Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,8,Mod(32,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.32");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.d (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: | \(10.3087058410\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 32.4 | ||
Character | \(\chi\) | \(=\) | 33.32 |
Dual form | 33.8.d.b.32.3 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −17.1890 | −1.51930 | −0.759652 | − | 0.650330i | \(-0.774631\pi\) | ||||
−0.759652 | + | 0.650330i | \(0.774631\pi\) | |||||||
\(3\) | −43.8101 | + | 16.3606i | −0.936807 | + | 0.349845i | ||||
\(4\) | 167.460 | 1.30828 | ||||||||
\(5\) | 90.8965i | 0.325201i | 0.986692 | + | 0.162601i | \(0.0519882\pi\) | ||||
−0.986692 | + | 0.162601i | \(0.948012\pi\) | |||||||
\(6\) | 753.051 | − | 281.222i | 1.42329 | − | 0.531521i | ||||
\(7\) | − | 1506.19i | − | 1.65973i | −0.557963 | − | 0.829866i | \(-0.688417\pi\) | ||
0.557963 | − | 0.829866i | \(-0.311583\pi\) | |||||||
\(8\) | −678.279 | −0.468375 | ||||||||
\(9\) | 1651.66 | − | 1433.52i | 0.755216 | − | 0.655476i | ||||
\(10\) | − | 1562.42i | − | 0.494079i | ||||||
\(11\) | 981.685 | + | 4303.89i | 0.222381 | + | 0.974960i | ||||
\(12\) | −7336.45 | + | 2739.76i | −1.22561 | + | 0.457697i | ||||
\(13\) | − | 3566.16i | − | 0.450193i | −0.974336 | − | 0.225097i | \(-0.927730\pi\) | ||
0.974336 | − | 0.225097i | \(-0.0722698\pi\) | |||||||
\(14\) | 25889.9i | 2.52164i | ||||||||
\(15\) | −1487.13 | − | 3982.19i | −0.113770 | − | 0.304651i | ||||
\(16\) | −9775.99 | −0.596679 | ||||||||
\(17\) | −13457.6 | −0.664349 | −0.332174 | − | 0.943218i | \(-0.607782\pi\) | ||||
−0.332174 | + | 0.943218i | \(0.607782\pi\) | |||||||
\(18\) | −28390.3 | + | 24640.8i | −1.14740 | + | 0.995866i | ||||
\(19\) | 26772.8i | 0.895481i | 0.894164 | + | 0.447740i | \(0.147771\pi\) | ||||
−0.894164 | + | 0.447740i | \(0.852229\pi\) | |||||||
\(20\) | 15221.5i | 0.425455i | ||||||||
\(21\) | 24642.3 | + | 65986.6i | 0.580650 | + | 1.55485i | ||||
\(22\) | −16874.1 | − | 73979.4i | −0.337864 | − | 1.48126i | ||||
\(23\) | − | 40415.9i | − | 0.692635i | −0.938117 | − | 0.346318i | \(-0.887432\pi\) | ||
0.938117 | − | 0.346318i | \(-0.112568\pi\) | |||||||
\(24\) | 29715.5 | − | 11097.1i | 0.438777 | − | 0.163859i | ||||
\(25\) | 69862.8 | 0.894244 | ||||||||
\(26\) | 61298.6i | 0.683980i | ||||||||
\(27\) | −48906.0 | + | 89825.1i | −0.478177 | + | 0.878263i | ||||
\(28\) | − | 252228.i | − | 2.17140i | ||||||
\(29\) | −142803. | −1.08728 | −0.543642 | − | 0.839317i | \(-0.682955\pi\) | ||||
−0.543642 | + | 0.839317i | \(0.682955\pi\) | |||||||
\(30\) | 25562.1 | + | 68449.7i | 0.172851 | + | 0.462857i | ||||
\(31\) | −158528. | −0.955739 | −0.477869 | − | 0.878431i | \(-0.658591\pi\) | ||||
−0.477869 | + | 0.878431i | \(0.658591\pi\) | |||||||
\(32\) | 254859. | 1.37491 | ||||||||
\(33\) | −113422. | − | 172493.i | −0.549413 | − | 0.835551i | ||||
\(34\) | 231322. | 1.00935 | ||||||||
\(35\) | 136908. | 0.539747 | ||||||||
\(36\) | 276587. | − | 240058.i | 0.988036 | − | 0.857547i | ||||
\(37\) | 286564. | 0.930069 | 0.465035 | − | 0.885292i | \(-0.346042\pi\) | ||||
0.465035 | + | 0.885292i | \(0.346042\pi\) | |||||||
\(38\) | − | 460197.i | − | 1.36051i | ||||||
\(39\) | 58344.7 | + | 156234.i | 0.157498 | + | 0.421745i | ||||
\(40\) | − | 61653.2i | − | 0.152316i | ||||||
\(41\) | −434415. | −0.984378 | −0.492189 | − | 0.870488i | \(-0.663803\pi\) | ||||
−0.492189 | + | 0.870488i | \(0.663803\pi\) | |||||||
\(42\) | −423576. | − | 1.13424e6i | −0.882183 | − | 2.36229i | ||||
\(43\) | 689840.i | 1.32315i | 0.749880 | + | 0.661574i | \(0.230111\pi\) | ||||
−0.749880 | + | 0.661574i | \(0.769889\pi\) | |||||||
\(44\) | 164393. | + | 720730.i | 0.290937 | + | 1.27552i | ||||
\(45\) | 130302. | + | 150130.i | 0.213161 | + | 0.245597i | ||||
\(46\) | 694707.i | 1.05232i | ||||||||
\(47\) | 1.28647e6i | 1.80741i | 0.428155 | + | 0.903705i | \(0.359164\pi\) | ||||
−0.428155 | + | 0.903705i | \(0.640836\pi\) | |||||||
\(48\) | 428288. | − | 159942.i | 0.558974 | − | 0.208746i | ||||
\(49\) | −1.44508e6 | −1.75471 | ||||||||
\(50\) | −1.20087e6 | −1.35863 | ||||||||
\(51\) | 589579. | − | 220175.i | 0.622367 | − | 0.232419i | ||||
\(52\) | − | 597190.i | − | 0.588980i | ||||||
\(53\) | 406111.i | 0.374696i | 0.982294 | + | 0.187348i | \(0.0599892\pi\) | ||||
−0.982294 | + | 0.187348i | \(0.940011\pi\) | |||||||
\(54\) | 840643. | − | 1.54400e6i | 0.726496 | − | 1.33435i | ||||
\(55\) | −391208. | + | 89231.7i | −0.317058 | + | 0.0723186i | ||||
\(56\) | 1.02162e6i | 0.777377i | ||||||||
\(57\) | −438020. | − | 1.17292e6i | −0.313280 | − | 0.838893i | ||||
\(58\) | 2.45463e6 | 1.65192 | ||||||||
\(59\) | 622324.i | 0.394489i | 0.980354 | + | 0.197244i | \(0.0631993\pi\) | ||||
−0.980354 | + | 0.197244i | \(0.936801\pi\) | |||||||
\(60\) | −249034. | − | 666858.i | −0.148843 | − | 0.398569i | ||||
\(61\) | 901495.i | 0.508521i | 0.967136 | + | 0.254261i | \(0.0818321\pi\) | ||||
−0.967136 | + | 0.254261i | \(0.918168\pi\) | |||||||
\(62\) | 2.72492e6 | 1.45206 | ||||||||
\(63\) | −2.15917e6 | − | 2.48772e6i | −1.08791 | − | 1.25346i | ||||
\(64\) | −3.12943e6 | −1.49223 | ||||||||
\(65\) | 324151. | 0.146403 | ||||||||
\(66\) | 1.94961e6 | + | 2.96497e6i | 0.834726 | + | 1.26945i | ||||
\(67\) | 2.03178e6 | 0.825308 | 0.412654 | − | 0.910888i | \(-0.364602\pi\) | ||||
0.412654 | + | 0.910888i | \(0.364602\pi\) | |||||||
\(68\) | −2.25361e6 | −0.869156 | ||||||||
\(69\) | 661230. | + | 1.77063e6i | 0.242315 | + | 0.648866i | ||||
\(70\) | −2.35330e6 | −0.820039 | ||||||||
\(71\) | 2.52259e6i | 0.836455i | 0.908342 | + | 0.418228i | \(0.137349\pi\) | ||||
−0.908342 | + | 0.418228i | \(0.862651\pi\) | |||||||
\(72\) | −1.12029e6 | + | 972330.i | −0.353724 | + | 0.307008i | ||||
\(73\) | − | 1.13869e6i | − | 0.342589i | −0.985220 | − | 0.171295i | \(-0.945205\pi\) | ||
0.985220 | − | 0.171295i | \(-0.0547950\pi\) | |||||||
\(74\) | −4.92573e6 | −1.41306 | ||||||||
\(75\) | −3.06070e6 | + | 1.14300e6i | −0.837735 | + | 0.312847i | ||||
\(76\) | 4.48338e6i | 1.17154i | ||||||||
\(77\) | 6.48250e6 | − | 1.47861e6i | 1.61817 | − | 0.369093i | ||||
\(78\) | −1.00288e6 | − | 2.68550e6i | −0.239287 | − | 0.640758i | ||||
\(79\) | − | 1.22674e6i | − | 0.279934i | −0.990156 | − | 0.139967i | \(-0.955300\pi\) | ||
0.990156 | − | 0.139967i | \(-0.0446997\pi\) | |||||||
\(80\) | − | 888604.i | − | 0.194041i | ||||||
\(81\) | 672982. | − | 4.73539e6i | 0.140704 | − | 0.990052i | ||||
\(82\) | 7.46715e6 | 1.49557 | ||||||||
\(83\) | −5.90164e6 | −1.13292 | −0.566460 | − | 0.824089i | \(-0.691687\pi\) | ||||
−0.566460 | + | 0.824089i | \(0.691687\pi\) | |||||||
\(84\) | 4.12661e6 | + | 1.10501e7i | 0.759654 | + | 2.03418i | ||||
\(85\) | − | 1.22325e6i | − | 0.216047i | ||||||
\(86\) | − | 1.18576e7i | − | 2.01026i | ||||||
\(87\) | 6.25621e6 | − | 2.33634e6i | 1.01858 | − | 0.380382i | ||||
\(88\) | −665856. | − | 2.91924e6i | −0.104158 | − | 0.456646i | ||||
\(89\) | 7.09843e6i | 1.06733i | 0.845697 | + | 0.533664i | \(0.179185\pi\) | ||||
−0.845697 | + | 0.533664i | \(0.820815\pi\) | |||||||
\(90\) | −2.23976e6 | − | 2.58058e6i | −0.323857 | − | 0.373137i | ||||
\(91\) | −5.37133e6 | −0.747200 | ||||||||
\(92\) | − | 6.76805e6i | − | 0.906163i | ||||||
\(93\) | 6.94512e6 | − | 2.59362e6i | 0.895343 | − | 0.334361i | ||||
\(94\) | − | 2.21131e7i | − | 2.74601i | ||||||
\(95\) | −2.43355e6 | −0.291211 | ||||||||
\(96\) | −1.11654e7 | + | 4.16966e6i | −1.28803 | + | 0.481006i | ||||
\(97\) | 8.09192e6 | 0.900224 | 0.450112 | − | 0.892972i | \(-0.351384\pi\) | ||||
0.450112 | + | 0.892972i | \(0.351384\pi\) | |||||||
\(98\) | 2.48394e7 | 2.66594 | ||||||||
\(99\) | 7.79114e6 | + | 5.70128e6i | 0.807008 | + | 0.590540i | ||||
\(100\) | 1.16992e7 | 1.16992 | ||||||||
\(101\) | 4.89863e6 | 0.473097 | 0.236548 | − | 0.971620i | \(-0.423984\pi\) | ||||
0.236548 | + | 0.971620i | \(0.423984\pi\) | |||||||
\(102\) | −1.01343e7 | + | 3.78458e6i | −0.945564 | + | 0.353116i | ||||
\(103\) | −1.63269e7 | −1.47223 | −0.736113 | − | 0.676859i | \(-0.763341\pi\) | ||||
−0.736113 | + | 0.676859i | \(0.763341\pi\) | |||||||
\(104\) | 2.41885e6i | 0.210859i | ||||||||
\(105\) | −5.99795e6 | + | 2.23990e6i | −0.505639 | + | 0.188828i | ||||
\(106\) | − | 6.98062e6i | − | 0.569276i | ||||||
\(107\) | −2.11142e7 | −1.66622 | −0.833108 | − | 0.553111i | \(-0.813441\pi\) | ||||
−0.833108 | + | 0.553111i | \(0.813441\pi\) | |||||||
\(108\) | −8.18981e6 | + | 1.50421e7i | −0.625591 | + | 1.14902i | ||||
\(109\) | 2.46933e7i | 1.82636i | 0.407559 | + | 0.913179i | \(0.366380\pi\) | ||||
−0.407559 | + | 0.913179i | \(0.633620\pi\) | |||||||
\(110\) | 6.72446e6 | − | 1.53380e6i | 0.481707 | − | 0.109874i | ||||
\(111\) | −1.25544e7 | + | 4.68837e6i | −0.871296 | + | 0.325380i | ||||
\(112\) | 1.47246e7i | 0.990328i | ||||||||
\(113\) | − | 2.80165e7i | − | 1.82658i | −0.407308 | − | 0.913291i | \(-0.633532\pi\) | ||
0.407308 | − | 0.913291i | \(-0.366468\pi\) | |||||||
