Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,8,Mod(129,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.129");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.9705665239\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.129 |
Dual form | 256.8.b.c.129.2 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 84.0000i | − 1.79620i | −0.439790 | − | 0.898100i | \(-0.644947\pi\) | ||||
0.439790 | − | 0.898100i | \(-0.355053\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 82.0000i | − 0.293372i | −0.989183 | − | 0.146686i | \(-0.953139\pi\) | ||||
0.989183 | − | 0.146686i | \(-0.0468607\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −456.000 | −0.502483 | −0.251242 | − | 0.967924i | \(-0.580839\pi\) | ||||
−0.251242 | + | 0.967924i | \(0.580839\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4869.00 | −2.22634 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2524.00i | 0.571762i | 0.958265 | + | 0.285881i | \(0.0922861\pi\) | ||||
−0.958265 | + | 0.285881i | \(0.907714\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10778.0i | 1.36062i | 0.732925 | + | 0.680309i | \(0.238155\pi\) | ||||
−0.732925 | + | 0.680309i | \(0.761845\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6888.00 | −0.526955 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11150.0 | −0.550432 | −0.275216 | − | 0.961382i | \(-0.588749\pi\) | ||||
−0.275216 | + | 0.961382i | \(0.588749\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4124.00i | 0.137937i | 0.997619 | + | 0.0689685i | \(0.0219708\pi\) | ||||
−0.997619 | + | 0.0689685i | \(0.978029\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 38304.0i | 0.902561i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 81704.0 | 1.40022 | 0.700109 | − | 0.714036i | \(-0.253135\pi\) | ||||
0.700109 | + | 0.714036i | \(0.253135\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 71401.0 | 0.913933 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 225288.i | 2.20275i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 99798.0i | − 0.759852i | −0.925017 | − | 0.379926i | \(-0.875949\pi\) | ||||
0.925017 | − | 0.379926i | \(-0.124051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 40480.0 | 0.244048 | 0.122024 | − | 0.992527i | \(-0.461062\pi\) | ||||
0.122024 | + | 0.992527i | \(0.461062\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 212016. | 1.02700 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 37392.0i | 0.147415i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 419442.i | − 1.36134i | −0.732591 | − | 0.680669i | \(-0.761689\pi\) | ||||
0.732591 | − | 0.680669i | \(-0.238311\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 905352. | 2.44394 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −141402. | −0.320414 | −0.160207 | − | 0.987083i | \(-0.551216\pi\) | ||||
−0.160207 | + | 0.987083i | \(0.551216\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 690428.i | 1.32428i | 0.749382 | + | 0.662138i | \(0.230351\pi\) | ||||
−0.749382 | + | 0.662138i | \(0.769649\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 399258.i | 0.653145i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 682032. | 0.958213 | 0.479107 | − | 0.877757i | \(-0.340961\pi\) | ||||
0.479107 | + | 0.877757i | \(0.340961\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −615607. | −0.747510 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 936600.i | 0.988686i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.81312e6i | 1.67286i | 0.548071 | + | 0.836432i | \(0.315362\pi\) | ||||
−0.548071 | + | 0.836432i | \(0.684638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 206968. | 0.167739 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 346416. | 0.247763 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 966028.i | 0.612361i | 0.951973 | + | 0.306181i | \(0.0990511\pi\) | ||||
−0.951973 | + | 0.306181i | \(0.900949\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.88767e6i | − 1.06481i | −0.846490 | − | 0.532404i | \(-0.821289\pi\) | ||||
0.846490 | − | 0.532404i | \(-0.178711\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.22026e6 | 1.11870 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 883796. | 0.399168 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.96587e6i | 1.20473i | 0.798220 | + | 0.602365i | \(0.205775\pi\) | ||||
−0.798220 | + | 0.602365i | \(0.794225\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 6.86314e6i | − 2.51507i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.54823e6 | −0.844957 | −0.422479 | − | 0.906373i | \(-0.638840\pi\) | ||||
−0.422479 | + | 0.906373i | \(0.638840\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.68033e6 | 0.505549 | 0.252775 | − | 0.967525i | \(-0.418657\pi\) | ||||
0.252775 | + | 0.967525i | \(0.418657\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 5.99768e6i | − 1.64161i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.15094e6i | − 0.287301i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.03806e6 | −0.921464 | −0.460732 | − | 0.887539i | \(-0.652413\pi\) | ||||
−0.460732 | + | 0.887539i | \(0.652413\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.27569e6 | 1.73024 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 5.38576e6i | − 1.03389i | −0.856019 | − | 0.516945i | \(-0.827069\pi\) | ||||
0.856019 | − | 0.516945i | \(-0.172931\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 914300.i | 0.161481i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.38303e6 | −1.36485 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.47305e6 | 0.973293 | 0.486647 | − | 0.873599i | \(-0.338220\pi\) | ||||
0.486647 | + | 0.873599i | \(0.338220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 4.91477e6i | − 0.683688i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 3.40032e6i | − 0.438359i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 338168. | 0.0404669 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.06576e6 | −0.674814 | −0.337407 | − | 0.941359i | \(-0.609550\pi\) | ||||
−0.337407 | + | 0.941359i | \(0.609550\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 1.22894e7i | − 1.27293i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.70069e6i | 0.936866i | 0.883499 | + | 0.468433i | \(0.155181\pi\) | ||||
−0.883499 | + | 0.468433i | \(0.844819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.10159e6 | 0.369847 | 0.184924 | − | 0.982753i | \(-0.440796\pi\) | ||||
0.184924 | + | 0.982753i | \(0.440796\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.14093e6 | 0.264786 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 72900.0i | − 0.00575287i | −0.999996 | − | 0.00287643i | \(-0.999084\pi\) | ||||
0.999996 | − | 0.00287643i | \(-0.000915598\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 9.55841e6i | − 0.706957i | −0.935443 | − | 0.353478i | \(-0.884999\pi\) | ||||
