Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [121,9,Mod(120,121)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(121, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("121.120");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 121 = 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 121.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(49.2928118174\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 11) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 120.17 | ||
Character | \(\chi\) | \(=\) | 121.120 |
Dual form | 121.9.b.b.120.12 |
$q$-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 \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.02107i | 0.438817i | 0.975633 | + | 0.219409i | \(0.0704127\pi\) | ||||
−0.975633 | + | 0.219409i | \(0.929587\pi\) | |||||||
\(3\) | 77.6168 | 0.958232 | 0.479116 | − | 0.877752i | \(-0.340957\pi\) | ||||
0.479116 | + | 0.877752i | \(0.340957\pi\) | |||||||
\(4\) | 206.705 | 0.807440 | ||||||||
\(5\) | −703.179 | −1.12509 | −0.562543 | − | 0.826768i | \(-0.690177\pi\) | ||||
−0.562543 | + | 0.826768i | \(0.690177\pi\) | |||||||
\(6\) | 544.953i | 0.420488i | ||||||||
\(7\) | − 1344.96i | − 0.560165i | −0.959976 | − | 0.280082i | \(-0.909638\pi\) | ||||
0.959976 | − | 0.280082i | \(-0.0903618\pi\) | |||||||
\(8\) | 3248.68i | 0.793135i | ||||||||
\(9\) | −536.638 | −0.0817921 | ||||||||
\(10\) | − 4937.07i | − 0.493707i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 16043.7 | 0.773714 | ||||||||
\(13\) | 19362.2i | 0.677926i | 0.940800 | + | 0.338963i | \(0.110076\pi\) | ||||
−0.940800 | + | 0.338963i | \(0.889924\pi\) | |||||||
\(14\) | 9443.03 | 0.245810 | ||||||||
\(15\) | −54578.5 | −1.07809 | ||||||||
\(16\) | 30107.1 | 0.459398 | ||||||||
\(17\) | − 68446.7i | − 0.819514i | −0.912195 | − | 0.409757i | \(-0.865613\pi\) | ||||
0.912195 | − | 0.409757i | \(-0.134387\pi\) | |||||||
\(18\) | − 3767.78i | − 0.0358918i | ||||||||
\(19\) | 199054.i | 1.52742i | 0.645562 | + | 0.763708i | \(0.276623\pi\) | ||||
−0.645562 | + | 0.763708i | \(0.723377\pi\) | |||||||
\(20\) | −145350. | −0.908440 | ||||||||
\(21\) | − 104391.i | − 0.536767i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −350509. | −1.25253 | −0.626265 | − | 0.779610i | \(-0.715417\pi\) | ||||
−0.626265 | + | 0.779610i | \(0.715417\pi\) | |||||||
\(24\) | 252152.i | 0.760007i | ||||||||
\(25\) | 103836. | 0.265820 | ||||||||
\(26\) | −135944. | −0.297485 | ||||||||
\(27\) | −550896. | −1.03661 | ||||||||
\(28\) | − 278008.i | − 0.452299i | ||||||||
\(29\) | 382400.i | 0.540662i | 0.962767 | + | 0.270331i | \(0.0871332\pi\) | ||||
−0.962767 | + | 0.270331i | \(0.912867\pi\) | |||||||
\(30\) | − 383200.i | − 0.473086i | ||||||||
\(31\) | −1.01139e6 | −1.09515 | −0.547575 | − | 0.836756i | \(-0.684449\pi\) | ||||
−0.547575 | + | 0.836756i | \(0.684449\pi\) | |||||||
\(32\) | 1.04305e6i | 0.994727i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 480569. | 0.359617 | ||||||||
\(35\) | 945744.i | 0.630234i | ||||||||
\(36\) | −110926. | −0.0660422 | ||||||||
\(37\) | 384405. | 0.205108 | 0.102554 | − | 0.994727i | \(-0.467299\pi\) | ||||
0.102554 | + | 0.994727i | \(0.467299\pi\) | |||||||
\(38\) | −1.39758e6 | −0.670256 | ||||||||
\(39\) | 1.50283e6i | 0.649610i | ||||||||
\(40\) | − 2.28441e6i | − 0.892346i | ||||||||
\(41\) | 3.18937e6i | 1.12868i | 0.825543 | + | 0.564339i | \(0.190869\pi\) | ||||
−0.825543 | + | 0.564339i | \(0.809131\pi\) | |||||||
\(42\) | 732937. | 0.235543 | ||||||||
\(43\) | − 823502.i | − 0.240875i | −0.992721 | − | 0.120437i | \(-0.961570\pi\) | ||||
0.992721 | − | 0.120437i | \(-0.0384297\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 377353. | 0.0920233 | ||||||||
\(46\) | − 2.46095e6i | − 0.549632i | ||||||||
\(47\) | −507245. | −0.103951 | −0.0519753 | − | 0.998648i | \(-0.516552\pi\) | ||||
−0.0519753 | + | 0.998648i | \(0.516552\pi\) | |||||||
\(48\) | 2.33682e6 | 0.440210 | ||||||||
\(49\) | 3.95590e6 | 0.686216 | ||||||||
\(50\) | 729040.i | 0.116646i | ||||||||
\(51\) | − 5.31261e6i | − 0.785285i | ||||||||
\(52\) | 4.00226e6i | 0.547384i | ||||||||
\(53\) | 7.24871e6 | 0.918666 | 0.459333 | − | 0.888264i | \(-0.348089\pi\) | ||||
0.459333 | + | 0.888264i | \(0.348089\pi\) | |||||||
\(54\) | − 3.86788e6i | − 0.454881i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.36933e6 | 0.444286 | ||||||||
\(57\) | 1.54500e7i | 1.46362i | ||||||||
\(58\) | −2.68486e6 | −0.237252 | ||||||||
\(59\) | −1.94016e7 | −1.60114 | −0.800569 | − | 0.599240i | \(-0.795469\pi\) | ||||
−0.800569 | + | 0.599240i | \(0.795469\pi\) | |||||||
\(60\) | −1.12816e7 | −0.870496 | ||||||||
\(61\) | 2.29541e7i | 1.65783i | 0.559373 | + | 0.828916i | \(0.311042\pi\) | ||||
−0.559373 | + | 0.828916i | \(0.688958\pi\) | |||||||
\(62\) | − 7.10108e6i | − 0.480571i | ||||||||
\(63\) | 721754.i | 0.0458171i | ||||||||
\(64\) | 384118. | 0.0228952 | ||||||||
\(65\) | − 1.36151e7i | − 0.762725i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.55334e7 | −1.76335 | −0.881673 | − | 0.471861i | \(-0.843583\pi\) | ||||
−0.881673 | + | 0.471861i | \(0.843583\pi\) | |||||||
\(68\) | − 1.41482e7i | − 0.661708i | ||||||||
\(69\) | −2.72054e7 | −1.20021 | ||||||||
\(70\) | −6.64014e6 | −0.276557 | ||||||||
\(71\) | −3.06113e7 | −1.20462 | −0.602309 | − | 0.798263i | \(-0.705752\pi\) | ||||
−0.602309 | + | 0.798263i | \(0.705752\pi\) | |||||||
\(72\) | − 1.74337e6i | − 0.0648722i | ||||||||
\(73\) | − 4.83861e7i | − 1.70384i | −0.523672 | − | 0.851920i | \(-0.675438\pi\) | ||||
0.523672 | − | 0.851920i | \(-0.324562\pi\) | |||||||
\(74\) | 2.69893e6i | 0.0900047i | ||||||||
\(75\) | 8.05941e6 | 0.254717 | ||||||||
\(76\) | 4.11455e7i | 1.23330i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.05515e7 | −0.285060 | ||||||||
\(79\) | 4.42610e7i | 1.13635i | 0.822907 | + | 0.568177i | \(0.192351\pi\) | ||||
−0.822907 | + | 0.568177i | \(0.807649\pi\) | |||||||
\(80\) | −2.11707e7 | −0.516863 | ||||||||
\(81\) | −3.92379e7 | −0.911518 | ||||||||
\(82\) | −2.23928e7 | −0.495283 | ||||||||
\(83\) | − 3.91863e7i | − 0.825699i | −0.910799 | − | 0.412849i | \(-0.864534\pi\) | ||||
0.910799 | − | 0.412849i | \(-0.135466\pi\) | |||||||
\(84\) | − 2.15781e7i | − 0.433407i | ||||||||
\(85\) | 4.81303e7i | 0.922025i | ||||||||
\(86\) | 5.78187e6 | 0.105700 | ||||||||
\(87\) | 2.96807e7i | 0.518080i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.40233e7 | −0.382888 | −0.191444 | − | 0.981503i | \(-0.561317\pi\) | ||||
−0.191444 | + | 0.981503i | \(0.561317\pi\) | |||||||
\(90\) | 2.64942e6i | 0.0403814i | ||||||||
\(91\) | 2.60413e7 | 0.379750 | ||||||||
\(92\) | −7.24519e7 | −1.01134 | ||||||||
\(93\) | −7.85012e7 | −1.04941 | ||||||||
\(94\) | − 3.56141e6i | − 0.0456153i | ||||||||
\(95\) | − 1.39971e8i | − 1.71848i | ||||||||
\(96\) | 8.09579e7i | 0.953179i | ||||||||
\(97\) | 1.22884e8 | 1.38806 | 0.694028 | − | 0.719948i | \(-0.255834\pi\) | ||||
0.694028 | + | 0.719948i | \(0.255834\pi\) | |||||||
\(98\) | 2.77746e7i | 0.301123i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.14634e7 | 0.214634 | ||||||||
\(101\) | 1.81445e6i | 0.0174365i | 0.999962 | + | 0.00871825i | \(0.00277514\pi\) | ||||
−0.999962 | + | 0.00871825i | \(0.997225\pi\) | |||||||
\(102\) | 3.73002e7 | 0.344596 | ||||||||
\(103\) | 6.36632e7 | 0.565640 | 0.282820 | − | 0.959173i | \(-0.408730\pi\) | ||||
0.282820 | + | 0.959173i | \(0.408730\pi\) | |||||||
\(104\) | −6.29018e7 | −0.537687 | ||||||||
\(105\) | 7.34056e7i | 0.603910i | ||||||||
\(106\) | 5.08937e7i | 0.403126i | ||||||||
\(107\) | − 2.33770e7i | − 0.178342i | −0.996016 | − | 0.0891710i | \(-0.971578\pi\) | ||||
