Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,25,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 25, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 25);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 25 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8980291355\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9921984x^{6} + 31297402621425x^{4} + 35629505313218665424x^{2} + 11190322069687119538557504 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{53}\cdot 3^{32}\cdot 17^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(-2234.51i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.25.b.a.5.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2896.31i | − | 0.707107i | ||||||
\(3\) | −490828. | − | 203759.i | −0.923579 | − | 0.383409i | ||||
\(4\) | −8.38861e6 | −0.500000 | ||||||||
\(5\) | 1.24013e8i | 0.507958i | 0.967210 | + | 0.253979i | \(0.0817394\pi\) | ||||
−0.967210 | + | 0.253979i | \(0.918261\pi\) | |||||||
\(6\) | −5.90150e8 | + | 1.42159e9i | −0.271111 | + | 0.653069i | ||||
\(7\) | 1.50611e10 | 1.08813 | 0.544066 | − | 0.839043i | \(-0.316884\pi\) | ||||
0.544066 | + | 0.839043i | \(0.316884\pi\) | |||||||
\(8\) | 2.42960e10i | 0.353553i | ||||||||
\(9\) | 1.99394e11 | + | 2.00021e11i | 0.705995 | + | 0.708216i | ||||
\(10\) | 3.59180e11 | 0.359180 | ||||||||
\(11\) | − | 2.25660e12i | − | 0.719023i | −0.933141 | − | 0.359512i | \(-0.882943\pi\) | ||
0.933141 | − | 0.359512i | \(-0.117057\pi\) | |||||||
\(12\) | 4.11736e12 | + | 1.70926e12i | 0.461789 | + | 0.191704i | ||||
\(13\) | 4.78761e12 | 0.205494 | 0.102747 | − | 0.994708i | \(-0.467237\pi\) | ||||
0.102747 | + | 0.994708i | \(0.467237\pi\) | |||||||
\(14\) | − | 4.36217e13i | − | 0.769425i | ||||||
\(15\) | 2.52688e13 | − | 6.08691e13i | 0.194756 | − | 0.469139i | ||||
\(16\) | 7.03687e13 | 0.250000 | ||||||||
\(17\) | 5.31661e14i | 0.912531i | 0.889844 | + | 0.456265i | \(0.150813\pi\) | ||||
−0.889844 | + | 0.456265i | \(0.849187\pi\) | |||||||
\(18\) | 5.79323e14 | − | 5.77507e14i | 0.500785 | − | 0.499214i | ||||
\(19\) | −2.04629e15 | −0.924537 | −0.462269 | − | 0.886740i | \(-0.652964\pi\) | ||||
−0.462269 | + | 0.886740i | \(0.652964\pi\) | |||||||
\(20\) | − | 1.04030e15i | − | 0.253979i | ||||||
\(21\) | −7.39242e15 | − | 3.06885e15i | −1.00498 | − | 0.417199i | ||||
\(22\) | −6.53582e15 | −0.508426 | ||||||||
\(23\) | − | 3.16079e16i | − | 1.44232i | −0.692768 | − | 0.721161i | \(-0.743609\pi\) | ||
0.692768 | − | 0.721161i | \(-0.256391\pi\) | |||||||
\(24\) | 4.95053e15 | − | 1.19251e16i | 0.135555 | − | 0.326534i | ||||
\(25\) | 4.42254e16 | 0.741979 | ||||||||
\(26\) | − | 1.38664e16i | − | 0.145306i | ||||||
\(27\) | −5.71119e16 | − | 1.38804e17i | −0.380506 | − | 0.924779i | ||||
\(28\) | −1.26342e17 | −0.544066 | ||||||||
\(29\) | − | 6.82228e17i | − | 1.92821i | −0.265527 | − | 0.964103i | \(-0.585546\pi\) | ||
0.265527 | − | 0.964103i | \(-0.414454\pi\) | |||||||
\(30\) | −1.76296e17 | − | 7.31863e16i | −0.331731 | − | 0.137713i | ||||
\(31\) | −6.83154e17 | −0.867318 | −0.433659 | − | 0.901077i | \(-0.642778\pi\) | ||||
−0.433659 | + | 0.901077i | \(0.642778\pi\) | |||||||
\(32\) | − | 2.03810e17i | − | 0.176777i | ||||||
\(33\) | −4.59804e17 | + | 1.10760e18i | −0.275680 | + | 0.664075i | ||||
\(34\) | 1.53985e18 | 0.645257 | ||||||||
\(35\) | 1.86778e18i | 0.552725i | ||||||||
\(36\) | −1.67264e18 | − | 1.67790e18i | −0.352998 | − | 0.354108i | ||||
\(37\) | 9.74472e18 | 1.48030 | 0.740148 | − | 0.672444i | \(-0.234755\pi\) | ||||
0.740148 | + | 0.672444i | \(0.234755\pi\) | |||||||
\(38\) | 5.92669e18i | 0.653747i | ||||||||
\(39\) | −2.34989e18 | − | 9.75520e17i | −0.189790 | − | 0.0787882i | ||||
\(40\) | −3.01302e18 | −0.179590 | ||||||||
\(41\) | 1.91167e19i | 0.847242i | 0.905840 | + | 0.423621i | \(0.139241\pi\) | ||||
−0.905840 | + | 0.423621i | \(0.860759\pi\) | |||||||
\(42\) | −8.88833e18 | + | 2.14107e19i | −0.295004 | + | 0.710625i | ||||
\(43\) | 6.07042e19 | 1.51914 | 0.759569 | − | 0.650426i | \(-0.225410\pi\) | ||||
0.759569 | + | 0.650426i | \(0.225410\pi\) | |||||||
\(44\) | 1.89298e19i | 0.359512i | ||||||||
\(45\) | −2.48053e19 | + | 2.47275e19i | −0.359744 | + | 0.358616i | ||||
\(46\) | −9.15463e19 | −1.01988 | ||||||||
\(47\) | − | 1.14305e20i | − | 0.983766i | −0.870661 | − | 0.491883i | \(-0.836309\pi\) | ||
0.870661 | − | 0.491883i | \(-0.163691\pi\) | |||||||
\(48\) | −3.45389e19 | − | 1.43383e19i | −0.230895 | − | 0.0958522i | ||||
\(49\) | 3.52568e19 | 0.184030 | ||||||||
\(50\) | − | 1.28090e20i | − | 0.524658i | ||||||
\(51\) | 1.08331e20 | − | 2.60954e20i | 0.349872 | − | 0.842794i | ||||
\(52\) | −4.01614e19 | −0.102747 | ||||||||
\(53\) | − | 5.21591e20i | − | 1.06174i | −0.847452 | − | 0.530872i | \(-0.821864\pi\) | ||
0.847452 | − | 0.530872i | \(-0.178136\pi\) | |||||||
\(54\) | −4.02020e20 | + | 1.65414e20i | −0.653917 | + | 0.269058i | ||||
\(55\) | 2.79848e20 | 0.365233 | ||||||||
\(56\) | 3.65926e20i | 0.384713i | ||||||||
\(57\) | 1.00438e21 | + | 4.16951e20i | 0.853883 | + | 0.354476i | ||||
\(58\) | −1.97594e21 | −1.36345 | ||||||||
\(59\) | − | 5.99992e20i | − | 0.337226i | −0.985682 | − | 0.168613i | \(-0.946071\pi\) | ||
0.985682 | − | 0.168613i | \(-0.0539289\pi\) | |||||||
\(60\) | −2.11970e20 | + | 5.10607e20i | −0.0973778 | + | 0.234570i | ||||
\(61\) | 7.42263e19 | 0.0279640 | 0.0139820 | − | 0.999902i | \(-0.495549\pi\) | ||||
