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 | 2.6 | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.71.b.a.2.17 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.74673e10i | − | 1.09044i | −0.838292 | − | 0.545221i | \(-0.816446\pi\) | ||
0.838292 | − | 0.545221i | \(-0.183554\pi\) | |||||||
\(3\) | −7.56180e15 | − | 4.94568e16i | −0.151141 | − | 0.988512i | ||||
\(4\) | −2.23206e20 | −0.189063 | ||||||||
\(5\) | 1.07403e24i | 0.369033i | 0.982829 | + | 0.184516i | \(0.0590719\pi\) | ||||
−0.982829 | + | 0.184516i | \(0.940928\pi\) | |||||||
\(6\) | −1.85301e27 | + | 2.83320e26i | −1.07791 | + | 0.164810i | ||||
\(7\) | 6.73954e29 | 1.77909 | 0.889547 | − | 0.456844i | \(-0.151020\pi\) | ||||
0.889547 | + | 0.456844i | \(0.151020\pi\) | |||||||
\(8\) | − | 3.58706e31i | − | 0.884279i | ||||||
\(9\) | −2.38879e33 | + | 7.47965e32i | −0.954313 | + | 0.298809i | ||||
\(10\) | 4.02409e34 | 0.402409 | ||||||||
\(11\) | 9.56510e35i | 0.340365i | 0.985413 | + | 0.170183i | \(0.0544358\pi\) | ||||
−0.985413 | + | 0.170183i | \(0.945564\pi\) | |||||||
\(12\) | 1.68784e36 | + | 1.10391e37i | 0.0285751 | + | 0.186891i | ||||
\(13\) | 9.40335e38 | 0.966641 | 0.483321 | − | 0.875443i | \(-0.339431\pi\) | ||||
0.483321 | + | 0.875443i | \(0.339431\pi\) | |||||||
\(14\) | − | 2.52512e40i | − | 1.94000i | ||||||
\(15\) | 5.31179e40 | − | 8.12158e39i | 0.364793 | − | 0.0557759i | ||||
\(16\) | −1.60749e42 | −1.15332 | ||||||||
\(17\) | 1.38452e43i | 1.19011i | 0.803686 | + | 0.595054i | \(0.202869\pi\) | ||||
−0.803686 | + | 0.595054i | \(0.797131\pi\) | |||||||
\(18\) | 2.80242e43 | + | 8.95016e43i | 0.325834 | + | 1.04062i | ||||
\(19\) | −4.21700e44 | −0.738971 | −0.369485 | − | 0.929237i | \(-0.620466\pi\) | ||||
−0.369485 | + | 0.929237i | \(0.620466\pi\) | |||||||
\(20\) | − | 2.39729e44i | − | 0.0697705i | ||||||
\(21\) | −5.09631e45 | − | 3.33316e46i | −0.268893 | − | 1.75866i | ||||
\(22\) | 3.58378e46 | 0.371149 | ||||||||
\(23\) | 7.41679e47i | 1.62085i | 0.585845 | + | 0.810423i | \(0.300763\pi\) | ||||
−0.585845 | + | 0.810423i | \(0.699237\pi\) | |||||||
\(24\) | −1.77405e48 | + | 2.71247e47i | −0.874121 | + | 0.133651i | ||||
\(25\) | 7.31680e48 | 0.863815 | ||||||||
\(26\) | − | 3.52318e49i | − | 1.05407i | ||||||
\(27\) | 5.50556e49 | + | 1.12486e50i | 0.439612 | + | 0.898188i | ||||
\(28\) | −1.50431e50 | −0.336361 | ||||||||
\(29\) | 6.56664e50i | 0.429945i | 0.976620 | + | 0.214973i | \(0.0689663\pi\) | ||||
−0.976620 | + | 0.214973i | \(0.931034\pi\) | |||||||
\(30\) | −3.04294e50 | − | 1.99018e51i | −0.0608203 | − | 0.397786i | ||||
\(31\) | 2.15139e52 | 1.36477 | 0.682386 | − | 0.730992i | \(-0.260942\pi\) | ||||
0.682386 | + | 0.730992i | \(0.260942\pi\) | |||||||
\(32\) | 1.78798e52i | 0.373347i | ||||||||
\(33\) | 4.73059e52 | − | 7.23294e51i | 0.336455 | − | 0.0514431i | ||||
\(34\) | 5.18742e53 | 1.29774 | ||||||||
\(35\) | 7.23844e53i | 0.656544i | ||||||||
\(36\) | 5.33194e53 | − | 1.66951e53i | 0.180425 | − | 0.0564937i | ||||
\(37\) | 4.93106e54 | 0.639559 | 0.319779 | − | 0.947492i | \(-0.396391\pi\) | ||||
0.319779 | + | 0.947492i | \(0.396391\pi\) | |||||||
\(38\) | 1.57999e55i | 0.805804i | ||||||||
\(39\) | −7.11063e54 | − | 4.65060e55i | −0.146099 | − | 0.955537i | ||||
\(40\) | 3.85260e55 | 0.326328 | ||||||||
\(41\) | − | 5.23895e55i | − | 0.186986i | −0.995620 | − | 0.0934930i | \(-0.970197\pi\) | ||
0.995620 | − | 0.0934930i | \(-0.0298033\pi\) | |||||||
\(42\) | −1.24884e57 | + | 1.90945e56i | −1.91771 | + | 0.293213i | ||||
\(43\) | 1.48232e57 | 0.998958 | 0.499479 | − | 0.866326i | \(-0.333525\pi\) | ||||
0.499479 | + | 0.866326i | \(0.333525\pi\) | |||||||
\(44\) | − | 2.13499e56i | − | 0.0643505i | ||||||
\(45\) | −8.03335e56 | − | 2.56563e57i | −0.110270 | − | 0.352173i | ||||
\(46\) | 2.77887e58 | 1.76744 | ||||||||
\(47\) | 1.27739e58i | 0.382735i | 0.981518 | + | 0.191367i | \(0.0612922\pi\) | ||||
−0.981518 | + | 0.191367i | \(0.938708\pi\) | |||||||
\(48\) | 1.21555e58 | + | 7.95014e58i | 0.174313 | + | 1.14007i | ||||
\(49\) | 3.10710e59 | 2.16517 | ||||||||
\(50\) | − | 2.74141e59i | − | 0.941940i | ||||||
\(51\) | 6.84738e59 | − | 1.04695e59i | 1.17644 | − | 0.179874i | ||||
\(52\) | −2.09889e59 | −0.182756 | ||||||||
\(53\) | 3.94947e60i | 1.76556i | 0.469782 | + | 0.882782i | \(0.344332\pi\) | ||||
−0.469782 | + | 0.882782i | \(0.655668\pi\) | |||||||
\(54\) | 4.21455e60 | − | 2.06278e60i | 0.979421 | − | 0.479371i | ||||
\(55\) | −1.02732e60 | −0.125606 | ||||||||
\(56\) | − | 2.41752e61i | − | 1.57322i | ||||||
\(57\) | 3.18881e60 | + | 2.08559e61i | 0.111689 | + | 0.730481i | ||||
\(58\) | 2.46034e61 | 0.468830 | ||||||||
\(59\) | 9.57573e61i | 1.00312i | 0.865124 | + | 0.501558i | \(0.167240\pi\) | ||||
−0.865124 | + | 0.501558i | \(0.832760\pi\) | |||||||
\(60\) | −1.18563e61 | + | 1.81279e60i | −0.0689689 | + | 0.0105452i | ||||
\(61\) | −2.37768e61 | −0.0775549 | −0.0387774 | − | 0.999248i | \(-0.512346\pi\) | ||||
−0.0387774 | + | 0.999248i | \(0.512346\pi\) | |||||||
\(62\) | − | 8.06068e62i | − | 1.48820i | ||||||
\(63\) | −1.60994e63 | + | 5.04094e62i | −1.69781 | + | 0.531609i | ||||
\(64\) | −1.22788e63 | −0.746205 | ||||||||
\(65\) | 1.00994e63i | 0.356722i | ||||||||
\(66\) | −2.70999e62 | − | 1.77242e63i | −0.0560957 | − | 0.366885i | ||||
\(67\) | −8.71513e63 | −1.06575 | −0.532875 | − | 0.846194i | \(-0.678889\pi\) | ||||
−0.532875 | + | 0.846194i | \(0.678889\pi\) | |||||||
\(68\) | − | 3.09033e63i | − | 0.225005i | ||||||
\(69\) | 3.66811e64 | − | 5.60843e63i | 1.60223 | − | 0.244976i | ||||
\(70\) | 2.71205e64 | 0.715923 | ||||||||
\(71\) | 4.27746e64i | 0.687296i | 0.939098 | + | 0.343648i | \(0.111663\pi\) | ||||
−0.939098 | + | 0.343648i | \(0.888337\pi\) | |||||||
\(72\) | 2.68300e64 | + | 8.56876e64i | 0.264231 | + | 0.843879i | ||||
\(73\) | 1.50425e65 | 0.914156 | 0.457078 | − | 0.889427i | \(-0.348896\pi\) | ||||
0.457078 | + | 0.889427i | \(0.348896\pi\) | |||||||
\(74\) | − | 1.84754e65i | − | 0.697401i | ||||||
\(75\) | −5.53282e64 | − | 3.61865e65i | −0.130558 | − | 0.853892i | ||||
\(76\) | 9.41260e64 | 0.139712 | ||||||||
\(77\) | 6.44644e65i | 0.605542i | ||||||||
\(78\) | −1.74245e66 | + | 2.66416e65i | −1.04196 | + | 0.159312i | ||||
\(79\) | −2.81029e66 | −1.07598 | −0.537988 | − | 0.842952i | \(-0.680815\pi\) | ||||
−0.537988 | + | 0.842952i | \(0.680815\pi\) | |||||||
\(80\) | − | 1.72649e66i | − | 0.425612i | ||||||
\(81\) | 5.14688e66 | − | 3.57347e66i | 0.821426 | − | 0.570314i | ||||
\(82\) | −1.96289e66 | −0.203897 | ||||||||
\(83\) | 1.40793e66i | 0.0956856i | 0.998855 | + | 0.0478428i | \(0.0152346\pi\) | ||||
−0.998855 | + | 0.0478428i | \(0.984765\pi\) | |||||||
\(84\) | 1.13753e66 | + | 7.43982e66i | 0.0508378 | + | 0.332497i | ||||
\(85\) | −1.48701e67 | −0.439189 | ||||||||
\(86\) | − | 5.55387e67i | − | 1.08931i | ||||||
\(87\) | 3.24765e67 | − | 4.96556e66i | 0.425006 | − | 0.0649823i | ||||
\(88\) | 3.43106e67 | 0.300978 | ||||||||
\(89\) | − | 8.71916e67i | − | 0.515020i | −0.966276 | − | 0.257510i | \(-0.917098\pi\) | ||
0.966276 | − | 0.257510i | \(-0.0829021\pi\) | |||||||
\(90\) | −9.61271e67 | + | 3.00988e67i | −0.384024 | + | 0.120243i | ||||
\(91\) | 6.33743e68 | 1.71975 | ||||||||
\(92\) | − | 1.65547e68i | − | 0.306442i | ||||||
\(93\) | −1.62684e68 | − | 1.06401e69i | −0.206273 | − | 1.34909i | ||||
\(94\) | 4.78603e68 | 0.417350 | ||||||||
\(95\) | − | 4.52917e68i | − | 0.272704i | ||||||
\(96\) | 8.84276e68 | − | 1.35203e68i | 0.369058 | − | 0.0564279i | ||||
\(97\) | −5.94495e69 | −1.72639 | −0.863193 | − | 0.504875i | \(-0.831539\pi\) | ||||
−0.863193 | + | 0.504875i | \(0.831539\pi\) | |||||||
\(98\) | − | 1.16415e70i | − | 2.36100i | ||||||
\(99\) | −7.15436e68 | − | 2.28491e69i | −0.101704 | − | 0.324815i | ||||
\(100\) | −1.63315e69 | −0.163315 | ||||||||
\(101\) | − | 6.40697e69i | − | 0.452277i | −0.974095 | − | 0.226139i | \(-0.927390\pi\) | ||
0.974095 | − | 0.226139i | \(-0.0726102\pi\) | |||||||
\(102\) | −3.92262e69 | − | 2.56553e70i | −0.196142 | − | 1.28284i | ||||
\(103\) | 1.41045e70 | 0.501251 | 0.250625 | − | 0.968084i | \(-0.419364\pi\) | ||||
0.250625 | + | 0.968084i | \(0.419364\pi\) | |||||||
\(104\) | − | 3.37304e70i | − | 0.854781i | ||||||
\(105\) | 3.57990e70 | − | 5.47357e69i | 0.649002 | − | 0.0992305i | ||||
\(106\) | 1.47976e71 | 1.92525 | ||||||||
\(107\) | − | 1.78393e71i | − | 1.67088i | −0.549578 | − | 0.835442i | \(-0.685212\pi\) | ||
0.549578 | − | 0.835442i | \(-0.314788\pi\) | |||||||
\(108\) | −1.22887e70 | − | 2.51076e70i | −0.0831144 | − | 0.169814i | ||||
\(109\) | 7.39284e70 | 0.362146 | 0.181073 | − | 0.983470i | \(-0.442043\pi\) | ||||
0.181073 | + | 0.983470i | \(0.442043\pi\) | |||||||
\(110\) | 3.84908e70i | 0.136966i | ||||||||
\(111\) | −3.72877e70 | − | 2.43875e71i | −0.0966634 | − | 0.632212i | ||||
\(112\) | −1.08337e72 | −2.05186 | ||||||||
\(113\) | − | 8.68793e71i | − | 1.20551i | −0.797926 | − | 0.602755i | \(-0.794070\pi\) | ||
