Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(1,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, 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("418.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.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: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.469.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 5x + 4 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.772866\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.772866 | 0.446214 | 0.223107 | − | 0.974794i | \(-0.428380\pi\) | ||||
0.223107 | + | 0.974794i | \(0.428380\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.22713 | 0.548791 | 0.274396 | − | 0.961617i | \(-0.411522\pi\) | ||||
0.274396 | + | 0.961617i | \(0.411522\pi\) | |||||||
\(6\) | 0.772866 | 0.315521 | ||||||||
\(7\) | 3.40268 | 1.28609 | 0.643046 | − | 0.765828i | \(-0.277670\pi\) | ||||
0.643046 | + | 0.765828i | \(0.277670\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.40268 | −0.800893 | ||||||||
\(10\) | 1.22713 | 0.388054 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.772866 | 0.223107 | ||||||||
\(13\) | −1.40268 | −0.389033 | −0.194517 | − | 0.980899i | \(-0.562314\pi\) | ||||
−0.194517 | + | 0.980899i | \(0.562314\pi\) | |||||||
\(14\) | 3.40268 | 0.909404 | ||||||||
\(15\) | 0.948410 | 0.244878 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.80536 | −1.16547 | −0.582735 | − | 0.812662i | \(-0.698018\pi\) | ||||
−0.582735 | + | 0.812662i | \(0.698018\pi\) | |||||||
\(18\) | −2.40268 | −0.566317 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 1.22713 | 0.274396 | ||||||||
\(21\) | 2.62981 | 0.573872 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 6.80536 | 1.41902 | 0.709508 | − | 0.704698i | \(-0.248917\pi\) | ||||
0.709508 | + | 0.704698i | \(0.248917\pi\) | |||||||
\(24\) | 0.772866 | 0.157761 | ||||||||
\(25\) | −3.49414 | −0.698828 | ||||||||
\(26\) | −1.40268 | −0.275088 | ||||||||
\(27\) | −4.17554 | −0.803584 | ||||||||
\(28\) | 3.40268 | 0.643046 | ||||||||
\(29\) | 8.03249 | 1.49160 | 0.745798 | − | 0.666172i | \(-0.232068\pi\) | ||||
0.745798 | + | 0.666172i | \(0.232068\pi\) | |||||||
\(30\) | 0.948410 | 0.173155 | ||||||||
\(31\) | −4.94841 | −0.888761 | −0.444380 | − | 0.895838i | \(-0.646576\pi\) | ||||
−0.444380 | + | 0.895838i | \(0.646576\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.772866 | −0.134539 | ||||||||
\(34\) | −4.80536 | −0.824112 | ||||||||
\(35\) | 4.17554 | 0.705796 | ||||||||
\(36\) | −2.40268 | −0.400446 | ||||||||
\(37\) | 2.35109 | 0.386517 | 0.193258 | − | 0.981148i | \(-0.438094\pi\) | ||||
0.193258 | + | 0.981148i | \(0.438094\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −1.08408 | −0.173592 | ||||||||
\(40\) | 1.22713 | 0.194027 | ||||||||
\(41\) | 2.94841 | 0.460464 | 0.230232 | − | 0.973136i | \(-0.426051\pi\) | ||||
0.230232 | + | 0.973136i | \(0.426051\pi\) | |||||||
\(42\) | 2.62981 | 0.405789 | ||||||||
\(43\) | −9.12395 | −1.39139 | −0.695695 | − | 0.718337i | \(-0.744903\pi\) | ||||
−0.695695 | + | 0.718337i | \(0.744903\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −2.94841 | −0.439523 | ||||||||
\(46\) | 6.80536 | 1.00340 | ||||||||
\(47\) | 5.25963 | 0.767195 | 0.383598 | − | 0.923500i | \(-0.374685\pi\) | ||||
0.383598 | + | 0.923500i | \(0.374685\pi\) | |||||||
\(48\) | 0.772866 | 0.111554 | ||||||||
\(49\) | 4.57822 | 0.654032 | ||||||||
\(50\) | −3.49414 | −0.494146 | ||||||||
\(51\) | −3.71390 | −0.520049 | ||||||||
\(52\) | −1.40268 | −0.194517 | ||||||||
\(53\) | −4.45427 | −0.611841 | −0.305920 | − | 0.952057i | \(-0.598964\pi\) | ||||
−0.305920 | + | 0.952057i | \(0.598964\pi\) | |||||||
\(54\) | −4.17554 | −0.568220 | ||||||||
\(55\) | −1.22713 | −0.165467 | ||||||||
\(56\) | 3.40268 | 0.454702 | ||||||||
\(57\) | −0.772866 | −0.102369 | ||||||||
\(58\) | 8.03249 | 1.05472 | ||||||||
\(59\) | −14.5193 | −1.89025 | −0.945123 | − | 0.326715i | \(-0.894058\pi\) | ||||
−0.945123 | + | 0.326715i | \(0.894058\pi\) | |||||||
\(60\) | 0.948410 | 0.122439 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | −4.94841 | −0.628449 | ||||||||
\(63\) | −8.17554 | −1.03002 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.72128 | −0.213498 | ||||||||
\(66\) | −0.772866 | −0.0951332 | ||||||||
\(67\) | 3.40268 | 0.415703 | 0.207852 | − | 0.978160i | \(-0.433353\pi\) | ||||
0.207852 | + | 0.978160i | \(0.433353\pi\) | |||||||
\(68\) | −4.80536 | −0.582735 | ||||||||
\(69\) | 5.25963 | 0.633185 | ||||||||
\(70\) | 4.17554 | 0.499073 | ||||||||
\(71\) | −7.57822 | −0.899370 | −0.449685 | − | 0.893187i | \(-0.648464\pi\) | ||||
−0.449685 | + | 0.893187i | \(0.648464\pi\) | |||||||
\(72\) | −2.40268 | −0.283158 | ||||||||
\(73\) | −10.0650 | −1.17802 | −0.589009 | − | 0.808127i | \(-0.700482\pi\) | ||||
−0.589009 | + | 0.808127i | \(0.700482\pi\) | |||||||
\(74\) | 2.35109 | 0.273309 | ||||||||
\(75\) | −2.70050 | −0.311827 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −3.40268 | −0.387771 | ||||||||
\(78\) | −1.08408 | −0.122748 | ||||||||
\(79\) | −3.71390 | −0.417846 | −0.208923 | − | 0.977932i | \(-0.566996\pi\) | ||||
−0.208923 | + | 0.977932i | \(0.566996\pi\) | |||||||
\(80\) | 1.22713 | 0.137198 | ||||||||
\(81\) | 3.98090 | 0.442322 | ||||||||
\(82\) | 2.94841 | 0.325597 | ||||||||
\(83\) | 10.6697 | 1.17115 | 0.585575 | − | 0.810618i | \(-0.300869\pi\) | ||||
0.585575 | + | 0.810618i | \(0.300869\pi\) | |||||||
\(84\) | 2.62981 | 0.286936 | ||||||||
\(85\) | −5.89682 | −0.639600 | ||||||||
\(86\) | −9.12395 | −0.983861 | ||||||||
\(87\) | 6.20804 | 0.665571 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 14.9883 | 1.58875 | 0.794377 | − | 0.607425i | \(-0.207797\pi\) | ||||
0.794377 | + | 0.607425i | \(0.207797\pi\) | |||||||
\(90\) | −2.94841 | −0.310790 | ||||||||
\(91\) | −4.77287 | −0.500332 | ||||||||
\(92\) | 6.80536 | 0.709508 | ||||||||
\(93\) | −3.82446 | −0.396578 | ||||||||
\(94\) | 5.25963 | 0.542489 | ||||||||
\(95\) | −1.22713 | −0.125901 | ||||||||
\(96\) | 0.772866 | 0.0788803 | ||||||||
\(97\) | 2.35109 | 0.238717 | 0.119358 | − | 0.992851i | \(-0.461916\pi\) | ||||
0.119358 | + | 0.992851i | \(0.461916\pi\) | |||||||
\(98\) | 4.57822 | 0.462470 | ||||||||
\(99\) | 2.40268 | 0.241478 | ||||||||
\(100\) | −3.49414 | −0.349414 | ||||||||
\(101\) | 14.0650 | 1.39952 | 0.699759 | − | 0.714379i | \(-0.253291\pi\) | ||||
0.699759 | + | 0.714379i | \(0.253291\pi\) | |||||||
\(102\) | −3.71390 | −0.367730 | ||||||||
\(103\) | −15.5782 | −1.53497 | −0.767484 | − | 0.641068i | \(-0.778492\pi\) | ||||
−0.767484 | + | 0.641068i | \(0.778492\pi\) | |||||||
\(104\) | −1.40268 | −0.137544 | ||||||||
\(105\) | 3.22713 | 0.314936 | ||||||||
\(106\) | −4.45427 | −0.432637 | ||||||||
\(107\) | −4.35109 | −0.420636 | −0.210318 | − | 0.977633i | \(-0.567450\pi\) | ||||
−0.210318 | + | 0.977633i | \(0.567450\pi\) | |||||||
\(108\) | −4.17554 | −0.401792 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | −1.22713 | −0.117003 | ||||||||
\(111\) | 1.81708 | 0.172469 | ||||||||
\(112\) | 3.40268 | 0.321523 | ||||||||
