Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(161,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.161");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 384x^{6} + 506x^{5} + 49869x^{4} + 29654x^{3} - 2235516x^{2} - 1528906x + 34180205 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.3 | ||
Root | \(-7.33903 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.161 |
Dual form | 320.6.d.b.161.6 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 15.6781i | − 1.00575i | −0.864360 | − | 0.502874i | \(-0.832276\pi\) | ||||
0.864360 | − | 0.502874i | \(-0.167724\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 25.0000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −164.681 | −1.27028 | −0.635139 | − | 0.772398i | \(-0.719057\pi\) | ||||
−0.635139 | + | 0.772398i | \(0.719057\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.80186 | −0.0115303 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 744.619i | − 1.85546i | −0.373249 | − | 0.927731i | \(-0.621756\pi\) | ||||
0.373249 | − | 0.927731i | \(-0.378244\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 873.876i | − 1.43414i | −0.697001 | − | 0.717070i | \(-0.745483\pi\) | ||||
0.697001 | − | 0.717070i | \(-0.254517\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −391.952 | −0.449784 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 984.464 | 0.826185 | 0.413093 | − | 0.910689i | \(-0.364449\pi\) | ||||
0.413093 | + | 0.910689i | \(0.364449\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1149.05i | 0.730223i | 0.930964 | + | 0.365111i | \(0.118969\pi\) | ||||
−0.930964 | + | 0.365111i | \(0.881031\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2581.88i | 1.27758i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 578.171 | 0.227896 | 0.113948 | − | 0.993487i | \(-0.463650\pi\) | ||||
0.113948 | + | 0.993487i | \(0.463650\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 3765.84i | − 0.994152i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 5863.72i | − 1.29473i | −0.762181 | − | 0.647364i | \(-0.775871\pi\) | ||||
0.762181 | − | 0.647364i | \(-0.224129\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9825.27 | −1.83629 | −0.918143 | − | 0.396249i | \(-0.870312\pi\) | ||||
−0.918143 | + | 0.396249i | \(0.870312\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11674.2 | −1.86613 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4117.03i | 0.568085i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 7885.71i | − 0.946970i | −0.880802 | − | 0.473485i | \(-0.842996\pi\) | ||||
0.880802 | − | 0.473485i | \(-0.157004\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13700.7 | −1.44238 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10485.2 | 0.974131 | 0.487066 | − | 0.873365i | \(-0.338067\pi\) | ||||
0.487066 | + | 0.873365i | \(0.338067\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19074.5i | 1.57320i | 0.617465 | + | 0.786598i | \(0.288160\pi\) | ||||
−0.617465 | + | 0.786598i | \(0.711840\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 70.0464i | 0.00515650i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2973.28 | 0.196332 | 0.0981659 | − | 0.995170i | \(-0.468702\pi\) | ||||
0.0981659 | + | 0.995170i | \(0.468702\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10312.8 | 0.613604 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 15434.5i | − 0.830935i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 35972.1i | 1.75904i | 0.475860 | + | 0.879521i | \(0.342137\pi\) | ||||
−0.475860 | + | 0.879521i | \(0.657863\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18615.5 | −0.829788 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18014.9 | 0.734421 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 19390.0i | − 0.725183i | −0.931948 | − | 0.362592i | \(-0.881892\pi\) | ||||
0.931948 | − | 0.362592i | \(-0.118108\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 37812.2i | 1.30109i | 0.759468 | + | 0.650544i | \(0.225459\pi\) | ||||
−0.759468 | + | 0.650544i | \(0.774541\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 461.413 | 0.0146466 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21846.9 | −0.641367 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11395.7i | − 0.310137i | −0.987904 | − | 0.155069i | \(-0.950440\pi\) | ||||
0.987904 | − | 0.155069i | \(-0.0495599\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 9064.61i | − 0.229206i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 33932.2 | 0.798851 | 0.399425 | − | 0.916766i | \(-0.369210\pi\) | ||||
0.399425 | + | 0.916766i | \(0.369210\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 22794.6 | 0.500640 | 0.250320 | − | 0.968163i | \(-0.419464\pi\) | ||||
0.250320 | + | 0.968163i | \(0.419464\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9798.79i | 0.201150i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 122625.i | 2.35695i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −94753.9 | −1.70816 | −0.854082 | − | 0.520139i | \(-0.825880\pi\) | ||||
−0.854082 | + | 0.520139i | \(0.825880\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −59722.0 | −1.01140 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 34722.9i | − 0.553249i | −0.960978 | − | 0.276625i | \(-0.910784\pi\) | ||||
0.960978 | − | 0.276625i | \(-0.0892158\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 24611.6i | − 0.369481i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −91931.8 | −1.30217 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −42021.6 | −0.562338 | −0.281169 | − | 0.959658i | \(-0.590722\pi\) | ||||
−0.281169 | + | 0.959658i | \(0.590722\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 143911.i | 1.82176i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 154041.i | 1.84684i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 28726.3 | 0.326566 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11466.2 | −0.123734 | −0.0618672 | − | 0.998084i | \(-0.519706\pi\) | ||||
−0.0618672 | + | 0.998084i | \(0.519706\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2086.31i | 0.0213940i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 65173.4i | 0.635722i | 0.948137 | + | 0.317861i | \(0.102964\pi\) | ||||
−0.948137 | + | 0.317861i | \(0.897036\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 47472.7 | 0.440911 | 0.220455 | − | 0.975397i | \(-0.429246\pi\) | ||||
0.220455 | + | 0.975397i | \(0.429246\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 64547.0 | 0.571351 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 93432.1i | − 0.788927i | −0.918912 | − | 0.394464i | \(-0.870930\pi\) | ||||
