Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,22,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (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: | \(58.6902423003\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.35 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.22.c.b.20.36 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2061.69i | − | 1.42367i | −0.702349 | − | 0.711833i | \(-0.747865\pi\) | ||
0.702349 | − | 0.711833i | \(-0.252135\pi\) | |||||||
\(3\) | 759.014 | + | 102273.i | 0.00742124 | + | 0.999972i | ||||
\(4\) | −2.15341e6 | −1.02682 | ||||||||
\(5\) | −1.95223e7 | −0.894017 | −0.447008 | − | 0.894530i | \(-0.647511\pi\) | ||||
−0.447008 | + | 0.894530i | \(0.647511\pi\) | |||||||
\(6\) | 2.10855e8 | − | 1.56485e6i | 1.42363 | − | 0.0105654i | ||||
\(7\) | −6.67328e8 | + | 3.36481e8i | −0.892914 | + | 0.450227i | ||||
\(8\) | 1.15978e8i | 0.0381884i | ||||||||
\(9\) | −1.04592e10 | + | 1.55253e8i | −0.999890 | + | 0.0148421i | ||||
\(10\) | 4.02489e10i | 1.27278i | ||||||||
\(11\) | − | 1.09823e11i | − | 1.27665i | −0.769768 | − | 0.638323i | \(-0.779628\pi\) | ||
0.769768 | − | 0.638323i | \(-0.220372\pi\) | |||||||
\(12\) | −1.63447e9 | − | 2.20235e11i | −0.00762031 | − | 1.02680i | ||||
\(13\) | 5.15271e11i | 1.03665i | 0.855185 | + | 0.518323i | \(0.173443\pi\) | ||||
−0.855185 | + | 0.518323i | \(0.826557\pi\) | |||||||
\(14\) | 6.93720e11 | + | 1.37582e12i | 0.640973 | + | 1.27121i | ||||
\(15\) | −1.48177e10 | − | 1.99660e12i | −0.00663472 | − | 0.893992i | ||||
\(16\) | −4.27691e12 | −0.972456 | ||||||||
\(17\) | −1.12356e13 | −1.35171 | −0.675855 | − | 0.737035i | \(-0.736225\pi\) | ||||
−0.675855 | + | 0.737035i | \(0.736225\pi\) | |||||||
\(18\) | 3.20084e11 | + | 2.15636e13i | 0.0211302 | + | 1.42351i | ||||
\(19\) | 4.21841e13i | 1.57847i | 0.614092 | + | 0.789235i | \(0.289522\pi\) | ||||
−0.614092 | + | 0.789235i | \(0.710478\pi\) | |||||||
\(20\) | 4.20394e13 | 0.917998 | ||||||||
\(21\) | −3.49195e13 | − | 6.79942e13i | −0.456841 | − | 0.889548i | ||||
\(22\) | −2.26421e14 | −1.81752 | ||||||||
\(23\) | − | 2.30898e14i | − | 1.16219i | −0.813836 | − | 0.581095i | \(-0.802625\pi\) | ||
0.813836 | − | 0.581095i | \(-0.197375\pi\) | |||||||
\(24\) | −1.18614e13 | + | 8.80291e10i | −0.0381873 | + | 0.000283405i | ||||
\(25\) | −9.57173e13 | −0.200734 | ||||||||
\(26\) | 1.06233e15 | 1.47584 | ||||||||
\(27\) | −2.38169e13 | − | 1.06958e15i | −0.0222621 | − | 0.999752i | ||||
\(28\) | 1.43703e15 | − | 7.24581e14i | 0.916866 | − | 0.462304i | ||||
\(29\) | 2.95496e15i | 1.30429i | 0.758095 | + | 0.652144i | \(0.226130\pi\) | ||||
−0.758095 | + | 0.652144i | \(0.773870\pi\) | |||||||
\(30\) | −4.11638e15 | + | 3.05495e13i | −1.27275 | + | 0.00944562i | ||||
\(31\) | − | 4.09546e15i | − | 0.897438i | −0.893673 | − | 0.448719i | \(-0.851880\pi\) | ||
0.893673 | − | 0.448719i | \(-0.148120\pi\) | |||||||
\(32\) | 9.06088e15i | 1.42264i | ||||||||
\(33\) | 1.12319e16 | − | 8.33573e13i | 1.27661 | − | 0.00947430i | ||||
\(34\) | 2.31643e16i | 1.92438i | ||||||||
\(35\) | 1.30278e16 | − | 6.56889e15i | 0.798280 | − | 0.402511i | ||||
\(36\) | 2.25229e16 | − | 3.34324e14i | 1.02671 | − | 0.0152402i | ||||
\(37\) | 2.53669e16 | 0.867260 | 0.433630 | − | 0.901091i | \(-0.357232\pi\) | ||||
0.433630 | + | 0.901091i | \(0.357232\pi\) | |||||||
\(38\) | 8.69705e16 | 2.24721 | ||||||||
\(39\) | −5.26983e16 | + | 3.91098e14i | −1.03662 | + | 0.00769320i | ||||
\(40\) | − | 2.26416e15i | − | 0.0341411i | ||||||
\(41\) | 1.05157e17 | 1.22351 | 0.611753 | − | 0.791049i | \(-0.290465\pi\) | ||||
0.611753 | + | 0.791049i | \(0.290465\pi\) | |||||||
\(42\) | −1.40183e17 | + | 7.19931e16i | −1.26642 | + | 0.650389i | ||||
\(43\) | 2.13460e17 | 1.50625 | 0.753127 | − | 0.657875i | \(-0.228545\pi\) | ||||
0.753127 | + | 0.657875i | \(0.228545\pi\) | |||||||
\(44\) | 2.36494e17i | 1.31089i | ||||||||
\(45\) | 2.04188e17 | − | 3.03090e15i | 0.893918 | − | 0.0132691i | ||||
\(46\) | −4.76039e17 | −1.65457 | ||||||||
\(47\) | −2.13141e17 | −0.591071 | −0.295535 | − | 0.955332i | \(-0.595498\pi\) | ||||
−0.295535 | + | 0.955332i | \(0.595498\pi\) | |||||||
\(48\) | −3.24623e15 | − | 4.37413e17i | −0.00721684 | − | 0.972430i | ||||
\(49\) | 3.32106e17 | − | 4.49087e17i | 0.594591 | − | 0.804028i | ||||
\(50\) | 1.97339e17i | 0.285778i | ||||||||
\(51\) | −8.52799e15 | − | 1.14910e18i | −0.0100314 | − | 1.35167i | ||||
\(52\) | − | 1.10959e18i | − | 1.06445i | ||||||
\(53\) | − | 1.61549e18i | − | 1.26884i | −0.772987 | − | 0.634421i | \(-0.781238\pi\) | ||
0.772987 | − | 0.634421i | \(-0.218762\pi\) | |||||||
\(54\) | −2.20513e18 | + | 4.91031e16i | −1.42331 | + | 0.0316938i | ||||
\(55\) | 2.14400e18i | 1.14134i | ||||||||
\(56\) | −3.90245e16 | − | 7.73954e16i | −0.0171934 | − | 0.0340989i | ||||
\(57\) | −4.31430e18 | + | 3.20183e16i | −1.57843 | + | 0.0117142i | ||||
\(58\) | 6.09222e18 | 1.85687 | ||||||||
\(59\) | −3.38337e18 | −0.861793 | −0.430896 | − | 0.902401i | \(-0.641803\pi\) | ||||
−0.430896 | + | 0.902401i | \(0.641803\pi\) | |||||||
\(60\) | 3.19085e16 | + | 4.29950e18i | 0.00681269 | + | 0.917973i | ||||
\(61\) | − | 5.43127e18i | − | 0.974851i | −0.873165 | − | 0.487426i | \(-0.837936\pi\) | ||
0.873165 | − | 0.487426i | \(-0.162064\pi\) | |||||||
\(62\) | −8.44356e18 | −1.27765 | ||||||||
\(63\) | 6.92747e18 | − | 3.62293e18i | 0.886133 | − | 0.463430i | ||||
\(64\) | 9.71137e18 | 1.05291 | ||||||||
\(65\) | − | 1.00593e19i | − | 0.926779i | ||||||
\(66\) | −1.71857e17 | − | 2.31568e19i | −0.0134882 | − | 1.81747i | ||||
\(67\) | 1.42533e19 | 0.955279 | 0.477640 | − | 0.878556i | \(-0.341492\pi\) | ||||
0.477640 | + | 0.878556i | \(0.341492\pi\) | |||||||
\(68\) | 2.41948e19 | 1.38797 | ||||||||
\(69\) | 2.36146e19 | − | 1.75255e17i | 1.16216 | − | 0.00862489i | ||||
\(70\) | −1.35430e19 | − | 2.68592e19i | −0.573041 | − | 1.13648i | ||||
\(71\) | 2.98894e19i | 1.08969i | 0.838536 | + | 0.544846i | \(0.183412\pi\) | ||||
−0.838536 | + | 0.544846i | \(0.816588\pi\) | |||||||
\(72\) | −1.80060e16 | − | 1.21304e18i | −0.000566795 | − | 0.0381842i | ||||
\(73\) | 3.08957e18i | 0.0841411i | 0.999115 | + | 0.0420706i | \(0.0133954\pi\) | ||||
−0.999115 | + | 0.0420706i | \(0.986605\pi\) | |||||||
\(74\) | − | 5.22987e19i | − | 1.23469i | ||||||
\(75\) | −7.26508e16 | − | 9.78930e18i | −0.00148969 | − | 0.200728i | ||||
\(76\) | − | 9.08395e19i | − | 1.62081i | ||||||
\(77\) | 3.69534e19 | + | 7.32880e19i | 0.574781 | + | 1.13994i | ||||
\(78\) | 8.06322e17 | + | 1.08648e20i | 0.0109525 | + | 1.47580i | ||||
\(79\) | −6.07045e19 | −0.721335 | −0.360667 | − | 0.932695i | \(-0.617451\pi\) | ||||
−0.360667 | + | 0.932695i | \(0.617451\pi\) | |||||||
\(80\) | 8.34951e19 | 0.869393 | ||||||||
\(81\) | 1.09371e20 | − | 3.24765e18i | 0.999559 | − | 0.0296809i | ||||
\(82\) | − | 2.16800e20i | − | 1.74186i | ||||||
\(83\) | −3.37951e19 | −0.239075 | −0.119538 | − | 0.992830i | \(-0.538141\pi\) | ||||
−0.119538 | + | 0.992830i | \(0.538141\pi\) | |||||||
\(84\) | 7.51958e19 | + | 1.46419e20i | 0.469096 | + | 0.913409i | ||||
\(85\) | 2.19345e20 | 1.20845 | ||||||||
\(86\) | − | 4.40088e20i | − | 2.14440i | ||||||
\(87\) | −3.02213e20 | + | 2.24286e18i | −1.30425 | + | 0.00967944i | ||||
\(88\) | 1.27371e19 | 0.0487531 | ||||||||
\(89\) | 4.45786e18 | 0.0151542 | 0.00757708 | − | 0.999971i | \(-0.497588\pi\) | ||||
0.00757708 | + | 0.999971i | \(0.497588\pi\) | |||||||
\(90\) | −6.24877e18 | − | 4.20971e20i | −0.0188907 | − | 1.27264i | ||||
\(91\) | −1.73379e20 | − | 3.43855e20i | −0.466726 | − | 0.925636i | ||||
\(92\) | 4.97216e20i | 1.19336i | ||||||||
\(93\) | 4.18855e20 | − | 3.10851e18i | 0.897414 | − | 0.00666011i | ||||
\(94\) | 4.39430e20i | 0.841487i | ||||||||
\(95\) | − | 8.23530e20i | − | 1.41118i | ||||||
\(96\) | −9.26683e20 | + | 6.87733e18i | −1.42260 | + | 0.0105578i | ||||
\(97\) | 8.29303e20i | 1.14185i | 0.821001 | + | 0.570926i | \(0.193416\pi\) | ||||
−0.821001 | + | 0.570926i | \(0.806584\pi\) | |||||||
\(98\) | −9.25877e20 | − | 6.84700e20i | −1.14467 | − | 0.846499i | ||||
\(99\) | 1.70504e19 | + | 1.14866e21i | 0.0189481 | + | 1.27651i | ||||
\(100\) | 2.06118e20 | 0.206118 | ||||||||
\(101\) | 1.30816e21 | 1.17839 | 0.589194 | − | 0.807992i | \(-0.299445\pi\) | ||||
0.589194 | + | 0.807992i | \(0.299445\pi\) | |||||||
\(102\) | −2.36909e21 | + | 1.75821e19i | −1.92433 | + | 0.0142813i | ||||
\(103\) | 4.95812e20i | 0.363518i | 0.983343 | + | 0.181759i | \(0.0581791\pi\) | ||||
−0.983343 | + | 0.181759i | \(0.941821\pi\) | |||||||
\(104\) | −5.97602e19 | −0.0395878 | ||||||||
\(105\) | 6.81708e20 | + | 1.32740e21i | 0.408424 | + | 0.795271i | ||||
\(106\) | −3.33064e21 | −1.80641 | ||||||||
\(107\) | − | 2.59201e21i | − | 1.27382i | −0.770940 | − | 0.636908i | \(-0.780213\pi\) | ||
0.770940 | − | 0.636908i | \(-0.219787\pi\) | |||||||
\(108\) | 5.12875e19 | + | 2.30323e21i | 0.0228593 | + | 1.02657i | ||||
\(109\) | 1.17517e21 | 0.475469 | 0.237734 | − | 0.971330i | \(-0.423595\pi\) | ||||
0.237734 | + | 0.971330i | \(0.423595\pi\) | |||||||
\(110\) | 4.42026e21 | 1.62489 | ||||||||
\(111\) | 1.92538e19 | + | 2.59435e21i | 0.00643615 | + | 0.867236i | ||||
\(112\) | 2.85410e21 | − | 1.43910e21i | 0.868320 | − | 0.437826i | ||||
\(113\) | 2.57912e21i | 0.714740i | 0.933963 | + | 0.357370i | \(0.116326\pi\) | ||||