\(113\) | −19.9618 | −1.87785 | −0.938924 | − | 0.344124i | \(-0.888176\pi\) | ||||
−0.938924 | + | 0.344124i | \(0.888176\pi\) | |||||||
\(114\) | −0.772866 | −0.0723855 | ||||||||
\(115\) | 8.35109 | 0.778743 | ||||||||
\(116\) | 8.03249 | 0.745798 | ||||||||
\(117\) | 3.37019 | 0.311574 | ||||||||
\(118\) | −14.5193 | −1.33661 | ||||||||
\(119\) | −16.3511 | −1.49890 | ||||||||
\(120\) | 0.948410 | 0.0865776 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | 2.27872 | 0.205466 | ||||||||
\(124\) | −4.94841 | −0.444380 | ||||||||
\(125\) | −10.4235 | −0.932302 | ||||||||
\(126\) | −8.17554 | −0.728335 | ||||||||
\(127\) | 11.7139 | 1.03944 | 0.519720 | − | 0.854337i | \(-0.326036\pi\) | ||||
0.519720 | + | 0.854337i | \(0.326036\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.05159 | −0.620858 | ||||||||
\(130\) | −1.72128 | −0.150966 | ||||||||
\(131\) | 1.85695 | 0.162242 | 0.0811211 | − | 0.996704i | \(-0.474150\pi\) | ||||
0.0811211 | + | 0.996704i | \(0.474150\pi\) | |||||||
\(132\) | −0.772866 | −0.0672693 | ||||||||
\(133\) | −3.40268 | −0.295050 | ||||||||
\(134\) | 3.40268 | 0.293947 | ||||||||
\(135\) | −5.12395 | −0.441000 | ||||||||
\(136\) | −4.80536 | −0.412056 | ||||||||
\(137\) | 10.5973 | 0.905390 | 0.452695 | − | 0.891665i | \(-0.350463\pi\) | ||||
0.452695 | + | 0.891665i | \(0.350463\pi\) | |||||||
\(138\) | 5.25963 | 0.447729 | ||||||||
\(139\) | 14.7347 | 1.24978 | 0.624889 | − | 0.780713i | \(-0.285144\pi\) | ||||
0.624889 | + | 0.780713i | \(0.285144\pi\) | |||||||
\(140\) | 4.17554 | 0.352898 | ||||||||
\(141\) | 4.06498 | 0.342333 | ||||||||
\(142\) | −7.57822 | −0.635950 | ||||||||
\(143\) | 1.40268 | 0.117298 | ||||||||
\(144\) | −2.40268 | −0.200223 | ||||||||
\(145\) | 9.85695 | 0.818575 | ||||||||
\(146\) | −10.0650 | −0.832984 | ||||||||
\(147\) | 3.53835 | 0.291838 | ||||||||
\(148\) | 2.35109 | 0.193258 | ||||||||
\(149\) | 18.3511 | 1.50338 | 0.751690 | − | 0.659517i | \(-0.229239\pi\) | ||||
0.751690 | + | 0.659517i | \(0.229239\pi\) | |||||||
\(150\) | −2.70050 | −0.220495 | ||||||||
\(151\) | −7.64891 | −0.622460 | −0.311230 | − | 0.950335i | \(-0.600741\pi\) | ||||
−0.311230 | + | 0.950335i | \(0.600741\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 11.5457 | 0.933417 | ||||||||
\(154\) | −3.40268 | −0.274196 | ||||||||
\(155\) | −6.07236 | −0.487744 | ||||||||
\(156\) | −1.08408 | −0.0867960 | ||||||||
\(157\) | 8.38358 | 0.669083 | 0.334541 | − | 0.942381i | \(-0.391419\pi\) | ||||
0.334541 | + | 0.942381i | \(0.391419\pi\) | |||||||
\(158\) | −3.71390 | −0.295462 | ||||||||
\(159\) | −3.44255 | −0.273012 | ||||||||
\(160\) | 1.22713 | 0.0970135 | ||||||||
\(161\) | 23.1564 | 1.82498 | ||||||||
\(162\) | 3.98090 | 0.312769 | ||||||||
\(163\) | −14.2479 | −1.11598 | −0.557991 | − | 0.829847i | \(-0.688428\pi\) | ||||
−0.557991 | + | 0.829847i | \(0.688428\pi\) | |||||||
\(164\) | 2.94841 | 0.230232 | ||||||||
\(165\) | −0.948410 | −0.0738336 | ||||||||
\(166\) | 10.6697 | 0.828128 | ||||||||
\(167\) | −10.8703 | −0.841172 | −0.420586 | − | 0.907253i | \(-0.638176\pi\) | ||||
−0.420586 | + | 0.907253i | \(0.638176\pi\) | |||||||
\(168\) | 2.62981 | 0.202894 | ||||||||
\(169\) | −11.0325 | −0.848653 | ||||||||
\(170\) | −5.89682 | −0.452265 | ||||||||
\(171\) | 2.40268 | 0.183737 | ||||||||
\(172\) | −9.12395 | −0.695695 | ||||||||
\(173\) | 3.39530 | 0.258140 | 0.129070 | − | 0.991635i | \(-0.458801\pi\) | ||||
0.129070 | + | 0.991635i | \(0.458801\pi\) | |||||||
\(174\) | 6.20804 | 0.470630 | ||||||||
\(175\) | −11.8894 | −0.898757 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −11.2214 | −0.843454 | ||||||||
\(178\) | 14.9883 | 1.12342 | ||||||||
\(179\) | −0.311217 | −0.0232614 | −0.0116307 | − | 0.999932i | \(-0.503702\pi\) | ||||
−0.0116307 | + | 0.999932i | \(0.503702\pi\) | |||||||
\(180\) | −2.94841 | −0.219762 | ||||||||
\(181\) | −15.3246 | −1.13907 | −0.569535 | − | 0.821967i | \(-0.692877\pi\) | ||||
−0.569535 | + | 0.821967i | \(0.692877\pi\) | |||||||
\(182\) | −4.77287 | −0.353788 | ||||||||
\(183\) | 1.54573 | 0.114264 | ||||||||
\(184\) | 6.80536 | 0.501698 | ||||||||
\(185\) | 2.88510 | 0.212117 | ||||||||
\(186\) | −3.82446 | −0.280423 | ||||||||
\(187\) | 4.80536 | 0.351403 | ||||||||
\(188\) | 5.25963 | 0.383598 | ||||||||
\(189\) | −14.2080 | −1.03348 | ||||||||
\(190\) | −1.22713 | −0.0890257 | ||||||||
\(191\) | 26.8703 | 1.94427 | 0.972135 | − | 0.234422i | \(-0.0753199\pi\) | ||||
0.972135 | + | 0.234422i | \(0.0753199\pi\) | |||||||
\(192\) | 0.772866 | 0.0557768 | ||||||||
\(193\) | 18.5665 | 1.33645 | 0.668223 | − | 0.743961i | \(-0.267055\pi\) | ||||
0.668223 | + | 0.743961i | \(0.267055\pi\) | |||||||
\(194\) | 2.35109 | 0.168798 | ||||||||
\(195\) | −1.33031 | −0.0952658 | ||||||||
\(196\) | 4.57822 | 0.327016 | ||||||||
\(197\) | 14.9085 | 1.06219 | 0.531095 | − | 0.847312i | \(-0.321781\pi\) | ||||
0.531095 | + | 0.847312i | \(0.321781\pi\) | |||||||
\(198\) | 2.40268 | 0.170751 | ||||||||
\(199\) | 15.1564 | 1.07441 | 0.537206 | − | 0.843451i | \(-0.319480\pi\) | ||||
0.537206 | + | 0.843451i | \(0.319480\pi\) | |||||||
\(200\) | −3.49414 | −0.247073 | ||||||||
\(201\) | 2.62981 | 0.185493 | ||||||||
\(202\) | 14.0650 | 0.989609 | ||||||||
\(203\) | 27.3320 | 1.91833 | ||||||||
\(204\) | −3.71390 | −0.260025 | ||||||||
\(205\) | 3.61810 | 0.252699 | ||||||||
\(206\) | −15.5782 | −1.08539 | ||||||||
\(207\) | −16.3511 | −1.13648 | ||||||||
\(208\) | −1.40268 | −0.0972583 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 3.22713 | 0.222693 | ||||||||
\(211\) | 11.1564 | 0.768041 | 0.384021 | − | 0.923324i | \(-0.374539\pi\) | ||||
0.384021 | + | 0.923324i | \(0.374539\pi\) | |||||||
\(212\) | −4.45427 | −0.305920 | ||||||||
\(213\) | −5.85695 | −0.401311 | ||||||||
\(214\) | −4.35109 | −0.297434 | ||||||||
\(215\) | −11.1963 | −0.763583 | ||||||||
\(216\) | −4.17554 | −0.284110 | ||||||||
\(217\) | −16.8378 | −1.14303 | ||||||||
\(218\) | 6.00000 | 0.406371 | ||||||||
\(219\) | −7.77888 | −0.525648 | ||||||||
\(220\) | −1.22713 | −0.0827334 | ||||||||
\(221\) | 6.74037 | 0.453407 | ||||||||
\(222\) | 1.81708 | 0.121954 | ||||||||
\(223\) | 1.61072 | 0.107861 | 0.0539307 | − | 0.998545i | \(-0.482825\pi\) | ||||
0.0539307 | + | 0.998545i | \(0.482825\pi\) | |||||||
\(224\) | 3.40268 | 0.227351 | ||||||||
\(225\) | 8.39530 | 0.559687 | ||||||||
\(226\) | −19.9618 | −1.32784 | ||||||||
\(227\) | −16.7672 | −1.11288 | −0.556438 | − | 0.830889i | \(-0.687832\pi\) | ||||
−0.556438 | + | 0.830889i | \(0.687832\pi\) | |||||||
\(228\) | −0.772866 | −0.0511843 | ||||||||
\(229\) | −8.55913 | −0.565603 | −0.282801 | − | 0.959178i | \(-0.591264\pi\) | ||||
−0.282801 | + | 0.959178i | \(0.591264\pi\) | |||||||
\(230\) | 8.35109 | 0.550654 | ||||||||
\(231\) | −2.62981 | −0.173029 | ||||||||
\(232\) | 8.03249 | 0.527359 | ||||||||
\(233\) | 5.44255 | 0.356553 | 0.178277 | − | 0.983980i | \(-0.442948\pi\) | ||||
0.178277 | + | 0.983980i | \(0.442948\pi\) | |||||||
\(234\) | 3.37019 | 0.220316 | ||||||||
\(235\) | 6.45427 | 0.421030 | ||||||||
\(236\) | −14.5193 | −0.945123 | ||||||||
\(237\) | −2.87034 | −0.186449 | ||||||||
