Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(73,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.73");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.z (of order \(6\), degree \(2\), 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: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} - 1751639 x^{18} + 15765036 x^{17} + 1288400424989 x^{16} - 10307560742020 x^{15} + \cdots + 51\!\cdots\!63 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | \( 2^{36}\cdot 3^{26}\cdot 7^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.7 | ||
Root | \(-285.330 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.145 |
Dual form | 252.9.z.e.73.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 428.745 | + | 247.536i | 0.685992 | + | 0.396058i | 0.802109 | − | 0.597178i | \(-0.203711\pi\) |
−0.116117 | + | 0.993236i | \(0.537045\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1933.79 | + | 1423.12i | 0.805409 | + | 0.592719i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1062.17 | − | 1839.73i | −0.0725475 | − | 0.125656i | 0.827470 | − | 0.561510i | \(-0.189780\pi\) |
−0.900017 | + | 0.435854i | \(0.856446\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 15639.3i | − | 0.547577i | −0.961790 | − | 0.273788i | \(-0.911723\pi\) | ||
0.961790 | − | 0.273788i | \(-0.0882768\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −48991.8 | + | 28285.4i | −0.586580 | + | 0.338662i | −0.763744 | − | 0.645519i | \(-0.776641\pi\) |
0.177164 | + | 0.984181i | \(0.443308\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −140021. | − | 80841.3i | −1.07443 | − | 0.620325i | −0.145044 | − | 0.989425i | \(-0.546332\pi\) |
−0.929390 | + | 0.369100i | \(0.879666\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 223626. | − | 387331.i | 0.799117 | − | 1.38411i | −0.121075 | − | 0.992643i | \(-0.538634\pi\) |
0.920192 | − | 0.391467i | \(-0.128032\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −72764.3 | − | 126031.i | −0.186277 | − | 0.322641i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.33434e6 | −1.88658 | −0.943291 | − | 0.331966i | \(-0.892288\pi\) | ||||
−0.943291 | + | 0.331966i | \(0.892288\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −467329. | + | 269813.i | −0.506030 | + | 0.292156i | −0.731200 | − | 0.682163i | \(-0.761039\pi\) |
0.225170 | + | 0.974319i | \(0.427706\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 476829. | + | 1.08884e6i | 0.317753 | + | 0.725589i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 531934. | − | 921336.i | 0.283825 | − | 0.491599i | −0.688499 | − | 0.725238i | \(-0.741730\pi\) |
0.972324 | + | 0.233638i | \(0.0750632\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.94716e6i | − | 1.75073i | −0.483459 | − | 0.875367i | \(-0.660620\pi\) | ||
0.483459 | − | 0.875367i | \(-0.339380\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.05532e6 | 0.601180 | 0.300590 | − | 0.953753i | \(-0.402816\pi\) | ||||
0.300590 | + | 0.953753i | \(0.402816\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.47316e6 | − | 1.42788e6i | −0.506828 | − | 0.292617i | 0.224701 | − | 0.974428i | \(-0.427859\pi\) |
−0.731529 | + | 0.681811i | \(0.761193\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.71427e6 | + | 5.50402e6i | 0.297368 | + | 0.954763i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.97472e6 | + | 1.20806e7i | 0.883941 | + | 1.53103i | 0.846923 | + | 0.531715i | \(0.178452\pi\) |
0.0370175 | + | 0.999315i | \(0.488214\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.05170e6i | − | 0.114932i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.87945e6 | + | 3.39450e6i | −0.485209 | + | 0.280136i | −0.722585 | − | 0.691282i | \(-0.757046\pi\) |
0.237376 | + | 0.971418i | \(0.423713\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 480161. | + | 277221.i | 0.0346791 | + | 0.0200220i | 0.517239 | − | 0.855841i | \(-0.326960\pi\) |
−0.482560 | + | 0.875863i | \(0.660293\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.87130e6 | − | 6.70529e6i | 0.216872 | − | 0.375633i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.71524e7 | − | 2.97088e7i | −0.851188 | − | 1.47430i | −0.880137 | − | 0.474720i | \(-0.842549\pi\) |
0.0289486 | − | 0.999581i | \(-0.490784\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.21608e7 | 0.872071 | 0.436036 | − | 0.899929i | \(-0.356382\pi\) | ||||
0.436036 | + | 0.899929i | \(0.356382\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.19338e7 | + | 6.89001e6i | −0.420232 | + | 0.242621i | −0.695177 | − | 0.718839i | \(-0.744674\pi\) |
0.274945 | + | 0.961460i | \(0.411340\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 564145. | − | 5.06924e6i | 0.0160483 | − | 0.144205i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.94917e7 | − | 3.37606e7i | 0.500428 | − | 0.866767i | −0.499572 | − | 0.866272i | \(-0.666509\pi\) |
1.00000 | 0.000494391i | \(-0.000157370\pi\) | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.23163e7i | 1.31307i | 0.754294 | + | 0.656537i | \(0.227979\pi\) | ||||
−0.754294 | + | 0.656537i | \(0.772021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.80066e7 | −0.536519 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.64932e7 | − | 2.68429e7i | −0.741019 | − | 0.427827i | 0.0814208 | − | 0.996680i | \(-0.474054\pi\) |
−0.822440 | + | 0.568852i | \(0.807388\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.22566e7 | − | 3.02432e7i | 0.324559 | − | 0.441023i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00223e7 | − | 6.93206e7i | −0.491369 | − | 0.851076i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.92340e7i | − | 0.330218i | −0.986275 | − | 0.165109i | \(-0.947202\pi\) | ||
0.986275 | − | 0.165109i | \(-0.0527977\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.15074e8 | − | 6.64378e7i | 1.10583 | − | 0.638454i | 0.168087 | − | 0.985772i | \(-0.446241\pi\) |
0.937747 | + | 0.347318i | \(0.112908\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.24124e7 | − | 4.75808e7i | −0.732224 | − | 0.422750i | 0.0870114 | − | 0.996207i | \(-0.472268\pi\) |