\(114\) | 7.52911e6 | + | 2.01613e7i | 0.475967 | + | 1.27453i | ||||
\(115\) | 3.67366e6 | 0.225246 | ||||||||
\(116\) | −2.39138e7 | −1.42248 | ||||||||
\(117\) | −5.11218e6 | − | 5.89008e6i | −0.295091 | − | 0.339993i | ||||
\(118\) | − | 1.06971e7i | − | 0.599348i | ||||||
\(119\) | 2.02698e7i | 1.10264i | ||||||||
\(120\) | 1.00869e6 | + | 2.70103e6i | 0.0532870 | + | 0.142691i | ||||
\(121\) | −1.75598e7 | + | 8.45013e6i | −0.901093 | + | 0.433625i | ||||
\(122\) | − | 1.54958e7i | − | 0.772598i | ||||||
\(123\) | 1.90318e7 | − | 7.10732e6i | 0.922172 | − | 0.344380i | ||||
\(124\) | −2.65471e7 | −1.25038 | ||||||||
\(125\) | 1.34516e7i | 0.616010i | ||||||||
\(126\) | 3.71138e7 | + | 4.27613e7i | 1.65287 | + | 1.90438i | ||||
\(127\) | 3.98549e7i | 1.72651i | 0.504768 | + | 0.863255i | \(0.331578\pi\) | ||||
−0.504768 | + | 0.863255i | \(0.668422\pi\) | |||||||
\(128\) | 2.11697e7 | 0.892236 | ||||||||
\(129\) | −1.12862e7 | − | 3.02220e7i | −0.462897 | − | 1.23954i | ||||
\(130\) | −5.57182e6 | −0.222431 | ||||||||
\(131\) | 1.80946e7 | 0.703232 | 0.351616 | − | 0.936144i | \(-0.385632\pi\) | ||||
0.351616 | + | 0.936144i | \(0.385632\pi\) | |||||||
\(132\) | −1.89937e7 | − | 2.88857e7i | −0.718788 | − | 1.09314i | ||||
\(133\) | 4.03251e7 | 1.48626 | ||||||||
\(134\) | −3.49242e7 | −1.25389 | ||||||||
\(135\) | −8.16479e6 | − | 4.44538e6i | −0.285612 | − | 0.155504i | ||||
\(136\) | 9.12800e6 | 0.311164 | ||||||||
\(137\) | − | 1.08842e7i | − | 0.361638i | −0.983516 | − | 0.180819i | \(-0.942125\pi\) | ||
0.983516 | − | 0.180819i | \(-0.0578747\pi\) | |||||||
\(138\) | −1.13659e7 | − | 3.04352e7i | −0.368150 | − | 0.985824i | ||||
\(139\) | − | 1.33599e6i | − | 0.0421942i | −0.999777 | − | 0.0210971i | \(-0.993284\pi\) | ||
0.999777 | − | 0.0210971i | \(-0.00671591\pi\) | |||||||
\(140\) | 2.29266e7 | 0.706141 | ||||||||
\(141\) | −2.10475e7 | − | 5.63604e7i | −0.632314 | − | 1.69320i | ||||
\(142\) | − | 4.33607e7i | − | 1.27083i | ||||||
\(143\) | 1.53484e7 | − | 3.50085e6i | 0.438920 | − | 0.100114i | ||||
\(144\) | −1.61466e7 | + | 1.40141e7i | −0.450622 | + | 0.391109i | ||||
\(145\) | − | 1.29803e7i | − | 0.353586i | ||||||
\(146\) | 1.95728e7i | 0.520497i | ||||||||
\(147\) | 6.33092e7 | − | 2.36425e7i | 1.64383 | − | 0.613878i | ||||
\(148\) | 4.79880e7 | 1.21679 | ||||||||
\(149\) | 3.30097e7 | 0.817503 | 0.408752 | − | 0.912646i | \(-0.365964\pi\) | ||||
0.408752 | + | 0.912646i | \(0.365964\pi\) | |||||||
\(150\) | 5.26102e7 | − | 1.96470e7i | 1.27277 | − | 0.475310i | ||||
\(151\) | − | 7.90394e6i | − | 0.186820i | −0.995628 | − | 0.0934102i | \(-0.970223\pi\) | ||
0.995628 | − | 0.0934102i | \(-0.0297768\pi\) | |||||||
\(152\) | − | 1.81594e7i | − | 0.419420i | ||||||
\(153\) | −2.22274e7 | + | 1.92918e7i | −0.501727 | + | 0.435464i | ||||
\(154\) | −1.11427e8 | + | 2.54157e7i | −2.45849 | + | 0.560764i | ||||
\(155\) | − | 1.44096e7i | − | 0.310807i | ||||||
\(156\) | 9.77041e6 | + | 2.61630e7i | 0.206052 | + | 0.551761i | ||||
\(157\) | 5.79006e6 | 0.119408 | 0.0597041 | − | 0.998216i | \(-0.480984\pi\) | ||||
0.0597041 | + | 0.998216i | \(0.480984\pi\) | |||||||
\(158\) | 2.10863e7i | 0.425305i | ||||||||
\(159\) | −6.64423e6 | − | 1.77918e7i | −0.131086 | − | 0.351018i | ||||
\(160\) | 2.31658e7i | 0.447123i | ||||||||
\(161\) | −6.08742e7 | −1.14959 | ||||||||
\(162\) | −1.15678e7 | + | 8.13963e7i | −0.213772 | + | 1.50419i | ||||
\(163\) | −1.67020e7 | −0.302073 | −0.151037 | − | 0.988528i | \(-0.548261\pi\) | ||||
−0.151037 | + | 0.988528i | \(0.548261\pi\) | |||||||
\(164\) | −7.27473e7 | −1.28784 | ||||||||
\(165\) | 1.56790e7 | − | 1.03097e7i | 0.271722 | − | 0.178670i | ||||
\(166\) | 1.01443e8 | 1.72125 | ||||||||
\(167\) | −5.41613e7 | −0.899873 | −0.449936 | − | 0.893061i | \(-0.648553\pi\) | ||||
−0.449936 | + | 0.893061i | \(0.648553\pi\) | |||||||
\(168\) | −1.67144e7 | − | 4.47573e7i | −0.271962 | − | 0.728252i | ||||
\(169\) | 5.00310e7 | 0.797326 | ||||||||
\(170\) | 2.10264e7i | 0.328241i | ||||||||
\(171\) | 3.83795e7 | + | 4.42195e7i | 0.586966 | + | 0.676282i | ||||
\(172\) | 1.15521e8i | 1.73105i | ||||||||
\(173\) | 1.03863e8 | 1.52511 | 0.762554 | − | 0.646924i | \(-0.223945\pi\) | ||||
0.762554 | + | 0.646924i | \(0.223945\pi\) | |||||||
\(174\) | −1.07538e8 | + | 4.01593e7i | −1.54753 | + | 0.577915i | ||||
\(175\) | − | 1.05227e8i | − | 1.48421i | ||||||
\(176\) | −9.59695e6 | − | 4.20748e7i | −0.132690 | − | 0.581738i | ||||
\(177\) | −1.01816e7 | − | 2.72641e7i | −0.138010 | − | 0.369560i | ||||
\(178\) | − | 1.22015e8i | − | 1.62159i | ||||||
\(179\) | − | 1.48451e7i | − | 0.193463i | −0.995311 | − | 0.0967316i | \(-0.969161\pi\) | ||
0.995311 | − | 0.0967316i | \(-0.0308389\pi\) | |||||||
\(180\) | 2.18205e7 | + | 2.51408e7i | 0.278875 | + | 0.321311i | ||||
\(181\) | −4.88799e7 | −0.612710 | −0.306355 | − | 0.951917i | \(-0.599109\pi\) | ||||
−0.306355 | + | 0.951917i | \(0.599109\pi\) | |||||||
\(182\) | 9.23276e7 | 1.13522 | ||||||||
\(183\) | −1.47490e7 | − | 3.94946e7i | −0.177904 | − | 0.476386i | ||||
\(184\) | 2.74132e7i | 0.324413i | ||||||||
\(185\) | 2.60476e7i | 0.302460i | ||||||||
\(186\) | −1.19379e8 | + | 4.45815e7i | −1.36030 | + | 0.507995i | ||||
\(187\) | −1.32111e7 | − | 5.79200e7i | −0.147739 | − | 0.647714i | ||||
\(188\) | 2.15432e8i | 2.36460i | ||||||||
\(189\) | 1.35294e8 | + | 7.36620e7i | 1.45768 | + | 0.793646i | ||||
\(190\) | 4.18302e7 | 0.442438 | ||||||||
\(191\) | 9.62151e7i | 0.999140i | 0.866273 | + | 0.499570i | \(0.166509\pi\) | ||||
−0.866273 | + | 0.499570i | \(0.833491\pi\) | |||||||
\(192\) | 1.37101e8 | − | 5.11995e7i | 1.39793 | − | 0.522049i | ||||
\(193\) | − | 1.60072e8i | − | 1.60275i | −0.598164 | − | 0.801374i | \(-0.704103\pi\) | ||
0.598164 | − | 0.801374i | \(-0.295897\pi\) | |||||||
\(194\) | −1.39092e8 | −1.36771 | ||||||||
\(195\) | −1.42011e7 | + | 5.30333e6i | −0.137152 | + | 0.0512186i | ||||
\(196\) | −2.41993e8 | −2.29566 | ||||||||
\(197\) | −1.66964e7 | −0.155593 | −0.0777965 | − | 0.996969i | \(-0.524788\pi\) | ||||
−0.0777965 | + | 0.996969i | \(0.524788\pi\) | |||||||
\(198\) | −1.33922e8 | − | 9.79991e7i | −1.22609 | − | 0.897210i | ||||
\(199\) | 1.14515e8 | 1.03009 | 0.515045 | − | 0.857163i | \(-0.327775\pi\) | ||||
0.515045 | + | 0.857163i | \(0.327775\pi\) | |||||||
\(200\) | −4.73865e7 | −0.418841 | ||||||||
\(201\) | −8.90128e7 | + | 3.32413e7i | −0.773154 | + | 0.288730i | ||||
\(202\) | −8.42023e7 | −0.718777 | ||||||||
\(203\) | 2.15089e8i | 1.80460i | ||||||||
\(204\) | 9.87310e7 | − | 3.68705e7i | 0.814232 | − | 0.304070i | ||||
\(205\) | − | 3.94868e7i | − | 0.320121i | ||||||
\(206\) | 2.80643e8 | 2.23676 | ||||||||
\(207\) | −5.79372e7 | − | 6.67532e7i | −0.454005 | − | 0.523089i | ||||
\(208\) | 3.48628e7i | 0.268621i | ||||||||
\(209\) | −1.15227e8 | + | 2.62825e7i | −0.873058 | + | 0.199138i | ||||
\(210\) | 1.03099e8 | − | 3.85016e7i | 0.768219 | − | 0.286887i | ||||
\(211\) | 1.51161e8i | 1.10778i | 0.832591 | + | 0.553889i | \(0.186857\pi\) | ||||
−0.832591 | + | 0.553889i | \(0.813143\pi\) | |||||||
\(212\) | 6.80073e7i | 0.490208i | ||||||||
\(213\) | −4.12712e7 | − | 1.10515e8i | −0.292630 | − | 0.783597i | ||||
\(214\) | 3.62931e8 | 2.53149 | ||||||||
\(215\) | −6.27040e7 | −0.430289 | ||||||||
\(216\) | 3.31719e7 | − | 6.09265e7i | 0.223966 | − | 0.411356i | ||||
\(217\) | 2.38774e8i | 1.58627i | ||||||||
\(218\) | − | 4.24451e8i | − | 2.77479i | ||||||
\(219\) | 1.86296e7 | + | 4.98860e7i | 0.119853 | + | 0.320940i | ||||
\(220\) | −6.55118e7 | + | 1.49428e7i | −0.414802 | + | 0.0946131i | ||||
\(221\) | 4.79919e7i | 0.299085i | ||||||||
\(222\) | 2.15797e8 | − | 8.05882e7i | 1.32376 | − | 0.494352i | ||||
\(223\) | −1.62697e8 | −0.982457 | −0.491228 | − | 0.871031i | \(-0.663452\pi\) | ||||
−0.491228 | + | 0.871031i | \(0.663452\pi\) | |||||||
\(224\) | − | 3.83867e8i | − | 2.28199i | ||||||
\(225\) | 1.15390e8 | − | 1.00150e8i | 0.675348 | − | 0.586155i | ||||
\(226\) | 4.81574e8i | 2.77513i | ||||||||
\(227\) | −2.43483e8 | −1.38158 | −0.690792 | − | 0.723053i | \(-0.742738\pi\) | ||||
−0.690792 | + | 0.723053i | \(0.742738\pi\) | |||||||
\(228\) | −7.33510e7 | − | 1.96417e8i | −0.409858 | − | 1.09751i | ||||
\(229\) | −7.10138e7 | −0.390767 | −0.195384 | − | 0.980727i | \(-0.562595\pi\) | ||||
−0.195384 | + | 0.980727i | \(0.562595\pi\) | |||||||
\(230\) | −6.31464e7 | −0.342217 | ||||||||
\(231\) | −2.59808e8 | + | 1.70836e8i | −1.38679 | + | 0.911879i | ||||
\(232\) | 9.68600e7 | 0.509257 | ||||||||
\(233\) | −3.81060e7 | −0.197355 | −0.0986774 | − | 0.995119i | \(-0.531461\pi\) | ||||
−0.0986774 | + | 0.995119i | \(0.531461\pi\) | |||||||
\(234\) | 8.78730e7 | + | 1.01244e8i | 0.448332 | + | 0.516553i | ||||
\(235\) | −1.16936e8 | −0.587772 | ||||||||
\(236\) | 1.04215e8i | 0.516103i | ||||||||
\(237\) | 2.00702e7 | + | 5.37435e7i | 0.0979338 | + | 0.262245i | ||||
\(238\) | − | 3.48416e8i | − | 1.67525i | ||||||
\(239\) | 3.32792e8 | 1.57681 | 0.788406 | − | 0.615156i | \(-0.210907\pi\) | ||||
