Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,10,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.a (trivial) |
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: | yes |
Analytic conductor: | \(46.8682610909\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 4752 x^{12} + 9346 x^{11} + 8576824 x^{10} - 26923636 x^{9} - 7450416552 x^{8} + \cdots - 24\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(33.1611\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −31.1611 | −1.37714 | −0.688570 | − | 0.725169i | \(-0.741761\pi\) | ||||
−0.688570 | + | 0.725169i | \(0.741761\pi\) | |||||||
\(3\) | −183.696 | −1.30935 | −0.654673 | − | 0.755912i | \(-0.727194\pi\) | ||||
−0.654673 | + | 0.755912i | \(0.727194\pi\) | |||||||
\(4\) | 459.017 | 0.896517 | ||||||||
\(5\) | −1660.96 | −1.18848 | −0.594242 | − | 0.804286i | \(-0.702548\pi\) | ||||
−0.594242 | + | 0.804286i | \(0.702548\pi\) | |||||||
\(6\) | 5724.18 | 1.80315 | ||||||||
\(7\) | 2401.00 | 0.377964 | ||||||||
\(8\) | 1651.02 | 0.142511 | ||||||||
\(9\) | 14061.3 | 0.714387 | ||||||||
\(10\) | 51757.3 | 1.63671 | ||||||||
\(11\) | −2168.88 | −0.0446652 | −0.0223326 | − | 0.999751i | \(-0.507109\pi\) | ||||
−0.0223326 | + | 0.999751i | \(0.507109\pi\) | |||||||
\(12\) | −84319.6 | −1.17385 | ||||||||
\(13\) | −28561.0 | −0.277350 | ||||||||
\(14\) | −74817.9 | −0.520510 | ||||||||
\(15\) | 305111. | 1.55614 | ||||||||
\(16\) | −286464. | −1.09277 | ||||||||
\(17\) | 32976.9 | 0.0957612 | 0.0478806 | − | 0.998853i | \(-0.484753\pi\) | ||||
0.0478806 | + | 0.998853i | \(0.484753\pi\) | |||||||
\(18\) | −438165. | −0.983811 | ||||||||
\(19\) | −448123. | −0.788871 | −0.394436 | − | 0.918924i | \(-0.629060\pi\) | ||||
−0.394436 | + | 0.918924i | \(0.629060\pi\) | |||||||
\(20\) | −762407. | −1.06550 | ||||||||
\(21\) | −441054. | −0.494886 | ||||||||
\(22\) | 67584.9 | 0.0615102 | ||||||||
\(23\) | −708849. | −0.528175 | −0.264088 | − | 0.964499i | \(-0.585071\pi\) | ||||
−0.264088 | + | 0.964499i | \(0.585071\pi\) | |||||||
\(24\) | −303286. | −0.186596 | ||||||||
\(25\) | 805651. | 0.412493 | ||||||||
\(26\) | 889993. | 0.381950 | ||||||||
\(27\) | 1.03269e6 | 0.373967 | ||||||||
\(28\) | 1.10210e6 | 0.338852 | ||||||||
\(29\) | −7.50446e6 | −1.97028 | −0.985141 | − | 0.171748i | \(-0.945059\pi\) | ||||
−0.985141 | + | 0.171748i | \(0.945059\pi\) | |||||||
\(30\) | −9.50762e6 | −2.14302 | ||||||||
\(31\) | −8.49151e6 | −1.65142 | −0.825710 | − | 0.564095i | \(-0.809225\pi\) | ||||
−0.825710 | + | 0.564095i | \(0.809225\pi\) | |||||||
\(32\) | 8.08123e6 | 1.36239 | ||||||||
\(33\) | 398415. | 0.0584822 | ||||||||
\(34\) | −1.02760e6 | −0.131877 | ||||||||
\(35\) | −3.98796e6 | −0.449205 | ||||||||
\(36\) | 6.45436e6 | 0.640460 | ||||||||
\(37\) | −1.77529e7 | −1.55726 | −0.778632 | − | 0.627481i | \(-0.784086\pi\) | ||||
−0.778632 | + | 0.627481i | \(0.784086\pi\) | |||||||
\(38\) | 1.39640e7 | 1.08639 | ||||||||
\(39\) | 5.24655e6 | 0.363147 | ||||||||
\(40\) | −2.74228e6 | −0.169372 | ||||||||
\(41\) | 2.82963e6 | 0.156388 | 0.0781938 | − | 0.996938i | \(-0.475085\pi\) | ||||
0.0781938 | + | 0.996938i | \(0.475085\pi\) | |||||||
\(42\) | 1.37438e7 | 0.681528 | ||||||||
\(43\) | −4.58688e6 | −0.204602 | −0.102301 | − | 0.994754i | \(-0.532620\pi\) | ||||
−0.102301 | + | 0.994754i | \(0.532620\pi\) | |||||||
\(44\) | −995553. | −0.0400431 | ||||||||
\(45\) | −2.33552e7 | −0.849037 | ||||||||
\(46\) | 2.20885e7 | 0.727372 | ||||||||
\(47\) | −3.19968e7 | −0.956459 | −0.478230 | − | 0.878235i | \(-0.658721\pi\) | ||||
−0.478230 | + | 0.878235i | \(0.658721\pi\) | |||||||
\(48\) | 5.26224e7 | 1.43082 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | −2.51050e7 | −0.568061 | ||||||||
\(51\) | −6.05773e6 | −0.125385 | ||||||||
\(52\) | −1.31100e7 | −0.248649 | ||||||||
\(53\) | −1.83900e7 | −0.320141 | −0.160070 | − | 0.987106i | \(-0.551172\pi\) | ||||
−0.160070 | + | 0.987106i | \(0.551172\pi\) | |||||||
\(54\) | −3.21798e7 | −0.515005 | ||||||||
\(55\) | 3.60242e6 | 0.0530838 | ||||||||
\(56\) | 3.96411e6 | 0.0538641 | ||||||||
\(57\) | 8.23185e7 | 1.03291 | ||||||||
\(58\) | 2.33847e8 | 2.71336 | ||||||||
\(59\) | 1.45660e8 | 1.56497 | 0.782487 | − | 0.622667i | \(-0.213951\pi\) | ||||
0.782487 | + | 0.622667i | \(0.213951\pi\) | |||||||
\(60\) | 1.40051e8 | 1.39510 | ||||||||
\(61\) | −1.05246e7 | −0.0973247 | −0.0486624 | − | 0.998815i | \(-0.515496\pi\) | ||||
−0.0486624 | + | 0.998815i | \(0.515496\pi\) | |||||||
\(62\) | 2.64605e8 | 2.27424 | ||||||||
\(63\) | 3.37611e7 | 0.270013 | ||||||||
\(64\) | −1.05151e8 | −0.783433 | ||||||||
\(65\) | 4.74386e7 | 0.329626 | ||||||||
\(66\) | −1.24151e7 | −0.0805382 | ||||||||
\(67\) | −3.52331e7 | −0.213606 | −0.106803 | − | 0.994280i | \(-0.534061\pi\) | ||||
−0.106803 | + | 0.994280i | \(0.534061\pi\) | |||||||
\(68\) | 1.51369e7 | 0.0858515 | ||||||||
\(69\) | 1.30213e8 | 0.691564 | ||||||||
\(70\) | 1.24269e8 | 0.618618 | ||||||||
\(71\) | −2.70612e7 | −0.126382 | −0.0631908 | − | 0.998001i | \(-0.520128\pi\) | ||||
−0.0631908 | + | 0.998001i | \(0.520128\pi\) | |||||||
\(72\) | 2.32155e7 | 0.101808 | ||||||||
\(73\) | −3.20807e8 | −1.32218 | −0.661090 | − | 0.750306i | \(-0.729906\pi\) | ||||
−0.661090 | + | 0.750306i | \(0.729906\pi\) | |||||||
\(74\) | 5.53201e8 | 2.14457 | ||||||||
\(75\) | −1.47995e8 | −0.540096 | ||||||||
\(76\) | −2.05696e8 | −0.707236 | ||||||||
\(77\) | −5.20749e6 | −0.0168818 | ||||||||
\(78\) | −1.63488e8 | −0.500105 | ||||||||
\(79\) | −3.48283e8 | −1.00603 | −0.503014 | − | 0.864278i | \(-0.667776\pi\) | ||||
−0.503014 | + | 0.864278i | \(0.667776\pi\) | |||||||
\(80\) | 4.75805e8 | 1.29874 | ||||||||
\(81\) | −4.66469e8 | −1.20404 | ||||||||
\(82\) | −8.81745e7 | −0.215368 | ||||||||
\(83\) | −1.46829e8 | −0.339593 | −0.169797 | − | 0.985479i | \(-0.554311\pi\) | ||||
−0.169797 | + | 0.985479i | \(0.554311\pi\) | |||||||
\(84\) | −2.02451e8 | −0.443674 | ||||||||
\(85\) | −5.47732e7 | −0.113811 | ||||||||
\(86\) | 1.42932e8 | 0.281765 | ||||||||
\(87\) | 1.37854e9 | 2.57978 | ||||||||
\(88\) | −3.58087e6 | −0.00636527 | ||||||||
\(89\) | −3.59036e8 | −0.606573 | −0.303286 | − | 0.952899i | \(-0.598084\pi\) | ||||
−0.303286 | + | 0.952899i | \(0.598084\pi\) | |||||||
\(90\) | 7.27773e8 | 1.16924 | ||||||||
\(91\) | −6.85750e7 | −0.104828 | ||||||||
\(92\) | −3.25373e8 | −0.473518 | ||||||||
\(93\) | 1.55986e9 | 2.16228 | ||||||||
\(94\) | 9.97057e8 | 1.31718 | ||||||||
\(95\) | 7.44313e8 | 0.937561 | ||||||||
\(96\) | −1.48449e9 | −1.78384 | ||||||||
\(97\) | −1.04226e9 | −1.19537 | −0.597687 | − | 0.801729i | \(-0.703914\pi\) | ||||
−0.597687 | + | 0.801729i | \(0.703914\pi\) | |||||||
\(98\) | −1.79638e8 | −0.196734 | ||||||||
\(99\) | −3.04973e7 | −0.0319082 | ||||||||
\(100\) | 3.69807e8 | 0.369807 | ||||||||
\(101\) | 1.84467e9 | 1.76389 | 0.881947 | − | 0.471348i | \(-0.156232\pi\) | ||||
0.881947 | + | 0.471348i | \(0.156232\pi\) | |||||||
\(102\) | 1.88766e8 | 0.172672 | ||||||||
\(103\) | −2.94224e8 | −0.257579 | −0.128790 | − | 0.991672i | \(-0.541109\pi\) | ||||
−0.128790 | + | 0.991672i | \(0.541109\pi\) | |||||||
\(104\) | −4.71549e7 | −0.0395254 | ||||||||
\(105\) | 7.32572e8 | 0.588164 | ||||||||
\(106\) | 5.73054e8 | 0.440879 | ||||||||
\(107\) | −1.05501e9 | −0.778093 | −0.389046 | − | 0.921218i | \(-0.627195\pi\) | ||||
−0.389046 | + | 0.921218i | \(0.627195\pi\) | |||||||
\(108\) | 4.74022e8 | 0.335267 | ||||||||
\(109\) | 7.00451e7 | 0.0475290 | 0.0237645 | − | 0.999718i | \(-0.492435\pi\) | ||||
