Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,10,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (of order \(3\), degree \(2\), not 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: | \(25.2367559720\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 427x^{4} - 3606x^{3} + 183492x^{2} - 858816x + 4064256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 30.3 | ||
Root | \(9.13724 - 15.8262i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.30 |
Dual form | 49.10.c.e.18.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 17.0813 | − | 29.5857i | 0.754896 | − | 1.30752i | −0.190531 | − | 0.981681i | \(-0.561021\pi\) |
0.945426 | − | 0.325836i | \(-0.105646\pi\) | |||||||
\(3\) | −39.8234 | − | 68.9762i | −0.283853 | − | 0.491648i | 0.688478 | − | 0.725258i | \(-0.258279\pi\) |
−0.972330 | + | 0.233610i | \(0.924946\pi\) | |||||||
\(4\) | −327.544 | − | 567.323i | −0.639735 | − | 1.10805i | ||||
\(5\) | 711.850 | − | 1232.96i | 0.509358 | − | 0.882235i | −0.490583 | − | 0.871395i | \(-0.663216\pi\) |
0.999941 | − | 0.0108401i | \(-0.00345057\pi\) | |||||||
\(6\) | −2720.95 | −0.857117 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4888.28 | −0.421940 | ||||||||
\(9\) | 6669.69 | − | 11552.2i | 0.338855 | − | 0.586914i | ||||
\(10\) | −24318.7 | − | 42121.2i | −0.769025 | − | 1.33199i | ||||
\(11\) | −34677.2 | − | 60062.6i | −0.714129 | − | 1.23691i | −0.963295 | − | 0.268447i | \(-0.913490\pi\) |
0.249166 | − | 0.968461i | \(-0.419844\pi\) | |||||||
\(12\) | −26087.9 | + | 45185.5i | −0.363181 | + | 0.629048i | ||||
\(13\) | −105959. | −1.02895 | −0.514473 | − | 0.857506i | \(-0.672013\pi\) | ||||
−0.514473 | + | 0.857506i | \(0.672013\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −113393. | −0.578331 | ||||||||
\(16\) | 84204.3 | − | 145846.i | 0.321214 | − | 0.556359i | ||||
\(17\) | 284134. | + | 492134.i | 0.825092 | + | 1.42910i | 0.901849 | + | 0.432051i | \(0.142210\pi\) |
−0.0767571 | + | 0.997050i | \(0.524457\pi\) | |||||||
\(18\) | −227854. | − | 394655.i | −0.511600 | − | 0.886118i | ||||
\(19\) | −198203. | + | 343297.i | −0.348914 | + | 0.604337i | −0.986057 | − | 0.166409i | \(-0.946783\pi\) |
0.637143 | + | 0.770746i | \(0.280116\pi\) | |||||||
\(20\) | −932649. | −1.30342 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.36933e6 | −2.15637 | ||||||||
\(23\) | 310382. | − | 537598.i | 0.231271 | − | 0.400574i | −0.726911 | − | 0.686731i | \(-0.759045\pi\) |
0.958182 | + | 0.286158i | \(0.0923782\pi\) | |||||||
\(24\) | 194668. | + | 337175.i | 0.119769 | + | 0.207446i | ||||
\(25\) | −36898.3 | − | 63909.8i | −0.0188920 | − | 0.0327218i | ||||
\(26\) | −1.80992e6 | + | 3.13488e6i | −0.776747 | + | 1.34537i | ||||
\(27\) | −2.63013e6 | −0.952446 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.87652e6 | 1.28032 | 0.640161 | − | 0.768241i | \(-0.278868\pi\) | ||||
0.640161 | + | 0.768241i | \(0.278868\pi\) | |||||||
\(30\) | −1.93691e6 | + | 3.35482e6i | −0.436580 | + | 0.756178i | ||||
\(31\) | −712408. | − | 1.23393e6i | −0.138548 | − | 0.239973i | 0.788399 | − | 0.615164i | \(-0.210910\pi\) |
−0.926947 | + | 0.375192i | \(0.877577\pi\) | |||||||
\(32\) | −4.12804e6 | − | 7.14998e6i | −0.695936 | − | 1.20540i | ||||
\(33\) | −2.76193e6 | + | 4.78380e6i | −0.405415 | + | 0.702199i | ||||
\(34\) | 1.94135e7 | 2.49143 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.73846e6 | −0.867109 | ||||||||
\(37\) | −6.55458e6 | + | 1.13529e7i | −0.574960 | + | 0.995859i | 0.421086 | + | 0.907021i | \(0.361649\pi\) |
−0.996046 | + | 0.0888388i | \(0.971684\pi\) | |||||||
\(38\) | 6.77113e6 | + | 1.17279e7i | 0.526787 | + | 0.912422i | ||||
\(39\) | 4.21965e6 | + | 7.30866e6i | 0.292069 | + | 0.505879i | ||||
\(40\) | −3.47972e6 | + | 6.02705e6i | −0.214919 | + | 0.372250i | ||||
\(41\) | 2.03049e7 | 1.12221 | 0.561105 | − | 0.827744i | \(-0.310376\pi\) | ||||
0.561105 | + | 0.827744i | \(0.310376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.11768e7 | −0.498551 | −0.249276 | − | 0.968433i | \(-0.580193\pi\) | ||||
−0.249276 | + | 0.968433i | \(0.580193\pi\) | |||||||
\(44\) | −2.27166e7 | + | 3.93463e7i | −0.913706 | + | 1.58259i | ||||
\(45\) | −9.49563e6 | − | 1.64469e7i | −0.345197 | − | 0.597899i | ||||
\(46\) | −1.06035e7 | − | 1.83658e7i | −0.349171 | − | 0.604782i | ||||
\(47\) | −9.96760e6 | + | 1.72644e7i | −0.297955 | + | 0.516073i | −0.975668 | − | 0.219254i | \(-0.929638\pi\) |
0.677713 | + | 0.735326i | \(0.262971\pi\) | |||||||
\(48\) | −1.34132e7 | −0.364710 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.52109e6 | −0.0570458 | ||||||||
\(51\) | 2.26304e7 | − | 3.91969e7i | 0.468409 | − | 0.811309i | ||||
\(52\) | 3.47063e7 | + | 6.01130e7i | 0.658253 | + | 1.14013i | ||||
\(53\) | −2.82503e7 | − | 4.89310e7i | −0.491793 | − | 0.851810i | 0.508162 | − | 0.861261i | \(-0.330325\pi\) |
−0.999955 | + | 0.00945100i | \(0.996992\pi\) | |||||||
\(54\) | −4.49261e7 | + | 7.78143e7i | −0.718997 | + | 1.24534i | ||||
\(55\) | −9.87398e7 | −1.45499 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.15725e7 | 0.396161 | ||||||||
\(58\) | 8.32975e7 | − | 1.44275e8i | 0.966509 | − | 1.67404i | ||||
\(59\) | −5.46701e7 | − | 9.46914e7i | −0.587375 | − | 1.01736i | −0.994575 | − | 0.104025i | \(-0.966828\pi\) |
0.407199 | − | 0.913339i | \(-0.366505\pi\) | |||||||
\(60\) | 3.71413e7 | + | 6.43306e7i | 0.369979 | + | 0.640822i | ||||
\(61\) | 1.60004e7 | − | 2.77135e7i | 0.147961 | − | 0.256275i | −0.782513 | − | 0.622634i | \(-0.786062\pi\) |
0.930474 | + | 0.366359i | \(0.119396\pi\) | |||||||
\(62\) | −4.86755e7 | −0.418358 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.95825e8 | −1.45901 | ||||||||
\(65\) | −7.54269e7 | + | 1.30643e8i | −0.524103 | + | 0.907773i | ||||
\(66\) | 9.43549e7 | + | 1.63427e8i | 0.612092 | + | 1.06017i | ||||
\(67\) | −4.01434e7 | − | 6.95305e7i | −0.243376 | − | 0.421540i | 0.718298 | − | 0.695736i | \(-0.244922\pi\) |
−0.961674 | + | 0.274196i | \(0.911588\pi\) | |||||||
\(68\) | 1.86133e8 | − | 3.22391e8i | 1.05568 | − | 1.82849i | ||||
\(69\) | −4.94420e7 | −0.262588 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.07893e8 | 0.970906 | 0.485453 | − | 0.874263i | \(-0.338655\pi\) | ||||
0.485453 | + | 0.874263i | \(0.338655\pi\) | |||||||
\(72\) | −3.26033e7 | + | 5.64705e7i | −0.142977 | + | 0.247643i | ||||
\(73\) | −1.35137e8 | − | 2.34064e8i | −0.556957 | − | 0.964677i | −0.997748 | − | 0.0670680i | \(-0.978636\pi\) |
0.440792 | − | 0.897609i | \(-0.354698\pi\) | |||||||
\(74\) | 2.23922e8 | + | 3.87844e8i | 0.868069 | + | 1.50354i | ||||
\(75\) | −2.93884e6 | + | 5.09022e6i | −0.0107251 | + | 0.0185764i | ||||
\(76\) | 2.59680e8 | 0.892849 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.88309e8 | 0.881928 | ||||||||
\(79\) | 2.58098e8 | − | 4.47039e8i | 0.745526 | − | 1.29129i | −0.204423 | − | 0.978883i | \(-0.565532\pi\) |
0.949949 | − | 0.312406i | \(-0.101135\pi\) | |||||||
\(80\) | −1.19882e8 | − | 2.07641e8i | −0.327226 | − | 0.566772i | ||||
\(81\) | −2.65386e7 | − | 4.59662e7i | −0.0685008 | − | 0.118647i | ||||
\(82\) | 3.46836e8 | − | 6.00737e8i | 0.847152 | − | 1.46731i | ||||
\(83\) | 6.82693e8 | 1.57897 | 0.789486 | − | 0.613769i | \(-0.210347\pi\) | ||||
0.789486 | + | 0.613769i | \(0.210347\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.09042e8 | 1.68107 | ||||||||
\(86\) | −1.90915e8 | + | 3.30674e8i | −0.376354 | + | 0.651865i | ||||
\(87\) | −1.94200e8 | − | 3.36364e8i | −0.363423 | − | 0.629467i | ||||
\(88\) | 1.69512e8 | + | 2.93603e8i | 0.301320 | + | 0.521901i | ||||
\(89\) | −7.35750e7 | + | 1.27436e8i | −0.124301 | + | 0.215296i | −0.921460 | − | 0.388474i | \(-0.873002\pi\) |
0.797158 | + | 0.603770i | \(0.206336\pi\) | |||||||
\(90\) | −6.48792e8 | −1.04235 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.06656e8 | −0.591809 | ||||||||
\(93\) | −5.67411e7 | + | 9.82784e7i | −0.0786546 | + | 0.136234i | ||||
\(94\) | 3.40520e8 | + | 5.89798e8i | 0.449849 | + | 0.779162i | ||||
\(95\) | 2.82181e8 | + | 4.88752e8i | 0.355445 | + | 0.615648i | ||||
\(96\) | −3.28786e8 | + | 5.69474e8i | −0.395087 | + | 0.684310i | ||||
\(97\) | −1.09643e9 | −1.25750 | −0.628750 | − | 0.777608i | \(-0.716433\pi\) | ||||
−0.628750 | + | 0.777608i | \(0.716433\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.25144e8 | −0.967945 | ||||||||
\(100\) | −2.41717e7 | + | 4.18666e7i | −0.0241717 | + | 0.0418666i | ||||
\(101\) | 1.04342e8 | + | 1.80725e8i | 0.0997727 | + | 0.172811i | 0.911591 | − | 0.411099i | \(-0.134855\pi\) |
−0.811818 | + | 0.583911i | \(0.801522\pi\) | |||||||
\(102\) | −7.73113e8 | − | 1.33907e9i | −0.707200 | − | 1.22491i | ||||
\(103\) | 3.39097e8 | − | 5.87333e8i | 0.296863 | − | 0.514182i | −0.678553 | − | 0.734551i | \(-0.737393\pi\) |
0.975417 | + | 0.220369i | \(0.0707261\pi\) | |||||||
\(104\) | 5.17957e8 | 0.434154 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.93021e9 | −1.48501 | ||||||||
\(107\) | 2.29771e8 | − | 3.97975e8i | 0.169461 | − | 0.293514i | −0.768770 | − | 0.639526i | \(-0.779131\pi\) |
0.938230 | + | 0.346011i | \(0.112464\pi\) | |||||||
\(108\) | 8.61483e8 | + | 1.49213e9i | 0.609312 | + | 1.05536i | ||||
\(109\) | −2.60543e8 | − | 4.51274e8i | −0.176791 | − | 0.306211i | 0.763989 | − | 0.645230i | \(-0.223238\pi\) |
−0.940780 | + | 0.339019i | \(0.889905\pi\) | |||||||
\(110\) | −1.68661e9 | + | 2.92129e9i | −1.09837 | + | 1.90243i | ||||
\(111\) | 1.04410e9 | 0.652816 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.45612e8 | 0.257101 | 0.128551 | − | 0.991703i | \(-0.458968\pi\) | ||||
