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 | 32.2 | ||
Character | \(\chi\) | \(=\) | 33.32 |
Dual form | 33.8.d.b.32.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −21.2791 | −1.88082 | −0.940412 | − | 0.340038i | \(-0.889560\pi\) | ||||
−0.940412 | + | 0.340038i | \(0.889560\pi\) | |||||||
\(3\) | 13.2650 | + | 44.8446i | 0.283651 | + | 0.958928i | ||||
\(4\) | 324.799 | 2.53750 | ||||||||
\(5\) | − | 116.081i | − | 0.415304i | −0.978203 | − | 0.207652i | \(-0.933418\pi\) | ||
0.978203 | − | 0.207652i | \(-0.0665821\pi\) | |||||||
\(6\) | −282.268 | − | 954.252i | −0.533497 | − | 1.80357i | ||||
\(7\) | 73.6975i | 0.0812100i | 0.999175 | + | 0.0406050i | \(0.0129285\pi\) | ||||
−0.999175 | + | 0.0406050i | \(0.987071\pi\) | |||||||
\(8\) | −4187.71 | −2.89176 | ||||||||
\(9\) | −1835.08 | + | 1189.73i | −0.839084 | + | 0.544001i | ||||
\(10\) | 2470.10i | 0.781113i | ||||||||
\(11\) | 1337.24 | − | 4207.01i | 0.302924 | − | 0.953015i | ||||
\(12\) | 4308.48 | + | 14565.5i | 0.719763 | + | 2.43327i | ||||
\(13\) | − | 11437.6i | − | 1.44388i | −0.691955 | − | 0.721940i | \(-0.743250\pi\) | ||
0.691955 | − | 0.721940i | \(-0.256750\pi\) | |||||||
\(14\) | − | 1568.22i | − | 0.152742i | ||||||
\(15\) | 5205.60 | − | 1539.82i | 0.398246 | − | 0.117801i | ||||
\(16\) | 47536.4 | 2.90139 | ||||||||
\(17\) | 19264.4 | 0.951007 | 0.475503 | − | 0.879714i | \(-0.342266\pi\) | ||||
0.475503 | + | 0.879714i | \(0.342266\pi\) | |||||||
\(18\) | 39048.8 | − | 25316.4i | 1.57817 | − | 1.02317i | ||||
\(19\) | 42528.5i | 1.42247i | 0.702956 | + | 0.711234i | \(0.251863\pi\) | ||||
−0.702956 | + | 0.711234i | \(0.748137\pi\) | |||||||
\(20\) | − | 37703.0i | − | 1.05383i | ||||||
\(21\) | −3304.93 | + | 977.600i | −0.0778745 | + | 0.0230353i | ||||
\(22\) | −28455.2 | + | 89521.4i | −0.569747 | + | 1.79245i | ||||
\(23\) | − | 38757.4i | − | 0.664212i | −0.943242 | − | 0.332106i | \(-0.892241\pi\) | ||
0.943242 | − | 0.332106i | \(-0.107759\pi\) | |||||||
\(24\) | −55550.2 | − | 187796.i | −0.820250 | − | 2.77299i | ||||
\(25\) | 64650.2 | 0.827523 | ||||||||
\(26\) | 243381.i | 2.71568i | ||||||||
\(27\) | −77695.4 | − | 66511.5i | −0.759665 | − | 0.650315i | ||||
\(28\) | 23936.9i | 0.206070i | ||||||||
\(29\) | 115979. | 0.883056 | 0.441528 | − | 0.897247i | \(-0.354437\pi\) | ||||
0.441528 | + | 0.897247i | \(0.354437\pi\) | |||||||
\(30\) | −110771. | + | 32765.9i | −0.749031 | + | 0.221563i | ||||
\(31\) | 157493. | 0.949502 | 0.474751 | − | 0.880120i | \(-0.342538\pi\) | ||||
0.474751 | + | 0.880120i | \(0.342538\pi\) | |||||||
\(32\) | −475503. | −2.56524 | ||||||||
\(33\) | 206400. | + | 4161.63i | 0.999797 | + | 0.0201588i | ||||
\(34\) | −409928. | −1.78868 | ||||||||
\(35\) | 8554.87 | 0.0337268 | ||||||||
\(36\) | −596032. | + | 386424.i | −2.12917 | + | 1.38040i | ||||
\(37\) | −205289. | −0.666284 | −0.333142 | − | 0.942877i | \(-0.608109\pi\) | ||||
−0.333142 | + | 0.942877i | \(0.608109\pi\) | |||||||
\(38\) | − | 904967.i | − | 2.67541i | ||||||
\(39\) | 512913. | − | 151720.i | 1.38458 | − | 0.409558i | ||||
\(40\) | 486114.i | 1.20096i | ||||||||
\(41\) | 457481. | 1.03664 | 0.518322 | − | 0.855185i | \(-0.326557\pi\) | ||||
0.518322 | + | 0.855185i | \(0.326557\pi\) | |||||||
\(42\) | 70326.0 | − | 20802.4i | 0.146468 | − | 0.0433253i | ||||
\(43\) | − | 215319.i | − | 0.412994i | −0.978447 | − | 0.206497i | \(-0.933794\pi\) | ||
0.978447 | − | 0.206497i | \(-0.0662063\pi\) | |||||||
\(44\) | 434334. | − | 1.36644e6i | 0.768669 | − | 2.41827i | ||||
\(45\) | 138105. | + | 213018.i | 0.225926 | + | 0.348475i | ||||
\(46\) | 824722.i | 1.24927i | ||||||||
\(47\) | 682721.i | 0.959181i | 0.877492 | + | 0.479591i | \(0.159215\pi\) | ||||
−0.877492 | + | 0.479591i | \(0.840785\pi\) | |||||||
\(48\) | 630572. | + | 2.13175e6i | 0.822982 | + | 2.78222i | ||||
\(49\) | 818112. | 0.993405 | ||||||||
\(50\) | −1.37570e6 | −1.55642 | ||||||||
\(51\) | 255543. | + | 863903.i | 0.269754 | + | 0.911947i | ||||
\(52\) | − | 3.71491e6i | − | 3.66384i | ||||||
\(53\) | − | 1.29875e6i | − | 1.19829i | −0.800642 | − | 0.599143i | \(-0.795508\pi\) | ||
0.800642 | − | 0.599143i | \(-0.204492\pi\) | |||||||
\(54\) | 1.65329e6 | + | 1.41530e6i | 1.42880 | + | 1.22313i | ||||
\(55\) | −488354. | − | 155228.i | −0.395791 | − | 0.125806i | ||||
\(56\) | − | 308624.i | − | 0.234840i | ||||||
\(57\) | −1.90717e6 | + | 564142.i | −1.36404 | + | 0.403484i | ||||
\(58\) | −2.46794e6 | −1.66087 | ||||||||
\(59\) | 2.61276e6i | 1.65622i | 0.560567 | + | 0.828109i | \(0.310583\pi\) | ||||
−0.560567 | + | 0.828109i | \(0.689417\pi\) | |||||||
\(60\) | 1.69078e6 | − | 500132.i | 1.01055 | − | 0.298920i | ||||
\(61\) | − | 1.67910e6i | − | 0.947156i | −0.880752 | − | 0.473578i | \(-0.842962\pi\) | ||
0.880752 | − | 0.473578i | \(-0.157038\pi\) | |||||||
\(62\) | −3.35131e6 | −1.78585 | ||||||||
\(63\) | −87680.2 | − | 135241.i | −0.0441783 | − | 0.0681420i | ||||
\(64\) | 4.03362e6 | 1.92338 | ||||||||
\(65\) | −1.32768e6 | −0.599649 | ||||||||
\(66\) | −4.39201e6 | − | 88555.7i | −1.88044 | − | 0.0379152i | ||||
\(67\) | 2.45218e6 | 0.996070 | 0.498035 | − | 0.867157i | \(-0.334055\pi\) | ||||
0.498035 | + | 0.867157i | \(0.334055\pi\) | |||||||
\(68\) | 6.25706e6 | 2.41318 | ||||||||
\(69\) | 1.73806e6 | − | 514118.i | 0.636932 | − | 0.188404i | ||||
\(70\) | −182040. | −0.0634342 | ||||||||
\(71\) | − | 658125.i | − | 0.218225i | −0.994029 | − | 0.109112i | \(-0.965199\pi\) | ||
0.994029 | − | 0.109112i | \(-0.0348009\pi\) | |||||||
\(72\) | 7.68478e6 | − | 4.98225e6i | 2.42643 | − | 1.57312i | ||||
\(73\) | − | 1.22508e6i | − | 0.368583i | −0.982872 | − | 0.184291i | \(-0.941001\pi\) | ||
0.982872 | − | 0.184291i | \(-0.0589990\pi\) | |||||||
\(74\) | 4.36836e6 | 1.25316 | ||||||||
\(75\) | 857588. | + | 2.89921e6i | 0.234728 | + | 0.793534i | ||||
\(76\) | 1.38132e7i | 3.60950i | ||||||||
\(77\) | 310046. | + | 98551.0i | 0.0773943 | + | 0.0246005i | ||||
\(78\) | −1.09143e7 | + | 3.22845e6i | −2.60415 | + | 0.770306i | ||||
\(79\) | − | 6.39822e6i | − | 1.46004i | −0.683426 | − | 0.730020i | \(-0.739511\pi\) | ||
0.683426 | − | 0.730020i | \(-0.260489\pi\) | |||||||
\(80\) | − | 5.51807e6i | − | 1.20496i | ||||||
\(81\) | 1.95205e6 | − | 4.36650e6i | 0.408125 | − | 0.912926i | ||||
\(82\) | −9.73478e6 | −1.94975 | ||||||||
\(83\) | −8.51697e6 | −1.63498 | −0.817488 | − | 0.575945i | \(-0.804634\pi\) | ||||
−0.817488 | + | 0.575945i | \(0.804634\pi\) | |||||||
\(84\) | −1.07344e6 | + | 317524.i | −0.197606 | + | 0.0584520i | ||||
\(85\) | − | 2.23623e6i | − | 0.394957i | ||||||
\(86\) | 4.58180e6i | 0.776768i | ||||||||
\(87\) | 1.53847e6 | + | 5.20105e6i | 0.250480 | + | 0.846787i | ||||
\(88\) | −5.59996e6 | + | 1.76178e7i | −0.875983 | + | 2.75589i | ||||
\(89\) | − | 2.50924e6i | − | 0.377292i | −0.982045 | − | 0.188646i | \(-0.939590\pi\) | ||
0.982045 | − | 0.188646i | \(-0.0604099\pi\) | |||||||
\(90\) | −2.93875e6 | − | 4.53282e6i | −0.424927 | − | 0.655420i | ||||
\(91\) | 842919. | 0.117258 | ||||||||
\(92\) | − | 1.25884e7i | − | 1.68544i | ||||||
\(93\) | 2.08915e6 | + | 7.06272e6i | 0.269327 | + | 0.910504i | ||||
\(94\) | − | 1.45277e7i | − | 1.80405i | ||||||
\(95\) | 4.93675e6 | 0.590756 | ||||||||
\(96\) | −6.30757e6 | − | 2.13238e7i | −0.727634 | − | 2.45988i | ||||
\(97\) | 5.77174e6 | 0.642104 | 0.321052 | − | 0.947062i | \(-0.395964\pi\) | ||||
0.321052 | + | 0.947062i | \(0.395964\pi\) | |||||||
\(98\) | −1.74087e7 | −1.86842 | ||||||||
\(99\) | 2.55128e6 | + | 9.31115e6i | 0.264262 | + | 0.964451i | ||||
\(100\) | 2.09984e7 | 2.09984 | ||||||||
\(101\) | −4.05710e6 | −0.391823 | −0.195912 | − | 0.980622i | \(-0.562767\pi\) | ||||
−0.195912 | + | 0.980622i | \(0.562767\pi\) | |||||||
\(102\) | −5.43771e6 | − | 1.83831e7i | −0.507359 | − | 1.71521i | ||||
\(103\) | −1.06050e7 | −0.956267 | −0.478133 | − | 0.878287i | \(-0.658686\pi\) | ||||
−0.478133 | + | 0.878287i | \(0.658686\pi\) | |||||||
\(104\) | 4.78972e7i | 4.17535i | ||||||||
\(105\) | 113481. | + | 383640.i | 0.00956664 | + | 0.0323416i | ||||
\(106\) | 2.76362e7i | 2.25376i | ||||||||
\(107\) | 1.68359e7 | 1.32860 | 0.664298 | − | 0.747468i | \(-0.268731\pi\) | ||||
0.664298 | + | 0.747468i | \(0.268731\pi\) | |||||||
\(108\) | −2.52354e7 | − | 2.16029e7i | −1.92765 | − | 1.65017i | ||||
\(109\) | 4.01015e6i | 0.296597i | 0.988943 | + | 0.148299i | \(0.0473797\pi\) | ||||
−0.988943 | + | 0.148299i | \(0.952620\pi\) | |||||||
\(110\) | 1.03917e7 | + | 3.30310e6i | 0.744412 | + | 0.236618i | ||||
\(111\) | −2.72317e6 | − | 9.20610e6i | −0.188992 | − | 0.638918i | ||||
\(112\) | 3.50331e6i | 0.235622i | ||||||||
\(113\) | − | 3.24480e6i | − | 0.211550i | −0.994390 | − | 0.105775i | \(-0.966268\pi\) | ||
0.994390 | − | 0.105775i | \(-0.0337324\pi\) | |||||||
\(114\) | 4.05829e7 | − | 1.20044e7i | 2.56552 | − | 0.758882i | ||||
\(115\) | −4.49899e6 | −0.275850 | ||||||||
\(116\) | 3.76701e7 | 2.24075 | ||||||||