−0.819235 | + | 0.573458i | \(0.805602\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.88716e7 | + | 6.73275e7i | −0.296549 | + | 0.513638i | −0.975344 | − | 0.220690i | \(-0.929169\pi\) |
0.678795 | + | 0.734328i | \(0.262503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.53205e7 | − | 2.65360e7i | −0.108535 | − | 0.187987i | 0.806642 | − | 0.591040i | \(-0.201282\pi\) |
−0.915177 | + | 0.403053i | \(0.867949\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.30284e8 | −0.799056 | −0.399528 | − | 0.916721i | \(-0.630826\pi\) | ||||
−0.399528 | + | 0.916721i | \(0.630826\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.91757e8 | − | 1.10711e8i | 1.09638 | − | 0.632993i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.34993e8 | − | 1.50231e7i | −0.673169 | − | 0.0749156i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.04923e8 | − | 1.81732e8i | 0.489474 | − | 0.847793i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.65435e8i | − | 1.08722i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.78124e8 | −1.06911 | −0.534557 | − | 0.845132i | \(-0.679522\pi\) | ||||
−0.534557 | + | 0.845132i | \(0.679522\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.16821e8 | + | 1.82917e8i | 1.07579 | + | 0.621110i | 0.929759 | − | 0.368169i | \(-0.120015\pi\) |
0.146036 | + | 0.989279i | \(0.453349\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.55725e8 | − | 3.55597e8i | −0.497681 | − | 1.13645i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.91348e8 | + | 3.31425e8i | 0.543178 | + | 0.940812i | 0.998719 | + | 0.0505971i | \(0.0161124\pi\) |
−0.455541 | + | 0.890215i | \(0.650554\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.95007e8i | − | 1.59391i | −0.604040 | − | 0.796954i | \(-0.706443\pi\) | ||
0.604040 | − | 0.796954i | \(-0.293557\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.87722e7 | + | 1.66116e7i | −0.0688063 | + | 0.0397253i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.72093e8 | − | 3.30298e8i | −1.29418 | − | 0.747196i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.12693e8 | + | 1.95190e8i | −0.228639 | + | 0.396015i | −0.957405 | − | 0.288748i | \(-0.906761\pi\) |
0.728766 | + | 0.684763i | \(0.240094\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.57375e8 | − | 7.92196e8i | −0.879760 | − | 1.52379i | −0.851604 | − | 0.524185i | \(-0.824370\pi\) |
−0.0281557 | − | 0.999604i | \(-0.508963\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.67153e8 | −0.462843 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.82590e8 | − | 1.05418e8i | 0.300523 | − | 0.173507i | −0.342155 | − | 0.939644i | \(-0.611157\pi\) |
0.642678 | + | 0.766136i | \(0.277823\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.83662e8 | − | 4.30770e8i | 1.46400 | − | 0.641124i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.37742e8 | − | 2.38576e8i | 0.195126 | − | 0.337969i | −0.751816 | − | 0.659373i | \(-0.770822\pi\) |
0.946942 | + | 0.321405i | \(0.104155\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.66593e8i | 0.728460i | 0.931309 | + | 0.364230i | \(0.118668\pi\) | ||||
−0.931309 | + | 0.364230i | \(0.881332\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.71142e8 | 0.700160 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.27950e9 | − | 7.38720e8i | −1.42842 | − | 0.824699i | −0.431425 | − | 0.902149i | \(-0.641989\pi\) |
−0.996996 | + | 0.0774499i | \(0.975322\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.86470e7 | − | 3.47270e8i | 0.0412063 | − | 0.370267i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.83010e8 | + | 6.63393e8i | 0.373077 | + | 0.646188i | 0.990037 | − | 0.140806i | \(-0.0449694\pi\) |
−0.616960 | + | 0.786994i | \(0.711636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.84765e9i | − | 1.72150i | −0.509030 | − | 0.860749i | \(-0.669996\pi\) | ||
0.509030 | − | 0.860749i | \(-0.330004\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.56128e8 | − | 2.63345e8i | 0.389403 | − | 0.224822i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.04075e8 | + | 6.00878e7i | 0.0851099 | + | 0.0491382i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.14741e8 | − | 1.98737e8i | 0.0862152 | − | 0.149329i | −0.819693 | − | 0.572803i | \(-0.805856\pi\) |
0.905908 | + | 0.423474i | \(0.139189\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.44633e8 | − | 1.28974e9i | −0.536677 | − | 0.929552i | −0.999080 | − | 0.0428820i | \(-0.986346\pi\) |
0.462403 | − | 0.886670i | \(-0.346987\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.44196e8 | −0.294924 | −0.147462 | − | 0.989068i | \(-0.547110\pi\) | ||||
−0.147462 | + | 0.989068i | \(0.547110\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.25444e9 | + | 7.24251e8i | −0.799904 | + | 0.461825i | −0.843437 | − | 0.537227i | \(-0.819472\pi\) |
0.0435338 | + | 0.999052i | \(0.486138\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.58034e9 | − | 1.89893e9i | −1.51947 | − | 1.11821i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.22460e9 | − | 2.12107e9i | 0.693392 | − | 1.20099i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.43469e8i | 0.180012i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.24503e8 | −0.0628129 | −0.0314065 | − | 0.999507i | \(-0.509999\pi\) | ||||
−0.0314065 | + | 0.999507i | \(0.509999\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.81206e8 | + | 5.08765e8i | 0.412405 | + | 0.238102i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.28769e9 | − | 1.43304e8i | −0.580728 | − | 0.0646280i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.42365e8 | + | 7.66199e8i | 0.185444 | + | 0.321198i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.07401e9i | − | 0.434300i | −0.976138 | − | 0.217150i | \(-0.930324\pi\) | ||
0.976138 | − | 0.217150i | \(-0.0696761\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.61590e9 | − | 2.08764e9i | 1.36180 | − | 0.786234i | 0.371935 | − | 0.928259i | \(-0.378695\pi\) |
