Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [207,2,Mod(1,207)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(207, 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("207.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 207 = 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 207.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: | \(1.65290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 69) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 207.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23607 | −1.58114 | −0.790569 | − | 0.612372i | \(-0.790215\pi\) | ||||
−0.790569 | + | 0.612372i | \(0.790215\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.00000 | 1.50000 | ||||||||
\(5\) | 3.23607 | 1.44721 | 0.723607 | − | 0.690212i | \(-0.242483\pi\) | ||||
0.723607 | + | 0.690212i | \(0.242483\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.23607 | −0.467190 | −0.233595 | − | 0.972334i | \(-0.575049\pi\) | ||||
−0.233595 | + | 0.972334i | \(0.575049\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.23607 | −2.28825 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | 2.76393 | 0.738692 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 7.23607 | 1.75500 | 0.877502 | − | 0.479573i | \(-0.159208\pi\) | ||||
0.877502 | + | 0.479573i | \(0.159208\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.76393 | 0.634089 | 0.317045 | − | 0.948411i | \(-0.397309\pi\) | ||||
0.317045 | + | 0.948411i | \(0.397309\pi\) | |||||||
\(20\) | 9.70820 | 2.17082 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.94427 | 1.90693 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | −10.0000 | −1.96116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.70820 | −0.700785 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.47214 | 0.444009 | 0.222004 | − | 0.975046i | \(-0.428740\pi\) | ||||
0.222004 | + | 0.975046i | \(0.428740\pi\) | |||||||
\(32\) | 6.70820 | 1.18585 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −16.1803 | −2.77491 | ||||||||
\(35\) | −4.00000 | −0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | −6.18034 | −1.00258 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.23607 | −1.14412 | ||||||||
\(41\) | −6.94427 | −1.08451 | −0.542257 | − | 0.840213i | \(-0.682430\pi\) | ||||
−0.542257 | + | 0.840213i | \(0.682430\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.70820 | 1.17549 | 0.587745 | − | 0.809046i | \(-0.300016\pi\) | ||||
0.587745 | + | 0.809046i | \(0.300016\pi\) | |||||||
\(44\) | −12.0000 | −1.80907 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.23607 | 0.329690 | ||||||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.47214 | −0.781734 | ||||||||
\(50\) | −12.2361 | −1.73044 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13.4164 | 1.86052 | ||||||||
\(53\) | 0.763932 | 0.104934 | 0.0524671 | − | 0.998623i | \(-0.483292\pi\) | ||||
0.0524671 | + | 0.998623i | \(0.483292\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.9443 | −1.74541 | ||||||||
\(56\) | 2.76393 | 0.369346 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.0000 | −1.31306 | ||||||||
\(59\) | −12.9443 | −1.68520 | −0.842600 | − | 0.538539i | \(-0.818976\pi\) | ||||
−0.842600 | + | 0.538539i | \(0.818976\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.47214 | −0.572598 | −0.286299 | − | 0.958140i | \(-0.592425\pi\) | ||||
−0.286299 | + | 0.958140i | \(0.592425\pi\) | |||||||
\(62\) | −5.52786 | −0.702039 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | 14.4721 | 1.79505 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.23607 | 0.639688 | 0.319844 | − | 0.947470i | \(-0.396370\pi\) | ||||
0.319844 | + | 0.947470i | \(0.396370\pi\) | |||||||
\(68\) | 21.7082 | 2.63251 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.94427 | 1.06904 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.9443 | −1.28093 | −0.640465 | − | 0.767987i | \(-0.721258\pi\) | ||||
−0.640465 | + | 0.767987i | \(0.721258\pi\) | |||||||
\(74\) | 10.0000 | 1.16248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.29180 | 0.951134 | ||||||||
\(77\) | 4.94427 | 0.563452 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.70820 | −0.417206 | −0.208603 | − | 0.978000i | \(-0.566892\pi\) | ||||
−0.208603 | + | 0.978000i | \(0.566892\pi\) | |||||||
\(80\) | −3.23607 | −0.361803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 15.5279 | 1.71477 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23.4164 | 2.53987 | ||||||||
\(86\) | −17.2361 | −1.85861 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.94427 | 0.953463 | ||||||||
\(89\) | −3.23607 | −0.343023 | −0.171511 | − | 0.985182i | \(-0.554865\pi\) | ||||
−0.171511 | + | 0.985182i | \(0.554865\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.52786 | −0.579478 | ||||||||
\(92\) | −3.00000 | −0.312772 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.94427 | −0.922531 | ||||||||
\(95\) | 8.94427 | 0.917663 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.472136 | −0.0479381 | −0.0239691 | − | 0.999713i | \(-0.507630\pi\) | ||||
−0.0239691 | + | 0.999713i | \(0.507630\pi\) | |||||||
\(98\) | 12.2361 | 1.23603 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 16.4164 | 1.64164 | ||||||||
\(101\) | −10.9443 | −1.08900 | −0.544498 | − | 0.838762i | \(-0.683280\pi\) | ||||
−0.544498 | + | 0.838762i | \(0.683280\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.76393 | −0.666470 | −0.333235 | − | 0.942844i | \(-0.608140\pi\) | ||||
−0.333235 | + | 0.942844i | \(0.608140\pi\) | |||||||
\(104\) | −10.0000 | −0.980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.70820 | −0.165915 | ||||||||
\(107\) | 0.944272 | 0.0912862 | 0.0456431 | − | 0.998958i | \(-0.485466\pi\) | ||||
0.0456431 | + | 0.998958i | \(0.485466\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.94427 | 0.282010 | 0.141005 | − | 0.990009i | \(-0.454967\pi\) | ||||
0.141005 | + | 0.990009i | \(0.454967\pi\) | |||||||
\(110\) | 28.9443 | 2.75973 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.23607 | 0.116797 | ||||||||
\(113\) | −16.1803 | −1.52212 | −0.761059 | − | 0.648682i | \(-0.775320\pi\) | ||||
−0.761059 | + | 0.648682i | \(0.775320\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.23607 | −0.301765 | ||||||||
\(116\) | 13.4164 | 1.24568 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 28.9443 | 2.66454 | ||||||||
\(119\) | −8.94427 | −0.819920 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 10.0000 | 0.905357 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.41641 | 0.666013 | ||||||||