0.0237645 | + | 0.999718i | \(0.492435\pi\) | |||||||
\(110\) | −1.12256e8 | −0.0731039 | ||||||||
\(111\) | 3.26114e9 | 2.03900 | ||||||||
\(112\) | −6.87801e8 | −0.413030 | ||||||||
\(113\) | −2.22556e9 | −1.28406 | −0.642030 | − | 0.766679i | \(-0.721908\pi\) | ||||
−0.642030 | + | 0.766679i | \(0.721908\pi\) | |||||||
\(114\) | −2.56514e9 | −1.42246 | ||||||||
\(115\) | 1.17737e9 | 0.627728 | ||||||||
\(116\) | −3.44467e9 | −1.76639 | ||||||||
\(117\) | −4.01604e8 | −0.198135 | ||||||||
\(118\) | −4.53894e9 | −2.15519 | ||||||||
\(119\) | 7.91775e7 | 0.0361943 | ||||||||
\(120\) | 5.03746e8 | 0.221766 | ||||||||
\(121\) | −2.35324e9 | −0.998005 | ||||||||
\(122\) | 3.27960e8 | 0.134030 | ||||||||
\(123\) | −5.19792e8 | −0.204765 | ||||||||
\(124\) | −3.89775e9 | −1.48053 | ||||||||
\(125\) | 1.90590e9 | 0.698242 | ||||||||
\(126\) | −1.05203e9 | −0.371846 | ||||||||
\(127\) | −5.19626e9 | −1.77245 | −0.886225 | − | 0.463254i | \(-0.846682\pi\) | ||||
−0.886225 | + | 0.463254i | \(0.846682\pi\) | |||||||
\(128\) | −8.60977e8 | −0.283496 | ||||||||
\(129\) | 8.42591e8 | 0.267894 | ||||||||
\(130\) | −1.47824e9 | −0.453941 | ||||||||
\(131\) | −1.68134e9 | −0.498811 | −0.249405 | − | 0.968399i | \(-0.580235\pi\) | ||||
−0.249405 | + | 0.968399i | \(0.580235\pi\) | |||||||
\(132\) | 1.82879e8 | 0.0524302 | ||||||||
\(133\) | −1.07594e9 | −0.298165 | ||||||||
\(134\) | 1.09790e9 | 0.294166 | ||||||||
\(135\) | −1.71525e9 | −0.444453 | ||||||||
\(136\) | 5.44456e7 | 0.0136470 | ||||||||
\(137\) | −6.67999e9 | −1.62007 | −0.810034 | − | 0.586383i | \(-0.800552\pi\) | ||||
−0.810034 | + | 0.586383i | \(0.800552\pi\) | |||||||
\(138\) | −4.05758e9 | −0.952382 | ||||||||
\(139\) | 2.74649e9 | 0.624039 | 0.312019 | − | 0.950076i | \(-0.398995\pi\) | ||||
0.312019 | + | 0.950076i | \(0.398995\pi\) | |||||||
\(140\) | −1.83054e9 | −0.402719 | ||||||||
\(141\) | 5.87769e9 | 1.25234 | ||||||||
\(142\) | 8.43257e8 | 0.174045 | ||||||||
\(143\) | 6.19455e7 | 0.0123879 | ||||||||
\(144\) | −4.02805e9 | −0.780664 | ||||||||
\(145\) | 1.24646e10 | 2.34165 | ||||||||
\(146\) | 9.99671e9 | 1.82083 | ||||||||
\(147\) | −1.05897e9 | −0.187049 | ||||||||
\(148\) | −8.14889e9 | −1.39611 | ||||||||
\(149\) | 3.95604e9 | 0.657540 | 0.328770 | − | 0.944410i | \(-0.393366\pi\) | ||||
0.328770 | + | 0.944410i | \(0.393366\pi\) | |||||||
\(150\) | 4.61169e9 | 0.743789 | ||||||||
\(151\) | −3.00865e9 | −0.470951 | −0.235475 | − | 0.971880i | \(-0.575665\pi\) | ||||
−0.235475 | + | 0.971880i | \(0.575665\pi\) | |||||||
\(152\) | −7.39861e8 | −0.112423 | ||||||||
\(153\) | 4.63697e8 | 0.0684105 | ||||||||
\(154\) | 1.62271e8 | 0.0232487 | ||||||||
\(155\) | 1.41040e10 | 1.96269 | ||||||||
\(156\) | 2.40825e9 | 0.325568 | ||||||||
\(157\) | −1.49559e9 | −0.196456 | −0.0982280 | − | 0.995164i | \(-0.531317\pi\) | ||||
−0.0982280 | + | 0.995164i | \(0.531317\pi\) | |||||||
\(158\) | 1.08529e10 | 1.38544 | ||||||||
\(159\) | 3.37818e9 | 0.419175 | ||||||||
\(160\) | −1.34226e10 | −1.61918 | ||||||||
\(161\) | −1.70195e9 | −0.199632 | ||||||||
\(162\) | 1.45357e10 | 1.65813 | ||||||||
\(163\) | 2.89358e9 | 0.321064 | 0.160532 | − | 0.987031i | \(-0.448679\pi\) | ||||
0.160532 | + | 0.987031i | \(0.448679\pi\) | |||||||
\(164\) | 1.29885e9 | 0.140204 | ||||||||
\(165\) | −6.61751e8 | −0.0695051 | ||||||||
\(166\) | 4.57535e9 | 0.467668 | ||||||||
\(167\) | 6.58005e9 | 0.654644 | 0.327322 | − | 0.944913i | \(-0.393854\pi\) | ||||
0.327322 | + | 0.944913i | \(0.393854\pi\) | |||||||
\(168\) | −7.28191e8 | −0.0705267 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | 1.70680e9 | 0.156733 | ||||||||
\(171\) | −6.30118e9 | −0.563559 | ||||||||
\(172\) | −2.10545e9 | −0.183429 | ||||||||
\(173\) | 6.76816e9 | 0.574464 | 0.287232 | − | 0.957861i | \(-0.407265\pi\) | ||||
0.287232 | + | 0.957861i | \(0.407265\pi\) | |||||||
\(174\) | −4.29569e10 | −3.55272 | ||||||||
\(175\) | 1.93437e9 | 0.155908 | ||||||||
\(176\) | 6.21307e8 | 0.0488090 | ||||||||
\(177\) | −2.67572e10 | −2.04909 | ||||||||
\(178\) | 1.11880e10 | 0.835336 | ||||||||
\(179\) | −4.69441e9 | −0.341777 | −0.170888 | − | 0.985290i | \(-0.554664\pi\) | ||||
−0.170888 | + | 0.985290i | \(0.554664\pi\) | |||||||
\(180\) | −1.07204e10 | −0.761176 | ||||||||
\(181\) | 5.31928e9 | 0.368383 | 0.184191 | − | 0.982890i | \(-0.441033\pi\) | ||||
0.184191 | + | 0.982890i | \(0.441033\pi\) | |||||||
\(182\) | 2.13687e9 | 0.144364 | ||||||||
\(183\) | 1.93334e9 | 0.127432 | ||||||||
\(184\) | −1.17033e9 | −0.0752708 | ||||||||
\(185\) | 2.94868e10 | 1.85078 | ||||||||
\(186\) | −4.86070e10 | −2.97776 | ||||||||
\(187\) | −7.15230e7 | −0.00427719 | ||||||||
\(188\) | −1.46871e10 | −0.857482 | ||||||||
\(189\) | 2.47949e9 | 0.141346 | ||||||||
\(190\) | −2.31936e10 | −1.29115 | ||||||||
\(191\) | 1.23028e10 | 0.668888 | 0.334444 | − | 0.942416i | \(-0.391451\pi\) | ||||
0.334444 | + | 0.942416i | \(0.391451\pi\) | |||||||
\(192\) | 1.93158e10 | 1.02578 | ||||||||
\(193\) | −5.33716e9 | −0.276887 | −0.138443 | − | 0.990370i | \(-0.544210\pi\) | ||||
−0.138443 | + | 0.990370i | \(0.544210\pi\) | |||||||
\(194\) | 3.24781e10 | 1.64620 | ||||||||
\(195\) | −8.71428e9 | −0.431595 | ||||||||
\(196\) | 2.64614e9 | 0.128074 | ||||||||
\(197\) | 2.81913e10 | 1.33357 | 0.666786 | − | 0.745249i | \(-0.267670\pi\) | ||||
0.666786 | + | 0.745249i | \(0.267670\pi\) | |||||||
\(198\) | 9.50329e8 | 0.0439421 | ||||||||
\(199\) | 2.59177e10 | 1.17154 | 0.585772 | − | 0.810476i | \(-0.300791\pi\) | ||||
0.585772 | + | 0.810476i | \(0.300791\pi\) | |||||||
\(200\) | 1.33015e9 | 0.0587848 | ||||||||
\(201\) | 6.47218e9 | 0.279685 | ||||||||
\(202\) | −5.74820e10 | −2.42913 | ||||||||
\(203\) | −1.80182e10 | −0.744697 | ||||||||
\(204\) | −2.78060e9 | −0.112409 | ||||||||
\(205\) | −4.69989e9 | −0.185864 | ||||||||
\(206\) | 9.16836e9 | 0.354723 | ||||||||
\(207\) | −9.96731e9 | −0.377322 | ||||||||
\(208\) | 8.18171e9 | 0.303081 | ||||||||
\(209\) | 9.71927e8 | 0.0352351 | ||||||||
\(210\) | −2.28278e10 | −0.809985 | ||||||||
\(211\) | 4.18680e10 | 1.45416 | 0.727079 | − | 0.686554i | \(-0.240877\pi\) | ||||
0.727079 | + | 0.686554i | \(0.240877\pi\) | |||||||
\(212\) | −8.44133e9 | −0.287012 | ||||||||
\(213\) | 4.97103e9 | 0.165477 | ||||||||
\(214\) | 3.28754e10 | 1.07154 | ||||||||
\(215\) | 7.61860e9 | 0.243166 | ||||||||
\(216\) | 1.70499e9 | 0.0532943 | ||||||||
\(217\) | −2.03881e10 | −0.624178 | ||||||||
\(218\) | −2.18269e9 | −0.0654541 | ||||||||
\(219\) | 5.89310e10 | 1.73119 | ||||||||
\(220\) | 1.65357e9 | 0.0475905 | ||||||||
\(221\) | −9.41853e8 | −0.0265594 | ||||||||
\(222\) | −1.01621e11 | −2.80799 | ||||||||
\(223\) | −2.89900e9 | −0.0785013 | −0.0392506 | − | 0.999229i | \(-0.512497\pi\) | ||||
−0.0392506 | + | 0.999229i | \(0.512497\pi\) | |||||||
\(224\) | 1.94030e10 | 0.514936 | ||||||||
\(225\) | 1.13285e10 | 0.294680 | ||||||||
\(226\) | 6.93509e10 | 1.76833 | ||||||||
\(227\) | 3.64280e10 | 0.910582 | 0.455291 | − | 0.890343i | \(-0.349535\pi\) | ||||
0.455291 | + | 0.890343i | \(0.349535\pi\) | |||||||
\(228\) | 3.77856e10 | 0.926017 | ||||||||
\(229\) | −5.37091e10 | −1.29059 | −0.645295 | − | 0.763933i | \(-0.723266\pi\) | ||||
−0.645295 | + | 0.763933i | \(0.723266\pi\) | |||||||
\(230\) | −3.66881e10 | −0.864470 | ||||||||
\(231\) | 9.56595e8 | 0.0221042 | ||||||||
\(232\) | −1.23900e10 | −0.280787 | ||||||||
\(233\) | −5.21834e10 | −1.15993 | −0.579963 | − | 0.814643i | \(-0.696933\pi\) | ||||
−0.579963 | + | 0.814643i | \(0.696933\pi\) | |||||||
