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 | 42.24 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.9.b.b.42.5 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 23.8212i | 1.48883i | 0.667720 | + | 0.744413i | \(0.267270\pi\) | ||||
−0.667720 | + | 0.744413i | \(0.732730\pi\) | |||||||
\(3\) | − | 128.615i | − | 1.58783i | −0.608026 | − | 0.793917i | \(-0.708039\pi\) | ||
0.608026 | − | 0.793917i | \(-0.291961\pi\) | |||||||
\(4\) | −311.450 | −1.21660 | ||||||||
\(5\) | − | 1187.44i | − | 1.89990i | −0.312406 | − | 0.949949i | \(-0.601135\pi\) | ||
0.312406 | − | 0.949949i | \(-0.398865\pi\) | |||||||
\(6\) | 3063.75 | 2.36401 | ||||||||
\(7\) | 1045.51i | 0.435448i | 0.976010 | + | 0.217724i | \(0.0698633\pi\) | ||||
−0.976010 | + | 0.217724i | \(0.930137\pi\) | |||||||
\(8\) | − | 1320.89i | − | 0.322482i | ||||||
\(9\) | −9980.70 | −1.52122 | ||||||||
\(10\) | 28286.2 | 2.82862 | ||||||||
\(11\) | −7720.54 | −0.527323 | −0.263662 | − | 0.964615i | \(-0.584930\pi\) | ||||
−0.263662 | + | 0.964615i | \(0.584930\pi\) | |||||||
\(12\) | 40057.0i | 1.93176i | ||||||||
\(13\) | −32771.9 | −1.14743 | −0.573717 | − | 0.819054i | \(-0.694499\pi\) | ||||
−0.573717 | + | 0.819054i | \(0.694499\pi\) | |||||||
\(14\) | −24905.4 | −0.648307 | ||||||||
\(15\) | −152722. | −3.01672 | ||||||||
\(16\) | −48266.1 | −0.736482 | ||||||||
\(17\) | 74818.8 | 0.895808 | 0.447904 | − | 0.894082i | \(-0.352171\pi\) | ||||
0.447904 | + | 0.894082i | \(0.352171\pi\) | |||||||
\(18\) | − | 237752.i | − | 2.26482i | ||||||
\(19\) | 221516.i | 1.69977i | 0.526966 | + | 0.849886i | \(0.323329\pi\) | ||||
−0.526966 | + | 0.849886i | \(0.676671\pi\) | |||||||
\(20\) | 369827.i | 2.31142i | ||||||||
\(21\) | 134468. | 0.691420 | ||||||||
\(22\) | − | 183913.i | − | 0.785092i | ||||||
\(23\) | 272622. | 0.974205 | 0.487102 | − | 0.873345i | \(-0.338054\pi\) | ||||
0.487102 | + | 0.873345i | \(0.338054\pi\) | |||||||
\(24\) | −169885. | −0.512047 | ||||||||
\(25\) | −1.01938e6 | −2.60961 | ||||||||
\(26\) | − | 780665.i | − | 1.70833i | ||||||
\(27\) | 439823.i | 0.827604i | ||||||||
\(28\) | − | 325625.i | − | 0.529767i | ||||||
\(29\) | − | 11057.0i | − | 0.0156332i | −0.999969 | − | 0.00781658i | \(-0.997512\pi\) | ||
0.999969 | − | 0.00781658i | \(-0.00248812\pi\) | |||||||
\(30\) | − | 3.63801e6i | − | 4.49137i | ||||||
\(31\) | −669910. | −0.725387 | −0.362694 | − | 0.931908i | \(-0.618143\pi\) | ||||
−0.362694 | + | 0.931908i | \(0.618143\pi\) | |||||||
\(32\) | − | 1.48790e6i | − | 1.41898i | ||||||
\(33\) | 992974.i | 0.837302i | ||||||||
\(34\) | 1.78227e6i | 1.33370i | ||||||||
\(35\) | 1.24148e6 | 0.827307 | ||||||||
\(36\) | 3.10849e6 | 1.85071 | ||||||||
\(37\) | − | 3.02251e6i | − | 1.61273i | −0.591421 | − | 0.806363i | \(-0.701433\pi\) | ||
0.591421 | − | 0.806363i | \(-0.298567\pi\) | |||||||
\(38\) | −5.27678e6 | −2.53066 | ||||||||
\(39\) | 4.21494e6i | 1.82193i | ||||||||
\(40\) | −1.56847e6 | −0.612682 | ||||||||
\(41\) | −874510. | −0.309478 | −0.154739 | − | 0.987955i | \(-0.549454\pi\) | ||||
−0.154739 | + | 0.987955i | \(0.549454\pi\) | |||||||
\(42\) | 3.20319e6i | 1.02940i | ||||||||
\(43\) | −3.02666e6 | + | 1.58983e6i | −0.885298 | + | 0.465025i | ||||
\(44\) | 2.40456e6 | 0.641542 | ||||||||
\(45\) | 1.18514e7i | 2.89015i | ||||||||
\(46\) | 6.49420e6i | 1.45042i | ||||||||
\(47\) | −2.23823e6 | −0.458685 | −0.229342 | − | 0.973346i | \(-0.573658\pi\) | ||||
−0.229342 | + | 0.973346i | \(0.573658\pi\) | |||||||
\(48\) | 6.20772e6i | 1.16941i | ||||||||
\(49\) | 4.67171e6 | 0.810385 | ||||||||
\(50\) | − | 2.42828e7i | − | 3.88525i | ||||||
\(51\) | − | 9.62278e6i | − | 1.42239i | ||||||
\(52\) | 1.02068e7 | 1.39597 | ||||||||
\(53\) | −1.95235e6 | −0.247431 | −0.123715 | − | 0.992318i | \(-0.539481\pi\) | ||||
−0.123715 | + | 0.992318i | \(0.539481\pi\) | |||||||
\(54\) | −1.04771e7 | −1.23216 | ||||||||
\(55\) | 9.16765e6i | 1.00186i | ||||||||
\(56\) | 1.38100e6 | 0.140424 | ||||||||
\(57\) | 2.84902e7 | 2.69896 | ||||||||
\(58\) | 263392. | 0.0232750 | ||||||||
\(59\) | −2.07104e7 | −1.70915 | −0.854574 | − | 0.519330i | \(-0.826182\pi\) | ||||
−0.854574 | + | 0.519330i | \(0.826182\pi\) | |||||||
\(60\) | 4.75651e7 | 3.67015 | ||||||||
\(61\) | − | 1.01183e7i | − | 0.730783i | −0.930854 | − | 0.365392i | \(-0.880935\pi\) | ||
0.930854 | − | 0.365392i | \(-0.119065\pi\) | |||||||
\(62\) | − | 1.59581e7i | − | 1.07997i | ||||||
\(63\) | − | 1.04349e7i | − | 0.662411i | ||||||
\(64\) | 2.30875e7 | 1.37612 | ||||||||
\(65\) | 3.89145e7i | 2.18001i | ||||||||
\(66\) | −2.36538e7 | −1.24660 | ||||||||
\(67\) | −2.69928e7 | −1.33952 | −0.669760 | − | 0.742577i | \(-0.733603\pi\) | ||||
−0.669760 | + | 0.742577i | \(0.733603\pi\) | |||||||
\(68\) | −2.33023e7 | −1.08984 | ||||||||
\(69\) | − | 3.50632e7i | − | 1.54688i | ||||||
\(70\) | 2.95735e7i | 1.23172i | ||||||||
\(71\) | − | 1.28888e7i | − | 0.507200i | −0.967309 | − | 0.253600i | \(-0.918385\pi\) | ||
0.967309 | − | 0.253600i | \(-0.0816148\pi\) | |||||||
\(72\) | 1.31834e7i | 0.490564i | ||||||||
\(73\) | − | 1.98955e7i | − | 0.700589i | −0.936640 | − | 0.350294i | \(-0.886082\pi\) | ||
0.936640 | − | 0.350294i | \(-0.113918\pi\) | |||||||
\(74\) | 7.19998e7 | 2.40107 | ||||||||
\(75\) | 1.31107e8i | 4.14363i | ||||||||
\(76\) | − | 6.89912e7i | − | 2.06795i | ||||||
\(77\) | − | 8.07192e6i | − | 0.229622i | ||||||
\(78\) | −1.00405e8 | −2.71254 | ||||||||
\(79\) | 4.68555e7 | 1.20296 | 0.601482 | − | 0.798886i | \(-0.294577\pi\) | ||||
0.601482 | + | 0.798886i | \(0.294577\pi\) | |||||||
\(80\) | 5.73129e7i | 1.39924i | ||||||||
\(81\) | −8.91576e6 | −0.207118 | ||||||||
\(82\) | − | 2.08319e7i | − | 0.460759i | ||||||
\(83\) | 2.60253e7 | 0.548382 | 0.274191 | − | 0.961675i | \(-0.411590\pi\) | ||||
0.274191 | + | 0.961675i | \(0.411590\pi\) | |||||||
\(84\) | −4.18801e7 | −0.841182 | ||||||||
\(85\) | − | 8.88425e7i | − | 1.70194i | ||||||
\(86\) | −3.78716e7 | − | 7.20986e7i | −0.692340 | − | 1.31805i | ||||
\(87\) | −1.42210e6 | −0.0248229 | ||||||||
\(88\) | 1.01979e7i | 0.170052i | ||||||||
\(89\) | 2.43427e7i | 0.387980i | 0.981004 | + | 0.193990i | \(0.0621429\pi\) | ||||
−0.981004 | + | 0.193990i | \(0.937857\pi\) | |||||||
\(90\) | −2.82316e8 | −4.30294 | ||||||||
\(91\) | − | 3.42634e7i | − | 0.499648i | ||||||
\(92\) | −8.49083e7 | −1.18522 | ||||||||
\(93\) | 8.61602e7i | 1.15179i | ||||||||
\(94\) | − | 5.33175e7i | − | 0.682901i | ||||||
\(95\) | 2.63036e8 | 3.22939 | ||||||||
\(96\) | −1.91366e8 | −2.25310 | ||||||||
\(97\) | 3.57432e6 | 0.0403744 | 0.0201872 | − | 0.999796i | \(-0.493574\pi\) | ||||
0.0201872 | + | 0.999796i | \(0.493574\pi\) | |||||||
\(98\) | 1.11286e8i | 1.20652i | ||||||||
\(99\) | 7.70564e7 | 0.802173 | ||||||||
\(100\) | 3.17486e8 | 3.17486 | ||||||||
\(101\) | −4.79756e7 | −0.461036 | −0.230518 | − | 0.973068i | \(-0.574042\pi\) | ||||
−0.230518 | + | 0.973068i | \(0.574042\pi\) | |||||||
\(102\) | 2.29226e8 | 2.11770 | ||||||||
\(103\) | 2.85028e7 | 0.253243 | 0.126622 | − | 0.991951i | \(-0.459587\pi\) | ||||
0.126622 | + | 0.991951i | \(0.459587\pi\) | |||||||
\(104\) | 4.32879e7i | 0.370027i | ||||||||
\(105\) | − | 1.59672e8i | − | 1.31363i | ||||||
\(106\) | − | 4.65073e7i | − | 0.368381i | ||||||
\(107\) | −1.05259e8 | −0.803016 | −0.401508 | − | 0.915855i | \(-0.631514\pi\) | ||||
−0.401508 | + | 0.915855i | \(0.631514\pi\) | |||||||
\(108\) | − | 1.36983e8i | − | 1.00686i | ||||||
\(109\) | 4.41249e7 | 0.312592 | 0.156296 | − | 0.987710i | \(-0.450045\pi\) | ||||
0.156296 | + | 0.987710i | \(0.450045\pi\) | |||||||
\(110\) | −2.18384e8 | −1.49160 | ||||||||
\(111\) | −3.88739e8 | −2.56074 | ||||||||
\(112\) | − | 5.04628e7i | − | 0.320700i | ||||||
\(113\) | − | 2.43450e8i | − | 1.49313i | −0.665314 | − | 0.746563i | \(-0.731702\pi\) | ||
