Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,6,Mod(65,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.65");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.b (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: | \(20.5291289361\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-29})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 28x^{2} + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.3 | ||
Root | \(-0.707107 - 3.80789i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.65 |
Dual form | 128.6.b.d.65.2 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 15.2315i | 0.977104i | 0.872535 | + | 0.488552i | \(0.162475\pi\) | ||||
−0.872535 | + | 0.488552i | \(0.837525\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 43.0813i | − 0.770662i | −0.922778 | − | 0.385331i | \(-0.874087\pi\) | ||||
0.922778 | − | 0.385331i | \(-0.125913\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.6274 | 0.174538 | 0.0872690 | − | 0.996185i | \(-0.472186\pi\) | ||||
0.0872690 | + | 0.996185i | \(0.472186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 11.0000 | 0.0452675 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 258.936i | 0.645225i | 0.946531 | + | 0.322613i | \(0.104561\pi\) | ||||
−0.946531 | + | 0.322613i | \(0.895439\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 990.870i | − 1.62614i | −0.582165 | − | 0.813071i | \(-0.697794\pi\) | ||||
0.582165 | − | 0.813071i | \(-0.302206\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 656.195 | 0.753017 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −218.000 | −0.182951 | −0.0914754 | − | 0.995807i | \(-0.529158\pi\) | ||||
−0.0914754 | + | 0.995807i | \(0.529158\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1995.33i | − 1.26804i | −0.773319 | − | 0.634018i | \(-0.781405\pi\) | ||||
0.773319 | − | 0.634018i | \(-0.218595\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 344.651i | 0.170542i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3416.74 | 1.34677 | 0.673383 | − | 0.739294i | \(-0.264840\pi\) | ||||
0.673383 | + | 0.739294i | \(0.264840\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1269.00 | 0.406080 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3868.81i | 1.02134i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4868.19i | 1.07491i | 0.843292 | + | 0.537455i | \(0.180614\pi\) | ||||
−0.843292 | + | 0.537455i | \(0.819386\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8688.93 | 1.62391 | 0.811955 | − | 0.583720i | \(-0.198403\pi\) | ||||
0.811955 | + | 0.583720i | \(0.198403\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3944.00 | −0.630452 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 974.819i | − 0.134510i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3231.10i | 0.388013i | 0.981000 | + | 0.194006i | \(0.0621482\pi\) | ||||
−0.981000 | + | 0.194006i | \(0.937852\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15092.5 | 1.58891 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8410.00 | 0.781333 | 0.390667 | − | 0.920532i | \(-0.372245\pi\) | ||||
0.390667 | + | 0.920532i | \(0.372245\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 685.420i | 0.0565308i | 0.999600 | + | 0.0282654i | \(0.00899836\pi\) | ||||
−0.999600 | + | 0.0282654i | \(0.991002\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 473.895i | − 0.0348859i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 18147.2 | 1.19830 | 0.599149 | − | 0.800638i | \(-0.295506\pi\) | ||||
0.599149 | + | 0.800638i | \(0.295506\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16295.0 | −0.969537 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 3320.48i | − 0.178762i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 26581.2i | − 1.29982i | −0.760010 | − | 0.649912i | \(-0.774806\pi\) | ||||
0.760010 | − | 0.649912i | \(-0.225194\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11155.3 | 0.497250 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 30392.0 | 1.23900 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 33798.8i | − 1.26407i | −0.774940 | − | 0.632035i | \(-0.782220\pi\) | ||||
0.774940 | − | 0.632035i | \(-0.217780\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 27356.6i | − 0.941322i | −0.882314 | − | 0.470661i | \(-0.844016\pi\) | ||||
0.882314 | − | 0.470661i | \(-0.155984\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 248.902 | 0.00790090 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −42688.0 | −1.25321 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 66729.4i | 1.81606i | 0.418905 | + | 0.908030i | \(0.362414\pi\) | ||||
−0.418905 | + | 0.908030i | \(0.637586\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 52042.2i | 1.31593i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −21609.2 | −0.508736 | −0.254368 | − | 0.967108i | \(-0.581867\pi\) | ||||
−0.254368 | + | 0.967108i | \(0.581867\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 43006.0 | 0.944543 | 0.472272 | − | 0.881453i | \(-0.343434\pi\) | ||||
0.472272 | + | 0.881453i | \(0.343434\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 19328.8i | 0.396782i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5859.06i | 0.112616i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −64759.7 | −1.16745 | −0.583723 | − | 0.811953i | \(-0.698405\pi\) | ||||
−0.583723 | + | 0.811953i | \(0.698405\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −56255.0 | −0.952683 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 70659.1i | − 1.12583i | −0.826515 | − | 0.562915i | \(-0.809680\pi\) | ||||
0.826515 | − | 0.562915i | \(-0.190320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9391.73i | 0.140993i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −74150.0 | −1.05030 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 93870.0 | 1.25618 | 0.628090 | − | 0.778141i | \(-0.283837\pi\) | ||||
0.628090 | + | 0.778141i | \(0.283837\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 22420.8i | − 0.283823i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 132346.i | 1.58673i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −85961.6 | −0.977227 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −81706.0 | −0.881708 | −0.440854 | − | 0.897579i | \(-0.645324\pi\) | ||||
−0.440854 | + | 0.897579i | \(0.645324\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2848.30i | 0.0292077i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 87412.0i | − 0.852644i | −0.904572 | − | 0.426322i | \(-0.859809\pi\) | ||||
0.904572 | − | 0.426322i | \(-0.140191\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −132665. | −1.23214 | −0.616072 | − | 0.787689i | \(-0.711277\pi\) | ||||
