Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,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, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
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: | \(119.955849786\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7628 x^{10} + 22070097 x^{8} - 30593373916 x^{6} + 21405948373596 x^{4} + \cdots + 90\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{57}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.6 | ||
Root | \(-19.8448 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.8.d.e.193.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 27.0000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 467.267i | 1.67175i | 0.548922 | + | 0.835873i | \(0.315038\pi\) | ||||
−0.548922 | + | 0.835873i | \(0.684962\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −31.2683 | −0.0344557 | −0.0172279 | − | 0.999852i | \(-0.505484\pi\) | ||||
−0.0172279 | + | 0.999852i | \(0.505484\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5276.60i | − 1.19531i | −0.801754 | − | 0.597654i | \(-0.796100\pi\) | ||||
0.801754 | − | 0.597654i | \(-0.203900\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 806.828i | − 0.101854i | −0.998702 | − | 0.0509271i | \(-0.983782\pi\) | ||||
0.998702 | − | 0.0509271i | \(-0.0162176\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12616.2 | 0.965183 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.4070 | 0.000908680 0 | 0.000454340 | − | 1.00000i | \(-0.499855\pi\) | ||||
0.000454340 | 1.00000i | \(0.499855\pi\) | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13657.0i | 0.456791i | 0.973568 | + | 0.228395i | \(0.0733479\pi\) | ||||
−0.973568 | + | 0.228395i | \(0.926652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 844.244i | 0.0198930i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 58696.4 | 1.00592 | 0.502961 | − | 0.864309i | \(-0.332244\pi\) | ||||
0.502961 | + | 0.864309i | \(0.332244\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −140214. | −1.79474 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 119183.i | 0.907444i | 0.891143 | + | 0.453722i | \(0.149904\pi\) | ||||
−0.891143 | + | 0.453722i | \(0.850096\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −101880. | −0.614216 | −0.307108 | − | 0.951675i | \(-0.599361\pi\) | ||||
−0.307108 | + | 0.951675i | \(0.599361\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −142468. | −0.690111 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 14610.7i | − 0.0576012i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 259208.i | − 0.841285i | −0.907227 | − | 0.420642i | \(-0.861805\pi\) | ||||
0.907227 | − | 0.420642i | \(-0.138195\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −21784.4 | −0.0588056 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −809267. | −1.83378 | −0.916892 | − | 0.399135i | \(-0.869311\pi\) | ||||
−0.916892 | + | 0.399135i | \(0.869311\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 15343.1i | − 0.0294289i | −0.999892 | − | 0.0147145i | \(-0.995316\pi\) | ||||
0.999892 | − | 0.0147145i | \(-0.00468392\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 340638.i | − 0.557249i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −183648. | −0.258015 | −0.129007 | − | 0.991644i | \(-0.541179\pi\) | ||||
−0.129007 | + | 0.991644i | \(0.541179\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −822565. | −0.998813 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 496.988i | 0 0.000524627i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 907643.i | 0.837431i | 0.908117 | + | 0.418716i | \(0.137520\pi\) | ||||
−0.908117 | + | 0.418716i | \(0.862480\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.46558e6 | 1.99825 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 368739. | 0.263728 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1.43398e6i | − 0.908993i | −0.890748 | − | 0.454497i | \(-0.849819\pi\) | ||||
0.890748 | − | 0.454497i | \(-0.150181\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 884055.i | − 0.498683i | −0.968416 | − | 0.249342i | \(-0.919786\pi\) | ||||
0.968416 | − | 0.249342i | \(-0.0802142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 22794.6 | 0.0114852 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 377004. | 0.170274 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.48901e6i | 1.01103i | 0.862817 | + | 0.505516i | \(0.168698\pi\) | ||||
−0.862817 | + | 0.505516i | \(0.831302\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 1.58480e6i | − 0.580769i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.68753e6 | 1.55432 | 0.777158 | − | 0.629305i | \(-0.216660\pi\) | ||||
0.777158 | + | 0.629305i | \(0.216660\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.46295e6 | 1.04188 | 0.520938 | − | 0.853594i | \(-0.325582\pi\) | ||||
0.520938 | + | 0.853594i | \(0.325582\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.78577e6i | 1.03619i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 164990.i | 0.0411852i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.34533e6 | −0.991580 | −0.495790 | − | 0.868442i | \(-0.665121\pi\) | ||||
−0.495790 | + | 0.868442i | \(0.665121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 8.38216e6i | − 1.60910i | −0.593886 | − | 0.804549i | \(-0.702407\pi\) | ||||
0.593886 | − | 0.804549i | \(-0.297593\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8600.98i | 0.00151908i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.21793e6 | 0.523913 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.29208e7 | 1.94278 | 0.971390 | − | 0.237489i | \(-0.0763245\pi\) | ||||
0.971390 | + | 0.237489i | \(0.0763245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25228.1i | 0.00350946i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.75075e6i | 0.354618i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.38146e6 | −0.763638 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.60705e6 | 0.512533 | 0.256266 | − | 0.966606i | \(-0.417508\pi\) | ||||
0.256266 | + | 0.966606i | \(0.417508\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.84664e6i | 0.398436i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.50932e7i | − 1.45766i | −0.684696 | − | 0.728829i | \(-0.740065\pi\) | ||||
0.684696 | − | 0.728829i | \(-0.259935\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.45820e6 | 0.582346 | 0.291173 | − | 0.956670i | \(-0.405954\pi\) | ||||
0.291173 | + | 0.956670i | \(0.405954\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −394488. | −0.0332561 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.43047e7i | − 1.12885i | −0.825484 | − | 0.564425i | \(-0.809098\pi\) | ||||