0.665314 | − | 0.746563i | \(-0.268298\pi\) | |||||||
\(114\) | 6.78671e8i | 4.01827i | ||||||||
\(115\) | − | 3.23722e8i | − | 1.85089i | ||||||
\(116\) | 3.44371e6i | 0.0190193i | ||||||||
\(117\) | 3.27086e8 | 1.74549 | ||||||||
\(118\) | − | 4.93346e8i | − | 2.54462i | ||||||
\(119\) | 7.82239e7i | 0.390078i | ||||||||
\(120\) | 2.01728e8i | 0.972838i | ||||||||
\(121\) | −1.54752e8 | −0.721930 | ||||||||
\(122\) | 2.41030e8 | 1.08801 | ||||||||
\(123\) | 1.12475e8i | 0.491399i | ||||||||
\(124\) | 2.08644e8 | 0.882507 | ||||||||
\(125\) | 7.46605e8i | 3.05809i | ||||||||
\(126\) | 2.48573e8 | 0.986215 | ||||||||
\(127\) | 4.14402e8 | 1.59297 | 0.796483 | − | 0.604661i | \(-0.206691\pi\) | ||||
0.796483 | + | 0.604661i | \(0.206691\pi\) | |||||||
\(128\) | 1.69070e8i | 0.629834i | ||||||||
\(129\) | 2.04475e8 | + | 3.89272e8i | 0.738382 | + | 1.40571i | ||||
\(130\) | −9.26990e8 | −3.24565 | ||||||||
\(131\) | − | 7.37862e7i | − | 0.250548i | −0.992122 | − | 0.125274i | \(-0.960019\pi\) | ||
0.992122 | − | 0.125274i | \(-0.0399809\pi\) | |||||||
\(132\) | − | 3.09262e8i | − | 1.01866i | ||||||
\(133\) | −2.31598e8 | −0.740163 | ||||||||
\(134\) | − | 6.43002e8i | − | 1.99431i | ||||||
\(135\) | 5.22261e8 | 1.57236 | ||||||||
\(136\) | − | 9.88270e7i | − | 0.288882i | ||||||
\(137\) | 3.82975e8i | 1.08715i | 0.839362 | + | 0.543573i | \(0.182929\pi\) | ||||
−0.839362 | + | 0.543573i | \(0.817071\pi\) | |||||||
\(138\) | 8.35248e8 | 2.30303 | ||||||||
\(139\) | −1.29166e8 | −0.346011 | −0.173005 | − | 0.984921i | \(-0.555348\pi\) | ||||
−0.173005 | + | 0.984921i | \(0.555348\pi\) | |||||||
\(140\) | −3.86658e8 | −1.00650 | ||||||||
\(141\) | 2.87869e8i | 0.728315i | ||||||||
\(142\) | 3.07027e8 | 0.755133 | ||||||||
\(143\) | 2.53017e8 | 0.605069 | ||||||||
\(144\) | 4.81729e8 | 1.12035 | ||||||||
\(145\) | −1.31295e7 | −0.0297014 | ||||||||
\(146\) | 4.73935e8 | 1.04305 | ||||||||
\(147\) | − | 6.00849e8i | − | 1.28676i | ||||||
\(148\) | 9.41360e8i | 1.96205i | ||||||||
\(149\) | − | 1.46858e8i | − | 0.297957i | −0.988840 | − | 0.148979i | \(-0.952401\pi\) | ||
0.988840 | − | 0.148979i | \(-0.0475985\pi\) | |||||||
\(150\) | −3.12313e9 | −6.16914 | ||||||||
\(151\) | − | 4.27850e7i | − | 0.0822970i | −0.999153 | − | 0.0411485i | \(-0.986898\pi\) | ||
0.999153 | − | 0.0411485i | \(-0.0131017\pi\) | |||||||
\(152\) | 2.92597e8 | 0.548146 | ||||||||
\(153\) | −7.46744e8 | −1.36272 | ||||||||
\(154\) | 1.92283e8 | 0.341867 | ||||||||
\(155\) | 7.95475e8i | 1.37816i | ||||||||
\(156\) | − | 1.31274e9i | − | 2.21657i | ||||||
\(157\) | − | 7.84735e8i | − | 1.29159i | −0.763511 | − | 0.645795i | \(-0.776526\pi\) | ||
0.763511 | − | 0.645795i | \(-0.223474\pi\) | |||||||
\(158\) | 1.11616e9i | 1.79100i | ||||||||
\(159\) | 2.51100e8i | 0.392879i | ||||||||
\(160\) | −1.76679e9 | −2.69591 | ||||||||
\(161\) | 2.85030e8i | 0.424216i | ||||||||
\(162\) | − | 2.12384e8i | − | 0.308363i | ||||||
\(163\) | − | 8.52878e8i | − | 1.20819i | −0.796911 | − | 0.604097i | \(-0.793534\pi\) | ||
0.796911 | − | 0.604097i | \(-0.206466\pi\) | |||||||
\(164\) | 2.72366e8 | 0.376511 | ||||||||
\(165\) | 1.17909e9 | 1.59079 | ||||||||
\(166\) | 6.19954e8i | 0.816446i | ||||||||
\(167\) | 6.08443e8 | 0.782266 | 0.391133 | − | 0.920334i | \(-0.372083\pi\) | ||||
0.391133 | + | 0.920334i | \(0.372083\pi\) | |||||||
\(168\) | − | 1.77617e8i | − | 0.222970i | ||||||
\(169\) | 2.58264e8 | 0.316605 | ||||||||
\(170\) | 2.11634e9 | 2.53390 | ||||||||
\(171\) | − | 2.21088e9i | − | 2.58572i | ||||||
\(172\) | 9.42652e8 | − | 4.95151e8i | 1.07705 | − | 0.565750i | ||||
\(173\) | −1.45079e9 | −1.61965 | −0.809824 | − | 0.586673i | \(-0.800437\pi\) | ||||
−0.809824 | + | 0.586673i | \(0.800437\pi\) | |||||||
\(174\) | − | 3.38760e7i | − | 0.0369569i | ||||||
\(175\) | − | 1.06577e9i | − | 1.13635i | ||||||
\(176\) | 3.72640e8 | 0.388364 | ||||||||
\(177\) | 2.66365e9i | 2.71384i | ||||||||
\(178\) | −5.79873e8 | −0.577634 | ||||||||
\(179\) | − | 4.36516e8i | − | 0.425194i | −0.977140 | − | 0.212597i | \(-0.931808\pi\) | ||
0.977140 | − | 0.212597i | \(-0.0681922\pi\) | |||||||
\(180\) | − | 3.69113e9i | − | 3.51617i | ||||||
\(181\) | 1.12797e9 | 1.05095 | 0.525474 | − | 0.850810i | \(-0.323888\pi\) | ||||
0.525474 | + | 0.850810i | \(0.323888\pi\) | |||||||
\(182\) | 8.16195e8 | 0.743889 | ||||||||
\(183\) | −1.30136e9 | −1.16036 | ||||||||
\(184\) | − | 3.60103e8i | − | 0.314163i | ||||||
\(185\) | −3.58904e9 | −3.06401 | ||||||||
\(186\) | −2.05244e9 | −1.71482 | ||||||||
\(187\) | −5.77642e8 | −0.472381 | ||||||||
\(188\) | 6.97098e8 | 0.558036 | ||||||||
\(189\) | −4.59840e8 | −0.360379 | ||||||||
\(190\) | 6.26584e9i | 4.80800i | ||||||||
\(191\) | − | 1.96549e9i | − | 1.47685i | −0.674335 | − | 0.738425i | \(-0.735570\pi\) | ||
0.674335 | − | 0.738425i | \(-0.264430\pi\) | |||||||
\(192\) | − | 2.96939e9i | − | 2.18506i | ||||||
\(193\) | 4.37331e8 | 0.315197 | 0.157598 | − | 0.987503i | \(-0.449625\pi\) | ||||
0.157598 | + | 0.987503i | \(0.449625\pi\) | |||||||
\(194\) | 8.51445e7i | 0.0601104i | ||||||||
\(195\) | 5.00497e9 | 3.46149 | ||||||||
\(196\) | −1.45500e9 | −0.985915 | ||||||||
\(197\) | −1.98231e9 | −1.31615 | −0.658077 | − | 0.752950i | \(-0.728630\pi\) | ||||
−0.658077 | + | 0.752950i | \(0.728630\pi\) | |||||||
\(198\) | 1.83558e9i | 1.19430i | ||||||||
\(199\) | 3.04777e9i | 1.94344i | 0.236143 | + | 0.971718i | \(0.424117\pi\) | ||||
−0.236143 | + | 0.971718i | \(0.575883\pi\) | |||||||
\(200\) | 1.34648e9i | 0.841552i | ||||||||
\(201\) | 3.47167e9i | 2.12694i | ||||||||
\(202\) | − | 1.14284e9i | − | 0.686402i | ||||||
\(203\) | 1.15603e7 | 0.00680744 | ||||||||
\(204\) | 2.99702e9i | 1.73049i | ||||||||
\(205\) | 1.03843e9i | 0.587976i | ||||||||
\(206\) | 6.78970e8i | 0.377035i | ||||||||
\(207\) | −2.72096e9 | −1.48198 | ||||||||
\(208\) | 1.58177e9 | 0.845065 | ||||||||
\(209\) | − | 1.71022e9i | − | 0.896330i | ||||||
\(210\) | 3.80358e9 | 1.95576 | ||||||||
\(211\) | − | 2.99574e8i | − | 0.151138i | −0.997141 | − | 0.0755690i | \(-0.975923\pi\) | ||
0.997141 | − | 0.0755690i | \(-0.0240773\pi\) | |||||||
\(212\) | 6.08059e8 | 0.301025 | ||||||||
\(213\) | −1.65769e9 | −0.805350 | ||||||||
\(214\) | − | 2.50740e9i | − | 1.19555i | ||||||
\(215\) | 1.88782e9 | + | 3.59396e9i | 0.883499 | + | 1.68197i | ||||
\(216\) | 5.80955e8 | 0.266887 | ||||||||
\(217\) | − | 7.00399e8i | − | 0.315869i | ||||||
\(218\) | 1.05111e9i | 0.465395i | ||||||||
\(219\) | −2.55885e9 | −1.11242 | ||||||||
\(220\) | − | 2.85526e9i | − | 1.21886i | ||||||
\(221\) | −2.45195e9 | −1.02788 | ||||||||
\(222\) | − | 9.26022e9i | − | 3.81250i | ||||||
\(223\) | − | 2.78431e9i | − | 1.12589i | −0.826493 | − | 0.562947i | \(-0.809667\pi\) | ||
0.826493 | − | 0.562947i | \(-0.190333\pi\) | |||||||
\(224\) | 1.55562e9 | 0.617891 | ||||||||
\(225\) | 1.01741e10 | 3.96978 | ||||||||
\(226\) | 5.79928e9 | 2.22301 | ||||||||
\(227\) | 9.25556e8i | 0.348578i | 0.984695 | + | 0.174289i | \(0.0557626\pi\) | ||||
−0.984695 | + | 0.174289i | \(0.944237\pi\) | |||||||
\(228\) | −8.87327e9 | −3.28355 | ||||||||
\(229\) | −4.49307e9 | −1.63381 | −0.816905 | − | 0.576772i | \(-0.804312\pi\) | ||||
−0.816905 | + | 0.576772i | \(0.804312\pi\) | |||||||
\(230\) | 7.71144e9 | 2.75565 | ||||||||
\(231\) | −1.03817e9 | −0.364602 | ||||||||
\(232\) | −1.46051e7 | −0.00504141 | ||||||||
\(233\) | 1.03025e9i | 0.349559i | 0.984608 | + | 0.174779i | \(0.0559212\pi\) | ||||
−0.984608 | + | 0.174779i | \(0.944079\pi\) | |||||||
\(234\) | 7.79158e9i | 2.59874i | ||||||||
\(235\) | 2.65776e9i | 0.871454i | ||||||||
\(236\) | 6.45024e9 | 2.07935 | ||||||||
\(237\) | − | 6.02630e9i | − | 1.91011i | ||||||
\(238\) | −1.86339e9 | −0.580758 | ||||||||
