Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,9,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.5172802326\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.6 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.9.b.b.42.23 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 23.5327i | − | 1.47080i | −0.677636 | − | 0.735398i | \(-0.736995\pi\) | ||
0.677636 | − | 0.735398i | \(-0.263005\pi\) | |||||||
\(3\) | 46.0777i | 0.568861i | 0.958697 | + | 0.284430i | \(0.0918044\pi\) | ||||
−0.958697 | + | 0.284430i | \(0.908196\pi\) | |||||||
\(4\) | −297.789 | −1.16324 | ||||||||
\(5\) | − | 373.886i | − | 0.598217i | −0.954219 | − | 0.299108i | \(-0.903311\pi\) | ||
0.954219 | − | 0.299108i | \(-0.0966892\pi\) | |||||||
\(6\) | 1084.33 | 0.836678 | ||||||||
\(7\) | − | 2487.41i | − | 1.03599i | −0.855384 | − | 0.517994i | \(-0.826679\pi\) | ||
0.855384 | − | 0.517994i | \(-0.173321\pi\) | |||||||
\(8\) | 983.414i | 0.240091i | ||||||||
\(9\) | 4437.84 | 0.676398 | ||||||||
\(10\) | −8798.55 | −0.879855 | ||||||||
\(11\) | 7400.35 | 0.505454 | 0.252727 | − | 0.967538i | \(-0.418673\pi\) | ||||
0.252727 | + | 0.967538i | \(0.418673\pi\) | |||||||
\(12\) | − | 13721.4i | − | 0.661721i | ||||||
\(13\) | −36285.4 | −1.27045 | −0.635227 | − | 0.772325i | \(-0.719094\pi\) | ||||
−0.635227 | + | 0.772325i | \(0.719094\pi\) | |||||||
\(14\) | −58535.4 | −1.52373 | ||||||||
\(15\) | 17227.8 | 0.340302 | ||||||||
\(16\) | −53091.6 | −0.810114 | ||||||||
\(17\) | −88832.2 | −1.06359 | −0.531795 | − | 0.846873i | \(-0.678482\pi\) | ||||
−0.531795 | + | 0.846873i | \(0.678482\pi\) | |||||||
\(18\) | − | 104435.i | − | 0.994843i | ||||||
\(19\) | 41818.3i | 0.320887i | 0.987045 | + | 0.160443i | \(0.0512924\pi\) | ||||
−0.987045 | + | 0.160443i | \(0.948708\pi\) | |||||||
\(20\) | 111339.i | 0.695869i | ||||||||
\(21\) | 114614. | 0.589332 | ||||||||
\(22\) | − | 174150.i | − | 0.743419i | ||||||
\(23\) | −294498. | −1.05238 | −0.526188 | − | 0.850368i | \(-0.676379\pi\) | ||||
−0.526188 | + | 0.850368i | \(0.676379\pi\) | |||||||
\(24\) | −45313.5 | −0.136579 | ||||||||
\(25\) | 250835. | 0.642137 | ||||||||
\(26\) | 853895.i | 1.86858i | ||||||||
\(27\) | 506802.i | 0.953637i | ||||||||
\(28\) | 740723.i | 1.20510i | ||||||||
\(29\) | 43140.9i | 0.0609954i | 0.999535 | + | 0.0304977i | \(0.00970923\pi\) | ||||
−0.999535 | + | 0.0304977i | \(0.990291\pi\) | |||||||
\(30\) | − | 405417.i | − | 0.500515i | ||||||
\(31\) | −557310. | −0.603463 | −0.301731 | − | 0.953393i | \(-0.597565\pi\) | ||||
−0.301731 | + | 0.953393i | \(0.597565\pi\) | |||||||
\(32\) | 1.50114e6i | 1.43160i | ||||||||
\(33\) | 340991.i | 0.287533i | ||||||||
\(34\) | 2.09046e6i | 1.56432i | ||||||||
\(35\) | −930005. | −0.619745 | ||||||||
\(36\) | −1.32154e6 | −0.786812 | ||||||||
\(37\) | − | 3.70010e6i | − | 1.97427i | −0.159887 | − | 0.987135i | \(-0.551113\pi\) | ||
0.159887 | − | 0.987135i | \(-0.448887\pi\) | |||||||
\(38\) | 984099. | 0.471959 | ||||||||
\(39\) | − | 1.67195e6i | − | 0.722711i | ||||||
\(40\) | 367684. | 0.143627 | ||||||||
\(41\) | 1.14292e6 | 0.404463 | 0.202232 | − | 0.979338i | \(-0.435181\pi\) | ||||
0.202232 | + | 0.979338i | \(0.435181\pi\) | |||||||
\(42\) | − | 2.69718e6i | − | 0.866787i | ||||||
\(43\) | −2.60367e6 | − | 2.21565e6i | −0.761574 | − | 0.648078i | ||||
\(44\) | −2.20374e6 | −0.587963 | ||||||||
\(45\) | − | 1.65925e6i | − | 0.404632i | ||||||
\(46\) | 6.93034e6i | 1.54783i | ||||||||
\(47\) | −721451. | −0.147848 | −0.0739240 | − | 0.997264i | \(-0.523552\pi\) | ||||
−0.0739240 | + | 0.997264i | \(0.523552\pi\) | |||||||
\(48\) | − | 2.44634e6i | − | 0.460842i | ||||||
\(49\) | −422388. | −0.0732702 | ||||||||
\(50\) | − | 5.90282e6i | − | 0.944452i | ||||||
\(51\) | − | 4.09318e6i | − | 0.605035i | ||||||
\(52\) | 1.08054e7 | 1.47784 | ||||||||
\(53\) | −8.22613e6 | −1.04254 | −0.521269 | − | 0.853392i | \(-0.674541\pi\) | ||||
−0.521269 | + | 0.853392i | \(0.674541\pi\) | |||||||
\(54\) | 1.19264e7 | 1.40260 | ||||||||
\(55\) | − | 2.76688e6i | − | 0.302371i | ||||||
\(56\) | 2.44615e6 | 0.248732 | ||||||||
\(57\) | −1.92689e6 | −0.182540 | ||||||||
\(58\) | 1.01522e6 | 0.0897118 | ||||||||
\(59\) | 5.76533e6 | 0.475791 | 0.237895 | − | 0.971291i | \(-0.423542\pi\) | ||||
0.237895 | + | 0.971291i | \(0.423542\pi\) | |||||||
\(60\) | −5.13025e6 | −0.395853 | ||||||||
\(61\) | 1.24108e7i | 0.896355i | 0.893945 | + | 0.448178i | \(0.147927\pi\) | ||||
−0.893945 | + | 0.448178i | \(0.852073\pi\) | |||||||
\(62\) | 1.31150e7i | 0.887570i | ||||||||
\(63\) | − | 1.10387e7i | − | 0.700740i | ||||||
\(64\) | 2.17346e7 | 1.29548 | ||||||||
\(65\) | 1.35666e7i | 0.760007i | ||||||||
\(66\) | 8.02445e6 | 0.422902 | ||||||||
\(67\) | 2.60940e7 | 1.29492 | 0.647458 | − | 0.762101i | \(-0.275832\pi\) | ||||
0.647458 | + | 0.762101i | \(0.275832\pi\) | |||||||
\(68\) | 2.64533e7 | 1.23721 | ||||||||
\(69\) | − | 1.35698e7i | − | 0.598655i | ||||||
\(70\) | 2.18856e7i | 0.911518i | ||||||||
\(71\) | − | 3.21676e7i | − | 1.26586i | −0.774209 | − | 0.632930i | \(-0.781852\pi\) | ||
0.774209 | − | 0.632930i | \(-0.218148\pi\) | |||||||
\(72\) | 4.36424e6i | 0.162397i | ||||||||
\(73\) | − | 1.56616e7i | − | 0.551498i | −0.961230 | − | 0.275749i | \(-0.911074\pi\) | ||
0.961230 | − | 0.275749i | \(-0.0889258\pi\) | |||||||
\(74\) | −8.70735e7 | −2.90375 | ||||||||
\(75\) | 1.15579e7i | 0.365286i | ||||||||
\(76\) | − | 1.24530e7i | − | 0.373268i | ||||||
\(77\) | − | 1.84077e7i | − | 0.523644i | ||||||
\(78\) | −3.93455e7 | −1.06296 | ||||||||
\(79\) | 2.11723e7 | 0.543576 | 0.271788 | − | 0.962357i | \(-0.412385\pi\) | ||||
0.271788 | + | 0.962357i | \(0.412385\pi\) | |||||||
\(80\) | 1.98502e7i | 0.484624i | ||||||||
\(81\) | 5.76445e6 | 0.133911 | ||||||||
\(82\) | − | 2.68960e7i | − | 0.594883i | ||||||
\(83\) | −5.69127e7 | −1.19921 | −0.599607 | − | 0.800294i | \(-0.704676\pi\) | ||||
−0.599607 | + | 0.800294i | \(0.704676\pi\) | |||||||
\(84\) | −3.41308e7 | −0.685535 | ||||||||
\(85\) | 3.32131e7i | 0.636258i | ||||||||
\(86\) | −5.21402e7 | + | 6.12715e7i | −0.953189 | + | 1.12012i | ||||
\(87\) | −1.98783e6 | −0.0346979 | ||||||||
\(88\) | 7.27761e6i | 0.121355i | ||||||||
\(89\) | − | 6.26121e7i | − | 0.997926i | −0.866623 | − | 0.498963i | \(-0.833714\pi\) | ||
0.866623 | − | 0.498963i | \(-0.166286\pi\) | |||||||
\(90\) | −3.90466e7 | −0.595132 | ||||||||
\(91\) | 9.02566e7i | 1.31617i | ||||||||
\(92\) | 8.76983e7 | 1.22417 | ||||||||
\(93\) | − | 2.56796e7i | − | 0.343286i | ||||||
\(94\) | 1.69777e7i | 0.217454i | ||||||||
\(95\) | 1.56353e7 | 0.191960 | ||||||||
\(96\) | −6.91693e7 | −0.814383 | ||||||||
\(97\) | 1.82440e7 | 0.206079 | 0.103039 | − | 0.994677i | \(-0.467143\pi\) | ||||
0.103039 | + | 0.994677i | \(0.467143\pi\) | |||||||
\(98\) | 9.93994e6i | 0.107765i | ||||||||
\(99\) | 3.28416e7 | 0.341888 | ||||||||
\(100\) | −7.46958e7 | −0.746958 | ||||||||
\(101\) | 1.12667e8 | 1.08271 | 0.541354 | − | 0.840795i | \(-0.317912\pi\) | ||||
0.541354 | + | 0.840795i | \(0.317912\pi\) | |||||||
\(102\) | −9.63237e7 | −0.889882 | ||||||||
\(103\) | 5.41519e6 | 0.0481132 | 0.0240566 | − | 0.999711i | \(-0.492342\pi\) | ||||
0.0240566 | + | 0.999711i | \(0.492342\pi\) | |||||||
\(104\) | − | 3.56836e7i | − | 0.305025i | ||||||
\(105\) | − | 4.28525e7i | − | 0.352549i | ||||||
\(106\) | 1.93583e8i | 1.53336i | ||||||||
\(107\) | 1.01525e8 | 0.774527 | 0.387264 | − | 0.921969i | \(-0.373420\pi\) | ||||
0.387264 | + | 0.921969i | \(0.373420\pi\) | |||||||
\(108\) | − | 1.50920e8i | − | 1.10931i | ||||||
\(109\) | 1.10356e8 | 0.781791 | 0.390896 | − | 0.920435i | \(-0.372165\pi\) | ||||
0.390896 | + | 0.920435i | \(0.372165\pi\) | |||||||
\(110\) | −6.51123e7 | −0.444726 | ||||||||
\(111\) | 1.70492e8 | 1.12308 | ||||||||
\(112\) | 1.32060e8i | 0.839268i | ||||||||
