Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(15,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, 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("224.15");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.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: | \(6.10355792167\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 15.8 | ||
Root | \(1.37098 + 1.45617i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.15 |
Dual form | 224.3.g.b.15.7 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | \(-0.163728\pi\) | ||||
0.870605 | + | 0.491982i | \(0.163728\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.26788i | 1.25358i | 0.779190 | + | 0.626788i | \(0.215631\pi\) | ||||
−0.779190 | + | 0.626788i | \(0.784369\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 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 | \(-0.435002\pi\) | ||||
0.202780 | + | 0.979224i | \(0.435002\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.77637 | −0.146125 | −0.0730624 | − | 0.997327i | \(-0.523277\pi\) | ||||
−0.0730624 | + | 0.997327i | \(0.523277\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.8204i | 0.658116i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 42.8332i | − 1.86231i | −0.364617 | − | 0.931157i | \(-0.618800\pi\) | ||||
0.364617 | − | 0.931157i | \(-0.381200\pi\) | |||||||
\(24\) | 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 | \(-0.777285\pi\) | ||||
0.765048 | − | 0.643974i | \(-0.222715\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −16.5833 | −0.473807 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 0.202653i | − 0.00547709i | −0.999996 | − | 0.00273855i | \(-0.999128\pi\) | ||||
0.999996 | − | 0.00273855i | \(-0.000871708\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.6231i | 0.323668i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 63.5494 | 1.54999 | 0.774993 | − | 0.631970i | \(-0.217753\pi\) | ||||
0.774993 | + | 0.631970i | \(0.217753\pi\) | |||||||
\(42\) | 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 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 36.0144 | 0.706165 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 54.6651i | − 1.03142i | −0.856764 | − | 0.515709i | \(-0.827529\pi\) | ||||
0.856764 | − | 0.515709i | \(-0.172471\pi\) | |||||||
\(54\) | 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 | \(-0.847970\pi\) | ||||
−0.888093 | + | 0.459665i | \(0.847970\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 43.7668i | 0.717489i | 0.933436 | + | 0.358745i | \(0.116795\pi\) | ||||
−0.933436 | + | 0.358745i | \(0.883205\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 48.3810i | 0.767953i | ||||||||
\(64\) | 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 | \(-0.947921\pi\) | ||||
0.986645 | − | 0.162883i | \(-0.0520794\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −69.2275 | −0.948322 | −0.474161 | − | 0.880438i | \(-0.657249\pi\) | ||||
−0.474161 | + | 0.880438i | \(0.657249\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −74.6264 | −0.995019 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 25.9466i | − 0.336968i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 19.9328i | − 0.252315i | −0.992010 | − | 0.126157i | \(-0.959736\pi\) | ||||
0.992010 | − | 0.126157i | \(-0.0402644\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 88.8125 | 1.09645 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.11617 | 0.0616406 | 0.0308203 | − | 0.999525i | \(-0.490188\pi\) | ||||
0.0308203 | + | 0.999525i | \(0.490188\pi\) | |||||||
\(84\) | 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 | \(-0.532224\pi\) | ||||
−0.101061 | + | 0.994880i | \(0.532224\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.39353 | −0.0702586 | ||||||||
\(92\) | 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 | \(-0.479498\pi\) | ||||
0.0643629 | + | 0.997927i | \(0.479498\pi\) | |||||||
\(98\) | 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 | ||||||||
\(105\) | −86.6248 | −0.824998 | ||||||||
\(106\) | 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 | \(0.0654332\pi\) | ||||
−0.978946 | + | 0.204120i | \(0.934567\pi\) | |||||||
\(110\) | 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 | ||||||||
\(119\) | 18.2412i | 0.153287i | ||||||||
