Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,2,Mod(1,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.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: | \(2.29170653801\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.633117.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 4x^{2} + 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.03121\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 287.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.03121 | 1.43628 | 0.718142 | − | 0.695897i | \(-0.244993\pi\) | ||||
0.718142 | + | 0.695897i | \(0.244993\pi\) | |||||||
\(3\) | 3.03121 | 1.75007 | 0.875036 | − | 0.484059i | \(-0.160838\pi\) | ||||
0.875036 | + | 0.484059i | \(0.160838\pi\) | |||||||
\(4\) | 2.12582 | 1.06291 | ||||||||
\(5\) | −3.82713 | −1.71155 | −0.855773 | − | 0.517351i | \(-0.826918\pi\) | ||||
−0.855773 | + | 0.517351i | \(0.826918\pi\) | |||||||
\(6\) | 6.15703 | 2.51360 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.255573 | 0.0903586 | ||||||||
\(9\) | 6.18825 | 2.06275 | ||||||||
\(10\) | −7.77372 | −2.45827 | ||||||||
\(11\) | −5.96294 | −1.79789 | −0.898947 | − | 0.438057i | \(-0.855667\pi\) | ||||
−0.898947 | + | 0.438057i | \(0.855667\pi\) | |||||||
\(12\) | 6.44382 | 1.86017 | ||||||||
\(13\) | 1.44574 | 0.400976 | 0.200488 | − | 0.979696i | \(-0.435747\pi\) | ||||
0.200488 | + | 0.979696i | \(0.435747\pi\) | |||||||
\(14\) | 2.03121 | 0.542864 | ||||||||
\(15\) | −11.6009 | −2.99533 | ||||||||
\(16\) | −3.73252 | −0.933131 | ||||||||
\(17\) | 6.06148 | 1.47012 | 0.735062 | − | 0.677999i | \(-0.237153\pi\) | ||||
0.735062 | + | 0.677999i | \(0.237153\pi\) | |||||||
\(18\) | 12.5696 | 2.96269 | ||||||||
\(19\) | −0.0743284 | −0.0170521 | −0.00852605 | − | 0.999964i | \(-0.502714\pi\) | ||||
−0.00852605 | + | 0.999964i | \(0.502714\pi\) | |||||||
\(20\) | −8.13581 | −1.81922 | ||||||||
\(21\) | 3.03121 | 0.661465 | ||||||||
\(22\) | −12.1120 | −2.58229 | ||||||||
\(23\) | −4.43383 | −0.924518 | −0.462259 | − | 0.886745i | \(-0.652961\pi\) | ||||
−0.462259 | + | 0.886745i | \(0.652961\pi\) | |||||||
\(24\) | 0.774695 | 0.158134 | ||||||||
\(25\) | 9.64695 | 1.92939 | ||||||||
\(26\) | 2.93660 | 0.575915 | ||||||||
\(27\) | 9.66425 | 1.85989 | ||||||||
\(28\) | 2.12582 | 0.401743 | ||||||||
\(29\) | −1.92662 | −0.357764 | −0.178882 | − | 0.983871i | \(-0.557248\pi\) | ||||
−0.178882 | + | 0.983871i | \(0.557248\pi\) | |||||||
\(30\) | −23.5638 | −4.30214 | ||||||||
\(31\) | 1.76471 | 0.316951 | 0.158476 | − | 0.987363i | \(-0.449342\pi\) | ||||
0.158476 | + | 0.987363i | \(0.449342\pi\) | |||||||
\(32\) | −8.09269 | −1.43060 | ||||||||
\(33\) | −18.0749 | −3.14644 | ||||||||
\(34\) | 12.3122 | 2.11152 | ||||||||
\(35\) | −3.82713 | −0.646904 | ||||||||
\(36\) | 13.1551 | 2.19252 | ||||||||
\(37\) | 0.497233 | 0.0817446 | 0.0408723 | − | 0.999164i | \(-0.486986\pi\) | ||||
0.0408723 | + | 0.999164i | \(0.486986\pi\) | |||||||
\(38\) | −0.150977 | −0.0244917 | ||||||||
\(39\) | 4.38234 | 0.701736 | ||||||||
\(40\) | −0.978111 | −0.154653 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 6.15703 | 0.950051 | ||||||||
\(43\) | 4.10393 | 0.625844 | 0.312922 | − | 0.949779i | \(-0.398692\pi\) | ||||
0.312922 | + | 0.949779i | \(0.398692\pi\) | |||||||
\(44\) | −12.6762 | −1.91100 | ||||||||
\(45\) | −23.6832 | −3.53049 | ||||||||
\(46\) | −9.00606 | −1.32787 | ||||||||
\(47\) | −2.92536 | −0.426708 | −0.213354 | − | 0.976975i | \(-0.568439\pi\) | ||||
−0.213354 | + | 0.976975i | \(0.568439\pi\) | |||||||
\(48\) | −11.3141 | −1.63305 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 19.5950 | 2.77115 | ||||||||
\(51\) | 18.3736 | 2.57282 | ||||||||
\(52\) | 3.07338 | 0.426202 | ||||||||
\(53\) | 3.08431 | 0.423663 | 0.211832 | − | 0.977306i | \(-0.432057\pi\) | ||||
0.211832 | + | 0.977306i | \(0.432057\pi\) | |||||||
\(54\) | 19.6301 | 2.67132 | ||||||||
\(55\) | 22.8210 | 3.07718 | ||||||||
\(56\) | 0.255573 | 0.0341523 | ||||||||
\(57\) | −0.225305 | −0.0298424 | ||||||||
\(58\) | −3.91337 | −0.513850 | ||||||||
\(59\) | 11.4408 | 1.48947 | 0.744735 | − | 0.667360i | \(-0.232576\pi\) | ||||
0.744735 | + | 0.667360i | \(0.232576\pi\) | |||||||
\(60\) | −24.6614 | −3.18377 | ||||||||
\(61\) | 2.94851 | 0.377517 | 0.188759 | − | 0.982023i | \(-0.439554\pi\) | ||||
0.188759 | + | 0.982023i | \(0.439554\pi\) | |||||||
\(62\) | 3.58450 | 0.455232 | ||||||||
\(63\) | 6.18825 | 0.779646 | ||||||||
\(64\) | −8.97293 | −1.12162 | ||||||||
\(65\) | −5.53303 | −0.686288 | ||||||||
\(66\) | −36.7140 | −4.51919 | ||||||||
\(67\) | −1.12488 | −0.137426 | −0.0687129 | − | 0.997636i | \(-0.521889\pi\) | ||||
−0.0687129 | + | 0.997636i | \(0.521889\pi\) | |||||||
\(68\) | 12.8856 | 1.56261 | ||||||||
\(69\) | −13.4399 | −1.61797 | ||||||||
\(70\) | −7.77372 | −0.929137 | ||||||||
\(71\) | 5.87671 | 0.697437 | 0.348719 | − | 0.937227i | \(-0.386617\pi\) | ||||
0.348719 | + | 0.937227i | \(0.386617\pi\) | |||||||
\(72\) | 1.58155 | 0.186387 | ||||||||
\(73\) | 15.7737 | 1.84617 | 0.923087 | − | 0.384591i | \(-0.125657\pi\) | ||||
0.923087 | + | 0.384591i | \(0.125657\pi\) | |||||||
\(74\) | 1.00999 | 0.117408 | ||||||||
\(75\) | 29.2420 | 3.37657 | ||||||||
\(76\) | −0.158009 | −0.0181249 | ||||||||
\(77\) | −5.96294 | −0.679540 | ||||||||
\(78\) | 8.90146 | 1.00789 | ||||||||
\(79\) | −14.5736 | −1.63965 | −0.819827 | − | 0.572611i | \(-0.805931\pi\) | ||||
−0.819827 | + | 0.572611i | \(0.805931\pi\) | |||||||
\(80\) | 14.2849 | 1.59710 | ||||||||
\(81\) | 10.7297 | 1.19218 | ||||||||
\(82\) | −2.03121 | −0.224310 | ||||||||
\(83\) | −14.4941 | −1.59093 | −0.795465 | − | 0.606000i | \(-0.792773\pi\) | ||||
−0.795465 | + | 0.606000i | \(0.792773\pi\) | |||||||
\(84\) | 6.44382 | 0.703078 | ||||||||
\(85\) | −23.1981 | −2.51619 | ||||||||
\(86\) | 8.33596 | 0.898890 | ||||||||
\(87\) | −5.83998 | −0.626112 | ||||||||
\(88\) | −1.52396 | −0.162455 | ||||||||
\(89\) | 0.670099 | 0.0710303 | 0.0355152 | − | 0.999369i | \(-0.488693\pi\) | ||||
0.0355152 | + | 0.999369i | \(0.488693\pi\) | |||||||
\(90\) | −48.1057 | −5.07079 | ||||||||
\(91\) | 1.44574 | 0.151555 | ||||||||
\(92\) | −9.42555 | −0.982681 | ||||||||
\(93\) | 5.34921 | 0.554687 | ||||||||
\(94\) | −5.94203 | −0.612873 | ||||||||
\(95\) | 0.284465 | 0.0291855 | ||||||||
\(96\) | −24.5307 | −2.50365 | ||||||||
\(97\) | −10.5587 | −1.07207 | −0.536036 | − | 0.844195i | \(-0.680079\pi\) | ||||
−0.536036 | + | 0.844195i | \(0.680079\pi\) | |||||||
\(98\) | 2.03121 | 0.205183 | ||||||||
\(99\) | −36.9002 | −3.70861 | ||||||||
\(100\) | 20.5077 | 2.05077 | ||||||||
\(101\) | −3.20947 | −0.319355 | −0.159677 | − | 0.987169i | \(-0.551045\pi\) | ||||
−0.159677 | + | 0.987169i | \(0.551045\pi\) | |||||||
\(102\) | 37.3207 | 3.69530 | ||||||||
\(103\) | 5.79008 | 0.570513 | 0.285257 | − | 0.958451i | \(-0.407921\pi\) | ||||
0.285257 | + | 0.958451i | \(0.407921\pi\) | |||||||
\(104\) | 0.369491 | 0.0362316 | ||||||||
\(105\) | −11.6009 | −1.13213 | ||||||||
\(106\) | 6.26490 | 0.608500 | ||||||||
\(107\) | −5.90146 | −0.570516 | −0.285258 | − | 0.958451i | \(-0.592079\pi\) | ||||
−0.285258 | + | 0.958451i | \(0.592079\pi\) | |||||||
\(108\) | 20.5445 | 1.97689 | ||||||||