−0.933963 | + | 0.357370i | \(0.883674\pi\) | |||||||
\(114\) | 6.60118e19 | + | 8.89474e21i | 0.0166771 | + | 2.24715i | ||||
\(115\) | 4.50765e21i | 1.03902i | ||||||||
\(116\) | − | 6.36324e21i | − | 1.33927i | ||||||
\(117\) | −7.99976e19 | − | 5.38932e21i | −0.0153860 | − | 1.03653i | ||||
\(118\) | 6.97545e21i | 1.22690i | ||||||||
\(119\) | 7.49784e21 | − | 3.78058e21i | 1.20696 | − | 0.608576i | ||||
\(120\) | 2.31562e20 | − | 1.71853e18i | 0.0341401 | − | 0.000253369i | ||||
\(121\) | −4.66087e21 | −0.629826 | ||||||||
\(122\) | −1.11976e22 | −1.38786 | ||||||||
\(123\) | 7.98154e19 | + | 1.07547e22i | 0.00907994 | + | 1.22347i | ||||
\(124\) | 8.81918e21i | 0.921511i | ||||||||
\(125\) | 1.11776e22 | 1.07348 | ||||||||
\(126\) | −7.46936e21 | − | 1.42823e22i | −0.659770 | − | 1.26156i | ||||
\(127\) | 1.10504e22 | 0.898337 | 0.449169 | − | 0.893447i | \(-0.351720\pi\) | ||||
0.449169 | + | 0.893447i | \(0.351720\pi\) | |||||||
\(128\) | − | 1.01979e21i | − | 0.0763493i | ||||||
\(129\) | 1.62019e20 | + | 2.18312e22i | 0.0111783 | + | 1.50621i | ||||
\(130\) | −2.07391e22 | −1.31942 | ||||||||
\(131\) | −1.58647e22 | −0.931289 | −0.465644 | − | 0.884972i | \(-0.654177\pi\) | ||||
−0.465644 | + | 0.884972i | \(0.654177\pi\) | |||||||
\(132\) | −2.41869e22 | + | 1.79502e20i | −1.31085 | + | 0.00972844i | ||||
\(133\) | −1.41942e22 | − | 2.81506e22i | −0.710670 | − | 1.40944i | ||||
\(134\) | − | 2.93859e22i | − | 1.36000i | ||||||
\(135\) | 4.64961e20 | + | 2.08806e22i | 0.0199027 | + | 0.893795i | ||||
\(136\) | − | 1.30309e21i | − | 0.0516196i | ||||||
\(137\) | − | 2.07157e21i | − | 0.0759859i | −0.999278 | − | 0.0379929i | \(-0.987904\pi\) | ||
0.999278 | − | 0.0379929i | \(-0.0120964\pi\) | |||||||
\(138\) | −3.61320e20 | − | 4.86859e22i | −0.0122790 | − | 1.65452i | ||||
\(139\) | − | 2.47227e22i | − | 0.778826i | −0.921063 | − | 0.389413i | \(-0.872678\pi\) | ||
0.921063 | − | 0.389413i | \(-0.127322\pi\) | |||||||
\(140\) | −2.80541e22 | + | 1.41455e22i | −0.819693 | + | 0.413308i | ||||
\(141\) | −1.61777e20 | − | 2.17986e22i | −0.00438648 | − | 0.591055i | ||||
\(142\) | 6.16226e22 | 1.55136 | ||||||||
\(143\) | 5.65887e22 | 1.32343 | ||||||||
\(144\) | 4.47330e22 | − | 6.64005e20i | 0.972349 | − | 0.0144333i | ||||
\(145\) | − | 5.76877e22i | − | 1.16606i | ||||||
\(146\) | 6.36973e21 | 0.119789 | ||||||||
\(147\) | 4.61815e22 | + | 3.36247e22i | 0.808419 | + | 0.588608i | ||||
\(148\) | −5.46253e22 | −0.890524 | ||||||||
\(149\) | 1.45149e22i | 0.220474i | 0.993905 | + | 0.110237i | \(0.0351610\pi\) | ||||
−0.993905 | + | 0.110237i | \(0.964839\pi\) | |||||||
\(150\) | −2.01825e22 | + | 1.49783e20i | −0.285770 | + | 0.00212083i | ||||
\(151\) | −1.14495e23 | −1.51192 | −0.755959 | − | 0.654619i | \(-0.772829\pi\) | ||||
−0.755959 | + | 0.654619i | \(0.772829\pi\) | |||||||
\(152\) | −4.89243e21 | −0.0602792 | ||||||||
\(153\) | 1.17516e23 | − | 1.74437e21i | 1.35156 | − | 0.0200622i | ||||
\(154\) | 1.51097e23 | − | 7.61865e22i | 1.62289 | − | 0.818296i | ||||
\(155\) | 7.99527e22i | 0.802325i | ||||||||
\(156\) | 1.13481e23 | − | 8.42193e20i | 1.06442 | − | 0.00789956i | ||||
\(157\) | 1.16658e23i | 1.02322i | 0.859219 | + | 0.511608i | \(0.170950\pi\) | ||||
−0.859219 | + | 0.511608i | \(0.829050\pi\) | |||||||
\(158\) | 1.25154e23i | 1.02694i | ||||||||
\(159\) | 1.65221e23 | − | 1.22618e21i | 1.26881 | − | 0.00941639i | ||||
\(160\) | − | 1.76889e23i | − | 1.27187i | ||||||
\(161\) | 7.76927e22 | + | 1.54084e23i | 0.523249 | + | 1.03774i | ||||
\(162\) | −6.69565e21 | − | 2.25488e23i | −0.0422557 | − | 1.42304i | ||||
\(163\) | 7.30065e22 | 0.431909 | 0.215954 | − | 0.976403i | \(-0.430714\pi\) | ||||
0.215954 | + | 0.976403i | \(0.430714\pi\) | |||||||
\(164\) | −2.26445e23 | −1.25633 | ||||||||
\(165\) | −2.19273e23 | + | 1.62733e21i | −1.14131 | + | 0.00847019i | ||||
\(166\) | 6.96750e22i | 0.340363i | ||||||||
\(167\) | −4.21191e22 | −0.193177 | −0.0965886 | − | 0.995324i | \(-0.530793\pi\) | ||||
−0.0965886 | + | 0.995324i | \(0.530793\pi\) | |||||||
\(168\) | 7.88585e21 | − | 4.04990e21i | 0.0339704 | − | 0.0174460i | ||||
\(169\) | −1.84396e22 | −0.0746348 | ||||||||
\(170\) | − | 4.52221e23i | − | 1.72043i | ||||||
\(171\) | −6.54923e21 | − | 4.41212e23i | −0.0234278 | − | 1.57830i | ||||
\(172\) | −4.59666e23 | −1.54666 | ||||||||
\(173\) | −1.09515e23 | −0.346729 | −0.173364 | − | 0.984858i | \(-0.555464\pi\) | ||||
−0.173364 | + | 0.984858i | \(0.555464\pi\) | |||||||
\(174\) | 4.62408e21 | + | 6.23070e23i | 0.0137803 | + | 1.85682i | ||||
\(175\) | 6.38748e22 | − | 3.22071e22i | 0.179238 | − | 0.0903758i | ||||
\(176\) | 4.69703e23i | 1.24148i | ||||||||
\(177\) | −2.56802e21 | − | 3.46027e23i | −0.00639557 | − | 0.861769i | ||||
\(178\) | − | 9.19072e21i | − | 0.0215744i | ||||||
\(179\) | 1.69301e22i | 0.0374716i | 0.999824 | + | 0.0187358i | \(0.00596414\pi\) | ||||
−0.999824 | + | 0.0187358i | \(0.994036\pi\) | |||||||
\(180\) | −4.39699e23 | + | 6.52676e21i | −0.917897 | + | 0.0136250i | ||||
\(181\) | 2.60312e23i | 0.512707i | 0.966583 | + | 0.256354i | \(0.0825212\pi\) | ||||
−0.966583 | + | 0.256354i | \(0.917479\pi\) | |||||||
\(182\) | −7.08921e23 | + | 3.57454e23i | −1.31780 | + | 0.664462i | ||||
\(183\) | 5.55473e23 | − | 4.12241e21i | 0.974824 | − | 0.00723461i | ||||
\(184\) | 2.67791e22 | 0.0443822 | ||||||||
\(185\) | −4.95220e23 | −0.775345 | ||||||||
\(186\) | −6.40878e21 | − | 8.63548e23i | −0.00948177 | − | 1.27762i | ||||
\(187\) | 1.23393e24i | 1.72565i | ||||||||
\(188\) | 4.58979e23 | 0.606926 | ||||||||
\(189\) | 3.75786e23 | + | 7.05744e23i | 0.469994 | + | 0.882670i | ||||
\(190\) | −1.69786e24 | −2.00905 | ||||||||
\(191\) | 9.15056e23i | 1.02470i | 0.858776 | + | 0.512351i | \(0.171225\pi\) | ||||
−0.858776 | + | 0.512351i | \(0.828775\pi\) | |||||||
\(192\) | 7.37107e21 | + | 9.93212e23i | 0.00781390 | + | 1.05288i | ||||
\(193\) | −4.03287e23 | −0.404820 | −0.202410 | − | 0.979301i | \(-0.564877\pi\) | ||||
−0.202410 | + | 0.979301i | \(0.564877\pi\) | |||||||
\(194\) | 1.70976e24 | 1.62562 | ||||||||
\(195\) | 1.02879e24 | − | 7.63513e21i | 0.926753 | − | 0.00687785i | ||||
\(196\) | −7.15160e23 | + | 9.67066e23i | −0.610540 | + | 0.825596i | ||||
\(197\) | − | 7.49247e23i | − | 0.606359i | −0.952933 | − | 0.303179i | \(-0.901952\pi\) | ||
0.952933 | − | 0.303179i | \(-0.0980482\pi\) | |||||||
\(198\) | 2.36818e24 | − | 3.51526e22i | 1.81732 | − | 0.0269757i | ||||
\(199\) | − | 1.86005e24i | − | 1.35384i | −0.736057 | − | 0.676919i | \(-0.763315\pi\) | ||
0.736057 | − | 0.676919i | \(-0.236685\pi\) | |||||||
\(200\) | − | 1.11011e22i | − | 0.00766570i | ||||||
\(201\) | 1.08185e22 | + | 1.45773e24i | 0.00708936 | + | 0.955253i | ||||
\(202\) | − | 2.69703e24i | − | 1.67763i | ||||||
\(203\) | −9.94291e23 | − | 1.97193e24i | −0.587226 | − | 1.16462i | ||||
\(204\) | 1.83642e22 | + | 2.47448e24i | 0.0103004 | + | 1.38793i | ||||
\(205\) | −2.05290e24 | −1.09384 | ||||||||
\(206\) | 1.02221e24 | 0.517528 | ||||||||
\(207\) | 3.58476e22 | + | 2.41500e24i | 0.0172493 | + | 1.16206i | ||||
\(208\) | − | 2.20377e24i | − | 1.00809i | ||||||
\(209\) | 4.63279e24 | 2.01515 | ||||||||
\(210\) | 2.73669e24 | − | 1.40547e24i | 1.13220 | − | 0.581459i | ||||
\(211\) | 9.62999e23 | 0.379018 | 0.189509 | − | 0.981879i | \(-0.439310\pi\) | ||||
0.189509 | + | 0.981879i | \(0.439310\pi\) | |||||||
\(212\) | 3.47881e24i | 1.30288i | ||||||||
\(213\) | −3.05688e24 | + | 2.26865e22i | −1.08966 | + | 0.00808688i | ||||
\(214\) | −5.34391e24 | −1.81349 | ||||||||
\(215\) | −4.16723e24 | −1.34662 | ||||||||
\(216\) | 1.24048e23 | − | 2.76224e21i | 0.0381789 | − | 0.000850154i | ||||
\(217\) | 1.37805e24 | + | 2.73301e24i | 0.404051 | + | 0.801335i | ||||
\(218\) | − | 2.42283e24i | − | 0.676908i | ||||||
\(219\) | −3.15980e23 | + | 2.34503e21i | −0.0841388 | + | 0.000624432i | ||||
\(220\) | − | 4.61690e24i | − | 1.17196i | ||||||
\(221\) | − | 5.78939e24i | − | 1.40124i | ||||||
\(222\) | 5.34874e24 | − | 3.96954e22i | 1.23465 | − | 0.00916293i | ||||
\(223\) | 9.70907e23i | 0.213785i | 0.994271 | + | 0.106892i | \(0.0340900\pi\) | ||||
−0.994271 | + | 0.106892i | \(0.965910\pi\) | |||||||
\(224\) | −3.04882e24 | − | 6.04657e24i | −0.640512 | − | 1.27030i | ||||
\(225\) | 1.00113e24 | − | 1.48604e22i | 0.200712 | − | 0.00297931i | ||||
\(226\) | 5.31734e24 | 1.01755 | ||||||||
\(227\) | −9.66778e24 | −1.76626 | −0.883131 | − | 0.469126i | \(-0.844569\pi\) | ||||
−0.883131 | + | 0.469126i | \(0.844569\pi\) | |||||||
\(228\) | 9.29043e24 | − | 6.89485e22i | 1.62077 | − | 0.0120284i | ||||
\(229\) | − | 4.10875e24i | − | 0.684600i | −0.939591 | − | 0.342300i | \(-0.888794\pi\) | ||
0.939591 | − | 0.342300i | \(-0.111206\pi\) | |||||||
\(230\) | 9.29337e24 | 1.47921 | ||||||||
\(231\) | −7.46734e24 | + | 3.83497e24i | −1.13564 | + | 0.583225i | ||||
\(232\) | −3.42711e23 | −0.0498086 | ||||||||
\(233\) | − | 1.50807e24i | − | 0.209501i | −0.994499 | − | 0.104750i | \(-0.966596\pi\) | ||
0.994499 | − | 0.104750i | \(-0.0334044\pi\) | |||||||
\(234\) | −1.11111e25 | + | 1.64930e23i | −1.47567 | + | 0.0219045i | ||||
\(235\) | 4.16100e24 | 0.528427 | ||||||||
\(236\) | 7.28576e24 | 0.884910 | ||||||||
\(237\) | −4.60756e22 | − | 6.20844e24i | −0.00535320 | − | 0.721315i | ||||
\(238\) | −7.79437e24 | − | 1.54582e25i | −0.866409 | − | 1.71831i | ||||