\(117\) | 1.36076e7 | + | 2.09888e7i | 0.785473 | + | 1.21154i | ||||
\(118\) | − | 5.55972e7i | − | 3.11505i | ||||||
\(119\) | 1.41974e6i | 0.0772313i | ||||||||
\(120\) | −2.17996e7 | + | 6.44832e6i | −1.15163 | + | 0.340653i | ||||
\(121\) | −1.59108e7 | − | 1.12515e7i | −0.816474 | − | 0.577382i | ||||
\(122\) | 3.57297e7i | 1.78143i | ||||||||
\(123\) | 6.06851e6 | + | 2.05156e7i | 0.294045 | + | 0.994067i | ||||
\(124\) | 5.11537e7 | 2.40936 | ||||||||
\(125\) | − | 1.65735e7i | − | 0.758977i | ||||||
\(126\) | 1.86575e6 | + | 2.87780e6i | 0.0830917 | + | 0.128163i | ||||
\(127\) | − | 2.48533e7i | − | 1.07664i | −0.842739 | − | 0.538322i | \(-0.819059\pi\) | ||
0.842739 | − | 0.538322i | \(-0.180941\pi\) | |||||||
\(128\) | −2.49673e7 | −1.05229 | ||||||||
\(129\) | 9.65591e6 | − | 2.85622e6i | 0.396031 | − | 0.117146i | ||||
\(130\) | 2.82519e7 | 1.12783 | ||||||||
\(131\) | 2.73219e7 | 1.06185 | 0.530924 | − | 0.847420i | \(-0.321845\pi\) | ||||
0.530924 | + | 0.847420i | \(0.321845\pi\) | |||||||
\(132\) | 6.70387e7 | + | 1.35170e6i | 2.53698 | + | 0.0511529i | ||||
\(133\) | −3.13424e6 | −0.115519 | ||||||||
\(134\) | −5.21801e7 | −1.87343 | ||||||||
\(135\) | −7.72072e6 | + | 9.01895e6i | −0.270078 | + | 0.315492i | ||||
\(136\) | −8.06737e7 | −2.75008 | ||||||||
\(137\) | − | 1.91331e7i | − | 0.635716i | −0.948138 | − | 0.317858i | \(-0.897036\pi\) | ||
0.948138 | − | 0.317858i | \(-0.102964\pi\) | |||||||
\(138\) | −3.69843e7 | + | 1.09400e7i | −1.19796 | + | 0.354355i | ||||
\(139\) | − | 8.95211e6i | − | 0.282731i | −0.989957 | − | 0.141366i | \(-0.954851\pi\) | ||
0.989957 | − | 0.141366i | \(-0.0451493\pi\) | |||||||
\(140\) | 2.77862e6 | 0.0855817 | ||||||||
\(141\) | −3.06164e7 | + | 9.05632e6i | −0.919786 | + | 0.272073i | ||||
\(142\) | 1.40043e7i | 0.410442i | ||||||||
\(143\) | −4.81180e7 | − | 1.52947e7i | −1.37604 | − | 0.437386i | ||||
\(144\) | −8.72329e7 | + | 5.65555e7i | −2.43451 | + | 1.57836i | ||||
\(145\) | − | 1.34630e7i | − | 0.366737i | ||||||
\(146\) | 2.60686e7i | 0.693239i | ||||||||
\(147\) | 1.08523e7 | + | 3.66879e7i | 0.281780 | + | 0.952603i | ||||
\(148\) | −6.66778e7 | −1.69069 | ||||||||
\(149\) | 96814.2 | 0.00239766 | 0.00119883 | − | 0.999999i | \(-0.499618\pi\) | ||||
0.00119883 | + | 0.999999i | \(0.499618\pi\) | |||||||
\(150\) | −1.82487e7 | − | 6.16926e7i | −0.441481 | − | 1.49250i | ||||
\(151\) | 6.10092e7i | 1.44204i | 0.692917 | + | 0.721018i | \(0.256325\pi\) | ||||
−0.692917 | + | 0.721018i | \(0.743675\pi\) | |||||||
\(152\) | − | 1.78097e8i | − | 4.11343i | ||||||
\(153\) | −3.53516e7 | + | 2.29194e7i | −0.797975 | + | 0.517349i | ||||
\(154\) | −6.59750e6 | − | 2.09707e6i | −0.145565 | − | 0.0462691i | ||||
\(155\) | − | 1.82820e7i | − | 0.394332i | ||||||
\(156\) | 1.66594e8 | − | 4.92784e7i | 3.51336 | − | 1.03925i | ||||
\(157\) | −1.55235e7 | −0.320141 | −0.160071 | − | 0.987106i | \(-0.551172\pi\) | ||||
−0.160071 | + | 0.987106i | \(0.551172\pi\) | |||||||
\(158\) | 1.36148e8i | 2.74608i | ||||||||
\(159\) | 5.82420e7 | − | 1.72280e7i | 1.14907 | − | 0.339895i | ||||
\(160\) | 5.51969e7i | 1.06536i | ||||||||
\(161\) | 2.85632e6 | 0.0539407 | ||||||||
\(162\) | −4.15378e7 | + | 9.29151e7i | −0.767611 | + | 1.71705i | ||||
\(163\) | 1.97076e7 | 0.356432 | 0.178216 | − | 0.983991i | \(-0.442967\pi\) | ||||
0.178216 | + | 0.983991i | \(0.442967\pi\) | |||||||
\(164\) | 1.48590e8 | 2.63048 | ||||||||
\(165\) | 483086. | − | 2.39592e7i | 0.00837203 | − | 0.415219i | ||||
\(166\) | 1.81233e8 | 3.07510 | ||||||||
\(167\) | −4.16534e7 | −0.692058 | −0.346029 | − | 0.938224i | \(-0.612470\pi\) | ||||
−0.346029 | + | 0.938224i | \(0.612470\pi\) | |||||||
\(168\) | 1.38401e7 | − | 4.09391e6i | 0.225194 | − | 0.0666125i | ||||
\(169\) | −6.80691e7 | −1.08479 | ||||||||
\(170\) | 4.75849e7i | 0.742844i | ||||||||
\(171\) | −5.05974e7 | − | 7.80431e7i | −0.773824 | − | 1.19357i | ||||
\(172\) | − | 6.99356e7i | − | 1.04797i | ||||||
\(173\) | −5.29067e7 | −0.776871 | −0.388436 | − | 0.921476i | \(-0.626984\pi\) | ||||
−0.388436 | + | 0.921476i | \(0.626984\pi\) | |||||||
\(174\) | −3.27373e7 | − | 1.10674e8i | −0.471108 | − | 1.59266i | ||||
\(175\) | 4.76456e6i | 0.0672031i | ||||||||
\(176\) | 6.35674e7 | − | 1.99986e8i | 0.878901 | − | 2.76507i | ||||
\(177\) | −1.17168e8 | + | 3.46584e7i | −1.58819 | + | 0.469788i | ||||
\(178\) | 5.33944e7i | 0.709620i | ||||||||
\(179\) | 1.87430e7i | 0.244260i | 0.992514 | + | 0.122130i | \(0.0389725\pi\) | ||||
−0.992514 | + | 0.122130i | \(0.961027\pi\) | |||||||
\(180\) | 4.48565e7 | + | 6.91880e7i | 0.573286 | + | 0.884254i | ||||
\(181\) | 1.34869e7 | 0.169059 | 0.0845293 | − | 0.996421i | \(-0.473061\pi\) | ||||
0.0845293 | + | 0.996421i | \(0.473061\pi\) | |||||||
\(182\) | −1.79365e7 | −0.220541 | ||||||||
\(183\) | 7.52985e7 | − | 2.22733e7i | 0.908254 | − | 0.268662i | ||||
\(184\) | 1.62305e8i | 1.92074i | ||||||||
\(185\) | 2.38301e7i | 0.276710i | ||||||||
\(186\) | −4.44553e7 | − | 1.50288e8i | −0.506557 | − | 1.71250i | ||||
\(187\) | 2.57610e7 | − | 8.10455e7i | 0.288083 | − | 0.906323i | ||||
\(188\) | 2.21747e8i | 2.43392i | ||||||||
\(189\) | 4.90173e6 | − | 5.72595e6i | 0.0528121 | − | 0.0616924i | ||||
\(190\) | −1.05049e8 | −1.11111 | ||||||||
\(191\) | − | 8.65128e7i | − | 0.898387i | −0.893434 | − | 0.449194i | \(-0.851711\pi\) | ||
0.893434 | − | 0.449194i | \(-0.148289\pi\) | |||||||
\(192\) | 5.35061e7 | + | 1.80886e8i | 0.545568 | + | 1.84438i | ||||
\(193\) | 1.50178e8i | 1.50368i | 0.659347 | + | 0.751838i | \(0.270833\pi\) | ||||
−0.659347 | + | 0.751838i | \(0.729167\pi\) | |||||||
\(194\) | −1.22817e8 | −1.20768 | ||||||||
\(195\) | −1.76118e7 | − | 5.95394e7i | −0.170091 | − | 0.575020i | ||||
\(196\) | 2.65722e8 | 2.52076 | ||||||||
\(197\) | −8.80966e7 | −0.820971 | −0.410485 | − | 0.911867i | \(-0.634641\pi\) | ||||
−0.410485 | + | 0.911867i | \(0.634641\pi\) | |||||||
\(198\) | −5.42890e7 | − | 1.98133e8i | −0.497031 | − | 1.81396i | ||||
\(199\) | −6.12483e6 | −0.0550945 | −0.0275472 | − | 0.999621i | \(-0.508770\pi\) | ||||
−0.0275472 | + | 0.999621i | \(0.508770\pi\) | |||||||
\(200\) | −2.70737e8 | −2.39300 | ||||||||
\(201\) | 3.25282e7 | + | 1.09967e8i | 0.282536 | + | 0.955159i | ||||
\(202\) | 8.63313e7 | 0.736951 | ||||||||
\(203\) | 8.54740e6i | 0.0717130i | ||||||||
\(204\) | 8.30001e7 | + | 2.80595e8i | 0.684499 | + | 2.31406i | ||||
\(205\) | − | 5.31049e7i | − | 0.430522i | ||||||
\(206\) | 2.25664e8 | 1.79857 | ||||||||
\(207\) | 4.61109e7 | + | 7.11228e7i | 0.361332 | + | 0.557330i | ||||
\(208\) | − | 5.43700e8i | − | 4.18926i | ||||||
\(209\) | 1.78918e8 | + | 5.68706e7i | 1.35563 | + | 0.430900i | ||||
\(210\) | −2.41477e6 | − | 8.16351e6i | −0.0179932 | − | 0.0608288i | ||||
\(211\) | 1.45369e8i | 1.06533i | 0.846327 | + | 0.532664i | \(0.178809\pi\) | ||||
−0.846327 | + | 0.532664i | \(0.821191\pi\) | |||||||
\(212\) | − | 4.21834e8i | − | 3.04065i | ||||||
\(213\) | 2.95134e7 | − | 8.73006e6i | 0.209262 | − | 0.0618997i | ||||
\(214\) | −3.58253e8 | −2.49885 | ||||||||
\(215\) | −2.49945e7 | −0.171518 | ||||||||
\(216\) | 3.25366e8 | + | 2.78531e8i | 2.19677 | + | 1.88055i | ||||
\(217\) | 1.16069e7i | 0.0771091i | ||||||||
\(218\) | − | 8.53322e7i | − | 0.557847i | ||||||
\(219\) | 5.49383e7 | − | 1.62508e7i | 0.353444 | − | 0.104549i | ||||
\(220\) | −1.58617e8 | − | 5.04179e7i | −1.00432 | − | 0.319231i | ||||
\(221\) | − | 2.20337e8i | − | 1.37314i | ||||||
\(222\) | 5.79465e7 | + | 1.95897e8i | 0.355461 | + | 1.20169i | ||||
\(223\) | 2.55101e8 | 1.54044 | 0.770220 | − | 0.637778i | \(-0.220146\pi\) | ||||
0.770220 | + | 0.637778i | \(0.220146\pi\) | |||||||
\(224\) | − | 3.50434e7i | − | 0.208323i | ||||||
\(225\) | −1.18638e8 | + | 7.69164e7i | −0.694361 | + | 0.450173i | ||||
\(226\) | 6.90464e7i | 0.397889i | ||||||||
\(227\) | 3.50553e7 | 0.198913 | 0.0994564 | − | 0.995042i | \(-0.468290\pi\) | ||||
0.0994564 | + | 0.995042i | \(0.468290\pi\) | |||||||
\(228\) | −6.19449e8 | + | 1.83233e8i | −3.46125 | + | 1.02384i | ||||
\(229\) | −9.43843e7 | −0.519369 | −0.259684 | − | 0.965694i | \(-0.583618\pi\) | ||||
−0.259684 | + | 0.965694i | \(0.583618\pi\) | |||||||
\(230\) | 9.57345e7 | 0.518825 | ||||||||
\(231\) | −306702. | + | 1.52112e7i | −0.00163710 | + | 0.0811935i | ||||
\(232\) | −4.85689e8 | −2.55358 | ||||||||
\(233\) | 1.32885e7 | 0.0688227 | 0.0344114 | − | 0.999408i | \(-0.489044\pi\) | ||||
0.0344114 | + | 0.999408i | \(0.489044\pi\) | |||||||
\(234\) | −2.89558e8 | − | 4.46622e8i | −1.47734 | − | 2.27869i | ||||
\(235\) | 7.92509e7 | 0.398352 | ||||||||
\(236\) | 8.48623e8i | 4.20265i | ||||||||
\(237\) | 2.86926e8 | − | 8.48727e7i | 1.40007 | − | 0.414141i | ||||
\(238\) | − | 3.02107e7i | − | 0.145258i | ||||||
\(239\) | 1.59568e8 | 0.756053 | 0.378026 | − | 0.925795i | \(-0.376603\pi\) | ||||
0.378026 | + | 0.925795i | \(0.376603\pi\) | |||||||
\(240\) | 2.47456e8 | − | 7.31974e7i | 1.15547 | − | 0.341788i | ||||
\(241\) | 2.64943e8i | 1.21925i | 0.792689 | + | 0.609626i | \(0.208680\pi\) | ||||