0.0139820 | + | 0.999902i | \(0.495549\pi\) | |||||||
\(62\) | 1.97862e21i | 0.613286i | ||||||||
\(63\) | 3.00310e21 | + | 3.01255e21i | 0.768216 | + | 0.770633i | ||||
\(64\) | −5.90296e20 | −0.125000 | ||||||||
\(65\) | 5.93727e20i | 0.104382i | ||||||||
\(66\) | 3.20796e21 | + | 1.33173e21i | 0.469572 | + | 0.194935i | ||||
\(67\) | 8.52972e21 | 1.04241 | 0.521203 | − | 0.853433i | \(-0.325483\pi\) | ||||
0.521203 | + | 0.853433i | \(0.325483\pi\) | |||||||
\(68\) | − | 4.45989e21i | − | 0.456265i | ||||||
\(69\) | −6.44041e21 | + | 1.55140e22i | −0.552999 | + | 1.33210i | ||||
\(70\) | 5.40967e21 | 0.390836 | ||||||||
\(71\) | − | 2.05121e22i | − | 1.25000i | −0.780625 | − | 0.624999i | \(-0.785099\pi\) | ||
0.780625 | − | 0.624999i | \(-0.214901\pi\) | |||||||
\(72\) | −4.85972e21 | + | 4.84448e21i | −0.250392 | + | 0.249607i | ||||
\(73\) | −3.58499e22 | −1.56536 | −0.782679 | − | 0.622425i | \(-0.786148\pi\) | ||||
−0.782679 | + | 0.622425i | \(0.786148\pi\) | |||||||
\(74\) | − | 2.82237e22i | − | 1.04673i | ||||||
\(75\) | −2.17070e22 | − | 9.01133e21i | −0.685276 | − | 0.284481i | ||||
\(76\) | 1.71655e22 | 0.462269 | ||||||||
\(77\) | − | 3.39870e22i | − | 0.782392i | ||||||
\(78\) | −2.82541e21 | + | 6.80602e21i | −0.0557116 | + | 0.134202i | ||||
\(79\) | 2.61248e22 | 0.442108 | 0.221054 | − | 0.975262i | \(-0.429050\pi\) | ||||
0.221054 | + | 0.975262i | \(0.429050\pi\) | |||||||
\(80\) | 8.72665e21i | 0.126989i | ||||||||
\(81\) | −2.50559e20 | + | 7.97660e22i | −0.00314115 | + | 0.999995i | ||||
\(82\) | 5.53680e22 | 0.599091 | ||||||||
\(83\) | − | 1.17460e23i | − | 1.09889i | −0.835530 | − | 0.549445i | \(-0.814839\pi\) | ||
0.835530 | − | 0.549445i | \(-0.185161\pi\) | |||||||
\(84\) | 6.20122e22 | + | 2.57433e22i | 0.502488 | + | 0.208600i | ||||
\(85\) | −6.59329e22 | −0.463527 | ||||||||
\(86\) | − | 1.75818e23i | − | 1.07419i | ||||||
\(87\) | −1.39010e23 | + | 3.34856e23i | −0.739291 | + | 1.78085i | ||||
\(88\) | 5.48264e22 | 0.254213 | ||||||||
\(89\) | 1.60364e23i | 0.649273i | 0.945839 | + | 0.324637i | \(0.105242\pi\) | ||||
−0.945839 | + | 0.324637i | \(0.894758\pi\) | |||||||
\(90\) | 7.16184e22 | + | 7.18437e22i | 0.253580 | + | 0.254377i | ||||
\(91\) | 7.21069e22 | 0.223604 | ||||||||
\(92\) | 2.65147e23i | 0.721161i | ||||||||
\(93\) | 3.35311e23 | + | 1.39199e23i | 0.801036 | + | 0.332537i | ||||
\(94\) | −3.31063e23 | −0.695628 | ||||||||
\(95\) | − | 2.53767e23i | − | 0.469626i | ||||||
\(96\) | −4.15281e22 | + | 1.00035e23i | −0.0677777 | + | 0.163267i | ||||
\(97\) | −8.32244e22 | −0.119947 | −0.0599736 | − | 0.998200i | \(-0.519102\pi\) | ||||
−0.0599736 | + | 0.998200i | \(0.519102\pi\) | |||||||
\(98\) | − | 1.02115e23i | − | 0.130129i | ||||||
\(99\) | 4.51369e23 | − | 4.49953e23i | 0.509224 | − | 0.507627i | ||||
\(100\) | −3.70989e23 | −0.370989 | ||||||||
\(101\) | − | 2.20951e24i | − | 1.96083i | −0.196945 | − | 0.980415i | \(-0.563102\pi\) | ||
0.196945 | − | 0.980415i | \(-0.436898\pi\) | |||||||
\(102\) | −7.55803e23 | − | 3.13759e23i | −0.595945 | − | 0.247397i | ||||
\(103\) | 3.85825e23 | 0.270610 | 0.135305 | − | 0.990804i | \(-0.456799\pi\) | ||||
0.135305 | + | 0.990804i | \(0.456799\pi\) | |||||||
\(104\) | 1.16320e23i | 0.0726530i | ||||||||
\(105\) | 3.80577e23 | − | 9.16758e23i | 0.211920 | − | 0.510485i | ||||
\(106\) | −1.51069e24 | −0.750767 | ||||||||
\(107\) | 3.07071e24i | 1.36343i | 0.731617 | + | 0.681716i | \(0.238766\pi\) | ||||
−0.731617 | + | 0.681716i | \(0.761234\pi\) | |||||||
\(108\) | 4.79089e23 | + | 1.16437e24i | 0.190253 | + | 0.462389i | ||||
\(109\) | 1.69282e24 | 0.601857 | 0.300929 | − | 0.953647i | \(-0.402703\pi\) | ||||
0.300929 | + | 0.953647i | \(0.402703\pi\) | |||||||
\(110\) | − | 8.10528e23i | − | 0.258259i | ||||||
\(111\) | −4.78298e24 | − | 1.98558e24i | −1.36717 | − | 0.567558i | ||||
\(112\) | 1.05983e24 | 0.272033 | ||||||||
\(113\) | 2.70784e24i | 0.624715i | 0.949965 | + | 0.312358i | \(0.101119\pi\) | ||||
−0.949965 | + | 0.312358i | \(0.898881\pi\) | |||||||
\(114\) | 1.20762e24 | − | 2.90899e24i | 0.250652 | − | 0.603786i | ||||
\(115\) | 3.91980e24 | 0.732638 | ||||||||
\(116\) | 5.72294e24i | 0.964103i | ||||||||
\(117\) | 9.54621e23 | + | 9.57624e23i | 0.145078 | + | 0.145534i | ||||
\(118\) | −1.73776e24 | −0.238455 | ||||||||
\(119\) | 8.00742e24i | 0.992954i | ||||||||
\(120\) | 1.47888e24 | + | 6.13931e23i | 0.165866 | + | 0.0688565i | ||||
\(121\) | 4.75748e24 | 0.483006 | ||||||||
\(122\) | − | 2.14982e23i | − | 0.0197736i | ||||||
\(123\) | 3.89521e24 | − | 9.38302e24i | 0.324840 | − | 0.782495i | ||||
\(124\) | 5.73071e24 | 0.433659 | ||||||||
\(125\) | 1.28763e25i | 0.884852i | ||||||||
\(126\) | 8.72527e24 | − | 8.69791e24i | 0.544920 | − | 0.543211i | ||||
\(127\) | −2.15801e25 | −1.22577 | −0.612886 | − | 0.790172i | \(-0.709991\pi\) | ||||
−0.612886 | + | 0.790172i | \(0.709991\pi\) | |||||||
\(128\) | 1.70968e24i | 0.0883883i | ||||||||
\(129\) | −2.97953e25 | − | 1.23690e25i | −1.40304 | − | 0.582451i | ||||
\(130\) | 1.71962e24 | 0.0738094 | ||||||||
\(131\) | − | 1.13650e25i | − | 0.444954i | −0.974938 | − | 0.222477i | \(-0.928586\pi\) | ||
0.974938 | − | 0.222477i | \(-0.0714143\pi\) | |||||||
\(132\) | 3.85711e24 | − | 9.29125e24i | 0.137840 | − | 0.332037i | ||||
\(133\) | −3.08195e25 | −1.00602 | ||||||||
\(134\) | − | 2.47047e25i | − | 0.737093i | ||||||
