Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,19,Mod(3,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 19, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.3");
S:= CuspForms(chi, 19);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 19 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.c (of order \(4\), degree \(2\), 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: | \(20.5386137710\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 15200484 x^{8} + 52963214026118 x^{6} + \cdots + 20\!\cdots\!04 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{8}\cdot 5^{17} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.5 | ||
Root | \(2026.71i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.7 |
Dual form | 10.19.c.b.3.5 |
$q$-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 \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −256.000 | − | 256.000i | −0.500000 | − | 0.500000i | ||||
\(3\) | 21673.0 | − | 21673.0i | 1.10110 | − | 1.10110i | 0.106822 | − | 0.994278i | \(-0.465932\pi\) |
0.994278 | − | 0.106822i | \(-0.0340676\pi\) | |||||||
\(4\) | 131072.i | 0.500000i | ||||||||
\(5\) | 839560. | + | 1.76347e6i | 0.429855 | + | 0.902898i | ||||
\(6\) | −1.10966e7 | −1.10110 | ||||||||
\(7\) | −2.81596e7 | − | 2.81596e7i | −0.697821 | − | 0.697821i | 0.266119 | − | 0.963940i | \(-0.414259\pi\) |
−0.963940 | + | 0.266119i | \(0.914259\pi\) | |||||||
\(8\) | 3.35544e7 | − | 3.35544e7i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 5.52014e8i | − | 1.42484i | ||||||
\(10\) | 2.36522e8 | − | 6.66376e8i | 0.236522 | − | 0.666376i | ||||
\(11\) | −2.01016e9 | −0.852502 | −0.426251 | − | 0.904605i | \(-0.640166\pi\) | ||||
−0.426251 | + | 0.904605i | \(0.640166\pi\) | |||||||
\(12\) | 2.84072e9 | + | 2.84072e9i | 0.550550 | + | 0.550550i | ||||
\(13\) | 8.61354e9 | − | 8.61354e9i | 0.812253 | − | 0.812253i | −0.172718 | − | 0.984971i | \(-0.555255\pi\) |
0.984971 | + | 0.172718i | \(0.0552549\pi\) | |||||||
\(14\) | 1.44177e10i | 0.697821i | ||||||||
\(15\) | 5.64154e10 | + | 2.00239e10i | 1.46749 | + | 0.520868i | ||||
\(16\) | −1.71799e10 | −0.250000 | ||||||||
\(17\) | −1.24094e11 | − | 1.24094e11i | −1.04643 | − | 1.04643i | −0.998868 | − | 0.0475664i | \(-0.984853\pi\) |
−0.0475664 | − | 0.998868i | \(-0.515147\pi\) | |||||||
\(18\) | −1.41316e11 | + | 1.41316e11i | −0.712422 | + | 0.712422i | ||||
\(19\) | − | 4.61669e11i | − | 1.43070i | −0.698767 | − | 0.715349i | \(-0.746268\pi\) | ||
0.698767 | − | 0.715349i | \(-0.253732\pi\) | |||||||
\(20\) | −2.31142e11 | + | 1.10043e11i | −0.451449 | + | 0.214927i | ||||
\(21\) | −1.22060e12 | −1.53674 | ||||||||
\(22\) | 5.14600e11 | + | 5.14600e11i | 0.426251 | + | 0.426251i | ||||
\(23\) | −9.96769e11 | + | 9.96769e11i | −0.553406 | + | 0.553406i | −0.927422 | − | 0.374016i | \(-0.877981\pi\) |
0.374016 | + | 0.927422i | \(0.377981\pi\) | |||||||
\(24\) | − | 1.45445e12i | − | 0.550550i | ||||||
\(25\) | −2.40498e12 | + | 2.96108e12i | −0.630450 | + | 0.776230i | ||||
\(26\) | −4.41013e12 | −0.812253 | ||||||||
\(27\) | −3.56723e12 | − | 3.56723e12i | −0.467796 | − | 0.467796i | ||||
\(28\) | 3.69094e12 | − | 3.69094e12i | 0.348911 | − | 0.348911i | ||||
\(29\) | − | 1.38376e13i | − | 0.953848i | −0.878944 | − | 0.476924i | \(-0.841752\pi\) | ||
0.878944 | − | 0.476924i | \(-0.158248\pi\) | |||||||
\(30\) | −9.31622e12 | − | 1.95685e13i | −0.473313 | − | 0.994181i | ||||
\(31\) | −2.65717e13 | −1.00499 | −0.502497 | − | 0.864579i | \(-0.667585\pi\) | ||||
−0.502497 | + | 0.864579i | \(0.667585\pi\) | |||||||
\(32\) | 4.39805e12 | + | 4.39805e12i | 0.125000 | + | 0.125000i | ||||
\(33\) | −4.35660e13 | + | 4.35660e13i | −0.938691 | + | 0.938691i | ||||
\(34\) | 6.35364e13i | 1.04643i | ||||||||
\(35\) | 2.60170e13 | − | 7.33004e13i | 0.330100 | − | 0.930024i | ||||
\(36\) | 7.23536e13 | 0.712422 | ||||||||
\(37\) | 1.40030e14 | + | 1.40030e14i | 1.07747 | + | 1.07747i | 0.996735 | + | 0.0807371i | \(0.0257274\pi\) |
0.0807371 | + | 0.996735i | \(0.474273\pi\) | |||||||
\(38\) | −1.18187e14 | + | 1.18187e14i | −0.715349 | + | 0.715349i | ||||
\(39\) | − | 3.73362e14i | − | 1.78875i | ||||||
\(40\) | 8.73433e13 | + | 3.10014e13i | 0.333188 | + | 0.118261i | ||||
\(41\) | −8.98236e13 | −0.274370 | −0.137185 | − | 0.990545i | \(-0.543805\pi\) | ||||
−0.137185 | + | 0.990545i | \(0.543805\pi\) | |||||||
\(42\) | 3.12475e14 | + | 3.12475e14i | 0.768372 | + | 0.768372i | ||||
\(43\) | 3.06959e13 | − | 3.06959e13i | 0.0610752 | − | 0.0610752i | −0.675909 | − | 0.736985i | \(-0.736249\pi\) |
0.736985 | + | 0.675909i | \(0.236249\pi\) | |||||||
\(44\) | − | 2.63475e14i | − | 0.426251i | ||||||
\(45\) | 9.73461e14 | − | 4.63449e14i | 1.28649 | − | 0.612476i | ||||
\(46\) | 5.10346e14 | 0.553406 | ||||||||
\(47\) | 7.03769e14 | + | 7.03769e14i | 0.628853 | + | 0.628853i | 0.947780 | − | 0.318926i | \(-0.103322\pi\) |
−0.318926 | + | 0.947780i | \(0.603322\pi\) | |||||||
\(48\) | −3.72339e14 | + | 3.72339e14i | −0.275275 | + | 0.275275i | ||||
\(49\) | − | 4.24859e13i | − | 0.0260904i | ||||||
\(50\) | 1.37371e15 | − | 1.42363e14i | 0.703340 | − | 0.0728901i | ||||
\(51\) | −5.37899e15 | −2.30446 | ||||||||
\(52\) | 1.12899e15 | + | 1.12899e15i | 0.406127 | + | 0.406127i | ||||
\(53\) | −1.18441e15 | + | 1.18441e15i | −0.358939 | + | 0.358939i | −0.863422 | − | 0.504483i | \(-0.831683\pi\) |
0.504483 | + | 0.863422i | \(0.331683\pi\) | |||||||
\(54\) | 1.82642e15i | 0.467796i | ||||||||
\(55\) | −1.68765e15 | − | 3.54486e15i | −0.366452 | − | 0.769723i | ||||
\(56\) | −1.88976e15 | −0.348911 | ||||||||
\(57\) | −1.00057e16 | − | 1.00057e16i | −1.57534 | − | 1.57534i | ||||
\(58\) | −3.54243e15 | + | 3.54243e15i | −0.476924 | + | 0.476924i | ||||
\(59\) | − | 1.13913e16i | − | 1.31494i | −0.753481 | − | 0.657470i | \(-0.771627\pi\) | ||
0.753481 | − | 0.657470i | \(-0.228373\pi\) | |||||||
\(60\) | −2.62458e15 | + | 7.39448e15i | −0.260434 | + | 0.733747i | ||||
\(61\) | 1.79758e16 | 1.53716 | 0.768579 | − | 0.639754i | \(-0.220964\pi\) | ||||
0.768579 | + | 0.639754i | \(0.220964\pi\) | |||||||
\(62\) | 6.80234e15 | + | 6.80234e15i | 0.502497 | + | 0.502497i | ||||
\(63\) | −1.55445e16 | + | 1.55445e16i | −0.994287 | + | 0.994287i | ||||
\(64\) | − | 2.25180e15i | − | 0.125000i | ||||||
\(65\) | 2.24213e16 | + | 7.95816e15i | 1.08253 | + | 0.384231i | ||||
\(66\) | 2.23058e16 | 0.938691 | ||||||||
\(67\) | −3.42502e16 | − | 3.42502e16i | −1.25890 | − | 1.25890i | −0.951620 | − | 0.307276i | \(-0.900583\pi\) |
−0.307276 | − | 0.951620i | \(-0.599417\pi\) | |||||||
\(68\) | 1.62653e16 | − | 1.62653e16i | 0.523217 | − | 0.523217i | ||||
\(69\) | 4.32059e16i | 1.21871i | ||||||||
\(70\) | −2.54253e16 | + | 1.21045e16i | −0.630062 | + | 0.299962i | ||||
\(71\) | 1.84976e16 | 0.403451 | 0.201726 | − | 0.979442i | \(-0.435345\pi\) | ||||
0.201726 | + | 0.979442i | \(0.435345\pi\) | |||||||
\(72\) | −1.85225e16 | − | 1.85225e16i | −0.356211 | − | 0.356211i | ||||
\(73\) | 5.63444e16 | − | 5.63444e16i | 0.957074 | − | 0.957074i | −0.0420421 | − | 0.999116i | \(-0.513386\pi\) |
0.999116 | + | 0.0420421i | \(0.0133864\pi\) | |||||||
\(74\) | − | 7.16955e16i | − | 1.07747i | ||||||
\(75\) | 1.20525e16 | + | 1.16298e17i | 0.160519 | + | 1.54890i | ||||
\(76\) | 6.05118e16 | 0.715349 | ||||||||
\(77\) | 5.66052e16 | + | 5.66052e16i | 0.594895 | + | 0.594895i | ||||
\(78\) | −9.55806e16 | + | 9.55806e16i | −0.894373 | + | 0.894373i | ||||
\(79\) | 4.85160e16i | 0.404801i | 0.979303 | + | 0.202400i | \(0.0648742\pi\) | ||||
−0.979303 | + | 0.202400i | \(0.935126\pi\) | |||||||
\(80\) | −1.44235e16 | − | 3.02962e16i | −0.107464 | − | 0.225725i | ||||
\(81\) | 5.92368e16 | 0.394663 | ||||||||
\(82\) | 2.29948e16 | + | 2.29948e16i | 0.137185 | + | 0.137185i | ||||
\(83\) | −1.33052e16 | + | 1.33052e16i | −0.0711738 | + | 0.0711738i | −0.741798 | − | 0.670624i | \(-0.766026\pi\) |
0.670624 | + | 0.741798i | \(0.266026\pi\) | |||||||
\(84\) | − | 1.59987e17i | − | 0.768372i | ||||||
\(85\) | 1.14652e17 | − | 3.23022e17i | 0.495009 | − | 1.39464i | ||||
\(86\) | −1.57163e16 | −0.0610752 | ||||||||
\(87\) | −2.99902e17 | − | 2.99902e17i | −1.05028 | − | 1.05028i | ||||
\(88\) | −6.74497e16 | + | 6.74497e16i | −0.213126 | + | 0.213126i | ||||
\(89\) | 4.56446e17i | 1.30280i | 0.758733 | + | 0.651402i | \(0.225819\pi\) | ||||
−0.758733 | + | 0.651402i | \(0.774181\pi\) | |||||||
\(90\) | −3.67849e17 | − | 1.30563e17i | −0.949483 | − | 0.337007i | ||||
\(91\) | −4.85108e17 | −1.13362 | ||||||||
\(92\) | −1.30649e17 | − | 1.30649e17i | −0.276703 | − | 0.276703i | ||||
\(93\) | −5.75886e17 | + | 5.75886e17i | −1.10660 | + | 1.10660i | ||||
\(94\) | − | 3.60330e17i | − | 0.628853i | ||||||
\(95\) | 8.14140e17 | − | 3.87598e17i | 1.29177 | − | 0.614992i | ||||
\(96\) | 1.90637e17 | 0.275275 | ||||||||
\(97\) | 6.31856e17 | + | 6.31856e17i | 0.831136 | + | 0.831136i | 0.987672 | − | 0.156536i | \(-0.0500327\pi\) |
−0.156536 | + | 0.987672i | \(0.550033\pi\) | |||||||
\(98\) | −1.08764e16 | + | 1.08764e16i | −0.0130452 | + | 0.0130452i | ||||
\(99\) | 1.10963e18i | 1.21468i | ||||||||
\(100\) | −3.88115e17 | − | 3.15225e17i | −0.388115 | − | 0.315225i | ||||
\(101\) | −4.70951e17 | −0.430609 | −0.215305 | − | 0.976547i | \(-0.569074\pi\) | ||||
−0.215305 | + | 0.976547i | \(0.569074\pi\) | |||||||
\(102\) | 1.37702e18 | + | 1.37702e18i | 1.15223 | + | 1.15223i | ||||
\(103\) | 1.00486e18 | − | 1.00486e18i | 0.770145 | − | 0.770145i | −0.207987 | − | 0.978132i | \(-0.566691\pi\) |
0.978132 | + | 0.207987i | \(0.0666911\pi\) | |||||||
\(104\) | − | 5.78045e17i | − | 0.406127i | ||||||
\(105\) | −1.02477e18 | − | 2.15250e18i | −0.660576 | − | 1.38752i | ||||
\(106\) | 6.06419e17 | 0.358939 | ||||||||
\(107\) | −2.70418e17 | − | 2.70418e17i | −0.147089 | − | 0.147089i | 0.629727 | − | 0.776816i | \(-0.283167\pi\) |
−0.776816 | + | 0.629727i | \(0.783167\pi\) | |||||||
\(108\) | 4.67563e17 | − | 4.67563e17i | 0.233898 | − | 0.233898i | ||||