−0.792689 | + | 0.609626i | \(0.791320\pi\) | |||||||
\(242\) | 3.38567e8 | + | 2.39423e8i | 1.53564 | + | 1.08595i | ||||
\(243\) | 2.21708e8 | + | 2.96172e7i | 0.991195 | + | 0.132410i | ||||
\(244\) | − | 5.45370e8i | − | 2.40340i | ||||||
\(245\) | − | 9.49672e7i | − | 0.412565i | ||||||
\(246\) | −1.29132e8 | − | 4.36553e8i | −0.553047 | − | 1.86966i | ||||
\(247\) | 4.86422e8 | 2.05387 | ||||||||
\(248\) | −6.59536e8 | −2.74573 | ||||||||
\(249\) | −1.12978e8 | − | 3.81940e8i | −0.463763 | − | 1.56782i | ||||
\(250\) | 3.52669e8i | 1.42750i | ||||||||
\(251\) | 7.51774e7i | 0.300075i | 0.988680 | + | 0.150037i | \(0.0479394\pi\) | ||||
−0.988680 | + | 0.150037i | \(0.952061\pi\) | |||||||
\(252\) | −2.84785e7 | − | 4.39261e7i | −0.112102 | − | 0.172910i | ||||
\(253\) | −1.63053e8 | − | 5.18278e7i | −0.633004 | − | 0.201206i | ||||
\(254\) | 5.28856e8i | 2.02498i | ||||||||
\(255\) | 1.00283e8 | − | 2.96636e7i | 0.378735 | − | 0.112030i | ||||
\(256\) | 1.49782e7 | 0.0557980 | ||||||||
\(257\) | − | 1.43540e8i | − | 0.527482i | −0.964593 | − | 0.263741i | \(-0.915044\pi\) | ||
0.964593 | − | 0.263741i | \(-0.0849565\pi\) | |||||||
\(258\) | −2.05469e8 | + | 6.07777e7i | −0.744864 | + | 0.220331i | ||||
\(259\) | − | 1.51293e7i | − | 0.0541090i | ||||||
\(260\) | −4.31230e8 | −1.52161 | ||||||||
\(261\) | −2.12831e8 | + | 1.37984e8i | −0.740958 | + | 0.480384i | ||||
\(262\) | −5.81386e8 | −1.99715 | ||||||||
\(263\) | −1.37060e8 | −0.464585 | −0.232293 | − | 0.972646i | \(-0.574623\pi\) | ||||
−0.232293 | + | 0.972646i | \(0.574623\pi\) | |||||||
\(264\) | −8.64346e8 | − | 1.74277e7i | −2.89117 | − | 0.0582944i | ||||
\(265\) | −1.50760e8 | −0.497653 | ||||||||
\(266\) | 6.66938e7 | 0.217270 | ||||||||
\(267\) | 1.12526e8 | − | 3.32852e7i | 0.361796 | − | 0.107019i | ||||
\(268\) | 7.96466e8 | 2.52752 | ||||||||
\(269\) | − | 5.97463e7i | − | 0.187145i | −0.995612 | − | 0.0935725i | \(-0.970171\pi\) | ||
0.995612 | − | 0.0935725i | \(-0.0298287\pi\) | |||||||
\(270\) | 1.64290e8 | − | 1.91915e8i | 0.507969 | − | 0.593384i | ||||
\(271\) | − | 5.05492e8i | − | 1.54284i | −0.636325 | − | 0.771421i | \(-0.719546\pi\) | ||
0.636325 | − | 0.771421i | \(-0.280454\pi\) | |||||||
\(272\) | 9.15758e8 | 2.75924 | ||||||||
\(273\) | 1.11814e7 | + | 3.78004e7i | 0.0332602 | + | 0.112442i | ||||
\(274\) | 4.07135e8i | 1.19567i | ||||||||
\(275\) | 8.64526e7 | − | 2.71984e8i | 0.250677 | − | 0.788641i | ||||
\(276\) | 5.64521e8 | − | 1.66985e8i | 1.61621 | − | 0.478076i | ||||
\(277\) | 4.20567e8i | 1.18893i | 0.804121 | + | 0.594465i | \(0.202636\pi\) | ||||
−0.804121 | + | 0.594465i | \(0.797364\pi\) | |||||||
\(278\) | 1.90493e8i | 0.531767i | ||||||||
\(279\) | −2.89012e8 | + | 1.87375e8i | −0.796712 | + | 0.516530i | ||||
\(280\) | −3.58254e7 | −0.0975298 | ||||||||
\(281\) | 2.17377e8 | 0.584442 | 0.292221 | − | 0.956351i | \(-0.405606\pi\) | ||||
0.292221 | + | 0.956351i | \(0.405606\pi\) | |||||||
\(282\) | 6.51488e8 | − | 1.92710e8i | 1.72995 | − | 0.511721i | ||||
\(283\) | − | 1.24453e8i | − | 0.326403i | −0.986593 | − | 0.163202i | \(-0.947818\pi\) | ||
0.986593 | − | 0.163202i | \(-0.0521821\pi\) | |||||||
\(284\) | − | 2.13759e8i | − | 0.553745i | ||||||
\(285\) | 6.54861e7 | + | 2.21386e8i | 0.167568 | + | 0.566492i | ||||
\(286\) | 1.02391e9 | + | 3.25457e8i | 2.58809 | + | 0.822646i | ||||
\(287\) | 3.37152e7i | 0.0841859i | ||||||||
\(288\) | 8.72585e8 | − | 5.65721e8i | 2.15246 | − | 1.39550i | ||||
\(289\) | −3.92227e7 | −0.0955862 | ||||||||
\(290\) | 2.86481e8i | 0.689767i | ||||||||
\(291\) | 7.65623e7 | + | 2.58831e8i | 0.182133 | + | 0.615731i | ||||
\(292\) | − | 3.97906e8i | − | 0.935277i | ||||||
\(293\) | −7.39068e8 | −1.71651 | −0.858257 | − | 0.513220i | \(-0.828453\pi\) | ||||
−0.858257 | + | 0.513220i | \(0.828453\pi\) | |||||||
\(294\) | −2.30927e8 | − | 7.80685e8i | −0.529979 | − | 1.79168i | ||||
\(295\) | 3.03292e8 | 0.687834 | ||||||||
\(296\) | 8.59691e8 | 1.92673 | ||||||||
\(297\) | −3.83712e8 | + | 2.37924e8i | −0.849880 | + | 0.526976i | ||||
\(298\) | −2.06012e6 | −0.00450957 | ||||||||
\(299\) | −4.43290e8 | −0.959044 | ||||||||
\(300\) | 2.78544e8 | + | 9.41663e8i | 0.595620 | + | 2.01359i | ||||
\(301\) | 1.58685e7 | 0.0335392 | ||||||||
\(302\) | − | 1.29822e9i | − | 2.71221i | ||||||
\(303\) | −5.38175e7 | − | 1.81939e8i | −0.111141 | − | 0.375730i | ||||
\(304\) | 2.02165e9i | 4.12713i | ||||||||
\(305\) | −1.94911e8 | −0.393358 | ||||||||
\(306\) | 7.52250e8 | − | 4.87704e8i | 1.50085 | − | 0.973042i | ||||
\(307\) | 6.55755e8i | 1.29347i | 0.762713 | + | 0.646737i | \(0.223867\pi\) | ||||
−0.762713 | + | 0.646737i | \(0.776133\pi\) | |||||||
\(308\) | 1.00703e8 | + | 3.20093e7i | 0.196388 | + | 0.0624236i | ||||
\(309\) | −1.40675e8 | − | 4.75576e8i | −0.271246 | − | 0.916991i | ||||
\(310\) | 3.89023e8i | 0.741669i | ||||||||
\(311\) | 6.55393e8i | 1.23549i | 0.786377 | + | 0.617746i | \(0.211954\pi\) | ||||
−0.786377 | + | 0.617746i | \(0.788046\pi\) | |||||||
\(312\) | −2.14793e9 | + | 6.35358e8i | −4.00386 | + | 1.18434i | ||||
\(313\) | −8.32166e8 | −1.53393 | −0.766963 | − | 0.641691i | \(-0.778233\pi\) | ||||
−0.766963 | + | 0.641691i | \(0.778233\pi\) | |||||||
\(314\) | 3.30326e8 | 0.602129 | ||||||||
\(315\) | −1.56989e7 | + | 1.01780e7i | −0.0282997 | + | 0.0183474i | ||||
\(316\) | − | 2.07814e9i | − | 3.70484i | ||||||
\(317\) | − | 7.71297e7i | − | 0.135992i | −0.997686 | − | 0.0679961i | \(-0.978339\pi\) | ||
0.997686 | − | 0.0679961i | \(-0.0216605\pi\) | |||||||
\(318\) | −1.23934e9 | + | 3.66596e8i | −2.16120 | + | 0.639282i | ||||
\(319\) | 1.55092e8 | − | 4.87927e8i | 0.267499 | − | 0.841565i | ||||
\(320\) | − | 4.68226e8i | − | 0.798787i | ||||||
\(321\) | 2.23329e8 | + | 7.54999e8i | 0.376858 | + | 1.27403i | ||||
\(322\) | −6.07799e7 | −0.101453 | ||||||||
\(323\) | 8.19284e8i | 1.35278i | ||||||||
\(324\) | 6.34025e8 | − | 1.41824e9i | 1.03562 | − | 2.31655i | ||||
\(325\) | − | 7.39440e8i | − | 1.19484i | ||||||
\(326\) | −4.19359e8 | −0.670386 | ||||||||
\(327\) | −1.79833e8 | + | 5.31947e7i | −0.284416 | + | 0.0841301i | ||||
\(328\) | −1.91580e9 | −2.99773 | ||||||||
\(329\) | −5.03148e7 | −0.0778951 | ||||||||
\(330\) | −1.02796e7 | + | 5.09829e8i | −0.0157463 | + | 0.780954i | ||||
\(331\) | −6.98515e8 | −1.05871 | −0.529356 | − | 0.848400i | \(-0.677566\pi\) | ||||
−0.529356 | + | 0.848400i | \(0.677566\pi\) | |||||||
\(332\) | −2.76631e9 | −4.14875 | ||||||||
\(333\) | 3.76721e8 | − | 2.44239e8i | 0.559069 | − | 0.362460i | ||||
\(334\) | 8.86346e8 | 1.30164 | ||||||||
\(335\) | − | 2.84651e8i | − | 0.413672i | ||||||
\(336\) | −1.57105e8 | + | 4.64716e7i | −0.225944 | + | 0.0668344i | ||||
\(337\) | − | 5.36311e8i | − | 0.763330i | −0.924301 | − | 0.381665i | \(-0.875351\pi\) | ||
0.924301 | − | 0.381665i | \(-0.124649\pi\) | |||||||
\(338\) | 1.44845e9 | 2.04030 | ||||||||
\(339\) | 1.45512e8 | − | 4.30424e7i | 0.202861 | − | 0.0600064i | ||||
\(340\) | − | 7.26325e8i | − | 1.00220i | ||||||
\(341\) | 2.10606e8 | − | 6.62576e8i | 0.287627 | − | 0.904889i | ||||
\(342\) | 1.07667e9 | + | 1.66068e9i | 1.45543 | + | 2.24489i | ||||
\(343\) | 1.20986e8i | 0.161884i | ||||||||
\(344\) | 9.01695e8i | 1.19428i | ||||||||
\(345\) | −5.96793e7 | − | 2.01756e8i | −0.0782451 | − | 0.264520i | ||||
\(346\) | 1.12581e9 | 1.46116 | ||||||||
\(347\) | 5.95942e8 | 0.765687 | 0.382843 | − | 0.923813i | \(-0.374945\pi\) | ||||
0.382843 | + | 0.923813i | \(0.374945\pi\) | |||||||
\(348\) | 4.99695e8 | + | 1.68930e9i | 0.635591 | + | 2.14872i | ||||
\(349\) | − | 7.19204e8i | − | 0.905655i | −0.891598 | − | 0.452828i | \(-0.850415\pi\) | ||
0.891598 | − | 0.452828i | \(-0.149585\pi\) | |||||||
\(350\) | − | 1.01385e8i | − | 0.126397i | ||||||
\(351\) | −7.60729e8 | + | 8.88645e8i | −0.938977 | + | 1.09687i | ||||
\(352\) | −6.35860e8 | + | 2.00045e9i | −0.777074 | + | 2.44471i | ||||
\(353\) | 1.09245e8i | 0.132188i | 0.997813 | + | 0.0660938i | \(0.0210536\pi\) | ||||
−0.997813 | + | 0.0660938i | \(0.978946\pi\) | |||||||
\(354\) | 2.49323e9 | − | 7.37498e8i | 2.98711 | − | 0.883588i | ||||
\(355\) | −7.63958e7 | −0.0906296 | ||||||||
\(356\) | − | 8.15001e8i | − | 0.957378i | ||||||
\(357\) | −6.36675e7 | + | 1.88328e7i | −0.0740592 | + | 0.0219067i | ||||
\(358\) | − | 3.98833e8i | − | 0.459410i | ||||||
\(359\) | 1.53339e9 | 1.74913 | 0.874567 | − | 0.484904i | \(-0.161146\pi\) | ||||
0.874567 | + | 0.484904i | \(0.161146\pi\) | |||||||
\(360\) | −5.78345e8 | − | 8.92056e8i | −0.653323 | − | 1.00771i | ||||
\(361\) | −9.14800e8 | −1.02341 | ||||||||
\(362\) | −2.86989e8 | −0.317970 | ||||||||
\(363\) | 2.93514e8 | − | 8.62764e8i | 0.322074 | − | 0.946714i | ||||
\(364\) | 2.73780e8 | 0.297541 | ||||||||
\(365\) | −1.42209e8 | −0.153074 | ||||||||
\(366\) | −1.60228e9 | + | 4.73955e8i | −1.70827 | + | 0.505305i | ||||
\(367\) | −4.93917e8 | −0.521582 | −0.260791 | − | 0.965395i | \(-0.583983\pi\) | ||||