\(239\) | −4.62921e8 | −0.141878 | −0.0709390 | − | 0.997481i | \(-0.522600\pi\) | ||||
−0.0709390 | + | 0.997481i | \(0.522600\pi\) | |||||||
\(240\) | 7.37127e9 | 2.22176 | ||||||||
\(241\) | − | 2.39828e9i | − | 0.710938i | −0.934688 | − | 0.355469i | \(-0.884321\pi\) | ||
0.934688 | − | 0.355469i | \(-0.115679\pi\) | |||||||
\(242\) | − | 3.68638e9i | − | 1.07483i | ||||||
\(243\) | 4.03237e9i | 1.15647i | ||||||||
\(244\) | 3.15135e9i | 0.889072i | ||||||||
\(245\) | − | 5.54735e9i | − | 1.53965i | ||||||
\(246\) | −2.67928e9 | −0.731608 | ||||||||
\(247\) | − | 7.25949e9i | − | 1.95038i | ||||||
\(248\) | 8.84875e8i | 0.233924i | ||||||||
\(249\) | − | 3.34723e9i | − | 0.870740i | ||||||
\(250\) | −1.77850e10 | −4.55297 | ||||||||
\(251\) | 6.66643e9 | 1.67957 | 0.839786 | − | 0.542918i | \(-0.182681\pi\) | ||||
0.839786 | + | 0.542918i | \(0.182681\pi\) | |||||||
\(252\) | 3.24996e9i | 0.805890i | ||||||||
\(253\) | −2.10479e9 | −0.513721 | ||||||||
\(254\) | 9.87155e9i | 2.37165i | ||||||||
\(255\) | −1.14264e10 | −2.70240 | ||||||||
\(256\) | 1.88296e9 | 0.438412 | ||||||||
\(257\) | 5.34258e9i | 1.22467i | 0.790599 | + | 0.612334i | \(0.209769\pi\) | ||||
−0.790599 | + | 0.612334i | \(0.790231\pi\) | |||||||
\(258\) | −9.27293e9 | + | 4.87084e9i | −2.09285 | + | 1.09932i | ||||
\(259\) | 3.16007e9 | 0.702259 | ||||||||
\(260\) | − | 1.21199e10i | − | 2.65220i | ||||||
\(261\) | 1.10357e8i | 0.0237814i | ||||||||
\(262\) | 1.75768e9 | 0.373022 | ||||||||
\(263\) | 1.45518e9i | 0.304155i | 0.988369 | + | 0.152078i | \(0.0485964\pi\) | ||||
−0.988369 | + | 0.152078i | \(0.951404\pi\) | |||||||
\(264\) | 1.31160e9 | 0.270015 | ||||||||
\(265\) | 2.31829e9i | 0.470093i | ||||||||
\(266\) | − | 5.51694e9i | − | 1.10197i | ||||||
\(267\) | 3.13083e9 | 0.616047 | ||||||||
\(268\) | 8.40692e9 | 1.62966 | ||||||||
\(269\) | −3.65582e9 | −0.698194 | −0.349097 | − | 0.937087i | \(-0.613512\pi\) | ||||
−0.349097 | + | 0.937087i | \(0.613512\pi\) | |||||||
\(270\) | 1.24409e10i | 2.34097i | ||||||||
\(271\) | −7.70139e9 | −1.42788 | −0.713940 | − | 0.700207i | \(-0.753091\pi\) | ||||
−0.713940 | + | 0.700207i | \(0.753091\pi\) | |||||||
\(272\) | −3.61121e9 | −0.659747 | ||||||||
\(273\) | −4.40677e9 | −0.793359 | ||||||||
\(274\) | −9.12293e9 | −1.61857 | ||||||||
\(275\) | 7.87016e9 | 1.37611 | ||||||||
\(276\) | 1.09204e10i | 1.88193i | ||||||||
\(277\) | − | 2.17850e9i | − | 0.370032i | −0.982736 | − | 0.185016i | \(-0.940766\pi\) | ||
0.982736 | − | 0.185016i | \(-0.0592336\pi\) | |||||||
\(278\) | − | 3.07690e9i | − | 0.515150i | ||||||
\(279\) | 6.68617e9 | 1.10347 | ||||||||
\(280\) | − | 1.63985e9i | − | 0.266792i | ||||||
\(281\) | 2.46057e9 | 0.394649 | 0.197324 | − | 0.980338i | \(-0.436775\pi\) | ||||
0.197324 | + | 0.980338i | \(0.436775\pi\) | |||||||
\(282\) | −6.85740e9 | −1.08433 | ||||||||
\(283\) | −2.55764e9 | −0.398744 | −0.199372 | − | 0.979924i | \(-0.563890\pi\) | ||||
−0.199372 | + | 0.979924i | \(0.563890\pi\) | |||||||
\(284\) | 4.01422e9i | 0.617061i | ||||||||
\(285\) | − | 3.38303e10i | − | 5.12774i | ||||||
\(286\) | 6.02716e9i | 0.900842i | ||||||||
\(287\) | − | 9.14311e8i | − | 0.134762i | ||||||
\(288\) | 1.48503e10i | 2.15857i | ||||||||
\(289\) | −1.37791e9 | −0.197528 | ||||||||
\(290\) | − | 3.12761e8i | − | 0.0442202i | ||||||
\(291\) | − | 4.59709e8i | − | 0.0641078i | ||||||
\(292\) | 6.19645e9i | 0.852338i | ||||||||
\(293\) | 8.21345e9 | 1.11444 | 0.557218 | − | 0.830366i | \(-0.311869\pi\) | ||||
0.557218 | + | 0.830366i | \(0.311869\pi\) | |||||||
\(294\) | 1.43130e10 | 1.91576 | ||||||||
\(295\) | 2.45922e10i | 3.24721i | ||||||||
\(296\) | −3.99239e9 | −0.520075 | ||||||||
\(297\) | − | 3.39567e9i | − | 0.436415i | ||||||
\(298\) | 3.49834e9 | 0.443606 | ||||||||
\(299\) | −8.93435e9 | −1.11784 | ||||||||
\(300\) | − | 4.08333e10i | − | 5.04114i | ||||||
\(301\) | −1.66218e9 | − | 3.16441e9i | −0.202494 | − | 0.385502i | ||||
\(302\) | 1.01919e9 | 0.122526 | ||||||||
\(303\) | 6.17036e9i | 0.732048i | ||||||||
\(304\) | − | 1.06917e10i | − | 1.25185i | ||||||
\(305\) | −1.20148e10 | −1.38841 | ||||||||
\(306\) | − | 1.77883e10i | − | 2.02885i | ||||||
\(307\) | 1.23393e10 | 1.38911 | 0.694554 | − | 0.719441i | \(-0.255602\pi\) | ||||
0.694554 | + | 0.719441i | \(0.255602\pi\) | |||||||
\(308\) | 2.51400e9i | 0.279359i | ||||||||
\(309\) | − | 3.66587e9i | − | 0.402108i | ||||||
\(310\) | −1.89492e10 | −2.05184 | ||||||||
\(311\) | 1.48263e10 | 1.58486 | 0.792430 | − | 0.609963i | \(-0.208816\pi\) | ||||
0.792430 | + | 0.609963i | \(0.208816\pi\) | |||||||
\(312\) | 5.56745e9 | 0.587541 | ||||||||
\(313\) | 4.43851e8i | 0.0462445i | 0.999733 | + | 0.0231223i | \(0.00736070\pi\) | ||||
−0.999733 | + | 0.0231223i | \(0.992639\pi\) | |||||||
\(314\) | 1.86933e10 | 1.92295 | ||||||||
\(315\) | −1.23908e10 | −1.25851 | ||||||||
\(316\) | −1.45932e10 | −1.46353 | ||||||||
\(317\) | 1.69495e10 | 1.67850 | 0.839249 | − | 0.543748i | \(-0.182995\pi\) | ||||
0.839249 | + | 0.543748i | \(0.182995\pi\) | |||||||
\(318\) | −5.98151e9 | −0.584928 | ||||||||
\(319\) | 8.53663e7i | 0.00824373i | ||||||||
\(320\) | − | 2.74150e10i | − | 2.61450i | ||||||
\(321\) | 1.35378e10i | 1.27506i | ||||||||
\(322\) | −6.78976e9 | −0.631584 | ||||||||
\(323\) | 1.65736e10i | 1.52267i | ||||||||
\(324\) | 2.77681e9 | 0.251980 | ||||||||
\(325\) | 3.34069e10 | 2.99436 | ||||||||
\(326\) | 2.03166e10 | 1.79879 | ||||||||
\(327\) | − | 5.67510e9i | − | 0.496344i | ||||||
\(328\) | 1.15513e9i | 0.0998010i | ||||||||
\(329\) | − | 2.34010e9i | − | 0.199734i | ||||||
\(330\) | 2.80874e10i | 2.36841i | ||||||||
\(331\) | − | 1.21801e10i | − | 1.01470i | −0.861740 | − | 0.507351i | \(-0.830625\pi\) | ||
0.861740 | − | 0.507351i | \(-0.169375\pi\) | |||||||
\(332\) | −8.10558e9 | −0.667163 | ||||||||
\(333\) | 3.01667e10i | 2.45330i | ||||||||
\(334\) | 1.44939e10i | 1.16466i | ||||||||
\(335\) | 3.20523e10i | 2.54495i | ||||||||
\(336\) | −6.49025e9 | −0.509218 | ||||||||
\(337\) | 1.06848e10 | 0.828411 | 0.414205 | − | 0.910183i | \(-0.364059\pi\) | ||||
0.414205 | + | 0.910183i | \(0.364059\pi\) | |||||||
\(338\) | 6.15217e9i | 0.471369i | ||||||||
\(339\) | −3.13113e10 | −2.37084 | ||||||||
\(340\) | 2.76700e10i | 2.07059i | ||||||||
\(341\) | 5.17207e9 | 0.382514 | ||||||||
\(342\) | 5.26659e10 | 3.84969 | ||||||||
\(343\) | 1.09115e10i | 0.788329i | ||||||||
\(344\) | 2.09998e9 | + | 3.99787e9i | 0.149962 | + | 0.285492i | ||||
\(345\) | −4.16353e10 | −2.93890 | ||||||||
\(346\) | − | 3.45596e10i | − | 2.41137i | ||||||
\(347\) | − | 4.88319e9i | − | 0.336810i | −0.985718 | − | 0.168405i | \(-0.946138\pi\) | ||
0.985718 | − | 0.168405i | \(-0.0538617\pi\) | |||||||
\(348\) | 4.42912e8 | 0.0301995 | ||||||||
\(349\) | − | 1.60675e10i | − | 1.08304i | −0.840687 | − | 0.541521i | \(-0.817848\pi\) | ||
0.840687 | − | 0.541521i | \(-0.182152\pi\) | |||||||
\(350\) | 2.53880e10 | 1.69183 | ||||||||
\(351\) | − | 1.44138e10i | − | 0.949621i | ||||||
\(352\) | 1.14874e10i | 0.748259i | ||||||||
\(353\) | 1.51491e10 | 0.975634 | 0.487817 | − | 0.872946i | \(-0.337793\pi\) | ||||
0.487817 | + | 0.872946i | \(0.337793\pi\) | |||||||
\(354\) | −6.34514e10 | −4.04044 | ||||||||
\(355\) | −1.53046e10 | −0.963629 | ||||||||
\(356\) | − | 7.58154e9i | − | 0.472017i | ||||||
\(357\) | 1.00607e10 | 0.619379 | ||||||||
\(358\) | 1.03983e10 | 0.633040 | ||||||||
\(359\) | −1.52025e10 | −0.915242 | −0.457621 | − | 0.889147i | \(-0.651298\pi\) | ||||
−0.457621 | + | 0.889147i | \(0.651298\pi\) | |||||||
\(360\) | 1.56544e10 | 0.932022 | ||||||||
\(361\) | −3.20858e10 | −1.88923 | ||||||||
\(362\) | 2.68695e10i | 1.56468i | ||||||||
\(363\) | 1.99034e10i | 1.14630i | ||||||||
\(364\) | 1.06713e10i | 0.607873i | ||||||||