0.918912 | − | 0.394464i | \(-0.129070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 164332.i | 1.32482i | 0.749143 | + | 0.662408i | \(0.230466\pi\) | ||||
−0.749143 | + | 0.662408i | \(0.769534\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −123633. | −0.952414 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 162453. | 1.19683 | 0.598415 | − | 0.801186i | \(-0.295797\pi\) | ||||
0.598415 | + | 0.801186i | \(0.295797\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 14454.3i | − 0.101918i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2448.48i | 0.0165360i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −162122. | −1.04948 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −393406. | −2.44274 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 164388.i | − 0.979731i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −127181. | −0.699700 | −0.349850 | − | 0.936806i | \(-0.613767\pi\) | ||||
−0.349850 | + | 0.936806i | \(0.613767\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 299052. | 1.58224 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 192224.i | 0.978655i | 0.872100 | + | 0.489328i | \(0.162758\pi\) | ||||
−0.872100 | + | 0.489328i | \(0.837242\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 189227.i | − 0.927585i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −94146.1 | −0.444598 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 354980. | 1.61586 | 0.807928 | − | 0.589281i | \(-0.200589\pi\) | ||||
0.807928 | + | 0.589281i | \(0.200589\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 38205.1i | − 0.167720i | −0.996478 | − | 0.0838600i | \(-0.973275\pi\) | ||||
0.996478 | − | 0.0838600i | \(-0.0267248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 46615.2i | − 0.197460i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −650704. | −2.66099 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −146593. | −0.579020 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 161686.i | − 0.617132i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 135301.i | − 0.499271i | −0.968340 | − | 0.249636i | \(-0.919689\pi\) | ||||
0.968340 | − | 0.249636i | \(-0.0803108\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −219371. | −0.782955 | −0.391477 | − | 0.920188i | \(-0.628036\pi\) | ||||
−0.391477 | + | 0.920188i | \(0.628036\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2758.33 | −0.00952614 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 245632.i | 0.821212i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 99927.5i | − 0.323546i | −0.986828 | − | 0.161773i | \(-0.948279\pi\) | ||||
0.986828 | − | 0.161773i | \(-0.0517212\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 563973. | 1.76915 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −95213.9 | −0.289491 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 386516.i | 1.13946i | 0.821833 | + | 0.569729i | \(0.192952\pi\) | ||||
−0.821833 | + | 0.569729i | \(0.807048\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 291855.i | 0.834558i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 317945. | 0.882187 | 0.441094 | − | 0.897461i | \(-0.354591\pi\) | ||||
0.441094 | + | 0.897461i | \(0.354591\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −392367. | −1.05676 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 3219.48i | − 0.00841967i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 142037.i | − 0.360815i | −0.983592 | − | 0.180408i | \(-0.942258\pi\) | ||||
0.983592 | − | 0.180408i | \(-0.0577417\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 102926. | 0.254055 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −303998. | −0.729352 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 461274.i | − 1.07603i | −0.842934 | − | 0.538017i | \(-0.819173\pi\) | ||||
0.842934 | − | 0.538017i | \(-0.180827\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 117514.i | 0.266620i | 0.991074 | + | 0.133310i | \(0.0425607\pi\) | ||||
−0.991074 | + | 0.133310i | \(0.957439\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 592822. | 1.30857 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −197143. | −0.423498 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 733050.i | − 1.53296i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 620163.i | 1.26285i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −226621. | −0.449486 | −0.224743 | − | 0.974418i | \(-0.572154\pi\) | ||||
−0.224743 | + | 0.974418i | \(0.572154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21404.0 | −0.0413620 | −0.0206810 | − | 0.999786i | \(-0.506583\pi\) | ||||
−0.0206810 | + | 0.999786i | \(0.506583\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 342517.i | 0.645054i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 707471.i | − 1.29880i | −0.760446 | − | 0.649401i | \(-0.775020\pi\) | ||||
0.760446 | − | 0.649401i | \(-0.224980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 387592. | 0.693812 | 0.346906 | − | 0.937900i | \(-0.387232\pi\) | ||||
0.346906 | + | 0.937900i | \(0.387232\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −178663. | −0.311920 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 965644.i | 1.64466i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 262130.i | − 0.435645i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1619.95 | −0.00262771 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 855605. | 1.35490 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 209622.i | − 0.324139i | −0.986779 | − | 0.162070i | \(-0.948183\pi\) | ||||
0.986779 | − | 0.162070i | \(-0.0518169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 531991.i | − 0.803443i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 476863. | 0.703555 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.61804e6 | 2.33259 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 357376.i | − 0.503518i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 860299.i | − 1.18487i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 454449. | 0.611960 | 0.305980 | − | 0.952038i | \(-0.401016\pi\) | ||||
0.305980 | + | 0.952038i | \(0.401016\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1751.16 | 0.00230606 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 569941.i | − 0.734117i | −0.930198 | − | 0.367059i | \(-0.880365\pi\) | ||||
0.930198 | − | 0.367059i | \(-0.119635\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 319567.i | − 0.402692i | −0.979520 | − | 0.201346i | \(-0.935468\pi\) | ||||
0.979520 | − | 0.201346i | \(-0.0645316\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.92252e6 | 2.37050 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 313094. | 0.377820 | 0.188910 | − | 0.981994i | \(-0.439505\pi\) | ||||
