Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.84847 | −1.30707 | −0.653533 | − | 0.756898i | \(-0.726714\pi\) | ||||
−0.653533 | + | 0.756898i | \(0.726714\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.41684 | 0.708420 | ||||||||
\(5\) | 3.30338 | 1.47731 | 0.738657 | − | 0.674081i | \(-0.235460\pi\) | ||||
0.738657 | + | 0.674081i | \(0.235460\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.95713 | −1.49565 | −0.747827 | − | 0.663893i | \(-0.768903\pi\) | ||||
−0.747827 | + | 0.663893i | \(0.768903\pi\) | |||||||
\(8\) | 1.07795 | 0.381114 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.10619 | −1.93095 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.98905 | −0.829013 | −0.414507 | − | 0.910046i | \(-0.636046\pi\) | ||||
−0.414507 | + | 0.910046i | \(0.636046\pi\) | |||||||
\(14\) | 7.31464 | 1.95492 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.82624 | −1.20656 | ||||||||
\(17\) | 2.21325 | 0.536792 | 0.268396 | − | 0.963309i | \(-0.413506\pi\) | ||||
0.268396 | + | 0.963309i | \(0.413506\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.56465 | 0.817787 | 0.408894 | − | 0.912582i | \(-0.365915\pi\) | ||||
0.408894 | + | 0.912582i | \(0.365915\pi\) | |||||||
\(20\) | 4.68036 | 1.04656 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.84847 | −0.394095 | ||||||||
\(23\) | 4.72434 | 0.985092 | 0.492546 | − | 0.870286i | \(-0.336066\pi\) | ||||
0.492546 | + | 0.870286i | \(0.336066\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.91229 | 1.18246 | ||||||||
\(26\) | 5.52517 | 1.08357 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.60662 | −1.05955 | ||||||||
\(29\) | −9.75580 | −1.81161 | −0.905803 | − | 0.423699i | \(-0.860732\pi\) | ||||
−0.905803 | + | 0.423699i | \(0.860732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.49208 | −0.806801 | −0.403400 | − | 0.915024i | \(-0.632172\pi\) | ||||
−0.403400 | + | 0.915024i | \(0.632172\pi\) | |||||||
\(32\) | 6.76526 | 1.19594 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.09113 | −0.701623 | ||||||||
\(35\) | −13.0719 | −2.20955 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.68381 | −0.934413 | −0.467207 | − | 0.884148i | \(-0.654740\pi\) | ||||
−0.467207 | + | 0.884148i | \(0.654740\pi\) | |||||||
\(38\) | −6.58915 | −1.06890 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.56088 | 0.563025 | ||||||||
\(41\) | 1.33980 | 0.209242 | 0.104621 | − | 0.994512i | \(-0.466637\pi\) | ||||
0.104621 | + | 0.994512i | \(0.466637\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.84241 | −0.280965 | −0.140482 | − | 0.990083i | \(-0.544865\pi\) | ||||
−0.140482 | + | 0.990083i | \(0.544865\pi\) | |||||||
\(44\) | 1.41684 | 0.213597 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.73279 | −1.28758 | ||||||||
\(47\) | 3.92388 | 0.572357 | 0.286178 | − | 0.958176i | \(-0.407615\pi\) | ||||
0.286178 | + | 0.958176i | \(0.407615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.65888 | 1.23698 | ||||||||
\(50\) | −10.9287 | −1.54555 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.23501 | −0.587290 | ||||||||
\(53\) | 8.83416 | 1.21347 | 0.606733 | − | 0.794906i | \(-0.292480\pi\) | ||||
0.606733 | + | 0.794906i | \(0.292480\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.30338 | 0.445427 | ||||||||
\(56\) | −4.26560 | −0.570015 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 18.0333 | 2.36789 | ||||||||
\(59\) | −14.2933 | −1.86083 | −0.930415 | − | 0.366508i | \(-0.880553\pi\) | ||||
−0.930415 | + | 0.366508i | \(0.880553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 8.30347 | 1.05454 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.85289 | −0.356612 | ||||||||
\(65\) | −9.87396 | −1.22471 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.8404 | 1.44653 | 0.723267 | − | 0.690568i | \(-0.242640\pi\) | ||||
0.723267 | + | 0.690568i | \(0.242640\pi\) | |||||||
\(68\) | 3.13582 | 0.380275 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 24.1630 | 2.88803 | ||||||||
\(71\) | 10.1261 | 1.20175 | 0.600875 | − | 0.799343i | \(-0.294819\pi\) | ||||
0.600875 | + | 0.799343i | \(0.294819\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.19928 | −0.842612 | −0.421306 | − | 0.906918i | \(-0.638428\pi\) | ||||
−0.421306 | + | 0.906918i | \(0.638428\pi\) | |||||||
\(74\) | 10.5064 | 1.22134 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.05054 | 0.579337 | ||||||||
\(77\) | −3.95713 | −0.450957 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.49052 | 0.842750 | 0.421375 | − | 0.906887i | \(-0.361548\pi\) | ||||
0.421375 | + | 0.906887i | \(0.361548\pi\) | |||||||
\(80\) | −15.9429 | −1.78247 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.47659 | −0.273493 | ||||||||
\(83\) | −15.2439 | −1.67323 | −0.836616 | − | 0.547789i | \(-0.815470\pi\) | ||||
−0.836616 | + | 0.547789i | \(0.815470\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.31120 | 0.793011 | ||||||||
\(86\) | 3.40564 | 0.367239 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.07795 | 0.114910 | ||||||||
\(89\) | 4.27782 | 0.453448 | 0.226724 | − | 0.973959i | \(-0.427198\pi\) | ||||
0.226724 | + | 0.973959i | \(0.427198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.8281 | 1.23992 | ||||||||
\(92\) | 6.69363 | 0.697859 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.25317 | −0.748108 | ||||||||
\(95\) | 11.7754 | 1.20813 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.72931 | −0.886327 | −0.443164 | − | 0.896441i | \(-0.646144\pi\) | ||||
−0.443164 | + | 0.896441i | \(0.646144\pi\) | |||||||
\(98\) | −16.0057 | −1.61682 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.37678 | 0.837678 | ||||||||
\(101\) | −8.41434 | −0.837258 | −0.418629 | − | 0.908157i | \(-0.637489\pi\) | ||||
−0.418629 | + | 0.908157i | \(0.637489\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0092 | −1.18330 | −0.591652 | − | 0.806194i | \(-0.701524\pi\) | ||||
−0.591652 | + | 0.806194i | \(0.701524\pi\) | |||||||
\(104\) | −3.22205 | −0.315948 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.3297 | −1.58608 | ||||||||
\(107\) | −4.38059 | −0.423488 | −0.211744 | − | 0.977325i | \(-0.567914\pi\) | ||||
−0.211744 | + | 0.977325i | \(0.567914\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.23951 | 0.406072 | 0.203036 | − | 0.979171i | \(-0.434919\pi\) | ||||
0.203036 | + | 0.979171i | \(0.434919\pi\) | |||||||
\(110\) | −6.10619 | −0.582202 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 19.0981 | 1.80460 | ||||||||
\(113\) | 4.63806 | 0.436312 | 0.218156 | − | 0.975914i | \(-0.429996\pi\) | ||||