\(365\) | −2.36246e10 | −1.33105 | ||||||||
\(366\) | − | 3.10000e10i | − | 1.72758i | ||||||
\(367\) | −9.87809e9 | −0.544514 | −0.272257 | − | 0.962225i | \(-0.587770\pi\) | ||||
−0.272257 | + | 0.962225i | \(0.587770\pi\) | |||||||
\(368\) | −1.31584e10 | −0.717485 | ||||||||
\(369\) | 8.72822e9 | 0.470783 | ||||||||
\(370\) | − | 8.54952e10i | − | 4.56178i | ||||||
\(371\) | − | 2.04120e9i | − | 0.107743i | ||||||
\(372\) | − | 2.68346e10i | − | 1.40127i | ||||||
\(373\) | 2.67857e10i | 1.38378i | 0.722002 | + | 0.691891i | \(0.243222\pi\) | ||||
−0.722002 | + | 0.691891i | \(0.756778\pi\) | |||||||
\(374\) | − | 1.37601e10i | − | 0.703292i | ||||||
\(375\) | 9.60243e10 | 4.85575 | ||||||||
\(376\) | 2.95645e9i | 0.147917i | ||||||||
\(377\) | 3.62360e8i | 0.0179380i | ||||||||
\(378\) | − | 1.09539e10i | − | 0.536541i | ||||||
\(379\) | 1.56805e10 | 0.759983 | 0.379991 | − | 0.924990i | \(-0.375927\pi\) | ||||
0.379991 | + | 0.924990i | \(0.375927\pi\) | |||||||
\(380\) | −8.19226e10 | −3.92888 | ||||||||
\(381\) | − | 5.32981e10i | − | 2.52937i | ||||||
\(382\) | 4.68203e10 | 2.19877 | ||||||||
\(383\) | 2.95831e10i | 1.37483i | 0.726266 | + | 0.687414i | \(0.241254\pi\) | ||||
−0.726266 | + | 0.687414i | \(0.758746\pi\) | |||||||
\(384\) | 2.17448e10 | 1.00007 | ||||||||
\(385\) | −9.58488e9 | −0.436259 | ||||||||
\(386\) | 1.04178e10i | 0.469273i | ||||||||
\(387\) | 3.02081e10 | − | 1.58676e10i | 1.34673 | − | 0.707403i | ||||
\(388\) | −1.11322e9 | −0.0491195 | ||||||||
\(389\) | 1.92230e10i | 0.839502i | 0.907639 | + | 0.419751i | \(0.137883\pi\) | ||||
−0.907639 | + | 0.419751i | \(0.862117\pi\) | |||||||
\(390\) | 1.19224e11i | 5.15355i | ||||||||
\(391\) | 2.03973e10 | 0.872701 | ||||||||
\(392\) | − | 6.17079e9i | − | 0.261334i | ||||||
\(393\) | −9.48998e9 | −0.397828 | ||||||||
\(394\) | − | 4.72210e10i | − | 1.95952i | ||||||
\(395\) | − | 5.56380e10i | − | 2.28551i | ||||||
\(396\) | −2.39992e10 | −0.975924 | ||||||||
\(397\) | −2.76966e10 | −1.11497 | −0.557486 | − | 0.830186i | \(-0.688234\pi\) | ||||
−0.557486 | + | 0.830186i | \(0.688234\pi\) | |||||||
\(398\) | −7.26016e10 | −2.89344 | ||||||||
\(399\) | 2.97868e10i | 1.17526i | ||||||||
\(400\) | 4.92015e10 | 1.92193 | ||||||||
\(401\) | −3.55121e10 | −1.37340 | −0.686702 | − | 0.726939i | \(-0.740942\pi\) | ||||
−0.686702 | + | 0.726939i | \(0.740942\pi\) | |||||||
\(402\) | −8.26994e10 | −3.16664 | ||||||||
\(403\) | 2.19542e10 | 0.832334 | ||||||||
\(404\) | 1.49420e10 | 0.560897 | ||||||||
\(405\) | 1.05869e10i | 0.393503i | ||||||||
\(406\) | 2.75379e8i | 0.0101351i | ||||||||
\(407\) | 2.33354e10i | 0.850428i | ||||||||
\(408\) | −1.27106e10 | −0.458696 | ||||||||
\(409\) | 5.61655e9i | 0.200713i | 0.994952 | + | 0.100357i | \(0.0319984\pi\) | ||||
−0.994952 | + | 0.100357i | \(0.968002\pi\) | |||||||
\(410\) | −2.47365e10 | −0.875394 | ||||||||
\(411\) | 4.92561e10 | 1.72621 | ||||||||
\(412\) | −8.87718e9 | −0.308096 | ||||||||
\(413\) | − | 2.16529e10i | − | 0.744246i | ||||||
\(414\) | − | 6.48166e10i | − | 2.20640i | ||||||
\(415\) | − | 3.09034e10i | − | 1.04187i | ||||||
\(416\) | 4.87614e10i | 1.62818i | ||||||||
\(417\) | 1.66127e10i | 0.549408i | ||||||||
\(418\) | 4.07396e10 | 1.33448 | ||||||||
\(419\) | − | 3.04720e10i | − | 0.988655i | −0.869276 | − | 0.494328i | \(-0.835414\pi\) | ||
0.869276 | − | 0.494328i | \(-0.164586\pi\) | |||||||
\(420\) | 4.97299e10i | 1.59816i | ||||||||
\(421\) | − | 2.98892e10i | − | 0.951449i | −0.879594 | − | 0.475724i | \(-0.842186\pi\) | ||
0.879594 | − | 0.475724i | \(-0.157814\pi\) | |||||||
\(422\) | 7.13620e9 | 0.225018 | ||||||||
\(423\) | 2.23391e10 | 0.697758 | ||||||||
\(424\) | 2.57883e9i | 0.0797919i | ||||||||
\(425\) | −7.62687e10 | −2.33771 | ||||||||
\(426\) | − | 3.94882e10i | − | 1.19903i | ||||||
\(427\) | 1.05788e10 | 0.318219 | ||||||||
\(428\) | 3.27829e10 | 0.976951 | ||||||||
\(429\) | − | 3.25416e10i | − | 0.960749i | ||||||
\(430\) | −8.56125e10 | + | 4.49701e10i | −2.50417 | + | 1.31538i | ||||
\(431\) | 1.21255e10 | 0.351390 | 0.175695 | − | 0.984445i | \(-0.443783\pi\) | ||||
0.175695 | + | 0.984445i | \(0.443783\pi\) | |||||||
\(432\) | − | 2.12285e10i | − | 0.609516i | ||||||
\(433\) | 6.14766e9i | 0.174887i | 0.996169 | + | 0.0874436i | \(0.0278698\pi\) | ||||
−0.996169 | + | 0.0874436i | \(0.972130\pi\) | |||||||
\(434\) | 1.66844e10 | 0.470273 | ||||||||
\(435\) | 1.68865e9i | 0.0471609i | ||||||||
\(436\) | −1.37427e10 | −0.380300 | ||||||||
\(437\) | 6.03903e10i | 1.65593i | ||||||||
\(438\) | − | 6.09549e10i | − | 1.65620i | ||||||
\(439\) | 2.09828e10 | 0.564945 | 0.282472 | − | 0.959275i | \(-0.408845\pi\) | ||||
0.282472 | + | 0.959275i | \(0.408845\pi\) | |||||||
\(440\) | 1.21094e10 | 0.323082 | ||||||||
\(441\) | −4.66269e10 | −1.23277 | ||||||||
\(442\) | − | 5.84084e10i | − | 1.53033i | ||||||
\(443\) | 4.56919e10 | 1.18638 | 0.593191 | − | 0.805062i | \(-0.297868\pi\) | ||||
0.593191 | + | 0.805062i | \(0.297868\pi\) | |||||||
\(444\) | 1.21073e11 | 3.11540 | ||||||||
\(445\) | 2.89054e10 | 0.737122 | ||||||||
\(446\) | 6.63256e10 | 1.67626 | ||||||||
\(447\) | −1.88881e10 | −0.473106 | ||||||||
\(448\) | 2.41383e10i | 0.599231i | ||||||||
\(449\) | − | 4.66900e10i | − | 1.14878i | −0.818580 | − | 0.574392i | \(-0.805238\pi\) | ||
0.818580 | − | 0.574392i | \(-0.194762\pi\) | |||||||
\(450\) | 2.42360e11i | 5.91031i | ||||||||
\(451\) | 6.75169e9 | 0.163195 | ||||||||
\(452\) | 7.58226e10i | 1.81654i | ||||||||
\(453\) | −5.50278e9 | −0.130674 | ||||||||
\(454\) | −2.20479e10 | −0.518971 | ||||||||
\(455\) | −4.06856e10 | −0.949281 | ||||||||
\(456\) | − | 3.76323e10i | − | 0.870364i | ||||||
\(457\) | 5.13987e10i | 1.17839i | 0.807992 | + | 0.589193i | \(0.200554\pi\) | ||||
−0.807992 | + | 0.589193i | \(0.799446\pi\) | |||||||
\(458\) | − | 1.07030e11i | − | 2.43246i | ||||||
\(459\) | 3.29070e10i | 0.741374i | ||||||||
\(460\) | 1.00823e11i | 2.25179i | ||||||||
\(461\) | −5.31807e9 | −0.117747 | −0.0588736 | − | 0.998265i | \(-0.518751\pi\) | ||||
−0.0588736 | + | 0.998265i | \(0.518751\pi\) | |||||||
\(462\) | − | 2.47304e10i | − | 0.542828i | ||||||
\(463\) | − | 1.73963e10i | − | 0.378558i | −0.981923 | − | 0.189279i | \(-0.939385\pi\) | ||
0.981923 | − | 0.189279i | \(-0.0606151\pi\) | |||||||
\(464\) | 5.33680e8i | 0.0115135i | ||||||||
\(465\) | 1.02310e11 | 2.18829 | ||||||||
\(466\) | −2.45419e10 | −0.520432 | ||||||||
\(467\) | 1.29922e10i | 0.273158i | 0.990629 | + | 0.136579i | \(0.0436108\pi\) | ||||
−0.990629 | + | 0.136579i | \(0.956389\pi\) | |||||||
\(468\) | −1.01871e11 | −2.12357 | ||||||||
\(469\) | − | 2.82213e10i | − | 0.583292i | ||||||
\(470\) | −6.33111e10 | −1.29744 | ||||||||
\(471\) | −1.00928e11 | −2.05083 | ||||||||
\(472\) | 2.73560e10i | 0.551169i | ||||||||
\(473\) | 2.33674e10 | − | 1.22743e10i | 0.466838 | − | 0.245218i | ||||
\(474\) | 1.43554e11 | 2.84382 | ||||||||
\(475\) | − | 2.25809e11i | − | 4.43574i | ||||||
\(476\) | − | 2.43628e10i | − | 0.474570i | ||||||
\(477\) | 1.94858e10 | 0.376396 | ||||||||
\(478\) | − | 1.10273e10i | − | 0.211231i | ||||||
\(479\) | −4.10168e10 | −0.779148 | −0.389574 | − | 0.920995i | \(-0.627378\pi\) | ||||
−0.389574 | + | 0.920995i | \(0.627378\pi\) | |||||||
\(480\) | 2.27235e11i | 4.28065i | ||||||||
\(481\) | 9.90532e10i | 1.85050i | ||||||||
\(482\) | 5.71299e10 | 1.05846 | ||||||||
\(483\) | 3.66590e10 | 0.673584 | ||||||||
\(484\) | 4.81975e10 | 0.878301 | ||||||||
\(485\) | − | 4.24427e9i | − | 0.0767072i | ||||||
\(486\) | −9.60560e10 | −1.72179 | ||||||||
\(487\) | −1.49123e10 | −0.265112 | −0.132556 | − | 0.991176i | \(-0.542318\pi\) | ||||
−0.132556 | + | 0.991176i | \(0.542318\pi\) | |||||||
\(488\) | −1.33651e10 | −0.235664 | ||||||||
\(489\) | −1.09692e11 | −1.91841 | ||||||||
