Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(1,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, 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("1148.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.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: | \(9.16682615204\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.470117.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 8x^{2} + 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.94177\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.94177 | −1.12108 | −0.560541 | − | 0.828127i | \(-0.689407\pi\) | ||||
−0.560541 | + | 0.828127i | \(0.689407\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.68629 | 1.20135 | 0.600673 | − | 0.799495i | \(-0.294899\pi\) | ||||
0.600673 | + | 0.799495i | \(0.294899\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.770473 | 0.256824 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.616576 | −0.185905 | −0.0929524 | − | 0.995671i | \(-0.529630\pi\) | ||||
−0.0929524 | + | 0.995671i | \(0.529630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.70117 | −0.471819 | −0.235910 | − | 0.971775i | \(-0.575807\pi\) | ||||
−0.235910 | + | 0.971775i | \(0.575807\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.21616 | −1.34681 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.91582 | −0.707190 | −0.353595 | − | 0.935399i | \(-0.615041\pi\) | ||||
−0.353595 | + | 0.935399i | \(0.615041\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.49649 | 0.343319 | 0.171659 | − | 0.985156i | \(-0.445087\pi\) | ||||
0.171659 | + | 0.985156i | \(0.445087\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.94177 | 0.423729 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.22765 | −1.92410 | −0.962049 | − | 0.272878i | \(-0.912025\pi\) | ||||
−0.962049 | + | 0.272878i | \(0.912025\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.21616 | 0.443232 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.32923 | 0.833161 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.4723 | 1.94465 | 0.972327 | − | 0.233623i | \(-0.0750581\pi\) | ||||
0.972327 | + | 0.233623i | \(0.0750581\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.02889 | −1.26243 | −0.631213 | − | 0.775610i | \(-0.717442\pi\) | ||||
−0.631213 | + | 0.775610i | \(0.717442\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.19725 | 0.208414 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.68629 | −0.454066 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.62554 | −0.760434 | −0.380217 | − | 0.924897i | \(-0.624151\pi\) | ||||
−0.380217 | + | 0.924897i | \(0.624151\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.30328 | 0.528948 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.88909 | 0.745579 | 0.372789 | − | 0.927916i | \(-0.378401\pi\) | ||||
0.372789 | + | 0.927916i | \(0.378401\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.06972 | 0.308535 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.96813 | −0.724677 | −0.362338 | − | 0.932047i | \(-0.618021\pi\) | ||||
−0.362338 | + | 0.932047i | \(0.618021\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.66185 | 0.792818 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.14053 | −1.11819 | −0.559094 | − | 0.829104i | \(-0.688851\pi\) | ||||
−0.559094 | + | 0.829104i | \(0.688851\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.65630 | −0.223336 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.90584 | −0.384888 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.71628 | −1.26495 | −0.632476 | − | 0.774580i | \(-0.717961\pi\) | ||||
−0.632476 | + | 0.774580i | \(0.717961\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.04890 | −0.902519 | −0.451260 | − | 0.892393i | \(-0.649025\pi\) | ||||
−0.451260 | + | 0.892393i | \(0.649025\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.770473 | −0.0970705 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.56983 | −0.566818 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.8776 | −1.32891 | −0.664457 | − | 0.747327i | \(-0.731337\pi\) | ||||
−0.664457 | + | 0.747327i | \(0.731337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.9180 | 2.15707 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.23698 | −0.265480 | −0.132740 | − | 0.991151i | \(-0.542378\pi\) | ||||
−0.132740 | + | 0.991151i | \(0.542378\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.30479 | 0.854961 | 0.427480 | − | 0.904025i | \(-0.359401\pi\) | ||||
0.427480 | + | 0.904025i | \(0.359401\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.30328 | −0.496900 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.616576 | 0.0702654 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0081 | −1.35101 | −0.675507 | − | 0.737354i | \(-0.736075\pi\) | ||||
−0.675507 | + | 0.737354i | \(0.736075\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7178 | −1.19087 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.9105 | −1.74641 | −0.873203 | − | 0.487356i | \(-0.837961\pi\) | ||||
−0.873203 | + | 0.487356i | \(0.837961\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.83274 | −0.849580 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20.3348 | −2.18012 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.3418 | 1.09623 | 0.548115 | − | 0.836403i | \(-0.315346\pi\) | ||||
0.548115 | + | 0.836403i | \(0.315346\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.70117 | 0.178331 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.6485 | 1.41528 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.02001 | 0.412445 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.32921 | 0.947237 | 0.473619 | − | 0.880730i | \(-0.342947\pi\) | ||||
0.473619 | + | 0.880730i | \(0.342947\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.475055 | −0.0477449 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.01932 | 0.897456 | 0.448728 | − | 0.893668i | \(-0.351877\pi\) | ||||
0.448728 | + | 0.893668i | \(0.351877\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.3637 | 1.71089 | 0.855446 | − | 0.517892i | \(-0.173283\pi\) | ||||
0.855446 | + | 0.517892i | \(0.173283\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.21616 | 0.509045 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.1830 | −1.08110 | −0.540552 | − | 0.841311i | \(-0.681784\pi\) | ||||
−0.540552 | + | 0.841311i | \(0.681784\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.97808 | −0.859944 | −0.429972 | − | 0.902842i | \(-0.641477\pi\) | ||||