0.797926 | − | 0.602755i | \(-0.205930\pi\) | |||||||
\(114\) | 7.81414e71 | − | 1.19476e71i | 0.796547 | − | 0.121790i | ||||
\(115\) | −7.96583e71 | −0.598145 | ||||||||
\(116\) | − | 1.46572e71i | − | 0.0812868i | ||||||
\(117\) | −2.24627e72 | + | 7.03338e71i | −0.922478 | + | 0.288841i | ||||
\(118\) | 3.58777e72 | 1.09384 | ||||||||
\(119\) | 9.33101e72i | 2.11731i | ||||||||
\(120\) | −2.91326e71 | − | 1.90537e72i | −0.0493215 | − | 0.322579i | ||||
\(121\) | 6.98256e72 | 0.884151 | ||||||||
\(122\) | 8.90852e71i | 0.0845691i | ||||||||
\(123\) | −2.59101e72 | + | 3.96159e71i | −0.184838 | + | 0.0282612i | ||||
\(124\) | −4.80204e72 | −0.258028 | ||||||||
\(125\) | 1.69558e73i | 0.687809i | ||||||||
\(126\) | 1.88870e73 | + | 6.03200e73i | 0.579689 | + | 1.85136i | ||||
\(127\) | −4.17415e73 | −0.971490 | −0.485745 | − | 0.874101i | \(-0.661452\pi\) | ||||
−0.485745 | + | 0.874101i | \(0.661452\pi\) | |||||||
\(128\) | 6.71142e73i | 1.18704i | ||||||||
\(129\) | −1.12090e73 | − | 7.33110e73i | −0.150983 | − | 0.987482i | ||||
\(130\) | 3.78399e73 | 0.388985 | ||||||||
\(131\) | 4.79654e73i | 0.377079i | 0.982066 | + | 0.188540i | \(0.0603754\pi\) | ||||
−0.982066 | + | 0.188540i | \(0.939625\pi\) | |||||||
\(132\) | −1.05590e73 | + | 1.61444e72i | −0.0636113 | + | 0.00972599i | ||||
\(133\) | −2.84206e74 | −1.31470 | ||||||||
\(134\) | 3.26532e74i | 1.16214i | ||||||||
\(135\) | −1.20813e74 | + | 5.91311e73i | −0.331461 | + | 0.162231i | ||||
\(136\) | 4.96636e74 | 1.05239 | ||||||||
\(137\) | − | 3.85815e74i | − | 0.632643i | −0.948652 | − | 0.316322i | \(-0.897552\pi\) | ||
0.948652 | − | 0.316322i | \(-0.102448\pi\) | |||||||
\(138\) | −2.10133e74 | − | 1.37434e75i | −0.267132 | − | 1.74713i | ||||
\(139\) | −2.92083e73 | −0.0288395 | −0.0144198 | − | 0.999896i | \(-0.504590\pi\) | ||||
−0.0144198 | + | 0.999896i | \(0.504590\pi\) | |||||||
\(140\) | − | 1.61567e74i | − | 0.124128i | ||||||
\(141\) | 6.31755e74 | − | 9.65936e73i | 0.378338 | − | 0.0578468i | ||||
\(142\) | 1.60265e75 | 0.749457 | ||||||||
\(143\) | 8.99440e74i | 0.329011i | ||||||||
\(144\) | 3.83996e75 | − | 1.20235e75i | 1.10063 | − | 0.344622i | ||||
\(145\) | −7.05275e74 | −0.158664 | ||||||||
\(146\) | − | 5.63602e75i | − | 0.996834i | ||||||
\(147\) | −2.34953e75 | − | 1.53667e76i | −0.327246 | − | 2.14030i | ||||
\(148\) | −1.10064e75 | −0.120917 | ||||||||
\(149\) | 7.65280e75i | 0.664204i | 0.943244 | + | 0.332102i | \(0.107758\pi\) | ||||
−0.943244 | + | 0.332102i | \(0.892242\pi\) | |||||||
\(150\) | −1.35581e76 | + | 2.07300e75i | −0.931119 | + | 0.142365i | ||||
\(151\) | −1.71428e76 | −0.933016 | −0.466508 | − | 0.884517i | \(-0.654488\pi\) | ||||
−0.466508 | + | 0.884517i | \(0.654488\pi\) | |||||||
\(152\) | 1.51266e76i | 0.653456i | ||||||||
\(153\) | −1.03557e76 | − | 3.30733e76i | −0.355615 | − | 1.13574i | ||||
\(154\) | 2.41530e76 | 0.660308 | ||||||||
\(155\) | 2.31065e76i | 0.503646i | ||||||||
\(156\) | 1.58714e75 | + | 1.03804e76i | 0.0276219 | + | 0.180657i | ||||
\(157\) | 4.83802e76 | 0.673256 | 0.336628 | − | 0.941638i | \(-0.390714\pi\) | ||||
0.336628 | + | 0.941638i | \(0.390714\pi\) | |||||||
\(158\) | 1.05294e77i | 1.17329i | ||||||||
\(159\) | 1.95328e77 | − | 2.98651e76i | 1.74528 | − | 0.266849i | ||||
\(160\) | −1.92033e76 | −0.137777 | ||||||||
\(161\) | 4.99857e77i | 2.88364i | ||||||||
\(162\) | −1.33888e77 | − | 1.92840e77i | −0.621895 | − | 0.895718i | ||||
\(163\) | −2.68918e77 | −1.00706 | −0.503528 | − | 0.863979i | \(-0.667965\pi\) | ||||
−0.503528 | + | 0.863979i | \(0.667965\pi\) | |||||||
\(164\) | 1.16937e76i | 0.0353521i | ||||||||
\(165\) | 7.76837e75 | + | 5.08078e76i | 0.0189842 | + | 0.124163i | ||||
\(166\) | 5.27512e76 | 0.104340 | ||||||||
\(167\) | − | 2.52508e76i | − | 0.0404761i | −0.999795 | − | 0.0202380i | \(-0.993558\pi\) | ||
0.999795 | − | 0.0202380i | \(-0.00644241\pi\) | |||||||
\(168\) | −1.19563e78 | + | 1.82808e77i | −1.55514 | + | 0.237777i | ||||
\(169\) | −6.20825e76 | −0.0656046 | ||||||||
\(170\) | 5.57142e77i | 0.478910i | ||||||||
\(171\) | 1.00735e78 | − | 3.15417e77i | 0.705209 | − | 0.220811i | ||||
\(172\) | −3.30864e77 | −0.188866 | ||||||||
\(173\) | − | 1.78943e78i | − | 0.833877i | −0.908935 | − | 0.416938i | \(-0.863103\pi\) | ||
0.908935 | − | 0.416938i | \(-0.136897\pi\) | |||||||
\(174\) | −1.86046e77 | − | 1.21681e78i | −0.0708594 | − | 0.463445i | ||||
\(175\) | 4.93118e78 | 1.53681 | ||||||||
\(176\) | − | 1.53758e78i | − | 0.392550i | ||||||
\(177\) | 4.73585e78 | − | 7.24098e77i | 0.991593 | − | 0.151612i | ||||
\(178\) | −3.26683e78 | −0.561600 | ||||||||
\(179\) | − | 3.48527e78i | − | 0.492471i | −0.969210 | − | 0.246235i | \(-0.920806\pi\) | ||
0.969210 | − | 0.246235i | \(-0.0791937\pi\) | |||||||
\(180\) | 1.79309e77 | + | 5.72664e77i | 0.0208480 | + | 0.0665828i | ||||
\(181\) | −1.09292e79 | −1.04674 | −0.523371 | − | 0.852105i | \(-0.675326\pi\) | ||||
−0.523371 | + | 0.852105i | \(0.675326\pi\) | |||||||
\(182\) | − | 2.37446e79i | − | 1.87528i | ||||||
\(183\) | 1.79795e77 | + | 1.17592e78i | 0.0117217 | + | 0.0766639i | ||||
\(184\) | 2.66045e79 | 1.43328 | ||||||||
\(185\) | 5.29610e78i | 0.236018i | ||||||||
\(186\) | −3.98655e79 | + | 6.09533e78i | −1.47111 | + | 0.224928i | ||||
\(187\) | −1.32431e79 | −0.405072 | ||||||||
\(188\) | − | 2.85121e78i | − | 0.0723610i | ||||||
\(189\) | 3.71049e79 | + | 7.58105e79i | 0.782111 | + | 1.59796i | ||||
\(190\) | −1.69696e79 | −0.297368 | ||||||||
\(191\) | − | 1.08457e80i | − | 1.58158i | −0.612088 | − | 0.790789i | \(-0.709670\pi\) | ||
0.612088 | − | 0.790789i | \(-0.290330\pi\) | |||||||
\(192\) | 9.28502e78 | + | 6.07272e79i | 0.112782 | + | 0.737633i | ||||
\(193\) | −5.69826e79 | −0.577080 | −0.288540 | − | 0.957468i | \(-0.593170\pi\) | ||||
−0.288540 | + | 0.957468i | \(0.593170\pi\) | |||||||
\(194\) | 2.22741e80i | 1.88252i | ||||||||
\(195\) | 4.99486e79 | − | 7.63701e78i | 0.352624 | − | 0.0539153i | ||||
\(196\) | −6.93525e79 | −0.409354 | ||||||||
\(197\) | 9.63743e79i | 0.476040i | 0.971260 | + | 0.238020i | \(0.0764983\pi\) | ||||
−0.971260 | + | 0.238020i | \(0.923502\pi\) | |||||||
\(198\) | −8.56092e79 | + | 2.68055e79i | −0.354192 | + | 0.110903i | ||||
\(199\) | 5.16960e80 | 1.79308 | 0.896540 | − | 0.442963i | \(-0.146073\pi\) | ||||
0.896540 | + | 0.442963i | \(0.146073\pi\) | |||||||
\(200\) | − | 2.62458e80i | − | 0.763854i | ||||||
\(201\) | 6.59021e79 | + | 4.31022e80i | 0.161078 | + | 1.05351i | ||||
\(202\) | −2.40052e80 | −0.493182 | ||||||||
\(203\) | 4.42561e80i | 0.764913i | ||||||||
\(204\) | −1.52838e80 | + | 2.33685e79i | −0.222421 | + | 0.0340075i | ||||
\(205\) | 5.62677e79 | 0.0690039 | ||||||||
\(206\) | − | 5.28458e80i | − | 0.546585i | ||||||
\(207\) | −5.54750e80 | − | 1.77172e81i | −0.484323 | − | 1.54679i | ||||
\(208\) | −1.51158e81 | −1.11484 | ||||||||
\(209\) | − | 4.03360e80i | − | 0.251520i | ||||||
\(210\) | −2.05080e80 | − | 1.34129e81i | −0.108205 | − | 0.707698i | ||||
\(211\) | 2.13952e81 | 0.955938 | 0.477969 | − | 0.878377i | \(-0.341373\pi\) | ||||
0.477969 | + | 0.878377i | \(0.341373\pi\) | |||||||
\(212\) | − | 8.81547e80i | − | 0.333803i | ||||||
\(213\) | 2.11550e81 | − | 3.23453e80i | 0.679401 | − | 0.103878i | ||||
\(214\) | −6.68392e81 | −1.82200 | ||||||||
\(215\) | 1.59206e81i | 0.368648i | ||||||||
\(216\) | 4.03495e81 | − | 1.97488e81i | 0.794249 | − | 0.388740i | ||||
\(217\) | 1.44994e82 | 2.42806 | ||||||||
\(218\) | − | 2.76990e81i | − | 0.394899i | ||||||
\(219\) | −1.13749e81 | − | 7.43955e81i | −0.138166 | − | 0.903655i | ||||
\(220\) | 2.29304e80 | 0.0237475 | ||||||||
\(221\) | 1.30191e82i | 1.15041i | ||||||||
\(222\) | −9.13732e81 | + | 1.39707e81i | −0.689390 | + | 0.105406i | ||||
\(223\) | 6.95888e81 | 0.448610 | 0.224305 | − | 0.974519i | \(-0.427989\pi\) | ||||
0.224305 | + | 0.974519i | \(0.427989\pi\) | |||||||
\(224\) | 1.20501e82i | 0.664219i | ||||||||
\(225\) | −1.74783e82 | + | 5.47271e81i | −0.824350 | + | 0.258116i | ||||
\(226\) | −3.25513e82 | −1.31454 | ||||||||
\(227\) | 7.59143e81i | 0.262675i | 0.991338 | + | 0.131337i | \(0.0419271\pi\) | ||||
−0.991338 | + | 0.131337i | \(0.958073\pi\) | |||||||
\(228\) | −7.11762e80 | − | 4.65517e81i | −0.0211162 | − | 0.138107i | ||||
\(229\) | −3.55819e82 | −0.905705 | −0.452853 | − | 0.891585i | \(-0.649594\pi\) | ||||
−0.452853 | + | 0.891585i | \(0.649594\pi\) | |||||||
\(230\) | 2.98458e82i | 0.652242i | ||||||||
\(231\) | 3.18820e82 | − | 4.87467e81i | 0.598586 | − | 0.0915221i | ||||
\(232\) | 2.35550e82 | 0.380192 | ||||||||
\(233\) | 3.22793e82i | 0.448194i | 0.974567 | + | 0.224097i | \(0.0719433\pi\) | ||||
−0.974567 | + | 0.224097i | \(0.928057\pi\) | |||||||
\(234\) | 2.63522e82 | + | 8.41615e82i | 0.314964 | + | 1.00591i | ||||
\(235\) | −1.37195e82 | −0.141242 | ||||||||
\(236\) | − | 2.13736e82i | − | 0.189652i | ||||||
\(237\) | 2.12509e82 | + | 1.38988e83i | 0.162624 | + | 1.06362i | ||||
\(238\) | 3.49608e83 | 2.30881 | ||||||||
