Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(2\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | −7.00000 | −1.34715 | −0.673575 | − | 0.739119i | \(-0.735242\pi\) | ||||
−0.673575 | + | 0.739119i | \(0.735242\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 13.0000 | 1.16276 | 0.581378 | − | 0.813634i | \(-0.302514\pi\) | ||||
0.581378 | + | 0.813634i | \(0.302514\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.0000 | −0.863919 | −0.431959 | − | 0.901893i | \(-0.642178\pi\) | ||||
−0.431959 | + | 0.901893i | \(0.642178\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 22.0000 | 0.814815 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −45.0000 | −1.23346 | −0.616728 | − | 0.787177i | \(-0.711542\pi\) | ||||
−0.616728 | + | 0.787177i | \(0.711542\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −61.0000 | −1.30141 | −0.650706 | − | 0.759330i | \(-0.725527\pi\) | ||||
−0.650706 | + | 0.759330i | \(0.725527\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −91.0000 | −1.56641 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −102.000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −68.0000 | −0.821067 | −0.410533 | − | 0.911846i | \(-0.634657\pi\) | ||||
−0.410533 | + | 0.911846i | \(0.634657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 112.000 | 1.16383 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −194.000 | −1.75877 | −0.879387 | − | 0.476108i | \(-0.842047\pi\) | ||||
−0.879387 | + | 0.476108i | \(0.842047\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.0000 | 0.352000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 35.0000 | 0.249472 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −149.000 | −0.863264 | −0.431632 | − | 0.902050i | \(-0.642062\pi\) | ||||
−0.431632 | + | 0.902050i | \(0.642062\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 315.000 | 1.66165 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −208.000 | −1.00453 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −400.000 | −1.77729 | −0.888643 | − | 0.458599i | \(-0.848351\pi\) | ||||
−0.888643 | + | 0.458599i | \(0.848351\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 427.000 | 1.75320 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 280.000 | 1.06655 | 0.533276 | − | 0.845941i | \(-0.320961\pi\) | ||||
0.533276 | + | 0.845941i | \(0.320961\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 263.000 | 0.932724 | 0.466362 | − | 0.884594i | \(-0.345564\pi\) | ||||
0.466362 | + | 0.884594i | \(0.345564\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 286.000 | 0.947430 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −509.000 | −1.57969 | −0.789843 | − | 0.613309i | \(-0.789838\pi\) | ||||
−0.789843 | + | 0.613309i | \(0.789838\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −87.0000 | −0.253644 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 714.000 | 1.96039 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 605.000 | 1.56798 | 0.783992 | − | 0.620771i | \(-0.213180\pi\) | ||||
0.783992 | + | 0.620771i | \(0.213180\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −585.000 | −1.43421 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 476.000 | 1.10610 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −578.000 | −1.27541 | −0.637705 | − | 0.770281i | \(-0.720116\pi\) | ||||
−0.637705 | + | 0.770281i | \(0.720116\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 718.000 | 1.50706 | 0.753529 | − | 0.657415i | \(-0.228350\pi\) | ||||
0.753529 | + | 0.657415i | \(0.228350\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −352.000 | −0.703934 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −793.000 | −1.51322 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −260.000 | −0.474090 | −0.237045 | − | 0.971499i | \(-0.576179\pi\) | ||||
−0.237045 | + | 0.971499i | \(0.576179\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1358.00 | 2.36933 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −738.000 | −1.23358 | −0.616792 | − | 0.787126i | \(-0.711568\pi\) | ||||
−0.616792 | + | 0.787126i | \(0.711568\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 652.000 | 1.04535 | 0.522677 | − | 0.852531i | \(-0.324933\pi\) | ||||
0.522677 | + | 0.852531i | \(0.324933\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −308.000 | −0.474197 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 720.000 | 1.06561 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 917.000 | 1.30596 | 0.652978 | − | 0.757377i | \(-0.273519\pi\) | ||||
0.652978 | + | 0.757377i | \(0.273519\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −839.000 | −1.15089 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 678.000 | 0.896629 | 0.448314 | − | 0.893876i | \(-0.352025\pi\) | ||||
0.448314 | + | 0.893876i | \(0.352025\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1326.00 | −1.69206 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −203.000 | −0.250160 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1008.00 | −1.20054 | −0.600268 | − | 0.799799i | \(-0.704940\pi\) | ||||
−0.600268 | + | 0.799799i | \(0.704940\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 976.000 | 1.12431 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1043.00 | 1.16295 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −884.000 | −0.954700 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1764.00 | −1.84646 | −0.923232 | − | 0.384242i | \(-0.874463\pi\) | ||||
−0.923232 | + | 0.384242i | \(0.874463\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −990.000 | −1.00504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1360.00 | 1.33985 | 0.669926 | − | 0.742428i | \(-0.266326\pi\) | ||||
0.669926 | + | 0.742428i | \(0.266326\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1498.00 | −1.43303 | −0.716516 | − | 0.697571i | \(-0.754264\pi\) | ||||
−0.716516 | + | 0.697571i | \(0.754264\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1456.00 | 1.35325 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −772.000 | −0.697496 | −0.348748 | − | 0.937217i | \(-0.613393\pi\) | ||||
−0.348748 | + | 0.937217i | \(0.613393\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −763.000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2800.00 | 2.39427 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1218.00 | −1.01398 | −0.506990 | − | 0.861952i | \(-0.669242\pi\) | ||||
