Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [208,12,Mod(129,208)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(208, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("208.129");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 208 = 2^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 208.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(159.815381556\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 18433 x^{10} + 121088056 x^{8} + 340607607312 x^{6} + 380893885719552 x^{4} + \cdots + 14\!\cdots\!56 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{31}\cdot 3^{4}\cdot 13^{4} \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.11 | ||
Root | \(-25.1535i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 208.129 |
Dual form | 208.12.f.b.129.12 |
$q$-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 \(\left(\mathbb{Z}/208\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 638.702 | 1.51751 | 0.758755 | − | 0.651377i | \(-0.225808\pi\) | ||||
0.758755 | + | 0.651377i | \(0.225808\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 9287.93i | − | 1.32918i | −0.747208 | − | 0.664590i | \(-0.768606\pi\) | ||
0.747208 | − | 0.664590i | \(-0.231394\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 25239.3i | − | 0.567595i | −0.958884 | − | 0.283797i | \(-0.908406\pi\) | ||
0.958884 | − | 0.283797i | \(-0.0915943\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 230793. | 1.30283 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 809580.i | − | 1.51565i | −0.652456 | − | 0.757827i | \(-0.726261\pi\) | ||
0.652456 | − | 0.757827i | \(-0.273739\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 738773. | − | 1.11641e6i | 0.551852 | − | 0.833942i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 5.93222e6i | − | 2.01704i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.09516e7 | 1.87072 | 0.935361 | − | 0.353693i | \(-0.115074\pi\) | ||||
0.935361 | + | 0.353693i | \(0.115074\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.08406e7i | − | 1.00440i | −0.864751 | − | 0.502201i | \(-0.832524\pi\) | ||
0.864751 | − | 0.502201i | \(-0.167476\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.61204e7i | − | 0.861330i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.65347e6 | 0.183152 | 0.0915761 | − | 0.995798i | \(-0.470810\pi\) | ||||
0.0915761 | + | 0.995798i | \(0.470810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.74375e7 | −0.766719 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.42639e7 | 0.459554 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.64007e7 | 0.691685 | 0.345842 | − | 0.938293i | \(-0.387593\pi\) | ||||
0.345842 | + | 0.938293i | \(0.387593\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.22306e8i | 0.767287i | 0.923481 | + | 0.383643i | \(0.125331\pi\) | ||||
−0.923481 | + | 0.383643i | \(0.874669\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 5.17080e8i | − | 2.30002i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.34421e8 | −0.754435 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.45819e7i | 0.129401i | 0.997905 | + | 0.0647007i | \(0.0206093\pi\) | ||||
−0.997905 | + | 0.0647007i | \(0.979391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.71856e8 | − | 7.13054e8i | 0.837440 | − | 1.26551i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.95844e8i | 1.34239i | 0.741279 | + | 0.671197i | \(0.234220\pi\) | ||||
−0.741279 | + | 0.671197i | \(0.765780\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.96262e8 | 0.411060 | 0.205530 | − | 0.978651i | \(-0.434108\pi\) | ||||
0.205530 | + | 0.978651i | \(0.434108\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 2.14359e9i | − | 1.73170i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.01264e8i | 0.446008i | 0.974817 | + | 0.223004i | \(0.0715864\pi\) | ||||
−0.974817 | + | 0.223004i | \(0.928414\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.34030e9 | 0.677836 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.99482e9 | 2.83884 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.66216e8 | 0.218825 | 0.109413 | − | 0.993996i | \(-0.465103\pi\) | ||||
0.109413 | + | 0.993996i | \(0.465103\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.51932e9 | −2.01458 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.92389e9i | − | 1.52419i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 2.42983e9i | − | 0.442476i | −0.975220 | − | 0.221238i | \(-0.928990\pi\) | ||
0.975220 | − | 0.221238i | \(-0.0710098\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.91257e9 | −1.35110 | −0.675552 | − | 0.737312i | \(-0.736095\pi\) | ||||
−0.675552 | + | 0.737312i | \(0.736095\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 5.82506e9i | − | 0.739482i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.03692e10 | − | 6.86167e9i | −1.10846 | − | 0.733510i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.44060e9i | 0.582794i | 0.956602 | + | 0.291397i | \(0.0941200\pi\) | ||||
−0.956602 | + | 0.291397i | \(0.905880\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.61088e9 | 0.277935 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.38964e10i | − | 0.914073i | −0.889448 | − | 0.457037i | \(-0.848911\pi\) | ||
0.889448 | − | 0.457037i | \(-0.151089\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.48127e10i | − | 0.836296i | −0.908379 | − | 0.418148i | \(-0.862679\pi\) | ||
0.908379 | − | 0.418148i | \(-0.137321\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.39114e10 | −1.16350 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.04332e10 | −0.860277 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.96608e10 | −1.08451 | −0.542256 | − | 0.840213i | \(-0.682430\pi\) | ||||
−0.542256 | + | 0.840213i | \(0.682430\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.89999e10 | −0.605457 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.25290e10i | 0.349129i | 0.984646 | + | 0.174564i | \(0.0558517\pi\) | ||||
−0.984646 | + | 0.174564i | \(0.944148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.01718e11i | − | 2.48653i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.87973e10 | 1.04964 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.03892e10i | 1.71582i | 0.513800 | + | 0.857910i | \(0.328237\pi\) | ||||
−0.513800 | + | 0.857910i | \(0.671763\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.81775e10 | − | 1.86461e10i | −0.473341 | − | 0.313228i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.81170e10i | 1.16436i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00686e11 | −1.33503 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5.24967e10i | − | 0.620708i | −0.950621 | − | 0.310354i | \(-0.899552\pi\) | ||
0.950621 | − | 0.310354i | \(-0.100448\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.86845e11i | − | 1.97464i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.66125e10 | 0.630650 | 0.315325 | − | 0.948984i | \(-0.397887\pi\) | ||||