0.935443 | − | 0.353478i | \(-0.115001\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.52331e7 | −2.44524 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.33890e6 | 0.608865 | 0.304433 | − | 0.952534i | \(-0.401533\pi\) | ||||
0.304433 | + | 0.952534i | \(0.401533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 6.69973e6i | − 0.410785i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 5.24781e7i | − 3.02920i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.08440e6 | 0.276583 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.31166e7 | 0.673089 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.18778e7i | 0.575529i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.22611e7i | − 0.561495i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.59794e7 | 1.55862 | 0.779311 | − | 0.626637i | \(-0.215569\pi\) | ||||
0.779311 | + | 0.626637i | \(0.215569\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.79960e7 | 2.37867 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 676052.i | − 0.0262743i | −0.999914 | − | 0.0131371i | \(-0.995818\pi\) | ||||
0.999914 | − | 0.0131371i | \(-0.00418180\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.88054e6i | − 0.0693111i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.84736e7 | 0.646225 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.95841e7 | 0.982962 | 0.491481 | − | 0.870888i | \(-0.336456\pi\) | ||||
0.491481 | + | 0.870888i | \(0.336456\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.19084e7i | 1.00775i | 0.863776 | + | 0.503876i | \(0.168093\pi\) | ||||
−0.863776 | + | 0.503876i | \(0.831907\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 5.72907e7i | − 1.72114i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.72037e7 | −0.777949 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.18344e6 | −0.222919 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.17110e7i | 1.34268i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1.16603e7i | − 0.288773i | −0.989521 | − | 0.144386i | \(-0.953879\pi\) | ||||
0.989521 | − | 0.144386i | \(-0.0461208\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.76295e7 | −0.416698 | −0.208349 | − | 0.978055i | \(-0.566809\pi\) | ||||
−0.208349 | + | 0.978055i | \(0.566809\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.42894e7 | 1.22545 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 3.31936e6i | − 0.0715968i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 6.34658e6i | − 0.130885i | −0.997856 | − | 0.0654427i | \(-0.979154\pi\) | ||||
0.997856 | − | 0.0654427i | \(-0.0208460\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.52302e8 | 3.00480 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.72570e7 | −0.703587 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.04234e7i | 1.45454i | 0.686351 | + | 0.727271i | \(0.259211\pi\) | ||||
−0.686351 | + | 0.727271i | \(0.740789\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 1.73853e7i | − 0.301293i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.14767e8 | 1.90682 | 0.953411 | − | 0.301673i | \(-0.0975451\pi\) | ||||
0.953411 | + | 0.301673i | \(0.0975451\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.34168e7 | −0.851283 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.00798e7i | − 0.307095i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.33755e7i | 0.930594i | 0.885155 | + | 0.465297i | \(0.154053\pi\) | ||||
−0.885155 | + | 0.465297i | \(0.845947\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.25589e7 | −0.459236 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.11464e7 | 1.09992 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1.13228e7i | − 0.147559i | −0.997275 | − | 0.0737796i | \(-0.976494\pi\) | ||||
0.997275 | − | 0.0737796i | \(-0.0235061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 5.22650e6i | − 0.0655143i | −0.999463 | − | 0.0327571i | \(-0.989571\pi\) | ||||
0.999463 | − | 0.0327571i | \(-0.0104288\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.58564e8 | −1.91261 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.43942e7 | −0.399379 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.81426e7i | − 0.314716i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.02731e8i | − 1.10684i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.50301e7 | 0.882990 | 0.441495 | − | 0.897264i | \(-0.354448\pi\) | ||||
0.441495 | + | 0.897264i | \(0.354448\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.15092e8 | 1.15237 | 0.576186 | − | 0.817319i | \(-0.304540\pi\) | ||||
0.576186 | + | 0.817319i | \(0.304540\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 7.42389e7i | − 0.716985i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.38522e8i | − 1.29088i | −0.763810 | − | 0.645441i | \(-0.776674\pi\) | ||||
0.763810 | − | 0.645441i | \(-0.223326\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.19614e7 | −0.197548 | −0.0987742 | − | 0.995110i | \(-0.531492\pi\) | ||||
−0.0987742 | + | 0.995110i | \(0.531492\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.49133e8 | 2.16394 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.55079e7i | 0.381813i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.15950e7i | 0.0940007i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.97817e8 | −3.11736 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.04090e7 | −0.0788671 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 6.10208e7i | − 0.447187i | −0.974682 | − | 0.223594i | \(-0.928221\pi\) | ||||
0.974682 | − | 0.223594i | \(-0.0717789\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.14051e8i | 1.51771i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.66151e7 | 0.388506 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.84589e7 | −0.122630 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1.41147e8i | − 0.908068i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.20175e8i | − 0.748928i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.22448e7 | 0.255098 | 0.127549 | − | 0.991832i | \(-0.459289\pi\) | ||||
0.127549 | + | 0.991832i | \(0.459289\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.47651e8 | −2.03472 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2.39102e8i | − 1.35673i | −0.734726 | − | 0.678364i | \(-0.762689\pi\) | ||||
0.734726 | − | 0.678364i | \(-0.237311\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 4.67889e7i | − 0.257465i | −0.991679 | − | 0.128733i | \(-0.958909\pi\) | ||||
0.991679 | − | 0.128733i | \(-0.0410909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.66793e7 | −0.516050 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.45225e8 | −1.78795 | −0.893977 | − | 0.448113i | \(-0.852096\pi\) | ||||