\(239\) | − | 6.01108e24i | − | 0.639402i | −0.947518 | − | 0.319701i | \(-0.896417\pi\) | ||
0.947518 | − | 0.319701i | \(-0.103583\pi\) | |||||||
\(240\) | 6.33739e22 | + | 8.53929e24i | 0.00645197 | + | 0.869369i | ||||
\(241\) | − | 1.33812e24i | − | 0.130411i | −0.997872 | − | 0.0652057i | \(-0.979230\pi\) | ||
0.997872 | − | 0.0652057i | \(-0.0207704\pi\) | |||||||
\(242\) | 9.60926e24i | 0.896661i | ||||||||
\(243\) | 4.15161e23 | + | 1.11832e25i | 0.0370980 | + | 0.999312i | ||||
\(244\) | 1.16957e25i | 1.00100i | ||||||||
\(245\) | −6.48348e24 | + | 8.76720e24i | −0.531574 | + | 0.718815i | ||||
\(246\) | 2.21728e25 | − | 1.64554e23i | 1.74182 | − | 0.0129268i | ||||
\(247\) | −2.17362e25 | −1.63631 | ||||||||
\(248\) | 4.74984e23 | 0.0342717 | ||||||||
\(249\) | −2.56510e22 | − | 3.45633e24i | −0.00177423 | − | 0.239068i | ||||
\(250\) | − | 2.30447e25i | − | 1.52827i | ||||||
\(251\) | 2.97642e25 | 1.89287 | 0.946434 | − | 0.322897i | \(-0.104657\pi\) | ||||
0.946434 | + | 0.322897i | \(0.104657\pi\) | |||||||
\(252\) | −1.49177e25 | + | 7.80164e24i | −0.909903 | + | 0.475861i | ||||
\(253\) | −2.53579e25 | −1.48371 | ||||||||
\(254\) | − | 2.27825e25i | − | 1.27893i | ||||||
\(255\) | 1.66486e23 | + | 2.24331e25i | 0.00896821 | + | 1.20842i | ||||
\(256\) | 1.82637e25 | 0.944213 | ||||||||
\(257\) | 9.49079e24 | 0.470982 | 0.235491 | − | 0.971877i | \(-0.424330\pi\) | ||||
0.235491 | + | 0.971877i | \(0.424330\pi\) | |||||||
\(258\) | 4.50092e25 | − | 3.34033e23i | 2.14434 | − | 0.0159141i | ||||
\(259\) | −1.69280e25 | + | 8.53549e24i | −0.774389 | + | 0.390464i | ||||
\(260\) | 2.16617e25i | 0.951639i | ||||||||
\(261\) | −4.58768e23 | − | 3.09066e25i | −0.0193583 | − | 1.30414i | ||||
\(262\) | 3.27081e25i | 1.32584i | ||||||||
\(263\) | 2.22155e25i | 0.865208i | 0.901584 | + | 0.432604i | \(0.142405\pi\) | ||||
−0.901584 | + | 0.432604i | \(0.857595\pi\) | |||||||
\(264\) | 9.66763e21 | + | 1.30266e24i | 0.000361808 | + | 0.0487517i | ||||
\(265\) | 3.15381e25i | 1.13437i | ||||||||
\(266\) | −5.80378e25 | + | 2.92639e25i | −2.00657 | + | 1.01176i | ||||
\(267\) | 3.38358e21 | + | 4.55919e23i | 0.000112463 | + | 0.0151537i | ||||
\(268\) | −3.06932e25 | −0.980904 | ||||||||
\(269\) | −2.52837e25 | −0.777038 | −0.388519 | − | 0.921441i | \(-0.627013\pi\) | ||||
−0.388519 | + | 0.921441i | \(0.627013\pi\) | |||||||
\(270\) | 4.30493e25 | − | 9.58604e23i | 1.27247 | − | 0.0283348i | ||||
\(271\) | 6.86265e24i | 0.195126i | 0.995229 | + | 0.0975628i | \(0.0311047\pi\) | ||||
−0.995229 | + | 0.0975628i | \(0.968895\pi\) | |||||||
\(272\) | 4.80537e25 | 1.31448 | ||||||||
\(273\) | 3.50355e25 | − | 1.79930e25i | 0.922147 | − | 0.473583i | ||||
\(274\) | −4.27092e24 | −0.108178 | ||||||||
\(275\) | 1.05120e25i | 0.256266i | ||||||||
\(276\) | −5.08518e25 | + | 3.77394e23i | −1.19333 | + | 0.00885625i | ||||
\(277\) | −5.78389e24 | −0.130672 | −0.0653360 | − | 0.997863i | \(-0.520812\pi\) | ||||
−0.0653360 | + | 0.997863i | \(0.520812\pi\) | |||||||
\(278\) | −5.09705e25 | −1.10879 | ||||||||
\(279\) | 6.35834e23 | + | 4.28352e25i | 0.0133199 | + | 0.897340i | ||||
\(280\) | 7.61847e23 | + | 1.51094e24i | 0.0153712 | + | 0.0304850i | ||||
\(281\) | − | 2.45601e25i | − | 0.477324i | −0.971103 | − | 0.238662i | \(-0.923291\pi\) | ||
0.971103 | − | 0.238662i | \(-0.0767089\pi\) | |||||||
\(282\) | −4.49419e25 | + | 3.33534e23i | −0.841464 | + | 0.00624488i | ||||
\(283\) | 3.50073e25i | 0.631541i | 0.948836 | + | 0.315770i | \(0.102263\pi\) | ||||
−0.948836 | + | 0.315770i | \(0.897737\pi\) | |||||||
\(284\) | − | 6.43640e25i | − | 1.11892i | ||||||
\(285\) | 8.42250e25 | − | 6.25071e23i | 1.41114 | − | 0.0104727i | ||||
\(286\) | − | 1.16668e26i | − | 1.88412i | ||||||
\(287\) | −7.01739e25 | + | 3.53833e25i | −1.09249 | + | 0.550856i | ||||
\(288\) | −1.40673e24 | − | 9.47695e25i | −0.0211150 | − | 1.42248i | ||||
\(289\) | 5.71472e25 | 0.827118 | ||||||||
\(290\) | −1.18934e26 | −1.66007 | ||||||||
\(291\) | −8.48154e25 | + | 6.29453e23i | −1.14182 | + | 0.00847397i | ||||
\(292\) | − | 6.65310e24i | − | 0.0863981i | ||||||
\(293\) | 6.39934e25 | 0.801724 | 0.400862 | − | 0.916138i | \(-0.368711\pi\) | ||||
0.400862 | + | 0.916138i | \(0.368711\pi\) | |||||||
\(294\) | 6.93236e25 | − | 9.52119e25i | 0.837981 | − | 1.15092i | ||||
\(295\) | 6.60511e25 | 0.770457 | ||||||||
\(296\) | 2.94201e24i | 0.0331193i | ||||||||
\(297\) | −1.17464e26 | + | 2.61565e24i | −1.27633 | + | 0.0284208i | ||||
\(298\) | 2.99252e25 | 0.313882 | ||||||||
\(299\) | 1.18975e26 | 1.20478 | ||||||||
\(300\) | 1.56447e23 | + | 2.10803e25i | 0.00152965 | + | 0.206113i | ||||
\(301\) | −1.42448e26 | + | 7.18254e25i | −1.34496 | + | 0.678156i | ||||
\(302\) | 2.36053e26i | 2.15247i | ||||||||
\(303\) | 9.92916e23 | + | 1.33790e26i | 0.00874510 | + | 1.17835i | ||||
\(304\) | − | 1.80418e26i | − | 1.53499i | ||||||
\(305\) | 1.06031e26i | 0.871533i | ||||||||
\(306\) | −3.59634e24 | − | 2.42280e26i | −0.0285618 | − | 1.92417i | ||||
\(307\) | 3.28116e25i | 0.251811i | 0.992042 | + | 0.125905i | \(0.0401836\pi\) | ||||
−0.992042 | + | 0.125905i | \(0.959816\pi\) | |||||||
\(308\) | −7.95758e25 | − | 1.57819e26i | −0.590199 | − | 1.17051i | ||||
\(309\) | −5.07082e25 | + | 3.76328e23i | −0.363508 | + | 0.00269776i | ||||
\(310\) | 1.64838e26 | 1.14224 | ||||||||
\(311\) | 2.76734e26 | 1.85387 | 0.926933 | − | 0.375228i | \(-0.122436\pi\) | ||||
0.926933 | + | 0.375228i | \(0.122436\pi\) | |||||||
\(312\) | −4.53588e22 | − | 6.11186e24i | −0.000293791 | − | 0.0395867i | ||||
\(313\) | 1.79304e26i | 1.12299i | 0.827481 | + | 0.561494i | \(0.189773\pi\) | ||||
−0.827481 | + | 0.561494i | \(0.810227\pi\) | |||||||
\(314\) | 2.40512e26 | 1.45672 | ||||||||
\(315\) | −1.35240e26 | + | 7.07279e25i | −0.792218 | + | 0.414314i | ||||
\(316\) | 1.30722e26 | 0.740684 | ||||||||
\(317\) | 1.17639e26i | 0.644808i | 0.946602 | + | 0.322404i | \(0.104491\pi\) | ||||
−0.946602 | + | 0.322404i | \(0.895509\pi\) | |||||||
\(318\) | −2.52800e24 | − | 3.40635e26i | −0.0134058 | − | 1.80636i | ||||
\(319\) | 3.24523e26 | 1.66511 | ||||||||
\(320\) | −1.89588e26 | −0.941319 | ||||||||
\(321\) | 2.65092e26 | − | 1.96737e24i | 1.27378 | − | 0.00945329i | ||||
\(322\) | 3.17674e26 | − | 1.60178e26i | 1.47739 | − | 0.744932i | ||||
\(323\) | − | 4.73965e26i | − | 2.13363i | ||||||
\(324\) | −2.35520e26 | + | 6.99351e24i | −1.02637 | + | 0.0304770i | ||||
\(325\) | − | 4.93204e25i | − | 0.208090i | ||||||
\(326\) | − | 1.50517e26i | − | 0.614893i | ||||||
\(327\) | 8.91969e23 | + | 1.20188e26i | 0.00352857 | + | 0.475455i | ||||
\(328\) | 1.21959e25i | 0.0467237i | ||||||||
\(329\) | 1.42235e26 | − | 7.17180e25i | 0.527776 | − | 0.266116i | ||||
\(330\) | 3.35504e24 | + | 4.52073e26i | 0.0120587 | + | 1.62485i | ||||
\(331\) | 1.90496e26 | 0.663271 | 0.331635 | − | 0.943408i | \(-0.392400\pi\) | ||||
0.331635 | + | 0.943408i | \(0.392400\pi\) | |||||||
\(332\) | 7.27747e25 | 0.245488 | ||||||||
\(333\) | −2.65318e26 | + | 3.93830e24i | −0.867165 | + | 0.0128719i | ||||
\(334\) | 8.68364e25i | 0.275020i | ||||||||
\(335\) | −2.78257e26 | −0.854036 | ||||||||
\(336\) | 1.49347e26 | + | 2.90805e26i | 0.444258 | + | 0.865047i | ||||
\(337\) | −6.53084e26 | −1.88302 | −0.941510 | − | 0.336985i | \(-0.890593\pi\) | ||||
−0.941510 | + | 0.336985i | \(0.890593\pi\) | |||||||
\(338\) | 3.80167e25i | 0.106255i | ||||||||
\(339\) | −2.63775e26 | + | 1.95759e24i | −0.714720 | + | 0.00530426i | ||||
\(340\) | −4.72339e26 | −1.24087 | ||||||||
\(341\) | −4.49776e26 | −1.14571 | ||||||||
\(342\) | −9.09642e26 | + | 1.35025e25i | −2.24696 | + | 0.0333533i | ||||
\(343\) | −7.05144e25 | + | 4.11436e26i | −0.168923 | + | 0.985629i | ||||
\(344\) | 2.47567e25i | 0.0575214i | ||||||||
\(345\) | −4.61011e26 | + | 3.42137e24i | −1.03899 | + | 0.00771080i | ||||
\(346\) | 2.25786e26i | 0.493626i | ||||||||
\(347\) | − | 3.77882e26i | − | 0.801487i | −0.916190 | − | 0.400744i | \(-0.868752\pi\) | ||
0.916190 | − | 0.400744i | \(-0.131248\pi\) | |||||||
\(348\) | 6.50788e26 | − | 4.82979e24i | 1.33924 | − | 0.00993908i | ||||
\(349\) | 3.41611e26i | 0.682126i | 0.940040 | + | 0.341063i | \(0.110787\pi\) | ||||
−0.940040 | + | 0.341063i | \(0.889213\pi\) | |||||||
\(350\) | −6.64010e25 | − | 1.31690e26i | −0.128665 | − | 0.255175i | ||||
\(351\) | 5.51122e26 | − | 1.22722e25i | 1.03639 | − | 0.0230779i | ||||
\(352\) | 9.95094e26 | 1.81621 | ||||||||
\(353\) | −8.74403e25 | −0.154909 | −0.0774546 | − | 0.996996i | \(-0.524679\pi\) | ||||
−0.0774546 | + | 0.996996i | \(0.524679\pi\) | |||||||
\(354\) | −7.13400e26 | + | 5.29446e24i | −1.22687 | + | 0.00910516i | ||||
\(355\) | − | 5.83509e26i | − | 0.974204i | ||||||
\(356\) | −9.59959e24 | −0.0155606 | ||||||||
\(357\) | 3.92342e26 | + | 7.63957e26i | 0.617517 | + | 1.20241i | ||||
\(358\) | 3.49045e25 | 0.0533470 | ||||||||
\(359\) | − | 1.11054e27i | − | 1.64832i | −0.566359 | − | 0.824159i | \(-0.691648\pi\) | ||
0.566359 | − | 0.824159i | \(-0.308352\pi\) | |||||||
\(360\) | 3.51518e23 | + | 2.36813e25i | 0.000506724 | + | 0.0341373i | ||||
\(361\) | −1.06529e27 | −1.49156 | ||||||||
\(362\) | 5.36683e26 | 0.729924 | ||||||||
\(363\) | −3.53767e24 | − | 4.76681e26i | −0.00467409 | − | 0.629808i | ||||
\(364\) | 3.73356e26 | + | 7.40458e26i | 0.479246 | + | 0.950465i | ||||