\(120\) | 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 | \(0.172452\pi\) | ||||
−0.856795 | + | 0.515657i | \(0.827548\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 184.595 | 1.43097 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 53.3311 | 0.407108 | 0.203554 | − | 0.979064i | \(-0.434751\pi\) | ||||
0.203554 | + | 0.979064i | \(0.434751\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 7.34558i | − 0.0552299i | ||||||||
\(134\) | 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 | \(-0.287042\pi\) | ||||
0.620224 | + | 0.784425i | \(0.287042\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | −36.5654 | −0.248744 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 219.529i | 1.47335i | 0.676249 | + | 0.736673i | \(0.263604\pi\) | ||||
−0.676249 | + | 0.736673i | \(0.736396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 185.668i | 1.22959i | 0.788687 | + | 0.614795i | \(0.210761\pi\) | ||||
−0.788687 | + | 0.614795i | \(0.789239\pi\) | |||||||
\(152\) | 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 | ||||||||
\(161\) | 113.326 | 0.703889 | ||||||||
\(162\) | 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 | ||||||||
\(175\) | − 37.7980i | − 0.215989i | ||||||||
\(176\) | 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 | ||||||||
\(189\) | 128.341i | 0.679052i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 178.459i | 0.934342i | 0.884167 | + | 0.467171i | \(0.154727\pi\) | ||||
−0.884167 | + | 0.467171i | \(0.845273\pi\) | |||||||
\(192\) | 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 | \(-0.789168\pi\) | ||||
0.788550 | − | 0.614970i | \(-0.210832\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 98.8201 | 0.486798 | ||||||||
\(204\) | 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 | ||||||||
\(217\) | −18.9657 | −0.0873994 | ||||||||
\(218\) | 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 | \(-0.505740\pi\) | ||||
−0.0180308 | + | 0.999837i | \(0.505740\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 332.252i | − 1.45088i | −0.688285 | − | 0.725440i | \(-0.741636\pi\) | ||||
0.688285 | − | 0.725440i | \(-0.258364\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 135.535i | − 0.586733i | ||||||||
\(232\) | 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 | \(-0.906971\pi\) | ||||
0.957596 | − | 0.288115i | \(-0.0930286\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 201.854 | 0.837567 | 0.418783 | − | 0.908086i | \(-0.362457\pi\) | ||||
0.418783 | + | 0.908086i | \(0.362457\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 27.3492 | 0.112548 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 43.8752i | − 0.179082i | ||||||||
\(246\) | 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 | \(-0.319836\pi\) | ||||
0.536261 | + | 0.844052i | \(0.319836\pi\) | |||||||
\(252\) | 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 | \(-0.656293\pi\) | ||||
−0.471516 | + | 0.881858i | \(0.656293\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.536168 | 0.00207015 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 683.002i | − 2.61687i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 33.8470i | 0.128696i | 0.997928 | + | 0.0643479i | \(0.0204967\pi\) | ||||
−0.997928 | + | 0.0643479i | \(0.979503\pi\) | |||||||
\(264\) | 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 | ||||||||
\(273\) | −33.3975 | −0.122335 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 140.104 | 0.509470 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 478.358i | 1.72693i | 0.504413 | + | 0.863463i | \(0.331709\pi\) | ||||
−0.504413 | + | 0.863463i | \(0.668291\pi\) | |||||||
\(278\) | 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 | \(-0.351469\pi\) | ||||
0.449873 | + | 0.893093i | \(0.351469\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 90.9014i | − 0.318952i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 168.136i | 0.585840i | ||||||||
\(288\) | 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 | ||||||||
\(301\) | 93.4966i | 0.310620i | ||||||||
\(302\) | 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 | \(-0.645957\pi\) | ||||
−0.442636 | + | 0.896701i | \(0.645957\pi\) | |||||||
\(308\) | 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 | \(-0.848287\pi\) | ||||