0.788406 | + | 0.615156i | \(0.210907\pi\) | |||||||
\(240\) | 1.45381e7 | + | 3.89299e7i | 0.0678843 | + | 0.181779i | ||||
\(241\) | 2.13039e7i | 0.0980390i | 0.998798 | + | 0.0490195i | \(0.0156097\pi\) | ||||
−0.998798 | + | 0.0490195i | \(0.984390\pi\) | |||||||
\(242\) | 3.01834e8 | − | 1.45249e8i | 1.36903 | − | 0.658808i | ||||
\(243\) | 4.79906e7 | + | 2.18468e8i | 0.214553 | + | 0.976712i | ||||
\(244\) | 1.50965e8i | 0.665289i | ||||||||
\(245\) | − | 1.31353e8i | − | 0.570634i | ||||||
\(246\) | −3.27137e8 | + | 1.22167e8i | −1.40106 | + | 0.523218i | ||||
\(247\) | 9.54761e7 | 0.403139 | ||||||||
\(248\) | 1.07526e8 | 0.447644 | ||||||||
\(249\) | 2.58552e8 | − | 9.65546e7i | 1.06133 | − | 0.396347i | ||||
\(250\) | − | 2.31218e8i | − | 0.935907i | ||||||
\(251\) | 2.36907e8i | 0.945629i | 0.881162 | + | 0.472814i | \(0.156762\pi\) | ||||
−0.881162 | + | 0.472814i | \(0.843238\pi\) | |||||||
\(252\) | −3.61575e8 | − | 4.16594e8i | −1.42330 | − | 1.63988i | ||||
\(253\) | 1.73945e8 | − | 3.96757e7i | 0.675292 | − | 0.154029i | ||||
\(254\) | − | 6.85065e8i | − | 2.62309i | ||||||
\(255\) | 2.00131e7 | + | 5.35907e7i | 0.0755831 | + | 0.202394i | ||||
\(256\) | 3.66821e7 | 0.136651 | ||||||||
\(257\) | 1.83527e8i | 0.674425i | 0.941429 | + | 0.337212i | \(0.109484\pi\) | ||||
−0.941429 | + | 0.337212i | \(0.890516\pi\) | |||||||
\(258\) | 1.93998e8 | + | 5.19484e8i | 0.703282 | + | 1.88323i | ||||
\(259\) | − | 4.31621e8i | − | 1.54367i | ||||||
\(260\) | 5.42824e7 | 0.191537 | ||||||||
\(261\) | −2.35861e8 | + | 2.04711e8i | −0.821135 | + | 0.712689i | ||||
\(262\) | −3.11027e8 | −1.06842 | ||||||||
\(263\) | 3.47905e8 | 1.17928 | 0.589638 | − | 0.807667i | \(-0.299270\pi\) | ||||
0.589638 | + | 0.807667i | \(0.299270\pi\) | |||||||
\(264\) | 7.69319e7 | + | 1.16998e8i | 0.257331 | + | 0.391351i | ||||
\(265\) | −3.69140e7 | −0.121851 | ||||||||
\(266\) | −6.93146e8 | −2.25808 | ||||||||
\(267\) | −1.16135e8 | − | 3.10983e8i | −0.373399 | − | 0.999880i | ||||
\(268\) | 3.40243e8 | 1.07974 | ||||||||
\(269\) | − | 5.51585e8i | − | 1.72774i | −0.503711 | − | 0.863872i | \(-0.668032\pi\) | ||
0.503711 | − | 0.863872i | \(-0.331968\pi\) | |||||||
\(270\) | 1.40344e8 | + | 7.64115e7i | 0.433932 | + | 0.236257i | ||||
\(271\) | 2.83981e8i | 0.866755i | 0.901213 | + | 0.433377i | \(0.142678\pi\) | ||||
−0.901213 | + | 0.433377i | \(0.857322\pi\) | |||||||
\(272\) | 1.31561e8 | 0.396403 | ||||||||
\(273\) | 2.35319e8 | − | 8.78785e7i | 0.699983 | − | 0.261405i | ||||
\(274\) | 1.87088e8i | 0.549437i | ||||||||
\(275\) | 6.85833e7 | + | 3.00682e8i | 0.198863 | + | 0.871852i | ||||
\(276\) | 1.10730e8 | + | 2.96509e8i | 0.317017 | + | 0.848900i | ||||
\(277\) | − | 3.38232e8i | − | 0.956170i | −0.878313 | − | 0.478085i | \(-0.841331\pi\) | ||
0.878313 | − | 0.478085i | \(-0.158669\pi\) | |||||||
\(278\) | 2.29643e7i | 0.0641058i | ||||||||
\(279\) | −2.61834e8 | + | 2.27253e8i | −0.721790 | + | 0.626463i | ||||
\(280\) | −9.28617e7 | −0.252804 | ||||||||
\(281\) | −3.57886e8 | −0.962216 | −0.481108 | − | 0.876661i | \(-0.659765\pi\) | ||||
−0.481108 | + | 0.876661i | \(0.659765\pi\) | |||||||
\(282\) | 3.61784e8 | + | 9.68776e8i | 0.960677 | + | 2.57248i | ||||
\(283\) | − | 1.65581e8i | − | 0.434267i | −0.976142 | − | 0.217134i | \(-0.930329\pi\) | ||
0.976142 | − | 0.217134i | \(-0.0696707\pi\) | |||||||
\(284\) | 4.22433e8i | 1.09432i | ||||||||
\(285\) | 1.06614e8 | − | 3.98145e7i | 0.272809 | − | 0.101879i | ||||
\(286\) | −2.63822e8 | + | 6.01759e7i | −0.666853 | + | 0.152104i | ||||
\(287\) | 6.54314e8i | 1.63380i | ||||||||
\(288\) | 4.20940e8 | − | 3.65346e8i | 1.03836 | − | 0.901221i | ||||
\(289\) | −2.29232e8 | −0.558640 | ||||||||
\(290\) | 2.23117e8i | 0.537205i | ||||||||
\(291\) | −3.54508e8 | + | 1.32389e8i | −0.843337 | + | 0.314939i | ||||
\(292\) | − | 1.90685e8i | − | 0.448204i | ||||||
\(293\) | −3.27097e8 | −0.759695 | −0.379847 | − | 0.925049i | \(-0.624024\pi\) | ||||
−0.379847 | + | 0.925049i | \(0.624024\pi\) | |||||||
\(294\) | −1.08822e9 | + | 4.06389e8i | −2.49747 | + | 0.932666i | ||||
\(295\) | −5.65671e7 | −0.128288 | ||||||||
\(296\) | −1.94370e8 | −0.435621 | ||||||||
\(297\) | −4.34608e8 | − | 1.22306e8i | −0.962609 | − | 0.270895i | ||||
\(298\) | −5.67402e8 | −1.24204 | ||||||||
\(299\) | −1.44129e8 | −0.311820 | ||||||||
\(300\) | −5.12545e8 | + | 1.91407e8i | −1.09599 | + | 0.409293i | ||||
\(301\) | 1.03903e9 | 2.19607 | ||||||||
\(302\) | 1.35860e8i | 0.283837i | ||||||||
\(303\) | −2.14610e8 | + | 8.01448e7i | −0.443200 | + | 0.165511i | ||||
\(304\) | − | 2.61731e8i | − | 0.534315i | ||||||
\(305\) | −8.19427e7 | −0.165372 | ||||||||
\(306\) | 3.82065e8 | − | 3.31606e8i | 0.762276 | − | 0.661603i | ||||
\(307\) | 3.94124e8i | 0.777408i | 0.921363 | + | 0.388704i | \(0.127077\pi\) | ||||
−0.921363 | + | 0.388704i | \(0.872923\pi\) | |||||||
\(308\) | 1.08556e9 | − | 2.47608e8i | 2.11703 | − | 0.482878i | ||||
\(309\) | 7.15285e8 | − | 2.67119e8i | 1.37919 | − | 0.515051i | ||||
\(310\) | 2.47686e8i | 0.472211i | ||||||||
\(311\) | 1.72708e8i | 0.325575i | 0.986661 | + | 0.162788i | \(0.0520485\pi\) | ||||
−0.986661 | + | 0.162788i | \(0.947951\pi\) | |||||||
\(312\) | −3.95740e7 | − | 1.05970e8i | −0.0737681 | − | 0.197534i | ||||
\(313\) | −2.48533e8 | −0.458119 | −0.229060 | − | 0.973412i | \(-0.573565\pi\) | ||||
−0.229060 | + | 0.973412i | \(0.573565\pi\) | |||||||
\(314\) | −9.95251e7 | −0.181417 | ||||||||
\(315\) | 2.26125e8 | − | 1.96261e8i | 0.407626 | − | 0.353791i | ||||
\(316\) | − | 2.05429e8i | − | 0.366233i | ||||||
\(317\) | − | 6.99051e8i | − | 1.23254i | −0.787534 | − | 0.616271i | \(-0.788643\pi\) | ||
0.787534 | − | 0.616271i | \(-0.211357\pi\) | |||||||
\(318\) | 1.14207e8 | + | 3.05822e8i | 0.199159 | + | 0.533302i | ||||
\(319\) | −1.40187e8 | − | 6.14607e8i | −0.241792 | − | 1.06006i | ||||
\(320\) | − | 2.84454e8i | − | 0.485274i | ||||||
\(321\) | 9.25016e8 | − | 3.45442e8i | 1.56092 | − | 0.582918i | ||||
\(322\) | 1.04636e9 | 1.74657 | ||||||||
\(323\) | − | 3.60298e8i | − | 0.594912i | ||||||
\(324\) | 1.12698e8 | − | 7.92989e8i | 0.184080 | − | 1.29527i | ||||
\(325\) | − | 2.49142e8i | − | 0.402583i | ||||||
\(326\) | 2.87090e8 | 0.458941 | ||||||||
\(327\) | −4.03998e8 | − | 1.08182e9i | −0.638943 | − | 1.71095i | ||||
\(328\) | 2.94655e8 | 0.461058 | ||||||||
\(329\) | 1.93767e9 | 2.99982 | ||||||||
\(330\) | −2.69506e8 | + | 1.77213e8i | −0.412828 | + | 0.271454i | ||||
\(331\) | −6.14954e8 | −0.932062 | −0.466031 | − | 0.884768i | \(-0.654317\pi\) | ||||
−0.466031 | + | 0.884768i | \(0.654317\pi\) | |||||||
\(332\) | −9.88289e8 | −1.48218 | ||||||||
\(333\) | 4.73306e8 | − | 4.10796e8i | 0.702404 | − | 0.609638i | ||||
\(334\) | 9.30975e8 | 1.36718 | ||||||||
\(335\) | 1.84682e8i | 0.268391i | ||||||||
\(336\) | −2.40903e8 | − | 6.45085e8i | −0.346462 | − | 0.927747i | ||||
\(337\) | 3.16600e8i | 0.450616i | 0.974288 | + | 0.225308i | \(0.0723388\pi\) | ||||
−0.974288 | + | 0.225308i | \(0.927661\pi\) | |||||||
\(338\) | −8.59981e8 | −1.21138 | ||||||||
\(339\) | 4.58368e8 | + | 1.22741e9i | 0.639021 | + | 1.71116i | ||||
\(340\) | − | 2.04845e8i | − | 0.282651i | ||||||
\(341\) | −1.55624e8 | − | 6.82286e8i | −0.212538 | − | 0.931807i | ||||
\(342\) | −6.59703e8 | − | 7.60087e8i | −0.891779 | − | 1.02748i | ||||
\(343\) | 9.36156e8i | 1.25262i | ||||||||
\(344\) | − | 4.67904e8i | − | 0.619729i | ||||||
\(345\) | −1.60944e8 | + | 6.01035e7i | −0.211012 | + | 0.0788012i | ||||
\(346\) | −1.78530e9 | −2.31710 | ||||||||
\(347\) | −1.05014e9 | −1.34925 | −0.674626 | − | 0.738160i | \(-0.735695\pi\) | ||||
−0.674626 | + | 0.738160i | \(0.735695\pi\) | |||||||
\(348\) | 1.04767e9 | − | 3.91245e8i | 1.33259 | − | 0.497647i | ||||
\(349\) | 8.07445e8i | 1.01677i | 0.861129 | + | 0.508386i | \(0.169758\pi\) | ||||
−0.861129 | + | 0.508386i | \(0.830242\pi\) | |||||||
\(350\) | 1.80874e9i | 2.25496i | ||||||||
\(351\) | 3.20331e8 | + | 1.74407e8i | 0.395388 | + | 0.215272i | ||||
\(352\) | 2.50191e8 | + | 1.09688e9i | 0.305754 | + | 1.34048i | ||||
\(353\) | − | 6.42480e8i | − | 0.777406i | −0.921363 | − | 0.388703i | \(-0.872923\pi\) | ||
0.921363 | − | 0.388703i | \(-0.127077\pi\) | |||||||
\(354\) | 1.75012e8 | + | 4.68642e8i | 0.209679 | + | 0.561474i | ||||
\(355\) | −2.29295e8 | −0.272016 | ||||||||
\(356\) | 1.18870e9i | 1.39637i | ||||||||
\(357\) | −3.31626e8 | − | 8.88021e8i | −0.385754 | − | 1.03296i | ||||
\(358\) | 2.55172e8i | 0.293929i | ||||||||
\(359\) | −1.21411e9 | −1.38493 | −0.692464 | − | 0.721452i | \(-0.743475\pi\) | ||||
−0.692464 | + | 0.721452i | \(0.743475\pi\) | |||||||
\(360\) | −8.83814e7 | − | 1.01830e8i | −0.0998394 | − | 0.115032i | ||||
\(361\) | 1.77089e8 | 0.198114 | ||||||||
\(362\) | 8.40194e8 | 0.930892 | ||||||||
\(363\) | 6.31046e8 | − | 6.57490e8i | 0.692449 | − | 0.721467i | ||||
\(364\) | −8.99484e8 | −0.977549 | ||||||||
\(365\) | 1.03503e8 | 0.111410 | ||||||||
\(366\) | 2.53521e8 | + | 6.78871e8i | 0.270290 | + | 0.723775i | ||||