\(234\) | 1.25144e10 | 0.272860 | ||||||||
\(235\) | 5.31453e10 | 1.13674 | ||||||||
\(236\) | 6.68605e10 | 1.40303 | ||||||||
\(237\) | 6.39782e10 | 1.31724 | ||||||||
\(238\) | −2.46726e9 | −0.0498447 | ||||||||
\(239\) | 1.56130e10 | 0.309524 | 0.154762 | − | 0.987952i | \(-0.450539\pi\) | ||||
0.154762 | + | 0.987952i | \(0.450539\pi\) | |||||||
\(240\) | −8.74035e10 | −1.70051 | ||||||||
\(241\) | 1.79029e10 | 0.341859 | 0.170930 | − | 0.985283i | \(-0.445323\pi\) | ||||
0.170930 | + | 0.985283i | \(0.445323\pi\) | |||||||
\(242\) | 7.33298e10 | 1.37439 | ||||||||
\(243\) | 6.53622e10 | 1.20254 | ||||||||
\(244\) | −4.83099e9 | −0.0872533 | ||||||||
\(245\) | −9.57508e9 | −0.169783 | ||||||||
\(246\) | 1.61973e10 | 0.281991 | ||||||||
\(247\) | 1.27988e10 | 0.218794 | ||||||||
\(248\) | −1.40197e10 | −0.235345 | ||||||||
\(249\) | 2.69718e10 | 0.444645 | ||||||||
\(250\) | −5.93901e10 | −0.961578 | ||||||||
\(251\) | −1.11916e11 | −1.77976 | −0.889878 | − | 0.456199i | \(-0.849211\pi\) | ||||
−0.889878 | + | 0.456199i | \(0.849211\pi\) | |||||||
\(252\) | 1.54969e10 | 0.242071 | ||||||||
\(253\) | 1.53741e9 | 0.0235910 | ||||||||
\(254\) | 1.61921e11 | 2.44091 | ||||||||
\(255\) | 1.00616e10 | 0.149017 | ||||||||
\(256\) | 8.06661e10 | 1.17385 | ||||||||
\(257\) | −1.00270e11 | −1.43375 | −0.716874 | − | 0.697203i | \(-0.754428\pi\) | ||||
−0.716874 | + | 0.697203i | \(0.754428\pi\) | |||||||
\(258\) | −2.62561e10 | −0.368928 | ||||||||
\(259\) | −4.26248e10 | −0.588590 | ||||||||
\(260\) | 2.17751e10 | 0.295515 | ||||||||
\(261\) | −1.05522e11 | −1.40754 | ||||||||
\(262\) | 5.23926e10 | 0.686933 | ||||||||
\(263\) | 9.81760e10 | 1.26533 | 0.632666 | − | 0.774425i | \(-0.281961\pi\) | ||||
0.632666 | + | 0.774425i | \(0.281961\pi\) | |||||||
\(264\) | 6.57793e8 | 0.00833435 | ||||||||
\(265\) | 3.05450e10 | 0.380482 | ||||||||
\(266\) | 3.35276e10 | 0.410616 | ||||||||
\(267\) | 6.59535e10 | 0.794214 | ||||||||
\(268\) | −1.61726e10 | −0.191502 | ||||||||
\(269\) | 1.06526e11 | 1.24043 | 0.620213 | − | 0.784433i | \(-0.287046\pi\) | ||||
0.620213 | + | 0.784433i | \(0.287046\pi\) | |||||||
\(270\) | 5.34492e10 | 0.612075 | ||||||||
\(271\) | −9.45652e10 | −1.06505 | −0.532525 | − | 0.846415i | \(-0.678757\pi\) | ||||
−0.532525 | + | 0.846415i | \(0.678757\pi\) | |||||||
\(272\) | −9.44670e9 | −0.104645 | ||||||||
\(273\) | 1.25970e10 | 0.137257 | ||||||||
\(274\) | 2.08156e11 | 2.23106 | ||||||||
\(275\) | −1.74736e9 | −0.0184241 | ||||||||
\(276\) | 5.97698e10 | 0.619999 | ||||||||
\(277\) | −2.28335e8 | −0.00233031 | −0.00116515 | − | 0.999999i | \(-0.500371\pi\) | ||||
−0.00116515 | + | 0.999999i | \(0.500371\pi\) | |||||||
\(278\) | −8.55838e10 | −0.859389 | ||||||||
\(279\) | −1.19402e11 | −1.17975 | ||||||||
\(280\) | −6.58421e9 | −0.0640166 | ||||||||
\(281\) | 2.74740e10 | 0.262871 | 0.131436 | − | 0.991325i | \(-0.458041\pi\) | ||||
0.131436 | + | 0.991325i | \(0.458041\pi\) | |||||||
\(282\) | −1.83156e11 | −1.72464 | ||||||||
\(283\) | −2.21355e10 | −0.205140 | −0.102570 | − | 0.994726i | \(-0.532707\pi\) | ||||
−0.102570 | + | 0.994726i | \(0.532707\pi\) | |||||||
\(284\) | −1.24215e10 | −0.113303 | ||||||||
\(285\) | −1.36727e11 | −1.22759 | ||||||||
\(286\) | −1.93029e9 | −0.0170599 | ||||||||
\(287\) | 6.79394e9 | 0.0591089 | ||||||||
\(288\) | 1.13632e11 | 0.973276 | ||||||||
\(289\) | −1.17500e11 | −0.990830 | ||||||||
\(290\) | −3.88410e11 | −3.22478 | ||||||||
\(291\) | 1.91460e11 | 1.56516 | ||||||||
\(292\) | −1.47256e11 | −1.18536 | ||||||||
\(293\) | −3.00864e10 | −0.238487 | −0.119244 | − | 0.992865i | \(-0.538047\pi\) | ||||
−0.119244 | + | 0.992865i | \(0.538047\pi\) | |||||||
\(294\) | 3.29988e10 | 0.257593 | ||||||||
\(295\) | −2.41935e11 | −1.85995 | ||||||||
\(296\) | −2.93105e10 | −0.221927 | ||||||||
\(297\) | −2.23978e9 | −0.0167033 | ||||||||
\(298\) | −1.23275e11 | −0.905526 | ||||||||
\(299\) | 2.02454e10 | 0.146490 | ||||||||
\(300\) | −6.79322e10 | −0.484206 | ||||||||
\(301\) | −1.10131e10 | −0.0773321 | ||||||||
\(302\) | 9.37530e10 | 0.648565 | ||||||||
\(303\) | −3.38859e11 | −2.30955 | ||||||||
\(304\) | 1.28371e11 | 0.862058 | ||||||||
\(305\) | 1.74810e10 | 0.115669 | ||||||||
\(306\) | −1.44493e10 | −0.0942110 | ||||||||
\(307\) | −1.26253e11 | −0.811185 | −0.405592 | − | 0.914054i | \(-0.632935\pi\) | ||||
−0.405592 | + | 0.914054i | \(0.632935\pi\) | |||||||
\(308\) | −2.39032e9 | −0.0151349 | ||||||||
\(309\) | 5.40478e10 | 0.337260 | ||||||||
\(310\) | −4.39498e11 | −2.70289 | ||||||||
\(311\) | −2.72563e11 | −1.65213 | −0.826066 | − | 0.563574i | \(-0.809426\pi\) | ||||
−0.826066 | + | 0.563574i | \(0.809426\pi\) | |||||||
\(312\) | 8.66217e9 | 0.0517524 | ||||||||
\(313\) | 2.58487e11 | 1.52226 | 0.761131 | − | 0.648598i | \(-0.224644\pi\) | ||||
0.761131 | + | 0.648598i | \(0.224644\pi\) | |||||||
\(314\) | 4.66044e10 | 0.270548 | ||||||||
\(315\) | −5.60757e10 | −0.320906 | ||||||||
\(316\) | −1.59868e11 | −0.901921 | ||||||||
\(317\) | 2.80288e11 | 1.55897 | 0.779486 | − | 0.626420i | \(-0.215480\pi\) | ||||
0.779486 | + | 0.626420i | \(0.215480\pi\) | |||||||
\(318\) | −1.05268e11 | −0.577263 | ||||||||
\(319\) | 1.62763e10 | 0.0880030 | ||||||||
\(320\) | 1.74651e11 | 0.931097 | ||||||||
\(321\) | 1.93802e11 | 1.01879 | ||||||||
\(322\) | 5.30346e10 | 0.274921 | ||||||||
\(323\) | −1.47777e10 | −0.0755433 | ||||||||
\(324\) | −2.14117e11 | −1.07944 | ||||||||
\(325\) | −2.30102e10 | −0.114405 | ||||||||
\(326\) | −9.01672e10 | −0.442150 | ||||||||
\(327\) | −1.28670e10 | −0.0622319 | ||||||||
\(328\) | 4.67178e9 | 0.0222869 | ||||||||
\(329\) | −7.68244e10 | −0.361508 | ||||||||
\(330\) | 2.06209e10 | 0.0957183 | ||||||||
\(331\) | −9.04934e10 | −0.414373 | −0.207186 | − | 0.978302i | \(-0.566431\pi\) | ||||
−0.207186 | + | 0.978302i | \(0.566431\pi\) | |||||||
\(332\) | −6.73968e10 | −0.304451 | ||||||||
\(333\) | −2.49629e11 | −1.11249 | ||||||||
\(334\) | −2.05042e11 | −0.901537 | ||||||||
\(335\) | 5.85206e10 | 0.253868 | ||||||||
\(336\) | 1.26346e11 | 0.540799 | ||||||||
\(337\) | −1.00307e10 | −0.0423640 | −0.0211820 | − | 0.999776i | \(-0.506743\pi\) | ||||
−0.0211820 | + | 0.999776i | \(0.506743\pi\) | |||||||
\(338\) | −2.54191e10 | −0.105934 | ||||||||
\(339\) | 4.08826e11 | 1.68128 | ||||||||
\(340\) | −2.51418e10 | −0.102033 | ||||||||
\(341\) | 1.84171e10 | 0.0737610 | ||||||||
\(342\) | 1.96352e11 | 0.776100 | ||||||||
\(343\) | 1.38413e10 | 0.0539949 | ||||||||
\(344\) | −7.57304e9 | −0.0291580 | ||||||||
\(345\) | −2.16278e11 | −0.821913 | ||||||||
\(346\) | −2.10904e11 | −0.791118 | ||||||||
\(347\) | −2.98414e11 | −1.10494 | −0.552468 | − | 0.833534i | \(-0.686314\pi\) | ||||
−0.552468 | + | 0.833534i | \(0.686314\pi\) | |||||||
\(348\) | 6.32773e11 | 2.31282 | ||||||||
\(349\) | 4.74116e11 | 1.71069 | 0.855343 | − | 0.518061i | \(-0.173346\pi\) | ||||
0.855343 | + | 0.518061i | \(0.173346\pi\) | |||||||
\(350\) | −6.02771e10 | −0.214707 | ||||||||
\(351\) | −2.94946e10 | −0.103720 | ||||||||
\(352\) | −1.75272e10 | −0.0608515 | ||||||||
\(353\) | 5.42384e11 | 1.85918 | 0.929588 | − | 0.368600i | \(-0.120163\pi\) | ||||
0.929588 | + | 0.368600i | \(0.120163\pi\) | |||||||
\(354\) | 8.33786e11 | 2.82189 | ||||||||
\(355\) | 4.49474e10 | 0.150203 | ||||||||
\(356\) | −1.64804e11 | −0.543803 | ||||||||
\(357\) | −1.45446e10 | −0.0473909 | ||||||||
\(358\) | 1.46283e11 | 0.470675 | ||||||||
\(359\) | 8.05321e10 | 0.255885 | 0.127942 | − | 0.991782i | \(-0.459163\pi\) | ||||
0.127942 | + | 0.991782i | \(0.459163\pi\) | |||||||