\(109\) | −13.4426 | −1.28756 | −0.643782 | − | 0.765209i | \(-0.722636\pi\) | ||||
−0.643782 | + | 0.765209i | \(0.722636\pi\) | |||||||
\(110\) | 46.3542 | 4.41970 | ||||||||
\(111\) | 1.50722 | 0.143059 | ||||||||
\(112\) | −3.73252 | −0.352690 | ||||||||
\(113\) | 6.01283 | 0.565639 | 0.282820 | − | 0.959173i | \(-0.408730\pi\) | ||||
0.282820 | + | 0.959173i | \(0.408730\pi\) | |||||||
\(114\) | −0.457643 | −0.0428622 | ||||||||
\(115\) | 16.9689 | 1.58236 | ||||||||
\(116\) | −4.09564 | −0.380271 | ||||||||
\(117\) | 8.94659 | 0.827112 | ||||||||
\(118\) | 23.2388 | 2.13930 | ||||||||
\(119\) | 6.06148 | 0.555655 | ||||||||
\(120\) | −2.96486 | −0.270654 | ||||||||
\(121\) | 24.5567 | 2.23242 | ||||||||
\(122\) | 5.98904 | 0.542222 | ||||||||
\(123\) | −3.03121 | −0.273315 | ||||||||
\(124\) | 3.75146 | 0.336891 | ||||||||
\(125\) | −17.7845 | −1.59070 | ||||||||
\(126\) | 12.5696 | 1.11979 | ||||||||
\(127\) | −6.27284 | −0.556625 | −0.278312 | − | 0.960491i | \(-0.589775\pi\) | ||||
−0.278312 | + | 0.960491i | \(0.589775\pi\) | |||||||
\(128\) | −2.04053 | −0.180360 | ||||||||
\(129\) | 12.4399 | 1.09527 | ||||||||
\(130\) | −11.2388 | −0.985705 | ||||||||
\(131\) | 12.0382 | 1.05178 | 0.525892 | − | 0.850551i | \(-0.323732\pi\) | ||||
0.525892 | + | 0.850551i | \(0.323732\pi\) | |||||||
\(132\) | −38.4241 | −3.34439 | ||||||||
\(133\) | −0.0743284 | −0.00644509 | ||||||||
\(134\) | −2.28487 | −0.197382 | ||||||||
\(135\) | −36.9864 | −3.18328 | ||||||||
\(136\) | 1.54915 | 0.132838 | ||||||||
\(137\) | 6.46697 | 0.552510 | 0.276255 | − | 0.961084i | \(-0.410907\pi\) | ||||
0.276255 | + | 0.961084i | \(0.410907\pi\) | |||||||
\(138\) | −27.2993 | −2.32387 | ||||||||
\(139\) | −8.66331 | −0.734812 | −0.367406 | − | 0.930061i | \(-0.619754\pi\) | ||||
−0.367406 | + | 0.930061i | \(0.619754\pi\) | |||||||
\(140\) | −8.13581 | −0.687601 | ||||||||
\(141\) | −8.86739 | −0.746769 | ||||||||
\(142\) | 11.9368 | 1.00172 | ||||||||
\(143\) | −8.62085 | −0.720912 | ||||||||
\(144\) | −23.0978 | −1.92481 | ||||||||
\(145\) | 7.37342 | 0.612329 | ||||||||
\(146\) | 32.0398 | 2.65163 | ||||||||
\(147\) | 3.03121 | 0.250010 | ||||||||
\(148\) | 1.05703 | 0.0868872 | ||||||||
\(149\) | 8.01997 | 0.657022 | 0.328511 | − | 0.944500i | \(-0.393453\pi\) | ||||
0.328511 | + | 0.944500i | \(0.393453\pi\) | |||||||
\(150\) | 59.3966 | 4.84971 | ||||||||
\(151\) | −4.83256 | −0.393268 | −0.196634 | − | 0.980477i | \(-0.563001\pi\) | ||||
−0.196634 | + | 0.980477i | \(0.563001\pi\) | |||||||
\(152\) | −0.0189963 | −0.00154080 | ||||||||
\(153\) | 37.5099 | 3.03250 | ||||||||
\(154\) | −12.1120 | −0.976013 | ||||||||
\(155\) | −6.75378 | −0.542477 | ||||||||
\(156\) | 9.31608 | 0.745883 | ||||||||
\(157\) | −10.2117 | −0.814982 | −0.407491 | − | 0.913209i | \(-0.633596\pi\) | ||||
−0.407491 | + | 0.913209i | \(0.633596\pi\) | |||||||
\(158\) | −29.6020 | −2.35501 | ||||||||
\(159\) | 9.34921 | 0.741441 | ||||||||
\(160\) | 30.9718 | 2.44854 | ||||||||
\(161\) | −4.43383 | −0.349435 | ||||||||
\(162\) | 21.7942 | 1.71232 | ||||||||
\(163\) | −19.2954 | −1.51133 | −0.755665 | − | 0.654958i | \(-0.772686\pi\) | ||||
−0.755665 | + | 0.654958i | \(0.772686\pi\) | |||||||
\(164\) | −2.12582 | −0.165999 | ||||||||
\(165\) | 69.1752 | 5.38528 | ||||||||
\(166\) | −29.4405 | −2.28503 | ||||||||
\(167\) | 2.42397 | 0.187572 | 0.0937861 | − | 0.995592i | \(-0.470103\pi\) | ||||
0.0937861 | + | 0.995592i | \(0.470103\pi\) | |||||||
\(168\) | 0.774695 | 0.0597690 | ||||||||
\(169\) | −10.9098 | −0.839218 | ||||||||
\(170\) | −47.1202 | −3.61396 | ||||||||
\(171\) | −0.459963 | −0.0351742 | ||||||||
\(172\) | 8.72423 | 0.665217 | ||||||||
\(173\) | −8.79388 | −0.668587 | −0.334293 | − | 0.942469i | \(-0.608498\pi\) | ||||
−0.334293 | + | 0.942469i | \(0.608498\pi\) | |||||||
\(174\) | −11.8622 | −0.899274 | ||||||||
\(175\) | 9.64695 | 0.729241 | ||||||||
\(176\) | 22.2568 | 1.67767 | ||||||||
\(177\) | 34.6796 | 2.60668 | ||||||||
\(178\) | 1.36111 | 0.102020 | ||||||||
\(179\) | 14.4831 | 1.08252 | 0.541259 | − | 0.840856i | \(-0.317948\pi\) | ||||
0.541259 | + | 0.840856i | \(0.317948\pi\) | |||||||
\(180\) | −50.3464 | −3.75260 | ||||||||
\(181\) | −3.07539 | −0.228592 | −0.114296 | − | 0.993447i | \(-0.536461\pi\) | ||||
−0.114296 | + | 0.993447i | \(0.536461\pi\) | |||||||
\(182\) | 2.93660 | 0.217675 | ||||||||
\(183\) | 8.93755 | 0.660682 | ||||||||
\(184\) | −1.13317 | −0.0835382 | ||||||||
\(185\) | −1.90298 | −0.139910 | ||||||||
\(186\) | 10.8654 | 0.796688 | ||||||||
\(187\) | −36.1442 | −2.64313 | ||||||||
\(188\) | −6.21880 | −0.453552 | ||||||||
\(189\) | 9.66425 | 0.702971 | ||||||||
\(190\) | 0.577808 | 0.0419186 | ||||||||
\(191\) | 4.90956 | 0.355243 | 0.177622 | − | 0.984099i | \(-0.443160\pi\) | ||||
0.177622 | + | 0.984099i | \(0.443160\pi\) | |||||||
\(192\) | −27.1988 | −1.96291 | ||||||||
\(193\) | 11.3050 | 0.813754 | 0.406877 | − | 0.913483i | \(-0.366618\pi\) | ||||
0.406877 | + | 0.913483i | \(0.366618\pi\) | |||||||
\(194\) | −21.4469 | −1.53980 | ||||||||
\(195\) | −16.7718 | −1.20105 | ||||||||
\(196\) | 2.12582 | 0.151844 | ||||||||
\(197\) | −17.8594 | −1.27243 | −0.636215 | − | 0.771512i | \(-0.719501\pi\) | ||||
−0.636215 | + | 0.771512i | \(0.719501\pi\) | |||||||
\(198\) | −74.9520 | −5.32661 | ||||||||
\(199\) | 13.6330 | 0.966419 | 0.483209 | − | 0.875505i | \(-0.339471\pi\) | ||||
0.483209 | + | 0.875505i | \(0.339471\pi\) | |||||||
\(200\) | 2.46550 | 0.174337 | ||||||||
\(201\) | −3.40974 | −0.240505 | ||||||||
\(202\) | −6.51912 | −0.458684 | ||||||||
\(203\) | −1.92662 | −0.135222 | ||||||||
\(204\) | 39.0591 | 2.73468 | ||||||||
\(205\) | 3.82713 | 0.267299 | ||||||||
\(206\) | 11.7609 | 0.819419 | ||||||||
\(207\) | −27.4377 | −1.90705 | ||||||||
\(208\) | −5.39625 | −0.374163 | ||||||||
\(209\) | 0.443216 | 0.0306579 | ||||||||
\(210\) | −23.5638 | −1.62606 | ||||||||
\(211\) | 22.4460 | 1.54525 | 0.772625 | − | 0.634863i | \(-0.218944\pi\) | ||||
0.772625 | + | 0.634863i | \(0.218944\pi\) | |||||||
\(212\) | 6.55670 | 0.450316 | ||||||||
\(213\) | 17.8136 | 1.22056 | ||||||||
\(214\) | −11.9871 | −0.819423 | ||||||||
\(215\) | −15.7063 | −1.07116 | ||||||||
\(216\) | 2.46992 | 0.168057 | ||||||||
\(217\) | 1.76471 | 0.119796 | ||||||||
\(218\) | −27.3047 | −1.84931 | ||||||||
\(219\) | 47.8135 | 3.23094 | ||||||||
\(220\) | 48.5133 | 3.27077 | ||||||||
\(221\) | 8.76331 | 0.589484 | ||||||||
\(222\) | 3.06148 | 0.205473 | ||||||||
\(223\) | 4.08663 | 0.273661 | 0.136831 | − | 0.990594i | \(-0.456308\pi\) | ||||
0.136831 | + | 0.990594i | \(0.456308\pi\) | |||||||
\(224\) | −8.09269 | −0.540716 | ||||||||
\(225\) | 59.6977 | 3.97985 | ||||||||
\(226\) | 12.2133 | 0.812419 | ||||||||
\(227\) | −19.5310 | −1.29632 | −0.648158 | − | 0.761506i | \(-0.724460\pi\) | ||||
−0.648158 | + | 0.761506i | \(0.724460\pi\) | |||||||
\(228\) | −0.478959 | −0.0317198 | ||||||||
\(229\) | 23.0456 | 1.52290 | 0.761449 | − | 0.648225i | \(-0.224488\pi\) | ||||
0.761449 | + | 0.648225i | \(0.224488\pi\) | |||||||
\(230\) | 34.4674 | 2.27271 | ||||||||
\(231\) | −18.0749 | −1.18924 | ||||||||
\(232\) | −0.492390 | −0.0323270 | ||||||||
