Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,3,Mod(1023,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.1023");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.d (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: | \(48.8284633734\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{14} + 48x^{12} + 180x^{10} + 1056x^{8} + 2880x^{6} + 12288x^{4} + 20480x^{2} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{38} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1023.15 | ||
Root | \(-1.45617 - 1.37098i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1023 |
Dual form | 1792.3.d.j.1023.1 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 5.22363i | 1.74121i | 0.491982 | + | 0.870605i | \(0.336272\pi\) | ||||
−0.491982 | + | 0.870605i | \(0.663728\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.26788 | −1.25358 | −0.626788 | − | 0.779190i | \(-0.715631\pi\) | ||||
−0.626788 | + | 0.779190i | \(0.715631\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −18.2863 | −2.03181 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.80688i | 0.891535i | 0.895149 | + | 0.445767i | \(0.147069\pi\) | ||||
−0.895149 | + | 0.445767i | \(0.852931\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.41653 | 0.185887 | 0.0929434 | − | 0.995671i | \(-0.470372\pi\) | ||||
0.0929434 | + | 0.995671i | \(0.470372\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | − 2.77637i | − 0.146125i | −0.997327 | − | 0.0730624i | \(-0.976723\pi\) | ||||
0.997327 | − | 0.0730624i | \(-0.0232772\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −13.8204 | −0.658116 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | − 48.5083i | − 1.79660i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −37.3505 | −1.28795 | −0.643974 | − | 0.765048i | \(-0.722715\pi\) | ||||
−0.643974 | + | 0.765048i | \(0.722715\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 7.16835i | − 0.231237i | −0.993294 | − | 0.115619i | \(-0.963115\pi\) | ||||
0.993294 | − | 0.115619i | \(-0.0368850\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −51.2275 | −1.55235 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 16.5833i | − 0.473807i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.202653 | 0.00547709 | 0.00273855 | − | 0.999996i | \(-0.499128\pi\) | ||||
0.00273855 | + | 0.999996i | \(0.499128\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | − 35.3384i | − 0.821823i | −0.911675 | − | 0.410911i | \(-0.865211\pi\) | ||||
0.911675 | − | 0.410911i | \(-0.134789\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 114.616 | 2.54703 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 37.9129i | − 0.806657i | −0.915055 | − | 0.403329i | \(-0.867853\pi\) | ||||
0.915055 | − | 0.403329i | \(-0.132147\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 36.0144i | 0.706165i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 54.6651 | 1.03142 | 0.515709 | − | 0.856764i | \(-0.327529\pi\) | ||||
0.515709 | + | 0.856764i | \(0.327529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 61.4684i | − 1.11761i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.5027 | 0.254434 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 104.795i | 1.77619i | 0.459665 | + | 0.888093i | \(0.347970\pi\) | ||||
−0.459665 | + | 0.888093i | \(0.652030\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 43.7668 | 0.717489 | 0.358745 | − | 0.933436i | \(-0.383205\pi\) | ||||
0.358745 | + | 0.933436i | \(0.383205\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 48.3810i | − 0.767953i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.1465 | −0.233023 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 31.1021i | − 0.464210i | −0.972691 | − | 0.232105i | \(-0.925439\pi\) | ||||
0.972691 | − | 0.232105i | \(-0.0745613\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 223.745 | 3.24268 | ||||||||
\(70\) | 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 | \(-0.342751\pi\) | ||||
0.474161 | + | 0.880438i | \(0.342751\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 74.6264i | 0.995019i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −25.9466 | −0.336968 | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 5.11617i | 0.0616406i | 0.999525 | + | 0.0308203i | \(0.00981197\pi\) | ||||
−0.999525 | + | 0.0308203i | \(0.990188\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −43.2140 | −0.508400 | ||||||||
\(86\) | 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 | ||||||||
\(91\) | 6.39353i | 0.0702586i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 37.4448 | 0.402632 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | − 179.332i | − 1.81143i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 68.0753 | 0.674013 | 0.337006 | − | 0.941502i | \(-0.390586\pi\) | ||||
0.337006 | + | 0.941502i | \(0.390586\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | 135.868i | 1.26979i | 0.772597 | + | 0.634897i | \(0.218957\pi\) | ||||
−0.772597 | + | 0.634897i | \(0.781043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 44.4981 | 0.408239 | 0.204120 | − | 0.978946i | \(-0.434567\pi\) | ||||