−0.888550 | + | 0.458780i | \(0.848287\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −303.247 | −0.962688 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 387.459i | − 1.22227i | −0.791527 | − | 0.611134i | \(-0.790714\pi\) | ||||
0.791527 | − | 0.611134i | \(-0.209286\pi\) | |||||||
\(318\) | 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 | ||||||||
\(329\) | −100.308 | −0.304888 | ||||||||
\(330\) | 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 | ||||||||
\(343\) | − 18.5203i | − 0.0539949i | ||||||||
\(344\) | 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 | \(-0.358382\pi\) | ||||
0.430373 | + | 0.902651i | \(0.358382\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 144.972 | 0.408373 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 95.2852i | 0.266905i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 116.130i | − 0.323481i | −0.986833 | − | 0.161741i | \(-0.948289\pi\) | ||||
0.986833 | − | 0.161741i | \(-0.0517108\pi\) | |||||||
\(360\) | 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 | ||||||||
\(371\) | 144.630 | 0.389839 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 49.2857i | 0.132133i | 0.997815 | + | 0.0660666i | \(0.0210450\pi\) | ||||
−0.997815 | + | 0.0660666i | \(0.978955\pi\) | |||||||
\(374\) | 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 | ||||||||
\(385\) | 162.630 | 0.422416 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 646.209 | 1.66979 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 709.398i | 1.82365i | 0.410584 | + | 0.911823i | \(0.365325\pi\) | ||||
−0.410584 | + | 0.911823i | \(0.634675\pi\) | |||||||
\(390\) | 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 | ||||||||
\(399\) | − 38.3706i | − 0.0961669i | ||||||||
\(400\) | 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 | \(-0.769552\pi\) | ||||
−0.749181 | + | 0.662366i | \(0.769552\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −301.497 | −0.733569 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 277.261i | − 0.671335i | ||||||||
\(414\) | 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 | \(-0.408477\pi\) | ||||
0.283583 | + | 0.958948i | \(0.408477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 394.516i | − 0.937092i | −0.883439 | − | 0.468546i | \(-0.844778\pi\) | ||||
0.883439 | − | 0.468546i | \(-0.155222\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 693.287i | 1.63898i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −98.4973 | −0.231758 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −115.796 | −0.271185 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 123.793i | − 0.288561i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 363.359i | 0.843059i | 0.906815 | + | 0.421530i | \(0.138507\pi\) | ||||
−0.906815 | + | 0.421530i | \(0.861493\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 119.733 | 0.276520 | 0.138260 | − | 0.990396i | \(-0.455849\pi\) | ||||
0.138260 | + | 0.990396i | \(0.455849\pi\) | |||||||
\(434\) | 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 | ||||||||
\(441\) | −128.004 | −0.290259 | ||||||||
\(442\) | 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 | ||||||||
\(455\) | − 40.0739i | − 0.0880745i | ||||||||
\(456\) | 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 | \(-0.960311\pi\) | ||||
0.992237 | − | 0.124363i | \(-0.0396889\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −234.700 | −0.504730 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −603.424 | −1.29213 | −0.646064 | − | 0.763283i | \(-0.723586\pi\) | ||||
−0.646064 | + | 0.763283i | \(0.723586\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 82.2884i | − 0.175455i | ||||||||
\(470\) | 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 | ||||||||
\(483\) | 591.974 | 1.22562 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 78.2633i | 0.161368i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 106.987i | 0.219687i | 0.993949 | + | 0.109843i | \(0.0350349\pi\) | ||||
−0.993949 | + | 0.109843i | \(0.964965\pi\) | |||||||
\(488\) | 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 | ||||||||
\(497\) | 61.1947 | 0.123128 | ||||||||
\(498\) | 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 | ||||||||
\(511\) | − 183.159i | − 0.358432i | ||||||||
\(512\) | 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 | \(-0.469943\pi\) | ||||
