Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(197,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.197");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 4002260 x^{14} + 6534459751956 x^{12} + \cdots + 19\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{37}\cdot 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.6 | ||
Root | \(-491.437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.197 |
Dual form | 252.9.c.a.197.11 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 491.437i | − 0.786300i | −0.919474 | − | 0.393150i | \(-0.871385\pi\) | ||||
0.919474 | − | 0.393150i | \(-0.128615\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −907.493 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5999.21i | 0.409754i | 0.978788 | + | 0.204877i | \(0.0656795\pi\) | ||||
−0.978788 | + | 0.204877i | \(0.934321\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −47598.9 | −1.66657 | −0.833285 | − | 0.552843i | \(-0.813543\pi\) | ||||
−0.833285 | + | 0.552843i | \(0.813543\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 106621.i | 1.27658i | 0.769795 | + | 0.638291i | \(0.220358\pi\) | ||||
−0.769795 | + | 0.638291i | \(0.779642\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 137232. | 1.05303 | 0.526514 | − | 0.850166i | \(-0.323499\pi\) | ||||
0.526514 | + | 0.850166i | \(0.323499\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 80032.4i | − 0.285993i | −0.989723 | − | 0.142996i | \(-0.954326\pi\) | ||||
0.989723 | − | 0.142996i | \(-0.0456737\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 149114. | 0.381733 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 46364.8i | − 0.0655536i | −0.999463 | − | 0.0327768i | \(-0.989565\pi\) | ||||
0.999463 | − | 0.0327768i | \(-0.0104350\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 941453. | 1.01942 | 0.509708 | − | 0.860347i | \(-0.329753\pi\) | ||||
0.509708 | + | 0.860347i | \(0.329753\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 445976.i | 0.297193i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.33907e6 | −0.714492 | −0.357246 | − | 0.934010i | \(-0.616284\pi\) | ||||
−0.357246 | + | 0.934010i | \(0.616284\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.74791e6i | 1.68022i | 0.542415 | + | 0.840111i | \(0.317510\pi\) | ||||
−0.542415 | + | 0.840111i | \(0.682490\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.35655e6 | 0.689292 | 0.344646 | − | 0.938733i | \(-0.387999\pi\) | ||||
0.344646 | + | 0.938733i | \(0.387999\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 2.73617e6i | − 0.560727i | −0.959894 | − | 0.280364i | \(-0.909545\pi\) | ||||
0.959894 | − | 0.280364i | \(-0.0904551\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 823543. | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.15514e7i | − 1.46397i | −0.681322 | − | 0.731984i | \(-0.738595\pi\) | ||||
0.681322 | − | 0.731984i | \(-0.261405\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.94824e6 | 0.322189 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1.65119e7i | − 1.36267i | −0.731974 | − | 0.681333i | \(-0.761401\pi\) | ||||
0.731974 | − | 0.681333i | \(-0.238599\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.01747e7 | −0.734859 | −0.367429 | − | 0.930051i | \(-0.619762\pi\) | ||||
−0.367429 | + | 0.930051i | \(0.619762\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.33919e7i | 1.31042i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.21775e7 | −0.604310 | −0.302155 | − | 0.953259i | \(-0.597706\pi\) | ||||
−0.302155 | + | 0.953259i | \(0.597706\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 5.40380e6i | − 0.212650i | −0.994331 | − | 0.106325i | \(-0.966092\pi\) | ||||
0.994331 | − | 0.106325i | \(-0.0339084\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.94313e7 | 1.38851 | 0.694257 | − | 0.719727i | \(-0.255733\pi\) | ||||
0.694257 | + | 0.719727i | \(0.255733\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 5.44424e6i | − 0.154873i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.34681e7 | −1.88621 | −0.943106 | − | 0.332493i | \(-0.892110\pi\) | ||||
−0.943106 | + | 0.332493i | \(0.892110\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.14266e7i | 0.662194i | 0.943597 | + | 0.331097i | \(0.107419\pi\) | ||||
−0.943597 | + | 0.331097i | \(0.892581\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.23977e7 | 1.00378 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 8.79931e7i | − 1.40245i | −0.712938 | − | 0.701227i | \(-0.752636\pi\) | ||||
0.712938 | − | 0.701227i | \(-0.247364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.31957e7 | 0.629905 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 6.74408e7i | − 0.827996i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00964e7 | −0.114046 | −0.0570231 | − | 0.998373i | \(-0.518161\pi\) | ||||
−0.0570231 | + | 0.998373i | \(0.518161\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.06293e8i | − 1.02145i | −0.859743 | − | 0.510727i | \(-0.829376\pi\) | ||||
0.859743 | − | 0.510727i | \(-0.170624\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.33130e8 | 1.18285 | 0.591423 | − | 0.806361i | \(-0.298566\pi\) | ||||
