Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,8,Mod(35,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.35");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.f (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: | \(22.4917218349\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 35.28 | ||
Character | \(\chi\) | \(=\) | 72.35 |
Dual form | 72.8.f.a.35.27 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 11.3087 | + | 0.338231i | 0.999553 | + | 0.0298957i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 127.771 | + | 7.64988i | 0.998212 | + | 0.0597647i | ||||
\(5\) | −93.0830 | −0.333024 | −0.166512 | − | 0.986039i | \(-0.553250\pi\) | ||||
−0.166512 | + | 0.986039i | \(0.553250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1025.06i | − | 1.12956i | −0.825243 | − | 0.564778i | \(-0.808962\pi\) | ||
0.825243 | − | 0.564778i | \(-0.191038\pi\) | |||||||
\(8\) | 1442.33 | + | 129.726i | 0.995980 | + | 0.0895803i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1052.64 | − | 31.4836i | −0.332875 | − | 0.00995598i | ||||
\(11\) | − | 1545.61i | − | 0.350126i | −0.984557 | − | 0.175063i | \(-0.943987\pi\) | ||
0.984557 | − | 0.175063i | \(-0.0560130\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5677.41i | − | 0.716719i | −0.933584 | − | 0.358359i | \(-0.883336\pi\) | ||
0.933584 | − | 0.358359i | \(-0.116664\pi\) | |||||||
\(14\) | 346.709 | − | 11592.1i | 0.0337689 | − | 1.12905i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16267.0 | + | 1954.87i | 0.992856 | + | 0.119316i | ||||
\(17\) | − | 15703.6i | − | 0.775227i | −0.921822 | − | 0.387613i | \(-0.873300\pi\) | ||
0.921822 | − | 0.387613i | \(-0.126700\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 33939.0 | 1.13517 | 0.567586 | − | 0.823314i | \(-0.307877\pi\) | ||||
0.567586 | + | 0.823314i | \(0.307877\pi\) | |||||||
\(20\) | −11893.3 | − | 712.074i | −0.332428 | − | 0.0199031i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 522.773 | − | 17478.7i | 0.0104673 | − | 0.349970i | ||||
\(23\) | 30068.2 | 0.515300 | 0.257650 | − | 0.966238i | \(-0.417052\pi\) | ||||
0.257650 | + | 0.966238i | \(0.417052\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −69460.6 | −0.889095 | ||||||||
\(26\) | 1920.28 | − | 64203.9i | 0.0214268 | − | 0.716398i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7841.62 | − | 130974.i | 0.0675076 | − | 1.12754i | ||||
\(29\) | 99025.6 | 0.753971 | 0.376985 | − | 0.926219i | \(-0.376961\pi\) | ||||
0.376985 | + | 0.926219i | \(0.376961\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 152785.i | − | 0.921115i | −0.887630 | − | 0.460558i | \(-0.847649\pi\) | ||
0.887630 | − | 0.460558i | \(-0.152351\pi\) | |||||||
\(32\) | 183296. | + | 27608.9i | 0.988846 | + | 0.148945i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5311.46 | − | 177587.i | 0.0231760 | − | 0.774880i | ||||
\(35\) | 95416.0i | 0.376169i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 336316.i | − | 1.09154i | −0.837933 | − | 0.545772i | \(-0.816236\pi\) | ||
0.837933 | − | 0.545772i | \(-0.183764\pi\) | |||||||
\(38\) | 383805. | + | 11479.2i | 1.13467 | + | 0.0339368i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −134257. | − | 12075.3i | −0.331685 | − | 0.0298324i | ||||
\(41\) | 663449.i | 1.50336i | 0.659527 | + | 0.751681i | \(0.270757\pi\) | ||||
−0.659527 | + | 0.751681i | \(0.729243\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −707879. | −1.35775 | −0.678874 | − | 0.734255i | \(-0.737532\pi\) | ||||
−0.678874 | + | 0.734255i | \(0.737532\pi\) | |||||||
\(44\) | 11823.7 | − | 197484.i | 0.0209252 | − | 0.349500i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 340031. | + | 10170.0i | 0.515069 | + | 0.0154052i | ||||
\(47\) | 402012. | 0.564802 | 0.282401 | − | 0.959296i | \(-0.408869\pi\) | ||||
0.282401 | + | 0.959296i | \(0.408869\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −227213. | −0.275896 | ||||||||
\(50\) | −785505. | − | 23493.7i | −0.888698 | − | 0.0265801i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 43431.5 | − | 725410.i | 0.0428345 | − | 0.715438i | ||||
\(53\) | 662469. | 0.611223 | 0.305612 | − | 0.952156i | \(-0.401139\pi\) | ||||
0.305612 | + | 0.952156i | \(0.401139\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 143870.i | 0.116600i | ||||||||
\(56\) | 132977. | − | 1.47848e6i | 0.101186 | − | 1.12501i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.11985e6 | + | 33493.6i | 0.753634 | + | 0.0225405i | ||||
\(59\) | 1.74805e6i | 1.10808i | 0.832489 | + | 0.554041i | \(0.186915\pi\) | ||||
−0.832489 | + | 0.554041i | \(0.813085\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 321803.i | − | 0.181525i | −0.995873 | − | 0.0907624i | \(-0.971070\pi\) | ||
0.995873 | − | 0.0907624i | \(-0.0289304\pi\) | |||||||
\(62\) | 51676.6 | − | 1.72779e6i | 0.0275374 | − | 0.920704i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.06349e6 | + | 374216.i | 0.983951 | + | 0.178440i | ||||
\(65\) | 528470.i | 0.238684i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −464913. | −0.188847 | −0.0944234 | − | 0.995532i | \(-0.530101\pi\) | ||||
−0.0944234 | + | 0.995532i | \(0.530101\pi\) | |||||||
\(68\) | 120131. | − | 2.00647e6i | 0.0463312 | − | 0.773841i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −32272.7 | + | 1.07903e6i | −0.0112458 | + | 0.376001i | ||||
\(71\) | −3.53880e6 | −1.17342 | −0.586708 | − | 0.809799i | \(-0.699576\pi\) | ||||
−0.586708 | + | 0.809799i | \(0.699576\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.41741e6 | −1.02817 | −0.514087 | − | 0.857738i | \(-0.671869\pi\) | ||||
−0.514087 | + | 0.857738i | \(0.671869\pi\) | |||||||
\(74\) | 113753. | − | 3.80328e6i | 0.0326325 | − | 1.09106i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.33643e6 | + | 259630.i | 1.13314 | + | 0.0678433i | ||||
\(77\) | −1.58435e6 | −0.395487 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.60430e6i | 1.73526i | 0.497210 | + | 0.867630i | \(0.334358\pi\) | ||||
−0.497210 | + | 0.867630i | \(0.665642\pi\) | |||||||
\(80\) | −1.51418e6 | − | 181965.i | −0.330645 | − | 0.0397350i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −224399. | + | 7.50271e6i | −0.0449441 | + | 1.50269i | ||||
\(83\) | 8.11070e6i | 1.55699i | 0.627653 | + | 0.778494i | \(0.284016\pi\) | ||||
−0.627653 | + | 0.778494i | \(0.715984\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.46174e6i | 0.258169i | ||||||||
\(86\) | −8.00515e6 | − | 239427.i | −1.35714 | − | 0.0405908i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 200506. | − | 2.22928e6i | 0.0313644 | − | 0.348719i | ||||
\(89\) | 1.00923e7i | 1.51749i | 0.651387 | + | 0.758746i | \(0.274187\pi\) | ||||
−0.651387 | + | 0.758746i | \(0.725813\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.81971e6 | −0.809574 | ||||||||
\(92\) | 3.84185e6 | + | 230018.i | 0.514379 | + | 0.0307967i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.54621e6 | + | 135973.i | 0.564550 | + | 0.0168852i | ||||
\(95\) | −3.15915e6 | −0.378039 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.88229e6 | −0.654403 | −0.327201 | − | 0.944955i | \(-0.606106\pi\) | ||||
−0.327201 | + | 0.944955i | \(0.606106\pi\) | |||||||
\(98\) | −2.56947e6 | − | 76850.4i | −0.275773 | − | 0.00824812i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.87506e6 | − | 531365.i | −0.887506 | − | 0.0531365i | ||||
\(101\) | 1.32223e7 | 1.27697 | 0.638486 | − | 0.769633i | \(-0.279561\pi\) | ||||
0.638486 | + | 0.769633i | \(0.279561\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.86665e6i | 0.799520i | 0.916620 | + | 0.399760i | \(0.130907\pi\) | ||||
−0.916620 | + | 0.399760i | \(0.869093\pi\) | |||||||
\(104\) | 736508. | − | 8.18872e6i | 0.0642038 | − | 0.713837i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.49163e6 | + | 224068.i | 0.610950 | + | 0.0182729i | ||||
\(107\) | − | 4.71318e6i | − | 0.371938i | −0.982556 | − | 0.185969i | \(-0.940458\pi\) | ||
0.982556 | − | 0.185969i | \(-0.0595424\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.63965e7i | − | 1.95233i | −0.217027 | − | 0.976166i | \(-0.569636\pi\) | ||
0.217027 | − | 0.976166i | \(-0.430364\pi\) | |||||||
\(110\) | −48661.2 | + | 1.62697e6i | −0.00348585 | + | 0.116548i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00387e6 | − | 1.66747e7i | 0.134774 | − | 1.12149i | ||||