0.989863 | + | 0.142025i | \(0.0453612\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.27312e9 | − | 1.31238e9i | −0.826571 | − | 0.477221i | 0.0261064 | − | 0.999659i | \(-0.491689\pi\) |
−0.852677 | + | 0.522438i | \(0.825022\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.84691e8 | + | 1.18592e9i | −0.232312 | + | 0.402376i | −0.958488 | − | 0.285133i | \(-0.907962\pi\) |
0.726176 | + | 0.687509i | \(0.241296\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.06903e8 | − | 1.22439e9i | −0.231786 | − | 0.401466i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.37306e9 | −0.727307 | −0.363653 | − | 0.931534i | \(-0.618471\pi\) | ||||
−0.363653 | + | 0.931534i | \(0.618471\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.85917e9 | − | 1.65074e9i | 0.847564 | − | 0.489341i | −0.0122645 | − | 0.999925i | \(-0.503904\pi\) |
0.859828 | + | 0.510584i | \(0.170571\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.27458e8 | + | 2.78416e9i | −0.174149 | + | 0.772735i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.26430e9 | + | 2.18984e9i | −0.339675 | + | 0.588335i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.12960e7i | 0.00788487i | 0.999992 | + | 0.00394244i | \(0.00125492\pi\) | ||||
−0.999992 | + | 0.00394244i | \(0.998745\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.50112e8 | −0.231896 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.40586e8 | + | 3.69842e8i | 0.146840 | + | 0.0847782i | 0.571620 | − | 0.820518i | \(-0.306315\pi\) |
−0.424780 | + | 0.905297i | \(0.639648\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.33982e9 | − | 1.02466e9i | 0.519975 | − | 0.227710i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.59579e9 | + | 4.49604e9i | 0.542558 | + | 0.939738i | 0.998756 | + | 0.0498601i | \(0.0158775\pi\) |
−0.456198 | + | 0.889878i | \(0.650789\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.90598e9i | 1.40037i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.76648e9 | − | 2.17458e9i | 0.719328 | − | 0.415304i | −0.0951772 | − | 0.995460i | \(-0.530342\pi\) |
0.814505 | + | 0.580156i | \(0.197008\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.75508e9 | + | 2.16799e9i | 0.696212 | + | 0.401958i | 0.805935 | − | 0.592004i | \(-0.201663\pi\) |
−0.109723 | + | 0.993962i | \(0.534996\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.54576e8 | + | 2.67733e8i | −0.0270278 | + | 0.0468136i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.19364e9 | + | 8.99565e9i | 0.882171 | + | 1.52797i | 0.848922 | + | 0.528518i | \(0.177252\pi\) |
0.0332491 | + | 0.999447i | \(0.489415\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.25066e9 | −0.842149 | −0.421074 | − | 0.907026i | \(-0.638347\pi\) | ||||
−0.421074 | + | 0.907026i | \(0.638347\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.61734e8 | + | 2.66582e8i | −0.0719857 | + | 0.0415610i | −0.535561 | − | 0.844497i | \(-0.679900\pi\) |
0.463575 | + | 0.886058i | \(0.346566\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.04039e9 | − | 9.56675e9i | 1.03769 | − | 1.41006i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.88775e9 | + | 3.26968e9i | −0.270616 | + | 0.468720i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.02293e9i | 0.545849i | 0.962036 | + | 0.272924i | \(0.0879908\pi\) | ||||
−0.962036 | + | 0.272924i | \(0.912009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.36105e9 | −0.443799 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.05760e9 | − | 3.49736e9i | −0.757907 | − | 0.437578i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.97454e9 | + | 2.92496e9i | 0.484196 | + | 0.356331i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.37245e8 | + | 2.37714e8i | 0.0158597 | + | 0.0274699i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.66029e9i | 0.862366i | 0.902265 | + | 0.431183i | \(0.141904\pi\) | ||||
−0.902265 | + | 0.431183i | \(0.858096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.30940e10 | + | 7.55982e9i | −1.39969 | + | 0.808109i | −0.994359 | − | 0.106063i | \(-0.966175\pi\) |
−0.405326 | + | 0.914172i | \(0.632842\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.40149e9 | + | 1.38650e9i | 0.250209 | + | 0.144458i | 0.619860 | − | 0.784712i | \(-0.287189\pi\) |
−0.369651 | + | 0.929171i | \(0.620523\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.98768e9 | + | 3.44277e9i | −0.196839 | + | 0.340934i | −0.947502 | − | 0.319751i | \(-0.896401\pi\) |
0.750663 | + | 0.660685i | \(0.229734\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.41730e9 | + | 2.45483e9i | 0.136867 | + | 0.237061i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.14652e9 | 0.840322 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.97105e9 | + | 1.13799e9i | −0.176670 | + | 0.102001i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.75052e9 | − | 6.28081e9i | −0.234764 | − | 0.536083i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.95902e9 | + | 8.58927e9i | −0.413127 | + | 0.715557i | −0.995230 | − | 0.0975583i | \(-0.968897\pi\) |
0.582103 | + | 0.813115i | \(0.302230\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.69833e10i | − | 1.34848i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.98626e9 | 0.619189 | 0.309595 | − | 0.950869i | \(-0.399807\pi\) | ||||
0.309595 | + | 0.950869i | \(0.399807\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.92765e8 | + | 5.73173e8i | 0.0734224 | + | 0.0423905i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.51784e9 | + | 1.30832e10i | −0.326403 | + | 0.945231i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.76637e9 | − | 3.05945e9i | −0.121833 | − | 0.211021i | 0.798658 | − | 0.601786i | \(-0.205544\pi\) |
−0.920491 | + | 0.390765i | \(0.872211\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.17888e10i | 0.794638i | 0.917680 | + | 0.397319i | \(0.130059\pi\) | ||||
−0.917680 | + | 0.397319i | \(0.869941\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.39483e10 | − | 8.05305e9i | 0.898301 | − | 0.518634i | 0.0216525 | − | 0.999766i | \(-0.493107\pi\) |