−0.429972 | + | 0.902842i | \(0.641477\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.98173 | 0.852508 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.6550 | −1.75492 | −0.877460 | − | 0.479651i | \(-0.840763\pi\) | ||||
−0.877460 | + | 0.479651i | \(0.840763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.7882 | −2.31151 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.31070 | −0.121175 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.91582 | 0.267293 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6198 | −0.965439 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.94177 | −0.175084 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.47820 | −0.668871 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.56174 | −0.316053 | −0.158027 | − | 0.987435i | \(-0.550513\pi\) | ||||
−0.158027 | + | 0.987435i | \(0.550513\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.49349 | −0.835855 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.34370 | 0.728992 | 0.364496 | − | 0.931205i | \(-0.381241\pi\) | ||||
0.364496 | + | 0.931205i | \(0.381241\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.49649 | −0.129762 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.6296 | 1.00091 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.12563 | 0.523348 | 0.261674 | − | 0.965156i | \(-0.415725\pi\) | ||||
0.261674 | + | 0.965156i | \(0.415725\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.1886 | 1.54273 | 0.771367 | − | 0.636391i | \(-0.219573\pi\) | ||||
0.771367 | + | 0.636391i | \(0.219573\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.64697 | 0.812422 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.04890 | 0.0877134 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28.1316 | 2.33620 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.94177 | −0.160155 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.02297 | −0.657267 | −0.328634 | − | 0.944457i | \(-0.606588\pi\) | ||||
−0.328634 | + | 0.944457i | \(0.606588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.66146 | 0.297966 | 0.148983 | − | 0.988840i | \(-0.452400\pi\) | ||||
0.148983 | + | 0.988840i | \(0.452400\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.24656 | −0.181624 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.8816 | −1.51661 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.63702 | −0.769118 | −0.384559 | − | 0.923100i | \(-0.625647\pi\) | ||||
−0.384559 | + | 0.923100i | \(0.625647\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.8070 | 1.25358 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.22765 | 0.727241 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.71077 | 0.603954 | 0.301977 | − | 0.953315i | \(-0.402353\pi\) | ||||
0.301977 | + | 0.953315i | \(0.402353\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.21616 | 0.250378 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.37813 | −0.648319 | −0.324160 | − | 0.946002i | \(-0.605081\pi\) | ||||
−0.324160 | + | 0.946002i | \(0.605081\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1060 | −0.777387 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.15301 | 0.0881726 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.38847 | 0.409678 | 0.204839 | − | 0.978796i | \(-0.434333\pi\) | ||||
0.204839 | + | 0.978796i | \(0.434333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.21616 | −0.167526 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.8668 | 1.41811 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.74603 | 0.429479 | 0.214739 | − | 0.976671i | \(-0.431110\pi\) | ||||
0.214739 | + | 0.976671i | \(0.431110\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.17203 | −0.607422 | −0.303711 | − | 0.952764i | \(-0.598226\pi\) | ||||
−0.303711 | + | 0.952764i | \(0.598226\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.6873 | 1.01180 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.4255 | −0.913544 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.79782 | 0.131470 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.32923 | −0.314905 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.5766 | 1.41651 | 0.708255 | − | 0.705956i | \(-0.249483\pi\) | ||||
0.708255 | + | 0.705956i | \(0.249483\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.21001 | −0.0870985 | −0.0435493 | − | 0.999051i | \(-0.513867\pi\) | ||||
−0.0435493 | + | 0.999051i | \(0.513867\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.87357 | 0.635449 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.3611 | 1.02319 | 0.511594 | − | 0.859227i | \(-0.329055\pi\) | ||||
0.511594 | + | 0.859227i | \(0.329055\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.93456 | 0.562466 | 0.281233 | − | 0.959640i | \(-0.409257\pi\) | ||||
0.281233 | + | 0.959640i | \(0.409257\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.1219 | 1.48982 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.4723 | −0.735010 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.68629 | 0.187619 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.10965 | −0.494155 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.922701 | −0.0638246 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.6704 | −0.872266 | −0.436133 | − | 0.899882i | \(-0.643652\pi\) | ||||
−0.436133 | + | 0.899882i | \(0.643652\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.34370 | 0.297625 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.1335 | 0.895698 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.02889 | 0.477152 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.1842 | −0.958481 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.96030 | 0.333666 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.8487 | 0.994342 | 0.497171 | − | 0.867653i | \(-0.334372\pi\) | ||||
0.497171 | + | 0.867653i | \(0.334372\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.70749 | 0.113833 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.5836 | 1.56530 | 0.782651 | − | 0.622461i | \(-0.213867\pi\) | ||||
0.782651 | + | 0.622461i | \(0.213867\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.26135 | −0.347680 | −0.173840 | − | 0.984774i | \(-0.555618\pi\) | ||||
−0.173840 | + | 0.984774i | \(0.555618\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.19725 | −0.0787732 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.0100 | 0.852312 | 0.426156 | − | 0.904650i | \(-0.359868\pi\) | ||||