0.591423 | + | 0.806361i | \(0.298566\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.17472e7i | 0.318487i | 0.987239 | + | 0.159244i | \(0.0509055\pi\) | ||||
−0.987239 | + | 0.159244i | \(0.949094\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.20761e8 | 1.56393 | 0.781964 | − | 0.623323i | \(-0.214218\pi\) | ||||
0.781964 | + | 0.623323i | \(0.214218\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.31146e8i | 0.804341i | 0.915565 | + | 0.402171i | \(0.131744\pi\) | ||||
−0.915565 | + | 0.402171i | \(0.868256\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.93309e7 | −0.224876 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 9.67582e7i | − 0.482503i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.78368e8 | 0.832102 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 2.65248e8i | − 1.08646i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −434.944 | −1.67193e−6 0 | −8.35966e−7 | − | 1.00000i | \(-0.500000\pi\) | ||||
−8.35966e−7 | 1.00000i | \(0.500000\pi\) | ||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 3.36763e8i | − 1.14351i | −0.820425 | − | 0.571754i | \(-0.806263\pi\) | ||||
0.820425 | − | 0.571754i | \(-0.193737\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.24537e8 | −0.398007 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.24216e6i | 0.0262356i | 0.999914 | + | 0.0131178i | \(0.00417565\pi\) | ||||
−0.999914 | + | 0.0131178i | \(0.995824\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.35507e7 | 0.116664 | 0.0583319 | − | 0.998297i | \(-0.481422\pi\) | ||||
0.0583319 | + | 0.998297i | \(0.481422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 2.85556e8i | − 0.682884i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.27854e7 | −0.0515448 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 8.91966e8i | − 1.80969i | −0.425746 | − | 0.904843i | \(-0.639988\pi\) | ||||
0.425746 | − | 0.904843i | \(-0.360012\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.81506e8 | 0.733827 | 0.366914 | − | 0.930255i | \(-0.380414\pi\) | ||||
0.366914 | + | 0.930255i | \(0.380414\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.62665e8i | − 0.801567i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.26816e8 | 0.373314 | 0.186657 | − | 0.982425i | \(-0.440235\pi\) | ||||
0.186657 | + | 0.982425i | \(0.440235\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.26288e7i | 0.108095i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.59270e8 | 0.225623 | 0.112811 | − | 0.993616i | \(-0.464014\pi\) | ||||
0.112811 | + | 0.993616i | \(0.464014\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1.47027e9i | − 1.89031i | −0.326625 | − | 0.945154i | \(-0.605911\pi\) | ||||
0.326625 | − | 0.945154i | \(-0.394089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.44993e9 | 1.77746 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.54399e8i | 0.172370i | 0.996279 | + | 0.0861849i | \(0.0274676\pi\) | ||||
−0.996279 | + | 0.0861849i | \(0.972532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.35320e8 | −0.144282 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.46569e8i | 0.434987i | 0.976062 | + | 0.217494i | \(0.0697882\pi\) | ||||
−0.976062 | + | 0.217494i | \(0.930212\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.55769e8 | 0.331477 | 0.165739 | − | 0.986170i | \(-0.446999\pi\) | ||||
0.165739 | + | 0.986170i | \(0.446999\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.58071e8i | 0.561805i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.39644e8 | −0.523085 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 2.17843e9i | − 1.63686i | −0.574608 | − | 0.818429i | \(-0.694845\pi\) | ||||
0.574608 | − | 0.818429i | \(-0.305155\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.79560e8 | −0.129414 | −0.0647069 | − | 0.997904i | \(-0.520611\pi\) | ||||
−0.0647069 | + | 0.997904i | \(0.520611\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.46094e9i | − 0.969991i | −0.874517 | − | 0.484996i | \(-0.838821\pi\) | ||||
0.874517 | − | 0.484996i | \(-0.161179\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.06149e9 | 1.31452 | 0.657261 | − | 0.753663i | \(-0.271715\pi\) | ||||
0.657261 | + | 0.753663i | \(0.271715\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.20757e7i | 0.0247769i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.33330e9 | 1.32116 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.23282e8i | 0.431483i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.03874e9 | 1.53307 | 0.766537 | − | 0.642200i | \(-0.221978\pi\) | ||||
0.766537 | + | 0.642200i | \(0.221978\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 1.15810e9i | − 0.541990i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.54362e8 | −0.385303 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 5.07507e9i | − 2.12751i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.03325e7 | 0.00417819 | 0.00208909 | − | 0.999998i | \(-0.499335\pi\) | ||||
0.00208909 | + | 0.999998i | \(0.499335\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.11020e9i | 0.794733i | 0.917660 | + | 0.397366i | \(0.130076\pi\) | ||||
