Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (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: | \(197.773761087\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 300700 x^{18} + 6140664 x^{17} + 35387063979 x^{16} - 1130222504088 x^{15} + \cdots + 12\!\cdots\!52 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{175}\cdot 3^{32} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.17 | ||
Root | \(-271.678 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.10.d.f.193.4 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 81.0000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 573.512i | 0.410372i | 0.978723 | + | 0.205186i | \(0.0657799\pi\) | ||||
−0.978723 | + | 0.205186i | \(0.934220\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2185.20 | 0.343994 | 0.171997 | − | 0.985097i | \(-0.444978\pi\) | ||||
0.171997 | + | 0.985097i | \(0.444978\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6561.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 25190.5i | − 0.518764i | −0.965775 | − | 0.259382i | \(-0.916481\pi\) | ||||
0.965775 | − | 0.259382i | \(-0.0835189\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 170686.i | − 1.65750i | −0.559622 | − | 0.828748i | \(-0.689054\pi\) | ||||
0.559622 | − | 0.828748i | \(-0.310946\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −46454.5 | −0.236928 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 461173. | 1.33919 | 0.669597 | − | 0.742725i | \(-0.266467\pi\) | ||||
0.669597 | + | 0.742725i | \(0.266467\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 165769.i | 0.291818i | 0.989298 | + | 0.145909i | \(0.0466107\pi\) | ||||
−0.989298 | + | 0.145909i | \(0.953389\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 177001.i | 0.198605i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 953690. | 0.710611 | 0.355306 | − | 0.934750i | \(-0.384377\pi\) | ||||
0.355306 | + | 0.934750i | \(0.384377\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.62421e6 | 0.831595 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 531441.i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.12414e6i | 0.295141i | 0.989052 | + | 0.147570i | \(0.0471453\pi\) | ||||
−0.989052 | + | 0.147570i | \(0.952855\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −886392. | −0.172385 | −0.0861923 | − | 0.996279i | \(-0.527470\pi\) | ||||
−0.0861923 | + | 0.996279i | \(0.527470\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.04043e6 | 0.299509 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.25324e6i | 0.141165i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.04360e7i | 0.915434i | 0.889098 | + | 0.457717i | \(0.151333\pi\) | ||||
−0.889098 | + | 0.457717i | \(0.848667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.38256e7 | 0.956956 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.74090e7 | −1.51484 | −0.757420 | − | 0.652928i | \(-0.773540\pi\) | ||||
−0.757420 | + | 0.652928i | \(0.773540\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.48442e7i | − 1.55426i | −0.629342 | − | 0.777128i | \(-0.716676\pi\) | ||||
0.629342 | − | 0.777128i | \(-0.283324\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 3.76281e6i | − 0.136791i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.83629e7 | −1.74460 | −0.872301 | − | 0.488970i | \(-0.837373\pi\) | ||||
−0.872301 | + | 0.488970i | \(0.837373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.55785e7 | −0.881668 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.73550e7i | 0.773184i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.24392e7i | − 0.738797i | −0.929271 | − | 0.369399i | \(-0.879564\pi\) | ||||
0.929271 | − | 0.369399i | \(-0.120436\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.44471e7 | 0.212886 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.34273e7 | −0.168481 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.50758e7i | 0.591734i | 0.955229 | + | 0.295867i | \(0.0956086\pi\) | ||||
−0.955229 | + | 0.295867i | \(0.904391\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 3.22137e7i | − 0.297890i | −0.988845 | − | 0.148945i | \(-0.952412\pi\) | ||||
0.988845 | − | 0.148945i | \(-0.0475877\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.43371e7 | −0.114665 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.78904e7 | 0.680190 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1.97628e8i | − 1.19815i | −0.800692 | − | 0.599076i | \(-0.795535\pi\) | ||||
0.800692 | − | 0.599076i | \(-0.204465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.72489e7i | 0.410272i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.31495e8 | −0.614111 | −0.307056 | − | 0.951692i | \(-0.599344\pi\) | ||||
−0.307056 | + | 0.951692i | \(0.599344\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.88866e7 | 0.0778398 | 0.0389199 | − | 0.999242i | \(-0.487608\pi\) | ||||
0.0389199 | + | 0.999242i | \(0.487608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.31561e8i | 0.480122i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 5.50464e7i | − 0.178452i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.76946e7 | −0.195538 | −0.0977692 | − | 0.995209i | \(-0.531171\pi\) | ||||
−0.0977692 | + | 0.995209i | \(0.531171\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.73246e8i | 0.863264i | 0.902050 | + | 0.431632i | \(0.142062\pi\) | ||||
−0.902050 | + | 0.431632i | \(0.857938\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.64488e8i | 0.549567i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.10553e7 | −0.170400 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.50175e8 | −0.422658 | −0.211329 | − | 0.977415i | \(-0.567779\pi\) | ||||
−0.211329 | + | 0.977415i | \(0.567779\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 3.72983e8i | − 0.570168i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 7.17978e7i | − 0.0995262i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.50706e7 | −0.119754 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.73257e8 | −0.886852 | −0.443426 | − | 0.896311i | \(-0.646237\pi\) | ||||
−0.443426 | + | 0.896311i | \(0.646237\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.65275e8i | 0.172921i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 8.34597e8i | − 0.798051i | −0.916940 | − | 0.399025i | \(-0.869349\pi\) | ||||
0.916940 | − | 0.399025i | \(-0.130651\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.44701e9 | −1.26678 | −0.633392 | − | 0.773831i | \(-0.718338\pi\) | ||||
−0.633392 | + | 0.773831i | \(0.718338\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.01513e8 | −0.0815019 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.20932e8i | 0.162942i | 0.996676 | + | 0.0814708i | \(0.0259617\pi\) | ||||