\(238\) | −16.3511 | −1.05988 | ||||||||
\(239\) | 11.2921 | 0.730426 | 0.365213 | − | 0.930924i | \(-0.380996\pi\) | ||||
0.365213 | + | 0.930924i | \(0.380996\pi\) | |||||||
\(240\) | 0.948410 | 0.0612196 | ||||||||
\(241\) | 11.4101 | 0.734987 | 0.367493 | − | 0.930026i | \(-0.380216\pi\) | ||||
0.367493 | + | 0.930026i | \(0.380216\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 15.6033 | 1.00095 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 5.61810 | 0.358927 | ||||||||
\(246\) | 2.27872 | 0.145286 | ||||||||
\(247\) | 1.40268 | 0.0892503 | ||||||||
\(248\) | −4.94841 | −0.314224 | ||||||||
\(249\) | 8.24623 | 0.522584 | ||||||||
\(250\) | −10.4235 | −0.659237 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | −8.17554 | −0.515011 | ||||||||
\(253\) | −6.80536 | −0.427849 | ||||||||
\(254\) | 11.7139 | 0.734995 | ||||||||
\(255\) | −4.55745 | −0.285399 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.2331 | 1.51162 | 0.755811 | − | 0.654790i | \(-0.227243\pi\) | ||||
0.755811 | + | 0.654790i | \(0.227243\pi\) | |||||||
\(258\) | −7.05159 | −0.439013 | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | −1.72128 | −0.106749 | ||||||||
\(261\) | −19.2995 | −1.19461 | ||||||||
\(262\) | 1.85695 | 0.114723 | ||||||||
\(263\) | 20.5665 | 1.26819 | 0.634093 | − | 0.773257i | \(-0.281374\pi\) | ||||
0.634093 | + | 0.773257i | \(0.281374\pi\) | |||||||
\(264\) | −0.772866 | −0.0475666 | ||||||||
\(265\) | −5.46599 | −0.335773 | ||||||||
\(266\) | −3.40268 | −0.208632 | ||||||||
\(267\) | 11.5839 | 0.708925 | ||||||||
\(268\) | 3.40268 | 0.207852 | ||||||||
\(269\) | −1.36281 | −0.0830918 | −0.0415459 | − | 0.999137i | \(-0.513228\pi\) | ||||
−0.0415459 | + | 0.999137i | \(0.513228\pi\) | |||||||
\(270\) | −5.12395 | −0.311834 | ||||||||
\(271\) | −23.1963 | −1.40908 | −0.704538 | − | 0.709666i | \(-0.748846\pi\) | ||||
−0.704538 | + | 0.709666i | \(0.748846\pi\) | |||||||
\(272\) | −4.80536 | −0.291368 | ||||||||
\(273\) | −3.68878 | −0.223255 | ||||||||
\(274\) | 10.5973 | 0.640208 | ||||||||
\(275\) | 3.49414 | 0.210705 | ||||||||
\(276\) | 5.25963 | 0.316592 | ||||||||
\(277\) | 31.0385 | 1.86492 | 0.932462 | − | 0.361269i | \(-0.117656\pi\) | ||||
0.932462 | + | 0.361269i | \(0.117656\pi\) | |||||||
\(278\) | 14.7347 | 0.883727 | ||||||||
\(279\) | 11.8894 | 0.711802 | ||||||||
\(280\) | 4.17554 | 0.249537 | ||||||||
\(281\) | −2.77287 | −0.165415 | −0.0827076 | − | 0.996574i | \(-0.526357\pi\) | ||||
−0.0827076 | + | 0.996574i | \(0.526357\pi\) | |||||||
\(282\) | 4.06498 | 0.242066 | ||||||||
\(283\) | −9.23451 | −0.548935 | −0.274467 | − | 0.961596i | \(-0.588502\pi\) | ||||
−0.274467 | + | 0.961596i | \(0.588502\pi\) | |||||||
\(284\) | −7.57822 | −0.449685 | ||||||||
\(285\) | −0.948410 | −0.0561790 | ||||||||
\(286\) | 1.40268 | 0.0829421 | ||||||||
\(287\) | 10.0325 | 0.592199 | ||||||||
\(288\) | −2.40268 | −0.141579 | ||||||||
\(289\) | 6.09146 | 0.358321 | ||||||||
\(290\) | 9.85695 | 0.578820 | ||||||||
\(291\) | 1.81708 | 0.106519 | ||||||||
\(292\) | −10.0650 | −0.589009 | ||||||||
\(293\) | 17.7390 | 1.03632 | 0.518162 | − | 0.855283i | \(-0.326616\pi\) | ||||
0.518162 | + | 0.855283i | \(0.326616\pi\) | |||||||
\(294\) | 3.53835 | 0.206361 | ||||||||
\(295\) | −17.8171 | −1.03735 | ||||||||
\(296\) | 2.35109 | 0.136654 | ||||||||
\(297\) | 4.17554 | 0.242290 | ||||||||
\(298\) | 18.3511 | 1.06305 | ||||||||
\(299\) | −9.54573 | −0.552044 | ||||||||
\(300\) | −2.70050 | −0.155914 | ||||||||
\(301\) | −31.0459 | −1.78946 | ||||||||
\(302\) | −7.64891 | −0.440145 | ||||||||
\(303\) | 10.8703 | 0.624485 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 2.45427 | 0.140531 | ||||||||
\(306\) | 11.5457 | 0.660026 | ||||||||
\(307\) | 20.9735 | 1.19702 | 0.598511 | − | 0.801115i | \(-0.295759\pi\) | ||||
0.598511 | + | 0.801115i | \(0.295759\pi\) | |||||||
\(308\) | −3.40268 | −0.193886 | ||||||||
\(309\) | −12.0399 | −0.684924 | ||||||||
\(310\) | −6.07236 | −0.344887 | ||||||||
\(311\) | −3.36281 | −0.190687 | −0.0953436 | − | 0.995444i | \(-0.530395\pi\) | ||||
−0.0953436 | + | 0.995444i | \(0.530395\pi\) | |||||||
\(312\) | −1.08408 | −0.0613741 | ||||||||
\(313\) | −4.94103 | −0.279284 | −0.139642 | − | 0.990202i | \(-0.544595\pi\) | ||||
−0.139642 | + | 0.990202i | \(0.544595\pi\) | |||||||
\(314\) | 8.38358 | 0.473113 | ||||||||
\(315\) | −10.0325 | −0.565267 | ||||||||
\(316\) | −3.71390 | −0.208923 | ||||||||
\(317\) | 14.2861 | 0.802388 | 0.401194 | − | 0.915993i | \(-0.368595\pi\) | ||||
0.401194 | + | 0.915993i | \(0.368595\pi\) | |||||||
\(318\) | −3.44255 | −0.193049 | ||||||||
\(319\) | −8.03249 | −0.449733 | ||||||||
\(320\) | 1.22713 | 0.0685989 | ||||||||
\(321\) | −3.36281 | −0.187694 | ||||||||
\(322\) | 23.1564 | 1.29046 | ||||||||
\(323\) | 4.80536 | 0.267377 | ||||||||
\(324\) | 3.98090 | 0.221161 | ||||||||
\(325\) | 4.90116 | 0.271867 | ||||||||
\(326\) | −14.2479 | −0.789119 | ||||||||
\(327\) | 4.63719 | 0.256437 | ||||||||
\(328\) | 2.94841 | 0.162799 | ||||||||
\(329\) | 17.8968 | 0.986684 | ||||||||
\(330\) | −0.948410 | −0.0522082 | ||||||||
\(331\) | −31.9293 | −1.75499 | −0.877497 | − | 0.479582i | \(-0.840788\pi\) | ||||
−0.877497 | + | 0.479582i | \(0.840788\pi\) | |||||||
\(332\) | 10.6697 | 0.585575 | ||||||||
\(333\) | −5.64891 | −0.309558 | ||||||||
\(334\) | −10.8703 | −0.594799 | ||||||||
\(335\) | 4.17554 | 0.228134 | ||||||||
\(336\) | 2.62981 | 0.143468 | ||||||||
\(337\) | −8.84523 | −0.481830 | −0.240915 | − | 0.970546i | \(-0.577448\pi\) | ||||
−0.240915 | + | 0.970546i | \(0.577448\pi\) | |||||||
\(338\) | −11.0325 | −0.600088 | ||||||||
\(339\) | −15.4278 | −0.837923 | ||||||||
\(340\) | −5.89682 | −0.319800 | ||||||||
\(341\) | 4.94841 | 0.267971 | ||||||||
\(342\) | 2.40268 | 0.129922 | ||||||||
\(343\) | −8.24053 | −0.444947 | ||||||||
\(344\) | −9.12395 | −0.491931 | ||||||||
\(345\) | 6.45427 | 0.347486 | ||||||||
\(346\) | 3.39530 | 0.182532 | ||||||||
\(347\) | 5.27439 | 0.283144 | 0.141572 | − | 0.989928i | \(-0.454784\pi\) | ||||
0.141572 | + | 0.989928i | \(0.454784\pi\) | |||||||
\(348\) | 6.20804 | 0.332786 | ||||||||
\(349\) | −10.9085 | −0.583921 | −0.291960 | − | 0.956430i | \(-0.594308\pi\) | ||||
−0.291960 | + | 0.956430i | \(0.594308\pi\) | |||||||
\(350\) | −11.8894 | −0.635517 | ||||||||
\(351\) | 5.85695 | 0.312621 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −22.1300 | −1.17786 | −0.588930 | − | 0.808184i | \(-0.700451\pi\) | ||||
−0.588930 | + | 0.808184i | \(0.700451\pi\) | |||||||
\(354\) | −11.2214 | −0.596412 | ||||||||
\(355\) | −9.29950 | −0.493566 | ||||||||
\(356\) | 14.9883 | 0.794377 | ||||||||
\(357\) | −12.6372 | −0.668831 | ||||||||
\(358\) | −0.311217 | −0.0164483 | ||||||||
\(359\) | −16.3910 | −0.865082 | −0.432541 | − | 0.901614i | \(-0.642383\pi\) | ||||
−0.432541 | + | 0.901614i | \(0.642383\pi\) | |||||||
\(360\) | −2.94841 | −0.155395 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −15.3246 | −0.805444 | ||||||||
\(363\) | 0.772866 | 0.0405649 | ||||||||
\(364\) | −4.77287 | −0.250166 | ||||||||
\(365\) | −12.3511 | −0.646486 | ||||||||
\(366\) | 1.54573 | 0.0807967 | ||||||||