−0.616072 | + | 0.787689i | \(0.711277\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14848.0 | 0.131430 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 87870.8i | 0.741968i | 0.928639 | + | 0.370984i | \(0.120980\pi\) | ||||
−0.928639 | + | 0.370984i | \(0.879020\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 121791.i | − 0.981858i | −0.871200 | − | 0.490929i | \(-0.836657\pi\) | ||||
0.871200 | − | 0.490929i | \(-0.163343\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −49214.6 | −0.379129 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −29614.0 | −0.218173 | −0.109086 | − | 0.994032i | \(-0.534793\pi\) | ||||
−0.109086 | + | 0.994032i | \(0.534793\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 147198.i | − 1.03790i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 10899.6i | − 0.0736114i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4932.78 | −0.0319318 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 94003.0 | 0.583685 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 128097.i | 0.763444i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 189299.i | − 1.08361i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −60551.0 | −0.333128 | −0.166564 | − | 0.986031i | \(-0.553267\pi\) | ||||
−0.166564 | + | 0.986031i | \(0.553267\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10440.0 | −0.0552365 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 186754.i | 0.950805i | 0.879768 | + | 0.475403i | \(0.157698\pi\) | ||||
−0.879768 | + | 0.475403i | \(0.842302\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 45149.2i | − 0.221320i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 166674. | 0.787104 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −182054. | −0.828703 | −0.414351 | − | 0.910117i | \(-0.635992\pi\) | ||||
−0.414351 | + | 0.910117i | \(0.635992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 45131.1i | − 0.198125i | −0.995081 | − | 0.0990624i | \(-0.968416\pi\) | ||||
0.995081 | − | 0.0990624i | \(-0.0315843\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 276410.i | 1.17086i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 256572. | 1.04923 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 209728. | 0.828393 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 248198.i | − 0.947338i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 262408.i | 0.968304i | 0.874984 | + | 0.484152i | \(0.160872\pi\) | ||||
−0.874984 | + | 0.484152i | \(0.839128\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 113839. | 0.406300 | 0.203150 | − | 0.979148i | \(-0.434882\pi\) | ||||
0.203150 | + | 0.979148i | \(0.434882\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2398.00 | −0.00828172 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 374330.i | − 1.25149i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 114898.i | − 0.372017i | −0.982548 | − | 0.186009i | \(-0.940445\pi\) | ||||
0.982548 | − | 0.186009i | \(-0.0595552\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 404872. | 1.27006 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 77312.0 | 0.235062 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 284784.i | 0.839551i | 0.907628 | + | 0.419775i | \(0.137891\pi\) | ||||
−0.907628 | + | 0.419775i | \(0.862109\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 169913.i | 0.485865i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 425871. | 1.18164 | 0.590822 | − | 0.806802i | \(-0.298804\pi\) | ||||
0.590822 | + | 0.806802i | \(0.298804\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −610531. | −1.64434 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 21948.7i | − 0.0574008i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 165131.i | 0.419481i | 0.977757 | + | 0.209741i | \(0.0672620\pi\) | ||||
−0.977757 | + | 0.209741i | \(0.932738\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 28714.2 | 0.0708764 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 514808. | 1.23513 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 724671.i | 1.69047i | 0.534392 | + | 0.845237i | \(0.320541\pi\) | ||||
−0.534392 | + | 0.845237i | \(0.679459\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 45709.3i | − 0.103707i | −0.998655 | − | 0.0518535i | \(-0.983487\pi\) | ||||
0.998655 | − | 0.0518535i | \(-0.0165129\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 416684. | 0.919769 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 139200. | 0.299027 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 56448.1i | − 0.118044i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 87541.2i | 0.178262i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 434537. | 0.861873 | 0.430936 | − | 0.902382i | \(-0.358183\pi\) | ||||
0.430936 | + | 0.902382i | \(0.358183\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 277878. | 0.536983 | 0.268492 | − | 0.963282i | \(-0.413475\pi\) | ||||
0.268492 | + | 0.963282i | \(0.413475\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 650204.i | − 1.22451i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.00539e6i | − 1.84573i | −0.385122 | − | 0.922866i | \(-0.625841\pi\) | ||||
0.385122 | − | 0.922866i | \(-0.374159\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −477506. | −0.854765 | −0.427382 | − | 0.904071i | \(-0.640564\pi\) | ||||
−0.427382 | + | 0.904071i | \(0.640564\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.01639e6 | −1.77448 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 110155.i | 0.187613i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 362314.i | − 0.602144i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 37584.1 | 0.0609647 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 516664. | 0.818168 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 18871.9i | − 0.0291816i | −0.999894 | − | 0.0145908i | \(-0.995355\pi\) | ||||
0.999894 | − | 0.0145908i | \(-0.00464456\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 329141.i | − 0.497088i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29528.8 | 0.0435662 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 196608. | 0.283434 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 655048.i | 0.922917i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 216010.i | 0.297504i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.23636e6 | −1.66488 | −0.832441 | − | 0.554114i | \(-0.813057\pi\) | ||||
−0.832441 | + | 0.554114i | \(0.813057\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13959.0 | 0.0183822 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 802261.i | − 1.03336i | −0.856179 | − | 0.516679i | \(-0.827168\pi\) | ||||
0.856179 | − | 0.516679i | \(-0.172832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.39579e6i | 1.75886i | 0.476026 | + | 0.879431i | \(0.342077\pi\) | ||||