\(109\) | − | 7.79245e17i | − | 0.358786i | −0.983777 | − | 0.179393i | \(-0.942587\pi\) | ||
0.983777 | − | 0.179393i | \(-0.0574134\pi\) | |||||||
\(110\) | −4.75446e17 | + | 1.33952e18i | −0.201635 | + | 0.568088i | ||||
\(111\) | 6.06974e18 | 2.37281 | ||||||||
\(112\) | 4.83778e17 | + | 4.83778e17i | 0.174455 | + | 0.174455i | ||||
\(113\) | −1.20994e17 | + | 1.20994e17i | −0.0402772 | + | 0.0402772i | −0.726959 | − | 0.686681i | \(-0.759067\pi\) |
0.686681 | + | 0.726959i | \(0.259067\pi\) | |||||||
\(114\) | 5.12293e18i | 1.57534i | ||||||||
\(115\) | −2.59462e18 | − | 9.20928e17i | −0.737554 | − | 0.261785i | ||||
\(116\) | 1.81372e18 | 0.476924 | ||||||||
\(117\) | −4.75479e18 | − | 4.75479e18i | −1.15733 | − | 1.15733i | ||||
\(118\) | −2.91618e18 | + | 2.91618e18i | −0.657470 | + | 0.657470i | ||||
\(119\) | 6.98890e18i | 1.46045i | ||||||||
\(120\) | 2.56488e18 | − | 1.22110e18i | 0.497091 | − | 0.236657i | ||||
\(121\) | −1.51919e18 | −0.273240 | ||||||||
\(122\) | −4.60180e18 | − | 4.60180e18i | −0.768579 | − | 0.768579i | ||||
\(123\) | −1.94674e18 | + | 1.94674e18i | −0.302108 | + | 0.302108i | ||||
\(124\) | − | 3.48280e18i | − | 0.502497i | ||||||
\(125\) | −7.24091e18 | − | 1.75510e18i | −0.971858 | − | 0.235566i | ||||
\(126\) | 7.95878e18 | 0.994287 | ||||||||
\(127\) | −8.83476e18 | − | 8.83476e18i | −1.02792 | − | 1.02792i | −0.999599 | − | 0.0283254i | \(-0.990983\pi\) |
−0.0283254 | − | 0.999599i | \(-0.509017\pi\) | |||||||
\(128\) | −5.76461e17 | + | 5.76461e17i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 1.33054e18i | − | 0.134500i | ||||||
\(130\) | −3.70257e18 | − | 7.77715e18i | −0.349151 | − | 0.733382i | ||||
\(131\) | 1.51094e19 | 1.32986 | 0.664931 | − | 0.746905i | \(-0.268461\pi\) | ||||
0.664931 | + | 0.746905i | \(0.268461\pi\) | |||||||
\(132\) | −5.71029e18 | − | 5.71029e18i | −0.469345 | − | 0.469345i | ||||
\(133\) | −1.30004e19 | + | 1.30004e19i | −0.998372 | + | 0.998372i | ||||
\(134\) | 1.75361e19i | 1.25890i | ||||||||
\(135\) | 3.29581e18 | − | 9.28561e18i | 0.221288 | − | 0.623457i | ||||
\(136\) | −8.32784e18 | −0.523217 | ||||||||
\(137\) | 2.18638e19 | + | 2.18638e19i | 1.28600 | + | 1.28600i | 0.937195 | + | 0.348806i | \(0.113413\pi\) |
0.348806 | + | 0.937195i | \(0.386587\pi\) | |||||||
\(138\) | 1.10607e19 | − | 1.10607e19i | 0.609356 | − | 0.609356i | ||||
\(139\) | − | 9.45473e18i | − | 0.488108i | −0.969762 | − | 0.244054i | \(-0.921523\pi\) | ||
0.969762 | − | 0.244054i | \(-0.0784774\pi\) | |||||||
\(140\) | 9.60763e18 | + | 3.41010e18i | 0.465012 | + | 0.165050i | ||||
\(141\) | 3.05055e19 | 1.38486 | ||||||||
\(142\) | −4.73540e18 | − | 4.73540e18i | −0.201726 | − | 0.201726i | ||||
\(143\) | −1.73146e19 | + | 1.73146e19i | −0.692448 | + | 0.692448i | ||||
\(144\) | 9.48353e18i | 0.356211i | ||||||||
\(145\) | 2.44023e19 | − | 1.16175e19i | 0.861228 | − | 0.410016i | ||||
\(146\) | −2.88484e19 | −0.957074 | ||||||||
\(147\) | −9.20796e17 | − | 9.20796e17i | −0.0287281 | − | 0.0287281i | ||||
\(148\) | −1.83540e19 | + | 1.83540e19i | −0.538736 | + | 0.538736i | ||||
\(149\) | − | 7.57728e18i | − | 0.209333i | −0.994507 | − | 0.104666i | \(-0.966623\pi\) | ||
0.994507 | − | 0.104666i | \(-0.0333775\pi\) | |||||||
\(150\) | 2.66869e19 | − | 3.28578e19i | 0.694189 | − | 0.854707i | ||||
\(151\) | 4.54551e19 | 1.11376 | 0.556878 | − | 0.830594i | \(-0.311999\pi\) | ||||
0.556878 | + | 0.830594i | \(0.311999\pi\) | |||||||
\(152\) | −1.54910e19 | − | 1.54910e19i | −0.357674 | − | 0.357674i | ||||
\(153\) | −6.85019e19 | + | 6.85019e19i | −1.49101 | + | 1.49101i | ||||
\(154\) | − | 2.89819e19i | − | 0.594895i | ||||||
\(155\) | −2.23085e19 | − | 4.68584e19i | −0.432001 | − | 0.907407i | ||||
\(156\) | 4.89373e19 | 0.894373 | ||||||||
\(157\) | 3.39679e19 | + | 3.39679e19i | 0.586099 | + | 0.586099i | 0.936573 | − | 0.350473i | \(-0.113979\pi\) |
−0.350473 | + | 0.936573i | \(0.613979\pi\) | |||||||
\(158\) | 1.24201e19 | − | 1.24201e19i | 0.202400 | − | 0.202400i | ||||
\(159\) | 5.13395e19i | 0.790455i | ||||||||
\(160\) | −4.06341e18 | + | 1.14483e19i | −0.0591304 | + | 0.166594i | ||||
\(161\) | 5.61373e19 | 0.772358 | ||||||||
\(162\) | −1.51646e19 | − | 1.51646e19i | −0.197332 | − | 0.197332i | ||||
\(163\) | 2.84690e19 | − | 2.84690e19i | 0.350497 | − | 0.350497i | −0.509798 | − | 0.860294i | \(-0.670280\pi\) |
0.860294 | + | 0.509798i | \(0.170280\pi\) | |||||||
\(164\) | − | 1.17734e19i | − | 0.137185i | ||||||
\(165\) | −1.13404e20 | − | 4.02512e19i | −1.25104 | − | 0.444041i | ||||
\(166\) | 6.81229e18 | 0.0711738 | ||||||||
\(167\) | −3.24829e19 | − | 3.24829e19i | −0.321519 | − | 0.321519i | 0.527831 | − | 0.849350i | \(-0.323006\pi\) |
−0.849350 | + | 0.527831i | \(0.823006\pi\) | |||||||
\(168\) | −4.09567e19 | + | 4.09567e19i | −0.384186 | + | 0.384186i | ||||
\(169\) | − | 3.59308e19i | − | 0.319511i | ||||||
\(170\) | −1.12045e20 | + | 5.33426e19i | −0.944824 | + | 0.449815i | ||||
\(171\) | −2.54847e20 | −2.03852 | ||||||||
\(172\) | 4.02338e18 | + | 4.02338e18i | 0.0305376 | + | 0.0305376i | ||||
\(173\) | 4.31333e19 | − | 4.31333e19i | 0.310741 | − | 0.310741i | −0.534456 | − | 0.845196i | \(-0.679483\pi\) |
0.845196 | + | 0.534456i | \(0.179483\pi\) | |||||||
\(174\) | 1.53550e20i | 1.05028i | ||||||||
\(175\) | 1.51106e20 | − | 1.56598e19i | 0.981611 | − | 0.101729i | ||||
\(176\) | 3.45342e19 | 0.213126 | ||||||||
\(177\) | −2.46884e20 | − | 2.46884e20i | −1.44788 | − | 1.44788i | ||||
\(178\) | 1.16850e20 | − | 1.16850e20i | 0.651402 | − | 0.651402i | ||||
\(179\) | 6.14185e19i | 0.325553i | 0.986663 | + | 0.162777i | \(0.0520450\pi\) | ||||
−0.986663 | + | 0.162777i | \(0.947955\pi\) | |||||||
\(180\) | 6.07452e19 | + | 1.27594e20i | 0.306238 | + | 0.643245i | ||||
\(181\) | −1.18309e20 | −0.567430 | −0.283715 | − | 0.958909i | \(-0.591567\pi\) | ||||
−0.283715 | + | 0.958909i | \(0.591567\pi\) | |||||||
\(182\) | 1.24188e20 | + | 1.24188e20i | 0.566808 | + | 0.566808i | ||||
\(183\) | 3.89588e20 | − | 3.89588e20i | 1.69257 | − | 1.69257i | ||||
\(184\) | 6.68921e19i | 0.276703i | ||||||||
\(185\) | −1.29376e20 | + | 3.64503e20i | −0.509691 | + | 1.43600i | ||||
\(186\) | 2.94854e20 | 1.10660 | ||||||||
\(187\) | 2.49449e20 | + | 2.49449e20i | 0.892088 | + | 0.892088i | ||||
\(188\) | −9.22444e19 | + | 9.22444e19i | −0.314427 | + | 0.314427i | ||||
\(189\) | 2.00903e20i | 0.652877i | ||||||||
\(190\) | −3.07645e20 | − | 1.09195e20i | −0.953383 | − | 0.338391i | ||||
\(191\) | 3.91502e20 | 1.15727 | 0.578634 | − | 0.815588i | \(-0.303586\pi\) | ||||
0.578634 | + | 0.815588i | \(0.303586\pi\) | |||||||
\(192\) | −4.88032e19 | − | 4.88032e19i | −0.137638 | − | 0.137638i | ||||
\(193\) | −1.22942e20 | + | 1.22942e20i | −0.330891 | + | 0.330891i | −0.852925 | − | 0.522034i | \(-0.825174\pi\) |
0.522034 | + | 0.852925i | \(0.325174\pi\) | |||||||
\(194\) | − | 3.23510e20i | − | 0.831136i | ||||||
\(195\) | 6.58413e20 | − | 3.13460e20i | 1.61505 | − | 0.768901i | ||||
\(196\) | 5.56872e18 | 0.0130452 | ||||||||
\(197\) | 1.46541e20 | + | 1.46541e20i | 0.327917 | + | 0.327917i | 0.851794 | − | 0.523877i | \(-0.175515\pi\) |
−0.523877 | + | 0.851794i | \(0.675515\pi\) | |||||||
\(198\) | 2.84066e20 | − | 2.84066e20i | 0.607342 | − | 0.607342i | ||||
\(199\) | − | 6.13745e20i | − | 1.25404i | −0.779005 | − | 0.627018i | \(-0.784275\pi\) | ||
0.779005 | − | 0.627018i | \(-0.215725\pi\) | |||||||
\(200\) | 1.86599e19 | + | 1.80055e20i | 0.0364450 | + | 0.351670i | ||||
\(201\) | −1.48461e21 | −2.77234 | ||||||||
\(202\) | 1.20563e20 | + | 1.20563e20i | 0.215305 | + | 0.215305i | ||||
\(203\) | −3.89662e20 | + | 3.89662e20i | −0.665616 | + | 0.665616i | ||||
\(204\) | − | 7.05035e20i | − | 1.15223i | ||||||
\(205\) | −7.54123e19 | − | 1.58402e20i | −0.117939 | − | 0.247728i | ||||
\(206\) | −5.14491e20 | −0.770145 | ||||||||
\(207\) | 5.50231e20 | + | 5.50231e20i | 0.788518 | + | 0.788518i | ||||
\(208\) | −1.47979e20 | + | 1.47979e20i | −0.203063 | + | 0.203063i | ||||
\(209\) | 9.28026e20i | 1.21967i | ||||||||
\(210\) | −2.88699e20 | + | 8.13382e20i | −0.363473 | + | 1.02405i | ||||
\(211\) | −3.98223e20 | −0.480379 | −0.240190 | − | 0.970726i | \(-0.577210\pi\) | ||||
−0.240190 | + | 0.970726i | \(0.577210\pi\) | |||||||
\(212\) | −1.55243e20 | − | 1.55243e20i | −0.179469 | − | 0.179469i | ||||
\(213\) | 4.00899e20 | − | 4.00899e20i | 0.444241 | − | 0.444241i | ||||
\(214\) | 1.38454e20i | 0.147089i | ||||||||
\(215\) | 7.99025e19 | + | 2.83604e19i | 0.0813981 | + | 0.0288912i | ||||
\(216\) | −2.39392e20 | −0.233898 | ||||||||
\(217\) | 7.48247e20 | + | 7.48247e20i | 0.701306 | + | 0.701306i | ||||
\(218\) | −1.99487e20 | + | 1.99487e20i | −0.179393 | + | 0.179393i | ||||
\(219\) | − | 2.44230e21i | − | 2.10767i | ||||||
\(220\) | 4.64631e20 | − | 2.21203e20i | 0.384861 | − | 0.183226i | ||||
\(221\) | −2.13779e21 | −1.69994 | ||||||||
\(222\) | −1.55385e21 | − | 1.55385e21i | −1.18641 | − | 1.18641i | ||||
\(223\) | −1.16848e20 | + | 1.16848e20i | −0.0856793 | + | 0.0856793i | −0.748648 | − | 0.662968i | \(-0.769296\pi\) |
0.662968 | + | 0.748648i | \(0.269296\pi\) | |||||||
\(224\) | − | 2.47695e20i | − | 0.174455i | ||||||
\(225\) | 1.63456e21 | + | 1.32758e21i | 1.10601 | + | 0.898293i | ||||
\(226\) | 6.19491e19 | 0.0402772 | ||||||||
\(227\) | 7.21268e20 | + | 7.21268e20i | 0.450676 | + | 0.450676i | 0.895579 | − | 0.444903i | \(-0.146762\pi\) |
−0.444903 | + | 0.895579i | \(0.646762\pi\) | |||||||
\(228\) | 1.31147e21 | − | 1.31147e21i | 0.787671 | − | 0.787671i | ||||
\(229\) | − | 3.25492e21i | − | 1.87941i | −0.341987 | − | 0.939705i | \(-0.611100\pi\) | ||
0.341987 | − | 0.939705i | \(-0.388900\pi\) | |||||||
\(230\) | 4.28466e20 | + | 8.99981e20i | 0.237884 | + | 0.499670i | ||||
\(231\) | 2.45361e21 | 1.31008 | ||||||||
\(232\) | −4.64313e20 | − | 4.64313e20i | −0.238462 | − | 0.238462i | ||||
\(233\) | −2.39551e21 | + | 2.39551e21i | −1.18357 | + | 1.18357i | −0.204759 | + | 0.978812i | \(0.565641\pi\) |