\(233\) | 7.69494 | 0.504112 | 0.252056 | − | 0.967713i | \(-0.418893\pi\) | ||||
0.252056 | + | 0.967713i | \(0.418893\pi\) | |||||||
\(234\) | 18.1724 | 1.18797 | ||||||||
\(235\) | 11.1957 | 0.730330 | ||||||||
\(236\) | 24.3212 | 1.58317 | ||||||||
\(237\) | −44.1756 | −2.86951 | ||||||||
\(238\) | 12.3122 | 0.798078 | ||||||||
\(239\) | −12.2279 | −0.790960 | −0.395480 | − | 0.918475i | \(-0.629422\pi\) | ||||
−0.395480 | + | 0.918475i | \(0.629422\pi\) | |||||||
\(240\) | 43.3005 | 2.79503 | ||||||||
\(241\) | −3.68209 | −0.237184 | −0.118592 | − | 0.992943i | \(-0.537838\pi\) | ||||
−0.118592 | + | 0.992943i | \(0.537838\pi\) | |||||||
\(242\) | 49.8798 | 3.20640 | ||||||||
\(243\) | 3.53112 | 0.226521 | ||||||||
\(244\) | 6.26800 | 0.401268 | ||||||||
\(245\) | −3.82713 | −0.244507 | ||||||||
\(246\) | −6.15703 | −0.392558 | ||||||||
\(247\) | −0.107459 | −0.00683748 | ||||||||
\(248\) | 0.451011 | 0.0286393 | ||||||||
\(249\) | −43.9346 | −2.78424 | ||||||||
\(250\) | −36.1241 | −2.28469 | ||||||||
\(251\) | −27.1519 | −1.71381 | −0.856907 | − | 0.515472i | \(-0.827617\pi\) | ||||
−0.856907 | + | 0.515472i | \(0.827617\pi\) | |||||||
\(252\) | 13.1551 | 0.828694 | ||||||||
\(253\) | 26.4387 | 1.66219 | ||||||||
\(254\) | −12.7415 | −0.799471 | ||||||||
\(255\) | −70.3183 | −4.40351 | ||||||||
\(256\) | 13.8011 | 0.862568 | ||||||||
\(257\) | −4.46344 | −0.278422 | −0.139211 | − | 0.990263i | \(-0.544457\pi\) | ||||
−0.139211 | + | 0.990263i | \(0.544457\pi\) | |||||||
\(258\) | 25.2681 | 1.57312 | ||||||||
\(259\) | 0.497233 | 0.0308965 | ||||||||
\(260\) | −11.7623 | −0.729464 | ||||||||
\(261\) | −11.9224 | −0.737977 | ||||||||
\(262\) | 24.4522 | 1.51066 | ||||||||
\(263\) | 16.6595 | 1.02727 | 0.513633 | − | 0.858010i | \(-0.328299\pi\) | ||||
0.513633 | + | 0.858010i | \(0.328299\pi\) | |||||||
\(264\) | −4.61946 | −0.284308 | ||||||||
\(265\) | −11.8041 | −0.725119 | ||||||||
\(266\) | −0.150977 | −0.00925698 | ||||||||
\(267\) | 2.03121 | 0.124308 | ||||||||
\(268\) | −2.39129 | −0.146071 | ||||||||
\(269\) | 3.43160 | 0.209229 | 0.104614 | − | 0.994513i | \(-0.466639\pi\) | ||||
0.104614 | + | 0.994513i | \(0.466639\pi\) | |||||||
\(270\) | −75.1272 | −4.57210 | ||||||||
\(271\) | 27.8083 | 1.68924 | 0.844618 | − | 0.535370i | \(-0.179828\pi\) | ||||
0.844618 | + | 0.535370i | \(0.179828\pi\) | |||||||
\(272\) | −22.6246 | −1.37182 | ||||||||
\(273\) | 4.38234 | 0.265231 | ||||||||
\(274\) | 13.1358 | 0.793561 | ||||||||
\(275\) | −57.5242 | −3.46884 | ||||||||
\(276\) | −28.5708 | −1.71976 | ||||||||
\(277\) | −13.5938 | −0.816774 | −0.408387 | − | 0.912809i | \(-0.633909\pi\) | ||||
−0.408387 | + | 0.912809i | \(0.633909\pi\) | |||||||
\(278\) | −17.5970 | −1.05540 | ||||||||
\(279\) | 10.9205 | 0.653791 | ||||||||
\(280\) | −0.978111 | −0.0584533 | ||||||||
\(281\) | 2.37494 | 0.141677 | 0.0708384 | − | 0.997488i | \(-0.477433\pi\) | ||||
0.0708384 | + | 0.997488i | \(0.477433\pi\) | |||||||
\(282\) | −18.0115 | −1.07257 | ||||||||
\(283\) | −22.9301 | −1.36305 | −0.681526 | − | 0.731794i | \(-0.738683\pi\) | ||||
−0.681526 | + | 0.731794i | \(0.738683\pi\) | |||||||
\(284\) | 12.4928 | 0.741314 | ||||||||
\(285\) | 0.862273 | 0.0510767 | ||||||||
\(286\) | −17.5108 | −1.03543 | ||||||||
\(287\) | −1.00000 | −0.0590281 | ||||||||
\(288\) | −50.0796 | −2.95097 | ||||||||
\(289\) | 19.7415 | 1.16127 | ||||||||
\(290\) | 14.9770 | 0.879478 | ||||||||
\(291\) | −32.0056 | −1.87620 | ||||||||
\(292\) | 33.5321 | 1.96232 | ||||||||
\(293\) | −7.30314 | −0.426654 | −0.213327 | − | 0.976981i | \(-0.568430\pi\) | ||||
−0.213327 | + | 0.976981i | \(0.568430\pi\) | |||||||
\(294\) | 6.15703 | 0.359086 | ||||||||
\(295\) | −43.7856 | −2.54930 | ||||||||
\(296\) | 0.127079 | 0.00738632 | ||||||||
\(297\) | −57.6274 | −3.34388 | ||||||||
\(298\) | 16.2903 | 0.943670 | ||||||||
\(299\) | −6.41016 | −0.370709 | ||||||||
\(300\) | 62.1632 | 3.58900 | ||||||||
\(301\) | 4.10393 | 0.236547 | ||||||||
\(302\) | −9.81595 | −0.564845 | ||||||||
\(303\) | −9.72860 | −0.558893 | ||||||||
\(304\) | 0.277433 | 0.0159118 | ||||||||
\(305\) | −11.2843 | −0.646139 | ||||||||
\(306\) | 76.1906 | 4.35553 | ||||||||
\(307\) | 16.2292 | 0.926247 | 0.463124 | − | 0.886294i | \(-0.346729\pi\) | ||||
0.463124 | + | 0.886294i | \(0.346729\pi\) | |||||||
\(308\) | −12.6762 | −0.722291 | ||||||||
\(309\) | 17.5509 | 0.998439 | ||||||||
\(310\) | −13.7184 | −0.779150 | ||||||||
\(311\) | 24.8162 | 1.40720 | 0.703599 | − | 0.710598i | \(-0.251575\pi\) | ||||
0.703599 | + | 0.710598i | \(0.251575\pi\) | |||||||
\(312\) | 1.12001 | 0.0634079 | ||||||||
\(313\) | 1.00459 | 0.0567828 | 0.0283914 | − | 0.999597i | \(-0.490962\pi\) | ||||
0.0283914 | + | 0.999597i | \(0.490962\pi\) | |||||||
\(314\) | −20.7421 | −1.17055 | ||||||||
\(315\) | −23.6832 | −1.33440 | ||||||||
\(316\) | −30.9808 | −1.74281 | ||||||||
\(317\) | −29.9777 | −1.68372 | −0.841859 | − | 0.539697i | \(-0.818539\pi\) | ||||
−0.841859 | + | 0.539697i | \(0.818539\pi\) | |||||||
\(318\) | 18.9902 | 1.06492 | ||||||||
\(319\) | 11.4883 | 0.643221 | ||||||||
\(320\) | 34.3406 | 1.91970 | ||||||||
\(321\) | −17.8886 | −0.998443 | ||||||||
\(322\) | −9.00606 | −0.501888 | ||||||||
\(323\) | −0.450540 | −0.0250687 | ||||||||
\(324\) | 22.8094 | 1.26719 | ||||||||
\(325\) | 13.9470 | 0.773639 | ||||||||
\(326\) | −39.1930 | −2.17070 | ||||||||
\(327\) | −40.7473 | −2.25333 | ||||||||
\(328\) | −0.255573 | −0.0141116 | ||||||||
\(329\) | −2.92536 | −0.161280 | ||||||||
\(330\) | 140.510 | 7.73480 | ||||||||
\(331\) | −25.1471 | −1.38221 | −0.691106 | − | 0.722754i | \(-0.742876\pi\) | ||||
−0.691106 | + | 0.722754i | \(0.742876\pi\) | |||||||
\(332\) | −30.8118 | −1.69102 | ||||||||
\(333\) | 3.07700 | 0.168619 | ||||||||
\(334\) | 4.92359 | 0.269407 | ||||||||
\(335\) | 4.30506 | 0.235210 | ||||||||
\(336\) | −11.3141 | −0.617233 | ||||||||
\(337\) | 1.81608 | 0.0989285 | 0.0494642 | − | 0.998776i | \(-0.484249\pi\) | ||||
0.0494642 | + | 0.998776i | \(0.484249\pi\) | |||||||
\(338\) | −22.1602 | −1.20536 | ||||||||
\(339\) | 18.2262 | 0.989909 | ||||||||
\(340\) | −49.3150 | −2.67448 | ||||||||
\(341\) | −10.5229 | −0.569845 | ||||||||
\(342\) | −0.934282 | −0.0505202 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.04885 | 0.0565504 | ||||||||
\(345\) | 51.4363 | 2.76924 | ||||||||
\(346\) | −17.8622 | −0.960280 | ||||||||
\(347\) | 23.5712 | 1.26537 | 0.632685 | − | 0.774409i | \(-0.281953\pi\) | ||||
0.632685 | + | 0.774409i | \(0.281953\pi\) | |||||||
\(348\) | −12.4148 | −0.665501 | ||||||||
\(349\) | 22.3613 | 1.19697 | 0.598486 | − | 0.801133i | \(-0.295769\pi\) | ||||
0.598486 | + | 0.801133i | \(0.295769\pi\) | |||||||
\(350\) | 19.5950 | 1.04740 | ||||||||
\(351\) | 13.9720 | 0.745769 | ||||||||
\(352\) | 48.2562 | 2.57207 | ||||||||
\(353\) | 12.0297 | 0.640277 | 0.320139 | − | 0.947371i | \(-0.396271\pi\) | ||||
0.320139 | + | 0.947371i | \(0.396271\pi\) | |||||||
\(354\) | 70.4416 | 3.74393 | ||||||||
\(355\) | −22.4910 | −1.19370 | ||||||||
\(356\) | 1.42451 | 0.0754990 | ||||||||
\(357\) | 18.3736 | 0.972436 | ||||||||
\(358\) | 29.4182 | 1.55480 | ||||||||
\(359\) | −29.0810 | −1.53483 | −0.767417 | − | 0.641148i | \(-0.778459\pi\) | ||||
