Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80081 | −1.27337 | −0.636683 | − | 0.771126i | \(-0.719694\pi\) | ||||
−0.636683 | + | 0.771126i | \(0.719694\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.24292 | 0.621458 | ||||||||
\(5\) | −2.17778 | −0.973932 | −0.486966 | − | 0.873421i | \(-0.661896\pi\) | ||||
−0.486966 | + | 0.873421i | \(0.661896\pi\) | |||||||
\(6\) | −1.80081 | −0.735178 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.36336 | 0.482022 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.92176 | 1.24017 | ||||||||
\(11\) | −0.798673 | −0.240809 | −0.120404 | − | 0.992725i | \(-0.538419\pi\) | ||||
−0.120404 | + | 0.992725i | \(0.538419\pi\) | |||||||
\(12\) | 1.24292 | 0.358799 | ||||||||
\(13\) | 1.19276 | 0.330813 | 0.165406 | − | 0.986225i | \(-0.447106\pi\) | ||||
0.165406 | + | 0.986225i | \(0.447106\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.17778 | −0.562300 | ||||||||
\(16\) | −4.94099 | −1.23525 | ||||||||
\(17\) | −5.17880 | −1.25604 | −0.628021 | − | 0.778196i | \(-0.716135\pi\) | ||||
−0.628021 | + | 0.778196i | \(0.716135\pi\) | |||||||
\(18\) | −1.80081 | −0.424455 | ||||||||
\(19\) | −4.47213 | −1.02598 | −0.512989 | − | 0.858395i | \(-0.671462\pi\) | ||||
−0.512989 | + | 0.858395i | \(0.671462\pi\) | |||||||
\(20\) | −2.70680 | −0.605258 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.43826 | 0.306638 | ||||||||
\(23\) | 6.71919 | 1.40105 | 0.700524 | − | 0.713629i | \(-0.252950\pi\) | ||||
0.700524 | + | 0.713629i | \(0.252950\pi\) | |||||||
\(24\) | 1.36336 | 0.278295 | ||||||||
\(25\) | −0.257287 | −0.0514574 | ||||||||
\(26\) | −2.14794 | −0.421246 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.22854 | 0.785220 | 0.392610 | − | 0.919705i | \(-0.371572\pi\) | ||||
0.392610 | + | 0.919705i | \(0.371572\pi\) | |||||||
\(30\) | 3.92176 | 0.716013 | ||||||||
\(31\) | 0.168434 | 0.0302517 | 0.0151258 | − | 0.999886i | \(-0.495185\pi\) | ||||
0.0151258 | + | 0.999886i | \(0.495185\pi\) | |||||||
\(32\) | 6.17106 | 1.09090 | ||||||||
\(33\) | −0.798673 | −0.139031 | ||||||||
\(34\) | 9.32603 | 1.59940 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.24292 | 0.207153 | ||||||||
\(37\) | −5.83538 | −0.959330 | −0.479665 | − | 0.877452i | \(-0.659242\pi\) | ||||
−0.479665 | + | 0.877452i | \(0.659242\pi\) | |||||||
\(38\) | 8.05346 | 1.30644 | ||||||||
\(39\) | 1.19276 | 0.190995 | ||||||||
\(40\) | −2.96910 | −0.469456 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.82010 | 0.277563 | 0.138782 | − | 0.990323i | \(-0.455681\pi\) | ||||
0.138782 | + | 0.990323i | \(0.455681\pi\) | |||||||
\(44\) | −0.992684 | −0.149653 | ||||||||
\(45\) | −2.17778 | −0.324644 | ||||||||
\(46\) | −12.1000 | −1.78405 | ||||||||
\(47\) | −5.26975 | −0.768672 | −0.384336 | − | 0.923193i | \(-0.625570\pi\) | ||||
−0.384336 | + | 0.923193i | \(0.625570\pi\) | |||||||
\(48\) | −4.94099 | −0.713171 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.463325 | 0.0655241 | ||||||||
\(51\) | −5.17880 | −0.725177 | ||||||||
\(52\) | 1.48251 | 0.205587 | ||||||||
\(53\) | −1.21884 | −0.167421 | −0.0837103 | − | 0.996490i | \(-0.526677\pi\) | ||||
−0.0837103 | + | 0.996490i | \(0.526677\pi\) | |||||||
\(54\) | −1.80081 | −0.245059 | ||||||||
\(55\) | 1.73933 | 0.234531 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.47213 | −0.592348 | ||||||||
\(58\) | −7.61479 | −0.999871 | ||||||||
\(59\) | 11.7353 | 1.52780 | 0.763900 | − | 0.645334i | \(-0.223282\pi\) | ||||
0.763900 | + | 0.645334i | \(0.223282\pi\) | |||||||
\(60\) | −2.70680 | −0.349446 | ||||||||
\(61\) | −12.5796 | −1.61065 | −0.805325 | − | 0.592833i | \(-0.798009\pi\) | ||||
−0.805325 | + | 0.592833i | \(0.798009\pi\) | |||||||
\(62\) | −0.303318 | −0.0385214 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.23093 | −0.153866 | ||||||||
\(65\) | −2.59757 | −0.322189 | ||||||||
\(66\) | 1.43826 | 0.177037 | ||||||||
\(67\) | −2.41092 | −0.294541 | −0.147271 | − | 0.989096i | \(-0.547049\pi\) | ||||
−0.147271 | + | 0.989096i | \(0.547049\pi\) | |||||||
\(68\) | −6.43681 | −0.780578 | ||||||||
\(69\) | 6.71919 | 0.808895 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.255861 | 0.0303651 | 0.0151826 | − | 0.999885i | \(-0.495167\pi\) | ||||
0.0151826 | + | 0.999885i | \(0.495167\pi\) | |||||||
\(72\) | 1.36336 | 0.160674 | ||||||||
\(73\) | −5.27880 | −0.617837 | −0.308918 | − | 0.951089i | \(-0.599967\pi\) | ||||
−0.308918 | + | 0.951089i | \(0.599967\pi\) | |||||||
\(74\) | 10.5084 | 1.22158 | ||||||||
\(75\) | −0.257287 | −0.0297089 | ||||||||
\(76\) | −5.55849 | −0.637602 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.14794 | −0.243206 | ||||||||
\(79\) | 13.1519 | 1.47970 | 0.739851 | − | 0.672771i | \(-0.234896\pi\) | ||||
0.739851 | + | 0.672771i | \(0.234896\pi\) | |||||||
\(80\) | 10.7604 | 1.20305 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.80081 | 0.198866 | ||||||||
\(83\) | 10.9425 | 1.20109 | 0.600546 | − | 0.799590i | \(-0.294950\pi\) | ||||
0.600546 | + | 0.799590i | \(0.294950\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.2783 | 1.22330 | ||||||||
\(86\) | −3.27766 | −0.353439 | ||||||||
\(87\) | 4.22854 | 0.453347 | ||||||||
\(88\) | −1.08888 | −0.116075 | ||||||||
\(89\) | −9.74201 | −1.03265 | −0.516325 | − | 0.856392i | \(-0.672700\pi\) | ||||
−0.516325 | + | 0.856392i | \(0.672700\pi\) | |||||||
\(90\) | 3.92176 | 0.413390 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.35140 | 0.870693 | ||||||||
\(93\) | 0.168434 | 0.0174658 | ||||||||
\(94\) | 9.48982 | 0.978800 | ||||||||
\(95\) | 9.73931 | 0.999232 | ||||||||
\(96\) | 6.17106 | 0.629831 | ||||||||
\(97\) | 4.79462 | 0.486820 | 0.243410 | − | 0.969923i | \(-0.421734\pi\) | ||||
0.243410 | + | 0.969923i | \(0.421734\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.798673 | −0.0802696 | ||||||||
\(100\) | −0.319786 | −0.0319786 | ||||||||
\(101\) | −2.54061 | −0.252800 | −0.126400 | − | 0.991979i | \(-0.540342\pi\) | ||||
−0.126400 | + | 0.991979i | \(0.540342\pi\) | |||||||
\(102\) | 9.32603 | 0.923415 | ||||||||
\(103\) | −5.43950 | −0.535970 | −0.267985 | − | 0.963423i | \(-0.586358\pi\) | ||||
−0.267985 | + | 0.963423i | \(0.586358\pi\) | |||||||
\(104\) | 1.62617 | 0.159459 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.19490 | 0.213188 | ||||||||
\(107\) | 16.2891 | 1.57473 | 0.787364 | − | 0.616489i | \(-0.211445\pi\) | ||||
0.787364 | + | 0.616489i | \(0.211445\pi\) | |||||||
\(108\) | 1.24292 | 0.119600 | ||||||||
\(109\) | 10.3602 | 0.992326 | 0.496163 | − | 0.868229i | \(-0.334742\pi\) | ||||
0.496163 | + | 0.868229i | \(0.334742\pi\) | |||||||
\(110\) | −3.13221 | −0.298644 | ||||||||
\(111\) | −5.83538 | −0.553869 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.79770 | 0.263185 | 0.131593 | − | 0.991304i | \(-0.457991\pi\) | ||||
0.131593 | + | 0.991304i | \(0.457991\pi\) | |||||||
\(114\) | 8.05346 | 0.754276 | ||||||||
