Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,13,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.31195053821\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 5 x^{9} + 468 x^{8} + 1496 x^{7} + 710096 x^{6} + 29155008 x^{5} + 143571008 x^{4} + 28213427840 x^{3} + 1335549648384 x^{2} + \cdots + 824967906703360 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{45}\cdot 3^{3}\cdot 23 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.2 | ||
Root | \(-25.4137 - 6.09761i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.13.d.b.3.1 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −62.8274 | + | 12.1952i | −0.981677 | + | 0.190550i | ||||
\(3\) | 24.0930 | 0.0330494 | 0.0165247 | − | 0.999863i | \(-0.494740\pi\) | ||||
0.0165247 | + | 0.999863i | \(0.494740\pi\) | |||||||
\(4\) | 3798.55 | − | 1532.39i | 0.927381 | − | 0.374118i | ||||
\(5\) | 25133.2i | 1.60853i | 0.594273 | + | 0.804264i | \(0.297440\pi\) | ||||
−0.594273 | + | 0.804264i | \(0.702560\pi\) | |||||||
\(6\) | −1513.70 | + | 293.819i | −0.0324438 | + | 0.00629757i | ||||
\(7\) | − | 190438.i | − | 1.61870i | −0.587329 | − | 0.809348i | \(-0.699820\pi\) | ||
0.587329 | − | 0.809348i | \(-0.300180\pi\) | |||||||
\(8\) | −219965. | + | 142600.i | −0.839101 | + | 0.543976i | ||||
\(9\) | −530861. | −0.998908 | ||||||||
\(10\) | −306505. | − | 1.57906e6i | −0.306505 | − | 1.57906i | ||||
\(11\) | −1.60494e6 | −0.905946 | −0.452973 | − | 0.891524i | \(-0.649637\pi\) | ||||
−0.452973 | + | 0.891524i | \(0.649637\pi\) | |||||||
\(12\) | 91518.6 | − | 36919.8i | 0.0306494 | − | 0.0123644i | ||||
\(13\) | − | 3.13062e6i | − | 0.648590i | −0.945956 | − | 0.324295i | \(-0.894873\pi\) | ||
0.945956 | − | 0.324295i | \(-0.105127\pi\) | |||||||
\(14\) | 2.32243e6 | + | 1.19647e7i | 0.308443 | + | 1.58904i | ||||
\(15\) | 605535.i | 0.0531609i | ||||||||
\(16\) | 1.20808e7 | − | 1.16417e7i | 0.720072 | − | 0.693900i | ||||
\(17\) | −1.87119e7 | −0.775218 | −0.387609 | − | 0.921824i | \(-0.626699\pi\) | ||||
−0.387609 | + | 0.921824i | \(0.626699\pi\) | |||||||
\(18\) | 3.33526e7 | − | 6.47396e6i | 0.980605 | − | 0.190342i | ||||
\(19\) | −2.37206e7 | −0.504202 | −0.252101 | − | 0.967701i | \(-0.581122\pi\) | ||||
−0.252101 | + | 0.967701i | \(0.581122\pi\) | |||||||
\(20\) | 3.85138e7 | + | 9.54700e7i | 0.601779 | + | 1.49172i | ||||
\(21\) | − | 4.58823e6i | − | 0.0534969i | ||||||
\(22\) | 1.00834e8 | − | 1.95726e7i | 0.889347 | − | 0.172628i | ||||
\(23\) | − | 9.22388e7i | − | 0.623084i | −0.950232 | − | 0.311542i | \(-0.899154\pi\) | ||
0.950232 | − | 0.311542i | \(-0.100846\pi\) | |||||||
\(24\) | −5.29963e6 | + | 3.43566e6i | −0.0277318 | + | 0.0179781i | ||||
\(25\) | −3.87539e8 | −1.58736 | ||||||||
\(26\) | 3.81786e7 | + | 1.96689e8i | 0.123589 | + | 0.636706i | ||||
\(27\) | −2.55940e7 | −0.0660627 | ||||||||
\(28\) | −2.91825e8 | − | 7.23389e8i | −0.605583 | − | 1.50115i | ||||
\(29\) | − | 4.84649e8i | − | 0.814779i | −0.913255 | − | 0.407389i | \(-0.866439\pi\) | ||
0.913255 | − | 0.407389i | \(-0.133561\pi\) | |||||||
\(30\) | −7.38463e6 | − | 3.80442e7i | −0.0101298 | − | 0.0521868i | ||||
\(31\) | 6.86189e8i | 0.773168i | 0.922254 | + | 0.386584i | \(0.126345\pi\) | ||||
−0.922254 | + | 0.386584i | \(0.873655\pi\) | |||||||
\(32\) | −6.17032e8 | + | 8.78745e8i | −0.574656 | + | 0.818395i | ||||
\(33\) | −3.86678e7 | −0.0299410 | ||||||||
\(34\) | 1.17562e9 | − | 2.28195e8i | 0.761014 | − | 0.147718i | ||||
\(35\) | 4.78633e9 | 2.60372 | ||||||||
\(36\) | −2.01650e9 | + | 8.13483e8i | −0.926368 | + | 0.373709i | ||||
\(37\) | 2.95206e9i | 1.15057i | 0.817952 | + | 0.575287i | \(0.195110\pi\) | ||||
−0.817952 | + | 0.575287i | \(0.804890\pi\) | |||||||
\(38\) | 1.49030e9 | − | 2.89278e8i | 0.494964 | − | 0.0960758i | ||||
\(39\) | − | 7.54260e7i | − | 0.0214355i | ||||||
\(40\) | −3.58400e9 | − | 5.52844e9i | −0.875000 | − | 1.34972i | ||||
\(41\) | −4.28864e9 | −0.902852 | −0.451426 | − | 0.892308i | \(-0.649085\pi\) | ||||
−0.451426 | + | 0.892308i | \(0.649085\pi\) | |||||||
\(42\) | 5.59544e7 | + | 2.88266e8i | 0.0101939 | + | 0.0525167i | ||||
\(43\) | 5.06490e9 | 0.801235 | 0.400617 | − | 0.916245i | \(-0.368796\pi\) | ||||
0.400617 | + | 0.916245i | \(0.368796\pi\) | |||||||
\(44\) | −6.09645e9 | + | 2.45939e9i | −0.840157 | + | 0.338930i | ||||
\(45\) | − | 1.33422e10i | − | 1.60677i | ||||||
\(46\) | 1.12487e9 | + | 5.79512e9i | 0.118729 | + | 0.611668i | ||||
\(47\) | 8.78567e9i | 0.815056i | 0.913193 | + | 0.407528i | \(0.133609\pi\) | ||||
−0.913193 | + | 0.407528i | \(0.866391\pi\) | |||||||
\(48\) | 2.91063e8 | − | 2.80484e8i | 0.0237979 | − | 0.0229330i | ||||
\(49\) | −2.24254e10 | −1.62018 | ||||||||
\(50\) | 2.43481e10 | − | 4.72612e9i | 1.55828 | − | 0.302472i | ||||
\(51\) | −4.50825e8 | −0.0256205 | ||||||||
\(52\) | −4.79732e9 | − | 1.18918e10i | −0.242649 | − | 0.601490i | ||||
\(53\) | 1.91993e10i | 0.866222i | 0.901341 | + | 0.433111i | \(0.142584\pi\) | ||||
−0.901341 | + | 0.433111i | \(0.857416\pi\) | |||||||
\(54\) | 1.60801e9 | − | 3.12125e8i | 0.0648522 | − | 0.0125883i | ||||
\(55\) | − | 4.03373e10i | − | 1.45724i | ||||||
\(56\) | 2.71565e10 | + | 4.18898e10i | 0.880532 | + | 1.35825i | ||||
\(57\) | −5.71501e8 | −0.0166636 | ||||||||
\(58\) | 5.91040e9 | + | 3.04492e10i | 0.155256 | + | 0.799850i | ||||
\(59\) | −3.49769e9 | −0.0829219 | −0.0414609 | − | 0.999140i | \(-0.513201\pi\) | ||||
−0.0414609 | + | 0.999140i | \(0.513201\pi\) | |||||||
\(60\) | 9.27914e8 | + | 2.30016e9i | 0.0198884 | + | 0.0493004i | ||||
\(61\) | − | 2.44704e10i | − | 0.474965i | −0.971392 | − | 0.237482i | \(-0.923678\pi\) | ||
0.971392 | − | 0.237482i | \(-0.0763222\pi\) | |||||||
\(62\) | −8.36822e9 | − | 4.31115e10i | −0.147327 | − | 0.759001i | ||||
\(63\) | 1.01096e11i | 1.61693i | ||||||||
\(64\) | 2.80500e10 | − | 6.27341e10i | 0.408181 | − | 0.912901i | ||||
\(65\) | 7.86826e10 | 1.04327 | ||||||||
\(66\) | 2.42940e9 | − | 4.71562e8i | 0.0293924 | − | 0.00570526i | ||||
\(67\) | −8.26763e10 | −0.913971 | −0.456985 | − | 0.889474i | \(-0.651071\pi\) | ||||
−0.456985 | + | 0.889474i | \(0.651071\pi\) | |||||||
\(68\) | −7.10780e10 | + | 2.86738e10i | −0.718922 | + | 0.290023i | ||||
\(69\) | − | 2.22231e9i | − | 0.0205926i | ||||||
\(70\) | −3.00712e11 | + | 5.83703e10i | −2.55601 | + | 0.496139i | ||||
\(71\) | − | 1.93928e11i | − | 1.51388i | −0.653486 | − | 0.756939i | \(-0.726694\pi\) | ||
0.653486 | − | 0.756939i | \(-0.273306\pi\) | |||||||
\(72\) | 1.16771e11 | − | 7.57007e10i | 0.838184 | − | 0.543381i | ||||
\(73\) | 1.67338e11 | 1.10575 | 0.552874 | − | 0.833265i | \(-0.313531\pi\) | ||||
0.552874 | + | 0.833265i | \(0.313531\pi\) | |||||||
\(74\) | −3.60010e10 | − | 1.85470e11i | −0.219242 | − | 1.12949i | ||||
\(75\) | −9.33698e9 | −0.0524613 | ||||||||
\(76\) | −9.01041e10 | + | 3.63492e10i | −0.467587 | + | 0.188631i | ||||
\(77\) | 3.05641e11i | 1.46645i | ||||||||
\(78\) | 9.19837e8 | + | 4.73882e9i | 0.00408454 | + | 0.0210427i | ||||
\(79\) | 1.86669e11i | 0.767910i | 0.923352 | + | 0.383955i | \(0.125438\pi\) | ||||
−0.923352 | + | 0.383955i | \(0.874562\pi\) | |||||||
\(80\) | 2.92594e11 | + | 3.03630e11i | 1.11616 | + | 1.15826i | ||||
\(81\) | 2.81504e11 | 0.996724 | ||||||||
\(82\) | 2.69444e11 | − | 5.23009e10i | 0.886310 | − | 0.172039i | ||||
\(83\) | −1.03167e11 | −0.315553 | −0.157777 | − | 0.987475i | \(-0.550433\pi\) | ||||
−0.157777 | + | 0.987475i | \(0.550433\pi\) | |||||||
\(84\) | −7.03093e9 | − | 1.74286e10i | −0.0200142 | − | 0.0496121i | ||||
\(85\) | − | 4.70290e11i | − | 1.24696i | ||||||
\(86\) | −3.18214e11 | + | 6.17675e10i | −0.786554 | + | 0.152675i | ||||
\(87\) | − | 1.16767e10i | − | 0.0269279i | ||||||
\(88\) | 3.53031e11 | − | 2.28864e11i | 0.760180 | − | 0.492813i | ||||
\(89\) | −4.34582e11 | −0.874444 | −0.437222 | − | 0.899354i | \(-0.644038\pi\) | ||||
−0.437222 | + | 0.899354i | \(0.644038\pi\) | |||||||
\(90\) | 1.62712e11 | + | 8.38258e11i | 0.306170 | + | 1.57733i | ||||
\(91\) | −5.96189e11 | −1.04987 | ||||||||
\(92\) | −1.41346e11 | − | 3.50374e11i | −0.233107 | − | 0.577837i | ||||
\(93\) | 1.65324e10i | 0.0255527i | ||||||||
\(94\) | −1.07143e11 | − | 5.51980e11i | −0.155309 | − | 0.800123i | ||||
\(95\) | − | 5.96176e11i | − | 0.811023i | ||||||
\(96\) | −1.48661e10 | + | 2.11716e10i | −0.0189920 | + | 0.0270475i | ||||
\(97\) | −1.22566e12 | −1.47143 | −0.735713 | − | 0.677293i | \(-0.763153\pi\) | ||||
−0.735713 | + | 0.677293i | \(0.763153\pi\) | |||||||
\(98\) | 1.40893e12 | − | 2.73482e11i | 1.59049 | − | 0.308726i | ||||
\(99\) | 8.51999e11 | 0.904956 | ||||||||
\(100\) | −1.47209e12 | + | 5.93860e11i | −1.47209 | + | 0.593860i | ||||
\(101\) | 1.80880e11i | 0.170397i | 0.996364 | + | 0.0851983i | \(0.0271524\pi\) | ||||
−0.996364 | + | 0.0851983i | \(0.972848\pi\) | |||||||
\(102\) | 2.83242e10 | − | 5.49791e9i | 0.0251510 | − | 0.00488199i | ||||
\(103\) | 8.06974e11i | 0.675828i | 0.941177 | + | 0.337914i | \(0.109721\pi\) | ||||
−0.941177 | + | 0.337914i | \(0.890279\pi\) | |||||||
\(104\) | 4.46426e11 | + | 6.88628e11i | 0.352817 | + | 0.544232i | ||||
\(105\) | 1.15317e11 | 0.0860513 | ||||||||
\(106\) | −2.34139e11 | − | 1.20624e12i | −0.165059 | − | 0.850350i | ||||
\(107\) | 1.97329e12 | 1.31488 | 0.657442 | − | 0.753505i | \(-0.271638\pi\) | ||||
0.657442 | + | 0.753505i | \(0.271638\pi\) | |||||||
\(108\) | −9.72203e10 | + | 3.92199e10i | −0.0612653 | + | 0.0247152i | ||||
\(109\) | − | 5.54844e11i | − | 0.330835i | −0.986224 | − | 0.165418i | \(-0.947103\pi\) | ||
0.986224 | − | 0.165418i | \(-0.0528972\pi\) | |||||||
\(110\) | 4.91922e11 | + | 2.53429e12i | 0.277677 | + | 1.43054i | ||||