\(113\) | − | 5.64521e7i | − | 0.346231i | −0.984901 | − | 0.173116i | \(-0.944617\pi\) | ||
0.984901 | − | 0.173116i | \(-0.0553835\pi\) | |||||||
\(114\) | 4.53450e7i | 0.268479i | ||||||||
\(115\) | 1.10109e8i | 0.629549i | ||||||||
\(116\) | − | 1.28469e7i | − | 0.0709523i | ||||||
\(117\) | −1.61029e8 | −0.859332 | ||||||||
\(118\) | − | 1.35674e8i | − | 0.699791i | ||||||
\(119\) | 2.20962e8i | 1.10187i | ||||||||
\(120\) | 1.69421e7i | 0.0817036i | ||||||||
\(121\) | −1.59594e8 | −0.744517 | ||||||||
\(122\) | 2.92060e8 | 1.31836 | ||||||||
\(123\) | 5.26630e7i | 0.230083i | ||||||||
\(124\) | 1.65961e8 | 0.701971 | ||||||||
\(125\) | − | 2.39832e8i | − | 0.982354i | ||||||
\(126\) | −2.59771e8 | −1.03064 | ||||||||
\(127\) | −3.89323e6 | −0.0149656 | −0.00748281 | − | 0.999972i | \(-0.502382\pi\) | ||||
−0.00748281 | + | 0.999972i | \(0.502382\pi\) | |||||||
\(128\) | − | 1.27181e8i | − | 0.473785i | ||||||
\(129\) | 1.02092e8 | − | 1.19971e8i | 0.368666 | − | 0.433230i | ||||
\(130\) | 3.19259e8 | 1.11782 | ||||||||
\(131\) | − | 5.05331e8i | − | 1.71590i | −0.513736 | − | 0.857948i | \(-0.671739\pi\) | ||
0.513736 | − | 0.857948i | \(-0.328261\pi\) | |||||||
\(132\) | − | 1.01543e8i | − | 0.334469i | ||||||
\(133\) | 1.04019e8 | 0.332435 | ||||||||
\(134\) | − | 6.14063e8i | − | 1.90456i | ||||||
\(135\) | 1.89486e8 | 0.570481 | ||||||||
\(136\) | − | 8.73588e7i | − | 0.255359i | ||||||
\(137\) | 2.61606e8i | 0.742618i | 0.928509 | + | 0.371309i | \(0.121091\pi\) | ||||
−0.928509 | + | 0.371309i | \(0.878909\pi\) | |||||||
\(138\) | −3.19334e8 | −0.880500 | ||||||||
\(139\) | 6.91310e8 | 1.85188 | 0.925942 | − | 0.377666i | \(-0.123273\pi\) | ||||
0.925942 | + | 0.377666i | \(0.123273\pi\) | |||||||
\(140\) | 2.76946e8 | 0.720912 | ||||||||
\(141\) | − | 3.32428e7i | − | 0.0841048i | ||||||
\(142\) | −7.56992e8 | −1.86182 | ||||||||
\(143\) | −2.68525e8 | −0.642156 | ||||||||
\(144\) | −2.35612e8 | −0.547959 | ||||||||
\(145\) | 1.61298e7 | 0.0364885 | ||||||||
\(146\) | −3.68559e8 | −0.811141 | ||||||||
\(147\) | − | 1.94627e7i | − | 0.0416805i | ||||||
\(148\) | 1.10185e9i | 2.29655i | ||||||||
\(149\) | − | 5.93902e8i | − | 1.20495i | −0.798137 | − | 0.602476i | \(-0.794181\pi\) | ||
0.798137 | − | 0.602476i | \(-0.205819\pi\) | |||||||
\(150\) | 2.71989e8 | 0.537261 | ||||||||
\(151\) | 1.81225e8i | 0.348587i | 0.984694 | + | 0.174293i | \(0.0557641\pi\) | ||||
−0.984694 | + | 0.174293i | \(0.944236\pi\) | |||||||
\(152\) | −4.11247e7 | −0.0770422 | ||||||||
\(153\) | −3.94223e8 | −0.719410 | ||||||||
\(154\) | −4.33183e8 | −0.770173 | ||||||||
\(155\) | 2.08370e8i | 0.361002i | ||||||||
\(156\) | 4.97889e8i | 0.840686i | ||||||||
\(157\) | − | 2.30311e8i | − | 0.379067i | −0.981874 | − | 0.189533i | \(-0.939302\pi\) | ||
0.981874 | − | 0.189533i | \(-0.0606975\pi\) | |||||||
\(158\) | − | 4.98243e8i | − | 0.799489i | ||||||
\(159\) | − | 3.79041e8i | − | 0.593059i | ||||||
\(160\) | 5.61256e8 | 0.856409 | ||||||||
\(161\) | 7.32536e8i | 1.09025i | ||||||||
\(162\) | − | 1.35653e8i | − | 0.196956i | ||||||
\(163\) | 8.19691e8i | 1.16118i | 0.814196 | + | 0.580590i | \(0.197178\pi\) | ||||
−0.814196 | + | 0.580590i | \(0.802822\pi\) | |||||||
\(164\) | −3.40348e8 | −0.470488 | ||||||||
\(165\) | 1.27492e8 | 0.172007 | ||||||||
\(166\) | 1.33931e9i | 1.76380i | ||||||||
\(167\) | 2.35824e8 | 0.303195 | 0.151597 | − | 0.988442i | \(-0.451558\pi\) | ||||
0.151597 | + | 0.988442i | \(0.451558\pi\) | |||||||
\(168\) | 1.12713e8i | 0.141494i | ||||||||
\(169\) | 5.00903e8 | 0.614054 | ||||||||
\(170\) | 7.81594e8 | 0.935805 | ||||||||
\(171\) | 1.85583e8i | 0.217047i | ||||||||
\(172\) | 7.75345e8 | + | 6.59796e8i | 0.885893 | + | 0.753869i | ||||
\(173\) | −1.31006e9 | −1.46254 | −0.731270 | − | 0.682088i | \(-0.761072\pi\) | ||||
−0.731270 | + | 0.682088i | \(0.761072\pi\) | |||||||
\(174\) | 4.67792e7i | 0.0510335i | ||||||||
\(175\) | − | 6.23927e8i | − | 0.665245i | ||||||
\(176\) | −3.92896e8 | −0.409475 | ||||||||
\(177\) | 2.65653e8i | 0.270659i | ||||||||
\(178\) | −1.47343e9 | −1.46774 | ||||||||
\(179\) | − | 5.68976e8i | − | 0.554219i | −0.960838 | − | 0.277110i | \(-0.910623\pi\) | ||
0.960838 | − | 0.277110i | \(-0.0893765\pi\) | |||||||
\(180\) | 4.94106e8i | 0.470684i | ||||||||
\(181\) | 3.63916e8 | 0.339068 | 0.169534 | − | 0.985524i | \(-0.445774\pi\) | ||||
0.169534 | + | 0.985524i | \(0.445774\pi\) | |||||||
\(182\) | 2.12398e9 | 1.93582 | ||||||||
\(183\) | −5.71861e8 | −0.509901 | ||||||||
\(184\) | − | 2.89614e8i | − | 0.252667i | ||||||
\(185\) | −1.38341e9 | −1.18104 | ||||||||
\(186\) | −6.04311e8 | −0.504904 | ||||||||
\(187\) | −6.57389e8 | −0.537596 | ||||||||
\(188\) | 2.14840e8 | 0.171982 | ||||||||
\(189\) | 1.26062e9 | 0.987956 | ||||||||
\(190\) | − | 3.67940e8i | − | 0.282334i | ||||||
\(191\) | − | 1.85510e9i | − | 1.39390i | −0.717118 | − | 0.696952i | \(-0.754539\pi\) | ||
0.717118 | − | 0.696952i | \(-0.245461\pi\) | |||||||
\(192\) | 1.00148e9i | 0.736948i | ||||||||
\(193\) | −2.33960e9 | −1.68621 | −0.843105 | − | 0.537749i | \(-0.819275\pi\) | ||||
−0.843105 | + | 0.537749i | \(0.819275\pi\) | |||||||
\(194\) | − | 4.29331e8i | − | 0.303099i | ||||||
\(195\) | −6.25118e8 | −0.432338 | ||||||||
\(196\) | 1.25783e8 | 0.0852307 | ||||||||
\(197\) | 2.19809e8 | 0.145942 | 0.0729710 | − | 0.997334i | \(-0.476752\pi\) | ||||
0.0729710 | + | 0.997334i | \(0.476752\pi\) | |||||||
\(198\) | − | 7.72852e8i | − | 0.502847i | ||||||
\(199\) | − | 4.33133e8i | − | 0.276190i | −0.990419 | − | 0.138095i | \(-0.955902\pi\) | ||
0.990419 | − | 0.138095i | \(-0.0440980\pi\) | |||||||
\(200\) | 2.46674e8i | 0.154171i | ||||||||
\(201\) | 1.20235e9i | 0.736627i | ||||||||
\(202\) | − | 2.65136e9i | − | 1.59244i | ||||||
\(203\) | 1.07309e8 | 0.0631905 | ||||||||
\(204\) | 1.21891e9i | 0.703800i | ||||||||
\(205\) | − | 4.27320e8i | − | 0.241957i | ||||||
\(206\) | − | 1.27434e8i | − | 0.0707647i | ||||||
\(207\) | −1.30694e9 | −0.711825 | ||||||||
\(208\) | 1.92645e9 | 1.02921 | ||||||||
\(209\) | 3.09470e8i | 0.162193i | ||||||||
\(210\) | −1.00844e9 | −0.518527 | ||||||||
\(211\) | − | 1.78019e9i | − | 0.898127i | −0.893500 | − | 0.449063i | \(-0.851758\pi\) | ||
0.893500 | − | 0.449063i | \(-0.148242\pi\) | |||||||
\(212\) | 2.44965e9 | 1.21272 | ||||||||
\(213\) | 1.48221e9 | 0.720097 | ||||||||
\(214\) | − | 2.38915e9i | − | 1.13917i | ||||||
\(215\) | −8.28399e8 | + | 9.73475e8i | −0.387691 | + | 0.455587i | ||||
\(216\) | −4.98396e8 | −0.228960 | ||||||||
\(217\) | 1.38626e9i | 0.625180i | ||||||||
\(218\) | − | 2.59698e9i | − | 1.14986i | ||||||
\(219\) | 7.21649e8 | 0.313725 | ||||||||
\(220\) | 8.23948e8i | 0.351730i | ||||||||
\(221\) | 3.22331e9 | 1.35124 | ||||||||
\(222\) | − | 4.01215e9i | − | 1.65183i | ||||||
\(223\) | 1.99684e8i | 0.0807465i | 0.999185 | + | 0.0403732i | \(0.0128547\pi\) | ||||
−0.999185 | + | 0.0403732i | \(0.987145\pi\) | |||||||
\(224\) | 3.73396e9 | 1.48312 | ||||||||
\(225\) | 1.11317e9 | 0.434340 | ||||||||
\(226\) | −1.32847e9 | −0.509236 | ||||||||
\(227\) | 5.20422e9i | 1.95998i | 0.199036 | + | 0.979992i | \(0.436219\pi\) | ||||
−0.199036 | + | 0.979992i | \(0.563781\pi\) | |||||||
\(228\) | 5.73808e8 | 0.212338 | ||||||||
\(229\) | −3.23276e9 | −1.17552 | −0.587762 | − | 0.809034i | \(-0.699991\pi\) | ||||
−0.587762 | + | 0.809034i | \(0.699991\pi\) | |||||||
\(230\) | 2.59115e9 | 0.925938 | ||||||||
\(231\) | 8.48183e8 | 0.297880 | ||||||||
\(232\) | −4.24254e7 | −0.0146445 | ||||||||
\(233\) | − | 2.31185e9i | − | 0.784397i | −0.919881 | − | 0.392199i | \(-0.871715\pi\) | ||
0.919881 | − | 0.392199i | \(-0.128285\pi\) | |||||||
\(234\) | 3.78946e9i | 1.26390i | ||||||||
\(235\) | 2.69740e8i | 0.0884451i | ||||||||
\(236\) | −1.71685e9 | −0.553458 | ||||||||
