Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,21,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(20.2811012082\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 66008406614424 x^{16} + \cdots + 53\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.4 | ||
Root | \(-20011.7 + 4.20507e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.21.d.b.3.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −980.704 | + | 294.612i | −0.957718 | + | 0.287707i | ||||
\(3\) | −86392.9 | −1.46307 | −0.731536 | − | 0.681803i | \(-0.761196\pi\) | ||||
−0.731536 | + | 0.681803i | \(0.761196\pi\) | |||||||
\(4\) | 874983. | − | 577854.i | 0.834449 | − | 0.551085i | ||||
\(5\) | − | 1.68203e7i | − | 1.72240i | −0.508269 | − | 0.861199i | \(-0.669714\pi\) | ||
0.508269 | − | 0.861199i | \(-0.330286\pi\) | |||||||
\(6\) | 8.47258e7 | − | 2.54524e7i | 1.40121 | − | 0.420936i | ||||
\(7\) | 3.64653e8i | 1.29092i | 0.763794 | + | 0.645460i | \(0.223334\pi\) | ||||
−0.763794 | + | 0.645460i | \(0.776666\pi\) | |||||||
\(8\) | −6.87856e8 | + | 8.24485e8i | −0.640616 | + | 0.767861i | ||||
\(9\) | 3.97695e9 | 1.14058 | ||||||||
\(10\) | 4.95546e9 | + | 1.64957e10i | 0.495546 | + | 1.64957i | ||||
\(11\) | 2.95556e10 | 1.13949 | 0.569747 | − | 0.821820i | \(-0.307041\pi\) | ||||
0.569747 | + | 0.821820i | \(0.307041\pi\) | |||||||
\(12\) | −7.55923e10 | + | 4.99225e10i | −1.22086 | + | 0.806276i | ||||
\(13\) | − | 1.06510e11i | − | 0.772600i | −0.922373 | − | 0.386300i | \(-0.873753\pi\) | ||
0.922373 | − | 0.386300i | \(-0.126247\pi\) | |||||||
\(14\) | −1.07431e11 | − | 3.57616e11i | −0.371407 | − | 1.23634i | ||||
\(15\) | 1.45315e12i | 2.51999i | ||||||||
\(16\) | 4.31680e11 | − | 1.01123e12i | 0.392611 | − | 0.919705i | ||||
\(17\) | 2.31198e12 | 1.14682 | 0.573410 | − | 0.819269i | \(-0.305620\pi\) | ||||
0.573410 | + | 0.819269i | \(0.305620\pi\) | |||||||
\(18\) | −3.90021e12 | + | 1.17166e12i | −1.09235 | + | 0.328152i | ||||
\(19\) | −8.42253e11 | −0.137375 | −0.0686873 | − | 0.997638i | \(-0.521881\pi\) | ||||
−0.0686873 | + | 0.997638i | \(0.521881\pi\) | |||||||
\(20\) | −9.71968e12 | − | 1.47175e13i | −0.949187 | − | 1.43725i | ||||
\(21\) | − | 3.15034e13i | − | 1.88871i | ||||||
\(22\) | −2.89852e13 | + | 8.70743e12i | −1.09132 | + | 0.327841i | ||||
\(23\) | − | 2.92728e12i | − | 0.0706621i | −0.999376 | − | 0.0353310i | \(-0.988751\pi\) | ||
0.999376 | − | 0.0353310i | \(-0.0112486\pi\) | |||||||
\(24\) | 5.94259e13 | − | 7.12296e13i | 0.937267 | − | 1.12344i | ||||
\(25\) | −1.87555e14 | −1.96665 | ||||||||
\(26\) | 3.13790e13 | + | 1.04454e14i | 0.222283 | + | 0.739934i | ||||
\(27\) | −4.23466e13 | −0.205675 | ||||||||
\(28\) | 2.10716e14 | + | 3.19065e14i | 0.711407 | + | 1.07721i | ||||
\(29\) | − | 2.89106e14i | − | 0.687190i | −0.939118 | − | 0.343595i | \(-0.888355\pi\) | ||
0.939118 | − | 0.343595i | \(-0.111645\pi\) | |||||||
\(30\) | −4.28117e14 | − | 1.42511e15i | −0.725019 | − | 2.41344i | ||||
\(31\) | − | 6.94432e14i | − | 0.847252i | −0.905837 | − | 0.423626i | \(-0.860757\pi\) | ||
0.905837 | − | 0.423626i | \(-0.139243\pi\) | |||||||
\(32\) | −1.25431e14 | + | 1.11889e15i | −0.111405 | + | 0.993775i | ||||
\(33\) | −2.55339e15 | −1.66716 | ||||||||
\(34\) | −2.26737e15 | + | 6.81138e14i | −1.09833 | + | 0.329948i | ||||
\(35\) | 6.13357e15 | 2.22348 | ||||||||
\(36\) | 3.47976e15 | − | 2.29810e15i | 0.951754 | − | 0.628555i | ||||
\(37\) | 2.39031e15i | 0.497092i | 0.968620 | + | 0.248546i | \(0.0799527\pi\) | ||||
−0.968620 | + | 0.248546i | \(0.920047\pi\) | |||||||
\(38\) | 8.26001e14 | − | 2.48138e14i | 0.131566 | − | 0.0395237i | ||||
\(39\) | 9.20166e15i | 1.13037i | ||||||||
\(40\) | 1.38681e16 | + | 1.15699e16i | 1.32256 | + | 1.10340i | ||||
\(41\) | −8.44047e15 | −0.628822 | −0.314411 | − | 0.949287i | \(-0.601807\pi\) | ||||
−0.314411 | + | 0.949287i | \(0.601807\pi\) | |||||||
\(42\) | 9.28129e15 | + | 3.08955e16i | 0.543395 | + | 1.80885i | ||||
\(43\) | −2.60268e16 | −1.20431 | −0.602153 | − | 0.798381i | \(-0.705690\pi\) | ||||
−0.602153 | + | 0.798381i | \(0.705690\pi\) | |||||||
\(44\) | 2.58606e16 | − | 1.70788e16i | 0.950850 | − | 0.627958i | ||||
\(45\) | − | 6.68934e16i | − | 1.96453i | ||||||
\(46\) | 8.62413e14 | + | 2.87080e15i | 0.0203300 | + | 0.0676744i | ||||
\(47\) | − | 4.58565e16i | − | 0.871811i | −0.899992 | − | 0.435906i | \(-0.856428\pi\) | ||
0.899992 | − | 0.435906i | \(-0.143572\pi\) | |||||||
\(48\) | −3.72941e16 | + | 8.73627e16i | −0.574418 | + | 1.34559i | ||||
\(49\) | −5.31795e16 | −0.666475 | ||||||||
\(50\) | 1.83935e17 | − | 5.52559e16i | 1.88350 | − | 0.565820i | ||||
\(51\) | −1.99739e17 | −1.67788 | ||||||||
\(52\) | −6.15470e16 | − | 9.31941e16i | −0.425768 | − | 0.644696i | ||||
\(53\) | 2.23880e17i | 1.28014i | 0.768318 | + | 0.640068i | \(0.221094\pi\) | ||||
−0.768318 | + | 0.640068i | \(0.778906\pi\) | |||||||
\(54\) | 4.15294e16 | − | 1.24758e16i | 0.196978 | − | 0.0591740i | ||||
\(55\) | − | 4.97133e17i | − | 1.96266i | ||||||
\(56\) | −3.00651e17 | − | 2.50829e17i | −0.991247 | − | 0.826984i | ||||
\(57\) | 7.27647e16 | 0.200989 | ||||||||
\(58\) | 8.51741e16 | + | 2.83527e17i | 0.197710 | + | 0.658135i | ||||
\(59\) | −3.72686e17 | −0.729161 | −0.364580 | − | 0.931172i | \(-0.618788\pi\) | ||||
−0.364580 | + | 0.931172i | \(0.618788\pi\) | |||||||
\(60\) | 8.39711e17 | + | 1.27148e18i | 1.38873 | + | 2.10280i | ||||
\(61\) | − | 1.14075e18i | − | 1.59917i | −0.600556 | − | 0.799583i | \(-0.705054\pi\) | ||
0.600556 | − | 0.799583i | \(-0.294946\pi\) | |||||||
\(62\) | 2.04588e17 | + | 6.81032e17i | 0.243761 | + | 0.811429i | ||||
\(63\) | 1.45021e18i | 1.47239i | ||||||||
\(64\) | −2.06628e17 | − | 1.13425e18i | −0.179222 | − | 0.983809i | ||||
\(65\) | −1.79152e18 | −1.33072 | ||||||||
\(66\) | 2.50412e18 | − | 7.52260e17i | 1.59667 | − | 0.479654i | ||||
\(67\) | 1.69388e18 | 0.929257 | 0.464628 | − | 0.885506i | \(-0.346188\pi\) | ||||
0.464628 | + | 0.885506i | \(0.346188\pi\) | |||||||
\(68\) | 2.02295e18 | − | 1.33599e18i | 0.956963 | − | 0.631995i | ||||
\(69\) | 2.52896e17i | 0.103384i | ||||||||
\(70\) | −6.01521e18 | + | 1.80702e18i | −2.12947 | + | 0.639710i | ||||
\(71\) | 1.43248e18i | 0.440054i | 0.975494 | + | 0.220027i | \(0.0706146\pi\) | ||||
−0.975494 | + | 0.220027i | \(0.929385\pi\) | |||||||
\(72\) | −2.73557e18 | + | 3.27893e18i | −0.730672 | + | 0.875805i | ||||
\(73\) | 6.55444e17 | 0.152513 | 0.0762565 | − | 0.997088i | \(-0.475703\pi\) | ||||
0.0762565 | + | 0.997088i | \(0.475703\pi\) | |||||||
\(74\) | −7.04214e17 | − | 2.34419e18i | −0.143017 | − | 0.476074i | ||||
\(75\) | 1.62034e19 | 2.87735 | ||||||||
\(76\) | −7.36958e17 | + | 4.86700e17i | −0.114632 | + | 0.0757051i | ||||
\(77\) | 1.07775e19i | 1.47100i | ||||||||
\(78\) | −2.71092e18 | − | 9.02411e18i | −0.325215 | − | 1.08258i | ||||
\(79\) | − | 3.74112e18i | − | 0.395121i | −0.980291 | − | 0.197561i | \(-0.936698\pi\) | ||
0.980291 | − | 0.197561i | \(-0.0633019\pi\) | |||||||
\(80\) | −1.70091e19 | − | 7.26098e18i | −1.58410 | − | 0.676232i | ||||
\(81\) | −1.02083e19 | −0.839661 | ||||||||
\(82\) | 8.27760e18 | − | 2.48666e18i | 0.602235 | − | 0.180917i | ||||
\(83\) | −1.51998e19 | −0.979621 | −0.489811 | − | 0.871829i | \(-0.662934\pi\) | ||||
−0.489811 | + | 0.871829i | \(0.662934\pi\) | |||||||
\(84\) | −1.82044e19 | − | 2.75650e19i | −1.04084 | − | 1.57603i | ||||
\(85\) | − | 3.88882e19i | − | 1.97528i | ||||||
\(86\) | 2.55246e19 | − | 7.66782e18i | 1.15339 | − | 0.346488i | ||||
\(87\) | 2.49767e19i | 1.00541i | ||||||||
\(88\) | −2.03300e19 | + | 2.43681e19i | −0.729979 | + | 0.874974i | ||||
\(89\) | 2.12767e19 | 0.682346 | 0.341173 | − | 0.940000i | \(-0.389176\pi\) | ||||
0.341173 | + | 0.940000i | \(0.389176\pi\) | |||||||
\(90\) | 1.97076e19 | + | 6.56026e19i | 0.565209 | + | 1.88146i | ||||
\(91\) | 3.88390e19 | 0.997365 | ||||||||
\(92\) | −1.69154e18 | − | 2.56132e18i | −0.0389408 | − | 0.0589639i | ||||
\(93\) | 5.99940e19i | 1.23959i | ||||||||
\(94\) | 1.35099e19 | + | 4.49717e19i | 0.250826 | + | 0.834950i | ||||
\(95\) | 1.41669e19i | 0.236614i | ||||||||
\(96\) | 1.08363e19 | − | 9.66643e19i | 0.162993 | − | 1.45396i | ||||
\(97\) | −6.94557e19 | −0.941868 | −0.470934 | − | 0.882168i | \(-0.656083\pi\) | ||||
−0.470934 | + | 0.882168i | \(0.656083\pi\) | |||||||
\(98\) | 5.21533e19 | − | 1.56673e19i | 0.638295 | − | 0.191750i | ||||
\(99\) | 1.17541e20 | 1.29968 | ||||||||
\(100\) | −1.64107e20 | + | 1.08379e20i | −1.64107 | + | 1.08379i | ||||
\(101\) | − | 6.91127e19i | − | 0.625668i | −0.949808 | − | 0.312834i | \(-0.898722\pi\) | ||
0.949808 | − | 0.312834i | \(-0.101278\pi\) | |||||||
\(102\) | 1.95885e20 | − | 5.88455e19i | 1.60694 | − | 0.482738i | ||||
\(103\) | − | 7.42626e18i | − | 0.0552584i | −0.999618 | − | 0.0276292i | \(-0.991204\pi\) | ||
0.999618 | − | 0.0276292i | \(-0.00879576\pi\) | |||||||
\(104\) | 8.78155e19 | + | 7.32633e19i | 0.593250 | + | 0.494940i | ||||
\(105\) | −5.29897e20 | −3.25311 | ||||||||
\(106\) | −6.59577e19 | − | 2.19560e20i | −0.368305 | − | 1.22601i | ||||
\(107\) | 1.94444e20 | 0.988453 | 0.494227 | − | 0.869333i | \(-0.335451\pi\) | ||||
0.494227 | + | 0.869333i | \(0.335451\pi\) | |||||||
\(108\) | −3.70525e19 | + | 2.44701e19i | −0.171625 | + | 0.113344i | ||||
\(109\) | − | 3.23383e20i | − | 1.36601i | −0.730415 | − | 0.683003i | \(-0.760673\pi\) | ||
0.730415 | − | 0.683003i | \(-0.239327\pi\) | |||||||
\(110\) | 1.46461e20 | + | 4.87540e20i | 0.564672 | + | 1.87968i | ||||
\(111\) | − | 2.06506e20i | − | 0.727281i | ||||||