\(125\) | 1.52786 | 0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.4721 | 0.929252 | 0.464626 | − | 0.885507i | \(-0.346189\pi\) | ||||
0.464626 | + | 0.885507i | \(0.346189\pi\) | |||||||
\(128\) | 15.6525 | 1.38350 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −32.3607 | −2.83822 | ||||||||
\(131\) | 0.944272 | 0.0825014 | 0.0412507 | − | 0.999149i | \(-0.486866\pi\) | ||||
0.0412507 | + | 0.999149i | \(0.486866\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.41641 | −0.296240 | ||||||||
\(134\) | −11.7082 | −1.01143 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.1803 | −1.38745 | ||||||||
\(137\) | −3.23607 | −0.276476 | −0.138238 | − | 0.990399i | \(-0.544144\pi\) | ||||
−0.138238 | + | 0.990399i | \(0.544144\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.94427 | 0.758643 | 0.379322 | − | 0.925265i | \(-0.376157\pi\) | ||||
0.379322 | + | 0.925265i | \(0.376157\pi\) | |||||||
\(140\) | −12.0000 | −1.01419 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −17.8885 | −1.50117 | ||||||||
\(143\) | −17.8885 | −1.49592 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.4721 | 1.20185 | ||||||||
\(146\) | 24.4721 | 2.02533 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.4164 | −1.10282 | ||||||||
\(149\) | −1.70820 | −0.139942 | −0.0699708 | − | 0.997549i | \(-0.522291\pi\) | ||||
−0.0699708 | + | 0.997549i | \(0.522291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | −6.18034 | −0.501292 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.0557 | −0.890896 | ||||||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.4721 | −0.995385 | −0.497692 | − | 0.867354i | \(-0.665819\pi\) | ||||
−0.497692 | + | 0.867354i | \(0.665819\pi\) | |||||||
\(158\) | 8.29180 | 0.659660 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 21.7082 | 1.71618 | ||||||||
\(161\) | 1.23607 | 0.0974158 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.4164 | −1.52081 | −0.760405 | − | 0.649449i | \(-0.775000\pi\) | ||||
−0.760405 | + | 0.649449i | \(0.775000\pi\) | |||||||
\(164\) | −20.8328 | −1.62677 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.94427 | 0.694210 | ||||||||
\(167\) | 4.94427 | 0.382599 | 0.191300 | − | 0.981532i | \(-0.438730\pi\) | ||||
0.191300 | + | 0.981532i | \(0.438730\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | −52.3607 | −4.01588 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 23.1246 | 1.76324 | ||||||||
\(173\) | 4.47214 | 0.340010 | 0.170005 | − | 0.985443i | \(-0.445622\pi\) | ||||
0.170005 | + | 0.985443i | \(0.445622\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.76393 | −0.511305 | ||||||||
\(176\) | 4.00000 | 0.301511 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.23607 | 0.542366 | ||||||||
\(179\) | −3.05573 | −0.228396 | −0.114198 | − | 0.993458i | \(-0.536430\pi\) | ||||
−0.114198 | + | 0.993458i | \(0.536430\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.8885 | 1.77562 | 0.887811 | − | 0.460209i | \(-0.152225\pi\) | ||||
0.887811 | + | 0.460209i | \(0.152225\pi\) | |||||||
\(182\) | 12.3607 | 0.916235 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.23607 | 0.164845 | ||||||||
\(185\) | −14.4721 | −1.06401 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.9443 | −2.11661 | ||||||||
\(188\) | 12.0000 | 0.875190 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.0000 | −1.45095 | ||||||||
\(191\) | −10.4721 | −0.757737 | −0.378869 | − | 0.925450i | \(-0.623687\pi\) | ||||
−0.378869 | + | 0.925450i | \(0.623687\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.41641 | −0.677808 | −0.338904 | − | 0.940821i | \(-0.610056\pi\) | ||||
−0.338904 | + | 0.940821i | \(0.610056\pi\) | |||||||
\(194\) | 1.05573 | 0.0757969 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.4164 | −1.17260 | ||||||||
\(197\) | 9.41641 | 0.670891 | 0.335446 | − | 0.942060i | \(-0.391113\pi\) | ||||
0.335446 | + | 0.942060i | \(0.391113\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.70820 | −0.262868 | −0.131434 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131434 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(200\) | −12.2361 | −0.865221 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.4721 | 1.72185 | ||||||||
\(203\) | −5.52786 | −0.387980 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.4721 | −1.56952 | ||||||||
\(206\) | 15.1246 | 1.05378 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.47214 | −0.310087 | ||||||||
\(209\) | −11.0557 | −0.764741 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.4721 | 1.54705 | 0.773523 | − | 0.633768i | \(-0.218493\pi\) | ||||
0.773523 | + | 0.633768i | \(0.218493\pi\) | |||||||
\(212\) | 2.29180 | 0.157401 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.11146 | −0.144336 | ||||||||
\(215\) | 24.9443 | 1.70119 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.05573 | −0.207436 | ||||||||
\(218\) | −6.58359 | −0.445897 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −38.8328 | −2.61811 | ||||||||
\(221\) | 32.3607 | 2.17681 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.88854 | 0.662186 | 0.331093 | − | 0.943598i | \(-0.392583\pi\) | ||||
0.331093 | + | 0.943598i | \(0.392583\pi\) | |||||||
\(224\) | −8.29180 | −0.554019 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 36.1803 | 2.40668 | ||||||||
\(227\) | 22.4721 | 1.49153 | 0.745764 | − | 0.666210i | \(-0.232085\pi\) | ||||
0.745764 | + | 0.666210i | \(0.232085\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.9443 | −0.987545 | −0.493773 | − | 0.869591i | \(-0.664382\pi\) | ||||
−0.493773 | + | 0.869591i | \(0.664382\pi\) | |||||||
\(230\) | 7.23607 | 0.477132 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.0000 | −0.656532 | ||||||||
\(233\) | 14.0000 | 0.917170 | 0.458585 | − | 0.888650i | \(-0.348356\pi\) | ||||
0.458585 | + | 0.888650i | \(0.348356\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.9443 | 0.844391 | ||||||||
\(236\) | −38.8328 | −2.52780 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 20.0000 | 1.29641 | ||||||||
\(239\) | 12.9443 | 0.837295 | 0.418648 | − | 0.908149i | \(-0.362504\pi\) | ||||
0.418648 | + | 0.908149i | \(0.362504\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.4721 | 1.83405 | 0.917026 | − | 0.398828i | \(-0.130583\pi\) | ||||
0.917026 | + | 0.398828i | \(0.130583\pi\) | |||||||
\(242\) | −11.1803 | −0.718699 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.4164 | −0.858898 | ||||||||
\(245\) | −17.7082 | −1.13134 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.3607 | 0.786491 | ||||||||