−0.893977 | + | 0.448113i | \(0.852096\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 5.59266e7i | − 0.281113i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.39197e8i | 1.65513i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.34413e8 | −1.11068 | −0.555340 | − | 0.831624i | \(-0.687412\pi\) | ||||
−0.555340 | + | 0.831624i | \(0.687412\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.09557e8 | −0.504175 | −0.252087 | − | 0.967705i | \(-0.581117\pi\) | ||||
−0.252087 | + | 0.967705i | \(0.581117\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 2.02453e8i | − 0.905112i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.04798e7i | 0.219299i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.44485e7 | −0.187680 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.52404e8 | −1.85707 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.94031e8i | 1.57280i | 0.617720 | + | 0.786398i | \(0.288057\pi\) | ||||
−0.617720 | + | 0.786398i | \(0.711943\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.06221e8i | 0.800591i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.68012e7 | 0.290053 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.19064e8 | 1.17250 | 0.586248 | − | 0.810131i | \(-0.300604\pi\) | ||||
0.586248 | + | 0.810131i | \(0.300604\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.91266e8i | 0.684050i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.85916e8i | 1.69169i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.19359e8 | 0.743549 | 0.371774 | − | 0.928323i | \(-0.378750\pi\) | ||||
0.371774 | + | 0.928323i | \(0.378750\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.48676e8 | 0.490772 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 5.43736e8i | − 1.74823i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.48033e8i | 0.463687i | 0.972753 | + | 0.231844i | \(0.0744757\pi\) | ||||
−0.972753 | + | 0.231844i | \(0.925524\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.69934e8 | 1.12910 | 0.564549 | − | 0.825399i | \(-0.309050\pi\) | ||||
0.564549 | + | 0.825399i | \(0.309050\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.12841e8 | −1.22804 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.80216e8i | 0.522552i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3.95860e8i | − 1.11908i | −0.828803 | − | 0.559541i | \(-0.810977\pi\) | ||||
0.828803 | − | 0.559541i | \(-0.189023\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.97097e8 | −0.543332 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.97760e8 | 1.60714 | 0.803572 | − | 0.595208i | \(-0.202930\pi\) | ||||
0.803572 | + | 0.595208i | \(0.202930\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 8.05797e7i | − 0.211336i | −0.994401 | − | 0.105668i | \(-0.966302\pi\) | ||||
0.994401 | − | 0.105668i | \(-0.0336981\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 2.84061e7i | − 0.0726867i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.44793e7 | 0.161003 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.86016e8 | −0.697025 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.09524e8i | 1.21210i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.54530e8i | 1.75243i | 0.481924 | + | 0.876213i | \(0.339938\pi\) | ||||
−0.481924 | + | 0.876213i | \(0.660062\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.92143e7 | 0.179650 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.68627e8 | −1.25945 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.80606e8i | 1.90516i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3.14835e8i | − 0.665427i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.14858e8 | 1.68280 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.54789e8 | −0.312385 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.20472e8i | 1.61838i | 0.587549 | + | 0.809188i | \(0.300093\pi\) | ||||
−0.587549 | + | 0.809188i | \(0.699907\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 3.44534e8i | − 0.664320i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.53503e8 | 1.23193 | 0.615965 | − | 0.787773i | \(-0.288766\pi\) | ||||
0.615965 | + | 0.787773i | \(0.288766\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.63587e8 | −1.22319 | −0.611594 | − | 0.791172i | \(-0.709471\pi\) | ||||
−0.611594 | + | 0.791172i | \(0.709471\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1.82062e8i | − 0.328195i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.54718e8i | 0.625426i | 0.949848 | + | 0.312713i | \(0.101238\pi\) | ||||
−0.949848 | + | 0.312713i | \(0.898762\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.51890e8 | 0.434454 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.12360e6 | −0.0103333 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 4.59826e7i | − 0.0759250i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.69560e8i | 1.24351i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.02906e8 | −1.26984 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.11007e8 | −0.481486 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.05543e8i | 0.463100i | 0.972823 | + | 0.231550i | \(0.0743797\pi\) | ||||
−0.972823 | + | 0.231550i | \(0.925620\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.04226e9i | 3.03080i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.43201e8 | 0.353434 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.54965e7 | 0.0505220 | 0.0252610 | − | 0.999681i | \(-0.491958\pi\) | ||||
0.0252610 | + | 0.999681i | \(0.491958\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 7.84467e8i | − 1.09364i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.02172e8i | 0.139537i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.56252e8 | 0.878095 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.62777e8 | −0.737853 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.90594e8i | 0.244882i | 0.992476 | + | 0.122441i | \(0.0390723\pi\) | ||||
−0.992476 | + | 0.122441i | \(0.960928\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 8.60864e8i | − 1.08404i | −0.840366 | − | 0.542020i | \(-0.817660\pi\) | ||||
0.840366 | − | 0.542020i | \(-0.182340\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.42815e9 | −2.99710 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.04544e9 | −1.26500 | −0.632498 | − | 0.774562i | \(-0.717970\pi\) | ||||
−0.632498 | + | 0.774562i | \(0.717970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.08955e8i | 0.247887i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 4.27090e8i | − 0.496798i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.63303e8 | 0.870696 | 0.435348 | − | 0.900262i | \(-0.356625\pi\) | ||||
0.435348 | + | 0.900262i | \(0.356625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.76864e8 | 0.980973 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.10179e9i | − 1.20900i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.37787e8i | − 0.148314i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.38692e9 | 1.46460 | 0.732302 | − | 0.680980i | \(-0.238446\pi\) | ||||