\(490\) | 1.32145e11 | 2.29227 | ||||||||
\(491\) | 2.57099e10i | 0.442359i | 0.975233 | + | 0.221180i | \(0.0709907\pi\) | ||||
−0.975233 | + | 0.221180i | \(0.929009\pi\) | |||||||
\(492\) | − | 3.50303e10i | − | 0.597837i | ||||||
\(493\) | − | 8.27274e8i | − | 0.0140043i | ||||||
\(494\) | 1.72930e11 | 2.90377 | ||||||||
\(495\) | − | 9.14995e10i | − | 1.52405i | ||||||
\(496\) | 3.23340e10 | 0.534235 | ||||||||
\(497\) | 1.34754e10 | 0.220860 | ||||||||
\(498\) | 7.97351e10 | 1.29638 | ||||||||
\(499\) | − | 4.88036e10i | − | 0.787136i | −0.919296 | − | 0.393568i | \(-0.871241\pi\) | ||
0.919296 | − | 0.393568i | \(-0.128759\pi\) | |||||||
\(500\) | − | 2.32530e11i | − | 3.72048i | ||||||
\(501\) | − | 7.82546e10i | − | 1.24211i | ||||||
\(502\) | 1.58802e11i | 2.50059i | ||||||||
\(503\) | 6.69023e10i | 1.04513i | 0.852601 | + | 0.522563i | \(0.175024\pi\) | ||||
−0.852601 | + | 0.522563i | \(0.824976\pi\) | |||||||
\(504\) | −1.37834e10 | −0.213616 | ||||||||
\(505\) | 5.69679e10i | 0.875921i | ||||||||
\(506\) | − | 5.01387e10i | − | 0.764841i | ||||||
\(507\) | − | 3.32165e10i | − | 0.502716i | ||||||
\(508\) | −1.29065e11 | −1.93800 | ||||||||
\(509\) | −3.93507e9 | −0.0586248 | −0.0293124 | − | 0.999570i | \(-0.509332\pi\) | ||||
−0.0293124 | + | 0.999570i | \(0.509332\pi\) | |||||||
\(510\) | − | 2.72192e11i | − | 4.02341i | ||||||
\(511\) | 2.08010e10 | 0.305070 | ||||||||
\(512\) | 8.81363e10i | 1.28255i | ||||||||
\(513\) | −9.74278e10 | −1.40674 | ||||||||
\(514\) | −1.27267e11 | −1.82332 | ||||||||
\(515\) | − | 3.38452e10i | − | 0.481136i | ||||||
\(516\) | −6.36837e10 | − | 1.21239e11i | −0.898316 | − | 1.71018i | ||||
\(517\) | 1.72804e10 | 0.241875 | ||||||||
\(518\) | 7.52767e10i | 1.04554i | ||||||||
\(519\) | 1.86593e11i | 2.57173i | ||||||||
\(520\) | 5.14016e10 | 0.703012 | ||||||||
\(521\) | − | 2.38175e10i | − | 0.323256i | −0.986852 | − | 0.161628i | \(-0.948326\pi\) | ||
0.986852 | − | 0.161628i | \(-0.0516744\pi\) | |||||||
\(522\) | −2.62884e9 | −0.0354064 | ||||||||
\(523\) | 8.63612e10i | 1.15428i | 0.816645 | + | 0.577141i | \(0.195832\pi\) | ||||
−0.816645 | + | 0.577141i | \(0.804168\pi\) | |||||||
\(524\) | 2.29807e10i | 0.304817i | ||||||||
\(525\) | −1.37074e11 | −1.80434 | ||||||||
\(526\) | −3.46643e10 | −0.452834 | ||||||||
\(527\) | −5.01219e10 | −0.649808 | ||||||||
\(528\) | − | 4.79270e10i | − | 0.616658i | ||||||
\(529\) | −3.98798e9 | −0.0509250 | ||||||||
\(530\) | −5.52244e10 | −0.699887 | ||||||||
\(531\) | 2.06704e11 | 2.59998 | ||||||||
\(532\) | 7.21311e10 | 0.900484 | ||||||||
\(533\) | 2.86593e10 | 0.355105 | ||||||||
\(534\) | 7.45801e10i | 0.917187i | ||||||||
\(535\) | 1.24988e11i | 1.52565i | ||||||||
\(536\) | 3.56544e10i | 0.431971i | ||||||||
\(537\) | −5.61422e10 | −0.675138 | ||||||||
\(538\) | − | 8.70861e10i | − | 1.03949i | ||||||
\(539\) | −3.60681e10 | −0.427335 | ||||||||
\(540\) | −1.62658e11 | −1.91294 | ||||||||
\(541\) | 1.11202e11 | 1.29815 | 0.649074 | − | 0.760725i | \(-0.275157\pi\) | ||||
0.649074 | + | 0.760725i | \(0.275157\pi\) | |||||||
\(542\) | − | 1.83456e11i | − | 2.12586i | ||||||
\(543\) | − | 1.45073e11i | − | 1.66873i | ||||||
\(544\) | − | 1.11323e11i | − | 1.27113i | ||||||
\(545\) | − | 5.23955e10i | − | 0.593892i | ||||||
\(546\) | − | 1.04975e11i | − | 1.18117i | ||||||
\(547\) | −4.80348e10 | −0.536546 | −0.268273 | − | 0.963343i | \(-0.586453\pi\) | ||||
−0.268273 | + | 0.963343i | \(0.586453\pi\) | |||||||
\(548\) | − | 1.19278e11i | − | 1.32262i | ||||||
\(549\) | 1.00988e11i | 1.11168i | ||||||||
\(550\) | 1.87477e11i | 2.04879i | ||||||||
\(551\) | 2.44931e9 | 0.0265728 | ||||||||
\(552\) | −4.63145e10 | −0.498839 | ||||||||
\(553\) | 4.89880e10i | 0.523829i | ||||||||
\(554\) | 5.18945e10 | 0.550912 | ||||||||
\(555\) | 4.61602e11i | 4.86515i | ||||||||
\(556\) | 4.02288e10 | 0.420957 | ||||||||
\(557\) | −4.60143e10 | −0.478049 | −0.239024 | − | 0.971014i | \(-0.576828\pi\) | ||||
−0.239024 | + | 0.971014i | \(0.576828\pi\) | |||||||
\(558\) | 1.59273e11i | 1.64287i | ||||||||
\(559\) | 9.91892e10 | − | 5.21016e10i | 1.01582 | − | 0.533585i | ||||
\(560\) | −5.99213e10 | −0.609297 | ||||||||
\(561\) | 7.42931e10i | 0.750062i | ||||||||
\(562\) | 5.86138e10i | 0.587563i | ||||||||
\(563\) | 3.36946e10 | 0.335372 | 0.167686 | − | 0.985840i | \(-0.446371\pi\) | ||||
0.167686 | + | 0.985840i | \(0.446371\pi\) | |||||||
\(564\) | − | 8.96569e10i | − | 0.886069i | ||||||
\(565\) | −2.89082e11 | −2.83679 | ||||||||
\(566\) | − | 6.09261e10i | − | 0.593660i | ||||||
\(567\) | − | 9.32153e9i | − | 0.0901893i | ||||||
\(568\) | −1.70246e10 | −0.163563 | ||||||||
\(569\) | −4.56726e10 | −0.435719 | −0.217860 | − | 0.975980i | \(-0.569907\pi\) | ||||
−0.217860 | + | 0.975980i | \(0.569907\pi\) | |||||||
\(570\) | 8.05878e11 | 7.63431 | ||||||||
\(571\) | 1.77572e10i | 0.167043i | 0.996506 | + | 0.0835217i | \(0.0266168\pi\) | ||||
−0.996506 | + | 0.0835217i | \(0.973383\pi\) | |||||||
\(572\) | −7.88020e10 | −0.736128 | ||||||||
\(573\) | −2.52790e11 | −2.34499 | ||||||||
\(574\) | 2.17800e10 | 0.200637 | ||||||||
\(575\) | −2.77906e11 | −2.54229 | ||||||||
\(576\) | −2.30430e11 | −2.09338 | ||||||||
\(577\) | − | 1.55926e11i | − | 1.40675i | −0.710821 | − | 0.703373i | \(-0.751677\pi\) | ||
0.710821 | − | 0.703373i | \(-0.248323\pi\) | |||||||
\(578\) | − | 3.28234e10i | − | 0.294085i | ||||||
\(579\) | − | 5.62472e10i | − | 0.500480i | ||||||
\(580\) | 4.08919e9 | 0.0361348 | ||||||||
\(581\) | 2.72098e10i | 0.238792i | ||||||||
\(582\) | 1.09508e10 | 0.0954454 | ||||||||
\(583\) | 1.50732e10 | 0.130476 | ||||||||
\(584\) | −2.62797e10 | −0.225927 | ||||||||
\(585\) | − | 3.88394e11i | − | 3.31626i | ||||||
\(586\) | 1.95654e11i | 1.65920i | ||||||||
\(587\) | 2.42355e10i | 0.204127i | 0.994778 | + | 0.102063i | \(0.0325445\pi\) | ||||
−0.994778 | + | 0.102063i | \(0.967456\pi\) | |||||||
\(588\) | 1.87134e11i | 1.56547i | ||||||||
\(589\) | − | 1.48396e11i | − | 1.23299i | ||||||
\(590\) | −5.85817e11 | −4.83452 | ||||||||
\(591\) | 2.54954e11i | 2.08983i | ||||||||
\(592\) | 1.45885e11i | 1.18774i | ||||||||
\(593\) | − | 6.73194e10i | − | 0.544404i | −0.962240 | − | 0.272202i | \(-0.912248\pi\) | ||
0.962240 | − | 0.272202i | \(-0.0877519\pi\) | |||||||
\(594\) | 8.08889e10 | 0.649746 | ||||||||
\(595\) | 9.28859e10 | 0.741109 | ||||||||
\(596\) | 4.57390e10i | 0.362495i | ||||||||
\(597\) | 3.91988e11 | 3.08585 | ||||||||
\(598\) | − | 2.12827e11i | − | 1.66426i | ||||||
\(599\) | 6.22767e10 | 0.483747 | 0.241874 | − | 0.970308i | \(-0.422238\pi\) | ||||
0.241874 | + | 0.970308i | \(0.422238\pi\) | |||||||
\(600\) | 1.73177e11 | 1.33624 | ||||||||
\(601\) | − | 1.57836e11i | − | 1.20979i | −0.796307 | − | 0.604893i | \(-0.793216\pi\) | ||
0.796307 | − | 0.604893i | \(-0.206784\pi\) | |||||||
\(602\) | 7.53800e10 | − | 3.95952e10i | 0.573945 | − | 0.301479i | ||||
\(603\) | 2.69407e11 | 2.03770 | ||||||||
\(604\) | 1.33254e10i | 0.100123i | ||||||||
\(605\) | 1.83758e11i | 1.37159i | ||||||||
\(606\) | −1.46985e11 | −1.08989 | ||||||||
\(607\) | − | 1.00707e11i | − | 0.741833i | −0.928666 | − | 0.370917i | \(-0.879044\pi\) | ||
0.928666 | − | 0.370917i | \(-0.120956\pi\) | |||||||
\(608\) | 3.29595e11 | 2.41194 | ||||||||
\(609\) | − | 1.48682e9i | − | 0.0108091i | ||||||
\(610\) | − | 2.86208e11i | − | 2.06711i | ||||||
\(611\) | 7.33511e10 | 0.526310 | ||||||||
\(612\) | 2.32573e11 | 1.65788 | ||||||||
\(613\) | −1.80424e11 | −1.27777 | −0.638884 | − | 0.769303i | \(-0.720604\pi\) | ||||
−0.638884 | + | 0.769303i | \(0.720604\pi\) | |||||||
\(614\) | 2.93936e11i | 2.06814i | ||||||||
\(615\) | 1.33557e11 | 0.933608 | ||||||||
\(616\) | −1.06621e10 | −0.0740490 | ||||||||