\(115\) | −14.6329 | −1.36452 | ||||||||
\(116\) | 5.25572 | 0.487981 | ||||||||
\(117\) | 1.19276 | 0.110271 | ||||||||
\(118\) | −21.1330 | −1.94545 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.96910 | −0.271041 | ||||||||
\(121\) | −10.3621 | −0.942011 | ||||||||
\(122\) | 22.6534 | 2.05095 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 0.209350 | 0.0188001 | ||||||||
\(125\) | 11.4492 | 1.02405 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.5164 | −1.28812 | −0.644062 | − | 0.764973i | \(-0.722752\pi\) | ||||
−0.644062 | + | 0.764973i | \(0.722752\pi\) | |||||||
\(128\) | −10.1255 | −0.894972 | ||||||||
\(129\) | 1.82010 | 0.160251 | ||||||||
\(130\) | 4.67773 | 0.410264 | ||||||||
\(131\) | 0.770663 | 0.0673331 | 0.0336666 | − | 0.999433i | \(-0.489282\pi\) | ||||
0.0336666 | + | 0.999433i | \(0.489282\pi\) | |||||||
\(132\) | −0.992684 | −0.0864020 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.34161 | 0.375058 | ||||||||
\(135\) | −2.17778 | −0.187433 | ||||||||
\(136\) | −7.06058 | −0.605440 | ||||||||
\(137\) | 4.75720 | 0.406435 | 0.203218 | − | 0.979134i | \(-0.434860\pi\) | ||||
0.203218 | + | 0.979134i | \(0.434860\pi\) | |||||||
\(138\) | −12.1000 | −1.03002 | ||||||||
\(139\) | 0.628119 | 0.0532764 | 0.0266382 | − | 0.999645i | \(-0.491520\pi\) | ||||
0.0266382 | + | 0.999645i | \(0.491520\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.26975 | −0.443793 | ||||||||
\(142\) | −0.460758 | −0.0386659 | ||||||||
\(143\) | −0.952627 | −0.0796627 | ||||||||
\(144\) | −4.94099 | −0.411749 | ||||||||
\(145\) | −9.20881 | −0.764750 | ||||||||
\(146\) | 9.50612 | 0.786732 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.25289 | −0.596184 | ||||||||
\(149\) | −0.960953 | −0.0787243 | −0.0393622 | − | 0.999225i | \(-0.512533\pi\) | ||||
−0.0393622 | + | 0.999225i | \(0.512533\pi\) | |||||||
\(150\) | 0.463325 | 0.0378303 | ||||||||
\(151\) | −5.66573 | −0.461071 | −0.230535 | − | 0.973064i | \(-0.574048\pi\) | ||||
−0.230535 | + | 0.973064i | \(0.574048\pi\) | |||||||
\(152\) | −6.09714 | −0.494543 | ||||||||
\(153\) | −5.17880 | −0.418681 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.366812 | −0.0294630 | ||||||||
\(156\) | 1.48251 | 0.118695 | ||||||||
\(157\) | −14.1792 | −1.13162 | −0.565812 | − | 0.824534i | \(-0.691437\pi\) | ||||
−0.565812 | + | 0.824534i | \(0.691437\pi\) | |||||||
\(158\) | −23.6840 | −1.88420 | ||||||||
\(159\) | −1.21884 | −0.0966603 | ||||||||
\(160\) | −13.4392 | −1.06246 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.80081 | −0.141485 | ||||||||
\(163\) | 10.5373 | 0.825346 | 0.412673 | − | 0.910879i | \(-0.364595\pi\) | ||||
0.412673 | + | 0.910879i | \(0.364595\pi\) | |||||||
\(164\) | −1.24292 | −0.0970555 | ||||||||
\(165\) | 1.73933 | 0.135407 | ||||||||
\(166\) | −19.7053 | −1.52943 | ||||||||
\(167\) | 13.9834 | 1.08207 | 0.541034 | − | 0.841001i | \(-0.318033\pi\) | ||||
0.541034 | + | 0.841001i | \(0.318033\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5773 | −0.890563 | ||||||||
\(170\) | −20.3100 | −1.55771 | ||||||||
\(171\) | −4.47213 | −0.341992 | ||||||||
\(172\) | 2.26224 | 0.172494 | ||||||||
\(173\) | 5.17342 | 0.393328 | 0.196664 | − | 0.980471i | \(-0.436989\pi\) | ||||
0.196664 | + | 0.980471i | \(0.436989\pi\) | |||||||
\(174\) | −7.61479 | −0.577276 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.94624 | 0.297459 | ||||||||
\(177\) | 11.7353 | 0.882076 | ||||||||
\(178\) | 17.5435 | 1.31494 | ||||||||
\(179\) | −0.884735 | −0.0661282 | −0.0330641 | − | 0.999453i | \(-0.510527\pi\) | ||||
−0.0330641 | + | 0.999453i | \(0.510527\pi\) | |||||||
\(180\) | −2.70680 | −0.201753 | ||||||||
\(181\) | −10.6540 | −0.791905 | −0.395952 | − | 0.918271i | \(-0.629586\pi\) | ||||
−0.395952 | + | 0.918271i | \(0.629586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.5796 | −0.929910 | ||||||||
\(184\) | 9.16069 | 0.675335 | ||||||||
\(185\) | 12.7081 | 0.934321 | ||||||||
\(186\) | −0.303318 | −0.0222403 | ||||||||
\(187\) | 4.13616 | 0.302466 | ||||||||
\(188\) | −6.54986 | −0.477698 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −17.5386 | −1.27239 | ||||||||
\(191\) | −5.78471 | −0.418567 | −0.209283 | − | 0.977855i | \(-0.567113\pi\) | ||||
−0.209283 | + | 0.977855i | \(0.567113\pi\) | |||||||
\(192\) | −1.23093 | −0.0888345 | ||||||||
\(193\) | 16.6099 | 1.19561 | 0.597803 | − | 0.801643i | \(-0.296040\pi\) | ||||
0.597803 | + | 0.801643i | \(0.296040\pi\) | |||||||
\(194\) | −8.63420 | −0.619900 | ||||||||
\(195\) | −2.59757 | −0.186016 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.2889 | −1.16054 | −0.580268 | − | 0.814426i | \(-0.697052\pi\) | ||||
−0.580268 | + | 0.814426i | \(0.697052\pi\) | |||||||
\(198\) | 1.43826 | 0.102213 | ||||||||
\(199\) | 21.9239 | 1.55414 | 0.777070 | − | 0.629414i | \(-0.216705\pi\) | ||||
0.777070 | + | 0.629414i | \(0.216705\pi\) | |||||||
\(200\) | −0.350776 | −0.0248036 | ||||||||
\(201\) | −2.41092 | −0.170053 | ||||||||
\(202\) | 4.57515 | 0.321907 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.43681 | −0.450667 | ||||||||
\(205\) | 2.17778 | 0.152103 | ||||||||
\(206\) | 9.79550 | 0.682485 | ||||||||
\(207\) | 6.71919 | 0.467016 | ||||||||
\(208\) | −5.89343 | −0.408636 | ||||||||
\(209\) | 3.57177 | 0.247064 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.48428 | −0.652925 | −0.326462 | − | 0.945210i | \(-0.605857\pi\) | ||||
−0.326462 | + | 0.945210i | \(0.605857\pi\) | |||||||
\(212\) | −1.51492 | −0.104045 | ||||||||
\(213\) | 0.255861 | 0.0175313 | ||||||||
\(214\) | −29.3336 | −2.00520 | ||||||||
\(215\) | −3.96378 | −0.270327 | ||||||||
\(216\) | 1.36336 | 0.0927651 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.6567 | −1.26359 | ||||||||
\(219\) | −5.27880 | −0.356708 | ||||||||
\(220\) | 2.16184 | 0.145752 | ||||||||
\(221\) | −6.17708 | −0.415515 | ||||||||
\(222\) | 10.5084 | 0.705278 | ||||||||
\(223\) | 5.77091 | 0.386449 | 0.193224 | − | 0.981155i | \(-0.438105\pi\) | ||||
0.193224 | + | 0.981155i | \(0.438105\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.257287 | −0.0171525 | ||||||||
\(226\) | −5.03813 | −0.335131 | ||||||||
\(227\) | −0.172461 | −0.0114466 | −0.00572332 | − | 0.999984i | \(-0.501822\pi\) | ||||
−0.00572332 | + | 0.999984i | \(0.501822\pi\) | |||||||
\(228\) | −5.55849 | −0.368120 | ||||||||
\(229\) | 2.34851 | 0.155194 | 0.0775970 | − | 0.996985i | \(-0.475275\pi\) | ||||
0.0775970 | + | 0.996985i | \(0.475275\pi\) | |||||||
\(230\) | 26.3511 | 1.73754 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.76503 | 0.378493 | ||||||||
\(233\) | −2.17060 | −0.142201 | −0.0711004 | − | 0.997469i | \(-0.522651\pi\) | ||||
−0.0711004 | + | 0.997469i | \(0.522651\pi\) | |||||||
\(234\) | −2.14794 | −0.140415 | ||||||||
\(235\) | 11.4763 | 0.748634 | ||||||||
\(236\) | 14.5860 | 0.949465 | ||||||||