−0.260791 | + | 0.965395i | \(0.583983\pi\) | |||||||
\(368\) | − | 1.84239e9i | − | 1.92714i | ||||||
\(369\) | −8.39514e8 | + | 5.44280e8i | −0.869832 | + | 0.563936i | ||||
\(370\) | − | 5.07084e8i | − | 0.520443i | ||||||
\(371\) | 9.57147e7 | 0.0973128 | ||||||||
\(372\) | 6.78556e8 | + | 2.29397e9i | 0.683416 | + | 2.31040i | ||||
\(373\) | 1.69102e9i | 1.68721i | 0.536965 | + | 0.843605i | \(0.319571\pi\) | ||||
−0.536965 | + | 0.843605i | \(0.680429\pi\) | |||||||
\(374\) | −5.48171e8 | + | 1.72457e9i | −0.541833 | + | 1.70463i | ||||
\(375\) | 7.43231e8 | − | 2.19848e8i | 0.727804 | − | 0.215285i | ||||
\(376\) | − | 2.85904e9i | − | 2.77372i | ||||||
\(377\) | − | 1.32652e9i | − | 1.27503i | ||||||
\(378\) | −1.04304e8 | + | 1.21843e8i | −0.0993301 | + | 0.116032i | ||||
\(379\) | 9.30338e8 | 0.877817 | 0.438908 | − | 0.898532i | \(-0.355365\pi\) | ||||
0.438908 | + | 0.898532i | \(0.355365\pi\) | |||||||
\(380\) | 1.60345e9 | 1.49904 | ||||||||
\(381\) | 1.11454e9 | − | 3.29681e8i | 1.03242 | − | 0.305391i | ||||
\(382\) | 1.84091e9i | 1.68971i | ||||||||
\(383\) | 2.08513e8i | 0.189643i | 0.995494 | + | 0.0948214i | \(0.0302280\pi\) | ||||
−0.995494 | + | 0.0948214i | \(0.969772\pi\) | |||||||
\(384\) | −3.31192e8 | − | 1.11965e9i | −0.298484 | − | 1.00907i | ||||
\(385\) | 1.14399e7 | − | 3.59905e7i | 0.0102167 | − | 0.0321422i | ||||
\(386\) | − | 3.19564e9i | − | 2.82815i | ||||||
\(387\) | 2.56172e8 | + | 3.95127e8i | 0.224669 | + | 0.346536i | ||||
\(388\) | 1.87466e9 | 1.62934 | ||||||||
\(389\) | − | 6.01312e8i | − | 0.517936i | −0.965886 | − | 0.258968i | \(-0.916618\pi\) | ||
0.965886 | − | 0.258968i | \(-0.0833825\pi\) | |||||||
\(390\) | 3.74762e8 | + | 1.26694e9i | 0.319911 | + | 1.08151i | ||||
\(391\) | − | 7.46637e8i | − | 0.631671i | ||||||
\(392\) | −3.42602e9 | −2.87269 | ||||||||
\(393\) | 3.62427e8 | + | 1.22524e9i | 0.301194 | + | 1.01823i | ||||
\(394\) | 1.87462e9 | 1.54410 | ||||||||
\(395\) | −7.42712e8 | −0.606360 | ||||||||
\(396\) | 8.28655e8 | + | 3.02426e9i | 0.670565 | + | 2.44729i | ||||
\(397\) | −2.59934e8 | −0.208495 | −0.104248 | − | 0.994551i | \(-0.533243\pi\) | ||||
−0.104248 | + | 0.994551i | \(0.533243\pi\) | |||||||
\(398\) | 1.30331e8 | 0.103623 | ||||||||
\(399\) | −4.15758e7 | − | 1.40554e8i | −0.0327669 | − | 0.110774i | ||||
\(400\) | 3.07324e9 | 2.40097 | ||||||||
\(401\) | 1.85389e9i | 1.43575i | 0.696174 | + | 0.717873i | \(0.254884\pi\) | ||||
−0.696174 | + | 0.717873i | \(0.745116\pi\) | |||||||
\(402\) | −6.92171e8 | − | 2.34000e9i | −0.531401 | − | 1.79649i | ||||
\(403\) | − | 1.80134e9i | − | 1.37097i | ||||||
\(404\) | −1.31774e9 | −0.994250 | ||||||||
\(405\) | −5.06867e8 | − | 2.26596e8i | −0.379142 | − | 0.169496i | ||||
\(406\) | − | 1.81881e8i | − | 0.134879i | ||||||
\(407\) | −2.74520e8 | + | 8.63654e8i | −0.201834 | + | 0.634979i | ||||
\(408\) | −1.07014e9 | − | 3.61778e9i | −0.780063 | − | 2.63713i | ||||
\(409\) | 4.43794e8i | 0.320738i | 0.987057 | + | 0.160369i | \(0.0512684\pi\) | ||||
−0.987057 | + | 0.160369i | \(0.948732\pi\) | |||||||
\(410\) | 1.13002e9i | 0.809737i | ||||||||
\(411\) | 8.58016e8 | − | 2.53801e8i | 0.609606 | − | 0.180321i | ||||
\(412\) | −3.44449e9 | −2.42652 | ||||||||
\(413\) | −1.92554e8 | −0.134501 | ||||||||
\(414\) | −9.81197e8 | − | 1.51343e9i | −0.679602 | − | 1.04824i | ||||
\(415\) | 9.88658e8i | 0.679012i | ||||||||
\(416\) | 5.43859e9i | 3.70391i | ||||||||
\(417\) | 4.01454e8 | − | 1.18750e8i | 0.271119 | − | 0.0801969i | ||||
\(418\) | −3.80721e9 | − | 1.21016e9i | −2.54970 | − | 0.810446i | ||||
\(419\) | 9.87687e8i | 0.655950i | 0.944686 | + | 0.327975i | \(0.106366\pi\) | ||||
−0.944686 | + | 0.327975i | \(0.893634\pi\) | |||||||
\(420\) | 3.68585e7 | + | 1.24606e8i | 0.0242753 | + | 0.0820666i | ||||
\(421\) | 2.40008e8 | 0.156761 | 0.0783805 | − | 0.996924i | \(-0.475025\pi\) | ||||
0.0783805 | + | 0.996924i | \(0.475025\pi\) | |||||||
\(422\) | − | 3.09332e9i | − | 2.00369i | ||||||
\(423\) | −8.12254e8 | − | 1.25285e9i | −0.521796 | − | 0.804834i | ||||
\(424\) | 5.43880e9i | 3.46515i | ||||||||
\(425\) | 1.24545e9 | 0.786980 | ||||||||
\(426\) | −6.28017e8 | + | 1.85768e8i | −0.393585 | + | 0.116422i | ||||
\(427\) | 1.23745e8 | 0.0769185 | ||||||||
\(428\) | 5.46829e9 | 3.37131 | ||||||||
\(429\) | 4.75989e7 | − | 2.36072e9i | 0.0291069 | − | 1.44359i | ||||
\(430\) | 5.31859e8 | 0.322595 | ||||||||
\(431\) | −5.62589e8 | −0.338470 | −0.169235 | − | 0.985576i | \(-0.554130\pi\) | ||||
−0.169235 | + | 0.985576i | \(0.554130\pi\) | |||||||
\(432\) | −3.69336e9 | − | 3.16172e9i | −2.20408 | − | 1.88682i | ||||
\(433\) | 6.74068e8 | 0.399021 | 0.199511 | − | 0.979896i | \(-0.436065\pi\) | ||||
0.199511 | + | 0.979896i | \(0.436065\pi\) | |||||||
\(434\) | − | 2.46983e8i | − | 0.145029i | ||||||
\(435\) | 6.03743e8 | − | 1.78587e8i | 0.351674 | − | 0.104025i | ||||
\(436\) | 1.30249e9i | 0.752615i | ||||||||
\(437\) | 1.64829e9 | 0.944820 | ||||||||
\(438\) | −1.16904e9 | + | 3.45801e8i | −0.664766 | + | 0.196638i | ||||
\(439\) | 1.29876e9i | 0.732661i | 0.930485 | + | 0.366331i | \(0.119386\pi\) | ||||
−0.930485 | + | 0.366331i | \(0.880614\pi\) | |||||||
\(440\) | 2.04509e9 | + | 6.50049e8i | 1.14453 | + | 0.363799i | ||||
\(441\) | −1.50130e9 | + | 9.73333e8i | −0.833551 | + | 0.540414i | ||||
\(442\) | 4.68858e9i | 2.58263i | ||||||||
\(443\) | − | 9.82222e8i | − | 0.536780i | −0.963310 | − | 0.268390i | \(-0.913508\pi\) | ||
0.963310 | − | 0.268390i | \(-0.0864917\pi\) | |||||||
\(444\) | −8.84483e8 | − | 2.99014e9i | −0.479567 | − | 1.62125i | ||||
\(445\) | −2.91275e8 | −0.156691 | ||||||||
\(446\) | −5.42831e9 | −2.89730 | ||||||||
\(447\) | 1.28424e6 | + | 4.34159e6i | 0.000680098 | + | 0.00229918i | ||||
\(448\) | 2.97268e8i | 0.156198i | ||||||||
\(449\) | 3.16711e9i | 1.65120i | 0.564253 | + | 0.825602i | \(0.309164\pi\) | ||||
−0.564253 | + | 0.825602i | \(0.690836\pi\) | |||||||
\(450\) | 2.52451e9 | − | 1.63671e9i | 1.30597 | − | 0.846697i | ||||
\(451\) | 6.11761e8 | − | 1.92463e9i | 0.314025 | − | 0.987937i | ||||
\(452\) | − | 1.05391e9i | − | 0.536808i | ||||||
\(453\) | −2.73593e9 | + | 8.09289e8i | −1.38281 | + | 0.409035i | ||||
\(454\) | −7.45944e8 | −0.374120 | ||||||||
\(455\) | − | 9.78468e7i | − | 0.0486975i | ||||||
\(456\) | 7.98669e9 | − | 2.36246e9i | 3.94448 | − | 1.16678i | ||||
\(457\) | − | 3.03618e9i | − | 1.48806i | −0.668146 | − | 0.744031i | \(-0.732912\pi\) | ||
0.668146 | − | 0.744031i | \(-0.267088\pi\) | |||||||
\(458\) | 2.00841e9 | 0.976840 | ||||||||
\(459\) | −1.49675e9 | − | 1.28130e9i | −0.722446 | − | 0.618454i | ||||
\(460\) | −1.46127e9 | −0.699968 | ||||||||
\(461\) | −1.09519e9 | −0.520637 | −0.260319 | − | 0.965523i | \(-0.583828\pi\) | ||||
−0.260319 | + | 0.965523i | \(0.583828\pi\) | |||||||
\(462\) | 6.52634e6 | − | 3.23680e8i | 0.00307909 | − | 0.152711i | ||||
\(463\) | 3.57109e9 | 1.67212 | 0.836060 | − | 0.548639i | \(-0.184854\pi\) | ||||
0.836060 | + | 0.548639i | \(0.184854\pi\) | |||||||
\(464\) | 5.51324e9 | 2.56209 | ||||||||
\(465\) | 8.19847e8 | − | 2.42511e8i | 0.378136 | − | 0.111853i | ||||
\(466\) | −2.82768e8 | −0.129443 | ||||||||
\(467\) | 9.84786e8i | 0.447438i | 0.974654 | + | 0.223719i | \(0.0718198\pi\) | ||||
−0.974654 | + | 0.223719i | \(0.928180\pi\) | |||||||
\(468\) | 4.41974e9 | + | 6.81715e9i | 1.99313 | + | 3.07427i | ||||
\(469\) | 1.80719e8i | 0.0808909i | ||||||||
\(470\) | −1.68639e9 | −0.749229 | ||||||||
\(471\) | −2.05920e8 | − | 6.96146e8i | −0.0908083 | − | 0.306992i | ||||
\(472\) | − | 1.09415e10i | − | 4.78938i | ||||||
\(473\) | −9.05851e8 | − | 2.87933e8i | −0.393589 | − | 0.125106i | ||||
\(474\) | −6.10552e9 | + | 1.80601e9i | −2.63329 | + | 0.778927i | ||||
\(475\) | 2.74948e9i | 1.17712i | ||||||||
\(476\) | 4.61129e8i | 0.195974i | ||||||||
\(477\) | 1.54516e9 | + | 2.38331e9i | 0.651869 | + | 1.00546i | ||||
\(478\) | −3.39545e9 | −1.42200 | ||||||||
\(479\) | −1.72008e9 | −0.715113 | −0.357556 | − | 0.933892i | \(-0.616390\pi\) | ||||
−0.357556 | + | 0.933892i | \(0.616390\pi\) | |||||||
\(480\) | −2.47528e9 | + | 7.32189e8i | −1.02160 | + | 0.302189i | ||||
\(481\) | 2.34800e9i | 0.962035i | ||||||||
\(482\) | − | 5.63775e9i | − | 2.29320i | ||||||
\(483\) | 3.78892e7 | + | 1.28091e8i | 0.0153003 | + | 0.0517252i | ||||
\(484\) | −5.16781e9 | − | 3.65450e9i | −2.07180 | − | 1.46511i | ||||
\(485\) | − | 6.69989e8i | − | 0.266668i | ||||||
\(486\) | −4.71774e9 | − | 6.30226e8i | −1.86426 | − | 0.249040i | ||||
\(487\) | −1.16488e9 | −0.457015 | −0.228508 | − | 0.973542i | \(-0.573385\pi\) | ||||
−0.228508 | + | 0.973542i | \(0.573385\pi\) | |||||||
\(488\) | 7.03158e9i | 2.73895i | ||||||||
\(489\) | 2.61422e8 | + | 8.83779e8i | 0.101102 | + | 0.341793i | ||||
\(490\) | 2.02081e9i | 0.775962i | ||||||||
\(491\) | −2.41653e9 | −0.921313 | −0.460657 | − | 0.887578i | \(-0.652386\pi\) | ||||
−0.460657 | + | 0.887578i | \(0.652386\pi\) | |||||||
\(492\) | 1.97105e9 | + | 6.66345e9i | 0.746138 | + | 2.52244i | ||||