−0.917660 | + | 0.397366i | \(0.869924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.82730e9 | −1.02809 | −0.514044 | − | 0.857764i | \(-0.671853\pi\) | ||||
−0.514044 | + | 0.857764i | \(0.671853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.03733e9i | 0.691256i | 0.938372 | + | 0.345628i | \(0.112334\pi\) | ||||
−0.938372 | + | 0.345628i | \(0.887666\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.34466e9 | −0.440900 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.94533e9i | 1.82215i | 0.412240 | + | 0.911075i | \(0.364746\pi\) | ||||
−0.412240 | + | 0.911075i | \(0.635254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.09550e9 | 0.324746 | 0.162373 | − | 0.986729i | \(-0.448085\pi\) | ||||
0.162373 | + | 0.986729i | \(0.448085\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 4.04720e8i | − 0.112329i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.53208e9 | −1.75495 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 4.08687e9i | − 1.02967i | −0.857290 | − | 0.514833i | \(-0.827854\pi\) | ||||
0.857290 | − | 0.514833i | \(-0.172146\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.80131e8 | 0.117187 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 5.61577e9i | − 1.28729i | −0.765323 | − | 0.643646i | \(-0.777421\pi\) | ||||
0.765323 | − | 0.643646i | \(-0.222579\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.21520e9 | 0.270053 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.85186e9i | 1.64116i | 0.571535 | + | 0.820578i | \(0.306348\pi\) | ||||
−0.571535 | + | 0.820578i | \(0.693652\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.67679e9 | −1.15112 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 4.18792e9i | − 0.799815i | −0.916556 | − | 0.399907i | \(-0.869042\pi\) | ||||
0.916556 | − | 0.399907i | \(-0.130958\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.90063e9 | 1.09401 | 0.547005 | − | 0.837129i | \(-0.315768\pi\) | ||||
0.547005 | + | 0.837129i | \(0.315768\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.94569e8i | 0.156417i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.65342e9 | 0.790411 | 0.395206 | − | 0.918593i | \(-0.370673\pi\) | ||||
0.395206 | + | 0.918593i | \(0.370673\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.79692e9i | 0.288206i | 0.989563 | + | 0.144103i | \(0.0460296\pi\) | ||||
−0.989563 | + | 0.144103i | \(0.953970\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.76770e9 | 0.275590 | 0.137795 | − | 0.990461i | \(-0.455998\pi\) | ||||
0.137795 | + | 0.990461i | \(0.455998\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 4.30869e9i | − 0.635064i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.39237e9 | −0.629663 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.70982e9i | 1.04610i | 0.852301 | + | 0.523051i | \(0.175206\pi\) | ||||
−0.852301 | + | 0.523051i | \(0.824794\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.11457e9 | −1.07146 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.80946e9i | 0.476627i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.13855e9 | −0.260528 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.00025e9i | 0.577819i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.19818e9 | −0.472615 | −0.236308 | − | 0.971678i | \(-0.575937\pi\) | ||||
−0.236308 | + | 0.971678i | \(0.575937\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.39143e9i | 0.576318i | 0.957583 | + | 0.288159i | \(0.0930432\pi\) | ||||
−0.957583 | + | 0.288159i | \(0.906957\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.50941e9 | −0.886588 | −0.443294 | − | 0.896376i | \(-0.646190\pi\) | ||||
−0.443294 | + | 0.896376i | \(0.646190\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.92300e10i | 1.90433i | 0.305577 | + | 0.952167i | \(0.401151\pi\) | ||||
−0.305577 | + | 0.952167i | \(0.598849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.78152e8 | 0.0268609 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.46318e10i | 1.34428i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.09769e9 | −0.636185 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.48305e9i | 0.211935i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.32387e8 | −0.0526831 | −0.0263415 | − | 0.999653i | \(-0.508386\pi\) | ||||
−0.0263415 | + | 0.999653i | \(0.508386\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.98449e9i | 0.475169i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.67516e10 | 1.29878 | 0.649391 | − | 0.760455i | \(-0.275024\pi\) | ||||
0.649391 | + | 0.760455i | \(0.275024\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.64797e9i | 0.417710i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.47359e8 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.77019e9i | 0.535937i | 0.963428 | + | 0.267969i | \(0.0863524\pi\) | ||||
−0.963428 | + | 0.267969i | \(0.913648\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.05365e9 | −0.273240 | −0.136620 | − | 0.990624i | \(-0.543624\pi\) | ||||
−0.136620 | + | 0.990624i | \(0.543624\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.37233e9i | − 0.0883812i | −0.999023 | − | 0.0441906i | \(-0.985929\pi\) | ||||