\(248\) | −5.52786 | −0.351020 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.41641 | −0.216073 | ||||||||
\(251\) | 1.52786 | 0.0964379 | 0.0482190 | − | 0.998837i | \(-0.484645\pi\) | ||||
0.0482190 | + | 0.998837i | \(0.484645\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | −23.4164 | −1.46928 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | 22.0000 | 1.37232 | 0.686161 | − | 0.727450i | \(-0.259294\pi\) | ||||
0.686161 | + | 0.727450i | \(0.259294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.52786 | 0.343485 | ||||||||
\(260\) | 43.4164 | 2.69257 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.11146 | −0.130446 | ||||||||
\(263\) | 2.47214 | 0.152438 | 0.0762192 | − | 0.997091i | \(-0.475715\pi\) | ||||
0.0762192 | + | 0.997091i | \(0.475715\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.47214 | 0.151862 | ||||||||
\(266\) | 7.63932 | 0.468397 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.7082 | 0.959531 | ||||||||
\(269\) | −8.47214 | −0.516555 | −0.258278 | − | 0.966071i | \(-0.583155\pi\) | ||||
−0.258278 | + | 0.966071i | \(0.583155\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.4721 | −1.60807 | −0.804034 | − | 0.594583i | \(-0.797317\pi\) | ||||
−0.804034 | + | 0.594583i | \(0.797317\pi\) | |||||||
\(272\) | −7.23607 | −0.438751 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.23607 | 0.437147 | ||||||||
\(275\) | −21.8885 | −1.31993 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.8885 | −1.19499 | −0.597493 | − | 0.801874i | \(-0.703837\pi\) | ||||
−0.597493 | + | 0.801874i | \(0.703837\pi\) | |||||||
\(278\) | −20.0000 | −1.19952 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.94427 | 0.534522 | ||||||||
\(281\) | 6.65248 | 0.396853 | 0.198427 | − | 0.980116i | \(-0.436417\pi\) | ||||
0.198427 | + | 0.980116i | \(0.436417\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.70820 | −0.458205 | −0.229103 | − | 0.973402i | \(-0.573579\pi\) | ||||
−0.229103 | + | 0.973402i | \(0.573579\pi\) | |||||||
\(284\) | 24.0000 | 1.42414 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 40.0000 | 2.36525 | ||||||||
\(287\) | 8.58359 | 0.506673 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.3607 | 2.08004 | ||||||||
\(290\) | −32.3607 | −1.90028 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −32.8328 | −1.92140 | ||||||||
\(293\) | 5.70820 | 0.333477 | 0.166738 | − | 0.986001i | \(-0.446676\pi\) | ||||
0.166738 | + | 0.986001i | \(0.446676\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −41.8885 | −2.43885 | ||||||||
\(296\) | 10.0000 | 0.581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.81966 | 0.221267 | ||||||||
\(299\) | −4.47214 | −0.258630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.52786 | −0.549177 | ||||||||
\(302\) | 35.7771 | 2.05874 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.76393 | −0.158522 | ||||||||
\(305\) | −14.4721 | −0.828672 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.47214 | −0.369384 | −0.184692 | − | 0.982796i | \(-0.559129\pi\) | ||||
−0.184692 | + | 0.982796i | \(0.559129\pi\) | |||||||
\(308\) | 14.8328 | 0.845178 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.8885 | −1.01600 | ||||||||
\(311\) | −24.9443 | −1.41446 | −0.707230 | − | 0.706984i | \(-0.750055\pi\) | ||||
−0.707230 | + | 0.706984i | \(0.750055\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.9443 | 1.29689 | 0.648443 | − | 0.761263i | \(-0.275420\pi\) | ||||
0.648443 | + | 0.761263i | \(0.275420\pi\) | |||||||
\(314\) | 27.8885 | 1.57384 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.1246 | −0.625808 | ||||||||
\(317\) | −29.4164 | −1.65219 | −0.826095 | − | 0.563531i | \(-0.809443\pi\) | ||||
−0.826095 | + | 0.563531i | \(0.809443\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.8885 | −1.00157 | ||||||||
\(320\) | −42.0689 | −2.35172 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.76393 | −0.154028 | ||||||||
\(323\) | 20.0000 | 1.11283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.4721 | 1.35747 | ||||||||
\(326\) | 43.4164 | 2.40461 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.5279 | 0.857383 | ||||||||
\(329\) | −4.94427 | −0.272587 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.41641 | −0.187783 | −0.0938914 | − | 0.995582i | \(-0.529931\pi\) | ||||
−0.0938914 | + | 0.995582i | \(0.529931\pi\) | |||||||
\(332\) | −12.0000 | −0.658586 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.0557 | −0.604943 | ||||||||
\(335\) | 16.9443 | 0.925764 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.3607 | 1.65385 | 0.826926 | − | 0.562311i | \(-0.190088\pi\) | ||||
0.826926 | + | 0.562311i | \(0.190088\pi\) | |||||||
\(338\) | −15.6525 | −0.851382 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 70.2492 | 3.80980 | ||||||||
\(341\) | −9.88854 | −0.535495 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4164 | 0.832408 | ||||||||
\(344\) | −17.2361 | −0.929307 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.0000 | −0.537603 | ||||||||
\(347\) | −25.8885 | −1.38977 | −0.694885 | − | 0.719121i | \(-0.744545\pi\) | ||||
−0.694885 | + | 0.719121i | \(0.744545\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.4721 | −1.73819 | −0.869097 | − | 0.494642i | \(-0.835299\pi\) | ||||
−0.869097 | + | 0.494642i | \(0.835299\pi\) | |||||||
\(350\) | 15.1246 | 0.808445 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −26.8328 | −1.43019 | ||||||||
\(353\) | −9.41641 | −0.501185 | −0.250592 | − | 0.968093i | \(-0.580625\pi\) | ||||
−0.250592 | + | 0.968093i | \(0.580625\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.8885 | 1.37402 | ||||||||
\(356\) | −9.70820 | −0.514534 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.83282 | 0.361126 | ||||||||
\(359\) | 2.47214 | 0.130474 | 0.0652372 | − | 0.997870i | \(-0.479220\pi\) | ||||
0.0652372 | + | 0.997870i | \(0.479220\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3607 | −0.597931 | ||||||||
\(362\) | −53.4164 | −2.80750 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.5836 | −0.869216 | ||||||||
\(365\) | −35.4164 | −1.85378 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.2918 | 0.641627 | 0.320813 | − | 0.947142i | \(-0.396044\pi\) | ||||
0.320813 | + | 0.947142i | \(0.396044\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 32.3607 | 1.68235 | ||||||||
\(371\) | −0.944272 | −0.0490242 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.5279 | 0.596890 | 0.298445 | − | 0.954427i | \(-0.403532\pi\) | ||||
0.298445 | + | 0.954427i | \(0.403532\pi\) | |||||||
\(374\) | 64.7214 | 3.34666 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.94427 | −0.461266 | ||||||||