−0.978812 | + | 0.204759i | \(0.934359\pi\) | |||||||
\(234\) | 2.43445e21i | 1.15733i | ||||||||
\(235\) | −6.50221e20 | + | 1.83193e21i | −0.297475 | + | 0.838106i | ||||
\(236\) | 1.49308e21 | 0.657470 | ||||||||
\(237\) | 1.05149e21 | + | 1.05149e21i | 0.445726 | + | 0.445726i | ||||
\(238\) | 1.78916e21 | − | 1.78916e21i | 0.730224 | − | 0.730224i | ||||
\(239\) | 2.96344e21i | 1.16470i | 0.812937 | + | 0.582351i | \(0.197867\pi\) | ||||
−0.812937 | + | 0.582351i | \(0.802133\pi\) | |||||||
\(240\) | −9.69210e20 | − | 3.44008e20i | −0.366874 | − | 0.130217i | ||||
\(241\) | 3.77663e20 | 0.137705 | 0.0688527 | − | 0.997627i | \(-0.478066\pi\) | ||||
0.0688527 | + | 0.997627i | \(0.478066\pi\) | |||||||
\(242\) | 3.88912e20 | + | 3.88912e20i | 0.136620 | + | 0.136620i | ||||
\(243\) | 2.66585e21 | − | 2.66585e21i | 0.902360 | − | 0.902360i | ||||
\(244\) | 2.35612e21i | 0.768579i | ||||||||
\(245\) | 7.49228e19 | − | 3.56695e19i | 0.0235570 | − | 0.0112151i | ||||
\(246\) | 9.96733e20 | 0.302108 | ||||||||
\(247\) | −3.97660e21 | − | 3.97660e21i | −1.16209 | − | 1.16209i | ||||
\(248\) | −8.91597e20 | + | 8.91597e20i | −0.251248 | + | 0.251248i | ||||
\(249\) | 5.76728e20i | 0.156739i | ||||||||
\(250\) | 1.40437e21 | + | 2.30298e21i | 0.368146 | + | 0.603712i | ||||
\(251\) | 8.95398e20 | 0.226440 | 0.113220 | − | 0.993570i | \(-0.463884\pi\) | ||||
0.113220 | + | 0.993570i | \(0.463884\pi\) | |||||||
\(252\) | −2.03745e21 | − | 2.03745e21i | −0.497143 | − | 0.497143i | ||||
\(253\) | 2.00366e21 | − | 2.00366e21i | 0.471780 | − | 0.471780i | ||||
\(254\) | 4.52339e21i | 1.02792i | ||||||||
\(255\) | −4.51598e21 | − | 9.48570e21i | −0.990583 | − | 2.08069i | ||||
\(256\) | 2.95148e20 | 0.0625000 | ||||||||
\(257\) | 2.44830e21 | + | 2.44830e21i | 0.500571 | + | 0.500571i | 0.911615 | − | 0.411044i | \(-0.134836\pi\) |
−0.411044 | + | 0.911615i | \(0.634836\pi\) | |||||||
\(258\) | −3.40619e20 | + | 3.40619e20i | −0.0672499 | + | 0.0672499i | ||||
\(259\) | − | 7.88639e21i | − | 1.50377i | ||||||
\(260\) | −1.04309e21 | + | 2.93881e21i | −0.192116 | + | 0.541266i | ||||
\(261\) | −7.63856e21 | −1.35909 | ||||||||
\(262\) | −3.86801e21 | − | 3.86801e21i | −0.664931 | − | 0.664931i | ||||
\(263\) | −4.66735e21 | + | 4.66735e21i | −0.775298 | + | 0.775298i | −0.979027 | − | 0.203729i | \(-0.934694\pi\) |
0.203729 | + | 0.979027i | \(0.434694\pi\) | |||||||
\(264\) | 2.92367e21i | 0.469345i | ||||||||
\(265\) | −3.08307e21 | − | 1.09429e21i | −0.478377 | − | 0.169794i | ||||
\(266\) | 6.65621e21 | 0.998372 | ||||||||
\(267\) | 9.89253e21 | + | 9.89253e21i | 1.43452 | + | 1.43452i | ||||
\(268\) | 4.48924e21 | − | 4.48924e21i | 0.629448 | − | 0.629448i | ||||
\(269\) | − | 1.31883e21i | − | 0.178821i | −0.995995 | − | 0.0894107i | \(-0.971502\pi\) | ||
0.995995 | − | 0.0894107i | \(-0.0284984\pi\) | |||||||
\(270\) | −3.22084e21 | + | 1.53339e21i | −0.422372 | + | 0.201084i | ||||
\(271\) | 6.33690e20 | 0.0803810 | 0.0401905 | − | 0.999192i | \(-0.487204\pi\) | ||||
0.0401905 | + | 0.999192i | \(0.487204\pi\) | |||||||
\(272\) | 2.13193e21 | + | 2.13193e21i | 0.261609 | + | 0.261609i | ||||
\(273\) | −1.05137e22 | + | 1.05137e22i | −1.24822 | + | 1.24822i | ||||
\(274\) | − | 1.11943e22i | − | 1.28600i | ||||||
\(275\) | 4.83438e21 | − | 5.95224e21i | 0.537460 | − | 0.661738i | ||||
\(276\) | −5.66308e21 | −0.609356 | ||||||||
\(277\) | −6.90617e20 | − | 6.90617e20i | −0.0719315 | − | 0.0719315i | 0.670226 | − | 0.742157i | \(-0.266197\pi\) |
−0.742157 | + | 0.670226i | \(0.766197\pi\) | |||||||
\(278\) | −2.42041e21 | + | 2.42041e21i | −0.244054 | + | 0.244054i | ||||
\(279\) | 1.46679e22i | 1.43196i | ||||||||
\(280\) | −1.58657e21 | − | 3.33254e21i | −0.149981 | − | 0.315031i | ||||
\(281\) | −4.40026e21 | −0.402830 | −0.201415 | − | 0.979506i | \(-0.564554\pi\) | ||||
−0.201415 | + | 0.979506i | \(0.564554\pi\) | |||||||
\(282\) | −7.80941e21 | − | 7.80941e21i | −0.692431 | − | 0.692431i | ||||
\(283\) | −5.52989e21 | + | 5.52989e21i | −0.474939 | + | 0.474939i | −0.903509 | − | 0.428569i | \(-0.859018\pi\) |
0.428569 | + | 0.903509i | \(0.359018\pi\) | |||||||
\(284\) | 2.42452e21i | 0.201726i | ||||||||
\(285\) | 9.24442e21 | − | 2.60452e22i | 0.745205 | − | 2.09954i | ||||
\(286\) | 8.86506e21 | 0.692448 | ||||||||
\(287\) | 2.52940e21 | + | 2.52940e21i | 0.191461 | + | 0.191461i | ||||
\(288\) | 2.42778e21 | − | 2.42778e21i | 0.178106 | − | 0.178106i | ||||
\(289\) | 1.67358e22i | 1.19005i | ||||||||
\(290\) | −9.22106e21 | − | 3.27290e21i | −0.635622 | − | 0.225606i | ||||
\(291\) | 2.73884e22 | 1.83033 | ||||||||
\(292\) | 7.38518e21 | + | 7.38518e21i | 0.478537 | + | 0.478537i | ||||
\(293\) | 7.93653e21 | − | 7.93653e21i | 0.498680 | − | 0.498680i | −0.412347 | − | 0.911027i | \(-0.635291\pi\) |
0.911027 | + | 0.412347i | \(0.135291\pi\) | |||||||
\(294\) | 4.71448e20i | 0.0287281i | ||||||||
\(295\) | 2.00883e22 | − | 9.56370e21i | 1.18726 | − | 0.565233i | ||||
\(296\) | 9.39727e21 | 0.538736 | ||||||||
\(297\) | 7.17068e21 | + | 7.17068e21i | 0.398797 | + | 0.398797i | ||||
\(298\) | −1.93978e21 | + | 1.93978e21i | −0.104666 | + | 0.104666i | ||||
\(299\) | 1.71714e22i | 0.899012i | ||||||||
\(300\) | −1.52435e22 | + | 1.57974e21i | −0.774448 | + | 0.0802593i | ||||
\(301\) | −1.72877e21 | −0.0852392 | ||||||||
\(302\) | −1.16365e22 | − | 1.16365e22i | −0.556878 | − | 0.556878i | ||||
\(303\) | −1.02069e22 | + | 1.02069e22i | −0.474144 | + | 0.474144i | ||||
\(304\) | 7.93141e21i | 0.357674i | ||||||||
\(305\) | 1.50917e22 | + | 3.16998e22i | 0.660755 | + | 1.38790i | ||||
\(306\) | 3.50730e22 | 1.49101 | ||||||||
\(307\) | −2.17651e22 | − | 2.17651e22i | −0.898495 | − | 0.898495i | 0.0968085 | − | 0.995303i | \(-0.469137\pi\) |
−0.995303 | + | 0.0968085i | \(0.969137\pi\) | |||||||
\(308\) | −7.41936e21 | + | 7.41936e21i | −0.297447 | + | 0.297447i | ||||
\(309\) | − | 4.35568e22i | − | 1.69601i | ||||||
\(310\) | −6.28477e21 | + | 1.77067e22i | −0.237703 | + | 0.669704i | ||||
\(311\) | −1.64905e22 | −0.605885 | −0.302943 | − | 0.953009i | \(-0.597969\pi\) | ||||
−0.302943 | + | 0.953009i | \(0.597969\pi\) | |||||||
\(312\) | −1.25279e22 | − | 1.25279e22i | −0.447186 | − | 0.447186i | ||||
\(313\) | 8.39391e21 | − | 8.39391e21i | 0.291116 | − | 0.291116i | −0.546405 | − | 0.837521i | \(-0.684004\pi\) |
0.837521 | + | 0.546405i | \(0.184004\pi\) | |||||||
\(314\) | − | 1.73915e22i | − | 0.586099i | ||||||
\(315\) | −4.04628e22 | − | 1.43618e22i | −1.32514 | − | 0.470341i | ||||
\(316\) | −6.35909e21 | −0.202400 | ||||||||
\(317\) | −1.53965e22 | − | 1.53965e22i | −0.476310 | − | 0.476310i | 0.427640 | − | 0.903949i | \(-0.359345\pi\) |
−0.903949 | + | 0.427640i | \(0.859345\pi\) | |||||||
\(318\) | 1.31429e22 | − | 1.31429e22i | 0.395228 | − | 0.395228i | ||||
\(319\) | 2.78158e22i | 0.813158i | ||||||||
\(320\) | 3.97099e21 | − | 1.89052e21i | 0.112862 | − | 0.0537318i | ||||
\(321\) | −1.17215e22 | −0.323921 | ||||||||
\(322\) | −1.43711e22 | − | 1.43711e22i | −0.386179 | − | 0.386179i | ||||
\(323\) | −5.72905e22 | + | 5.72905e22i | −1.49713 | + | 1.49713i | ||||
\(324\) | 7.76429e21i | 0.197332i | ||||||||
\(325\) | 4.79005e21 | + | 4.62208e22i | 0.118410 | + | 1.14258i | ||||
\(326\) | −1.45761e22 | −0.350497 | ||||||||
\(327\) | −1.68885e22 | − | 1.68885e22i | −0.395059 | − | 0.395059i | ||||
\(328\) | −3.01398e21 | + | 3.01398e21i | −0.0685924 | + | 0.0685924i | ||||
\(329\) | − | 3.96357e22i | − | 0.877655i | ||||||
\(330\) | 1.87271e22 | + | 3.93357e22i | 0.403501 | + | 0.847542i | ||||
\(331\) | −2.29878e22 | −0.481998 | −0.240999 | − | 0.970525i | \(-0.577475\pi\) | ||||
−0.240999 | + | 0.970525i | \(0.577475\pi\) | |||||||
\(332\) | −1.74395e21 | − | 1.74395e21i | −0.0355869 | − | 0.0355869i | ||||
\(333\) | 7.72986e22 | − | 7.72986e22i | 1.53523 | − | 1.53523i | ||||
\(334\) | 1.66312e22i | 0.321519i | ||||||||
\(335\) | 3.16442e22 | − | 8.91544e22i | 0.595513 | − | 1.67780i | ||||
\(336\) | 2.09698e22 | 0.384186 | ||||||||
\(337\) | 6.20976e22 | + | 6.20976e22i | 1.10766 | + | 1.10766i | 0.993458 | + | 0.114201i | \(0.0364308\pi\) |
0.114201 | + | 0.993458i | \(0.463569\pi\) | |||||||
\(338\) | −9.19827e21 | + | 9.19827e21i | −0.159756 | + | 0.159756i | ||||
\(339\) | 5.24461e21i | 0.0886985i | ||||||||
\(340\) | 4.23391e22 | + | 1.50277e22i | 0.697319 | + | 0.247504i | ||||
\(341\) | 5.34132e22 | 0.856760 | ||||||||
\(342\) | 6.52410e22 | + | 6.52410e22i | 1.01926 | + | 1.01926i | ||||
\(343\) | −4.70519e22 | + | 4.70519e22i | −0.716028 | + | 0.716028i | ||||
\(344\) | − | 2.05997e21i | − | 0.0305376i | ||||||
\(345\) | −7.61924e22 | + | 3.62739e22i | −1.10037 | + | 0.523869i | ||||
\(346\) | −2.20843e22 | −0.310741 | ||||||||
\(347\) | −3.20550e22 | − | 3.20550e22i | −0.439471 | − | 0.439471i | 0.452363 | − | 0.891834i | \(-0.350581\pi\) |
−0.891834 | + | 0.452363i | \(0.850581\pi\) | |||||||
\(348\) | 3.93088e22 | − | 3.93088e22i | 0.525141 | − | 0.525141i | ||||
\(349\) | − | 1.42412e23i | − | 1.85403i | −0.375020 | − | 0.927017i | \(-0.622364\pi\) | ||
0.375020 | − | 0.927017i | \(-0.377636\pi\) | |||||||
\(350\) | −4.26921e22 | − | 3.46743e22i | −0.541670 | − | 0.439941i | ||||
\(351\) | −6.14529e22 | −0.759938 | ||||||||
\(352\) | −8.84076e21 | − | 8.84076e21i | −0.106563 | − | 0.106563i | ||||
\(353\) | 9.43648e22 | − | 9.43648e22i | 1.10876 | − | 1.10876i | 0.115447 | − | 0.993314i | \(-0.463170\pi\) |
0.993314 | − | 0.115447i | \(-0.0368301\pi\) | |||||||
\(354\) | 1.26404e23i | 1.44788i | ||||||||
\(355\) | 1.55299e22 | + | 3.26201e22i | 0.173426 | + | 0.364276i | ||||
\(356\) | −5.98272e22 | −0.651402 | ||||||||
\(357\) | 1.51470e23 | + | 1.51470e23i | 1.60810 | + | 1.60810i | ||||
\(358\) | 1.57231e22 | − | 1.57231e22i | 0.162777 | − | 0.162777i | ||||
\(359\) | − | 5.14231e21i | − | 0.0519168i | −0.999663 | − | 0.0259584i | \(-0.991736\pi\) | ||
0.999663 | − | 0.0259584i | \(-0.00826374\pi\) | |||||||
\(360\) | 1.71132e22 | − | 4.82147e22i | 0.168503 | − | 0.474741i | ||||