\(111\) | 7.11240e10i | 0.0380258i | ||||||||
\(112\) | −2.21702e12 | − | 2.30064e12i | −1.12321 | − | 1.16558i | ||||
\(113\) | 3.67045e11 | 0.176298 | 0.0881491 | − | 0.996107i | \(-0.471905\pi\) | ||||
0.0881491 | + | 0.996107i | \(0.471905\pi\) | |||||||
\(114\) | 3.59059e10 | − | 6.96958e9i | 0.0163582 | − | 0.00317525i | ||||
\(115\) | 2.31826e12 | 1.00225 | ||||||||
\(116\) | −7.42670e11 | − | 1.84097e12i | −0.304823 | − | 0.755611i | ||||
\(117\) | 1.66192e12i | 0.647881i | ||||||||
\(118\) | 2.19751e11 | − | 4.26551e10i | 0.0814025 | − | 0.0158008i | ||||
\(119\) | 3.56345e12i | 1.25484i | ||||||||
\(120\) | −8.63493e10 | − | 1.33197e11i | −0.0289182 | − | 0.0446073i | ||||
\(121\) | −5.62601e11 | −0.179262 | ||||||||
\(122\) | 2.98421e11 | + | 1.53741e12i | 0.0905047 | + | 0.466262i | ||||
\(123\) | −1.03326e11 | −0.0298387 | ||||||||
\(124\) | 1.05151e12 | + | 2.60653e12i | 0.289256 | + | 0.717021i | ||||
\(125\) | − | 3.60407e12i | − | 0.944786i | ||||||
\(126\) | −1.23289e12 | − | 6.35160e12i | −0.308106 | − | 1.58730i | ||||
\(127\) | − | 6.92557e12i | − | 1.65057i | −0.564718 | − | 0.825284i | \(-0.691015\pi\) | ||
0.564718 | − | 0.825284i | \(-0.308985\pi\) | |||||||
\(128\) | −9.97251e11 | + | 4.28349e12i | −0.226749 | + | 0.973953i | ||||
\(129\) | 1.22029e11 | 0.0264803 | ||||||||
\(130\) | −4.94342e12 | + | 9.59551e11i | −1.02416 | + | 0.198796i | ||||
\(131\) | −9.09784e12 | −1.80016 | −0.900079 | − | 0.435727i | \(-0.856491\pi\) | ||||
−0.900079 | + | 0.435727i | \(0.856491\pi\) | |||||||
\(132\) | −1.46882e11 | + | 5.92540e10i | −0.0277667 | + | 0.0112014i | ||||
\(133\) | 4.51731e12i | 0.816150i | ||||||||
\(134\) | 5.19433e12 | − | 1.00826e12i | 0.897224 | − | 0.174157i | ||||
\(135\) | − | 6.43261e11i | − | 0.106264i | ||||||
\(136\) | 4.11596e12 | − | 2.66831e12i | 0.650486 | − | 0.421699i | ||||
\(137\) | −1.11865e12 | −0.169189 | −0.0845943 | − | 0.996415i | \(-0.526959\pi\) | ||||
−0.0845943 | + | 0.996415i | \(0.526959\pi\) | |||||||
\(138\) | 2.71016e10 | + | 1.39622e11i | 0.00392392 | + | 0.0202152i | ||||
\(139\) | −3.44169e12 | −0.477181 | −0.238590 | − | 0.971120i | \(-0.576685\pi\) | ||||
−0.238590 | + | 0.971120i | \(0.576685\pi\) | |||||||
\(140\) | 1.81811e13 | − | 7.33450e12i | 2.41464 | − | 0.974097i | ||||
\(141\) | 2.11673e11i | 0.0269371i | ||||||||
\(142\) | 2.36499e12 | + | 1.21840e13i | 0.288470 | + | 1.48614i | ||||
\(143\) | 5.02445e12i | 0.587587i | ||||||||
\(144\) | −6.41322e12 | + | 6.18012e12i | −0.719285 | + | 0.693142i | ||||
\(145\) | 1.21808e13 | 1.31059 | ||||||||
\(146\) | −1.05134e13 | + | 2.04072e12i | −1.08549 | + | 0.210701i | ||||
\(147\) | −5.40295e11 | −0.0535460 | ||||||||
\(148\) | 4.52369e12 | + | 1.12136e13i | 0.430450 | + | 1.06702i | ||||
\(149\) | − | 1.15080e13i | − | 1.05167i | −0.850586 | − | 0.525837i | \(-0.823752\pi\) | ||
0.850586 | − | 0.525837i | \(-0.176248\pi\) | |||||||
\(150\) | 5.86618e11 | − | 1.13867e11i | 0.0515001 | − | 0.00999651i | ||||
\(151\) | − | 1.45861e12i | − | 0.123049i | −0.998106 | − | 0.0615246i | \(-0.980404\pi\) | ||
0.998106 | − | 0.0615246i | \(-0.0195963\pi\) | |||||||
\(152\) | 5.21771e12 | − | 3.38256e12i | 0.423076 | − | 0.274274i | ||||
\(153\) | 9.93339e12 | 0.774371 | ||||||||
\(154\) | −3.72736e12 | − | 1.92026e13i | −0.279433 | − | 1.43958i | ||||
\(155\) | −1.72462e13 | −1.24366 | ||||||||
\(156\) | −1.15582e11 | − | 2.86510e11i | −0.00801940 | − | 0.0198789i | ||||
\(157\) | 2.09908e13i | 1.40162i | 0.713348 | + | 0.700810i | \(0.247178\pi\) | ||||
−0.713348 | + | 0.700810i | \(0.752822\pi\) | |||||||
\(158\) | −2.27647e12 | − | 1.17279e13i | −0.146325 | − | 0.753840i | ||||
\(159\) | 4.62568e11i | 0.0286281i | ||||||||
\(160\) | −2.20857e13 | − | 1.55080e13i | −1.31641 | − | 0.924349i | ||||
\(161\) | −1.75658e13 | −1.00858 | ||||||||
\(162\) | −1.76862e13 | + | 3.43301e12i | −0.978462 | + | 0.189926i | ||||
\(163\) | 3.15997e13 | 1.68483 | 0.842417 | − | 0.538826i | \(-0.181132\pi\) | ||||
0.842417 | + | 0.538826i | \(0.181132\pi\) | |||||||
\(164\) | −1.62906e13 | + | 6.57186e12i | −0.837288 | + | 0.337773i | ||||
\(165\) | − | 9.71847e11i | − | 0.0481609i | ||||||
\(166\) | 6.48171e12 | − | 1.25814e12i | 0.309771 | − | 0.0601287i | ||||
\(167\) | − | 3.19093e13i | − | 1.47102i | −0.677515 | − | 0.735509i | \(-0.736943\pi\) | ||
0.677515 | − | 0.735509i | \(-0.263057\pi\) | |||||||
\(168\) | 6.54281e11 | + | 1.00925e12i | 0.0291010 | + | 0.0448893i | ||||
\(169\) | 1.34973e13 | 0.579331 | ||||||||
\(170\) | 5.73529e12 | + | 2.95471e13i | 0.237608 | + | 1.22411i | ||||
\(171\) | 1.25923e13 | 0.503651 | ||||||||
\(172\) | 1.92393e13 | − | 7.76138e12i | 0.743050 | − | 0.299756i | ||||
\(173\) | − | 6.15011e12i | − | 0.229407i | −0.993400 | − | 0.114703i | \(-0.963408\pi\) | ||
0.993400 | − | 0.114703i | \(-0.0365918\pi\) | |||||||
\(174\) | 1.42399e11 | + | 7.33614e11i | 0.00513113 | + | 0.0264346i | ||||
\(175\) | 7.38022e13i | 2.56946i | ||||||||
\(176\) | −1.93889e13 | + | 1.86842e13i | −0.652346 | + | 0.628635i | ||||
\(177\) | −8.42698e10 | −0.00274052 | ||||||||
\(178\) | 2.73036e13 | − | 5.29982e12i | 0.858422 | − | 0.166625i | ||||
\(179\) | 1.73833e12 | 0.0528462 | 0.0264231 | − | 0.999651i | \(-0.491588\pi\) | ||||
0.0264231 | + | 0.999651i | \(0.491588\pi\) | |||||||
\(180\) | −2.04455e13 | − | 5.06812e13i | −0.601121 | − | 1.49009i | ||||
\(181\) | − | 3.18525e13i | − | 0.905884i | −0.891540 | − | 0.452942i | \(-0.850374\pi\) | ||
0.891540 | − | 0.452942i | \(-0.149626\pi\) | |||||||
\(182\) | 3.74570e13 | − | 7.27065e12i | 1.03063 | − | 0.200053i | ||||
\(183\) | − | 5.89565e11i | − | 0.0156973i | ||||||
\(184\) | 1.31533e13 | + | 2.02893e13i | 0.338943 | + | 0.522831i | ||||
\(185\) | −7.41948e13 | −1.85073 | ||||||||
\(186\) | −2.01616e11 | − | 1.03868e12i | −0.00486908 | − | 0.0250845i | ||||
\(187\) | 3.00314e13 | 0.702305 | ||||||||
\(188\) | 1.34630e13 | + | 3.33728e13i | 0.304927 | + | 0.755868i | ||||
\(189\) | 4.87408e12i | 0.106935i | ||||||||
\(190\) | 7.27050e12 | + | 3.74562e13i | 0.154541 | + | 0.796163i | ||||
\(191\) | − | 8.30187e13i | − | 1.70992i | −0.518694 | − | 0.854960i | \(-0.673582\pi\) | ||
0.518694 | − | 0.854960i | \(-0.326418\pi\) | |||||||
\(192\) | 6.75808e11 | − | 1.51145e12i | 0.0134901 | − | 0.0301708i | ||||
\(193\) | −4.06576e13 | −0.786680 | −0.393340 | − | 0.919393i | \(-0.628680\pi\) | ||||
−0.393340 | + | 0.919393i | \(0.628680\pi\) | |||||||
\(194\) | 7.70048e13 | − | 1.49471e13i | 1.44447 | − | 0.280381i | ||||
\(195\) | 1.89570e12 | 0.0344796 | ||||||||
\(196\) | −8.51840e13 | + | 3.43643e13i | −1.50252 | + | 0.606138i | ||||
\(197\) | 6.98237e13i | 1.19455i | 0.802035 | + | 0.597277i | \(0.203751\pi\) | ||||
−0.802035 | + | 0.597277i | \(0.796249\pi\) | |||||||
\(198\) | −5.35288e13 | + | 1.03903e13i | −0.888375 | + | 0.172440i | ||||
\(199\) | − | 6.00170e12i | − | 0.0966398i | −0.998832 | − | 0.0483199i | \(-0.984613\pi\) | ||
0.998832 | − | 0.0483199i | \(-0.0153867\pi\) | |||||||
\(200\) | 8.52452e13 | − | 5.52631e13i | 1.33196 | − | 0.863485i | ||||
\(201\) | −1.99192e12 | −0.0302062 | ||||||||
\(202\) | −2.20586e12 | − | 1.13642e13i | −0.0324691 | − | 0.167275i | ||||
\(203\) | −9.22957e13 | −1.31888 | ||||||||
\(204\) | −1.71248e12 | + | 6.90838e11i | −0.0237599 | + | 0.00958507i | ||||
\(205\) | − | 1.07788e14i | − | 1.45226i | ||||||
\(206\) | −9.84122e12 | − | 5.07000e13i | −0.128779 | − | 0.663445i | ||||
\(207\) | 4.89660e13i | 0.622404i | ||||||||
\(208\) | −3.64457e13 | − | 3.78204e13i | −0.450056 | − | 0.467031i | ||||
\(209\) | 3.80701e13 | 0.456780 | ||||||||
\(210\) | −7.24506e12 | + | 1.40632e12i | −0.0844746 | + | 0.0163971i | ||||
\(211\) | 5.39452e13 | 0.611305 | 0.305653 | − | 0.952143i | \(-0.401125\pi\) | ||||
0.305653 | + | 0.952143i | \(0.401125\pi\) | |||||||
\(212\) | 2.94207e13 | + | 7.29294e13i | 0.324069 | + | 0.803318i | ||||
\(213\) | − | 4.67231e12i | − | 0.0500327i | ||||||
\(214\) | −1.23976e14 | + | 2.40647e13i | −1.29079 | + | 0.250551i | ||||
\(215\) | 1.27297e14i | 1.28881i | ||||||||
\(216\) | 5.62980e12 | − | 3.64971e12i | 0.0554333 | − | 0.0359365i | ||||
\(217\) | 1.30677e14 | 1.25152 | ||||||||
\(218\) | 6.76644e12 | + | 3.48594e13i | 0.0630408 | + | 0.324774i | ||||
\(219\) | 4.03167e12 | 0.0365443 | ||||||||
\(220\) | −6.18123e13 | − | 1.53223e14i | −0.545179 | − | 1.35142i | ||||
\(221\) | 5.85797e13i | 0.502798i | ||||||||
\(222\) | −8.67372e11 | − | 4.46853e12i | −0.00724582 | − | 0.0373290i | ||||
\(223\) | − | 1.68020e14i | − | 1.36626i | −0.730299 | − | 0.683128i | \(-0.760619\pi\) | ||
0.730299 | − | 0.683128i | \(-0.239381\pi\) | |||||||
\(224\) | 1.67347e14 | + | 1.17506e14i | 1.32473 | + | 0.930193i | ||||
\(225\) | 2.05729e14 | 1.58563 | ||||||||
\(226\) | −2.30604e13 | + | 4.47619e12i | −0.173068 | + | 0.0335937i | ||||
\(227\) | 2.18840e13 | 0.159946 | 0.0799728 | − | 0.996797i | \(-0.474517\pi\) | ||||
0.0799728 | + | 0.996797i | \(0.474517\pi\) | |||||||
\(228\) | −2.17088e12 | + | 8.75761e11i | −0.0154535 | + | 0.00623414i | ||||
\(229\) | 2.42819e14i | 1.68372i | 0.539699 | + | 0.841858i | \(0.318538\pi\) | ||||
−0.539699 | + | 0.841858i | \(0.681462\pi\) | |||||||
\(230\) | −1.45650e14 | + | 2.82717e13i | −0.983885 | + | 0.190979i | ||||
\(231\) | 7.36382e12i | 0.0484653i | ||||||||
\(232\) | 6.91110e13 | + | 1.06606e14i | 0.443220 | + | 0.683682i | ||||
\(233\) | 6.71846e13 | 0.419889 | 0.209944 | − | 0.977713i | \(-0.432672\pi\) | ||||
0.209944 | + | 0.977713i | \(0.432672\pi\) | |||||||
\(234\) | −2.02675e13 | − | 1.04414e14i | −0.123454 | − | 0.636011i | ||||
\(235\) | −2.20812e14 | −1.31104 | ||||||||