0.128551 | + | 0.991703i | \(0.458968\pi\) | |||||||
\(114\) | 5.39300e8 | − | 9.34095e8i | 0.299060 | − | 0.517987i | ||||
\(115\) | −4.41891e8 | − | 7.65378e8i | −0.235600 | − | 0.408071i | ||||
\(116\) | −1.59728e9 | − | 2.76656e9i | −0.819066 | − | 1.41866i | ||||
\(117\) | −7.06714e8 | + | 1.22406e9i | −0.348664 | + | 0.603904i | ||||
\(118\) | −3.73535e9 | −1.77363 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.54298e8 | 0.244021 | ||||||||
\(121\) | −1.22604e9 | + | 2.12356e9i | −0.519960 | + | 0.900598i | ||||
\(122\) | −5.46616e8 | − | 9.46766e8i | −0.223390 | − | 0.386922i | ||||
\(123\) | −8.08613e8 | − | 1.40056e9i | −0.318543 | − | 0.551732i | ||||
\(124\) | −4.66690e8 | + | 8.08331e8i | −0.177268 | + | 0.307038i | ||||
\(125\) | 2.67560e9 | 0.980226 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.28626e8 | 0.316755 | 0.158378 | − | 0.987379i | \(-0.449374\pi\) | ||||
0.158378 | + | 0.987379i | \(0.449374\pi\) | |||||||
\(128\) | −1.23139e9 | + | 2.13283e9i | −0.405463 | + | 0.702282i | ||||
\(129\) | 4.45099e8 | + | 7.70934e8i | 0.141515 | + | 0.245112i | ||||
\(130\) | 2.57679e9 | + | 4.46312e9i | 0.791286 | + | 1.37055i | ||||
\(131\) | 1.28847e9 | − | 2.23169e9i | 0.382255 | − | 0.662084i | −0.609130 | − | 0.793071i | \(-0.708481\pi\) |
0.991384 | + | 0.130986i | \(0.0418144\pi\) | |||||||
\(132\) | 3.61862e9 | 1.03743 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.74281e9 | −0.734894 | ||||||||
\(135\) | −1.87226e9 | + | 3.24285e9i | −0.485136 | + | 0.840280i | ||||
\(136\) | −1.38892e9 | − | 2.40568e9i | −0.348139 | − | 0.602995i | ||||
\(137\) | 2.22058e9 | + | 3.84616e9i | 0.538548 | + | 0.932792i | 0.998983 | + | 0.0450984i | \(0.0143601\pi\) |
−0.460435 | + | 0.887693i | \(0.652307\pi\) | |||||||
\(138\) | −8.44535e8 | + | 1.46278e9i | −0.198227 | + | 0.343338i | ||||
\(139\) | 7.28389e9 | 1.65499 | 0.827497 | − | 0.561470i | \(-0.189764\pi\) | ||||
0.827497 | + | 0.561470i | \(0.189764\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.58778e9 | 0.338301 | ||||||||
\(142\) | 3.55109e9 | − | 6.15067e9i | 0.732933 | − | 1.26948i | ||||
\(143\) | 3.67436e9 | + | 6.36418e9i | 0.734801 | + | 1.27271i | ||||
\(144\) | −1.12323e9 | − | 1.94550e9i | −0.217690 | − | 0.377050i | ||||
\(145\) | 3.47135e9 | − | 6.01256e9i | 0.652142 | − | 1.12954i | ||||
\(146\) | −9.23328e9 | −1.68178 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.58766e9 | 1.47129 | ||||||||
\(149\) | −2.43678e9 | + | 4.22062e9i | −0.405021 | + | 0.701517i | −0.994324 | − | 0.106395i | \(-0.966069\pi\) |
0.589303 | + | 0.807912i | \(0.299402\pi\) | |||||||
\(150\) | 1.00399e8 | + | 1.73895e8i | 0.0161926 | + | 0.0280464i | ||||
\(151\) | 4.31888e9 | + | 7.48052e9i | 0.676044 | + | 1.17094i | 0.976163 | + | 0.217041i | \(0.0696404\pi\) |
−0.300119 | + | 0.953902i | \(0.597026\pi\) | |||||||
\(152\) | 9.68869e8 | − | 1.67813e9i | 0.147221 | − | 0.254994i | ||||
\(153\) | 7.58033e9 | 1.11835 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.02851e9 | −0.282283 | ||||||||
\(156\) | 2.76425e9 | − | 4.78781e9i | 0.373694 | − | 0.647257i | ||||
\(157\) | −4.67085e9 | − | 8.09015e9i | −0.613546 | − | 1.06269i | −0.990638 | − | 0.136517i | \(-0.956409\pi\) |
0.377091 | − | 0.926176i | \(-0.376924\pi\) | |||||||
\(158\) | −8.81732e9 | − | 1.52720e10i | −1.12559 | − | 1.94958i | ||||
\(159\) | −2.25005e9 | + | 3.89720e9i | −0.279194 | + | 0.483577i | ||||
\(160\) | −1.17542e10 | −1.41792 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.81326e9 | −0.206844 | ||||||||
\(163\) | 1.05340e9 | − | 1.82454e9i | 0.116883 | − | 0.202447i | −0.801648 | − | 0.597796i | \(-0.796043\pi\) |
0.918531 | + | 0.395350i | \(0.129377\pi\) | |||||||
\(164\) | −6.65077e9 | − | 1.15195e10i | −0.717917 | − | 1.24347i | ||||
\(165\) | 3.93216e9 | + | 6.81070e9i | 0.413003 | + | 0.715342i | ||||
\(166\) | 1.16613e10 | − | 2.01980e10i | 1.19196 | − | 2.06453i | ||||
\(167\) | −1.39800e10 | −1.39086 | −0.695431 | − | 0.718593i | \(-0.744787\pi\) | ||||
−0.695431 | + | 0.718593i | \(0.744787\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.22820e8 | 0.0587316 | ||||||||
\(170\) | 1.38195e10 | − | 2.39361e10i | 1.26903 | − | 2.19803i | ||||
\(171\) | 2.64390e9 | + | 4.57937e9i | 0.236463 | + | 0.409565i | ||||
\(172\) | 3.66090e9 | + | 6.34086e9i | 0.318941 | + | 0.552421i | ||||
\(173\) | −6.22177e9 | + | 1.07764e10i | −0.528088 | + | 0.914675i | 0.471376 | + | 0.881932i | \(0.343758\pi\) |
−0.999464 | + | 0.0327427i | \(0.989576\pi\) | |||||||
\(174\) | −1.32688e10 | −1.09739 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.16799e10 | −0.917553 | ||||||||
\(177\) | −4.35430e9 | + | 7.54187e9i | −0.333456 | + | 0.577563i | ||||
\(178\) | 2.51352e9 | + | 4.35354e9i | 0.187669 | + | 0.325052i | ||||
\(179\) | −3.65089e9 | − | 6.32353e9i | −0.265803 | − | 0.460384i | 0.701971 | − | 0.712206i | \(-0.252304\pi\) |
−0.967774 | + | 0.251821i | \(0.918970\pi\) | |||||||
\(180\) | −6.22048e9 | + | 1.07742e10i | −0.441669 | + | 0.764994i | ||||
\(181\) | 1.27074e10 | 0.880038 | 0.440019 | − | 0.897988i | \(-0.354972\pi\) | ||||
0.440019 | + | 0.897988i | \(0.354972\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.54876e9 | −0.167996 | ||||||||
\(184\) | −1.51723e9 | + | 2.62793e9i | −0.0975826 | + | 0.169018i | ||||
\(185\) | 9.33176e9 | + | 1.61631e10i | 0.585721 | + | 1.01450i | ||||
\(186\) | 1.93843e9 | + | 3.35745e9i | 0.118752 | + | 0.205685i | ||||
\(187\) | 1.97059e10 | − | 3.41316e10i | 1.17844 | − | 2.04113i | ||||
\(188\) | 1.30593e10 | 0.762448 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.92801e10 | 1.07329 | ||||||||
\(191\) | −8.07734e9 | + | 1.39904e10i | −0.439155 | + | 0.760639i | −0.997625 | − | 0.0688860i | \(-0.978056\pi\) |
0.558469 | + | 0.829525i | \(0.311389\pi\) | |||||||
\(192\) | 7.79842e9 | + | 1.35073e10i | 0.414144 | + | 0.717318i | ||||
\(193\) | 7.64204e9 | + | 1.32364e10i | 0.396462 | + | 0.686692i | 0.993287 | − | 0.115679i | \(-0.0369045\pi\) |
−0.596825 | + | 0.802372i | \(0.703571\pi\) | |||||||
\(194\) | −1.87285e10 | + | 3.24387e10i | −0.949281 | + | 1.64420i | ||||
\(195\) | 1.20150e10 | 0.595072 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.33886e10 | 1.10639 | 0.553193 | − | 0.833053i | \(-0.313409\pi\) | ||||
0.553193 | + | 0.833053i | \(0.313409\pi\) | |||||||
\(198\) | −1.58027e10 | + | 2.73711e10i | −0.730697 | + | 1.26561i | ||||
\(199\) | −1.26805e10 | − | 2.19633e10i | −0.573189 | − | 0.992792i | −0.996236 | − | 0.0866844i | \(-0.972373\pi\) |
0.423047 | − | 0.906108i | \(-0.360961\pi\) | |||||||
\(200\) | 1.80369e8 | + | 3.12409e8i | 0.00797127 | + | 0.0138066i | ||||
\(201\) | −3.19730e9 | + | 5.53789e9i | −0.138166 | + | 0.239310i | ||||
\(202\) | 7.12918e9 | 0.301272 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.96498e10 | −1.19863 | ||||||||
\(205\) | 1.44541e10 | − | 2.50352e10i | 0.571608 | − | 0.990053i | ||||
\(206\) | −1.15845e10 | − | 2.00649e10i | −0.448202 | − | 0.776308i | ||||
\(207\) | −4.14030e9 | − | 7.17122e9i | −0.156735 | − | 0.271473i | ||||
\(208\) | −8.92221e9 | + | 1.54537e10i | −0.330512 | + | 0.572464i | ||||
\(209\) | 2.74924e10 | 0.996678 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.23757e8 | −0.0320838 | −0.0160419 | − | 0.999871i | \(-0.505107\pi\) | ||||
−0.0160419 | + | 0.999871i | \(0.505107\pi\) | |||||||
\(212\) | −1.85065e10 | + | 3.20541e10i | −0.629234 | + | 1.08986i | ||||
\(213\) | −8.27902e9 | − | 1.43397e10i | −0.275595 | − | 0.477344i | ||||
\(214\) | −7.84960e9 | − | 1.35959e10i | −0.255850 | − | 0.443145i | ||||
\(215\) | −7.95621e9 | + | 1.37806e10i | −0.253941 | + | 0.439839i | ||||
\(216\) | 1.28568e10 | 0.401875 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.78017e10 | −0.533835 | ||||||||
\(219\) | −1.07632e10 | + | 1.86425e10i | −0.316188 | + | 0.547653i | ||||
\(220\) | 3.23416e10 | + | 5.60174e10i | 0.930808 | + | 1.61221i | ||||
\(221\) | −3.01065e10 | − | 5.21460e10i | −0.848976 | − | 1.47047i | ||||
\(222\) | 1.78347e10 | − | 3.08906e10i | 0.492808 | − | 0.853568i | ||||
\(223\) | −6.68635e9 | −0.181058 | −0.0905290 | − | 0.995894i | \(-0.528856\pi\) | ||||
−0.0905290 | + | 0.995894i | \(0.528856\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.84401e8 | −0.0256065 | ||||||||
\(226\) | 7.61165e9 | − | 1.31838e10i | 0.194085 | − | 0.336164i | ||||
\(227\) | −2.41438e10 | − | 4.18183e10i | −0.603516 | − | 1.04532i | −0.992284 | − | 0.123985i | \(-0.960432\pi\) |
0.388768 | − | 0.921336i | \(-0.372901\pi\) | |||||||
\(228\) | −1.03414e10 | − | 1.79118e10i | −0.253438 | − | 0.438967i | ||||
\(229\) | −1.17132e10 | + | 2.02878e10i | −0.281459 | + | 0.487501i | −0.971744 | − | 0.236036i | \(-0.924152\pi\) |
0.690285 | + | 0.723537i | \(0.257485\pi\) | |||||||
\(230\) | −3.01924e10 | −0.711413 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.38378e10 | −0.540219 | ||||||||
\(233\) | 1.64570e10 | − | 2.85044e10i | 0.365805 | − | 0.633592i | −0.623100 | − | 0.782142i | \(-0.714127\pi\) |
0.988905 | + | 0.148550i | \(0.0474605\pi\) | |||||||
\(234\) | 2.41432e10 | + | 4.18173e10i | 0.526410 | + | 0.911768i | ||||
\(235\) | 1.41909e10 | + | 2.45793e10i | 0.303531 | + | 0.525732i | ||||
\(236\) | −3.58137e10 | + | 6.20312e10i | −0.751529 | + | 1.30169i | ||||
\(237\) | −4.11134e10 | −0.846479 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.51973e10 | 0.499533 | 0.249766 | − | 0.968306i | \(-0.419646\pi\) | ||||
