Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,22,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (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: | \(58.6902423003\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.27 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.22.c.b.20.28 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2822.55i | − | 1.94907i | −0.224245 | − | 0.974533i | \(-0.571991\pi\) | ||
0.224245 | − | 0.974533i | \(-0.428009\pi\) | |||||||
\(3\) | −20847.2 | − | 100129.i | −0.203833 | − | 0.979006i | ||||
\(4\) | −5.86963e6 | −2.79886 | ||||||||
\(5\) | 4.54821e6 | 0.208284 | 0.104142 | − | 0.994562i | \(-0.466790\pi\) | ||||
0.104142 | + | 0.994562i | \(0.466790\pi\) | |||||||
\(6\) | −2.82618e8 | + | 5.88423e7i | −1.90815 | + | 0.397285i | ||||
\(7\) | 2.96411e8 | + | 6.86066e8i | 0.396611 | + | 0.917987i | ||||
\(8\) | 1.06480e10i | 3.50609i | ||||||||
\(9\) | −9.59114e9 | + | 4.17481e9i | −0.916904 | + | 0.399108i | ||||
\(10\) | − | 1.28375e10i | − | 0.405959i | ||||||
\(11\) | 7.30549e10i | 0.849232i | 0.905374 | + | 0.424616i | \(0.139591\pi\) | ||||
−0.905374 | + | 0.424616i | \(0.860409\pi\) | |||||||
\(12\) | 1.22366e11 | + | 5.87718e11i | 0.570500 | + | 2.74010i | ||||
\(13\) | − | 3.14236e11i | − | 0.632194i | −0.948727 | − | 0.316097i | \(-0.897628\pi\) | ||
0.948727 | − | 0.316097i | \(-0.102372\pi\) | |||||||
\(14\) | 1.93645e12 | − | 8.36633e11i | 1.78922 | − | 0.773020i | ||||
\(15\) | −9.48176e10 | − | 4.55406e11i | −0.0424552 | − | 0.203911i | ||||
\(16\) | 1.77450e13 | 4.03475 | ||||||||
\(17\) | −1.38799e13 | −1.66983 | −0.834916 | − | 0.550377i | \(-0.814484\pi\) | ||||
−0.834916 | + | 0.550377i | \(0.814484\pi\) | |||||||
\(18\) | 1.17836e13 | + | 2.70715e13i | 0.777888 | + | 1.78711i | ||||
\(19\) | 1.99201e13i | 0.745382i | 0.927955 | + | 0.372691i | \(0.121565\pi\) | ||||
−0.927955 | + | 0.372691i | \(0.878435\pi\) | |||||||
\(20\) | −2.66963e13 | −0.582957 | ||||||||
\(21\) | 6.25155e13 | − | 4.39818e13i | 0.817872 | − | 0.575400i | ||||
\(22\) | 2.06201e14 | 1.65521 | ||||||||
\(23\) | − | 2.36645e14i | − | 1.19112i | −0.803312 | − | 0.595558i | \(-0.796931\pi\) | ||
0.803312 | − | 0.595558i | \(-0.203069\pi\) | |||||||
\(24\) | 1.06617e15 | − | 2.21981e14i | 3.43248 | − | 0.714658i | ||||
\(25\) | −4.56151e14 | −0.956618 | ||||||||
\(26\) | −8.86945e14 | −1.23219 | ||||||||
\(27\) | 6.17967e14 | + | 8.73315e14i | 0.577624 | + | 0.816303i | ||||
\(28\) | −1.73982e15 | − | 4.02695e15i | −1.11006 | − | 2.56931i | ||||
\(29\) | − | 4.13478e14i | − | 0.182504i | −0.995828 | − | 0.0912521i | \(-0.970913\pi\) | ||
0.995828 | − | 0.0912521i | \(-0.0290869\pi\) | |||||||
\(30\) | −1.28541e15 | + | 2.67627e14i | −0.397436 | + | 0.0827479i | ||||
\(31\) | − | 4.96475e15i | − | 1.08793i | −0.839109 | − | 0.543963i | \(-0.816923\pi\) | ||
0.839109 | − | 0.543963i | \(-0.183077\pi\) | |||||||
\(32\) | − | 2.77556e16i | − | 4.35789i | ||||||
\(33\) | 7.31489e15 | − | 1.52299e15i | 0.831403 | − | 0.173102i | ||||
\(34\) | 3.91767e16i | 3.25461i | ||||||||
\(35\) | 1.34814e15 | + | 3.12037e15i | 0.0826076 | + | 0.191202i | ||||
\(36\) | 5.62964e16 | − | 2.45046e16i | 2.56628 | − | 1.11705i | ||||
\(37\) | 1.68899e16 | 0.577442 | 0.288721 | − | 0.957413i | \(-0.406770\pi\) | ||||
0.288721 | + | 0.957413i | \(0.406770\pi\) | |||||||
\(38\) | 5.62255e16 | 1.45280 | ||||||||
\(39\) | −3.14640e16 | + | 6.55094e15i | −0.618921 | + | 0.128862i | ||||
\(40\) | 4.84294e16i | 0.730262i | ||||||||
\(41\) | 3.82916e16 | 0.445526 | 0.222763 | − | 0.974873i | \(-0.428492\pi\) | ||||
0.222763 | + | 0.974873i | \(0.428492\pi\) | |||||||
\(42\) | −1.24141e17 | − | 1.76453e17i | −1.12149 | − | 1.59409i | ||||
\(43\) | 1.23817e17 | 0.873698 | 0.436849 | − | 0.899535i | \(-0.356094\pi\) | ||||
0.436849 | + | 0.899535i | \(0.356094\pi\) | |||||||
\(44\) | − | 4.28805e17i | − | 2.37688i | ||||||
\(45\) | −4.36225e16 | + | 1.89879e16i | −0.190976 | + | 0.0831277i | ||||
\(46\) | −6.67941e17 | −2.32157 | ||||||||
\(47\) | 5.21576e17 | 1.44641 | 0.723203 | − | 0.690635i | \(-0.242669\pi\) | ||||
0.723203 | + | 0.690635i | \(0.242669\pi\) | |||||||
\(48\) | −3.69934e17 | − | 1.77678e18i | −0.822416 | − | 3.95004i | ||||
\(49\) | −3.82827e17 | + | 4.06714e17i | −0.685400 | + | 0.728167i | ||||
\(50\) | 1.28751e18i | 1.86451i | ||||||||
\(51\) | 2.89358e17 | + | 1.38978e18i | 0.340368 | + | 1.63478i | ||||
\(52\) | 1.84445e18i | 1.76942i | ||||||||
\(53\) | − | 4.78164e17i | − | 0.375561i | −0.982211 | − | 0.187780i | \(-0.939871\pi\) | ||
0.982211 | − | 0.187780i | \(-0.0601293\pi\) | |||||||
\(54\) | 2.46497e18 | − | 1.74424e18i | 1.59103 | − | 1.12583i | ||||
\(55\) | 3.32269e17i | 0.176881i | ||||||||
\(56\) | −7.30523e18 | + | 3.15618e18i | −3.21855 | + | 1.39055i | ||||
\(57\) | 1.99457e18 | − | 4.15279e17i | 0.729733 | − | 0.151934i | ||||
\(58\) | −1.16706e18 | −0.355713 | ||||||||
\(59\) | 4.67014e18 | 1.18955 | 0.594777 | − | 0.803891i | \(-0.297240\pi\) | ||||
0.594777 | + | 0.803891i | \(0.297240\pi\) | |||||||
\(60\) | 5.56544e17 | + | 2.67307e18i | 0.118826 | + | 0.570718i | ||||
\(61\) | 6.18188e18i | 1.10958i | 0.831992 | + | 0.554788i | \(0.187201\pi\) | ||||
−0.831992 | + | 0.554788i | \(0.812799\pi\) | |||||||
\(62\) | −1.40132e19 | −2.12044 | ||||||||
\(63\) | −5.70711e18 | − | 5.34270e18i | −0.730030 | − | 0.683415i | ||||
\(64\) | −4.11277e19 | −4.45907 | ||||||||
\(65\) | − | 1.42921e18i | − | 0.131676i | ||||||
\(66\) | −4.29872e18 | − | 2.06466e19i | −0.337387 | − | 1.62046i | ||||
\(67\) | −4.47340e18 | −0.299814 | −0.149907 | − | 0.988700i | \(-0.547897\pi\) | ||||
−0.149907 | + | 0.988700i | \(0.547897\pi\) | |||||||
\(68\) | 8.14699e19 | 4.67362 | ||||||||
\(69\) | −2.36949e19 | + | 4.93338e18i | −1.16611 | + | 0.242789i | ||||
\(70\) | 8.80740e18 | − | 3.80518e18i | 0.372665 | − | 0.161008i | ||||
\(71\) | − | 1.47479e19i | − | 0.537674i | −0.963186 | − | 0.268837i | \(-0.913361\pi\) | ||
0.963186 | − | 0.268837i | \(-0.0866392\pi\) | |||||||
\(72\) | −4.44534e19 | − | 1.02126e20i | −1.39931 | − | 3.21475i | ||||
\(73\) | − | 3.45031e18i | − | 0.0939653i | −0.998896 | − | 0.0469827i | \(-0.985039\pi\) | ||
0.998896 | − | 0.0469827i | \(-0.0149606\pi\) | |||||||
\(74\) | − | 4.76725e19i | − | 1.12547i | ||||||
\(75\) | 9.50948e18 | + | 4.56738e19i | 0.194991 | + | 0.936534i | ||||
\(76\) | − | 1.16924e20i | − | 2.08622i | ||||||
\(77\) | −5.01205e19 | + | 2.16542e19i | −0.779584 | + | 0.336814i | ||||
\(78\) | 1.84903e19 | + | 8.88086e19i | 0.251161 | + | 1.20632i | ||||
\(79\) | 9.44267e19 | 1.12204 | 0.561022 | − | 0.827801i | \(-0.310408\pi\) | ||||
0.561022 | + | 0.827801i | \(0.310408\pi\) | |||||||
\(80\) | 8.07080e19 | 0.840372 | ||||||||
\(81\) | 7.45609e19 | − | 8.00824e19i | 0.681426 | − | 0.731887i | ||||
\(82\) | − | 1.08080e20i | − | 0.868359i | ||||||
\(83\) | 4.40648e19 | 0.311725 | 0.155863 | − | 0.987779i | \(-0.450184\pi\) | ||||
0.155863 | + | 0.987779i | \(0.450184\pi\) | |||||||
\(84\) | −3.66943e20 | + | 2.58157e20i | −2.28911 | + | 1.61046i | ||||
\(85\) | −6.31288e19 | −0.347799 | ||||||||
\(86\) | − | 3.49479e20i | − | 1.70289i | ||||||
\(87\) | −4.14009e19 | + | 8.61986e18i | −0.178673 | + | 0.0372004i | ||||
\(88\) | −7.77889e20 | −2.97748 | ||||||||
\(89\) | −1.20740e20 | −0.410447 | −0.205224 | − | 0.978715i | \(-0.565792\pi\) | ||||
−0.205224 | + | 0.978715i | \(0.565792\pi\) | |||||||
\(90\) | 5.35943e19 | + | 1.23127e20i | 0.162021 | + | 0.372225i | ||||
\(91\) | 2.15586e20 | − | 9.31427e19i | 0.580346 | − | 0.250735i | ||||
\(92\) | 1.38902e21i | 3.33377i | ||||||||
\(93\) | −4.97113e20 | + | 1.03501e20i | −1.06509 | + | 0.221756i | ||||
\(94\) | − | 1.47217e21i | − | 2.81914i | ||||||
\(95\) | 9.06009e19i | 0.155251i | ||||||||
\(96\) | −2.77914e21 | + | 5.78628e20i | −4.26640 | + | 0.888284i | ||||
\(97\) | 8.64106e20i | 1.18977i | 0.803810 | + | 0.594886i | \(0.202803\pi\) | ||||
−0.803810 | + | 0.594886i | \(0.797197\pi\) | |||||||
\(98\) | 1.14797e21 | + | 1.08055e21i | 1.41924 | + | 1.33589i | ||||
\(99\) | −3.04990e20 | − | 7.00680e20i | −0.338935 | − | 0.778664i | ||||
\(100\) | 2.67744e21 | 2.67744 | ||||||||
\(101\) | 1.20647e21 | 1.08678 | 0.543391 | − | 0.839480i | \(-0.317140\pi\) | ||||
0.543391 | + | 0.839480i | \(0.317140\pi\) | |||||||
\(102\) | 3.92271e21 | − | 8.16726e20i | 3.18629 | − | 0.663399i | ||||
\(103\) | 1.96297e21i | 1.43920i | 0.694386 | + | 0.719602i | \(0.255676\pi\) | ||||
−0.694386 | + | 0.719602i | \(0.744324\pi\) | |||||||
\(104\) | 3.34598e21 | 2.21653 | ||||||||
\(105\) | 2.84334e20 | − | 2.00038e20i | 0.170349 | − | 0.119847i | ||||
\(106\) | −1.34964e21 | −0.731993 | ||||||||
\(107\) | − | 2.10165e20i | − | 0.103284i | −0.998666 | − | 0.0516418i | \(-0.983555\pi\) | ||
0.998666 | − | 0.0516418i | \(-0.0164454\pi\) | |||||||
\(108\) | −3.62724e21 | − | 5.12603e21i | −1.61669 | − | 2.28471i | ||||
\(109\) | −2.61048e21 | −1.05619 | −0.528095 | − | 0.849186i | \(-0.677093\pi\) | ||||
−0.528095 | + | 0.849186i | \(0.677093\pi\) | |||||||
\(110\) | 9.37846e20 | 0.344753 | ||||||||
\(111\) | −3.52107e20 | − | 1.69116e21i | −0.117702 | − | 0.565319i | ||||
\(112\) | 5.25980e21 | + | 1.21742e22i | 1.60022 | + | 3.70384i | ||||
\(113\) | − | 2.84927e21i | − | 0.789606i | −0.918766 | − | 0.394803i | \(-0.870813\pi\) | ||