\(237\) | 9.75573e8i | 0.309219i | ||||||||
\(238\) | 5.19983e9 | 1.62062 | ||||||||
\(239\) | 1.60464e9 | 0.491798 | 0.245899 | − | 0.969295i | \(-0.420917\pi\) | ||||
0.245899 | + | 0.969295i | \(0.420917\pi\) | |||||||
\(240\) | −9.14651e8 | −0.275683 | ||||||||
\(241\) | 2.76525e9i | 0.819723i | 0.912148 | + | 0.409861i | \(0.134423\pi\) | ||||
−0.912148 | + | 0.409861i | \(0.865577\pi\) | |||||||
\(242\) | 3.75568e9i | 1.09503i | ||||||||
\(243\) | 3.59074e9i | 1.02981i | ||||||||
\(244\) | − | 3.69580e9i | − | 1.04268i | ||||||
\(245\) | 1.57925e8i | 0.0438314i | ||||||||
\(246\) | 1.23930e9 | 0.338406 | ||||||||
\(247\) | − | 1.51740e9i | − | 0.407672i | ||||||
\(248\) | − | 5.48067e8i | − | 0.144886i | ||||||
\(249\) | − | 2.62241e9i | − | 0.682186i | ||||||
\(250\) | −5.64391e9 | −1.44484 | ||||||||
\(251\) | 4.50337e9 | 1.13460 | 0.567299 | − | 0.823512i | \(-0.307988\pi\) | ||||
0.567299 | + | 0.823512i | \(0.307988\pi\) | |||||||
\(252\) | 3.28721e9i | 0.815128i | ||||||||
\(253\) | −2.17939e9 | −0.531927 | ||||||||
\(254\) | 9.16182e7i | 0.0220114i | ||||||||
\(255\) | −1.53038e9 | −0.361942 | ||||||||
\(256\) | 2.57114e9 | 0.598640 | ||||||||
\(257\) | 4.59914e9i | 1.05425i | 0.849787 | + | 0.527126i | \(0.176730\pi\) | ||||
−0.849787 | + | 0.527126i | \(0.823270\pi\) | |||||||
\(258\) | −2.82325e9 | − | 2.40250e9i | −0.637192 | − | 0.542232i | ||||
\(259\) | −9.20365e9 | −2.04532 | ||||||||
\(260\) | − | 4.03999e9i | − | 0.884070i | ||||||
\(261\) | 1.91453e8i | 0.0412572i | ||||||||
\(262\) | −1.18918e10 | −2.52373 | ||||||||
\(263\) | − | 4.72634e9i | − | 0.987875i | −0.869498 | − | 0.493937i | \(-0.835557\pi\) | ||
0.869498 | − | 0.493937i | \(-0.164443\pi\) | |||||||
\(264\) | −3.35335e8 | −0.0690341 | ||||||||
\(265\) | 3.07563e9i | 0.623664i | ||||||||
\(266\) | − | 2.44785e9i | − | 0.488944i | ||||||
\(267\) | 2.88502e9 | 0.567681 | ||||||||
\(268\) | −7.77052e9 | −1.50630 | ||||||||
\(269\) | −6.99220e9 | −1.33538 | −0.667690 | − | 0.744440i | \(-0.732717\pi\) | ||||
−0.667690 | + | 0.744440i | \(0.732717\pi\) | |||||||
\(270\) | − | 4.45912e9i | − | 0.839062i | ||||||
\(271\) | 4.98868e8 | 0.0924929 | 0.0462464 | − | 0.998930i | \(-0.485274\pi\) | ||||
0.0462464 | + | 0.998930i | \(0.485274\pi\) | |||||||
\(272\) | 4.71624e9 | 0.861630 | ||||||||
\(273\) | −4.15882e9 | −0.748720 | ||||||||
\(274\) | 6.15631e9 | 1.09224 | ||||||||
\(275\) | 1.85626e9 | 0.324570 | ||||||||
\(276\) | 4.04094e9i | 0.696379i | ||||||||
\(277\) | 2.44613e9i | 0.415489i | 0.978183 | + | 0.207745i | \(0.0666123\pi\) | ||||
−0.978183 | + | 0.207745i | \(0.933388\pi\) | |||||||
\(278\) | − | 1.62684e10i | − | 2.72374i | ||||||
\(279\) | −2.47326e9 | −0.408181 | ||||||||
\(280\) | − | 9.14581e8i | − | 0.148796i | ||||||
\(281\) | 5.33032e9 | 0.854925 | 0.427462 | − | 0.904033i | \(-0.359408\pi\) | ||||
0.427462 | + | 0.904033i | \(0.359408\pi\) | |||||||
\(282\) | −7.82293e8 | −0.123701 | ||||||||
\(283\) | 6.55249e9 | 1.02155 | 0.510776 | − | 0.859714i | \(-0.329358\pi\) | ||||
0.510776 | + | 0.859714i | \(0.329358\pi\) | |||||||
\(284\) | 9.57917e9i | 1.47250i | ||||||||
\(285\) | 7.20437e8i | 0.109198i | ||||||||
\(286\) | 6.31912e9i | 0.944480i | ||||||||
\(287\) | − | 2.84290e9i | − | 0.419019i | ||||||
\(288\) | 6.66185e9i | 0.968333i | ||||||||
\(289\) | 9.15395e8 | 0.131225 | ||||||||
\(290\) | − | 3.79577e8i | − | 0.0536671i | ||||||
\(291\) | 8.40641e8i | 0.117230i | ||||||||
\(292\) | 4.66385e9i | 0.641524i | ||||||||
\(293\) | −6.99212e9 | −0.948720 | −0.474360 | − | 0.880331i | \(-0.657321\pi\) | ||||
−0.474360 | + | 0.880331i | \(0.657321\pi\) | |||||||
\(294\) | −4.58010e8 | −0.0613035 | ||||||||
\(295\) | − | 2.15557e9i | − | 0.284626i | ||||||
\(296\) | 3.63873e9 | 0.474005 | ||||||||
\(297\) | 3.75051e9i | 0.482019i | ||||||||
\(298\) | −1.39761e10 | −1.77224 | ||||||||
\(299\) | 1.06860e10 | 1.33700 | ||||||||
\(300\) | − | 3.44181e9i | − | 0.424915i | ||||||
\(301\) | −5.51122e9 | + | 6.47639e9i | −0.671400 | + | 0.788982i | ||||
\(302\) | 4.26472e9 | 0.512700 | ||||||||
\(303\) | 5.19144e9i | 0.615910i | ||||||||
\(304\) | − | 2.22020e9i | − | 0.259955i | ||||||
\(305\) | 4.64022e9 | 0.536215 | ||||||||
\(306\) | 9.27715e9i | 1.05811i | ||||||||
\(307\) | 1.24677e10 | 1.40357 | 0.701783 | − | 0.712391i | \(-0.252387\pi\) | ||||
0.701783 | + | 0.712391i | \(0.252387\pi\) | |||||||
\(308\) | 5.48161e9i | 0.609123i | ||||||||
\(309\) | 2.49519e8i | 0.0273697i | ||||||||
\(310\) | 4.90352e9 | 0.530959 | ||||||||
\(311\) | 7.46273e9 | 0.797731 | 0.398865 | − | 0.917010i | \(-0.369404\pi\) | ||||
0.398865 | + | 0.917010i | \(0.369404\pi\) | |||||||
\(312\) | 1.64422e9 | 0.173517 | ||||||||
\(313\) | − | 1.52569e10i | − | 1.58960i | −0.606869 | − | 0.794802i | \(-0.707575\pi\) | ||
0.606869 | − | 0.794802i | \(-0.292425\pi\) | |||||||
\(314\) | −5.41984e9 | −0.557530 | ||||||||
\(315\) | −4.12722e9 | −0.419194 | ||||||||
\(316\) | −6.30489e9 | −0.632309 | ||||||||
\(317\) | 2.80977e9 | 0.278250 | 0.139125 | − | 0.990275i | \(-0.455571\pi\) | ||||
0.139125 | + | 0.990275i | \(0.455571\pi\) | |||||||
\(318\) | −8.91988e9 | −0.872269 | ||||||||
\(319\) | 3.19258e8i | 0.0308304i | ||||||||
\(320\) | − | 8.12624e9i | − | 0.774979i | ||||||
\(321\) | 4.67803e9i | 0.440598i | ||||||||
\(322\) | 1.72386e10 | 1.60353 | ||||||||
\(323\) | − | 3.71481e9i | − | 0.341292i | ||||||
\(324\) | −1.71659e9 | −0.155771 | ||||||||
\(325\) | −9.10164e9 | −0.815805 | ||||||||
\(326\) | 1.92896e10 | 1.70786 | ||||||||
\(327\) | 5.08496e9i | 0.444730i | ||||||||
\(328\) | 1.12396e9i | 0.0971082i | ||||||||
\(329\) | 1.79454e9i | 0.153169i | ||||||||
\(330\) | − | 3.00023e9i | − | 0.252987i | ||||||
\(331\) | − | 6.18867e9i | − | 0.515567i | −0.966203 | − | 0.257784i | \(-0.917008\pi\) | ||
0.966203 | − | 0.257784i | \(-0.0829922\pi\) | |||||||
\(332\) | 1.69480e10 | 1.39497 | ||||||||
\(333\) | − | 1.64205e10i | − | 1.33539i | ||||||
\(334\) | − | 5.54957e9i | − | 0.445937i | ||||||
\(335\) | − | 9.75617e9i | − | 0.774641i | ||||||
\(336\) | −6.08504e9 | −0.477426 | ||||||||
\(337\) | 1.61697e10 | 1.25367 | 0.626835 | − | 0.779152i | \(-0.284350\pi\) | ||||
0.626835 | + | 0.779152i | \(0.284350\pi\) | |||||||
\(338\) | − | 1.17876e10i | − | 0.903148i | ||||||
\(339\) | 2.60118e9 | 0.196957 | ||||||||
\(340\) | − | 9.89049e9i | − | 0.740120i | ||||||
\(341\) | −4.12429e9 | −0.305022 | ||||||||
\(342\) | 4.36728e9 | 0.319232 | ||||||||
\(343\) | − | 1.32888e10i | − | 0.960081i | ||||||
\(344\) | 2.17890e9 | − | 2.56049e9i | 0.155598 | − | 0.182847i | ||||
\(345\) | −5.07355e9 | −0.358126 | ||||||||
\(346\) | 3.08294e10i | 2.15110i | ||||||||
\(347\) | − | 2.32144e10i | − | 1.60118i | −0.599214 | − | 0.800589i | \(-0.704520\pi\) | ||
0.599214 | − | 0.800589i | \(-0.295480\pi\) | |||||||
\(348\) | 5.91956e8 | 0.0403620 | ||||||||
\(349\) | 1.73500e10i | 1.16949i | 0.811216 | + | 0.584747i | \(0.198806\pi\) | ||||
−0.811216 | + | 0.584747i | \(0.801194\pi\) | |||||||
\(350\) | −1.46827e10 | −0.978440 | ||||||||
\(351\) | − | 1.83895e10i | − | 1.21155i | ||||||
\(352\) | 1.11090e10i | 0.723609i | ||||||||
\(353\) | −1.64013e10 | −1.05628 | −0.528139 | − | 0.849158i | \(-0.677110\pi\) | ||||
−0.528139 | + | 0.849158i | \(0.677110\pi\) | |||||||
\(354\) | 6.25154e9 | 0.398083 | ||||||||
\(355\) | −1.20270e10 | −0.757258 | ||||||||
\(356\) | 1.86452e10i | 1.16083i | ||||||||
\(357\) | −1.01814e10 | −0.626809 | ||||||||
\(358\) | −1.33896e10 | −0.815143 | ||||||||
\(359\) | −3.19339e10 | −1.92254 | −0.961269 | − | 0.275613i | \(-0.911119\pi\) | ||||
−0.961269 | + | 0.275613i | \(0.911119\pi\) | |||||||
\(360\) | 1.63173e9 | 0.0971488 | ||||||||
\(361\) | 1.52348e10 | 0.897032 | ||||||||
\(362\) | − | 8.56394e9i | − | 0.498700i | ||||||
\(363\) | − | 7.35371e9i | − | 0.423526i | ||||||