0.999023 | − | 0.0441906i | \(-0.0140709\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.65563e9 | −0.167207 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 8.16787e9i | − 0.491735i | −0.969303 | − | 0.245867i | \(-0.920927\pi\) | ||||
0.969303 | − | 0.245867i | \(-0.0790727\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.84899e9 | 0.108869 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.93780e10i | − 1.09179i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.92285e10 | −1.61117 | −0.805587 | − | 0.592477i | \(-0.798150\pi\) | ||||
−0.805587 | + | 0.592477i | \(0.798150\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.04828e10i | 0.553328i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.42210e9 | −0.435096 | −0.217548 | − | 0.976050i | \(-0.569806\pi\) | ||||
−0.217548 | + | 0.976050i | \(0.569806\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.20692e9i | 0.109250i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.32101e10 | −1.12491 | −0.562457 | − | 0.826826i | \(-0.690144\pi\) | ||||
−0.562457 | + | 0.826826i | \(0.690144\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.47468e10i | 0.685336i | 0.939457 | + | 0.342668i | \(0.111331\pi\) | ||||
−0.939457 | + | 0.342668i | \(0.888669\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.67550e9 | −0.121776 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6.70446e9i | − 0.292796i | −0.989226 | − | 0.146398i | \(-0.953232\pi\) | ||||
0.989226 | − | 0.146398i | \(-0.0467680\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.53317e9 | 0.365093 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.61050e10i | 1.48313i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.04252e10 | −0.419682 | −0.209841 | − | 0.977735i | \(-0.567295\pi\) | ||||
−0.209841 | + | 0.977735i | \(0.567295\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 2.66893e10i | − 1.03219i | −0.856532 | − | 0.516094i | \(-0.827385\pi\) | ||||
0.856532 | − | 0.516094i | \(-0.172615\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.48122e10 | −1.69893 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 8.03339e9i | − 0.292766i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.20725e10 | 1.14614 | 0.573072 | − | 0.819505i | \(-0.305752\pi\) | ||||
0.573072 | + | 0.819505i | \(0.305752\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.49844e10i | 0.515039i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.54442e10 | 0.520683 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 6.50024e9i | − 0.210898i | −0.994425 | − | 0.105449i | \(-0.966372\pi\) | ||||
0.994425 | − | 0.105449i | \(-0.0336280\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.35499e10 | 0.431327 | 0.215664 | − | 0.976468i | \(-0.430809\pi\) | ||||
0.215664 | + | 0.976468i | \(0.430809\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.58988e10i | 0.487314i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.23350e9 | 0.277751 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.10549e9i | 0.176934i | 0.996079 | + | 0.0884671i | \(0.0281968\pi\) | ||||
−0.996079 | + | 0.0884671i | \(0.971803\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.28877e10 | 1.22006 | 0.610030 | − | 0.792378i | \(-0.291157\pi\) | ||||
0.610030 | + | 0.792378i | \(0.291157\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.09830e10i | − 0.301158i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.18244e10 | 0.587604 | 0.293802 | − | 0.955866i | \(-0.405079\pi\) | ||||
0.293802 | + | 0.955866i | \(0.405079\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.20937e10i | 0.314011i | 0.987598 | + | 0.157005i | \(0.0501840\pi\) | ||||
−0.987598 | + | 0.157005i | \(0.949816\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.32431e10 | −1.10275 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 3.64601e10i | − 0.897083i | −0.893762 | − | 0.448542i | \(-0.851944\pi\) | ||||
0.893762 | − | 0.448542i | \(-0.148056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.84837e10 | −0.688478 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 2.12280e10i | − 0.495294i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.95062e10 | 1.59353 | 0.796763 | − | 0.604293i | \(-0.206544\pi\) | ||||
0.796763 | + | 0.604293i | \(0.206544\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2.44898e9i | − 0.0542227i | −0.999632 | − | 0.0271114i | \(-0.991369\pi\) | ||||
0.999632 | − | 0.0271114i | \(-0.00863087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.19882e10 | −0.913698 | −0.456849 | − | 0.889544i | \(-0.651022\pi\) | ||||
−0.456849 | + | 0.889544i | \(0.651022\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 5.55739e10i | − 1.16843i | −0.811599 | − | 0.584216i | \(-0.801402\pi\) | ||||
0.811599 | − | 0.584216i | \(-0.198598\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.10510e10 | 0.228408 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.41375e10i | 0.282440i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.04632e10 | 0.401976 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 3.59246e10i | − 0.682417i | −0.939988 | − | 0.341208i | \(-0.889164\pi\) | ||||
