Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,12,Mod(55,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.55");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.b (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: | \(64.5408271670\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.2 | ||
Character | \(\chi\) | \(=\) | 84.55 |
Dual form | 84.12.b.a.55.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −45.2221 | + | 1.72065i | −0.999277 | + | 0.0380213i | ||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 2042.08 | − | 155.623i | 0.997109 | − | 0.0759877i | ||||
\(5\) | − | 479.067i | − | 0.0685585i | −0.999412 | − | 0.0342793i | \(-0.989086\pi\) | ||
0.999412 | − | 0.0342793i | \(-0.0109136\pi\) | |||||||
\(6\) | 10989.0 | − | 418.118i | 0.576933 | − | 0.0219516i | ||||
\(7\) | 18444.0 | + | 40461.6i | 0.414779 | + | 0.909922i | ||||
\(8\) | −92079.3 | + | 10551.3i | −0.993499 | + | 0.113844i | ||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 824.307 | + | 21664.4i | 0.00260669 | + | 0.0685089i | ||||
\(11\) | − | 617971.i | − | 1.15693i | −0.815706 | − | 0.578467i | \(-0.803651\pi\) | ||
0.815706 | − | 0.578467i | \(-0.196349\pi\) | |||||||
\(12\) | −496225. | + | 37816.3i | −0.575681 | + | 0.0438715i | ||||
\(13\) | 805412.i | 0.601630i | 0.953682 | + | 0.300815i | \(0.0972587\pi\) | ||||
−0.953682 | + | 0.300815i | \(0.902741\pi\) | |||||||
\(14\) | −903698. | − | 1.79803e6i | −0.449075 | − | 0.893494i | ||||
\(15\) | 116413.i | 0.0395823i | ||||||||
\(16\) | 4.14587e6 | − | 635588.i | 0.988452 | − | 0.151536i | ||||
\(17\) | − | 6.15701e6i | − | 1.05172i | −0.850570 | − | 0.525861i | \(-0.823743\pi\) | ||
0.850570 | − | 0.525861i | \(-0.176257\pi\) | |||||||
\(18\) | −2.67032e6 | + | 101603.i | −0.333092 | + | 0.0126738i | ||||
\(19\) | 3.03570e6 | 0.281264 | 0.140632 | − | 0.990062i | \(-0.455087\pi\) | ||||
0.140632 | + | 0.990062i | \(0.455087\pi\) | |||||||
\(20\) | −74553.8 | − | 978293.i | −0.00520960 | − | 0.0683603i | ||||
\(21\) | −4.48190e6 | − | 9.83218e6i | −0.239473 | − | 0.525344i | ||||
\(22\) | 1.06331e6 | + | 2.79460e7i | 0.0439882 | + | 1.15610i | ||||
\(23\) | 6.78832e6i | 0.219917i | 0.993936 | + | 0.109959i | \(0.0350718\pi\) | ||||
−0.993936 | + | 0.109959i | \(0.964928\pi\) | |||||||
\(24\) | 2.23753e7 | − | 2.56396e6i | 0.573597 | − | 0.0657280i | ||||
\(25\) | 4.85986e7 | 0.995300 | ||||||||
\(26\) | −1.38583e6 | − | 3.64224e7i | −0.0228748 | − | 0.601195i | ||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 4.39609e7 | + | 7.97555e7i | 0.482723 | + | 0.875773i | ||||
\(29\) | −2.53110e7 | −0.229150 | −0.114575 | − | 0.993415i | \(-0.536551\pi\) | ||||
−0.114575 | + | 0.993415i | \(0.536551\pi\) | |||||||
\(30\) | −200307. | − | 5.26446e6i | −0.00150497 | − | 0.0395537i | ||||
\(31\) | −2.54102e8 | −1.59411 | −0.797057 | − | 0.603904i | \(-0.793611\pi\) | ||||
−0.797057 | + | 0.603904i | \(0.793611\pi\) | |||||||
\(32\) | −1.86391e8 | + | 3.58762e7i | −0.981975 | + | 0.189009i | ||||
\(33\) | 1.50167e8i | 0.667956i | ||||||||
\(34\) | 1.05941e7 | + | 2.78433e8i | 0.0399879 | + | 1.05096i | ||||
\(35\) | 1.93838e7 | − | 8.83593e6i | 0.0623829 | − | 0.0284366i | ||||
\(36\) | 1.20583e8 | − | 9.18937e6i | 0.332370 | − | 0.0253292i | ||||
\(37\) | −3.76158e8 | −0.891786 | −0.445893 | − | 0.895086i | \(-0.647114\pi\) | ||||
−0.445893 | + | 0.895086i | \(0.647114\pi\) | |||||||
\(38\) | −1.37281e8 | + | 5.22338e6i | −0.281061 | + | 0.0106940i | ||||
\(39\) | − | 1.95715e8i | − | 0.347351i | ||||||
\(40\) | 5.05478e6 | + | 4.41122e7i | 0.00780499 | + | 0.0681128i | ||||
\(41\) | 6.88640e8i | 0.928285i | 0.885761 | + | 0.464142i | \(0.153637\pi\) | ||||
−0.885761 | + | 0.464142i | \(0.846363\pi\) | |||||||
\(42\) | 2.19599e8 | + | 4.36920e8i | 0.259274 | + | 0.515859i | ||||
\(43\) | 1.05610e9i | 1.09554i | 0.836629 | + | 0.547770i | \(0.184523\pi\) | ||||
−0.836629 | + | 0.547770i | \(0.815477\pi\) | |||||||
\(44\) | −9.61704e7 | − | 1.26195e9i | −0.0879127 | − | 1.15359i | ||||
\(45\) | − | 2.82884e7i | − | 0.0228528i | ||||||
\(46\) | −1.16803e7 | − | 3.06982e8i | −0.00836154 | − | 0.219758i | ||||
\(47\) | 1.61462e9 | 1.02691 | 0.513453 | − | 0.858117i | \(-0.328366\pi\) | ||||
0.513453 | + | 0.858117i | \(0.328366\pi\) | |||||||
\(48\) | −1.00745e9 | + | 1.54448e8i | −0.570683 | + | 0.0874893i | ||||
\(49\) | −1.29696e9 | + | 1.49255e9i | −0.655917 | + | 0.754833i | ||||
\(50\) | −2.19773e9 | + | 8.36212e7i | −0.994580 | + | 0.0378426i | ||||
\(51\) | 1.49615e9i | 0.607212i | ||||||||
\(52\) | 1.25340e8 | + | 1.64471e9i | 0.0457165 | + | 0.599891i | ||||
\(53\) | 2.86554e9 | 0.941216 | 0.470608 | − | 0.882342i | \(-0.344035\pi\) | ||||
0.470608 | + | 0.882342i | \(0.344035\pi\) | |||||||
\(54\) | 6.48888e8 | − | 2.46894e7i | 0.192311 | − | 0.00731721i | ||||
\(55\) | −2.96050e8 | −0.0793177 | ||||||||
\(56\) | −2.12524e9 | − | 3.53107e9i | −0.515672 | − | 0.856786i | ||||
\(57\) | −7.37675e8 | −0.162388 | ||||||||
\(58\) | 1.14462e9 | − | 4.35514e7i | 0.228985 | − | 0.00871261i | ||||
\(59\) | −5.63596e9 | −1.02632 | −0.513159 | − | 0.858293i | \(-0.671525\pi\) | ||||
−0.513159 | + | 0.858293i | \(0.671525\pi\) | |||||||
\(60\) | 1.81166e7 | + | 2.37725e8i | 0.00300777 | + | 0.0394678i | ||||
\(61\) | − | 7.15254e9i | − | 1.08429i | −0.840284 | − | 0.542146i | \(-0.817612\pi\) | ||
0.840284 | − | 0.542146i | \(-0.182388\pi\) | |||||||
\(62\) | 1.14910e10 | − | 4.37221e8i | 1.59296 | − | 0.0606103i | ||||
\(63\) | 1.08910e9 | + | 2.38922e9i | 0.138260 | + | 0.303307i | ||||
\(64\) | 8.36728e9 | − | 1.94311e9i | 0.974079 | − | 0.226208i | ||||
\(65\) | 3.85847e8 | 0.0412469 | ||||||||
\(66\) | −2.58385e8 | − | 6.79087e9i | −0.0253966 | − | 0.667473i | ||||
\(67\) | − | 3.11480e9i | − | 0.281850i | −0.990020 | − | 0.140925i | \(-0.954992\pi\) | ||
0.990020 | − | 0.140925i | \(-0.0450077\pi\) | |||||||
\(68\) | −9.58172e8 | − | 1.25731e10i | −0.0799180 | − | 1.04868i | ||||
\(69\) | − | 1.64956e9i | − | 0.126969i | ||||||
\(70\) | −8.61375e8 | + | 4.32932e8i | −0.0612566 | + | 0.0307879i | ||||
\(71\) | − | 1.04104e10i | − | 0.684772i | −0.939559 | − | 0.342386i | \(-0.888765\pi\) | ||
0.939559 | − | 0.342386i | \(-0.111235\pi\) | |||||||
\(72\) | −5.43719e9 | + | 6.23043e8i | −0.331166 | + | 0.0379481i | ||||
\(73\) | − | 2.84639e10i | − | 1.60701i | −0.595297 | − | 0.803506i | \(-0.702966\pi\) | ||
0.595297 | − | 0.803506i | \(-0.297034\pi\) | |||||||
\(74\) | 1.70107e10 | − | 6.47236e8i | 0.891141 | − | 0.0339069i | ||||
\(75\) | −1.18095e10 | −0.574637 | ||||||||
\(76\) | 6.19914e9 | − | 4.72424e8i | 0.280451 | − | 0.0213726i | ||||
\(77\) | 2.50041e10 | − | 1.13979e10i | 1.05272 | − | 0.479872i | ||||
\(78\) | 3.36757e8 | + | 8.85065e9i | 0.0132068 | + | 0.347100i | ||||
\(79\) | 4.17004e10i | 1.52472i | 0.647150 | + | 0.762362i | \(0.275961\pi\) | ||||
−0.647150 | + | 0.762362i | \(0.724039\pi\) | |||||||
\(80\) | −3.04489e8 | − | 1.98615e9i | −0.0103891 | − | 0.0677668i | ||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −1.18491e9 | − | 3.11418e10i | −0.0352946 | − | 0.927614i | ||||
\(83\) | 3.43032e10 | 0.955883 | 0.477942 | − | 0.878392i | \(-0.341383\pi\) | ||||
0.477942 | + | 0.878392i | \(0.341383\pi\) | |||||||
\(84\) | −1.06825e10 | − | 1.93806e10i | −0.278700 | − | 0.505628i | ||||
\(85\) | −2.94962e9 | −0.0721045 | ||||||||
\(86\) | −1.81718e9 | − | 4.77591e10i | −0.0416539 | − | 1.09475i | ||||
\(87\) | 6.15058e9 | 0.132300 | ||||||||
\(88\) | 6.52040e9 | + | 5.69024e10i | 0.131710 | + | 1.14941i | ||||
\(89\) | − | 1.68359e10i | − | 0.319589i | −0.987150 | − | 0.159795i | \(-0.948917\pi\) | ||
0.987150 | − | 0.159795i | \(-0.0510832\pi\) | |||||||
\(90\) | 4.86745e7 | + | 1.27926e9i | 0.000868896 | + | 0.0228363i | ||||
\(91\) | −3.25883e10 | + | 1.48550e10i | −0.547437 | + | 0.249544i | ||||
\(92\) | 1.05642e9 | + | 1.38623e10i | 0.0167110 | + | 0.219281i | ||||
\(93\) | 6.17468e10 | 0.920362 | ||||||||
\(94\) | −7.30163e10 | + | 2.77819e9i | −1.02616 | + | 0.0390444i | ||||
\(95\) | − | 1.45430e9i | − | 0.0192830i | ||||||
\(96\) | 4.52931e10 | − | 8.71792e9i | 0.566944 | − | 0.109124i | ||||
\(97\) | − | 1.64842e11i | − | 1.94905i | −0.224284 | − | 0.974524i | \(-0.572004\pi\) | ||
0.224284 | − | 0.974524i | \(-0.427996\pi\) | |||||||
\(98\) | 5.60832e10 | − | 6.97280e10i | 0.626743 | − | 0.779226i | ||||
\(99\) | − | 3.64906e10i | − | 0.385645i | ||||||
\(100\) | 9.92422e10 | − | 7.56305e9i | 0.992422 | − | 0.0756305i | ||||
\(101\) | − | 1.82562e11i | − | 1.72840i | −0.503150 | − | 0.864199i | \(-0.667826\pi\) | ||
0.503150 | − | 0.864199i | \(-0.332174\pi\) | |||||||
\(102\) | −2.57436e9 | − | 6.76593e10i | −0.0230870 | − | 0.606773i | ||||
\(103\) | 2.10558e10 | 0.178964 | 0.0894822 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894822 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(104\) | −8.49814e9 | − | 7.41618e10i | −0.0684921 | − | 0.597719i | ||||
\(105\) | −4.71027e9 | + | 2.14713e9i | −0.0360168 | + | 0.0164179i | ||||
\(106\) | −1.29586e11 | + | 4.93059e9i | −0.940536 | + | 0.0357863i | ||||
\(107\) | − | 5.95206e10i | − | 0.410257i | −0.978735 | − | 0.205129i | \(-0.934239\pi\) | ||
0.978735 | − | 0.205129i | \(-0.0657613\pi\) | |||||||
\(108\) | −2.93016e10 | + | 2.23302e9i | −0.191894 | + | 0.0146238i | ||||
\(109\) | 1.72861e11 | 1.07610 | 0.538049 | − | 0.842914i | \(-0.319162\pi\) | ||||
0.538049 | + | 0.842914i | \(0.319162\pi\) | |||||||
\(110\) | 1.33880e10 | − | 5.09398e8i | 0.0792603 | − | 0.00301576i | ||||
\(111\) | 9.14063e10 | 0.514873 | ||||||||
\(112\) | 1.02183e11 | + | 1.56026e11i | 0.547875 | + | 0.836560i | ||||
\(113\) | 4.09553e10 | 0.209112 | 0.104556 | − | 0.994519i | \(-0.466658\pi\) | ||||
0.104556 | + | 0.994519i | \(0.466658\pi\) | |||||||
\(114\) | 3.33592e10 | − | 1.26928e9i | 0.162270 | − | 0.00617420i | ||||
\(115\) | 3.25206e9 | 0.0150772 | ||||||||