0.426156 | + | 0.904650i | \(0.359868\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.3459 | −0.870587 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.3169 | 1.51460 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.8401 | 1.47740 | 0.738700 | − | 0.674034i | \(-0.235440\pi\) | ||||
0.738700 | + | 0.674034i | \(0.235440\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.5969 | 1.58443 | 0.792214 | − | 0.610244i | \(-0.208929\pi\) | ||||
0.792214 | + | 0.610244i | \(0.208929\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.82380 | 0.501897 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.68629 | 0.171621 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.54578 | −0.161984 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 30.8946 | 1.95786 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.4545 | 1.48043 | 0.740217 | − | 0.672368i | \(-0.234723\pi\) | ||||
0.740217 | + | 0.672368i | \(0.234723\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.68955 | 0.357699 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.2094 | 0.952448 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.5565 | −1.15752 | −0.578762 | − | 0.815497i | \(-0.696464\pi\) | ||||
−0.578762 | + | 0.815497i | \(0.696464\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.62554 | 0.287417 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.06861 | 0.499435 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.0340 | 0.803714 | 0.401857 | − | 0.915702i | \(-0.368365\pi\) | ||||
0.401857 | + | 0.915702i | \(0.368365\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.8678 | −1.34333 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.0814 | −1.22896 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.32781 | −0.507755 | −0.253878 | − | 0.967236i | \(-0.581706\pi\) | ||||
−0.253878 | + | 0.967236i | \(0.581706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.09297 | −0.127139 | −0.0635694 | − | 0.997977i | \(-0.520248\pi\) | ||||
−0.0635694 | + | 0.997977i | \(0.520248\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.30328 | −0.199923 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.36643 | −0.0823990 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.18490 | −0.491783 | −0.245891 | − | 0.969297i | \(-0.579081\pi\) | ||||
−0.245891 | + | 0.969297i | \(0.579081\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.41557 | −0.324222 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.3834 | 0.798388 | 0.399194 | − | 0.916866i | \(-0.369290\pi\) | ||||
0.399194 | + | 0.916866i | \(0.369290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.1644 | −0.782541 | −0.391270 | − | 0.920276i | \(-0.627964\pi\) | ||||
−0.391270 | + | 0.920276i | \(0.627964\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.80594 | −0.462384 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.00000 | −0.0590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.49800 | −0.499883 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.1152 | −1.06193 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.7152 | 1.56072 | 0.780359 | − | 0.625332i | \(-0.215036\pi\) | ||||
0.780359 | + | 0.625332i | \(0.215036\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.1008 | −1.51964 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.66930 | −0.154889 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.6978 | 0.907826 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.88909 | −0.281802 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.5135 | −1.00612 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.9354 | −1.08424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.9998 | −0.627790 | −0.313895 | − | 0.949458i | \(-0.601634\pi\) | ||||
−0.313895 | + | 0.949458i | \(0.601634\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −33.7163 | −1.91805 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.1242 | 0.914320 | 0.457160 | − | 0.889384i | \(-0.348867\pi\) | ||||
0.457160 | + | 0.889384i | \(0.348867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.2400 | −1.48317 | −0.741586 | − | 0.670858i | \(-0.765926\pi\) | ||||
−0.741586 | + | 0.670858i | \(0.765926\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.06972 | −0.116615 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.6496 | 0.766637 | 0.383319 | − | 0.923616i | \(-0.374781\pi\) | ||||
0.383319 | + | 0.923616i | \(0.374781\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.45696 | −0.361521 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.7149 | 1.21201 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.36350 | −0.242792 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.77006 | −0.209125 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.4334 | 0.964068 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.96813 | 0.273902 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0230 | −0.770772 | −0.385386 | − | 0.922755i | \(-0.625932\pi\) | ||||
−0.385386 | + | 0.922755i | \(0.625932\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.56385 | −0.195298 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −29.2205 | −1.59649 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.1990 | −1.15478 | −0.577391 | − | 0.816467i | \(-0.695929\pi\) | ||||
−0.577391 | + | 0.816467i | \(0.695929\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.2238 | 1.96741 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.33384 | 0.234691 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 48.1329 | 2.59139 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.65520 | 0.196222 | 0.0981108 | − | 0.995176i | \(-0.468720\pi\) | ||||
0.0981108 | + | 0.995176i | \(0.468720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.9786 | −1.60472 | −0.802359 | − | 0.596841i | \(-0.796422\pi\) | ||||
−0.802359 | + | 0.596841i | \(0.796422\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.36475 | −0.393101 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.5294 | −0.666870 | −0.333435 | − | 0.942773i | \(-0.608208\pi\) | ||||
−0.333435 | + | 0.942773i | \(0.608208\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00917 | −0.318934 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.66185 | −0.299657 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.233065 | 0.0123007 | 0.00615034 | − | 0.999981i | \(-0.498042\pi\) | ||||
