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 | 2.1 | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.71.b.a.2.22 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 6.63817e10i | − | 1.93196i | −0.258614 | − | 0.965981i | \(-0.583266\pi\) | ||
0.258614 | − | 0.965981i | \(-0.416734\pi\) | |||||||
\(3\) | 2.36972e16 | − | 4.40636e16i | 0.473645 | − | 0.880716i | ||||
\(4\) | −3.22594e21 | −2.73248 | ||||||||
\(5\) | 6.32737e23i | 0.217407i | 0.994074 | + | 0.108703i | \(0.0346699\pi\) | ||||
−0.994074 | + | 0.108703i | \(0.965330\pi\) | |||||||
\(6\) | −2.92502e27 | − | 1.57306e27i | −1.70151 | − | 0.915063i | ||||
\(7\) | −2.54650e29 | −0.672222 | −0.336111 | − | 0.941822i | \(-0.609112\pi\) | ||||
−0.336111 | + | 0.941822i | \(0.609112\pi\) | |||||||
\(8\) | 1.35774e32i | 3.34708i | ||||||||
\(9\) | −1.38004e33 | − | 2.08836e33i | −0.551322 | − | 0.834293i | ||||
\(10\) | 4.20021e34 | 0.420021 | ||||||||
\(11\) | − | 1.33911e36i | − | 0.476509i | −0.971203 | − | 0.238255i | \(-0.923425\pi\) | ||
0.971203 | − | 0.238255i | \(-0.0765753\pi\) | |||||||
\(12\) | −7.64456e37 | + | 1.42146e38i | −1.29422 | + | 2.40654i | ||||
\(13\) | −1.53510e39 | −1.57804 | −0.789022 | − | 0.614365i | \(-0.789412\pi\) | ||||
−0.789022 | + | 0.614365i | \(0.789412\pi\) | |||||||
\(14\) | 1.69041e40i | 1.29871i | ||||||||
\(15\) | 2.78806e40 | + | 1.49941e40i | 0.191474 | + | 0.102973i | ||||
\(16\) | 5.20436e42 | 3.73395 | ||||||||
\(17\) | 7.59069e42i | 0.652483i | 0.945287 | + | 0.326241i | \(0.105782\pi\) | ||||
−0.945287 | + | 0.326241i | \(0.894218\pi\) | |||||||
\(18\) | −1.38629e44 | + | 9.16097e43i | −1.61182 | + | 1.06513i | ||||
\(19\) | 8.19873e44 | 1.43671 | 0.718357 | − | 0.695674i | \(-0.244894\pi\) | ||||
0.718357 | + | 0.695674i | \(0.244894\pi\) | |||||||
\(20\) | − | 2.04117e45i | − | 0.594058i | ||||||
\(21\) | −6.03449e45 | + | 1.12208e46i | −0.318394 | + | 0.592037i | ||||
\(22\) | −8.88922e46 | −0.920597 | ||||||||
\(23\) | 6.91248e47i | 1.51063i | 0.655359 | + | 0.755317i | \(0.272517\pi\) | ||||
−0.655359 | + | 0.755317i | \(0.727483\pi\) | |||||||
\(24\) | 5.98267e48 | + | 3.21745e48i | 2.94782 | + | 1.58532i | ||||
\(25\) | 8.06997e48 | 0.952734 | ||||||||
\(26\) | 1.01902e50i | 3.04872i | ||||||||
\(27\) | −1.24724e50 | + | 1.13214e49i | −0.995906 | + | 0.0903997i | ||||
\(28\) | 8.21487e50 | 1.83683 | ||||||||
\(29\) | − | 4.05488e50i | − | 0.265490i | −0.991150 | − | 0.132745i | \(-0.957621\pi\) | ||
0.991150 | − | 0.132745i | \(-0.0423791\pi\) | |||||||
\(30\) | 9.95332e50 | − | 1.85076e51i | 0.198941 | − | 0.369920i | ||||
\(31\) | −1.63946e52 | −1.04002 | −0.520011 | − | 0.854160i | \(-0.674072\pi\) | ||||
−0.520011 | + | 0.854160i | \(0.674072\pi\) | |||||||
\(32\) | − | 1.85181e53i | − | 3.86677i | ||||||
\(33\) | −5.90059e52 | − | 3.17330e52i | −0.419669 | − | 0.225696i | ||||
\(34\) | 5.03883e53 | 1.26057 | ||||||||
\(35\) | − | 1.61127e53i | − | 0.146146i | ||||||
\(36\) | 4.45194e54 | + | 6.73693e54i | 1.50647 | + | 2.27968i | ||||
\(37\) | 3.41760e54 | 0.443263 | 0.221631 | − | 0.975131i | \(-0.428862\pi\) | ||||
0.221631 | + | 0.975131i | \(0.428862\pi\) | |||||||
\(38\) | − | 5.44246e55i | − | 2.77568i | ||||||
\(39\) | −3.63775e55 | + | 6.76420e55i | −0.747432 | + | 1.38981i | ||||
\(40\) | −8.59089e55 | −0.727677 | ||||||||
\(41\) | − | 4.15548e56i | − | 1.48315i | −0.670868 | − | 0.741577i | \(-0.734078\pi\) | ||
0.670868 | − | 0.741577i | \(-0.265922\pi\) | |||||||
\(42\) | 7.44856e56 | + | 4.00580e56i | 1.14379 | + | 0.615126i | ||||
\(43\) | −8.83584e56 | −0.595459 | −0.297730 | − | 0.954650i | \(-0.596229\pi\) | ||||
−0.297730 | + | 0.954650i | \(0.596229\pi\) | |||||||
\(44\) | 4.31988e57i | 1.30205i | ||||||||
\(45\) | 1.32138e57 | − | 8.73204e56i | 0.181381 | − | 0.119861i | ||||
\(46\) | 4.58862e58 | 2.91849 | ||||||||
\(47\) | − | 4.77253e57i | − | 0.142996i | −0.997441 | − | 0.0714979i | \(-0.977222\pi\) | ||
0.997441 | − | 0.0714979i | \(-0.0227779\pi\) | |||||||
\(48\) | 1.23329e59 | − | 2.29323e59i | 1.76856 | − | 3.28855i | ||||
\(49\) | −7.86568e58 | −0.548117 | ||||||||
\(50\) | − | 5.35699e59i | − | 1.84065i | ||||||
\(51\) | 3.34473e59 | + | 1.79878e59i | 0.574652 | + | 0.309045i | ||||
\(52\) | 4.95213e60 | 4.31197 | ||||||||
\(53\) | − | 5.62909e59i | − | 0.251642i | −0.992053 | − | 0.125821i | \(-0.959844\pi\) | ||
0.992053 | − | 0.125821i | \(-0.0401564\pi\) | |||||||
\(54\) | 7.51531e59 | + | 8.27939e60i | 0.174649 | + | 1.92405i | ||||
\(55\) | 8.47302e59 | 0.103596 | ||||||||
\(56\) | − | 3.45748e61i | − | 2.24998i | ||||||
\(57\) | 1.94287e61 | − | 3.61265e61i | 0.680492 | − | 1.26534i | ||||
\(58\) | −2.69170e61 | −0.512916 | ||||||||
\(59\) | 9.59463e61i | 1.00510i | 0.864549 | + | 0.502548i | \(0.167604\pi\) | ||||
−0.864549 | + | 0.502548i | \(0.832396\pi\) | |||||||
\(60\) | −8.99412e61 | − | 4.83699e61i | −0.523197 | − | 0.281373i | ||||
\(61\) | −8.18161e61 | −0.266867 | −0.133433 | − | 0.991058i | \(-0.542600\pi\) | ||||
−0.133433 | + | 0.991058i | \(0.542600\pi\) | |||||||
\(62\) | 1.08830e63i | 2.00928i | ||||||||
\(63\) | 3.51429e62 | + | 5.31803e62i | 0.370611 | + | 0.560830i | ||||
\(64\) | −6.14843e63 | −3.73650 | ||||||||
\(65\) | − | 9.71313e62i | − | 0.343077i | ||||||
\(66\) | −2.10649e63 | + | 3.91691e63i | −0.436036 | + | 0.810785i | ||||
\(67\) | 2.40454e63 | 0.294045 | 0.147022 | − | 0.989133i | \(-0.453031\pi\) | ||||
0.147022 | + | 0.989133i | \(0.453031\pi\) | |||||||
\(68\) | − | 2.44871e64i | − | 1.78289i | ||||||
\(69\) | 3.04588e64 | + | 1.63806e64i | 1.33044 | + | 0.715504i | ||||
\(70\) | −1.06959e64 | −0.282348 | ||||||||
\(71\) | 7.14405e64i | 1.14789i | 0.818892 | + | 0.573947i | \(0.194589\pi\) | ||||
−0.818892 | + | 0.573947i | \(0.805411\pi\) | |||||||
\(72\) | 2.83545e65 | − | 1.87373e65i | 2.79244 | − | 1.84532i | ||||
\(73\) | 1.52365e65 | 0.925947 | 0.462974 | − | 0.886372i | \(-0.346782\pi\) | ||||
0.462974 | + | 0.886372i | \(0.346782\pi\) | |||||||
\(74\) | − | 2.26866e65i | − | 0.856366i | ||||||
\(75\) | 1.91236e65 | − | 3.55592e65i | 0.451257 | − | 0.839088i | ||||
\(76\) | −2.64486e66 | −3.92579 | ||||||||
\(77\) | 3.41004e65i | 0.320320i | ||||||||
\(78\) | 4.49019e66 | + | 2.41480e66i | 2.68506 | + | 1.44401i | ||||
\(79\) | −2.33890e66 | −0.895495 | −0.447748 | − | 0.894160i | \(-0.647774\pi\) | ||||
−0.447748 | + | 0.894160i | \(0.647774\pi\) | |||||||
\(80\) | 3.29299e66i | 0.811785i | ||||||||
\(81\) | −2.45675e66 | + | 5.76407e66i | −0.392089 | + | 0.919927i | ||||
\(82\) | −2.75848e67 | −2.86540 | ||||||||
\(83\) | − | 2.67747e67i | − | 1.81966i | −0.414976 | − | 0.909832i | \(-0.636210\pi\) | ||
0.414976 | − | 0.909832i | \(-0.363790\pi\) | |||||||
\(84\) | 1.94669e67 | − | 3.61976e67i | 0.870005 | − | 1.61773i | ||||
\(85\) | −4.80291e66 | −0.141854 | ||||||||
\(86\) | 5.86538e67i | 1.15040i | ||||||||
\(87\) | −1.78672e67 | − | 9.60891e66i | −0.233821 | − | 0.125748i | ||||
\(88\) | 1.81815e68 | 1.59491 | ||||||||
\(89\) | 5.29244e67i | 0.312612i | 0.987709 | + | 0.156306i | \(0.0499586\pi\) | ||||
−0.987709 | + | 0.156306i | \(0.950041\pi\) | |||||||
\(90\) | −5.79648e67 | − | 8.77158e67i | −0.231567 | − | 0.350421i | ||||
\(91\) | 3.90914e68 | 1.06080 | ||||||||
\(92\) | − | 2.22992e69i | − | 4.12777i | ||||||
\(93\) | −3.88506e68 | + | 7.22406e68i | −0.492601 | + | 0.915964i | ||||
\(94\) | −3.16809e68 | −0.276263 | ||||||||
\(95\) | 5.18764e68i | 0.312351i | ||||||||
\(96\) | −8.15976e69 | − | 4.38828e69i | −3.40553 | − | 1.83147i | ||||
\(97\) | 4.21837e69 | 1.22499 | 0.612497 | − | 0.790473i | \(-0.290165\pi\) | ||||
0.612497 | + | 0.790473i | \(0.290165\pi\) | |||||||
\(98\) | 5.22137e69i | 1.05894i | ||||||||
\(99\) | −2.79654e69 | + | 1.84803e69i | −0.397548 | + | 0.262710i | ||||
\(100\) | −2.60332e70 | −2.60332 | ||||||||
\(101\) | 5.84441e69i | 0.412565i | 0.978492 | + | 0.206283i | \(0.0661366\pi\) | ||||
−0.978492 | + | 0.206283i | \(0.933863\pi\) | |||||||
\(102\) | 1.19406e70 | − | 2.22029e70i | 0.597063 | − | 1.11021i | ||||
\(103\) | 5.53027e69 | 0.196537 | 0.0982684 | − | 0.995160i | \(-0.468670\pi\) | ||||
0.0982684 | + | 0.995160i | \(0.468670\pi\) | |||||||
\(104\) | − | 2.08426e71i | − | 5.28183i | ||||||
\(105\) | −7.09982e69 | − | 3.81825e69i | −0.128713 | − | 0.0692211i | ||||
\(106\) | −3.73668e70 | −0.486162 | ||||||||
\(107\) | 3.46547e70i | 0.324586i | 0.986743 | + | 0.162293i | \(0.0518890\pi\) | ||||
−0.986743 | + | 0.162293i | \(0.948111\pi\) | |||||||
\(108\) | 4.02352e71 | − | 3.65220e70i | 2.72129 | − | 0.247015i | ||||
\(109\) | −1.46497e71 | −0.717631 | −0.358815 | − | 0.933409i | \(-0.616819\pi\) | ||||
−0.358815 | + | 0.933409i | \(0.616819\pi\) | |||||||
\(110\) | − | 5.62453e70i | − | 0.200144i | ||||||
\(111\) | 8.09875e70 | − | 1.50592e71i | 0.209949 | − | 0.390388i | ||||
\(112\) | −1.32529e72 | −2.51004 | ||||||||
\(113\) | 2.60988e71i | 0.362139i | 0.983470 | + | 0.181069i | \(0.0579559\pi\) | ||||