−0.767417 | + | 0.641148i | \(0.778459\pi\) | |||||||
\(360\) | −6.05279 | −0.319010 | ||||||||
\(361\) | −18.9945 | −0.999709 | ||||||||
\(362\) | −6.24677 | −0.328323 | ||||||||
\(363\) | 74.4365 | 3.90690 | ||||||||
\(364\) | 3.07338 | 0.161089 | ||||||||
\(365\) | −60.3681 | −3.15981 | ||||||||
\(366\) | 18.1541 | 0.948928 | ||||||||
\(367\) | −34.9839 | −1.82615 | −0.913073 | − | 0.407796i | \(-0.866298\pi\) | ||||
−0.913073 | + | 0.407796i | \(0.866298\pi\) | |||||||
\(368\) | 16.5494 | 0.862697 | ||||||||
\(369\) | −6.18825 | −0.322147 | ||||||||
\(370\) | −3.86535 | −0.200950 | ||||||||
\(371\) | 3.08431 | 0.160130 | ||||||||
\(372\) | 11.3715 | 0.589583 | ||||||||
\(373\) | 25.0688 | 1.29801 | 0.649006 | − | 0.760783i | \(-0.275185\pi\) | ||||
0.649006 | + | 0.760783i | \(0.275185\pi\) | |||||||
\(374\) | −73.4166 | −3.79628 | ||||||||
\(375\) | −53.9086 | −2.78383 | ||||||||
\(376\) | −0.747642 | −0.0385567 | ||||||||
\(377\) | −2.78538 | −0.143455 | ||||||||
\(378\) | 19.6301 | 1.00967 | ||||||||
\(379\) | 16.2692 | 0.835695 | 0.417848 | − | 0.908517i | \(-0.362785\pi\) | ||||
0.417848 | + | 0.908517i | \(0.362785\pi\) | |||||||
\(380\) | 0.604722 | 0.0310216 | ||||||||
\(381\) | −19.0143 | −0.974133 | ||||||||
\(382\) | 9.97235 | 0.510230 | ||||||||
\(383\) | −7.88034 | −0.402667 | −0.201333 | − | 0.979523i | \(-0.564527\pi\) | ||||
−0.201333 | + | 0.979523i | \(0.564527\pi\) | |||||||
\(384\) | −6.18529 | −0.315642 | ||||||||
\(385\) | 22.8210 | 1.16306 | ||||||||
\(386\) | 22.9629 | 1.16878 | ||||||||
\(387\) | 25.3962 | 1.29096 | ||||||||
\(388\) | −22.4459 | −1.13952 | ||||||||
\(389\) | 28.0477 | 1.42208 | 0.711038 | − | 0.703154i | \(-0.248225\pi\) | ||||
0.711038 | + | 0.703154i | \(0.248225\pi\) | |||||||
\(390\) | −34.0671 | −1.72505 | ||||||||
\(391\) | −26.8756 | −1.35916 | ||||||||
\(392\) | 0.255573 | 0.0129084 | ||||||||
\(393\) | 36.4904 | 1.84070 | ||||||||
\(394\) | −36.2762 | −1.82757 | ||||||||
\(395\) | 55.7750 | 2.80634 | ||||||||
\(396\) | −78.4432 | −3.94192 | ||||||||
\(397\) | 12.8210 | 0.643466 | 0.321733 | − | 0.946830i | \(-0.395735\pi\) | ||||
0.321733 | + | 0.946830i | \(0.395735\pi\) | |||||||
\(398\) | 27.6915 | 1.38805 | ||||||||
\(399\) | −0.225305 | −0.0112794 | ||||||||
\(400\) | −36.0075 | −1.80037 | ||||||||
\(401\) | −1.81684 | −0.0907285 | −0.0453643 | − | 0.998971i | \(-0.514445\pi\) | ||||
−0.0453643 | + | 0.998971i | \(0.514445\pi\) | |||||||
\(402\) | −6.92591 | −0.345433 | ||||||||
\(403\) | 2.55131 | 0.127090 | ||||||||
\(404\) | −6.82277 | −0.339446 | ||||||||
\(405\) | −41.0638 | −2.04048 | ||||||||
\(406\) | −3.91337 | −0.194217 | ||||||||
\(407\) | −2.96497 | −0.146968 | ||||||||
\(408\) | 4.69580 | 0.232477 | ||||||||
\(409\) | −35.2528 | −1.74314 | −0.871569 | − | 0.490273i | \(-0.836897\pi\) | ||||
−0.871569 | + | 0.490273i | \(0.836897\pi\) | |||||||
\(410\) | 7.77372 | 0.383917 | ||||||||
\(411\) | 19.6027 | 0.966932 | ||||||||
\(412\) | 12.3087 | 0.606405 | ||||||||
\(413\) | 11.4408 | 0.562967 | ||||||||
\(414\) | −55.7317 | −2.73906 | ||||||||
\(415\) | 55.4707 | 2.72295 | ||||||||
\(416\) | −11.6999 | −0.573636 | ||||||||
\(417\) | −26.2603 | −1.28597 | ||||||||
\(418\) | 0.900266 | 0.0440334 | ||||||||
\(419\) | 16.1804 | 0.790464 | 0.395232 | − | 0.918581i | \(-0.370664\pi\) | ||||
0.395232 | + | 0.918581i | \(0.370664\pi\) | |||||||
\(420\) | −24.6614 | −1.20335 | ||||||||
\(421\) | −8.95139 | −0.436264 | −0.218132 | − | 0.975919i | \(-0.569996\pi\) | ||||
−0.218132 | + | 0.975919i | \(0.569996\pi\) | |||||||
\(422\) | 45.5927 | 2.21942 | ||||||||
\(423\) | −18.1028 | −0.880191 | ||||||||
\(424\) | 0.788266 | 0.0382816 | ||||||||
\(425\) | 58.4748 | 2.83644 | ||||||||
\(426\) | 36.1831 | 1.75308 | ||||||||
\(427\) | 2.94851 | 0.142688 | ||||||||
\(428\) | −12.5455 | −0.606408 | ||||||||
\(429\) | −26.1316 | −1.26165 | ||||||||
\(430\) | −31.9028 | −1.53849 | ||||||||
\(431\) | 12.5790 | 0.605907 | 0.302954 | − | 0.953005i | \(-0.402027\pi\) | ||||
0.302954 | + | 0.953005i | \(0.402027\pi\) | |||||||
\(432\) | −36.0720 | −1.73552 | ||||||||
\(433\) | 16.4245 | 0.789309 | 0.394654 | − | 0.918830i | \(-0.370864\pi\) | ||||
0.394654 | + | 0.918830i | \(0.370864\pi\) | |||||||
\(434\) | 3.58450 | 0.172061 | ||||||||
\(435\) | 22.3504 | 1.07162 | ||||||||
\(436\) | −28.5765 | −1.36857 | ||||||||
\(437\) | 0.329560 | 0.0157650 | ||||||||
\(438\) | 97.1193 | 4.64054 | ||||||||
\(439\) | −25.2770 | −1.20640 | −0.603202 | − | 0.797589i | \(-0.706109\pi\) | ||||
−0.603202 | + | 0.797589i | \(0.706109\pi\) | |||||||
\(440\) | 5.83242 | 0.278050 | ||||||||
\(441\) | 6.18825 | 0.294678 | ||||||||
\(442\) | 17.8002 | 0.846667 | ||||||||
\(443\) | −0.450540 | −0.0214058 | −0.0107029 | − | 0.999943i | \(-0.503407\pi\) | ||||
−0.0107029 | + | 0.999943i | \(0.503407\pi\) | |||||||
\(444\) | 3.20408 | 0.152059 | ||||||||
\(445\) | −2.56456 | −0.121572 | ||||||||
\(446\) | 8.30082 | 0.393055 | ||||||||
\(447\) | 24.3102 | 1.14983 | ||||||||
\(448\) | −8.97293 | −0.423931 | ||||||||
\(449\) | −18.2531 | −0.861418 | −0.430709 | − | 0.902491i | \(-0.641736\pi\) | ||||
−0.430709 | + | 0.902491i | \(0.641736\pi\) | |||||||
\(450\) | 121.259 | 5.71619 | ||||||||
\(451\) | 5.96294 | 0.280784 | ||||||||
\(452\) | 12.7822 | 0.601224 | ||||||||
\(453\) | −14.6485 | −0.688247 | ||||||||
\(454\) | −39.6716 | −1.86188 | ||||||||
\(455\) | −5.53303 | −0.259393 | ||||||||
\(456\) | −0.0575818 | −0.00269652 | ||||||||
\(457\) | 28.5308 | 1.33461 | 0.667307 | − | 0.744783i | \(-0.267447\pi\) | ||||
0.667307 | + | 0.744783i | \(0.267447\pi\) | |||||||
\(458\) | 46.8105 | 2.18731 | ||||||||
\(459\) | 58.5797 | 2.73426 | ||||||||
\(460\) | 36.0728 | 1.68190 | ||||||||
\(461\) | −7.30314 | −0.340141 | −0.170071 | − | 0.985432i | \(-0.554400\pi\) | ||||
−0.170071 | + | 0.985432i | \(0.554400\pi\) | |||||||
\(462\) | −36.7140 | −1.70809 | ||||||||
\(463\) | −16.5369 | −0.768535 | −0.384268 | − | 0.923222i | \(-0.625546\pi\) | ||||
−0.384268 | + | 0.923222i | \(0.625546\pi\) | |||||||
\(464\) | 7.19114 | 0.333840 | ||||||||
\(465\) | −20.4721 | −0.949373 | ||||||||
\(466\) | 15.6301 | 0.724048 | ||||||||
\(467\) | −16.6909 | −0.772363 | −0.386181 | − | 0.922423i | \(-0.626206\pi\) | ||||
−0.386181 | + | 0.922423i | \(0.626206\pi\) | |||||||
\(468\) | 19.0189 | 0.879147 | ||||||||
\(469\) | −1.12488 | −0.0519420 | ||||||||
\(470\) | 22.7409 | 1.04896 | ||||||||
\(471\) | −30.9538 | −1.42628 | ||||||||
\(472\) | 2.92396 | 0.134586 | ||||||||
\(473\) | −24.4715 | −1.12520 | ||||||||
\(474\) | −89.7300 | −4.12143 | ||||||||
\(475\) | −0.717043 | −0.0329002 | ||||||||
\(476\) | 12.8856 | 0.590612 | ||||||||
\(477\) | 19.0865 | 0.873911 | ||||||||
\(478\) | −24.8376 | −1.13604 | ||||||||
\(479\) | 7.64133 | 0.349141 | 0.174571 | − | 0.984645i | \(-0.444146\pi\) | ||||
0.174571 | + | 0.984645i | \(0.444146\pi\) | |||||||
\(480\) | 93.8821 | 4.28511 | ||||||||
\(481\) | 0.718869 | 0.0327776 | ||||||||
\(482\) | −7.47911 | −0.340664 | ||||||||
\(483\) | −13.4399 | −0.611536 | ||||||||
\(484\) | 52.2031 | 2.37287 | ||||||||
\(485\) | 40.4095 | 1.83490 | ||||||||
\(486\) | 7.17245 | 0.325349 | ||||||||