−0.476026 | + | 0.879431i | \(0.657923\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −89242.5 | −0.110038 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −812898. | −0.980949 | −0.490474 | − | 0.871456i | \(-0.663176\pi\) | ||||
−0.490474 | + | 0.871456i | \(0.663176\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 781805.i | − 0.923483i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 986390.i | − 1.14072i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −403537. | −0.456971 | −0.228486 | − | 0.973547i | \(-0.573377\pi\) | ||||
−0.228486 | + | 0.973547i | \(0.573377\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 560262. | 0.621368 | 0.310684 | − | 0.950513i | \(-0.399442\pi\) | ||||
0.310684 | + | 0.950513i | \(0.399442\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 83270.9i | 0.0904643i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 702010.i | 0.747185i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.97712e6 | −2.06201 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.07625e6 | 1.10005 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 901784.i | 0.903479i | 0.892150 | + | 0.451740i | \(0.149196\pi\) | ||||
−0.892150 | + | 0.451740i | \(0.850804\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 884718.i | 0.868968i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −143051. | −0.137765 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −870558. | −0.822176 | −0.411088 | − | 0.911596i | \(-0.634851\pi\) | ||||
−0.411088 | + | 0.911596i | \(0.634851\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 73111.4i | 0.0677229i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 53550.1i | 0.0486585i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −231954. | −0.206782 | −0.103391 | − | 0.994641i | \(-0.532969\pi\) | ||||
−0.103391 | + | 0.994641i | \(0.532969\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.14515e6 | −1.00172 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.42979e6i | 1.22742i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.43396e6i | 1.20825i | 0.796890 | + | 0.604125i | \(0.206477\pi\) | ||||
−0.796890 | + | 0.604125i | \(0.793523\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.59627e6 | −1.32034 | −0.660168 | − | 0.751118i | \(-0.729515\pi\) | ||||
−0.660168 | + | 0.751118i | \(0.729515\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 341504. | 0.277325 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 328590.i | 0.262013i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.38278e6i | − 1.08281i | −0.840761 | − | 0.541407i | \(-0.817892\pi\) | ||||
0.840761 | − | 0.541407i | \(-0.182108\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 95578.2 | 0.0735103 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.39301e6 | 1.80791 | 0.903957 | − | 0.427622i | \(-0.140649\pi\) | ||||
0.903957 | + | 0.427622i | \(0.140649\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 597671.i | − 0.443604i | −0.975092 | − | 0.221802i | \(-0.928806\pi\) | ||||
0.975092 | − | 0.221802i | \(-0.0711939\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.30933e6i | − 0.954852i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 190297. | 0.136372 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.37233e6 | −0.966529 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1.24451e6i | − 0.861520i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 874680.i | 0.595224i | 0.954687 | + | 0.297612i | \(0.0961901\pi\) | ||||
−0.954687 | + | 0.297612i | \(0.903810\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.45610e6 | −0.974171 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00178e6 | −0.658991 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 3.38555e6i | − 2.19003i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15509.3i | 0.00986678i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.33142e6 | 0.833122 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.17856e6 | −0.725441 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.70313e6i | 1.63689i | 0.574582 | + | 0.818447i | \(0.305165\pi\) | ||||
−0.574582 | + | 0.818447i | \(0.694835\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 2.02069e6i | − 1.20393i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.49642e6 | 1.46358 | 0.731789 | − | 0.681531i | \(-0.238686\pi\) | ||||
0.731789 | + | 0.681531i | \(0.238686\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.92331e6 | 1.68661 | 0.843303 | − | 0.537439i | \(-0.180608\pi\) | ||||
0.843303 | + | 0.537439i | \(0.180608\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 10723.0i | − 0.00608892i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.61671e6i | − 0.903618i | −0.892115 | − | 0.451809i | \(-0.850779\pi\) | ||||
0.892115 | − | 0.451809i | \(-0.149221\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.26055e6 | −0.693559 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.33841e6 | −0.724980 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 434982.i | 0.231988i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1.25741e6i | − 0.660344i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.85506e6 | 0.959377 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 410624. | 0.209148 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.14774e6i | 0.575804i | 0.957660 | + | 0.287902i | \(0.0929577\pi\) | ||||
−0.957660 | + | 0.287902i | \(0.907042\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 35542.1i | 0.0175644i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.87479e6 | 1.39957 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 371378. | 0.178132 | 0.0890659 | − | 0.996026i | \(-0.471612\pi\) | ||||
0.0890659 | + | 0.996026i | \(0.471612\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 451067.i | − 0.213178i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.24988e6i | 1.04779i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −749013. | −0.343759 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.24205e6 | 1.01414 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.13912e6i | − 0.507863i | −0.967222 | − | 0.253931i | \(-0.918276\pi\) | ||||
0.967222 | − | 0.253931i | \(-0.0817238\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.08105e6i | 1.79353i | 0.442508 | + | 0.896764i | \(0.354089\pi\) | ||||
−0.442508 | + | 0.896764i | \(0.645911\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.83349e6 | 1.66084 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.90953e6 | −1.66989 | −0.834946 | − | 0.550332i | \(-0.814501\pi\) | ||||
−0.834946 | + | 0.550332i | \(0.814501\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 930952.i | 0.392064i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 75133.8i | − 0.0312007i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.62028e6 | 1.07303 | 0.536514 | − | 0.843891i | \(-0.319741\pi\) | ||||