\(237\) | 13.1519 | 0.854306 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.2909 | 1.05377 | 0.526886 | − | 0.849936i | \(-0.323359\pi\) | ||||
0.526886 | + | 0.849936i | \(0.323359\pi\) | |||||||
\(240\) | 10.7604 | 0.694579 | ||||||||
\(241\) | 22.5603 | 1.45324 | 0.726619 | − | 0.687041i | \(-0.241091\pi\) | ||||
0.726619 | + | 0.687041i | \(0.241091\pi\) | |||||||
\(242\) | 18.6602 | 1.19952 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −15.6354 | −1.00095 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.80081 | 0.114815 | ||||||||
\(247\) | −5.33419 | −0.339407 | ||||||||
\(248\) | 0.229637 | 0.0145819 | ||||||||
\(249\) | 10.9425 | 0.693451 | ||||||||
\(250\) | −20.6178 | −1.30399 | ||||||||
\(251\) | 15.9372 | 1.00594 | 0.502972 | − | 0.864303i | \(-0.332240\pi\) | ||||
0.502972 | + | 0.864303i | \(0.332240\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.36643 | −0.337385 | ||||||||
\(254\) | 26.1413 | 1.64025 | ||||||||
\(255\) | 11.2783 | 0.706272 | ||||||||
\(256\) | 20.6959 | 1.29349 | ||||||||
\(257\) | 4.67166 | 0.291410 | 0.145705 | − | 0.989328i | \(-0.453455\pi\) | ||||
0.145705 | + | 0.989328i | \(0.453455\pi\) | |||||||
\(258\) | −3.27766 | −0.204058 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.22857 | −0.200227 | ||||||||
\(261\) | 4.22854 | 0.261740 | ||||||||
\(262\) | −1.38782 | −0.0857397 | ||||||||
\(263\) | −27.7645 | −1.71203 | −0.856017 | − | 0.516948i | \(-0.827068\pi\) | ||||
−0.856017 | + | 0.516948i | \(0.827068\pi\) | |||||||
\(264\) | −1.08888 | −0.0670160 | ||||||||
\(265\) | 2.65436 | 0.163056 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.74201 | −0.596201 | ||||||||
\(268\) | −2.99658 | −0.183045 | ||||||||
\(269\) | 0.216531 | 0.0132021 | 0.00660106 | − | 0.999978i | \(-0.497899\pi\) | ||||
0.00660106 | + | 0.999978i | \(0.497899\pi\) | |||||||
\(270\) | 3.92176 | 0.238671 | ||||||||
\(271\) | 15.4909 | 0.941007 | 0.470504 | − | 0.882398i | \(-0.344072\pi\) | ||||
0.470504 | + | 0.882398i | \(0.344072\pi\) | |||||||
\(272\) | 25.5884 | 1.55152 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.56682 | −0.517540 | ||||||||
\(275\) | 0.205488 | 0.0123914 | ||||||||
\(276\) | 8.35140 | 0.502695 | ||||||||
\(277\) | 2.35151 | 0.141289 | 0.0706443 | − | 0.997502i | \(-0.477494\pi\) | ||||
0.0706443 | + | 0.997502i | \(0.477494\pi\) | |||||||
\(278\) | −1.13112 | −0.0678403 | ||||||||
\(279\) | 0.168434 | 0.0100839 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.8868 | 1.42497 | 0.712483 | − | 0.701690i | \(-0.247571\pi\) | ||||
0.712483 | + | 0.701690i | \(0.247571\pi\) | |||||||
\(282\) | 9.48982 | 0.565111 | ||||||||
\(283\) | −7.09006 | −0.421461 | −0.210730 | − | 0.977544i | \(-0.567584\pi\) | ||||
−0.210730 | + | 0.977544i | \(0.567584\pi\) | |||||||
\(284\) | 0.318014 | 0.0188707 | ||||||||
\(285\) | 9.73931 | 0.576907 | ||||||||
\(286\) | 1.71550 | 0.101440 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.17106 | 0.363633 | ||||||||
\(289\) | 9.81994 | 0.577644 | ||||||||
\(290\) | 16.5833 | 0.973806 | ||||||||
\(291\) | 4.79462 | 0.281066 | ||||||||
\(292\) | −6.56111 | −0.383960 | ||||||||
\(293\) | −29.3669 | −1.71563 | −0.857815 | − | 0.513958i | \(-0.828179\pi\) | ||||
−0.857815 | + | 0.513958i | \(0.828179\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.5568 | −1.48797 | ||||||||
\(296\) | −7.95573 | −0.462418 | ||||||||
\(297\) | −0.798673 | −0.0463437 | ||||||||
\(298\) | 1.73049 | 0.100245 | ||||||||
\(299\) | 8.01440 | 0.463485 | ||||||||
\(300\) | −0.319786 | −0.0184629 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.2029 | 0.587111 | ||||||||
\(303\) | −2.54061 | −0.145954 | ||||||||
\(304\) | 22.0968 | 1.26734 | ||||||||
\(305\) | 27.3955 | 1.56866 | ||||||||
\(306\) | 9.32603 | 0.533134 | ||||||||
\(307\) | −30.7496 | −1.75497 | −0.877485 | − | 0.479604i | \(-0.840780\pi\) | ||||
−0.877485 | + | 0.479604i | \(0.840780\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.43950 | −0.309442 | ||||||||
\(310\) | 0.660558 | 0.0375172 | ||||||||
\(311\) | 17.9250 | 1.01644 | 0.508218 | − | 0.861228i | \(-0.330304\pi\) | ||||
0.508218 | + | 0.861228i | \(0.330304\pi\) | |||||||
\(312\) | 1.62617 | 0.0920637 | ||||||||
\(313\) | 15.7109 | 0.888035 | 0.444018 | − | 0.896018i | \(-0.353553\pi\) | ||||
0.444018 | + | 0.896018i | \(0.353553\pi\) | |||||||
\(314\) | 25.5340 | 1.44097 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.3467 | 0.919573 | ||||||||
\(317\) | −3.37598 | −0.189614 | −0.0948070 | − | 0.995496i | \(-0.530223\pi\) | ||||
−0.0948070 | + | 0.995496i | \(0.530223\pi\) | |||||||
\(318\) | 2.19490 | 0.123084 | ||||||||
\(319\) | −3.37722 | −0.189088 | ||||||||
\(320\) | 2.68069 | 0.149855 | ||||||||
\(321\) | 16.2891 | 0.909169 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.1603 | 1.28867 | ||||||||
\(324\) | 1.24292 | 0.0690509 | ||||||||
\(325\) | −0.306882 | −0.0170228 | ||||||||
\(326\) | −18.9757 | −1.05097 | ||||||||
\(327\) | 10.3602 | 0.572920 | ||||||||
\(328\) | −1.36336 | −0.0752791 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.13221 | −0.172422 | ||||||||
\(331\) | 22.9215 | 1.25988 | 0.629940 | − | 0.776644i | \(-0.283079\pi\) | ||||
0.629940 | + | 0.776644i | \(0.283079\pi\) | |||||||
\(332\) | 13.6006 | 0.746429 | ||||||||
\(333\) | −5.83538 | −0.319777 | ||||||||
\(334\) | −25.1815 | −1.37787 | ||||||||
\(335\) | 5.25045 | 0.286863 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.3916 | 1.00185 | 0.500927 | − | 0.865489i | \(-0.332992\pi\) | ||||
0.500927 | + | 0.865489i | \(0.332992\pi\) | |||||||
\(338\) | 20.8485 | 1.13401 | ||||||||
\(339\) | 2.79770 | 0.151950 | ||||||||
\(340\) | 14.0179 | 0.760230 | ||||||||
\(341\) | −0.134524 | −0.00728487 | ||||||||
\(342\) | 8.05346 | 0.435481 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.48146 | 0.133791 | ||||||||
\(345\) | −14.6329 | −0.787809 | ||||||||
\(346\) | −9.31635 | −0.500850 | ||||||||
\(347\) | 8.01891 | 0.430477 | 0.215239 | − | 0.976561i | \(-0.430947\pi\) | ||||
0.215239 | + | 0.976561i | \(0.430947\pi\) | |||||||
\(348\) | 5.25572 | 0.281736 | ||||||||
\(349\) | −14.8361 | −0.794159 | −0.397079 | − | 0.917784i | \(-0.629976\pi\) | ||||
−0.397079 | + | 0.917784i | \(0.629976\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.19276 | 0.0636650 | ||||||||
\(352\) | −4.92866 | −0.262698 | ||||||||
\(353\) | 31.7462 | 1.68968 | 0.844840 | − | 0.535020i | \(-0.179696\pi\) | ||||
0.844840 | + | 0.535020i | \(0.179696\pi\) | |||||||
\(354\) | −21.1330 | −1.12320 | ||||||||
\(355\) | −0.557209 | −0.0295736 | ||||||||
\(356\) | −12.1085 | −0.641750 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.59324 | 0.0842054 | ||||||||
\(359\) | 20.9734 | 1.10693 | 0.553466 | − | 0.832872i | \(-0.313305\pi\) | ||||
0.553466 | + | 0.832872i | \(0.313305\pi\) | |||||||
\(360\) | −2.96910 | −0.156485 | ||||||||
\(361\) | 0.999965 | 0.0526297 | ||||||||
\(362\) | 19.1858 | 1.00838 | ||||||||