\(113\) | 3.41021e6i | 0.222334i | 0.993802 | + | 0.111167i | \(0.0354589\pi\) | ||||
−0.993802 | + | 0.111167i | \(0.964541\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.79884e6 | −0.171607 | ||||||||
\(116\) | 1.26526e7 | + | 757534.i | 0.752623 | + | 0.0450608i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −591246. | + | 1.97681e7i | −0.0331269 | + | 1.10759i | ||||
\(119\) | −1.60972e7 | −0.875662 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.70983e7 | 0.877412 | ||||||||
\(122\) | 108844. | − | 3.63916e6i | 0.00542681 | − | 0.181444i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.16879e6 | − | 1.95215e7i | 0.0550502 | − | 0.919469i | ||||
\(125\) | 1.37377e7 | 0.629114 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.87499e6i | 0.427783i | 0.976857 | + | 0.213892i | \(0.0686139\pi\) | ||||
−0.976857 | + | 0.213892i | \(0.931386\pi\) | |||||||
\(128\) | 2.32088e7 | + | 4.92982e6i | 0.978176 | + | 0.207776i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −178745. | + | 5.97629e6i | −0.00713564 | + | 0.238578i | ||||
\(131\) | − | 2.16683e7i | − | 0.842124i | −0.907032 | − | 0.421062i | \(-0.861658\pi\) | ||
0.907032 | − | 0.421062i | \(-0.138342\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.47897e7i | − | 1.28224i | ||||||
\(134\) | −5.25754e6 | − | 157248.i | −0.188762 | − | 0.00564571i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.03717e6 | − | 2.26499e7i | 0.0694450 | − | 0.772110i | ||||
\(137\) | − | 5.12379e7i | − | 1.70243i | −0.524818 | − | 0.851214i | \(-0.675867\pi\) | ||
0.524818 | − | 0.851214i | \(-0.324133\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.92028e7 | 1.23813 | 0.619063 | − | 0.785341i | \(-0.287512\pi\) | ||||
0.619063 | + | 0.785341i | \(0.287512\pi\) | |||||||
\(140\) | −729921. | + | 1.21914e7i | −0.0224816 | + | 0.375497i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00191e7 | − | 1.19693e6i | −1.17289 | − | 0.0350801i | ||||
\(143\) | −8.77505e6 | −0.250942 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.21760e6 | −0.251090 | ||||||||
\(146\) | −3.86463e7 | − | 1.15587e6i | −1.02771 | − | 0.0307380i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.57278e6 | − | 4.29715e7i | 0.0652359 | − | 1.08959i | ||||
\(149\) | 7.23566e7 | 1.79195 | 0.895975 | − | 0.444104i | \(-0.146478\pi\) | ||||
0.895975 | + | 0.444104i | \(0.146478\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.61796e7i | 1.32788i | 0.747786 | + | 0.663940i | \(0.231117\pi\) | ||||
−0.747786 | + | 0.663940i | \(0.768883\pi\) | |||||||
\(152\) | 4.89514e7 | + | 4.40278e6i | 1.13061 | + | 0.101689i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.79168e7 | − | 535875.i | −0.395310 | − | 0.0118234i | ||||
\(155\) | 1.42217e7i | 0.306753i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.29634e7i | − | 1.71095i | −0.517843 | − | 0.855476i | \(-0.673265\pi\) | ||
0.517843 | − | 0.855476i | \(-0.326735\pi\) | |||||||
\(158\) | −2.57201e6 | + | 8.59944e7i | −0.0518768 | + | 1.73448i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.70618e7 | − | 2.56992e6i | −0.329309 | − | 0.0496021i | ||||
\(161\) | − | 3.08218e7i | − | 0.582060i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.32708e7 | 0.240017 | 0.120008 | − | 0.992773i | \(-0.461708\pi\) | ||||
0.120008 | + | 0.992773i | \(0.461708\pi\) | |||||||
\(164\) | −5.07530e6 | + | 8.47696e7i | −0.0898480 | + | 1.50068i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.74329e6 | + | 9.17211e7i | −0.0465472 | + | 1.55629i | ||||
\(167\) | −6.62945e7 | −1.10146 | −0.550732 | − | 0.834682i | \(-0.685651\pi\) | ||||
−0.550732 | + | 0.834682i | \(0.685651\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.05155e7 | 0.486314 | ||||||||
\(170\) | −494406. | + | 1.65303e7i | −0.00771814 | + | 0.258054i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.04465e7 | − | 5.41519e6i | −1.35532 | − | 0.0811454i | ||||
\(173\) | −5.99909e7 | −0.880895 | −0.440448 | − | 0.897778i | \(-0.645180\pi\) | ||||
−0.440448 | + | 0.897778i | \(0.645180\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.12015e7i | 1.00428i | ||||||||
\(176\) | 3.02146e6 | − | 2.51423e7i | 0.0417756 | − | 0.347625i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.41354e6 | + | 1.14131e8i | −0.0453665 | + | 1.51681i | ||||
\(179\) | − | 8.01095e7i | − | 1.04399i | −0.852947 | − | 0.521997i | \(-0.825187\pi\) | ||
0.852947 | − | 0.521997i | \(-0.174813\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.83641e7i | 0.480894i | 0.970662 | + | 0.240447i | \(0.0772941\pi\) | ||||
−0.970662 | + | 0.240447i | \(0.922706\pi\) | |||||||
\(182\) | −6.58131e7 | − | 1.96841e6i | −0.809212 | − | 0.0242028i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.33683e7 | + | 3.90063e6i | 0.513228 | + | 0.0461607i | ||||
\(185\) | 3.13053e7i | 0.363510i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.42716e7 | −0.271427 | ||||||||
\(188\) | 5.13655e7 | + | 3.07534e6i | 0.563792 | + | 0.0337552i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.57257e7 | − | 1.06852e6i | −0.377871 | − | 0.0113018i | ||||
\(191\) | −1.26246e8 | −1.31100 | −0.655499 | − | 0.755196i | \(-0.727542\pi\) | ||||
−0.655499 | + | 0.755196i | \(0.727542\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.20271e8 | 1.20423 | 0.602115 | − | 0.798409i | \(-0.294325\pi\) | ||||
0.602115 | + | 0.798409i | \(0.294325\pi\) | |||||||
\(194\) | −6.65207e7 | − | 1.98957e6i | −0.654110 | − | 0.0195638i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.90312e7 | − | 1.73815e6i | −0.275403 | − | 0.0164889i | ||||
\(197\) | 1.23903e8 | 1.15465 | 0.577326 | − | 0.816514i | \(-0.304096\pi\) | ||||
0.577326 | + | 0.816514i | \(0.304096\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.68027e8i | 1.51145i | 0.654888 | + | 0.755726i | \(0.272716\pi\) | ||||
−0.654888 | + | 0.755726i | \(0.727284\pi\) | |||||||
\(200\) | −1.00185e8 | − | 9.01085e6i | −0.885521 | − | 0.0796454i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.49526e8 | + | 4.47219e6i | 1.27640 | + | 0.0381760i | ||||
\(203\) | − | 1.01508e8i | − | 0.851652i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 6.17558e7i | − | 0.500655i | ||||||
\(206\) | −2.99898e6 | + | 1.00270e8i | −0.0239022 | + | 0.799163i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.10986e7 | − | 9.23542e7i | 0.0855158 | − | 0.711599i | ||||
\(209\) | − | 5.24564e7i | − | 0.397454i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.24919e7 | 0.604537 | 0.302268 | − | 0.953223i | \(-0.402256\pi\) | ||||
0.302268 | + | 0.953223i | \(0.402256\pi\) | |||||||
\(212\) | 8.46444e7 | + | 5.06781e6i | 0.610130 | + | 0.0365296i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.59414e6 | − | 5.32997e7i | 0.0111194 | − | 0.371772i | ||||
\(215\) | 6.58914e7 | 0.452162 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.56614e8 | −1.04045 | ||||||||
\(218\) | 8.92812e6 | − | 2.98509e8i | 0.0583663 | − | 1.95146i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.10059e6 | + | 1.83824e7i | −0.00696858 | + | 0.116392i | ||||
\(221\) | −8.91560e7 | −0.555620 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.10837e8i | − | 0.669296i | −0.942343 | − | 0.334648i | \(-0.891383\pi\) | ||
0.942343 | − | 0.334648i | \(-0.108617\pi\) | |||||||
\(224\) | 2.83009e7 | − | 1.87890e8i | 0.168241 | − | 1.11696i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.15344e6 | + | 3.85649e7i | −0.00664685 | + | 0.222235i | ||||
\(227\) | 2.44393e8i | 1.38675i | 0.720576 | + | 0.693376i | \(0.243877\pi\) | ||||
−0.720576 | + | 0.693376i | \(0.756123\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.49235e7i | − | 0.137146i | −0.997646 | − | 0.0685732i | \(-0.978155\pi\) | ||
0.997646 | − | 0.0685732i | \(-0.0218447\pi\) | |||||||
\(230\) | −3.16511e7 | − | 946654.i | −0.171530 | − | 0.00513031i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.42828e8 | + | 1.28462e7i | 0.750940 | + | 0.0675409i | ||||
\(233\) | 8.59209e7i | 0.444993i | 0.974934 | + | 0.222496i | \(0.0714206\pi\) | ||||
−0.974934 | + | 0.222496i | \(0.928579\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.74204e7 | −0.188092 | ||||||||
\(236\) | −1.33724e7 | + | 2.23351e8i | −0.0662242 | + | 1.10610i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.82038e8 | − | 5.44458e6i | −0.875271 | − | 0.0261785i | ||||