\(377\) | 20.0000 | 1.03005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0689 | −1.44180 | −0.720901 | − | 0.693038i | \(-0.756272\pi\) | ||||
−0.720901 | + | 0.693038i | \(0.756272\pi\) | |||||||
\(380\) | 26.8328 | 1.37649 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 23.4164 | 1.19809 | ||||||||
\(383\) | −34.4721 | −1.76144 | −0.880722 | − | 0.473634i | \(-0.842942\pi\) | ||||
−0.880722 | + | 0.473634i | \(0.842942\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | 21.0557 | 1.07171 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.41641 | −0.0719072 | ||||||||
\(389\) | 10.6525 | 0.540102 | 0.270051 | − | 0.962846i | \(-0.412959\pi\) | ||||
0.270051 | + | 0.962846i | \(0.412959\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.23607 | −0.365944 | ||||||||
\(392\) | 12.2361 | 0.618015 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.0557 | −1.06077 | ||||||||
\(395\) | −12.0000 | −0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.00000 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | 8.29180 | 0.415630 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.47214 | −0.273607 | ||||||||
\(401\) | 38.0689 | 1.90107 | 0.950535 | − | 0.310618i | \(-0.100536\pi\) | ||||
0.950535 | + | 0.310618i | \(0.100536\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.0557 | 0.550725 | ||||||||
\(404\) | −32.8328 | −1.63349 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.3607 | 0.613450 | ||||||||
\(407\) | 17.8885 | 0.886702 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.41641 | −0.465611 | −0.232806 | − | 0.972523i | \(-0.574791\pi\) | ||||
−0.232806 | + | 0.972523i | \(0.574791\pi\) | |||||||
\(410\) | 50.2492 | 2.48163 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.2918 | −0.999705 | ||||||||
\(413\) | 16.0000 | 0.787309 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.9443 | −0.635409 | ||||||||
\(416\) | 30.0000 | 1.47087 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 24.7214 | 1.20916 | ||||||||
\(419\) | 21.8885 | 1.06933 | 0.534663 | − | 0.845066i | \(-0.320439\pi\) | ||||
0.534663 | + | 0.845066i | \(0.320439\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0557 | −0.636297 | −0.318149 | − | 0.948041i | \(-0.603061\pi\) | ||||
−0.318149 | + | 0.948041i | \(0.603061\pi\) | |||||||
\(422\) | −50.2492 | −2.44609 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.70820 | −0.0829577 | ||||||||
\(425\) | 39.5967 | 1.92072 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.52786 | 0.267512 | ||||||||
\(428\) | 2.83282 | 0.136929 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −55.7771 | −2.68981 | ||||||||
\(431\) | −8.00000 | −0.385346 | −0.192673 | − | 0.981263i | \(-0.561716\pi\) | ||||
−0.192673 | + | 0.981263i | \(0.561716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.88854 | −0.379099 | −0.189550 | − | 0.981871i | \(-0.560703\pi\) | ||||
−0.189550 | + | 0.981871i | \(0.560703\pi\) | |||||||
\(434\) | 6.83282 | 0.327986 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.83282 | 0.423015 | ||||||||
\(437\) | −2.76393 | −0.132217 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.8885 | 1.23559 | 0.617796 | − | 0.786338i | \(-0.288026\pi\) | ||||
0.617796 | + | 0.786338i | \(0.288026\pi\) | |||||||
\(440\) | 28.9443 | 1.37986 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −72.3607 | −3.44185 | ||||||||
\(443\) | −18.8328 | −0.894774 | −0.447387 | − | 0.894340i | \(-0.647645\pi\) | ||||
−0.447387 | + | 0.894340i | \(0.647645\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.4721 | −0.496427 | ||||||||
\(446\) | −22.1115 | −1.04701 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.0689 | 0.759183 | ||||||||
\(449\) | 2.94427 | 0.138949 | 0.0694744 | − | 0.997584i | \(-0.477868\pi\) | ||||
0.0694744 | + | 0.997584i | \(0.477868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.7771 | 1.30797 | ||||||||
\(452\) | −48.5410 | −2.28318 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −50.2492 | −2.35831 | ||||||||
\(455\) | −17.8885 | −0.838628 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.472136 | −0.0220856 | −0.0110428 | − | 0.999939i | \(-0.503515\pi\) | ||||
−0.0110428 | + | 0.999939i | \(0.503515\pi\) | |||||||
\(458\) | 33.4164 | 1.56145 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.70820 | −0.452647 | ||||||||
\(461\) | −21.4164 | −0.997462 | −0.498731 | − | 0.866757i | \(-0.666200\pi\) | ||||
−0.498731 | + | 0.866757i | \(0.666200\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.94427 | 0.229780 | 0.114890 | − | 0.993378i | \(-0.463348\pi\) | ||||
0.114890 | + | 0.993378i | \(0.463348\pi\) | |||||||
\(464\) | −4.47214 | −0.207614 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −31.3050 | −1.45017 | ||||||||
\(467\) | 24.3607 | 1.12728 | 0.563639 | − | 0.826021i | \(-0.309401\pi\) | ||||
0.563639 | + | 0.826021i | \(0.309401\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.47214 | −0.298855 | ||||||||
\(470\) | −28.9443 | −1.33510 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 28.9443 | 1.33227 | ||||||||
\(473\) | −30.8328 | −1.41769 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.1246 | 0.693965 | ||||||||
\(476\) | −26.8328 | −1.22988 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −28.9443 | −1.32388 | ||||||||
\(479\) | −1.88854 | −0.0862898 | −0.0431449 | − | 0.999069i | \(-0.513738\pi\) | ||||
−0.0431449 | + | 0.999069i | \(0.513738\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | −0.911922 | ||||||||
\(482\) | −63.6656 | −2.89989 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.0000 | 0.681818 | ||||||||
\(485\) | −1.52786 | −0.0693767 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.0000 | 1.08754 | 0.543772 | − | 0.839233i | \(-0.316996\pi\) | ||||
0.543772 | + | 0.839233i | \(0.316996\pi\) | |||||||
\(488\) | 10.0000 | 0.452679 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 39.5967 | 1.78880 | ||||||||
\(491\) | −40.0000 | −1.80517 | −0.902587 | − | 0.430507i | \(-0.858335\pi\) | ||||
−0.902587 | + | 0.430507i | \(0.858335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.3607 | 1.45745 | ||||||||
\(494\) | −27.6393 | −1.24355 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.47214 | −0.111002 | ||||||||
\(497\) | −9.88854 | −0.443562 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.3607 | 1.44866 | 0.724331 | − | 0.689452i | \(-0.242149\pi\) | ||||
0.724331 | + | 0.689452i | \(0.242149\pi\) | |||||||
\(500\) | 4.58359 | 0.204984 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.41641 | −0.152482 | ||||||||