\(363\) | −10.3621 | −0.543870 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.4961 | 0.601731 | ||||||||
\(366\) | 22.6534 | 1.18411 | ||||||||
\(367\) | 9.23972 | 0.482309 | 0.241155 | − | 0.970487i | \(-0.422474\pi\) | ||||
0.241155 | + | 0.970487i | \(0.422474\pi\) | |||||||
\(368\) | −33.1995 | −1.73064 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −22.8850 | −1.18973 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.209350 | 0.0108543 | ||||||||
\(373\) | 35.1745 | 1.82127 | 0.910634 | − | 0.413214i | \(-0.135594\pi\) | ||||
0.910634 | + | 0.413214i | \(0.135594\pi\) | |||||||
\(374\) | −7.44845 | −0.385150 | ||||||||
\(375\) | 11.4492 | 0.591234 | ||||||||
\(376\) | −7.18458 | −0.370517 | ||||||||
\(377\) | 5.04364 | 0.259761 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.1280 | 1.44484 | 0.722419 | − | 0.691456i | \(-0.243030\pi\) | ||||
0.722419 | + | 0.691456i | \(0.243030\pi\) | |||||||
\(380\) | 12.1051 | 0.620981 | ||||||||
\(381\) | −14.5164 | −0.743699 | ||||||||
\(382\) | 10.4172 | 0.532988 | ||||||||
\(383\) | 1.11304 | 0.0568738 | 0.0284369 | − | 0.999596i | \(-0.490947\pi\) | ||||
0.0284369 | + | 0.999596i | \(0.490947\pi\) | |||||||
\(384\) | −10.1255 | −0.516713 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −29.9113 | −1.52244 | ||||||||
\(387\) | 1.82010 | 0.0925210 | ||||||||
\(388\) | 5.95932 | 0.302538 | ||||||||
\(389\) | −24.4665 | −1.24050 | −0.620251 | − | 0.784404i | \(-0.712969\pi\) | ||||
−0.620251 | + | 0.784404i | \(0.712969\pi\) | |||||||
\(390\) | 4.67773 | 0.236866 | ||||||||
\(391\) | −34.7973 | −1.75978 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.770663 | 0.0388748 | ||||||||
\(394\) | 29.3332 | 1.47779 | ||||||||
\(395\) | −28.6419 | −1.44113 | ||||||||
\(396\) | −0.992684 | −0.0498842 | ||||||||
\(397\) | 4.87136 | 0.244487 | 0.122243 | − | 0.992500i | \(-0.460991\pi\) | ||||
0.122243 | + | 0.992500i | \(0.460991\pi\) | |||||||
\(398\) | −39.4807 | −1.97899 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.27125 | 0.0635626 | ||||||||
\(401\) | −8.56547 | −0.427739 | −0.213869 | − | 0.976862i | \(-0.568607\pi\) | ||||
−0.213869 | + | 0.976862i | \(0.568607\pi\) | |||||||
\(402\) | 4.34161 | 0.216540 | ||||||||
\(403\) | 0.200902 | 0.0100076 | ||||||||
\(404\) | −3.15777 | −0.157105 | ||||||||
\(405\) | −2.17778 | −0.108215 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.66056 | 0.231015 | ||||||||
\(408\) | −7.06058 | −0.349551 | ||||||||
\(409\) | −30.9507 | −1.53041 | −0.765207 | − | 0.643784i | \(-0.777363\pi\) | ||||
−0.765207 | + | 0.643784i | \(0.777363\pi\) | |||||||
\(410\) | −3.92176 | −0.193682 | ||||||||
\(411\) | 4.75720 | 0.234655 | ||||||||
\(412\) | −6.76085 | −0.333083 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.1000 | −0.594682 | ||||||||
\(415\) | −23.8303 | −1.16978 | ||||||||
\(416\) | 7.36061 | 0.360884 | ||||||||
\(417\) | 0.628119 | 0.0307591 | ||||||||
\(418\) | −6.43208 | −0.314603 | ||||||||
\(419\) | −21.7112 | −1.06066 | −0.530331 | − | 0.847791i | \(-0.677932\pi\) | ||||
−0.530331 | + | 0.847791i | \(0.677932\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4470 | 1.33768 | 0.668841 | − | 0.743405i | \(-0.266791\pi\) | ||||
0.668841 | + | 0.743405i | \(0.266791\pi\) | |||||||
\(422\) | 17.0794 | 0.831412 | ||||||||
\(423\) | −5.26975 | −0.256224 | ||||||||
\(424\) | −1.66172 | −0.0807003 | ||||||||
\(425\) | 1.33244 | 0.0646327 | ||||||||
\(426\) | −0.460758 | −0.0223238 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 20.2460 | 0.978628 | ||||||||
\(429\) | −0.952627 | −0.0459933 | ||||||||
\(430\) | 7.13801 | 0.344226 | ||||||||
\(431\) | 17.8045 | 0.857611 | 0.428806 | − | 0.903397i | \(-0.358934\pi\) | ||||
0.428806 | + | 0.903397i | \(0.358934\pi\) | |||||||
\(432\) | −4.94099 | −0.237724 | ||||||||
\(433\) | −13.7451 | −0.660549 | −0.330274 | − | 0.943885i | \(-0.607141\pi\) | ||||
−0.330274 | + | 0.943885i | \(0.607141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.20881 | −0.441529 | ||||||||
\(436\) | 12.8769 | 0.616690 | ||||||||
\(437\) | −30.0491 | −1.43744 | ||||||||
\(438\) | 9.50612 | 0.454220 | ||||||||
\(439\) | −4.70167 | −0.224398 | −0.112199 | − | 0.993686i | \(-0.535789\pi\) | ||||
−0.112199 | + | 0.993686i | \(0.535789\pi\) | |||||||
\(440\) | 2.37134 | 0.113049 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.1237 | 0.529103 | ||||||||
\(443\) | 31.8616 | 1.51379 | 0.756894 | − | 0.653537i | \(-0.226716\pi\) | ||||
0.756894 | + | 0.653537i | \(0.226716\pi\) | |||||||
\(444\) | −7.25289 | −0.344207 | ||||||||
\(445\) | 21.2159 | 1.00573 | ||||||||
\(446\) | −10.3923 | −0.492091 | ||||||||
\(447\) | −0.960953 | −0.0454515 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.7586 | 1.45159 | 0.725795 | − | 0.687911i | \(-0.241472\pi\) | ||||
0.725795 | + | 0.687911i | \(0.241472\pi\) | |||||||
\(450\) | 0.463325 | 0.0218414 | ||||||||
\(451\) | 0.798673 | 0.0376080 | ||||||||
\(452\) | 3.47731 | 0.163559 | ||||||||
\(453\) | −5.66573 | −0.266199 | ||||||||
\(454\) | 0.310569 | 0.0145757 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.09714 | −0.285525 | ||||||||
\(457\) | 4.85756 | 0.227227 | 0.113614 | − | 0.993525i | \(-0.463757\pi\) | ||||
0.113614 | + | 0.993525i | \(0.463757\pi\) | |||||||
\(458\) | −4.22922 | −0.197619 | ||||||||
\(459\) | −5.17880 | −0.241726 | ||||||||
\(460\) | −18.1875 | −0.847995 | ||||||||
\(461\) | 34.9988 | 1.63006 | 0.815028 | − | 0.579422i | \(-0.196722\pi\) | ||||
0.815028 | + | 0.579422i | \(0.196722\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.712122 | −0.0330951 | −0.0165476 | − | 0.999863i | \(-0.505267\pi\) | ||||
−0.0165476 | + | 0.999863i | \(0.505267\pi\) | |||||||
\(464\) | −20.8932 | −0.969941 | ||||||||
\(465\) | −0.366812 | −0.0170105 | ||||||||
\(466\) | 3.90884 | 0.181073 | ||||||||
\(467\) | 20.5280 | 0.949922 | 0.474961 | − | 0.880007i | \(-0.342462\pi\) | ||||
0.474961 | + | 0.880007i | \(0.342462\pi\) | |||||||
\(468\) | 1.48251 | 0.0685288 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −20.6667 | −0.953284 | ||||||||
\(471\) | −14.1792 | −0.653343 | ||||||||
\(472\) | 15.9994 | 0.736433 | ||||||||
\(473\) | −1.45367 | −0.0668397 | ||||||||
\(474\) | −23.6840 | −1.08784 | ||||||||
\(475\) | 1.15062 | 0.0527941 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.21884 | −0.0558069 | ||||||||
\(478\) | −29.3369 | −1.34184 | ||||||||
\(479\) | 41.3853 | 1.89094 | 0.945471 | − | 0.325705i | \(-0.105602\pi\) | ||||
0.945471 | + | 0.325705i | \(0.105602\pi\) | |||||||
\(480\) | −13.4392 | −0.613413 | ||||||||
\(481\) | −6.96022 | −0.317359 | ||||||||
\(482\) | −40.6268 | −1.85050 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.8793 | −0.585421 | ||||||||
\(485\) | −10.4416 | −0.474129 | ||||||||
\(486\) | −1.80081 | −0.0816864 | ||||||||
\(487\) | 9.90202 | 0.448703 | 0.224352 | − | 0.974508i | \(-0.427974\pi\) | ||||
0.224352 | + | 0.974508i | \(0.427974\pi\) | |||||||