\(364\) | − | 2.68775e10i | − | 1.53103i | ||||||
\(365\) | −5.85563e9 | −0.329915 | ||||||||
\(366\) | 1.34574e10i | 0.749960i | ||||||||
\(367\) | −4.75693e9 | −0.262218 | −0.131109 | − | 0.991368i | \(-0.541854\pi\) | ||||
−0.131109 | + | 0.991368i | \(0.541854\pi\) | |||||||
\(368\) | 1.56354e10 | 0.852545 | ||||||||
\(369\) | 5.07209e9 | 0.273578 | ||||||||
\(370\) | 3.25555e10i | 1.73707i | ||||||||
\(371\) | 2.04617e10i | 1.08006i | ||||||||
\(372\) | 7.64711e9i | 0.399324i | ||||||||
\(373\) | − | 1.66167e10i | − | 0.858439i | −0.903200 | − | 0.429220i | \(-0.858789\pi\) | ||
0.903200 | − | 0.429220i | \(-0.141211\pi\) | |||||||
\(374\) | 1.54702e10i | 0.790693i | ||||||||
\(375\) | 1.10509e10 | 0.558822 | ||||||||
\(376\) | − | 7.09485e8i | − | 0.0354970i | ||||||
\(377\) | − | 1.56539e9i | − | 0.0774919i | ||||||
\(378\) | − | 2.96659e10i | − | 1.45308i | ||||||
\(379\) | 3.60255e10 | 1.74603 | 0.873017 | − | 0.487689i | \(-0.162160\pi\) | ||||
0.873017 | + | 0.487689i | \(0.162160\pi\) | |||||||
\(380\) | −4.65601e9 | −0.223295 | ||||||||
\(381\) | − | 1.79391e8i | − | 0.00851335i | ||||||
\(382\) | −4.36555e10 | −2.05015 | ||||||||
\(383\) | − | 5.37123e9i | − | 0.249619i | −0.992181 | − | 0.124810i | \(-0.960168\pi\) | ||
0.992181 | − | 0.124810i | \(-0.0398320\pi\) | |||||||
\(384\) | 5.86020e9 | 0.269518 | ||||||||
\(385\) | −6.88236e9 | −0.313252 | ||||||||
\(386\) | 5.50571e10i | 2.48007i | ||||||||
\(387\) | −1.15547e10 | − | 9.83270e9i | −0.515127 | − | 0.438358i | ||||
\(388\) | −5.43286e9 | −0.239719 | ||||||||
\(389\) | 3.33530e10i | 1.45659i | 0.685266 | + | 0.728293i | \(0.259686\pi\) | ||||
−0.685266 | + | 0.728293i | \(0.740314\pi\) | |||||||
\(390\) | 1.47107e10i | 0.635881i | ||||||||
\(391\) | 2.61609e10 | 1.11930 | ||||||||
\(392\) | − | 4.15382e8i | − | 0.0175915i | ||||||
\(393\) | 2.32845e10 | 0.976106 | ||||||||
\(394\) | − | 5.17270e9i | − | 0.214651i | ||||||
\(395\) | − | 7.91603e9i | − | 0.325176i | ||||||
\(396\) | −9.77987e9 | −0.397697 | ||||||||
\(397\) | 3.58311e10 | 1.44244 | 0.721220 | − | 0.692706i | \(-0.243582\pi\) | ||||
0.721220 | + | 0.692706i | \(0.243582\pi\) | |||||||
\(398\) | −1.01928e10 | −0.406220 | ||||||||
\(399\) | 4.79296e9i | 0.189109i | ||||||||
\(400\) | −1.33172e10 | −0.520204 | ||||||||
\(401\) | −3.38981e10 | −1.31098 | −0.655492 | − | 0.755202i | \(-0.727539\pi\) | ||||
−0.655492 | + | 0.755202i | \(0.727539\pi\) | |||||||
\(402\) | 2.82946e10 | 1.08343 | ||||||||
\(403\) | 2.02223e10 | 0.766672 | ||||||||
\(404\) | −3.35511e10 | −1.25945 | ||||||||
\(405\) | − | 2.15524e9i | − | 0.0801081i | ||||||
\(406\) | − | 2.52527e9i | − | 0.0929403i | ||||||
\(407\) | − | 2.73820e10i | − | 0.997902i | ||||||
\(408\) | 4.02529e9 | 0.145264 | ||||||||
\(409\) | 3.60185e10i | 1.28716i | 0.765380 | + | 0.643579i | \(0.222551\pi\) | ||||
−0.765380 | + | 0.643579i | \(0.777449\pi\) | |||||||
\(410\) | −1.00560e10 | −0.355869 | ||||||||
\(411\) | −1.20542e10 | −0.422446 | ||||||||
\(412\) | −1.61258e9 | −0.0559672 | ||||||||
\(413\) | − | 1.43407e10i | − | 0.492913i | ||||||
\(414\) | 3.07558e10i | 1.04695i | ||||||||
\(415\) | 2.12788e10i | 0.717390i | ||||||||
\(416\) | − | 5.44697e10i | − | 1.81879i | ||||||
\(417\) | 3.18540e10i | 1.05346i | ||||||||
\(418\) | 7.28267e9 | 0.238553 | ||||||||
\(419\) | − | 5.29067e9i | − | 0.171654i | −0.996310 | − | 0.0858271i | \(-0.972647\pi\) | ||
0.996310 | − | 0.0858271i | \(-0.0273533\pi\) | |||||||
\(420\) | 1.27610e10i | 0.410098i | ||||||||
\(421\) | 4.80310e10i | 1.52895i | 0.644654 | + | 0.764474i | \(0.277001\pi\) | ||||
−0.644654 | + | 0.764474i | \(0.722999\pi\) | |||||||
\(422\) | −4.18928e10 | −1.32096 | ||||||||
\(423\) | −3.20169e9 | −0.100004 | ||||||||
\(424\) | − | 8.08970e9i | − | 0.250305i | ||||||
\(425\) | −2.22822e10 | −0.682970 | ||||||||
\(426\) | − | 3.48804e10i | − | 1.05912i | ||||||
\(427\) | 3.08707e10 | 0.928613 | ||||||||
\(428\) | −3.02330e10 | −0.900960 | ||||||||
\(429\) | − | 1.23730e10i | − | 0.365297i | ||||||
\(430\) | 2.29085e10 | + | 1.94945e10i | 0.670075 | + | 0.570214i | ||||
\(431\) | 2.78280e10 | 0.806442 | 0.403221 | − | 0.915103i | \(-0.367891\pi\) | ||||
0.403221 | + | 0.915103i | \(0.367891\pi\) | |||||||
\(432\) | − | 2.69069e10i | − | 0.772554i | ||||||
\(433\) | 2.80139e10i | 0.796932i | 0.917183 | + | 0.398466i | \(0.130457\pi\) | ||||
−0.917183 | + | 0.398466i | \(0.869543\pi\) | |||||||
\(434\) | 3.26224e10 | 0.919512 | ||||||||
\(435\) | 7.43223e8i | 0.0207569i | ||||||||
\(436\) | −3.28629e10 | −0.909410 | ||||||||
\(437\) | − | 1.23154e10i | − | 0.337694i | ||||||
\(438\) | − | 1.69824e10i | − | 0.461426i | ||||||
\(439\) | −4.49882e10 | −1.21127 | −0.605634 | − | 0.795743i | \(-0.707081\pi\) | ||||
−0.605634 | + | 0.795743i | \(0.707081\pi\) | |||||||
\(440\) | 2.72099e9 | 0.0725967 | ||||||||
\(441\) | −1.87449e9 | −0.0495598 | ||||||||
\(442\) | − | 7.58534e10i | − | 1.98740i | ||||||
\(443\) | 2.77199e10 | 0.719742 | 0.359871 | − | 0.933002i | \(-0.382821\pi\) | ||||
0.359871 | + | 0.933002i | \(0.382821\pi\) | |||||||
\(444\) | −5.07707e10 | −1.30642 | ||||||||
\(445\) | −2.34098e10 | −0.596976 | ||||||||
\(446\) | 4.69911e9 | 0.118762 | ||||||||
\(447\) | 2.73657e10 | 0.685450 | ||||||||
\(448\) | − | 5.40627e10i | − | 1.34210i | ||||||
\(449\) | − | 5.79249e10i | − | 1.42521i | −0.701564 | − | 0.712607i | \(-0.747514\pi\) | ||
0.701564 | − | 0.712607i | \(-0.252486\pi\) | |||||||
\(450\) | − | 2.61958e10i | − | 0.638825i | ||||||
\(451\) | 8.45798e9 | 0.204438 | ||||||||
\(452\) | 1.68108e10i | 0.402750i | ||||||||
\(453\) | −8.35045e9 | −0.198297 | ||||||||
\(454\) | 1.22470e11 | 2.88274 | ||||||||
\(455\) | 3.37456e10 | 0.787358 | ||||||||
\(456\) | − | 1.89493e9i | − | 0.0438263i | ||||||
\(457\) | 6.50756e10i | 1.49195i | 0.665975 | + | 0.745974i | \(0.268016\pi\) | ||||
−0.665975 | + | 0.745974i | \(0.731984\pi\) | |||||||
\(458\) | 7.60756e10i | 1.72895i | ||||||||
\(459\) | − | 4.50203e10i | − | 1.01428i | ||||||
\(460\) | − | 3.27891e10i | − | 0.732316i | ||||||
\(461\) | −1.47188e10 | −0.325888 | −0.162944 | − | 0.986635i | \(-0.552099\pi\) | ||||
−0.162944 | + | 0.986635i | \(0.552099\pi\) | |||||||
\(462\) | − | 1.99601e10i | − | 0.438121i | ||||||
\(463\) | − | 2.13619e10i | − | 0.464854i | −0.972614 | − | 0.232427i | \(-0.925333\pi\) | ||
0.972614 | − | 0.232427i | \(-0.0746667\pi\) | |||||||
\(464\) | − | 2.29042e9i | − | 0.0494132i | ||||||
\(465\) | −9.60123e9 | −0.205360 | ||||||||
\(466\) | −5.44042e10 | −1.15369 | ||||||||
\(467\) | 4.57818e10i | 0.962554i | 0.876569 | + | 0.481277i | \(0.159827\pi\) | ||||
−0.876569 | + | 0.481277i | \(0.840173\pi\) | |||||||
\(468\) | 4.79528e10 | 0.999609 | ||||||||
\(469\) | − | 6.49064e10i | − | 1.34152i | ||||||
\(470\) | 6.34772e9 | 0.130085 | ||||||||
\(471\) | 1.06122e10 | 0.215636 | ||||||||
\(472\) | 5.66971e9i | 0.114233i | ||||||||
\(473\) | −1.92681e10 | − | 1.63966e10i | −0.384941 | − | 0.327573i | ||||
\(474\) | 2.29579e10 | 0.454798 | ||||||||
\(475\) | 1.04895e10i | 0.206053i | ||||||||
\(476\) | − | 6.58000e10i | − | 1.28173i | ||||||
\(477\) | −3.65063e10 | −0.705171 | ||||||||
\(478\) | − | 3.77616e10i | − | 0.723334i | ||||||
\(479\) | 1.62487e10 | 0.308658 | 0.154329 | − | 0.988020i | \(-0.450678\pi\) | ||||
0.154329 | + | 0.988020i | \(0.450678\pi\) | |||||||
\(480\) | 2.58614e10i | 0.487177i | ||||||||
\(481\) | 1.34260e11i | 2.50822i | ||||||||
\(482\) | 6.50740e10 | 1.20564 | ||||||||
\(483\) | −3.37536e10 | −0.620200 | ||||||||
\(484\) | 4.75253e10 | 0.866051 | ||||||||
\(485\) | − | 6.82116e9i | − | 0.123280i | ||||||
\(486\) | 8.44998e10 | 1.51464 | ||||||||
\(487\) | 7.51248e10 | 1.33557 | 0.667786 | − | 0.744353i | \(-0.267242\pi\) | ||||
0.667786 | + | 0.744353i | \(0.267242\pi\) | |||||||
\(488\) | −1.22050e10 | −0.215207 | ||||||||