\(361\) | −1.09011e23 | −1.04690 | ||||||||
\(362\) | 3.02872e22 | + | 3.02872e22i | 0.283715 | + | 0.283715i | ||||
\(363\) | −3.29253e22 | + | 3.29253e22i | −0.300864 | + | 0.300864i | ||||
\(364\) | − | 6.35841e22i | − | 0.566808i | ||||||
\(365\) | 1.46666e23 | + | 5.20574e22i | 1.27554 | + | 0.452737i | ||||
\(366\) | −1.99469e23 | −1.69257 | ||||||||
\(367\) | 1.00104e23 | + | 1.00104e23i | 0.828817 | + | 0.828817i | 0.987353 | − | 0.158536i | \(-0.0506775\pi\) |
−0.158536 | + | 0.987353i | \(0.550678\pi\) | |||||||
\(368\) | 1.71244e22 | − | 1.71244e22i | 0.138352 | − | 0.138352i | ||||
\(369\) | 4.95839e22i | 0.390934i | ||||||||
\(370\) | 1.26433e23 | − | 6.01926e22i | 0.972848 | − | 0.463157i | ||||
\(371\) | 6.67052e22 | 0.500950 | ||||||||
\(372\) | −7.54826e22 | − | 7.54826e22i | −0.553299 | − | 0.553299i | ||||
\(373\) | −8.80250e22 | + | 8.80250e22i | −0.629835 | + | 0.629835i | −0.948026 | − | 0.318192i | \(-0.896924\pi\) |
0.318192 | + | 0.948026i | \(0.396924\pi\) | |||||||
\(374\) | − | 1.27718e23i | − | 0.892088i | ||||||
\(375\) | −1.94970e23 | + | 1.18894e23i | −1.32950 | + | 0.810732i | ||||
\(376\) | 4.72291e22 | 0.314427 | ||||||||
\(377\) | −1.19191e23 | − | 1.19191e23i | −0.774767 | − | 0.774767i | ||||
\(378\) | 5.14313e22 | − | 5.14313e22i | 0.326438 | − | 0.326438i | ||||
\(379\) | 2.05289e22i | 0.127237i | 0.997974 | + | 0.0636185i | \(0.0202641\pi\) | ||||
−0.997974 | + | 0.0636185i | \(0.979736\pi\) | |||||||
\(380\) | 5.08033e22 | + | 1.06711e23i | 0.307496 | + | 0.645887i | ||||
\(381\) | −3.82951e23 | −2.26370 | ||||||||
\(382\) | −1.00225e23 | − | 1.00225e23i | −0.578634 | − | 0.578634i | ||||
\(383\) | 2.34489e23 | − | 2.34489e23i | 1.32231 | − | 1.32231i | 0.410414 | − | 0.911899i | \(-0.365384\pi\) |
0.911899 | − | 0.410414i | \(-0.134616\pi\) | |||||||
\(384\) | 2.49872e22i | 0.137638i | ||||||||
\(385\) | −5.22983e22 | + | 1.47345e23i | −0.281411 | + | 0.792847i | ||||
\(386\) | 6.29464e22 | 0.330891 | ||||||||
\(387\) | −1.69446e22 | − | 1.69446e22i | −0.0870226 | − | 0.0870226i | ||||
\(388\) | −8.28186e22 | + | 8.28186e22i | −0.415568 | + | 0.415568i | ||||
\(389\) | − | 1.96355e23i | − | 0.962710i | −0.876526 | − | 0.481355i | \(-0.840145\pi\) | ||
0.876526 | − | 0.481355i | \(-0.159855\pi\) | |||||||
\(390\) | −2.48800e23 | − | 8.83082e22i | −1.19198 | − | 0.423077i | ||||
\(391\) | 2.47387e23 | 1.15821 | ||||||||
\(392\) | −1.42559e21 | − | 1.42559e21i | −0.00652260 | − | 0.00652260i | ||||
\(393\) | 3.27466e23 | − | 3.27466e23i | 1.46431 | − | 1.46431i | ||||
\(394\) | − | 7.50292e22i | − | 0.327917i | ||||||
\(395\) | −8.55566e22 | + | 4.07321e22i | −0.365494 | + | 0.174005i | ||||
\(396\) | −1.45442e23 | −0.607342 | ||||||||
\(397\) | −1.56434e23 | − | 1.56434e23i | −0.638581 | − | 0.638581i | 0.311625 | − | 0.950205i | \(-0.399127\pi\) |
−0.950205 | + | 0.311625i | \(0.899127\pi\) | |||||||
\(398\) | −1.57119e23 | + | 1.57119e23i | −0.627018 | + | 0.627018i | ||||
\(399\) | 5.63515e23i | 2.19862i | ||||||||
\(400\) | 4.13172e22 | − | 5.08710e22i | 0.157612 | − | 0.194057i | ||||
\(401\) | 2.24216e23 | 0.836309 | 0.418154 | − | 0.908376i | \(-0.362677\pi\) | ||||
0.418154 | + | 0.908376i | \(0.362677\pi\) | |||||||
\(402\) | 3.80059e23 | + | 3.80059e23i | 1.38617 | + | 1.38617i | ||||
\(403\) | −2.28876e23 | + | 2.28876e23i | −0.816310 | + | 0.816310i | ||||
\(404\) | − | 6.17285e22i | − | 0.215305i | ||||||
\(405\) | 4.97328e22 | + | 1.04462e23i | 0.169648 | + | 0.356340i | ||||
\(406\) | 1.99507e23 | 0.665616 | ||||||||
\(407\) | −2.81483e23 | − | 2.81483e23i | −0.918548 | − | 0.918548i | ||||
\(408\) | −1.80489e23 | + | 1.80489e23i | −0.576115 | + | 0.576115i | ||||
\(409\) | 1.24937e23i | 0.390104i | 0.980793 | + | 0.195052i | \(0.0624876\pi\) | ||||
−0.980793 | + | 0.195052i | \(0.937512\pi\) | |||||||
\(410\) | −2.12452e22 | + | 5.98563e22i | −0.0648943 | + | 0.182833i | ||||
\(411\) | 9.47708e23 | 2.83203 | ||||||||
\(412\) | 1.31710e23 | + | 1.31710e23i | 0.385072 | + | 0.385072i | ||||
\(413\) | −3.20775e23 | + | 3.20775e23i | −0.917594 | + | 0.917594i | ||||
\(414\) | − | 2.81718e23i | − | 0.788518i | ||||||
\(415\) | −3.46340e22 | − | 1.22929e22i | −0.0948571 | − | 0.0336683i | ||||
\(416\) | 7.57655e22 | 0.203063 | ||||||||
\(417\) | −2.04912e23 | − | 2.04912e23i | −0.537456 | − | 0.537456i | ||||
\(418\) | 2.37575e23 | − | 2.37575e23i | 0.609837 | − | 0.609837i | ||||
\(419\) | − | 4.44206e23i | − | 1.11599i | −0.829846 | − | 0.557993i | \(-0.811572\pi\) | ||
0.829846 | − | 0.557993i | \(-0.188428\pi\) | |||||||
\(420\) | 2.82133e23 | − | 1.34319e23i | 0.693761 | − | 0.330288i | ||||
\(421\) | −3.69953e23 | −0.890446 | −0.445223 | − | 0.895420i | \(-0.646876\pi\) | ||||
−0.445223 | + | 0.895420i | \(0.646876\pi\) | |||||||
\(422\) | 1.01945e23 | + | 1.01945e23i | 0.240190 | + | 0.240190i | ||||
\(423\) | 3.88490e23 | − | 3.88490e23i | 0.896018 | − | 0.896018i | ||||
\(424\) | 7.94846e22i | 0.179469i | ||||||||
\(425\) | 6.65898e23 | − | 6.90098e22i | 1.47200 | − | 0.152549i | ||||
\(426\) | −2.05260e23 | −0.444241 | ||||||||
\(427\) | −5.06191e23 | − | 5.06191e23i | −1.07266 | − | 1.07266i | ||||
\(428\) | 3.54442e22 | − | 3.54442e22i | 0.0735447 | − | 0.0735447i | ||||
\(429\) | 7.50516e23i | 1.52491i | ||||||||
\(430\) | −1.31948e22 | − | 2.77153e22i | −0.0262535 | − | 0.0551447i | ||||
\(431\) | −3.27398e23 | −0.637942 | −0.318971 | − | 0.947765i | \(-0.603337\pi\) | ||||
−0.318971 | + | 0.947765i | \(0.603337\pi\) | |||||||
\(432\) | 6.12845e22 | + | 6.12845e22i | 0.116949 | + | 0.116949i | ||||
\(433\) | −3.28782e23 | + | 3.28782e23i | −0.614493 | + | 0.614493i | −0.944113 | − | 0.329621i | \(-0.893079\pi\) |
0.329621 | + | 0.944113i | \(0.393079\pi\) | |||||||
\(434\) | − | 3.83103e23i | − | 0.701306i | ||||||
\(435\) | 2.77083e23 | − | 7.80655e23i | 0.496829 | − | 1.39977i | ||||
\(436\) | 1.02137e23 | 0.179393 | ||||||||
\(437\) | 4.60177e23 | + | 4.60177e23i | 0.791757 | + | 0.791757i | ||||
\(438\) | −6.25229e23 | + | 6.25229e23i | −1.05383 | + | 1.05383i | ||||
\(439\) | − | 2.94245e23i | − | 0.485880i | −0.970041 | − | 0.242940i | \(-0.921888\pi\) | ||
0.970041 | − | 0.242940i | \(-0.0781118\pi\) | |||||||
\(440\) | −1.75574e23 | − | 6.23176e22i | −0.284044 | − | 0.100818i | ||||
\(441\) | −2.34528e22 | −0.0371747 | ||||||||
\(442\) | 5.47273e23 | + | 5.47273e23i | 0.849970 | + | 0.849970i | ||||
\(443\) | −8.40443e23 | + | 8.40443e23i | −1.27901 | + | 1.27901i | −0.337792 | + | 0.941221i | \(0.609680\pi\) |
−0.941221 | + | 0.337792i | \(0.890320\pi\) | |||||||
\(444\) | 7.95573e23i | 1.18641i | ||||||||
\(445\) | −8.04929e23 | + | 3.83213e23i | −1.17630 | + | 0.560016i | ||||
\(446\) | 5.98259e22 | 0.0856793 | ||||||||
\(447\) | −1.64222e23 | − | 1.64222e23i | −0.230496 | − | 0.230496i | ||||
\(448\) | −6.34098e22 | + | 6.34098e22i | −0.0872277 | + | 0.0872277i | ||||
\(449\) | − | 4.24066e23i | − | 0.571764i | −0.958265 | − | 0.285882i | \(-0.907714\pi\) | ||
0.958265 | − | 0.285882i | \(-0.0922865\pi\) | |||||||
\(450\) | −7.85866e22 | − | 7.58307e23i | −0.103857 | − | 1.00215i | ||||
\(451\) | 1.80560e23 | 0.233901 | ||||||||
\(452\) | −1.58590e22 | − | 1.58590e22i | −0.0201386 | − | 0.0201386i | ||||
\(453\) | 9.85146e23 | − | 9.85146e23i | 1.22636 | − | 1.22636i | ||||
\(454\) | − | 3.69289e23i | − | 0.450676i | ||||||
\(455\) | −4.07277e23 | − | 8.55475e23i | −0.487290 | − | 1.02354i | ||||
\(456\) | −6.71473e23 | −0.787671 | ||||||||
\(457\) | −9.31623e23 | − | 9.31623e23i | −1.07151 | − | 1.07151i | −0.997238 | − | 0.0742673i | \(-0.976338\pi\) |
−0.0742673 | − | 0.997238i | \(-0.523662\pi\) | |||||||
\(458\) | −8.33260e23 | + | 8.33260e23i | −0.939705 | + | 0.939705i | ||||
\(459\) | 8.85346e23i | 0.979036i | ||||||||
\(460\) | 1.20708e23 | − | 3.40082e23i | 0.130893 | − | 0.368777i | ||||
\(461\) | 1.99127e23 | 0.211749 | 0.105874 | − | 0.994380i | \(-0.466236\pi\) | ||||
0.105874 | + | 0.994380i | \(0.466236\pi\) | |||||||
\(462\) | −6.28123e23 | − | 6.28123e23i | −0.655039 | − | 0.655039i | ||||
\(463\) | −1.39613e23 | + | 1.39613e23i | −0.142789 | + | 0.142789i | −0.774888 | − | 0.632099i | \(-0.782194\pi\) |
0.632099 | + | 0.774888i | \(0.282194\pi\) | |||||||
\(464\) | 2.37728e23i | 0.238462i | ||||||||
\(465\) | −1.49905e24 | − | 5.32069e23i | −1.47482 | − | 0.523469i | ||||
\(466\) | 1.22650e24 | 1.18357 | ||||||||
\(467\) | 8.53068e23 | + | 8.53068e23i | 0.807480 | + | 0.807480i | 0.984252 | − | 0.176772i | \(-0.0565656\pi\) |
−0.176772 | + | 0.984252i | \(0.556566\pi\) | |||||||
\(468\) | 6.23220e23 | − | 6.23220e23i | 0.578667 | − | 0.578667i | ||||
\(469\) | 1.92895e24i | 1.75697i | ||||||||
\(470\) | 6.35432e23 | − | 3.02518e23i | 0.567790 | − | 0.270316i | ||||
\(471\) | 1.47237e24 | 1.29071 | ||||||||
\(472\) | −3.82229e23 | − | 3.82229e23i | −0.328735 | − | 0.328735i | ||||
\(473\) | −6.17036e22 | + | 6.17036e22i | −0.0520668 | + | 0.0520668i | ||||
\(474\) | − | 5.38360e23i | − | 0.445726i | ||||||
\(475\) | 1.36704e24 | + | 1.11030e24i | 1.11055 | + | 0.901983i | ||||
\(476\) | −9.16050e23 | −0.730224 | ||||||||
\(477\) | 6.53812e23 | + | 6.53812e23i | 0.511432 | + | 0.511432i | ||||
\(478\) | 7.58641e23 | − | 7.58641e23i | 0.582351 | − | 0.582351i | ||||
\(479\) | 3.14908e22i | 0.0237227i | 0.999930 | + | 0.0118614i | \(0.00377567\pi\) | ||||
−0.999930 | + | 0.0118614i | \(0.996224\pi\) | |||||||
\(480\) | 1.60052e23 | + | 3.36184e23i | 0.118328 | + | 0.248545i | ||||
\(481\) | 2.41231e24 | 1.75036 | ||||||||
\(482\) | −9.66816e22 | − | 9.66816e22i | −0.0688527 | − | 0.0688527i | ||||
\(483\) | 1.21666e24 | − | 1.21666e24i | 0.850443 | − | 0.850443i | ||||
\(484\) | − | 1.99123e23i | − | 0.136620i | ||||||
\(485\) | −5.83780e23 | + | 1.64474e24i | −0.393164 | + | 1.10770i | ||||
\(486\) | −1.36492e24 | −0.902360 | ||||||||
\(487\) | 6.85335e23 | + | 6.85335e23i | 0.444777 | + | 0.444777i | 0.893614 | − | 0.448837i | \(-0.148161\pi\) |
−0.448837 | + | 0.893614i | \(0.648161\pi\) | |||||||