\(367\) | −32.3511 | −1.68871 | −0.844357 | − | 0.535782i | \(-0.820017\pi\) | ||||
−0.844357 | + | 0.535782i | \(0.820017\pi\) | |||||||
\(368\) | 6.80536 | 0.354754 | ||||||||
\(369\) | −7.08408 | −0.368783 | ||||||||
\(370\) | 2.88510 | 0.149989 | ||||||||
\(371\) | −15.1564 | −0.786883 | ||||||||
\(372\) | −3.82446 | −0.198289 | ||||||||
\(373\) | 17.5782 | 0.910166 | 0.455083 | − | 0.890449i | \(-0.349610\pi\) | ||||
0.455083 | + | 0.890449i | \(0.349610\pi\) | |||||||
\(374\) | 4.80536 | 0.248479 | ||||||||
\(375\) | −8.05593 | −0.416006 | ||||||||
\(376\) | 5.25963 | 0.271245 | ||||||||
\(377\) | −11.2670 | −0.580280 | ||||||||
\(378\) | −14.2080 | −0.730783 | ||||||||
\(379\) | 8.93365 | 0.458891 | 0.229445 | − | 0.973322i | \(-0.426309\pi\) | ||||
0.229445 | + | 0.973322i | \(0.426309\pi\) | |||||||
\(380\) | −1.22713 | −0.0629507 | ||||||||
\(381\) | 9.05327 | 0.463813 | ||||||||
\(382\) | 26.8703 | 1.37481 | ||||||||
\(383\) | −16.0399 | −0.819599 | −0.409800 | − | 0.912176i | \(-0.634401\pi\) | ||||
−0.409800 | + | 0.912176i | \(0.634401\pi\) | |||||||
\(384\) | 0.772866 | 0.0394401 | ||||||||
\(385\) | −4.17554 | −0.212805 | ||||||||
\(386\) | 18.5665 | 0.945010 | ||||||||
\(387\) | 21.9219 | 1.11435 | ||||||||
\(388\) | 2.35109 | 0.119358 | ||||||||
\(389\) | 17.2271 | 0.873450 | 0.436725 | − | 0.899595i | \(-0.356138\pi\) | ||||
0.436725 | + | 0.899595i | \(0.356138\pi\) | |||||||
\(390\) | −1.33031 | −0.0673631 | ||||||||
\(391\) | −32.7022 | −1.65382 | ||||||||
\(392\) | 4.57822 | 0.231235 | ||||||||
\(393\) | 1.43517 | 0.0723948 | ||||||||
\(394\) | 14.9085 | 0.751081 | ||||||||
\(395\) | −4.55745 | −0.229310 | ||||||||
\(396\) | 2.40268 | 0.120739 | ||||||||
\(397\) | 15.0784 | 0.756762 | 0.378381 | − | 0.925650i | \(-0.376481\pi\) | ||||
0.378381 | + | 0.925650i | \(0.376481\pi\) | |||||||
\(398\) | 15.1564 | 0.759724 | ||||||||
\(399\) | −2.62981 | −0.131655 | ||||||||
\(400\) | −3.49414 | −0.174707 | ||||||||
\(401\) | −13.1564 | −0.657002 | −0.328501 | − | 0.944504i | \(-0.606543\pi\) | ||||
−0.328501 | + | 0.944504i | \(0.606543\pi\) | |||||||
\(402\) | 2.62981 | 0.131163 | ||||||||
\(403\) | 6.94103 | 0.345757 | ||||||||
\(404\) | 14.0650 | 0.699759 | ||||||||
\(405\) | 4.88510 | 0.242743 | ||||||||
\(406\) | 27.3320 | 1.35646 | ||||||||
\(407\) | −2.35109 | −0.116539 | ||||||||
\(408\) | −3.71390 | −0.183865 | ||||||||
\(409\) | −16.3836 | −0.810116 | −0.405058 | − | 0.914291i | \(-0.632749\pi\) | ||||
−0.405058 | + | 0.914291i | \(0.632749\pi\) | |||||||
\(410\) | 3.61810 | 0.178685 | ||||||||
\(411\) | 8.19030 | 0.403998 | ||||||||
\(412\) | −15.5782 | −0.767484 | ||||||||
\(413\) | −49.4044 | −2.43103 | ||||||||
\(414\) | −16.3511 | −0.803612 | ||||||||
\(415\) | 13.0931 | 0.642717 | ||||||||
\(416\) | −1.40268 | −0.0687720 | ||||||||
\(417\) | 11.3879 | 0.557669 | ||||||||
\(418\) | 1.00000 | 0.0489116 | ||||||||
\(419\) | 1.12966 | 0.0551874 | 0.0275937 | − | 0.999619i | \(-0.491216\pi\) | ||||
0.0275937 | + | 0.999619i | \(0.491216\pi\) | |||||||
\(420\) | 3.22713 | 0.157468 | ||||||||
\(421\) | −2.63719 | −0.128529 | −0.0642645 | − | 0.997933i | \(-0.520470\pi\) | ||||
−0.0642645 | + | 0.997933i | \(0.520470\pi\) | |||||||
\(422\) | 11.1564 | 0.543087 | ||||||||
\(423\) | −12.6372 | −0.614441 | ||||||||
\(424\) | −4.45427 | −0.216318 | ||||||||
\(425\) | 16.7906 | 0.814464 | ||||||||
\(426\) | −5.85695 | −0.283770 | ||||||||
\(427\) | 6.80536 | 0.329334 | ||||||||
\(428\) | −4.35109 | −0.210318 | ||||||||
\(429\) | 1.08408 | 0.0523400 | ||||||||
\(430\) | −11.1963 | −0.539934 | ||||||||
\(431\) | −28.4958 | −1.37260 | −0.686298 | − | 0.727321i | \(-0.740765\pi\) | ||||
−0.686298 | + | 0.727321i | \(0.740765\pi\) | |||||||
\(432\) | −4.17554 | −0.200896 | ||||||||
\(433\) | −37.5075 | −1.80250 | −0.901249 | − | 0.433302i | \(-0.857348\pi\) | ||||
−0.901249 | + | 0.433302i | \(0.857348\pi\) | |||||||
\(434\) | −16.8378 | −0.808243 | ||||||||
\(435\) | 7.61810 | 0.365260 | ||||||||
\(436\) | 6.00000 | 0.287348 | ||||||||
\(437\) | −6.80536 | −0.325544 | ||||||||
\(438\) | −7.77888 | −0.371689 | ||||||||
\(439\) | −32.1300 | −1.53348 | −0.766740 | − | 0.641958i | \(-0.778122\pi\) | ||||
−0.766740 | + | 0.641958i | \(0.778122\pi\) | |||||||
\(440\) | −1.22713 | −0.0585013 | ||||||||
\(441\) | −11.0000 | −0.523810 | ||||||||
\(442\) | 6.74037 | 0.320607 | ||||||||
\(443\) | 33.0385 | 1.56971 | 0.784853 | − | 0.619681i | \(-0.212738\pi\) | ||||
0.784853 | + | 0.619681i | \(0.212738\pi\) | |||||||
\(444\) | 1.81708 | 0.0862346 | ||||||||
\(445\) | 18.3926 | 0.871895 | ||||||||
\(446\) | 1.61072 | 0.0762696 | ||||||||
\(447\) | 14.1829 | 0.670829 | ||||||||
\(448\) | 3.40268 | 0.160761 | ||||||||
\(449\) | 7.88206 | 0.371977 | 0.185989 | − | 0.982552i | \(-0.440451\pi\) | ||||
0.185989 | + | 0.982552i | \(0.440451\pi\) | |||||||
\(450\) | 8.39530 | 0.395758 | ||||||||
\(451\) | −2.94841 | −0.138835 | ||||||||
\(452\) | −19.9618 | −0.938924 | ||||||||
\(453\) | −5.91158 | −0.277750 | ||||||||
\(454\) | −16.7672 | −0.786922 | ||||||||
\(455\) | −5.85695 | −0.274578 | ||||||||
\(456\) | −0.772866 | −0.0361927 | ||||||||
\(457\) | 24.9353 | 1.16643 | 0.583213 | − | 0.812320i | \(-0.301795\pi\) | ||||
0.583213 | + | 0.812320i | \(0.301795\pi\) | |||||||
\(458\) | −8.55913 | −0.399942 | ||||||||
\(459\) | 20.0650 | 0.936553 | ||||||||
\(460\) | 8.35109 | 0.389372 | ||||||||
\(461\) | −26.6874 | −1.24296 | −0.621478 | − | 0.783431i | \(-0.713468\pi\) | ||||
−0.621478 | + | 0.783431i | \(0.713468\pi\) | |||||||
\(462\) | −2.62981 | −0.122350 | ||||||||
\(463\) | −32.7022 | −1.51980 | −0.759900 | − | 0.650041i | \(-0.774752\pi\) | ||||
−0.759900 | + | 0.650041i | \(0.774752\pi\) | |||||||
\(464\) | 8.03249 | 0.372899 | ||||||||
\(465\) | −4.69312 | −0.217638 | ||||||||
\(466\) | 5.44255 | 0.252121 | ||||||||
\(467\) | 11.3776 | 0.526491 | 0.263246 | − | 0.964729i | \(-0.415207\pi\) | ||||
0.263246 | + | 0.964729i | \(0.415207\pi\) | |||||||
\(468\) | 3.37019 | 0.155787 | ||||||||
\(469\) | 11.5782 | 0.534633 | ||||||||
\(470\) | 6.45427 | 0.297713 | ||||||||
\(471\) | 6.47938 | 0.298554 | ||||||||
\(472\) | −14.5193 | −0.668303 | ||||||||
\(473\) | 9.12395 | 0.419520 | ||||||||
\(474\) | −2.87034 | −0.131839 | ||||||||
\(475\) | 3.49414 | 0.160322 | ||||||||
\(476\) | −16.3511 | −0.749451 | ||||||||
\(477\) | 10.7022 | 0.490019 | ||||||||
\(478\) | 11.2921 | 0.516489 | ||||||||
\(479\) | −12.5973 | −0.575586 | −0.287793 | − | 0.957693i | \(-0.592922\pi\) | ||||
−0.287793 | + | 0.957693i | \(0.592922\pi\) | |||||||
\(480\) | 0.948410 | 0.0432888 | ||||||||
\(481\) | −3.29782 | −0.150368 | ||||||||
\(482\) | 11.4101 | 0.519714 | ||||||||
\(483\) | 17.8968 | 0.814334 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 2.88510 | 0.131006 | ||||||||
\(486\) | 15.6033 | 0.707782 | ||||||||
\(487\) | 9.69616 | 0.439375 | 0.219688 | − | 0.975570i | \(-0.429496\pi\) | ||||
0.219688 | + | 0.975570i | \(0.429496\pi\) | |||||||
\(488\) | 2.00000 | 0.0905357 | ||||||||
\(489\) | −11.0117 | −0.497967 | ||||||||
\(490\) | 5.61810 | 0.253800 | ||||||||
