Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,3,Mod(351,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.351");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(21.7984211488\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.1827904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 14x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 351.2 | ||
Root | \(-1.37720i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.351 |
Dual form | 800.3.b.i.351.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 2.75441i | − 0.918135i | −0.888401 | − | 0.459068i | \(-0.848184\pi\) | ||||
0.888401 | − | 0.459068i | \(-0.151816\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.84997i | 0.549995i | 0.961445 | + | 0.274998i | \(0.0886771\pi\) | ||||
−0.961445 | + | 0.274998i | \(0.911323\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.41325 | 0.157028 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 6.19112i | − 0.562829i | −0.959586 | − | 0.281415i | \(-0.909196\pi\) | ||||
0.959586 | − | 0.281415i | \(-0.0908037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.1132 | 1.23948 | 0.619738 | − | 0.784809i | \(-0.287239\pi\) | ||||
0.619738 | + | 0.784809i | \(0.287239\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.20875 | −0.306397 | −0.153198 | − | 0.988195i | \(-0.548957\pi\) | ||||
−0.153198 | + | 0.988195i | \(0.548957\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 36.2264i | 1.90665i | 0.301944 | + | 0.953326i | \(0.402364\pi\) | ||||
−0.301944 | + | 0.953326i | \(0.597636\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.6044 | 0.504970 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 22.0411i | − 0.958308i | −0.877731 | − | 0.479154i | \(-0.840943\pi\) | ||||
0.877731 | − | 0.479154i | \(-0.159057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 28.6823i | − 1.06231i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 20.0352 | 0.690871 | 0.345435 | − | 0.938443i | \(-0.387731\pi\) | ||||
0.345435 | + | 0.938443i | \(0.387731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.4175i | 0.852177i | 0.904681 | + | 0.426089i | \(0.140109\pi\) | ||||
−0.904681 | + | 0.426089i | \(0.859891\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.0529 | −0.516754 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 69.3219 | 1.87357 | 0.936783 | − | 0.349911i | \(-0.113788\pi\) | ||||
0.936783 | + | 0.349911i | \(0.113788\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 44.3822i | − 1.13801i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.6220 | 0.283463 | 0.141732 | − | 0.989905i | \(-0.454733\pi\) | ||||
0.141732 | + | 0.989905i | \(0.454733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 25.8542i | 0.601261i | 0.953741 | + | 0.300630i | \(0.0971971\pi\) | ||||
−0.953741 | + | 0.300630i | \(0.902803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 66.1853i | − 1.40820i | −0.710102 | − | 0.704099i | \(-0.751351\pi\) | ||||
0.710102 | − | 0.704099i | \(-0.248649\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 34.1777 | 0.697505 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.3470i | 0.281314i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 39.5751 | 0.746699 | 0.373350 | − | 0.927691i | \(-0.378209\pi\) | ||||
0.373350 | + | 0.927691i | \(0.378209\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 99.7821 | 1.75056 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 27.7736i | 0.470739i | 0.971906 | + | 0.235370i | \(0.0756301\pi\) | ||||
−0.971906 | + | 0.235370i | \(0.924370\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −54.1954 | −0.888449 | −0.444224 | − | 0.895916i | \(-0.646521\pi\) | ||||
−0.444224 | + | 0.895916i | \(0.646521\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.44096i | 0.0863645i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 107.507i | − 1.60459i | −0.596931 | − | 0.802293i | \(-0.703613\pi\) | ||||
0.596931 | − | 0.802293i | \(-0.296387\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −60.7101 | −0.879857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 70.7997i | − 0.997179i | −0.866838 | − | 0.498590i | \(-0.833851\pi\) | ||||
0.866838 | − | 0.498590i | \(-0.166149\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −37.4351 | −0.512810 | −0.256405 | − | 0.966569i | \(-0.582538\pi\) | ||||
−0.256405 | + | 0.966569i | \(0.582538\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23.8356 | 0.309554 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 97.6530i | − 1.23611i | −0.786133 | − | 0.618057i | \(-0.787920\pi\) | ||||
0.786133 | − | 0.618057i | \(-0.212080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −66.2835 | −0.818315 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 126.163i | − 1.52003i | −0.649904 | − | 0.760017i | \(-0.725191\pi\) | ||||
0.649904 | − | 0.760017i | \(-0.274809\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 55.1852i | − 0.634313i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −133.635 | −1.50151 | −0.750757 | − | 0.660579i | \(-0.770311\pi\) | ||||
−0.750757 | + | 0.660579i | \(0.770311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 62.0352i | 0.681706i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 72.7645 | 0.782414 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.40900 | 0.0660722 | 0.0330361 | − | 0.999454i | \(-0.489482\pi\) | ||||
0.0330361 | + | 0.999454i | \(0.489482\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 8.74960i | − 0.0883798i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 121.564 | 1.20361 | 0.601803 | − | 0.798644i | \(-0.294449\pi\) | ||||
0.601803 | + | 0.798644i | \(0.294449\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.95891i | 0.0966884i | 0.998831 | + | 0.0483442i | \(0.0153944\pi\) | ||||
−0.998831 | + | 0.0483442i | \(0.984606\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 134.842i | 1.26020i | 0.776512 | + | 0.630102i | \(0.216987\pi\) | ||||