\(239\) | − | 3.24392e83i | − | 1.84988i | −0.380116 | − | 0.924939i | \(-0.624116\pi\) | ||
0.380116 | − | 0.924939i | \(-0.375884\pi\) | |||||||
\(240\) | −8.53866e82 | + | 1.30554e82i | −0.420723 | + | 0.0643273i | ||||
\(241\) | −2.13929e83 | −0.911326 | −0.455663 | − | 0.890152i | \(-0.650598\pi\) | ||||
−0.455663 | + | 0.890152i | \(0.650598\pi\) | |||||||
\(242\) | − | 2.61618e83i | − | 0.964115i | ||||||
\(243\) | −2.15652e83 | − | 2.27526e83i | −0.687914 | − | 0.725792i | ||||
\(244\) | 5.30713e81 | 0.0146628 | ||||||||
\(245\) | 3.33711e83i | 0.799020i | ||||||||
\(246\) | 1.48430e82 | + | 9.70783e82i | 0.0308172 | + | 0.201555i | ||||
\(247\) | −3.96539e83 | −0.714319 | ||||||||
\(248\) | − | 7.71718e83i | − | 1.20684i | ||||||
\(249\) | 6.96315e82 | − | 1.06465e82i | 0.0945864 | − | 0.0144620i | ||||
\(250\) | 6.35288e83 | 0.750015 | ||||||||
\(251\) | − | 1.84142e84i | − | 1.89048i | −0.326376 | − | 0.945240i | \(-0.605828\pi\) | ||
0.326376 | − | 0.945240i | \(-0.394172\pi\) | |||||||
\(252\) | 3.59348e83 | − | 1.12517e83i | 0.320993 | − | 0.100508i | ||||
\(253\) | −7.09423e83 | −0.551680 | ||||||||
\(254\) | 1.56394e84i | 1.05935i | ||||||||
\(255\) | 1.12445e83 | + | 7.35427e83i | 0.0663793 | + | 0.434144i | ||||
\(256\) | 1.06496e84 | 0.548193 | ||||||||
\(257\) | 2.78141e84i | 1.24912i | 0.780976 | + | 0.624562i | \(0.214722\pi\) | ||||
−0.780976 | + | 0.624562i | \(0.785278\pi\) | |||||||
\(258\) | −2.74676e84 | + | 4.19972e83i | −1.07679 | + | 0.164638i | ||||
\(259\) | 3.32331e84 | 1.13783 | ||||||||
\(260\) | − | 2.25426e83i | − | 0.0674430i | ||||||
\(261\) | −4.91162e83 | − | 1.56863e84i | −0.128472 | − | 0.410302i | ||||
\(262\) | 1.79713e84 | 0.411183 | ||||||||
\(263\) | 2.55167e84i | 0.510944i | 0.966817 | + | 0.255472i | \(0.0822308\pi\) | ||||
−0.966817 | + | 0.255472i | \(0.917769\pi\) | |||||||
\(264\) | −2.59450e83 | − | 1.69689e84i | −0.0454901 | − | 0.297521i | ||||
\(265\) | −4.24184e84 | −0.651551 | ||||||||
\(266\) | 1.06484e85i | 1.43360i | ||||||||
\(267\) | −4.31222e84 | + | 6.59326e83i | −0.509104 | + | 0.0778406i | ||||
\(268\) | 1.94527e84 | 0.201494 | ||||||||
\(269\) | 1.62397e85i | 1.47655i | 0.674500 | + | 0.738275i | \(0.264359\pi\) | ||||
−0.674500 | + | 0.738275i | \(0.735641\pi\) | |||||||
\(270\) | 2.21548e84 | + | 4.52654e84i | 0.176904 | + | 0.361439i | ||||
\(271\) | −1.84202e84 | −0.129231 | −0.0646157 | − | 0.997910i | \(-0.520582\pi\) | ||||
−0.0646157 | + | 0.997910i | \(0.520582\pi\) | |||||||
\(272\) | − | 2.22560e85i | − | 1.37257i | ||||||
\(273\) | −4.79224e84 | − | 3.13429e85i | −0.259924 | − | 1.69999i | ||||
\(274\) | −1.44554e85 | −0.689861 | ||||||||
\(275\) | 6.99859e84i | 0.294013i | ||||||||
\(276\) | −8.18744e84 | + | 1.25184e84i | −0.302922 | + | 0.0463159i | ||||
\(277\) | 4.99183e85 | 1.62730 | 0.813650 | − | 0.581355i | \(-0.197477\pi\) | ||||
0.813650 | + | 0.581355i | \(0.197477\pi\) | |||||||
\(278\) | 1.09436e84i | 0.0314478i | ||||||||
\(279\) | −5.13923e85 | + | 1.60917e85i | −1.30242 | + | 0.407806i | ||||
\(280\) | 2.59648e85 | 0.580568 | ||||||||
\(281\) | − | 8.02187e85i | − | 1.58327i | −0.610995 | − | 0.791634i | \(-0.709231\pi\) | ||
0.610995 | − | 0.791634i | \(-0.290769\pi\) | |||||||
\(282\) | −3.61910e84 | − | 2.36702e85i | −0.0630786 | − | 0.412555i | ||||
\(283\) | 1.22156e86 | 1.88101 | 0.940505 | − | 0.339780i | \(-0.110353\pi\) | ||||
0.940505 | + | 0.339780i | \(0.110353\pi\) | |||||||
\(284\) | − | 9.54757e84i | − | 0.129942i | ||||||
\(285\) | −2.23998e85 | + | 3.42487e84i | −0.269572 | + | 0.0412167i | ||||
\(286\) | 3.36996e85 | 0.358768 | ||||||||
\(287\) | − | 3.53081e85i | − | 0.332665i | ||||||
\(288\) | −1.33734e85 | − | 4.27111e85i | −0.111559 | − | 0.356290i | ||||
\(289\) | −5.63496e85 | −0.416358 | ||||||||
\(290\) | 2.64247e85i | 0.173014i | ||||||||
\(291\) | 4.49546e85 | + | 2.94018e86i | 0.260927 | + | 1.70655i | ||||
\(292\) | −3.35758e85 | −0.172833 | ||||||||
\(293\) | − | 2.05294e86i | − | 0.937582i | −0.883309 | − | 0.468791i | \(-0.844690\pi\) | ||
0.883309 | − | 0.468791i | \(-0.155310\pi\) | |||||||
\(294\) | −5.75750e86 | + | 8.80305e85i | −2.33387 | + | 0.356843i | ||||
\(295\) | −1.02846e86 | −0.370183 | ||||||||
\(296\) | − | 1.76880e86i | − | 0.565549i | ||||||
\(297\) | −1.07594e86 | + | 5.26612e85i | −0.305712 | + | 0.149629i | ||||
\(298\) | 2.86730e86 | 0.724275 | ||||||||
\(299\) | 6.97427e86i | 1.56678i | ||||||||
\(300\) | 1.23496e85 | + | 8.07706e85i | 0.0246836 | + | 0.161439i | ||||
\(301\) | 9.99018e86 | 1.77724 | ||||||||
\(302\) | 6.42295e86i | 1.01740i | ||||||||
\(303\) | −3.16868e86 | + | 4.84483e85i | −0.447081 | + | 0.0683575i | ||||
\(304\) | 6.77878e86 | 0.852268 | ||||||||
\(305\) | − | 2.55369e85i | − | 0.0286203i | ||||||
\(306\) | −1.23917e87 | + | 3.88001e86i | −1.23845 | + | 0.387777i | ||||
\(307\) | 1.48515e87 | 1.32412 | 0.662058 | − | 0.749453i | \(-0.269683\pi\) | ||||
0.662058 | + | 0.749453i | \(0.269683\pi\) | |||||||
\(308\) | − | 1.43888e86i | − | 0.114486i | ||||||
\(309\) | −1.06656e86 | − | 6.97564e86i | −0.0757594 | − | 0.495493i | ||||
\(310\) | 8.65739e86 | 0.549196 | ||||||||
\(311\) | − | 1.60180e87i | − | 0.907808i | −0.891051 | − | 0.453904i | \(-0.850031\pi\) | ||
0.891051 | − | 0.453904i | \(-0.149969\pi\) | |||||||
\(312\) | −1.66820e87 | + | 2.55063e86i | −0.844962 | + | 0.129192i | ||||
\(313\) | −2.72246e87 | −1.23285 | −0.616423 | − | 0.787415i | \(-0.711419\pi\) | ||||
−0.616423 | + | 0.787415i | \(0.711419\pi\) | |||||||
\(314\) | − | 1.81268e87i | − | 0.734146i | ||||||
\(315\) | −5.41410e86 | − | 1.72911e87i | −0.196181 | − | 0.626548i | ||||
\(316\) | 6.27274e86 | 0.203427 | ||||||||
\(317\) | 4.70724e87i | 1.36676i | 0.730063 | + | 0.683380i | \(0.239491\pi\) | ||||
−0.730063 | + | 0.683380i | \(0.760509\pi\) | |||||||
\(318\) | −1.11897e87 | − | 7.31842e87i | −0.290983 | − | 1.90313i | ||||
\(319\) | −6.28106e86 | −0.146339 | ||||||||
\(320\) | − | 1.31878e87i | − | 0.275374i | ||||||
\(321\) | −8.82276e87 | + | 1.34898e87i | −1.65169 | + | 0.252539i | ||||
\(322\) | 1.87283e88 | 3.14444 | ||||||||
\(323\) | − | 5.83851e87i | − | 0.879455i | ||||||
\(324\) | −1.14882e87 | + | 7.97621e86i | −0.155301 | + | 0.107825i | ||||
\(325\) | 6.88024e87 | 0.834999 | ||||||||
\(326\) | 1.00756e88i | 1.09814i | ||||||||
\(327\) | −5.59032e86 | − | 3.65626e87i | −0.0547350 | − | 0.357986i | ||||
\(328\) | −1.87924e87 | −0.165348 | ||||||||
\(329\) | 8.60901e87i | 0.680921i | ||||||||
\(330\) | 1.90363e87 | − | 2.91060e86i | 0.135393 | − | 0.0207011i | ||||
\(331\) | −2.84891e86 | −0.0182263 | −0.00911317 | − | 0.999958i | \(-0.502901\pi\) | ||||
−0.00911317 | + | 0.999958i | \(0.502901\pi\) | |||||||
\(332\) | − | 3.14258e86i | − | 0.0180906i | ||||||
\(333\) | −1.17793e88 | + | 3.68826e87i | −0.610339 | + | 0.191106i | ||||
\(334\) | −9.46079e86 | −0.0441368 | ||||||||
\(335\) | − | 9.36028e87i | − | 0.393297i | ||||||
\(336\) | 8.19227e87 | + | 5.35802e88i | 0.310120 | + | 2.02829i | ||||
\(337\) | −3.03137e88 | −1.03417 | −0.517086 | − | 0.855933i | \(-0.672983\pi\) | ||||
−0.517086 | + | 0.855933i | \(0.672983\pi\) | |||||||
\(338\) | 2.32606e87i | 0.0715380i | ||||||||
\(339\) | −4.29677e88 | + | 6.56964e87i | −1.19166 | + | 0.182202i | ||||
\(340\) | 3.31910e87 | 0.0830344 | ||||||||
\(341\) | 2.05783e88i | 0.464521i | ||||||||
\(342\) | −1.18178e88 | − | 3.77428e88i | −0.240782 | − | 0.768989i | ||||
\(343\) | 1.12690e89 | 2.07295 | ||||||||
\(344\) | − | 5.31719e88i | − | 0.883358i | ||||||
\(345\) | 6.02360e87 | + | 3.93964e88i | 0.0904041 | + | 0.591274i | ||||
\(346\) | −6.70452e88 | −0.909294 | ||||||||
\(347\) | 7.95172e88i | 0.974831i | 0.873170 | + | 0.487416i | \(0.162060\pi\) | ||||
−0.873170 | + | 0.487416i | \(0.837940\pi\) | |||||||
\(348\) | −7.24896e87 | + | 1.10835e87i | −0.0803530 | + | 0.0122857i | ||||
\(349\) | 3.95452e88 | 0.396464 | 0.198232 | − | 0.980155i | \(-0.436480\pi\) | ||||
0.198232 | + | 0.980155i | \(0.436480\pi\) | |||||||
\(350\) | − | 1.84758e89i | − | 1.67580i | ||||||
\(351\) | 5.17707e88 | + | 1.05775e89i | 0.424947 | + | 0.868225i | ||||
\(352\) | −1.71022e88 | −0.127074 | ||||||||
\(353\) | − | 1.92807e89i | − | 1.29720i | −0.761129 | − | 0.648601i | \(-0.775355\pi\) | ||
0.761129 | − | 0.648601i | \(-0.224645\pi\) | |||||||
\(354\) | −2.71300e88 | − | 1.77439e89i | −0.165324 | − | 1.08127i | ||||
\(355\) | −4.59411e88 | −0.253635 | ||||||||
\(356\) | 1.94617e88i | 0.0973713i | ||||||||
\(357\) | 4.61482e89 | − | 7.05593e88i | 2.09299 | − | 0.320012i | ||||
\(358\) | −1.30584e89 | −0.537011 | ||||||||
\(359\) | 8.63288e87i | 0.0321996i | 0.999870 | + | 0.0160998i | \(0.00512494\pi\) | ||||
−0.999870 | + | 0.0160998i | \(0.994875\pi\) | |||||||
\(360\) | −9.20307e88 | + | 2.88161e88i | −0.311419 | + | 0.0975097i | ||||
\(361\) | −1.47820e89 | −0.453923 | ||||||||
\(362\) | 4.09489e89i | 1.14141i | ||||||||
\(363\) | −5.28007e88 | − | 3.45335e89i | −0.133631 | − | 0.873994i | ||||
\(364\) | −1.41455e89 | −0.325140 | ||||||||