\(491\) | −11.7538 | −0.530440 | −0.265220 | − | 0.964188i | \(-0.585445\pi\) | ||||
−0.265220 | + | 0.964188i | \(0.585445\pi\) | |||||||
\(492\) | 2.27872 | 0.102733 | ||||||||
\(493\) | −38.5990 | −1.73841 | ||||||||
\(494\) | 1.40268 | 0.0631095 | ||||||||
\(495\) | 2.94841 | 0.132521 | ||||||||
\(496\) | −4.94841 | −0.222190 | ||||||||
\(497\) | −25.7863 | −1.15667 | ||||||||
\(498\) | 8.24623 | 0.369523 | ||||||||
\(499\) | 26.6640 | 1.19364 | 0.596822 | − | 0.802374i | \(-0.296430\pi\) | ||||
0.596822 | + | 0.802374i | \(0.296430\pi\) | |||||||
\(500\) | −10.4235 | −0.466151 | ||||||||
\(501\) | −8.40131 | −0.375343 | ||||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | 11.1622 | 0.497696 | 0.248848 | − | 0.968543i | \(-0.419948\pi\) | ||||
0.248848 | + | 0.968543i | \(0.419948\pi\) | |||||||
\(504\) | −8.17554 | −0.364168 | ||||||||
\(505\) | 17.2596 | 0.768043 | ||||||||
\(506\) | −6.80536 | −0.302535 | ||||||||
\(507\) | −8.52663 | −0.378681 | ||||||||
\(508\) | 11.7139 | 0.519720 | ||||||||
\(509\) | −35.9618 | −1.59398 | −0.796989 | − | 0.603993i | \(-0.793575\pi\) | ||||
−0.796989 | + | 0.603993i | \(0.793575\pi\) | |||||||
\(510\) | −4.55745 | −0.201807 | ||||||||
\(511\) | −34.2479 | −1.51504 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.17554 | 0.184355 | ||||||||
\(514\) | 24.2331 | 1.06888 | ||||||||
\(515\) | −19.1166 | −0.842377 | ||||||||
\(516\) | −7.05159 | −0.310429 | ||||||||
\(517\) | −5.25963 | −0.231318 | ||||||||
\(518\) | 8.00000 | 0.351500 | ||||||||
\(519\) | 2.62411 | 0.115186 | ||||||||
\(520\) | −1.72128 | −0.0754829 | ||||||||
\(521\) | 10.1300 | 0.443802 | 0.221901 | − | 0.975069i | \(-0.428774\pi\) | ||||
0.221901 | + | 0.975069i | \(0.428774\pi\) | |||||||
\(522\) | −19.2995 | −0.844716 | ||||||||
\(523\) | −7.93502 | −0.346974 | −0.173487 | − | 0.984836i | \(-0.555503\pi\) | ||||
−0.173487 | + | 0.984836i | \(0.555503\pi\) | |||||||
\(524\) | 1.85695 | 0.0811211 | ||||||||
\(525\) | −9.18894 | −0.401038 | ||||||||
\(526\) | 20.5665 | 0.896742 | ||||||||
\(527\) | 23.7789 | 1.03582 | ||||||||
\(528\) | −0.772866 | −0.0336347 | ||||||||
\(529\) | 23.3129 | 1.01360 | ||||||||
\(530\) | −5.46599 | −0.237427 | ||||||||
\(531\) | 34.8851 | 1.51388 | ||||||||
\(532\) | −3.40268 | −0.147525 | ||||||||
\(533\) | −4.13567 | −0.179136 | ||||||||
\(534\) | 11.5839 | 0.501286 | ||||||||
\(535\) | −5.33937 | −0.230841 | ||||||||
\(536\) | 3.40268 | 0.146973 | ||||||||
\(537\) | −0.240529 | −0.0103796 | ||||||||
\(538\) | −1.36281 | −0.0587548 | ||||||||
\(539\) | −4.57822 | −0.197198 | ||||||||
\(540\) | −5.12395 | −0.220500 | ||||||||
\(541\) | 10.8436 | 0.466201 | 0.233100 | − | 0.972453i | \(-0.425113\pi\) | ||||
0.233100 | + | 0.972453i | \(0.425113\pi\) | |||||||
\(542\) | −23.1963 | −0.996367 | ||||||||
\(543\) | −11.8439 | −0.508269 | ||||||||
\(544\) | −4.80536 | −0.206028 | ||||||||
\(545\) | 7.36281 | 0.315388 | ||||||||
\(546\) | −3.68878 | −0.157865 | ||||||||
\(547\) | −10.3129 | −0.440947 | −0.220474 | − | 0.975393i | \(-0.570760\pi\) | ||||
−0.220474 | + | 0.975393i | \(0.570760\pi\) | |||||||
\(548\) | 10.5973 | 0.452695 | ||||||||
\(549\) | −4.80536 | −0.205088 | ||||||||
\(550\) | 3.49414 | 0.148991 | ||||||||
\(551\) | −8.03249 | −0.342196 | ||||||||
\(552\) | 5.25963 | 0.223865 | ||||||||
\(553\) | −12.6372 | −0.537388 | ||||||||
\(554\) | 31.0385 | 1.31870 | ||||||||
\(555\) | 2.22980 | 0.0946496 | ||||||||
\(556\) | 14.7347 | 0.624889 | ||||||||
\(557\) | −14.4811 | −0.613582 | −0.306791 | − | 0.951777i | \(-0.599255\pi\) | ||||
−0.306791 | + | 0.951777i | \(0.599255\pi\) | |||||||
\(558\) | 11.8894 | 0.503320 | ||||||||
\(559\) | 12.7980 | 0.541297 | ||||||||
\(560\) | 4.17554 | 0.176449 | ||||||||
\(561\) | 3.71390 | 0.156801 | ||||||||
\(562\) | −2.77287 | −0.116966 | ||||||||
\(563\) | 10.5340 | 0.443956 | 0.221978 | − | 0.975052i | \(-0.428749\pi\) | ||||
0.221978 | + | 0.975052i | \(0.428749\pi\) | |||||||
\(564\) | 4.06498 | 0.171167 | ||||||||
\(565\) | −24.4958 | −1.03055 | ||||||||
\(566\) | −9.23451 | −0.388156 | ||||||||
\(567\) | 13.5457 | 0.568867 | ||||||||
\(568\) | −7.57822 | −0.317975 | ||||||||
\(569\) | 10.3762 | 0.434993 | 0.217496 | − | 0.976061i | \(-0.430211\pi\) | ||||
0.217496 | + | 0.976061i | \(0.430211\pi\) | |||||||
\(570\) | −0.948410 | −0.0397245 | ||||||||
\(571\) | 33.2847 | 1.39292 | 0.696461 | − | 0.717594i | \(-0.254757\pi\) | ||||
0.696461 | + | 0.717594i | \(0.254757\pi\) | |||||||
\(572\) | 1.40268 | 0.0586489 | ||||||||
\(573\) | 20.7672 | 0.867561 | ||||||||
\(574\) | 10.0325 | 0.418748 | ||||||||
\(575\) | −23.7789 | −0.991648 | ||||||||
\(576\) | −2.40268 | −0.100112 | ||||||||
\(577\) | −2.93365 | −0.122129 | −0.0610647 | − | 0.998134i | \(-0.519450\pi\) | ||||
−0.0610647 | + | 0.998134i | \(0.519450\pi\) | |||||||
\(578\) | 6.09146 | 0.253371 | ||||||||
\(579\) | 14.3494 | 0.596341 | ||||||||
\(580\) | 9.85695 | 0.409287 | ||||||||
\(581\) | 36.3055 | 1.50621 | ||||||||
\(582\) | 1.81708 | 0.0753202 | ||||||||
\(583\) | 4.45427 | 0.184477 | ||||||||
\(584\) | −10.0650 | −0.416492 | ||||||||
\(585\) | 4.13567 | 0.170989 | ||||||||
\(586\) | 17.7390 | 0.732792 | ||||||||
\(587\) | 8.90854 | 0.367695 | 0.183847 | − | 0.982955i | \(-0.441145\pi\) | ||||
0.183847 | + | 0.982955i | \(0.441145\pi\) | |||||||
\(588\) | 3.53835 | 0.145919 | ||||||||
\(589\) | 4.94841 | 0.203896 | ||||||||
\(590\) | −17.8171 | −0.733517 | ||||||||
\(591\) | 11.5223 | 0.473964 | ||||||||
\(592\) | 2.35109 | 0.0966292 | ||||||||
\(593\) | 16.3129 | 0.669890 | 0.334945 | − | 0.942238i | \(-0.391282\pi\) | ||||
0.334945 | + | 0.942238i | \(0.391282\pi\) | |||||||
\(594\) | 4.17554 | 0.171325 | ||||||||
\(595\) | −20.0650 | −0.822584 | ||||||||
\(596\) | 18.3511 | 0.751690 | ||||||||
\(597\) | 11.7139 | 0.479418 | ||||||||
\(598\) | −9.54573 | −0.390354 | ||||||||
\(599\) | 40.9826 | 1.67450 | 0.837251 | − | 0.546818i | \(-0.184161\pi\) | ||||
0.837251 | + | 0.546818i | \(0.184161\pi\) | |||||||
\(600\) | −2.70050 | −0.110248 | ||||||||
\(601\) | 0.349413 | 0.0142528 | 0.00712642 | − | 0.999975i | \(-0.497732\pi\) | ||||
0.00712642 | + | 0.999975i | \(0.497732\pi\) | |||||||
\(602\) | −31.0459 | −1.26534 | ||||||||
\(603\) | −8.17554 | −0.332934 | ||||||||
\(604\) | −7.64891 | −0.311230 | ||||||||
\(605\) | 1.22713 | 0.0498901 | ||||||||
\(606\) | 10.8703 | 0.441577 | ||||||||
\(607\) | 5.56049 | 0.225693 | 0.112847 | − | 0.993612i | \(-0.464003\pi\) | ||||
0.112847 | + | 0.993612i | \(0.464003\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 21.1240 | 0.855986 | ||||||||
\(610\) | 2.45427 | 0.0993704 | ||||||||
\(611\) | −7.37757 | −0.298464 | ||||||||
\(612\) | 11.5457 | 0.466709 | ||||||||
\(613\) | −19.7407 | −0.797319 | −0.398659 | − | 0.917099i | \(-0.630524\pi\) | ||||
−0.398659 | + | 0.917099i | \(0.630524\pi\) | |||||||
\(614\) | 20.9735 | 0.846422 | ||||||||
\(615\) | 2.79630 | 0.112758 | ||||||||
\(616\) | −3.40268 | −0.137098 | ||||||||
\(617\) | 10.5973 | 0.426632 | 0.213316 | − | 0.976983i | \(-0.431574\pi\) | ||||
0.213316 | + | 0.976983i | \(0.431574\pi\) | |||||||
\(618\) | −12.0399 | −0.484315 | ||||||||