0.536514 | + | 0.843891i | \(0.319741\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.50525e6 | −0.607913 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.43181e6i | 0.570321i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.85276e6i | − 0.727924i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.65266e6 | −0.640499 | −0.320250 | − | 0.947333i | \(-0.603767\pi\) | ||||
−0.320250 | + | 0.947333i | \(0.603767\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 92510.0 | 0.0353690 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 601463.i | − 0.226869i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.09630e6i | 1.15231i | 0.817339 | + | 0.576157i | \(0.195448\pi\) | ||||
−0.817339 | + | 0.576157i | \(0.804552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.88332e6 | 1.05880 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.82374e6 | 1.74796 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 647478.i | 0.231540i | 0.993276 | + | 0.115770i | \(0.0369336\pi\) | ||||
−0.993276 | + | 0.115770i | \(0.963066\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 922285.i | − 0.325501i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.42168e6 | 0.843566 | 0.421783 | − | 0.906697i | \(-0.361404\pi\) | ||||
0.421783 | + | 0.906697i | \(0.361404\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 252416. | 0.0867891 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7539.62i | 0.00255901i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.06441e6i | 0.356644i | 0.983972 | + | 0.178322i | \(0.0570669\pi\) | ||||
−0.983972 | + | 0.178322i | \(0.942933\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −744849. | −0.246392 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.84455e6 | −0.929036 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.78993e6i | 0.899706i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 734235.i | − 0.233808i | −0.993143 | − | 0.116904i | \(-0.962703\pi\) | ||||
0.993143 | − | 0.116904i | \(-0.0372969\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 687692. | 0.216253 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −448218. | −0.139197 | −0.0695983 | − | 0.997575i | \(-0.522172\pi\) | ||||
−0.0695983 | + | 0.997575i | \(0.522172\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 8.60960e6i | − 2.64071i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.42354e6i | 0.734197i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −836649. | −0.250356 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −84854.0 | −0.0250821 | −0.0125411 | − | 0.999921i | \(-0.503992\pi\) | ||||
−0.0125411 | + | 0.999921i | \(0.503992\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 2.77296e6i | − 0.809729i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 764780.i | − 0.220628i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.04409e6 | −0.867635 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 687416. | 0.193588 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.75650e6i | 0.767048i | 0.923531 | + | 0.383524i | \(0.125290\pi\) | ||||
−0.923531 | + | 0.383524i | \(0.874710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 6.94647e6i | − 1.91011i | −0.296423 | − | 0.955057i | \(-0.595794\pi\) | ||||
0.296423 | − | 0.955057i | \(-0.404206\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 199619. | 0.0542439 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −276642. | −0.0742926 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 619010.i | − 0.164296i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.90799e6i | 1.02520i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.08227e6 | 0.280635 | 0.140318 | − | 0.990107i | \(-0.455188\pi\) | ||||
0.140318 | + | 0.990107i | \(0.455188\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.26093e6 | 0.579520 | 0.289760 | − | 0.957099i | \(-0.406425\pi\) | ||||
0.289760 | + | 0.957099i | \(0.406425\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.19448e6i | 0.809426i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 6.81753e6i | − 1.70775i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.16645e6 | −1.52712 | −0.763561 | − | 0.645736i | \(-0.776551\pi\) | ||||
−0.763561 | + | 0.645736i | \(0.776551\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −179245. | −0.0438885 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.61587e6i | 1.60169i | 0.598874 | + | 0.800843i | \(0.295615\pi\) | ||||
−0.598874 | + | 0.800843i | \(0.704385\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 4.04404e6i | − 0.968090i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.99688e6 | −0.946134 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −807882. | −0.189118 | −0.0945588 | − | 0.995519i | \(-0.530144\pi\) | ||||
−0.0945588 | + | 0.995519i | \(0.530144\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.17765e6i | 0.504136i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.73394e6i | 0.396998i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −965919. | −0.218732 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.20353e6 | −1.38947 | −0.694733 | − | 0.719267i | \(-0.744478\pi\) | ||||
−0.694733 | + | 0.719267i | \(0.744478\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 843401.i | − 0.186854i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.93853e6i | 0.424835i | 0.977179 | + | 0.212417i | \(0.0681337\pi\) | ||||
−0.977179 | + | 0.212417i | \(0.931866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.96413e6 | −1.50978 | −0.754891 | − | 0.655850i | \(-0.772310\pi\) | ||||
−0.754891 | + | 0.655850i | \(0.772310\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.70163e6 | 1.22283 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 4.65298e6i | − 0.987277i | −0.869667 | − | 0.493638i | \(-0.835667\pi\) | ||||
0.869667 | − | 0.493638i | \(-0.164333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.50991e6i | 0.316971i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.75007e6 | 0.363499 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −177480. | −0.0364751 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2.53208e6i | − 0.514924i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 292393.i | − 0.0588398i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.10743e6 | −0.419676 | −0.209838 | − | 0.977736i | \(-0.567294\pi\) | ||||
−0.209838 | + | 0.977736i | \(0.567294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.20160e6 | 0.630964 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.17758e6i | 0.229680i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.52000e6i | 0.679499i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.02334e6 | −1.72403 | −0.862015 | − | 0.506883i | \(-0.830798\pi\) | ||||