\(135\) | 1.72136e25 | − | 7.08262e24i | 0.469748 | − | 0.193281i | ||||
\(136\) | −1.29172e25 | −0.322628 | ||||||||
\(137\) | − | 1.38297e25i | − | 0.316349i | −0.987411 | − | 0.158175i | \(-0.949439\pi\) | ||
0.987411 | − | 0.158175i | \(-0.0505609\pi\) | |||||||
\(138\) | 4.49335e25 | + | 1.86534e25i | 0.941935 | + | 0.391029i | ||||
\(139\) | 6.91088e25 | 1.32848 | 0.664241 | − | 0.747518i | \(-0.268755\pi\) | ||||
0.664241 | + | 0.747518i | \(0.268755\pi\) | |||||||
\(140\) | − | 1.56681e25i | − | 0.276362i | ||||||
\(141\) | −2.32907e25 | + | 5.61042e25i | −0.377185 | + | 0.908586i | ||||
\(142\) | −5.94093e25 | −0.883882 | ||||||||
\(143\) | − | 1.08037e25i | − | 0.147755i | ||||||
\(144\) | 1.40311e25 | + | 1.40752e25i | 0.176499 | + | 0.177054i | ||||
\(145\) | 8.46052e25 | 0.979448 | ||||||||
\(146\) | 1.03832e26i | 1.10688i | ||||||||
\(147\) | −1.73050e25 | − | 7.18389e24i | −0.169967 | − | 0.0705589i | ||||
\(148\) | −8.17446e25 | −0.740148 | ||||||||
\(149\) | 1.45823e25i | 0.121785i | 0.998144 | + | 0.0608923i | \(0.0193946\pi\) | ||||
−0.998144 | + | 0.0608923i | \(0.980605\pi\) | |||||||
\(150\) | −2.60996e25 | + | 6.28703e25i | −0.201159 | + | 0.484563i | ||||
\(151\) | 1.28532e26 | 0.914720 | 0.457360 | − | 0.889282i | \(-0.348795\pi\) | ||||
0.457360 | + | 0.889282i | \(0.348795\pi\) | |||||||
\(152\) | − | 4.97167e25i | − | 0.326873i | ||||||
\(153\) | −1.06343e26 | + | 1.06010e26i | −0.646269 | + | 0.644242i | ||||
\(154\) | −9.84369e25 | −0.553235 | ||||||||
\(155\) | − | 8.47200e25i | − | 0.440561i | ||||||
\(156\) | 1.97123e25 | + | 8.18326e24i | 0.0948949 | + | 0.0393941i | ||||
\(157\) | 1.95529e26 | 0.871796 | 0.435898 | − | 0.899996i | \(-0.356431\pi\) | ||||
0.435898 | + | 0.899996i | \(0.356431\pi\) | |||||||
\(158\) | − | 7.56656e25i | − | 0.312617i | ||||||
\(159\) | −1.06279e26 | + | 2.56011e26i | −0.407082 | + | 0.980604i | ||||
\(160\) | 2.52751e25 | 0.0897951 | ||||||||
\(161\) | − | 4.76052e26i | − | 1.56944i | ||||||
\(162\) | 2.31027e26 | + | 7.25695e23i | 0.707103 | + | 0.00222113i | ||||
\(163\) | 1.44368e26 | 0.410413 | 0.205206 | − | 0.978719i | \(-0.434213\pi\) | ||||
0.205206 | + | 0.978719i | \(0.434213\pi\) | |||||||
\(164\) | − | 1.60363e26i | − | 0.423621i | ||||||
\(165\) | −1.37357e26 | − | 5.70217e25i | −0.337322 | − | 0.140034i | ||||
\(166\) | −3.40202e26 | −0.777033 | ||||||||
\(167\) | − | 4.74707e26i | − | 1.00885i | −0.863455 | − | 0.504426i | \(-0.831704\pi\) | ||
0.863455 | − | 0.504426i | \(-0.168296\pi\) | |||||||
\(168\) | 7.45607e25 | − | 1.79606e26i | 0.147502 | − | 0.355312i | ||||
\(169\) | −5.19880e26 | −0.957772 | ||||||||
\(170\) | 1.90962e26i | 0.327763i | ||||||||
\(171\) | −4.08018e26 | − | 4.09302e26i | −0.652719 | − | 0.654772i | ||||
\(172\) | −5.09224e26 | −0.759569 | ||||||||
\(173\) | 7.88219e26i | 1.09671i | 0.836244 | + | 0.548357i | \(0.184747\pi\) | ||||
−0.836244 | + | 0.548357i | \(0.815253\pi\) | |||||||
\(174\) | 9.69848e26 | + | 4.02617e26i | 1.25925 | + | 0.522758i | ||||
\(175\) | 6.66085e26 | 0.807371 | ||||||||
\(176\) | − | 1.58794e26i | − | 0.179756i | ||||||
\(177\) | −1.22254e26 | + | 2.94493e26i | −0.129296 | + | 0.311455i | ||||
\(178\) | 4.64465e26 | 0.459106 | ||||||||
\(179\) | 1.71671e27i | 1.58657i | 0.608847 | + | 0.793287i | \(0.291632\pi\) | ||||
−0.608847 | + | 0.793287i | \(0.708368\pi\) | |||||||
\(180\) | 2.08082e26 | − | 2.07429e26i | 0.179872 | − | 0.179308i | ||||
\(181\) | −6.59970e26 | −0.533804 | −0.266902 | − | 0.963724i | \(-0.586000\pi\) | ||||
−0.266902 | + | 0.963724i | \(0.586000\pi\) | |||||||
\(182\) | − | 2.08844e26i | − | 0.158112i | ||||||
\(183\) | −3.64323e25 | − | 1.51243e25i | −0.0258270 | − | 0.0107217i | ||||
\(184\) | 7.67946e26 | 0.509938 | ||||||||
\(185\) | 1.20847e27i | 0.751928i | ||||||||
\(186\) | 4.03163e26 | − | 9.71164e26i | 0.235139 | − | 0.566418i | ||||
\(187\) | 1.19975e27 | 0.656131 | ||||||||
\(188\) | 9.58862e26i | 0.491883i | ||||||||
\(189\) | −8.60170e26 | − | 2.09055e27i | −0.414040 | − | 1.00628i | ||||
\(190\) | −7.34988e26 | −0.332076 | ||||||||
\(191\) | − | 8.80733e26i | − | 0.373632i | −0.982395 | − | 0.186816i | \(-0.940183\pi\) | ||
0.982395 | − | 0.186816i | \(-0.0598168\pi\) | |||||||
\(192\) | 2.89733e26 | + | 1.20278e26i | 0.115447 | + | 0.0479261i | ||||
\(193\) | −1.65998e27 | −0.621461 | −0.310730 | − | 0.950498i | \(-0.600574\pi\) | ||||
−0.310730 | + | 0.950498i | \(0.600574\pi\) | |||||||
\(194\) | 2.41044e26i | 0.0848155i | ||||||||
\(195\) | 1.20977e26 | − | 2.91418e26i | 0.0400211 | − | 0.0964052i | ||||
\(196\) | −2.95755e26 | −0.0920152 | ||||||||
\(197\) | 2.80575e27i | 0.821209i | 0.911814 | + | 0.410604i | \(0.134682\pi\) | ||||
−0.911814 | + | 0.410604i | \(0.865318\pi\) | |||||||
\(198\) | −1.30320e27 | − | 1.30730e27i | −0.358947 | − | 0.360076i | ||||
\(199\) | 6.04163e27 | 1.56645 | 0.783226 | − | 0.621737i | \(-0.213573\pi\) | ||||
0.783226 | + | 0.621737i | \(0.213573\pi\) | |||||||
\(200\) | 1.07450e27i | 0.262329i | ||||||||
\(201\) | −4.18662e27 | − | 1.73801e27i | −0.962745 | − | 0.399668i | ||||
\(202\) | −6.39943e27 | −1.38652 | ||||||||
\(203\) | − | 1.02751e28i | − | 2.09814i | ||||||
\(204\) | −9.08744e26 | + | 2.18904e27i | −0.174936 | + | 0.421397i | ||||
\(205\) | −2.37073e27 | −0.430363 | ||||||||
\(206\) | − | 1.11747e27i | − | 0.191350i | ||||||
\(207\) | 6.32226e27 | − | 6.30243e27i | 1.02148 | − | 1.01827i | ||||