0.732302 | + | 0.680980i | \(0.238446\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.88486e8 | 0.713351 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 8.26782e8i | − 0.840586i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.77105e8i | 0.476029i | 0.971262 | + | 0.238015i | \(0.0764966\pi\) | ||||
−0.971262 | + | 0.238015i | \(0.923503\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.02994e9 | −1.00856 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.07562e9 | 1.03387 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.92468e8i | 0.370311i | 0.982709 | + | 0.185156i | \(0.0592789\pi\) | ||||
−0.982709 | + | 0.185156i | \(0.940721\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 3.02227e9i | − 2.79960i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.10409e9 | −1.91368 | −0.956839 | − | 0.290617i | \(-0.906139\pi\) | ||||
−0.956839 | + | 0.290617i | \(0.906139\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.43774e7 | −0.0842860 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3.36169e9i | − 2.94829i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 1.26019e9i | − 1.08546i | −0.839907 | − | 0.542730i | \(-0.817391\pi\) | ||||
0.839907 | − | 0.542730i | \(-0.182609\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.11000e8 | −0.770725 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.67884e7 | −0.0471939 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.31121e8i | 0.270332i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.81298e8i | 0.787107i | 0.919302 | + | 0.393554i | \(0.128754\pi\) | ||||
−0.919302 | + | 0.393554i | \(0.871246\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.57966e8 | −0.124497 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.09981e8 | 0.704737 | 0.352369 | − | 0.935861i | \(-0.385376\pi\) | ||||
0.352369 | + | 0.935861i | \(0.385376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.36293e8i | 0.332056i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 6.78606e8i | − 0.507604i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.05867e9 | 0.778361 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.55609e7 | 0.0257004 | 0.0128502 | − | 0.999917i | \(-0.495910\pi\) | ||||
0.0128502 | + | 0.999917i | \(0.495910\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 2.48507e9i | − 1.76560i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.40509e8i | − 0.307701i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.41633e8 | −0.303314 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.68031e9 | 1.81013 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.65360e9i | 1.76233i | 0.472813 | + | 0.881163i | \(0.343239\pi\) | ||||
−0.472813 | + | 0.881163i | \(0.656761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.12113e9i | − 0.732264i | −0.930563 | − | 0.366132i | \(-0.880682\pi\) | ||||
0.930563 | − | 0.366132i | \(-0.119318\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.32081e9 | −2.13331 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.96121e8 | −0.503058 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.60778e8i | 0.535049i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.28511e9i | 1.39735i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.06344e9 | 0.639799 | 0.319900 | − | 0.947451i | \(-0.396351\pi\) | ||||
0.319900 | + | 0.947451i | \(0.396351\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.05962e8 | −0.417901 | −0.208951 | − | 0.977926i | \(-0.567005\pi\) | ||||
−0.208951 | + | 0.977926i | \(0.567005\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.87409e8i | 0.400408i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.36947e8i | 0.193142i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.48506e9 | 0.837760 | 0.418880 | − | 0.908042i | \(-0.362423\pi\) | ||||
0.418880 | + | 0.908042i | \(0.362423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.99739e9 | 1.66421 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.22153e8i | 0.394654i | 0.980338 | + | 0.197327i | \(0.0632260\pi\) | ||||
−0.980338 | + | 0.197327i | \(0.936774\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 5.30790e8i | − 0.285537i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.79462e8 | −0.518694 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.22968e9 | −0.641109 | −0.320554 | − | 0.947230i | \(-0.603869\pi\) | ||||
−0.320554 | + | 0.947230i | \(0.603869\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 3.56899e8i | − 0.183201i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.48088e9i | 0.748473i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.03011e8 | −0.200575 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.85551e7 | 0.0434017 | 0.0217009 | − | 0.999765i | \(-0.493092\pi\) | ||||
0.0217009 | + | 0.999765i | \(0.493092\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2.51196e9i | − 1.21246i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2.10937e8i | − 0.100277i | −0.998742 | − | 0.0501384i | \(-0.984034\pi\) | ||||
0.998742 | − | 0.0501384i | \(-0.0159662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.29775e9 | 1.54413 | 0.772066 | − | 0.635543i | \(-0.219224\pi\) | ||||
0.772066 | + | 0.635543i | \(0.219224\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.78826e8 | −0.128602 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.82873e7i | 0.0401134i | 0.999799 | + | 0.0200567i | \(0.00638467\pi\) | ||||
−0.999799 | + | 0.0200567i | \(0.993615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1.35244e9i | − 0.605357i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.33113e8 | −0.235096 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.74264e9 | −0.757171 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.94458e8i | 0.126065i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 8.82807e9i | − 3.72436i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.51507e9 | 1.87711 | 0.938557 | − | 0.345125i | \(-0.112164\pi\) | ||||
0.938557 | + | 0.345125i | \(0.112164\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.52075e9 | 1.85226 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.12959e9i | 1.26378i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.97392e8i | 0.197972i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.31338e9 | 1.29993 | 0.649964 | − | 0.759965i | \(-0.274784\pi\) | ||||
0.649964 | + | 0.759965i | \(0.274784\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.75557e9 | 2.61265 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.01694e9i | 1.53147i | 0.643154 | + | 0.765737i | \(0.277626\pi\) | ||||
−0.643154 | + | 0.765737i | \(0.722374\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.11275e9i | 0.418247i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.00773e9 | −0.373443 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.16199e9 | 0.424577 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.70976e9i | 0.976290i | 0.872763 | + | 0.488145i | \(0.162326\pi\) | ||||