\(360\) | −3.85599e10 | −0.120997 | ||||||||
\(361\) | −1.21873e11 | −0.377682 | ||||||||
\(362\) | −1.65755e11 | −0.507315 | ||||||||
\(363\) | 4.32282e11 | 1.30673 | ||||||||
\(364\) | −3.14770e10 | −0.0939805 | ||||||||
\(365\) | 5.32846e11 | 1.57139 | ||||||||
\(366\) | −6.02450e10 | −0.175491 | ||||||||
\(367\) | −9.90111e10 | −0.284896 | −0.142448 | − | 0.989802i | \(-0.545497\pi\) | ||||
−0.142448 | + | 0.989802i | \(0.545497\pi\) | |||||||
\(368\) | 2.03060e11 | 0.577177 | ||||||||
\(369\) | 3.97882e10 | 0.111721 | ||||||||
\(370\) | −9.18843e11 | −2.54879 | ||||||||
\(371\) | −4.41545e10 | −0.121002 | ||||||||
\(372\) | 7.16001e11 | 1.93852 | ||||||||
\(373\) | −5.64158e11 | −1.50908 | −0.754538 | − | 0.656257i | \(-0.772139\pi\) | ||||
−0.754538 | + | 0.656257i | \(0.772139\pi\) | |||||||
\(374\) | 2.22874e9 | 0.00589029 | ||||||||
\(375\) | −3.50107e11 | −0.914240 | ||||||||
\(376\) | −5.28275e10 | −0.136306 | ||||||||
\(377\) | 2.14335e11 | 0.546458 | ||||||||
\(378\) | −7.72636e10 | −0.194653 | ||||||||
\(379\) | −1.87576e11 | −0.466982 | −0.233491 | − | 0.972359i | \(-0.575015\pi\) | ||||
−0.233491 | + | 0.972359i | \(0.575015\pi\) | |||||||
\(380\) | 3.41652e11 | 0.840539 | ||||||||
\(381\) | 9.54533e11 | 2.32075 | ||||||||
\(382\) | −3.83369e11 | −0.921153 | ||||||||
\(383\) | −2.75353e11 | −0.653877 | −0.326938 | − | 0.945046i | \(-0.606017\pi\) | ||||
−0.326938 | + | 0.945046i | \(0.606017\pi\) | |||||||
\(384\) | 1.58158e11 | 0.371194 | ||||||||
\(385\) | 8.64941e9 | 0.0200638 | ||||||||
\(386\) | 1.66312e11 | 0.381312 | ||||||||
\(387\) | −6.44973e10 | −0.146165 | ||||||||
\(388\) | −4.78416e11 | −1.07167 | ||||||||
\(389\) | 5.23050e11 | 1.15816 | 0.579082 | − | 0.815269i | \(-0.303411\pi\) | ||||
0.579082 | + | 0.815269i | \(0.303411\pi\) | |||||||
\(390\) | 2.71547e11 | 0.594366 | ||||||||
\(391\) | −2.33756e10 | −0.0505787 | ||||||||
\(392\) | 9.51782e9 | 0.0203587 | ||||||||
\(393\) | 3.08856e11 | 0.653116 | ||||||||
\(394\) | −8.78472e11 | −1.83652 | ||||||||
\(395\) | 5.78482e11 | 1.19565 | ||||||||
\(396\) | −1.39987e10 | −0.0286062 | ||||||||
\(397\) | −1.33964e11 | −0.270665 | −0.135333 | − | 0.990800i | \(-0.543210\pi\) | ||||
−0.135333 | + | 0.990800i | \(0.543210\pi\) | |||||||
\(398\) | −8.07627e11 | −1.61338 | ||||||||
\(399\) | 1.97647e11 | 0.390402 | ||||||||
\(400\) | −2.30790e11 | −0.450762 | ||||||||
\(401\) | 8.10802e11 | 1.56590 | 0.782952 | − | 0.622082i | \(-0.213713\pi\) | ||||
0.782952 | + | 0.622082i | \(0.213713\pi\) | |||||||
\(402\) | −2.01681e11 | −0.385165 | ||||||||
\(403\) | 2.42526e11 | 0.458022 | ||||||||
\(404\) | 8.46735e11 | 1.58136 | ||||||||
\(405\) | 7.74785e11 | 1.43098 | ||||||||
\(406\) | 5.61468e11 | 1.02555 | ||||||||
\(407\) | 3.85040e10 | 0.0695555 | ||||||||
\(408\) | −1.00014e10 | −0.0178687 | ||||||||
\(409\) | −4.86152e10 | −0.0859048 | −0.0429524 | − | 0.999077i | \(-0.513676\pi\) | ||||
−0.0429524 | + | 0.999077i | \(0.513676\pi\) | |||||||
\(410\) | 1.46454e11 | 0.255961 | ||||||||
\(411\) | 1.22709e12 | 2.12123 | ||||||||
\(412\) | −1.35054e11 | −0.230924 | ||||||||
\(413\) | 3.49730e11 | 0.591504 | ||||||||
\(414\) | 3.10593e11 | 0.519625 | ||||||||
\(415\) | 2.43876e11 | 0.403601 | ||||||||
\(416\) | −2.30808e11 | −0.377860 | ||||||||
\(417\) | −5.04520e11 | −0.817082 | ||||||||
\(418\) | −3.02863e10 | −0.0485237 | ||||||||
\(419\) | −6.91424e11 | −1.09593 | −0.547963 | − | 0.836503i | \(-0.684597\pi\) | ||||
−0.547963 | + | 0.836503i | \(0.684597\pi\) | |||||||
\(420\) | 3.36263e11 | 0.527299 | ||||||||
\(421\) | −3.17438e11 | −0.492481 | −0.246241 | − | 0.969209i | \(-0.579195\pi\) | ||||
−0.246241 | + | 0.969209i | \(0.579195\pi\) | |||||||
\(422\) | −1.30466e12 | −2.00258 | ||||||||
\(423\) | −4.49916e11 | −0.683282 | ||||||||
\(424\) | −3.03624e10 | −0.0456236 | ||||||||
\(425\) | 2.65679e10 | 0.0395009 | ||||||||
\(426\) | −1.54903e11 | −0.227886 | ||||||||
\(427\) | −2.52697e10 | −0.0367853 | ||||||||
\(428\) | −4.84269e11 | −0.697573 | ||||||||
\(429\) | −1.13791e10 | −0.0162200 | ||||||||
\(430\) | −2.37404e11 | −0.334873 | ||||||||
\(431\) | 7.71117e11 | 1.07640 | 0.538198 | − | 0.842818i | \(-0.319105\pi\) | ||||
0.538198 | + | 0.842818i | \(0.319105\pi\) | |||||||
\(432\) | −2.95829e11 | −0.408661 | ||||||||
\(433\) | 3.28343e11 | 0.448882 | 0.224441 | − | 0.974488i | \(-0.427944\pi\) | ||||
0.224441 | + | 0.974488i | \(0.427944\pi\) | |||||||
\(434\) | 6.35317e11 | 0.859581 | ||||||||
\(435\) | −2.28969e12 | −3.06603 | ||||||||
\(436\) | 3.21519e10 | 0.0426105 | ||||||||
\(437\) | 3.17651e11 | 0.416662 | ||||||||
\(438\) | −1.83636e12 | −2.38409 | ||||||||
\(439\) | −3.77562e11 | −0.485175 | −0.242587 | − | 0.970130i | \(-0.577996\pi\) | ||||
−0.242587 | + | 0.970130i | \(0.577996\pi\) | |||||||
\(440\) | 5.94768e9 | 0.00756502 | ||||||||
\(441\) | 8.10604e10 | 0.102055 | ||||||||
\(442\) | 2.93492e10 | 0.0365760 | ||||||||
\(443\) | −1.02879e12 | −1.26914 | −0.634569 | − | 0.772866i | \(-0.718822\pi\) | ||||
−0.634569 | + | 0.772866i | \(0.718822\pi\) | |||||||
\(444\) | 1.49692e12 | 1.82800 | ||||||||
\(445\) | 5.96343e11 | 0.720902 | ||||||||
\(446\) | 9.03362e10 | 0.108107 | ||||||||
\(447\) | −7.26709e11 | −0.860948 | ||||||||
\(448\) | −2.52467e11 | −0.296110 | ||||||||
\(449\) | 3.88014e11 | 0.450545 | 0.225273 | − | 0.974296i | \(-0.427673\pi\) | ||||
0.225273 | + | 0.974296i | \(0.427673\pi\) | |||||||
\(450\) | −3.53008e11 | −0.405816 | ||||||||
\(451\) | −6.13714e9 | −0.00698508 | ||||||||
\(452\) | −1.02157e12 | −1.15118 | ||||||||
\(453\) | 5.52677e11 | 0.616637 | ||||||||
\(454\) | −1.13514e12 | −1.25400 | ||||||||
\(455\) | 1.13900e11 | 0.124587 | ||||||||
\(456\) | 1.35910e11 | 0.147200 | ||||||||
\(457\) | 7.08194e11 | 0.759503 | 0.379752 | − | 0.925089i | \(-0.376009\pi\) | ||||
0.379752 | + | 0.925089i | \(0.376009\pi\) | |||||||
\(458\) | 1.67364e12 | 1.77732 | ||||||||
\(459\) | 3.40549e10 | 0.0358115 | ||||||||
\(460\) | 5.40431e11 | 0.562769 | ||||||||
\(461\) | −1.80238e11 | −0.185862 | −0.0929311 | − | 0.995673i | \(-0.529624\pi\) | ||||
−0.0929311 | + | 0.995673i | \(0.529624\pi\) | |||||||
\(462\) | −2.98086e10 | −0.0304406 | ||||||||
\(463\) | −8.36615e11 | −0.846079 | −0.423040 | − | 0.906111i | \(-0.639037\pi\) | ||||
−0.423040 | + | 0.906111i | \(0.639037\pi\) | |||||||
\(464\) | 2.14976e12 | 2.15307 | ||||||||
\(465\) | −2.59086e12 | −2.56983 | ||||||||
\(466\) | 1.62609e12 | 1.59738 | ||||||||
\(467\) | 6.45255e11 | 0.627777 | 0.313889 | − | 0.949460i | \(-0.398368\pi\) | ||||
0.313889 | + | 0.949460i | \(0.398368\pi\) | |||||||
\(468\) | −1.84343e11 | −0.177632 | ||||||||
\(469\) | −8.45946e10 | −0.0807356 | ||||||||
\(470\) | −1.65607e12 | −1.56545 | ||||||||
\(471\) | 2.74735e11 | 0.257229 | ||||||||
\(472\) | 2.40488e11 | 0.223026 | ||||||||
\(473\) | 9.94840e9 | 0.00913856 | ||||||||
\(474\) | −1.99363e12 | −1.81402 | ||||||||
\(475\) | −3.61031e11 | −0.325404 | ||||||||
\(476\) | 3.63438e10 | 0.0324488 | ||||||||
\(477\) | −2.58587e11 | −0.228704 | ||||||||
\(478\) | −4.86518e11 | −0.426258 | ||||||||
\(479\) | 1.17577e12 | 1.02050 | 0.510249 | − | 0.860027i | \(-0.329553\pi\) | ||||
0.510249 | + | 0.860027i | \(0.329553\pi\) | |||||||
\(480\) | 2.46567e12 | 2.12007 | ||||||||
\(481\) | 5.07041e11 | 0.431907 | ||||||||
\(482\) | −5.57876e11 | −0.470788 | ||||||||
\(483\) | 3.12641e11 | 0.261387 | ||||||||
\(484\) | −1.08018e12 | −0.894728 | ||||||||
\(485\) | 1.73115e12 | 1.42068 | ||||||||
\(486\) | −2.03676e12 | −1.65606 | ||||||||