\(503\) | 36.9443 | 1.64726 | 0.823632 | − | 0.567125i | \(-0.191944\pi\) | ||||
0.823632 | + | 0.567125i | \(0.191944\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.4164 | −1.57601 | ||||||||
\(506\) | −8.94427 | −0.397621 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 31.4164 | 1.39388 | ||||||||
\(509\) | 7.52786 | 0.333667 | 0.166833 | − | 0.985985i | \(-0.446646\pi\) | ||||
0.166833 | + | 0.985985i | \(0.446646\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.5279 | 0.598437 | ||||||||
\(512\) | −11.1803 | −0.494106 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −49.1935 | −2.16983 | ||||||||
\(515\) | −21.8885 | −0.964524 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.0000 | −0.703679 | ||||||||
\(518\) | −12.3607 | −0.543097 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −32.3607 | −1.41911 | ||||||||
\(521\) | 28.7639 | 1.26017 | 0.630085 | − | 0.776526i | \(-0.283020\pi\) | ||||
0.630085 | + | 0.776526i | \(0.283020\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.5967 | −1.46908 | −0.734542 | − | 0.678564i | \(-0.762603\pi\) | ||||
−0.734542 | + | 0.678564i | \(0.762603\pi\) | |||||||
\(524\) | 2.83282 | 0.123752 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.52786 | −0.241026 | ||||||||
\(527\) | 17.8885 | 0.779237 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −5.52786 | −0.240115 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.2492 | −0.444360 | ||||||||
\(533\) | −31.0557 | −1.34517 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.05573 | 0.132111 | ||||||||
\(536\) | −11.7082 | −0.505717 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.9443 | 0.816746 | ||||||||
\(539\) | 21.8885 | 0.942806 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.4721 | −1.05214 | −0.526070 | − | 0.850441i | \(-0.676335\pi\) | ||||
−0.526070 | + | 0.850441i | \(0.676335\pi\) | |||||||
\(542\) | 59.1935 | 2.54258 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 48.5410 | 2.08118 | ||||||||
\(545\) | 9.52786 | 0.408129 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.4721 | 0.960839 | 0.480420 | − | 0.877039i | \(-0.340484\pi\) | ||||
0.480420 | + | 0.877039i | \(0.340484\pi\) | |||||||
\(548\) | −9.70820 | −0.414714 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 48.9443 | 2.08699 | ||||||||
\(551\) | 12.3607 | 0.526583 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.58359 | 0.194914 | ||||||||
\(554\) | 44.4721 | 1.88944 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 26.8328 | 1.13796 | ||||||||
\(557\) | 19.8197 | 0.839786 | 0.419893 | − | 0.907574i | \(-0.362068\pi\) | ||||
0.419893 | + | 0.907574i | \(0.362068\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.4721 | 1.45802 | ||||||||
\(560\) | 4.00000 | 0.169031 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.8754 | −0.627480 | ||||||||
\(563\) | −19.4164 | −0.818304 | −0.409152 | − | 0.912466i | \(-0.634175\pi\) | ||||
−0.409152 | + | 0.912466i | \(0.634175\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −52.3607 | −2.20283 | ||||||||
\(566\) | 17.2361 | 0.724486 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.8885 | −0.750587 | ||||||||
\(569\) | 15.2361 | 0.638729 | 0.319365 | − | 0.947632i | \(-0.396531\pi\) | ||||
0.319365 | + | 0.947632i | \(0.396531\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.2918 | 0.681790 | 0.340895 | − | 0.940101i | \(-0.389270\pi\) | ||||
0.340895 | + | 0.940101i | \(0.389270\pi\) | |||||||
\(572\) | −53.6656 | −2.24387 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.1935 | −0.801121 | ||||||||
\(575\) | −5.47214 | −0.228204 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.4721 | 0.685744 | 0.342872 | − | 0.939382i | \(-0.388600\pi\) | ||||
0.342872 | + | 0.939382i | \(0.388600\pi\) | |||||||
\(578\) | −79.0689 | −3.28883 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 43.4164 | 1.80277 | ||||||||
\(581\) | 4.94427 | 0.205123 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.05573 | −0.126555 | ||||||||
\(584\) | 24.4721 | 1.01266 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.7639 | −0.527273 | ||||||||
\(587\) | −16.9443 | −0.699365 | −0.349682 | − | 0.936868i | \(-0.613711\pi\) | ||||
−0.349682 | + | 0.936868i | \(0.613711\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.83282 | 0.281541 | ||||||||
\(590\) | 93.6656 | 3.85615 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.47214 | 0.183804 | ||||||||
\(593\) | −34.0000 | −1.39621 | −0.698106 | − | 0.715994i | \(-0.745974\pi\) | ||||
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.9443 | −1.18660 | ||||||||
\(596\) | −5.12461 | −0.209912 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.0000 | 0.408930 | ||||||||
\(599\) | 20.9443 | 0.855760 | 0.427880 | − | 0.903836i | \(-0.359261\pi\) | ||||
0.427880 | + | 0.903836i | \(0.359261\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.36068 | 0.0962941 | 0.0481471 | − | 0.998840i | \(-0.484668\pi\) | ||||
0.0481471 | + | 0.998840i | \(0.484668\pi\) | |||||||
\(602\) | 21.3050 | 0.868325 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −48.0000 | −1.95309 | ||||||||
\(605\) | 16.1803 | 0.657824 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.8328 | 1.57618 | 0.788088 | − | 0.615563i | \(-0.211071\pi\) | ||||
0.788088 | + | 0.615563i | \(0.211071\pi\) | |||||||
\(608\) | 18.5410 | 0.751938 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 32.3607 | 1.31025 | ||||||||
\(611\) | 17.8885 | 0.723693 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.5279 | −1.27340 | −0.636699 | − | 0.771112i | \(-0.719701\pi\) | ||||
−0.636699 | + | 0.771112i | \(0.719701\pi\) | |||||||
\(614\) | 14.4721 | 0.584048 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.0557 | −0.445448 | ||||||||
\(617\) | 33.7082 | 1.35704 | 0.678521 | − | 0.734581i | \(-0.262621\pi\) | ||||
0.678521 | + | 0.734581i | \(0.262621\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.1246 | 1.25100 | 0.625502 | − | 0.780223i | \(-0.284894\pi\) | ||||
0.625502 | + | 0.780223i | \(0.284894\pi\) | |||||||
\(620\) | 24.0000 | 0.963863 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 55.7771 | 2.23646 | ||||||||
\(623\) | 4.00000 | 0.160257 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | −51.3050 | −2.05056 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −37.4164 | −1.49308 | ||||||||
\(629\) | −32.3607 | −1.29030 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.18034 | 0.246035 | 0.123018 | − | 0.992404i | \(-0.460743\pi\) | ||||
0.123018 | + | 0.992404i | \(0.460743\pi\) | |||||||