−0.872763 | + | 0.488145i | \(0.837674\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 9.64045e9i | − 3.42504i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.04579e8 | 0.106712 | 0.0533558 | − | 0.998576i | \(-0.483008\pi\) | ||||
0.0533558 | + | 0.998576i | \(0.483008\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.95456e8 | 0.274850 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.48701e9i | 1.52908i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.88202e8i | 0.0632575i | 0.999500 | + | 0.0316287i | \(0.0100694\pi\) | ||||
−0.999500 | + | 0.0316287i | \(0.989931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.66229e8 | −0.254030 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.29088e8 | −0.303841 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 3.36331e8i | − 0.108503i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.72145e9i | 0.547870i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.32355e9 | 1.67153 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.14963e9 | −1.28552 | −0.642758 | − | 0.766069i | \(-0.722210\pi\) | ||||
−0.642758 | + | 0.766069i | \(0.722210\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.51360e9i | − 0.768318i | −0.923267 | − | 0.384159i | \(-0.874491\pi\) | ||||
0.923267 | − | 0.384159i | \(-0.125509\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.73494e9i | 0.824880i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.51352e8 | −0.134332 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.27072e9 | 0.960613 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 4.70359e9i | − 1.36332i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.52403e9i | − 0.435962i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.97780e6 | −0.00168773 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.51112e8 | −0.265046 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.55379e9i | − 0.427398i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.32416e9i | 0.359543i | 0.983708 | + | 0.179772i | \(0.0575358\pi\) | ||||
−0.983708 | + | 0.179772i | \(0.942464\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.39026e8 | −0.117677 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.83789e8 | −0.207401 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.58047e8i | 0.145786i | 0.997340 | + | 0.0728929i | \(0.0232231\pi\) | ||||
−0.997340 | + | 0.0728929i | \(0.976777\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.19107e9i | 2.37062i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.11567e8 | 0.104812 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.84136e9 | 0.463020 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.88912e9i | 0.717364i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.30331e9i | 0.809946i | 0.914329 | + | 0.404973i | \(0.132719\pi\) | ||||
−0.914329 | + | 0.404973i | \(0.867281\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.44143e9 | −1.80184 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.36398e9 | −0.565293 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.22011e8i | − 0.0288152i | −0.999896 | − | 0.0144076i | \(-0.995414\pi\) | ||||
0.999896 | − | 0.0144076i | \(-0.00458623\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 7.65790e8i | − 0.178624i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.77371e9 | −0.869417 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.00925e8 | −0.113993 | −0.0569967 | − | 0.998374i | \(-0.518152\pi\) | ||||
−0.0569967 | + | 0.998374i | \(0.518152\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.98702e9i | 1.57060i | 0.619116 | + | 0.785300i | \(0.287491\pi\) | ||||
−0.619116 | + | 0.785300i | \(0.712509\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 7.14253e9i | − 1.58603i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.83375e9 | 1.27971 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.16573e9 | −1.76962 | −0.884809 | − | 0.465954i | \(-0.845711\pi\) | ||||
−0.884809 | + | 0.465954i | \(0.845711\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 9.66769e9i | − 2.06989i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.45591e9i | 0.519512i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.57631e9 | −0.956479 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.30320e9 | −0.888682 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 8.53182e9i | − 1.74104i | −0.492135 | − | 0.870519i | \(-0.663783\pi\) | ||||
0.492135 | − | 0.870519i | \(-0.336217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.66940e8i | 0.0336632i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.16358e10 | −2.31868 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.71175e9 | −0.337092 | −0.168546 | − | 0.985694i | \(-0.553907\pi\) | ||||
−0.168546 | + | 0.985694i | \(0.553907\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4.16921e8i | − 0.0811417i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.84475e9i | 0.354836i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.77362e9 | −0.907516 | −0.453758 | − | 0.891125i | \(-0.649917\pi\) | ||||
−0.453758 | + | 0.891125i | \(0.649917\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.89998e8 | −0.148445 | −0.0742224 | − | 0.997242i | \(-0.523647\pi\) | ||||
−0.0742224 | + | 0.997242i | \(0.523647\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.44408e10i | − 2.68214i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1.07556e9i | − 0.197465i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.82652e9 | 0.331485 | 0.165743 | − | 0.986169i | \(-0.446998\pi\) | ||||
0.165743 | + | 0.986169i | \(0.446998\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.82266e9 | 0.685813 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.35094e9i | 1.30376i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 6.90339e9i | − 1.21046i | −0.796050 | − | 0.605231i | \(-0.793081\pi\) | ||||
0.796050 | − | 0.605231i | \(-0.206919\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.73977e8 | 0.168844 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.69235e9 | 0.975649 | 0.487825 | − | 0.872942i | \(-0.337791\pi\) | ||||
0.487825 | + | 0.872942i | \(0.337791\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.28594e9i | 0.726321i | 0.931727 | + | 0.363161i | \(0.118302\pi\) | ||||
−0.931727 | + | 0.363161i | \(0.881698\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.84069e10i | 3.08433i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.95171e9 | −0.489064 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.57279e9 | 0.749206 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.74354e8i | 0.141661i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.67678e9i | 0.749324i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.61602e8 | −0.0889869 | −0.0444935 | − | 0.999010i | \(-0.514167\pi\) | ||||