\(617\) | 3.85259e10 | 0.265835 | 0.132918 | − | 0.991127i | \(-0.457565\pi\) | ||||
0.132918 | + | 0.991127i | \(0.457565\pi\) | |||||||
\(618\) | 8.73254e10 | 0.598669 | ||||||||
\(619\) | −5.48744e9 | −0.0373773 | −0.0186886 | − | 0.999825i | \(-0.505949\pi\) | ||||
−0.0186886 | + | 0.999825i | \(0.505949\pi\) | |||||||
\(620\) | − | 2.47751e11i | − | 1.67667i | ||||||
\(621\) | 1.19906e11i | 0.806256i | ||||||||
\(622\) | 3.53180e11i | 2.35958i | ||||||||
\(623\) | −2.54506e10 | −0.168945 | ||||||||
\(624\) | − | 2.03439e11i | − | 1.34182i | ||||||
\(625\) | 4.88351e11 | 3.20046 | ||||||||
\(626\) | −1.05731e10 | −0.0688500 | ||||||||
\(627\) | −2.19960e11 | −1.42322 | ||||||||
\(628\) | 2.44406e11i | 1.57135i | ||||||||
\(629\) | − | 2.26140e11i | − | 1.44469i | ||||||
\(630\) | − | 2.95164e11i | − | 1.87371i | ||||||
\(631\) | − | 1.07158e11i | − | 0.675936i | −0.941158 | − | 0.337968i | \(-0.890260\pi\) | ||
0.941158 | − | 0.337968i | \(-0.109740\pi\) | |||||||
\(632\) | − | 6.18908e10i | − | 0.387934i | ||||||
\(633\) | −3.85295e10 | −0.239982 | ||||||||
\(634\) | 4.03758e11i | 2.49899i | ||||||||
\(635\) | − | 4.92075e11i | − | 3.02647i | ||||||
\(636\) | − | 7.82052e10i | − | 0.477977i | ||||||
\(637\) | −1.53101e11 | −0.929863 | ||||||||
\(638\) | −2.03353e9 | −0.0122735 | ||||||||
\(639\) | 1.28639e11i | 0.771561i | ||||||||
\(640\) | 2.00759e11 | 1.19662 | ||||||||
\(641\) | − | 3.02938e10i | − | 0.179441i | −0.995967 | − | 0.0897203i | \(-0.971403\pi\) | ||
0.995967 | − | 0.0897203i | \(-0.0285973\pi\) | |||||||
\(642\) | −3.22488e11 | −1.89834 | ||||||||
\(643\) | 5.55577e10 | 0.325013 | 0.162506 | − | 0.986707i | \(-0.448042\pi\) | ||||
0.162506 | + | 0.986707i | \(0.448042\pi\) | |||||||
\(644\) | − | 8.87726e10i | − | 0.516102i | ||||||
\(645\) | 4.62236e11 | − | 2.42801e11i | 2.67070 | − | 1.40285i | ||||
\(646\) | −3.94802e11 | −2.26699 | ||||||||
\(647\) | 2.27072e10i | 0.129583i | 0.997899 | + | 0.0647913i | \(0.0206382\pi\) | ||||
−0.997899 | + | 0.0647913i | \(0.979362\pi\) | |||||||
\(648\) | 1.17767e10i | 0.0667919i | ||||||||
\(649\) | 1.59895e11 | 0.901274 | ||||||||
\(650\) | 7.95794e11i | 4.45807i | ||||||||
\(651\) | −9.00815e10 | −0.501547 | ||||||||
\(652\) | 2.65629e11i | 1.46989i | ||||||||
\(653\) | − | 6.93373e10i | − | 0.381341i | −0.981654 | − | 0.190671i | \(-0.938934\pi\) | ||
0.981654 | − | 0.190671i | \(-0.0610663\pi\) | |||||||
\(654\) | 1.35188e11 | 0.738969 | ||||||||
\(655\) | −8.76164e10 | −0.476015 | ||||||||
\(656\) | 4.22092e10 | 0.227925 | ||||||||
\(657\) | 1.98571e11i | 1.06575i | ||||||||
\(658\) | 5.57440e10 | 0.297368 | ||||||||
\(659\) | 7.72055e10 | 0.409361 | 0.204680 | − | 0.978829i | \(-0.434384\pi\) | ||||
0.204680 | + | 0.978829i | \(0.434384\pi\) | |||||||
\(660\) | −3.67228e11 | −1.93535 | ||||||||
\(661\) | −1.37353e11 | −0.719501 | −0.359750 | − | 0.933049i | \(-0.617138\pi\) | ||||
−0.359750 | + | 0.933049i | \(0.617138\pi\) | |||||||
\(662\) | 2.90144e11 | 1.51071 | ||||||||
\(663\) | 3.15357e11i | 1.63210i | ||||||||
\(664\) | − | 3.43764e10i | − | 0.176843i | ||||||
\(665\) | 2.75007e11i | 1.40623i | ||||||||
\(666\) | −7.18608e11 | −3.65254 | ||||||||
\(667\) | − | 3.01440e9i | − | 0.0152299i | ||||||
\(668\) | −1.89500e11 | −0.951705 | ||||||||
\(669\) | −3.58102e11 | −1.78773 | ||||||||
\(670\) | −7.63524e11 | −3.78899 | ||||||||
\(671\) | 7.81188e10i | 0.385359i | ||||||||
\(672\) | − | 2.00075e11i | − | 0.981108i | ||||||
\(673\) | 1.37895e11i | 0.672184i | 0.941829 | + | 0.336092i | \(0.109105\pi\) | ||||
−0.941829 | + | 0.336092i | \(0.890895\pi\) | |||||||
\(674\) | 2.54524e11i | 1.23336i | ||||||||
\(675\) | − | 4.48346e11i | − | 2.15972i | ||||||
\(676\) | −8.04364e10 | −0.385182 | ||||||||
\(677\) | 2.93763e11i | 1.39844i | 0.714908 | + | 0.699218i | \(0.246468\pi\) | ||||
−0.714908 | + | 0.699218i | \(0.753532\pi\) | |||||||
\(678\) | − | 7.45872e11i | − | 3.52976i | ||||||
\(679\) | 3.73699e9i | 0.0175810i | ||||||||
\(680\) | −1.17351e11 | −0.548846 | ||||||||
\(681\) | 1.19040e11 | 0.553483 | ||||||||
\(682\) | 1.23205e11i | 0.569496i | ||||||||
\(683\) | −1.66608e11 | −0.765619 | −0.382810 | − | 0.923827i | \(-0.625044\pi\) | ||||
−0.382810 | + | 0.923827i | \(0.625044\pi\) | |||||||
\(684\) | 6.88580e11i | 3.14579i | ||||||||
\(685\) | 4.54758e11 | 2.06547 | ||||||||
\(686\) | −2.59925e11 | −1.17368 | ||||||||
\(687\) | 5.77875e11i | 2.59422i | ||||||||
\(688\) | 1.46085e11 | − | 7.67347e10i | 0.652006 | − | 0.342482i | ||||
\(689\) | 6.39821e10 | 0.283911 | ||||||||
\(690\) | − | 9.91803e11i | − | 4.37552i | ||||||
\(691\) | − | 3.05698e11i | − | 1.34085i | −0.741977 | − | 0.670425i | \(-0.766112\pi\) | ||
0.741977 | − | 0.670425i | \(-0.233888\pi\) | |||||||
\(692\) | 4.51849e11 | 1.97047 | ||||||||
\(693\) | 8.05634e10i | 0.349305i | ||||||||
\(694\) | 1.16323e11 | 0.501452 | ||||||||
\(695\) | 1.53377e11i | 0.657385i | ||||||||
\(696\) | 1.87843e9i | 0.00800492i | ||||||||
\(697\) | −6.54298e10 | −0.277233 | ||||||||
\(698\) | 3.82746e11 | 1.61246 | ||||||||
\(699\) | 1.32505e11 | 0.555041 | ||||||||
\(700\) | 3.31935e11i | 1.38249i | ||||||||
\(701\) | 2.10620e11 | 0.872221 | 0.436111 | − | 0.899893i | \(-0.356356\pi\) | ||||
0.436111 | + | 0.899893i | \(0.356356\pi\) | |||||||
\(702\) | 3.43354e11 | 1.41382 | ||||||||
\(703\) | 6.69534e11 | 2.74127 | ||||||||
\(704\) | −1.78248e11 | −0.725663 | ||||||||
\(705\) | 3.41827e11 | 1.38372 | ||||||||
\(706\) | 3.60869e11i | 1.45255i | ||||||||
\(707\) | − | 5.01590e10i | − | 0.200757i | ||||||
\(708\) | − | 8.29595e11i | − | 3.30166i | ||||||
\(709\) | −3.74546e11 | −1.48225 | −0.741123 | − | 0.671369i | \(-0.765707\pi\) | ||||
−0.741123 | + | 0.671369i | \(0.765707\pi\) | |||||||
\(710\) | − | 3.64575e11i | − | 1.43468i | ||||||
\(711\) | −4.67651e11 | −1.82997 | ||||||||
\(712\) | 3.21539e10 | 0.125116 | ||||||||
\(713\) | −1.82633e11 | −0.706676 | ||||||||
\(714\) | 2.39659e11i | 0.922148i | ||||||||
\(715\) | − | 3.00441e11i | − | 1.14957i | ||||||
\(716\) | 1.35953e11i | 0.517292i | ||||||||
\(717\) | 5.95383e10i | 0.225279i | ||||||||
\(718\) | − | 3.62141e11i | − | 1.36264i | ||||||
\(719\) | −7.82761e10 | −0.292896 | −0.146448 | − | 0.989218i | \(-0.546784\pi\) | ||||
−0.146448 | + | 0.989218i | \(0.546784\pi\) | |||||||
\(720\) | − | 5.72023e11i | − | 2.12855i | ||||||
\(721\) | 2.98000e10i | 0.110274i | ||||||||
\(722\) | − | 7.64323e11i | − | 2.81273i | ||||||
\(723\) | −3.08454e11 | −1.12885 | ||||||||
\(724\) | −3.51305e11 | −1.27859 | ||||||||
\(725\) | 1.12713e10i | 0.0407965i | ||||||||
\(726\) | −4.74122e11 | −1.70665 | ||||||||
\(727\) | − | 3.82480e11i | − | 1.36921i | −0.728913 | − | 0.684606i | \(-0.759974\pi\) | ||
0.728913 | − | 0.684606i | \(-0.240026\pi\) | |||||||
\(728\) | −4.52580e10 | −0.161127 | ||||||||
\(729\) | 4.60125e11 | 1.62917 | ||||||||
\(730\) | − | 5.62767e11i | − | 1.98170i | ||||||
\(731\) | −2.26451e11 | + | 1.18949e11i | −0.793057 | + | 0.416573i | ||||
\(732\) | 4.05309e11 | 1.41170 | ||||||||
\(733\) | 1.33780e11i | 0.463421i | 0.972785 | + | 0.231711i | \(0.0744322\pi\) | ||||
−0.972785 | + | 0.231711i | \(0.925568\pi\) | |||||||
\(734\) | − | 2.35308e11i | − | 0.810686i | ||||||
\(735\) | −7.13470e11 | −2.44470 | ||||||||
\(736\) | − | 4.05636e11i | − | 1.38237i | ||||||
\(737\) | 2.08399e11 | 0.706360 | ||||||||
\(738\) | 2.07917e11i | 0.700913i | ||||||||
\(739\) | 1.57627e11i | 0.528509i | 0.964453 | + | 0.264254i | \(0.0851259\pi\) | ||||
−0.964453 | + | 0.264254i | \(0.914874\pi\) | |||||||
\(740\) | 1.11780e12 | 3.72768 | ||||||||
\(741\) | −9.33676e11 | −3.09687 | ||||||||
\(742\) | 4.86239e10 | 0.160411 | ||||||||
\(743\) | 1.29006e11i | 0.423307i | 0.977345 | + | 0.211654i | \(0.0678848\pi\) | ||||
−0.977345 | + | 0.211654i | \(0.932115\pi\) | |||||||