−0.506990 | + | 0.861952i | \(0.669242\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2522.00 | −2.04502 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1342.00 | −1.06041 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1632.00 | 1.25719 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 694.000 | 0.521412 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1960.00 | −1.43681 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1053.00 | −0.753465 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1544.00 | −1.07880 | −0.539401 | − | 0.842049i | \(-0.681349\pi\) | ||||
−0.539401 | + | 0.842049i | \(0.681349\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1841.00 | −1.25652 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1916.00 | −1.27788 | −0.638938 | − | 0.769258i | \(-0.720626\pi\) | ||||
−0.638938 | + | 0.769258i | \(0.720626\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1088.00 | 0.709335 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 455.000 | 0.290075 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 72.0000 | 0.0449005 | 0.0224503 | − | 0.999748i | \(-0.492853\pi\) | ||||
0.0224503 | + | 0.999748i | \(0.492853\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1394.00 | 0.850630 | 0.425315 | − | 0.905045i | \(-0.360163\pi\) | ||||
0.425315 | + | 0.905045i | \(0.360163\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3563.00 | 2.12808 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2745.00 | 1.60523 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 377.000 | 0.215918 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 609.000 | 0.341697 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 135.000 | 0.0742257 | 0.0371129 | − | 0.999311i | \(-0.488184\pi\) | ||||
0.0371129 | + | 0.999311i | \(0.488184\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1708.00 | 0.920497 | 0.460249 | − | 0.887790i | \(-0.347760\pi\) | ||||
0.460249 | + | 0.887790i | \(0.347760\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2244.00 | −1.18573 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1937.00 | −1.00377 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −128.000 | −0.0650670 | −0.0325335 | − | 0.999471i | \(-0.510358\pi\) | ||||
−0.0325335 | + | 0.999471i | \(0.510358\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4235.00 | −2.11231 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3104.00 | 1.51944 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1235.00 | 0.593452 | 0.296726 | − | 0.954963i | \(-0.404105\pi\) | ||||
0.296726 | + | 0.954963i | \(0.404105\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4095.00 | 1.93209 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2398.00 | 1.11115 | 0.555577 | − | 0.831465i | \(-0.312497\pi\) | ||||
0.555577 | + | 0.831465i | \(0.312497\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1524.00 | 0.693673 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1496.00 | −0.669017 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1258.00 | 0.552855 | 0.276428 | − | 0.961035i | \(-0.410849\pi\) | ||||
0.276428 | + | 0.961035i | \(0.410849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −704.000 | −0.304099 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4046.00 | 1.71817 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 154.000 | 0.0643045 | 0.0321522 | − | 0.999483i | \(-0.489764\pi\) | ||||
0.0321522 | + | 0.999483i | \(0.489764\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3089.00 | −1.26853 | −0.634264 | − | 0.773117i | \(-0.718697\pi\) | ||||
−0.634264 | + | 0.773117i | \(0.718697\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5026.00 | −2.03023 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5200.00 | −2.06655 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4590.00 | 1.79494 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −560.000 | −0.215524 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1088.00 | 0.412172 | 0.206086 | − | 0.978534i | \(-0.433927\pi\) | ||||
0.206086 | + | 0.978534i | \(0.433927\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −228.000 | −0.0850352 | −0.0425176 | − | 0.999096i | \(-0.513538\pi\) | ||||
−0.0425176 | + | 0.999096i | \(0.513538\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5551.00 | 2.03854 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2226.00 | −0.805055 | −0.402528 | − | 0.915408i | \(-0.631868\pi\) | ||||
−0.402528 | + | 0.915408i | \(0.631868\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1908.00 | 0.679671 | 0.339836 | − | 0.940485i | \(-0.389629\pi\) | ||||
0.339836 | + | 0.940485i | \(0.389629\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1820.00 | 0.638671 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −464.000 | −0.160426 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3640.00 | 1.24014 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4268.00 | −1.43307 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3060.00 | 1.01275 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 583.000 | 0.190215 | 0.0951075 | − | 0.995467i | \(-0.469681\pi\) | ||||
0.0951075 | + | 0.995467i | \(0.469681\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5166.00 | 1.66182 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3419.00 | 1.08453 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2384.00 | 0.745790 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4564.00 | −1.40825 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6222.00 | 1.89383 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1594.00 | 0.478664 | 0.239332 | − | 0.970938i | \(-0.423072\pi\) | ||||
0.239332 | + | 0.970938i | \(0.423072\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 968.000 | 0.286815 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2682.00 | 0.784188 | 0.392094 | − | 0.919925i | \(-0.371751\pi\) | ||||
0.392094 | + | 0.919925i | \(0.371751\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 960.000 | 0.277024 | 0.138512 | − | 0.990361i | \(-0.455768\pi\) | ||||
0.138512 | + | 0.990361i | \(0.455768\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5040.00 | −1.43553 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1225.00 | −0.344431 | −0.172215 | − | 0.985059i | \(-0.555093\pi\) | ||||
−0.172215 | + | 0.985059i | \(0.555093\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6617.00 | −1.83679 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6419.00 | −1.75932 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1650.00 | 0.446567 | 0.223284 | − | 0.974753i | \(-0.428322\pi\) | ||||