0.825484 | − | 0.564425i | \(-0.190902\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.46215e7i | − 1.08143i | −0.841206 | − | 0.540715i | \(-0.818154\pi\) | ||||
0.841206 | − | 0.540715i | \(-0.181846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.99863e6 | −0.485716 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.44884e7 | −0.944596 | −0.472298 | − | 0.881439i | \(-0.656575\pi\) | ||||
−0.472298 | + | 0.881439i | \(0.656575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.74269e7i | 1.68165i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 588177.i | 0.0339514i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −575.555 | −3.13092e−5 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.35532e6 | −0.428760 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.18502e7i | 1.05874i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 2.90121e7i | − 1.32860i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.06200e7 | 0.460055 | 0.230028 | − | 0.973184i | \(-0.426118\pi\) | ||||
0.230028 | + | 0.973184i | \(0.426118\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −414264. | −0.0169908 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 4.85018e7i | − 1.88499i | −0.334227 | − | 0.942493i | \(-0.608475\pi\) | ||||
0.334227 | − | 0.942493i | \(-0.391525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 427031.i | − 0.0157390i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.19722e6 | −0.321728 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.66799e7 | −1.21873 | −0.609363 | − | 0.792892i | \(-0.708575\pi\) | ||||
−0.609363 | + | 0.792892i | \(0.708575\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 5.99325e6i | − 0.189282i | −0.995511 | − | 0.0946412i | \(-0.969830\pi\) | ||||
0.995511 | − | 0.0946412i | \(-0.0301704\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.95850e6i | 0.148965i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.25731e6 | −0.121747 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.56902e7 | −1.51702 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.22093e7i | 0.576665i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 5.10670e7i | − 1.26470i | −0.774682 | − | 0.632351i | \(-0.782090\pi\) | ||||
0.774682 | − | 0.632351i | \(-0.217910\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.49428e7 | −1.53501 | −0.767506 | − | 0.641042i | \(-0.778502\pi\) | ||||
−0.767506 | + | 0.641042i | \(0.778502\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13418.7 | −0.000302893 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.76050e7i | − 1.02681i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 8.27200e7i | − 1.70593i | −0.521967 | − | 0.852966i | \(-0.674802\pi\) | ||||
0.521967 | − | 0.852966i | \(-0.325198\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.45063e7 | 0.483491 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.83534e6 | −0.0346598 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.55553e7i | 0.823915i | 0.911203 | + | 0.411958i | \(0.135155\pi\) | ||||
−0.911203 | + | 0.411958i | \(0.864845\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 6.65707e7i | − 1.15369i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.80939e7 | −1.46365 | −0.731827 | − | 0.681491i | \(-0.761332\pi\) | ||||
−0.731827 | + | 0.681491i | \(0.761332\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.20975e7 | 0.989626 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 9.95594e6i | − 0.152264i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.34223e6i | 0.0343929i | 0.999852 | + | 0.0171965i | \(0.00547407\pi\) | ||||
−0.999852 | + | 0.0171965i | \(0.994526\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.38425e6 | 0.0618389 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.87174e7 | −0.524807 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.96459e7i | 0.777312i | 0.921383 | + | 0.388656i | \(0.127061\pi\) | ||||
−0.921383 | + | 0.388656i | \(0.872939\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 4.32379e7i | − 0.541987i | −0.962581 | − | 0.270994i | \(-0.912648\pi\) | ||||
0.962581 | − | 0.270994i | \(-0.0873522\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.38695e7 | −0.287915 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.21120e8 | 1.40642 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 97126.2i | − 0.00108615i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 615454.i | − 0.00663100i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.53658e8 | 1.59565 | 0.797826 | − | 0.602887i | \(-0.205983\pi\) | ||||
0.797826 | + | 0.602887i | \(0.205983\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.22178e7 | 0.723093 | 0.361546 | − | 0.932354i | \(-0.382249\pi\) | ||||
0.361546 | + | 0.932354i | \(0.382249\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1.01791e7i | − 0.0983080i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.48312e8i | − 1.38212i | −0.722799 | − | 0.691058i | \(-0.757145\pi\) | ||||
0.722799 | − | 0.691058i | \(-0.242855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.21013e8 | 1.08855 | 0.544274 | − | 0.838907i | \(-0.316805\pi\) | ||||
0.544274 | + | 0.838907i | \(0.316805\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.72033e7 | 0.583720 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 3.72664e6i | − 0.0312666i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 3.78144e8i | − 3.06562i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.27897e7 | −0.335307 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.20624e7 | 0.546005 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.37134e8i | − 1.00498i | −0.864584 | − | 0.502489i | \(-0.832418\pi\) | ||||
0.864584 | − | 0.502489i | \(-0.167582\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.26563e8i | − 0.897385i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.16934e6 | 0.0491977 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.18560e6 | 0.0211632 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 9.34996e7i | − 0.601528i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 14851.3i | 0 9.25529e-5i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.14479e8 | 1.29514 | 0.647572 | − | 0.762004i | \(-0.275785\pi\) | ||||
0.647572 | + | 0.762004i | \(0.275785\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.02216e8 | 0.598246 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.91532e8i | 1.65423i | 0.562035 | + | 0.827113i | \(0.310019\pi\) | ||||
−0.562035 | + | 0.827113i | \(0.689981\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.31691e8i | 0.724657i | 0.932050 | + | 0.362329i | \(0.118018\pi\) | ||||