0.188910 | + | 0.981994i | \(0.439505\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 74331.9i | − 0.0878023i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.48556e6i | 1.71798i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 129520. | 0.146671 | 0.0733353 | − | 0.997307i | \(-0.476636\pi\) | ||||
0.0733353 | + | 0.997307i | \(0.476636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.61051e6 | −1.78616 | −0.893081 | − | 0.449897i | \(-0.851461\pi\) | ||||
−0.893081 | + | 0.449897i | \(0.851461\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21225.8i | 0.0230594i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 257821.i | − 0.274412i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00413e6 | 1.04724 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −544388. | −0.556429 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 196054.i | − 0.196422i | −0.995166 | − | 0.0982111i | \(-0.968688\pi\) | ||||
0.995166 | − | 0.0982111i | \(-0.0313120\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 430517.i | − 0.422853i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −385862. | −0.371605 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.58199e6 | −1.49407 | −0.747034 | − | 0.664786i | \(-0.768523\pi\) | ||||
−0.747034 | + | 0.664786i | \(0.768523\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.29863e6i | 1.20291i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16429.3i | 0.0149286i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 231519. | 0.206394 | 0.103197 | − | 0.994661i | \(-0.467093\pi\) | ||||
0.103197 | + | 0.994661i | \(0.467093\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 899303. | 0.786668 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 658818.i | 0.565571i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 2.34536e6i | − 1.97619i | −0.153841 | − | 0.988096i | \(-0.549164\pi\) | ||||
0.153841 | − | 0.988096i | \(-0.450836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 398969. | 0.330002 | 0.165001 | − | 0.986293i | \(-0.447237\pi\) | ||||
0.165001 | + | 0.986293i | \(0.447237\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.25624e6 | 1.83223 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 465387.i | 0.371092i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.74046e6i | − 1.36290i | −0.731863 | − | 0.681451i | \(-0.761349\pi\) | ||||
0.731863 | − | 0.681451i | \(-0.238651\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 27529.0 | 0.0211729 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −812193. | −0.613612 | −0.306806 | − | 0.951772i | \(-0.599260\pi\) | ||||
−0.306806 | + | 0.951772i | \(0.599260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 516938.i | − 0.383683i | −0.981426 | − | 0.191841i | \(-0.938554\pi\) | ||||
0.981426 | − | 0.191841i | \(-0.0614459\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 450373.i | − 0.328443i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.72672e6 | −1.23742 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −450688. | −0.317418 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 179768.i | 0.124446i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.78836e6i | 1.21699i | 0.793558 | + | 0.608495i | \(0.208227\pi\) | ||||
−0.793558 | + | 0.608495i | \(0.791773\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −484750. | −0.324312 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.80412e6 | −1.84461 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 505250.i | − 0.326835i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3.14121e6i | − 1.99839i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.02179e6 | 0.639376 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 945304. | 0.581865 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 804925.i | − 0.487427i | −0.969847 | − | 0.243713i | \(-0.921634\pi\) | ||||
0.969847 | − | 0.243713i | \(-0.0783656\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 744280.i | − 0.443445i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −478186. | −0.280347 | −0.140173 | − | 0.990127i | \(-0.544766\pi\) | ||||
−0.140173 | + | 0.990127i | \(0.544766\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.14478e6 | 1.81439 | 0.907194 | − | 0.420713i | \(-0.138220\pi\) | ||||
0.907194 | + | 0.420713i | \(0.138220\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 11535.3i | − 0.00655018i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.93977e6i | − 1.08418i | −0.840320 | − | 0.542090i | \(-0.817633\pi\) | ||||
0.840320 | − | 0.542090i | \(-0.182367\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.36624e6 | −2.40232 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.46484e6 | −0.793462 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.13120e6i | 0.603299i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 546173.i | 0.286828i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.57641e6 | 1.33243 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −489642. | −0.249396 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 3.59866e6i | − 1.80539i | −0.430281 | − | 0.902695i | \(-0.641586\pi\) | ||||
0.430281 | − | 0.902695i | \(-0.358414\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22094.6i | 0.0109188i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −284893. | −0.138698 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.58986e6 | 0.762577 | 0.381289 | − | 0.924456i | \(-0.375480\pi\) | ||||
0.381289 | + | 0.924456i | \(0.375480\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 2.54695e6i | − 1.20371i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.31608e6i | 3.40716i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.06946e6 | 0.490830 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −226615. | −0.102504 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.16369e6i | 0.964655i | 0.875991 | + | 0.482327i | \(0.160208\pi\) | ||||
−0.875991 | + | 0.482327i | \(0.839792\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 403328.i | 0.177253i | 0.996065 | + | 0.0886267i | \(0.0282478\pi\) | ||||
−0.996065 | + | 0.0886267i | \(0.971752\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.29088e6 | −1.42575 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −74007.2 | −0.0316109 | −0.0158055 | − | 0.999875i | \(-0.505031\pi\) | ||||
−0.0158055 | + | 0.999875i | \(0.505031\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 848304.i | − 0.357257i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.54177e6i | 1.05552i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.37764e6 | 1.79269 | 0.896343 | − | 0.443361i | \(-0.146214\pi\) | ||||