0.996016 | − | 0.0891710i | \(-0.0284217\pi\) | |||||||
\(108\) | −1.13873e8 | −0.836998 | ||||||||
\(109\) | − 1.51242e8i | − 1.07144i | −0.844396 | − | 0.535719i | \(-0.820041\pi\) | ||||
0.844396 | − | 0.535719i | \(-0.179959\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.98362e7 | 0.196541 | ||||||||
\(112\) | − 4.04927e7i | − 0.257339i | ||||||||
\(113\) | −1.30764e8 | −0.802003 | −0.401001 | − | 0.916077i | \(-0.631338\pi\) | ||||
−0.401001 | + | 0.916077i | \(0.631338\pi\) | |||||||
\(114\) | −1.08475e8 | −0.642261 | ||||||||
\(115\) | 2.46471e8 | 1.40921 | ||||||||
\(116\) | 7.90439e7i | 0.436552i | ||||||||
\(117\) | − 1.03905e7i | − 0.0554490i | ||||||||
\(118\) | − 1.36220e8i | − 0.702607i | ||||||||
\(119\) | −9.20577e7 | −0.459063 | ||||||||
\(120\) | − 1.77308e8i | − 0.855074i | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.61162e8 | −0.727485 | ||||||||
\(123\) | 2.47549e8i | 1.08153i | ||||||||
\(124\) | −2.09060e8 | −0.884268 | ||||||||
\(125\) | 2.01664e8 | 0.826016 | ||||||||
\(126\) | −5.06749e6 | −0.0201053 | ||||||||
\(127\) | 3.35006e8i | 1.28777i | 0.765123 | + | 0.643884i | \(0.222678\pi\) | ||||
−0.765123 | + | 0.643884i | \(0.777322\pi\) | |||||||
\(128\) | 2.69717e8i | 1.00477i | ||||||||
\(129\) | − 6.39176e7i | − 0.230814i | ||||||||
\(130\) | 9.55928e7 | 0.334697 | ||||||||
\(131\) | 3.32594e8i | 1.12935i | 0.825312 | + | 0.564677i | \(0.190999\pi\) | ||||
−0.825312 | + | 0.564677i | \(0.809001\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.67719e8 | 0.855604 | ||||||||
\(134\) | − 2.49483e8i | − 0.773786i | ||||||||
\(135\) | 3.87378e8 | 1.16627 | ||||||||
\(136\) | 2.22361e8 | 0.649986 | ||||||||
\(137\) | 7.71773e7 | 0.219082 | 0.109541 | − | 0.993982i | \(-0.465062\pi\) | ||||
0.109541 | + | 0.993982i | \(0.465062\pi\) | |||||||
\(138\) | − 1.91011e8i | − 0.526675i | ||||||||
\(139\) | 2.97102e8i | 0.795878i | 0.917412 | + | 0.397939i | \(0.130274\pi\) | ||||
−0.917412 | + | 0.397939i | \(0.869726\pi\) | |||||||
\(140\) | 1.95490e8i | 0.508876i | ||||||||
\(141\) | −3.93708e7 | −0.0996087 | ||||||||
\(142\) | − 2.14924e8i | − 0.528607i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.61566e7 | −0.0375752 | ||||||||
\(145\) | − 2.68896e8i | − 0.608292i | ||||||||
\(146\) | 3.39722e8 | 0.747674 | ||||||||
\(147\) | 3.07044e8 | 0.657554 | ||||||||
\(148\) | 7.94582e7 | 0.165612 | ||||||||
\(149\) | − 8.04396e8i | − 1.63202i | −0.578039 | − | 0.816009i | \(-0.696182\pi\) | ||||
0.578039 | − | 0.816009i | \(-0.303818\pi\) | |||||||
\(150\) | 5.65857e7i | 0.111774i | ||||||||
\(151\) | − 2.47501e8i | − 0.476069i | −0.971257 | − | 0.238034i | \(-0.923497\pi\) | ||||
0.971257 | − | 0.238034i | \(-0.0765031\pi\) | |||||||
\(152\) | −6.46664e8 | −1.21145 | ||||||||
\(153\) | 3.67311e7i | 0.0670298i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.11192e8 | 1.23214 | ||||||||
\(156\) | 3.10643e8i | 0.524521i | ||||||||
\(157\) | 3.50938e8 | 0.577606 | 0.288803 | − | 0.957389i | \(-0.406743\pi\) | ||||
0.288803 | + | 0.957389i | \(0.406743\pi\) | |||||||
\(158\) | −3.10760e8 | −0.498651 | ||||||||
\(159\) | 5.62622e8 | 0.880294 | ||||||||
\(160\) | − 7.33449e8i | − 1.11915i | ||||||||
\(161\) | 4.71420e8i | 0.701623i | ||||||||
\(162\) | − 2.75492e8i | − 0.399990i | ||||||||
\(163\) | 4.07923e8 | 0.577867 | 0.288934 | − | 0.957349i | \(-0.406699\pi\) | ||||
0.288934 | + | 0.957349i | \(0.406699\pi\) | |||||||
\(164\) | 6.59258e8i | 0.911339i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.75130e8 | 0.362331 | ||||||||
\(167\) | − 1.07018e9i | − 1.37591i | −0.725754 | − | 0.687955i | \(-0.758509\pi\) | ||||
0.725754 | − | 0.687955i | \(-0.241491\pi\) | |||||||
\(168\) | 3.39133e8 | 0.425729 | ||||||||
\(169\) | 4.40834e8 | 0.540416 | ||||||||
\(170\) | −3.37926e8 | −0.404600 | ||||||||
\(171\) | − 1.06820e8i | − 0.124931i | ||||||||
\(172\) | − 1.70222e8i | − 0.194492i | ||||||||
\(173\) | − 4.59404e7i | − 0.0512873i | −0.999671 | − | 0.0256437i | \(-0.991836\pi\) | ||||
0.999671 | − | 0.0256437i | \(-0.00816352\pi\) | |||||||
\(174\) | −2.08390e8 | −0.227342 | ||||||||
\(175\) | − 1.39655e8i | − 0.148903i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.50589e9 | −1.53426 | ||||||||
\(178\) | − 1.68669e8i | − 0.168018i | ||||||||
\(179\) | −1.02935e9 | −1.00265 | −0.501326 | − | 0.865258i | \(-0.667154\pi\) | ||||
−0.501326 | + | 0.865258i | \(0.667154\pi\) | |||||||
\(180\) | 7.80005e7 | 0.0743032 | ||||||||
\(181\) | 8.18745e8 | 0.762842 | 0.381421 | − | 0.924402i | \(-0.375435\pi\) | ||||
0.381421 | + | 0.924402i | \(0.375435\pi\) | |||||||
\(182\) | 1.82838e8i | 0.166641i | ||||||||
\(183\) | 1.78162e9i | 1.58859i | ||||||||
\(184\) | − 1.13869e9i | − 0.993426i | ||||||||
\(185\) | −2.70305e8 | −0.230764 | ||||||||
\(186\) | − 5.51162e8i | − 0.460498i | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.04850e8 | −0.0839338 | ||||||||
\(189\) | 7.40930e8i | 0.580671i | ||||||||
\(190\) | 9.82746e8 | 0.754096 | ||||||||
\(191\) | 6.67535e8 | 0.501581 | 0.250790 | − | 0.968041i | \(-0.419310\pi\) | ||||
0.250790 | + | 0.968041i | \(0.419310\pi\) | |||||||
\(192\) | 2.98140e7 | 0.0219389 | ||||||||
\(193\) | 2.20519e9i | 1.58934i | 0.607040 | + | 0.794671i | \(0.292357\pi\) | ||||
−0.607040 | + | 0.794671i | \(0.707643\pi\) | |||||||
\(194\) | 8.62775e8i | 0.609103i | ||||||||
\(195\) | − 1.05676e9i | − 0.730868i | ||||||||
\(196\) | 8.17702e8 | 0.554078 | ||||||||
\(197\) | − 2.23782e8i | − 0.148580i | −0.997237 | − | 0.0742899i | \(-0.976331\pi\) | ||||
0.997237 | − | 0.0742899i | \(-0.0236690\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.49591e9 | 0.953880 | 0.476940 | − | 0.878936i | \(-0.341746\pi\) | ||||
0.476940 | + | 0.878936i | \(0.341746\pi\) | |||||||
\(200\) | 3.37330e8i | 0.210831i | ||||||||
\(201\) | −2.75799e9 | −1.68969 | ||||||||
\(202\) | −1.27394e7 | −0.00765143 | ||||||||
\(203\) | 5.14311e8 | 0.302860 | ||||||||
\(204\) | − 1.09814e9i | − 0.634070i | ||||||||
\(205\) | − 2.24270e9i | − 1.26986i | ||||||||
\(206\) | 4.46984e8i | 0.248212i | ||||||||
\(207\) | 1.88097e8 | 0.102447 | ||||||||
\(208\) | 5.82942e8i | 0.311438i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −5.15386e8 | −0.265006 | ||||||||
\(211\) | − 1.54592e9i | − 0.779933i | −0.920829 | − | 0.389966i | \(-0.872487\pi\) | ||||
0.920829 | − | 0.389966i | \(-0.127513\pi\) | |||||||
\(212\) | 1.49834e9 | 0.741767 | ||||||||
\(213\) | −2.37595e9 | −1.15430 | ||||||||
\(214\) | 1.64132e8 | 0.0782595 | ||||||||
\(215\) | 5.79070e8i | 0.271005i | ||||||||
\(216\) | − 1.78968e9i | − 0.822170i | ||||||||
\(217\) | 1.36028e9i | 0.613465i | ||||||||
\(218\) | 1.06188e9 | 0.470165 | ||||||||
\(219\) | − 3.75557e9i | − 1.63267i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.32528e9 | 0.555570 | ||||||||
\(222\) | 2.09482e8i | 0.0862454i | ||||||||
\(223\) | 1.96463e9 | 0.794440 | 0.397220 | − | 0.917723i | \(-0.369975\pi\) | ||||
0.397220 | + | 0.917723i | \(0.369975\pi\) | |||||||
\(224\) | 1.40285e9 | 0.557211 | ||||||||
\(225\) | −5.57224e7 | −0.0217420 | ||||||||
\(226\) | − 9.18106e8i | − 0.351932i | ||||||||
\(227\) | − 6.58101e8i | − 0.247850i | −0.992292 | − | 0.123925i | \(-0.960452\pi\) | ||||
0.992292 | − | 0.123925i | \(-0.0395482\pi\) | |||||||
\(228\) | 3.19358e9i | 1.18178i | ||||||||
\(229\) | 1.18612e8 | 0.0431306 | 0.0215653 | − | 0.999767i | \(-0.493135\pi\) | ||||
0.0215653 | + | 0.999767i | \(0.493135\pi\) | |||||||
\(230\) | 1.73049e9i | 0.618383i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.24230e9 | −0.428818 | ||||||||