−0.932050 | + | 0.362329i | \(0.881982\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.45474e6 | 0.0237783 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.40022e8 | −0.725189 | −0.362595 | − | 0.931947i | \(-0.618109\pi\) | ||||
−0.362595 | + | 0.931947i | \(0.618109\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 8.58129e7i | − 0.431335i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.17324e8i | 0.572489i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.32407e8 | −1.57499 | −0.787495 | − | 0.616321i | \(-0.788622\pi\) | ||||
−0.787495 | + | 0.616321i | \(0.788622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.15264e8 | 0.530436 | 0.265218 | − | 0.964188i | \(-0.414556\pi\) | ||||
0.265218 | + | 0.964188i | \(0.414556\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.43489e7i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.84358e8i | − 1.66976i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.10188e7 | 0.0465261 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.26318e8 | −0.929014 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.42315e7i | 0.256384i | 0.991749 | + | 0.128192i | \(0.0409173\pi\) | ||||
−0.991749 | + | 0.128192i | \(0.959083\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 3.09718e8i | − 1.20239i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 232226. | 0.000877043 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.87951e8 | −0.690682 | −0.345341 | − | 0.938477i | \(-0.612237\pi\) | ||||
−0.345341 | + | 0.938477i | \(0.612237\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.10501e6i | 0.0289871i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 8.68841e7i | − 0.302481i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.53334e8 | 1.53664 | 0.768322 | − | 0.640064i | \(-0.221092\pi\) | ||||
0.768322 | + | 0.640064i | \(0.221092\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.24112e8 | −1.39997 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3.48861e8i | − 1.12166i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 3.11428e8i | − 0.975495i | −0.872985 | − | 0.487747i | \(-0.837819\pi\) | ||||
0.872985 | − | 0.487747i | \(-0.162181\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.59086e8 | −1.09599 | −0.547994 | − | 0.836483i | \(-0.684608\pi\) | ||||
−0.547994 | + | 0.836483i | \(0.684608\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 681160. | 0.00202619 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.39852e8i | 2.14526i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.12866e8i | 0.601767i | 0.953661 | + | 0.300883i | \(0.0972815\pi\) | ||||
−0.953661 | + | 0.300883i | \(0.902719\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.42702e7 | 0.204739 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.34768e8 | −0.631200 | −0.315600 | − | 0.948892i | \(-0.602206\pi\) | ||||
−0.315600 | + | 0.948892i | \(0.602206\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4.61638e8i | − 1.21073i | −0.795947 | − | 0.605367i | \(-0.793026\pi\) | ||||
0.795947 | − | 0.605367i | \(-0.206974\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.72299e8i | 0.440887i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.53044e7 | 0.0631843 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.10338e8 | −0.999999 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1.24390e8i | − 0.295911i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 2.81937e8i | − 0.654811i | −0.944884 | − | 0.327406i | \(-0.893826\pi\) | ||||
0.944884 | − | 0.327406i | \(-0.106174\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.70051e8 | 1.51961 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.03859e8 | 0.230037 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 4.73579e7i | − 0.102457i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 479753.i | 0.00101399i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.07515e8 | −0.841579 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.13090e8 | 0.833672 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.31592e8i | 0.456813i | 0.973566 | + | 0.228407i | \(0.0733515\pi\) | ||||
−0.973566 | + | 0.228407i | \(0.926648\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1.74371e8i | − 0.336218i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.15818e8 | −1.16089 | −0.580445 | − | 0.814299i | \(-0.697121\pi\) | ||||
−0.580445 | + | 0.814299i | \(0.697121\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.86280e8 | 0.527699 | 0.263849 | − | 0.964564i | \(-0.415008\pi\) | ||||
0.263849 | + | 0.964564i | \(0.415008\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.06512e7i | 0.0192004i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.20478e8i | 0.565055i | 0.959259 | + | 0.282527i | \(0.0911728\pi\) | ||||
−0.959259 | + | 0.282527i | \(0.908827\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.28879e8 | 1.08467 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.86228e8 | −0.651742 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 251384.i | 0 0.000415077i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.13128e8i | 0.182802i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.94780e8 | −0.624364 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.74237e6 | 0.00889008 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 6.95072e8i | − 1.05349i | −0.850022 | − | 0.526746i | \(-0.823412\pi\) | ||||
0.850022 | − | 0.526746i | \(-0.176588\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.88963e8i | 0.280428i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.16303e9 | −1.69019 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.90458e8 | 1.12506 | 0.562528 | − | 0.826778i | \(-0.309829\pi\) | ||||
0.562528 | + | 0.826778i | \(0.309829\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.91187e8i | 0.545363i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.37577e8i | 0.734177i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.14710e7 | 0.0688705 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.40527e8 | 0.970899 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 8.49503e8i | − 1.09147i | −0.837958 | − | 0.545735i | \(-0.816251\pi\) | ||||
0.837958 | − | 0.545735i | \(-0.183749\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 3.96115e8i | − 0.498806i | −0.968400 | − | 0.249403i | \(-0.919766\pi\) | ||||
0.968400 | − | 0.249403i | \(-0.0802345\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.58808e7 | 0.0196019 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.57428e8 | 0.795494 | 0.397747 | − | 0.917495i | \(-0.369792\pi\) | ||||
0.397747 | + | 0.917495i | \(0.369792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.19033e9i | 2.59842i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15540.0i | 0 1.80764e-5i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.97068e8 | −0.681072 | −0.340536 | − | 0.940231i | \(-0.610609\pi\) | ||||