\(365\) | − | 6.03155e25i | − | 0.0752236i | ||||||
\(366\) | −8.49913e24 | − | 1.14521e27i | −0.0102997 | − | 1.38782i | ||||
\(367\) | 8.92501e26i | 1.05103i | 0.850784 | + | 0.525515i | \(0.176127\pi\) | ||||
−0.850784 | + | 0.525515i | \(0.823873\pi\) | |||||||
\(368\) | 9.87528e26i | 1.13018i | ||||||||
\(369\) | −1.09985e27 | + | 1.63259e25i | −1.22337 | + | 0.0181594i | ||||
\(370\) | 1.02099e27i | 1.10383i | ||||||||
\(371\) | 5.43583e26 | + | 1.07806e27i | 0.571268 | + | 1.13297i | ||||
\(372\) | −9.01965e26 | + | 6.69388e24i | −0.921486 | + | 0.00683876i | ||||
\(373\) | 1.74259e27 | 1.73082 | 0.865410 | − | 0.501064i | \(-0.167058\pi\) | ||||
0.865410 | + | 0.501064i | \(0.167058\pi\) | |||||||
\(374\) | 2.54398e27 | 2.45676 | ||||||||
\(375\) | 8.48394e24 | + | 1.14316e27i | 0.00796653 | + | 1.07345i | ||||
\(376\) | − | 2.47197e25i | − | 0.0225720i | ||||||
\(377\) | −1.52261e27 | −1.35208 | ||||||||
\(378\) | 1.45502e27 | − | 7.74754e26i | 1.25663 | − | 0.669114i | ||||
\(379\) | 7.52589e25 | 0.0632188 | 0.0316094 | − | 0.999500i | \(-0.489937\pi\) | ||||
0.0316094 | + | 0.999500i | \(0.489937\pi\) | |||||||
\(380\) | 1.77340e27i | 1.44903i | ||||||||
\(381\) | 8.38742e24 | + | 1.13016e27i | 0.00666678 | + | 0.898312i | ||||
\(382\) | 1.88656e27 | 1.45883 | ||||||||
\(383\) | −2.06634e26 | −0.155458 | −0.0777291 | − | 0.996975i | \(-0.524767\pi\) | ||||
−0.0777291 | + | 0.996975i | \(0.524767\pi\) | |||||||
\(384\) | 1.04297e26 | − | 7.74033e23i | 0.0763472 | − | 0.000566607i | ||||
\(385\) | −7.21416e26 | − | 1.43075e27i | −0.513864 | − | 1.01912i | ||||
\(386\) | 8.31451e26i | 0.576328i | ||||||||
\(387\) | −2.23262e27 | + | 3.31404e25i | −1.50609 | + | 0.0223559i | ||||
\(388\) | − | 1.78583e27i | − | 1.17248i | ||||||
\(389\) | − | 1.21725e27i | − | 0.777871i | −0.921265 | − | 0.388936i | \(-0.872843\pi\) | ||
0.921265 | − | 0.388936i | \(-0.127157\pi\) | |||||||
\(390\) | −1.57413e25 | − | 2.12105e27i | −0.00979176 | − | 1.31939i | ||||
\(391\) | 2.59428e27i | 1.57094i | ||||||||
\(392\) | 5.20842e25 | + | 3.85171e25i | 0.0307045 | + | 0.0227065i | ||||
\(393\) | −1.20416e25 | − | 1.62254e27i | −0.00691132 | − | 0.931263i | ||||
\(394\) | −1.54471e27 | −0.863252 | ||||||||
\(395\) | 1.18509e27 | 0.644885 | ||||||||
\(396\) | −3.67165e25 | − | 2.47354e27i | −0.0194563 | − | 1.31075i | ||||
\(397\) | − | 3.28608e27i | − | 1.69581i | −0.530148 | − | 0.847905i | \(-0.677864\pi\) | ||
0.530148 | − | 0.847905i | \(-0.322136\pi\) | |||||||
\(398\) | −3.83484e27 | −1.92741 | ||||||||
\(399\) | 2.86828e27 | − | 1.47305e27i | 1.40412 | − | 0.721110i | ||||
\(400\) | 4.09374e26 | 0.195205 | ||||||||
\(401\) | 1.23718e27i | 0.574667i | 0.957831 | + | 0.287333i | \(0.0927688\pi\) | ||||
−0.957831 | + | 0.287333i | \(0.907231\pi\) | |||||||
\(402\) | 3.00538e27 | − | 2.23043e25i | 1.35996 | − | 0.0100929i | ||||
\(403\) | 2.11027e27 | 0.930326 | ||||||||
\(404\) | −2.81701e27 | −1.21000 | ||||||||
\(405\) | −2.13517e27 | + | 6.34016e25i | −0.893623 | + | 0.0265352i | ||||
\(406\) | −4.06550e27 | + | 2.04992e27i | −1.65802 | + | 0.836013i | ||||
\(407\) | − | 2.78587e27i | − | 1.10718i | ||||||
\(408\) | 1.33271e26 | − | 9.89061e23i | 0.0516182 | − | 0.000383082i | ||||
\(409\) | − | 2.84104e27i | − | 1.07246i | −0.844071 | − | 0.536232i | \(-0.819847\pi\) | ||
0.844071 | − | 0.536232i | \(-0.180153\pi\) | |||||||
\(410\) | 4.23244e27i | 1.55726i | ||||||||
\(411\) | 2.11865e26 | − | 1.57235e24i | 0.0759838 | − | 0.000563910i | ||||
\(412\) | − | 1.06768e27i | − | 0.373269i | ||||||
\(413\) | 2.25781e27 | − | 1.13844e27i | 0.769507 | − | 0.388003i | ||||
\(414\) | 4.97898e27 | − | 7.39066e25i | 1.65439 | − | 0.0245573i | ||||
\(415\) | 6.59759e26 | 0.213737 | ||||||||
\(416\) | −4.66881e27 | −1.47478 | ||||||||
\(417\) | 2.52847e27 | − | 1.87649e25i | 0.778805 | − | 0.00577986i | ||||
\(418\) | − | 9.55137e27i | − | 2.86890i | ||||||
\(419\) | −3.50430e27 | −1.02649 | −0.513244 | − | 0.858243i | \(-0.671556\pi\) | ||||
−0.513244 | + | 0.858243i | \(0.671556\pi\) | |||||||
\(420\) | −1.46800e27 | − | 2.85844e27i | −0.419379 | − | 0.816603i | ||||
\(421\) | −2.61126e27 | −0.727593 | −0.363797 | − | 0.931478i | \(-0.618520\pi\) | ||||
−0.363797 | + | 0.931478i | \(0.618520\pi\) | |||||||
\(422\) | − | 1.98540e27i | − | 0.539595i | ||||||
\(423\) | 2.22929e27 | − | 3.30909e25i | 0.591006 | − | 0.00877272i | ||||
\(424\) | 1.87362e26 | 0.0484551 | ||||||||
\(425\) | 1.07544e27 | 0.271334 | ||||||||
\(426\) | 4.67724e25 | + | 6.30233e27i | 0.0115130 | + | 1.55132i | ||||
\(427\) | 1.82752e27 | + | 3.62444e27i | 0.438904 | + | 0.870458i | ||||
\(428\) | 5.58164e27i | 1.30798i | ||||||||
\(429\) | 4.29516e25 | + | 5.78750e27i | 0.00982150 | + | 1.32339i | ||||
\(430\) | 8.59153e27i | 1.91713i | ||||||||
\(431\) | − | 4.32301e27i | − | 0.941401i | −0.882293 | − | 0.470701i | \(-0.844001\pi\) | ||
0.882293 | − | 0.470701i | \(-0.155999\pi\) | |||||||
\(432\) | 1.01863e26 | + | 4.57448e27i | 0.0216489 | + | 0.972215i | ||||
\(433\) | − | 6.00077e27i | − | 1.24475i | −0.782717 | − | 0.622377i | \(-0.786167\pi\) | ||
0.782717 | − | 0.622377i | \(-0.213833\pi\) | |||||||
\(434\) | 5.63462e27 | − | 2.84110e27i | 1.14083 | − | 0.575234i | ||||
\(435\) | 5.89990e27 | − | 4.37858e25i | 1.16602 | − | 0.00865358i | ||||
\(436\) | −2.53061e27 | −0.488223 | ||||||||
\(437\) | 9.74021e27 | 1.83448 | ||||||||
\(438\) | 4.83472e24 | + | 6.51452e26i | 0.000888982 | + | 0.119786i | ||||
\(439\) | 3.42115e27i | 0.614179i | 0.951681 | + | 0.307089i | \(0.0993550\pi\) | ||||
−0.951681 | + | 0.307089i | \(0.900645\pi\) | |||||||
\(440\) | −2.48657e26 | −0.0435861 | ||||||||
\(441\) | −3.40385e27 | + | 4.74865e27i | −0.582592 | + | 0.812765i | ||||
\(442\) | −1.19359e28 | −1.99490 | ||||||||
\(443\) | 3.58900e27i | 0.585780i | 0.956146 | + | 0.292890i | \(0.0946169\pi\) | ||||
−0.956146 | + | 0.292890i | \(0.905383\pi\) | |||||||
\(444\) | −4.14613e25 | − | 5.58669e27i | −0.00660879 | − | 0.890499i | ||||
\(445\) | −8.70277e25 | −0.0135481 | ||||||||
\(446\) | 2.00171e27 | 0.304358 | ||||||||
\(447\) | −1.48448e27 | + | 1.10170e25i | −0.220468 | + | 0.00163619i | ||||
\(448\) | −6.48067e27 | + | 3.26770e27i | −0.940157 | + | 0.474048i | ||||
\(449\) | 4.67066e27i | 0.661899i | 0.943648 | + | 0.330950i | \(0.107369\pi\) | ||||
−0.943648 | + | 0.330950i | \(0.892631\pi\) | |||||||
\(450\) | −3.06376e25 | − | 2.06401e27i | −0.00424154 | − | 0.285746i | ||||
\(451\) | − | 1.15486e28i | − | 1.56199i | ||||||
\(452\) | − | 5.55389e27i | − | 0.733912i | ||||||
\(453\) | −8.69033e25 | − | 1.17097e28i | −0.0112203 | − | 1.51188i | ||||
\(454\) | 1.99319e28i | 2.51457i | ||||||||
\(455\) | 3.38476e27 | + | 6.71283e27i | 0.417261 | + | 0.827534i | ||||
\(456\) | −3.71343e24 | − | 5.00364e26i | −0.000447347 | − | 0.0602775i | ||||
\(457\) | 1.37696e27 | 0.162107 | 0.0810534 | − | 0.996710i | \(-0.474172\pi\) | ||||
0.0810534 | + | 0.996710i | \(0.474172\pi\) | |||||||
\(458\) | −8.47095e27 | −0.974641 | ||||||||
\(459\) | 2.67598e26 | + | 1.20174e28i | 0.0300919 | + | 1.35137i | ||||
\(460\) | − | 9.70680e27i | − | 1.06689i | ||||||
\(461\) | 1.09639e28 | 1.17789 | 0.588944 | − | 0.808174i | \(-0.299544\pi\) | ||||
0.588944 | + | 0.808174i | \(0.299544\pi\) | |||||||
\(462\) | 7.90651e27 | + | 1.53953e28i | 0.830317 | + | 1.61677i | ||||
\(463\) | 5.06009e27 | 0.519467 | 0.259733 | − | 0.965680i | \(-0.416365\pi\) | ||||
0.259733 | + | 0.965680i | \(0.416365\pi\) | |||||||
\(464\) | − | 1.26381e28i | − | 1.26836i | ||||||
\(465\) | −8.17701e27 | + | 6.06852e25i | −0.802303 | + | 0.00595425i | ||||
\(466\) | −3.10918e27 | −0.298259 | ||||||||
\(467\) | 5.77790e27 | 0.541930 | 0.270965 | − | 0.962589i | \(-0.412657\pi\) | ||||
0.270965 | + | 0.962589i | \(0.412657\pi\) | |||||||
\(468\) | 1.72267e26 | + | 1.16054e28i | 0.0157987 | + | 1.06434i | ||||
\(469\) | −9.51163e27 | + | 4.79597e27i | −0.852982 | + | 0.430093i | ||||
\(470\) | − | 8.57869e27i | − | 0.752304i | ||||||
\(471\) | −1.19309e28 | + | 8.85449e25i | −1.02319 | + | 0.00759354i | ||||
\(472\) | − | 3.92397e26i | − | 0.0329105i | ||||||
\(473\) | − | 2.34429e28i | − | 1.92295i | ||||||
\(474\) | −1.27999e28 | + | 9.49935e25i | −1.02691 | + | 0.00762117i | ||||
\(475\) | − | 4.03775e27i | − | 0.316852i | ||||||
\(476\) | −1.61459e28 | + | 8.14112e27i | −1.23934 | + | 0.624901i | ||||
\(477\) | 2.50810e26 | + | 1.68967e28i | 0.0188323 | + | 1.26870i | ||||
\(478\) | −1.23930e28 | −0.910295 | ||||||||
\(479\) | −9.85556e27 | −0.708204 | −0.354102 | − | 0.935207i | \(-0.615213\pi\) | ||||
−0.354102 | + | 0.935207i | \(0.615213\pi\) | |||||||
\(480\) | 1.80910e28 | − | 1.34261e26i | 1.27183 | − | 0.00943882i | ||||
\(481\) | 1.30708e28i | 0.899042i | ||||||||
\(482\) | −2.75878e27 | −0.185662 | ||||||||
\(483\) | −1.56997e28 | + | 8.06282e27i | −1.03382 | + | 0.530936i | ||||
\(484\) | 1.00367e28 | 0.646720 | ||||||||
\(485\) | − | 1.61899e28i | − | 1.02084i | ||||||
\(486\) | 2.30563e28 | − | 8.55933e26i | 1.42269 | − | 0.0528152i | ||||
\(487\) | 1.39895e27 | 0.0844786 | 0.0422393 | − | 0.999108i | \(-0.486551\pi\) | ||||
0.0422393 | + | 0.999108i | \(0.486551\pi\) | |||||||
\(488\) | 6.29909e26 | 0.0372280 | ||||||||
\(489\) | 5.54130e25 | + | 7.46660e27i | 0.00320530 | + | 0.431897i | ||||
\(490\) | 1.80752e28 | + | 1.33669e28i | 1.02335 | + | 0.756784i | ||||