\(367\) | 2.98569e8 | 0.315292 | 0.157646 | − | 0.987496i | \(-0.449609\pi\) | ||||
0.157646 | + | 0.987496i | \(0.449609\pi\) | |||||||
\(368\) | 3.95105e8i | 0.413281i | ||||||||
\(369\) | −7.17506e8 | + | 6.22745e8i | −0.743418 | + | 0.645235i | ||||
\(370\) | − | 4.47732e8i | − | 0.459528i | ||||||
\(371\) | 6.11682e8 | 0.621895 | ||||||||
\(372\) | 1.16303e9 | − | 4.34327e8i | 1.17136 | − | 0.437438i | ||||
\(373\) | 1.65310e9i | 1.64937i | 0.565594 | + | 0.824684i | \(0.308647\pi\) | ||||
−0.565594 | + | 0.824684i | \(0.691353\pi\) | |||||||
\(374\) | 2.27085e8 | + | 9.95584e8i | 0.224460 | + | 0.984073i | ||||
\(375\) | −2.20076e8 | − | 5.89315e8i | −0.215508 | − | 0.577083i | ||||
\(376\) | − | 8.72585e8i | − | 0.846545i | ||||||
\(377\) | 5.09257e8i | 0.489488i | ||||||||
\(378\) | −2.32557e9 | − | 1.26617e9i | −2.21466 | − | 1.20579i | ||||
\(379\) | −1.56573e8 | −0.147734 | −0.0738669 | − | 0.997268i | \(-0.523534\pi\) | ||||
−0.0738669 | + | 0.997268i | \(0.523534\pi\) | |||||||
\(380\) | −4.07523e8 | −0.380987 | ||||||||
\(381\) | −6.52053e8 | − | 1.74605e9i | −0.604011 | − | 1.61741i | ||||
\(382\) | − | 1.65384e9i | − | 1.51800i | ||||||
\(383\) | − | 1.20689e9i | − | 1.09767i | −0.835932 | − | 0.548834i | \(-0.815072\pi\) | ||
0.835932 | − | 0.548834i | \(-0.184928\pi\) | |||||||
\(384\) | −9.27447e8 | + | 3.46350e8i | −0.835853 | + | 0.312145i | ||||
\(385\) | 1.34400e8 | + | 5.89236e8i | 0.120030 | + | 0.526232i | ||||
\(386\) | 2.75147e9i | 2.43506i | ||||||||
\(387\) | 9.88903e8 | + | 1.13938e9i | 0.867292 | + | 0.999264i | ||||
\(388\) | 1.35507e9 | 1.17775 | ||||||||
\(389\) | 8.41324e7i | 0.0724669i | 0.999343 | + | 0.0362335i | \(0.0115360\pi\) | ||||
−0.999343 | + | 0.0362335i | \(0.988464\pi\) | |||||||
\(390\) | 2.44102e8 | − | 9.11587e7i | 0.208375 | − | 0.0778165i | ||||
\(391\) | 5.43901e8i | 0.460151i | ||||||||
\(392\) | 9.80167e8 | 0.821862 | ||||||||
\(393\) | −7.92726e8 | + | 2.96039e8i | −0.658793 | + | 0.246023i | ||||
\(394\) | 2.86993e8 | 0.236393 | ||||||||
\(395\) | 1.11506e8 | 0.0910350 | ||||||||
\(396\) | 1.30471e9 | + | 9.54738e8i | 1.05579 | + | 0.772594i | ||||
\(397\) | 2.75369e8 | 0.220876 | 0.110438 | − | 0.993883i | \(-0.464775\pi\) | ||||
0.110438 | + | 0.993883i | \(0.464775\pi\) | |||||||
\(398\) | −1.96839e9 | −1.56502 | ||||||||
\(399\) | −1.76665e9 | + | 6.59744e8i | −1.39234 | + | 0.519961i | ||||
\(400\) | −6.82979e8 | −0.533577 | ||||||||
\(401\) | 1.02279e8i | 0.0792103i | 0.999215 | + | 0.0396051i | \(0.0126100\pi\) | ||||
−0.999215 | + | 0.0396051i | \(0.987390\pi\) | |||||||
\(402\) | 1.53004e9 | − | 5.71383e8i | 1.17466 | − | 0.438668i | ||||
\(403\) | 5.65335e8i | 0.430267i | ||||||||
\(404\) | 8.20325e8 | 0.618944 | ||||||||
\(405\) | 4.30430e8 | + | 6.11717e7i | 0.321966 | + | 0.0457570i | ||||
\(406\) | − | 3.69715e9i | − | 2.74174i | ||||||
\(407\) | 2.81316e8 | + | 1.23334e9i | 0.206830 | + | 0.906780i | ||||
\(408\) | −3.99899e8 | + | 1.49340e8i | −0.291501 | + | 0.108859i | ||||
\(409\) | − | 2.21805e9i | − | 1.60303i | −0.597977 | − | 0.801513i | \(-0.704029\pi\) | ||
0.597977 | − | 0.801513i | \(-0.295971\pi\) | |||||||
\(410\) | 6.78737e8i | 0.486360i | ||||||||
\(411\) | 1.78072e8 | + | 4.76837e8i | 0.126517 | + | 0.338785i | ||||
\(412\) | −2.73411e9 | −1.92609 | ||||||||
\(413\) | 9.37342e8 | 0.654746 | ||||||||
\(414\) | 9.95879e8 | + | 1.14742e9i | 0.689772 | + | 0.794732i | ||||
\(415\) | − | 5.36438e8i | − | 0.368427i | ||||||
\(416\) | − | 9.08867e8i | − | 0.618976i | ||||||
\(417\) | 2.18577e7 | + | 5.85301e7i | 0.0147614 | + | 0.0395278i | ||||
\(418\) | 1.98063e9 | − | 4.51768e8i | 1.32644 | − | 0.302551i | ||||
\(419\) | − | 1.77010e9i | − | 1.17557i | −0.809016 | − | 0.587786i | \(-0.800000\pi\) | ||
0.809016 | − | 0.587786i | \(-0.200000\pi\) | |||||||
\(420\) | −1.00442e9 | + | 3.75094e8i | −0.661519 | + | 0.247040i | ||||
\(421\) | −4.18994e7 | −0.0273666 | −0.0136833 | − | 0.999906i | \(-0.504356\pi\) | ||||
−0.0136833 | + | 0.999906i | \(0.504356\pi\) | |||||||
\(422\) | − | 2.59831e9i | − | 1.68305i | ||||||
\(423\) | 1.84419e9 | + | 2.12481e9i | 1.18471 | + | 1.36499i | ||||
\(424\) | − | 2.75456e8i | − | 0.175498i | ||||||
\(425\) | −9.40186e8 | −0.594090 | ||||||||
\(426\) | 7.09409e8 | + | 1.89964e9i | 0.444594 | + | 1.19052i | ||||
\(427\) | 1.35783e9 | 0.844009 | ||||||||
\(428\) | −3.53578e9 | −2.17988 | ||||||||
\(429\) | −6.15138e8 | + | 4.04482e8i | −0.376159 | + | 0.247342i | ||||
\(430\) | 1.07782e9 | 0.653740 | ||||||||
\(431\) | 1.47449e9 | 0.887096 | 0.443548 | − | 0.896251i | \(-0.353720\pi\) | ||||
0.443548 | + | 0.896251i | \(0.353720\pi\) | |||||||
\(432\) | 4.78105e8 | − | 8.78130e8i | 0.285319 | − | 0.524042i | ||||
\(433\) | −1.82639e9 | −1.08115 | −0.540575 | − | 0.841296i | \(-0.681793\pi\) | ||||
−0.540575 | + | 0.841296i | \(0.681793\pi\) | |||||||
\(434\) | − | 4.10427e9i | − | 2.41003i | ||||||
\(435\) | 2.12365e8 | + | 5.68667e8i | 0.123701 | + | 0.331242i | ||||
\(436\) | 4.13514e9i | 2.38939i | ||||||||
\(437\) | 1.08205e9 | 0.620242 | ||||||||
\(438\) | −3.20224e8 | − | 8.57488e8i | −0.182094 | − | 0.487606i | ||||
\(439\) | − | 8.64064e8i | − | 0.487439i | −0.969846 | − | 0.243719i | \(-0.921632\pi\) | ||
0.969846 | − | 0.243719i | \(-0.0783676\pi\) | |||||||
\(440\) | 2.65348e8 | − | 6.05240e7i | 0.148502 | − | 0.0338722i | ||||
\(441\) | −2.38678e9 | + | 2.07156e9i | −1.32519 | + | 1.15017i | ||||
\(442\) | − | 8.24931e8i | − | 0.454402i | ||||||
\(443\) | − | 1.93792e9i | − | 1.05907i | −0.848289 | − | 0.529533i | \(-0.822367\pi\) | ||
0.848289 | − | 0.529533i | \(-0.177633\pi\) | |||||||
\(444\) | −2.10236e9 | + | 7.85115e8i | −1.13990 | + | 0.425690i | ||||
\(445\) | −6.45223e8 | −0.347096 | ||||||||
\(446\) | 2.79660e9 | 1.49265 | ||||||||
\(447\) | −1.44616e9 | + | 5.40060e8i | −0.765843 | + | 0.286000i | ||||
\(448\) | 4.71353e9i | 2.47670i | ||||||||
\(449\) | 2.62445e9i | 1.36828i | 0.729350 | + | 0.684141i | \(0.239823\pi\) | ||||
−0.729350 | + | 0.684141i | \(0.760177\pi\) | |||||||
\(450\) | −1.98343e9 | + | 1.72148e9i | −1.02606 | + | 0.890547i | ||||
\(451\) | −4.26459e8 | − | 1.86968e9i | −0.218907 | − | 0.959729i | ||||
\(452\) | − | 4.69165e9i | − | 2.38969i | ||||||
\(453\) | 1.29314e8 | + | 3.46273e8i | 0.0653583 | + | 0.175015i | ||||
\(454\) | 4.18521e9 | 2.09905 | ||||||||
\(455\) | − | 4.88235e8i | − | 0.242990i | ||||||
\(456\) | 2.97100e8 | + | 7.95567e8i | 0.146732 | + | 0.392916i | ||||
\(457\) | 1.97630e8i | 0.0968602i | 0.998827 | + | 0.0484301i | \(0.0154218\pi\) | ||||
−0.998827 | + | 0.0484301i | \(0.984578\pi\) | |||||||
\(458\) | 1.22065e9 | 0.593694 | ||||||||
\(459\) | 6.58157e8 | − | 1.20883e9i | 0.317677 | − | 0.583473i | ||||
\(460\) | 6.15192e8 | 0.294685 | ||||||||
\(461\) | −2.12787e9 | −1.01156 | −0.505781 | − | 0.862662i | \(-0.668795\pi\) | ||||
−0.505781 | + | 0.862662i | \(0.668795\pi\) | |||||||
\(462\) | 4.46583e9 | − | 2.93649e9i | 2.10696 | − | 1.38542i | ||||
\(463\) | −1.17054e9 | −0.548091 | −0.274045 | − | 0.961717i | \(-0.588362\pi\) | ||||
−0.274045 | + | 0.961717i | \(0.588362\pi\) | |||||||
\(464\) | 1.39604e9 | 0.648760 | ||||||||
\(465\) | 2.35751e8 | + | 6.31287e8i | 0.108734 | + | 0.291167i | ||||
\(466\) | 6.55002e8 | 0.299842 | ||||||||
\(467\) | − | 9.29267e8i | − | 0.422213i | −0.977463 | − | 0.211107i | \(-0.932293\pi\) | ||
0.977463 | − | 0.211107i | \(-0.0677067\pi\) | |||||||
\(468\) | −8.56086e8 | − | 9.86353e8i | −0.386062 | − | 0.444807i | ||||
\(469\) | − | 3.06026e9i | − | 1.36979i | ||||||
\(470\) | 2.01000e9 | 0.893004 | ||||||||
\(471\) | −2.53663e8 | + | 9.47292e7i | −0.111863 | + | 0.0417744i | ||||
\(472\) | − | 4.22110e8i | − | 0.184769i | ||||||
\(473\) | −2.96899e9 | + | 6.77206e8i | −1.29002 | + | 0.294243i | ||||
\(474\) | −3.44986e8 | − | 9.23795e8i | −0.148791 | − | 0.398429i | ||||
\(475\) | 1.87042e9i | 0.800778i | ||||||||
\(476\) | 3.39438e9i | 1.44257i | ||||||||
\(477\) | 5.82170e8 | + | 6.70756e8i | 0.245604 | + | 0.282976i | ||||
\(478\) | −5.72034e9 | −2.39565 | ||||||||
\(479\) | 2.34570e9 | 0.975209 | 0.487605 | − | 0.873065i | \(-0.337871\pi\) | ||||
0.487605 | + | 0.873065i | \(0.337871\pi\) | |||||||
\(480\) | −3.79007e8 | − | 1.01490e9i | −0.156424 | − | 0.418868i | ||||
\(481\) | − | 1.02193e9i | − | 0.418711i | ||||||
\(482\) | − | 3.66191e8i | − | 0.148951i | ||||||
\(483\) | 2.66691e9 | − | 9.95941e8i | 1.07694 | − | 0.402178i | ||||
\(484\) | −2.94056e9 | + | 1.41506e9i | −1.17888 | + | 0.567304i | ||||
\(485\) | 7.35527e8i | 0.292754i | ||||||||
\(486\) | −8.24908e8 | − | 3.75524e9i | −0.325971 | − | 1.48392i | ||||
\(487\) | 2.47213e9 | 0.969882 | 0.484941 | − | 0.874547i | \(-0.338841\pi\) | ||||
0.484941 | + | 0.874547i | \(0.338841\pi\) | |||||||
\(488\) | − | 6.11465e8i | − | 0.238178i | ||||||
\(489\) | 7.31718e8 | − | 2.73256e8i | 0.282985 | − | 0.105679i | ||||
\(490\) | 2.25782e9i | 0.866966i | ||||||||
\(491\) | −4.41850e9 | −1.68457 | −0.842287 | − | 0.539030i | \(-0.818791\pi\) | ||||