\(112\) | 3.68747e20 | + | 1.57413e20i | 1.18727 | + | 0.506829i | ||||
\(113\) | −4.42432e20 | −1.30335 | −0.651677 | − | 0.758496i | \(-0.725934\pi\) | ||||
−0.651677 | + | 0.758496i | \(0.725934\pi\) | |||||||
\(114\) | −7.13606e19 | + | 2.14374e19i | −0.192491 | + | 0.0578260i | ||||
\(115\) | −4.92377e19 | −0.121708 | ||||||||
\(116\) | −1.67061e20 | − | 2.52963e20i | −0.378700 | − | 0.573425i | ||||
\(117\) | − | 4.23583e20i | − | 0.881210i | ||||||
\(118\) | 3.65495e20 | − | 1.09798e20i | 0.698331 | − | 0.209785i | ||||
\(119\) | 8.43071e20i | 1.48045i | ||||||||
\(120\) | −1.19810e21 | − | 9.99561e20i | −1.93500 | − | 1.61435i | ||||
\(121\) | 2.00781e20 | 0.298448 | ||||||||
\(122\) | 3.36080e20 | + | 1.11874e21i | 0.460091 | + | 1.53155i | ||||
\(123\) | 7.29196e20 | 0.920012 | ||||||||
\(124\) | −4.01281e20 | − | 6.07616e20i | −0.466908 | − | 0.706989i | ||||
\(125\) | 1.55061e21i | 1.66496i | ||||||||
\(126\) | −4.27248e20 | − | 1.42222e21i | −0.423618 | − | 1.41014i | ||||
\(127\) | − | 4.00904e20i | − | 0.367285i | −0.982993 | − | 0.183643i | \(-0.941211\pi\) | ||
0.982993 | − | 0.183643i | \(-0.0587889\pi\) | |||||||
\(128\) | 5.36806e20 | + | 1.05149e21i | 0.454693 | + | 0.890648i | ||||
\(129\) | 2.24853e21 | 1.76199 | ||||||||
\(130\) | 1.75695e21 | − | 5.27804e20i | 1.27446 | − | 0.382859i | ||||
\(131\) | 7.08938e20 | 0.476316 | 0.238158 | − | 0.971226i | \(-0.423456\pi\) | ||||
0.238158 | + | 0.971226i | \(0.423456\pi\) | |||||||
\(132\) | −2.23417e21 | + | 1.47549e21i | −1.39116 | + | 0.918748i | ||||
\(133\) | − | 3.07130e20i | − | 0.177340i | ||||||
\(134\) | −1.66120e21 | + | 4.99039e20i | −0.889966 | + | 0.267354i | ||||
\(135\) | 7.12281e20i | 0.354253i | ||||||||
\(136\) | −1.59031e21 | + | 1.90619e21i | −0.734671 | + | 0.880598i | ||||
\(137\) | 8.38295e20 | 0.359908 | 0.179954 | − | 0.983675i | \(-0.442405\pi\) | ||||
0.179954 | + | 0.983675i | \(0.442405\pi\) | |||||||
\(138\) | −7.45063e19 | − | 2.48016e20i | −0.0297442 | − | 0.0990124i | ||||
\(139\) | −3.16274e21 | −1.17467 | −0.587335 | − | 0.809344i | \(-0.699823\pi\) | ||||
−0.587335 | + | 0.809344i | \(0.699823\pi\) | |||||||
\(140\) | 5.36677e21 | − | 3.54431e21i | 1.85538 | − | 1.22532i | ||||
\(141\) | 3.96168e21i | 1.27552i | ||||||||
\(142\) | −4.22027e20 | − | 1.40484e21i | −0.126607 | − | 0.421448i | ||||
\(143\) | − | 3.14795e21i | − | 0.880374i | ||||||
\(144\) | 1.71677e21 | − | 4.02159e21i | 0.447803 | − | 1.04899i | ||||
\(145\) | −4.86284e21 | −1.18361 | ||||||||
\(146\) | −6.42796e20 | + | 1.93102e20i | −0.146064 | + | 0.0438791i | ||||
\(147\) | 4.59433e21 | 0.975100 | ||||||||
\(148\) | 1.38125e21 | + | 2.09148e21i | 0.273940 | + | 0.414798i | ||||
\(149\) | − | 1.03338e22i | − | 1.91602i | −0.286740 | − | 0.958008i | \(-0.592572\pi\) | ||
0.286740 | − | 0.958008i | \(-0.407428\pi\) | |||||||
\(150\) | −1.58907e22 | + | 4.77371e21i | −2.75569 | + | 0.827835i | ||||
\(151\) | 8.08356e21i | 1.31170i | 0.754893 | + | 0.655848i | \(0.227689\pi\) | ||||
−0.754893 | + | 0.655848i | \(0.772311\pi\) | |||||||
\(152\) | 5.79349e20 | − | 6.94425e20i | 0.0880045 | − | 0.105485i | ||||
\(153\) | 9.19463e21 | 1.30804 | ||||||||
\(154\) | −3.17519e21 | − | 1.05696e22i | −0.423216 | − | 1.40880i | ||||
\(155\) | −1.16805e22 | −1.45931 | ||||||||
\(156\) | 5.31722e21 | + | 8.05130e21i | 0.622929 | + | 0.943236i | ||||
\(157\) | − | 3.88131e21i | − | 0.426562i | −0.976991 | − | 0.213281i | \(-0.931585\pi\) | ||
0.976991 | − | 0.213281i | \(-0.0684149\pi\) | |||||||
\(158\) | 1.10218e21 | + | 3.66893e21i | 0.113679 | + | 0.378415i | ||||
\(159\) | − | 1.93416e22i | − | 1.87293i | ||||||
\(160\) | 1.88201e22 | + | 2.10978e21i | 1.71168 | + | 0.191884i | ||||
\(161\) | 1.06744e21 | 0.0912191 | ||||||||
\(162\) | 1.00113e22 | − | 3.00749e21i | 0.804159 | − | 0.241576i | ||||
\(163\) | −2.16871e22 | −1.63804 | −0.819020 | − | 0.573765i | \(-0.805482\pi\) | ||||
−0.819020 | + | 0.573765i | \(0.805482\pi\) | |||||||
\(164\) | −7.38527e21 | + | 4.87736e21i | −0.524720 | + | 0.346534i | ||||
\(165\) | 4.29488e22i | 2.87152i | ||||||||
\(166\) | 1.49065e22 | − | 4.47806e21i | 0.938201 | − | 0.281844i | ||||
\(167\) | 1.36722e22i | 0.810352i | 0.914239 | + | 0.405176i | \(0.132790\pi\) | ||||
−0.914239 | + | 0.405176i | \(0.867210\pi\) | |||||||
\(168\) | 2.59741e22 | + | 2.16698e22i | 1.45027 | + | 1.20994i | ||||
\(169\) | 7.66069e21 | 0.403089 | ||||||||
\(170\) | 1.14569e22 | + | 3.81378e22i | 0.568302 | + | 1.89176i | ||||
\(171\) | −3.34960e21 | −0.156686 | ||||||||
\(172\) | −2.27731e22 | + | 1.50397e22i | −1.00493 | + | 0.663675i | ||||
\(173\) | − | 3.92487e22i | − | 1.63442i | −0.576339 | − | 0.817211i | \(-0.695519\pi\) | ||
0.576339 | − | 0.817211i | \(-0.304481\pi\) | |||||||
\(174\) | −7.35844e21 | − | 2.44947e22i | −0.289263 | − | 0.962898i | ||||
\(175\) | − | 6.83923e22i | − | 2.53879i | ||||||
\(176\) | 1.27585e22 | − | 2.98873e22i | 0.447378 | − | 1.04800i | ||||
\(177\) | 3.21974e22 | 1.06681 | ||||||||
\(178\) | −2.08662e22 | + | 6.26838e21i | −0.653496 | + | 0.196316i | ||||
\(179\) | −4.77271e22 | −1.41330 | −0.706651 | − | 0.707562i | \(-0.749795\pi\) | ||||
−0.706651 | + | 0.707562i | \(0.749795\pi\) | |||||||
\(180\) | −3.86546e22 | − | 5.85306e22i | −1.08262 | − | 1.63930i | ||||
\(181\) | 1.43094e22i | 0.379171i | 0.981864 | + | 0.189585i | \(0.0607144\pi\) | ||||
−0.981864 | + | 0.189585i | \(0.939286\pi\) | |||||||
\(182\) | −3.80896e22 | + | 1.14424e22i | −0.955195 | + | 0.286949i | ||||
\(183\) | 9.85530e22i | 2.33969i | ||||||||
\(184\) | 2.41350e21 | + | 2.01355e21i | 0.0542586 | + | 0.0452673i | ||||
\(185\) | 4.02057e22 | 0.856190 | ||||||||
\(186\) | −1.76750e22 | − | 5.88363e22i | −0.356639 | − | 1.18718i | ||||
\(187\) | 6.83319e22 | 1.30680 | ||||||||
\(188\) | −2.64984e22 | − | 4.01237e22i | −0.480442 | − | 0.727482i | ||||
\(189\) | − | 1.54418e22i | − | 0.265509i | ||||||
\(190\) | −4.17375e21 | − | 1.38936e22i | −0.0680755 | − | 0.226609i | ||||
\(191\) | 8.04614e22i | 1.24524i | 0.782524 | + | 0.622621i | \(0.213932\pi\) | ||||
−0.782524 | + | 0.622621i | \(0.786068\pi\) | |||||||
\(192\) | 1.78512e22 | + | 9.79915e22i | 0.262214 | + | 1.43938i | ||||
\(193\) | −1.11689e23 | −1.55753 | −0.778766 | − | 0.627315i | \(-0.784154\pi\) | ||||
−0.778766 | + | 0.627315i | \(0.784154\pi\) | |||||||
\(194\) | 6.81154e22 | − | 2.04625e22i | 0.902045 | − | 0.270982i | ||||
\(195\) | 1.54775e23 | 1.94694 | ||||||||
\(196\) | −4.65312e22 | + | 3.07300e22i | −0.556139 | + | 0.367284i | ||||
\(197\) | − | 1.72505e22i | − | 0.195948i | −0.995189 | − | 0.0979738i | \(-0.968764\pi\) | ||
0.995189 | − | 0.0979738i | \(-0.0312361\pi\) | |||||||
\(198\) | −1.15273e23 | + | 3.46290e22i | −1.24473 | + | 0.373928i | ||||
\(199\) | − | 1.69597e23i | − | 1.74135i | −0.491858 | − | 0.870676i | \(-0.663682\pi\) | ||
0.491858 | − | 0.870676i | \(-0.336318\pi\) | |||||||
\(200\) | 1.29011e23 | − | 1.54636e23i | 1.25987 | − | 1.51012i | ||||
\(201\) | −1.46340e23 | −1.35957 | ||||||||
\(202\) | 2.03614e22 | + | 6.77791e22i | 0.180009 | + | 0.599214i | ||||
\(203\) | 1.05423e23 | 0.887108 | ||||||||
\(204\) | −1.74768e23 | + | 1.15420e23i | −1.40010 | + | 0.924654i | ||||
\(205\) | 1.41971e23i | 1.08308i | ||||||||
\(206\) | 2.18787e21 | + | 7.28296e21i | 0.0158982 | + | 0.0529219i | ||||
\(207\) | − | 1.16416e22i | − | 0.0805955i | ||||||
\(208\) | −1.07705e23 | − | 4.59780e22i | −0.710564 | − | 0.303331i | ||||
\(209\) | −2.48933e22 | −0.156538 | ||||||||
\(210\) | 5.19672e23 | − | 1.56114e23i | 3.11556 | − | 0.935942i | ||||
\(211\) | −1.06851e22 | −0.0610877 | −0.0305439 | − | 0.999533i | \(-0.509724\pi\) | ||||
−0.0305439 | + | 0.999533i | \(0.509724\pi\) | |||||||
\(212\) | 1.29370e23 | + | 1.95891e23i | 0.705464 | + | 1.06821i | ||||
\(213\) | − | 1.23756e23i | − | 0.643831i | ||||||
\(214\) | −1.90692e23 | + | 5.72855e22i | −0.946660 | + | 0.284385i | ||||
\(215\) | 4.37779e23i | 2.07429i | ||||||||
\(216\) | 2.91284e22 | − | 3.49141e22i | 0.131758 | − | 0.157929i | ||||
\(217\) | 2.53227e23 | 1.09374 | ||||||||
\(218\) | 9.52727e22 | + | 3.17143e23i | 0.393010 | + | 1.30825i | ||||
\(219\) | −5.66257e22 | −0.223137 | ||||||||
\(220\) | −2.87270e23 | − | 4.34983e23i | −1.08159 | − | 1.63774i | ||||
\(221\) | − | 2.46248e23i | − | 0.886033i | ||||||
\(222\) | 6.08391e22 | + | 2.02521e23i | 0.209244 | + | 0.696531i | ||||
\(223\) | − | 6.34169e22i | − | 0.208524i | −0.994550 | − | 0.104262i | \(-0.966752\pi\) | ||
0.994550 | − | 0.104262i | \(-0.0332481\pi\) | |||||||
\(224\) | −4.08007e23 | − | 4.57387e22i | −1.28288 | − | 0.143815i | ||||
\(225\) | −7.45895e23 | −2.24312 | ||||||||
\(226\) | 4.33895e23 | − | 1.30346e23i | 1.24825 | − | 0.374984i | ||||
\(227\) | −1.13881e23 | −0.313468 | −0.156734 | − | 0.987641i | \(-0.550097\pi\) | ||||
−0.156734 | + | 0.987641i | \(0.550097\pi\) | |||||||
\(228\) | 6.36679e22 | − | 4.20474e22i | 0.167715 | − | 0.110762i | ||||
\(229\) | − | 3.51437e23i | − | 0.886121i | −0.896492 | − | 0.443060i | \(-0.853893\pi\) | ||
0.896492 | − | 0.443060i | \(-0.146107\pi\) | |||||||
\(230\) | 4.82876e22 | − | 1.45060e22i | 0.116562 | − | 0.0350163i | ||||
\(231\) | − | 9.31101e23i | − | 2.15217i | ||||||
\(232\) | 2.38363e23 | + | 1.98863e23i | 0.527667 | + | 0.440225i | ||||
\(233\) | 4.48445e23 | 0.950933 | 0.475466 | − | 0.879734i | \(-0.342279\pi\) | ||||
0.475466 | + | 0.879734i | \(0.342279\pi\) | |||||||
\(234\) | 1.24793e23 | + | 4.15409e23i | 0.253531 | + | 0.843951i | ||||
\(235\) | −7.71320e23 | −1.50161 | ||||||||
\(236\) | −3.26094e23 | + | 2.15358e23i | −0.608448 | + | 0.401830i | ||||