0.204120 | + | 0.978946i | \(0.434567\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 268.474i | 2.33455i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −44.1894 | −0.377687 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.2412i | 0.153287i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.8251 | 0.205166 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 331.959i | − 2.69885i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 67.1521 | 0.537217 | ||||||||
\(126\) | 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 | ||||||||
\(131\) | 53.3311i | 0.407108i | 0.979064 | + | 0.203554i | \(0.0652492\pi\) | ||||
−0.979064 | + | 0.203554i | \(0.934751\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.34558 | 0.0552299 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 304.044i | 2.25218i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 57.7179 | 0.421299 | 0.210649 | − | 0.977562i | \(-0.432442\pi\) | ||||
0.210649 | + | 0.977562i | \(0.432442\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 172.422i | − 1.24045i | −0.784425 | − | 0.620224i | \(-0.787042\pi\) | ||||
0.784425 | − | 0.620224i | \(-0.212958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 198.043 | 1.40456 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.6986i | 0.165725i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 234.108 | 1.61454 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 36.5654i | − 0.248744i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −219.529 | −1.47335 | −0.736673 | − | 0.676249i | \(-0.763604\pi\) | ||||
−0.736673 | + | 0.676249i | \(0.763604\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 44.9304i | 0.289873i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −188.182 | −1.19861 | −0.599305 | − | 0.800521i | \(-0.704556\pi\) | ||||
−0.599305 | + | 0.800521i | \(0.704556\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 285.550i | 1.79591i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 113.326 | 0.703889 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 54.5154i | − 0.334450i | −0.985919 | − | 0.167225i | \(-0.946519\pi\) | ||||
0.985919 | − | 0.167225i | \(-0.0534806\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 321.088 | 1.94599 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 50.7696i | 0.296898i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 114.835 | 0.663786 | 0.331893 | − | 0.943317i | \(-0.392313\pi\) | ||||
0.331893 | + | 0.943317i | \(0.392313\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 37.7980i | 0.215989i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −547.410 | −3.09271 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 112.849i | − 0.630439i | −0.949019 | − | 0.315220i | \(-0.897922\pi\) | ||||
0.949019 | − | 0.315220i | \(-0.102078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −60.9470 | −0.336724 | −0.168362 | − | 0.985725i | \(-0.553848\pi\) | ||||
−0.168362 | + | 0.985725i | \(0.553848\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 228.622i | 1.24930i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.27020 | −0.00686595 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 67.6138i | 0.361571i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 128.341 | 0.679052 | ||||||||
\(190\) | 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 | ||||||||
\(195\) | − 79.1198i | − 0.405742i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 242.298 | 1.22994 | 0.614970 | − | 0.788550i | \(-0.289168\pi\) | ||||
0.614970 | + | 0.788550i | \(0.289168\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | − 98.8201i | − 0.486798i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 398.320 | 1.94302 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 783.262i | 3.78388i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.2275 | 0.130275 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 141.020i | 0.668341i | 0.942513 | + | 0.334171i | \(0.108456\pi\) | ||||
−0.942513 | + | 0.334171i | \(0.891544\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 120.820 | 0.567228 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 221.497i | 1.03022i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.9657 | 0.0873994 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 361.619i | 1.65123i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.6608 | 0.0753883 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 40.8267i | − 0.183079i | −0.995801 | − | 0.0915396i | \(-0.970821\pi\) | ||||
0.995801 | − | 0.0915396i | \(-0.0291788\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −261.244 | −1.16108 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 8.18598i | − 0.0360616i | −0.999837 | − | 0.0180308i | \(-0.994260\pi\) | ||||
0.999837 | − | 0.0180308i | \(-0.00573969\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 332.252 | 1.45088 | 0.725440 | − | 0.688285i | \(-0.241636\pi\) | ||||
0.725440 | + | 0.688285i | \(0.241636\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 135.535i | − 0.586733i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −329.260 | −1.41314 | −0.706568 | − | 0.707646i | \(-0.749757\pi\) | ||||
−0.706568 | + | 0.707646i | \(0.749757\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 237.633i | 1.01121i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −104.122 | −0.439333 | ||||||||
\(238\) | 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 | \(-0.362457\pi\) | ||||