\(493\) | 2.23427e9 | 0.839792 | ||||||||
\(494\) | −1.03506e10 | −3.86297 | ||||||||
\(495\) | 1.08085e9 | − | 2.96155e8i | 0.400540 | − | 0.109749i | ||||
\(496\) | 7.48666e9 | 2.75488 | ||||||||
\(497\) | 4.85022e7 | 0.0177220 | ||||||||
\(498\) | 2.40407e9 | + | 8.12733e9i | 0.872255 | + | 2.94880i | ||||
\(499\) | −3.43329e9 | −1.23697 | −0.618484 | − | 0.785797i | \(-0.712253\pi\) | ||||
−0.618484 | + | 0.785797i | \(0.712253\pi\) | |||||||
\(500\) | − | 5.38306e9i | − | 1.92590i | ||||||
\(501\) | −5.52534e8 | − | 1.86793e9i | −0.196303 | − | 0.663634i | ||||
\(502\) | − | 1.59971e9i | − | 0.564387i | ||||||
\(503\) | 1.05168e9 | 0.368464 | 0.184232 | − | 0.982883i | \(-0.441020\pi\) | ||||
0.184232 | + | 0.982883i | \(0.441020\pi\) | |||||||
\(504\) | 3.67179e8 | + | 5.66349e8i | 0.127753 | + | 0.197050i | ||||
\(505\) | 4.70952e8i | 0.162726i | ||||||||
\(506\) | 3.46962e9 | + | 1.10285e9i | 1.19057 | + | 0.378433i | ||||
\(507\) | −9.02939e8 | − | 3.05253e9i | −0.307702 | − | 1.04024i | ||||
\(508\) | − | 8.07235e9i | − | 2.73198i | ||||||
\(509\) | 7.06309e7i | 0.0237401i | 0.999930 | + | 0.0118700i | \(0.00377844\pi\) | ||||
−0.999930 | + | 0.0118700i | \(0.996222\pi\) | |||||||
\(510\) | −2.13392e9 | + | 6.31215e8i | −0.712333 | + | 0.210708i | ||||
\(511\) | 9.02855e7 | 0.0299326 | ||||||||
\(512\) | 2.87709e9 | 0.947347 | ||||||||
\(513\) | 2.82863e9 | − | 3.30427e9i | 0.925051 | − | 1.08060i | ||||
\(514\) | 3.05441e9i | 0.992101i | ||||||||
\(515\) | 1.23103e9i | 0.397141i | ||||||||
\(516\) | 3.13623e9 | − | 9.27698e8i | 1.00493 | − | 0.297257i | ||||
\(517\) | 2.87222e9 | + | 9.12959e8i | 0.914114 | + | 0.290559i | ||||
\(518\) | 3.21937e8i | 0.101769i | ||||||||
\(519\) | −7.01809e8 | − | 2.37258e9i | −0.220360 | − | 0.744963i | ||||
\(520\) | 5.55995e9 | 1.73404 | ||||||||
\(521\) | 3.88780e9i | 1.20440i | 0.798344 | + | 0.602202i | \(0.205710\pi\) | ||||
−0.798344 | + | 0.602202i | \(0.794290\pi\) | |||||||
\(522\) | 4.52886e9 | − | 2.93618e9i | 1.39361 | − | 0.903517i | ||||
\(523\) | 1.58766e9i | 0.485292i | 0.970115 | + | 0.242646i | \(0.0780153\pi\) | ||||
−0.970115 | + | 0.242646i | \(0.921985\pi\) | |||||||
\(524\) | 8.87415e9 | 2.69443 | ||||||||
\(525\) | −2.13665e8 | + | 6.32020e7i | −0.0644429 | + | 0.0190622i | ||||
\(526\) | 2.91651e9 | 0.873802 | ||||||||
\(527\) | 3.03401e9 | 0.902983 | ||||||||
\(528\) | 9.81153e9 | + | 1.97829e8i | 2.90080 | + | 0.0584886i | ||||
\(529\) | 1.90269e9 | 0.558822 | ||||||||
\(530\) | 3.20804e9 | 0.935997 | ||||||||
\(531\) | −3.10848e9 | − | 4.79462e9i | −0.900985 | − | 1.38971i | ||||
\(532\) | −1.01800e9 | −0.293128 | ||||||||
\(533\) | − | 5.23247e9i | − | 1.49679i | ||||||
\(534\) | −2.39445e9 | + | 7.08279e8i | −0.680474 | + | 0.201284i | ||||
\(535\) | − | 1.95433e9i | − | 0.551771i | ||||||
\(536\) | −1.02690e10 | −2.88039 | ||||||||
\(537\) | −8.40521e8 | + | 2.48626e8i | −0.234228 | + | 0.0692847i | ||||
\(538\) | 1.27135e9i | 0.351987i | ||||||||
\(539\) | 1.09401e9 | − | 3.44181e9i | 0.300926 | − | 0.946729i | ||||
\(540\) | −2.50769e9 | + | 2.92935e9i | −0.685322 | + | 0.800559i | ||||
\(541\) | − | 5.30861e8i | − | 0.144142i | −0.997400 | − | 0.0720709i | \(-0.977039\pi\) | ||
0.997400 | − | 0.0720709i | \(-0.0229608\pi\) | |||||||
\(542\) | 1.07564e10i | 2.90181i | ||||||||
\(543\) | 1.78904e8 | + | 6.04815e8i | 0.0479536 | + | 0.162115i | ||||
\(544\) | −9.16027e9 | −2.43956 | ||||||||
\(545\) | 4.65502e8 | 0.123178 | ||||||||
\(546\) | −2.37929e8 | − | 8.04357e8i | −0.0625566 | − | 0.211483i | ||||
\(547\) | 3.43126e9i | 0.896391i | 0.893936 | + | 0.448195i | \(0.147933\pi\) | ||||
−0.893936 | + | 0.448195i | \(0.852067\pi\) | |||||||
\(548\) | − | 6.21442e9i | − | 1.61313i | ||||||
\(549\) | 1.99767e9 | + | 3.08127e9i | 0.515254 | + | 0.794744i | ||||
\(550\) | −1.83963e9 | + | 5.78758e9i | −0.471478 | + | 1.48329i | ||||
\(551\) | 4.93243e9i | 1.25612i | ||||||||
\(552\) | −7.27849e9 | + | 2.15298e9i | −1.84185 | + | 0.544820i | ||||
\(553\) | 4.71533e8 | 0.118570 | ||||||||
\(554\) | − | 8.94929e9i | − | 2.23617i | ||||||
\(555\) | −1.06865e9 | + | 3.16108e8i | −0.265345 | + | 0.0784892i | ||||
\(556\) | − | 2.90764e9i | − | 0.717429i | ||||||
\(557\) | 1.86574e9 | 0.457464 | 0.228732 | − | 0.973489i | \(-0.426542\pi\) | ||||
0.228732 | + | 0.973489i | \(0.426542\pi\) | |||||||
\(558\) | 6.14992e9 | − | 3.98716e9i | 1.49848 | − | 0.971502i | ||||
\(559\) | −2.46273e9 | −0.596313 | ||||||||
\(560\) | 4.06668e8 | 0.0978547 | ||||||||
\(561\) | 3.97617e9 | + | 8.01712e7i | 0.950813 | + | 0.0191712i | ||||
\(562\) | −4.62558e9 | −1.09923 | ||||||||
\(563\) | 5.10827e9 | 1.20641 | 0.603204 | − | 0.797587i | \(-0.293890\pi\) | ||||
0.603204 | + | 0.797587i | \(0.293890\pi\) | |||||||
\(564\) | −9.94418e9 | + | 2.94149e9i | −2.33395 | + | 0.690383i | ||||
\(565\) | −3.76660e8 | −0.0878576 | ||||||||
\(566\) | 2.64825e9i | 0.613906i | ||||||||
\(567\) | 3.21800e8 | + | 1.43861e8i | 0.0741387 | + | 0.0331438i | ||||
\(568\) | 2.75604e9i | 0.631054i | ||||||||
\(569\) | 1.72525e8 | 0.0392607 | 0.0196303 | − | 0.999807i | \(-0.493751\pi\) | ||||
0.0196303 | + | 0.999807i | \(0.493751\pi\) | |||||||
\(570\) | −1.39349e9 | − | 4.71090e9i | −0.315167 | − | 1.06547i | ||||
\(571\) | 2.09567e9i | 0.471083i | 0.971864 | + | 0.235541i | \(0.0756863\pi\) | ||||
−0.971864 | + | 0.235541i | \(0.924314\pi\) | |||||||
\(572\) | −1.56287e10 | − | 4.96771e9i | −3.49170 | − | 1.10987i | ||||
\(573\) | 3.87963e9 | − | 1.14760e9i | 0.861488 | − | 0.254828i | ||||
\(574\) | − | 7.17429e8i | − | 0.158339i | ||||||
\(575\) | − | 2.50567e9i | − | 0.549651i | ||||||
\(576\) | −7.40200e9 | + | 4.79892e9i | −1.61388 | + | 1.04632i | ||||
\(577\) | 9.05678e8 | 0.196272 | 0.0981360 | − | 0.995173i | \(-0.468712\pi\) | ||||
0.0981360 | + | 0.995173i | \(0.468712\pi\) | |||||||
\(578\) | 8.34624e8 | 0.179781 | ||||||||
\(579\) | −6.73465e9 | + | 1.99211e9i | −1.44192 | + | 0.426519i | ||||
\(580\) | − | 4.37278e9i | − | 0.930592i | ||||||
\(581\) | − | 6.27679e8i | − | 0.132776i | ||||||
\(582\) | −1.62918e9 | − | 5.50769e9i | −0.342561 | − | 1.15808i | ||||
\(583\) | −5.46386e9 | − | 1.73674e9i | −1.14198 | − | 0.362990i | ||||
\(584\) | 5.13029e9i | 1.06585i | ||||||||
\(585\) | 2.43640e9 | − | 1.57958e9i | 0.503156 | − | 0.326210i | ||||
\(586\) | 1.57267e10 | 3.22846 | ||||||||
\(587\) | 2.37789e9i | 0.485241i | 0.970121 | + | 0.242621i | \(0.0780070\pi\) | ||||
−0.970121 | + | 0.242621i | \(0.921993\pi\) | |||||||
\(588\) | 3.52482e9 | + | 1.19162e10i | 0.715016 | + | 2.41723i | ||||
\(589\) | 6.69795e9i | 1.35064i | ||||||||
\(590\) | −6.45377e9 | −1.29369 | ||||||||
\(591\) | −1.16861e9 | − | 3.95066e9i | −0.232869 | − | 0.787251i | ||||
\(592\) | −9.75869e9 | −1.93315 | ||||||||
\(593\) | −6.48663e9 | −1.27740 | −0.638701 | − | 0.769455i | \(-0.720528\pi\) | ||||
−0.638701 | + | 0.769455i | \(0.720528\pi\) | |||||||
\(594\) | 8.16504e9 | − | 5.06281e9i | 1.59847 | − | 0.991148i | ||||
\(595\) | 1.64804e8 | 0.0320744 | ||||||||
\(596\) | 3.14452e7 | 0.00608405 | ||||||||
\(597\) | −8.12461e7 | − | 2.74666e8i | −0.0156276 | − | 0.0528316i | ||||
\(598\) | 9.43280e9 | 1.80379 | ||||||||
\(599\) | 1.63992e9i | 0.311767i | 0.987775 | + | 0.155883i | \(0.0498224\pi\) | ||||
−0.987775 | + | 0.155883i | \(0.950178\pi\) | |||||||
\(600\) | −3.59133e9 | − | 1.21411e10i | −0.678775 | − | 2.29471i | ||||
\(601\) | 2.98244e9i | 0.560416i | 0.959939 | + | 0.280208i | \(0.0904035\pi\) | ||||
−0.959939 | + | 0.280208i | \(0.909597\pi\) | |||||||
\(602\) | −3.37667e8 | −0.0630813 | ||||||||
\(603\) | −4.49994e9 | + | 2.91743e9i | −0.835787 | + | 0.541864i | ||||
\(604\) | 1.98157e10i | 3.65916i | ||||||||
\(605\) | −1.30609e9 | + | 1.84694e9i | −0.239789 | + | 0.339085i | ||||
\(606\) | 1.14519e9 | + | 3.87149e9i | 0.209037 | + | 0.706682i | ||||
\(607\) | 8.17709e9i | 1.48402i | 0.670391 | + | 0.742008i | \(0.266126\pi\) | ||||
−0.670391 | + | 0.742008i | \(0.733874\pi\) | |||||||
\(608\) | − | 2.02224e10i | − | 3.64897i | ||||||
\(609\) | −3.83305e8 | + | 1.13382e8i | −0.0687676 | + | 0.0203414i | ||||
\(610\) | 4.14753e9 | 0.739836 | ||||||||
\(611\) | 7.80866e9 | 1.38494 | ||||||||
\(612\) | −1.14822e10 | + | 7.44421e9i | −2.02486 | + | 1.31277i | ||||
\(613\) | − | 1.01160e10i | − | 1.77378i | −0.461985 | − | 0.886888i | \(-0.652863\pi\) | ||
0.461985 | − | 0.886888i | \(-0.347137\pi\) | |||||||
\(614\) | − | 1.39539e10i | − | 2.43279i | ||||||
\(615\) | 2.38147e9 | − | 7.04438e8i | 0.412840 | − | 0.122118i | ||||
\(616\) | −1.29839e9 | − | 4.12703e8i | −0.223806 | − | 0.0711386i | ||||
\(617\) | − | 1.05718e10i | − | 1.81198i | −0.423303 | − | 0.905988i | \(-0.639130\pi\) | ||
0.423303 | − | 0.905988i | \(-0.360870\pi\) | |||||||
\(618\) | 2.99344e9 | + | 1.01198e10i | 0.510166 | + | 1.72470i | ||||
\(619\) | −6.19329e9 | −1.04955 | −0.524776 | − | 0.851240i | \(-0.675851\pi\) | ||||
−0.524776 | + | 0.851240i | \(0.675851\pi\) | |||||||