0.218156 | + | 0.975914i | \(0.429996\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.6063 | 1.45529 | ||||||||
\(116\) | −13.8224 | −1.28338 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 26.4207 | 2.43223 | ||||||||
\(119\) | −8.75812 | −0.802856 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.84847 | −0.167353 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.36456 | −0.571554 | ||||||||
\(125\) | 3.01365 | 0.269549 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.86801 | −0.431966 | −0.215983 | − | 0.976397i | \(-0.569296\pi\) | ||||
−0.215983 | + | 0.976397i | \(0.569296\pi\) | |||||||
\(128\) | −8.25704 | −0.729826 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 18.2517 | 1.60078 | ||||||||
\(131\) | −15.3923 | −1.34483 | −0.672414 | − | 0.740175i | \(-0.734743\pi\) | ||||
−0.672414 | + | 0.740175i | \(0.734743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.1058 | −1.22313 | ||||||||
\(134\) | −21.8866 | −1.89071 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.38578 | 0.204579 | ||||||||
\(137\) | −10.4869 | −0.895953 | −0.447976 | − | 0.894045i | \(-0.647855\pi\) | ||||
−0.447976 | + | 0.894045i | \(0.647855\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.8531 | 1.34464 | 0.672321 | − | 0.740259i | \(-0.265297\pi\) | ||||
0.672321 | + | 0.740259i | \(0.265297\pi\) | |||||||
\(140\) | −18.5208 | −1.56529 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −18.7178 | −1.57077 | ||||||||
\(143\) | −2.98905 | −0.249957 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −32.2271 | −2.67631 | ||||||||
\(146\) | 13.3077 | 1.10135 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.05306 | −0.661957 | ||||||||
\(149\) | −23.5778 | −1.93157 | −0.965783 | − | 0.259352i | \(-0.916491\pi\) | ||||
−0.965783 | + | 0.259352i | \(0.916491\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.83173 | −0.637337 | −0.318668 | − | 0.947866i | \(-0.603236\pi\) | ||||
−0.318668 | + | 0.947866i | \(0.603236\pi\) | |||||||
\(152\) | 3.84253 | 0.311670 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.31464 | 0.589430 | ||||||||
\(155\) | −14.8390 | −1.19190 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.23571 | 0.258238 | 0.129119 | − | 0.991629i | \(-0.458785\pi\) | ||||
0.129119 | + | 0.991629i | \(0.458785\pi\) | |||||||
\(158\) | −13.8460 | −1.10153 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 22.3482 | 1.76678 | ||||||||
\(161\) | −18.6948 | −1.47336 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.2249 | −0.800875 | −0.400437 | − | 0.916324i | \(-0.631142\pi\) | ||||
−0.400437 | + | 0.916324i | \(0.631142\pi\) | |||||||
\(164\) | 1.89829 | 0.148231 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 28.1778 | 2.18703 | ||||||||
\(167\) | 16.3966 | 1.26881 | 0.634405 | − | 0.773000i | \(-0.281245\pi\) | ||||
0.634405 | + | 0.773000i | \(0.281245\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.06558 | −0.312737 | ||||||||
\(170\) | −13.5145 | −1.03652 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.61040 | −0.199041 | ||||||||
\(173\) | 5.35272 | 0.406960 | 0.203480 | − | 0.979079i | \(-0.434775\pi\) | ||||
0.203480 | + | 0.979079i | \(0.434775\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −23.3957 | −1.76855 | ||||||||
\(176\) | −4.82624 | −0.363792 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.90743 | −0.592687 | ||||||||
\(179\) | −0.134569 | −0.0100582 | −0.00502909 | − | 0.999987i | \(-0.501601\pi\) | ||||
−0.00502909 | + | 0.999987i | \(0.501601\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.95147 | 0.145051 | 0.0725257 | − | 0.997367i | \(-0.476894\pi\) | ||||
0.0725257 | + | 0.997367i | \(0.476894\pi\) | |||||||
\(182\) | −21.8638 | −1.62065 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.09261 | 0.375432 | ||||||||
\(185\) | −18.7758 | −1.38042 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.21325 | 0.161849 | ||||||||
\(188\) | 5.55951 | 0.405469 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −21.7664 | −1.57910 | ||||||||
\(191\) | 23.0282 | 1.66626 | 0.833130 | − | 0.553078i | \(-0.186547\pi\) | ||||
0.833130 | + | 0.553078i | \(0.186547\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.6738 | 1.41615 | 0.708076 | − | 0.706136i | \(-0.249563\pi\) | ||||
0.708076 | + | 0.706136i | \(0.249563\pi\) | |||||||
\(194\) | 16.1359 | 1.15849 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.2683 | 0.876304 | ||||||||
\(197\) | −4.30898 | −0.307002 | −0.153501 | − | 0.988149i | \(-0.549055\pi\) | ||||
−0.153501 | + | 0.988149i | \(0.549055\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.33897 | 0.520246 | 0.260123 | − | 0.965576i | \(-0.416237\pi\) | ||||
0.260123 | + | 0.965576i | \(0.416237\pi\) | |||||||
\(200\) | 6.37317 | 0.450651 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.5537 | 1.09435 | ||||||||
\(203\) | 38.6050 | 2.70954 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.42587 | 0.309116 | ||||||||
\(206\) | 22.1987 | 1.54665 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.4259 | 1.00026 | ||||||||
\(209\) | 3.56465 | 0.246572 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.5685 | −1.20947 | −0.604733 | − | 0.796428i | \(-0.706720\pi\) | ||||
−0.604733 | + | 0.796428i | \(0.706720\pi\) | |||||||
\(212\) | 12.5166 | 0.859644 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.09740 | 0.553527 | ||||||||
\(215\) | −6.08617 | −0.415073 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.7757 | 1.20670 | ||||||||
\(218\) | −7.83661 | −0.530762 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.68036 | 0.315550 | ||||||||
\(221\) | −6.61552 | −0.445008 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.0149 | −1.27333 | −0.636666 | − | 0.771140i | \(-0.719687\pi\) | ||||
−0.636666 | + | 0.771140i | \(0.719687\pi\) | |||||||
\(224\) | −26.7710 | −1.78871 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.57331 | −0.570288 | ||||||||
\(227\) | 21.0709 | 1.39852 | 0.699262 | − | 0.714866i | \(-0.253512\pi\) | ||||
0.699262 | + | 0.714866i | \(0.253512\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.19206 | −0.409183 | −0.204592 | − | 0.978847i | \(-0.565587\pi\) | ||||
−0.204592 | + | 0.978847i | \(0.565587\pi\) | |||||||
\(230\) | −28.8477 | −1.90216 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.5163 | −0.690428 | ||||||||
\(233\) | −10.4925 | −0.687387 | −0.343694 | − | 0.939082i | \(-0.611678\pi\) | ||||
−0.343694 | + | 0.939082i | \(0.611678\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.9621 | 0.845551 | ||||||||
\(236\) | −20.2513 | −1.31825 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.1891 | 1.04939 | ||||||||