\(489\) | −3.77695e10 | −0.660549 | ||||||||
\(490\) | 3.71640e9 | 0.0644671 | ||||||||
\(491\) | − | 1.57898e10i | − | 0.271676i | −0.990731 | − | 0.135838i | \(-0.956627\pi\) | ||
0.990731 | − | 0.135838i | \(-0.0433726\pi\) | |||||||
\(492\) | − | 1.56825e10i | − | 0.267642i | ||||||
\(493\) | − | 3.83230e9i | − | 0.0648742i | ||||||
\(494\) | −3.57085e10 | −0.599602 | ||||||||
\(495\) | − | 1.22790e10i | − | 0.204523i | ||||||
\(496\) | 2.95885e10 | 0.488873 | ||||||||
\(497\) | −8.00139e10 | −1.31141 | ||||||||
\(498\) | −6.17124e10 | −1.00336 | ||||||||
\(499\) | 1.13287e11i | 1.82716i | 0.406657 | + | 0.913581i | \(0.366694\pi\) | ||||
−0.406657 | + | 0.913581i | \(0.633306\pi\) | |||||||
\(500\) | 7.14195e10i | 1.14271i | ||||||||
\(501\) | 1.08662e10i | 0.172475i | ||||||||
\(502\) | − | 1.05976e11i | − | 1.66876i | ||||||
\(503\) | 6.13184e10i | 0.957897i | 0.877843 | + | 0.478949i | \(0.158982\pi\) | ||||
−0.877843 | + | 0.478949i | \(0.841018\pi\) | |||||||
\(504\) | 1.08556e10 | 0.168242 | ||||||||
\(505\) | − | 4.21246e10i | − | 0.647695i | ||||||
\(506\) | 5.12869e10i | 0.782356i | ||||||||
\(507\) | 2.30804e10i | 0.349311i | ||||||||
\(508\) | 1.15936e9 | 0.0174086 | ||||||||
\(509\) | −3.60434e10 | −0.536976 | −0.268488 | − | 0.963283i | \(-0.586524\pi\) | ||||
−0.268488 | + | 0.963283i | \(0.586524\pi\) | |||||||
\(510\) | 3.60141e10i | 0.532343i | ||||||||
\(511\) | −3.89567e10 | −0.571345 | ||||||||
\(512\) | − | 9.30642e10i | − | 1.35426i | ||||||
\(513\) | −2.11936e10 | −0.306010 | ||||||||
\(514\) | 1.08230e11 | 1.55059 | ||||||||
\(515\) | − | 2.02466e9i | − | 0.0287822i | ||||||
\(516\) | −3.04019e10 | + | 3.57261e10i | −0.428846 | + | 0.503950i | ||||
\(517\) | −5.33898e9 | −0.0747303 | ||||||||
\(518\) | 2.16587e11i | 3.00825i | ||||||||
\(519\) | − | 6.03647e10i | − | 0.831982i | ||||||
\(520\) | −1.33416e10 | −0.182471 | ||||||||
\(521\) | − | 3.97439e10i | − | 0.539411i | −0.962943 | − | 0.269705i | \(-0.913074\pi\) | ||
0.962943 | − | 0.269705i | \(-0.0869263\pi\) | |||||||
\(522\) | 4.50540e9 | 0.0606809 | ||||||||
\(523\) | − | 1.18662e11i | − | 1.58601i | −0.609218 | − | 0.793003i | \(-0.708517\pi\) | ||
0.609218 | − | 0.793003i | \(-0.291483\pi\) | |||||||
\(524\) | 1.50482e11i | 1.99600i | ||||||||
\(525\) | 2.87491e10 | 0.378432 | ||||||||
\(526\) | −1.11224e11 | −1.45296 | ||||||||
\(527\) | 4.95071e10 | 0.641837 | ||||||||
\(528\) | − | 1.81038e10i | − | 0.232934i | ||||||
\(529\) | 8.41811e9 | 0.107496 | ||||||||
\(530\) | 7.23780e10 | 0.917283 | ||||||||
\(531\) | 2.55856e10 | 0.321824 | ||||||||
\(532\) | −3.09758e10 | −0.386701 | ||||||||
\(533\) | −4.14713e10 | −0.513852 | ||||||||
\(534\) | − | 6.78924e10i | − | 0.834942i | ||||||
\(535\) | − | 3.79586e10i | − | 0.463335i | ||||||
\(536\) | 2.56612e10i | 0.310898i | ||||||||
\(537\) | 2.62171e10 | 0.315274 | ||||||||
\(538\) | 1.64546e11i | 1.96407i | ||||||||
\(539\) | −3.12582e9 | −0.0370347 | ||||||||
\(540\) | −5.64268e10 | −0.663606 | ||||||||
\(541\) | −1.01448e11 | −1.18428 | −0.592141 | − | 0.805834i | \(-0.701717\pi\) | ||||
−0.592141 | + | 0.805834i | \(0.701717\pi\) | |||||||
\(542\) | − | 1.17397e10i | − | 0.136038i | ||||||
\(543\) | 1.67684e10i | 0.192883i | ||||||||
\(544\) | − | 1.33350e11i | − | 1.52264i | ||||||
\(545\) | − | 4.12606e10i | − | 0.467681i | ||||||
\(546\) | 9.78683e10i | 1.10121i | ||||||||
\(547\) | −8.17603e10 | −0.913257 | −0.456629 | − | 0.889657i | \(-0.650943\pi\) | ||||
−0.456629 | + | 0.889657i | \(0.650943\pi\) | |||||||
\(548\) | − | 7.79035e10i | − | 0.863843i | ||||||
\(549\) | 5.50772e10i | 0.606293i | ||||||||
\(550\) | − | 4.36829e10i | − | 0.477376i | ||||||
\(551\) | −1.80408e9 | −0.0195726 | ||||||||
\(552\) | 1.33447e10 | 0.143732 | ||||||||
\(553\) | − | 5.26642e10i | − | 0.563138i | ||||||
\(554\) | 5.75640e10 | 0.611100 | ||||||||
\(555\) | − | 6.37446e10i | − | 0.671848i | ||||||
\(556\) | −2.05865e11 | −2.15418 | ||||||||
\(557\) | −1.33090e11 | −1.38269 | −0.691343 | − | 0.722526i | \(-0.742981\pi\) | ||||
−0.691343 | + | 0.722526i | \(0.742981\pi\) | |||||||
\(558\) | 5.82025e10i | 0.600350i | ||||||||
\(559\) | 9.44754e10 | + | 8.03958e10i | 0.967545 | + | 0.823353i | ||||
\(560\) | 4.93755e10 | 0.502064 | ||||||||
\(561\) | − | 3.02910e10i | − | 0.305817i | ||||||
\(562\) | − | 1.25437e11i | − | 1.25742i | ||||||
\(563\) | −7.48660e10 | −0.745162 | −0.372581 | − | 0.928000i | \(-0.621527\pi\) | ||||
−0.372581 | + | 0.928000i | \(0.621527\pi\) | |||||||
\(564\) | 9.89934e9i | 0.0978340i | ||||||||
\(565\) | −2.11066e10 | −0.207122 | ||||||||
\(566\) | − | 1.54198e11i | − | 1.50250i | ||||||
\(567\) | − | 1.43385e10i | − | 0.138731i | ||||||
\(568\) | 3.16341e10 | 0.303922 | ||||||||
\(569\) | −1.64918e11 | −1.57333 | −0.786663 | − | 0.617383i | \(-0.788193\pi\) | ||||
−0.786663 | + | 0.617383i | \(0.788193\pi\) | |||||||
\(570\) | 1.69538e10 | 0.160609 | ||||||||
\(571\) | − | 2.56402e10i | − | 0.241200i | −0.992701 | − | 0.120600i | \(-0.961518\pi\) | ||
0.992701 | − | 0.120600i | \(-0.0384818\pi\) | |||||||
\(572\) | 7.99638e10 | 0.746981 | ||||||||
\(573\) | 8.54785e10 | 0.792937 | ||||||||
\(574\) | −6.69012e10 | −0.616291 | ||||||||
\(575\) | −7.38703e10 | −0.675769 | ||||||||
\(576\) | 9.64547e10 | 0.876261 | ||||||||
\(577\) | − | 7.01456e10i | − | 0.632844i | −0.948618 | − | 0.316422i | \(-0.897518\pi\) | ||
0.948618 | − | 0.316422i | \(-0.102482\pi\) | |||||||
\(578\) | − | 2.15417e10i | − | 0.193005i | ||||||
\(579\) | − | 1.07803e11i | − | 0.959218i | ||||||
\(580\) | −4.80327e9 | −0.0424449 | ||||||||
\(581\) | 1.41565e11i | 1.24237i | ||||||||
\(582\) | 1.97826e10 | 0.172421 | ||||||||
\(583\) | −6.08762e10 | −0.526955 | ||||||||
\(584\) | 1.54018e10 | 0.132410 | ||||||||
\(585\) | 6.02065e10i | 0.514067i | ||||||||
\(586\) | 1.64544e11i | 1.39537i | ||||||||
\(587\) | 1.89363e11i | 1.59493i | 0.603363 | + | 0.797467i | \(0.293827\pi\) | ||||
−0.603363 | + | 0.797467i | \(0.706173\pi\) | |||||||
\(588\) | 5.79577e9i | 0.0484844i | ||||||||
\(589\) | − | 2.33058e10i | − | 0.193643i | ||||||
\(590\) | −5.07265e10 | −0.418627 | ||||||||
\(591\) | 1.01283e10i | 0.0830207i | ||||||||
\(592\) | 1.96444e11i | 1.59938i | ||||||||
\(593\) | 6.58027e10i | 0.532139i | 0.963954 | + | 0.266069i | \(0.0857250\pi\) | ||||
−0.963954 | + | 0.266069i | \(0.914275\pi\) | |||||||
\(594\) | 8.82597e10 | 0.708951 | ||||||||
\(595\) | 8.26144e10 | 0.659155 | ||||||||
\(596\) | 1.76858e11i | 1.40165i | ||||||||
\(597\) | 1.99578e10 | 0.157114 | ||||||||
\(598\) | − | 2.51471e11i | − | 1.96645i | ||||||
\(599\) | 9.67186e10 | 0.751282 | 0.375641 | − | 0.926765i | \(-0.377423\pi\) | ||||
0.375641 | + | 0.926765i | \(0.377423\pi\) | |||||||
\(600\) | −1.13662e10 | −0.0877021 | ||||||||
\(601\) | 8.07367e10i | 0.618833i | 0.950927 | + | 0.309416i | \(0.100134\pi\) | ||||
−0.950927 | + | 0.309416i | \(0.899866\pi\) | |||||||
\(602\) | 1.52407e11 | + | 1.29694e11i | 1.16043 | + | 0.987492i | ||||
\(603\) | 1.15801e11 | 0.875878 | ||||||||
\(604\) | − | 5.39669e10i | − | 0.405490i | ||||||
\(605\) | 5.96698e10i | 0.445382i | ||||||||
\(606\) | 1.22169e11 | 0.905878 | ||||||||
\(607\) | − | 2.18215e11i | − | 1.60742i | −0.595019 | − | 0.803712i | \(-0.702855\pi\) | ||
0.595019 | − | 0.803712i | \(-0.297145\pi\) | |||||||
\(608\) | −6.27753e10 | −0.459383 | ||||||||
\(609\) | 4.94455e9i | 0.0359466i | ||||||||
\(610\) | − | 1.09197e11i | − | 0.788662i | ||||||
\(611\) | 2.61782e10 | 0.187834 | ||||||||
\(612\) | 1.17395e11 | 0.836846 | ||||||||
\(613\) | 2.66467e11 | 1.88713 | 0.943564 | − | 0.331189i | \(-0.107450\pi\) | ||||
0.943564 | + | 0.331189i | \(0.107450\pi\) | |||||||
\(614\) | − | 2.93399e11i | − | 2.06436i | ||||||
\(615\) | 1.96899e10 | 0.137640 | ||||||||
\(616\) | 1.81024e10 | 0.125722 | ||||||||