0.00615034 | + | 0.999981i | \(0.498042\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7605 | −0.882132 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.6213 | 1.08234 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.6228 | 1.02710 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.1545 | −1.20865 | −0.604326 | − | 0.796737i | \(-0.706558\pi\) | ||||
−0.604326 | + | 0.796737i | \(0.706558\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.770473 | 0.0401092 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.14053 | 0.422635 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.7029 | 0.657732 | 0.328866 | − | 0.944377i | \(-0.393334\pi\) | ||||
0.328866 | + | 0.944377i | \(0.393334\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.5210 | 0.749859 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.8151 | −0.917525 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9179 | −0.766283 | −0.383141 | − | 0.923690i | \(-0.625158\pi\) | ||||
−0.383141 | + | 0.923690i | \(0.625158\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.91608 | 0.354321 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.921522 | 0.0470876 | 0.0235438 | − | 0.999723i | \(-0.492505\pi\) | ||||
0.0235438 | + | 0.999723i | \(0.492505\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.65630 | 0.0844131 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.76691 | 0.191483 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.0151 | −1.21761 | −0.608807 | − | 0.793318i | \(-0.708352\pi\) | ||||
−0.608807 | + | 0.793318i | \(0.708352\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.9061 | 1.36070 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.2015 | −0.817260 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −32.2572 | −1.62303 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.9949 | 0.652196 | 0.326098 | − | 0.945336i | \(-0.394266\pi\) | ||||
0.326098 | + | 0.945336i | \(0.394266\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.90584 | 0.145474 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.2074 | 0.959171 | 0.479586 | − | 0.877495i | \(-0.340787\pi\) | ||||
0.479586 | + | 0.877495i | \(0.340787\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.9573 | 0.595636 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −28.7911 | −1.43064 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.85200 | 0.141368 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.8957 | 0.884884 | 0.442442 | − | 0.896797i | \(-0.354112\pi\) | ||||
0.442442 | + | 0.896797i | \(0.354112\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.8946 | −0.586716 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.71628 | 0.478107 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −42.7403 | −2.09804 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −35.3180 | −1.72953 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.1277 | 1.12986 | 0.564932 | − | 0.825138i | \(-0.308903\pi\) | ||||
0.564932 | + | 0.825138i | \(0.308903\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.2191 | −0.936683 | −0.468341 | − | 0.883548i | \(-0.655148\pi\) | ||||
−0.468341 | + | 0.883548i | \(0.655148\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.82781 | −0.186115 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.46193 | −0.313449 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.04890 | 0.341120 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.03672 | −0.0983339 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.8211 | −1.67727 | −0.838637 | − | 0.544691i | \(-0.816647\pi\) | ||||
−0.838637 | + | 0.544691i | \(0.816647\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.6604 | 0.992875 | 0.496437 | − | 0.868073i | \(-0.334641\pi\) | ||||
0.496437 | + | 0.868073i | \(0.334641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −54.6251 | −2.61907 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.8091 | −0.660579 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.5338 | 0.836841 | 0.418421 | − | 0.908253i | \(-0.362584\pi\) | ||||
0.418421 | + | 0.908253i | \(0.362584\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.770473 | 0.0366892 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.9057 | 1.04077 | 0.520386 | − | 0.853931i | \(-0.325788\pi\) | ||||
0.520386 | + | 0.853931i | \(0.325788\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.7811 | 1.31695 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.5788 | 0.736851 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.4998 | −1.06183 | −0.530915 | − | 0.847425i | \(-0.678152\pi\) | ||||
−0.530915 | + | 0.847425i | \(0.678152\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.616576 | −0.0290334 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.10972 | −0.334044 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.56983 | 0.214237 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.25908 | −0.292787 | −0.146394 | − | 0.989226i | \(-0.546767\pi\) | ||||
−0.146394 | + | 0.989226i | \(0.546767\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.6232 | −0.589203 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.8716 | 0.506343 | 0.253172 | − | 0.967421i | \(-0.418526\pi\) | ||||
0.253172 | + | 0.967421i | \(0.418526\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.78513 | 0.222384 | 0.111192 | − | 0.993799i | \(-0.464533\pi\) | ||||
0.111192 | + | 0.993799i | \(0.464533\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 36.6638 | 1.70024 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.974072 | −0.0450747 | −0.0225373 | − | 0.999746i | \(-0.507174\pi\) | ||||
−0.0225373 | + | 0.999746i | \(0.507174\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.8776 | 0.502282 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.7129 | 0.862244 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.01450 | −0.138607 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.31647 | 0.152170 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.27206 | −0.287178 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.62638 | 0.439840 | 0.219920 | − | 0.975518i | \(-0.429420\pi\) | ||||
0.219920 | + | 0.975518i | \(0.429420\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.86882 | 0.358787 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −17.9180 | −0.815296 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.0610 | 1.13796 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.00149 | −0.317268 | −0.158634 | − | 0.987337i | \(-0.550709\pi\) | ||||
