Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,71,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 71, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 71);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 71 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(93.0951693564\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.3 | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.71.b.a.2.20 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 5.67567e10i | − | 1.65184i | −0.563790 | − | 0.825918i | \(-0.690657\pi\) | ||
0.563790 | − | 0.825918i | \(-0.309343\pi\) | |||||||
\(3\) | 2.16075e15 | + | 4.99849e16i | 0.0431877 | + | 0.999067i | ||||
\(4\) | −2.04073e21 | −1.72856 | ||||||||
\(5\) | 2.61507e24i | 0.898530i | 0.893399 | + | 0.449265i | \(0.148314\pi\) | ||||
−0.893399 | + | 0.449265i | \(0.851686\pi\) | |||||||
\(6\) | 2.83697e27 | − | 1.22637e26i | 1.65030 | − | 0.0713391i | ||||
\(7\) | −2.08517e29 | −0.550439 | −0.275220 | − | 0.961381i | \(-0.588751\pi\) | ||||
−0.275220 | + | 0.961381i | \(0.588751\pi\) | |||||||
\(8\) | 4.88185e31i | 1.20347i | ||||||||
\(9\) | −2.49382e33 | + | 2.16009e32i | −0.996270 | + | 0.0862948i | ||||
\(10\) | 1.48422e35 | 1.48422 | ||||||||
\(11\) | 2.44874e36i | 0.871361i | 0.900101 | + | 0.435681i | \(0.143492\pi\) | ||||
−0.900101 | + | 0.435681i | \(0.856508\pi\) | |||||||
\(12\) | −4.40950e36 | − | 1.02006e38i | −0.0746527 | − | 1.72695i | ||||
\(13\) | 1.52613e39 | 1.56882 | 0.784412 | − | 0.620240i | \(-0.212965\pi\) | ||||
0.784412 | + | 0.620240i | \(0.212965\pi\) | |||||||
\(14\) | 1.18347e40i | 0.909235i | ||||||||
\(15\) | −1.30714e41 | + | 5.65050e39i | −0.897691 | + | 0.0388054i | ||||
\(16\) | 3.61509e41 | 0.259370 | ||||||||
\(17\) | 1.39013e43i | 1.19493i | 0.801894 | + | 0.597467i | \(0.203826\pi\) | ||||
−0.801894 | + | 0.597467i | \(0.796174\pi\) | |||||||
\(18\) | 1.22600e43 | + | 1.41541e44i | 0.142545 | + | 1.64567i | ||||
\(19\) | 6.05007e44 | 1.06019 | 0.530096 | − | 0.847938i | \(-0.322156\pi\) | ||||
0.530096 | + | 0.847938i | \(0.322156\pi\) | |||||||
\(20\) | − | 5.33664e45i | − | 1.55317i | ||||||
\(21\) | −4.50552e44 | − | 1.04227e46i | −0.0237722 | − | 0.549925i | ||||
\(22\) | 1.38982e47 | 1.43935 | ||||||||
\(23\) | − | 5.18745e47i | − | 1.13365i | −0.823838 | − | 0.566826i | \(-0.808171\pi\) | ||
0.823838 | − | 0.566826i | \(-0.191829\pi\) | |||||||
\(24\) | −2.44019e48 | + | 1.05484e47i | −1.20235 | + | 0.0519751i | ||||
\(25\) | 1.63176e48 | 0.192644 | ||||||||
\(26\) | − | 8.66181e49i | − | 2.59144i | ||||||
\(27\) | −1.61857e49 | − | 1.24186e50i | −0.129241 | − | 0.991613i | ||||
\(28\) | 4.25526e50 | 0.951469 | ||||||||
\(29\) | 1.74998e50i | 0.114579i | 0.998358 | + | 0.0572894i | \(0.0182458\pi\) | ||||
−0.998358 | + | 0.0572894i | \(0.981754\pi\) | |||||||
\(30\) | 3.20703e50 | + | 7.41887e51i | 0.0641003 | + | 1.48284i | ||||
\(31\) | 1.83290e52 | 1.16273 | 0.581366 | − | 0.813642i | \(-0.302519\pi\) | ||||
0.581366 | + | 0.813642i | \(0.302519\pi\) | |||||||
\(32\) | 3.71167e52i | 0.775032i | ||||||||
\(33\) | −1.22400e53 | + | 5.29111e51i | −0.870548 | + | 0.0376321i | ||||
\(34\) | 7.88993e53 | 1.97384 | ||||||||
\(35\) | − | 5.45285e53i | − | 0.494586i | ||||||
\(36\) | 5.08920e54 | − | 4.40817e53i | 1.72212 | − | 0.149166i | ||||
\(37\) | −5.50074e54 | −0.713446 | −0.356723 | − | 0.934210i | \(-0.616106\pi\) | ||||
−0.356723 | + | 0.934210i | \(0.616106\pi\) | |||||||
\(38\) | − | 3.43382e55i | − | 1.75126i | ||||||
\(39\) | 3.29758e54 | + | 7.62834e55i | 0.0677540 | + | 1.56736i | ||||
\(40\) | −1.27664e56 | −1.08135 | ||||||||
\(41\) | 3.14908e56i | 1.12395i | 0.827153 | + | 0.561977i | \(0.189959\pi\) | ||||
−0.827153 | + | 0.561977i | \(0.810041\pi\) | |||||||
\(42\) | −5.91556e56 | + | 2.55718e55i | −0.908387 | + | 0.0392678i | ||||
\(43\) | −1.00222e57 | −0.675410 | −0.337705 | − | 0.941252i | \(-0.609651\pi\) | ||||
−0.337705 | + | 0.941252i | \(0.609651\pi\) | |||||||
\(44\) | − | 4.99721e57i | − | 1.50620i | ||||||
\(45\) | −5.64879e56 | − | 6.52150e57i | −0.0775385 | − | 0.895178i | ||||
\(46\) | −2.94422e58 | −1.87261 | ||||||||
\(47\) | 4.95679e58i | 1.48517i | 0.669754 | + | 0.742583i | \(0.266400\pi\) | ||||
−0.669754 | + | 0.742583i | \(0.733600\pi\) | |||||||
\(48\) | 7.81130e56 | + | 1.80700e58i | 0.0112016 | + | 0.259128i | ||||
\(49\) | −1.00024e59 | −0.697017 | ||||||||
\(50\) | − | 9.26134e58i | − | 0.318217i | ||||||
\(51\) | −6.94856e59 | + | 3.00373e58i | −1.19382 | + | 0.0516065i | ||||
\(52\) | −3.11442e60 | −2.71181 | ||||||||
\(53\) | − | 2.19350e60i | − | 0.980578i | −0.871560 | − | 0.490289i | \(-0.836891\pi\) | ||
0.871560 | − | 0.490289i | \(-0.163109\pi\) | |||||||
\(54\) | −7.04841e60 | + | 9.18647e59i | −1.63798 | + | 0.213485i | ||||
\(55\) | −6.40361e60 | −0.782944 | ||||||||
\(56\) | − | 1.01795e61i | − | 0.662436i | ||||||
\(57\) | 1.30727e60 | + | 3.02412e61i | 0.0457872 | + | 1.05920i | ||||
\(58\) | 9.93233e60 | 0.189265 | ||||||||
\(59\) | 7.59389e61i | 0.795507i | 0.917492 | + | 0.397753i | \(0.130210\pi\) | ||||
−0.917492 | + | 0.397753i | \(0.869790\pi\) | |||||||
\(60\) | 2.66751e62 | − | 1.15311e61i | 1.55172 | − | 0.0670777i | ||||
\(61\) | 2.47919e62 | 0.808661 | 0.404330 | − | 0.914613i | \(-0.367505\pi\) | ||||
0.404330 | + | 0.914613i | \(0.367505\pi\) | |||||||
\(62\) | − | 1.04029e63i | − | 1.92064i | ||||||
\(63\) | 5.20002e62 | − | 4.50415e61i | 0.548386 | − | 0.0475001i | ||||
\(64\) | 2.53341e63 | 1.53960 | ||||||||
\(65\) | 3.99093e63i | 1.40964i | ||||||||
\(66\) | 3.00306e62 | + | 6.94701e63i | 0.0621621 | + | 1.43800i | ||||
\(67\) | −1.18377e64 | −1.44761 | −0.723804 | − | 0.690006i | \(-0.757608\pi\) | ||||
−0.723804 | + | 0.690006i | \(0.757608\pi\) | |||||||
\(68\) | − | 2.83688e64i | − | 2.06552i | ||||||
\(69\) | 2.59294e64 | − | 1.12088e63i | 1.13259 | − | 0.0489598i | ||||
\(70\) | −3.09485e64 | −0.816975 | ||||||||
\(71\) | 6.04004e64i | 0.970505i | 0.874374 | + | 0.485253i | \(0.161272\pi\) | ||||
−0.874374 | + | 0.485253i | \(0.838728\pi\) | |||||||
\(72\) | −1.05453e64 | − | 1.21744e65i | −0.103853 | − | 1.19898i | ||||
\(73\) | −2.84733e65 | −1.73037 | −0.865183 | − | 0.501457i | \(-0.832798\pi\) | ||||
−0.865183 | + | 0.501457i | \(0.832798\pi\) | |||||||
\(74\) | 3.12204e65i | 1.17850i | ||||||||
\(75\) | 3.52583e63 | + | 8.15634e64i | 0.00831988 | + | 0.192465i | ||||
\(76\) | −1.23465e66 | −1.83261 | ||||||||
\(77\) | − | 5.10603e65i | − | 0.479631i | ||||||
\(78\) | 4.32959e66 | − | 1.87160e65i | 2.58902 | − | 0.111918i | ||||
\(79\) | −1.26491e66 | −0.484296 | −0.242148 | − | 0.970239i | \(-0.577852\pi\) | ||||
−0.242148 | + | 0.970239i | \(0.577852\pi\) | |||||||
\(80\) | 9.45369e65i | 0.233052i | ||||||||
\(81\) | 6.17247e66 | − | 1.07738e66i | 0.985106 | − | 0.171946i | ||||
\(82\) | 1.78731e67 | 1.85659 | ||||||||
\(83\) | 7.76052e65i | 0.0527421i | 0.999652 | + | 0.0263711i | \(0.00839515\pi\) | ||||
−0.999652 | + | 0.0263711i | \(0.991605\pi\) | |||||||
\(84\) | 9.19454e65 | + | 2.12698e67i | 0.0410918 | + | 0.950581i | ||||
\(85\) | −3.63529e67 | −1.07368 | ||||||||
\(86\) | 5.68828e67i | 1.11567i | ||||||||
\(87\) | −8.74727e66 | + | 3.78127e65i | −0.114472 | + | 0.00494840i | ||||
\(88\) | −1.19544e68 | −1.04866 | ||||||||
\(89\) | − | 2.51424e68i | − | 1.48510i | −0.669788 | − | 0.742552i | \(-0.733615\pi\) | ||
0.669788 | − | 0.742552i | \(-0.266385\pi\) | |||||||
\(90\) | −3.70138e68 | + | 3.20606e67i | −1.47869 | + | 0.128081i | ||||
\(91\) | −3.18224e68 | −0.863542 | ||||||||
\(92\) | 1.05862e69i | 1.95959i | ||||||||
\(93\) | 3.96044e67 | + | 9.16173e68i | 0.0502157 | + | 1.16165i | ||||
\(94\) | 2.81331e69 | 2.45325 | ||||||||
\(95\) | 1.58213e69i | 0.952613i | ||||||||
\(96\) | −1.85527e69 | + | 8.01998e67i | −0.774309 | + | 0.0334719i | ||||
\(97\) | 5.38387e69 | 1.56345 | 0.781725 | − | 0.623623i | \(-0.214340\pi\) | ||||
0.781725 | + | 0.623623i | \(0.214340\pi\) | |||||||
\(98\) | 5.67705e69i | 1.15136i | ||||||||
\(99\) | −5.28951e68 | − | 6.10671e69i | −0.0751940 | − | 0.868111i | ||||
\(100\) | −3.32998e69 | −0.332998 | ||||||||
\(101\) | 1.86953e70i | 1.31973i | 0.751384 | + | 0.659865i | \(0.229386\pi\) | ||||
−0.751384 | + | 0.659865i | \(0.770614\pi\) | |||||||
\(102\) | 1.70481e69 | + | 3.94377e70i | 0.0852454 | + | 1.97199i | ||||
\(103\) | −1.60989e70 | −0.572128 | −0.286064 | − | 0.958210i | \(-0.592347\pi\) | ||||
−0.286064 | + | 0.958210i | \(0.592347\pi\) | |||||||
\(104\) | 7.45034e70i | 1.88803i | ||||||||
\(105\) | 2.72560e70 | − | 1.17822e69i | 0.494124 | − | 0.0213600i | ||||
\(106\) | −1.24496e71 | −1.61975 | ||||||||
\(107\) | − | 1.16190e71i | − | 1.08827i | −0.838996 | − | 0.544137i | \(-0.816857\pi\) | ||
0.838996 | − | 0.544137i | \(-0.183143\pi\) | |||||||
\(108\) | 3.30306e70 | + | 2.53431e71i | 0.223401 | + | 1.71407i | ||||
\(109\) | −1.47058e71 | −0.720378 | −0.360189 | − | 0.932879i | \(-0.617288\pi\) | ||||
−0.360189 | + | 0.932879i | \(0.617288\pi\) | |||||||
\(110\) | 3.63448e71i | 1.29330i | ||||||||
