Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(687,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.687");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.g (of order \(2\), degree \(1\), not 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: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.292213762624.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 687.2 | ||
Root | \(1.37098 - 1.45617i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.687 |
Dual form | 1568.3.g.m.687.1 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −5.22363 | −1.74121 | −0.870605 | − | 0.491982i | \(-0.836272\pi\) | ||||
−0.870605 | + | 0.491982i | \(0.836272\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.26788i | 1.25358i | 0.779190 | + | 0.626788i | \(0.215631\pi\) | ||||
−0.779190 | + | 0.626788i | \(0.784369\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 18.2863 | 2.03181 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.80688 | −0.891535 | −0.445767 | − | 0.895149i | \(-0.647069\pi\) | ||||
−0.445767 | + | 0.895149i | \(0.647069\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.41653i | 0.185887i | 0.995671 | + | 0.0929434i | \(0.0296276\pi\) | ||||
−0.995671 | + | 0.0929434i | \(0.970372\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 32.7411i | − 2.18274i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.89452 | −0.405560 | −0.202780 | − | 0.979224i | \(-0.564998\pi\) | ||||
−0.202780 | + | 0.979224i | \(0.564998\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.77637 | 0.146125 | 0.0730624 | − | 0.997327i | \(-0.476723\pi\) | ||||
0.0730624 | + | 0.997327i | \(0.476723\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 42.8332i | 1.86231i | 0.364617 | + | 0.931157i | \(0.381200\pi\) | ||||
−0.364617 | + | 0.931157i | \(0.618800\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.2863 | −0.571453 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −48.5083 | −1.79660 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 37.3505i | 1.28795i | 0.765048 | + | 0.643974i | \(0.222715\pi\) | ||||
−0.765048 | + | 0.643974i | \(0.777285\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.16835i | 0.231237i | 0.993294 | + | 0.115619i | \(0.0368850\pi\) | ||||
−0.993294 | + | 0.115619i | \(0.963115\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 51.2275 | 1.55235 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.202653i | 0.00547709i | 0.999996 | + | 0.00273855i | \(0.000871708\pi\) | ||||
−0.999996 | + | 0.00273855i | \(0.999128\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 12.6231i | − 0.323668i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −63.5494 | −1.54999 | −0.774993 | − | 0.631970i | \(-0.782247\pi\) | ||||
−0.774993 | + | 0.631970i | \(0.782247\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 35.3384 | 0.821823 | 0.410911 | − | 0.911675i | \(-0.365211\pi\) | ||||
0.410911 | + | 0.911675i | \(0.365211\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 114.616i | 2.54703i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 37.9129i | 0.806657i | 0.915055 | + | 0.403329i | \(0.132147\pi\) | ||||
−0.915055 | + | 0.403329i | \(0.867853\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 36.0144 | 0.706165 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 54.6651i | 1.03142i | 0.856764 | + | 0.515709i | \(0.172471\pi\) | ||||
−0.856764 | + | 0.515709i | \(0.827529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 61.4684i | − 1.11761i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.5027 | −0.254434 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 104.795 | 1.77619 | 0.888093 | − | 0.459665i | \(-0.152030\pi\) | ||||
0.888093 | + | 0.459665i | \(0.152030\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 43.7668i | 0.717489i | 0.933436 | + | 0.358745i | \(0.116795\pi\) | ||||
−0.933436 | + | 0.358745i | \(0.883205\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.1465 | −0.233023 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −31.1021 | −0.464210 | −0.232105 | − | 0.972691i | \(-0.574561\pi\) | ||||
−0.232105 | + | 0.972691i | \(0.574561\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 223.745i | − 3.24268i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 23.1294i | 0.325766i | 0.986645 | + | 0.162883i | \(0.0520794\pi\) | ||||
−0.986645 | + | 0.162883i | \(0.947921\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 69.2275 | 0.948322 | 0.474161 | − | 0.880438i | \(-0.342751\pi\) | ||||
0.474161 | + | 0.880438i | \(0.342751\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 74.6264 | 0.995019 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 19.9328i | 0.252315i | 0.992010 | + | 0.126157i | \(0.0402644\pi\) | ||||
−0.992010 | + | 0.126157i | \(0.959736\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 88.8125 | 1.09645 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.11617 | −0.0616406 | −0.0308203 | − | 0.999525i | \(-0.509812\pi\) | ||||
−0.0308203 | + | 0.999525i | \(0.509812\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 43.2140i | − 0.508400i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 195.105i | − 2.24259i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.9889 | 0.202122 | 0.101061 | − | 0.994880i | \(-0.467776\pi\) | ||||
0.101061 | + | 0.994880i | \(0.467776\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 37.4448i | − 0.402632i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17.4019i | 0.183178i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.4864 | −0.128726 | −0.0643629 | − | 0.997927i | \(-0.520502\pi\) | ||||
−0.0643629 | + | 0.997927i | \(0.520502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −179.332 | −1.81143 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 68.0753i | − 0.674013i | −0.941502 | − | 0.337006i | \(-0.890586\pi\) | ||||
0.941502 | − | 0.337006i | \(-0.109414\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 58.2931i | 0.565952i | 0.959127 | + | 0.282976i | \(0.0913217\pi\) | ||||
−0.959127 | + | 0.282976i | \(0.908678\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −135.868 | −1.26979 | −0.634897 | − | 0.772597i | \(-0.718957\pi\) | ||||
