Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.121819537.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 25x^{4} + 55x^{3} + 224x^{2} - 252x - 728 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(3.07801\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.80194 | 1.27416 | 0.637081 | − | 0.770797i | \(-0.280142\pi\) | ||||
0.637081 | + | 0.770797i | \(0.280142\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.24698 | 0.623490 | ||||||||
\(5\) | 2.07801 | 0.929313 | 0.464657 | − | 0.885491i | \(-0.346178\pi\) | ||||
0.464657 | + | 0.885491i | \(0.346178\pi\) | |||||||
\(6\) | −1.80194 | −0.735638 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.35690 | −0.479735 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.74444 | 1.18410 | ||||||||
\(11\) | −5.11428 | −1.54201 | −0.771007 | − | 0.636826i | \(-0.780247\pi\) | ||||
−0.771007 | + | 0.636826i | \(0.780247\pi\) | |||||||
\(12\) | −1.24698 | −0.359972 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.80194 | 0.481588 | ||||||||
\(15\) | −2.07801 | −0.536539 | ||||||||
\(16\) | −4.93900 | −1.23475 | ||||||||
\(17\) | −0.185116 | −0.0448972 | −0.0224486 | − | 0.999748i | \(-0.507146\pi\) | ||||
−0.0224486 | + | 0.999748i | \(0.507146\pi\) | |||||||
\(18\) | 1.80194 | 0.424721 | ||||||||
\(19\) | 0.591233 | 0.135638 | 0.0678191 | − | 0.997698i | \(-0.478396\pi\) | ||||
0.0678191 | + | 0.997698i | \(0.478396\pi\) | |||||||
\(20\) | 2.59123 | 0.579417 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −9.21562 | −1.96478 | ||||||||
\(23\) | −2.78930 | −0.581608 | −0.290804 | − | 0.956783i | \(-0.593923\pi\) | ||||
−0.290804 | + | 0.956783i | \(0.593923\pi\) | |||||||
\(24\) | 1.35690 | 0.276975 | ||||||||
\(25\) | −0.681883 | −0.136377 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.24698 | 0.235657 | ||||||||
\(29\) | −9.95951 | −1.84943 | −0.924717 | − | 0.380654i | \(-0.875699\pi\) | ||||
−0.924717 | + | 0.380654i | \(0.875699\pi\) | |||||||
\(30\) | −3.74444 | −0.683638 | ||||||||
\(31\) | −5.23122 | −0.939554 | −0.469777 | − | 0.882785i | \(-0.655666\pi\) | ||||
−0.469777 | + | 0.882785i | \(0.655666\pi\) | |||||||
\(32\) | −6.18598 | −1.09354 | ||||||||
\(33\) | 5.11428 | 0.890282 | ||||||||
\(34\) | −0.333567 | −0.0572063 | ||||||||
\(35\) | 2.07801 | 0.351247 | ||||||||
\(36\) | 1.24698 | 0.207830 | ||||||||
\(37\) | 2.97441 | 0.488990 | 0.244495 | − | 0.969651i | \(-0.421378\pi\) | ||||
0.244495 | + | 0.969651i | \(0.421378\pi\) | |||||||
\(38\) | 1.06537 | 0.172825 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.81964 | −0.445824 | ||||||||
\(41\) | 10.0533 | 1.57006 | 0.785030 | − | 0.619458i | \(-0.212648\pi\) | ||||
0.785030 | + | 0.619458i | \(0.212648\pi\) | |||||||
\(42\) | −1.80194 | −0.278045 | ||||||||
\(43\) | 5.25454 | 0.801310 | 0.400655 | − | 0.916229i | \(-0.368783\pi\) | ||||
0.400655 | + | 0.916229i | \(0.368783\pi\) | |||||||
\(44\) | −6.37741 | −0.961430 | ||||||||
\(45\) | 2.07801 | 0.309771 | ||||||||
\(46\) | −5.02614 | −0.741063 | ||||||||
\(47\) | −12.6067 | −1.83887 | −0.919437 | − | 0.393238i | \(-0.871355\pi\) | ||||
−0.919437 | + | 0.393238i | \(0.871355\pi\) | |||||||
\(48\) | 4.93900 | 0.712883 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.22871 | −0.173766 | ||||||||
\(51\) | 0.185116 | 0.0259214 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.51955 | −0.758168 | −0.379084 | − | 0.925362i | \(-0.623761\pi\) | ||||
−0.379084 | + | 0.925362i | \(0.623761\pi\) | |||||||
\(54\) | −1.80194 | −0.245213 | ||||||||
\(55\) | −10.6275 | −1.43301 | ||||||||
\(56\) | −1.35690 | −0.181323 | ||||||||
\(57\) | −0.591233 | −0.0783108 | ||||||||
\(58\) | −17.9464 | −2.35648 | ||||||||
\(59\) | −6.46823 | −0.842091 | −0.421046 | − | 0.907039i | \(-0.638337\pi\) | ||||
−0.421046 | + | 0.907039i | \(0.638337\pi\) | |||||||
\(60\) | −2.59123 | −0.334527 | ||||||||
\(61\) | 8.43351 | 1.07980 | 0.539900 | − | 0.841729i | \(-0.318462\pi\) | ||||
0.539900 | + | 0.841729i | \(0.318462\pi\) | |||||||
\(62\) | −9.42632 | −1.19714 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −1.26875 | −0.158594 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.21562 | 1.13436 | ||||||||
\(67\) | −9.58967 | −1.17156 | −0.585782 | − | 0.810468i | \(-0.699213\pi\) | ||||
−0.585782 | + | 0.810468i | \(0.699213\pi\) | |||||||
\(68\) | −0.230836 | −0.0279929 | ||||||||
\(69\) | 2.78930 | 0.335792 | ||||||||
\(70\) | 3.74444 | 0.447546 | ||||||||
\(71\) | 1.60894 | 0.190946 | 0.0954728 | − | 0.995432i | \(-0.469564\pi\) | ||||
0.0954728 | + | 0.995432i | \(0.469564\pi\) | |||||||
\(72\) | −1.35690 | −0.159912 | ||||||||
\(73\) | −9.17303 | −1.07362 | −0.536811 | − | 0.843702i | \(-0.680371\pi\) | ||||
−0.536811 | + | 0.843702i | \(0.680371\pi\) | |||||||
\(74\) | 5.35970 | 0.623053 | ||||||||
\(75\) | 0.681883 | 0.0787371 | ||||||||
\(76\) | 0.737256 | 0.0845691 | ||||||||
\(77\) | −5.11428 | −0.582827 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.42070 | 0.609876 | 0.304938 | − | 0.952372i | \(-0.401364\pi\) | ||||
0.304938 | + | 0.952372i | \(0.401364\pi\) | |||||||
\(80\) | −10.2633 | −1.14747 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 18.1154 | 2.00051 | ||||||||
\(83\) | −3.99899 | −0.438946 | −0.219473 | − | 0.975619i | \(-0.570434\pi\) | ||||
−0.219473 | + | 0.975619i | \(0.570434\pi\) | |||||||
\(84\) | −1.24698 | −0.136057 | ||||||||
\(85\) | −0.384672 | −0.0417235 | ||||||||
\(86\) | 9.46836 | 1.02100 | ||||||||
\(87\) | 9.95951 | 1.06777 | ||||||||
\(88\) | 6.93955 | 0.739758 | ||||||||
\(89\) | 9.63632 | 1.02145 | 0.510724 | − | 0.859745i | \(-0.329377\pi\) | ||||
0.510724 | + | 0.859745i | \(0.329377\pi\) | |||||||
\(90\) | 3.74444 | 0.394699 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.47819 | −0.362627 | ||||||||
\(93\) | 5.23122 | 0.542452 | ||||||||
\(94\) | −22.7165 | −2.34302 | ||||||||
\(95\) | 1.22859 | 0.126050 | ||||||||
\(96\) | 6.18598 | 0.631354 | ||||||||
\(97\) | 3.05048 | 0.309729 | 0.154864 | − | 0.987936i | \(-0.450506\pi\) | ||||
0.154864 | + | 0.987936i | \(0.450506\pi\) | |||||||
\(98\) | 1.80194 | 0.182023 | ||||||||
\(99\) | −5.11428 | −0.514005 | ||||||||
\(100\) | −0.850295 | −0.0850295 | ||||||||
\(101\) | −8.65561 | −0.861265 | −0.430633 | − | 0.902527i | \(-0.641710\pi\) | ||||
−0.430633 | + | 0.902527i | \(0.641710\pi\) | |||||||
\(102\) | 0.333567 | 0.0330281 | ||||||||
\(103\) | 14.0880 | 1.38813 | 0.694066 | − | 0.719911i | \(-0.255818\pi\) | ||||
0.694066 | + | 0.719911i | \(0.255818\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.07801 | −0.202793 | ||||||||
\(106\) | −9.94588 | −0.966029 | ||||||||
\(107\) | 4.66386 | 0.450873 | 0.225436 | − | 0.974258i | \(-0.427619\pi\) | ||||
0.225436 | + | 0.974258i | \(0.427619\pi\) | |||||||
\(108\) | −1.24698 | −0.119991 | ||||||||
\(109\) | 2.35477 | 0.225546 | 0.112773 | − | 0.993621i | \(-0.464027\pi\) | ||||
0.112773 | + | 0.993621i | \(0.464027\pi\) | |||||||
\(110\) | −19.1501 | −1.82589 | ||||||||
\(111\) | −2.97441 | −0.282319 | ||||||||