\(239\) | −7.59425 | −0.491231 | −0.245616 | − | 0.969367i | \(-0.578990\pi\) | ||||
−0.245616 | + | 0.969367i | \(0.578990\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.8949 | −1.08829 | −0.544147 | − | 0.838990i | \(-0.683147\pi\) | ||||
−0.544147 | + | 0.838990i | \(0.683147\pi\) | |||||||
\(242\) | −1.84847 | −0.118824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.41684 | 0.0907039 | ||||||||
\(245\) | 28.6035 | 1.82741 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.6549 | −0.677957 | ||||||||
\(248\) | −4.84225 | −0.307483 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.57065 | −0.352319 | ||||||||
\(251\) | 11.9875 | 0.756646 | 0.378323 | − | 0.925674i | \(-0.376501\pi\) | ||||
0.378323 | + | 0.925674i | \(0.376501\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.72434 | 0.297016 | ||||||||
\(254\) | 8.99837 | 0.564608 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9687 | 1.31054 | ||||||||
\(257\) | 1.46850 | 0.0916027 | 0.0458014 | − | 0.998951i | \(-0.485416\pi\) | ||||
0.0458014 | + | 0.998951i | \(0.485416\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.4916 | 1.39756 | ||||||||
\(260\) | −13.9898 | −0.867612 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 28.4521 | 1.75778 | ||||||||
\(263\) | −5.52056 | −0.340412 | −0.170206 | − | 0.985408i | \(-0.554443\pi\) | ||||
−0.170206 | + | 0.985408i | \(0.554443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 29.1826 | 1.79267 | ||||||||
\(266\) | 26.0741 | 1.59871 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.7759 | 1.02475 | ||||||||
\(269\) | 17.4972 | 1.06682 | 0.533412 | − | 0.845856i | \(-0.320910\pi\) | ||||
0.533412 | + | 0.845856i | \(0.320910\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.52293 | −0.456985 | −0.228493 | − | 0.973546i | \(-0.573380\pi\) | ||||
−0.228493 | + | 0.973546i | \(0.573380\pi\) | |||||||
\(272\) | −10.6817 | −0.647673 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.3846 | 1.17107 | ||||||||
\(275\) | 5.91229 | 0.356525 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.90278 | −0.474832 | −0.237416 | − | 0.971408i | \(-0.576300\pi\) | ||||
−0.237416 | + | 0.971408i | \(0.576300\pi\) | |||||||
\(278\) | −29.3040 | −1.75754 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −14.0909 | −0.842091 | ||||||||
\(281\) | 0.766106 | 0.0457020 | 0.0228510 | − | 0.999739i | \(-0.492726\pi\) | ||||
0.0228510 | + | 0.999739i | \(0.492726\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.2211 | 0.845357 | 0.422678 | − | 0.906280i | \(-0.361090\pi\) | ||||
0.422678 | + | 0.906280i | \(0.361090\pi\) | |||||||
\(284\) | 14.3471 | 0.851344 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.52517 | 0.326710 | ||||||||
\(287\) | −5.30178 | −0.312954 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.1015 | −0.711854 | ||||||||
\(290\) | 59.5708 | 3.49812 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.2002 | −0.596924 | ||||||||
\(293\) | −3.44663 | −0.201354 | −0.100677 | − | 0.994919i | \(-0.532101\pi\) | ||||
−0.100677 | + | 0.994919i | \(0.532101\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −47.2162 | −2.74903 | ||||||||
\(296\) | −6.12688 | −0.356118 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 43.5828 | 2.52468 | ||||||||
\(299\) | −14.1213 | −0.816655 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.29065 | 0.420226 | ||||||||
\(302\) | 14.4767 | 0.833041 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −17.2039 | −0.986710 | ||||||||
\(305\) | 3.30338 | 0.189151 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.4971 | −0.656171 | −0.328086 | − | 0.944648i | \(-0.606403\pi\) | ||||
−0.328086 | + | 0.944648i | \(0.606403\pi\) | |||||||
\(308\) | −5.60662 | −0.319467 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 27.4295 | 1.55789 | ||||||||
\(311\) | 14.3564 | 0.814075 | 0.407038 | − | 0.913411i | \(-0.366562\pi\) | ||||
0.407038 | + | 0.913411i | \(0.366562\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.6147 | −0.995644 | −0.497822 | − | 0.867279i | \(-0.665867\pi\) | ||||
−0.497822 | + | 0.867279i | \(0.665867\pi\) | |||||||
\(314\) | −5.98112 | −0.337534 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.6129 | 0.597021 | ||||||||
\(317\) | −13.7541 | −0.772506 | −0.386253 | − | 0.922393i | \(-0.626231\pi\) | ||||
−0.386253 | + | 0.922393i | \(0.626231\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.75580 | −0.546220 | ||||||||
\(320\) | −9.42418 | −0.526828 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 34.5568 | 1.92577 | ||||||||
\(323\) | 7.88947 | 0.438982 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.6721 | −0.980274 | ||||||||
\(326\) | 18.9004 | 1.04680 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.44424 | 0.0797450 | ||||||||
\(329\) | −15.5273 | −0.856048 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.7124 | 1.63314 | 0.816569 | − | 0.577247i | \(-0.195873\pi\) | ||||
0.816569 | + | 0.577247i | \(0.195873\pi\) | |||||||
\(332\) | −21.5981 | −1.18535 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −30.3087 | −1.65842 | ||||||||
\(335\) | 39.1133 | 2.13699 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.1870 | −0.663867 | −0.331933 | − | 0.943303i | \(-0.607701\pi\) | ||||
−0.331933 | + | 0.943303i | \(0.607701\pi\) | |||||||
\(338\) | 7.51510 | 0.408767 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.3588 | 0.561785 | ||||||||
\(341\) | −4.49208 | −0.243260 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.56440 | −0.354445 | ||||||||
\(344\) | −1.98603 | −0.107080 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.89434 | −0.531923 | ||||||||
\(347\) | 28.8989 | 1.55137 | 0.775686 | − | 0.631119i | \(-0.217404\pi\) | ||||
0.775686 | + | 0.631119i | \(0.217404\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.51210 | −0.509171 | −0.254585 | − | 0.967050i | \(-0.581939\pi\) | ||||
−0.254585 | + | 0.967050i | \(0.581939\pi\) | |||||||
\(350\) | 43.2463 | 2.31161 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.76526 | 0.360590 | ||||||||
\(353\) | −4.38429 | −0.233352 | −0.116676 | − | 0.993170i | \(-0.537224\pi\) | ||||
−0.116676 | + | 0.993170i | \(0.537224\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.4504 | 1.77536 | ||||||||
\(356\) | 6.06099 | 0.321232 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.248747 | 0.0131467 | ||||||||
\(359\) | −34.8151 | −1.83747 | −0.918735 | − | 0.394874i | \(-0.870788\pi\) | ||||
−0.918735 | + | 0.394874i | \(0.870788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.29326 | −0.331224 | ||||||||