0.0942861 | + | 0.995545i | \(0.469943\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 574.764 | 1.09898 | 0.549488 | − | 0.835502i | \(-0.314823\pi\) | ||||
0.549488 | + | 0.835502i | \(0.314823\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 197.443i | − 0.376082i | ||||||||
\(526\) | 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 | ||||||||
\(539\) | 68.6482 | 0.127362 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 370.654i | − 0.685128i | −0.939495 | − | 0.342564i | \(-0.888705\pi\) | ||||
0.939495 | − | 0.342564i | \(-0.111295\pi\) | |||||||
\(542\) | 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 | ||||||||
\(553\) | 52.7374 | 0.0953659 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.63506 | 0.0119551 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 151.525i | − 0.272037i | −0.990706 | − | 0.136019i | \(-0.956569\pi\) | ||||
0.990706 | − | 0.136019i | \(-0.0434307\pi\) | |||||||
\(558\) | 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 | \(-0.408850\pi\) | ||||
0.282458 | + | 0.959280i | \(0.408850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 836.076i | − 1.47978i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 234.976i | 0.414419i | ||||||||
\(568\) | 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 | \(-0.266924\pi\) | ||||
0.668530 | + | 0.743685i | \(0.266924\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1157.49 | 1.99912 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.5361i | 0.0232980i | ||||||||
\(582\) | 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 | \(-0.539244\pi\) | ||||
−0.122978 | + | 0.992409i | \(0.539244\pi\) | |||||||
\(588\) | 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 | \(-0.249887\pi\) | ||||
0.707357 | + | 0.706856i | \(0.249887\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −114.334 | −0.192157 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1551.66i | 2.59910i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 711.341i | − 1.18755i | −0.804632 | − | 0.593774i | \(-0.797637\pi\) | ||||
0.804632 | − | 0.593774i | \(-0.202363\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −356.394 | −0.593002 | −0.296501 | − | 0.955033i | \(-0.595820\pi\) | ||||
−0.296501 | + | 0.955033i | \(0.595820\pi\) | |||||||
\(602\) | 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 | ||||||||
\(609\) | 516.199 | 0.847618 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −91.6176 | −0.149947 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 482.989i | 0.787911i | 0.919130 | + | 0.393955i | \(0.128894\pi\) | ||||
−0.919130 | + | 0.393955i | \(0.871106\pi\) | |||||||
\(614\) | 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 | \(-0.476045\pi\) | ||||
0.0751872 | + | 0.997169i | \(0.476045\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2077.77i | − 3.34584i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 47.5941i | − 0.0763951i | ||||||||
\(624\) | 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 | \(-0.839251\pi\) | ||||
0.875171 | − | 0.483814i | \(-0.160749\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 736.636 | 1.16372 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −820.947 | −1.29283 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 16.9157i | − 0.0265553i | ||||||||
\(638\) | 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 | \(-0.435711\pi\) | ||||
0.200600 | + | 0.979673i | \(0.435711\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | −99.0696 | −0.152181 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 952.773i | − 1.45907i | −0.683943 | − | 0.729535i | \(-0.739736\pi\) | ||||
0.683943 | − | 0.729535i | \(-0.260264\pi\) | |||||||
\(654\) | 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 | ||||||||
\(665\) | 46.0412 | 0.0692349 | ||||||||
\(666\) | 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 | ||||||||
\(679\) | 33.0359i | 0.0486538i | ||||||||
\(680\) | 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 | \(-0.363447\pi\) | ||||
0.415956 | + | 0.909385i | \(0.363447\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 474.467i | − 0.684657i | ||||||||
\(694\) | 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 | \(-0.967445\pi\) | ||||