\(239\) | 1.03442e8 | 0.490122 | 0.245061 | − | 0.969508i | \(-0.421192\pi\) | ||||
0.245061 | + | 0.969508i | \(0.421192\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.12373e8 | −0.977325 | −0.488662 | − | 0.872473i | \(-0.662515\pi\) | ||||
−0.488662 | + | 0.872473i | \(0.662515\pi\) | |||||||
\(242\) | 1.93358e8 | + | 5.78317e6i | 0.877019 | + | 0.0262308i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.46176e6 | − | 4.11172e7i | 0.0108488 | − | 0.181200i | ||||
\(245\) | 2.11496e7 | 0.0918801 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.92686e8i | − | 0.813599i | ||||||
\(248\) | 1.98202e7 | − | 2.20366e8i | 0.0825137 | − | 0.917412i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.55355e8 | + | 4.64652e6i | 0.628832 | + | 0.0188078i | ||||
\(251\) | 2.88318e8i | 1.15084i | 0.817859 | + | 0.575418i | \(0.195161\pi\) | ||||
−0.817859 | + | 0.575418i | \(0.804839\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.64736e7i | − | 0.180420i | ||||||
\(254\) | −3.34003e6 | + | 1.11673e8i | −0.0127889 | + | 0.427592i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.60792e8 | + | 6.35995e7i | 0.971528 | + | 0.236927i | ||||
\(257\) | 3.06607e8i | 1.12672i | 0.826211 | + | 0.563361i | \(0.190492\pi\) | ||||
−0.826211 | + | 0.563361i | \(0.809508\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.44745e8 | −1.23296 | ||||||||
\(260\) | −4.04274e6 | + | 6.75233e7i | −0.0142649 | + | 0.238258i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.32891e6 | − | 2.45040e8i | 0.0251759 | − | 0.841747i | ||||
\(263\) | 7.85030e7 | 0.266098 | 0.133049 | − | 0.991109i | \(-0.457523\pi\) | ||||
0.133049 | + | 0.991109i | \(0.457523\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.16645e7 | −0.203552 | ||||||||
\(266\) | 1.17670e7 | − | 3.93424e8i | 0.0383335 | − | 1.28167i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.94025e7 | − | 3.55653e6i | −0.188509 | − | 0.0112864i | ||||
\(269\) | 2.64506e8 | 0.828519 | 0.414259 | − | 0.910159i | \(-0.364041\pi\) | ||||
0.414259 | + | 0.910159i | \(0.364041\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.60573e8i | − | 1.10053i | −0.834991 | − | 0.550263i | \(-0.814527\pi\) | ||
0.834991 | − | 0.550263i | \(-0.185473\pi\) | |||||||
\(272\) | 3.06985e7 | − | 2.55450e8i | 0.0924968 | − | 0.769689i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.73302e7 | − | 5.79431e8i | 0.0508953 | − | 1.70167i | ||||
\(275\) | 1.07359e8i | 0.311296i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.46978e8i | 0.698198i | 0.937086 | + | 0.349099i | \(0.113512\pi\) | ||||
−0.937086 | + | 0.349099i | \(0.886488\pi\) | |||||||
\(278\) | 4.43331e8 | + | 1.32596e7i | 1.23757 | + | 0.0370147i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.23779e7 | + | 1.37622e8i | −0.0336973 | + | 0.374657i | ||||
\(281\) | 1.16347e8i | 0.312812i | 0.987693 | + | 0.156406i | \(0.0499908\pi\) | ||||
−0.987693 | + | 0.156406i | \(0.950009\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.05548e8 | −0.801358 | −0.400679 | − | 0.916219i | \(-0.631226\pi\) | ||||
−0.400679 | + | 0.916219i | \(0.631226\pi\) | |||||||
\(284\) | −4.52157e8 | − | 2.70714e7i | −1.17132 | − | 0.0701289i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.92340e7 | − | 2.96800e6i | −0.250830 | − | 0.00750209i | ||||
\(287\) | 6.80077e8 | 1.69813 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.63735e8 | 0.399023 | ||||||||
\(290\) | −1.04239e8 | − | 3.11768e6i | −0.250978 | − | 0.00750652i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.36646e8 | − | 2.61428e7i | −1.02634 | − | 0.0614485i | ||||
\(293\) | −7.14442e8 | −1.65932 | −0.829661 | − | 0.558268i | \(-0.811466\pi\) | ||||
−0.829661 | + | 0.558268i | \(0.811466\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.62714e8i | − | 0.369018i | ||||||
\(296\) | 4.36290e7 | − | 4.85080e8i | 0.0977809 | − | 1.08716i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.18255e8 | + | 2.44733e7i | 1.79115 | + | 0.0535716i | ||||
\(299\) | − | 1.70709e8i | − | 0.369325i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.25621e8i | 1.53365i | ||||||||
\(302\) | −1.90017e7 | + | 6.35315e8i | −0.0396979 | + | 1.32729i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.52085e8 | + | 6.63464e7i | 1.12706 | + | 0.135444i | ||||
\(305\) | 2.99544e7i | 0.0604521i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.95766e8 | 0.780647 | 0.390323 | − | 0.920678i | \(-0.372363\pi\) | ||||
0.390323 | + | 0.920678i | \(0.372363\pi\) | |||||||
\(308\) | −2.02434e8 | − | 1.21201e7i | −0.394780 | − | 0.0236362i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.81021e6 | + | 1.60828e8i | −0.00917061 | + | 0.306616i | ||||
\(311\) | −4.17018e8 | −0.786129 | −0.393064 | − | 0.919511i | \(-0.628585\pi\) | ||||
−0.393064 | + | 0.919511i | \(0.628585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.16149e8 | 0.398426 | 0.199213 | − | 0.979956i | \(-0.436161\pi\) | ||||
0.199213 | + | 0.979956i | \(0.436161\pi\) | |||||||
\(314\) | 2.80608e7 | − | 9.38204e8i | 0.0511501 | − | 1.71019i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.81720e7 | + | 9.71611e8i | −0.103707 | + | 1.73216i | ||||
\(317\) | −6.69525e8 | −1.18048 | −0.590241 | − | 0.807227i | \(-0.700967\pi\) | ||||
−0.590241 | + | 0.807227i | \(0.700967\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.53055e8i | − | 0.263985i | ||||||
\(320\) | −1.92076e8 | − | 3.48332e7i | −0.327679 | − | 0.0594248i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.04249e7 | − | 3.48553e8i | 0.0174011 | − | 0.581800i | ||||
\(323\) | − | 5.32966e8i | − | 0.880016i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.94356e8i | 0.637231i | ||||||||
\(326\) | 1.50075e8 | + | 4.48862e6i | 0.239910 | + | 0.00717548i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.60666e7 | + | 9.56913e8i | −0.134672 | + | 1.49732i | ||||
\(329\) | − | 4.12088e8i | − | 0.637975i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.27775e8 | 0.345230 | 0.172615 | − | 0.984989i | \(-0.444778\pi\) | ||||
0.172615 | + | 0.984989i | \(0.444778\pi\) | |||||||
\(332\) | −6.20459e7 | + | 1.03631e9i | −0.0930529 | + | 1.55420i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.49702e8 | − | 2.24229e7i | −1.10097 | − | 0.0329290i | ||||
\(335\) | 4.32755e7 | 0.0628905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.09334e8 | −0.440274 | −0.220137 | − | 0.975469i | \(-0.570650\pi\) | ||||
−0.220137 | + | 0.975469i | \(0.570650\pi\) | |||||||
\(338\) | 3.45089e8 | + | 1.03213e7i | 0.486097 | + | 0.0145387i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.11821e7 | + | 1.86768e8i | −0.0154294 | + | 0.257707i | ||||
\(341\) | −2.36145e8 | −0.322507 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.11277e8i | − | 0.817915i | ||||||
\(344\) | −1.02100e9 | − | 9.18303e7i | −1.35229 | − | 0.121627i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.78417e8 | − | 2.02908e7i | −0.880502 | − | 0.0263350i | ||||
\(347\) | 4.22835e8i | 0.543272i | 0.962400 | + | 0.271636i | \(0.0875647\pi\) | ||||
−0.962400 | + | 0.271636i | \(0.912435\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.23470e9i | 1.55479i | 0.629011 | + | 0.777396i | \(0.283460\pi\) | ||||
−0.629011 | + | 0.777396i | \(0.716540\pi\) | |||||||
\(350\) | −2.40826e7 | + | 8.05193e8i | −0.0300237 | + | 1.00383i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.26726e7 | − | 2.83304e8i | 0.0521494 | − | 0.346221i | ||||
\(353\) | − | 1.17813e8i | − | 0.142554i | −0.997457 | − | 0.0712772i | \(-0.977292\pi\) | ||
0.997457 | − | 0.0712772i | \(-0.0227075\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.29402e8 | 0.390775 | ||||||||
\(356\) | −7.72051e7 | + | 1.28951e9i | −0.0906924 | + | 1.51478i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.70955e7 | − | 9.05930e8i | 0.0312110 | − | 1.04353i | ||||
\(359\) | 1.21083e9 | 1.38119 | 0.690595 | − | 0.723242i | \(-0.257349\pi\) | ||||
0.690595 | + | 0.723242i | \(0.257349\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.57987e8 | 0.288617 | ||||||||
\(362\) | −1.29759e7 | + | 4.33846e8i | −0.0143767 | + | 0.480679i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.43591e8 | − | 4.45201e7i | −0.808127 | − | 0.0483839i | ||||
