106194 | + | 0.999944i | \(0.503380\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.0032 | 1.28368 | 0.641838 | − | 0.766841i | \(-0.278172\pi\) | ||||
0.641838 | + | 0.766841i | \(0.278172\pi\) | |||||||
\(662\) | −18.4258 | −0.716139 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.7872 | −0.690279 | ||||||||
\(665\) | −1.43334 | −0.0555826 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −2.85956 | −0.110640 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.0813 | −0.466741 | ||||||||
\(671\) | 32.3294 | 1.24806 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.7564 | 1.95652 | 0.978259 | − | 0.207389i | \(-0.0664964\pi\) | ||||
0.978259 | + | 0.207389i | \(0.0664964\pi\) | |||||||
\(674\) | 18.1275 | 0.698245 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.1302 | 0.505007 | ||||||||
\(677\) | 33.9999 | 1.30672 | 0.653362 | − | 0.757046i | \(-0.273358\pi\) | ||||
0.653362 | + | 0.757046i | \(0.273358\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.4059 | −1.20525 | ||||||||
\(680\) | −16.0175 | −0.614244 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.9042 | 0.494126 | ||||||||
\(683\) | −10.9943 | −0.420686 | −0.210343 | − | 0.977628i | \(-0.567458\pi\) | ||||
−0.210343 | + | 0.977628i | \(0.567458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.31077 | −0.0500819 | ||||||||
\(686\) | 31.1691 | 1.19004 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −32.9675 | −1.25687 | ||||||||
\(689\) | 13.9795 | 0.532577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.5308 | −1.65599 | −0.827994 | − | 0.560736i | \(-0.810518\pi\) | ||||
−0.827994 | + | 0.560736i | \(0.810518\pi\) | |||||||
\(692\) | 5.81197 | 0.220938 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.527504 | −0.0200238 | ||||||||
\(695\) | −4.24313 | −0.160951 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −44.7565 | −1.69527 | ||||||||
\(698\) | 21.2666 | 0.804954 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.67433 | −0.176673 | ||||||||
\(701\) | −49.4520 | −1.86778 | −0.933889 | − | 0.357564i | \(-0.883607\pi\) | ||||
−0.933889 | + | 0.357564i | \(0.883607\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.77560 | −0.104684 | ||||||||
\(704\) | 19.3234 | 0.728279 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.0893 | 0.868976 | ||||||||
\(707\) | −13.5549 | −0.509785 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.65262 | −0.287400 | −0.143700 | − | 0.989621i | \(-0.545900\pi\) | ||||
−0.143700 | + | 0.989621i | \(0.545900\pi\) | |||||||
\(710\) | −1.40953 | −0.0528988 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.70089 | 0.0637435 | ||||||||
\(713\) | 2.00112 | 0.0749424 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.4199 | 1.13764 | ||||||||
\(716\) | −13.7983 | −0.515666 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.5014 | 0.615828 | ||||||||
\(719\) | −41.8360 | −1.56022 | −0.780110 | − | 0.625642i | \(-0.784837\pi\) | ||||
−0.780110 | + | 0.625642i | \(0.784837\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.4531 | 1.61828 | ||||||||
\(722\) | 29.9677 | 1.11528 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.48592 | 0.352542 | ||||||||
\(725\) | −3.46928 | −0.128846 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.6803 | −1.84254 | −0.921270 | − | 0.388924i | \(-0.872847\pi\) | ||||
−0.921270 | + | 0.388924i | \(0.872847\pi\) | |||||||
\(728\) | 34.7877 | 1.28932 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −27.4664 | −1.01658 | ||||||||
\(731\) | −38.3821 | −1.41961 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.24207 | 0.119749 | 0.0598744 | − | 0.998206i | \(-0.480930\pi\) | ||||
0.0598744 | + | 0.998206i | \(0.480930\pi\) | |||||||
\(734\) | 7.51573 | 0.277411 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.01220 | −0.111031 | ||||||||
\(737\) | 24.7266 | 0.910817 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.53356 | −0.240341 | −0.120170 | − | 0.992753i | \(-0.538344\pi\) | ||||
−0.120170 | + | 0.992753i | \(0.538344\pi\) | |||||||
\(740\) | 3.99377 | 0.146814 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.03781 | −0.331788 | ||||||||
\(743\) | 13.1158 | 0.481173 | 0.240587 | − | 0.970628i | \(-0.422660\pi\) | ||||
0.240587 | + | 0.970628i | \(0.422660\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.8163 | −0.726012 | ||||||||