0.876649 | + | 0.481131i | \(0.159774\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.50133e9 | + | 5.48560e9i | 0.598234 | + | 0.345391i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.78100e9 | + | 8.28093e9i | −0.287833 | + | 0.498541i | −0.973292 | − | 0.229570i | \(-0.926268\pi\) |
0.685459 | + | 0.728111i | \(0.259601\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.57886e9 | + | 7.93082e9i | 0.269605 | + | 0.466970i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.82210e9 | −0.384368 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.48860e10 | + | 1.43680e10i | −1.37180 | + | 0.792010i | −0.991155 | − | 0.132710i | \(-0.957632\pi\) |
−0.380647 | + | 0.924720i | \(0.624299\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.70445e9 | + | 3.32871e10i | −0.195537 | + | 1.75703i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.48457e9 | − | 4.30341e9i | 0.128356 | − | 0.222319i | −0.794684 | − | 0.607024i | \(-0.792363\pi\) |
0.923040 | + | 0.384704i | \(0.125697\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.08683e10i | 1.03305i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.03220e10 | 1.46961 | 0.734804 | − | 0.678280i | \(-0.237274\pi\) | ||||
0.734804 | + | 0.678280i | \(0.237274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.45211e10 | + | 8.38379e9i | 0.674848 | + | 0.389624i | 0.797911 | − | 0.602775i | \(-0.205938\pi\) |
−0.123063 | + | 0.992399i | \(0.539272\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.49669e9 | − | 2.03376e9i | 0.0681224 | − | 0.0925674i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.83553e9 | − | 6.64334e9i | −0.167505 | − | 0.290127i | 0.770037 | − | 0.637999i | \(-0.220238\pi\) |
−0.937542 | + | 0.347872i | \(0.886904\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.53014e10i | 1.08252i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.67140e10 | − | 9.64980e9i | 0.686579 | − | 0.396397i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.70191e10 | + | 9.82597e9i | 0.685132 | + | 0.395561i | 0.801786 | − | 0.597612i | \(-0.203884\pi\) |
−0.116654 | + | 0.993173i | \(0.537217\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.16330e10 | − | 3.74694e10i | 0.836639 | − | 1.44910i | −0.0560491 | − | 0.998428i | \(-0.517850\pi\) |
0.892689 | − | 0.450674i | \(-0.148816\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.21969e9 | + | 7.30872e9i | 0.159978 | + | 0.277090i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.26001e9 | −0.0823632 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.76795e10 | − | 1.02073e10i | 0.631796 | − | 0.364768i | −0.149651 | − | 0.988739i | \(-0.547815\pi\) |
0.781447 | + | 0.623971i | \(0.214482\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.62004e10 | − | 1.80291e9i | −0.556834 | − | 0.0619688i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.54255e10 | + | 2.67178e10i | −0.520053 | + | 0.900758i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.55195e10i | 0.503524i | 0.967789 | + | 0.251762i | \(0.0810101\pi\) | ||||
−0.967789 | + | 0.251762i | \(0.918990\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.58425e9 | −0.0822633 | −0.0411317 | − | 0.999154i | \(-0.513096\pi\) | ||||
−0.0411317 | + | 0.999154i | \(0.513096\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.12971e9 | + | 4.11634e9i | 0.218532 | + | 0.126170i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.34011e8 | + | 1.21941e9i | 0.0160635 | + | 0.0366809i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.10297e10 | − | 1.91041e10i | −0.319637 | − | 0.553627i | 0.660776 | − | 0.750583i | \(-0.270227\pi\) |
−0.980412 | + | 0.196957i | \(0.936894\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.09726e10i | − | 1.73453i | −0.497843 | − | 0.867267i | \(-0.665874\pi\) | ||
0.497843 | − | 0.867267i | \(-0.334126\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.26247e10 | + | 3.61564e10i | −1.71720 | + | 0.991424i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.10681e10 | − | 2.94842e10i | −1.37497 | − | 0.793836i | −0.383417 | − | 0.923575i | \(-0.625253\pi\) |
−0.991548 | + | 0.129739i | \(0.958586\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.02703e10 | + | 1.77888e10i | −0.266668 | + | 0.461882i | −0.967999 | − | 0.250953i | \(-0.919256\pi\) |
0.701332 | + | 0.712835i | \(0.252589\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.32891e10 | − | 2.30175e10i | −0.338889 | − | 0.586972i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.11616e10 | 1.50485 | 0.752425 | − | 0.658678i | \(-0.228884\pi\) | ||||
0.752425 | + | 0.658678i | \(0.228884\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.10143e9 | + | 5.25471e9i | −0.219990 | + | 0.127011i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.70287e10 | − | 7.45729e9i | 0.397316 | − | 0.173994i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.93723e9 | − | 1.20156e10i | 0.159045 | − | 0.275475i | −0.775479 | − | 0.631373i | \(-0.782492\pi\) |
0.934525 | + | 0.355898i | \(0.115825\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.22295e10i | − | 1.59923i | −0.600513 | − | 0.799615i | \(-0.705037\pi\) | ||
0.600513 | − | 0.799615i | \(-0.294963\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.19540e10 | −1.13056 | −0.565281 | − | 0.824898i | \(-0.691232\pi\) | ||||
−0.565281 | + | 0.824898i | \(0.691232\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.77578e10 | − | 3.33465e10i | −1.21435 | − | 0.701104i | −0.250644 | − | 0.968079i | \(-0.580642\pi\) |
−0.963703 | + | 0.266975i | \(0.913976\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.11008e9 | − | 8.18604e10i | 0.188291 | − | 1.69193i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.18309e9 | − | 3.78122e9i | −0.0436141 | − | 0.0755419i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.35295e10i | 0.462208i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.78886e10 | + | 2.18750e10i | −0.719724 | + | 0.415533i | −0.814651 | − | 0.579951i | \(-0.803072\pi\) |