0.918766 | − | 0.394803i | \(-0.129187\pi\) | |||||||
\(114\) | −1.17215e21 | − | 5.62978e21i | −0.296129 | − | 1.42230i | ||||
\(115\) | − | 1.07631e21i | − | 0.248090i | ||||||
\(116\) | 2.42696e21i | 0.510803i | ||||||||
\(117\) | 1.31187e21 | + | 3.01388e21i | 0.252313 | + | 0.579661i | ||||
\(118\) | − | 1.31817e22i | − | 2.31852i | ||||||
\(119\) | −4.11415e21 | − | 9.52254e21i | −0.662273 | − | 1.53288i | ||||
\(120\) | 4.84917e21 | − | 1.00962e21i | 0.714931 | − | 0.148852i | ||||
\(121\) | 2.06323e21 | 0.278806 | ||||||||
\(122\) | 1.74487e22 | 2.16264 | ||||||||
\(123\) | −7.98273e20 | − | 3.83408e21i | −0.0908130 | − | 0.436172i | ||||
\(124\) | 2.91412e22i | 3.04495i | ||||||||
\(125\) | −4.24343e21 | −0.407532 | ||||||||
\(126\) | −1.50800e22 | + | 1.61086e22i | −1.33202 | + | 1.42288i | ||||
\(127\) | 1.93411e22 | 1.57232 | 0.786162 | − | 0.618021i | \(-0.212065\pi\) | ||||
0.786162 | + | 0.618021i | \(0.212065\pi\) | |||||||
\(128\) | 5.78771e22i | 4.33314i | ||||||||
\(129\) | −2.58124e21 | − | 1.23976e22i | −0.178089 | − | 0.855355i | ||||
\(130\) | −4.03401e21 | −0.256645 | ||||||||
\(131\) | 2.69309e22 | 1.58089 | 0.790445 | − | 0.612533i | \(-0.209849\pi\) | ||||
0.790445 | + | 0.612533i | \(0.209849\pi\) | |||||||
\(132\) | −4.29357e22 | + | 8.93940e21i | −2.32698 | + | 0.484487i | ||||
\(133\) | −1.36665e22 | + | 5.90453e21i | −0.684251 | + | 0.295626i | ||||
\(134\) | 1.26264e22i | 0.584357i | ||||||||
\(135\) | 2.81064e21 | + | 3.97202e21i | 0.120310 | + | 0.170023i | ||||
\(136\) | − | 1.47793e23i | − | 5.85459i | ||||||
\(137\) | − | 2.02386e22i | − | 0.742361i | −0.928561 | − | 0.371181i | \(-0.878953\pi\) | ||
0.928561 | − | 0.371181i | \(-0.121047\pi\) | |||||||
\(138\) | 1.39247e22 | + | 6.68800e22i | 0.473212 | + | 2.27283i | ||||
\(139\) | − | 8.93099e21i | − | 0.281348i | −0.990056 | − | 0.140674i | \(-0.955073\pi\) | ||
0.990056 | − | 0.140674i | \(-0.0449270\pi\) | |||||||
\(140\) | −7.91307e21 | − | 1.83154e22i | −0.231207 | − | 0.535147i | ||||
\(141\) | −1.08734e22 | − | 5.22247e22i | −0.294826 | − | 1.41604i | ||||
\(142\) | −4.16268e22 | −1.04796 | ||||||||
\(143\) | 2.29564e22 | 0.536879 | ||||||||
\(144\) | −1.70195e23 | + | 7.40820e22i | −3.69947 | + | 1.61030i | ||||
\(145\) | − | 1.88058e21i | − | 0.0380127i | ||||||
\(146\) | −9.73866e21 | −0.183145 | ||||||||
\(147\) | 4.87047e22 | + | 2.98531e22i | 0.852587 | + | 0.522586i | ||||
\(148\) | −9.91373e22 | −1.61618 | ||||||||
\(149\) | − | 6.95768e22i | − | 1.05684i | −0.848983 | − | 0.528419i | \(-0.822785\pi\) | ||
0.848983 | − | 0.528419i | \(-0.177215\pi\) | |||||||
\(150\) | 1.28916e23 | − | 2.68410e22i | 1.82537 | − | 0.380049i | ||||
\(151\) | 9.93310e22 | 1.31168 | 0.655838 | − | 0.754901i | \(-0.272315\pi\) | ||||
0.655838 | + | 0.754901i | \(0.272315\pi\) | |||||||
\(152\) | −2.12109e23 | −2.61338 | ||||||||
\(153\) | 1.33124e23 | − | 5.79460e22i | 1.53108 | − | 0.666444i | ||||
\(154\) | 6.11202e22 | + | 1.41468e23i | 0.656473 | + | 1.51946i | ||||
\(155\) | − | 2.25807e22i | − | 0.226597i | ||||||
\(156\) | 1.84682e23 | − | 3.84516e22i | 1.73227 | − | 0.360667i | ||||
\(157\) | 8.43714e22i | 0.740029i | 0.929026 | + | 0.370014i | \(0.120647\pi\) | ||||
−0.929026 | + | 0.370014i | \(0.879353\pi\) | |||||||
\(158\) | − | 2.66524e23i | − | 2.18694i | ||||||
\(159\) | −4.78779e22 | + | 9.96839e21i | −0.367676 | + | 0.0765518i | ||||
\(160\) | − | 1.26239e23i | − | 0.907679i | ||||||
\(161\) | 1.62354e23 | − | 7.01440e22i | 1.09343 | − | 0.472410i | ||||
\(162\) | −2.26036e23 | − | 2.10452e23i | −1.42650 | − | 1.32814i | ||||
\(163\) | −4.43058e22 | −0.262114 | −0.131057 | − | 0.991375i | \(-0.541837\pi\) | ||||
−0.131057 | + | 0.991375i | \(0.541837\pi\) | |||||||
\(164\) | −2.24757e23 | −1.24696 | ||||||||
\(165\) | 3.32697e22 | − | 6.92689e21i | 0.173168 | − | 0.0360543i | ||||
\(166\) | − | 1.24375e23i | − | 0.607573i | ||||||
\(167\) | 7.95970e22 | 0.365068 | 0.182534 | − | 0.983200i | \(-0.441570\pi\) | ||||
0.182534 | + | 0.983200i | \(0.441570\pi\) | |||||||
\(168\) | 4.68318e23 | + | 6.65665e23i | 2.01741 | + | 2.86753i | ||||
\(169\) | 1.48321e23 | 0.600331 | ||||||||
\(170\) | 1.78184e23i | 0.677883i | ||||||||
\(171\) | −8.31627e22 | − | 1.91057e23i | −0.297488 | − | 0.683444i | ||||
\(172\) | −7.26760e23 | −2.44536 | ||||||||
\(173\) | −3.57085e23 | −1.13054 | −0.565272 | − | 0.824905i | \(-0.691229\pi\) | ||||
−0.565272 | + | 0.824905i | \(0.691229\pi\) | |||||||
\(174\) | 2.43300e22 | + | 1.16856e23i | 0.0725061 | + | 0.348245i | ||||
\(175\) | −1.35208e23 | − | 3.12950e23i | −0.379405 | − | 0.878163i | ||||
\(176\) | 1.29636e24i | 3.42643i | ||||||||
\(177\) | −9.73595e22 | − | 4.67615e23i | −0.242471 | − | 1.16458i | ||||
\(178\) | 3.40796e23i | 0.799989i | ||||||||
\(179\) | − | 4.41100e23i | − | 0.976294i | −0.872761 | − | 0.488147i | \(-0.837673\pi\) | ||
0.872761 | − | 0.488147i | \(-0.162327\pi\) | |||||||
\(180\) | 2.56048e23 | − | 1.11452e23i | 0.534515 | − | 0.232663i | ||||
\(181\) | 7.85797e23i | 1.54769i | 0.633372 | + | 0.773847i | \(0.281670\pi\) | ||||
−0.633372 | + | 0.773847i | \(0.718330\pi\) | |||||||
\(182\) | −2.62900e23 | − | 6.08503e23i | −0.488698 | − | 1.13113i | ||||
\(183\) | 6.18983e23 | − | 1.28875e23i | 1.08628 | − | 0.226169i | ||||
\(184\) | 2.51979e24 | 4.17616 | ||||||||
\(185\) | 7.68187e22 | 0.120272 | ||||||||
\(186\) | 2.92137e23 | + | 1.40313e24i | 0.432216 | + | 2.07592i | ||||
\(187\) | − | 1.01400e24i | − | 1.41808i | ||||||
\(188\) | −3.06146e24 | −4.04829 | ||||||||
\(189\) | −4.15980e23 | + | 6.82826e23i | −0.520263 | + | 0.854006i | ||||
\(190\) | 2.55725e23 | 0.302595 | ||||||||
\(191\) | − | 4.96369e22i | − | 0.0555846i | −0.999614 | − | 0.0277923i | \(-0.991152\pi\) | ||
0.999614 | − | 0.0277923i | \(-0.00884770\pi\) | |||||||
\(192\) | 8.57399e23 | + | 4.11806e24i | 0.908908 | + | 4.36546i | ||||
\(193\) | −5.47484e23 | −0.549565 | −0.274783 | − | 0.961506i | \(-0.588606\pi\) | ||||
−0.274783 | + | 0.961506i | \(0.588606\pi\) | |||||||
\(194\) | 2.43898e24 | 2.31894 | ||||||||
\(195\) | −1.43105e23 | + | 2.97951e22i | −0.128911 | + | 0.0268399i | ||||
\(196\) | 2.24706e24 | − | 2.38726e24i | 1.91834 | − | 2.03803i | ||||
\(197\) | 1.48828e24i | 1.20445i | 0.798325 | + | 0.602226i | \(0.205720\pi\) | ||||
−0.798325 | + | 0.602226i | \(0.794280\pi\) | |||||||
\(198\) | −1.97770e24 | + | 8.60850e23i | −1.51767 | + | 0.660607i | ||||
\(199\) | 2.48286e24i | 1.80715i | 0.428430 | + | 0.903575i | \(0.359067\pi\) | ||||
−0.428430 | + | 0.903575i | \(0.640933\pi\) | |||||||
\(200\) | − | 4.85710e24i | − | 3.35399i | ||||||
\(201\) | 9.32579e22 | + | 4.47915e23i | 0.0611121 | + | 0.293520i | ||||
\(202\) | − | 3.40532e24i | − | 2.11821i | ||||||
\(203\) | 2.83673e23 | − | 1.22559e23i | 0.167537 | − | 0.0723831i | ||||
\(204\) | −1.69842e24 | − | 8.15747e24i | −0.952640 | − | 4.57550i | ||||
\(205\) | 1.74158e23 | 0.0927958 | ||||||||
\(206\) | 5.54058e24 | 2.80510 | ||||||||
\(207\) | 9.87946e23 | + | 2.26969e24i | 0.475384 | + | 1.09214i | ||||
\(208\) | − | 5.57611e24i | − | 2.55074i | ||||||
\(209\) | −1.45526e24 | −0.633002 | ||||||||
\(210\) | −5.64618e23 | − | 8.02546e23i | −0.233589 | − | 0.332022i | ||||
\(211\) | −2.81283e24 | −1.10708 | −0.553538 | − | 0.832824i | \(-0.686723\pi\) | ||||
−0.553538 | + | 0.832824i | \(0.686723\pi\) | |||||||
\(212\) | 2.80665e24i | 1.05114i | ||||||||
\(213\) | −1.47669e24 | + | 3.07454e23i | −0.526386 | + | 0.109596i | ||||
\(214\) | −5.93202e23 | −0.201306 | ||||||||
\(215\) | 5.63146e23 | 0.181977 | ||||||||
\(216\) | −9.29906e24 | + | 6.58011e24i | −2.86203 | + | 2.02520i | ||||
\(217\) | 3.40614e24 | − | 1.47160e24i | 0.998702 | − | 0.431483i | ||||
\(218\) | 7.36820e24i | 2.05858i | ||||||||
\(219\) | −3.45475e23 | + | 7.19293e22i | −0.0919926 | + | 0.0191533i | ||||
\(220\) | − | 1.95030e24i | − | 0.495065i | ||||||
\(221\) | 4.36156e24i | 1.05566i | ||||||||
\(222\) | −4.77338e24 | + | 9.93839e23i | −1.10184 | + | 0.229409i | ||||
\(223\) | 2.10755e24i | 0.464063i | 0.972708 | + | 0.232032i | \(0.0745373\pi\) | ||||
−0.972708 | + | 0.232032i | \(0.925463\pi\) | |||||||
\(224\) | 1.90422e25 | − | 8.22707e24i | 4.00049 | − | 1.72839i | ||||
\(225\) | 4.37501e24 | − | 1.90434e24i | 0.877127 | − | 0.381794i | ||||
\(226\) | −8.04222e24 | −1.53899 | ||||||||
\(227\) | −4.72952e24 | −0.864063 | −0.432031 | − | 0.901859i | \(-0.642203\pi\) | ||||
−0.432031 | + | 0.901859i | \(0.642203\pi\) | |||||||
\(228\) | −1.17074e25 | + | 2.43753e24i | −2.04242 | + | 0.425241i | ||||
\(229\) | 1.23459e24i | 0.205708i | 0.994696 | + | 0.102854i | \(0.0327974\pi\) | ||||
−0.994696 | + | 0.102854i | \(0.967203\pi\) | |||||||
\(230\) | −3.03794e24 | −0.483544 | ||||||||
\(231\) | 3.21308e24 | + | 4.56707e24i | 0.488648 | + | 0.694563i | ||||
\(232\) | 4.40271e24 | 0.639877 | ||||||||
\(233\) | 1.30483e25i | 1.81266i | 0.422571 | + | 0.906330i | \(0.361128\pi\) | ||||
−0.422571 | + | 0.906330i | \(0.638872\pi\) | |||||||
\(234\) | 8.50682e24 | − | 3.70283e24i | 1.12980 | − | 0.491776i | ||||
\(235\) | 2.37224e24 | 0.301263 | ||||||||
\(236\) | −2.74120e25 | −3.32939 | ||||||||
\(237\) | −1.96853e24 | − | 9.45481e24i | −0.228710 | − | 1.09849i | ||||