\(746\) | 9.10207 | 0.333250 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.3285 | −0.450776 | ||||||||
\(749\) | −4.56865 | −0.166935 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.48871 | −0.127305 | −0.0636525 | − | 0.997972i | \(-0.520275\pi\) | ||||
−0.0636525 | + | 0.997972i | \(0.520275\pi\) | |||||||
\(752\) | 40.1435 | 1.46388 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.70981 | −0.353610 | ||||||||
\(755\) | −10.4302 | −0.379593 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.2975 | −0.665032 | −0.332516 | − | 0.943098i | \(-0.607898\pi\) | ||||
−0.332516 | + | 0.943098i | \(0.607898\pi\) | |||||||
\(758\) | 11.1484 | 0.404926 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.34864 | −0.0489202 | ||||||||
\(761\) | 29.1438 | 1.05646 | 0.528231 | − | 0.849101i | \(-0.322855\pi\) | ||||
0.528231 | + | 0.849101i | \(0.322855\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.65103 | −0.132176 | ||||||||
\(764\) | 4.15314 | 0.150255 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −43.7936 | −1.58233 | ||||||||
\(767\) | 40.8627 | 1.47547 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.4216 | −0.556117 | −0.278059 | − | 0.960564i | \(-0.589691\pi\) | ||||
−0.278059 | + | 0.960564i | \(0.589691\pi\) | |||||||
\(770\) | −19.6666 | −0.708735 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.0994 | 0.543440 | ||||||||
\(773\) | 14.1320 | 0.508291 | 0.254146 | − | 0.967166i | \(-0.418206\pi\) | ||||
0.254146 | + | 0.967166i | \(0.418206\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.94243 | 0.249380 | ||||||||
\(776\) | −29.5499 | −1.06078 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 48.6570 | 1.74444 | ||||||||
\(779\) | −3.76839 | −0.135017 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.88488 | 0.103229 | ||||||||
\(782\) | −8.90752 | −0.318532 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.42797 | 0.158142 | ||||||||
\(785\) | −4.05106 | −0.144588 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.3022 | −0.973219 | −0.486609 | − | 0.873620i | \(-0.661767\pi\) | ||||
−0.486609 | + | 0.873620i | \(0.661767\pi\) | |||||||
\(788\) | 5.03256 | 0.179277 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.98113 | −0.141642 | ||||||||
\(791\) | −24.8703 | −0.884285 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.6800 | 1.72868 | ||||||||
\(794\) | 38.2888 | 1.35882 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.38177 | −0.155308 | ||||||||
\(797\) | 31.0268 | 1.09902 | 0.549512 | − | 0.835486i | \(-0.314814\pi\) | ||||
0.549512 | + | 0.835486i | \(0.314814\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.7367 | 1.65342 | ||||||||
\(800\) | −10.4502 | −0.369469 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 33.5611 | 1.18508 | ||||||||
\(803\) | 56.2152 | 1.98379 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.04981 | −0.107492 | ||||||||
\(806\) | 19.4305 | 0.684409 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.7539 | −0.448680 | ||||||||
\(809\) | −6.99136 | −0.245803 | −0.122902 | − | 0.992419i | \(-0.539220\pi\) | ||||
−0.122902 | + | 0.992419i | \(0.539220\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.7374 | −0.517499 | −0.258750 | − | 0.965944i | \(-0.583310\pi\) | ||||
−0.258750 | + | 0.965944i | \(0.583310\pi\) | |||||||
\(812\) | 1.34735 | 0.0472826 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −38.0835 | −1.33483 | ||||||||
\(815\) | −3.50138 | −0.122648 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.23168 | −0.113062 | ||||||||
\(818\) | −36.8507 | −1.28845 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.42227 | 0.189354 | ||||||||
\(821\) | 32.5264 | 1.13518 | 0.567590 | − | 0.823312i | \(-0.307876\pi\) | ||||
0.567590 | + | 0.823312i | \(0.307876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.1514 | −1.67845 | −0.839226 | − | 0.543783i | \(-0.816991\pi\) | ||||
−0.839226 | + | 0.543783i | \(0.816991\pi\) | |||||||
\(824\) | 40.8852 | 1.42430 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −26.4179 | −0.919197 | ||||||||
\(827\) | 39.9441 | 1.38899 | 0.694497 | − | 0.719496i | \(-0.255627\pi\) | ||||
0.694497 | + | 0.719496i | \(0.255627\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.4169 | −1.12589 | −0.562944 | − | 0.826495i | \(-0.690331\pi\) | ||||
−0.562944 | + | 0.826495i | \(0.690331\pi\) | |||||||