\(236\) | −1.32862e13 | + | 5.35981e12i | −0.0769002 | + | 0.0310225i | ||||
\(237\) | 4.49743e12i | 0.0253790i | ||||||||
\(238\) | −4.34571e13 | − | 2.23882e14i | −0.239110 | − | 1.23185i | ||||
\(239\) | − | 6.19250e13i | − | 0.332260i | −0.986104 | − | 0.166130i | \(-0.946873\pi\) | ||
0.986104 | − | 0.166130i | \(-0.0531272\pi\) | |||||||
\(240\) | 7.04946e12 | + | 7.31535e12i | 0.0368883 | + | 0.0382796i | ||||
\(241\) | −2.92732e14 | −1.49406 | −0.747030 | − | 0.664791i | \(-0.768521\pi\) | ||||
−0.747030 | + | 0.664791i | \(0.768521\pi\) | |||||||
\(242\) | 3.53467e13 | − | 6.86103e12i | 0.175977 | − | 0.0341584i | ||||
\(243\) | 2.03840e13 | 0.0990038 | ||||||||
\(244\) | −3.74981e13 | − | 9.29520e13i | −0.177693 | − | 0.440474i | ||||
\(245\) | − | 5.63622e14i | − | 2.60610i | ||||||
\(246\) | 6.49172e12 | − | 1.26009e12i | 0.0292920 | − | 0.00568578i | ||||
\(247\) | 7.42602e13i | 0.327020i | ||||||||
\(248\) | −9.78505e13 | − | 1.50938e14i | −0.420584 | − | 0.648766i | ||||
\(249\) | −2.48560e12 | −0.0104288 | ||||||||
\(250\) | 4.39524e13 | + | 2.26434e14i | 0.180029 | + | 0.927475i | ||||
\(251\) | −4.22767e14 | −1.69067 | −0.845335 | − | 0.534236i | \(-0.820599\pi\) | ||||
−0.845335 | + | 0.534236i | \(0.820599\pi\) | |||||||
\(252\) | 1.54918e14 | + | 3.84019e14i | 0.604922 | + | 1.49951i | ||||
\(253\) | 1.48038e14i | 0.564481i | ||||||||
\(254\) | 8.44588e13 | + | 4.35115e14i | 0.314516 | + | 1.62033i | ||||
\(255\) | − | 1.13307e13i | − | 0.0412112i | ||||||
\(256\) | 1.04165e13 | − | 2.81282e14i | 0.0370069 | − | 0.999315i | ||||
\(257\) | 5.23143e13 | 0.181561 | 0.0907803 | − | 0.995871i | \(-0.471064\pi\) | ||||
0.0907803 | + | 0.995871i | \(0.471064\pi\) | |||||||
\(258\) | −7.66673e12 | + | 1.48816e12i | −0.0259951 | + | 0.00504583i | ||||
\(259\) | 5.62184e14 | 1.86243 | ||||||||
\(260\) | 2.98880e14 | − | 1.20572e14i | 0.967513 | − | 0.390307i | ||||
\(261\) | 2.57281e14i | 0.813889i | ||||||||
\(262\) | 5.71593e14 | − | 1.10950e14i | 1.76717 | − | 0.343020i | ||||
\(263\) | 1.22242e13i | 0.0369391i | 0.999829 | + | 0.0184695i | \(0.00587937\pi\) | ||||
−0.999829 | + | 0.0184695i | \(0.994121\pi\) | |||||||
\(264\) | 8.50557e12 | − | 5.51403e12i | 0.0251235 | − | 0.0162872i | ||||
\(265\) | −4.82539e14 | −1.39334 | ||||||||
\(266\) | −5.50896e13 | − | 2.83811e14i | −0.155518 | − | 0.801196i | ||||
\(267\) | −1.04704e13 | −0.0288998 | ||||||||
\(268\) | −3.14050e14 | + | 1.26692e14i | −0.847599 | + | 0.341933i | ||||
\(269\) | 1.96941e14i | 0.519783i | 0.965638 | + | 0.259892i | \(0.0836869\pi\) | ||||
−0.965638 | + | 0.259892i | \(0.916313\pi\) | |||||||
\(270\) | 7.84471e12 | + | 4.04144e13i | 0.0202486 | + | 0.104317i | ||||
\(271\) | 8.50754e13i | 0.214777i | 0.994217 | + | 0.107389i | \(0.0342489\pi\) | ||||
−0.994217 | + | 0.107389i | \(0.965751\pi\) | |||||||
\(272\) | −2.26054e14 | + | 2.17838e14i | −0.558212 | + | 0.537923i | ||||
\(273\) | −1.43640e13 | −0.0346976 | ||||||||
\(274\) | 7.02819e13 | − | 1.36422e13i | 0.166089 | − | 0.0322389i | ||||
\(275\) | 6.21977e14 | 1.43806 | ||||||||
\(276\) | −3.40544e12 | − | 8.44157e12i | −0.00770404 | − | 0.0190972i | ||||
\(277\) | − | 5.61149e14i | − | 1.24222i | −0.783722 | − | 0.621112i | \(-0.786681\pi\) | ||
0.783722 | − | 0.621112i | \(-0.213319\pi\) | |||||||
\(278\) | 2.16232e14 | − | 4.19721e13i | 0.468438 | − | 0.0909269i | ||||
\(279\) | − | 3.64271e14i | − | 0.772323i | ||||||
\(280\) | −1.05283e15 | + | 6.82530e14i | −2.18478 | + | 1.41636i | ||||
\(281\) | 1.07441e14 | 0.218239 | 0.109119 | − | 0.994029i | \(-0.465197\pi\) | ||||
0.109119 | + | 0.994029i | \(0.465197\pi\) | |||||||
\(282\) | −2.58140e12 | − | 1.32989e13i | −0.00513287 | − | 0.0264436i | ||||
\(283\) | 2.56049e14 | 0.498430 | 0.249215 | − | 0.968448i | \(-0.419827\pi\) | ||||
0.249215 | + | 0.968448i | \(0.419827\pi\) | |||||||
\(284\) | −2.97173e14 | − | 7.36646e14i | −0.566368 | − | 1.40394i | ||||
\(285\) | − | 1.43637e13i | − | 0.0268038i | ||||||
\(286\) | −6.12743e13 | − | 3.15673e14i | −0.111965 | − | 0.576821i | ||||
\(287\) | 8.16721e14i | 1.46144i | ||||||||
\(288\) | 3.27558e14 | − | 4.66491e14i | 0.574028 | − | 0.817501i | ||||
\(289\) | −2.32488e14 | −0.399038 | ||||||||
\(290\) | −7.65288e14 | + | 1.48548e14i | −1.28658 | + | 0.249734i | ||||
\(291\) | −2.95298e13 | −0.0486297 | ||||||||
\(292\) | 6.35641e14 | − | 2.56426e14i | 1.02545 | − | 0.413680i | ||||
\(293\) | 8.02439e14i | 1.26825i | 0.773229 | + | 0.634127i | \(0.218640\pi\) | ||||
−0.773229 | + | 0.634127i | \(0.781360\pi\) | |||||||
\(294\) | 3.39453e13 | − | 6.58901e12i | 0.0525649 | − | 0.0102032i | ||||
\(295\) | − | 8.79083e13i | − | 0.133382i | ||||||
\(296\) | −4.20963e14 | − | 6.49350e14i | −0.625884 | − | 0.965448i | ||||
\(297\) | 4.10769e13 | 0.0598492 | ||||||||
\(298\) | 1.40342e14 | + | 7.23015e14i | 0.200397 | + | 1.03240i | ||||
\(299\) | −2.88765e14 | −0.404126 | ||||||||
\(300\) | −3.54670e13 | + | 1.43079e13i | −0.0486516 | + | 0.0196267i | ||||
\(301\) | − | 9.64549e14i | − | 1.29696i | ||||||
\(302\) | 1.77881e13 | + | 9.16409e13i | 0.0234471 | + | 0.120795i | ||||
\(303\) | 4.35793e12i | 0.00563151i | ||||||||
\(304\) | −2.86564e14 | + | 2.76148e14i | −0.363062 | + | 0.349866i | ||||
\(305\) | 6.15020e14 | 0.763994 | ||||||||
\(306\) | −6.24089e14 | + | 1.21140e14i | −0.760182 | + | 0.147557i | ||||
\(307\) | 9.10083e14 | 1.08705 | 0.543527 | − | 0.839392i | \(-0.317089\pi\) | ||||
0.543527 | + | 0.839392i | \(0.317089\pi\) | |||||||
\(308\) | 4.68361e14 | + | 1.16100e15i | 0.548626 | + | 1.35996i | ||||
\(309\) | 1.94424e13i | 0.0223357i | ||||||||
\(310\) | 1.08353e15 | − | 2.10321e14i | 1.22087 | − | 0.236980i | ||||
\(311\) | − | 1.09063e15i | − | 1.20535i | −0.797986 | − | 0.602676i | \(-0.794101\pi\) | ||
0.797986 | − | 0.602676i | \(-0.205899\pi\) | |||||||
\(312\) | 1.07557e13 | + | 1.65911e13i | 0.0116604 | + | 0.0179865i | ||||
\(313\) | −1.36097e14 | −0.144738 | −0.0723688 | − | 0.997378i | \(-0.523056\pi\) | ||||
−0.0723688 | + | 0.997378i | \(0.523056\pi\) | |||||||
\(314\) | −2.55987e14 | − | 1.31879e15i | −0.267079 | − | 1.37594i | ||||
\(315\) | −2.54087e15 | −2.60087 | ||||||||
\(316\) | 2.86050e14 | + | 7.09073e14i | 0.287289 | + | 0.712145i | ||||
\(317\) | 6.95183e14i | 0.685083i | 0.939503 | + | 0.342542i | \(0.111288\pi\) | ||||
−0.939503 | + | 0.342542i | \(0.888712\pi\) | |||||||
\(318\) | −5.64111e12 | − | 2.90619e13i | −0.00545509 | − | 0.0281036i | ||||
\(319\) | 7.77833e14i | 0.738146i | ||||||||
\(320\) | 1.57671e15 | + | 7.04987e14i | 1.46843 | + | 0.656570i | ||||
\(321\) | 4.75424e13 | 0.0434561 | ||||||||
\(322\) | 1.10361e15 | − | 2.14219e14i | 0.990105 | − | 0.192186i | ||||
\(323\) | 4.43857e14 | 0.390866 | ||||||||
\(324\) | 1.06931e15 | − | 4.31373e14i | 0.924343 | − | 0.372892i | ||||
\(325\) | 1.21324e15i | 1.02955i | ||||||||
\(326\) | −1.98532e15 | + | 3.85365e14i | −1.65396 | + | 0.321045i | ||||
\(327\) | − | 1.33679e13i | − | 0.0109339i | ||||||
\(328\) | 9.43353e14 | − | 6.11560e14i | 0.757584 | − | 0.491130i | ||||
\(329\) | 1.67313e15 | 1.31933 | ||||||||
\(330\) | 1.18519e13 | + | 6.10586e13i | 0.00917706 | + | 0.0472784i | ||||
\(331\) | −1.71367e15 | −1.30304 | −0.651522 | − | 0.758630i | \(-0.725869\pi\) | ||||
−0.651522 | + | 0.758630i | \(0.725869\pi\) | |||||||
\(332\) | −3.91886e14 | + | 1.58092e14i | −0.292638 | + | 0.118054i | ||||
\(333\) | − | 1.56713e15i | − | 1.14932i | ||||||
\(334\) | 3.89140e14 | + | 2.00477e15i | 0.280303 | + | 1.44407i | ||||
\(335\) | − | 2.07792e15i | − | 1.47015i | ||||||
\(336\) | −5.34148e13 | − | 5.54294e13i | −0.0371215 | − | 0.0385216i | ||||
\(337\) | −1.43398e15 | −0.978959 | −0.489480 | − | 0.872015i | \(-0.662813\pi\) | ||||
−0.489480 | + | 0.872015i | \(0.662813\pi\) | |||||||
\(338\) | −8.48000e14 | + | 1.64603e14i | −0.568716 | + | 0.110392i | ||||
\(339\) | 8.84321e12 | 0.00582655 | ||||||||
\(340\) | −7.20666e14 | − | 1.78642e15i | −0.466509 | − | 1.15641i | ||||
\(341\) | − | 1.10129e15i | − | 0.700448i | ||||||
\(342\) | −7.91144e14 | + | 1.53566e14i | −0.494423 | + | 0.0959709i | ||||
\(343\) | 1.63474e15i | 1.00388i | ||||||||
\(344\) | −1.11410e15 | + | 7.22254e14i | −0.672317 | + | 0.435852i | ||||
\(345\) | 5.58539e13 | 0.0331237 | ||||||||
\(346\) | 7.50019e13 | + | 3.86395e14i | 0.0437135 | + | 0.225204i | ||||
\(347\) | −2.28118e15 | −1.30672 | −0.653360 | − | 0.757047i | \(-0.726641\pi\) | ||||
−0.653360 | + | 0.757047i | \(0.726641\pi\) | |||||||
\(348\) | −1.78932e13 | − | 4.43544e13i | −0.0100742 | − | 0.0249725i | ||||
\(349\) | 4.21458e14i | 0.233239i | 0.993177 | + | 0.116620i | \(0.0372058\pi\) | ||||
−0.993177 | + | 0.116620i | \(0.962794\pi\) | |||||||
\(350\) | −9.00034e14 | − | 4.63680e15i | −0.489610 | − | 2.52238i | ||||
\(351\) | 8.01252e13i | 0.0428476i | ||||||||
\(352\) | 9.90298e14 | − | 1.41033e15i | 0.520607 | − | 0.741422i | ||||
\(353\) | 2.36861e15 | 1.22418 | 0.612091 | − | 0.790787i | \(-0.290329\pi\) | ||||
0.612091 | + | 0.790787i | \(0.290329\pi\) | |||||||
\(354\) | 5.29445e12 | − | 1.02769e12i | 0.00269030 | − | 0.000522206i | ||||
\(355\) | 4.87404e15 | 2.43511 | ||||||||
\(356\) | −1.65078e15 | + | 6.65948e14i | −0.810943 | + | 0.327145i | ||||
\(357\) | 8.58543e13i | 0.0414718i | ||||||||
\(358\) | −1.09215e14 | + | 2.11993e13i | −0.0518780 | + | 0.0100699i | ||||
\(359\) | 2.67033e15i | 1.24738i | 0.781673 | + | 0.623689i | \(0.214367\pi\) | ||||
−0.781673 | + | 0.623689i | \(0.785633\pi\) | |||||||
\(360\) | 1.90260e15 | + | 2.93483e15i | 0.874044 | + | 1.34824i | ||||
\(361\) | −1.65065e15 | −0.745780 | ||||||||
\(362\) | 3.88449e14 | + | 2.00121e15i | 0.172616 | + | 0.889286i | ||||