0.315325 | + | 0.948984i | \(0.397887\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.97201e10 | −0.847574 | −0.423787 | − | 0.905762i | \(-0.639300\pi\) | ||||
−0.423787 | + | 0.905762i | \(0.639300\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.49725e11 | −1.14486 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.29206e11 | 1.57985 | 0.789923 | − | 0.613207i | \(-0.210121\pi\) | ||||
0.789923 | + | 0.613207i | \(0.210121\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.26351e11i | 0.786559i | 0.919419 | + | 0.393279i | \(0.128660\pi\) | ||||
−0.919419 | + | 0.393279i | \(0.871340\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.48615e10i | 0.196368i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.83959e11 | 1.44985 | 0.724927 | − | 0.688825i | \(-0.241873\pi\) | ||||
0.724927 | + | 0.688825i | \(0.241873\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.25090e10i | − | 0.243442i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.70504e11 | − | 2.57660e11i | 0.718971 | − | 1.08649i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.76411e11i | − | 1.06181i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.70108e11 | −1.29720 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.36048e11i | 2.03710i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.05796e11i | − | 0.310072i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.13296e11 | 0.304294 | 0.152147 | − | 0.988358i | \(-0.451381\pi\) | ||||
0.152147 | + | 0.988358i | \(0.451381\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.53093e11 | 0.623788 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.66543e11 | −0.603636 | −0.301818 | − | 0.953366i | \(-0.597594\pi\) | ||||
−0.301818 | + | 0.953366i | \(0.597594\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.73609e11 | −0.570093 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 3.18241e11i | − | 0.610829i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.54368e11i | 0.981375i | 0.871336 | + | 0.490688i | \(0.163254\pi\) | ||||
−0.871336 | + | 0.490688i | \(0.836746\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.49505e11 | 0.734772 | 0.367386 | − | 0.930069i | \(-0.380253\pi\) | ||||
0.367386 | + | 0.930069i | \(0.380253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.47898e11i | 0.676822i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.03824e11 | − | 5.98095e11i | −1.26397 | − | 0.836416i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.09604e11i | − | 0.919373i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.56055e11 | 1.02862 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.82945e11i | 0.204078i | 0.994780 | + | 0.102039i | \(0.0325367\pi\) | ||||
−0.994780 | + | 0.102039i | \(0.967463\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.63643e12i | 1.69639i | 0.529687 | + | 0.848193i | \(0.322309\pi\) | ||||
−0.529687 | + | 0.848193i | \(0.677691\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.52756e12 | 2.43724 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.13597e12 | 1.01986 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.12984e12 | 0.945300 | 0.472650 | − | 0.881250i | \(-0.343297\pi\) | ||||
0.472650 | + | 0.881250i | \(0.343297\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.25513e11 | 0.332069 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.42690e11i | − | 0.103956i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.19794e12i | 0.815461i | 0.913102 | + | 0.407730i | \(0.133680\pi\) | ||||
−0.913102 | + | 0.407730i | \(0.866320\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.80260e12 | −3.05714 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.60628e12i | 0.956932i | 0.878106 | + | 0.478466i | \(0.158807\pi\) | ||||
−0.878106 | + | 0.478466i | \(0.841193\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00590e11 | − | 1.64955e12i | −0.390919 | − | 0.920425i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 2.50193e12i | − | 1.30857i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.48270e12 | −1.70869 | −0.854344 | − | 0.519707i | \(-0.826041\pi\) | ||||
−0.854344 | + | 0.519707i | \(0.826041\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.44896e11i | 0.435186i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1.55194e12i | − | 0.671462i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.99582e12 | −0.811762 | −0.405881 | − | 0.913926i | \(-0.633035\pi\) | ||||
−0.405881 | + | 0.913926i | \(0.633035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.10025e12 | −0.803598 | −0.401799 | − | 0.915728i | \(-0.631615\pi\) | ||||
−0.401799 | + | 0.915728i | \(0.631615\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.69248e12 | −2.05031 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.06952e11 | 0.171998 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 8.86621e12i | − | 2.83537i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 8.64797e11i | − | 0.260840i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.56924e11 | −0.0446689 | −0.0223344 | − | 0.999751i | \(-0.507110\pi\) | ||||
−0.0223344 | + | 0.999751i | \(0.507110\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 8.94216e11i | − | 0.240368i | −0.992752 | − | 0.120184i | \(-0.961651\pi\) | ||
0.992752 | − | 0.120184i | \(-0.0383485\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.62280e12 | − | 4.38256e12i | −1.68210 | − | 1.11311i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.78108e12i | − | 0.907928i | −0.891020 | − | 0.453964i | \(-0.850009\pi\) | ||
0.891020 | − | 0.453964i | \(-0.149991\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.20196e12 | −0.500170 | −0.250085 | − | 0.968224i | \(-0.580459\pi\) | ||||
−0.250085 | + | 0.968224i | \(0.580459\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.11362e12i | 0.884395i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.92830e12i | − | 0.392597i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.24933e12 | 1.78428 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.30478e12 | 0.238617 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.77631e12 | −1.52232 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.45222e12 | 1.55590 | 0.777948 | − | 0.628329i | \(-0.216261\pi\) | ||||
0.777948 | + | 0.628329i | \(0.216261\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.87565e12i | − | 1.38711i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3.68045e12i | − | 0.546373i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.08691e12 | 0.435508 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 9.46093e12i | − | 1.26909i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.09076e12 | − | 1.22265e13i | 1.03236 | − | 1.56007i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.58107e12i | − | 0.313417i | −0.987645 | − | 0.156709i | \(-0.949912\pi\) | ||
0.987645 | − | 0.156709i | \(-0.0500883\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.64031e12 | −0.998908 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 7.72832e12i | − | 0.851027i | −0.904952 | − | 0.425513i | \(-0.860094\pi\) | ||