\(744\) | 1.13808e11 | 0.371433 | ||||||||
\(745\) | −1.74385e11 | −0.566088 | ||||||||
\(746\) | −6.38068e11 | −2.06021 | ||||||||
\(747\) | −2.59751e11 | −0.834208 | ||||||||
\(748\) | 1.79906e11 | 0.574699 | ||||||||
\(749\) | − | 1.10050e11i | − | 0.349672i | ||||||
\(750\) | 2.28741e12i | 7.22936i | ||||||||
\(751\) | 2.48684e11i | 0.781788i | 0.920436 | + | 0.390894i | \(0.127834\pi\) | ||||
−0.920436 | + | 0.390894i | \(0.872166\pi\) | |||||||
\(752\) | 1.08031e11 | 0.337813 | ||||||||
\(753\) | − | 8.57400e11i | − | 2.66688i | ||||||
\(754\) | −8.63185e9 | −0.0267066 | ||||||||
\(755\) | −5.08045e10 | −0.156356 | ||||||||
\(756\) | 1.43217e11 | 0.438438 | ||||||||
\(757\) | 1.23839e11i | 0.377117i | 0.982062 | + | 0.188558i | \(0.0603814\pi\) | ||||
−0.982062 | + | 0.188558i | \(0.939619\pi\) | |||||||
\(758\) | 3.73529e11i | 1.13148i | ||||||||
\(759\) | 2.70707e11i | 0.815703i | ||||||||
\(760\) | − | 3.47441e11i | − | 1.04142i | ||||||
\(761\) | 2.24574e9i | 0.00669608i | 0.999994 | + | 0.00334804i | \(0.00106572\pi\) | ||||
−0.999994 | + | 0.00334804i | \(0.998934\pi\) | |||||||
\(762\) | 1.26962e12 | 3.76578 | ||||||||
\(763\) | 4.61331e10i | 0.136118i | ||||||||
\(764\) | 6.12151e11i | 1.79674i | ||||||||
\(765\) | 8.86710e11i | 2.58902i | ||||||||
\(766\) | −7.04705e11 | −2.04688 | ||||||||
\(767\) | 6.78717e11 | 1.96113 | ||||||||
\(768\) | − | 2.42177e11i | − | 0.696125i | ||||||
\(769\) | −2.16341e10 | −0.0618635 | −0.0309317 | − | 0.999521i | \(-0.509847\pi\) | ||||
−0.0309317 | + | 0.999521i | \(0.509847\pi\) | |||||||
\(770\) | − | 2.28324e11i | − | 0.649513i | ||||||
\(771\) | 6.87133e11 | 1.94457 | ||||||||
\(772\) | −1.36207e11 | −0.383469 | ||||||||
\(773\) | 1.23331e11i | 0.345425i | 0.984972 | + | 0.172712i | \(0.0552531\pi\) | ||||
−0.984972 | + | 0.172712i | \(0.944747\pi\) | |||||||
\(774\) | 3.77985e11 | + | 7.19595e11i | 1.05320 | + | 2.00504i | ||||
\(775\) | 6.82892e11 | 1.89298 | ||||||||
\(776\) | − | 4.72126e9i | − | 0.0130200i | ||||||
\(777\) | − | 4.06431e11i | − | 1.11507i | ||||||
\(778\) | −4.57914e11 | −1.24987 | ||||||||
\(779\) | − | 1.93718e11i | − | 0.526042i | ||||||
\(780\) | −1.55880e12 | −4.21125 | ||||||||
\(781\) | 9.95086e10i | 0.267459i | ||||||||
\(782\) | 4.85888e11i | 1.29930i | ||||||||
\(783\) | 4.86314e9 | 0.0129381 | ||||||||
\(784\) | −2.25485e11 | −0.596834 | ||||||||
\(785\) | −9.31823e11 | −2.45389 | ||||||||
\(786\) | − | 2.26063e11i | − | 0.592296i | ||||||
\(787\) | −2.14761e11 | −0.559831 | −0.279915 | − | 0.960025i | \(-0.590306\pi\) | ||||
−0.279915 | + | 0.960025i | \(0.590306\pi\) | |||||||
\(788\) | 6.17391e11 | 1.60124 | ||||||||
\(789\) | 1.87158e11 | 0.482948 | ||||||||
\(790\) | 1.32536e12 | 3.40272 | ||||||||
\(791\) | 2.54530e11 | 0.650180 | ||||||||
\(792\) | − | 1.01783e11i | − | 0.258686i | ||||||
\(793\) | 3.31596e11i | 0.838526i | ||||||||
\(794\) | − | 6.59766e11i | − | 1.66000i | ||||||
\(795\) | 2.98166e11 | 0.746430 | ||||||||
\(796\) | − | 9.49229e11i | − | 2.36439i | ||||||
\(797\) | 4.86223e11 | 1.20504 | 0.602521 | − | 0.798103i | \(-0.294163\pi\) | ||||
0.602521 | + | 0.798103i | \(0.294163\pi\) | |||||||
\(798\) | −7.09558e11 | −1.74975 | ||||||||
\(799\) | −1.67462e11 | −0.410893 | ||||||||
\(800\) | 1.51674e12i | 3.70297i | ||||||||
\(801\) | − | 2.42957e11i | − | 0.590201i | ||||||
\(802\) | − | 8.45940e11i | − | 2.04476i | ||||||
\(803\) | 1.53604e11i | 0.369437i | ||||||||
\(804\) | − | 1.08125e12i | − | 2.58763i | ||||||
\(805\) | 3.38455e11 | 0.805967 | ||||||||
\(806\) | 5.22976e11i | 1.23920i | ||||||||
\(807\) | 4.70192e11i | 1.10862i | ||||||||
\(808\) | 6.33702e10i | 0.148676i | ||||||||
\(809\) | 4.55725e11 | 1.06392 | 0.531959 | − | 0.846770i | \(-0.321456\pi\) | ||||
0.531959 | + | 0.846770i | \(0.321456\pi\) | |||||||
\(810\) | −2.52193e11 | −0.585858 | ||||||||
\(811\) | − | 3.83583e10i | − | 0.0886698i | −0.999017 | − | 0.0443349i | \(-0.985883\pi\) | ||
0.999017 | − | 0.0443349i | \(-0.0141169\pi\) | |||||||
\(812\) | −3.60044e9 | −0.00828194 | ||||||||
\(813\) | 9.90510e11i | 2.26724i | ||||||||
\(814\) | −5.55877e11 | −1.26614 | ||||||||
\(815\) | −1.01274e12 | −2.29544 | ||||||||
\(816\) | 4.64454e11i | 1.04757i | ||||||||
\(817\) | −3.52172e11 | − | 6.70453e11i | −0.790436 | − | 1.50480i | ||||
\(818\) | −1.33793e11 | −0.298827 | ||||||||
\(819\) | 3.41972e11i | 0.760073i | ||||||||
\(820\) | − | 3.23417e11i | − | 0.715333i | ||||||
\(821\) | 7.24878e11 | 1.59548 | 0.797741 | − | 0.603000i | \(-0.206028\pi\) | ||||
0.797741 | + | 0.603000i | \(0.206028\pi\) | |||||||
\(822\) | 1.17334e12i | 2.57002i | ||||||||
\(823\) | 4.18426e11 | 0.912052 | 0.456026 | − | 0.889967i | \(-0.349272\pi\) | ||||
0.456026 | + | 0.889967i | \(0.349272\pi\) | |||||||
\(824\) | − | 3.76489e10i | − | 0.0816663i | ||||||
\(825\) | − | 1.01222e12i | − | 2.18503i | ||||||
\(826\) | 5.15799e11 | 1.10805 | ||||||||
\(827\) | −1.75466e11 | −0.375122 | −0.187561 | − | 0.982253i | \(-0.560058\pi\) | ||||
−0.187561 | + | 0.982253i | \(0.560058\pi\) | |||||||
\(828\) | 8.47444e11 | 1.80297 | ||||||||
\(829\) | 3.36853e10i | 0.0713217i | 0.999364 | + | 0.0356608i | \(0.0113536\pi\) | ||||
−0.999364 | + | 0.0356608i | \(0.988646\pi\) | |||||||
\(830\) | 7.36156e11 | 1.55116 | ||||||||
\(831\) | −2.80187e11 | −0.587549 | ||||||||
\(832\) | −7.56622e11 | −1.57901 | ||||||||
\(833\) | 3.49531e11 | 0.725949 | ||||||||
\(834\) | −3.95733e11 | −0.817972 | ||||||||
\(835\) | − | 7.22487e11i | − | 1.48622i | ||||||
\(836\) | 5.32649e11i | 1.09048i | ||||||||
\(837\) | − | 2.94642e11i | − | 0.600333i | ||||||
\(838\) | 7.25880e11 | 1.47194 | ||||||||
\(839\) | 4.53076e11i | 0.914372i | 0.889371 | + | 0.457186i | \(0.151143\pi\) | ||||
−0.889371 | + | 0.457186i | \(0.848857\pi\) | |||||||
\(840\) | −2.10909e11 | −0.423621 | ||||||||
\(841\) | 5.00124e11 | 0.999756 | ||||||||
\(842\) | 7.11996e11 | 1.41654 | ||||||||
\(843\) | − | 3.16465e11i | − | 0.626637i | ||||||
\(844\) | 9.33022e10i | 0.183875i | ||||||||
\(845\) | − | 3.06672e11i | − | 0.601517i | ||||||
\(846\) | 5.32145e11i | 1.03884i | ||||||||
\(847\) | − | 1.61795e11i | − | 0.314363i | ||||||
\(848\) | 9.42323e10 | 0.182228 | ||||||||
\(849\) | 3.28950e11i | 0.633139i | ||||||||
\(850\) | − | 1.81681e12i | − | 3.48044i | ||||||
\(851\) | − | 8.24004e11i | − | 1.57113i | ||||||
\(852\) | 5.16287e11 | 0.979790 | ||||||||
\(853\) | −9.50642e11 | −1.79565 | −0.897824 | − | 0.440355i | \(-0.854853\pi\) | ||||
−0.897824 | + | 0.440355i | \(0.854853\pi\) | |||||||
\(854\) | 2.52000e11i | 0.473772i | ||||||||
\(855\) | −2.62528e12 | −4.91260 | ||||||||
\(856\) | 1.39035e11i | 0.258958i | ||||||||
\(857\) | −6.23613e11 | −1.15609 | −0.578045 | − | 0.816005i | \(-0.696184\pi\) | ||||
−0.578045 | + | 0.816005i | \(0.696184\pi\) | |||||||
\(858\) | 7.75180e11 | 1.43039 | ||||||||
\(859\) | − | 7.70810e11i | − | 1.41571i | −0.706357 | − | 0.707855i | \(-0.749663\pi\) | ||
0.706357 | − | 0.707855i | \(-0.250337\pi\) | |||||||
\(860\) | −5.87960e11 | − | 1.11934e12i | −1.07487 | − | 2.04629i | ||||
\(861\) | −1.17594e11 | −0.213979 | ||||||||
\(862\) | 2.88843e11i | 0.523159i | ||||||||
\(863\) | − | 9.80353e11i | − | 1.76742i | −0.468037 | − | 0.883709i | \(-0.655039\pi\) | ||
0.468037 | − | 0.883709i | \(-0.344961\pi\) | |||||||
\(864\) | 6.54414e11 | 1.17435 | ||||||||
\(865\) | 1.72272e12i | 3.07716i | ||||||||
\(866\) | −1.46445e11 | −0.260377 | ||||||||
\(867\) | 1.77219e11i | 0.313641i | ||||||||
\(868\) | 2.18139e11i | 0.384286i | ||||||||
\(869\) | −3.61750e11 | −0.634351 | ||||||||
\(870\) | −4.02256e10 | −0.0702143 | ||||||||
\(871\) | 8.84606e11 | 1.53701 | ||||||||
\(872\) | − | 5.82839e10i | − | 0.100805i | ||||||
\(873\) | −3.56742e10 | −0.0614182 | ||||||||
\(874\) | −1.43857e12 | −2.46539 | ||||||||