\(112\) | −4.93900 | −0.466692 | ||||||||
\(113\) | −6.58305 | −0.619281 | −0.309641 | − | 0.950854i | \(-0.600209\pi\) | ||||
−0.309641 | + | 0.950854i | \(0.600209\pi\) | |||||||
\(114\) | −1.06537 | −0.0997806 | ||||||||
\(115\) | −5.79618 | −0.540496 | ||||||||
\(116\) | −12.4193 | −1.15310 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.6553 | −1.07296 | ||||||||
\(119\) | −0.185116 | −0.0169695 | ||||||||
\(120\) | 2.81964 | 0.257397 | ||||||||
\(121\) | 15.1559 | 1.37781 | ||||||||
\(122\) | 15.1967 | 1.37584 | ||||||||
\(123\) | −10.0533 | −0.906474 | ||||||||
\(124\) | −6.52322 | −0.585802 | ||||||||
\(125\) | −11.8070 | −1.05605 | ||||||||
\(126\) | 1.80194 | 0.160529 | ||||||||
\(127\) | −5.34744 | −0.474509 | −0.237254 | − | 0.971448i | \(-0.576247\pi\) | ||||
−0.237254 | + | 0.971448i | \(0.576247\pi\) | |||||||
\(128\) | 10.0858 | 0.891463 | ||||||||
\(129\) | −5.25454 | −0.462637 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.8419 | −1.47148 | −0.735742 | − | 0.677262i | \(-0.763166\pi\) | ||||
−0.735742 | + | 0.677262i | \(0.763166\pi\) | |||||||
\(132\) | 6.37741 | 0.555082 | ||||||||
\(133\) | 0.591233 | 0.0512664 | ||||||||
\(134\) | −17.2800 | −1.49276 | ||||||||
\(135\) | −2.07801 | −0.178846 | ||||||||
\(136\) | 0.251183 | 0.0215387 | ||||||||
\(137\) | 22.1369 | 1.89128 | 0.945642 | − | 0.325209i | \(-0.105435\pi\) | ||||
0.945642 | + | 0.325209i | \(0.105435\pi\) | |||||||
\(138\) | 5.02614 | 0.427853 | ||||||||
\(139\) | −18.2956 | −1.55181 | −0.775905 | − | 0.630850i | \(-0.782706\pi\) | ||||
−0.775905 | + | 0.630850i | \(0.782706\pi\) | |||||||
\(140\) | 2.59123 | 0.218999 | ||||||||
\(141\) | 12.6067 | 1.06167 | ||||||||
\(142\) | 2.89920 | 0.243296 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.93900 | −0.411583 | ||||||||
\(145\) | −20.6959 | −1.71870 | ||||||||
\(146\) | −16.5292 | −1.36797 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 3.70903 | 0.304880 | ||||||||
\(149\) | −21.8601 | −1.79085 | −0.895427 | − | 0.445209i | \(-0.853129\pi\) | ||||
−0.895427 | + | 0.445209i | \(0.853129\pi\) | |||||||
\(150\) | 1.22871 | 0.100324 | ||||||||
\(151\) | 6.89601 | 0.561190 | 0.280595 | − | 0.959826i | \(-0.409468\pi\) | ||||
0.280595 | + | 0.959826i | \(0.409468\pi\) | |||||||
\(152\) | −0.802242 | −0.0650704 | ||||||||
\(153\) | −0.185116 | −0.0149657 | ||||||||
\(154\) | −9.21562 | −0.742616 | ||||||||
\(155\) | −10.8705 | −0.873140 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.87082 | 0.388734 | 0.194367 | − | 0.980929i | \(-0.437735\pi\) | ||||
0.194367 | + | 0.980929i | \(0.437735\pi\) | |||||||
\(158\) | 9.76776 | 0.777081 | ||||||||
\(159\) | 5.51955 | 0.437729 | ||||||||
\(160\) | −12.8545 | −1.01624 | ||||||||
\(161\) | −2.78930 | −0.219827 | ||||||||
\(162\) | 1.80194 | 0.141574 | ||||||||
\(163\) | 21.1276 | 1.65485 | 0.827423 | − | 0.561580i | \(-0.189806\pi\) | ||||
0.827423 | + | 0.561580i | \(0.189806\pi\) | |||||||
\(164\) | 12.5362 | 0.978916 | ||||||||
\(165\) | 10.6275 | 0.827351 | ||||||||
\(166\) | −7.20593 | −0.559289 | ||||||||
\(167\) | 0.804062 | 0.0622202 | 0.0311101 | − | 0.999516i | \(-0.490096\pi\) | ||||
0.0311101 | + | 0.999516i | \(0.490096\pi\) | |||||||
\(168\) | 1.35690 | 0.104687 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.693155 | −0.0531626 | ||||||||
\(171\) | 0.591233 | 0.0452127 | ||||||||
\(172\) | 6.55231 | 0.499609 | ||||||||
\(173\) | 18.2281 | 1.38586 | 0.692929 | − | 0.721006i | \(-0.256320\pi\) | ||||
0.692929 | + | 0.721006i | \(0.256320\pi\) | |||||||
\(174\) | 17.9464 | 1.36051 | ||||||||
\(175\) | −0.681883 | −0.0515455 | ||||||||
\(176\) | 25.2594 | 1.90400 | ||||||||
\(177\) | 6.46823 | 0.486182 | ||||||||
\(178\) | 17.3641 | 1.30149 | ||||||||
\(179\) | −20.7087 | −1.54784 | −0.773921 | − | 0.633282i | \(-0.781707\pi\) | ||||
−0.773921 | + | 0.633282i | \(0.781707\pi\) | |||||||
\(180\) | 2.59123 | 0.193139 | ||||||||
\(181\) | −9.66053 | −0.718061 | −0.359031 | − | 0.933326i | \(-0.616893\pi\) | ||||
−0.359031 | + | 0.933326i | \(0.616893\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.43351 | −0.623423 | ||||||||
\(184\) | 3.78478 | 0.279018 | ||||||||
\(185\) | 6.18085 | 0.454425 | ||||||||
\(186\) | 9.42632 | 0.691172 | ||||||||
\(187\) | 0.946734 | 0.0692321 | ||||||||
\(188\) | −15.7203 | −1.14652 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 2.21384 | 0.160609 | ||||||||
\(191\) | −10.4151 | −0.753609 | −0.376804 | − | 0.926293i | \(-0.622977\pi\) | ||||
−0.376804 | + | 0.926293i | \(0.622977\pi\) | |||||||
\(192\) | 1.26875 | 0.0915641 | ||||||||
\(193\) | −26.2530 | −1.88973 | −0.944867 | − | 0.327455i | \(-0.893809\pi\) | ||||
−0.944867 | + | 0.327455i | \(0.893809\pi\) | |||||||
\(194\) | 5.49677 | 0.394645 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.24698 | 0.0890700 | ||||||||
\(197\) | 12.4560 | 0.887451 | 0.443725 | − | 0.896163i | \(-0.353657\pi\) | ||||
0.443725 | + | 0.896163i | \(0.353657\pi\) | |||||||
\(198\) | −9.21562 | −0.654926 | ||||||||
\(199\) | −10.3098 | −0.730841 | −0.365421 | − | 0.930843i | \(-0.619075\pi\) | ||||
−0.365421 | + | 0.930843i | \(0.619075\pi\) | |||||||
\(200\) | 0.925245 | 0.0654247 | ||||||||
\(201\) | 9.58967 | 0.676403 | ||||||||
\(202\) | −15.5969 | −1.09739 | ||||||||
\(203\) | −9.95951 | −0.699021 | ||||||||
\(204\) | 0.230836 | 0.0161617 | ||||||||
\(205\) | 20.8908 | 1.45908 | ||||||||
\(206\) | 25.3857 | 1.76871 | ||||||||
\(207\) | −2.78930 | −0.193869 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.02374 | −0.209156 | ||||||||
\(210\) | −3.74444 | −0.258391 | ||||||||
\(211\) | 14.0679 | 0.968473 | 0.484237 | − | 0.874937i | \(-0.339097\pi\) | ||||
0.484237 | + | 0.874937i | \(0.339097\pi\) | |||||||
\(212\) | −6.88276 | −0.472710 | ||||||||
\(213\) | −1.60894 | −0.110242 | ||||||||
\(214\) | 8.40399 | 0.574485 | ||||||||
\(215\) | 10.9190 | 0.744669 | ||||||||
\(216\) | 1.35690 | 0.0923251 | ||||||||
\(217\) | −5.23122 | −0.355118 | ||||||||
\(218\) | 4.24315 | 0.287383 | ||||||||
\(219\) | 9.17303 | 0.619856 | ||||||||
\(220\) | −13.2523 | −0.893470 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.35970 | −0.359720 | ||||||||
\(223\) | −23.4082 | −1.56753 | −0.783763 | − | 0.621060i | \(-0.786702\pi\) | ||||
−0.783763 | + | 0.621060i | \(0.786702\pi\) | |||||||
\(224\) | −6.18598 | −0.413318 | ||||||||
\(225\) | −0.681883 | −0.0454589 | ||||||||
\(226\) | −11.8622 | −0.789065 | ||||||||
\(227\) | −1.79773 | −0.119319 | −0.0596596 | − | 0.998219i | \(-0.519002\pi\) | ||||
−0.0596596 | + | 0.998219i | \(0.519002\pi\) | |||||||
\(228\) | −0.737256 | −0.0488260 | ||||||||
\(229\) | 4.80163 | 0.317301 | 0.158650 | − | 0.987335i | \(-0.449286\pi\) | ||||
0.158650 | + | 0.987335i | \(0.449286\pi\) | |||||||
\(230\) | −10.4444 | −0.688680 | ||||||||
\(231\) | 5.11428 | 0.336495 | ||||||||
\(232\) | 13.5140 | 0.887239 | ||||||||
\(233\) | −18.1525 | −1.18921 | −0.594605 | − | 0.804018i | \(-0.702692\pi\) | ||||
−0.594605 | + | 0.804018i | \(0.702692\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.1968 | −1.70889 | ||||||||