0.418783 | + | 0.908086i | \(0.362457\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 27.3492i | 0.112548i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 43.8752 | 0.179082 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 6.70917i | − 0.0271627i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −26.7250 | −0.107329 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 269.203i | − 1.07252i | −0.844052 | − | 0.536261i | \(-0.819836\pi\) | ||||
0.844052 | − | 0.536261i | \(-0.180164\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 420.061 | 1.66032 | ||||||||
\(254\) | 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 | ||||||||
\(259\) | 0.536168i | 0.00207015i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 683.002 | 2.61687 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 93.9673i | 0.351937i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −165.598 | −0.615606 | −0.307803 | − | 0.951450i | \(-0.599594\pi\) | ||||
−0.307803 | + | 0.951450i | \(0.599594\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 148.308i | − 0.547263i | −0.961835 | − | 0.273632i | \(-0.911775\pi\) | ||||
0.961835 | − | 0.273632i | \(-0.0882249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −33.3975 | −0.122335 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 140.104i | 0.509470i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −478.358 | −1.72693 | −0.863463 | − | 0.504413i | \(-0.831709\pi\) | ||||
−0.863463 | + | 0.504413i | \(0.831709\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 131.083i | 0.469830i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 226.066 | 0.804506 | 0.402253 | − | 0.915528i | \(-0.368227\pi\) | ||||
0.402253 | + | 0.915528i | \(0.368227\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 254.628i | − 0.899745i | −0.893093 | − | 0.449873i | \(-0.851469\pi\) | ||||
0.893093 | − | 0.449873i | \(-0.148531\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −90.9014 | −0.318952 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 168.136i | − 0.585840i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −241.466 | −0.835521 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 65.2244i | 0.224139i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −149.558 | −0.510437 | −0.255218 | − | 0.966883i | \(-0.582147\pi\) | ||||
−0.255218 | + | 0.966883i | \(0.582147\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 656.842i | − 2.22658i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 475.715 | 1.60173 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 103.508i | − 0.346180i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 93.4966 | 0.310620 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 355.600i | 1.17360i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −274.325 | −0.899427 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 271.779i | − 0.885272i | −0.896701 | − | 0.442636i | \(-0.854043\pi\) | ||||
0.896701 | − | 0.442636i | \(-0.145957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −304.502 | −0.985442 | ||||||||
\(310\) | 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 | ||||||||
\(315\) | 303.247i | 0.962688i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −387.459 | −1.22227 | −0.611134 | − | 0.791527i | \(-0.709286\pi\) | ||||
−0.611134 | + | 0.791527i | \(0.709286\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 366.292i | − 1.14825i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −709.724 | −2.21098 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 19.1417i | − 0.0592624i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.5233 | 0.106225 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 232.442i | 0.710830i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 100.308 | 0.304888 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 383.205i | − 1.15772i | −0.815427 | − | 0.578860i | \(-0.803498\pi\) | ||||
0.815427 | − | 0.578860i | \(-0.196502\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.70577 | −0.0111284 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 696.783i | − 2.05541i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 70.2992 | 0.206156 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 18.5203i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1402.41 | −4.06495 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 51.5890i | 0.148671i | 0.997233 | + | 0.0743357i | \(0.0236836\pi\) | ||||
−0.997233 | + | 0.0743357i | \(0.976316\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −586.383 | −1.68018 | −0.840090 | − | 0.542447i | \(-0.817498\pi\) | ||||
−0.840090 | + | 0.542447i | \(0.817498\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 144.972i | 0.408373i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −95.2852 | −0.266905 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 129.677i | 0.357237i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −433.910 | −1.18879 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 476.288i | − 1.29779i | −0.760879 | − | 0.648894i | \(-0.775232\pi\) | ||||
0.760879 | − | 0.648894i | \(-0.224768\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1162.08 | 3.14928 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 144.630i | 0.389839i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −49.2857 | −0.132133 | −0.0660666 | − | 0.997815i | \(-0.521045\pi\) | ||||