\(488\) | 6.03166e23 | − | 6.03166e23i | 0.384290 | − | 0.384290i | ||||
\(489\) | − | 1.23402e24i | − | 0.771864i | ||||||
\(490\) | −2.83116e22 | − | 1.00488e22i | −0.0173860 | − | 0.00617094i | ||||
\(491\) | 7.58996e23 | 0.457621 | 0.228811 | − | 0.973471i | \(-0.426516\pi\) | ||||
0.228811 | + | 0.973471i | \(0.426516\pi\) | |||||||
\(492\) | −2.55164e23 | − | 2.55164e23i | −0.151054 | − | 0.151054i | ||||
\(493\) | −1.71717e24 | + | 1.71717e24i | −0.998140 | + | 0.998140i | ||||
\(494\) | 2.03602e24i | 1.16209i | ||||||||
\(495\) | −1.95681e24 | + | 9.31604e23i | −1.09674 | + | 0.522137i | ||||
\(496\) | 4.56498e23 | 0.251248 | ||||||||
\(497\) | −5.20887e23 | − | 5.20887e23i | −0.281537 | − | 0.281537i | ||||
\(498\) | 1.47642e23 | − | 1.47642e23i | 0.0783695 | − | 0.0783695i | ||||
\(499\) | − | 2.27644e24i | − | 1.18673i | −0.804934 | − | 0.593364i | \(-0.797799\pi\) | ||
0.804934 | − | 0.593364i | \(-0.202201\pi\) | |||||||
\(500\) | 2.30045e23 | − | 9.49080e23i | 0.117783 | − | 0.485929i | ||||
\(501\) | −1.40800e24 | −0.708049 | ||||||||
\(502\) | −2.29222e23 | − | 2.29222e23i | −0.113220 | − | 0.113220i | ||||
\(503\) | 1.72617e24 | − | 1.72617e24i | 0.837474 | − | 0.837474i | −0.151052 | − | 0.988526i | \(-0.548266\pi\) |
0.988526 | + | 0.151052i | \(0.0482660\pi\) | |||||||
\(504\) | 1.04317e24i | 0.497143i | ||||||||
\(505\) | −3.95392e23 | − | 8.30509e23i | −0.185099 | − | 0.388796i | ||||
\(506\) | −1.02588e24 | −0.471780 | ||||||||
\(507\) | −7.78726e23 | − | 7.78726e23i | −0.351814 | − | 0.351814i | ||||
\(508\) | 1.15799e24 | − | 1.15799e24i | 0.513962 | − | 0.513962i | ||||
\(509\) | − | 5.34569e23i | − | 0.233101i | −0.993185 | − | 0.116550i | \(-0.962816\pi\) | ||
0.993185 | − | 0.116550i | \(-0.0371837\pi\) | |||||||
\(510\) | −1.27225e24 | + | 3.58443e24i | −0.545055 | + | 1.53564i | ||||
\(511\) | −3.17328e24 | −1.33573 | ||||||||
\(512\) | −7.55579e22 | − | 7.55579e22i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −1.64688e24 | + | 1.64688e24i | −0.669275 | + | 0.669275i | ||||
\(514\) | − | 1.25353e24i | − | 0.500571i | ||||||
\(515\) | 2.61569e24 | + | 9.28407e23i | 1.02641 | + | 0.364312i | ||||
\(516\) | 1.74397e23 | 0.0672499 | ||||||||
\(517\) | −1.41469e24 | − | 1.41469e24i | −0.536099 | − | 0.536099i | ||||
\(518\) | −2.01892e24 | + | 2.01892e24i | −0.751883 | + | 0.751883i | ||||
\(519\) | − | 1.86965e24i | − | 0.684313i | ||||||
\(520\) | 1.01937e24 | − | 4.85303e23i | 0.366691 | − | 0.174575i | ||||
\(521\) | −3.06229e24 | −1.08270 | −0.541348 | − | 0.840798i | \(-0.682086\pi\) | ||||
−0.541348 | + | 0.840798i | \(0.682086\pi\) | |||||||
\(522\) | 1.95547e24 | + | 1.95547e24i | 0.679543 | + | 0.679543i | ||||
\(523\) | 1.53641e24 | − | 1.53641e24i | 0.524797 | − | 0.524797i | −0.394219 | − | 0.919016i | \(-0.628985\pi\) |
0.919016 | + | 0.394219i | \(0.128985\pi\) | |||||||
\(524\) | 1.98042e24i | 0.664931i | ||||||||
\(525\) | 2.93552e24 | − | 3.61431e24i | 0.968839 | − | 1.19287i | ||||
\(526\) | 2.38968e24 | 0.775298 | ||||||||
\(527\) | 3.29739e24 | + | 3.29739e24i | 1.05166 | + | 1.05166i | ||||
\(528\) | 7.48459e23 | − | 7.48459e23i | 0.234673 | − | 0.234673i | ||||
\(529\) | 1.25705e24i | 0.387483i | ||||||||
\(530\) | 5.09126e23 | + | 1.06940e24i | 0.154292 | + | 0.324085i | ||||
\(531\) | −6.28817e24 | −1.87359 | ||||||||
\(532\) | −1.70399e24 | − | 1.70399e24i | −0.499186 | − | 0.499186i | ||||
\(533\) | −7.73699e23 | + | 7.73699e23i | −0.222858 | + | 0.222858i | ||||
\(534\) | − | 5.06497e24i | − | 1.43452i | ||||||
\(535\) | 2.49843e23 | − | 7.03907e23i | 0.0695797 | − | 0.196034i | ||||
\(536\) | −2.29849e24 | −0.629448 | ||||||||
\(537\) | 1.33112e24 | + | 1.33112e24i | 0.358467 | + | 0.358467i | ||||
\(538\) | −3.37621e23 | + | 3.37621e23i | −0.0894107 | + | 0.0894107i | ||||
\(539\) | 8.54034e22i | 0.0222421i | ||||||||
\(540\) | 1.21708e24 | + | 4.31988e23i | 0.311728 | + | 0.110644i | ||||
\(541\) | 4.40201e23 | 0.110886 | 0.0554428 | − | 0.998462i | \(-0.482343\pi\) | ||||
0.0554428 | + | 0.998462i | \(0.482343\pi\) | |||||||
\(542\) | −1.62225e23 | − | 1.62225e23i | −0.0401905 | − | 0.0401905i | ||||
\(543\) | −2.56411e24 | + | 2.56411e24i | −0.624797 | + | 0.624797i | ||||
\(544\) | − | 1.09155e24i | − | 0.261609i | ||||||
\(545\) | 1.37418e24 | − | 6.54223e23i | 0.323947 | − | 0.154226i | ||||
\(546\) | 5.38303e24 | 1.24822 | ||||||||
\(547\) | −1.18120e24 | − | 1.18120e24i | −0.269424 | − | 0.269424i | 0.559444 | − | 0.828868i | \(-0.311015\pi\) |
−0.828868 | + | 0.559444i | \(0.811015\pi\) | |||||||
\(548\) | −2.86574e24 | + | 2.86574e24i | −0.643001 | + | 0.643001i | ||||
\(549\) | − | 9.92287e24i | − | 2.19021i | ||||||
\(550\) | −2.76137e24 | + | 2.86173e23i | −0.599599 | + | 0.0621390i | ||||
\(551\) | −6.38839e24 | −1.36467 | ||||||||
\(552\) | 1.44975e24 | + | 1.44975e24i | 0.304678 | + | 0.304678i | ||||
\(553\) | 1.36619e24 | − | 1.36619e24i | 0.282478 | − | 0.282478i | ||||
\(554\) | 3.53596e23i | 0.0719315i | ||||||||
\(555\) | 5.09591e24 | + | 1.07038e25i | 1.01996 | + | 2.14241i | ||||
\(556\) | 1.23925e24 | 0.244054 | ||||||||
\(557\) | 5.77137e24 | + | 5.77137e24i | 1.11836 | + | 1.11836i | 0.991982 | + | 0.126380i | \(0.0403360\pi\) |
0.126380 | + | 0.991982i | \(0.459664\pi\) | |||||||
\(558\) | 3.75499e24 | − | 3.75499e24i | 0.715980 | − | 0.715980i | ||||
\(559\) | − | 5.28801e23i | − | 0.0992171i | ||||||
\(560\) | −4.46969e23 | + | 1.25929e24i | −0.0825250 | + | 0.232506i | ||||
\(561\) | 1.08126e25 | 1.96456 | ||||||||
\(562\) | 1.12647e24 | + | 1.12647e24i | 0.201415 | + | 0.201415i | ||||
\(563\) | 3.51547e23 | − | 3.51547e23i | 0.0618597 | − | 0.0618597i | −0.675500 | − | 0.737360i | \(-0.736072\pi\) |
0.737360 | + | 0.675500i | \(0.236072\pi\) | |||||||
\(564\) | 3.99842e24i | 0.692431i | ||||||||
\(565\) | −3.14952e23 | − | 1.11788e23i | −0.0536795 | − | 0.0190529i | ||||
\(566\) | 2.83130e24 | 0.474939 | ||||||||
\(567\) | −1.66809e24 | − | 1.66809e24i | −0.275404 | − | 0.275404i | ||||
\(568\) | 6.20678e23 | − | 6.20678e23i | 0.100863 | − | 0.100863i | ||||
\(569\) | 5.74910e24i | 0.919580i | 0.888028 | + | 0.459790i | \(0.152075\pi\) | ||||
−0.888028 | + | 0.459790i | \(0.847925\pi\) | |||||||
\(570\) | −9.03415e24 | + | 4.30101e24i | −1.42237 | + | 0.677168i | ||||
\(571\) | −1.10385e25 | −1.71075 | −0.855375 | − | 0.518009i | \(-0.826673\pi\) | ||||
−0.855375 | + | 0.518009i | \(0.826673\pi\) | |||||||
\(572\) | −2.26945e24 | − | 2.26945e24i | −0.346224 | − | 0.346224i | ||||
\(573\) | 8.48501e24 | − | 8.48501e24i | 1.27427 | − | 1.27427i | ||||
\(574\) | − | 1.29505e24i | − | 0.191461i | ||||||
\(575\) | −5.54311e23 | − | 5.34872e24i | −0.0806757 | − | 0.778466i | ||||
\(576\) | −1.24302e24 | −0.178106 | ||||||||
\(577\) | 4.10073e24 | + | 4.10073e24i | 0.578467 | + | 0.578467i | 0.934481 | − | 0.356014i | \(-0.115864\pi\) |
−0.356014 | + | 0.934481i | \(0.615864\pi\) | |||||||
\(578\) | 4.28436e24 | − | 4.28436e24i | 0.595025 | − | 0.595025i | ||||
\(579\) | 5.32904e24i | 0.728689i | ||||||||
\(580\) | 1.52273e24 | + | 3.19845e24i | 0.205008 | + | 0.430614i | ||||
\(581\) | 7.49341e23 | 0.0993332 | ||||||||
\(582\) | −7.01142e24 | − | 7.01142e24i | −0.915165 | − | 0.915165i | ||||
\(583\) | 2.38086e24 | − | 2.38086e24i | 0.305996 | − | 0.305996i | ||||
\(584\) | − | 3.78121e24i | − | 0.478537i | ||||||
\(585\) | 4.39301e24 | − | 1.23769e25i | 0.547469 | − | 1.54244i | ||||
\(586\) | −4.06350e24 | −0.498680 | ||||||||
\(587\) | −2.35372e24 | − | 2.35372e24i | −0.284454 | − | 0.284454i | 0.550428 | − | 0.834883i | \(-0.314465\pi\) |
−0.834883 | + | 0.550428i | \(0.814465\pi\) | |||||||
\(588\) | 1.20691e23 | − | 1.20691e23i | 0.0143641 | − | 0.0143641i | ||||
\(589\) | 1.22673e25i | 1.43784i | ||||||||
\(590\) | −7.59091e24 | − | 2.69429e24i | −0.876245 | − | 0.311012i | ||||
\(591\) | 6.35197e24 | 0.722140 | ||||||||
\(592\) | −2.40570e24 | − | 2.40570e24i | −0.269368 | − | 0.269368i | ||||
\(593\) | −9.78054e24 | + | 9.78054e24i | −1.07862 | + | 1.07862i | −0.0819919 | + | 0.996633i | \(0.526128\pi\) |
−0.996633 | + | 0.0819919i | \(0.973872\pi\) | |||||||
\(594\) | − | 3.67139e24i | − | 0.398797i | ||||||
\(595\) | −1.23247e25 | + | 5.86760e24i | −1.31864 | + | 0.627781i | ||||
\(596\) | 9.93169e23 | 0.104666 | ||||||||
\(597\) | −1.33017e25 | − | 1.33017e25i | −1.38082 | − | 1.38082i | ||||
\(598\) | 4.39589e24 | − | 4.39589e24i | 0.449506 | − | 0.449506i | ||||
\(599\) | − | 3.41830e24i | − | 0.344325i | −0.985069 | − | 0.172162i | \(-0.944925\pi\) | ||
0.985069 | − | 0.172162i | \(-0.0550754\pi\) | |||||||
\(600\) | 4.30674e24 | + | 3.49791e24i | 0.427354 | + | 0.347094i | ||||
\(601\) | −2.54521e23 | −0.0248802 | −0.0124401 | − | 0.999923i | \(-0.503960\pi\) | ||||
−0.0124401 | + | 0.999923i | \(0.503960\pi\) | |||||||
\(602\) | 4.42566e23 | + | 4.42566e23i | 0.0426196 | + | 0.0426196i | ||||
\(603\) | −1.89066e25 | + | 1.89066e25i | −1.79373 | + | 1.79373i | ||||
\(604\) | 5.95789e24i | 0.556878i | ||||||||
\(605\) | −1.27545e24 | − | 2.67905e24i | −0.117453 | − | 0.246707i | ||||
\(606\) | 5.22593e24 | 0.474144 | ||||||||
\(607\) | 3.01333e24 | + | 3.01333e24i | 0.269370 | + | 0.269370i | 0.828846 | − | 0.559477i | \(-0.188998\pi\) |
−0.559477 | + | 0.828846i | \(0.688998\pi\) | |||||||
\(608\) | 2.03044e24 | − | 2.03044e24i | 0.178837 | − | 0.178837i | ||||
\(609\) | 1.68903e25i | 1.46582i | ||||||||
\(610\) | 4.25166e24 | − | 1.19786e25i | 0.363571 | − | 1.02433i | ||||
\(611\) | 1.21239e25 | 1.02158 | ||||||||
\(612\) | −8.97868e24 | − | 8.97868e24i | −0.745503 | − | 0.745503i | ||||
\(613\) | 5.96667e24 | − | 5.96667e24i | 0.488188 | − | 0.488188i | −0.419546 | − | 0.907734i | \(-0.637811\pi\) |
0.907734 | + | 0.419546i | \(0.137811\pi\) | |||||||
\(614\) | 1.11437e25i | 0.898495i | ||||||||
\(615\) | −5.06744e24 | − | 1.79862e24i | −0.402636 | − | 0.142910i | ||||
\(616\) | 3.79871e24 | 0.297447 | ||||||||