0.896343 | + | 0.443361i | \(0.146214\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.15578e6 | 0.466775 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.16784e6i | 2.45678i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 569866.i | − 0.223893i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 547770. | 0.212292 | 0.106146 | − | 0.994351i | \(-0.466149\pi\) | ||||
0.106146 | + | 0.994351i | \(0.466149\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −29378.1 | −0.0112320 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 5.92393e6i | − 2.23447i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1.33289e6i | − 0.496045i | −0.968754 | − | 0.248023i | \(-0.920219\pi\) | ||||
0.968754 | − | 0.248023i | \(-0.0797807\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 244970. | 0.0899569 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.12417e6 | −1.85682 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.65535e6i | 1.30717i | 0.756855 | + | 0.653583i | \(0.226735\pi\) | ||||
−0.756855 | + | 0.653583i | \(0.773265\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.99395e6i | 0.703722i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.69148e6 | −1.28589 | −0.642945 | − | 0.765913i | \(-0.722287\pi\) | ||||
−0.642945 | + | 0.765913i | \(0.722287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.06561e6 | 1.05406 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 53444.1i | − 0.0181394i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.20539e6i | 0.403880i | 0.979398 | + | 0.201940i | \(0.0647247\pi\) | ||||
−0.979398 | + | 0.201940i | \(0.935275\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 569189. | 0.188284 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.01370e6 | 0.984281 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.36885e6i | 0.763914i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.96565e6i | 1.26281i | 0.775453 | + | 0.631406i | \(0.217522\pi\) | ||||
−0.775453 | + | 0.631406i | \(0.782478\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.96671e6 | −0.932918 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.45029e6 | 0.760951 | 0.380475 | − | 0.924791i | \(-0.375760\pi\) | ||||
0.380475 | + | 0.924791i | \(0.375760\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.58607e6i | 2.63349i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.49305e6i | 0.452311i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.87184e6 | −1.75707 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.78101e6 | −1.41323 | −0.706613 | − | 0.707600i | \(-0.749778\pi\) | ||||
−0.706613 | + | 0.707600i | \(0.749778\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 5.56540e6i | − 1.62514i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.19316e6i | 0.921183i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −868072. | −0.247420 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −598983. | −0.168684 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.46113e6i | 0.406586i | 0.979118 | + | 0.203293i | \(0.0651645\pi\) | ||||
−0.979118 | + | 0.203293i | \(0.934836\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 5.32662e6i | − 1.46469i | −0.680932 | − | 0.732347i | \(-0.738425\pi\) | ||||
0.680932 | − | 0.732347i | \(-0.261575\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8330.70 | −0.00226376 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −615290. | −0.165237 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6.22695e6i | − 1.65274i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.02018e7i | 2.67629i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 363772. | 0.0943270 | 0.0471635 | − | 0.998887i | \(-0.484982\pi\) | ||||
0.0471635 | + | 0.998887i | \(0.484982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.45960e6 | −1.14308 | −0.571540 | − | 0.820574i | \(-0.693654\pi\) | ||||
−0.571540 | + | 0.820574i | \(0.693654\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.29830e6i | 0.582348i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 664349.i | 0.166415i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.13055e6 | 1.27058 | 0.635290 | − | 0.772273i | \(-0.280880\pi\) | ||||
0.635290 | + | 0.772273i | \(0.280880\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −28895.1 | −0.00707503 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 320762.i | − 0.0776557i | −0.999246 | − | 0.0388279i | \(-0.987638\pi\) | ||||
0.999246 | − | 0.0388279i | \(-0.0123624\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.05054e6i | 0.251485i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.12126e6 | −0.502141 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 557835. | 0.130584 | 0.0652920 | − | 0.997866i | \(-0.479202\pi\) | ||||
0.0652920 | + | 0.997866i | \(0.479202\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 7.80748e6i | − 1.80746i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.43931e6i | 0.787456i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.59777e6 | 0.814714 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.78896e6 | −0.624672 | −0.312336 | − | 0.949972i | \(-0.601112\pi\) | ||||
−0.312336 | + | 0.949972i | \(0.601112\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 3.70734e6i | − 0.821354i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 733222.i | − 0.160688i | −0.996767 | − | 0.0803439i | \(-0.974398\pi\) | ||||
0.996767 | − | 0.0803439i | \(-0.0256019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.80938e6 | −1.47623 | −0.738117 | − | 0.674672i | \(-0.764285\pi\) | ||||
−0.738117 | + | 0.674672i | \(0.764285\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.85103e6 | 0.825933 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.33064e6i | 0.706701i | 0.935491 | + | 0.353351i | \(0.114958\pi\) | ||||
−0.935491 | + | 0.353351i | \(0.885042\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.87666e6i | 0.393960i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.56667e6 | −0.325406 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.42033e7 | 2.91901 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 718157.i | − 0.146045i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 100789.i | − 0.0202822i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.58735e6 | −1.31181 | −0.655907 | − | 0.754842i | \(-0.727713\pi\) | ||||
−0.655907 | + | 0.754842i | \(0.727713\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.89113e6 | −1.35809 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.49277e6i | 0.291156i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 286655.i | 0.0553357i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.26167e6 | 0.623186 | 0.311593 | − | 0.950216i | \(-0.399137\pi\) | ||||