0.994775 | − | 0.102096i | \(-0.0325548\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.562638i | 0 0.000800339i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1241.31 | −1.76072 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 180.110 | 0.254753 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 255.311i | 0.360101i | 0.983657 | + | 0.180050i | \(0.0576261\pi\) | ||||
−0.983657 | + | 0.180050i | \(0.942374\pi\) | |||||||
\(710\) | 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 | ||||||||
\(721\) | −154.229 | −0.213910 | ||||||||
\(722\) | 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 | ||||||||
\(735\) | − 229.188i | − 0.311820i | ||||||||
\(736\) | 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 | \(0.360207\pi\) | ||||
−0.425191 | + | 0.905104i | \(0.639793\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1375.98 | −1.84695 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 93.5560 | 0.125242 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 359.473i | − 0.479937i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.6931i | 0.0368749i | 0.999830 | + | 0.0184375i | \(0.00586916\pi\) | ||||
−0.999830 | + | 0.0184375i | \(0.994131\pi\) | |||||||
\(752\) | 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 | \(-0.653341\pi\) | ||||
0.463318 | − | 0.886192i | \(-0.346659\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2194.24i | 2.89096i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −112.001 | −0.147176 | −0.0735881 | − | 0.997289i | \(-0.523445\pi\) | ||||
−0.0735881 | + | 0.997289i | \(0.523445\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −117.731 | −0.154300 | ||||||||
\(764\) | 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 | \(-0.470829\pi\) | ||||
0.0915142 | + | 0.995804i | \(0.470829\pi\) | |||||||
\(770\) | 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 | ||||||||
\(777\) | 2.80074 | 0.00360456 | ||||||||
\(778\) | 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 | \(-0.433220\pi\) | ||||
0.208260 | + | 0.978074i | \(0.433220\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 176.804i | 0.224086i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 352.918i | − 0.446167i | ||||||||
\(792\) | 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 | ||||||||
\(805\) | 710.314i | 0.882378i | ||||||||
\(806\) | 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 | \(-0.347277\pi\) | ||||
0.461595 | + | 0.887091i | \(0.347277\pi\) | |||||||
\(812\) | 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 | ||||||||
\(819\) | −116.914 | −0.142752 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 554.169i | − 0.674993i | −0.941327 | − | 0.337496i | \(-0.890420\pi\) | ||||
0.941327 | − | 0.337496i | \(-0.109580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 121.452i | 0.147572i | 0.997274 | + | 0.0737861i | \(0.0235082\pi\) | ||||
−0.997274 | + | 0.0737861i | \(0.976492\pi\) | |||||||
\(824\) | 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 | ||||||||
\(833\) | −48.2617 | −0.0579372 | ||||||||
\(834\) | 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 | ||||||||
\(847\) | − 65.6810i | − 0.0775454i | ||||||||
\(848\) | 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 | \(-0.422727\pi\) | ||||
0.240384 | + | 0.970678i | \(0.422727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −159.993 | −0.186255 | −0.0931274 | − | 0.995654i | \(-0.529686\pi\) | ||||
−0.0931274 | + | 0.995654i | \(0.529686\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 878.280i | 1.02007i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 992.910i | 1.15053i | 0.817966 | + | 0.575266i | \(0.195102\pi\) | ||||
−0.817966 | + | 0.575266i | \(0.804898\pi\) | |||||||
\(864\) | 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 | ||||||||
\(875\) | −177.668 | −0.203049 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 825.096i | 0.940817i | 0.882449 | + | 0.470408i | \(0.155893\pi\) | ||||
−0.882449 | + | 0.470408i | \(0.844107\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 781.236i | 0.888778i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1352.83 | 1.53556 | 0.767780 | − | 0.640714i | \(-0.221361\pi\) | ||||
0.767780 | + | 0.640714i | \(0.221361\pi\) | |||||||
\(882\) | 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 | ||||||||
\(889\) | −346.532 | −0.389800 | ||||||||