\(487\) | −11.6260 | −0.526825 | −0.263412 | − | 0.964683i | \(-0.584848\pi\) | ||||
−0.263412 | + | 0.964683i | \(0.584848\pi\) | |||||||
\(488\) | 0.753557 | 0.0341119 | ||||||||
\(489\) | −58.4884 | −2.64494 | ||||||||
\(490\) | −7.77372 | −0.351181 | ||||||||
\(491\) | 25.9788 | 1.17241 | 0.586204 | − | 0.810164i | \(-0.300622\pi\) | ||||
0.586204 | + | 0.810164i | \(0.300622\pi\) | |||||||
\(492\) | −6.44382 | −0.290510 | ||||||||
\(493\) | −11.6781 | −0.525957 | ||||||||
\(494\) | −0.218273 | −0.00982056 | ||||||||
\(495\) | 141.222 | 6.34745 | ||||||||
\(496\) | −6.58682 | −0.295757 | ||||||||
\(497\) | 5.87671 | 0.263606 | ||||||||
\(498\) | −89.2404 | −3.99896 | ||||||||
\(499\) | −23.1920 | −1.03821 | −0.519107 | − | 0.854709i | \(-0.673736\pi\) | ||||
−0.519107 | + | 0.854709i | \(0.673736\pi\) | |||||||
\(500\) | −37.8067 | −1.69077 | ||||||||
\(501\) | 7.34756 | 0.328265 | ||||||||
\(502\) | −55.1513 | −2.46152 | ||||||||
\(503\) | 10.6434 | 0.474564 | 0.237282 | − | 0.971441i | \(-0.423743\pi\) | ||||
0.237282 | + | 0.971441i | \(0.423743\pi\) | |||||||
\(504\) | 1.58155 | 0.0704477 | ||||||||
\(505\) | 12.2831 | 0.546590 | ||||||||
\(506\) | 53.7026 | 2.38737 | ||||||||
\(507\) | −33.0700 | −1.46869 | ||||||||
\(508\) | −13.3350 | −0.591643 | ||||||||
\(509\) | 1.33530 | 0.0591860 | 0.0295930 | − | 0.999562i | \(-0.490579\pi\) | ||||
0.0295930 | + | 0.999562i | \(0.490579\pi\) | |||||||
\(510\) | −142.831 | −6.32468 | ||||||||
\(511\) | 15.7737 | 0.697788 | ||||||||
\(512\) | 32.1140 | 1.41925 | ||||||||
\(513\) | −0.718329 | −0.0317150 | ||||||||
\(514\) | −9.06619 | −0.399893 | ||||||||
\(515\) | −22.1594 | −0.976460 | ||||||||
\(516\) | 26.4450 | 1.16418 | ||||||||
\(517\) | 17.4438 | 0.767175 | ||||||||
\(518\) | 1.00999 | 0.0443762 | ||||||||
\(519\) | −26.6561 | −1.17007 | ||||||||
\(520\) | −1.41409 | −0.0620120 | ||||||||
\(521\) | 26.5594 | 1.16359 | 0.581795 | − | 0.813335i | \(-0.302351\pi\) | ||||
0.581795 | + | 0.813335i | \(0.302351\pi\) | |||||||
\(522\) | −24.2169 | −1.05994 | ||||||||
\(523\) | −9.41507 | −0.411692 | −0.205846 | − | 0.978584i | \(-0.565995\pi\) | ||||
−0.205846 | + | 0.978584i | \(0.565995\pi\) | |||||||
\(524\) | 25.5911 | 1.11795 | ||||||||
\(525\) | 29.2420 | 1.27622 | ||||||||
\(526\) | 33.8389 | 1.47545 | ||||||||
\(527\) | 10.6968 | 0.465958 | ||||||||
\(528\) | 67.4651 | 2.93604 | ||||||||
\(529\) | −3.34111 | −0.145266 | ||||||||
\(530\) | −23.9766 | −1.04148 | ||||||||
\(531\) | 70.7987 | 3.07240 | ||||||||
\(532\) | −0.158009 | −0.00685056 | ||||||||
\(533\) | −1.44574 | −0.0626219 | ||||||||
\(534\) | 4.12582 | 0.178542 | ||||||||
\(535\) | 22.5857 | 0.976464 | ||||||||
\(536\) | −0.287488 | −0.0124176 | ||||||||
\(537\) | 43.9013 | 1.89448 | ||||||||
\(538\) | 6.97032 | 0.300512 | ||||||||
\(539\) | −5.96294 | −0.256842 | ||||||||
\(540\) | −78.6265 | −3.38355 | ||||||||
\(541\) | −8.71416 | −0.374651 | −0.187325 | − | 0.982298i | \(-0.559982\pi\) | ||||
−0.187325 | + | 0.982298i | \(0.559982\pi\) | |||||||
\(542\) | 56.4846 | 2.42622 | ||||||||
\(543\) | −9.32217 | −0.400052 | ||||||||
\(544\) | −49.0537 | −2.10316 | ||||||||
\(545\) | 51.4465 | 2.20373 | ||||||||
\(546\) | 8.90146 | 0.380947 | ||||||||
\(547\) | −16.6541 | −0.712079 | −0.356040 | − | 0.934471i | \(-0.615873\pi\) | ||||
−0.356040 | + | 0.934471i | \(0.615873\pi\) | |||||||
\(548\) | 13.7476 | 0.587269 | ||||||||
\(549\) | 18.2461 | 0.778724 | ||||||||
\(550\) | −116.844 | −4.98224 | ||||||||
\(551\) | 0.143202 | 0.00610062 | ||||||||
\(552\) | −3.43487 | −0.146198 | ||||||||
\(553\) | −14.5736 | −0.619731 | ||||||||
\(554\) | −27.6119 | −1.17312 | ||||||||
\(555\) | −5.76833 | −0.244852 | ||||||||
\(556\) | −18.4167 | −0.781040 | ||||||||
\(557\) | 8.98351 | 0.380643 | 0.190322 | − | 0.981722i | \(-0.439047\pi\) | ||||
0.190322 | + | 0.981722i | \(0.439047\pi\) | |||||||
\(558\) | 22.1818 | 0.939029 | ||||||||
\(559\) | 5.93321 | 0.250948 | ||||||||
\(560\) | 14.2849 | 0.603646 | ||||||||
\(561\) | −109.561 | −4.62566 | ||||||||
\(562\) | 4.82400 | 0.203488 | ||||||||
\(563\) | −6.35931 | −0.268013 | −0.134007 | − | 0.990980i | \(-0.542784\pi\) | ||||
−0.134007 | + | 0.990980i | \(0.542784\pi\) | |||||||
\(564\) | −18.8505 | −0.793749 | ||||||||
\(565\) | −23.0119 | −0.968118 | ||||||||
\(566\) | −46.5759 | −1.95773 | ||||||||
\(567\) | 10.7297 | 0.450603 | ||||||||
\(568\) | 1.50193 | 0.0630194 | ||||||||
\(569\) | −5.92160 | −0.248246 | −0.124123 | − | 0.992267i | \(-0.539612\pi\) | ||||
−0.124123 | + | 0.992267i | \(0.539612\pi\) | |||||||
\(570\) | 1.75146 | 0.0733606 | ||||||||
\(571\) | 45.8163 | 1.91735 | 0.958676 | − | 0.284502i | \(-0.0918281\pi\) | ||||
0.958676 | + | 0.284502i | \(0.0918281\pi\) | |||||||
\(572\) | −18.3264 | −0.766266 | ||||||||
\(573\) | 14.8819 | 0.621701 | ||||||||
\(574\) | −2.03121 | −0.0847812 | ||||||||
\(575\) | −42.7730 | −1.78376 | ||||||||
\(576\) | −55.5267 | −2.31361 | ||||||||
\(577\) | 37.9400 | 1.57946 | 0.789731 | − | 0.613453i | \(-0.210220\pi\) | ||||
0.789731 | + | 0.613453i | \(0.210220\pi\) | |||||||
\(578\) | 40.0992 | 1.66791 | ||||||||
\(579\) | 34.2679 | 1.42413 | ||||||||
\(580\) | 15.6746 | 0.650852 | ||||||||
\(581\) | −14.4941 | −0.601315 | ||||||||
\(582\) | −65.0102 | −2.69476 | ||||||||
\(583\) | −18.3916 | −0.761702 | ||||||||
\(584\) | 4.03133 | 0.166818 | ||||||||
\(585\) | −34.2398 | −1.41564 | ||||||||
\(586\) | −14.8342 | −0.612796 | ||||||||
\(587\) | 5.81661 | 0.240077 | 0.120039 | − | 0.992769i | \(-0.461698\pi\) | ||||
0.120039 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(588\) | 6.44382 | 0.265739 | ||||||||
\(589\) | −0.131168 | −0.00540469 | ||||||||
\(590\) | −88.9379 | −3.66151 | ||||||||
\(591\) | −54.1357 | −2.22684 | ||||||||
\(592\) | −1.85593 | −0.0762784 | ||||||||
\(593\) | −16.7778 | −0.688980 | −0.344490 | − | 0.938790i | \(-0.611948\pi\) | ||||
−0.344490 | + | 0.938790i | \(0.611948\pi\) | |||||||
\(594\) | −117.053 | −4.80276 | ||||||||
\(595\) | −23.1981 | −0.951029 | ||||||||
\(596\) | 17.0490 | 0.698356 | ||||||||
\(597\) | 41.3245 | 1.69130 | ||||||||
\(598\) | −13.0204 | −0.532444 | ||||||||
\(599\) | −13.8344 | −0.565260 | −0.282630 | − | 0.959229i | \(-0.591207\pi\) | ||||
−0.282630 | + | 0.959229i | \(0.591207\pi\) | |||||||
\(600\) | 7.47344 | 0.305102 | ||||||||
\(601\) | 22.2486 | 0.907539 | 0.453769 | − | 0.891119i | \(-0.350079\pi\) | ||||
0.453769 | + | 0.891119i | \(0.350079\pi\) | |||||||
\(602\) | 8.33596 | 0.339748 | ||||||||
\(603\) | −6.96102 | −0.283475 | ||||||||
\(604\) | −10.2732 | −0.418009 | ||||||||
\(605\) | −93.9817 | −3.82090 | ||||||||
\(606\) | −19.7608 | −0.802729 | ||||||||
\(607\) | −2.39107 | −0.0970505 | −0.0485252 | − | 0.998822i | \(-0.515452\pi\) | ||||
−0.0485252 | + | 0.998822i | \(0.515452\pi\) | |||||||
\(608\) | 0.601517 | 0.0243947 | ||||||||
\(609\) | −5.83998 | −0.236648 | ||||||||
\(610\) | −22.9209 | −0.928038 | ||||||||
\(611\) | −4.22931 | −0.171099 | ||||||||
\(612\) | 79.7395 | 3.22328 | ||||||||
\(613\) | 38.0777 | 1.53795 | 0.768973 | − | 0.639282i | \(-0.220768\pi\) | ||||
0.768973 | + | 0.639282i | \(0.220768\pi\) | |||||||
\(614\) | 32.9649 | 1.33035 | ||||||||