\(488\) | −17.1505 | −0.776368 | ||||||||
\(489\) | 10.5373 | 0.476513 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.9292 | −1.35069 | −0.675343 | − | 0.737504i | \(-0.736004\pi\) | ||||
−0.675343 | + | 0.737504i | \(0.736004\pi\) | |||||||
\(492\) | −1.24292 | −0.0560350 | ||||||||
\(493\) | −21.8987 | −0.986269 | ||||||||
\(494\) | 9.60587 | 0.432189 | ||||||||
\(495\) | 1.73933 | 0.0781771 | ||||||||
\(496\) | −0.832231 | −0.0373683 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −19.7053 | −0.883017 | ||||||||
\(499\) | −26.4456 | −1.18387 | −0.591934 | − | 0.805986i | \(-0.701635\pi\) | ||||
−0.591934 | + | 0.805986i | \(0.701635\pi\) | |||||||
\(500\) | 14.2304 | 0.636403 | ||||||||
\(501\) | 13.9834 | 0.624733 | ||||||||
\(502\) | −28.6998 | −1.28093 | ||||||||
\(503\) | 0.150863 | 0.00672665 | 0.00336333 | − | 0.999994i | \(-0.498929\pi\) | ||||
0.00336333 | + | 0.999994i | \(0.498929\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.53288 | 0.246210 | ||||||||
\(506\) | 9.66393 | 0.429614 | ||||||||
\(507\) | −11.5773 | −0.514167 | ||||||||
\(508\) | −18.0427 | −0.800516 | ||||||||
\(509\) | 36.0422 | 1.59754 | 0.798771 | − | 0.601635i | \(-0.205484\pi\) | ||||
0.798771 | + | 0.601635i | \(0.205484\pi\) | |||||||
\(510\) | −20.3100 | −0.899343 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −17.0184 | −0.752116 | ||||||||
\(513\) | −4.47213 | −0.197449 | ||||||||
\(514\) | −8.41276 | −0.371071 | ||||||||
\(515\) | 11.8460 | 0.521998 | ||||||||
\(516\) | 2.26224 | 0.0995894 | ||||||||
\(517\) | 4.20881 | 0.185103 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.17342 | 0.227088 | ||||||||
\(520\) | −3.54143 | −0.155302 | ||||||||
\(521\) | 20.8532 | 0.913594 | 0.456797 | − | 0.889571i | \(-0.348996\pi\) | ||||
0.456797 | + | 0.889571i | \(0.348996\pi\) | |||||||
\(522\) | −7.61479 | −0.333290 | ||||||||
\(523\) | 14.0673 | 0.615122 | 0.307561 | − | 0.951528i | \(-0.400487\pi\) | ||||
0.307561 | + | 0.951528i | \(0.400487\pi\) | |||||||
\(524\) | 0.957870 | 0.0418448 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 49.9986 | 2.18004 | ||||||||
\(527\) | −0.872286 | −0.0379974 | ||||||||
\(528\) | 3.94624 | 0.171738 | ||||||||
\(529\) | 22.1475 | 0.962935 | ||||||||
\(530\) | −4.78000 | −0.207630 | ||||||||
\(531\) | 11.7353 | 0.509267 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.19276 | −0.0516643 | ||||||||
\(534\) | 17.5435 | 0.759182 | ||||||||
\(535\) | −35.4741 | −1.53368 | ||||||||
\(536\) | −3.28696 | −0.141975 | ||||||||
\(537\) | −0.884735 | −0.0381791 | ||||||||
\(538\) | −0.389931 | −0.0168111 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.70680 | −0.116482 | ||||||||
\(541\) | 16.8592 | 0.724835 | 0.362417 | − | 0.932016i | \(-0.381952\pi\) | ||||
0.362417 | + | 0.932016i | \(0.381952\pi\) | |||||||
\(542\) | −27.8962 | −1.19825 | ||||||||
\(543\) | −10.6540 | −0.457207 | ||||||||
\(544\) | −31.9587 | −1.37022 | ||||||||
\(545\) | −22.5622 | −0.966458 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.789938 | −0.0337753 | −0.0168877 | − | 0.999857i | \(-0.505376\pi\) | ||||
−0.0168877 | + | 0.999857i | \(0.505376\pi\) | |||||||
\(548\) | 5.91281 | 0.252583 | ||||||||
\(549\) | −12.5796 | −0.536884 | ||||||||
\(550\) | −0.370045 | −0.0157788 | ||||||||
\(551\) | −18.9106 | −0.805618 | ||||||||
\(552\) | 9.16069 | 0.389905 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.23463 | −0.179912 | ||||||||
\(555\) | 12.7081 | 0.539431 | ||||||||
\(556\) | 0.780700 | 0.0331091 | ||||||||
\(557\) | 22.2700 | 0.943610 | 0.471805 | − | 0.881703i | \(-0.343603\pi\) | ||||
0.471805 | + | 0.881703i | \(0.343603\pi\) | |||||||
\(558\) | −0.303318 | −0.0128405 | ||||||||
\(559\) | 2.17095 | 0.0918215 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.13616 | 0.174629 | ||||||||
\(562\) | −43.0155 | −1.81450 | ||||||||
\(563\) | 0.488170 | 0.0205739 | 0.0102870 | − | 0.999947i | \(-0.496726\pi\) | ||||
0.0102870 | + | 0.999947i | \(0.496726\pi\) | |||||||
\(564\) | −6.54986 | −0.275799 | ||||||||
\(565\) | −6.09277 | −0.256325 | ||||||||
\(566\) | 12.7679 | 0.536673 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.348832 | 0.0146367 | ||||||||
\(569\) | 20.2741 | 0.849936 | 0.424968 | − | 0.905208i | \(-0.360285\pi\) | ||||
0.424968 | + | 0.905208i | \(0.360285\pi\) | |||||||
\(570\) | −17.5386 | −0.734613 | ||||||||
\(571\) | 29.6973 | 1.24279 | 0.621397 | − | 0.783496i | \(-0.286566\pi\) | ||||
0.621397 | + | 0.783496i | \(0.286566\pi\) | |||||||
\(572\) | −1.18404 | −0.0495071 | ||||||||
\(573\) | −5.78471 | −0.241660 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.72876 | −0.0720943 | ||||||||
\(576\) | −1.23093 | −0.0512886 | ||||||||
\(577\) | −38.6879 | −1.61060 | −0.805300 | − | 0.592868i | \(-0.797996\pi\) | ||||
−0.805300 | + | 0.592868i | \(0.797996\pi\) | |||||||
\(578\) | −17.6838 | −0.735551 | ||||||||
\(579\) | 16.6099 | 0.690284 | ||||||||
\(580\) | −11.4458 | −0.475260 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.63420 | −0.357899 | ||||||||
\(583\) | 0.973455 | 0.0403164 | ||||||||
\(584\) | −7.19692 | −0.297811 | ||||||||
\(585\) | −2.59757 | −0.107396 | ||||||||
\(586\) | 52.8841 | 2.18462 | ||||||||
\(587\) | 9.27772 | 0.382932 | 0.191466 | − | 0.981499i | \(-0.438676\pi\) | ||||
0.191466 | + | 0.981499i | \(0.438676\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.753259 | −0.0310375 | ||||||||
\(590\) | 46.0229 | 1.89473 | ||||||||
\(591\) | −16.2889 | −0.670036 | ||||||||
\(592\) | 28.8325 | 1.18501 | ||||||||
\(593\) | −42.3599 | −1.73951 | −0.869756 | − | 0.493482i | \(-0.835724\pi\) | ||||
−0.869756 | + | 0.493482i | \(0.835724\pi\) | |||||||
\(594\) | 1.43826 | 0.0590124 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.19438 | −0.0489239 | ||||||||
\(597\) | 21.9239 | 0.897284 | ||||||||
\(598\) | −14.4324 | −0.590185 | ||||||||
\(599\) | 12.3390 | 0.504159 | 0.252080 | − | 0.967706i | \(-0.418886\pi\) | ||||
0.252080 | + | 0.967706i | \(0.418886\pi\) | |||||||
\(600\) | −0.350776 | −0.0143204 | ||||||||
\(601\) | −16.6041 | −0.677297 | −0.338648 | − | 0.940913i | \(-0.609970\pi\) | ||||
−0.338648 | + | 0.940913i | \(0.609970\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.41092 | −0.0981803 | ||||||||
\(604\) | −7.04203 | −0.286536 | ||||||||
\(605\) | 22.5664 | 0.917454 | ||||||||
\(606\) | 4.57515 | 0.185853 | ||||||||
\(607\) | 3.93533 | 0.159730 | 0.0798652 | − | 0.996806i | \(-0.474551\pi\) | ||||
0.0798652 | + | 0.996806i | \(0.474551\pi\) | |||||||
\(608\) | −27.5978 | −1.11924 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −49.3342 | −1.99748 | ||||||||
\(611\) | −6.28556 | −0.254287 | ||||||||
\(612\) | −6.43681 | −0.260193 | ||||||||
\(613\) | 31.1638 | 1.25870 | 0.629348 | − | 0.777124i | \(-0.283322\pi\) | ||||
0.629348 | + | 0.777124i | \(0.283322\pi\) | |||||||
\(614\) | 55.3741 | 2.23472 | ||||||||