\(237\) | 3.23206e23i | 0.578090i | ||||||||
\(238\) | −2.48379e23 | − | 8.26803e23i | −0.425937 | − | 1.41786i | ||||
\(239\) | 6.35130e22i | 0.104444i | 0.998635 | + | 0.0522220i | \(0.0166304\pi\) | ||||
−0.998635 | + | 0.0522220i | \(0.983370\pi\) | |||||||
\(240\) | 1.46947e24 | + | 6.27297e23i | 2.31765 | + | 0.989375i | ||||
\(241\) | −1.20735e24 | −1.82668 | −0.913338 | − | 0.407202i | \(-0.866504\pi\) | ||||
−0.913338 | + | 0.407202i | \(0.866504\pi\) | |||||||
\(242\) | −1.96907e23 | + | 5.91525e22i | −0.285829 | + | 0.0858657i | ||||
\(243\) | 1.02958e24 | 1.43416 | ||||||||
\(244\) | −6.59189e23 | − | 9.98140e23i | −0.881276 | − | 1.33442i | ||||
\(245\) | 8.94495e23i | 1.14793i | ||||||||
\(246\) | −7.15126e23 | + | 2.14830e23i | −0.881112 | + | 0.264694i | ||||
\(247\) | 8.97080e22i | 0.106136i | ||||||||
\(248\) | 5.72549e23 | + | 4.77670e23i | 0.650572 | + | 0.542764i | ||||
\(249\) | 1.31316e24 | 1.43326 | ||||||||
\(250\) | −4.56830e23 | − | 1.52069e24i | −0.479021 | − | 1.59456i | ||||
\(251\) | 1.33605e24 | 1.34613 | 0.673065 | − | 0.739583i | \(-0.264977\pi\) | ||||
0.673065 | + | 0.739583i | \(0.264977\pi\) | |||||||
\(252\) | 8.38008e23 | + | 1.26891e24i | 0.811414 | + | 1.22864i | ||||
\(253\) | − | 8.65175e22i | − | 0.0805190i | ||||||
\(254\) | 1.18111e23 | + | 3.93168e23i | 0.105671 | + | 0.351756i | ||||
\(255\) | 3.35966e24i | 2.88997i | ||||||||
\(256\) | −8.36230e23 | − | 8.73052e23i | −0.691713 | − | 0.722172i | ||||
\(257\) | 1.56338e24 | 1.24375 | 0.621875 | − | 0.783117i | \(-0.286371\pi\) | ||||
0.621875 | + | 0.783117i | \(0.286371\pi\) | |||||||
\(258\) | −2.20515e24 | + | 6.62445e23i | −1.68749 | + | 0.506936i | ||||
\(259\) | −8.71633e23 | −0.641706 | ||||||||
\(260\) | −1.56755e24 | + | 1.03524e24i | −1.11042 | + | 0.733342i | ||||
\(261\) | − | 1.14976e24i | − | 0.783794i | ||||||
\(262\) | −6.95258e23 | + | 2.08862e23i | −0.456177 | + | 0.137040i | ||||
\(263\) | − | 2.63570e24i | − | 1.66471i | −0.554244 | − | 0.832354i | \(-0.686993\pi\) | ||
0.554244 | − | 0.832354i | \(-0.313007\pi\) | |||||||
\(264\) | 1.75637e24 | − | 2.10523e24i | 1.06801 | − | 1.28015i | ||||
\(265\) | 3.76572e24 | 2.20490 | ||||||||
\(266\) | 9.04843e22 | + | 3.01204e23i | 0.0510219 | + | 0.169842i | ||||
\(267\) | −1.83816e24 | −0.998321 | ||||||||
\(268\) | 1.48212e24 | − | 9.78819e23i | 0.775418 | − | 0.512099i | ||||
\(269\) | 3.33951e24i | 1.68329i | 0.540027 | + | 0.841647i | \(0.318414\pi\) | ||||
−0.540027 | + | 0.841647i | \(0.681586\pi\) | |||||||
\(270\) | −2.09847e23 | − | 6.98537e23i | −0.101921 | − | 0.339275i | ||||
\(271\) | − | 8.24630e23i | − | 0.385981i | −0.981201 | − | 0.192991i | \(-0.938181\pi\) | ||
0.981201 | − | 0.192991i | \(-0.0618187\pi\) | |||||||
\(272\) | 9.98037e23 | − | 2.33794e24i | 0.450254 | − | 1.05474i | ||||
\(273\) | −3.35541e24 | −1.45922 | ||||||||
\(274\) | −8.22119e23 | + | 2.46972e23i | −0.344690 | + | 0.103548i | ||||
\(275\) | −5.54328e24 | −2.24099 | ||||||||
\(276\) | 1.46137e23 | + | 2.21280e23i | 0.0569732 | + | 0.0862684i | ||||
\(277\) | − | 1.73553e24i | − | 0.652580i | −0.945270 | − | 0.326290i | \(-0.894201\pi\) | ||
0.945270 | − | 0.326290i | \(-0.105799\pi\) | |||||||
\(278\) | 3.10171e24 | − | 9.31782e23i | 1.12500 | − | 0.337961i | ||||
\(279\) | − | 2.76172e24i | − | 0.966357i | ||||||
\(280\) | −4.21901e24 | + | 5.05703e24i | −1.42440 | + | 1.70732i | ||||
\(281\) | 2.59074e24 | 0.844036 | 0.422018 | − | 0.906587i | \(-0.361322\pi\) | ||||
0.422018 | + | 0.906587i | \(0.361322\pi\) | |||||||
\(282\) | −1.16716e24 | − | 3.88523e24i | −0.366977 | − | 1.22159i | ||||
\(283\) | −1.50077e24 | −0.455459 | −0.227730 | − | 0.973724i | \(-0.573130\pi\) | ||||
−0.227730 | + | 0.973724i | \(0.573130\pi\) | |||||||
\(284\) | 8.27767e23 | + | 1.25340e24i | 0.242507 | + | 0.367203i | ||||
\(285\) | − | 1.22392e24i | − | 0.346183i | ||||||
\(286\) | 9.27424e23 | + | 3.08720e24i | 0.253290 | + | 0.843150i | ||||
\(287\) | − | 3.07784e24i | − | 0.811759i | ||||||
\(288\) | −4.98832e23 | + | 4.44977e24i | −0.127066 | + | 1.13348i | ||||
\(289\) | 1.28103e24 | 0.315196 | ||||||||
\(290\) | 4.76901e24 | − | 1.43265e24i | 1.13357 | − | 0.340534i | ||||
\(291\) | 6.00047e24 | 1.37802 | ||||||||
\(292\) | 5.73502e23 | − | 3.78751e23i | 0.127264 | − | 0.0840476i | ||||
\(293\) | 5.50029e24i | 1.17953i | 0.807574 | + | 0.589766i | \(0.200780\pi\) | ||||
−0.807574 | + | 0.589766i | \(0.799220\pi\) | |||||||
\(294\) | −4.50568e24 | + | 1.35355e24i | −0.933871 | + | 0.280543i | ||||
\(295\) | 6.26869e24i | 1.25590i | ||||||||
\(296\) | −1.97077e24 | − | 1.64419e24i | −0.381698 | − | 0.318445i | ||||
\(297\) | −1.25158e24 | −0.234365 | ||||||||
\(298\) | 3.04448e24 | + | 1.01344e25i | 0.551252 | + | 1.83500i | ||||
\(299\) | −3.11783e23 | −0.0545935 | ||||||||
\(300\) | 1.41777e25 | − | 9.36320e24i | 2.40100 | − | 1.58567i | ||||
\(301\) | − | 9.49076e24i | − | 1.55466i | ||||||
\(302\) | −2.38151e24 | − | 7.92758e24i | −0.377384 | − | 1.25624i | ||||
\(303\) | 5.97084e24i | 0.915397i | ||||||||
\(304\) | −3.63584e23 | + | 8.51709e23i | −0.0539348 | + | 0.126344i | ||||
\(305\) | −1.91878e25 | −2.75440 | ||||||||
\(306\) | −9.01721e24 | + | 2.70885e24i | −1.25273 | + | 0.376331i | ||||
\(307\) | −2.32060e24 | −0.312044 | −0.156022 | − | 0.987754i | \(-0.549867\pi\) | ||||
−0.156022 | + | 0.987754i | \(0.549867\pi\) | |||||||
\(308\) | 6.22784e24 | + | 9.43015e24i | 0.810644 | + | 1.22747i | ||||
\(309\) | 6.41576e23i | 0.0808469i | ||||||||
\(310\) | 1.14552e25 | − | 3.44123e24i | 1.39760 | − | 0.419853i | ||||
\(311\) | − | 3.94846e24i | − | 0.466470i | −0.972420 | − | 0.233235i | \(-0.925069\pi\) | ||
0.972420 | − | 0.233235i | \(-0.0749312\pi\) | |||||||
\(312\) | −7.58663e24 | − | 6.32942e24i | −0.867967 | − | 0.724133i | ||||
\(313\) | 5.88598e24 | 0.652192 | 0.326096 | − | 0.945337i | \(-0.394267\pi\) | ||||
0.326096 | + | 0.945337i | \(0.394267\pi\) | |||||||
\(314\) | 1.14348e24 | + | 3.80642e24i | 0.122725 | + | 0.408526i | ||||
\(315\) | 2.43929e25 | 2.53605 | ||||||||
\(316\) | −2.16182e24 | − | 3.27341e24i | −0.217745 | − | 0.329709i | ||||
\(317\) | − | 1.40352e25i | − | 1.36970i | −0.728685 | − | 0.684849i | \(-0.759868\pi\) | ||
0.728685 | − | 0.684849i | \(-0.240132\pi\) | |||||||
\(318\) | 5.69828e24 | + | 1.89684e25i | 0.538856 | + | 1.79374i | ||||
\(319\) | − | 8.54469e24i | − | 0.783050i | ||||||
\(320\) | −1.90785e25 | + | 3.47555e24i | −1.69451 | + | 0.308691i | ||||
\(321\) | −1.67986e25 | −1.44618 | ||||||||
\(322\) | −1.04684e24 | + | 3.14481e23i | −0.0873622 | + | 0.0262444i | ||||
\(323\) | −1.94727e24 | −0.157544 | ||||||||
\(324\) | −8.93211e24 | + | 5.89892e24i | −0.700654 | + | 0.462724i | ||||
\(325\) | 1.99763e25i | 1.51944i | ||||||||
\(326\) | 2.12686e25 | − | 6.38927e24i | 1.56878 | − | 0.471276i | ||||
\(327\) | 2.79380e25i | 1.99857i | ||||||||
\(328\) | 5.80583e24 | − | 6.95904e24i | 0.402834 | − | 0.482848i | ||||
\(329\) | 1.67217e25 | 1.12544 | ||||||||
\(330\) | −1.26532e25 | − | 4.21200e25i | −0.826155 | − | 2.75010i | ||||
\(331\) | −1.16179e25 | −0.735951 | −0.367976 | − | 0.929835i | \(-0.619949\pi\) | ||||
−0.367976 | + | 0.929835i | \(0.619949\pi\) | |||||||
\(332\) | −1.32996e25 | + | 8.78329e24i | −0.817444 | + | 0.539854i | ||||
\(333\) | 9.50613e24i | 0.566972i | ||||||||
\(334\) | −4.02799e24 | − | 1.34084e25i | −0.233144 | − | 0.776089i | ||||
\(335\) | − | 2.84916e25i | − | 1.60055i | ||||||
\(336\) | −3.18571e25 | − | 1.35994e25i | −1.73705 | − | 0.741527i | ||||
\(337\) | 7.90893e24 | 0.418619 | 0.209309 | − | 0.977849i | \(-0.432878\pi\) | ||||
0.209309 | + | 0.977849i | \(0.432878\pi\) | |||||||
\(338\) | −7.51286e24 | + | 2.25693e24i | −0.386046 | + | 0.115972i | ||||
\(339\) | 3.82230e25 | 1.90690 | ||||||||
\(340\) | −2.24717e25 | − | 3.40265e25i | −1.08855 | − | 1.64827i | ||||
\(341\) | − | 2.05243e25i | − | 0.965440i | ||||||
\(342\) | 3.28496e24 | − | 9.86832e23i | 0.150062 | − | 0.0450798i | ||||
\(343\) | 9.70442e24i | 0.430555i | ||||||||
\(344\) | 1.79027e25 | − | 2.14587e25i | 0.771498 | − | 0.924740i | ||||
\(345\) | 4.25379e24 | 0.178068 | ||||||||
\(346\) | 1.15631e25 | + | 3.84913e25i | 0.470235 | + | 1.56532i | ||||
\(347\) | −3.29133e25 | −1.30040 | −0.650200 | − | 0.759763i | \(-0.725315\pi\) | ||||
−0.650200 | + | 0.759763i | \(0.725315\pi\) | |||||||
\(348\) | 1.44329e25 | + | 2.18542e25i | 0.554065 | + | 0.838962i | ||||
\(349\) | 4.94005e25i | 1.84279i | 0.388623 | + | 0.921397i | \(0.372951\pi\) | ||||
−0.388623 | + | 0.921397i | \(0.627049\pi\) | |||||||
\(350\) | 2.01492e25 | + | 6.70726e25i | 0.730428 | + | 2.43145i | ||||
\(351\) | 4.51031e24i | 0.158904i | ||||||||
\(352\) | −3.70718e24 | + | 3.30695e25i | −0.126945 | + | 1.13240i | ||||
\(353\) | 1.62932e25 | 0.542326 | 0.271163 | − | 0.962534i | \(-0.412592\pi\) | ||||
0.271163 | + | 0.962534i | \(0.412592\pi\) | |||||||
\(354\) | −3.15762e25 | + | 9.48576e24i | −1.02171 | + | 0.306930i | ||||
\(355\) | 2.40948e25 | 0.757948 | ||||||||
\(356\) | 1.86168e25 | − | 1.22949e25i | 0.569383 | − | 0.376031i | ||||
\(357\) | − | 7.28353e25i | − | 2.16601i | ||||||
\(358\) | 4.68062e25 | − | 1.40610e25i | 1.35355 | − | 0.406617i | ||||
\(359\) | 5.41413e25i | 1.52259i | 0.648403 | + | 0.761297i | \(0.275437\pi\) | ||||
−0.648403 | + | 0.761297i | \(0.724563\pi\) | |||||||
\(360\) | 5.51526e25 | + | 4.60130e25i | 1.50848 | + | 1.25851i | ||||
\(361\) | −3.68806e25 | −0.981128 | ||||||||
\(362\) | −4.21571e24 | − | 1.40333e25i | −0.109090 | − | 0.363139i | ||||
\(363\) | −1.73461e25 | −0.436651 | ||||||||