\(365\) | 3.18102e8 | 0.342406 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.02237e8i | − | 0.213565i | −0.994282 | − | 0.106782i | \(-0.965945\pi\) | ||
0.994282 | − | 0.106782i | \(-0.0340548\pi\) | |||||||
\(368\) | 4.89118e8 | + | 5.87794e7i | 0.511618 | + | 0.0614833i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.05884e7 | + | 3.54021e8i | −0.0108674 | + | 0.363348i | ||||
\(371\) | − | 6.79072e8i | − | 0.690411i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.43859e8i | − | 0.143534i | −0.997421 | − | 0.0717671i | \(-0.977136\pi\) | ||
0.997421 | − | 0.0717671i | \(-0.0228638\pi\) | |||||||
\(374\) | −2.74480e8 | − | 8.20943e6i | −0.271306 | − | 0.00811451i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.79835e8 | + | 5.21514e7i | 0.562531 | + | 0.0505951i | ||||
\(377\) | − | 5.62209e8i | − | 0.540385i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.77228e8 | 0.827705 | 0.413852 | − | 0.910344i | \(-0.364183\pi\) | ||||
0.413852 | + | 0.910344i | \(0.364183\pi\) | |||||||
\(380\) | −4.03648e8 | − | 2.41671e7i | −0.377364 | − | 0.0225934i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.42768e9 | − | 4.27005e7i | −1.31041 | − | 0.0391932i | ||||
\(383\) | −2.04366e8 | −0.185871 | −0.0929356 | − | 0.995672i | \(-0.529625\pi\) | ||||
−0.0929356 | + | 0.995672i | \(0.529625\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.47476e8 | 0.131707 | ||||||||
\(386\) | 1.36010e9 | + | 4.06793e7i | 1.20369 | + | 0.0360013i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.51587e8 | − | 4.49988e7i | −0.653233 | − | 0.0391102i | ||||
\(389\) | −1.58576e9 | −1.36589 | −0.682943 | − | 0.730472i | \(-0.739300\pi\) | ||||
−0.682943 | + | 0.730472i | \(0.739300\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.72180e8i | − | 0.399474i | ||||||
\(392\) | −3.27716e8 | − | 2.94754e7i | −0.274787 | − | 0.0247149i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.40118e9 | + | 4.19080e7i | 1.15414 | + | 0.0345191i | ||||
\(395\) | − | 7.07831e8i | − | 0.577883i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.83002e8i | − | 0.146787i | −0.997303 | − | 0.0733935i | \(-0.976617\pi\) | ||
0.997303 | − | 0.0733935i | \(-0.0233829\pi\) | |||||||
\(398\) | −5.68321e7 | + | 1.90016e9i | −0.0451859 | + | 1.51078i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.12991e9 | − | 1.35786e8i | −0.882744 | − | 0.106083i | ||||
\(401\) | − | 1.57329e9i | − | 1.21844i | −0.793001 | − | 0.609220i | \(-0.791483\pi\) | ||
0.793001 | − | 0.609220i | \(-0.208517\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.67422e8 | −0.660181 | ||||||||
\(404\) | 1.68943e9 | + | 1.01149e8i | 1.27469 | + | 0.0763178i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.43330e7 | − | 1.14791e9i | 0.0254607 | − | 0.851271i | ||||
\(407\) | −5.19813e8 | −0.382179 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.66645e9 | 1.20437 | 0.602187 | − | 0.798355i | \(-0.294296\pi\) | ||||
0.602187 | + | 0.798355i | \(0.294296\pi\) | |||||||
\(410\) | 2.08877e7 | − | 6.98374e8i | 0.0149675 | − | 0.500432i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.78288e7 | + | 1.13290e9i | −0.0477831 | + | 0.798091i | ||||
\(413\) | 1.79186e9 | 1.25164 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.54968e8i | − | 0.518514i | ||||||
\(416\) | 1.56747e8 | − | 1.04065e9i | 0.106751 | − | 0.708724i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.77424e7 | − | 5.93211e8i | 0.0118822 | − | 0.397276i | ||||
\(419\) | − | 8.92118e8i | − | 0.592479i | −0.955114 | − | 0.296240i | \(-0.904267\pi\) | ||
0.955114 | − | 0.296240i | \(-0.0957327\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.98849e9i | − | 1.29878i | −0.760455 | − | 0.649391i | \(-0.775024\pi\) | ||
0.760455 | − | 0.649391i | \(-0.224976\pi\) | |||||||
\(422\) | 9.32872e8 | + | 2.79013e7i | 0.604267 | + | 0.0180731i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.55500e8 | + | 8.59394e7i | 0.608766 | + | 0.0547535i | ||||
\(425\) | 1.09078e9i | 0.689250i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.29869e8 | −0.205042 | ||||||||
\(428\) | 3.60552e7 | − | 6.02208e8i | 0.0222288 | − | 0.371273i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.45143e8 | + | 2.22865e7i | 0.451960 | + | 0.0135177i | ||||
\(431\) | 9.29190e8 | 0.559029 | 0.279514 | − | 0.960142i | \(-0.409827\pi\) | ||||
0.279514 | + | 0.960142i | \(0.409827\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.65923e9 | 0.982197 | 0.491099 | − | 0.871104i | \(-0.336595\pi\) | ||||
0.491099 | + | 0.871104i | \(0.336595\pi\) | |||||||
\(434\) | −1.77109e9 | − | 5.29718e7i | −1.03999 | − | 0.0311050i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.01930e8 | − | 3.37271e9i | 0.116680 | − | 1.94884i | ||||
\(437\) | 1.02049e9 | 0.584954 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.17987e7i | 0.0517858i | 0.999665 | + | 0.0258929i | \(0.00824288\pi\) | ||||
−0.999665 | + | 0.0258929i | \(0.991757\pi\) | |||||||
\(440\) | −1.86636e7 | + | 2.07508e8i | −0.0104451 | + | 0.116132i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.00823e9 | − | 3.01553e7i | −0.555371 | − | 0.0166106i | ||||
\(443\) | − | 7.47135e8i | − | 0.408306i | −0.978939 | − | 0.204153i | \(-0.934556\pi\) | ||
0.978939 | − | 0.204153i | \(-0.0654441\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 9.39424e8i | − | 0.505361i | ||||||
\(446\) | 3.74886e7 | − | 1.25342e9i | 0.0200091 | − | 0.668996i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.83595e8 | − | 2.11521e9i | 0.201558 | − | 1.11143i | ||||
\(449\) | − | 3.67451e8i | − | 0.191574i | −0.995402 | − | 0.0957871i | \(-0.969463\pi\) | ||
0.995402 | − | 0.0957871i | \(-0.0305368\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.02543e9 | 0.526367 | ||||||||
\(452\) | −2.60877e7 | + | 4.35727e8i | −0.0132877 | + | 0.221937i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.26615e7 | + | 2.76376e9i | −0.0414579 | + | 1.38613i | ||||
\(455\) | 5.41716e8 | 0.269607 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.88980e9 | −1.90643 | −0.953215 | − | 0.302292i | \(-0.902248\pi\) | ||||
−0.953215 | + | 0.302292i | \(0.902248\pi\) | |||||||
\(458\) | 8.42990e6 | − | 2.81851e8i | 0.00410009 | − | 0.137085i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.57611e8 | − | 2.14108e7i | −0.171300 | − | 0.0102560i | ||||
\(461\) | 7.45672e8 | 0.354482 | 0.177241 | − | 0.984167i | \(-0.443283\pi\) | ||||
0.177241 | + | 0.984167i | \(0.443283\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.76294e9i | 0.825473i | 0.910850 | + | 0.412737i | \(0.135427\pi\) | ||||
−0.910850 | + | 0.412737i | \(0.864573\pi\) | |||||||
\(464\) | 1.61085e9 | + | 1.93582e8i | 0.748585 | + | 0.0899606i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.90611e7 | + | 9.71649e8i | −0.0133034 | + | 0.444794i | ||||
\(467\) | 2.95161e9i | 1.34106i | 0.741881 | + | 0.670531i | \(0.233934\pi\) | ||||
−0.741881 | + | 0.670531i | \(0.766066\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.76565e8i | 0.213313i | ||||||||
\(470\) | −4.23175e8 | − | 1.26568e7i | −0.188008 | − | 0.00562316i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.26768e8 | + | 2.52127e9i | −0.0992623 | + | 1.10363i | ||||
\(473\) | 1.09410e9i | 0.475383i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.35742e9 | −1.00928 | ||||||||
\(476\) | −2.05676e9 | − | 1.23142e8i | −0.874097 | − | 0.0523337i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.16979e9 | + | 3.49873e7i | 0.489903 | + | 0.0146526i | ||||
\(479\) | −4.12030e9 | −1.71299 | −0.856495 | − | 0.516156i | \(-0.827363\pi\) | ||||
−0.856495 | + | 0.516156i | \(0.827363\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.90941e9 | −0.782331 | ||||||||
\(482\) | −2.40165e9 | − | 7.18311e7i | −0.976888 | − | 0.0292178i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.18467e9 | + | 1.30800e8i | 0.875843 | + | 0.0524382i | ||||
\(485\) | 5.47541e8 | 0.217932 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.42855e9i | 1.73744i | 0.495304 | + | 0.868720i | \(0.335057\pi\) | ||||
−0.495304 | + | 0.868720i | \(0.664943\pi\) | |||||||
\(488\) | 4.17463e7 | − | 4.64147e8i | 0.0162610 | − | 0.180795i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.39174e8 | + | 7.15347e6i | 0.0918390 | + | 0.00274682i | ||||
\(491\) | 4.43647e9i | 1.69142i | 0.533641 | + | 0.845711i | \(0.320823\pi\) | ||||