−0.0660666 | + | 0.997815i | \(0.521045\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 350.778i | 0.935407i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −90.2585 | −0.239412 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 167.511i | 0.441983i | 0.975276 | + | 0.220991i | \(0.0709292\pi\) | ||||
−0.975276 | + | 0.220991i | \(0.929071\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 684.174 | 1.79573 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 513.207i | − 1.33997i | −0.742376 | − | 0.669983i | \(-0.766301\pi\) | ||||
0.742376 | − | 0.669983i | \(-0.233699\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 162.630 | 0.422416 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 646.209i | 1.66979i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −709.398 | −1.82365 | −0.911823 | − | 0.410584i | \(-0.865325\pi\) | ||||
−0.911823 | + | 0.410584i | \(0.865325\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 295.315i | − 0.755281i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −278.582 | −0.708860 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 124.937i | − 0.316295i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 309.404 | 0.779355 | 0.389677 | − | 0.920951i | \(-0.372587\pi\) | ||||
0.389677 | + | 0.920951i | \(0.372587\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − 17.3225i | − 0.0429839i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −556.666 | −1.37448 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 301.497i | 0.733569i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −277.261 | −0.671335 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 32.0676i | − 0.0772712i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 900.670 | 2.15988 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 237.642i | 0.567165i | 0.958948 | + | 0.283583i | \(0.0915230\pi\) | ||||
−0.958948 | + | 0.283583i | \(0.908477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 394.516 | 0.937092 | 0.468546 | − | 0.883439i | \(-0.344778\pi\) | ||||
0.468546 | + | 0.883439i | \(0.344778\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 693.287i | 1.63898i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 98.4973 | 0.231758 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 115.796i | 0.271185i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −123.793 | −0.288561 | ||||||||
\(430\) | 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 | \(-0.455849\pi\) | ||||
0.138260 | + | 0.990396i | \(0.455849\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1222.89i | 2.81125i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −118.921 | −0.272130 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | − 343.956i | − 0.776424i | −0.921570 | − | 0.388212i | \(-0.873093\pi\) | ||||
0.921570 | − | 0.388212i | \(-0.126907\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −112.752 | −0.253376 | ||||||||
\(446\) | 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 | ||||||||
\(451\) | − 623.222i | − 1.38187i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −969.861 | −2.14097 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 40.0739i | − 0.0880745i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 42.2571 | 0.0924662 | 0.0462331 | − | 0.998931i | \(-0.485278\pi\) | ||||
0.0462331 | + | 0.998931i | \(0.485278\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 334.441i | − 0.728631i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 816.370 | 1.77087 | 0.885434 | − | 0.464766i | \(-0.153861\pi\) | ||||
0.885434 | + | 0.464766i | \(0.153861\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | − 603.424i | − 1.29213i | −0.763283 | − | 0.646064i | \(-0.776414\pi\) | ||||
0.763283 | − | 0.646064i | \(-0.223586\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 82.2884 | 0.175455 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 982.992i | − 2.08703i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 346.559 | 0.732684 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 39.6641i | − 0.0835034i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −999.624 | −2.09565 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 158.595i | 0.331097i | 0.986202 | + | 0.165548i | \(0.0529394\pi\) | ||||
−0.986202 | + | 0.165548i | \(0.947061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.489715 | 0.00101812 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 591.974i | 1.22562i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −78.2633 | −0.161368 | ||||||||
\(486\) | 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 | ||||||||
\(491\) | 616.591i | 1.25579i | 0.778299 | + | 0.627893i | \(0.216083\pi\) | ||||
−0.778299 | + | 0.627893i | \(0.783917\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −257.514 | −0.522340 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1124.03i | 2.27077i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 61.1947 | 0.123128 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 554.090i | − 1.11040i | −0.831717 | − | 0.555200i | \(-0.812642\pi\) | ||||