\(238\) | −2.68778e25 | + | 1.16124e25i | −2.98769 | + | 1.29081i | ||||
\(239\) | − | 1.74054e24i | − | 0.185142i | −0.995706 | − | 0.0925711i | \(-0.970491\pi\) | ||
0.995706 | − | 0.0925711i | \(-0.0295085\pi\) | |||||||
\(240\) | −1.68254e24 | − | 8.08118e24i | −0.171296 | − | 0.822729i | ||||
\(241\) | 1.57536e24i | 0.153532i | 0.997049 | + | 0.0767662i | \(0.0244595\pi\) | ||||
−0.997049 | + | 0.0767662i | \(0.975541\pi\) | |||||||
\(242\) | − | 5.82357e24i | − | 0.543410i | ||||||
\(243\) | −9.57293e24 | − | 5.79619e24i | −0.855419 | − | 0.517937i | ||||
\(244\) | − | 3.62853e25i | − | 3.10555i | ||||||
\(245\) | −1.74118e24 | + | 1.84982e24i | −0.142758 | + | 0.151665i | ||||
\(246\) | −1.08219e25 | + | 2.25317e24i | −0.850128 | + | 0.177000i | ||||
\(247\) | 6.25961e24 | 0.471226 | ||||||||
\(248\) | 5.28646e25 | 3.81437 | ||||||||
\(249\) | −9.18630e23 | − | 4.41215e24i | −0.0635400 | − | 0.305181i | ||||
\(250\) | 1.19773e25i | 0.794306i | ||||||||
\(251\) | −1.19217e25 | −0.758167 | −0.379083 | − | 0.925363i | \(-0.623761\pi\) | ||||
−0.379083 | + | 0.925363i | \(0.623761\pi\) | |||||||
\(252\) | 3.34986e25 | + | 3.13597e25i | 2.04325 | + | 1.91278i | ||||
\(253\) | 1.72880e25 | 1.01153 | ||||||||
\(254\) | − | 5.45912e25i | − | 3.06456i | ||||||
\(255\) | 1.31606e24 | + | 6.32100e24i | 0.0708931 | + | 0.340497i | ||||
\(256\) | 7.71100e25 | 3.98649 | ||||||||
\(257\) | 2.64268e25 | 1.31144 | 0.655718 | − | 0.755006i | \(-0.272366\pi\) | ||||
0.655718 | + | 0.755006i | \(0.272366\pi\) | |||||||
\(258\) | −3.49929e25 | + | 7.28568e24i | −1.66714 | + | 0.347107i | ||||
\(259\) | 5.00634e24 | + | 1.15876e25i | 0.229020 | + | 0.530084i | ||||
\(260\) | 8.38893e24i | 0.368542i | ||||||||
\(261\) | 1.72619e24 | + | 3.96572e24i | 0.0728389 | + | 0.167339i | ||||
\(262\) | − | 7.60137e25i | − | 3.08126i | ||||||
\(263\) | 1.97989e25i | 0.771092i | 0.922689 | + | 0.385546i | \(0.125987\pi\) | ||||
−0.922689 | + | 0.385546i | \(0.874013\pi\) | |||||||
\(264\) | 1.62168e25 | + | 7.78889e25i | 0.606910 | + | 2.91497i | ||||
\(265\) | − | 2.17479e24i | − | 0.0782232i | ||||||
\(266\) | 1.66658e25 | + | 3.85744e25i | 0.576195 | + | 1.33365i | ||||
\(267\) | 2.51710e24 | + | 1.20896e25i | 0.0836629 | + | 0.401830i | ||||
\(268\) | 2.62572e25 | 0.839137 | ||||||||
\(269\) | 2.88993e25 | 0.888155 | 0.444077 | − | 0.895988i | \(-0.353532\pi\) | ||||
0.444077 | + | 0.895988i | \(0.353532\pi\) | |||||||
\(270\) | 1.12112e25 | − | 7.93318e24i | 0.331385 | − | 0.234492i | ||||
\(271\) | 2.99441e25i | 0.851400i | 0.904864 | + | 0.425700i | \(0.139972\pi\) | ||||
−0.904864 | + | 0.425700i | \(0.860028\pi\) | |||||||
\(272\) | −2.46299e26 | −6.73735 | ||||||||
\(273\) | −1.38206e25 | − | 1.96446e25i | −0.363764 | − | 0.517053i | ||||
\(274\) | −5.71246e25 | −1.44691 | ||||||||
\(275\) | − | 3.33241e25i | − | 0.812390i | ||||||
\(276\) | 1.39080e26 | − | 2.89571e25i | 3.26378 | − | 0.679533i | ||||
\(277\) | −1.50940e25 | −0.341010 | −0.170505 | − | 0.985357i | \(-0.554540\pi\) | ||||
−0.170505 | + | 0.985357i | \(0.554540\pi\) | |||||||
\(278\) | −2.52082e25 | −0.548366 | ||||||||
\(279\) | 2.07269e25 | + | 4.76176e25i | 0.434200 | + | 0.997524i | ||||
\(280\) | −3.32257e25 | + | 1.43550e25i | −0.670371 | + | 0.289630i | ||||
\(281\) | − | 9.89724e25i | − | 1.92352i | −0.273886 | − | 0.961762i | \(-0.588309\pi\) | ||
0.273886 | − | 0.961762i | \(-0.411691\pi\) | |||||||
\(282\) | −1.47407e26 | + | 3.06908e25i | −2.75996 | + | 0.574635i | ||||
\(283\) | − | 2.13079e25i | − | 0.384400i | −0.981356 | − | 0.192200i | \(-0.938438\pi\) | ||
0.981356 | − | 0.192200i | \(-0.0615623\pi\) | |||||||
\(284\) | 8.65650e25i | 1.50487i | ||||||||
\(285\) | 9.07174e24 | − | 1.88878e24i | 0.151992 | − | 0.0316453i | ||||
\(286\) | − | 6.47957e25i | − | 1.04641i | ||||||
\(287\) | 1.13500e25 | + | 2.62706e25i | 0.176700 | + | 0.408987i | ||||
\(288\) | 1.15875e26 | + | 2.66208e26i | 1.73927 | + | 3.99577i | ||||
\(289\) | 1.23560e26 | 1.78834 | ||||||||
\(290\) | −5.30804e24 | −0.0740892 | ||||||||
\(291\) | 8.65218e25 | − | 1.80142e25i | 1.16479 | − | 0.242515i | ||||
\(292\) | 2.02520e25i | 0.262996i | ||||||||
\(293\) | −1.82697e25 | −0.228888 | −0.114444 | − | 0.993430i | \(-0.536509\pi\) | ||||
−0.114444 | + | 0.993430i | \(0.536509\pi\) | |||||||
\(294\) | 8.42619e25 | − | 1.37471e26i | 1.01855 | − | 1.66175i | ||||
\(295\) | 2.12408e25 | 0.247765 | ||||||||
\(296\) | 1.79843e26i | 2.02456i | ||||||||
\(297\) | −6.37999e25 | + | 4.51455e25i | −0.693230 | + | 0.490537i | ||||
\(298\) | −1.96384e26 | −2.05985 | ||||||||
\(299\) | −7.43622e25 | −0.753017 | ||||||||
\(300\) | −5.58171e25 | − | 2.68088e26i | −0.545751 | − | 2.62123i | ||||
\(301\) | 3.67007e25 | + | 8.49466e25i | 0.346518 | + | 0.802043i | ||||
\(302\) | − | 2.80366e26i | − | 2.55654i | ||||||
\(303\) | −2.51516e25 | − | 1.20802e26i | −0.221522 | − | 1.06397i | ||||
\(304\) | 3.53482e26i | 3.00743i | ||||||||
\(305\) | 2.81165e25i | 0.231107i | ||||||||
\(306\) | −1.63555e26 | − | 3.75749e26i | −1.29894 | − | 2.98417i | ||||
\(307\) | 1.29125e26i | 0.990960i | 0.868619 | + | 0.495480i | \(0.165008\pi\) | ||||
−0.868619 | + | 0.495480i | \(0.834992\pi\) | |||||||
\(308\) | 2.94189e26 | − | 1.27102e26i | 2.18194 | − | 0.942695i | ||||
\(309\) | 1.96549e26 | − | 4.09225e25i | 1.40899 | − | 0.293358i | ||||
\(310\) | −6.37352e25 | −0.441653 | ||||||||
\(311\) | 1.10962e26 | 0.743345 | 0.371673 | − | 0.928364i | \(-0.378784\pi\) | ||||
0.371673 | + | 0.928364i | \(0.378784\pi\) | |||||||
\(312\) | −6.97544e25 | − | 3.35029e26i | −0.451802 | − | 2.16999i | ||||
\(313\) | − | 1.36190e26i | − | 0.852959i | −0.904497 | − | 0.426480i | \(-0.859754\pi\) | ||
0.904497 | − | 0.426480i | \(-0.140246\pi\) | |||||||
\(314\) | 2.38142e26 | 1.44237 | ||||||||
\(315\) | −2.59571e25 | − | 2.42997e25i | −0.152053 | − | 0.142344i | ||||
\(316\) | −5.54250e26 | −3.14044 | ||||||||
\(317\) | − | 3.98342e25i | − | 0.218340i | −0.994023 | − | 0.109170i | \(-0.965181\pi\) | ||
0.994023 | − | 0.109170i | \(-0.0348194\pi\) | |||||||
\(318\) | 2.81363e25 | + | 1.35138e26i | 0.149204 | + | 0.716625i | ||||
\(319\) | 3.02066e25 | 0.154988 | ||||||||
\(320\) | −1.87057e26 | −0.928753 | ||||||||
\(321\) | −2.10436e25 | + | 4.38136e24i | −0.101115 | + | 0.0210526i | ||||
\(322\) | −1.97985e26 | − | 4.58252e26i | −0.920757 | − | 2.13117i | ||||
\(323\) | − | 2.76489e26i | − | 1.24466i | ||||||
\(324\) | −4.37645e26 | + | 4.70054e26i | −1.90721 | + | 2.04845i | ||||
\(325\) | 1.43339e26i | 0.604768i | ||||||||
\(326\) | 1.25055e26i | 0.510878i | ||||||||
\(327\) | 5.44212e25 | + | 2.61384e26i | 0.215287 | + | 1.03402i | ||||
\(328\) | 4.07729e26i | 1.56205i | ||||||||
\(329\) | 1.54601e26 | + | 3.57836e26i | 0.573660 | + | 1.32778i | ||||
\(330\) | −1.95515e25 | − | 9.39052e25i | −0.0702722 | − | 0.337515i | ||||
\(331\) | 3.34913e26 | 1.16611 | 0.583053 | − | 0.812434i | \(-0.301858\pi\) | ||||
0.583053 | + | 0.812434i | \(0.301858\pi\) | |||||||
\(332\) | −2.58644e26 | −0.872475 | ||||||||
\(333\) | −1.61993e26 | + | 7.05120e25i | −0.529459 | + | 0.230462i | ||||
\(334\) | − | 2.24667e26i | − | 0.711542i | ||||||
\(335\) | −2.03459e25 | −0.0624464 | ||||||||
\(336\) | 1.10934e27 | − | 7.80456e26i | 3.29991 | − | 2.32159i | ||||
\(337\) | 2.58313e26 | 0.744787 | 0.372394 | − | 0.928075i | \(-0.378537\pi\) | ||||
0.372394 | + | 0.928075i | \(0.378537\pi\) | |||||||
\(338\) | − | 4.18642e26i | − | 1.17008i | ||||||
\(339\) | −2.85294e26 | + | 5.93995e25i | −0.773029 | + | 0.160948i | ||||
\(340\) | 3.70542e26 | 0.973440 | ||||||||
\(341\) | 3.62699e26 | 0.923901 | ||||||||
\(342\) | −5.39267e26 | + | 2.34731e26i | −1.33208 | + | 0.579824i | ||||
\(343\) | −3.92507e26 | − | 1.42090e26i | −0.940284 | − | 0.340390i | ||||
\(344\) | 1.31840e27i | 3.06327i | ||||||||
\(345\) | −1.07769e26 | + | 2.24381e25i | −0.242882 | + | 0.0505691i | ||||
\(346\) | 1.00789e27i | 2.20350i | ||||||||
\(347\) | 6.04754e26i | 1.28268i | 0.767256 | + | 0.641341i | \(0.221622\pi\) | ||||
−0.767256 | + | 0.641341i | \(0.778378\pi\) | |||||||
\(348\) | 2.43008e26 | − | 5.05954e25i | 0.500079 | − | 0.104119i | ||||
\(349\) | − | 6.47340e26i | − | 1.29260i | −0.763082 | − | 0.646302i | \(-0.776315\pi\) | ||
0.763082 | − | 0.646302i | \(-0.223685\pi\) | |||||||
\(350\) | −8.83316e26 | + | 3.81631e26i | −1.71160 | + | 0.739485i | ||||
\(351\) | 2.74427e26 | − | 1.94187e26i | 0.516061 | − | 0.365171i | ||||
\(352\) | 2.02769e27 | 3.70086 | ||||||||
\(353\) | 5.10240e26 | 0.903941 | 0.451971 | − | 0.892033i | \(-0.350721\pi\) | ||||
0.451971 | + | 0.892033i | \(0.350721\pi\) | |||||||
\(354\) | −1.31987e27 | + | 2.74802e26i | −2.26984 | + | 0.472591i | ||||
\(355\) | − | 6.70768e25i | − | 0.111989i | ||||||
\(356\) | 7.08701e26 | 1.14878 | ||||||||
\(357\) | −8.67710e26 | + | 6.10463e26i | −1.36571 | + | 0.960822i | ||||
\(358\) | −1.24503e27 | −1.90286 | ||||||||
\(359\) | 7.66525e26i | 1.13772i | 0.822435 | + | 0.568859i | \(0.192615\pi\) | ||||
−0.822435 | + | 0.568859i | \(0.807385\pi\) | |||||||
\(360\) | −2.02183e26 | − | 4.64493e26i | −0.291453 | − | 0.669580i | ||||
\(361\) | 3.17399e26 | 0.444405 | ||||||||
\(362\) | 2.21795e27 | 3.01656 | ||||||||
\(363\) | −4.30127e25 | − | 2.06589e26i | −0.0568299 | − | 0.272952i | ||||