−0.533641 | + | 0.845711i | \(0.679177\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.55506e9i | − | 0.584498i | ||||||
\(494\) | 6.51724e7 | − | 2.17902e9i | 0.0243231 | − | 0.813236i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.98674e8 | − | 2.48534e9i | 0.109904 | − | 0.914535i | ||||
\(497\) | 3.62750e9i | 1.32544i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.41428e9 | 1.23012 | 0.615060 | − | 0.788481i | \(-0.289132\pi\) | ||||
0.615060 | + | 0.788481i | \(0.289132\pi\) | |||||||
\(500\) | 1.75528e9 | + | 1.05092e8i | 0.627989 | + | 0.0375988i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.75182e7 | + | 3.26049e9i | −0.0344051 | + | 1.15032i | ||||
\(503\) | −2.56937e9 | −0.900201 | −0.450100 | − | 0.892978i | \(-0.648612\pi\) | ||||
−0.450100 | + | 0.892978i | \(0.648612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.23077e9 | −0.425262 | ||||||||
\(506\) | 1.57188e7 | − | 5.25554e8i | 0.00539378 | − | 0.180339i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.55425e7 | + | 1.26174e9i | −0.0255663 | + | 0.427019i | ||||
\(509\) | −1.06039e9 | −0.356414 | −0.178207 | − | 0.983993i | \(-0.557030\pi\) | ||||
−0.178207 | + | 0.983993i | \(0.557030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.50306e9i | 1.16138i | ||||||||
\(512\) | 2.92770e9 | + | 8.07433e8i | 0.964010 | + | 0.265865i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.03704e8 | + | 3.46731e9i | −0.0336841 | + | 1.12622i | ||||
\(515\) | − | 8.25334e8i | − | 0.266259i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6.21352e8i | − | 0.197752i | ||||||
\(518\) | −3.89861e9 | − | 1.16604e8i | −1.23241 | − | 0.0368602i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.85564e7 | + | 7.62230e8i | −0.0213814 | + | 0.237725i | ||||
\(521\) | 4.18471e8i | 0.129638i | 0.997897 | + | 0.0648191i | \(0.0206470\pi\) | ||||
−0.997897 | + | 0.0648191i | \(0.979353\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.84414e9 | −1.17502 | −0.587508 | − | 0.809218i | \(-0.699891\pi\) | ||||
−0.587508 | + | 0.809218i | \(0.699891\pi\) | |||||||
\(524\) | 1.65760e8 | − | 2.76859e9i | 0.0503293 | − | 0.840618i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.87763e8 | + | 2.65522e7i | 0.265979 | + | 0.00795518i | ||||
\(527\) | −2.39927e9 | −0.714073 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.50073e9 | −0.734466 | ||||||||
\(530\) | −6.97343e8 | − | 2.08569e7i | −0.203461 | − | 0.00608533i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.66137e8 | − | 4.44512e9i | 0.0766327 | − | 1.27995i | ||||
\(533\) | 3.76667e9 | 1.07749 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.38717e8i | 0.123864i | ||||||||
\(536\) | −6.70559e8 | − | 6.03113e7i | −0.188088 | − | 0.0169169i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.99120e9 | + | 8.94642e7i | 0.828148 | + | 0.0247692i | ||||
\(539\) | 3.51181e8i | 0.0965986i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 3.23668e9i | − | 0.878838i | −0.898282 | − | 0.439419i | \(-0.855184\pi\) | ||
0.898282 | − | 0.439419i | \(-0.144816\pi\) | |||||||
\(542\) | 1.21957e8 | − | 4.07759e9i | 0.0329010 | − | 1.10003i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.33560e8 | − | 2.87842e9i | 0.115466 | − | 0.766580i | ||||
\(545\) | 2.45706e9i | 0.650173i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.94425e9 | −1.29165 | −0.645824 | − | 0.763486i | \(-0.723486\pi\) | ||||
−0.645824 | + | 0.763486i | \(0.723486\pi\) | |||||||
\(548\) | 3.91963e8 | − | 6.54672e9i | 0.101745 | − | 1.69939i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.63121e7 | + | 1.21408e9i | −0.00930640 | + | 0.311156i | ||||
\(551\) | 3.36083e9 | 0.855887 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.79490e9 | 1.96007 | ||||||||
\(554\) | −8.35356e7 | + | 2.79299e9i | −0.0208731 | + | 0.697886i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.00899e9 | + | 2.99897e8i | 1.23591 | + | 0.0739963i | ||||
\(557\) | −1.48349e9 | −0.363740 | −0.181870 | − | 0.983323i | \(-0.558215\pi\) | ||||
−0.181870 | + | 0.983323i | \(0.558215\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.01892e9i | 0.973123i | ||||||||
\(560\) | −1.86526e8 | + | 1.55213e9i | −0.0448829 | + | 0.373482i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.93522e7 | + | 1.31573e9i | −0.00935174 | + | 0.312672i | ||||
\(563\) | − | 4.65548e9i | − | 1.09947i | −0.835338 | − | 0.549737i | \(-0.814728\pi\) | ||
0.835338 | − | 0.549737i | \(-0.185272\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 3.17433e8i | − | 0.0740426i | ||||||
\(566\) | −3.45533e9 | − | 1.03346e8i | −0.801000 | − | 0.0239572i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.10413e9 | − | 4.59075e8i | −1.16870 | − | 0.105115i | ||||
\(569\) | − | 4.03603e9i | − | 0.918462i | −0.888317 | − | 0.459231i | \(-0.848125\pi\) | ||
0.888317 | − | 0.459231i | \(-0.151875\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.33338e9 | 0.974094 | 0.487047 | − | 0.873376i | \(-0.338074\pi\) | ||||
0.487047 | + | 0.873376i | \(0.338074\pi\) | |||||||
\(572\) | −1.12120e9 | − | 6.71281e7i | −0.250493 | − | 0.0149975i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.69075e9 | + | 2.30023e8i | 1.69737 | + | 0.0507669i | ||||
\(575\) | −2.08855e9 | −0.458150 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.65483e9 | 0.358623 | 0.179311 | − | 0.983792i | \(-0.442613\pi\) | ||||
0.179311 | + | 0.983792i | \(0.442613\pi\) | |||||||
\(578\) | 1.85162e9 | + | 5.53802e7i | 0.398845 | + | 0.0119291i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.17774e9 | − | 7.05135e7i | −0.250641 | − | 0.0150063i | ||||
\(581\) | 8.31398e9 | 1.75870 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.02392e9i | − | 0.214005i | ||||||
\(584\) | −4.92904e9 | − | 4.43327e8i | −1.02404 | − | 0.0921041i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.07938e9 | − | 2.41647e8i | −1.65858 | − | 0.0496066i | ||||
\(587\) | 5.30362e9i | 1.08228i | 0.840933 | + | 0.541140i | \(0.182007\pi\) | ||||
−0.840933 | + | 0.541140i | \(0.817993\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.18537e9i | − | 1.04563i | ||||||
\(590\) | 5.50349e7 | − | 1.84007e9i | 0.0110320 | − | 0.368853i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.57454e8 | − | 5.47084e9i | 0.130238 | − | 1.08375i | ||||
\(593\) | − | 7.54656e7i | − | 0.0148613i | −0.999972 | − | 0.00743066i | \(-0.997635\pi\) | ||
0.999972 | − | 0.00743066i | \(-0.00236527\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.49838e9 | 0.291616 | ||||||||
\(596\) | 9.24508e9 | + | 5.53519e8i | 1.78875 | + | 0.107095i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.77393e7 | − | 1.93049e9i | 0.0110412 | − | 0.369160i | ||||
\(599\) | −7.13988e9 | −1.35737 | −0.678683 | − | 0.734431i | \(-0.737449\pi\) | ||||
−0.678683 | + | 0.734431i | \(0.737449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.21234e9 | −1.73105 | −0.865524 | − | 0.500867i | \(-0.833015\pi\) | ||||
−0.865524 | + | 0.500867i | \(0.833015\pi\) | |||||||
\(602\) | −2.45428e8 | + | 8.20579e9i | −0.0458496 | + | 1.53297i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.29767e8 | + | 7.17813e9i | −0.0793604 | + | 1.32551i | ||||
\(605\) | −1.59156e9 | −0.292199 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.53391e9i | − | 0.459866i | −0.973206 | − | 0.229933i | \(-0.926149\pi\) | ||
0.973206 | − | 0.229933i | \(-0.0738507\pi\) | |||||||
\(608\) | 6.22090e9 | + | 9.37020e8i | 1.12251 | + | 0.169078i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.01315e7 | + | 3.38744e8i | −0.00180726 | + | 0.0604251i | ||||
\(611\) | − | 2.28239e9i | − | 0.404804i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 2.83258e9i | − | 0.496674i | −0.968674 | − | 0.248337i | \(-0.920116\pi\) | ||
0.968674 | − | 0.248337i | \(-0.0798840\pi\) | |||||||
\(614\) | 4.47558e9 | + | 1.33861e8i | 0.780298 | + | 0.0233380i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.28515e9 | − | 2.05531e8i | −0.393897 | − | 0.0354278i | ||||
\(617\) | − | 1.09456e9i | − | 0.187604i | −0.995591 | − | 0.0938018i | \(-0.970098\pi\) | ||
0.995591 | − | 0.0938018i | \(-0.0299020\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.22342e9 | −0.546260 | −0.273130 | − | 0.961977i | \(-0.588059\pi\) | ||||
−0.273130 | + | 0.961977i | \(0.588059\pi\) | |||||||