\(491\) | − | 1.11135e28i | − | 0.615879i | −0.951406 | − | 0.307939i | \(-0.900361\pi\) | ||
0.951406 | − | 0.307939i | \(-0.0996394\pi\) | |||||||
\(492\) | −1.71875e26 | − | 2.31592e28i | −0.00932350 | − | 1.25629i | ||||
\(493\) | − | 3.32009e28i | − | 1.76302i | ||||||
\(494\) | 4.48134e28i | 2.32956i | ||||||||
\(495\) | −3.32863e26 | − | 2.24245e28i | −0.0169399 | − | 1.14122i | ||||
\(496\) | 1.75159e28i | 0.872720i | ||||||||
\(497\) | −1.00572e28 | − | 1.99460e28i | −0.490609 | − | 0.973002i | ||||
\(498\) | −7.12588e27 | + | 5.28843e25i | −0.340354 | + | 0.00252592i | ||||
\(499\) | 3.06648e28 | 1.43411 | 0.717057 | − | 0.697014i | \(-0.245489\pi\) | ||||
0.717057 | + | 0.697014i | \(0.245489\pi\) | |||||||
\(500\) | −2.40699e28 | −1.10227 | ||||||||
\(501\) | −3.19690e25 | − | 4.30765e27i | −0.00143362 | − | 0.193172i | ||||
\(502\) | − | 6.13645e28i | − | 2.69481i | ||||||
\(503\) | 3.08475e28 | 1.32665 | 0.663324 | − | 0.748332i | \(-0.269145\pi\) | ||||
0.663324 | + | 0.748332i | \(0.269145\pi\) | |||||||
\(504\) | 4.20181e26 | + | 8.03436e26i | 0.0176977 | + | 0.0338400i | ||||
\(505\) | −2.55384e28 | −1.05350 | ||||||||
\(506\) | 5.22801e28i | 2.11230i | ||||||||
\(507\) | −1.39959e25 | − | 1.88588e27i | −0.000553883 | − | 0.0746328i | ||||
\(508\) | −2.37960e28 | −0.922434 | ||||||||
\(509\) | 2.68589e28 | 1.01988 | 0.509942 | − | 0.860209i | \(-0.329667\pi\) | ||||
0.509942 | + | 0.860209i | \(0.329667\pi\) | |||||||
\(510\) | 4.62500e28 | − | 3.43242e26i | 1.72038 | − | 0.0127677i | ||||
\(511\) | −1.03958e27 | − | 2.06176e27i | −0.0378826 | − | 0.0751308i | ||||
\(512\) | − | 3.97928e28i | − | 1.42059i | ||||||
\(513\) | 4.51191e28 | − | 1.00470e27i | 1.57808 | − | 0.0351400i | ||||
\(514\) | − | 1.95670e28i | − | 0.670521i | ||||||
\(515\) | − | 9.67939e27i | − | 0.324991i | ||||||
\(516\) | −3.48893e26 | − | 4.70115e28i | −0.0114781 | − | 1.54661i | ||||
\(517\) | 2.34078e28i | 0.754589i | ||||||||
\(518\) | 1.75975e28 | + | 3.49003e28i | 0.555890 | + | 1.10247i | ||||
\(519\) | −8.31235e25 | − | 1.12004e28i | −0.00257316 | − | 0.346719i | ||||
\(520\) | 1.16666e27 | 0.0353922 | ||||||||
\(521\) | −5.78769e28 | −1.72071 | −0.860357 | − | 0.509691i | \(-0.829760\pi\) | ||||
−0.860357 | + | 0.509691i | \(0.829760\pi\) | |||||||
\(522\) | −6.37197e28 | + | 9.45837e26i | −1.85666 | + | 0.0275598i | ||||
\(523\) | − | 3.94058e28i | − | 1.12536i | −0.826673 | − | 0.562682i | \(-0.809770\pi\) | ||
0.826673 | − | 0.562682i | \(-0.190230\pi\) | |||||||
\(524\) | 3.41632e28 | 0.956270 | ||||||||
\(525\) | 3.34240e27 | + | 6.50823e27i | 0.0917035 | + | 0.178562i | ||||
\(526\) | 4.58014e28 | 1.23177 | ||||||||
\(527\) | 4.60150e28i | 1.21308i | ||||||||
\(528\) | −4.80380e28 | + | 3.56512e26i | −1.24145 | + | 0.00921335i | ||||
\(529\) | −1.38421e28 | −0.350685 | ||||||||
\(530\) | 6.50217e28 | 1.61496 | ||||||||
\(531\) | 3.53873e28 | − | 5.25279e26i | 0.861698 | − | 0.0127908i | ||||
\(532\) | 3.05658e28 | + | 6.06197e28i | 0.729733 | + | 1.44724i | ||||
\(533\) | 5.41842e28i | 1.26834i | ||||||||
\(534\) | 9.39963e26 | − | 6.97589e24i | 0.0215739 | − | 0.000160109i | ||||
\(535\) | 5.06019e28i | 1.13881i | ||||||||
\(536\) | 1.65307e27i | 0.0364806i | ||||||||
\(537\) | −1.73149e27 | + | 1.28502e25i | −0.0374706 | + | 0.000278086i | ||||
\(538\) | 5.21272e28i | 1.10624i | ||||||||
\(539\) | −4.93201e28 | − | 3.64730e28i | −1.02646 | − | 0.759083i | ||||
\(540\) | −1.00125e27 | − | 4.49644e28i | −0.0204366 | − | 0.917770i | ||||
\(541\) | 3.13623e28 | 0.627822 | 0.313911 | − | 0.949452i | \(-0.398361\pi\) | ||||
0.313911 | + | 0.949452i | \(0.398361\pi\) | |||||||
\(542\) | 1.41486e28 | 0.277794 | ||||||||
\(543\) | −2.66229e28 | + | 1.97581e26i | −0.512693 | + | 0.00380493i | ||||
\(544\) | − | 1.01805e29i | − | 1.92300i | ||||||
\(545\) | −2.29420e28 | −0.425077 | ||||||||
\(546\) | −3.70960e28 | − | 7.22322e28i | −0.674223 | − | 1.31283i | ||||
\(547\) | −4.58701e27 | −0.0817830 | −0.0408915 | − | 0.999164i | \(-0.513020\pi\) | ||||
−0.0408915 | + | 0.999164i | \(0.513020\pi\) | |||||||
\(548\) | 4.46092e27i | 0.0780241i | ||||||||
\(549\) | 8.43223e26 | + | 5.68068e28i | 0.0144688 | + | 0.974744i | ||||
\(550\) | 2.16724e28 | 0.364837 | ||||||||
\(551\) | −1.24653e29 | −2.05878 | ||||||||
\(552\) | 2.03257e25 | + | 2.73878e27i | 0.000329371 | + | 0.0443809i | ||||
\(553\) | 4.05098e28 | − | 2.04260e28i | 0.644090 | − | 0.324764i | ||||
\(554\) | 1.19246e28i | 0.186033i | ||||||||
\(555\) | −3.75879e26 | − | 5.06477e28i | −0.00575403 | − | 0.775324i | ||||
\(556\) | 5.32380e28i | 0.799718i | ||||||||
\(557\) | − | 5.57923e28i | − | 0.822422i | −0.911540 | − | 0.411211i | \(-0.865106\pi\) | ||
0.911540 | − | 0.411211i | \(-0.134894\pi\) | |||||||
\(558\) | 8.83129e28 | − | 1.31089e27i | 1.27751 | − | 0.0189630i | ||||
\(559\) | 1.09990e29i | 1.56145i | ||||||||
\(560\) | −5.57186e28 | + | 2.80945e28i | −0.776293 | + | 0.391424i | ||||
\(561\) | −1.26198e29 | + | 9.36571e26i | −1.72561 | + | 0.0128065i | ||||
\(562\) | −5.06352e28 | −0.679550 | ||||||||
\(563\) | 5.51297e27 | 0.0726185 | 0.0363093 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363093 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(564\) | 3.48372e26 | + | 4.69412e28i | 0.00450414 | + | 0.606909i | ||||
\(565\) | − | 5.03503e28i | − | 0.638989i | ||||||
\(566\) | 7.21742e28 | 0.899103 | ||||||||
\(567\) | −7.18934e28 | + | 3.89685e28i | −0.879158 | + | 0.476531i | ||||
\(568\) | −3.46651e27 | −0.0416136 | ||||||||
\(569\) | 4.19217e28i | 0.494038i | 0.969011 | + | 0.247019i | \(0.0794509\pi\) | ||||
−0.969011 | + | 0.247019i | \(0.920549\pi\) | |||||||
\(570\) | −1.28870e27 | − | 1.73646e29i | −0.0149096 | − | 2.00899i | ||||
\(571\) | 1.07694e29 | 1.22325 | 0.611623 | − | 0.791150i | \(-0.290517\pi\) | ||||
0.611623 | + | 0.791150i | \(0.290517\pi\) | |||||||
\(572\) | −1.21858e29 | −1.35893 | ||||||||
\(573\) | −9.35856e28 | + | 6.94541e26i | −1.02467 | + | 0.00760456i | ||||
\(574\) | 7.29493e28 | + | 1.44677e29i | 0.784235 | + | 1.55534i | ||||
\(575\) | 2.21009e28i | 0.233291i | ||||||||
\(576\) | −1.01573e29 | + | 1.50772e27i | −1.05279 | + | 0.0156274i | ||||
\(577\) | 1.13427e29i | 1.15444i | 0.816590 | + | 0.577218i | \(0.195862\pi\) | ||||
−0.816590 | + | 0.577218i | \(0.804138\pi\) | |||||||
\(578\) | − | 1.17820e29i | − | 1.17754i | ||||||
\(579\) | −3.06100e26 | − | 4.12454e28i | −0.00300427 | − | 0.404809i | ||||
\(580\) | 1.24225e29i | 1.19733i | ||||||||
\(581\) | 2.25524e28 | − | 1.13714e28i | 0.213473 | − | 0.107638i | ||||
\(582\) | 1.29774e27 | + | 1.74863e29i | 0.0120641 | + | 1.62557i | ||||
\(583\) | −1.77418e29 | −1.61986 | ||||||||
\(584\) | −3.58323e26 | −0.00321321 | ||||||||
\(585\) | 1.56174e27 | + | 1.05212e29i | 0.0137553 | + | 0.926677i | ||||
\(586\) | − | 1.31934e29i | − | 1.14139i | ||||||
\(587\) | 1.89698e29 | 1.61199 | 0.805997 | − | 0.591920i | \(-0.201630\pi\) | ||||
0.805997 | + | 0.591920i | \(0.201630\pi\) | |||||||
\(588\) | −9.94476e28 | − | 7.24076e28i | −0.830104 | − | 0.604397i | ||||
\(589\) | 1.72763e29 | 1.41658 | ||||||||
\(590\) | − | 1.36177e29i | − | 1.09687i | ||||||
\(591\) | 7.66278e28 | − | 5.68689e26i | 0.606342 | − | 0.00449994i | ||||
\(592\) | −1.08492e29 | −0.843373 | ||||||||
\(593\) | 2.34077e29 | 1.78766 | 0.893830 | − | 0.448407i | \(-0.148008\pi\) | ||||
0.893830 | + | 0.448407i | \(0.148008\pi\) | |||||||
\(594\) | 5.39265e27 | + | 2.42175e29i | 0.0404618 | + | 1.81707i | ||||
\(595\) | −1.46375e29 | + | 7.38055e28i | −1.07904 | + | 0.544077i | ||||
\(596\) | − | 3.12565e28i | − | 0.226388i | ||||||
\(597\) | 1.90233e29 | − | 1.41180e27i | 1.35380 | − | 0.0100472i | ||||
\(598\) | − | 2.45289e29i | − | 1.71520i | ||||||
\(599\) | − | 1.27627e29i | − | 0.876922i | −0.898750 | − | 0.438461i | \(-0.855524\pi\) | ||
0.898750 | − | 0.438461i | \(-0.144476\pi\) | |||||||
\(600\) | 1.13535e27 | − | 8.42591e24i | 0.00766549 | − | 5.68890e-5i | ||||
\(601\) | 1.03497e29i | 0.686666i | 0.939214 | + | 0.343333i | \(0.111556\pi\) | ||||
−0.939214 | + | 0.343333i | \(0.888444\pi\) | |||||||
\(602\) | 1.48082e29 | + | 2.93683e29i | 0.965468 | + | 1.91477i | ||||
\(603\) | −1.49078e29 | + | 2.21287e27i | −0.955174 | + | 0.0141783i | ||||
\(604\) | 2.46554e29 | 1.55247 | ||||||||
\(605\) | 9.09908e28 | 0.563075 | ||||||||
\(606\) | 2.75833e29 | − | 2.04708e27i | 1.67758 | − | 0.0124501i | ||||
\(607\) | 7.57714e28i | 0.452922i | 0.974020 | + | 0.226461i | \(0.0727156\pi\) | ||||
−0.974020 | + | 0.226461i | \(0.927284\pi\) | |||||||
\(608\) | −3.82225e29 | −2.24560 | ||||||||
\(609\) | 2.00921e29 | − | 1.03186e29i | 1.16023 | − | 0.595852i | ||||
\(610\) | 2.18603e29 | 1.24077 | ||||||||
\(611\) | − | 1.09825e29i | − | 0.612731i | ||||||
\(612\) | −2.53059e29 | + | 3.75633e27i | −1.38781 | + | 0.0206003i | ||||
\(613\) | −8.06116e28 | −0.434573 | −0.217287 | − | 0.976108i | \(-0.569721\pi\) | ||||
−0.217287 | + | 0.976108i | \(0.569721\pi\) | |||||||
\(614\) | 6.76473e28 | 0.358495 | ||||||||
\(615\) | −1.55818e27 | − | 2.09956e29i | −0.00811762 | − | 1.09381i | ||||
\(616\) | −8.49981e27 | + | 4.28579e27i | −0.0435323 | + | 0.0219500i | ||||
\(617\) | 1.68400e29i | 0.847905i | 0.905684 | + | 0.423953i | \(0.139358\pi\) | ||||
−0.905684 | + | 0.423953i | \(0.860642\pi\) | |||||||