\(615\) | 2.17778 | 0.0878164 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.9486 | 0.883615 | 0.441808 | − | 0.897110i | \(-0.354337\pi\) | ||||
0.441808 | + | 0.897110i | \(0.354337\pi\) | |||||||
\(618\) | 9.79550 | 0.394033 | ||||||||
\(619\) | −17.1921 | −0.691010 | −0.345505 | − | 0.938417i | \(-0.612292\pi\) | ||||
−0.345505 | + | 0.938417i | \(0.612292\pi\) | |||||||
\(620\) | −0.455917 | −0.0183101 | ||||||||
\(621\) | 6.71919 | 0.269632 | ||||||||
\(622\) | −32.2796 | −1.29429 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.89343 | −0.235926 | ||||||||
\(625\) | −23.6474 | −0.945895 | ||||||||
\(626\) | −28.2924 | −1.13079 | ||||||||
\(627\) | 3.57177 | 0.142643 | ||||||||
\(628\) | −17.6236 | −0.703257 | ||||||||
\(629\) | 30.2202 | 1.20496 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5560 | −0.499847 | −0.249923 | − | 0.968266i | \(-0.580405\pi\) | ||||
−0.249923 | + | 0.968266i | \(0.580405\pi\) | |||||||
\(632\) | 17.9308 | 0.713248 | ||||||||
\(633\) | −9.48428 | −0.376966 | ||||||||
\(634\) | 6.07950 | 0.241448 | ||||||||
\(635\) | 31.6135 | 1.25454 | ||||||||
\(636\) | −1.51492 | −0.0600704 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.08173 | 0.240778 | ||||||||
\(639\) | 0.255861 | 0.0101217 | ||||||||
\(640\) | 22.0510 | 0.871642 | ||||||||
\(641\) | −28.6102 | −1.13003 | −0.565017 | − | 0.825079i | \(-0.691130\pi\) | ||||
−0.565017 | + | 0.825079i | \(0.691130\pi\) | |||||||
\(642\) | −29.3336 | −1.15770 | ||||||||
\(643\) | −0.325302 | −0.0128287 | −0.00641434 | − | 0.999979i | \(-0.502042\pi\) | ||||
−0.00641434 | + | 0.999979i | \(0.502042\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.96378 | −0.156074 | ||||||||
\(646\) | −41.7072 | −1.64095 | ||||||||
\(647\) | −2.72658 | −0.107193 | −0.0535965 | − | 0.998563i | \(-0.517068\pi\) | ||||
−0.0535965 | + | 0.998563i | \(0.517068\pi\) | |||||||
\(648\) | 1.36336 | 0.0535579 | ||||||||
\(649\) | −9.37263 | −0.367908 | ||||||||
\(650\) | 0.552637 | 0.0216762 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.0970 | 0.512918 | ||||||||
\(653\) | −3.40058 | −0.133075 | −0.0665375 | − | 0.997784i | \(-0.521195\pi\) | ||||
−0.0665375 | + | 0.997784i | \(0.521195\pi\) | |||||||
\(654\) | −18.6567 | −0.729536 | ||||||||
\(655\) | −1.67833 | −0.0655779 | ||||||||
\(656\) | 4.94099 | 0.192913 | ||||||||
\(657\) | −5.27880 | −0.205946 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.29196 | 0.245100 | 0.122550 | − | 0.992462i | \(-0.460893\pi\) | ||||
0.122550 | + | 0.992462i | \(0.460893\pi\) | |||||||
\(660\) | 2.16184 | 0.0841497 | ||||||||
\(661\) | −16.2199 | −0.630880 | −0.315440 | − | 0.948945i | \(-0.602152\pi\) | ||||
−0.315440 | + | 0.948945i | \(0.602152\pi\) | |||||||
\(662\) | −41.2773 | −1.60429 | ||||||||
\(663\) | −6.17708 | −0.239898 | ||||||||
\(664\) | 14.9186 | 0.578953 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.5084 | 0.407192 | ||||||||
\(667\) | 28.4123 | 1.10013 | ||||||||
\(668\) | 17.3802 | 0.672461 | ||||||||
\(669\) | 5.77091 | 0.223116 | ||||||||
\(670\) | −9.45507 | −0.365281 | ||||||||
\(671\) | 10.0470 | 0.387859 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.2265 | 0.625486 | 0.312743 | − | 0.949838i | \(-0.398752\pi\) | ||||
0.312743 | + | 0.949838i | \(0.398752\pi\) | |||||||
\(674\) | −33.1198 | −1.27573 | ||||||||
\(675\) | −0.257287 | −0.00990298 | ||||||||
\(676\) | −14.3896 | −0.553448 | ||||||||
\(677\) | −34.2117 | −1.31486 | −0.657432 | − | 0.753514i | \(-0.728357\pi\) | ||||
−0.657432 | + | 0.753514i | \(0.728357\pi\) | |||||||
\(678\) | −5.03813 | −0.193488 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15.3764 | 0.589657 | ||||||||
\(681\) | −0.172461 | −0.00660872 | ||||||||
\(682\) | 0.242252 | 0.00927629 | ||||||||
\(683\) | 3.88638 | 0.148708 | 0.0743540 | − | 0.997232i | \(-0.476311\pi\) | ||||
0.0743540 | + | 0.997232i | \(0.476311\pi\) | |||||||
\(684\) | −5.55849 | −0.212534 | ||||||||
\(685\) | −10.3601 | −0.395840 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.34851 | 0.0896013 | ||||||||
\(688\) | −8.99311 | −0.342859 | ||||||||
\(689\) | −1.45379 | −0.0553849 | ||||||||
\(690\) | 26.3511 | 1.00317 | ||||||||
\(691\) | 47.1900 | 1.79519 | 0.897595 | − | 0.440821i | \(-0.145313\pi\) | ||||
0.897595 | + | 0.440821i | \(0.145313\pi\) | |||||||
\(692\) | 6.43013 | 0.244437 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.4405 | −0.548155 | ||||||||
\(695\) | −1.36790 | −0.0518876 | ||||||||
\(696\) | 5.76503 | 0.218523 | ||||||||
\(697\) | 5.17880 | 0.196161 | ||||||||
\(698\) | 26.7170 | 1.01125 | ||||||||
\(699\) | −2.17060 | −0.0820997 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.0103 | 0.642469 | 0.321234 | − | 0.947000i | \(-0.395902\pi\) | ||||
0.321234 | + | 0.947000i | \(0.395902\pi\) | |||||||
\(702\) | −2.14794 | −0.0810688 | ||||||||
\(703\) | 26.0966 | 0.984251 | ||||||||
\(704\) | 0.983108 | 0.0370523 | ||||||||
\(705\) | 11.4763 | 0.432224 | ||||||||
\(706\) | −57.1689 | −2.15158 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 14.5860 | 0.548174 | ||||||||
\(709\) | 24.8723 | 0.934100 | 0.467050 | − | 0.884231i | \(-0.345317\pi\) | ||||
0.467050 | + | 0.884231i | \(0.345317\pi\) | |||||||
\(710\) | 1.00343 | 0.0376580 | ||||||||
\(711\) | 13.1519 | 0.493234 | ||||||||
\(712\) | −13.2819 | −0.497760 | ||||||||
\(713\) | 1.13174 | 0.0423840 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.07461 | 0.0775860 | ||||||||
\(716\) | −1.09965 | −0.0410959 | ||||||||
\(717\) | 16.2909 | 0.608396 | ||||||||
\(718\) | −37.7690 | −1.40953 | ||||||||
\(719\) | 24.7701 | 0.923768 | 0.461884 | − | 0.886940i | \(-0.347174\pi\) | ||||
0.461884 | + | 0.886940i | \(0.347174\pi\) | |||||||
\(720\) | 10.7604 | 0.401016 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.80075 | −0.0670169 | ||||||||
\(723\) | 22.5603 | 0.839027 | ||||||||
\(724\) | −13.2420 | −0.492136 | ||||||||
\(725\) | −1.08795 | −0.0404054 | ||||||||
\(726\) | 18.6602 | 0.692545 | ||||||||
\(727\) | 29.1958 | 1.08281 | 0.541406 | − | 0.840761i | \(-0.317892\pi\) | ||||
0.541406 | + | 0.840761i | \(0.317892\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −20.7022 | −0.766223 | ||||||||
\(731\) | −9.42595 | −0.348631 | ||||||||
\(732\) | −15.6354 | −0.577900 | ||||||||
\(733\) | 17.8678 | 0.659961 | 0.329981 | − | 0.943988i | \(-0.392958\pi\) | ||||
0.329981 | + | 0.943988i | \(0.392958\pi\) | |||||||
\(734\) | −16.6390 | −0.614156 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 41.4645 | 1.52840 | ||||||||
\(737\) | 1.92554 | 0.0709281 | ||||||||
\(738\) | 1.80081 | 0.0662887 | ||||||||
\(739\) | 14.4976 | 0.533303 | 0.266651 | − | 0.963793i | \(-0.414083\pi\) | ||||
0.266651 | + | 0.963793i | \(0.414083\pi\) | |||||||
\(740\) | 15.7952 | 0.580642 | ||||||||
\(741\) | −5.33419 | −0.195956 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.9665 | 1.06268 | 0.531339 | − | 0.847160i | \(-0.321689\pi\) | ||||
0.531339 | + | 0.847160i | \(0.321689\pi\) | |||||||