\(620\) | −1.08794e8 | + | 1.81712e9i | −0.0183330 | + | 0.306205i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.71591e9 | − | 1.41049e8i | −0.785777 | − | 0.0235019i | ||||
\(623\) | 1.03453e10 | 1.71409 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.14786e9 | 0.679585 | ||||||||
\(626\) | 2.44435e9 | + | 7.31084e7i | 0.398248 | + | 0.0119112i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.34660e8 | − | 1.06003e10i | 0.102255 | − | 1.70789i | ||||
\(629\) | −5.28138e9 | −0.846195 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.31648e9i | − | 1.31776i | −0.752248 | − | 0.658880i | \(-0.771030\pi\) | ||
0.752248 | − | 0.658880i | \(-0.228970\pi\) | |||||||
\(632\) | −9.86476e8 | + | 1.09679e10i | −0.155445 | + | 1.72828i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.57143e9 | − | 2.26454e8i | −1.17995 | − | 0.0352914i | ||||
\(635\) | − | 9.19193e8i | − | 0.142462i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.28998e9i | 0.197740i | ||||||||
\(638\) | 5.17679e7 | − | 1.73084e9i | 0.00789202 | − | 0.263867i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.16034e9 | − | 4.58882e8i | −0.325756 | − | 0.0691945i | ||||
\(641\) | − | 8.71195e9i | − | 1.30651i | −0.757138 | − | 0.653255i | \(-0.773403\pi\) | ||
0.757138 | − | 0.653255i | \(-0.226597\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.96578e9 | 1.47834 | 0.739168 | − | 0.673522i | \(-0.235219\pi\) | ||||
0.739168 | + | 0.673522i | \(0.235219\pi\) | |||||||
\(644\) | 2.35783e8 | − | 3.93814e9i | 0.0347866 | − | 0.581019i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.80266e8 | − | 6.02713e9i | 0.0263087 | − | 0.879623i | ||||
\(647\) | 4.53985e9 | 0.658987 | 0.329493 | − | 0.944158i | \(-0.393122\pi\) | ||||
0.329493 | + | 0.944158i | \(0.393122\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.70180e9 | 0.387969 | ||||||||
\(650\) | −1.33384e8 | + | 4.45964e9i | −0.0190505 | + | 0.636946i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.69563e9 | + | 1.01520e8i | 0.239588 | + | 0.0143445i | ||||
\(653\) | 2.90772e9 | 0.408655 | 0.204328 | − | 0.978903i | \(-0.434499\pi\) | ||||
0.204328 | + | 0.978903i | \(0.434499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.01695e9i | 0.280447i | ||||||||
\(656\) | −1.29695e9 | + | 1.07923e10i | −0.179375 | + | 1.49262i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.39381e8 | − | 4.66016e9i | 0.0190727 | − | 0.637690i | ||||
\(659\) | − | 3.96130e9i | − | 0.539186i | −0.962974 | − | 0.269593i | \(-0.913111\pi\) | ||
0.962974 | − | 0.269593i | \(-0.0868892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.86484e9i | 0.655184i | 0.944819 | + | 0.327592i | \(0.106237\pi\) | ||||
−0.944819 | + | 0.327592i | \(0.893763\pi\) | |||||||
\(662\) | 2.57583e9 | + | 7.70408e7i | 0.345076 | + | 0.0103209i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.05217e9 | + | 1.16983e10i | −0.139475 | + | 1.55073i | ||||
\(665\) | 3.23833e9i | 0.427017i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.97752e9 | 0.388521 | ||||||||
\(668\) | −8.47053e9 | − | 5.07145e8i | −1.09949 | − | 0.0658286i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.89387e8 | + | 1.46371e7i | 0.0628624 | + | 0.00188016i | ||||
\(671\) | −4.97381e8 | −0.0635566 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.43436e9 | −0.307845 | −0.153923 | − | 0.988083i | \(-0.549191\pi\) | ||||
−0.153923 | + | 0.988083i | \(0.549191\pi\) | |||||||
\(674\) | −3.49815e9 | − | 1.04626e8i | −0.440077 | − | 0.0131623i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.89900e9 | + | 2.33440e8i | 0.485445 | + | 0.0290644i | ||||
\(677\) | 1.30568e9 | 0.161725 | 0.0808624 | − | 0.996725i | \(-0.474233\pi\) | ||||
0.0808624 | + | 0.996725i | \(0.474233\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.02972e9i | 0.739184i | ||||||||
\(680\) | −1.89626e8 | + | 2.10832e9i | −0.0231268 | + | 0.257131i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.67048e9 | − | 7.98717e7i | −0.322363 | − | 0.00964157i | ||||
\(683\) | − | 7.27394e9i | − | 0.873569i | −0.899566 | − | 0.436785i | \(-0.856117\pi\) | ||
0.899566 | − | 0.436785i | \(-0.143883\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.76937e9i | 0.566949i | ||||||||
\(686\) | 2.06753e8 | − | 6.91271e9i | 0.0244522 | − | 0.817550i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.15150e10 | − | 1.38381e9i | −1.34805 | − | 0.162001i | ||||
\(689\) | − | 3.76111e9i | − | 0.438075i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.01649e9 | −0.232500 | −0.116250 | − | 0.993220i | \(-0.537087\pi\) | ||||
−0.116250 | + | 0.993220i | \(0.537087\pi\) | |||||||
\(692\) | −7.66511e9 | − | 4.58924e8i | −0.879321 | − | 0.0526464i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.43016e8 | + | 4.78169e9i | −0.0162415 | + | 0.543030i | ||||
\(695\) | −3.64911e9 | −0.412326 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.04185e10 | 1.16545 | ||||||||
\(698\) | −4.17614e8 | + | 1.39628e10i | −0.0464816 | + | 1.55410i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.44683e8 | + | 9.09750e9i | −0.0600206 | + | 1.00249i | ||||
\(701\) | −1.51344e10 | −1.65940 | −0.829700 | − | 0.558210i | \(-0.811488\pi\) | ||||
−0.829700 | + | 0.558210i | \(0.811488\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.14142e10i | − | 1.23909i | ||||||
\(704\) | 5.78391e8 | − | 3.18935e9i | 0.0624766 | − | 0.344507i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.98480e7 | − | 1.33230e9i | 0.00426177 | − | 0.142491i | ||||
\(707\) | − | 1.35537e10i | − | 1.44241i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.47287e10i | 1.55204i | 0.630708 | + | 0.776020i | \(0.282765\pi\) | ||||
−0.630708 | + | 0.776020i | \(0.717235\pi\) | |||||||
\(710\) | 3.72509e9 | + | 1.11414e8i | 0.390601 | + | 0.0116825i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.30924e9 | + | 1.45565e10i | −0.135937 | + | 1.51139i | ||||
\(713\) | − | 4.59396e9i | − | 0.474650i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.16808e8 | 0.0835697 | ||||||||
\(716\) | 6.12828e8 | − | 1.02357e10i | 0.0623940 | − | 1.04213i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.36929e10 | + | 4.09541e8i | 1.38057 | + | 0.0412916i | ||||
\(719\) | −2.99832e9 | −0.300834 | −0.150417 | − | 0.988623i | \(-0.548062\pi\) | ||||
−0.150417 | + | 0.988623i | \(0.548062\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.08888e9 | 0.903103 | ||||||||
\(722\) | 2.91748e9 | + | 8.72592e7i | 0.288488 | + | 0.00862842i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.93481e8 | + | 4.90182e9i | −0.0287405 | + | 0.480035i | ||||
\(725\) | −6.87837e9 | −0.670352 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.00906e9i | − | 0.869579i | −0.900532 | − | 0.434789i | \(-0.856823\pi\) | ||
0.900532 | − | 0.434789i | \(-0.143177\pi\) | |||||||
\(728\) | −8.39396e9 | − | 7.54968e8i | −0.806319 | − | 0.0725218i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.59731e9 | + | 1.07592e8i | 0.342253 | + | 0.0102365i | ||||
\(731\) | 1.11163e10i | 1.05256i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.89008e9i | 0.833761i | 0.908961 | + | 0.416880i | \(0.136877\pi\) | ||||
−0.908961 | + | 0.416880i | \(0.863123\pi\) | |||||||
\(734\) | 6.84029e7 | − | 2.28703e9i | 0.00638467 | − | 0.213469i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.51138e9 | + | 8.30150e8i | 0.509552 | + | 0.0767511i | ||||
\(737\) | 7.18573e8i | 0.0661202i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.53349e9 | 0.777806 | 0.388903 | − | 0.921279i | \(-0.372854\pi\) | ||||
0.388903 | + | 0.921279i | \(0.372854\pi\) | |||||||
\(740\) | −2.39482e8 | + | 3.99992e9i | −0.0217251 | + | 0.362861i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.29684e8 | − | 7.67939e9i | 0.0206403 | − | 0.690102i | ||||
\(743\) | 1.12936e10 | 1.01011 | 0.505057 | − | 0.863086i | \(-0.331472\pi\) | ||||
0.505057 | + | 0.863086i | \(0.331472\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.73516e9 | −0.596762 | ||||||||
\(746\) | 4.86576e7 | − | 1.62685e9i | 0.00429106 | − | 0.143470i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.10122e9 | − | 1.85675e8i | −0.270942 | − | 0.0162218i | ||||
\(749\) | −4.83131e9 | −0.420125 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 6.47122e9i | − | 0.557502i | −0.960363 | − | 0.278751i | \(-0.910080\pi\) | ||