\(111\) | −1.18857e70 | − | 2.74954e71i | −0.0308121 | − | 0.712780i | ||||
\(112\) | −7.53806e70 | −0.142767 | ||||||||
\(113\) | 1.03401e72i | 1.43476i | 0.696684 | + | 0.717378i | \(0.254658\pi\) | ||||
−0.696684 | + | 0.717378i | \(0.745342\pi\) | |||||||
\(114\) | 1.71639e72 | − | 7.41961e70i | 1.74963 | − | 0.0756330i | ||||
\(115\) | 1.35655e72 | 1.01862 | ||||||||
\(116\) | − | 3.57124e71i | − | 0.198057i | ||||||
\(117\) | −3.80589e72 | + | 3.29659e71i | −1.56297 | + | 0.135382i | ||||
\(118\) | 4.31004e72 | 1.31405 | ||||||||
\(119\) | − | 2.89866e72i | − | 0.657738i | ||||||
\(120\) | −2.75849e71 | − | 6.38125e72i | −0.0467012 | − | 1.08034i | ||||
\(121\) | 1.90115e72 | 0.240729 | ||||||||
\(122\) | − | 1.40711e73i | − | 1.33578i | ||||||
\(123\) | −1.57406e73 | + | 6.80437e71i | −1.12291 | + | 0.0485410i | ||||
\(124\) | −3.74045e73 | −2.00986 | ||||||||
\(125\) | 2.64176e73i | 1.07163i | ||||||||
\(126\) | −2.55641e72 | − | 2.95136e73i | −0.0784623 | − | 0.905844i | ||||
\(127\) | 6.94331e72 | 0.161598 | 0.0807990 | − | 0.996730i | \(-0.474253\pi\) | ||||
0.0807990 | + | 0.996730i | \(0.474253\pi\) | |||||||
\(128\) | − | 9.99685e73i | − | 1.76813i | ||||||
\(129\) | −2.16555e72 | − | 5.00959e73i | −0.0291694 | − | 0.674780i | ||||
\(130\) | 2.26512e74 | 2.32849 | ||||||||
\(131\) | − | 1.85604e74i | − | 1.45912i | −0.683917 | − | 0.729560i | \(-0.739725\pi\) | ||
0.683917 | − | 0.729560i | \(-0.260275\pi\) | |||||||
\(132\) | 2.49785e74 | − | 1.07977e73i | 1.50480 | − | 0.0650495i | ||||
\(133\) | −1.26154e74 | −0.583571 | ||||||||
\(134\) | 6.71871e74i | 2.39121i | ||||||||
\(135\) | 3.24756e74 | − | 4.23267e73i | 0.890994 | − | 0.116127i | ||||
\(136\) | −6.78642e74 | −1.43807 | ||||||||
\(137\) | 4.72325e74i | 0.774499i | 0.921975 | + | 0.387250i | \(0.126575\pi\) | ||||
−0.921975 | + | 0.387250i | \(0.873425\pi\) | |||||||
\(138\) | −6.36172e73 | − | 1.47167e75i | −0.0808736 | − | 1.87086i | ||||
\(139\) | −1.55543e75 | −1.53579 | −0.767896 | − | 0.640574i | \(-0.778696\pi\) | ||||
−0.767896 | + | 0.640574i | \(0.778696\pi\) | |||||||
\(140\) | 1.11278e75i | 0.854923i | ||||||||
\(141\) | −2.47764e75 | + | 1.07104e74i | −1.48378 | + | 0.0641409i | ||||
\(142\) | 3.42813e75 | 1.60312 | ||||||||
\(143\) | 3.73709e75i | 1.36701i | ||||||||
\(144\) | −9.01537e74 | + | 7.80893e73i | −0.258402 | + | 0.0223823i | ||||
\(145\) | −4.57632e74 | −0.102952 | ||||||||
\(146\) | 1.61605e76i | 2.85828i | ||||||||
\(147\) | −2.16128e74 | − | 4.99971e75i | −0.0301026 | − | 0.696367i | ||||
\(148\) | 1.12255e76 | 1.23324 | ||||||||
\(149\) | − | 6.27147e75i | − | 0.544314i | −0.962253 | − | 0.272157i | \(-0.912263\pi\) | ||
0.962253 | − | 0.272157i | \(-0.0877371\pi\) | |||||||
\(150\) | 4.62927e75 | − | 2.00114e74i | 0.317920 | − | 0.0137431i | ||||
\(151\) | 1.35242e76 | 0.736068 | 0.368034 | − | 0.929812i | \(-0.380031\pi\) | ||||
0.368034 | + | 0.929812i | \(0.380031\pi\) | |||||||
\(152\) | 2.95355e76i | 1.27591i | ||||||||
\(153\) | −3.00282e75 | − | 3.46674e76i | −0.103117 | − | 1.19048i | ||||
\(154\) | −2.89801e76 | −0.792273 | ||||||||
\(155\) | 4.79315e76i | 1.04475i | ||||||||
\(156\) | −6.72947e75 | − | 1.55674e77i | −0.117117 | − | 2.70928i | ||||
\(157\) | −7.43206e76 | −1.03424 | −0.517120 | − | 0.855913i | \(-0.672996\pi\) | ||||
−0.517120 | + | 0.855913i | \(0.672996\pi\) | |||||||
\(158\) | 7.17920e76i | 0.799978i | ||||||||
\(159\) | 1.09642e77 | − | 4.73960e75i | 0.979663 | − | 0.0423489i | ||||
\(160\) | −9.70625e76 | −0.696389 | ||||||||
\(161\) | 1.08167e77i | 0.624006i | ||||||||
\(162\) | −6.11483e76 | − | 3.50329e77i | −0.284026 | − | 1.62723i | ||||
\(163\) | −2.31545e76 | −0.0867100 | −0.0433550 | − | 0.999060i | \(-0.513805\pi\) | ||||
−0.0433550 | + | 0.999060i | \(0.513805\pi\) | |||||||
\(164\) | − | 6.42642e77i | − | 1.94283i | ||||||
\(165\) | −1.38366e76 | − | 3.20084e77i | −0.0338136 | − | 0.782214i | ||||
\(166\) | 4.40461e76 | 0.0871214 | ||||||||
\(167\) | 3.77615e77i | 0.605304i | 0.953101 | + | 0.302652i | \(0.0978719\pi\) | ||||
−0.953101 | + | 0.302652i | \(0.902128\pi\) | |||||||
\(168\) | 5.08819e77 | − | 2.19953e76i | 0.661818 | − | 0.0286091i | ||||
\(169\) | 1.38276e78 | 1.46121 | ||||||||
\(170\) | 2.06327e78i | 1.77355i | ||||||||
\(171\) | −1.50878e78 | + | 1.30687e77i | −1.05624 | + | 0.0914890i | ||||
\(172\) | 2.04526e78 | 1.16749 | ||||||||
\(173\) | − | 8.86986e77i | − | 0.413336i | −0.978411 | − | 0.206668i | \(-0.933738\pi\) | ||
0.978411 | − | 0.206668i | \(-0.0662620\pi\) | |||||||
\(174\) | 2.14613e76 | + | 4.96466e77i | 0.00817394 | + | 0.189089i | ||||
\(175\) | −3.40249e77 | −0.106039 | ||||||||
\(176\) | 8.85241e77i | 0.226005i | ||||||||
\(177\) | −3.79580e78 | + | 1.64085e77i | −0.794765 | + | 0.0343561i | ||||
\(178\) | −1.42700e79 | −2.45315 | ||||||||
\(179\) | − | 2.15731e78i | − | 0.304829i | −0.988317 | − | 0.152414i | \(-0.951295\pi\) | ||
0.988317 | − | 0.152414i | \(-0.0487048\pi\) | |||||||
\(180\) | 1.15276e78 | + | 1.33086e79i | 0.134030 | + | 1.54737i | ||||
\(181\) | −1.27122e78 | −0.121751 | −0.0608754 | − | 0.998145i | \(-0.519389\pi\) | ||||
−0.0608754 | + | 0.998145i | \(0.519389\pi\) | |||||||
\(182\) | 1.80613e79i | 1.42643i | ||||||||
\(183\) | 5.35692e77 | + | 1.23922e79i | 0.0349242 | + | 0.807906i | ||||
\(184\) | 2.53243e79 | 1.36431 | ||||||||
\(185\) | − | 1.43848e79i | − | 0.641052i | ||||||
\(186\) | 5.19989e79 | − | 2.24781e78i | 1.91885 | − | 0.0829482i | ||||
\(187\) | −3.40407e79 | −1.04122 | ||||||||
\(188\) | − | 1.01155e80i | − | 2.56721i | ||||||
\(189\) | 3.37499e78 | + | 2.58949e79i | 0.0711393 | + | 0.545823i | ||||
\(190\) | 8.97966e79 | 1.57356 | ||||||||
\(191\) | 1.66680e78i | 0.0243062i | 0.999926 | + | 0.0121531i | \(0.00386855\pi\) | ||||
−0.999926 | + | 0.0121531i | \(0.996131\pi\) | |||||||
\(192\) | 5.47407e78 | + | 1.26632e80i | 0.0664917 | + | 1.53816i | ||||
\(193\) | −1.63414e80 | −1.65495 | −0.827473 | − | 0.561505i | \(-0.810222\pi\) | ||||
−0.827473 | + | 0.561505i | \(0.810222\pi\) | |||||||
\(194\) | − | 3.05571e80i | − | 2.58256i | ||||||
\(195\) | −1.99486e80 | + | 8.62340e78i | −1.40832 | + | 0.0608789i | ||||
\(196\) | 2.04123e80 | 1.20484 | ||||||||
\(197\) | − | 8.93355e79i | − | 0.441272i | −0.975356 | − | 0.220636i | \(-0.929187\pi\) | ||
0.975356 | − | 0.220636i | \(-0.0708133\pi\) | |||||||
\(198\) | −3.46596e80 | + | 3.00215e79i | −1.43398 | + | 0.124208i | ||||
\(199\) | −3.93386e80 | −1.36446 | −0.682230 | − | 0.731138i | \(-0.738990\pi\) | ||||
−0.682230 | + | 0.731138i | \(0.738990\pi\) | |||||||
\(200\) | 7.96602e79i | 0.231842i | ||||||||
\(201\) | −2.55784e79 | − | 5.91708e80i | −0.0625189 | − | 1.44626i | ||||
\(202\) | 1.06108e81 | 2.17998 | ||||||||
\(203\) | − | 3.64901e79i | − | 0.0630686i | ||||||
\(204\) | 1.41801e81 | − | 6.12979e79i | 2.06359 | − | 0.0892051i | ||||
\(205\) | −8.23505e80 | −1.00991 | ||||||||
\(206\) | 9.13720e80i | 0.945062i | ||||||||
\(207\) | 1.12054e80 | + | 1.29365e81i | 0.0978283 | + | 1.12942i | ||||
\(208\) | 5.51710e80 | 0.406906 | ||||||||
\(209\) | 1.48150e81i | 0.923810i | ||||||||
\(210\) | −6.68720e79 | − | 1.54696e81i | −0.0352833 | − | 0.816213i | ||||
\(211\) | 6.66814e80 | 0.297933 | 0.148966 | − | 0.988842i | \(-0.452405\pi\) | ||||
0.148966 | + | 0.988842i | \(0.452405\pi\) | |||||||
\(212\) | 4.47634e81i | 1.69499i | ||||||||
\(213\) | −3.01911e81 | + | 1.30510e80i | −0.969600 | + | 0.0419139i | ||||
\(214\) | −6.59458e81 | −1.79765 | ||||||||
\(215\) | − | 2.62088e81i | − | 0.606876i | ||||||
\(216\) | 6.06259e81 | − | 7.90162e80i | 1.19338 | − | 0.155537i | ||||
\(217\) | −3.82190e81 | −0.640013 | ||||||||
\(218\) | 8.34650e81i | 1.18995i | ||||||||
\(219\) | −6.15237e80 | − | 1.42323e82i | −0.0747305 | − | 1.72875i | ||||
\(220\) | 1.30680e82 | 1.35337 | ||||||||
\(221\) | 2.12152e82i | 1.87464i | ||||||||
\(222\) | −1.56055e82 | + | 6.74594e80i | −1.17740 | + | 0.0508966i | ||||
\(223\) | −1.34100e82 | −0.864488 | −0.432244 | − | 0.901757i | \(-0.642278\pi\) | ||||
−0.432244 | + | 0.901757i | \(0.642278\pi\) | |||||||
\(224\) | − | 7.73944e81i | − | 0.426608i | ||||||
\(225\) | −4.06932e81 | + | 3.52476e80i | −0.191926 | + | 0.0166242i | ||||
\(226\) | 5.86868e82 | 2.36998 | ||||||||
\(227\) | − | 3.01073e82i | − | 1.04176i | −0.853631 | − | 0.520878i | \(-0.825604\pi\) | ||
0.853631 | − | 0.520878i | \(-0.174396\pi\) | |||||||
\(228\) | −2.66778e81 | − | 6.17140e82i | −0.0791462 | − | 1.83090i | ||||
\(229\) | 1.52276e82 | 0.387604 | 0.193802 | − | 0.981041i | \(-0.437918\pi\) | ||||
0.193802 | + | 0.981041i | \(0.437918\pi\) | |||||||
\(230\) | − | 7.69934e82i | − | 1.68259i | ||||||
\(231\) | 2.55224e82 | − | 1.10328e81i | 0.479184 | − | 0.0207142i | ||||
\(232\) | −8.54316e81 | −0.137892 | ||||||||
\(233\) | 5.76506e82i | 0.800473i | 0.916412 | + | 0.400237i | \(0.131072\pi\) | ||||
−0.916412 | + | 0.400237i | \(0.868928\pi\) | |||||||
\(234\) | 1.87103e82 | + | 2.16010e83i | 0.223628 | + | 2.58178i | ||||
\(235\) | −1.29623e83 | −1.33447 | ||||||||