\(364\) | 3.39835e25 | − | 2.24433e25i | 0.832251 | − | 0.549633i | ||||
\(365\) | − | 1.10247e25i | − | 0.262688i | ||||||
\(366\) | −2.90349e25 | − | 9.66513e25i | −0.673146 | − | 2.24077i | ||||
\(367\) | − | 2.12308e25i | − | 0.478968i | −0.970900 | − | 0.239484i | \(-0.923022\pi\) | ||
0.970900 | − | 0.239484i | \(-0.0769782\pi\) | |||||||
\(368\) | −2.96014e24 | − | 1.26365e24i | −0.0649882 | − | 0.0277427i | ||||
\(369\) | −3.35673e25 | −0.717220 | ||||||||
\(370\) | −3.94299e25 | + | 1.18451e25i | −0.819989 | + | 0.246332i | ||||
\(371\) | −8.16385e25 | −1.65255 | ||||||||
\(372\) | 3.46678e25 | + | 5.24937e25i | 0.683120 | + | 1.03438i | ||||
\(373\) | 4.08340e25i | 0.783309i | 0.920112 | + | 0.391655i | \(0.128097\pi\) | ||||
−0.920112 | + | 0.391655i | \(0.871903\pi\) | |||||||
\(374\) | −6.70134e25 | + | 2.01314e25i | −1.25154 | + | 0.375974i | ||||
\(375\) | − | 1.33962e26i | − | 2.43595i | ||||||
\(376\) | 3.78080e25 | + | 3.15427e25i | 0.669430 | + | 0.558496i | ||||
\(377\) | −3.07925e25 | −0.530923 | ||||||||
\(378\) | 4.54934e24 | + | 1.51438e25i | 0.0763890 | + | 0.254283i | ||||
\(379\) | 6.13221e25 | 1.00282 | 0.501412 | − | 0.865209i | \(-0.332814\pi\) | ||||
0.501412 | + | 0.865209i | \(0.332814\pi\) | |||||||
\(380\) | 8.18643e24 | + | 1.23958e25i | 0.130394 | + | 0.197442i | ||||
\(381\) | 3.46353e25i | 0.537364i | ||||||||
\(382\) | −2.37049e25 | − | 7.89087e25i | −0.358265 | − | 1.19259i | ||||
\(383\) | 5.66622e24i | 0.0834268i | 0.999130 | + | 0.0417134i | \(0.0132816\pi\) | ||||
−0.999130 | + | 0.0417134i | \(0.986718\pi\) | |||||||
\(384\) | −4.63763e25 | − | 9.08414e25i | −0.665248 | − | 1.30308i | ||||
\(385\) | 1.81281e26 | 2.53364 | ||||||||
\(386\) | 1.09534e26 | − | 3.29049e25i | 1.49168 | − | 0.448113i | ||||
\(387\) | −1.03507e26 | −1.37360 | ||||||||
\(388\) | −6.07725e25 | + | 4.01353e25i | −0.785941 | + | 0.519050i | ||||
\(389\) | − | 2.56636e25i | − | 0.323461i | −0.986835 | − | 0.161730i | \(-0.948292\pi\) | ||
0.986835 | − | 0.161730i | \(-0.0517075\pi\) | |||||||
\(390\) | −1.51788e26 | + | 4.55985e25i | −1.86463 | + | 0.560150i | ||||
\(391\) | − | 6.76782e24i | − | 0.0810366i | ||||||
\(392\) | 3.65799e25 | − | 4.38457e25i | 0.426954 | − | 0.511760i | ||||
\(393\) | −6.12472e25 | −0.696884 | ||||||||
\(394\) | 5.08221e24 | + | 1.69177e25i | 0.0563755 | + | 0.187663i | ||||
\(395\) | −6.29266e25 | −0.680556 | ||||||||
\(396\) | 1.02846e26 | − | 6.79215e25i | 1.08452 | − | 0.716235i | ||||
\(397\) | − | 4.41470e25i | − | 0.453938i | −0.973902 | − | 0.226969i | \(-0.927118\pi\) | ||
0.973902 | − | 0.226969i | \(-0.0728816\pi\) | |||||||
\(398\) | 4.99652e25 | + | 1.66324e26i | 0.500999 | + | 1.66772i | ||||
\(399\) | 2.65339e25i | 0.259461i | ||||||||
\(400\) | −8.09636e25 | + | 1.89660e26i | −0.772129 | + | 1.80874i | ||||
\(401\) | 8.39617e25 | 0.780976 | 0.390488 | − | 0.920608i | \(-0.372306\pi\) | ||||
0.390488 | + | 0.920608i | \(0.372306\pi\) | |||||||
\(402\) | 1.43516e26 | − | 4.31134e25i | 1.30208 | − | 0.391158i | ||||
\(403\) | −7.39636e25 | −0.654587 | ||||||||
\(404\) | −3.99371e25 | − | 6.04724e25i | −0.344796 | − | 0.522088i | ||||
\(405\) | 1.71707e26i | 1.44623i | ||||||||
\(406\) | −1.03389e26 | + | 3.10590e25i | −0.849599 | + | 0.255227i | ||||
\(407\) | 7.06469e25i | 0.566434i | ||||||||
\(408\) | 1.37392e26 | − | 1.64682e26i | 1.07488 | − | 1.28838i | ||||
\(409\) | 1.78278e26 | 1.36102 | 0.680508 | − | 0.732740i | \(-0.261759\pi\) | ||||
0.680508 | + | 0.732740i | \(0.261759\pi\) | |||||||
\(410\) | −4.18264e25 | − | 1.39232e26i | −0.311610 | − | 1.03729i | ||||
\(411\) | −7.24227e25 | −0.526571 | ||||||||
\(412\) | −4.29130e24 | − | 6.49786e24i | −0.0304520 | − | 0.0461103i | ||||
\(413\) | − | 1.35901e26i | − | 0.941288i | ||||||
\(414\) | 3.42977e24 | + | 1.14170e25i | 0.0231879 | + | 0.0771878i | ||||
\(415\) | 2.55666e26i | 1.68730i | ||||||||
\(416\) | 1.19173e26 | + | 1.33596e25i | 0.767791 | + | 0.0860715i | ||||
\(417\) | 2.73238e26 | 1.71862 | ||||||||
\(418\) | 2.44129e25 | − | 7.33386e24i | 0.149919 | − | 0.0450370i | ||||
\(419\) | 2.19481e26 | 1.31600 | 0.658000 | − | 0.753018i | \(-0.271403\pi\) | ||||
0.658000 | + | 0.753018i | \(0.271403\pi\) | |||||||
\(420\) | −4.63651e26 | + | 3.06203e26i | −2.71455 | + | 1.79274i | ||||
\(421\) | 2.80463e25i | 0.160345i | 0.996781 | + | 0.0801723i | \(0.0255471\pi\) | ||||
−0.996781 | + | 0.0801723i | \(0.974453\pi\) | |||||||
\(422\) | 1.04789e25 | − | 3.14796e24i | 0.0585048 | − | 0.0175754i | ||||
\(423\) | − | 1.82369e26i | − | 0.994368i | ||||||
\(424\) | −1.84586e26 | − | 1.53997e26i | −0.982967 | − | 0.820076i | ||||
\(425\) | −4.33623e26 | −2.25540 | ||||||||
\(426\) | 3.64601e25 | + | 1.21368e26i | 0.185235 | + | 0.616608i | ||||
\(427\) | 4.15979e26 | 2.06439 | ||||||||
\(428\) | 1.70135e26 | − | 1.12360e26i | 0.824814 | − | 0.544722i | ||||
\(429\) | 2.71960e26i | 1.28805i | ||||||||
\(430\) | −1.28975e26 | − | 4.29331e26i | −0.596789 | − | 1.98659i | ||||
\(431\) | − | 2.93226e26i | − | 1.32565i | −0.748773 | − | 0.662826i | \(-0.769357\pi\) | ||
0.748773 | − | 0.662826i | \(-0.230643\pi\) | |||||||
\(432\) | −1.82802e25 | + | 4.28219e25i | −0.0807501 | + | 0.189160i | ||||
\(433\) | −3.63565e26 | −1.56929 | −0.784646 | − | 0.619945i | \(-0.787155\pi\) | ||||
−0.784646 | + | 0.619945i | \(0.787155\pi\) | |||||||
\(434\) | −2.48340e26 | + | 7.46037e25i | −1.04749 | + | 0.314675i | ||||
\(435\) | 4.20115e26 | 1.73171 | ||||||||
\(436\) | −1.86869e26 | − | 2.82955e26i | −0.752786 | − | 1.13986i | ||||
\(437\) | 2.46551e24i | 0.00970718i | ||||||||
\(438\) | 5.55330e25 | − | 1.66826e25i | 0.213703 | − | 0.0641982i | ||||
\(439\) | 5.58045e24i | 0.0209906i | 0.999945 | + | 0.0104953i | \(0.00334081\pi\) | ||||
−0.999945 | + | 0.0104953i | \(0.996659\pi\) | |||||||
\(440\) | 4.09878e26 | + | 3.41956e26i | 1.50705 | + | 1.25731i | ||||
\(441\) | −2.11492e26 | −0.760166 | ||||||||
\(442\) | 7.25477e25 | + | 2.41496e26i | 0.254918 | + | 0.848570i | ||||
\(443\) | −3.86486e26 | −1.32769 | −0.663845 | − | 0.747870i | \(-0.731077\pi\) | ||||
−0.663845 | + | 0.747870i | \(0.731077\pi\) | |||||||
\(444\) | −1.19330e26 | − | 1.80689e26i | −0.400794 | − | 0.606879i | ||||
\(445\) | − | 3.57881e26i | − | 1.17527i | ||||||
\(446\) | 1.86834e25 | + | 6.21932e25i | 0.0599939 | + | 0.199707i | ||||
\(447\) | 8.92771e26i | 2.80327i | ||||||||
\(448\) | 4.13609e26 | − | 7.53477e25i | 1.27002 | − | 0.231361i | ||||
\(449\) | −2.54008e26 | −0.762753 | −0.381377 | − | 0.924420i | \(-0.624550\pi\) | ||||
−0.381377 | + | 0.924420i | \(0.624550\pi\) | |||||||
\(450\) | 7.31502e26 | − | 2.19750e26i | 2.14828 | − | 0.645361i | ||||
\(451\) | −2.49463e26 | −0.716540 | ||||||||
\(452\) | −3.87121e26 | + | 2.55662e26i | −1.08758 | + | 0.718259i | ||||
\(453\) | − | 6.98362e26i | − | 1.91910i | ||||||
\(454\) | 1.11684e26 | − | 3.35508e25i | 0.300214 | − | 0.0901870i | ||||
\(455\) | − | 6.53283e26i | − | 1.71786i | ||||||
\(456\) | −5.00517e25 | + | 5.99934e25i | −0.128757 | + | 0.154332i | ||||
\(457\) | −4.82016e26 | −1.21311 | −0.606554 | − | 0.795042i | \(-0.707449\pi\) | ||||
−0.606554 | + | 0.795042i | \(0.707449\pi\) | |||||||
\(458\) | 1.03538e26 | + | 3.44656e26i | 0.254943 | + | 0.848654i | ||||
\(459\) | −9.79045e25 | −0.235872 | ||||||||
\(460\) | −4.30822e25 | + | 2.84522e25i | −0.101559 | + | 0.0670715i | ||||
\(461\) | − | 4.12032e26i | − | 0.950434i | −0.879869 | − | 0.475217i | \(-0.842370\pi\) | ||
0.879869 | − | 0.475217i | \(-0.157630\pi\) | |||||||
\(462\) | 2.74314e26 | + | 9.13134e26i | 0.619196 | + | 2.06118i | ||||
\(463\) | − | 2.63607e26i | − | 0.582300i | −0.956677 | − | 0.291150i | \(-0.905962\pi\) | ||
0.956677 | − | 0.291150i | \(-0.0940378\pi\) | |||||||
\(464\) | −2.92351e26 | − | 1.24801e26i | −0.632012 | − | 0.269798i | ||||
\(465\) | 1.00912e27 | 2.13507 | ||||||||
\(466\) | −4.39792e26 | + | 1.32117e26i | −0.910726 | + | 0.273590i | ||||
\(467\) | 2.33101e26 | 0.472471 | 0.236236 | − | 0.971696i | \(-0.424086\pi\) | ||||
0.236236 | + | 0.971696i | \(0.424086\pi\) | |||||||
\(468\) | −2.44769e26 | − | 3.70628e26i | −0.485622 | − | 0.735325i | ||||
\(469\) | 6.17680e26i | 1.19960i | ||||||||
\(470\) | 7.56436e26 | − | 2.27240e26i | 1.43812 | − | 0.432023i | ||||
\(471\) | 3.35318e26i | 0.624090i | ||||||||
\(472\) | 2.56355e26 | − | 3.07274e26i | 0.467112 | − | 0.559894i | ||||
\(473\) | −7.69238e26 | −1.37230 | ||||||||
\(474\) | −9.52204e25 | − | 3.16969e26i | −0.166321 | − | 0.553648i | ||||
\(475\) | 1.57968e26 | 0.270168 | ||||||||
\(476\) | 4.87172e26 | + | 7.37673e26i | 0.815855 | + | 1.23536i | ||||
\(477\) | 8.90358e26i | 1.46009i | ||||||||
\(478\) | −1.87117e25 | − | 6.22875e25i | −0.0300493 | − | 0.100028i | ||||
\(479\) | 3.33329e25i | 0.0524226i | 0.999656 | + | 0.0262113i | \(0.00834427\pi\) | ||||
−0.999656 | + | 0.0262113i | \(0.991656\pi\) | |||||||
\(480\) | −1.62592e27 | − | 1.82270e26i | −2.50430 | − | 0.280739i | ||||
\(481\) | 2.54591e26 | 0.384054 | ||||||||
\(482\) | 1.18405e27 | − | 3.55699e26i | 1.74944 | − | 0.525548i | ||||
\(483\) | −9.22194e25 | −0.133460 | ||||||||
\(484\) | 1.75680e26 | − | 1.16022e26i | 0.249040 | − | 0.164470i | ||||
\(485\) | 1.16826e27i | 1.62227i | ||||||||
\(486\) | −1.00971e27 | + | 3.03327e26i | −1.37352 | + | 0.412618i | ||||
\(487\) | 5.35339e26i | 0.713410i | 0.934217 | + | 0.356705i | \(0.116100\pi\) | ||||
−0.934217 | + | 0.356705i | \(0.883900\pi\) | |||||||
\(488\) | 9.40534e26 | + | 7.84675e26i | 1.22794 | + | 1.02445i | ||||
\(489\) | 1.87361e27 | 2.39657 | ||||||||