\(116\) | −5.16871e10 | + | 3.93897e9i | −0.228488 | + | 0.0174126i | ||||
\(117\) | 4.75588e10i | 0.200543i | ||||||||
\(118\) | 2.54870e11 | − | 9.69752e9i | 1.02558 | − | 0.0390220i | ||||
\(119\) | 2.49123e11 | − | 1.13560e11i | 0.956986 | − | 0.436232i | ||||
\(120\) | −1.22831e9 | − | 1.07193e10i | −0.00450621 | − | 0.0393249i | ||||
\(121\) | −9.65769e10 | −0.338496 | ||||||||
\(122\) | 1.23070e10 | + | 3.23453e11i | 0.0412262 | + | 1.08351i | ||||
\(123\) | − | 1.67340e11i | − | 0.535945i | ||||||
\(124\) | −5.18897e11 | + | 3.95441e10i | −1.58950 | + | 0.121133i | ||||
\(125\) | − | 4.66740e10i | − | 0.136795i | ||||||
\(126\) | −5.33625e10 | − | 1.06172e11i | −0.149692 | − | 0.297831i | ||||
\(127\) | − | 4.58978e10i | − | 0.123274i | −0.998099 | − | 0.0616370i | \(-0.980368\pi\) | ||
0.998099 | − | 0.0616370i | \(-0.0196321\pi\) | |||||||
\(128\) | −3.75042e11 | + | 1.02269e11i | −0.964774 | + | 0.263080i | ||||
\(129\) | − | 2.56632e11i | − | 0.632511i | ||||||
\(130\) | −1.74488e10 | + | 6.63907e8i | −0.0412171 | + | 0.00156826i | ||||
\(131\) | −6.01350e11 | −1.36187 | −0.680935 | − | 0.732344i | \(-0.738426\pi\) | ||||
−0.680935 | + | 0.732344i | \(0.738426\pi\) | |||||||
\(132\) | 2.33694e10 | + | 3.06653e11i | 0.0507564 | + | 0.666025i | ||||
\(133\) | 5.59906e10 | + | 1.22829e11i | 0.116662 | + | 0.255928i | ||||
\(134\) | 5.35947e9 | + | 1.40858e11i | 0.0107163 | + | 0.281646i | ||||
\(135\) | 6.87409e9i | 0.0131941i | ||||||||
\(136\) | 6.49645e10 | + | 5.66934e11i | 0.119732 | + | 1.04488i | ||||
\(137\) | 6.29401e10 | 0.111420 | 0.0557102 | − | 0.998447i | \(-0.482258\pi\) | ||||
0.0557102 | + | 0.998447i | \(0.482258\pi\) | |||||||
\(138\) | 2.83832e9 | + | 7.45966e10i | 0.00482754 | + | 0.126877i | ||||
\(139\) | −4.56494e11 | −0.746198 | −0.373099 | − | 0.927792i | \(-0.621705\pi\) | ||||
−0.373099 | + | 0.927792i | \(0.621705\pi\) | |||||||
\(140\) | 3.82083e10 | − | 2.10602e10i | 0.0600417 | − | 0.0330947i | ||||
\(141\) | −3.92352e11 | −0.592885 | ||||||||
\(142\) | 1.79126e10 | + | 4.70780e11i | 0.0260360 | + | 0.684277i | ||||
\(143\) | 4.97722e11 | 0.696047 | ||||||||
\(144\) | 2.44809e11 | − | 3.75308e10i | 0.329484 | − | 0.0505120i | ||||
\(145\) | 1.21257e10i | 0.0157102i | ||||||||
\(146\) | 4.89764e10 | + | 1.28720e12i | 0.0611007 | + | 1.60585i | ||||
\(147\) | 3.15162e11 | − | 3.62690e11i | 0.378694 | − | 0.435803i | ||||
\(148\) | −7.68144e11 | + | 5.85387e10i | −0.889208 | + | 0.0677648i | ||||
\(149\) | 7.80967e11 | 0.871181 | 0.435591 | − | 0.900145i | \(-0.356540\pi\) | ||||
0.435591 | + | 0.900145i | \(0.356540\pi\) | |||||||
\(150\) | 5.34049e11 | − | 2.03199e10i | 0.574221 | − | 0.0218485i | ||||
\(151\) | 1.59890e12i | 1.65748i | 0.559637 | + | 0.828738i | \(0.310941\pi\) | ||||
−0.559637 | + | 0.828738i | \(0.689059\pi\) | |||||||
\(152\) | −2.79525e11 | + | 3.20306e10i | −0.279435 | + | 0.0320203i | ||||
\(153\) | − | 3.63566e11i | − | 0.350574i | ||||||
\(154\) | −1.11113e12 | + | 5.58460e11i | −1.03371 | + | 0.519551i | ||||
\(155\) | 1.21732e11i | 0.109290i | ||||||||
\(156\) | −3.04577e10 | − | 3.99666e11i | −0.0263944 | − | 0.346347i | ||||
\(157\) | − | 1.17727e12i | − | 0.984978i | −0.870319 | − | 0.492489i | \(-0.836087\pi\) | ||
0.870319 | − | 0.492489i | \(-0.163913\pi\) | |||||||
\(158\) | −7.17518e10 | − | 1.88578e12i | −0.0579721 | − | 1.52362i | ||||
\(159\) | −6.96327e11 | −0.543412 | ||||||||
\(160\) | 1.71871e10 | + | 8.92939e10i | 0.0129582 | + | 0.0673228i | ||||
\(161\) | −2.74666e11 | + | 1.25204e11i | −0.200107 | + | 0.0912170i | ||||
\(162\) | −1.57680e11 | + | 5.99953e9i | −0.111031 | + | 0.00422459i | ||||
\(163\) | 3.34549e11i | 0.227734i | 0.993496 | + | 0.113867i | \(0.0363238\pi\) | ||||
−0.993496 | + | 0.113867i | \(0.963676\pi\) | |||||||
\(164\) | 1.07168e11 | + | 1.40626e12i | 0.0705382 | + | 0.925601i | ||||
\(165\) | 7.19401e10 | 0.0457941 | ||||||||
\(166\) | −1.55126e12 | + | 5.90237e10i | −0.955192 | + | 0.0363440i | ||||
\(167\) | 1.18173e12 | 0.704008 | 0.352004 | − | 0.935998i | \(-0.385500\pi\) | ||||
0.352004 | + | 0.935998i | \(0.385500\pi\) | |||||||
\(168\) | 5.16433e11 | + | 8.58051e11i | 0.297723 | + | 0.494666i | ||||
\(169\) | 1.14347e12 | 0.638041 | ||||||||
\(170\) | 1.33388e11 | − | 5.07527e9i | 0.0720524 | − | 0.00274151i | ||||
\(171\) | 1.79255e11 | 0.0937547 | ||||||||
\(172\) | 1.64353e11 | + | 2.15664e12i | 0.0832476 | + | 1.09237i | ||||
\(173\) | − | 3.74576e12i | − | 1.83775i | −0.394548 | − | 0.918875i | \(-0.629099\pi\) | ||
0.394548 | − | 0.918875i | \(-0.370901\pi\) | |||||||
\(174\) | −2.78142e11 | + | 1.05830e10i | −0.132204 | + | 0.00503023i | ||||
\(175\) | 8.96355e11 | + | 1.96638e12i | 0.412829 | + | 0.905645i | ||||
\(176\) | −3.92775e11 | − | 2.56203e12i | −0.175317 | − | 1.14357i | ||||
\(177\) | 1.36954e12 | 0.592545 | ||||||||
\(178\) | 2.89687e10 | + | 7.61356e11i | 0.0121512 | + | 0.319358i | ||||
\(179\) | − | 3.01633e12i | − | 1.22684i | −0.789758 | − | 0.613419i | \(-0.789794\pi\) | ||
0.789758 | − | 0.613419i | \(-0.210206\pi\) | |||||||
\(180\) | −4.40233e9 | − | 5.77672e10i | −0.00173653 | − | 0.0227868i | ||||
\(181\) | − | 6.31151e11i | − | 0.241491i | −0.992683 | − | 0.120746i | \(-0.961471\pi\) | ||
0.992683 | − | 0.120746i | \(-0.0385285\pi\) | |||||||
\(182\) | 1.44815e12 | − | 7.27850e11i | 0.537553 | − | 0.270177i | ||||
\(183\) | 1.73807e12i | 0.626016i | ||||||||
\(184\) | −7.16255e10 | − | 6.25064e11i | −0.0250363 | − | 0.218487i | ||||
\(185\) | 1.80205e11i | 0.0611395i | ||||||||
\(186\) | −2.79232e12 | + | 1.06245e11i | −0.919696 | + | 0.0349934i | ||||
\(187\) | −3.80486e12 | −1.21677 | ||||||||
\(188\) | 3.29717e12 | − | 2.51271e11i | 1.02394 | − | 0.0780323i | ||||
\(189\) | −2.64652e11 | − | 5.80580e11i | −0.0798242 | − | 0.175115i | ||||
\(190\) | 2.50235e9 | + | 6.57667e10i | 0.000733167 | + | 0.0192691i | ||||
\(191\) | − | 3.16029e12i | − | 0.899587i | −0.893133 | − | 0.449793i | \(-0.851498\pi\) | ||
0.893133 | − | 0.449793i | \(-0.148502\pi\) | |||||||
\(192\) | −2.03325e12 | + | 4.72176e11i | −0.562385 | + | 0.130601i | ||||
\(193\) | 1.77257e12 | 0.476474 | 0.238237 | − | 0.971207i | \(-0.423430\pi\) | ||||
0.238237 | + | 0.971207i | \(0.423430\pi\) | |||||||
\(194\) | 2.83635e11 | + | 7.45449e12i | 0.0741054 | + | 1.94764i | ||||
\(195\) | −9.37607e10 | −0.0238139 | ||||||||
\(196\) | −2.41622e12 | + | 3.24974e12i | −0.596662 | + | 0.802492i | ||||
\(197\) | −1.17677e12 | −0.282572 | −0.141286 | − | 0.989969i | \(-0.545124\pi\) | ||||
−0.141286 | + | 0.989969i | \(0.545124\pi\) | |||||||
\(198\) | 6.27875e10 | + | 1.65018e12i | 0.0146627 | + | 0.385366i | ||||
\(199\) | −3.32981e11 | −0.0756358 | −0.0378179 | − | 0.999285i | \(-0.512041\pi\) | ||||
−0.0378179 | + | 0.999285i | \(0.512041\pi\) | |||||||
\(200\) | −4.47493e12 | + | 5.12778e11i | −0.988829 | + | 0.113309i | ||||
\(201\) | 7.56895e11i | 0.162726i | ||||||||
\(202\) | 3.14126e11 | + | 8.25586e12i | 0.0657160 | + | 1.72715i | ||||
\(203\) | −4.66837e11 | − | 1.02413e12i | −0.0950468 | − | 0.208509i | ||||
\(204\) | 2.32836e11 | + | 3.05527e12i | 0.0461407 | + | 0.605457i | ||||
\(205\) | 3.29905e11 | 0.0636418 | ||||||||
\(206\) | −9.52187e11 | + | 3.62296e10i | −0.178835 | + | 0.00680447i | ||||
\(207\) | 4.00843e11i | 0.0733057i | ||||||||
\(208\) | 5.11910e11 | + | 3.33913e12i | 0.0911686 | + | 0.594682i | ||||
\(209\) | − | 1.87598e12i | − | 0.325404i | ||||||
\(210\) | 2.09314e11 | − | 1.05203e11i | 0.0353665 | − | 0.0177754i | ||||
\(211\) | − | 3.77872e12i | − | 0.622002i | −0.950410 | − | 0.311001i | \(-0.899336\pi\) | ||
0.950410 | − | 0.311001i | \(-0.100664\pi\) | |||||||
\(212\) | 5.85166e12 | − | 4.45944e11i | 0.938495 | − | 0.0715209i | ||||
\(213\) | 2.52973e12i | 0.395354i | ||||||||
\(214\) | 1.02414e11 | + | 2.69165e12i | 0.0155985 | + | 0.409961i | ||||
\(215\) | 5.05943e11 | 0.0751086 | ||||||||
\(216\) | 1.32124e12 | − | 1.51400e11i | 0.191199 | − | 0.0219093i | ||||
\(217\) | −4.68667e12 | − | 1.02814e13i | −0.661205 | − | 1.45052i | ||||
\(218\) | −7.81714e12 | + | 2.97433e11i | −1.07532 | + | 0.0409147i | ||||
\(219\) | 6.91673e12i | 0.927808i | ||||||||
\(220\) | −6.04557e11 | + | 4.60721e10i | −0.0790884 | + | 0.00602717i | ||||
\(221\) | 4.95893e12 | 0.632748 | ||||||||
\(222\) | −4.13359e12 | + | 1.57278e11i | −0.514501 | + | 0.0195762i | ||||
\(223\) | 8.50333e12 | 1.03255 | 0.516276 | − | 0.856422i | \(-0.327318\pi\) | ||||
0.516276 | + | 0.856422i | \(0.327318\pi\) | |||||||
\(224\) | −4.88942e12 | − | 6.87999e12i | −0.579286 | − | 0.815124i | ||||
\(225\) | 2.86970e12 | 0.331767 | ||||||||
\(226\) | −1.85209e12 | + | 7.04698e10i | −0.208961 | + | 0.00795072i | ||||
\(227\) | 6.84775e12 | 0.754060 | 0.377030 | − | 0.926201i | \(-0.376945\pi\) | ||||
0.377030 | + | 0.926201i | \(0.376945\pi\) | |||||||
\(228\) | −1.50639e12 | + | 1.14799e11i | −0.161918 | + | 0.0123395i | ||||
\(229\) | − | 7.51129e12i | − | 0.788169i | −0.919074 | − | 0.394085i | \(-0.871062\pi\) | ||
0.919074 | − | 0.394085i | \(-0.128938\pi\) | |||||||
\(230\) | −1.47065e11 | + | 5.59565e9i | −0.0150663 | + | 0.000573255i | ||||
\(231\) | −6.07600e12 | + | 2.76969e12i | −0.607788 | + | 0.277054i | ||||
\(232\) | 2.33062e12 | − | 2.67064e11i | 0.227661 | − | 0.0260874i | ||||
\(233\) | 1.39492e13 | 1.33074 | 0.665369 | − | 0.746515i | \(-0.268274\pi\) | ||||
0.665369 | + | 0.746515i | \(0.268274\pi\) | |||||||
\(234\) | −8.18320e10 | − | 2.15071e12i | −0.00762493 | − | 0.200398i | ||||
\(235\) | − | 7.73510e11i | − | 0.0704032i | ||||||
\(236\) | −1.15091e13 | + | 8.77085e11i | −1.02335 | + | 0.0779876i | ||||
\(237\) | − | 1.01332e13i | − | 0.880300i | ||||||
\(238\) | −1.10705e13 | + | 5.56408e12i | −0.939707 | + | 0.472303i | ||||
\(239\) | − | 2.57628e12i | − | 0.213700i | −0.994275 | − | 0.106850i | \(-0.965923\pi\) | ||
0.994275 | − | 0.106850i | \(-0.0340765\pi\) | |||||||