−0.340536 | + | 0.940231i | \(0.610609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.07359e8 | 0.791342 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.25594e8i | 0.247545i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.61812e9i | 1.74175i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.31319e8 | −0.244275 | −0.122138 | − | 0.992513i | \(-0.538975\pi\) | ||||
−0.122138 | + | 0.992513i | \(0.538975\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.89956e8 | 0.611262 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2.83804e7i | − 0.0288543i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.47548e9i | 1.47215i | 0.676897 | + | 0.736077i | \(0.263324\pi\) | ||||
−0.676897 | + | 0.736077i | \(0.736676\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.83326e8 | −0.767067 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.61599e7 | 0.0924270 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 9.58315e8i | − 0.904214i | −0.891964 | − | 0.452107i | \(-0.850673\pi\) | ||||
0.891964 | − | 0.452107i | \(-0.149327\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 2.86739e8i | − 0.265613i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.90346e9 | 1.73121 | 0.865603 | − | 0.500731i | \(-0.166935\pi\) | ||||
0.865603 | + | 0.500731i | \(0.166935\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.70946e7 | −0.0688512 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.11851e7i | 0.00980963i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.68380e9i | 1.45033i | 0.688575 | + | 0.725165i | \(0.258236\pi\) | ||||
−0.688575 | + | 0.725165i | \(0.741764\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.08042e6 | 0.000914061 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.30955e9 | −1.08830 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 2.03043e9i | − 1.65767i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.50529e8i | 0.762428i | 0.924487 | + | 0.381214i | \(0.124494\pi\) | ||||
−0.924487 | + | 0.381214i | \(0.875506\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.15298e7 | −0.00908694 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.52085e8 | −0.427564 | −0.213782 | − | 0.976881i | \(-0.568578\pi\) | ||||
−0.213782 | + | 0.976881i | \(0.568578\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.21992e7i | 0.0625605i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.48325e8i | 0.185750i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.36774e9 | −1.00559 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.84172e8 | −0.349919 | −0.174960 | − | 0.984576i | \(-0.555980\pi\) | ||||
−0.174960 | + | 0.984576i | \(0.555980\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.90357e8i | 0.703631i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.48381e7i | 0.0313200i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.91671e9 | 2.69001 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.61818e8 | −0.109282 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 4.02693e8i | − 0.267439i | −0.991019 | − | 0.133719i | \(-0.957308\pi\) | ||||
0.991019 | − | 0.133719i | \(-0.0426921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.16230e9i | − 0.759159i | −0.925159 | − | 0.379579i | \(-0.876069\pi\) | ||||
0.925159 | − | 0.379579i | \(-0.123931\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.33880e8 | 0.0860049 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.58091e6 | −0.00163084 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.76429e7i | 0.0171825i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.14947e8i | 0.0702907i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.65230e8 | −0.520548 | −0.260274 | − | 0.965535i | \(-0.583813\pi\) | ||||
−0.260274 | + | 0.965535i | \(0.583813\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.88729e9 | −1.11720 | −0.558599 | − | 0.829438i | \(-0.688661\pi\) | ||||
−0.558599 | + | 0.829438i | \(0.688661\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.50363e9i | 0.875850i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.01616e8i | 0.459496i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.78047e9 | 1.00440 | 0.502202 | − | 0.864751i | \(-0.332524\pi\) | ||||
0.502202 | + | 0.864751i | \(0.332524\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.99650e8 | 0.332938 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2.21282e9i | − 1.20930i | −0.796492 | − | 0.604649i | \(-0.793314\pi\) | ||||
0.796492 | − | 0.604649i | \(-0.206686\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.03746e9i | 3.24784i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.37881e9 | −0.730176 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.81035e9 | −0.943844 | −0.471922 | − | 0.881640i | \(-0.656440\pi\) | ||||
−0.471922 | + | 0.881640i | \(0.656440\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.27018e9i | 2.19194i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.75346e9i | 0.886239i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.17883e7 | −0.00586693 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.26015e9 | −1.10772 | −0.553861 | − | 0.832609i | \(-0.686846\pi\) | ||||
−0.553861 | + | 0.832609i | \(0.686846\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 362304.i | 0 0.000174876i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2.29944e8i | − 0.109312i | −0.998505 | − | 0.0546561i | \(-0.982594\pi\) | ||||
0.998505 | − | 0.0546561i | \(-0.0174062\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.87071e9 | 1.34418 | 0.672088 | − | 0.740472i | \(-0.265398\pi\) | ||||
0.672088 | + | 0.740472i | \(0.265398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.28533e9 | −0.592831 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.25672e8i | 0.375145i | 0.982251 | + | 0.187572i | \(0.0600619\pi\) | ||||
−0.982251 | + | 0.187572i | \(0.939938\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 7.78272e7i | − 0.0348359i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.23344e9 | −0.984920 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.09595e7 | −0.0351766 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.91490e9i | − 0.819819i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 6.61671e8i | − 0.279144i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.09397e9 | −1.28630 | −0.643150 | − | 0.765740i | \(-0.722373\pi\) | ||||
−0.643150 | + | 0.765740i | \(0.722373\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.09137e8 | −0.0856884 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.95541e7i | 0.0200108i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.15272e9i | 0.856825i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.88844e9 | 1.13321 | 0.566607 | − | 0.823988i | \(-0.308256\pi\) | ||||