\(236\) | − | 1.54971e83i | − | 1.37508i | ||||||
\(237\) | −2.73315e81 | − | 6.32263e82i | −0.0209156 | − | 0.483844i | ||||
\(238\) | −1.64518e83 | −1.08648 | ||||||||
\(239\) | 6.75327e81i | 0.0385112i | 0.999815 | + | 0.0192556i | \(0.00612963\pi\) | ||||
−0.999815 | + | 0.0192556i | \(0.993870\pi\) | |||||||
\(240\) | −4.72542e82 | + | 2.04271e81i | −0.232834 | + | 0.0100650i | ||||
\(241\) | 1.62791e83 | 0.693480 | 0.346740 | − | 0.937961i | \(-0.387289\pi\) | ||||
0.346740 | + | 0.937961i | \(0.387289\pi\) | |||||||
\(242\) | − | 1.07903e83i | − | 0.397645i | ||||||
\(243\) | 6.71897e82 | + | 3.06202e83i | 0.214330 | + | 0.976761i | ||||
\(244\) | −5.05936e83 | −1.39782 | ||||||||
\(245\) | − | 2.61570e83i | − | 0.626290i | ||||||
\(246\) | 3.86193e82 | + | 8.93386e83i | 0.0801818 | + | 1.85486i | ||||
\(247\) | 9.23319e83 | 1.66325 | ||||||||
\(248\) | 8.94794e83i | 1.39931i | ||||||||
\(249\) | −3.87909e82 | + | 1.67685e81i | −0.0526929 | + | 0.00227781i | ||||
\(250\) | 1.49938e84 | 1.77015 | ||||||||
\(251\) | 3.34403e82i | 0.0343313i | 0.999853 | + | 0.0171657i | \(0.00546427\pi\) | ||||
−0.999853 | + | 0.0171657i | \(0.994536\pi\) | |||||||
\(252\) | −1.06118e84 | + | 9.19176e82i | −0.947920 | + | 0.0821069i | ||||
\(253\) | 1.27027e84 | 0.987820 | ||||||||
\(254\) | − | 3.94079e83i | − | 0.266934i | ||||||
\(255\) | −7.85494e82 | − | 1.81709e84i | −0.0463699 | − | 1.07268i | ||||
\(256\) | −2.68295e84 | −1.38106 | ||||||||
\(257\) | 1.99841e84i | 0.897483i | 0.893662 | + | 0.448742i | \(0.148128\pi\) | ||||
−0.893662 | + | 0.448742i | \(0.851872\pi\) | |||||||
\(258\) | −2.84328e84 | + | 1.22909e83i | −1.11463 | + | 0.0481831i | ||||
\(259\) | 1.14700e84 | 0.392708 | ||||||||
\(260\) | − | 8.14441e84i | − | 2.43665i | ||||||
\(261\) | −3.78013e82 | − | 4.36414e83i | −0.00988756 | − | 0.114151i | ||||
\(262\) | −1.05342e85 | −2.41023 | ||||||||
\(263\) | 3.03310e84i | 0.607345i | 0.952777 | + | 0.303672i | \(0.0982128\pi\) | ||||
−0.952777 | + | 0.303672i | \(0.901787\pi\) | |||||||
\(264\) | −2.58304e83 | − | 5.97538e84i | −0.0452891 | − | 1.04768i | ||||
\(265\) | 5.73615e84 | 0.881079 | ||||||||
\(266\) | 7.16008e84i | 0.963963i | ||||||||
\(267\) | 1.25674e85 | − | 5.43265e83i | 1.48372 | − | 0.0641383i | ||||
\(268\) | 2.41576e85 | 2.50228 | ||||||||
\(269\) | 2.16129e84i | 0.196510i | 0.995161 | + | 0.0982549i | \(0.0313260\pi\) | ||||
−0.995161 | + | 0.0982549i | \(0.968674\pi\) | |||||||
\(270\) | −2.40232e84 | − | 1.84320e85i | −0.191823 | − | 1.47178i | ||||
\(271\) | −1.24350e85 | −0.872407 | −0.436203 | − | 0.899848i | \(-0.643677\pi\) | ||||
−0.436203 | + | 0.899848i | \(0.643677\pi\) | |||||||
\(272\) | 5.02545e84i | 0.309930i | ||||||||
\(273\) | −6.87601e83 | − | 1.59064e85i | −0.0372944 | − | 0.862737i | ||||
\(274\) | 2.68076e85 | 1.27935 | ||||||||
\(275\) | 3.99576e84i | 0.167863i | ||||||||
\(276\) | −5.29148e85 | + | 2.28741e84i | −1.95776 | + | 0.0846302i | ||||
\(277\) | −5.47997e84 | −0.178643 | −0.0893215 | − | 0.996003i | \(-0.528470\pi\) | ||||
−0.0893215 | + | 0.996003i | \(0.528470\pi\) | |||||||
\(278\) | 8.82811e85i | 2.53688i | ||||||||
\(279\) | −4.57092e85 | + | 3.95924e84i | −1.15839 | + | 0.100338i | ||||
\(280\) | 2.66200e85 | 0.595219 | ||||||||
\(281\) | − | 8.73444e84i | − | 0.172391i | −0.996278 | − | 0.0861954i | \(-0.972529\pi\) | ||
0.996278 | − | 0.0861954i | \(-0.0274709\pi\) | |||||||
\(282\) | 6.07885e84 | + | 1.40623e86i | 0.105950 | + | 2.45096i | ||||
\(283\) | −8.28406e85 | −1.27561 | −0.637805 | − | 0.770198i | \(-0.720157\pi\) | ||||
−0.637805 | + | 0.770198i | \(0.720157\pi\) | |||||||
\(284\) | − | 1.23261e86i | − | 1.67758i | ||||||
\(285\) | −7.90827e85 | + | 3.41859e84i | −0.951724 | + | 0.0411412i | ||||
\(286\) | 2.12105e86 | 2.25808 | ||||||||
\(287\) | − | 6.56635e85i | − | 0.618668i | ||||||
\(288\) | −8.01755e84 | − | 9.25622e85i | −0.0668813 | − | 0.772141i | ||||
\(289\) | −5.79072e85 | −0.427866 | ||||||||
\(290\) | 2.59737e85i | 0.170061i | ||||||||
\(291\) | 1.16332e85 | + | 2.69112e86i | 0.0675219 | + | 1.56199i | ||||
\(292\) | 5.81063e86 | 2.99105 | ||||||||
\(293\) | 3.51835e85i | 0.160684i | 0.996767 | + | 0.0803419i | \(0.0256012\pi\) | ||||
−0.996767 | + | 0.0803419i | \(0.974399\pi\) | |||||||
\(294\) | −2.83767e86 | + | 1.22667e85i | −1.15028 | + | 0.0497245i | ||||
\(295\) | −1.98585e86 | −0.714787 | ||||||||
\(296\) | − | 2.68538e86i | − | 0.858610i | ||||||
\(297\) | 3.04100e86 | − | 3.96346e85i | 0.864054 | − | 0.112616i | ||||
\(298\) | −3.55948e86 | −0.899119 | ||||||||
\(299\) | − | 7.91672e86i | − | 1.77850i | ||||||
\(300\) | −7.19526e84 | − | 1.66449e86i | −0.0143814 | − | 0.332688i | ||||
\(301\) | 2.08980e86 | 0.371772 | ||||||||
\(302\) | − | 7.67588e86i | − | 1.21586i | ||||||
\(303\) | −9.34483e86 | + | 4.03959e85i | −1.31850 | + | 0.0569961i | ||||
\(304\) | 2.18715e86 | 0.274982 | ||||||||
\(305\) | 6.48326e86i | 0.726606i | ||||||||
\(306\) | −1.96760e87 | + | 1.70430e86i | −1.96647 | + | 0.170332i | ||||
\(307\) | 1.56704e87 | 1.39713 | 0.698566 | − | 0.715546i | \(-0.253822\pi\) | ||||
0.698566 | + | 0.715546i | \(0.253822\pi\) | |||||||
\(308\) | 1.04200e87i | 0.829074i | ||||||||
\(309\) | −3.47857e85 | − | 8.04701e86i | −0.0247089 | − | 0.571594i | ||||
\(310\) | 2.72043e87 | 1.72575 | ||||||||
\(311\) | 2.62923e86i | 0.149010i | 0.997221 | + | 0.0745050i | \(0.0237377\pi\) | ||||
−0.997221 | + | 0.0745050i | \(0.976262\pi\) | |||||||
\(312\) | −3.72404e87 | + | 1.60983e86i | −1.88627 | + | 0.0815398i | ||||
\(313\) | 1.17384e87 | 0.531564 | 0.265782 | − | 0.964033i | \(-0.414370\pi\) | ||||
0.265782 | + | 0.964033i | \(0.414370\pi\) | |||||||
\(314\) | 4.21819e87i | 1.70840i | ||||||||
\(315\) | 1.17787e86 | + | 1.35984e87i | 0.0426802 | + | 0.492741i | ||||
\(316\) | 2.58134e87 | 0.837137 | ||||||||
\(317\) | − | 8.39797e86i | − | 0.243837i | −0.992540 | − | 0.121919i | \(-0.961095\pi\) | ||
0.992540 | − | 0.121919i | \(-0.0389047\pi\) | |||||||
\(318\) | −2.69004e86 | − | 6.22290e87i | −0.0699535 | − | 1.61824i | ||||
\(319\) | −4.28525e86 | −0.0998395 | ||||||||
\(320\) | 6.62504e87i | 1.38337i | ||||||||
\(321\) | 5.80776e87 | − | 2.51058e86i | 1.08726 | − | 0.0470001i | ||||
\(322\) | 6.13919e87 | 1.03076 | ||||||||
\(323\) | 8.41039e87i | 1.26686i | ||||||||
\(324\) | −1.25963e88 | + | 2.19863e87i | −1.70282 | + | 0.297219i | ||||
\(325\) | 2.49028e87 | 0.302225 | ||||||||
\(326\) | 1.31417e87i | 0.143231i | ||||||||
\(327\) | −3.17755e86 | − | 7.35066e87i | −0.0311115 | − | 0.719705i | ||||
\(328\) | −1.53733e88 | −1.35264 | ||||||||
\(329\) | − | 1.03357e88i | − | 0.817493i | ||||||
\(330\) | −1.81669e88 | + | 7.85319e86i | −1.29209 | + | 0.0558545i | ||||
\(331\) | −1.45913e88 | −0.933503 | −0.466751 | − | 0.884389i | \(-0.654576\pi\) | ||||
−0.466751 | + | 0.884389i | \(0.654576\pi\) | |||||||
\(332\) | − | 1.58371e87i | − | 0.0911682i | ||||||
\(333\) | 1.37179e88 | − | 1.18821e87i | 0.710785 | − | 0.0615667i | ||||
\(334\) | 2.14322e88 | 0.999863 | ||||||||
\(335\) | − | 3.09565e88i | − | 1.30072i | ||||||
\(336\) | −1.62879e86 | − | 3.76789e87i | −0.00616580 | − | 0.142634i | ||||
\(337\) | 4.65867e88 | 1.58934 | 0.794668 | − | 0.607045i | \(-0.207645\pi\) | ||||
0.794668 | + | 0.607045i | \(0.207645\pi\) | |||||||
\(338\) | − | 7.84810e88i | − | 2.41368i | ||||||
\(339\) | −5.16847e88 | + | 2.23423e87i | −1.43342 | + | 0.0619639i | ||||
\(340\) | 7.41863e88 | 1.85593 | ||||||||
\(341\) | 4.48829e88i | 1.01316i | ||||||||
\(342\) | 7.41737e87 | + | 8.56331e88i | 0.151125 | + | 1.74473i | ||||
\(343\) | 5.07796e88 | 0.934104 | ||||||||
\(344\) | − | 4.89270e88i | − | 0.812836i | ||||||
\(345\) | 2.93117e87 | + | 6.78070e88i | 0.0439918 | + | 1.01767i | ||||
\(346\) | −5.03424e88 | −0.682764 | ||||||||
\(347\) | − | 1.55148e88i | − | 0.190202i | −0.995468 | − | 0.0951011i | \(-0.969683\pi\) | ||
0.995468 | − | 0.0951011i | \(-0.0303174\pi\) | |||||||
\(348\) | 1.78508e88 | − | 7.71656e86i | 0.197872 | − | 0.00855362i | ||||
\(349\) | −1.82726e89 | −1.83194 | −0.915968 | − | 0.401252i | \(-0.868575\pi\) | ||||
−0.915968 | + | 0.401252i | \(0.868575\pi\) | |||||||
\(350\) | 1.93114e88i | 0.175159i | ||||||||
\(351\) | −2.47015e88 | − | 1.89525e89i | −0.202756 | − | 1.55567i | ||||
\(352\) | −9.08890e88 | −0.675333 | ||||||||
\(353\) | − | 9.00675e88i | − | 0.605973i | −0.952995 | − | 0.302987i | \(-0.902016\pi\) | ||
0.952995 | − | 0.302987i | \(-0.0979837\pi\) | |||||||
\(354\) | 9.31291e87 | + | 2.15437e89i | 0.0567507 | + | 1.31282i | ||||
\(355\) | −1.57951e89 | −0.872028 | ||||||||
\(356\) | 5.13089e89i | 2.56710i | ||||||||
\(357\) | 1.44889e89 | − | 6.26327e87i | 0.657124 | − | 0.0284062i | ||||
\(358\) | −1.22442e89 | −0.503527 | ||||||||
\(359\) | 1.92502e89i | 0.718009i | 0.933336 | + | 0.359004i | \(0.116884\pi\) | ||||
−0.933336 | + | 0.359004i | \(0.883116\pi\) | |||||||
\(360\) | 3.18370e89 | − | 2.75765e88i | 1.07732 | − | 0.0933152i | ||||
\(361\) | 4.03824e88 | 0.124005 | ||||||||