\(236\) | −8.06575 | −0.525035 | ||||||||
\(237\) | −5.42070 | −0.352112 | ||||||||
\(238\) | −0.333567 | −0.0216219 | ||||||||
\(239\) | 17.0258 | 1.10131 | 0.550654 | − | 0.834733i | \(-0.314378\pi\) | ||||
0.550654 | + | 0.834733i | \(0.314378\pi\) | |||||||
\(240\) | 10.2633 | 0.662492 | ||||||||
\(241\) | −10.2368 | −0.659412 | −0.329706 | − | 0.944084i | \(-0.606950\pi\) | ||||
−0.329706 | + | 0.944084i | \(0.606950\pi\) | |||||||
\(242\) | 27.3100 | 1.75555 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.5164 | 0.673244 | ||||||||
\(245\) | 2.07801 | 0.132759 | ||||||||
\(246\) | −18.1154 | −1.15500 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 7.09821 | 0.450737 | ||||||||
\(249\) | 3.99899 | 0.253426 | ||||||||
\(250\) | −21.2755 | −1.34558 | ||||||||
\(251\) | 17.3844 | 1.09730 | 0.548648 | − | 0.836053i | \(-0.315143\pi\) | ||||
0.548648 | + | 0.836053i | \(0.315143\pi\) | |||||||
\(252\) | 1.24698 | 0.0785523 | ||||||||
\(253\) | 14.2652 | 0.896848 | ||||||||
\(254\) | −9.63576 | −0.604601 | ||||||||
\(255\) | 0.384672 | 0.0240891 | ||||||||
\(256\) | 20.7114 | 1.29446 | ||||||||
\(257\) | −1.26764 | −0.0790733 | −0.0395366 | − | 0.999218i | \(-0.512588\pi\) | ||||
−0.0395366 | + | 0.999218i | \(0.512588\pi\) | |||||||
\(258\) | −9.46836 | −0.589474 | ||||||||
\(259\) | 2.97441 | 0.184821 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.95951 | −0.616478 | ||||||||
\(262\) | −30.3480 | −1.87491 | ||||||||
\(263\) | 14.3084 | 0.882294 | 0.441147 | − | 0.897435i | \(-0.354572\pi\) | ||||
0.441147 | + | 0.897435i | \(0.354572\pi\) | |||||||
\(264\) | −6.93955 | −0.427100 | ||||||||
\(265\) | −11.4697 | −0.704576 | ||||||||
\(266\) | 1.06537 | 0.0653218 | ||||||||
\(267\) | −9.63632 | −0.589733 | ||||||||
\(268\) | −11.9581 | −0.730459 | ||||||||
\(269\) | −6.23326 | −0.380049 | −0.190024 | − | 0.981779i | \(-0.560857\pi\) | ||||
−0.190024 | + | 0.981779i | \(0.560857\pi\) | |||||||
\(270\) | −3.74444 | −0.227879 | ||||||||
\(271\) | −10.8204 | −0.657290 | −0.328645 | − | 0.944454i | \(-0.606592\pi\) | ||||
−0.328645 | + | 0.944454i | \(0.606592\pi\) | |||||||
\(272\) | 0.914287 | 0.0554368 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 39.8893 | 2.40980 | ||||||||
\(275\) | 3.48734 | 0.210295 | ||||||||
\(276\) | 3.47819 | 0.209363 | ||||||||
\(277\) | 16.5661 | 0.995359 | 0.497679 | − | 0.867361i | \(-0.334186\pi\) | ||||
0.497679 | + | 0.867361i | \(0.334186\pi\) | |||||||
\(278\) | −32.9675 | −1.97726 | ||||||||
\(279\) | −5.23122 | −0.313185 | ||||||||
\(280\) | −2.81964 | −0.168506 | ||||||||
\(281\) | 21.4915 | 1.28208 | 0.641039 | − | 0.767508i | \(-0.278504\pi\) | ||||
0.641039 | + | 0.767508i | \(0.278504\pi\) | |||||||
\(282\) | 22.7165 | 1.35275 | ||||||||
\(283\) | −24.4327 | −1.45237 | −0.726185 | − | 0.687499i | \(-0.758709\pi\) | ||||
−0.726185 | + | 0.687499i | \(0.758709\pi\) | |||||||
\(284\) | 2.00631 | 0.119053 | ||||||||
\(285\) | −1.22859 | −0.0727753 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.0533 | 0.593427 | ||||||||
\(288\) | −6.18598 | −0.364512 | ||||||||
\(289\) | −16.9657 | −0.997984 | ||||||||
\(290\) | −37.2928 | −2.18991 | ||||||||
\(291\) | −3.05048 | −0.178822 | ||||||||
\(292\) | −11.4386 | −0.669393 | ||||||||
\(293\) | −11.1636 | −0.652187 | −0.326094 | − | 0.945337i | \(-0.605732\pi\) | ||||
−0.326094 | + | 0.945337i | \(0.605732\pi\) | |||||||
\(294\) | −1.80194 | −0.105091 | ||||||||
\(295\) | −13.4410 | −0.782567 | ||||||||
\(296\) | −4.03597 | −0.234586 | ||||||||
\(297\) | 5.11428 | 0.296761 | ||||||||
\(298\) | −39.3906 | −2.28184 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.850295 | 0.0490918 | ||||||||
\(301\) | 5.25454 | 0.302867 | ||||||||
\(302\) | 12.4262 | 0.715047 | ||||||||
\(303\) | 8.65561 | 0.497252 | ||||||||
\(304\) | −2.92010 | −0.167479 | ||||||||
\(305\) | 17.5249 | 1.00347 | ||||||||
\(306\) | −0.333567 | −0.0190688 | ||||||||
\(307\) | 2.87863 | 0.164292 | 0.0821461 | − | 0.996620i | \(-0.473823\pi\) | ||||
0.0821461 | + | 0.996620i | \(0.473823\pi\) | |||||||
\(308\) | −6.37741 | −0.363386 | ||||||||
\(309\) | −14.0880 | −0.801438 | ||||||||
\(310\) | −19.5880 | −1.11252 | ||||||||
\(311\) | 27.7786 | 1.57518 | 0.787590 | − | 0.616199i | \(-0.211328\pi\) | ||||
0.787590 | + | 0.616199i | \(0.211328\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.2336 | 1.20019 | 0.600096 | − | 0.799928i | \(-0.295129\pi\) | ||||
0.600096 | + | 0.799928i | \(0.295129\pi\) | |||||||
\(314\) | 8.77691 | 0.495310 | ||||||||
\(315\) | 2.07801 | 0.117082 | ||||||||
\(316\) | 6.75950 | 0.380252 | ||||||||
\(317\) | −1.54637 | −0.0868530 | −0.0434265 | − | 0.999057i | \(-0.513827\pi\) | ||||
−0.0434265 | + | 0.999057i | \(0.513827\pi\) | |||||||
\(318\) | 9.94588 | 0.557737 | ||||||||
\(319\) | 50.9358 | 2.85186 | ||||||||
\(320\) | −2.63647 | −0.147383 | ||||||||
\(321\) | −4.66386 | −0.260312 | ||||||||
\(322\) | −5.02614 | −0.280096 | ||||||||
\(323\) | −0.109447 | −0.00608977 | ||||||||
\(324\) | 1.24698 | 0.0692766 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 38.0707 | 2.10854 | ||||||||
\(327\) | −2.35477 | −0.130219 | ||||||||
\(328\) | −13.6413 | −0.753213 | ||||||||
\(329\) | −12.6067 | −0.695029 | ||||||||
\(330\) | 19.1501 | 1.05418 | ||||||||
\(331\) | 24.2044 | 1.33039 | 0.665197 | − | 0.746668i | \(-0.268347\pi\) | ||||
0.665197 | + | 0.746668i | \(0.268347\pi\) | |||||||
\(332\) | −4.98666 | −0.273678 | ||||||||
\(333\) | 2.97441 | 0.162997 | ||||||||
\(334\) | 1.44887 | 0.0792786 | ||||||||
\(335\) | −19.9274 | −1.08875 | ||||||||
\(336\) | 4.93900 | 0.269445 | ||||||||
\(337\) | −11.8094 | −0.643297 | −0.321648 | − | 0.946859i | \(-0.604237\pi\) | ||||
−0.321648 | + | 0.946859i | \(0.604237\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.58305 | 0.357542 | ||||||||
\(340\) | −0.479678 | −0.0260142 | ||||||||
\(341\) | 26.7539 | 1.44881 | ||||||||
\(342\) | 1.06537 | 0.0576084 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −7.12987 | −0.384417 | ||||||||
\(345\) | 5.79618 | 0.312056 | ||||||||
\(346\) | 32.8459 | 1.76581 | ||||||||
\(347\) | −3.90357 | −0.209555 | −0.104777 | − | 0.994496i | \(-0.533413\pi\) | ||||
−0.104777 | + | 0.994496i | \(0.533413\pi\) | |||||||
\(348\) | 12.4193 | 0.665745 | ||||||||
\(349\) | 3.89952 | 0.208736 | 0.104368 | − | 0.994539i | \(-0.466718\pi\) | ||||
0.104368 | + | 0.994539i | \(0.466718\pi\) | |||||||
\(350\) | −1.22871 | −0.0656774 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 31.6369 | 1.68625 | ||||||||
\(353\) | 10.0452 | 0.534650 | 0.267325 | − | 0.963606i | \(-0.413860\pi\) | ||||
0.267325 | + | 0.963606i | \(0.413860\pi\) | |||||||
\(354\) | 11.6553 | 0.619474 | ||||||||
\(355\) | 3.34338 | 0.177448 | ||||||||
\(356\) | 12.0163 | 0.636863 | ||||||||
\(357\) | 0.185116 | 0.00979737 | ||||||||
\(358\) | −37.3158 | −1.97220 | ||||||||
\(359\) | 27.3427 | 1.44309 | 0.721547 | − | 0.692365i | \(-0.243431\pi\) | ||||
0.721547 | + | 0.692365i | \(0.243431\pi\) | |||||||