0.223284 | + | 0.974753i | \(0.428322\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3503.00 | −0.936299 | −0.468150 | − | 0.883649i | \(-0.655079\pi\) | ||||
−0.468150 | + | 0.883649i | \(0.655079\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4928.00 | 1.30095 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1131.00 | −0.294926 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4148.00 | 1.06855 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4746.00 | −1.20789 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5571.00 | −1.40095 | −0.700475 | − | 0.713677i | \(-0.747028\pi\) | ||||
−0.700475 | + | 0.713677i | \(0.747028\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8730.00 | 2.16937 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9282.00 | 2.27946 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4891.00 | −1.18713 | −0.593565 | − | 0.804786i | \(-0.702280\pi\) | ||||
−0.593565 | + | 0.804786i | \(0.702280\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6400.00 | 1.53543 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 638.000 | 0.151307 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1287.00 | 0.301748 | 0.150874 | − | 0.988553i | \(-0.451791\pi\) | ||||
0.150874 | + | 0.988553i | \(0.451791\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7865.00 | 1.82318 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7056.00 | 1.61730 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3826.00 | 0.867195 | 0.433597 | − | 0.901107i | \(-0.357244\pi\) | ||||
0.433597 | + | 0.901107i | \(0.357244\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1713.00 | 0.383975 | 0.191988 | − | 0.981397i | \(-0.438507\pi\) | ||||
0.191988 | + | 0.981397i | \(0.438507\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6832.00 | −1.51462 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1980.00 | −0.434176 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7086.00 | −1.53703 | −0.768513 | − | 0.639834i | \(-0.779003\pi\) | ||||
−0.768513 | + | 0.639834i | \(0.779003\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3278.00 | −0.703400 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7063.00 | 1.49944 | 0.749721 | − | 0.661754i | \(-0.230188\pi\) | ||||
0.749721 | + | 0.661754i | \(0.230188\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5002.00 | −1.05066 | −0.525332 | − | 0.850897i | \(-0.676059\pi\) | ||||
−0.525332 | + | 0.850897i | \(0.676059\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6188.00 | 1.28612 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4480.00 | −0.921415 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5491.00 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12348.0 | 2.48747 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4086.00 | −0.814699 | −0.407349 | − | 0.913272i | \(-0.633547\pi\) | ||||
−0.407349 | + | 0.913272i | \(0.633547\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7514.00 | −1.48299 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1575.00 | −0.307713 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11834.0 | 2.28889 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4208.00 | −0.805798 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9520.00 | −1.80498 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9334.00 | 1.75234 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1909.00 | −0.354894 | −0.177447 | − | 0.984130i | \(-0.556784\pi\) | ||||
−0.177447 | + | 0.984130i | \(0.556784\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10486.0 | 1.93051 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5808.00 | 1.05898 | 0.529488 | − | 0.848317i | \(-0.322384\pi\) | ||||
0.529488 | + | 0.848317i | \(0.322384\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6783.00 | −1.22491 | −0.612457 | − | 0.790504i | \(-0.709819\pi\) | ||||
−0.612457 | + | 0.790504i | \(0.709819\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4576.00 | −0.818503 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6090.00 | 1.07902 | 0.539509 | − | 0.841980i | \(-0.318610\pi\) | ||||
0.539509 | + | 0.841980i | \(0.318610\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1305.00 | −0.229047 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5404.00 | 0.939632 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6936.00 | 1.19483 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2684.00 | −0.458097 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5341.00 | 0.903235 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8144.00 | 1.36472 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3801.00 | −0.631184 | −0.315592 | − | 0.948895i | \(-0.602203\pi\) | ||||
−0.315592 | + | 0.948895i | \(0.602203\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8800.00 | −1.44816 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3380.00 | −0.551251 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2374.00 | −0.383739 | −0.191869 | − | 0.981420i | \(-0.561455\pi\) | ||||
−0.191869 | + | 0.981420i | \(0.561455\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8526.00 | 1.36598 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6705.00 | 1.06480 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6880.00 | 1.08305 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17654.0 | 2.75495 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5346.00 | −0.827056 | −0.413528 | − | 0.910491i | \(-0.635704\pi\) | ||||
−0.413528 | + | 0.910491i | \(0.635704\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9003.00 | −1.38086 | −0.690429 | − | 0.723400i | \(-0.742578\pi\) | ||||
−0.690429 | + | 0.723400i | \(0.742578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2135.00 | −0.324666 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10222.0 | 1.54125 | 0.770626 | − | 0.637287i | \(-0.219944\pi\) | ||||
0.770626 | + | 0.637287i | \(0.219944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9594.00 | −1.43436 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11424.0 | −1.69362 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −719.000 | −0.105703 | −0.0528515 | − | 0.998602i | \(-0.516831\pi\) | ||||