0.249766 | + | 0.968306i | \(0.419646\pi\) | |||||||
\(240\) | −9.54820e9 | + | 1.65380e10i | −0.185768 | + | 0.321760i | ||||
\(241\) | 3.50407e10 | + | 6.06923e10i | 0.669109 | + | 1.15893i | 0.978154 | + | 0.207883i | \(0.0666573\pi\) |
−0.309045 | + | 0.951047i | \(0.600009\pi\) | |||||||
\(242\) | 4.18848e10 | + | 7.25466e10i | 0.785032 | + | 1.35971i | ||||
\(243\) | −2.79981e10 | + | 4.84942e10i | −0.515111 | + | 0.892199i | ||||
\(244\) | −2.09633e10 | −0.378622 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.52488e10 | −0.961866 | ||||||||
\(247\) | 2.10014e10 | − | 3.63754e10i | 0.359014 | − | 0.621830i | ||||
\(248\) | 3.48244e9 | + | 6.03177e9i | 0.0584590 | + | 0.101254i | ||||
\(249\) | −2.71872e10 | − | 4.70896e10i | −0.448196 | − | 0.776297i | ||||
\(250\) | 4.57028e10 | − | 7.91596e10i | 0.739968 | − | 1.28166i | ||||
\(251\) | −4.19681e10 | −0.667401 | −0.333701 | − | 0.942679i | \(-0.608297\pi\) | ||||
−0.333701 | + | 0.942679i | \(0.608297\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.30527e10 | −0.660630 | ||||||||
\(254\) | 1.58622e10 | − | 2.74741e10i | 0.239117 | − | 0.414163i | ||||
\(255\) | −3.22188e10 | − | 5.58047e10i | −0.477176 | − | 0.826494i | ||||
\(256\) | −8.06355e9 | − | 1.39665e10i | −0.117340 | − | 0.203239i | ||||
\(257\) | 4.18797e10 | − | 7.25378e10i | 0.598832 | − | 1.03721i | −0.394162 | − | 0.919041i | \(-0.628965\pi\) |
0.992994 | − | 0.118166i | \(-0.0377015\pi\) | |||||||
\(258\) | 3.04116e10 | 0.427317 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.88226e10 | 1.34115 | ||||||||
\(261\) | 3.25249e10 | − | 5.63347e10i | 0.433843 | − | 0.751439i | ||||
\(262\) | −4.40175e10 | − | 7.62405e10i | −0.577125 | − | 0.999609i | ||||
\(263\) | 1.17302e9 | + | 2.03173e9i | 0.0151184 | + | 0.0261858i | 0.873486 | − | 0.486850i | \(-0.161854\pi\) |
−0.858367 | + | 0.513036i | \(0.828521\pi\) | |||||||
\(264\) | 1.35011e10 | − | 2.33845e10i | 0.171061 | − | 0.296286i | ||||
\(265\) | −8.04400e10 | −1.00200 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.17200e10 | 0.141133 | ||||||||
\(268\) | −2.62975e10 | + | 4.55486e10i | −0.311392 | + | 0.539347i | ||||
\(269\) | −3.22330e10 | − | 5.58291e10i | −0.375332 | − | 0.650093i | 0.615045 | − | 0.788492i | \(-0.289138\pi\) |
−0.990377 | + | 0.138399i | \(0.955804\pi\) | |||||||
\(270\) | 6.39613e10 | + | 1.10784e11i | 0.732454 | + | 1.26865i | ||||
\(271\) | −7.02649e9 | + | 1.21702e10i | −0.0791365 | + | 0.137068i | −0.902878 | − | 0.429898i | \(-0.858550\pi\) |
0.823741 | + | 0.566966i | \(0.191883\pi\) | |||||||
\(272\) | 9.57011e10 | 1.06012 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.51722e11 | 1.62619 | ||||||||
\(275\) | −2.55906e9 | + | 4.43242e9i | −0.0269826 | + | 0.0467352i | ||||
\(276\) | 1.61944e10 | + | 2.80496e10i | 0.167987 | + | 0.290961i | ||||
\(277\) | 3.76384e10 | + | 6.51916e10i | 0.384124 | + | 0.665323i | 0.991647 | − | 0.128979i | \(-0.0411700\pi\) |
−0.607523 | + | 0.794302i | \(0.707837\pi\) | |||||||
\(278\) | 1.24419e11 | − | 2.15499e11i | 1.24935 | − | 2.16393i | ||||
\(279\) | −1.90061e10 | −0.187791 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.56085e10 | 0.914783 | 0.457391 | − | 0.889266i | \(-0.348784\pi\) | ||||
0.457391 | + | 0.889266i | \(0.348784\pi\) | |||||||
\(282\) | 2.71213e10 | − | 4.69756e10i | 0.255382 | − | 0.442335i | ||||
\(283\) | 2.41403e10 | + | 4.18122e10i | 0.223719 | + | 0.387493i | 0.955934 | − | 0.293580i | \(-0.0948468\pi\) |
−0.732215 | + | 0.681073i | \(0.761513\pi\) | |||||||
\(284\) | −6.80941e10 | − | 1.17942e11i | −0.621122 | − | 1.07582i | ||||
\(285\) | 2.24749e10 | − | 3.89276e10i | 0.201788 | − | 0.349507i | ||||
\(286\) | 2.51052e11 | 2.21879 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.10131e11 | −0.943286 | ||||||||
\(289\) | −1.02170e11 | + | 1.76963e11i | −0.861553 | + | 1.49225i | ||||
\(290\) | −1.18591e11 | − | 2.05405e11i | −0.984599 | − | 1.70538i | ||||
\(291\) | 4.36636e10 | + | 7.56276e10i | 0.356945 | + | 0.618247i | ||||
\(292\) | −8.85267e10 | + | 1.53333e11i | −0.712609 | + | 1.23428i | ||||
\(293\) | 7.07439e10 | 0.560770 | 0.280385 | − | 0.959888i | \(-0.409538\pi\) | ||||
0.280385 | + | 0.959888i | \(0.409538\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.55668e11 | −1.19674 | ||||||||
\(296\) | 3.20406e10 | − | 5.54960e10i | 0.242598 | − | 0.420193i | ||||
\(297\) | 9.12055e10 | + | 1.57973e11i | 0.680169 | + | 1.17809i | ||||
\(298\) | 8.32468e10 | + | 1.44188e11i | 0.611497 | + | 1.05914i | ||||
\(299\) | −3.28878e10 | + | 5.69634e10i | −0.237966 | + | 0.412169i | ||||
\(300\) | 3.85040e9 | 0.0274448 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.95089e11 | 2.04137 | ||||||||
\(303\) | 8.31049e9 | − | 1.43942e10i | 0.0566415 | − | 0.0981060i | ||||
\(304\) | 3.33790e10 | + | 5.78142e10i | 0.224152 | + | 0.388243i | ||||
\(305\) | −2.27797e10 | − | 3.94557e10i | −0.150730 | − | 0.261072i | ||||
\(306\) | 1.29482e11 | − | 2.24270e11i | 0.844235 | − | 1.46226i | ||||
\(307\) | −1.30493e11 | −0.838429 | −0.419214 | − | 0.907887i | \(-0.637694\pi\) | ||||
−0.419214 | + | 0.907887i | \(0.637694\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.40161e10 | −0.337062 | ||||||||
\(310\) | −3.46497e10 | + | 6.00150e10i | −0.213094 | + | 0.369090i | ||||
\(311\) | 4.25858e10 | + | 7.37607e10i | 0.258132 | + | 0.447099i | 0.965742 | − | 0.259505i | \(-0.0835596\pi\) |
−0.707609 | + | 0.706604i | \(0.750226\pi\) | |||||||
\(312\) | −2.06268e10 | − | 3.57267e10i | −0.123236 | − | 0.213451i | ||||
\(313\) | −6.08723e10 | + | 1.05434e11i | −0.358484 | + | 0.620913i | −0.987708 | − | 0.156311i | \(-0.950040\pi\) |
0.629223 | + | 0.777224i | \(0.283373\pi\) | |||||||
\(314\) | −3.19137e11 | −1.85265 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.38154e11 | −1.90775 | ||||||||
\(317\) | 1.07297e11 | − | 1.85845e11i | 0.596791 | − | 1.03367i | −0.396500 | − | 0.918035i | \(-0.629775\pi\) |
0.993291 | − | 0.115638i | \(-0.0368913\pi\) | |||||||
\(318\) | 7.68678e10 | + | 1.33139e11i | 0.421524 | + | 0.730101i | ||||
\(319\) | −1.69104e11 | − | 2.92897e11i | −0.914315 | − | 1.58364i | ||||
\(320\) | −1.39398e11 | + | 2.41444e11i | −0.743158 | + | 1.28719i | ||||
\(321\) | −3.66011e10 | −0.192407 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.25264e11 | −1.15154 | ||||||||
\(324\) | −1.73851e10 | + | 3.01119e10i | −0.0876446 | + | 0.151805i | ||||
\(325\) | 3.90971e9 | + | 6.77182e9i | 0.0194388 | + | 0.0336690i | ||||
\(326\) | −3.59870e10 | − | 6.23313e10i | −0.176468 | − | 0.305652i | ||||
\(327\) | −2.07515e10 | + | 3.59426e10i | −0.100365 | + | 0.173838i | ||||
\(328\) | −9.92562e10 | −0.473506 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.68666e11 | 1.24710 | ||||||||
\(331\) | 2.74000e10 | − | 4.74582e10i | 0.125466 | − | 0.217313i | −0.796449 | − | 0.604705i | \(-0.793291\pi\) |
0.921915 | + | 0.387393i | \(0.126624\pi\) | |||||||
\(332\) | −2.23612e11 | − | 3.87308e11i | −1.01012 | − | 1.74958i | ||||
\(333\) | 8.74340e10 | + | 1.51440e11i | 0.389656 | + | 0.674904i | ||||
\(334\) | −2.38798e11 | + | 4.13610e11i | −1.04996 | + | 1.81858i | ||||
\(335\) | −1.14304e11 | −0.495863 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.34297e11 | −0.989538 | −0.494769 | − | 0.869025i | \(-0.664747\pi\) | ||||
−0.494769 | + | 0.869025i | \(0.664747\pi\) | |||||||
\(338\) | 1.06386e10 | − | 1.84266e10i | 0.0443362 | − | 0.0767926i | ||||
\(339\) | −1.77458e10 | − | 3.07366e10i | −0.0729789 | − | 0.126403i | ||||
\(340\) | −2.64997e11 | − | 4.58988e11i | −1.07544 | − | 1.86271i | ||||
\(341\) | −4.94086e10 | + | 8.55782e10i | −0.197883 | + | 0.342743i | ||||
\(342\) | 1.80645e11 | 0.714018 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.46353e10 | 0.210359 | ||||||||
\(345\) | −3.51953e10 | + | 6.09600e10i | −0.133751 | + | 0.231664i | ||||
\(346\) | 2.12552e11 | + | 3.68151e11i | 0.797302 | + | 1.38097i | ||||
\(347\) | −1.71725e10 | − | 2.97436e10i | −0.0635843 | − | 0.110131i | 0.832481 | − | 0.554054i | \(-0.186920\pi\) |
−0.896065 | + | 0.443923i | \(0.853587\pi\) | |||||||
\(348\) | −1.27218e11 | + | 2.20348e11i | −0.464988 | + | 0.805383i | ||||
\(349\) | 2.13485e11 | 0.770288 | 0.385144 | − | 0.922856i | \(-0.374152\pi\) | ||||
0.385144 | + | 0.922856i | \(0.374152\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.78686e11 | 0.980016 | ||||||||
\(352\) | −2.86298e11 | + | 4.95882e11i | −0.993976 | + | 1.72162i | ||||
\(353\) | 1.37941e11 | + | 2.38921e11i | 0.472832 | + | 0.818969i | 0.999517 | − | 0.0310916i | \(-0.00989837\pi\) |
−0.526684 | + | 0.850061i | \(0.676565\pi\) | |||||||
\(354\) | 1.48755e11 | + | 2.57651e11i | 0.503449 | + | 0.872000i | ||||
\(355\) | 1.47989e11 | − | 2.56324e11i | 0.494539 | − | 0.856567i | ||||
\(356\) | 9.63962e10 | 0.318079 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.49448e11 | −0.802614 | ||||||||
\(359\) | 1.73119e11 | − | 2.99851e11i | 0.550073 | − | 0.952754i | −0.448196 | − | 0.893935i | \(-0.647933\pi\) |
0.998269 | − | 0.0588186i | \(-0.0187334\pi\) | |||||||
\(360\) | 4.64173e10 | + | 8.03971e10i | 0.145653 | + | 0.252278i | ||||
\(361\) | 8.27752e10 | + | 1.43371e11i | 0.256518 | + | 0.444302i | ||||
\(362\) | 2.17059e11 | − | 3.75957e11i | 0.664337 | − | 1.15067i | ||||
\(363\) | 1.95300e11 | 0.590369 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.84789e11 | −1.13476 | ||||||||
\(366\) | −4.35362e10 | + | 7.54070e10i | −0.126820 | + | 0.219658i | ||||