0.0949269 | + | 0.995484i | \(0.469738\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.44091e10 | − | 8.31909e9i | −0.269188 | − | 0.155416i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.23647e9 | − | 1.25339e10i | 0.130786 | − | 0.226527i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.08822e9 | − | 3.61691e9i | −0.0371245 | − | 0.0643016i | 0.846866 | − | 0.531806i | \(-0.178486\pi\) |
−0.883991 | + | 0.467505i | \(0.845153\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.01240e10 | 0.518307 | 0.259153 | − | 0.965836i | \(-0.416557\pi\) | ||||
0.259153 | + | 0.965836i | \(0.416557\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.53719e10 | − | 3.77425e10i | 1.10663 | − | 0.638915i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.28543e10 | + | 3.15374e10i | 0.702374 | + | 0.516893i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.25369e10 | − | 5.63555e10i | 0.524776 | − | 0.908938i | −0.474808 | − | 0.880089i | \(-0.657483\pi\) |
0.999584 | − | 0.0288486i | \(-0.00918408\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.63371e10i | 0.723864i | 0.932204 | + | 0.361932i | \(0.117883\pi\) | ||||
−0.932204 | + | 0.361932i | \(0.882117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.57830e10 | 1.01146 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.46633e10 | + | 2.00129e10i | 0.516415 | + | 0.298152i | 0.735466 | − | 0.677561i | \(-0.236963\pi\) |
−0.219052 | + | 0.975713i | \(0.570296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.28828e10 | − | 3.65946e9i | −0.482265 | − | 0.0536702i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.35559e10 | − | 4.08001e10i | −0.334866 | − | 0.580006i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.06659e9i | 0.0849146i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.05814e10 | + | 2.34297e10i | −0.550777 | + | 0.317992i | −0.749436 | − | 0.662077i | \(-0.769675\pi\) |
0.198658 | + | 0.980069i | \(0.436342\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.50830e10 | − | 4.33492e10i | −1.00354 | − | 0.579395i | −0.0942468 | − | 0.995549i | \(-0.530044\pi\) |
−0.909294 | + | 0.416154i | \(0.863378\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.52635e10 | − | 2.64372e10i | 0.197885 | − | 0.342746i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.08613e10 | − | 1.05415e11i | −0.777175 | − | 1.34611i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.73702e10 | −0.958661 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.33320e10 | + | 1.92442e10i | −0.406861 | + | 0.234901i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.30506e9 | − | 8.99999e9i | 0.0983984 | − | 0.106632i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.33406e10 | − | 5.77477e10i | 0.389211 | − | 0.674133i | −0.603133 | − | 0.797641i | \(-0.706081\pi\) |
0.992344 | + | 0.123508i | \(0.0394145\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.51695e10i | − | 0.171944i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.37378e10 | −0.376849 | −0.188425 | − | 0.982088i | \(-0.560338\pi\) | ||||
−0.188425 | + | 0.982088i | \(0.560338\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.86837e11 | + | 1.07870e11i | 2.02701 | + | 1.17029i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.57382e10 | − | 3.75469e10i | 0.916799 | − | 0.401489i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.38794e10 | + | 4.13604e10i | 0.248087 | + | 0.429699i | 0.962995 | − | 0.269520i | \(-0.0868649\pi\) |
−0.714908 | + | 0.699218i | \(0.753532\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.21438e10i | − | 0.329192i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.30170e10 | − | 5.37034e10i | 0.925825 | − | 0.534525i | 0.0403360 | − | 0.999186i | \(-0.487157\pi\) |
0.885489 | + | 0.464661i | \(0.153824\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.58586e10 | − | 3.22500e10i | −0.548146 | − | 0.316472i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.54714e10 | + | 2.67973e10i | −0.147598 | + | 0.255648i | −0.930339 | − | 0.366700i | \(-0.880488\pi\) |
0.782741 | + | 0.622348i | \(0.213821\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.37493e10 | − | 9.30965e10i | −0.505625 | − | 0.875768i | −0.999979 | − | 0.00650703i | \(-0.997929\pi\) |
0.494354 | − | 0.869261i | \(-0.335405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.50878e10 | −0.595427 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.22110e10 | + | 3.01440e10i | −0.471041 | + | 0.271955i | −0.716675 | − | 0.697407i | \(-0.754337\pi\) |
0.245635 | + | 0.969363i | \(0.421004\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.86834e10 | + | 1.20506e11i | −0.778284 | + | 1.05756i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.48167e10 | − | 2.56632e10i | 0.128255 | − | 0.222145i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 2.16561e10i | − | 0.182401i | −0.995833 | − | 0.0912005i | \(-0.970930\pi\) | ||
0.995833 | − | 0.0912005i | \(-0.0290704\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.72480e10 | 0.724927 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.44121e11 | − | 8.32084e10i | −1.16549 | − | 0.672897i | −0.212878 | − | 0.977079i | \(-0.568284\pi\) |
−0.952614 | + | 0.304182i | \(0.901617\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.41589e10 | − | 3.98568e10i | −0.432118 | − | 0.318005i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.40903e10 | − | 1.45649e11i | −0.653189 | − | 1.13136i | −0.982345 | − | 0.187080i | \(-0.940098\pi\) |
0.329156 | − | 0.944276i | \(-0.393236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.87638e10i | − | 0.603710i | −0.953354 | − | 0.301855i | \(-0.902394\pi\) | ||
0.953354 | − | 0.301855i | \(-0.0976059\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.99705e10 | − | 5.19445e10i | 0.671550 | − | 0.387720i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.54048e10 | − | 1.46674e10i | −0.187137 | − | 0.108044i | 0.403504 | − | 0.914978i | \(-0.367792\pi\) |
−0.590642 | + | 0.806934i | \(0.701125\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.23311e10 | + | 3.86785e10i | −0.160230 | + | 0.277527i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.10346e10 | − | 8.83945e10i | −0.361429 | − | 0.626013i | 0.626767 | − | 0.779206i | \(-0.284378\pi\) |