−0.634897 | + | 0.772597i | \(0.718957\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 44.4981i | − 0.408239i | −0.978946 | − | 0.204120i | \(-0.934567\pi\) | ||||
0.978946 | − | 0.204120i | \(-0.0654332\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 1.05858i | − 0.00953677i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −133.391 | −1.18045 | −0.590224 | − | 0.807240i | \(-0.700961\pi\) | ||||
−0.590224 | + | 0.807240i | \(0.700961\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −268.474 | −2.33455 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 44.1894i | 0.377687i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24.8251 | −0.205166 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 331.959 | 2.69885 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 67.1521i | 0.537217i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 130.977i | − 1.03131i | −0.856795 | − | 0.515657i | \(-0.827548\pi\) | ||||
0.856795 | − | 0.515657i | \(-0.172452\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −184.595 | −1.43097 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −53.3311 | −0.407108 | −0.203554 | − | 0.979064i | \(-0.565249\pi\) | ||||
−0.203554 | + | 0.979064i | \(0.565249\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 304.044i | − 2.25218i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −57.7179 | −0.421299 | −0.210649 | − | 0.977562i | \(-0.567558\pi\) | ||||
−0.210649 | + | 0.977562i | \(0.567558\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −172.422 | −1.24045 | −0.620224 | − | 0.784425i | \(-0.712958\pi\) | ||||
−0.620224 | + | 0.784425i | \(0.712958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 198.043i | − 1.40456i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 23.6986i | − 0.165725i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −234.108 | −1.61454 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 219.529i | − 1.47335i | −0.676249 | − | 0.736673i | \(-0.736396\pi\) | ||||
0.676249 | − | 0.736673i | \(-0.263604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 185.668i | − 1.22959i | −0.788687 | − | 0.614795i | \(-0.789239\pi\) | ||||
0.788687 | − | 0.614795i | \(-0.210761\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −126.075 | −0.824022 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −44.9304 | −0.289873 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 188.182i | − 1.19861i | −0.800521 | − | 0.599305i | \(-0.795444\pi\) | ||||
0.800521 | − | 0.599305i | \(-0.204556\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 285.550i | − 1.79591i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −54.5154 | −0.334450 | −0.167225 | − | 0.985919i | \(-0.553481\pi\) | ||||
−0.167225 | + | 0.985919i | \(0.553481\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 321.088i | 1.94599i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 266.435i | − 1.59542i | −0.603042 | − | 0.797709i | \(-0.706045\pi\) | ||||
0.603042 | − | 0.797709i | \(-0.293955\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 163.160 | 0.965446 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 50.7696 | 0.296898 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 114.835i | 0.663786i | 0.943317 | + | 0.331893i | \(0.107687\pi\) | ||||
−0.943317 | + | 0.331893i | \(0.892313\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −547.410 | −3.09271 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −112.849 | −0.630439 | −0.315220 | − | 0.949019i | \(-0.602078\pi\) | ||||
−0.315220 | + | 0.949019i | \(0.602078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 60.9470i | 0.336724i | 0.985725 | + | 0.168362i | \(0.0538477\pi\) | ||||
−0.985725 | + | 0.168362i | \(0.946152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 228.622i | − 1.24930i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.27020 | −0.00686595 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 67.6138 | 0.361571 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 178.459i | − 0.934342i | −0.884167 | − | 0.467171i | \(-0.845273\pi\) | ||||
0.884167 | − | 0.467171i | \(-0.154727\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 221.588 | 1.14812 | 0.574062 | − | 0.818812i | \(-0.305367\pi\) | ||||
0.574062 | + | 0.818812i | \(0.305367\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 79.1198 | 0.405742 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 242.298i | 1.22994i | 0.788550 | + | 0.614970i | \(0.210832\pi\) | ||||
−0.788550 | + | 0.614970i | \(0.789168\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 297.047i | 1.49270i | 0.665555 | + | 0.746349i | \(0.268195\pi\) | ||||
−0.665555 | + | 0.746349i | \(0.731805\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 162.466 | 0.808287 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 398.320i | − 1.94302i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 783.262i | 3.78388i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.2275 | −0.130275 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 141.020 | 0.668341 | 0.334171 | − | 0.942513i | \(-0.391544\pi\) | ||||
0.334171 | + | 0.942513i | \(0.391544\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 120.820i | − 0.567228i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 221.497i | 1.03022i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −361.619 | −1.65123 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 16.6608i | − 0.0753883i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 40.8267i | 0.183079i | 0.995801 | + | 0.0915396i | \(0.0291788\pi\) | ||||
−0.995801 | + | 0.0915396i | \(0.970821\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −261.244 | −1.16108 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.18598 | 0.0360616 | 0.0180308 | − | 0.999837i | \(-0.494260\pi\) | ||||
0.0180308 | + | 0.999837i | \(0.494260\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 332.252i | − 1.45088i | −0.688285 | − | 0.725440i | \(-0.741636\pi\) | ||||
0.688285 | − | 0.725440i | \(-0.258364\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 329.260 | 1.41314 | 0.706568 | − | 0.707646i | \(-0.250243\pi\) | ||||