0.311593 | + | 0.950216i | \(0.399137\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.05982e6 | 1.14601 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 5.26941e6i | − 0.986412i | −0.869912 | − | 0.493206i | \(-0.835825\pi\) | ||||
0.869912 | − | 0.493206i | \(-0.164175\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.77262e6i | − 1.06968i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 52157.9 | 0.00956768 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.58798e6 | −1.01476 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.56847e6i | 0.821333i | 0.911786 | + | 0.410666i | \(0.134704\pi\) | ||||
−0.911786 | + | 0.410666i | \(0.865296\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 4.98476e6i | − 0.887259i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.34743e6 | −1.11861 | −0.559304 | − | 0.828962i | \(-0.688932\pi\) | ||||
−0.559304 | + | 0.828962i | \(0.688932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.62933e6 | 0.284303 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.15155e6i | 1.06283i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 5.80648e6i | − 0.993388i | −0.867926 | − | 0.496694i | \(-0.834547\pi\) | ||||
0.867926 | − | 0.496694i | \(-0.165453\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.75384e6 | −0.635951 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.32715e6 | 0.725953 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 1.18682e6i | − 0.197181i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.21396e6i | − 0.364286i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.22686e6 | −0.362889 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.75153e6 | −1.57390 | −0.786952 | − | 0.617014i | \(-0.788342\pi\) | ||||
−0.786952 | + | 0.617014i | \(0.788342\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.86264e6i | 1.41680i | 0.705811 | + | 0.708401i | \(0.250583\pi\) | ||||
−0.705811 | + | 0.708401i | \(0.749417\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1.61368e6i | − 0.255516i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.67262e6 | −1.51711 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.10206e6 | −0.948063 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 54328.0i | 0.00836156i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 9.16277e6i | − 1.39704i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.33580e6 | −0.352819 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.23188e6 | −1.08222 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 7.67914e6i | − 1.13852i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.43686e6i | 1.09244i | 0.837643 | + | 0.546218i | \(0.183933\pi\) | ||||
−0.837643 | + | 0.546218i | \(0.816067\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.84239e6 | 0.268153 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.10830e6 | 0.592476 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 6.65237e6i | − 0.950623i | −0.879818 | − | 0.475311i | \(-0.842335\pi\) | ||||
0.879818 | − | 0.475311i | \(-0.157665\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 105944.i | − 0.0150019i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.73772e6 | 0.945440 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.56042e7 | 2.16984 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.09082e6i | 0.425932i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1.02580e6i | − 0.140095i | −0.997544 | − | 0.0700477i | \(-0.977685\pi\) | ||||
0.997544 | − | 0.0700477i | \(-0.0223152\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.66688e7 | 2.25618 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.14928e7 | −1.54177 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.06816e6i | 0.407950i | 0.978976 | + | 0.203975i | \(0.0653861\pi\) | ||||
−0.978976 | + | 0.203975i | \(0.934614\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 4.06133e6i | − 0.535239i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.83508e6 | 1.28475 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.05690e7 | −1.36853 | −0.684263 | − | 0.729236i | \(-0.739876\pi\) | ||||
−0.684263 | + | 0.729236i | \(0.739876\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.22219e7i | 1.56873i | 0.620298 | + | 0.784366i | \(0.287012\pi\) | ||||
−0.620298 | + | 0.784366i | \(0.712988\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.55298e6i | 0.452070i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −361357. | −0.0455792 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.08742e6 | 0.386061 | 0.193031 | − | 0.981193i | \(-0.438168\pi\) | ||||
0.193031 | + | 0.981193i | \(0.438168\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 335573.i | 0.0415998i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.71820e6i | 0.702780i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.67855e7 | 3.26384 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 61211.9 | 0.00739514 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 7.45584e6i | − 0.893103i | −0.894758 | − | 0.446551i | \(-0.852652\pi\) | ||||
0.894758 | − | 0.446551i | \(-0.147348\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.12897e7i | − 1.34090i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.10918e7 | −1.30627 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.10599e7 | 1.29156 | 0.645780 | − | 0.763523i | \(-0.276532\pi\) | ||||
0.645780 | + | 0.763523i | \(0.276532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.05306e6i | 0.469344i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 6.07669e6i | − 0.697800i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.08444e7 | −1.23492 | −0.617460 | − | 0.786602i | \(-0.711838\pi\) | ||||
−0.617460 | + | 0.786602i | \(0.711838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.41110e6 | 0.272289 | 0.136144 | − | 0.990689i | \(-0.456529\pi\) | ||||
0.136144 | + | 0.990689i | \(0.456529\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31929.1i | 0.00357597i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.83515e6i | 1.09243i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.25003e7 | 1.37704 | 0.688521 | − | 0.725216i | \(-0.258260\pi\) | ||||
0.688521 | + | 0.725216i | \(0.258260\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.51394e7 | 1.65412 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2.59828e6i | − 0.281567i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.22386e6i | 0.454002i | 0.973894 | + | 0.227001i | \(0.0728921\pi\) | ||||