−0.996676 | + | 0.0814708i | \(0.974038\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 8.53497e8i | − 0.579139i | −0.957157 | − | 0.289570i | \(-0.906488\pi\) | ||||
0.957157 | − | 0.289570i | \(-0.0935122\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.45318e8 | −0.528526 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.25755e9 | 0.725560 | 0.362780 | − | 0.931875i | \(-0.381828\pi\) | ||||
0.362780 | + | 0.931875i | \(0.381828\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.46953e8i | 0.291615i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.11987e9i | 0.552499i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00776e9 | 0.460674 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.72339e9 | 0.730884 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 2.22013e9i | − 0.874593i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.05164e9i | 0.751635i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.98428e9 | −1.01794 | −0.508971 | − | 0.860783i | \(-0.669974\pi\) | ||||
−0.508971 | + | 0.860783i | \(0.669974\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.82238e9 | 0.897351 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 2.24225e9i | − 0.665217i | −0.943065 | − | 0.332609i | \(-0.892071\pi\) | ||||
0.943065 | − | 0.332609i | \(-0.107929\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.62239e8i | 0.100384i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.04788e8 | 0.0789761 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.92870e8 | −0.0467759 | −0.0233879 | − | 0.999726i | \(-0.507445\pi\) | ||||
−0.0233879 | + | 0.999726i | \(0.507445\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.70374e9i | 1.29596i | 0.761655 | + | 0.647982i | \(0.224387\pi\) | ||||
−0.761655 | + | 0.647982i | \(0.775613\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 4.72739e9i | − 1.00725i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.29966e9 | −0.859849 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.44708e8 | −0.121117 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2.88186e9i | − 0.509031i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 8.87026e9i | − 1.47434i | −0.675707 | − | 0.737171i | \(-0.736161\pi\) | ||||
0.675707 | − | 0.737171i | \(-0.263839\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.12257e10 | 1.75719 | 0.878595 | − | 0.477568i | \(-0.158481\pi\) | ||||
0.878595 | + | 0.477568i | \(0.158481\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.02575e9 | −0.446398 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 5.08357e8i | − 0.0707418i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 6.26221e9i | − 0.822582i | −0.911504 | − | 0.411291i | \(-0.865078\pi\) | ||||
0.911504 | − | 0.411291i | \(-0.134922\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.43757e9 | 0.426545 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.08401e9 | 0.244446 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.06846e9i | − 0.451425i | −0.974194 | − | 0.225712i | \(-0.927529\pi\) | ||||
0.974194 | − | 0.225712i | \(-0.0724710\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.17021e9i | 0.122910i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.42771e9 | −0.738976 | −0.369488 | − | 0.929235i | \(-0.620467\pi\) | ||||
−0.369488 | + | 0.929235i | \(0.620467\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.85292e10 | −1.74729 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 1.08761e9i | − 0.0972727i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.15808e9i | 0.777315i | 0.921382 | + | 0.388658i | \(0.127061\pi\) | ||||
−0.921382 | + | 0.388658i | \(0.872939\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.54923e9 | 0.286064 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.46114e9 | −0.341638 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.24462e10i | 1.63420i | 0.576499 | + | 0.817098i | \(0.304418\pi\) | ||||
−0.576499 | + | 0.817098i | \(0.695582\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1.01662e10i | − 0.704049i | −0.935991 | − | 0.352025i | \(-0.885493\pi\) | ||||
0.935991 | − | 0.352025i | \(-0.114507\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.60931e9 | 0.171987 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.98519e9 | −0.375669 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.16172e10i | − 0.694726i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.16131e9i | − 0.0662017i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.71383e10 | 1.47548 | 0.737738 | − | 0.675088i | \(-0.235894\pi\) | ||||
0.737738 | + | 0.675088i | \(0.235894\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.59970e10 | 1.34870 | 0.674350 | − | 0.738412i | \(-0.264424\pi\) | ||||
0.674350 | + | 0.738412i | \(0.264424\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.92912e9i | 0.392708i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.11903e10i | − 0.529351i | −0.964337 | − | 0.264676i | \(-0.914735\pi\) | ||||
0.964337 | − | 0.264676i | \(-0.0852649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.24980e10 | −1.01696 | −0.508482 | − | 0.861073i | \(-0.669793\pi\) | ||||
−0.508482 | + | 0.861073i | \(0.669793\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.60079e10 | 0.691753 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.45647e9i | 0.101527i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1.57194e10i | − 0.621648i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.25716e9 | −0.236870 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.17581e9 | 0.151385 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2.12635e10i | − 0.738521i | −0.929326 | − | 0.369261i | \(-0.879611\pi\) | ||||
0.929326 | − | 0.369261i | \(-0.120389\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.06511e10i | − 0.354557i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.99836e10 | 0.637823 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.93695e9 | −0.0592992 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.52982e9i | 0.0449408i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 7.87156e10i | − 2.21971i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.72002e10 | 0.736546 | 0.368273 | − | 0.929718i | \(-0.379949\pi\) | ||||
0.368273 | + | 0.929718i | \(0.379949\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.06564e10 | −0.277198 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.16425e9i | 0.104093i | 0.998645 | + | 0.0520464i | \(0.0165744\pi\) | ||||
−0.998645 | + | 0.0520464i | \(0.983426\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 5.12064e10i | − 1.23045i | −0.788351 | − | 0.615226i | \(-0.789065\pi\) | ||||
0.788351 | − | 0.615226i | \(-0.210935\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.45876e9 | 0.103029 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.39479e10 | −0.532311 | −0.266155 | − | 0.963930i | \(-0.585753\pi\) | ||||