−0.983470 | + | 0.181069i | \(0.942044\pi\) | |||||||
\(114\) | −2.39814e72 | − | 1.28971e72i | −2.44458 | − | 1.31468i | ||||
\(115\) | −4.37378e71 | −0.328422 | ||||||||
\(116\) | 1.30808e72i | 0.725444i | ||||||||
\(117\) | 2.11850e72 | + | 3.20585e72i | 0.870010 | + | 1.31655i | ||||
\(118\) | 6.36908e72 | 1.94181 | ||||||||
\(119\) | − | 1.93297e72i | − | 0.438614i | ||||||
\(120\) | −2.03580e72 | + | 3.78545e72i | −0.344660 | + | 0.640877i | ||||
\(121\) | 6.10426e72 | 0.772939 | ||||||||
\(122\) | 5.43109e72i | 0.515577i | ||||||||
\(123\) | −1.83105e73 | − | 9.84731e72i | −1.30624 | − | 0.702488i | ||||
\(124\) | 5.28881e73 | 2.84183 | ||||||||
\(125\) | 1.04657e73i | 0.424537i | ||||||||
\(126\) | 3.53020e73 | − | 2.33284e73i | 1.08350 | − | 0.716006i | ||||
\(127\) | −2.34346e73 | −0.545415 | −0.272708 | − | 0.962097i | \(-0.587919\pi\) | ||||
−0.272708 | + | 0.962097i | \(0.587919\pi\) | |||||||
\(128\) | 1.89519e74i | 3.35201i | ||||||||
\(129\) | −2.09384e73 | + | 3.89339e73i | −0.282036 | + | 0.524431i | ||||
\(130\) | −6.44774e73 | −0.662812 | ||||||||
\(131\) | − | 3.03202e73i | − | 0.238362i | −0.992873 | − | 0.119181i | \(-0.961973\pi\) | ||
0.992873 | − | 0.119181i | \(-0.0380269\pi\) | |||||||
\(132\) | 1.90349e74 | + | 1.02369e74i | 1.14674 | + | 0.616709i | ||||
\(133\) | −2.08781e74 | −0.965792 | ||||||||
\(134\) | − | 1.59617e74i | − | 0.568083i | ||||||
\(135\) | −7.16344e72 | − | 7.89174e73i | −0.0196535 | − | 0.216516i | ||||
\(136\) | −1.03062e75 | −2.18391 | ||||||||
\(137\) | 9.01556e74i | 1.47833i | 0.673522 | + | 0.739167i | \(0.264781\pi\) | ||||
−0.673522 | + | 0.739167i | \(0.735219\pi\) | |||||||
\(138\) | 1.08737e75 | − | 2.02191e75i | 1.38233 | − | 2.57036i | ||||
\(139\) | 6.69019e74 | 0.660572 | 0.330286 | − | 0.943881i | \(-0.392855\pi\) | ||||
0.330286 | + | 0.943881i | \(0.392855\pi\) | |||||||
\(140\) | 5.19785e74i | 0.399339i | ||||||||
\(141\) | −2.10295e74 | − | 1.13095e74i | −0.125939 | − | 0.0677292i | ||||
\(142\) | 4.74234e75 | 2.21769 | ||||||||
\(143\) | 2.05566e75i | 0.751952i | ||||||||
\(144\) | −7.18225e75 | − | 1.08686e76i | −2.05861 | − | 3.11521i | ||||
\(145\) | 2.56567e74 | 0.0577192 | ||||||||
\(146\) | − | 1.01143e76i | − | 1.78889i | ||||||
\(147\) | −1.86394e75 | + | 3.46590e75i | −0.259613 | + | 0.482735i | ||||
\(148\) | −1.10250e76 | −1.21120 | ||||||||
\(149\) | 3.80767e75i | 0.330476i | 0.986254 | + | 0.165238i | \(0.0528392\pi\) | ||||
−0.986254 | + | 0.165238i | \(0.947161\pi\) | |||||||
\(150\) | −2.36048e76 | − | 1.26945e76i | −1.62109 | − | 0.871812i | ||||
\(151\) | −6.40778e75 | −0.348750 | −0.174375 | − | 0.984679i | \(-0.555790\pi\) | ||||
−0.174375 | + | 0.984679i | \(0.555790\pi\) | |||||||
\(152\) | 1.11317e77i | 4.80879i | ||||||||
\(153\) | 1.58521e76 | − | 1.04755e76i | 0.544362 | − | 0.359728i | ||||
\(154\) | 2.26364e76 | 0.618846 | ||||||||
\(155\) | − | 1.03735e76i | − | 0.226108i | ||||||
\(156\) | 1.17352e77 | − | 2.18209e77i | 2.04234 | − | 3.79762i | ||||
\(157\) | −6.98741e76 | −0.972363 | −0.486181 | − | 0.873858i | \(-0.661611\pi\) | ||||
−0.486181 | + | 0.873858i | \(0.661611\pi\) | |||||||
\(158\) | 1.55260e77i | 1.73006i | ||||||||
\(159\) | −2.48038e76 | − | 1.33393e76i | −0.221625 | − | 0.119189i | ||||
\(160\) | 1.17171e77 | 0.840661 | ||||||||
\(161\) | − | 1.76026e77i | − | 1.01548i | ||||||
\(162\) | 3.82629e77 | + | 1.63083e77i | 1.77726 | + | 0.757501i | ||||
\(163\) | 4.49284e77 | 1.68250 | 0.841250 | − | 0.540646i | \(-0.181820\pi\) | ||||
0.841250 | + | 0.540646i | \(0.181820\pi\) | |||||||
\(164\) | 1.34053e78i | 4.05268i | ||||||||
\(165\) | 2.00787e76 | − | 3.73352e76i | 0.0490678 | − | 0.0912389i | ||||
\(166\) | −1.77735e78 | −3.51552 | ||||||||
\(167\) | 2.65948e77i | 0.426305i | 0.977019 | + | 0.213152i | \(0.0683731\pi\) | ||||
−0.977019 | + | 0.213152i | \(0.931627\pi\) | |||||||
\(168\) | −1.52349e78 | − | 8.19325e77i | −1.98159 | − | 1.06569i | ||||
\(169\) | 1.41022e78 | 1.49022 | ||||||||
\(170\) | 3.18825e77i | 0.274057i | ||||||||
\(171\) | −1.13146e78 | − | 1.71219e78i | −0.792092 | − | 1.19864i | ||||
\(172\) | 2.85039e78 | 1.62708 | ||||||||
\(173\) | − | 5.17414e77i | − | 0.241115i | −0.992706 | − | 0.120558i | \(-0.961532\pi\) | ||
0.992706 | − | 0.120558i | \(-0.0384682\pi\) | |||||||
\(174\) | −6.37856e77 | + | 1.18606e78i | −0.242940 | + | 0.451733i | ||||
\(175\) | −2.05502e78 | −0.640449 | ||||||||
\(176\) | − | 6.96920e78i | − | 1.77926i | ||||||
\(177\) | 4.22774e78 | + | 2.27366e78i | 0.885205 | + | 0.476058i | ||||
\(178\) | 3.51321e78 | 0.603954 | ||||||||
\(179\) | − | 6.60972e78i | − | 0.933957i | −0.884269 | − | 0.466978i | \(-0.845343\pi\) | ||
0.884269 | − | 0.466978i | \(-0.154657\pi\) | |||||||
\(180\) | −4.26271e78 | + | 2.81690e78i | −0.495619 | + | 0.327517i | ||||
\(181\) | 1.35420e79 | 1.29698 | 0.648488 | − | 0.761225i | \(-0.275402\pi\) | ||||
0.648488 | + | 0.761225i | \(0.275402\pi\) | |||||||
\(182\) | − | 2.59495e79i | − | 2.04942i | ||||||
\(183\) | −1.93881e78 | + | 3.60511e78i | −0.126400 | + | 0.235034i | ||||
\(184\) | −9.38532e79 | −5.05621 | ||||||||
\(185\) | 2.16244e78i | 0.0963682i | ||||||||
\(186\) | 4.79546e79 | + | 2.57897e79i | 1.76961 | + | 0.951685i | ||||
\(187\) | 1.01647e79 | 0.310914 | ||||||||
\(188\) | 1.53959e79i | 0.390733i | ||||||||
\(189\) | 3.17610e79 | − | 2.88299e78i | 0.669470 | − | 0.0607687i | ||||
\(190\) | 3.44364e79 | 0.603451 | ||||||||
\(191\) | 2.69940e79i | 0.393640i | 0.980440 | + | 0.196820i | \(0.0630614\pi\) | ||||
−0.980440 | + | 0.196820i | \(0.936939\pi\) | |||||||
\(192\) | −1.45700e80 | + | 2.70922e80i | −1.76977 | + | 3.29080i | ||||
\(193\) | 9.29560e79 | 0.941394 | 0.470697 | − | 0.882295i | \(-0.344002\pi\) | ||||
0.470697 | + | 0.882295i | \(0.344002\pi\) | |||||||
\(194\) | − | 2.80023e80i | − | 2.36664i | ||||||
\(195\) | −4.27995e79 | − | 2.30174e79i | −0.302154 | − | 0.162497i | ||||
\(196\) | 2.53742e80 | 1.49772 | ||||||||
\(197\) | − | 3.36879e80i | − | 1.66401i | −0.554768 | − | 0.832005i | \(-0.687193\pi\) | ||
0.554768 | − | 0.832005i | \(-0.312807\pi\) | |||||||
\(198\) | 1.22675e80 | + | 1.85639e80i | 0.507545 | + | 0.768048i | ||||
\(199\) | 2.89620e80 | 1.00455 | 0.502275 | − | 0.864708i | \(-0.332497\pi\) | ||||
0.502275 | + | 0.864708i | \(0.332497\pi\) | |||||||
\(200\) | 1.09569e81i | 3.18888i | ||||||||
\(201\) | 5.69807e79 | − | 1.05952e80i | 0.139273 | − | 0.258970i | ||||
\(202\) | 3.87962e80 | 0.797060 | ||||||||
\(203\) | 1.03258e80i | 0.178468i | ||||||||
\(204\) | −1.07899e81 | − | 5.80275e80i | −1.57022 | − | 0.844458i | ||||
\(205\) | 2.62933e80 | 0.322448 | ||||||||
\(206\) | − | 3.67109e80i | − | 0.379701i | ||||||
\(207\) | 1.44358e81 | − | 9.53952e80i | 1.26031 | − | 0.832845i | ||||
\(208\) | −7.98921e81 | −5.89233 | ||||||||
\(209\) | − | 1.09790e81i | − | 0.684608i | ||||||
\(210\) | −2.53462e80 | + | 4.71298e80i | −0.133732 | + | 0.248668i | ||||
\(211\) | 3.31637e81 | 1.48176 | 0.740878 | − | 0.671639i | \(-0.234410\pi\) | ||||
0.740878 | + | 0.671639i | \(0.234410\pi\) | |||||||
\(212\) | 1.81591e81i | 0.687605i | ||||||||
\(213\) | 3.14792e81 | + | 1.69294e81i | 1.01097 | + | 0.543694i | ||||
\(214\) | 2.30044e81 | 0.627089 | ||||||||
\(215\) | − | 5.59076e80i | − | 0.129457i | ||||||
\(216\) | −1.53714e81 | − | 1.69342e82i | −0.302575 | − | 3.33337i | ||||
\(217\) | 4.17490e81 | 0.699126 | ||||||||
\(218\) | 9.72471e81i | 1.38644i | ||||||||
\(219\) | 3.61063e81 | − | 6.71377e81i | 0.438570 | − | 0.815497i | ||||
\(220\) | −2.73334e81 | −0.283074 | ||||||||
\(221\) | − | 1.16525e82i | − | 1.02965i | ||||||
\(222\) | −9.99654e81 | − | 5.37609e81i | −0.754216 | − | 0.405613i | ||||
\(223\) | 1.00171e82 | 0.645764 | 0.322882 | − | 0.946439i | \(-0.395348\pi\) | ||||
0.322882 | + | 0.946439i | \(0.395348\pi\) | |||||||
\(224\) | 4.71565e82i | 2.59933i | ||||||||
\(225\) | −1.11369e82 | − | 1.68530e82i | −0.525263 | − | 0.794859i | ||||
\(226\) | 1.73248e82 | 0.699638 | ||||||||
\(227\) | 1.32377e82i | 0.458045i | 0.973421 | + | 0.229022i | \(0.0735529\pi\) | ||||
−0.973421 | + | 0.229022i | \(0.926447\pi\) | |||||||
\(228\) | −6.26757e82 | + | 1.16542e83i | −1.85943 | + | 3.45751i | ||||
\(229\) | −2.29576e82 | −0.584366 | −0.292183 | − | 0.956362i | \(-0.594382\pi\) | ||||
−0.292183 | + | 0.956362i | \(0.594382\pi\) | |||||||
\(230\) | 2.90339e82i | 0.634499i | ||||||||
\(231\) | 1.50259e82 | + | 8.08083e81i | 0.282111 | + | 0.151718i | ||||
\(232\) | 5.50545e82 | 0.888614 | ||||||||
\(233\) | − | 1.67406e82i | − | 0.232442i | −0.993223 | − | 0.116221i | \(-0.962922\pi\) | ||
0.993223 | − | 0.116221i | \(-0.0370780\pi\) | |||||||
\(234\) | 2.12809e83 | − | 1.40630e83i | 2.54352 | − | 1.68083i | ||||
\(235\) | 3.01975e81 | 0.0310883 | ||||||||
\(236\) | − | 3.09517e83i | − | 2.74640i | ||||||
\(237\) | −5.54253e82 | + | 1.03060e83i | −0.424146 | + | 0.788677i | ||||
\(238\) | −1.28314e83 | −0.847385 | ||||||||