\(363\) | −1.35547e13 | −0.00592450 | ||||||||
\(364\) | −2.26466e15 | + | 9.13592e14i | −0.973630 | + | 0.392775i | ||||
\(365\) | 4.20574e15i | 1.77863i | ||||||||
\(366\) | 7.18987e12 | + | 3.70408e13i | 0.00299112 | + | 0.0154097i | ||||
\(367\) | − | 3.55243e15i | − | 1.45388i | −0.686700 | − | 0.726941i | \(-0.740941\pi\) | ||
0.686700 | − | 0.726941i | \(-0.259059\pi\) | |||||||
\(368\) | −1.07382e15 | − | 1.11432e15i | −0.432358 | − | 0.448665i | ||||
\(369\) | 2.27667e15 | 0.901866 | ||||||||
\(370\) | 4.66146e15 | − | 9.04822e14i | 1.81682 | − | 0.352657i | ||||
\(371\) | 3.65627e15 | 1.40215 | ||||||||
\(372\) | 2.53340e13 | + | 6.27991e13i | 0.00955973 | + | 0.0236971i | ||||
\(373\) | − | 1.18076e15i | − | 0.438439i | −0.975676 | − | 0.219220i | \(-0.929649\pi\) | ||
0.975676 | − | 0.219220i | \(-0.0703511\pi\) | |||||||
\(374\) | −1.88679e15 | + | 3.66239e14i | −0.689437 | + | 0.133824i | ||||
\(375\) | − | 8.68329e13i | − | 0.0312246i | ||||||
\(376\) | −1.25284e15 | − | 1.93254e15i | −0.443371 | − | 0.683915i | ||||
\(377\) | −1.51725e15 | −0.528457 | ||||||||
\(378\) | −5.94404e13 | − | 3.06226e14i | −0.0203766 | − | 0.104976i | ||||
\(379\) | 2.57544e15 | 0.868991 | 0.434496 | − | 0.900674i | \(-0.356927\pi\) | ||||
0.434496 | + | 0.900674i | \(0.356927\pi\) | |||||||
\(380\) | −9.13572e14 | − | 2.26461e15i | −0.303418 | − | 0.752127i | ||||
\(381\) | − | 1.66858e14i | − | 0.0545503i | ||||||
\(382\) | 1.01243e15 | + | 5.21584e15i | 0.325826 | + | 1.67859i | ||||
\(383\) | 2.65161e15i | 0.840074i | 0.907507 | + | 0.420037i | \(0.137983\pi\) | ||||
−0.907507 | + | 0.420037i | \(0.862017\pi\) | |||||||
\(384\) | −2.40268e13 | + | 1.03202e14i | −0.00749390 | + | 0.0321886i | ||||
\(385\) | −7.68176e15 | −2.35883 | ||||||||
\(386\) | 2.55441e15 | − | 4.95828e14i | 0.772266 | − | 0.149902i | ||||
\(387\) | −2.68875e15 | −0.800360 | ||||||||
\(388\) | −4.65572e15 | + | 1.87818e15i | −1.36457 | + | 0.550487i | ||||
\(389\) | − | 6.46338e15i | − | 1.86536i | −0.360709 | − | 0.932678i | \(-0.617465\pi\) | ||
0.360709 | − | 0.932678i | \(-0.382535\pi\) | |||||||
\(390\) | −1.19102e14 | + | 2.31185e13i | −0.0338478 | + | 0.00657009i | ||||
\(391\) | 1.72596e15i | 0.483026i | ||||||||
\(392\) | 4.93280e15 | − | 3.19786e15i | 1.35949 | − | 0.881338i | ||||
\(393\) | −2.19194e14 | −0.0594941 | ||||||||
\(394\) | −8.51515e14 | − | 4.38684e15i | −0.227622 | − | 1.17267i | ||||
\(395\) | −4.69161e15 | −1.23520 | ||||||||
\(396\) | 3.23636e15 | − | 1.30559e15i | 0.839240 | − | 0.338560i | ||||
\(397\) | − | 3.33297e15i | − | 0.851312i | −0.904885 | − | 0.425656i | \(-0.860043\pi\) | ||
0.904885 | − | 0.425656i | \(-0.139957\pi\) | |||||||
\(398\) | 7.31920e13 | + | 3.77071e14i | 0.0184147 | + | 0.0948691i | ||||
\(399\) | 1.08836e14i | 0.0269733i | ||||||||
\(400\) | −4.68178e15 | + | 4.51162e15i | −1.14301 | + | 1.10147i | ||||
\(401\) | 4.76253e14 | 0.114544 | 0.0572719 | − | 0.998359i | \(-0.481760\pi\) | ||||
0.0572719 | + | 0.998359i | \(0.481760\pi\) | |||||||
\(402\) | 1.25147e14 | − | 2.42919e13i | 0.0296527 | − | 0.00575579i | ||||
\(403\) | 2.14820e15 | 0.501469 | ||||||||
\(404\) | 2.77177e14 | + | 6.87081e14i | 0.0637484 | + | 0.158023i | ||||
\(405\) | 7.07512e15i | 1.60326i | ||||||||
\(406\) | 5.79870e15 | − | 1.12557e15i | 1.29471 | − | 0.251313i | ||||
\(407\) | − | 4.73787e15i | − | 1.04236i | ||||||
\(408\) | 9.91659e13 | − | 6.42876e13i | 0.0214982 | − | 0.0139369i | ||||
\(409\) | −3.11273e15 | −0.664969 | −0.332484 | − | 0.943109i | \(-0.607887\pi\) | ||||
−0.332484 | + | 0.943109i | \(0.607887\pi\) | |||||||
\(410\) | 1.31449e15 | + | 6.77200e15i | 0.276729 | + | 1.42565i | ||||
\(411\) | −2.69517e13 | −0.00559158 | ||||||||
\(412\) | 1.23660e15 | + | 3.06533e15i | 0.252839 | + | 0.626750i | ||||
\(413\) | 6.66093e14i | 0.134225i | ||||||||
\(414\) | −5.97150e14 | − | 3.07640e15i | −0.118599 | − | 0.611000i | ||||
\(415\) | − | 2.59292e15i | − | 0.507576i | ||||||
\(416\) | 2.75102e15 | + | 1.93169e15i | 0.530803 | + | 0.372716i | ||||
\(417\) | −8.29206e13 | −0.0157705 | ||||||||
\(418\) | −2.39185e15 | + | 4.64274e14i | −0.448410 | + | 0.0870395i | ||||
\(419\) | 2.81541e15 | 0.520305 | 0.260152 | − | 0.965568i | \(-0.416227\pi\) | ||||
0.260152 | + | 0.965568i | \(0.416227\pi\) | |||||||
\(420\) | 4.38038e14 | − | 1.76710e14i | 0.0798024 | − | 0.0321933i | ||||
\(421\) | 2.35273e15i | 0.422551i | 0.977427 | + | 0.211275i | \(0.0677617\pi\) | ||||
−0.977427 | + | 0.211275i | \(0.932238\pi\) | |||||||
\(422\) | −3.38924e15 | + | 6.57873e14i | −0.600105 | + | 0.116484i | ||||
\(423\) | − | 4.66397e15i | − | 0.814166i | ||||||
\(424\) | −2.73781e15 | − | 4.22317e15i | −0.471203 | − | 0.726847i | ||||
\(425\) | 7.25158e15 | 1.23055 | ||||||||
\(426\) | 5.69798e13 | + | 2.93549e14i | 0.00953375 | + | 0.0491160i | ||||
\(427\) | −4.66009e15 | −0.768824 | ||||||||
\(428\) | 7.49563e15 | − | 3.02384e15i | 1.21940 | − | 0.491921i | ||||
\(429\) | 1.21054e14i | 0.0194194i | ||||||||
\(430\) | −1.55242e15 | − | 7.99775e15i | −0.245583 | − | 1.26519i | ||||
\(431\) | 1.20497e16i | 1.87981i | 0.341434 | + | 0.939906i | \(0.389087\pi\) | ||||
−0.341434 | + | 0.939906i | \(0.610913\pi\) | |||||||
\(432\) | −3.09196e14 | + | 2.97958e14i | −0.0475699 | + | 0.0458409i | ||||
\(433\) | 5.48809e15 | 0.832710 | 0.416355 | − | 0.909202i | \(-0.363307\pi\) | ||||
0.416355 | + | 0.909202i | \(0.363307\pi\) | |||||||
\(434\) | −8.21006e15 | + | 1.59363e15i | −1.22859 | + | 0.238478i | ||||
\(435\) | 2.93472e14 | 0.0433143 | ||||||||
\(436\) | −8.50235e14 | − | 2.10760e15i | −0.123771 | − | 0.306811i | ||||
\(437\) | 2.18796e15i | 0.314160i | ||||||||
\(438\) | −2.53299e14 | + | 4.91670e13i | −0.0358747 | + | 0.00696353i | ||||
\(439\) | 5.61937e15i | 0.785056i | 0.919740 | + | 0.392528i | \(0.128399\pi\) | ||||
−0.919740 | + | 0.392528i | \(0.871601\pi\) | |||||||
\(440\) | 5.75210e15 | + | 8.87281e15i | 0.792703 | + | 1.22277i | ||||
\(441\) | 1.19047e16 | 1.61841 | ||||||||
\(442\) | −7.14392e14 | − | 3.68041e15i | −0.0958083 | − | 0.493586i | ||||
\(443\) | −8.80399e15 | −1.16482 | −0.582408 | − | 0.812897i | \(-0.697889\pi\) | ||||
−0.582408 | + | 0.812897i | \(0.697889\pi\) | |||||||
\(444\) | 1.08989e14 | + | 2.70168e14i | 0.0142261 | + | 0.0352644i | ||||
\(445\) | − | 1.09225e16i | − | 1.40657i | ||||||
\(446\) | 2.04904e15 | + | 1.05563e16i | 0.260340 | + | 1.34122i | ||||
\(447\) | − | 2.77261e14i | − | 0.0347572i | ||||||
\(448\) | −1.19470e16 | − | 5.34179e15i | −1.47771 | − | 0.660721i | ||||
\(449\) | 5.50713e15 | 0.672121 | 0.336061 | − | 0.941840i | \(-0.390905\pi\) | ||||
0.336061 | + | 0.941840i | \(0.390905\pi\) | |||||||
\(450\) | −1.29254e16 | + | 2.50891e15i | −1.55657 | + | 0.302142i | ||||
\(451\) | 6.88301e15 | 0.817936 | ||||||||
\(452\) | 1.39424e15 | − | 5.62454e14i | 0.163496 | − | 0.0659563i | ||||
\(453\) | − | 3.51424e13i | − | 0.00406670i | ||||||
\(454\) | −1.37492e15 | + | 2.66881e14i | −0.157015 | + | 0.0304777i | ||||
\(455\) | − | 1.49842e16i | − | 1.68875i | ||||||
\(456\) | 1.25710e14 | − | 8.14960e13i | 0.0139824 | − | 0.00906458i | ||||
\(457\) | −1.11057e16 | −1.21912 | −0.609561 | − | 0.792739i | \(-0.708654\pi\) | ||||
−0.609561 | + | 0.792739i | \(0.708654\pi\) | |||||||
\(458\) | −2.96122e15 | − | 1.52556e16i | −0.320833 | − | 1.65287i | ||||
\(459\) | 4.78912e14 | 0.0512130 | ||||||||
\(460\) | 8.80604e15 | − | 3.55247e15i | 0.929466 | − | 0.374959i | ||||
\(461\) | 1.21877e16i | 1.26975i | 0.772616 | + | 0.634874i | \(0.218948\pi\) | ||||
−0.772616 | + | 0.634874i | \(0.781052\pi\) | |||||||
\(462\) | −8.98034e13 | − | 4.62649e14i | −0.00923508 | − | 0.0475773i | ||||
\(463\) | − | 1.17797e14i | − | 0.0119578i | −0.999982 | − | 0.00597888i | \(-0.998097\pi\) | ||
0.999982 | − | 0.00597888i | \(-0.00190315\pi\) | |||||||
\(464\) | −5.64214e15 | − | 5.85495e15i | −0.565375 | − | 0.586699i | ||||
\(465\) | −4.15512e14 | −0.0411023 | ||||||||
\(466\) | −4.22103e15 | + | 8.19331e14i | −0.412195 | + | 0.0800099i | ||||
\(467\) | −1.73578e16 | −1.67337 | −0.836687 | − | 0.547681i | \(-0.815511\pi\) | ||||
−0.836687 | + | 0.547681i | \(0.815511\pi\) | |||||||
\(468\) | 2.54671e15 | + | 6.31290e15i | 0.242384 | + | 0.600833i | ||||
\(469\) | 1.57447e16i | 1.47944i | ||||||||
\(470\) | 1.38731e16 | − | 2.69285e15i | 1.28702 | − | 0.249819i | ||||
\(471\) | 5.05731e14i | 0.0463227i | ||||||||
\(472\) | 7.69370e14 | − | 4.98770e14i | 0.0695798 | − | 0.0451075i | ||||
\(473\) | −8.12885e15 | −0.725876 | ||||||||
\(474\) | −5.48471e13 | − | 2.82561e14i | −0.00483597 | − | 0.0249140i | ||||
\(475\) | 9.19267e15 | 0.800350 | ||||||||
\(476\) | 5.46058e15 | + | 1.35360e16i | 0.469459 | + | 1.16372i | ||||
\(477\) | − | 1.01921e16i | − | 0.865276i | ||||||
\(478\) | 7.55189e14 | + | 3.89058e15i | 0.0633123 | + | 0.326173i | ||||
\(479\) | − | 9.01540e15i | − | 0.746400i | −0.927751 | − | 0.373200i | \(-0.878260\pi\) | ||
0.927751 | − | 0.373200i | \(-0.121740\pi\) | |||||||
\(480\) | −5.32111e14 | − | 3.73635e14i | −0.0435066 | − | 0.0305492i | ||||
\(481\) | 9.24177e15 | 0.746251 | ||||||||
\(482\) | 1.83916e16 | − | 3.56993e15i | 1.46668 | − | 0.284693i | ||||
\(483\) | −4.23213e14 | −0.0333331 | ||||||||
\(484\) | −2.13707e15 | + | 8.62121e14i | −0.166244 | + | 0.0670650i | ||||
\(485\) | − | 3.08047e16i | − | 2.36683i | ||||||
\(486\) | −1.28067e15 | + | 2.48587e14i | −0.0971898 | + | 0.0188652i | ||||
\(487\) | 1.44952e16i | 1.08655i | 0.839554 | + | 0.543276i | \(0.182816\pi\) | ||||
−0.839554 | + | 0.543276i | \(0.817184\pi\) | |||||||
\(488\) | 3.48947e15 | + | 5.38263e15i | 0.258369 | + | 0.398544i | ||||