−0.266155 | + | 0.963930i | \(0.585753\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 3.34718e10i | − 0.715935i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 5.48326e9i | − 0.112894i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.69723e9 | 0.152596 | 0.0762981 | − | 0.997085i | \(-0.475690\pi\) | ||||
0.0762981 | + | 0.997085i | \(0.475690\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.87829e8 | −0.0188628 | −0.00943138 | − | 0.999956i | \(-0.503002\pi\) | ||||
−0.00943138 | + | 0.999956i | \(0.503002\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.48678e9i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2.04047e10i | − 0.361812i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.82944e10 | 0.483687 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.02329e10 | −0.498406 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.00907e10i | 0.478521i | 0.970955 | + | 0.239261i | \(0.0769050\pi\) | ||||
−0.970955 | + | 0.239261i | \(0.923095\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.40239e10i | − 0.368640i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.14235e10 | −0.317293 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.68520e10 | 0.240963 | 0.120482 | − | 0.992716i | \(-0.461556\pi\) | ||||
0.120482 | + | 0.992716i | \(0.461556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.28048e10i | 0.314904i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 7.37548e9i | − 0.0983803i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.47935e10 | −0.319548 | −0.159774 | − | 0.987154i | \(-0.551077\pi\) | ||||
−0.159774 | + | 0.987154i | \(0.551077\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.43394e10 | 0.303182 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2.02642e10i | − 0.244022i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1.44586e11i | − 1.68361i | −0.539785 | − | 0.841803i | \(-0.681494\pi\) | ||||
0.539785 | − | 0.841803i | \(-0.318506\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.33109e10 | −1.05092 | −0.525461 | − | 0.850818i | \(-0.676107\pi\) | ||||
−0.525461 | + | 0.850818i | \(0.676107\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.02116e10 | 0.329187 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 4.09146e10i | − 0.431402i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.41736e11i | − 1.44651i | −0.690583 | − | 0.723253i | \(-0.742646\pi\) | ||||
0.690583 | − | 0.723253i | \(-0.257354\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.81562e9 | 0.0574615 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.57492e10 | 0.437729 | 0.218864 | − | 0.975755i | \(-0.429765\pi\) | ||||
0.218864 | + | 0.975755i | \(0.429765\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.57214e10i | 0.794420i | 0.917728 | + | 0.397210i | \(0.130022\pi\) | ||||
−0.917728 | + | 0.397210i | \(0.869978\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 7.70072e9i | − 0.0691400i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.98944e10 | −0.521096 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.40923e10 | 0.793440 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 6.26338e10i | − 0.512024i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 7.92826e10i | − 0.628454i | −0.949348 | − | 0.314227i | \(-0.898255\pi\) | ||||
0.949348 | − | 0.314227i | \(-0.101745\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.15866e10 | −0.242831 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.33873e10 | −0.0998362 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.62781e11i | − 1.17784i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 7.61417e10i | − 0.534655i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.76023e10 | 0.460755 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.84749e10 | 0.122246 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.70824e11i | 1.74006i | 0.492996 | + | 0.870031i | \(0.335902\pi\) | ||||
−0.492996 | + | 0.870031i | \(0.664098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1.17207e11i | − 0.731378i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.53125e11 | −1.53431 | −0.767155 | − | 0.641462i | \(-0.778328\pi\) | ||||
−0.767155 | + | 0.641462i | \(0.778328\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.80905e10 | −0.224320 | −0.112160 | − | 0.993690i | \(-0.535777\pi\) | ||||
−0.112160 | + | 0.993690i | \(0.535777\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 8.22251e9i | − 0.0470551i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.66537e11i | − 1.48249i | −0.671235 | − | 0.741245i | \(-0.734236\pi\) | ||||
0.671235 | − | 0.741245i | \(-0.265764\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.83176e10 | 0.153108 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.78955e10 | −0.0940744 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.64482e10i | 0.390801i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2.77229e11i | − 1.37836i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.91333e10 | 0.334366 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.27535e11 | −0.600132 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 1.32548e11i | − 0.606942i | −0.952841 | − | 0.303471i | \(-0.901854\pi\) | ||||
0.952841 | − | 0.303471i | \(-0.0981456\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 6.84707e10i | − 0.305145i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.13342e11 | 0.491688 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.91693e11 | −1.65429 | −0.827145 | − | 0.561988i | \(-0.810037\pi\) | ||||
−0.827145 | + | 0.561988i | \(0.810037\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.01862e11i | 0.418903i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.23287e10i | 0.0894269i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.65927e11 | −0.647282 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.43032e10 | −0.168364 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 5.17702e10i | − 0.191689i | −0.995396 | − | 0.0958445i | \(-0.969445\pi\) | ||||
0.995396 | − | 0.0958445i | \(-0.0305551\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 2.61383e11i | − 0.943113i | −0.881836 | − | 0.471556i | \(-0.843692\pi\) | ||||
0.881836 | − | 0.471556i | \(-0.156308\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.07095e10 | −0.318985 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.46204e11 | −0.843934 | −0.421967 | − | 0.906611i | \(-0.638660\pi\) | ||||
−0.421967 | + | 0.906611i | \(0.638660\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 7.54141e10i | − 0.252014i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.16282e10i | 0.265971i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.40472e11 | 1.39956 | 0.699782 | − | 0.714356i | \(-0.253280\pi\) | ||||