0.939988 | − | 0.341208i | \(-0.110836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.37385e10 | 1.19075 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.96176e9i | 0.0896745i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.03441e10 | 1.60614 | 0.803071 | − | 0.595884i | \(-0.203198\pi\) | ||||
0.803071 | + | 0.595884i | \(0.203198\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.45844e10i | 0.767108i | 0.923518 | + | 0.383554i | \(0.125300\pi\) | ||||
−0.923518 | + | 0.383554i | \(0.874700\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.94348e9 | 0.0836846 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.90391e9i | 0.0803742i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.06435e10 | −0.655525 | −0.327762 | − | 0.944760i | \(-0.606295\pi\) | ||||
−0.327762 | + | 0.944760i | \(0.606295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 1.09003e10i | − 0.170282i | −0.996369 | − | 0.0851409i | \(-0.972866\pi\) | ||||
0.996369 | − | 0.0851409i | \(-0.0271340\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.22363e10 | −0.803169 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 7.87110e10i | − 1.17264i | −0.810080 | − | 0.586319i | \(-0.800576\pi\) | ||||
0.810080 | − | 0.586319i | \(-0.199424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.57837e10 | −0.524809 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 6.54253e10i | − 0.930072i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.64149e10 | 0.229760 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 4.77689e10i | − 0.648327i | −0.946001 | − | 0.324164i | \(-0.894917\pi\) | ||||
0.946001 | − | 0.324164i | \(-0.105083\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.39395e11 | 1.86312 | 0.931562 | − | 0.363582i | \(-0.118446\pi\) | ||||
0.931562 | + | 0.363582i | \(0.118446\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.00379e11i | 1.30137i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.19058e10 | 0.918208 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 2.25995e11i | − 2.80021i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.05161e10 | 0.250426 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.94061e9i | 0.0585363i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.97193e10 | −1.04736 | −0.523681 | − | 0.851914i | \(-0.675442\pi\) | ||||
−0.523681 | + | 0.851914i | \(0.675442\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 1.08490e11i | − 1.22972i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.81538e9 | 0.0426176 | 0.0213088 | − | 0.999773i | \(-0.493217\pi\) | ||||
0.0213088 | + | 0.999773i | \(0.493217\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 6.36272e9i | − 0.0690298i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.66718e10 | 0.712921 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 7.53991e10i | − 0.783332i | −0.920108 | − | 0.391666i | \(-0.871899\pi\) | ||||
0.920108 | − | 0.391666i | \(-0.128101\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.12169e11 | −1.14875 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 5.47694e10i | − 0.545136i | −0.962137 | − | 0.272568i | \(-0.912127\pi\) | ||||
0.962137 | − | 0.272568i | \(-0.0878729\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.44499e10 | 0.632453 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 2.13904e10i | − 0.204066i | −0.994781 | − | 0.102033i | \(-0.967465\pi\) | ||||
0.994781 | − | 0.102033i | \(-0.0325347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.98254e10 | −0.844996 | −0.422498 | − | 0.906364i | \(-0.638847\pi\) | ||||
−0.422498 | + | 0.906364i | \(0.638847\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 1.19340e10i | − 0.109173i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.66116e10 | 0.600962 | 0.300481 | − | 0.953788i | \(-0.402853\pi\) | ||||
0.300481 | + | 0.953788i | \(0.402853\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 2.85194e10i | − 0.250286i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.92993e10 | 0.599867 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.87389e11i | 1.57831i | 0.614195 | + | 0.789154i | \(0.289481\pi\) | ||||
−0.614195 | + | 0.789154i | \(0.710519\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.29197e11 | 1.07348 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.25162e11i | − 1.01217i | −0.862483 | − | 0.506085i | \(-0.831092\pi\) | ||||
0.862483 | − | 0.506085i | \(-0.168908\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.75506e10 | −0.379392 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.83190e11i | 1.42296i | 0.702704 | + | 0.711482i | \(0.251976\pi\) | ||||
−0.702704 | + | 0.711482i | \(0.748024\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.92487e10 | 0.684076 | 0.342038 | − | 0.939686i | \(-0.388883\pi\) | ||||
0.342038 | + | 0.939686i | \(0.388883\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 8.76568e10i | − 0.654281i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.61679e11 | −1.19097 | −0.595484 | − | 0.803367i | \(-0.703040\pi\) | ||||