−0.0528515 | + | 0.998602i | \(0.516831\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2235.00 | −0.325849 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4858.00 | −0.702421 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8476.00 | 1.21549 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6084.00 | 0.865347 | 0.432673 | − | 0.901551i | \(-0.357570\pi\) | ||||
0.432673 | + | 0.901551i | \(0.357570\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6160.00 | 0.869043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9680.00 | −1.35461 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1451.00 | 0.201421 | 0.100710 | − | 0.994916i | \(-0.467888\pi\) | ||||
0.100710 | + | 0.994916i | \(0.467888\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7371.00 | 1.01503 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1769.00 | −0.241666 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 896.000 | 0.121436 | 0.0607182 | − | 0.998155i | \(-0.480661\pi\) | ||||
0.0607182 | + | 0.998155i | \(0.480661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10808.0 | 1.45331 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13016.0 | −1.73652 | −0.868259 | − | 0.496111i | \(-0.834761\pi\) | ||||
−0.868259 | + | 0.496111i | \(0.834761\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9360.00 | 1.23904 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5786.00 | 0.759997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6560.00 | 0.855026 | 0.427513 | − | 0.904009i | \(-0.359390\pi\) | ||||
0.427513 | + | 0.904009i | \(0.359390\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19788.0 | 2.55939 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13412.0 | 1.72149 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11921.0 | 1.51851 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2757.00 | −0.348539 | −0.174269 | − | 0.984698i | \(-0.555756\pi\) | ||||
−0.174269 | + | 0.984698i | \(0.555756\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7616.00 | −0.955581 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4995.00 | 0.622041 | 0.311020 | − | 0.950403i | \(-0.399329\pi\) | ||||
0.311020 | + | 0.950403i | \(0.399329\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9089.00 | 1.12346 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10907.0 | −1.33821 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18000.0 | 2.19220 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3930.00 | 0.475125 | 0.237562 | − | 0.971372i | \(-0.423652\pi\) | ||||
0.237562 | + | 0.971372i | \(0.423652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −504.000 | −0.0604878 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9248.00 | 1.10185 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8814.00 | 1.04256 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9758.00 | −1.14593 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3230.00 | −0.376601 | −0.188301 | − | 0.982111i | \(-0.560298\pi\) | ||||
−0.188301 | + | 0.982111i | \(0.560298\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6110.00 | −0.707323 | −0.353662 | − | 0.935373i | \(-0.615064\pi\) | ||||
−0.353662 | + | 0.935373i | \(0.615064\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11198.0 | −1.28715 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4488.00 | −0.512235 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11488.0 | −1.30197 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19215.0 | −2.16249 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14218.0 | −1.58900 | −0.794498 | − | 0.607267i | \(-0.792266\pi\) | ||||
−0.794498 | + | 0.607267i | \(0.792266\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10008.0 | −1.11075 | −0.555374 | − | 0.831601i | \(-0.687425\pi\) | ||||
−0.555374 | + | 0.831601i | \(0.687425\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2639.00 | −0.290874 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13192.0 | 1.44407 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11338.0 | 1.23265 | 0.616325 | − | 0.787492i | \(-0.288621\pi\) | ||||
0.616325 | + | 0.787492i | \(0.288621\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1914.00 | −0.206673 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10180.0 | 1.09180 | 0.545899 | − | 0.837851i | \(-0.316188\pi\) | ||||
0.545899 | + | 0.837851i | \(0.316188\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13104.0 | −1.39593 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −945.000 | −0.0999932 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −90.0000 | −0.00945960 | −0.00472980 | − | 0.999989i | \(-0.501506\pi\) | ||||
−0.00472980 | + | 0.999989i | \(0.501506\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12600.0 | −1.31555 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11956.0 | −1.24005 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12688.0 | 1.30730 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8906.00 | −0.911609 | −0.455804 | − | 0.890080i | \(-0.650648\pi\) | ||||
−0.455804 | + | 0.890080i | \(0.650648\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3570.00 | −0.363036 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9646.00 | 0.974531 | 0.487266 | − | 0.873254i | \(-0.337994\pi\) | ||||
0.487266 | + | 0.873254i | \(0.337994\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11578.0 | −1.16215 | −0.581075 | − | 0.813850i | \(-0.697368\pi\) | ||||
−0.581075 | + | 0.813850i | \(0.697368\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13559.0 | 1.35222 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4671.00 | 0.462844 | 0.231422 | − | 0.972853i | \(-0.425662\pi\) | ||||
0.231422 | + | 0.972853i | \(0.425662\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4160.00 | 0.409576 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 896.000 | 0.0876550 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11835.0 | −1.15047 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2992.00 | −0.289016 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13310.0 | 1.27762 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −195.000 | −0.0186008 | −0.00930039 | − | 0.999957i | \(-0.502960\pi\) | ||||
−0.00930039 | + | 0.999957i | \(0.502960\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24400.0 | 2.31298 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −21728.0 | −2.04691 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22932.0 | −2.14699 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15604.0 | −1.45192 | −0.725960 | − | 0.687737i | \(-0.758604\pi\) | ||||