\(487\) | 1.48367e11 | 0.119524 | 0.0597621 | − | 0.998213i | \(-0.480966\pi\) | ||||
0.0597621 | + | 0.998213i | \(0.480966\pi\) | |||||||
\(488\) | −1.73764e10 | −0.0138698 | ||||||||
\(489\) | −5.31539e11 | −0.420383 | ||||||||
\(490\) | 2.98370e11 | 0.233816 | ||||||||
\(491\) | −1.67861e12 | −1.30342 | −0.651708 | − | 0.758470i | \(-0.725947\pi\) | ||||
−0.651708 | + | 0.758470i | \(0.725947\pi\) | |||||||
\(492\) | −2.38593e11 | −0.183576 | ||||||||
\(493\) | −2.47474e11 | −0.188677 | ||||||||
\(494\) | −3.98827e11 | −0.301309 | ||||||||
\(495\) | 5.06546e10 | 0.0379224 | ||||||||
\(496\) | 2.43252e12 | 1.80463 | ||||||||
\(497\) | −6.49739e10 | −0.0477678 | ||||||||
\(498\) | −8.40474e11 | −0.612339 | ||||||||
\(499\) | −6.00497e11 | −0.433569 | −0.216785 | − | 0.976219i | \(-0.569557\pi\) | ||||
−0.216785 | + | 0.976219i | \(0.569557\pi\) | |||||||
\(500\) | 8.74842e11 | 0.625986 | ||||||||
\(501\) | −1.20873e12 | −0.857156 | ||||||||
\(502\) | 3.48743e12 | 2.45097 | ||||||||
\(503\) | −7.25643e9 | −0.00505437 | −0.00252718 | − | 0.999997i | \(-0.500804\pi\) | ||||
−0.00252718 | + | 0.999997i | \(0.500804\pi\) | |||||||
\(504\) | 5.57404e10 | 0.0384798 | ||||||||
\(505\) | −3.06392e12 | −2.09636 | ||||||||
\(506\) | −4.79074e10 | −0.0324882 | ||||||||
\(507\) | −1.49847e11 | −0.100719 | ||||||||
\(508\) | −2.38517e12 | −1.58903 | ||||||||
\(509\) | 2.50852e12 | 1.65648 | 0.828241 | − | 0.560371i | \(-0.189342\pi\) | ||||
0.828241 | + | 0.560371i | \(0.189342\pi\) | |||||||
\(510\) | −3.13532e11 | −0.205218 | ||||||||
\(511\) | −7.70257e11 | −0.499737 | ||||||||
\(512\) | −2.07283e12 | −1.33306 | ||||||||
\(513\) | −4.62772e11 | −0.295011 | ||||||||
\(514\) | 3.12453e12 | 1.97447 | ||||||||
\(515\) | 4.88693e11 | 0.306129 | ||||||||
\(516\) | 3.86763e11 | 0.240172 | ||||||||
\(517\) | 6.93974e10 | 0.0427204 | ||||||||
\(518\) | 1.32824e12 | 0.810572 | ||||||||
\(519\) | −1.24329e12 | −0.752173 | ||||||||
\(520\) | 7.83222e10 | 0.0469753 | ||||||||
\(521\) | 1.83929e12 | 1.09366 | 0.546829 | − | 0.837244i | \(-0.315835\pi\) | ||||
0.546829 | + | 0.837244i | \(0.315835\pi\) | |||||||
\(522\) | 3.28819e12 | 1.93839 | ||||||||
\(523\) | −2.67195e12 | −1.56160 | −0.780801 | − | 0.624779i | \(-0.785189\pi\) | ||||
−0.780801 | + | 0.624779i | \(0.785189\pi\) | |||||||
\(524\) | −7.71765e11 | −0.447192 | ||||||||
\(525\) | −3.55336e11 | −0.204137 | ||||||||
\(526\) | −3.05928e12 | −1.74254 | ||||||||
\(527\) | −2.80024e11 | −0.158142 | ||||||||
\(528\) | −1.14132e11 | −0.0639078 | ||||||||
\(529\) | −1.29869e12 | −0.721031 | ||||||||
\(530\) | −9.51818e11 | −0.523978 | ||||||||
\(531\) | 2.04817e12 | 1.11800 | ||||||||
\(532\) | −4.93876e11 | −0.267310 | ||||||||
\(533\) | −8.08170e10 | −0.0433741 | ||||||||
\(534\) | −2.05519e12 | −1.09374 | ||||||||
\(535\) | 1.75233e12 | 0.924750 | ||||||||
\(536\) | −5.81706e10 | −0.0304412 | ||||||||
\(537\) | 8.62345e11 | 0.447504 | ||||||||
\(538\) | −3.31948e12 | −1.70824 | ||||||||
\(539\) | −1.25032e10 | −0.00638074 | ||||||||
\(540\) | −7.87329e11 | −0.398460 | ||||||||
\(541\) | 7.07819e10 | 0.0355250 | 0.0177625 | − | 0.999842i | \(-0.494346\pi\) | ||||
0.0177625 | + | 0.999842i | \(0.494346\pi\) | |||||||
\(542\) | 2.94676e12 | 1.46672 | ||||||||
\(543\) | −9.77131e11 | −0.482340 | ||||||||
\(544\) | 2.66494e11 | 0.130464 | ||||||||
\(545\) | −1.16342e11 | −0.0564874 | ||||||||
\(546\) | −3.92536e11 | −0.189022 | ||||||||
\(547\) | 2.46809e12 | 1.17874 | 0.589369 | − | 0.807864i | \(-0.299376\pi\) | ||||
0.589369 | + | 0.807864i | \(0.299376\pi\) | |||||||
\(548\) | −3.06623e12 | −1.45242 | ||||||||
\(549\) | −1.47990e11 | −0.0695275 | ||||||||
\(550\) | 5.44498e10 | 0.0253726 | ||||||||
\(551\) | 3.36292e12 | 1.55430 | ||||||||
\(552\) | 2.14984e11 | 0.0985555 | ||||||||
\(553\) | −8.36227e11 | −0.380243 | ||||||||
\(554\) | 7.11517e9 | 0.00320916 | ||||||||
\(555\) | −5.41662e12 | −2.42331 | ||||||||
\(556\) | 1.26068e12 | 0.559461 | ||||||||
\(557\) | −3.04875e12 | −1.34207 | −0.671033 | − | 0.741427i | \(-0.734149\pi\) | ||||
−0.671033 | + | 0.741427i | \(0.734149\pi\) | |||||||
\(558\) | 3.72069e12 | 1.62469 | ||||||||
\(559\) | 1.31006e11 | 0.0567463 | ||||||||
\(560\) | 1.14241e12 | 0.490879 | ||||||||
\(561\) | 1.31385e10 | 0.00560032 | ||||||||
\(562\) | −8.56121e11 | −0.362011 | ||||||||
\(563\) | −2.04691e12 | −0.858638 | −0.429319 | − | 0.903153i | \(-0.641246\pi\) | ||||
−0.429319 | + | 0.903153i | \(0.641246\pi\) | |||||||
\(564\) | 2.69796e12 | 1.12274 | ||||||||
\(565\) | 3.69655e12 | 1.52609 | ||||||||
\(566\) | 6.89766e11 | 0.282506 | ||||||||
\(567\) | −1.11999e12 | −0.455084 | ||||||||
\(568\) | −4.46786e10 | −0.0180108 | ||||||||
\(569\) | −1.21106e12 | −0.484353 | −0.242176 | − | 0.970232i | \(-0.577861\pi\) | ||||
−0.242176 | + | 0.970232i | \(0.577861\pi\) | |||||||
\(570\) | 4.26058e12 | 1.69057 | ||||||||
\(571\) | −2.71050e12 | −1.06706 | −0.533528 | − | 0.845782i | \(-0.679134\pi\) | ||||
−0.533528 | + | 0.845782i | \(0.679134\pi\) | |||||||
\(572\) | 2.84340e10 | 0.0111060 | ||||||||
\(573\) | −2.25998e12 | −0.875806 | ||||||||
\(574\) | −2.11707e11 | −0.0814013 | ||||||||
\(575\) | −5.71085e11 | −0.217869 | ||||||||
\(576\) | −1.47855e12 | −0.559674 | ||||||||
\(577\) | −3.60856e11 | −0.135532 | −0.0677661 | − | 0.997701i | \(-0.521587\pi\) | ||||
−0.0677661 | + | 0.997701i | \(0.521587\pi\) | |||||||
\(578\) | 3.66145e12 | 1.36451 | ||||||||
\(579\) | 9.80416e11 | 0.362541 | ||||||||
\(580\) | 5.72145e12 | 2.09933 | ||||||||
\(581\) | −3.52535e11 | −0.128354 | ||||||||
\(582\) | −5.96610e12 | −2.15544 | ||||||||
\(583\) | 3.98858e10 | 0.0142991 | ||||||||
\(584\) | −5.29659e11 | −0.188425 | ||||||||
\(585\) | 6.67047e11 | 0.235480 | ||||||||
\(586\) | 9.37525e11 | 0.328431 | ||||||||
\(587\) | −2.53212e12 | −0.880263 | −0.440132 | − | 0.897933i | \(-0.645068\pi\) | ||||
−0.440132 | + | 0.897933i | \(0.645068\pi\) | |||||||
\(588\) | −4.86086e11 | −0.167693 | ||||||||
\(589\) | 3.80524e12 | 1.30276 | ||||||||
\(590\) | 7.53898e12 | 2.56141 | ||||||||
\(591\) | −5.17862e12 | −1.74611 | ||||||||
\(592\) | 5.08558e12 | 1.70174 | ||||||||
\(593\) | 5.57792e11 | 0.185236 | 0.0926182 | − | 0.995702i | \(-0.470476\pi\) | ||||
0.0926182 | + | 0.995702i | \(0.470476\pi\) | |||||||
\(594\) | 6.97942e10 | 0.0230028 | ||||||||
\(595\) | −1.31510e11 | −0.0430164 | ||||||||
\(596\) | 1.81589e12 | 0.589496 | ||||||||
\(597\) | −4.76099e12 | −1.53396 | ||||||||
\(598\) | −6.30870e11 | −0.201737 | ||||||||
\(599\) | −5.40325e12 | −1.71488 | −0.857441 | − | 0.514582i | \(-0.827947\pi\) | ||||
−0.857441 | + | 0.514582i | \(0.827947\pi\) | |||||||
\(600\) | −2.44343e11 | −0.0769696 | ||||||||
\(601\) | 3.75368e10 | 0.0117361 | 0.00586803 | − | 0.999983i | \(-0.498132\pi\) | ||||
0.00586803 | + | 0.999983i | \(0.498132\pi\) | |||||||
\(602\) | 3.43180e11 | 0.106497 | ||||||||
\(603\) | −4.95422e11 | −0.152597 | ||||||||
\(604\) | −1.38102e12 | −0.422215 | ||||||||
\(605\) | 3.90864e12 | 1.18611 | ||||||||
\(606\) | 1.05592e13 | 3.18057 | ||||||||
\(607\) | −2.89398e12 | −0.865260 | −0.432630 | − | 0.901571i | \(-0.642414\pi\) | ||||
−0.432630 | + | 0.901571i | \(0.642414\pi\) | |||||||
\(608\) | −3.62139e12 | −1.07475 | ||||||||
\(609\) | 3.30987e12 | 0.975065 | ||||||||
\(610\) | −5.44727e11 | −0.159292 | ||||||||
\(611\) | 9.13861e11 | 0.265274 | ||||||||
\(612\) | 2.12845e11 | 0.0613312 | ||||||||
\(613\) | −3.90117e12 | −1.11589 | −0.557946 | − | 0.829877i | \(-0.688411\pi\) | ||||
−0.557946 | + | 0.829877i | \(0.688411\pi\) | |||||||