−0.595484 | + | 0.803367i | \(0.703040\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.30239e11i | 0.934492i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.43758e10 | 0.243450 | 0.121725 | − | 0.992564i | \(-0.461157\pi\) | ||||
0.121725 | + | 0.992564i | \(0.461157\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.50411e11i | 1.03786i | 0.854817 | + | 0.518930i | \(0.173669\pi\) | ||||
−0.854817 | + | 0.518930i | \(0.826331\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.96128e11 | −1.33591 | −0.667953 | − | 0.744203i | \(-0.732829\pi\) | ||||
−0.667953 | + | 0.744203i | \(0.732829\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.98531e10i | 0.530078i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.21049e10 | −0.472547 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.42774e11i | − 0.912109i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.34299e11 | 1.47792 | 0.738962 | − | 0.673747i | \(-0.235316\pi\) | ||||
0.738962 | + | 0.673747i | \(0.235316\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 213748.i | 0 1.31464e-6i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.91998e10 | −0.238082 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.73910e9i | 0.0399181i | 0.999801 | + | 0.0199591i | \(0.00635359\pi\) | ||||
−0.999801 | + | 0.0199591i | \(0.993646\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.90111e11 | 1.11215 | 0.556074 | − | 0.831133i | \(-0.312307\pi\) | ||||
0.556074 | + | 0.831133i | \(0.312307\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.82979e11i | 1.04420i | 0.852885 | + | 0.522099i | \(0.174851\pi\) | ||||
−0.852885 | + | 0.522099i | \(0.825149\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.90584e10 | 0.558358 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 2.11840e11i | − 1.16508i | −0.812802 | − | 0.582540i | \(-0.802059\pi\) | ||||
0.812802 | − | 0.582540i | \(-0.197941\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.65498e11 | −0.899140 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 2.25407e11i | − 1.19516i | −0.801810 | − | 0.597579i | \(-0.796129\pi\) | ||||
0.801810 | − | 0.597579i | \(-0.203871\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.85024e11 | 0.969222 | 0.484611 | − | 0.874730i | \(-0.338961\pi\) | ||||
0.484611 | + | 0.874730i | \(0.338961\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.12020e10i | 0.312953i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.71069e9 | −0.0187478 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 6.10404e10i | − 0.301112i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.14867e10 | 0.104739 | 0.0523696 | − | 0.998628i | \(-0.483323\pi\) | ||||
0.0523696 | + | 0.998628i | \(0.483323\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 2.67075e11i | − 1.27139i | −0.771940 | − | 0.635695i | \(-0.780714\pi\) | ||||
0.771940 | − | 0.635695i | \(-0.219286\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.16244e9 | 0.0431054 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.89664e11i | 1.33110i | 0.746351 | + | 0.665552i | \(0.231804\pi\) | ||||
−0.746351 | + | 0.665552i | \(0.768196\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.54194e9 | 0.0206291 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.49835e11i | 2.43981i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.34359e11 | −0.589326 | −0.294663 | − | 0.955601i | \(-0.595207\pi\) | ||||
−0.294663 | + | 0.955601i | \(0.595207\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 2.14024e10i | − 0.0917327i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.06229e11 | −2.14494 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.57810e11i | 1.89589i | 0.318434 | + | 0.947945i | \(0.396843\pi\) | ||||
−0.318434 | + | 0.947945i | \(0.603157\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.83763e11 | −0.752381 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.64601e10i | 0.386074i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.69596e10 | −0.383712 | −0.191856 | − | 0.981423i | \(-0.561451\pi\) | ||||
−0.191856 | + | 0.981423i | \(0.561451\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 7.53468e10i | − 0.291546i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.40333e11 | −0.536952 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.45199e11i | 0.543310i | 0.962395 | + | 0.271655i | \(0.0875709\pi\) | ||||
−0.962395 | + | 0.271655i | \(0.912429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.20815e11 | −0.447074 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 6.91367e9i | − 0.0250240i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.37599e11 | −1.56653 | −0.783265 | − | 0.621688i | \(-0.786447\pi\) | ||||
−0.783265 | + | 0.621688i | \(0.786447\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.51259e11i | 0.879938i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.99110e10 | 0.172894 | 0.0864471 | − | 0.996256i | \(-0.472449\pi\) | ||||
0.0864471 | + | 0.996256i | \(0.472449\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 7.30556e10i | − 0.247619i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.34218e11 | 1.45590 | 0.727948 | − | 0.685632i | \(-0.240474\pi\) | ||||