0.699782 | + | 0.714356i | \(0.253280\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.95208e11 | 0.914842 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.39594e11i | 0.421976i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.08317e10i | 0.0319433i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.54837e11 | −0.733271 | −0.366636 | − | 0.930365i | \(-0.619490\pi\) | ||||
−0.366636 | + | 0.930365i | \(0.619490\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.79831e11 | 0.504947 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 9.27382e10i | − 0.254142i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 4.92490e11i | − 1.31737i | −0.752419 | − | 0.658685i | \(-0.771113\pi\) | ||||
0.752419 | − | 0.658685i | \(-0.228887\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.66183e11 | −0.433957 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.91875e11 | 0.489195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 6.04503e11i | − 1.50495i | −0.658621 | − | 0.752475i | \(-0.728860\pi\) | ||||
0.658621 | − | 0.752475i | \(-0.271140\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 2.41727e11i | − 0.587710i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.93960e10 | 0.236034 | 0.118017 | − | 0.993012i | \(-0.462346\pi\) | ||||
0.118017 | + | 0.993012i | \(0.462346\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.15698e10 | 0.0732315 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.28613e11i | 0.518086i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 8.77921e11i | − 1.94394i | −0.235109 | − | 0.971969i | \(-0.575545\pi\) | ||||
0.235109 | − | 0.971969i | \(-0.424455\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.39816e11 | 0.951646 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.81622e11 | 0.384063 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 3.88237e10i | − 0.0802435i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.40922e9i | 0.00688808i | 0.999994 | + | 0.00344404i | \(0.00109627\pi\) | ||||
−0.999994 | + | 0.00344404i | \(0.998904\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.93414e10 | −0.0579565 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.36366e11 | 0.842755 | 0.421378 | − | 0.906885i | \(-0.361547\pi\) | ||||
0.421378 | + | 0.906885i | \(0.361547\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.51295e11i | 0.285727i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.46878e10i | 0.0455969i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.62889e11 | 0.474894 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.53167e9 | 0.00270652 | 0.00135326 | − | 0.999999i | \(-0.499569\pi\) | ||||
0.00135326 | + | 0.999999i | \(0.499569\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.56225e10i | − 0.0270061i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.20352e11i | 0.203553i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.14061e11 | −0.354259 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.62003e11 | −0.748226 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.95996e11i | 1.26168i | 0.775915 | + | 0.630838i | \(0.217289\pi\) | ||||
−0.775915 | + | 0.630838i | \(0.782711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.16602e11i | 1.11175i | 0.831265 | + | 0.555877i | \(0.187617\pi\) | ||||
−0.831265 | + | 0.555877i | \(0.812383\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.82919e11 | 0.581534 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.49041e11 | 1.11367 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 7.03934e10i | − 0.102472i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 3.48273e11i | − 0.496434i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.72042e11 | −0.379741 | −0.189871 | − | 0.981809i | \(-0.560807\pi\) | ||||
−0.189871 | + | 0.981809i | \(0.560807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.93461e11 | −0.401195 | −0.200598 | − | 0.979674i | \(-0.564288\pi\) | ||||
−0.200598 | + | 0.979674i | \(0.564288\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 5.22213e10i | − 0.0699272i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.58092e11i | 0.207369i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.95559e11 | −0.379799 | −0.189900 | − | 0.981804i | \(-0.560816\pi\) | ||||
−0.189900 | + | 0.981804i | \(0.560816\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.33430e11 | 0.293889 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 1.41221e12i | − 1.74214i | −0.491163 | − | 0.871068i | \(-0.663428\pi\) | ||||
0.491163 | − | 0.871068i | \(-0.336572\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.43479e11i | − 0.173447i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.18491e11 | 0.851211 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.27145e11 | −0.960447 | −0.480223 | − | 0.877146i | \(-0.659444\pi\) | ||||
−0.480223 | + | 0.877146i | \(0.659444\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.90448e11i | 0.785844i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.09285e11i | 1.01451i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.13910e11 | 0.233981 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.57958e11 | −0.920117 | −0.460058 | − | 0.887889i | \(-0.652172\pi\) | ||||
−0.460058 | + | 0.887889i | \(0.652172\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2.45086e11i | − 0.257728i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.68707e11i | 0.483334i | 0.970359 | + | 0.241667i | \(0.0776941\pi\) | ||||
−0.970359 | + | 0.241667i | \(0.922306\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.90051e11 | 0.900120 | 0.450060 | − | 0.892998i | \(-0.351403\pi\) | ||||
0.450060 | + | 0.892998i | \(0.351403\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.11769e10 | 0.0408428 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.17567e12i | 1.14383i | 0.820314 | + | 0.571913i | \(0.193799\pi\) | ||||
−0.820314 | + | 0.571913i | \(0.806201\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 4.31857e11i | − 0.412157i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.07239e11 | 0.474918 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.77744e11 | −0.806293 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.69244e11i | 0.242674i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.78443e11i | 0.246266i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.61386e11 | 0.660838 | 0.330419 | − | 0.943834i | \(-0.392810\pi\) | ||||
0.330419 | + | 0.943834i | \(0.392810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.78128e12 | 1.51733 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.68805e11i | 0.141131i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4.43473e11i | − 0.363939i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.08842e12 | −1.68243 | −0.841217 | − | 0.540698i | \(-0.818160\pi\) | ||||