\(617\) | 1.98336e11 | 1.36855 | 0.684277 | − | 0.729222i | \(-0.260118\pi\) | ||||
0.684277 | + | 0.729222i | \(0.260118\pi\) | |||||||
\(618\) | 5.87187e9 | 0.0402553 | ||||||||
\(619\) | 2.63949e11 | 1.79786 | 0.898932 | − | 0.438088i | \(-0.144344\pi\) | ||||
0.898932 | + | 0.438088i | \(0.144344\pi\) | |||||||
\(620\) | − | 6.20504e10i | − | 0.419931i | ||||||
\(621\) | − | 1.49252e11i | − | 1.00358i | ||||||
\(622\) | − | 1.75618e11i | − | 1.17330i | ||||||
\(623\) | −1.55742e11 | −1.03384 | ||||||||
\(624\) | 8.87665e10i | 0.585478i | ||||||||
\(625\) | 8.31237e9 | 0.0544759 | ||||||||
\(626\) | −3.59036e11 | −2.33798 | ||||||||
\(627\) | −1.42597e10 | −0.0922655 | ||||||||
\(628\) | 6.85841e10i | 0.440945i | ||||||||
\(629\) | 3.28688e11i | 2.09982i | ||||||||
\(630\) | 9.71247e10i | 0.616549i | ||||||||
\(631\) | − | 7.50901e10i | − | 0.473658i | −0.971551 | − | 0.236829i | \(-0.923892\pi\) | ||
0.971551 | − | 0.236829i | \(-0.0761082\pi\) | |||||||
\(632\) | 2.08212e10i | 0.130508i | ||||||||
\(633\) | 8.20273e10 | 0.510909 | ||||||||
\(634\) | − | 6.61217e10i | − | 0.409248i | ||||||
\(635\) | 1.45562e9i | 0.00895269i | ||||||||
\(636\) | 1.12874e11i | 0.689870i | ||||||||
\(637\) | 1.53265e10 | 0.0930864 | ||||||||
\(638\) | 7.51300e9 | 0.0453452 | ||||||||
\(639\) | − | 1.42755e11i | − | 0.856224i | ||||||
\(640\) | −4.75510e10 | −0.283426 | ||||||||
\(641\) | − | 1.48724e11i | − | 0.880948i | −0.897765 | − | 0.440474i | \(-0.854810\pi\) | ||
0.897765 | − | 0.440474i | \(-0.145190\pi\) | |||||||
\(642\) | 1.10087e11 | 0.648029 | ||||||||
\(643\) | −1.86069e11 | −1.08851 | −0.544253 | − | 0.838921i | \(-0.683187\pi\) | ||||
−0.544253 | + | 0.838921i | \(0.683187\pi\) | |||||||
\(644\) | − | 2.18141e11i | − | 1.26822i | ||||||
\(645\) | −4.48555e10 | − | 3.81707e10i | −0.259165 | − | 0.220542i | ||||
\(646\) | −8.74196e10 | −0.501971 | ||||||||
\(647\) | 8.09539e10i | 0.461977i | 0.972956 | + | 0.230989i | \(0.0741960\pi\) | ||||
−0.972956 | + | 0.230989i | \(0.925804\pi\) | |||||||
\(648\) | 5.66884e9i | 0.0321510i | ||||||||
\(649\) | 4.26654e10 | 0.240490 | ||||||||
\(650\) | 2.14187e11i | 1.19988i | ||||||||
\(651\) | −6.38756e10 | −0.355640 | ||||||||
\(652\) | − | 2.44095e11i | − | 1.35073i | ||||||
\(653\) | 4.75870e10i | 0.261719i | 0.991401 | + | 0.130860i | \(0.0417737\pi\) | ||||
−0.991401 | + | 0.130860i | \(0.958226\pi\) | |||||||
\(654\) | 1.19663e11 | 0.654107 | ||||||||
\(655\) | −1.88936e11 | −1.02648 | ||||||||
\(656\) | −6.06793e10 | −0.327661 | ||||||||
\(657\) | − | 6.95036e10i | − | 0.373032i | ||||||
\(658\) | 4.22304e10 | 0.225280 | ||||||||
\(659\) | 1.65374e10 | 0.0876850 | 0.0438425 | − | 0.999038i | \(-0.486040\pi\) | ||||
0.0438425 | + | 0.999038i | \(0.486040\pi\) | |||||||
\(660\) | −3.79656e10 | −0.200085 | ||||||||
\(661\) | 1.78227e11 | 0.933615 | 0.466808 | − | 0.884359i | \(-0.345404\pi\) | ||||
0.466808 | + | 0.884359i | \(0.345404\pi\) | |||||||
\(662\) | −1.45636e11 | −0.758294 | ||||||||
\(663\) | 1.48523e11i | 0.768669i | ||||||||
\(664\) | − | 5.59688e10i | − | 0.287921i | ||||||
\(665\) | − | 3.88912e10i | − | 0.198868i | ||||||
\(666\) | −3.86419e11 | −1.96409 | ||||||||
\(667\) | − | 1.27049e10i | − | 0.0641902i | ||||||
\(668\) | −7.02258e10 | −0.352688 | ||||||||
\(669\) | −9.20098e9 | −0.0459335 | ||||||||
\(670\) | −2.29589e11 | −1.13934 | ||||||||
\(671\) | 9.18442e10i | 0.453066i | ||||||||
\(672\) | 1.72052e11i | 0.843690i | ||||||||
\(673\) | 4.02539e11i | 1.96222i | 0.193456 | + | 0.981109i | \(0.438030\pi\) | ||||
−0.193456 | + | 0.981109i | \(0.561970\pi\) | |||||||
\(674\) | − | 3.80518e11i | − | 1.84389i | ||||||
\(675\) | 1.27123e11i | 0.612365i | ||||||||
\(676\) | −1.49163e11 | −0.714292 | ||||||||
\(677\) | − | 3.11966e11i | − | 1.48509i | −0.669796 | − | 0.742545i | \(-0.733618\pi\) | ||
0.669796 | − | 0.742545i | \(-0.266382\pi\) | |||||||
\(678\) | − | 6.12130e10i | − | 0.289684i | ||||||
\(679\) | − | 4.53802e10i | − | 0.213495i | ||||||
\(680\) | −3.26622e10 | −0.152760 | ||||||||
\(681\) | −2.39799e11 | −1.11496 | ||||||||
\(682\) | 9.70558e10i | 0.448626i | ||||||||
\(683\) | 2.47854e11 | 1.13897 | 0.569487 | − | 0.822000i | \(-0.307142\pi\) | ||||
0.569487 | + | 0.822000i | \(0.307142\pi\) | |||||||
\(684\) | − | 5.52647e10i | − | 0.252478i | ||||||
\(685\) | 9.78108e10 | 0.444247 | ||||||||
\(686\) | −3.12721e11 | −1.41208 | ||||||||
\(687\) | − | 1.48958e11i | − | 0.668709i | ||||||
\(688\) | 1.38233e11 | + | 1.17632e11i | 0.616962 | + | 0.525017i | ||||
\(689\) | 2.98489e11 | 1.32450 | ||||||||
\(690\) | 1.19394e11i | 0.526730i | ||||||||
\(691\) | − | 1.76475e11i | − | 0.774052i | −0.922069 | − | 0.387026i | \(-0.873502\pi\) | ||
0.922069 | − | 0.387026i | \(-0.126498\pi\) | |||||||
\(692\) | 3.90123e11 | 1.70128 | ||||||||
\(693\) | − | 8.16904e10i | − | 0.354191i | ||||||
\(694\) | −5.46298e11 | −2.35501 | ||||||||
\(695\) | − | 2.58471e11i | − | 1.10783i | ||||||
\(696\) | − | 1.95487e9i | − | 0.00833067i | ||||||
\(697\) | −1.01528e11 | −0.430184 | ||||||||
\(698\) | 4.08293e11 | 1.72009 | ||||||||
\(699\) | 1.06525e11 | 0.446213 | ||||||||
\(700\) | 1.85799e11i | 0.773840i | ||||||||
\(701\) | −2.51419e11 | −1.04118 | −0.520589 | − | 0.853807i | \(-0.674288\pi\) | ||||
−0.520589 | + | 0.853807i | \(0.674288\pi\) | |||||||
\(702\) | −4.32756e11 | −1.78194 | ||||||||
\(703\) | 1.54732e11 | 0.633518 | ||||||||
\(704\) | 1.60843e11 | 0.654806 | ||||||||
\(705\) | −1.24290e10 | −0.0503129 | ||||||||
\(706\) | 3.85966e11i | 1.55357i | ||||||||
\(707\) | − | 2.80249e11i | − | 1.12167i | ||||||
\(708\) | − | 7.91086e10i | − | 0.314841i | ||||||
\(709\) | 2.53180e11 | 1.00195 | 0.500973 | − | 0.865463i | \(-0.332976\pi\) | ||||
0.500973 | + | 0.865463i | \(0.332976\pi\) | |||||||
\(710\) | 2.83028e11i | 1.11377i | ||||||||
\(711\) | 9.39595e10 | 0.367674 | ||||||||
\(712\) | 6.15736e10 | 0.239593 | ||||||||
\(713\) | 1.64127e11 | 0.635070 | ||||||||
\(714\) | 2.39596e11i | 0.921907i | ||||||||
\(715\) | 1.00398e11i | 0.384148i | ||||||||
\(716\) | 1.69435e11i | 0.644690i | ||||||||
\(717\) | 7.39382e10i | 0.279764i | ||||||||
\(718\) | 7.51493e11i | 2.82766i | ||||||||
\(719\) | −2.91790e11 | −1.09183 | −0.545914 | − | 0.837841i | \(-0.683818\pi\) | ||||
−0.545914 | + | 0.837841i | \(0.683818\pi\) | |||||||
\(720\) | 8.80921e10i | 0.327798i | ||||||||
\(721\) | − | 1.34698e10i | − | 0.0498447i | ||||||
\(722\) | − | 3.58516e11i | − | 1.31935i | ||||||
\(723\) | −1.27417e11 | −0.466308 | ||||||||
\(724\) | −1.08370e11 | −0.394418 | ||||||||
\(725\) | 1.08212e10i | 0.0391674i | ||||||||
\(726\) | −1.73053e11 | −0.622920 | ||||||||
\(727\) | 7.09422e10i | 0.253961i | 0.991905 | + | 0.126980i | \(0.0405285\pi\) | ||||
−0.991905 | + | 0.126980i | \(0.959471\pi\) | |||||||
\(728\) | −8.87597e10 | −0.316002 | ||||||||
\(729\) | −1.27632e11 | −0.451909 | ||||||||
\(730\) | 1.37799e11i | 0.485238i | ||||||||
\(731\) | 2.31290e11 | + | 1.96821e11i | 0.810003 | + | 0.689289i | ||||
\(732\) | 1.70294e11 | 0.593137 | ||||||||
\(733\) | 5.49791e11i | 1.90450i | 0.305316 | + | 0.952251i | \(0.401238\pi\) | ||||
−0.305316 | + | 0.952251i | \(0.598762\pi\) | |||||||
\(734\) | 1.11944e11i | 0.385669i | ||||||||
\(735\) | −7.27681e9 | −0.0249340 | ||||||||
\(736\) | − | 4.42084e11i | − | 1.50659i | ||||||
\(737\) | 1.93105e11 | 0.654520 | ||||||||
\(738\) | − | 1.19360e11i | − | 0.402377i | ||||||
\(739\) | 2.61314e11i | 0.876162i | 0.898936 | + | 0.438081i | \(0.144342\pi\) | ||||
−0.898936 | + | 0.438081i | \(0.855658\pi\) | |||||||
\(740\) | 4.11966e11 | 1.37383 | ||||||||
\(741\) | 6.99181e10 | 0.231909 | ||||||||
\(742\) | 4.81520e11 | 1.58854 | ||||||||
\(743\) | 1.87745e11i | 0.616045i | 0.951379 | + | 0.308023i | \(0.0996673\pi\) | ||||
−0.951379 | + | 0.308023i | \(0.900333\pi\) | |||||||
\(744\) | 2.52537e10 | 0.0824201 | ||||||||