\(489\) | 7.61331e14 | 0.0556827 | ||||||||
\(490\) | 6.87350e15 | + | 3.54109e16i | 0.496594 | + | 2.55835i | ||||
\(491\) | 8.18112e15 | 0.583880 | 0.291940 | − | 0.956437i | \(-0.405699\pi\) | ||||
0.291940 | + | 0.956437i | \(0.405699\pi\) | |||||||
\(492\) | −3.92491e14 | + | 1.58336e14i | −0.0276719 | + | 0.0111632i | ||||
\(493\) | 9.06870e15i | 0.631631i | ||||||||
\(494\) | −9.05620e14 | − | 4.66558e15i | −0.0623138 | − | 0.321028i | ||||
\(495\) | 2.14135e16i | 1.45565i | ||||||||
\(496\) | 7.98841e15 | + | 8.28971e15i | 0.536501 | + | 0.556736i | ||||
\(497\) | −3.69313e16 | −2.45051 | ||||||||
\(498\) | 1.56164e14 | − | 3.03125e13i | 0.0102378 | − | 0.00198722i | ||||
\(499\) | 1.38967e16 | 0.900135 | 0.450067 | − | 0.892995i | \(-0.351400\pi\) | ||||
0.450067 | + | 0.892995i | \(0.351400\pi\) | |||||||
\(500\) | −5.52283e15 | − | 1.36903e16i | −0.353461 | − | 0.876176i | ||||
\(501\) | − | 7.68790e14i | − | 0.0486162i | ||||||
\(502\) | 2.65614e16 | − | 5.15574e15i | 1.65969 | − | 0.322158i | ||||
\(503\) | − | 1.70388e15i | − | 0.105203i | −0.998616 | − | 0.0526017i | \(-0.983249\pi\) | ||
0.998616 | − | 0.0526017i | \(-0.0167514\pi\) | |||||||
\(504\) | −1.44163e16 | − | 2.22376e16i | −0.879570 | − | 1.35677i | ||||
\(505\) | −4.54609e15 | −0.274088 | ||||||||
\(506\) | −1.80535e15 | − | 9.30082e15i | −0.107562 | − | 0.554138i | ||||
\(507\) | 3.25191e14 | 0.0191465 | ||||||||
\(508\) | −1.06127e16 | − | 2.63072e16i | −0.617507 | − | 1.53071i | ||||
\(509\) | 1.60688e16i | 0.924012i | 0.886877 | + | 0.462006i | \(0.152870\pi\) | ||||
−0.886877 | + | 0.462006i | \(0.847130\pi\) | |||||||
\(510\) | 1.38180e14 | + | 7.11878e14i | 0.00785281 | + | 0.0404561i | ||||
\(511\) | − | 3.18675e16i | − | 1.78987i | ||||||
\(512\) | 2.77585e15 | + | 1.77992e16i | 0.154091 | + | 0.988057i | ||||
\(513\) | 6.07107e14 | 0.0333089 | ||||||||
\(514\) | −3.28677e15 | + | 6.37984e14i | −0.178234 | + | 0.0345964i | ||||
\(515\) | −2.02819e16 | −1.08709 | ||||||||
\(516\) | 4.63532e14 | − | 1.86995e14i | 0.0245574 | − | 0.00990676i | ||||
\(517\) | − | 1.41005e16i | − | 0.738397i | ||||||
\(518\) | −3.53206e16 | + | 6.85596e15i | −1.82831 | + | 0.354887i | ||||
\(519\) | − | 1.48175e14i | − | 0.00758176i | ||||||
\(520\) | −1.73074e16 | + | 1.12201e16i | −0.875413 | + | 0.567516i | ||||
\(521\) | −2.05693e15 | −0.102847 | −0.0514236 | − | 0.998677i | \(-0.516376\pi\) | ||||
−0.0514236 | + | 0.998677i | \(0.516376\pi\) | |||||||
\(522\) | −3.13760e15 | − | 1.61643e16i | −0.155087 | − | 0.798976i | ||||
\(523\) | 3.83630e16 | 1.87458 | 0.937288 | − | 0.348557i | \(-0.113328\pi\) | ||||
0.937288 | + | 0.348557i | \(0.113328\pi\) | |||||||
\(524\) | −3.45586e16 | + | 1.39414e16i | −1.66943 | + | 0.673471i | ||||
\(525\) | 1.77812e15i | 0.0849189i | ||||||||
\(526\) | −1.49077e14 | − | 7.68015e14i | −0.00703875 | − | 0.0362623i | ||||
\(527\) | − | 1.28399e16i | − | 0.599373i | ||||||
\(528\) | −4.67138e14 | + | 4.50159e14i | −0.0215596 | + | 0.0207760i | ||||
\(529\) | 1.34066e16 | 0.611766 | ||||||||
\(530\) | 3.03167e16 | − | 5.88467e15i | 1.36781 | − | 0.265502i | ||||
\(531\) | 1.85679e15 | 0.0828313 | ||||||||
\(532\) | 6.92226e15 | + | 1.71592e16i | 0.305336 | + | 0.756882i | ||||
\(533\) | 1.34261e16i | 0.585581i | ||||||||
\(534\) | 6.57827e14 | − | 1.27689e14i | 0.0283703 | − | 0.00550687i | ||||
\(535\) | 4.95951e16i | 2.11503i | ||||||||
\(536\) | 1.81859e16 | − | 1.17896e16i | 0.766914 | − | 0.497178i | ||||
\(537\) | 4.18816e13 | 0.00174654 | ||||||||
\(538\) | −2.40174e15 | − | 1.23733e16i | −0.0990448 | − | 0.510260i | ||||
\(539\) | 3.59913e16 | 1.46780 | ||||||||
\(540\) | −9.85724e14 | − | 2.44346e15i | −0.0397551 | − | 0.0985469i | ||||
\(541\) | − | 3.00552e15i | − | 0.119877i | −0.998202 | − | 0.0599386i | \(-0.980910\pi\) | ||
0.998202 | − | 0.0599386i | \(-0.0190905\pi\) | |||||||
\(542\) | −1.03751e15 | − | 5.34506e15i | −0.0409258 | − | 0.210842i | ||||
\(543\) | − | 7.67423e14i | − | 0.0299389i | ||||||
\(544\) | 1.15458e16 | − | 1.64430e16i | 0.445483 | − | 0.634434i | ||||
\(545\) | 1.39450e16 | 0.532158 | ||||||||
\(546\) | 9.02451e14 | − | 1.75172e14i | 0.0340618 | − | 0.00661163i | ||||
\(547\) | −4.32641e16 | −1.61512 | −0.807559 | − | 0.589787i | \(-0.799212\pi\) | ||||
−0.807559 | + | 0.589787i | \(0.799212\pi\) | |||||||
\(548\) | −4.24926e15 | + | 1.71421e15i | −0.156902 | + | 0.0632965i | ||||
\(549\) | 1.29904e16i | 0.474446i | ||||||||
\(550\) | −3.90771e16 | + | 7.58514e15i | −1.41171 | + | 0.274023i | ||||
\(551\) | 1.14962e16i | 0.410813i | ||||||||
\(552\) | 3.16901e14 | + | 4.88831e14i | 0.0112018 | + | 0.0172792i | ||||
\(553\) | 3.55489e16 | 1.24301 | ||||||||
\(554\) | 6.84334e15 | + | 3.52555e16i | 0.236706 | + | 1.21946i | ||||
\(555\) | −1.78758e15 | −0.0611655 | ||||||||
\(556\) | −1.30734e16 | + | 5.27400e15i | −0.442528 | + | 0.178522i | ||||
\(557\) | − | 2.58426e16i | − | 0.865377i | −0.901544 | − | 0.432688i | \(-0.857565\pi\) | ||
0.901544 | − | 0.432688i | \(-0.142435\pi\) | |||||||
\(558\) | 4.44236e15 | + | 2.28862e16i | 0.147166 | + | 0.758172i | ||||
\(559\) | − | 1.58563e16i | − | 0.519673i | ||||||
\(560\) | 5.78227e16 | − | 5.57210e16i | 1.87486 | − | 1.80672i | ||||
\(561\) | 7.23547e14 | 0.0232108 | ||||||||
\(562\) | −6.75024e15 | + | 1.31027e15i | −0.214240 | + | 0.0415855i | ||||
\(563\) | −2.30517e16 | −0.723858 | −0.361929 | − | 0.932206i | \(-0.617882\pi\) | ||||
−0.361929 | + | 0.932206i | \(0.617882\pi\) | |||||||
\(564\) | 3.24365e14 | + | 8.04052e14i | 0.0100777 | + | 0.0249810i | ||||
\(565\) | 9.22502e15i | 0.283581i | ||||||||
\(566\) | −1.60869e16 | + | 3.12257e15i | −0.489297 | + | 0.0949759i | ||||
\(567\) | − | 5.36092e16i | − | 1.61339i | ||||||
\(568\) | 2.76541e16 | + | 4.26575e16i | 0.823512 | + | 1.27030i | ||||
\(569\) | 2.64650e15 | 0.0779828 | 0.0389914 | − | 0.999240i | \(-0.487585\pi\) | ||||
0.0389914 | + | 0.999240i | \(0.487585\pi\) | |||||||
\(570\) | 1.75168e14 | + | 9.02432e14i | 0.00510747 | + | 0.0263127i | ||||
\(571\) | −5.11842e16 | −1.47679 | −0.738396 | − | 0.674368i | \(-0.764416\pi\) | ||||
−0.738396 | + | 0.674368i | \(0.764416\pi\) | |||||||
\(572\) | 7.69940e15 | + | 1.90856e16i | 0.219827 | + | 0.544917i | ||||
\(573\) | − | 2.00017e15i | − | 0.0565118i | ||||||
\(574\) | −9.96009e15 | − | 5.13124e16i | −0.278479 | − | 1.43467i | ||||
\(575\) | 3.57462e16i | 0.989059i | ||||||||
\(576\) | −1.48906e16 | + | 3.33030e16i | −0.407735 | + | 0.911904i | ||||
\(577\) | −1.35781e16 | −0.367945 | −0.183972 | − | 0.982931i | \(-0.558896\pi\) | ||||
−0.183972 | + | 0.982931i | \(0.558896\pi\) | |||||||
\(578\) | 1.46066e16 | − | 2.83524e15i | 0.391726 | − | 0.0760367i | ||||
\(579\) | −9.79564e14 | −0.0259993 | ||||||||
\(580\) | 4.62695e16 | − | 1.86657e16i | 1.21542 | − | 0.490317i | ||||
\(581\) | 1.96469e16i | 0.510785i | ||||||||
\(582\) | 1.85528e15 | − | 3.60122e14i | 0.0477387 | − | 0.00926641i | ||||
\(583\) | − | 3.08136e16i | − | 0.784750i | ||||||
\(584\) | −3.68085e16 | + | 2.38623e16i | −0.927835 | + | 0.601500i | ||||
\(585\) | −4.17695e16 | −1.04213 | ||||||||
\(586\) | −9.78591e15 | − | 5.04151e16i | −0.241666 | − | 1.24502i | ||||
\(587\) | −2.85301e15 | −0.0697387 | −0.0348694 | − | 0.999392i | \(-0.511102\pi\) | ||||
−0.0348694 | + | 0.999392i | \(0.511102\pi\) | |||||||
\(588\) | −2.05234e15 | + | 8.27940e14i | −0.0496575 | + | 0.0200325i | ||||
\(589\) | − | 1.62768e16i | − | 0.389833i | ||||||
\(590\) | 1.07206e15 | + | 5.52304e15i | 0.0254160 | + | 0.130938i | ||||
\(591\) | 1.68226e15i | 0.0394793i | ||||||||
\(592\) | 3.43670e16 | + | 3.56632e16i | 0.798383 | + | 0.828496i | ||||
\(593\) | 4.45903e16 | 1.02544 | 0.512722 | − | 0.858555i | \(-0.328637\pi\) | ||||
0.512722 | + | 0.858555i | \(0.328637\pi\) | |||||||
\(594\) | −2.58075e15 | + | 5.00941e14i | −0.0587526 | + | 0.0114043i | ||||
\(595\) | −8.95611e16 | −2.01845 | ||||||||
\(596\) | −1.76346e16 | − | 4.37136e16i | −0.393450 | − | 0.975302i | ||||
\(597\) | − | 1.44599e14i | − | 0.00319389i | ||||||
\(598\) | 1.81423e16 | − | 3.52155e15i | 0.396722 | − | 0.0770063i | ||||
\(599\) | − | 1.40027e16i | − | 0.303146i | −0.988446 | − | 0.151573i | \(-0.951566\pi\) | ||
0.988446 | − | 0.151573i | \(-0.0484338\pi\) | |||||||
\(600\) | 2.05381e15 | − | 1.33145e15i | 0.0440203 | − | 0.0285377i | ||||
\(601\) | 1.60858e14 | 0.00341347 | 0.00170673 | − | 0.999999i | \(-0.499457\pi\) | ||||
0.00170673 | + | 0.999999i | \(0.499457\pi\) | |||||||
\(602\) | 1.17629e16 | + | 6.06001e16i | 0.247135 | + | 1.27319i | ||||
\(603\) | 4.38896e16 | 0.912972 | ||||||||
\(604\) | −2.23516e15 | − | 5.54063e15i | −0.0460349 | − | 0.114114i | ||||
\(605\) | − | 1.41400e16i | − | 0.288348i | ||||||
\(606\) | −5.31459e13 | − | 2.73797e14i | −0.00107308 | − | 0.00552832i | ||||
\(607\) | 1.11179e16i | 0.222274i | 0.993805 | + | 0.111137i | \(0.0354493\pi\) | ||||
−0.993805 | + | 0.111137i | \(0.964551\pi\) | |||||||
\(608\) | 1.46364e16 | − | 2.08444e16i | 0.289742 | − | 0.412637i | ||||
\(609\) | −2.22368e15 | −0.0435882 | ||||||||
\(610\) | −3.86401e16 | + | 7.50030e15i | −0.749996 | + | 0.145579i | ||||
\(611\) | 2.75046e16 | 0.528637 | ||||||||
\(612\) | 3.77325e16 | − | 1.52218e16i | 0.718137 | − | 0.289706i | ||||
\(613\) | 2.67476e16i | 0.504106i | 0.967713 | + | 0.252053i | \(0.0811057\pi\) | ||||
−0.967713 | + | 0.252053i | \(0.918894\pi\) | |||||||
\(614\) | −5.71781e16 | + | 1.10987e16i | −1.06714 | + | 0.207138i | ||||
\(615\) | − | 2.59693e15i | − | 0.0479964i | ||||||
\(616\) | −4.35845e16 | − | 6.72305e16i | −0.797714 | − | 1.23050i | ||||
\(617\) | 3.68437e16 | 0.667808 | 0.333904 | − | 0.942607i | \(-0.391634\pi\) | ||||