−0.841217 | + | 0.540698i | \(0.818160\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.29545e11 | 0.260630 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 5.35372e11i | − 0.415709i | −0.978160 | − | 0.207854i | \(-0.933352\pi\) | ||||
0.978160 | − | 0.207854i | \(-0.0666480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.18422e11i | 0.395251i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.47872e10 | −0.0709621 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.87344e11 | −0.211251 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.24709e12i | 0.900422i | 0.892922 | + | 0.450211i | \(0.148651\pi\) | ||||
−0.892922 | + | 0.450211i | \(0.851349\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 6.01644e11i | − 0.426648i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.38151e11 | −0.305188 | −0.152594 | − | 0.988289i | \(-0.548763\pi\) | ||||
−0.152594 | + | 0.988289i | \(0.548763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.78651e11 | 0.327498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1.50086e12i | − 1.00880i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 8.18520e11i | − 0.540505i | −0.962790 | − | 0.270252i | \(-0.912893\pi\) | ||||
0.962790 | − | 0.270252i | \(-0.0871071\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.12712e10 | 0.0267764 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.80965e10 | 0.0561604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 8.29875e11i | − 0.519853i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.47019e12i | 0.905037i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.41805e11 | −0.448783 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.40738e12 | 0.836835 | 0.418418 | − | 0.908255i | \(-0.362585\pi\) | ||||
0.418418 | + | 0.908255i | \(0.362585\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.18942e12i | − 0.695147i | −0.937653 | − | 0.347574i | \(-0.887006\pi\) | ||||
0.937653 | − | 0.347574i | \(-0.112994\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.87487e11i | 0.165159i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.08780e11 | −0.230856 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.91627e11 | −0.495032 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 3.61352e11i | − 0.197245i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.67834e12i | 2.51084i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.26707e11 | −0.0668667 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.81814e12 | −0.943503 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.96240e11i | 0.457378i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.99696e12i | 1.50416i | 0.659072 | + | 0.752080i | \(0.270949\pi\) | ||||
−0.659072 | + | 0.752080i | \(0.729051\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.23459e11 | 0.406483 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.89491e11 | 0.237662 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.19878e12i | 0.572527i | 0.958151 | + | 0.286264i | \(0.0924133\pi\) | ||||
−0.958151 | + | 0.286264i | \(0.907587\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.11354e11i | 0.0992966i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.86348e11 | −0.0861274 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.47927e11 | −0.0672640 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 4.84800e11i | − 0.216892i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.94419e12i | 1.29604i | 0.761625 | + | 0.648018i | \(0.224402\pi\) | ||||
−0.761625 | + | 0.648018i | \(0.775598\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.94742e12 | −2.57617 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.40991e11 | 0.401100 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.99061e12i | 1.25450i | 0.778816 | + | 0.627252i | \(0.215820\pi\) | ||||
−0.778816 | + | 0.627252i | \(0.784180\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.21222e11i | 0.297750i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.40658e10 | 0.0382215 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.33223e12 | −1.33269 | −0.666346 | − | 0.745643i | \(-0.732142\pi\) | ||||
−0.666346 | + | 0.745643i | \(0.732142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 3.69698e12i | − 1.45541i | −0.685891 | − | 0.727704i | \(-0.740587\pi\) | ||||
0.685891 | − | 0.727704i | \(-0.259413\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.19820e12i | 0.851866i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.54899e12 | 0.590941 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.68443e12 | −0.632647 | −0.316323 | − | 0.948651i | \(-0.602448\pi\) | ||||
−0.316323 | + | 0.948651i | \(0.602448\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.10576e12i | 0.778672i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.15618e11i | 0.296958i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.06906e12 | −0.383262 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.42259e11 | −0.226730 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 5.18518e12i | − 1.80257i | −0.433224 | − | 0.901286i | \(-0.642624\pi\) | ||||
0.433224 | − | 0.901286i | \(-0.357376\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.46936e11i | − 0.0503049i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.06415e11 | 0.305621 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.75208e10 | 0.0191020 | 0.00955100 | − | 0.999954i | \(-0.496960\pi\) | ||||
0.00955100 | + | 0.999954i | \(0.496960\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.77960e11i | 0.189048i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.82234e12i | − 0.587144i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.13376e12 | 1.62935 | 0.814677 | − | 0.579916i | \(-0.196914\pi\) | ||||
0.814677 | + | 0.579916i | \(0.196914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.69179e12 | 0.528947 | 0.264474 | − | 0.964393i | \(-0.414802\pi\) | ||||
0.264474 | + | 0.964393i | \(0.414802\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.29664e12i | 0.399384i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.88383e11i | 0.299934i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.63728e12 | −0.489524 | −0.244762 | − | 0.969583i | \(-0.578710\pi\) | ||||
−0.244762 | + | 0.969583i | \(0.578710\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.98974e11 | −0.0586164 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.96171e12i | 2.89167i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.61028e12i | 0.746646i | 0.927701 | + | 0.373323i | \(0.121782\pi\) | ||||