\(632\) | 8.29180 | 0.329830 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 65.7771 | 2.61234 | ||||||||
\(635\) | 33.8885 | 1.34483 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.4721 | −0.969621 | ||||||||
\(638\) | 40.0000 | 1.58362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 50.6525 | 2.00221 | ||||||||
\(641\) | 27.0132 | 1.06696 | 0.533478 | − | 0.845814i | \(-0.320885\pi\) | ||||
0.533478 | + | 0.845814i | \(0.320885\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.0689 | −0.791440 | −0.395720 | − | 0.918371i | \(-0.629505\pi\) | ||||
−0.395720 | + | 0.918371i | \(0.629505\pi\) | |||||||
\(644\) | 3.70820 | 0.146124 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −44.7214 | −1.75954 | ||||||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.7771 | 2.03243 | ||||||||
\(650\) | −54.7214 | −2.14635 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −58.2492 | −2.28122 | ||||||||
\(653\) | 5.05573 | 0.197846 | 0.0989230 | − | 0.995095i | \(-0.468460\pi\) | ||||
0.0989230 | + | 0.995095i | \(0.468460\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.05573 | 0.119397 | ||||||||
\(656\) | 6.94427 | 0.271128 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.0557 | 0.430997 | ||||||||
\(659\) | 8.36068 | 0.325686 | 0.162843 | − | 0.986652i | \(-0.447934\pi\) | ||||
0.162843 | + | 0.986652i | \(0.447934\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.4721 | −0.796274 | −0.398137 | − | 0.917326i | \(-0.630343\pi\) | ||||
−0.398137 | + | 0.917326i | \(0.630343\pi\) | |||||||
\(662\) | 7.63932 | 0.296911 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.94427 | 0.347105 | ||||||||
\(665\) | −11.0557 | −0.428723 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.47214 | −0.173162 | ||||||||
\(668\) | 14.8328 | 0.573899 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −37.8885 | −1.46376 | ||||||||
\(671\) | 17.8885 | 0.690580 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.4164 | 1.13392 | 0.566960 | − | 0.823746i | \(-0.308120\pi\) | ||||
0.566960 | + | 0.823746i | \(0.308120\pi\) | |||||||
\(674\) | −67.8885 | −2.61497 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.0000 | 0.807692 | ||||||||
\(677\) | −37.4853 | −1.44068 | −0.720338 | − | 0.693623i | \(-0.756013\pi\) | ||||
−0.720338 | + | 0.693623i | \(0.756013\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.583592 | 0.0223962 | ||||||||
\(680\) | −52.3607 | −2.00794 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 22.1115 | 0.846691 | ||||||||
\(683\) | 20.0000 | 0.765279 | 0.382639 | − | 0.923898i | \(-0.375015\pi\) | ||||
0.382639 | + | 0.923898i | \(0.375015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.4721 | −0.400120 | ||||||||
\(686\) | −34.4721 | −1.31615 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.70820 | −0.293873 | ||||||||
\(689\) | 3.41641 | 0.130155 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.3607 | −1.53539 | −0.767696 | − | 0.640814i | \(-0.778597\pi\) | ||||
−0.767696 | + | 0.640814i | \(0.778597\pi\) | |||||||
\(692\) | 13.4164 | 0.510015 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 57.8885 | 2.19742 | ||||||||
\(695\) | 28.9443 | 1.09792 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.2492 | −1.90333 | ||||||||
\(698\) | 72.6099 | 2.74833 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −20.2918 | −0.766958 | ||||||||
\(701\) | −20.7639 | −0.784243 | −0.392121 | − | 0.919913i | \(-0.628259\pi\) | ||||
−0.392121 | + | 0.919913i | \(0.628259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.3607 | −0.466192 | ||||||||
\(704\) | 52.0000 | 1.95982 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.0557 | 0.792443 | ||||||||
\(707\) | 13.5279 | 0.508768 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.8328 | 0.782393 | 0.391196 | − | 0.920307i | \(-0.372061\pi\) | ||||
0.391196 | + | 0.920307i | \(0.372061\pi\) | |||||||
\(710\) | −57.8885 | −2.17252 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.23607 | 0.271183 | ||||||||
\(713\) | −2.47214 | −0.0925822 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −57.8885 | −2.16491 | ||||||||
\(716\) | −9.16718 | −0.342594 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.52786 | −0.206298 | ||||||||
\(719\) | −4.00000 | −0.149175 | −0.0745874 | − | 0.997214i | \(-0.523764\pi\) | ||||
−0.0745874 | + | 0.997214i | \(0.523764\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.36068 | 0.311368 | ||||||||
\(722\) | 25.4033 | 0.945411 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 71.6656 | 2.66343 | ||||||||
\(725\) | 24.4721 | 0.908872 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.6525 | 1.21101 | 0.605507 | − | 0.795840i | \(-0.292971\pi\) | ||||
0.605507 | + | 0.795840i | \(0.292971\pi\) | |||||||
\(728\) | 12.3607 | 0.458117 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 79.1935 | 2.93108 | ||||||||
\(731\) | 55.7771 | 2.06299 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.0000 | 0.812589 | 0.406294 | − | 0.913742i | \(-0.366821\pi\) | ||||
0.406294 | + | 0.913742i | \(0.366821\pi\) | |||||||
\(734\) | −27.4853 | −1.01450 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.70820 | −0.247268 | ||||||||
\(737\) | −20.9443 | −0.771492 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.8328 | 0.987061 | 0.493531 | − | 0.869728i | \(-0.335706\pi\) | ||||
0.493531 | + | 0.869728i | \(0.335706\pi\) | |||||||
\(740\) | −43.4164 | −1.59602 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.11146 | 0.0775140 | ||||||||
\(743\) | −20.3607 | −0.746961 | −0.373480 | − | 0.927638i | \(-0.621836\pi\) | ||||
−0.373480 | + | 0.927638i | \(0.621836\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.52786 | −0.202525 | ||||||||
\(746\) | −25.7771 | −0.943766 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −86.8328 | −3.17492 | ||||||||
\(749\) | −1.16718 | −0.0426480 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.06888 | −0.294438 | −0.147219 | − | 0.989104i | \(-0.547032\pi\) | ||||
−0.147219 | + | 0.989104i | \(0.547032\pi\) | |||||||
\(752\) | −4.00000 | −0.145865 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −44.7214 | −1.62866 | ||||||||
\(755\) | −51.7771 | −1.88436 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.11146 | 0.149433 | 0.0747167 | − | 0.997205i | \(-0.476195\pi\) | ||||
0.0747167 | + | 0.997205i | \(0.476195\pi\) | |||||||
\(758\) | 62.7639 | 2.27969 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20.0000 | −0.725476 | ||||||||
\(761\) | 2.36068 | 0.0855746 | 0.0427873 | − | 0.999084i | \(-0.486376\pi\) | ||||