−0.776512 | + | 0.630102i | \(0.783013\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 28.2306 | 0.258996 | 0.129498 | − | 0.991580i | \(-0.458663\pi\) | ||||
0.129498 | + | 0.991580i | \(0.458663\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 190.941i | − 1.72019i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 190.052 | 1.68188 | 0.840939 | − | 0.541130i | \(-0.182003\pi\) | ||||
0.840939 | + | 0.541130i | \(0.182003\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 22.7719 | 0.194632 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 20.0535i | − 0.168517i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 82.6700 | 0.683223 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 32.0117i | − 0.260258i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 60.0646i | − 0.472950i | −0.971638 | − | 0.236475i | \(-0.924008\pi\) | ||||
0.971638 | − | 0.236475i | \(-0.0759921\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 71.2130 | 0.552039 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 111.985i | 0.854848i | 0.904051 | + | 0.427424i | \(0.140579\pi\) | ||||
−0.904051 | + | 0.427424i | \(0.859421\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −139.470 | −1.04865 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −42.6439 | −0.311269 | −0.155635 | − | 0.987815i | \(-0.549742\pi\) | ||||
−0.155635 | + | 0.987815i | \(0.549742\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 222.332i | 1.59951i | 0.600325 | + | 0.799756i | \(0.295038\pi\) | ||||
−0.600325 | + | 0.799756i | \(0.704962\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −182.301 | −1.29292 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 99.7587i | − 0.697614i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 94.1394i | − 0.640404i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.0981 | −0.134887 | −0.0674434 | − | 0.997723i | \(-0.521484\pi\) | ||||
−0.0674434 | + | 0.997723i | \(0.521484\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 86.0522i | 0.569882i | 0.958545 | + | 0.284941i | \(0.0919741\pi\) | ||||
−0.958545 | + | 0.284941i | \(0.908026\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.36126 | −0.0481128 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.0342 | −0.102129 | −0.0510643 | − | 0.998695i | \(-0.516261\pi\) | ||||
−0.0510643 | + | 0.998695i | \(0.516261\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 109.006i | − 0.685571i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 84.8575 | 0.527065 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 179.157i | 1.09912i | 0.835454 | + | 0.549561i | \(0.185205\pi\) | ||||
−0.835454 | + | 0.549561i | \(0.814795\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 137.800i | 0.825149i | 0.910924 | + | 0.412574i | \(0.135370\pi\) | ||||
−0.910924 | + | 0.412574i | \(0.864630\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 90.6347 | 0.536300 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 51.1969i | 0.299397i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −62.8895 | −0.363523 | −0.181762 | − | 0.983343i | \(-0.558180\pi\) | ||||
−0.181762 | + | 0.983343i | \(0.558180\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 76.4998 | 0.432203 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 238.020i | 1.32972i | 0.746967 | + | 0.664861i | \(0.231509\pi\) | ||||
−0.746967 | + | 0.664861i | \(0.768491\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 186.718 | 1.03159 | 0.515795 | − | 0.856712i | \(-0.327497\pi\) | ||||
0.515795 | + | 0.856712i | \(0.327497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 149.276i | 0.815716i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 32.2480i | 0.172449i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 110.426 | 0.584264 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 123.447i | 0.646319i | 0.946344 | + | 0.323160i | \(0.104745\pi\) | ||||
−0.946344 | + | 0.323160i | \(0.895255\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −162.355 | −0.841220 | −0.420610 | − | 0.907242i | \(-0.638184\pi\) | ||||
−0.420610 | + | 0.907242i | \(0.638184\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −113.540 | −0.576344 | −0.288172 | − | 0.957579i | \(-0.593048\pi\) | ||||
−0.288172 | + | 0.957579i | \(0.593048\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 325.928i | − 1.63783i | −0.573915 | − | 0.818915i | \(-0.694576\pi\) | ||||
0.573915 | − | 0.818915i | \(-0.305424\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −296.118 | −1.47323 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 77.1351i | 0.379976i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 31.1496i | − 0.150481i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 224.282 | 1.07312 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 130.731i | − 0.619580i | −0.950805 | − | 0.309790i | \(-0.899741\pi\) | ||||
0.950805 | − | 0.309790i | \(-0.100259\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −195.011 | −0.915546 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −101.707 | −0.468694 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 103.112i | 0.470829i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −83.9295 | −0.379772 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 93.3889i | 0.418784i | 0.977832 | + | 0.209392i | \(0.0671485\pi\) | ||||
−0.977832 | + | 0.209392i | \(0.932851\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.9957i | 0.0660602i | 0.999454 | + | 0.0330301i | \(0.0105157\pi\) | ||||
−0.999454 | + | 0.0330301i | \(0.989484\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 144.106 | 0.629283 | 0.314641 | − | 0.949211i | \(-0.398116\pi\) | ||||
0.314641 | + | 0.949211i | \(0.398116\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 65.6530i | − 0.284212i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 126.528 | 0.543040 | 0.271520 | − | 0.962433i | \(-0.412474\pi\) | ||||
0.271520 | + | 0.962433i | \(0.412474\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −268.976 | −1.13492 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 1.65300i | − 0.00691630i | −0.999994 | − | 0.00345815i | \(-0.998899\pi\) | ||||