\(360\) | −2.81964 | −0.148608 | ||||||||
\(361\) | −18.6504 | −0.981602 | ||||||||
\(362\) | −17.4077 | −0.914927 | ||||||||
\(363\) | −15.1559 | −0.795478 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.0616 | −0.997732 | ||||||||
\(366\) | −15.1967 | −0.794342 | ||||||||
\(367\) | −16.0870 | −0.839734 | −0.419867 | − | 0.907586i | \(-0.637923\pi\) | ||||
−0.419867 | + | 0.907586i | \(0.637923\pi\) | |||||||
\(368\) | 13.7763 | 0.718141 | ||||||||
\(369\) | 10.0533 | 0.523353 | ||||||||
\(370\) | 11.1375 | 0.579011 | ||||||||
\(371\) | −5.51955 | −0.286561 | ||||||||
\(372\) | 6.52322 | 0.338213 | ||||||||
\(373\) | −8.23352 | −0.426315 | −0.213158 | − | 0.977018i | \(-0.568375\pi\) | ||||
−0.213158 | + | 0.977018i | \(0.568375\pi\) | |||||||
\(374\) | 1.70596 | 0.0882129 | ||||||||
\(375\) | 11.8070 | 0.609711 | ||||||||
\(376\) | 17.1060 | 0.882172 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.80194 | −0.0926817 | ||||||||
\(379\) | −8.18484 | −0.420427 | −0.210214 | − | 0.977655i | \(-0.567416\pi\) | ||||
−0.210214 | + | 0.977655i | \(0.567416\pi\) | |||||||
\(380\) | 1.53202 | 0.0785912 | ||||||||
\(381\) | 5.34744 | 0.273958 | ||||||||
\(382\) | −18.7673 | −0.960220 | ||||||||
\(383\) | −26.3188 | −1.34483 | −0.672413 | − | 0.740176i | \(-0.734742\pi\) | ||||
−0.672413 | + | 0.740176i | \(0.734742\pi\) | |||||||
\(384\) | −10.0858 | −0.514686 | ||||||||
\(385\) | −10.6275 | −0.541629 | ||||||||
\(386\) | −47.3063 | −2.40783 | ||||||||
\(387\) | 5.25454 | 0.267103 | ||||||||
\(388\) | 3.80388 | 0.193113 | ||||||||
\(389\) | 29.0722 | 1.47402 | 0.737010 | − | 0.675882i | \(-0.236237\pi\) | ||||
0.737010 | + | 0.675882i | \(0.236237\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.516343 | 0.0261126 | ||||||||
\(392\) | −1.35690 | −0.0685336 | ||||||||
\(393\) | 16.8419 | 0.849561 | ||||||||
\(394\) | 22.4449 | 1.13076 | ||||||||
\(395\) | 11.2643 | 0.566766 | ||||||||
\(396\) | −6.37741 | −0.320477 | ||||||||
\(397\) | 5.11134 | 0.256531 | 0.128265 | − | 0.991740i | \(-0.459059\pi\) | ||||
0.128265 | + | 0.991740i | \(0.459059\pi\) | |||||||
\(398\) | −18.5776 | −0.931210 | ||||||||
\(399\) | −0.591233 | −0.0295987 | ||||||||
\(400\) | 3.36782 | 0.168391 | ||||||||
\(401\) | 14.9970 | 0.748913 | 0.374456 | − | 0.927245i | \(-0.377829\pi\) | ||||
0.374456 | + | 0.927245i | \(0.377829\pi\) | |||||||
\(402\) | 17.2800 | 0.861847 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −10.7934 | −0.536990 | ||||||||
\(405\) | 2.07801 | 0.103257 | ||||||||
\(406\) | −17.9464 | −0.890666 | ||||||||
\(407\) | −15.2120 | −0.754030 | ||||||||
\(408\) | −0.251183 | −0.0124354 | ||||||||
\(409\) | 32.1645 | 1.59043 | 0.795217 | − | 0.606325i | \(-0.207357\pi\) | ||||
0.795217 | + | 0.606325i | \(0.207357\pi\) | |||||||
\(410\) | 37.6439 | 1.85910 | ||||||||
\(411\) | −22.1369 | −1.09193 | ||||||||
\(412\) | 17.5674 | 0.865486 | ||||||||
\(413\) | −6.46823 | −0.318281 | ||||||||
\(414\) | −5.02614 | −0.247021 | ||||||||
\(415\) | −8.30993 | −0.407919 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.2956 | 0.895938 | ||||||||
\(418\) | −5.44858 | −0.266499 | ||||||||
\(419\) | −22.8601 | −1.11679 | −0.558395 | − | 0.829575i | \(-0.688583\pi\) | ||||
−0.558395 | + | 0.829575i | \(0.688583\pi\) | |||||||
\(420\) | −2.59123 | −0.126439 | ||||||||
\(421\) | 24.3260 | 1.18558 | 0.592789 | − | 0.805358i | \(-0.298027\pi\) | ||||
0.592789 | + | 0.805358i | \(0.298027\pi\) | |||||||
\(422\) | 25.3495 | 1.23399 | ||||||||
\(423\) | −12.6067 | −0.612958 | ||||||||
\(424\) | 7.48945 | 0.363720 | ||||||||
\(425\) | 0.126227 | 0.00612293 | ||||||||
\(426\) | −2.89920 | −0.140467 | ||||||||
\(427\) | 8.43351 | 0.408126 | ||||||||
\(428\) | 5.81574 | 0.281115 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.6753 | 0.948829 | ||||||||
\(431\) | −25.1639 | −1.21210 | −0.606051 | − | 0.795426i | \(-0.707247\pi\) | ||||
−0.606051 | + | 0.795426i | \(0.707247\pi\) | |||||||
\(432\) | 4.93900 | 0.237628 | ||||||||
\(433\) | −29.9618 | −1.43987 | −0.719936 | − | 0.694040i | \(-0.755829\pi\) | ||||
−0.719936 | + | 0.694040i | \(0.755829\pi\) | |||||||
\(434\) | −9.42632 | −0.452478 | ||||||||
\(435\) | 20.6959 | 0.992295 | ||||||||
\(436\) | 2.93635 | 0.140626 | ||||||||
\(437\) | −1.64912 | −0.0788883 | ||||||||
\(438\) | 16.5292 | 0.789797 | ||||||||
\(439\) | 19.1986 | 0.916299 | 0.458150 | − | 0.888875i | \(-0.348512\pi\) | ||||
0.458150 | + | 0.888875i | \(0.348512\pi\) | |||||||
\(440\) | 14.4204 | 0.687467 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.61112 | −0.409127 | −0.204563 | − | 0.978853i | \(-0.565577\pi\) | ||||
−0.204563 | + | 0.978853i | \(0.565577\pi\) | |||||||
\(444\) | −3.70903 | −0.176023 | ||||||||
\(445\) | 20.0244 | 0.949245 | ||||||||
\(446\) | −42.1800 | −1.99728 | ||||||||
\(447\) | 21.8601 | 1.03395 | ||||||||
\(448\) | −1.26875 | −0.0599428 | ||||||||
\(449\) | −20.7380 | −0.978686 | −0.489343 | − | 0.872091i | \(-0.662763\pi\) | ||||
−0.489343 | + | 0.872091i | \(0.662763\pi\) | |||||||
\(450\) | −1.22871 | −0.0579220 | ||||||||
\(451\) | −51.4153 | −2.42105 | ||||||||
\(452\) | −8.20893 | −0.386116 | ||||||||
\(453\) | −6.89601 | −0.324003 | ||||||||
\(454\) | −3.23939 | −0.152032 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.802242 | 0.0375684 | ||||||||
\(457\) | 17.2267 | 0.805833 | 0.402916 | − | 0.915237i | \(-0.367997\pi\) | ||||
0.402916 | + | 0.915237i | \(0.367997\pi\) | |||||||
\(458\) | 8.65224 | 0.404293 | ||||||||
\(459\) | 0.185116 | 0.00864046 | ||||||||
\(460\) | −7.22772 | −0.336994 | ||||||||
\(461\) | 37.3236 | 1.73833 | 0.869167 | − | 0.494519i | \(-0.164656\pi\) | ||||
0.869167 | + | 0.494519i | \(0.164656\pi\) | |||||||
\(462\) | 9.21562 | 0.428749 | ||||||||
\(463\) | 0.678707 | 0.0315422 | 0.0157711 | − | 0.999876i | \(-0.494980\pi\) | ||||
0.0157711 | + | 0.999876i | \(0.494980\pi\) | |||||||
\(464\) | 49.1900 | 2.28359 | ||||||||
\(465\) | 10.8705 | 0.504108 | ||||||||
\(466\) | −32.7097 | −1.51525 | ||||||||
\(467\) | −21.2872 | −0.985055 | −0.492527 | − | 0.870297i | \(-0.663927\pi\) | ||||
−0.492527 | + | 0.870297i | \(0.663927\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.58967 | −0.442810 | ||||||||
\(470\) | −47.2050 | −2.17740 | ||||||||
\(471\) | −4.87082 | −0.224435 | ||||||||
\(472\) | 8.77671 | 0.403981 | ||||||||
\(473\) | −26.8732 | −1.23563 | ||||||||
\(474\) | −9.76776 | −0.448648 | ||||||||
\(475\) | −0.403152 | −0.0184979 | ||||||||
\(476\) | −0.230836 | −0.0105803 | ||||||||
\(477\) | −5.51955 | −0.252723 | ||||||||
\(478\) | 30.6795 | 1.40325 | ||||||||
\(479\) | 5.01859 | 0.229305 | 0.114653 | − | 0.993406i | \(-0.463425\pi\) | ||||
0.114653 | + | 0.993406i | \(0.463425\pi\) | |||||||
\(480\) | 12.8545 | 0.586726 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −18.4461 | −0.840198 | ||||||||
\(483\) | 2.78930 | 0.126917 | ||||||||
\(484\) | 18.8991 | 0.859049 | ||||||||
\(485\) | 6.33891 | 0.287835 | ||||||||
\(486\) | −1.80194 | −0.0817376 | ||||||||