−0.725960 | + | 0.687737i | \(0.758604\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8645.00 | −0.799469 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18507.0 | −1.70104 | −0.850519 | − | 0.525945i | \(-0.823712\pi\) | ||||
−0.850519 | + | 0.525945i | \(0.823712\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2958.00 | −0.270226 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12870.0 | −1.16861 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11808.0 | 1.06572 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1882.00 | −0.168837 | −0.0844187 | − | 0.996430i | \(-0.526903\pi\) | ||||
−0.0844187 | + | 0.996430i | \(0.526903\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16786.0 | −1.49689 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7645.00 | 0.677681 | 0.338841 | − | 0.940844i | \(-0.389965\pi\) | ||||
0.338841 | + | 0.940844i | \(0.389965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17680.0 | 1.55792 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10668.0 | −0.934482 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1255.00 | −0.109287 | −0.0546433 | − | 0.998506i | \(-0.517402\pi\) | ||||
−0.0546433 | + | 0.998506i | \(0.517402\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10432.0 | −0.903101 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2380.00 | −0.204833 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19474.0 | −1.66627 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22905.0 | 1.94847 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8806.00 | −0.744779 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −873.000 | −0.0734104 | −0.0367052 | − | 0.999326i | \(-0.511686\pi\) | ||||
−0.0367052 | + | 0.999326i | \(0.511686\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14996.0 | 1.25378 | 0.626892 | − | 0.779106i | \(-0.284327\pi\) | ||||
0.626892 | + | 0.779106i | \(0.284327\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4928.00 | 0.409668 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15198.0 | 1.25623 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25469.0 | 2.09329 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12716.0 | −1.03922 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17080.0 | −1.38802 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10036.0 | −0.811017 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1078.00 | −0.0866278 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3915.00 | 0.312859 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2672.00 | −0.212344 | −0.106172 | − | 0.994348i | \(-0.533859\pi\) | ||||
−0.106172 | + | 0.994348i | \(0.533859\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21623.0 | 1.70890 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9919.00 | −0.779602 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4776.00 | −0.373322 | −0.186661 | − | 0.982424i | \(-0.559767\pi\) | ||||
−0.186661 | + | 0.982424i | \(0.559767\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15796.0 | 1.22797 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1972.00 | −0.152468 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14672.0 | −1.12824 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 36400.0 | 2.78395 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 134.000 | 0.0101935 | 0.00509673 | − | 0.999987i | \(-0.498378\pi\) | ||||
0.00509673 | + | 0.999987i | \(0.498378\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16043.0 | −1.21386 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32130.0 | −2.41806 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −437.000 | −0.0327129 | −0.0163564 | − | 0.999866i | \(-0.505207\pi\) | ||||
−0.0163564 | + | 0.999866i | \(0.505207\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15834.0 | −1.17901 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13424.0 | 0.994277 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23990.0 | −1.76751 | −0.883755 | − | 0.467950i | \(-0.844993\pi\) | ||||
−0.883755 | + | 0.467950i | \(0.844993\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −100.000 | −0.00732902 | −0.00366451 | − | 0.999993i | \(-0.501166\pi\) | ||||
−0.00366451 | + | 0.999993i | \(0.501166\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7616.00 | −0.555258 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8536.00 | −0.619088 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6078.00 | 0.438528 | 0.219264 | − | 0.975666i | \(-0.429634\pi\) | ||||
0.219264 | + | 0.975666i | \(0.429634\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1596.00 | 0.114555 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10848.0 | −0.774614 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27225.0 | −1.93404 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17446.0 | −1.23300 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4214.00 | −0.296304 | −0.148152 | − | 0.988965i | \(-0.547332\pi\) | ||||
−0.148152 | + | 0.988965i | \(0.547332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10132.0 | 0.708798 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15582.0 | 1.08453 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28293.0 | −1.95928 | −0.979641 | − | 0.200757i | \(-0.935660\pi\) | ||||
−0.979641 | + | 0.200757i | \(0.935660\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21216.0 | 1.46180 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13356.0 | −0.915619 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8843.00 | −0.603197 | −0.301599 | − | 0.953435i | \(-0.597520\pi\) | ||||
−0.301599 | + | 0.953435i | \(0.597520\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22548.0 | −1.53037 | −0.765185 | − | 0.643811i | \(-0.777352\pi\) | ||||
−0.765185 | + | 0.643811i | \(0.777352\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5720.00 | −0.386296 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9022.00 | 0.606275 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17061.0 | 1.14083 | 0.570416 | − | 0.821356i | \(-0.306782\pi\) | ||||
0.570416 | + | 0.821356i | \(0.306782\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3248.00 | 0.216118 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31049.0 | 2.05582 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21251.0 | −1.40020 | −0.700098 | − | 0.714047i | \(-0.746860\pi\) | ||||
−0.700098 | + | 0.714047i | \(0.746860\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −25480.0 | −1.67065 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 200.000 | 0.0130498 | 0.00652488 | − | 0.999979i | \(-0.497923\pi\) | ||||