0.333904 | + | 0.942607i | \(0.391634\pi\) | |||||||
\(618\) | −2.37105e14 | − | 1.22152e15i | −0.00425607 | − | 0.0219264i | ||||
\(619\) | 8.60978e16 | 1.53055 | 0.765276 | − | 0.643702i | \(-0.222603\pi\) | ||||
0.765276 | + | 0.643702i | \(0.222603\pi\) | |||||||
\(620\) | −6.55105e16 | + | 2.64278e16i | −1.15335 | + | 0.465276i | ||||
\(621\) | 2.36076e15i | 0.0411626i | ||||||||
\(622\) | 1.33004e16 | + | 6.85212e16i | 0.229680 | + | 1.18327i | ||||
\(623\) | 8.27610e16i | 1.41546i | ||||||||
\(624\) | −8.78087e14 | − | 9.11207e14i | −0.0148741 | − | 0.0154351i | ||||
\(625\) | −4.03208e15 | −0.0676471 | ||||||||
\(626\) | 8.55059e15 | − | 1.65973e15i | 0.142086 | − | 0.0275798i | ||||
\(627\) | 9.17224e14 | 0.0150963 | ||||||||
\(628\) | 3.21660e16 | + | 7.97345e16i | 0.524371 | + | 1.29984i | ||||
\(629\) | − | 5.52385e16i | − | 0.891945i | ||||||
\(630\) | 1.59636e17 | − | 3.09865e16i | 2.55322 | − | 0.495597i | ||||
\(631\) | − | 1.95166e16i | − | 0.309192i | −0.987978 | − | 0.154596i | \(-0.950592\pi\) | ||
0.987978 | − | 0.154596i | \(-0.0494076\pi\) | |||||||
\(632\) | −2.66190e16 | − | 4.10608e16i | −0.417724 | − | 0.644354i | ||||
\(633\) | 1.29970e15 | 0.0202033 | ||||||||
\(634\) | −8.47790e15 | − | 4.36765e16i | −0.130543 | − | 0.672531i | ||||
\(635\) | 1.74062e17 | 2.65498 | ||||||||
\(636\) | 7.08832e14 | + | 1.75709e15i | 0.0107103 | + | 0.0265492i | ||||
\(637\) | 7.02053e16i | 1.05083i | ||||||||
\(638\) | −9.48584e15 | − | 4.88692e16i | −0.140654 | − | 0.724621i | ||||
\(639\) | 1.02949e17i | 1.51222i | ||||||||
\(640\) | −1.07658e17 | − | 2.50641e16i | −1.56663 | − | 0.364731i | ||||
\(641\) | −6.95403e16 | −1.00251 | −0.501254 | − | 0.865300i | \(-0.667128\pi\) | ||||
−0.501254 | + | 0.865300i | \(0.667128\pi\) | |||||||
\(642\) | −2.98696e15 | + | 5.79790e14i | −0.0426599 | + | 0.00828057i | ||||
\(643\) | −1.06417e17 | −1.50573 | −0.752863 | − | 0.658177i | \(-0.771328\pi\) | ||||
−0.752863 | + | 0.658177i | \(0.771328\pi\) | |||||||
\(644\) | −6.67246e16 | + | 2.69176e16i | −0.935343 | + | 0.377329i | ||||
\(645\) | 3.06697e15i | 0.0425943i | ||||||||
\(646\) | −2.78864e16 | + | 5.41293e15i | −0.383705 | + | 0.0744797i | ||||
\(647\) | − | 2.80616e16i | − | 0.382549i | −0.981537 | − | 0.191274i | \(-0.938738\pi\) | ||
0.981537 | − | 0.191274i | \(-0.0612620\pi\) | |||||||
\(648\) | −6.19212e16 | + | 4.01425e16i | −0.836352 | + | 0.542194i | ||||
\(649\) | 5.61358e15 | 0.0751227 | ||||||||
\(650\) | −1.47957e16 | − | 7.62245e16i | −0.196180 | − | 1.01068i | ||||
\(651\) | 3.14839e15 | 0.0413621 | ||||||||
\(652\) | 1.20033e17 | − | 4.84229e16i | 1.56248 | − | 0.630326i | ||||
\(653\) | 3.61637e16i | 0.466437i | 0.972424 | + | 0.233219i | \(0.0749258\pi\) | ||||
−0.972424 | + | 0.233219i | \(0.925074\pi\) | |||||||
\(654\) | 1.63024e14 | + | 8.39867e14i | 0.00208346 | + | 0.0107336i | ||||
\(655\) | − | 2.28658e17i | − | 2.89560i | ||||||
\(656\) | −5.18102e16 | + | 4.99271e16i | −0.650119 | + | 0.626489i | ||||
\(657\) | −8.88329e16 | −1.10454 | ||||||||
\(658\) | −1.05118e17 | + | 2.04041e16i | −1.29516 | + | 0.251399i | ||||
\(659\) | 5.19401e16 | 0.634147 | 0.317074 | − | 0.948401i | \(-0.397300\pi\) | ||||
0.317074 | + | 0.948401i | \(0.397300\pi\) | |||||||
\(660\) | −1.48924e15 | − | 3.69161e15i | −0.0180178 | − | 0.0446635i | ||||
\(661\) | − | 1.42475e17i | − | 1.70817i | −0.520135 | − | 0.854084i | \(-0.674118\pi\) | ||
0.520135 | − | 0.854084i | \(-0.325882\pi\) | |||||||
\(662\) | 1.07665e17 | − | 2.08986e16i | 1.27917 | − | 0.248295i | ||||
\(663\) | 1.41136e15i | 0.0166172i | ||||||||
\(664\) | 2.26932e16 | − | 1.47116e16i | 0.264781 | − | 0.171653i | ||||
\(665\) | −1.13535e17 | −1.31280 | ||||||||
\(666\) | 1.91115e16 | + | 9.84587e16i | 0.219003 | + | 1.12826i | ||||
\(667\) | −4.47035e16 | −0.507676 | ||||||||
\(668\) | −4.88973e16 | − | 1.21209e17i | −0.550334 | − | 1.36419i | ||||
\(669\) | − | 4.04811e15i | − | 0.0451539i | ||||||
\(670\) | 2.53407e16 | + | 1.30550e17i | 0.280137 | + | 1.44321i | ||||
\(671\) | 3.92734e16i | 0.430293i | ||||||||
\(672\) | 4.03188e15 | + | 2.83108e15i | 0.0437817 | + | 0.0307423i | ||||
\(673\) | 4.48938e16 | 0.483165 | 0.241583 | − | 0.970380i | \(-0.422333\pi\) | ||||
0.241583 | + | 0.970380i | \(0.422333\pi\) | |||||||
\(674\) | 9.00934e16 | − | 1.74877e16i | 0.961022 | − | 0.186541i | ||||
\(675\) | 9.91869e15 | 0.104865 | ||||||||
\(676\) | 5.12702e16 | − | 2.06831e16i | 0.537261 | − | 0.216738i | ||||
\(677\) | 1.04649e17i | 1.08693i | 0.839431 | + | 0.543466i | \(0.182888\pi\) | ||||
−0.839431 | + | 0.543466i | \(0.817112\pi\) | |||||||
\(678\) | −5.55595e14 | + | 1.07845e14i | −0.00571979 | + | 0.00111025i | ||||
\(679\) | 2.33412e17i | 2.38179i | ||||||||
\(680\) | 6.70633e16 | + | 1.03447e17i | 0.678315 | + | 1.04632i | ||||
\(681\) | 5.27252e14 | 0.00528611 | ||||||||
\(682\) | 1.34305e16 | + | 6.91912e16i | 0.133471 | + | 0.687614i | ||||
\(683\) | −3.83475e16 | −0.377757 | −0.188879 | − | 0.982000i | \(-0.560485\pi\) | ||||
−0.188879 | + | 0.982000i | \(0.560485\pi\) | |||||||
\(684\) | 4.78327e16 | − | 1.92963e16i | 0.467077 | − | 0.188425i | ||||
\(685\) | − | 2.81153e16i | − | 0.272145i | ||||||
\(686\) | −1.99360e16 | − | 1.02706e17i | −0.191290 | − | 0.985490i | ||||
\(687\) | 5.85023e15i | 0.0556458i | ||||||||
\(688\) | 6.11880e16 | − | 5.89640e16i | 0.576947 | − | 0.555977i | ||||
\(689\) | 6.01055e16 | 0.561823 | ||||||||
\(690\) | −3.50915e15 | + | 6.81150e14i | −0.0325168 | + | 0.00631173i | ||||
\(691\) | −1.07827e17 | −0.990510 | −0.495255 | − | 0.868748i | \(-0.664925\pi\) | ||||
−0.495255 | + | 0.868748i | \(0.664925\pi\) | |||||||
\(692\) | −9.42435e15 | − | 2.33615e16i | −0.0858252 | − | 0.212748i | ||||
\(693\) | − | 1.62253e17i | − | 1.46485i | ||||||
\(694\) | 1.43320e17 | − | 2.78195e16i | 1.28278 | − | 0.248996i | ||||
\(695\) | − | 8.65008e16i | − | 0.767558i | ||||||
\(696\) | 1.66509e15 | + | 2.56846e15i | 0.0146481 | + | 0.0225953i | ||||
\(697\) | 8.02485e16 | 0.699907 | ||||||||
\(698\) | −5.13977e15 | − | 2.64791e16i | −0.0444438 | − | 0.228966i | ||||
\(699\) | 1.61868e15 | 0.0138771 | ||||||||
\(700\) | 1.13094e17 | + | 2.80342e17i | 0.961279 | + | 2.38286i | ||||
\(701\) | 1.68907e16i | 0.142344i | 0.997464 | + | 0.0711719i | \(0.0226739\pi\) | ||||
−0.997464 | + | 0.0711719i | \(0.977326\pi\) | |||||||
\(702\) | −9.77144e14 | − | 5.03405e15i | −0.00816462 | − | 0.0420625i | ||||
\(703\) | − | 7.00247e16i | − | 0.580122i | ||||||
\(704\) | −4.50185e16 | + | 1.00684e17i | −0.369790 | + | 0.827039i | ||||
\(705\) | −5.32003e15 | −0.0433291 | ||||||||
\(706\) | −1.48814e17 | + | 2.88857e16i | −1.20175 | + | 0.233268i | ||||
\(707\) | 3.44463e16 | 0.275821 | ||||||||
\(708\) | −3.20104e14 | + | 1.29134e14i | −0.00254150 | + | 0.00102528i | ||||
\(709\) | 1.88733e17i | 1.48584i | 0.669382 | + | 0.742919i | \(0.266559\pi\) | ||||
−0.669382 | + | 0.742919i | \(0.733441\pi\) | |||||||
\(710\) | −3.06223e17 | + | 5.94400e16i | −2.39050 | + | 0.464011i | ||||
\(711\) | − | 9.90954e16i | − | 0.767071i | ||||||
\(712\) | 9.55930e16 | − | 6.19714e16i | 0.733747 | − | 0.475676i | ||||
\(713\) | 6.32933e16 | 0.481749 | ||||||||
\(714\) | −1.04701e15 | − | 5.39400e15i | −0.00790246 | − | 0.0407119i | ||||
\(715\) | −1.26281e17 | −0.945150 | ||||||||
\(716\) | 6.60314e15 | − | 2.66379e15i | 0.0490086 | − | 0.0197707i | ||||
\(717\) | − | 1.49196e15i | − | 0.0109810i | ||||||
\(718\) | −3.25652e16 | − | 1.67770e17i | −0.237688 | − | 1.22452i | ||||
\(719\) | − | 1.50283e17i | − | 1.08777i | −0.839160 | − | 0.543884i | \(-0.816953\pi\) | ||
0.839160 | − | 0.543884i | \(-0.183047\pi\) | |||||||
\(720\) | −1.55326e17 | − | 1.61185e17i | −1.11494 | − | 1.15699i | ||||
\(721\) | 1.53679e17 | 1.09396 | ||||||||
\(722\) | 1.03706e17 | − | 2.01300e16i | 0.732116 | − | 0.142109i | ||||
\(723\) | −7.05279e15 | −0.0493778 | ||||||||
\(724\) | −4.88104e16 | − | 1.20994e17i | −0.338907 | − | 0.840100i | ||||
\(725\) | 1.87821e17i | 1.29335i | ||||||||
\(726\) | 8.51608e14 | − | 1.65303e14i | 0.00581594 | − | 0.00112891i | ||||
\(727\) | 1.88422e17i | 1.27622i | 0.769947 | + | 0.638108i | \(0.220283\pi\) | ||||
−0.769947 | + | 0.638108i | \(0.779717\pi\) | |||||||
\(728\) | 1.31141e17 | − | 8.50165e16i | 0.880947 | − | 0.571104i | ||||
\(729\) | −1.49112e17 | −0.993452 | ||||||||
\(730\) | −5.12899e16 | − | 2.64235e17i | −0.338918 | − | 1.74604i | ||||
\(731\) | −9.47737e16 | −0.621131 | ||||||||
\(732\) | −9.03441e14 | − | 2.23949e15i | −0.00587264 | − | 0.0145574i | ||||
\(733\) | − | 4.73850e16i | − | 0.305504i | −0.988265 | − | 0.152752i | \(-0.951186\pi\) | ||
0.988265 | − | 0.152752i | \(-0.0488136\pi\) | |||||||
\(734\) | 4.33227e16 | + | 2.23190e17i | 0.277038 | + | 1.42724i | ||||
\(735\) | − | 1.35794e16i | − | 0.0861301i | ||||||
\(736\) | 8.10545e16 | + | 5.69143e16i | 0.509929 | + | 0.358059i | ||||
\(737\) | 1.32690e17 | 0.828008 | ||||||||
\(738\) | −1.43037e17 | + | 2.77645e16i | −0.885342 | + | 0.171851i | ||||
\(739\) | 9.08599e16 | 0.557835 | 0.278917 | − | 0.960315i | \(-0.410024\pi\) | ||||
0.278917 | + | 0.960315i | \(0.410024\pi\) | |||||||
\(740\) | −2.81833e17 | + | 1.13695e17i | −1.71633 | + | 0.692391i | ||||
\(741\) | 1.78915e15i | 0.0108078i | ||||||||
\(742\) | −2.29714e17 | + | 4.45890e16i | −1.37646 | + | 0.267180i | ||||
\(743\) | 8.47788e16i | 0.503912i | 0.967739 | + | 0.251956i | \(0.0810737\pi\) | ||||
−0.967739 | + | 0.251956i | \(0.918926\pi\) | |||||||
\(744\) | −2.35751e15 | − | 3.63655e15i | −0.0139001 | − | 0.0214413i | ||||
\(745\) | 2.89232e17 | 1.69165 | ||||||||
\(746\) | 1.43996e16 | + | 7.41841e16i | 0.0835447 | + | 0.430406i | ||||