\(487\) | 16.2859 | 0.737986 | 0.368993 | − | 0.929432i | \(-0.379703\pi\) | ||||
0.368993 | + | 0.929432i | \(0.379703\pi\) | |||||||
\(488\) | −11.4434 | −0.518018 | ||||||||
\(489\) | −21.1276 | −0.955425 | ||||||||
\(490\) | 3.74444 | 0.169157 | ||||||||
\(491\) | −3.69624 | −0.166809 | −0.0834045 | − | 0.996516i | \(-0.526579\pi\) | ||||
−0.0834045 | + | 0.996516i | \(0.526579\pi\) | |||||||
\(492\) | −12.5362 | −0.565177 | ||||||||
\(493\) | 1.84366 | 0.0830344 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.6275 | −0.477672 | ||||||||
\(496\) | 25.8370 | 1.16011 | ||||||||
\(497\) | 1.60894 | 0.0721706 | ||||||||
\(498\) | 7.20593 | 0.322905 | ||||||||
\(499\) | 40.5061 | 1.81330 | 0.906652 | − | 0.421880i | \(-0.138630\pi\) | ||||
0.906652 | + | 0.421880i | \(0.138630\pi\) | |||||||
\(500\) | −14.7231 | −0.658436 | ||||||||
\(501\) | −0.804062 | −0.0359228 | ||||||||
\(502\) | 31.3257 | 1.39813 | ||||||||
\(503\) | −31.3688 | −1.39867 | −0.699333 | − | 0.714796i | \(-0.746520\pi\) | ||||
−0.699333 | + | 0.714796i | \(0.746520\pi\) | |||||||
\(504\) | −1.35690 | −0.0604409 | ||||||||
\(505\) | −17.9864 | −0.800385 | ||||||||
\(506\) | 25.7051 | 1.14273 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.66815 | −0.295851 | ||||||||
\(509\) | 27.0022 | 1.19685 | 0.598426 | − | 0.801178i | \(-0.295793\pi\) | ||||
0.598426 | + | 0.801178i | \(0.295793\pi\) | |||||||
\(510\) | 0.693155 | 0.0306934 | ||||||||
\(511\) | −9.17303 | −0.405791 | ||||||||
\(512\) | 17.1491 | 0.757892 | ||||||||
\(513\) | −0.591233 | −0.0261036 | ||||||||
\(514\) | −2.28421 | −0.100752 | ||||||||
\(515\) | 29.2750 | 1.29001 | ||||||||
\(516\) | −6.55231 | −0.288449 | ||||||||
\(517\) | 64.4742 | 2.83557 | ||||||||
\(518\) | 5.35970 | 0.235492 | ||||||||
\(519\) | −18.2281 | −0.800126 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.6292 | 1.07902 | 0.539512 | − | 0.841978i | \(-0.318609\pi\) | ||||
0.539512 | + | 0.841978i | \(0.318609\pi\) | |||||||
\(522\) | −17.9464 | −0.785493 | ||||||||
\(523\) | 6.84384 | 0.299260 | 0.149630 | − | 0.988742i | \(-0.452192\pi\) | ||||
0.149630 | + | 0.988742i | \(0.452192\pi\) | |||||||
\(524\) | −21.0015 | −0.917455 | ||||||||
\(525\) | 0.681883 | 0.0297598 | ||||||||
\(526\) | 25.7829 | 1.12419 | ||||||||
\(527\) | 0.968380 | 0.0421833 | ||||||||
\(528\) | −25.2594 | −1.09928 | ||||||||
\(529\) | −15.2198 | −0.661732 | ||||||||
\(530\) | −20.6676 | −0.897744 | ||||||||
\(531\) | −6.46823 | −0.280697 | ||||||||
\(532\) | 0.737256 | 0.0319641 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −17.3641 | −0.751416 | ||||||||
\(535\) | 9.69155 | 0.419002 | ||||||||
\(536\) | 13.0122 | 0.562041 | ||||||||
\(537\) | 20.7087 | 0.893647 | ||||||||
\(538\) | −11.2320 | −0.484244 | ||||||||
\(539\) | −5.11428 | −0.220288 | ||||||||
\(540\) | −2.59123 | −0.111509 | ||||||||
\(541\) | −26.4753 | −1.13826 | −0.569130 | − | 0.822247i | \(-0.692720\pi\) | ||||
−0.569130 | + | 0.822247i | \(0.692720\pi\) | |||||||
\(542\) | −19.4976 | −0.837494 | ||||||||
\(543\) | 9.66053 | 0.414573 | ||||||||
\(544\) | 1.14512 | 0.0490967 | ||||||||
\(545\) | 4.89323 | 0.209603 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7444 | 0.673183 | 0.336592 | − | 0.941651i | \(-0.390726\pi\) | ||||
0.336592 | + | 0.941651i | \(0.390726\pi\) | |||||||
\(548\) | 27.6043 | 1.17920 | ||||||||
\(549\) | 8.43351 | 0.359933 | ||||||||
\(550\) | 6.28398 | 0.267950 | ||||||||
\(551\) | −5.88840 | −0.250854 | ||||||||
\(552\) | −3.78478 | −0.161091 | ||||||||
\(553\) | 5.42070 | 0.230512 | ||||||||
\(554\) | 29.8510 | 1.26825 | ||||||||
\(555\) | −6.18085 | −0.262362 | ||||||||
\(556\) | −22.8142 | −0.967538 | ||||||||
\(557\) | −14.4151 | −0.610788 | −0.305394 | − | 0.952226i | \(-0.598788\pi\) | ||||
−0.305394 | + | 0.952226i | \(0.598788\pi\) | |||||||
\(558\) | −9.42632 | −0.399048 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −10.2633 | −0.433703 | ||||||||
\(561\) | −0.946734 | −0.0399712 | ||||||||
\(562\) | 38.7264 | 1.63358 | ||||||||
\(563\) | −22.7569 | −0.959088 | −0.479544 | − | 0.877518i | \(-0.659198\pi\) | ||||
−0.479544 | + | 0.877518i | \(0.659198\pi\) | |||||||
\(564\) | 15.7203 | 0.661943 | ||||||||
\(565\) | −13.6796 | −0.575506 | ||||||||
\(566\) | −44.0261 | −1.85056 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −2.18316 | −0.0916033 | ||||||||
\(569\) | −23.4397 | −0.982642 | −0.491321 | − | 0.870978i | \(-0.663486\pi\) | ||||
−0.491321 | + | 0.870978i | \(0.663486\pi\) | |||||||
\(570\) | −2.21384 | −0.0927275 | ||||||||
\(571\) | −2.24053 | −0.0937634 | −0.0468817 | − | 0.998900i | \(-0.514928\pi\) | ||||
−0.0468817 | + | 0.998900i | \(0.514928\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.4151 | 0.435096 | ||||||||
\(574\) | 18.1154 | 0.756122 | ||||||||
\(575\) | 1.90197 | 0.0793178 | ||||||||
\(576\) | −1.26875 | −0.0528646 | ||||||||
\(577\) | 39.6538 | 1.65081 | 0.825405 | − | 0.564541i | \(-0.190947\pi\) | ||||
0.825405 | + | 0.564541i | \(0.190947\pi\) | |||||||
\(578\) | −30.5712 | −1.27159 | ||||||||
\(579\) | 26.2530 | 1.09104 | ||||||||
\(580\) | −25.8074 | −1.07159 | ||||||||
\(581\) | −3.99899 | −0.165906 | ||||||||
\(582\) | −5.49677 | −0.227848 | ||||||||
\(583\) | 28.2285 | 1.16911 | ||||||||
\(584\) | 12.4469 | 0.515054 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.1162 | −0.830993 | ||||||||
\(587\) | 14.1384 | 0.583555 | 0.291777 | − | 0.956486i | \(-0.405753\pi\) | ||||
0.291777 | + | 0.956486i | \(0.405753\pi\) | |||||||
\(588\) | −1.24698 | −0.0514246 | ||||||||
\(589\) | −3.09287 | −0.127439 | ||||||||
\(590\) | −24.2199 | −0.997117 | ||||||||
\(591\) | −12.4560 | −0.512370 | ||||||||
\(592\) | −14.6906 | −0.603781 | ||||||||
\(593\) | 8.38386 | 0.344284 | 0.172142 | − | 0.985072i | \(-0.444931\pi\) | ||||
0.172142 | + | 0.985072i | \(0.444931\pi\) | |||||||
\(594\) | 9.21562 | 0.378121 | ||||||||
\(595\) | −0.384672 | −0.0157700 | ||||||||
\(596\) | −27.2592 | −1.11658 | ||||||||
\(597\) | 10.3098 | 0.421951 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.7481 | −1.29719 | −0.648596 | − | 0.761133i | \(-0.724644\pi\) | ||||
−0.648596 | + | 0.761133i | \(0.724644\pi\) | |||||||
\(600\) | −0.925245 | −0.0377730 | ||||||||
\(601\) | 4.22823 | 0.172473 | 0.0862365 | − | 0.996275i | \(-0.472516\pi\) | ||||
0.0862365 | + | 0.996275i | \(0.472516\pi\) | |||||||
\(602\) | 9.46836 | 0.385902 | ||||||||
\(603\) | −9.58967 | −0.390522 | ||||||||
\(604\) | 8.59919 | 0.349896 | ||||||||
\(605\) | 31.4941 | 1.28042 | ||||||||
\(606\) | 15.5969 | 0.633580 | ||||||||
\(607\) | 44.1087 | 1.79032 | 0.895158 | − | 0.445749i | \(-0.147063\pi\) | ||||
0.895158 | + | 0.445749i | \(0.147063\pi\) | |||||||
\(608\) | −3.65736 | −0.148325 | ||||||||
\(609\) | 9.95951 | 0.403580 | ||||||||
\(610\) | 31.5788 | 1.27859 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.230836 | −0.00933098 | ||||||||
\(613\) | 46.2247 | 1.86700 | 0.933499 | − | 0.358580i | \(-0.116739\pi\) | ||||
0.933499 | + | 0.358580i | \(0.116739\pi\) | |||||||
\(614\) | 5.18711 | 0.209335 | ||||||||