0.00652488 | + | 0.999979i | \(0.497923\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19533.0 | −1.26833 | −0.634166 | − | 0.773197i | \(-0.718656\pi\) | ||||
−0.634166 | + | 0.773197i | \(0.718656\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6790.00 | −0.438765 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16128.0 | 1.03717 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19189.0 | −1.22810 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21420.0 | −1.36433 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 40800.0 | 2.58633 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12570.0 | −0.793033 | −0.396516 | − | 0.918028i | \(-0.629781\pi\) | ||||
−0.396516 | + | 0.918028i | \(0.629781\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4081.00 | −0.256248 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20072.0 | −1.25438 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5307.00 | 0.330096 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16236.0 | −1.00514 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17446.0 | 1.07500 | 0.537500 | − | 0.843263i | \(-0.319369\pi\) | ||||
0.537500 | + | 0.843263i | \(0.319369\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11324.0 | −0.694518 | −0.347259 | − | 0.937769i | \(-0.612887\pi\) | ||||
−0.347259 | + | 0.937769i | \(0.612887\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23933.0 | −1.46102 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2922.00 | −0.177551 | −0.0887756 | − | 0.996052i | \(-0.528295\pi\) | ||||
−0.0887756 | + | 0.996052i | \(0.528295\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26010.0 | 1.57316 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16688.0 | −1.00469 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23120.0 | −1.38554 | −0.692768 | − | 0.721160i | \(-0.743609\pi\) | ||||
−0.692768 | + | 0.721160i | \(0.743609\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24908.0 | −1.48586 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14344.0 | 0.851770 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32901.0 | 1.94483 | 0.972414 | − | 0.233264i | \(-0.0749406\pi\) | ||||
0.972414 | + | 0.233264i | \(0.0749406\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18494.0 | 1.08825 | 0.544125 | − | 0.839004i | \(-0.316862\pi\) | ||||
0.544125 | + | 0.839004i | \(0.316862\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −43554.0 | −2.55128 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14144.0 | 0.824783 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5626.00 | −0.326596 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11158.0 | −0.644833 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32310.0 | −1.85889 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15119.0 | −0.865965 | −0.432983 | − | 0.901402i | \(-0.642539\pi\) | ||||
−0.432983 | + | 0.901402i | \(0.642539\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1540.00 | 0.0878143 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6946.00 | −0.394323 | −0.197161 | − | 0.980371i | \(-0.563172\pi\) | ||||
−0.197161 | + | 0.980371i | \(0.563172\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28224.0 | 1.59520 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18774.0 | −1.05642 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31124.0 | 1.74367 | 0.871835 | − | 0.489799i | \(-0.162930\pi\) | ||||
0.871835 | + | 0.489799i | \(0.162930\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 936.000 | 0.0522084 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6720.00 | −0.373194 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36905.0 | −2.04059 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12664.0 | 0.697194 | 0.348597 | − | 0.937273i | \(-0.386658\pi\) | ||||
0.348597 | + | 0.937273i | \(0.386658\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15840.0 | 0.868271 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18122.0 | 0.989074 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28560.0 | −1.55206 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8575.00 | 0.464000 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18715.0 | 1.00835 | 0.504177 | − | 0.863600i | \(-0.331796\pi\) | ||||
0.504177 | + | 0.863600i | \(0.331796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27200.0 | 1.45927 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 46319.0 | 2.47443 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21760.0 | −1.15752 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7531.00 | 0.398918 | 0.199459 | − | 0.979906i | \(-0.436082\pi\) | ||||
0.199459 | + | 0.979906i | \(0.436082\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20174.0 | 1.06411 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28906.0 | 1.51829 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35685.0 | 1.86649 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11550.0 | −0.601594 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35338.0 | −1.83294 | −0.916471 | − | 0.400102i | \(-0.868975\pi\) | ||||
−0.916471 | + | 0.400102i | \(0.868975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23968.0 | 1.23802 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24521.0 | 1.26134 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1276.00 | 0.0653648 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13976.0 | 0.712986 | 0.356493 | − | 0.934298i | \(-0.383972\pi\) | ||||
0.356493 | + | 0.934298i | \(0.383972\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26826.0 | −1.35731 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7172.00 | −0.361397 | −0.180698 | − | 0.983539i | \(-0.557836\pi\) | ||||
−0.180698 | + | 0.983539i | \(0.557836\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7917.00 | 0.397310 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11700.0 | 0.584769 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35091.0 | −1.74674 | −0.873372 | − | 0.487054i | \(-0.838071\pi\) | ||||
−0.873372 | + | 0.487054i | \(0.838071\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −29036.0 | −1.43949 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10992.0 | 0.542742 | 0.271371 | − | 0.962475i | \(-0.412523\pi\) | ||||