0.566607 | + | 0.823988i | \(0.308256\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.22999e9 | 0.475688 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 3.69018e9i | − 1.40690i | −0.710746 | − | 0.703449i | \(-0.751643\pi\) | ||||
0.710746 | − | 0.703449i | \(-0.248357\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.19379e6i | 0 0.000824577i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.79741e9 | −0.666084 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.46571e8 | −0.0535551 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 1.03673e9i | − 0.373519i | −0.982406 | − | 0.186759i | \(-0.940202\pi\) | ||||
0.982406 | − | 0.186759i | \(-0.0597985\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.37854e9i | 0.845040i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.16186e8 | 0.215886 | 0.107943 | − | 0.994157i | \(-0.465574\pi\) | ||||
0.107943 | + | 0.994157i | \(0.465574\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.05254e9 | 2.43683 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1.67663e9i | − 0.571361i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.70431e9i | − 0.572844i | −0.958103 | − | 0.286422i | \(-0.907534\pi\) | ||||
0.958103 | − | 0.286422i | \(-0.0924660\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.08281e8 | −0.0358986 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.68810e8 | −0.0879094 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.01771e9i | 0.973535i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.69038e8i | 0.308407i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.32403e7 | 0.0198568 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.12737e9 | −0.349249 | −0.174624 | − | 0.984635i | \(-0.555871\pi\) | ||||
−0.174624 | + | 0.984635i | \(0.555871\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.00952e8i | 0.214256i | 0.994245 | + | 0.107128i | \(0.0341654\pi\) | ||||
−0.994245 | + | 0.107128i | \(0.965835\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1.18375e8i | − 0.0357027i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.87529e6 | −0.000558126 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.04465e7 | 0.0118792 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.04537e9i | 0.302998i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.52939e8i | 0.186779i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.68413e9 | 1.88715 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.61044e9 | 0.448781 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.34035e9i | 1.19389i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.93472e9i | 0.796851i | 0.917201 | + | 0.398425i | \(0.130443\pi\) | ||||
−0.917201 | + | 0.398425i | \(0.869557\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.16742e9 | −0.312916 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.83214e9 | 1.80788 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.77357e9i | − 0.985819i | −0.870080 | − | 0.492910i | \(-0.835933\pi\) | ||||
0.870080 | − | 0.492910i | \(-0.164067\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.44476e8i | 0.166228i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.62767e9 | −0.414512 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.35871e8 | 0.0341656 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 3.27023e9i | − 0.811994i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.41429e9i | 0.346774i | 0.984854 | + | 0.173387i | \(0.0554711\pi\) | ||||
−0.984854 | + | 0.173387i | \(0.944529\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.23793e7 | −0.00299746 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.62241e6 | −0.000627090 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.13087e9i | 1.44791i | 0.689845 | + | 0.723957i | \(0.257679\pi\) | ||||
−0.689845 | + | 0.723957i | \(0.742321\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 6.76996e9i | − 1.57913i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.66173e7 | −0.00382841 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.93798e9 | 0.441017 | 0.220509 | − | 0.975385i | \(-0.429228\pi\) | ||||
0.220509 | + | 0.975385i | \(0.429228\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 8.05170e8i | − 0.180993i | −0.995897 | − | 0.0904964i | \(-0.971155\pi\) | ||||
0.995897 | − | 0.0904964i | \(-0.0288453\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 4.14877e9i | − 0.921250i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.23005e9 | −1.80537 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.00273e9 | −0.217305 | −0.108653 | − | 0.994080i | \(-0.534654\pi\) | ||||
−0.108653 | + | 0.994080i | \(0.534654\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1.94988e9i | − 0.417478i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.62096e8i | 0.0554426i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.78927e9 | 1.00099 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.74836e8 | −0.0567582 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.87262e9i | 0.382135i | 0.981577 | + | 0.191067i | \(0.0611949\pi\) | ||||
−0.981577 | + | 0.191067i | \(0.938805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.39137e9i | − 0.280568i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.00442e9 | −0.797965 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.41357e9 | 1.06609 | 0.533043 | − | 0.846088i | \(-0.321048\pi\) | ||||
0.533043 | + | 0.846088i | \(0.321048\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 268938.i | 0 5.23411e-5i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 3.26736e9i | − 0.628474i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.71914e9 | −0.897159 | −0.448579 | − | 0.893743i | \(-0.648070\pi\) | ||||
−0.448579 | + | 0.893743i | \(0.648070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.69993e9 | −0.507331 | −0.253666 | − | 0.967292i | \(-0.581636\pi\) | ||||
−0.253666 | + | 0.967292i | \(0.581636\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.81449e9i | − 0.337011i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.90417e9i | − 0.716778i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.86996e8 | 0.0702337 | 0.0351169 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351169 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.00619e8 | −0.0180518 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.48173e8i | 0.0262799i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 7.20217e9i | − 1.26285i | −0.775437 | − | 0.631425i | \(-0.782470\pi\) | ||||