\(615\) | −20.8908 | −0.842399 | ||||||||
\(616\) | 6.93955 | 0.279602 | ||||||||
\(617\) | 23.6252 | 0.951114 | 0.475557 | − | 0.879685i | \(-0.342247\pi\) | ||||
0.475557 | + | 0.879685i | \(0.342247\pi\) | |||||||
\(618\) | −25.3857 | −1.02116 | ||||||||
\(619\) | −15.8607 | −0.637495 | −0.318747 | − | 0.947840i | \(-0.603262\pi\) | ||||
−0.318747 | + | 0.947840i | \(0.603262\pi\) | |||||||
\(620\) | −13.5553 | −0.544394 | ||||||||
\(621\) | 2.78930 | 0.111931 | ||||||||
\(622\) | 50.0553 | 2.00704 | ||||||||
\(623\) | 9.63632 | 0.386071 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.1256 | −0.845025 | ||||||||
\(626\) | 38.2616 | 1.52924 | ||||||||
\(627\) | 3.02374 | 0.120756 | ||||||||
\(628\) | 6.07381 | 0.242371 | ||||||||
\(629\) | −0.550610 | −0.0219543 | ||||||||
\(630\) | 3.74444 | 0.149182 | ||||||||
\(631\) | −0.782536 | −0.0311523 | −0.0155761 | − | 0.999879i | \(-0.504958\pi\) | ||||
−0.0155761 | + | 0.999879i | \(0.504958\pi\) | |||||||
\(632\) | −7.35532 | −0.292579 | ||||||||
\(633\) | −14.0679 | −0.559148 | ||||||||
\(634\) | −2.78647 | −0.110665 | ||||||||
\(635\) | −11.1120 | −0.440967 | ||||||||
\(636\) | 6.88276 | 0.272919 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 91.7831 | 3.63373 | ||||||||
\(639\) | 1.60894 | 0.0636485 | ||||||||
\(640\) | 20.9583 | 0.828449 | ||||||||
\(641\) | 45.1286 | 1.78247 | 0.891237 | − | 0.453538i | \(-0.149838\pi\) | ||||
0.891237 | + | 0.453538i | \(0.149838\pi\) | |||||||
\(642\) | −8.40399 | −0.331679 | ||||||||
\(643\) | −30.1683 | −1.18972 | −0.594861 | − | 0.803828i | \(-0.702793\pi\) | ||||
−0.594861 | + | 0.803828i | \(0.702793\pi\) | |||||||
\(644\) | −3.47819 | −0.137060 | ||||||||
\(645\) | −10.9190 | −0.429935 | ||||||||
\(646\) | −0.197216 | −0.00775936 | ||||||||
\(647\) | −32.8978 | −1.29334 | −0.646672 | − | 0.762768i | \(-0.723840\pi\) | ||||
−0.646672 | + | 0.762768i | \(0.723840\pi\) | |||||||
\(648\) | −1.35690 | −0.0533039 | ||||||||
\(649\) | 33.0803 | 1.29852 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.23122 | 0.205027 | ||||||||
\(652\) | 26.3457 | 1.03178 | ||||||||
\(653\) | −18.7526 | −0.733848 | −0.366924 | − | 0.930251i | \(-0.619589\pi\) | ||||
−0.366924 | + | 0.930251i | \(0.619589\pi\) | |||||||
\(654\) | −4.24315 | −0.165920 | ||||||||
\(655\) | −34.9976 | −1.36747 | ||||||||
\(656\) | −49.6532 | −1.93863 | ||||||||
\(657\) | −9.17303 | −0.357874 | ||||||||
\(658\) | −22.7165 | −0.885580 | ||||||||
\(659\) | −30.9219 | −1.20455 | −0.602274 | − | 0.798289i | \(-0.705739\pi\) | ||||
−0.602274 | + | 0.798289i | \(0.705739\pi\) | |||||||
\(660\) | 13.2523 | 0.515845 | ||||||||
\(661\) | −31.2501 | −1.21549 | −0.607743 | − | 0.794133i | \(-0.707925\pi\) | ||||
−0.607743 | + | 0.794133i | \(0.707925\pi\) | |||||||
\(662\) | 43.6148 | 1.69514 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.42621 | 0.210578 | ||||||||
\(665\) | 1.22859 | 0.0476426 | ||||||||
\(666\) | 5.35970 | 0.207684 | ||||||||
\(667\) | 27.7800 | 1.07565 | ||||||||
\(668\) | 1.00265 | 0.0387937 | ||||||||
\(669\) | 23.4082 | 0.905012 | ||||||||
\(670\) | −35.9079 | −1.38725 | ||||||||
\(671\) | −43.1314 | −1.66507 | ||||||||
\(672\) | 6.18598 | 0.238629 | ||||||||
\(673\) | 1.80497 | 0.0695765 | 0.0347883 | − | 0.999395i | \(-0.488924\pi\) | ||||
0.0347883 | + | 0.999395i | \(0.488924\pi\) | |||||||
\(674\) | −21.2797 | −0.819665 | ||||||||
\(675\) | 0.681883 | 0.0262457 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.4596 | −1.24752 | −0.623762 | − | 0.781614i | \(-0.714397\pi\) | ||||
−0.623762 | + | 0.781614i | \(0.714397\pi\) | |||||||
\(678\) | 11.8622 | 0.455567 | ||||||||
\(679\) | 3.05048 | 0.117067 | ||||||||
\(680\) | 0.521960 | 0.0200162 | ||||||||
\(681\) | 1.79773 | 0.0688890 | ||||||||
\(682\) | 48.2089 | 1.84601 | ||||||||
\(683\) | −21.4439 | −0.820529 | −0.410265 | − | 0.911967i | \(-0.634564\pi\) | ||||
−0.410265 | + | 0.911967i | \(0.634564\pi\) | |||||||
\(684\) | 0.737256 | 0.0281897 | ||||||||
\(685\) | 46.0007 | 1.75760 | ||||||||
\(686\) | 1.80194 | 0.0687983 | ||||||||
\(687\) | −4.80163 | −0.183194 | ||||||||
\(688\) | −25.9522 | −0.989418 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 10.4444 | 0.397610 | ||||||||
\(691\) | 9.69999 | 0.369005 | 0.184502 | − | 0.982832i | \(-0.440933\pi\) | ||||
0.184502 | + | 0.982832i | \(0.440933\pi\) | |||||||
\(692\) | 22.7301 | 0.864068 | ||||||||
\(693\) | −5.11428 | −0.194276 | ||||||||
\(694\) | −7.03399 | −0.267007 | ||||||||
\(695\) | −38.0183 | −1.44212 | ||||||||
\(696\) | −13.5140 | −0.512248 | ||||||||
\(697\) | −1.86102 | −0.0704912 | ||||||||
\(698\) | 7.02669 | 0.265964 | ||||||||
\(699\) | 18.1525 | 0.686591 | ||||||||
\(700\) | −0.850295 | −0.0321381 | ||||||||
\(701\) | −18.2679 | −0.689969 | −0.344984 | − | 0.938608i | \(-0.612116\pi\) | ||||
−0.344984 | + | 0.938608i | \(0.612116\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.75857 | 0.0663258 | ||||||||
\(704\) | 6.48875 | 0.244554 | ||||||||
\(705\) | 26.1968 | 0.986628 | ||||||||
\(706\) | 18.1008 | 0.681231 | ||||||||
\(707\) | −8.65561 | −0.325528 | ||||||||
\(708\) | 8.06575 | 0.303129 | ||||||||
\(709\) | 42.0282 | 1.57840 | 0.789201 | − | 0.614135i | \(-0.210495\pi\) | ||||
0.789201 | + | 0.614135i | \(0.210495\pi\) | |||||||
\(710\) | 6.02457 | 0.226098 | ||||||||
\(711\) | 5.42070 | 0.203292 | ||||||||
\(712\) | −13.0755 | −0.490025 | ||||||||
\(713\) | 14.5914 | 0.546452 | ||||||||
\(714\) | 0.333567 | 0.0124834 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.8234 | −0.965064 | ||||||||
\(717\) | −17.0258 | −0.635841 | ||||||||
\(718\) | 49.2699 | 1.83874 | ||||||||
\(719\) | 18.9870 | 0.708094 | 0.354047 | − | 0.935228i | \(-0.384805\pi\) | ||||
0.354047 | + | 0.935228i | \(0.384805\pi\) | |||||||
\(720\) | −10.2633 | −0.382490 | ||||||||
\(721\) | 14.0880 | 0.524665 | ||||||||
\(722\) | −33.6069 | −1.25072 | ||||||||
\(723\) | 10.2368 | 0.380712 | ||||||||
\(724\) | −12.0465 | −0.447704 | ||||||||
\(725\) | 6.79123 | 0.252220 | ||||||||
\(726\) | −27.3100 | −1.01357 | ||||||||
\(727\) | 24.0558 | 0.892180 | 0.446090 | − | 0.894988i | \(-0.352816\pi\) | ||||
0.446090 | + | 0.894988i | \(0.352816\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −34.3479 | −1.27127 | ||||||||
\(731\) | −0.972699 | −0.0359766 | ||||||||
\(732\) | −10.5164 | −0.388698 | ||||||||
\(733\) | −13.1128 | −0.484333 | −0.242166 | − | 0.970235i | \(-0.577858\pi\) | ||||
−0.242166 | + | 0.970235i | \(0.577858\pi\) | |||||||
\(734\) | −28.9878 | −1.06996 | ||||||||
\(735\) | −2.07801 | −0.0766485 | ||||||||
\(736\) | 17.2545 | 0.636010 | ||||||||
\(737\) | 49.0443 | 1.80657 | ||||||||
\(738\) | 18.1154 | 0.666837 | ||||||||
\(739\) | −2.80795 | −0.103292 | −0.0516461 | − | 0.998665i | \(-0.516447\pi\) | ||||
−0.0516461 | + | 0.998665i | \(0.516447\pi\) | |||||||
\(740\) | 7.70739 | 0.283329 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.94588 | −0.365125 | ||||||||
\(743\) | 13.2186 | 0.484945 | 0.242472 | − | 0.970158i | \(-0.422042\pi\) | ||||