\(490\) | −2.63529e26 | − | 8.77234e26i | −0.330269 | − | 1.09940i | ||||
\(491\) | −3.93131e26 | −0.482750 | −0.241375 | − | 0.970432i | \(-0.577598\pi\) | ||||
−0.241375 | + | 0.970432i | \(0.577598\pi\) | |||||||
\(492\) | 6.38035e26 | − | 4.21369e26i | 0.767703 | − | 0.507005i | ||||
\(493\) | − | 6.68408e26i | − | 0.788083i | ||||||
\(494\) | −2.64291e25 | − | 8.79770e25i | −0.0305360 | − | 0.101648i | ||||
\(495\) | − | 1.97707e27i | − | 2.23857i | ||||||
\(496\) | −7.02228e26 | − | 2.99773e26i | −0.779222 | − | 0.332640i | ||||
\(497\) | −5.22359e26 | −0.568075 | ||||||||
\(498\) | −1.28782e27 | + | 3.86872e26i | −1.37266 | + | 0.412358i | ||||
\(499\) | 3.50826e26 | 0.366511 | 0.183255 | − | 0.983065i | \(-0.441336\pi\) | ||||
0.183255 | + | 0.983065i | \(0.441336\pi\) | |||||||
\(500\) | 8.96029e26 | + | 1.35676e27i | 0.917534 | + | 1.38932i | ||||
\(501\) | − | 1.18118e27i | − | 1.18560i | ||||||
\(502\) | −1.31027e27 | + | 3.93618e26i | −1.28921 | + | 0.387291i | ||||
\(503\) | 7.83816e26i | 0.756022i | 0.925801 | + | 0.378011i | \(0.123392\pi\) | ||||
−0.925801 | + | 0.378011i | \(0.876608\pi\) | |||||||
\(504\) | −1.19567e27 | − | 9.97533e26i | −1.13059 | − | 0.943240i | ||||
\(505\) | −1.16250e27 | −1.07765 | ||||||||
\(506\) | 2.54891e25 | + | 8.48480e25i | 0.0231659 | + | 0.0771146i | ||||
\(507\) | −6.61829e26 | −0.589747 | ||||||||
\(508\) | −2.31664e26 | − | 3.50785e26i | −0.202405 | − | 0.306481i | ||||
\(509\) | − | 1.14995e27i | − | 0.985148i | −0.870271 | − | 0.492574i | \(-0.836056\pi\) | ||
0.870271 | − | 0.492574i | \(-0.163944\pi\) | |||||||
\(510\) | −9.89798e26 | − | 3.29483e27i | −0.831466 | − | 2.76778i | ||||
\(511\) | 2.39009e26i | 0.196882i | ||||||||
\(512\) | 1.07731e27 | + | 6.09842e26i | 0.870241 | + | 0.492627i | ||||
\(513\) | 3.56665e25 | 0.0282545 | ||||||||
\(514\) | −1.53321e27 | + | 4.60590e26i | −1.19116 | + | 0.357836i | ||||
\(515\) | −1.24912e26 | −0.0951768 | ||||||||
\(516\) | 1.96743e27 | − | 1.29933e27i | 1.47029 | − | 0.971004i | ||||
\(517\) | − | 1.35531e27i | − | 0.993424i | ||||||
\(518\) | 8.54814e26 | − | 2.56794e26i | 0.614574 | − | 0.184623i | ||||
\(519\) | 3.39081e27i | 2.39128i | ||||||||
\(520\) | 1.23231e27 | − | 1.47708e27i | 0.852484 | − | 1.02181i | ||||
\(521\) | 1.79868e27 | 1.22061 | 0.610306 | − | 0.792166i | \(-0.291047\pi\) | ||||
0.610306 | + | 0.792166i | \(0.291047\pi\) | |||||||
\(522\) | 3.38733e26 | + | 1.12757e27i | 0.225503 | + | 0.750654i | ||||
\(523\) | 1.23394e27 | 0.805890 | 0.402945 | − | 0.915224i | \(-0.367987\pi\) | ||||
0.402945 | + | 0.915224i | \(0.367987\pi\) | |||||||
\(524\) | 6.20309e26 | − | 4.09663e26i | 0.397461 | − | 0.262491i | ||||
\(525\) | 5.90861e27i | 3.71443i | ||||||||
\(526\) | 7.76509e26 | + | 2.58484e27i | 0.478949 | + | 1.59432i | ||||
\(527\) | − | 1.60551e27i | − | 0.971646i | ||||||
\(528\) | −1.10225e27 | + | 2.58205e27i | −0.654546 | + | 1.53330i | ||||
\(529\) | 1.70759e27 | 0.995007 | ||||||||
\(530\) | −3.69306e27 | + | 1.10943e27i | −2.11168 | + | 0.634367i | ||||
\(531\) | −1.48215e27 | −0.831664 | ||||||||
\(532\) | −1.77477e26 | − | 2.68734e26i | −0.0977293 | − | 0.147981i | ||||
\(533\) | 8.98990e26i | 0.485828i | ||||||||
\(534\) | 1.80269e27 | − | 5.41544e26i | 0.956111 | − | 0.287224i | ||||
\(535\) | − | 3.27060e27i | − | 1.70251i | ||||||
\(536\) | −1.16515e27 | + | 1.39658e27i | −0.595297 | + | 0.713540i | ||||
\(537\) | 4.12328e27 | 2.06776 | ||||||||
\(538\) | −9.83861e26 | − | 3.27507e27i | −0.484296 | − | 1.61212i | ||||
\(539\) | −1.57175e27 | −0.759444 | ||||||||
\(540\) | 4.11595e26 | + | 6.23234e26i | 0.195224 | + | 0.295606i | ||||
\(541\) | − | 3.90282e26i | − | 0.181721i | −0.995864 | − | 0.0908607i | \(-0.971038\pi\) | ||
0.995864 | − | 0.0908607i | \(-0.0289618\pi\) | |||||||
\(542\) | 2.42946e26 | + | 8.08718e26i | 0.111050 | + | 0.369662i | ||||
\(543\) | − | 1.23623e27i | − | 0.554754i | ||||||
\(544\) | −2.89994e26 | + | 2.58686e27i | −0.127761 | + | 1.13968i | ||||
\(545\) | −5.43940e27 | −2.35281 | ||||||||
\(546\) | 3.29067e27 | − | 9.88546e26i | 1.39752 | − | 0.419827i | ||||
\(547\) | −5.54597e26 | −0.231262 | −0.115631 | − | 0.993292i | \(-0.536889\pi\) | ||||
−0.115631 | + | 0.993292i | \(0.536889\pi\) | |||||||
\(548\) | 7.33494e26 | − | 4.84412e26i | 0.300325 | − | 0.198340i | ||||
\(549\) | − | 4.53672e27i | − | 1.82397i | ||||||
\(550\) | 5.43632e27 | − | 1.63312e27i | 2.14624 | − | 0.644749i | ||||
\(551\) | 2.43500e26i | 0.0944026i | ||||||||
\(552\) | −2.08509e26 | − | 1.73956e26i | −0.0793843 | − | 0.0662292i | ||||
\(553\) | 1.36421e27 | 0.510070 | ||||||||
\(554\) | 5.11308e26 | + | 1.70204e27i | 0.187752 | + | 0.624988i | ||||
\(555\) | −3.47349e27 | −1.25267 | ||||||||
\(556\) | −2.76735e27 | + | 1.82760e27i | −0.980202 | + | 0.647343i | ||||
\(557\) | − | 2.54412e27i | − | 0.885087i | −0.896747 | − | 0.442543i | \(-0.854076\pi\) | ||
0.896747 | − | 0.442543i | \(-0.145924\pi\) | |||||||
\(558\) | 8.13636e26 | + | 2.70843e27i | 0.278028 | + | 0.925498i | ||||
\(559\) | 2.77211e27i | 0.930447i | ||||||||
\(560\) | 2.64774e27 | − | 6.20242e27i | 0.872961 | − | 2.04494i | ||||
\(561\) | −5.90339e27 | −1.91193 | ||||||||
\(562\) | −2.54075e27 | + | 7.63264e26i | −0.808349 | + | 0.242835i | ||||
\(563\) | −1.04936e27 | −0.327976 | −0.163988 | − | 0.986462i | \(-0.552436\pi\) | ||||
−0.163988 | + | 0.986462i | \(0.552436\pi\) | |||||||
\(564\) | 2.28927e27 | + | 3.46640e27i | 0.702921 | + | 1.06436i | ||||
\(565\) | 7.44184e27i | 2.24489i | ||||||||
\(566\) | 1.47181e27 | − | 4.42145e26i | 0.436202 | − | 0.131039i | ||||
\(567\) | − | 3.72249e27i | − | 1.08393i | ||||||
\(568\) | −1.18106e27 | − | 9.85343e26i | −0.337900 | − | 0.281906i | ||||
\(569\) | 1.91505e27 | 0.538340 | 0.269170 | − | 0.963093i | \(-0.413251\pi\) | ||||
0.269170 | + | 0.963093i | \(0.413251\pi\) | |||||||
\(570\) | 3.60583e26 | + | 1.20031e27i | 0.0995993 | + | 0.331546i | ||||
\(571\) | 9.26020e26 | 0.251339 | 0.125669 | − | 0.992072i | \(-0.459892\pi\) | ||||
0.125669 | + | 0.992072i | \(0.459892\pi\) | |||||||
\(572\) | −1.81906e27 | − | 2.75440e27i | −0.485161 | − | 0.734627i | ||||
\(573\) | − | 6.95129e27i | − | 1.82188i | ||||||
\(574\) | 9.06769e26 | + | 3.01845e27i | 0.233549 | + | 0.777437i | ||||
\(575\) | 5.49025e26i | 0.138968i | ||||||||
\(576\) | −8.21750e26 | − | 4.51087e27i | −0.204416 | − | 1.12211i | ||||
\(577\) | −8.98956e26 | −0.219776 | −0.109888 | − | 0.993944i | \(-0.535049\pi\) | ||||
−0.109888 | + | 0.993944i | \(0.535049\pi\) | |||||||
\(578\) | −1.25631e27 | + | 3.77406e26i | −0.301869 | + | 0.0906840i | ||||
\(579\) | 9.64912e27 | 2.27878 | ||||||||
\(580\) | −4.25491e27 | + | 2.81002e27i | −0.987666 | + | 0.652272i | ||||
\(581\) | − | 5.54267e27i | − | 1.26461i | ||||||
\(582\) | −5.88469e27 | + | 1.76781e27i | −1.31976 | + | 0.396466i | ||||
\(583\) | 6.61689e27i | 1.45871i | ||||||||
\(584\) | −4.50851e26 | + | 5.40403e26i | −0.0977023 | + | 0.117109i | ||||
\(585\) | −7.12478e27 | −1.51779 | ||||||||
\(586\) | −1.62045e27 | − | 5.39416e27i | −0.339360 | − | 1.12966i | ||||
\(587\) | 8.28104e26 | 0.170492 | 0.0852460 | − | 0.996360i | \(-0.472832\pi\) | ||||
0.0852460 | + | 0.996360i | \(0.472832\pi\) | |||||||
\(588\) | 4.01996e27 | − | 2.65486e27i | 0.813671 | − | 0.537363i | ||||
\(589\) | 5.84888e26i | 0.116391i | ||||||||
\(590\) | −1.84683e27 | − | 6.14773e27i | −0.361333 | − | 1.20280i | ||||
\(591\) | 1.49032e27i | 0.286685i | ||||||||
\(592\) | 2.41714e27 | + | 1.03185e27i | 0.457178 | + | 0.195164i | ||||
\(593\) | 2.16861e27 | 0.403306 | 0.201653 | − | 0.979457i | \(-0.435369\pi\) | ||||
0.201653 | + | 0.979457i | \(0.435369\pi\) | |||||||
\(594\) | 1.22743e27 | − | 3.68730e26i | 0.224456 | − | 0.0674285i | ||||
\(595\) | 1.41807e28 | 2.54993 | ||||||||
\(596\) | −5.97146e27 | − | 9.04194e27i | −1.05589 | − | 1.59882i | ||||
\(597\) | 1.46519e28i | 2.54772i | ||||||||
\(598\) | 3.05767e26 | − | 9.18552e25i | 0.0522852 | − | 0.0157069i | ||||
\(599\) | − | 6.16313e26i | − | 0.103641i | −0.998656 | − | 0.0518207i | \(-0.983498\pi\) | ||
0.998656 | − | 0.0518207i | \(-0.0165024\pi\) | |||||||
\(600\) | −1.11456e28 | + | 1.33594e28i | −1.84328 | + | 2.20941i | ||||
\(601\) | −8.17765e26 | −0.133010 | −0.0665049 | − | 0.997786i | \(-0.521185\pi\) | ||||
−0.0665049 | + | 0.997786i | \(0.521185\pi\) | |||||||
\(602\) | 2.79609e27 | + | 9.30763e27i | 0.447288 | + | 1.48893i | ||||
\(603\) | 6.73649e27 | 1.05989 | ||||||||
\(604\) | 4.67112e27 | + | 7.07298e27i | 0.722856 | + | 1.09454i | ||||
\(605\) | − | 3.37719e27i | − | 0.514046i | ||||||
\(606\) | −1.75908e27 | − | 5.85563e27i | −0.263366 | − | 0.876692i | ||||
\(607\) | 7.48374e27i | 1.10213i | 0.834463 | + | 0.551064i | \(0.185778\pi\) | ||||
−0.834463 | + | 0.551064i | \(0.814222\pi\) | |||||||
\(608\) | 1.05645e26 | − | 9.42390e26i | 0.0153042 | − | 0.136520i | ||||
\(609\) | −9.10783e27 | −1.29790 | ||||||||
\(610\) | 1.88175e28 | − | 5.65296e27i | 2.63794 | − | 0.792460i | ||||
\(611\) | −4.88416e27 | −0.673562 | ||||||||
\(612\) | 8.04515e27 | − | 5.31316e27i | 1.09149 | − | 0.720839i | ||||
\(613\) | − | 2.92871e27i | − | 0.390906i | −0.980713 | − | 0.195453i | \(-0.937382\pi\) | ||
0.980713 | − | 0.195453i | \(-0.0626177\pi\) | |||||||
\(614\) | 2.27582e27 | − | 6.83676e26i | 0.298850 | − | 0.0897773i | ||||
\(615\) | − | 1.22653e28i | − | 1.58463i | ||||||
\(616\) | −8.88590e27 | − | 7.41339e27i | −1.12952 | − | 0.942344i | ||||
\(617\) | 1.27218e28 | 1.59109 | 0.795547 | − | 0.605891i | \(-0.207183\pi\) | ||||
0.795547 | + | 0.605891i | \(0.207183\pi\) | |||||||