\(240\) | 7.39909e10 | + | 4.82634e11i | 0.00599814 | + | 0.0391252i | ||||
\(241\) | − | 4.33765e12i | − | 0.343685i | −0.985124 | − | 0.171843i | \(-0.945028\pi\) | ||
0.985124 | − | 0.171843i | \(-0.0549720\pi\) | |||||||
\(242\) | 4.36741e12 | − | 1.66175e11i | 0.338252 | − | 0.0128701i | ||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | −1.11310e12 | − | 1.46060e13i | −0.0823928 | − | 1.08116i | ||||
\(245\) | 7.15033e11 | + | 6.21332e11i | 0.0517502 | + | 0.0449687i | ||||
\(246\) | 2.87933e11 | + | 7.56745e12i | 0.0203774 | + | 0.535558i | ||||
\(247\) | 2.44499e12i | 0.169217i | ||||||||
\(248\) | 2.33976e13 | − | 2.68111e12i | 1.58375 | − | 0.181481i | ||||
\(249\) | −8.33567e12 | −0.551879 | ||||||||
\(250\) | 8.03095e10 | + | 2.11070e12i | 0.00520112 | + | 0.136696i | ||||
\(251\) | 2.49868e12 | 0.158309 | 0.0791546 | − | 0.996862i | \(-0.474778\pi\) | ||||
0.0791546 | + | 0.996862i | \(0.474778\pi\) | |||||||
\(252\) | 2.59585e12 | + | 4.70949e12i | 0.160908 | + | 0.291924i | ||||
\(253\) | 4.19499e12 | 0.254430 | ||||||||
\(254\) | 7.89741e10 | + | 2.07560e12i | 0.00468704 | + | 0.123185i | ||||
\(255\) | 7.16759e11 | 0.0416296 | ||||||||
\(256\) | 1.67842e13 | − | 5.27013e12i | 0.954074 | − | 0.299572i | ||||
\(257\) | − | 1.97217e13i | − | 1.09727i | −0.836063 | − | 0.548634i | \(-0.815148\pi\) | ||
0.836063 | − | 0.548634i | \(-0.184852\pi\) | |||||||
\(258\) | 4.41574e11 | + | 1.16055e13i | 0.0240489 | + | 0.632053i | ||||
\(259\) | −6.93787e12 | − | 1.52200e13i | −0.369894 | − | 0.811456i | ||||
\(260\) | 7.87929e11 | − | 6.00465e10i | 0.0411276 | − | 0.00313426i | ||||
\(261\) | −1.49459e12 | −0.0763835 | ||||||||
\(262\) | 2.71943e13 | − | 1.03471e12i | 1.36088 | − | 0.0517801i | ||||
\(263\) | 2.01705e10i | 0.000988463i | 1.00000 | 0.000494232i | \(0.000157319\pi\) | |||||
−1.00000 | 0.000494232i | \(0.999843\pi\) | ||||||||
\(264\) | −1.58446e12 | − | 1.38273e13i | −0.0760429 | − | 0.663614i | ||||
\(265\) | − | 1.37279e12i | − | 0.0645284i | ||||||
\(266\) | −2.74336e12 | − | 5.45827e12i | −0.126309 | − | 0.251308i | ||||
\(267\) | 4.09113e12i | 0.184515i | ||||||||
\(268\) | −4.84733e11 | − | 6.36066e12i | −0.0214171 | − | 0.281035i | ||||
\(269\) | − | 1.36960e13i | − | 0.592865i | −0.955054 | − | 0.296432i | \(-0.904203\pi\) | ||
0.955054 | − | 0.296432i | \(-0.0957969\pi\) | |||||||
\(270\) | −1.18279e10 | − | 3.10861e11i | −0.000501657 | − | 0.0131846i | ||||
\(271\) | −3.80787e12 | −0.158253 | −0.0791263 | − | 0.996865i | \(-0.525213\pi\) | ||||
−0.0791263 | + | 0.996865i | \(0.525213\pi\) | |||||||
\(272\) | −3.91332e12 | − | 2.55262e13i | −0.159374 | − | 1.03958i | ||||
\(273\) | 7.91896e12 | − | 3.60978e12i | 0.316063 | − | 0.144074i | ||||
\(274\) | −2.84629e12 | + | 1.08298e11i | −0.111340 | + | 0.00423635i | ||||
\(275\) | − | 3.00326e13i | − | 1.15150i | ||||||
\(276\) | −2.56709e11 | − | 3.36853e12i | −0.00964810 | − | 0.126602i | ||||
\(277\) | 4.43508e13 | 1.63404 | 0.817021 | − | 0.576608i | \(-0.195624\pi\) | ||||
0.817021 | + | 0.576608i | \(0.195624\pi\) | |||||||
\(278\) | 2.06436e13 | − | 7.85467e11i | 0.745658 | − | 0.0283714i | ||||
\(279\) | −1.50045e13 | −0.531371 | ||||||||
\(280\) | −1.69162e12 | + | 1.01813e12i | −0.0587400 | + | 0.0353537i | ||||
\(281\) | −1.76790e13 | −0.601968 | −0.300984 | − | 0.953629i | \(-0.597315\pi\) | ||||
−0.300984 | + | 0.953629i | \(0.597315\pi\) | |||||||
\(282\) | 1.77430e13 | − | 6.75100e11i | 0.592456 | − | 0.0225423i | ||||
\(283\) | 3.92550e13 | 1.28549 | 0.642747 | − | 0.766079i | \(-0.277795\pi\) | ||||
0.642747 | + | 0.766079i | \(0.277795\pi\) | |||||||
\(284\) | −1.62009e12 | − | 2.12588e13i | −0.0520343 | − | 0.682793i | ||||
\(285\) | 3.53396e11i | 0.0111331i | ||||||||
\(286\) | −2.25080e13 | + | 8.56404e11i | −0.695543 | + | 0.0264646i | ||||
\(287\) | −2.78635e13 | + | 1.27013e13i | −0.844667 | + | 0.385033i | ||||
\(288\) | −1.10062e13 | + | 2.11845e12i | −0.327325 | + | 0.0630029i | ||||
\(289\) | −3.63693e12 | −0.106120 | ||||||||
\(290\) | −2.08640e10 | − | 5.48349e11i | −0.000597323 | − | 0.0156989i | ||||
\(291\) | 4.00565e13i | 1.12528i | ||||||||
\(292\) | −4.42963e12 | − | 5.81256e13i | −0.122113 | − | 1.60237i | ||||
\(293\) | 1.66541e13i | 0.450556i | 0.974295 | + | 0.225278i | \(0.0723290\pi\) | ||||
−0.974295 | + | 0.225278i | \(0.927671\pi\) | |||||||
\(294\) | −1.36282e13 | + | 1.69439e13i | −0.361850 | + | 0.449886i | ||||
\(295\) | 2.70001e12i | 0.0703629i | ||||||||
\(296\) | 3.46364e13 | − | 3.96895e12i | 0.885988 | − | 0.101525i | ||||
\(297\) | 8.86721e12i | 0.222652i | ||||||||
\(298\) | −3.53170e13 | + | 1.34377e12i | −0.870551 | + | 0.0331235i | ||||
\(299\) | −5.46739e12 | −0.132309 | ||||||||
\(300\) | −2.41159e13 | + | 1.83782e12i | −0.572975 | + | 0.0436653i | ||||
\(301\) | −4.27315e13 | + | 1.94787e13i | −0.996856 | + | 0.454407i | ||||
\(302\) | −2.75114e12 | − | 7.23055e13i | −0.0630195 | − | 1.65628i | ||||
\(303\) | 4.43627e13i | 0.997891i | ||||||||
\(304\) | 1.25856e13 | − | 1.92945e12i | 0.278016 | − | 0.0426216i | ||||
\(305\) | −3.42655e12 | −0.0743374 | ||||||||
\(306\) | 6.25569e11 | + | 1.64412e13i | 0.0133293 | + | 0.350321i | ||||
\(307\) | −4.82817e13 | −1.01047 | −0.505233 | − | 0.862983i | \(-0.668593\pi\) | ||||
−0.505233 | + | 0.862983i | \(0.668593\pi\) | |||||||
\(308\) | 4.92866e13 | − | 2.71666e13i | 1.01321 | − | 0.558478i | ||||
\(309\) | −5.11656e12 | −0.103325 | ||||||||
\(310\) | −2.09458e11 | − | 5.50498e12i | −0.00415535 | − | 0.109211i | ||||
\(311\) | 9.15050e13 | 1.78346 | 0.891729 | − | 0.452570i | \(-0.149493\pi\) | ||||
0.891729 | + | 0.452570i | \(0.149493\pi\) | |||||||
\(312\) | 2.06505e12 | + | 1.80213e13i | 0.0395439 | + | 0.345093i | ||||
\(313\) | 7.94015e13i | 1.49395i | 0.664855 | + | 0.746973i | \(0.268493\pi\) | ||||
−0.664855 | + | 0.746973i | \(0.731507\pi\) | |||||||
\(314\) | 2.02566e12 | + | 5.32385e13i | 0.0374502 | + | 0.984266i | ||||
\(315\) | 1.14460e12 | − | 5.21753e11i | 0.0207943 | − | 0.00947888i | ||||
\(316\) | 6.48954e12 | + | 8.51555e13i | 0.115860 | + | 1.52032i | ||||
\(317\) | −8.50957e13 | −1.49308 | −0.746538 | − | 0.665343i | \(-0.768285\pi\) | ||||
−0.746538 | + | 0.665343i | \(0.768285\pi\) | |||||||
\(318\) | 3.14894e13 | − | 1.19813e12i | 0.543019 | − | 0.0206612i | ||||
\(319\) | 1.56415e13i | 0.265112i | ||||||||
\(320\) | −9.30881e11 | − | 4.00849e12i | −0.0155085 | − | 0.0667814i | ||||
\(321\) | 1.44635e13i | 0.236862i | ||||||||
\(322\) | 1.22056e13 | − | 6.13459e12i | 0.196495 | − | 0.0987594i | ||||
\(323\) | − | 1.86909e13i | − | 0.295812i | ||||||
\(324\) | 7.12029e12 | − | 5.42623e11i | 0.110790 | − | 0.00844308i | ||||
\(325\) | 3.91419e13i | 0.598802i | ||||||||
\(326\) | −5.75642e11 | − | 1.51290e13i | −0.00865875 | − | 0.227569i | ||||
\(327\) | −4.20053e13 | −0.621285 | ||||||||
\(328\) | −7.26605e12 | − | 6.34095e13i | −0.105680 | − | 0.922250i | ||||
\(329\) | 2.97800e13 | + | 6.53300e13i | 0.425939 | + | 0.934405i | ||||
\(330\) | −3.25328e12 | + | 1.23784e11i | −0.0457610 | + | 0.00174115i | ||||
\(331\) | 3.95604e13i | 0.547276i | 0.961833 | + | 0.273638i | \(0.0882271\pi\) | ||||
−0.961833 | + | 0.273638i | \(0.911773\pi\) | |||||||
\(332\) | 7.00498e13 | − | 5.33836e12i | 0.953120 | − | 0.0726354i | ||||
\(333\) | −2.22117e13 | −0.297262 | ||||||||
\(334\) | −5.34403e13 | + | 2.03334e12i | −0.703499 | + | 0.0267673i | ||||
\(335\) | −1.49220e12 | −0.0193232 | ||||||||
\(336\) | −2.48306e13 | − | 3.79143e13i | −0.316316 | − | 0.482988i | ||||
\(337\) | −4.49990e13 | −0.563947 | −0.281974 | − | 0.959422i | \(-0.590989\pi\) | ||||
−0.281974 | + | 0.959422i | \(0.590989\pi\) | |||||||
\(338\) | −5.17102e13 | + | 1.96751e12i | −0.637580 | + | 0.0242592i | ||||
\(339\) | −9.95215e12 | −0.120731 | ||||||||
\(340\) | −6.02336e12 | + | 4.59029e11i | −0.0718961 | + | 0.00547906i | ||||
\(341\) | 1.57028e14i | 1.84428i | ||||||||
\(342\) | −8.10629e12 | + | 3.08435e11i | −0.0936869 | + | 0.00356468i | ||||
\(343\) | −8.43123e13 | − | 2.49485e13i | −0.958900 | − | 0.283744i | ||||
\(344\) | −1.11432e13 | − | 9.72450e13i | −0.124721 | − | 1.08842i | ||||
\(345\) | −7.90251e11 | −0.00870482 | ||||||||
\(346\) | 6.44514e12 | + | 1.69391e14i | 0.0698737 | + | 1.83642i | ||||
\(347\) | − | 1.31702e14i | − | 1.40534i | −0.711518 | − | 0.702668i | \(-0.751992\pi\) | ||
0.711518 | − | 0.702668i | \(-0.248008\pi\) | |||||||
\(348\) | 1.25600e13 | − | 9.57170e11i | 0.131918 | − | 0.0100532i | ||||
\(349\) | 1.29885e14i | 1.34283i | 0.741083 | + | 0.671413i | \(0.234312\pi\) | ||||
−0.741083 | + | 0.671413i | \(0.765688\pi\) | |||||||
\(350\) | −4.39185e13 | − | 8.73815e13i | −0.446965 | − | 0.889294i | ||||
\(351\) | − | 1.15568e13i | − | 0.115784i | ||||||
\(352\) | 2.21705e13 | + | 1.15184e14i | 0.218671 | + | 1.13608i | ||||
\(353\) | 1.43551e14i | 1.39395i | 0.717097 | + | 0.696974i | \(0.245471\pi\) | ||||
−0.717097 | + | 0.696974i | \(0.754529\pi\) | |||||||
\(354\) | −6.19335e13 | + | 2.35650e12i | −0.592117 | + | 0.0225294i | ||||
\(355\) | −4.98728e12 | −0.0469470 | ||||||||
\(356\) | −2.62005e12 | − | 3.43803e13i | −0.0242848 | − | 0.318665i | ||||
\(357\) | −6.05369e13 | + | 2.75951e13i | −0.552516 | + | 0.251859i | ||||
\(358\) | 5.19005e12 | + | 1.36405e14i | 0.0466460 | + | 1.22595i | ||||
\(359\) | − | 1.68359e14i | − | 1.49011i | −0.667006 | − | 0.745053i | \(-0.732424\pi\) | ||
0.667006 | − | 0.745053i | \(-0.267576\pi\) | |||||||
\(360\) | 2.98480e11 | + | 2.60478e12i | 0.00260166 | + | 0.0227043i | ||||
\(361\) | −1.07275e14 | −0.920891 | ||||||||
\(362\) | 1.08599e12 | + | 2.85420e13i | 0.00918182 | + | 0.241317i | ||||
\(363\) | 2.34682e13 | 0.195431 | ||||||||
\(364\) | −6.42361e13 | + | 3.54067e13i | −0.526892 | + | 0.290421i | ||||
\(365\) | −1.36361e13 | −0.110174 | ||||||||
\(366\) | −2.99060e12 | − | 7.85991e13i | −0.0238020 | − | 0.625563i | ||||