0.999994 | − | 0.00345815i | \(-0.00110077\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 206.928 | 0.858622 | 0.429311 | − | 0.903157i | \(-0.358756\pi\) | ||||
0.429311 | + | 0.903157i | \(0.358756\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 75.5692i | − 0.310984i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 583.722i | 2.36325i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −347.503 | −1.39560 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 74.1206i | − 0.295301i | −0.989040 | − | 0.147651i | \(-0.952829\pi\) | ||||
0.989040 | − | 0.147651i | \(-0.0471711\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −136.459 | −0.539364 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −274.682 | −1.06880 | −0.534402 | − | 0.845231i | \(-0.679463\pi\) | ||||
−0.534402 | + | 0.845231i | \(0.679463\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 266.887i | 1.03045i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 28.3148 | 0.108486 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 75.5382i | − 0.287218i | −0.989635 | − | 0.143609i | \(-0.954129\pi\) | ||||
0.989635 | − | 0.143609i | \(-0.0458707\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 368.084i | 1.37859i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −314.087 | −1.16761 | −0.583804 | − | 0.811895i | \(-0.698436\pi\) | ||||
−0.583804 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 128.158i | 0.472908i | 0.971643 | + | 0.236454i | \(0.0759852\pi\) | ||||
−0.971643 | + | 0.236454i | \(0.924015\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 170.870 | 0.625898 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −242.118 | −0.874073 | −0.437037 | − | 0.899444i | \(-0.643972\pi\) | ||||
−0.437037 | + | 0.899444i | \(0.643972\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 37.3345i | 0.133815i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.8562 | 0.102691 | 0.0513456 | − | 0.998681i | \(-0.483649\pi\) | ||||
0.0513456 | + | 0.998681i | \(0.483649\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 269.993i | 0.954039i | 0.878893 | + | 0.477020i | \(0.158283\pi\) | ||||
−0.878893 | + | 0.477020i | \(0.841717\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 44.7443i | 0.155904i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −261.869 | −0.906121 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 17.6530i | − 0.0606632i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 353.448 | 1.20631 | 0.603154 | − | 0.797625i | \(-0.293911\pi\) | ||||
0.603154 | + | 0.797625i | \(0.293911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −177.576 | −0.597898 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 355.152i | − 1.18780i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −99.5379 | −0.330691 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 334.837i | − 1.10507i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 260.946i | 0.849985i | 0.905197 | + | 0.424993i | \(0.139723\pi\) | ||||
−0.905197 | + | 0.424993i | \(0.860277\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.4309 | 0.0887730 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 141.570i | − 0.455208i | −0.973754 | − | 0.227604i | \(-0.926911\pi\) | ||||
0.973754 | − | 0.227604i | \(-0.0730892\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −365.950 | −1.16917 | −0.584584 | − | 0.811333i | \(-0.698742\pi\) | ||||
−0.584584 | + | 0.811333i | \(0.698742\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.22805 | 0.0291106 | 0.0145553 | − | 0.999894i | \(-0.495367\pi\) | ||||
0.0145553 | + | 0.999894i | \(0.495367\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 124.041i | − 0.388842i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 371.409 | 1.15704 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 188.694i | − 0.584192i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 77.7586i | − 0.237794i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 254.811 | 0.774502 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 53.3799i | 0.161268i | 0.996744 | + | 0.0806342i | \(0.0256946\pi\) | ||||
−0.996744 | + | 0.0806342i | \(0.974305\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 97.9692 | 0.294202 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −350.458 | −1.03994 | −0.519968 | − | 0.854186i | \(-0.674056\pi\) | ||||
−0.519968 | + | 0.854186i | \(0.674056\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 523.481i | − 1.54419i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 163.554 | 0.479630 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 320.232i | 0.933620i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 70.8302i | − 0.204122i | −0.994778 | − | 0.102061i | \(-0.967456\pi\) | ||||
0.994778 | − | 0.102061i | \(-0.0325436\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −373.045 | −1.06890 | −0.534449 | − | 0.845201i | \(-0.679481\pi\) | ||||
−0.534449 | + | 0.845201i | \(0.679481\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 462.163i | − 1.31670i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −543.568 | −1.53985 | −0.769927 | − | 0.638132i | \(-0.779707\pi\) | ||||
−0.769927 | + | 0.638132i | \(0.779707\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −55.2355 | −0.154721 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 500.805i | 1.39500i | 0.716585 | + | 0.697500i | \(0.245704\pi\) | ||||
−0.716585 | + | 0.697500i | \(0.754296\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −951.350 | −2.63532 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 227.707i | − 0.627291i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 142.499i | − 0.388281i | −0.980974 | − | 0.194140i | \(-0.937808\pi\) | ||||
0.980974 | − | 0.194140i | \(-0.0621918\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.4248 | 0.0445116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 152.363i | 0.410681i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 160.000 | 0.428954 | 0.214477 | − | 0.976729i | \(-0.431195\pi\) | ||||