−0.862015 | + | 0.506883i | \(0.830798\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.33770e6 | −0.820328 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 2.69262e6i | − 0.504047i | −0.967721 | − | 0.252023i | \(-0.918904\pi\) | ||||
0.967721 | − | 0.252023i | \(-0.0810960\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.06127e6i | − 0.196656i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 122708. | 0.0225093 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −488960. | −0.0887937 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.32456e6i | 0.777482i | 0.921347 | + | 0.388741i | \(0.127090\pi\) | ||||
−0.921347 | + | 0.388741i | \(0.872910\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.48667e6i | 1.15459i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.58525e6 | −0.455599 | −0.227799 | − | 0.973708i | \(-0.573153\pi\) | ||||
−0.227799 | + | 0.973708i | \(0.573153\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.76582e6 | −0.657100 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 9.29933e6i | − 1.60669i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.02746e6i | 0.689027i | 0.938781 | + | 0.344514i | \(0.111956\pi\) | ||||
−0.938781 | + | 0.344514i | \(0.888044\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 973115. | 0.164859 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.71957e6 | 1.29509 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.71536e6i | 0.949567i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.69897e6i | 0.773172i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.51520e6 | −0.409877 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.11324e6 | 0.341079 | 0.170539 | − | 0.985351i | \(-0.445449\pi\) | ||||
0.170539 | + | 0.985351i | \(0.445449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.72110e6i | 0.435001i | 0.976060 | + | 0.217501i | \(0.0697904\pi\) | ||||
−0.976060 | + | 0.217501i | \(0.930210\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 437362.i | 0.0692536i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.89419e6 | −0.297096 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.23777e6 | 0.813780 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 371787.i | − 0.0572213i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 8.33322e6i | − 1.27056i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.78559e6 | 0.571806 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.10379e7 | −1.65177 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 4.21937e6i | − 0.625569i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 1.05683e6i | − 0.155243i | −0.996983 | − | 0.0776213i | \(-0.975267\pi\) | ||||
0.996983 | − | 0.0776213i | \(-0.0247325\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 696223. | 0.101333 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.24691e6 | −0.756680 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.14920e6i | − 0.450020i | −0.974356 | − | 0.225010i | \(-0.927759\pi\) | ||||
0.974356 | − | 0.225010i | \(-0.0722415\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 300923.i | − 0.0426113i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.71366e6 | 1.36302 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.46534e6 | −0.203764 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.12023e6i | 0.292180i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 3.91932e6i | − 0.535270i | −0.963520 | − | 0.267635i | \(-0.913758\pi\) | ||||
0.963520 | − | 0.267635i | \(-0.0862422\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 679162. | 0.0919272 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 859792. | 0.115342 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.62499e6i | − 0.349025i | −0.984655 | − | 0.174513i | \(-0.944165\pi\) | ||||
0.984655 | − | 0.174513i | \(-0.0558349\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.27581e6i | 0.168138i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.27291e6 | −0.166279 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.56020e6 | 0.849448 | 0.424724 | − | 0.905323i | \(-0.360371\pi\) | ||||
0.424724 | + | 0.905323i | \(0.360371\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.14800e7i | 1.47350i | 0.676165 | + | 0.736751i | \(0.263641\pi\) | ||||
−0.676165 | + | 0.736751i | \(0.736359\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.61867e6i | 0.842140i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.33584e6 | 0.546895 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.04493e7 | 1.30662 | 0.653308 | − | 0.757092i | \(-0.273381\pi\) | ||||
0.653308 | + | 0.757092i | \(0.273381\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.23251e6i | 0.524689i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1.59883e6i | − 0.196500i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.88283e6 | 0.838679 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −469568. | −0.0567295 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.24714e6i | 0.748318i | 0.927365 | + | 0.374159i | \(0.122069\pi\) | ||||
−0.927365 | + | 0.374159i | \(0.877931\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.73373e7i | − 2.05917i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.53136e7 | 1.80347 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.31288e6 | −0.737209 | −0.368605 | − | 0.929586i | \(-0.620164\pi\) | ||||
−0.368605 | + | 0.929586i | \(0.620164\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 212511.i | 0.0246087i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 7.27316e6i | − 0.835194i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.21797e6 | 0.138697 | 0.0693487 | − | 0.997592i | \(-0.477908\pi\) | ||||
0.0693487 | + | 0.997592i | \(0.477908\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.05226e7 | −1.18833 | −0.594167 | − | 0.804342i | \(-0.702518\pi\) | ||||
−0.594167 | + | 0.804342i | \(0.702518\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 734023.i | 0.0822085i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 4.04977e6i | − 0.449824i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.18789e6 | 0.241020 | 0.120510 | − | 0.992712i | \(-0.461547\pi\) | ||||
0.120510 | + | 0.992712i | \(0.461547\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.67782e6 | −0.183317 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1.79815e7i | − 1.94860i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 3.98593e6i | − 0.428428i | −0.976787 | − | 0.214214i | \(-0.931281\pi\) | ||||
0.976787 | − | 0.214214i | \(-0.0687190\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.51860e6 | 0.588357 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.42965e7 | 1.51188 | 0.755938 | − | 0.654643i | \(-0.227181\pi\) | ||||