0.271371 | + | 0.962475i | \(0.412523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1755.00 | 0.0863063 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14916.0 | 0.730586 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12352.0 | 0.602580 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20988.0 | 1.01979 | 0.509895 | − | 0.860236i | \(-0.329684\pi\) | ||||
0.509895 | + | 0.860236i | \(0.329684\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 38997.0 | 1.88729 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22204.0 | 1.07031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39094.0 | 1.87701 | 0.938504 | − | 0.345267i | \(-0.112212\pi\) | ||||
0.938504 | + | 0.345267i | \(0.112212\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −61110.0 | −2.92247 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27270.0 | −1.29900 | −0.649499 | − | 0.760363i | \(-0.725021\pi\) | ||||
−0.649499 | + | 0.760363i | \(0.725021\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12208.0 | 0.579239 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −29172.0 | −1.37871 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35258.0 | 1.65983 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3462.00 | 0.162344 | 0.0811722 | − | 0.996700i | \(-0.474134\pi\) | ||||
0.0811722 | + | 0.996700i | \(0.474134\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34237.0 | 1.59924 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10632.0 | 0.494704 | 0.247352 | − | 0.968926i | \(-0.420440\pi\) | ||||
0.247352 | + | 0.968926i | \(0.420440\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6556.00 | −0.303869 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −44800.0 | −2.06846 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19040.0 | −0.875711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33210.0 | 1.52157 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1015.00 | 0.0463259 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1664.00 | −0.0756570 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3754.00 | −0.170033 | −0.0850163 | − | 0.996380i | \(-0.527094\pi\) | ||||
−0.0850163 | + | 0.996380i | \(0.527094\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9009.00 | −0.406500 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19488.0 | 0.875997 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −43798.0 | −1.96130 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −55055.0 | −2.45610 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9378.00 | −0.416795 | −0.208398 | − | 0.978044i | \(-0.566825\pi\) | ||||
−0.208398 | + | 0.978044i | \(0.566825\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51918.0 | 2.29878 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22176.0 | −0.978215 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29340.0 | −1.28940 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40352.0 | 1.76673 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26782.0 | −1.16824 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3708.00 | −0.161145 | −0.0805725 | − | 0.996749i | \(-0.525675\pi\) | ||||
−0.0805725 | + | 0.996749i | \(0.525675\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13232.0 | 0.572920 | 0.286460 | − | 0.958092i | \(-0.407521\pi\) | ||||
0.286460 | + | 0.958092i | \(0.407521\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11991.0 | −0.517273 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16055.0 | 0.690039 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17884.0 | −0.765829 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21472.0 | 0.916108 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5445.00 | −0.231464 | −0.115732 | − | 0.993280i | \(-0.536921\pi\) | ||||
−0.115732 | + | 0.993280i | \(0.536921\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17576.0 | 0.744424 | 0.372212 | − | 0.928148i | \(-0.378599\pi\) | ||||
0.372212 | + | 0.928148i | \(0.378599\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13860.0 | 0.584901 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10143.0 | 0.426489 | 0.213245 | − | 0.976999i | \(-0.431597\pi\) | ||||
0.213245 | + | 0.976999i | \(0.431597\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8558.00 | 0.358542 | 0.179271 | − | 0.983800i | \(-0.442626\pi\) | ||||
0.179271 | + | 0.983800i | \(0.442626\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 49602.0 | 2.07061 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8874.00 | 0.369107 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31174.0 | 1.29200 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5215.00 | −0.215361 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30467.0 | 1.25368 | 0.626840 | − | 0.779148i | \(-0.284348\pi\) | ||||
0.626840 | + | 0.779148i | \(0.284348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −49441.0 | −2.01997 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19812.0 | 0.806572 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11104.0 | −0.450458 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35014.0 | 1.41540 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 77600.0 | 3.12584 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 154.000 | 0.00618155 | 0.00309077 | − | 0.999995i | \(-0.499016\pi\) | ||||
0.00309077 | + | 0.999995i | \(0.499016\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19448.0 | −0.777904 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10463.0 | −0.417047 | −0.208523 | − | 0.978017i | \(-0.566866\pi\) | ||||
−0.208523 | + | 0.978017i | \(0.566866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24749.0 | 0.983033 | 0.491516 | − | 0.870868i | \(-0.336443\pi\) | ||||
0.491516 | + | 0.870868i | \(0.336443\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31360.0 | 1.24128 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20586.0 | 0.812000 | 0.406000 | − | 0.913873i | \(-0.366923\pi\) | ||||
0.406000 | + | 0.913873i | \(0.366923\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16354.0 | 0.642835 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −38437.0 | −1.50564 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41265.0 | −1.61084 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15860.0 | 0.616987 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −38808.0 | −1.50453 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16848.0 | 0.650933 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5051.00 | −0.194481 | −0.0972407 | − | 0.995261i | \(-0.531002\pi\) | ||||