−0.988196 | + | 0.153193i | \(0.951044\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.49461e11 | 1.72132 | 0.860661 | − | 0.509179i | \(-0.170051\pi\) | ||||
0.860661 | + | 0.509179i | \(0.170051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.46061e11 | + | 8.43281e10i | −0.994879 | + | 0.574394i | −0.906729 | − | 0.421713i | \(-0.861429\pi\) |
−0.0881501 | + | 0.996107i | \(0.528096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.17074e10 | − | 1.18074e11i | −0.343242 | − | 0.783792i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.72811e10 | − | 6.45728e10i | 0.244325 | − | 0.423184i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.01839e10i | 0.384483i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.03011e10 | 0.506529 | 0.253265 | − | 0.967397i | \(-0.418496\pi\) | ||||
0.253265 | + | 0.967397i | \(0.418496\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.19244e11 | − | 6.88458e10i | −0.733404 | − | 0.423431i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.60792e10 | − | 2.68100e10i | 0.522806 | − | 0.162832i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.51587e10 | + | 7.82172e10i | 0.267491 | + | 0.463308i | 0.968213 | − | 0.250126i | \(-0.0804721\pi\) |
−0.700722 | + | 0.713434i | \(0.747139\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.94542e11i | 1.72307i | 0.507696 | + | 0.861536i | \(0.330497\pi\) | ||||
−0.507696 | + | 0.861536i | \(0.669503\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.46833e11 | + | 8.47741e10i | −0.837928 | + | 0.483778i | −0.856559 | − | 0.516048i | \(-0.827402\pi\) |
0.0186314 | + | 0.999826i | \(0.494069\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.24899e10 | + | 7.21107e9i | 0.0704015 | + | 0.0406463i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.31238e10 | + | 7.46926e10i | −0.237172 | + | 0.410795i | −0.959902 | − | 0.280337i | \(-0.909554\pi\) |
0.722729 | + | 0.691131i | \(0.242887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.05571e10 | + | 1.56849e11i | 0.491991 | + | 0.852153i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.84405e10 | −0.415909 | −0.207955 | − | 0.978138i | \(-0.566681\pi\) | ||||
−0.207955 | + | 0.978138i | \(0.566681\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.79270e11 | − | 1.03502e11i | 0.939080 | − | 0.542178i | 0.0494080 | − | 0.998779i | \(-0.484267\pi\) |
0.889672 | + | 0.456601i | \(0.150933\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.12569e10 | − | 1.91008e11i | 0.108696 | − | 0.976708i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.98394e11 | + | 5.16833e11i | −1.50760 | + | 2.61124i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.17782e9i | − | 0.00581018i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.74989e11 | 1.82792 | 0.913961 | − | 0.405801i | \(-0.133008\pi\) | ||||
0.913961 | + | 0.405801i | \(0.133008\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.82953e11 | − | 1.05628e11i | −0.870932 | − | 0.502833i | −0.00327401 | − | 0.999995i | \(-0.501042\pi\) |
−0.867658 | + | 0.497162i | \(0.834375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.16034e10 | − | 5.65323e10i | 0.195727 | − | 0.265961i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.80288e11 | + | 3.12268e11i | 0.828484 | + | 1.43498i | 0.899227 | + | 0.437482i | \(0.144130\pi\) |
−0.0707428 | + | 0.997495i | \(0.522537\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.89462e11i | 0.860519i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.88932e11 | − | 1.09080e11i | 0.838356 | − | 0.484025i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.19035e11 | − | 6.87249e10i | −0.522110 | − | 0.301441i | 0.215687 | − | 0.976462i | \(-0.430801\pi\) |
−0.737798 | + | 0.675022i | \(0.764134\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.47286e11 | − | 2.55106e11i | 0.631279 | − | 1.09341i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.39932e11 | + | 2.42370e11i | 0.592908 | + | 1.02695i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.01153e11 | −1.24714 | −0.623570 | − | 0.781767i | \(-0.714318\pi\) | ||||
−0.623570 | + | 0.781767i | \(0.714318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.48964e11 | + | 8.60044e10i | −0.609902 | + | 0.352127i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.17077e11 | + | 3.52868e10i | 1.26907 | + | 0.141232i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.24726e11 | − | 2.16031e11i | 0.493595 | − | 0.854931i | −0.506378 | − | 0.862312i | \(-0.669016\pi\) |
0.999973 | + | 0.00738024i | \(0.00234922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.41348e11i | 0.933868i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.64479e10 | −0.0629341 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.58304e11 | + | 1.49132e11i | 0.966531 | + | 0.558027i | 0.898177 | − | 0.439634i | \(-0.144892\pi\) |
0.0683543 | + | 0.997661i | \(0.478225\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.16550e10 | − | 2.09294e11i | −0.339168 | − | 0.774489i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.70926e10 | + | 1.68169e11i | 0.351426 | + | 0.608688i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.07469e11i | 1.81665i | 0.418263 | + | 0.908326i | \(0.362639\pi\) | ||||
−0.418263 | + | 0.908326i | \(0.637361\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.00694e11 | + | 5.81354e10i | −0.352640 | + | 0.203597i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.01877e9 | + | 4.05229e9i | 0.0243134 | + | 0.0140373i | 0.512107 | − | 0.858921i | \(-0.328865\pi\) |
−0.487794 | + | 0.872959i | \(0.662198\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.64375e10 | + | 6.31116e10i | −0.123503 | + | 0.213914i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.21836e11 | + | 2.11026e11i | 0.408506 | + | 0.707553i | 0.994723 | − | 0.102601i | \(-0.0327166\pi\) |
−0.586217 | + | 0.810154i | \(0.699383\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.89064e11 | −0.620376 | −0.310188 | − | 0.950675i | \(-0.600392\pi\) | ||||