0.904952 | − | 0.425513i | \(-0.139906\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.52739e13i | − | 1.60271i | −0.598192 | − | 0.801353i | \(-0.704114\pi\) | ||
0.598192 | − | 0.801353i | \(-0.295886\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.30507e13 | −1.30548 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.77378e12 | −0.360014 | −0.180007 | − | 0.983665i | \(-0.557612\pi\) | ||||
−0.180007 | + | 0.983665i | \(0.557612\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.51329e12 | 0.592826 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.89444e13 | −1.64576 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.60079e13i | 1.32784i | 0.747805 | + | 0.663919i | \(0.231108\pi\) | ||||
−0.747805 | + | 0.663919i | \(0.768892\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.89827e13i | 1.50406i | 0.659132 | + | 0.752028i | \(0.270924\pi\) | ||||
−0.659132 | + | 0.752028i | \(0.729076\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.82050e13 | −1.37834 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.24486e13i | − | 0.900966i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.21025e13 | − | 8.00872e12i | −0.837613 | − | 0.554281i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.00227e12i | 0.529806i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.01879e13 | 0.645473 | 0.322736 | − | 0.946489i | \(-0.395397\pi\) | ||||
0.322736 | + | 0.946489i | \(0.395397\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.57694e12i | − | 0.277595i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 6.49674e13i | − | 3.77333i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.75191e12 | 0.264384 | 0.132192 | − | 0.991224i | \(-0.457798\pi\) | ||||
0.132192 | + | 0.991224i | \(0.457798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.37761e12 | 0.0734475 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.76328e13 | 0.901150 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.41999e12 | 0.167598 | 0.0837989 | − | 0.996483i | \(-0.473295\pi\) | ||||
0.0837989 | + | 0.996483i | \(0.473295\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.18776e12i | − | 0.290858i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.77318e13i | 2.60377i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.29606e13 | −0.993905 | −0.496953 | − | 0.867778i | \(-0.665548\pi\) | ||||
−0.496953 | + | 0.867778i | \(0.665548\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.51961e12i | 0.229392i | 0.993401 | + | 0.114696i | \(0.0365893\pi\) | ||||
−0.993401 | + | 0.114696i | \(0.963411\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.79970e13 | − | 1.19093e13i | −0.718300 | − | 0.475327i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.03086e13i | 1.16208i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.44914e13 | −0.533915 | −0.266957 | − | 0.963708i | \(-0.586018\pi\) | ||||
−0.266957 | + | 0.963708i | \(0.586018\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.82273e13i | 0.999648i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.56226e13i | 0.531948i | 0.963980 | + | 0.265974i | \(0.0856936\pi\) | ||||
−0.963980 | + | 0.265974i | \(0.914306\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.17544e13 | −0.384924 | −0.192462 | − | 0.981304i | \(-0.561647\pi\) | ||||
−0.192462 | + | 0.981304i | \(0.561647\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.43086e13 | −2.02592 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.51344e13 | 0.761936 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.56662e13 | 2.49960 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 3.35297e13i | − | 0.941930i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.44993e13i | − | 0.662799i | −0.943491 | − | 0.331399i | \(-0.892479\pi\) | ||
0.943491 | − | 0.331399i | \(-0.107521\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.25681e13 | −0.588131 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.77394e13i | − | 0.696524i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.17663e12 | − | 6.31160e12i | 0.101073 | − | 0.152738i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.00014e13i | − | 0.233316i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.25455e13 | 0.957017 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.27793e13i | 1.79586i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.49589e13i | 1.77807i | 0.457843 | + | 0.889033i | \(0.348622\pi\) | ||||
−0.457843 | + | 0.889033i | \(0.651378\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.36914e13 | −1.28620 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.90036e13 | −0.565289 | −0.282644 | − | 0.959225i | \(-0.591212\pi\) | ||||
−0.282644 | + | 0.959225i | \(0.591212\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.29452e13 | 0.808017 | 0.404009 | − | 0.914755i | \(-0.367617\pi\) | ||||
0.404009 | + | 0.914755i | \(0.367617\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.41027e13 | −0.982904 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.21340e13i | − | 0.212901i | −0.994318 | − | 0.106450i | \(-0.966052\pi\) | ||
0.994318 | − | 0.106450i | \(-0.0339485\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.18524e13i | − | 1.04835i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.46394e14 | 2.39743 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.18722e14i | − | 1.87896i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.76578e13 | + | 4.17956e13i | −0.423115 | + | 0.639400i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.07003e13i | 1.19361i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.76994e13 | 0.253152 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 9.04525e13i | − | 1.25131i | −0.780098 | − | 0.625657i | \(-0.784831\pi\) | ||
0.780098 | − | 0.625657i | \(-0.215169\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.25971e13i | 0.168589i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.98198e13 | 0.774638 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.34962e14 | −1.69140 | −0.845701 | − | 0.533657i | \(-0.820818\pi\) | ||||
−0.845701 | + | 0.533657i | \(0.820818\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.81365e14 | 2.20017 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.90163e13 | 1.16294 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.37347e13i | − | 0.952331i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 3.35376e13i | − | 0.369426i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.61562e13 | −1.02604 | −0.513021 | − | 0.858376i | \(-0.671474\pi\) | ||||
−0.513021 | + | 0.858376i | \(0.671474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.77772e14i | − | 1.83791i | −0.394361 | − | 0.918956i | \(-0.629034\pi\) | ||
0.394361 | − | 0.918956i | \(-0.370966\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.53132e13 | − | 3.82526e13i | 0.253605 | − | 0.383241i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.37066e13i | 0.909933i | 0.890509 | + | 0.454966i | \(0.150349\pi\) | ||||