\(617\) | 1.05403e25 | + | 1.05403e25i | 0.813371 | + | 0.813371i | 0.985138 | − | 0.171767i | \(-0.0549476\pi\) |
−0.171767 | + | 0.985138i | \(0.554948\pi\) | |||||||
\(618\) | −1.11505e25 | + | 1.11505e25i | −0.848007 | + | 0.848007i | ||||
\(619\) | − | 1.30457e25i | − | 0.977807i | −0.872338 | − | 0.488903i | \(-0.837397\pi\) | ||
0.872338 | − | 0.488903i | \(-0.162603\pi\) | |||||||
\(620\) | 6.14182e24 | − | 2.92402e24i | 0.453703 | − | 0.216001i | ||||
\(621\) | 7.11140e24 | 0.517763 | ||||||||
\(622\) | 4.22157e24 | + | 4.22157e24i | 0.302943 | + | 0.302943i | ||||
\(623\) | 1.28533e25 | − | 1.28533e25i | 0.909124 | − | 0.909124i | ||||
\(624\) | 6.41431e24i | 0.447186i | ||||||||
\(625\) | −2.98410e24 | − | 1.42427e25i | −0.205066 | − | 0.978748i | ||||
\(626\) | −4.29768e24 | −0.291116 | ||||||||
\(627\) | 2.01131e25 | + | 2.01131e25i | 1.34298 | + | 1.34298i | ||||
\(628\) | −4.45224e24 | + | 4.45224e24i | −0.293050 | + | 0.293050i | ||||
\(629\) | − | 3.47539e25i | − | 2.25501i | ||||||
\(630\) | 6.68188e24 | + | 1.40351e25i | 0.427399 | + | 0.897740i | ||||
\(631\) | −1.23499e25 | −0.778755 | −0.389378 | − | 0.921078i | \(-0.627310\pi\) | ||||
−0.389378 | + | 0.921078i | \(0.627310\pi\) | |||||||
\(632\) | 1.62793e24 | + | 1.62793e24i | 0.101200 | + | 0.101200i | ||||
\(633\) | −8.63067e24 | + | 8.63067e24i | −0.528946 | + | 0.528946i | ||||
\(634\) | 7.88302e24i | 0.476310i | ||||||||
\(635\) | 8.16254e24 | − | 2.29972e25i | 0.486253 | − | 1.36997i | ||||
\(636\) | −6.72917e24 | −0.395228 | ||||||||
\(637\) | −3.65954e23 | − | 3.65954e23i | −0.0211920 | − | 0.0211920i | ||||
\(638\) | 7.12084e24 | − | 7.12084e24i | 0.406579 | − | 0.406579i | ||||
\(639\) | − | 1.02110e25i | − | 0.574856i | ||||||
\(640\) | −1.50055e24 | − | 5.32599e23i | −0.0832970 | − | 0.0295652i | ||||
\(641\) | −7.78434e24 | −0.426088 | −0.213044 | − | 0.977043i | \(-0.568338\pi\) | ||||
−0.213044 | + | 0.977043i | \(0.568338\pi\) | |||||||
\(642\) | 3.00071e24 | + | 3.00071e24i | 0.161960 | + | 0.161960i | ||||
\(643\) | −8.62731e23 | + | 8.62731e23i | −0.0459174 | + | 0.0459174i | −0.729693 | − | 0.683775i | \(-0.760337\pi\) |
0.683775 | + | 0.729693i | \(0.260337\pi\) | |||||||
\(644\) | 7.35803e24i | 0.386179i | ||||||||
\(645\) | 2.34638e24 | − | 1.11707e24i | 0.121440 | − | 0.0578154i | ||||
\(646\) | 2.93327e25 | 1.49713 | ||||||||
\(647\) | −4.00425e24 | − | 4.00425e24i | −0.201550 | − | 0.201550i | 0.599114 | − | 0.800664i | \(-0.295520\pi\) |
−0.800664 | + | 0.599114i | \(0.795520\pi\) | |||||||
\(648\) | 1.98766e24 | − | 1.98766e24i | 0.0986658 | − | 0.0986658i | ||||
\(649\) | 2.28983e25i | 1.12099i | ||||||||
\(650\) | 1.06063e25 | − | 1.30588e25i | 0.512085 | − | 0.630495i | ||||
\(651\) | 3.24335e25 | 1.54442 | ||||||||
\(652\) | 3.73149e24 | + | 3.73149e24i | 0.175248 | + | 0.175248i | ||||
\(653\) | −6.73509e24 | + | 6.73509e24i | −0.311979 | + | 0.311979i | −0.845676 | − | 0.533697i | \(-0.820802\pi\) |
0.533697 | + | 0.845676i | \(0.320802\pi\) | |||||||
\(654\) | 8.64693e24i | 0.395059i | ||||||||
\(655\) | 1.26853e25 | + | 2.66451e25i | 0.571647 | + | 1.20073i | ||||
\(656\) | 1.54316e24 | 0.0685924 | ||||||||
\(657\) | −3.11029e25 | − | 3.11029e25i | −1.36368 | − | 1.36368i | ||||
\(658\) | −1.01467e25 | + | 1.01467e25i | −0.438827 | + | 0.438827i | ||||
\(659\) | − | 1.78789e24i | − | 0.0762730i | −0.999273 | − | 0.0381365i | \(-0.987858\pi\) | ||
0.999273 | − | 0.0381365i | \(-0.0121422\pi\) | |||||||
\(660\) | 5.27581e24 | − | 1.48641e25i | 0.222021 | − | 0.625521i | ||||
\(661\) | 1.99846e25 | 0.829624 | 0.414812 | − | 0.909907i | \(-0.363847\pi\) | ||||
0.414812 | + | 0.909907i | \(0.363847\pi\) | |||||||
\(662\) | 5.88487e24 | + | 5.88487e24i | 0.240999 | + | 0.240999i | ||||
\(663\) | −4.63321e25 | + | 4.63321e25i | −1.87180 | + | 1.87180i | ||||
\(664\) | 8.92900e23i | 0.0355869i | ||||||||
\(665\) | −3.38405e25 | − | 1.20112e25i | −1.33058 | − | 0.472273i | ||||
\(666\) | −3.95769e25 | −1.53523 | ||||||||
\(667\) | 1.37929e25 | + | 1.37929e25i | 0.527866 | + | 0.527866i | ||||
\(668\) | 4.25760e24 | − | 4.25760e24i | 0.160760 | − | 0.160760i | ||||
\(669\) | 5.06486e24i | 0.188683i | ||||||||
\(670\) | −3.09244e25 | + | 1.47226e25i | −1.13666 | + | 0.541143i | ||||
\(671\) | −3.61341e25 | −1.31043 | ||||||||
\(672\) | −5.36827e24 | − | 5.36827e24i | −0.192093 | − | 0.192093i | ||||
\(673\) | −5.81796e24 | + | 5.81796e24i | −0.205416 | + | 0.205416i | −0.802316 | − | 0.596900i | \(-0.796399\pi\) |
0.596900 | + | 0.802316i | \(0.296399\pi\) | |||||||
\(674\) | − | 3.17940e25i | − | 1.10766i | ||||||
\(675\) | 1.91419e25 | − | 1.98376e24i | 0.658040 | − | 0.0681954i | ||||
\(676\) | 4.70952e24 | 0.159756 | ||||||||
\(677\) | −9.58000e24 | − | 9.58000e24i | −0.320677 | − | 0.320677i | 0.528350 | − | 0.849027i | \(-0.322811\pi\) |
−0.849027 | + | 0.528350i | \(0.822811\pi\) | |||||||
\(678\) | 1.34262e24 | − | 1.34262e24i | 0.0443492 | − | 0.0443492i | ||||
\(679\) | − | 3.55856e25i | − | 1.15997i | ||||||
\(680\) | −6.99172e24 | − | 1.46859e25i | −0.224907 | − | 0.472412i | ||||
\(681\) | 3.12640e25 | 0.992479 | ||||||||
\(682\) | −1.36738e25 | − | 1.36738e25i | −0.428380 | − | 0.428380i | ||||
\(683\) | 3.34343e25 | − | 3.34343e25i | 1.03373 | − | 1.03373i | 0.0343157 | − | 0.999411i | \(-0.489075\pi\) |
0.999411 | − | 0.0343157i | \(-0.0109252\pi\) | |||||||
\(684\) | − | 3.34034e25i | − | 1.01926i | ||||||
\(685\) | −2.02003e25 | + | 5.69123e25i | −0.608334 | + | 1.71392i | ||||
\(686\) | 2.40906e25 | 0.716028 | ||||||||
\(687\) | −7.05438e25 | − | 7.05438e25i | −2.06942 | − | 2.06942i | ||||
\(688\) | −5.27352e23 | + | 5.27352e23i | −0.0152688 | + | 0.0152688i | ||||
\(689\) | 2.04040e25i | 0.583098i | ||||||||
\(690\) | 2.87914e25 | + | 1.02191e25i | 0.812121 | + | 0.288252i | ||||
\(691\) | 2.94336e25 | 0.819486 | 0.409743 | − | 0.912201i | \(-0.365618\pi\) | ||||
0.409743 | + | 0.912201i | \(0.365618\pi\) | |||||||
\(692\) | 5.65357e24 | + | 5.65357e24i | 0.155370 | + | 0.155370i | ||||
\(693\) | 3.12469e25 | − | 3.12469e25i | 0.847632 | − | 0.847632i | ||||
\(694\) | 1.64121e25i | 0.439471i | ||||||||
\(695\) | 1.66732e25 | − | 7.93781e24i | 0.440712 | − | 0.209816i | ||||
\(696\) | −2.01261e25 | −0.525141 | ||||||||
\(697\) | 1.11466e25 | + | 1.11466e25i | 0.287110 | + | 0.287110i | ||||
\(698\) | −3.64575e25 | + | 3.64575e25i | −0.927017 | + | 0.927017i | ||||
\(699\) | 1.03836e26i | 2.60646i | ||||||||
\(700\) | 2.05256e24 | + | 1.98058e25i | 0.0508643 | + | 0.490806i | ||||
\(701\) | −4.86804e25 | −1.19095 | −0.595473 | − | 0.803375i | \(-0.703035\pi\) | ||||
−0.595473 | + | 0.803375i | \(0.703035\pi\) | |||||||
\(702\) | 1.57319e25 | + | 1.57319e25i | 0.379969 | + | 0.379969i | ||||
\(703\) | 6.46475e25 | − | 6.46475e25i | 1.54154 | − | 1.54154i | ||||
\(704\) | 4.52647e24i | 0.106563i | ||||||||
\(705\) | 2.56112e25 | + | 5.37956e25i | 0.595289 | + | 1.25039i | ||||
\(706\) | −4.83148e25 | −1.10876 | ||||||||
\(707\) | 1.32618e25 | + | 1.32618e25i | 0.300488 | + | 0.300488i | ||||
\(708\) | 3.23595e25 | − | 3.23595e25i | 0.723941 | − | 0.723941i | ||||
\(709\) | 2.38652e25i | 0.527167i | 0.964637 | + | 0.263584i | \(0.0849045\pi\) | ||||
−0.964637 | + | 0.263584i | \(0.915095\pi\) | |||||||
\(710\) | 4.37509e24 | − | 1.23264e25i | 0.0954250 | − | 0.268851i | ||||
\(711\) | 2.67815e25 | 0.576778 | ||||||||
\(712\) | 1.53158e25 | + | 1.53158e25i | 0.325701 | + | 0.325701i | ||||
\(713\) | 2.64858e25 | − | 2.64858e25i | 0.556170 | − | 0.556170i | ||||
\(714\) | − | 7.75528e25i | − | 1.60810i | ||||||
\(715\) | −4.50704e25 | − | 1.59971e25i | −0.922862 | − | 0.327558i | ||||
\(716\) | −8.05025e24 | −0.162777 | ||||||||
\(717\) | 6.42265e25 | + | 6.42265e25i | 1.28245 | + | 1.28245i | ||||
\(718\) | −1.31643e24 | + | 1.31643e24i | −0.0259584 | + | 0.0259584i | ||||
\(719\) | 2.39320e25i | 0.466035i | 0.972473 | + | 0.233018i | \(0.0748600\pi\) | ||||
−0.972473 | + | 0.233018i | \(0.925140\pi\) | |||||||
\(720\) | −1.67239e25 | + | 7.96199e24i | −0.321622 | + | 0.153119i | ||||
\(721\) | −5.65932e25 | −1.07485 | ||||||||
\(722\) | 2.79067e25 | + | 2.79067e25i | 0.523448 | + | 0.523448i | ||||
\(723\) | 8.18507e24 | − | 8.18507e24i | 0.151627 | − | 0.151627i | ||||
\(724\) | − | 1.55070e25i | − | 0.283715i | ||||||
\(725\) | 4.09743e25 | + | 3.32791e25i | 0.740406 | + | 0.601354i | ||||
\(726\) | 1.68578e25 | 0.300864 | ||||||||
\(727\) | −4.32047e25 | − | 4.32047e25i | −0.761590 | − | 0.761590i | 0.215020 | − | 0.976610i | \(-0.431018\pi\) |
−0.976610 | + | 0.215020i | \(0.931018\pi\) | |||||||
\(728\) | −1.62775e25 | + | 1.62775e25i | −0.283404 | + | 0.283404i | ||||
\(729\) | − | 9.26043e25i | − | 1.59251i | ||||||
\(730\) | −2.42199e25 | − | 5.08733e25i | −0.411403 | − | 0.864140i | ||||
\(731\) | −7.61839e24 | −0.127822 | ||||||||
\(732\) | 5.10641e25 | + | 5.10641e25i | 0.846283 | + | 0.846283i | ||||
\(733\) | 3.46694e24 | − | 3.46694e24i | 0.0567558 | − | 0.0567558i | −0.678159 | − | 0.734915i | \(-0.737222\pi\) |
0.734915 | + | 0.678159i | \(0.237222\pi\) | |||||||
\(734\) | − | 5.12534e25i | − | 0.828817i | ||||||
\(735\) | 8.50735e23 | − | 2.39686e24i | 0.0135897 | − | 0.0382875i | ||||
\(736\) | −8.76768e24 | −0.138352 | ||||||||
\(737\) | 6.88483e25 | + | 6.88483e25i | 1.07321 | + | 1.07321i | ||||
\(738\) | 1.26935e25 | − | 1.26935e25i | 0.195467 | − | 0.195467i | ||||
\(739\) | − | 2.57729e25i | − | 0.392069i | −0.980597 | − | 0.196035i | \(-0.937194\pi\) | ||
0.980597 | − | 0.196035i | \(-0.0628065\pi\) | |||||||
\(740\) | −4.77762e25 | − | 1.69575e25i | −0.718002 | − | 0.254846i | ||||
\(741\) | −1.72369e26 | −2.55915 | ||||||||
\(742\) | −1.70765e25 | − | 1.70765e25i | −0.250475 | − | 0.250475i | ||||
\(743\) | −2.88959e25 | + | 2.88959e25i | −0.418733 | + | 0.418733i | −0.884767 | − | 0.466034i | \(-0.845683\pi\) |
0.466034 | + | 0.884767i | \(0.345683\pi\) | |||||||
\(744\) | 3.86471e25i | 0.553299i | ||||||||
\(745\) | 1.33623e25 | − | 6.36158e24i | 0.189006 | − | 0.0899826i | ||||
\(746\) | 4.50688e25 | 0.629835 | ||||||||