0.214477 | + | 0.976729i | \(0.431195\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 322.832 | 0.856317 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 192.796i | − 0.508698i | −0.967113 | − | 0.254349i | \(-0.918139\pi\) | ||||
0.967113 | − | 0.254349i | \(-0.0818611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −165.442 | −0.434232 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 605.286i | 1.58038i | 0.612861 | + | 0.790191i | \(0.290019\pi\) | ||||
−0.612861 | + | 0.790191i | \(0.709981\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 36.5384i | 0.0944146i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 522.159 | 1.34231 | 0.671155 | − | 0.741317i | \(-0.265798\pi\) | ||||
0.671155 | + | 0.741317i | \(0.265798\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 114.806i | 0.293623i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 308.452 | 0.784866 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 357.537 | 0.900598 | 0.450299 | − | 0.892878i | \(-0.351317\pi\) | ||||
0.450299 | + | 0.892878i | \(0.351317\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 384.158i | 0.962802i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 262.506 | 0.654629 | 0.327315 | − | 0.944915i | \(-0.393856\pi\) | ||||
0.327315 | + | 0.944915i | \(0.393856\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 425.670i | 1.05625i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 429.181i | − 1.05450i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 63.2015 | 0.154527 | 0.0772634 | − | 0.997011i | \(-0.475382\pi\) | ||||
0.0772634 | + | 0.997011i | \(0.475382\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 117.459i | 0.285787i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −106.928 | −0.258905 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 612.393 | 1.46857 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 673.390i | − 1.60714i | −0.595213 | − | 0.803568i | \(-0.702932\pi\) | ||||
0.595213 | − | 0.803568i | \(-0.297068\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 84.6877 | 0.201158 | 0.100579 | − | 0.994929i | \(-0.467930\pi\) | ||||
0.100579 | + | 0.994929i | \(0.467930\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 93.5363i | − 0.221126i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 208.650i | − 0.488643i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −274.776 | −0.640504 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 672.158i | 1.55953i | 0.626072 | + | 0.779766i | \(0.284662\pi\) | ||||
−0.626072 | + | 0.779766i | \(0.715338\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −562.185 | −1.29835 | −0.649174 | − | 0.760640i | \(-0.724885\pi\) | ||||
−0.649174 | + | 0.760640i | \(0.724885\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 798.469 | 1.82716 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 384.842i | 0.876633i | 0.898821 | + | 0.438316i | \(0.144425\pi\) | ||||
−0.898821 | + | 0.438316i | \(0.855575\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 48.3017 | 0.109528 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 461.625i | − 1.04204i | −0.853544 | − | 0.521021i | \(-0.825551\pi\) | ||||
0.853544 | − | 0.521021i | \(-0.174449\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 55.3584i | 0.123844i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −48.7390 | −0.108550 | −0.0542750 | − | 0.998526i | \(-0.517285\pi\) | ||||
−0.0542750 | + | 0.998526i | \(0.517285\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 71.9532i | − 0.159542i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 237.023 | 0.523229 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −762.588 | −1.66868 | −0.834341 | − | 0.551248i | \(-0.814152\pi\) | ||||
−0.834341 | + | 0.551248i | \(0.814152\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 149.399i | 0.325488i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −406.436 | −0.881639 | −0.440820 | − | 0.897596i | \(-0.645312\pi\) | ||||
−0.440820 | + | 0.897596i | \(0.645312\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 260.743i | − 0.563159i | −0.959538 | − | 0.281580i | \(-0.909142\pi\) | ||||
0.959538 | − | 0.281580i | \(-0.0908583\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 594.738i | − 1.27353i | −0.771058 | − | 0.636765i | \(-0.780272\pi\) | ||||
0.771058 | − | 0.636765i | \(-0.219728\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 413.899 | 0.882515 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 44.1647i | 0.0937679i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 160.067 | 0.338407 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 55.9294 | 0.117252 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 534.894i | 1.11669i | 0.829609 | + | 0.558344i | \(0.188563\pi\) | ||||
−0.829609 | + | 0.558344i | \(0.811437\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1117.00 | 2.32224 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 233.732i | − 0.483917i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 264.298i | − 0.542706i | −0.962480 | − | 0.271353i | \(-0.912529\pi\) | ||||
0.962480 | − | 0.271353i | \(-0.0874711\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 493.471 | 1.00914 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 539.150i | − 1.09807i | −0.835801 | − | 0.549033i | \(-0.814996\pi\) | ||||
0.835801 | − | 0.549033i | \(-0.185004\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −104.359 | −0.211681 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 272.577 | 0.548444 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 138.218i | 0.276991i | 0.990363 | + | 0.138495i | \(0.0442266\pi\) | ||||
−0.990363 | + | 0.138495i | \(0.955773\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 379.557 | 0.757598 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 389.170i | − 0.773697i | −0.922143 | − | 0.386848i | \(-0.873564\pi\) | ||||