\(362\) | −3.60723 | −0.189592 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16.7585 | 0.878383 | ||||||||
\(365\) | −23.7819 | −1.24480 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.614056 | 0.0320535 | 0.0160267 | − | 0.999872i | \(-0.494898\pi\) | ||||
0.0160267 | + | 0.999872i | \(0.494898\pi\) | |||||||
\(368\) | −22.8008 | −1.18857 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 34.7065 | 1.80430 | ||||||||
\(371\) | −34.9579 | −1.81493 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.38763 | −0.278961 | −0.139481 | − | 0.990225i | \(-0.544543\pi\) | ||||
−0.139481 | + | 0.990225i | \(0.544543\pi\) | |||||||
\(374\) | −4.09113 | −0.211547 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.22976 | 0.218133 | ||||||||
\(377\) | 29.1606 | 1.50185 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.5494 | −0.952819 | −0.476410 | − | 0.879223i | \(-0.658062\pi\) | ||||
−0.476410 | + | 0.879223i | \(0.658062\pi\) | |||||||
\(380\) | 16.6838 | 0.855863 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −42.5669 | −2.17791 | ||||||||
\(383\) | −8.41132 | −0.429798 | −0.214899 | − | 0.976636i | \(-0.568942\pi\) | ||||
−0.214899 | + | 0.976636i | \(0.568942\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.0719 | −0.666205 | ||||||||
\(386\) | −36.3664 | −1.85100 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.3680 | −0.627892 | ||||||||
\(389\) | −20.5368 | −1.04126 | −0.520628 | − | 0.853784i | \(-0.674302\pi\) | ||||
−0.520628 | + | 0.853784i | \(0.674302\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.4561 | 0.528790 | ||||||||
\(392\) | 9.33386 | 0.471431 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.96501 | 0.401271 | ||||||||
\(395\) | 24.7440 | 1.24501 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.7098 | 1.29034 | 0.645169 | − | 0.764040i | \(-0.276787\pi\) | ||||
0.645169 | + | 0.764040i | \(0.276787\pi\) | |||||||
\(398\) | −13.5659 | −0.679995 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −28.5342 | −1.42671 | ||||||||
\(401\) | −26.9601 | −1.34633 | −0.673163 | − | 0.739494i | \(-0.735065\pi\) | ||||
−0.673163 | + | 0.739494i | \(0.735065\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.4270 | 0.668849 | ||||||||
\(404\) | −11.9218 | −0.593131 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −71.3601 | −3.54154 | ||||||||
\(407\) | −5.68381 | −0.281736 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.6253 | −0.574833 | −0.287416 | − | 0.957806i | \(-0.592796\pi\) | ||||
−0.287416 | + | 0.957806i | \(0.592796\pi\) | |||||||
\(410\) | −8.18109 | −0.404035 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.0151 | −0.838276 | ||||||||
\(413\) | 56.5605 | 2.78316 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −50.3563 | −2.47189 | ||||||||
\(416\) | −20.2217 | −0.991451 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.58915 | −0.322286 | ||||||||
\(419\) | −34.0716 | −1.66451 | −0.832254 | − | 0.554394i | \(-0.812950\pi\) | ||||
−0.832254 | + | 0.554394i | \(0.812950\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6562 | 0.665563 | 0.332781 | − | 0.943004i | \(-0.392013\pi\) | ||||
0.332781 | + | 0.943004i | \(0.392013\pi\) | |||||||
\(422\) | 32.4749 | 1.58085 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.52281 | 0.462468 | ||||||||
\(425\) | 13.0854 | 0.634735 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.95713 | −0.191499 | ||||||||
\(428\) | −6.20660 | −0.300008 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.2501 | 0.542528 | ||||||||
\(431\) | −27.0917 | −1.30496 | −0.652481 | − | 0.757805i | \(-0.726272\pi\) | ||||
−0.652481 | + | 0.757805i | \(0.726272\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.42284 | −0.212548 | −0.106274 | − | 0.994337i | \(-0.533892\pi\) | ||||
−0.106274 | + | 0.994337i | \(0.533892\pi\) | |||||||
\(434\) | −32.8579 | −1.57723 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.00672 | 0.287670 | ||||||||
\(437\) | 16.8406 | 0.805596 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.4951 | −1.16909 | −0.584544 | − | 0.811362i | \(-0.698726\pi\) | ||||
−0.584544 | + | 0.811362i | \(0.698726\pi\) | |||||||
\(440\) | 3.56088 | 0.169758 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.2286 | 0.581655 | ||||||||
\(443\) | −14.2630 | −0.677655 | −0.338827 | − | 0.940849i | \(-0.610030\pi\) | ||||
−0.338827 | + | 0.940849i | \(0.610030\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.1313 | 0.669886 | ||||||||
\(446\) | 35.1484 | 1.66433 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11.2893 | 0.533368 | ||||||||
\(449\) | 0.585554 | 0.0276340 | 0.0138170 | − | 0.999905i | \(-0.495602\pi\) | ||||
0.0138170 | + | 0.999905i | \(0.495602\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.33980 | 0.0630889 | ||||||||
\(452\) | 6.57139 | 0.309092 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −38.9489 | −1.82796 | ||||||||
\(455\) | 39.0725 | 1.83175 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4744 | 0.817416 | 0.408708 | − | 0.912665i | \(-0.365979\pi\) | ||||
0.408708 | + | 0.912665i | \(0.365979\pi\) | |||||||
\(458\) | 11.4458 | 0.534829 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 22.1116 | 1.03096 | ||||||||
\(461\) | 20.5326 | 0.956300 | 0.478150 | − | 0.878278i | \(-0.341308\pi\) | ||||
0.478150 | + | 0.878278i | \(0.341308\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.88087 | 0.412729 | 0.206365 | − | 0.978475i | \(-0.433837\pi\) | ||||
0.206365 | + | 0.978475i | \(0.433837\pi\) | |||||||
\(464\) | 47.0839 | 2.18581 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.3951 | 0.898460 | ||||||||
\(467\) | 3.46933 | 0.160541 | 0.0802707 | − | 0.996773i | \(-0.474422\pi\) | ||||
0.0802707 | + | 0.996773i | \(0.474422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −46.8540 | −2.16352 | ||||||||
\(470\) | −23.9600 | −1.10519 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.4075 | −0.709188 | ||||||||
\(473\) | −1.84241 | −0.0847141 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.0753 | 0.967000 | ||||||||
\(476\) | −12.4089 | −0.568759 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.0377 | 0.642072 | ||||||||
\(479\) | −16.0150 | −0.731745 | −0.365873 | − | 0.930665i | \(-0.619229\pi\) | ||||
−0.365873 | + | 0.930665i | \(0.619229\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.9892 | 0.774641 | ||||||||
\(482\) | 31.2296 | 1.42247 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.41684 | 0.0644018 | ||||||||
\(485\) | −28.8362 | −1.30938 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.12455 | 0.322844 | 0.161422 | − | 0.986885i | \(-0.448392\pi\) | ||||