\(614\) | 3.93419e12 | 1.11712 | ||||||||
\(615\) | 8.63352e11 | 0.243360 | ||||||||
\(616\) | −8.59768e9 | −0.00240585 | ||||||||
\(617\) | 4.57281e12 | 1.27028 | 0.635141 | − | 0.772396i | \(-0.280942\pi\) | ||||
0.635141 | + | 0.772396i | \(0.280942\pi\) | |||||||
\(618\) | −1.68419e12 | −0.464455 | ||||||||
\(619\) | −7.82457e10 | −0.0214216 | −0.0107108 | − | 0.999943i | \(-0.503409\pi\) | ||||
−0.0107108 | + | 0.999943i | \(0.503409\pi\) | |||||||
\(620\) | 6.47399e12 | 1.75958 | ||||||||
\(621\) | −7.32020e11 | −0.197520 | ||||||||
\(622\) | 8.49336e12 | 2.27522 | ||||||||
\(623\) | −8.62046e11 | −0.229263 | ||||||||
\(624\) | −1.50295e12 | −0.396838 | ||||||||
\(625\) | −4.73916e12 | −1.24234 | ||||||||
\(626\) | −8.05476e12 | −2.09637 | ||||||||
\(627\) | −1.78539e11 | −0.0461349 | ||||||||
\(628\) | −6.86503e11 | −0.176126 | ||||||||
\(629\) | −5.85436e11 | −0.149125 | ||||||||
\(630\) | 1.74738e12 | 0.441932 | ||||||||
\(631\) | 7.59017e12 | 1.90599 | 0.952993 | − | 0.302993i | \(-0.0979860\pi\) | ||||
0.952993 | + | 0.302993i | \(0.0979860\pi\) | |||||||
\(632\) | −5.75023e11 | −0.143370 | ||||||||
\(633\) | −7.69100e12 | −1.90400 | ||||||||
\(634\) | −8.73410e12 | −2.14692 | ||||||||
\(635\) | 8.63076e12 | 2.10653 | ||||||||
\(636\) | 1.55064e12 | 0.375798 | ||||||||
\(637\) | −1.64648e11 | −0.0396214 | ||||||||
\(638\) | −5.07188e11 | −0.121193 | ||||||||
\(639\) | −3.80515e11 | −0.0902854 | ||||||||
\(640\) | 1.43004e12 | 0.336930 | ||||||||
\(641\) | −8.44275e12 | −1.97525 | −0.987627 | − | 0.156823i | \(-0.949875\pi\) | ||||
−0.987627 | + | 0.156823i | \(0.949875\pi\) | |||||||
\(642\) | −6.03909e12 | −1.40302 | ||||||||
\(643\) | −5.90952e12 | −1.36334 | −0.681668 | − | 0.731661i | \(-0.738745\pi\) | ||||
−0.681668 | + | 0.731661i | \(0.738745\pi\) | |||||||
\(644\) | −7.81221e11 | −0.178973 | ||||||||
\(645\) | −1.39951e12 | −0.318388 | ||||||||
\(646\) | 4.60490e11 | 0.104034 | ||||||||
\(647\) | −3.06115e11 | −0.0686776 | −0.0343388 | − | 0.999410i | \(-0.510933\pi\) | ||||
−0.0343388 | + | 0.999410i | \(0.510933\pi\) | |||||||
\(648\) | −7.70151e11 | −0.171589 | ||||||||
\(649\) | −3.15920e11 | −0.0698998 | ||||||||
\(650\) | 7.17024e11 | 0.157552 | ||||||||
\(651\) | 3.74522e12 | 0.817265 | ||||||||
\(652\) | 1.32820e12 | 0.287839 | ||||||||
\(653\) | −2.75098e12 | −0.592078 | −0.296039 | − | 0.955176i | \(-0.595666\pi\) | ||||
−0.296039 | + | 0.955176i | \(0.595666\pi\) | |||||||
\(654\) | 4.00951e11 | 0.0857021 | ||||||||
\(655\) | 2.79264e12 | 0.592828 | ||||||||
\(656\) | −8.10588e11 | −0.170896 | ||||||||
\(657\) | −4.51095e12 | −0.944548 | ||||||||
\(658\) | 2.39393e12 | 0.497847 | ||||||||
\(659\) | −8.30422e11 | −0.171520 | −0.0857599 | − | 0.996316i | \(-0.527332\pi\) | ||||
−0.0857599 | + | 0.996316i | \(0.527332\pi\) | |||||||
\(660\) | −3.03755e11 | −0.0623125 | ||||||||
\(661\) | 6.29780e12 | 1.28316 | 0.641582 | − | 0.767054i | \(-0.278278\pi\) | ||||
0.641582 | + | 0.767054i | \(0.278278\pi\) | |||||||
\(662\) | 2.81988e12 | 0.570649 | ||||||||
\(663\) | 1.73015e11 | 0.0347754 | ||||||||
\(664\) | −2.42417e11 | −0.0483958 | ||||||||
\(665\) | 1.78710e12 | 0.354365 | ||||||||
\(666\) | 7.77872e12 | 1.53205 | ||||||||
\(667\) | 5.31952e12 | 1.04065 | ||||||||
\(668\) | 3.02035e12 | 0.586900 | ||||||||
\(669\) | 5.32536e11 | 0.102785 | ||||||||
\(670\) | −1.82357e12 | −0.349611 | ||||||||
\(671\) | 2.28267e10 | 0.00434703 | ||||||||
\(672\) | −3.56426e12 | −0.674230 | ||||||||
\(673\) | 7.18852e12 | 1.35074 | 0.675370 | − | 0.737479i | \(-0.263984\pi\) | ||||
0.675370 | + | 0.737479i | \(0.263984\pi\) | |||||||
\(674\) | 3.12568e11 | 0.0583411 | ||||||||
\(675\) | 8.31987e11 | 0.154259 | ||||||||
\(676\) | 3.74434e11 | 0.0689628 | ||||||||
\(677\) | −4.60851e12 | −0.843162 | −0.421581 | − | 0.906791i | \(-0.638525\pi\) | ||||
−0.421581 | + | 0.906791i | \(0.638525\pi\) | |||||||
\(678\) | −1.27395e13 | −2.31536 | ||||||||
\(679\) | −2.50247e12 | −0.451809 | ||||||||
\(680\) | −9.04318e10 | −0.0162193 | ||||||||
\(681\) | −6.69168e12 | −1.19227 | ||||||||
\(682\) | −5.73898e11 | −0.101579 | ||||||||
\(683\) | 5.50395e12 | 0.967791 | 0.483895 | − | 0.875126i | \(-0.339221\pi\) | ||||
0.483895 | + | 0.875126i | \(0.339221\pi\) | |||||||
\(684\) | −2.89235e12 | −0.505240 | ||||||||
\(685\) | 1.10952e13 | 1.92542 | ||||||||
\(686\) | −4.31310e11 | −0.0743586 | ||||||||
\(687\) | 9.86616e12 | 1.68983 | ||||||||
\(688\) | 1.31398e12 | 0.223583 | ||||||||
\(689\) | 5.25238e11 | 0.0887911 | ||||||||
\(690\) | 6.73946e12 | 1.13189 | ||||||||
\(691\) | 7.67282e12 | 1.28028 | 0.640138 | − | 0.768260i | \(-0.278877\pi\) | ||||
0.640138 | + | 0.768260i | \(0.278877\pi\) | |||||||
\(692\) | 3.10670e12 | 0.515017 | ||||||||
\(693\) | −7.32239e10 | −0.0120602 | ||||||||
\(694\) | 9.29893e12 | 1.52165 | ||||||||
\(695\) | −4.56180e12 | −0.741660 | ||||||||
\(696\) | 2.27600e12 | 0.367647 | ||||||||
\(697\) | 9.33124e10 | 0.0149759 | ||||||||
\(698\) | −1.47740e13 | −2.35586 | ||||||||
\(699\) | 9.58588e12 | 1.51874 | ||||||||
\(700\) | 8.87907e11 | 0.139774 | ||||||||
\(701\) | −9.37860e11 | −0.146692 | −0.0733461 | − | 0.997307i | \(-0.523368\pi\) | ||||
−0.0733461 | + | 0.997307i | \(0.523368\pi\) | |||||||
\(702\) | 9.19087e11 | 0.142837 | ||||||||
\(703\) | 7.95550e12 | 1.22848 | ||||||||
\(704\) | 2.28059e11 | 0.0349922 | ||||||||
\(705\) | −9.76259e12 | −1.48838 | ||||||||
\(706\) | −1.69013e13 | −2.56035 | ||||||||
\(707\) | 4.42905e12 | 0.666690 | ||||||||
\(708\) | −1.22820e13 | −1.83705 | ||||||||
\(709\) | 8.95196e12 | 1.33049 | 0.665243 | − | 0.746627i | \(-0.268328\pi\) | ||||
0.665243 | + | 0.746627i | \(0.268328\pi\) | |||||||
\(710\) | −1.40061e12 | −0.206850 | ||||||||
\(711\) | −4.89730e12 | −0.718693 | ||||||||
\(712\) | −5.92777e11 | −0.0864433 | ||||||||
\(713\) | 6.01920e12 | 0.872240 | ||||||||
\(714\) | 4.53227e11 | 0.0652640 | ||||||||
\(715\) | −1.02889e11 | −0.0147228 | ||||||||
\(716\) | −2.15481e12 | −0.306409 | ||||||||
\(717\) | −2.86804e12 | −0.405274 | ||||||||
\(718\) | −2.50947e12 | −0.352389 | ||||||||
\(719\) | −4.59577e11 | −0.0641325 | −0.0320662 | − | 0.999486i | \(-0.510209\pi\) | ||||
−0.0320662 | + | 0.999486i | \(0.510209\pi\) | |||||||
\(720\) | 6.69042e12 | 0.927806 | ||||||||
\(721\) | −7.06432e11 | −0.0973557 | ||||||||
\(722\) | 3.79771e12 | 0.520121 | ||||||||
\(723\) | −3.28870e12 | −0.447612 | ||||||||
\(724\) | 2.44164e12 | 0.330261 | ||||||||
\(725\) | −6.04598e12 | −0.812728 | ||||||||
\(726\) | −1.34704e13 | −1.79956 | ||||||||
\(727\) | −1.01063e13 | −1.34180 | −0.670898 | − | 0.741549i | \(-0.734091\pi\) | ||||
−0.670898 | + | 0.741549i | \(0.734091\pi\) | |||||||
\(728\) | −1.13219e11 | −0.0149392 | ||||||||
\(729\) | −2.82526e12 | −0.370497 | ||||||||
\(730\) | −1.66041e13 | −2.16403 | ||||||||
\(731\) | −1.51261e11 | −0.0195929 | ||||||||
\(732\) | 8.87434e11 | 0.114245 | ||||||||
\(733\) | 1.25171e13 | 1.60153 | 0.800765 | − | 0.598979i | \(-0.204427\pi\) | ||||
0.800765 | + | 0.598979i | \(0.204427\pi\) | |||||||
\(734\) | 3.08530e12 | 0.392342 | ||||||||
\(735\) | 1.75891e12 | 0.222305 | ||||||||
\(736\) | −5.72837e12 | −0.719583 | ||||||||
\(737\) | 7.64164e10 | 0.00954076 | ||||||||
\(738\) | −1.23985e12 | −0.153856 | ||||||||
\(739\) | −1.26664e13 | −1.56226 | −0.781128 | − | 0.624370i | \(-0.785356\pi\) | ||||
−0.781128 | + | 0.624370i | \(0.785356\pi\) | |||||||
\(740\) | 1.35349e13 | 1.65926 | ||||||||
\(741\) | −2.35110e12 | −0.286476 | ||||||||
\(742\) | 1.37590e12 | 0.166637 | ||||||||