\(615\) | 11.6009 | 0.467792 | ||||||||
\(616\) | −1.52396 | −0.0614023 | ||||||||
\(617\) | −22.6988 | −0.913819 | −0.456910 | − | 0.889513i | \(-0.651044\pi\) | ||||
−0.456910 | + | 0.889513i | \(0.651044\pi\) | |||||||
\(618\) | 35.6497 | 1.43404 | ||||||||
\(619\) | −33.3077 | −1.33875 | −0.669376 | − | 0.742924i | \(-0.733438\pi\) | ||||
−0.669376 | + | 0.742924i | \(0.733438\pi\) | |||||||
\(620\) | −14.3573 | −0.576605 | ||||||||
\(621\) | −42.8497 | −1.71950 | ||||||||
\(622\) | 50.4070 | 2.02113 | ||||||||
\(623\) | 0.670099 | 0.0268469 | ||||||||
\(624\) | −16.3572 | −0.654811 | ||||||||
\(625\) | 19.8289 | 0.793158 | ||||||||
\(626\) | 2.04053 | 0.0815562 | ||||||||
\(627\) | 1.34348 | 0.0536535 | ||||||||
\(628\) | −21.7083 | −0.866254 | ||||||||
\(629\) | 3.01397 | 0.120175 | ||||||||
\(630\) | −48.1057 | −1.91658 | ||||||||
\(631\) | −5.52118 | −0.219795 | −0.109897 | − | 0.993943i | \(-0.535052\pi\) | ||||
−0.109897 | + | 0.993943i | \(0.535052\pi\) | |||||||
\(632\) | −3.72461 | −0.148157 | ||||||||
\(633\) | 68.0387 | 2.70430 | ||||||||
\(634\) | −60.8912 | −2.41830 | ||||||||
\(635\) | 24.0070 | 0.952689 | ||||||||
\(636\) | 19.8748 | 0.788086 | ||||||||
\(637\) | 1.44574 | 0.0572822 | ||||||||
\(638\) | 23.3352 | 0.923848 | ||||||||
\(639\) | 36.3665 | 1.43864 | ||||||||
\(640\) | 7.80940 | 0.308694 | ||||||||
\(641\) | 12.7799 | 0.504775 | 0.252387 | − | 0.967626i | \(-0.418784\pi\) | ||||
0.252387 | + | 0.967626i | \(0.418784\pi\) | |||||||
\(642\) | −36.3355 | −1.43405 | ||||||||
\(643\) | 19.0687 | 0.751998 | 0.375999 | − | 0.926620i | \(-0.377300\pi\) | ||||
0.375999 | + | 0.926620i | \(0.377300\pi\) | |||||||
\(644\) | −9.42555 | −0.371419 | ||||||||
\(645\) | −47.6091 | −1.87461 | ||||||||
\(646\) | −0.915143 | −0.0360058 | ||||||||
\(647\) | 20.9933 | 0.825331 | 0.412665 | − | 0.910883i | \(-0.364598\pi\) | ||||
0.412665 | + | 0.910883i | \(0.364598\pi\) | |||||||
\(648\) | 2.74221 | 0.107724 | ||||||||
\(649\) | −68.2210 | −2.67791 | ||||||||
\(650\) | 28.3293 | 1.11116 | ||||||||
\(651\) | 5.34921 | 0.209652 | ||||||||
\(652\) | −41.0185 | −1.60641 | ||||||||
\(653\) | −36.4523 | −1.42649 | −0.713244 | − | 0.700916i | \(-0.752775\pi\) | ||||
−0.713244 | + | 0.700916i | \(0.752775\pi\) | |||||||
\(654\) | −82.7663 | −3.23642 | ||||||||
\(655\) | −46.0719 | −1.80018 | ||||||||
\(656\) | 3.73252 | 0.145731 | ||||||||
\(657\) | 97.6117 | 3.80819 | ||||||||
\(658\) | −5.94203 | −0.231644 | ||||||||
\(659\) | −20.9058 | −0.814373 | −0.407187 | − | 0.913345i | \(-0.633490\pi\) | ||||
−0.407187 | + | 0.913345i | \(0.633490\pi\) | |||||||
\(660\) | 147.054 | 5.72408 | ||||||||
\(661\) | 51.0624 | 1.98610 | 0.993048 | − | 0.117709i | \(-0.0375550\pi\) | ||||
0.993048 | + | 0.117709i | \(0.0375550\pi\) | |||||||
\(662\) | −51.0792 | −1.98525 | ||||||||
\(663\) | 26.5635 | 1.03164 | ||||||||
\(664\) | −3.70428 | −0.143754 | ||||||||
\(665\) | 0.284465 | 0.0110311 | ||||||||
\(666\) | 6.25004 | 0.242184 | ||||||||
\(667\) | 8.54230 | 0.330759 | ||||||||
\(668\) | 5.15293 | 0.199373 | ||||||||
\(669\) | 12.3875 | 0.478927 | ||||||||
\(670\) | 8.74449 | 0.337829 | ||||||||
\(671\) | −17.5818 | −0.678737 | ||||||||
\(672\) | −24.5307 | −0.946291 | ||||||||
\(673\) | 42.4278 | 1.63547 | 0.817736 | − | 0.575594i | \(-0.195229\pi\) | ||||
0.817736 | + | 0.575594i | \(0.195229\pi\) | |||||||
\(674\) | 3.68885 | 0.142089 | ||||||||
\(675\) | 93.2306 | 3.58845 | ||||||||
\(676\) | −23.1924 | −0.892015 | ||||||||
\(677\) | 15.1486 | 0.582209 | 0.291105 | − | 0.956691i | \(-0.405977\pi\) | ||||
0.291105 | + | 0.956691i | \(0.405977\pi\) | |||||||
\(678\) | 37.0212 | 1.42179 | ||||||||
\(679\) | −10.5587 | −0.405205 | ||||||||
\(680\) | −5.92880 | −0.227359 | ||||||||
\(681\) | −59.2025 | −2.26865 | ||||||||
\(682\) | −21.3742 | −0.818459 | ||||||||
\(683\) | 8.69113 | 0.332557 | 0.166278 | − | 0.986079i | \(-0.446825\pi\) | ||||
0.166278 | + | 0.986079i | \(0.446825\pi\) | |||||||
\(684\) | −0.977799 | −0.0373871 | ||||||||
\(685\) | −24.7499 | −0.945647 | ||||||||
\(686\) | 2.03121 | 0.0775520 | ||||||||
\(687\) | 69.8562 | 2.66518 | ||||||||
\(688\) | −15.3180 | −0.583994 | ||||||||
\(689\) | 4.45911 | 0.169879 | ||||||||
\(690\) | 104.478 | 3.97741 | ||||||||
\(691\) | 24.8701 | 0.946102 | 0.473051 | − | 0.881035i | \(-0.343153\pi\) | ||||
0.473051 | + | 0.881035i | \(0.343153\pi\) | |||||||
\(692\) | −18.6942 | −0.710648 | ||||||||
\(693\) | −36.9002 | −1.40172 | ||||||||
\(694\) | 47.8782 | 1.81743 | ||||||||
\(695\) | 33.1556 | 1.25767 | ||||||||
\(696\) | −1.49254 | −0.0565746 | ||||||||
\(697\) | −6.06148 | −0.229595 | ||||||||
\(698\) | 45.4205 | 1.71919 | ||||||||
\(699\) | 23.3250 | 0.882233 | ||||||||
\(700\) | 20.5077 | 0.775119 | ||||||||
\(701\) | 38.5821 | 1.45723 | 0.728613 | − | 0.684926i | \(-0.240165\pi\) | ||||
0.728613 | + | 0.684926i | \(0.240165\pi\) | |||||||
\(702\) | 28.3801 | 1.07114 | ||||||||
\(703\) | −0.0369585 | −0.00139392 | ||||||||
\(704\) | 53.5050 | 2.01655 | ||||||||
\(705\) | 33.9367 | 1.27813 | ||||||||
\(706\) | 24.4349 | 0.919620 | ||||||||
\(707\) | −3.20947 | −0.120705 | ||||||||
\(708\) | 73.7227 | 2.77067 | ||||||||
\(709\) | 13.3306 | 0.500642 | 0.250321 | − | 0.968163i | \(-0.419464\pi\) | ||||
0.250321 | + | 0.968163i | \(0.419464\pi\) | |||||||
\(710\) | −45.6839 | −1.71449 | ||||||||
\(711\) | −90.1848 | −3.38220 | ||||||||
\(712\) | 0.171259 | 0.00641820 | ||||||||
\(713\) | −7.82443 | −0.293027 | ||||||||
\(714\) | 37.3207 | 1.39669 | ||||||||
\(715\) | 32.9932 | 1.23387 | ||||||||
\(716\) | 30.7885 | 1.15062 | ||||||||
\(717\) | −37.0655 | −1.38424 | ||||||||
\(718\) | −59.0696 | −2.20446 | ||||||||
\(719\) | 19.0012 | 0.708625 | 0.354312 | − | 0.935127i | \(-0.384715\pi\) | ||||
0.354312 | + | 0.935127i | \(0.384715\pi\) | |||||||
\(720\) | 88.3983 | 3.29441 | ||||||||
\(721\) | 5.79008 | 0.215634 | ||||||||
\(722\) | −38.5818 | −1.43587 | ||||||||
\(723\) | −11.1612 | −0.415090 | ||||||||
\(724\) | −6.53774 | −0.242973 | ||||||||
\(725\) | −18.5860 | −0.690266 | ||||||||
\(726\) | 151.196 | 5.61142 | ||||||||
\(727\) | 19.0336 | 0.705916 | 0.352958 | − | 0.935639i | \(-0.385176\pi\) | ||||
0.352958 | + | 0.935639i | \(0.385176\pi\) | |||||||
\(728\) | 0.369491 | 0.0136943 | ||||||||
\(729\) | −21.4854 | −0.795756 | ||||||||
\(730\) | −122.620 | −4.53839 | ||||||||
\(731\) | 24.8759 | 0.920069 | ||||||||
\(732\) | 18.9996 | 0.702247 | ||||||||
\(733\) | 50.7508 | 1.87452 | 0.937261 | − | 0.348628i | \(-0.113352\pi\) | ||||
0.937261 | + | 0.348628i | \(0.113352\pi\) | |||||||
\(734\) | −71.0598 | −2.62286 | ||||||||
\(735\) | −11.6009 | −0.427904 | ||||||||
\(736\) | 35.8817 | 1.32262 | ||||||||
\(737\) | 6.70758 | 0.247077 | ||||||||
\(738\) | −12.5696 | −0.462695 | ||||||||
\(739\) | −6.70443 | −0.246626 | −0.123313 | − | 0.992368i | \(-0.539352\pi\) | ||||
−0.123313 | + | 0.992368i | \(0.539352\pi\) | |||||||
\(740\) | −4.04539 | −0.148712 | ||||||||
\(741\) | −0.325732 | −0.0119661 | ||||||||
\(742\) | 6.26490 | 0.229992 | ||||||||
\(743\) | 30.7597 | 1.12846 | 0.564232 | − | 0.825617i | \(-0.309173\pi\) | ||||
0.564232 | + | 0.825617i | \(0.309173\pi\) | |||||||
\(744\) | 1.36711 | 0.0501207 | ||||||||