−0.927701 | + | 0.373323i | \(0.878218\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.27327e12 | 0.358908 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.80946e11 | 0.189160 | 0.0945800 | − | 0.995517i | \(-0.469849\pi\) | ||||
0.0945800 | + | 0.995517i | \(0.469849\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 5.97226e12i | − 1.63505i | −0.575894 | − | 0.817524i | \(-0.695346\pi\) | ||||
0.575894 | − | 0.817524i | \(-0.304654\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 5.06830e11i | − 0.136757i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.46684e11 | −0.145392 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.99564e12 | 0.523145 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.38240e11i | 0.0874020i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.81281e12i | 1.22594i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.38581e12 | −1.35244 | −0.676221 | − | 0.736698i | \(-0.736384\pi\) | ||||
−0.676221 | + | 0.736698i | \(0.736384\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.72234e12 | 0.426386 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.71152e12i | − 0.417735i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.07275e12i | 1.46136i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.62740e11 | 0.204704 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.98854e12 | 1.63503 | 0.817514 | − | 0.575909i | \(-0.195352\pi\) | ||||
0.817514 | + | 0.575909i | \(0.195352\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.21879e12i | 0.281176i | 0.990068 | + | 0.140588i | \(0.0448994\pi\) | ||||
−0.990068 | + | 0.140588i | \(0.955101\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.61867e12i | 0.368247i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.11593e11 | −0.182083 | −0.0910414 | − | 0.995847i | \(-0.529020\pi\) | ||||
−0.0910414 | + | 0.995847i | \(0.529020\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.38739e12 | 0.306970 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 1.56893e11i | − 0.0342364i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.33692e12i | 0.502962i | 0.967862 | + | 0.251481i | \(0.0809175\pi\) | ||||
−0.967862 | + | 0.251481i | \(0.919082\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.28596e12 | 0.272986 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.23915e11 | −0.0259466 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 5.06294e12i | − 1.04573i | −0.852416 | − | 0.522863i | \(-0.824864\pi\) | ||||
0.852416 | − | 0.522863i | \(-0.175136\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.34073e12i | 0.273170i | 0.990628 | + | 0.136585i | \(0.0436127\pi\) | ||||
−0.990628 | + | 0.136585i | \(0.956387\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.37597e12 | 1.28155 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.07749e11 | −0.0411946 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.07208e12i | 0.209730i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.20321e12i | 0.425245i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.11478e11 | −0.154535 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.40610e12 | 0.827916 | 0.413958 | − | 0.910296i | \(-0.364146\pi\) | ||||
0.413958 | + | 0.910296i | \(0.364146\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 8.63171e11i | − 0.160041i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 2.41655e12i | − 0.442126i | −0.975259 | − | 0.221063i | \(-0.929047\pi\) | ||||
0.975259 | − | 0.221063i | \(-0.0709527\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.68972e12 | −0.305072 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.37304e11 | −0.0600980 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.19393e12i | 0.561606i | 0.959765 | + | 0.280803i | \(0.0906008\pi\) | ||||
−0.959765 | + | 0.280803i | \(0.909399\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.10613e11i | − 0.0191955i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.14772e12 | 0.710401 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.24376e12 | −1.22455 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.11051e13i | 1.85298i | 0.376318 | + | 0.926491i | \(0.377190\pi\) | ||||
−0.376318 | + | 0.926491i | \(0.622810\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.61159e11i | 0.0594839i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.27116e12 | −0.531828 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.26403e13 | −2.02866 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1.93978e12i | − 0.307330i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.08592e12i | 0.169850i | 0.996387 | + | 0.0849249i | \(0.0270650\pi\) | ||||
−0.996387 | + | 0.0849249i | \(0.972935\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.72997e12 | −0.267140 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.71122e12 | 0.413346 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.82376e12i | − 0.274525i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.38234e12i | 0.651325i | 0.945486 | + | 0.325662i | \(0.105587\pi\) | ||||
−0.945486 | + | 0.325662i | \(0.894413\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.44144e11 | 0.0651795 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.45344e11 | −0.122498 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.46591e12i | − 0.352858i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.23475e11i | 0.0881015i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.08321e13 | 1.51158 | 0.755789 | − | 0.654815i | \(-0.227253\pi\) | ||||
0.755789 | + | 0.654815i | \(0.227253\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.16200e12 | −0.435766 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 8.00142e10i | − 0.0108904i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.82584e12i | 0.245438i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.52246e12 | −0.600440 | −0.300220 | − | 0.953870i | \(-0.597060\pi\) | ||||
−0.300220 | + | 0.953870i | \(0.597060\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.82430e11 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.60692e13i | − 2.08145i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.16220e13i | − 1.48701i | −0.668729 | − | 0.743506i | \(-0.733161\pi\) | ||||
0.668729 | − | 0.743506i | \(-0.266839\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.65278e12 | 0.208892 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.97835e12 | −0.621558 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.43315e12i | 0.300102i | 0.988678 | + | 0.150051i | \(0.0479438\pi\) | ||||
−0.988678 | + | 0.150051i | \(0.952056\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.29185e12i | 0.279257i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.63463e13 | 1.96774 | 0.983872 | − | 0.178875i | \(-0.0572457\pi\) | ||||