0.0427873 | + | 0.999084i | \(0.486376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.63932 | −0.131752 | ||||||||
\(764\) | −31.4164 | −1.13661 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 77.0820 | 2.78509 | ||||||||
\(767\) | −57.8885 | −2.09023 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.8328 | −1.32823 | −0.664113 | − | 0.747633i | \(-0.731190\pi\) | ||||
−0.664113 | + | 0.747633i | \(0.731190\pi\) | |||||||
\(770\) | −35.7771 | −1.28932 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −28.2492 | −1.01671 | ||||||||
\(773\) | −49.7082 | −1.78788 | −0.893940 | − | 0.448187i | \(-0.852070\pi\) | ||||
−0.893940 | + | 0.448187i | \(0.852070\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.5279 | 0.485935 | ||||||||
\(776\) | 1.05573 | 0.0378984 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.8197 | −0.853976 | ||||||||
\(779\) | −19.1935 | −0.687678 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 16.1803 | 0.578608 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.47214 | 0.195433 | ||||||||
\(785\) | −40.3607 | −1.44053 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.291796 | −0.0104014 | −0.00520070 | − | 0.999986i | \(-0.501655\pi\) | ||||
−0.00520070 | + | 0.999986i | \(0.501655\pi\) | |||||||
\(788\) | 28.2492 | 1.00634 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26.8328 | 0.954669 | ||||||||
\(791\) | 20.0000 | 0.711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | −0.710221 | ||||||||
\(794\) | 4.47214 | 0.158710 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.1246 | −0.394301 | ||||||||
\(797\) | 18.6525 | 0.660705 | 0.330352 | − | 0.943858i | \(-0.392832\pi\) | ||||
0.330352 | + | 0.943858i | \(0.392832\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.9443 | 1.02397 | ||||||||
\(800\) | 36.7082 | 1.29783 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −85.1246 | −3.00585 | ||||||||
\(803\) | 43.7771 | 1.54486 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | −24.7214 | −0.870773 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 24.4721 | 0.860927 | ||||||||
\(809\) | −19.3050 | −0.678726 | −0.339363 | − | 0.940655i | \(-0.610211\pi\) | ||||
−0.339363 | + | 0.940655i | \(0.610211\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.41641 | 0.119966 | 0.0599832 | − | 0.998199i | \(-0.480895\pi\) | ||||
0.0599832 | + | 0.998199i | \(0.480895\pi\) | |||||||
\(812\) | −16.5836 | −0.581970 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −40.0000 | −1.40200 | ||||||||
\(815\) | −62.8328 | −2.20094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.3050 | 0.745366 | ||||||||
\(818\) | 21.0557 | 0.736196 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −67.4164 | −2.35428 | ||||||||
\(821\) | −47.8885 | −1.67132 | −0.835661 | − | 0.549246i | \(-0.814915\pi\) | ||||
−0.835661 | + | 0.549246i | \(0.814915\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.4721 | −1.20162 | −0.600812 | − | 0.799391i | \(-0.705156\pi\) | ||||
−0.600812 | + | 0.799391i | \(0.705156\pi\) | |||||||
\(824\) | 15.1246 | 0.526891 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −35.7771 | −1.24484 | ||||||||
\(827\) | −35.4164 | −1.23155 | −0.615775 | − | 0.787922i | \(-0.711157\pi\) | ||||
−0.615775 | + | 0.787922i | \(0.711157\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.3607 | −1.19340 | −0.596698 | − | 0.802466i | \(-0.703521\pi\) | ||||
−0.596698 | + | 0.802466i | \(0.703521\pi\) | |||||||
\(830\) | 28.9443 | 1.00467 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −58.1378 | −2.01556 | ||||||||
\(833\) | −39.5967 | −1.37195 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000 | 0.553703 | ||||||||
\(836\) | −33.1672 | −1.14711 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −48.9443 | −1.69075 | ||||||||
\(839\) | 39.4164 | 1.36081 | 0.680403 | − | 0.732838i | \(-0.261805\pi\) | ||||
0.680403 | + | 0.732838i | \(0.261805\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 29.1935 | 1.00607 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 67.4164 | 2.32057 | ||||||||
\(845\) | 22.6525 | 0.779269 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.18034 | −0.212359 | ||||||||
\(848\) | −0.763932 | −0.0262335 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −88.5410 | −3.03693 | ||||||||
\(851\) | 4.47214 | 0.153303 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0000 | 0.753266 | 0.376633 | − | 0.926363i | \(-0.377082\pi\) | ||||
0.376633 | + | 0.926363i | \(0.377082\pi\) | |||||||
\(854\) | −12.3607 | −0.422974 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.11146 | −0.0721681 | ||||||||
\(857\) | 25.0557 | 0.855887 | 0.427944 | − | 0.903805i | \(-0.359238\pi\) | ||||
0.427944 | + | 0.903805i | \(0.359238\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.9443 | −0.851088 | −0.425544 | − | 0.904938i | \(-0.639917\pi\) | ||||
−0.425544 | + | 0.904938i | \(0.639917\pi\) | |||||||
\(860\) | 74.8328 | 2.55178 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.8885 | 0.609286 | ||||||||
\(863\) | 4.00000 | 0.136162 | 0.0680808 | − | 0.997680i | \(-0.478312\pi\) | ||||
0.0680808 | + | 0.997680i | \(0.478312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.4721 | 0.492067 | ||||||||
\(866\) | 17.6393 | 0.599409 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.16718 | −0.311155 | ||||||||
\(869\) | 14.8328 | 0.503169 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.4164 | 0.793435 | ||||||||
\(872\) | −6.58359 | −0.222949 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.18034 | 0.209053 | ||||||||
\(875\) | −1.88854 | −0.0638444 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.9443 | 1.72027 | 0.860133 | − | 0.510070i | \(-0.170381\pi\) | ||||
0.860133 | + | 0.510070i | \(0.170381\pi\) | |||||||
\(878\) | −57.8885 | −1.95364 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12.9443 | 0.436351 | ||||||||
\(881\) | 40.5410 | 1.36586 | 0.682931 | − | 0.730483i | \(-0.260705\pi\) | ||||
0.682931 | + | 0.730483i | \(0.260705\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.4164 | 0.653414 | 0.326707 | − | 0.945126i | \(-0.394061\pi\) | ||||
0.326707 | + | 0.945126i | \(0.394061\pi\) | |||||||
\(884\) | 97.0820 | 3.26522 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 42.1115 | 1.41476 | ||||||||
\(887\) | −48.9443 | −1.64339 | −0.821694 | − | 0.569929i | \(-0.806971\pi\) | ||||
−0.821694 | + | 0.569929i | \(0.806971\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.9443 | −0.434137 | ||||||||
\(890\) | 23.4164 | 0.784920 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 29.6656 | 0.993279 | ||||||||