0.775437 | − | 0.631425i | \(-0.217530\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.02099e10 | −1.76994 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.11331e10 | −1.90817 | −0.954087 | − | 0.299531i | \(-0.903170\pi\) | ||||
−0.954087 | + | 0.299531i | \(0.903170\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 5.50625e9i | − 0.933123i | −0.884489 | − | 0.466561i | \(-0.845493\pi\) | ||||
0.884489 | − | 0.466561i | \(-0.154507\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.15532e9i | 0.193590i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.04011e8 | −0.0669399 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.60219e9 | 0.426343 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.94569e9i | − 0.315236i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 4.77124e6i | 0 0.000764459i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.99750e9 | 0.791863 | 0.395931 | − | 0.918280i | \(-0.370422\pi\) | ||||
0.395931 | + | 0.918280i | \(0.370422\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.70262e9 | −0.580224 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.96236e9i | 0.769096i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.63669e8i | 0.101733i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.41721e9 | −0.518106 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.92704e9 | −1.33877 | −0.669383 | − | 0.742918i | \(-0.733441\pi\) | ||||
−0.669383 | + | 0.742918i | \(0.733441\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.87437e9i | − 0.278046i | −0.990289 | − | 0.139023i | \(-0.955604\pi\) | ||||
0.990289 | − | 0.139023i | \(-0.0443963\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 1.93572e8i | − 0.0284043i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.12131e9 | −0.888545 | −0.444273 | − | 0.895892i | \(-0.646538\pi\) | ||||
−0.444273 | + | 0.895892i | \(0.646538\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.56653e9 | −1.08653 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 8.60112e7i | − 0.0122186i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 3.55775e9i | − 0.500010i | −0.968245 | − | 0.250005i | \(-0.919568\pi\) | ||||
0.968245 | − | 0.250005i | \(-0.0804323\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.26633e10 | 3.15122 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.52449e9 | −0.347292 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.14258e9i | 0.291634i | 0.989312 | + | 0.145817i | \(0.0465811\pi\) | ||||
−0.989312 | + | 0.145817i | \(0.953419\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.02631e9i | 0.138221i | 0.997609 | + | 0.0691105i | \(0.0220161\pi\) | ||||
−0.997609 | + | 0.0691105i | \(0.977984\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −400984. | −5.34355e−5 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.99537e8 | 0.0263117 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.99560e9i | 0.912818i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 5.79094e9i | − 0.747752i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.66480e9 | −0.596080 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.26856e9 | −0.539794 | −0.269897 | − | 0.962889i | \(-0.586990\pi\) | ||||
−0.269897 | + | 0.962889i | \(0.586990\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 2.75983e9i | − 0.345397i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 5.61660e9i | − 0.695686i | −0.937553 | − | 0.347843i | \(-0.886914\pi\) | ||||
0.937553 | − | 0.347843i | \(-0.113086\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.44055e8 | −0.0176597 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.87135e9 | 0.955068 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.51352e9i | 0.662150i | 0.943604 | + | 0.331075i | \(0.107411\pi\) | ||||
−0.943604 | + | 0.331075i | \(0.892589\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.71393e10i | − 2.03740i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.55566e9 | 0.418381 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.32311e8 | 0.0852959 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1.03033e10i | − 1.18796i | −0.804480 | − | 0.593980i | \(-0.797556\pi\) | ||||
0.804480 | − | 0.593980i | \(-0.202444\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.20278e8i | − 0.0137284i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.80045e9 | 0.316432 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.48962e7 | −0.00166632 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.78060e9i | 0.418688i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.05192e10i | − 1.15337i | −0.816966 | − | 0.576686i | \(-0.804345\pi\) | ||||
0.816966 | − | 0.576686i | \(-0.195655\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.54000e9 | 0.384291 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.31695e9 | −0.249031 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.71938e8i | 0.0502246i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 7.67229e9i | − 0.808468i | −0.914656 | − | 0.404234i | \(-0.867538\pi\) | ||||
0.914656 | − | 0.404234i | \(-0.132462\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.16774e9 | 0.330527 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.97996e9 | −0.617853 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.98930e9i | − 0.203530i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.97500e9i | 0.909321i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.54882e10 | 1.55400 | 0.776999 | − | 0.629502i | \(-0.216741\pi\) | ||||
0.776999 | + | 0.629502i | \(0.216741\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.01937e8 | −0.0200652 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 3.11212e9i | − 0.306247i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1.67110e10i | − 1.62862i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.36057e9 | −0.131326 | −0.0656631 | − | 0.997842i | \(-0.520916\pi\) | ||||
−0.0656631 | + | 0.997842i | \(0.520916\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 282420.i | 0 2.67415e-5i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.50290e8i | 0.0891235i | 0.999007 | + | 0.0445617i | \(0.0141891\pi\) | ||||
−0.999007 | + | 0.0445617i | \(0.985811\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.03777e10 | −0.964037 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.31335e10 | 1.20850 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.61058e10i | 1.46800i | 0.679150 | + | 0.733999i | \(0.262349\pi\) | ||||
−0.679150 | + | 0.733999i | \(0.737651\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 2.97508e8i | − 0.0268618i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.62026e10 | −1.44918 | −0.724592 | − | 0.689178i | \(-0.757972\pi\) | ||||