\(362\) | 7.21504e88i | 0.201112i | ||||||||
\(363\) | 4.10791e87 | + | 9.50288e88i | 0.0103965 | + | 0.240505i | ||||
\(364\) | 6.49408e89 | 1.49269 | ||||||||
\(365\) | − | 7.44596e89i | − | 1.55478i | ||||||
\(366\) | 7.03341e89 | − | 3.04041e88i | 1.33453 | − | 0.0576891i | ||||
\(367\) | −8.49328e87 | −0.0146475 | −0.00732375 | − | 0.999973i | \(-0.502331\pi\) | ||||
−0.00732375 | + | 0.999973i | \(0.502331\pi\) | |||||||
\(368\) | − | 1.87531e89i | − | 0.294035i | ||||||
\(369\) | −6.80231e88 | − | 7.85323e89i | −0.0969915 | − | 1.11976i | ||||
\(370\) | −8.16434e89 | −1.05891 | ||||||||
\(371\) | 4.57381e89i | 0.539748i | ||||||||
\(372\) | −8.08217e88 | − | 1.86966e90i | −0.0868011 | − | 2.00798i | ||||
\(373\) | −6.27000e89 | −0.612997 | −0.306498 | − | 0.951871i | \(-0.599157\pi\) | ||||
−0.306498 | + | 0.951871i | \(0.599157\pi\) | |||||||
\(374\) | 1.93204e90i | 1.71992i | ||||||||
\(375\) | −1.32048e90 | + | 5.70819e88i | −1.07063 | + | 0.0462811i | ||||
\(376\) | −2.41983e90 | −1.78735 | ||||||||
\(377\) | 2.67070e89i | 0.179754i | ||||||||
\(378\) | 1.46971e90 | − | 1.91553e89i | 0.901610 | − | 0.117510i | ||||
\(379\) | 7.01306e89 | 0.392225 | 0.196113 | − | 0.980581i | \(-0.437168\pi\) | ||||
0.196113 | + | 0.980581i | \(0.437168\pi\) | |||||||
\(380\) | − | 3.22870e90i | − | 1.64665i | ||||||
\(381\) | 1.50027e88 | + | 3.47060e89i | 0.00697905 | + | 0.161447i | ||||
\(382\) | 9.46023e88 | 0.0401499 | ||||||||
\(383\) | − | 3.88315e90i | − | 1.50393i | −0.659205 | − | 0.751963i | \(-0.729107\pi\) | ||
0.659205 | − | 0.751963i | \(-0.270893\pi\) | |||||||
\(384\) | 4.99691e90 | − | 2.16007e89i | 1.76648 | − | 0.0763615i | ||||
\(385\) | 1.33526e90 | 0.430963 | ||||||||
\(386\) | 9.27485e90i | 2.73370i | ||||||||
\(387\) | 2.49936e90 | − | 2.16489e89i | 0.672891 | − | 0.0582844i | ||||
\(388\) | −1.09870e91 | −2.70252 | ||||||||
\(389\) | − | 4.45418e90i | − | 1.00122i | −0.865672 | − | 0.500612i | \(-0.833108\pi\) | ||
0.865672 | − | 0.500612i | \(-0.166892\pi\) | |||||||
\(390\) | 4.89436e89 | + | 1.13222e91i | 0.100562 | + | 2.32632i | ||||
\(391\) | 7.21124e90 | 1.35464 | ||||||||
\(392\) | − | 4.88304e90i | − | 0.838838i | ||||||
\(393\) | 9.27737e90 | − | 4.01043e89i | 1.45776 | − | 0.0630161i | ||||
\(394\) | −5.07039e90 | −0.728909 | ||||||||
\(395\) | − | 3.30782e90i | − | 0.435154i | ||||||
\(396\) | 1.07944e90 | + | 1.24621e91i | 0.129978 | + | 1.50059i | ||||
\(397\) | −1.05757e91 | −1.16584 | −0.582921 | − | 0.812529i | \(-0.698090\pi\) | ||||
−0.582921 | + | 0.812529i | \(0.698090\pi\) | |||||||
\(398\) | 2.23273e91i | 2.25386i | ||||||||
\(399\) | −2.72587e89 | − | 6.30579e90i | −0.0252031 | − | 0.583026i | ||||
\(400\) | 5.89897e89 | 0.0499662 | ||||||||
\(401\) | − | 8.84401e90i | − | 0.686430i | −0.939257 | − | 0.343215i | \(-0.888484\pi\) | ||
0.939257 | − | 0.343215i | \(-0.111516\pi\) | |||||||
\(402\) | −3.35834e91 | + | 1.45174e90i | −2.38898 | + | 0.103271i | ||||
\(403\) | 2.79725e91 | 1.82412 | ||||||||
\(404\) | − | 3.81521e91i | − | 2.28124i | ||||||
\(405\) | 2.81741e90 | + | 1.61414e91i | 0.154498 | + | 0.885147i | ||||
\(406\) | −2.07105e90 | −0.104179 | ||||||||
\(407\) | − | 1.34699e91i | − | 0.621669i | ||||||
\(408\) | −1.46637e90 | − | 3.39218e91i | −0.0621068 | − | 1.43672i | ||||
\(409\) | −2.98698e91 | −1.16123 | −0.580613 | − | 0.814180i | \(-0.697187\pi\) | ||||
−0.580613 | + | 0.814180i | \(0.697187\pi\) | |||||||
\(410\) | 4.67394e91i | 1.66820i | ||||||||
\(411\) | −2.36091e91 | + | 1.02057e90i | −0.773776 | + | 0.0334488i | ||||
\(412\) | 3.28535e91 | 0.988960 | ||||||||
\(413\) | − | 1.58345e91i | − | 0.437878i | ||||||
\(414\) | 7.34236e91 | − | 6.35980e90i | 1.86562 | − | 0.161596i | ||||
\(415\) | −2.02943e90 | −0.0473904 | ||||||||
\(416\) | 5.66449e91i | 1.21589i | ||||||||
\(417\) | −3.36089e90 | − | 7.77480e91i | −0.0663274 | − | 1.53436i | ||||
\(418\) | 8.40852e91 | 1.52598 | ||||||||
\(419\) | − | 6.14188e91i | − | 1.02520i | −0.858626 | − | 0.512602i | \(-0.828682\pi\) | ||
0.858626 | − | 0.512602i | \(-0.171318\pi\) | |||||||
\(420\) | −5.56220e91 | + | 2.40443e90i | −0.854126 | + | 0.0369222i | ||||
\(421\) | −5.49596e91 | −0.776552 | −0.388276 | − | 0.921543i | \(-0.626929\pi\) | ||||
−0.388276 | + | 0.921543i | \(0.626929\pi\) | |||||||
\(422\) | − | 3.78461e91i | − | 0.492137i | ||||||
\(423\) | −1.07071e91 | − | 1.23613e92i | −0.128162 | − | 1.47963i | ||||
\(424\) | 1.07083e92 | 1.18010 | ||||||||
\(425\) | 2.26836e91i | 0.230197i | ||||||||
\(426\) | 7.40732e90 | + | 1.71355e92i | 0.0692349 | + | 1.60162i | ||||
\(427\) | −5.16953e91 | −0.445118 | ||||||||
\(428\) | 2.37113e92i | 1.88115i | ||||||||
\(429\) | −1.86798e92 | + | 8.07492e90i | −1.36574 | + | 0.0590382i | ||||
\(430\) | −1.48752e92 | −1.00246 | ||||||||
\(431\) | 1.61558e92i | 1.00375i | 0.864940 | + | 0.501875i | \(0.167356\pi\) | ||||
−0.864940 | + | 0.501875i | \(0.832644\pi\) | |||||||
\(432\) | −5.85128e90 | − | 4.48945e91i | −0.0335212 | − | 0.257195i | ||||
\(433\) | 3.16030e91 | 0.166975 | 0.0834876 | − | 0.996509i | \(-0.473394\pi\) | ||||
0.0834876 | + | 0.996509i | \(0.473394\pi\) | |||||||
\(434\) | 2.16918e92i | 1.05720i | ||||||||
\(435\) | −9.88828e89 | − | 2.28747e91i | −0.00444628 | − | 0.102856i | ||||
\(436\) | 3.00105e92 | 1.24522 | ||||||||
\(437\) | − | 3.13844e92i | − | 1.20189i | ||||||
\(438\) | −8.07781e92 | + | 3.49188e91i | −2.85561 | + | 0.123443i | ||||
\(439\) | −1.03963e91 | −0.0339329 | −0.0169664 | − | 0.999856i | \(-0.505401\pi\) | ||||
−0.0169664 | + | 0.999856i | \(0.505401\pi\) | |||||||
\(440\) | − | 3.12615e92i | − | 0.942249i | ||||||
\(441\) | 2.49443e92 | − | 2.16062e91i | 0.694417 | − | 0.0601490i | ||||
\(442\) | 1.20411e93 | 3.09660 | ||||||||
\(443\) | 2.96785e91i | 0.0705200i | 0.999378 | + | 0.0352600i | \(0.0112259\pi\) | ||||
−0.999378 | + | 0.0352600i | \(0.988774\pi\) | |||||||
\(444\) | 2.42555e91 | + | 5.61106e92i | 0.0532607 | + | 1.23209i | ||||
\(445\) | 6.57491e92 | 1.33441 | ||||||||
\(446\) | 7.61108e92i | 1.42799i | ||||||||
\(447\) | 3.13479e92 | − | 1.35511e91i | 0.543807 | − | 0.0235077i | ||||
\(448\) | −5.28259e92 | −0.847454 | ||||||||
\(449\) | − | 1.07715e93i | − | 1.59829i | −0.601140 | − | 0.799144i | \(-0.705287\pi\) | ||
0.601140 | − | 0.799144i | \(-0.294713\pi\) | |||||||
\(450\) | 2.00054e91 | + | 2.30961e92i | 0.0274605 | + | 0.317030i | ||||
\(451\) | −7.71127e92 | −0.979370 | ||||||||
\(452\) | − | 2.11013e93i | − | 2.48007i | ||||||
\(453\) | 2.92224e91 | + | 6.76005e92i | 0.0317891 | + | 0.735381i | ||||
\(454\) | −1.70879e93 | −1.72081 | ||||||||
\(455\) | − | 8.32176e92i | − | 0.775918i | ||||||
\(456\) | −1.47633e93 | + | 6.38188e91i | −1.27472 | + | 0.0551035i | ||||
\(457\) | 6.34409e92 | 0.507344 | 0.253672 | − | 0.967290i | \(-0.418362\pi\) | ||||
0.253672 | + | 0.967290i | \(0.418362\pi\) | |||||||
\(458\) | − | 8.64266e92i | − | 0.640259i | ||||||
\(459\) | 1.72635e93 | − | 2.25003e92i | 1.18491 | − | 0.154434i | ||||
\(460\) | −2.76835e93 | −1.76075 | ||||||||
\(461\) | 8.34085e92i | 0.491675i | 0.969311 | + | 0.245837i | \(0.0790629\pi\) | ||||
−0.969311 | + | 0.245837i | \(0.920937\pi\) | |||||||
\(462\) | −6.26187e91 | − | 1.44857e93i | −0.0342164 | − | 0.791533i | ||||
\(463\) | 1.16626e93 | 0.590829 | 0.295415 | − | 0.955369i | \(-0.404542\pi\) | ||||
0.295415 | + | 0.955369i | \(0.404542\pi\) | |||||||
\(464\) | 6.32635e91i | 0.0297183i | ||||||||
\(465\) | −2.39585e93 | + | 1.03568e92i | −1.04377 | + | 0.0451203i | ||||
\(466\) | 3.27206e93 | 1.32225 | ||||||||
\(467\) | 4.59677e93i | 1.72331i | 0.507499 | + | 0.861653i | \(0.330570\pi\) | ||||
−0.507499 | + | 0.861653i | \(0.669430\pi\) | |||||||
\(468\) | 7.76679e93 | − | 6.72744e92i | 2.70170 | − | 0.234016i | ||||
\(469\) | 2.46837e93 | 0.796820 | ||||||||
\(470\) | 7.35698e93i | 2.20432i | ||||||||
\(471\) | −1.60588e92 | − | 3.71491e93i | −0.0446665 | − | 1.03328i | ||||
\(472\) | −3.70722e93 | −0.957368 | ||||||||
\(473\) | − | 2.45418e93i | − | 0.588527i | ||||||
\(474\) | −3.58851e93 | + | 1.55124e92i | −0.799232 | + | 0.0345492i | ||||
\(475\) | 9.87227e92 | 0.204240 | ||||||||
\(476\) | 5.91537e93i | 1.13694i | ||||||||
\(477\) | 4.73817e92 | + | 5.47019e93i | 0.0846188 | + | 0.976920i | ||||
\(478\) | 3.83293e92 | 0.0636143 | ||||||||
\(479\) | − | 1.82658e93i | − | 0.281771i | −0.990026 | − | 0.140885i | \(-0.955005\pi\) | ||
0.990026 | − | 0.140885i | \(-0.0449949\pi\) | |||||||
\(480\) | −2.09728e92 | − | 4.85166e93i | −0.0300755 | − | 0.695740i | ||||
\(481\) | −8.39486e93 | −1.11927 | ||||||||
\(482\) | − | 9.23948e93i | − | 1.14552i | ||||||
\(483\) | −5.40671e93 | + | 2.33721e92i | −0.623424 | + | 0.0269494i | ||||
\(484\) | −3.87973e93 | −0.416116 | ||||||||
\(485\) | 1.40792e94i | 1.40481i | ||||||||
\(486\) | 1.73790e94 | − | 3.81346e93i | 1.61345 | − | 0.354038i | ||||
\(487\) | −2.05417e94 | −1.77469 | −0.887346 | − | 0.461105i | \(-0.847453\pi\) | ||||
−0.887346 | + | 0.461105i | \(0.847453\pi\) | |||||||
\(488\) | 1.21031e94i | 0.973198i | ||||||||