0.706568 | + | 0.707646i | \(0.250243\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −237.633 | −1.01121 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 104.122i | − 0.439333i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 137.719i | 0.576230i | 0.957596 | + | 0.288115i | \(0.0930286\pi\) | ||||
−0.957596 | + | 0.288115i | \(0.906971\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −201.854 | −0.837567 | −0.418783 | − | 0.908086i | \(-0.637543\pi\) | ||||
−0.418783 | + | 0.908086i | \(0.637543\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −27.3492 | −0.112548 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.70917i | 0.0271627i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 26.7250 | 0.107329 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −269.203 | −1.07252 | −0.536261 | − | 0.844052i | \(-0.680164\pi\) | ||||
−0.536261 | + | 0.844052i | \(0.680164\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 420.061i | − 1.66032i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 225.734i | 0.885232i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 242.359 | 0.943032 | 0.471516 | − | 0.881858i | \(-0.343707\pi\) | ||||
0.471516 | + | 0.881858i | \(0.343707\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 683.002i | 2.61687i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 33.8470i | − 0.128696i | −0.997928 | − | 0.0643479i | \(-0.979503\pi\) | ||||
0.997928 | − | 0.0643479i | \(-0.0204967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −342.634 | −1.29296 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −93.9673 | −0.351937 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 165.598i | − 0.615606i | −0.951450 | − | 0.307803i | \(-0.900406\pi\) | ||||
0.951450 | − | 0.307803i | \(-0.0995938\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 148.308i | 0.547263i | 0.961835 | + | 0.273632i | \(0.0882249\pi\) | ||||
−0.961835 | + | 0.273632i | \(0.911775\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 140.104 | 0.509470 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 478.358i | − 1.72693i | −0.504413 | − | 0.863463i | \(-0.668291\pi\) | ||||
0.504413 | − | 0.863463i | \(-0.331709\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 131.083i | 0.469830i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −226.066 | −0.804506 | −0.402253 | − | 0.915528i | \(-0.631773\pi\) | ||||
−0.402253 | + | 0.915528i | \(0.631773\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −254.628 | −0.899745 | −0.449873 | − | 0.893093i | \(-0.648531\pi\) | ||||
−0.449873 | + | 0.893093i | \(0.648531\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 90.9014i | − 0.318952i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −241.466 | −0.835521 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 65.2244 | 0.224139 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 149.558i | 0.510437i | 0.966883 | + | 0.255218i | \(0.0821474\pi\) | ||||
−0.966883 | + | 0.255218i | \(0.917853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 656.842i | 2.22658i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 475.715 | 1.60173 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −103.508 | −0.346180 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 355.600i | 1.17360i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −274.325 | −0.899427 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 271.779 | 0.885272 | 0.442636 | − | 0.896701i | \(-0.354043\pi\) | ||||
0.442636 | + | 0.896701i | \(0.354043\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 304.502i | − 0.985442i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 534.180i | − 1.71762i | −0.512293 | − | 0.858811i | \(-0.671204\pi\) | ||||
0.512293 | − | 0.858811i | \(-0.328796\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 556.232 | 1.77710 | 0.888550 | − | 0.458780i | \(-0.151713\pi\) | ||||
0.888550 | + | 0.458780i | \(0.151713\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 387.459i | 1.22227i | 0.791527 | + | 0.611134i | \(0.209286\pi\) | ||||
−0.791527 | + | 0.611134i | \(0.790714\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 366.292i | − 1.14825i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 709.724 | 2.21098 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.1417 | −0.0592624 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 34.5233i | − 0.106225i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 232.442i | 0.710830i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 383.205 | 1.15772 | 0.578860 | − | 0.815427i | \(-0.303498\pi\) | ||||
0.578860 | + | 0.815427i | \(0.303498\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.70577i | 0.0111284i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 194.944i | − 0.581923i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 563.726 | 1.67278 | 0.836388 | − | 0.548138i | \(-0.184663\pi\) | ||||
0.836388 | + | 0.548138i | \(0.184663\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 696.783 | 2.05541 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 70.2992i | − 0.206156i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1402.41 | 4.06495 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −51.5890 | −0.148671 | −0.0743357 | − | 0.997233i | \(-0.523684\pi\) | ||||
−0.0743357 | + | 0.997233i | \(0.523684\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 586.383i | − 1.68018i | −0.542447 | − | 0.840090i | \(-0.682502\pi\) | ||||
0.542447 | − | 0.840090i | \(-0.317498\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 117.222i | − 0.333965i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −303.844 | −0.860746 | −0.430373 | − | 0.902651i | \(-0.641618\pi\) | ||||
−0.430373 | + | 0.902651i | \(0.641618\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −144.972 | −0.408373 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 116.130i | 0.323481i | 0.986833 | + | 0.161741i | \(0.0517108\pi\) | ||||
−0.986833 | + | 0.161741i | \(0.948289\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −353.292 | −0.978648 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 129.677 | 0.357237 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 433.910i | 1.18879i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 476.288i | 1.29779i | 0.760879 | + | 0.648894i | \(0.224768\pi\) | ||||