−0.0444935 | + | 0.999010i | \(0.514167\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.12575e9 | −0.803238 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 2.95031e9i | − 0.457256i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6.63501e9i | − 1.01708i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.24073e10 | 1.88116 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.17445e9 | 0.775998 | 0.387999 | − | 0.921660i | \(-0.373166\pi\) | ||||
0.387999 | + | 0.921660i | \(0.373166\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.04374e10i | − 1.54830i | −0.633004 | − | 0.774148i | \(-0.718178\pi\) | ||||
0.633004 | − | 0.774148i | \(-0.281822\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 4.75567e9i | − 0.697835i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.71623e8 | −0.141037 | −0.0705185 | − | 0.997510i | \(-0.522465\pi\) | ||||
−0.0705185 | + | 0.997510i | \(0.522465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.43825e9 | −0.350125 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.55055e9i | 0.220268i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.25223e9i | 1.01924i | 0.860400 | + | 0.509619i | \(0.170214\pi\) | ||||
−0.860400 | + | 0.509619i | \(0.829786\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.54363e7 | −0.00770814 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.18151e9 | −1.12552 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.81924e9i | 0.519851i | 0.965629 | + | 0.259925i | \(0.0836979\pi\) | ||||
−0.965629 | + | 0.259925i | \(0.916302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.07881e10i | 1.45292i | 0.687210 | + | 0.726459i | \(0.258835\pi\) | ||||
−0.687210 | + | 0.726459i | \(0.741165\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.00947e10 | −1.34523 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.54205e8 | −0.0203339 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 8.15390e9i | − 1.06396i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 3.54857e9i | − 0.458207i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.76448e9 | 0.608817 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.34833e9 | −0.802798 | −0.401399 | − | 0.915903i | \(-0.631476\pi\) | ||||
−0.401399 | + | 0.915903i | \(0.631476\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.60858e10i | 2.01316i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.82566e9i | 1.09317i | 0.837404 | + | 0.546584i | \(0.184072\pi\) | ||||
−0.837404 | + | 0.546584i | \(0.815928\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.76599e9 | 0.339083 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.00846e10 | −2.43696 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 4.92331e9i | − 0.591268i | −0.955301 | − | 0.295634i | \(-0.904469\pi\) | ||||
0.955301 | − | 0.295634i | \(-0.0955309\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 2.42590e9i | − 0.288374i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.93027e9 | −0.462459 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.95418e10 | −2.27613 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 5.68449e9i | − 0.655418i | −0.944779 | − | 0.327709i | \(-0.893723\pi\) | ||||
0.944779 | − | 0.327709i | \(-0.106277\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.60395e9i | 0.639628i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.61649e9 | 0.295646 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.57663e9 | 0.176366 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.89989e10i | 3.21152i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.70567e9i | 0.187017i | 0.995618 | + | 0.0935085i | \(0.0298082\pi\) | ||||
−0.995618 | + | 0.0935085i | \(0.970192\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.72978e9 | 0.187779 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.69784e9 | −0.504936 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.42351e9i | − 0.470760i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.52189e9i | 0.476495i | 0.971204 | + | 0.238248i | \(0.0765730\pi\) | ||||
−0.971204 | + | 0.238248i | \(0.923427\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.96613e10 | 2.05149 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.30738e9 | 0.341720 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.23070e9i | 0.228229i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.96907e10i | 1.99500i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.09206e9 | 0.310239 | 0.155120 | − | 0.987896i | \(-0.450424\pi\) | ||||
0.155120 | + | 0.987896i | \(0.450424\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.87033e9 | −0.185842 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.20280e9i | 0.905599i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 7.12568e9i | − 0.694453i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.44622e10 | 1.39593 | 0.697965 | − | 0.716132i | \(-0.254089\pi\) | ||||
0.697965 | + | 0.716132i | \(0.254089\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.09288e9 | 0.104478 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 7.69827e9i | − 0.728924i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 3.15415e9i | − 0.295814i | −0.989001 | − | 0.147907i | \(-0.952746\pi\) | ||||
0.989001 | − | 0.147907i | \(-0.0472536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.24030e9 | 0.393905 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.48585e9 | −0.688819 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.54236e10i | 1.40582i | 0.711277 | + | 0.702912i | \(0.248117\pi\) | ||||
−0.711277 | + | 0.702912i | \(0.751883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.73367e9i | 0.337111i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.59520e10 | −1.42677 | −0.713385 | − | 0.700772i | \(-0.752839\pi\) | ||||
−0.713385 | + | 0.700772i | \(0.752839\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.56141e8 | −0.0847179 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.62233e10i | 2.30179i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.32424e7i | 0.00289072i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.13964e9 | −0.528936 | −0.264468 | − | 0.964395i | \(-0.585196\pi\) | ||||
−0.264468 | + | 0.964395i | \(0.585196\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.30986e10 | 2.82506 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.44562e9i | 0.122248i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.42818e10i | − 1.19660i | −0.801273 | − | 0.598299i | \(-0.795843\pi\) | ||||
0.801273 | − | 0.598299i | \(-0.204157\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.73226e10 | 1.43802 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.47536e10 | −1.21353 | −0.606767 | − | 0.794880i | \(-0.707534\pi\) | ||||