\(489\) | −5.00310e91 | − | 1.15737e93i | −0.00374481 | − | 0.0866291i | ||||
\(490\) | −1.48459e94 | −1.03453 | ||||||||
\(491\) | 3.14396e93i | 0.203997i | 0.994785 | + | 0.101999i | \(0.0325238\pi\) | ||||
−0.994785 | + | 0.101999i | \(0.967476\pi\) | |||||||
\(492\) | 3.21223e94 | − | 1.38859e93i | 1.94101 | − | 0.0839063i | ||||
\(493\) | −2.43271e93 | −0.136914 | ||||||||
\(494\) | − | 5.24045e94i | − | 2.74742i | ||||||
\(495\) | 1.59694e94 | − | 1.38324e93i | 0.780023 | − | 0.0675640i | ||||
\(496\) | 6.62610e93 | 0.301578 | ||||||||
\(497\) | − | 1.25945e94i | − | 0.534204i | ||||||
\(498\) | 9.51726e91 | + | 2.20164e93i | 0.00376257 | + | 0.0870401i | ||||
\(499\) | 4.32031e94 | 1.59219 | 0.796097 | − | 0.605169i | \(-0.206894\pi\) | ||||
0.796097 | + | 0.605169i | \(0.206894\pi\) | |||||||
\(500\) | − | 5.39112e94i | − | 1.85238i | ||||||
\(501\) | −1.88751e94 | + | 8.15932e92i | −0.604739 | + | 0.0261417i | ||||
\(502\) | 1.89796e93 | 0.0567097 | ||||||||
\(503\) | 4.87887e94i | 1.35969i | 0.733356 | + | 0.679845i | \(0.237953\pi\) | ||||
−0.733356 | + | 0.679845i | \(0.762047\pi\) | |||||||
\(504\) | 2.19886e93 | + | 2.53857e94i | 0.0571648 | + | 0.659965i | ||||
\(505\) | −4.88895e94 | −1.18582 | ||||||||
\(506\) | − | 7.20963e94i | − | 1.63172i | ||||||
\(507\) | 2.98780e93 | + | 6.91172e94i | 0.0631064 | + | 1.45985i | ||||
\(508\) | −1.41694e94 | −0.279333 | ||||||||
\(509\) | 8.02521e94i | 1.47684i | 0.674340 | + | 0.738421i | \(0.264428\pi\) | ||||
−0.674340 | + | 0.738421i | \(0.735572\pi\) | |||||||
\(510\) | −1.03132e95 | + | 4.45820e93i | −1.77189 | + | 0.0765956i | ||||
\(511\) | 5.93716e94 | 0.952461 | ||||||||
\(512\) | 3.42535e94i | 0.513164i | ||||||||
\(513\) | −9.79247e93 | − | 7.51336e94i | −0.137020 | − | 1.05130i | ||||
\(514\) | 1.13423e95 | 1.48250 | ||||||||
\(515\) | − | 4.20997e94i | − | 0.514074i | ||||||
\(516\) | 4.41930e93 | + | 1.02232e95i | 0.0504212 | + | 1.16640i | ||||
\(517\) | −1.21379e95 | −1.29412 | ||||||||
\(518\) | − | 6.50997e94i | − | 0.648690i | ||||||
\(519\) | 4.43359e94 | − | 1.91655e93i | 0.412950 | − | 0.0178510i | ||||
\(520\) | −1.94831e95 | −1.69645 | ||||||||
\(521\) | − | 2.62710e94i | − | 0.213873i | −0.994266 | − | 0.106937i | \(-0.965896\pi\) | ||
0.994266 | − | 0.106937i | \(-0.0341042\pi\) | |||||||
\(522\) | −2.47694e94 | + | 2.14548e93i | −0.188559 | + | 0.0163326i | ||||
\(523\) | 2.04777e95 | 1.45788 | 0.728941 | − | 0.684576i | \(-0.240013\pi\) | ||||
0.728941 | + | 0.684576i | \(0.240013\pi\) | |||||||
\(524\) | 3.78767e95i | 2.52218i | ||||||||
\(525\) | −7.35193e92 | − | 1.70073e94i | −0.00457958 | − | 0.105940i | ||||
\(526\) | 1.72149e95 | 1.00323 | ||||||||
\(527\) | 2.54797e95i | 1.38939i | ||||||||
\(528\) | −4.42486e94 | + | 1.91278e93i | −0.225794 | + | 0.00976064i | ||||
\(529\) | −5.97097e94 | −0.285165 | ||||||||
\(530\) | − | 3.25565e95i | − | 1.45540i | ||||||
\(531\) | −1.64035e94 | − | 1.89378e95i | −0.0686482 | − | 0.792539i | ||||
\(532\) | 2.57446e95 | 1.00874 | ||||||||
\(533\) | 4.80591e95i | 1.76329i | ||||||||
\(534\) | −3.08339e94 | − | 7.13284e95i | −0.105946 | − | 2.45086i | ||||
\(535\) | 3.03846e95 | 0.977847 | ||||||||
\(536\) | − | 5.77901e95i | − | 1.74215i | ||||||
\(537\) | 1.07833e95 | − | 4.66140e93i | 0.304544 | − | 0.0131649i | ||||
\(538\) | 1.22668e95 | 0.324602 | ||||||||
\(539\) | − | 2.44934e95i | − | 0.607354i | ||||||
\(540\) | −6.62738e95 | + | 8.63773e94i | −1.54014 | + | 0.200733i | ||||
\(541\) | −4.06029e95 | −0.884408 | −0.442204 | − | 0.896914i | \(-0.645803\pi\) | ||||
−0.442204 | + | 0.896914i | \(0.645803\pi\) | |||||||
\(542\) | 7.05767e95i | 1.44107i | ||||||||
\(543\) | −2.74679e93 | − | 6.35419e94i | −0.00525814 | − | 0.121637i | ||||
\(544\) | −5.15971e95 | −0.926112 | ||||||||
\(545\) | − | 3.84565e95i | − | 0.647281i | ||||||
\(546\) | −9.02792e95 | + | 3.90260e94i | −1.42510 | + | 0.0616043i | ||||
\(547\) | 7.77500e95 | 1.15118 | 0.575591 | − | 0.817738i | \(-0.304772\pi\) | ||||
0.575591 | + | 0.817738i | \(0.304772\pi\) | |||||||
\(548\) | − | 9.63887e95i | − | 1.33877i | ||||||
\(549\) | −6.18266e95 | + | 5.35529e94i | −0.805644 | + | 0.0697833i | ||||
\(550\) | 2.26786e95 | 0.277282 | ||||||||
\(551\) | 1.05875e95i | 0.121475i | ||||||||
\(552\) | 5.47195e94 | + | 1.26583e96i | 0.0589216 | + | 1.36304i | ||||
\(553\) | 2.63754e95 | 0.266576 | ||||||||
\(554\) | 3.11025e95i | 0.295089i | ||||||||
\(555\) | 7.19023e95 | − | 3.10819e94i | 0.640454 | − | 0.0276856i | ||||
\(556\) | 3.17421e96 | 2.65472 | ||||||||
\(557\) | − | 1.00134e96i | − | 0.786411i | −0.919451 | − | 0.393206i | \(-0.871366\pi\) | ||
0.919451 | − | 0.393206i | \(-0.128634\pi\) | |||||||
\(558\) | 2.24713e95 | + | 2.59430e96i | 0.165742 | + | 1.91348i | ||||
\(559\) | −1.52952e96 | −1.05960 | ||||||||
\(560\) | − | 1.97125e95i | − | 0.128281i | ||||||
\(561\) | −7.35534e94 | − | 1.70152e96i | −0.0449679 | − | 1.04025i | ||||
\(562\) | −4.95738e95 | −0.284761 | ||||||||
\(563\) | 3.73226e95i | 0.201455i | 0.994914 | + | 0.100728i | \(0.0321171\pi\) | ||||
−0.994914 | + | 0.100728i | \(0.967883\pi\) | |||||||
\(564\) | 5.05620e96 | − | 2.18569e95i | 2.56481 | − | 0.110872i | ||||
\(565\) | −2.70400e96 | −1.28917 | ||||||||
\(566\) | 4.70176e96i | 2.10710i | ||||||||
\(567\) | −1.28706e96 | + | 2.24651e95i | −0.542241 | + | 0.0946457i | ||||
\(568\) | −2.94866e96 | −1.16797 | ||||||||
\(569\) | 9.68853e95i | 0.360851i | 0.983589 | + | 0.180426i | \(0.0577476\pi\) | ||||
−0.983589 | + | 0.180426i | \(0.942252\pi\) | |||||||
\(570\) | 1.94028e95 | + | 4.48847e96i | 0.0679585 | + | 1.57209i | ||||
\(571\) | 8.32759e95 | 0.274319 | 0.137159 | − | 0.990549i | \(-0.456203\pi\) | ||||
0.137159 | + | 0.990549i | \(0.456203\pi\) | |||||||
\(572\) | − | 7.62640e96i | − | 2.36297i | ||||||
\(573\) | −8.33150e94 | + | 3.60155e93i | −0.0242835 | + | 0.00104973i | ||||
\(574\) | −3.72684e96 | −1.02194 | ||||||||
\(575\) | − | 8.46468e95i | − | 0.218392i | ||||||
\(576\) | −6.31787e96 | + | 5.47241e95i | −1.53385 | + | 0.132859i | ||||
\(577\) | −4.79842e96 | −1.09634 | −0.548169 | − | 0.836367i | \(-0.684675\pi\) | ||||
−0.548169 | + | 0.836367i | \(0.684675\pi\) | |||||||
\(578\) | 3.28662e96i | 0.706765i | ||||||||
\(579\) | −3.53097e95 | − | 8.16824e96i | −0.0714734 | − | 1.65340i | ||||
\(580\) | 9.33903e95 | 0.177960 | ||||||||
\(581\) | − | 1.61820e95i | − | 0.0290313i | ||||||
\(582\) | 1.52739e97 | − | 6.60261e95i | 2.58015 | − | 0.111535i | ||||
\(583\) | 5.37131e96 | 0.854438 | ||||||||
\(584\) | − | 1.39002e97i | − | 2.08244i | ||||||
\(585\) | −8.62079e95 | − | 9.95266e96i | −0.121644 | − | 1.40438i | ||||
\(586\) | 1.99690e96 | 0.265423 | ||||||||
\(587\) | 3.76796e96i | 0.471816i | 0.971775 | + | 0.235908i | \(0.0758064\pi\) | ||||
−0.971775 | + | 0.235908i | \(0.924194\pi\) | |||||||
\(588\) | 4.41058e95 | + | 1.02030e97i | 0.0520342 | + | 1.20371i | ||||
\(589\) | 1.10892e97 | 1.23272 | ||||||||
\(590\) | 1.12710e97i | 1.18071i | ||||||||
\(591\) | 4.46542e96 | − | 1.93032e95i | 0.440860 | − | 0.0190575i | ||||
\(592\) | −1.98857e96 | −0.185046 | ||||||||
\(593\) | 1.96744e97i | 1.72579i | 0.505386 | + | 0.862894i | \(0.331350\pi\) | ||||
−0.505386 | + | 0.862894i | \(0.668650\pi\) | |||||||
\(594\) | −2.24953e96 | − | 1.72597e97i | −0.186023 | − | 1.42728i | ||||
\(595\) | 7.58017e96 | 0.590997 | ||||||||
\(596\) | 1.27984e97i | 0.940882i | ||||||||
\(597\) | −8.50007e95 | − | 1.96633e97i | −0.0589279 | − | 1.36319i | ||||
\(598\) | −4.49327e97 | −2.93779 | ||||||||
\(599\) | − | 2.03648e97i | − | 1.25586i | −0.778269 | − | 0.627931i | \(-0.783902\pi\) | ||
0.778269 | − | 0.627931i | \(-0.216098\pi\) | |||||||
\(600\) | −3.98180e96 | + | 1.72126e95i | −0.231625 | + | 0.0100127i | ||||
\(601\) | −8.18342e96 | −0.449085 | −0.224542 | − | 0.974464i | \(-0.572089\pi\) | ||||
−0.224542 | + | 0.974464i | \(0.572089\pi\) | |||||||
\(602\) | − | 1.18610e97i | − | 0.614107i | ||||||
\(603\) | 2.95212e97 | − | 2.55706e96i | 1.44221 | − | 0.124921i | ||||
\(604\) | −2.75992e97 | −1.27234 | ||||||||
\(605\) | 4.97163e96i | 0.216302i | ||||||||
\(606\) | 2.29274e96 | + | 5.30382e97i | 0.0941482 | + | 2.17794i | ||||
\(607\) | −3.58526e97 | −1.38969 | −0.694843 | − | 0.719162i | \(-0.744526\pi\) | ||||
−0.694843 | + | 0.719162i | \(0.744526\pi\) | |||||||
\(608\) | 2.24558e97i | 0.821682i | ||||||||
\(609\) | 1.82395e96 | − | 7.88459e94i | 0.0630098 | − | 0.00272379i | ||||
\(610\) | 3.67968e97 | 1.20023 | ||||||||
\(611\) | 7.56470e97i | 2.32997i | ||||||||
\(612\) | 6.12793e96 | + | 7.07467e97i | 0.178244 | + | 2.05781i | ||||
\(613\) | 3.98148e97 | 1.09377 | 0.546887 | − | 0.837207i | \(-0.315813\pi\) | ||||
0.546887 | + | 0.837207i | \(0.315813\pi\) | |||||||
\(614\) | − | 8.89401e97i | − | 2.30783i | ||||||
\(615\) | −1.77939e96 | − | 4.11628e97i | −0.0436155 | − | 1.00896i | ||||
\(616\) | 2.49268e97 | 0.577221 | ||||||||
\(617\) | − | 8.90028e96i | − | 0.194725i | −0.995249 | − | 0.0973627i | \(-0.968959\pi\) | ||
0.995249 | − | 0.0973627i | \(-0.0310407\pi\) | |||||||