−0.760879 | + | 0.648894i | \(0.775232\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1162.08 | −3.14928 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 49.2857i | − 0.132133i | −0.997815 | − | 0.0660666i | \(-0.978955\pi\) | ||||
0.997815 | − | 0.0660666i | \(-0.0210450\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 350.778i | − 0.935407i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −90.2585 | −0.239412 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −167.511 | −0.441983 | −0.220991 | − | 0.975276i | \(-0.570929\pi\) | ||||
−0.220991 | + | 0.975276i | \(0.570929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 684.174i | 1.79573i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 513.207i | 1.33997i | 0.742376 | + | 0.669983i | \(0.233699\pi\) | ||||
−0.742376 | + | 0.669983i | \(0.766301\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 646.209 | 1.66979 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 709.398i | − 1.82365i | −0.410584 | − | 0.911823i | \(-0.634675\pi\) | ||||
0.410584 | − | 0.911823i | \(-0.365325\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 295.315i | − 0.755281i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 278.582 | 0.708860 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −124.937 | −0.316295 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 309.404i | 0.779355i | 0.920951 | + | 0.389677i | \(0.127413\pi\) | ||||
−0.920951 | + | 0.389677i | \(0.872587\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −528.073 | −1.31689 | −0.658445 | − | 0.752629i | \(-0.728785\pi\) | ||||
−0.658445 | + | 0.752629i | \(0.728785\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.3225 | −0.0429839 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 556.666i | 1.37448i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.98739i | − 0.00488302i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 612.830 | 1.49836 | 0.749181 | − | 0.662366i | \(-0.230448\pi\) | ||||
0.749181 | + | 0.662366i | \(0.230448\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 301.497 | 0.733569 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 32.0676i | − 0.0772712i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 900.670 | 2.15988 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −237.642 | −0.567165 | −0.283583 | − | 0.958948i | \(-0.591523\pi\) | ||||
−0.283583 | + | 0.958948i | \(0.591523\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 394.516i | 0.937092i | 0.883439 | + | 0.468546i | \(0.155222\pi\) | ||||
−0.883439 | + | 0.468546i | \(0.844778\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 693.287i | 1.63898i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 98.4973 | 0.231758 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 123.793i | 0.288561i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 363.359i | − 0.843059i | −0.906815 | − | 0.421530i | \(-0.861493\pi\) | ||||
0.906815 | − | 0.421530i | \(-0.138507\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −119.733 | −0.276520 | −0.138260 | − | 0.990396i | \(-0.544151\pi\) | ||||
−0.138260 | + | 0.990396i | \(0.544151\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1222.89 | 2.81125 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 118.921i | 0.272130i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 871.477i | − 1.98514i | −0.121672 | − | 0.992570i | \(-0.538826\pi\) | ||||
0.121672 | − | 0.992570i | \(-0.461174\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 343.956 | 0.776424 | 0.388212 | − | 0.921570i | \(-0.373093\pi\) | ||||
0.388212 | + | 0.921570i | \(0.373093\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 112.752i | 0.253376i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1146.74i | 2.56541i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −242.849 | −0.540866 | −0.270433 | − | 0.962739i | \(-0.587167\pi\) | ||||
−0.270433 | + | 0.962739i | \(0.587167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 623.222 | 1.38187 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 969.861i | 2.14097i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −42.2571 | −0.0924662 | −0.0462331 | − | 0.998931i | \(-0.514722\pi\) | ||||
−0.0462331 | + | 0.998931i | \(0.514722\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 334.441 | 0.728631 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 816.370i | 1.77087i | 0.464766 | + | 0.885434i | \(0.346139\pi\) | ||||
−0.464766 | + | 0.885434i | \(0.653861\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 115.161i | 0.248727i | 0.992237 | + | 0.124363i | \(0.0396889\pi\) | ||||
−0.992237 | + | 0.124363i | \(0.960311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 234.700 | 0.504730 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 603.424 | 1.29213 | 0.646064 | − | 0.763283i | \(-0.276414\pi\) | ||||
0.646064 | + | 0.763283i | \(0.276414\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 982.992i | 2.08703i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −346.559 | −0.732684 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −39.6641 | −0.0835034 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 999.624i | 2.09565i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 158.595i | − 0.331097i | −0.986202 | − | 0.165548i | \(-0.947061\pi\) | ||||
0.986202 | − | 0.165548i | \(-0.0529394\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.489715 | −0.00101812 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 78.2633i | − 0.161368i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 106.987i | − 0.219687i | −0.993949 | − | 0.109843i | \(-0.964965\pi\) | ||||
0.993949 | − | 0.109843i | \(-0.0350349\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 284.768 | 0.582348 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −616.591 | −1.25579 | −0.627893 | − | 0.778299i | \(-0.716083\pi\) | ||||
−0.627893 | + | 0.778299i | \(0.716083\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 257.514i | − 0.522340i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 1124.03i | − 2.27077i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −554.090 | −1.11040 | −0.555200 | − | 0.831717i | \(-0.687358\pi\) | ||||