\(208\) | 3.36898e26 | 0.0513735 | ||||||||
\(209\) | 4.61767e27i | 0.664764i | ||||||||
\(210\) | −2.65521e27 | − | 1.10227e27i | −0.360967 | − | 0.149850i | ||||
\(211\) | 9.62629e27 | 1.23615 | 0.618073 | − | 0.786121i | \(-0.287914\pi\) | ||||
0.618073 | + | 0.786121i | \(0.287914\pi\) | |||||||
\(212\) | 4.37543e27i | 0.530872i | ||||||||
\(213\) | −4.17952e27 | + | 1.00679e28i | −0.479260 | + | 1.15447i | ||||
\(214\) | 8.89372e27 | 0.964092 | ||||||||
\(215\) | 7.52812e27i | 0.771658i | ||||||||
\(216\) | 3.37239e27 | − | 1.38759e27i | 0.326959 | − | 0.134529i | ||||
\(217\) | −1.02891e28 | −0.943756 | ||||||||
\(218\) | − | 4.90294e27i | − | 0.425577i | ||||||
\(219\) | 1.75961e28 | + | 7.30475e27i | 1.44573 | + | 0.600172i | ||||
\(220\) | −2.34754e27 | −0.182617 | ||||||||
\(221\) | 2.54539e27i | 0.187519i | ||||||||
\(222\) | −5.75084e27 | + | 1.38530e28i | −0.401324 | + | 0.966735i | ||||
\(223\) | −1.86863e28 | −1.23556 | −0.617782 | − | 0.786349i | \(-0.711969\pi\) | ||||
−0.617782 | + | 0.786349i | \(0.711969\pi\) | |||||||
\(224\) | − | 3.06961e27i | − | 0.192356i | ||||||
\(225\) | 8.81827e27 | + | 8.84602e27i | 0.523834 | + | 0.525482i | ||||
\(226\) | 7.84275e27 | 0.441741 | ||||||||
\(227\) | − | 1.80444e28i | − | 0.963901i | −0.876198 | − | 0.481951i | \(-0.839928\pi\) | ||
0.876198 | − | 0.481951i | \(-0.160072\pi\) | |||||||
\(228\) | −8.42532e27 | − | 3.49764e27i | −0.426941 | − | 0.177238i | ||||
\(229\) | −1.96660e28 | −0.945562 | −0.472781 | − | 0.881180i | \(-0.656750\pi\) | ||||
−0.472781 | + | 0.881180i | \(0.656750\pi\) | |||||||
\(230\) | − | 1.13529e28i | − | 0.518054i | ||||||
\(231\) | −6.92517e27 | + | 1.66818e28i | −0.299976 | + | 0.722601i | ||||
\(232\) | 1.65754e28 | 0.681724 | ||||||||
\(233\) | − | 3.90415e28i | − | 1.52495i | −0.647018 | − | 0.762474i | \(-0.723984\pi\) | ||
0.647018 | − | 0.762474i | \(-0.276016\pi\) | |||||||
\(234\) | 2.77358e27 | − | 2.76488e27i | 0.102908 | − | 0.102585i | ||||
\(235\) | 1.41754e28 | 0.499712 | ||||||||
\(236\) | 5.03310e27i | 0.168613i | ||||||||
\(237\) | −1.28228e28 | − | 5.32317e27i | −0.408321 | − | 0.169508i | ||||
\(238\) | 2.31920e28 | 0.702124 | ||||||||
\(239\) | 1.14900e28i | 0.330785i | 0.986228 | + | 0.165392i | \(0.0528891\pi\) | ||||
−0.986228 | + | 0.165392i | \(0.947111\pi\) | |||||||
\(240\) | 1.77813e27 | − | 4.28328e27i | 0.0486889 | − | 0.117285i | ||||
\(241\) | −2.26729e28 | −0.590612 | −0.295306 | − | 0.955403i | \(-0.595422\pi\) | ||||
−0.295306 | + | 0.955403i | \(0.595422\pi\) | |||||||
\(242\) | − | 1.37791e28i | − | 0.341537i | ||||||
\(243\) | 1.63760e28 | − | 3.91003e28i | 0.386308 | − | 0.922370i | ||||
\(244\) | −6.22655e26 | −0.0139820 | ||||||||
\(245\) | 4.37231e27i | 0.0934797i | ||||||||
\(246\) | −2.71761e28 | − | 1.12817e28i | −0.553307 | − | 0.229697i | ||||
\(247\) | −9.79685e27 | −0.189987 | ||||||||
\(248\) | − | 1.65979e28i | − | 0.306643i | ||||||
\(249\) | −2.39336e28 | + | 5.76528e28i | −0.421324 | + | 1.01491i | ||||
\(250\) | 3.72937e28 | 0.625685 | ||||||||
\(251\) | 2.74981e27i | 0.0439762i | 0.999758 | + | 0.0219881i | \(0.00699960\pi\) | ||||
−0.999758 | + | 0.0219881i | \(0.993000\pi\) | |||||||
\(252\) | −2.51918e28 | − | 2.52711e28i | −0.384108 | − | 0.385316i | ||||
\(253\) | −7.13265e28 | −1.03706 | ||||||||
\(254\) | 6.25027e28i | 0.866751i | ||||||||
\(255\) | 3.23617e28 | + | 1.34344e28i | 0.428104 | + | 0.177720i | ||||
\(256\) | 4.95176e27 | 0.0625000 | ||||||||
\(257\) | 1.14943e29i | 1.38447i | 0.721671 | + | 0.692236i | \(0.243374\pi\) | ||||
−0.721671 | + | 0.692236i | \(0.756626\pi\) | |||||||
\(258\) | −3.58246e28 | + | 8.62964e28i | −0.411855 | + | 0.992102i | ||||
\(259\) | 1.46767e29 | 1.61076 | ||||||||
\(260\) | − | 4.98054e27i | − | 0.0521911i | ||||||
\(261\) | 1.36460e29 | − | 1.36032e29i | 1.36559 | − | 1.36130i | ||||
\(262\) | −3.29167e28 | −0.314630 | ||||||||
\(263\) | 1.67988e28i | 0.153394i | 0.997054 | + | 0.0766970i | \(0.0244374\pi\) | ||||
−0.997054 | + | 0.0766970i | \(0.975563\pi\) | |||||||
\(264\) | −2.69103e28 | − | 1.11714e28i | −0.234786 | − | 0.0974675i | ||||
\(265\) | 6.46842e28 | 0.539321 | ||||||||
\(266\) | 8.92628e28i | 0.711362i | ||||||||
\(267\) | 3.26757e28 | − | 7.87112e28i | 0.248937 | − | 0.599655i | ||||
\(268\) | −7.15525e28 | −0.521203 | ||||||||
\(269\) | 7.11629e28i | 0.495708i | 0.968797 | + | 0.247854i | \(0.0797254\pi\) | ||||
−0.968797 | + | 0.247854i | \(0.920275\pi\) | |||||||
\(270\) | −2.05135e28 | − | 4.98558e28i | −0.136670 | − | 0.332162i | ||||
\(271\) | −8.35305e28 | −0.532370 | −0.266185 | − | 0.963922i | \(-0.585763\pi\) | ||||
−0.266185 | + | 0.963922i | \(0.585763\pi\) | |||||||
\(272\) | 3.74123e28i | 0.228133i | ||||||||
\(273\) | −3.53921e28 | − | 1.46924e28i | −0.206516 | − | 0.0857319i | ||||
\(274\) | −4.00552e28 | −0.223693 | ||||||||
\(275\) | − | 9.97991e28i | − | 0.533500i | ||||||
\(276\) | 5.40260e28 | − | 1.30141e29i | 0.276499 | − | 0.666049i | ||||
\(277\) | −1.50267e29 | −0.736389 | −0.368194 | − | 0.929749i | \(-0.620024\pi\) | ||||
−0.368194 | + | 0.929749i | \(0.620024\pi\) | |||||||
\(278\) | − | 2.00161e29i | − | 0.939379i | ||||||
\(279\) | −1.36217e29 | − | 1.36645e29i | −0.612322 | − | 0.614249i | ||||
\(280\) | −4.53796e28 | −0.195418 | ||||||||
\(281\) | − | 1.37645e29i | − | 0.567918i | −0.958836 | − | 0.283959i | \(-0.908352\pi\) | ||