0.831717 | − | 0.555200i | \(-0.187358\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1391.76 | 2.77796 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | − 852.290i | − 1.68104i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −182.889 | −0.359310 | −0.179655 | − | 0.983730i | \(-0.557498\pi\) | ||||
−0.179655 | + | 0.983730i | \(0.557498\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 183.159i | 0.358432i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −134.677 | −0.262528 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 365.374i | − 0.709464i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 371.807 | 0.719163 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | − 574.764i | − 1.09898i | −0.835502 | − | 0.549488i | \(-0.814823\pi\) | ||||
0.835502 | − | 0.549488i | \(-0.185177\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −197.443 | −0.376082 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 49.4223i | − 0.0937805i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1305.69 | −2.46822 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1916.31i | − 3.60888i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −153.569 | −0.288122 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 851.604i | − 1.59178i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 589.480 | 1.09773 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 68.6482i | − 0.127362i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −370.654 | −0.685128 | −0.342564 | − | 0.939495i | \(-0.611295\pi\) | ||||
−0.342564 | + | 0.939495i | \(0.611295\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 318.365i | − 0.586307i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −278.909 | −0.511759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 56.5966i | 0.103467i | 0.998661 | + | 0.0517336i | \(0.0164747\pi\) | ||||
−0.998661 | + | 0.0517336i | \(0.983525\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −800.334 | −1.45780 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 103.699i | 0.188201i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −52.7374 | −0.0953659 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 6.63506i | − 0.0119551i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −151.525 | −0.272037 | −0.136019 | − | 0.990706i | \(-0.543431\pi\) | ||||
−0.136019 | + | 0.990706i | \(0.543431\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 85.3962i | − 0.152766i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −353.189 | −0.629571 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 318.048i | 0.564917i | 0.959280 | + | 0.282458i | \(0.0911499\pi\) | ||||
−0.959280 | + | 0.282458i | \(0.908850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 836.076 | 1.47978 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 234.976i | 0.414419i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −356.654 | −0.626808 | −0.313404 | − | 0.949620i | \(-0.601469\pi\) | ||||
−0.313404 | + | 0.949620i | \(0.601469\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 831.014i | 1.45537i | 0.685914 | + | 0.727683i | \(0.259403\pi\) | ||||
−0.685914 | + | 0.727683i | \(0.740597\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 932.205 | 1.62689 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 1157.49i | 1.99912i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.5361 | −0.0232980 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 536.094i | 0.919544i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 276.974 | 0.473460 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 144.376i | 0.245956i | 0.992409 | + | 0.122978i | \(0.0392445\pi\) | ||||
−0.992409 | + | 0.122978i | \(0.960756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.9020 | −0.0337894 | ||||||||
\(590\) | 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 | ||||||||
\(595\) | − 114.334i | − 0.192157i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1551.66 | −2.59910 | ||||||||
\(598\) | 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 | \(-0.404180\pi\) | ||||
0.296501 | + | 0.955033i | \(0.404180\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 568.742i | 0.943188i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −155.601 | −0.257191 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 60.3719i | 0.0994595i | 0.998763 | + | 0.0497298i | \(0.0158360\pi\) | ||||
−0.998763 | + | 0.0497298i | \(0.984164\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 516.199 | 0.847618 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 91.6176i | − 0.149947i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −482.989 | −0.787911 | −0.393955 | − | 0.919130i | \(-0.628894\pi\) | ||||
−0.393955 | + | 0.919130i | \(0.628894\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2080.68i | 3.38321i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −712.490 | −1.15476 | −0.577382 | − | 0.816474i | \(-0.695926\pi\) | ||||
−0.577382 | + | 0.816474i | \(0.695926\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 93.0817i | − 0.150374i | −0.997169 | − | 0.0751872i | \(-0.976045\pi\) | ||||
0.997169 | − | 0.0751872i | \(-0.0239554\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2077.77 | −3.34584 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 47.5941i | 0.0763951i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −778.059 | −1.24489 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 142.227i | 0.226837i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.39719 | 0.00222129 | ||||||||