\(618\) | −1.89016e26 | − | 6.29196e26i | −0.0232602 | − | 0.0774286i | ||||
\(619\) | −1.60929e28 | −1.94863 | −0.974314 | − | 0.225195i | \(-0.927698\pi\) | ||||
−0.974314 | + | 0.225195i | \(0.927698\pi\) | |||||||
\(620\) | −1.02203e28 | + | 6.74965e27i | −1.21772 | + | 0.804201i | ||||
\(621\) | 1.23960e26i | 0.0145334i | ||||||||
\(622\) | 1.16326e27 | + | 3.87227e27i | 0.134207 | + | 0.446747i | ||||
\(623\) | 7.75862e27i | 0.880854i | ||||||||
\(624\) | 9.30496e27 | + | 3.97218e27i | 1.03961 | + | 0.443795i | ||||
\(625\) | 8.19518e27 | 0.901069 | ||||||||
\(626\) | −5.77240e27 | + | 1.73408e27i | −0.624616 | + | 0.187640i | ||||
\(627\) | 2.15060e27 | 0.229026 | ||||||||
\(628\) | −2.24283e27 | − | 3.39608e27i | −0.235072 | − | 0.355944i | ||||
\(629\) | 5.52635e27i | 0.570075i | ||||||||
\(630\) | −2.39222e28 | + | 7.18644e27i | −2.42882 | + | 0.729639i | ||||
\(631\) | − | 9.82154e27i | − | 0.981490i | −0.871303 | − | 0.490745i | \(-0.836725\pi\) | ||
0.871303 | − | 0.490745i | \(-0.163275\pi\) | |||||||
\(632\) | 3.08449e27 | + | 2.57335e27i | 0.303398 | + | 0.253121i | ||||
\(633\) | 9.23116e26 | 0.0893757 | ||||||||
\(634\) | 4.13493e27 | + | 1.37643e28i | 0.394072 | + | 1.31178i | ||||
\(635\) | −6.74332e27 | −0.632611 | ||||||||
\(636\) | −1.11766e28 | − | 1.69236e28i | −1.03214 | − | 1.56287i | ||||
\(637\) | 5.66412e27i | 0.514918i | ||||||||
\(638\) | 2.51737e27 | + | 8.37981e27i | 0.225289 | + | 0.749941i | ||||
\(639\) | 5.69691e27i | 0.501916i | ||||||||
\(640\) | 1.76864e28 | − | 9.02924e27i | 1.53405 | − | 0.783161i | ||||
\(641\) | 7.29542e27 | 0.622974 | 0.311487 | − | 0.950250i | \(-0.399173\pi\) | ||||
0.311487 | + | 0.950250i | \(0.399173\pi\) | |||||||
\(642\) | 1.64744e28 | − | 4.94906e27i | 1.38503 | − | 0.416076i | ||||
\(643\) | −3.08089e26 | −0.0255016 | −0.0127508 | − | 0.999919i | \(-0.504059\pi\) | ||||
−0.0127508 | + | 0.999919i | \(0.504059\pi\) | |||||||
\(644\) | 9.33994e26 | − | 6.16826e26i | 0.0761177 | − | 0.0502694i | ||||
\(645\) | − | 3.78210e28i | − | 3.03484i | ||||||
\(646\) | 1.90970e27 | − | 5.73691e26i | 0.150883 | − | 0.0453265i | ||||
\(647\) | − | 4.11006e27i | − | 0.319746i | −0.987138 | − | 0.159873i | \(-0.948891\pi\) | ||
0.987138 | − | 0.159873i | \(-0.0511085\pi\) | |||||||
\(648\) | 7.02186e27 | − | 8.41660e27i | 0.537900 | − | 0.644743i | ||||
\(649\) | −1.10150e28 | −0.830875 | ||||||||
\(650\) | −5.88527e27 | − | 1.95909e28i | −0.437153 | − | 1.45519i | ||||
\(651\) | −2.18770e28 | −1.60021 | ||||||||
\(652\) | −1.89758e28 | + | 1.25320e28i | −1.36686 | + | 0.902699i | ||||
\(653\) | 2.18243e28i | 1.54813i | 0.633105 | + | 0.774066i | \(0.281780\pi\) | ||||
−0.633105 | + | 0.774066i | \(0.718220\pi\) | |||||||
\(654\) | −8.23088e27 | − | 2.73989e28i | −0.575001 | − | 1.91406i | ||||
\(655\) | − | 1.19245e28i | − | 0.820405i | ||||||
\(656\) | −3.64358e27 | + | 8.53522e27i | −0.246882 | + | 0.578331i | ||||
\(657\) | 2.60666e27 | 0.173953 | ||||||||
\(658\) | −1.63990e28 | + | 4.92642e27i | −1.07785 | + | 0.323797i | ||||
\(659\) | −1.03384e28 | −0.669265 | −0.334632 | − | 0.942349i | \(-0.608612\pi\) | ||||
−0.334632 | + | 0.942349i | \(0.608612\pi\) | |||||||
\(660\) | 2.48181e28 | + | 3.75794e28i | 1.58245 | + | 2.39613i | ||||
\(661\) | − | 3.34206e27i | − | 0.209894i | −0.994478 | − | 0.104947i | \(-0.966533\pi\) | ||
0.994478 | − | 0.104947i | \(-0.0334672\pi\) | |||||||
\(662\) | 1.13938e28 | − | 3.42279e27i | 0.704834 | − | 0.211739i | ||||
\(663\) | 2.12741e28i | 1.29633i | ||||||||
\(664\) | 1.04553e28 | − | 1.25320e28i | 0.627561 | − | 0.752213i | ||||
\(665\) | −5.16602e27 | −0.305450 | ||||||||
\(666\) | −2.80062e27 | − | 9.32270e27i | −0.163122 | − | 0.543000i | ||||
\(667\) | −8.46295e26 | −0.0485583 | ||||||||
\(668\) | 7.90054e27 | + | 1.19629e28i | 0.446573 | + | 0.676197i | ||||
\(669\) | 5.47877e27i | 0.305086i | ||||||||
\(670\) | 8.39398e27 | + | 2.79418e28i | 0.460490 | + | 1.53288i | ||||
\(671\) | − | 3.37156e28i | − | 1.82224i | ||||||
\(672\) | 3.52489e28 | + | 3.95150e27i | 1.87695 | + | 0.210412i | ||||
\(673\) | −7.36345e27 | −0.386306 | −0.193153 | − | 0.981169i | \(-0.561871\pi\) | ||||
−0.193153 | + | 0.981169i | \(0.561871\pi\) | |||||||
\(674\) | −7.75632e27 | + | 2.33007e27i | −0.400919 | + | 0.120440i | ||||
\(675\) | 7.94229e27 | 0.404490 | ||||||||
\(676\) | 6.70297e27 | − | 4.42676e27i | 0.336357 | − | 0.222136i | ||||
\(677\) | 1.68918e28i | 0.835199i | 0.908631 | + | 0.417600i | \(0.137129\pi\) | ||||
−0.908631 | + | 0.417600i | \(0.862871\pi\) | |||||||
\(678\) | −3.74855e28 | + | 1.12610e28i | −1.82627 | + | 0.548629i | ||||
\(679\) | − | 2.53272e28i | − | 1.21588i | ||||||
\(680\) | 3.20627e28 | + | 2.67495e28i | 1.51674 | + | 1.26540i | ||||
\(681\) | 9.83853e27 | 0.458626 | ||||||||
\(682\) | 6.04672e27 | + | 2.01283e28i | 0.277764 | + | 0.924619i | ||||
\(683\) | 2.83245e28 | 1.28220 | 0.641100 | − | 0.767457i | \(-0.278478\pi\) | ||||
0.641100 | + | 0.767457i | \(0.278478\pi\) | |||||||
\(684\) | −2.93084e27 | + | 1.93558e27i | −0.130747 | + | 0.0863475i | ||||
\(685\) | − | 1.41004e28i | − | 0.619904i | ||||||
\(686\) | −2.85904e27 | − | 9.51716e27i | −0.123874 | − | 0.412350i | ||||
\(687\) | 3.03617e28i | 1.29646i | ||||||||
\(688\) | −1.12353e28 | + | 2.63190e28i | −0.472824 | + | 1.10761i | ||||
\(689\) | 2.38453e28 | 0.989034 | ||||||||
\(690\) | −4.17171e27 | + | 1.25322e27i | −0.170539 | + | 0.0512313i | ||||
\(691\) | 9.01687e26 | 0.0363308 | 0.0181654 | − | 0.999835i | \(-0.494217\pi\) | ||||
0.0181654 | + | 0.999835i | \(0.494217\pi\) | |||||||
\(692\) | −2.26800e28 | − | 3.43420e28i | −0.900705 | − | 1.36384i | ||||
\(693\) | 4.28616e28i | 1.67779i | ||||||||
\(694\) | 3.22782e28 | − | 9.69666e27i | 1.24542 | − | 0.374134i | ||||
\(695\) | 5.31982e28i | 2.02325i | ||||||||
\(696\) | −2.05929e28 | − | 1.71804e28i | −0.772014 | − | 0.644081i | ||||
\(697\) | −1.95142e28 | −0.721146 | ||||||||
\(698\) | −1.45540e28 | − | 4.84472e28i | −0.530185 | − | 1.76488i | ||||
\(699\) | −3.87425e28 | −1.39128 | ||||||||
\(700\) | −3.95208e28 | − | 5.98422e28i | −1.39909 | − | 2.11849i | ||||
\(701\) | − | 1.13211e28i | − | 0.395100i | −0.980293 | − | 0.197550i | \(-0.936702\pi\) | ||
0.980293 | − | 0.197550i | \(-0.0632985\pi\) | |||||||
\(702\) | −1.32879e27 | − | 4.42328e27i | −0.0457179 | − | 0.152186i | ||||
\(703\) | − | 2.01325e27i | − | 0.0682879i | ||||||
\(704\) | −6.10702e27 | − | 3.35235e28i | −0.204222 | − | 1.12104i | ||||
\(705\) | 6.66365e28 | 2.19696 | ||||||||
\(706\) | −1.59788e28 | + | 4.80018e27i | −0.519395 | + | 0.156031i | ||||
\(707\) | 2.52021e28 | 0.807687 | ||||||||
\(708\) | 2.81722e28 | − | 1.86054e28i | 0.890202 | − | 0.587905i | ||||
\(709\) | − | 5.95923e28i | − | 1.85664i | −0.371783 | − | 0.928320i | \(-0.621253\pi\) | ||
0.371783 | − | 0.928320i | \(-0.378747\pi\) | |||||||
\(710\) | −2.36298e28 | + | 7.09861e27i | −0.725901 | + | 0.218067i | ||||
\(711\) | − | 1.48782e28i | − | 0.450666i | ||||||
\(712\) | −1.46353e28 | + | 1.75423e28i | −0.437122 | + | 0.523947i | ||||
\(713\) | −2.03280e27 | −0.0598686 | ||||||||
\(714\) | 2.14582e28 | + | 7.14299e28i | 0.623176 | + | 2.07443i | ||||
\(715\) | −5.29494e28 | −1.51635 | ||||||||
\(716\) | −4.17604e28 | + | 2.75793e28i | −1.17933 | + | 0.778849i | ||||
\(717\) | − | 5.48707e27i | − | 0.152809i | ||||||
\(718\) | −1.59507e28 | − | 5.30966e28i | −0.438061 | − | 1.45822i | ||||
\(719\) | − | 2.54256e28i | − | 0.688623i | −0.938855 | − | 0.344312i | \(-0.888112\pi\) | ||
0.938855 | − | 0.344312i | \(-0.111888\pi\) | |||||||
\(720\) | −6.76443e28 | − | 2.88765e28i | −1.80678 | − | 0.771295i | ||||
\(721\) | 2.70801e27 | 0.0713341 | ||||||||
\(722\) | 3.61689e28 | − | 1.08655e28i | 0.939645 | − | 0.282278i | ||||
\(723\) | 1.04306e29 | 2.67256 | ||||||||
\(724\) | 8.26873e27 | + | 1.25205e28i | 0.208955 | + | 0.316399i | ||||
\(725\) | 5.42231e28i | 1.35146i | ||||||||
\(726\) | 1.70113e28 | − | 5.11036e27i | 0.418189 | − | 0.125628i | ||||
\(727\) | 4.74565e28i | 1.15067i | 0.817917 | + | 0.575337i | \(0.195129\pi\) | ||||
−0.817917 | + | 0.575337i | \(0.804871\pi\) | |||||||
\(728\) | −2.67157e28 | + | 3.20222e28i | −0.638928 | + | 0.765838i | ||||
\(729\) | −5.33541e28 | −1.25861 | ||||||||
\(730\) | 3.24802e27 | + | 1.08120e28i | 0.0755772 | + | 0.251581i | ||||
\(731\) | −6.01736e28 | −1.38112 | ||||||||
\(732\) | 5.69493e28 | + | 8.62322e28i | 1.28937 | + | 1.95236i | ||||
\(733\) | − | 3.45216e27i | − | 0.0770995i | −0.999257 | − | 0.0385498i | \(-0.987726\pi\) | ||
0.999257 | − | 0.0385498i | \(-0.0122738\pi\) | |||||||
\(734\) | 6.25486e27 | + | 2.08211e28i | 0.137802 | + | 0.458716i | ||||
\(735\) | − | 7.72780e28i | − | 1.67951i | ||||||
\(736\) | 3.27531e27 | + | 3.67172e26i | 0.0702222 | + | 0.00787211i | ||||
\(737\) | 5.00637e28 | 1.05888 | ||||||||
\(738\) | 3.29196e28 | − | 9.88933e27i | 0.686895 | − | 0.206349i | ||||
\(739\) | 6.30447e28 | 1.29779 | 0.648895 | − | 0.760878i | \(-0.275232\pi\) | ||||
0.648895 | + | 0.760878i | \(0.275232\pi\) | |||||||
\(740\) | 3.51793e28 | − | 2.32330e28i | 0.714447 | − | 0.471833i | ||||
\(741\) | − | 7.75013e27i | − | 0.155284i | ||||||
\(742\) | 8.00631e28 | − | 2.40517e28i | 1.58268 | − | 0.475452i | ||||
\(743\) | 1.06032e28i | 0.206799i | 0.994640 | + | 0.103400i | \(0.0329721\pi\) | ||||
−0.994640 | + | 0.103400i | \(0.967028\pi\) | |||||||
\(744\) | −4.94641e28 | − | 4.12673e28i | −0.951833 | − | 0.794102i | ||||
\(745\) | −1.73818e29 | −3.30014 | ||||||||
\(746\) | −1.20302e28 | − | 4.00460e28i | −0.225364 | − | 0.750190i | ||||
\(747\) | −6.04490e28 | −1.11733 | ||||||||