\(745\) | −2.22052e11 | −0.720823 | ||||||||
\(746\) | −3.91036e11 | −1.26259 | ||||||||
\(747\) | −2.52570e11 | −0.811146 | ||||||||
\(748\) | 1.95763e11 | 0.625352 | ||||||||
\(749\) | − | 2.52533e11i | − | 0.802400i | ||||||
\(750\) | − | 2.60059e11i | − | 0.821913i | ||||||
\(751\) | − | 1.34471e10i | − | 0.0422736i | −0.999777 | − | 0.0211368i | \(-0.993271\pi\) | ||
0.999777 | − | 0.0211368i | \(-0.00672855\pi\) | |||||||
\(752\) | 3.83030e10 | 0.119774 | ||||||||
\(753\) | 2.07505e11i | 0.645429i | ||||||||
\(754\) | −3.68378e10 | −0.113975 | ||||||||
\(755\) | 6.77575e10 | 0.208531 | ||||||||
\(756\) | −3.75399e11 | −1.14923 | ||||||||
\(757\) | − | 2.39956e11i | − | 0.730716i | −0.930867 | − | 0.365358i | \(-0.880947\pi\) | ||
0.930867 | − | 0.365358i | \(-0.119053\pi\) | |||||||
\(758\) | − | 8.47778e11i | − | 2.56806i | ||||||
\(759\) | − | 1.00421e11i | − | 0.302593i | ||||||
\(760\) | 1.53759e10i | 0.0460879i | ||||||||
\(761\) | − | 1.35338e11i | − | 0.403535i | −0.979433 | − | 0.201768i | \(-0.935331\pi\) | ||
0.979433 | − | 0.201768i | \(-0.0646686\pi\) | |||||||
\(762\) | −4.22156e9 | −0.0125214 | ||||||||
\(763\) | − | 2.74501e11i | − | 0.809926i | ||||||
\(764\) | 5.52427e11i | 1.62144i | ||||||||
\(765\) | 1.47394e11i | 0.430363i | ||||||||
\(766\) | −1.26400e11 | −0.367139 | ||||||||
\(767\) | −2.09197e11 | −0.604470 | ||||||||
\(768\) | 1.18472e11i | 0.340543i | ||||||||
\(769\) | −5.25701e11 | −1.50326 | −0.751629 | − | 0.659586i | \(-0.770732\pi\) | ||||
−0.751629 | + | 0.659586i | \(0.770732\pi\) | |||||||
\(770\) | 1.61961e11i | 0.460730i | ||||||||
\(771\) | −2.11918e11 | −0.599722 | ||||||||
\(772\) | 6.96707e11 | 1.96147 | ||||||||
\(773\) | − | 3.97129e11i | − | 1.11228i | −0.831089 | − | 0.556140i | \(-0.812282\pi\) | ||
0.831089 | − | 0.556140i | \(-0.187718\pi\) | |||||||
\(774\) | −2.31390e11 | + | 2.71913e11i | −0.644735 | + | 0.757647i | ||||
\(775\) | −1.39793e11 | −0.387505 | ||||||||
\(776\) | 1.79414e10i | 0.0494777i | ||||||||
\(777\) | − | 4.24083e11i | − | 1.16350i | ||||||
\(778\) | 7.84886e11 | 2.14234 | ||||||||
\(779\) | 4.77949e10i | 0.129787i | ||||||||
\(780\) | 1.86153e11 | 0.502913 | ||||||||
\(781\) | − | 2.38051e11i | − | 0.639833i | ||||||
\(782\) | − | 6.15637e11i | − | 1.64626i | ||||||
\(783\) | −2.18639e10 | −0.0581675 | ||||||||
\(784\) | 2.24253e10 | 0.0593572 | ||||||||
\(785\) | −8.61099e10 | −0.226764 | ||||||||
\(786\) | − | 5.47948e11i | − | 1.43565i | ||||||
\(787\) | 4.89399e11 | 1.27575 | 0.637873 | − | 0.770141i | \(-0.279814\pi\) | ||||
0.637873 | + | 0.770141i | \(0.279814\pi\) | |||||||
\(788\) | −6.54567e10 | −0.169766 | ||||||||
\(789\) | 2.17779e11 | 0.561963 | ||||||||
\(790\) | −1.86286e11 | −0.478268 | ||||||||
\(791\) | −1.40419e11 | −0.358691 | ||||||||
\(792\) | 3.22969e10i | 0.0820843i | ||||||||
\(793\) | − | 4.50331e11i | − | 1.13878i | ||||||
\(794\) | − | 8.43202e11i | − | 2.12153i | ||||||
\(795\) | −1.41718e11 | −0.354778 | ||||||||
\(796\) | 1.28982e11i | 0.321275i | ||||||||
\(797\) | 5.70493e11 | 1.41389 | 0.706947 | − | 0.707266i | \(-0.250072\pi\) | ||||
0.706947 | + | 0.707266i | \(0.250072\pi\) | |||||||
\(798\) | 1.12791e11 | 0.278141 | ||||||||
\(799\) | 6.40880e10 | 0.157250 | ||||||||
\(800\) | 3.76539e11i | 0.919285i | ||||||||
\(801\) | − | 2.77863e11i | − | 0.674995i | ||||||
\(802\) | 7.97714e11i | 1.92819i | ||||||||
\(803\) | − | 1.15901e11i | − | 0.278757i | ||||||
\(804\) | − | 3.58048e11i | − | 0.856873i | ||||||
\(805\) | 2.73885e11 | 0.652205 | ||||||||
\(806\) | − | 4.75885e11i | − | 1.12762i | ||||||
\(807\) | − | 3.22185e11i | − | 0.759645i | ||||||
\(808\) | 1.10798e11i | 0.259949i | ||||||||
\(809\) | −4.95126e11 | −1.15590 | −0.577952 | − | 0.816071i | \(-0.696148\pi\) | ||||
−0.577952 | + | 0.816071i | \(0.696148\pi\) | |||||||
\(810\) | −5.07188e10 | −0.117823 | ||||||||
\(811\) | 3.93370e11i | 0.909323i | 0.890664 | + | 0.454661i | \(0.150240\pi\) | ||||
−0.890664 | + | 0.454661i | \(0.849760\pi\) | |||||||
\(812\) | −3.19555e10 | −0.0735057 | ||||||||
\(813\) | 2.29867e10i | 0.0526155i | ||||||||
\(814\) | −6.44374e11 | −1.46771 | ||||||||
\(815\) | 3.06470e11 | 0.694637 | ||||||||
\(816\) | 2.17314e11i | 0.490147i | ||||||||
\(817\) | 9.26546e10 | − | 1.08881e11i | 0.207960 | − | 0.244379i | ||||
\(818\) | 8.47613e11 | 1.89315 | ||||||||
\(819\) | 4.00545e11i | 0.890257i | ||||||||
\(820\) | 1.27251e11i | 0.281454i | ||||||||
\(821\) | −5.77560e11 | −1.27123 | −0.635615 | − | 0.772006i | \(-0.719253\pi\) | ||||
−0.635615 | + | 0.772006i | \(0.719253\pi\) | |||||||
\(822\) | 2.83669e11i | 0.621332i | ||||||||
\(823\) | −4.32530e11 | −0.942794 | −0.471397 | − | 0.881921i | \(-0.656250\pi\) | ||||
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(824\) | 5.32537e9i | 0.0115516i | ||||||||
\(825\) | 8.55323e10i | 0.184635i | ||||||||
\(826\) | −3.37476e11 | −0.724975 | ||||||||
\(827\) | −7.27704e11 | −1.55572 | −0.777862 | − | 0.628435i | \(-0.783696\pi\) | ||||
−0.777862 | + | 0.628435i | \(0.783696\pi\) | |||||||
\(828\) | 3.89192e11 | 0.828023 | ||||||||
\(829\) | 4.79249e10i | 0.101471i | 0.998712 | + | 0.0507356i | \(0.0161566\pi\) | ||||
−0.998712 | + | 0.0507356i | \(0.983843\pi\) | |||||||
\(830\) | 5.00749e11 | 1.05513 | ||||||||
\(831\) | −1.12712e11 | −0.236356 | ||||||||
\(832\) | −7.88649e11 | −1.64585 | ||||||||
\(833\) | 3.75216e10 | 0.0779295 | ||||||||
\(834\) | 7.49611e11 | 1.54943 | ||||||||
\(835\) | − | 8.81711e10i | − | 0.181376i | ||||||
\(836\) | − | 9.21568e10i | − | 0.188670i | ||||||
\(837\) | − | 2.82446e11i | − | 0.575484i | ||||||
\(838\) | −1.24504e11 | −0.252468 | ||||||||
\(839\) | 2.04478e11i | 0.412667i | 0.978482 | + | 0.206333i | \(0.0661531\pi\) | ||||
−0.978482 | + | 0.206333i | \(0.933847\pi\) | |||||||
\(840\) | 4.21418e10 | 0.0846439 | ||||||||
\(841\) | 4.98385e11 | 0.996280 | ||||||||
\(842\) | 1.13030e12 | 2.24877 | ||||||||
\(843\) | 2.45609e11i | 0.486333i | ||||||||
\(844\) | 5.30123e11i | 1.04474i | ||||||||
\(845\) | − | 1.87280e11i | − | 0.367337i | ||||||
\(846\) | 7.53444e10i | 0.147085i | ||||||||
\(847\) | 3.96974e11i | 0.771310i | ||||||||
\(848\) | 4.36739e11 | 0.844575 | ||||||||
\(849\) | 3.01924e11i | 0.581121i | ||||||||
\(850\) | 5.24360e11i | 1.00451i | ||||||||
\(851\) | 1.08967e12i | 2.07768i | ||||||||
\(852\) | −4.41386e11 | −0.837646 | ||||||||
\(853\) | 7.68747e11 | 1.45207 | 0.726034 | − | 0.687658i | \(-0.241361\pi\) | ||||
0.726034 | + | 0.687658i | \(0.241361\pi\) | |||||||
\(854\) | − | 7.26471e11i | − | 1.36580i | ||||||
\(855\) | 6.93869e10 | 0.129841 | ||||||||
\(856\) | 9.98409e10i | 0.185957i | ||||||||
\(857\) | −3.77473e11 | −0.699782 | −0.349891 | − | 0.936790i | \(-0.613781\pi\) | ||||
−0.349891 | + | 0.936790i | \(0.613781\pi\) | |||||||
\(858\) | −2.91171e11 | −0.537277 | ||||||||
\(859\) | − | 2.09913e11i | − | 0.385538i | −0.981244 | − | 0.192769i | \(-0.938253\pi\) | ||
0.981244 | − | 0.192769i | \(-0.0617468\pi\) | |||||||
\(860\) | 2.46688e11 | − | 2.89890e11i | 0.450977 | − | 0.529956i | ||||
\(861\) | 1.30994e11 | 0.238363 | ||||||||
\(862\) | − | 6.54869e11i | − | 1.18611i | ||||||
\(863\) | 3.75693e11i | 0.677314i | 0.940910 | + | 0.338657i | \(0.109973\pi\) | ||||
−0.940910 | + | 0.338657i | \(0.890027\pi\) | |||||||
\(864\) | −7.60782e11 | −1.36523 | ||||||||
\(865\) | 4.89814e11i | 0.874917i | ||||||||
\(866\) | 6.59243e11 | 1.17212 | ||||||||
\(867\) | 4.21793e10i | 0.0746488i | ||||||||
\(868\) | − | 4.12813e11i | − | 0.727234i | ||||||
\(869\) | 1.56683e11 | 0.274753 | ||||||||
\(870\) | 1.74901e10 | 0.0305291 | ||||||||
\(871\) | −9.46833e11 | −1.64513 | ||||||||
\(872\) | 1.08526e11i | 0.187701i | ||||||||
\(873\) | 8.09640e10 | 0.139391 | ||||||||
\(874\) | −2.89815e11 | −0.496679 | ||||||||
\(875\) | −5.96561e11 | −1.01771 | ||||||||