\(630\) | 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 | ||||||||
\(635\) | 820.947i | 1.29283i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.9157 | −0.0265553 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 257.971i | 0.401199i | 0.979673 | + | 0.200600i | \(0.0642890\pi\) | ||||
−0.979673 | + | 0.200600i | \(0.935711\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1157.02 | −1.79383 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 99.0696i | 0.152181i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −952.773 | −1.45907 | −0.729535 | − | 0.683943i | \(-0.760264\pi\) | ||||
−0.729535 | + | 0.683943i | \(0.760264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 334.273i | − 0.510340i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1265.92 | −1.92681 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 963.119i | 1.46149i | 0.682653 | + | 0.730743i | \(0.260826\pi\) | ||||
−0.682653 | + | 0.730743i | \(0.739174\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −71.6817 | −0.108444 | −0.0542222 | − | 0.998529i | \(-0.517268\pi\) | ||||
−0.0542222 | + | 0.998529i | \(0.517268\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 87.0299i | 0.131267i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −46.0412 | −0.0692349 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1599.84i | 2.39856i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 213.263 | 0.318779 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | − 693.005i | − 1.02667i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −767.527 | −1.13372 | −0.566859 | − | 0.823815i | \(-0.691841\pi\) | ||||
−0.566859 | + | 0.823815i | \(0.691841\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.0359i | 0.0486538i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.7605 | 0.0627908 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 484.354i | − 0.709156i | −0.935026 | − | 0.354578i | \(-0.884625\pi\) | ||||
0.935026 | − | 0.354578i | \(-0.115375\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −361.769 | −0.528130 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1735.56i | 2.52629i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 132.100 | 0.191727 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 574.851i | 0.831912i | 0.909385 | + | 0.415956i | \(0.136553\pi\) | ||||
−0.909385 | + | 0.415956i | \(0.863447\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 474.467 | 0.684657 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1080.72i | 1.55500i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −438.143 | −0.628612 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1719.94i | − 2.46057i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −143.138 | −0.204191 | −0.102096 | − | 0.994775i | \(-0.532555\pi\) | ||||
−0.102096 | + | 0.994775i | \(0.532555\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 0.562638i | 0 0.000800339i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1241.31 | −1.76072 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 180.110i | 0.254753i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −255.311 | −0.360101 | −0.180050 | − | 0.983657i | \(-0.557626\pi\) | ||||
−0.180050 | + | 0.983657i | \(0.557626\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 364.498i | − 0.512656i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −307.044 | −0.430636 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 148.540i | − 0.207748i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −719.393 | −1.00334 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 415.630i | − 0.578067i | −0.957319 | − | 0.289034i | \(-0.906666\pi\) | ||||
0.957319 | − | 0.289034i | \(-0.0933340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −154.229 | −0.213910 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1054.41i | 1.45838i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −533.601 | −0.736001 | ||||||||
\(726\) | 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 | ||||||||
\(731\) | − 243.641i | − 0.333299i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 509.059 | 0.694487 | 0.347244 | − | 0.937775i | \(-0.387118\pi\) | ||||
0.347244 | + | 0.937775i | \(0.387118\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 229.188i | 0.311820i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 305.014 | 0.413859 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 741.427i | − 1.00328i | −0.865075 | − | 0.501642i | \(-0.832729\pi\) | ||||
0.865075 | − | 0.501642i | \(-0.167271\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35.0463 | 0.0472959 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | − 93.5560i | − 0.125242i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −359.473 | −0.479937 | ||||||||
\(750\) | 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 | ||||||||
\(755\) | − 1163.74i | − 1.54138i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1341.69 | 1.77238 | 0.886192 | − | 0.463318i | \(-0.153341\pi\) | ||||