\(618\) | 7.75872e26 | + | 1.04545e29i | 0.00384070 | + | 0.517514i | ||||
\(619\) | − | 3.43525e29i | − | 1.67188i | −0.548817 | − | 0.835942i | \(-0.684922\pi\) | ||
0.548817 | − | 0.835942i | \(-0.315078\pi\) | |||||||
\(620\) | − | 1.72171e29i | − | 0.823847i | ||||||
\(621\) | −2.46963e29 | + | 5.49927e27i | −1.16190 | + | 0.0258728i | ||||
\(622\) | − | 5.70539e29i | − | 2.63928i | ||||||
\(623\) | −2.97485e27 | + | 1.49999e27i | −0.0135314 | + | 0.00682281i | ||||
\(624\) | 2.25386e29 | − | 1.67269e27i | 1.00807 | − | 0.00748130i | ||||
\(625\) | −1.72570e29 | −0.758972 | ||||||||
\(626\) | 3.69670e29 | 1.59876 | ||||||||
\(627\) | 3.51635e27 | + | 4.73810e29i | 0.0149549 | + | 2.01509i | ||||
\(628\) | − | 2.51212e29i | − | 1.05066i | ||||||
\(629\) | −2.85013e29 | −1.17228 | ||||||||
\(630\) | 1.45819e29 | + | 2.78823e29i | 0.589845 | + | 1.12785i | ||||
\(631\) | −2.86972e29 | −1.14165 | −0.570823 | − | 0.821073i | \(-0.693376\pi\) | ||||
−0.570823 | + | 0.821073i | \(0.693376\pi\) | |||||||
\(632\) | − | 7.04040e27i | − | 0.0275466i | ||||||
\(633\) | 7.30930e26 | + | 9.84888e28i | 0.00281279 | + | 0.379008i | ||||
\(634\) | 2.42536e29 | 0.917990 | ||||||||
\(635\) | −2.15729e29 | −0.803128 | ||||||||
\(636\) | −3.55788e29 | + | 2.64046e27i | −1.30284 | + | 0.00966898i | ||||
\(637\) | 2.31401e29 | + | 1.71125e29i | 0.833493 | + | 0.616380i | ||||
\(638\) | − | 6.69066e29i | − | 2.37057i | ||||||
\(639\) | −4.64043e27 | − | 3.12619e29i | −0.0161733 | − | 1.08957i | ||||
\(640\) | 1.99086e28i | 0.0682576i | ||||||||
\(641\) | 2.02581e29i | 0.683265i | 0.939834 | + | 0.341632i | \(0.110980\pi\) | ||||
−0.939834 | + | 0.341632i | \(0.889020\pi\) | |||||||
\(642\) | −4.05610e27 | − | 5.46538e29i | −0.0134583 | − | 1.81344i | ||||
\(643\) | 3.24332e29i | 1.05870i | 0.848402 | + | 0.529352i | \(0.177565\pi\) | ||||
−0.848402 | + | 0.529352i | \(0.822435\pi\) | |||||||
\(644\) | −1.67304e29 | − | 3.31806e29i | −0.537285 | − | 1.06557i | ||||
\(645\) | −3.16299e27 | − | 4.26196e29i | −0.00999357 | − | 1.34658i | ||||
\(646\) | −9.77167e29 | −3.03758 | ||||||||
\(647\) | 3.72570e29 | 1.13950 | 0.569748 | − | 0.821819i | \(-0.307041\pi\) | ||||
0.569748 | + | 0.821819i | \(0.307041\pi\) | |||||||
\(648\) | 3.76657e26 | + | 1.26846e28i | 0.00113347 | + | 0.0381716i | ||||
\(649\) | 3.71572e29i | 1.10020i | ||||||||
\(650\) | −1.01683e29 | −0.296250 | ||||||||
\(651\) | −2.78468e29 | + | 1.43011e29i | −0.798315 | + | 0.409987i | ||||
\(652\) | −1.57213e29 | −0.443494 | ||||||||
\(653\) | 5.73406e29i | 1.59175i | 0.605464 | + | 0.795873i | \(0.292988\pi\) | ||||
−0.605464 | + | 0.795873i | \(0.707012\pi\) | |||||||
\(654\) | 2.47790e29 | − | 1.83896e27i | 0.676890 | − | 0.00502350i | ||||
\(655\) | 3.09716e29 | 0.832588 | ||||||||
\(656\) | −4.49745e29 | −1.18981 | ||||||||
\(657\) | −4.79667e26 | − | 3.23145e28i | −0.00124883 | − | 0.0841319i | ||||
\(658\) | −1.47860e29 | − | 2.93244e29i | −0.378860 | − | 0.751376i | ||||
\(659\) | 3.15527e28i | 0.0795682i | 0.999208 | + | 0.0397841i | \(0.0126670\pi\) | ||||
−0.999208 | + | 0.0397841i | \(0.987333\pi\) | |||||||
\(660\) | 4.72184e29 | − | 3.50429e27i | 1.17193 | − | 0.00869739i | ||||
\(661\) | − | 3.17504e29i | − | 0.775594i | −0.921745 | − | 0.387797i | \(-0.873236\pi\) | ||
0.921745 | − | 0.387797i | \(-0.126764\pi\) | |||||||
\(662\) | − | 3.92743e29i | − | 0.944276i | ||||||
\(663\) | 5.92098e29 | − | 4.39423e27i | 1.40121 | − | 0.0103990i | ||||
\(664\) | − | 3.91950e27i | − | 0.00912989i | ||||||
\(665\) | 2.77103e29 | + | 5.49565e29i | 0.635351 | + | 1.26006i | ||||
\(666\) | 8.11954e27 | + | 5.47002e29i | 0.0183253 | + | 1.23455i | ||||
\(667\) | 6.82294e29 | 1.51583 | ||||||||
\(668\) | 9.06995e28 | 0.198359 | ||||||||
\(669\) | −9.92976e28 | + | 7.36932e26i | −0.213779 | + | 0.00158655i | ||||
\(670\) | 5.73680e29i | 1.21586i | ||||||||
\(671\) | −5.96479e29 | −1.24454 | ||||||||
\(672\) | 6.16087e29 | − | 3.16401e29i | 1.26551 | − | 0.649921i | ||||
\(673\) | 3.93458e29 | 0.795684 | 0.397842 | − | 0.917454i | \(-0.369759\pi\) | ||||
0.397842 | + | 0.917454i | \(0.369759\pi\) | |||||||
\(674\) | 1.34645e30i | 2.68079i | ||||||||
\(675\) | 2.27969e27 | + | 1.02377e29i | 0.00446876 | + | 0.200684i | ||||
\(676\) | 3.97080e28 | 0.0766368 | ||||||||
\(677\) | −5.39053e29 | −1.02435 | −0.512177 | − | 0.858880i | \(-0.671161\pi\) | ||||
−0.512177 | + | 0.858880i | \(0.671161\pi\) | |||||||
\(678\) | 4.03594e27 | + | 5.43821e29i | 0.00755149 | + | 1.01752i | ||||
\(679\) | −2.79045e29 | − | 5.53417e29i | −0.514093 | − | 1.01958i | ||||
\(680\) | 2.54392e28i | 0.0461488i | ||||||||
\(681\) | −7.33798e27 | − | 9.88753e29i | −0.0131079 | − | 1.76621i | ||||
\(682\) | 9.27298e29i | 1.63111i | ||||||||
\(683\) | − | 1.34724e29i | − | 0.233360i | −0.993170 | − | 0.116680i | \(-0.962775\pi\) | ||
0.993170 | − | 0.116680i | \(-0.0372252\pi\) | |||||||
\(684\) | 1.41031e28 | + | 9.50109e29i | 0.0240562 | + | 1.62063i | ||||
\(685\) | 4.04417e28i | 0.0679327i | ||||||||
\(686\) | 8.48252e29 | + | 1.45379e29i | 1.40321 | + | 0.240490i | ||||
\(687\) | 4.20214e29 | − | 3.11860e27i | 0.684581 | − | 0.00508058i | ||||
\(688\) | −9.12950e29 | −1.46477 | ||||||||
\(689\) | 8.32416e29 | 1.31534 | ||||||||
\(690\) | 7.05380e27 | + | 9.50461e29i | 0.0109776 | + | 1.47917i | ||||
\(691\) | − | 7.84599e29i | − | 1.20262i | −0.799016 | − | 0.601309i | \(-0.794646\pi\) | ||
0.799016 | − | 0.601309i | \(-0.205354\pi\) | |||||||
\(692\) | 2.35830e29 | 0.356029 | ||||||||
\(693\) | −3.97882e29 | − | 7.60797e29i | −0.591637 | − | 1.13128i | ||||
\(694\) | −7.79075e29 | −1.14105 | ||||||||
\(695\) | 4.82644e29i | 0.696284i | ||||||||
\(696\) | −2.60123e26 | − | 3.50501e28i | −0.000369642 | − | 0.0498073i | ||||
\(697\) | −1.18150e30 | −1.65383 | ||||||||
\(698\) | 7.04295e29 | 0.971120 | ||||||||
\(699\) | 1.54235e29 | − | 1.14465e27i | 0.209495 | − | 0.00155476i | ||||
\(700\) | −1.37548e29 | + | 6.93550e28i | −0.184046 | + | 0.0928000i | ||||
\(701\) | − | 7.51986e29i | − | 0.991222i | −0.868545 | − | 0.495611i | \(-0.834944\pi\) | ||
0.868545 | − | 0.495611i | \(-0.165056\pi\) | |||||||
\(702\) | −2.53014e28 | − | 1.13624e30i | −0.0328552 | − | 1.47547i | ||||
\(703\) | 1.07008e30i | 1.36894i | ||||||||
\(704\) | − | 1.06653e30i | − | 1.34419i | ||||||
\(705\) | 3.15826e27 | + | 4.25558e29i | 0.00392159 | + | 0.528413i | ||||
\(706\) | 1.80275e29i | 0.220539i | ||||||||
\(707\) | −8.72975e29 | + | 4.40173e29i | −1.05220 | + | 0.530542i | ||||
\(708\) | 5.53000e27 | + | 7.45137e29i | 0.00656713 | + | 0.884885i | ||||
\(709\) | 1.55784e30 | 1.82279 | 0.911394 | − | 0.411534i | \(-0.135007\pi\) | ||||
0.911394 | + | 0.411534i | \(0.135007\pi\) | |||||||
\(710\) | −1.20301e30 | −1.38694 | ||||||||
\(711\) | 6.34921e29 | − | 9.42459e27i | 0.721255 | − | 0.0107061i | ||||
\(712\) | 5.17015e26i | 0.000578713i | ||||||||
\(713\) | −9.45631e29 | −1.04299 | ||||||||
\(714\) | 1.57504e30 | − | 8.08887e29i | 1.71183 | − | 0.879137i | ||||
\(715\) | −1.10474e30 | −1.18317 | ||||||||
\(716\) | − | 3.64573e28i | − | 0.0384767i | ||||||
\(717\) | 6.14771e29 | − | 4.56249e27i | 0.639385 | − | 0.00474516i | ||||
\(718\) | −2.28958e30 | −2.34665 | ||||||||
\(719\) | 1.78661e28 | 0.0180459 | 0.00902293 | − | 0.999959i | \(-0.497128\pi\) | ||||
0.00902293 | + | 0.999959i | \(0.497128\pi\) | |||||||
\(720\) | −8.73292e29 | + | 1.29629e28i | −0.869297 | + | 0.0129036i | ||||
\(721\) | −1.66832e29 | − | 3.30869e29i | −0.163666 | − | 0.324591i | ||||
\(722\) | 2.19629e30i | 2.12349i | ||||||||
\(723\) | 1.36853e29 | − | 1.01565e27i | 0.130408 | − | 0.000967815i | ||||
\(724\) | − | 5.60558e29i | − | 0.526460i | ||||||
\(725\) | − | 2.82841e29i | − | 0.261815i | ||||||
\(726\) | −9.82768e29 | + | 7.29356e27i | −0.896637 | + | 0.00665434i | ||||
\(727\) | − | 1.04360e30i | − | 0.938475i | −0.883072 | − | 0.469238i | \(-0.844529\pi\) | ||
0.883072 | − | 0.469238i | \(-0.155471\pi\) | |||||||
\(728\) | 3.98796e28 | − | 2.01082e28i | 0.0353485 | − | 0.0178235i | ||||
\(729\) | −1.14343e30 | + | 5.09480e28i | −0.999009 | + | 0.0445132i | ||||
\(730\) | −1.24352e29 | −0.107093 | ||||||||
\(731\) | −2.39836e30 | −2.03602 | ||||||||
\(732\) | −1.19616e30 | + | 8.87723e27i | −1.00097 | + | 0.00742867i | ||||
\(733\) | − | 2.13525e29i | − | 0.176139i | −0.996114 | − | 0.0880697i | \(-0.971930\pi\) | ||
0.996114 | − | 0.0880697i | \(-0.0280698\pi\) | |||||||
\(734\) | 1.84006e30 | 1.49632 | ||||||||
\(735\) | −9.01569e29 | − | 6.56431e29i | −0.722740 | − | 0.526225i | ||||
\(736\) | 2.09213e30 | 1.65338 | ||||||||
\(737\) | − | 1.56534e30i | − | 1.21955i | ||||||
\(738\) | 3.36590e28 | + | 2.26756e30i | 0.0258529 | + | 1.74167i | ||||
\(739\) | 1.74393e30 | 1.32057 | 0.660287 | − | 0.751013i | \(-0.270435\pi\) | ||||
0.660287 | + | 0.751013i | \(0.270435\pi\) | |||||||
\(740\) | 1.06641e30 | 0.796143 | ||||||||
\(741\) | −1.64981e28 | − | 2.22303e30i | −0.0121435 | − | 1.63627i | ||||
\(742\) | 2.22263e30 | − | 1.12070e30i | 1.61297 | − | 0.813294i | ||||
\(743\) | − | 8.08005e28i | − | 0.0578138i | −0.999582 | − | 0.0289069i | \(-0.990797\pi\) | ||
0.999582 | − | 0.0289069i | \(-0.00920264\pi\) | |||||||
\(744\) | 3.60519e26 | + | 4.85780e28i | 0.000254339 | + | 0.0342708i | ||||
\(745\) | − | 2.83364e29i | − | 0.197108i | ||||||
\(746\) | − | 3.59267e30i | − | 2.46411i | ||||||