\(743\) | 2.79839e12 | 0.336867 | 0.168433 | − | 0.985713i | \(-0.446129\pi\) | ||||
0.168433 | + | 0.985713i | \(0.446129\pi\) | |||||||
\(744\) | 2.57536e12 | 0.308148 | ||||||||
\(745\) | −6.57081e12 | −0.781476 | ||||||||
\(746\) | 1.75798e13 | 2.07821 | ||||||||
\(747\) | −2.06460e12 | −0.242601 | ||||||||
\(748\) | −3.28303e10 | −0.00383457 | ||||||||
\(749\) | −2.53309e12 | −0.294091 | ||||||||
\(750\) | 1.09097e13 | 1.25904 | ||||||||
\(751\) | 1.15286e13 | 1.32251 | 0.661253 | − | 0.750163i | \(-0.270025\pi\) | ||||
0.661253 | + | 0.750163i | \(0.270025\pi\) | |||||||
\(752\) | 9.16595e12 | 1.04519 | ||||||||
\(753\) | 2.05585e13 | 2.33032 | ||||||||
\(754\) | −6.67892e12 | −0.752549 | ||||||||
\(755\) | 4.99724e12 | 0.559717 | ||||||||
\(756\) | 1.13813e12 | 0.126719 | ||||||||
\(757\) | −8.40849e12 | −0.930651 | −0.465325 | − | 0.885140i | \(-0.654063\pi\) | ||||
−0.465325 | + | 0.885140i | \(0.654063\pi\) | |||||||
\(758\) | 5.84507e12 | 0.643100 | ||||||||
\(759\) | −2.82416e11 | −0.0308888 | ||||||||
\(760\) | 1.22888e12 | 0.133613 | ||||||||
\(761\) | −1.19871e13 | −1.29563 | −0.647816 | − | 0.761797i | \(-0.724318\pi\) | ||||
−0.647816 | + | 0.761797i | \(0.724318\pi\) | |||||||
\(762\) | −2.97443e13 | −3.19600 | ||||||||
\(763\) | 1.68178e11 | 0.0179643 | ||||||||
\(764\) | 5.64719e12 | 0.599670 | ||||||||
\(765\) | −7.70181e11 | −0.0813048 | ||||||||
\(766\) | 8.58032e12 | 0.900480 | ||||||||
\(767\) | −4.16020e12 | −0.434046 | ||||||||
\(768\) | −1.48181e13 | −1.53697 | ||||||||
\(769\) | 3.39698e12 | 0.350288 | 0.175144 | − | 0.984543i | \(-0.443961\pi\) | ||||
0.175144 | + | 0.984543i | \(0.443961\pi\) | |||||||
\(770\) | −2.69525e11 | −0.0276307 | ||||||||
\(771\) | 1.84193e13 | 1.87727 | ||||||||
\(772\) | −2.44984e12 | −0.248234 | ||||||||
\(773\) | 1.45175e13 | 1.46246 | 0.731228 | − | 0.682133i | \(-0.238948\pi\) | ||||
0.731228 | + | 0.682133i | \(0.238948\pi\) | |||||||
\(774\) | 2.00981e12 | 0.201289 | ||||||||
\(775\) | −6.84120e12 | −0.681200 | ||||||||
\(776\) | −1.72080e12 | −0.170354 | ||||||||
\(777\) | 7.83001e12 | 0.770668 | ||||||||
\(778\) | −1.62988e13 | −1.59496 | ||||||||
\(779\) | −1.26802e12 | −0.123370 | ||||||||
\(780\) | −4.00000e12 | −0.386932 | ||||||||
\(781\) | 5.86925e10 | 0.00564486 | ||||||||
\(782\) | 7.28411e11 | 0.0696540 | ||||||||
\(783\) | −7.74977e12 | −0.736820 | ||||||||
\(784\) | −1.65141e12 | −0.156111 | ||||||||
\(785\) | 2.48412e12 | 0.233485 | ||||||||
\(786\) | −9.62432e12 | −0.899432 | ||||||||
\(787\) | −1.78281e13 | −1.65660 | −0.828300 | − | 0.560284i | \(-0.810692\pi\) | ||||
−0.828300 | + | 0.560284i | \(0.810692\pi\) | |||||||
\(788\) | 1.29403e13 | 1.19557 | ||||||||
\(789\) | −1.80346e13 | −1.65676 | ||||||||
\(790\) | −1.80262e13 | −1.64658 | ||||||||
\(791\) | −5.34356e12 | −0.485329 | ||||||||
\(792\) | −5.03517e10 | −0.00454727 | ||||||||
\(793\) | 3.00594e11 | 0.0269930 | ||||||||
\(794\) | 4.17448e12 | 0.372744 | ||||||||
\(795\) | −5.61101e12 | −0.498183 | ||||||||
\(796\) | 1.18967e13 | 1.05031 | ||||||||
\(797\) | −5.09625e12 | −0.447392 | −0.223696 | − | 0.974659i | \(-0.571812\pi\) | ||||
−0.223696 | + | 0.974659i | \(0.571812\pi\) | |||||||
\(798\) | −6.15890e12 | −0.537638 | ||||||||
\(799\) | −1.05516e12 | −0.0915917 | ||||||||
\(800\) | 6.51065e12 | 0.561978 | ||||||||
\(801\) | −5.04850e12 | −0.433328 | ||||||||
\(802\) | −2.52655e13 | −2.15647 | ||||||||
\(803\) | 6.95792e11 | 0.0590554 | ||||||||
\(804\) | 2.97084e12 | 0.250742 | ||||||||
\(805\) | 2.82686e12 | 0.237259 | ||||||||
\(806\) | −7.55739e12 | −0.630760 | ||||||||
\(807\) | −1.95684e13 | −1.62415 | ||||||||
\(808\) | 3.04559e12 | 0.251374 | ||||||||
\(809\) | −1.58582e13 | −1.30162 | −0.650811 | − | 0.759240i | \(-0.725571\pi\) | ||||
−0.650811 | + | 0.759240i | \(0.725571\pi\) | |||||||
\(810\) | −2.41432e13 | −1.97066 | ||||||||
\(811\) | −8.27659e12 | −0.671827 | −0.335914 | − | 0.941893i | \(-0.609045\pi\) | ||||
−0.335914 | + | 0.941893i | \(0.609045\pi\) | |||||||
\(812\) | −8.27066e12 | −0.667633 | ||||||||
\(813\) | 1.73713e13 | 1.39452 | ||||||||
\(814\) | −1.19983e12 | −0.0957877 | ||||||||
\(815\) | −4.80611e12 | −0.381579 | ||||||||
\(816\) | 1.73532e12 | 0.137017 | ||||||||
\(817\) | 2.05549e12 | 0.161404 | ||||||||
\(818\) | 1.51491e12 | 0.118303 | ||||||||
\(819\) | −9.64251e11 | −0.0748881 | ||||||||
\(820\) | −2.15733e12 | −0.166630 | ||||||||
\(821\) | 1.81620e13 | 1.39515 | 0.697575 | − | 0.716512i | \(-0.254263\pi\) | ||||
0.697575 | + | 0.716512i | \(0.254263\pi\) | |||||||
\(822\) | −3.82375e13 | −2.92123 | ||||||||
\(823\) | −1.73956e11 | −0.0132172 | −0.00660861 | − | 0.999978i | \(-0.502104\pi\) | ||||
−0.00660861 | + | 0.999978i | \(0.502104\pi\) | |||||||
\(824\) | −4.85771e11 | −0.0367078 | ||||||||
\(825\) | 3.20984e11 | 0.0241235 | ||||||||
\(826\) | −1.08980e13 | −0.814585 | ||||||||
\(827\) | −6.27403e12 | −0.466414 | −0.233207 | − | 0.972427i | \(-0.574922\pi\) | ||||
−0.233207 | + | 0.972427i | \(0.574922\pi\) | |||||||
\(828\) | −4.57516e12 | −0.338275 | ||||||||
\(829\) | −3.58695e12 | −0.263773 | −0.131886 | − | 0.991265i | \(-0.542103\pi\) | ||||
−0.131886 | + | 0.991265i | \(0.542103\pi\) | |||||||
\(830\) | −7.59945e12 | −0.555816 | ||||||||
\(831\) | 4.19442e10 | 0.00305118 | ||||||||
\(832\) | 3.00321e12 | 0.217285 | ||||||||
\(833\) | 1.90105e11 | 0.0136802 | ||||||||
\(834\) | 1.57214e13 | 1.12524 | ||||||||
\(835\) | −1.09292e13 | −0.778034 | ||||||||
\(836\) | 4.46130e11 | 0.0315888 | ||||||||
\(837\) | −8.76910e12 | −0.617576 | ||||||||
\(838\) | 2.15456e13 | 1.50924 | ||||||||
\(839\) | 1.66816e13 | 1.16228 | 0.581138 | − | 0.813805i | \(-0.302608\pi\) | ||||
0.581138 | + | 0.813805i | \(0.302608\pi\) | |||||||
\(840\) | 1.20949e12 | 0.0838198 | ||||||||
\(841\) | 4.18098e13 | 2.88201 | ||||||||
\(842\) | 9.89173e12 | 0.678216 | ||||||||
\(843\) | −5.04687e12 | −0.344190 | ||||||||
\(844\) | 1.92181e13 | 1.30368 | ||||||||
\(845\) | −1.35489e12 | −0.0914218 | ||||||||
\(846\) | 1.40199e13 | 0.940975 | ||||||||
\(847\) | −5.65014e12 | −0.377210 | ||||||||
\(848\) | 5.26809e12 | 0.349842 | ||||||||
\(849\) | 4.06620e12 | 0.268599 | ||||||||
\(850\) | −8.27885e11 | −0.0543983 | ||||||||
\(851\) | 1.25841e13 | 0.822509 | ||||||||
\(852\) | 2.28179e12 | 0.148353 | ||||||||
\(853\) | 1.55052e13 | 1.00278 | 0.501390 | − | 0.865221i | \(-0.332822\pi\) | ||||
0.501390 | + | 0.865221i | \(0.332822\pi\) | |||||||
\(854\) | 7.87432e11 | 0.0506585 | ||||||||
\(855\) | 1.04660e13 | 0.669781 | ||||||||
\(856\) | −1.74185e12 | −0.110887 | ||||||||
\(857\) | −2.15563e13 | −1.36509 | −0.682544 | − | 0.730845i | \(-0.739126\pi\) | ||||
−0.682544 | + | 0.730845i | \(0.739126\pi\) | |||||||
\(858\) | 3.54587e11 | 0.0223373 | ||||||||
\(859\) | 2.44363e13 | 1.53132 | 0.765661 | − | 0.643244i | \(-0.222412\pi\) | ||||
0.765661 | + | 0.643244i | \(0.222412\pi\) | |||||||
\(860\) | 3.49706e12 | 0.218002 | ||||||||
\(861\) | −1.24802e12 | −0.0773941 | ||||||||
\(862\) | −2.40289e13 | −1.48235 | ||||||||
\(863\) | 2.00361e12 | 0.122960 | 0.0614801 | − | 0.998108i | \(-0.480418\pi\) | ||||
0.0614801 | + | 0.998108i | \(0.480418\pi\) | |||||||
\(864\) | 8.34540e12 | 0.509490 | ||||||||
\(865\) | −1.12416e13 | −0.682742 | ||||||||
\(866\) | −1.02315e13 | −0.618174 | ||||||||
\(867\) | 2.15844e13 | 1.29734 | ||||||||
\(868\) | −9.35849e12 | −0.559586 | ||||||||
\(869\) | 7.55384e11 | 0.0449344 | ||||||||
\(870\) | 7.13495e13 | 4.22235 | ||||||||
\(871\) | 1.00629e12 | 0.0592437 | ||||||||