\(890\) | 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 | ||||||||
\(903\) | 488.392i | 0.540854i | ||||||||
\(904\) | 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 | \(0.127799\pi\) | ||||
−0.920479 | + | 0.390792i | \(0.872201\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −50.1737 | −0.0549548 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1432.97 | −1.56609 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 141.101i | 0.153872i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 786.783i | − 0.856129i | −0.903748 | − | 0.428065i | \(-0.859196\pi\) | ||||
0.903748 | − | 0.428065i | \(-0.140804\pi\) | |||||||
\(920\) | 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 | \(-0.850947\pi\) | ||||
−0.892353 | + | 0.451338i | \(0.850947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.4346 | 0.0208750 | ||||||||
\(932\) | 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 | \(-0.443009\pi\) | ||||
0.178088 | + | 0.984015i | \(0.443009\pi\) | |||||||
\(938\) | 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 | ||||||||
\(945\) | −804.425 | −0.851243 | ||||||||
\(946\) | 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 | ||||||||
\(959\) | − 152.707i | − 0.159236i | ||||||||
\(960\) | 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 | \(-0.842016\pi\) | ||||
0.879340 | − | 0.476195i | \(-0.157984\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −99.9894 | −0.103188 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1327.31 | −1.36695 | −0.683476 | − | 0.729973i | \(-0.739532\pi\) | ||||
−0.683476 | + | 0.729973i | \(0.739532\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 456.186i | 0.468845i | ||||||||
\(974\) | 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 | ||||||||
\(987\) | −523.972 | −0.530874 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1513.66i | − 1.53049i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1139.22i | 1.14957i | 0.818304 | + | 0.574785i | \(0.194914\pi\) | ||||
−0.818304 | + | 0.574785i | \(0.805086\pi\) | |||||||
\(992\) | 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 | 224.3.g.b.15.8 | 8 | ||
3.2 | odd | 2 | 2016.3.g.b.1135.1 | 8 | |||
4.3 | odd | 2 | 56.3.g.b.43.6 | yes | 8 | ||
7.6 | odd | 2 | 1568.3.g.m.687.1 | 8 | |||
8.3 | odd | 2 | inner | 224.3.g.b.15.7 | 8 | ||
8.5 | even | 2 | 56.3.g.b.43.5 | ✓ | 8 | ||
12.11 | even | 2 | 504.3.g.b.379.3 | 8 | |||
16.3 | odd | 4 | 1792.3.d.j.1023.2 | 16 | |||
16.5 | even | 4 | 1792.3.d.j.1023.1 | 16 | |||
16.11 | odd | 4 | 1792.3.d.j.1023.15 | 16 | |||
16.13 | even | 4 | 1792.3.d.j.1023.16 | 16 | |||
24.5 | odd | 2 | 504.3.g.b.379.4 | 8 | |||
24.11 | even | 2 | 2016.3.g.b.1135.8 | 8 | |||
28.3 | even | 6 | 392.3.k.n.275.1 | 16 | |||
28.11 | odd | 6 | 392.3.k.o.275.1 | 16 | |||
28.19 | even | 6 | 392.3.k.n.67.6 | 16 | |||
28.23 | odd | 6 | 392.3.k.o.67.6 | 16 | |||
28.27 | even | 2 | 392.3.g.m.99.6 | 8 | |||
56.5 | odd | 6 | 392.3.k.n.67.1 | 16 | |||
56.13 | odd | 2 | 392.3.g.m.99.5 | 8 | |||
56.27 | even | 2 | 1568.3.g.m.687.2 | 8 | |||
56.37 | even | 6 | 392.3.k.o.67.1 | 16 | |||
56.45 | odd | 6 | 392.3.k.n.275.6 | 16 | |||
56.53 | even | 6 | 392.3.k.o.275.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.5 | ✓ | 8 | 8.5 | even | 2 | ||
56.3.g.b.43.6 | yes | 8 | 4.3 | odd | 2 | ||
224.3.g.b.15.7 | 8 | 8.3 | odd | 2 | inner | ||
224.3.g.b.15.8 | 8 | 1.1 | even | 1 | trivial | ||
392.3.g.m.99.5 | 8 | 56.13 | odd | 2 | |||
392.3.g.m.99.6 | 8 | 28.27 | even | 2 | |||
392.3.k.n.67.1 | 16 | 56.5 | odd | 6 | |||
392.3.k.n.67.6 | 16 | 28.19 | even | 6 | |||
392.3.k.n.275.1 | 16 | 28.3 | even | 6 | |||
392.3.k.n.275.6 | 16 | 56.45 | odd | 6 | |||
392.3.k.o.67.1 | 16 | 56.37 | even | 6 | |||
392.3.k.o.67.6 | 16 | 28.23 | odd | 6 | |||
392.3.k.o.275.1 | 16 | 28.11 | odd | 6 | |||
392.3.k.o.275.6 | 16 | 56.53 | even | 6 | |||
504.3.g.b.379.3 | 8 | 12.11 | even | 2 | |||
504.3.g.b.379.4 | 8 | 24.5 | odd | 2 | |||
1568.3.g.m.687.1 | 8 | 7.6 | odd | 2 | |||
1568.3.g.m.687.2 | 8 | 56.27 | even | 2 | |||
1792.3.d.j.1023.1 | 16 | 16.5 | even | 4 | |||
1792.3.d.j.1023.2 | 16 | 16.3 | odd | 4 | |||
1792.3.d.j.1023.15 | 16 | 16.11 | odd | 4 | |||
1792.3.d.j.1023.16 | 16 | 16.13 | even | 4 | |||
2016.3.g.b.1135.1 | 8 | 3.2 | odd | 2 | |||
2016.3.g.b.1135.8 | 8 | 24.11 | even | 2 |