\(233\) | − 1.88981e7i | − 0.00641203i | −0.999995 | − | 0.00320601i | \(-0.998979\pi\) | ||||
0.999995 | − | 0.00320601i | \(-0.00102051\pi\) | |||||||
\(234\) | 7.29526e7 | 0.0243320 | ||||||||
\(235\) | 3.56684e8 | 0.116953 | ||||||||
\(236\) | −4.01039e9 | −1.29282 | ||||||||
\(237\) | 3.43540e9i | 1.08889i | ||||||||
\(238\) | − 6.46344e8i | − 0.201445i | ||||||||
\(239\) | 1.34719e9i | 0.412894i | 0.978458 | + | 0.206447i | \(0.0661900\pi\) | ||||
−0.978458 | + | 0.206447i | \(0.933810\pi\) | |||||||
\(240\) | −1.64320e9 | −0.495274 | ||||||||
\(241\) | 5.25935e9i | 1.55906i | 0.626363 | + | 0.779531i | \(0.284543\pi\) | ||||
−0.626363 | + | 0.779531i | \(0.715457\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.68911e8 | 0.163162 | ||||||||
\(244\) | 4.74471e9i | 1.33860i | ||||||||
\(245\) | −2.78170e9 | −0.772052 | ||||||||
\(246\) | −1.73806e9 | −0.474596 | ||||||||
\(247\) | −3.85414e9 | −1.03548 | ||||||||
\(248\) | − 3.28570e9i | − 0.868603i | ||||||||
\(249\) | − 3.04151e9i | − 0.791211i | ||||||||
\(250\) | 1.41590e9i | 0.362470i | ||||||||
\(251\) | 5.98408e7 | 0.0150766 | 0.00753828 | − | 0.999972i | \(-0.497600\pi\) | ||||
0.00753828 | + | 0.999972i | \(0.497600\pi\) | |||||||
\(252\) | 1.49190e8i | 0.0369945i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.35210e9 | −0.565095 | ||||||||
\(255\) | 3.73572e9i | 0.883513i | ||||||||
\(256\) | −1.79537e9 | −0.418017 | ||||||||
\(257\) | −1.20842e9 | −0.277004 | −0.138502 | − | 0.990362i | \(-0.544229\pi\) | ||||
−0.138502 | + | 0.990362i | \(0.544229\pi\) | |||||||
\(258\) | 4.48770e8 | 0.101285 | ||||||||
\(259\) | − 5.17007e8i | − 0.114894i | ||||||||
\(260\) | − 2.81431e9i | − 0.615855i | ||||||||
\(261\) | − 2.05211e8i | − 0.0442219i | ||||||||
\(262\) | −2.33517e9 | −0.495580 | ||||||||
\(263\) | − 4.22692e8i | − 0.0883490i | −0.999024 | − | 0.0441745i | \(-0.985934\pi\) | ||||
0.999024 | − | 0.0441745i | \(-0.0140658\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.09714e9 | −1.03358 | ||||||||
\(266\) | 1.87968e9i | 0.375454i | ||||||||
\(267\) | −1.86461e9 | −0.366896 | ||||||||
\(268\) | −7.34492e9 | −1.42380 | ||||||||
\(269\) | −4.44912e9 | −0.849700 | −0.424850 | − | 0.905264i | \(-0.639673\pi\) | ||||
−0.424850 | + | 0.905264i | \(0.639673\pi\) | |||||||
\(270\) | 2.71981e9i | 0.511781i | ||||||||
\(271\) | 1.41774e9i | 0.262857i | 0.991326 | + | 0.131428i | \(0.0419563\pi\) | ||||
−0.991326 | + | 0.131428i | \(0.958044\pi\) | |||||||
\(272\) | − 2.06073e9i | − 0.376484i | ||||||||
\(273\) | 2.02124e9 | 0.363889 | ||||||||
\(274\) | 5.41868e8i | 0.0961371i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.62348e9 | −0.969101 | ||||||||
\(277\) | − 3.39043e9i | − 0.575885i | −0.957648 | − | 0.287943i | \(-0.907029\pi\) | ||||
0.957648 | − | 0.287943i | \(-0.0929713\pi\) | |||||||
\(278\) | −2.08597e9 | −0.349245 | ||||||||
\(279\) | 5.42753e8 | 0.0895747 | ||||||||
\(280\) | −3.07242e9 | −0.499861 | ||||||||
\(281\) | 9.12882e9i | 1.46416i | 0.681217 | + | 0.732081i | \(0.261451\pi\) | ||||
−0.681217 | + | 0.732081i | \(0.738549\pi\) | |||||||
\(282\) | − 2.76425e8i | − 0.0437100i | ||||||||
\(283\) | 6.49110e9i | 1.01198i | 0.862539 | + | 0.505991i | \(0.168873\pi\) | ||||
−0.862539 | + | 0.505991i | \(0.831127\pi\) | |||||||
\(284\) | −6.32750e9 | −0.972656 | ||||||||
\(285\) | − 1.08641e10i | − 1.64670i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.28956e9 | 0.632245 | ||||||||
\(288\) | − 5.59739e8i | − 0.0813609i | ||||||||
\(289\) | 2.29081e9 | 0.328396 | ||||||||
\(290\) | 1.88794e9 | 0.266929 | ||||||||
\(291\) | 9.53783e9 | 1.33008 | ||||||||
\(292\) | − 1.00016e10i | − 1.37575i | ||||||||
\(293\) | − 9.28248e9i | − 1.25949i | −0.776803 | − | 0.629743i | \(-0.783160\pi\) | ||||
0.776803 | − | 0.629743i | \(-0.216840\pi\) | |||||||
\(294\) | 2.15578e9i | 0.288546i | ||||||||
\(295\) | 1.36428e10 | 1.80142 | ||||||||
\(296\) | 1.24881e9i | 0.162678i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.64773e9 | 0.716157 | ||||||||
\(299\) | − 6.78665e9i | − 0.849123i | ||||||||
\(300\) | 1.66592e9 | 0.205669 | ||||||||
\(301\) | −1.10757e9 | −0.134929 | ||||||||
\(302\) | 1.73772e9 | 0.208907 | ||||||||
\(303\) | 1.40832e8i | 0.0167082i | ||||||||
\(304\) | 5.99296e9i | 0.701693i | ||||||||
\(305\) | − 1.61408e10i | − 1.86520i | ||||||||
\(306\) | −2.57892e8 | −0.0294138 | ||||||||
\(307\) | 3.17364e9i | 0.357276i | 0.983915 | + | 0.178638i | \(0.0571691\pi\) | ||||
−0.983915 | + | 0.178638i | \(0.942831\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.94133e9 | 0.542014 | ||||||||
\(310\) | 4.99333e9i | 0.540684i | ||||||||
\(311\) | 1.86968e9 | 0.199859 | 0.0999297 | − | 0.994994i | \(-0.468138\pi\) | ||||
0.0999297 | + | 0.994994i | \(0.468138\pi\) | |||||||
\(312\) | −4.88223e9 | −0.515229 | ||||||||
\(313\) | 1.75095e9 | 0.182430 | 0.0912152 | − | 0.995831i | \(-0.470925\pi\) | ||||
0.0912152 | + | 0.995831i | \(0.470925\pi\) | |||||||
\(314\) | 2.46396e9i | 0.253463i | ||||||||
\(315\) | − 5.07523e8i | − 0.0515482i | ||||||||
\(316\) | 9.14896e9i | 0.917537i | ||||||||
\(317\) | 1.68758e10 | 1.67119 | 0.835596 | − | 0.549344i | \(-0.185122\pi\) | ||||
0.835596 | + | 0.549344i | \(0.185122\pi\) | |||||||
\(318\) | 3.95021e9i | 0.386288i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.70104e8 | −0.0257591 | ||||||||
\(321\) | − 1.81445e9i | − 0.170893i | ||||||||
\(322\) | −3.30987e9 | −0.307884 | ||||||||
\(323\) | 1.36246e10 | 1.25174 | ||||||||
\(324\) | −8.11064e9 | −0.735996 | ||||||||
\(325\) | 2.01050e9i | 0.180206i | ||||||||
\(326\) | 2.86406e9i | 0.253578i | ||||||||
\(327\) | − 1.17389e10i | − 1.02669i | ||||||||
\(328\) | −1.03613e10 | −0.895194 | ||||||||
\(329\) | 6.82222e8i | 0.0582294i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.80681e9 | 0.317138 | 0.158569 | − | 0.987348i | \(-0.449312\pi\) | ||||
0.158569 | + | 0.987348i | \(0.449312\pi\) | |||||||
\(332\) | − 8.09998e9i | − 0.666702i | ||||||||
\(333\) | −2.06286e8 | −0.0167762 | ||||||||
\(334\) | 7.51379e9 | 0.603773 | ||||||||
\(335\) | 2.49863e10 | 1.98392 | ||||||||
\(336\) | − 3.14292e9i | − 0.246590i | ||||||||
\(337\) | 1.61926e10i | 1.25544i | 0.778439 | + | 0.627720i | \(0.216012\pi\) | ||||
−0.778439 | + | 0.627720i | \(0.783988\pi\) | |||||||
\(338\) | 3.09513e9i | 0.237144i | ||||||||
\(339\) | −1.01495e10 | −0.768504 | ||||||||
\(340\) | 9.94874e9i | 0.744479i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.49992e8 | 0.0548217 | ||||||||
\(343\) | − 1.30739e10i | − 0.944558i | ||||||||
\(344\) | 2.67530e9 | 0.191046 | ||||||||
\(345\) | 1.91303e10 | 1.35035 | ||||||||
\(346\) | 3.22551e8 | 0.0225057 | ||||||||
\(347\) | − 5.67555e9i | − 0.391462i | −0.980658 | − | 0.195731i | \(-0.937292\pi\) | ||||
0.980658 | − | 0.195731i | \(-0.0627080\pi\) | |||||||
\(348\) | 6.13513e9i | 0.418318i | ||||||||
\(349\) | − 1.48337e10i | − 0.999880i | −0.866060 | − | 0.499940i | \(-0.833355\pi\) | ||||
0.866060 | − | 0.499940i | \(-0.166645\pi\) | |||||||
\(350\) | 9.80526e8 | 0.0653412 | ||||||||
\(351\) | − 1.06666e10i | − 0.702743i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.89071e9 | −0.636984 | −0.318492 | − | 0.947926i | \(-0.603176\pi\) | ||||
−0.318492 | + | 0.947926i | \(0.603176\pi\) | |||||||
\(354\) | − 1.05729e10i | − 0.673260i | ||||||||
\(355\) | 2.15253e10 | 1.35530 | ||||||||
\(356\) | −4.96572e9 | −0.309159 | ||||||||
\(357\) | −7.14522e9 | −0.439889 | ||||||||
\(358\) | − 7.22714e9i | − 0.439981i | ||||||||
\(359\) | 1.29873e10i | 0.781881i | 0.920416 | + | 0.390940i | \(0.127850\pi\) | ||||
−0.920416 | + | 0.390940i | \(0.872150\pi\) | |||||||