−0.555200 | + | 0.831717i | \(0.687358\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1391.76i | 2.77796i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 148.158i | − 0.294548i | −0.989096 | − | 0.147274i | \(-0.952950\pi\) | ||||
0.989096 | − | 0.147274i | \(-0.0470499\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 426.688 | 0.844926 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −852.290 | −1.68104 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 182.889i | − 0.359310i | −0.983730 | − | 0.179655i | \(-0.942502\pi\) | ||||
0.983730 | − | 0.179655i | \(-0.0574981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −134.677 | −0.262528 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −365.374 | −0.709464 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 371.807i | − 0.719163i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 599.856i | − 1.15579i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −98.2461 | −0.188572 | −0.0942861 | − | 0.995545i | \(-0.530057\pi\) | ||||
−0.0942861 | + | 0.995545i | \(0.530057\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −574.764 | −1.09898 | −0.549488 | − | 0.835502i | \(-0.685177\pi\) | ||||
−0.549488 | + | 0.835502i | \(0.685177\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 49.4223i | − 0.0937805i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1305.69 | −2.46822 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1916.31 | 3.60888 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 153.569i | − 0.288122i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 851.604i | − 1.59178i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 589.480 | 1.09773 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 370.654i | 0.685128i | 0.939495 | + | 0.342564i | \(0.111295\pi\) | ||||
−0.939495 | + | 0.342564i | \(0.888705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 318.365i | − 0.586307i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 278.909 | 0.511759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 56.5966 | 0.103467 | 0.0517336 | − | 0.998661i | \(-0.483525\pi\) | ||||
0.0517336 | + | 0.998661i | \(0.483525\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 800.334i | 1.45780i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 103.699i | 0.188201i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.63506 | 0.0119551 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 151.525i | 0.272037i | 0.990706 | + | 0.136019i | \(0.0434307\pi\) | ||||
−0.990706 | + | 0.136019i | \(0.956569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 85.3962i | 0.152766i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −353.189 | −0.629571 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −318.048 | −0.564917 | −0.282458 | − | 0.959280i | \(-0.591150\pi\) | ||||
−0.282458 | + | 0.959280i | \(0.591150\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 836.076i | − 1.47978i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 356.654 | 0.626808 | 0.313404 | − | 0.949620i | \(-0.398531\pi\) | ||||
0.313404 | + | 0.949620i | \(0.398531\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −831.014 | −1.45537 | −0.727683 | − | 0.685914i | \(-0.759403\pi\) | ||||
−0.727683 | + | 0.685914i | \(0.759403\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 932.205i | 1.62689i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 611.929i | − 1.06422i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −771.483 | −1.33706 | −0.668530 | − | 0.743685i | \(-0.733076\pi\) | ||||
−0.668530 | + | 0.743685i | \(0.733076\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1157.49 | −1.99912 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 536.094i | − 0.919544i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −276.974 | −0.473460 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 144.376 | 0.245956 | 0.122978 | − | 0.992409i | \(-0.460756\pi\) | ||||
0.122978 | + | 0.992409i | \(0.460756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.9020i | 0.0337894i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 1265.68i | − 2.14158i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −838.926 | −1.41471 | −0.707357 | − | 0.706856i | \(-0.750113\pi\) | ||||
−0.707357 | + | 0.706856i | \(0.750113\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1551.66i | − 2.59910i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 711.341i | 1.18755i | 0.804632 | + | 0.593774i | \(0.202363\pi\) | ||||
−0.804632 | + | 0.593774i | \(0.797637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 356.394 | 0.593002 | 0.296501 | − | 0.955033i | \(-0.404180\pi\) | ||||
0.296501 | + | 0.955033i | \(0.404180\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −568.742 | −0.943188 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 155.601i | − 0.257191i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 60.3719i | − 0.0994595i | −0.998763 | − | 0.0497298i | \(-0.984164\pi\) | ||||
0.998763 | − | 0.0497298i | \(-0.0158360\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −91.6176 | −0.149947 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 482.989i | − 0.787911i | −0.919130 | − | 0.393955i | \(-0.871106\pi\) | ||||
0.919130 | − | 0.393955i | \(-0.128894\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2080.68i | 3.38321i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 712.490 | 1.15476 | 0.577382 | − | 0.816474i | \(-0.304074\pi\) | ||||
0.577382 | + | 0.816474i | \(0.304074\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −93.0817 | −0.150374 | −0.0751872 | − | 0.997169i | \(-0.523955\pi\) | ||||
−0.0751872 | + | 0.997169i | \(0.523955\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2077.77i | − 3.34584i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −778.059 | −1.24489 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 142.227 | 0.226837 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.39719i | − 0.00222129i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 610.573i | 0.967628i | 0.875171 | + | 0.483814i | \(0.160749\pi\) | ||||
−0.875171 | + | 0.483814i | \(0.839251\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −736.636 | −1.16372 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 820.947 | 1.29283 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 422.952i | 0.661897i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 590.153 | 0.920676 | 0.460338 | − | 0.887744i | \(-0.347728\pi\) | ||||