\(745\) | −30.6935 | −1.12452 | ||||||||
\(746\) | 50.9200 | 1.86432 | ||||||||
\(747\) | −89.6928 | −3.28169 | ||||||||
\(748\) | −76.8363 | −2.80941 | ||||||||
\(749\) | −5.90146 | −0.215635 | ||||||||
\(750\) | −109.500 | −3.99837 | ||||||||
\(751\) | −38.8738 | −1.41852 | −0.709262 | − | 0.704945i | \(-0.750972\pi\) | ||||
−0.709262 | + | 0.704945i | \(0.750972\pi\) | |||||||
\(752\) | 10.9190 | 0.398174 | ||||||||
\(753\) | −82.3032 | −2.99930 | ||||||||
\(754\) | −5.65770 | −0.206041 | ||||||||
\(755\) | 18.4948 | 0.673096 | ||||||||
\(756\) | 20.5445 | 0.747196 | ||||||||
\(757\) | 3.89914 | 0.141717 | 0.0708583 | − | 0.997486i | \(-0.477426\pi\) | ||||
0.0708583 | + | 0.997486i | \(0.477426\pi\) | |||||||
\(758\) | 33.0463 | 1.20030 | ||||||||
\(759\) | 80.1413 | 2.90894 | ||||||||
\(760\) | 0.0727014 | 0.00263716 | ||||||||
\(761\) | 13.9575 | 0.505959 | 0.252979 | − | 0.967472i | \(-0.418590\pi\) | ||||
0.252979 | + | 0.967472i | \(0.418590\pi\) | |||||||
\(762\) | −38.6221 | −1.39913 | ||||||||
\(763\) | −13.4426 | −0.486653 | ||||||||
\(764\) | 10.4369 | 0.377592 | ||||||||
\(765\) | −143.556 | −5.19026 | ||||||||
\(766\) | −16.0067 | −0.578344 | ||||||||
\(767\) | 16.5405 | 0.597241 | ||||||||
\(768\) | 41.8340 | 1.50956 | ||||||||
\(769\) | 9.40607 | 0.339192 | 0.169596 | − | 0.985514i | \(-0.445754\pi\) | ||||
0.169596 | + | 0.985514i | \(0.445754\pi\) | |||||||
\(770\) | 46.3542 | 1.67049 | ||||||||
\(771\) | −13.5296 | −0.487258 | ||||||||
\(772\) | 24.0325 | 0.864948 | ||||||||
\(773\) | 6.38151 | 0.229527 | 0.114764 | − | 0.993393i | \(-0.463389\pi\) | ||||
0.114764 | + | 0.993393i | \(0.463389\pi\) | |||||||
\(774\) | 51.5850 | 1.85418 | ||||||||
\(775\) | 17.0241 | 0.611523 | ||||||||
\(776\) | −2.69851 | −0.0968709 | ||||||||
\(777\) | 1.50722 | 0.0540711 | ||||||||
\(778\) | 56.9709 | 2.04250 | ||||||||
\(779\) | 0.0743284 | 0.00266309 | ||||||||
\(780\) | −35.6539 | −1.27661 | ||||||||
\(781\) | −35.0425 | −1.25392 | ||||||||
\(782\) | −54.5900 | −1.95214 | ||||||||
\(783\) | −18.6193 | −0.665400 | ||||||||
\(784\) | −3.73252 | −0.133304 | ||||||||
\(785\) | 39.0815 | 1.39488 | ||||||||
\(786\) | 74.1197 | 2.64376 | ||||||||
\(787\) | −31.4514 | −1.12112 | −0.560561 | − | 0.828113i | \(-0.689414\pi\) | ||||
−0.560561 | + | 0.828113i | \(0.689414\pi\) | |||||||
\(788\) | −37.9659 | −1.35248 | ||||||||
\(789\) | 50.4984 | 1.79779 | ||||||||
\(790\) | 113.291 | 4.03071 | ||||||||
\(791\) | 6.01283 | 0.213792 | ||||||||
\(792\) | −9.43067 | −0.335104 | ||||||||
\(793\) | 4.26277 | 0.151375 | ||||||||
\(794\) | 26.0421 | 0.924200 | ||||||||
\(795\) | −35.7807 | −1.26901 | ||||||||
\(796\) | 28.9814 | 1.02722 | ||||||||
\(797\) | −12.7701 | −0.452339 | −0.226170 | − | 0.974088i | \(-0.572620\pi\) | ||||
−0.226170 | + | 0.974088i | \(0.572620\pi\) | |||||||
\(798\) | −0.457643 | −0.0162004 | ||||||||
\(799\) | −17.7320 | −0.627313 | ||||||||
\(800\) | −78.0698 | −2.76018 | ||||||||
\(801\) | 4.14674 | 0.146518 | ||||||||
\(802\) | −3.69038 | −0.130312 | ||||||||
\(803\) | −94.0578 | −3.31923 | ||||||||
\(804\) | −7.24851 | −0.255635 | ||||||||
\(805\) | 16.9689 | 0.598074 | ||||||||
\(806\) | 5.18225 | 0.182537 | ||||||||
\(807\) | 10.4019 | 0.366165 | ||||||||
\(808\) | −0.820254 | −0.0288564 | ||||||||
\(809\) | 37.8116 | 1.32939 | 0.664693 | − | 0.747117i | \(-0.268563\pi\) | ||||
0.664693 | + | 0.747117i | \(0.268563\pi\) | |||||||
\(810\) | −83.4094 | −2.93071 | ||||||||
\(811\) | −29.0566 | −1.02031 | −0.510157 | − | 0.860081i | \(-0.670413\pi\) | ||||
−0.510157 | + | 0.860081i | \(0.670413\pi\) | |||||||
\(812\) | −4.09564 | −0.143729 | ||||||||
\(813\) | 84.2929 | 2.95628 | ||||||||
\(814\) | −6.02248 | −0.211088 | ||||||||
\(815\) | 73.8460 | 2.58671 | ||||||||
\(816\) | −68.5800 | −2.40078 | ||||||||
\(817\) | −0.305039 | −0.0106720 | ||||||||
\(818\) | −71.6059 | −2.50364 | ||||||||
\(819\) | 8.94659 | 0.312619 | ||||||||
\(820\) | 8.13581 | 0.284115 | ||||||||
\(821\) | −22.1598 | −0.773381 | −0.386691 | − | 0.922209i | \(-0.626382\pi\) | ||||
−0.386691 | + | 0.922209i | \(0.626382\pi\) | |||||||
\(822\) | 39.8173 | 1.38879 | ||||||||
\(823\) | −44.5895 | −1.55429 | −0.777147 | − | 0.629319i | \(-0.783334\pi\) | ||||
−0.777147 | + | 0.629319i | \(0.783334\pi\) | |||||||
\(824\) | 1.47978 | 0.0515507 | ||||||||
\(825\) | −174.368 | −6.07072 | ||||||||
\(826\) | 23.2388 | 0.808580 | ||||||||
\(827\) | 17.7093 | 0.615814 | 0.307907 | − | 0.951416i | \(-0.400371\pi\) | ||||
0.307907 | + | 0.951416i | \(0.400371\pi\) | |||||||
\(828\) | −58.3276 | −2.02702 | ||||||||
\(829\) | 29.8270 | 1.03594 | 0.517968 | − | 0.855400i | \(-0.326689\pi\) | ||||
0.517968 | + | 0.855400i | \(0.326689\pi\) | |||||||
\(830\) | 112.673 | 3.91093 | ||||||||
\(831\) | −41.2058 | −1.42941 | ||||||||
\(832\) | −12.9725 | −0.449741 | ||||||||
\(833\) | 6.06148 | 0.210018 | ||||||||
\(834\) | −53.3403 | −1.84702 | ||||||||
\(835\) | −9.27685 | −0.321039 | ||||||||
\(836\) | 0.942199 | 0.0325866 | ||||||||
\(837\) | 17.0546 | 0.589493 | ||||||||
\(838\) | 32.8658 | 1.13533 | ||||||||
\(839\) | 31.3123 | 1.08102 | 0.540511 | − | 0.841337i | \(-0.318231\pi\) | ||||
0.540511 | + | 0.841337i | \(0.318231\pi\) | |||||||
\(840\) | −2.96486 | −0.102297 | ||||||||
\(841\) | −25.2881 | −0.872005 | ||||||||
\(842\) | −18.1822 | −0.626599 | ||||||||
\(843\) | 7.19894 | 0.247945 | ||||||||
\(844\) | 47.7163 | 1.64246 | ||||||||
\(845\) | 41.7534 | 1.43636 | ||||||||
\(846\) | −36.7707 | −1.26420 | ||||||||
\(847\) | 24.5567 | 0.843777 | ||||||||
\(848\) | −11.5123 | −0.395333 | ||||||||
\(849\) | −69.5060 | −2.38544 | ||||||||
\(850\) | 118.775 | 4.07394 | ||||||||
\(851\) | −2.20465 | −0.0755744 | ||||||||
\(852\) | 37.8685 | 1.29735 | ||||||||
\(853\) | 33.0949 | 1.13315 | 0.566574 | − | 0.824011i | \(-0.308269\pi\) | ||||
0.566574 | + | 0.824011i | \(0.308269\pi\) | |||||||
\(854\) | 5.98904 | 0.204941 | ||||||||
\(855\) | 1.76034 | 0.0602023 | ||||||||
\(856\) | −1.50825 | −0.0515510 | ||||||||
\(857\) | −20.0025 | −0.683272 | −0.341636 | − | 0.939832i | \(-0.610981\pi\) | ||||
−0.341636 | + | 0.939832i | \(0.610981\pi\) | |||||||
\(858\) | −53.0789 | −1.81208 | ||||||||
\(859\) | −37.3721 | −1.27512 | −0.637559 | − | 0.770401i | \(-0.720056\pi\) | ||||
−0.637559 | + | 0.770401i | \(0.720056\pi\) | |||||||
\(860\) | −33.3888 | −1.13855 | ||||||||
\(861\) | −3.03121 | −0.103303 | ||||||||
\(862\) | 25.5505 | 0.870255 | ||||||||
\(863\) | 46.4668 | 1.58175 | 0.790875 | − | 0.611978i | \(-0.209626\pi\) | ||||
0.790875 | + | 0.611978i | \(0.209626\pi\) | |||||||
\(864\) | −78.2098 | −2.66075 | ||||||||
\(865\) | 33.6554 | 1.14432 | ||||||||
\(866\) | 33.3615 | 1.13367 | ||||||||
\(867\) | 59.8408 | 2.03230 | ||||||||
\(868\) | 3.75146 | 0.127333 | ||||||||
\(869\) | 86.9013 | 2.94793 | ||||||||
\(870\) | 45.3984 | 1.53915 | ||||||||
\(871\) | −1.62628 | −0.0551044 | ||||||||
\(872\) | −3.43555 | −0.116342 | ||||||||
\(873\) | −65.3397 | −2.21142 | ||||||||
\(874\) | 0.669406 | 0.0226430 | ||||||||
\(875\) | −17.7845 | −0.601226 | ||||||||
\(876\) | 101.643 | 3.43420 | ||||||||
\(877\) | −10.5546 | −0.356404 | −0.178202 | − | 0.983994i | \(-0.557028\pi\) | ||||