−0.842287 | + | 0.539030i | \(0.818791\pi\) | |||||||
\(492\) | 3.18707e9 | − | 1.19019e9i | 1.20646 | − | 0.450546i | ||||
\(493\) | 1.92178e9 | 0.722337 | ||||||||
\(494\) | −1.64113e9 | −0.612491 | ||||||||
\(495\) | −5.18227e8 | + | 7.08187e8i | −0.192044 | + | 0.262440i | ||||
\(496\) | 1.54977e9 | 0.570270 | ||||||||
\(497\) | 3.79951e9 | 1.38829 | ||||||||
\(498\) | −4.44423e9 | + | 1.65967e9i | −1.61248 | + | 0.602171i | ||||
\(499\) | 2.81853e9 | 1.01548 | 0.507740 | − | 0.861510i | \(-0.330481\pi\) | ||||
0.507740 | + | 0.861510i | \(0.330481\pi\) | |||||||
\(500\) | 2.25260e9i | 0.805916i | ||||||||
\(501\) | 2.37281e9 | − | 8.86113e8i | 0.843008 | − | 0.314816i | ||||
\(502\) | − | 4.07219e9i | − | 1.43670i | ||||||
\(503\) | 1.28396e9 | 0.449844 | 0.224922 | − | 0.974377i | \(-0.427787\pi\) | ||||
0.224922 | + | 0.974377i | \(0.427787\pi\) | |||||||
\(504\) | 1.46452e9 | + | 1.68737e9i | 0.509551 | + | 0.587088i | ||||
\(505\) | 4.45268e8i | 0.153852i | ||||||||
\(506\) | −2.98994e9 | + | 6.81983e8i | −1.02597 | + | 0.234017i | ||||
\(507\) | −2.19187e9 | + | 8.18540e8i | −0.746941 | + | 0.278941i | ||||
\(508\) | 6.67411e9i | 2.25876i | ||||||||
\(509\) | 6.98994e8i | 0.234942i | 0.993076 | + | 0.117471i | \(0.0374788\pi\) | ||||
−0.993076 | + | 0.117471i | \(0.962521\pi\) | |||||||
\(510\) | −3.44005e8 | − | 9.21168e8i | −0.114834 | − | 0.307499i | ||||
\(511\) | −1.71508e9 | −0.568607 | ||||||||
\(512\) | −3.34025e9 | −1.09985 | ||||||||
\(513\) | −2.40487e9 | − | 1.30935e9i | −0.786468 | − | 0.428199i | ||||
\(514\) | − | 3.15463e9i | − | 1.02466i | ||||||
\(515\) | − | 1.48406e9i | − | 0.478769i | ||||||
\(516\) | −1.88999e9 | − | 5.06098e9i | −0.605601 | − | 1.62166i | ||||
\(517\) | −5.53682e9 | + | 1.26291e9i | −1.76215 | + | 0.401934i | ||||
\(518\) | 7.41911e9i | 2.34530i | ||||||||
\(519\) | −4.55027e9 | + | 1.69927e9i | −1.42873 | + | 0.533552i | ||||
\(520\) | −2.19865e8 | −0.0685716 | ||||||||
\(521\) | 2.63160e9i | 0.815245i | 0.913151 | + | 0.407622i | \(0.133642\pi\) | ||||
−0.913151 | + | 0.407622i | \(0.866358\pi\) | |||||||
\(522\) | 4.05421e9 | − | 3.51877e9i | 1.24755 | − | 1.08279i | ||||
\(523\) | − | 8.06360e8i | − | 0.246475i | −0.992377 | − | 0.123238i | \(-0.960672\pi\) | ||
0.992377 | − | 0.123238i | \(-0.0393277\pi\) | |||||||
\(524\) | 3.03012e9 | 0.920027 | ||||||||
\(525\) | 1.72158e9 | + | 4.61001e9i | 0.519243 | + | 1.39042i | ||||
\(526\) | −5.98013e9 | −1.79168 | ||||||||
\(527\) | 2.13340e9 | 0.634944 | ||||||||
\(528\) | 1.10881e9 | + | 1.68629e9i | 0.327824 | + | 0.498556i | ||||
\(529\) | 1.77138e9 | 0.520256 | ||||||||
\(530\) | 6.34513e8 | 0.185129 | ||||||||
\(531\) | 8.92118e8 | + | 1.02787e9i | 0.258578 | + | 0.297925i | ||||
\(532\) | 6.75284e9 | 1.94445 | ||||||||
\(533\) | 1.54919e9i | 0.443160i | ||||||||
\(534\) | 1.99624e9 | + | 5.34548e9i | 0.567307 | + | 1.51912i | ||||
\(535\) | − | 1.91921e9i | − | 0.541855i | ||||||
\(536\) | −1.37812e9 | −0.386553 | ||||||||
\(537\) | 2.42876e8 | + | 6.50367e8i | 0.0676822 | + | 0.181238i | ||||
\(538\) | 9.48117e9i | 2.62497i | ||||||||
\(539\) | −1.41861e9 | − | 6.21947e9i | −0.390215 | − | 1.71077i | ||||
\(540\) | −1.36728e9 | − | 7.44425e8i | −0.373662 | − | 0.203443i | ||||
\(541\) | 6.85116e8i | 0.186026i | 0.995665 | + | 0.0930130i | \(0.0296498\pi\) | ||||
−0.995665 | + | 0.0930130i | \(0.970350\pi\) | |||||||
\(542\) | − | 4.88133e9i | − | 1.31686i | ||||||
\(543\) | 2.14143e9 | − | 7.99706e8i | 0.573991 | − | 0.214354i | ||||
\(544\) | −3.42979e9 | −0.913421 | ||||||||
\(545\) | −2.24453e9 | −0.593934 | ||||||||
\(546\) | −4.04489e9 | + | 1.51054e9i | −1.06349 | + | 0.397153i | ||||
\(547\) | 3.43701e9i | 0.897893i | 0.893559 | + | 0.448946i | \(0.148201\pi\) | ||||
−0.893559 | + | 0.448946i | \(0.851799\pi\) | |||||||
\(548\) | − | 1.82267e9i | − | 0.473124i | ||||||
\(549\) | 1.29232e9 | + | 1.48896e9i | 0.333323 | + | 0.384043i | ||||
\(550\) | −1.17888e9 | − | 5.16841e9i | −0.302133 | − | 1.32461i | ||||
\(551\) | − | 3.82323e9i | − | 0.973643i | ||||||
\(552\) | −4.48498e8 | − | 1.20098e9i | −0.113494 | − | 0.303912i | ||||
\(553\) | −1.84770e9 | −0.464616 | ||||||||
\(554\) | 5.81385e9i | 1.45271i | ||||||||
\(555\) | −4.26156e8 | − | 1.14115e9i | −0.105814 | − | 0.283346i | ||||
\(556\) | − | 2.23726e8i | − | 0.0552019i | ||||||
\(557\) | 4.55366e9 | 1.11652 | 0.558261 | − | 0.829665i | \(-0.311469\pi\) | ||||
0.558261 | + | 0.829665i | \(0.311469\pi\) | |||||||
\(558\) | 4.50064e9 | − | 3.90625e9i | 1.09662 | − | 0.951788i | ||||
\(559\) | 2.46008e9 | 0.595673 | ||||||||
\(560\) | −1.33841e9 | −0.322056 | ||||||||
\(561\) | 1.52639e9 | + | 2.32134e9i | 0.365002 | + | 0.555097i | ||||
\(562\) | 6.15168e9 | 1.46190 | ||||||||
\(563\) | 1.43713e9 | 0.339405 | 0.169702 | − | 0.985495i | \(-0.445719\pi\) | ||||
0.169702 | + | 0.985495i | \(0.445719\pi\) | |||||||
\(564\) | −3.52461e9 | − | 9.43812e9i | −0.827246 | − | 2.21518i | ||||
\(565\) | 2.54660e9 | 0.594007 | ||||||||
\(566\) | 2.84616e9i | 0.659784i | ||||||||
\(567\) | −7.13242e9 | − | 1.01364e9i | −1.64322 | − | 0.233531i | ||||
\(568\) | − | 1.71102e9i | − | 0.391774i | ||||||
\(569\) | −4.72921e9 | −1.07621 | −0.538103 | − | 0.842879i | \(-0.680859\pi\) | ||||
−0.538103 | + | 0.842879i | \(0.680859\pi\) | |||||||
\(570\) | −1.83259e9 | + | 6.84370e8i | −0.414480 | + | 0.154785i | ||||
\(571\) | − | 5.46491e9i | − | 1.22845i | −0.789132 | − | 0.614224i | \(-0.789469\pi\) | ||
0.789132 | − | 0.614224i | \(-0.210531\pi\) | |||||||
\(572\) | 2.57024e9 | − | 5.86252e8i | 0.574232 | − | 0.130978i | ||||
\(573\) | −1.57414e9 | − | 4.21520e9i | −0.349545 | − | 0.936002i | ||||
\(574\) | − | 1.12470e10i | − | 2.48224i | ||||||
\(575\) | − | 2.82357e9i | − | 0.619385i | ||||||
\(576\) | −5.16875e9 | + | 4.48612e9i | −1.12696 | + | 0.978119i | ||||
\(577\) | 1.40691e9 | 0.304896 | 0.152448 | − | 0.988311i | \(-0.451284\pi\) | ||||
0.152448 | + | 0.988311i | \(0.451284\pi\) | |||||||
\(578\) | 3.94025e9 | 0.848744 | ||||||||
\(579\) | 2.61888e9 | + | 7.01278e9i | 0.560714 | + | 1.50147i | ||||
\(580\) | − | 2.17368e9i | − | 0.462591i | ||||||
\(581\) | 8.88902e9i | 1.88034i | ||||||||
\(582\) | 6.09363e9 | − | 2.27563e9i | 1.28128 | − | 0.478488i | ||||
\(583\) | −1.74785e9 | + | 3.98673e8i | −0.365313 | + | 0.0833252i | ||||
\(584\) | 7.72347e8i | 0.160460i | ||||||||
\(585\) | 5.35387e8 | − | 4.64679e8i | 0.110566 | − | 0.0959638i | ||||
\(586\) | 5.62245e9 | 1.15421 | ||||||||
\(587\) | − | 2.19542e9i | − | 0.448007i | −0.974588 | − | 0.224003i | \(-0.928087\pi\) | ||
0.974588 | − | 0.224003i | \(-0.0719127\pi\) | |||||||
\(588\) | 1.06018e10 | − | 3.95917e9i | 2.15059 | − | 0.803125i | ||||
\(589\) | − | 4.24423e9i | − | 0.855846i | ||||||
\(590\) | 9.72329e8 | 0.194909 | ||||||||
\(591\) | 7.31470e8 | − | 2.73163e8i | 0.145761 | − | 0.0544335i | ||||
\(592\) | −2.80145e9 | −0.554953 | ||||||||
\(593\) | −3.84584e9 | −0.757355 | −0.378677 | − | 0.925529i | \(-0.623621\pi\) | ||||
−0.378677 | + | 0.925529i | \(0.623621\pi\) | |||||||
\(594\) | 7.47045e9 | + | 2.10231e9i | 1.46250 | + | 0.411571i | ||||
\(595\) | −1.84245e9 | −0.358580 | ||||||||
\(596\) | 5.52781e9 | 1.06953 | ||||||||
\(597\) | −5.01690e9 | + | 1.87353e9i | −0.964996 | + | 0.360372i | ||||
\(598\) | 2.47744e9 | 0.473749 | ||||||||
\(599\) | 3.80221e9i | 0.722840i | 0.932403 | + | 0.361420i | \(0.117708\pi\) | ||||
−0.932403 | + | 0.361420i | \(0.882292\pi\) | |||||||
\(600\) | 2.07601e9 | − | 7.75274e8i | 0.392374 | − | 0.146530i | ||||
\(601\) | 2.11400e9i | 0.397233i | 0.980077 | + | 0.198616i | \(0.0636448\pi\) | ||||
−0.980077 | + | 0.198616i | \(0.936355\pi\) | |||||||
\(602\) | −1.78599e10 | −3.33650 | ||||||||
\(603\) | 3.35581e9 | − | 2.91261e9i | 0.623286 | − | 0.540969i | ||||
\(604\) | − | 1.32360e9i | − | 0.244414i | ||||||
\(605\) | −7.68087e8 | − | 1.59612e9i | −0.141015 | − | 0.293037i | ||||
\(606\) | 3.68892e9 | − | 1.37760e9i | 0.673356 | − | 0.251461i | ||||
\(607\) | 4.49197e9i | 0.815223i | 0.913155 | + | 0.407611i | \(0.133638\pi\) | ||||
−0.913155 | + | 0.407611i | \(0.866362\pi\) | |||||||
\(608\) | 6.82329e9i | 1.23121i | ||||||||
\(609\) | −3.51899e9 | − | 9.42307e9i | −0.631332 | − | 1.69056i | ||||
\(610\) | 1.40851e9 | 0.251250 | ||||||||
\(611\) | 4.58776e9 | 0.813684 | ||||||||
\(612\) | −3.72220e9 | + | 3.23061e9i | −0.656401 | + | 0.569711i | ||||
\(613\) | − | 9.04115e8i | − | 0.158530i | −0.996854 | − | 0.0792651i | \(-0.974743\pi\) | ||
0.996854 | − | 0.0792651i | \(-0.0252574\pi\) | |||||||
\(614\) | − | 6.77458e9i | − | 1.18112i | ||||||
\(615\) | 6.46030e8 | + | 1.72992e9i | 0.111993 | + | 0.299891i | ||||
\(616\) | −4.39694e9 | + | 1.00291e9i | −0.757911 | + | 0.172874i | ||||
\(617\) | − | 1.22475e9i | − | 0.209918i | −0.994477 | − | 0.104959i | \(-0.966529\pi\) | ||
0.994477 | − | 0.104959i | \(-0.0334712\pi\) | |||||||
\(618\) | −1.22950e10 | + | 4.59150e9i | −2.09541 | + | 0.782519i | ||||
\(619\) | −6.43876e9 | −1.09115 | −0.545576 | − | 0.838062i | \(-0.683689\pi\) | ||||