\(747\) | 3.53470e29 | − | 5.24681e27i | 0.239049 | − | 0.00354837i | ||||
\(748\) | − | 2.65715e30i | − | 1.77194i | ||||||
\(749\) | 8.72162e29 | + | 1.72972e30i | 0.573506 | + | 1.13741i | ||||
\(750\) | 2.35685e30 | − | 1.74912e28i | 1.52823 | − | 0.0113417i | ||||
\(751\) | 2.52556e30 | 1.61487 | 0.807437 | − | 0.589954i | \(-0.200854\pi\) | ||||
0.807437 | + | 0.589954i | \(0.200854\pi\) | |||||||
\(752\) | 9.11585e29 | 0.574791 | ||||||||
\(753\) | 2.25915e28 | + | 3.04408e30i | 0.0140474 | + | 1.89282i | ||||
\(754\) | 3.13914e30i | 1.92492i | ||||||||
\(755\) | 2.23520e30 | 1.35168 | ||||||||
\(756\) | −8.09221e29 | − | 1.51975e30i | −0.482601 | − | 0.906346i | ||||
\(757\) | −1.56975e30 | −0.923261 | −0.461630 | − | 0.887072i | \(-0.652735\pi\) | ||||
−0.461630 | + | 0.887072i | \(0.652735\pi\) | |||||||
\(758\) | − | 1.55160e29i | − | 0.0900025i | ||||||
\(759\) | −1.92470e28 | − | 2.59343e30i | −0.0110109 | − | 1.48366i | ||||
\(760\) | 9.55115e28 | 0.0538906 | ||||||||
\(761\) | −1.72012e30 | −0.957235 | −0.478618 | − | 0.878023i | \(-0.658862\pi\) | ||||
−0.478618 | + | 0.878023i | \(0.658862\pi\) | |||||||
\(762\) | 2.33004e30 | − | 1.72922e28i | 1.27890 | − | 0.00949126i | ||||
\(763\) | −7.84222e29 | + | 3.95422e29i | −0.424553 | + | 0.214069i | ||||
\(764\) | − | 1.97049e30i | − | 1.05219i | ||||||
\(765\) | −2.29417e30 | + | 3.40541e28i | −1.20832 | + | 0.0179359i | ||||
\(766\) | 4.26014e29i | 0.221321i | ||||||||
\(767\) | − | 1.74335e30i | − | 0.893374i | ||||||
\(768\) | 1.38624e28 | + | 1.86789e30i | 0.00700724 | + | 0.944187i | ||||
\(769\) | 5.97512e29i | 0.297934i | 0.988842 | + | 0.148967i | \(0.0475948\pi\) | ||||
−0.988842 | + | 0.148967i | \(0.952405\pi\) | |||||||
\(770\) | −2.94976e30 | + | 1.48733e30i | −1.45089 | + | 0.731570i | ||||
\(771\) | 7.20364e27 | + | 9.70652e29i | 0.00349527 | + | 0.470969i | ||||
\(772\) | 8.68440e29 | 0.415679 | ||||||||
\(773\) | 2.40153e30 | 1.13397 | 0.566987 | − | 0.823727i | \(-0.308109\pi\) | ||||
0.566987 | + | 0.823727i | \(0.308109\pi\) | |||||||
\(774\) | 6.83252e28 | + | 4.60297e30i | 0.0318274 | + | 2.14417i | ||||
\(775\) | 3.92006e29i | 0.180146i | ||||||||
\(776\) | −9.61811e28 | −0.0436055 | ||||||||
\(777\) | −8.85800e29 | − | 1.72480e30i | −0.396200 | − | 0.771470i | ||||
\(778\) | −2.50958e30 | −1.10743 | ||||||||
\(779\) | 4.43594e30i | 1.93127i | ||||||||
\(780\) | −2.21541e30 | + | 1.64415e28i | −0.951613 | + | 0.00706234i | ||||
\(781\) | 3.28254e30 | 1.39115 | ||||||||
\(782\) | 5.34859e30 | 2.23650 | ||||||||
\(783\) | 3.16056e30 | − | 7.03782e28i | 1.30396 | − | 0.0290362i | ||||
\(784\) | −1.42039e30 | + | 1.92070e30i | −0.578214 | + | 0.781883i | ||||
\(785\) | − | 2.27743e30i | − | 0.914773i | ||||||
\(786\) | −3.34516e30 | + | 2.48259e28i | −1.32581 | + | 0.00983941i | ||||
\(787\) | − | 1.42038e30i | − | 0.555483i | −0.960656 | − | 0.277741i | \(-0.910414\pi\) | ||
0.960656 | − | 0.277741i | \(-0.0895858\pi\) | |||||||
\(788\) | 1.61343e30i | 0.622624i | ||||||||
\(789\) | −2.27204e30 | + | 1.68619e28i | −0.865184 | + | 0.00642092i | ||||
\(790\) | − | 2.44329e30i | − | 0.918101i | ||||||
\(791\) | −8.67826e29 | − | 1.72112e30i | −0.321795 | − | 0.638201i | ||||
\(792\) | −1.33220e29 | + | 1.97748e27i | −0.0487477 | + | 0.000723597i | ||||
\(793\) | 2.79858e30 | 1.01058 | ||||||||
\(794\) | −6.77487e30 | −2.41427 | ||||||||
\(795\) | −3.22550e30 | + | 2.39379e28i | −1.13434 | + | 0.00841841i | ||||
\(796\) | 4.00544e30i | 1.39015i | ||||||||
\(797\) | 4.23430e30 | 1.45034 | 0.725170 | − | 0.688570i | \(-0.241761\pi\) | ||||
0.725170 | + | 0.688570i | \(0.241761\pi\) | |||||||
\(798\) | −3.03696e30 | − | 5.91349e30i | −1.02662 | − | 1.99900i | ||||
\(799\) | 2.39477e30 | 0.798956 | ||||||||
\(800\) | − | 8.67283e29i | − | 0.285572i | ||||||
\(801\) | −4.66257e28 | + | 6.92098e26i | −0.0151525 | + | 0.000224919i | ||||
\(802\) | 2.55067e30 | 0.818133 | ||||||||
\(803\) | 3.39306e29 | 0.107418 | ||||||||
\(804\) | −2.32965e28 | − | 3.13908e30i | −0.00727952 | − | 0.980877i | ||||
\(805\) | −1.51674e30 | − | 3.00808e30i | −0.467794 | − | 0.927753i | ||||
\(806\) | − | 4.35072e30i | − | 1.32447i | ||||||
\(807\) | −1.91907e28 | − | 2.58584e30i | −0.00576659 | − | 0.777017i | ||||
\(808\) | 1.51719e29i | 0.0450007i | ||||||||
\(809\) | − | 4.80366e30i | − | 1.40641i | −0.710986 | − | 0.703206i | \(-0.751751\pi\) | ||
0.710986 | − | 0.703206i | \(-0.248249\pi\) | |||||||
\(810\) | 1.30714e29 | + | 4.40205e30i | 0.0377773 | + | 1.27222i | ||||
\(811\) | 8.54703e29i | 0.243835i | 0.992540 | + | 0.121918i | \(0.0389043\pi\) | ||||
−0.992540 | + | 0.121918i | \(0.961096\pi\) | |||||||
\(812\) | 2.14111e30 | + | 4.24636e30i | 0.602977 | + | 1.19586i | ||||
\(813\) | −7.01864e29 | + | 5.20885e27i | −0.195120 | + | 0.00144807i | ||||
\(814\) | −5.74360e30 | −1.57626 | ||||||||
\(815\) | −1.42525e30 | −0.386134 | ||||||||
\(816\) | 3.64734e28 | + | 4.91460e30i | 0.00975506 | + | 1.31444i | ||||
\(817\) | 9.00463e30i | 2.37757i | ||||||||
\(818\) | −5.85734e30 | −1.52683 | ||||||||
\(819\) | 1.86679e30 | + | 3.56953e30i | 0.480413 | + | 0.918607i | ||||
\(820\) | 4.42073e30 | 1.12318 | ||||||||
\(821\) | 6.10606e30i | 1.53164i | 0.643052 | + | 0.765822i | \(0.277668\pi\) | ||||
−0.643052 | + | 0.765822i | \(0.722332\pi\) | |||||||
\(822\) | −3.24169e27 | − | 4.36800e29i | −0.000802819 | − | 0.108176i | ||||
\(823\) | 2.44508e30 | 0.597854 | 0.298927 | − | 0.954276i | \(-0.403371\pi\) | ||||
0.298927 | + | 0.954276i | \(0.403371\pi\) | |||||||
\(824\) | −5.75034e28 | −0.0138822 | ||||||||
\(825\) | −1.07509e30 | + | 7.97874e27i | −0.256259 | + | 0.00190181i | ||||
\(826\) | −2.34711e30 | − | 4.65491e30i | −0.552386 | − | 1.09552i | ||||
\(827\) | 7.46910e28i | 0.0173564i | 0.999962 | + | 0.00867821i | \(0.00276240\pi\) | ||||
−0.999962 | + | 0.00867821i | \(0.997238\pi\) | |||||||
\(828\) | −7.71945e28 | − | 5.20048e30i | −0.0177120 | − | 1.19323i | ||||
\(829\) | 5.33913e30i | 1.20962i | 0.796371 | + | 0.604809i | \(0.206750\pi\) | ||||
−0.796371 | + | 0.604809i | \(0.793250\pi\) | |||||||
\(830\) | − | 1.36022e30i | − | 0.304290i | ||||||
\(831\) | −4.39006e27 | − | 5.91536e29i | −0.000969749 | − | 0.130668i | ||||
\(832\) | 5.00399e30i | 1.09149i | ||||||||
\(833\) | −3.73142e30 | + | 5.04577e30i | −0.803714 | + | 1.08681i | ||||
\(834\) | −3.86873e28 | − | 5.21291e30i | −0.00822859 | − | 1.10876i | ||||
\(835\) | 8.22261e29 | 0.172704 | ||||||||
\(836\) | −9.97628e30 | −2.06920 | ||||||||
\(837\) | −4.38041e30 | + | 9.75412e28i | −0.897216 | + | 0.0199789i | ||||
\(838\) | 7.22476e30i | 1.46137i | ||||||||
\(839\) | 6.79091e30 | 1.35652 | 0.678262 | − | 0.734821i | \(-0.262734\pi\) | ||||
0.678262 | + | 0.734821i | \(0.262734\pi\) | |||||||
\(840\) | −1.53950e29 | + | 7.90633e28i | −0.0303701 | + | 0.0155970i | ||||
\(841\) | −3.59897e30 | −0.701166 | ||||||||
\(842\) | 5.38361e30i | 1.03585i | ||||||||
\(843\) | 2.51184e30 | − | 1.86415e28i | 0.477311 | − | 0.00354234i | ||||
\(844\) | −2.07373e30 | −0.389185 | ||||||||
\(845\) | 3.59984e29 | 0.0667248 | ||||||||
\(846\) | −6.82231e28 | − | 4.59609e30i | −0.0124894 | − | 0.841395i | ||||
\(847\) | 3.11033e30 | − | 1.56830e30i | 0.562380 | − | 0.283565i | ||||
\(848\) | 6.90931e30i | 1.23389i | ||||||||
\(849\) | −3.58031e30 | + | 2.65711e28i | −0.631524 | + | 0.00468682i | ||||
\(850\) | − | 2.21723e30i | − | 0.386289i | ||||||
\(851\) | − | 5.85716e30i | − | 1.00792i | ||||||
\(852\) | 6.58270e30 | − | 4.88532e28i | 1.11889 | − | 0.00830380i | ||||
\(853\) | − | 5.44553e30i | − | 0.914272i | −0.889397 | − | 0.457136i | \(-0.848875\pi\) | ||
0.889397 | − | 0.457136i | \(-0.151125\pi\) | |||||||
\(854\) | 7.47246e30 | − | 3.76778e30i | 1.23924 | − | 0.624853i | ||||
\(855\) | 1.27856e29 | + | 8.61347e30i | 0.0209448 | + | 1.41102i | ||||
\(856\) | 3.00616e29 | 0.0486449 | ||||||||
\(857\) | 8.68907e30 | 1.38891 | 0.694456 | − | 0.719535i | \(-0.255645\pi\) | ||||
0.694456 | + | 0.719535i | \(0.255645\pi\) | |||||||
\(858\) | 1.19320e31 | − | 8.85528e28i | 1.88407 | − | 0.0139825i | ||||
\(859\) | − | 5.86174e30i | − | 0.914321i | −0.889384 | − | 0.457160i | \(-0.848867\pi\) | ||
0.889384 | − | 0.457160i | \(-0.151133\pi\) | |||||||
\(860\) | 8.97374e30 | 1.38274 | ||||||||
\(861\) | −3.67202e30 | − | 7.15005e30i | −0.558948 | − | 1.08837i | ||||
\(862\) | −8.91270e30 | −1.34024 | ||||||||
\(863\) | − | 2.61010e30i | − | 0.387742i | −0.981027 | − | 0.193871i | \(-0.937896\pi\) | ||
0.981027 | − | 0.193871i | \(-0.0621044\pi\) | |||||||
\(864\) | 9.69130e30 | − | 2.15802e29i | 1.42229 | − | 0.0316710i | ||||
\(865\) | 2.13799e30 | 0.309981 | ||||||||
\(866\) | −1.23717e31 | −1.77211 | ||||||||
\(867\) | 4.33755e28 | + | 5.84462e30i | 0.00613824 | + | 0.827095i | ||||
\(868\) | −2.96749e30 | − | 5.88528e30i | −0.414889 | − | 0.822830i | ||||
\(869\) | 6.66676e30i | 0.920889i | ||||||||
\(870\) | −9.02726e28 | − | 1.21637e31i | −0.0123198 | − | 1.66003i | ||||
\(871\) | 7.34432e30i | 0.990286i | ||||||||
\(872\) | 1.36294e29i | 0.0181574i | ||||||||
\(873\) | −1.28752e29 | − | 8.67385e30i | −0.0169475 | − | 1.14173i | ||||
\(874\) | − | 2.00813e31i | − | 2.61169i | ||||||
\(875\) | −7.45910e30 | + | 3.76105e30i | −0.958522 | + | 0.483308i | ||||
\(876\) | 6.80433e29 | − | 5.04980e27i | 0.0863957 | − | 0.000641182i | ||||