0.161422 | + | 0.986885i | \(0.448392\pi\) | |||||||
\(488\) | 1.07795 | 0.0487966 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −52.8728 | −2.38855 | ||||||||
\(491\) | −24.6208 | −1.11112 | −0.555561 | − | 0.831476i | \(-0.687496\pi\) | ||||
−0.555561 | + | 0.831476i | \(0.687496\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.5920 | −0.972456 | ||||||||
\(494\) | 19.6953 | 0.886134 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21.6799 | 0.973454 | ||||||||
\(497\) | −40.0704 | −1.79740 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.6515 | 1.59598 | 0.797991 | − | 0.602669i | \(-0.205896\pi\) | ||||
0.797991 | + | 0.602669i | \(0.205896\pi\) | |||||||
\(500\) | 4.26987 | 0.190954 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.1586 | −0.988986 | ||||||||
\(503\) | 34.2193 | 1.52576 | 0.762881 | − | 0.646539i | \(-0.223784\pi\) | ||||
0.762881 | + | 0.646539i | \(0.223784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.7957 | −1.23689 | ||||||||
\(506\) | −8.73279 | −0.388220 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.89719 | −0.306013 | ||||||||
\(509\) | −4.88930 | −0.216714 | −0.108357 | − | 0.994112i | \(-0.534559\pi\) | ||||
−0.108357 | + | 0.994112i | \(0.534559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.4885 | 1.26026 | ||||||||
\(512\) | −22.2459 | −0.983138 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.71448 | −0.119731 | ||||||||
\(515\) | −39.6710 | −1.74811 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.92388 | 0.172572 | ||||||||
\(518\) | −41.5750 | −1.82670 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.6437 | −0.466755 | ||||||||
\(521\) | −0.638526 | −0.0279743 | −0.0139872 | − | 0.999902i | \(-0.504452\pi\) | ||||
−0.0139872 | + | 0.999902i | \(0.504452\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.03487 | −0.176433 | −0.0882163 | − | 0.996101i | \(-0.528117\pi\) | ||||
−0.0882163 | + | 0.996101i | \(0.528117\pi\) | |||||||
\(524\) | −21.8084 | −0.952704 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.2046 | 0.444941 | ||||||||
\(527\) | −9.94210 | −0.433084 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.680653 | −0.0295936 | ||||||||
\(530\) | −53.9431 | −2.34314 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −19.9857 | −0.866488 | ||||||||
\(533\) | −4.00474 | −0.173464 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.4708 | −0.625625 | ||||||||
\(536\) | 12.7634 | 0.551294 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −32.3430 | −1.39441 | ||||||||
\(539\) | 8.65888 | 0.372964 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.47979 | −0.0636213 | −0.0318107 | − | 0.999494i | \(-0.510127\pi\) | ||||
−0.0318107 | + | 0.999494i | \(0.510127\pi\) | |||||||
\(542\) | 13.9059 | 0.597310 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 14.9732 | 0.641972 | ||||||||
\(545\) | 14.0047 | 0.599896 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.12677 | 0.133691 | 0.0668454 | − | 0.997763i | \(-0.478707\pi\) | ||||
0.0668454 | + | 0.997763i | \(0.478707\pi\) | |||||||
\(548\) | −14.8582 | −0.634711 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.9287 | −0.466001 | ||||||||
\(551\) | −34.7760 | −1.48151 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29.6410 | −1.26046 | ||||||||
\(554\) | 14.6081 | 0.620637 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.4613 | 0.952572 | ||||||||
\(557\) | 23.5146 | 0.996347 | 0.498174 | − | 0.867077i | \(-0.334004\pi\) | ||||
0.498174 | + | 0.867077i | \(0.334004\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.50705 | 0.232924 | ||||||||
\(560\) | 63.0881 | 2.66596 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.41612 | −0.0597356 | ||||||||
\(563\) | 22.9262 | 0.966226 | 0.483113 | − | 0.875558i | \(-0.339506\pi\) | ||||
0.483113 | + | 0.875558i | \(0.339506\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.3213 | 0.644570 | ||||||||
\(566\) | −26.2873 | −1.10494 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.9155 | 0.458003 | ||||||||
\(569\) | −33.6211 | −1.40947 | −0.704734 | − | 0.709471i | \(-0.748934\pi\) | ||||
−0.704734 | + | 0.709471i | \(0.748934\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.9729 | −1.12878 | −0.564391 | − | 0.825507i | \(-0.690889\pi\) | ||||
−0.564391 | + | 0.825507i | \(0.690889\pi\) | |||||||
\(572\) | −4.23501 | −0.177075 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.80017 | 0.409051 | ||||||||
\(575\) | 27.9317 | 1.16483 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.22915 | 0.134431 | 0.0672157 | − | 0.997738i | \(-0.478588\pi\) | ||||
0.0672157 | + | 0.997738i | \(0.478588\pi\) | |||||||
\(578\) | 22.3693 | 0.930440 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −45.6606 | −1.89595 | ||||||||
\(581\) | 60.3220 | 2.50258 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.83416 | 0.365874 | ||||||||
\(584\) | −7.76049 | −0.321131 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.37099 | 0.263183 | ||||||||
\(587\) | 1.21224 | 0.0500345 | 0.0250173 | − | 0.999687i | \(-0.492036\pi\) | ||||
0.0250173 | + | 0.999687i | \(0.492036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0127 | −0.659791 | ||||||||
\(590\) | 87.2777 | 3.59316 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 27.4315 | 1.12743 | ||||||||
\(593\) | −20.2271 | −0.830627 | −0.415314 | − | 0.909678i | \(-0.636328\pi\) | ||||
−0.415314 | + | 0.909678i | \(0.636328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.9314 | −1.18607 | ||||||||
\(596\) | −33.4059 | −1.36836 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26.1028 | 1.06742 | ||||||||
\(599\) | 35.5417 | 1.45219 | 0.726097 | − | 0.687593i | \(-0.241332\pi\) | ||||
0.726097 | + | 0.687593i | \(0.241332\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.4502 | −1.28288 | −0.641440 | − | 0.767173i | \(-0.721663\pi\) | ||||
−0.641440 | + | 0.767173i | \(0.721663\pi\) | |||||||
\(602\) | −13.4766 | −0.549263 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.0963 | −0.451502 | ||||||||
\(605\) | 3.30338 | 0.134301 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.2027 | 1.63178 | 0.815890 | − | 0.578208i | \(-0.196248\pi\) | ||||
0.815890 | + | 0.578208i | \(0.196248\pi\) | |||||||
\(608\) | 24.1158 | 0.978025 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.10619 | −0.247232 | ||||||||
\(611\) | −11.7287 | −0.474492 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.3320 | −0.982761 | −0.491381 | − | 0.870945i | \(-0.663508\pi\) | ||||
−0.491381 | + | 0.870945i | \(0.663508\pi\) | |||||||
\(614\) | 21.2520 | 0.857659 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.26560 | −0.171866 | ||||||||