\(367\) | 1.78421e11 | + | 3.09034e11i | 0.513391 | + | 0.889220i | 0.999879 | + | 0.0155325i | \(0.00494436\pi\) |
−0.486488 | + | 0.873687i | \(0.661722\pi\) | |||||||
\(368\) | −5.22711e10 | − | 9.05361e10i | −0.148575 | − | 0.257340i | ||||
\(369\) | 1.35428e11 | − | 2.34568e11i | 0.380267 | − | 0.658642i | ||||
\(370\) | 6.37596e11 | 1.76863 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.43408e10 | 0.201272 | ||||||||
\(373\) | −3.36917e11 | + | 5.83557e11i | −0.901224 | + | 1.56097i | −0.0753159 | + | 0.997160i | \(0.523997\pi\) |
−0.825908 | + | 0.563805i | \(0.809337\pi\) | |||||||
\(374\) | −6.73206e11 | − | 1.16603e12i | −1.77920 | − | 3.08167i | ||||
\(375\) | −1.06552e11 | − | 1.84553e11i | −0.278240 | − | 0.481926i | ||||
\(376\) | 4.87244e10 | − | 8.43931e10i | 0.125719 | − | 0.217752i | ||||
\(377\) | −5.16711e11 | −1.31738 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.90163e11 | 1.46925 | 0.734625 | − | 0.678473i | \(-0.237358\pi\) | ||||
0.734625 | + | 0.678473i | \(0.237358\pi\) | |||||||
\(380\) | 1.84854e11 | − | 3.20176e11i | 0.454780 | − | 0.787703i | ||||
\(381\) | −3.69811e10 | − | 6.40531e10i | −0.0899119 | − | 0.155732i | ||||
\(382\) | 2.75943e11 | + | 4.77948e11i | 0.663033 | + | 1.14841i | ||||
\(383\) | −7.94657e10 | + | 1.37639e11i | −0.188706 | + | 0.326848i | −0.944819 | − | 0.327593i | \(-0.893763\pi\) |
0.756113 | + | 0.654441i | \(0.227096\pi\) | |||||||
\(384\) | 1.96153e11 | 0.460367 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.22145e11 | 1.19715 | ||||||||
\(387\) | −7.45458e10 | + | 1.29117e11i | −0.168937 | + | 0.292607i | ||||
\(388\) | 3.59129e11 | + | 6.22030e11i | 0.804466 | + | 1.39338i | ||||
\(389\) | 1.87717e11 | + | 3.25135e11i | 0.415652 | + | 0.719931i | 0.995497 | − | 0.0947965i | \(-0.0302201\pi\) |
−0.579845 | + | 0.814727i | \(0.696887\pi\) | |||||||
\(390\) | 2.05233e11 | − | 3.55474e11i | 0.449217 | − | 0.778067i | ||||
\(391\) | 3.52760e11 | 0.763280 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.05245e11 | −0.434016 | ||||||||
\(394\) | 3.99509e11 | − | 6.91970e11i | 0.835206 | − | 1.44662i | ||||
\(395\) | −3.67454e11 | − | 6.36449e11i | −0.759480 | − | 1.31546i | ||||
\(396\) | 3.03025e11 | + | 5.24855e11i | 0.619228 | + | 1.07253i | ||||
\(397\) | −2.16754e11 | + | 3.75428e11i | −0.437935 | + | 0.758525i | −0.997530 | − | 0.0702410i | \(-0.977623\pi\) |
0.559596 | + | 0.828766i | \(0.310957\pi\) | |||||||
\(398\) | −8.66400e11 | −1.73079 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.24280e10 | −0.0242734 | ||||||||
\(401\) | 8.89025e10 | − | 1.53984e11i | 0.171698 | − | 0.297389i | −0.767316 | − | 0.641269i | \(-0.778408\pi\) |
0.939013 | + | 0.343880i | \(0.111741\pi\) | |||||||
\(402\) | 1.09228e11 | + | 1.89189e11i | 0.208602 | + | 0.361309i | ||||
\(403\) | 7.54860e10 | + | 1.30746e11i | 0.142559 | + | 0.246919i | ||||
\(404\) | 6.83530e10 | − | 1.18391e11i | 0.127656 | − | 0.221107i | ||||
\(405\) | −7.55660e10 | −0.139566 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.09178e11 | 1.64238 | ||||||||
\(408\) | −1.10623e11 | + | 1.91605e11i | −0.197641 | + | 0.342324i | ||||
\(409\) | −3.83935e11 | − | 6.64995e11i | −0.678427 | − | 1.17507i | −0.975455 | − | 0.220201i | \(-0.929329\pi\) |
0.297028 | − | 0.954869i | \(-0.404005\pi\) | |||||||
\(410\) | −4.93790e11 | − | 8.55269e11i | −0.863008 | − | 1.49477i | ||||
\(411\) | 1.76862e11 | − | 3.06335e11i | 0.305737 | − | 0.529551i | ||||
\(412\) | −4.44277e11 | −0.759655 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.82888e11 | −0.473274 | ||||||||
\(415\) | 4.85975e11 | − | 8.41734e11i | 0.804262 | − | 1.39302i | ||||
\(416\) | 4.37403e11 | + | 7.57605e11i | 0.716081 | + | 1.24029i | ||||
\(417\) | −2.90069e11 | − | 5.02415e11i | −0.469775 | − | 0.813674i | ||||
\(418\) | 4.69608e11 | − | 8.13384e11i | 0.752388 | − | 1.30317i | ||||
\(419\) | −4.96552e11 | −0.787048 | −0.393524 | − | 0.919314i | \(-0.628744\pi\) | ||||
−0.393524 | + | 0.919314i | \(0.628744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.48514e11 | −0.695835 | −0.347917 | − | 0.937525i | \(-0.613111\pi\) | ||||
−0.347917 | + | 0.937525i | \(0.613111\pi\) | |||||||
\(422\) | −1.57790e10 | + | 2.73300e10i | −0.0242200 | + | 0.0419502i | ||||
\(423\) | 1.32962e11 | + | 2.30296e11i | 0.201927 | + | 0.349748i | ||||
\(424\) | 1.38095e11 | + | 2.39188e11i | 0.207507 | + | 0.359413i | ||||
\(425\) | 2.09681e10 | − | 3.63178e10i | 0.0311752 | − | 0.0539970i | ||||
\(426\) | −5.65667e11 | −0.832180 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.01041e11 | −0.433639 | ||||||||
\(429\) | 2.92651e11 | − | 5.06887e11i | 0.417151 | − | 0.722526i | ||||
\(430\) | 2.71805e11 | + | 4.70781e11i | 0.383398 | + | 0.664065i | ||||
\(431\) | 8.29702e10 | + | 1.43709e11i | 0.115817 | + | 0.200602i | 0.918106 | − | 0.396334i | \(-0.129718\pi\) |
−0.802289 | + | 0.596936i | \(0.796385\pi\) | |||||||
\(432\) | −2.21468e11 | + | 3.83594e11i | −0.305939 | + | 0.529902i | ||||
\(433\) | 4.10674e11 | 0.561438 | 0.280719 | − | 0.959790i | \(-0.409427\pi\) | ||||
0.280719 | + | 0.959790i | \(0.409427\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.52965e11 | −0.740450 | ||||||||
\(436\) | −1.70679e11 | + | 2.95624e11i | −0.226199 | + | 0.391788i | ||||
\(437\) | 1.23037e11 | + | 2.13107e11i | 0.161388 | + | 0.279531i | ||||
\(438\) | 3.67701e11 | + | 6.36877e11i | 0.477377 | + | 0.826841i | ||||
\(439\) | −1.64797e11 | + | 2.85436e11i | −0.211767 | + | 0.366791i | −0.952268 | − | 0.305265i | \(-0.901255\pi\) |
0.740501 | + | 0.672056i | \(0.234588\pi\) | |||||||
\(440\) | 4.82667e11 | 0.613919 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.05704e12 | −2.56355 | ||||||||
\(443\) | −2.54545e11 | + | 4.40886e11i | −0.314014 | + | 0.543888i | −0.979227 | − | 0.202765i | \(-0.935007\pi\) |
0.665214 | + | 0.746653i | \(0.268340\pi\) | |||||||
\(444\) | −3.41990e11 | − | 5.92345e11i | −0.417629 | − | 0.723354i | ||||
\(445\) | 1.04749e11 | + | 1.81430e11i | 0.126628 | + | 0.219326i | ||||
\(446\) | −1.14212e11 | + | 1.97821e11i | −0.136680 | + | 0.236736i | ||||
\(447\) | 3.88163e11 | 0.459865 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.49596e12 | 1.73705 | 0.868525 | − | 0.495646i | \(-0.165069\pi\) | ||||
0.868525 | + | 0.495646i | \(0.165069\pi\) | |||||||
\(450\) | −1.68149e10 | + | 2.91242e10i | −0.0193303 | + | 0.0334810i | ||||
\(451\) | −7.04118e11 | − | 1.21957e12i | −0.801403 | − | 1.38807i | ||||
\(452\) | −1.45958e11 | − | 2.52806e11i | −0.164476 | − | 0.284882i | ||||
\(453\) | 3.43985e11 | − | 5.95800e11i | 0.383794 | − | 0.664751i | ||||
\(454\) | −1.64963e12 | −1.82237 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.54335e11 | −0.167156 | ||||||||
\(457\) | −7.19600e11 | + | 1.24638e12i | −0.771735 | + | 1.33668i | 0.164876 | + | 0.986314i | \(0.447278\pi\) |
−0.936611 | + | 0.350370i | \(0.886056\pi\) | |||||||
\(458\) | 4.00153e11 | + | 6.93086e11i | 0.424944 | + | 0.736025i | ||||
\(459\) | −7.47308e11 | − | 1.29438e12i | −0.785855 | − | 1.36114i | ||||
\(460\) | −2.89478e11 | + | 5.01390e11i | −0.301443 | + | 0.522114i | ||||
\(461\) | 1.37741e12 | 1.42039 | 0.710195 | − | 0.704005i | \(-0.248607\pi\) | ||||
0.710195 | + | 0.704005i | \(0.248607\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.76612e12 | 1.78610 | 0.893049 | − | 0.449960i | \(-0.148562\pi\) | ||||
0.893049 | + | 0.449960i | \(0.148562\pi\) | |||||||
\(464\) | 4.10624e11 | − | 7.11222e11i | 0.411257 | − | 0.712318i | ||||
\(465\) | 8.07823e10 | + | 1.39919e11i | 0.0801268 | + | 0.138784i | ||||
\(466\) | −5.62215e11 | − | 9.73785e11i | −0.552288 | − | 0.956592i | ||||
\(467\) | −5.86617e11 | + | 1.01605e12i | −0.570727 | + | 0.988528i | 0.425764 | + | 0.904834i | \(0.360005\pi\) |
−0.996491 | + | 0.0836942i | \(0.973328\pi\) | |||||||
\(468\) | 9.25919e11 | 0.892209 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.69596e11 | 0.916538 | ||||||||
\(471\) | −3.72019e11 | + | 6.44355e11i | −0.348314 | + | 0.603297i | ||||
\(472\) | 2.67242e11 | + | 4.62878e11i | 0.247837 | + | 0.429267i | ||||
\(473\) | 3.87580e11 | + | 6.71309e11i | 0.356030 | + | 0.616662i | ||||
\(474\) | −7.02272e11 | + | 1.21637e12i | −0.639003 | + | 1.10679i | ||||
\(475\) | 2.92534e10 | 0.0263667 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.53683e11 | −0.666586 | ||||||||
\(478\) | 4.30404e11 | − | 7.45482e11i | 0.377095 | − | 0.653148i | ||||
\(479\) | −9.93617e11 | − | 1.72100e12i | −0.862401 | − | 1.49372i | −0.869605 | − | 0.493749i | \(-0.835626\pi\) |
0.00720347 | − | 0.999974i | \(-0.497707\pi\) | |||||||
\(480\) | 4.68092e11 | + | 8.10760e11i | 0.402482 | + | 0.697118i | ||||
\(481\) | 6.94517e11 | − | 1.20294e12i | 0.591603 | − | 1.02469i | ||||
\(482\) | 2.39417e12 | 2.02043 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.60633e12 | 1.33055 | ||||||||
\(485\) | −7.80493e11 | + | 1.35185e12i | −0.640518 | + | 1.10941i | ||||
\(486\) | 9.56491e11 | + | 1.65669e12i | 0.777710 | + | 1.34703i | ||||
\(487\) | 6.16202e11 | + | 1.06729e12i | 0.496413 | + | 0.859812i | 0.999991 | − | 0.00413747i | \(-0.00131700\pi\) |
−0.503579 | + | 0.863949i | \(0.667984\pi\) | |||||||
\(488\) | −7.82142e10 | + | 1.35471e11i | −0.0624305 | + | 0.108133i | ||||
\(489\) | −1.67800e11 | −0.132710 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.03763e12 | −1.58219 | −0.791095 | − | 0.611693i | \(-0.790489\pi\) | ||||
−0.791095 | + | 0.611693i | \(0.790489\pi\) | |||||||
\(492\) | −5.29713e11 | + | 9.17490e11i | −0.407566 | + | 0.705924i | ||||