\(239\) | 1.85976e83i | 1.06055i | 0.847826 | + | 0.530275i | \(0.177911\pi\) | ||||
−0.847826 | + | 0.530275i | \(0.822089\pi\) | |||||||
\(240\) | 1.45101e83 | + | 7.80346e82i | 0.714952 | + | 0.384498i | ||||
\(241\) | −6.16463e82 | −0.262609 | −0.131305 | − | 0.991342i | \(-0.541917\pi\) | ||||
−0.131305 | + | 0.991342i | \(0.541917\pi\) | |||||||
\(242\) | − | 4.05211e83i | − | 1.49329i | ||||||
\(243\) | 1.95768e83 | + | 2.44845e83i | 0.624484 | + | 0.781038i | ||||
\(244\) | 2.63934e83 | 0.729207 | ||||||||
\(245\) | − | 4.97690e82i | − | 0.119164i | ||||||
\(246\) | −6.53681e83 | + | 1.21548e84i | −1.35718 | + | 2.52360i | ||||
\(247\) | −1.25859e84 | −2.26720 | ||||||||
\(248\) | − | 2.22596e84i | − | 3.48103i | ||||||
\(249\) | −1.17979e84 | − | 6.34485e83i | −1.60261 | − | 0.861874i | ||||
\(250\) | 6.94728e83 | 0.820190 | ||||||||
\(251\) | 7.79373e83i | 0.800138i | 0.916485 | + | 0.400069i | \(0.131014\pi\) | ||||
−0.916485 | + | 0.400069i | \(0.868986\pi\) | |||||||
\(252\) | −1.13369e84 | − | 1.71556e84i | −1.01269 | − | 1.53246i | ||||
\(253\) | 9.25654e83 | 0.719831 | ||||||||
\(254\) | 1.55563e84i | 1.05372i | ||||||||
\(255\) | −1.13815e83 | + | 2.11633e83i | −0.0671884 | + | 0.124933i | ||||
\(256\) | 5.32184e84 | 2.73945 | ||||||||
\(257\) | 1.89034e84i | 0.848945i | 0.905441 | + | 0.424472i | \(0.139540\pi\) | ||||
−0.905441 | + | 0.424472i | \(0.860460\pi\) | |||||||
\(258\) | 2.58450e84 | + | 1.38993e84i | 1.01318 | + | 0.544883i | ||||
\(259\) | −8.70294e83 | −0.297971 | ||||||||
\(260\) | 3.13340e84i | 0.937450i | ||||||||
\(261\) | −8.46806e83 | + | 5.59591e83i | −0.221496 | + | 0.146370i | ||||
\(262\) | −2.01271e84 | −0.460506 | ||||||||
\(263\) | − | 7.44706e84i | − | 1.49119i | −0.666399 | − | 0.745596i | \(-0.732165\pi\) | ||
0.666399 | − | 0.745596i | \(-0.267835\pi\) | |||||||
\(264\) | 4.30851e84 | − | 8.01144e84i | 0.755422 | − | 1.40467i | ||||
\(265\) | 3.56173e83 | 0.0547086 | ||||||||
\(266\) | 1.38592e85i | 1.86587i | ||||||||
\(267\) | 2.33204e84 | + | 1.25416e84i | 0.275322 | + | 0.148067i | ||||
\(268\) | −7.75688e84 | −0.803470 | ||||||||
\(269\) | 1.38025e85i | 1.25496i | 0.778633 | + | 0.627479i | \(0.215913\pi\) | ||||
−0.778633 | + | 0.627479i | \(0.784087\pi\) | |||||||
\(270\) | −5.23867e84 | + | 4.75521e83i | −0.418302 | + | 0.0379698i | ||||
\(271\) | −1.67408e85 | −1.17450 | −0.587248 | − | 0.809407i | \(-0.699789\pi\) | ||||
−0.587248 | + | 0.809407i | \(0.699789\pi\) | |||||||
\(272\) | 3.95047e85i | 2.43634i | ||||||||
\(273\) | 9.26354e84 | − | 1.72251e85i | 0.502440 | − | 0.934260i | ||||
\(274\) | 5.98468e85 | 2.85609 | ||||||||
\(275\) | − | 1.08066e85i | − | 0.453987i | ||||||
\(276\) | −9.82584e85 | − | 5.28428e85i | −3.63540 | − | 1.95510i | ||||
\(277\) | −1.46289e85 | −0.476891 | −0.238446 | − | 0.971156i | \(-0.576638\pi\) | ||||
−0.238446 | + | 0.971156i | \(0.576638\pi\) | |||||||
\(278\) | − | 4.44106e85i | − | 1.27620i | ||||||
\(279\) | 2.26253e85 | + | 3.42380e85i | 0.573386 | + | 0.867682i | ||||
\(280\) | 2.18767e85 | 0.489161 | ||||||||
\(281\) | − | 3.86508e85i | − | 0.762846i | −0.924401 | − | 0.381423i | \(-0.875434\pi\) | ||
0.924401 | − | 0.381423i | \(-0.124566\pi\) | |||||||
\(282\) | −7.50747e84 | + | 1.39597e85i | −0.130850 | + | 0.243309i | ||||
\(283\) | 9.93234e85 | 1.52942 | 0.764709 | − | 0.644375i | \(-0.222883\pi\) | ||||
0.764709 | + | 0.644375i | \(0.222883\pi\) | |||||||
\(284\) | − | 2.30463e86i | − | 3.13659i | ||||||
\(285\) | 2.28586e85 | + | 1.22932e85i | 0.275093 | + | 0.147944i | ||||
\(286\) | 1.36458e86 | 1.45274 | ||||||||
\(287\) | 1.05820e86i | 0.997010i | ||||||||
\(288\) | −3.86726e86 | + | 2.55558e86i | −3.22602 | + | 2.13183i | ||||
\(289\) | 7.77209e85 | 0.574266 | ||||||||
\(290\) | − | 1.70313e85i | − | 0.111511i | ||||||
\(291\) | 9.99635e85 | − | 1.85877e86i | 0.580212 | − | 1.07887i | ||||
\(292\) | −4.91521e86 | −2.53013 | ||||||||
\(293\) | 4.64538e85i | 0.212155i | 0.994358 | + | 0.106078i | \(0.0338292\pi\) | ||||
−0.994358 | + | 0.106078i | \(0.966171\pi\) | |||||||
\(294\) | 2.30072e86 | + | 1.23732e86i | 0.932626 | + | 0.501562i | ||||
\(295\) | −6.07087e85 | −0.218515 | ||||||||
\(296\) | 4.64020e86i | 1.48363i | ||||||||
\(297\) | 1.51605e85 | + | 1.67019e86i | 0.0430763 | + | 0.474558i | ||||
\(298\) | 2.52760e86 | 0.638467 | ||||||||
\(299\) | − | 1.06113e87i | − | 2.38385i | ||||||
\(300\) | −6.16914e86 | + | 1.14712e87i | −1.23305 | + | 2.29279i | ||||
\(301\) | 2.25005e86 | 0.400281 | ||||||||
\(302\) | 4.25359e86i | 0.673772i | ||||||||
\(303\) | 2.57526e86 | + | 1.38496e86i | 0.363353 | + | 0.195409i | ||||
\(304\) | 4.26692e87 | 5.36462 | ||||||||
\(305\) | − | 5.17681e85i | − | 0.0580186i | ||||||
\(306\) | −6.95381e86 | − | 1.05229e87i | −0.694980 | − | 1.05169i | ||||
\(307\) | −4.92341e86 | −0.438958 | −0.219479 | − | 0.975617i | \(-0.570436\pi\) | ||||
−0.219479 | + | 0.975617i | \(0.570436\pi\) | |||||||
\(308\) | − | 1.10006e87i | − | 0.875267i | ||||||
\(309\) | 1.31052e86 | − | 2.43684e86i | 0.0930886 | − | 0.173093i | ||||
\(310\) | −6.88609e86 | −0.436831 | ||||||||
\(311\) | 1.62337e87i | 0.920033i | 0.887910 | + | 0.460016i | \(0.152156\pi\) | ||||
−0.887910 | + | 0.460016i | \(0.847844\pi\) | |||||||
\(312\) | −9.18399e87 | − | 4.93910e87i | −4.65180 | − | 2.50171i | ||||
\(313\) | −1.00197e87 | −0.453736 | −0.226868 | − | 0.973926i | \(-0.572849\pi\) | ||||
−0.226868 | + | 0.973926i | \(0.572849\pi\) | |||||||
\(314\) | 4.63836e87i | 1.87857i | ||||||||
\(315\) | −3.36491e86 | + | 2.22362e86i | −0.121928 | + | 0.0805733i | ||||
\(316\) | 7.54514e87 | 2.44692 | ||||||||
\(317\) | 1.77919e87i | 0.516593i | 0.966066 | + | 0.258296i | \(0.0831611\pi\) | ||||
−0.966066 | + | 0.258296i | \(0.916839\pi\) | |||||||
\(318\) | −8.85488e86 | + | 1.64652e87i | −0.230268 | + | 0.428171i | ||||
\(319\) | −5.42991e86 | −0.126508 | ||||||||
\(320\) | − | 3.89034e87i | − | 0.812340i | ||||||
\(321\) | 1.52701e87 | + | 8.21219e86i | 0.285869 | + | 0.153739i | ||||
\(322\) | −1.16849e88 | −1.96187 | ||||||||
\(323\) | 6.22340e87i | 0.937432i | ||||||||
\(324\) | 7.92531e87 | − | 1.85945e88i | 1.07137 | − | 2.51368i | ||||
\(325\) | −1.23882e88 | −1.50346 | ||||||||
\(326\) | − | 2.98243e88i | − | 3.25053i | ||||||
\(327\) | −3.47156e87 | + | 6.45518e87i | −0.339902 | + | 0.632029i | ||||
\(328\) | 5.64205e88 | 4.96423 | ||||||||
\(329\) | 1.21533e87i | 0.0961250i | ||||||||
\(330\) | −2.47837e87 | − | 1.33286e87i | −0.176270 | − | 0.0947971i | ||||
\(331\) | −1.46985e88 | −0.940357 | −0.470178 | − | 0.882571i | \(-0.655810\pi\) | ||||
−0.470178 | + | 0.882571i | \(0.655810\pi\) | |||||||
\(332\) | 8.63735e88i | 4.97219i | ||||||||
\(333\) | −4.71644e87 | − | 7.13720e87i | −0.244380 | − | 0.369811i | ||||
\(334\) | 1.76541e88 | 0.823604 | ||||||||
\(335\) | 1.52144e87i | 0.0639272i | ||||||||
\(336\) | −3.14057e88 | + | 5.83972e88i | −1.18887 | + | 2.21064i | ||||
\(337\) | −9.50112e87 | −0.324137 | −0.162068 | − | 0.986780i | \(-0.551817\pi\) | ||||
−0.162068 | + | 0.986780i | \(0.551817\pi\) | |||||||
\(338\) | − | 9.36125e88i | − | 2.87905i | ||||||
\(339\) | 1.15001e88 | + | 6.18468e87i | 0.318942 | + | 0.171525i | ||||
\(340\) | 1.54939e88 | 0.387613 | ||||||||
\(341\) | 2.19542e88i | 0.495580i | ||||||||
\(342\) | −1.13658e89 | + | 7.51083e88i | −2.31573 | + | 1.53029i | ||||
\(343\) | 5.65732e88 | 1.04068 | ||||||||
\(344\) | − | 1.19967e89i | − | 1.99305i | ||||||
\(345\) | −1.03646e88 | + | 1.92724e88i | −0.155555 | + | 0.289246i | ||||
\(346\) | −3.43468e88 | −0.465825 | ||||||||
\(347\) | − | 7.07834e88i | − | 0.867760i | −0.900971 | − | 0.433880i | \(-0.857144\pi\) | ||
0.900971 | − | 0.433880i | \(-0.142856\pi\) | |||||||
\(348\) | 5.76386e88 | + | 3.09977e88i | 0.638910 | + | 0.343603i | ||||
\(349\) | 1.31421e89 | 1.31758 | 0.658788 | − | 0.752328i | \(-0.271069\pi\) | ||||
0.658788 | + | 0.752328i | \(0.271069\pi\) | |||||||
\(350\) | 1.36416e89i | 1.23732i | ||||||||
\(351\) | 1.91464e89 | − | 1.73794e88i | 1.57158 | − | 0.142655i | ||||
\(352\) | −2.47978e89 | −1.84255 | ||||||||
\(353\) | − | 5.79360e88i | − | 0.389793i | −0.980824 | − | 0.194897i | \(-0.937563\pi\) | ||
0.980824 | − | 0.194897i | \(-0.0624371\pi\) | |||||||
\(354\) | 1.50929e89 | − | 2.80644e89i | 0.919727 | − | 1.71018i | ||||
\(355\) | −4.52030e88 | −0.249560 | ||||||||
\(356\) | − | 1.70731e89i | − | 0.854205i | ||||||
\(357\) | −8.51737e88 | − | 4.58060e88i | −0.386294 | − | 0.207747i | ||||
\(358\) | −4.38764e89 | −1.80437 | ||||||||
\(359\) | 1.99472e89i | 0.744004i | 0.928232 | + | 0.372002i | \(0.121329\pi\) | ||||
−0.928232 | + | 0.372002i | \(0.878671\pi\) | |||||||
\(360\) | 1.18558e89 | + | 1.79409e89i | 0.401184 | + | 0.607095i | ||||
\(361\) | 3.46541e89 | 1.06415 | ||||||||
\(362\) | − | 8.98940e89i | − | 2.50571i | ||||||
\(363\) | 1.44654e89 | − | 2.68976e89i | 0.366098 | − | 0.680740i | ||||
\(364\) | −1.26106e90 | −2.89860 | ||||||||