\(747\) | 5.47673e16 | 0.315209 | ||||||||
\(748\) | 1.14076e17 | − | 4.60197e16i | 0.651305 | − | 0.262745i | ||||
\(749\) | − | 3.75789e17i | − | 2.12840i | ||||||
\(750\) | 1.05895e15 | + | 5.45548e15i | 0.00594985 | + | 0.0306525i | ||||
\(751\) | 1.48426e17i | 0.827315i | 0.910433 | + | 0.413657i | \(0.135749\pi\) | ||||
−0.910433 | + | 0.413657i | \(0.864251\pi\) | |||||||
\(752\) | 1.02280e17 | + | 1.06138e17i | 0.565567 | + | 0.586899i | ||||
\(753\) | −1.01857e16 | −0.0558756 | ||||||||
\(754\) | 9.53250e16 | − | 1.85032e16i | 0.518775 | − | 0.100698i | ||||
\(755\) | 3.66597e16 | 0.197928 | ||||||||
\(756\) | 7.46897e15 | + | 1.85145e16i | 0.0400065 | + | 0.0991699i | ||||
\(757\) | − | 9.42029e16i | − | 0.500598i | −0.968169 | − | 0.250299i | \(-0.919471\pi\) | ||
0.968169 | − | 0.250299i | \(-0.0805289\pi\) | |||||||
\(758\) | −1.61808e17 | + | 3.14080e16i | −0.853069 | + | 0.165586i | ||||
\(759\) | 3.56667e15i | 0.0186557i | ||||||||
\(760\) | 8.50147e16 | + | 1.31138e17i | 0.441177 | + | 0.680530i | ||||
\(761\) | −6.48622e16 | −0.333952 | −0.166976 | − | 0.985961i | \(-0.553400\pi\) | ||||
−0.166976 | + | 0.985961i | \(0.553400\pi\) | |||||||
\(762\) | 2.03487e15 | + | 1.04832e16i | 0.0103946 | + | 0.0535508i | ||||
\(763\) | −1.05663e17 | −0.535522 | ||||||||
\(764\) | −1.27217e17 | − | 3.15351e17i | −0.639711 | − | 1.58575i | ||||
\(765\) | 2.49658e17i | 1.24560i | ||||||||
\(766\) | −3.23370e16 | − | 1.66594e17i | −0.160076 | − | 0.824682i | ||||
\(767\) | 1.09499e16i | 0.0537823i | ||||||||
\(768\) | 2.50966e14 | − | 6.77693e15i | 0.00122306 | − | 0.0330268i | ||||
\(769\) | −1.78979e17 | −0.865454 | −0.432727 | − | 0.901525i | \(-0.642449\pi\) | ||||
−0.432727 | + | 0.901525i | \(0.642449\pi\) | |||||||
\(770\) | 4.82625e17 | − | 9.36807e16i | 2.31561 | − | 0.449475i | ||||
\(771\) | 1.26041e15 | 0.00600047 | ||||||||
\(772\) | −1.54440e17 | + | 6.23032e16i | −0.729552 | + | 0.294311i | ||||
\(773\) | 1.22731e17i | 0.575278i | 0.957739 | + | 0.287639i | \(0.0928703\pi\) | ||||
−0.957739 | + | 0.287639i | \(0.907130\pi\) | |||||||
\(774\) | 1.68927e17 | − | 3.27899e16i | 0.785695 | − | 0.152509i | ||||
\(775\) | − | 2.65925e17i | − | 1.22730i | ||||||
\(776\) | 2.69602e17 | − | 1.74779e17i | 1.23468 | − | 0.800420i | ||||
\(777\) | 1.35447e16 | 0.0615522 | ||||||||
\(778\) | 7.88223e16 | + | 4.06077e17i | 0.355444 | + | 1.83118i | ||||
\(779\) | 1.01729e17 | 0.455220 | ||||||||
\(780\) | 7.20092e15 | − | 2.90495e15i | 0.0319757 | − | 0.0128994i | ||||
\(781\) | 3.11243e17i | 1.37149i | ||||||||
\(782\) | −2.10485e16 | − | 1.08438e17i | −0.0920407 | − | 0.474176i | ||||
\(783\) | 1.24041e16i | 0.0538265i | ||||||||
\(784\) | −2.70916e17 | + | 2.61070e17i | −1.16665 | + | 1.12424i | ||||
\(785\) | −5.27566e17 | −2.25454 | ||||||||
\(786\) | 1.37714e16 | − | 2.67312e15i | 0.0584040 | − | 0.0113366i | ||||
\(787\) | 3.54881e17 | 1.49360 | 0.746800 | − | 0.665049i | \(-0.231589\pi\) | ||||
0.746800 | + | 0.665049i | \(0.231589\pi\) | |||||||
\(788\) | 1.06997e17 | + | 2.65229e17i | 0.446904 | + | 1.10781i | ||||
\(789\) | 2.94518e14i | 0.00122081i | ||||||||
\(790\) | 2.94761e17 | − | 5.72151e16i | 1.21257 | − | 0.235369i | ||||
\(791\) | − | 6.98993e16i | − | 0.285374i | ||||||
\(792\) | −1.87410e17 | + | 1.21495e17i | −0.759350 | + | 0.492274i | ||||
\(793\) | −7.66074e16 | −0.308057 | ||||||||
\(794\) | 4.06463e16 | + | 2.09402e17i | 0.162218 | + | 0.835713i | ||||
\(795\) | −1.16258e16 | −0.0460491 | ||||||||
\(796\) | −9.19692e15 | − | 2.27978e16i | −0.0361547 | − | 0.0896219i | ||||
\(797\) | − | 3.68183e17i | − | 1.43653i | −0.695771 | − | 0.718264i | \(-0.744937\pi\) | ||
0.695771 | − | 0.718264i | \(-0.255063\pi\) | |||||||
\(798\) | −1.32727e15 | − | 6.83785e15i | −0.00513976 | − | 0.0264790i | ||||
\(799\) | − | 1.64396e17i | − | 0.631846i | ||||||
\(800\) | 2.39124e17 | − | 3.40548e17i | 0.912186 | − | 1.29909i | ||||
\(801\) | 2.30703e17 | 0.873489 | ||||||||
\(802\) | −2.99217e16 | + | 5.80801e15i | −0.112445 | + | 0.0218264i | ||||
\(803\) | −2.68567e17 | −1.00175 | ||||||||
\(804\) | −7.56642e15 | + | 3.05239e15i | −0.0280126 | + | 0.0113007i | ||||
\(805\) | − | 4.41485e17i | − | 1.62234i | ||||||
\(806\) | −1.34966e17 | + | 2.61977e16i | −0.492280 | + | 0.0955550i | ||||
\(807\) | 4.74490e15i | 0.0171785i | ||||||||
\(808\) | −2.57934e16 | − | 3.97872e16i | −0.0926916 | − | 0.142980i | ||||
\(809\) | −5.30501e17 | −1.89232 | −0.946161 | − | 0.323696i | \(-0.895075\pi\) | ||||
−0.946161 | + | 0.323696i | \(0.895075\pi\) | |||||||
\(810\) | −8.62826e16 | − | 4.44511e17i | −0.305501 | − | 1.57388i | ||||
\(811\) | −1.81588e17 | −0.638208 | −0.319104 | − | 0.947720i | \(-0.603382\pi\) | ||||
−0.319104 | + | 0.947720i | \(0.603382\pi\) | |||||||
\(812\) | −3.50590e17 | + | 1.41433e17i | −1.22310 | + | 0.493416i | ||||
\(813\) | 2.04972e15i | 0.00709825i | ||||||||
\(814\) | 5.77794e16 | + | 2.97668e17i | 0.198622 | + | 1.02326i | ||||
\(815\) | 7.94202e17i | 2.71010i | ||||||||
\(816\) | −5.44633e15 | + | 5.24837e15i | −0.0184486 | + | 0.0177780i | ||||
\(817\) | −1.20143e17 | −0.403984 | ||||||||
\(818\) | 1.95564e17 | − | 3.79604e16i | 0.652785 | − | 0.126710i | ||||
\(819\) | 3.16493e17 | 1.04872 | ||||||||
\(820\) | −1.65172e17 | − | 4.09437e17i | −0.543317 | − | 1.34680i | ||||
\(821\) | − | 1.83914e17i | − | 0.600559i | −0.953851 | − | 0.300280i | \(-0.902920\pi\) | ||
0.953851 | − | 0.300280i | \(-0.0970800\pi\) | |||||||
\(822\) | 1.69330e15 | − | 3.28681e14i | 0.00548913 | − | 0.00106548i | ||||
\(823\) | − | 1.97259e17i | − | 0.634800i | −0.948292 | − | 0.317400i | \(-0.897190\pi\) | ||
0.948292 | − | 0.317400i | \(-0.102810\pi\) | |||||||
\(824\) | −1.15074e17 | − | 1.77506e17i | −0.367634 | − | 0.567088i | ||||
\(825\) | 1.49853e16 | 0.0475271 | ||||||||
\(826\) | −8.12315e15 | − | 4.18489e16i | −0.0255767 | − | 0.131766i | ||||
\(827\) | −3.28518e17 | −1.02690 | −0.513448 | − | 0.858121i | \(-0.671632\pi\) | ||||
−0.513448 | + | 0.858121i | \(0.671632\pi\) | |||||||
\(828\) | 7.50348e16 | + | 1.86000e17i | 0.232852 | + | 0.577206i | ||||
\(829\) | 3.57199e17i | 1.10048i | 0.835006 | + | 0.550241i | \(0.185464\pi\) | ||||
−0.835006 | + | 0.550241i | \(0.814536\pi\) | |||||||
\(830\) | 3.16213e16 | + | 1.62906e17i | 0.0967187 | + | 0.498276i | ||||
\(831\) | − | 1.35198e16i | − | 0.0410547i | ||||||
\(832\) | −1.96397e17 | − | 8.78138e16i | −0.592098 | − | 0.264742i | ||||
\(833\) | 4.19621e17 | 1.25599 | ||||||||
\(834\) | 5.20969e15 | − | 1.01124e15i | 0.0154816 | − | 0.00300508i | ||||
\(835\) | 8.01983e17 | 2.36617 | ||||||||
\(836\) | 1.44611e17 | − | 5.83382e16i | 0.423609 | − | 0.170889i | ||||
\(837\) | − | 1.75624e16i | − | 0.0510775i | ||||||
\(838\) | −1.76885e17 | + | 3.43346e16i | −0.510772 | + | 0.0991442i | ||||
\(839\) | − | 3.98851e17i | − | 1.14351i | −0.820426 | − | 0.571753i | \(-0.806263\pi\) | ||
0.820426 | − | 0.571753i | \(-0.193737\pi\) | |||||||
\(840\) | −2.53657e16 | + | 1.64442e16i | −0.0722057 | + | 0.0468098i | ||||
\(841\) | 1.18930e17 | 0.336135 | ||||||||
\(842\) | −2.86920e16 | − | 1.47816e17i | −0.0805171 | − | 0.414809i | ||||
\(843\) | 2.58858e15 | 0.00721266 | ||||||||
\(844\) | 2.04914e17 | − | 8.26649e16i | 0.566913 | − | 0.228700i | ||||
\(845\) | 3.39231e17i | 0.931870i | ||||||||
\(846\) | 5.68781e16 | + | 2.93025e17i | 0.155140 | + | 0.799249i | ||||
\(847\) | 1.07141e17i | 0.290171i | ||||||||
\(848\) | 2.23512e17 | + | 2.31942e17i | 0.601071 | + | 0.623742i | ||||
\(849\) | 6.16898e15 | 0.0164728 | ||||||||
\(850\) | −4.55598e17 | + | 8.84346e16i | −1.20800 | + | 0.234482i | ||||
\(851\) | 2.72294e17 | 0.716905 | ||||||||
\(852\) | −7.15978e15 | − | 1.77480e16i | −0.0187181 | − | 0.0463994i | ||||
\(853\) | 5.41457e17i | 1.40563i | 0.711375 | + | 0.702813i | \(0.248073\pi\) | ||||
−0.711375 | + | 0.702813i | \(0.751927\pi\) | |||||||
\(854\) | 2.92781e17 | − | 5.68308e16i | 0.754737 | − | 0.146500i | ||||
\(855\) | 3.16486e17i | 0.810137i | ||||||||
\(856\) | −4.34055e17 | + | 2.81391e17i | −1.10332 | + | 0.715265i | ||||
\(857\) | 5.21930e17 | 1.31743 | 0.658714 | − | 0.752393i | \(-0.271101\pi\) | ||||
0.658714 | + | 0.752393i | \(0.271101\pi\) | |||||||
\(858\) | −1.47628e15 | − | 7.60551e15i | −0.00370037 | − | 0.0190636i | ||||
\(859\) | −2.55344e17 | −0.635575 | −0.317787 | − | 0.948162i | \(-0.602940\pi\) | ||||
−0.317787 | + | 0.948162i | \(0.602940\pi\) | |||||||
\(860\) | 1.95069e17 | + | 4.83545e17i | 0.482166 | + | 1.19522i | ||||
\(861\) | 1.96773e16i | 0.0482999i | ||||||||
\(862\) | −1.46949e17 | − | 7.57054e17i | −0.358198 | − | 1.84537i | ||||
\(863\) | − | 5.24738e17i | − | 1.27022i | −0.772423 | − | 0.635108i | \(-0.780956\pi\) | ||
0.772423 | − | 0.635108i | \(-0.219044\pi\) | |||||||
\(864\) | 1.57923e16 | − | 2.24906e16i | 0.0379633 | − | 0.0540654i | ||||
\(865\) | 1.54572e17 | 0.369007 | ||||||||
\(866\) | −3.44802e17 | + | 6.69284e16i | −0.817453 | + | 0.158673i | ||||
\(867\) | −5.60134e15 | −0.0131880 | ||||||||
\(868\) | 4.96382e17 | − | 2.00247e17i | 1.16064 | − | 0.468217i | ||||
\(869\) | − | 2.99593e17i | − | 0.695685i | ||||||
\(870\) | −1.84381e16 | + | 3.57896e15i | −0.0425207 | + | 0.00825356i | ||||
\(871\) | 2.58828e17i | 0.592792i | ||||||||
\(872\) | 7.91207e16 | + | 1.22046e17i | 0.179966 | + | 0.277604i | ||||
\(873\) | 6.50653e17 | 1.46982 | ||||||||
\(874\) | −2.66827e16 | − | 1.37464e17i | −0.0598633 | − | 0.308404i | ||||
\(875\) | −6.86352e17 | −1.52932 | ||||||||
\(876\) | 1.53145e16 | − | 6.17807e15i | 0.0338905 | − | 0.0136719i | ||||
\(877\) | − | 3.45631e17i | − | 0.759653i | −0.925058 | − | 0.379827i | \(-0.875984\pi\) | ||