\(364\) | −1.26541e27 | + | 5.46713e26i | −1.62430 | + | 0.701771i | ||||
\(365\) | − | 1.56927e25i | − | 0.0195715i | ||||||
\(366\) | −3.63756e26 | − | 1.74711e27i | −0.440818 | − | 2.11723i | ||||
\(367\) | − | 1.93862e26i | − | 0.228296i | −0.993464 | − | 0.114148i | \(-0.963586\pi\) | ||
0.993464 | − | 0.114148i | \(-0.0364138\pi\) | |||||||
\(368\) | − | 4.19926e27i | − | 4.80585i | ||||||
\(369\) | −3.67260e26 | + | 1.59860e26i | −0.408504 | + | 0.177813i | ||||
\(370\) | − | 2.16825e26i | − | 0.234418i | ||||||
\(371\) | 3.28052e26 | − | 1.41733e26i | 0.344760 | − | 0.148951i | ||||
\(372\) | 2.91787e27 | − | 6.07514e26i | 2.98102 | − | 0.620662i | ||||
\(373\) | 2.33075e26 | 0.231501 | 0.115750 | − | 0.993278i | \(-0.463073\pi\) | ||||
0.115750 | + | 0.993278i | \(0.463073\pi\) | |||||||
\(374\) | −2.86205e27 | −2.76392 | ||||||||
\(375\) | 8.84637e25 | + | 4.24889e26i | 0.0830686 | + | 0.398976i | ||||
\(376\) | 5.55375e27i | 5.07123i | ||||||||
\(377\) | −1.29929e26 | −0.115378 | ||||||||
\(378\) | 1.92731e27 | + | 1.17412e27i | 1.66451 | + | 1.01403i | ||||
\(379\) | −2.00863e26 | −0.168728 | −0.0843642 | − | 0.996435i | \(-0.526886\pi\) | ||||
−0.0843642 | + | 0.996435i | \(0.526886\pi\) | |||||||
\(380\) | − | 5.31794e26i | − | 0.434526i | ||||||
\(381\) | −4.03208e26 | − | 1.93660e27i | −0.320492 | − | 1.53931i | ||||
\(382\) | −1.40103e26 | −0.108338 | ||||||||
\(383\) | −1.83208e27 | −1.37834 | −0.689170 | − | 0.724600i | \(-0.742025\pi\) | ||||
−0.689170 | + | 0.724600i | \(0.742025\pi\) | |||||||
\(384\) | 5.79516e27 | − | 1.20658e27i | 4.24216 | − | 0.883238i | ||||
\(385\) | −2.27959e26 | + | 9.84881e25i | −0.162375 | + | 0.0701530i | ||||
\(386\) | 1.54530e27i | 1.07114i | ||||||||
\(387\) | −1.18755e27 | + | 5.16912e26i | −0.801097 | + | 0.348700i | ||||
\(388\) | − | 5.07198e27i | − | 3.33000i | ||||||
\(389\) | 2.27075e27i | 1.45110i | 0.688167 | + | 0.725552i | \(0.258416\pi\) | ||||
−0.688167 | + | 0.725552i | \(0.741584\pi\) | |||||||
\(390\) | 8.40980e25 | + | 4.03920e26i | 0.0523127 | + | 0.251257i | ||||
\(391\) | 3.28461e27i | 1.98897i | ||||||||
\(392\) | −4.33070e27 | − | 4.07635e27i | −2.55302 | − | 2.40308i | ||||
\(393\) | −5.61434e26 | − | 2.69655e27i | −0.322238 | − | 1.54770i | ||||
\(394\) | 4.20075e27 | 2.34756 | ||||||||
\(395\) | 4.29472e26 | 0.233704 | ||||||||
\(396\) | 1.79018e27 | + | 4.11273e27i | 0.948631 | + | 2.17937i | ||||
\(397\) | − | 1.23637e27i | − | 0.638042i | −0.947748 | − | 0.319021i | \(-0.896646\pi\) | ||
0.947748 | − | 0.319021i | \(-0.103354\pi\) | |||||||
\(398\) | 7.00798e27 | 3.52225 | ||||||||
\(399\) | 8.76122e26 | + | 1.24532e27i | 0.428893 | + | 0.609627i | ||||
\(400\) | −8.09440e27 | −3.85971 | ||||||||
\(401\) | − | 8.93304e26i | − | 0.414938i | −0.978242 | − | 0.207469i | \(-0.933477\pi\) | ||
0.978242 | − | 0.207469i | \(-0.0665226\pi\) | |||||||
\(402\) | 1.26426e27 | − | 2.63225e26i | 0.572089 | − | 0.119111i | ||||
\(403\) | −1.56010e27 | −0.687780 | ||||||||
\(404\) | −7.08154e27 | −3.04175 | ||||||||
\(405\) | 3.39119e26 | − | 3.64231e26i | 0.141930 | − | 0.152440i | ||||
\(406\) | −3.45929e26 | − | 8.00681e26i | −0.141079 | − | 0.326540i | ||||
\(407\) | 1.23389e27i | 0.490382i | ||||||||
\(408\) | −1.47983e28 | + | 3.08108e27i | −5.73167 | + | 1.19336i | ||||
\(409\) | − | 7.11975e26i | − | 0.268764i | −0.990930 | − | 0.134382i | \(-0.957095\pi\) | ||
0.990930 | − | 0.134382i | \(-0.0429048\pi\) | |||||||
\(410\) | − | 4.91570e26i | − | 0.180865i | ||||||
\(411\) | −2.02647e27 | + | 4.21920e26i | −0.726776 | + | 0.151318i | ||||
\(412\) | − | 1.15219e28i | − | 4.02813i | ||||||
\(413\) | 1.38428e27 | + | 3.20403e27i | 0.471789 | + | 1.09199i | ||||
\(414\) | 6.40632e27 | − | 2.78853e27i | 2.12865 | − | 0.926555i | ||||
\(415\) | 2.00416e26 | 0.0649273 | ||||||||
\(416\) | −8.72181e27 | −2.75503 | ||||||||
\(417\) | −8.94248e26 | + | 1.86186e26i | −0.275442 | + | 0.0573482i | ||||
\(418\) | 4.10755e27i | 1.23376i | ||||||||
\(419\) | 4.68503e27 | 1.37235 | 0.686175 | − | 0.727436i | \(-0.259288\pi\) | ||||
0.686175 | + | 0.727436i | \(0.259288\pi\) | |||||||
\(420\) | −1.66893e27 | + | 1.17415e27i | −0.476784 | + | 0.335433i | ||||
\(421\) | 1.27528e27 | 0.355339 | 0.177669 | − | 0.984090i | \(-0.443144\pi\) | ||||
0.177669 | + | 0.984090i | \(0.443144\pi\) | |||||||
\(422\) | 7.93935e27i | 2.15776i | ||||||||
\(423\) | −5.00251e27 | + | 2.17748e27i | −1.32622 | + | 0.577272i | ||||
\(424\) | 5.09149e27 | 1.31675 | ||||||||
\(425\) | 6.33133e27 | 1.59739 | ||||||||
\(426\) | 8.67803e26 | + | 4.16803e27i | 0.213609 | + | 1.02596i | ||||
\(427\) | −4.24118e27 | + | 1.83237e27i | −1.01858 | + | 0.440070i | ||||
\(428\) | 1.23359e27i | 0.289076i | ||||||||
\(429\) | −4.78578e26 | − | 2.29860e27i | −0.109434 | − | 0.525607i | ||||
\(430\) | − | 1.58951e27i | − | 0.354685i | ||||||
\(431\) | − | 7.89964e27i | − | 1.72027i | −0.510068 | − | 0.860134i | \(-0.670380\pi\) | ||
0.510068 | − | 0.860134i | \(-0.329620\pi\) | |||||||
\(432\) | 1.09658e28 | + | 1.54970e28i | 2.33057 | + | 3.29357i | ||||
\(433\) | − | 1.65572e27i | − | 0.343450i | −0.985145 | − | 0.171725i | \(-0.945066\pi\) | ||
0.985145 | − | 0.171725i | \(-0.0549341\pi\) | |||||||
\(434\) | −4.15367e27 | − | 9.61401e27i | −0.840989 | − | 1.94654i | ||||
\(435\) | −1.88300e26 | + | 3.92049e25i | −0.0372146 | + | 0.00774825i | ||||
\(436\) | 1.53225e28 | 2.95612 | ||||||||
\(437\) | 4.71399e27 | 0.887837 | ||||||||
\(438\) | 2.03024e26 | + | 9.75119e26i | 0.0373310 | + | 0.179300i | ||||
\(439\) | − | 2.42738e27i | − | 0.435774i | −0.975974 | − | 0.217887i | \(-0.930084\pi\) | ||
0.975974 | − | 0.217887i | \(-0.0699163\pi\) | |||||||
\(440\) | −3.53800e27 | −0.620162 | ||||||||
\(441\) | 1.97380e27 | − | 5.49909e27i | 0.337829 | − | 0.941207i | ||||
\(442\) | 1.23107e28 | 2.05755 | ||||||||
\(443\) | − | 2.42490e27i | − | 0.395780i | −0.980224 | − | 0.197890i | \(-0.936591\pi\) | ||
0.980224 | − | 0.197890i | \(-0.0634089\pi\) | |||||||
\(444\) | 2.06674e27 | + | 9.92648e27i | 0.329431 | + | 1.58225i | ||||
\(445\) | −5.49153e26 | −0.0854896 | ||||||||
\(446\) | 5.94867e27 | 0.904490 | ||||||||
\(447\) | −6.96663e27 | + | 1.45048e27i | −1.03465 | + | 0.215419i | ||||
\(448\) | −1.21907e28 | − | 2.82163e28i | −1.76852 | − | 4.09337i | ||||
\(449\) | − | 9.06997e27i | − | 1.28534i | −0.766142 | − | 0.642672i | \(-0.777826\pi\) | ||
0.766142 | − | 0.642672i | \(-0.222174\pi\) | |||||||
\(450\) | −5.37510e27 | − | 1.23487e28i | −0.744141 | − | 1.70958i | ||||
\(451\) | 2.79739e27i | 0.378355i | ||||||||
\(452\) | 1.67242e28i | 2.21000i | ||||||||
\(453\) | −2.07078e27 | − | 9.94588e27i | −0.267363 | − | 1.28414i | ||||
\(454\) | 1.33493e28i | 1.68412i | ||||||||
\(455\) | 9.80532e26 | − | 4.23633e26i | 0.120877 | − | 0.0522240i | ||||
\(456\) | 4.42189e27 | + | 2.12382e28i | 0.532694 | + | 2.55851i | ||||
\(457\) | −3.56460e27 | −0.419653 | −0.209826 | − | 0.977739i | \(-0.567290\pi\) | ||||
−0.209826 | + | 0.977739i | \(0.567290\pi\) | |||||||
\(458\) | 3.48469e27 | 0.400938 | ||||||||
\(459\) | −8.57732e27 | − | 1.21215e28i | −0.964536 | − | 1.36309i | ||||
\(460\) | 6.31754e27i | 0.694370i | ||||||||
\(461\) | −2.71423e27 | −0.291600 | −0.145800 | − | 0.989314i | \(-0.546576\pi\) | ||||
−0.145800 | + | 0.989314i | \(0.546576\pi\) | |||||||
\(462\) | 1.28908e28 | − | 9.06908e27i | 1.35375 | − | 0.952407i | ||||
\(463\) | −1.90778e28 | −1.95852 | −0.979261 | − | 0.202601i | \(-0.935061\pi\) | ||||
−0.979261 | + | 0.202601i | \(0.935061\pi\) | |||||||
\(464\) | − | 7.33716e27i | − | 0.736358i | ||||||
\(465\) | −2.26098e27 | + | 4.70745e26i | −0.221840 | + | 0.0461881i | ||||
\(466\) | 3.68294e28 | 3.53299 | ||||||||
\(467\) | 1.87542e28 | 1.75902 | 0.879510 | − | 0.475881i | \(-0.157871\pi\) | ||||
0.879510 | + | 0.475881i | \(0.157871\pi\) | |||||||
\(468\) | −7.70021e27 | − | 1.76903e28i | −0.706189 | − | 1.62239i | ||||
\(469\) | −1.32596e27 | − | 3.06905e27i | −0.118909 | − | 0.275225i | ||||
\(470\) | − | 6.69576e27i | − | 0.587182i | ||||||
\(471\) | 8.44799e27 | − | 1.75891e27i | 0.724493 | − | 0.150843i | ||||
\(472\) | 4.97277e28i | 4.17068i | ||||||||
\(473\) | 9.04544e27i | 0.741972i | ||||||||
\(474\) | −2.66867e28 | + | 5.55628e27i | −2.14103 | + | 0.445771i | ||||
\(475\) | − | 9.08658e27i | − | 0.713046i | ||||||
\(476\) | 2.41486e28 | + | 5.58938e28i | 1.85361 | + | 4.29033i | ||||
\(477\) | 1.99624e27 | + | 4.58614e27i | 0.149889 | + | 0.344353i | ||||
\(478\) | −4.91275e27 | −0.360854 | ||||||||
\(479\) | 5.46163e27 | 0.392463 | 0.196232 | − | 0.980558i | \(-0.437130\pi\) | ||||
0.196232 | + | 0.980558i | \(0.437130\pi\) | |||||||
\(480\) | −1.26401e28 | + | 2.63172e27i | −0.888622 | + | 0.185015i | ||||
\(481\) | − | 5.30740e27i | − | 0.365055i | ||||||
\(482\) | 4.44652e27 | 0.299245 | ||||||||
\(483\) | −1.04080e28 | − | 1.47940e28i | −0.685369 | − | 0.974181i | ||||
\(484\) | −1.21104e28 | −0.780337 | ||||||||
\(485\) | 3.93014e27i | 0.247810i | ||||||||
\(486\) | −1.63600e28 | + | 2.70201e28i | −1.00949 | + | 1.66727i | ||||
\(487\) | 1.36909e28 | 0.826754 | 0.413377 | − | 0.910560i | \(-0.364349\pi\) | ||||
0.413377 | + | 0.910560i | \(0.364349\pi\) | |||||||
\(488\) | −6.58247e28 | −3.89028 | ||||||||
\(489\) | 9.23653e26 | + | 4.43628e27i | 0.0534276 | + | 0.256611i | ||||