0.958836 | − | 0.283959i | \(-0.0916479\pi\) | |||||||
\(282\) | 1.62495e29 | + | 6.74572e28i | 0.642467 | + | 0.266710i | ||||
\(283\) | −4.27935e28 | −0.162159 | −0.0810794 | − | 0.996708i | \(-0.525837\pi\) | ||||
−0.0810794 | + | 0.996708i | \(0.525837\pi\) | |||||||
\(284\) | 1.72068e29i | 0.624999i | ||||||||
\(285\) | −5.17074e28 | + | 1.24556e29i | −0.180059 | + | 0.433737i | ||||
\(286\) | −3.12910e28 | −0.104478 | ||||||||
\(287\) | 2.87920e29i | 0.921911i | ||||||||
\(288\) | 4.07663e28 | − | 4.06384e28i | 0.125196 | − | 0.124804i | ||||
\(289\) | 5.67855e28 | 0.167288 | ||||||||
\(290\) | − | 2.45043e29i | − | 0.692574i | ||||||
\(291\) | 4.08489e28 | + | 1.69577e28i | 0.110781 | + | 0.0459888i | ||||
\(292\) | 3.00731e29 | 0.782679 | ||||||||
\(293\) | − | 1.71498e29i | − | 0.428397i | −0.976790 | − | 0.214199i | \(-0.931286\pi\) | ||
0.976790 | − | 0.214199i | \(-0.0687140\pi\) | |||||||
\(294\) | −2.08068e28 | + | 5.01206e28i | −0.0498927 | + | 0.120185i | ||||
\(295\) | 7.44069e28 | 0.171297 | ||||||||
\(296\) | 2.36758e29i | 0.523364i | ||||||||
\(297\) | −3.13226e29 | + | 1.28879e29i | −0.664937 | + | 0.273593i | ||||
\(298\) | 4.22350e28 | 0.0861147 | ||||||||
\(299\) | − | 1.51327e29i | − | 0.296388i | ||||||
\(300\) | 1.82092e29 | + | 7.55925e28i | 0.342638 | + | 0.142241i | ||||
\(301\) | 9.14275e29 | 1.65302 | ||||||||
\(302\) | − | 3.72269e29i | − | 0.646805i | ||||||
\(303\) | −4.50208e29 | + | 1.08449e30i | −0.751799 | + | 1.81098i | ||||
\(304\) | −1.43995e29 | −0.231134 | ||||||||
\(305\) | 9.20503e27i | 0.0142045i | ||||||||
\(306\) | 3.07038e29 | + | 3.08004e29i | 0.455548 | + | 0.456981i | ||||
\(307\) | −9.60156e29 | −1.36988 | −0.684938 | − | 0.728601i | \(-0.740171\pi\) | ||||
−0.684938 | + | 0.728601i | \(0.740171\pi\) | |||||||
\(308\) | 2.85104e29i | 0.391196i | ||||||||
\(309\) | −1.89374e29 | − | 7.86154e28i | −0.249930 | − | 0.103754i | ||||
\(310\) | −2.45375e29 | −0.311523 | ||||||||
\(311\) | 1.83314e29i | 0.223909i | 0.993713 | + | 0.111955i | \(0.0357111\pi\) | ||||
−0.993713 | + | 0.111955i | \(0.964289\pi\) | |||||||
\(312\) | 2.37012e28 | − | 5.70930e28i | 0.0278558 | − | 0.0671008i | ||||
\(313\) | 1.66337e30 | 1.88130 | 0.940648 | − | 0.339385i | \(-0.110219\pi\) | ||||
0.940648 | + | 0.339385i | \(0.110219\pi\) | |||||||
\(314\) | − | 5.66312e29i | − | 0.616453i | ||||||
\(315\) | −3.73596e29 | + | 3.72424e29i | −0.391449 | + | 0.390221i | ||||
\(316\) | −2.19151e29 | −0.221054 | ||||||||
\(317\) | − | 5.50864e29i | − | 0.534975i | −0.963561 | − | 0.267487i | \(-0.913807\pi\) | ||
0.963561 | − | 0.267487i | \(-0.0861934\pi\) | |||||||
\(318\) | 7.41488e29 | + | 3.07817e29i | 0.693392 | + | 0.287851i | ||||
\(319\) | −1.53952e30 | −1.38643 | ||||||||
\(320\) | − | 7.32044e28i | − | 0.0634947i | ||||||
\(321\) | 6.25685e29 | − | 1.50719e30i | 0.522752 | − | 1.25924i | ||||
\(322\) | −1.37879e30 | −1.10976 | ||||||||
\(323\) | − | 1.08793e30i | − | 0.843669i | ||||||
\(324\) | 2.10184e27 | − | 6.69126e29i | 0.00157058 | − | 0.499998i | ||||
\(325\) | 2.11734e29 | 0.152472 | ||||||||
\(326\) | − | 4.18136e29i | − | 0.290206i | ||||||
\(327\) | −8.30884e29 | − | 3.44928e29i | −0.555862 | − | 0.230757i | ||||
\(328\) | −4.64460e29 | −0.299545 | ||||||||
\(329\) | − | 1.72157e30i | − | 1.07047i | ||||||
\(330\) | −1.65152e29 | + | 3.97829e29i | −0.0990188 | + | 0.238523i | ||||
\(331\) | 2.52531e30 | 1.46009 | 0.730045 | − | 0.683399i | \(-0.239499\pi\) | ||||
0.730045 | + | 0.683399i | \(0.239499\pi\) | |||||||
\(332\) | 9.85329e29i | 0.549445i | ||||||||
\(333\) | 1.94304e30 | + | 1.94915e30i | 1.04508 | + | 1.04837i | ||||
\(334\) | −1.37490e30 | −0.713366 | ||||||||
\(335\) | 1.05780e30i | 0.529499i | ||||||||
\(336\) | −5.20196e29 | − | 2.15951e29i | −0.251244 | − | 0.104300i | ||||
\(337\) | 6.18579e29 | 0.288295 | 0.144147 | − | 0.989556i | \(-0.453956\pi\) | ||||
0.144147 | + | 0.989556i | \(0.453956\pi\) | |||||||
\(338\) | 1.50573e30i | 0.677247i | ||||||||
\(339\) | 5.51748e29 | − | 1.32908e30i | 0.239521 | − | 0.576974i | ||||
\(340\) | 5.53085e29 | 0.231764 | ||||||||
\(341\) | 1.54161e30i | 0.623621i | ||||||||
\(342\) | −1.18546e30 | + | 1.18175e30i | −0.462994 | + | 0.461542i | ||||
\(343\) | −2.35442e30 | −0.887882 | ||||||||
\(344\) | 1.47487e30i | 0.537097i | ||||||||
\(345\) | −1.92395e30 | − | 7.98695e29i | −0.676649 | − | 0.280900i | ||||
\(346\) | 2.28292e30 | 0.775494 | ||||||||
\(347\) | 3.27882e30i | 1.07588i | 0.842983 | + | 0.537940i | \(0.180797\pi\) | ||||
−0.842983 | + | 0.537940i | \(0.819203\pi\) | |||||||
\(348\) | 1.16610e30 | − | 2.80898e30i | 0.369646 | − | 0.890425i | ||||
\(349\) | −1.23269e30 | −0.377527 | −0.188764 | − | 0.982023i | \(-0.560448\pi\) | ||||
−0.188764 | + | 0.982023i | \(0.560448\pi\) | |||||||
\(350\) | − | 1.92919e30i | − | 0.570897i | ||||||
\(351\) | −2.73430e29 | − | 6.64541e29i | −0.0781916 | − | 0.190036i | ||||
\(352\) | −4.59917e29 | −0.127107 | ||||||||
\(353\) | 5.25121e30i | 1.40269i | 0.712820 | + | 0.701347i | \(0.247418\pi\) | ||||
−0.712820 | + | 0.701347i | \(0.752582\pi\) | |||||||
\(354\) | 8.52942e29 | + | 3.54085e29i | 0.220232 | + | 0.0914258i | ||||
\(355\) | 2.54377e30 | 0.634946 | ||||||||
\(356\) | − | 1.34523e30i | − | 0.324637i | ||||||
\(357\) | 1.63158e30 | − | 3.93026e30i | 0.380707 | − | 0.917071i | ||||
\(358\) | 4.97212e30 | 1.12188 | ||||||||