−0.545576 | + | 0.838062i | \(0.683689\pi\) | |||||||
\(620\) | − | 2.41304e9i | − | 0.406624i | ||||||
\(621\) | 3.63036e9 | + | 1.97658e9i | 0.608316 | + | 0.331202i | ||||
\(622\) | − | 2.96867e9i | − | 0.494648i | ||||||
\(623\) | 1.06916e10 | 1.77148 | ||||||||
\(624\) | −5.70377e8 | − | 1.52734e9i | −0.0939758 | − | 0.251646i | ||||
\(625\) | 4.23533e9 | 0.693917 | ||||||||
\(626\) | 4.27202e9 | 0.696022 | ||||||||
\(627\) | 4.61812e9 | − | 3.03663e9i | 0.748220 | − | 0.491989i | ||||
\(628\) | 9.69605e8 | 0.156220 | ||||||||
\(629\) | −3.85646e9 | −0.617891 | ||||||||
\(630\) | −3.88685e9 | + | 3.37352e9i | −0.619307 | + | 0.537516i | ||||
\(631\) | 1.66316e9 | 0.263530 | 0.131765 | − | 0.991281i | \(-0.457936\pi\) | ||||
0.131765 | + | 0.991281i | \(0.457936\pi\) | |||||||
\(632\) | 8.32069e8i | 0.131114i | ||||||||
\(633\) | −2.47310e9 | − | 6.62241e9i | −0.387551 | − | 1.03777i | ||||
\(634\) | 1.20160e10i | 1.87260i | ||||||||
\(635\) | −3.62267e9 | −0.561463 | ||||||||
\(636\) | −1.11264e9 | − | 2.97941e9i | −0.171497 | − | 0.459230i | ||||
\(637\) | 5.15339e9i | 0.789959i | ||||||||
\(638\) | 2.40967e9 | + | 1.05645e10i | 0.367355 | + | 1.61055i | ||||
\(639\) | 3.61620e9 | + | 4.16646e9i | 0.548276 | + | 0.631705i | ||||
\(640\) | 1.92425e9i | 0.290156i | ||||||||
\(641\) | 2.73222e9i | 0.409744i | 0.978789 | + | 0.204872i | \(0.0656778\pi\) | ||||
−0.978789 | + | 0.204872i | \(0.934322\pi\) | |||||||
\(642\) | −1.59001e10 | + | 5.93778e9i | −2.37152 | + | 0.885629i | ||||
\(643\) | 1.02739e10 | 1.52405 | 0.762023 | − | 0.647550i | \(-0.224206\pi\) | ||||
0.762023 | + | 0.647550i | \(0.224206\pi\) | |||||||
\(644\) | −1.01940e10 | −1.50399 | ||||||||
\(645\) | 2.74707e9 | − | 1.02588e9i | 0.403098 | − | 0.150535i | ||||
\(646\) | 6.19314e9i | 0.903851i | ||||||||
\(647\) | − | 4.55706e9i | − | 0.661485i | −0.943721 | − | 0.330742i | \(-0.892701\pi\) | ||
0.943721 | − | 0.330742i | \(-0.107299\pi\) | |||||||
\(648\) | −4.56469e8 | + | 3.21191e9i | −0.0659021 | + | 0.463715i | ||||
\(649\) | −2.67842e9 | + | 6.10927e8i | −0.384611 | + | 0.0877269i | ||||
\(650\) | 4.28249e9i | 0.611645i | ||||||||
\(651\) | −3.90649e9 | − | 1.04607e10i | −0.554949 | − | 1.48603i | ||||
\(652\) | −2.79692e9 | −0.395197 | ||||||||
\(653\) | 3.74412e8i | 0.0526203i | 0.999654 | + | 0.0263101i | \(0.00837574\pi\) | ||||
−0.999654 | + | 0.0263101i | \(0.991624\pi\) | |||||||
\(654\) | 6.94430e9 | + | 1.85953e10i | 0.970748 | + | 2.59944i | ||||
\(655\) | 1.64473e9i | 0.228692i | ||||||||
\(656\) | 4.24684e9 | 0.587358 | ||||||||
\(657\) | −1.63233e9 | − | 1.88072e9i | −0.224559 | − | 0.258729i | ||||
\(658\) | −3.33066e10 | −4.55763 | ||||||||
\(659\) | 1.99436e9 | 0.271459 | 0.135730 | − | 0.990746i | \(-0.456662\pi\) | ||||
0.135730 | + | 0.990746i | \(0.456662\pi\) | |||||||
\(660\) | 2.62561e9 | − | 1.72646e9i | 0.355489 | − | 0.233751i | ||||
\(661\) | −3.02625e9 | −0.407567 | −0.203784 | − | 0.979016i | \(-0.565324\pi\) | ||||
−0.203784 | + | 0.979016i | \(0.565324\pi\) | |||||||
\(662\) | 1.05704e10 | 1.41609 | ||||||||
\(663\) | −7.85179e8 | − | 2.10253e9i | −0.104634 | − | 0.280186i | ||||
\(664\) | 4.00296e9 | 0.530631 | ||||||||
\(665\) | 3.66541e9i | 0.483333i | ||||||||
\(666\) | −8.13563e9 | + | 7.06116e9i | −1.06716 | + | 0.926225i | ||||
\(667\) | 5.77149e9i | 0.753092i | ||||||||
\(668\) | −9.06985e9 | −1.17729 | ||||||||
\(669\) | 7.12780e9 | − | 2.66183e9i | 0.920373 | − | 0.343708i | ||||
\(670\) | − | 3.17449e9i | − | 0.407767i | ||||||
\(671\) | −3.87994e9 | + | 8.84984e8i | −0.495788 | + | 0.113085i | ||||
\(672\) | 6.28031e9 | + | 1.68173e10i | 0.798342 | + | 2.13778i | ||||
\(673\) | − | 7.32088e9i | − | 0.925786i | −0.886414 | − | 0.462893i | \(-0.846811\pi\) | ||
0.886414 | − | 0.462893i | \(-0.153189\pi\) | |||||||
\(674\) | − | 5.44202e9i | − | 0.684622i | ||||||
\(675\) | −3.41671e9 | + | 6.27544e9i | −0.427607 | + | 0.785382i | ||||
\(676\) | 8.37820e9 | 1.04313 | ||||||||
\(677\) | −7.83766e9 | −0.970792 | −0.485396 | − | 0.874295i | \(-0.661324\pi\) | ||||
−0.485396 | + | 0.874295i | \(0.661324\pi\) | |||||||
\(678\) | −7.87887e9 | − | 2.10978e10i | −0.970867 | − | 2.59976i | ||||
\(679\) | − | 1.21880e10i | − | 1.49413i | ||||||
\(680\) | 8.29704e8i | 0.101191i | ||||||||
\(681\) | 1.06670e10 | − | 3.98353e9i | 1.29428 | − | 0.483341i | ||||
\(682\) | 2.67502e9 | + | 1.17278e10i | 0.322910 | + | 1.41570i | ||||
\(683\) | − | 9.04868e9i | − | 1.08671i | −0.839504 | − | 0.543354i | \(-0.817154\pi\) | ||
0.839504 | − | 0.543354i | \(-0.182846\pi\) | |||||||
\(684\) | 6.42703e9 | + | 7.40501e9i | 0.767917 | + | 0.884768i | ||||
\(685\) | 9.89333e8 | 0.117605 | ||||||||
\(686\) | − | 1.60915e10i | − | 1.90311i | ||||||
\(687\) | 3.11112e9 | − | 1.16183e9i | 0.366074 | − | 0.136708i | ||||
\(688\) | − | 6.74387e9i | − | 0.789496i | ||||||
\(689\) | 1.44826e9 | 0.168686 | ||||||||
\(690\) | 2.76645e9 | − | 1.03312e9i | 0.320591 | − | 0.119723i | ||||
\(691\) | −3.93165e9 | −0.453316 | −0.226658 | − | 0.973974i | \(-0.572780\pi\) | ||||
−0.226658 | + | 0.973974i | \(0.572780\pi\) | |||||||
\(692\) | 1.73930e10 | 1.99527 | ||||||||
\(693\) | 8.58725e9 | − | 1.17350e10i | 0.980139 | − | 1.33942i | ||||
\(694\) | 1.80508e10 | 2.04992 | ||||||||
\(695\) | 1.21437e8 | 0.0137216 | ||||||||
\(696\) | −4.24345e9 | + | 1.58469e9i | −0.477075 | + | 0.178161i | ||||
\(697\) | 5.84619e9 | 0.653970 | ||||||||
\(698\) | − | 1.38791e10i | − | 1.54479i | ||||||
\(699\) | 1.66943e9 | − | 6.23439e8i | 0.184883 | − | 0.0690437i | ||||
\(700\) | − | 1.76213e10i | − | 1.94176i | ||||||
\(701\) | 5.21221e9 | 0.571490 | 0.285745 | − | 0.958306i | \(-0.407759\pi\) | ||||
0.285745 | + | 0.958306i | \(0.407759\pi\) | |||||||
\(702\) | −5.50615e9 | − | 2.99787e9i | −0.600715 | − | 0.327064i | ||||
\(703\) | 7.67212e9i | 0.832859i | ||||||||
\(704\) | −3.07211e9 | − | 1.34687e10i | −0.331843 | − | 1.45486i | ||||
\(705\) | 5.12296e9 | − | 1.91314e9i | 0.550629 | − | 0.205629i | ||||
\(706\) | 1.10436e10i | 1.18112i | ||||||||
\(707\) | − | 7.37829e9i | − | 0.785214i | ||||||
\(708\) | −1.70502e9 | − | 4.56566e9i | −0.180556 | − | 0.483489i | ||||
\(709\) | −7.80610e8 | −0.0822569 | −0.0411285 | − | 0.999154i | \(-0.513095\pi\) | ||||
−0.0411285 | + | 0.999154i | \(0.513095\pi\) | |||||||
\(710\) | 3.94134e9 | 0.413275 | ||||||||
\(711\) | −1.75856e9 | − | 2.02615e9i | −0.183490 | − | 0.211411i | ||||
\(712\) | − | 4.81472e9i | − | 0.499909i | ||||||
\(713\) | 6.40703e9i | 0.661978i | ||||||||
\(714\) | 5.70031e9 | + | 1.52642e10i | 0.586077 | + | 1.56938i | ||||
\(715\) | 3.18215e8 | + | 1.39511e9i | 0.0325574 | + | 0.142737i | ||||
\(716\) | − | 2.48597e9i | − | 0.253105i | ||||||
\(717\) | −1.45797e10 | + | 5.44469e9i | −1.47717 | + | 0.551640i | ||||
\(718\) | 2.08693e10 | 2.10413 | ||||||||
\(719\) | 1.70514e10i | 1.71084i | 0.517936 | + | 0.855419i | \(0.326700\pi\) | ||||
−0.517936 | + | 0.855419i | \(0.673300\pi\) | |||||||
\(720\) | −1.27384e9 | − | 1.46767e9i | −0.127189 | − | 0.146543i | ||||
\(721\) | 2.45915e10i | 2.44350i | ||||||||
\(722\) | −3.04397e9 | −0.300996 | ||||||||
\(723\) | −3.48545e8 | − | 9.33326e8i | −0.0342985 | − | 0.0918437i | ||||
\(724\) | −8.18543e9 | −0.801598 | ||||||||
\(725\) | −9.97660e9 | −0.972298 | ||||||||
\(726\) | −1.08470e10 | + | 1.13016e10i | −1.05204 | + | 1.09613i | ||||
\(727\) | −1.69760e10 | −1.63857 | −0.819285 | − | 0.573386i | \(-0.805630\pi\) | ||||
−0.819285 | + | 0.573386i | \(0.805630\pi\) | |||||||
\(728\) | 3.64326e9 | 0.349970 | ||||||||
\(729\) | −5.67676e9 | − | 8.78598e9i | −0.542693 | − | 0.839931i | ||||
\(730\) | −1.77910e9 | −0.169266 | ||||||||
\(731\) | − | 9.28358e9i | − | 0.879032i | ||||||
\(732\) | −2.46988e9 | − | 6.61378e9i | −0.232748 | − | 0.623248i | ||||
\(733\) | − | 2.18459e7i | − | 0.00204883i | −0.999999 | − | 0.00102442i | \(-0.999674\pi\) | ||
0.999999 | − | 0.00102442i | \(-0.000326082\pi\) | |||||||
\(734\) | −5.13209e9 | −0.479025 | ||||||||
\(735\) | 2.14902e9 | + | 5.75458e9i | 0.199634 | + | 0.534574i | ||||
\(736\) | − | 1.03003e10i | − | 0.952312i | ||||||
\(737\) | 1.99457e9 | + | 8.74458e9i | 0.183533 | + | 0.804642i | ||||
\(738\) | 1.23332e10 | − | 1.07043e10i | 1.12948 | − | 0.980308i | ||||
\(739\) | 3.00892e9i | 0.274256i | 0.990553 | + | 0.137128i | \(0.0437871\pi\) | ||||
−0.990553 | + | 0.137128i | \(0.956213\pi\) | |||||||
\(740\) | 4.36194e9i | 0.395703i | ||||||||
\(741\) | −4.18282e9 | + | 1.56205e9i | −0.377664 | + | 0.141036i | ||||
\(742\) | −1.05142e10 | −0.944846 | ||||||||
\(743\) | 4.99839e9 | 0.447063 | 0.223532 | − | 0.974697i | \(-0.428241\pi\) | ||||
0.223532 | + | 0.974697i | \(0.428241\pi\) | |||||||
\(744\) | −4.71073e9 | + | 1.75919e9i | −0.419356 | + | 0.156606i | ||||
\(745\) | 3.00047e9i | 0.265853i | ||||||||
\(746\) | − | 2.84150e10i | − | 2.50589i | ||||||
\(747\) | −9.74749e9 | + | 8.46014e9i | −0.855600 | + | 0.742601i | ||||
\(748\) | −2.21234e9 | − | 9.69929e9i | −0.193284 | − | 0.847392i | ||||