0.960363 | − | 0.278751i | \(-0.0899204\pi\) | |||||||
\(752\) | 6.53951e9 | + | 7.85880e8i | 0.560767 | + | 0.0673898i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.90157e8 | − | 6.35783e9i | 0.0161552 | − | 0.540143i | ||||
\(755\) | − | 5.22936e9i | − | 0.442216i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.70372e9i | 0.394100i | 0.980393 | + | 0.197050i | \(0.0631361\pi\) | ||||
−0.980393 | + | 0.197050i | \(0.936864\pi\) | |||||||
\(758\) | 9.92027e9 | + | 2.96706e8i | 0.827335 | + | 0.0247448i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.55654e9 | − | 4.09824e8i | −0.376520 | − | 0.0338649i | ||||
\(761\) | 9.44372e9i | 0.776778i | 0.921496 | + | 0.388389i | \(0.126968\pi\) | ||||
−0.921496 | + | 0.388389i | \(0.873032\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.70581e10 | −2.20527 | ||||||||
\(764\) | −1.61306e10 | − | 9.65770e8i | −1.30865 | − | 0.0783514i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.31110e9 | − | 6.91228e7i | −0.185788 | − | 0.00555675i | ||||
\(767\) | 9.92441e9 | 0.794183 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.19374e9 | −0.411849 | −0.205925 | − | 0.978568i | \(-0.566020\pi\) | ||||
−0.205925 | + | 0.978568i | \(0.566020\pi\) | |||||||
\(770\) | 1.66775e9 | + | 4.98809e7i | 0.131648 | + | 0.00393746i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.53671e10 | + | 9.20057e8i | 1.20208 | + | 0.0719704i | ||||
\(773\) | −1.43367e10 | −1.11640 | −0.558202 | − | 0.829705i | \(-0.688509\pi\) | ||||
−0.558202 | + | 0.829705i | \(0.688509\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.06125e10i | 0.818959i | ||||||||
\(776\) | −8.48421e9 | − | 7.63086e8i | −0.651772 | − | 0.0586216i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.79328e10 | − | 5.36355e8i | −1.36528 | − | 0.0408341i | ||||
\(779\) | 2.25168e10i | 1.70658i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.46960e9i | 0.410844i | ||||||||
\(782\) | 1.59706e8 | − | 5.33972e9i | 0.0119426 | − | 0.399296i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.69606e9 | − | 4.44171e8i | −0.273926 | − | 0.0329188i | ||||
\(785\) | 7.72248e9i | 0.569788i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.32430e9 | 0.462489 | 0.231244 | − | 0.972896i | \(-0.425720\pi\) | ||||
0.231244 | + | 0.972896i | \(0.425720\pi\) | |||||||
\(788\) | 1.58313e10 | + | 9.47846e8i | 1.15259 | + | 0.0690074i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.39411e8 | − | 8.00462e9i | 0.0172762 | − | 0.577625i | ||||
\(791\) | 3.49568e9 | 0.251139 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.82701e9 | −0.130102 | ||||||||
\(794\) | 6.18968e7 | − | 2.06950e9i | 0.00438830 | − | 0.146721i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.28539e9 | + | 2.14691e10i | −0.0903315 | + | 1.50875i | ||||
\(797\) | 1.99261e10 | 1.39418 | 0.697091 | − | 0.716983i | \(-0.254477\pi\) | ||||
0.697091 | + | 0.716983i | \(0.254477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.31304e9i | − | 0.437850i | ||||||
\(800\) | −1.27319e10 | − | 1.91773e9i | −0.879178 | − | 0.132426i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.32137e8 | − | 1.77918e10i | 0.0364261 | − | 1.21790i | ||||
\(803\) | 5.28197e9i | 0.359991i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.86899e9i | 0.193840i | ||||||||
\(806\) | −9.80937e9 | − | 2.93389e8i | −0.659885 | − | 0.0197366i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.90709e10 | + | 1.71527e9i | 1.27184 | + | 0.114391i | ||||
\(809\) | 4.18784e9i | 0.278080i | 0.990287 | + | 0.139040i | \(0.0444017\pi\) | ||||
−0.990287 | + | 0.139040i | \(0.955598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.77264e9 | −0.248355 | −0.124177 | − | 0.992260i | \(-0.539629\pi\) | ||||
−0.124177 | + | 0.992260i | \(0.539629\pi\) | |||||||
\(812\) | 7.76521e8 | − | 1.29697e10i | 0.0508987 | − | 0.850130i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.87838e9 | − | 1.75817e8i | −0.382008 | − | 0.0114255i | ||||
\(815\) | −1.23529e9 | −0.0799314 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.40247e10 | −1.54128 | ||||||||
\(818\) | 1.88453e10 | + | 5.63646e8i | 1.20384 | + | 0.0360056i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.72424e8 | − | 7.89061e9i | 0.0299215 | − | 0.499761i | ||||
\(821\) | −8.35665e9 | −0.527025 | −0.263512 | − | 0.964656i | \(-0.584881\pi\) | ||||
−0.263512 | + | 0.964656i | \(0.584881\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.54233e10i | − | 1.58977i | −0.606763 | − | 0.794883i | \(-0.707532\pi\) | ||
0.606763 | − | 0.794883i | \(-0.292468\pi\) | |||||||
\(824\) | −1.15024e9 | + | 1.27887e10i | −0.0716212 | + | 0.796306i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.02636e10 | + | 6.06064e8i | 1.25108 | + | 0.0374187i | ||||
\(827\) | 2.71179e10i | 1.66720i | 0.552371 | + | 0.833599i | \(0.313723\pi\) | ||||
−0.552371 | + | 0.833599i | \(0.686277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.95618e10i | 1.19252i | 0.802790 | + | 0.596262i | \(0.203348\pi\) | ||||
−0.802790 | + | 0.596262i | \(0.796652\pi\) | |||||||
\(830\) | 2.55354e8 | − | 8.53767e9i | 0.0155013 | − | 0.518282i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.12458e9 | − | 1.17153e10i | 0.127891 | − | 0.705216i | ||||
\(833\) | 3.56806e9i | 0.213882i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.17089e9 | 0.366813 | ||||||||
\(836\) | 4.01285e8 | − | 6.70242e9i | 0.0237537 | − | 0.396743i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.01742e8 | − | 1.00886e10i | 0.0177126 | − | 0.592214i | ||||
\(839\) | 1.86844e10 | 1.09223 | 0.546113 | − | 0.837711i | \(-0.316107\pi\) | ||||
0.546113 | + | 0.837711i | \(0.316107\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.44381e9 | −0.431528 | ||||||||
\(842\) | 6.72570e8 | − | 2.24871e10i | 0.0388280 | − | 1.29820i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.05401e10 | + | 6.31053e8i | 0.603456 | + | 0.0361300i | ||||
\(845\) | −2.84047e9 | −0.161954 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.75268e10i | − | 0.991085i | ||||||
\(848\) | 1.07763e10 | + | 1.29504e9i | 0.606857 | + | 0.0729285i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.68937e8 | + | 1.23353e10i | −0.0206056 | + | 0.688942i | ||||
\(851\) | − | 1.01124e10i | − | 0.562473i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.55557e10i | − | 1.96150i | −0.195273 | − | 0.980749i | \(-0.562559\pi\) | ||
0.195273 | − | 0.980749i | \(-0.437441\pi\) | |||||||
\(854\) | −3.73037e9 | − | 1.11572e8i | −0.204951 | − | 0.00612989i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.11422e8 | − | 6.79797e9i | 0.0333183 | − | 0.370443i | ||||
\(857\) | 4.79883e6i | 0.000260437i | 1.00000 | 0.000130218i | \(4.14498e-5\pi\) | |||||
−1.00000 | 0.000130218i | \(0.999959\pi\) | ||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.84728e10 | −0.994388 | −0.497194 | − | 0.867639i | \(-0.665636\pi\) | ||||
−0.497194 | + | 0.867639i | \(0.665636\pi\) | |||||||
\(860\) | 8.41903e9 | + | 5.04062e8i | 0.451354 | + | 0.0270233i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.05079e10 | + | 3.14281e8i | 0.558779 | + | 0.0167126i | ||||
\(863\) | 6.22171e9 | 0.329513 | 0.164756 | − | 0.986334i | \(-0.447316\pi\) | ||||
0.164756 | + | 0.986334i | \(0.447316\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.58414e9 | 0.293359 | ||||||||
\(866\) | 1.87636e10 | + | 5.61203e8i | 0.981758 | + | 0.0293635i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.00108e10 | − | 1.19808e9i | −1.03859 | − | 0.0621823i | ||||
\(869\) | 1.17533e10 | 0.607560 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.63950e9i | 0.135350i | ||||||||
\(872\) | 3.42431e9 | − | 3.80725e10i | 0.174890 | − | 1.94448i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.15403e10 | + | 3.45160e8i | 0.584693 | + | 0.0174876i | ||||
\(875\) | − | 1.40820e10i | − | 0.710619i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.16634e10i | − | 0.583884i | −0.956436 | − | 0.291942i | \(-0.905699\pi\) | ||
0.956436 | − | 0.291942i | \(-0.0943014\pi\) | |||||||
\(878\) | −3.10492e7 | + | 1.03812e9i | −0.00154817 | + | 0.0517626i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.81246e8 | + | 2.34032e9i | −0.0139123 | + | 0.115767i | ||||
\(881\) | 9.09495e9i | 0.448110i | 0.974577 | + | 0.224055i | \(0.0719295\pi\) | ||||