\(490\) | 5.22122e27 | + | 4.91456e27i | 0.295606 | + | 0.278244i | ||||
\(491\) | 2.04125e28i | 1.13120i | 0.824679 | + | 0.565601i | \(0.191356\pi\) | ||||
−0.824679 | + | 0.565601i | \(0.808644\pi\) | |||||||
\(492\) | 4.68557e27 | + | 2.25047e28i | 0.254173 | + | 1.22078i | ||||
\(493\) | 5.73903e27i | 0.304752i | ||||||||
\(494\) | − | 1.76680e28i | − | 0.918450i | ||||||
\(495\) | −1.38716e27 | − | 3.18684e27i | −0.0705947 | − | 0.162183i | ||||
\(496\) | − | 8.80994e28i | − | 4.38950i | ||||||
\(497\) | 1.01181e28 | − | 4.37145e27i | 0.493577 | − | 0.213247i | ||||
\(498\) | −1.24535e28 | + | 2.59288e27i | −0.594818 | + | 0.123844i | ||||
\(499\) | −4.24208e26 | −0.0198392 | −0.00991958 | − | 0.999951i | \(-0.503158\pi\) | ||||
−0.00991958 | + | 0.999951i | \(0.503158\pi\) | |||||||
\(500\) | 2.49073e28 | 1.14062 | ||||||||
\(501\) | −1.65938e27 | − | 7.96994e27i | −0.0744131 | − | 0.357404i | ||||
\(502\) | 3.36496e28i | 1.47772i | ||||||||
\(503\) | 3.41707e27 | 0.146957 | 0.0734785 | − | 0.997297i | \(-0.476590\pi\) | ||||
0.0734785 | + | 0.997297i | \(0.476590\pi\) | |||||||
\(504\) | 5.68891e28 | − | 6.07693e28i | 2.39612 | − | 2.55955i | ||||
\(505\) | 5.48728e27 | 0.226359 | ||||||||
\(506\) | − | 4.87964e28i | − | 1.97155i | ||||||
\(507\) | −3.09207e27 | − | 1.48511e28i | −0.122367 | − | 0.587728i | ||||
\(508\) | −1.13525e29 | −4.40071 | ||||||||
\(509\) | −2.92017e27 | −0.110884 | −0.0554422 | − | 0.998462i | \(-0.517657\pi\) | ||||
−0.0554422 | + | 0.998462i | \(0.517657\pi\) | |||||||
\(510\) | 1.78413e28 | − | 3.71464e27i | 0.663652 | − | 0.138175i | ||||
\(511\) | 2.36714e27 | − | 1.02271e27i | 0.0862590 | − | 0.0372676i | ||||
\(512\) | − | 9.62696e28i | − | 3.43680i | ||||||
\(513\) | −1.73965e28 | + | 1.23100e28i | −0.608457 | + | 0.430551i | ||||
\(514\) | − | 7.45910e28i | − | 2.55608i | ||||||
\(515\) | 8.92800e27i | 0.299763i | ||||||||
\(516\) | 1.51509e28 | + | 7.27695e28i | 0.498445 | + | 2.39402i | ||||
\(517\) | 3.81037e28i | 1.22833i | ||||||||
\(518\) | 3.27065e28 | − | 1.41306e28i | 1.03317 | − | 0.446374i | ||||
\(519\) | 7.44423e27 | + | 3.57544e28i | 0.230442 | + | 1.10681i | ||||
\(520\) | 1.52182e28 | 0.461667 | ||||||||
\(521\) | 1.46429e28 | 0.435344 | 0.217672 | − | 0.976022i | \(-0.430154\pi\) | ||||
0.217672 | + | 0.976022i | \(0.430154\pi\) | |||||||
\(522\) | 1.11934e28 | − | 4.87226e27i | 0.326154 | − | 0.141968i | ||||
\(523\) | − | 2.32580e28i | − | 0.664208i | −0.943243 | − | 0.332104i | \(-0.892241\pi\) | ||
0.943243 | − | 0.332104i | \(-0.107759\pi\) | |||||||
\(524\) | −1.58074e29 | −4.42468 | ||||||||
\(525\) | −2.85165e28 | + | 2.00623e28i | −0.782391 | + | 0.550438i | ||||
\(526\) | 5.58834e28 | 1.50291 | ||||||||
\(527\) | 6.89103e28i | 1.81665i | ||||||||
\(528\) | 1.29803e29 | − | 2.70255e28i | 3.35450 | − | 0.698421i | ||||
\(529\) | −1.65291e28 | −0.418759 | ||||||||
\(530\) | −6.13845e27 | −0.152462 | ||||||||
\(531\) | −4.47920e28 | + | 1.94970e28i | −1.09071 | + | 0.474760i | ||||
\(532\) | 8.02174e28 | − | 3.46574e28i | 1.91512 | − | 0.827416i | ||||
\(533\) | − | 1.20326e28i | − | 0.281659i | ||||||
\(534\) | 3.41234e28 | − | 7.10465e27i | 0.783194 | − | 0.163064i | ||||
\(535\) | − | 9.55876e26i | − | 0.0215123i | ||||||
\(536\) | − | 4.76327e28i | − | 1.05118i | ||||||
\(537\) | −4.41668e28 | + | 9.19572e27i | −0.955797 | + | 0.199001i | ||||
\(538\) | − | 8.15697e28i | − | 1.73107i | ||||||
\(539\) | −2.97125e28 | − | 2.79674e28i | −0.618382 | − | 0.582063i | ||||
\(540\) | −1.64974e28 | − | 2.33143e28i | −0.336730 | − | 0.475869i | ||||
\(541\) | 3.43629e28 | 0.687889 | 0.343944 | − | 0.938990i | \(-0.388237\pi\) | ||||
0.343944 | + | 0.938990i | \(0.388237\pi\) | |||||||
\(542\) | 8.45186e28 | 1.65943 | ||||||||
\(543\) | 7.86808e28 | − | 1.63817e28i | 1.51520 | − | 0.315472i | ||||
\(544\) | 3.85246e29i | 7.27695i | ||||||||
\(545\) | −1.18730e28 | −0.219987 | ||||||||
\(546\) | −5.54478e28 | + | 3.90094e28i | −1.00777 | + | 0.709001i | ||||
\(547\) | −6.34601e28 | −1.13145 | −0.565723 | − | 0.824595i | \(-0.691403\pi\) | ||||
−0.565723 | + | 0.824595i | \(0.691403\pi\) | |||||||
\(548\) | 1.18793e29i | 2.07776i | ||||||||
\(549\) | −2.58082e28 | − | 5.92913e28i | −0.442841 | − | 1.01737i | ||||
\(550\) | −9.40588e28 | −1.58340 | ||||||||
\(551\) | 8.23652e27 | 0.136035 | ||||||||
\(552\) | −5.25307e28 | − | 2.52303e29i | −0.851241 | − | 4.08849i | ||||
\(553\) | 2.79891e28 | + | 6.47829e28i | 0.445015 | + | 1.03002i | ||||
\(554\) | 4.26036e28i | 0.664652i | ||||||||
\(555\) | −1.60146e27 | − | 7.69175e27i | −0.0245154 | − | 0.117747i | ||||
\(556\) | 5.24216e28i | 0.787454i | ||||||||
\(557\) | 1.18605e28i | 0.174832i | 0.996172 | + | 0.0874162i | \(0.0278610\pi\) | ||||
−0.996172 | + | 0.0874162i | \(0.972139\pi\) | |||||||
\(558\) | 1.34403e29 | − | 5.85026e28i | 1.94424 | − | 0.846284i | ||||
\(559\) | − | 3.89077e28i | − | 0.552346i | ||||||
\(560\) | 2.39227e28 | + | 5.53710e28i | 0.333300 | + | 0.771451i | ||||
\(561\) | −1.01530e29 | + | 2.11390e28i | −1.38830 | + | 0.289051i | ||||
\(562\) | −2.79354e29 | −3.74908 | ||||||||
\(563\) | −8.27726e28 | −1.09031 | −0.545153 | − | 0.838337i | \(-0.683528\pi\) | ||||
−0.545153 | + | 0.838337i | \(0.683528\pi\) | |||||||
\(564\) | 6.38230e28 | + | 3.06540e29i | 0.825176 | + | 3.96329i | ||||
\(565\) | − | 1.29591e28i | − | 0.164462i | ||||||
\(566\) | −6.01426e28 | −0.749221 | ||||||||
\(567\) | 7.70424e28 | + | 2.74165e28i | 0.942124 | + | 0.335266i | ||||
\(568\) | 1.57036e29 | 1.88513 | ||||||||
\(569\) | 4.84740e27i | 0.0571255i | 0.999592 | + | 0.0285628i | \(0.00909304\pi\) | ||||
−0.999592 | + | 0.0285628i | \(0.990907\pi\) | |||||||
\(570\) | −5.33117e27 | − | 2.56054e28i | −0.0616788 | − | 0.296242i | ||||
\(571\) | 5.95415e28 | 0.676302 | 0.338151 | − | 0.941092i | \(-0.390199\pi\) | ||||
0.338151 | + | 0.941092i | \(0.390199\pi\) | |||||||
\(572\) | −1.34746e29 | −1.50265 | ||||||||
\(573\) | −4.97008e27 | + | 1.03479e27i | −0.0544176 | + | 0.0113300i | ||||
\(574\) | 7.41499e28 | − | 3.20360e28i | 0.797142 | − | 0.344400i | ||||
\(575\) | 1.07946e29i | 1.13944i | ||||||||
\(576\) | 3.94462e29 | − | 1.71700e29i | 4.08854 | − | 1.77965i | ||||
\(577\) | 4.08708e28i | 0.415975i | 0.978131 | + | 0.207988i | \(0.0666914\pi\) | ||||
−0.978131 | + | 0.207988i | \(0.933309\pi\) | |||||||
\(578\) | − | 3.48754e29i | − | 3.48560i | ||||||
\(579\) | 1.14135e28 | + | 5.48188e28i | 0.112020 | + | 0.538028i | ||||
\(580\) | 1.10383e28i | 0.106392i | ||||||||
\(581\) | 1.30613e28 | + | 3.02314e28i | 0.123634 | + | 0.286160i | ||||
\(582\) | −5.08460e28 | − | 2.44212e29i | −0.472678 | − | 2.27026i | ||||
\(583\) | 3.49322e28 | 0.318938 | ||||||||
\(584\) | 3.67389e28 | 0.329451 | ||||||||
\(585\) | 5.96668e27 | + | 1.37077e28i | 0.0525528 | + | 0.120734i | ||||
\(586\) | 5.15672e28i | 0.446117i | ||||||||
\(587\) | 2.08509e29 | 1.77184 | 0.885919 | − | 0.463839i | \(-0.153528\pi\) | ||||
0.885919 | + | 0.463839i | \(0.153528\pi\) | |||||||
\(588\) | −2.85878e29 | − | 1.75227e29i | −2.38627 | − | 1.46264i | ||||
\(589\) | 9.88983e28 | 0.810921 | ||||||||
\(590\) | − | 5.99532e28i | − | 0.482910i | ||||||
\(591\) | 1.49020e29 | − | 3.10266e28i | 1.17917 | − | 0.245508i | ||||
\(592\) | 2.99711e29 | 2.32983 | ||||||||
\(593\) | −8.48106e28 | −0.647703 | −0.323852 | − | 0.946108i | \(-0.604978\pi\) | ||||
−0.323852 | + | 0.946108i | \(0.604978\pi\) | |||||||
\(594\) | 1.27425e29 | + | 1.80078e29i | 0.956089 | + | 1.35115i | ||||
\(595\) | −1.87120e28 | − | 4.33105e28i | −0.137941 | − | 0.319275i | ||||
\(596\) | 4.08390e29i | 2.95794i | ||||||||
\(597\) | 2.48605e29 | − | 5.17607e28i | 1.76921 | − | 0.368357i | ||||
\(598\) | 2.09891e29i | 1.46768i | ||||||||
\(599\) | − | 1.25037e29i | − | 0.859129i | −0.903036 | − | 0.429565i | \(-0.858667\pi\) | ||
0.903036 | − | 0.429565i | \(-0.141333\pi\) | |||||||
\(600\) | −4.86334e29 | + | 1.01257e29i | −3.28357 | + | 0.683655i | ||||
\(601\) | 9.97492e28i | 0.661801i | 0.943666 | + | 0.330900i | \(0.107352\pi\) | ||||
−0.943666 | + | 0.330900i | \(0.892648\pi\) | |||||||
\(602\) | 2.39766e29 | − | 1.03589e29i | 1.56324 | − | 0.675386i | ||||
\(603\) | 4.29050e28 | − | 1.86756e28i | 0.274901 | − | 0.119658i | ||||
\(604\) | −5.83036e29 | −3.67120 | ||||||||
\(605\) | 9.38401e27 | 0.0580707 | ||||||||
\(606\) | −3.40970e29 | + | 7.09915e28i | −2.07374 | + | 0.431762i | ||||
\(607\) | − | 9.31313e28i | − | 0.556691i | −0.960481 | − | 0.278346i | \(-0.910214\pi\) | ||
0.960481 | − | 0.278346i | \(-0.0897861\pi\) | |||||||
\(608\) | 5.52896e29 | 3.24830 | ||||||||
\(609\) | −1.81855e28 | − | 2.58488e28i | −0.105013 | − | 0.149265i | ||||
\(610\) | 7.93602e28 | 0.450442 | ||||||||
\(611\) | − | 1.63898e29i | − | 0.914409i | ||||||
\(612\) | −7.81390e29 | + | 3.40121e29i | −4.28526 | + | 1.86528i | ||||
\(613\) | −7.95015e28 | −0.428588 | −0.214294 | − | 0.976769i | \(-0.568745\pi\) | ||||
−0.214294 | + | 0.976769i | \(0.568745\pi\) | |||||||
\(614\) | 3.64461e29 | 1.93145 | ||||||||
\(615\) | −3.63072e27 | − | 1.74382e28i | −0.0189149 | − | 0.0908476i | ||||
\(616\) | −2.30574e29 | − | 5.33683e29i | −1.18090 | − | 2.73329i | ||||
\(617\) | − | 1.87702e29i | − | 0.945092i | −0.881306 | − | 0.472546i | \(-0.843335\pi\) | ||
0.881306 | − | 0.472546i | \(-0.156665\pi\) | |||||||