0.460338 | + | 0.887744i | \(0.347728\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −257.971 | −0.401199 | −0.200600 | − | 0.979673i | \(-0.564289\pi\) | ||||
−0.200600 | + | 0.979673i | \(0.564289\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 1157.02i | − 1.79383i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 379.964i | − 0.587271i | −0.955918 | − | 0.293635i | \(-0.905135\pi\) | ||||
0.955918 | − | 0.293635i | \(-0.0948651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1027.71 | −1.58353 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 952.773i | 1.45907i | 0.683943 | + | 0.729535i | \(0.260264\pi\) | ||||
−0.683943 | + | 0.729535i | \(0.739736\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 334.273i | − 0.510340i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1265.92 | 1.92681 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 963.119 | 1.46149 | 0.730743 | − | 0.682653i | \(-0.239174\pi\) | ||||
0.730743 | + | 0.682653i | \(0.239174\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 71.6817i | 0.108444i | 0.998529 | + | 0.0542222i | \(0.0172679\pi\) | ||||
−0.998529 | + | 0.0542222i | \(0.982732\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 87.0299i | 0.131267i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1599.84 | −2.39856 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 213.263i | − 0.318779i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 429.216i | − 0.639667i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −712.783 | −1.05911 | −0.529556 | − | 0.848275i | \(-0.677642\pi\) | ||||
−0.529556 | + | 0.848275i | \(0.677642\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 693.005 | 1.02667 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 767.527i | 1.13372i | 0.823815 | + | 0.566859i | \(0.191841\pi\) | ||||
−0.823815 | + | 0.566859i | \(0.808159\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.7605 | −0.0627908 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 484.354 | 0.709156 | 0.354578 | − | 0.935026i | \(-0.384625\pi\) | ||||
0.354578 | + | 0.935026i | \(0.384625\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 361.769i | − 0.528130i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1735.56i | 2.52629i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −132.100 | −0.191727 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −574.851 | −0.831912 | −0.415956 | − | 0.909385i | \(-0.636553\pi\) | ||||
−0.415956 | + | 0.909385i | \(0.636553\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1080.72i | − 1.55500i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 438.143 | 0.628612 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1719.94 | −2.46057 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 143.138i | 0.204191i | 0.994775 | + | 0.102096i | \(0.0325548\pi\) | ||||
−0.994775 | + | 0.102096i | \(0.967445\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.562638i | 0 0.000800339i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1241.31 | 1.76072 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 255.311i | − 0.360101i | −0.983657 | − | 0.180050i | \(-0.942374\pi\) | ||||
0.983657 | − | 0.180050i | \(-0.0576261\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 364.498i | 0.512656i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −307.044 | −0.430636 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 148.540 | 0.207748 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 719.393i | − 1.00334i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 415.630i | 0.578067i | 0.957319 | + | 0.289034i | \(0.0933340\pi\) | ||||
−0.957319 | + | 0.289034i | \(0.906666\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1054.41 | 1.45838 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 533.601i | − 0.736001i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 896.838i | 1.23361i | 0.787114 | + | 0.616807i | \(0.211574\pi\) | ||||
−0.787114 | + | 0.616807i | \(0.788426\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −656.451 | −0.900481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −243.641 | −0.333299 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 509.059i | 0.694487i | 0.937775 | + | 0.347244i | \(0.112882\pi\) | ||||
−0.937775 | + | 0.347244i | \(0.887118\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 305.014 | 0.413859 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −741.427 | −1.00328 | −0.501642 | − | 0.865075i | \(-0.667271\pi\) | ||||
−0.501642 | + | 0.865075i | \(0.667271\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 35.0463i | − 0.0472959i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1344.98i | − 1.81021i | −0.425191 | − | 0.905104i | \(-0.639793\pi\) | ||||
0.425191 | − | 0.905104i | \(-0.360207\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1375.98 | 1.84695 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −93.5560 | −0.125242 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 27.6931i | − 0.0368749i | −0.999830 | − | 0.0184375i | \(-0.994131\pi\) | ||||
0.999830 | − | 0.0184375i | \(-0.00586916\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1406.22 | 1.86749 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1163.74 | 1.54138 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1341.69i | 1.77238i | 0.463318 | + | 0.886192i | \(0.346659\pi\) | ||||
−0.463318 | + | 0.886192i | \(0.653341\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2194.24i | 2.89096i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 112.001 | 0.147176 | 0.0735881 | − | 0.997289i | \(-0.476555\pi\) | ||||
0.0735881 | + | 0.997289i | \(0.476555\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 790.226i | − 1.03297i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 253.240i | 0.330169i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −140.749 | −0.183028 | −0.0915142 | − | 0.995804i | \(-0.529171\pi\) | ||||
−0.0915142 | + | 0.995804i | \(0.529171\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1265.99 | −1.64202 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1325.14i | 1.71428i | 0.515087 | + | 0.857138i | \(0.327760\pi\) | ||||