\(360\) | 1.22590e9i | 0.0729869i | ||||||||
\(361\) | −2.26391e10 | −1.33300 | ||||||||
\(362\) | 5.74847e9i | 0.334748i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.38286e9 | 0.306625 | ||||||||
\(365\) | 3.40241e10i | 1.91697i | ||||||||
\(366\) | −1.25089e10 | −0.697099 | ||||||||
\(367\) | −1.78932e10 | −0.986336 | −0.493168 | − | 0.869934i | \(-0.664161\pi\) | ||||
−0.493168 | + | 0.869934i | \(0.664161\pi\) | |||||||
\(368\) | −1.05528e10 | −0.575411 | ||||||||
\(369\) | − 1.71154e9i | − 0.0923170i | ||||||||
\(370\) | − 1.89783e9i | − 0.101263i | ||||||||
\(371\) | − 9.74919e9i | − 0.514604i | ||||||||
\(372\) | −1.62266e10 | −0.847334 | ||||||||
\(373\) | − 1.91399e10i | − 0.988789i | −0.869238 | − | 0.494394i | \(-0.835390\pi\) | ||||
0.869238 | − | 0.494394i | \(-0.164610\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.56525e10 | 0.791515 | ||||||||
\(376\) | − 1.64788e9i | − 0.0824468i | ||||||||
\(377\) | −7.40413e9 | −0.366529 | ||||||||
\(378\) | −5.20212e9 | −0.254808 | ||||||||
\(379\) | 2.33972e10 | 1.13398 | 0.566992 | − | 0.823723i | \(-0.308107\pi\) | ||||
0.566992 | + | 0.823723i | \(0.308107\pi\) | |||||||
\(380\) | − 2.89326e10i | − 1.38757i | ||||||||
\(381\) | 2.60021e10i | 1.23398i | ||||||||
\(382\) | 4.68681e9i | 0.220102i | ||||||||
\(383\) | −4.28407e9 | −0.199096 | −0.0995478 | − | 0.995033i | \(-0.531740\pi\) | ||||
−0.0995478 | + | 0.995033i | \(0.531740\pi\) | |||||||
\(384\) | 2.09346e10i | 0.962806i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.54828e10 | −0.697431 | ||||||||
\(387\) | 4.41923e8i | 0.0197017i | ||||||||
\(388\) | 2.54006e10 | 1.12077 | ||||||||
\(389\) | 2.43100e10 | 1.06166 | 0.530831 | − | 0.847478i | \(-0.321880\pi\) | ||||
0.530831 | + | 0.847478i | \(0.321880\pi\) | |||||||
\(390\) | 7.41960e9 | 0.320717 | ||||||||
\(391\) | 2.39912e10i | 1.02647i | ||||||||
\(392\) | 1.28515e10i | 0.544262i | ||||||||
\(393\) | 2.58149e10i | 1.08218i | ||||||||
\(394\) | 1.57119e9 | 0.0651993 | ||||||||
\(395\) | − 3.11234e10i | − 1.27850i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.11498e9 | 0.366939 | 0.183469 | − | 0.983025i | \(-0.441267\pi\) | ||||
0.183469 | + | 0.983025i | \(0.441267\pi\) | |||||||
\(398\) | 1.05029e10i | 0.418579i | ||||||||
\(399\) | 2.07795e10 | 0.819867 | ||||||||
\(400\) | 3.12620e9 | 0.122117 | ||||||||
\(401\) | −7.76346e9 | −0.300247 | −0.150123 | − | 0.988667i | \(-0.547967\pi\) | ||||
−0.150123 | + | 0.988667i | \(0.547967\pi\) | |||||||
\(402\) | − 1.93640e10i | − 0.741467i | ||||||||
\(403\) | − 1.95829e10i | − 0.742431i | ||||||||
\(404\) | 3.75055e8i | 0.0140789i | ||||||||
\(405\) | 2.75912e10 | 1.02554 | ||||||||
\(406\) | 3.61102e9i | 0.132900i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.72590e10 | 0.622837 | ||||||||
\(409\) | − 3.88260e10i | − 1.38749i | −0.720221 | − | 0.693745i | \(-0.755959\pi\) | ||||
0.720221 | − | 0.693745i | \(-0.244041\pi\) | |||||||
\(410\) | 1.57462e10 | 0.557236 | ||||||||
\(411\) | 5.99025e9 | 0.209932 | ||||||||
\(412\) | 1.31595e10 | 0.456720 | ||||||||
\(413\) | 2.60942e10i | 0.896901i | ||||||||
\(414\) | 1.32064e9i | 0.0449556i | ||||||||
\(415\) | 2.75550e10i | 0.928983i | ||||||||
\(416\) | −2.01957e10 | −0.674351 | ||||||||
\(417\) | 2.30601e10i | 0.762635i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.41027e9 | −0.0782005 | −0.0391003 | − | 0.999235i | \(-0.512449\pi\) | ||||
−0.0391003 | + | 0.999235i | \(0.512449\pi\) | |||||||
\(420\) | 1.51733e10i | 0.487621i | ||||||||
\(421\) | −4.87583e10 | −1.55210 | −0.776051 | − | 0.630670i | \(-0.782780\pi\) | ||||
−0.776051 | + | 0.630670i | \(0.782780\pi\) | |||||||
\(422\) | 1.08540e10 | 0.342248 | ||||||||
\(423\) | 2.72207e8 | 0.00850234 | ||||||||
\(424\) | 2.35488e10i | 0.728626i | ||||||||
\(425\) | − 7.10722e9i | − 0.217843i | ||||||||
\(426\) | − 1.66817e10i | − 0.506528i | ||||||||
\(427\) | 3.08722e10 | 0.928659 | ||||||||
\(428\) | − 4.83213e9i | − 0.144000i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.06569e9 | −0.118922 | ||||||||
\(431\) | − 6.82411e9i | − 0.197759i | −0.995099 | − | 0.0988796i | \(-0.968474\pi\) | ||||
0.995099 | − | 0.0988796i | \(-0.0315259\pi\) | |||||||
\(432\) | −1.65859e10 | −0.476216 | ||||||||
\(433\) | −3.12920e10 | −0.890188 | −0.445094 | − | 0.895484i | \(-0.646830\pi\) | ||||
−0.445094 | + | 0.895484i | \(0.646830\pi\) | |||||||
\(434\) | −9.55063e9 | −0.269199 | ||||||||
\(435\) | − 2.08708e10i | − 0.582885i | ||||||||
\(436\) | − 3.12625e10i | − 0.865122i | ||||||||
\(437\) | − 6.97705e10i | − 1.91314i | ||||||||
\(438\) | 2.63681e10 | 0.716445 | ||||||||
\(439\) | − 3.21529e9i | − 0.0865689i | −0.999063 | − | 0.0432845i | \(-0.986218\pi\) | ||||
0.999063 | − | 0.0432845i | \(-0.0137822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.12289e9 | −0.0561271 | ||||||||
\(442\) | 9.30489e9i | 0.243794i | ||||||||
\(443\) | −4.82442e10 | −1.25265 | −0.626326 | − | 0.779561i | \(-0.715442\pi\) | ||||
−0.626326 | + | 0.779561i | \(0.715442\pi\) | |||||||
\(444\) | 6.16729e9 | 0.158695 | ||||||||
\(445\) | 1.68927e10 | 0.430783 | ||||||||
\(446\) | 1.37938e10i | 0.348614i | ||||||||
\(447\) | − 6.24346e10i | − 1.56385i | ||||||||
\(448\) | − 5.16621e8i | − 0.0128251i | ||||||||
\(449\) | −3.15412e10 | −0.776056 | −0.388028 | − | 0.921648i | \(-0.626844\pi\) | ||||
−0.388028 | + | 0.921648i | \(0.626844\pi\) | |||||||
\(450\) | − 3.91231e8i | − 0.00954076i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −2.70296e10 | −0.647569 | ||||||||
\(453\) | − 1.92102e10i | − 0.456184i | ||||||||
\(454\) | 4.62057e9 | 0.108761 | ||||||||
\(455\) | −1.83117e10 | −0.427252 | ||||||||
\(456\) | −5.01920e10 | −1.16085 | ||||||||
\(457\) | 5.03796e10i | 1.15502i | 0.816383 | + | 0.577510i | \(0.195976\pi\) | ||||
−0.816383 | + | 0.577510i | \(0.804024\pi\) | |||||||
\(458\) | 8.32782e8i | 0.0189265i | ||||||||
\(459\) | 3.77070e10i | 0.849515i | ||||||||
\(460\) | 5.09467e10 | 1.13785 | ||||||||
\(461\) | 5.01336e10i | 1.11001i | 0.831849 | + | 0.555003i | \(0.187283\pi\) | ||||
−0.831849 | + | 0.555003i | \(0.812717\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.36331e10 | 0.514276 | 0.257138 | − | 0.966375i | \(-0.417221\pi\) | ||||
0.257138 | + | 0.966375i | \(0.417221\pi\) | |||||||
\(464\) | 1.15130e10i | 0.248379i | ||||||||
\(465\) | 5.52004e10 | 1.18068 | ||||||||
\(466\) | 1.32685e8 | 0.00281371 | ||||||||
\(467\) | −8.22609e10 | −1.72952 | −0.864760 | − | 0.502185i | \(-0.832530\pi\) | ||||
−0.864760 | + | 0.502185i | \(0.832530\pi\) | |||||||
\(468\) | − 2.14777e9i | − 0.0447717i | ||||||||
\(469\) | 4.77908e10i | 0.987764i | ||||||||
\(470\) | 2.50431e9i | 0.0513211i | ||||||||
\(471\) | 2.72387e10 | 0.553480 | ||||||||
\(472\) | − 6.30295e10i | − 1.26992i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2.41202e10 | −0.477823 | ||||||||
\(475\) | 2.06690e10i | 0.406018i | ||||||||
\(476\) | −1.90287e10 | −0.370666 | ||||||||
\(477\) | −3.88994e9 | −0.0751396 | ||||||||
\(478\) | −9.45874e9 | −0.181185 | ||||||||
\(479\) | 6.36700e9i | 0.120946i | 0.998170 | + | 0.0604732i | \(0.0192610\pi\) | ||||
−0.998170 | + | 0.0604732i | \(0.980739\pi\) | |||||||
\(480\) | − 5.69279e10i | − 1.07241i | ||||||||
\(481\) | 7.44294e9i | 0.139048i | ||||||||
\(482\) | −3.69263e10 | −0.684143 | ||||||||
\(483\) | 3.65901e10i | 0.672318i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.64092e10 | −1.56168 | ||||||||
\(486\) | 3.99437e9i | 0.0715983i | ||||||||
\(487\) | −4.68524e10 | −0.832944 | −0.416472 | − | 0.909149i | \(-0.636734\pi\) | ||||
−0.416472 | + | 0.909149i | \(0.636734\pi\) | |||||||