\(367\) | 1.46547e14 | 1.14898 | 0.574491 | − | 0.818511i | \(-0.305200\pi\) | ||||
0.574491 | + | 0.818511i | \(0.305200\pi\) | |||||||
\(368\) | 4.31457e12 | + | 2.81435e13i | 0.0333254 | + | 0.217377i | ||||
\(369\) | 4.06635e13i | 0.309428i | ||||||||
\(370\) | −3.10069e11 | − | 8.14924e12i | −0.00232461 | − | 0.0610953i | ||||
\(371\) | 5.28522e13 | + | 1.15945e14i | 0.390397 | + | 0.856434i | ||||
\(372\) | 1.26092e14 | − | 9.60922e12i | 0.917701 | − | 0.0699362i | ||||
\(373\) | −1.23191e14 | −0.883446 | −0.441723 | − | 0.897152i | \(-0.645633\pi\) | ||||
−0.441723 | + | 0.897152i | \(0.645633\pi\) | |||||||
\(374\) | 1.72064e14 | − | 6.54683e12i | 1.21589 | − | 0.0462634i | ||||
\(375\) | 1.13418e13i | 0.0789785i | ||||||||
\(376\) | −1.48673e14 | + | 1.70363e13i | −1.02023 | + | 0.116907i | ||||
\(377\) | − | 2.03858e13i | − | 0.137864i | ||||||
\(378\) | 1.29671e13 | + | 2.57997e13i | 0.0864246 | + | 0.171953i | ||||
\(379\) | − | 7.21254e12i | − | 0.0473775i | −0.999719 | − | 0.0236888i | \(-0.992459\pi\) | ||
0.999719 | − | 0.0236888i | \(-0.00754108\pi\) | |||||||
\(380\) | −2.26323e11 | − | 2.96980e12i | −0.00146527 | − | 0.0192273i | ||||
\(381\) | 1.11532e13i | 0.0711723i | ||||||||
\(382\) | 5.43775e12 | + | 1.42915e14i | 0.0342035 | + | 0.898936i | ||||
\(383\) | −1.36525e14 | −0.846484 | −0.423242 | − | 0.906017i | \(-0.639108\pi\) | ||||
−0.423242 | + | 0.906017i | \(0.639108\pi\) | |||||||
\(384\) | 9.11353e13 | − | 2.48513e13i | 0.557013 | − | 0.151889i | ||||
\(385\) | −5.46035e12 | − | 1.19787e13i | −0.0328993 | − | 0.0721729i | ||||
\(386\) | −8.01596e13 | + | 3.04998e12i | −0.476130 | + | 0.0181162i | ||||
\(387\) | 6.23616e13i | 0.365180i | ||||||||
\(388\) | −2.56531e13 | − | 3.36620e14i | −0.148104 | − | 1.94341i | ||||
\(389\) | 2.34420e14 | 1.33436 | 0.667178 | − | 0.744899i | \(-0.267502\pi\) | ||||
0.667178 | + | 0.744899i | \(0.267502\pi\) | |||||||
\(390\) | 4.24006e12 | − | 1.61329e11i | 0.0237967 | − | 0.000905436i | ||||
\(391\) | 4.17958e13 | 0.231292 | ||||||||
\(392\) | 1.03675e14 | − | 1.51118e14i | 0.565719 | − | 0.824598i | ||||
\(393\) | 1.46128e14 | 0.786276 | ||||||||
\(394\) | 5.32162e13 | − | 2.02482e12i | 0.282368 | − | 0.0107438i | ||||
\(395\) | 1.99773e13 | 0.104533 | ||||||||
\(396\) | −5.67877e12 | − | 7.45167e13i | −0.0293042 | − | 0.384530i | ||||
\(397\) | − | 1.70986e14i | − | 0.870187i | −0.900385 | − | 0.435093i | \(-0.856715\pi\) | ||
0.900385 | − | 0.435093i | \(-0.143285\pi\) | |||||||
\(398\) | 1.50581e13 | − | 5.72944e11i | 0.0755811 | − | 0.00287578i | ||||
\(399\) | −1.36057e13 | − | 2.98475e13i | −0.0673550 | − | 0.147760i | ||||
\(400\) | 2.01483e14 | − | 3.08887e13i | 0.983806 | − | 0.150824i | ||||
\(401\) | −1.38987e14 | −0.669391 | −0.334695 | − | 0.942326i | \(-0.608633\pi\) | ||||
−0.334695 | + | 0.942326i | \(0.608633\pi\) | |||||||
\(402\) | −1.30235e12 | − | 3.42284e13i | −0.00618707 | − | 0.162609i | ||||
\(403\) | − | 2.04657e14i | − | 0.959067i | ||||||
\(404\) | −2.84109e13 | − | 3.72807e14i | −0.131337 | − | 1.72340i | ||||
\(405\) | − | 1.67040e12i | − | 0.00761761i | ||||||
\(406\) | 2.28735e13 | + | 4.55099e13i | 0.102906 | + | 0.204745i | ||||
\(407\) | 2.32455e14i | 1.03174i | ||||||||
\(408\) | −1.57864e13 | − | 1.37765e14i | −0.0691276 | − | 0.603264i | ||||
\(409\) | − | 1.00762e14i | − | 0.435331i | −0.976023 | − | 0.217666i | \(-0.930156\pi\) | ||
0.976023 | − | 0.217666i | \(-0.0698442\pi\) | |||||||
\(410\) | −1.49190e13 | + | 5.67651e11i | −0.0635958 | + | 0.00241975i | ||||
\(411\) | −1.52945e13 | −0.0643286 | ||||||||
\(412\) | 4.29976e13 | − | 3.27676e12i | 0.178447 | − | 0.0135991i | ||||
\(413\) | −1.03950e14 | − | 2.28040e14i | −0.425695 | − | 0.933870i | ||||
\(414\) | −6.89711e11 | − | 1.81270e13i | −0.00278718 | − | 0.0732527i | ||||
\(415\) | − | 1.64335e13i | − | 0.0655339i | ||||||
\(416\) | −2.88951e13 | − | 1.50122e14i | −0.113713 | − | 0.590786i | ||||
\(417\) | 1.10928e14 | 0.430818 | ||||||||
\(418\) | 3.22790e12 | + | 8.48356e13i | 0.0123723 | + | 0.325169i | ||||
\(419\) | −1.05522e14 | −0.399177 | −0.199589 | − | 0.979880i | \(-0.563961\pi\) | ||||
−0.199589 | + | 0.979880i | \(0.563961\pi\) | |||||||
\(420\) | −9.28461e12 | + | 5.11764e12i | −0.0346651 | + | 0.0191073i | ||||
\(421\) | 4.71336e14 | 1.73692 | 0.868459 | − | 0.495760i | \(-0.165111\pi\) | ||||
0.868459 | + | 0.495760i | \(0.165111\pi\) | |||||||
\(422\) | 6.50186e12 | + | 1.70882e14i | 0.0236493 | + | 0.621552i | ||||
\(423\) | 9.53415e13 | 0.342302 | ||||||||
\(424\) | −2.63857e14 | + | 3.02352e13i | −0.935097 | + | 0.107152i | ||||
\(425\) | − | 2.99222e14i | − | 1.04678i | ||||||
\(426\) | −4.35277e12 | − | 1.14400e14i | −0.0150319 | − | 0.395068i | ||||
\(427\) | 2.89403e14 | − | 1.31922e14i | 0.986621 | − | 0.449741i | ||||
\(428\) | −9.26276e12 | − | 1.21546e14i | −0.0311745 | − | 0.409071i | ||||
\(429\) | −1.20946e14 | −0.401863 | ||||||||
\(430\) | −2.28798e13 | + | 8.70550e11i | −0.0750543 | + | 0.00285573i | ||||
\(431\) | 5.92339e14i | 1.91843i | 0.282680 | + | 0.959214i | \(0.408777\pi\) | ||||
−0.282680 | + | 0.959214i | \(0.591223\pi\) | |||||||
\(432\) | −5.94887e13 | + | 9.11999e12i | −0.190228 | + | 0.0291631i | ||||
\(433\) | − | 9.08413e12i | − | 0.0286814i | −0.999897 | − | 0.0143407i | \(-0.995435\pi\) | ||
0.999897 | − | 0.0143407i | \(-0.00456494\pi\) | |||||||
\(434\) | 2.29632e14 | + | 4.56882e14i | 0.715877 | + | 1.42433i | ||||
\(435\) | − | 2.94654e12i | − | 0.00907030i | ||||||
\(436\) | 3.52996e14 | − | 2.69011e13i | 1.07299 | − | 0.0817702i | ||||
\(437\) | 2.06073e13i | 0.0618548i | ||||||||
\(438\) | −1.19013e13 | − | 3.12789e14i | −0.0352765 | − | 0.927138i | ||||
\(439\) | −4.78753e14 | −1.40138 | −0.700692 | − | 0.713464i | \(-0.747125\pi\) | ||||
−0.700692 | + | 0.713464i | \(0.747125\pi\) | |||||||
\(440\) | 2.72601e13 | − | 3.12371e12i | 0.0788020 | − | 0.00902986i | ||||
\(441\) | −7.65843e13 | + | 8.81337e13i | −0.218639 | + | 0.251611i | ||||
\(442\) | −2.24253e14 | + | 8.53259e12i | −0.632290 | + | 0.0240579i | ||||
\(443\) | 1.26020e14i | 0.350929i | 0.984486 | + | 0.175465i | \(0.0561428\pi\) | ||||
−0.984486 | + | 0.175465i | \(0.943857\pi\) | |||||||
\(444\) | 1.86659e14 | − | 1.42249e13i | 0.513384 | − | 0.0391240i | ||||
\(445\) | −8.06554e12 | −0.0219106 | ||||||||
\(446\) | −3.84539e14 | + | 1.46312e13i | −1.03181 | + | 0.0392590i | ||||
\(447\) | −1.89775e14 | −0.502977 | ||||||||
\(448\) | 2.32948e14 | + | 3.02715e14i | 0.609859 | + | 0.792510i | ||||
\(449\) | −2.95747e14 | −0.764832 | −0.382416 | − | 0.923990i | \(-0.624908\pi\) | ||||
−0.382416 | + | 0.923990i | \(0.624908\pi\) | |||||||
\(450\) | −1.29774e14 | + | 4.93775e12i | −0.331527 | + | 0.0126142i | ||||
\(451\) | 4.25560e14 | 1.07396 | ||||||||
\(452\) | 8.36340e13 | − | 6.37358e12i | 0.208507 | − | 0.0158899i | ||||
\(453\) | − | 3.88532e14i | − | 0.956944i | ||||||
\(454\) | −3.09670e14 | + | 1.17826e13i | −0.753515 | + | 0.0286704i | ||||
\(455\) | 7.11657e12 | + | 1.56120e13i | 0.0171083 | + | 0.0375315i | ||||
\(456\) | 6.79246e13 | − | 7.78343e12i | 0.161332 | − | 0.0184869i | ||||
\(457\) | 8.79287e13 | 0.206344 | 0.103172 | − | 0.994664i | \(-0.467101\pi\) | ||||
0.103172 | + | 0.994664i | \(0.467101\pi\) | |||||||
\(458\) | 1.29243e13 | + | 3.39677e14i | 0.0299673 | + | 0.787600i | ||||
\(459\) | 8.83464e13i | 0.202404i | ||||||||
\(460\) | 6.64096e12 | − | 5.06095e11i | 0.0150336 | − | 0.00114568i | ||||
\(461\) | − | 3.26239e14i | − | 0.729760i | −0.931055 | − | 0.364880i | \(-0.881110\pi\) | ||
0.931055 | − | 0.364880i | \(-0.118890\pi\) | |||||||
\(462\) | 2.70004e14 | − | 1.35706e14i | 0.596815 | − | 0.299963i | ||||
\(463\) | − | 8.05662e14i | − | 1.75978i | −0.475181 | − | 0.879888i | \(-0.657618\pi\) | ||
0.475181 | − | 0.879888i | \(-0.342382\pi\) | |||||||
\(464\) | −1.04936e14 | + | 1.60874e13i | −0.226504 | + | 0.0347245i | ||||
\(465\) | − | 2.95809e13i | − | 0.0630986i | ||||||
\(466\) | −6.30813e14 | + | 2.40017e13i | −1.32978 | + | 0.0505964i | ||||
\(467\) | −4.34161e14 | −0.904498 | −0.452249 | − | 0.891892i | \(-0.649378\pi\) | ||||
−0.452249 | + | 0.891892i | \(0.649378\pi\) | |||||||
\(468\) | 7.40123e12 | + | 9.71188e13i | 0.0152388 | + | 0.199964i | ||||
\(469\) | 1.26030e14 | − | 5.74494e13i | 0.256462 | − | 0.116905i | ||||
\(470\) | 1.33094e12 | + | 3.49797e13i | 0.00267682 | + | 0.0703523i | ||||
\(471\) | 2.86076e14i | 0.568677i | ||||||||
\(472\) | 5.18956e14 | − | 5.94667e13i | 1.01965 | − | 0.116840i | ||||
\(473\) | 6.52639e14 | 1.26747 | ||||||||
\(474\) | 1.74357e13 | + | 4.58245e14i | 0.0334702 | + | 0.879664i | ||||
\(475\) | 1.47531e14 | 0.279942 | ||||||||
\(476\) | 4.91056e14 | − | 2.70668e14i | 0.921070 | − | 0.507690i | ||||
\(477\) | 1.69207e14 | 0.313739 | ||||||||
\(478\) | 4.43288e12 | + | 1.16505e14i | 0.00812517 | + | 0.213546i | ||||
\(479\) | 1.91239e14 | 0.346523 | 0.173262 | − | 0.984876i | \(-0.444569\pi\) | ||||
0.173262 | + | 0.984876i | \(0.444569\pi\) | |||||||
\(480\) | −4.17647e12 | − | 2.16984e13i | −0.00748139 | − | 0.0388688i | ||||
\(481\) | − | 3.02962e14i | − | 0.536525i | ||||||
\(482\) | 7.46357e12 | + | 1.96158e14i | 0.0130674 | + | 0.343437i | ||||
\(483\) | 6.67439e13 | − | 3.04246e13i | 0.115532 | − | 0.0526641i | ||||
\(484\) | −1.97218e14 | + | 1.50296e13i | −0.337518 | + | 0.0257216i | ||||
\(485\) | −7.89702e13 | −0.133624 | ||||||||
\(486\) | 3.83162e13 | − | 1.45789e12i | 0.0641036 | − | 0.00243907i | ||||
\(487\) | − | 3.73321e14i | − | 0.617552i | −0.951135 | − | 0.308776i | \(-0.900081\pi\) | ||
0.951135 | − | 0.308776i | \(-0.0999193\pi\) | |||||||
\(488\) | 7.54685e13 | + | 6.58601e14i | 0.123440 | + | 1.07724i | ||||
\(489\) | − | 8.12954e13i | − | 0.131482i | ||||||
\(490\) | −3.34044e13 | − | 2.68676e13i | −0.0534226 | − | 0.0429686i | ||||
\(491\) | 7.98177e14i | 1.26227i | 0.775674 | + | 0.631133i | \(0.217410\pi\) | ||||