\(493\) | 1.38558e12 | + | 2.39990e12i | 1.05638 | + | 1.82971i | ||||
\(494\) | −7.17463e11 | − | 1.24268e12i | −0.542036 | − | 0.938834i | ||||
\(495\) | −6.58563e11 | + | 1.14067e12i | −0.493031 | + | 0.853955i | ||||
\(496\) | −2.39951e11 | −0.178014 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.85758e12 | −1.35336 | ||||||||
\(499\) | 1.63150e11 | − | 2.82583e11i | 0.117797 | − | 0.204030i | −0.801097 | − | 0.598534i | \(-0.795750\pi\) |
0.918894 | + | 0.394504i | \(0.129084\pi\) | |||||||
\(500\) | −8.76377e11 | − | 1.51793e12i | −0.627084 | − | 1.08614i | ||||
\(501\) | 5.56733e11 | + | 9.64290e11i | 0.394800 | + | 0.683814i | ||||
\(502\) | −7.16870e11 | + | 1.24166e12i | −0.503818 | + | 0.872639i | ||||
\(503\) | 4.46869e11 | 0.311261 | 0.155630 | − | 0.987815i | \(-0.450259\pi\) | ||||
0.155630 | + | 0.987815i | \(0.450259\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.97103e11 | 0.203280 | ||||||||
\(506\) | −7.35398e11 | + | 1.27375e12i | −0.498707 | + | 0.863785i | ||||
\(507\) | −2.48028e10 | − | 4.29597e10i | −0.0166711 | − | 0.0288753i | ||||
\(508\) | −3.04166e11 | − | 5.26831e11i | −0.202639 | − | 0.350982i | ||||
\(509\) | 6.70502e11 | − | 1.16134e12i | 0.442761 | − | 0.766885i | −0.555132 | − | 0.831762i | \(-0.687332\pi\) |
0.997893 | + | 0.0648771i | \(0.0206655\pi\) | |||||||
\(510\) | −2.20136e12 | −1.44087 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.81189e12 | −1.16524 | ||||||||
\(513\) | 5.21299e11 | − | 9.02916e11i | 0.332322 | − | 0.575598i | ||||
\(514\) | −1.43072e12 | − | 2.47809e12i | −0.904111 | − | 1.56597i | ||||
\(515\) | −4.82772e11 | − | 8.36186e11i | −0.302420 | − | 0.523806i | ||||
\(516\) | 2.91579e11 | − | 5.05030e11i | 0.181064 | − | 0.313613i | ||||
\(517\) | 1.38259e12 | 0.851112 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.91089e11 | 0.599597 | ||||||||
\(520\) | 3.68708e11 | − | 6.38620e11i | 0.221140 | − | 0.383026i | ||||
\(521\) | 1.49262e12 | + | 2.58529e12i | 0.887520 | + | 1.53723i | 0.842798 | + | 0.538230i | \(0.180907\pi\) |
0.0447221 | + | 0.998999i | \(0.485760\pi\) | |||||||
\(522\) | −1.11114e12 | − | 1.92454e12i | −0.655013 | − | 1.13452i | ||||
\(523\) | 8.23253e11 | − | 1.42592e12i | 0.481145 | − | 0.833367i | −0.518621 | − | 0.855004i | \(-0.673554\pi\) |
0.999766 | + | 0.0216371i | \(0.00688783\pi\) | |||||||
\(524\) | −1.68812e12 | −0.978166 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.01470e10 | 0.0456511 | ||||||||
\(527\) | 4.04838e11 | − | 7.01200e11i | 0.228630 | − | 0.395999i | ||||
\(528\) | 4.65133e11 | + | 8.05634e11i | 0.260450 | + | 0.451113i | ||||
\(529\) | 7.07902e11 | + | 1.22612e12i | 0.393027 | + | 0.680743i | ||||
\(530\) | −1.37402e12 | + | 2.37988e12i | −0.756402 | + | 1.31013i | ||||
\(531\) | −1.45853e12 | −0.796141 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.15149e12 | −1.15470 | ||||||||
\(534\) | 2.00194e11 | − | 3.46746e11i | 0.106541 | − | 0.184534i | ||||
\(535\) | −3.27125e11 | − | 5.66597e11i | −0.172632 | − | 0.299008i | ||||
\(536\) | 1.96232e11 | + | 3.39884e11i | 0.102690 | + | 0.177864i | ||||
\(537\) | −2.90782e11 | + | 5.03649e11i | −0.150898 | + | 0.261363i | ||||
\(538\) | −2.20233e12 | −1.13334 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.45299e12 | 1.24143 | ||||||||
\(541\) | 2.28984e11 | − | 3.96612e11i | 0.114926 | − | 0.199057i | −0.802824 | − | 0.596216i | \(-0.796670\pi\) |
0.917750 | + | 0.397158i | \(0.130004\pi\) | |||||||
\(542\) | 2.40044e11 | + | 4.15768e11i | 0.119480 | + | 0.206945i | ||||
\(543\) | −5.06051e11 | − | 8.76506e11i | −0.249801 | − | 0.432669i | ||||
\(544\) | 2.34583e12 | − | 4.06310e12i | 1.14842 | − | 1.98913i | ||||
\(545\) | −7.41871e11 | −0.360200 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.39624e12 | 1.14443 | 0.572213 | − | 0.820105i | \(-0.306085\pi\) | ||||
0.572213 | + | 0.820105i | \(0.306085\pi\) | |||||||
\(548\) | 1.45468e12 | − | 2.51957e12i | 0.689055 | − | 1.19348i | ||||
\(549\) | −2.13435e11 | − | 3.69680e11i | −0.100274 | − | 0.173680i | ||||
\(550\) | 8.74244e10 | + | 1.51423e11i | 0.0407381 | + | 0.0705604i | ||||
\(551\) | −9.66539e11 | + | 1.67410e12i | −0.446722 | + | 0.773745i | ||||
\(552\) | 2.41686e11 | 0.110796 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.57166e12 | 1.15990 | ||||||||
\(555\) | 7.43246e11 | − | 1.28734e12i | 0.332517 | − | 0.575937i | ||||
\(556\) | −2.38579e12 | − | 4.13232e12i | −1.05876 | − | 1.83382i | ||||
\(557\) | −5.39315e11 | − | 9.34121e11i | −0.237407 | − | 0.411201i | 0.722562 | − | 0.691306i | \(-0.242964\pi\) |
−0.959970 | + | 0.280104i | \(0.909631\pi\) | |||||||
\(558\) | −3.24650e11 | + | 5.62311e11i | −0.141763 | + | 0.245540i | ||||
\(559\) | 1.18428e12 | 0.512983 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.13903e12 | −1.33802 | ||||||||
\(562\) | 1.63312e12 | − | 2.82865e12i | 0.690565 | − | 1.19609i | ||||
\(563\) | 1.16570e11 | + | 2.01905e11i | 0.0488988 | + | 0.0846952i | 0.889439 | − | 0.457054i | \(-0.151095\pi\) |
−0.840540 | + | 0.541749i | \(0.817762\pi\) | |||||||
\(564\) | −5.20067e11 | − | 9.00782e11i | −0.216423 | − | 0.374855i | ||||
\(565\) | 3.17209e11 | − | 5.49422e11i | 0.130957 | − | 0.226824i | ||||
\(566\) | 1.64939e12 | 0.675539 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.01624e12 | −0.409664 | ||||||||
\(569\) | −2.25267e11 | + | 3.90174e11i | −0.0900934 | + | 0.156046i | −0.907550 | − | 0.419943i | \(-0.862050\pi\) |
0.817457 | + | 0.575990i | \(0.195383\pi\) | |||||||
\(570\) | −7.67801e11 | − | 1.32987e12i | −0.304658 | − | 0.527682i | ||||
\(571\) | 2.19420e12 | + | 3.80046e12i | 0.863800 | + | 1.49615i | 0.868234 | + | 0.496155i | \(0.165255\pi\) |
−0.00443402 | + | 0.999990i | \(0.501411\pi\) | |||||||
\(572\) | 2.40703e12 | − | 4.16910e12i | 0.940155 | − | 1.62840i | ||||
\(573\) | 1.28667e12 | 0.498622 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.58104e10 | −0.0174767 | ||||||||
\(576\) | −1.30609e12 | + | 2.26221e12i | −0.494392 | + | 0.856313i | ||||
\(577\) | 1.56997e12 | + | 2.71927e12i | 0.589658 | + | 1.02132i | 0.994277 | + | 0.106832i | \(0.0340708\pi\) |
−0.404619 | + | 0.914485i | \(0.632596\pi\) | |||||||
\(578\) | 3.49039e12 | + | 6.04554e12i | 1.30077 | + | 2.25299i | ||||
\(579\) | 6.08665e11 | − | 1.05424e12i | 0.225074 | − | 0.389839i | ||||
\(580\) | −4.54808e12 | −1.66879 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.98333e12 | 1.07782 | ||||||||
\(583\) | −1.95928e12 | + | 3.39358e12i | −0.702407 | + | 1.21660i | ||||
\(584\) | 6.60587e11 | + | 1.14417e12i | 0.235002 | + | 0.407036i | ||||
\(585\) | 1.00615e12 | + | 1.74270e12i | 0.355190 | + | 0.615207i | ||||
\(586\) | 1.20840e12 | − | 2.09301e12i | 0.423323 | − | 0.733216i | ||||
\(587\) | −2.52512e12 | −0.877829 | −0.438915 | − | 0.898529i | \(-0.644637\pi\) | ||||
−0.438915 | + | 0.898529i | \(0.644637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.64805e11 | 0.193366 | ||||||||
\(590\) | −2.65901e12 | + | 4.60554e12i | −0.903412 | + | 1.56476i | ||||
\(591\) | −9.31416e11 | − | 1.61326e12i | −0.314051 | − | 0.543952i | ||||
\(592\) | 1.10385e12 | + | 1.91192e12i | 0.369370 | + | 0.639768i | ||||
\(593\) | −4.67708e11 | + | 8.10095e11i | −0.155321 | + | 0.269023i | −0.933176 | − | 0.359421i | \(-0.882974\pi\) |
0.777855 | + | 0.628444i | \(0.216308\pi\) | |||||||
\(594\) | 6.23165e12 | 2.05383 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.19261e12 | 1.03642 | ||||||||
\(597\) | −1.00996e12 | + | 1.74931e12i | −0.325403 | + | 0.563614i | ||||
\(598\) | 1.12354e12 | + | 1.94602e12i | 0.359279 | + | 0.622289i | ||||
\(599\) | −2.36793e12 | − | 4.10138e12i | −0.751534 | − | 1.30169i | −0.947079 | − | 0.321000i | \(-0.895981\pi\) |
0.195545 | − | 0.980695i | \(-0.437352\pi\) | |||||||
\(600\) | 1.43659e10 | − | 2.48824e10i | 0.00452533 | − | 0.00783811i | ||||
\(601\) | 5.99855e12 | 1.87548 | 0.937738 | − | 0.347344i | \(-0.112916\pi\) | ||||
0.937738 | + | 0.347344i | \(0.112916\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.07098e12 | −0.329877 | ||||||||
\(604\) | 2.82925e12 | − | 4.90040e12i | 0.864977 | − | 1.49818i | ||||
\(605\) | 1.74551e12 | + | 3.02332e12i | 0.529692 | + | 0.917454i | ||||
\(606\) | −2.83909e11 | − | 4.91744e11i | −0.0855169 | − | 0.148120i | ||||
\(607\) | 1.71857e12 | − | 2.97666e12i | 0.513830 | − | 0.889979i | −0.486041 | − | 0.873936i | \(-0.661560\pi\) |
0.999871 | − | 0.0160437i | \(-0.00510708\pi\) | |||||||
\(608\) | 3.27276e12 | 0.971287 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.55643e12 | −0.455141 | ||||||||
\(611\) | 1.05616e12 | − | 1.82932e12i | 0.306580 | − | 0.531011i | ||||
\(612\) | −2.48289e12 | − | 4.30049e12i | −0.715445 | − | 1.23919i | ||||
\(613\) | −2.07637e12 | − | 3.59637e12i | −0.593925 | − | 1.02871i | −0.993698 | − | 0.112094i | \(-0.964244\pi\) |
0.399772 | − | 0.916615i | \(-0.369089\pi\) | |||||||
\(614\) | −2.22900e12 | + | 3.86075e12i | −0.632926 | + | 1.09626i | ||||
\(615\) | −2.30244e12 | −0.649010 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.12196e12 | −0.311669 | −0.155834 | − | 0.987783i | \(-0.549807\pi\) | ||||
−0.155834 | + | 0.987783i | \(0.549807\pi\) | |||||||
\(618\) | −9.22666e11 | + | 1.59811e12i | −0.254447 | + | 0.440714i | ||||
\(619\) | −2.99470e12 | − | 5.18697e12i | −0.819871 | − | 1.42006i | −0.905777 | − | 0.423754i | \(-0.860712\pi\) |
0.0859067 | − | 0.996303i | \(-0.472621\pi\) | |||||||
\(620\) | 6.64426e11 | + | 1.15082e12i | 0.180586 | + | 0.312784i | ||||
\(621\) | −8.16346e11 | + | 1.41395e12i | −0.220273 | + | 0.381525i | ||||