\(620\) | − | 5.93797e9i | − | 1.00062i | ||||||
\(621\) | −2.57781e9 | + | 3.01127e9i | −0.431947 | + | 0.504579i | ||||
\(622\) | − | 1.39462e10i | − | 2.32374i | ||||||
\(623\) | 1.84925e8 | 0.0306399 | ||||||||
\(624\) | 2.43820e10 | − | 7.21220e9i | 4.01720 | − | 1.18829i | ||||
\(625\) | 3.12693e9 | 0.512317 | ||||||||
\(626\) | 1.77077e10 | 2.88504 | ||||||||
\(627\) | −1.76988e8 | + | 8.77790e9i | −0.0286753 | + | 1.42218i | ||||
\(628\) | −5.04203e9 | −0.812357 | ||||||||
\(629\) | −3.95476e9 | −0.633641 | ||||||||
\(630\) | 3.34057e8 | − | 2.16579e8i | 0.0532266 | − | 0.0345083i | ||||
\(631\) | −3.29651e9 | −0.522338 | −0.261169 | − | 0.965293i | \(-0.584108\pi\) | ||||
−0.261169 | + | 0.965293i | \(0.584108\pi\) | |||||||
\(632\) | 2.67939e10i | 4.22208i | ||||||||
\(633\) | −6.51902e9 | + | 1.92833e9i | −1.02157 | + | 0.302181i | ||||
\(634\) | 1.64125e9i | 0.255777i | ||||||||
\(635\) | −2.88500e9 | −0.447134 | ||||||||
\(636\) | 1.89170e10 | − | 5.59564e9i | 2.91576 | − | 0.862482i | ||||
\(637\) | − | 9.35720e9i | − | 1.43436i | ||||||
\(638\) | −3.30022e9 | + | 1.03826e10i | −0.503118 | + | 1.58284i | ||||
\(639\) | 7.82992e8 | + | 1.20771e9i | 0.118715 | + | 0.183109i | ||||
\(640\) | 2.89823e9i | 0.437021i | ||||||||
\(641\) | − | 1.09738e10i | − | 1.64571i | −0.568253 | − | 0.822854i | \(-0.692380\pi\) | ||
0.568253 | − | 0.822854i | \(-0.307620\pi\) | |||||||
\(642\) | −4.75223e9 | − | 1.60657e10i | −0.708802 | − | 2.39622i | ||||
\(643\) | −8.87778e9 | −1.31694 | −0.658470 | − | 0.752607i | \(-0.728796\pi\) | ||||
−0.658470 | + | 0.752607i | \(0.728796\pi\) | |||||||
\(644\) | 9.27732e8 | 0.136874 | ||||||||
\(645\) | −3.31553e8 | − | 1.12087e9i | −0.0486512 | − | 0.164473i | ||||
\(646\) | − | 1.74336e10i | − | 2.54433i | ||||||
\(647\) | 1.21358e10i | 1.76159i | 0.473498 | + | 0.880795i | \(0.342991\pi\) | ||||
−0.473498 | + | 0.880795i | \(0.657009\pi\) | |||||||
\(648\) | −8.17462e9 | + | 1.82856e10i | −1.18020 | + | 2.63996i | ||||
\(649\) | 1.09919e10 | + | 3.49388e9i | 1.57840 | + | 0.501708i | ||||
\(650\) | 1.57346e10i | 2.24729i | ||||||||
\(651\) | −5.20505e8 | + | 1.53965e8i | −0.0739420 | + | 0.0218721i | ||||
\(652\) | 6.40101e9 | 0.904445 | ||||||||
\(653\) | 1.91875e9i | 0.269663i | 0.990869 | + | 0.134832i | \(0.0430493\pi\) | ||||
−0.990869 | + | 0.134832i | \(0.956951\pi\) | |||||||
\(654\) | 3.82669e9 | − | 1.13194e9i | 0.534935 | − | 0.158234i | ||||
\(655\) | − | 3.17156e9i | − | 0.440989i | ||||||
\(656\) | 2.17470e10 | 3.00771 | ||||||||
\(657\) | 1.45752e9 | + | 2.24812e9i | 0.200510 | + | 0.309272i | ||||
\(658\) | 1.07065e9 | 0.146507 | ||||||||
\(659\) | −1.08084e10 | −1.47117 | −0.735587 | − | 0.677431i | \(-0.763093\pi\) | ||||
−0.735587 | + | 0.677431i | \(0.763093\pi\) | |||||||
\(660\) | 1.56906e8 | − | 7.78192e9i | 0.0212440 | − | 1.05362i | ||||
\(661\) | −6.26254e9 | −0.843423 | −0.421711 | − | 0.906730i | \(-0.638570\pi\) | ||||
−0.421711 | + | 0.906730i | \(0.638570\pi\) | |||||||
\(662\) | 1.48638e10 | 1.99125 | ||||||||
\(663\) | 9.88094e9 | − | 2.92278e9i | 1.31674 | − | 0.389493i | ||||
\(664\) | 3.56666e10 | 4.72796 | ||||||||
\(665\) | 3.63826e8i | 0.0479753i | ||||||||
\(666\) | −8.01628e9 | + | 5.19717e9i | −1.05151 | + | 0.681722i | ||||
\(667\) | − | 4.49506e9i | − | 0.586537i | ||||||
\(668\) | −1.35290e10 | −1.75610 | ||||||||
\(669\) | 3.38392e9 | + | 1.14399e10i | 0.436947 | + | 1.47717i | ||||
\(670\) | 6.05711e9i | 0.778044i | ||||||||
\(671\) | −7.06399e9 | − | 2.24535e9i | −0.902654 | − | 0.286916i | ||||
\(672\) | 1.57151e9 | − | 4.64852e8i | 0.199767 | − | 0.0590911i | ||||
\(673\) | − | 1.29760e10i | − | 1.64093i | −0.571699 | − | 0.820463i | \(-0.693716\pi\) | ||
0.571699 | − | 0.820463i | \(-0.306284\pi\) | |||||||
\(674\) | 1.14122e10i | 1.43569i | ||||||||
\(675\) | −5.02302e9 | − | 4.29998e9i | −0.628640 | − | 0.538150i | ||||
\(676\) | −2.21088e10 | −2.75266 | ||||||||
\(677\) | 1.37621e10 | 1.70461 | 0.852305 | − | 0.523045i | \(-0.175204\pi\) | ||||
0.852305 | + | 0.523045i | \(0.175204\pi\) | |||||||
\(678\) | −3.09636e9 | + | 9.15903e8i | −0.381546 | + | 0.112861i | ||||
\(679\) | 4.25362e8i | 0.0521453i | ||||||||
\(680\) | 9.36467e9i | 1.14212i | ||||||||
\(681\) | 4.65010e8 | + | 1.57204e9i | 0.0564218 | + | 0.190743i | ||||
\(682\) | −4.48150e9 | + | 1.40990e10i | −0.540976 | + | 1.70194i | ||||
\(683\) | − | 4.38092e9i | − | 0.526130i | −0.964778 | − | 0.263065i | \(-0.915267\pi\) | ||
0.964778 | − | 0.263065i | \(-0.0847334\pi\) | |||||||
\(684\) | −1.64340e10 | − | 2.53483e10i | −1.96358 | − | 3.02868i | ||||
\(685\) | −2.22099e9 | −0.264015 | ||||||||
\(686\) | − | 2.57447e9i | − | 0.304476i | ||||||
\(687\) | −1.25201e9 | − | 4.23263e9i | −0.147319 | − | 0.498037i | ||||
\(688\) | − | 1.02355e10i | − | 1.19826i | ||||||
\(689\) | −1.48545e10 | −1.73018 | ||||||||
\(690\) | 1.26992e9 | + | 4.29318e9i | 0.147165 | + | 0.497516i | ||||
\(691\) | −1.01743e10 | −1.17309 | −0.586544 | − | 0.809917i | \(-0.699512\pi\) | ||||
−0.586544 | + | 0.809917i | \(0.699512\pi\) | |||||||
\(692\) | −1.71841e10 | −1.97131 | ||||||||
\(693\) | −6.86208e8 | + | 1.88023e8i | −0.0783231 | + | 0.0214607i | ||||
\(694\) | −1.26811e10 | −1.44012 | ||||||||
\(695\) | −1.03917e9 | −0.117419 | ||||||||
\(696\) | −6.44268e9 | − | 2.17805e10i | −0.724326 | − | 2.44870i | ||||
\(697\) | 8.81309e9 | 0.985856 | ||||||||
\(698\) | 1.53040e10i | 1.70338i | ||||||||
\(699\) | 1.76273e8 | + | 5.95920e8i | 0.0195216 | + | 0.0659960i | ||||
\(700\) | 1.54753e9i | 0.170528i | ||||||||
\(701\) | −7.87337e9 | −0.863272 | −0.431636 | − | 0.902048i | \(-0.642063\pi\) | ||||
−0.431636 | + | 0.902048i | \(0.642063\pi\) | |||||||
\(702\) | 1.61876e10 | − | 1.89096e10i | 1.76605 | − | 2.06301i | ||||
\(703\) | − | 8.73063e9i | − | 0.947768i | ||||||
\(704\) | 5.39390e9 | − | 1.69695e10i | 0.582638 | − | 1.83301i | ||||
\(705\) | 1.05127e9 | + | 3.55398e9i | 0.112993 | + | 0.381991i | ||||
\(706\) | − | 2.32464e9i | − | 0.248621i | ||||||
\(707\) | − | 2.98998e8i | − | 0.0318200i | ||||||
\(708\) | −3.80562e10 | + | 1.12570e10i | −4.03003 | + | 1.19208i | ||||
\(709\) | 1.55379e10 | 1.63731 | 0.818654 | − | 0.574287i | \(-0.194721\pi\) | ||||
0.818654 | + | 0.574287i | \(0.194721\pi\) | |||||||
\(710\) | 1.62563e9 | 0.170458 | ||||||||
\(711\) | 7.61216e9 | + | 1.17412e10i | 0.794263 | + | 1.22510i | ||||
\(712\) | 1.05080e10i | 1.09104i | ||||||||
\(713\) | − | 6.10403e9i | − | 0.630671i | ||||||
\(714\) | 1.35479e9 | − | 4.00746e8i | 0.139292 | − | 0.0412027i | ||||
\(715\) | −1.77542e9 | + | 5.58558e9i | −0.181648 | + | 0.571475i | ||||
\(716\) | 6.08771e9i | 0.619810i | ||||||||
\(717\) | 2.11667e9 | + | 7.15575e9i | 0.214455 | + | 0.725000i | ||||
\(718\) | −3.26292e10 | −3.28981 | ||||||||
\(719\) | − | 7.61998e8i | − | 0.0764545i | −0.999269 | − | 0.0382272i | \(-0.987829\pi\) | ||
0.999269 | − | 0.0382272i | \(-0.0121711\pi\) | |||||||
\(720\) | 6.56502e9 | + | 1.01261e10i | 0.655499 | + | 1.01106i | ||||
\(721\) | − | 7.81559e8i | − | 0.0776584i | ||||||
\(722\) | 1.94661e10 | 1.92486 | ||||||||
\(723\) | −1.18813e10 | + | 3.51448e9i | −1.16917 | + | 0.345842i | ||||
\(724\) | 4.38054e9 | 0.428986 | ||||||||
\(725\) | 7.49810e9 | 0.730749 | ||||||||
\(726\) | −6.24571e9 | + | 1.83588e10i | −0.605765 | + | 1.78060i | ||||
\(727\) | 1.10918e10 | 1.07061 | 0.535307 | − | 0.844658i | \(-0.320196\pi\) | ||||
0.535307 | + | 0.844658i | \(0.320196\pi\) | |||||||
\(728\) | −3.52990e9 | −0.339081 | ||||||||
\(729\) | 1.61279e9 | + | 1.03353e10i | 0.154182 | + | 0.988043i | ||||
\(730\) | 3.02607e9 | 0.287905 | ||||||||
\(731\) | − | 4.14799e9i | − | 0.392760i | ||||||
\(732\) | 2.44569e10 | − | 7.23435e9i | 2.30469 | − | 0.681728i | ||||
\(733\) | 1.36766e10i | 1.28267i | 0.767262 | + | 0.641333i | \(0.221618\pi\) | ||||
−0.767262 | + | 0.641333i | \(0.778382\pi\) | |||||||
\(734\) | 1.05101e10 | 0.981003 | ||||||||
\(735\) | 4.25877e9 | − | 1.25974e9i | 0.395620 | − | 0.117024i | ||||
\(736\) | 1.84293e10i | 1.70387i | ||||||||
\(737\) | 3.27914e9 | − | 1.03163e10i | 0.301734 | − | 0.949270i | ||||
\(738\) | 1.78641e10 | − | 1.15818e10i | 1.63600 | − | 1.06066i | ||||
\(739\) | − | 1.59670e10i | − | 1.45536i | −0.685919 | − | 0.727678i | \(-0.740600\pi\) | ||
0.685919 | − | 0.727678i | \(-0.259400\pi\) | |||||||
\(740\) | 7.74002e9i | 0.702152i | ||||||||
\(741\) | 6.45240e9 | + | 2.18134e10i | 0.582583 | + | 1.96952i | ||||
\(742\) | −2.03672e9 | −0.183028 | ||||||||
\(743\) | −1.12516e10 | −1.00636 | −0.503180 | − | 0.864182i | \(-0.667837\pi\) | ||||
−0.503180 | + | 0.864182i | \(0.667837\pi\) | |||||||
\(744\) | −8.74878e9 | − | 2.95767e10i | −0.778829 | − | 2.63296i | ||||
\(745\) | − | 1.12383e7i | − | 0.000995756i | ||||||
\(746\) | − | 3.59834e10i | − | 3.17334i | ||||||
\(747\) | 1.56293e10 | − | 1.01329e10i | 1.37188 | − | 0.889430i | ||||
\(748\) | 8.36717e9 | − | 2.63235e10i | 0.731009 | − | 2.29979i | ||||
\(749\) | 1.24076e9i | 0.107895i | ||||||||