\(365\) | 1.61561e89i | 0.337354i | ||||||||
\(366\) | 4.40587e88 | − | 6.73645e87i | 0.0835976 | − | 0.0127818i | ||||
\(367\) | −3.37495e89 | −0.582043 | −0.291022 | − | 0.956716i | \(-0.593995\pi\) | ||||
−0.291022 | + | 0.956716i | \(0.593995\pi\) | |||||||
\(368\) | − | 1.19224e90i | − | 1.86935i | ||||||
\(369\) | 3.91855e88 | + | 1.25148e89i | 0.0558731 | + | 0.178443i | ||||
\(370\) | 1.98430e89 | 0.257364 | ||||||||
\(371\) | 2.66176e90i | 3.14110i | ||||||||
\(372\) | 3.63121e88 | + | 2.37494e89i | 0.0389985 | + | 0.255064i | ||||
\(373\) | −1.82806e90 | −1.78723 | −0.893616 | − | 0.448832i | \(-0.851840\pi\) | ||||
−0.893616 | + | 0.448832i | \(0.851840\pi\) | |||||||
\(374\) | 4.96181e89i | 0.441707i | ||||||||
\(375\) | 8.38579e89 | − | 1.28216e89i | 0.679907 | − | 0.103956i | ||||
\(376\) | 4.58207e89 | 0.338444 | ||||||||
\(377\) | 6.17484e89i | 0.415603i | ||||||||
\(378\) | 2.84041e90 | − | 1.39022e90i | 1.74248 | − | 0.852846i | ||||
\(379\) | 1.23841e90 | 0.692614 | 0.346307 | − | 0.938121i | \(-0.387436\pi\) | ||||
0.346307 | + | 0.938121i | \(0.387436\pi\) | |||||||
\(380\) | 1.01094e89i | 0.0515583i | ||||||||
\(381\) | 3.15641e89 | + | 2.06440e90i | 0.146832 | + | 0.960329i | ||||
\(382\) | −4.06360e90 | −1.72462 | ||||||||
\(383\) | − | 1.59350e90i | − | 0.617156i | −0.951199 | − | 0.308578i | \(-0.900147\pi\) | ||
0.951199 | − | 0.308578i | \(-0.0998532\pi\) | |||||||
\(384\) | 3.31925e90 | − | 5.07504e89i | 1.17340 | − | 0.179410i | ||||
\(385\) | −6.92364e89 | −0.223465 | ||||||||
\(386\) | 2.13498e90i | 0.629272i | ||||||||
\(387\) | −3.54097e90 | + | 1.10873e90i | −0.953318 | + | 0.298498i | ||||
\(388\) | 1.32695e90 | 0.326396 | ||||||||
\(389\) | − | 3.53522e90i | − | 0.794657i | −0.917676 | − | 0.397329i | \(-0.869937\pi\) | ||
0.917676 | − | 0.397329i | \(-0.130063\pi\) | |||||||
\(390\) | −2.86138e89 | − | 1.87144e90i | −0.0587915 | − | 0.384516i | ||||
\(391\) | −1.02687e91 | −1.92898 | ||||||||
\(392\) | − | 1.11454e91i | − | 1.91462i | ||||||
\(393\) | 2.37221e90 | − | 3.62705e89i | 0.372747 | − | 0.0569920i | ||||
\(394\) | 3.61088e90 | 0.519094 | ||||||||
\(395\) | − | 3.01832e90i | − | 0.397070i | ||||||
\(396\) | 1.59690e89 | + | 5.10005e89i | 0.0192285 | + | 0.0614106i | ||||
\(397\) | 3.96451e90 | 0.437040 | 0.218520 | − | 0.975832i | \(-0.429877\pi\) | ||||
0.218520 | + | 0.975832i | \(0.429877\pi\) | |||||||
\(398\) | − | 1.93691e91i | − | 1.95525i | ||||||
\(399\) | 2.14911e90 | + | 1.40559e91i | 0.198704 | + | 1.29959i | ||||
\(400\) | −1.17617e91 | −0.996253 | ||||||||
\(401\) | 2.23372e91i | 1.73371i | 0.498563 | + | 0.866854i | \(0.333861\pi\) | ||||
−0.498563 | + | 0.866854i | \(0.666139\pi\) | |||||||
\(402\) | 1.61492e91 | − | 2.46917e90i | 1.14879 | − | 0.175647i | ||||
\(403\) | 2.02303e91 | 1.31925 | ||||||||
\(404\) | 1.43008e90i | 0.0855089i | ||||||||
\(405\) | 3.83800e90 | + | 5.52789e90i | 0.210465 | + | 0.303133i | ||||
\(406\) | 1.65816e91 | 0.834093 | ||||||||
\(407\) | 4.71661e90i | 0.217684i | ||||||||
\(408\) | −3.75546e90 | − | 2.45620e91i | −0.159059 | − | 1.04030i | ||||
\(409\) | −2.96339e91 | −1.15205 | −0.576027 | − | 0.817431i | \(-0.695398\pi\) | ||||
−0.576027 | + | 0.817431i | \(0.695398\pi\) | |||||||
\(410\) | − | 2.10820e90i | − | 0.0752448i | ||||||
\(411\) | −1.90812e91 | + | 2.91745e90i | −0.625376 | + | 0.0956182i | ||||
\(412\) | −3.14821e90 | −0.0947680 | ||||||||
\(413\) | 6.45360e91i | 1.78464i | ||||||||
\(414\) | −6.63815e91 | + | 2.07850e91i | −1.68669 | + | 0.528126i | ||||
\(415\) | −1.51215e90 | −0.0353111 | ||||||||
\(416\) | 1.68130e91i | 0.360892i | ||||||||
\(417\) | 2.20867e89 | + | 1.44455e90i | 0.00435883 | + | 0.0285082i | ||||
\(418\) | −1.51128e91 | −0.274268 | ||||||||
\(419\) | 5.73588e90i | 0.0957435i | 0.998853 | + | 0.0478718i | \(0.0152439\pi\) | ||||
−0.998853 | + | 0.0478718i | \(0.984756\pi\) | |||||||
\(420\) | −7.99057e90 | + | 1.22173e90i | −0.122702 | + | 0.0187608i | ||||
\(421\) | 5.52037e91 | 0.780000 | 0.390000 | − | 0.920815i | \(-0.372475\pi\) | ||||
0.390000 | + | 0.920815i | \(0.372475\pi\) | |||||||
\(422\) | − | 8.01619e91i | − | 1.04240i | ||||||
\(423\) | −9.55442e90 | − | 3.05142e91i | −0.114365 | − | 0.365249i | ||||
\(424\) | 1.41670e92 | 1.56125 | ||||||||
\(425\) | 1.01302e92i | 1.02803i | ||||||||
\(426\) | −1.21189e91 | − | 7.92619e91i | −0.113273 | − | 0.740847i | ||||
\(427\) | −1.60245e91 | −0.137977 | ||||||||
\(428\) | 3.98185e91i | 0.315903i | ||||||||
\(429\) | 4.44834e91 | − | 6.80139e90i | 0.325232 | − | 0.0497270i | ||||
\(430\) | 5.96500e91 | 0.401989 | ||||||||
\(431\) | 1.88079e92i | 1.16852i | 0.811567 | + | 0.584259i | \(0.198615\pi\) | ||||
−0.811567 | + | 0.584259i | \(0.801385\pi\) | |||||||
\(432\) | −8.85013e91 | − | 1.80820e92i | −0.507012 | − | 1.03590i | ||||
\(433\) | 8.12054e91 | 0.429051 | 0.214525 | − | 0.976718i | \(-0.431180\pi\) | ||||
0.214525 | + | 0.976718i | \(0.431180\pi\) | |||||||
\(434\) | − | 5.43253e92i | − | 2.64765i | ||||||
\(435\) | 5.33315e90 | + | 3.48806e91i | 0.0239806 | + | 0.156841i | ||||
\(436\) | −1.65013e91 | −0.0684685 | ||||||||
\(437\) | − | 3.12766e92i | − | 1.19776i | ||||||
\(438\) | −2.78740e92 | + | 4.26185e91i | −0.985383 | + | 0.150662i | ||||
\(439\) | 2.15018e92 | 0.701806 | 0.350903 | − | 0.936412i | \(-0.385875\pi\) | ||||
0.350903 | + | 0.936412i | \(0.385875\pi\) | |||||||
\(440\) | 3.68505e91i | 0.111071i | ||||||||
\(441\) | −7.42223e92 | + | 2.32400e92i | −2.06625 | + | 0.646973i | ||||
\(442\) | 4.87791e92 | 1.25445 | ||||||||
\(443\) | 6.12999e92i | 1.45656i | 0.685279 | + | 0.728281i | \(0.259680\pi\) | ||||
−0.685279 | + | 0.728281i | \(0.740320\pi\) | |||||||
\(444\) | 8.32286e90 | + | 5.44343e91i | 0.0182755 | + | 0.119528i | ||||
\(445\) | 9.36461e91 | 0.190059 | ||||||||
\(446\) | − | 2.60730e92i | − | 0.489183i | ||||||
\(447\) | 3.78483e92 | − | 5.78690e91i | 0.656573 | − | 0.100388i | ||||
\(448\) | −8.27537e92 | −1.32757 | ||||||||
\(449\) | − | 6.85161e92i | − | 1.01665i | −0.861166 | − | 0.508324i | \(-0.830265\pi\) | ||
0.861166 | − | 0.508324i | \(-0.169735\pi\) | |||||||
\(450\) | 2.05048e92 | + | 6.54865e92i | 0.281460 | + | 0.898905i | ||||
\(451\) | 5.01110e91 | 0.0636436 | ||||||||
\(452\) | 1.93920e92i | 0.227917i | ||||||||
\(453\) | 1.29631e92 | + | 8.47829e92i | 0.141017 | + | 0.922298i | ||||
\(454\) | 2.84430e92 | 0.286432 | ||||||||
\(455\) | 6.80656e92i | 0.634642i | ||||||||
\(456\) | 7.48115e92 | − | 1.14385e92i | 0.645950 | − | 0.0987639i | ||||
\(457\) | 1.14924e92 | 0.0919057 | 0.0459529 | − | 0.998944i | \(-0.485368\pi\) | ||||
0.0459529 | + | 0.998944i | \(0.485368\pi\) | |||||||
\(458\) | 1.33316e93i | 0.987619i | ||||||||
\(459\) | −1.55739e93 | + | 7.62254e92i | −1.06894 | + | 0.523186i | ||||
\(460\) | 1.77802e92 | 0.113087 | ||||||||
\(461\) | − | 1.66396e91i | − | 0.00980866i | −0.999988 | − | 0.00490433i | \(-0.998439\pi\) | ||
0.999988 | − | 0.00490433i | \(-0.00156110\pi\) | |||||||
\(462\) | −1.82641e92 | − | 1.19453e93i | −0.0997995 | − | 0.652723i | ||||
\(463\) | 3.91041e92 | 0.198101 | 0.0990507 | − | 0.995082i | \(-0.468419\pi\) | ||||
0.0990507 | + | 0.995082i | \(0.468419\pi\) | |||||||
\(464\) | − | 1.05558e93i | − | 0.495864i | ||||||
\(465\) | 1.14277e93 | − | 1.74727e92i | 0.497860 | − | 0.0761214i | ||||
\(466\) | 1.20942e93 | 0.488730 | ||||||||
\(467\) | − | 1.16552e93i | − | 0.436946i | −0.975843 | − | 0.218473i | \(-0.929892\pi\) | ||
0.975843 | − | 0.218473i | \(-0.0701075\pi\) | |||||||
\(468\) | 5.01381e92 | − | 1.56989e92i | 0.174407 | − | 0.0546092i | ||||
\(469\) | −5.87360e93 | −1.89607 | ||||||||
\(470\) | 5.14032e92i | 0.154016i | ||||||||
\(471\) | −3.65842e92 | − | 2.39273e93i | −0.101756 | − | 0.665522i | ||||
\(472\) | 3.43488e93 | 0.887036 | ||||||||
\(473\) | 1.41786e93i | 0.340011i | ||||||||
\(474\) | 5.20750e93 | − | 7.96212e92i | 1.15981 | − | 0.177332i | ||||
\(475\) | −3.08549e93 | −0.638334 | ||||||||
\(476\) | − | 2.08274e93i | − | 0.400306i | ||||||
\(477\) | −2.95407e93 | − | 9.43447e93i | −0.527566 | − | 1.68490i | ||||
\(478\) | −1.21541e94 | −2.01718 | ||||||||
\(479\) | − | 2.30295e93i | − | 0.355257i | −0.984098 | − | 0.177628i | \(-0.943158\pi\) | ||
0.984098 | − | 0.177628i | \(-0.0568425\pi\) | |||||||
\(480\) | 1.45212e92 | + | 9.49735e92i | 0.0208237 | + | 0.136194i | ||||
\(481\) | 4.63685e93 | 0.618224 | ||||||||
\(482\) | 8.01535e93i | 0.993748i | ||||||||
\(483\) | 2.47213e94 | − | 3.77982e93i | 2.85051 | − | 0.435835i | ||||
\(484\) | −1.55855e93 | −0.167160 | ||||||||
\(485\) | − | 6.38504e93i | − | 0.637093i | ||||||
\(486\) | −8.52480e93 | + | 8.07990e93i | −0.791434 | + | 0.750130i | ||||
\(487\) | 1.78355e93 | 0.154089 | 0.0770443 | − | 0.997028i | \(-0.475452\pi\) | ||||
0.0770443 | + | 0.997028i | \(0.475452\pi\) | |||||||
\(488\) | 8.52889e92i | 0.0685802i | ||||||||
\(489\) | 2.03350e93 | + | 1.32998e94i | 0.152207 | + | 0.995487i | ||||
\(490\) | 1.25032e94 | 0.871285 | ||||||||
\(491\) | − | 1.05458e93i | − | 0.0684269i | −0.999415 | − | 0.0342135i | \(-0.989107\pi\) | ||