0.922143 | − | 0.386848i | \(-0.126436\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 249.645i | − 0.492396i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 468.599 | 0.920627 | 0.460314 | − | 0.887756i | \(-0.347737\pi\) | ||||
0.460314 | + | 0.887756i | \(0.347737\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 144.124i | − 0.282043i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1039.06 | 2.02545 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −409.761 | −0.792575 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 173.223i | 0.333764i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −931.151 | −1.78724 | −0.893619 | − | 0.448826i | \(-0.851842\pi\) | ||||
−0.893619 | + | 0.448826i | \(0.851842\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 227.656i | 0.435289i | 0.976028 | + | 0.217645i | \(0.0698374\pi\) | ||||
−0.976028 | + | 0.217645i | \(0.930163\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 137.602i | − 0.261104i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 43.1902 | 0.0816451 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 39.2511i | 0.0739191i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 187.267 | 0.351346 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 655.605 | 1.22087 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 211.599i | − 0.392576i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 388.174 | 0.717511 | 0.358756 | − | 0.933431i | \(-0.383201\pi\) | ||||
0.358756 | + | 0.933431i | \(0.383201\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 514.296i | − 0.947139i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 473.059i | 0.864824i | 0.901676 | + | 0.432412i | \(0.142337\pi\) | ||||
−0.901676 | + | 0.432412i | \(0.857663\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −76.5916 | −0.139511 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 725.804i | 1.31725i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 375.961 | 0.679857 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 419.101 | 0.752426 | 0.376213 | − | 0.926533i | \(-0.377226\pi\) | ||||
0.376213 | + | 0.926533i | \(0.377226\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 416.594i | 0.745248i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 88.8241 | 0.158332 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 145.910i | 0.259165i | 0.991569 | + | 0.129582i | \(0.0413637\pi\) | ||||
−0.991569 | + | 0.129582i | \(0.958636\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 255.189i | − 0.450069i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −950.513 | −1.67050 | −0.835249 | − | 0.549872i | \(-0.814677\pi\) | ||||
−0.835249 | + | 0.549872i | \(0.814677\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 404.107i | − 0.707717i | −0.935299 | − | 0.353859i | \(-0.884869\pi\) | ||||
0.935299 | − | 0.353859i | \(-0.115131\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 340.023 | 0.593408 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 847.944 | 1.46957 | 0.734787 | − | 0.678298i | \(-0.237282\pi\) | ||||
0.734787 | + | 0.678298i | \(0.237282\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 447.193i | 0.772354i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 485.723 | 0.836011 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 245.014i | − 0.420264i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 658.243i | − 1.12137i | −0.828030 | − | 0.560684i | \(-0.810538\pi\) | ||||
0.828030 | − | 0.560684i | \(-0.189462\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −957.010 | −1.62480 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 312.735i | 0.529162i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 282.430 | 0.476274 | 0.238137 | − | 0.971232i | \(-0.423463\pi\) | ||||
0.238137 | + | 0.971232i | \(0.423463\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −897.739 | −1.50375 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 498.597i | − 0.832382i | −0.909277 | − | 0.416191i | \(-0.863365\pi\) | ||||
0.909277 | − | 0.416191i | \(-0.136635\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −287.496 | −0.478363 | −0.239182 | − | 0.970975i | \(-0.576879\pi\) | ||||
−0.239182 | + | 0.970975i | \(0.576879\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 151.934i | − 0.251964i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 844.260i | 1.39087i | 0.718587 | + | 0.695437i | \(0.244789\pi\) | ||||
−0.718587 | + | 0.695437i | \(0.755211\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 212.461 | 0.348869 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1066.46i | − 1.74543i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −975.340 | −1.59109 | −0.795547 | − | 0.605892i | \(-0.792816\pi\) | ||||
−0.795547 | + | 0.605892i | \(0.792816\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 319.229 | 0.517389 | 0.258695 | − | 0.965959i | \(-0.416708\pi\) | ||||
0.258695 | + | 0.965959i | \(0.416708\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 845.837i | − 1.36646i | −0.730205 | − | 0.683228i | \(-0.760575\pi\) | ||||
0.730205 | − | 0.683228i | \(-0.239425\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −632.190 | −1.01802 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 514.489i | − 0.825826i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 617.764i | − 0.985269i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −361.080 | −0.574055 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 322.653i | − 0.511335i | −0.966765 | − | 0.255668i | \(-0.917705\pi\) | ||||
0.966765 | − | 0.255668i | \(-0.0822953\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −360.087 | −0.568858 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 550.712 | 0.864541 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 100.058i | − 0.156585i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 167.659 | 0.261558 | 0.130779 | − | 0.991412i | \(-0.458252\pi\) | ||||