\(619\) | 4.22112 | 0.169661 | 0.0848306 | − | 0.996395i | \(-0.472965\pi\) | ||||
0.0848306 | + | 0.996395i | \(0.472965\pi\) | |||||||
\(620\) | −6.07236 | −0.243872 | ||||||||
\(621\) | −28.4161 | −1.14030 | ||||||||
\(622\) | −3.36281 | −0.134836 | ||||||||
\(623\) | 51.0003 | 2.04328 | ||||||||
\(624\) | −1.08408 | −0.0433980 | ||||||||
\(625\) | 4.67973 | 0.187189 | ||||||||
\(626\) | −4.94103 | −0.197483 | ||||||||
\(627\) | 0.772866 | 0.0308653 | ||||||||
\(628\) | 8.38358 | 0.334541 | ||||||||
\(629\) | −11.2978 | −0.450474 | ||||||||
\(630\) | −10.0325 | −0.399704 | ||||||||
\(631\) | 13.6905 | 0.545009 | 0.272504 | − | 0.962155i | \(-0.412148\pi\) | ||||
0.272504 | + | 0.962155i | \(0.412148\pi\) | |||||||
\(632\) | −3.71390 | −0.147731 | ||||||||
\(633\) | 8.62243 | 0.342711 | ||||||||
\(634\) | 14.2861 | 0.567374 | ||||||||
\(635\) | 14.3745 | 0.570436 | ||||||||
\(636\) | −3.44255 | −0.136506 | ||||||||
\(637\) | −6.42178 | −0.254440 | ||||||||
\(638\) | −8.03249 | −0.318009 | ||||||||
\(639\) | 18.2080 | 0.720299 | ||||||||
\(640\) | 1.22713 | 0.0485067 | ||||||||
\(641\) | −42.9883 | −1.69794 | −0.848968 | − | 0.528445i | \(-0.822775\pi\) | ||||
−0.848968 | + | 0.528445i | \(0.822775\pi\) | |||||||
\(642\) | −3.36281 | −0.132719 | ||||||||
\(643\) | 16.3658 | 0.645406 | 0.322703 | − | 0.946500i | \(-0.395408\pi\) | ||||
0.322703 | + | 0.946500i | \(0.395408\pi\) | |||||||
\(644\) | 23.1564 | 0.912492 | ||||||||
\(645\) | −8.65325 | −0.340721 | ||||||||
\(646\) | 4.80536 | 0.189064 | ||||||||
\(647\) | 39.9886 | 1.57211 | 0.786057 | − | 0.618154i | \(-0.212119\pi\) | ||||
0.786057 | + | 0.618154i | \(0.212119\pi\) | |||||||
\(648\) | 3.98090 | 0.156385 | ||||||||
\(649\) | 14.5193 | 0.569931 | ||||||||
\(650\) | 4.90116 | 0.192239 | ||||||||
\(651\) | −13.0134 | −0.510035 | ||||||||
\(652\) | −14.2479 | −0.557991 | ||||||||
\(653\) | −37.5976 | −1.47131 | −0.735655 | − | 0.677357i | \(-0.763125\pi\) | ||||
−0.735655 | + | 0.677357i | \(0.763125\pi\) | |||||||
\(654\) | 4.63719 | 0.181329 | ||||||||
\(655\) | 2.27872 | 0.0890371 | ||||||||
\(656\) | 2.94841 | 0.115116 | ||||||||
\(657\) | 24.1829 | 0.943466 | ||||||||
\(658\) | 17.8968 | 0.697691 | ||||||||
\(659\) | −11.5075 | −0.448270 | −0.224135 | − | 0.974558i | \(-0.571956\pi\) | ||||
−0.224135 | + | 0.974558i | \(0.571956\pi\) | |||||||
\(660\) | −0.948410 | −0.0369168 | ||||||||
\(661\) | −29.2362 | −1.13716 | −0.568578 | − | 0.822629i | \(-0.692506\pi\) | ||||
−0.568578 | + | 0.822629i | \(0.692506\pi\) | |||||||
\(662\) | −31.9293 | −1.24097 | ||||||||
\(663\) | 5.20940 | 0.202316 | ||||||||
\(664\) | 10.6697 | 0.414064 | ||||||||
\(665\) | −4.17554 | −0.161921 | ||||||||
\(666\) | −5.64891 | −0.218891 | ||||||||
\(667\) | 54.6640 | 2.11660 | ||||||||
\(668\) | −10.8703 | −0.420586 | ||||||||
\(669\) | 1.24487 | 0.0481293 | ||||||||
\(670\) | 4.17554 | 0.161315 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 2.62981 | 0.101447 | ||||||||
\(673\) | −47.0784 | −1.81474 | −0.907369 | − | 0.420335i | \(-0.861913\pi\) | ||||
−0.907369 | + | 0.420335i | \(0.861913\pi\) | |||||||
\(674\) | −8.84523 | −0.340706 | ||||||||
\(675\) | 14.5899 | 0.561567 | ||||||||
\(676\) | −11.0325 | −0.424327 | ||||||||
\(677\) | 43.2539 | 1.66238 | 0.831192 | − | 0.555986i | \(-0.187659\pi\) | ||||
0.831192 | + | 0.555986i | \(0.187659\pi\) | |||||||
\(678\) | −15.4278 | −0.592501 | ||||||||
\(679\) | 8.00000 | 0.307012 | ||||||||
\(680\) | −5.89682 | −0.226133 | ||||||||
\(681\) | −12.9588 | −0.496581 | ||||||||
\(682\) | 4.94841 | 0.189484 | ||||||||
\(683\) | 34.8556 | 1.33371 | 0.666856 | − | 0.745187i | \(-0.267640\pi\) | ||||
0.666856 | + | 0.745187i | \(0.267640\pi\) | |||||||
\(684\) | 2.40268 | 0.0918687 | ||||||||
\(685\) | 13.0043 | 0.496870 | ||||||||
\(686\) | −8.24053 | −0.314625 | ||||||||
\(687\) | −6.61505 | −0.252380 | ||||||||
\(688\) | −9.12395 | −0.347847 | ||||||||
\(689\) | 6.24791 | 0.238026 | ||||||||
\(690\) | 6.45427 | 0.245710 | ||||||||
\(691\) | 28.4811 | 1.08347 | 0.541735 | − | 0.840549i | \(-0.317768\pi\) | ||||
0.541735 | + | 0.840549i | \(0.317768\pi\) | |||||||
\(692\) | 3.39530 | 0.129070 | ||||||||
\(693\) | 8.17554 | 0.310563 | ||||||||
\(694\) | 5.27439 | 0.200213 | ||||||||
\(695\) | 18.0814 | 0.685867 | ||||||||
\(696\) | 6.20804 | 0.235315 | ||||||||
\(697\) | −14.1682 | −0.536657 | ||||||||
\(698\) | −10.9085 | −0.412894 | ||||||||
\(699\) | 4.20636 | 0.159099 | ||||||||
\(700\) | −11.8894 | −0.449379 | ||||||||
\(701\) | 12.8703 | 0.486106 | 0.243053 | − | 0.970013i | \(-0.421851\pi\) | ||||
0.243053 | + | 0.970013i | \(0.421851\pi\) | |||||||
\(702\) | 5.85695 | 0.221056 | ||||||||
\(703\) | −2.35109 | −0.0886730 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 4.98828 | 0.187870 | ||||||||
\(706\) | −22.1300 | −0.832872 | ||||||||
\(707\) | 47.8586 | 1.79991 | ||||||||
\(708\) | −11.2214 | −0.421727 | ||||||||
\(709\) | 1.41744 | 0.0532330 | 0.0266165 | − | 0.999646i | \(-0.491527\pi\) | ||||
0.0266165 | + | 0.999646i | \(0.491527\pi\) | |||||||
\(710\) | −9.29950 | −0.349004 | ||||||||
\(711\) | 8.92330 | 0.334650 | ||||||||
\(712\) | 14.9883 | 0.561710 | ||||||||
\(713\) | −33.6757 | −1.26116 | ||||||||
\(714\) | −12.6372 | −0.472935 | ||||||||
\(715\) | 1.72128 | 0.0643721 | ||||||||
\(716\) | −0.311217 | −0.0116307 | ||||||||
\(717\) | 8.72729 | 0.325927 | ||||||||
\(718\) | −16.3910 | −0.611705 | ||||||||
\(719\) | −31.1564 | −1.16194 | −0.580970 | − | 0.813925i | \(-0.697327\pi\) | ||||
−0.580970 | + | 0.813925i | \(0.697327\pi\) | |||||||
\(720\) | −2.94841 | −0.109881 | ||||||||
\(721\) | −53.0077 | −1.97411 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 8.81844 | 0.327961 | ||||||||
\(724\) | −15.3246 | −0.569535 | ||||||||
\(725\) | −28.0667 | −1.04237 | ||||||||
\(726\) | 0.772866 | 0.0286837 | ||||||||
\(727\) | −8.57221 | −0.317926 | −0.158963 | − | 0.987285i | \(-0.550815\pi\) | ||||
−0.158963 | + | 0.987285i | \(0.550815\pi\) | |||||||
\(728\) | −4.77287 | −0.176894 | ||||||||
\(729\) | 0.116574 | 0.00431757 | ||||||||
\(730\) | −12.3511 | −0.457134 | ||||||||
\(731\) | 43.8439 | 1.62162 | ||||||||
\(732\) | 1.54573 | 0.0571319 | ||||||||
\(733\) | 44.6787 | 1.65025 | 0.825123 | − | 0.564952i | \(-0.191105\pi\) | ||||
0.825123 | + | 0.564952i | \(0.191105\pi\) | |||||||
\(734\) | −32.3511 | −1.19410 | ||||||||
\(735\) | 4.34203 | 0.160158 | ||||||||
\(736\) | 6.80536 | 0.250849 | ||||||||
\(737\) | −3.40268 | −0.125339 | ||||||||
\(738\) | −7.08408 | −0.260769 | ||||||||
\(739\) | 29.4898 | 1.08480 | 0.542400 | − | 0.840120i | \(-0.317516\pi\) | ||||
0.542400 | + | 0.840120i | \(0.317516\pi\) | |||||||
\(740\) | 2.88510 | 0.106058 | ||||||||
\(741\) | 1.08408 | 0.0398248 | ||||||||
\(742\) | −15.1564 | −0.556411 | ||||||||
\(743\) | −13.2596 | −0.486449 | −0.243224 | − | 0.969970i | \(-0.578205\pi\) | ||||
−0.243224 | + | 0.969970i | \(0.578205\pi\) | |||||||
\(744\) | −3.82446 | −0.140211 | ||||||||
\(745\) | 22.5193 | 0.825042 | ||||||||
\(746\) | 17.5782 | 0.643584 | ||||||||
\(747\) | −25.6358 | −0.937966 | ||||||||
\(748\) | 4.80536 | 0.175701 | ||||||||
\(749\) | −14.8054 | −0.540976 | ||||||||