0.886192 | + | 0.463318i | \(0.153341\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 117.731i | 0.154300i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 790.226 | 1.03297 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | − 1265.99i | − 1.64202i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1325.14 | −1.71428 | −0.857138 | − | 0.515087i | \(-0.827760\pi\) | ||||
−0.857138 | + | 0.515087i | \(0.827760\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 102.409i | − 0.132141i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.80074 | −0.00360456 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 176.437i | 0.226491i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 226.827 | 0.290432 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1811.81i | 2.31393i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1179.50 | 1.50255 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 327.801i | 0.416519i | 0.978074 | + | 0.208260i | \(0.0667799\pi\) | ||||
−0.978074 | + | 0.208260i | \(0.933220\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −176.804 | −0.224086 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 352.918i | − 0.446167i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 105.764 | 0.133372 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1789.80i | − 2.25132i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −393.650 | −0.493915 | −0.246958 | − | 0.969026i | \(-0.579431\pi\) | ||||
−0.246958 | + | 0.969026i | \(0.579431\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 261.391i | − 0.327148i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −328.950 | −0.410675 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 678.906i | 0.845462i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −710.314 | −0.882378 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 865.023i | − 1.07190i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −416.641 | −0.515008 | −0.257504 | − | 0.966277i | \(-0.582900\pi\) | ||||
−0.257504 | + | 0.966277i | \(0.582900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 748.707i | − 0.923190i | −0.887091 | − | 0.461595i | \(-0.847277\pi\) | ||||
0.887091 | − | 0.461595i | \(-0.152723\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 774.708 | 0.952901 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 341.696i | 0.419259i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −98.1124 | −0.120089 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 116.914i | − 0.142752i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 554.169 | 0.674993 | 0.337496 | − | 0.941327i | \(-0.390420\pi\) | ||||
0.337496 | + | 0.941327i | \(0.390420\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | − 1516.61i | − 1.83386i | −0.399043 | − | 0.916932i | \(-0.630657\pi\) | ||||
0.399043 | − | 0.916932i | \(-0.369343\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 325.042 | 0.392089 | 0.196044 | − | 0.980595i | \(-0.437190\pi\) | ||||
0.196044 | + | 0.980595i | \(0.437190\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 2498.77i | − 3.00694i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −48.2617 | −0.0579372 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1669.98i | 1.99998i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −347.724 | −0.415441 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 1180.89i | 1.40081i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1022.67 | 1.21026 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 65.6810i | 0.0775454i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1330.08 | 1.56665 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 8.68026i | − 0.0102001i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −151.949 | −0.178134 | −0.0890672 | − | 0.996026i | \(-0.528389\pi\) | ||||
−0.0890672 | + | 0.996026i | \(0.528389\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | 159.993i | 0.186255i | 0.995654 | + | 0.0931274i | \(0.0296864\pi\) | ||||
−0.995654 | + | 0.0931274i | \(0.970314\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 878.280 | 1.02007 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | − 1261.33i | − 1.45482i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −195.479 | −0.224947 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 75.1590i | − 0.0862905i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −228.330 | −0.261547 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 177.668i | 0.203049i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 825.096 | 0.940817 | 0.470408 | − | 0.882449i | \(-0.344107\pi\) | ||||
0.470408 | + | 0.882449i | \(0.344107\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 1013.40i | 1.14768i | 0.818969 | + | 0.573838i | \(0.194546\pi\) | ||||
−0.818969 | + | 0.573838i | \(0.805454\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3431.10 | 3.87695 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 870.974i | 0.977524i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −105.260 | −0.117873 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 707.322i | 0.790304i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 540.686 | 0.602772 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 267.741i | 0.297821i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 376.890 | 0.418302 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 488.392i | 0.540854i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 382.008 | 0.422109 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 203.590i | − 0.224465i | −0.993682 | − | 0.112233i | \(-0.964200\pi\) | ||||