0.999415 | − | 0.0342135i | \(-0.0108926\pi\) | |||||||
\(492\) | 5.78331e92 | − | 8.84251e91i | 0.0349460 | − | 0.00534315i | ||||
\(493\) | −9.09163e93 | −0.511682 | ||||||||
\(494\) | 1.48572e94i | 0.778924i | ||||||||
\(495\) | 2.45405e93 | − | 7.68398e92i | 0.119867 | − | 0.0375322i | ||||
\(496\) | −3.45834e94 | −1.57402 | ||||||||
\(497\) | 2.88281e94i | 1.22276i | ||||||||
\(498\) | −3.98894e92 | − | 2.60890e93i | −0.0157700 | − | 0.103141i | ||||
\(499\) | 3.61226e93 | 0.133125 | 0.0665625 | − | 0.997782i | \(-0.478797\pi\) | ||||
0.0665625 | + | 0.997782i | \(0.478797\pi\) | |||||||
\(500\) | − | 3.78464e93i | − | 0.130039i | ||||||
\(501\) | −1.24882e93 | + | 1.90942e92i | −0.0400111 | + | 0.00611759i | ||||
\(502\) | −6.89929e94 | −2.06146 | ||||||||
\(503\) | − | 5.80394e94i | − | 1.61750i | −0.588154 | − | 0.808749i | \(-0.700145\pi\) | ||
0.588154 | − | 0.808749i | \(-0.299855\pi\) | |||||||
\(504\) | 1.80822e94 | + | 5.77495e94i | 0.470091 | + | 1.50134i | ||||
\(505\) | 6.88126e93 | 0.166905 | ||||||||
\(506\) | 2.65802e94i | 0.601575i | ||||||||
\(507\) | 4.69456e92 | + | 3.07040e93i | 0.00991553 | + | 0.0648510i | ||||
\(508\) | 9.31697e93 | 0.183673 | ||||||||
\(509\) | − | 7.93157e94i | − | 1.45961i | −0.683655 | − | 0.729805i | \(-0.739611\pi\) | ||
0.683655 | − | 0.729805i | \(-0.260389\pi\) | |||||||
\(510\) | 2.75545e94 | − | 4.21300e93i | 0.473408 | − | 0.0723828i | ||||
\(511\) | 1.01380e95 | 1.62637 | ||||||||
\(512\) | 3.93334e94i | 0.589268i | ||||||||
\(513\) | −2.32169e94 | − | 4.74353e94i | −0.324860 | − | 0.663734i | ||||
\(514\) | 1.04212e95 | 1.36210 | ||||||||
\(515\) | 1.51486e94i | 0.184978i | ||||||||
\(516\) | 2.50193e93 | + | 1.63635e94i | 0.0285453 | + | 0.186696i | ||||
\(517\) | −1.22183e94 | −0.130270 | ||||||||
\(518\) | − | 1.24515e95i | − | 1.24074i | ||||||
\(519\) | −8.84996e94 | + | 1.35313e94i | −0.824298 | + | 0.126033i | ||||
\(520\) | 3.62274e94 | 0.315442 | ||||||||
\(521\) | − | 1.22143e95i | − | 0.994372i | −0.867644 | − | 0.497186i | \(-0.834367\pi\) | ||
0.867644 | − | 0.497186i | \(-0.165633\pi\) | |||||||
\(522\) | −5.87725e94 | + | 1.84025e94i | −0.447411 | + | 0.140091i | ||||
\(523\) | −4.52157e94 | −0.321907 | −0.160953 | − | 0.986962i | \(-0.551457\pi\) | ||||
−0.160953 | + | 0.986962i | \(0.551457\pi\) | |||||||
\(524\) | − | 1.07062e94i | − | 0.0712917i | ||||||
\(525\) | −3.72886e94 | − | 2.43881e95i | −0.232274 | − | 1.51915i | ||||
\(526\) | 9.56041e94 | 0.557154 | ||||||||
\(527\) | 2.97864e95i | 1.62423i | ||||||||
\(528\) | −7.60438e94 | + | 1.16269e94i | −0.388040 | + | 0.0593303i | ||||
\(529\) | −3.40701e95 | −1.62714 | ||||||||
\(530\) | 1.58930e95i | 0.710479i | ||||||||
\(531\) | −7.16231e94 | − | 2.28744e95i | −0.299740 | − | 0.957287i | ||||
\(532\) | 6.34366e94 | 0.248561 | ||||||||
\(533\) | − | 4.92636e94i | − | 0.180748i | ||||||
\(534\) | 2.47032e94 | + | 1.61567e95i | 0.0848806 | + | 0.555148i | ||||
\(535\) | 1.91599e95 | 0.616611 | ||||||||
\(536\) | 3.12617e95i | 0.942422i | ||||||||
\(537\) | −1.72370e95 | + | 2.63549e94i | −0.486814 | + | 0.0744324i | ||||
\(538\) | 6.08458e95 | 1.61009 | ||||||||
\(539\) | 2.97197e95i | 0.736950i | ||||||||
\(540\) | 2.69662e94 | − | 1.31984e94i | 0.0626670 | − | 0.0306719i | ||||
\(541\) | 3.52145e95 | 0.767039 | 0.383520 | − | 0.923533i | \(-0.374712\pi\) | ||||
0.383520 | + | 0.923533i | \(0.374712\pi\) | |||||||
\(542\) | 6.90153e94i | 0.140919i | ||||||||
\(543\) | 8.26447e94 | + | 5.40525e95i | 0.158205 | + | 1.03472i | ||||
\(544\) | −2.47549e95 | −0.444323 | ||||||||
\(545\) | 7.94011e94i | 0.133644i | ||||||||
\(546\) | −1.17433e96 | + | 1.79552e95i | −1.85374 | + | 0.283431i | ||||
\(547\) | 9.52447e95 | 1.41021 | 0.705106 | − | 0.709102i | \(-0.250900\pi\) | ||||
0.705106 | + | 0.709102i | \(0.250900\pi\) | |||||||
\(548\) | 8.61162e94i | 0.119609i | ||||||||
\(549\) | 5.67979e94 | − | 1.77842e94i | 0.0740116 | − | 0.0231741i | ||||
\(550\) | 2.62218e95 | 0.320604 | ||||||||
\(551\) | − | 2.76915e95i | − | 0.317717i | ||||||
\(552\) | −2.01178e95 | − | 1.31577e96i | −0.216627 | − | 1.41682i | ||||
\(553\) | −1.89400e96 | −1.91426 | ||||||||
\(554\) | − | 1.87030e96i | − | 1.77448i | ||||||
\(555\) | 2.61928e95 | − | 4.00480e94i | 0.233307 | − | 0.0356719i | ||||
\(556\) | 6.51947e93 | 0.00545249 | ||||||||
\(557\) | 1.40954e96i | 1.10699i | 0.832851 | + | 0.553497i | \(0.186707\pi\) | ||||
−0.832851 | + | 0.553497i | \(0.813293\pi\) | |||||||
\(558\) | 6.02911e95 | + | 1.92553e96i | 0.444689 | + | 1.42021i | ||||
\(559\) | 1.39388e96 | 0.965634 | ||||||||
\(560\) | − | 1.16357e96i | − | 0.757204i | ||||||
\(561\) | 1.00141e95 | + | 6.54959e95i | 0.0612228 | + | 0.400418i | ||||
\(562\) | −3.00558e96 | −1.72646 | ||||||||
\(563\) | − | 1.95346e96i | − | 1.05442i | −0.849736 | − | 0.527208i | \(-0.823239\pi\) | ||
0.849736 | − | 0.527208i | \(-0.176761\pi\) | |||||||
\(564\) | −1.41012e95 | + | 2.15603e94i | −0.0715297 | + | 0.0109367i | ||||
\(565\) | 9.33107e95 | 0.444873 | ||||||||
\(566\) | − | 4.57687e96i | − | 2.05113i | ||||||
\(567\) | 3.46876e96 | − | 2.40835e96i | 1.46139 | − | 1.01464i | ||||
\(568\) | 1.53435e96 | 0.607762 | ||||||||
\(569\) | 2.31100e96i | 0.860739i | 0.902653 | + | 0.430369i | \(0.141617\pi\) | ||||
−0.902653 | + | 0.430369i | \(0.858383\pi\) | |||||||
\(570\) | 1.28320e95 | + | 8.39260e95i | 0.0449444 | + | 0.293952i | ||||
\(571\) | 6.42257e95 | 0.211566 | 0.105783 | − | 0.994389i | \(-0.466265\pi\) | ||||
0.105783 | + | 0.994389i | \(0.466265\pi\) | |||||||
\(572\) | − | 2.00761e95i | − | 0.0622039i | ||||||
\(573\) | −5.36395e96 | + | 8.20133e95i | −1.56341 | + | 0.239041i | ||||
\(574\) | −1.32290e96 | −0.362752 | ||||||||
\(575\) | 5.42671e96i | 1.40011i | ||||||||
\(576\) | 2.93316e96 | − | 9.18415e95i | 0.712113 | − | 0.222973i | ||||
\(577\) | −1.41993e96 | −0.324424 | −0.162212 | − | 0.986756i | \(-0.551863\pi\) | ||||
−0.162212 | + | 0.986756i | \(0.551863\pi\) | |||||||
\(578\) | 2.11127e96i | 0.454014i | ||||||||
\(579\) | 4.30891e95 | + | 2.81818e96i | 0.0872203 | + | 0.570451i | ||||
\(580\) | 1.57422e95 | 0.0299975 | ||||||||
\(581\) | 9.48877e95i | 0.170234i | ||||||||
\(582\) | 1.10161e97 | − | 1.68433e96i | 1.86090 | − | 0.284526i | ||||
\(583\) | −3.77771e96 | −0.600937 | ||||||||
\(584\) | − | 5.39585e96i | − | 0.808369i | ||||||
\(585\) | −7.55404e95 | − | 2.41255e96i | −0.106592 | − | 0.340425i | ||||
\(586\) | −7.69181e96 | −1.02238 | ||||||||
\(587\) | 1.55094e97i | 1.94205i | 0.238973 | + | 0.971026i | \(0.423189\pi\) | ||||
−0.238973 | + | 0.971026i | \(0.576811\pi\) | |||||||
\(588\) | 5.24430e95 | + | 3.42995e96i | 0.0618701 | + | 0.404652i | ||||
\(589\) | −9.07241e96 | −1.00853 | ||||||||
\(590\) | 3.85336e96i | 0.403663i | ||||||||
\(591\) | 4.76636e96 | − | 7.28763e95i | 0.470571 | − | 0.0719490i | ||||
\(592\) | −7.92664e96 | −0.737615 | ||||||||
\(593\) | 3.07126e96i | 0.269403i | 0.990886 | + | 0.134702i | \(0.0430076\pi\) | ||||
−0.990886 | + | 0.134702i | \(0.956992\pi\) | |||||||
\(594\) | 1.97307e96 | + | 4.03126e96i | 0.163161 | + | 0.333361i | ||||
\(595\) | −1.00218e97 | −0.781358 | ||||||||
\(596\) | − | 1.70815e96i | − | 0.125576i | ||||||
\(597\) | −3.90915e96 | − | 2.55672e97i | −0.271007 | − | 1.77248i | ||||
\(598\) | 2.61307e97 | 1.70848 | ||||||||
\(599\) | 1.12034e97i | 0.690893i | 0.938438 | + | 0.345447i | \(0.112273\pi\) | ||||
−0.938438 | + | 0.345447i | \(0.887727\pi\) | |||||||
\(600\) | −1.29803e97 | + | 1.98466e96i | −0.755079 | + | 0.115449i | ||||
\(601\) | 6.51749e96 | 0.357663 | 0.178831 | − | 0.983880i | \(-0.442768\pi\) | ||||
0.178831 | + | 0.983880i | \(0.442768\pi\) | |||||||
\(602\) | − | 3.74305e97i | − | 1.93798i | ||||||
\(603\) | 2.08186e97 | − | 6.51861e96i | 1.01706 | − | 0.318456i | ||||
\(604\) | 3.82639e96 | 0.176399 | ||||||||
\(605\) | 7.49945e96i | 0.326281i | ||||||||
\(606\) | 1.81522e96 | + | 1.18722e97i | 0.0745399 | + | 0.487516i | ||||
\(607\) | −8.71897e96 | −0.337957 | −0.168978 | − | 0.985620i | \(-0.554047\pi\) | ||||
−0.168978 | + | 0.985620i | \(0.554047\pi\) | |||||||
\(608\) | − | 7.53989e96i | − | 0.275892i | ||||||
\(609\) | 2.18877e97 | − | 3.34656e96i | 0.756126 | − | 0.115610i | ||||
\(610\) | −9.56799e95 | −0.0312088 | ||||||||
\(611\) | 1.20117e97i | 0.369967i | ||||||||
\(612\) | 2.31146e96 | + | 7.38216e96i | 0.0672336 | + | 0.214726i | ||||
\(613\) | 3.08337e96 | 0.0847050 | 0.0423525 | − | 0.999103i | \(-0.486515\pi\) | ||||
0.0423525 | + | 0.999103i | \(0.486515\pi\) | |||||||
\(614\) | − | 5.56444e97i | − | 1.44387i | ||||||
\(615\) | −4.25485e95 | − | 2.78282e96i | −0.0104293 | − | 0.0682112i | ||||
\(616\) | 2.31238e97 | 0.535468 | ||||||||
\(617\) | − | 3.48898e97i | − | 0.763339i | −0.924299 | − | 0.381669i | \(-0.875349\pi\) | ||
0.924299 | − | 0.381669i | \(-0.124651\pi\) | |||||||
\(618\) | −2.61358e97 | + | 3.99609e96i | −0.540306 | + | 0.0826112i | ||||
\(619\) | −2.02151e97 | −0.394916 | −0.197458 | − | 0.980311i | \(-0.563269\pi\) | ||||