−0.515087 | + | 0.857138i | \(0.672240\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 102.409i | − 0.132141i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −176.437 | −0.226491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 226.827i | − 0.290432i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 1811.81i | − 2.31393i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1179.50 | 1.50255 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −327.801 | −0.416519 | −0.208260 | − | 0.978074i | \(-0.566780\pi\) | ||||
−0.208260 | + | 0.978074i | \(0.566780\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 176.804i | 0.224086i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −105.764 | −0.133372 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1789.80 | 2.25132 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 393.650i | − 0.493915i | −0.969026 | − | 0.246958i | \(-0.920569\pi\) | ||||
0.969026 | − | 0.246958i | \(-0.0794308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 261.391i | − 0.327148i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 328.950 | 0.410675 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −678.906 | −0.845462 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 865.023i | 1.07190i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 416.641 | 0.515008 | 0.257504 | − | 0.966277i | \(-0.417100\pi\) | ||||
0.257504 | + | 0.966277i | \(0.417100\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −748.707 | −0.923190 | −0.461595 | − | 0.887091i | \(-0.652723\pi\) | ||||
−0.461595 | + | 0.887091i | \(0.652723\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 774.708i | − 0.952901i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 341.696i | − 0.419259i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 98.1124 | 0.120089 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 554.169i | 0.674993i | 0.941327 | + | 0.337496i | \(0.109580\pi\) | ||||
−0.941327 | + | 0.337496i | \(0.890420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 121.452i | − 0.147572i | −0.997274 | − | 0.0737861i | \(-0.976492\pi\) | ||||
0.997274 | − | 0.0737861i | \(-0.0235082\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −731.853 | −0.887094 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1516.61 | 1.83386 | 0.916932 | − | 0.399043i | \(-0.130657\pi\) | ||||
0.916932 | + | 0.399043i | \(0.130657\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 325.042i | 0.392089i | 0.980595 | + | 0.196044i | \(0.0628097\pi\) | ||||
−0.980595 | + | 0.196044i | \(0.937190\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2498.77i | 3.00694i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1669.98 | 1.99998 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 347.724i | − 0.415441i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1165.70i | − 1.38939i | −0.719303 | − | 0.694696i | \(-0.755539\pi\) | ||||
0.719303 | − | 0.694696i | \(-0.244461\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −554.058 | −0.658808 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1180.89 | 1.40081 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1022.67i | 1.21026i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1330.08 | 1.56665 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.68026 | −0.0102001 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 151.949i | 0.178134i | 0.996026 | + | 0.0890672i | \(0.0283886\pi\) | ||||
−0.996026 | + | 0.0890672i | \(0.971611\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 318.218i | 0.372184i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −412.018 | −0.480768 | −0.240384 | − | 0.970678i | \(-0.577273\pi\) | ||||
−0.240384 | + | 0.970678i | \(0.577273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 159.993 | 0.186255 | 0.0931274 | − | 0.995654i | \(-0.470314\pi\) | ||||
0.0931274 | + | 0.995654i | \(0.470314\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 992.910i | − 1.15053i | −0.817966 | − | 0.575266i | \(-0.804898\pi\) | ||||
0.817966 | − | 0.575266i | \(-0.195102\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −719.772 | −0.832107 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1261.33 | 1.45482 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 195.479i | − 0.224947i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 75.1590i | − 0.0862905i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −228.330 | −0.261547 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 825.096i | − 0.940817i | −0.882449 | − | 0.470408i | \(-0.844107\pi\) | ||||
0.882449 | − | 0.470408i | \(-0.155893\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 781.236i | − 0.888778i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1352.83 | −1.53556 | −0.767780 | − | 0.640714i | \(-0.778639\pi\) | ||||
−0.767780 | + | 0.640714i | \(0.778639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1013.40 | 1.14768 | 0.573838 | − | 0.818969i | \(-0.305454\pi\) | ||||
0.573838 | + | 0.818969i | \(0.305454\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 3431.10i | − 3.87695i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 233.760i | − 0.263540i | −0.991280 | − | 0.131770i | \(-0.957934\pi\) | ||||
0.991280 | − | 0.131770i | \(-0.0420661\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −870.974 | −0.977524 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 105.260i | 0.117873i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 707.322i | − 0.790304i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 540.686 | 0.602772 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −267.741 | −0.297821 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 376.890i | − 0.418302i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −382.008 | −0.422109 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 203.590 | 0.224465 | 0.112233 | − | 0.993682i | \(-0.464200\pi\) | ||||
0.112233 | + | 0.993682i | \(0.464200\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 1244.85i | − 1.36947i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 712.022i | − 0.781583i | −0.920479 | − | 0.390792i | \(-0.872201\pi\) | ||||