0.925058 | − | 0.379827i | \(-0.124016\pi\) | |||||||
\(878\) | −6.85295e16 | − | 3.53050e17i | −0.149593 | − | 0.770672i | ||||
\(879\) | 1.93332e16i | 0.0419150i | ||||||||
\(880\) | −4.69595e17 | − | 4.87307e17i | −1.01118 | − | 1.04932i | ||||
\(881\) | 5.86814e16 | 0.125500 | 0.0627502 | − | 0.998029i | \(-0.480013\pi\) | ||||
0.0627502 | + | 0.998029i | \(0.480013\pi\) | |||||||
\(882\) | −7.47944e17 | + | 1.45181e17i | −1.58876 | + | 0.308388i | ||||
\(883\) | −5.84143e17 | −1.23241 | −0.616205 | − | 0.787586i | \(-0.711331\pi\) | ||||
−0.616205 | + | 0.787586i | \(0.711331\pi\) | |||||||
\(884\) | 8.97668e16 | + | 2.22518e17i | 0.188106 | + | 0.466286i | ||||
\(885\) | − | 2.11797e15i | − | 0.00440820i | ||||||
\(886\) | 5.53132e17 | − | 1.07367e17i | 1.14347 | − | 0.221956i | ||||
\(887\) | 1.24494e17i | 0.255627i | 0.991798 | + | 0.127813i | \(0.0407958\pi\) | ||||
−0.991798 | + | 0.127813i | \(0.959204\pi\) | |||||||
\(888\) | −1.01423e16 | − | 1.56448e16i | −0.0206851 | − | 0.0319075i | ||||
\(889\) | −1.31889e18 | −2.67177 | ||||||||
\(890\) | 1.33202e17 | + | 6.86229e17i | 0.268022 | + | 1.38079i | ||||
\(891\) | −4.51797e17 | −0.902978 | ||||||||
\(892\) | −2.57472e17 | − | 6.38233e17i | −0.511141 | − | 1.26704i | ||||
\(893\) | − | 2.08402e17i | − | 0.410953i | ||||||
\(894\) | 3.38126e15 | + | 1.74196e16i | 0.00662299 | + | 0.0341203i | ||||
\(895\) | 4.36899e16i | 0.0850046i | ||||||||
\(896\) | 8.15740e17 | + | 1.89915e17i | 1.57654 | + | 0.367037i | ||||
\(897\) | −6.95721e15 | −0.0133561 | ||||||||
\(898\) | −3.45999e17 | + | 6.71607e16i | −0.659806 | + | 0.128073i | ||||
\(899\) | 3.32561e17 | 0.629961 | ||||||||
\(900\) | 7.81474e17 | − | 3.15257e17i | 1.47048 | − | 0.593211i | ||||
\(901\) | − | 3.59254e17i | − | 0.671510i | ||||||
\(902\) | −4.32441e17 | + | 8.39398e16i | −0.802949 | + | 0.155858i | ||||
\(903\) | − | 2.32389e16i | − | 0.0428636i | ||||||
\(904\) | −8.07371e16 | + | 5.23405e16i | −0.147932 | + | 0.0959020i | ||||
\(905\) | 8.00557e17 | 1.45714 | ||||||||
\(906\) | 4.28569e14 | + | 2.20790e15i | 0.000774911 | + | 0.00399219i | ||||
\(907\) | −3.14671e17 | −0.565213 | −0.282607 | − | 0.959236i | \(-0.591199\pi\) | ||||
−0.282607 | + | 0.959236i | \(0.591199\pi\) | |||||||
\(908\) | 8.31277e16 | − | 3.35348e16i | 0.148331 | − | 0.0598385i | ||||
\(909\) | − | 9.60218e16i | − | 0.170211i | ||||||
\(910\) | 1.82735e17 | + | 9.41415e17i | 0.321791 | + | 1.65780i | ||||
\(911\) | − | 1.09959e18i | − | 1.92362i | −0.273716 | − | 0.961811i | \(-0.588253\pi\) | ||
0.273716 | − | 0.961811i | \(-0.411747\pi\) | |||||||
\(912\) | −6.90419e15 | + | 6.65325e15i | −0.0119990 | + | 0.0115628i | ||||
\(913\) | 1.65577e17 | 0.285874 | ||||||||
\(914\) | 6.97740e17 | − | 1.35436e17i | 1.19679 | − | 0.232304i | ||||
\(915\) | 1.48177e16 | 0.0252495 | ||||||||
\(916\) | 3.72092e17 | + | 9.22359e17i | 0.629908 | + | 1.56145i | ||||
\(917\) | 1.73258e18i | 2.91391i | ||||||||
\(918\) | −3.00888e16 | + | 5.84044e15i | −0.0502746 | + | 0.00975864i | ||||
\(919\) | 3.89660e17i | 0.646834i | 0.946257 | + | 0.323417i | \(0.104832\pi\) | ||||
−0.946257 | + | 0.323417i | \(0.895168\pi\) | |||||||
\(920\) | −5.09937e17 | + | 3.30584e17i | −0.840988 | + | 0.545199i | ||||
\(921\) | 2.19266e16 | 0.0359264 | ||||||||
\(922\) | −1.48632e17 | − | 7.65723e17i | −0.241951 | − | 1.24648i | ||||
\(923\) | −6.07115e17 | −0.981885 | ||||||||
\(924\) | 1.12842e16 | + | 2.79719e16i | 0.0181317 | + | 0.0449459i | ||||
\(925\) | − | 1.14404e18i | − | 1.82638i | ||||||
\(926\) | 1.43656e15 | + | 7.40090e15i | 0.00227855 | + | 0.0117387i | ||||
\(927\) | − | 4.28390e17i | − | 0.675090i | ||||||
\(928\) | 4.25883e17 | + | 2.99044e17i | 0.666811 | + | 0.468217i | ||||
\(929\) | −9.01757e17 | −1.40280 | −0.701399 | − | 0.712769i | \(-0.747441\pi\) | ||||
−0.701399 | + | 0.712769i | \(0.747441\pi\) | |||||||
\(930\) | 2.61055e16 | − | 5.06726e15i | 0.0403492 | − | 0.00783204i | ||||
\(931\) | 5.31944e17 | 0.816898 | ||||||||
\(932\) | 2.55204e17 | − | 1.02953e17i | 0.389397 | − | 0.157088i | ||||
\(933\) | − | 2.62765e16i | − | 0.0398361i | ||||||
\(934\) | 1.09054e18 | − | 2.11682e17i | 1.64271 | − | 0.318862i | ||||
\(935\) | 7.54786e17i | 1.12968i | ||||||||
\(936\) | −2.36990e17 | − | 3.65565e17i | −0.352432 | − | 0.543638i | ||||
\(937\) | 2.84937e17 | 0.421028 | 0.210514 | − | 0.977591i | \(-0.432486\pi\) | ||||
0.210514 | + | 0.977591i | \(0.432486\pi\) | |||||||
\(938\) | −1.92010e17 | − | 9.89199e17i | −0.281908 | − | 1.45233i | ||||
\(939\) | −3.27898e15 | −0.00478349 | ||||||||
\(940\) | −8.38768e17 | + | 3.38370e17i | −1.21583 | + | 0.490484i | ||||
\(941\) | 7.97698e17i | 1.14895i | 0.818522 | + | 0.574475i | \(0.194794\pi\) | ||||
−0.818522 | + | 0.574475i | \(0.805206\pi\) | |||||||
\(942\) | −6.16749e15 | − | 3.17737e16i | −0.00882680 | − | 0.0454739i | ||||
\(943\) | 3.95580e17i | 0.562553i | ||||||||
\(944\) | −4.22549e16 | + | 4.07191e16i | −0.0597097 | + | 0.0575395i | ||||
\(945\) | −1.22501e17 | −0.172009 | ||||||||
\(946\) | 5.10714e17 | − | 9.91330e16i | 0.712576 | − | 0.138316i | ||||
\(947\) | 8.11827e17 | 1.12555 | 0.562773 | − | 0.826611i | \(-0.309734\pi\) | ||||
0.562773 | + | 0.826611i | \(0.309734\pi\) | |||||||
\(948\) | 6.89179e15 | + | 1.70837e16i | 0.00949472 | + | 0.0235360i | ||||
\(949\) | − | 5.23870e17i | − | 0.717177i | ||||||
\(950\) | −5.77551e17 | + | 1.12107e17i | −0.785686 | + | 0.152507i | ||||
\(951\) | 1.67490e16i | 0.0226416i | ||||||||
\(952\) | −5.08148e17 | − | 7.83836e17i | −0.682604 | − | 1.05294i | ||||
\(953\) | −5.02264e17 | −0.670463 | −0.335231 | − | 0.942136i | \(-0.608814\pi\) | ||||
−0.335231 | + | 0.942136i | \(0.608814\pi\) | |||||||
\(954\) | 1.24295e17 | + | 6.40344e17i | 0.164878 | + | 0.849421i | ||||
\(955\) | 2.08653e18 | 2.75045 | ||||||||
\(956\) | −9.48930e16 | − | 2.35225e17i | −0.124305 | − | 0.308132i | ||||
\(957\) | 1.87403e16i | 0.0243953i | ||||||||
\(958\) | 1.09945e17 | + | 5.66414e17i | 0.142227 | + | 0.732724i | ||||
\(959\) | 2.13034e17i | 0.273865i | ||||||||
\(960\) | 3.79877e16 | + | 1.69853e16i | 0.0485306 | + | 0.0216992i | ||||
\(961\) | 3.16807e17 | 0.402212 | ||||||||
\(962\) | −5.80636e17 | + | 1.12705e17i | −0.732578 | + | 0.142198i | ||||
\(963\) | −1.04754e18 | −1.31345 | ||||||||
\(964\) | −1.11196e18 | + | 4.48578e17i | −1.38556 | + | 0.558954i | ||||
\(965\) | − | 1.02186e18i | − | 1.26540i | ||||||
\(966\) | 2.65893e16 | − | 5.16117e15i | 0.0327224 | − | 0.00635163i | ||||
\(967\) | − | 5.04696e17i | − | 0.617264i | −0.951182 | − | 0.308632i | \(-0.900129\pi\) | ||
0.951182 | − | 0.308632i | \(-0.0998711\pi\) | |||||||
\(968\) | 1.23753e17 | − | 8.02268e16i | 0.150419 | − | 0.0975141i | ||||
\(969\) | 1.06939e16 | 0.0129179 | ||||||||
\(970\) | 3.75670e17 | + | 1.93538e18i | 0.451000 | + | 2.32346i | ||||
\(971\) | 3.85943e16 | 0.0460477 | 0.0230238 | − | 0.999735i | \(-0.492671\pi\) | ||||
0.0230238 | + | 0.999735i | \(0.492671\pi\) | |||||||
\(972\) | 7.74297e16 | − | 3.12362e16i | 0.0918143 | − | 0.0370391i | ||||
\(973\) | 6.55429e17i | 0.772411i | ||||||||
\(974\) | −1.76772e17 | − | 9.10695e17i | −0.207043 | − | 1.06664i | ||||
\(975\) | 2.92305e16i | 0.0340259i | ||||||||
\(976\) | −2.84877e17 | − | 2.95622e17i | −0.329578 | − | 0.342009i | ||||
\(977\) | 6.44700e17 | 0.741294 | 0.370647 | − | 0.928774i | \(-0.379136\pi\) | ||||
0.370647 | + | 0.928774i | \(0.379136\pi\) | |||||||
\(978\) | −4.78324e16 | + | 9.28460e15i | −0.0546625 | + | 0.0106104i | ||||
\(979\) | 6.97478e17 | 0.792199 | ||||||||
\(980\) | −8.63687e17 | − | 2.14095e18i | −0.974990 | − | 2.41685i | ||||
\(981\) | 2.94545e17i | 0.330474i | ||||||||
\(982\) | −5.13998e17 | + | 9.97705e16i | −0.573182 | + | 0.111258i | ||||
\(983\) | 5.46969e16i | 0.0606236i | 0.999540 | + | 0.0303118i | \(0.00965003\pi\) | ||||
−0.999540 | + | 0.0303118i | \(0.990350\pi\) | |||||||
\(984\) | 2.27282e16 | − | 1.47343e16i | 0.0250377 | − | 0.0162315i | ||||
\(985\) | −1.75490e18 | −1.92147 | ||||||||
\(986\) | −1.10595e17 | − | 5.69762e17i | −0.120357 | − | 0.620058i | ||||
\(987\) | 4.03106e16 | 0.0436030 | ||||||||
\(988\) | 1.13795e17 | + | 2.82082e17i | 0.122344 | + | 0.303272i | ||||
\(989\) | − | 4.67180e17i | − | 0.499237i | ||||||
\(990\) | −2.61142e17 | − | 1.34535e18i | −0.277374 | − | 1.42898i | ||||
\(991\) | 1.53333e18i | 1.61880i | 0.587259 | + | 0.809399i | \(0.300207\pi\) | ||||
−0.587259 | + | 0.809399i | \(0.699793\pi\) | |||||||
\(992\) | −6.02986e17 | − | 4.23400e17i | −0.632757 | − | 0.444305i | ||||
\(993\) | −4.12875e16 | −0.0430648 | ||||||||
\(994\) | 2.32030e18 | − | 4.50385e17i | 2.40561 | − | 0.466945i | ||||
\(995\) | 1.50842e17 | 0.155448 | ||||||||
\(996\) | −9.44170e15 | + | 3.80891e15i | −0.00967151 | + | 0.00390161i | ||||
\(997\) | 4.69347e17i | 0.477885i | 0.971034 | + | 0.238942i | \(0.0768007\pi\) | ||||
−0.971034 | + | 0.238942i | \(0.923199\pi\) | |||||||
\(998\) | −8.73091e17 | + | 1.69473e17i | −0.883642 | + | 0.171521i | ||||
\(999\) | − | 7.55551e16i | − | 0.0760100i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8.13.d.b.3.2 | yes | 10 | |
3.2 | odd | 2 | 72.13.b.b.19.9 | 10 | |||
4.3 | odd | 2 | 32.13.d.b.15.6 | 10 | |||
8.3 | odd | 2 | inner | 8.13.d.b.3.1 | ✓ | 10 | |
8.5 | even | 2 | 32.13.d.b.15.5 | 10 | |||
24.11 | even | 2 | 72.13.b.b.19.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.13.d.b.3.1 | ✓ | 10 | 8.3 | odd | 2 | inner | |
8.13.d.b.3.2 | yes | 10 | 1.1 | even | 1 | trivial | |
32.13.d.b.15.5 | 10 | 8.5 | even | 2 | |||
32.13.d.b.15.6 | 10 | 4.3 | odd | 2 | |||
72.13.b.b.19.9 | 10 | 3.2 | odd | 2 | |||
72.13.b.b.19.10 | 10 | 24.11 | even | 2 |