−0.197458 | + | 0.980311i | \(0.563269\pi\) | |||||||
\(620\) | − | 5.15752e96i | − | 0.0952208i | ||||||
\(621\) | −8.34286e97 | + | 4.08335e97i | −1.45582 | + | 0.712543i | ||||
\(622\) | −6.00150e97 | −0.989911 | ||||||||
\(623\) | − | 5.87631e97i | − | 0.916269i | ||||||
\(624\) | 1.14303e97 | + | 7.47579e97i | 0.168498 | + | 1.10204i | ||||
\(625\) | 4.37647e97 | 0.609991 | ||||||||
\(626\) | 1.02003e98i | 1.34435i | ||||||||
\(627\) | −1.99489e97 | + | 3.05013e96i | −0.248631 | + | 0.0380149i | ||||
\(628\) | −1.07988e97 | −0.127288 | ||||||||
\(629\) | 6.82715e97i | 0.761144i | ||||||||
\(630\) | −6.47853e97 | + | 2.02852e97i | −0.683214 | + | 0.213924i | ||||
\(631\) | 8.63445e97 | 0.861404 | 0.430702 | − | 0.902494i | \(-0.358266\pi\) | ||||
0.430702 | + | 0.902494i | \(0.358266\pi\) | |||||||
\(632\) | 1.00807e98i | 0.951464i | ||||||||
\(633\) | −1.61786e97 | − | 1.05814e98i | −0.144481 | − | 0.944957i | ||||
\(634\) | 1.76368e98 | 1.49037 | ||||||||
\(635\) | − | 4.48315e97i | − | 0.358511i | ||||||
\(636\) | −4.35985e97 | + | 6.66608e96i | −0.329968 | + | 0.0504512i | ||||
\(637\) | 2.92172e98 | 2.09295 | ||||||||
\(638\) | 2.35334e97i | 0.159574i | ||||||||
\(639\) | −3.19939e97 | − | 1.02180e98i | −0.205370 | − | 0.655896i | ||||
\(640\) | −7.20824e97 | −0.438057 | ||||||||
\(641\) | 1.78330e98i | 1.02611i | 0.858357 | + | 0.513054i | \(0.171486\pi\) | ||||
−0.858357 | + | 0.513054i | \(0.828514\pi\) | |||||||
\(642\) | 5.05425e97 | + | 3.30565e98i | 0.275379 | + | 1.80107i | ||||
\(643\) | −1.54596e98 | −0.797652 | −0.398826 | − | 0.917027i | \(-0.630582\pi\) | ||||
−0.398826 | + | 0.917027i | \(0.630582\pi\) | |||||||
\(644\) | − | 1.11571e98i | − | 0.545189i | ||||||
\(645\) | 7.87380e97 | − | 1.20388e97i | 0.364413 | − | 0.0557177i | ||||
\(646\) | −2.18753e98 | −0.958994 | ||||||||
\(647\) | 7.33049e96i | 0.0304427i | 0.999884 | + | 0.0152214i | \(0.00484529\pi\) | ||||
−0.999884 | + | 0.0152214i | \(0.995155\pi\) | |||||||
\(648\) | −1.28183e98 | − | 1.84622e98i | −0.504317 | − | 0.726371i | ||||
\(649\) | −9.15928e97 | −0.341426 | ||||||||
\(650\) | − | 2.57784e98i | − | 0.910518i | ||||||
\(651\) | −1.09642e98 | − | 7.17093e98i | −0.366978 | − | 2.40016i | ||||
\(652\) | 6.00241e97 | 0.190397 | ||||||||
\(653\) | − | 1.43275e98i | − | 0.430734i | −0.976533 | − | 0.215367i | \(-0.930905\pi\) | ||
0.976533 | − | 0.215367i | \(-0.0690948\pi\) | |||||||
\(654\) | −1.36990e98 | + | 2.09454e97i | −0.390363 | + | 0.0596854i | ||||
\(655\) | −5.15161e97 | −0.139155 | ||||||||
\(656\) | 8.42156e97i | 0.215654i | ||||||||
\(657\) | −3.59335e98 | + | 1.12513e98i | −0.872391 | + | 0.273158i | ||||
\(658\) | 3.22556e98 | 0.742504 | ||||||||
\(659\) | 2.16793e98i | 0.473211i | 0.971606 | + | 0.236605i | \(0.0760349\pi\) | ||||
−0.971606 | + | 0.236605i | \(0.923965\pi\) | |||||||
\(660\) | −1.73395e96 | − | 1.13406e97i | −0.00358921 | − | 0.0234746i | ||||
\(661\) | 8.01711e98 | 1.57386 | 0.786931 | − | 0.617041i | \(-0.211669\pi\) | ||||
0.786931 | + | 0.617041i | \(0.211669\pi\) | |||||||
\(662\) | 1.06741e97i | 0.0198748i | ||||||||
\(663\) | 6.43884e98 | − | 9.84480e97i | 1.13719 | − | 0.173873i | ||||
\(664\) | 5.05032e97 | 0.0846128 | ||||||||
\(665\) | − | 3.05245e98i | − | 0.485166i | ||||||
\(666\) | 1.38189e98 | + | 4.41338e98i | 0.208390 | + | 0.665539i | ||||
\(667\) | −4.87034e98 | −0.696875 | ||||||||
\(668\) | 5.63614e96i | 0.00765253i | ||||||||
\(669\) | −5.26217e97 | − | 3.44164e98i | −0.0678032 | − | 0.443456i | ||||
\(670\) | −3.50704e98 | −0.428867 | ||||||||
\(671\) | − | 2.27427e97i | − | 0.0263970i | ||||||
\(672\) | 5.95961e98 | − | 9.11207e97i | 0.656588 | − | 0.100391i | ||||
\(673\) | 1.53899e97 | 0.0160956 | 0.00804781 | − | 0.999968i | \(-0.497438\pi\) | ||||
0.00804781 | + | 0.999968i | \(0.497438\pi\) | |||||||
\(674\) | 1.13577e99i | 1.12770i | ||||||||
\(675\) | 4.02830e98 | + | 8.23038e98i | 0.379743 | + | 0.775868i | ||||
\(676\) | 1.38572e97 | 0.0124034 | ||||||||
\(677\) | − | 8.33012e98i | − | 0.708024i | −0.935241 | − | 0.354012i | \(-0.884817\pi\) | ||
0.935241 | − | 0.354012i | \(-0.115183\pi\) | |||||||
\(678\) | 2.46147e98 | + | 1.60988e99i | 0.198680 | + | 1.29944i | ||||
\(679\) | −4.00662e99 | −3.07140 | ||||||||
\(680\) | 5.33400e98i | 0.388366i | ||||||||
\(681\) | 3.75448e98 | − | 5.74049e97i | 0.259657 | − | 0.0397009i | ||||
\(682\) | 7.71012e98 | 0.506533 | ||||||||
\(683\) | 4.93620e98i | 0.308084i | 0.988064 | + | 0.154042i | \(0.0492290\pi\) | ||||
−0.988064 | + | 0.154042i | \(0.950771\pi\) | |||||||
\(684\) | −2.24848e98 | + | 7.04030e97i | −0.133329 | + | 0.0417472i | ||||
\(685\) | 4.14375e98 | 0.233466 | ||||||||
\(686\) | − | 4.22217e99i | − | 2.26043i | ||||||
\(687\) | 2.69063e98 | + | 1.75977e99i | 0.136889 | + | 0.895301i | ||||
\(688\) | −2.38282e99 | −1.15212 | ||||||||
\(689\) | 3.71383e99i | 1.70667i | ||||||||
\(690\) | 1.47608e99 | − | 2.25688e98i | 0.644750 | − | 0.0985804i | ||||
\(691\) | 1.52452e98 | 0.0632998 | 0.0316499 | − | 0.999499i | \(-0.489924\pi\) | ||||
0.0316499 | + | 0.999499i | \(0.489924\pi\) | |||||||
\(692\) | 3.99413e98i | 0.157655i | ||||||||
\(693\) | −4.82171e98 | − | 1.53992e99i | −0.180941 | − | 0.577877i | ||||
\(694\) | 2.97929e99 | 1.06300 | ||||||||
\(695\) | − | 3.13705e97i | − | 0.0106427i | ||||||
\(696\) | −1.78118e98 | − | 1.16495e99i | −0.0574625 | − | 0.375824i | ||||
\(697\) | 7.25342e98 | 0.222533 | ||||||||
\(698\) | − | 1.48165e99i | − | 0.432321i | ||||||
\(699\) | 1.59643e99 | − | 2.44090e98i | 0.443046 | − | 0.0677404i | ||||
\(700\) | −1.10067e99 | −0.290553 | ||||||||
\(701\) | − | 3.87093e99i | − | 0.972042i | −0.873947 | − | 0.486021i | \(-0.838448\pi\) | ||
0.873947 | − | 0.486021i | \(-0.161552\pi\) | |||||||
\(702\) | 3.96309e99 | − | 1.93971e99i | 0.946749 | − | 0.463380i | ||||
\(703\) | −2.07943e99 | −0.472615 | ||||||||
\(704\) | − | 1.17448e99i | − | 0.253983i | ||||||
\(705\) | 1.03744e98 | + | 6.78522e98i | 0.0213474 | + | 0.139619i | ||||
\(706\) | −7.22394e99 | −1.41452 | ||||||||
\(707\) | − | 4.31800e99i | − | 0.804643i | ||||||
\(708\) | −1.05707e99 | + | 1.61623e98i | −0.187474 | + | 0.0286642i | ||||
\(709\) | 9.32705e99 | 1.57444 | 0.787220 | − | 0.616673i | \(-0.211520\pi\) | ||||
0.787220 | + | 0.616673i | \(0.211520\pi\) | |||||||
\(710\) | 1.72129e99i | 0.276574i | ||||||||
\(711\) | 6.71320e99 | − | 2.10200e99i | 1.02682 | − | 0.321511i | ||||
\(712\) | −3.12762e99 | −0.455422 | ||||||||
\(713\) | 1.59564e100i | 2.21209i | ||||||||
\(714\) | −2.64367e99 | − | 1.72905e100i | −0.348955 | − | 2.28228i | ||||
\(715\) | −9.66022e98 | −0.121416 | ||||||||
\(716\) | 7.77934e98i | 0.0931081i | ||||||||
\(717\) | −1.60434e100 | + | 2.45299e99i | −1.82863 | + | 0.279592i | ||||
\(718\) | 3.23451e98 | 0.0351118 | ||||||||
\(719\) | − | 1.22951e99i | − | 0.127122i | −0.997978 | − | 0.0635610i | \(-0.979754\pi\) | ||
0.997978 | − | 0.0635610i | \(-0.0202457\pi\) | |||||||
\(720\) | 1.29135e99 | + | 4.12422e99i | 0.127177 | + | 0.406167i | ||||
\(721\) | 9.50579e99 | 0.891772 | ||||||||
\(722\) | 5.53842e99i | 0.494976i | ||||||||
\(723\) | 1.61769e99 | + | 1.05803e100i | 0.137738 | + | 0.900857i | ||||
\(724\) | 2.43947e99 | 0.197900 | ||||||||
\(725\) | 4.80468e99i | 0.371393i | ||||||||
\(726\) | −1.29388e100 | + | 1.97830e99i | −0.953040 | + | 0.145717i | ||||
\(727\) | −6.23831e99 | −0.437887 | −0.218944 | − | 0.975737i | \(-0.570261\pi\) | ||||
−0.218944 | + | 0.975737i | \(0.570261\pi\) | |||||||
\(728\) | − | 2.27327e100i | − | 1.52074i | ||||||
\(729\) | −9.62201e99 | + | 1.23860e100i | −0.613483 | + | 0.789708i | ||||
\(730\) | 6.05324e99 | 0.367864 | ||||||||
\(731\) | 2.05230e100i | 1.18887i | ||||||||
\(732\) | −4.01315e97 | − | 2.62474e98i | −0.00221614 | − | 0.0144943i | ||||
\(733\) | 1.63823e100 | 0.862452 | 0.431226 | − | 0.902244i | \(-0.358081\pi\) | ||||
0.431226 | + | 0.902244i | \(0.358081\pi\) | |||||||
\(734\) | 1.26450e100i | 0.634684i | ||||||||
\(735\) | 1.65043e100 | − | 2.52346e99i | 0.789841 | − | 0.120764i | ||||
\(736\) | −1.32610e100 | −0.605138 | ||||||||
\(737\) | − | 8.33611e99i | − | 0.362745i | ||||||
\(738\) | 4.68894e99 | − | 1.46817e99i | 0.194582 | − | 0.0609263i | ||||
\(739\) | −2.58809e100 | −1.02429 | −0.512145 | − | 0.858899i | \(-0.671149\pi\) | ||||
−0.512145 | + | 0.858899i | \(0.671149\pi\) | |||||||
\(740\) | − | 1.18212e99i | − | 0.0446223i | ||||||
\(741\) | 2.99855e99 | + | 1.96115e100i | 0.107963 | + | 0.706114i | ||||
\(742\) | 9.97290e100 | 3.42519 | ||||||||
\(743\) | − | 3.25238e100i | − | 1.06560i | −0.846242 | − | 0.532799i | \(-0.821140\pi\) | ||
0.846242 | − | 0.532799i | \(-0.178860\pi\) | |||||||
\(744\) | −3.81667e100 | + | 5.83558e99i | −1.19298 | + | 0.182403i | ||||
\(745\) | −8.21932e99 | −0.245113 | ||||||||
\(746\) | 6.84924e100i | 1.94887i | ||||||||
\(747\) | −1.05308e99 | − | 3.36324e99i | −0.0285917 | − | 0.0913140i | ||||
\(748\) | 2.95593e99 | 0.0765841 | ||||||||