\(488\) | −7.45705e10 | −1.31488 | ||||||||
\(489\) | 3.16617e10 | 0.553731 | ||||||||
\(490\) | − 1.95305e10i | − 0.338790i | ||||||||
\(491\) | − 4.92867e10i | − 0.848016i | −0.905659 | − | 0.424008i | \(-0.860623\pi\) | ||||
0.905659 | − | 0.424008i | \(-0.139377\pi\) | |||||||
\(492\) | 5.11695e10i | 0.873274i | ||||||||
\(493\) | 2.61740e10 | 0.443081 | ||||||||
\(494\) | − 2.70602e10i | − 0.454384i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.04502e10 | −0.503110 | ||||||||
\(497\) | 4.11709e10i | 0.674784i | ||||||||
\(498\) | 2.13547e10 | 0.347197 | ||||||||
\(499\) | −9.36586e10 | −1.51059 | −0.755293 | − | 0.655388i | \(-0.772505\pi\) | ||||
−0.755293 | + | 0.655388i | \(0.772505\pi\) | |||||||
\(500\) | 4.16849e10 | 0.666958 | ||||||||
\(501\) | − 8.30637e10i | − 1.31844i | ||||||||
\(502\) | 4.20147e8i | 0.00661585i | ||||||||
\(503\) | 1.16402e11i | 1.81840i | 0.416361 | + | 0.909199i | \(0.363305\pi\) | ||||
−0.416361 | + | 0.909199i | \(0.636695\pi\) | |||||||
\(504\) | −2.34475e9 | −0.0363391 | ||||||||
\(505\) | − 1.27588e9i | − 0.0196176i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.42161e10 | 0.517844 | ||||||||
\(508\) | 6.92473e10i | 1.03980i | ||||||||
\(509\) | −5.87268e10 | −0.874913 | −0.437457 | − | 0.899240i | \(-0.644121\pi\) | ||||
−0.437457 | + | 0.899240i | \(0.644121\pi\) | |||||||
\(510\) | −2.62287e10 | −0.387701 | ||||||||
\(511\) | −6.50771e10 | −0.954431 | ||||||||
\(512\) | 5.64421e10i | 0.821341i | ||||||||
\(513\) | − 1.09658e11i | − 1.58333i | ||||||||
\(514\) | − 8.48442e9i | − 0.121554i | ||||||||
\(515\) | −4.47667e10 | −0.636394 | ||||||||
\(516\) | − 1.32121e10i | − 0.186368i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.62994e9 | 0.0504174 | ||||||||
\(519\) | − 3.56574e9i | − 0.0491451i | ||||||||
\(520\) | 4.42312e10 | 0.604944 | ||||||||
\(521\) | 3.75217e10 | 0.509251 | 0.254625 | − | 0.967040i | \(-0.418048\pi\) | ||||
0.254625 | + | 0.967040i | \(0.418048\pi\) | |||||||
\(522\) | 1.44080e9 | 0.0194053 | ||||||||
\(523\) | − 7.09987e10i | − 0.948951i | −0.880269 | − | 0.474475i | \(-0.842638\pi\) | ||||
0.880269 | − | 0.474475i | \(-0.157362\pi\) | |||||||
\(524\) | 6.87488e10i | 0.911885i | ||||||||
\(525\) | − 1.08395e10i | − 0.142684i | ||||||||
\(526\) | 2.96775e9 | 0.0387690 | ||||||||
\(527\) | 6.92266e10i | 0.897492i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.45459e10 | 0.568833 | ||||||||
\(530\) | − 3.57874e10i | − 0.453552i | ||||||||
\(531\) | 1.04116e10 | 0.130961 | ||||||||
\(532\) | 5.53388e10 | 0.690849 | ||||||||
\(533\) | −6.17534e10 | −0.765160 | ||||||||
\(534\) | − 1.30916e10i | − 0.161000i | ||||||||
\(535\) | 1.64382e10i | 0.200650i | ||||||||
\(536\) | − 1.15437e11i | − 1.39857i | ||||||||
\(537\) | −7.98948e10 | −0.960774 | ||||||||
\(538\) | − 3.12376e10i | − 0.372863i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.00729e10 | 0.941695 | ||||||||
\(541\) | 1.02085e10i | 0.119172i | 0.998223 | + | 0.0595860i | \(0.0189781\pi\) | ||||
−0.998223 | + | 0.0595860i | \(0.981022\pi\) | |||||||
\(542\) | −9.95405e9 | −0.115346 | ||||||||
\(543\) | 6.35483e10 | 0.730979 | ||||||||
\(544\) | 7.13931e10 | 0.815193 | ||||||||
\(545\) | 1.06350e11i | 1.20546i | ||||||||
\(546\) | 1.41913e10i | 0.159680i | ||||||||
\(547\) | 1.07484e11i | 1.20059i | 0.799779 | + | 0.600295i | \(0.204950\pi\) | ||||
−0.799779 | + | 0.600295i | \(0.795050\pi\) | |||||||
\(548\) | 1.59529e10 | 0.176896 | ||||||||
\(549\) | − 1.23180e10i | − 0.135598i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.61185e10 | −0.825817 | ||||||||
\(552\) | − 8.83817e10i | − 0.951933i | ||||||||
\(553\) | 5.95291e10 | 0.636545 | ||||||||
\(554\) | 2.38045e10 | 0.252708 | ||||||||
\(555\) | −2.09802e10 | −0.221125 | ||||||||
\(556\) | 6.14123e10i | 0.642623i | ||||||||
\(557\) | 1.21741e11i | 1.26478i | 0.774648 | + | 0.632392i | \(0.217927\pi\) | ||||
−0.774648 | + | 0.632392i | \(0.782073\pi\) | |||||||
\(558\) | 3.81071e9i | 0.0393069i | ||||||||
\(559\) | 1.59449e10 | 0.163295 | ||||||||
\(560\) | 2.84737e10i | 0.289528i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.40941e10 | −0.642499 | ||||||||
\(563\) | 2.54979e9i | 0.0253787i | 0.999919 | + | 0.0126894i | \(0.00403926\pi\) | ||||
−0.999919 | + | 0.0126894i | \(0.995961\pi\) | |||||||
\(564\) | −8.13811e9 | −0.0804280 | ||||||||
\(565\) | 9.19508e10 | 0.902322 | ||||||||
\(566\) | −4.55745e10 | −0.444075 | ||||||||
\(567\) | 5.27732e10i | 0.510600i | ||||||||
\(568\) | − 9.94465e10i | − 0.955424i | ||||||||
\(569\) | − 2.01383e11i | − 1.92120i | −0.277928 | − | 0.960602i | \(-0.589648\pi\) | ||||
0.277928 | − | 0.960602i | \(-0.410352\pi\) | |||||||
\(570\) | 7.62776e10 | 0.722599 | ||||||||
\(571\) | − 1.60852e10i | − 0.151315i | −0.997134 | − | 0.0756575i | \(-0.975894\pi\) | ||||
0.997134 | − | 0.0756575i | \(-0.0241056\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.18119e10 | 0.480631 | ||||||||
\(574\) | 3.01173e10i | 0.277440i | ||||||||
\(575\) | −3.63955e10 | −0.332948 | ||||||||
\(576\) | −2.06132e8 | −0.00187265 | ||||||||
\(577\) | 9.97880e10 | 0.900274 | 0.450137 | − | 0.892959i | \(-0.351375\pi\) | ||||
0.450137 | + | 0.892959i | \(0.351375\pi\) | |||||||
\(578\) | 1.60840e10i | 0.144106i | ||||||||
\(579\) | 1.71160e11i | 1.52296i | ||||||||
\(580\) | − 5.55820e10i | − 0.491159i | ||||||||
\(581\) | −5.27038e10 | −0.462527 | ||||||||
\(582\) | 6.69658e10i | 0.583662i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.57191e11 | 1.35138 | ||||||||
\(585\) | 7.30640e9i | 0.0623849i | ||||||||
\(586\) | 6.51729e10 | 0.552684 | ||||||||
\(587\) | 1.55828e10 | 0.131248 | 0.0656241 | − | 0.997844i | \(-0.479096\pi\) | ||||
0.0656241 | + | 0.997844i | \(0.479096\pi\) | |||||||
\(588\) | 6.34674e10 | 0.530935 | ||||||||
\(589\) | − 2.01323e11i | − 1.67275i | ||||||||
\(590\) | 9.57870e10i | 0.790494i | ||||||||
\(591\) | − 1.73692e10i | − 0.142374i | ||||||||
\(592\) | 1.15733e10 | 0.0942261 | ||||||||
\(593\) | − 5.77849e10i | − 0.467300i | −0.972321 | − | 0.233650i | \(-0.924933\pi\) | ||||
0.972321 | − | 0.233650i | \(-0.0750670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.47330e10 | 0.516486 | ||||||||
\(596\) | − 1.66272e11i | − 1.31776i | ||||||||
\(597\) | 1.16108e11 | 0.914038 | ||||||||
\(598\) | 4.76496e10 | 0.372610 | ||||||||
\(599\) | 1.55883e11 | 1.21085 | 0.605425 | − | 0.795902i | \(-0.293003\pi\) | ||||
0.605425 | + | 0.795902i | \(0.293003\pi\) | |||||||
\(600\) | 2.61825e10i | 0.202025i | ||||||||
\(601\) | − 2.12533e10i | − 0.162903i | −0.996677 | − | 0.0814513i | \(-0.974044\pi\) | ||||
0.996677 | − | 0.0814513i | \(-0.0259555\pi\) | |||||||
\(602\) | − 7.77636e9i | − 0.0592093i | ||||||||
\(603\) | 1.90686e10 | 0.144228 | ||||||||
\(604\) | − 5.11596e10i | − 0.384397i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.88789e8 | −0.00733184 | ||||||||
\(607\) | 2.67103e10i | 0.196754i | 0.995149 | + | 0.0983772i | \(0.0313652\pi\) | ||||
−0.995149 | + | 0.0983772i | \(0.968635\pi\) | |||||||
\(608\) | −2.07623e11 | −1.51936 | ||||||||
\(609\) | 3.99192e10 | 0.290210 | ||||||||
\(610\) | 1.13326e11 | 0.818483 | ||||||||
\(611\) | − 9.82141e9i | − 0.0704708i | ||||||||
\(612\) | 7.59248e9i | 0.0541225i | ||||||||
\(613\) | 1.43939e11i | 1.01938i | 0.860358 | + | 0.509690i | \(0.170240\pi\) | ||||
−0.860358 | + | 0.509690i | \(0.829760\pi\) | |||||||
\(614\) | −2.22823e10 | −0.156779 | ||||||||
\(615\) | − 1.74071e11i | − 1.21682i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.08135e11 | −0.746152 | −0.373076 | − | 0.927801i | \(-0.621697\pi\) | ||||