0.242472 | + | 0.970158i | \(0.422042\pi\) | |||||||
\(744\) | −7.09821 | −0.260233 | ||||||||
\(745\) | −45.4256 | −1.66426 | ||||||||
\(746\) | −14.8363 | −0.543195 | ||||||||
\(747\) | −3.99899 | −0.146315 | ||||||||
\(748\) | 1.18056 | 0.0431655 | ||||||||
\(749\) | 4.66386 | 0.170414 | ||||||||
\(750\) | 21.2755 | 0.776871 | ||||||||
\(751\) | −5.25633 | −0.191806 | −0.0959031 | − | 0.995391i | \(-0.530574\pi\) | ||||
−0.0959031 | + | 0.995391i | \(0.530574\pi\) | |||||||
\(752\) | 62.2644 | 2.27055 | ||||||||
\(753\) | −17.3844 | −0.633524 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.3300 | 0.521521 | ||||||||
\(756\) | −1.24698 | −0.0453522 | ||||||||
\(757\) | −33.7607 | −1.22705 | −0.613526 | − | 0.789675i | \(-0.710249\pi\) | ||||
−0.613526 | + | 0.789675i | \(0.710249\pi\) | |||||||
\(758\) | −14.7486 | −0.535692 | ||||||||
\(759\) | −14.2652 | −0.517796 | ||||||||
\(760\) | −1.66707 | −0.0604708 | ||||||||
\(761\) | −24.6020 | −0.891823 | −0.445911 | − | 0.895077i | \(-0.647120\pi\) | ||||
−0.445911 | + | 0.895077i | \(0.647120\pi\) | |||||||
\(762\) | 9.63576 | 0.349067 | ||||||||
\(763\) | 2.35477 | 0.0852485 | ||||||||
\(764\) | −12.9874 | −0.469867 | ||||||||
\(765\) | −0.384672 | −0.0139078 | ||||||||
\(766\) | −47.4248 | −1.71353 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −20.7114 | −0.747358 | ||||||||
\(769\) | −26.9935 | −0.973411 | −0.486705 | − | 0.873566i | \(-0.661801\pi\) | ||||
−0.486705 | + | 0.873566i | \(0.661801\pi\) | |||||||
\(770\) | −19.1501 | −0.690123 | ||||||||
\(771\) | 1.26764 | 0.0456530 | ||||||||
\(772\) | −32.7370 | −1.17823 | ||||||||
\(773\) | 43.0722 | 1.54920 | 0.774599 | − | 0.632453i | \(-0.217952\pi\) | ||||
0.774599 | + | 0.632453i | \(0.217952\pi\) | |||||||
\(774\) | 9.46836 | 0.340333 | ||||||||
\(775\) | 3.56708 | 0.128133 | ||||||||
\(776\) | −4.13918 | −0.148588 | ||||||||
\(777\) | −2.97441 | −0.106706 | ||||||||
\(778\) | 52.3863 | 1.87814 | ||||||||
\(779\) | 5.94384 | 0.212960 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.22855 | −0.294441 | ||||||||
\(782\) | 0.930417 | 0.0332717 | ||||||||
\(783\) | 9.95951 | 0.355924 | ||||||||
\(784\) | −4.93900 | −0.176393 | ||||||||
\(785\) | 10.1216 | 0.361255 | ||||||||
\(786\) | 30.3480 | 1.08248 | ||||||||
\(787\) | −20.8945 | −0.744807 | −0.372403 | − | 0.928071i | \(-0.621466\pi\) | ||||
−0.372403 | + | 0.928071i | \(0.621466\pi\) | |||||||
\(788\) | 15.5323 | 0.553316 | ||||||||
\(789\) | −14.3084 | −0.509393 | ||||||||
\(790\) | 20.2975 | 0.722152 | ||||||||
\(791\) | −6.58305 | −0.234066 | ||||||||
\(792\) | 6.93955 | 0.246586 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.21031 | 0.326862 | ||||||||
\(795\) | 11.4697 | 0.406787 | ||||||||
\(796\) | −12.8561 | −0.455672 | ||||||||
\(797\) | −8.62449 | −0.305495 | −0.152748 | − | 0.988265i | \(-0.548812\pi\) | ||||
−0.152748 | + | 0.988265i | \(0.548812\pi\) | |||||||
\(798\) | −1.06537 | −0.0377135 | ||||||||
\(799\) | 2.33370 | 0.0825602 | ||||||||
\(800\) | 4.21812 | 0.149133 | ||||||||
\(801\) | 9.63632 | 0.340483 | ||||||||
\(802\) | 27.0236 | 0.954236 | ||||||||
\(803\) | 46.9135 | 1.65554 | ||||||||
\(804\) | 11.9581 | 0.421730 | ||||||||
\(805\) | −5.79618 | −0.204288 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.23326 | 0.219421 | ||||||||
\(808\) | 11.7448 | 0.413179 | ||||||||
\(809\) | 25.7533 | 0.905439 | 0.452720 | − | 0.891653i | \(-0.350454\pi\) | ||||
0.452720 | + | 0.891653i | \(0.350454\pi\) | |||||||
\(810\) | 3.74444 | 0.131566 | ||||||||
\(811\) | 22.3107 | 0.783433 | 0.391717 | − | 0.920086i | \(-0.371881\pi\) | ||||
0.391717 | + | 0.920086i | \(0.371881\pi\) | |||||||
\(812\) | −12.4193 | −0.435832 | ||||||||
\(813\) | 10.8204 | 0.379487 | ||||||||
\(814\) | −27.4110 | −0.960757 | ||||||||
\(815\) | 43.9034 | 1.53787 | ||||||||
\(816\) | −0.914287 | −0.0320064 | ||||||||
\(817\) | 3.10666 | 0.108688 | ||||||||
\(818\) | 57.9585 | 2.02647 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 26.0504 | 0.909720 | ||||||||
\(821\) | 18.3608 | 0.640797 | 0.320399 | − | 0.947283i | \(-0.396183\pi\) | ||||
0.320399 | + | 0.947283i | \(0.396183\pi\) | |||||||
\(822\) | −39.8893 | −1.39130 | ||||||||
\(823\) | 31.6172 | 1.10211 | 0.551053 | − | 0.834470i | \(-0.314226\pi\) | ||||
0.551053 | + | 0.834470i | \(0.314226\pi\) | |||||||
\(824\) | −19.1160 | −0.665936 | ||||||||
\(825\) | −3.48734 | −0.121414 | ||||||||
\(826\) | −11.6553 | −0.405541 | ||||||||
\(827\) | 25.2749 | 0.878893 | 0.439446 | − | 0.898269i | \(-0.355175\pi\) | ||||
0.439446 | + | 0.898269i | \(0.355175\pi\) | |||||||
\(828\) | −3.47819 | −0.120876 | ||||||||
\(829\) | 32.3697 | 1.12425 | 0.562123 | − | 0.827054i | \(-0.309985\pi\) | ||||
0.562123 | + | 0.827054i | \(0.309985\pi\) | |||||||
\(830\) | −14.9740 | −0.519754 | ||||||||
\(831\) | −16.5661 | −0.574671 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.185116 | −0.00641388 | ||||||||
\(834\) | 32.9675 | 1.14157 | ||||||||
\(835\) | 1.67085 | 0.0578221 | ||||||||
\(836\) | −3.77054 | −0.130407 | ||||||||
\(837\) | 5.23122 | 0.180817 | ||||||||
\(838\) | −41.1925 | −1.42297 | ||||||||
\(839\) | 39.1606 | 1.35197 | 0.675987 | − | 0.736914i | \(-0.263718\pi\) | ||||
0.675987 | + | 0.736914i | \(0.263718\pi\) | |||||||
\(840\) | 2.81964 | 0.0972868 | ||||||||
\(841\) | 70.1919 | 2.42041 | ||||||||
\(842\) | 43.8340 | 1.51062 | ||||||||
\(843\) | −21.4915 | −0.740208 | ||||||||
\(844\) | 17.5424 | 0.603833 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −22.7165 | −0.781008 | ||||||||
\(847\) | 15.1559 | 0.520763 | ||||||||
\(848\) | 27.2611 | 0.936148 | ||||||||
\(849\) | 24.4327 | 0.838527 | ||||||||
\(850\) | 0.227454 | 0.00780160 | ||||||||
\(851\) | −8.29651 | −0.284401 | ||||||||
\(852\) | −2.00631 | −0.0687351 | ||||||||
\(853\) | −42.6091 | −1.45891 | −0.729454 | − | 0.684029i | \(-0.760226\pi\) | ||||
−0.729454 | + | 0.684029i | \(0.760226\pi\) | |||||||
\(854\) | 15.1967 | 0.520019 | ||||||||
\(855\) | 1.22859 | 0.0420168 | ||||||||
\(856\) | −6.32838 | −0.216300 | ||||||||
\(857\) | −33.6003 | −1.14776 | −0.573882 | − | 0.818938i | \(-0.694563\pi\) | ||||
−0.573882 | + | 0.818938i | \(0.694563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.3846 | −1.78734 | −0.893670 | − | 0.448725i | \(-0.851878\pi\) | ||||
−0.893670 | + | 0.448725i | \(0.851878\pi\) | |||||||
\(860\) | 13.6158 | 0.464293 | ||||||||
\(861\) | −10.0533 | −0.342615 | ||||||||
\(862\) | −45.3437 | −1.54441 | ||||||||
\(863\) | −26.1175 | −0.889048 | −0.444524 | − | 0.895767i | \(-0.646627\pi\) | ||||
−0.444524 | + | 0.895767i | \(0.646627\pi\) | |||||||
\(864\) | 6.18598 | 0.210451 | ||||||||
\(865\) | 37.8782 | 1.28790 | ||||||||
\(866\) | −53.9893 | −1.83463 | ||||||||
\(867\) | 16.9657 | 0.576186 | ||||||||
\(868\) | −6.52322 | −0.221412 | ||||||||
\(869\) | −27.7230 | −0.940438 | ||||||||
\(870\) | 37.2928 | 1.26434 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.19518 | −0.108202 | ||||||||
\(873\) | 3.05048 | 0.103243 | ||||||||
\(874\) | −2.97162 | −0.100517 | ||||||||