0.130779 | + | 0.991412i | \(0.458252\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 118.227i | − 0.183867i | −0.995765 | − | 0.0919335i | \(-0.970695\pi\) | ||||
0.995765 | − | 0.0919335i | \(-0.0293047\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 783.464i | − 1.21092i | −0.795876 | − | 0.605459i | \(-0.792989\pi\) | ||||
0.795876 | − | 0.605459i | \(-0.207011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 171.950 | 0.264946 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 280.141i | 0.430324i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.4352 | 0.0435455 | 0.0217727 | − | 0.999763i | \(-0.493069\pi\) | ||||
0.0217727 | + | 0.999763i | \(0.493069\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −52.9051 | −0.0805253 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 594.296i | − 0.901814i | −0.892571 | − | 0.450907i | \(-0.851101\pi\) | ||||
0.892571 | − | 0.450907i | \(-0.148899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −495.511 | −0.749638 | −0.374819 | − | 0.927098i | \(-0.622295\pi\) | ||||
−0.374819 | + | 0.927098i | \(0.622295\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 231.176i | 0.348682i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 441.599i | − 0.662067i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 257.231 | 0.384501 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 335.530i | 0.500045i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 168.874 | 0.250927 | 0.125464 | − | 0.992098i | \(-0.459958\pi\) | ||||
0.125464 | + | 0.992098i | \(0.459958\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 895.899 | 1.32334 | 0.661668 | − | 0.749797i | \(-0.269849\pi\) | ||||
0.661668 | + | 0.749797i | \(0.269849\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.6745i | 0.0363394i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41.3042 | 0.0606522 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 359.410i | 0.526223i | 0.964765 | + | 0.263112i | \(0.0847487\pi\) | ||||
−0.964765 | + | 0.263112i | \(0.915251\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 396.926i | − 0.577767i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 637.680 | 0.925516 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 515.701i | 0.746311i | 0.927769 | + | 0.373155i | \(0.121724\pi\) | ||||
−0.927769 | + | 0.373155i | \(0.878276\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 33.6857 | 0.0486085 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −60.5360 | −0.0868523 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 348.510i | − 0.498584i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1370.37 | −1.95488 | −0.977438 | − | 0.211221i | \(-0.932256\pi\) | ||||
−0.977438 | + | 0.211221i | \(0.932256\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2511.28i | 3.57224i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 468.018i | 0.661978i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 662.128 | 0.933890 | 0.466945 | − | 0.884286i | \(-0.345355\pi\) | ||||
0.466945 | + | 0.884286i | \(0.345355\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 138.008i | − 0.194104i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 582.270 | 0.816649 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.55302 | −0.00635010 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 370.003i | − 0.514608i | −0.966331 | − | 0.257304i | \(-0.917166\pi\) | ||||
0.966331 | − | 0.257304i | \(-0.0828341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.3415 | −0.0531782 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 569.964i | − 0.788331i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 607.695i | − 0.835894i | −0.908471 | − | 0.417947i | \(-0.862750\pi\) | ||||
0.908471 | − | 0.417947i | \(-0.137250\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −804.700 | −1.10384 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 134.668i | − 0.184224i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1066.76 | −1.45533 | −0.727666 | − | 0.685931i | \(-0.759395\pi\) | ||||
−0.727666 | + | 0.685931i | \(0.759395\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −665.591 | −0.903108 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 558.366i | − 0.755570i | −0.925893 | − | 0.377785i | \(-0.876686\pi\) | ||||
0.925893 | − | 0.377785i | \(-0.123314\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1607.81 | 2.16978 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1112.00i | − 1.49664i | −0.663339 | − | 0.748319i | \(-0.730861\pi\) | ||||
0.663339 | − | 0.748319i | \(-0.269139\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 178.299i | − 0.238687i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −519.137 | −0.693107 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1207.34i | − 1.60764i | −0.594873 | − | 0.803820i | \(-0.702798\pi\) | ||||
0.594873 | − | 0.803820i | \(-0.297202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −204.158 | −0.271127 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 87.7776 | 0.115955 | 0.0579773 | − | 0.998318i | \(-0.481535\pi\) | ||||
0.0579773 | + | 0.998318i | \(0.481535\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 375.864i | 0.495209i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 67.0202 | 0.0880686 | 0.0440343 | − | 0.999030i | \(-0.485979\pi\) | ||||
0.0440343 | + | 0.999030i | \(0.485979\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 108.687i | 0.142447i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 447.522i | 0.583470i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −342.869 | −0.445863 | −0.222932 | − | 0.974834i | \(-0.571563\pi\) | ||||
−0.222932 | + | 0.974834i | \(0.571563\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 756.587i | 0.981306i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 244.756 | 0.316631 | 0.158316 | − | 0.987389i | \(-0.449394\pi\) | ||||