−0.0972407 | + | 0.995261i | \(0.531002\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28602.0 | 1.09752 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38990.0 | −1.49104 | −0.745520 | − | 0.666483i | \(-0.767799\pi\) | ||||
−0.745520 | + | 0.666483i | \(0.767799\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27180.0 | −1.03588 | −0.517939 | − | 0.855418i | \(-0.673300\pi\) | ||||
−0.517939 | + | 0.855418i | \(0.673300\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 52598.0 | 1.99781 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17435.0 | 0.659989 | 0.329994 | − | 0.943983i | \(-0.392953\pi\) | ||||
0.329994 | + | 0.943983i | \(0.392953\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24704.0 | 0.931997 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37755.0 | 1.41957 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34612.0 | 1.29703 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2002.00 | 0.0747704 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −82838.0 | −3.08348 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4321.00 | −0.160304 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −61710.0 | −2.28175 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 29456.0 | 1.08553 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40157.0 | −1.47499 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11500.0 | −0.421005 | −0.210502 | − | 0.977593i | \(-0.567510\pi\) | ||||
−0.210502 | + | 0.977593i | \(0.567510\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29920.0 | 1.09173 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7969.00 | 0.289819 | 0.144909 | − | 0.989445i | \(-0.453711\pi\) | ||||
0.144909 | + | 0.989445i | \(0.453711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30510.0 | −1.10595 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −65338.0 | −2.36066 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30656.0 | 1.10398 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24414.0 | 0.876326 | 0.438163 | − | 0.898896i | \(-0.355629\pi\) | ||||
0.438163 | + | 0.898896i | \(0.355629\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13363.0 | 0.478095 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45018.0 | 1.60540 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17600.0 | −0.625605 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −32956.0 | −1.16766 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18694.0 | −0.660205 | −0.330102 | − | 0.943945i | \(-0.607083\pi\) | ||||
−0.330102 | + | 0.943945i | \(0.607083\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5916.00 | 0.208259 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −40656.0 | −1.42660 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 59670.0 | 2.08708 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14394.0 | 0.501848 | 0.250924 | − | 0.968007i | \(-0.419266\pi\) | ||||
0.250924 | + | 0.968007i | \(0.419266\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 47481.0 | 1.65014 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11925.0 | 0.413118 | 0.206559 | − | 0.978434i | \(-0.433773\pi\) | ||||
0.206559 | + | 0.978434i | \(0.433773\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −54320.0 | −1.87582 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7280.00 | −0.250602 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53321.0 | −1.82967 | −0.914836 | − | 0.403825i | \(-0.867680\pi\) | ||||
−0.914836 | + | 0.403825i | \(0.867680\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39772.0 | −1.36044 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −42630.0 | −1.45360 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38301.0 | −1.30188 | −0.650940 | − | 0.759129i | \(-0.725625\pi\) | ||||
−0.650940 | + | 0.759129i | \(0.725625\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14144.0 | 0.479256 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9135.00 | 0.308561 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1152.00 | −0.0387904 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7590.00 | −0.254775 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16984.0 | −0.568330 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2964.00 | −0.0988752 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40011.0 | 1.33058 | 0.665288 | − | 0.746587i | \(-0.268309\pi\) | ||||
0.665288 | + | 0.746587i | \(0.268309\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −48552.0 | −1.60961 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53500.0 | −1.76817 | −0.884087 | − | 0.467323i | \(-0.845219\pi\) | ||||
−0.884087 | + | 0.467323i | \(0.845219\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22304.0 | −0.734875 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18788.0 | 0.617126 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28449.0 | 0.931591 | 0.465795 | − | 0.884892i | \(-0.345768\pi\) | ||||
0.465795 | + | 0.884892i | \(0.345768\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45360.0 | 1.48081 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16786.0 | −0.546316 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48529.0 | −1.57460 | −0.787301 | − | 0.616568i | \(-0.788522\pi\) | ||||
−0.787301 | + | 0.616568i | \(0.788522\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28938.0 | −0.936083 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −57008.0 | −1.83848 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51022.0 | −1.64045 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8142.00 | −0.260988 | −0.130494 | − | 0.991449i | \(-0.541656\pi\) | ||||
−0.130494 | + | 0.991449i | \(0.541656\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26607.0 | 0.850300 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24804.0 | 0.790291 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30572.0 | 0.971138 | 0.485569 | − | 0.874198i | \(-0.338612\pi\) | ||||
0.485569 | + | 0.874198i | \(0.338612\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14000.0 | −0.443384 |
(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 | 1856.4.a.b.1.1 | 1 | ||
4.3 | odd | 2 | 1856.4.a.e.1.1 | 1 | |||
8.3 | odd | 2 | 928.4.a.a.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 928.4.a.b.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.a.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
928.4.a.b.1.1 | yes | 1 | 8.5 | even | 2 | ||
1856.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1856.4.a.e.1.1 | 1 | 4.3 | odd | 2 |