\(618\) | −1.15506e29 | − | 5.54770e29i | −0.571774 | − | 2.74621i | ||||
\(619\) | − | 5.03814e28i | − | 0.245199i | −0.992456 | − | 0.122599i | \(-0.960877\pi\) | ||
0.992456 | − | 0.122599i | \(-0.0391230\pi\) | |||||||
\(620\) | 1.32540e29i | 0.634214i | ||||||||
\(621\) | 2.06665e29 | − | 1.46239e29i | 0.972312 | − | 0.688018i | ||||
\(622\) | − | 3.13196e29i | − | 1.44883i | ||||||
\(623\) | −3.57887e28 | − | 8.28359e28i | −0.162788 | − | 0.376785i | ||||
\(624\) | −5.58328e29 | + | 1.16246e29i | −2.49719 | + | 0.519926i | ||||
\(625\) | 1.98210e29 | 0.871736 | ||||||||
\(626\) | −3.84402e29 | −1.66247 | ||||||||
\(627\) | 3.03382e28 | + | 1.45713e29i | 0.129027 | + | 0.619713i | ||||
\(628\) | − | 4.95229e29i | − | 2.07124i | ||||||
\(629\) | −2.34430e29 | −0.964232 | ||||||||
\(630\) | −6.85871e28 | + | 7.32653e28i | −0.277439 | + | 0.296362i | ||||
\(631\) | 1.89931e29 | 0.755591 | 0.377795 | − | 0.925889i | \(-0.376682\pi\) | ||||
0.377795 | + | 0.925889i | \(0.376682\pi\) | |||||||
\(632\) | 1.00546e30i | 3.93399i | ||||||||
\(633\) | 5.86397e28 | + | 2.81645e29i | 0.225659 | + | 1.08383i | ||||
\(634\) | −1.12434e29 | −0.425560 | ||||||||
\(635\) | 8.79674e28 | 0.327490 | ||||||||
\(636\) | 2.81026e29 | − | 5.85108e28i | 1.02907 | − | 0.214258i | ||||
\(637\) | 1.27804e29 | + | 1.20298e29i | 0.460342 | + | 0.433306i | ||||
\(638\) | − | 8.52595e28i | − | 0.302083i | ||||||
\(639\) | 6.15699e28 | + | 1.41450e29i | 0.214590 | + | 0.492995i | ||||
\(640\) | 2.63237e29i | 0.902522i | ||||||||
\(641\) | − | 1.01567e29i | − | 0.342565i | −0.985222 | − | 0.171283i | \(-0.945209\pi\) | ||
0.985222 | − | 0.171283i | \(-0.0547912\pi\) | |||||||
\(642\) | 1.23666e28 | + | 5.93965e28i | 0.0410330 | + | 0.197080i | ||||
\(643\) | 1.50938e29i | 0.492701i | 0.969181 | + | 0.246350i | \(0.0792314\pi\) | ||||
−0.969181 | + | 0.246350i | \(0.920769\pi\) | |||||||
\(644\) | −9.52957e29 | + | 4.11719e29i | −3.06035 | + | 1.32221i | ||||
\(645\) | −1.17400e28 | − | 5.63870e28i | −0.0370930 | − | 0.178157i | ||||
\(646\) | −7.80405e29 | −2.42593 | ||||||||
\(647\) | −3.02033e29 | −0.923761 | −0.461880 | − | 0.886942i | \(-0.652825\pi\) | ||||
−0.461880 | + | 0.886942i | \(0.652825\pi\) | |||||||
\(648\) | 8.52717e29 | + | 7.93925e29i | 2.56606 | + | 2.38914i | ||||
\(649\) | 3.41177e29i | 1.01021i | ||||||||
\(650\) | 4.04581e29 | 1.17873 | ||||||||
\(651\) | −2.18358e29 | − | 3.10374e29i | −0.625993 | − | 0.889784i | ||||
\(652\) | 2.60059e29 | 0.733621 | ||||||||
\(653\) | 1.39825e29i | 0.388147i | 0.980987 | + | 0.194073i | \(0.0621700\pi\) | ||||
−0.980987 | + | 0.194073i | \(0.937830\pi\) | |||||||
\(654\) | 7.37768e29 | − | 1.53607e29i | 2.01536 | − | 0.419608i | ||||
\(655\) | 1.22487e29 | 0.329274 | ||||||||
\(656\) | 6.79484e29 | 1.79758 | ||||||||
\(657\) | 1.44044e28 | + | 3.30924e28i | 0.0375023 | + | 0.0861572i | ||||
\(658\) | 1.01001e30 | − | 4.36368e29i | 2.58794 | − | 1.11810i | ||||
\(659\) | − | 7.66724e29i | − | 1.93349i | −0.255738 | − | 0.966746i | \(-0.582319\pi\) | ||
0.255738 | − | 0.966746i | \(-0.417681\pi\) | |||||||
\(660\) | −1.95281e29 | + | 4.06583e28i | −0.484672 | + | 0.100911i | ||||
\(661\) | − | 1.65340e28i | − | 0.0403889i | −0.999796 | − | 0.0201945i | \(-0.993571\pi\) | ||
0.999796 | − | 0.0201945i | \(-0.00642853\pi\) | |||||||
\(662\) | − | 9.45308e29i | − | 2.27282i | ||||||
\(663\) | 4.36717e29 | − | 9.09265e28i | 1.03349 | − | 0.215178i | ||||
\(664\) | 4.69202e29i | 1.09294i | ||||||||
\(665\) | −6.21582e28 | + | 2.68551e28i | −0.142518 | + | 0.0615742i | ||||
\(666\) | 1.99024e29 | + | 4.57234e29i | 0.449185 | + | 1.03195i | ||||
\(667\) | −9.78472e28 | −0.217384 | ||||||||
\(668\) | −4.67205e29 | −1.02177 | ||||||||
\(669\) | 2.11026e29 | − | 4.39366e28i | 0.454320 | − | 0.0945915i | ||||
\(670\) | 5.74274e28i | 0.121712i | ||||||||
\(671\) | −4.51617e29 | −0.942287 | ||||||||
\(672\) | −1.22074e30 | − | 1.73516e30i | −2.50753 | − | 3.56420i | ||||
\(673\) | −6.92774e29 | −1.40098 | −0.700492 | − | 0.713660i | \(-0.747036\pi\) | ||||
−0.700492 | + | 0.713660i | \(0.747036\pi\) | |||||||
\(674\) | − | 7.29101e29i | − | 1.45164i | ||||||
\(675\) | −2.81886e29 | − | 3.98363e29i | −0.552566 | − | 0.780890i | ||||
\(676\) | −8.70587e29 | −1.68024 | ||||||||
\(677\) | 9.41956e28 | 0.178999 | 0.0894993 | − | 0.995987i | \(-0.471473\pi\) | ||||
0.0894993 | + | 0.995987i | \(0.471473\pi\) | |||||||
\(678\) | 1.67658e29 | + | 8.05256e29i | 0.313698 | + | 1.50668i | ||||
\(679\) | −5.92834e29 | + | 2.56130e29i | −1.09220 | + | 0.471876i | ||||
\(680\) | − | 6.72195e29i | − | 1.21942i | ||||||
\(681\) | 9.85973e28 | + | 4.73560e29i | 0.176125 | + | 0.845922i | ||||
\(682\) | − | 1.02374e30i | − | 1.80074i | ||||||
\(683\) | 1.09202e30i | 1.89153i | 0.324857 | + | 0.945763i | \(0.394684\pi\) | ||||
−0.324857 | + | 0.945763i | \(0.605316\pi\) | |||||||
\(684\) | 4.88134e29 | + | 1.12143e30i | 0.832626 | + | 1.91286i | ||||
\(685\) | − | 9.20496e28i | − | 0.154622i | ||||||
\(686\) | −4.01057e29 | + | 1.10787e30i | −0.663442 | + | 1.83268i | ||||
\(687\) | 1.23618e29 | − | 2.57378e28i | 0.201389 | − | 0.0419301i | ||||
\(688\) | 2.19713e30 | 3.52515 | ||||||||
\(689\) | −1.50256e29 | −0.237427 | ||||||||
\(690\) | 6.33326e28 | + | 3.04184e29i | 0.0985625 | + | 0.473393i | ||||
\(691\) | 4.19332e29i | 0.642744i | 0.946953 | + | 0.321372i | \(0.104144\pi\) | ||||
−0.946953 | + | 0.321372i | \(0.895856\pi\) | |||||||
\(692\) | 2.09596e30 | 3.16423 | ||||||||
\(693\) | 3.90310e29 | − | 4.16932e29i | 0.580378 | − | 0.619964i | ||||
\(694\) | 1.70695e30 | 2.50003 | ||||||||
\(695\) | − | 4.06200e28i | − | 0.0586003i | ||||||
\(696\) | −9.17843e28 | − | 4.40837e29i | −0.130428 | − | 0.626443i | ||||
\(697\) | −5.31484e29 | −0.743954 | ||||||||
\(698\) | −1.82715e30 | −2.51937 | ||||||||
\(699\) | 1.30651e30 | − | 2.72021e29i | 1.77460 | − | 0.369480i | ||||
\(700\) | 7.93621e29 | + | 1.83690e30i | 1.06190 | + | 2.45785i | ||||
\(701\) | − | 2.35911e29i | − | 0.310963i | −0.987839 | − | 0.155482i | \(-0.950307\pi\) | ||
0.987839 | − | 0.155482i | \(-0.0496929\pi\) | |||||||
\(702\) | −5.48103e29 | − | 7.74582e29i | −0.711741 | − | 1.00584i | ||||
\(703\) | 3.36448e29i | 0.430415i | ||||||||
\(704\) | − | 3.00458e30i | − | 3.78679i | ||||||
\(705\) | −4.94546e28 | − | 2.37529e29i | −0.0614075 | − | 0.294938i | ||||
\(706\) | − | 1.44018e30i | − | 1.76184i | ||||||
\(707\) | 3.57611e29 | + | 8.27719e29i | 0.431029 | + | 0.997652i | ||||
\(708\) | 5.71464e29 | + | 2.74473e30i | 0.678641 | + | 3.25949i | ||||
\(709\) | 4.53953e29 | 0.531160 | 0.265580 | − | 0.964089i | \(-0.414436\pi\) | ||||
0.265580 | + | 0.964089i | \(0.414436\pi\) | |||||||
\(710\) | −1.89327e29 | −0.218273 | ||||||||
\(711\) | −9.05659e29 | + | 3.94213e29i | −1.02881 | + | 0.447817i | ||||
\(712\) | − | 1.28564e30i | − | 1.43907i | ||||||
\(713\) | −1.17488e30 | −1.29585 | ||||||||
\(714\) | 1.72306e30 | + | 2.44915e30i | 1.87271 | + | 2.66186i | ||||
\(715\) | 1.04411e29 | 0.111823 | ||||||||
\(716\) | 2.58910e30i | 2.73251i | ||||||||
\(717\) | −1.74278e29 | + | 3.62854e28i | −0.181255 | + | 0.0377381i | ||||
\(718\) | 2.16355e30 | 2.21749 | ||||||||
\(719\) | −1.00116e30 | −1.01123 | −0.505615 | − | 0.862759i | \(-0.668734\pi\) | ||||
−0.505615 | + | 0.862759i | \(0.668734\pi\) | |||||||
\(720\) | −7.74082e29 | + | 3.36940e29i | −0.770541 | + | 0.335399i | ||||
\(721\) | −1.34673e30 | + | 5.81845e29i | −1.32117 | + | 0.570804i | ||||
\(722\) | − | 8.95873e29i | − | 0.866175i | ||||||
\(723\) | 1.57738e29 | − | 3.28418e28i | 0.150309 | − | 0.0312950i | ||||
\(724\) | − | 4.61234e30i | − | 4.33178i | ||||||
\(725\) | 1.88608e29i | 0.174587i | ||||||||
\(726\) | −5.83106e29 | + | 1.21405e29i | −0.532002 | + | 0.110765i | ||||
\(727\) | − | 3.47338e29i | − | 0.312349i | −0.987729 | − | 0.156175i | \(-0.950084\pi\) | ||
0.987729 | − | 0.156175i | \(-0.0499163\pi\) | |||||||
\(728\) | 9.91784e29 | + | 2.29556e30i | 0.879099 | + | 2.03474i | ||||
\(729\) | −3.80796e29 | + | 1.07936e30i | −0.332700 | + | 0.943033i | ||||
\(730\) | −4.42935e28 | −0.0381461 | ||||||||
\(731\) | −1.71857e30 | −1.45893 | ||||||||
\(732\) | −3.63320e30 | + | 7.56449e29i | −3.04035 | + | 0.633014i | ||||
\(733\) | − | 8.39113e29i | − | 0.692195i | −0.938198 | − | 0.346098i | \(-0.887507\pi\) | ||
0.938198 | − | 0.346098i | \(-0.112493\pi\) | |||||||
\(734\) | −5.47184e29 | −0.444964 | ||||||||
\(735\) | 2.21519e29 | + | 1.35778e29i | 0.177580 | + | 0.108846i | ||||
\(736\) | −6.56822e30 | −5.19076 | ||||||||
\(737\) | − | 3.26803e29i | − | 0.254612i | ||||||
\(738\) | 4.51213e29 | + | 1.03661e30i | 0.346569 | + | 0.796202i | ||||
\(739\) | 5.00868e29 | 0.379277 | 0.189639 | − | 0.981854i | \(-0.439268\pi\) | ||||
0.189639 | + | 0.981854i | \(0.439268\pi\) | |||||||
\(740\) | −4.50897e29 | −0.336624 | ||||||||
\(741\) | −1.30495e29 | − | 6.26766e29i | −0.0960515 | − | 0.461333i | ||||
\(742\) | −4.00048e29 | − | 9.25943e29i | −0.290316 | − | 0.671960i | ||||
\(743\) | − | 6.56737e29i | − | 0.469904i | −0.972007 | − | 0.234952i | \(-0.924507\pi\) | ||
0.972007 | − | 0.234952i | \(-0.0754932\pi\) | |||||||
\(744\) | −1.10208e30 | − | 5.29326e30i | −0.777495 | − | 3.73429i | ||||
\(745\) | − | 3.16450e29i | − | 0.220122i | ||||||