\(622\) | 2.90969e12 | 0.779452 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.42125e12 | 0.375267 | ||||||||
\(625\) | 1.97669e12 | − | 3.42373e12i | 0.518178 | − | 0.897511i | ||||
\(626\) | 2.07956e12 | + | 3.60191e12i | 0.541237 | + | 0.937449i | ||||
\(627\) | −1.09484e12 | − | 1.89633e12i | −0.282910 | − | 0.490014i | ||||
\(628\) | −3.05982e12 | + | 5.29976e12i | −0.785013 | + | 1.35968i | ||||
\(629\) | −7.44951e12 | −1.89758 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.97135e12 | 1.24837 | 0.624184 | − | 0.781277i | \(-0.285432\pi\) | ||||
0.624184 | + | 0.781277i | \(0.285432\pi\) | |||||||
\(632\) | −1.26165e12 | + | 2.18525e12i | −0.314567 | + | 0.544846i | ||||
\(633\) | 3.67872e10 | + | 6.37172e10i | 0.00910709 | + | 0.0157739i | ||||
\(634\) | −3.66557e12 | − | 6.34895e12i | −0.901030 | − | 1.56063i | ||||
\(635\) | 6.61042e11 | − | 1.14496e12i | 0.161342 | − | 0.279453i | ||||
\(636\) | 2.94796e12 | 0.714439 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.15541e13 | −2.76085 | ||||||||
\(639\) | 1.38658e12 | − | 2.40163e12i | 0.328997 | − | 0.569839i | ||||
\(640\) | 1.75313e12 | + | 3.03651e12i | 0.413052 | + | 0.715426i | ||||
\(641\) | 1.20590e12 | + | 2.08869e12i | 0.282131 | + | 0.488666i | 0.971909 | − | 0.235355i | \(-0.0756253\pi\) |
−0.689778 | + | 0.724021i | \(0.742292\pi\) | |||||||
\(642\) | −6.25196e11 | + | 1.08287e12i | −0.145247 | + | 0.251576i | ||||
\(643\) | −6.86804e12 | −1.58447 | −0.792234 | − | 0.610217i | \(-0.791082\pi\) | ||||
−0.792234 | + | 0.610217i | \(0.791082\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.26738e12 | 0.288328 | ||||||||
\(646\) | −3.84781e12 | + | 6.66461e12i | −0.869296 | + | 1.50566i | ||||
\(647\) | −8.66968e11 | − | 1.50163e12i | −0.194506 | − | 0.336895i | 0.752232 | − | 0.658898i | \(-0.228977\pi\) |
−0.946739 | + | 0.322003i | \(0.895644\pi\) | |||||||
\(648\) | 1.29728e11 | + | 2.24695e11i | 0.0289032 | + | 0.0500618i | ||||
\(649\) | −3.79161e12 | + | 6.56726e12i | −0.838924 | + | 1.45306i | ||||
\(650\) | 2.67132e11 | 0.0586971 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.38014e12 | −0.299095 | ||||||||
\(653\) | −1.43220e10 | + | 2.48065e10i | −0.00308244 | + | 0.00533894i | −0.867563 | − | 0.497328i | \(-0.834315\pi\) |
0.864480 | + | 0.502667i | \(0.167648\pi\) | |||||||
\(654\) | 7.08925e11 | + | 1.22789e12i | 0.151531 | + | 0.262459i | ||||
\(655\) | −1.83439e12 | − | 3.17726e12i | −0.389409 | − | 0.674476i | ||||
\(656\) | 1.70976e12 | − | 2.96140e12i | 0.360470 | − | 0.624352i | ||||
\(657\) | −3.60529e12 | −0.754911 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.31728e12 | −1.30481 | −0.652403 | − | 0.757872i | \(-0.726239\pi\) | ||||
−0.652403 | + | 0.757872i | \(0.726239\pi\) | |||||||
\(660\) | 2.57591e12 | − | 4.46161e12i | 0.528425 | − | 0.915259i | ||||
\(661\) | −1.74779e12 | − | 3.02726e12i | −0.356109 | − | 0.616798i | 0.631199 | − | 0.775621i | \(-0.282563\pi\) |
−0.987307 | + | 0.158823i | \(0.949230\pi\) | |||||||
\(662\) | −9.36058e11 | − | 1.62130e12i | −0.189427 | − | 0.328097i | ||||
\(663\) | −2.39789e12 | + | 4.15327e12i | −0.481968 | + | 0.834794i | ||||
\(664\) | −3.33719e12 | −0.666231 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.97396e12 | 1.17660 | ||||||||
\(667\) | 1.51359e12 | − | 2.62161e12i | 0.296102 | − | 0.512863i | ||||
\(668\) | 4.57908e12 | + | 7.93120e12i | 0.889783 | + | 1.54115i | ||||
\(669\) | 2.66274e11 | + | 4.61200e11i | 0.0513938 | + | 0.0890167i | ||||
\(670\) | −1.95247e12 | + | 3.38178e12i | −0.374324 | + | 0.648349i | ||||
\(671\) | −2.21939e12 | −0.422652 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.02535e12 | −1.50798 | −0.753991 | − | 0.656885i | \(-0.771874\pi\) | ||||
−0.753991 | + | 0.656885i | \(0.771874\pi\) | |||||||
\(674\) | −4.00211e12 | + | 6.93185e12i | −0.746998 | + | 1.29384i | ||||
\(675\) | 9.70474e10 | + | 1.68091e11i | 0.0179936 | + | 0.0311658i | ||||
\(676\) | −2.04001e11 | − | 3.53340e11i | −0.0375727 | − | 0.0650777i | ||||
\(677\) | 5.85814e11 | − | 1.01466e12i | 0.107179 | − | 0.185640i | −0.807447 | − | 0.589940i | \(-0.799151\pi\) |
0.914626 | + | 0.404300i | \(0.132485\pi\) | |||||||
\(678\) | −1.21249e12 | −0.220366 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.95482e12 | −0.709311 | ||||||||
\(681\) | −1.92298e12 | + | 3.33070e12i | −0.342620 | + | 0.593435i | ||||
\(682\) | 1.68793e12 | + | 2.92358e12i | 0.298761 | + | 0.517470i | ||||
\(683\) | −2.34877e12 | − | 4.06819e12i | −0.412997 | − | 0.715333i | 0.582218 | − | 0.813032i | \(-0.302185\pi\) |
−0.995216 | + | 0.0976998i | \(0.968852\pi\) | |||||||
\(684\) | 1.73199e12 | − | 2.99989e12i | 0.302547 | − | 0.524026i | ||||
\(685\) | 6.32288e12 | 1.09726 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.86584e12 | 0.319572 | ||||||||
\(688\) | −9.41136e11 | + | 1.63009e12i | −0.160142 | + | 0.277373i | ||||
\(689\) | 2.99338e12 | + | 5.18468e12i | 0.506029 | + | 0.876467i | ||||
\(690\) | 1.20236e12 | + | 2.08256e12i | 0.201937 | + | 0.349765i | ||||
\(691\) | −3.91597e12 | + | 6.78265e12i | −0.653413 | + | 1.13174i | 0.328876 | + | 0.944373i | \(0.393330\pi\) |
−0.982289 | + | 0.187372i | \(0.940003\pi\) | |||||||
\(692\) | 8.15161e12 | 1.35134 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.17332e12 | −0.191998 | ||||||||
\(695\) | 5.18503e12 | − | 8.98074e12i | 0.842985 | − | 1.46009i | ||||
\(696\) | 9.49302e11 | + | 1.64424e12i | 0.153343 | + | 0.265597i | ||||
\(697\) | 5.76932e12 | + | 9.99275e12i | 0.925927 | + | 1.60375i | ||||
\(698\) | 3.64661e12 | − | 6.31612e12i | 0.581487 | − | 1.00717i | ||||
\(699\) | −2.62150e12 | −0.415339 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.13243e12 | 1.11559 | 0.557797 | − | 0.829977i | \(-0.311647\pi\) | ||||
0.557797 | + | 0.829977i | \(0.311647\pi\) | |||||||
\(702\) | 4.76033e12 | − | 8.24513e12i | 0.739810 | − | 1.28139i | ||||
\(703\) | −2.59827e12 | − | 4.50034e12i | −0.401223 | − | 0.694938i | ||||
\(704\) | 6.79065e12 | + | 1.17617e13i | 1.04192 | + | 1.80466i | ||||
\(705\) | 1.13026e12 | − | 1.95767e12i | 0.172317 | − | 0.298461i | ||||
\(706\) | 9.42486e12 | 1.42776 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.70491e12 | 0.853294 | ||||||||
\(709\) | −4.32637e12 | + | 7.49349e12i | −0.643007 | + | 1.11372i | 0.341751 | + | 0.939790i | \(0.388980\pi\) |
−0.984758 | + | 0.173930i | \(0.944353\pi\) | |||||||
\(710\) | −5.05569e12 | − | 8.75671e12i | −0.746651 | − | 1.29324i | ||||
\(711\) | −3.44287e12 | − | 5.96322e12i | −0.505251 | − | 0.875120i | ||||
\(712\) | 3.59655e11 | − | 6.22940e11i | 0.0524476 | − | 0.0908420i | ||||
\(713\) | −8.84475e11 | −0.128169 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.04624e13 | 1.49711 | ||||||||
\(716\) | −2.39165e12 | + | 4.14247e12i | −0.340087 | + | 0.589048i | ||||
\(717\) | −1.00344e12 | − | 1.73802e12i | −0.141794 | − | 0.245594i | ||||
\(718\) | −5.91421e12 | − | 1.02437e13i | −0.830495 | − | 1.43846i | ||||
\(719\) | 2.29223e11 | − | 3.97026e11i | 0.0319873 | − | 0.0554037i | −0.849589 | − | 0.527446i | \(-0.823150\pi\) |
0.881576 | + | 0.472042i | \(0.156483\pi\) | |||||||
\(720\) | −3.19829e12 | −0.443529 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.65565e12 | 0.774577 | ||||||||
\(723\) | 2.79089e12 | − | 4.83396e12i | 0.379857 | − | 0.657931i | ||||
\(724\) | −4.16222e12 | − | 7.20918e12i | −0.562991 | − | 0.975129i | ||||
\(725\) | −1.79935e11 | − | 3.11657e11i | −0.0241878 | − | 0.0418944i | ||||
\(726\) | 3.33599e12 | − | 5.77811e12i | 0.445667 | − | 0.771918i | ||||
\(727\) | 2.53850e12 | 0.337033 | 0.168517 | − | 0.985699i | \(-0.446102\pi\) | ||||
0.168517 | + | 0.985699i | \(0.446102\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.41521e12 | 0.447861 | ||||||||
\(730\) | −6.57271e12 | + | 1.13843e13i | −0.856627 | + | 1.48372i | ||||
\(731\) | −3.17571e12 | − | 5.50049e12i | −0.411351 | − | 0.712480i | ||||
\(732\) | 8.34832e11 | + | 1.44597e12i | 0.107473 | + | 0.186149i | ||||
\(733\) | 5.46805e12 | − | 9.47095e12i | 0.699624 | − | 1.21178i | −0.268972 | − | 0.963148i | \(-0.586684\pi\) |
0.968597 | − | 0.248637i | \(-0.0799826\pi\) | |||||||
\(734\) | 1.21907e13 | 1.55023 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.12509e12 | −0.643800 | ||||||||
\(737\) | −2.78412e12 | + | 4.82224e12i | −0.347604 | + | 0.602067i | ||||
\(738\) | −4.62657e12 | − | 8.01345e12i | −0.574124 | − | 0.994411i | ||||
\(739\) | −3.67498e12 | − | 6.36525e12i | −0.453268 | − | 0.785083i | 0.545319 | − | 0.838229i | \(-0.316409\pi\) |
−0.998587 | + | 0.0531455i | \(0.983075\pi\) | |||||||
\(740\) | 6.11313e12 | − | 1.05882e13i | 0.749412 | − | 1.29802i | ||||
\(741\) | −3.34539e12 | −0.407628 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.60813e12 | −0.193584 | −0.0967922 | − | 0.995305i | \(-0.530858\pi\) | ||||
−0.0967922 | + | 0.995305i | \(0.530858\pi\) | |||||||
\(744\) | 2.77366e11 | − | 4.80412e11i | 0.0331875 | − | 0.0574825i | ||||
\(745\) | 3.46924e12 | + | 6.00890e12i | 0.412602 | + | 0.714647i | ||||
\(746\) | 1.15100e13 | + | 1.99358e13i | 1.36066 | + | 2.35673i | ||||
\(747\) | 4.55335e12 | − | 7.88663e12i | 0.535043 | − | 0.926721i | ||||
\(748\) | −2.58182e13 | −3.01557 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.28018e12 | −0.840168 | ||||||||
\(751\) | 1.47952e12 | − | 2.56260e12i | 0.169723 | − | 0.293968i | −0.768600 | − | 0.639730i | \(-0.779046\pi\) |
0.938322 | + | 0.345762i | \(0.112379\pi\) | |||||||