0.755938 | + | 0.654643i | \(0.227181\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1.32078e7i | − 1.38549i | −0.721182 | − | 0.692746i | \(-0.756401\pi\) | ||||
0.721182 | − | 0.692746i | \(-0.243599\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.32187e7i | 1.37550i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.12404e6 | 0.219251 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.18964e6 | −0.429019 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.86959e6i | 0.799435i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 704380.i | − 0.0709872i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.51047e7 | 1.51021 | 0.755107 | − | 0.655602i | \(-0.227585\pi\) | ||||
0.755107 | + | 0.655602i | \(0.227585\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 287448. | 0.0285135 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.60862e6i | 0.256729i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.61462e7i | 1.57660i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −237701. | −0.0230292 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.88071e6 | −0.661437 | −0.330718 | − | 0.943729i | \(-0.607291\pi\) | ||||
−0.330718 | + | 0.943729i | \(0.607291\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.44561e7i | − 1.37887i | −0.724346 | − | 0.689437i | \(-0.757858\pi\) | ||||
0.724346 | − | 0.689437i | \(-0.242142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 449769.i | 0.0425687i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.83310e6 | −0.453905 | −0.226953 | − | 0.973906i | \(-0.572876\pi\) | ||||
−0.226953 | + | 0.973906i | \(0.572876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.75174e6 | 0.815610 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.99464e6i | 0.276944i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.22289e6i | 0.754643i | 0.926082 | + | 0.377321i | \(0.123155\pi\) | ||||
−0.926082 | + | 0.377321i | \(0.876845\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.04561e6 | 0.732750 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 473066. | 0.0427571 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.93447e6i | 0.532315i | 0.963930 | + | 0.266157i | \(0.0857541\pi\) | ||||
−0.963930 | + | 0.266157i | \(0.914246\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.07425e6i | 0.540741i | 0.962756 | + | 0.270370i | \(0.0871461\pi\) | ||||
−0.962756 | + | 0.270370i | \(0.912854\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.29016e6 | −0.290692 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.94509e6 | −0.170563 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.66333e7i | 1.44765i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.88317e7i | − 1.62676i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.08363e6 | 0.607364 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.01847e6 | −0.341998 | −0.170999 | − | 0.985271i | \(-0.554699\pi\) | ||||
−0.170999 | + | 0.985271i | \(0.554699\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.90952e6i | 0.414744i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.84827e7i | 1.54986i | 0.632044 | + | 0.774932i | \(0.282216\pi\) | ||||
−0.632044 | + | 0.774932i | \(0.717784\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.84880e6 | −0.153891 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.22197e7 | 1.00970 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.40610e6i | − 0.115336i | −0.998336 | − | 0.0576679i | \(-0.981634\pi\) | ||||
0.998336 | − | 0.0576679i | \(-0.0183665\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.84313e6i | 0.638650i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.12601e7 | −1.71859 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.63385e7 | −2.11370 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.01640e6i | 0.559009i | 0.960144 | + | 0.279505i | \(0.0901702\pi\) | ||||
−0.960144 | + | 0.279505i | \(0.909830\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 64449.7i | 0.00509786i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.94431e6 | −0.152687 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.83338e6 | −0.142946 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1.23817e7i | − 0.958489i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.28008e7i | − 0.983879i | −0.870629 | − | 0.491940i | \(-0.836288\pi\) | ||||
0.870629 | − | 0.491940i | \(-0.163712\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.44712e6 | 0.492014 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.19081e7 | 0.902339 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.97791e6i | − 0.148819i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.05442e6i | 0.228199i | 0.993469 | + | 0.114099i | \(0.0363982\pi\) | ||||
−0.993469 | + | 0.114099i | \(0.963602\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −712356. | −0.0528474 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.96878e7 | 2.18703 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.10535e7i | − 0.808600i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 6.14650e6i | − 0.446509i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.99890e7 | −1.44201 | −0.721006 | − | 0.692928i | \(-0.756320\pi\) | ||||
−0.721006 | + | 0.692928i | \(0.756320\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.00186e6 | −0.215056 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.53366e6i | 0.607141i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.17773e6i | 0.436500i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.34254e7 | −0.942088 | −0.471044 | − | 0.882110i | \(-0.656123\pi\) | ||||
−0.471044 | + | 0.882110i | \(0.656123\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.49383e7 | −1.04108 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 149421.i | − 0.0103424i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.89485e6i | − 0.130261i | −0.997877 | − | 0.0651304i | \(-0.979254\pi\) | ||||
0.997877 | − | 0.0651304i | \(-0.0207463\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.06927e7 | −0.730078 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.72787e7 | −1.17177 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.52333e7i | 1.02608i | 0.858364 | + | 0.513041i | \(0.171481\pi\) | ||||
−0.858364 | + | 0.513041i | \(0.828519\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 3.01145e7i | − 2.01479i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.79078e7 | −1.19006 | −0.595031 | − | 0.803703i | \(-0.702860\pi\) | ||||
−0.595031 | + | 0.803703i | \(0.702860\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.13049e7 | 0.746235 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 777251.i | − 0.0509635i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.98829e6i | 0.129502i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.08382e7 | 1.34822 | 0.674109 | − | 0.738632i | \(-0.264528\pi\) | ||||