\(617\) | −41.3610 | −1.66513 | −0.832565 | − | 0.553928i | \(-0.813128\pi\) | ||||
−0.832565 | + | 0.553928i | \(0.813128\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.0276 | 0.523625 | 0.261813 | − | 0.965119i | \(-0.415680\pi\) | ||||
0.261813 | + | 0.965119i | \(0.415680\pi\) | |||||||
\(620\) | −21.0245 | −0.844365 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.5373 | −1.06405 | ||||||||
\(623\) | −16.9279 | −0.678202 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.6062 | −0.784250 | ||||||||
\(626\) | 32.5603 | 1.30137 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.58449 | 0.182941 | ||||||||
\(629\) | −12.5797 | −0.501586 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.09168 | −0.123078 | −0.0615388 | − | 0.998105i | \(-0.519601\pi\) | ||||
−0.0615388 | + | 0.998105i | \(0.519601\pi\) | |||||||
\(632\) | 8.07443 | 0.321183 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.4240 | 1.00972 | ||||||||
\(635\) | −16.0809 | −0.638150 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.8818 | −1.02548 | ||||||||
\(638\) | 18.0333 | 0.713945 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −27.2761 | −1.07818 | ||||||||
\(641\) | −31.6850 | −1.25148 | −0.625740 | − | 0.780031i | \(-0.715203\pi\) | ||||
−0.625740 | + | 0.780031i | \(0.715203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.9634 | −1.65488 | −0.827438 | − | 0.561557i | \(-0.810203\pi\) | ||||
−0.827438 | + | 0.561557i | \(0.810203\pi\) | |||||||
\(644\) | −26.4876 | −1.04376 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.5834 | −0.573778 | ||||||||
\(647\) | 6.08892 | 0.239380 | 0.119690 | − | 0.992811i | \(-0.461810\pi\) | ||||
0.119690 | + | 0.992811i | \(0.461810\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.2933 | −0.561061 | ||||||||
\(650\) | 32.6664 | 1.28128 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.4870 | −0.567356 | ||||||||
\(653\) | −3.83537 | −0.150090 | −0.0750449 | − | 0.997180i | \(-0.523910\pi\) | ||||
−0.0750449 | + | 0.997180i | \(0.523910\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −50.8465 | −1.98674 | ||||||||
\(656\) | −6.46622 | −0.252463 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 28.7018 | 1.11891 | ||||||||
\(659\) | −42.8074 | −1.66754 | −0.833769 | − | 0.552113i | \(-0.813822\pi\) | ||||
−0.833769 | + | 0.552113i | \(0.813822\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.43048 | 0.133430 | 0.0667151 | − | 0.997772i | \(-0.478748\pi\) | ||||
0.0667151 | + | 0.997772i | \(0.478748\pi\) | |||||||
\(662\) | −54.9224 | −2.13462 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.4322 | −0.637692 | ||||||||
\(665\) | −46.5967 | −1.80694 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −46.0897 | −1.78460 | ||||||||
\(668\) | 23.2314 | 0.898851 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −72.2997 | −2.79318 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.2194 | −1.66599 | −0.832993 | − | 0.553283i | \(-0.813375\pi\) | ||||
−0.832993 | + | 0.553283i | \(0.813375\pi\) | |||||||
\(674\) | 22.5273 | 0.867718 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.76027 | −0.221549 | ||||||||
\(677\) | 19.5997 | 0.753276 | 0.376638 | − | 0.926360i | \(-0.377080\pi\) | ||||
0.376638 | + | 0.926360i | \(0.377080\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.5430 | 1.32564 | ||||||||
\(680\) | 7.88113 | 0.302228 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.30347 | 0.317956 | ||||||||
\(683\) | −5.19077 | −0.198619 | −0.0993096 | − | 0.995057i | \(-0.531663\pi\) | ||||
−0.0993096 | + | 0.995057i | \(0.531663\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34.6420 | −1.32360 | ||||||||
\(686\) | 12.1341 | 0.463282 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.89192 | 0.339001 | ||||||||
\(689\) | −26.4058 | −1.00598 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.2822 | −0.657446 | −0.328723 | − | 0.944426i | \(-0.606618\pi\) | ||||
−0.328723 | + | 0.944426i | \(0.606618\pi\) | |||||||
\(692\) | 7.58395 | 0.288298 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −53.4187 | −2.02775 | ||||||||
\(695\) | 52.3688 | 1.98646 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.96532 | 0.112320 | ||||||||
\(698\) | 17.5828 | 0.665520 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −33.1480 | −1.25288 | ||||||||
\(701\) | −49.5798 | −1.87260 | −0.936301 | − | 0.351199i | \(-0.885774\pi\) | ||||
−0.936301 | + | 0.351199i | \(0.885774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.2608 | −0.764151 | ||||||||
\(704\) | −2.85289 | −0.107522 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.10423 | 0.305007 | ||||||||
\(707\) | 33.2966 | 1.25225 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.6865 | −0.438895 | −0.219448 | − | 0.975624i | \(-0.570425\pi\) | ||||
−0.219448 | + | 0.975624i | \(0.570425\pi\) | |||||||
\(710\) | −61.8320 | −2.32052 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.61129 | 0.172815 | ||||||||
\(713\) | −21.2221 | −0.794773 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.87396 | −0.369265 | ||||||||
\(716\) | −0.190663 | −0.00712542 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 64.3547 | 2.40169 | ||||||||
\(719\) | −36.7278 | −1.36971 | −0.684857 | − | 0.728677i | \(-0.740136\pi\) | ||||
−0.684857 | + | 0.728677i | \(0.740136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.5220 | 1.76981 | ||||||||
\(722\) | 11.6329 | 0.432932 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.76492 | 0.102757 | ||||||||
\(725\) | −57.6792 | −2.14215 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.1648 | 1.48963 | 0.744815 | − | 0.667270i | \(-0.232537\pi\) | ||||
0.744815 | + | 0.667270i | \(0.232537\pi\) | |||||||
\(728\) | 12.7501 | 0.472550 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 43.9602 | 1.62704 | ||||||||
\(731\) | −4.07771 | −0.150820 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.6513 | 1.27988 | 0.639938 | − | 0.768427i | \(-0.278960\pi\) | ||||
0.639938 | + | 0.768427i | \(0.278960\pi\) | |||||||
\(734\) | −1.13506 | −0.0418960 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 31.9614 | 1.17811 | ||||||||
\(737\) | 11.8404 | 0.436146 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.3526 | −1.66832 | −0.834161 | − | 0.551520i | \(-0.814048\pi\) | ||||
−0.834161 | + | 0.551520i | \(0.814048\pi\) | |||||||
\(740\) | −26.6023 | −0.977919 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 64.6187 | 2.37223 | ||||||||
\(743\) | −5.06913 | −0.185968 | −0.0929842 | − | 0.995668i | \(-0.529641\pi\) | ||||