−0.606767 | + | 0.794880i | \(0.707534\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.35863e9i | 0.355234i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 4.45173e9i | − 0.359512i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.04118e10 | −0.833190 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.97592e10 | 1.56685 | 0.783424 | − | 0.621487i | \(-0.213471\pi\) | ||||
0.783424 | + | 0.621487i | \(0.213471\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 2.68014e10i | − 2.10604i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.01370e10i | 0.789374i | 0.918816 | + | 0.394687i | \(0.129147\pi\) | ||||
−0.918816 | + | 0.394687i | \(0.870853\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.89031e9 | 0.223043 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.60663e10 | 1.22869 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 5.83142e8i | − 0.0441970i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 6.43174e9i | − 0.483114i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.24833e10 | 1.67376 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.20420e8 | −0.0383981 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.27882e10i | − 0.935188i | −0.883943 | − | 0.467594i | \(-0.845121\pi\) | ||||
0.883943 | − | 0.467594i | \(-0.154879\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1.84261e10i | − 1.33556i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.25854e9 | −0.305945 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.03453e10 | 1.44880 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.24888e10i | − 0.881524i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.38617e9i | 0.516791i | 0.966039 | + | 0.258396i | \(0.0831938\pi\) | ||||
−0.966039 | + | 0.258396i | \(0.916806\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.60466e9 | −0.527431 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.15173e10 | −2.16688 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.24114e9i | 0.289054i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.05508e9i | 0.206413i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.24348e10 | 0.832875 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.53742e10 | −1.02087 | −0.510437 | − | 0.859915i | \(-0.670516\pi\) | ||||
−0.510437 | + | 0.859915i | \(0.670516\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 9.77882e9i | − 0.643744i | −0.946783 | − | 0.321872i | \(-0.895688\pi\) | ||||
0.946783 | − | 0.321872i | \(-0.104312\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 3.10745e10i | − 2.02809i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.59472e9 | 0.426722 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.84733e9 | −0.182667 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.39300e10i | 1.52212i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.83470e10i | 1.15708i | 0.815654 | + | 0.578540i | \(0.196377\pi\) | ||||
−0.815654 | + | 0.578540i | \(0.803623\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.16960e10 | −1.98201 | −0.991004 | − | 0.133829i | \(-0.957273\pi\) | ||||
−0.991004 | + | 0.133829i | \(0.957273\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.51382e10 | 0.938608 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.12845e9i | 0.376774i | 0.982095 | + | 0.188387i | \(0.0603260\pi\) | ||||
−0.982095 | + | 0.188387i | \(0.939674\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.24652e10i | 0.759904i | 0.925006 | + | 0.379952i | \(0.124060\pi\) | ||||
−0.925006 | + | 0.379952i | \(0.875940\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.32522e10 | −2.01010 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.86402e9 | 0.411454 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 9.41091e9i | − 0.559409i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.11966e9i | 0.537575i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.82237e10 | −1.06530 | −0.532648 | − | 0.846337i | \(-0.678803\pi\) | ||||
−0.532648 | + | 0.846337i | \(0.678803\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.29024e9 | 0.422625 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 5.02118e10i | − 2.88675i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.38017e9i | 0.249743i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.98117e9 | −0.338216 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.76870e9 | −0.379602 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 3.42701e10i | − 1.90617i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.48619e10i | − 1.37155i | −0.727812 | − | 0.685777i | \(-0.759463\pi\) | ||||
0.727812 | − | 0.685777i | \(-0.240537\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.64654e9 | −0.0900930 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.96761e10 | −1.61055 | −0.805275 | − | 0.592902i | \(-0.797982\pi\) | ||||
−0.805275 | + | 0.592902i | \(0.797982\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1.14772e10i | − 0.617819i | −0.951091 | − | 0.308910i | \(-0.900036\pi\) | ||||
0.951091 | − | 0.308910i | \(-0.0999640\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 5.41626e9i | − 0.289194i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.13485e10 | −1.13066 | −0.565328 | − | 0.824866i | \(-0.691250\pi\) | ||||
−0.565328 | + | 0.824866i | \(0.691250\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.19679e9 | 0.273010 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.40254e10i | 1.25200i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.01921e10i | − 0.526858i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.19661e10 | −1.63918 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.95342e10 | 1.50236 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.59108e9i | 0.282142i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.92753e9i | 0.396862i | 0.980115 | + | 0.198431i | \(0.0635846\pi\) | ||||
−0.980115 | + | 0.198431i | \(0.936415\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.33805e10 | 3.14771 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.32045e9 | 0.360680 | 0.180340 | − | 0.983604i | \(-0.442280\pi\) | ||||
0.180340 | + | 0.983604i | \(0.442280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3.54988e9i | − 0.173521i | −0.996229 | − | 0.0867604i | \(-0.972349\pi\) | ||||
0.996229 | − | 0.0867604i | \(-0.0276514\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 6.65400e9i | − 0.322687i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.80634e9 | 0.279364 | 0.139682 | − | 0.990196i | \(-0.455392\pi\) | ||||