−0.724592 | + | 0.689178i | \(0.757972\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.38619e10 | 2.11426 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.11060e9i | 0.536366i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.47284e8i | 0.0388953i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.60043e10 | 1.37879 | 0.689393 | − | 0.724388i | \(-0.257878\pi\) | ||||
0.689393 | + | 0.724388i | \(0.257878\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.73425e9 | 0.148023 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 3.03457e10i | − 2.56615i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.44950e10i | 1.21446i | 0.794527 | + | 0.607229i | \(0.207719\pi\) | ||||
−0.794527 | + | 0.607229i | \(0.792281\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.36237e9 | −0.694198 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.48731e8 | 0.0286843 | 0.0143421 | − | 0.999897i | \(-0.495435\pi\) | ||||
0.0143421 | + | 0.999897i | \(0.495435\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.57189e8i | 0.0372615i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 6.27011e6i | 0 0.000506361i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.15697e9 | −0.0925848 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.31946e9 | −0.342521 | −0.171260 | − | 0.985226i | \(-0.554784\pi\) | ||||
−0.171260 | + | 0.985226i | \(0.554784\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.07467e9i | 0.398765i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.47386e10i | − 1.14770i | −0.818961 | − | 0.573849i | \(-0.805449\pi\) | ||||
0.818961 | − | 0.573849i | \(-0.194551\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.42849e10 | 1.10236 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.18835e8 | 0.0167357 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.10521e10i | − 0.837655i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 2.47342e10i | − 1.85789i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.34587e9 | −0.174638 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.86523e10 | 2.85189 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.74976e9i | 0.639859i | 0.947441 | + | 0.319930i | \(0.103659\pi\) | ||||
−0.947441 | + | 0.319930i | \(0.896341\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1.22400e10i | − 0.887182i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.53028e8 | 0.0325467 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.13280e8 | −0.0507930 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.14510e10i | 0.808275i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.95855e9i | − 0.137035i | −0.997650 | − | 0.0685173i | \(-0.978173\pi\) | ||||
0.997650 | − | 0.0685173i | \(-0.0218268\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.38041e6 | −0.000234453 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.41925e9 | −0.647593 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.82726e10i | − 1.24536i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 8.57594e8i | − 0.0579423i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.40856e9 | −0.563202 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.64242e10 | −1.09060 | −0.545299 | − | 0.838242i | \(-0.683584\pi\) | ||||
−0.545299 | + | 0.838242i | \(0.683584\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.27404e10i | 1.49701i | 0.663127 | + | 0.748507i | \(0.269229\pi\) | ||||
−0.663127 | + | 0.748507i | \(0.730771\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.69531e9i | 0.632768i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.12865e10 | −1.37738 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.09541e8 | 0.0134428 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 1.83913e7i | − 0.00116982i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 2.18898e9i | − 0.138052i | −0.997615 | − | 0.0690258i | \(-0.978011\pi\) | ||||
0.997615 | − | 0.0690258i | \(-0.0219891\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.09467e10 | 1.30983 | 0.654916 | − | 0.755702i | \(-0.272704\pi\) | ||||
0.654916 | + | 0.755702i | \(0.272704\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.99760e10 | 1.23857 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.60221e10i | 0.985033i | 0.870303 | + | 0.492517i | \(0.163923\pi\) | ||||
−0.870303 | + | 0.492517i | \(0.836077\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.26352e9i | 0.503761i | 0.967758 | + | 0.251880i | \(0.0810490\pi\) | ||||
−0.967758 | + | 0.251880i | \(0.918951\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.74739e9 | 0.347430 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.51409e7 | −0.000907601 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 4.11634e10i | − 2.44686i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2.00529e9i | − 0.118206i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.38387e9 | 0.548549 | 0.274274 | − | 0.961651i | \(-0.411562\pi\) | ||||
0.274274 | + | 0.961651i | \(0.411562\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.04538e9 | 0.176545 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.33874e9i | 0.364424i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.90162e10i | 1.65440i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.61257e8 | 0.0147732 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.24642e10 | −0.699017 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.52146e10i | − 0.846267i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.49929e10i | 1.93045i | 0.261424 | + | 0.965224i | \(0.415808\pi\) | ||||
−0.261424 | + | 0.965224i | \(0.584192\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.65209e9 | 0.254546 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.73150e10 | −1.48241 | −0.741205 | − | 0.671279i | \(-0.765745\pi\) | ||||
−0.741205 | + | 0.671279i | \(0.765745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.65662e10i | 1.96836i | 0.177181 | + | 0.984178i | \(0.443302\pi\) | ||||
−0.177181 | + | 0.984178i | \(0.556698\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 6.83219e8i | − 0.0364795i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.34559e10 | −0.712646 | −0.356323 | − | 0.934363i | \(-0.615970\pi\) | ||||
−0.356323 | + | 0.934363i | \(0.615970\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.09445e9 | −0.0574962 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.10791e10i | 0.577350i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.29286e10i | 1.18524i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00820e9 | 0.102978 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.35854e9 | −0.170844 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.07158e8i | 0.0457778i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.73698e10i | − 1.87078i | −0.353624 | − | 0.935388i | \(-0.615051\pi\) | ||||