−0.373076 | + | 0.927801i | \(0.621697\pi\) | |||||||
\(618\) | 3.46935e10i | 0.237845i | ||||||||
\(619\) | 1.70618e11 | 1.16215 | 0.581074 | − | 0.813851i | \(-0.302633\pi\) | ||||
0.581074 | + | 0.813851i | \(0.302633\pi\) | |||||||
\(620\) | 1.47007e11 | 0.994878 | ||||||||
\(621\) | 1.93094e11 | 1.29838 | ||||||||
\(622\) | 1.31271e10i | 0.0877017i | ||||||||
\(623\) | 3.23102e10i | 0.214481i | ||||||||
\(624\) | 4.52460e10i | 0.298430i | ||||||||
\(625\) | −1.82367e11 | −1.19516 | ||||||||
\(626\) | 1.22936e10i | 0.0800536i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.25405e10 | 0.466382 | ||||||||
\(629\) | − 2.63112e10i | − 0.168089i | ||||||||
\(630\) | 3.56335e9 | 0.0226202 | ||||||||
\(631\) | −1.99135e11 | −1.25612 | −0.628060 | − | 0.778165i | \(-0.716151\pi\) | ||||
−0.628060 | + | 0.778165i | \(0.716151\pi\) | |||||||
\(632\) | −1.43790e11 | −0.901282 | ||||||||
\(633\) | − 1.19989e11i | − 0.747356i | ||||||||
\(634\) | 1.18486e11i | 0.733348i | ||||||||
\(635\) | − 2.35569e11i | − 1.44885i | ||||||||
\(636\) | 1.16296e11 | 0.710785 | ||||||||
\(637\) | 7.65950e10i | 0.465203i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.64272e10 | 0.0985282 | ||||||||
\(640\) | − 1.89659e11i | − 1.13046i | ||||||||
\(641\) | −2.83608e10 | −0.167991 | −0.0839957 | − | 0.996466i | \(-0.526768\pi\) | ||||
−0.0839957 | + | 0.996466i | \(0.526768\pi\) | |||||||
\(642\) | 1.27394e10 | 0.0749907 | ||||||||
\(643\) | −1.99392e11 | −1.16644 | −0.583221 | − | 0.812313i | \(-0.698208\pi\) | ||||
−0.583221 | + | 0.812313i | \(0.698208\pi\) | |||||||
\(644\) | 9.74446e10i | 0.566519i | ||||||||
\(645\) | 4.49455e10i | 0.259685i | ||||||||
\(646\) | 9.56594e10i | 0.549285i | ||||||||
\(647\) | −2.79365e10 | −0.159425 | −0.0797123 | − | 0.996818i | \(-0.525400\pi\) | ||||
−0.0797123 | + | 0.996818i | \(0.525400\pi\) | |||||||
\(648\) | − 1.27471e11i | − 0.722957i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.41158e10 | −0.0790776 | ||||||||
\(651\) | 1.05581e11i | 0.587841i | ||||||||
\(652\) | 8.43196e10 | 0.466593 | ||||||||
\(653\) | −1.92931e11 | −1.06108 | −0.530542 | − | 0.847659i | \(-0.678011\pi\) | ||||
−0.530542 | + | 0.847659i | \(0.678011\pi\) | |||||||
\(654\) | 8.24199e10 | 0.450527 | ||||||||
\(655\) | − 2.33874e11i | − 1.27062i | ||||||||
\(656\) | 9.60229e10i | 0.518513i | ||||||||
\(657\) | 2.59658e10i | 0.139361i | ||||||||
\(658\) | −4.78993e9 | −0.0255521 | ||||||||
\(659\) | 2.89730e11i | 1.53621i | 0.640322 | + | 0.768107i | \(0.278801\pi\) | ||||
−0.640322 | + | 0.768107i | \(0.721199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.56337e10 | −0.291428 | −0.145714 | − | 0.989327i | \(-0.546548\pi\) | ||||
−0.145714 | + | 0.989327i | \(0.546548\pi\) | |||||||
\(662\) | 2.67279e10i | 0.139166i | ||||||||
\(663\) | 1.02864e11 | 0.532365 | ||||||||
\(664\) | 1.27304e11 | 0.654891 | ||||||||
\(665\) | −1.88255e11 | −0.962629 | ||||||||
\(666\) | − 1.44835e9i | − 0.00736168i | ||||||||
\(667\) | − 1.34035e11i | − 0.677196i | ||||||||
\(668\) | − 2.21211e11i | − 1.11096i | ||||||||
\(669\) | 1.52488e11 | 0.761258 | ||||||||
\(670\) | 1.75431e11i | 0.870577i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.08885e11 | 0.533937 | ||||||||
\(673\) | 1.72745e11i | 0.842064i | 0.907046 | + | 0.421032i | \(0.138332\pi\) | ||||
−0.907046 | + | 0.421032i | \(0.861668\pi\) | |||||||
\(674\) | −1.13689e11 | −0.550909 | ||||||||
\(675\) | −5.72028e10 | −0.275551 | ||||||||
\(676\) | 9.11225e10 | 0.436354 | ||||||||
\(677\) | − 7.32817e10i | − 0.348852i | −0.984670 | − | 0.174426i | \(-0.944193\pi\) | ||||
0.984670 | − | 0.174426i | \(-0.0558069\pi\) | |||||||
\(678\) | − 7.12604e10i | − 0.337233i | ||||||||
\(679\) | − 1.65273e11i | − 0.777540i | ||||||||
\(680\) | −1.56360e11 | −0.731290 | ||||||||
\(681\) | − 5.10797e10i | − 0.237498i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.37571e11 | −1.55125 | −0.775625 | − | 0.631194i | \(-0.782565\pi\) | ||||
−0.775625 | + | 0.631194i | \(0.782565\pi\) | |||||||
\(684\) | − 2.20802e10i | − 0.100874i | ||||||||
\(685\) | −5.42695e10 | −0.246487 | ||||||||
\(686\) | 9.17928e10 | 0.414488 | ||||||||
\(687\) | 9.20626e9 | 0.0413291 | ||||||||
\(688\) | − 2.47933e10i | − 0.110657i | ||||||||
\(689\) | 1.40351e11i | 0.622787i | ||||||||
\(690\) | 1.34315e11i | 0.592555i | ||||||||
\(691\) | −2.55262e11 | −1.11963 | −0.559813 | − | 0.828619i | \(-0.689127\pi\) | ||||
−0.559813 | + | 0.828619i | \(0.689127\pi\) | |||||||
\(692\) | − 9.49608e9i | − 0.0414114i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.98484e10 | 0.171780 | ||||||||
\(695\) | − 2.08916e11i | − 0.895431i | ||||||||
\(696\) | −9.64231e10 | −0.410907 | ||||||||
\(697\) | 2.18302e11 | 0.924968 | ||||||||
\(698\) | 1.04149e11 | 0.438764 | ||||||||
\(699\) | − 1.46681e9i | − 0.00614421i | ||||||||
\(700\) | − 2.88673e10i | − 0.120230i | ||||||||
\(701\) | 4.73174e10i | 0.195951i | 0.995189 | + | 0.0979757i | \(0.0312367\pi\) | ||||
−0.995189 | + | 0.0979757i | \(0.968763\pi\) | |||||||
\(702\) | 7.48908e10 | 0.308376 | ||||||||
\(703\) | 7.65174e10i | 0.313285i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.76847e10 | 0.112068 | ||||||||
\(706\) | − 6.94434e10i | − 0.279519i | ||||||||
\(707\) | 2.44035e9 | 0.00976731 | ||||||||
\(708\) | −3.11274e11 | −1.23882 | ||||||||
\(709\) | −3.31666e11 | −1.31255 | −0.656276 | − | 0.754521i | \(-0.727869\pi\) | ||||
−0.656276 | + | 0.754521i | \(0.727869\pi\) | |||||||
\(710\) | 1.51130e11i | 0.594728i | ||||||||
\(711\) | − 2.37522e10i | − 0.0929448i | ||||||||
\(712\) | − 7.80440e10i | − 0.303682i | ||||||||
\(713\) | 3.54503e11 | 1.37171 | ||||||||
\(714\) | − 5.01671e10i | − 0.193031i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.12771e11 | −0.809582 | ||||||||
\(717\) | 1.04565e11i | 0.395648i | ||||||||
\(718\) | −9.11846e10 | −0.343102 | ||||||||
\(719\) | 3.88790e11 | 1.45479 | 0.727394 | − | 0.686220i | \(-0.240731\pi\) | ||||
0.727394 | + | 0.686220i | \(0.240731\pi\) | |||||||
\(720\) | 1.13610e10 | 0.0422753 | ||||||||
\(721\) | − 8.56242e10i | − 0.316851i | ||||||||
\(722\) | − 1.58951e11i | − 0.584943i | ||||||||
\(723\) | 4.08213e11i | 1.49394i | ||||||||
\(724\) | 1.69238e11 | 0.615949 | ||||||||
\(725\) | 3.97069e10i | 0.143719i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.54660e11 | 1.26962 | 0.634812 | − | 0.772667i | \(-0.281078\pi\) | ||||
0.634812 | + | 0.772667i | \(0.281078\pi\) | |||||||
\(728\) | 8.46001e10i | 0.301193i | ||||||||
\(729\) | 3.01597e11 | 1.06787 | ||||||||
\(730\) | −2.38886e11 | −0.841198 | ||||||||
\(731\) | −5.63660e10 | −0.197400 | ||||||||
\(732\) | 3.68269e11i | 1.28269i | ||||||||
\(733\) | − 5.63516e11i | − 1.95205i | −0.217664 | − | 0.976024i | \(-0.569844\pi\) | ||||
0.217664 | − | 0.976024i | \(-0.430156\pi\) | |||||||
\(734\) | − 1.25630e11i | − 0.432821i | ||||||||
\(735\) | −2.15907e11 | −0.739805 | ||||||||
\(736\) | − 3.65598e11i | − 1.24593i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.20168e10 | 0.0405103 | ||||||||
\(739\) | − 1.88021e11i | − 0.630420i | −0.949022 | − | 0.315210i | \(-0.897925\pi\) | ||||
0.949022 | − | 0.315210i | \(-0.102075\pi\) | |||||||
\(740\) | −5.58733e10 | −0.186328 | ||||||||
\(741\) | −2.99146e11 | −0.992225 | ||||||||
\(742\) | 6.84498e10 | 0.225817 | ||||||||
\(743\) | 4.07212e11i | 1.33618i | 0.744080 | + | 0.668090i | \(0.232888\pi\) | ||||
−0.744080 | + | 0.668090i | \(0.767112\pi\) | |||||||
\(744\) | − 2.55025e11i | − 0.832323i | ||||||||
\(745\) | 5.65635e11i | 1.83616i | ||||||||
\(746\) | 1.34382e11 | 0.433897 | ||||||||