−0.973894 | + | 0.227001i | \(0.927108\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.10970e6 | −0.438149 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.02123e7 | 1.07997 | 0.539984 | − | 0.841675i | \(-0.318430\pi\) | ||||
0.539984 | + | 0.841675i | \(0.318430\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 458202.i | 0.0480651i | 0.999711 | + | 0.0240326i | \(0.00765054\pi\) | ||||
−0.999711 | + | 0.0240326i | \(0.992349\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.17730e6i | − 0.226563i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.92016e6 | 0.714325 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.34142e7i | − 1.36269i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 7.76319e6i | − 0.782373i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.10444e7 | 1.10426 | 0.552128 | − | 0.833760i | \(-0.313816\pi\) | ||||
0.552128 | + | 0.833760i | \(0.313816\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.28647e6 | −0.326002 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.17952e6i | 0.312915i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 9.01215e6i | − 0.879994i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −95073.1 | −0.00921097 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.64212e7 | −1.57856 | −0.789278 | − | 0.614036i | \(-0.789545\pi\) | ||||
−0.789278 | + | 0.614036i | \(0.789545\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.96664e6i | 0.664501i | 0.943191 | + | 0.332251i | \(0.107808\pi\) | ||||
−0.943191 | + | 0.332251i | \(0.892192\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 7.47630e6i | − 0.707599i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.37322e7 | 1.28967 | 0.644834 | − | 0.764322i | \(-0.276926\pi\) | ||||
0.644834 | + | 0.764322i | \(0.276926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.44381e7 | −1.34555 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 2.53677e7i | − 2.34600i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.32515e7i | 1.21613i | 0.793886 | + | 0.608067i | \(0.208055\pi\) | ||||
−0.793886 | + | 0.608067i | \(0.791945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.80560e6 | 0.437668 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −63867.3 | −0.00577251 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.01216e6i | − 0.0907892i | −0.998969 | − | 0.0453946i | \(-0.985545\pi\) | ||||
0.998969 | − | 0.0453946i | \(-0.0144545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 2.17387e7i | − 1.93522i | −0.252447 | − | 0.967611i | \(-0.581235\pi\) | ||||
0.252447 | − | 0.967611i | \(-0.418765\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.34878e7 | −1.19168 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.73067e6 | −0.414829 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 3.39024e6i | − 0.295063i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 7.12489e6i | − 0.615478i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.81556e7 | 2.41412 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.30341e6 | −0.621567 | −0.310783 | − | 0.950481i | \(-0.600591\pi\) | ||||
−0.310783 | + | 0.950481i | \(0.600591\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.35365e6i | 0.198830i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.35855e6i | 0.700905i | 0.936580 | + | 0.350453i | \(0.113972\pi\) | ||||
−0.936580 | + | 0.350453i | \(0.886028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.88827e6 | 0.157177 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.93558e6 | −0.738337 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.85500e7i | 1.52157i | 0.649004 | + | 0.760785i | \(0.275186\pi\) | ||||
−0.649004 | + | 0.760785i | \(0.724814\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 8.87450e6i | − 0.722633i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.01020e6 | −0.405007 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.14352e7 | 2.52271 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 858046.i | − 0.0683621i | −0.999416 | − | 0.0341810i | \(-0.989118\pi\) | ||||
0.999416 | − | 0.0341810i | \(-0.0108823\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 343576.i | − 0.0271763i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −955128. | −0.0750066 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.03223e7 | 0.804813 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 4.90871e6i | − 0.379992i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.28710e7i | 1.75788i | 0.476928 | + | 0.878942i | \(0.341750\pi\) | ||||
−0.476928 | + | 0.878942i | \(0.658250\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.06108e6 | 0.691499 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.16538e6 | −0.0883070 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.07328e7i | − 0.807543i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.64348e6i | − 0.122786i | −0.998114 | − | 0.0613930i | \(-0.980446\pi\) | ||||
0.998114 | − | 0.0613930i | \(-0.0195543\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 265487. | 0.0196956 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.68069e6 | −0.418483 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.62676e7i | 1.19003i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.03063e6i | − 0.147514i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.22486e6 | 0.0883614 | 0.0441807 | − | 0.999024i | \(-0.485932\pi\) | ||||
0.0441807 | + | 0.999024i | \(0.485932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.81785e6 | −0.560079 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.52497e7i | 1.79643i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.66483e6i | 0.258945i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.07644e7 | −0.755362 | −0.377681 | − | 0.925936i | \(-0.623278\pi\) | ||||
−0.377681 | + | 0.925936i | \(0.623278\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.41797e7 | −0.988205 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.87782e7i | 1.29975i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.45041e7i | − 1.68453i | −0.539065 | − | 0.842264i | \(-0.681222\pi\) | ||||
0.539065 | − | 0.842264i | \(-0.318778\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.04214e6 | −0.275990 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.48545e6 | −0.575448 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.80906e7i | − 1.21855i | −0.792960 | − | 0.609274i | \(-0.791461\pi\) | ||||
0.792960 | − | 0.609274i | \(-0.208539\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1.57428e7i | − 1.05326i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.48284e6 | 0.497272 | 0.248636 | − | 0.968597i | \(-0.420018\pi\) | ||||