\(365\) | 9.64072e88i | 0.201307i | ||||||||
\(366\) | 2.39313e89 | + | 1.28702e89i | 0.454077 | + | 0.244200i | ||||
\(367\) | 2.13853e89 | 0.368810 | 0.184405 | − | 0.982850i | \(-0.440964\pi\) | ||||
0.184405 | + | 0.982850i | \(0.440964\pi\) | |||||||
\(368\) | 3.59750e90i | 5.64063i | ||||||||
\(369\) | −8.67816e89 | + | 5.73475e89i | −1.23738 | + | 0.817695i | ||||
\(370\) | 1.43547e89 | 0.186180 | ||||||||
\(371\) | 1.43345e89i | 0.169159i | ||||||||
\(372\) | 1.25330e90 | − | 2.33044e90i | 1.34602 | − | 2.50285i | ||||
\(373\) | 1.92012e90 | 1.87724 | 0.938619 | − | 0.344957i | \(-0.112106\pi\) | ||||
0.938619 | + | 0.344957i | \(0.112106\pi\) | |||||||
\(374\) | − | 6.74753e89i | − | 0.600674i | ||||||
\(375\) | 4.61154e89 | + | 2.48006e89i | 0.373897 | + | 0.201080i | ||||
\(376\) | 6.47983e89 | 0.478618 | ||||||||
\(377\) | 6.22464e89i | 0.418954i | ||||||||
\(378\) | −1.91378e89 | − | 2.10835e90i | −0.117403 | − | 1.29339i | ||||
\(379\) | −2.93102e90 | −1.63925 | −0.819626 | − | 0.572899i | \(-0.805819\pi\) | ||||
−0.819626 | + | 0.572899i | \(0.805819\pi\) | |||||||
\(380\) | − | 1.67350e90i | − | 0.853492i | ||||||
\(381\) | −5.55333e89 | + | 1.03261e90i | −0.258333 | + | 0.480356i | ||||
\(382\) | 1.79191e90 | 0.760497 | ||||||||
\(383\) | 2.91177e90i | 1.12772i | 0.825871 | + | 0.563859i | \(0.190684\pi\) | ||||
−0.825871 | + | 0.563859i | \(0.809316\pi\) | |||||||
\(384\) | 8.35091e90 | + | 4.49107e90i | 2.95217 | + | 1.58766i | ||||
\(385\) | −2.15766e89 | −0.0696397 | ||||||||
\(386\) | − | 6.17058e90i | − | 1.81874i | ||||||
\(387\) | 1.21939e90 | + | 1.84525e90i | 0.328290 | + | 0.496787i | ||||
\(388\) | −1.36082e91 | −3.34727 | ||||||||
\(389\) | 3.00943e90i | 0.676469i | 0.941062 | + | 0.338235i | \(0.109830\pi\) | ||||
−0.941062 | + | 0.338235i | \(0.890170\pi\) | |||||||
\(390\) | −1.52793e90 | + | 2.84111e90i | −0.313937 | + | 0.583749i | ||||
\(391\) | −5.24705e90 | −0.985663 | ||||||||
\(392\) | − | 1.06795e91i | − | 1.83459i | ||||||
\(393\) | −1.33602e90 | − | 7.18503e89i | −0.209929 | − | 0.112899i | ||||
\(394\) | −2.23626e91 | −3.21480 | ||||||||
\(395\) | − | 1.47991e90i | − | 0.194687i | ||||||
\(396\) | 9.02148e90 | − | 5.96162e90i | 1.08629 | − | 0.717848i | ||||
\(397\) | 6.05978e90 | 0.668020 | 0.334010 | − | 0.942570i | \(-0.391598\pi\) | ||||
0.334010 | + | 0.942570i | \(0.391598\pi\) | |||||||
\(398\) | − | 1.92255e91i | − | 1.94075i | ||||||
\(399\) | −4.94752e90 | + | 9.19964e90i | −0.457442 | + | 0.850588i | ||||
\(400\) | 4.19991e91 | 3.55746 | ||||||||
\(401\) | 2.06431e91i | 1.60222i | 0.598520 | + | 0.801108i | \(0.295756\pi\) | ||||
−0.598520 | + | 0.801108i | \(0.704244\pi\) | |||||||
\(402\) | −7.03331e90 | − | 3.78248e90i | −0.500320 | − | 0.269069i | ||||
\(403\) | 2.51674e91 | 1.64120 | ||||||||
\(404\) | − | 1.88537e91i | − | 1.12732i | ||||||
\(405\) | −3.64714e90 | − | 1.55447e90i | −0.199998 | − | 0.0852427i | ||||
\(406\) | 6.85441e90 | 0.344794 | ||||||||
\(407\) | − | 4.57653e90i | − | 0.211219i | ||||||
\(408\) | −2.44227e91 | + | 4.54126e91i | −1.03440 | + | 1.92340i | ||||
\(409\) | −1.88971e91 | −0.734650 | −0.367325 | − | 0.930093i | \(-0.619726\pi\) | ||||
−0.367325 | + | 0.930093i | \(0.619726\pi\) | |||||||
\(410\) | − | 1.74539e91i | − | 0.622956i | ||||||
\(411\) | 3.97258e91 | + | 2.13643e91i | 1.30199 | + | 0.700205i | ||||
\(412\) | −1.78403e91 | −0.537032 | ||||||||
\(413\) | − | 2.44328e91i | − | 0.675648i | ||||||
\(414\) | −6.33250e91 | − | 9.58271e91i | −1.60903 | − | 2.43487i | ||||
\(415\) | 1.69413e91 | 0.395607 | ||||||||
\(416\) | 2.84272e92i | 6.10193i | ||||||||
\(417\) | 1.58539e91 | − | 2.94794e91i | 0.312876 | − | 0.581777i | ||||
\(418\) | −7.28803e91 | −1.32264 | ||||||||
\(419\) | 1.15475e92i | 1.92751i | 0.266789 | + | 0.963755i | \(0.414037\pi\) | ||||
−0.266789 | + | 0.963755i | \(0.585963\pi\) | |||||||
\(420\) | 2.29036e91 | + | 1.23174e91i | 0.351705 | + | 0.189145i | ||||
\(421\) | 4.31281e91 | 0.609379 | 0.304689 | − | 0.952452i | \(-0.401447\pi\) | ||||
0.304689 | + | 0.952452i | \(0.401447\pi\) | |||||||
\(422\) | − | 2.20146e92i | − | 2.86270i | ||||||
\(423\) | −9.96678e90 | + | 6.58630e90i | −0.119300 | + | 0.0788367i | ||||
\(424\) | 7.64281e91 | 0.842264 | ||||||||
\(425\) | 6.12567e91i | 0.621643i | ||||||||
\(426\) | 1.12380e92 | − | 2.08964e92i | 1.05040 | − | 1.95315i | ||||
\(427\) | 2.08345e91 | 0.179394 | ||||||||
\(428\) | − | 1.11794e92i | − | 0.886925i | ||||||
\(429\) | 9.05798e91 | + | 4.87134e91i | 0.662256 | + | 0.356158i | ||||
\(430\) | −3.71124e91 | −0.250106 | ||||||||
\(431\) | − | 2.22171e92i | − | 1.38033i | −0.723652 | − | 0.690165i | \(-0.757538\pi\) | ||
0.723652 | − | 0.690165i | \(-0.242462\pi\) | |||||||
\(432\) | −6.49109e92 | + | 5.89205e91i | −3.71866 | + | 0.337548i | ||||
\(433\) | 2.53676e92 | 1.34030 | 0.670151 | − | 0.742225i | \(-0.266229\pi\) | ||||
0.670151 | + | 0.742225i | \(0.266229\pi\) | |||||||
\(434\) | − | 2.77137e92i | − | 1.35068i | ||||||
\(435\) | 6.07991e90 | − | 1.13053e91i | 0.0273384 | − | 0.0508342i | ||||
\(436\) | 4.72590e92 | 1.96091 | ||||||||
\(437\) | 5.66735e92i | 2.17035i | ||||||||
\(438\) | −4.45671e92 | − | 2.39680e92i | −1.57551 | − | 0.847300i | ||||
\(439\) | 2.94727e91 | 0.0961970 | 0.0480985 | − | 0.998843i | \(-0.484684\pi\) | ||||
0.0480985 | + | 0.998843i | \(0.484684\pi\) | |||||||
\(440\) | 1.15041e92i | 0.346745i | ||||||||
\(441\) | 1.08550e92 | + | 1.64264e92i | 0.302189 | + | 0.457290i | ||||
\(442\) | −7.73510e92 | −1.98924 | ||||||||
\(443\) | 1.72364e92i | 0.409558i | 0.978808 | + | 0.204779i | \(0.0656475\pi\) | ||||
−0.978808 | + | 0.204779i | \(0.934352\pi\) | |||||||
\(444\) | −2.61261e92 | + | 4.85800e92i | −0.573680 | + | 1.06673i | ||||
\(445\) | −3.34872e91 | −0.0679639 | ||||||||
\(446\) | − | 6.64955e92i | − | 1.24759i | ||||||
\(447\) | 1.67780e92 | + | 9.02310e91i | 0.291056 | + | 0.156528i | ||||
\(448\) | 1.56570e93 | 2.51176 | ||||||||
\(449\) | − | 1.03310e93i | − | 1.53292i | −0.642290 | − | 0.766462i | \(-0.722015\pi\) | ||
0.642290 | − | 0.766462i | \(-0.277985\pi\) | |||||||
\(450\) | −1.11873e93 | + | 7.39288e92i | −1.53564 | + | 1.01479i | ||||
\(451\) | −5.56463e92 | −0.706737 | ||||||||
\(452\) | − | 8.41931e92i | − | 0.989536i | ||||||
\(453\) | −1.51846e92 | + | 2.82350e92i | −0.165184 | + | 0.307150i | ||||
\(454\) | 8.78742e92 | 0.884925 | ||||||||
\(455\) | 2.47345e92i | 0.230624i | ||||||||
\(456\) | 4.90503e93 | + | 2.63790e93i | 4.23518 | + | 2.27766i | ||||
\(457\) | −2.36615e93 | −1.89224 | −0.946118 | − | 0.323822i | \(-0.895032\pi\) | ||||
−0.946118 | + | 0.323822i | \(0.895032\pi\) | |||||||
\(458\) | 1.52396e93i | 1.12897i | ||||||||
\(459\) | −8.59369e91 | − | 9.46741e92i | −0.0589842 | − | 0.649811i | ||||
\(460\) | 1.41095e93 | 0.897405 | ||||||||
\(461\) | 2.35999e93i | 1.39116i | 0.718449 | + | 0.695580i | \(0.244853\pi\) | ||||
−0.718449 | + | 0.695580i | \(0.755147\pi\) | |||||||
\(462\) | 5.36419e92 | − | 9.97442e92i | 0.293113 | − | 0.545028i | ||||
\(463\) | 8.48600e92 | 0.429901 | 0.214950 | − | 0.976625i | \(-0.431041\pi\) | ||||
0.214950 | + | 0.976625i | \(0.431041\pi\) | |||||||
\(464\) | − | 2.11031e93i | − | 0.991325i | ||||||
\(465\) | −4.57093e92 | − | 2.45822e92i | −0.199137 | − | 0.107095i | ||||
\(466\) | −1.11127e93 | −0.449068 | ||||||||
\(467\) | 6.86184e92i | 0.257247i | 0.991694 | + | 0.128623i | \(0.0410558\pi\) | ||||
−0.991694 | + | 0.128623i | \(0.958944\pi\) | |||||||
\(468\) | −6.83416e93 | − | 1.03419e94i | −2.37728 | − | 3.59744i | ||||
\(469\) | −6.12316e92 | −0.197663 | ||||||||
\(470\) | − | 2.00456e92i | − | 0.0600613i | ||||||
\(471\) | −1.65582e93 | + | 3.07890e93i | −0.460554 | + | 0.856376i | ||||
\(472\) | −1.30270e94 | −3.36414 | ||||||||
\(473\) | 1.18321e93i | 0.283742i | ||||||||
\(474\) | 6.84132e93 | + | 3.67922e93i | 1.52369 | + | 0.819435i | ||||
\(475\) | 6.61635e93 | 1.36881 | ||||||||
\(476\) | 6.23565e93i | 1.19850i | ||||||||
\(477\) | −1.17556e93 | + | 7.76839e92i | −0.209943 | + | 0.138735i | ||||
\(478\) | 1.23454e94 | 2.04894 | ||||||||
\(479\) | − | 6.99075e93i | − | 1.07840i | −0.842177 | − | 0.539201i | \(-0.818726\pi\) | ||
0.842177 | − | 0.539201i | \(-0.181274\pi\) | |||||||
\(480\) | 2.77662e93 | − | 5.16298e93i | 0.398175 | − | 0.740384i | ||||
\(481\) | −5.24636e93 | −0.699488 | ||||||||
\(482\) | 4.09218e93i | 0.507351i | ||||||||
\(483\) | −7.75636e93 | − | 4.17133e93i | −0.894352 | − | 0.480978i | ||||
\(484\) | −1.96920e94 | −2.11204 | ||||||||
\(485\) | 2.66912e93i | 0.266322i | ||||||||
\(486\) | 1.62532e94 | − | 1.29954e94i | 1.50893 | − | 1.20648i | ||||
\(487\) | 8.04645e93 | 0.695170 | 0.347585 | − | 0.937649i | \(-0.387002\pi\) | ||||
0.347585 | + | 0.937649i | \(0.387002\pi\) | |||||||
\(488\) | − | 1.11085e94i | − | 0.893224i | ||||||
\(489\) | 1.06468e94 | − | 1.97971e94i | 0.796907 | − | 1.48180i | ||||
\(490\) | −3.30375e93 | −0.230221 | ||||||||