\(749\) | − | 1.20229e101i | − | 2.97266i | ||||||
\(750\) | −4.80392e99 | − | 3.14193e100i | −0.113358 | − | 0.741399i | ||||
\(751\) | −2.15441e100 | −0.485210 | −0.242605 | − | 0.970125i | \(-0.578002\pi\) | ||||
−0.242605 | + | 0.970125i | \(0.578002\pi\) | |||||||
\(752\) | − | 2.05339e100i | − | 0.441415i | ||||||
\(753\) | −9.10706e100 | + | 1.39244e100i | −1.86876 | + | 0.285729i | ||||
\(754\) | 2.31355e100 | 0.453191 | ||||||||
\(755\) | − | 1.84118e100i | − | 0.344314i | ||||||
\(756\) | −8.28205e99 | − | 1.69214e100i | −0.147868 | − | 0.302115i | ||||
\(757\) | −3.19520e100 | −0.544681 | −0.272340 | − | 0.962201i | \(-0.587798\pi\) | ||||
−0.272340 | + | 0.962201i | \(0.587798\pi\) | |||||||
\(758\) | − | 4.63997e100i | − | 0.755255i | ||||||
\(759\) | 5.36452e99 | + | 3.50858e100i | 0.0833813 | + | 0.545342i | ||||
\(760\) | −1.62464e100 | −0.241147 | ||||||||
\(761\) | 2.01704e100i | 0.285925i | 0.989728 | + | 0.142962i | \(0.0456628\pi\) | ||||
−0.989728 | + | 0.142962i | \(0.954337\pi\) | |||||||
\(762\) | 7.73476e100 | − | 1.18262e100i | 1.04718 | − | 0.160111i | ||||
\(763\) | 4.98243e100 | 0.644292 | ||||||||
\(764\) | 2.42083e100i | 0.299018i | ||||||||
\(765\) | 3.55216e100 | − | 1.11223e100i | 0.419124 | − | 0.131234i | ||||
\(766\) | −5.97042e100 | −0.672973 | ||||||||
\(767\) | 9.00440e100i | 0.969654i | ||||||||
\(768\) | −8.05300e99 | − | 5.26694e100i | −0.0828542 | − | 0.541895i | ||||
\(769\) | −4.20089e98 | −0.00412971 | −0.00206486 | − | 0.999998i | \(-0.500657\pi\) | ||||
−0.00206486 | + | 0.999998i | \(0.500657\pi\) | |||||||
\(770\) | 2.59410e100i | 0.243675i | ||||||||
\(771\) | 1.37560e101 | − | 2.10325e100i | 1.23477 | − | 0.188793i | ||||
\(772\) | 1.27189e100 | 0.109105 | ||||||||
\(773\) | − | 4.81153e100i | − | 0.394458i | −0.980357 | − | 0.197229i | \(-0.936806\pi\) | ||
0.980357 | − | 0.197229i | \(-0.0631942\pi\) | |||||||
\(774\) | 4.15410e100 | + | 1.32670e101i | 0.325494 | + | 1.03954i | ||||
\(775\) | 1.57413e101 | 1.17891 | ||||||||
\(776\) | 2.13249e101i | 1.52661i | ||||||||
\(777\) | −2.51302e100 | − | 1.64360e101i | −0.171973 | − | 1.12476i | ||||
\(778\) | −1.32455e101 | −0.866527 | ||||||||
\(779\) | 2.20926e100i | 0.138177i | ||||||||
\(780\) | −1.11488e100 | + | 1.70463e99i | −0.0666682 | + | 0.0101934i | ||||
\(781\) | −4.09144e100 | −0.233932 | ||||||||
\(782\) | 3.84740e101i | 2.10344i | ||||||||
\(783\) | −7.38656e100 | + | 3.61530e100i | −0.386172 | + | 0.189009i | ||||
\(784\) | −4.99464e101 | −2.49713 | ||||||||
\(785\) | 5.19617e100i | 0.248454i | ||||||||
\(786\) | −1.35896e100 | − | 8.88804e100i | −0.0621465 | − | 0.406459i | ||||
\(787\) | 1.22010e101 | 0.533679 | 0.266840 | − | 0.963741i | \(-0.414021\pi\) | ||||
0.266840 | + | 0.963741i | \(0.414021\pi\) | |||||||
\(788\) | − | 2.15113e100i | − | 0.0900015i | ||||||
\(789\) | 1.26197e101 | − | 1.92952e100i | 0.505074 | − | 0.0772244i | ||||
\(790\) | −1.13088e101 | −0.432982 | ||||||||
\(791\) | − | 5.85527e101i | − | 2.14472i | ||||||
\(792\) | −8.19610e100 | + | 2.56632e100i | −0.287227 | + | 0.0899350i | ||||
\(793\) | −2.23582e100 | −0.0749677 | ||||||||
\(794\) | − | 1.48539e101i | − | 0.476567i | ||||||
\(795\) | 3.20759e100 | + | 2.09788e101i | 0.0984759 | + | 0.644066i | ||||
\(796\) | −1.15389e101 | −0.339005 | ||||||||
\(797\) | 7.77697e100i | 0.218660i | 0.994006 | + | 0.109330i | \(0.0348705\pi\) | ||||
−0.994006 | + | 0.109330i | \(0.965129\pi\) | |||||||
\(798\) | 5.26637e101 | − | 8.05213e100i | 1.41713 | − | 0.216676i | ||||
\(799\) | −1.76857e101 | −0.455496 | ||||||||
\(800\) | 1.30823e101i | 0.322502i | ||||||||
\(801\) | 6.52163e100 | + | 2.08283e101i | 0.153893 | + | 0.491491i | ||||
\(802\) | 8.36914e101 | 1.89051 | ||||||||
\(803\) | 1.43883e101i | 0.311147i | ||||||||
\(804\) | −1.47098e100 | − | 9.62069e100i | −0.0304540 | − | 0.199179i | ||||
\(805\) | −5.36860e101 | −1.06416 | ||||||||
\(806\) | − | 7.57974e101i | − | 1.43856i | ||||||
\(807\) | 8.03164e101 | − | 1.22801e101i | 1.45959 | − | 0.223167i | ||||
\(808\) | −2.29822e101 | −0.399939 | ||||||||
\(809\) | − | 8.91757e101i | − | 1.48610i | −0.669236 | − | 0.743050i | \(-0.733378\pi\) | ||
0.669236 | − | 0.743050i | \(-0.266622\pi\) | |||||||
\(810\) | 2.07115e101 | − | 1.43799e101i | 0.330549 | − | 0.229499i | ||||
\(811\) | 4.01682e101 | 0.613977 | 0.306989 | − | 0.951713i | \(-0.400679\pi\) | ||||
0.306989 | + | 0.951713i | \(0.400679\pi\) | |||||||
\(812\) | − | 9.87824e100i | − | 0.144617i | ||||||
\(813\) | 1.39290e100 | + | 9.11002e100i | 0.0195321 | + | 0.127747i | ||||
\(814\) | 1.76719e101 | 0.237371 | ||||||||
\(815\) | − | 2.88825e101i | − | 0.371636i | ||||||
\(816\) | −1.10071e102 | + | 1.68296e101i | −1.35681 | + | 0.207452i | ||||
\(817\) | −6.25095e101 | −0.738200 | ||||||||
\(818\) | 1.11030e102i | 1.25625i | ||||||||
\(819\) | −1.51388e102 | + | 4.74017e101i | −1.64118 | + | 0.513875i | ||||
\(820\) | −1.25593e100 | −0.0130461 | ||||||||
\(821\) | − | 4.66174e100i | − | 0.0464021i | −0.999731 | − | 0.0232011i | \(-0.992614\pi\) | ||
0.999731 | − | 0.0232011i | \(-0.00738579\pi\) | |||||||
\(822\) | 1.09309e101 | + | 7.14919e101i | 0.104266 | + | 0.681936i | ||||
\(823\) | −1.18842e102 | −1.08636 | −0.543182 | − | 0.839615i | \(-0.682781\pi\) | ||||
−0.543182 | + | 0.839615i | \(0.682781\pi\) | |||||||
\(824\) | − | 5.05938e101i | − | 0.443246i | ||||||
\(825\) | 3.46128e101 | − | 5.29220e100i | 0.290635 | − | 0.0444373i | ||||
\(826\) | 2.41799e102 | 1.94604 | ||||||||
\(827\) | 7.49819e99i | 0.00578447i | 0.999996 | + | 0.00289223i | \(0.000920628\pi\) | ||||
−0.999996 | + | 0.00289223i | \(0.999079\pi\) | |||||||
\(828\) | 1.23824e101 | + | 3.95459e101i | 0.0915676 | + | 0.292442i | ||||
\(829\) | 6.46738e101 | 0.458479 | 0.229240 | − | 0.973370i | \(-0.426376\pi\) | ||||
0.229240 | + | 0.973370i | \(0.426376\pi\) | |||||||
\(830\) | 5.66561e100i | 0.0385047i | ||||||||
\(831\) | −3.77472e101 | − | 2.46880e102i | −0.245951 | − | 1.60861i | ||||
\(832\) | −1.15462e102 | −0.721313 | ||||||||
\(833\) | 4.30184e102i | 2.57679i | ||||||||
\(834\) | 5.41233e100 | − | 8.27530e99i | 0.0310865 | − | 0.00475305i | ||||
\(835\) | 2.71200e100 | 0.0149370 | ||||||||
\(836\) | 9.00324e100i | 0.0475531i | ||||||||
\(837\) | 1.18446e102 | + | 2.42002e102i | 0.599970 | + | 1.22582i | ||||
\(838\) | 2.14908e101 | 0.104403 | ||||||||
\(839\) | 3.16527e102i | 1.47483i | 0.675440 | + | 0.737415i | \(0.263954\pi\) | ||||
−0.675440 | + | 0.737415i | \(0.736046\pi\) | |||||||
\(840\) | −1.96340e101 | − | 1.28413e102i | −0.0877475 | − | 0.573899i | ||||
\(841\) | 1.90150e102 | 0.815147 | ||||||||
\(842\) | − | 2.06833e102i | − | 0.850544i | ||||||
\(843\) | −3.96736e102 | + | 6.06598e101i | −1.56508 | + | 0.239296i | ||||
\(844\) | −4.77554e101 | −0.180733 | ||||||||
\(845\) | − | 6.66783e100i | − | 0.0242103i | ||||||
\(846\) | −1.14328e102 | + | 3.57978e101i | −0.398282 | + | 0.124708i | ||||
\(847\) | 4.70592e102 | 1.57299 | ||||||||
\(848\) | − | 6.34874e102i | − | 2.03626i | ||||||
\(849\) | −9.23723e101 | − | 6.04147e102i | −0.284297 | − | 1.85940i | ||||
\(850\) | 3.79553e102 | 1.12101 | ||||||||
\(851\) | 3.65727e102i | 1.03663i | ||||||||
\(852\) | −4.72192e101 | + | 7.21968e100i | −0.128450 | + | 0.0196396i | ||||
\(853\) | −5.41555e101 | −0.141392 | −0.0706962 | − | 0.997498i | \(-0.522522\pi\) | ||||
−0.0706962 | + | 0.997498i | \(0.522522\pi\) | |||||||
\(854\) | 6.00393e101i | 0.150456i | ||||||||
\(855\) | 3.38766e101 | + | 1.08192e102i | 0.0814865 | + | 0.260245i | ||||
\(856\) | −6.39908e102 | −1.47753 | ||||||||
\(857\) | 2.60836e101i | 0.0578148i | 0.999582 | + | 0.0289074i | \(0.00920280\pi\) | ||||
−0.999582 | + | 0.0289074i | \(0.990797\pi\) | |||||||
\(858\) | −2.54830e101 | − | 1.66667e102i | −0.0542244 | − | 0.354646i | ||||
\(859\) | −1.06634e102 | −0.217839 | −0.108919 | − | 0.994051i | \(-0.534739\pi\) | ||||
−0.108919 | + | 0.994051i | \(0.534739\pi\) | |||||||
\(860\) | − | 3.55357e101i | − | 0.0696977i | ||||||
\(861\) | −1.74622e102 | + | 2.66993e101i | −0.328844 | + | 0.0502793i | ||||
\(862\) | 7.04680e102 | 1.27420 | ||||||||
\(863\) | − | 7.06229e102i | − | 1.22622i | −0.789999 | − | 0.613109i | \(-0.789919\pi\) | ||
0.789999 | − | 0.613109i | \(-0.210081\pi\) | |||||||
\(864\) | −2.01122e102 | + | 9.84380e101i | −0.335336 | + | 0.164128i | ||||
\(865\) | 1.92190e102 | 0.307728 | ||||||||
\(866\) | − | 3.04255e102i | − | 0.467855i | ||||||
\(867\) | 4.26105e101 | + | 2.78687e102i | 0.0629286 | + | 0.411575i | ||||
\(868\) | −3.23635e102 | −0.459056 | ||||||||
\(869\) | − | 2.68807e102i | − | 0.366225i | ||||||
\(870\) | 1.30688e102 | − | 1.99819e101i | 0.171026 | − | 0.0261494i | ||||
\(871\) | −8.19514e102 | −1.03020 | ||||||||
\(872\) | − | 2.65186e102i | − | 0.320238i | ||||||
\(873\) | 1.42013e103 | − | 4.44662e102i | 1.64751 | − | 0.515859i | ||||
\(874\) | −1.17185e103 | −1.30608 | ||||||||
\(875\) | 1.14274e103i | 1.22368i | ||||||||
\(876\) | 2.53894e101 | + | 1.66055e102i | 0.0261221 | + | 0.170848i | ||||