\(877\) | 1.12364e30 | 0.140972 | 0.0704858 | − | 0.997513i | \(-0.477545\pi\) | ||||
0.0704858 | + | 0.997513i | \(0.477545\pi\) | |||||||
\(878\) | 7.05334e30 | 0.874385 | ||||||||
\(879\) | 4.85719e28 | + | 6.54480e30i | 0.00594979 | + | 0.801702i | ||||
\(880\) | − | 9.16969e30i | − | 1.10991i | ||||||
\(881\) | −1.10064e31 | −1.31643 | −0.658216 | − | 0.752829i | \(-0.728689\pi\) | ||||
−0.658216 | + | 0.752829i | \(0.728689\pi\) | |||||||
\(882\) | 9.79023e30 | + | 7.01767e30i | 1.15711 | + | 0.829416i | ||||
\(883\) | 1.30249e31 | 1.52120 | 0.760599 | − | 0.649222i | \(-0.224906\pi\) | ||||
0.760599 | + | 0.649222i | \(0.224906\pi\) | |||||||
\(884\) | 1.24669e31i | 1.43883i | ||||||||
\(885\) | 5.01337e28 | + | 6.75524e30i | 0.00571775 | + | 0.770436i | ||||
\(886\) | 7.39940e30 | 0.833955 | ||||||||
\(887\) | −3.68363e30 | −0.410277 | −0.205139 | − | 0.978733i | \(-0.565765\pi\) | ||||
−0.205139 | + | 0.978733i | \(0.565765\pi\) | |||||||
\(888\) | −3.00888e29 | + | 2.23303e27i | −0.0331184 | + | 0.000245786i | ||||
\(889\) | −7.37424e30 | + | 3.71826e30i | −0.802138 | + | 0.404456i | ||||
\(890\) | 1.79424e29i | 0.0192879i | ||||||||
\(891\) | −3.56667e29 | − | 1.20114e31i | −0.0378920 | − | 1.27608i | ||||
\(892\) | − | 2.09076e30i | − | 0.219519i | ||||||
\(893\) | − | 8.99117e30i | − | 0.932987i | ||||||
\(894\) | 2.27136e28 | + | 3.06054e30i | 0.00232939 | + | 0.313873i | ||||
\(895\) | − | 3.30514e29i | − | 0.0335002i | ||||||
\(896\) | 3.43140e29 | + | 6.80532e29i | 0.0343745 | + | 0.0681734i | ||||
\(897\) | 9.03036e28 | + | 1.21679e31i | 0.00894096 | + | 1.20475i | ||||
\(898\) | 9.62945e30 | 0.942323 | ||||||||
\(899\) | 1.21019e31 | 1.17052 | ||||||||
\(900\) | −2.15583e30 | + | 3.20006e28i | −0.206096 | + | 0.00305922i | ||||
\(901\) | 1.81510e31i | 1.71511i | ||||||||
\(902\) | −2.38097e31 | −2.22374 | ||||||||
\(903\) | −7.45392e30 | − | 1.45141e31i | −0.688119 | − | 1.33989i | ||||
\(904\) | −2.99122e29 | −0.0272948 | ||||||||
\(905\) | − | 5.08189e30i | − | 0.458369i | ||||||
\(906\) | −2.41418e31 | + | 1.79167e29i | −2.15241 | + | 0.0159740i | ||||
\(907\) | −7.33469e30 | −0.646406 | −0.323203 | − | 0.946330i | \(-0.604760\pi\) | ||||
−0.323203 | + | 0.946330i | \(0.604760\pi\) | |||||||
\(908\) | 2.08186e31 | 1.81364 | ||||||||
\(909\) | −1.36824e31 | + | 2.03097e29i | −1.17826 | + | 0.0174897i | ||||
\(910\) | 1.38398e31 | − | 6.97831e30i | 1.17813 | − | 0.594040i | ||||
\(911\) | − | 1.97607e31i | − | 1.66287i | −0.555622 | − | 0.831435i | \(-0.687520\pi\) | ||
0.555622 | − | 0.831435i | \(-0.312480\pi\) | |||||||
\(912\) | 1.84519e31 | − | 1.36940e29i | 1.53495 | − | 0.0113916i | ||||
\(913\) | 3.71149e30i | 0.305214i | ||||||||
\(914\) | − | 2.83886e30i | − | 0.230786i | ||||||
\(915\) | −1.08441e31 | + | 8.04789e28i | −0.871509 | + | 0.00646786i | ||||
\(916\) | 8.84780e30i | 0.702963i | ||||||||
\(917\) | 1.05870e31 | − | 5.33819e30i | 0.831561 | − | 0.419291i | ||||
\(918\) | 2.47760e31 | − | 5.51703e29i | 1.92391 | − | 0.0428408i | ||||
\(919\) | −2.29564e31 | −1.76235 | −0.881173 | − | 0.472793i | \(-0.843246\pi\) | ||||
−0.881173 | + | 0.472793i | \(0.843246\pi\) | |||||||
\(920\) | −5.22789e29 | −0.0396784 | ||||||||
\(921\) | −3.35574e30 | + | 2.49045e28i | −0.251804 | + | 0.00186875i | ||||
\(922\) | − | 2.26041e31i | − | 1.67692i | ||||||
\(923\) | −1.54011e31 | −1.12963 | ||||||||
\(924\) | 1.60802e31 | − | 8.25824e30i | 1.16610 | − | 0.598869i | ||||
\(925\) | −2.42805e30 | −0.174088 | ||||||||
\(926\) | − | 1.04323e31i | − | 0.739547i | ||||||
\(927\) | −7.69765e28 | − | 5.18580e30i | −0.00539537 | − | 0.363478i | ||||
\(928\) | −2.67746e31 | −1.85553 | ||||||||
\(929\) | −1.17358e31 | −0.804167 | −0.402083 | − | 0.915603i | \(-0.631714\pi\) | ||||
−0.402083 | + | 0.915603i | \(0.631714\pi\) | |||||||
\(930\) | 1.25114e29 | + | 1.68584e31i | 0.00847686 | + | 1.14221i | ||||
\(931\) | 1.89443e31 | + | 1.40096e31i | 1.26913 | + | 0.938544i | ||||
\(932\) | 3.24750e30i | 0.215120i | ||||||||
\(933\) | 2.10045e29 | + | 2.83024e31i | 0.0137580 | + | 1.85381i | ||||
\(934\) | − | 1.19122e31i | − | 0.771527i | ||||||
\(935\) | − | 2.40892e31i | − | 1.54276i | ||||||
\(936\) | 6.25044e29 | − | 9.27797e27i | 0.0395835 | − | 0.000587566i | ||||
\(937\) | 1.34665e31i | 0.843313i | 0.906756 | + | 0.421656i | \(0.138551\pi\) | ||||
−0.906756 | + | 0.421656i | \(0.861449\pi\) | |||||||
\(938\) | 9.88780e30 | + | 1.96100e31i | 0.612308 | + | 1.21436i | ||||
\(939\) | −1.83380e31 | + | 1.36095e29i | −1.12296 | + | 0.00833397i | ||||
\(940\) | −8.96033e30 | −0.542602 | ||||||||
\(941\) | 1.87253e31 | 1.12134 | 0.560671 | − | 0.828039i | \(-0.310543\pi\) | ||||
0.560671 | + | 0.828039i | \(0.310543\pi\) | |||||||
\(942\) | 1.82552e29 | + | 2.45979e31i | 0.0108107 | + | 1.45668i | ||||
\(943\) | − | 2.42804e31i | − | 1.42195i | ||||||
\(944\) | 1.44703e31 | 0.838056 | ||||||||
\(945\) | −7.33621e30 | − | 1.37777e31i | −0.420182 | − | 0.789122i | ||||
\(946\) | −4.83319e31 | −2.73764 | ||||||||
\(947\) | 2.57059e31i | 1.43998i | 0.693982 | + | 0.719992i | \(0.255855\pi\) | ||||
−0.693982 | + | 0.719992i | \(0.744145\pi\) | |||||||
\(948\) | 9.92195e28 | + | 1.33693e31i | 0.00549679 | + | 0.740663i | ||||
\(949\) | −1.59197e30 | −0.0872246 | ||||||||
\(950\) | −8.32458e30 | −0.451091 | ||||||||
\(951\) | −1.20313e31 | + | 8.92899e28i | −0.644790 | + | 0.00478527i | ||||
\(952\) | 4.38464e29 | + | 8.69585e29i | 0.0232405 | + | 0.0460919i | ||||
\(953\) | − | 2.74399e31i | − | 1.43849i | −0.694756 | − | 0.719246i | \(-0.744488\pi\) | ||
0.694756 | − | 0.719246i | \(-0.255512\pi\) | |||||||
\(954\) | 3.48358e31 | − | 5.17093e29i | 1.80621 | − | 0.0268109i | ||||
\(955\) | − | 1.78640e31i | − | 0.916101i | ||||||
\(956\) | 1.29443e31i | 0.656554i | ||||||||
\(957\) | 2.46318e29 | + | 3.31900e31i | 0.0123572 | + | 1.66507i | ||||
\(958\) | 2.03191e31i | 1.00825i | ||||||||
\(959\) | 6.97044e29 | + | 1.38241e30i | 0.0342109 | + | 0.0678489i | ||||
\(960\) | −1.43900e29 | − | 1.93898e31i | −0.00698575 | − | 0.941293i | ||||
\(961\) | 4.05273e30 | 0.194604 | ||||||||
\(962\) | 2.69480e31 | 1.27994 | ||||||||
\(963\) | 4.02418e29 | + | 2.71103e31i | 0.0189061 | + | 1.27367i | ||||
\(964\) | 2.88151e30i | 0.133910i | ||||||||
\(965\) | 7.87308e30 | 0.361916 | ||||||||
\(966\) | 1.66230e31 | + | 3.23679e31i | 0.755876 | + | 1.47182i | ||||
\(967\) | 4.46138e30 | 0.200674 | 0.100337 | − | 0.994954i | \(-0.468008\pi\) | ||||
0.100337 | + | 0.994954i | \(0.468008\pi\) | |||||||
\(968\) | − | 5.40559e29i | − | 0.0240520i | ||||||
\(969\) | 4.84738e31 | − | 3.59746e29i | 2.13357 | − | 0.0158342i | ||||
\(970\) | −3.33785e31 | −1.45333 | ||||||||
\(971\) | −2.17554e31 | −0.937054 | −0.468527 | − | 0.883449i | \(-0.655215\pi\) | ||||
−0.468527 | + | 0.883449i | \(0.655215\pi\) | |||||||
\(972\) | −8.94011e29 | − | 2.40820e31i | −0.0380932 | − | 1.02612i | ||||
\(973\) | 8.31873e30 | + | 1.64981e31i | 0.350649 | + | 0.695425i | ||||
\(974\) | − | 2.88419e30i | − | 0.120269i | ||||||
\(975\) | 5.04414e30 | − | 3.74349e28i | 0.208084 | − | 0.00154429i | ||||
\(976\) | 2.32291e31i | 0.948000i | ||||||||
\(977\) | 3.04944e31i | 1.23120i | 0.788060 | + | 0.615599i | \(0.211086\pi\) | ||||
−0.788060 | + | 0.615599i | \(0.788914\pi\) | |||||||
\(978\) | 1.53938e31 | − | 1.14244e29i | 0.614876 | − | 0.00456327i | ||||
\(979\) | − | 4.89576e29i | − | 0.0193465i | ||||||
\(980\) | 1.39616e31 | − | 1.88793e31i | 0.545833 | − | 0.738096i | ||||
\(981\) | −1.22913e31 | + | 1.82449e29i | −0.475416 | + | 0.00705694i | ||||
\(982\) | −2.29126e31 | −0.876805 | ||||||||
\(983\) | 2.98752e31 | 1.13109 | 0.565547 | − | 0.824716i | \(-0.308665\pi\) | ||||
0.565547 | + | 0.824716i | \(0.308665\pi\) | |||||||
\(984\) | −1.24731e30 | + | 9.25684e27i | −0.0467225 | + | 0.000346748i | ||||
\(985\) | 1.46270e31i | 0.542095i | ||||||||
\(986\) | −6.84498e31 | −2.50995 | ||||||||
\(987\) | 7.44278e30 | + | 1.44924e31i | 0.270026 | + | 0.525786i | ||||
\(988\) | 4.68070e31 | 1.68021 | ||||||||
\(989\) | − | 4.92874e31i | − | 1.75055i | ||||||
\(990\) | −4.62324e31 | + | 6.86260e29i | −1.62471 | + | 0.0241168i | ||||
\(991\) | 4.64507e30 | 0.161517 | 0.0807587 | − | 0.996734i | \(-0.474266\pi\) | ||||
0.0807587 | + | 0.996734i | \(0.474266\pi\) | |||||||
\(992\) | 3.71084e31 | 1.27673 | ||||||||
\(993\) | 1.44589e29 | + | 1.94826e31i | 0.00492230 | + | 0.663253i | ||||
\(994\) | −4.11224e31 | + | 2.07348e31i | −1.38523 | + | 0.698464i | ||||
\(995\) | 3.63124e31i | 1.21035i | ||||||||
\(996\) | 5.52370e28 | + | 7.44289e30i | 0.00182183 | + | 0.245481i | ||||
\(997\) | − | 4.49952e30i | − | 0.146847i | −0.997301 | − | 0.0734237i | \(-0.976607\pi\) | ||
0.997301 | − | 0.0734237i | \(-0.0233926\pi\) | |||||||
\(998\) | − | 6.32212e31i | − | 2.04170i | ||||||
\(999\) | −6.04162e29 | − | 2.71319e31i | −0.0193070 | − | 0.867045i |
(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 | 21.22.c.b.20.35 | yes | 52 | |
3.2 | odd | 2 | inner | 21.22.c.b.20.18 | yes | 52 | |
7.6 | odd | 2 | inner | 21.22.c.b.20.17 | ✓ | 52 | |
21.20 | even | 2 | inner | 21.22.c.b.20.36 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.22.c.b.20.17 | ✓ | 52 | 7.6 | odd | 2 | inner | |
21.22.c.b.20.18 | yes | 52 | 3.2 | odd | 2 | inner | |
21.22.c.b.20.35 | yes | 52 | 1.1 | even | 1 | trivial | |
21.22.c.b.20.36 | yes | 52 | 21.20 | even | 2 | inner |