\(875\) | −7.80584e11 | −1.33164 | ||||||||
\(876\) | 7.96954e11 | 1.35337 | ||||||||
\(877\) | 1.96302e11 | 0.331839 | 0.165919 | − | 0.986139i | \(-0.446941\pi\) | ||||
0.165919 | + | 0.986139i | \(0.446941\pi\) | |||||||
\(878\) | 4.99836e11i | 0.841104i | ||||||||
\(879\) | − | 1.05637e12i | − | 1.76954i | ||||||
\(880\) | − | 4.42487e11i | − | 0.737852i | ||||||
\(881\) | −1.18673e12 | −1.96992 | −0.984962 | − | 0.172771i | \(-0.944728\pi\) | ||||
−0.984962 | + | 0.172771i | \(0.944728\pi\) | |||||||
\(882\) | − | 1.11071e12i | − | 1.83538i | ||||||
\(883\) | 2.15504e11 | 0.354497 | 0.177249 | − | 0.984166i | \(-0.443280\pi\) | ||||
0.177249 | + | 0.984166i | \(0.443280\pi\) | |||||||
\(884\) | 7.63660e11 | 1.25052 | ||||||||
\(885\) | 3.16292e12 | 5.15602 | ||||||||
\(886\) | 1.08844e12i | 1.76632i | ||||||||
\(887\) | 2.28915e11i | 0.369812i | 0.982756 | + | 0.184906i | \(0.0591980\pi\) | ||||
−0.982756 | + | 0.184906i | \(0.940802\pi\) | |||||||
\(888\) | 5.13479e11i | 0.825792i | ||||||||
\(889\) | 4.33262e11i | 0.693655i | ||||||||
\(890\) | 6.88562e11i | 1.09745i | ||||||||
\(891\) | 6.88345e10 | 0.109218 | ||||||||
\(892\) | 8.67172e11i | 1.36976i | ||||||||
\(893\) | − | 4.95805e11i | − | 0.779660i | ||||||
\(894\) | − | 4.49938e11i | − | 0.704373i | ||||||
\(895\) | −5.18334e11 | −0.807826 | ||||||||
\(896\) | −1.76764e11 | −0.274260 | ||||||||
\(897\) | 1.14909e12i | 1.77494i | ||||||||
\(898\) | 1.11221e12 | 1.71034 | ||||||||
\(899\) | 7.40722e9i | 0.0113401i | ||||||||
\(900\) | −3.16873e12 | −4.82964 | ||||||||
\(901\) | −1.46072e11 | −0.221651 | ||||||||
\(902\) | 1.60834e11i | 0.242969i | ||||||||
\(903\) | −4.06989e11 | + | 2.13781e11i | −0.612112 | + | 0.321527i | ||||
\(904\) | −3.21570e11 | −0.481506 | ||||||||
\(905\) | − | 1.33939e12i | − | 1.99669i | ||||||
\(906\) | − | 1.31083e11i | − | 0.194551i | ||||||
\(907\) | −1.53390e11 | −0.226657 | −0.113328 | − | 0.993558i | \(-0.536151\pi\) | ||||
−0.113328 | + | 0.993558i | \(0.536151\pi\) | |||||||
\(908\) | − | 2.88264e11i | − | 0.424080i | ||||||
\(909\) | 4.78830e11 | 0.701335 | ||||||||
\(910\) | − | 9.69179e11i | − | 1.41331i | ||||||
\(911\) | − | 1.45999e11i | − | 0.211971i | −0.994368 | − | 0.105985i | \(-0.966200\pi\) | ||
0.994368 | − | 0.105985i | \(-0.0337997\pi\) | |||||||
\(912\) | −1.37511e12 | −1.98773 | ||||||||
\(913\) | −2.00929e11 | −0.289175 | ||||||||
\(914\) | −1.22438e12 | −1.75441 | ||||||||
\(915\) | 1.54528e12i | 2.20457i | ||||||||
\(916\) | 1.39937e12 | 1.98770 | ||||||||
\(917\) | 7.71444e10 | 0.109101 | ||||||||
\(918\) | −7.83885e11 | −1.10378 | ||||||||
\(919\) | −1.10838e11 | −0.155391 | −0.0776957 | − | 0.996977i | \(-0.524756\pi\) | ||||
−0.0776957 | + | 0.996977i | \(0.524756\pi\) | |||||||
\(920\) | −4.27599e11 | −0.596878 | ||||||||
\(921\) | − | 1.58701e12i | − | 2.20567i | ||||||
\(922\) | − | 1.26683e11i | − | 0.175305i | ||||||
\(923\) | 4.22391e11i | 0.581979i | ||||||||
\(924\) | 3.23337e11 | 0.443575 | ||||||||
\(925\) | 3.08108e12i | 4.20859i | ||||||||
\(926\) | 4.14401e11 | 0.563607 | ||||||||
\(927\) | −2.84477e11 | −0.385238 | ||||||||
\(928\) | −1.64518e10 | −0.0221831 | ||||||||
\(929\) | − | 1.01988e12i | − | 1.36927i | −0.728888 | − | 0.684633i | \(-0.759963\pi\) | ||
0.728888 | − | 0.684633i | \(-0.240037\pi\) | |||||||
\(930\) | 2.43714e12i | 3.25798i | ||||||||
\(931\) | 1.03486e12i | 1.37747i | ||||||||
\(932\) | − | 3.20872e11i | − | 0.425273i | ||||||
\(933\) | − | 1.90688e12i | − | 2.51649i | ||||||
\(934\) | −3.09489e11 | −0.406685 | ||||||||
\(935\) | 6.85912e11i | 0.897475i | ||||||||
\(936\) | − | 4.32043e11i | − | 0.562890i | ||||||
\(937\) | − | 7.67098e11i | − | 0.995158i | −0.867419 | − | 0.497579i | \(-0.834222\pi\) | ||
0.867419 | − | 0.497579i | \(-0.165778\pi\) | |||||||
\(938\) | 6.72266e11 | 0.868420 | ||||||||
\(939\) | 5.70857e10 | 0.0734286 | ||||||||
\(940\) | − | 8.27759e11i | − | 1.06021i | ||||||
\(941\) | −4.08673e11 | −0.521215 | −0.260608 | − | 0.965445i | \(-0.583923\pi\) | ||||
−0.260608 | + | 0.965445i | \(0.583923\pi\) | |||||||
\(942\) | − | 2.40424e12i | − | 3.05333i | ||||||
\(943\) | −2.38411e11 | −0.301495 | ||||||||
\(944\) | 9.99609e11 | 1.25876 | ||||||||
\(945\) | 5.46030e11i | 0.684683i | ||||||||
\(946\) | 2.92389e11 | + | 5.56640e11i | 0.365087 | + | 0.695041i | ||||
\(947\) | 6.69336e11 | 0.832231 | 0.416116 | − | 0.909312i | \(-0.363391\pi\) | ||||
0.416116 | + | 0.909312i | \(0.363391\pi\) | |||||||
\(948\) | 1.87689e12i | 2.32384i | ||||||||
\(949\) | 6.52012e11i | 0.803880i | ||||||||
\(950\) | 5.37904e12 | 6.60405 | ||||||||
\(951\) | − | 2.17996e12i | − | 2.66517i | ||||||
\(952\) | 1.03325e11 | 0.125793 | ||||||||
\(953\) | 6.17905e11i | 0.749118i | 0.927203 | + | 0.374559i | \(0.122206\pi\) | ||||
−0.927203 | + | 0.374559i | \(0.877794\pi\) | |||||||
\(954\) | 4.64175e11i | 0.560388i | ||||||||
\(955\) | −2.33389e12 | −2.80586 | ||||||||
\(956\) | 1.44177e11 | 0.172609 | ||||||||
\(957\) | 1.09793e10 | 0.0130897 | ||||||||
\(958\) | − | 9.77070e11i | − | 1.16002i | ||||||
\(959\) | −4.00405e11 | −0.473396 | ||||||||
\(960\) | −3.52596e12 | −4.15138 | ||||||||
\(961\) | −4.04111e11 | −0.473814 | ||||||||
\(962\) | −2.35957e12 | −2.75507 | ||||||||
\(963\) | 1.05056e12 | 1.22156 | ||||||||
\(964\) | 7.46945e11i | 0.864928i | ||||||||
\(965\) | − | 5.19303e11i | − | 0.598841i | ||||||
\(966\) | 8.73262e11i | 1.00285i | ||||||||
\(967\) | 1.66198e12 | 1.90072 | 0.950362 | − | 0.311145i | \(-0.100713\pi\) | ||||
0.950362 | + | 0.311145i | \(0.100713\pi\) | |||||||
\(968\) | 2.04410e11i | 0.232809i | ||||||||
\(969\) | 2.13160e12 | 2.41775 | ||||||||
\(970\) | 1.01104e11 | 0.114204 | ||||||||
\(971\) | 1.24122e11 | 0.139628 | 0.0698138 | − | 0.997560i | \(-0.477759\pi\) | ||||
0.0698138 | + | 0.997560i | \(0.477759\pi\) | |||||||
\(972\) | − | 1.25588e12i | − | 1.40697i | ||||||
\(973\) | − | 1.35045e11i | − | 0.150670i | ||||||
\(974\) | − | 3.55230e11i | − | 0.394706i | ||||||
\(975\) | − | 4.29662e12i | − | 4.75454i | ||||||
\(976\) | 4.88372e11i | 0.538209i | ||||||||
\(977\) | −7.69622e11 | −0.844694 | −0.422347 | − | 0.906434i | \(-0.638794\pi\) | ||||
−0.422347 | + | 0.906434i | \(0.638794\pi\) | |||||||
\(978\) | − | 2.61301e12i | − | 2.85618i | ||||||
\(979\) | − | 1.87939e11i | − | 0.204591i | ||||||
\(980\) | 1.72772e12i | 1.87314i | ||||||||
\(981\) | −4.40397e11 | −0.475520 | ||||||||
\(982\) | −6.12442e11 | −0.658596 | ||||||||
\(983\) | 5.29094e11i | 0.566655i | 0.959023 | + | 0.283327i | \(0.0914383\pi\) | ||||
−0.959023 | + | 0.283327i | \(0.908562\pi\) | |||||||
\(984\) | 1.48566e11 | 0.158467 | ||||||||
\(985\) | 2.35387e12i | 2.50056i | ||||||||
\(986\) | 1.97067e10 | 0.0208500 | ||||||||
\(987\) | −3.00971e11 | −0.317144 | ||||||||
\(988\) | 2.26097e12i | 2.37283i | ||||||||
\(989\) | −8.25135e11 | + | 4.33422e11i | −0.862461 | + | 0.453029i | ||||
\(990\) | 2.17963e12 | 2.26904 | ||||||||
\(991\) | 9.90323e11i | 1.02679i | 0.858152 | + | 0.513396i | \(0.171613\pi\) | ||||
−0.858152 | + | 0.513396i | \(0.828387\pi\) | |||||||
\(992\) | 9.96762e11i | 1.02931i | ||||||||
\(993\) | −1.56654e12 | −1.61118 | ||||||||
\(994\) | 3.21001e11i | 0.328822i | ||||||||
\(995\) | 3.61904e12 | 3.69233 | ||||||||
\(996\) | 1.04250e12i | 1.05934i | ||||||||
\(997\) | 1.72782e12i | 1.74871i | 0.485285 | + | 0.874356i | \(0.338716\pi\) | ||||
−0.485285 | + | 0.874356i | \(0.661284\pi\) | |||||||
\(998\) | 1.16256e12 | 1.17191 | ||||||||
\(999\) | 1.32937e12 | 1.33470 |
(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.42.24 | yes | 28 | |
43.42 | odd | 2 | inner | 43.9.b.b.42.5 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.9.b.b.42.5 | ✓ | 28 | 43.42 | odd | 2 | inner | |
43.9.b.b.42.24 | yes | 28 | 1.1 | even | 1 | trivial |