\(877\) | 1.27965e103 | 1.26504 | 0.632520 | − | 0.774544i | \(-0.282020\pi\) | ||||
0.632520 | + | 0.774544i | \(0.282020\pi\) | |||||||
\(878\) | − | 8.05615e102i | − | 0.765279i | ||||||
\(879\) | −1.01532e103 | + | 1.55239e102i | −0.926812 | + | 0.141707i | ||||
\(880\) | 1.65140e102 | 0.144864 | ||||||||
\(881\) | 2.03421e103i | 1.71490i | 0.514567 | + | 0.857450i | \(0.327953\pi\) | ||||
−0.514567 | + | 0.857450i | \(0.672047\pi\) | |||||||
\(882\) | 8.70741e102 | + | 2.78091e103i | 0.705487 | + | 2.25313i | ||||
\(883\) | 4.77812e100 | 0.00372077 | 0.00186038 | − | 0.999998i | \(-0.499408\pi\) | ||||
0.00186038 | + | 0.999998i | \(0.499408\pi\) | |||||||
\(884\) | − | 2.90595e102i | − | 0.217500i | ||||||
\(885\) | 7.77701e101 | + | 5.08643e102i | 0.0559497 | + | 0.365930i | ||||
\(886\) | 2.29674e103 | 1.58830 | ||||||||
\(887\) | − | 1.96441e103i | − | 1.30589i | −0.757407 | − | 0.652943i | \(-0.773534\pi\) | ||
0.757407 | − | 0.652943i | \(-0.226466\pi\) | |||||||
\(888\) | −8.74794e102 | + | 1.33754e102i | −0.559052 | + | 0.0854774i | ||||
\(889\) | −2.81319e103 | −1.72837 | ||||||||
\(890\) | − | 3.50867e102i | − | 0.207249i | ||||||
\(891\) | 3.41806e102 | + | 4.92305e102i | 0.194115 | + | 0.279585i | ||||
\(892\) | −1.55326e102 | −0.0848156 | ||||||||
\(893\) | − | 5.38674e102i | − | 0.282830i | ||||||
\(894\) | −2.16820e102 | − | 1.41807e103i | −0.109467 | − | 0.715955i | ||||
\(895\) | 3.74328e102 | 0.181738 | ||||||||
\(896\) | 4.52319e103i | 2.11186i | ||||||||
\(897\) | 3.44925e103 | − | 5.27380e102i | 1.54878 | − | 0.236804i | ||||
\(898\) | −2.56711e103 | −1.10860 | ||||||||
\(899\) | 1.41274e103i | 0.586777i | ||||||||
\(900\) | 3.90127e102 | − | 1.22154e102i | 0.155854 | − | 0.0488001i | ||||
\(901\) | −5.46812e103 | −2.10121 | ||||||||
\(902\) | − | 1.87752e102i | − | 0.0693996i | ||||||
\(903\) | −7.55438e102 | − | 4.94082e103i | −0.268613 | − | 1.75682i | ||||
\(904\) | −3.11642e103 | −1.06601 | ||||||||
\(905\) | − | 1.17383e103i | − | 0.386282i | ||||||
\(906\) | 3.17659e103 | − | 4.85691e102i | 1.00571 | − | 0.153771i | ||||
\(907\) | 2.06701e103 | 0.629632 | 0.314816 | − | 0.949153i | \(-0.398057\pi\) | ||||
0.314816 | + | 0.949153i | \(0.398057\pi\) | |||||||
\(908\) | − | 1.69445e102i | − | 0.0496621i | ||||||
\(909\) | 4.79219e102 | + | 1.53049e103i | 0.135144 | + | 0.431614i | ||||
\(910\) | 2.55023e103 | 0.692040 | ||||||||
\(911\) | − | 7.29561e103i | − | 1.90510i | −0.304377 | − | 0.952552i | \(-0.598448\pi\) | ||
0.304377 | − | 0.952552i | \(-0.401552\pi\) | |||||||
\(912\) | −5.12598e102 | − | 3.35257e103i | −0.128812 | − | 0.842478i | ||||
\(913\) | −1.34669e102 | −0.0325681 | ||||||||
\(914\) | − | 4.30588e102i | − | 0.100218i | ||||||
\(915\) | −1.26297e102 | + | 1.93105e101i | −0.0282915 | + | 0.00432569i | ||||
\(916\) | 7.94210e102 | 0.171235 | ||||||||
\(917\) | 3.23264e103i | 0.670859i | ||||||||
\(918\) | 2.85596e103 | + | 5.83512e103i | 0.570503 | + | 1.16562i | ||||
\(919\) | 1.02760e104 | 1.97596 | 0.987982 | − | 0.154568i | \(-0.0493985\pi\) | ||||
0.987982 | + | 0.154568i | \(0.0493985\pi\) | |||||||
\(920\) | 2.85739e103i | 0.528927i | ||||||||
\(921\) | −1.12304e103 | − | 7.34505e103i | −0.200128 | − | 1.30890i | ||||
\(922\) | −6.23439e101 | −0.0106958 | ||||||||
\(923\) | 4.02225e103i | 0.664369i | ||||||||
\(924\) | −7.11626e102 | + | 1.08806e102i | −0.113170 | + | 0.0173034i | ||||
\(925\) | 3.60796e103 | 0.552460 | ||||||||
\(926\) | − | 1.46512e103i | − | 0.216018i | ||||||
\(927\) | −3.36928e103 | + | 1.05497e103i | −0.478350 | + | 0.149778i | ||||
\(928\) | −1.17410e103 | −0.160519 | ||||||||
\(929\) | − | 5.83401e103i | − | 0.768099i | −0.923313 | − | 0.384050i | \(-0.874529\pi\) | ||
0.923313 | − | 0.384050i | \(-0.125471\pi\) | |||||||
\(930\) | −6.54655e102 | − | 4.28167e103i | −0.0830059 | − | 0.542887i | ||||
\(931\) | −1.31026e104 | −1.60000 | ||||||||
\(932\) | − | 7.20493e102i | − | 0.0847370i | ||||||
\(933\) | −7.92197e103 | + | 1.21125e103i | −0.897379 | + | 0.137207i | ||||
\(934\) | −4.36687e103 | −0.476464 | ||||||||
\(935\) | − | 1.42234e103i | − | 0.149485i | ||||||
\(936\) | 2.52292e103 | + | 8.05750e103i | 0.255416 | + | 0.815729i | ||||
\(937\) | −3.69929e103 | −0.360771 | −0.180386 | − | 0.983596i | \(-0.557735\pi\) | ||||
−0.180386 | + | 0.983596i | \(0.557735\pi\) | |||||||
\(938\) | 2.20068e104i | 2.06755i | ||||||||
\(939\) | 2.05867e103 | + | 1.34644e104i | 0.186333 | + | 1.21868i | ||||
\(940\) | 3.06228e102 | 0.0267036 | ||||||||
\(941\) | − | 8.37545e103i | − | 0.703674i | −0.936061 | − | 0.351837i | \(-0.885557\pi\) | ||
0.936061 | − | 0.351837i | \(-0.114443\pi\) | |||||||
\(942\) | −8.96492e103 | + | 1.37071e103i | −0.725713 | + | 0.110959i | ||||
\(943\) | 3.88562e103 | 0.303075 | ||||||||
\(944\) | − | 1.53929e104i | − | 1.15691i | ||||||
\(945\) | −8.14224e103 | + | 3.98517e103i | −0.589700 | + | 0.288624i | ||||
\(946\) | 5.31233e103 | 0.370762 | ||||||||
\(947\) | 1.34182e104i | 0.902494i | 0.892399 | + | 0.451247i | \(0.149021\pi\) | ||||
−0.892399 | + | 0.451247i | \(0.850979\pi\) | |||||||
\(948\) | −4.74332e102 | − | 3.10230e103i | −0.0307462 | − | 0.201090i | ||||
\(949\) | 1.41450e104 | 0.883661 | ||||||||
\(950\) | 1.15605e104i | 0.696066i | ||||||||
\(951\) | 2.32805e104 | − | 3.55952e103i | 1.35106 | − | 0.206573i | ||||
\(952\) | 3.34709e104 | 1.87230 | ||||||||
\(953\) | − | 1.44176e104i | − | 0.777392i | −0.921366 | − | 0.388696i | \(-0.872926\pi\) | ||
0.921366 | − | 0.388696i | \(-0.127074\pi\) | |||||||
\(954\) | −3.53484e104 | + | 1.10681e104i | −1.83729 | + | 0.575280i | ||||
\(955\) | 1.16486e104 | 0.583654 | ||||||||
\(956\) | 7.24062e103i | 0.349743i | ||||||||
\(957\) | 4.74961e102 | + | 3.10641e103i | 0.0221177 | + | 0.144657i | ||||
\(958\) | −8.62854e103 | −0.387387 | ||||||||
\(959\) | − | 2.60021e104i | − | 1.12553i | ||||||
\(960\) | −6.52227e103 | + | 9.97236e102i | −0.272211 | + | 0.0416203i | ||||
\(961\) | 2.14353e104 | 0.862603 | ||||||||
\(962\) | − | 1.73730e104i | − | 0.674137i | ||||||
\(963\) | 1.33432e104 | + | 4.26145e104i | 0.499275 | + | 1.59455i | ||||
\(964\) | 4.77503e103 | 0.172298 | ||||||||
\(965\) | − | 6.12008e103i | − | 0.212962i | ||||||
\(966\) | −1.41620e104 | − | 9.26242e104i | −0.475253 | − | 3.10831i | ||||
\(967\) | −3.39129e104 | −1.09758 | −0.548792 | − | 0.835959i | \(-0.684912\pi\) | ||||
−0.548792 | + | 0.835959i | \(0.684912\pi\) | |||||||
\(968\) | − | 2.50469e104i | − | 0.781837i | ||||||
\(969\) | −2.88754e104 | + | 4.41497e103i | −0.869352 | + | 0.132921i | ||||
\(970\) | −2.39230e104 | −0.694712 | ||||||||
\(971\) | 3.72372e104i | 1.04305i | 0.853237 | + | 0.521523i | \(0.174636\pi\) | ||||
−0.853237 | + | 0.521523i | \(0.825364\pi\) | |||||||
\(972\) | 4.81349e103 | + | 5.07853e103i | 0.130059 | + | 0.137221i | ||||
\(973\) | −1.96850e103 | −0.0513082 | ||||||||
\(974\) | − | 6.68246e103i | − | 0.168025i | ||||||
\(975\) | −5.20270e103 | − | 3.40275e104i | −0.126202 | − | 0.825407i | ||||
\(976\) | 3.82210e103 | 0.0894454 | ||||||||
\(977\) | 2.47114e104i | 0.557941i | 0.960300 | + | 0.278970i | \(0.0899931\pi\) | ||||
−0.960300 | + | 0.278970i | \(0.910007\pi\) | |||||||
\(978\) | 4.98308e104 | − | 7.61899e103i | 1.08552 | − | 0.165973i | ||||
\(979\) | 8.33996e103 | 0.175295 | ||||||||
\(980\) | − | 7.44864e103i | − | 0.151065i | ||||||
\(981\) | −1.76600e104 | + | 5.52959e103i | −0.345601 | + | 0.108213i | ||||
\(982\) | −3.95122e103 | −0.0746156 | ||||||||
\(983\) | − | 5.18570e104i | − | 0.945006i | −0.881329 | − | 0.472503i | \(-0.843351\pi\) | ||
0.881329 | − | 0.472503i | \(-0.156649\pi\) | |||||||
\(984\) | 1.42105e103 | + | 9.29413e103i | 0.0249908 | + | 0.163448i | ||||
\(985\) | −1.03509e104 | −0.175674 | ||||||||
\(986\) | 3.40639e104i | 0.557959i | ||||||||
\(987\) | 4.25774e104 | − | 6.50996e103i | 0.673099 | − | 0.102915i | ||||
\(988\) | 8.85100e103 | 0.135051 | ||||||||
\(989\) | 1.09941e105i | 1.61916i | ||||||||
\(990\) | −2.87898e103 | − | 9.19466e103i | −0.0409267 | − | 0.130708i | ||||
\(991\) | −1.65940e104 | −0.227706 | −0.113853 | − | 0.993498i | \(-0.536319\pi\) | ||||
−0.113853 | + | 0.993498i | \(0.536319\pi\) | |||||||
\(992\) | 3.84664e104i | 0.509533i | ||||||||
\(993\) | 2.15429e102 | + | 1.40898e103i | 0.00275474 | + | 0.0180170i | ||||
\(994\) | 1.08011e105 | 1.33335 | ||||||||
\(995\) | 5.55229e104i | 0.661705i | ||||||||
\(996\) | −1.55422e103 | + | 2.37636e102i | −0.0178828 | + | 0.00273423i | ||||
\(997\) | −8.04145e104 | −0.893314 | −0.446657 | − | 0.894705i | \(-0.647386\pi\) | ||||
−0.446657 | + | 0.894705i | \(0.647386\pi\) | |||||||
\(998\) | − | 1.35341e104i | − | 0.145165i | ||||||
\(999\) | 2.71483e104 | + | 5.54676e104i | 0.281158 | + | 0.574444i |
(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.2.6 | ✓ | 22 | |
3.2 | odd | 2 | inner | 3.71.b.a.2.17 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.71.b.a.2.6 | ✓ | 22 | 1.1 | even | 1 | trivial | |
3.71.b.a.2.17 | yes | 22 | 3.2 | odd | 2 | inner |