\(893\) | 11.0557 | 0.369966 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.88854 | −0.330538 | ||||||||
\(896\) | −19.3475 | −0.646355 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.58359 | −0.219697 | ||||||||
\(899\) | 11.0557 | 0.368729 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.52786 | 0.184160 | ||||||||
\(902\) | −62.1115 | −2.06809 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 36.1803 | 1.20334 | ||||||||
\(905\) | 77.3050 | 2.56970 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.1246 | 1.29911 | 0.649556 | − | 0.760314i | \(-0.274955\pi\) | ||||
0.649556 | + | 0.760314i | \(0.274955\pi\) | |||||||
\(908\) | 67.4164 | 2.23729 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 40.0000 | 1.32599 | ||||||||
\(911\) | −48.7214 | −1.61421 | −0.807105 | − | 0.590407i | \(-0.798967\pi\) | ||||
−0.807105 | + | 0.590407i | \(0.798967\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.0000 | 0.529523 | ||||||||
\(914\) | 1.05573 | 0.0349204 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −44.8328 | −1.48132 | ||||||||
\(917\) | −1.16718 | −0.0385438 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.0132 | 1.74874 | 0.874371 | − | 0.485257i | \(-0.161274\pi\) | ||||
0.874371 | + | 0.485257i | \(0.161274\pi\) | |||||||
\(920\) | 7.23607 | 0.238566 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 47.8885 | 1.57713 | ||||||||
\(923\) | 35.7771 | 1.17762 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.4721 | −0.804639 | ||||||||
\(926\) | −11.0557 | −0.363314 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 30.0000 | 0.984798 | ||||||||
\(929\) | −24.8328 | −0.814738 | −0.407369 | − | 0.913264i | \(-0.633554\pi\) | ||||
−0.407369 | + | 0.913264i | \(0.633554\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.1246 | −0.495689 | ||||||||
\(932\) | 42.0000 | 1.37576 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −54.4721 | −1.78238 | ||||||||
\(935\) | −93.6656 | −3.06319 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.8328 | 1.33395 | 0.666975 | − | 0.745080i | \(-0.267589\pi\) | ||||
0.666975 | + | 0.745080i | \(0.267589\pi\) | |||||||
\(938\) | 14.4721 | 0.472532 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 38.8328 | 1.26659 | ||||||||
\(941\) | −24.5410 | −0.800014 | −0.400007 | − | 0.916512i | \(-0.630992\pi\) | ||||
−0.400007 | + | 0.916512i | \(0.630992\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.94427 | 0.226137 | ||||||||
\(944\) | 12.9443 | 0.421300 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 68.9443 | 2.24157 | ||||||||
\(947\) | 54.8328 | 1.78183 | 0.890914 | − | 0.454173i | \(-0.150065\pi\) | ||||
0.890914 | + | 0.454173i | \(0.150065\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.9443 | −1.58880 | ||||||||
\(950\) | −33.8197 | −1.09725 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 20.0000 | 0.648204 | ||||||||
\(953\) | 46.0689 | 1.49232 | 0.746159 | − | 0.665768i | \(-0.231896\pi\) | ||||
0.746159 | + | 0.665768i | \(0.231896\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.8885 | −1.09661 | ||||||||
\(956\) | 38.8328 | 1.25594 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.22291 | 0.136436 | ||||||||
\(959\) | 4.00000 | 0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8885 | −0.802856 | ||||||||
\(962\) | 44.7214 | 1.44187 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 85.4164 | 2.75108 | ||||||||
\(965\) | −30.4721 | −0.980933 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.3607 | −1.68381 | −0.841903 | − | 0.539629i | \(-0.818565\pi\) | ||||
−0.841903 | + | 0.539629i | \(0.818565\pi\) | |||||||
\(968\) | −11.1803 | −0.359350 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.41641 | 0.109694 | ||||||||
\(971\) | 45.3050 | 1.45391 | 0.726953 | − | 0.686688i | \(-0.240936\pi\) | ||||
0.726953 | + | 0.686688i | \(0.240936\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.0557 | −0.354430 | ||||||||
\(974\) | −53.6656 | −1.71956 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.47214 | 0.143150 | ||||||||
\(977\) | −26.0689 | −0.834017 | −0.417009 | − | 0.908902i | \(-0.636922\pi\) | ||||
−0.417009 | + | 0.908902i | \(0.636922\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.9443 | 0.413701 | ||||||||
\(980\) | −53.1246 | −1.69700 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 89.4427 | 2.85423 | ||||||||
\(983\) | 30.8328 | 0.983414 | 0.491707 | − | 0.870761i | \(-0.336373\pi\) | ||||
0.491707 | + | 0.870761i | \(0.336373\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.4721 | 0.970923 | ||||||||
\(986\) | −72.3607 | −2.30443 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 37.0820 | 1.17974 | ||||||||
\(989\) | −7.70820 | −0.245107 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.4721 | −0.332658 | −0.166329 | − | 0.986070i | \(-0.553191\pi\) | ||||
−0.166329 | + | 0.986070i | \(0.553191\pi\) | |||||||
\(992\) | 16.5836 | 0.526530 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22.1115 | 0.701333 | ||||||||
\(995\) | −12.0000 | −0.380426 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.36068 | −0.0747635 | −0.0373817 | − | 0.999301i | \(-0.511902\pi\) | ||||
−0.0373817 | + | 0.999301i | \(0.511902\pi\) | |||||||
\(998\) | −72.3607 | −2.29054 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 207.2.a.c.1.1 | 2 | ||
3.2 | odd | 2 | 69.2.a.b.1.2 | ✓ | 2 | ||
4.3 | odd | 2 | 3312.2.a.bb.1.2 | 2 | |||
5.4 | even | 2 | 5175.2.a.bk.1.2 | 2 | |||
12.11 | even | 2 | 1104.2.a.m.1.1 | 2 | |||
15.2 | even | 4 | 1725.2.b.o.1174.4 | 4 | |||
15.8 | even | 4 | 1725.2.b.o.1174.1 | 4 | |||
15.14 | odd | 2 | 1725.2.a.ba.1.1 | 2 | |||
21.20 | even | 2 | 3381.2.a.t.1.2 | 2 | |||
23.22 | odd | 2 | 4761.2.a.v.1.1 | 2 | |||
24.5 | odd | 2 | 4416.2.a.bm.1.2 | 2 | |||
24.11 | even | 2 | 4416.2.a.bg.1.2 | 2 | |||
33.32 | even | 2 | 8349.2.a.i.1.1 | 2 | |||
69.68 | even | 2 | 1587.2.a.i.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.2.a.b.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
207.2.a.c.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1104.2.a.m.1.1 | 2 | 12.11 | even | 2 | |||
1587.2.a.i.1.2 | 2 | 69.68 | even | 2 | |||
1725.2.a.ba.1.1 | 2 | 15.14 | odd | 2 | |||
1725.2.b.o.1174.1 | 4 | 15.8 | even | 4 | |||
1725.2.b.o.1174.4 | 4 | 15.2 | even | 4 | |||
3312.2.a.bb.1.2 | 2 | 4.3 | odd | 2 | |||
3381.2.a.t.1.2 | 2 | 21.20 | even | 2 | |||
4416.2.a.bg.1.2 | 2 | 24.11 | even | 2 | |||
4416.2.a.bm.1.2 | 2 | 24.5 | odd | 2 | |||
4761.2.a.v.1.1 | 2 | 23.22 | odd | 2 | |||
5175.2.a.bk.1.2 | 2 | 5.4 | even | 2 | |||
8349.2.a.i.1.1 | 2 | 33.32 | even | 2 |