−0.775674 | + | 0.631133i | \(0.782590\pi\) | |||||||
\(492\) | −2.60419e13 | − | 3.41721e14i | −0.0407253 | − | 0.534396i | ||||
\(493\) | 1.55840e14i | 0.241003i | ||||||||
\(494\) | −4.20697e12 | − | 1.10568e14i | −0.00643385 | − | 0.169095i | ||||
\(495\) | −1.74814e13 | −0.0264392 | ||||||||
\(496\) | −1.05347e15 | + | 1.61504e14i | −1.57570 | + | 0.241566i | ||||
\(497\) | 4.21222e14 | − | 1.92010e14i | 0.623090 | − | 0.284029i | ||||
\(498\) | 3.76957e14 | − | 1.43428e13i | 0.551480 | − | 0.0209832i | ||||
\(499\) | − | 1.18142e15i | − | 1.70943i | −0.519096 | − | 0.854716i | \(-0.673731\pi\) | ||
0.519096 | − | 0.854716i | \(-0.326269\pi\) | |||||||
\(500\) | −7.26353e12 | − | 9.53119e13i | −0.0103947 | − | 0.136399i | ||||
\(501\) | −2.87160e14 | −0.406459 | ||||||||
\(502\) | −1.12996e14 | + | 4.29936e12i | −0.158195 | + | 0.00601913i | ||||
\(503\) | −1.12155e15 | −1.55309 | −0.776545 | − | 0.630062i | \(-0.783029\pi\) | ||||
−0.776545 | + | 0.630062i | \(0.783029\pi\) | |||||||
\(504\) | −1.25493e14 | − | 2.08506e14i | −0.171891 | − | 0.285595i | ||||
\(505\) | −8.74597e13 | −0.118496 | ||||||||
\(506\) | −1.89706e14 | + | 7.21810e12i | −0.254246 | + | 0.00967375i | ||||
\(507\) | −2.77864e14 | −0.368373 | ||||||||
\(508\) | −7.14275e12 | − | 9.37270e13i | −0.00936731 | − | 0.122918i | ||||
\(509\) | 3.59317e14i | 0.466154i | 0.972458 | + | 0.233077i | \(0.0748795\pi\) | ||||
−0.972458 | + | 0.233077i | \(0.925121\pi\) | |||||||
\(510\) | −3.24133e13 | + | 1.23329e12i | −0.0415995 | + | 0.00158281i | ||||
\(511\) | 1.15170e15 | − | 5.24989e14i | 1.46226 | − | 0.666554i | ||||
\(512\) | −7.49951e14 | + | 2.67206e14i | −0.941994 | + | 0.335631i | ||||
\(513\) | −4.35590e13 | −0.0541293 | ||||||||
\(514\) | 3.39342e13 | + | 8.91858e14i | 0.0417196 | + | 1.09647i | ||||
\(515\) | − | 1.00871e13i | − | 0.0122695i | ||||||
\(516\) | −3.99378e13 | − | 5.24063e14i | −0.0480630 | − | 0.630682i | ||||
\(517\) | − | 9.97786e14i | − | 1.18806i | ||||||
\(518\) | 3.39933e14 | + | 6.76341e14i | 0.400479 | + | 0.796805i | ||||
\(519\) | 9.10220e14i | 1.06103i | ||||||||
\(520\) | −3.55285e13 | + | 4.07118e12i | −0.0409787 | + | 0.00469572i | ||||
\(521\) | − | 1.10878e15i | − | 1.26543i | −0.774386 | − | 0.632713i | \(-0.781941\pi\) | ||
0.774386 | − | 0.632713i | \(-0.218059\pi\) | |||||||
\(522\) | 6.75885e13 | − | 2.57167e12i | 0.0763283 | − | 0.00290420i | ||||
\(523\) | 1.37899e15 | 1.54100 | 0.770501 | − | 0.637439i | \(-0.220006\pi\) | ||||
0.770501 | + | 0.637439i | \(0.220006\pi\) | |||||||
\(524\) | −1.22800e15 | + | 9.35838e13i | −1.35793 | + | 0.103485i | ||||
\(525\) | −2.17814e14 | − | 4.77830e14i | −0.238347 | − | 0.522875i | ||||
\(526\) | −3.47064e10 | − | 9.12154e11i | −3.75827e−5 | − | 0.000987749i | ||||
\(527\) | 1.56451e15i | 1.67656i | ||||||||
\(528\) | 9.54444e13 | + | 6.22573e14i | 0.101219 | + | 0.660242i | ||||
\(529\) | 9.06729e14 | 0.951636 | ||||||||
\(530\) | 2.36209e12 | + | 6.20803e13i | 0.00245346 | + | 0.0644817i | ||||
\(531\) | −3.32798e14 | −0.342106 | ||||||||
\(532\) | 1.33452e14 | + | 2.42114e14i | 0.135772 | + | 0.246323i | ||||
\(533\) | −5.54639e14 | −0.558484 | ||||||||
\(534\) | −7.03940e12 | − | 1.85009e14i | −0.00701550 | − | 0.184381i | ||||
\(535\) | −2.85144e13 | −0.0281266 | ||||||||
\(536\) | 3.28651e13 | + | 2.86808e14i | 0.0320870 | + | 0.280018i | ||||
\(537\) | 7.32968e14i | 0.708315i | ||||||||
\(538\) | 2.35660e13 | + | 6.19361e14i | 0.0225415 | + | 0.592436i | ||||
\(539\) | 9.22354e14 | + | 8.01485e14i | 0.873292 | + | 0.758853i | ||||
\(540\) | 1.06977e12 | + | 1.40374e13i | 0.00100259 | + | 0.0131559i | ||||
\(541\) | 9.54173e14 | 0.885202 | 0.442601 | − | 0.896719i | \(-0.354056\pi\) | ||||
0.442601 | + | 0.896719i | \(0.354056\pi\) | |||||||
\(542\) | 1.72200e14 | − | 6.55201e12i | 0.158138 | − | 0.00601698i | ||||
\(543\) | 1.53370e14i | 0.139425i | ||||||||
\(544\) | 2.20890e14 | + | 1.14761e15i | 0.198785 | + | 1.03277i | ||||
\(545\) | − | 8.28121e13i | − | 0.0737756i | ||||||
\(546\) | −3.51901e14 | + | 1.76867e14i | −0.310356 | + | 0.155987i | ||||
\(547\) | − | 1.98826e15i | − | 1.73597i | −0.496588 | − | 0.867987i | \(-0.665414\pi\) | ||
0.496588 | − | 0.867987i | \(-0.334586\pi\) | |||||||
\(548\) | 1.28529e14 | − | 9.79492e12i | 0.111098 | − | 0.00846658i | ||||
\(549\) | − | 4.22350e14i | − | 0.361431i | ||||||
\(550\) | 5.16755e13 | + | 1.35814e15i | 0.0437814 | + | 1.15066i | ||||
\(551\) | −7.68367e13 | −0.0644518 | ||||||||
\(552\) | 1.74050e13 | + | 1.51890e14i | 0.0144547 | + | 0.126144i | ||||
\(553\) | −1.68727e15 | + | 7.69124e14i | −1.38738 | + | 0.632424i | ||||
\(554\) | −2.00564e15 | + | 7.63122e13i | −1.63286 | + | 0.0621284i | ||||
\(555\) | − | 4.37898e13i | − | 0.0352989i | ||||||
\(556\) | −9.32198e14 | + | 7.10409e13i | −0.744041 | + | 0.0567019i | ||||
\(557\) | 1.11764e15 | 0.883281 | 0.441640 | − | 0.897192i | \(-0.354397\pi\) | ||||
0.441640 | + | 0.897192i | \(0.354397\pi\) | |||||||
\(558\) | 6.78534e14 | − | 2.58175e13i | 0.530987 | − | 0.0202034i | ||||
\(559\) | −8.50595e14 | −0.659110 | ||||||||
\(560\) | 7.47468e13 | − | 4.89527e13i | 0.0573533 | − | 0.0375615i | ||||
\(561\) | 9.24581e14 | 0.702504 | ||||||||
\(562\) | 7.99482e14 | − | 3.04194e13i | 0.601532 | − | 0.0228876i | ||||
\(563\) | −1.17479e15 | −0.875317 | −0.437659 | − | 0.899141i | \(-0.644192\pi\) | ||||
−0.437659 | + | 0.899141i | \(0.644192\pi\) | |||||||
\(564\) | −8.01213e14 | + | 6.10589e13i | −0.591171 | + | 0.0450520i | ||||
\(565\) | − | 1.96204e13i | − | 0.0143364i | ||||||
\(566\) | −1.77520e15 | + | 6.75442e13i | −1.28456 | + | 0.0488762i | ||||
\(567\) | 6.43104e13 | + | 1.41081e14i | 0.0460865 | + | 0.101102i | ||||
\(568\) | 1.09843e14 | + | 9.58582e14i | 0.0779573 | + | 0.680321i | ||||
\(569\) | −1.75027e15 | −1.23024 | −0.615118 | − | 0.788435i | \(-0.710892\pi\) | ||||
−0.615118 | + | 0.788435i | \(0.710892\pi\) | |||||||
\(570\) | −6.08071e11 | − | 1.59813e13i | −0.000423294 | − | 0.0111250i | ||||
\(571\) | − | 2.54403e15i | − | 1.75398i | −0.480509 | − | 0.876990i | \(-0.659548\pi\) | ||
0.480509 | − | 0.876990i | \(-0.340452\pi\) | |||||||
\(572\) | 1.01639e15 | − | 7.74568e13i | 0.694034 | − | 0.0528910i | ||||
\(573\) | 7.67950e14i | 0.519377i | ||||||||
\(574\) | 1.23819e15 | − | 6.22323e14i | 0.829417 | − | 0.416870i | ||||
\(575\) | 3.29903e14i | 0.218883i | ||||||||
\(576\) | 4.94079e14 | − | 1.14739e14i | 0.324693 | − | 0.0754027i | ||||
\(577\) | − | 3.34837e14i | − | 0.217955i | −0.994044 | − | 0.108977i | \(-0.965242\pi\) | ||
0.994044 | − | 0.108977i | \(-0.0347576\pi\) | |||||||
\(578\) | 1.64470e14 | − | 6.25788e12i | 0.106043 | − | 0.00403482i | ||||
\(579\) | −4.30736e14 | −0.275092 | ||||||||
\(580\) | 1.88703e12 | + | 2.47616e13i | 0.00119378 | + | 0.0156648i | ||||
\(581\) | 6.32689e14 | + | 1.38796e15i | 0.396480 | + | 0.869779i | ||||
\(582\) | −6.89232e13 | − | 1.81144e15i | −0.0427848 | − | 1.12447i | ||||
\(583\) | − | 1.77082e15i | − | 1.08893i | ||||||
\(584\) | 3.00331e14 | + | 2.62094e15i | 0.182949 | + | 1.59656i | ||||
\(585\) | 2.27839e13 | 0.0137490 | ||||||||
\(586\) | −2.86558e13 | − | 7.53133e14i | −0.0171307 | − | 0.450230i | ||||
\(587\) | −1.69749e15 | −1.00530 | −0.502652 | − | 0.864489i | \(-0.667642\pi\) | ||||
−0.502652 | + | 0.864489i | \(0.667642\pi\) | |||||||
\(588\) | 5.87142e14 | − | 7.89688e14i | 0.344483 | − | 0.463319i | ||||
\(589\) | −7.71378e14 | −0.448367 | ||||||||
\(590\) | −4.64576e12 | − | 1.22100e14i | −0.00267529 | − | 0.0703120i | ||||
\(591\) | 2.85956e14 | 0.163143 | ||||||||
\(592\) | −1.55950e15 | + | 2.39081e14i | −0.881487 | + | 0.135138i | ||||
\(593\) | − | 1.60063e14i | − | 0.0896376i | −0.998995 | − | 0.0448188i | \(-0.985729\pi\) | ||
0.998995 | − | 0.0448188i | \(-0.0142711\pi\) | |||||||
\(594\) | −1.52574e13 | − | 4.00994e14i | −0.00846553 | − | 0.222491i | ||||
\(595\) | −5.44030e13 | − | 1.19347e14i | −0.0299074 | − | 0.0656095i | ||||
\(596\) | 1.59480e15 | − | 1.21536e14i | 0.868662 | − | 0.0661990i | ||||
\(597\) | 8.09144e13 | 0.0436684 | ||||||||
\(598\) | 2.47247e14 | − | 9.40746e12i | 0.132213 | − | 0.00503056i | ||||
\(599\) | 2.88578e15i | 1.52903i | 0.644607 | + | 0.764514i | \(0.277021\pi\) | ||||
−0.644607 | + | 0.764514i | \(0.722979\pi\) | |||||||
\(600\) | 1.08741e15 | − | 1.24605e14i | 0.570901 | − | 0.0654190i | ||||
\(601\) | − | 1.50759e14i | − | 0.0784282i | −0.999231 | − | 0.0392141i | \(-0.987515\pi\) | ||
0.999231 | − | 0.0392141i | \(-0.0124854\pi\) | |||||||
\(602\) | 1.89889e15 | − | 9.54396e14i | 0.978859 | − | 0.491980i | ||||
\(603\) | − | 1.83926e14i | − | 0.0939500i | ||||||
\(604\) | 2.48825e14 | + | 3.26507e15i | 0.125948 | + | 1.65268i | ||||
\(605\) | 4.62668e13i | 0.0232068i | ||||||||
\(606\) | −7.63326e13 | − | 2.00617e15i | −0.0379412 | − | 0.997170i | ||||
\(607\) | 2.11779e15 | 1.04315 | 0.521574 | − | 0.853206i | \(-0.325345\pi\) | ||||
0.521574 | + | 0.853206i | \(0.325345\pi\) | |||||||
\(608\) | −5.65828e14 | + | 1.08909e14i | −0.276194 | + | 0.0531613i | ||||
\(609\) | 1.13441e14 | + | 2.48863e14i | 0.0548753 | + | 0.120383i | ||||
\(610\) | 1.54956e14 | − | 5.89589e12i | 0.0742837 | − | 0.00282641i | ||||
\(611\) | 1.30043e15i | 0.617818i | ||||||||
\(612\) | −5.65791e13 | − | 7.42429e14i | −0.0266393 | − | 0.349561i | ||||
\(613\) | −1.19459e15 | −0.557426 | −0.278713 | − | 0.960374i | \(-0.589908\pi\) | ||||
−0.278713 | + | 0.960374i | \(0.589908\pi\) | |||||||
\(614\) | 2.18340e15 | − | 8.30759e13i | 1.00973 | − | 0.0384193i | ||||
\(615\) | −8.01669e13 | −0.0367436 | ||||||||
\(616\) | −2.18210e15 | + | 1.31334e15i | −0.991245 | + | 0.596598i | ||||
\(617\) | −4.98737e14 | −0.224545 | −0.112272 | − | 0.993677i | \(-0.535813\pi\) | ||||
−0.112272 | + | 0.993677i | \(0.535813\pi\) | |||||||
\(618\) | 2.31382e14 | − | 8.80380e12i | 0.103250 | − | 0.00392856i | ||||