\(875\) | −11.8070 | −0.399149 | ||||||||
\(876\) | 11.4386 | 0.386474 | ||||||||
\(877\) | −46.4595 | −1.56883 | −0.784414 | − | 0.620238i | \(-0.787036\pi\) | ||||
−0.784414 | + | 0.620238i | \(0.787036\pi\) | |||||||
\(878\) | 34.5947 | 1.16751 | ||||||||
\(879\) | 11.1636 | 0.376541 | ||||||||
\(880\) | 52.4893 | 1.76942 | ||||||||
\(881\) | 9.96703 | 0.335798 | 0.167899 | − | 0.985804i | \(-0.446302\pi\) | ||||
0.167899 | + | 0.985804i | \(0.446302\pi\) | |||||||
\(882\) | 1.80194 | 0.0606744 | ||||||||
\(883\) | 18.4968 | 0.622469 | 0.311234 | − | 0.950333i | \(-0.399258\pi\) | ||||
0.311234 | + | 0.950333i | \(0.399258\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.4410 | 0.451815 | ||||||||
\(886\) | −15.5167 | −0.521294 | ||||||||
\(887\) | 3.55868 | 0.119489 | 0.0597443 | − | 0.998214i | \(-0.480971\pi\) | ||||
0.0597443 | + | 0.998214i | \(0.480971\pi\) | |||||||
\(888\) | 4.03597 | 0.135438 | ||||||||
\(889\) | −5.34744 | −0.179347 | ||||||||
\(890\) | 36.0826 | 1.20949 | ||||||||
\(891\) | −5.11428 | −0.171335 | ||||||||
\(892\) | −29.1895 | −0.977336 | ||||||||
\(893\) | −7.45349 | −0.249422 | ||||||||
\(894\) | 39.3906 | 1.31742 | ||||||||
\(895\) | −43.0329 | −1.43843 | ||||||||
\(896\) | 10.0858 | 0.336941 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −37.3685 | −1.24700 | ||||||||
\(899\) | 52.1004 | 1.73764 | ||||||||
\(900\) | −0.850295 | −0.0283432 | ||||||||
\(901\) | 1.02176 | 0.0340396 | ||||||||
\(902\) | −92.6472 | −3.08482 | ||||||||
\(903\) | −5.25454 | −0.174860 | ||||||||
\(904\) | 8.93251 | 0.297091 | ||||||||
\(905\) | −20.0746 | −0.667304 | ||||||||
\(906\) | −12.4262 | −0.412832 | ||||||||
\(907\) | 11.9822 | 0.397862 | 0.198931 | − | 0.980014i | \(-0.436253\pi\) | ||||
0.198931 | + | 0.980014i | \(0.436253\pi\) | |||||||
\(908\) | −2.24173 | −0.0743943 | ||||||||
\(909\) | −8.65561 | −0.287088 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.98797 | 0.198390 | 0.0991952 | − | 0.995068i | \(-0.468373\pi\) | ||||
0.0991952 | + | 0.995068i | \(0.468373\pi\) | |||||||
\(912\) | 2.92010 | 0.0966943 | ||||||||
\(913\) | 20.4520 | 0.676861 | ||||||||
\(914\) | 31.0415 | 1.02676 | ||||||||
\(915\) | −17.5249 | −0.579355 | ||||||||
\(916\) | 5.98754 | 0.197834 | ||||||||
\(917\) | −16.8419 | −0.556168 | ||||||||
\(918\) | 0.333567 | 0.0110094 | ||||||||
\(919\) | −46.7567 | −1.54236 | −0.771180 | − | 0.636617i | \(-0.780333\pi\) | ||||
−0.771180 | + | 0.636617i | \(0.780333\pi\) | |||||||
\(920\) | 7.86481 | 0.259295 | ||||||||
\(921\) | −2.87863 | −0.0948541 | ||||||||
\(922\) | 67.2548 | 2.21492 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 6.37741 | 0.209801 | ||||||||
\(925\) | −2.02820 | −0.0666869 | ||||||||
\(926\) | 1.22299 | 0.0401899 | ||||||||
\(927\) | 14.0880 | 0.462711 | ||||||||
\(928\) | 61.6093 | 2.02243 | ||||||||
\(929\) | 53.8880 | 1.76801 | 0.884004 | − | 0.467480i | \(-0.154838\pi\) | ||||
0.884004 | + | 0.467480i | \(0.154838\pi\) | |||||||
\(930\) | 19.5880 | 0.642315 | ||||||||
\(931\) | 0.591233 | 0.0193769 | ||||||||
\(932\) | −22.6358 | −0.741461 | ||||||||
\(933\) | −27.7786 | −0.909431 | ||||||||
\(934\) | −38.3582 | −1.25512 | ||||||||
\(935\) | 1.96732 | 0.0643383 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.58874 | −0.313251 | −0.156625 | − | 0.987658i | \(-0.550062\pi\) | ||||
−0.156625 | + | 0.987658i | \(0.550062\pi\) | |||||||
\(938\) | −17.2800 | −0.564212 | ||||||||
\(939\) | −21.2336 | −0.692931 | ||||||||
\(940\) | −32.6669 | −1.06548 | ||||||||
\(941\) | −19.5667 | −0.637857 | −0.318929 | − | 0.947779i | \(-0.603323\pi\) | ||||
−0.318929 | + | 0.947779i | \(0.603323\pi\) | |||||||
\(942\) | −8.77691 | −0.285967 | ||||||||
\(943\) | −28.0416 | −0.913160 | ||||||||
\(944\) | 31.9466 | 1.03977 | ||||||||
\(945\) | −2.07801 | −0.0675976 | ||||||||
\(946\) | −48.4239 | −1.57440 | ||||||||
\(947\) | −44.3870 | −1.44238 | −0.721191 | − | 0.692736i | \(-0.756405\pi\) | ||||
−0.721191 | + | 0.692736i | \(0.756405\pi\) | |||||||
\(948\) | −6.75950 | −0.219538 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.726455 | −0.0235693 | ||||||||
\(951\) | 1.54637 | 0.0501446 | ||||||||
\(952\) | 0.251183 | 0.00814088 | ||||||||
\(953\) | −60.0690 | −1.94583 | −0.972913 | − | 0.231172i | \(-0.925744\pi\) | ||||
−0.972913 | + | 0.231172i | \(0.925744\pi\) | |||||||
\(954\) | −9.94588 | −0.322010 | ||||||||
\(955\) | −21.6426 | −0.700338 | ||||||||
\(956\) | 21.2308 | 0.686655 | ||||||||
\(957\) | −50.9358 | −1.64652 | ||||||||
\(958\) | 9.04318 | 0.292172 | ||||||||
\(959\) | 22.1369 | 0.714838 | ||||||||
\(960\) | 2.63647 | 0.0850918 | ||||||||
\(961\) | −3.63439 | −0.117238 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.66386 | 0.150291 | ||||||||
\(964\) | −12.7651 | −0.411137 | ||||||||
\(965\) | −54.5540 | −1.75615 | ||||||||
\(966\) | 5.02614 | 0.161713 | ||||||||
\(967\) | 50.5268 | 1.62483 | 0.812416 | − | 0.583078i | \(-0.198152\pi\) | ||||
0.812416 | + | 0.583078i | \(0.198152\pi\) | |||||||
\(968\) | −20.5650 | −0.660983 | ||||||||
\(969\) | 0.109447 | 0.00351593 | ||||||||
\(970\) | 11.4223 | 0.366749 | ||||||||
\(971\) | −50.4985 | −1.62057 | −0.810287 | − | 0.586033i | \(-0.800689\pi\) | ||||
−0.810287 | + | 0.586033i | \(0.800689\pi\) | |||||||
\(972\) | −1.24698 | −0.0399969 | ||||||||
\(973\) | −18.2956 | −0.586529 | ||||||||
\(974\) | 29.3462 | 0.940314 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −41.6531 | −1.33328 | ||||||||
\(977\) | −39.0091 | −1.24801 | −0.624006 | − | 0.781420i | \(-0.714496\pi\) | ||||
−0.624006 | + | 0.781420i | \(0.714496\pi\) | |||||||
\(978\) | −38.0707 | −1.21737 | ||||||||
\(979\) | −49.2829 | −1.57509 | ||||||||
\(980\) | 2.59123 | 0.0827739 | ||||||||
\(981\) | 2.35477 | 0.0751821 | ||||||||
\(982\) | −6.66040 | −0.212542 | ||||||||
\(983\) | −35.4127 | −1.12949 | −0.564744 | − | 0.825266i | \(-0.691025\pi\) | ||||
−0.564744 | + | 0.825266i | \(0.691025\pi\) | |||||||
\(984\) | 13.6413 | 0.434867 | ||||||||
\(985\) | 25.8836 | 0.824720 | ||||||||
\(986\) | 3.32217 | 0.105799 | ||||||||
\(987\) | 12.6067 | 0.401275 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.6565 | −0.466049 | ||||||||
\(990\) | −19.1501 | −0.608631 | ||||||||
\(991\) | 46.8170 | 1.48719 | 0.743596 | − | 0.668629i | \(-0.233119\pi\) | ||||
0.743596 | + | 0.668629i | \(0.233119\pi\) | |||||||
\(992\) | 32.3602 | 1.02744 | ||||||||
\(993\) | −24.2044 | −0.768104 | ||||||||
\(994\) | 2.89920 | 0.0919571 | ||||||||
\(995\) | −21.4238 | −0.679180 | ||||||||
\(996\) | 4.98666 | 0.158008 | ||||||||
\(997\) | −20.4746 | −0.648436 | −0.324218 | − | 0.945982i | \(-0.605101\pi\) | ||||
−0.324218 | + | 0.945982i | \(0.605101\pi\) | |||||||
\(998\) | 72.9895 | 2.31044 | ||||||||
\(999\) | −2.97441 | −0.0941062 |
(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 | 3549.2.a.z.1.6 | yes | 6 | |
13.12 | even | 2 | 3549.2.a.y.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.y.1.1 | ✓ | 6 | 13.12 | even | 2 | ||
3549.2.a.z.1.6 | yes | 6 | 1.1 | even | 1 | trivial |