0.158316 | + | 0.987389i | \(0.449394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 735.116 | 0.946095 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 421.023i | 0.540466i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −438.330 | −0.561242 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 574.657i | − 0.733917i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1120.38i | 1.42361i | 0.702376 | + | 0.711806i | \(0.252123\pi\) | ||||
−0.702376 | + | 0.711806i | \(0.747877\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −208.063 | −0.263705 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 731.695i | 0.925025i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −873.260 | −1.10121 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1344.51 | −1.68696 | −0.843480 | − | 0.537161i | \(-0.819497\pi\) | ||||
−0.843480 | + | 0.537161i | \(0.819497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 344.742i | 0.431467i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −188.859 | −0.235779 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 231.765i | 0.288624i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 865.122i | 1.07202i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −345.363 | −0.426901 | −0.213451 | − | 0.976954i | \(-0.568470\pi\) | ||||
−0.213451 | + | 0.976954i | \(0.568470\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1275.44i | 1.57268i | 0.617797 | + | 0.786338i | \(0.288025\pi\) | ||||
−0.617797 | + | 0.786338i | \(0.711975\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 352.999 | 0.434193 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −936.604 | −1.14639 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 87.6713i | 0.107047i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1257.99 | 1.53226 | 0.766131 | − | 0.642684i | \(-0.222179\pi\) | ||||
0.766131 | + | 0.642684i | \(0.222179\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 206.093i | 0.250417i | 0.992130 | + | 0.125208i | \(0.0399600\pi\) | ||||
−0.992130 | + | 0.125208i | \(0.960040\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 615.606i | 0.744384i | 0.928156 | + | 0.372192i | \(0.121394\pi\) | ||||
−0.928156 | + | 0.372192i | \(0.878606\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1214.12 | 1.46456 | 0.732281 | − | 0.681002i | \(-0.238456\pi\) | ||||
0.732281 | + | 0.681002i | \(0.238456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 666.892i | 0.802518i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −178.023 | −0.213713 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 757.715 | 0.905275 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1338.99i | 1.59593i | 0.602701 | + | 0.797967i | \(0.294091\pi\) | ||||
−0.602701 | + | 0.797967i | \(0.705909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −439.589 | −0.522698 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 79.4817i | − 0.0942844i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 318.277i | 0.375769i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 743.671 | 0.875937 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1527.93i | − 1.79545i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 112.066 | 0.131379 | 0.0656893 | − | 0.997840i | \(-0.479075\pi\) | ||||
0.0656893 | + | 0.997840i | \(0.479075\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1089.15 | −1.27089 | −0.635443 | − | 0.772148i | \(-0.719183\pi\) | ||||
−0.635443 | + | 0.772148i | \(0.719183\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 719.610i | 0.837729i | 0.908049 | + | 0.418865i | \(0.137572\pi\) | ||||
−0.908049 | + | 0.418865i | \(0.862428\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 123.244 | 0.143141 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 114.135i | 0.132254i | 0.997811 | + | 0.0661269i | \(0.0210642\pi\) | ||||
−0.997811 | + | 0.0661269i | \(0.978936\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 721.293i | 0.831942i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −604.582 | −0.695721 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1732.28i | − 1.98884i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.05752 | 0.0103752 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1427.99 | −1.62827 | −0.814135 | − | 0.580675i | \(-0.802789\pi\) | ||||
−0.814135 | + | 0.580675i | \(0.802789\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 973.539i | − 1.10755i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 364.165 | 0.413354 | 0.206677 | − | 0.978409i | \(-0.433735\pi\) | ||||
0.206677 | + | 0.978409i | \(0.433735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 800.458i | 0.906521i | 0.891378 | + | 0.453260i | \(0.149739\pi\) | ||||
−0.891378 | + | 0.453260i | \(0.850261\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 591.672i | 0.667049i | 0.942741 | + | 0.333524i | \(0.108238\pi\) | ||||
−0.942741 | + | 0.333524i | \(0.891762\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 231.247 | 0.260120 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 410.369i | 0.460572i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2397.65 | 2.68494 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −978.233 | −1.09056 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 529.281i | 0.588744i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −206.136 | −0.228786 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 274.168i | 0.303619i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 545.657i | 0.601606i | 0.953686 | + | 0.300803i | \(0.0972547\pi\) | ||||
−0.953686 | + | 0.300803i | \(0.902745\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 171.801 | 0.189000 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 929.286i | − 1.02007i | −0.860153 | − | 0.510036i | \(-0.829632\pi\) | ||||
0.860153 | − | 0.510036i | \(-0.170368\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −781.089 | −0.855520 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −431.139 | −0.470163 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 171.353i | − 0.186456i | −0.995645 | − | 0.0932278i | \(-0.970282\pi\) | ||||