−0.158634 | + | 0.987337i | \(0.550709\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.9726 | −0.677082 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.6278 | −1.87864 | −0.939318 | − | 0.343047i | \(-0.888541\pi\) | ||||
−0.939318 | + | 0.343047i | \(0.888541\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.5353 | −1.37524 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.27614 | −0.0573581 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.23698 | 0.100342 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.4714 | 0.558298 | 0.279149 | − | 0.960248i | \(-0.409948\pi\) | ||||
0.279149 | + | 0.960248i | \(0.409948\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.2684 | 0.726819 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.28274 | 0.413897 | 0.206949 | − | 0.978352i | \(-0.433647\pi\) | ||||
0.206949 | + | 0.978352i | \(0.433647\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.2285 | 1.07816 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.6236 | 0.871514 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.5231 | 0.998320 | 0.499160 | − | 0.866510i | \(-0.333642\pi\) | ||||
0.499160 | + | 0.866510i | \(0.333642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.30479 | −0.323145 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.47866 | 0.286040 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 46.6439 | 2.05537 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.06323 | 0.134721 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.4632 | −0.459283 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.7247 | 1.03940 | 0.519699 | − | 0.854349i | \(-0.326044\pi\) | ||||
0.519699 | + | 0.854349i | \(0.326044\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.9534 | −1.39722 | −0.698612 | − | 0.715500i | \(-0.746199\pi\) | ||||
−0.698612 | + | 0.715500i | \(0.746199\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.30328 | 0.187810 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.4950 | 0.892774 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 62.1495 | 2.70215 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.48613 | −0.324870 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.70117 | −0.0736858 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.0408 | −1.29878 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.1575 | −0.481481 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.616576 | −0.0265578 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.39512 | −0.102974 | −0.0514871 | − | 0.998674i | \(-0.516396\pi\) | ||||
−0.0514871 | + | 0.998674i | \(0.516396\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.8682 | 0.680970 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.1177 | −1.03309 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.5941 | −0.452970 | −0.226485 | − | 0.974015i | \(-0.572723\pi\) | ||||
−0.226485 | + | 0.974015i | \(0.572723\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.43099 | −0.231789 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.6717 | 0.667636 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0081 | 0.510635 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.1276 | 1.02416 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.4085 | −1.37319 | −0.686596 | − | 0.727039i | \(-0.740896\pi\) | ||||
−0.686596 | + | 0.727039i | \(0.740896\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.31716 | −0.351778 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.49096 | −0.147389 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5658 | 0.445296 | 0.222648 | − | 0.974899i | \(-0.428530\pi\) | ||||
0.222648 | + | 0.974899i | \(0.428530\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −50.1129 | −2.10827 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.7178 | 0.450105 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.4511 | 1.06697 | 0.533484 | − | 0.845810i | \(-0.320883\pi\) | ||||
0.533484 | + | 0.845810i | \(0.320883\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.2975 | 1.22606 | 0.613031 | − | 0.790059i | \(-0.289950\pi\) | ||||
0.613031 | + | 0.790059i | \(0.289950\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −38.0132 | −1.58802 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.4500 | −0.852822 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.00667 | −0.374953 | −0.187476 | − | 0.982269i | \(-0.560031\pi\) | ||||
−0.187476 | + | 0.982269i | \(0.560031\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.34957 | 0.0976446 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.9105 | 0.660080 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.01926 | 0.207876 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.52093 | −0.145573 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −40.3386 | −1.66495 | −0.832476 | − | 0.554061i | \(-0.813078\pi\) | ||||
−0.832476 | + | 0.554061i | \(0.813078\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.5187 | −0.433414 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.8860 | −1.14708 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.2750 | 1.12005 | 0.560024 | − | 0.828476i | \(-0.310792\pi\) | ||||
0.560024 | + | 0.828476i | \(0.310792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.83274 | 0.321111 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.4071 | −0.630570 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.64567 | −0.230676 | −0.115338 | − | 0.993326i | \(-0.536795\pi\) | ||||
−0.115338 | + | 0.993326i | \(0.536795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.39390 | −0.301603 | −0.150802 | − | 0.988564i | \(-0.548185\pi\) | ||||
−0.150802 | + | 0.988564i | \(0.548185\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.38092 | −0.341297 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28.5280 | −1.15983 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.66935 | −0.108346 | −0.0541728 | − | 0.998532i | \(-0.517252\pi\) | ||||
−0.0541728 | + | 0.998532i | \(0.517252\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.3348 | 0.824007 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.45163 | 0.341916 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.6940 | −1.19933 | −0.599664 | − | 0.800252i | \(-0.704699\pi\) | ||||