\(491\) | − | 2.13489e94i | − | 1.38524i | −0.721305 | − | 0.692618i | \(-0.756457\pi\) | ||
0.721305 | − | 0.692618i | \(-0.243543\pi\) | |||||||
\(492\) | 5.90687e94 | + | 3.17668e94i | 3.56926 | + | 1.91953i | ||||
\(493\) | 3.07793e93 | 0.173227 | ||||||||
\(494\) | 8.35471e94i | 4.38014i | ||||||||
\(495\) | −1.16931e93 | − | 1.76948e93i | −0.0571149 | − | 0.0864296i | ||||
\(496\) | −8.53236e94 | −3.88339 | ||||||||
\(497\) | − | 1.81923e94i | − | 0.771641i | ||||||
\(498\) | −4.21182e94 | + | 7.83164e94i | −1.66511 | + | 3.09618i | ||||
\(499\) | 1.02687e94 | 0.378440 | 0.189220 | − | 0.981935i | \(-0.439404\pi\) | ||||
0.189220 | + | 0.981935i | \(0.439404\pi\) | |||||||
\(500\) | − | 3.37616e94i | − | 1.16004i | ||||||
\(501\) | 1.17186e94 | + | 6.30221e93i | 0.375453 | + | 0.201917i | ||||
\(502\) | 5.17361e94 | 1.54584 | ||||||||
\(503\) | − | 8.86184e93i | − | 0.246970i | −0.992346 | − | 0.123485i | \(-0.960593\pi\) | ||
0.992346 | − | 0.123485i | \(-0.0394071\pi\) | |||||||
\(504\) | −7.22048e94 | + | 4.77147e94i | −1.87714 | + | 1.24046i | ||||
\(505\) | −3.69797e93 | −0.0896944 | ||||||||
\(506\) | − | 6.14465e94i | − | 1.39069i | ||||||
\(507\) | 3.34181e94 | − | 6.21392e94i | 0.705835 | − | 1.31246i | ||||
\(508\) | 7.55985e94 | 1.49033 | ||||||||
\(509\) | 2.07219e94i | 0.381335i | 0.981655 | + | 0.190668i | \(0.0610653\pi\) | ||||
−0.981655 | + | 0.190668i | \(0.938935\pi\) | |||||||
\(510\) | 1.40486e94 | + | 7.55525e93i | 0.241366 | + | 0.129805i | ||||
\(511\) | −3.87999e94 | −0.622443 | ||||||||
\(512\) | − | 1.29528e95i | − | 1.94050i | ||||||
\(513\) | −1.02258e95 | + | 9.28208e93i | −1.43083 | + | 0.129879i | ||||
\(514\) | 1.25484e95 | 1.64013 | ||||||||
\(515\) | 3.49921e93i | 0.0427284i | ||||||||
\(516\) | 6.75461e94 | − | 1.25598e95i | 0.770657 | − | 1.43299i | ||||
\(517\) | −6.39093e93 | −0.0681389 | ||||||||
\(518\) | 5.77716e94i | 0.575669i | ||||||||
\(519\) | −2.27991e94 | − | 1.22612e94i | −0.212354 | − | 0.114203i | ||||
\(520\) | 1.31879e95 | 1.14831 | ||||||||
\(521\) | − | 2.19735e93i | − | 0.0178887i | −0.999960 | − | 0.00894437i | \(-0.997153\pi\) | ||
0.999960 | − | 0.00894437i | \(-0.00284712\pi\) | |||||||
\(522\) | 3.71466e94 | + | 5.62124e94i | 0.282782 | + | 0.427922i | ||||
\(523\) | −1.60824e95 | −1.14497 | −0.572483 | − | 0.819916i | \(-0.694020\pi\) | ||||
−0.572483 | + | 0.819916i | \(0.694020\pi\) | |||||||
\(524\) | 9.78111e94i | 0.651318i | ||||||||
\(525\) | −4.86982e94 | + | 9.05517e94i | −0.303345 | + | 0.564054i | ||||
\(526\) | −4.94348e95 | −2.88092 | ||||||||
\(527\) | − | 1.24447e95i | − | 0.678596i | ||||||
\(528\) | −3.07088e95 | − | 1.65150e95i | −1.56702 | − | 0.842737i | ||||
\(529\) | −2.68437e95 | −1.28202 | ||||||||
\(530\) | − | 2.36434e94i | − | 0.105695i | ||||||
\(531\) | 2.00371e95 | − | 1.32410e95i | 0.838545 | − | 0.554131i | ||||
\(532\) | 6.73515e95 | 2.63900 | ||||||||
\(533\) | 6.37907e95i | 2.34048i | ||||||||
\(534\) | 8.32532e94 | − | 1.54805e95i | 0.286060 | − | 0.531912i | ||||
\(535\) | −2.19273e94 | −0.0705673 | ||||||||
\(536\) | 3.26472e95i | 0.984190i | ||||||||
\(537\) | −2.91248e95 | − | 1.56632e95i | −0.822551 | − | 0.442363i | ||||
\(538\) | 9.16237e95 | 2.42453 | ||||||||
\(539\) | 1.05330e95i | 0.261183i | ||||||||
\(540\) | 2.31088e94 | + | 2.54583e95i | 0.0537027 | + | 0.591626i | ||||
\(541\) | 6.59796e94 | 0.143716 | 0.0718580 | − | 0.997415i | \(-0.477107\pi\) | ||||
0.0718580 | + | 0.997415i | \(0.477107\pi\) | |||||||
\(542\) | 1.11128e96i | 2.26908i | ||||||||
\(543\) | 3.20907e95 | − | 5.96708e95i | 0.614306 | − | 1.14227i | ||||
\(544\) | 1.40565e96 | 2.52300 | ||||||||
\(545\) | − | 9.26940e94i | − | 0.156018i | ||||||
\(546\) | −1.14343e96 | − | 6.14930e95i | −1.80496 | − | 0.970696i | ||||
\(547\) | 1.26128e95 | 0.186748 | 0.0933742 | − | 0.995631i | \(-0.470235\pi\) | ||||
0.0933742 | + | 0.995631i | \(0.470235\pi\) | |||||||
\(548\) | − | 2.90836e96i | − | 4.03951i | ||||||
\(549\) | 1.12910e95 | + | 1.70862e95i | 0.147130 | + | 0.222645i | ||||
\(550\) | −7.17358e95 | −0.877085 | ||||||||
\(551\) | − | 3.32448e95i | − | 0.381433i | ||||||
\(552\) | −2.22405e96 | + | 4.13551e96i | −2.39485 | + | 4.45309i | ||||
\(553\) | 5.95602e95 | 0.601972 | ||||||||
\(554\) | 9.71090e95i | 0.921335i | ||||||||
\(555\) | 9.52849e94 | + | 5.12437e94i | 0.0848730 | + | 0.0456443i | ||||
\(556\) | −2.15821e96 | −1.80500 | ||||||||
\(557\) | 8.69547e94i | 0.0682906i | 0.999417 | + | 0.0341453i | \(0.0108709\pi\) | ||||
−0.999417 | + | 0.0341453i | \(0.989129\pi\) | |||||||
\(558\) | 2.27277e96 | − | 1.50191e96i | 1.67633 | − | 1.10776i | ||||
\(559\) | 1.35639e96 | 0.939661 | ||||||||
\(560\) | − | 8.38562e95i | − | 0.545700i | ||||||
\(561\) | 2.40876e95 | − | 4.47895e95i | 0.147263 | − | 0.273827i | ||||
\(562\) | −2.56570e96 | −1.47379 | ||||||||
\(563\) | 4.14614e95i | 0.223795i | 0.993720 | + | 0.111897i | \(0.0356928\pi\) | ||||
−0.993720 | + | 0.111897i | \(0.964307\pi\) | |||||||
\(564\) | 6.78398e95 | + | 3.64839e95i | 0.344125 | + | 0.185068i | ||||
\(565\) | −1.65137e95 | −0.0787314 | ||||||||
\(566\) | − | 6.59326e96i | − | 2.95478i | ||||||
\(567\) | 6.25611e95 | − | 1.46782e96i | 0.263571 | − | 0.618396i | ||||
\(568\) | −9.69973e96 | −3.84209 | ||||||||
\(569\) | 3.82499e96i | 1.42463i | 0.701861 | + | 0.712314i | \(0.252353\pi\) | ||||
−0.701861 | + | 0.712314i | \(0.747647\pi\) | |||||||
\(570\) | 8.16045e95 | − | 1.51739e96i | 0.285821 | − | 0.531469i | ||||
\(571\) | 5.46607e96 | 1.80057 | 0.900287 | − | 0.435296i | \(-0.143356\pi\) | ||||
0.900287 | + | 0.435296i | \(0.143356\pi\) | |||||||
\(572\) | − | 6.63144e96i | − | 2.05469i | ||||||
\(573\) | 1.18945e96 | + | 6.39681e95i | 0.346685 | + | 0.186445i | ||||
\(574\) | 7.02448e96 | 1.92618 | ||||||||
\(575\) | 5.57835e96i | 1.43923i | ||||||||
\(576\) | 8.48510e96 | + | 1.28402e97i | 2.06001 | + | 3.11733i | ||||
\(577\) | −1.64095e96 | −0.374923 | −0.187462 | − | 0.982272i | \(-0.560026\pi\) | ||||
−0.187462 | + | 0.982272i | \(0.560026\pi\) | |||||||
\(578\) | − | 5.15925e96i | − | 1.10946i | ||||||
\(579\) | 2.20279e96 | − | 4.09597e96i | 0.445886 | − | 0.829101i | ||||
\(580\) | −8.27669e95 | −0.157716 | ||||||||
\(581\) | 6.81819e96i | 1.22322i | ||||||||
\(582\) | −1.23388e97 | − | 6.63575e96i | −2.08434 | − | 1.12095i | ||||
\(583\) | −7.53795e95 | −0.119910 | ||||||||
\(584\) | 2.06872e97i | 3.09922i | ||||||||
\(585\) | −2.02846e96 | + | 1.34045e96i | −0.286227 | + | 0.189146i | ||||
\(586\) | 3.08368e96 | 0.409876 | ||||||||
\(587\) | − | 5.92660e96i | − | 0.742116i | −0.928610 | − | 0.371058i | \(-0.878995\pi\) | ||
0.928610 | − | 0.371058i | \(-0.121005\pi\) | |||||||
\(588\) | 6.01296e96 | − | 1.11808e97i | 0.709385 | − | 1.31906i | ||||
\(589\) | −1.34415e97 | −1.49421 | ||||||||
\(590\) | 4.02995e96i | 0.422162i | ||||||||
\(591\) | −1.48441e97 | − | 7.98308e96i | −1.46552 | − | 0.788149i | ||||
\(592\) | 1.77864e97 | 1.65512 | ||||||||
\(593\) | 2.21183e97i | 1.94016i | 0.242786 | + | 0.970080i | \(0.421939\pi\) | ||||
−0.242786 | + | 0.970080i | \(0.578061\pi\) | |||||||
\(594\) | 1.10870e97 | − | 1.00638e96i | 0.916828 | − | 0.0832217i | ||||
\(595\) | 1.22306e96 | 0.0953575 | ||||||||
\(596\) | − | 1.22833e97i | − | 0.903018i | ||||||
\(597\) | 6.86318e96 | − | 1.27617e97i | 0.475799 | − | 0.884723i | ||||
\(598\) | −7.04398e97 | −4.60550 | ||||||||
\(599\) | 2.52028e97i | 1.55421i | 0.629371 | + | 0.777105i | \(0.283313\pi\) | ||||
−0.629371 | + | 0.777105i | \(0.716687\pi\) | |||||||
\(600\) | 4.82800e97 | + | 2.59647e97i | 2.80849 | + | 1.51039i | ||||
\(601\) | 1.48371e97 | 0.814220 | 0.407110 | − | 0.913379i | \(-0.366537\pi\) | ||||
0.407110 | + | 0.913379i | \(0.366537\pi\) | |||||||
\(602\) | − | 1.49362e97i | − | 0.773328i | ||||||
\(603\) | −3.31837e96 | − | 5.02155e96i | −0.162113 | − | 0.245319i | ||||
\(604\) | 2.06711e97 | 0.952951 | ||||||||
\(605\) | 3.86239e96i | 0.168042i | ||||||||
\(606\) | 9.19359e96 | − | 1.70950e97i | 0.377523 | − | 0.701983i | ||||
\(607\) | 2.49382e97 | 0.966632 | 0.483316 | − | 0.875446i | \(-0.339432\pi\) | ||||
0.483316 | + | 0.875446i | \(0.339432\pi\) | |||||||
\(608\) | − | 1.51825e98i | − | 5.55544i | ||||||
\(609\) | 4.54990e96 | + | 2.44691e96i | 0.157180 | + | 0.0845305i | ||||
\(610\) | −3.43645e96 | −0.112090 | ||||||||
\(611\) | 7.32630e96i | 0.225654i | ||||||||
\(612\) | −5.11380e97 | + | 3.37933e97i | −1.48745 | + | 0.982948i | ||||
\(613\) | −6.24289e97 | −1.71502 | −0.857510 | − | 0.514467i | \(-0.827990\pi\) | ||||
−0.857510 | + | 0.514467i | \(0.827990\pi\) | |||||||
\(614\) | 3.26824e97i | 0.848050i | ||||||||
\(615\) | 6.23076e96 | − | 1.15857e97i | 0.152726 | − | 0.283985i | ||||
\(616\) | −4.62993e97 | −1.07214 | ||||||||
\(617\) | 2.78657e97i | 0.609662i | 0.952406 | + | 0.304831i | \(0.0985999\pi\) | ||||
−0.952406 | + | 0.304831i | \(0.901400\pi\) | |||||||
\(618\) | −1.61761e97 | − | 8.69944e96i | −0.334409 | − | 0.179844i | ||||