\(747\) | 2.10289e10i | 0.0675357i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.14410e10 | −0.0999008 | ||||||||
\(750\) | 1.09897e11i | 0.347330i | ||||||||
\(751\) | −3.75624e11 | −1.18085 | −0.590424 | − | 0.807094i | \(-0.701039\pi\) | ||||
−0.590424 | + | 0.807094i | \(0.701039\pi\) | |||||||
\(752\) | −1.52717e10 | −0.0477547 | ||||||||
\(753\) | 4.64465e9 | 0.0144468 | ||||||||
\(754\) | − 5.19849e10i | − 0.160839i | ||||||||
\(755\) | 1.74038e11i | 0.535619i | ||||||||
\(756\) | 1.53154e11i | 0.468857i | ||||||||
\(757\) | 4.01108e11 | 1.22146 | 0.610728 | − | 0.791841i | \(-0.290877\pi\) | ||||
0.610728 | + | 0.791841i | \(0.290877\pi\) | |||||||
\(758\) | 1.64273e11i | 0.497611i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.54721e11 | 1.36298 | ||||||||
\(761\) | 5.63938e11i | 1.68148i | 0.541437 | + | 0.840741i | \(0.317880\pi\) | ||||
−0.541437 | + | 0.840741i | \(0.682120\pi\) | |||||||
\(762\) | −1.82562e11 | −0.541491 | ||||||||
\(763\) | −2.03414e11 | −0.600182 | ||||||||
\(764\) | 1.37983e11 | 0.404996 | ||||||||
\(765\) | − 2.58285e10i | − 0.0754144i | ||||||||
\(766\) | − 3.00788e10i | − 0.0873665i | ||||||||
\(767\) | − 3.75658e11i | − 1.08545i | ||||||||
\(768\) | −1.39351e11 | −0.400557 | ||||||||
\(769\) | − 3.98817e11i | − 1.14043i | −0.821495 | − | 0.570215i | \(-0.806860\pi\) | ||||
0.821495 | − | 0.570215i | \(-0.193140\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.37938e10 | −0.265434 | ||||||||
\(772\) | 4.55824e11i | 1.28330i | ||||||||
\(773\) | 1.42881e11 | 0.400180 | 0.200090 | − | 0.979777i | \(-0.435877\pi\) | ||||
0.200090 | + | 0.979777i | \(0.435877\pi\) | |||||||
\(774\) | −3.10277e9 | −0.00864542 | ||||||||
\(775\) | −1.05019e11 | −0.291113 | ||||||||
\(776\) | 3.99210e11i | 1.10092i | ||||||||
\(777\) | − 4.01284e10i | − 0.110095i | ||||||||
\(778\) | 1.70682e11i | 0.465876i | ||||||||
\(779\) | −6.34859e11 | −1.72396 | ||||||||
\(780\) | − 2.18437e11i | − 0.590131i | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.68444e11 | −0.450431 | ||||||||
\(783\) | − 2.10663e11i | − 0.560455i | ||||||||
\(784\) | 1.19101e11 | 0.315246 | ||||||||
\(785\) | −2.46772e11 | −0.649857 | ||||||||
\(786\) | −1.81248e11 | −0.474880 | ||||||||
\(787\) | − 2.65211e11i | − 0.691342i | −0.938356 | − | 0.345671i | \(-0.887651\pi\) | ||||
0.938356 | − | 0.345671i | \(-0.112349\pi\) | |||||||
\(788\) | − 4.62567e10i | − 0.119969i | ||||||||
\(789\) | − 3.28080e10i | − 0.0846588i | ||||||||
\(790\) | 2.18520e11 | 0.561026 | ||||||||
\(791\) | 1.75872e11i | 0.449253i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.44442e11 | −1.12389 | ||||||||
\(794\) | 6.39969e10i | 0.161019i | ||||||||
\(795\) | −3.95624e11 | −0.990408 | ||||||||
\(796\) | 3.09212e11 | 0.770200 | ||||||||
\(797\) | −4.31220e11 | −1.06872 | −0.534362 | − | 0.845256i | \(-0.679448\pi\) | ||||
−0.534362 | + | 0.845256i | \(0.679448\pi\) | |||||||
\(798\) | 1.45894e11i | 0.359772i | ||||||||
\(799\) | 3.47193e10i | 0.0851890i | ||||||||
\(800\) | 1.08306e11i | 0.264418i | ||||||||
\(801\) | 1.28918e10 | 0.0313173 | ||||||||
\(802\) | − 5.45078e10i | − 0.131753i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −5.70089e11 | −1.36433 | ||||||||
\(805\) | − 3.31492e11i | − 0.789387i | ||||||||
\(806\) | 1.37493e11 | 0.325791 | ||||||||
\(807\) | −3.45327e11 | −0.814209 | ||||||||
\(808\) | −5.89457e9 | −0.0138295 | ||||||||
\(809\) | 6.85663e10i | 0.160072i | 0.996792 | + | 0.0800362i | \(0.0255036\pi\) | ||||
−0.996792 | + | 0.0800362i | \(0.974496\pi\) | |||||||
\(810\) | 1.93720e11i | 0.450023i | ||||||||
\(811\) | 1.82889e11i | 0.422770i | 0.977403 | + | 0.211385i | \(0.0677973\pi\) | ||||
−0.977403 | + | 0.211385i | \(0.932203\pi\) | |||||||
\(812\) | 1.06310e11 | 0.244541 | ||||||||
\(813\) | 1.10040e11i | 0.251878i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.86843e11 | −0.650151 | ||||||||
\(816\) | − 1.59947e11i | − 0.360758i | ||||||||
\(817\) | 1.63922e11 | 0.367916 | ||||||||
\(818\) | 2.72600e11 | 0.608854 | ||||||||
\(819\) | −1.39748e10 | −0.0310606 | ||||||||
\(820\) | − 4.63577e11i | − 1.02534i | ||||||||
\(821\) | − 8.72789e11i | − 1.92104i | −0.278208 | − | 0.960521i | \(-0.589740\pi\) | ||||
0.278208 | − | 0.960521i | \(-0.410260\pi\) | |||||||
\(822\) | 4.20580e10i | 0.0921216i | ||||||||
\(823\) | 7.70194e10 | 0.167881 | 0.0839404 | − | 0.996471i | \(-0.473249\pi\) | ||||
0.0839404 | + | 0.996471i | \(0.473249\pi\) | |||||||
\(824\) | 2.06822e11i | 0.448629i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.83210e11 | −0.393575 | ||||||||
\(827\) | − 2.53077e10i | − 0.0541042i | −0.999634 | − | 0.0270521i | \(-0.991388\pi\) | ||||
0.999634 | − | 0.0270521i | \(-0.00861200\pi\) | |||||||
\(828\) | 3.88805e10 | 0.0827199 | ||||||||
\(829\) | 5.47357e10 | 0.115892 | 0.0579459 | − | 0.998320i | \(-0.481545\pi\) | ||||
0.0579459 | + | 0.998320i | \(0.481545\pi\) | |||||||
\(830\) | −1.93465e11 | −0.407653 | ||||||||
\(831\) | − 2.63154e11i | − 0.551832i | ||||||||
\(832\) | 7.43738e9i | 0.0155212i | ||||||||
\(833\) | − 2.70768e11i | − 0.562364i | ||||||||
\(834\) | −1.61907e11 | −0.334657 | ||||||||
\(835\) | 7.52526e11i | 1.54802i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.57173e11 | 1.13524 | ||||||||
\(838\) | − 1.69227e10i | − 0.0343157i | ||||||||
\(839\) | −5.10452e11 | −1.03017 | −0.515083 | − | 0.857141i | \(-0.672239\pi\) | ||||
−0.515083 | + | 0.857141i | \(0.672239\pi\) | |||||||
\(840\) | −2.38472e11 | −0.478982 | ||||||||
\(841\) | 3.54016e11 | 0.707684 | ||||||||
\(842\) | − 3.42336e11i | − 0.681089i | ||||||||
\(843\) | 7.08549e11i | 1.40301i | ||||||||
\(844\) | − 3.19549e11i | − 0.629749i | ||||||||
\(845\) | −3.09986e11 | −0.608015 | ||||||||
\(846\) | 1.91119e9i | 0.00373097i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.18238e11 | 0.422033 | ||||||||
\(849\) | 5.03818e11i | 0.969713i | ||||||||
\(850\) | 4.99003e10 | 0.0955934 | ||||||||
\(851\) | −1.34737e11 | −0.256904 | ||||||||
\(852\) | −4.91120e11 | −0.932029 | ||||||||
\(853\) | 7.88006e11i | 1.48845i | 0.667931 | + | 0.744224i | \(0.267180\pi\) | ||||
−0.667931 | + | 0.744224i | \(0.732820\pi\) | |||||||
\(854\) | 2.16756e11i | 0.407511i | ||||||||
\(855\) | 7.51137e10i | 0.140558i | ||||||||
\(856\) | 7.59444e10 | 0.141449 | ||||||||
\(857\) | 1.32237e11i | 0.245150i | 0.992459 | + | 0.122575i | \(0.0391151\pi\) | ||||
−0.992459 | + | 0.122575i | \(0.960885\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.70268e11 | 0.680055 | 0.340027 | − | 0.940416i | \(-0.389564\pi\) | ||||
0.340027 | + | 0.940416i | \(0.389564\pi\) | |||||||
\(860\) | 1.19696e11i | 0.218820i | ||||||||
\(861\) | 3.32942e11 | 0.605837 | ||||||||
\(862\) | 4.79126e10 | 0.0867801 | ||||||||
\(863\) | −5.12080e11 | −0.923198 | −0.461599 | − | 0.887089i | \(-0.652724\pi\) | ||||
−0.461599 | + | 0.887089i | \(0.652724\pi\) | |||||||
\(864\) | − 5.74610e11i | − 1.03114i | ||||||||
\(865\) | 3.23043e10i | 0.0577027i | ||||||||
\(866\) | − 2.19703e11i | − 0.390630i | ||||||||
\(867\) | 1.77806e11 | 0.314680 | ||||||||
\(868\) | 2.81176e11i | 0.495336i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.46536e11 | 0.255780 | ||||||||
\(871\) | − 6.88006e11i | − 1.19542i | ||||||||
\(872\) | 4.91338e11 | 0.849796 | ||||||||
\(873\) | −6.59441e10 | −0.113532 | ||||||||
\(874\) | 4.89863e11 | 0.839517 | ||||||||
\(875\) | − 2.71229e11i | − 0.462705i | ||||||||
\(876\) | − 7.76293e11i | − 1.31829i | ||||||||
\(877\) | 1.31113e11i | 0.221640i | 0.993841 | + | 0.110820i | \(0.0353477\pi\) | ||||
−0.993841 | + | 0.110820i | \(0.964652\pi\) | |||||||
\(878\) | 2.25748e10 | 0.0379879 | ||||||||