−0.310188 | + | 0.950675i | \(0.600392\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.66329e10 | + | 5.57910e10i | −0.313689 | + | 0.181109i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.70984e11 | + | 7.48783e10i | −0.543287 | + | 0.237919i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.32130e11 | + | 4.02061e11i | −0.729746 | + | 1.26396i | 0.227245 | + | 0.973838i | \(0.427028\pi\) |
−0.956991 | + | 0.290119i | \(0.906305\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 4.52867e11i | − | 1.39374i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.81923e11 | 0.858513 | 0.429257 | − | 0.903183i | \(-0.358776\pi\) | ||||
0.429257 | + | 0.903183i | \(0.358776\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.54973e9 | + | 1.47209e9i | 0.00760248 | + | 0.00438929i | 0.503796 | − | 0.863822i | \(-0.331936\pi\) |
−0.496194 | + | 0.868212i | \(0.665270\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.13713e9 | − | 7.31178e10i | 0.0240089 | − | 0.215737i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.30878e10 | + | 9.19508e10i | 0.153396 | + | 0.265689i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.03649e11i | 0.868293i | 0.900842 | + | 0.434146i | \(0.142950\pi\) | ||||
−0.900842 | + | 0.434146i | \(0.857050\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.73971e11 | − | 2.73647e11i | 1.32750 | − | 0.766431i | 0.342585 | − | 0.939487i | \(-0.388698\pi\) |
0.984912 | + | 0.173056i | \(0.0553642\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.80098e10 | + | 3.92654e10i | 0.188523 | + | 0.108844i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.99935e11 | + | 6.92707e11i | −1.08602 | + | 1.88105i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.35385e10 | − | 4.07699e10i | −0.0632666 | − | 0.109581i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.04379e11 | 0.274875 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.54149e11 | + | 2.04468e11i | −0.923182 | + | 0.532999i | −0.884649 | − | 0.466258i | \(-0.845602\pi\) |
−0.0385331 | + | 0.999257i | \(0.512268\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.51942e11 | − | 1.85410e11i | −0.643567 | − | 0.473616i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.33556e9 | − | 7.50940e9i | 0.0109636 | − | 0.0189895i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.43730e11i | − | 0.604055i | −0.953299 | − | 0.302027i | \(-0.902337\pi\) | ||
0.953299 | − | 0.302027i | \(-0.0976634\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.61553e11 | 0.396394 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.53515e10 | + | 1.46367e10i | 0.0609736 | + | 0.0352031i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.28371e11 | + | 5.88013e10i | 1.25822 | + | 0.140024i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.88172e11 | − | 3.25924e11i | −0.439300 | − | 0.760890i | 0.558335 | − | 0.829615i | \(-0.311440\pi\) |
−0.997636 | + | 0.0687249i | \(0.978107\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.15386e11i | 1.42254i | 0.702920 | + | 0.711269i | \(0.251879\pi\) | ||||
−0.702920 | + | 0.711269i | \(0.748121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.18112e11 | − | 6.81922e10i | 0.267710 | − | 0.154563i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.87788e11 | − | 1.66154e11i | −0.645928 | − | 0.372927i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.08388e11 | − | 5.34144e11i | 0.678774 | − | 1.17567i | −0.296576 | − | 0.955009i | \(-0.595845\pi\) |
0.975350 | − | 0.220662i | \(-0.0708218\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.77630e10 | − | 6.54074e10i | −0.0823127 | − | 0.142570i | 0.821930 | − | 0.569588i | \(-0.192897\pi\) |
−0.904243 | + | 0.427018i | \(0.859564\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.93362e11 | −0.413380 | −0.206690 | − | 0.978406i | \(-0.566269\pi\) | ||||
−0.206690 | + | 0.978406i | \(0.566269\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.02147e11 | + | 5.89748e10i | −0.216276 | + | 0.124867i | −0.604225 | − | 0.796814i | \(-0.706517\pi\) |
0.387949 | + | 0.921681i | \(0.373184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.39669e11 | − | 2.21163e11i | −0.497773 | − | 0.459338i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.40252e11 | + | 2.42924e11i | −0.288512 | + | 0.499718i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.17469e11i | 1.44796i | 0.689823 | + | 0.723978i | \(0.257688\pi\) | ||||
−0.689823 | + | 0.723978i | \(0.742312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.28023e12 | 2.55920 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.44874e11 | + | 1.41378e11i | 0.480304 | + | 0.277304i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.61525e11 | − | 2.02113e11i | 0.896730 | − | 0.392700i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.37908e11 | − | 4.12069e11i | −0.453618 | − | 0.785690i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.84954e11i | 1.29379i | 0.762577 | + | 0.646897i | \(0.223934\pi\) | ||||
−0.762577 | + | 0.646897i | \(0.776066\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.95605e11 | + | 2.86137e11i | −0.918781 | + | 0.530458i | −0.883246 | − | 0.468910i | \(-0.844647\pi\) |
−0.0355351 | + | 0.999368i | \(0.511314\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.20619e11 | − | 6.96395e10i | −0.221536 | − | 0.127904i | 0.385126 | − | 0.922864i | \(-0.374158\pi\) |
−0.606661 | + | 0.794961i | \(0.707491\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.25312e11 | + | 3.90251e11i | −0.406200 | + | 0.703560i | −0.994460 | − | 0.105112i | \(-0.966480\pi\) |
0.588260 | + | 0.808672i | \(0.299813\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.65720e11 | − | 6.33445e11i | −0.653257 | − | 1.13147i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.28140e10 | −0.145219 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.64626e11 | + | 2.68252e11i | −0.807293 | + | 0.466091i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.77745e11 | − | 5.13294e11i | 0.644416 | − | 0.875658i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.71149e11 | − | 2.96439e11i | 0.289319 | − | 0.501114i | −0.684329 | − | 0.729174i | \(-0.739905\pi\) |