\(747\) | 7.34468e24 | + | 7.34468e24i | 0.101412 | + | 0.101412i | ||||
\(748\) | −3.26958e25 | + | 3.26958e25i | −0.446044 | + | 0.446044i | ||||
\(749\) | 1.52297e25i | 0.205284i | ||||||||
\(750\) | 8.03492e25 | + | 1.94756e25i | 1.07011 | + | 0.259382i | ||||
\(751\) | 1.19196e26 | 1.56856 | 0.784282 | − | 0.620404i | \(-0.213032\pi\) | ||||
0.784282 | + | 0.620404i | \(0.213032\pi\) | |||||||
\(752\) | −1.20907e25 | − | 1.20907e25i | −0.157213 | − | 0.157213i | ||||
\(753\) | 1.94059e25 | − | 1.94059e25i | 0.249333 | − | 0.249333i | ||||
\(754\) | 6.10257e25i | 0.774767i | ||||||||
\(755\) | 3.81623e25 | + | 8.01588e25i | 0.478753 | + | 1.00561i | ||||
\(756\) | −2.63328e25 | −0.326438 | ||||||||
\(757\) | −1.26082e25 | − | 1.26082e25i | −0.154451 | − | 0.154451i | 0.625652 | − | 0.780102i | \(-0.284833\pi\) |
−0.780102 | + | 0.625652i | \(0.784833\pi\) | |||||||
\(758\) | 5.25540e24 | − | 5.25540e24i | 0.0636185 | − | 0.0636185i | ||||
\(759\) | − | 8.68506e25i | − | 1.03896i | ||||||
\(760\) | 1.43124e25 | − | 4.03237e25i | 0.169196 | − | 0.476692i | ||||
\(761\) | −9.90307e25 | −1.15693 | −0.578466 | − | 0.815706i | \(-0.696348\pi\) | ||||
−0.578466 | + | 0.815706i | \(0.696348\pi\) | |||||||
\(762\) | 9.80354e25 | + | 9.80354e25i | 1.13185 | + | 1.13185i | ||||
\(763\) | −2.19432e25 | + | 2.19432e25i | −0.250369 | + | 0.250369i | ||||
\(764\) | 5.13150e25i | 0.578634i | ||||||||
\(765\) | −1.78313e26 | − | 6.32897e25i | −1.98714 | − | 0.705311i | ||||
\(766\) | −1.20059e26 | −1.32231 | ||||||||
\(767\) | −9.81196e25 | − | 9.81196e25i | −1.06806 | − | 1.06806i | ||||
\(768\) | 6.39673e24 | − | 6.39673e24i | 0.0688188 | − | 0.0688188i | ||||
\(769\) | − | 1.32343e26i | − | 1.40722i | −0.710586 | − | 0.703611i | \(-0.751570\pi\) | ||
0.710586 | − | 0.703611i | \(-0.248430\pi\) | |||||||
\(770\) | 5.11087e25 | − | 2.43320e25i | 0.537129 | − | 0.255718i | ||||
\(771\) | 1.06124e26 | 1.10236 | ||||||||
\(772\) | −1.61143e25 | − | 1.61143e25i | −0.165446 | − | 0.165446i | ||||
\(773\) | 1.20740e24 | − | 1.20740e24i | 0.0122528 | − | 0.0122528i | −0.700954 | − | 0.713207i | \(-0.747242\pi\) |
0.713207 | + | 0.700954i | \(0.247242\pi\) | |||||||
\(774\) | 8.67563e24i | 0.0870226i | ||||||||
\(775\) | 6.39042e25 | − | 7.86809e25i | 0.633598 | − | 0.780106i | ||||
\(776\) | 4.24031e25 | 0.415568 | ||||||||
\(777\) | −1.70921e26 | − | 1.70921e26i | −1.65580 | − | 1.65580i | ||||
\(778\) | −5.02669e25 | + | 5.02669e25i | −0.481355 | + | 0.481355i | ||||
\(779\) | 4.14687e25i | 0.392540i | ||||||||
\(780\) | 4.10858e25 | + | 8.62996e25i | 0.384450 | + | 0.807527i | ||||
\(781\) | −3.71832e25 | −0.343943 | ||||||||
\(782\) | −6.33311e25 | − | 6.33311e25i | −0.579104 | − | 0.579104i | ||||
\(783\) | −4.93619e25 | + | 4.93619e25i | −0.446207 | + | 0.446207i | ||||
\(784\) | 7.29903e23i | 0.00652260i | ||||||||
\(785\) | −3.13833e25 | + | 8.84195e25i | −0.277250 | + | 0.781126i | ||||
\(786\) | −1.67663e26 | −1.46431 | ||||||||
\(787\) | 1.14752e26 | + | 1.14752e26i | 0.990800 | + | 0.990800i | 0.999958 | − | 0.00915769i | \(-0.00291502\pi\) |
−0.00915769 | + | 0.999958i | \(0.502915\pi\) | |||||||
\(788\) | −1.92075e25 | + | 1.92075e25i | −0.163959 | + | 0.163959i | ||||
\(789\) | 2.02311e26i | 1.70736i | ||||||||
\(790\) | 3.23299e25 | + | 1.14751e25i | 0.269750 | + | 0.0957441i | ||||
\(791\) | 6.81431e24 | 0.0562126 | ||||||||
\(792\) | 3.72331e25 | + | 3.72331e25i | 0.303671 | + | 0.303671i | ||||
\(793\) | 1.54835e26 | − | 1.54835e26i | 1.24856 | − | 1.24856i | ||||
\(794\) | 8.00941e25i | 0.638581i | ||||||||
\(795\) | −9.05358e25 | + | 4.31026e25i | −0.713701 | + | 0.339781i | ||||
\(796\) | 8.04448e25 | 0.627018 | ||||||||
\(797\) | 1.36534e26 | + | 1.36534e26i | 1.05224 | + | 1.05224i | 0.998558 | + | 0.0536868i | \(0.0170972\pi\) |
0.0536868 | + | 0.998558i | \(0.482903\pi\) | |||||||
\(798\) | 1.44260e26 | − | 1.44260e26i | 1.09931 | − | 1.09931i | ||||
\(799\) | − | 1.74668e26i | − | 1.31611i | ||||||
\(800\) | −2.36002e25 | + | 2.44578e24i | −0.175835 | + | 0.0182225i | ||||
\(801\) | 2.51964e26 | 1.85629 | ||||||||
\(802\) | −5.73992e25 | − | 5.73992e25i | −0.418154 | − | 0.418154i | ||||
\(803\) | −1.13261e26 | + | 1.13261e26i | −0.815908 | + | 0.815908i | ||||
\(804\) | − | 1.94590e26i | − | 1.38617i | ||||||
\(805\) | 4.71306e25 | + | 9.89966e25i | 0.332002 | + | 0.697360i | ||||
\(806\) | 1.17185e26 | 0.816310 | ||||||||
\(807\) | −2.85830e25 | − | 2.85830e25i | −0.196900 | − | 0.196900i | ||||
\(808\) | −1.58025e25 | + | 1.58025e25i | −0.107652 | + | 0.107652i | ||||
\(809\) | 1.19623e26i | 0.805896i | 0.915223 | + | 0.402948i | \(0.132014\pi\) | ||||
−0.915223 | + | 0.402948i | \(0.867986\pi\) | |||||||
\(810\) | 1.40108e25 | − | 3.94740e25i | 0.0933464 | − | 0.262994i | ||||
\(811\) | 2.46399e26 | 1.62349 | 0.811747 | − | 0.584010i | \(-0.198517\pi\) | ||||
0.811747 | + | 0.584010i | \(0.198517\pi\) | |||||||
\(812\) | −5.10738e25 | − | 5.10738e25i | −0.332808 | − | 0.332808i | ||||
\(813\) | 1.37339e25 | − | 1.37339e25i | 0.0885075 | − | 0.0885075i | ||||
\(814\) | 1.44119e26i | 0.918548i | ||||||||
\(815\) | 7.41058e25 | + | 2.63029e25i | 0.467125 | + | 0.165800i | ||||
\(816\) | 9.24103e25 | 0.576115 | ||||||||
\(817\) | −1.41714e25 | − | 1.41714e25i | −0.0873802 | − | 0.0873802i | ||||
\(818\) | 3.19838e25 | − | 3.19838e25i | 0.195052 | − | 0.195052i | ||||
\(819\) | 2.67786e26i | 1.61523i | ||||||||
\(820\) | 2.07620e25 | − | 9.88444e24i | 0.123864 | − | 0.0589695i | ||||
\(821\) | 1.47376e26 | 0.869639 | 0.434819 | − | 0.900518i | \(-0.356812\pi\) | ||||
0.434819 | + | 0.900518i | \(0.356812\pi\) | |||||||
\(822\) | −2.42613e26 | − | 2.42613e26i | −1.41602 | − | 1.41602i | ||||
\(823\) | −2.13336e26 | + | 2.13336e26i | −1.23159 | + | 1.23159i | −0.268238 | + | 0.963353i | \(0.586442\pi\) |
−0.963353 | + | 0.268238i | \(0.913558\pi\) | |||||||
\(824\) | − | 6.74353e25i | − | 0.385072i | ||||||
\(825\) | −2.42274e25 | − | 2.33778e26i | −0.136842 | − | 1.32044i | ||||
\(826\) | 1.64237e26 | 0.917594 | ||||||||
\(827\) | −1.90505e26 | − | 1.90505e26i | −1.05283 | − | 1.05283i | −0.998525 | − | 0.0543008i | \(-0.982707\pi\) |
−0.0543008 | − | 0.998525i | \(-0.517293\pi\) | |||||||
\(828\) | −7.21198e25 | + | 7.21198e25i | −0.394259 | + | 0.394259i | ||||
\(829\) | − | 2.37733e26i | − | 1.28558i | −0.766043 | − | 0.642790i | \(-0.777777\pi\) | ||
0.766043 | − | 0.642790i | \(-0.222223\pi\) | |||||||
\(830\) | 5.71932e24 | + | 1.20133e25i | 0.0305944 | + | 0.0642627i | ||||
\(831\) | −2.99354e25 | −0.158408 | ||||||||
\(832\) | −1.93960e25 | − | 1.93960e25i | −0.101532 | − | 0.101532i | ||||
\(833\) | −5.27227e24 | + | 5.27227e24i | −0.0273019 | + | 0.0273019i | ||||
\(834\) | 1.04915e26i | 0.537456i | ||||||||
\(835\) | 3.00114e25 | − | 8.45541e25i | 0.152092 | − | 0.428505i | ||||
\(836\) | −1.21638e26 | −0.609837 | ||||||||
\(837\) | 9.47871e25 | + | 9.47871e25i | 0.470132 | + | 0.470132i | ||||
\(838\) | −1.13717e26 | + | 1.13717e26i | −0.557993 | + | 0.557993i | ||||
\(839\) | − | 5.87426e25i | − | 0.285165i | −0.989783 | − | 0.142582i | \(-0.954459\pi\) | ||
0.989783 | − | 0.142582i | \(-0.0455406\pi\) | |||||||
\(840\) | −1.06612e26 | − | 3.78404e25i | −0.512025 | − | 0.181737i | ||||
\(841\) | 1.89776e25 | 0.0901734 | ||||||||
\(842\) | 9.47080e25 | + | 9.47080e25i | 0.445223 | + | 0.445223i | ||||
\(843\) | −9.53667e25 | + | 9.53667e25i | −0.443556 | + | 0.443556i | ||||
\(844\) | − | 5.21959e25i | − | 0.240190i | ||||||
\(845\) | 6.33629e25 | − | 3.01660e25i | 0.288486 | − | 0.137343i | ||||
\(846\) | −1.98907e26 | −0.896018 | ||||||||
\(847\) | 4.27798e25 | + | 4.27798e25i | 0.190672 | + | 0.190672i | ||||
\(848\) | 2.03481e25 | − | 2.03481e25i | 0.0897347 | − | 0.0897347i | ||||
\(849\) | 2.39698e26i | 1.04591i | ||||||||
\(850\) | −1.88136e26 | − | 1.52803e26i | −0.812274 | − | 0.659724i | ||||
\(851\) | −2.79156e26 | −1.19256 | ||||||||
\(852\) | 5.25466e25 | + | 5.25466e25i | 0.222120 | + | 0.222120i | ||||
\(853\) | −9.24585e25 | + | 9.24585e25i | −0.386728 | + | 0.386728i | −0.873519 | − | 0.486791i | \(-0.838167\pi\) |
0.486791 | + | 0.873519i | \(0.338167\pi\) | |||||||
\(854\) | 2.59170e26i | 1.07266i | ||||||||
\(855\) | −2.13960e26 | − | 4.49417e26i | −0.876268 | − | 1.84058i | ||||
\(856\) | −1.81474e25 | −0.0735447 | ||||||||
\(857\) | 1.93037e25 | + | 1.93037e25i | 0.0774130 | + | 0.0774130i | 0.744753 | − | 0.667340i | \(-0.232567\pi\) |
−0.667340 | + | 0.744753i | \(0.732567\pi\) | |||||||
\(858\) | 1.92132e26 | − | 1.92132e26i | 0.762455 | − | 0.762455i | ||||
\(859\) | − | 2.04874e25i | − | 0.0804541i | −0.999191 | − | 0.0402270i | \(-0.987192\pi\) | ||
0.999191 | − | 0.0402270i | \(-0.0128081\pi\) | |||||||
\(860\) | −3.71725e24 | + | 1.04730e25i | −0.0144456 | + | 0.0406991i | ||||
\(861\) | 1.09639e26 | 0.421635 | ||||||||
\(862\) | 8.38140e25 | + | 8.38140e25i | 0.318971 | + | 0.318971i | ||||
\(863\) | −1.92698e26 | + | 1.92698e26i | −0.725738 | + | 0.725738i | −0.969768 | − | 0.244030i | \(-0.921531\pi\) |
0.244030 | + | 0.969768i | \(0.421531\pi\) | |||||||
\(864\) | − | 3.13777e25i | − | 0.116949i | ||||||
\(865\) | 1.12277e26 | + | 3.98514e25i | 0.414140 | + | 0.146994i | ||||
\(866\) | 1.68336e26 | 0.614493 | ||||||||
\(867\) | 3.62714e26 | + | 3.62714e26i | 1.31037 | + | 1.31037i | ||||
\(868\) | −9.80743e25 | + | 9.80743e25i | −0.350653 | + | 0.350653i | ||||
\(869\) | − | 9.75247e25i | − | 0.345093i | ||||||
\(870\) | −2.70781e26 | + | 1.28914e26i | −0.948298 | + | 0.451469i | ||||
\(871\) | −5.90031e26 | −2.04509 | ||||||||
\(872\) | −2.61471e25 | − | 2.61471e25i | −0.0896965 | − | 0.0896965i | ||||
\(873\) | 3.48793e26 | − | 3.48793e26i | 1.18424 | − | 1.18424i | ||||
\(874\) | − | 2.35611e26i | − | 0.791757i | ||||||
\(875\) | 1.54478e26 | + | 2.53324e26i | 0.513801 | + | 0.842567i | ||||
\(876\) | 3.20117e26 | 1.05383 | ||||||||
\(877\) | 2.00014e25 | + | 2.00014e25i | 0.0651726 | + | 0.0651726i | 0.738942 | − | 0.673769i | \(-0.235326\pi\) |