\(748\) | 5.97893e28 | − | 3.94859e28i | 1.09045 | − | 0.720155i | ||||
\(749\) | 7.09045e28i | 1.27601i | ||||||||
\(750\) | 3.94668e28 | + | 1.31377e29i | 0.700841 | + | 2.33296i | ||||
\(751\) | 1.67963e28i | 0.294316i | 0.989113 | + | 0.147158i | \(0.0470126\pi\) | ||||
−0.989113 | + | 0.147158i | \(0.952987\pi\) | |||||||
\(752\) | −4.63713e28 | − | 1.97953e28i | −0.801809 | − | 0.342283i | ||||
\(753\) | −1.15426e29 | −1.96948 | ||||||||
\(754\) | 3.01983e28 | − | 9.07185e27i | 0.508475 | − | 0.152750i | ||||
\(755\) | 1.35968e29 | 2.25926 | ||||||||
\(756\) | −8.92311e27 | − | 1.35113e28i | −0.146318 | − | 0.221554i | ||||
\(757\) | − | 3.68923e28i | − | 0.597003i | −0.954409 | − | 0.298502i | \(-0.903513\pi\) | ||
0.954409 | − | 0.298502i | \(-0.0964868\pi\) | |||||||
\(758\) | −6.01388e28 | + | 1.80662e28i | −0.960423 | + | 0.288520i | ||||
\(759\) | 7.47449e27i | 0.117805i | ||||||||
\(760\) | −1.16804e28 | − | 9.74482e27i | −0.181687 | − | 0.151579i | ||||
\(761\) | 7.29129e28 | 1.11933 | 0.559664 | − | 0.828719i | \(-0.310930\pi\) | ||||
0.559664 | + | 0.828719i | \(0.310930\pi\) | |||||||
\(762\) | −1.02040e28 | − | 3.39669e28i | −0.154604 | − | 0.514644i | ||||
\(763\) | 1.17923e29 | 1.76341 | ||||||||
\(764\) | 4.64949e28 | + | 7.04023e28i | 0.686234 | + | 1.03909i | ||||
\(765\) | − | 1.54656e29i | − | 2.25296i | ||||||
\(766\) | −1.66934e27 | − | 5.55688e27i | −0.0240025 | − | 0.0798994i | ||||
\(767\) | 3.96946e28i | 0.563350i | ||||||||
\(768\) | 7.22443e28 | + | 7.54255e28i | 1.01203 | + | 1.05659i | ||||
\(769\) | 1.07688e28 | 0.148904 | 0.0744519 | − | 0.997225i | \(-0.476279\pi\) | ||||
0.0744519 | + | 0.997225i | \(0.476279\pi\) | |||||||
\(770\) | −1.77783e29 | + | 5.34076e28i | −2.42651 | + | 0.728947i | ||||
\(771\) | −1.35065e29 | −1.81969 | ||||||||
\(772\) | −9.77259e28 | + | 6.45399e28i | −1.29968 | + | 0.858332i | ||||
\(773\) | − | 1.12471e29i | − | 1.47654i | −0.674503 | − | 0.738272i | \(-0.735642\pi\) | ||
0.674503 | − | 0.738272i | \(-0.264358\pi\) | |||||||
\(774\) | 1.01510e29 | − | 3.04945e28i | 1.31553 | − | 0.395196i | ||||
\(775\) | 1.30244e29i | 1.66625i | ||||||||
\(776\) | 4.77755e28 | − | 5.72651e28i | 0.603376 | − | 0.723224i | ||||
\(777\) | 7.53029e28 | 0.938862 | ||||||||
\(778\) | 7.56081e27 | + | 2.51684e28i | 0.0930620 | + | 0.309784i | ||||
\(779\) | 7.10901e27 | 0.0863843 | ||||||||
\(780\) | 1.35425e29 | − | 8.94372e28i | 1.62463 | − | 1.07293i | ||||
\(781\) | 4.23378e28i | 0.501439i | ||||||||
\(782\) | 1.99388e27 | + | 6.63723e27i | 0.0233148 | + | 0.0776103i | ||||
\(783\) | 1.22426e28i | 0.141338i | ||||||||
\(784\) | −2.29565e28 | + | 5.37765e28i | −0.261665 | + | 0.612960i | ||||
\(785\) | −6.52848e28 | −0.734709 | ||||||||
\(786\) | 6.00653e28 | − | 1.80442e28i | 0.667419 | − | 0.200499i | ||||
\(787\) | 5.39829e28 | 0.592255 | 0.296128 | − | 0.955148i | \(-0.404305\pi\) | ||||
0.296128 | + | 0.955148i | \(0.404305\pi\) | |||||||
\(788\) | −9.96829e27 | − | 1.50939e28i | −0.107984 | − | 0.163508i | ||||
\(789\) | 2.27706e29i | 2.43559i | ||||||||
\(790\) | 6.17124e28 | − | 1.85390e28i | 0.651781 | − | 0.195801i | ||||
\(791\) | − | 1.61334e29i | − | 1.68253i | ||||||
\(792\) | −8.08513e28 | + | 9.69107e28i | −0.832597 | + | 0.997975i | ||||
\(793\) | −1.21501e29 | −1.23552 | ||||||||
\(794\) | 1.30062e28 | + | 4.32951e28i | 0.130601 | + | 0.434745i | ||||
\(795\) | −3.25332e29 | −3.22593 | ||||||||
\(796\) | −9.80021e28 | − | 1.48394e29i | −0.959632 | − | 1.45307i | ||||
\(797\) | − | 7.35071e28i | − | 0.710798i | −0.934715 | − | 0.355399i | \(-0.884345\pi\) | ||
0.934715 | − | 0.355399i | \(-0.115655\pi\) | |||||||
\(798\) | −7.81720e27 | − | 2.60219e28i | −0.0746487 | − | 0.248490i | ||||
\(799\) | − | 1.06019e29i | − | 0.999810i | ||||||
\(800\) | 2.35251e28 | − | 2.09853e29i | 0.219095 | − | 1.95441i | ||||
\(801\) | 8.46164e28 | 0.778269 | ||||||||
\(802\) | −8.23416e28 | + | 2.47361e28i | −0.747955 | + | 0.224692i | ||||
\(803\) | 1.93720e28 | 0.173788 | ||||||||
\(804\) | −1.28045e29 | + | 8.45630e28i | −1.13449 | + | 0.749238i | ||||
\(805\) | − | 1.79547e28i | − | 0.157115i | ||||||
\(806\) | 7.25364e28 | − | 2.17906e28i | 0.626910 | − | 0.188330i | ||||
\(807\) | − | 2.88510e29i | − | 2.46278i | ||||||
\(808\) | 5.69823e28 | + | 4.75396e28i | 0.480426 | + | 0.400813i | ||||
\(809\) | 2.02377e29 | 1.68529 | 0.842646 | − | 0.538468i | \(-0.180997\pi\) | ||||
0.842646 | + | 0.538468i | \(0.180997\pi\) | |||||||
\(810\) | −5.05869e28 | − | 1.68393e29i | −0.416091 | − | 1.38508i | ||||
\(811\) | −1.16708e28 | −0.0948182 | −0.0474091 | − | 0.998876i | \(-0.515096\pi\) | ||||
−0.0474091 | + | 0.998876i | \(0.515096\pi\) | |||||||
\(812\) | 9.22437e28 | − | 6.09193e28i | 0.740246 | − | 0.488872i | ||||
\(813\) | 7.12422e28i | 0.564718i | ||||||||
\(814\) | −2.08134e28 | − | 6.92837e28i | −0.162967 | − | 0.542484i | ||||
\(815\) | 3.64783e29i | 2.82136i | ||||||||
\(816\) | −8.62233e28 | + | 2.01981e29i | −0.658753 | + | 1.54315i | ||||
\(817\) | 2.19212e28 | 0.165441 | ||||||||
\(818\) | −1.74837e29 | + | 5.25227e28i | −1.30347 | + | 0.391574i | ||||
\(819\) | 1.54461e29 | 1.13757 | ||||||||
\(820\) | 8.20386e28 | + | 1.24222e29i | 0.596870 | + | 0.903777i | ||||
\(821\) | 1.11995e29i | 0.804946i | 0.915432 | + | 0.402473i | \(0.131849\pi\) | ||||
−0.915432 | + | 0.402473i | \(0.868151\pi\) | |||||||
\(822\) | 7.10252e28 | − | 2.13366e28i | 0.504306 | − | 0.151498i | ||||
\(823\) | − | 1.93588e29i | − | 1.35794i | −0.734168 | − | 0.678968i | \(-0.762427\pi\) | ||
0.734168 | − | 0.678968i | \(-0.237573\pi\) | |||||||
\(824\) | 6.12284e27 | + | 5.10820e27i | 0.0424307 | + | 0.0353994i | ||||
\(825\) | 4.78900e29 | 3.27873 | ||||||||
\(826\) | 4.00381e28 | + | 1.33279e29i | 0.270815 | + | 0.901489i | ||||
\(827\) | −2.00807e29 | −1.34191 | −0.670956 | − | 0.741497i | \(-0.734116\pi\) | ||||
−0.670956 | + | 0.741497i | \(0.734116\pi\) | |||||||
\(828\) | −6.72718e27 | − | 1.01862e28i | −0.0444150 | − | 0.0672529i | ||||
\(829\) | 1.38032e29i | 0.900396i | 0.892929 | + | 0.450198i | \(0.148647\pi\) | ||||
−0.892929 | + | 0.450198i | \(0.851353\pi\) | |||||||
\(830\) | −7.53222e28 | − | 2.50732e29i | −0.485447 | − | 1.61596i | ||||
\(831\) | 1.49937e29i | 0.954771i | ||||||||
\(832\) | −1.20809e29 | + | 2.20079e28i | −0.760091 | + | 0.138467i | ||||
\(833\) | −1.22950e29 | −0.764326 | ||||||||
\(834\) | −2.67966e29 | + | 8.04993e28i | −1.64596 | + | 0.494461i | ||||
\(835\) | 2.29970e29 | 1.39575 | ||||||||
\(836\) | −2.17812e28 | + | 1.43847e28i | −0.130623 | + | 0.0862656i | ||||
\(837\) | 2.94068e28i | 0.174258i | ||||||||
\(838\) | −2.15245e29 | + | 6.46616e28i | −1.26036 | + | 0.378623i | ||||
\(839\) | 3.34163e29i | 1.93348i | 0.255767 | + | 0.966738i | \(0.417672\pi\) | ||||
−0.255767 | + | 0.966738i | \(0.582328\pi\) | |||||||
\(840\) | 3.64493e29 | − | 4.36892e29i | 2.08399 | − | 2.49793i | ||||
\(841\) | 9.34124e28 | 0.527770 | ||||||||
\(842\) | −8.26278e27 | − | 2.75051e28i | −0.0461323 | − | 0.153565i | ||||
\(843\) | −2.23822e29 | −1.23488 | ||||||||
\(844\) | −9.34928e27 | + | 6.17443e27i | −0.0509746 | + | 0.0336645i | ||||
\(845\) | − | 1.28855e29i | − | 0.694279i | ||||||
\(846\) | 5.37281e28 | + | 1.78850e29i | 0.286087 | + | 0.952325i | ||||
\(847\) | 7.32154e28i | 0.385273i | ||||||||
\(848\) | 2.26393e29 | + | 9.66445e28i | 1.17735 | + | 0.502596i | ||||
\(849\) | 1.29656e29 | 0.666370 | ||||||||
\(850\) | 4.25255e29 | − | 1.27751e29i | 2.16003 | − | 0.648894i | ||||
\(851\) | 6.99711e27 | 0.0351256 | ||||||||
\(852\) | −7.15132e28 | − | 1.08285e29i | −0.354805 | − | 0.537244i | ||||
\(853\) | − | 3.64380e29i | − | 1.78675i | −0.449311 | − | 0.893375i | \(-0.648331\pi\) | ||
0.449311 | − | 0.893375i | \(-0.351669\pi\) | |||||||
\(854\) | −4.07952e29 | + | 1.22553e29i | −1.97711 | + | 0.593941i | ||||
\(855\) | 5.63412e28i | 0.269876i | ||||||||
\(856\) | −1.33749e29 | + | 1.60316e29i | −0.633219 | + | 0.758995i | ||||
\(857\) | −1.92262e29 | −0.899676 | −0.449838 | − | 0.893110i | \(-0.648518\pi\) | ||||
−0.449838 | + | 0.893110i | \(0.648518\pi\) | |||||||
\(858\) | −8.01228e28 | − | 2.66713e29i | −0.370581 | − | 1.23359i | ||||
\(859\) | 3.17854e29 | 1.45310 | 0.726551 | − | 0.687113i | \(-0.241122\pi\) | ||||
0.726551 | + | 0.687113i | \(0.241122\pi\) | |||||||
\(860\) | 2.52972e29 | + | 3.83049e29i | 1.14311 | + | 1.73089i | ||||
\(861\) | 2.65904e29i | 1.18766i | ||||||||
\(862\) | 8.63879e28 | + | 2.87568e29i | 0.381400 | + | 1.26960i | ||||
\(863\) | − | 3.79268e29i | − | 1.65515i | −0.561353 | − | 0.827576i | \(-0.689719\pi\) | ||
0.561353 | − | 0.827576i | \(-0.310281\pi\) | |||||||
\(864\) | 5.31157e27 | − | 4.73812e28i | 0.0229132 | − | 0.204394i | ||||
\(865\) | −6.60174e29 | −2.81512 | ||||||||
\(866\) | 3.56550e29 | − | 1.07111e29i | 1.50294 | − | 0.451496i | ||||
\(867\) | −1.10672e29 | −0.461154 | ||||||||
\(868\) | 2.21569e29 | − | 1.46328e29i | 0.912666 | − | 0.602741i | ||||
\(869\) | − | 1.10571e29i | − | 0.450239i | ||||||
\(870\) | −4.12008e29 | + | 1.23771e29i | −1.65849 | + | 0.498226i | ||||
\(871\) | − | 1.80415e29i | − | 0.717944i | ||||||
\(872\) | 2.66625e29 | + | 2.22441e29i | 1.04890 | + | 0.875086i | ||||
\(873\) | −2.76221e29 | −1.07427 | ||||||||
\(874\) | −7.26370e26 | − | 2.41794e27i | −0.00279282 | − | 0.00929674i | ||||
\(875\) | −5.65436e29 | −2.14933 | ||||||||
\(876\) | −4.95465e28 | + | 3.27214e28i | −0.186197 | + | 0.122968i | ||||
\(877\) | 2.00911e29i | 0.746464i | 0.927738 | + | 0.373232i | \(0.121750\pi\) | ||||
−0.927738 | + | 0.373232i | \(0.878250\pi\) | |||||||