−0.178202 | + | 0.983994i | \(0.557028\pi\) | |||||||
\(878\) | −51.3429 | −1.73274 | ||||||||
\(879\) | −22.1374 | −0.746675 | ||||||||
\(880\) | −85.1798 | −2.87141 | ||||||||
\(881\) | −25.0214 | −0.842993 | −0.421497 | − | 0.906830i | \(-0.638495\pi\) | ||||
−0.421497 | + | 0.906830i | \(0.638495\pi\) | |||||||
\(882\) | 12.5696 | 0.423242 | ||||||||
\(883\) | 14.4626 | 0.486704 | 0.243352 | − | 0.969938i | \(-0.421753\pi\) | ||||
0.243352 | + | 0.969938i | \(0.421753\pi\) | |||||||
\(884\) | 18.6293 | 0.626570 | ||||||||
\(885\) | −132.723 | −4.46145 | ||||||||
\(886\) | −0.915143 | −0.0307448 | ||||||||
\(887\) | −5.65795 | −0.189975 | −0.0949877 | − | 0.995478i | \(-0.530281\pi\) | ||||
−0.0949877 | + | 0.995478i | \(0.530281\pi\) | |||||||
\(888\) | 0.385204 | 0.0129266 | ||||||||
\(889\) | −6.27284 | −0.210384 | ||||||||
\(890\) | −5.20916 | −0.174612 | ||||||||
\(891\) | −63.9803 | −2.14342 | ||||||||
\(892\) | 8.68746 | 0.290878 | ||||||||
\(893\) | 0.217437 | 0.00727626 | ||||||||
\(894\) | 49.3792 | 1.65149 | ||||||||
\(895\) | −55.4288 | −1.85278 | ||||||||
\(896\) | −2.04053 | −0.0681695 | ||||||||
\(897\) | −19.4306 | −0.648768 | ||||||||
\(898\) | −37.0759 | −1.23724 | ||||||||
\(899\) | −3.39992 | −0.113394 | ||||||||
\(900\) | 126.907 | 4.23023 | ||||||||
\(901\) | 18.6955 | 0.622838 | ||||||||
\(902\) | 12.1120 | 0.403285 | ||||||||
\(903\) | 12.4399 | 0.413974 | ||||||||
\(904\) | 1.53671 | 0.0511104 | ||||||||
\(905\) | 11.7699 | 0.391246 | ||||||||
\(906\) | −29.7542 | −0.988518 | ||||||||
\(907\) | −45.9050 | −1.52425 | −0.762126 | − | 0.647429i | \(-0.775844\pi\) | ||||
−0.762126 | + | 0.647429i | \(0.775844\pi\) | |||||||
\(908\) | −41.5194 | −1.37787 | ||||||||
\(909\) | −19.8610 | −0.658748 | ||||||||
\(910\) | −11.2388 | −0.372562 | ||||||||
\(911\) | 42.5495 | 1.40973 | 0.704864 | − | 0.709342i | \(-0.251008\pi\) | ||||
0.704864 | + | 0.709342i | \(0.251008\pi\) | |||||||
\(912\) | 0.840957 | 0.0278469 | ||||||||
\(913\) | 86.4272 | 2.86032 | ||||||||
\(914\) | 57.9521 | 1.91688 | ||||||||
\(915\) | −34.2052 | −1.13079 | ||||||||
\(916\) | 48.9909 | 1.61870 | ||||||||
\(917\) | 12.0382 | 0.397537 | ||||||||
\(918\) | 118.988 | 3.92718 | ||||||||
\(919\) | −25.1999 | −0.831269 | −0.415634 | − | 0.909532i | \(-0.636440\pi\) | ||||
−0.415634 | + | 0.909532i | \(0.636440\pi\) | |||||||
\(920\) | 4.33678 | 0.142979 | ||||||||
\(921\) | 49.1940 | 1.62100 | ||||||||
\(922\) | −14.8342 | −0.488539 | ||||||||
\(923\) | 8.49618 | 0.279655 | ||||||||
\(924\) | −38.4241 | −1.26406 | ||||||||
\(925\) | 4.79678 | 0.157717 | ||||||||
\(926\) | −33.5900 | −1.10384 | ||||||||
\(927\) | 35.8304 | 1.17683 | ||||||||
\(928\) | 15.5915 | 0.511816 | ||||||||
\(929\) | 37.0410 | 1.21528 | 0.607639 | − | 0.794214i | \(-0.292117\pi\) | ||||
0.607639 | + | 0.794214i | \(0.292117\pi\) | |||||||
\(930\) | −41.5833 | −1.36357 | ||||||||
\(931\) | −0.0743284 | −0.00243602 | ||||||||
\(932\) | 16.3581 | 0.535827 | ||||||||
\(933\) | 75.2231 | 2.46270 | ||||||||
\(934\) | −33.9027 | −1.10933 | ||||||||
\(935\) | 138.329 | 4.52384 | ||||||||
\(936\) | 2.28650 | 0.0747367 | ||||||||
\(937\) | 24.4307 | 0.798115 | 0.399058 | − | 0.916926i | \(-0.369337\pi\) | ||||
0.399058 | + | 0.916926i | \(0.369337\pi\) | |||||||
\(938\) | −2.28487 | −0.0746035 | ||||||||
\(939\) | 3.04512 | 0.0993739 | ||||||||
\(940\) | 23.8002 | 0.776276 | ||||||||
\(941\) | −42.4153 | −1.38270 | −0.691350 | − | 0.722520i | \(-0.742984\pi\) | ||||
−0.691350 | + | 0.722520i | \(0.742984\pi\) | |||||||
\(942\) | −62.8738 | −2.04854 | ||||||||
\(943\) | 4.43383 | 0.144386 | ||||||||
\(944\) | −42.7032 | −1.38987 | ||||||||
\(945\) | −36.9864 | −1.20317 | ||||||||
\(946\) | −49.7068 | −1.61611 | ||||||||
\(947\) | −10.0783 | −0.327501 | −0.163750 | − | 0.986502i | \(-0.552359\pi\) | ||||
−0.163750 | + | 0.986502i | \(0.552359\pi\) | |||||||
\(948\) | −93.9095 | −3.05004 | ||||||||
\(949\) | 22.8047 | 0.740271 | ||||||||
\(950\) | −1.45647 | −0.0472540 | ||||||||
\(951\) | −90.8689 | −2.94663 | ||||||||
\(952\) | 1.54915 | 0.0502082 | ||||||||
\(953\) | −50.1799 | −1.62549 | −0.812743 | − | 0.582623i | \(-0.802026\pi\) | ||||
−0.812743 | + | 0.582623i | \(0.802026\pi\) | |||||||
\(954\) | 38.7687 | 1.25518 | ||||||||
\(955\) | −18.7895 | −0.608015 | ||||||||
\(956\) | −25.9944 | −0.840720 | ||||||||
\(957\) | 34.8235 | 1.12568 | ||||||||
\(958\) | 15.5212 | 0.501466 | ||||||||
\(959\) | 6.46697 | 0.208829 | ||||||||
\(960\) | 104.094 | 3.35961 | ||||||||
\(961\) | −27.8858 | −0.899542 | ||||||||
\(962\) | 1.46017 | 0.0470779 | ||||||||
\(963\) | −36.5197 | −1.17683 | ||||||||
\(964\) | −7.82748 | −0.252106 | ||||||||
\(965\) | −43.2659 | −1.39278 | ||||||||
\(966\) | −27.2993 | −0.878340 | ||||||||
\(967\) | 33.4107 | 1.07441 | 0.537207 | − | 0.843450i | \(-0.319479\pi\) | ||||
0.537207 | + | 0.843450i | \(0.319479\pi\) | |||||||
\(968\) | 6.27601 | 0.201719 | ||||||||
\(969\) | −1.36568 | −0.0438721 | ||||||||
\(970\) | 82.0803 | 2.63544 | ||||||||
\(971\) | −57.1446 | −1.83386 | −0.916929 | − | 0.399051i | \(-0.869340\pi\) | ||||
−0.916929 | + | 0.399051i | \(0.869340\pi\) | |||||||
\(972\) | 7.50653 | 0.240772 | ||||||||
\(973\) | −8.66331 | −0.277733 | ||||||||
\(974\) | −23.6149 | −0.756670 | ||||||||
\(975\) | 42.2762 | 1.35392 | ||||||||
\(976\) | −11.0054 | −0.352273 | ||||||||
\(977\) | −5.17315 | −0.165504 | −0.0827519 | − | 0.996570i | \(-0.526371\pi\) | ||||
−0.0827519 | + | 0.996570i | \(0.526371\pi\) | |||||||
\(978\) | −118.802 | −3.79888 | ||||||||
\(979\) | −3.99576 | −0.127705 | ||||||||
\(980\) | −8.13581 | −0.259889 | ||||||||
\(981\) | −83.1859 | −2.65592 | ||||||||
\(982\) | 52.7685 | 1.68391 | ||||||||
\(983\) | 53.4989 | 1.70635 | 0.853175 | − | 0.521624i | \(-0.174674\pi\) | ||||
0.853175 | + | 0.521624i | \(0.174674\pi\) | |||||||
\(984\) | −0.774695 | −0.0246964 | ||||||||
\(985\) | 68.3503 | 2.17782 | ||||||||
\(986\) | −23.7208 | −0.755424 | ||||||||
\(987\) | −8.86739 | −0.282252 | ||||||||
\(988\) | −0.228440 | −0.00726764 | ||||||||
\(989\) | −18.1962 | −0.578604 | ||||||||
\(990\) | 286.852 | 9.11674 | ||||||||
\(991\) | 16.6924 | 0.530252 | 0.265126 | − | 0.964214i | \(-0.414587\pi\) | ||||
0.265126 | + | 0.964214i | \(0.414587\pi\) | |||||||
\(992\) | −14.2813 | −0.453430 | ||||||||
\(993\) | −76.2263 | −2.41897 | ||||||||
\(994\) | 11.9368 | 0.378614 | ||||||||
\(995\) | −52.1754 | −1.65407 | ||||||||
\(996\) | −93.3971 | −2.95940 | ||||||||
\(997\) | 0.818514 | 0.0259226 | 0.0129613 | − | 0.999916i | \(-0.495874\pi\) | ||||
0.0129613 | + | 0.999916i | \(0.495874\pi\) | |||||||
\(998\) | −47.1078 | −1.49117 | ||||||||
\(999\) | 4.80538 | 0.152036 |
(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 | 287.2.a.e.1.5 | ✓ | 5 | |
3.2 | odd | 2 | 2583.2.a.r.1.1 | 5 | |||
4.3 | odd | 2 | 4592.2.a.bb.1.1 | 5 | |||
5.4 | even | 2 | 7175.2.a.n.1.1 | 5 | |||
7.6 | odd | 2 | 2009.2.a.n.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.a.e.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
2009.2.a.n.1.5 | 5 | 7.6 | odd | 2 | |||
2583.2.a.r.1.1 | 5 | 3.2 | odd | 2 | |||
4592.2.a.bb.1.1 | 5 | 4.3 | odd | 2 | |||
7175.2.a.n.1.1 | 5 | 5.4 | even | 2 |