−0.0929842 | + | 0.995668i | \(0.529641\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −77.8862 | −2.85353 | ||||||||
\(746\) | 9.95888 | 0.364620 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.13582 | 0.114657 | ||||||||
\(749\) | 17.3346 | 0.633392 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.1802 | −1.06480 | −0.532400 | − | 0.846493i | \(-0.678710\pi\) | ||||
−0.532400 | + | 0.846493i | \(0.678710\pi\) | |||||||
\(752\) | −18.9376 | −0.690583 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −53.9024 | −1.96301 | ||||||||
\(755\) | −25.8711 | −0.941547 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.6485 | 1.36836 | 0.684179 | − | 0.729314i | \(-0.260161\pi\) | ||||
0.684179 | + | 0.729314i | \(0.260161\pi\) | |||||||
\(758\) | 34.2880 | 1.24540 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.6933 | 0.460435 | ||||||||
\(761\) | 7.57930 | 0.274749 | 0.137375 | − | 0.990519i | \(-0.456134\pi\) | ||||
0.137375 | + | 0.990519i | \(0.456134\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.7763 | −0.607343 | ||||||||
\(764\) | 32.6272 | 1.18041 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.5481 | 0.561774 | ||||||||
\(767\) | 42.7234 | 1.54265 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.43737 | −0.0518330 | −0.0259165 | − | 0.999664i | \(-0.508250\pi\) | ||||
−0.0259165 | + | 0.999664i | \(0.508250\pi\) | |||||||
\(770\) | 24.1630 | 0.870774 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 27.8747 | 1.00323 | ||||||||
\(773\) | −25.8996 | −0.931544 | −0.465772 | − | 0.884905i | \(-0.654223\pi\) | ||||
−0.465772 | + | 0.884905i | \(0.654223\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.5585 | −0.954009 | ||||||||
\(776\) | −9.40978 | −0.337791 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.9616 | 1.36099 | ||||||||
\(779\) | 4.77593 | 0.171115 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.1261 | 0.362341 | ||||||||
\(782\) | −19.3279 | −0.691163 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −41.7899 | −1.49250 | ||||||||
\(785\) | 10.6888 | 0.381499 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.0848 | 1.67839 | 0.839196 | − | 0.543830i | \(-0.183026\pi\) | ||||
0.839196 | + | 0.543830i | \(0.183026\pi\) | |||||||
\(788\) | −6.10513 | −0.217486 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −45.7386 | −1.62730 | ||||||||
\(791\) | −18.3534 | −0.652572 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.98905 | −0.106144 | ||||||||
\(794\) | −47.5238 | −1.68656 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.3981 | 0.368553 | ||||||||
\(797\) | −18.7516 | −0.664217 | −0.332109 | − | 0.943241i | \(-0.607760\pi\) | ||||
−0.332109 | + | 0.943241i | \(0.607760\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.68454 | 0.307237 | ||||||||
\(800\) | 39.9982 | 1.41415 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 49.8350 | 1.75974 | ||||||||
\(803\) | −7.19928 | −0.254057 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −61.7560 | −2.17661 | ||||||||
\(806\) | −24.8195 | −0.874229 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.07026 | −0.319091 | ||||||||
\(809\) | −32.1859 | −1.13160 | −0.565799 | − | 0.824543i | \(-0.691432\pi\) | ||||
−0.565799 | + | 0.824543i | \(0.691432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.3819 | −1.76915 | −0.884574 | − | 0.466401i | \(-0.845551\pi\) | ||||
−0.884574 | + | 0.466401i | \(0.845551\pi\) | |||||||
\(812\) | 54.6971 | 1.91949 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.5064 | 0.368248 | ||||||||
\(815\) | −33.7766 | −1.18314 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.56755 | −0.229769 | ||||||||
\(818\) | 21.4890 | 0.751344 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.27076 | 0.218984 | ||||||||
\(821\) | 42.9668 | 1.49955 | 0.749776 | − | 0.661692i | \(-0.230161\pi\) | ||||
0.749776 | + | 0.661692i | \(0.230161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.8913 | 1.84367 | 0.921837 | − | 0.387578i | \(-0.126688\pi\) | ||||
0.921837 | + | 0.387578i | \(0.126688\pi\) | |||||||
\(824\) | −12.9454 | −0.450973 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −104.550 | −3.63777 | ||||||||
\(827\) | 5.30584 | 0.184502 | 0.0922510 | − | 0.995736i | \(-0.470594\pi\) | ||||
0.0922510 | + | 0.995736i | \(0.470594\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.9232 | −0.900349 | −0.450174 | − | 0.892941i | \(-0.648638\pi\) | ||||
−0.450174 | + | 0.892941i | \(0.648638\pi\) | |||||||
\(830\) | 93.0820 | 3.23092 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.52744 | 0.295636 | ||||||||
\(833\) | 19.1643 | 0.664003 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.1643 | 1.87443 | ||||||||
\(836\) | 5.05054 | 0.174677 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 62.9804 | 2.17562 | ||||||||
\(839\) | −11.8004 | −0.407394 | −0.203697 | − | 0.979034i | \(-0.565296\pi\) | ||||
−0.203697 | + | 0.979034i | \(0.565296\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 66.1756 | 2.28192 | ||||||||
\(842\) | −25.2431 | −0.869934 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −24.8918 | −0.856810 | ||||||||
\(845\) | −13.4301 | −0.462011 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.95713 | −0.135969 | ||||||||
\(848\) | −42.6358 | −1.46412 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −24.1880 | −0.829640 | ||||||||
\(851\) | −26.8522 | −0.920483 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.0587 | −0.789514 | −0.394757 | − | 0.918785i | \(-0.629171\pi\) | ||||
−0.394757 | + | 0.918785i | \(0.629171\pi\) | |||||||
\(854\) | 7.31464 | 0.250302 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.72207 | −0.161397 | ||||||||
\(857\) | −39.0031 | −1.33232 | −0.666161 | − | 0.745808i | \(-0.732064\pi\) | ||||
−0.666161 | + | 0.745808i | \(0.732064\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.832111 | 0.0283913 | 0.0141956 | − | 0.999899i | \(-0.495481\pi\) | ||||
0.0141956 | + | 0.999899i | \(0.495481\pi\) | |||||||
\(860\) | −8.62313 | −0.294046 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 50.0783 | 1.70567 | ||||||||
\(863\) | −10.3690 | −0.352965 | −0.176482 | − | 0.984304i | \(-0.556472\pi\) | ||||
−0.176482 | + | 0.984304i | \(0.556472\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.6820 | 0.601207 | ||||||||
\(866\) | 8.17548 | 0.277814 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 25.1854 | 0.854847 | ||||||||
\(869\) | 7.49052 | 0.254099 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.3915 | −1.19920 | ||||||||
\(872\) | 4.57000 | 0.154760 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −31.1294 | −1.05297 | ||||||||