\(359\) | 3.10562e30i | 0.677664i | 0.940847 | + | 0.338832i | \(0.110032\pi\) | ||||
−0.940847 | + | 0.338832i | \(0.889968\pi\) | |||||||
\(360\) | −6.00779e29 | − | 6.02669e29i | −0.126790 | − | 0.127189i | ||||
\(361\) | −7.11452e29 | −0.145231 | ||||||||
\(362\) | 1.91148e30i | 0.377456i | ||||||||
\(363\) | −2.33510e30 | − | 9.69379e29i | −0.446094 | − | 0.185189i | ||||
\(364\) | −6.04877e29 | −0.111802 | ||||||||
\(365\) | − | 4.44586e30i | − | 0.795136i | ||||||
\(366\) | −4.38046e28 | + | 1.05519e29i | −0.00758135 | + | 0.0182624i | ||||
\(367\) | −1.54480e30 | −0.258749 | −0.129374 | − | 0.991596i | \(-0.541297\pi\) | ||||
−0.129374 | + | 0.991596i | \(0.541297\pi\) | |||||||
\(368\) | − | 2.22421e30i | − | 0.360580i | ||||||
\(369\) | −3.82375e30 | + | 3.81176e30i | −0.600031 | + | 0.598149i | ||||
\(370\) | 3.50011e30 | 0.531693 | ||||||||
\(371\) | − | 7.85576e30i | − | 1.15532i | ||||||
\(372\) | −2.81279e30 | − | 1.16768e30i | −0.400518 | − | 0.166269i | ||||
\(373\) | −8.17121e30 | −1.12663 | −0.563314 | − | 0.826243i | \(-0.690474\pi\) | ||||
−0.563314 | + | 0.826243i | \(0.690474\pi\) | |||||||
\(374\) | − | 3.47484e30i | − | 0.463955i | ||||||
\(375\) | 2.62366e30 | − | 6.32004e30i | 0.339260 | − | 0.817230i | ||||
\(376\) | 2.77716e30 | 0.347814 | ||||||||
\(377\) | − | 3.26624e30i | − | 0.396235i | ||||||
\(378\) | −6.05488e30 | + | 2.49132e30i | −0.711548 | + | 0.292771i | ||||
\(379\) | −1.36135e31 | −1.54989 | −0.774944 | − | 0.632029i | \(-0.782222\pi\) | ||||
−0.774944 | + | 0.632029i | \(0.782222\pi\) | |||||||
\(380\) | 2.12875e30i | 0.234813i | ||||||||
\(381\) | 1.05921e31 | + | 4.39715e30i | 1.13210 | + | 0.469971i | ||||
\(382\) | −2.55087e30 | −0.264197 | ||||||||
\(383\) | 2.14155e29i | 0.0214953i | 0.999942 | + | 0.0107477i | \(0.00342115\pi\) | ||||
−0.999942 | + | 0.0107477i | \(0.996579\pi\) | |||||||
\(384\) | 3.48363e29 | − | 8.39158e29i | 0.0338889 | − | 0.0816336i | ||||
\(385\) | 4.21484e30 | 0.397422 | ||||||||
\(386\) | 4.80780e30i | 0.439439i | ||||||||
\(387\) | 1.21041e31 | + | 1.21421e31i | 1.07250 | + | 1.07588i | ||||
\(388\) | 6.98137e29 | 0.0599736 | ||||||||
\(389\) | 2.46642e30i | 0.205433i | 0.994711 | + | 0.102717i | \(0.0327535\pi\) | ||||
−0.994711 | + | 0.102717i | \(0.967246\pi\) | |||||||
\(390\) | −8.44035e29 | − | 3.50388e29i | −0.0681688 | − | 0.0282992i | ||||
\(391\) | 1.68047e31 | 1.31616 | ||||||||
\(392\) | 8.56599e29i | 0.0650646i | ||||||||
\(393\) | −2.31573e30 | + | 5.57828e30i | −0.170599 | + | 0.410950i | ||||
\(394\) | 8.12631e30 | 0.580682 | ||||||||
\(395\) | 3.23982e30i | 0.224572i | ||||||||
\(396\) | −3.78635e30 | + | 3.77448e30i | −0.254612 | + | 0.253814i | ||||
\(397\) | −1.20449e31 | −0.785809 | −0.392904 | − | 0.919579i | \(-0.628530\pi\) | ||||
−0.392904 | + | 0.919579i | \(0.628530\pi\) | |||||||
\(398\) | − | 1.74984e31i | − | 1.10765i | ||||||
\(399\) | 1.51271e31 | + | 6.27976e30i | 0.929137 | + | 0.385716i | ||||
\(400\) | 3.11208e30 | 0.185495 | ||||||||
\(401\) | − | 4.88143e30i | − | 0.282367i | −0.989983 | − | 0.141184i | \(-0.954909\pi\) | ||
0.989983 | − | 0.141184i | \(-0.0450908\pi\) | |||||||
\(402\) | −5.03381e30 | + | 1.21258e31i | −0.282608 | + | 0.680763i | ||||
\(403\) | −3.27068e30 | −0.178228 | ||||||||
\(404\) | 1.85347e31i | 0.980415i | ||||||||
\(405\) | −9.89204e30 | − | 3.10726e28i | −0.507955 | − | 0.00159557i | ||||
\(406\) | −2.97600e31 | −1.48361 | ||||||||
\(407\) | − | 2.19900e31i | − | 1.06437i | ||||||
\(408\) | 6.34013e30 | + | 2.63200e30i | 0.297973 | + | 0.123699i | ||||
\(409\) | 2.14098e31 | 0.977085 | 0.488543 | − | 0.872540i | \(-0.337529\pi\) | ||||
0.488543 | + | 0.872540i | \(0.337529\pi\) | |||||||
\(410\) | 6.86636e30i | 0.304313i | ||||||||
\(411\) | −2.81793e30 | + | 6.78801e30i | −0.121291 | + | 0.292173i | ||||
\(412\) | −3.23654e30 | −0.135305 | ||||||||
\(413\) | − | 9.03657e30i | − | 0.366947i | ||||||
\(414\) | −1.82538e31 | − | 1.83112e31i | −0.720027 | − | 0.722292i | ||||
\(415\) | 1.45666e31 | 0.558190 | ||||||||
\(416\) | − | 9.75762e29i | − | 0.0363265i | ||||||
\(417\) | −3.39205e31 | − | 1.40816e31i | −1.22696 | − | 0.509352i | ||||
\(418\) | 1.33742e31 | 0.470059 | ||||||||
\(419\) | − | 9.90044e28i | − | 0.00338132i | −0.999999 | − | 0.00169066i | \(-0.999462\pi\) | ||
0.999999 | − | 0.00169066i | \(-0.000538154\pi\) | |||||||
\(420\) | −3.19251e30 | + | 7.69032e30i | −0.105960 | + | 0.255243i | ||||
\(421\) | −1.38801e31 | −0.447720 | −0.223860 | − | 0.974621i | \(-0.571866\pi\) | ||||
−0.223860 | + | 0.974621i | \(0.571866\pi\) | |||||||
\(422\) | − | 2.78807e31i | − | 0.874087i | ||||||
\(423\) | 2.28635e31 | − | 2.27918e31i | 0.696720 | − | 0.694535i | ||||
\(424\) | 1.26726e31 | 0.375383 | ||||||||
\(425\) | 2.35129e31i | 0.677079i | ||||||||
\(426\) | 2.91597e31 | + | 1.21052e31i | 0.816335 | + | 0.338888i | ||||
\(427\) | 1.11793e30 | 0.0304285 | ||||||||
\(428\) | − | 2.57590e31i | − | 0.681716i | ||||||
\(429\) | −2.20136e30 | + | 5.30277e30i | −0.0566505 | + | 0.136463i | ||||
\(430\) | 2.18038e31 | 0.545645 | ||||||||
\(431\) | − | 4.58411e31i | − | 1.11565i | −0.829959 | − | 0.557824i | \(-0.811636\pi\) | ||
0.829959 | − | 0.557824i | \(-0.188364\pi\) | |||||||
\(432\) | −4.01889e30 | − | 9.76748e30i | −0.0951265 | − | 0.231195i | ||||
\(433\) | −6.04562e31 | −1.39183 | −0.695915 | − | 0.718124i | \(-0.745001\pi\) | ||||
−0.695915 | + | 0.718124i | \(0.745001\pi\) | |||||||