0.139682 | + | 0.990196i | \(0.455392\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.64066e10 | −0.783182 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.08878e10i | 0.989285i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.81270e9i | 0.132173i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.28466e8 | −0.0432898 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.39709e10 | 3.42206 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 4.03982e9i | − 0.185440i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2.02163e10i | − 0.920798i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.64462e10 | −1.19524 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.28573e8 | −0.0192201 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.78240e10i | − 0.793196i | −0.917992 | − | 0.396598i | \(-0.870191\pi\) | ||||
0.917992 | − | 0.396598i | \(-0.129809\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 4.72326e10i | − 2.08578i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.87703e10 | −0.822538 | −0.411269 | − | 0.911514i | \(-0.634914\pi\) | ||||
−0.411269 | + | 0.911514i | \(0.634914\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.35937e10 | 0.591138 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.30023e10i | 0.561107i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.08280e8i | 0.0132024i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.75844e10 | 1.59736 | 0.798681 | − | 0.601754i | \(-0.205531\pi\) | ||||
0.798681 | + | 0.601754i | \(0.205531\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.89197e10 | 2.90693 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2.74648e10i | − 1.14966i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 2.99486e10i | − 1.24417i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.99707e10 | −0.823404 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.92372e10 | −0.787205 | −0.393602 | − | 0.919281i | \(-0.628771\pi\) | ||||
−0.393602 | + | 0.919281i | \(0.628771\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2.53876e9i | − 0.103109i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 5.48943e10i | − 2.21279i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.30769e9 | −0.0923289 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.04732e9 | −0.0415900 | −0.0207950 | − | 0.999784i | \(-0.506620\pi\) | ||||
−0.0207950 | + | 0.999784i | \(0.506620\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.57413e10i | 2.19709i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.97861e9i | 0.312150i | 0.987745 | + | 0.156075i | \(0.0498842\pi\) | ||||
−0.987745 | + | 0.156075i | \(0.950116\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.15531e10 | −0.448650 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.42397e9 | −0.324717 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.26943e9i | − 0.163360i | −0.996659 | − | 0.0816799i | \(-0.973971\pi\) | ||||
0.996659 | − | 0.0816799i | \(-0.0260285\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.81106e10i | 0.687860i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.97963e10 | 1.12339 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.06048e10 | 0.396897 | 0.198449 | − | 0.980111i | \(-0.436410\pi\) | ||||
0.198449 | + | 0.980111i | \(0.436410\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 6.97247e9i | − 0.259045i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.11588e10i | − 0.780367i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.34904e10 | −0.493922 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.58740e10 | −0.940441 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.54950e8i | 0.0128078i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 9.43750e9i | − 0.338074i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.65090e10 | −0.587123 | −0.293562 | − | 0.955940i | \(-0.594841\pi\) | ||||
−0.293562 | + | 0.955940i | \(0.594841\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.86254e9 | −0.136377 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.46094e10i | 0.862649i | 0.902197 | + | 0.431324i | \(0.141954\pi\) | ||||
−0.902197 | + | 0.431324i | \(0.858046\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.45503e10i | − 0.506379i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.46430e10 | 2.23360 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.53886e10 | −0.870979 | −0.435489 | − | 0.900194i | \(-0.643425\pi\) | ||||
−0.435489 | + | 0.900194i | \(0.643425\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.63380e10i | 0.556492i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.65399e10i | 1.57392i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.87585e10 | 0.629884 | 0.314942 | − | 0.949111i | \(-0.398015\pi\) | ||||
0.314942 | + | 0.949111i | \(0.398015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.13588e10 | −0.378709 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.61246e10i | 0.864846i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.64107e10i | 1.85428i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.59792e9 | 0.117434 | 0.0587170 | − | 0.998275i | \(-0.481299\pi\) | ||||
0.0587170 | + | 0.998275i | \(0.481299\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.56656e10 | 0.831821 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.80083e9i | 0.0579552i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.34287e10i | − 0.429143i | −0.976708 | − | 0.214571i | \(-0.931165\pi\) | ||||
0.976708 | − | 0.214571i | \(-0.0688354\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.44952e10 | 2.99868 |
(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 | 256.8.b.c.129.1 | 2 | ||
4.3 | odd | 2 | 256.8.b.e.129.2 | 2 | |||
8.3 | odd | 2 | 256.8.b.e.129.1 | 2 | |||
8.5 | even | 2 | inner | 256.8.b.c.129.2 | 2 | ||
16.3 | odd | 4 | 8.8.a.a.1.1 | ✓ | 1 | ||
16.5 | even | 4 | 64.8.a.a.1.1 | 1 | |||
16.11 | odd | 4 | 64.8.a.g.1.1 | 1 | |||
16.13 | even | 4 | 16.8.a.c.1.1 | 1 | |||
48.5 | odd | 4 | 576.8.a.k.1.1 | 1 | |||
48.11 | even | 4 | 576.8.a.j.1.1 | 1 | |||
48.29 | odd | 4 | 144.8.a.g.1.1 | 1 | |||
48.35 | even | 4 | 72.8.a.d.1.1 | 1 | |||
80.3 | even | 4 | 200.8.c.a.49.1 | 2 | |||
80.13 | odd | 4 | 400.8.c.b.49.2 | 2 | |||
80.19 | odd | 4 | 200.8.a.i.1.1 | 1 | |||
80.29 | even | 4 | 400.8.a.b.1.1 | 1 | |||
80.67 | even | 4 | 200.8.c.a.49.2 | 2 | |||
80.77 | odd | 4 | 400.8.c.b.49.1 | 2 | |||
112.83 | even | 4 | 392.8.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.8.a.a.1.1 | ✓ | 1 | 16.3 | odd | 4 | ||
16.8.a.c.1.1 | 1 | 16.13 | even | 4 | |||
64.8.a.a.1.1 | 1 | 16.5 | even | 4 | |||
64.8.a.g.1.1 | 1 | 16.11 | odd | 4 | |||
72.8.a.d.1.1 | 1 | 48.35 | even | 4 | |||
144.8.a.g.1.1 | 1 | 48.29 | odd | 4 | |||
200.8.a.i.1.1 | 1 | 80.19 | odd | 4 | |||
200.8.c.a.49.1 | 2 | 80.3 | even | 4 | |||
200.8.c.a.49.2 | 2 | 80.67 | even | 4 | |||
256.8.b.c.129.1 | 2 | 1.1 | even | 1 | trivial | ||
256.8.b.c.129.2 | 2 | 8.5 | even | 2 | inner | ||
256.8.b.e.129.1 | 2 | 8.3 | odd | 2 | |||
256.8.b.e.129.2 | 2 | 4.3 | odd | 2 | |||
392.8.a.d.1.1 | 1 | 112.83 | even | 4 | |||
400.8.a.b.1.1 | 1 | 80.29 | even | 4 | |||
400.8.c.b.49.1 | 2 | 80.77 | odd | 4 | |||
400.8.c.b.49.2 | 2 | 80.13 | odd | 4 | |||
576.8.a.j.1.1 | 1 | 48.11 | even | 4 | |||
576.8.a.k.1.1 | 1 | 48.5 | odd | 4 |