0.920479 | − | 0.390792i | \(-0.127799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.1737 | 0.0549548 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1432.97 | 1.56609 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 786.783i | 0.856129i | 0.903748 | + | 0.428065i | \(0.140804\pi\) | ||||
−0.903748 | + | 0.428065i | \(0.859196\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1419.67 | −1.54145 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −55.8929 | −0.0605557 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 2.89516i | − 0.00312990i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1065.97i | 1.14991i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1657.99 | 1.78471 | 0.892353 | − | 0.451338i | \(-0.149053\pi\) | ||||
0.892353 | + | 0.451338i | \(0.149053\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2790.36i | 2.99074i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 423.795i | 0.453257i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −333.736 | −0.356175 | −0.178088 | − | 0.984015i | \(-0.556991\pi\) | ||||
−0.178088 | + | 0.984015i | \(0.556991\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2905.55 | −3.09430 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 543.324i | − 0.577390i | −0.957421 | − | 0.288695i | \(-0.906779\pi\) | ||||
0.957421 | − | 0.288695i | \(-0.0932214\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2722.03i | − 2.88656i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 359.728 | 0.379861 | 0.189930 | − | 0.981798i | \(-0.439174\pi\) | ||||
0.189930 | + | 0.981798i | \(0.439174\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 167.290i | 0.176281i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 2023.94i | − 2.12823i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −904.225 | −0.948820 | −0.474410 | − | 0.880304i | \(-0.657339\pi\) | ||||
−0.474410 | + | 0.880304i | \(0.657339\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1118.56 | 1.17127 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1913.37i | 1.99934i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 909.615 | 0.946529 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2484.52 | −2.57998 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1388.89i | 1.43926i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 920.961i | 0.952390i | 0.879340 | + | 0.476195i | \(0.157984\pi\) | ||||
−0.879340 | + | 0.476195i | \(0.842016\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 99.9894 | 0.103188 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1327.31 | 1.36695 | 0.683476 | − | 0.729973i | \(-0.260468\pi\) | ||||
0.683476 | + | 0.729973i | \(0.260468\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 180.337i | 0.184961i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −688.490 | −0.704698 | −0.352349 | − | 0.935869i | \(-0.614617\pi\) | ||||
−0.352349 | + | 0.935869i | \(0.614617\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −176.415 | −0.180199 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 813.706i | − 0.829466i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1687.08i | 1.71625i | 0.513438 | + | 0.858127i | \(0.328372\pi\) | ||||
−0.513438 | + | 0.858127i | \(0.671628\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1518.70 | −1.54182 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1513.66i | 1.53049i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1139.22i | − 1.14957i | −0.818304 | − | 0.574785i | \(-0.805086\pi\) | ||||
0.818304 | − | 0.574785i | \(-0.194914\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2001.72 | −2.01583 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1861.85 | −1.87121 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 206.085i | 0.206705i | 0.994645 | + | 0.103353i | \(0.0329570\pi\) | ||||
−0.994645 | + | 0.103353i | \(0.967043\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 9.83033i | − 0.00984017i |
(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 | 1568.3.g.m.687.2 | 8 | ||
4.3 | odd | 2 | 392.3.g.m.99.5 | 8 | |||
7.6 | odd | 2 | 224.3.g.b.15.7 | 8 | |||
8.3 | odd | 2 | inner | 1568.3.g.m.687.1 | 8 | ||
8.5 | even | 2 | 392.3.g.m.99.6 | 8 | |||
21.20 | even | 2 | 2016.3.g.b.1135.8 | 8 | |||
28.3 | even | 6 | 392.3.k.o.275.6 | 16 | |||
28.11 | odd | 6 | 392.3.k.n.275.6 | 16 | |||
28.19 | even | 6 | 392.3.k.o.67.1 | 16 | |||
28.23 | odd | 6 | 392.3.k.n.67.1 | 16 | |||
28.27 | even | 2 | 56.3.g.b.43.5 | ✓ | 8 | ||
56.5 | odd | 6 | 392.3.k.o.67.6 | 16 | |||
56.13 | odd | 2 | 56.3.g.b.43.6 | yes | 8 | ||
56.27 | even | 2 | 224.3.g.b.15.8 | 8 | |||
56.37 | even | 6 | 392.3.k.n.67.6 | 16 | |||
56.45 | odd | 6 | 392.3.k.o.275.1 | 16 | |||
56.53 | even | 6 | 392.3.k.n.275.1 | 16 | |||
84.83 | odd | 2 | 504.3.g.b.379.4 | 8 | |||
112.13 | odd | 4 | 1792.3.d.j.1023.15 | 16 | |||
112.27 | even | 4 | 1792.3.d.j.1023.16 | 16 | |||
112.69 | odd | 4 | 1792.3.d.j.1023.2 | 16 | |||
112.83 | even | 4 | 1792.3.d.j.1023.1 | 16 | |||
168.83 | odd | 2 | 2016.3.g.b.1135.1 | 8 | |||
168.125 | even | 2 | 504.3.g.b.379.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.5 | ✓ | 8 | 28.27 | even | 2 | ||
56.3.g.b.43.6 | yes | 8 | 56.13 | odd | 2 | ||
224.3.g.b.15.7 | 8 | 7.6 | odd | 2 | |||
224.3.g.b.15.8 | 8 | 56.27 | even | 2 | |||
392.3.g.m.99.5 | 8 | 4.3 | odd | 2 | |||
392.3.g.m.99.6 | 8 | 8.5 | even | 2 | |||
392.3.k.n.67.1 | 16 | 28.23 | odd | 6 | |||
392.3.k.n.67.6 | 16 | 56.37 | even | 6 | |||
392.3.k.n.275.1 | 16 | 56.53 | even | 6 | |||
392.3.k.n.275.6 | 16 | 28.11 | odd | 6 | |||
392.3.k.o.67.1 | 16 | 28.19 | even | 6 | |||
392.3.k.o.67.6 | 16 | 56.5 | odd | 6 | |||
392.3.k.o.275.1 | 16 | 56.45 | odd | 6 | |||
392.3.k.o.275.6 | 16 | 28.3 | even | 6 | |||
504.3.g.b.379.3 | 8 | 168.125 | even | 2 | |||
504.3.g.b.379.4 | 8 | 84.83 | odd | 2 | |||
1568.3.g.m.687.1 | 8 | 8.3 | odd | 2 | inner | ||
1568.3.g.m.687.2 | 8 | 1.1 | even | 1 | trivial | ||
1792.3.d.j.1023.1 | 16 | 112.83 | even | 4 | |||
1792.3.d.j.1023.2 | 16 | 112.69 | odd | 4 | |||
1792.3.d.j.1023.15 | 16 | 112.13 | odd | 4 | |||
1792.3.d.j.1023.16 | 16 | 112.27 | even | 4 | |||
2016.3.g.b.1135.1 | 8 | 168.83 | odd | 2 | |||
2016.3.g.b.1135.8 | 8 | 21.20 | even | 2 |