−0.599664 | + | 0.800252i | \(0.704699\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.21616 | −0.210336 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.47295 | 0.341108 | 0.170554 | − | 0.985348i | \(-0.445444\pi\) | ||||
0.170554 | + | 0.985348i | \(0.445444\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.44345 | 0.0982104 | 0.0491052 | − | 0.998794i | \(-0.484363\pi\) | ||||
0.0491052 | + | 0.998794i | \(0.484363\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −39.9486 | −1.60308 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.3418 | −0.414336 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1694 | −1.24678 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.79167 | 0.0715526 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.4872 | 0.537771 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.246928 | 0.00983004 | 0.00491502 | − | 0.999988i | \(-0.498435\pi\) | ||||
0.00491502 | + | 0.999988i | \(0.498435\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.6030 | 0.977882 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.56787 | −0.379689 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.70117 | −0.0674027 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.72353 | −0.0681818 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.6671 | −0.500320 | −0.250160 | − | 0.968204i | \(-0.580483\pi\) | ||||
−0.250160 | + | 0.968204i | \(0.580483\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.4641 | 1.75349 | 0.876746 | − | 0.480953i | \(-0.159709\pi\) | ||||
0.876746 | + | 0.480953i | \(0.159709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −25.5023 | −1.00415 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.0143 | −1.49450 | −0.747249 | − | 0.664544i | \(-0.768626\pi\) | ||||
−0.747249 | + | 0.664544i | \(0.768626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.99083 | 0.235161 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.6485 | −0.534926 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.8090 | 0.462123 | 0.231062 | − | 0.972939i | \(-0.425780\pi\) | ||||
0.231062 | + | 0.972939i | \(0.425780\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.4136 | 0.875772 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.62814 | 0.219575 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.1657 | 1.72045 | 0.860225 | − | 0.509914i | \(-0.170323\pi\) | ||||
0.860225 | + | 0.509914i | \(0.170323\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.7184 | 0.728061 | 0.364030 | − | 0.931387i | \(-0.381400\pi\) | ||||
0.364030 | + | 0.931387i | \(0.381400\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.63176 | −0.374066 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.02001 | −0.155889 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −96.6346 | −3.74171 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −28.8328 | −1.11474 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.34618 | 0.167783 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.79888 | −0.262078 | −0.131039 | − | 0.991377i | \(-0.541831\pi\) | ||||
−0.131039 | + | 0.991377i | \(0.541831\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.59427 | 0.369284 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.8599 | −0.532681 | −0.266340 | − | 0.963879i | \(-0.585815\pi\) | ||||
−0.266340 | + | 0.963879i | \(0.585815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.32921 | −0.358022 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −45.7940 | −1.75483 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.9460 | 1.29891 | 0.649454 | − | 0.760401i | \(-0.274997\pi\) | ||||
0.649454 | + | 0.760401i | \(0.274997\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.4552 | 0.628722 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.2163 | 0.389777 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.8484 | 0.527582 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.8016 | 0.905456 | 0.452728 | − | 0.891649i | \(-0.350451\pi\) | ||||
0.452728 | + | 0.891649i | \(0.350451\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.475055 | 0.0180459 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 48.8598 | 1.85336 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.91582 | −0.110444 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.2624 | −0.955511 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.9994 | 1.85068 | 0.925340 | − | 0.379138i | \(-0.123779\pi\) | ||||
0.925340 | + | 0.379138i | \(0.123779\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.92208 | −0.261071 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.9146 | 0.976000 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.01932 | −0.339207 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.8902 | −1.42300 | −0.711499 | − | 0.702687i | \(-0.751983\pi\) | ||||
−0.711499 | + | 0.702687i | \(0.751983\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.25190 | −0.346973 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 64.8601 | 2.42903 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.81765 | 0.105374 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −44.3501 | −1.65629 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −47.4091 | −1.76806 | −0.884031 | − | 0.467429i | \(-0.845180\pi\) | ||||
−0.884031 | + | 0.467429i | \(0.845180\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.3637 | −0.646657 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −47.7616 | −1.77627 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.2083 | 0.861934 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.4720 | −1.57520 | −0.787600 | − | 0.616187i | \(-0.788677\pi\) | ||||
−0.787600 | + | 0.616187i | \(0.788677\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.9613 | 0.628198 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.2557 | −0.527266 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.79759 | −0.177203 | −0.0886015 | − | 0.996067i | \(-0.528240\pi\) | ||||
−0.0886015 | + | 0.996067i | \(0.528240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.21616 | −0.192401 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.70689 | 0.247051 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.6982 | −1.20282 | −0.601411 | − | 0.798940i | \(-0.705395\pi\) | ||||
−0.601411 | + | 0.798940i | \(0.705395\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.94333 | 0.181598 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.4685 | −0.604172 | −0.302086 | − | 0.953281i | \(-0.597683\pi\) | ||||