\(752\) | 1.67863e12 | + | 2.90747e12i | 0.191414 | + | 0.331539i | ||||
\(753\) | 1.67131e12 | + | 2.89480e12i | 0.189444 | + | 0.328126i | ||||
\(754\) | −8.82612e12 | + | 1.52873e13i | −0.994486 | + | 1.72250i | ||||
\(755\) | 1.22976e13 | 1.37739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.83223e12 | −0.534830 | −0.267415 | − | 0.963581i | \(-0.586170\pi\) | ||||
−0.267415 | + | 0.963581i | \(0.586170\pi\) | |||||||
\(758\) | 1.00808e13 | − | 1.74604e13i | 1.10913 | − | 1.92107i | ||||
\(759\) | 1.71451e12 | + | 2.96962e12i | 0.187522 | + | 0.324797i | ||||
\(760\) | −1.37938e12 | − | 2.38915e12i | −0.149976 | − | 0.259766i | ||||
\(761\) | 1.57607e12 | − | 2.72982e12i | 0.170350 | − | 0.295056i | −0.768192 | − | 0.640220i | \(-0.778843\pi\) |
0.938542 | + | 0.345164i | \(0.112177\pi\) | |||||||
\(762\) | −2.52675e12 | −0.271496 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.05827e13 | 1.12377 | ||||||||
\(765\) | 5.39605e12 | − | 9.34624e12i | 0.569639 | − | 0.986644i | ||||
\(766\) | 2.71476e12 | + | 4.70211e12i | 0.284906 | + | 0.493472i | ||||
\(767\) | 5.79279e12 | + | 1.00334e13i | 0.604378 | + | 1.04681i | ||||
\(768\) | −6.42237e11 | + | 1.11239e12i | −0.0666146 | + | 0.115380i | ||||
\(769\) | 6.87650e12 | 0.709086 | 0.354543 | − | 0.935040i | \(-0.384636\pi\) | ||||
0.354543 | + | 0.935040i | \(0.384636\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.67118e12 | −0.679920 | ||||||||
\(772\) | 5.00621e12 | − | 8.67101e12i | 0.507261 | − | 0.878602i | ||||
\(773\) | 5.80414e12 | + | 1.00531e13i | 0.584696 | + | 1.01272i | 0.994913 | + | 0.100735i | \(0.0321194\pi\) |
−0.410218 | + | 0.911988i | \(0.634547\pi\) | |||||||
\(774\) | 2.54668e12 | + | 4.41099e12i | 0.255059 | + | 0.441775i | ||||
\(775\) | −5.25733e10 | + | 9.10597e10i | −0.00523489 | + | 0.00906710i | ||||
\(776\) | 5.35965e12 | 0.530590 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.28258e13 | 1.25510 | ||||||||
\(779\) | −4.02450e12 | + | 6.97063e12i | −0.391555 | + | 0.678193i | ||||
\(780\) | −3.93546e12 | − | 6.81641e12i | −0.380688 | − | 0.659371i | ||||
\(781\) | −7.20914e12 | − | 1.24866e13i | −0.693352 | − | 1.20092i | ||||
\(782\) | 6.02561e12 | − | 1.04367e13i | 0.576197 | − | 0.998002i | ||||
\(783\) | −1.28259e13 | −1.21944 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.32998e13 | −1.25006 | ||||||||
\(786\) | −3.50586e12 | + | 6.07232e12i | −0.327637 | + | 0.567484i | ||||
\(787\) | −1.25003e12 | − | 2.16511e12i | −0.116154 | − | 0.201184i | 0.802087 | − | 0.597208i | \(-0.203723\pi\) |
−0.918240 | + | 0.396024i | \(0.870390\pi\) | |||||||
\(788\) | −7.66081e12 | − | 1.32689e13i | −0.707794 | − | 1.22593i | ||||
\(789\) | 9.34274e10 | − | 1.61821e11i | 0.00858278 | − | 0.0148658i | ||||
\(790\) | −2.51064e13 | −2.29331 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.52236e12 | 0.408415 | ||||||||
\(793\) | −1.69538e12 | + | 2.93649e12i | −0.152244 | + | 0.263694i | ||||
\(794\) | 7.40489e12 | + | 1.28256e13i | 0.661190 | + | 1.14521i | ||||
\(795\) | 3.20340e12 | + | 5.54845e12i | 0.284419 | + | 0.492628i | ||||
\(796\) | −8.30685e12 | + | 1.43879e13i | −0.733377 | + | 1.27025i | ||||
\(797\) | −2.77023e12 | −0.243194 | −0.121597 | − | 0.992580i | \(-0.538802\pi\) | ||||
−0.121597 | + | 0.992580i | \(0.538802\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.13285e13 | −0.983360 | ||||||||
\(800\) | −3.04636e11 | + | 5.27645e11i | −0.0262952 | + | 0.0455446i | ||||
\(801\) | 9.81444e11 | + | 1.69991e12i | 0.0842402 | + | 0.145908i | ||||
\(802\) | −3.03715e12 | − | 5.26049e12i | −0.259228 | − | 0.448995i | ||||
\(803\) | −9.37234e12 | + | 1.62334e13i | −0.795478 | + | 1.37781i | ||||
\(804\) | 4.18903e12 | 0.353558 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.15761e12 | 0.430468 | ||||||||
\(807\) | −2.56726e12 | + | 4.44662e12i | −0.213078 | + | 0.369062i | ||||
\(808\) | −5.10051e11 | − | 8.83434e11i | −0.0420981 | − | 0.0729160i | ||||
\(809\) | 1.48320e12 | + | 2.56898e12i | 0.121739 | + | 0.210859i | 0.920454 | − | 0.390852i | \(-0.127819\pi\) |
−0.798714 | + | 0.601710i | \(0.794486\pi\) | |||||||
\(810\) | −1.29077e12 | + | 2.23568e12i | −0.105358 | + | 0.182485i | ||||
\(811\) | 9.01447e12 | 0.731722 | 0.365861 | − | 0.930669i | \(-0.380775\pi\) | ||||
0.365861 | + | 0.930669i | \(0.380775\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.11928e12 | 0.0898524 | ||||||||
\(814\) | 1.55300e13 | − | 2.68987e13i | 1.23983 | − | 2.14744i | ||||
\(815\) | −1.49973e12 | − | 2.59760e12i | −0.119070 | − | 0.206236i | ||||
\(816\) | −3.81115e12 | − | 6.60110e12i | −0.300919 | − | 0.521207i | ||||
\(817\) | 2.21527e12 | − | 3.83697e12i | 0.173952 | − | 0.301293i | ||||
\(818\) | −2.62325e13 | −2.04857 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.89374e13 | −1.46271 | ||||||||
\(821\) | −6.25882e12 | + | 1.08406e13i | −0.480782 | + | 0.832738i | −0.999757 | − | 0.0220510i | \(-0.992980\pi\) |
0.518975 | + | 0.854789i | \(0.326314\pi\) | |||||||
\(822\) | −6.04209e12 | − | 1.04652e13i | −0.461598 | − | 0.799512i | ||||
\(823\) | 7.51738e12 | + | 1.30205e13i | 0.571172 | + | 0.989300i | 0.996446 | + | 0.0842347i | \(0.0268445\pi\) |
−0.425274 | + | 0.905065i | \(0.639822\pi\) | |||||||
\(824\) | −1.65760e12 | + | 2.87105e12i | −0.125258 | + | 0.216954i | ||||
\(825\) | 4.07642e11 | 0.0306363 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.31522e13 | 1.72115 | 0.860574 | − | 0.509325i | \(-0.170105\pi\) | ||||
0.860574 | + | 0.509325i | \(0.170105\pi\) | |||||||
\(828\) | −2.71226e12 | + | 4.69778e12i | −0.200537 | + | 0.347341i | ||||
\(829\) | 2.44036e12 | + | 4.22682e12i | 0.179456 | + | 0.310827i | 0.941694 | − | 0.336470i | \(-0.109233\pi\) |
−0.762238 | + | 0.647296i | \(0.775900\pi\) | |||||||
\(830\) | −1.66022e13 | − | 2.87559e13i | −1.21427 | − | 2.10317i | ||||
\(831\) | 2.99778e12 | − | 5.19231e12i | 0.218070 | − | 0.377708i | ||||
\(832\) | 2.07494e13 | 1.50124 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.98191e13 | −1.41852 | ||||||||
\(835\) | −9.95169e12 | + | 1.72368e13i | −0.708448 | + | 1.22707i | ||||
\(836\) | −9.00499e12 | − | 1.55971e13i | −0.637610 | − | 1.10437i | ||||
\(837\) | 1.87372e12 | + | 3.24539e12i | 0.131960 | + | 0.228561i | ||||
\(838\) | −8.48177e12 | + | 1.46908e13i | −0.594139 | + | 1.02908i | ||||
\(839\) | 1.18015e13 | 0.822258 | 0.411129 | − | 0.911577i | \(-0.365135\pi\) | ||||
0.411129 | + | 0.911577i | \(0.365135\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.27330e12 | 0.639223 | ||||||||
\(842\) | −7.66121e12 | + | 1.32696e13i | −0.525283 | + | 0.909816i | ||||
\(843\) | −3.80746e12 | − | 6.59471e12i | −0.259664 | − | 0.449751i | ||||
\(844\) | 3.02571e11 | + | 5.24068e11i | 0.0205251 | + | 0.0355506i | ||||
\(845\) | 4.43354e11 | − | 7.67912e11i | 0.0299154 | − | 0.0518151i | ||||
\(846\) | 9.08464e12 | 0.609735 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.51520e12 | −0.631883 | ||||||||
\(849\) | 1.92270e12 | − | 3.33021e12i | 0.127007 | − | 0.219982i | ||||
\(850\) | −7.16327e11 | − | 1.24071e12i | −0.0470680 | − | 0.0815242i | ||||
\(851\) | 4.06885e12 | + | 7.04746e12i | 0.265943 | + | 0.460627i | ||||
\(852\) | −5.42349e12 | + | 9.39375e12i | −0.352615 | + | 0.610747i | ||||
\(853\) | 2.54707e13 | 1.64729 | 0.823646 | − | 0.567104i | \(-0.191936\pi\) | ||||
0.823646 | + | 0.567104i | \(0.191936\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.52824e12 | 0.481777 | ||||||||
\(856\) | −1.12318e12 | + | 1.94541e12i | −0.0715022 | + | 0.123845i | ||||
\(857\) | 6.32921e12 | + | 1.09625e13i | 0.400807 | + | 0.694219i | 0.993824 | − | 0.110972i | \(-0.0353963\pi\) |
−0.593016 | + | 0.805191i | \(0.702063\pi\) | |||||||
\(858\) | −9.99775e12 | − | 1.73166e13i | −0.629810 | − | 1.09086i | ||||
\(859\) | 1.00694e13 | − | 1.74406e13i | 0.631004 | − | 1.09293i | −0.356342 | − | 0.934355i | \(-0.615976\pi\) |
0.987347 | − | 0.158576i | \(-0.0506904\pi\) | |||||||
\(860\) | 1.04240e13 | 0.649820 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.66896e12 | 0.349720 | ||||||||
\(863\) | 7.24887e12 | − | 1.25554e13i | 0.444858 | − | 0.770517i | −0.553184 | − | 0.833059i | \(-0.686587\pi\) |
0.998042 | + | 0.0625420i | \(0.0199207\pi\) | |||||||
\(864\) | 1.08573e13 | + | 1.88054e13i | 0.662841 | + | 1.14807i | ||||
\(865\) | 8.85793e12 | + | 1.53424e13i | 0.537972 | + | 0.931795i | ||||
\(866\) | 7.01487e12 | − | 1.21501e13i | 0.423827 | − | 0.734090i | ||||
\(867\) | 1.62750e13 | 0.978217 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.58004e13 | −2.12961 | ||||||||
\(870\) | −9.44537e12 | + | 1.63599e13i | −0.558962 | + | 0.968151i | ||||
\(871\) | 4.25356e12 | + | 7.36738e12i | 0.250421 | + | 0.433742i | ||||
\(872\) | 1.27361e12 | + | 2.20595e12i | 0.0745953 | + | 0.129203i | ||||
\(873\) | −7.31284e12 | + | 1.26662e13i | −0.426110 | + | 0.738045i | ||||
\(874\) | 8.40656e12 | 0.487323 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.41018e13 | 0.809104 | ||||||||
\(877\) | −9.16483e12 | + | 1.58740e13i | −0.523150 | + | 0.906122i | 0.476487 | + | 0.879181i | \(0.341910\pi\) |
−0.999637 | + | 0.0269409i | \(0.991423\pi\) | |||||||
\(878\) | 5.62990e12 | + | 9.75126e12i | 0.319724 | + | 0.553778i | ||||
\(879\) | −2.81727e12 | − | 4.87965e12i | −0.159176 | − | 0.275701i | ||||
\(880\) | −8.31432e12 | + | 1.44008e13i | −0.467363 | + | 0.809497i | ||||
\(881\) | −4.57369e12 | −0.255785 | −0.127892 | − | 0.991788i | \(-0.540821\pi\) | ||||