\(744\) | 0.229637 | 0.00841889 | ||||||||
\(745\) | 2.09274 | 0.0766721 | ||||||||
\(746\) | −63.3426 | −2.31914 | ||||||||
\(747\) | 10.9425 | 0.400364 | ||||||||
\(748\) | 5.14091 | 0.187970 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −20.6178 | −0.752857 | ||||||||
\(751\) | −22.0943 | −0.806234 | −0.403117 | − | 0.915148i | \(-0.632073\pi\) | ||||
−0.403117 | + | 0.915148i | \(0.632073\pi\) | |||||||
\(752\) | 26.0378 | 0.949501 | ||||||||
\(753\) | 15.9372 | 0.580782 | ||||||||
\(754\) | −9.08264 | −0.330770 | ||||||||
\(755\) | 12.3387 | 0.449051 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.0884 | 1.49338 | 0.746692 | − | 0.665170i | \(-0.231641\pi\) | ||||
0.746692 | + | 0.665170i | \(0.231641\pi\) | |||||||
\(758\) | −50.6532 | −1.83981 | ||||||||
\(759\) | −5.36643 | −0.194789 | ||||||||
\(760\) | 13.2782 | 0.481651 | ||||||||
\(761\) | −23.2864 | −0.844132 | −0.422066 | − | 0.906565i | \(-0.638695\pi\) | ||||
−0.422066 | + | 0.906565i | \(0.638695\pi\) | |||||||
\(762\) | 26.1413 | 0.947000 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.18991 | −0.260122 | ||||||||
\(765\) | 11.2783 | 0.407767 | ||||||||
\(766\) | −2.00438 | −0.0724212 | ||||||||
\(767\) | 13.9974 | 0.505416 | ||||||||
\(768\) | 20.6959 | 0.746798 | ||||||||
\(769\) | −15.2750 | −0.550832 | −0.275416 | − | 0.961325i | \(-0.588816\pi\) | ||||
−0.275416 | + | 0.961325i | \(0.588816\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.67166 | 0.168246 | ||||||||
\(772\) | 20.6447 | 0.743020 | ||||||||
\(773\) | 9.69680 | 0.348770 | 0.174385 | − | 0.984678i | \(-0.444206\pi\) | ||||
0.174385 | + | 0.984678i | \(0.444206\pi\) | |||||||
\(774\) | −3.27766 | −0.117813 | ||||||||
\(775\) | −0.0433359 | −0.00155667 | ||||||||
\(776\) | 6.53681 | 0.234658 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 44.0595 | 1.57961 | ||||||||
\(779\) | 4.47213 | 0.160231 | ||||||||
\(780\) | −3.22857 | −0.115601 | ||||||||
\(781\) | −0.204349 | −0.00731220 | ||||||||
\(782\) | 62.6634 | 2.24084 | ||||||||
\(783\) | 4.22854 | 0.151116 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.8791 | 1.10212 | ||||||||
\(786\) | −1.38782 | −0.0495018 | ||||||||
\(787\) | −18.3462 | −0.653972 | −0.326986 | − | 0.945029i | \(-0.606033\pi\) | ||||
−0.326986 | + | 0.945029i | \(0.606033\pi\) | |||||||
\(788\) | −20.2458 | −0.721225 | ||||||||
\(789\) | −27.7645 | −0.988443 | ||||||||
\(790\) | 51.5786 | 1.83508 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.08888 | −0.0386917 | ||||||||
\(793\) | −15.0045 | −0.532824 | ||||||||
\(794\) | −8.77240 | −0.311321 | ||||||||
\(795\) | 2.65436 | 0.0941406 | ||||||||
\(796\) | 27.2495 | 0.965834 | ||||||||
\(797\) | −29.5627 | −1.04717 | −0.523583 | − | 0.851975i | \(-0.675405\pi\) | ||||
−0.523583 | + | 0.851975i | \(0.675405\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.2910 | 0.965485 | ||||||||
\(800\) | −1.58773 | −0.0561349 | ||||||||
\(801\) | −9.74201 | −0.344217 | ||||||||
\(802\) | 15.4248 | 0.544668 | ||||||||
\(803\) | 4.21603 | 0.148781 | ||||||||
\(804\) | −2.99658 | −0.105681 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.361786 | −0.0127434 | ||||||||
\(807\) | 0.216531 | 0.00762224 | ||||||||
\(808\) | −3.46377 | −0.121855 | ||||||||
\(809\) | −18.4302 | −0.647970 | −0.323985 | − | 0.946062i | \(-0.605023\pi\) | ||||
−0.323985 | + | 0.946062i | \(0.605023\pi\) | |||||||
\(810\) | 3.92176 | 0.137797 | ||||||||
\(811\) | 19.9706 | 0.701264 | 0.350632 | − | 0.936513i | \(-0.385967\pi\) | ||||
0.350632 | + | 0.936513i | \(0.385967\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.4909 | 0.543291 | ||||||||
\(814\) | −8.39277 | −0.294167 | ||||||||
\(815\) | −22.9479 | −0.803830 | ||||||||
\(816\) | 25.5884 | 0.895773 | ||||||||
\(817\) | −8.13974 | −0.284774 | ||||||||
\(818\) | 55.7364 | 1.94878 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.70680 | 0.0945254 | ||||||||
\(821\) | 37.2773 | 1.30099 | 0.650493 | − | 0.759512i | \(-0.274562\pi\) | ||||
0.650493 | + | 0.759512i | \(0.274562\pi\) | |||||||
\(822\) | −8.56682 | −0.298802 | ||||||||
\(823\) | 42.9513 | 1.49719 | 0.748593 | − | 0.663029i | \(-0.230730\pi\) | ||||
0.748593 | + | 0.663029i | \(0.230730\pi\) | |||||||
\(824\) | −7.41601 | −0.258349 | ||||||||
\(825\) | 0.205488 | 0.00715418 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.0895 | 1.42882 | 0.714411 | − | 0.699726i | \(-0.246695\pi\) | ||||
0.714411 | + | 0.699726i | \(0.246695\pi\) | |||||||
\(828\) | 8.35140 | 0.290231 | ||||||||
\(829\) | 9.71580 | 0.337444 | 0.168722 | − | 0.985664i | \(-0.446036\pi\) | ||||
0.168722 | + | 0.985664i | \(0.446036\pi\) | |||||||
\(830\) | 42.9138 | 1.48956 | ||||||||
\(831\) | 2.35151 | 0.0815730 | ||||||||
\(832\) | −1.46820 | −0.0509008 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.13112 | −0.0391676 | ||||||||
\(835\) | −30.4527 | −1.05386 | ||||||||
\(836\) | 4.43941 | 0.153540 | ||||||||
\(837\) | 0.168434 | 0.00582193 | ||||||||
\(838\) | 39.0978 | 1.35061 | ||||||||
\(839\) | 18.1433 | 0.626378 | 0.313189 | − | 0.949691i | \(-0.398603\pi\) | ||||
0.313189 | + | 0.949691i | \(0.398603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.1195 | −0.383430 | ||||||||
\(842\) | −49.4268 | −1.70336 | ||||||||
\(843\) | 23.8868 | 0.822704 | ||||||||
\(844\) | −11.7882 | −0.405766 | ||||||||
\(845\) | 25.2128 | 0.867347 | ||||||||
\(846\) | 9.48982 | 0.326267 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.02228 | 0.206806 | ||||||||
\(849\) | −7.09006 | −0.243330 | ||||||||
\(850\) | −2.39947 | −0.0823010 | ||||||||
\(851\) | −39.2090 | −1.34407 | ||||||||
\(852\) | 0.318014 | 0.0108950 | ||||||||
\(853\) | −3.18526 | −0.109061 | −0.0545306 | − | 0.998512i | \(-0.517366\pi\) | ||||
−0.0545306 | + | 0.998512i | \(0.517366\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.73931 | 0.333077 | ||||||||
\(856\) | 22.2080 | 0.759053 | ||||||||
\(857\) | 23.0555 | 0.787562 | 0.393781 | − | 0.919204i | \(-0.371167\pi\) | ||||
0.393781 | + | 0.919204i | \(0.371167\pi\) | |||||||
\(858\) | 1.71550 | 0.0585662 | ||||||||
\(859\) | 7.33171 | 0.250155 | 0.125077 | − | 0.992147i | \(-0.460082\pi\) | ||||
0.125077 | + | 0.992147i | \(0.460082\pi\) | |||||||
\(860\) | −4.92665 | −0.167997 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.0625 | −1.09205 | ||||||||
\(863\) | 27.6924 | 0.942660 | 0.471330 | − | 0.881957i | \(-0.343774\pi\) | ||||
0.471330 | + | 0.881957i | \(0.343774\pi\) | |||||||
\(864\) | 6.17106 | 0.209944 | ||||||||
\(865\) | −11.2666 | −0.383074 | ||||||||
\(866\) | 24.7524 | 0.841120 | ||||||||
\(867\) | 9.81994 | 0.333503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.5040 | −0.356325 | ||||||||
\(870\) | 16.5833 | 0.562227 | ||||||||
\(871\) | −2.87566 | −0.0974380 | ||||||||
\(872\) | 14.1247 | 0.478323 | ||||||||
\(873\) | 4.79462 | 0.162273 | ||||||||
\(874\) | 54.1127 | 1.83039 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.56111 | −0.221679 | ||||||||