\(876\) | −2.14899e11 | −0.364938 | ||||||||
\(877\) | −2.74793e11 | −0.464523 | −0.232262 | − | 0.972653i | \(-0.574613\pi\) | ||||
−0.232262 | + | 0.972653i | \(0.574613\pi\) | |||||||
\(878\) | 1.05869e12i | 1.78153i | ||||||||
\(879\) | − | 3.22181e11i | − | 0.539690i | ||||||
\(880\) | 1.46898e11i | 0.244955i | ||||||||
\(881\) | 3.90265e11 | 0.647823 | 0.323911 | − | 0.946087i | \(-0.395002\pi\) | ||||
0.323911 | + | 0.946087i | \(0.395002\pi\) | |||||||
\(882\) | 4.41119e10i | 0.0728923i | ||||||||
\(883\) | 3.41392e11 | 0.561579 | 0.280789 | − | 0.959769i | \(-0.409404\pi\) | ||||
0.280789 | + | 0.959769i | \(0.409404\pi\) | |||||||
\(884\) | −9.59868e11 | −1.57182 | ||||||||
\(885\) | 9.93239e10 | 0.161913 | ||||||||
\(886\) | − | 6.52325e11i | − | 1.05859i | ||||||
\(887\) | 6.14485e11i | 0.992698i | 0.868123 | + | 0.496349i | \(0.165326\pi\) | ||||
−0.868123 | + | 0.496349i | \(0.834674\pi\) | |||||||
\(888\) | 1.67664e11i | 0.269643i | ||||||||
\(889\) | 9.68404e9i | 0.0155042i | ||||||||
\(890\) | 5.50895e11i | 0.878030i | ||||||||
\(891\) | 4.26589e10 | 0.0676860 | ||||||||
\(892\) | − | 5.94637e10i | − | 0.0939275i | ||||||
\(893\) | − | 3.01698e10i | − | 0.0474425i | ||||||
\(894\) | − | 6.43989e11i | − | 1.00816i | ||||||
\(895\) | −2.12732e11 | −0.331543 | ||||||||
\(896\) | −3.16350e11 | −0.490835 | ||||||||
\(897\) | 4.92386e11i | 0.760564i | ||||||||
\(898\) | −1.36313e12 | −2.09620 | ||||||||
\(899\) | − | 2.40429e10i | − | 0.0368085i | ||||||
\(900\) | −3.31489e11 | −0.505241 | ||||||||
\(901\) | 7.30745e11 | 1.10883 | ||||||||
\(902\) | − | 1.99039e11i | − | 0.300686i | ||||||
\(903\) | −2.98417e11 | − | 2.53944e11i | −0.448821 | − | 0.381933i | ||||
\(904\) | 5.55158e10 | 0.0831272 | ||||||||
\(905\) | − | 1.36063e11i | − | 0.202836i | ||||||
\(906\) | 1.96509e11i | 0.291655i | ||||||||
\(907\) | 5.42630e11 | 0.801815 | 0.400908 | − | 0.916118i | \(-0.368695\pi\) | ||||
0.400908 | + | 0.916118i | \(0.368695\pi\) | |||||||
\(908\) | − | 1.54976e12i | − | 2.27993i | ||||||
\(909\) | 4.99999e11 | 0.732342 | ||||||||
\(910\) | − | 7.94127e11i | − | 1.15804i | ||||||
\(911\) | − | 1.37471e11i | − | 0.199590i | −0.995008 | − | 0.0997949i | \(-0.968181\pi\) | ||
0.995008 | − | 0.0997949i | \(-0.0318187\pi\) | |||||||
\(912\) | 1.02302e11 | 0.147878 | ||||||||
\(913\) | −4.21174e11 | −0.606147 | ||||||||
\(914\) | 1.53141e12 | 2.19435 | ||||||||
\(915\) | 2.13811e11i | 0.305031i | ||||||||
\(916\) | 9.62681e11 | 1.36742 | ||||||||
\(917\) | −1.25696e12 | −1.77765 | ||||||||
\(918\) | −1.05945e12 | −1.49180 | ||||||||
\(919\) | 2.61231e11 | 0.366237 | 0.183119 | − | 0.983091i | \(-0.441381\pi\) | ||||
0.183119 | + | 0.983091i | \(0.441381\pi\) | |||||||
\(920\) | −1.08282e11 | −0.151149 | ||||||||
\(921\) | 5.74483e11i | 0.798434i | ||||||||
\(922\) | 3.46373e11i | 0.479314i | ||||||||
\(923\) | 1.16722e12i | 1.60822i | ||||||||
\(924\) | −2.52580e11 | −0.346506 | ||||||||
\(925\) | − | 9.28113e11i | − | 1.26775i | ||||||
\(926\) | −5.02705e11 | −0.683706 | ||||||||
\(927\) | 2.40318e10 | 0.0325437 | ||||||||
\(928\) | −6.47608e10 | −0.0873213 | ||||||||
\(929\) | 8.83331e10i | 0.118593i | 0.998240 | + | 0.0592967i | \(0.0188858\pi\) | ||||
−0.998240 | + | 0.0592967i | \(0.981114\pi\) | |||||||
\(930\) | 2.25943e11i | 0.302042i | ||||||||
\(931\) | − | 1.76635e10i | − | 0.0235114i | ||||||
\(932\) | 6.88444e11i | 0.912442i | ||||||||
\(933\) | 3.43866e11i | 0.453797i | ||||||||
\(934\) | 1.07737e12 | 1.41572 | ||||||||
\(935\) | 2.45788e11i | 0.321599i | ||||||||
\(936\) | − | 1.58358e11i | − | 0.206318i | ||||||
\(937\) | − | 7.68952e11i | − | 0.997564i | −0.866728 | − | 0.498782i | \(-0.833781\pi\) | ||
0.866728 | − | 0.498782i | \(-0.166219\pi\) | |||||||
\(938\) | −1.52742e12 | −1.97310 | ||||||||
\(939\) | 7.03003e11 | 0.904263 | ||||||||
\(940\) | − | 8.03257e10i | − | 0.102883i | ||||||
\(941\) | −9.97007e11 | −1.27157 | −0.635784 | − | 0.771867i | \(-0.719323\pi\) | ||||
−0.635784 | + | 0.771867i | \(0.719323\pi\) | |||||||
\(942\) | − | 2.49734e11i | − | 0.317157i | ||||||
\(943\) | −3.36587e11 | −0.425648 | ||||||||
\(944\) | −3.06091e11 | −0.385445 | ||||||||
\(945\) | − | 4.71328e11i | − | 0.591012i | ||||||
\(946\) | −3.85856e11 | + | 4.53430e11i | −0.481793 | + | 0.566169i | ||||
\(947\) | −2.90821e11 | −0.361598 | −0.180799 | − | 0.983520i | \(-0.557868\pi\) | ||||
−0.180799 | + | 0.983520i | \(0.557868\pi\) | |||||||
\(948\) | − | 2.90515e11i | − | 0.359696i | ||||||
\(949\) | 5.68287e11i | 0.700653i | ||||||||
\(950\) | 2.46846e11 | 0.303062 | ||||||||
\(951\) | 1.29468e11i | 0.158285i | ||||||||
\(952\) | −2.17297e11 | −0.264549 | ||||||||
\(953\) | − | 4.33449e11i | − | 0.525493i | −0.964865 | − | 0.262746i | \(-0.915372\pi\) | ||
0.964865 | − | 0.262746i | \(-0.0846283\pi\) | |||||||
\(954\) | 8.59093e11i | 1.03716i | ||||||||
\(955\) | −6.93593e11 | −0.833857 | ||||||||
\(956\) | −4.77845e11 | −0.572079 | ||||||||
\(957\) | −1.47107e10 | −0.0175382 | ||||||||
\(958\) | − | 3.82377e11i | − | 0.453972i | ||||||
\(959\) | 6.50721e11 | 0.769343 | ||||||||
\(960\) | 3.74439e11 | 0.440855 | ||||||||
\(961\) | −5.42296e11 | −0.635833 | ||||||||
\(962\) | 3.15950e12 | 3.68908 | ||||||||
\(963\) | 4.50551e11 | 0.523888 | ||||||||
\(964\) | − | 8.23463e11i | − | 0.953533i | ||||||
\(965\) | 8.74741e11i | 1.00872i | ||||||||
\(966\) | 7.94314e11i | 0.912187i | ||||||||
\(967\) | −1.00411e12 | −1.14835 | −0.574175 | − | 0.818733i | \(-0.694677\pi\) | ||||
−0.574175 | + | 0.818733i | \(0.694677\pi\) | |||||||
\(968\) | − | 1.56947e11i | − | 0.178752i | ||||||
\(969\) | 1.71170e11 | 0.194148 | ||||||||
\(970\) | −1.60521e11 | −0.181319 | ||||||||
\(971\) | 4.65426e11 | 0.523569 | 0.261785 | − | 0.965126i | \(-0.415689\pi\) | ||||
0.261785 | + | 0.965126i | \(0.415689\pi\) | |||||||
\(972\) | − | 1.06928e12i | − | 1.19792i | ||||||
\(973\) | − | 1.71957e12i | − | 1.91853i | ||||||
\(974\) | − | 1.76789e12i | − | 1.96435i | ||||||
\(975\) | − | 4.19383e11i | − | 0.464079i | ||||||
\(976\) | − | 6.58909e11i | − | 0.726150i | ||||||
\(977\) | 1.62647e12 | 1.78512 | 0.892560 | − | 0.450930i | \(-0.148907\pi\) | ||||
0.892560 | + | 0.450930i | \(0.148907\pi\) | |||||||
\(978\) | 8.88818e11i | 0.971533i | ||||||||
\(979\) | − | 4.63351e11i | − | 0.504405i | ||||||
\(980\) | − | 4.70283e10i | − | 0.0509865i | ||||||
\(981\) | 4.89744e11 | 0.528802 | ||||||||
\(982\) | −3.71577e11 | −0.399580 | ||||||||
\(983\) | − | 2.12076e11i | − | 0.227131i | −0.993530 | − | 0.113566i | \(-0.963773\pi\) | ||
0.993530 | − | 0.113566i | \(-0.0362272\pi\) | |||||||
\(984\) | −5.17896e10 | −0.0552410 | ||||||||
\(985\) | − | 8.21834e10i | − | 0.0873050i | ||||||
\(986\) | −9.01845e10 | −0.0954166 | ||||||||
\(987\) | −8.26883e10 | −0.0871316 | ||||||||
\(988\) | 4.51864e11i | 0.474220i | ||||||||
\(989\) | 7.66776e11 | + | 6.52504e11i | 0.801463 | + | 0.682021i | ||||
\(990\) | −2.88958e11 | −0.300811 | ||||||||
\(991\) | − | 6.41703e11i | − | 0.665334i | −0.943044 | − | 0.332667i | \(-0.892052\pi\) | ||
0.943044 | − | 0.332667i | \(-0.107948\pi\) | |||||||
\(992\) | − | 8.36604e11i | − | 0.863919i | ||||||
\(993\) | 2.85160e11 | 0.293286 | ||||||||
\(994\) | 1.88295e12i | 1.92882i | ||||||||
\(995\) | −1.61942e11 | −0.165222 | ||||||||
\(996\) | 7.80924e11i | 0.793545i | ||||||||
\(997\) | 1.47250e10i | 0.0149030i | 0.999972 | + | 0.00745151i | \(0.00237191\pi\) | ||||
−0.999972 | + | 0.00745151i | \(0.997628\pi\) | |||||||
\(998\) | 2.66595e12 | 2.68738 | ||||||||
\(999\) | 1.87522e12 | 1.88274 |
(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 | 43.9.b.b.42.6 | ✓ | 28 | |
43.42 | odd | 2 | inner | 43.9.b.b.42.23 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.9.b.b.42.6 | ✓ | 28 | 1.1 | even | 1 | trivial | |
43.9.b.b.42.23 | yes | 28 | 43.42 | odd | 2 | inner |