\(830\) | 15.1414 | 0.525565 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 29.0963 | 1.00873 | ||||||||
\(833\) | 5.15522 | 0.178618 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.47279 | −0.224000 | ||||||||
\(836\) | −1.03803 | −0.0359012 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −64.5727 | −2.23063 | ||||||||
\(839\) | 26.8967 | 0.928577 | 0.464289 | − | 0.885684i | \(-0.346310\pi\) | ||||
0.464289 | + | 0.885684i | \(0.346310\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 25.4973 | 0.878696 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.7805 | 0.439923 | ||||||||
\(845\) | 29.7210 | 1.02243 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.1360 | 0.451357 | ||||||||
\(848\) | −11.0153 | −0.378266 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −30.9027 | −1.05995 | ||||||||
\(851\) | −5.90581 | −0.202449 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.2014 | 1.44495 | 0.722474 | − | 0.691398i | \(-0.243005\pi\) | ||||
0.722474 | + | 0.691398i | \(0.243005\pi\) | |||||||
\(854\) | −31.4718 | −1.07694 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.29866 | −0.146925 | ||||||||
\(857\) | 28.4265 | 0.971030 | 0.485515 | − | 0.874228i | \(-0.338632\pi\) | ||||
0.485515 | + | 0.874228i | \(0.338632\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.8157 | −0.676103 | −0.338051 | − | 0.941128i | \(-0.609768\pi\) | ||||
−0.338051 | + | 0.941128i | \(0.609768\pi\) | |||||||
\(860\) | 4.65001 | 0.158564 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.8072 | 0.436214 | ||||||||
\(863\) | −14.3006 | −0.486797 | −0.243399 | − | 0.969926i | \(-0.578262\pi\) | ||||
−0.243399 | + | 0.969926i | \(0.578262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.1557 | 0.447309 | ||||||||
\(866\) | 24.5199 | 0.833221 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.69620 | −0.0915150 | ||||||||
\(869\) | 8.14813 | 0.276406 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.2322 | 1.26156 | ||||||||
\(872\) | −3.43527 | −0.116333 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.749992 | −0.0253689 | ||||||||
\(875\) | −25.8297 | −0.873202 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.1559 | 1.35597 | 0.677984 | − | 0.735077i | \(-0.262854\pi\) | ||||
0.677984 | + | 0.735077i | \(0.262854\pi\) | |||||||
\(878\) | −3.41407 | −0.115219 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −23.9697 | −0.808017 | ||||||||
\(881\) | 34.8681 | 1.17474 | 0.587368 | − | 0.809320i | \(-0.300164\pi\) | ||||
0.587368 | + | 0.809320i | \(0.300164\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.2214 | 1.72374 | 0.861868 | − | 0.507132i | \(-0.169295\pi\) | ||||
0.861868 | + | 0.507132i | \(0.169295\pi\) | |||||||
\(884\) | −18.5637 | −0.624366 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −37.8420 | −1.27133 | ||||||||
\(887\) | −2.84962 | −0.0956809 | −0.0478405 | − | 0.998855i | \(-0.515234\pi\) | ||||
−0.0478405 | + | 0.998855i | \(0.515234\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.5619 | 0.723162 | ||||||||
\(890\) | −1.44788 | −0.0485331 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.47047 | −0.0827176 | ||||||||
\(893\) | 3.93511 | 0.131684 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.2332 | −1.04401 | ||||||||
\(896\) | −33.6612 | −1.12454 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −52.4394 | −1.74993 | ||||||||
\(899\) | −2.00112 | −0.0667410 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.8244 | −0.427244 | ||||||||
\(902\) | −51.7053 | −1.72160 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23.4005 | −0.778290 | ||||||||
\(905\) | 21.4720 | 0.713753 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.5438 | 1.14701 | 0.573504 | − | 0.819203i | \(-0.305584\pi\) | ||||
0.573504 | + | 0.819203i | \(0.305584\pi\) | |||||||
\(908\) | 8.77049 | 0.291059 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −29.6130 | −0.981663 | ||||||||
\(911\) | −57.6795 | −1.91101 | −0.955503 | − | 0.294980i | \(-0.904687\pi\) | ||||
−0.955503 | + | 0.294980i | \(0.904687\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.9897 | −1.02561 | ||||||||
\(914\) | 28.1020 | 0.929533 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.76575 | −0.223547 | ||||||||
\(917\) | −4.09407 | −0.135198 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.5597 | −0.942096 | −0.471048 | − | 0.882108i | \(-0.656124\pi\) | ||||