\(434\) | 2.98003e31i | 0.667336i | ||||||||
\(435\) | −4.15266e31 | − | 1.72391e31i | −0.904597 | − | 0.375529i | ||||
\(436\) | −1.42004e31 | −0.300929 | ||||||||
\(437\) | 6.46790e31i | 1.33348i | ||||||||
\(438\) | 2.11568e31 | − | 5.09638e31i | 0.424386 | − | 1.02229i | ||||
\(439\) | 4.04585e31 | 0.789652 | 0.394826 | − | 0.918756i | \(-0.370805\pi\) | ||||
0.394826 | + | 0.918756i | \(0.370805\pi\) | |||||||
\(440\) | 6.79920e30i | 0.129130i | ||||||||
\(441\) | 7.02999e30 | + | 7.05211e30i | 0.129925 | + | 0.130333i | ||||
\(442\) | 7.37223e30 | 0.132596 | ||||||||
\(443\) | 1.03672e32i | 1.81474i | 0.420329 | + | 0.907372i | \(0.361915\pi\) | ||||
−0.420329 | + | 0.907372i | \(0.638085\pi\) | |||||||
\(444\) | 4.01225e31 | + | 1.66562e31i | 0.683585 | + | 0.283779i | ||||
\(445\) | −1.98873e31 | −0.329803 | ||||||||
\(446\) | 5.41214e31i | 0.873676i | ||||||||
\(447\) | 2.97129e30 | − | 7.15742e30i | 0.0466933 | − | 0.112478i | ||||
\(448\) | −8.89053e30 | −0.136016 | ||||||||
\(449\) | 5.40229e31i | 0.804677i | 0.915491 | + | 0.402338i | \(0.131803\pi\) | ||||
−0.915491 | + | 0.402338i | \(0.868197\pi\) | |||||||
\(450\) | 2.56208e31 | − | 2.55404e31i | 0.371572 | − | 0.370406i | ||||
\(451\) | 4.31389e31 | 0.609187 | ||||||||
\(452\) | − | 2.27150e31i | − | 0.312358i | ||||||
\(453\) | −6.30871e31 | − | 2.61896e31i | −0.844816 | − | 0.350712i | ||||
\(454\) | −5.22622e31 | −0.681581 | ||||||||
\(455\) | 8.94221e30i | 0.113582i | ||||||||
\(456\) | −1.01302e31 | + | 2.44023e31i | −0.125326 | + | 0.301893i | ||||
\(457\) | 5.79920e31 | 0.698834 | 0.349417 | − | 0.936967i | \(-0.386380\pi\) | ||||
0.349417 | + | 0.936967i | \(0.386380\pi\) | |||||||
\(458\) | 5.69588e31i | 0.668613i | ||||||||
\(459\) | 7.37968e31 | − | 3.03641e31i | 0.843889 | − | 0.347223i | ||||
\(460\) | −3.28817e31 | −0.366319 | ||||||||
\(461\) | − | 5.22421e31i | − | 0.567034i | −0.958967 | − | 0.283517i | \(-0.908499\pi\) | ||
0.958967 | − | 0.283517i | \(-0.0915013\pi\) | |||||||
\(462\) | 4.83156e31 | + | 2.00574e31i | 0.510956 | + | 0.212115i | ||||
\(463\) | −2.10907e31 | −0.217330 | −0.108665 | − | 0.994078i | \(-0.534658\pi\) | ||||
−0.108665 | + | 0.994078i | \(0.534658\pi\) | |||||||
\(464\) | − | 4.80075e31i | − | 0.482052i | ||||||
\(465\) | −1.72625e31 | + | 4.15829e31i | −0.168915 | + | 0.406893i | ||||
\(466\) | −1.13076e32 | −1.07830 | ||||||||
\(467\) | − | 1.62891e32i | − | 1.51389i | −0.653479 | − | 0.756945i | \(-0.726691\pi\) | ||
0.653479 | − | 0.756945i | \(-0.273309\pi\) | |||||||
\(468\) | −8.00794e30 | − | 8.03314e30i | −0.0725389 | − | 0.0727671i | ||||
\(469\) | 1.28467e32 | 1.13428 | ||||||||
\(470\) | − | 4.10562e31i | − | 0.353350i | ||||||
\(471\) | −9.59709e31 | − | 3.98408e31i | −0.805172 | − | 0.334254i | ||||
\(472\) | 1.45774e31 | 0.119228 | ||||||||
\(473\) | − | 1.36985e32i | − | 1.09230i | ||||||
\(474\) | −1.54176e31 | + | 3.71387e31i | −0.119860 | + | 0.288727i | ||||
\(475\) | −9.04981e31 | −0.685987 | ||||||||
\(476\) | − | 6.71711e31i | − | 0.496477i | ||||||
\(477\) | 1.04329e32 | − | 1.04002e32i | 0.751945 | − | 0.749587i | ||||
\(478\) | 3.32786e31 | 0.233900 | ||||||||
\(479\) | 1.75158e32i | 1.20062i | 0.799769 | + | 0.600308i | \(0.204955\pi\) | ||||
−0.799769 | + | 0.600308i | \(0.795045\pi\) | |||||||
\(480\) | −1.24057e31 | − | 5.15003e30i | −0.0829328 | − | 0.0344282i | ||||
\(481\) | 4.66539e31 | 0.304192 | ||||||||
\(482\) | 6.56677e31i | 0.417626i | ||||||||
\(483\) | −9.69999e31 | + | 2.33659e32i | −0.601735 | + | 1.44950i | ||||
\(484\) | −3.99086e31 | −0.241503 | ||||||||
\(485\) | − | 1.03209e31i | − | 0.0609281i | ||||||
\(486\) | −1.13247e32 | − | 4.74301e31i | −0.652214 | − | 0.273161i | ||||
\(487\) | −7.23439e31 | −0.406494 | −0.203247 | − | 0.979127i | \(-0.565149\pi\) | ||||
−0.203247 | + | 0.979127i | \(0.565149\pi\) | |||||||
\(488\) | 1.80340e30i | 0.00988678i | ||||||||
\(489\) | −7.08600e31 | − | 2.94164e31i | −0.379049 | − | 0.157356i | ||||
\(490\) | 1.26635e31 | 0.0661001 | ||||||||
\(491\) | − | 1.04300e32i | − | 0.531260i | −0.964075 | − | 0.265630i | \(-0.914420\pi\) | ||
0.964075 | − | 0.265630i | \(-0.0855799\pi\) | |||||||
\(492\) | −3.26754e31 | + | 7.87105e31i | −0.162420 | + | 0.391247i | ||||
\(493\) | 3.62714e32 | 1.75955 | ||||||||
\(494\) | 2.83747e31i | 0.134341i | ||||||||
\(495\) | 5.58001e31 | + | 5.59756e31i | 0.257853 | + | 0.258664i | ||||
\(496\) | −4.80727e31 | −0.216829 | ||||||||
\(497\) | − | 3.08935e32i | − | 1.36016i | ||||||
\(498\) | 1.66980e32 | + | 6.93192e31i | 0.717651 | + | 0.297921i | ||||
\(499\) | −1.57053e32 | −0.658931 | −0.329466 | − | 0.944168i | \(-0.606869\pi\) | ||||
−0.329466 | + | 0.944168i | \(0.606869\pi\) | |||||||
\(500\) | − | 1.08014e32i | − | 0.442426i | ||||||
\(501\) | −9.67258e31 | + | 2.32999e32i | −0.386803 | + | 0.931755i | ||||
\(502\) | 7.96430e30 | 0.0310959 | ||||||||
\(503\) | 2.71086e32i | 1.03345i | 0.856151 | + | 0.516726i | \(0.172850\pi\) | ||||
−0.856151 | + | 0.516726i | \(0.827150\pi\) | |||||||
\(504\) | −7.31929e31 | + | 7.29633e31i | −0.272460 | + | 0.271605i | ||||
\(505\) | 2.74008e32 | 0.996019 | ||||||||
\(506\) | 2.06584e32i | 0.733314i | ||||||||
\(507\) | 2.55171e32 | + | 1.05930e32i | 0.884578 | + | 0.367218i | ||||
\(508\) | 1.81027e32 | 0.612886 | ||||||||
\(509\) | − | 2.32358e31i | − | 0.0768324i | −0.999262 | − | 0.0384162i | \(-0.987769\pi\) | ||