0.995645 | − | 0.0932278i | \(-0.0297185\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 718.750 | 0.780402 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1140.81i | − 1.23598i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.0744i | 0.0151828i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1178.62 | 1.26870 | 0.634350 | − | 0.773046i | \(-0.281268\pi\) | ||||
0.634350 | + | 0.773046i | \(0.281268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1238.14i | 1.32990i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −389.940 | −0.417943 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −412.624 | −0.440367 | −0.220183 | − | 0.975458i | \(-0.570666\pi\) | ||||
−0.220183 | + | 0.975458i | \(0.570666\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1007.97i | 1.07346i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1121.33 | −1.19163 | −0.595817 | − | 0.803120i | \(-0.703172\pi\) | ||||
−0.595817 | + | 0.803120i | \(0.703172\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 256.161i | − 0.271645i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1395.22i | 1.47331i | 0.676271 | + | 0.736653i | \(0.263595\pi\) | ||||
−0.676271 | + | 0.736653i | \(0.736405\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −603.199 | −0.635615 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 25.4178i | − 0.0267275i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −476.331 | −0.499822 | −0.249911 | − | 0.968269i | \(-0.580401\pi\) | ||||
−0.249911 | + | 0.968269i | \(0.580401\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −341.658 | −0.357010 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 164.178i | − 0.171197i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 263.116 | 0.273794 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 190.565i | 0.197887i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 140.846i | − 0.145653i | −0.997345 | − | 0.0728263i | \(-0.976798\pi\) | ||||
0.997345 | − | 0.0728263i | \(-0.0232019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −519.740 | −0.536367 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1144.98i | − 1.17918i | −0.807704 | − | 0.589588i | \(-0.799290\pi\) | ||||
0.807704 | − | 0.589588i | \(-0.200710\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −855.971 | −0.879724 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.8912 | 0.0572070 | 0.0286035 | − | 0.999591i | \(-0.490894\pi\) | ||||
0.0286035 | + | 0.999591i | \(0.490894\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 827.349i | 0.845096i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.8969 | 0.0406696 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1028.74i | 1.04653i | 0.852169 | + | 0.523267i | \(0.175287\pi\) | ||||
−0.852169 | + | 0.523267i | \(0.824713\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 701.853i | − 0.711098i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 569.855 | 0.576193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 666.207i | 0.672257i | 0.941816 | + | 0.336129i | \(0.109118\pi\) | ||||
−0.941816 | + | 0.336129i | \(0.890882\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 147.030 | 0.148066 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −737.006 | −0.739224 | −0.369612 | − | 0.929186i | \(-0.620509\pi\) | ||||
−0.369612 | + | 0.929186i | \(0.620509\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 1988.31i | − 1.99030i |
(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 | 800.3.b.i.351.2 | 6 | ||
4.3 | odd | 2 | inner | 800.3.b.i.351.5 | 6 | ||
5.2 | odd | 4 | 160.3.h.b.159.1 | yes | 6 | ||
5.3 | odd | 4 | 160.3.h.a.159.6 | yes | 6 | ||
5.4 | even | 2 | 800.3.b.h.351.5 | 6 | |||
8.3 | odd | 2 | 1600.3.b.w.1151.2 | 6 | |||
8.5 | even | 2 | 1600.3.b.w.1151.5 | 6 | |||
15.2 | even | 4 | 1440.3.j.b.1279.2 | 6 | |||
15.8 | even | 4 | 1440.3.j.a.1279.1 | 6 | |||
20.3 | even | 4 | 160.3.h.b.159.2 | yes | 6 | ||
20.7 | even | 4 | 160.3.h.a.159.5 | ✓ | 6 | ||
20.19 | odd | 2 | 800.3.b.h.351.2 | 6 | |||
40.3 | even | 4 | 320.3.h.f.319.5 | 6 | |||
40.13 | odd | 4 | 320.3.h.g.319.1 | 6 | |||
40.19 | odd | 2 | 1600.3.b.v.1151.5 | 6 | |||
40.27 | even | 4 | 320.3.h.g.319.2 | 6 | |||
40.29 | even | 2 | 1600.3.b.v.1151.2 | 6 | |||
40.37 | odd | 4 | 320.3.h.f.319.6 | 6 | |||
60.23 | odd | 4 | 1440.3.j.b.1279.1 | 6 | |||
60.47 | odd | 4 | 1440.3.j.a.1279.2 | 6 | |||
80.3 | even | 4 | 1280.3.e.h.639.2 | 6 | |||
80.13 | odd | 4 | 1280.3.e.i.639.5 | 6 | |||
80.27 | even | 4 | 1280.3.e.i.639.2 | 6 | |||
80.37 | odd | 4 | 1280.3.e.h.639.5 | 6 | |||
80.43 | even | 4 | 1280.3.e.f.639.5 | 6 | |||
80.53 | odd | 4 | 1280.3.e.g.639.2 | 6 | |||
80.67 | even | 4 | 1280.3.e.g.639.5 | 6 | |||
80.77 | odd | 4 | 1280.3.e.f.639.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.3.h.a.159.5 | ✓ | 6 | 20.7 | even | 4 | ||
160.3.h.a.159.6 | yes | 6 | 5.3 | odd | 4 | ||
160.3.h.b.159.1 | yes | 6 | 5.2 | odd | 4 | ||
160.3.h.b.159.2 | yes | 6 | 20.3 | even | 4 | ||
320.3.h.f.319.5 | 6 | 40.3 | even | 4 | |||
320.3.h.f.319.6 | 6 | 40.37 | odd | 4 | |||
320.3.h.g.319.1 | 6 | 40.13 | odd | 4 | |||
320.3.h.g.319.2 | 6 | 40.27 | even | 4 | |||
800.3.b.h.351.2 | 6 | 20.19 | odd | 2 | |||
800.3.b.h.351.5 | 6 | 5.4 | even | 2 | |||
800.3.b.i.351.2 | 6 | 1.1 | even | 1 | trivial | ||
800.3.b.i.351.5 | 6 | 4.3 | odd | 2 | inner | ||
1280.3.e.f.639.2 | 6 | 80.77 | odd | 4 | |||
1280.3.e.f.639.5 | 6 | 80.43 | even | 4 | |||
1280.3.e.g.639.2 | 6 | 80.53 | odd | 4 | |||
1280.3.e.g.639.5 | 6 | 80.67 | even | 4 | |||
1280.3.e.h.639.2 | 6 | 80.3 | even | 4 | |||
1280.3.e.h.639.5 | 6 | 80.37 | odd | 4 | |||
1280.3.e.i.639.2 | 6 | 80.27 | even | 4 | |||
1280.3.e.i.639.5 | 6 | 80.13 | odd | 4 | |||
1440.3.j.a.1279.1 | 6 | 15.8 | even | 4 | |||
1440.3.j.a.1279.2 | 6 | 60.47 | odd | 4 | |||
1440.3.j.b.1279.1 | 6 | 60.23 | odd | 4 | |||
1440.3.j.b.1279.2 | 6 | 15.2 | even | 4 | |||
1600.3.b.v.1151.2 | 6 | 40.29 | even | 2 | |||
1600.3.b.v.1151.5 | 6 | 40.19 | odd | 2 | |||
1600.3.b.w.1151.2 | 6 | 8.3 | odd | 2 | |||
1600.3.b.w.1151.5 | 6 | 8.5 | even | 2 |