\(875\) | −11.9254 | −0.403153 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.6809 | 1.71137 | 0.855686 | − | 0.517496i | \(-0.173136\pi\) | ||||
0.855686 | + | 0.517496i | \(0.173136\pi\) | |||||||
\(878\) | 45.2785 | 1.52807 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15.9429 | −0.537435 | ||||||||
\(881\) | −16.3346 | −0.550327 | −0.275164 | − | 0.961397i | \(-0.588732\pi\) | ||||
−0.275164 | + | 0.961397i | \(0.588732\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.1354 | 0.778569 | 0.389285 | − | 0.921118i | \(-0.372722\pi\) | ||||
0.389285 | + | 0.921118i | \(0.372722\pi\) | |||||||
\(884\) | −9.37314 | −0.315253 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 26.3647 | 0.885739 | ||||||||
\(887\) | −29.4067 | −0.987379 | −0.493689 | − | 0.869638i | \(-0.664352\pi\) | ||||
−0.493689 | + | 0.869638i | \(0.664352\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.2633 | 0.646072 | ||||||||
\(890\) | −26.1212 | −0.875585 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −26.9411 | −0.902054 | ||||||||
\(893\) | 13.9873 | 0.468066 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.444533 | −0.0148591 | ||||||||
\(896\) | 32.6742 | 1.09157 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.08238 | −0.0361194 | ||||||||
\(899\) | 43.8238 | 1.46161 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.5522 | 0.651379 | ||||||||
\(902\) | −2.47659 | −0.0824613 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.99961 | 0.166284 | ||||||||
\(905\) | 6.44643 | 0.214287 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.3225 | −1.40530 | −0.702648 | − | 0.711537i | \(-0.747999\pi\) | ||||
−0.702648 | + | 0.711537i | \(0.747999\pi\) | |||||||
\(908\) | 29.8541 | 0.990742 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −72.2244 | −2.39422 | ||||||||
\(911\) | 26.5480 | 0.879575 | 0.439788 | − | 0.898102i | \(-0.355054\pi\) | ||||
0.439788 | + | 0.898102i | \(0.355054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.2439 | −0.504499 | ||||||||
\(914\) | −32.3008 | −1.06842 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.77317 | −0.289874 | ||||||||
\(917\) | 60.9092 | 2.01140 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.5096 | −0.676550 | −0.338275 | − | 0.941047i | \(-0.609843\pi\) | ||||
−0.338275 | + | 0.941047i | \(0.609843\pi\) | |||||||
\(920\) | 16.8228 | 0.554632 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −37.9540 | −1.24995 | ||||||||
\(923\) | −30.2675 | −0.996267 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33.6044 | −1.10491 | ||||||||
\(926\) | −16.4160 | −0.539464 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −66.0005 | −2.16657 | ||||||||
\(929\) | −56.6319 | −1.85803 | −0.929016 | − | 0.370039i | \(-0.879344\pi\) | ||||
−0.929016 | + | 0.370039i | \(0.879344\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.8659 | 1.01159 | ||||||||
\(932\) | −14.8662 | −0.486959 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.41295 | −0.209838 | ||||||||
\(935\) | 7.31120 | 0.239102 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.0886 | 0.688934 | 0.344467 | − | 0.938798i | \(-0.388060\pi\) | ||||
0.344467 | + | 0.938798i | \(0.388060\pi\) | |||||||
\(938\) | 86.6081 | 2.82786 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18.3652 | 0.599006 | ||||||||
\(941\) | −16.2132 | −0.528536 | −0.264268 | − | 0.964449i | \(-0.585130\pi\) | ||||
−0.264268 | + | 0.964449i | \(0.585130\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.32968 | 0.206123 | ||||||||
\(944\) | 68.9830 | 2.24520 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.40564 | 0.110727 | ||||||||
\(947\) | 7.65428 | 0.248731 | 0.124365 | − | 0.992236i | \(-0.460311\pi\) | ||||
0.124365 | + | 0.992236i | \(0.460311\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.5190 | 0.698537 | ||||||||
\(950\) | −38.9570 | −1.26393 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.44084 | −0.305980 | ||||||||
\(953\) | −19.9857 | −0.647400 | −0.323700 | − | 0.946160i | \(-0.604927\pi\) | ||||
−0.323700 | + | 0.946160i | \(0.604927\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 76.0707 | 2.46159 | ||||||||
\(956\) | −10.7598 | −0.347998 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.6033 | 0.956439 | ||||||||
\(959\) | 41.4979 | 1.34004 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.8212 | −0.349073 | ||||||||
\(962\) | −31.4040 | −1.01251 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.9373 | −0.770970 | ||||||||
\(965\) | 64.9900 | 2.09210 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.9320 | 1.05902 | 0.529511 | − | 0.848303i | \(-0.322376\pi\) | ||||
0.529511 | + | 0.848303i | \(0.322376\pi\) | |||||||
\(968\) | 1.07795 | 0.0346467 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 53.3028 | 1.71145 | ||||||||
\(971\) | 28.1643 | 0.903834 | 0.451917 | − | 0.892060i | \(-0.350740\pi\) | ||||
0.451917 | + | 0.892060i | \(0.350740\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −62.7328 | −2.01112 | ||||||||
\(974\) | −13.1695 | −0.421978 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.82624 | −0.154484 | ||||||||
\(977\) | −33.0812 | −1.05836 | −0.529180 | − | 0.848510i | \(-0.677500\pi\) | ||||
−0.529180 | + | 0.848510i | \(0.677500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.27782 | 0.136720 | ||||||||
\(980\) | 40.5267 | 1.29458 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 45.5108 | 1.45231 | ||||||||
\(983\) | −51.5783 | −1.64509 | −0.822547 | − | 0.568698i | \(-0.807447\pi\) | ||||
−0.822547 | + | 0.568698i | \(0.807447\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.2342 | −0.453538 | ||||||||
\(986\) | 39.9122 | 1.27106 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.0963 | −0.480278 | ||||||||
\(989\) | −8.70416 | −0.276776 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.8494 | 1.42469 | 0.712345 | − | 0.701830i | \(-0.247633\pi\) | ||||
0.712345 | + | 0.701830i | \(0.247633\pi\) | |||||||
\(992\) | −30.3901 | −0.964886 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 74.0689 | 2.34932 | ||||||||
\(995\) | 24.2434 | 0.768567 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.9286 | −0.852838 | −0.426419 | − | 0.904526i | \(-0.640225\pi\) | ||||
−0.426419 | + | 0.904526i | \(0.640225\pi\) | |||||||
\(998\) | −65.9008 | −2.08605 | ||||||||
\(999\) | 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 | 6039.2.a.m.1.7 | ✓ | 25 | |
3.2 | odd | 2 | 6039.2.a.p.1.19 | yes | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.m.1.7 | ✓ | 25 | 1.1 | even | 1 | trivial | |
6039.2.a.p.1.19 | yes | 25 | 3.2 | odd | 2 |