−0.890509 | + | 0.454966i | \(0.849651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.29069e14 | −1.21497 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1.76545e14i | − | 1.61131i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.23925e13i | 0.286698i | 0.989672 | + | 0.143349i | \(0.0457872\pi\) | ||||
−0.989672 | + | 0.143349i | \(0.954213\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.02770e12 | −0.00882218 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.36388e14 | −1.96852 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.37580e14 | −1.11159 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.22124e14 | 0.957499 | 0.478749 | − | 0.877952i | \(-0.341090\pi\) | ||||
0.478749 | + | 0.877952i | \(0.341090\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.29834e14i | 1.74892i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.68148e13i | − | 0.124204i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.80298e13 | −0.272726 | −0.136363 | − | 0.990659i | \(-0.543541\pi\) | ||||
−0.136363 | + | 0.990659i | \(0.543541\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 6.75718e13i | − | 0.470537i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.64427e13 | − | 8.52946e13i | 0.381707 | − | 0.576825i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.21824e13i | 0.539838i | 0.962883 | + | 0.269919i | \(0.0869969\pi\) | ||||
−0.962883 | + | 0.269919i | \(0.913003\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.23623e13 | 0.461770 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.83489e13i | 0.485780i | 0.970054 | + | 0.242890i | \(0.0780954\pi\) | ||||
−0.970054 | + | 0.242890i | \(0.921905\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.89782e14i | 1.14346i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.14545e13 | 0.535544 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.76093e14 | 1.00235 | 0.501176 | − | 0.865345i | \(-0.332901\pi\) | ||||
0.501176 | + | 0.865345i | \(0.332901\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.19147e13 | 0.342627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.70242e14 | −0.916024 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.75488e14i | 1.44151i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 5.25583e13i | − | 0.267481i | −0.991016 | − | 0.133741i | \(-0.957301\pi\) | ||
0.991016 | − | 0.133741i | \(-0.0426989\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.74754e14 | −0.865121 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.98075e13i | 0.336208i | 0.985769 | + | 0.168104i | \(0.0537644\pi\) | ||||
−0.985769 | + | 0.168104i | \(0.946236\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.36544e14 | + | 9.03562e13i | 0.639873 | + | 0.423429i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.76470e14i | 0.804762i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.41884e13 | 0.196128 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.03685e12i | 0.00879996i | 0.999990 | + | 0.00439998i | \(0.00140056\pi\) | ||||
−0.999990 | + | 0.00439998i | \(0.998599\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.54076e14i | 1.48925i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.13273e13 | −0.251147 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.16368e14 | 0.464055 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.87099e14 | 1.11502 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.11635e13 | −0.0800591 | −0.0400296 | − | 0.999198i | \(-0.512745\pi\) | ||||
−0.0400296 | + | 0.999198i | \(0.512745\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.53231e14i | 1.67020i | 0.550098 | + | 0.835100i | \(0.314590\pi\) | ||||
−0.550098 | + | 0.835100i | \(0.685410\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.61847e14i | 0.581075i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.10001e14 | −1.43432 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.24947e14i | 0.766880i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.77274e14 | − | 3.82005e14i | −1.91808 | − | 1.26927i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.32051e14i | 0.751551i | 0.926711 | + | 0.375775i | \(0.122624\pi\) | ||||
−0.926711 | + | 0.375775i | \(0.877376\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.22668e14 | 1.01876 | 0.509381 | − | 0.860541i | \(-0.329874\pi\) | ||||
0.509381 | + | 0.860541i | \(0.329874\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 4.53225e14i | − | 1.39516i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.12868e13i | − | 0.183958i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.43942e13 | 0.0421341 | 0.0210671 | − | 0.999778i | \(-0.493294\pi\) | ||||
0.0210671 | + | 0.999778i | \(0.493294\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.09333e14 | 0.883108 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.12647e13 | 0.0592159 | 0.0296079 | − | 0.999562i | \(-0.490574\pi\) | ||||
0.0296079 | + | 0.999562i | \(0.490574\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.39529e14 | 2.28063 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.16848e14i | 0.309691i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.13580e14i | − | 0.293729i | −0.989157 | − | 0.146865i | \(-0.953082\pi\) | ||
0.989157 | − | 0.146865i | \(-0.0469182\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.06215e14 | 2.03460 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.04519e15i | 2.57428i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.73184e14 | + | 2.61710e14i | −0.416337 | + | 0.629156i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.88690e14i | 0.677473i | 0.940881 | + | 0.338737i | \(0.110000\pi\) | ||||
−0.940881 | + | 0.338737i | \(0.890000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.75245e14 | 0.859697 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.07352e14i | − | 0.687514i | −0.939059 | − | 0.343757i | \(-0.888300\pi\) | ||
0.939059 | − | 0.343757i | \(-0.111700\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.18580e14i | − | 0.914288i | −0.889393 | − | 0.457144i | \(-0.848872\pi\) | ||
0.889393 | − | 0.457144i | \(-0.151128\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.25545e14 | 1.54765 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.56891e14 | 0.951853 | 0.475926 | − | 0.879485i | \(-0.342113\pi\) | ||||
0.475926 | + | 0.879485i | \(0.342113\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.62556e14 | 0.330791 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.21633e14 | 1.43450 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 3.20806e14i | − | 0.623025i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.05844e14i | 0.770094i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.53758e14 | 0.285093 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.50737e14i | 1.54152i | 0.637124 | + | 0.770762i | \(0.280124\pi\) | ||||
−0.637124 | + | 0.770762i | \(0.719876\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.09358e13 | + | 4.03236e13i | 0.107913 | + | 0.0714104i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 9.11362e13i | − | 0.157754i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.87585e14 | −0.825032 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.78950e14i | − | 1.12313i | −0.827434 | − | 0.561563i | \(-0.810200\pi\) | ||