−0.302086 | + | 0.953281i | \(0.597683\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.5520 | −0.789606 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.2586 | −0.448520 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.1830 | 0.408619 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.4542 | 1.91408 | 0.957040 | − | 0.289956i | \(-0.0936408\pi\) | ||||
0.957040 | + | 0.289956i | \(0.0936408\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −45.5432 | −1.65969 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.83576 | 0.357960 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.0448 | −1.27372 | −0.636862 | − | 0.770978i | \(-0.719768\pi\) | ||||
−0.636862 | + | 0.770978i | \(0.719768\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.0478 | −0.401010 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.0743581 | −0.00269548 | −0.00134774 | − | 0.999999i | \(-0.500429\pi\) | ||||
−0.00134774 | + | 0.999999i | \(0.500429\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.97808 | 0.325028 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.03491 | −0.218193 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.5290 | 0.596828 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.06711 | 0.0745418 | 0.0372709 | − | 0.999305i | \(-0.488134\pi\) | ||||
0.0372709 | + | 0.999305i | \(0.488134\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.0325 | 1.29768 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.1292 | −1.19157 | −0.595787 | − | 0.803143i | \(-0.703160\pi\) | ||||
−0.595787 | + | 0.803143i | \(0.703160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.5771 | −0.559548 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.98173 | −0.322218 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.49649 | 0.0536174 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.37927 | 0.0493541 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 45.3369 | 1.62021 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.8879 | −0.923977 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.7134 | 0.809646 | 0.404823 | − | 0.914395i | \(-0.367333\pi\) | ||||
0.404823 | + | 0.914395i | \(0.367333\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.3091 | −0.901029 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.6550 | 0.663297 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.9914 | 0.425826 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 42.4623 | 1.50598 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.3885 | −0.367978 | −0.183989 | − | 0.982928i | \(-0.558901\pi\) | ||||
−0.183989 | + | 0.982928i | \(0.558901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.4862 | 0.512484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.96809 | 0.281539 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.50396 | −0.158941 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.7882 | 0.873668 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.1707 | 0.569235 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.1639 | −1.41209 | −0.706044 | − | 0.708168i | \(-0.749522\pi\) | ||||
−0.706044 | + | 0.708168i | \(0.749522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.0648 | −1.19618 | −0.598089 | − | 0.801430i | \(-0.704073\pi\) | ||||
−0.598089 | + | 0.801430i | \(0.704073\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.06406 | 0.142533 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.7134 | 0.725558 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.31648 | 0.255971 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.31070 | 0.0457997 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.84366 | −0.169045 | −0.0845225 | − | 0.996422i | \(-0.526936\pi\) | ||||
−0.0845225 | + | 0.996422i | \(0.526936\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.9308 | 0.625027 | 0.312513 | − | 0.949913i | \(-0.398829\pi\) | ||||
0.312513 | + | 0.949913i | \(0.398829\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.65330 | 0.0923760 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.5813 | −1.65456 | −0.827281 | − | 0.561788i | \(-0.810114\pi\) | ||||
−0.827281 | + | 0.561788i | \(0.810114\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.0618 | 0.592580 | 0.296290 | − | 0.955098i | \(-0.404251\pi\) | ||||
0.296290 | + | 0.955098i | \(0.404251\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.8932 | 0.551329 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.91582 | −0.101027 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.5061 | −0.778856 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.4297 | −1.05180 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.06960 | 0.278594 | 0.139297 | − | 0.990251i | \(-0.455516\pi\) | ||||
0.139297 | + | 0.990251i | \(0.455516\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 80.6688 | 2.78168 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.9875 | −0.895058 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −27.1477 | −0.933911 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6198 | 0.364902 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.5622 | 0.877292 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.6828 | 1.46315 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.8221 | −1.12381 | −0.561904 | − | 0.827203i | \(-0.689931\pi\) | ||||
−0.561904 | + | 0.827203i | \(0.689931\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.09731 | 0.105926 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.35655 | 0.319614 | 0.159807 | − | 0.987148i | \(-0.448913\pi\) | ||||
0.159807 | + | 0.987148i | \(0.448913\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.2909 | −0.862913 | −0.431457 | − | 0.902134i | \(-0.642000\pi\) | ||||
−0.431457 | + | 0.902134i | \(0.642000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.94177 | 0.0661754 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.5622 | 1.51692 | 0.758458 | − | 0.651722i | \(-0.225953\pi\) | ||||
0.758458 | + | 0.651722i | \(0.225953\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.4750 | 0.492165 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.5012 | 0.560409 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.40389 | 0.251160 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.5047 | 0.627007 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.18790 | 0.243274 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.47820 | 0.252809 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.83308 | −0.332040 | −0.166020 | − | 0.986122i | \(-0.553092\pi\) | ||||