\(618\) | −4.56722e97 | + | 1.97432e96i | −0.944180 | + | 0.0408151i | ||||
\(619\) | 9.61328e97 | 1.87801 | 0.939007 | − | 0.343897i | \(-0.111747\pi\) | ||||
0.939007 | + | 0.343897i | \(0.111747\pi\) | |||||||
\(620\) | − | 9.78152e97i | − | 1.80592i | ||||||
\(621\) | −6.44210e97 | + | 8.39626e96i | −1.12414 | + | 0.146514i | ||||
\(622\) | 1.49226e97 | 0.246140 | ||||||||
\(623\) | 5.24261e97i | 0.817459i | ||||||||
\(624\) | 1.19211e96 | + | 2.75771e97i | 0.0175733 | + | 0.406526i | ||||
\(625\) | −5.52623e97 | −0.770244 | ||||||||
\(626\) | − | 6.66230e97i | − | 0.878057i | ||||||
\(627\) | −7.40527e97 | + | 3.20116e96i | −0.922948 | + | 0.0398972i | ||||
\(628\) | 1.51668e98 | 1.78775 | ||||||||
\(629\) | − | 7.64676e97i | − | 0.852521i | ||||||
\(630\) | 7.71800e97 | − | 6.68518e96i | 0.813927 | − | 0.0705007i | ||||
\(631\) | −5.73538e97 | −0.572182 | −0.286091 | − | 0.958202i | \(-0.592356\pi\) | ||||
−0.286091 | + | 0.958202i | \(0.592356\pi\) | |||||||
\(632\) | − | 6.17510e97i | − | 0.582835i | ||||||
\(633\) | 1.44082e96 | + | 3.33306e97i | 0.0128670 | + | 0.297655i | ||||
\(634\) | −4.76641e97 | −0.402779 | ||||||||
\(635\) | 1.81572e97i | 0.145201i | ||||||||
\(636\) | −2.23749e98 | + | 9.67224e96i | −1.69341 | + | 0.0732029i | ||||
\(637\) | −1.52650e98 | −1.09350 | ||||||||
\(638\) | 2.43217e97i | 0.164919i | ||||||||
\(639\) | −1.30471e97 | − | 1.50628e98i | −0.0837496 | − | 0.966885i | ||||
\(640\) | 2.61424e98 | 1.58872 | ||||||||
\(641\) | 2.69039e98i | 1.54805i | 0.633155 | + | 0.774025i | \(0.281760\pi\) | ||||
−0.633155 | + | 0.774025i | \(0.718240\pi\) | |||||||
\(642\) | −1.42492e97 | − | 3.29629e98i | −0.0776364 | − | 1.79597i | ||||
\(643\) | −2.68340e98 | −1.38453 | −0.692264 | − | 0.721644i | \(-0.743387\pi\) | ||||
−0.692264 | + | 0.721644i | \(0.743387\pi\) | |||||||
\(644\) | − | 2.20739e98i | − | 1.07863i | ||||||
\(645\) | 1.31004e98 | − | 5.66305e96i | 0.606310 | − | 0.0262096i | ||||
\(646\) | 4.77346e98 | 2.09264 | ||||||||
\(647\) | 4.16208e98i | 1.72847i | 0.503092 | + | 0.864233i | \(0.332196\pi\) | ||||
−0.503092 | + | 0.864233i | \(0.667804\pi\) | |||||||
\(648\) | 5.25959e97 | + | 3.01331e98i | 0.206932 | + | 1.18554i | ||||
\(649\) | −1.85955e98 | −0.693174 | ||||||||
\(650\) | − | 1.41340e98i | − | 0.499227i | ||||||
\(651\) | −8.25817e96 | − | 1.91037e98i | −0.0276407 | − | 0.639416i | ||||
\(652\) | 4.72520e97 | 0.149884 | ||||||||
\(653\) | 5.73970e98i | 1.72555i | 0.505588 | + | 0.862775i | \(0.331276\pi\) | ||||
−0.505588 | + | 0.862775i | \(0.668724\pi\) | |||||||
\(654\) | −4.17199e98 | + | 1.80347e97i | −1.18884 | + | 0.0513911i | ||||
\(655\) | 4.85366e98 | 1.31106 | ||||||||
\(656\) | 1.13842e98i | 0.291520i | ||||||||
\(657\) | 7.10072e98 | − | 6.15050e97i | 1.72391 | − | 0.149322i | ||||
\(658\) | −5.86621e98 | −1.35037 | ||||||||
\(659\) | − | 1.44836e98i | − | 0.316145i | −0.987428 | − | 0.158072i | \(-0.949472\pi\) | ||
0.987428 | − | 0.158072i | \(-0.0505279\pi\) | |||||||
\(660\) | 2.82367e97 | + | 6.53204e98i | 0.0584489 | + | 1.35211i | ||||
\(661\) | 6.45779e98 | 1.26775 | 0.633874 | − | 0.773436i | \(-0.281464\pi\) | ||||
0.633874 | + | 0.773436i | \(0.281464\pi\) | |||||||
\(662\) | 8.28156e98i | 1.54199i | ||||||||
\(663\) | −1.06044e99 | + | 4.58408e97i | −1.87289 | + | 0.0809615i | ||||
\(664\) | −3.78857e97 | −0.0634735 | ||||||||
\(665\) | − | 3.29901e98i | − | 0.524355i | ||||||
\(666\) | −6.74390e97 | − | 7.78580e98i | −0.101698 | − | 1.17410i | ||||
\(667\) | 9.07795e97 | 0.129892 | ||||||||
\(668\) | − | 7.70611e98i | − | 1.04631i | ||||||
\(669\) | −2.89757e97 | − | 6.70298e98i | −0.0373353 | − | 0.863682i | ||||
\(670\) | −1.75699e99 | −2.14857 | ||||||||
\(671\) | 6.07090e98i | 0.704636i | ||||||||
\(672\) | 3.86855e98 | − | 1.67230e97i | 0.426210 | − | 0.0184242i | ||||
\(673\) | 1.84898e99 | 1.93377 | 0.966885 | − | 0.255211i | \(-0.0821451\pi\) | ||||
0.966885 | + | 0.255211i | \(0.0821451\pi\) | |||||||
\(674\) | − | 2.64411e99i | − | 2.62532i | ||||||
\(675\) | −2.64112e97 | − | 2.02643e98i | −0.0248976 | − | 0.191029i | ||||
\(676\) | −2.82184e99 | −2.52580 | ||||||||
\(677\) | 1.38220e99i | 1.17481i | 0.809293 | + | 0.587406i | \(0.199851\pi\) | ||||
−0.809293 | + | 0.587406i | \(0.800149\pi\) | |||||||
\(678\) | 1.26807e98 | + | 2.93345e99i | 0.102354 | + | 2.36777i | ||||
\(679\) | −1.12263e99 | −0.860584 | ||||||||
\(680\) | − | 1.77469e99i | − | 1.29214i | ||||||
\(681\) | 1.50491e99 | − | 6.50542e97i | 1.04078 | − | 0.0449911i | ||||
\(682\) | 2.54741e99 | 1.67357 | ||||||||
\(683\) | 3.87946e98i | 0.242129i | 0.992645 | + | 0.121064i | \(0.0386307\pi\) | ||||
−0.992645 | + | 0.121064i | \(0.961369\pi\) | |||||||
\(684\) | 3.07900e99 | − | 2.66697e98i | 1.82577 | − | 0.158145i | ||||
\(685\) | −1.23516e99 | −0.695910 | ||||||||
\(686\) | − | 2.88208e99i | − | 1.54299i | ||||||
\(687\) | 3.29029e97 | + | 7.61148e98i | 0.0167398 | + | 0.387243i | ||||
\(688\) | −3.62312e98 | −0.175181 | ||||||||
\(689\) | − | 3.34757e99i | − | 1.53836i | ||||||
\(690\) | 3.84850e99 | − | 1.66363e98i | 1.68102 | − | 0.0726673i | ||||
\(691\) | 3.02076e98 | 0.125425 | 0.0627126 | − | 0.998032i | \(-0.480025\pi\) | ||||
0.0627126 | + | 0.998032i | \(0.480025\pi\) | |||||||
\(692\) | 1.81010e99i | 0.714478i | ||||||||
\(693\) | 1.10295e98 | + | 1.27335e99i | 0.0413897 | + | 0.477842i | ||||
\(694\) | −8.80570e98 | −0.314183 | ||||||||
\(695\) | − | 4.06755e99i | − | 1.37996i | ||||||
\(696\) | −1.84596e97 | − | 4.27029e98i | −0.00595524 | − | 0.137763i | ||||
\(697\) | −4.37764e99 | −1.34305 | ||||||||
\(698\) | 1.03709e100i | 3.02606i | ||||||||
\(699\) | −2.88166e99 | + | 1.24569e98i | −0.799726 | + | 0.0345706i | ||||
\(700\) | 6.94357e98 | 0.183295 | ||||||||
\(701\) | 5.56802e99i | 1.39820i | 0.715022 | + | 0.699102i | \(0.246417\pi\) | ||||
−0.715022 | + | 0.699102i | \(0.753583\pi\) | |||||||
\(702\) | −1.07568e100 | + | 1.40198e99i | −2.56971 | + | 0.334920i | ||||
\(703\) | −3.32799e99 | −0.756389 | ||||||||
\(704\) | 6.20367e99i | 1.34155i | ||||||||
\(705\) | −2.80083e98 | − | 6.47920e99i | −0.0576325 | − | 1.33322i | ||||
\(706\) | −5.11193e99 | −1.00097 | ||||||||
\(707\) | − | 3.89828e99i | − | 0.726430i | ||||||
\(708\) | 7.74619e99 | − | 3.34853e98i | 1.37380 | − | 0.0593868i | ||||
\(709\) | 8.83625e99 | 1.49159 | 0.745795 | − | 0.666175i | \(-0.232070\pi\) | ||||
0.745795 | + | 0.666175i | \(0.232070\pi\) | |||||||
\(710\) | 8.96478e99i | 1.44045i | ||||||||
\(711\) | 3.15445e99 | − | 2.73232e98i | 0.482490 | − | 0.0417923i | ||||
\(712\) | 1.22742e100 | 1.78728 | ||||||||
\(713\) | − | 9.50807e99i | − | 1.31813i | ||||||
\(714\) | −3.55482e98 | − | 8.22341e99i | −0.0469224 | − | 1.08546i | ||||
\(715\) | −9.77275e99 | −1.22830 | ||||||||
\(716\) | 4.40248e99i | 0.526916i | ||||||||
\(717\) | −3.37561e98 | + | 1.45921e97i | −0.0384753 | + | 0.00166321i | ||||
\(718\) | 1.09258e100 | 1.18603 | ||||||||
\(719\) | 3.32168e99i | 0.343436i | 0.985146 | + | 0.171718i | \(0.0549319\pi\) | ||||
−0.985146 | + | 0.171718i | \(0.945068\pi\) | |||||||
\(720\) | −2.04209e98 | − | 2.35758e99i | −0.0201112 | − | 0.232182i | ||||
\(721\) | 3.35689e99 | 0.314922 | ||||||||
\(722\) | − | 2.29197e99i | − | 0.204837i | ||||||
\(723\) | 3.51750e98 | + | 8.13709e99i | 0.0299498 | + | 0.692833i | ||||
\(724\) | 2.59422e99 | 0.210454 | ||||||||
\(725\) | 2.85556e98i | 0.0220730i | ||||||||
\(726\) | 5.39352e99 | − | 2.33151e98i | 0.397274 | − | 0.0171734i | ||||
\(727\) | 1.73653e100 | 1.21893 | 0.609464 | − | 0.792814i | \(-0.291385\pi\) | ||||
0.609464 | + | 0.792814i | \(0.291385\pi\) | |||||||
\(728\) | − | 1.55352e100i | − | 1.03925i | ||||||
\(729\) | −1.51603e100 | + | 4.02009e99i | −0.966594 | + | 0.256314i | ||||
\(730\) | −4.22608e100 | −2.56825 | ||||||||
\(731\) | − | 1.39322e100i | − | 0.807071i | ||||||
\(732\) | −1.09320e99 | − | 2.52892e100i | −0.0603687 | − | 1.39652i | ||||
\(733\) | −2.82348e100 | −1.48643 | −0.743217 | − | 0.669051i | \(-0.766701\pi\) | ||||
−0.743217 | + | 0.669051i | \(0.766701\pi\) | |||||||
\(734\) | 4.82051e98i | 0.0241953i | ||||||||
\(735\) | 1.30746e100 | − | 5.65188e98i | 0.625706 | − | 0.0270481i | ||||
\(736\) | 1.92541e100 | 0.878616 | ||||||||
\(737\) | − | 2.89875e100i | − | 1.26139i | ||||||
\(738\) | −4.45723e100 | + | 3.86076e99i | −1.84966 | + | 0.160214i | ||||
\(739\) | 2.00648e100 | 0.794109 | 0.397054 | − | 0.917795i | \(-0.370032\pi\) | ||||
0.397054 | + | 0.917795i | \(0.370032\pi\) | |||||||
\(740\) | 2.93555e100i | 1.10810i | ||||||||
\(741\) | 1.99506e99 | + | 4.61520e100i | 0.0718322 | + | 1.66170i | ||||
\(742\) | 2.59594e100 | 0.891576 | ||||||||
\(743\) | − | 6.05584e100i | − | 1.98411i | −0.125803 | − | 0.992055i | \(-0.540151\pi\) | ||
0.125803 | − | 0.992055i | \(-0.459849\pi\) | |||||||
\(744\) | −4.47262e100 | + | 1.93343e99i | −1.39801 | + | 0.0604331i | ||||
\(745\) | 1.64003e100 | 0.489083 | ||||||||
\(746\) | 3.55864e100i | 1.01257i | ||||||||