\(619\) | 2.81197e97 | 0.549337 | 0.274668 | − | 0.961539i | \(-0.411432\pi\) | ||||
0.274668 | + | 0.961539i | \(0.411432\pi\) | |||||||
\(620\) | 3.34642e97i | 0.617834i | ||||||||
\(621\) | −7.82586e96 | − | 8.62151e97i | −0.136561 | − | 1.50445i | ||||
\(622\) | 1.07762e98 | 1.77747 | ||||||||
\(623\) | − | 1.34772e97i | − | 0.210145i | ||||||
\(624\) | −1.89322e98 | + | 3.52033e98i | −2.79087 | + | 5.18947i | ||||
\(625\) | 6.17333e97 | 0.860437 | ||||||||
\(626\) | 6.65125e97i | 0.876600i | ||||||||
\(627\) | −4.83773e97 | − | 2.60171e97i | −0.602945 | − | 0.324261i | ||||
\(628\) | 2.25410e98 | 2.65696 | ||||||||
\(629\) | 2.59420e97i | 0.289221i | ||||||||
\(630\) | 1.47608e97 | + | 2.23369e97i | 0.155664 | + | 0.235561i | ||||
\(631\) | −1.71915e98 | −1.71509 | −0.857544 | − | 0.514410i | \(-0.828011\pi\) | ||||
−0.857544 | + | 0.514410i | \(0.828011\pi\) | |||||||
\(632\) | − | 3.17561e98i | − | 2.99729i | ||||||
\(633\) | 7.85885e97 | − | 1.46131e98i | 0.701826 | − | 1.30501i | ||||
\(634\) | 1.18106e98 | 0.998038 | ||||||||
\(635\) | − | 1.48279e97i | − | 0.118577i | ||||||
\(636\) | 8.00154e97 | + | 4.30319e97i | 0.605584 | + | 0.325680i | ||||
\(637\) | 1.20746e98 | 0.864953 | ||||||||
\(638\) | 3.60447e97i | 0.244409i | ||||||||
\(639\) | 1.49194e98 | − | 9.85910e97i | 0.957680 | − | 0.632859i | ||||
\(640\) | −1.19916e98 | −0.728748 | ||||||||
\(641\) | 7.69412e97i | 0.442719i | 0.975192 | + | 0.221359i | \(0.0710494\pi\) | ||||
−0.975192 | + | 0.221359i | \(0.928951\pi\) | |||||||
\(642\) | 5.45139e97 | − | 1.01366e98i | 0.297017 | − | 0.552287i | ||||
\(643\) | −7.45449e97 | −0.384622 | −0.192311 | − | 0.981334i | \(-0.561598\pi\) | ||||
−0.192311 | + | 0.981334i | \(0.561598\pi\) | |||||||
\(644\) | 5.67851e98i | 2.77478i | ||||||||
\(645\) | −2.46349e97 | − | 1.32485e97i | −0.114015 | − | 0.0613165i | ||||
\(646\) | 4.13120e98 | 1.81108 | ||||||||
\(647\) | 1.69399e98i | 0.703493i | 0.936095 | + | 0.351747i | \(0.114412\pi\) | ||||
−0.936095 | + | 0.351747i | \(0.885588\pi\) | |||||||
\(648\) | −7.82608e98 | − | 3.33561e98i | −3.07907 | − | 1.31235i | ||||
\(649\) | 1.28482e98 | 0.478938 | ||||||||
\(650\) | 8.22350e98i | 2.90462i | ||||||||
\(651\) | 9.89333e97 | − | 1.83961e98i | 0.331137 | − | 0.615731i | ||||
\(652\) | −1.44936e99 | −4.59739 | ||||||||
\(653\) | − | 5.57852e98i | − | 1.67709i | −0.544830 | − | 0.838547i | \(-0.683406\pi\) | ||
0.544830 | − | 0.838547i | \(-0.316594\pi\) | |||||||
\(654\) | 4.28506e98 | + | 2.30448e98i | 1.22106 | + | 0.656677i | ||||
\(655\) | 1.91847e97 | 0.0518215 | ||||||||
\(656\) | − | 2.16266e99i | − | 5.53802i | ||||||
\(657\) | −2.10271e98 | − | 3.18195e98i | −0.510495 | − | 0.772511i | ||||
\(658\) | 8.06754e97 | 0.185710 | ||||||||
\(659\) | 8.39543e98i | 1.83254i | 0.400561 | + | 0.916270i | \(0.368815\pi\) | ||||
−0.400561 | + | 0.916270i | \(0.631185\pi\) | |||||||
\(660\) | −6.47725e97 | + | 1.20441e98i | −0.134077 | + | 0.249308i | ||||
\(661\) | −8.60076e98 | −1.68844 | −0.844220 | − | 0.535997i | \(-0.819936\pi\) | ||||
−0.844220 | + | 0.535997i | \(0.819936\pi\) | |||||||
\(662\) | 9.75710e98i | 1.81673i | ||||||||
\(663\) | −5.13449e98 | − | 2.76130e98i | −0.906826 | − | 0.487686i | ||||
\(664\) | 3.63530e99 | 6.09056 | ||||||||
\(665\) | − | 1.32103e98i | − | 0.209970i | ||||||
\(666\) | −4.73779e98 | + | 3.13085e98i | −0.714460 | + | 0.472133i | ||||
\(667\) | 2.80292e98 | 0.401058 | ||||||||
\(668\) | − | 8.57931e98i | − | 1.16487i | ||||||
\(669\) | 2.37378e98 | − | 4.41391e98i | 0.305863 | − | 0.568735i | ||||
\(670\) | 1.00996e98 | 0.123505 | ||||||||
\(671\) | 1.09561e98i | 0.127165i | ||||||||
\(672\) | 2.07789e99 | + | 1.11748e99i | 2.28927 | + | 1.23116i | ||||
\(673\) | 3.13253e98 | 0.327619 | 0.163809 | − | 0.986492i | \(-0.447622\pi\) | ||||
0.163809 | + | 0.986492i | \(0.447622\pi\) | |||||||
\(674\) | 6.30701e98i | 0.626220i | ||||||||
\(675\) | −1.00652e99 | + | 9.13631e97i | −0.948833 | + | 0.0861269i | ||||
\(676\) | −4.54927e99 | −4.07199 | ||||||||
\(677\) | 6.53853e98i | 0.555746i | 0.960618 | + | 0.277873i | \(0.0896295\pi\) | ||||
−0.960618 | + | 0.277873i | \(0.910370\pi\) | |||||||
\(678\) | 4.10549e98 | − | 7.63394e98i | 0.331380 | − | 0.616183i | ||||
\(679\) | −1.07421e99 | −0.823469 | ||||||||
\(680\) | − | 6.52108e98i | − | 0.474797i | ||||||
\(681\) | 5.83301e98 | + | 3.13696e98i | 0.403407 | + | 0.216950i | ||||
\(682\) | 1.45735e99 | 0.957441 | ||||||||
\(683\) | 2.94286e98i | 0.183673i | 0.995774 | + | 0.0918364i | \(0.0292737\pi\) | ||||
−0.995774 | + | 0.0918364i | \(0.970726\pi\) | |||||||
\(684\) | 3.65002e99 | + | 5.52343e99i | 2.16437 | + | 3.27526i | ||||
\(685\) | −5.70447e98 | −0.321400 | ||||||||
\(686\) | − | 3.75543e99i | − | 2.01055i | ||||||
\(687\) | −5.44030e98 | + | 1.01159e99i | −0.276782 | + | 0.514660i | ||||
\(688\) | −4.59850e99 | −2.22341 | ||||||||
\(689\) | 8.64120e98i | 0.397101i | ||||||||
\(690\) | 1.27934e99 | + | 6.88021e98i | 0.558813 | + | 0.300527i | ||||
\(691\) | 7.70743e98 | 0.320021 | 0.160010 | − | 0.987115i | \(-0.448847\pi\) | ||||
0.160010 | + | 0.987115i | \(0.448847\pi\) | |||||||
\(692\) | 1.66914e99i | 0.658841i | ||||||||
\(693\) | 7.12141e98 | − | 4.70601e98i | 0.267241 | − | 0.176599i | ||||
\(694\) | −4.69872e99 | −1.67648 | ||||||||
\(695\) | 4.23313e98i | 0.143613i | ||||||||
\(696\) | 1.30464e99 | − | 2.42590e99i | 0.420887 | − | 0.782617i | ||||
\(697\) | 3.15430e99 | 0.967733 | ||||||||
\(698\) | − | 8.72397e99i | − | 2.54551i | ||||||
\(699\) | −7.37651e98 | − | 3.96705e98i | −0.204715 | − | 0.110095i | ||||
\(700\) | 6.62937e99 | 1.75001 | ||||||||
\(701\) | 2.68663e99i | 0.674648i | 0.941389 | + | 0.337324i | \(0.109522\pi\) | ||||
−0.941389 | + | 0.337324i | \(0.890478\pi\) | |||||||
\(702\) | −1.15367e99 | − | 1.27097e100i | −0.275603 | − | 3.03624i | ||||
\(703\) | 2.80200e99 | 0.636842 | ||||||||
\(704\) | 8.23340e99i | 1.78048i | ||||||||
\(705\) | 7.15596e97 | − | 1.33061e98i | 0.0147248 | − | 0.0273799i | ||||
\(706\) | −3.84589e99 | −0.753065 | ||||||||
\(707\) | − | 1.48828e99i | − | 0.277335i | ||||||
\(708\) | −1.36384e100 | − | 7.33467e99i | −2.41880 | − | 1.30082i | ||||
\(709\) | 4.51807e99 | 0.762667 | 0.381333 | − | 0.924438i | \(-0.375465\pi\) | ||||
0.381333 | + | 0.924438i | \(0.375465\pi\) | |||||||
\(710\) | 3.00065e99i | 0.482140i | ||||||||
\(711\) | 3.22778e99 | + | 4.88447e99i | 0.493706 | + | 0.747105i | ||||
\(712\) | −7.18573e99 | −1.04634 | ||||||||
\(713\) | − | 1.13327e100i | − | 1.57109i | ||||||
\(714\) | −3.04068e99 | + | 5.65397e99i | −0.401359 | + | 0.746305i | ||||
\(715\) | −1.30069e99 | −0.163479 | ||||||||
\(716\) | 2.13225e100i | 2.55201i | ||||||||
\(717\) | 8.19479e99 | + | 4.40711e99i | 0.934044 | + | 0.502324i | ||||
\(718\) | 1.32413e100 | 1.43739 | ||||||||
\(719\) | 9.22457e99i | 0.953751i | 0.878971 | + | 0.476876i | \(0.158231\pi\) | ||||
−0.878971 | + | 0.476876i | \(0.841769\pi\) | |||||||
\(720\) | 6.87697e99 | − | 4.54447e99i | 0.677267 | − | 0.447555i | ||||
\(721\) | −1.40829e99 | −0.132116 | ||||||||
\(722\) | − | 2.30040e100i | − | 2.05590i | ||||||
\(723\) | −1.46084e99 | + | 2.71636e99i | −0.124384 | + | 0.231284i | ||||
\(724\) | −4.36856e100 | −3.54396 | ||||||||
\(725\) | − | 3.27227e99i | − | 0.252941i | ||||||
\(726\) | −1.78551e100 | − | 9.60236e99i | −1.31516 | − | 0.707288i | ||||
\(727\) | 2.22427e100 | 1.56129 | 0.780644 | − | 0.624976i | \(-0.214891\pi\) | ||||
0.780644 | + | 0.624976i | \(0.214891\pi\) | |||||||
\(728\) | 5.30757e100i | 3.55057i | ||||||||
\(729\) | 1.54279e100 | − | 2.82409e99i | 0.983656 | − | 0.180059i | ||||
\(730\) | 6.39967e99 | 0.388918 | ||||||||
\(731\) | − | 6.70702e99i | − | 0.388527i | ||||||
\(732\) | 6.25448e99 | − | 1.16299e100i | 0.345385 | − | 0.642225i | ||||
\(733\) | −3.64397e100 | −1.91839 | −0.959193 | − | 0.282752i | \(-0.908753\pi\) | ||||
−0.959193 | + | 0.282752i | \(0.908753\pi\) | |||||||
\(734\) | − | 1.41959e100i | − | 0.712527i | ||||||
\(735\) | −2.19300e99 | − | 1.17938e99i | −0.104950 | − | 0.0564415i | ||||
\(736\) | 1.28006e101 | 5.84127 | ||||||||
\(737\) | − | 3.21993e99i | − | 0.140115i | ||||||
\(738\) | 3.80682e100 | + | 5.76071e100i | 1.57976 | + | 2.39058i | ||||
\(739\) | 5.10703e99 | 0.202122 | 0.101061 | − | 0.994880i | \(-0.467776\pi\) | ||||
0.101061 | + | 0.994880i | \(0.467776\pi\) | |||||||
\(740\) | − | 6.97590e99i | − | 0.263324i | ||||||
\(741\) | −2.98249e100 | + | 5.54578e100i | −1.07385 | + | 1.99676i | ||||
\(742\) | 9.51548e99 | 0.326809 | ||||||||
\(743\) | − | 2.04411e100i | − | 0.669723i | −0.942267 | − | 0.334861i | \(-0.891311\pi\) | ||
0.942267 | − | 0.334861i | \(-0.108689\pi\) | |||||||
\(744\) | −9.80837e100 | − | 5.27489e100i | −3.06580 | − | 1.64877i | ||||
\(745\) | −2.40925e99 | −0.0718477 | ||||||||
\(746\) | − | 1.27461e101i | − | 3.62675i | ||||||
\(747\) | −5.59153e100 | + | 3.69503e100i | −1.51813 | + | 1.00322i | ||||