\(750\) | −8.05593 | −0.294161 | ||||||||
\(751\) | −10.1829 | −0.371580 | −0.185790 | − | 0.982589i | \(-0.559484\pi\) | ||||
−0.185790 | + | 0.982589i | \(0.559484\pi\) | |||||||
\(752\) | 5.25963 | 0.191799 | ||||||||
\(753\) | −9.27439 | −0.337977 | ||||||||
\(754\) | −11.2670 | −0.410320 | ||||||||
\(755\) | −9.38624 | −0.341600 | ||||||||
\(756\) | −14.2080 | −0.516741 | ||||||||
\(757\) | 40.1122 | 1.45790 | 0.728952 | − | 0.684565i | \(-0.240008\pi\) | ||||
0.728952 | + | 0.684565i | \(0.240008\pi\) | |||||||
\(758\) | 8.93365 | 0.324485 | ||||||||
\(759\) | −5.25963 | −0.190912 | ||||||||
\(760\) | −1.22713 | −0.0445128 | ||||||||
\(761\) | −38.7819 | −1.40584 | −0.702922 | − | 0.711267i | \(-0.748122\pi\) | ||||
−0.702922 | + | 0.711267i | \(0.748122\pi\) | |||||||
\(762\) | 9.05327 | 0.327965 | ||||||||
\(763\) | 20.4161 | 0.739111 | ||||||||
\(764\) | 26.8703 | 0.972135 | ||||||||
\(765\) | 14.1682 | 0.512251 | ||||||||
\(766\) | −16.0399 | −0.579544 | ||||||||
\(767\) | 20.3658 | 0.735368 | ||||||||
\(768\) | 0.772866 | 0.0278884 | ||||||||
\(769\) | 8.15340 | 0.294019 | 0.147010 | − | 0.989135i | \(-0.453035\pi\) | ||||
0.147010 | + | 0.989135i | \(0.453035\pi\) | |||||||
\(770\) | −4.17554 | −0.150476 | ||||||||
\(771\) | 18.7290 | 0.674507 | ||||||||
\(772\) | 18.5665 | 0.668223 | ||||||||
\(773\) | −24.3893 | −0.877222 | −0.438611 | − | 0.898677i | \(-0.644529\pi\) | ||||
−0.438611 | + | 0.898677i | \(0.644529\pi\) | |||||||
\(774\) | 21.9219 | 0.787968 | ||||||||
\(775\) | 17.2904 | 0.621091 | ||||||||
\(776\) | 2.35109 | 0.0843992 | ||||||||
\(777\) | 6.18292 | 0.221811 | ||||||||
\(778\) | 17.2271 | 0.617623 | ||||||||
\(779\) | −2.94841 | −0.105638 | ||||||||
\(780\) | −1.33031 | −0.0476329 | ||||||||
\(781\) | 7.57822 | 0.271170 | ||||||||
\(782\) | −32.7022 | −1.16943 | ||||||||
\(783\) | −33.5400 | −1.19862 | ||||||||
\(784\) | 4.57822 | 0.163508 | ||||||||
\(785\) | 10.2878 | 0.367187 | ||||||||
\(786\) | 1.43517 | 0.0511909 | ||||||||
\(787\) | −46.3779 | −1.65319 | −0.826596 | − | 0.562795i | \(-0.809726\pi\) | ||||
−0.826596 | + | 0.562795i | \(0.809726\pi\) | |||||||
\(788\) | 14.9085 | 0.531095 | ||||||||
\(789\) | 15.8951 | 0.565882 | ||||||||
\(790\) | −4.55745 | −0.162147 | ||||||||
\(791\) | −67.9236 | −2.41509 | ||||||||
\(792\) | 2.40268 | 0.0853755 | ||||||||
\(793\) | −2.80536 | −0.0996212 | ||||||||
\(794\) | 15.0784 | 0.535112 | ||||||||
\(795\) | −4.22447 | −0.149827 | ||||||||
\(796\) | 15.1564 | 0.537206 | ||||||||
\(797\) | 3.89682 | 0.138032 | 0.0690162 | − | 0.997616i | \(-0.478014\pi\) | ||||
0.0690162 | + | 0.997616i | \(0.478014\pi\) | |||||||
\(798\) | −2.62981 | −0.0930944 | ||||||||
\(799\) | −25.2744 | −0.894144 | ||||||||
\(800\) | −3.49414 | −0.123537 | ||||||||
\(801\) | −36.0120 | −1.27242 | ||||||||
\(802\) | −13.1564 | −0.464570 | ||||||||
\(803\) | 10.0650 | 0.355186 | ||||||||
\(804\) | 2.62981 | 0.0927464 | ||||||||
\(805\) | 28.4161 | 1.00153 | ||||||||
\(806\) | 6.94103 | 0.244487 | ||||||||
\(807\) | −1.05327 | −0.0370767 | ||||||||
\(808\) | 14.0650 | 0.494804 | ||||||||
\(809\) | −43.3896 | −1.52550 | −0.762748 | − | 0.646695i | \(-0.776151\pi\) | ||||
−0.762748 | + | 0.646695i | \(0.776151\pi\) | |||||||
\(810\) | 4.88510 | 0.171645 | ||||||||
\(811\) | −12.9233 | −0.453798 | −0.226899 | − | 0.973918i | \(-0.572859\pi\) | ||||
−0.226899 | + | 0.973918i | \(0.572859\pi\) | |||||||
\(812\) | 27.3320 | 0.959165 | ||||||||
\(813\) | −17.9276 | −0.628750 | ||||||||
\(814\) | −2.35109 | −0.0824056 | ||||||||
\(815\) | −17.4841 | −0.612441 | ||||||||
\(816\) | −3.71390 | −0.130012 | ||||||||
\(817\) | 9.12395 | 0.319207 | ||||||||
\(818\) | −16.3836 | −0.572838 | ||||||||
\(819\) | 11.4677 | 0.400713 | ||||||||
\(820\) | 3.61810 | 0.126349 | ||||||||
\(821\) | −36.5842 | −1.27680 | −0.638399 | − | 0.769705i | \(-0.720403\pi\) | ||||
−0.638399 | + | 0.769705i | \(0.720403\pi\) | |||||||
\(822\) | 8.19030 | 0.285670 | ||||||||
\(823\) | −21.6107 | −0.753302 | −0.376651 | − | 0.926355i | \(-0.622924\pi\) | ||||
−0.376651 | + | 0.926355i | \(0.622924\pi\) | |||||||
\(824\) | −15.5782 | −0.542693 | ||||||||
\(825\) | 2.70050 | 0.0940194 | ||||||||
\(826\) | −49.4044 | −1.71900 | ||||||||
\(827\) | −34.8851 | −1.21307 | −0.606537 | − | 0.795055i | \(-0.707442\pi\) | ||||
−0.606537 | + | 0.795055i | \(0.707442\pi\) | |||||||
\(828\) | −16.3511 | −0.568240 | ||||||||
\(829\) | 31.7407 | 1.10240 | 0.551200 | − | 0.834373i | \(-0.314170\pi\) | ||||
0.551200 | + | 0.834373i | \(0.314170\pi\) | |||||||
\(830\) | 13.0931 | 0.454469 | ||||||||
\(831\) | 23.9886 | 0.832155 | ||||||||
\(832\) | −1.40268 | −0.0486291 | ||||||||
\(833\) | −22.0000 | −0.762255 | ||||||||
\(834\) | 11.3879 | 0.394331 | ||||||||
\(835\) | −13.3394 | −0.461628 | ||||||||
\(836\) | 1.00000 | 0.0345857 | ||||||||
\(837\) | 20.6623 | 0.714194 | ||||||||
\(838\) | 1.12966 | 0.0390234 | ||||||||
\(839\) | 13.4603 | 0.464701 | 0.232350 | − | 0.972632i | \(-0.425358\pi\) | ||||
0.232350 | + | 0.972632i | \(0.425358\pi\) | |||||||
\(840\) | 3.22713 | 0.111347 | ||||||||
\(841\) | 35.5209 | 1.22486 | ||||||||
\(842\) | −2.63719 | −0.0908837 | ||||||||
\(843\) | −2.14305 | −0.0738106 | ||||||||
\(844\) | 11.1564 | 0.384021 | ||||||||
\(845\) | −13.5384 | −0.465733 | ||||||||
\(846\) | −12.6372 | −0.434476 | ||||||||
\(847\) | 3.40268 | 0.116917 | ||||||||
\(848\) | −4.45427 | −0.152960 | ||||||||
\(849\) | −7.13704 | −0.244943 | ||||||||
\(850\) | 16.7906 | 0.575913 | ||||||||
\(851\) | 16.0000 | 0.548473 | ||||||||
\(852\) | −5.85695 | −0.200656 | ||||||||
\(853\) | 36.2981 | 1.24282 | 0.621412 | − | 0.783484i | \(-0.286559\pi\) | ||||
0.621412 | + | 0.783484i | \(0.286559\pi\) | |||||||
\(854\) | 6.80536 | 0.232875 | ||||||||
\(855\) | 2.94841 | 0.100833 | ||||||||
\(856\) | −4.35109 | −0.148717 | ||||||||
\(857\) | −43.8569 | −1.49812 | −0.749062 | − | 0.662499i | \(-0.769496\pi\) | ||||
−0.749062 | + | 0.662499i | \(0.769496\pi\) | |||||||
\(858\) | 1.08408 | 0.0370100 | ||||||||
\(859\) | −41.1980 | −1.40566 | −0.702829 | − | 0.711359i | \(-0.748080\pi\) | ||||
−0.702829 | + | 0.711359i | \(0.748080\pi\) | |||||||
\(860\) | −11.1963 | −0.381791 | ||||||||
\(861\) | 7.75377 | 0.264248 | ||||||||
\(862\) | −28.4958 | −0.970571 | ||||||||
\(863\) | −24.8720 | −0.846653 | −0.423327 | − | 0.905977i | \(-0.639138\pi\) | ||||
−0.423327 | + | 0.905977i | \(0.639138\pi\) | |||||||
\(864\) | −4.17554 | −0.142055 | ||||||||
\(865\) | 4.16649 | 0.141665 | ||||||||
\(866\) | −37.5075 | −1.27456 | ||||||||
\(867\) | 4.70788 | 0.159888 | ||||||||
\(868\) | −16.8378 | −0.571514 | ||||||||
\(869\) | 3.71390 | 0.125985 | ||||||||
\(870\) | 7.61810 | 0.258278 | ||||||||
\(871\) | −4.77287 | −0.161722 | ||||||||
\(872\) | 6.00000 | 0.203186 | ||||||||
\(873\) | −5.64891 | −0.191187 | ||||||||
\(874\) | −6.80536 | −0.230195 | ||||||||
\(875\) | −35.4677 | −1.19903 | ||||||||
\(876\) | −7.77888 | −0.262824 | ||||||||
\(877\) | 39.8911 | 1.34703 | 0.673514 | − | 0.739175i | \(-0.264784\pi\) | ||||
0.673514 | + | 0.739175i | \(0.264784\pi\) | |||||||
\(878\) | −32.1300 | −1.08433 | ||||||||