0.827434 | − | 0.561563i | \(-0.189800\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.65126e14i | 1.23747i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.96695e14 | −0.311060 | −0.155530 | − | 0.987831i | \(-0.549709\pi\) | ||||
−0.155530 | + | 0.987831i | \(0.549709\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.36711e14 | 1.29395 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.73541e15 | −2.62466 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.50735e14 | −0.518823 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.12395e14i | 1.03078i | 0.856954 | + | 0.515392i | \(0.172354\pi\) | ||||
−0.856954 | + | 0.515392i | \(0.827646\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.02594e15i | 1.45215i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.36394e15 | 1.88874 | 0.944368 | − | 0.328892i | \(-0.106675\pi\) | ||||
0.944368 | + | 0.328892i | \(0.106675\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 6.18692e14i | − | 0.838247i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.47468e14 | − | 1.05357e15i | −0.593224 | − | 1.39675i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 6.73249e12i | − | 0.00873430i | −0.999990 | − | 0.00436715i | \(-0.998610\pi\) | ||
0.999990 | − | 0.00436715i | \(-0.00139011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.73864e14 | −0.474677 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.71440e14i | − | 0.461576i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.26193e14i | 1.12658i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.67729e14 | 0.675994 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.22441e15 | −2.59295 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.59359e15 | −1.81873 | −0.909364 | − | 0.416000i | \(-0.863432\pi\) | ||||
−0.909364 | + | 0.416000i | \(0.863432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.42512e14 | 0.271003 | 0.135501 | − | 0.990777i | \(-0.456735\pi\) | ||||
0.135501 | + | 0.990777i | \(0.456735\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.03507e14i | 0.660399i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.33945e15i | 1.43538i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.20848e14 | −0.966455 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 5.60788e14i | − | 0.576473i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.11177e15 | + | 7.35703e14i | 1.11948 | + | 0.740803i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.12885e15i | − | 2.09990i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.27473e15 | −1.23186 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.08508e15i | − | 1.02736i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 2.45829e13i | − | 0.0228059i | −0.999935 | − | 0.0114030i | \(-0.996370\pi\) | ||
0.999935 | − | 0.0114030i | \(-0.00362976\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.34143e15 | −1.21947 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.17353e15 | 1.04548 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.94712e15 | 1.70006 | 0.850028 | − | 0.526737i | \(-0.176585\pi\) | ||||
0.850028 | + | 0.526737i | \(0.176585\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.05696e15 | −1.76027 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.28227e14i | − | 0.694729i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.48619e14i | 0.615563i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.23791e14 | 0.261008 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.17444e15i | − | 0.928170i | −0.885791 | − | 0.464085i | \(-0.846383\pi\) | ||
0.885791 | − | 0.464085i | \(-0.153617\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.92747e14 | − | 4.42391e14i | 0.226844 | − | 0.342801i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 5.66287e15i | − | 4.30270i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.20559e15 | −0.898266 | −0.449133 | − | 0.893465i | \(-0.648267\pi\) | ||||
−0.449133 | + | 0.893465i | \(0.648267\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.63739e15i | − | 1.92712i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.79544e14i | 0.343654i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.51790e14 | −0.668996 | −0.334498 | − | 0.942396i | \(-0.608567\pi\) | ||||
−0.334498 | + | 0.942396i | \(0.608567\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.03752e15 | 0.715318 | 0.357659 | − | 0.933852i | \(-0.383575\pi\) | ||||
0.357659 | + | 0.933852i | \(0.383575\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.00227e14 | −0.0677854 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.11652e14 | −0.140426 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.50976e14i | 0.358645i | 0.983790 | + | 0.179323i | \(0.0573906\pi\) | ||||
−0.983790 | + | 0.179323i | \(0.942609\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 5.71137e14i | − | 0.364761i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.16222e14 | 0.198164 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.39355e14i | − | 0.331663i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.39313e15 | − | 1.58363e15i | −1.44414 | − | 0.955642i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.76515e15i | 1.04537i | 0.852525 | + | 0.522686i | \(0.175070\pi\) | ||||
−0.852525 | + | 0.522686i | \(0.824930\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.32586e15 | 0.770664 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 2.41498e15i | − | 1.37779i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.34735e14i | 0.355461i | 0.984079 | + | 0.177730i | \(0.0568755\pi\) | ||||
−0.984079 | + | 0.177730i | \(0.943125\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.56729e15 | −1.41134 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.40640e15 | −0.759013 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.65843e15 | −0.878720 | −0.439360 | − | 0.898311i | \(-0.644795\pi\) | ||||
−0.439360 | + | 0.898311i | \(0.644795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.05963e14 | 0.419282 | 0.209641 | − | 0.977778i | \(-0.432771\pi\) | ||||
0.209641 | + | 0.977778i | \(0.432771\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.48645e15i | 0.759283i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.43753e15i | 1.72422i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.27550e15 | −0.628266 | −0.314133 | − | 0.949379i | \(-0.601714\pi\) | ||||
−0.314133 | + | 0.949379i | \(0.601714\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 1.23161e15i | − | 0.595769i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.82899e14 | + | 5.18075e14i | 0.371945 | + | 0.246131i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.84979e15i | 1.32978i | 0.746941 | + | 0.664891i | \(0.231522\pi\) | ||||