−0.673769 | + | 0.738942i | \(0.735326\pi\) | |||||||
\(878\) | −7.53268e25 | + | 7.53268e25i | −0.242940 | + | 0.242940i | ||||
\(879\) | − | 3.44016e26i | − | 1.09819i | ||||||
\(880\) | 2.89936e25 | + | 6.09002e25i | 0.0916131 | + | 0.192431i | ||||
\(881\) | −4.19858e26 | −1.31316 | −0.656582 | − | 0.754255i | \(-0.727998\pi\) | ||||
−0.656582 | + | 0.754255i | \(0.727998\pi\) | |||||||
\(882\) | 6.00392e24 | + | 6.00392e24i | 0.0185874 | + | 0.0185874i | ||||
\(883\) | −5.48338e25 | + | 5.48338e25i | −0.168036 | + | 0.168036i | −0.786115 | − | 0.618080i | \(-0.787911\pi\) |
0.618080 | + | 0.786115i | \(0.287911\pi\) | |||||||
\(884\) | − | 2.80204e26i | − | 0.849970i | ||||||
\(885\) | 2.28099e26 | − | 6.42646e26i | 0.684911 | − | 1.92967i | ||||
\(886\) | 4.30307e26 | 1.27901 | ||||||||
\(887\) | −3.29199e26 | − | 3.29199e26i | −0.968604 | − | 0.968604i | 0.0309183 | − | 0.999522i | \(-0.490157\pi\) |
−0.999522 | + | 0.0309183i | \(0.990157\pi\) | |||||||
\(888\) | 2.03667e26 | − | 2.03667e26i | 0.593203 | − | 0.593203i | ||||
\(889\) | 4.97567e26i | 1.43462i | ||||||||
\(890\) | 3.04165e26 | + | 1.07959e26i | 0.868158 | + | 0.308141i | ||||
\(891\) | −1.19075e26 | −0.336451 | ||||||||
\(892\) | −1.53154e25 | − | 1.53154e25i | −0.0428396 | − | 0.0428396i | ||||
\(893\) | 3.24908e26 | − | 3.24908e26i | 0.899699 | − | 0.899699i | ||||
\(894\) | 8.40817e25i | 0.230496i | ||||||||
\(895\) | −1.08310e26 | + | 5.15645e25i | −0.293941 | + | 0.139941i | ||||
\(896\) | 3.24658e25 | 0.0872277 | ||||||||
\(897\) | 3.72156e26 | + | 3.72156e26i | 0.989903 | + | 0.989903i | ||||
\(898\) | −1.08561e26 | + | 1.08561e26i | −0.285882 | + | 0.285882i | ||||
\(899\) | 3.67688e26i | 0.958612i | ||||||||
\(900\) | −1.74009e26 | + | 2.14245e26i | −0.449146 | + | 0.553003i | ||||
\(901\) | 2.93958e26 | 0.751212 | ||||||||
\(902\) | −4.62232e25 | − | 4.62232e25i | −0.116950 | − | 0.116950i | ||||
\(903\) | −3.74676e25 | + | 3.74676e25i | −0.0938569 | + | 0.0938569i | ||||
\(904\) | 8.11980e24i | 0.0201386i | ||||||||
\(905\) | −9.93278e25 | − | 2.08635e26i | −0.243912 | − | 0.512331i | ||||
\(906\) | −5.04395e26 | −1.22636 | ||||||||
\(907\) | 1.20580e26 | + | 1.20580e26i | 0.290275 | + | 0.290275i | 0.837189 | − | 0.546914i | \(-0.184197\pi\) |
−0.546914 | + | 0.837189i | \(0.684197\pi\) | |||||||
\(908\) | −9.45381e25 | + | 9.45381e25i | −0.225338 | + | 0.225338i | ||||
\(909\) | 2.59972e26i | 0.613551i | ||||||||
\(910\) | −1.14739e26 | + | 3.23264e26i | −0.268125 | + | 0.755415i | ||||
\(911\) | 8.14540e26 | 1.88472 | 0.942360 | − | 0.334600i | \(-0.108601\pi\) | ||||
0.942360 | + | 0.334600i | \(0.108601\pi\) | |||||||
\(912\) | 1.71897e26 | + | 1.71897e26i | 0.393836 | + | 0.393836i | ||||
\(913\) | 2.67456e25 | − | 2.67456e25i | 0.0606758 | − | 0.0606758i | ||||
\(914\) | 4.76991e26i | 1.07151i | ||||||||
\(915\) | 1.01411e27 | + | 3.59945e26i | 2.25577 | + | 0.800657i | ||||
\(916\) | 4.26629e26 | 0.939705 | ||||||||
\(917\) | −4.25476e26 | − | 4.25476e26i | −0.928006 | − | 0.928006i | ||||
\(918\) | 2.26649e26 | − | 2.26649e26i | 0.489518 | − | 0.489518i | ||||
\(919\) | − | 3.19256e26i | − | 0.682809i | −0.939917 | − | 0.341404i | \(-0.889097\pi\) | ||
0.939917 | − | 0.341404i | \(-0.110903\pi\) | |||||||
\(920\) | −1.17962e26 | + | 5.61599e25i | −0.249835 | + | 0.118942i | ||||
\(921\) | −9.43429e26 | −1.97867 | ||||||||
\(922\) | −5.09764e25 | − | 5.09764e25i | −0.105874 | − | 0.105874i | ||||
\(923\) | 1.59330e26 | − | 1.59330e26i | 0.327705 | − | 0.327705i | ||||
\(924\) | 3.21599e26i | 0.655039i | ||||||||
\(925\) | −7.51410e26 | + | 7.78718e25i | −1.51566 | + | 0.157074i | ||||
\(926\) | 7.14816e25 | 0.142789 | ||||||||
\(927\) | −5.54699e26 | − | 5.54699e26i | −1.09734 | − | 1.09734i | ||||
\(928\) | 6.08585e25 | − | 6.08585e25i | 0.119231 | − | 0.119231i | ||||
\(929\) | − | 6.83658e26i | − | 1.32647i | −0.748411 | − | 0.663235i | \(-0.769183\pi\) | ||
0.748411 | − | 0.663235i | \(-0.230817\pi\) | |||||||
\(930\) | 2.47547e26 | + | 5.19967e26i | 0.475677 | + | 0.999146i | ||||
\(931\) | −1.96144e25 | −0.0373275 | ||||||||
\(932\) | −3.13984e26 | − | 3.13984e26i | −0.591786 | − | 0.591786i | ||||
\(933\) | −3.57398e26 | + | 3.57398e26i | −0.667141 | + | 0.667141i | ||||
\(934\) | − | 4.36771e26i | − | 0.807480i | ||||||
\(935\) | −2.30469e26 | + | 6.49325e26i | −0.421996 | + | 1.18893i | ||||
\(936\) | −3.19089e26 | −0.578667 | ||||||||
\(937\) | 1.72845e26 | + | 1.72845e26i | 0.310456 | + | 0.310456i | 0.845086 | − | 0.534630i | \(-0.179549\pi\) |
−0.534630 | + | 0.845086i | \(0.679549\pi\) | |||||||
\(938\) | 4.93810e26 | − | 4.93810e26i | 0.878485 | − | 0.878485i | ||||
\(939\) | − | 3.63842e26i | − | 0.641095i | ||||||
\(940\) | −2.40115e26 | − | 8.52258e25i | −0.419053 | − | 0.148737i | ||||
\(941\) | 2.95805e26 | 0.511328 | 0.255664 | − | 0.966766i | \(-0.417706\pi\) | ||||
0.255664 | + | 0.966766i | \(0.417706\pi\) | |||||||
\(942\) | −3.76926e26 | − | 3.76926e26i | −0.645354 | − | 0.645354i | ||||
\(943\) | 8.95334e25 | − | 8.95334e25i | 0.151838 | − | 0.151838i | ||||
\(944\) | 1.95701e26i | 0.328735i | ||||||||
\(945\) | −3.54288e26 | + | 1.68670e26i | −0.589481 | + | 0.280642i | ||||
\(946\) | 3.15923e25 | 0.0520668 | ||||||||
\(947\) | 5.46582e26 | + | 5.46582e26i | 0.892288 | + | 0.892288i | 0.994738 | − | 0.102450i | \(-0.0326681\pi\) |
−0.102450 | + | 0.994738i | \(0.532668\pi\) | |||||||
\(948\) | −1.37820e26 | + | 1.37820e26i | −0.222863 | + | 0.222863i | ||||
\(949\) | − | 9.70650e26i | − | 1.55477i | ||||||
\(950\) | −6.57247e25 | − | 6.34199e26i | −0.104284 | − | 1.00627i | ||||
\(951\) | −6.67376e26 | −1.04893 | ||||||||
\(952\) | 2.34509e26 | + | 2.34509e26i | 0.365112 | + | 0.365112i | ||||
\(953\) | −8.99405e25 | + | 8.99405e25i | −0.138714 | + | 0.138714i | −0.773054 | − | 0.634340i | \(-0.781272\pi\) |
0.634340 | + | 0.773054i | \(0.281272\pi\) | |||||||
\(954\) | − | 3.34752e26i | − | 0.511432i | ||||||
\(955\) | 3.28689e26 | + | 6.90403e26i | 0.497457 | + | 1.04489i | ||||
\(956\) | −3.88424e26 | −0.582351 | ||||||||
\(957\) | 6.02850e26 | + | 6.02850e26i | 0.895369 | + | 0.895369i | ||||
\(958\) | 8.06165e24 | − | 8.06165e24i | 0.0118614 | − | 0.0118614i | ||||
\(959\) | − | 1.23135e27i | − | 1.79480i | ||||||
\(960\) | 4.50899e25 | − | 1.27036e26i | 0.0651085 | − | 0.183437i | ||||
\(961\) | 6.99912e24 | 0.0100123 | ||||||||
\(962\) | −6.17552e26 | − | 6.17552e26i | −0.875181 | − | 0.875181i | ||||
\(963\) | −1.49274e26 | + | 1.49274e26i | −0.209580 | + | 0.209580i | ||||
\(964\) | 4.95010e25i | 0.0688527i | ||||||||
\(965\) | −3.20023e26 | − | 1.13588e26i | −0.440996 | − | 0.156526i | ||||
\(966\) | −6.22930e26 | −0.850443 | ||||||||
\(967\) | 3.04683e26 | + | 3.04683e26i | 0.412107 | + | 0.412107i | 0.882472 | − | 0.470365i | \(-0.155878\pi\) |
−0.470365 | + | 0.882472i | \(0.655878\pi\) | |||||||
\(968\) | −5.09755e25 | + | 5.09755e25i | −0.0683099 | + | 0.0683099i | ||||
\(969\) | 2.48331e27i | 3.29698i | ||||||||
\(970\) | 5.70501e26 | − | 2.71606e26i | 0.750432 | − | 0.357268i | ||||
\(971\) | −1.33377e26 | −0.173824 | −0.0869119 | − | 0.996216i | \(-0.527700\pi\) | ||||
−0.0869119 | + | 0.996216i | \(0.527700\pi\) | |||||||
\(972\) | 3.49419e26 | + | 3.49419e26i | 0.451180 | + | 0.451180i | ||||
\(973\) | −2.66242e26 | + | 2.66242e26i | −0.340612 | + | 0.340612i | ||||
\(974\) | − | 3.50892e26i | − | 0.444777i | ||||||
\(975\) | 1.10556e27 | + | 8.97926e26i | 1.38848 | + | 1.12771i | ||||
\(976\) | −3.08821e26 | −0.384290 | ||||||||
\(977\) | 3.39872e26 | + | 3.39872e26i | 0.419048 | + | 0.419048i | 0.884876 | − | 0.465827i | \(-0.154243\pi\) |
−0.465827 | + | 0.884876i | \(0.654243\pi\) | |||||||
\(978\) | −3.15908e26 | + | 3.15908e26i | −0.385932 | + | 0.385932i | ||||
\(979\) | − | 9.17527e26i | − | 1.11064i | ||||||
\(980\) | 4.67527e24 | + | 9.82028e24i | 0.00560754 | + | 0.0117785i | ||||
\(981\) | −4.30154e26 | −0.511214 | ||||||||
\(982\) | −1.94303e26 | − | 1.94303e26i | −0.228811 | − | 0.228811i | ||||
\(983\) | 1.10437e27 | − | 1.10437e27i | 1.28864 | − | 1.28864i | 0.353030 | − | 0.935612i | \(-0.385151\pi\) |
0.935612 | − | 0.353030i | \(-0.114849\pi\) | |||||||
\(984\) | 1.30644e26i | 0.151054i | ||||||||
\(985\) | −1.35391e26 | + | 3.81452e26i | −0.155119 | + | 0.437033i | ||||
\(986\) | 8.79192e26 | 0.998140 | ||||||||
\(987\) | −8.59023e26 | − | 8.59023e26i | −0.966386 | − | 0.966386i | ||||
\(988\) | 5.21221e26 | − | 5.21221e26i | 0.581045 | − | 0.581045i | ||||
\(989\) | 6.11936e25i | 0.0675988i | ||||||||
\(990\) | 7.39434e26 | + | 2.62453e26i | 0.809436 | + | 0.287299i | ||||
\(991\) | −1.18012e27 | −1.28015 | −0.640076 | − | 0.768311i | \(-0.721097\pi\) | ||||
−0.640076 | + | 0.768311i | \(0.721097\pi\) | |||||||
\(992\) | −1.16863e26 | − | 1.16863e26i | −0.125624 | − | 0.125624i | ||||
\(993\) | −4.98213e26 | + | 4.98213e26i | −0.530728 | + | 0.530728i | ||||
\(994\) | 2.66694e26i | 0.281537i | ||||||||
\(995\) | 1.08232e27 | − | 5.15276e26i | 1.13227 | − | 0.539053i | ||||
\(996\) | −7.55929e25 | −0.0783695 | ||||||||
\(997\) | 8.35834e26 | + | 8.35834e26i | 0.858744 | + | 0.858744i | 0.991190 | − | 0.132446i | \(-0.0422832\pi\) |
−0.132446 | + | 0.991190i | \(0.542283\pi\) | |||||||
\(998\) | −5.82769e26 | + | 5.82769e26i | −0.593364 | + | 0.593364i | ||||
\(999\) | − | 9.99039e26i | − | 1.00808i |
(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 | 10.19.c.b.7.5 | yes | 10 | |
3.2 | odd | 2 | 90.19.g.b.37.2 | 10 | |||
5.2 | odd | 4 | 50.19.c.d.43.1 | 10 | |||
5.3 | odd | 4 | inner | 10.19.c.b.3.5 | ✓ | 10 | |
5.4 | even | 2 | 50.19.c.d.7.1 | 10 | |||
15.8 | even | 4 | 90.19.g.b.73.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.19.c.b.3.5 | ✓ | 10 | 5.3 | odd | 4 | inner | |
10.19.c.b.7.5 | yes | 10 | 1.1 | even | 1 | trivial | |
50.19.c.d.7.1 | 10 | 5.4 | even | 2 | |||
50.19.c.d.43.1 | 10 | 5.2 | odd | 4 | |||
90.19.g.b.37.2 | 10 | 3.2 | odd | 2 | |||
90.19.g.b.73.2 | 10 | 15.8 | even | 4 |