−0.127892 | + | 0.991788i | \(0.540821\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.07854e13 | 1.70420 | 0.852101 | − | 0.523377i | \(-0.175328\pi\) | ||||
0.852101 | + | 0.523377i | \(0.175328\pi\) | |||||||
\(884\) | −1.97224e13 | + | 3.41602e13i | −1.08624 | + | 1.88142i | ||||
\(885\) | 6.19922e12 | + | 1.07374e13i | 0.339698 | + | 0.588373i | ||||
\(886\) | 8.69595e12 | + | 1.50618e13i | 0.474095 | + | 0.821157i | ||||
\(887\) | −1.29401e13 | + | 2.24130e13i | −0.701911 | + | 1.21575i | 0.265883 | + | 0.964005i | \(0.414336\pi\) |
−0.967795 | + | 0.251741i | \(0.918997\pi\) | |||||||
\(888\) | −5.10387e12 | −0.275449 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.15699e12 | 0.382363 | ||||||||
\(891\) | −1.84057e12 | + | 3.18796e12i | −0.0978368 | + | 0.169458i | ||||
\(892\) | 2.19008e12 | + | 3.79332e12i | 0.115829 | + | 0.200622i | ||||
\(893\) | −3.95121e12 | − | 6.84370e12i | −0.207921 | − | 0.360130i | ||||
\(894\) | 6.63035e12 | − | 1.14841e13i | 0.347150 | − | 0.601282i | ||||
\(895\) | −1.03955e13 | −0.541556 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.23882e12 | 0.270189 | ||||||||
\(898\) | 2.55530e13 | − | 4.42592e13i | 1.31129 | − | 2.27122i | ||||
\(899\) | −3.47407e12 | − | 6.01727e12i | −0.177386 | − | 0.307242i | ||||
\(900\) | 3.22435e11 | + | 5.58474e11i | 0.0163814 | + | 0.0283734i | ||||
\(901\) | 1.60537e13 | − | 2.78059e13i | 0.811549 | − | 1.40564i | ||||
\(902\) | −4.81091e13 | −2.41990 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.17827e12 | −0.108481 | ||||||||
\(905\) | 9.04573e12 | − | 1.56677e13i | 0.448255 | − | 0.776400i | ||||
\(906\) | −1.17515e13 | − | 2.03541e13i | −0.579449 | − | 1.00363i | ||||
\(907\) | −4.82059e12 | − | 8.34951e12i | −0.236520 | − | 0.409664i | 0.723193 | − | 0.690645i | \(-0.242673\pi\) |
−0.959713 | + | 0.280981i | \(0.909340\pi\) | |||||||
\(908\) | −1.58163e13 | + | 2.73947e13i | −0.772181 | + | 1.33746i | ||||
\(909\) | 2.78371e12 | 0.135234 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.28746e12 | 0.350545 | 0.175272 | − | 0.984520i | \(-0.443919\pi\) | ||||
0.175272 | + | 0.984520i | \(0.443919\pi\) | |||||||
\(912\) | 2.65854e12 | − | 4.60472e12i | 0.127252 | − | 0.220408i | ||||
\(913\) | −2.36739e13 | − | 4.10044e13i | −1.12759 | − | 1.95304i | ||||
\(914\) | 2.45835e13 | + | 4.25798e13i | 1.16516 | + | 2.01811i | ||||
\(915\) | −1.81434e12 | + | 3.14252e12i | −0.0855702 | + | 0.148212i | ||||
\(916\) | 1.53463e13 | 0.720236 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.10601e13 | −2.37295 | ||||||||
\(919\) | −1.36638e13 | + | 2.36664e13i | −0.631906 | + | 1.09449i | 0.355256 | + | 0.934769i | \(0.384394\pi\) |
−0.987162 | + | 0.159724i | \(0.948940\pi\) | |||||||
\(920\) | 2.16009e12 | + | 3.74138e12i | 0.0994090 | + | 0.172181i | ||||
\(921\) | 5.19670e12 | + | 9.00095e12i | 0.237990 | + | 0.412211i | ||||
\(922\) | 2.35279e13 | − | 4.07516e13i | 1.07225 | − | 1.85719i | ||||
\(923\) | −2.20281e13 | −0.999011 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.67413e11 | 0.0434484 | ||||||||
\(926\) | 3.01676e13 | − | 5.22519e13i | 1.34832 | − | 2.33535i | ||||
\(927\) | −4.52334e12 | − | 7.83466e12i | −0.201187 | − | 0.348467i | ||||
\(928\) | −2.01305e13 | − | 3.48670e13i | −0.891022 | − | 1.54329i | ||||
\(929\) | −3.60903e12 | + | 6.25101e12i | −0.158971 | + | 0.275347i | −0.934498 | − | 0.355968i | \(-0.884151\pi\) |
0.775527 | + | 0.631315i | \(0.217484\pi\) | |||||||
\(930\) | 5.51948e12 | 0.241949 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.15616e13 | −0.936071 | ||||||||
\(933\) | 3.39182e12 | − | 5.87481e12i | 0.146543 | − | 0.253820i | ||||
\(934\) | 2.00404e13 | + | 3.47110e13i | 0.861679 | + | 1.49247i | ||||
\(935\) | −2.80553e13 | − | 4.85932e13i | −1.20050 | − | 2.07933i | ||||
\(936\) | 3.45461e12 | − | 5.98356e12i | 0.147115 | − | 0.254811i | ||||
\(937\) | −1.41988e13 | −0.601761 | −0.300880 | − | 0.953662i | \(-0.597281\pi\) | ||||
−0.300880 | + | 0.953662i | \(0.597281\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.69658e12 | 0.407027 | ||||||||
\(940\) | 9.29627e12 | − | 1.61016e13i | 0.388359 | − | 0.672658i | ||||
\(941\) | −1.26621e13 | − | 2.19314e13i | −0.526445 | − | 0.911830i | −0.999525 | − | 0.0308103i | \(-0.990191\pi\) |
0.473080 | − | 0.881019i | \(-0.343142\pi\) | |||||||
\(942\) | 1.27091e13 | + | 2.20129e13i | 0.525881 | + | 0.910852i | ||||
\(943\) | 6.30230e12 | − | 1.09159e13i | 0.259535 | − | 0.449528i | ||||
\(944\) | −1.84138e13 | −0.754693 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.64816e13 | 1.07506 | ||||||||
\(947\) | 6.85800e12 | − | 1.18784e13i | 0.277091 | − | 0.479936i | −0.693570 | − | 0.720390i | \(-0.743963\pi\) |
0.970661 | + | 0.240454i | \(0.0772963\pi\) | |||||||
\(948\) | 1.34665e13 | + | 2.33246e13i | 0.541522 | + | 0.937943i | ||||
\(949\) | 1.43190e13 | + | 2.48012e13i | 0.573079 | + | 0.992602i | ||||
\(950\) | 4.99687e11 | − | 8.65484e11i | 0.0199041 | − | 0.0344749i | ||||
\(951\) | −1.70918e13 | −0.677604 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.44096e13 | 0.958610 | 0.479305 | − | 0.877648i | \(-0.340889\pi\) | ||||
0.479305 | + | 0.877648i | \(0.340889\pi\) | |||||||
\(954\) | −1.28739e13 | + | 2.22983e13i | −0.503203 | + | 0.871573i | ||||
\(955\) | 1.14997e13 | + | 1.99181e13i | 0.447375 | + | 0.774876i | ||||
\(956\) | −8.25324e12 | − | 1.42950e13i | −0.319568 | − | 0.553509i | ||||
\(957\) | −1.34686e13 | + | 2.33283e13i | −0.519062 | + | 0.899041i | ||||
\(958\) | −6.78892e13 | −2.60409 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.22052e13 | 0.843790 | ||||||||
\(961\) | 1.22048e13 | − | 2.11393e13i | 0.461609 | − | 0.799530i | ||||
\(962\) | −2.37266e13 | − | 4.10956e13i | −0.893197 | − | 1.54706i | ||||
\(963\) | −3.06500e12 | − | 5.30874e12i | −0.114845 | − | 0.198918i | ||||
\(964\) | 2.29548e13 | − | 3.97588e13i | 0.856104 | − | 1.48282i | ||||
\(965\) | 2.17600e13 | 0.807765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.19850e13 | −1.54410 | −0.772049 | − | 0.635563i | \(-0.780768\pi\) | ||||
−0.772049 | + | 0.635563i | \(0.780768\pi\) | |||||||
\(968\) | 5.99322e12 | − | 1.03806e13i | 0.219392 | − | 0.379998i | ||||
\(969\) | 8.97079e12 | + | 1.55379e13i | 0.326869 | + | 0.566154i | ||||
\(970\) | 2.66637e13 | + | 4.61830e13i | 0.967049 | + | 1.67498i | ||||
\(971\) | 1.56627e12 | − | 2.71286e12i | 0.0565432 | − | 0.0979357i | −0.836368 | − | 0.548168i | \(-0.815325\pi\) |
0.892911 | + | 0.450232i | \(0.148659\pi\) | |||||||
\(972\) | 3.66825e13 | 1.31814 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.21022e13 | 1.49896 | ||||||||
\(975\) | 3.11397e11 | − | 5.39355e11i | 0.0110355 | − | 0.0191141i | ||||
\(976\) | −2.69460e12 | − | 4.66719e12i | −0.0950540 | − | 0.164638i | ||||
\(977\) | −2.26562e13 | − | 3.92417e13i | −0.795539 | − | 1.37791i | −0.922496 | − | 0.386006i | \(-0.873854\pi\) |
0.126957 | − | 0.991908i | \(-0.459479\pi\) | |||||||
\(978\) | −2.86625e12 | + | 4.96450e12i | −0.100182 | + | 0.173520i | ||||
\(979\) | 1.02055e13 | 0.355068 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.95097e12 | −0.239626 | ||||||||
\(982\) | −3.48055e13 | + | 6.02848e13i | −1.19439 | + | 2.06874i | ||||
\(983\) | −1.27241e13 | − | 2.20387e13i | −0.434645 | − | 0.752828i | 0.562621 | − | 0.826715i | \(-0.309793\pi\) |
−0.997267 | + | 0.0738871i | \(0.976460\pi\) | |||||||
\(984\) | 3.95272e12 | + | 6.84632e12i | 0.134406 | + | 0.232798i | ||||
\(985\) | 1.66492e13 | − | 2.88373e13i | 0.563547 | − | 0.976092i | ||||
\(986\) | 9.46704e13 | 3.18983 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.75155e13 | −0.918694 | ||||||||
\(989\) | −3.46908e12 | + | 6.00863e12i | −0.115301 | + | 0.199706i | ||||
\(990\) | 2.24983e13 | + | 3.89682e13i | 0.744374 | + | 1.28929i | ||||
\(991\) | 2.70845e13 | + | 4.69118e13i | 0.892052 | + | 1.54508i | 0.837412 | + | 0.546573i | \(0.184068\pi\) |
0.0546399 | + | 0.998506i | \(0.482599\pi\) | |||||||
\(992\) | −5.88170e12 | + | 1.01874e13i | −0.192841 | + | 0.334011i | ||||
\(993\) | −4.36465e12 | −0.142455 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.61065e13 | −1.16783 | ||||||||
\(996\) | −1.78100e13 | + | 3.08479e13i | −0.573452 | + | 0.993249i | ||||
\(997\) | −2.14664e13 | − | 3.71810e13i | −0.688069 | − | 1.19177i | −0.972462 | − | 0.233062i | \(-0.925126\pi\) |
0.284393 | − | 0.958708i | \(-0.408208\pi\) | |||||||
\(998\) | −5.57363e12 | − | 9.65380e12i | −0.177849 | − | 0.308043i | ||||
\(999\) | 1.72394e13 | − | 2.98595e13i | 0.547618 | − | 0.948502i |
(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 | 49.10.c.e.30.3 | 6 | ||
7.2 | even | 3 | 49.10.a.c.1.1 | 3 | |||
7.3 | odd | 6 | 49.10.c.d.18.3 | 6 | |||
7.4 | even | 3 | inner | 49.10.c.e.18.3 | 6 | ||
7.5 | odd | 6 | 7.10.a.b.1.1 | ✓ | 3 | ||
7.6 | odd | 2 | 49.10.c.d.30.3 | 6 | |||
21.5 | even | 6 | 63.10.a.e.1.3 | 3 | |||
28.19 | even | 6 | 112.10.a.h.1.3 | 3 | |||
35.12 | even | 12 | 175.10.b.d.99.2 | 6 | |||
35.19 | odd | 6 | 175.10.a.d.1.3 | 3 | |||
35.33 | even | 12 | 175.10.b.d.99.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.10.a.b.1.1 | ✓ | 3 | 7.5 | odd | 6 | ||
49.10.a.c.1.1 | 3 | 7.2 | even | 3 | |||
49.10.c.d.18.3 | 6 | 7.3 | odd | 6 | |||
49.10.c.d.30.3 | 6 | 7.6 | odd | 2 | |||
49.10.c.e.18.3 | 6 | 7.4 | even | 3 | inner | ||
49.10.c.e.30.3 | 6 | 1.1 | even | 1 | trivial | ||
63.10.a.e.1.3 | 3 | 21.5 | even | 6 | |||
112.10.a.h.1.3 | 3 | 28.19 | even | 6 | |||
175.10.a.d.1.3 | 3 | 35.19 | odd | 6 | |||
175.10.b.d.99.2 | 6 | 35.12 | even | 12 | |||
175.10.b.d.99.5 | 6 | 35.33 | even | 12 |