\(619\) | 2.24819e15 | 0.994337 | 0.497168 | − | 0.867654i | \(-0.334373\pi\) | ||||
0.497168 | + | 0.867654i | \(0.334373\pi\) | |||||||
\(620\) | 1.89443e13 | + | 2.48586e14i | 0.00830470 | + | 0.108974i | ||||
\(621\) | − | 9.74049e13i | − | 0.0423231i | ||||||
\(622\) | −4.13805e15 | + | 1.57448e14i | −1.78217 | + | 0.0678095i | ||||
\(623\) | 6.81209e14 | − | 3.10522e14i | 0.290801 | − | 0.132559i | ||||
\(624\) | −1.24394e14 | − | 8.11409e14i | −0.0526362 | − | 0.343340i | ||||
\(625\) | 2.35062e15 | 0.985921 | ||||||||
\(626\) | −1.36622e14 | − | 3.59070e15i | −0.0568018 | − | 1.49286i | ||||
\(627\) | 4.55862e14i | 0.187872i | ||||||||
\(628\) | −1.83209e14 | − | 2.40407e15i | −0.0748462 | − | 0.982130i | ||||
\(629\) | 2.31601e15i | 0.937911i | ||||||||
\(630\) | −5.08633e13 | + | 2.55642e13i | −0.0204189 | + | 0.0102626i | ||||
\(631\) | 3.11509e15i | 1.23968i | 0.784729 | + | 0.619839i | \(0.212802\pi\) | ||||
−0.784729 | + | 0.619839i | \(0.787198\pi\) | |||||||
\(632\) | −4.39993e14 | − | 3.83975e15i | −0.173581 | − | 1.51481i | ||||
\(633\) | 9.18230e14i | 0.359113i | ||||||||
\(634\) | 3.84821e15 | − | 1.46420e14i | 1.49200 | − | 0.0567687i | ||||
\(635\) | −2.19881e13 | −0.00845149 | ||||||||
\(636\) | −1.42195e15 | + | 1.08364e14i | −0.541840 | + | 0.0412926i | ||||
\(637\) | −1.20212e15 | − | 1.04459e15i | −0.454130 | − | 0.394619i | ||||
\(638\) | −2.69135e13 | − | 7.07341e14i | −0.0100799 | − | 0.264920i | ||||
\(639\) | − | 6.14723e14i | − | 0.228257i | ||||||
\(640\) | 4.89936e13 | + | 1.79671e14i | 0.0180364 | + | 0.0661435i | ||||
\(641\) | −3.10799e15 | −1.13439 | −0.567193 | − | 0.823585i | \(-0.691971\pi\) | ||||
−0.567193 | + | 0.823585i | \(0.691971\pi\) | |||||||
\(642\) | −2.48866e13 | − | 6.54070e14i | −0.00900582 | − | 0.236691i | ||||
\(643\) | −4.25049e15 | −1.52503 | −0.762515 | − | 0.646970i | \(-0.776036\pi\) | ||||
−0.762515 | + | 0.646970i | \(0.776036\pi\) | |||||||
\(644\) | −5.41406e14 | + | 2.98421e14i | −0.192598 | + | 0.106159i | ||||
\(645\) | −1.22944e14 | −0.0433640 | ||||||||
\(646\) | 3.21604e13 | + | 8.45240e14i | 0.0112472 | + | 0.295598i | ||||
\(647\) | 8.92140e14 | 0.309357 | 0.154678 | − | 0.987965i | \(-0.450566\pi\) | ||||
0.154678 | + | 0.987965i | \(0.450566\pi\) | |||||||
\(648\) | −3.21061e14 | + | 3.67901e13i | −0.110389 | + | 0.0126494i | ||||
\(649\) | 3.48286e15i | 1.18738i | ||||||||
\(650\) | −6.73495e13 | − | 1.77008e15i | −0.0227673 | − | 0.598369i | ||||
\(651\) | 1.13886e15 | + | 2.49838e15i | 0.381747 | + | 0.837458i | ||||
\(652\) | 5.20635e13 | + | 6.83176e14i | 0.0173050 | + | 0.227076i | ||||
\(653\) | 2.75032e15 | 0.906485 | 0.453242 | − | 0.891387i | \(-0.350267\pi\) | ||||
0.453242 | + | 0.891387i | \(0.350267\pi\) | |||||||
\(654\) | 1.89957e15 | − | 7.22763e13i | 0.620836 | − | 0.0236221i | ||||
\(655\) | 2.88087e14i | 0.0933678i | ||||||||
\(656\) | 4.37692e14 | + | 2.85501e15i | 0.140669 | + | 0.917565i | ||||
\(657\) | − | 1.68077e15i | − | 0.535670i | ||||||
\(658\) | −1.45913e15 | − | 2.90312e15i | −0.461159 | − | 0.917535i | ||||
\(659\) | − | 2.26220e15i | − | 0.709024i | −0.935051 | − | 0.354512i | \(-0.884647\pi\) | ||
0.935051 | − | 0.354512i | \(-0.115353\pi\) | |||||||
\(660\) | 1.46907e14 | − | 1.11955e13i | 0.0456617 | − | 0.00347979i | ||||
\(661\) | 2.84098e15i | 0.875709i | 0.899046 | + | 0.437854i | \(0.144261\pi\) | ||||
−0.899046 | + | 0.437854i | \(0.855739\pi\) | |||||||
\(662\) | −6.80696e13 | − | 1.78900e15i | −0.0208082 | − | 0.546880i | ||||
\(663\) | −1.20502e15 | −0.365317 | ||||||||
\(664\) | −3.15861e15 | + | 3.61943e14i | −0.949669 | + | 0.108822i | ||||
\(665\) | 5.88435e13 | − | 2.68232e13i | 0.0175461 | − | 0.00799820i | ||||
\(666\) | 1.00446e15 | − | 3.82186e13i | 0.297047 | − | 0.0113023i | ||||
\(667\) | − | 1.71819e14i | − | 0.0503941i | ||||||
\(668\) | 2.41319e15 | − | 1.83904e14i | 0.701973 | − | 0.0534959i | ||||
\(669\) | −2.06631e15 | −0.596145 | ||||||||
\(670\) | 6.74803e13 | − | 2.56755e12i | 0.0193093 | − | 0.000734695i | ||||
\(671\) | −4.42006e15 | −1.25445 | ||||||||
\(672\) | 1.18813e15 | + | 1.67184e15i | 0.334451 | + | 0.470612i | ||||
\(673\) | −7.57562e14 | −0.211512 | −0.105756 | − | 0.994392i | \(-0.533726\pi\) | ||||
−0.105756 | + | 0.994392i | \(0.533726\pi\) | |||||||
\(674\) | 2.03495e15 | − | 7.74275e13i | 0.563539 | − | 0.0214420i | ||||
\(675\) | −6.97337e14 | −0.191546 | ||||||||
\(676\) | 2.33506e15 | − | 1.77950e14i | 0.636196 | − | 0.0484833i | ||||
\(677\) | − | 2.30576e15i | − | 0.623126i | −0.950226 | − | 0.311563i | \(-0.899148\pi\) | ||
0.950226 | − | 0.311563i | \(-0.100852\pi\) | |||||||
\(678\) | 4.50057e14 | − | 1.71242e13i | 0.120644 | − | 0.00459035i | ||||
\(679\) | 6.66976e15 | − | 3.04035e15i | 1.77348 | − | 0.808424i | ||||
\(680\) | 2.71599e14 | − | 3.11223e13i | 0.0716357 | − | 0.00820868i | ||||
\(681\) | −1.66400e15 | −0.435357 | ||||||||
\(682\) | −2.70190e14 | − | 7.10113e15i | −0.0701221 | − | 1.84295i | ||||
\(683\) | − | 1.73464e15i | − | 0.446576i | −0.974753 | − | 0.223288i | \(-0.928321\pi\) | ||
0.974753 | − | 0.223288i | \(-0.0716790\pi\) | |||||||
\(684\) | 3.66053e14 | − | 2.78962e13i | 0.0934836 | − | 0.00712420i | ||||
\(685\) | − | 3.01526e13i | − | 0.00763882i | ||||||
\(686\) | 3.85571e15 | + | 9.83154e14i | 0.968995 | + | 0.247081i | ||||
\(687\) | 1.82524e15i | 0.455050i | ||||||||
\(688\) | 6.71244e14 | + | 4.37845e15i | 0.166014 | + | 1.08289i | ||||
\(689\) | 2.30794e15i | 0.566264i | ||||||||
\(690\) | 3.57368e13 | − | 1.35974e12i | 0.00869853 | − | 0.000330969i | ||||
\(691\) | −4.74208e15 | −1.14509 | −0.572544 | − | 0.819874i | \(-0.694044\pi\) | ||||
−0.572544 | + | 0.819874i | \(0.694044\pi\) | |||||||
\(692\) | −5.82926e14 | − | 7.64914e15i | −0.139646 | − | 1.83244i | ||||
\(693\) | 1.47647e15 | − | 6.73034e14i | 0.350907 | − | 0.159957i | ||||
\(694\) | 2.26613e14 | + | 5.95584e15i | 0.0534328 | + | 1.40432i | ||||
\(695\) | 2.18692e14i | 0.0511582i | ||||||||
\(696\) | −5.66341e14 | + | 6.48966e13i | −0.131440 | + | 0.0150616i | ||||
\(697\) | 4.23997e15 | 0.976298 | ||||||||
\(698\) | −2.23487e14 | − | 5.87368e15i | −0.0510560 | − | 1.34185i | ||||
\(699\) | −3.38966e15 | −0.768302 | ||||||||
\(700\) | 2.13644e15 | + | 3.87601e15i | 0.480454 | + | 0.871657i | ||||
\(701\) | 1.09344e15 | 0.243975 | 0.121987 | − | 0.992532i | \(-0.461073\pi\) | ||||
0.121987 | + | 0.992532i | \(0.461073\pi\) | |||||||
\(702\) | 1.98852e13 | + | 5.22622e14i | 0.00440226 | + | 0.115700i | ||||
\(703\) | −1.14190e15 | −0.250827 | ||||||||
\(704\) | −1.20079e15 | − | 5.17074e15i | −0.261708 | − | 1.12695i | ||||
\(705\) | 1.87963e14i | 0.0406473i | ||||||||
\(706\) | −2.47002e14 | − | 6.49170e15i | −0.0529998 | − | 1.39294i | ||||
\(707\) | 7.38678e15 | − | 3.36719e15i | 1.57271 | − | 0.716903i | ||||
\(708\) | 2.79671e15 | − | 2.13132e14i | 0.590832 | − | 0.0450262i | ||||
\(709\) | −3.08924e15 | −0.647586 | −0.323793 | − | 0.946128i | \(-0.604958\pi\) | ||||
−0.323793 | + | 0.946128i | \(0.604958\pi\) | |||||||
\(710\) | 2.25535e14 | − | 8.58136e12i | 0.0469130 | − | 0.00178499i | ||||
\(711\) | 2.46237e15i | 0.508242i | ||||||||
\(712\) | 1.77641e14 | + | 1.55024e15i | 0.0363833 | + | 0.317511i | ||||
\(713\) | − | 1.72493e15i | − | 0.350573i | ||||||
\(714\) | 2.69012e15 | − | 1.35207e15i | 0.542540 | − | 0.272684i | ||||
\(715\) | − | 2.38442e14i | − | 0.0477199i | ||||||
\(716\) | −4.69410e14 | − | 6.15958e15i | −0.0932246 | − | 1.22329i | ||||
\(717\) | 6.26037e14i | 0.123380i | ||||||||
\(718\) | 2.89687e14 | + | 7.61355e15i | 0.0566558 | + | 1.48903i | ||||
\(719\) | −1.26250e15 | −0.245032 | −0.122516 | − | 0.992467i | \(-0.539096\pi\) | ||||
−0.122516 | + | 0.992467i | \(0.539096\pi\) | |||||||
\(720\) | −1.79798e13 | − | 1.17280e14i | −0.00346303 | − | 0.0225889i | ||||
\(721\) | 3.88354e14 | + | 8.51952e14i | 0.0742307 | + | 0.162844i | ||||
\(722\) | 4.85119e15 | − | 1.84582e14i | 0.920225 | − | 0.0350135i | ||||
\(723\) | 1.05405e15i | 0.198427i | ||||||||
\(724\) | −9.82215e13 | − | 1.28886e15i | −0.0183504 | − | 0.240793i | ||||
\(725\) | −1.23008e15 | −0.228073 | ||||||||
\(726\) | −1.06128e15 | + | 4.03805e13i | −0.195290 | + | 0.00743055i | ||||
\(727\) | 4.48259e14 | 0.0818634 | 0.0409317 | − | 0.999162i | \(-0.486967\pi\) | ||||
0.0409317 | + | 0.999162i | \(0.486967\pi\) | |||||||
\(728\) | 2.84397e15 | − | 1.71169e15i | 0.515469 | − | 0.310244i | ||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 6.16655e14 | − | 2.34630e13i | 0.110095 | − | 0.00418898i | ||||
\(731\) | 6.50242e15 | 1.15220 | ||||||||
\(732\) | 2.70483e14 | + | 3.54927e15i | 0.0475695 | + | 0.624206i | ||||
\(733\) | − | 4.17763e15i | − | 0.729219i | −0.931161 | − | 0.364609i | \(-0.881203\pi\) | ||
0.931161 | − | 0.364609i | \(-0.118797\pi\) | |||||||
\(734\) | −6.62716e15 | + | 2.52156e14i | −1.14815 | + | 0.0436858i | ||||
\(735\) | −1.73753e14 | − | 1.50984e14i | −0.0298780 | − | 0.0259627i | ||||
\(736\) | −2.43539e14 | − | 1.26528e15i | −0.0415662 | − | 0.215953i | ||||
\(737\) | −1.92485e15 | −0.326082 | ||||||||
\(738\) | −6.99677e13 | − | 1.83889e15i | −0.0117649 | − | 0.309205i | ||||
\(739\) | − | 7.40374e14i | − | 0.123568i | −0.998090 | − | 0.0617841i | \(-0.980321\pi\) | ||
0.998090 | − | 0.0617841i | \(-0.0196790\pi\) | |||||||
\(740\) | 2.80440e13 | + | 3.67993e14i | 0.00464585 | + | 0.0609628i | ||||
\(741\) | − | 5.94132e14i | − | 0.0976974i | ||||||
\(742\) | −2.58959e15 | − | 5.15232e15i | −0.422677 | − | 0.840971i | ||||
\(743\) | − | 9.28702e15i | − | 1.50466i | −0.658787 | − | 0.752329i | \(-0.728930\pi\) | ||
0.658787 | − | 0.752329i | \(-0.271070\pi\) | |||||||
\(744\) | −5.68561e15 | + | 6.51509e14i | −0.914378 | + | 0.104778i | ||||
\(745\) | − | 3.74136e14i | − | 0.0597269i | ||||||
\(746\) | 5.57095e15 | − | 2.11968e14i | 0.882807 | − | 0.0335898i | ||||