0.727948 | + | 0.685632i | \(0.240474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.23440e10i | 0.106130i | 0.998591 | + | 0.0530650i | \(0.0168991\pi\) | ||||
−0.998591 | + | 0.0530650i | \(0.983101\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.38345e11 | −1.42295 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 3.78853e10i | − 0.120377i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.35441e11 | −1.68326 | −0.841631 | − | 0.540053i | \(-0.818404\pi\) | ||||
−0.841631 | + | 0.540053i | \(0.818404\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1.87486e11i | − 0.577008i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.72315e11 | 0.524736 | 0.262368 | − | 0.964968i | \(-0.415497\pi\) | ||||
0.262368 | + | 0.964968i | \(0.415497\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 6.61349e11i | − 1.97193i | −0.166946 | − | 0.985966i | \(-0.553391\pi\) | ||||
0.166946 | − | 0.985966i | \(-0.446609\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00339e11 | −0.591109 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.85949e11i | 2.27098i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.88022e11 | 0.823607 | 0.411803 | − | 0.911273i | \(-0.364899\pi\) | ||||
0.411803 | + | 0.911273i | \(0.364899\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.55828e10i | 0.0716524i | 0.999358 | + | 0.0358262i | \(0.0114063\pi\) | ||||
−0.999358 | + | 0.0358262i | \(0.988594\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.40384e11 | 0.389145 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.51563e11i | 1.76932i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.24185e10 | 0.0871343 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 1.11466e11i | − 0.293537i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.77507e10 | 0.202677 | 0.101339 | − | 0.994852i | \(-0.467687\pi\) | ||||
0.101339 | + | 0.994852i | \(0.467687\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 1.19014e11i | − 0.304012i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.84307e11 | 1.22469 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.89643e11i | 0.717845i | 0.933367 | + | 0.358922i | \(0.116856\pi\) | ||||
−0.933367 | + | 0.358922i | \(0.883144\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.91734e11 | 0.715815 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.36557e11i | 0.568949i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.56925e10 | 0.0849951 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.37144e11i | 0.553628i | 0.960924 | + | 0.276814i | \(0.0892786\pi\) | ||||
−0.960924 | + | 0.276814i | \(0.910721\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.30982e11 | −1.68975 | −0.844877 | − | 0.534961i | \(-0.820326\pi\) | ||||
−0.844877 | + | 0.534961i | \(0.820326\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 7.82711e10i | − 0.177407i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.23394e11 | 0.725844 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00241e11i | 1.98146i | 0.135835 | + | 0.990731i | \(0.456628\pi\) | ||||
−0.135835 | + | 0.990731i | \(0.543372\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.19062e11 | −1.56735 | −0.783676 | − | 0.621169i | \(-0.786658\pi\) | ||||
−0.783676 | + | 0.621169i | \(0.786658\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.80038e11i | − 0.812466i | −0.913770 | − | 0.406233i | \(-0.866842\pi\) | ||||
0.913770 | − | 0.406233i | \(-0.133158\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.57067e11 | 0.544288 | 0.272144 | − | 0.962257i | \(-0.412267\pi\) | ||||
0.272144 | + | 0.962257i | \(0.412267\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.78073e10i | 0.182369i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.22548e11 | −1.48635 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1.40281e11i | − 0.283108i | −0.989931 | − | 0.141554i | \(-0.954790\pi\) | ||||
0.989931 | − | 0.141554i | \(-0.0452098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.98097e11 | 0.995703 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 7.12548e11i | − 1.39761i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.61868e11 | −0.314505 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.07169e11i | 0.204339i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.23072e10 | 0.174357 | 0.0871786 | − | 0.996193i | \(-0.472215\pi\) | ||||
0.0871786 | + | 0.996193i | \(0.472215\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.32383e9i | 0.0172851i | 0.999963 | + | 0.00864254i | \(0.00275104\pi\) | ||||
−0.999963 | + | 0.00864254i | \(0.997249\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.42594e11 | 0.812892 | 0.406446 | − | 0.913675i | \(-0.366768\pi\) | ||||
0.406446 | + | 0.913675i | \(0.366768\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.42643e11i | 1.33887i | 0.742873 | + | 0.669433i | \(0.233463\pi\) | ||||
−0.742873 | + | 0.669433i | \(0.766537\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.58776e10 | 0.135534 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 4.40751e11i | − 0.772883i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.79637e11 | 1.00713 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.40711e11i | 0.410642i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.41714e11 | −1.25383 | −0.626914 | − | 0.779088i | \(-0.715682\pi\) | ||||