−0.471048 | + | 0.882108i | \(0.656124\pi\) | |||||||
\(920\) | −2.86957 | −0.0946070 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.9767 | −0.789631 | ||||||||
\(923\) | 4.34391 | 0.142981 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.4889 | −0.673671 | ||||||||
\(926\) | 1.61562 | 0.0530925 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.01220 | 0.0988802 | ||||||||
\(929\) | 2.84560 | 0.0933609 | 0.0466805 | − | 0.998910i | \(-0.485136\pi\) | ||||
0.0466805 | + | 0.998910i | \(0.485136\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.434057 | 0.0142257 | ||||||||
\(932\) | −7.03139 | −0.230321 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 50.8821 | 1.66491 | ||||||||
\(935\) | −27.9064 | −0.912638 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.5068 | 0.931276 | 0.465638 | − | 0.884975i | \(-0.345825\pi\) | ||||
0.465638 | + | 0.884975i | \(0.345825\pi\) | |||||||
\(938\) | −24.0707 | −0.785938 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.66217 | −0.184680 | ||||||||
\(941\) | 5.49695 | 0.179195 | 0.0895977 | − | 0.995978i | \(-0.471442\pi\) | ||||
0.0895977 | + | 0.995978i | \(0.471442\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.01822 | −0.261109 | ||||||||
\(944\) | −32.1981 | −1.04796 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −44.3413 | −1.44166 | ||||||||
\(947\) | 54.9545 | 1.78578 | 0.892891 | − | 0.450273i | \(-0.148673\pi\) | ||||
0.892891 | + | 0.450273i | \(0.148673\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 84.6462 | 2.74773 | ||||||||
\(950\) | −2.60193 | −0.0844178 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −31.9133 | −1.03432 | ||||||||
\(953\) | 10.0498 | 0.325546 | 0.162773 | − | 0.986664i | \(-0.447956\pi\) | ||||
0.162773 | + | 0.986664i | \(0.447956\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.40089 | 0.304206 | ||||||||
\(956\) | 7.96296 | 0.257541 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −56.2074 | −1.81598 | ||||||||
\(959\) | −2.61158 | −0.0843322 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.9955 | −0.870824 | ||||||||
\(962\) | −57.3443 | −1.84886 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.7504 | 0.507285 | ||||||||
\(965\) | 34.1785 | 1.10024 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.9191 | −1.34803 | −0.674014 | − | 0.738718i | \(-0.735431\pi\) | ||||
−0.674014 | + | 0.738718i | \(0.735431\pi\) | |||||||
\(968\) | 12.3597 | 0.397255 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 25.1544 | 0.807658 | ||||||||
\(971\) | 25.6453 | 0.822998 | 0.411499 | − | 0.911410i | \(-0.365005\pi\) | ||||
0.411499 | + | 0.911410i | \(0.365005\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.45402 | −0.271023 | ||||||||
\(974\) | 11.9569 | 0.383123 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.3579 | −1.22781 | ||||||||
\(977\) | 18.9681 | 0.606843 | 0.303422 | − | 0.952856i | \(-0.401871\pi\) | ||||
0.303422 | + | 0.952856i | \(0.401871\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.96336 | 0.0947095 | ||||||||
\(980\) | −0.624558 | −0.0199508 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 26.1512 | 0.834517 | ||||||||
\(983\) | 1.42191 | 0.0453519 | 0.0226760 | − | 0.999743i | \(-0.492781\pi\) | ||||
0.0226760 | + | 0.999743i | \(0.492781\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.3915 | 0.362964 | ||||||||
\(986\) | 8.90752 | 0.283673 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.56302 | −0.0497264 | ||||||||
\(989\) | −6.87624 | −0.218652 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.7528 | −1.38985 | −0.694927 | − | 0.719080i | \(-0.744563\pi\) | ||||
−0.694927 | + | 0.719080i | \(0.744563\pi\) | |||||||
\(992\) | −6.02776 | −0.191381 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.80835 | −0.0890756 | ||||||||
\(995\) | −9.91842 | −0.314435 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.221132 | 0.00700333 | 0.00350167 | − | 0.999994i | \(-0.498885\pi\) | ||||
0.00350167 | + | 0.999994i | \(0.498885\pi\) | |||||||
\(998\) | 45.5258 | 1.44109 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.w.1.8 | yes | 30 | |
3.2 | odd | 2 | 6003.2.a.v.1.23 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.v.1.23 | ✓ | 30 | 3.2 | odd | 2 | ||
6003.2.a.w.1.8 | yes | 30 | 1.1 | even | 1 | trivial |