\(749\) | 3.18021e10i | 2.76547i | ||||||||
\(750\) | 3.78288e9 | + | 1.01297e10i | 0.327423 | + | 0.876764i | ||||
\(751\) | −9.37269e9 | −0.807467 | −0.403733 | − | 0.914877i | \(-0.632288\pi\) | ||||
−0.403733 | + | 0.914877i | \(0.632288\pi\) | |||||||
\(752\) | − | 1.25765e10i | − | 1.07844i | ||||||
\(753\) | −3.87596e9 | − | 1.03790e10i | −0.330824 | − | 0.885872i | ||||
\(754\) | − | 8.75360e9i | − | 0.743681i | ||||||
\(755\) | 7.18440e8 | 0.0607542 | ||||||||
\(756\) | 2.26564e10 | + | 1.23354e10i | 1.90706 | + | 1.03831i | ||||
\(757\) | −3.29570e9 | −0.276129 | −0.138064 | − | 0.990423i | \(-0.544088\pi\) | ||||
−0.138064 | + | 0.990423i | \(0.544088\pi\) | |||||||
\(758\) | 2.69133e9 | 0.224452 | ||||||||
\(759\) | −6.97146e9 | + | 4.58406e9i | −0.578732 | + | 0.380543i | ||||
\(760\) | 1.65063e9 | 0.136396 | ||||||||
\(761\) | 7.79377e9 | 0.641064 | 0.320532 | − | 0.947238i | \(-0.396138\pi\) | ||||
0.320532 | + | 0.947238i | \(0.396138\pi\) | |||||||
\(762\) | 1.12081e10 | + | 3.00128e10i | 0.917677 | + | 2.45733i | ||||
\(763\) | 3.71929e10 | 3.03126 | ||||||||
\(764\) | 1.61122e10i | 1.30716i | ||||||||
\(765\) | −1.75356e9 | − | 2.02039e9i | −0.141614 | − | 0.163162i | ||||
\(766\) | 2.07451e10i | 1.66769i | ||||||||
\(767\) | 2.21931e9 | 0.177596 | ||||||||
\(768\) | −1.60705e9 | + | 6.00143e8i | −0.128016 | + | 0.0478069i | ||||
\(769\) | − | 1.81737e10i | − | 1.44112i | −0.693392 | − | 0.720560i | \(-0.743885\pi\) | ||
0.693392 | − | 0.720560i | \(-0.256115\pi\) | |||||||
\(770\) | −2.31020e9 | − | 1.01284e10i | −0.182361 | − | 0.799505i | ||||
\(771\) | −3.00262e9 | − | 8.04033e9i | −0.235944 | − | 0.631806i | ||||
\(772\) | − | 2.68057e10i | − | 2.09685i | ||||||
\(773\) | 6.21890e9i | 0.484268i | 0.970243 | + | 0.242134i | \(0.0778473\pi\) | ||||
−0.970243 | + | 0.242134i | \(0.922153\pi\) | |||||||
\(774\) | −1.69982e10 | − | 1.95847e10i | −1.31768 | − | 1.51818i | ||||
\(775\) | −1.10752e10 | −0.854664 | ||||||||
\(776\) | −5.48858e9 | −0.421642 | ||||||||
\(777\) | 7.06160e9 | + | 1.89094e10i | 0.540045 | + | 1.44612i | ||||
\(778\) | − | 1.44615e9i | − | 0.110099i | ||||||
\(779\) | − | 1.16305e10i | − | 0.881491i | ||||||
\(780\) | −2.37812e9 | + | 8.88096e8i | −0.179433 | + | 0.0670083i | ||||
\(781\) | −1.08570e10 | + | 2.47639e9i | −0.815510 | + | 0.186012i | ||||
\(782\) | − | 9.34908e9i | − | 0.699110i | ||||||
\(783\) | 6.98391e9 | − | 1.28273e10i | 0.519915 | − | 0.954922i | ||||
\(784\) | 1.41271e10 | 1.04700 | ||||||||
\(785\) | 5.26296e8i | 0.0388317i | ||||||||
\(786\) | 1.36261e10 | − | 5.08860e9i | 1.00091 | − | 0.373783i | ||||
\(787\) | − | 1.00229e9i | − | 0.0732965i | −0.999328 | − | 0.0366482i | \(-0.988332\pi\) | ||
0.999328 | − | 0.0366482i | \(-0.0116681\pi\) | |||||||
\(788\) | −2.79598e9 | −0.203560 | ||||||||
\(789\) | −1.52418e10 | + | 5.69195e9i | −1.10476 | + | 0.412565i | ||||
\(790\) | −1.91667e9 | −0.138310 | ||||||||
\(791\) | −4.21983e10 | −3.03164 | ||||||||
\(792\) | −5.28457e9 | − | 3.86706e9i | −0.377982 | − | 0.276594i | ||||
\(793\) | 3.21488e9 | 0.228933 | ||||||||
\(794\) | −4.73331e9 | −0.335578 | ||||||||
\(795\) | 1.61721e9 | − | 6.03937e8i | 0.114151 | − | 0.0426292i | ||||
\(796\) | 1.91766e10 | 1.34765 | ||||||||
\(797\) | 1.31177e10i | 0.917814i | 0.888484 | + | 0.458907i | \(0.151759\pi\) | ||||
−0.888484 | + | 0.458907i | \(0.848241\pi\) | |||||||
\(798\) | 3.03668e10 | − | 1.13403e10i | 2.11538 | − | 0.789978i | ||||
\(799\) | − | 1.73128e10i | − | 1.20075i | ||||||
\(800\) | 1.78052e10 | 1.22951 | ||||||||
\(801\) | 1.01758e10 | + | 1.17242e10i | 0.699607 | + | 0.806063i | ||||
\(802\) | − | 1.75807e9i | − | 0.120344i | ||||||
\(803\) | 4.90078e9 | − | 1.11783e9i | 0.334011 | − | 0.0761854i | ||||
\(804\) | −1.49061e10 | + | 5.56660e9i | −1.01150 | + | 0.377740i | ||||
\(805\) | − | 5.53325e9i | − | 0.373848i | ||||||
\(806\) | − | 9.71752e9i | − | 0.653706i | ||||||
\(807\) | 9.02429e9 | + | 2.41650e10i | 0.604443 | + | 1.61856i | ||||
\(808\) | −3.32264e9 | −0.221586 | ||||||||
\(809\) | 2.43034e10 | 1.61379 | 0.806895 | − | 0.590695i | \(-0.201146\pi\) | ||||
0.806895 | + | 0.590695i | \(0.201146\pi\) | |||||||
\(810\) | −7.39864e9 | − | 1.05148e9i | −0.489164 | − | 0.0695188i | ||||
\(811\) | 1.74656e10i | 1.14977i | 0.818234 | + | 0.574886i | \(0.194954\pi\) | ||||
−0.818234 | + | 0.574886i | \(0.805046\pi\) | |||||||
\(812\) | 3.60188e10i | 2.36093i | ||||||||
\(813\) | −4.64611e9 | − | 1.24412e10i | −0.303230 | − | 0.811982i | ||||
\(814\) | −4.83552e9 | − | 2.11998e10i | −0.314237 | − | 1.37767i | ||||
\(815\) | − | 1.51815e9i | − | 0.0982346i | ||||||
\(816\) | −5.76372e9 | + | 2.15243e9i | −0.371354 | + | 0.138680i | ||||
\(817\) | −1.84689e10 | −1.18485 | ||||||||
\(818\) | 3.81260e10i | 2.43548i | ||||||||
\(819\) | −8.87161e9 | + | 7.69994e9i | −0.564298 | + | 0.489772i | ||||
\(820\) | − | 6.61247e9i | − | 0.418808i | ||||||
\(821\) | −6.87118e9 | −0.433341 | −0.216671 | − | 0.976245i | \(-0.569520\pi\) | ||||
−0.216671 | + | 0.976245i | \(0.569520\pi\) | |||||||
\(822\) | −3.06087e9 | − | 8.19633e9i | −0.192218 | − | 0.514717i | ||||
\(823\) | 1.42413e9 | 0.0890534 | 0.0445267 | − | 0.999008i | \(-0.485822\pi\) | ||||
0.0445267 | + | 0.999008i | \(0.485822\pi\) | |||||||
\(824\) | 1.10742e10 | 0.689553 | ||||||||
\(825\) | −7.92400e9 | − | 1.20509e10i | −0.491310 | − | 0.747186i | ||||
\(826\) | −1.61119e10 | −0.994758 | ||||||||
\(827\) | −5.57924e9 | −0.343009 | −0.171505 | − | 0.985183i | \(-0.554863\pi\) | ||||
−0.171505 | + | 0.985183i | \(0.554863\pi\) | |||||||
\(828\) | −9.70217e9 | − | 1.11785e10i | −0.593967 | − | 0.684349i | ||||
\(829\) | −2.23224e10 | −1.36082 | −0.680408 | − | 0.732834i | \(-0.738197\pi\) | ||||
−0.680408 | + | 0.732834i | \(0.738197\pi\) | |||||||
\(830\) | 9.22081e9i | 0.559752i | ||||||||
\(831\) | 5.53369e9 | + | 1.48180e10i | 0.334512 | + | 0.895748i | ||||
\(832\) | 1.11600e10i | 0.671791i | ||||||||
\(833\) | 1.94473e10 | 1.16574 | ||||||||
\(834\) | −3.75712e8 | − | 1.00607e9i | −0.0224271 | − | 0.0600548i | ||||
\(835\) | − | 4.92307e9i | − | 0.292640i | ||||||
\(836\) | −1.92960e10 | + | 4.40127e9i | −1.14221 | + | 0.260529i | ||||
\(837\) | 7.75295e9 | − | 1.42398e10i | 0.457013 | − | 0.839390i | ||||
\(838\) | 3.04262e10i | 1.78605i | ||||||||
\(839\) | 7.88538e9i | 0.460952i | 0.973078 | + | 0.230476i | \(0.0740283\pi\) | ||||
−0.973078 | + | 0.230476i | \(0.925972\pi\) | |||||||
\(840\) | 4.06828e9 | − | 1.51928e9i | 0.236828 | − | 0.0884422i | ||||
\(841\) | 3.14273e9 | 0.182188 | ||||||||
\(842\) | 7.20206e8 | 0.0415781 | ||||||||
\(843\) | 1.56790e10 | − | 5.85525e9i | 0.901411 | − | 0.336627i | ||||
\(844\) | 2.53135e10i | 1.44929i | ||||||||
\(845\) | 4.54764e9i | 0.259291i | ||||||||
\(846\) | −3.16996e10 | − | 3.65232e10i | −1.79994 | − | 2.07383i | ||||
\(847\) | 1.27275e10 | + | 2.64484e10i | 0.719702 | + | 1.49557i | ||||
\(848\) | − | 3.97013e9i | − | 0.223573i | ||||||
\(849\) | 2.70901e9 | + | 7.25411e9i | 0.151926 | + | 0.406825i | ||||
\(850\) | 1.61608e10 | 0.902603 | ||||||||
\(851\) | − | 1.15817e10i | − | 0.644199i | ||||||
\(852\) | −6.91129e9 | − | 1.85069e10i | −0.382843 | − | 1.02517i | ||||
\(853\) | 2.40175e9i | 0.132497i | 0.997803 | + | 0.0662485i | \(0.0211030\pi\) | ||||
−0.997803 | + | 0.0662485i | \(0.978897\pi\) | |||||||
\(854\) | −2.33396e10 | −1.28231 | ||||||||
\(855\) | −4.01940e9 | + | 3.48856e9i | −0.219928 | + | 0.190882i | ||||
\(856\) | 1.43213e10 | 0.780413 | ||||||||
\(857\) | −2.70670e10 | −1.46895 | −0.734476 | − | 0.678635i | \(-0.762572\pi\) | ||||
−0.734476 | + | 0.678635i | \(0.762572\pi\) | |||||||
\(858\) | 1.05736e10 | − | 6.95262e9i | 0.571500 | − | 0.375788i | ||||
\(859\) | 1.53100e10 | 0.824137 | 0.412068 | − | 0.911153i | \(-0.364806\pi\) | ||||
0.412068 | + | 0.911153i | \(0.364806\pi\) | |||||||
\(860\) | −1.05004e10 | −0.562940 | ||||||||
\(861\) | −1.07050e10 | − | 2.86656e10i | −0.571579 | − | 1.53056i | ||||
\(862\) | −2.53449e10 | −1.34777 | ||||||||
\(863\) | − | 6.06233e9i | − | 0.321071i | −0.987030 | − | 0.160536i | \(-0.948678\pi\) | ||
0.987030 | − | 0.160536i | \(-0.0513222\pi\) | |||||||
\(864\) | −1.24641e10 | + | 2.28927e10i | −0.657452 | + | 1.20753i | ||||
\(865\) | 9.44081e9i | 0.495967i | ||||||||
\(866\) | 3.13937e10 | 1.64259 | ||||||||
\(867\) | 1.00427e10 | − | 3.75038e9i | 0.523339 | − | 0.195438i | ||||
\(868\) | 3.99851e10i | 2.07529i | ||||||||
\(869\) | 5.27974e9 | − | 1.20427e9i | 0.272925 | − | 0.0622521i | ||||
\(870\) | −3.65034e9 | − | 9.77479e9i | −0.187939 | − | 0.503257i | ||||
\(871\) | − | 7.24567e9i | − | 0.371548i | ||||||
\(872\) | − | 1.67489e10i | − | 0.855419i | ||||||
\(873\) | 1.33651e10 | − | 1.16000e10i | 0.679864 | − | 0.590075i | ||||
\(874\) | −1.85992e10 | −0.942335 | ||||||||
\(875\) | 2.02607e10 | 1.02241 | ||||||||
\(876\) | 3.11972e9 | + | 8.35392e9i | 0.156802 | + | 0.419881i | ||||
\(877\) | − | 3.16536e10i | − | 1.58462i | −0.610120 | − | 0.792309i | \(-0.708879\pi\) | ||
0.610120 | − | 0.792309i | \(-0.291121\pi\) | |||||||