\(746\) | − | 6.57865e29i | − | 0.451210i | ||||||
\(747\) | −4.22632e29 | + | 1.83962e29i | −0.285822 | + | 0.124412i | ||||
\(748\) | 5.95178e30i | 3.96899i | ||||||||
\(749\) | 1.44187e29 | − | 6.22952e28i | 0.0948129 | − | 0.0409633i | ||||
\(750\) | 1.19927e30 | − | 2.49693e29i | 0.777630 | − | 0.161906i | ||||
\(751\) | 3.70180e28 | 0.0236697 | 0.0118349 | − | 0.999930i | \(-0.496233\pi\) | ||||
0.0118349 | + | 0.999930i | \(0.496233\pi\) | |||||||
\(752\) | 9.25537e30 | 5.83588 | ||||||||
\(753\) | 2.48535e29 | + | 1.19371e30i | 0.154540 | + | 0.742249i | ||||
\(754\) | 3.66732e29i | 0.224879i | ||||||||
\(755\) | 4.51778e29 | 0.273201 | ||||||||
\(756\) | 2.44165e30 | − | 4.00793e30i | 1.45614 | − | 2.39024i | ||||
\(757\) | −8.95308e29 | −0.526581 | −0.263291 | − | 0.964717i | \(-0.584808\pi\) | ||||
−0.263291 | + | 0.964717i | \(0.584808\pi\) | |||||||
\(758\) | 5.66946e29i | 0.328863i | ||||||||
\(759\) | −3.60408e29 | − | 1.73103e30i | −0.206184 | − | 0.990298i | ||||
\(760\) | −9.64718e29 | −0.544324 | ||||||||
\(761\) | 2.77439e30 | 1.54393 | 0.771967 | − | 0.635662i | \(-0.219273\pi\) | ||||
0.771967 | + | 0.635662i | \(0.219273\pi\) | |||||||
\(762\) | −5.46614e30 | + | 1.13807e30i | −3.00022 | + | 0.624660i | ||||
\(763\) | −7.73773e29 | − | 1.79096e30i | −0.418896 | − | 0.969568i | ||||
\(764\) | 2.91350e29i | 0.155573i | ||||||||
\(765\) | 6.05477e29 | − | 2.63551e29i | 0.318898 | − | 0.138809i | ||||
\(766\) | 5.17112e30i | 2.68647i | ||||||||
\(767\) | − | 1.46752e30i | − | 0.752028i | ||||||
\(768\) | −1.60753e30 | − | 7.72092e30i | −0.812580 | − | 3.90280i | ||||
\(769\) | − | 1.12666e30i | − | 0.561779i | −0.959740 | − | 0.280890i | \(-0.909371\pi\) | ||
0.959740 | − | 0.280890i | \(-0.0906295\pi\) | |||||||
\(770\) | 2.77987e29 | + | 6.43424e29i | 0.136733 | + | 0.316479i | ||||
\(771\) | −5.50926e29 | − | 2.64608e30i | −0.267314 | − | 1.28390i | ||||
\(772\) | 3.21353e30 | 1.53816 | ||||||||
\(773\) | 3.15876e29 | 0.149153 | 0.0745766 | − | 0.997215i | \(-0.476239\pi\) | ||||
0.0745766 | + | 0.997215i | \(0.476239\pi\) | |||||||
\(774\) | 1.45901e30 | + | 3.35191e30i | 0.679639 | + | 1.56139i | ||||
\(775\) | 2.26467e30i | 1.04073i | ||||||||
\(776\) | −9.20100e30 | −4.17145 | ||||||||
\(777\) | 1.05588e30 | − | 7.42847e29i | 0.472274 | − | 0.332260i | ||||
\(778\) | 6.40930e30 | 2.82830 | ||||||||
\(779\) | 7.62773e29i | 0.332087i | ||||||||
\(780\) | 8.39972e29 | − | 1.74886e29i | 0.360804 | − | 0.0751210i | ||||
\(781\) | 1.07741e30 | 0.456610 | ||||||||
\(782\) | 9.27096e30 | 3.87663 | ||||||||
\(783\) | 3.61096e29 | − | 2.55515e29i | 0.148979 | − | 0.105419i | ||||
\(784\) | −6.79327e30 | + | 7.21715e30i | −2.76542 | + | 2.93797i | ||||
\(785\) | 3.83739e29i | 0.154136i | ||||||||
\(786\) | −7.61114e30 | + | 1.58467e30i | −3.01657 | + | 0.628063i | ||||
\(787\) | 3.13600e30i | 1.22643i | 0.789918 | + | 0.613213i | \(0.210123\pi\) | ||||
−0.789918 | + | 0.613213i | \(0.789877\pi\) | |||||||
\(788\) | − | 8.73566e30i | − | 3.37109i | ||||||
\(789\) | 1.98244e30 | − | 4.12753e29i | 0.754904 | − | 0.157174i | ||||
\(790\) | − | 1.21221e30i | − | 0.455504i | ||||||
\(791\) | 1.95479e30 | − | 8.44555e29i | 0.724848 | − | 0.313166i | ||||
\(792\) | 7.46084e30 | − | 3.24754e30i | 2.73007 | − | 1.18834i | ||||
\(793\) | 1.94257e30 | 0.701467 | ||||||||
\(794\) | −3.48972e30 | −1.24359 | ||||||||
\(795\) | −2.17759e29 | + | 4.53384e28i | −0.0765810 | + | 0.0159445i | ||||
\(796\) | − | 1.45734e31i | − | 5.05795i | ||||||
\(797\) | −1.83033e30 | −0.626926 | −0.313463 | − | 0.949600i | \(-0.601489\pi\) | ||||
−0.313463 | + | 0.949600i | \(0.601489\pi\) | |||||||
\(798\) | 3.51497e30 | − | 2.47290e30i | 1.18820 | − | 0.835941i | ||||
\(799\) | −7.23943e30 | −2.41526 | ||||||||
\(800\) | 1.26608e31i | 4.16884i | ||||||||
\(801\) | 1.15804e30 | − | 5.04068e29i | 0.376341 | − | 0.163813i | ||||
\(802\) | −2.52139e30 | −0.808741 | ||||||||
\(803\) | 2.52062e29 | 0.0797983 | ||||||||
\(804\) | −5.47389e29 | − | 2.62910e30i | −0.171044 | − | 0.821519i | ||||
\(805\) | 7.38419e29 | − | 3.19030e29i | 0.227744 | − | 0.0983953i | ||||
\(806\) | 4.40346e30i | 1.34053i | ||||||||
\(807\) | −6.02471e29 | − | 2.89365e30i | −0.181036 | − | 0.869509i | ||||
\(808\) | 1.28465e31i | 3.81036i | ||||||||
\(809\) | − | 4.25626e30i | − | 1.24615i | −0.782164 | − | 0.623073i | \(-0.785884\pi\) | ||
0.782164 | − | 0.623073i | \(-0.214116\pi\) | |||||||
\(810\) | −1.02806e30 | − | 9.57179e29i | −0.297116 | − | 0.276631i | ||||
\(811\) | 9.85036e29i | 0.281017i | 0.990079 | + | 0.140509i | \(0.0448738\pi\) | ||||
−0.990079 | + | 0.140509i | \(0.955126\pi\) | |||||||
\(812\) | −1.66505e30 | + | 7.19377e29i | −0.468911 | + | 0.202590i | ||||
\(813\) | 2.99826e30 | − | 6.24251e29i | 0.833525 | − | 0.173544i | ||||
\(814\) | 3.48271e30 | 0.955787 | ||||||||
\(815\) | −2.01512e29 | −0.0545942 | ||||||||
\(816\) | 5.13465e30 | + | 2.46616e31i | 1.37330 | + | 6.59590i | ||||
\(817\) | 2.46645e30i | 0.651239i | ||||||||
\(818\) | −2.00959e30 | −0.523838 | ||||||||
\(819\) | −1.67887e30 | + | 1.79338e30i | −0.432051 | + | 0.461520i | ||||
\(820\) | −1.02224e30 | −0.259722 | ||||||||
\(821\) | 4.06072e30i | 1.01859i | 0.860592 | + | 0.509296i | \(0.170094\pi\) | ||||
−0.860592 | + | 0.509296i | \(0.829906\pi\) | |||||||
\(822\) | 1.19089e30 | + | 5.71980e30i | 0.294929 | + | 1.41653i | ||||
\(823\) | −2.66549e30 | −0.651747 | −0.325873 | − | 0.945413i | \(-0.605658\pi\) | ||||
−0.325873 | + | 0.945413i | \(0.605658\pi\) | |||||||
\(824\) | −2.09017e31 | −5.04598 | ||||||||
\(825\) | −3.33669e30 | + | 6.94714e29i | −0.795335 | + | 0.165592i | ||||
\(826\) | 9.04352e30 | − | 3.90720e30i | 2.12837 | − | 0.919549i | ||||
\(827\) | 1.26604e30i | 0.294197i | 0.989122 | + | 0.147099i | \(0.0469935\pi\) | ||||
−0.989122 | + | 0.147099i | \(0.953007\pi\) | |||||||
\(828\) | −5.79888e30 | − | 1.33222e31i | −1.33053 | − | 3.05674i | ||||
\(829\) | − | 5.09586e30i | − | 1.15450i | −0.816567 | − | 0.577251i | \(-0.804125\pi\) | ||
0.816567 | − | 0.577251i | \(-0.195875\pi\) | |||||||
\(830\) | − | 5.65684e29i | − | 0.126548i | ||||||
\(831\) | 3.14669e29 | + | 1.51134e30i | 0.0695093 | + | 0.333851i | ||||
\(832\) | 1.29238e31i | 2.81900i | ||||||||
\(833\) | 5.31361e30 | − | 5.64516e30i | 1.14450 | − | 1.21592i | ||||
\(834\) | 5.25520e29 | + | 2.52406e30i | 0.111775 | + | 0.536854i | ||||
\(835\) | 3.62024e29 | 0.0760378 | ||||||||
\(836\) | 8.54185e30 | 1.77168 | ||||||||
\(837\) | 4.33579e30 | − | 3.06805e30i | 0.888077 | − | 0.628413i | ||||
\(838\) | − | 1.32237e31i | − | 2.67480i | ||||||
\(839\) | 5.57443e30 | 1.11352 | 0.556762 | − | 0.830672i | \(-0.312043\pi\) | ||||
0.556762 | + | 0.830672i | \(0.312043\pi\) | |||||||
\(840\) | 2.13001e30 | + | 3.02759e30i | 0.420193 | + | 0.597261i | ||||
\(841\) | 4.96188e30 | 0.966692 | ||||||||
\(842\) | − | 3.59953e30i | − | 0.692578i | ||||||
\(843\) | −9.90997e30 | + | 2.06330e30i | −1.88314 | + | 0.392078i | ||||
\(844\) | 1.65103e31 | 3.09855 | ||||||||
\(845\) | 6.74593e29 | 0.125039 | ||||||||
\(846\) | 6.14605e30 | + | 1.41198e31i | 1.12514 | + | 2.58488i | ||||
\(847\) | 6.11564e29 | + | 1.41551e30i | 0.110577 | + | 0.255940i | ||||
\(848\) | − | 8.48502e30i | − | 1.51529i | ||||||
\(849\) | −2.13353e30 | + | 4.44211e29i | −0.376330 | + | 0.0783535i | ||||
\(850\) | − | 1.78705e31i | − | 3.11342i | ||||||
\(851\) | − | 3.99690e30i | − | 0.687801i | ||||||
\(852\) | 8.66763e30 | − | 1.80464e30i | 1.47328 | − | 0.306743i | ||||
\(853\) | 2.97889e30i | 0.500138i | 0.968228 | + | 0.250069i | \(0.0804532\pi\) | ||||
−0.968228 | + | 0.250069i | \(0.919547\pi\) | |||||||
\(854\) | 5.17197e30 | + | 1.19709e31i | 0.857725 | + | 1.98527i | ||||
\(855\) | −3.78241e29 | − | 8.68966e29i | −0.0619619 | − | 0.142350i | ||||
\(856\) | 2.23784e30 | 0.362122 | ||||||||
\(857\) | −8.11612e30 | −1.29733 | −0.648664 | − | 0.761075i | \(-0.724672\pi\) | ||||
−0.648664 | + | 0.761075i | \(0.724672\pi\) | |||||||
\(858\) | −6.48791e30 | + | 1.35081e30i | −1.02444 | + | 0.213294i | ||||
\(859\) | 1.03931e31i | 1.62112i | 0.585653 | + | 0.810562i | \(0.300838\pi\) | ||||
−0.585653 | + | 0.810562i | \(0.699162\pi\) | |||||||
\(860\) | −3.30546e30 | −0.509328 | ||||||||
\(861\) | 2.39382e30 | − | 1.68413e30i | 0.364383 | − | 0.256356i | ||||
\(862\) | −2.22971e31 | −3.35291 | ||||||||
\(863\) | 2.75035e30i | 0.408577i | 0.978911 | + | 0.204289i | \(0.0654881\pi\) | ||||
−0.978911 | + | 0.204289i | \(0.934512\pi\) | |||||||
\(864\) | 2.42394e31 | − | 1.71521e31i | 3.55736 | − | 2.51723i | ||||
\(865\) | −1.62410e30 | −0.235474 | ||||||||
\(866\) | −4.67335e30 | −0.669407 | ||||||||
\(867\) | −2.57588e30 | − | 1.23719e31i | −0.364524 | − | 1.75080i | ||||
\(868\) | −1.99928e31 | + | 8.63777e30i | −2.79522 | + | 1.20766i | ||||
\(869\) | 6.89833e30i | 0.952876i | ||||||||
\(870\) | 1.10658e29 | + | 5.31487e29i | 0.0151018 | + | 0.0725338i | ||||
\(871\) | 1.40570e30i | 0.189541i | ||||||||
\(872\) | − | 2.77964e31i | − | 3.70310i | ||||||
\(873\) | −3.60748e30 | − | 8.28776e30i | −0.474847 | − | 1.09091i | ||||
\(874\) | − | 1.33055e31i | − | 1.73045i | ||||||
\(875\) | −1.25780e30 | − | 2.91127e30i | −0.161631 | − | 0.374109i | ||||
\(876\) | 2.02781e30 | − | 4.22199e29i | 0.257474 | − | 0.0536073i | ||||