0.248636 | + | 0.968597i | \(0.420018\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.38253e6 | −0.223281 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 97288.6i | 0.00637911i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.53865e7i | 1.00216i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.46162e6 | −0.159265 | −0.0796326 | − | 0.996824i | \(-0.525375\pi\) | ||||
−0.0796326 | + | 0.996824i | \(0.525375\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.07374e6 | −0.197551 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.48427e6i | 0.350148i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.46510e7i | 0.929239i | 0.885511 | + | 0.464619i | \(0.153809\pi\) | ||||
−0.885511 | + | 0.464619i | \(0.846191\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.74968e6 | −0.425284 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.15721e6 | 0.385409 | 0.192705 | − | 0.981257i | \(-0.438274\pi\) | ||||
0.192705 | + | 0.981257i | \(0.438274\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.70624e7i | − 1.68288i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 68958.2i | 0.00426022i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.69445e7 | −1.04001 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.10066e7 | 1.28097 | 0.640485 | − | 0.767970i | \(-0.278733\pi\) | ||||
0.640485 | + | 0.767970i | \(0.278733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.48025e7i | 1.50266i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 3.38948e6i | − 0.204025i | −0.994783 | − | 0.102013i | \(-0.967472\pi\) | ||||
0.994783 | − | 0.102013i | \(-0.0325282\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.14079e6 | 0.367257 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.03600e7 | 1.20983 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.20480e7i | 0.711333i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 2.52665e7i | − 1.48224i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.20819e7 | −1.28716 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.49819e6 | −0.144694 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.56364e7i | − 0.899914i | −0.893050 | − | 0.449957i | \(-0.851439\pi\) | ||||
0.893050 | − | 0.449957i | \(-0.148561\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 3.62977e6i | − 0.207580i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.67530e7 | −1.52031 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.30432e7 | 1.86594 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.40993e7i | − 0.791190i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2.17344e7i | − 1.21200i | −0.795466 | − | 0.605998i | \(-0.792774\pi\) | ||||
0.795466 | − | 0.605998i | \(-0.207226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.92708e6 | 0.162206 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 117739. | 0.00648391 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.69733e7i | − 0.928918i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.38035e6i | 0.129464i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.67707e7 | −1.98755 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.12327e7 | −1.67779 | −0.838897 | − | 0.544290i | \(-0.816799\pi\) | ||||
−0.838897 | + | 0.544290i | \(0.816799\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.82163e7i | − 0.972542i | −0.873808 | − | 0.486271i | \(-0.838357\pi\) | ||||
0.873808 | − | 0.486271i | \(-0.161643\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 6.25507e6i | − 0.331899i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.66290e6 | 0.509581 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.19176e7 | −1.14878 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 403218.i | − 0.0210053i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.38146e7i | 0.715286i | 0.933858 | + | 0.357643i | \(0.116420\pi\) | ||||
−0.933858 | + | 0.357643i | \(0.883580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.00873e7 | −0.519131 | −0.259566 | − | 0.965725i | \(-0.583579\pi\) | ||||
−0.259566 | + | 0.965725i | \(0.583579\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.29636e6 | 0.373226 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.12662e7i | 0.572813i | 0.958108 | + | 0.286406i | \(0.0924607\pi\) | ||||
−0.958108 | + | 0.286406i | \(0.907539\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 2.16824e6i | − 0.109577i | −0.998498 | − | 0.0547886i | \(-0.982552\pi\) | ||||
0.998498 | − | 0.0547886i | \(-0.0174485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.72871e7 | −1.37074 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.01526e7 | 0.506951 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 7.94862e6i | − 0.394526i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.70004e7i | 1.82555i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.39434e7 | −0.683856 | −0.341928 | − | 0.939726i | \(-0.611080\pi\) | ||||
−0.341928 | + | 0.939726i | \(0.611080\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.38721e7 | −0.676319 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.27336e7i | 0.617139i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.80917e6i | 0.472596i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.47865e7 | 3.10296 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.10459e6 | −0.385889 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 4.55929e6i | − 0.215811i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.37458e7i | 1.11741i | 0.829365 | + | 0.558707i | \(0.188702\pi\) | ||||
−0.829365 | + | 0.558707i | \(0.811298\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −80486.9 | −0.00376539 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.77323e7 | 1.28983 | 0.644917 | − | 0.764253i | \(-0.276892\pi\) | ||||
0.644917 | + | 0.764253i | \(0.276892\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1.63771e7i | − 0.757276i | −0.925545 | − | 0.378638i | \(-0.876392\pi\) | ||||
0.925545 | − | 0.378638i | \(-0.123608\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.70716e7i | 1.24453i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.12859e6 | −0.280113 | −0.140057 | − | 0.990143i | \(-0.544728\pi\) | ||||
−0.140057 | + | 0.990143i | \(0.544728\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.55091e6 | −0.161361 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.06593e6i | 0.319243i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.05555e7i | 3.16943i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.95843e6 | −0.444780 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 32126.7 | 0.00142669 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 2.57314e6i | − 0.113617i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.27843e7i | − 1.00031i | −0.865935 | − | 0.500157i | \(-0.833276\pi\) | ||||