−0.974577 | + | 0.224055i | \(0.928070\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.53416e10 | 0.749907 | 0.374954 | − | 0.927044i | \(-0.377659\pi\) | ||||
0.374954 | + | 0.927044i | \(0.377659\pi\) | |||||||
\(884\) | −1.13916e10 | − | 6.82033e8i | −0.554626 | − | 0.0332064i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.52705e8 | − | 8.44909e9i | 0.0122066 | − | 0.408124i | ||||
\(887\) | −2.84449e10 | −1.36858 | −0.684291 | − | 0.729209i | \(-0.739888\pi\) | ||||
−0.684291 | + | 0.729209i | \(0.739888\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.01225e10 | 0.483205 | ||||||||
\(890\) | 3.17742e8 | − | 1.06236e10i | 0.0151081 | − | 0.505135i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.47890e8 | − | 1.41618e10i | 0.0400002 | − | 0.668099i | ||||
\(893\) | 1.36439e10 | 0.641148 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.45683e9i | 0.347675i | ||||||||
\(896\) | 5.05338e9 | − | 2.37905e10i | 0.234695 | − | 1.10490i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.24283e8 | − | 4.15537e9i | 0.00572725 | − | 0.191489i | ||||
\(899\) | − | 1.51296e10i | − | 0.694494i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.04032e10i | − | 0.473837i | ||||||
\(902\) | 1.15962e10 | + | 3.46833e8i | 0.526131 | + | 0.0157361i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.42393e8 | + | 4.91866e9i | −0.0199168 | + | 0.221441i | ||||
\(905\) | − | 3.57104e9i | − | 0.160149i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.63965e10 | −0.729666 | −0.364833 | − | 0.931073i | \(-0.618874\pi\) | ||||
−0.364833 | + | 0.931073i | \(0.618874\pi\) | |||||||
\(908\) | −1.86958e9 | + | 3.12264e10i | −0.0828788 | + | 1.38427i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.12608e9 | + | 1.83225e8i | 0.269487 | + | 0.00806010i | ||||
\(911\) | 1.21999e10 | 0.534617 | 0.267309 | − | 0.963611i | \(-0.413866\pi\) | ||||
0.267309 | + | 0.963611i | \(0.413866\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.25360e10 | 0.545142 | ||||||||
\(914\) | −4.39884e10 | − | 1.31565e9i | −1.90558 | − | 0.0569941i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.90662e8 | − | 3.18450e9i | 0.00819651 | − | 0.136901i | ||||
\(917\) | −2.22114e10 | −0.951226 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.87196e10i | 1.64561i | 0.568326 | + | 0.822803i | \(0.307591\pi\) | ||||
−0.568326 | + | 0.822803i | \(0.692409\pi\) | |||||||
\(920\) | −4.03685e9 | − | 3.63082e8i | −0.170917 | − | 0.0153726i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.43255e9 | + | 2.52210e8i | 0.354324 | + | 0.0105975i | ||||
\(923\) | 2.00912e10i | 0.841009i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.33607e10i | 0.970487i | ||||||||
\(926\) | −5.96280e8 | + | 1.99364e10i | −0.0246781 | + | 0.825105i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.81510e10 | + | 2.73399e9i | 0.745561 | + | 0.112300i | ||||
\(929\) | 3.34318e10i | 1.36806i | 0.729455 | + | 0.684029i | \(0.239774\pi\) | ||||
−0.729455 | + | 0.684029i | \(0.760226\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.71138e9 | −0.313190 | ||||||||
\(932\) | −6.57284e8 | + | 1.09782e10i | −0.0265949 | + | 0.444197i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.98325e8 | + | 3.33787e10i | −0.0400920 | + | 1.34046i | ||||
\(935\) | 2.25928e9 | 0.0903917 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.13884e8 | −0.00452247 | −0.00226123 | − | 0.999997i | \(-0.500720\pi\) | ||||
−0.00226123 | + | 0.999997i | \(0.500720\pi\) | |||||||
\(938\) | −1.61189e8 | + | 5.38931e9i | −0.00637715 | + | 0.213218i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.78126e9 | − | 2.86262e8i | −0.187756 | − | 0.0112413i | ||||
\(941\) | 3.30760e10 | 1.29404 | 0.647022 | − | 0.762472i | \(-0.276014\pi\) | ||||
0.647022 | + | 0.762472i | \(0.276014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.99487e10i | 0.774682i | ||||||||
\(944\) | −3.41721e9 | + | 2.84355e10i | −0.132212 | + | 1.10017i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.70060e8 | + | 1.23728e10i | −0.0142119 | + | 0.475171i | ||||
\(947\) | − | 4.30694e10i | − | 1.64795i | −0.566627 | − | 0.823974i | \(-0.691752\pi\) | ||
0.566627 | − | 0.823974i | \(-0.308248\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.94020e10i | 0.736912i | ||||||||
\(950\) | −2.66593e10 | − | 7.97355e8i | −1.00883 | − | 0.0301730i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.32175e10 | − | 2.08823e9i | −0.872142 | − | 0.0784420i | ||||
\(953\) | − | 2.45613e10i | − | 0.919233i | −0.888118 | − | 0.459616i | \(-0.847987\pi\) | ||
0.888118 | − | 0.459616i | \(-0.152013\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.17514e10 | 0.436594 | ||||||||
\(956\) | 1.32169e10 | + | 7.91319e8i | 0.489246 | + | 0.0292920i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.65951e10 | − | 1.39362e9i | −1.71222 | − | 0.0512110i | ||||
\(959\) | −5.25221e10 | −1.92299 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.16944e9 | 0.151546 | ||||||||
\(962\) | −2.15928e10 | − | 6.45821e8i | −0.781981 | − | 0.0233883i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.71351e10 | − | 1.62463e9i | −0.975578 | − | 0.0584095i | ||||
\(965\) | −1.11952e10 | −0.401037 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.28479e10i | 0.812556i | 0.913750 | + | 0.406278i | \(0.133174\pi\) | ||||
−0.913750 | + | 0.406278i | \(0.866826\pi\) | |||||||
\(968\) | 2.46614e10 | + | 2.21809e9i | 0.873884 | + | 0.0785988i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.19195e9 | + | 1.85195e8i | 0.217834 | + | 0.00651522i | ||||
\(971\) | 4.59295e10i | 1.60999i | 0.593279 | + | 0.804997i | \(0.297833\pi\) | ||||
−0.593279 | + | 0.804997i | \(0.702167\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 4.01854e10i | − | 1.39853i | ||||||
\(974\) | −1.49787e9 | + | 5.00809e10i | −0.0519420 | + | 1.73666i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.29083e8 | − | 5.23476e9i | 0.0216588 | − | 0.180228i | ||||
\(977\) | − | 4.53672e10i | − | 1.55636i | −0.628038 | − | 0.778182i | \(-0.716142\pi\) | ||
0.628038 | − | 0.778182i | \(-0.283858\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.55988e10 | 0.531314 | ||||||||
\(980\) | 2.70231e9 | + | 1.61792e8i | 0.0917158 | + | 0.00549119i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.50055e9 | + | 5.01705e10i | −0.0505663 | + | 1.69067i | ||||
\(983\) | −2.77122e10 | −0.930536 | −0.465268 | − | 0.885170i | \(-0.654042\pi\) | ||||
−0.465268 | + | 0.885170i | \(0.654042\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.15333e10 | −0.384527 | ||||||||
\(986\) | 5.25971e8 | − | 1.75856e10i | 0.0174740 | − | 0.584237i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.47402e9 | − | 2.46197e10i | 0.0486245 | − | 0.812145i | ||||
\(989\) | −2.12846e10 | −0.699647 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.33226e9i | 0.239321i | 0.992815 | + | 0.119660i | \(0.0381806\pi\) | ||||
−0.992815 | + | 0.119660i | \(0.961819\pi\) | |||||||
\(992\) | 4.21822e9 | − | 2.80049e10i | 0.137195 | − | 0.910841i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.22693e9 | + | 4.10221e10i | −0.0396249 | + | 1.32485i | ||||
\(995\) | − | 1.56405e10i | − | 0.503350i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 2.27024e10i | − | 0.725502i | −0.931886 | − | 0.362751i | \(-0.881838\pi\) | ||
0.931886 | − | 0.362751i | \(-0.118162\pi\) | |||||||
\(998\) | 3.86109e10 | + | 1.15482e9i | 1.22957 | + | 0.0367753i | ||||
\(999\) | 0 | 0 |
(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 | 72.8.f.a.35.28 | yes | 28 | |
3.2 | odd | 2 | inner | 72.8.f.a.35.1 | ✓ | 28 | |
4.3 | odd | 2 | 288.8.f.a.143.14 | 28 | |||
8.3 | odd | 2 | inner | 72.8.f.a.35.2 | yes | 28 | |
8.5 | even | 2 | 288.8.f.a.143.15 | 28 | |||
12.11 | even | 2 | 288.8.f.a.143.16 | 28 | |||
24.5 | odd | 2 | 288.8.f.a.143.13 | 28 | |||
24.11 | even | 2 | inner | 72.8.f.a.35.27 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.8.f.a.35.1 | ✓ | 28 | 3.2 | odd | 2 | inner | |
72.8.f.a.35.2 | yes | 28 | 8.3 | odd | 2 | inner | |
72.8.f.a.35.27 | yes | 28 | 24.11 | even | 2 | inner | |
72.8.f.a.35.28 | yes | 28 | 1.1 | even | 1 | trivial | |
288.8.f.a.143.13 | 28 | 24.5 | odd | 2 | |||
288.8.f.a.143.14 | 28 | 4.3 | odd | 2 | |||
288.8.f.a.143.15 | 28 | 8.5 | even | 2 | |||
288.8.f.a.143.16 | 28 | 12.11 | even | 2 |