\(747\) | −1.67635e98 | − | 1.93533e99i | −0.00455138 | − | 0.0525454i | ||||
\(748\) | 6.94678e100 | 1.79981 | ||||||||
\(749\) | 2.42276e100i | 0.599028i | ||||||||
\(750\) | 3.23978e99 | + | 7.49461e100i | 0.0764488 | + | 1.76850i | ||||
\(751\) | 5.41700e100 | 1.22000 | 0.610001 | − | 0.792401i | \(-0.291169\pi\) | ||||
0.610001 | + | 0.792401i | \(0.291169\pi\) | |||||||
\(752\) | 1.79192e100i | 0.385207i | ||||||||
\(753\) | −1.67151e99 | + | 7.22562e97i | −0.0342993 | + | 0.00148269i | ||||
\(754\) | 1.51580e100 | 0.296924 | ||||||||
\(755\) | 3.53666e100i | 0.661379i | ||||||||
\(756\) | −6.88744e99 | − | 5.28445e100i | −0.122969 | − | 0.943489i | ||||
\(757\) | −3.52653e100 | −0.601162 | −0.300581 | − | 0.953756i | \(-0.597181\pi\) | ||||
−0.300581 | + | 0.953756i | \(0.597181\pi\) | |||||||
\(758\) | − | 3.98038e100i | − | 0.647892i | ||||||
\(759\) | 2.74473e99 | + | 6.34943e100i | 0.0426617 | + | 0.986898i | ||||
\(760\) | −7.72373e100 | −1.14644 | ||||||||
\(761\) | − | 1.98121e100i | − | 0.280845i | −0.990092 | − | 0.140422i | \(-0.955154\pi\) | ||
0.990092 | − | 0.140422i | \(-0.0448461\pi\) | |||||||
\(762\) | 1.96980e100 | − | 8.51506e98i | 0.266685 | − | 0.0115283i | ||||
\(763\) | 3.06640e100 | 0.396524 | ||||||||
\(764\) | − | 3.40150e99i | − | 0.0420148i | ||||||
\(765\) | 9.06574e100 | − | 7.85256e99i | 1.06968 | − | 0.0926533i | ||||
\(766\) | −2.20394e101 | −2.48424 | ||||||||
\(767\) | 1.15893e101i | 1.24801i | ||||||||
\(768\) | −5.79718e99 | − | 1.34107e101i | −0.0596450 | − | 1.37978i | ||||
\(769\) | −1.40777e101 | −1.38391 | −0.691957 | − | 0.721939i | \(-0.743251\pi\) | ||||
−0.691957 | + | 0.721939i | \(0.743251\pi\) | |||||||
\(770\) | − | 7.57849e100i | − | 0.711880i | ||||||
\(771\) | −9.98905e100 | + | 4.31807e99i | −0.896646 | + | 0.0387602i | ||||
\(772\) | 3.33484e101 | 2.86068 | ||||||||
\(773\) | − | 8.99852e100i | − | 0.737715i | −0.929486 | − | 0.368858i | \(-0.879749\pi\) | ||
0.929486 | − | 0.368858i | \(-0.120251\pi\) | |||||||
\(774\) | −1.22872e100 | − | 1.41855e101i | −0.0962764 | − | 1.11151i | ||||
\(775\) | 2.99086e100 | 0.223994 | ||||||||
\(776\) | 2.62833e101i | 1.88156i | ||||||||
\(777\) | 2.47837e99 | + | 5.73325e100i | 0.0169602 | + | 0.392342i | ||||
\(778\) | −2.52804e101 | −1.65386 | ||||||||
\(779\) | 1.90521e101i | 1.19161i | ||||||||
\(780\) | 4.07097e101 | − | 1.75980e100i | 2.43437 | − | 0.105233i | ||||
\(781\) | −1.47905e101 | −0.845661 | ||||||||
\(782\) | − | 4.09286e101i | − | 2.23764i | ||||||
\(783\) | 2.17324e100 | − | 2.83247e99i | 0.113618 | − | 0.0148083i | ||||
\(784\) | −3.61597e100 | −0.180785 | ||||||||
\(785\) | − | 1.94353e101i | − | 0.929296i | ||||||
\(786\) | −2.27619e100 | − | 5.26553e101i | −0.104092 | − | 2.40798i | ||||
\(787\) | 1.19724e101 | 0.523679 | 0.261839 | − | 0.965111i | \(-0.415671\pi\) | ||||
0.261839 | + | 0.965111i | \(0.415671\pi\) | |||||||
\(788\) | 1.82310e101i | 0.762767i | ||||||||
\(789\) | −1.51609e101 | + | 6.55376e99i | −0.606778 | + | 0.0262298i | ||||
\(790\) | −1.87741e101 | −0.718804 | ||||||||
\(791\) | − | 2.15608e101i | − | 0.789746i | ||||||
\(792\) | 2.98120e101 | − | 2.58226e100i | 1.04474 | − | 0.0904937i | ||||
\(793\) | 3.78358e101 | 1.26865 | ||||||||
\(794\) | 6.00239e101i | 1.92578i | ||||||||
\(795\) | 1.23944e100 | + | 2.86720e101i | 0.0380518 | + | 0.880256i | ||||
\(796\) | 8.02793e101 | 2.35856 | ||||||||
\(797\) | 4.79264e101i | 1.34751i | 0.738953 | + | 0.673757i | \(0.235321\pi\) | ||||
−0.738953 | + | 0.673757i | \(0.764679\pi\) | |||||||
\(798\) | −3.57896e101 | + | 1.54711e100i | −0.963064 | + | 0.0416314i | ||||
\(799\) | −6.89059e101 | −1.77468 | ||||||||
\(800\) | 6.05656e100i | 0.149306i | ||||||||
\(801\) | 5.43100e100 | + | 6.27006e101i | 0.128157 | + | 1.47956i | ||||
\(802\) | −5.01957e101 | −1.13387 | ||||||||
\(803\) | − | 6.97237e101i | − | 1.50777i | ||||||
\(804\) | 5.21985e100 | + | 1.20752e102i | 0.108068 | + | 2.49995i | ||||
\(805\) | −2.82863e101 | −0.560688 | ||||||||
\(806\) | − | 1.58762e102i | − | 3.01315i | ||||||
\(807\) | −1.08032e101 | + | 4.67001e99i | −0.196326 | + | 0.00848681i | ||||
\(808\) | −9.12678e101 | −1.58825 | ||||||||
\(809\) | 6.49307e101i | 1.08206i | 0.841003 | + | 0.541031i | \(0.181966\pi\) | ||||
−0.841003 | + | 0.541031i | \(0.818034\pi\) | |||||||
\(810\) | 9.16133e101 | − | 1.59907e101i | 1.46212 | − | 0.255206i | ||||
\(811\) | 2.30173e101 | 0.351823 | 0.175912 | − | 0.984406i | \(-0.443713\pi\) | ||||
0.175912 | + | 0.984406i | \(0.443713\pi\) | |||||||
\(812\) | 7.44663e100i | 0.109018i | ||||||||
\(813\) | −2.68688e100 | − | 6.21560e101i | −0.0376773 | − | 0.871593i | ||||
\(814\) | −7.64506e101 | −1.02690 | ||||||||
\(815\) | − | 6.05505e100i | − | 0.0779115i | ||||||
\(816\) | −2.51196e101 | + | 1.08587e100i | −0.309641 | + | 0.0133852i | ||||
\(817\) | −6.06351e101 | −0.716064 | ||||||||
\(818\) | 1.69531e102i | 1.91815i | ||||||||
\(819\) | 7.93592e101 | − | 6.87393e100i | 0.860321 | − | 0.0745193i | ||||
\(820\) | 1.68055e102 | 1.74569 | ||||||||
\(821\) | − | 7.15333e101i | − | 0.712029i | −0.934480 | − | 0.356015i | \(-0.884135\pi\) | ||
0.934480 | − | 0.356015i | \(-0.115865\pi\) | |||||||
\(822\) | 5.79244e100 | + | 1.33997e102i | 0.0552520 | + | 1.27815i | ||||
\(823\) | 1.36477e102 | 1.24757 | 0.623784 | − | 0.781597i | \(-0.285594\pi\) | ||||
0.623784 | + | 0.781597i | \(0.285594\pi\) | |||||||
\(824\) | − | 7.85924e101i | − | 0.688539i | ||||||
\(825\) | −1.99727e101 | + | 8.63383e99i | −0.167706 | + | 0.00724962i | ||||
\(826\) | −8.98715e101 | −0.723303 | ||||||||
\(827\) | 1.81733e101i | 0.140198i | 0.997540 | + | 0.0700990i | \(0.0223315\pi\) | ||||
−0.997540 | + | 0.0700990i | \(0.977668\pi\) | |||||||
\(828\) | −2.28671e101 | − | 2.64000e102i | −0.169102 | − | 1.95228i | ||||
\(829\) | 2.01560e102 | 1.42888 | 0.714441 | − | 0.699696i | \(-0.246681\pi\) | ||||
0.714441 | + | 0.699696i | \(0.246681\pi\) | |||||||
\(830\) | 1.15184e101i | 0.0782812i | ||||||||
\(831\) | −1.18408e100 | − | 2.73915e101i | −0.00771518 | − | 0.178476i | ||||
\(832\) | 3.86632e102 | 2.41536 | ||||||||
\(833\) | − | 1.39047e102i | − | 0.832889i | ||||||
\(834\) | −4.41272e102 | + | 1.90753e101i | −2.53451 | + | 0.109562i | ||||
\(835\) | −9.87489e101 | −0.543883 | ||||||||
\(836\) | − | 3.02335e102i | − | 1.59686i | ||||||
\(837\) | −2.96668e101 | − | 2.27621e102i | −0.150273 | − | 1.15298i | ||||
\(838\) | −3.48593e102 | −1.69347 | ||||||||
\(839\) | 6.38125e101i | 0.297329i | 0.988888 | + | 0.148664i | \(0.0474974\pi\) | ||||
−0.988888 | + | 0.148664i | \(0.952503\pi\) | |||||||
\(840\) | 5.75191e100 | + | 1.33060e102i | 0.0257061 | + | 0.594663i | ||||
\(841\) | 2.30208e102 | 0.986872 | ||||||||
\(842\) | 3.11933e102i | 1.28274i | ||||||||
\(843\) | 4.36590e101 | − | 1.88729e100i | 0.172230 | − | 0.00744516i | ||||
\(844\) | −1.36079e102 | −0.514996 | ||||||||
\(845\) | 3.61602e102i | 1.31294i | ||||||||
\(846\) | −7.01587e102 | + | 6.07701e101i | −2.44410 | + | 0.211703i | ||||
\(847\) | −3.96422e101 | −0.132507 | ||||||||
\(848\) | − | 7.92970e101i | − | 0.254332i | ||||||
\(849\) | −1.78998e101 | − | 4.14078e102i | −0.0550907 | − | 1.27442i | ||||
\(850\) | 1.28745e102 | 0.380248 | ||||||||
\(851\) | 2.85348e102i | 0.808799i | ||||||||
\(852\) | 6.16118e102 | − | 2.66336e101i | 1.67602 | − | 0.0724509i | ||||
\(853\) | −1.42229e102 | −0.371341 | −0.185671 | − | 0.982612i | \(-0.559446\pi\) | ||||
−0.185671 | + | 0.982612i | \(0.559446\pi\) | |||||||
\(854\) | 2.93405e102i | 0.735263i | ||||||||
\(855\) | −3.41755e101 | − | 3.94555e102i | −0.0822056 | − | 0.949060i | ||||
\(856\) | 5.67224e102 | 1.30970 | ||||||||
\(857\) | 5.12401e101i | 0.113575i | 0.998386 | + | 0.0567873i | \(0.0180857\pi\) | ||||
−0.998386 | + | 0.0567873i | \(0.981914\pi\) | |||||||
\(858\) | 4.58306e101 | + | 1.06020e103i | 0.0975215 | + | 2.25598i | ||||
\(859\) | −3.97003e102 | −0.811023 | −0.405512 | − | 0.914090i | \(-0.632907\pi\) | ||||
−0.405512 | + | 0.914090i | \(0.632907\pi\) | |||||||
\(860\) | 5.34849e102i | 1.04902i | ||||||||
\(861\) | 3.28218e102 | − | 1.41882e101i | 0.618091 | − | 0.0267189i | ||||
\(862\) | 9.16952e102 | 1.65803 | ||||||||
\(863\) | − | 3.08511e102i | − | 0.535665i | −0.963465 | − | 0.267833i | \(-0.913693\pi\) | ||
0.963465 | − | 0.267833i | \(-0.0863074\pi\) | |||||||
\(864\) | 4.60939e102 | − | 6.00760e101i | 0.768532 | − | 0.100166i | ||||
\(865\) | 2.31953e102 | 0.371395 | ||||||||
\(866\) | − | 1.79368e102i | − | 0.275816i | ||||||
\(867\) | −1.25123e101 | − | 2.89448e102i | −0.0184786 | − | 0.427467i | ||||
\(868\) | 7.79946e102 | 1.10630 | ||||||||
\(869\) | − | 3.09743e102i | − | 0.421997i | ||||||
\(870\) | −1.29829e102 | + | 5.61226e100i | −0.169902 | + | 0.00734453i | ||||
\(871\) | −1.80659e103 | −2.27104 | ||||||||
\(872\) | − | 7.17913e102i | − | 0.866952i | ||||||
\(873\) | −1.34264e103 | + | 1.16297e102i | −1.55762 | + | 0.134918i | ||||
\(874\) | −1.78127e103 | −1.98532 | ||||||||
\(875\) | − | 5.50851e102i | − | 0.589865i | ||||||
\(876\) | 1.25553e102 | + | 2.90444e103i | 0.129177 | + | 2.98826i | ||||