\(747\) | 2.02557e15 | 0.318628 | ||||||||
\(748\) | −7.76982e15 | + | 5.92123e14i | −1.21326 | + | 0.0924598i | ||||
\(749\) | 2.40830e15 | − | 1.09780e15i | 0.373302 | − | 0.170166i | ||||
\(750\) | −1.95152e13 | − | 5.12899e14i | −0.00300287 | − | 0.0789214i | ||||
\(751\) | − | 9.18866e14i | − | 0.140357i | −0.997534 | − | 0.0701783i | \(-0.977643\pi\) | ||
0.997534 | − | 0.0701783i | \(-0.0223568\pi\) | |||||||
\(752\) | 6.69398e15 | − | 1.02623e15i | 1.01505 | − | 0.155613i | ||||
\(753\) | −6.07180e14 | −0.0913998 | ||||||||
\(754\) | 3.50768e13 | + | 9.21889e14i | 0.00524177 | + | 0.137764i | ||||
\(755\) | 7.65979e14 | 0.113634 | ||||||||
\(756\) | −6.30791e14 | − | 1.14440e15i | −0.0929000 | − | 0.168543i | ||||
\(757\) | −3.02013e15 | −0.441569 | −0.220785 | − | 0.975323i | \(-0.570862\pi\) | ||||
−0.220785 | + | 0.975323i | \(0.570862\pi\) | |||||||
\(758\) | 1.24103e13 | + | 3.26166e14i | 0.00180136 | + | 0.0473433i | ||||
\(759\) | −1.01938e15 | −0.146895 | ||||||||
\(760\) | 1.53448e13 | + | 1.33911e14i | 0.00219526 | + | 0.0191577i | ||||
\(761\) | 5.06714e15i | 0.719692i | 0.933012 | + | 0.359846i | \(0.117171\pi\) | ||||
−0.933012 | + | 0.359846i | \(0.882829\pi\) | |||||||
\(762\) | −1.91907e13 | − | 5.04370e14i | −0.00270607 | − | 0.0711209i | ||||
\(763\) | 3.18826e15 | + | 6.99424e15i | 0.446343 | + | 0.979165i | ||||
\(764\) | −4.91813e14 | − | 6.45356e15i | −0.0683575 | − | 0.896986i | ||||
\(765\) | −1.74172e14 | −0.0240348 | ||||||||
\(766\) | 6.17395e15 | − | 2.34912e14i | 0.845872 | − | 0.0321844i | ||||
\(767\) | − | 4.53927e15i | − | 0.617464i | ||||||
\(768\) | −4.07857e15 | + | 1.28064e15i | −0.550835 | + | 0.172958i | ||||
\(769\) | 1.05380e16i | 1.41307i | 0.707679 | + | 0.706534i | \(0.249742\pi\) | ||||
−0.707679 | + | 0.706534i | \(0.750258\pi\) | |||||||
\(770\) | 2.67540e14 | + | 5.32305e14i | 0.0356196 | + | 0.0708699i | ||||
\(771\) | 4.79238e15i | 0.633508i | ||||||||
\(772\) | 3.61974e15 | − | 2.75853e14i | 0.475097 | − | 0.0362062i | ||||
\(773\) | 7.06227e15i | 0.920359i | 0.887826 | + | 0.460180i | \(0.152215\pi\) | ||||
−0.887826 | + | 0.460180i | \(0.847785\pi\) | |||||||
\(774\) | −1.07302e14 | − | 2.82012e15i | −0.0138846 | − | 0.364916i | ||||
\(775\) | −1.23490e16 | −1.58662 | ||||||||
\(776\) | 1.73929e15 | + | 1.51785e16i | 0.221888 | + | 1.93638i | ||||
\(777\) | 1.68590e15 | + | 3.69845e15i | 0.213558 | + | 0.468494i | ||||
\(778\) | −1.06010e16 | + | 4.03354e14i | −1.33339 | + | 0.0507340i | ||||
\(779\) | 2.09051e15i | 0.261093i | ||||||||
\(780\) | −1.91467e14 | + | 1.45913e13i | −0.0237450 | + | 0.00180956i | ||||
\(781\) | −6.43333e15 | −0.792237 | ||||||||
\(782\) | −1.89009e15 | + | 7.19159e13i | −0.231124 | + | 0.00879402i | ||||
\(783\) | 3.63186e14 | 0.0441000 | ||||||||
\(784\) | −4.42838e15 | + | 7.01225e15i | −0.533958 | + | 0.845511i | ||||
\(785\) | −5.63990e14 | −0.0675286 | ||||||||
\(786\) | −6.60822e15 | + | 2.51435e14i | −0.785707 | + | 0.0298953i | ||||
\(787\) | 9.62553e15 | 1.13648 | 0.568242 | − | 0.822861i | \(-0.307624\pi\) | ||||
0.568242 | + | 0.822861i | \(0.307624\pi\) | |||||||
\(788\) | −2.40307e15 | + | 1.83133e14i | −0.281755 | + | 0.0214720i | ||||
\(789\) | − | 4.90144e12i | − | 0.000570690i | ||||||
\(790\) | −9.03416e14 | + | 3.43739e13i | −0.104457 | + | 0.00397448i | ||||
\(791\) | 7.55382e14 | + | 1.65712e15i | 0.0867353 | + | 0.190276i | ||||
\(792\) | 3.85023e14 | + | 3.36003e15i | 0.0439034 | + | 0.383137i | ||||
\(793\) | 5.76074e15 | 0.652343 | ||||||||
\(794\) | 2.94207e14 | + | 7.73234e15i | 0.0330857 | + | 0.869557i | ||||
\(795\) | 3.33587e14i | 0.0372555i | ||||||||
\(796\) | −6.79973e14 | + | 5.18194e13i | −0.0754171 | + | 0.00574739i | ||||
\(797\) | 3.10132e15i | 0.341607i | 0.985305 | + | 0.170803i | \(0.0546363\pi\) | ||||
−0.985305 | + | 0.170803i | \(0.945364\pi\) | |||||||
\(798\) | 6.66636e14 | + | 1.32636e15i | 0.0729244 | + | 0.145093i | ||||
\(799\) | − | 9.94121e15i | − | 1.08002i | ||||||
\(800\) | −9.05836e15 | + | 1.74353e15i | −0.977360 | + | 0.188120i | ||||
\(801\) | − | 9.94144e14i | − | 0.106530i | ||||||
\(802\) | 6.28528e15 | − | 2.39148e14i | 0.668907 | − | 0.0254511i | ||||
\(803\) | −1.75899e16 | −1.85921 | ||||||||
\(804\) | 1.17790e14 | + | 1.54564e15i | 0.0123652 | + | 0.162256i | ||||
\(805\) | 5.99811e13 | + | 1.31584e14i | 0.00625370 | + | 0.0137191i | ||||
\(806\) | 3.52143e14 | + | 9.25502e15i | 0.0364650 | + | 0.958373i | ||||
\(807\) | 3.32812e15i | 0.342291i | ||||||||
\(808\) | 1.92627e15 | + | 1.68102e16i | 0.196768 | + | 1.71716i | ||||
\(809\) | −1.36082e16 | −1.38065 | −0.690325 | − | 0.723499i | \(-0.742533\pi\) | ||||
−0.690325 | + | 0.723499i | \(0.742533\pi\) | |||||||
\(810\) | 2.87418e12 | + | 7.55392e13i | 0.000289632 | + | 0.00761211i | ||||
\(811\) | 5.97769e15 | 0.598300 | 0.299150 | − | 0.954206i | \(-0.403297\pi\) | ||||
0.299150 | + | 0.954206i | \(0.403297\pi\) | |||||||
\(812\) | −1.11270e15 | − | 2.01869e15i | −0.110616 | − | 0.200684i | ||||
\(813\) | 9.25312e14 | 0.0913672 | ||||||||
\(814\) | −3.99973e14 | − | 1.05121e16i | −0.0392280 | − | 1.03099i | ||||
\(815\) | 1.60271e14 | 0.0156131 | ||||||||
\(816\) | 9.50938e14 | + | 6.20286e15i | 0.0920145 | + | 0.600200i | ||||
\(817\) | 3.20600e15i | 0.308136i | ||||||||
\(818\) | 1.73377e14 | + | 4.55668e15i | 0.0165519 | + | 0.435017i | ||||
\(819\) | −1.92431e15 | + | 8.77176e14i | −0.182479 | + | 0.0831812i | ||||
\(820\) | 6.73692e14 | − | 5.13407e13i | 0.0634578 | − | 0.00483600i | ||||
\(821\) | −2.81249e15 | −0.263150 | −0.131575 | − | 0.991306i | \(-0.542003\pi\) | ||||
−0.131575 | + | 0.991306i | \(0.542003\pi\) | |||||||
\(822\) | 6.91648e14 | − | 2.63164e13i | 0.0642821 | − | 0.00244586i | ||||
\(823\) | 3.93420e15i | 0.363210i | 0.983372 | + | 0.181605i | \(0.0581292\pi\) | ||||
−0.983372 | + | 0.181605i | \(0.941871\pi\) | |||||||
\(824\) | −1.93880e15 | + | 2.22166e14i | −0.177801 | + | 0.0203741i | ||||
\(825\) | 7.29791e15i | 0.664817i | ||||||||
\(826\) | 5.09321e15 | + | 1.01336e16i | 0.460894 | + | 0.917009i | ||||
\(827\) | 2.04668e16i | 1.83980i | 0.392153 | + | 0.919900i | \(0.371730\pi\) | ||||
−0.392153 | + | 0.919900i | \(0.628270\pi\) | |||||||
\(828\) | 6.23804e13 | + | 8.18554e14i | 0.00557033 | + | 0.0730938i | ||||
\(829\) | − | 3.72182e15i | − | 0.330145i | −0.986281 | − | 0.165073i | \(-0.947214\pi\) | ||
0.986281 | − | 0.165073i | \(-0.0527858\pi\) | |||||||
\(830\) | 2.82763e13 | + | 7.43159e14i | 0.00249169 | + | 0.0654866i | ||||
\(831\) | −1.07773e16 | −0.943414 | ||||||||
\(832\) | 1.56501e15 | + | 6.73910e15i | 0.136094 | + | 0.586035i | ||||
\(833\) | 9.18966e15 | + | 7.98541e15i | 0.793875 | + | 0.689842i | ||||
\(834\) | −5.01640e15 | + | 1.90868e14i | −0.430506 | + | 0.0163803i | ||||
\(835\) | − | 5.66128e14i | − | 0.0482657i | ||||||
\(836\) | −2.91945e14 | − | 3.83089e15i | −0.0247267 | − | 0.324463i | ||||
\(837\) | 3.64609e15 | 0.306787 | ||||||||
\(838\) | 4.77193e15 | − | 1.81566e14i | 0.398889 | − | 0.0151773i | ||||
\(839\) | 9.81366e15 | 0.814967 | 0.407484 | − | 0.913213i | \(-0.366406\pi\) | ||||
0.407484 | + | 0.913213i | \(0.366406\pi\) | |||||||
\(840\) | 4.11064e14 | − | 2.47406e14i | 0.0339136 | − | 0.0204115i | ||||
\(841\) | −1.15599e16 | −0.947490 | ||||||||
\(842\) | −2.13148e16 | + | 8.11005e14i | −1.73566 | + | 0.0660400i | ||||
\(843\) | 4.29600e15 | 0.347546 | ||||||||
\(844\) | −5.88055e14 | − | 7.71645e15i | −0.0472645 | − | 0.620203i | ||||
\(845\) | − | 5.47800e14i | − | 0.0437431i | ||||||
\(846\) | −4.31154e15 | + | 1.64049e14i | −0.342055 | + | 0.0130148i | ||||
\(847\) | −1.78127e15 | − | 3.90766e15i | −0.140401 | − | 0.308005i | ||||
\(848\) | 1.18802e16 | − | 1.82130e15i | 0.930347 | − | 0.142628i | ||||
\(849\) | −9.53898e15 | −0.742180 | ||||||||
\(850\) | 5.14857e14 | + | 1.35315e16i | 0.0397999 | + | 1.04602i | ||||
\(851\) | − | 2.55348e15i | − | 0.196119i | ||||||
\(852\) | 3.93683e14 | + | 5.16590e15i | 0.0300420 | + | 0.394211i | ||||
\(853\) | − | 1.77580e16i | − | 1.34640i | −0.739459 | − | 0.673202i | \(-0.764919\pi\) | ||
0.739459 | − | 0.673202i | \(-0.235081\pi\) | |||||||
\(854\) | −1.28604e16 | + | 6.46374e15i | −0.968808 | + | 0.486929i | ||||
\(855\) | − | 8.58752e13i | − | 0.00642768i | ||||||
\(856\) | 6.28019e14 | + | 5.48062e15i | 0.0467054 | + | 0.407590i | ||||
\(857\) | − | 1.92571e16i | − | 1.42298i | −0.702699 | − | 0.711488i | \(-0.748022\pi\) | ||
0.702699 | − | 0.711488i | \(-0.251978\pi\) | |||||||
\(858\) | 5.46945e15 | − | 2.08106e14i | 0.401572 | − | 0.0152794i | ||||
\(859\) | −1.07287e16 | −0.782683 | −0.391342 | − | 0.920245i | \(-0.627989\pi\) | ||||
−0.391342 | + | 0.920245i | \(0.627989\pi\) | |||||||
\(860\) | 1.03317e15 | − | 7.87362e13i | 0.0748915 | − | 0.00570733i | ||||
\(861\) | 6.77083e15 | − | 3.08642e15i | 0.487669 | − | 0.222299i | ||||
\(862\) | −1.01921e15 | − | 2.67868e16i | −0.0729412 | − | 1.91704i | ||||
\(863\) | − | 1.40265e16i | − | 0.997445i | −0.866762 | − | 0.498723i | \(-0.833803\pi\) | ||
0.866762 | − | 0.498723i | \(-0.166197\pi\) | |||||||
\(864\) | 2.67451e15 | − | 5.14784e14i | 0.188981 | − | 0.0363747i | ||||
\(865\) | −1.79447e15 | −0.125993 | ||||||||
\(866\) | 1.56306e13 | + | 4.10804e14i | 0.00109050 | + | 0.0286606i | ||||
\(867\) | 8.83774e14 | 0.0612684 | ||||||||
\(868\) | −1.11706e16 | − | 2.02661e16i | −0.769515 | − | 1.39608i | ||||
\(869\) | 2.57697e16 | 1.76401 | ||||||||
\(870\) | 5.06996e12 | + | 1.33249e14i | 0.000344865 | + | 0.00906374i | ||||
\(871\) | 2.50869e15 | 0.169570 | ||||||||
\(872\) | −1.59169e16 | + | 1.82391e15i | −1.06910 | + | 0.122507i | ||||
\(873\) | − | 9.73374e15i | − | 0.649683i | ||||||
\(874\) | −3.54579e13 | − | 9.31905e14i | −0.00235180 | − | 0.0618100i | ||||
\(875\) | 1.88850e15 | − | 8.60856e14i | 0.124473 | − | 0.0567396i | ||||
\(876\) | 1.07640e15 | + | 1.41245e16i | 0.0705020 | + | 0.925126i | ||||