−0.166020 | + | 0.986122i | \(0.553092\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −51.8748 | −1.74969 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.6685 | −0.797412 | −0.398706 | − | 0.917079i | \(-0.630541\pi\) | ||||
−0.398706 | + | 0.917079i | \(0.630541\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.7461 | −0.799120 | −0.399560 | − | 0.916707i | \(-0.630837\pi\) | ||||
−0.399560 | + | 0.916707i | \(0.630837\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 50.6817 | 1.70365 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.13770 | −0.172507 | −0.0862536 | − | 0.996273i | \(-0.527490\pi\) | ||||
−0.0862536 | + | 0.996273i | \(0.527490\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.56174 | 0.119457 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.60834 | 0.221388 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.43477 | −0.248795 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4355 | 0.515952 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.4815 | −1.01775 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −73.6085 | −2.45498 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.7363 | 0.790771 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.49349 | 0.315923 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.9525 | −0.729724 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.8817 | 1.58989 | 0.794943 | − | 0.606685i | \(-0.207501\pi\) | ||||
0.794943 | + | 0.606685i | \(0.207501\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.94914 | 0.230489 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.3791 | 1.13903 | 0.569516 | − | 0.821981i | \(-0.307131\pi\) | ||||
0.569516 | + | 0.821981i | \(0.307131\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.81005 | 0.324665 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.7682 | 1.21552 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.34370 | −0.275533 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.0563714 | 0.00185952 | 0.000929760 | − | 1.00000i | \(-0.499704\pi\) | ||||
0.000929760 | 1.00000i | \(0.499704\pi\) | ||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.3590 | 0.703804 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.80547 | 0.125259 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.2509 | −0.337049 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.3782 | 0.439399 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.49686 | 0.278773 | 0.139387 | − | 0.990238i | \(-0.455487\pi\) | ||||
0.139387 | + | 0.990238i | \(0.455487\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.49649 | 0.0490455 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.3095 | −1.02503 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.82948 | 0.157941 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.4166 | 0.470969 | 0.235485 | − | 0.971878i | \(-0.424332\pi\) | ||||
0.235485 | + | 0.971878i | \(0.424332\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 50.9520 | 1.66276 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.9747 | −1.62913 | −0.814565 | − | 0.580072i | \(-0.803024\pi\) | ||||
−0.814565 | + | 0.580072i | \(0.803024\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.22765 | −0.300494 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.6296 | −0.378310 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.2007 | −0.428965 | −0.214483 | − | 0.976728i | \(-0.568807\pi\) | ||||
−0.214483 | + | 0.976728i | \(0.568807\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.4267 | −0.403387 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.5044 | −0.859463 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.3461 | 0.885826 | 0.442913 | − | 0.896565i | \(-0.353945\pi\) | ||||
0.442913 | + | 0.896565i | \(0.353945\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 52.5884 | 1.70172 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.5379 | 0.405294 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.12563 | −0.197807 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.4052 | 0.593718 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.61621 | −0.277654 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.25044 | −0.104635 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.6323 | −1.27449 | −0.637245 | − | 0.770662i | \(-0.719926\pi\) | ||||
−0.637245 | + | 0.770662i | \(0.719926\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.47291 | 0.272189 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.7757 | 0.923456 | 0.461728 | − | 0.887022i | \(-0.347230\pi\) | ||||
0.461728 | + | 0.887022i | \(0.347230\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.1886 | −0.583099 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.32060 | 0.234447 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.0596 | 0.513793 | 0.256896 | − | 0.966439i | \(-0.417300\pi\) | ||||
0.256896 | + | 0.966439i | \(0.417300\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.37652 | −0.203794 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.91737 | −0.220855 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31.8476 | −1.01578 | −0.507890 | − | 0.861422i | \(-0.669575\pi\) | ||||
−0.507890 | + | 0.861422i | \(0.669575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.5782 | 1.22920 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.64697 | −0.307067 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −45.1148 | −1.43457 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.7518 | 0.341541 | 0.170771 | − | 0.985311i | \(-0.445374\pi\) | ||||
0.170771 | + | 0.985311i | \(0.445374\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.2294 | 0.864099 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.3145 | 0.675716 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.6437 | −0.875486 | −0.437743 | − | 0.899100i | \(-0.644222\pi\) | ||||
−0.437743 | + | 0.899100i | \(0.644222\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.0250 | −0.633563 |
(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 | 1148.2.a.c.1.2 | ✓ | 5 | |
4.3 | odd | 2 | 4592.2.a.be.1.4 | 5 | |||
7.6 | odd | 2 | 8036.2.a.l.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.a.c.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
4592.2.a.be.1.4 | 5 | 4.3 | odd | 2 | |||
8036.2.a.l.1.4 | 5 | 7.6 | odd | 2 |