\(748\) | −3.27908e100 | −0.849565 | ||||||||
\(749\) | − | 8.82484e99i | − | 0.218194i | ||||||
\(750\) | 1.64631e100 | − | 3.06122e100i | 0.388479 | − | 0.722355i | ||||
\(751\) | −2.05511e100 | −0.462848 | −0.231424 | − | 0.972853i | \(-0.574338\pi\) | ||||
−0.231424 | + | 0.972853i | \(0.574338\pi\) | |||||||
\(752\) | − | 2.48380e100i | − | 0.533939i | ||||||
\(753\) | 3.43420e100 | + | 1.84689e100i | 0.704695 | + | 0.378981i | ||||
\(754\) | 4.13202e100 | 0.809404 | ||||||||
\(755\) | − | 4.05443e99i | − | 0.0758206i | ||||||
\(756\) | −1.02459e101 | + | 9.30034e99i | −1.82931 | + | 0.166049i | ||||
\(757\) | −7.98590e100 | −1.36134 | −0.680672 | − | 0.732588i | \(-0.738312\pi\) | ||||
−0.680672 | + | 0.732588i | \(0.738312\pi\) | |||||||
\(758\) | 1.94566e101i | 3.16697i | ||||||||
\(759\) | 2.19354e100 | − | 4.07877e100i | 0.340944 | − | 0.633967i | ||||
\(760\) | −7.04344e100 | −1.04546 | ||||||||
\(761\) | 9.06307e100i | 1.28473i | 0.766398 | + | 0.642366i | \(0.222047\pi\) | ||||
−0.766398 | + | 0.642366i | \(0.777953\pi\) | |||||||
\(762\) | 6.85465e100 | + | 3.68640e100i | 0.928029 | + | 0.499089i | ||||
\(763\) | 3.73055e100 | 0.482407 | ||||||||
\(764\) | − | 8.70809e100i | − | 1.07561i | ||||||
\(765\) | 6.62822e99 | + | 1.00302e100i | 0.0782072 | + | 0.118348i | ||||
\(766\) | 1.93289e101 | 2.17871 | ||||||||
\(767\) | − | 1.47287e101i | − | 1.58609i | ||||||
\(768\) | 1.26113e101 | − | 2.34499e101i | 1.29752 | − | 2.41268i | ||||
\(769\) | 4.51479e100 | 0.443829 | 0.221915 | − | 0.975066i | \(-0.428769\pi\) | ||||
0.221915 | + | 0.975066i | \(0.428769\pi\) | |||||||
\(770\) | 1.43229e100i | 0.134541i | ||||||||
\(771\) | 8.32950e100 | + | 4.47956e100i | 0.747680 | + | 0.402098i | ||||
\(772\) | −2.99870e101 | −2.57234 | ||||||||
\(773\) | − | 1.64071e101i | − | 1.34509i | −0.740057 | − | 0.672544i | \(-0.765202\pi\) | ||
0.740057 | − | 0.672544i | \(-0.234798\pi\) | |||||||
\(774\) | 1.22491e101 | − | 8.09449e100i | 0.959774 | − | 0.634243i | ||||
\(775\) | −1.32304e101 | −0.990864 | ||||||||
\(776\) | 5.72744e101i | 4.10015i | ||||||||
\(777\) | −2.06235e100 | + | 3.83483e100i | −0.141132 | + | 0.262428i | ||||
\(778\) | 1.99771e101 | 1.30691 | ||||||||
\(779\) | − | 3.40697e101i | − | 2.13087i | ||||||
\(780\) | 1.38069e101 | + | 7.42526e100i | 0.825627 | + | 0.444018i | ||||
\(781\) | 9.56664e100 | 0.546982 | ||||||||
\(782\) | 3.48308e101i | 1.90426i | ||||||||
\(783\) | 4.59067e99 | + | 5.05740e100i | 0.0240002 | + | 0.264403i | ||||
\(784\) | −4.09358e101 | −2.04664 | ||||||||
\(785\) | − | 4.42119e100i | − | 0.211398i | ||||||
\(786\) | −4.76955e100 | + | 8.86871e100i | −0.218116 | + | 0.405575i | ||||
\(787\) | 2.67770e101 | 1.17124 | 0.585621 | − | 0.810585i | \(-0.300851\pi\) | ||||
0.585621 | + | 0.810585i | \(0.300851\pi\) | |||||||
\(788\) | 1.08675e102i | 4.54687i | ||||||||
\(789\) | −3.28144e101 | − | 1.76474e101i | −1.31332 | − | 0.706295i | ||||
\(790\) | −9.82387e100 | −0.376127 | ||||||||
\(791\) | − | 6.64607e100i | − | 0.243438i | ||||||
\(792\) | −2.50913e101 | − | 3.79697e101i | −0.879310 | − | 1.33062i | ||||
\(793\) | 1.25596e101 | 0.421128 | ||||||||
\(794\) | − | 4.02259e101i | − | 1.29059i | ||||||
\(795\) | 8.44029e99 | − | 1.56943e100i | 0.0259124 | − | 0.0481827i | ||||
\(796\) | −9.34297e101 | −2.74491 | ||||||||
\(797\) | − | 1.59526e101i | − | 0.448528i | −0.974528 | − | 0.224264i | \(-0.928002\pi\) | ||
0.974528 | − | 0.224264i | \(-0.0719977\pi\) | |||||||
\(798\) | 6.10688e101 | + | 3.28425e101i | 1.64330 | + | 0.883761i | ||||
\(799\) | 3.62268e100 | 0.0933023 | ||||||||
\(800\) | − | 1.49441e102i | − | 3.68400i | ||||||
\(801\) | 1.10525e101 | − | 7.30380e100i | 0.260810 | − | 0.172350i | ||||
\(802\) | 1.37032e102 | 3.09542 | ||||||||
\(803\) | − | 2.04034e101i | − | 0.441222i | ||||||
\(804\) | −1.83816e101 | + | 3.41796e101i | −0.380559 | + | 0.707629i | ||||
\(805\) | 1.11378e101 | 0.220773 | ||||||||
\(806\) | − | 1.67065e102i | − | 3.17073i | ||||||
\(807\) | 6.08190e101 | + | 3.27081e101i | 1.10526 | + | 0.594404i | ||||
\(808\) | −7.93516e101 | −1.38089 | ||||||||
\(809\) | 1.02101e102i | 1.70150i | 0.525569 | + | 0.850751i | \(0.323853\pi\) | ||||
−0.525569 | + | 0.850751i | \(0.676147\pi\) | |||||||
\(810\) | −1.03189e101 | + | 2.42103e101i | −0.164686 | + | 0.386389i | ||||
\(811\) | −5.68597e101 | −0.869109 | −0.434555 | − | 0.900645i | \(-0.643094\pi\) | ||||
−0.434555 | + | 0.900645i | \(0.643094\pi\) | |||||||
\(812\) | − | 3.33103e101i | − | 0.487660i | ||||||
\(813\) | −3.96710e101 | + | 7.37661e101i | −0.556294 | + | 1.03440i | ||||
\(814\) | −3.03798e101 | −0.408066 | ||||||||
\(815\) | 2.84279e101i | 0.365787i | ||||||||
\(816\) | 1.74072e102 | + | 9.36150e101i | 2.14572 | + | 1.15396i | ||||
\(817\) | −7.24427e101 | −0.855505 | ||||||||
\(818\) | 1.25442e102i | 1.41932i | ||||||||
\(819\) | −5.39478e101 | − | 8.16370e101i | −0.584840 | − | 0.885015i | ||||
\(820\) | −8.48204e101 | −0.881080 | ||||||||
\(821\) | − | 9.76445e101i | − | 0.971935i | −0.873977 | − | 0.485968i | \(-0.838467\pi\) | ||
0.873977 | − | 0.485968i | \(-0.161533\pi\) | |||||||
\(822\) | 1.41820e102 | − | 2.63707e102i | 1.35277 | − | 2.51540i | ||||
\(823\) | 1.73425e101 | 0.158532 | 0.0792659 | − | 0.996854i | \(-0.474742\pi\) | ||||
0.0792659 | + | 0.996854i | \(0.474742\pi\) | |||||||
\(824\) | 7.50865e101i | 0.657824i | ||||||||
\(825\) | −4.76176e101 | − | 2.56085e101i | −0.399833 | − | 0.215028i | ||||
\(826\) | −1.62189e102 | −1.30533 | ||||||||
\(827\) | 1.64045e102i | 1.26553i | 0.774345 | + | 0.632763i | \(0.218079\pi\) | ||||
−0.774345 | + | 0.632763i | \(0.781921\pi\) | |||||||
\(828\) | −4.65689e102 | + | 3.07739e102i | −3.44377 | + | 2.27573i | ||||
\(829\) | −9.95257e101 | −0.705548 | −0.352774 | − | 0.935709i | \(-0.614762\pi\) | ||||
−0.352774 | + | 0.935709i | \(0.614762\pi\) | |||||||
\(830\) | − | 1.12459e102i | − | 0.764298i | ||||||
\(831\) | −3.46663e101 | + | 6.44601e101i | −0.225877 | + | 0.420006i | ||||
\(832\) | 9.43844e102 | 5.89636 | ||||||||
\(833\) | − | 5.97059e101i | − | 0.357637i | ||||||
\(834\) | −1.95689e102 | − | 1.05241e102i | −1.12397 | − | 0.604465i | ||||
\(835\) | −1.68275e101 | −0.0926815 | ||||||||
\(836\) | 3.54175e102i | 1.87067i | ||||||||
\(837\) | 2.04480e102 | − | 1.85610e101i | 1.03576 | − | 0.0940176i | ||||
\(838\) | 7.66542e102 | 3.72387 | ||||||||
\(839\) | 2.90931e102i | 1.35557i | 0.735262 | + | 0.677783i | \(0.237059\pi\) | ||||
−0.735262 | + | 0.677783i | \(0.762941\pi\) | |||||||
\(840\) | 5.18417e101 | − | 9.63968e101i | 0.231688 | − | 0.430812i | ||||
\(841\) | 2.16828e102 | 0.929515 | ||||||||
\(842\) | − | 2.86292e102i | − | 1.17730i | ||||||
\(843\) | −1.70309e102 | − | 9.15914e101i | −0.671851 | − | 0.361318i | ||||
\(844\) | −1.06984e103 | −4.04886 | ||||||||
\(845\) | 8.92295e101i | 0.323984i | ||||||||
\(846\) | 4.37210e101 | + | 6.61612e101i | 0.152310 | + | 0.230484i | ||||
\(847\) | −1.55445e102 | −0.519587 | ||||||||
\(848\) | − | 2.92958e102i | − | 0.939617i | ||||||
\(849\) | 2.35368e102 | − | 4.37655e102i | 0.724401 | − | 1.34698i | ||||
\(850\) | 4.06632e102 | 1.20099 | ||||||||
\(851\) | 2.36241e102i | 0.669608i | ||||||||
\(852\) | −1.01550e103 | − | 5.46131e102i | −2.76245 | − | 1.48563i | ||||
\(853\) | 2.75552e102 | 0.719428 | 0.359714 | − | 0.933063i | \(-0.382874\pi\) | ||||
0.359714 | + | 0.933063i | \(0.382874\pi\) | |||||||
\(854\) | − | 1.38303e102i | − | 0.346582i | ||||||
\(855\) | 1.08337e102 | − | 7.15917e101i | 0.260592 | − | 0.172206i | ||||
\(856\) | −4.70520e102 | −1.08642 | ||||||||
\(857\) | 6.19181e102i | 1.37243i | 0.727401 | + | 0.686213i | \(0.240728\pi\) | ||||
−0.727401 | + | 0.686213i | \(0.759272\pi\) | |||||||
\(858\) | 3.23368e102 | − | 6.01284e102i | 0.688084 | − | 1.27945i | ||||
\(859\) | 3.27450e102 | 0.668935 | 0.334468 | − | 0.942407i | \(-0.391443\pi\) | ||||
0.334468 | + | 0.942407i | \(0.391443\pi\) | |||||||
\(860\) | 1.80355e102i | 0.353738i | ||||||||
\(861\) | 4.66279e102 | + | 2.50762e102i | 0.878082 | + | 0.472228i | ||||
\(862\) | −1.47481e103 | −2.66675 | ||||||||
\(863\) | 1.15167e102i | 0.199964i | 0.994989 | + | 0.0999820i | \(0.0318785\pi\) | ||||
−0.994989 | + | 0.0999820i | \(0.968121\pi\) | |||||||
\(864\) | 2.09651e102 | + | 2.30966e103i | 0.349555 | + | 3.85094i | ||||
\(865\) | 3.27387e101 | 0.0524200 | ||||||||
\(866\) | − | 1.68394e103i | − | 2.58941i | ||||||
\(867\) | 1.84177e102 | − | 3.42466e102i | 0.271998 | − | 0.505766i | ||||
\(868\) | −1.34680e103 | −1.91034 | ||||||||
\(869\) | 3.13204e102i | 0.426712i | ||||||||
\(870\) | −7.50462e101 | − | 4.03595e101i | −0.0982098 | − | 0.0528167i | ||||
\(871\) | −3.69120e102 | −0.464015 | ||||||||
\(872\) | − | 1.98904e103i | − | 2.40197i | ||||||
\(873\) | −5.82154e102 | − | 8.80950e102i | −0.675366 | − | 1.02200i | ||||
\(874\) | 3.76208e103 | 4.19303 | ||||||||
\(875\) | − | 2.66508e102i | − | 0.285384i | ||||||
\(876\) | −1.16477e103 | + | 2.16582e103i | −1.19838 | + | 2.22833i | ||||