−0.746941 | + | 0.664891i | \(0.768478\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.90756e15 | 2.70767 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 9.26977e14i | − | 0.417350i | −0.977985 | − | 0.208675i | \(-0.933085\pi\) | ||
0.977985 | − | 0.208675i | \(-0.0669151\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3.69032e15i | − | 1.63217i | −0.577932 | − | 0.816085i | \(-0.696140\pi\) | ||
0.577932 | − | 0.816085i | \(-0.303860\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.93710e14 | 0.0841682 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.28136e15 | 0.973890 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.81062e15 | −1.17886 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.60544e15 | −2.31014 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.97760e14i | 0.242074i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.66062e15i | 1.05882i | 0.848367 | + | 0.529408i | \(0.177586\pi\) | ||||
−0.848367 | + | 0.529408i | \(0.822414\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.03715e15 | 2.36109 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 1.05228e15i | − | 0.404462i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.90180e14 | − | 1.49633e15i | 0.374065 | − | 0.565276i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 3.20719e15i | − | 1.19089i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.06859e15 | 0.390023 | 0.195012 | − | 0.980801i | \(-0.437526\pi\) | ||||
0.195012 | + | 0.980801i | \(0.437526\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.45048e15i | 1.23799i | 0.785393 | + | 0.618997i | \(0.212461\pi\) | ||||
−0.785393 | + | 0.618997i | \(0.787539\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 2.35071e15i | − | 0.829127i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.12730e15 | −1.77793 | −0.888965 | − | 0.457974i | \(-0.848575\pi\) | ||||
−0.888965 | + | 0.457974i | \(0.848575\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.96714e15 | −0.670640 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.97162e15 | 0.660887 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.17199e15 | 0.715874 | 0.357937 | − | 0.933746i | \(-0.383480\pi\) | ||||
0.357937 | + | 0.933746i | \(0.383480\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.47563e15i | 0.802341i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 3.41868e15i | − | 1.08955i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.20683e15 | 1.00509 | 0.502546 | − | 0.864551i | \(-0.332397\pi\) | ||||
0.502546 | + | 0.864551i | \(0.332397\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.32193e14i | 0.256517i | 0.991741 | + | 0.128258i | \(0.0409387\pi\) | ||||
−0.991741 | + | 0.128258i | \(0.959061\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.16758e15 | − | 7.80910e15i | 1.56662 | − | 2.36743i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.54126e15i | 0.757756i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.31929e14 | 0.126684 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1.64853e15i | − | 0.475613i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.21544e15i | 2.04781i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.73256e15 | −1.32133 | −0.660667 | − | 0.750679i | \(-0.729727\pi\) | ||||
−0.660667 | + | 0.750679i | \(0.729727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.28275e15 | −0.352349 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.17475e15 | −1.12822 | −0.564109 | − | 0.825700i | \(-0.690780\pi\) | ||||
−0.564109 | + | 0.825700i | \(0.690780\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.32498e15 | −0.352310 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.93610e15i | − | 1.29144i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.95274e15i | − | 0.502725i | −0.967893 | − | 0.251362i | \(-0.919121\pi\) | ||
0.967893 | − | 0.251362i | \(-0.0808786\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.14893e15 | 1.30442 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 9.75545e15i | − | 2.43212i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.92182e14 | − | 7.43771e14i | 0.120759 | − | 0.182488i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.36443e15i | 0.812423i | 0.913779 | + | 0.406212i | \(0.133150\pi\) | ||||
−0.913779 | + | 0.406212i | \(0.866850\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.71585e15 | −1.12080 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 4.17497e15i | − | 0.976644i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.09061e16i | 2.51125i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.41032e15 | −0.546325 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.96043e15 | 0.437423 | 0.218711 | − | 0.975790i | \(-0.429815\pi\) | ||||
0.218711 | + | 0.975790i | \(0.429815\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.91699e14 | 0.129971 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.16005e15 | 0.899618 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.68125e15i | − | 0.357953i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.86748e15i | 0.391474i | 0.980656 | + | 0.195737i | \(0.0627098\pi\) | ||||
−0.980656 | + | 0.195737i | \(0.937290\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.84552e15 | −1.41294 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.91452e14i | 0.140530i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.55507e15 | + | 8.39465e15i | −1.11175 | + | 1.68004i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.02243e16i | 2.01501i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.66595e15 | 0.323334 | 0.161667 | − | 0.986845i | \(-0.448313\pi\) | ||||
0.161667 | + | 0.986845i | \(0.448313\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.51687e15i | 0.481079i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.21243e16i | 2.28242i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.86025e15 | −0.530328 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.12480e15 | −1.66642 | −0.833209 | − | 0.552958i | \(-0.813499\pi\) | ||||
−0.833209 | + | 0.552958i | \(0.813499\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.26181e15 | −1.48619 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.33971e15 | 0.768980 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.87654e15i | 0.676663i | 0.941027 | + | 0.338331i | \(0.109862\pi\) | ||||
−0.941027 | + | 0.338331i | \(0.890138\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 7.95097e15i | − | 1.36722i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.21418e15 | 0.883313 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.39355e15i | 0.232583i | 0.993215 | + | 0.116292i | \(0.0371007\pi\) | ||||
−0.993215 | + | 0.116292i | \(0.962899\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.72992e15 | − | 5.11518e15i | −1.27109 | − | 0.841126i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.07016e13i | 0.00173384i | 1.00000 | 0.000866919i | \(0.000275949\pi\) | |||||