0.983872 | + | 0.178875i | \(0.0572457\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.08720e12 | 0.605028 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 2.44887e12i | − 0.287755i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.82782e11i | 0.0560509i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.35795e13 | −1.55778 | −0.778888 | − | 0.627164i | \(-0.784216\pi\) | ||||
−0.778888 | + | 0.627164i | \(0.784216\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.43735e12 | −0.276274 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.43810e12i | 0.721101i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.13921e12i | 0.568807i | 0.958705 | + | 0.284403i | \(0.0917955\pi\) | ||||
−0.958705 | + | 0.284403i | \(0.908205\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.94594e12 | 0.212834 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.01011e13 | 1.09178 | 0.545892 | − | 0.837855i | \(-0.316191\pi\) | ||||
0.545892 | + | 0.837855i | \(0.316191\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.86507e12i | − 0.199220i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1.73531e12i | − 0.183189i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.40066e12 | 0.980797 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.55912e12 | −0.263889 | −0.131945 | − | 0.991257i | \(-0.542122\pi\) | ||||
−0.131945 | + | 0.991257i | \(0.542122\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.36501e12i | 0.139120i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.50470e13i | − 1.51580i | −0.652372 | − | 0.757899i | \(-0.726226\pi\) | ||||
0.652372 | − | 0.757899i | \(-0.273774\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.43969e12 | −0.143354 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.84719e12 | −0.181810 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 4.54357e12i | − 0.442058i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.31243e12i | 0.318579i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.97414e11 | 0.0567999 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.59145e12 | 0.337564 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.23403e13i | 1.14667i | 0.819320 | + | 0.573337i | \(0.194351\pi\) | ||||
−0.819320 | + | 0.573337i | \(0.805649\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 2.00827e12i | − 0.184491i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.74801e12 | 0.249588 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.49841e12 | −0.493751 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.97149e12i | 0.175042i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.96003e12i | 0.698799i | 0.936974 | + | 0.349399i | \(0.113614\pi\) | ||||
−0.936974 | + | 0.349399i | \(0.886386\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.69154e13 | −2.33636 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.64140e12 | 0.140886 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 4.75764e11i | − 0.0403805i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.19520e12i | 0.100314i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.17115e13 | 0.972030 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.33262e13 | 1.09380 | 0.546902 | − | 0.837197i | \(-0.315807\pi\) | ||||
0.546902 | + | 0.837197i | \(0.315807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 3.23877e12i | − 0.262897i | −0.991323 | − | 0.131449i | \(-0.958037\pi\) | ||||
0.991323 | − | 0.131449i | \(-0.0419628\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 7.55818e12i | − 0.606750i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.33331e12 | 0.185252 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.77609e12 | 0.453560 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.44714e12i | 0.190056i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.53482e13i | − 1.17900i | −0.807768 | − | 0.589501i | \(-0.799324\pi\) | ||||
0.807768 | − | 0.589501i | \(-0.200676\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.18794e13 | −1.66240 | −0.831202 | − | 0.555971i | \(-0.812347\pi\) | ||||
−0.831202 | + | 0.555971i | \(0.812347\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.31409e12 | 0.249070 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.40288e12i | 0.104291i | 0.998640 | + | 0.0521454i | \(0.0166059\pi\) | ||||
−0.998640 | + | 0.0521454i | \(0.983394\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1.59294e13i | − 1.17139i | −0.810530 | − | 0.585697i | \(-0.800821\pi\) | ||||
0.810530 | − | 0.585697i | \(-0.199179\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.14806e13 | 0.835140 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.64078e13 | −1.18072 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 4.25988e12i | − 0.303255i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.71065e11i | 0.0331754i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.81369e12 | 0.126367 | 0.0631836 | − | 0.998002i | \(-0.479875\pi\) | ||||
0.0631836 | + | 0.998002i | \(0.479875\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.32435e13 | 0.912892 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.70569e12i | 0.252723i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.06267e13i | − 0.717040i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.76595e12 | 0.251420 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.94343e12 | −0.458659 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.95273e12i | 0.650518i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.21558e13i | − 1.43290i | −0.697637 | − | 0.716451i | \(-0.745765\pi\) | ||||
0.697637 | − | 0.716451i | \(-0.254235\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.23758e11 | 0.0399180 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.33185e13 | −0.843416 | −0.421708 | − | 0.906732i | \(-0.638569\pi\) | ||||
−0.421708 | + | 0.906732i | \(0.638569\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 4.69713e12i | − 0.294349i | −0.989111 | − | 0.147175i | \(-0.952982\pi\) | ||||
0.989111 | − | 0.147175i | \(-0.0470179\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 4.85144e12i | − 0.300855i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.20688e12 | −0.0740653 | −0.0370326 | − | 0.999314i | \(-0.511791\pi\) | ||||
−0.0370326 | + | 0.999314i | \(0.511791\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.25227e12 | −0.318988 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.62148e12i | 0.458093i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.70526e12i | 0.101438i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.37323e13 | −1.98593 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.07334e12 | 0.295617 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.48326e12i | 0.258558i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.40216e13i | − 1.37121i | −0.727975 | − | 0.685604i | \(-0.759538\pi\) | ||||