\(878\) | −1.64407e27 | − | 5.47277e27i | −0.00603914 | − | 0.0201031i | ||||
\(879\) | − | 4.75186e29i | − | 1.72574i | ||||||
\(880\) | −5.02714e29 | − | 2.14602e29i | −1.80507 | − | 0.770563i | ||||
\(881\) | 1.90398e29 | 0.675931 | 0.337966 | − | 0.941158i | \(-0.390261\pi\) | ||||
0.337966 | + | 0.941158i | \(0.390261\pi\) | |||||||
\(882\) | 2.07411e29 | − | 6.23081e28i | 0.728025 | − | 0.218705i | ||||
\(883\) | 5.19250e29 | 1.80206 | 0.901031 | − | 0.433755i | \(-0.142812\pi\) | ||||
0.901031 | + | 0.433755i | \(0.142812\pi\) | |||||||
\(884\) | −1.42296e29 | − | 2.15463e29i | −0.488280 | − | 0.739350i | ||||
\(885\) | − | 5.41570e29i | − | 1.83748i | ||||||
\(886\) | 3.79028e29 | − | 1.13864e29i | 1.27155 | − | 0.381986i | ||||
\(887\) | − | 4.92436e29i | − | 1.63348i | −0.577007 | − | 0.816739i | \(-0.695780\pi\) | ||
0.577007 | − | 0.816739i | \(-0.304220\pi\) | |||||||
\(888\) | 1.70261e29 | + | 1.42046e29i | 0.558451 | + | 0.465908i | ||||
\(889\) | 1.46191e29 | 0.474136 | ||||||||
\(890\) | 1.05436e29 | + | 3.50975e29i | 0.338134 | + | 1.12558i | ||||
\(891\) | −3.01712e29 | −0.956789 | ||||||||
\(892\) | −3.66457e28 | − | 5.54887e28i | −0.114914 | − | 0.174003i | ||||
\(893\) | 3.86228e28i | 0.119765i | ||||||||
\(894\) | −2.63021e29 | − | 8.75544e29i | −0.806521 | − | 2.68474i | ||||
\(895\) | 8.02784e29i | 2.43427i | ||||||||
\(896\) | −3.83430e29 | + | 1.95748e29i | −1.14976 | + | 0.586972i | ||||
\(897\) | 2.69359e28 | 0.0798742 | ||||||||
\(898\) | 2.49107e29 | − | 7.48339e28i | 0.730503 | − | 0.219450i | ||||
\(899\) | −2.00764e29 | −0.582224 | ||||||||
\(900\) | −6.52645e29 | + | 4.31019e29i | −1.87177 | + | 1.23615i | ||||
\(901\) | 5.17606e29i | 1.46809i | ||||||||
\(902\) | 2.44649e29 | − | 7.34948e28i | 0.686243 | − | 0.206154i | ||||
\(903\) | 8.19935e29i | 2.27458i | ||||||||
\(904\) | 3.04330e29 | − | 3.64779e29i | 0.834950 | − | 1.00080i | ||||
\(905\) | 2.40688e29 | 0.653083 | ||||||||
\(906\) | 2.05746e29 | + | 6.84886e29i | 0.552140 | + | 1.83796i | ||||
\(907\) | −4.29545e29 | −1.14008 | −0.570041 | − | 0.821617i | \(-0.693073\pi\) | ||||
−0.570041 | + | 0.821617i | \(0.693073\pi\) | |||||||
\(908\) | −9.96442e28 | + | 6.58068e28i | −0.261573 | + | 0.172748i | ||||
\(909\) | − | 2.74857e29i | − | 0.713623i | ||||||
\(910\) | 1.92465e29 | + | 6.40677e29i | 0.494240 | + | 1.64523i | ||||
\(911\) | − | 5.20927e29i | − | 1.32310i | −0.749900 | − | 0.661551i | \(-0.769899\pi\) | ||
0.749900 | − | 0.661551i | \(-0.230101\pi\) | |||||||
\(912\) | 3.14111e28 | − | 7.35816e28i | 0.0789104 | − | 0.184850i | ||||
\(913\) | −4.49240e29 | −1.11627 | ||||||||
\(914\) | 4.72715e29 | − | 1.42008e29i | 1.16182 | − | 0.349020i | ||||
\(915\) | 1.65769e30 | 4.02988 | ||||||||
\(916\) | −2.03080e29 | − | 3.07502e29i | −0.488328 | − | 0.739423i | ||||
\(917\) | 2.58516e29i | 0.614886i | ||||||||
\(918\) | 9.60153e28 | − | 2.88438e28i | 0.225899 | − | 0.0678620i | ||||
\(919\) | 7.91946e29i | 1.84306i | 0.388302 | + | 0.921532i | \(0.373062\pi\) | ||||
−0.388302 | + | 0.921532i | \(0.626938\pi\) | |||||||
\(920\) | 3.38685e28 | − | 4.05958e28i | 0.0779682 | − | 0.0934549i | ||||
\(921\) | 2.00483e29 | 0.456543 | ||||||||
\(922\) | 1.21390e29 | + | 4.04082e29i | 0.273447 | + | 0.910248i | ||||
\(923\) | 1.52573e29 | 0.339986 | ||||||||
\(924\) | −5.38041e29 | − | 8.14698e29i | −1.18603 | − | 1.79588i | ||||
\(925\) | − | 4.48314e29i | − | 0.977607i | ||||||
\(926\) | 7.76617e28 | + | 2.58520e29i | 0.167532 | + | 0.557679i | ||||
\(927\) | − | 2.95338e28i | − | 0.0630264i | ||||||
\(928\) | 3.23478e29 | + | 3.62628e28i | 0.682913 | + | 0.0765564i | ||||
\(929\) | −1.01853e29 | −0.212723 | −0.106362 | − | 0.994328i | \(-0.533920\pi\) | ||||
−0.106362 | + | 0.994328i | \(0.533920\pi\) | |||||||
\(930\) | −9.89644e29 | + | 2.97298e29i | −2.04479 | + | 0.614274i | ||||
\(931\) | 4.47906e28 | 0.0915567 | ||||||||
\(932\) | 3.92382e29 | − | 2.59136e29i | 0.793505 | − | 0.524045i | ||||
\(933\) | 3.41119e29i | 0.682479i | ||||||||
\(934\) | −2.28603e29 | + | 6.86744e28i | −0.452494 | + | 0.135933i | ||||
\(935\) | − | 1.14936e30i | − | 2.25082i | ||||||
\(936\) | 3.49237e29 | + | 2.91364e29i | 0.676647 | + | 0.564518i | ||||
\(937\) | 7.68737e28 | 0.147361 | 0.0736804 | − | 0.997282i | \(-0.476526\pi\) | ||||
0.0736804 | + | 0.997282i | \(0.476526\pi\) | |||||||
\(938\) | −1.81976e29 | − | 6.05761e29i | −0.345132 | − | 1.14888i | ||||
\(939\) | −5.08507e29 | −0.954203 | ||||||||
\(940\) | −6.74892e29 | + | 4.45710e29i | −1.25301 | + | 0.827512i | ||||
\(941\) | − | 7.80777e29i | − | 1.43427i | −0.696935 | − | 0.717135i | \(-0.745453\pi\) | ||
0.696935 | − | 0.717135i | \(-0.254547\pi\) | |||||||
\(942\) | −9.87887e28 | − | 3.28847e29i | −0.179555 | − | 0.597703i | ||||
\(943\) | 2.47076e28i | 0.0444339i | ||||||||
\(944\) | −1.60881e29 | + | 3.76870e29i | −0.286276 | + | 0.670613i | ||||
\(945\) | −2.59735e29 | −0.457313 | ||||||||
\(946\) | 7.54394e29 | − | 2.26627e29i | 1.31428 | − | 0.394821i | ||||
\(947\) | −1.92963e29 | −0.332640 | −0.166320 | − | 0.986072i | \(-0.553188\pi\) | ||||
−0.166320 | + | 0.986072i | \(0.553188\pi\) | |||||||
\(948\) | 1.86766e29 | + | 2.82800e29i | 0.318577 | + | 0.482387i | ||||
\(949\) | − | 6.98110e28i | − | 0.117832i | ||||||
\(950\) | −1.54920e29 | + | 4.65394e28i | −0.258745 | + | 0.0777293i | ||||
\(951\) | 1.21254e30i | 2.00396i | ||||||||
\(952\) | −6.95099e29 | − | 5.79912e29i | −1.13678 | − | 0.948402i | ||||
\(953\) | −9.13861e29 | −1.47894 | −0.739471 | − | 0.673188i | \(-0.764924\pi\) | ||||
−0.739471 | + | 0.673188i | \(0.764924\pi\) | |||||||
\(954\) | −2.62310e29 | − | 8.73178e29i | −0.420080 | − | 1.39836i | ||||
\(955\) | 1.35338e30 | 2.14480 | ||||||||
\(956\) | 3.67013e28 | + | 5.55728e28i | 0.0575576 | + | 0.0871533i | ||||
\(957\) | 7.38200e29i | 1.14566i | ||||||||
\(958\) | −9.82029e27 | − | 3.26897e28i | −0.0150824 | − | 0.0502061i | ||||
\(959\) | 3.05687e29i | 0.464612i | ||||||||
\(960\) | 1.64825e30 | − | 3.00263e29i | 2.47919 | − | 0.451637i | ||||
\(961\) | 1.89555e29 | 0.282163 | ||||||||
\(962\) | −2.49678e29 | + | 7.50055e28i | −0.367815 | + | 0.110495i | ||||
\(963\) | 7.73292e29 | 1.12741 | ||||||||
\(964\) | −1.05641e30 | + | 6.97671e29i | −1.52427 | + | 1.00665i | ||||
\(965\) | 1.87864e30i | 2.68269i | ||||||||
\(966\) | 9.04399e28 | − | 2.71690e28i | 0.127817 | − | 0.0383974i | ||||
\(967\) | − | 4.43207e28i | − | 0.0619929i | −0.999519 | − | 0.0309964i | \(-0.990132\pi\) | ||
0.999519 | − | 0.0309964i | \(-0.00986805\pi\) | |||||||
\(968\) | −1.38109e29 | + | 1.65541e29i | −0.191191 | + | 0.229167i | ||||
\(969\) | 1.68231e29 | 0.230498 | ||||||||
\(970\) | −3.44185e29 | − | 1.14572e30i | −0.466739 | − | 1.55368i | ||||
\(971\) | −5.27622e29 | −0.708159 | −0.354079 | − | 0.935215i | \(-0.615206\pi\) | ||||
−0.354079 | + | 0.935215i | \(0.615206\pi\) | |||||||
\(972\) | 9.00865e29 | − | 5.94947e29i | 1.19673 | − | 0.790343i | ||||
\(973\) | − | 1.15330e30i | − | 1.51640i | ||||||
\(974\) | −1.57717e29 | − | 5.25009e29i | −0.205253 | − | 0.683246i | ||||
\(975\) | − | 1.72581e30i | − | 2.22304i | ||||||
\(976\) | −1.15356e30 | − | 4.92441e29i | −1.47076 | − | 0.627850i | ||||
\(977\) | 6.09552e29 | 0.769246 | 0.384623 | − | 0.923074i | \(-0.374331\pi\) | ||||
0.384623 | + | 0.923074i | \(0.374331\pi\) | |||||||
\(978\) | −1.83745e30 | + | 5.51988e29i | −2.29524 | + | 0.689510i | ||||
\(979\) | 6.28846e29 | 0.777530 | ||||||||
\(980\) | 5.16888e29 | + | 7.82668e29i | 0.632609 | + | 0.957893i | ||||
\(981\) | − | 1.28608e30i | − | 1.55804i | ||||||
\(982\) | 3.85545e29 | − | 1.15821e29i | 0.462338 | − | 0.138891i | ||||
\(983\) | 7.31189e29i | 0.867949i | 0.900925 | + | 0.433975i | \(0.142889\pi\) | ||||
−0.900925 | + | 0.433975i | \(0.857111\pi\) | |||||||
\(984\) | −5.01582e29 | + | 6.01211e29i | −0.589375 | + | 0.706441i | ||||
\(985\) | −2.90159e29 | −0.337500 | ||||||||
\(986\) | 1.96921e29 | + | 6.55510e29i | 0.226737 | + | 0.754762i | ||||
\(987\) | −1.44464e30 | −1.64660 | ||||||||
\(988\) | 5.18382e28 | + | 7.84930e28i | 0.0584898 | + | 0.0885649i | ||||
\(989\) | 7.61879e28i | 0.0850987i | ||||||||
\(990\) | 5.82469e29 | + | 1.93892e30i | 0.644052 | + | 2.14392i | ||||
\(991\) | − | 2.35361e29i | − | 0.257631i | −0.991669 | − | 0.128816i | \(-0.958882\pi\) | ||
0.991669 | − | 0.128816i | \(-0.0411175\pi\) | |||||||
\(992\) | 7.76994e29 | + | 8.71032e28i | 0.841978 | + | 0.0943881i | ||||
\(993\) | 1.00371e30 | 1.07675 | ||||||||
\(994\) | 5.12280e29 | − | 1.53893e29i | 0.544056 | − | 0.163439i | ||||
\(995\) | −2.85266e30 | −2.99930 | ||||||||
\(996\) | 1.14899e30 | − | 7.58814e29i | 1.19598 | − | 0.789845i | ||||
\(997\) | − | 1.40218e30i | − | 1.44494i | −0.691400 | − | 0.722472i | \(-0.743006\pi\) | ||
0.691400 | − | 0.722472i | \(-0.256994\pi\) | |||||||
\(998\) | −3.44057e29 | + | 1.03358e29i | −0.351014 | + | 0.105448i | ||||
\(999\) | − | 1.01221e29i | − | 0.102239i |
(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 | 8.21.d.b.3.4 | yes | 18 | |
3.2 | odd | 2 | 72.21.b.b.19.15 | 18 | |||
4.3 | odd | 2 | 32.21.d.b.15.15 | 18 | |||
8.3 | odd | 2 | inner | 8.21.d.b.3.3 | ✓ | 18 | |
8.5 | even | 2 | 32.21.d.b.15.16 | 18 | |||
24.11 | even | 2 | 72.21.b.b.19.16 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.21.d.b.3.3 | ✓ | 18 | 8.3 | odd | 2 | inner | |
8.21.d.b.3.4 | yes | 18 | 1.1 | even | 1 | trivial | |
32.21.d.b.15.15 | 18 | 4.3 | odd | 2 | |||
32.21.d.b.15.16 | 18 | 8.5 | even | 2 | |||
72.21.b.b.19.15 | 18 | 3.2 | odd | 2 | |||
72.21.b.b.19.16 | 18 | 24.11 | even | 2 |