0.993682 | − | 0.112233i | \(-0.0358002\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1244.85 | −1.36947 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | − 1432.97i | − 1.56609i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −141.101 | −0.153872 | ||||||||
\(918\) | 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 | ||||||||
\(923\) | − 55.8929i | − 0.0605557i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.89516 | 0.00312990 | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 19.4346i | 0.0208750i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2790.36 | 2.99074 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 2905.55i | 3.09430i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −543.324 | −0.577390 | −0.288695 | − | 0.957421i | \(-0.593221\pi\) | ||||
−0.288695 | + | 0.957421i | \(0.593221\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2722.03i | 2.88656i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −804.425 | −0.851243 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 359.728i | 0.379861i | 0.981798 | + | 0.189930i | \(0.0608262\pi\) | ||||
−0.981798 | + | 0.189930i | \(0.939174\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 167.290 | 0.176281 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 2023.94i | − 2.12823i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 904.225 | 0.948820 | 0.474410 | − | 0.880304i | \(-0.342661\pi\) | ||||
0.474410 | + | 0.880304i | \(0.342661\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1118.56i | 1.17127i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1913.37 | 1.99934 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 152.707i | 0.159236i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 909.615 | 0.946529 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 2484.52i | − 2.57998i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1388.89 | −1.43926 | ||||||||
\(966\) | 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 | ||||||||
\(971\) | 1327.31i | 1.36695i | 0.729973 | + | 0.683476i | \(0.239532\pi\) | ||||
−0.729973 | + | 0.683476i | \(0.760468\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 456.186 | 0.468845 | ||||||||
\(974\) | 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 | ||||||||
\(979\) | 176.415i | 0.180199i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −813.706 | −0.829466 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 523.972i | 0.530874i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1513.66 | −1.53049 | ||||||||
\(990\) | 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 | ||||||||
\(995\) | − 1861.85i | − 1.87121i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −206.085 | −0.206705 | −0.103353 | − | 0.994645i | \(-0.532957\pi\) | ||||
−0.103353 | + | 0.994645i | \(0.532957\pi\) | |||||||
\(998\) | 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 | 1792.3.d.j.1023.15 | 16 | ||
4.3 | odd | 2 | inner | 1792.3.d.j.1023.1 | 16 | ||
8.3 | odd | 2 | inner | 1792.3.d.j.1023.16 | 16 | ||
8.5 | even | 2 | inner | 1792.3.d.j.1023.2 | 16 | ||
16.3 | odd | 4 | 224.3.g.b.15.8 | 8 | |||
16.5 | even | 4 | 224.3.g.b.15.7 | 8 | |||
16.11 | odd | 4 | 56.3.g.b.43.5 | ✓ | 8 | ||
16.13 | even | 4 | 56.3.g.b.43.6 | yes | 8 | ||
48.5 | odd | 4 | 2016.3.g.b.1135.8 | 8 | |||
48.11 | even | 4 | 504.3.g.b.379.4 | 8 | |||
48.29 | odd | 4 | 504.3.g.b.379.3 | 8 | |||
48.35 | even | 4 | 2016.3.g.b.1135.1 | 8 | |||
112.11 | odd | 12 | 392.3.k.o.275.6 | 16 | |||
112.13 | odd | 4 | 392.3.g.m.99.6 | 8 | |||
112.27 | even | 4 | 392.3.g.m.99.5 | 8 | |||
112.45 | odd | 12 | 392.3.k.n.275.1 | 16 | |||
112.59 | even | 12 | 392.3.k.n.275.6 | 16 | |||
112.61 | odd | 12 | 392.3.k.n.67.6 | 16 | |||
112.69 | odd | 4 | 1568.3.g.m.687.2 | 8 | |||
112.75 | even | 12 | 392.3.k.n.67.1 | 16 | |||
112.83 | even | 4 | 1568.3.g.m.687.1 | 8 | |||
112.93 | even | 12 | 392.3.k.o.67.6 | 16 | |||
112.107 | odd | 12 | 392.3.k.o.67.1 | 16 | |||
112.109 | even | 12 | 392.3.k.o.275.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.5 | ✓ | 8 | 16.11 | odd | 4 | ||
56.3.g.b.43.6 | yes | 8 | 16.13 | even | 4 | ||
224.3.g.b.15.7 | 8 | 16.5 | even | 4 | |||
224.3.g.b.15.8 | 8 | 16.3 | odd | 4 | |||
392.3.g.m.99.5 | 8 | 112.27 | even | 4 | |||
392.3.g.m.99.6 | 8 | 112.13 | odd | 4 | |||
392.3.k.n.67.1 | 16 | 112.75 | even | 12 | |||
392.3.k.n.67.6 | 16 | 112.61 | odd | 12 | |||
392.3.k.n.275.1 | 16 | 112.45 | odd | 12 | |||
392.3.k.n.275.6 | 16 | 112.59 | even | 12 | |||
392.3.k.o.67.1 | 16 | 112.107 | odd | 12 | |||
392.3.k.o.67.6 | 16 | 112.93 | even | 12 | |||
392.3.k.o.275.1 | 16 | 112.109 | even | 12 | |||
392.3.k.o.275.6 | 16 | 112.11 | odd | 12 | |||
504.3.g.b.379.3 | 8 | 48.29 | odd | 4 | |||
504.3.g.b.379.4 | 8 | 48.11 | even | 4 | |||
1568.3.g.m.687.1 | 8 | 112.83 | even | 4 | |||
1568.3.g.m.687.2 | 8 | 112.69 | odd | 4 | |||
1792.3.d.j.1023.1 | 16 | 4.3 | odd | 2 | inner | ||
1792.3.d.j.1023.2 | 16 | 8.5 | even | 2 | inner | ||
1792.3.d.j.1023.15 | 16 | 1.1 | even | 1 | trivial | ||
1792.3.d.j.1023.16 | 16 | 8.3 | odd | 2 | inner | ||
2016.3.g.b.1135.1 | 8 | 48.35 | even | 4 | |||
2016.3.g.b.1135.8 | 8 | 48.5 | odd | 4 |