\(750\) | −1.58153e10 | + | 4.67816e9i | −1.36887 | + | 0.404912i | ||||
\(751\) | 1.39812e10 | 1.20449 | 0.602246 | − | 0.798310i | \(-0.294273\pi\) | ||||
0.602246 | + | 0.798310i | \(0.294273\pi\) | |||||||
\(752\) | 3.24541e10i | 2.78296i | ||||||||
\(753\) | −3.37130e9 | + | 9.97231e8i | −0.287750 | + | 0.0851164i | ||||
\(754\) | 2.82272e10i | 2.39810i | ||||||||
\(755\) | 7.08200e9 | 0.598883 | ||||||||
\(756\) | 1.59208e9 | − | 1.85979e9i | 0.134010 | − | 0.156544i | ||||
\(757\) | −2.10157e10 | −1.76079 | −0.880397 | − | 0.474237i | \(-0.842724\pi\) | ||||
−0.880397 | + | 0.474237i | \(0.842724\pi\) | |||||||
\(758\) | −1.97968e10 | −1.65102 | ||||||||
\(759\) | 1.61294e8 | − | 7.99954e9i | 0.0133897 | − | 0.664077i | ||||
\(760\) | −2.06737e10 | −1.70832 | ||||||||
\(761\) | 2.06241e10 | 1.69640 | 0.848200 | − | 0.529676i | \(-0.177686\pi\) | ||||
0.848200 | + | 0.529676i | \(0.177686\pi\) | |||||||
\(762\) | −2.37164e10 | + | 7.01530e9i | −1.94181 | + | 0.574386i | ||||
\(763\) | −2.95538e8 | −0.0240867 | ||||||||
\(764\) | − | 2.80993e10i | − | 2.27965i | ||||||
\(765\) | 2.66051e9 | + | 4.10365e9i | 0.214857 | + | 0.331402i | ||||
\(766\) | − | 4.43696e9i | − | 0.356685i | ||||||
\(767\) | 2.98836e10 | 2.39138 | ||||||||
\(768\) | 1.98686e8 | + | 6.71690e8i | 0.0158272 | + | 0.0535063i | ||||
\(769\) | − | 8.45536e9i | − | 0.670487i | −0.942132 | − | 0.335243i | \(-0.891181\pi\) | ||
0.942132 | − | 0.335243i | \(-0.108819\pi\) | |||||||
\(770\) | −2.43430e8 | + | 7.65845e8i | −0.0192157 | + | 0.0604537i | ||||
\(771\) | 6.43701e9 | − | 1.90407e9i | 0.505817 | − | 0.149621i | ||||
\(772\) | 4.87776e10i | 3.81557i | ||||||||
\(773\) | − | 3.75493e9i | − | 0.292397i | −0.989255 | − | 0.146199i | \(-0.953296\pi\) | ||
0.989255 | − | 0.146199i | \(-0.0467038\pi\) | |||||||
\(774\) | −5.45110e9 | − | 8.40795e9i | −0.422563 | − | 0.651774i | ||||
\(775\) | 1.01820e10 | 0.785735 | ||||||||
\(776\) | −2.41704e10 | −1.85681 | ||||||||
\(777\) | 6.78467e8 | − | 2.00690e8i | 0.0518866 | − | 0.0153481i | ||||
\(778\) | 1.27954e10i | 0.974147i | ||||||||
\(779\) | 1.94560e10i | 1.47459i | ||||||||
\(780\) | −5.72029e9 | − | 1.93384e10i | −0.431605 | − | 1.45911i | ||||
\(781\) | −2.76874e9 | − | 8.80069e8i | −0.207972 | − | 0.0661056i | ||||
\(782\) | 1.58877e10i | 1.18806i | ||||||||
\(783\) | −9.01107e9 | − | 7.71397e9i | −0.670827 | − | 0.574264i | ||||
\(784\) | 3.88901e10 | 2.88226 | ||||||||
\(785\) | 1.80199e9i | 0.132956i | ||||||||
\(786\) | −7.71211e9 | − | 2.60720e10i | −0.566492 | − | 1.91512i | ||||
\(787\) | 9.67085e9i | 0.707218i | 0.935393 | + | 0.353609i | \(0.115046\pi\) | ||||
−0.935393 | + | 0.353609i | \(0.884954\pi\) | |||||||
\(788\) | −2.86137e10 | −2.08321 | ||||||||
\(789\) | −1.81810e9 | − | 6.14640e9i | −0.131780 | − | 0.445504i | ||||
\(790\) | 1.58042e10 | 1.14046 | ||||||||
\(791\) | 2.39134e8 | 0.0171800 | ||||||||
\(792\) | −1.06840e10 | − | 3.89924e10i | −0.764183 | − | 2.78896i | ||||
\(793\) | −1.92048e10 | −1.36758 | ||||||||
\(794\) | 5.53116e9 | 0.392143 | ||||||||
\(795\) | −1.99984e9 | − | 6.76079e9i | −0.141160 | − | 0.477213i | ||||
\(796\) | −1.98934e9 | −0.139802 | ||||||||
\(797\) | − | 2.79433e9i | − | 0.195512i | −0.995210 | − | 0.0977559i | \(-0.968834\pi\) | ||
0.995210 | − | 0.0977559i | \(-0.0311665\pi\) | |||||||
\(798\) | 8.84696e8 | + | 2.99086e9i | 0.0616288 | + | 0.208346i | ||||
\(799\) | 1.31522e10i | 0.912188i | ||||||||
\(800\) | −3.07414e10 | −2.12280 | ||||||||
\(801\) | 2.98533e9 | + | 4.60466e9i | 0.205248 | + | 0.316580i | ||||
\(802\) | − | 3.94490e10i | − | 2.70038i | ||||||
\(803\) | −5.15394e9 | − | 1.63822e9i | −0.351265 | − | 0.111653i | ||||
\(804\) | 1.05652e10 | + | 3.57172e10i | 0.716935 | + | 2.42371i | ||||
\(805\) | − | 3.31565e8i | − | 0.0224018i | ||||||
\(806\) | 3.83308e10i | 2.57855i | ||||||||
\(807\) | 2.67930e9 | − | 7.92537e8i | 0.179459 | − | 0.0530838i | ||||
\(808\) | 1.69900e10 | 1.13306 | ||||||||
\(809\) | −1.68092e10 | −1.11616 | −0.558081 | − | 0.829787i | \(-0.688462\pi\) | ||||
−0.558081 | + | 0.829787i | \(0.688462\pi\) | |||||||
\(810\) | 1.07857e10 | + | 4.82175e9i | 0.713098 | + | 0.318792i | ||||
\(811\) | − | 4.67476e9i | − | 0.307742i | −0.988091 | − | 0.153871i | \(-0.950826\pi\) | ||
0.988091 | − | 0.153871i | \(-0.0491740\pi\) | |||||||
\(812\) | 2.77619e9i | 0.181971i | ||||||||
\(813\) | 2.26686e10 | − | 6.70537e9i | 1.47947 | − | 0.437629i | ||||
\(814\) | 5.84153e9 | − | 1.83778e10i | 0.379613 | − | 1.19428i | ||||
\(815\) | − | 2.28768e9i | − | 0.148028i | ||||||
\(816\) | 1.21476e10 | + | 4.10668e10i | 0.782661 | + | 2.64591i | ||||
\(817\) | 9.15720e9 | 0.587470 | ||||||||
\(818\) | − | 9.44354e9i | − | 0.603251i | ||||||
\(819\) | −1.54682e9 | + | 1.00285e9i | −0.0983890 | + | 0.0637883i | ||||
\(820\) | − | 1.72484e10i | − | 1.09245i | ||||||
\(821\) | −1.33329e10 | −0.840862 | −0.420431 | − | 0.907325i | \(-0.638121\pi\) | ||||
−0.420431 | + | 0.907325i | \(0.638121\pi\) | |||||||
\(822\) | −1.82578e10 | + | 5.40066e9i | −1.14656 | + | 0.339153i | ||||
\(823\) | 2.50853e10 | 1.56863 | 0.784314 | − | 0.620364i | \(-0.213015\pi\) | ||||
0.784314 | + | 0.620364i | \(0.213015\pi\) | |||||||
\(824\) | 4.44106e10 | 2.76529 | ||||||||
\(825\) | 1.33438e10 | + | 2.69050e8i | 0.827355 | + | 0.0166819i | ||||
\(826\) | 4.09737e9 | 0.252974 | ||||||||
\(827\) | −1.67010e9 | −0.102677 | −0.0513385 | − | 0.998681i | \(-0.516349\pi\) | ||||
−0.0513385 | + | 0.998681i | \(0.516349\pi\) | |||||||
\(828\) | 1.49768e10 | + | 2.31006e10i | 0.916880 | + | 1.41422i | ||||
\(829\) | −1.58908e10 | −0.968734 | −0.484367 | − | 0.874865i | \(-0.660950\pi\) | ||||
−0.484367 | + | 0.874865i | \(0.660950\pi\) | |||||||
\(830\) | − | 2.10377e10i | − | 1.27710i | ||||||
\(831\) | −1.88602e10 | + | 5.57884e9i | −1.14010 | + | 0.337241i | ||||
\(832\) | − | 4.61347e10i | − | 2.77713i | ||||||
\(833\) | 1.57604e10 | 0.944735 | ||||||||
\(834\) | −8.54257e9 | + | 2.52689e9i | −0.509926 | + | 0.150836i | ||||
\(835\) | 4.83517e9i | 0.287415i | ||||||||
\(836\) | 5.81125e10 | + | 1.84716e10i | 3.43991 | + | 1.09341i | ||||
\(837\) | −1.22365e10 | − | 1.04751e10i | −0.721303 | − | 0.617475i | ||||
\(838\) | − | 2.10171e10i | − | 1.23373i | ||||||
\(839\) | − | 2.09530e10i | − | 1.22484i | −0.790533 | − | 0.612419i | \(-0.790197\pi\) | ||
0.790533 | − | 0.612419i | \(-0.209803\pi\) | |||||||
\(840\) | −4.75225e8 | − | 1.60657e9i | −0.0276644 | − | 0.0935240i | ||||
\(841\) | −3.79863e9 | −0.220212 | ||||||||
\(842\) | −5.10714e9 | −0.294840 | ||||||||
\(843\) | 2.88351e9 | + | 9.74818e9i | 0.165777 | + | 0.560438i | ||||
\(844\) | 4.72158e10i | 2.70327i | ||||||||
\(845\) | 7.90153e9i | 0.450518i | ||||||||
\(846\) | 1.72840e10 | + | 2.66594e10i | 0.981406 | + | 1.51375i | ||||
\(847\) | 8.29211e8 | − | 1.17258e9i | 0.0468892 | − | 0.0663059i | ||||
\(848\) | − | 6.17379e10i | − | 3.47669i | ||||||
\(849\) | 5.58106e9 | − | 1.65088e9i | 0.312997 | − | 0.0925845i | ||||
\(850\) | −2.65019e10 | −1.48017 | ||||||||
\(851\) | 7.95646e9i | 0.442554i | ||||||||
\(852\) | 9.58593e9 | − | 2.83552e9i | 0.531001 | − | 0.157070i | ||||
\(853\) | 1.13843e10i | 0.628038i | 0.949417 | + | 0.314019i | \(0.101676\pi\) | ||||
−0.949417 | + | 0.314019i | \(0.898324\pi\) | |||||||
\(854\) | −2.63319e9 | −0.144670 | ||||||||
\(855\) | −9.05931e9 | + | 5.87340e9i | −0.495694 | + | 0.321372i | ||||
\(856\) | −7.05039e10 | −3.84198 | ||||||||
\(857\) | −9.61380e9 | −0.521749 | −0.260875 | − | 0.965373i | \(-0.584011\pi\) | ||||
−0.260875 | + | 0.965373i | \(0.584011\pi\) | |||||||
\(858\) | −1.01286e9 | + | 5.02339e10i | −0.0547450 | + | 2.71513i | ||||
\(859\) | 9.04935e9 | 0.487126 | 0.243563 | − | 0.969885i | \(-0.421684\pi\) | ||||
0.243563 | + | 0.969885i | \(0.421684\pi\) | |||||||
\(860\) | −8.11819e9 | −0.435226 | ||||||||
\(861\) | −1.51195e9 | + | 4.47234e8i | −0.0807282 | + | 0.0238794i | ||||
\(862\) | 1.19714e10 | 0.636603 | ||||||||
\(863\) | 2.62910e10i | 1.39242i | 0.717840 | + | 0.696208i | \(0.245131\pi\) | ||||
−0.717840 | + | 0.696208i | \(0.754869\pi\) | |||||||
\(864\) | 3.69444e10 | + | 3.16264e10i | 1.94873 | + | 1.66822i | ||||
\(865\) | 6.14146e9i | 0.322638i | ||||||||
\(866\) | −1.43435e10 | −0.750488 | ||||||||
\(867\) | −5.20291e8 | − | 1.75893e9i | −0.0271131 | − | 0.0916603i | ||||
\(868\) | 3.76990e9i | 0.195664i | ||||||||
\(869\) | −2.69174e10 | − | 8.55594e9i | −1.39144 | − | 0.442281i | ||||
\(870\) | −1.28471e10 | + | 3.80018e9i | −0.661436 | + | 0.195653i | ||||
\(871\) | − | 2.80469e10i | − | 1.43821i | ||||||
\(872\) | − | 1.67933e10i | − | 0.857688i | ||||||
\(873\) | −1.05916e10 | + | 6.86681e9i | −0.538780 | + | 0.349305i | ||||
\(874\) | −3.50742e10 | −1.77704 | ||||||||
\(875\) | 1.22142e9 | 0.0616365 | ||||||||
\(876\) | 1.78439e10 | − | 5.27824e9i | 0.896863 | − | 0.265292i | ||||
\(877\) | 2.46243e10i | 1.23272i | 0.787464 | + | 0.616361i | \(0.211394\pi\) | ||||
−0.787464 | + | 0.616361i | \(0.788606\pi\) | |||||||