0.973647 | + | 0.228059i | \(0.0732380\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.49186e11i | 1.07762i | 0.842427 | + | 0.538810i | \(0.181126\pi\) | ||||
−0.842427 | + | 0.538810i | \(0.818874\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.09905e11 | 0.180790 | 0.0903951 | − | 0.995906i | \(-0.471187\pi\) | ||||
0.0903951 | + | 0.995906i | \(0.471187\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.02639e11 | − | 1.74729e11i | −0.488912 | − | 0.282274i | 0.235211 | − | 0.971944i | \(-0.424422\pi\) |
−0.724123 | + | 0.689671i | \(0.757755\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.37833e11 | − | 3.95804e11i | −0.861074 | − | 0.633684i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.30863e11 | + | 3.99867e11i | 0.363035 | + | 0.628795i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.79235e11i | 0.591040i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.23578e11 | − | 3.60023e11i | 0.954667 | − | 0.551177i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.83408e11 | − | 3.94566e11i | −1.03700 | − | 0.598715i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.57361e11 | − | 7.92172e11i | 0.681812 | − | 1.18093i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.29895e11 | − | 9.17805e11i | −0.782998 | − | 1.35619i | −0.930188 | − | 0.367084i | \(-0.880356\pi\) |
0.147190 | − | 0.989108i | \(-0.452977\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.66809e11 | 1.11330 | 0.556652 | − | 0.830746i | \(-0.312086\pi\) | ||||
0.556652 | + | 0.830746i | \(0.312086\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.14645e11 | − | 6.61904e10i | 0.164996 | − | 0.0952603i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.52353e11 | + | 8.04597e11i | 0.498311 | + | 1.13789i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.25499e11 | − | 5.63780e11i | 0.456339 | − | 0.790402i | −0.542425 | − | 0.840104i | \(-0.682494\pi\) |
0.998764 | + | 0.0497021i | \(0.0158272\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 3.46580e11i | − | 0.477526i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.54823e11 | −0.211480 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.11519e11 | − | 5.26266e11i | −1.22378 | − | 0.706549i | −0.258058 | − | 0.966130i | \(-0.583082\pi\) |
−0.965722 | + | 0.259580i | \(0.916416\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.04918e11 | − | 9.09264e11i | 0.272760 | − | 1.21029i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.97478e10 | + | 5.15247e10i | 0.0389232 | + | 0.0674169i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.22936e11i | − | 0.418946i | −0.977814 | − | 0.209473i | \(-0.932825\pi\) | ||
0.977814 | − | 0.209473i | \(-0.0671748\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.73086e11 | + | 5.61812e11i | −1.24106 | + | 0.716526i | −0.969310 | − | 0.245841i | \(-0.920936\pi\) |
−0.271750 | + | 0.962368i | \(0.587602\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.91619e12 | − | 1.10631e12i | −2.42321 | − | 1.39904i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.59737e11 | + | 6.23083e11i | −0.447286 | + | 0.774723i | −0.998208 | − | 0.0598341i | \(-0.980943\pi\) |
0.550922 | + | 0.834557i | \(0.314276\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.07755e11 | + | 1.86637e11i | 0.132854 | + | 0.230109i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.43394e11 | 0.537549 | 0.268775 | − | 0.963203i | \(-0.413381\pi\) | ||||
0.268775 | + | 0.963203i | \(0.413381\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.83890e10 | − | 5.68049e10i | 0.118286 | − | 0.0682924i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.01630e11 | + | 9.13216e11i | −0.120156 | + | 1.07969i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.80848e11 | + | 4.86443e11i | −0.329289 | + | 0.570346i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 7.37294e11i | − | 0.850220i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.62631e12 | 1.85993 | 0.929965 | − | 0.367647i | \(-0.119837\pi\) | ||||
0.929965 | + | 0.367647i | \(0.119837\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.05556e12 | + | 6.09425e11i | 1.18742 | + | 0.685557i | 0.957719 | − | 0.287704i | \(-0.0928921\pi\) |
0.229700 | + | 0.973261i | \(0.426225\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.46766e11 | − | 1.15062e12i | 0.944739 | − | 1.28375i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.03817e11 | + | 1.04584e12i | 0.662715 | + | 1.14786i | 0.979899 | + | 0.199493i | \(0.0639294\pi\) |
−0.317184 | + | 0.948364i | \(0.602737\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.14047e11i | 0.124151i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.14970e11 | + | 1.81848e11i | −0.337330 | + | 0.194758i | −0.659091 | − | 0.752063i | \(-0.729059\pi\) |
0.321760 | + | 0.946821i | \(0.395725\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.90447e11 | − | 1.09955e11i | −0.202316 | − | 0.116807i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.59621e11 | − | 7.96087e11i | 0.480413 | − | 0.832100i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.17673e11 | − | 3.77021e11i | −0.225689 | − | 0.390905i | 0.730837 | − | 0.682552i | \(-0.239130\pi\) |
−0.956526 | + | 0.291647i | \(0.905797\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.17113e11 | −0.731637 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.88123e11 | + | 1.08613e11i | −0.190397 | + | 0.109926i | −0.592169 | − | 0.805814i | \(-0.701728\pi\) |
0.401771 | + | 0.915740i | \(0.368395\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.9.z.e.145.7 | yes | 20 | |
3.2 | odd | 2 | inner | 252.9.z.e.145.4 | yes | 20 | |
7.3 | odd | 6 | inner | 252.9.z.e.73.7 | yes | 20 | |
21.17 | even | 6 | inner | 252.9.z.e.73.4 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.z.e.73.4 | ✓ | 20 | 21.17 | even | 6 | inner | |
252.9.z.e.73.7 | yes | 20 | 7.3 | odd | 6 | inner | |
252.9.z.e.145.4 | yes | 20 | 3.2 | odd | 2 | inner | |
252.9.z.e.145.7 | yes | 20 | 1.1 | even | 1 | trivial |