\(877\) | 3.04085e16 | 1.97924 | 0.989618 | − | 0.143725i | \(-0.0459080\pi\) | ||||
0.989618 | + | 0.143725i | \(0.0459080\pi\) | |||||||
\(878\) | 2.16502e16 | − | 8.23767e14i | 1.40037 | − | 0.0532825i | ||||
\(879\) | − | 4.04694e15i | − | 0.260129i | ||||||
\(880\) | −1.22738e15 | + | 1.88166e14i | −0.0784017 | + | 0.0120195i | ||||
\(881\) | − | 2.66651e16i | − | 1.69269i | −0.532638 | − | 0.846343i | \(-0.678799\pi\) | ||
0.532638 | − | 0.846343i | \(-0.321201\pi\) | |||||||
\(882\) | 3.31166e15 | − | 4.11737e15i | 0.208914 | − | 0.259742i | ||||
\(883\) | 5.38302e15i | 0.337475i | 0.985661 | + | 0.168738i | \(0.0539691\pi\) | ||||
−0.985661 | + | 0.168738i | \(0.946031\pi\) | |||||||
\(884\) | 1.01265e16 | − | 7.71723e14i | 0.630919 | − | 0.0480811i | ||||
\(885\) | − | 6.56101e14i | − | 0.0406240i | ||||||
\(886\) | −2.16837e14 | − | 5.69890e15i | −0.0133428 | − | 0.350676i | ||||
\(887\) | 3.22721e15 | 0.197355 | 0.0986774 | − | 0.995119i | \(-0.468539\pi\) | ||||
0.0986774 | + | 0.995119i | \(0.468539\pi\) | |||||||
\(888\) | −8.41664e15 | + | 9.64455e14i | −0.511525 | + | 0.0586153i | ||||
\(889\) | 1.85710e15 | − | 8.46541e14i | 0.112170 | − | 0.0511315i | ||||
\(890\) | 3.64741e14 | − | 1.38780e13i | 0.0218947 | − | 0.000833068i | ||||
\(891\) | − | 2.15473e15i | − | 0.128548i | ||||||
\(892\) | 1.73645e16 | − | 1.32331e15i | 1.02957 | − | 0.0784613i | ||||
\(893\) | 4.90149e15 | 0.288832 | ||||||||
\(894\) | 8.58203e15 | − | 3.26536e14i | 0.502613 | − | 0.0191238i | ||||
\(895\) | −1.44502e15 | −0.0841102 | ||||||||
\(896\) | −1.10553e16 | − | 1.32886e16i | −0.639550 | − | 0.768749i | ||||
\(897\) | 1.32858e15 | 0.0763885 | ||||||||
\(898\) | 1.33743e16 | − | 5.08878e14i | 0.764279 | − | 0.0290799i | ||||
\(899\) | 6.43159e15 | 0.365292 | ||||||||
\(900\) | 5.86015e15 | − | 4.46591e14i | 0.330807 | − | 0.0252102i | ||||
\(901\) | − | 1.76432e16i | − | 0.989898i | ||||||
\(902\) | −1.92447e16 | + | 7.32240e14i | −1.07319 | + | 0.0408336i | ||||
\(903\) | 1.03838e16 | − | 4.73333e15i | 0.575535 | − | 0.262352i | ||||
\(904\) | −3.77114e15 | + | 4.32132e14i | −0.207753 | + | 0.0238062i | ||||
\(905\) | −3.02364e14 | −0.0165563 | ||||||||
\(906\) | 6.68527e14 | + | 1.75702e16i | 0.0363843 | + | 0.956252i | ||||
\(907\) | 1.23226e16i | 0.666596i | 0.942822 | + | 0.333298i | \(0.108161\pi\) | ||||
−0.942822 | + | 0.333298i | \(0.891839\pi\) | |||||||
\(908\) | 1.39837e16 | − | 1.06567e15i | 0.751880 | − | 0.0572993i | ||||
\(909\) | − | 1.07801e16i | − | 0.576133i | ||||||
\(910\) | −3.48689e14 | − | 6.93762e14i | −0.0185230 | − | 0.0368538i | ||||
\(911\) | − | 3.81405e15i | − | 0.201389i | −0.994917 | − | 0.100694i | \(-0.967894\pi\) | ||
0.994917 | − | 0.100694i | \(-0.0321065\pi\) | |||||||
\(912\) | −3.05830e15 | + | 4.68858e14i | −0.160513 | + | 0.0246076i | ||||
\(913\) | − | 2.11984e16i | − | 1.10589i | ||||||
\(914\) | −3.97632e15 | + | 1.51294e14i | −0.206195 | + | 0.00784547i | ||||
\(915\) | 8.32651e14 | 0.0429187 | ||||||||
\(916\) | −1.16893e15 | − | 1.53387e16i | −0.0598912 | − | 0.785891i | ||||
\(917\) | −1.10913e16 | − | 2.43316e16i | −0.564875 | − | 1.23920i | ||||
\(918\) | −1.52013e14 | − | 3.99521e15i | −0.00769567 | − | 0.202258i | ||||
\(919\) | 2.53007e16i | 1.27320i | 0.771193 | + | 0.636602i | \(0.219660\pi\) | ||||
−0.771193 | + | 0.636602i | \(0.780340\pi\) | |||||||
\(920\) | −2.99448e14 | + | 3.43134e13i | −0.0149792 | + | 0.00171645i | ||||
\(921\) | 1.17325e16 | 0.583393 | ||||||||
\(922\) | 5.61342e14 | + | 1.47532e16i | 0.0277465 | + | 0.729233i | ||||
\(923\) | 8.38466e15 | 0.411980 | ||||||||
\(924\) | −1.19767e16 | + | 6.60148e15i | −0.584978 | + | 0.322438i | ||||
\(925\) | −1.82808e16 | −0.887594 | ||||||||
\(926\) | 1.38626e15 | + | 3.64337e16i | 0.0669090 | + | 1.75850i | ||||
\(927\) | 1.24332e15 | 0.0596548 | ||||||||
\(928\) | 4.71775e15 | − | 9.08064e14i | 0.225020 | − | 0.0433114i | ||||
\(929\) | 9.59505e15i | 0.454947i | 0.973784 | + | 0.227473i | \(0.0730465\pi\) | ||||
−0.973784 | + | 0.227473i | \(0.926954\pi\) | |||||||
\(930\) | 5.08983e13 | + | 1.33771e15i | 0.00239909 | + | 0.0630530i | ||||
\(931\) | −3.93719e15 | + | 4.53094e15i | −0.184486 | + | 0.212307i | ||||
\(932\) | 2.84854e16 | − | 2.17082e15i | 1.32689 | − | 0.101120i | ||||
\(933\) | −2.22357e16 | −1.02968 | ||||||||
\(934\) | 1.96337e16 | − | 7.47039e14i | 0.903844 | − | 0.0343902i | ||||
\(935\) | 1.82278e15i | 0.0834202i | ||||||||
\(936\) | −5.01807e14 | − | 4.37918e15i | −0.0228307 | − | 0.199240i | ||||
\(937\) | 7.83284e15i | 0.354284i | 0.984185 | + | 0.177142i | \(0.0566851\pi\) | ||||
−0.984185 | + | 0.177142i | \(0.943315\pi\) | |||||||
\(938\) | −5.60048e15 | + | 2.81484e15i | −0.251831 | + | 0.126572i | ||||
\(939\) | − | 1.92946e16i | − | 0.862530i | ||||||
\(940\) | −1.20376e14 | − | 1.57957e15i | −0.00534978 | − | 0.0701997i | ||||
\(941\) | − | 7.72736e15i | − | 0.341420i | −0.985321 | − | 0.170710i | \(-0.945394\pi\) | ||
0.985321 | − | 0.170710i | \(-0.0546061\pi\) | |||||||
\(942\) | −4.92236e14 | − | 1.29369e16i | −0.0216219 | − | 0.568266i | ||||
\(943\) | −4.67471e15 | −0.204146 | ||||||||
\(944\) | −2.33660e16 | + | 3.58215e15i | −1.01447 | + | 0.155524i | ||||
\(945\) | −2.78137e14 | + | 1.26786e14i | −0.0120056 | + | 0.00547263i | ||||
\(946\) | −2.95137e16 | + | 1.12296e15i | −1.26655 | + | 0.0481908i | ||||
\(947\) | − | 3.11271e16i | − | 1.32805i | −0.747711 | − | 0.664024i | \(-0.768847\pi\) | ||
0.747711 | − | 0.664024i | \(-0.231153\pi\) | |||||||
\(948\) | −1.57696e15 | − | 2.06928e16i | −0.0668920 | − | 0.877755i | ||||
\(949\) | 2.29252e16 | 0.966827 | ||||||||
\(950\) | −6.67166e15 | + | 2.53849e14i | −0.279740 | + | 0.0106438i | ||||
\(951\) | 2.06783e16 | 0.862028 | ||||||||
\(952\) | −2.17409e16 | + | 1.30851e16i | −0.901101 | + | 0.542343i | ||||
\(953\) | 3.64258e16 | 1.50106 | 0.750531 | − | 0.660835i | \(-0.229798\pi\) | ||||
0.750531 | + | 0.660835i | \(0.229798\pi\) | |||||||
\(954\) | −7.65192e15 | + | 2.91147e14i | −0.313512 | + | 0.0119288i | ||||
\(955\) | −1.51399e15 | −0.0616743 | ||||||||
\(956\) | −4.00928e14 | − | 5.26097e15i | −0.0162386 | − | 0.213082i | ||||
\(957\) | − | 3.80088e15i | − | 0.153062i | ||||||
\(958\) | −8.64825e15 | + | 3.29056e14i | −0.346273 | + | 0.0131753i | ||||
\(959\) | 1.16087e15 | + | 2.54666e15i | 0.0462148 | + | 0.101384i | ||||
\(960\) | 2.26204e14 | + | 9.74062e14i | 0.00895383 | + | 0.0385563i | ||||
\(961\) | 3.91595e16 | 1.54120 | ||||||||
\(962\) | 5.21291e14 | + | 1.37006e16i | 0.0203994 | + | 0.536137i | ||||
\(963\) | − | 3.51463e15i | − | 0.136752i | ||||||
\(964\) | −6.75037e14 | − | 8.85782e15i | −0.0261158 | − | 0.342691i | ||||
\(965\) | − | 8.49182e14i | − | 0.0326664i | ||||||
\(966\) | −2.96595e15 | + | 1.49071e15i | −0.113446 | + | 0.0570187i | ||||
\(967\) | 1.27860e16i | 0.486284i | 0.969991 | + | 0.243142i | \(0.0781780\pi\) | ||||
−0.969991 | + | 0.243142i | \(0.921822\pi\) | |||||||
\(968\) | 8.89274e15 | − | 1.01901e15i | 0.336296 | − | 0.0385358i | ||||
\(969\) | 4.54188e15i | 0.170787i | ||||||||
\(970\) | 3.57120e15 | − | 1.35880e14i | 0.133527 | − | 0.00508056i | ||||
\(971\) | −4.45466e16 | −1.65618 | −0.828092 | − | 0.560592i | \(-0.810573\pi\) | ||||
−0.828092 | + | 0.560592i | \(0.810573\pi\) | |||||||
\(972\) | −1.73023e15 | + | 1.31857e14i | −0.0639646 | + | 0.00487461i | ||||
\(973\) | −8.41960e15 | − | 1.84705e16i | −0.309507 | − | 0.678982i | ||||
\(974\) | 6.42355e14 | + | 1.68824e16i | 0.0234801 | + | 0.617105i | ||||
\(975\) | − | 9.51149e15i | − | 0.345719i | ||||||
\(976\) | −4.54607e15 | − | 2.96535e16i | −0.164309 | − | 1.07177i | ||||
\(977\) | −3.92492e16 | −1.41062 | −0.705311 | − | 0.708898i | \(-0.749193\pi\) | ||||
−0.705311 | + | 0.708898i | \(0.749193\pi\) | |||||||
\(978\) | 1.39881e14 | + | 3.67635e15i | 0.00499913 | + | 0.131387i | ||||
\(979\) | −1.04041e16 | −0.369743 | ||||||||
\(980\) | 1.55685e15 | + | 1.15753e15i | 0.0550177 | + | 0.0409063i | ||||
\(981\) | 1.02073e16 | 0.358699 | ||||||||
\(982\) | −1.37338e15 | − | 3.60953e16i | −0.0479931 | − | 1.26135i | ||||
\(983\) | 3.27689e16 | 1.13872 | 0.569361 | − | 0.822088i | \(-0.307191\pi\) | ||||
0.569361 | + | 0.822088i | \(0.307191\pi\) | |||||||
\(984\) | 1.76565e15 | + | 1.54085e16i | 0.0610143 | + | 0.532461i | ||||
\(985\) | 5.63754e14i | 0.0193727i | ||||||||
\(986\) | −2.68147e14 | − | 7.04743e15i | −0.00916324 | − | 0.240828i | ||||
\(987\) | −7.23655e15 | − | 1.58752e16i | −0.245916 | − | 0.539479i | ||||
\(988\) | 3.80496e14 | + | 4.99286e15i | 0.0128584 | + | 0.168728i | ||||
\(989\) | −7.16914e15 | −0.240928 | ||||||||
\(990\) | 7.90548e14 | − | 3.00794e13i | 0.0264201 | − | 0.00100525i | ||||
\(991\) | 3.18758e15i | 0.105939i | 0.998596 | + | 0.0529695i | \(0.0168686\pi\) | ||||
−0.998596 | + | 0.0529695i | \(0.983131\pi\) | |||||||
\(992\) | 4.73624e16 | − | 9.11623e15i | 1.56538 | − | 0.301301i | ||||
\(993\) | − | 9.61317e15i | − | 0.315970i | ||||||
\(994\) | −1.87182e16 | + | 9.40786e15i | −0.611840 | + | 0.307515i | ||||
\(995\) | 1.59520e14i | 0.00518548i | ||||||||
\(996\) | −1.70221e16 | + | 1.29722e15i | −0.550284 | + | 0.0419360i | ||||
\(997\) | 3.91273e16i | 1.25793i | 0.777433 | + | 0.628965i | \(0.216521\pi\) | ||||
−0.777433 | + | 0.628965i | \(0.783479\pi\) | |||||||
\(998\) | 2.03281e15 | + | 5.34264e16i | 0.0649949 | + | 1.70820i | ||||
\(999\) | 5.39745e15 | 0.171624 |
(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 | 84.12.b.a.55.2 | yes | 44 | |
4.3 | odd | 2 | 84.12.b.b.55.1 | yes | 44 | ||
7.6 | odd | 2 | 84.12.b.b.55.2 | yes | 44 | ||
28.27 | even | 2 | inner | 84.12.b.a.55.1 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.b.a.55.1 | ✓ | 44 | 28.27 | even | 2 | inner | |
84.12.b.a.55.2 | yes | 44 | 1.1 | even | 1 | trivial | |
84.12.b.b.55.1 | yes | 44 | 4.3 | odd | 2 | ||
84.12.b.b.55.2 | yes | 44 | 7.6 | odd | 2 |