\(879\) | − 7.20476e11i | − 1.20688i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.82199e11 | 0.302443 | 0.151221 | − | 0.988500i | \(-0.451679\pi\) | ||||
0.151221 | + | 0.988500i | \(0.451679\pi\) | |||||||
\(882\) | − 1.49049e10i | − 0.0246295i | ||||||||
\(883\) | 1.32669e11 | 0.218236 | 0.109118 | − | 0.994029i | \(-0.465197\pi\) | ||||
0.109118 | + | 0.994029i | \(0.465197\pi\) | |||||||
\(884\) | 2.73942e11 | 0.448589 | ||||||||
\(885\) | 1.05891e12 | 1.72618 | ||||||||
\(886\) | − 3.38726e11i | − 0.549685i | ||||||||
\(887\) | 9.20909e11i | 1.48772i | 0.668333 | + | 0.743862i | \(0.267008\pi\) | ||||
−0.668333 | + | 0.743862i | \(0.732992\pi\) | |||||||
\(888\) | 9.69285e10i | 0.155883i | ||||||||
\(889\) | 4.50568e11 | 0.721362 | ||||||||
\(890\) | 1.18605e11i | 0.189035i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.06098e11 | 0.641463 | ||||||||
\(893\) | − 1.00969e11i | − 0.158776i | ||||||||
\(894\) | 4.38358e11 | 0.686245 | ||||||||
\(895\) | 7.23817e11 | 1.12807 | ||||||||
\(896\) | 3.62757e11 | 0.562839 | ||||||||
\(897\) | − 5.26758e11i | − 0.813657i | ||||||||
\(898\) | − 2.21453e11i | − 0.340546i | ||||||||
\(899\) | − 3.86758e11i | − 0.592107i | ||||||||
\(900\) | −1.15181e10 | −0.0175553 | ||||||||
\(901\) | − 4.96150e11i | − 0.752860i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.59663e10 | −0.129294 | ||||||||
\(904\) | − 4.24812e11i | − 0.636097i | ||||||||
\(905\) | −5.75724e11 | −0.858263 | ||||||||
\(906\) | 1.34877e11 | 0.200181 | ||||||||
\(907\) | 3.25840e11 | 0.481477 | 0.240738 | − | 0.970590i | \(-0.422610\pi\) | ||||
0.240738 | + | 0.970590i | \(0.422610\pi\) | |||||||
\(908\) | − 1.36032e11i | − 0.200124i | ||||||||
\(909\) | − 9.73703e8i | − 0.00142617i | ||||||||
\(910\) | − 1.28568e11i | − 0.187485i | ||||||||
\(911\) | 3.29495e11 | 0.478382 | 0.239191 | − | 0.970972i | \(-0.423118\pi\) | ||||
0.239191 | + | 0.970972i | \(0.423118\pi\) | |||||||
\(912\) | 4.65154e11i | 0.672384i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −3.53719e11 | −0.506843 | ||||||||
\(915\) | − 1.25280e12i | − 1.78730i | ||||||||
\(916\) | 2.45176e10 | 0.0348254 | ||||||||
\(917\) | 4.47325e11 | 0.632624 | ||||||||
\(918\) | −2.64743e11 | −0.372781 | ||||||||
\(919\) | 1.27480e12i | 1.78723i | 0.448839 | + | 0.893613i | \(0.351838\pi\) | ||||
−0.448839 | + | 0.893613i | \(0.648162\pi\) | |||||||
\(920\) | 8.00706e11i | 1.11769i | ||||||||
\(921\) | 2.46328e11i | 0.342353i | ||||||||
\(922\) | −3.51991e11 | −0.487089 | ||||||||
\(923\) | − 5.92704e11i | − 0.816641i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.99150e10 | 0.0545217 | ||||||||
\(926\) | 1.65930e11i | 0.225673i | ||||||||
\(927\) | −3.41641e10 | −0.0462649 | ||||||||
\(928\) | −3.98861e11 | −0.537812 | ||||||||
\(929\) | 5.43531e11 | 0.729729 | 0.364865 | − | 0.931061i | \(-0.381115\pi\) | ||||
0.364865 | + | 0.931061i | \(0.381115\pi\) | |||||||
\(930\) | 3.87566e11i | 0.518100i | ||||||||
\(931\) | 7.87439e11i | 1.04814i | ||||||||
\(932\) | − 3.90633e9i | − 0.00517733i | ||||||||
\(933\) | 1.45118e11 | 0.191512 | ||||||||
\(934\) | − 5.77560e11i | − 0.758943i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.37555e10 | 0.0439786 | ||||||||
\(937\) | 7.40437e11i | 0.960571i | 0.877112 | + | 0.480286i | \(0.159467\pi\) | ||||
−0.877112 | + | 0.480286i | \(0.840533\pi\) | |||||||
\(938\) | −3.35543e11 | −0.433448 | ||||||||
\(939\) | 1.35903e11 | 0.174811 | ||||||||
\(940\) | 7.37283e10 | 0.0944328 | ||||||||
\(941\) | 1.94941e11i | 0.248625i | 0.992243 | + | 0.124312i | \(0.0396725\pi\) | ||||
−0.992243 | + | 0.124312i | \(0.960327\pi\) | |||||||
\(942\) | 1.91245e11i | 0.242877i | ||||||||
\(943\) | − 1.11791e12i | − 1.41370i | ||||||||
\(944\) | −5.84126e11 | −0.735560 | ||||||||
\(945\) | − 5.21007e11i | − 0.653305i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.03034e11 | −0.376783 | −0.188392 | − | 0.982094i | \(-0.560327\pi\) | ||||
−0.188392 | + | 0.982094i | \(0.560327\pi\) | |||||||
\(948\) | 7.10113e11i | 0.879213i | ||||||||
\(949\) | 9.36863e11 | 1.15508 | ||||||||
\(950\) | −1.45119e11 | −0.178168 | ||||||||
\(951\) | 1.30984e12 | 1.60139 | ||||||||
\(952\) | − 2.99066e11i | − 0.364099i | ||||||||
\(953\) | 3.77448e11i | 0.457600i | 0.973473 | + | 0.228800i | \(0.0734802\pi\) | ||||
−0.973473 | + | 0.228800i | \(0.926520\pi\) | |||||||
\(954\) | − 2.73115e10i | − 0.0329725i | ||||||||
\(955\) | −4.69397e11 | −0.564322 | ||||||||
\(956\) | 2.78471e11i | 0.333387i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.47032e10 | −0.0530734 | ||||||||
\(959\) | − 1.03800e11i | − 0.122722i | ||||||||
\(960\) | −2.09646e10 | −0.0246832 | ||||||||
\(961\) | 1.70028e11 | 0.199355 | ||||||||
\(962\) | −5.22574e10 | −0.0610165 | ||||||||
\(963\) | 1.25450e10i | 0.0145870i | ||||||||
\(964\) | 1.08713e12i | 1.25885i | ||||||||
\(965\) | − 1.55065e12i | − 1.78815i | ||||||||
\(966\) | −2.56901e11 | −0.295024 | ||||||||
\(967\) | − 9.05058e10i | − 0.103507i | −0.998660 | − | 0.0517536i | \(-0.983519\pi\) | ||||
0.998660 | − | 0.0517536i | \(-0.0164810\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.05750e12 | 1.19946 | ||||||||
\(970\) | − 6.06685e11i | − 0.685294i | ||||||||
\(971\) | −7.80333e11 | −0.877815 | −0.438907 | − | 0.898532i | \(-0.644634\pi\) | ||||
−0.438907 | + | 0.898532i | \(0.644634\pi\) | |||||||
\(972\) | 1.17597e11 | 0.131744 | ||||||||
\(973\) | 3.99589e11 | 0.445822 | ||||||||
\(974\) | − 3.28954e11i | − 0.365510i | ||||||||
\(975\) | 1.56048e11i | 0.172679i | ||||||||
\(976\) | 6.91081e11i | 0.761605i | ||||||||
\(977\) | 3.35549e11 | 0.368280 | 0.184140 | − | 0.982900i | \(-0.441050\pi\) | ||||
0.184140 | + | 0.982900i | \(0.441050\pi\) | |||||||
\(978\) | 2.22299e11i | 0.242986i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −5.74991e11 | −0.623385 | ||||||||
\(981\) | 8.11624e10i | 0.0876352i | ||||||||
\(982\) | 3.46046e11 | 0.372124 | ||||||||
\(983\) | 1.01732e12 | 1.08954 | 0.544769 | − | 0.838586i | \(-0.316617\pi\) | ||||
0.544769 | + | 0.838586i | \(0.316617\pi\) | |||||||
\(984\) | −8.04208e11 | −0.857803 | ||||||||
\(985\) | 1.57359e11i | 0.167165i | ||||||||
\(986\) | 1.83770e11i | 0.194431i | ||||||||
\(987\) | 5.29519e10i | 0.0557973i | ||||||||
\(988\) | −7.96668e11 | −0.836084 | ||||||||
\(989\) | 2.88645e11i | 0.301703i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.14619e11 | 0.948299 | 0.474150 | − | 0.880444i | \(-0.342756\pi\) | ||||
0.474150 | + | 0.880444i | \(0.342756\pi\) | |||||||
\(992\) | − 1.05493e12i | − 1.08938i | ||||||||
\(993\) | 2.95472e11 | 0.303892 | ||||||||
\(994\) | −2.89064e11 | −0.296107 | ||||||||
\(995\) | −1.05189e12 | −1.07320 | ||||||||
\(996\) | − 6.28694e11i | − 0.638855i | ||||||||
\(997\) | − 1.32177e12i | − 1.33775i | −0.743376 | − | 0.668874i | \(-0.766777\pi\) | ||||
0.743376 | − | 0.668874i | \(-0.233223\pi\) | |||||||
\(998\) | − 6.57583e11i | − 0.662871i | ||||||||
\(999\) | −2.11767e11 | −0.212616 |
(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 | 121.9.b.b.120.17 | 28 | ||
11.3 | even | 5 | 11.9.d.a.2.5 | ✓ | 28 | ||
11.7 | odd | 10 | 11.9.d.a.6.5 | yes | 28 | ||
11.10 | odd | 2 | inner | 121.9.b.b.120.12 | 28 | ||
33.14 | odd | 10 | 99.9.k.a.46.3 | 28 | |||
33.29 | even | 10 | 99.9.k.a.28.3 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.9.d.a.2.5 | ✓ | 28 | 11.3 | even | 5 | ||
11.9.d.a.6.5 | yes | 28 | 11.7 | odd | 10 | ||
99.9.k.a.28.3 | 28 | 33.29 | even | 10 | |||
99.9.k.a.46.3 | 28 | 33.14 | odd | 10 | |||
121.9.b.b.120.12 | 28 | 11.10 | odd | 2 | inner | ||
121.9.b.b.120.17 | 28 | 1.1 | even | 1 | trivial |