\(877\) | 2.19361e102 | 0.216857 | 0.108429 | − | 0.994104i | \(-0.465418\pi\) | ||||
0.108429 | + | 0.994104i | \(0.465418\pi\) | |||||||
\(878\) | 5.90060e101i | 0.0560516i | ||||||||
\(879\) | −1.75864e102 | + | 7.60226e100i | −0.160534 | + | 0.00693957i | ||||
\(880\) | −2.31496e102 | −0.203072 | ||||||||
\(881\) | 1.00108e103i | 0.843941i | 0.906610 | + | 0.421971i | \(0.138661\pi\) | ||||
−0.906610 | + | 0.421971i | \(0.861339\pi\) | |||||||
\(882\) | −1.22630e102 | − | 1.41575e103i | −0.0993563 | − | 1.14706i | ||||
\(883\) | 8.39073e102 | 0.653394 | 0.326697 | − | 0.945129i | \(-0.394064\pi\) | ||||
0.326697 | + | 0.945129i | \(0.394064\pi\) | |||||||
\(884\) | − | 4.32945e103i | − | 3.24044i | ||||||
\(885\) | −4.29093e101 | − | 9.92626e102i | −0.0308700 | − | 0.714120i | ||||
\(886\) | 1.68446e102 | 0.116487 | ||||||||
\(887\) | − | 2.96647e101i | − | 0.0197203i | −0.999951 | − | 0.00986016i | \(-0.996861\pi\) | ||
0.999951 | − | 0.00986016i | \(-0.00313864\pi\) | |||||||
\(888\) | 1.34228e103 | − | 5.80243e101i | 0.857809 | − | 0.0370814i | ||||
\(889\) | −1.44779e102 | −0.0889499 | ||||||||
\(890\) | − | 3.73170e103i | − | 2.20423i | ||||||
\(891\) | 2.63821e102 | + | 1.51148e103i | 0.149827 | + | 0.858384i | ||||
\(892\) | 2.73662e103 | 1.49432 | ||||||||
\(893\) | 2.99889e103i | 1.57456i | ||||||||
\(894\) | −7.69113e101 | − | 1.77920e103i | −0.0388309 | − | 0.898280i | ||||
\(895\) | 5.64150e102 | 0.273898 | ||||||||
\(896\) | 2.08451e103i | 0.973248i | ||||||||
\(897\) | 3.95716e103 | − | 1.71060e102i | 1.77684 | − | 0.0768094i | ||||
\(898\) | −6.11355e103 | −2.64011 | ||||||||
\(899\) | 3.20755e102i | 0.133224i | ||||||||
\(900\) | 8.30437e102 | − | 7.19308e101i | 0.331756 | − | 0.0287360i | ||||
\(901\) | 3.04925e103 | 1.17173 | ||||||||
\(902\) | 4.37666e103i | 1.61776i | ||||||||
\(903\) | 4.51553e101 | + | 1.04458e103i | 0.0160560 | + | 0.371425i | ||||
\(904\) | −5.04787e103 | −1.72668 | ||||||||
\(905\) | − | 3.32433e102i | − | 0.109397i | ||||||
\(906\) | 3.83678e103 | − | 1.65856e102i | 1.21473 | − | 0.0525104i | ||||
\(907\) | −3.93503e101 | −0.0119865 | −0.00599326 | − | 0.999982i | \(-0.501908\pi\) | ||||
−0.00599326 | + | 0.999982i | \(0.501908\pi\) | |||||||
\(908\) | 6.14408e103i | 1.80074i | ||||||||
\(909\) | −4.03837e102 | − | 4.66227e103i | −0.113886 | − | 1.31481i | ||||
\(910\) | −4.72315e103 | −1.28169 | ||||||||
\(911\) | − | 1.58636e103i | − | 0.414245i | −0.978315 | − | 0.207123i | \(-0.933590\pi\) | ||
0.978315 | − | 0.207123i | \(-0.0664099\pi\) | |||||||
\(912\) | 4.72589e101 | + | 1.09325e103i | 0.0118758 | + | 0.274725i | ||||
\(913\) | −1.90035e102 | −0.0459575 | ||||||||
\(914\) | − | 3.60070e103i | − | 0.838050i | ||||||
\(915\) | −3.24065e103 | + | 1.40087e102i | −0.725928 | + | 0.0313804i | ||||
\(916\) | −3.10753e103 | −0.669999 | ||||||||
\(917\) | 3.87014e103i | 0.803157i | ||||||||
\(918\) | −1.27704e103 | − | 9.79822e103i | −0.255100 | − | 1.95728i | ||||
\(919\) | 3.54574e103 | 0.681812 | 0.340906 | − | 0.940097i | \(-0.389266\pi\) | ||||
0.340906 | + | 0.940097i | \(0.389266\pi\) | |||||||
\(920\) | 6.62248e103i | 1.22588i | ||||||||
\(921\) | 3.38598e102 | + | 7.83284e103i | 0.0603389 | + | 1.39583i | ||||
\(922\) | 4.73399e103 | 0.812167 | ||||||||
\(923\) | 9.21790e103i | 1.52255i | ||||||||
\(924\) | −5.20843e103 | + | 2.25150e102i | −0.828300 | + | 0.0358058i | ||||
\(925\) | −8.97591e102 | −0.137441 | ||||||||
\(926\) | − | 6.61933e103i | − | 0.975954i | ||||||
\(927\) | 4.01477e103 | − | 3.47751e102i | 0.569994 | − | 0.0493717i | ||||
\(928\) | −6.49536e102 | −0.0888022 | ||||||||
\(929\) | 9.90227e101i | 0.0130372i | 0.999979 | + | 0.00651861i | \(0.00207495\pi\) | ||||
−0.999979 | + | 0.00651861i | \(0.997925\pi\) | |||||||
\(930\) | 5.87817e102 | + | 1.35981e104i | 0.0745314 | + | 1.72414i | ||||
\(931\) | −6.05155e103 | −0.738971 | ||||||||
\(932\) | − | 1.17649e104i | − | 1.38367i | ||||||
\(933\) | −1.31422e103 | + | 5.68111e101i | −0.148871 | + | 0.00643540i | ||||
\(934\) | 2.60898e104 | 2.84662 | ||||||||
\(935\) | − | 8.90186e103i | − | 0.935566i | ||||||
\(936\) | −1.60934e103 | − | 1.85798e104i | −0.162927 | − | 1.88099i | ||||
\(937\) | −7.91783e103 | −0.772183 | −0.386092 | − | 0.922460i | \(-0.626175\pi\) | ||||
−0.386092 | + | 0.922460i | \(0.626175\pi\) | |||||||
\(938\) | − | 1.40096e104i | − | 1.31622i | ||||||
\(939\) | 2.53636e102 | + | 5.86740e103i | 0.0229570 | + | 0.531068i | ||||
\(940\) | 2.64526e104 | 2.30671 | ||||||||
\(941\) | − | 1.10499e104i | − | 0.928370i | −0.885738 | − | 0.464185i | \(-0.846347\pi\) | ||
0.885738 | − | 0.464185i | \(-0.153653\pi\) | |||||||
\(942\) | −2.10846e104 | + | 9.11445e102i | −1.70680 | + | 0.0737817i | ||||
\(943\) | 1.63357e104 | 1.27417 | ||||||||
\(944\) | 2.74526e103i | 0.206331i | ||||||||
\(945\) | −6.77169e103 | + | 8.82582e102i | −0.490438 | + | 0.0639207i | ||||
\(946\) | −1.39291e104 | −0.972150 | ||||||||
\(947\) | 4.56532e103i | 0.307059i | 0.988144 | + | 0.153530i | \(0.0490640\pi\) | ||||
−0.988144 | + | 0.153530i | \(0.950936\pi\) | |||||||
\(948\) | 5.57762e102 | + | 1.29028e104i | 0.0361540 | + | 0.836356i | ||||
\(949\) | −4.34540e104 | −2.71464 | ||||||||
\(950\) | − | 5.60317e103i | − | 0.337371i | ||||||
\(951\) | 4.19771e103 | − | 1.81459e102i | 0.243610 | − | 0.0105308i | ||||
\(952\) | 1.41508e104 | 0.791567 | ||||||||
\(953\) | 4.31607e103i | 0.232722i | 0.993207 | + | 0.116361i | \(0.0371229\pi\) | ||||
−0.993207 | + | 0.116361i | \(0.962877\pi\) | |||||||
\(954\) | 3.10470e104 | − | 2.68923e103i | 1.61371 | − | 0.139777i | ||||
\(955\) | −4.35880e102 | −0.0218398 | ||||||||
\(956\) | − | 1.37816e103i | − | 0.0665692i | ||||||
\(957\) | −9.25935e101 | − | 2.14198e103i | −0.00431184 | − | 0.0997464i | ||||
\(958\) | −1.03671e104 | −0.465439 | ||||||||
\(959\) | − | 9.84876e103i | − | 0.426314i | ||||||
\(960\) | −3.31152e104 | + | 1.43150e103i | −1.38208 | + | 0.0597447i | ||||
\(961\) | 8.74567e103 | 0.351945 | ||||||||
\(962\) | 4.76464e104i | 1.84885i | ||||||||
\(963\) | 2.50982e103 | + | 2.89758e104i | 0.0939124 | + | 1.08421i | ||||
\(964\) | −3.32212e104 | −1.19872 | ||||||||
\(965\) | − | 4.27339e104i | − | 1.48702i | ||||||
\(966\) | 1.32653e103 | + | 3.06867e104i | 0.0445160 | + | 1.02979i | ||||
\(967\) | 6.85055e103 | 0.221717 | 0.110858 | − | 0.993836i | \(-0.464640\pi\) | ||||
0.110858 | + | 0.993836i | \(0.464640\pi\) | |||||||
\(968\) | 9.28114e103i | 0.289710i | ||||||||
\(969\) | −4.20392e104 | + | 1.81727e103i | −1.26568 | + | 0.0547127i | ||||
\(970\) | 7.99087e104 | 2.32051 | ||||||||
\(971\) | − | 5.89247e104i | − | 1.65053i | −0.564744 | − | 0.825266i | \(-0.691025\pi\) | ||
0.564744 | − | 0.825266i | \(-0.308975\pi\) | |||||||
\(972\) | −1.37116e104 | − | 6.24875e104i | −0.370483 | − | 1.68839i | ||||
\(973\) | 3.24333e104 | 0.845360 | ||||||||
\(974\) | 1.16588e105i | 2.93150i | ||||||||
\(975\) | 5.38087e102 | + | 1.24476e104i | 0.0130524 | + | 0.301943i | ||||
\(976\) | 8.96251e103 | 0.209742 | ||||||||
\(977\) | 4.70080e104i | 1.06136i | 0.847573 | + | 0.530680i | \(0.178063\pi\) | ||||
−0.847573 | + | 0.530680i | \(0.821937\pi\) | |||||||
\(978\) | −6.56887e103 | + | 2.83959e102i | −0.143097 | + | 0.00618581i | ||||
\(979\) | 6.15672e104 | 1.29406 | ||||||||
\(980\) | 5.33794e104i | 1.08258i | ||||||||
\(981\) | 3.66735e104 | − | 3.17658e103i | 0.717690 | − | 0.0621649i | ||||
\(982\) | 1.78441e104 | 0.336970 | ||||||||
\(983\) | − | 3.35312e104i | − | 0.611049i | −0.952184 | − | 0.305524i | \(-0.901168\pi\) | ||
0.952184 | − | 0.305524i | \(-0.0988318\pi\) | |||||||
\(984\) | −3.32179e103 | − | 7.68434e104i | −0.0584176 | − | 1.35138i | ||||
\(985\) | 2.33618e104 | 0.396496 | ||||||||
\(986\) | 1.38072e104i | 0.226160i | ||||||||
\(987\) | 5.16630e104 | − | 2.23329e103i | 0.816731 | − | 0.0353057i | ||||
\(988\) | −1.88424e105 | −2.87504 | ||||||||
\(989\) | 5.19897e104i | 0.765680i | ||||||||
\(990\) | −7.85081e103 | − | 9.06372e104i | −0.111605 | − | 1.28847i | ||||
\(991\) | −5.86446e104 | −0.804730 | −0.402365 | − | 0.915479i | \(-0.631812\pi\) | ||||
−0.402365 | + | 0.915479i | \(0.631812\pi\) | |||||||
\(992\) | 6.80311e104i | 0.901154i | ||||||||
\(993\) | −3.15282e103 | − | 7.29347e104i | −0.0403159 | − | 0.932632i | ||||
\(994\) | −7.14821e104 | −0.882418 | ||||||||
\(995\) | − | 1.02873e105i | − | 1.22601i | ||||||
\(996\) | 7.91616e103 | − | 3.42200e102i | 0.0910831 | − | 0.00393735i | ||||
\(997\) | −3.40988e104 | −0.378799 | −0.189399 | − | 0.981900i | \(-0.560654\pi\) | ||||
−0.189399 | + | 0.981900i | \(0.560654\pi\) | |||||||
\(998\) | − | 2.45207e105i | − | 2.63004i | ||||||
\(999\) | 8.90335e103 | + | 6.83118e104i | 0.0922064 | + | 0.707462i |
(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 | 3.71.b.a.2.3 | ✓ | 22 | |
3.2 | odd | 2 | inner | 3.71.b.a.2.20 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.71.b.a.2.3 | ✓ | 22 | 1.1 | even | 1 | trivial | |
3.71.b.a.2.20 | yes | 22 | 3.2 | odd | 2 | inner |