0.674109 | + | 0.738632i | \(0.264528\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.37356e7 | −0.882793 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 4.90431e6i | − 0.313120i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.00548e6i | 0.190623i | 0.995448 | + | 0.0953113i | \(0.0303847\pi\) | ||||
−0.995448 | + | 0.0953113i | \(0.969615\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.34756e7 | −0.849072 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.28926e7 | 0.807013 | 0.403507 | − | 0.914977i | \(-0.367791\pi\) | ||||
0.403507 | + | 0.914977i | \(0.367791\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.75581e6i | − 0.171371i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 103309.i | 0.00638241i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.34902e7 | −2.05556 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.07309e7 | 0.654364 | 0.327182 | − | 0.944961i | \(-0.393901\pi\) | ||||
0.327182 | + | 0.944961i | \(0.393901\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1.32599e7i | − 0.803352i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.83952e7i | − 1.10728i | −0.832757 | − | 0.553639i | \(-0.813239\pi\) | ||||
0.832757 | − | 0.553639i | \(-0.186761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.10262e7 | 0.659437 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.11360e6 | −0.0661724 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.67807e7i | − 0.990758i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 5.59540e6i | − 0.328249i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.88341e7 | −1.09784 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.94995e6 | −0.286699 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.26448e6i | 0.245431i | 0.992442 | + | 0.122716i | \(0.0391603\pi\) | ||||
−0.992442 | + | 0.122716i | \(0.960840\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 3.53301e6i | − 0.202047i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −670088. | −0.0380795 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.71069e7 | −1.53072 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.74424e7i | − 0.978790i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.96002e7i | 1.65063i | 0.564676 | + | 0.825313i | \(0.309001\pi\) | ||||
−0.564676 | + | 0.825313i | \(0.690999\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.95609e6 | −0.219229 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.03257e6 | 0.0568641 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.11358e7i | 0.609443i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 3.33070e6i | − 0.181153i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.18415e7 | −1.18059 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.37728e7 | 1.81424 | 0.907121 | − | 0.420870i | \(-0.138275\pi\) | ||||
0.907121 | + | 0.420870i | \(0.138275\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.05658e7i | 1.09798i | 0.835830 | + | 0.548988i | \(0.184987\pi\) | ||||
−0.835830 | + | 0.548988i | \(0.815013\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.43137e7i | − 1.29010i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.22689e7 | 0.647010 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.36764e6 | 0.0716831 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 246629.i | − 0.0128480i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.78535e7i | 0.924414i | 0.886772 | + | 0.462207i | \(0.152942\pi\) | ||||
−0.886772 | + | 0.462207i | \(0.847058\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.13336e6 | 0.418572 | 0.209286 | − | 0.977854i | \(-0.432886\pi\) | ||||
0.209286 | + | 0.977854i | \(0.432886\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.00494e6 | −0.256014 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.12039e7i | 1.07808i | 0.842279 | + | 0.539042i | \(0.181213\pi\) | ||||
−0.842279 | + | 0.539042i | \(0.818787\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.73037e6i | 0.188523i | 0.995547 | + | 0.0942617i | \(0.0300491\pi\) | ||||
−0.995547 | + | 0.0942617i | \(0.969951\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.10619e7 | 1.05802 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.55231e6 | 0.177377 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1.83471e7i | − 0.910648i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.36158e7i | 1.65856i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.64106e7 | −0.804861 | −0.402430 | − | 0.915451i | \(-0.631834\pi\) | ||||
−0.402430 | + | 0.915451i | \(0.631834\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.18812e6 | −0.155433 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.64492e7i | 1.76652i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.63025e7i | 1.26723i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.12705e6 | 0.101875 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.10345e6 | 0.433448 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.10398e7i | 0.522563i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.74236e6i | 0.411392i | 0.978616 | + | 0.205696i | \(0.0659459\pi\) | ||||
−0.978616 | + | 0.205696i | \(0.934054\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −945577. | −0.0442366 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.31459e7 | −1.54162 | −0.770810 | − | 0.637065i | \(-0.780148\pi\) | ||||
−0.770810 | + | 0.637065i | \(0.780148\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 898006.i | 0.0415237i | 0.999784 | + | 0.0207619i | \(0.00660918\pi\) | ||||
−0.999784 | + | 0.0207619i | \(0.993391\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.89851e6i | 0.133250i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.63551e6 | −0.0747526 | −0.0373763 | − | 0.999301i | \(-0.511900\pi\) | ||||
−0.0373763 | + | 0.999301i | \(0.511900\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.11405e6 | 0.323278 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 2.09028e7i | − 0.944400i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.67686e7i | − 0.753266i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.61202e7 | 2.95317 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −898766. | −0.0399127 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 4.28335e6i | − 0.189132i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.42532e7i | 0.625770i | 0.949791 | + | 0.312885i | \(0.101295\pi\) | ||||
−0.949791 | + | 0.312885i | \(0.898705\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.33227e7 | −0.581595 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.24428e7 | −0.540105 | −0.270053 | − | 0.962846i | \(-0.587041\pi\) | ||||