\(877\) | 3.66484 | 0.123753 | 0.0618764 | − | 0.998084i | \(-0.480292\pi\) | ||||
0.0618764 | + | 0.998084i | \(0.480292\pi\) | |||||||
\(878\) | 8.46681 | 0.285741 | ||||||||
\(879\) | −29.3669 | −0.990520 | ||||||||
\(880\) | −8.59402 | −0.289704 | ||||||||
\(881\) | −15.2030 | −0.512203 | −0.256101 | − | 0.966650i | \(-0.582438\pi\) | ||||
−0.256101 | + | 0.966650i | \(0.582438\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.478768 | −0.0161118 | −0.00805591 | − | 0.999968i | \(-0.502564\pi\) | ||||
−0.00805591 | + | 0.999968i | \(0.502564\pi\) | |||||||
\(884\) | −7.67759 | −0.258225 | ||||||||
\(885\) | −25.5568 | −0.859082 | ||||||||
\(886\) | −57.3766 | −1.92761 | ||||||||
\(887\) | 2.63212 | 0.0883781 | 0.0441890 | − | 0.999023i | \(-0.485930\pi\) | ||||
0.0441890 | + | 0.999023i | \(0.485930\pi\) | |||||||
\(888\) | −7.95573 | −0.266977 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −38.2058 | −1.28066 | ||||||||
\(891\) | −0.798673 | −0.0267565 | ||||||||
\(892\) | 7.17277 | 0.240162 | ||||||||
\(893\) | 23.5670 | 0.788640 | ||||||||
\(894\) | 1.73049 | 0.0578764 | ||||||||
\(895\) | 1.92676 | 0.0644044 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.01440 | 0.267593 | ||||||||
\(898\) | −55.3905 | −1.84840 | ||||||||
\(899\) | 0.712230 | 0.0237542 | ||||||||
\(900\) | −0.319786 | −0.0106595 | ||||||||
\(901\) | 6.31213 | 0.210287 | ||||||||
\(902\) | −1.43826 | −0.0478888 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.81428 | 0.126861 | ||||||||
\(905\) | 23.2020 | 0.771261 | ||||||||
\(906\) | 10.2029 | 0.338969 | ||||||||
\(907\) | 11.6650 | 0.387329 | 0.193664 | − | 0.981068i | \(-0.437963\pi\) | ||||
0.193664 | + | 0.981068i | \(0.437963\pi\) | |||||||
\(908\) | −0.214355 | −0.00711361 | ||||||||
\(909\) | −2.54061 | −0.0842667 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.4241 | 0.676680 | 0.338340 | − | 0.941024i | \(-0.390135\pi\) | ||||
0.338340 | + | 0.941024i | \(0.390135\pi\) | |||||||
\(912\) | 22.0968 | 0.731697 | ||||||||
\(913\) | −8.73946 | −0.289234 | ||||||||
\(914\) | −8.74755 | −0.289343 | ||||||||
\(915\) | 27.3955 | 0.905668 | ||||||||
\(916\) | 2.91900 | 0.0964466 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 9.32603 | 0.307805 | ||||||||
\(919\) | −46.0665 | −1.51959 | −0.759797 | − | 0.650161i | \(-0.774702\pi\) | ||||
−0.759797 | + | 0.650161i | \(0.774702\pi\) | |||||||
\(920\) | −19.9499 | −0.657730 | ||||||||
\(921\) | −30.7496 | −1.01323 | ||||||||
\(922\) | −63.0261 | −2.07566 | ||||||||
\(923\) | 0.305182 | 0.0100452 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.50137 | 0.0493646 | ||||||||
\(926\) | 1.28240 | 0.0421422 | ||||||||
\(927\) | −5.43950 | −0.178657 | ||||||||
\(928\) | 26.0946 | 0.856596 | ||||||||
\(929\) | −9.23449 | −0.302974 | −0.151487 | − | 0.988459i | \(-0.548406\pi\) | ||||
−0.151487 | + | 0.988459i | \(0.548406\pi\) | |||||||
\(930\) | 0.660558 | 0.0216606 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.69788 | −0.0883719 | ||||||||
\(933\) | 17.9250 | 0.586840 | ||||||||
\(934\) | −36.9670 | −1.20960 | ||||||||
\(935\) | −9.00764 | −0.294581 | ||||||||
\(936\) | 1.62617 | 0.0531530 | ||||||||
\(937\) | 5.01754 | 0.163916 | 0.0819580 | − | 0.996636i | \(-0.473883\pi\) | ||||
0.0819580 | + | 0.996636i | \(0.473883\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.7109 | 0.512707 | ||||||||
\(940\) | 14.2641 | 0.465245 | ||||||||
\(941\) | −34.8594 | −1.13638 | −0.568191 | − | 0.822897i | \(-0.692357\pi\) | ||||
−0.568191 | + | 0.822897i | \(0.692357\pi\) | |||||||
\(942\) | 25.5340 | 0.831944 | ||||||||
\(943\) | −6.71919 | −0.218807 | ||||||||
\(944\) | −57.9838 | −1.88721 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.61778 | 0.0851113 | ||||||||
\(947\) | 0.0282576 | 0.000918248 0 | 0.000459124 | − | 1.00000i | \(-0.499854\pi\) | ||||
0.000459124 | 1.00000i | \(0.499854\pi\) | ||||||||
\(948\) | 16.3467 | 0.530916 | ||||||||
\(949\) | −6.29636 | −0.204388 | ||||||||
\(950\) | −2.07205 | −0.0672262 | ||||||||
\(951\) | −3.37598 | −0.109474 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.0320 | 1.49112 | 0.745562 | − | 0.666436i | \(-0.232181\pi\) | ||||
0.745562 | + | 0.666436i | \(0.232181\pi\) | |||||||
\(954\) | 2.19490 | 0.0710625 | ||||||||
\(955\) | 12.5978 | 0.407655 | ||||||||
\(956\) | 20.2483 | 0.654876 | ||||||||
\(957\) | −3.37722 | −0.109170 | ||||||||
\(958\) | −74.5271 | −2.40786 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.68069 | 0.0865187 | ||||||||
\(961\) | −30.9716 | −0.999085 | ||||||||
\(962\) | 12.5340 | 0.404113 | ||||||||
\(963\) | 16.2891 | 0.524909 | ||||||||
\(964\) | 28.0406 | 0.903127 | ||||||||
\(965\) | −36.1726 | −1.16444 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.8768 | −0.639196 | −0.319598 | − | 0.947553i | \(-0.603548\pi\) | ||||
−0.319598 | + | 0.947553i | \(0.603548\pi\) | |||||||
\(968\) | −14.1273 | −0.454070 | ||||||||
\(969\) | 23.1603 | 0.744015 | ||||||||
\(970\) | 18.8034 | 0.603740 | ||||||||
\(971\) | 11.5108 | 0.369400 | 0.184700 | − | 0.982795i | \(-0.440869\pi\) | ||||
0.184700 | + | 0.982795i | \(0.440869\pi\) | |||||||
\(972\) | 1.24292 | 0.0398666 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.8317 | −0.571363 | ||||||||
\(975\) | −0.306882 | −0.00982810 | ||||||||
\(976\) | 62.1556 | 1.98955 | ||||||||
\(977\) | 8.68854 | 0.277971 | 0.138985 | − | 0.990294i | \(-0.455616\pi\) | ||||
0.138985 | + | 0.990294i | \(0.455616\pi\) | |||||||
\(978\) | −18.9757 | −0.606776 | ||||||||
\(979\) | 7.78068 | 0.248671 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.3602 | 0.330775 | ||||||||
\(982\) | 53.8968 | 1.71992 | ||||||||
\(983\) | 7.47496 | 0.238414 | 0.119207 | − | 0.992869i | \(-0.461965\pi\) | ||||
0.119207 | + | 0.992869i | \(0.461965\pi\) | |||||||
\(984\) | −1.36336 | −0.0434624 | ||||||||
\(985\) | 35.4736 | 1.13028 | ||||||||
\(986\) | 39.4355 | 1.25588 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.62996 | −0.210927 | ||||||||
\(989\) | 12.2296 | 0.388879 | ||||||||
\(990\) | −3.13221 | −0.0995480 | ||||||||
\(991\) | −27.3575 | −0.869040 | −0.434520 | − | 0.900662i | \(-0.643082\pi\) | ||||
−0.434520 | + | 0.900662i | \(0.643082\pi\) | |||||||
\(992\) | 1.03942 | 0.0330015 | ||||||||
\(993\) | 22.9215 | 0.727392 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −47.7453 | −1.51363 | ||||||||
\(996\) | 13.6006 | 0.430951 | ||||||||
\(997\) | −28.2187 | −0.893695 | −0.446848 | − | 0.894610i | \(-0.647453\pi\) | ||||
−0.446848 | + | 0.894610i | \(0.647453\pi\) | |||||||
\(998\) | 47.6235 | 1.50750 | ||||||||
\(999\) | −5.83538 | −0.184623 |
(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 | 6027.2.a.bo.1.5 | yes | 24 | |
7.6 | odd | 2 | 6027.2.a.bn.1.5 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.5 | ✓ | 24 | 7.6 | odd | 2 | ||
6027.2.a.bo.1.5 | yes | 24 | 1.1 | even | 1 | trivial |