\(878\) | − | 2.76364e10i | − | 1.37801i | ||||||
\(879\) | −9.80376e9 | − | 3.31432e10i | −0.486891 | − | 1.64601i | ||||
\(880\) | −2.32146e10 | − | 7.37896e9i | −1.14834 | − | 0.365011i | ||||
\(881\) | − | 2.84916e10i | − | 1.40379i | −0.712282 | − | 0.701893i | \(-0.752338\pi\) | ||
0.712282 | − | 0.701893i | \(-0.247662\pi\) | |||||||
\(882\) | 3.19463e10 | − | 2.07116e10i | 1.56776 | − | 1.01642i | ||||
\(883\) | 1.42961e10 | 0.698802 | 0.349401 | − | 0.936973i | \(-0.386385\pi\) | ||||
0.349401 | + | 0.936973i | \(0.386385\pi\) | |||||||
\(884\) | − | 7.15654e10i | − | 3.48434i | ||||||
\(885\) | 4.02318e9 | + | 1.36010e10i | 0.195105 | + | 0.659583i | ||||
\(886\) | 2.09008e10i | 1.00959i | ||||||||
\(887\) | 2.01976e9 | 0.0971780 | 0.0485890 | − | 0.998819i | \(-0.484528\pi\) | ||||
0.0485890 | + | 0.998819i | \(0.484528\pi\) | |||||||
\(888\) | 1.14038e10 | + | 3.85525e10i | 0.546520 | + | 1.84760i | ||||
\(889\) | 1.83163e9 | 0.0874342 | ||||||||
\(890\) | 6.19808e9 | 0.294708 | ||||||||
\(891\) | −1.57596e10 | − | 1.40513e10i | −0.746401 | − | 0.665497i | ||||
\(892\) | 8.28566e10 | 3.90886 | ||||||||
\(893\) | −2.90351e10 | −1.36440 | ||||||||
\(894\) | −2.73275e7 | − | 9.23852e7i | −0.00127914 | − | 0.00432435i | ||||
\(895\) | 2.17570e9 | 0.101442 | ||||||||
\(896\) | − | 1.84003e9i | − | 0.0854567i | ||||||
\(897\) | −5.88025e9 | − | 1.98791e10i | −0.272034 | − | 0.919654i | ||||
\(898\) | − | 6.73932e10i | − | 3.10562i | ||||||
\(899\) | 1.82660e10 | 0.838463 | ||||||||
\(900\) | −3.85336e10 | + | 2.49824e10i | −1.76194 | + | 1.14231i | ||||
\(901\) | − | 2.50196e10i | − | 1.13958i | ||||||
\(902\) | −1.30177e10 | + | 4.09544e10i | −0.590625 | + | 1.85814i | ||||
\(903\) | 2.10496e8 | + | 7.11616e8i | 0.00951342 | + | 0.0321617i | ||||
\(904\) | 1.35883e10i | 0.611752i | ||||||||
\(905\) | − | 1.56557e9i | − | 0.0702107i | ||||||
\(906\) | 5.82181e10 | − | 1.72209e10i | 2.60082 | − | 0.769322i | ||||
\(907\) | −1.89029e10 | −0.841208 | −0.420604 | − | 0.907244i | \(-0.638182\pi\) | ||||
−0.420604 | + | 0.907244i | \(0.638182\pi\) | |||||||
\(908\) | 1.13859e10 | 0.504741 | ||||||||
\(909\) | 7.44509e9 | − | 4.82685e9i | 0.328773 | − | 0.213152i | ||||
\(910\) | 2.08209e9i | 0.0915914i | ||||||||
\(911\) | 1.87105e10i | 0.819918i | 0.912104 | + | 0.409959i | \(0.134457\pi\) | ||||
−0.912104 | + | 0.409959i | \(0.865543\pi\) | |||||||
\(912\) | −9.06601e10 | + | 2.68173e10i | −3.95762 | + | 1.17066i | ||||
\(913\) | −1.13892e10 | + | 3.58310e10i | −0.495274 | + | 1.55816i | ||||
\(914\) | 6.46071e10i | 2.79878i | ||||||||
\(915\) | −2.58551e9 | − | 8.74072e9i | −0.111576 | − | 0.377201i | ||||
\(916\) | −3.06560e10 | −1.31790 | ||||||||
\(917\) | 2.01356e9i | 0.0862326i | ||||||||
\(918\) | 3.18495e10 | + | 2.72649e10i | 1.35879 | + | 1.16320i | ||||
\(919\) | − | 6.43421e9i | − | 0.273458i | −0.990608 | − | 0.136729i | \(-0.956341\pi\) | ||
0.990608 | − | 0.136729i | \(-0.0436590\pi\) | |||||||
\(920\) | 1.88405e10 | 0.797691 | ||||||||
\(921\) | −2.94071e10 | + | 8.69862e9i | −1.24035 | + | 0.366895i | ||||
\(922\) | 2.33046e10 | 0.979226 | ||||||||
\(923\) | −7.52734e9 | −0.315091 | ||||||||
\(924\) | −9.96166e7 | + | 4.94059e9i | −0.00415413 | + | 0.206028i | ||||
\(925\) | −1.32720e10 | −0.551365 | ||||||||
\(926\) | −7.59895e10 | −3.14496 | ||||||||
\(927\) | 1.94609e10 | − | 1.26171e10i | 0.802388 | − | 0.520210i | ||||
\(928\) | −5.51486e10 | −2.26525 | ||||||||
\(929\) | 4.41197e9i | 0.180542i | 0.995917 | + | 0.0902708i | \(0.0287733\pi\) | ||||
−0.995917 | + | 0.0902708i | \(0.971227\pi\) | |||||||
\(930\) | −1.74456e10 | + | 5.16041e9i | −0.711206 | + | 0.210375i | ||||
\(931\) | 3.47930e10i | 1.41309i | ||||||||
\(932\) | 4.31611e9 | 0.174637 | ||||||||
\(933\) | −2.93908e10 | + | 8.69381e9i | −1.18475 | + | 0.350449i | ||||
\(934\) | − | 2.09553e10i | − | 0.841551i | ||||||
\(935\) | −9.40784e9 | − | 2.99036e9i | −0.376400 | − | 0.119642i | ||||
\(936\) | −5.69848e10 | − | 8.78951e10i | −2.27140 | − | 3.50347i | ||||
\(937\) | − | 2.10425e8i | − | 0.00835619i | −0.999991 | − | 0.00417809i | \(-0.998670\pi\) | ||
0.999991 | − | 0.00417809i | \(-0.00132993\pi\) | |||||||
\(938\) | − | 3.84554e9i | − | 0.152141i | ||||||
\(939\) | −1.10387e10 | − | 3.73181e10i | −0.435100 | − | 1.47092i | ||||
\(940\) | 2.57407e10 | 1.01082 | ||||||||
\(941\) | 3.06020e10 | 1.19725 | 0.598627 | − | 0.801028i | \(-0.295713\pi\) | ||||
0.598627 | + | 0.801028i | \(0.295713\pi\) | |||||||
\(942\) | 4.38179e9 | + | 1.48134e10i | 0.170794 | + | 0.577398i | ||||
\(943\) | − | 1.77308e10i | − | 0.688552i | ||||||
\(944\) | 1.24201e11i | 4.80534i | ||||||||
\(945\) | −6.64674e8 | − | 5.68998e8i | −0.0256211 | − | 0.0219331i | ||||
\(946\) | 1.92757e10 | + | 6.12694e9i | 0.740271 | + | 0.235302i | ||||
\(947\) | 1.68029e10i | 0.642925i | 0.946922 | + | 0.321463i | \(0.104174\pi\) | ||||
−0.946922 | + | 0.321463i | \(0.895826\pi\) | |||||||
\(948\) | 9.31934e10 | − | 2.75666e10i | 3.55268 | − | 1.05088i | ||||
\(949\) | −1.40119e10 | −0.532190 | ||||||||
\(950\) | − | 5.85063e10i | − | 2.21396i | ||||||
\(951\) | 3.45885e9 | − | 1.02313e9i | 0.130407 | − | 0.0385743i | ||||
\(952\) | − | 5.94545e9i | − | 0.223334i | ||||||
\(953\) | 4.57844e8 | 0.0171353 | 0.00856767 | − | 0.999963i | \(-0.497273\pi\) | ||||
0.00856767 | + | 0.999963i | \(0.497273\pi\) | |||||||
\(954\) | −3.28797e10 | − | 5.07146e10i | −1.22605 | − | 1.89110i | ||||
\(955\) | −1.00425e10 | −0.373104 | ||||||||
\(956\) | 5.18275e10 | 1.91848 | ||||||||
\(957\) | 2.39382e10 | + | 4.82664e8i | 0.882876 | + | 0.0178014i | ||||
\(958\) | 3.66017e10 | 1.34500 | ||||||||
\(959\) | 1.41006e9 | 0.0516265 | ||||||||
\(960\) | 2.09974e10 | − | 6.21104e9i | 0.765979 | − | 0.226577i | ||||
\(961\) | −2.70850e9 | −0.0984457 | ||||||||
\(962\) | − | 4.99634e10i | − | 1.80942i | ||||||
\(963\) | −3.08952e10 | + | 2.00302e10i | −1.11480 | + | 0.722758i | ||||
\(964\) | 8.60535e10i | 3.09385i | ||||||||
\(965\) | 1.74328e10 | 0.624483 | ||||||||
\(966\) | −8.06248e8 | − | 2.72565e9i | −0.0287772 | − | 0.0972860i | ||||
\(967\) | 1.99002e10i | 0.707726i | 0.935297 | + | 0.353863i | \(0.115132\pi\) | ||||
−0.935297 | + | 0.353863i | \(0.884868\pi\) | |||||||
\(968\) | 6.66297e10 | + | 4.71182e10i | 2.36105 | + | 1.66965i | ||||
\(969\) | −3.67405e10 | + | 1.08678e10i | −1.29721 | + | 0.383716i | ||||
\(970\) | 1.42567e10i | 0.501556i | ||||||||
\(971\) | 2.59685e10i | 0.910291i | 0.890417 | + | 0.455145i | \(0.150413\pi\) | ||||
−0.890417 | + | 0.455145i | \(0.849587\pi\) | |||||||
\(972\) | 7.20106e10 | + | 9.61964e9i | 2.51515 | + | 0.335990i | ||||
\(973\) | 6.59748e8 | 0.0229606 | ||||||||
\(974\) | 2.47876e10 | 0.859564 | ||||||||
\(975\) | 3.31599e10 | − | 9.80870e9i | 1.14577 | − | 0.338919i | ||||
\(976\) | − | 7.98182e10i | − | 2.74807i | ||||||
\(977\) | − | 2.89249e10i | − | 0.992296i | −0.868238 | − | 0.496148i | \(-0.834747\pi\) | ||
0.868238 | − | 0.496148i | \(-0.165253\pi\) | |||||||
\(978\) | −5.56282e9 | − | 1.88060e10i | −0.190156 | − | 0.642851i | ||||
\(979\) | −1.05564e10 | − | 3.35545e9i | −0.359565 | − | 0.114291i | ||||
\(980\) | − | 3.08453e10i | − | 1.04688i | ||||||
\(981\) | −4.77099e9 | − | 7.35893e9i | −0.161349 | − | 0.248870i | ||||
\(982\) | 5.14216e10 | 1.73283 | ||||||||
\(983\) | 5.49184e10i | 1.84408i | 0.387089 | + | 0.922042i | \(0.373481\pi\) | ||||
−0.387089 | + | 0.922042i | \(0.626519\pi\) | |||||||
\(984\) | −2.54132e10 | − | 8.59133e10i | −0.850307 | − | 2.87460i | ||||
\(985\) | 1.02263e10i | 0.340952i | ||||||||
\(986\) | −4.75433e10 | −1.57950 | ||||||||
\(987\) | −6.67428e8 | − | 2.25635e9i | −0.0220950 | − | 0.0746958i | ||||
\(988\) | 1.57990e11 | 5.21170 | ||||||||
\(989\) | −8.34521e9 | −0.274315 | ||||||||
\(990\) | −2.29994e10 | + | 6.30191e9i | −0.753345 | + | 0.206419i | ||||
\(991\) | 5.40673e10 | 1.76472 | 0.882362 | − | 0.470571i | \(-0.155952\pi\) | ||||
0.882362 | + | 0.470571i | \(0.155952\pi\) | |||||||
\(992\) | −7.48885e10 | −2.43570 | ||||||||
\(993\) | −9.26583e9 | − | 3.13246e10i | −0.300304 | − | 1.01523i | ||||
\(994\) | −1.03208e9 | −0.0333320 | ||||||||
\(995\) | 7.10976e8i | 0.0228810i | ||||||||
\(996\) | −3.66952e10 | − | 1.24054e11i | −1.17680 | − | 3.97835i | ||||
\(997\) | 3.57762e10i | 1.14330i | 0.820497 | + | 0.571651i | \(0.193697\pi\) | ||||
−0.820497 | + | 0.571651i | \(0.806303\pi\) | |||||||
\(998\) | 7.30573e10 | 2.32652 | ||||||||
\(999\) | 1.59500e10 | + | 1.36541e10i | 0.506153 | + | 0.433294i |
(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.32.2 | yes | 24 | |
3.2 | odd | 2 | inner | 33.8.d.b.32.23 | yes | 24 | |
11.10 | odd | 2 | inner | 33.8.d.b.32.24 | yes | 24 | |
33.32 | even | 2 | inner | 33.8.d.b.32.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.8.d.b.32.1 | ✓ | 24 | 33.32 | even | 2 | inner | |
33.8.d.b.32.2 | yes | 24 | 1.1 | even | 1 | trivial | |
33.8.d.b.32.23 | yes | 24 | 3.2 | odd | 2 | inner | |
33.8.d.b.32.24 | yes | 24 | 11.10 | odd | 2 | inner |