−1.00000 | 0.000866919i | \(0.999724\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.69918e15 | 0.271257 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.89160e15i | 0.454857i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 5.78499e15i | − | 0.896712i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.46539e14 | −0.0529337 | −0.0264668 | − | 0.999650i | \(-0.508426\pi\) | ||||
−0.0264668 | + | 0.999650i | \(0.508426\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.50701e15 | 0.979510 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.51991e16 | 2.25480 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.02514e15 | 1.02714 | 0.513568 | − | 0.858049i | \(-0.328324\pi\) | ||||
0.513568 | + | 0.858049i | \(0.328324\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 2.92330e15i | − | 0.421253i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.91316e15i | − | 0.555792i | −0.960611 | − | 0.277896i | \(-0.910363\pi\) | ||
0.960611 | − | 0.277896i | \(-0.0896371\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.18900e15 | 0.446447 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 2.34758e16i | − | 3.23953i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.71269e15 | − | 1.79509e15i | −0.369000 | − | 0.244181i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.94587e15i | − | 0.797298i | −0.917104 | − | 0.398649i | \(-0.869479\pi\) | ||
0.917104 | − | 0.398649i | \(-0.130521\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.03505e15 | 0.401206 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 6.92376e15i | − | 0.902308i | −0.892446 | − | 0.451154i | \(-0.851013\pi\) | ||
0.892446 | − | 0.451154i | \(-0.148987\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.57882e15i | − | 0.588294i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.79881e14 | 0.111457 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.07955e16 | 1.34830 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.12502e16 | −1.38542 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.61779e15 | 0.317866 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.04939e16i | − | 1.25647i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.36325e15i | 1.10552i | 0.833341 | + | 0.552759i | \(0.186425\pi\) | ||||
−0.833341 | + | 0.552759i | \(0.813575\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.18436e15 | 0.254331 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 7.16694e15i | − | 0.822930i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.58437e15 | + | 9.95010e15i | −0.745610 | + | 1.12674i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 3.95214e15i | − | 0.441380i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.64665e15 | 0.181377 | 0.0906883 | − | 0.995879i | \(-0.471093\pi\) | ||||
0.0906883 | + | 0.995879i | \(0.471093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.67998e15i | 0.834358i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.08612e16i | 2.23543i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.19921e16 | −1.26753 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.32529e15 | −0.138176 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.46650e16 | −1.50826 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.15540e15 | 0.725967 | 0.362984 | − | 0.931796i | \(-0.381758\pi\) | ||||
0.362984 | + | 0.931796i | \(0.381758\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.16278e16i | − | 1.16381i | −0.813258 | − | 0.581904i | \(-0.802308\pi\) | ||
0.813258 | − | 0.581904i | \(-0.197692\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.52539e15i | 0.348104i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.11264e16 | 1.08389 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.29570e15i | − | 0.412870i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.50317e15 | − | 4.30340e15i | −0.616685 | − | 0.408084i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.45685e15i | 0.229875i | 0.993373 | + | 0.114937i | \(0.0366667\pi\) | ||||
−0.993373 | + | 0.114937i | \(0.963333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.65791e15 | 0.891628 | 0.445814 | − | 0.895125i | \(-0.352914\pi\) | ||||
0.445814 | + | 0.895125i | \(0.352914\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.93582e16i | 1.76347i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.55380e16i | 1.39673i | 0.715740 | + | 0.698367i | \(0.246090\pi\) | ||||
−0.715740 | + | 0.698367i | \(0.753910\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.12675e16 | 0.999491 | 0.499745 | − | 0.866172i | \(-0.333427\pi\) | ||||
0.499745 | + | 0.866172i | \(0.333427\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.25570e15 | −0.810221 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.46785e16 | 1.26804 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.49190e16 | 1.27193 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.19068e15i | 0.352609i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.39925e15i | 0.199244i | 0.995025 | + | 0.0996220i | \(0.0317634\pi\) | ||||
−0.995025 | + | 0.0996220i | \(0.968237\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.36345e15 | −0.521572 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.97820e15i | 0.807236i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.53209e16 | + | 6.50703e15i | −1.22341 | + | 0.519602i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.34126e15i | 0.736286i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.50756e15 | −0.584126 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.08577e14i | 0.0237001i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.64529e16i | − | 1.24745i | −0.781643 | − | 0.623726i | \(-0.785618\pi\) | ||
0.781643 | − | 0.623726i | \(-0.214382\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.32377e16 | −1.73932 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.30993e15 | 0.244582 | 0.122291 | − | 0.992494i | \(-0.460976\pi\) | ||||
0.122291 | + | 0.992494i | \(0.460976\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.74823e16 | −1.27537 | −0.637685 | − | 0.770298i | \(-0.720108\pi\) | ||||
−0.637685 | + | 0.770298i | \(0.720108\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.60534e16 | 1.15624 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.44481e14i | − | 0.0173854i | −0.999962 | − | 0.00869272i | \(-0.997233\pi\) | ||
0.999962 | − | 0.00869272i | \(-0.00276701\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.23471e16i | 2.27116i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.47151e16 | 3.79317 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.40128e16i | 1.64374i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.19036e15 | + | 4.75814e15i | 0.486016 | + | 0.321616i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.21159e16i | − | 0.808679i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.67021e15 | −0.175995 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.53247e16i | − | 0.997460i | −0.866757 | − | 0.498730i | \(-0.833800\pi\) | ||
0.866757 | − | 0.498730i | \(-0.166200\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1.56477e16i | − | 1.00580i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.84693e16 | 1.80721 | 0.903607 | − | 0.428362i | \(-0.140909\pi\) | ||||