\(878\) | 1.48524e10i | 0.740567i | ||||||||
\(879\) | 1.43301e10 | − | 5.35151e9i | 0.711688 | − | 0.265776i | ||||
\(880\) | 3.82445e9 | − | 8.72329e8i | 0.189182 | − | 0.0431510i | ||||
\(881\) | − | 1.48267e10i | − | 0.730513i | −0.930907 | − | 0.365256i | \(-0.880981\pi\) | ||
0.930907 | − | 0.365256i | \(-0.119019\pi\) | |||||||
\(882\) | 4.10262e10 | − | 3.56079e10i | 2.01336 | − | 1.74746i | ||||
\(883\) | −1.66978e10 | −0.816201 | −0.408100 | − | 0.912937i | \(-0.633809\pi\) | ||||
−0.408100 | + | 0.912937i | \(0.633809\pi\) | |||||||
\(884\) | 8.03674e9i | 0.391288i | ||||||||
\(885\) | 2.47821e9 | − | 9.25475e8i | 0.120181 | − | 0.0448811i | ||||
\(886\) | 3.33108e10i | 1.60904i | ||||||||
\(887\) | −6.88613e9 | −0.331316 | −0.165658 | − | 0.986183i | \(-0.552975\pi\) | ||||
−0.165658 | + | 0.986183i | \(0.552975\pi\) | |||||||
\(888\) | 8.51539e9 | − | 3.18002e9i | 0.408093 | − | 0.152400i | ||||
\(889\) | 6.00293e10 | 2.86554 | ||||||||
\(890\) | 1.10907e10 | 0.527344 | ||||||||
\(891\) | 2.10412e10 | − | 1.75222e9i | 0.996551 | − | 0.0829883i | ||||
\(892\) | −2.72453e10 | −1.28533 | ||||||||
\(893\) | −3.44424e10 | −1.61850 | ||||||||
\(894\) | 2.48580e10 | − | 9.28307e9i | 1.16355 | − | 0.434520i | ||||
\(895\) | 1.34937e9 | 0.0629145 | ||||||||
\(896\) | − | 3.18857e10i | − | 1.48087i | ||||||
\(897\) | 6.31433e9 | − | 2.35805e9i | 0.292115 | − | 0.109089i | ||||
\(898\) | − | 4.51115e10i | − | 2.07884i | ||||||
\(899\) | 2.26382e10 | 1.03916 | ||||||||
\(900\) | 1.93231e10 | − | 1.67712e10i | 0.883546 | − | 0.766857i | ||||
\(901\) | − | 5.46527e9i | − | 0.248929i | ||||||
\(902\) | 7.33039e9 | + | 3.21378e10i | 0.332586 | + | 1.45812i | ||||
\(903\) | −4.55202e10 | + | 1.69993e10i | −2.05730 | + | 0.768286i | ||||
\(904\) | 1.90030e10i | 0.855525i | ||||||||
\(905\) | − | 4.44301e9i | − | 0.199254i | ||||||
\(906\) | −2.22277e9 | − | 5.95207e9i | −0.0992990 | − | 0.265901i | ||||
\(907\) | 2.35867e9 | 0.104964 | 0.0524822 | − | 0.998622i | \(-0.483287\pi\) | ||||
0.0524822 | + | 0.998622i | \(0.483287\pi\) | |||||||
\(908\) | −4.07736e10 | −1.80750 | ||||||||
\(909\) | 8.09086e9 | − | 7.02231e9i | 0.357290 | − | 0.310103i | ||||
\(910\) | 8.39225e9i | 0.369176i | ||||||||
\(911\) | 2.01599e10i | 0.883433i | 0.897155 | + | 0.441716i | \(0.145630\pi\) | ||||
−0.897155 | + | 0.441716i | \(0.854370\pi\) | |||||||
\(912\) | 4.28209e9 | + | 1.14665e10i | 0.186928 | + | 0.500550i | ||||
\(913\) | −5.79355e9 | − | 2.54000e10i | −0.251940 | − | 1.10455i | ||||
\(914\) | − | 3.39705e9i | − | 0.147160i | ||||||
\(915\) | 3.58992e9 | − | 1.34064e9i | 0.154921 | − | 0.0578545i | ||||
\(916\) | −1.18920e10 | −0.511234 | ||||||||
\(917\) | − | 2.72540e10i | − | 1.16718i | ||||||
\(918\) | −1.13130e10 | + | 2.07785e10i | −0.482647 | + | 0.886473i | ||||
\(919\) | − | 3.33135e10i | − | 1.41585i | −0.706289 | − | 0.707923i | \(-0.749632\pi\) | ||
0.706289 | − | 0.707923i | \(-0.250368\pi\) | |||||||
\(920\) | −2.49177e9 | −0.105499 | ||||||||
\(921\) | −6.44813e9 | − | 1.72666e10i | −0.271972 | − | 0.728281i | ||||
\(922\) | 3.65759e10 | 1.53687 | ||||||||
\(923\) | 8.99596e9 | 0.376567 | ||||||||
\(924\) | −4.35075e10 | + | 2.86082e10i | −1.81431 | + | 1.19300i | ||||
\(925\) | 2.00202e10 | 0.831709 | ||||||||
\(926\) | 2.01204e10 | 0.832716 | ||||||||
\(927\) | −2.69665e10 | + | 2.34051e10i | −1.11185 | + | 0.965008i | ||||
\(928\) | −3.63945e10 | −1.49492 | ||||||||
\(929\) | − | 3.78936e10i | − | 1.55064i | −0.631568 | − | 0.775320i | \(-0.717588\pi\) | ||
0.631568 | − | 0.775320i | \(-0.282412\pi\) | |||||||
\(930\) | −4.05231e9 | − | 1.08512e10i | −0.165201 | − | 0.442370i | ||||
\(931\) | − | 3.86888e10i | − | 1.57131i | ||||||
\(932\) | −6.38124e9 | −0.258196 | ||||||||
\(933\) | −2.82562e9 | − | 7.56637e9i | −0.113901 | − | 0.305001i | ||||
\(934\) | 1.59731e10i | 0.641470i | ||||||||
\(935\) | 5.26473e9 | − | 1.20084e9i | 0.210637 | − | 0.0480448i | ||||
\(936\) | 3.46748e9 | + | 3.99512e9i | 0.138213 | + | 0.159244i | ||||
\(937\) | 2.43061e10i | 0.965221i | 0.875835 | + | 0.482611i | \(0.160311\pi\) | ||||
−0.875835 | + | 0.482611i | \(0.839689\pi\) | |||||||
\(938\) | 5.26027e10i | 2.08113i | ||||||||
\(939\) | 1.08883e10 | − | 4.06616e9i | 0.429170 | − | 0.160271i | ||||
\(940\) | −1.95820e10 | −0.768972 | ||||||||
\(941\) | 3.55368e10 | 1.39032 | 0.695160 | − | 0.718855i | \(-0.255334\pi\) | ||||
0.695160 | + | 0.718855i | \(0.255334\pi\) | |||||||
\(942\) | 4.36021e9 | − | 1.62830e9i | 0.169953 | − | 0.0634680i | ||||
\(943\) | 1.75573e10i | 0.681815i | ||||||||
\(944\) | − | 6.08384e9i | − | 0.235383i | ||||||
\(945\) | −6.69561e9 | + | 1.22978e10i | −0.258095 | + | 0.474040i | ||||
\(946\) | 5.10339e10 | − | 1.16405e10i | 1.95993 | − | 0.447045i | ||||
\(947\) | − | 1.39578e10i | − | 0.534061i | −0.963688 | − | 0.267031i | \(-0.913957\pi\) | ||
0.963688 | − | 0.267031i | \(-0.0860425\pi\) | |||||||
\(948\) | 3.36096e9 | + | 8.99990e9i | 0.128125 | + | 0.343090i | ||||
\(949\) | −4.06074e9 | −0.154231 | ||||||||
\(950\) | − | 3.21506e10i | − | 1.21663i | ||||||
\(951\) | 1.14369e10 | + | 3.06255e10i | 0.431199 | + | 1.15465i | ||||
\(952\) | − | 1.37486e10i | − | 0.516449i | ||||||
\(953\) | −1.58704e10 | −0.593968 | −0.296984 | − | 0.954882i | \(-0.595981\pi\) | ||||
−0.296984 | + | 0.954882i | \(0.595981\pi\) | |||||||
\(954\) | −1.00069e10 | − | 1.15296e10i | −0.373147 | − | 0.429927i | ||||
\(955\) | −8.74562e9 | −0.324922 | ||||||||
\(956\) | 5.57293e10 | 2.06291 | ||||||||
\(957\) | 1.61970e10 | + | 2.46325e10i | 0.597369 | + | 0.908482i | ||||
\(958\) | −4.03201e10 | −1.48164 | ||||||||
\(959\) | −1.63937e10 | −0.600221 | ||||||||
\(960\) | 4.65385e9 | + | 1.24620e10i | 0.169771 | + | 0.454609i | ||||
\(961\) | −2.38159e9 | −0.0865637 | ||||||||
\(962\) | 1.75660e10i | 0.636149i | ||||||||
\(963\) | −3.48734e10 | + | 3.02677e10i | −1.25835 | + | 1.09216i | ||||
\(964\) | 3.56755e9i | 0.128263i | ||||||||
\(965\) | 1.45500e10 | 0.521215 | ||||||||
\(966\) | −4.58413e10 | + | 1.71192e10i | −1.63620 | + | 0.611031i | ||||
\(967\) | − | 1.26468e10i | − | 0.449767i | −0.974386 | − | 0.224884i | \(-0.927800\pi\) | ||
0.974386 | − | 0.224884i | \(-0.0722002\pi\) | |||||||
\(968\) | 1.19104e10 | − | 5.73155e9i | 0.422049 | − | 0.203099i | ||||
\(969\) | 5.89470e9 | + | 1.57847e10i | 0.208127 | + | 0.557318i | ||||
\(970\) | − | 1.26429e10i | − | 0.444782i | ||||||
\(971\) | − | 4.37988e10i | − | 1.53531i | −0.640866 | − | 0.767653i | \(-0.721425\pi\) | ||
0.640866 | − | 0.767653i | \(-0.278575\pi\) | |||||||
\(972\) | 8.03651e9 | + | 3.65848e10i | 0.280696 | + | 1.27782i | ||||
\(973\) | −2.01227e9 | −0.0700311 | ||||||||
\(974\) | −4.24932e10 | −1.47355 | ||||||||
\(975\) | 4.07613e9 | + | 1.09149e10i | 0.140842 | + | 0.377143i | ||||
\(976\) | − | 8.81301e9i | − | 0.303424i | ||||||
\(977\) | 1.33767e10i | 0.458899i | 0.973321 | + | 0.229450i | \(0.0736926\pi\) | ||||
−0.973321 | + | 0.229450i | \(0.926307\pi\) | |||||||
\(978\) | −1.25775e10 | + | 4.69698e9i | −0.429939 | + | 0.160558i | ||||
\(979\) | −3.05509e10 | + | 6.96843e9i | −1.04060 | + | 0.237353i | ||||
\(980\) | − | 2.19963e10i | − | 0.746551i | ||||||
\(981\) | 3.53984e10 | + | 4.07848e10i | 1.19713 | + | 1.37930i | ||||
\(982\) | 7.59494e10 | 2.55938 | ||||||||
\(983\) | 3.86027e10i | 1.29623i | 0.761544 | + | 0.648113i | \(0.224441\pi\) | ||||
−0.761544 | + | 0.648113i | \(0.775559\pi\) | |||||||
\(984\) | −1.29089e10 | + | 4.82074e9i | −0.431922 | + | 0.161299i | ||||
\(985\) | − | 1.51764e9i | − | 0.0505990i | ||||||
\(986\) | −3.30334e10 | −1.09745 | ||||||||
\(987\) | −8.48898e10 | + | 3.17016e10i | −2.81025 | + | 1.04947i | ||||
\(988\) | 1.59884e10 | 0.527420 | ||||||||
\(989\) | 2.78805e10 | 0.916459 | ||||||||
\(990\) | 8.90778e9 | − | 1.21730e10i | 0.291774 | − | 0.398726i | ||||
\(991\) | 4.44473e9 | 0.145073 | 0.0725366 | − | 0.997366i | \(-0.476891\pi\) | ||||
0.0725366 | + | 0.997366i | \(0.476891\pi\) | |||||||
\(992\) | −4.04022e10 | −1.31406 | ||||||||
\(993\) | 2.69412e10 | − | 1.00611e10i | 0.873163 | − | 0.326078i | ||||
\(994\) | −6.53097e10 | −2.10924 | ||||||||
\(995\) | 1.04090e10i | 0.334987i | ||||||||
\(996\) | 4.32971e10 | − | 1.61690e10i | 1.38852 | − | 0.518533i | ||||
\(997\) | 5.59898e10i | 1.78927i | 0.446799 | + | 0.894634i | \(0.352564\pi\) | ||||
−0.446799 | + | 0.894634i | \(0.647436\pi\) | |||||||
\(998\) | −4.84477e10 | −1.54282 | ||||||||
\(999\) | −1.40147e10 | + | 2.57406e10i | −0.444738 | + | 0.816846i |
(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 | 33.8.d.b.32.4 | yes | 24 | |
3.2 | odd | 2 | inner | 33.8.d.b.32.21 | yes | 24 | |
11.10 | odd | 2 | inner | 33.8.d.b.32.22 | yes | 24 | |
33.32 | even | 2 | inner | 33.8.d.b.32.3 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.8.d.b.32.3 | ✓ | 24 | 33.32 | even | 2 | inner | |
33.8.d.b.32.4 | yes | 24 | 1.1 | even | 1 | trivial | |
33.8.d.b.32.21 | yes | 24 | 3.2 | odd | 2 | inner | |
33.8.d.b.32.22 | yes | 24 | 11.10 | odd | 2 | inner |