\(872\) | 1.15646e11 | 0.00677340 | ||||||||
\(873\) | −1.46555e13 | −0.853960 | ||||||||
\(874\) | −9.89838e12 | −0.573803 | ||||||||
\(875\) | 4.57608e12 | 0.263911 | ||||||||
\(876\) | 2.70503e13 | 1.55204 | ||||||||
\(877\) | −2.95900e13 | −1.68907 | −0.844535 | − | 0.535501i | \(-0.820123\pi\) | ||||
−0.844535 | + | 0.535501i | \(0.820123\pi\) | |||||||
\(878\) | 1.17653e13 | 0.668154 | ||||||||
\(879\) | 5.52675e12 | 0.312263 | ||||||||
\(880\) | −1.03196e12 | −0.0580086 | ||||||||
\(881\) | 3.40701e13 | 1.90538 | 0.952691 | − | 0.303942i | \(-0.0983028\pi\) | ||||
0.952691 | + | 0.303942i | \(0.0983028\pi\) | |||||||
\(882\) | −2.52594e12 | −0.140544 | ||||||||
\(883\) | 3.28392e13 | 1.81790 | 0.908948 | − | 0.416910i | \(-0.136887\pi\) | ||||
0.908948 | + | 0.416910i | \(0.136887\pi\) | |||||||
\(884\) | −4.32326e11 | −0.0238109 | ||||||||
\(885\) | 4.44426e13 | 2.43531 | ||||||||
\(886\) | 3.20582e13 | 1.74778 | ||||||||
\(887\) | 2.46024e13 | 1.33451 | 0.667255 | − | 0.744829i | \(-0.267469\pi\) | ||||
0.667255 | + | 0.744829i | \(0.267469\pi\) | |||||||
\(888\) | 5.38422e12 | 0.290579 | ||||||||
\(889\) | −1.24762e13 | −0.669923 | ||||||||
\(890\) | −1.85827e13 | −0.992784 | ||||||||
\(891\) | 1.01172e12 | 0.0537786 | ||||||||
\(892\) | −1.33069e12 | −0.0703777 | ||||||||
\(893\) | 1.43385e13 | 0.754523 | ||||||||
\(894\) | 2.26451e13 | 1.18565 | ||||||||
\(895\) | 7.79721e12 | 0.406196 | ||||||||
\(896\) | −2.06720e12 | −0.107151 | ||||||||
\(897\) | −3.71901e12 | −0.191805 | ||||||||
\(898\) | −1.20909e13 | −0.620464 | ||||||||
\(899\) | 6.37242e13 | 3.25376 | ||||||||
\(900\) | 5.19996e12 | 0.264185 | ||||||||
\(901\) | −6.06446e11 | −0.0306571 | ||||||||
\(902\) | 1.91240e11 | 0.00961944 | ||||||||
\(903\) | 2.02306e12 | 0.101254 | ||||||||
\(904\) | −3.67444e12 | −0.182993 | ||||||||
\(905\) | −8.83509e12 | −0.437817 | ||||||||
\(906\) | −1.72221e13 | −0.849196 | ||||||||
\(907\) | 1.74939e13 | 0.858331 | 0.429166 | − | 0.903226i | \(-0.358808\pi\) | ||||
0.429166 | + | 0.903226i | \(0.358808\pi\) | |||||||
\(908\) | 1.67211e13 | 0.816352 | ||||||||
\(909\) | 2.59384e13 | 1.26010 | ||||||||
\(910\) | −3.54925e12 | −0.171574 | ||||||||
\(911\) | −3.56240e13 | −1.71360 | −0.856801 | − | 0.515648i | \(-0.827551\pi\) | ||||
−0.856801 | + | 0.515648i | \(0.827551\pi\) | |||||||
\(912\) | −2.35813e13 | −1.12873 | ||||||||
\(913\) | 3.18454e11 | 0.0151680 | ||||||||
\(914\) | −2.20681e13 | −1.04594 | ||||||||
\(915\) | −3.21119e12 | −0.151451 | ||||||||
\(916\) | −2.46534e13 | −1.15704 | ||||||||
\(917\) | −4.03691e12 | −0.188533 | ||||||||
\(918\) | −1.06119e12 | −0.0493175 | ||||||||
\(919\) | −1.60302e12 | −0.0741342 | −0.0370671 | − | 0.999313i | \(-0.511802\pi\) | ||||
−0.0370671 | + | 0.999313i | \(0.511802\pi\) | |||||||
\(920\) | 1.94386e12 | 0.0894581 | ||||||||
\(921\) | 2.31922e13 | 1.06212 | ||||||||
\(922\) | 5.61641e12 | 0.255958 | ||||||||
\(923\) | 7.72894e11 | 0.0350520 | ||||||||
\(924\) | 4.39093e11 | 0.0198168 | ||||||||
\(925\) | −1.43027e13 | −0.642361 | ||||||||
\(926\) | 2.60699e13 | 1.16517 | ||||||||
\(927\) | −4.13716e12 | −0.184011 | ||||||||
\(928\) | −6.06452e13 | −2.68430 | ||||||||
\(929\) | 1.79784e13 | 0.791919 | 0.395959 | − | 0.918268i | \(-0.370412\pi\) | ||||
0.395959 | + | 0.918268i | \(0.370412\pi\) | |||||||
\(930\) | 8.07341e13 | 3.53902 | ||||||||
\(931\) | −2.58334e12 | −0.112696 | ||||||||
\(932\) | −2.39530e13 | −1.03989 | ||||||||
\(933\) | 5.00687e13 | 2.16321 | ||||||||
\(934\) | −2.01069e13 | −0.864538 | ||||||||
\(935\) | 1.18797e11 | 0.00508337 | ||||||||
\(936\) | −6.63057e11 | −0.0282364 | ||||||||
\(937\) | −2.91204e13 | −1.23415 | −0.617077 | − | 0.786902i | \(-0.711683\pi\) | ||||
−0.617077 | + | 0.786902i | \(0.711683\pi\) | |||||||
\(938\) | 2.63606e12 | 0.111184 | ||||||||
\(939\) | −4.74831e13 | −1.99317 | ||||||||
\(940\) | 2.43946e13 | 1.01910 | ||||||||
\(941\) | −1.49397e13 | −0.621139 | −0.310569 | − | 0.950551i | \(-0.600520\pi\) | ||||
−0.310569 | + | 0.950551i | \(0.600520\pi\) | |||||||
\(942\) | −8.56105e12 | −0.354240 | ||||||||
\(943\) | −2.00578e12 | −0.0826001 | ||||||||
\(944\) | −4.17265e13 | −1.71016 | ||||||||
\(945\) | −4.11832e12 | −0.167988 | ||||||||
\(946\) | −3.10003e11 | −0.0125851 | ||||||||
\(947\) | −2.05716e13 | −0.831177 | −0.415589 | − | 0.909553i | \(-0.636424\pi\) | ||||
−0.415589 | + | 0.909553i | \(0.636424\pi\) | |||||||
\(948\) | 2.93671e13 | 1.18093 | ||||||||
\(949\) | 9.16256e12 | 0.366707 | ||||||||
\(950\) | 1.12501e13 | 0.448127 | ||||||||
\(951\) | −5.14879e13 | −2.04123 | ||||||||
\(952\) | 1.30724e11 | 0.00515809 | ||||||||
\(953\) | −4.75899e13 | −1.86894 | −0.934472 | − | 0.356035i | \(-0.884128\pi\) | ||||
−0.934472 | + | 0.356035i | \(0.884128\pi\) | |||||||
\(954\) | 8.05788e12 | 0.314958 | ||||||||
\(955\) | −2.04344e13 | −0.794963 | ||||||||
\(956\) | 7.16661e12 | 0.277494 | ||||||||
\(957\) | −2.98989e12 | −0.115226 | ||||||||
\(958\) | −3.66383e13 | −1.40537 | ||||||||
\(959\) | −1.60387e13 | −0.612328 | ||||||||
\(960\) | −3.20826e13 | −1.21913 | ||||||||
\(961\) | 4.56662e13 | 1.72719 | ||||||||
\(962\) | −1.58000e13 | −0.594797 | ||||||||
\(963\) | −1.48348e13 | −0.555859 | ||||||||
\(964\) | 8.21774e12 | 0.306483 | ||||||||
\(965\) | 8.86479e12 | 0.329075 | ||||||||
\(966\) | −9.74224e12 | −0.359966 | ||||||||
\(967\) | 7.90376e11 | 0.0290680 | 0.0145340 | − | 0.999894i | \(-0.495374\pi\) | ||||
0.0145340 | + | 0.999894i | \(0.495374\pi\) | |||||||
\(968\) | −3.88526e12 | −0.142227 | ||||||||
\(969\) | 2.71461e12 | 0.0989123 | ||||||||
\(970\) | −5.39447e13 | −1.95648 | ||||||||
\(971\) | −2.71117e13 | −0.978746 | −0.489373 | − | 0.872075i | \(-0.662774\pi\) | ||||
−0.489373 | + | 0.872075i | \(0.662774\pi\) | |||||||
\(972\) | 3.00023e13 | 1.07809 | ||||||||
\(973\) | 6.59432e12 | 0.235864 | ||||||||
\(974\) | −4.62327e12 | −0.164602 | ||||||||
\(975\) | 4.22689e12 | 0.149796 | ||||||||
\(976\) | 3.01493e12 | 0.106354 | ||||||||
\(977\) | −9.61551e12 | −0.337634 | −0.168817 | − | 0.985647i | \(-0.553995\pi\) | ||||
−0.168817 | + | 0.985647i | \(0.553995\pi\) | |||||||
\(978\) | 1.65634e13 | 0.578927 | ||||||||
\(979\) | 7.78707e11 | 0.0270927 | ||||||||
\(980\) | −4.39512e12 | −0.152214 | ||||||||
\(981\) | 9.84924e11 | 0.0339541 | ||||||||
\(982\) | 5.23074e13 | 1.79499 | ||||||||
\(983\) | −1.83268e13 | −0.626031 | −0.313016 | − | 0.949748i | \(-0.601339\pi\) | ||||
−0.313016 | + | 0.949748i | \(0.601339\pi\) | |||||||
\(984\) | −8.58188e11 | −0.0291813 | ||||||||
\(985\) | −4.68244e13 | −1.58493 | ||||||||
\(986\) | 7.71156e12 | 0.259834 | ||||||||
\(987\) | 1.41123e13 | 0.473339 | ||||||||
\(988\) | 5.87488e12 | 0.196152 | ||||||||
\(989\) | 3.25140e12 | 0.108066 | ||||||||
\(990\) | −1.57846e12 | −0.0522245 | ||||||||
\(991\) | −5.20026e13 | −1.71275 | −0.856374 | − | 0.516355i | \(-0.827288\pi\) | ||||
−0.856374 | + | 0.516355i | \(0.827288\pi\) | |||||||
\(992\) | −6.86219e13 | −2.24988 | ||||||||
\(993\) | 1.66233e13 | 0.542557 | ||||||||
\(994\) | 2.02466e12 | 0.0657829 | ||||||||
\(995\) | −4.30483e13 | −1.39236 | ||||||||
\(996\) | 1.23805e13 | 0.398632 | ||||||||
\(997\) | −1.11097e13 | −0.356103 | −0.178052 | − | 0.984021i | \(-0.556979\pi\) | ||||
−0.178052 | + | 0.984021i | \(0.556979\pi\) | |||||||
\(998\) | 1.87122e13 | 0.597086 | ||||||||
\(999\) | −1.83333e13 | −0.582365 |
(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 | 91.10.a.c.1.2 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.10.a.c.1.2 | ✓ | 14 | 1.1 | even | 1 | trivial |