0.903607 | + | 0.428362i | \(0.140909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.20988e15 | 0.0758506 | 0.0379253 | − | 0.999281i | \(-0.487925\pi\) | ||||
0.0379253 | + | 0.999281i | \(0.487925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.44143e16 | −0.892493 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.13464e16 | 1.91694 | 0.958469 | − | 0.285198i | \(-0.0920593\pi\) | ||||
0.958469 | + | 0.285198i | \(0.0920593\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2.85951e15i | − | 0.172716i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.53819e16i | 0.917663i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.60210e15 | 0.447972 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.85370e16i | 1.07898i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.66762e15 | − | 4.03123e15i | 0.153379 | − | 0.231782i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.34425e15i | 0.530721i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.29614e15 | 0.409361 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 6.38790e15i | − | 0.354059i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.95070e16i | 1.06813i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.40850e15 | 0.184384 | 0.0921920 | − | 0.995741i | \(-0.470613\pi\) | ||||
0.0921920 | + | 0.995741i | \(0.470613\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.53737e16 | 0.821632 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.09436e16 | −0.577840 | −0.288920 | − | 0.957353i | \(-0.593296\pi\) | ||||
−0.288920 | + | 0.957353i | \(0.593296\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.01432e16 | 0.529158 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.28713e16i | 2.72524i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.72737e15i | 0.342621i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.25304e15 | 0.314670 | 0.157335 | − | 0.987545i | \(-0.449710\pi\) | ||||
0.157335 | + | 0.987545i | \(0.449710\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.42634e16i | 2.69823i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.55141e16 | − | 1.02663e16i | −0.762284 | − | 0.504433i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.04341e15i | − | 0.0992146i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.30147e16 | −1.10425 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.65981e16i | 0.786996i | 0.919326 | + | 0.393498i | \(0.128735\pi\) | ||||
−0.919326 | + | 0.393498i | \(0.871265\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.45297e16i | − | 0.680820i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.85247e16 | −0.857831 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.23487e16 | −3.76871 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.21563e15 | 0.145445 | 0.0727225 | − | 0.997352i | \(-0.476831\pi\) | ||||
0.0727225 | + | 0.997352i | \(0.476831\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.74292e16 | 1.22617 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.00810e16i | 1.77091i | 0.464729 | + | 0.885453i | \(0.346152\pi\) | ||||
−0.464729 | + | 0.885453i | \(0.653848\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.62998e15i | 0.245862i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.03218e15 | −0.346704 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.94025e14i | 0.0210777i | 0.999944 | + | 0.0105389i | \(0.00335469\pi\) | ||||
−0.999944 | + | 0.0105389i | \(0.996645\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.65371e16 | − | 1.09433e16i | −0.697422 | − | 0.461511i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 7.74999e15i | − | 0.323078i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.84963e15 | −0.241056 | −0.120528 | − | 0.992710i | \(-0.538459\pi\) | ||||
−0.120528 | + | 0.992710i | \(0.538459\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.45750e15i | 0.0593730i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.95053e16i | − | 1.59089i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.39919e16 | 0.557023 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.04498e16 | 0.411271 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.28991e16 | 2.05828 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.30541e15 | −0.319493 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.46312e16i | − | 1.31711i | −0.752532 | − | 0.658555i | \(-0.771168\pi\) | ||
0.752532 | − | 0.658555i | \(-0.228832\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 7.58279e16i | − | 2.85133i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.55279e16 | −0.577307 | −0.288653 | − | 0.957434i | \(-0.593208\pi\) | ||||
−0.288653 | + | 0.957434i | \(0.593208\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.13452e16i | − | 0.417053i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.76651e16 | + | 2.66950e16i | −0.642082 | + | 0.970295i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.74397e16i | − | 0.626785i | −0.949624 | − | 0.313393i | \(-0.898534\pi\) | ||
0.949624 | − | 0.313393i | \(-0.101466\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.31773e16 | 2.60059 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.91608e16i | 1.02476i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 5.06070e16i | − | 1.75860i | −0.476272 | − | 0.879298i | \(-0.658012\pi\) | ||
0.476272 | − | 0.879298i | \(-0.341988\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.51184e16 | −1.20680 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.13046e16 | 0.384161 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.24025e15 | 0.0752866 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.03141e16 | 0.342789 | 0.171394 | − | 0.985202i | \(-0.445173\pi\) | ||||
0.171394 | + | 0.985202i | \(0.445173\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 5.77722e16i | − | 1.89888i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.04517e16i | 0.664816i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.12991e15 | −0.164925 | −0.0824624 | − | 0.996594i | \(-0.526278\pi\) | ||||
−0.0824624 | + | 0.996594i | \(0.526278\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.87019e15i | 0.0594669i |
(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 | 208.12.f.b.129.11 | 12 | ||
4.3 | odd | 2 | 13.12.b.a.12.8 | yes | 12 | ||
12.11 | even | 2 | 117.12.b.b.64.5 | 12 | |||
13.12 | even | 2 | inner | 208.12.f.b.129.12 | 12 | ||
52.31 | even | 4 | 169.12.a.e.1.8 | 12 | |||
52.47 | even | 4 | 169.12.a.e.1.5 | 12 | |||
52.51 | odd | 2 | 13.12.b.a.12.5 | ✓ | 12 | ||
156.155 | even | 2 | 117.12.b.b.64.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.12.b.a.12.5 | ✓ | 12 | 52.51 | odd | 2 | ||
13.12.b.a.12.8 | yes | 12 | 4.3 | odd | 2 | ||
117.12.b.b.64.5 | 12 | 12.11 | even | 2 | |||
117.12.b.b.64.8 | 12 | 156.155 | even | 2 | |||
169.12.a.e.1.5 | 12 | 52.47 | even | 4 | |||
169.12.a.e.1.8 | 12 | 52.31 | even | 4 | |||
208.12.f.b.129.11 | 12 | 1.1 | even | 1 | trivial | ||
208.12.f.b.129.12 | 12 | 13.12 | even | 2 | inner |