−0.626914 | + | 0.779088i | \(0.715682\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 3.16039e11i | − 0.524610i | −0.964985 | − | 0.262305i | \(-0.915517\pi\) | ||||
0.964985 | − | 0.262305i | \(-0.0844827\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.17818e11 | −0.687296 | −0.343648 | − | 0.939098i | \(-0.611663\pi\) | ||||
−0.343648 | + | 0.939098i | \(0.611663\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1.10372e12i | − 1.78306i | −0.452963 | − | 0.891529i | \(-0.649633\pi\) | ||||
0.452963 | − | 0.891529i | \(-0.350367\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 394709. | 6.31931e−7 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 3.75489e11i | − 0.590462i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.19461e11 | 0.342030 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 4.36503e10i | − 0.0668265i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.23163e12 | 1.86888 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 1.74838e11i | − 0.260640i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.80731e11 | 1.00588 | 0.502940 | − | 0.864321i | \(-0.332252\pi\) | ||||
0.502940 | + | 0.864321i | \(0.332252\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 2.03180e10i | − 0.0294990i | −0.999891 | − | 0.0147495i | \(-0.995305\pi\) | ||||
0.999891 | − | 0.0147495i | \(-0.00469508\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.88535e11 | −0.271337 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.05610e11i | 0.432205i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.05292e11 | −0.428010 | −0.214005 | − | 0.976833i | \(-0.568651\pi\) | ||||
−0.214005 | + | 0.976833i | \(0.568651\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.57215e11i | 0.354397i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.99675e11 | −0.272745 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 8.77155e11i | − 1.17764i | −0.808263 | − | 0.588821i | \(-0.799592\pi\) | ||||
0.808263 | − | 0.588821i | \(-0.200408\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.13016e11 | 0.150433 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.14345e11i | 0.411301i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.38579e11 | 1.21762 | 0.608811 | − | 0.793315i | \(-0.291647\pi\) | ||||
0.608811 | + | 0.793315i | \(0.291647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1.85800e11i | − 0.236967i | −0.992956 | − | 0.118484i | \(-0.962197\pi\) | ||||
0.992956 | − | 0.118484i | \(-0.0378033\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.79986e11 | 0.480531 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.46197e11i | − 0.554787i | −0.960756 | − | 0.277394i | \(-0.910529\pi\) | ||||
0.960756 | − | 0.277394i | \(-0.0894706\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.87689e12 | −2.31406 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 8.78364e11i | − 1.06488i | −0.846466 | − | 0.532442i | \(-0.821274\pi\) | ||||
0.846466 | − | 0.532442i | \(-0.178726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.07056e12 | −1.28706 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 8.38720e9i | − 0.00991613i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.34427e10 | 0.0392109 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.82425e10i | 0.101758i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.05174e12 | 1.20282 | 0.601412 | − | 0.798939i | \(-0.294605\pi\) | ||||
0.601412 | + | 0.798939i | \(0.294605\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.39307e12i | − 1.56710i | −0.621327 | − | 0.783552i | \(-0.713406\pi\) | ||||
0.621327 | − | 0.783552i | \(-0.286594\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.95220e10 | −0.0440948 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1.65500e11i | − 0.181643i | −0.995867 | − | 0.0908216i | \(-0.971051\pi\) | ||||
0.995867 | − | 0.0908216i | \(-0.0289493\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.27889e11 | 0.574661 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.64045e11i | 0.818286i | 0.912470 | + | 0.409143i | \(0.134172\pi\) | ||||
−0.912470 | + | 0.409143i | \(0.865828\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.17961e11 | −0.762704 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.88601e11i | − 0.197132i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.64848e10 | 0.0378283 | 0.0189142 | − | 0.999821i | \(-0.493979\pi\) | ||||
0.0189142 | + | 0.999821i | \(0.493979\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.01309e12i | − 1.03361i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.76241e11 | −0.583208 | −0.291604 | − | 0.956539i | \(-0.594189\pi\) | ||||
−0.291604 | + | 0.956539i | \(0.594189\pi\) | |||||||
\(998\) | 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.c.a.197.6 | ✓ | 16 | |
3.2 | odd | 2 | inner | 252.9.c.a.197.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.c.a.197.6 | ✓ | 16 | 1.1 | even | 1 | trivial | |
252.9.c.a.197.11 | yes | 16 | 3.2 | odd | 2 | inner |