\(879\) | 13.7099 | 0.462422 | ||||||||
\(880\) | −1.22713 | −0.0413667 | ||||||||
\(881\) | −2.88343 | −0.0971451 | −0.0485725 | − | 0.998820i | \(-0.515467\pi\) | ||||
−0.0485725 | + | 0.998820i | \(0.515467\pi\) | |||||||
\(882\) | −11.0000 | −0.370389 | ||||||||
\(883\) | −4.27134 | −0.143742 | −0.0718711 | − | 0.997414i | \(-0.522897\pi\) | ||||
−0.0718711 | + | 0.997414i | \(0.522897\pi\) | |||||||
\(884\) | 6.74037 | 0.226703 | ||||||||
\(885\) | −13.7702 | −0.462880 | ||||||||
\(886\) | 33.0385 | 1.10995 | ||||||||
\(887\) | 22.3129 | 0.749194 | 0.374597 | − | 0.927188i | \(-0.377781\pi\) | ||||
0.374597 | + | 0.927188i | \(0.377781\pi\) | |||||||
\(888\) | 1.81708 | 0.0609771 | ||||||||
\(889\) | 39.8586 | 1.33682 | ||||||||
\(890\) | 18.3926 | 0.616523 | ||||||||
\(891\) | −3.98090 | −0.133365 | ||||||||
\(892\) | 1.61072 | 0.0539307 | ||||||||
\(893\) | −5.25963 | −0.176007 | ||||||||
\(894\) | 14.1829 | 0.474348 | ||||||||
\(895\) | −0.381905 | −0.0127657 | ||||||||
\(896\) | 3.40268 | 0.113676 | ||||||||
\(897\) | −7.37757 | −0.246330 | ||||||||
\(898\) | 7.88206 | 0.263028 | ||||||||
\(899\) | −39.7481 | −1.32567 | ||||||||
\(900\) | 8.39530 | 0.279843 | ||||||||
\(901\) | 21.4044 | 0.713082 | ||||||||
\(902\) | −2.94841 | −0.0981713 | ||||||||
\(903\) | −23.9943 | −0.798480 | ||||||||
\(904\) | −19.9618 | −0.663920 | ||||||||
\(905\) | −18.8054 | −0.625111 | ||||||||
\(906\) | −5.91158 | −0.196399 | ||||||||
\(907\) | −35.5578 | −1.18068 | −0.590338 | − | 0.807156i | \(-0.701006\pi\) | ||||
−0.590338 | + | 0.807156i | \(0.701006\pi\) | |||||||
\(908\) | −16.7672 | −0.556438 | ||||||||
\(909\) | −33.7936 | −1.12086 | ||||||||
\(910\) | −5.85695 | −0.194156 | ||||||||
\(911\) | −49.1980 | −1.63000 | −0.815001 | − | 0.579459i | \(-0.803264\pi\) | ||||
−0.815001 | + | 0.579459i | \(0.803264\pi\) | |||||||
\(912\) | −0.772866 | −0.0255921 | ||||||||
\(913\) | −10.6697 | −0.353115 | ||||||||
\(914\) | 24.9353 | 0.824787 | ||||||||
\(915\) | 1.89682 | 0.0627069 | ||||||||
\(916\) | −8.55913 | −0.282801 | ||||||||
\(917\) | 6.31860 | 0.208658 | ||||||||
\(918\) | 20.0650 | 0.662243 | ||||||||
\(919\) | −8.47200 | −0.279466 | −0.139733 | − | 0.990189i | \(-0.544624\pi\) | ||||
−0.139733 | + | 0.990189i | \(0.544624\pi\) | |||||||
\(920\) | 8.35109 | 0.275327 | ||||||||
\(921\) | 16.2097 | 0.534128 | ||||||||
\(922\) | −26.6874 | −0.878903 | ||||||||
\(923\) | 10.6298 | 0.349885 | ||||||||
\(924\) | −2.62981 | −0.0865145 | ||||||||
\(925\) | −8.21504 | −0.270109 | ||||||||
\(926\) | −32.7022 | −1.07466 | ||||||||
\(927\) | 37.4295 | 1.22934 | ||||||||
\(928\) | 8.03249 | 0.263679 | ||||||||
\(929\) | −16.0017 | −0.524998 | −0.262499 | − | 0.964932i | \(-0.584547\pi\) | ||||
−0.262499 | + | 0.964932i | \(0.584547\pi\) | |||||||
\(930\) | −4.69312 | −0.153894 | ||||||||
\(931\) | −4.57822 | −0.150045 | ||||||||
\(932\) | 5.44255 | 0.178277 | ||||||||
\(933\) | −2.59900 | −0.0850874 | ||||||||
\(934\) | 11.3776 | 0.372285 | ||||||||
\(935\) | 5.89682 | 0.192847 | ||||||||
\(936\) | 3.37019 | 0.110158 | ||||||||
\(937\) | −15.9766 | −0.521932 | −0.260966 | − | 0.965348i | \(-0.584041\pi\) | ||||
−0.260966 | + | 0.965348i | \(0.584041\pi\) | |||||||
\(938\) | 11.5782 | 0.378042 | ||||||||
\(939\) | −3.81875 | −0.124620 | ||||||||
\(940\) | 6.45427 | 0.210515 | ||||||||
\(941\) | −21.0915 | −0.687562 | −0.343781 | − | 0.939050i | \(-0.611708\pi\) | ||||
−0.343781 | + | 0.939050i | \(0.611708\pi\) | |||||||
\(942\) | 6.47938 | 0.211110 | ||||||||
\(943\) | 20.0650 | 0.653406 | ||||||||
\(944\) | −14.5193 | −0.472561 | ||||||||
\(945\) | −17.4352 | −0.567166 | ||||||||
\(946\) | 9.12395 | 0.296645 | ||||||||
\(947\) | 20.9735 | 0.681548 | 0.340774 | − | 0.940145i | \(-0.389311\pi\) | ||||
0.340774 | + | 0.940145i | \(0.389311\pi\) | |||||||
\(948\) | −2.87034 | −0.0932244 | ||||||||
\(949\) | 14.1179 | 0.458288 | ||||||||
\(950\) | 3.49414 | 0.113365 | ||||||||
\(951\) | 11.0412 | 0.358037 | ||||||||
\(952\) | −16.3511 | −0.529942 | ||||||||
\(953\) | 3.27439 | 0.106068 | 0.0530339 | − | 0.998593i | \(-0.483111\pi\) | ||||
0.0530339 | + | 0.998593i | \(0.483111\pi\) | |||||||
\(954\) | 10.7022 | 0.346496 | ||||||||
\(955\) | 32.9735 | 1.06700 | ||||||||
\(956\) | 11.2921 | 0.365213 | ||||||||
\(957\) | −6.20804 | −0.200677 | ||||||||
\(958\) | −12.5973 | −0.407001 | ||||||||
\(959\) | 36.0593 | 1.16441 | ||||||||
\(960\) | 0.948410 | 0.0306098 | ||||||||
\(961\) | −6.51324 | −0.210104 | ||||||||
\(962\) | −3.29782 | −0.106326 | ||||||||
\(963\) | 10.4543 | 0.336884 | ||||||||
\(964\) | 11.4101 | 0.367493 | ||||||||
\(965\) | 22.7836 | 0.733430 | ||||||||
\(966\) | 17.8968 | 0.575821 | ||||||||
\(967\) | −29.2744 | −0.941401 | −0.470700 | − | 0.882293i | \(-0.655999\pi\) | ||||
−0.470700 | + | 0.882293i | \(0.655999\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 3.71390 | 0.119308 | ||||||||
\(970\) | 2.88510 | 0.0926350 | ||||||||
\(971\) | −38.3836 | −1.23179 | −0.615894 | − | 0.787829i | \(-0.711205\pi\) | ||||
−0.615894 | + | 0.787829i | \(0.711205\pi\) | |||||||
\(972\) | 15.6033 | 0.500477 | ||||||||
\(973\) | 50.1373 | 1.60733 | ||||||||
\(974\) | 9.69616 | 0.310685 | ||||||||
\(975\) | 3.78794 | 0.121311 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 10.9233 | 0.349467 | 0.174734 | − | 0.984616i | \(-0.444094\pi\) | ||||
0.174734 | + | 0.984616i | \(0.444094\pi\) | |||||||
\(978\) | −11.0117 | −0.352116 | ||||||||
\(979\) | −14.9883 | −0.479028 | ||||||||
\(980\) | 5.61810 | 0.179463 | ||||||||
\(981\) | −14.4161 | −0.460270 | ||||||||
\(982\) | −11.7538 | −0.375078 | ||||||||
\(983\) | −32.1196 | −1.02446 | −0.512228 | − | 0.858849i | \(-0.671180\pi\) | ||||
−0.512228 | + | 0.858849i | \(0.671180\pi\) | |||||||
\(984\) | 2.27872 | 0.0726431 | ||||||||
\(985\) | 18.2948 | 0.582920 | ||||||||
\(986\) | −38.5990 | −1.22924 | ||||||||
\(987\) | 13.8318 | 0.440272 | ||||||||
\(988\) | 1.40268 | 0.0446252 | ||||||||
\(989\) | −62.0918 | −1.97440 | ||||||||
\(990\) | 2.94841 | 0.0937066 | ||||||||
\(991\) | 4.37620 | 0.139015 | 0.0695073 | − | 0.997581i | \(-0.477857\pi\) | ||||
0.0695073 | + | 0.997581i | \(0.477857\pi\) | |||||||
\(992\) | −4.94841 | −0.157112 | ||||||||
\(993\) | −24.6771 | −0.783103 | ||||||||
\(994\) | −25.7863 | −0.817890 | ||||||||
\(995\) | 18.5990 | 0.589628 | ||||||||
\(996\) | 8.24623 | 0.261292 | ||||||||
\(997\) | −8.37788 | −0.265330 | −0.132665 | − | 0.991161i | \(-0.542353\pi\) | ||||
−0.132665 | + | 0.991161i | \(0.542353\pi\) | |||||||
\(998\) | 26.6640 | 0.844034 | ||||||||
\(999\) | −9.81708 | −0.310599 |
(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 | 418.2.a.h.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 3762.2.a.bd.1.2 | 3 | |||
4.3 | odd | 2 | 3344.2.a.p.1.2 | 3 | |||
11.10 | odd | 2 | 4598.2.a.bm.1.2 | 3 | |||
19.18 | odd | 2 | 7942.2.a.bc.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.a.h.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3344.2.a.p.1.2 | 3 | 4.3 | odd | 2 | |||
3762.2.a.bd.1.2 | 3 | 3.2 | odd | 2 | |||
4598.2.a.bm.1.2 | 3 | 11.10 | odd | 2 | |||
7942.2.a.bc.1.2 | 3 | 19.18 | odd | 2 |