−0.270053 | + | 0.962846i | \(0.587041\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 4.34630e7i | − 1.87593i | −0.346725 | − | 0.937967i | \(-0.612706\pi\) | ||||
0.346725 | − | 0.937967i | \(-0.387294\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2.21786e7i | − 0.951867i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.26973e6 | −0.182218 | −0.0911089 | − | 0.995841i | \(-0.529041\pi\) | ||||
−0.0911089 | + | 0.995841i | \(0.529041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.37011e6 | −0.0581436 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.45665e7i | − 0.614695i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 3.62097e7i | − 1.51948i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.12198e7 | 1.30278 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.15671e7 | 2.13989 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.22993e7i | 1.74556i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.79470e6i | 0.237804i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −236230. | −0.00964087 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.96922e6 | −0.0799230 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 3.88728e7i | − 1.56902i | −0.620119 | − | 0.784508i | \(-0.712916\pi\) | ||||
0.620119 | − | 0.784508i | \(-0.287084\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 961532.i | − 0.0385970i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.73840e7 | 1.09320 | 0.546602 | − | 0.837393i | \(-0.315921\pi\) | ||||
0.546602 | + | 0.837393i | \(0.315921\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.82962e7 | 0.726414 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1.79513e7i | − 0.708831i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.22576e6i | 0.165952i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.14731e7 | 1.22928 | 0.614640 | − | 0.788808i | \(-0.289301\pi\) | ||||
0.614640 | + | 0.788808i | \(0.289301\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.11728e7 | −1.59942 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.14119e7i | 0.827277i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.10026e6i | 0.157564i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.45931e6 | −0.0557761 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.58150e7 | −0.981371 | −0.490685 | − | 0.871337i | \(-0.663254\pi\) | ||||
−0.490685 | + | 0.871337i | \(0.663254\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.25139e7i | 1.22941i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.80243e7i | 1.43007i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.43186e6 | −0.0909723 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.77379e7 | −0.660014 | −0.330007 | − | 0.943979i | \(-0.607051\pi\) | ||||
−0.330007 | + | 0.943979i | \(0.607051\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.45265e7i | 1.64799i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 3.65458e7i | − 1.34544i | −0.739898 | − | 0.672719i | \(-0.765126\pi\) | ||||
0.739898 | − | 0.672719i | \(-0.234874\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.87348e7 | 1.05227 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.77139e6 | 0.137380 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.00234e7i | − 1.45024i | −0.688623 | − | 0.725119i | \(-0.741785\pi\) | ||||
0.688623 | − | 0.725119i | \(-0.258215\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 4.26134e7i | − 1.53596i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.46250e7 | 0.882928 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.61525e7 | 0.576114 | 0.288057 | − | 0.957613i | \(-0.406991\pi\) | ||||
0.288057 | + | 0.957613i | \(0.406991\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1.87204e7i | − 0.664213i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.92001e7i | − 0.677680i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.11941e6 | −0.144640 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.68683e7 | 1.63708 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 966579.i | 0.0335870i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1.19714e7i | − 0.413833i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.46946e7 | −0.505349 | −0.252674 | − | 0.967551i | \(-0.581310\pi\) | ||||
−0.252674 | + | 0.967551i | \(0.581310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.62546e6 | −0.226676 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 2.33873e7i | − 0.796034i | −0.917378 | − | 0.398017i | \(-0.869698\pi\) | ||||
0.917378 | − | 0.398017i | \(-0.130302\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.02120e6i | − 0.0345803i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.91524e7 | 0.645225 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.68638e7 | 1.23556 | 0.617779 | − | 0.786351i | \(-0.288032\pi\) | ||||
0.617779 | + | 0.786351i | \(0.288032\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.43063e7i | 0.810519i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.33970e6i | − 0.0444462i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.35629e7 | 0.447682 | 0.223841 | − | 0.974626i | \(-0.428140\pi\) | ||||
0.223841 | + | 0.974626i | \(0.428140\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.33135e7 | −1.42243 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.25444e6i | 0.204360i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.34190e6i | 0.0761338i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.33321e7 | 1.07815 | 0.539074 | − | 0.842258i | \(-0.318774\pi\) | ||||
0.539074 | + | 0.842258i | \(0.318774\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.74819e7 | −0.562620 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.05716e7i | 0.658735i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 3.52048e6i | − 0.112167i | −0.998426 | − | 0.0560833i | \(-0.982139\pi\) | ||||
0.998426 | − | 0.0560833i | \(-0.0178612\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.25005e7 | −0.396291 |
(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 | 128.6.b.d.65.3 | yes | 4 | |
4.3 | odd | 2 | inner | 128.6.b.d.65.1 | ✓ | 4 | |
8.3 | odd | 2 | inner | 128.6.b.d.65.4 | yes | 4 | |
8.5 | even | 2 | inner | 128.6.b.d.65.2 | yes | 4 | |
16.3 | odd | 4 | 256.6.a.m.1.3 | 4 | |||
16.5 | even | 4 | 256.6.a.m.1.4 | 4 | |||
16.11 | odd | 4 | 256.6.a.m.1.2 | 4 | |||
16.13 | even | 4 | 256.6.a.m.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.6.b.d.65.1 | ✓ | 4 | 4.3 | odd | 2 | inner | |
128.6.b.d.65.2 | yes | 4 | 8.5 | even | 2 | inner | |
128.6.b.d.65.3 | yes | 4 | 1.1 | even | 1 | trivial | |
128.6.b.d.65.4 | yes | 4 | 8.3 | odd | 2 | inner | |
256.6.a.m.1.1 | 4 | 16.13 | even | 4 | |||
256.6.a.m.1.2 | 4 | 16.11 | odd | 4 | |||
256.6.a.m.1.3 | 4 | 16.3 | odd | 4 | |||
256.6.a.m.1.4 | 4 | 16.5 | even | 4 |