\(877\) | 5.90447e102 | 0.583707 | 0.291854 | − | 0.956463i | \(-0.405728\pi\) | ||||
0.291854 | + | 0.956463i | \(0.405728\pi\) | |||||||
\(878\) | − | 1.95645e102i | − | 0.185849i | ||||||
\(879\) | 2.04692e102 | + | 1.10082e102i | 0.186849 | + | 0.100486i | ||||
\(880\) | 4.40967e102 | 0.386823 | ||||||||
\(881\) | − | 1.08160e103i | − | 0.911824i | −0.890025 | − | 0.455912i | \(-0.849313\pi\) | ||
0.890025 | − | 0.455912i | \(-0.150687\pi\) | |||||||
\(882\) | 1.09041e103 | − | 7.20572e102i | 0.883467 | − | 0.583817i | ||||
\(883\) | −2.86872e102 | −0.223390 | −0.111695 | − | 0.993743i | \(-0.535628\pi\) | ||||
−0.111695 | + | 0.993743i | \(0.535628\pi\) | |||||||
\(884\) | 3.75901e103i | 2.81348i | ||||||||
\(885\) | −1.43862e102 | + | 2.67504e102i | −0.103498 | + | 0.192449i | ||||
\(886\) | 1.14418e103 | 0.791250 | ||||||||
\(887\) | 2.06382e103i | 1.37197i | 0.727614 | + | 0.685987i | \(0.240629\pi\) | ||||
−0.727614 | + | 0.685987i | \(0.759371\pi\) | |||||||
\(888\) | 2.04464e103 | + | 1.09960e103i | 1.30666 | + | 0.702715i | ||||
\(889\) | 5.96763e102 | 0.366640 | ||||||||
\(890\) | 2.22294e102i | 0.131304i | ||||||||
\(891\) | 7.71870e102 | + | 3.28984e102i | 0.438354 | + | 0.186834i | ||||
\(892\) | −3.23147e103 | −1.76453 | ||||||||
\(893\) | − | 3.91287e102i | − | 0.205444i | ||||||
\(894\) | 5.98969e102 | − | 1.11375e103i | 0.302406 | − | 0.562308i | ||||
\(895\) | 4.18221e102 | 0.203048 | ||||||||
\(896\) | − | 4.82612e103i | − | 2.25329i | ||||||
\(897\) | −4.67573e103 | − | 2.51459e103i | −2.09949 | − | 1.12910i | ||||
\(898\) | −6.85790e103 | −2.96155 | ||||||||
\(899\) | 6.64782e102i | 0.276115i | ||||||||
\(900\) | 3.59270e103 | + | 5.43669e103i | 1.43527 | + | 2.17193i | ||||
\(901\) | 4.27286e102 | 0.164192 | ||||||||
\(902\) | 3.69390e103i | 1.36539i | ||||||||
\(903\) | 5.33198e102 | − | 9.91453e102i | 0.189591 | − | 0.352534i | ||||
\(904\) | −3.54353e103 | −1.21211 | ||||||||
\(905\) | 8.56851e102i | 0.281971i | ||||||||
\(906\) | 1.87428e103 | + | 1.00798e103i | 0.593401 | + | 0.319128i | ||||
\(907\) | −3.06332e103 | −0.933120 | −0.466560 | − | 0.884490i | \(-0.654507\pi\) | ||||
−0.466560 | + | 0.884490i | \(0.654507\pi\) | |||||||
\(908\) | − | 4.27040e103i | − | 1.25160i | ||||||
\(909\) | 1.22053e103 | − | 8.06554e102i | 0.344200 | − | 0.227456i | ||||
\(910\) | 1.64192e103 | 0.445557 | ||||||||
\(911\) | − | 1.38756e103i | − | 0.362334i | −0.983452 | − | 0.181167i | \(-0.942013\pi\) | ||
0.983452 | − | 0.181167i | \(-0.0579874\pi\) | |||||||
\(912\) | 1.01114e104 | − | 1.88016e104i | 2.54092 | − | 4.72471i | ||||
\(913\) | −3.58542e103 | −0.867087 | ||||||||
\(914\) | 1.57069e104i | 3.65573i | ||||||||
\(915\) | −2.28109e102 | − | 1.22676e102i | −0.0510979 | − | 0.0274802i | ||||
\(916\) | 7.40598e103 | 1.59677 | ||||||||
\(917\) | 7.72105e102i | 0.160232i | ||||||||
\(918\) | −6.28463e103 | + | 5.70464e102i | −1.25541 | + | 0.113955i | ||||
\(919\) | −4.69756e103 | −0.903295 | −0.451648 | − | 0.892196i | \(-0.649164\pi\) | ||||
−0.451648 | + | 0.892196i | \(0.649164\pi\) | |||||||
\(920\) | − | 5.93843e103i | − | 1.09925i | ||||||
\(921\) | −1.16671e103 | + | 2.16943e103i | −0.207910 | + | 0.386597i | ||||
\(922\) | 1.56660e104 | 2.68767 | ||||||||
\(923\) | − | 1.09668e104i | − | 1.81143i | ||||||
\(924\) | −4.84725e103 | − | 2.60683e103i | −0.770862 | − | 0.414565i | ||||
\(925\) | 2.75800e103 | 0.422311 | ||||||||
\(926\) | − | 5.63315e103i | − | 0.830552i | ||||||
\(927\) | −7.63202e102 | − | 1.15492e103i | −0.108355 | − | 0.163969i | ||||
\(928\) | −7.50888e103 | −1.02659 | ||||||||
\(929\) | 6.06252e103i | 0.798185i | 0.916911 | + | 0.399092i | \(0.130675\pi\) | ||||
−0.916911 | + | 0.399092i | \(0.869325\pi\) | |||||||
\(930\) | −1.63181e103 | + | 3.03426e103i | −0.206903 | + | 0.384724i | ||||
\(931\) | −6.44886e103 | −0.787488 | ||||||||
\(932\) | 5.40042e103i | 0.635141i | ||||||||
\(933\) | 7.15314e103 | + | 3.84692e103i | 0.810287 | + | 0.435768i | ||||
\(934\) | 4.55501e103 | 0.496991 | ||||||||
\(935\) | 6.43161e102i | 0.0675948i | ||||||||
\(936\) | −4.35269e104 | + | 2.87637e104i | −4.40660 | + | 2.91199i | ||||
\(937\) | 2.29002e103 | 0.223334 | 0.111667 | − | 0.993746i | \(-0.464381\pi\) | ||||
0.111667 | + | 0.993746i | \(0.464381\pi\) | |||||||
\(938\) | 4.06466e103i | 0.381878i | ||||||||
\(939\) | −2.37439e103 | + | 4.41504e103i | −0.214909 | + | 0.399612i | ||||
\(940\) | −9.74154e102 | −0.0849479 | ||||||||
\(941\) | − | 1.32612e104i | − | 1.11415i | −0.830461 | − | 0.557077i | \(-0.811923\pi\) | ||
0.830461 | − | 0.557077i | \(-0.188077\pi\) | |||||||
\(942\) | 2.04383e104 | + | 1.09916e104i | 1.65449 | + | 0.889773i | ||||
\(943\) | 2.87247e104 | 2.24050 | ||||||||
\(944\) | 4.99339e104i | 3.75298i | ||||||||
\(945\) | 1.82417e102 | + | 2.00964e103i | 0.0132115 | + | 0.145547i | ||||
\(946\) | 7.85437e103 | 0.548178 | ||||||||
\(947\) | − | 1.08526e104i | − | 0.729936i | −0.931020 | − | 0.364968i | \(-0.881080\pi\) | ||
0.931020 | − | 0.364968i | \(-0.118920\pi\) | |||||||
\(948\) | 1.78799e104 | − | 3.32466e104i | 1.15897 | − | 2.15504i | ||||
\(949\) | −2.33896e104 | −1.46119 | ||||||||
\(950\) | − | 4.39205e104i | − | 2.64448i | ||||||
\(951\) | 7.83975e103 | + | 4.21618e103i | 0.454972 | + | 0.244681i | ||||
\(952\) | 2.62447e104 | 1.46807 | ||||||||
\(953\) | 5.46083e103i | 0.294447i | 0.989103 | + | 0.147224i | \(0.0470337\pi\) | ||||
−0.989103 | + | 0.147224i | \(0.952966\pi\) | |||||||
\(954\) | 5.15679e103 | + | 7.80356e103i | 0.268032 | + | 0.405601i | ||||
\(955\) | −1.70801e103 | −0.0855799 | ||||||||
\(956\) | − | 5.99948e104i | − | 2.89793i | ||||||
\(957\) | −1.28674e103 | + | 2.39261e103i | −0.0599200 | + | 0.111418i | ||||
\(958\) | −4.64058e104 | −2.08343 | ||||||||
\(959\) | − | 2.29582e104i | − | 0.993770i | ||||||
\(960\) | −1.71422e104 | − | 9.21899e103i | −0.715441 | − | 0.384760i | ||||
\(961\) | 2.02884e103 | 0.0816449 | ||||||||
\(962\) | 3.48262e104i | 1.35138i | ||||||||
\(963\) | 7.23717e103 | − | 4.78251e103i | 0.270800 | − | 0.178952i | ||||
\(964\) | 1.98867e104 | 0.717574 | ||||||||
\(965\) | 5.88167e103i | 0.204665i | ||||||||
\(966\) | −2.76900e104 | + | 5.14880e104i | −0.929230 | + | 1.72785i | ||||
\(967\) | 4.10955e104 | 1.33005 | 0.665025 | − | 0.746821i | \(-0.268421\pi\) | ||||
0.665025 | + | 0.746821i | \(0.268421\pi\) | |||||||
\(968\) | 8.28798e104i | 2.58709i | ||||||||
\(969\) | 2.74225e104 | + | 1.47477e104i | 0.825611 | + | 0.444009i | ||||
\(970\) | 1.77181e104 | 0.514524 | ||||||||
\(971\) | − | 4.10883e104i | − | 1.15092i | −0.817830 | − | 0.575460i | \(-0.804823\pi\) | ||
0.817830 | − | 0.575460i | \(-0.195177\pi\) | |||||||
\(972\) | −6.31534e104 | − | 7.89855e104i | −1.70639 | − | 2.13417i | ||||
\(973\) | −1.70366e104 | −0.444051 | ||||||||
\(974\) | − | 5.34137e104i | − | 1.34304i | ||||||
\(975\) | −2.93565e104 | + | 5.45869e104i | −0.712104 | + | 1.32412i | ||||
\(976\) | −4.25801e104 | −0.996467 | ||||||||
\(977\) | 2.84359e104i | 0.642033i | 0.947074 | + | 0.321016i | \(0.104024\pi\) | ||||
−0.947074 | + | 0.321016i | \(0.895976\pi\) | |||||||
\(978\) | −1.31416e105 | − | 7.06750e104i | −2.86279 | − | 1.53959i | ||||
\(979\) | 7.08714e103 | 0.148962 | ||||||||
\(980\) | 1.60552e104i | 0.325614i | ||||||||
\(981\) | 2.02172e104 | + | 3.05939e104i | 0.395645 | + | 0.598714i | ||||
\(982\) | −1.41718e105 | −2.67622 | ||||||||
\(983\) | 8.43431e104i | 1.53701i | 0.639845 | + | 0.768504i | \(0.278999\pi\) | ||||
−0.639845 | + | 0.768504i | \(0.721001\pi\) | |||||||
\(984\) | 1.33701e105 | − | 2.48609e105i | 2.35128 | − | 4.37208i | ||||
\(985\) | 2.13156e104 | 0.361767 | ||||||||
\(986\) | − | 2.04318e104i | − | 0.334669i | ||||||
\(987\) | 5.35516e103 | + | 2.87998e103i | 0.0846589 | + | 0.0455291i | ||||
\(988\) | 4.06012e105 | 6.19507 | ||||||||
\(989\) | − | 6.10776e104i | − | 0.899521i | ||||||
\(990\) | −1.17461e104 | + | 7.76210e103i | −0.166979 | + | 0.110344i | ||||
\(991\) | −5.20468e104 | −0.714194 | −0.357097 | − | 0.934067i | \(-0.616233\pi\) | ||||
−0.357097 | + | 0.934067i | \(0.616233\pi\) | |||||||
\(992\) | 3.03598e105i | 4.02152i | ||||||||
\(993\) | −3.48312e104 | + | 6.47668e104i | −0.445395 | + | 0.828187i | ||||
\(994\) | −1.20764e105 | −1.49078 | ||||||||
\(995\) | 1.83253e104i | 0.218396i | ||||||||
\(996\) | 3.80593e105 | + | 2.04681e105i | 4.37909 | + | 2.35505i | ||||
\(997\) | −1.08854e105 | −1.20925 | −0.604623 | − | 0.796512i | \(-0.706676\pi\) | ||||
−0.604623 | + | 0.796512i | \(0.706676\pi\) | |||||||
\(998\) | − | 6.81654e104i | − | 0.731131i | ||||||
\(999\) | −4.26257e104 | + | 3.86919e103i | −0.441448 | + | 0.0400708i |
(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.2.1 | ✓ | 22 | |
3.2 | odd | 2 | inner | 3.71.b.a.2.22 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.71.b.a.2.1 | ✓ | 22 | 1.1 | even | 1 | trivial | |
3.71.b.a.2.22 | yes | 22 | 3.2 | odd | 2 | inner |