0.865935 | − | 0.500157i | \(-0.166724\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.80381e7 | 1.22399 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.49593e7 | −0.649339 | −0.324669 | − | 0.945828i | \(-0.605253\pi\) | ||||
−0.324669 | + | 0.945828i | \(0.605253\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.85756e7i | − 1.23337i | −0.787211 | − | 0.616684i | \(-0.788476\pi\) | ||||
0.787211 | − | 0.616684i | \(-0.211524\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.59994e6i | 0.326176i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.05017e7 | −0.874944 | −0.437472 | − | 0.899232i | \(-0.644126\pi\) | ||||
−0.437472 | + | 0.899232i | \(0.644126\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.09442e7 | 0.888812 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.44701e7i | 1.87661i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.41645e6i | 0.143366i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.15318e7 | −0.481217 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.92135e6 | −0.328714 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.76127e7i | 2.37749i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.54132e7i | 1.45329i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.92482e7 | −2.00988 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.93785e6 | 0.119236 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.27147e7i | 1.72409i | 0.506835 | + | 0.862043i | \(0.330815\pi\) | ||||
−0.506835 | + | 0.862043i | \(0.669185\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 182607.i | − 0.00733004i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.16615e7 | 0.864753 | 0.432376 | − | 0.901693i | \(-0.357675\pi\) | ||||
0.432376 | + | 0.901693i | \(0.357675\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.58553e7 | −1.02653 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1.48205e7i | − 0.585210i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 3.16557e7i | − 1.24316i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.49934e7 | 1.75736 | 0.878679 | − | 0.477413i | \(-0.158425\pi\) | ||||
0.878679 | + | 0.477413i | \(0.158425\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.26197e7 | −0.490229 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2.96525e7i | − 1.14566i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.92857e6i | 0.189394i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −133012. | −0.00508382 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.71344e7 | −0.651373 | −0.325686 | − | 0.945478i | \(-0.605595\pi\) | ||||
−0.325686 | + | 0.945478i | \(0.605595\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.18500e7i | 0.448068i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.49703e6i | 0.281959i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.83262e7 | −0.685558 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.36298e7 | −1.62343 | −0.811715 | − | 0.584053i | \(-0.801466\pi\) | ||||
−0.811715 | + | 0.584053i | \(0.801466\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 4.93041e7i | − 1.82482i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 930214.i | 0.0342459i | 0.999853 | + | 0.0171230i | \(0.00545067\pi\) | ||||
−0.999853 | + | 0.0171230i | \(0.994549\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.06225e6 | 0.222001 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.55041e7 | 0.564763 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.95330e7i | − 1.07012i | −0.844813 | − | 0.535061i | \(-0.820289\pi\) | ||||
0.844813 | − | 0.535061i | \(-0.179711\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.99197e7i | − 0.717988i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.04118e7 | −1.09041 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.63699e7 | −0.940538 | −0.470269 | − | 0.882523i | \(-0.655843\pi\) | ||||
−0.470269 | + | 0.882523i | \(0.655843\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.66552e6i | 0.201016i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.84542e7i | 2.41613i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.84585e7 | −2.05258 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.79068e7 | 2.37195 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 261783.i | 0.00909655i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 535100.i | 0.0184977i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 338149. | 0.0116290 | 0.00581449 | − | 0.999983i | \(-0.498149\pi\) | ||||
0.00581449 | + | 0.999983i | \(0.498149\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.77350e7 | 0.606767 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 2.00903e7i | − 0.683816i | −0.939734 | − | 0.341908i | \(-0.888927\pi\) | ||||
0.939734 | − | 0.341908i | \(-0.111073\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.29166e6i | 0.213051i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.56293e6 | 0.288477 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.04075e7 | 0.348826 | 0.174413 | − | 0.984673i | \(-0.444197\pi\) | ||||
0.174413 | + | 0.984673i | \(0.444197\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.12901e7i | 1.04340i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 460435.i | − 0.0152755i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.39326e6 | −0.0789963 | −0.0394982 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394982 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.76868e7 | −0.580842 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.67665e6i | 0.250830i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.10284e7i | 0.358525i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.23674e7 | 1.37040 | 0.685200 | − | 0.728355i | \(-0.259715\pi\) | ||||
0.685200 | + | 0.728355i | \(0.259715\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.64201e7 | −1.81577 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 9.68979e6i | − 0.310282i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.35670e6i | 0.0750873i | 0.999295 | + | 0.0375436i | \(0.0119533\pi\) | ||||
−0.999295 | + | 0.0375436i | \(0.988047\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.96963e7 | −0.941432 |
(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 | 320.6.d.b.161.3 | yes | 8 | |
4.3 | odd | 2 | 320.6.d.a.161.6 | yes | 8 | ||
8.3 | odd | 2 | 320.6.d.a.161.3 | ✓ | 8 | ||
8.5 | even | 2 | inner | 320.6.d.b.161.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.d.a.161.3 | ✓ | 8 | 8.3 | odd | 2 | ||
320.6.d.a.161.6 | yes | 8 | 4.3 | odd | 2 | ||
320.6.d.b.161.3 | yes | 8 | 1.1 | even | 1 | trivial | |
320.6.d.b.161.6 | yes | 8 | 8.5 | even | 2 | inner |