0.727975 | − | 0.685604i | \(-0.240462\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.42189e12 | 0.362838 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.51231e13 | −0.845765 | −0.422883 | − | 0.906184i | \(-0.638982\pi\) | ||||
−0.422883 | + | 0.906184i | \(0.638982\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.63940e13i | − 1.46111i | −0.682854 | − | 0.730555i | \(-0.739262\pi\) | ||||
0.682854 | − | 0.730555i | \(-0.260738\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2.55852e12i | − 0.140199i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.20527e13 | −1.19621 | −0.598103 | − | 0.801419i | \(-0.704079\pi\) | ||||
−0.598103 | + | 0.801419i | \(0.704079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.52127e12 | −0.350166 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.08437e12i | − 0.0576405i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 9.67476e12i | − 0.509106i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.28732e13 | −0.670628 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.31853e13 | 0.680023 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 9.96428e11i | − 0.0508777i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.95718e13i | − 0.989393i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.16748e12 | 0.308683 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.83041e12 | 0.288922 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 5.06988e12i | − 0.248751i | −0.992235 | − | 0.124376i | \(-0.960307\pi\) | ||||
0.992235 | − | 0.124376i | \(-0.0396927\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.47579e12i | 0.266017i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.16345e13 | 1.04067 | 0.520337 | − | 0.853961i | \(-0.325806\pi\) | ||||
0.520337 | + | 0.853961i | \(0.325806\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.40225e12 | 0.447830 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.49647e12i | 0.0705785i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.89978e12i | − 0.228831i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.37636e12 | 0.387378 | 0.193689 | − | 0.981063i | \(-0.437955\pi\) | ||||
0.193689 | + | 0.981063i | \(0.437955\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.19368e13 | −1.00463 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.24444e13i | 1.01789i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.69503e13i | 0.761271i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.49380e12 | 0.422261 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.81132e13 | 1.67882 | 0.839412 | − | 0.543496i | \(-0.182900\pi\) | ||||
0.839412 | + | 0.543496i | \(0.182900\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 5.89781e12i | − 0.257287i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 2.05031e13i | − 0.885834i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.66259e12 | 0.285096 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.86158e13 | 1.21277 | 0.606383 | − | 0.795172i | \(-0.292620\pi\) | ||||
0.606383 | + | 0.795172i | \(0.292620\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 3.08533e12i | − 0.129511i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 3.31159e13i | − 1.37684i | −0.725312 | − | 0.688421i | \(-0.758304\pi\) | ||||
0.725312 | − | 0.688421i | \(-0.241696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.61397e13 | −1.07646 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.66024e11 | 0.0271673 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 6.14318e12i | − 0.248209i | −0.992269 | − | 0.124105i | \(-0.960394\pi\) | ||||
0.992269 | − | 0.124105i | \(-0.0396059\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 3.22368e12i | − 0.129019i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.15895e13 | 0.855915 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.53935e13 | 0.604531 | 0.302266 | − | 0.953224i | \(-0.402257\pi\) | ||||
0.302266 | + | 0.953224i | \(0.402257\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.55641e13i | 0.605494i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.29373e12i | 0.0883972i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.21460e11 | −0.0160906 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.56539e13 | −0.970284 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.44954e12i | − 0.0543139i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.49096e13i | 0.553468i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.90791e13 | −1.80500 | −0.902500 | − | 0.430691i | \(-0.858270\pi\) | ||||
−0.902500 | + | 0.430691i | \(0.858270\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.19230e12 | −0.225629 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 2.88291e13i | − 1.04075i | −0.853939 | − | 0.520373i | \(-0.825793\pi\) | ||||
0.853939 | − | 0.520373i | \(-0.174207\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.24638e13i | 0.445804i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.24556e13 | 0.795799 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.64010e13 | −0.575899 | −0.287949 | − | 0.957646i | \(-0.592973\pi\) | ||||
−0.287949 | + | 0.957646i | \(0.592973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.30204e12i | 0.219260i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.59980e12i | 0.193046i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.06192e13 | 1.72912 | 0.864559 | − | 0.502531i | \(-0.167598\pi\) | ||||
0.864559 | + | 0.502531i | \(0.167598\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.41778e12 | 0.217231 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.03303e13i | − 0.346486i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 3.32306e13i | − 1.10447i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.53288e13 | −0.834225 | −0.417113 | − | 0.908855i | \(-0.636958\pi\) | ||||
−0.417113 | + | 0.908855i | \(0.636958\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.07364e13 | 0.350418 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.29029e13i | − 0.417333i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 5.28104e13i | − 1.69275i | −0.532591 | − | 0.846373i | \(-0.678782\pi\) | ||||
0.532591 | − | 0.846373i | \(-0.321218\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.54613e12 | 0.176175 |
(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 | 384.10.d.f.193.17 | yes | 20 | |
4.3 | odd | 2 | inner | 384.10.d.f.193.7 | yes | 20 | |
8.3 | odd | 2 | inner | 384.10.d.f.193.14 | yes | 20 | |
8.5 | even | 2 | inner | 384.10.d.f.193.4 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.d.f.193.4 | ✓ | 20 | 8.5 | even | 2 | inner | |
384.10.d.f.193.7 | yes | 20 | 4.3 | odd | 2 | inner | |
384.10.d.f.193.14 | yes | 20 | 8.3 | odd | 2 | inner | |
384.10.d.f.193.17 | yes | 20 | 1.1 | even | 1 | trivial |