\(877\) | 4.33521e30 | 0.543894 | 0.271947 | − | 0.962312i | \(-0.412333\pi\) | ||||
0.271947 | + | 0.962312i | \(0.412333\pi\) | |||||||
\(878\) | −6.85141e30 | −0.849351 | ||||||||
\(879\) | 3.80873e29 | + | 1.82932e30i | 0.0466549 | + | 0.224082i | ||||
\(880\) | 5.89611e30i | 0.713671i | ||||||||
\(881\) | 1.92140e30 | 0.229811 | 0.114906 | − | 0.993376i | \(-0.463343\pi\) | ||||
0.114906 | + | 0.993376i | \(0.463343\pi\) | |||||||
\(882\) | −1.55214e31 | − | 5.57113e30i | −1.83448 | − | 0.658451i | ||||
\(883\) | 4.99868e30 | 0.583805 | 0.291903 | − | 0.956448i | \(-0.405712\pi\) | ||||
0.291903 | + | 0.956448i | \(0.405712\pi\) | |||||||
\(884\) | − | 2.56008e31i | − | 2.95464i | ||||||
\(885\) | −4.42812e29 | − | 2.12681e30i | −0.0505027 | − | 0.242563i | ||||
\(886\) | −6.84439e30 | −0.771401 | ||||||||
\(887\) | 1.09139e31 | 1.21558 | 0.607788 | − | 0.794099i | \(-0.292057\pi\) | ||||
0.607788 | + | 0.794099i | \(0.292057\pi\) | |||||||
\(888\) | 1.80075e31 | − | 3.74924e30i | 1.98206 | − | 0.412674i | ||||
\(889\) | 5.73290e30 | + | 1.32693e31i | 0.623600 | + | 1.44337i | ||||
\(890\) | 1.55001e30i | 0.166625i | ||||||||
\(891\) | 5.85041e30 | + | 5.44704e30i | 0.621542 | + | 0.578688i | ||||
\(892\) | − | 1.23705e31i | − | 1.29885i | ||||||
\(893\) | 1.03899e31i | 1.07813i | ||||||||
\(894\) | 4.09406e30 | + | 1.96637e31i | 0.419866 | + | 2.01660i | ||||
\(895\) | − | 2.00622e30i | − | 0.203346i | ||||||
\(896\) | −3.97075e31 | + | 1.71554e31i | −3.97776 | + | 1.71857i | ||||
\(897\) | 1.55024e30 | + | 7.44578e30i | 0.153490 | + | 0.737207i | ||||
\(898\) | −2.56004e31 | −2.50522 | ||||||||
\(899\) | −2.05281e30 | −0.198551 | ||||||||
\(900\) | −2.56797e31 | + | 1.11778e31i | −2.45495 | + | 1.06859i | ||||
\(901\) | 6.63687e30i | 0.627124i | ||||||||
\(902\) | 7.89576e30 | 0.737438 | ||||||||
\(903\) | 7.74048e30 | − | 5.44569e30i | 0.714573 | − | 0.502726i | ||||
\(904\) | 3.03391e31 | 2.76843 | ||||||||
\(905\) | 3.57397e30i | 0.322360i | ||||||||
\(906\) | −2.80727e31 | + | 5.84486e30i | −2.50287 | + | 0.521109i | ||||
\(907\) | 5.96154e30 | 0.525390 | 0.262695 | − | 0.964879i | \(-0.415389\pi\) | ||||
0.262695 | + | 0.964879i | \(0.415389\pi\) | |||||||
\(908\) | 2.77605e31 | 2.41839 | ||||||||
\(909\) | −1.15714e31 | + | 5.03679e30i | −0.996475 | + | 0.433743i | ||||
\(910\) | −1.19572e30 | − | 2.76760e30i | −0.101788 | − | 0.235596i | ||||
\(911\) | 1.98630e31i | 1.67148i | 0.549122 | + | 0.835742i | \(0.314962\pi\) | ||||
−0.549122 | + | 0.835742i | \(0.685038\pi\) | |||||||
\(912\) | 3.53937e31 | − | 7.36913e30i | 2.94429 | − | 0.613014i | ||||
\(913\) | 3.21915e30i | 0.264727i | ||||||||
\(914\) | 1.00612e31i | 0.817931i | ||||||||
\(915\) | 2.81527e30 | − | 5.86151e29i | 0.226255 | − | 0.0471073i | ||||
\(916\) | − | 7.24659e30i | − | 0.575746i | ||||||
\(917\) | 7.98259e30 | + | 1.84763e31i | 0.626997 | + | 1.45124i | ||||
\(918\) | −3.42136e31 | + | 2.42099e31i | −2.65675 | + | 1.87994i | ||||
\(919\) | −7.89000e30 | −0.605709 | −0.302855 | − | 0.953037i | \(-0.597940\pi\) | ||||
−0.302855 | + | 0.953037i | \(0.597940\pi\) | |||||||
\(920\) | 1.14605e31 | 0.869827 | ||||||||
\(921\) | 1.29291e31 | − | 2.69189e30i | 0.970155 | − | 0.201991i | ||||
\(922\) | 7.66106e30i | 0.568348i | ||||||||
\(923\) | −4.63433e30 | −0.339914 | ||||||||
\(924\) | −1.88596e31 | − | 2.68070e31i | −1.36766 | − | 1.94398i | ||||
\(925\) | −7.70433e30 | −0.552391 | ||||||||
\(926\) | 5.38481e31i | 3.81729i | ||||||||
\(927\) | −8.19502e30 | − | 1.88271e31i | −0.574398 | − | 1.31961i | ||||
\(928\) | −1.14763e31 | −0.795334 | ||||||||
\(929\) | 2.45268e31 | 1.68065 | 0.840324 | − | 0.542084i | \(-0.182365\pi\) | ||||
0.840324 | + | 0.542084i | \(0.182365\pi\) | |||||||
\(930\) | 1.32870e30 | + | 6.38172e30i | 0.0900236 | + | 0.432381i | ||||
\(931\) | −8.10180e30 | − | 7.62597e30i | −0.542762 | − | 0.510885i | ||||
\(932\) | − | 7.65886e31i | − | 5.07338i | ||||||
\(933\) | −2.31325e30 | − | 1.11105e31i | −0.151518 | − | 0.727739i | ||||
\(934\) | − | 5.29346e31i | − | 3.42844i | ||||||
\(935\) | − | 4.61187e30i | − | 0.295362i | ||||||
\(936\) | −3.20918e31 | + | 1.39688e31i | −2.03234 | + | 0.884634i | ||||
\(937\) | 2.02136e31i | 1.26584i | 0.774218 | + | 0.632919i | \(0.218143\pi\) | ||||
−0.774218 | + | 0.632919i | \(0.781857\pi\) | |||||||
\(938\) | −8.66253e30 | + | 3.74259e30i | −0.536432 | + | 0.231762i | ||||
\(939\) | −1.36365e31 | + | 2.83917e30i | −0.835052 | + | 0.173861i | ||||
\(940\) | −1.39242e31 | −0.843193 | ||||||||
\(941\) | −2.54721e31 | −1.52536 | −0.762681 | − | 0.646775i | \(-0.776117\pi\) | ||||
−0.762681 | + | 0.646775i | \(0.776117\pi\) | |||||||
\(942\) | −4.96461e30 | − | 2.38449e31i | −0.294002 | − | 1.41208i | ||||
\(943\) | − | 9.06150e30i | − | 0.530673i | ||||||
\(944\) | 8.28717e31 | 4.79955 | ||||||||
\(945\) | −1.89196e30 | + | 3.10564e30i | −0.108362 | + | 0.177876i | ||||
\(946\) | 2.55312e31 | 1.44615 | ||||||||
\(947\) | 4.04525e30i | 0.226605i | 0.993561 | + | 0.113303i | \(0.0361430\pi\) | ||||
−0.993561 | + | 0.113303i | \(0.963857\pi\) | |||||||
\(948\) | 1.15546e31 | + | 5.54963e31i | 0.640127 | + | 3.07451i | ||||
\(949\) | −1.08421e30 | −0.0594043 | ||||||||
\(950\) | −2.56473e31 | −1.38977 | ||||||||
\(951\) | −3.98855e30 | + | 8.30433e29i | −0.213757 | + | 0.0445051i | ||||
\(952\) | 1.01396e32 | − | 4.38075e31i | 5.37443 | − | 2.32199i | ||||
\(953\) | − | 1.55994e31i | − | 0.817770i | −0.912586 | − | 0.408885i | \(-0.865918\pi\) | ||
0.912586 | − | 0.408885i | \(-0.134082\pi\) | |||||||
\(954\) | 1.29446e31 | − | 5.63450e30i | 0.671167 | − | 0.292144i | ||||
\(955\) | − | 2.25759e29i | − | 0.0115774i | ||||||
\(956\) | 1.02163e31i | 0.518187i | ||||||||
\(957\) | −6.29723e29 | − | 3.02454e30i | −0.0315918 | − | 0.151734i | ||||
\(958\) | − | 1.54157e31i | − | 0.764937i | ||||||
\(959\) | 1.38850e31 | − | 5.99895e30i | 0.681478 | − | 0.294428i | ||||
\(960\) | 3.89963e30 | + | 1.87298e31i | 0.189311 | + | 0.909254i | ||||
\(961\) | −3.82321e30 | −0.183583 | ||||||||
\(962\) | −1.49804e31 | −0.711517 | ||||||||
\(963\) | 8.77400e29 | + | 2.01572e30i | 0.0412213 | + | 0.0947011i | ||||
\(964\) | − | 9.24676e30i | − | 0.429715i | ||||||
\(965\) | −2.49007e30 | −0.114466 | ||||||||
\(966\) | −4.17567e31 | + | 2.93772e31i | −1.89874 | + | 1.33583i | ||||
\(967\) | 1.66736e31 | 0.749984 | 0.374992 | − | 0.927028i | \(-0.377646\pi\) | ||||
0.374992 | + | 0.927028i | \(0.377646\pi\) | |||||||
\(968\) | 2.19693e31i | 0.977518i | ||||||||
\(969\) | −2.76845e31 | + | 5.76404e30i | −1.21853 | + | 0.253704i | ||||
\(970\) | 1.10930e31 | 0.482998 | ||||||||
\(971\) | 2.26047e31 | 0.973635 | 0.486818 | − | 0.873504i | \(-0.338158\pi\) | ||||
0.486818 | + | 0.873504i | \(0.338158\pi\) | |||||||
\(972\) | 5.61895e31 | + | 3.40215e31i | 2.39420 | + | 1.44963i | ||||
\(973\) | 6.12725e30 | − | 2.64724e30i | 0.258274 | − | 0.111586i | ||||
\(974\) | − | 3.86431e31i | − | 1.61140i | ||||||
\(975\) | 1.43523e31 | − | 2.98822e30i | 0.592071 | − | 0.123272i | ||||
\(976\) | 1.09697e32i | 4.47686i | ||||||||
\(977\) | 7.72016e30i | 0.311698i | 0.987781 | + | 0.155849i | \(0.0498113\pi\) | ||||
−0.987781 | + | 0.155849i | \(0.950189\pi\) | |||||||
\(978\) | 1.25216e31 | − | 2.60706e30i | 0.500152 | − | 0.104134i | ||||
\(979\) | − | 8.82068e30i | − | 0.348565i | ||||||
\(980\) | 1.02201e31 | − | 1.08578e31i | 0.399559 | − | 0.424490i | ||||
\(981\) | 2.50375e31 | − | 1.08982e31i | 0.968424 | − | 0.421534i | ||||
\(982\) | 5.76153e31 | 2.20479 | ||||||||
\(983\) | −4.61990e31 | −1.74912 | −0.874562 | − | 0.484913i | \(-0.838851\pi\) | ||||
−0.874562 | + | 0.484913i | \(0.838851\pi\) | |||||||
\(984\) | 4.08253e31 | − | 8.50002e30i | 1.52926 | − | 0.318399i | ||||
\(985\) | 6.76902e30i | 0.250868i | ||||||||
\(986\) | 1.61987e31 | 0.593981 | ||||||||
\(987\) | 3.26066e31 | − | 2.29399e31i | 1.18298 | − | 0.832263i | ||||
\(988\) | −3.67416e31 | −1.31889 | ||||||||
\(989\) | − | 2.93006e31i | − | 1.04068i | ||||||
\(990\) | −8.99501e30 | + | 3.91533e30i | −0.316105 | + | 0.137594i | ||||
\(991\) | −3.83808e31 | −1.33457 | −0.667283 | − | 0.744804i | \(-0.732543\pi\) | ||||
−0.667283 | + | 0.744804i | \(0.732543\pi\) | |||||||
\(992\) | −1.37800e32 | −4.74106 | ||||||||
\(993\) | −6.98201e30 | − | 3.35344e31i | −0.237691 | − | 1.14162i | ||||
\(994\) | −1.23386e31 | − | 2.85587e31i | −0.415633 | − | 0.962015i | ||||
\(995\) | 1.12925e31i | 0.376400i | ||||||||
\(996\) | 5.39201e30 | + | 2.58977e31i | 0.177839 | + | 0.854158i | ||||
\(997\) | 4.67974e31i | 1.52729i | 0.645634 | + | 0.763647i | \(0.276593\pi\) | ||||
−0.645634 | + | 0.763647i | \(0.723407\pi\) | |||||||
\(998\) | 1.19735e30i | 0.0386678i | ||||||||
\(999\) | 1.04374e31 | + | 1.47502e31i | 0.333545 | + | 0.471367i |
(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 | 21.22.c.b.20.27 | yes | 52 | |
3.2 | odd | 2 | inner | 21.22.c.b.20.26 | yes | 52 | |
7.6 | odd | 2 | inner | 21.22.c.b.20.25 | ✓ | 52 | |
21.20 | even | 2 | inner | 21.22.c.b.20.28 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.22.c.b.20.25 | ✓ | 52 | 7.6 | odd | 2 | inner | |
21.22.c.b.20.26 | yes | 52 | 3.2 | odd | 2 | inner | |
21.22.c.b.20.27 | yes | 52 | 1.1 | even | 1 | trivial | |
21.22.c.b.20.28 | yes | 52 | 21.20 | even | 2 | inner |