0.353624 | − | 0.935388i | \(-0.384949\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.61231e9 | −0.378055 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.50627e10 | −1.72754 | −0.863772 | − | 0.503883i | \(-0.831904\pi\) | ||||
−0.863772 | + | 0.503883i | \(0.831904\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.59555e10i | 0.779918i | 0.920832 | + | 0.389959i | \(0.127511\pi\) | ||||
−0.920832 | + | 0.389959i | \(0.872489\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 1.80914e10i | − 0.877345i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.32602e10 | 0.637993 | 0.318996 | − | 0.947756i | \(-0.396654\pi\) | ||||
0.318996 | + | 0.947756i | \(0.396654\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.32068e8 | −0.0158515 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 2.80420e9i | − 0.132812i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 2.50808e9i | − 0.117859i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.78706e10 | −1.29947 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.27866e9 | −0.0591538 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.21423e10i | − 0.557366i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.67069e7i | 0 0.000760957i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.29533e7 | 0.000585429 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.02036e10 | 0.906065 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 4.01584e10i | − 1.78711i | −0.448953 | − | 0.893555i | \(-0.648203\pi\) | ||||
0.448953 | − | 0.893555i | \(-0.351797\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.10029e10i | 0.485886i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.17715e8 | −0.0402155 | −0.0201078 | − | 0.999798i | \(-0.506401\pi\) | ||||
−0.0201078 | + | 0.999798i | \(0.506401\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.42293e10 | −1.92337 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1.11534e10i | − 0.481321i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.51657e9i | 0.0649485i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.08713e10 | −0.462039 | −0.231019 | − | 0.972949i | \(-0.574206\pi\) | ||||
−0.231019 | + | 0.972949i | \(0.574206\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.25297e9 | 0.263741 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.78203e9i | − 0.158314i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.63446e10i | 1.50988i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.70803e9 | −0.194115 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.19109e9 | 0.212424 | 0.106212 | − | 0.994344i | \(-0.466128\pi\) | ||||
0.106212 | + | 0.994344i | \(0.466128\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.12338e10i | − 0.456248i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.66271e10i | 0.670240i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.53839e7 | 0.00181577 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.42896e10 | −0.567453 | −0.283727 | − | 0.958905i | \(-0.591571\pi\) | ||||
−0.283727 | + | 0.958905i | \(0.591571\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 7.72957e9i | − 0.304667i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.37976e10i | 1.71351i | 0.515722 | + | 0.856756i | \(0.327524\pi\) | ||||
−0.515722 | + | 0.856756i | \(0.672476\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.75011e10 | −1.84464 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.87582e8 | 0.0110854 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.19780e10i | − 0.458309i | −0.973390 | − | 0.229154i | \(-0.926404\pi\) | ||||
0.973390 | − | 0.229154i | \(-0.0735961\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 2.79400e9i | − 0.106120i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.65290e9 | 0.326234 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.67815e10 | −0.628068 | −0.314034 | − | 0.949412i | \(-0.601681\pi\) | ||||
−0.314034 | + | 0.949412i | \(0.601681\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.17994e10i | 2.66753i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.69797e10i | − 0.626237i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.14692e9 | 0.0419920 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.71332e10 | −0.622739 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.04281e10i | 0.376283i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.37450e10i | 1.20883i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.39750e9 | −0.263083 | −0.131541 | − | 0.991311i | \(-0.541993\pi\) | ||||
−0.131541 | + | 0.991311i | \(0.541993\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.78736e6 | 0.000239645 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.13191e10i | 1.09785i | 0.835872 | + | 0.548924i | \(0.184962\pi\) | ||||
−0.835872 | + | 0.548924i | \(0.815038\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.87399e8i | 0.00652186i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.05447e9 | 0.105541 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.00101e10 | 0.343405 | 0.171703 | − | 0.985149i | \(-0.445073\pi\) | ||||
0.171703 | + | 0.985149i | \(0.445073\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 6.81778e10i | − 2.32222i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.06591e10i | 0.360477i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.04299e10 | −1.35758 | −0.678789 | − | 0.734333i | \(-0.737495\pi\) | ||||
−0.678789 | + | 0.734333i | \(0.737495\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.93014e10 | 2.31055 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.55044e8i | − 0.00513269i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 9.00586e8i | − 0.0296032i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.02049e10 | 1.96505 | 0.982526 | − | 0.186125i | \(-0.0595930\pi\) | ||||
0.982526 | + | 0.186125i | \(0.0595930\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.87669e10 | −0.608234 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.65456e10i | 1.81978i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.18147e10i | 1.33628i | 0.744037 | + | 0.668138i | \(0.232909\pi\) | ||||
−0.744037 | + | 0.668138i | \(0.767091\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.10200e9 | 0.161905 |
(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 | 384.8.d.e.193.6 | yes | 12 | |
4.3 | odd | 2 | inner | 384.8.d.e.193.12 | yes | 12 | |
8.3 | odd | 2 | inner | 384.8.d.e.193.1 | ✓ | 12 | |
8.5 | even | 2 | inner | 384.8.d.e.193.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.d.e.193.1 | ✓ | 12 | 8.3 | odd | 2 | inner | |
384.8.d.e.193.6 | yes | 12 | 1.1 | even | 1 | trivial | |
384.8.d.e.193.7 | yes | 12 | 8.5 | even | 2 | inner | |
384.8.d.e.193.12 | yes | 12 | 4.3 | odd | 2 | inner |