0.999262 | − | 0.0384162i | \(-0.0122313\pi\) | |||||||
\(510\) | 3.89103e31 | − | 9.37295e31i | 0.125667 | − | 0.302715i | ||||
\(511\) | −5.39941e32 | −1.70332 | ||||||||
\(512\) | − | 1.43418e31i | − | 0.0441942i | ||||||
\(513\) | 1.16868e32 | + | 2.84034e32i | 0.351792 | + | 0.854992i | ||||
\(514\) | 3.32910e32 | 0.978970 | ||||||||
\(515\) | 4.78474e31i | 0.137458i | ||||||||
\(516\) | 2.49941e32 | + | 1.03759e32i | 0.701522 | + | 0.291226i | ||||
\(517\) | −2.57942e32 | −0.707351 | ||||||||
\(518\) | − | 4.25081e32i | − | 1.13898i | ||||||
\(519\) | 1.60607e32 | − | 3.86879e32i | 0.420490 | − | 1.01290i | ||||
\(520\) | −1.44252e31 | −0.0369047 | ||||||||
\(521\) | 2.99413e32i | 0.748546i | 0.927319 | + | 0.374273i | \(0.122108\pi\) | ||||
−0.927319 | + | 0.374273i | \(0.877892\pi\) | |||||||
\(522\) | −3.93991e32 | − | 3.95231e32i | −0.962588 | − | 0.965616i | ||||
\(523\) | −5.02363e32 | −1.19949 | −0.599746 | − | 0.800190i | \(-0.704732\pi\) | ||||
−0.599746 | + | 0.800190i | \(0.704732\pi\) | |||||||
\(524\) | 9.53369e31i | 0.222477i | ||||||||
\(525\) | −3.26933e32 | − | 1.35721e32i | −0.745670 | − | 0.309553i | ||||
\(526\) | 4.86544e31 | 0.108466 | ||||||||
\(527\) | − | 3.63206e32i | − | 0.791454i | ||||||
\(528\) | −3.23558e31 | + | 7.79406e31i | −0.0689200 | + | 0.166019i | ||||
\(529\) | −5.18810e32 | −1.08029 | ||||||||
\(530\) | − | 1.87345e32i | − | 0.381358i | ||||||
\(531\) | 1.20011e32 | − | 1.19635e32i | 0.238829 | − | 0.238080i | ||||
\(532\) | 2.58533e32 | 0.503009 | ||||||||
\(533\) | 9.15235e31i | 0.174103i | ||||||||
\(534\) | −2.27972e32 | − | 9.46389e31i | −0.424020 | − | 0.176025i | ||||
\(535\) | −3.80808e32 | −0.692566 | ||||||||
\(536\) | 2.07238e32i | 0.368546i | ||||||||
\(537\) | 3.49795e32 | − | 8.42609e32i | 0.608307 | − | 1.46533i | ||||
\(538\) | 2.06110e32 | 0.350519 | ||||||||
\(539\) | − | 7.95606e31i | − | 0.132322i | ||||||
\(540\) | −1.44398e32 | + | 5.94134e31i | −0.234874 | + | 0.0966405i | ||||
\(541\) | 1.14877e33 | 1.82754 | 0.913768 | − | 0.406236i | \(-0.133159\pi\) | ||||
0.913768 | + | 0.406236i | \(0.133159\pi\) | |||||||
\(542\) | 2.41930e32i | 0.376443i | ||||||||
\(543\) | 3.23932e32 | + | 1.34475e32i | 0.493010 | + | 0.204665i | ||||
\(544\) | 1.08358e32 | 0.161314 | ||||||||
\(545\) | 2.09932e32i | 0.305718i | ||||||||
\(546\) | −4.25539e31 | + | 1.02506e32i | −0.0606216 | + | 0.146029i | ||||
\(547\) | 2.72421e32 | 0.379658 | 0.189829 | − | 0.981817i | \(-0.439207\pi\) | ||||
0.189829 | + | 0.981817i | \(0.439207\pi\) | |||||||
\(548\) | 1.16012e32i | 0.158175i | ||||||||
\(549\) | 1.48003e31 | + | 1.48468e31i | 0.0197425 | + | 0.0198046i | ||||
\(550\) | −2.89049e32 | −0.377241 | ||||||||
\(551\) | 1.39604e33i | 1.78270i | ||||||||
\(552\) | −3.76929e32 | − | 1.56476e32i | −0.470967 | − | 0.195515i | ||||
\(553\) | 3.93470e32 | 0.481072 | ||||||||
\(554\) | 4.35221e32i | 0.520706i | ||||||||
\(555\) | 2.46237e32 | − | 5.93152e32i | 0.288296 | − | 0.694465i | ||||
\(556\) | −5.79727e32 | −0.664241 | ||||||||
\(557\) | − | 3.73854e32i | − | 0.419218i | −0.977785 | − | 0.209609i | \(-0.932781\pi\) | ||
0.977785 | − | 0.209609i | \(-0.0672191\pi\) | |||||||
\(558\) | −3.95767e32 | + | 3.94526e32i | −0.434339 | + | 0.432977i | ||||
\(559\) | 2.90628e32 | 0.312174 | ||||||||
\(560\) | 1.31433e32i | 0.138181i | ||||||||
\(561\) | −5.88869e32 | − | 2.44459e32i | −0.605988 | − | 0.251566i | ||||
\(562\) | −3.98663e32 | −0.401578 | ||||||||
\(563\) | − | 3.96278e32i | − | 0.390751i | −0.980729 | − | 0.195375i | \(-0.937408\pi\) | ||
0.980729 | − | 0.195375i | \(-0.0625925\pi\) | |||||||
\(564\) | 1.95377e32 | − | 4.70636e32i | 0.188592 | − | 0.454293i | ||||
\(565\) | −3.35808e32 | −0.317329 | ||||||||
\(566\) | 1.23943e32i | 0.114664i | ||||||||
\(567\) | −3.77370e30 | + | 1.20137e33i | −0.00341799 | + | 1.08813i | ||||
\(568\) | 4.98361e32 | 0.441941 | ||||||||
\(569\) | 1.91705e33i | 1.66451i | 0.554395 | + | 0.832254i | \(0.312950\pi\) | ||||
−0.554395 | + | 0.832254i | \(0.687050\pi\) | |||||||
\(570\) | 3.60752e32 | + | 1.49761e32i | 0.306698 | + | 0.127321i | ||||
\(571\) | 7.07277e32 | 0.588784 | 0.294392 | − | 0.955685i | \(-0.404883\pi\) | ||||
0.294392 | + | 0.955685i | \(0.404883\pi\) | |||||||
\(572\) | 9.06284e31i | 0.0738774i | ||||||||
\(573\) | −1.79457e32 | + | 4.32288e32i | −0.143254 | + | 0.345078i | ||||
\(574\) | 8.33905e32 | 0.651889 | ||||||||
\(575\) | − | 1.39787e33i | − | 1.07017i | ||||||
\(576\) | −1.17701e32 | − | 1.18072e32i | −0.0882494 | − | 0.0885271i | ||||
\(577\) | −5.60843e32 | −0.411843 | −0.205921 | − | 0.978569i | \(-0.566019\pi\) | ||||
−0.205921 | + | 0.978569i | \(0.566019\pi\) | |||||||
\(578\) | − | 1.64468e32i | − | 0.118290i | ||||||
\(579\) | 8.14762e32 | + | 3.38235e32i | 0.573968 | + | 0.238274i | ||||
\(580\) | −7.09720e32 | −0.489724 | ||||||||
\(581\) | − | 1.76909e33i | − | 1.19574i | ||||||
\(582\) | 4.91149e31 | − | 1.18311e32i | 0.0325190 | − | 0.0783338i | ||||
\(583\) | −1.17702e33 | −0.763419 | ||||||||
\(584\) | − | 8.71010e32i | − | 0.553438i | ||||||
\(585\) | −1.18758e32 | + | 1.18386e32i | −0.0739252 | + | 0.0736934i | ||||
\(586\) | −4.96710e32 | −0.302923 | ||||||||
\(587\) | − | 1.55484e33i | − | 0.929027i | −0.885566 | − | 0.464514i | \(-0.846229\pi\) | ||
0.885566 | − | 0.464514i | \(-0.153771\pi\) | |||||||
\(588\) | 1.45165e32 | + | 6.02629e31i | 0.0849833 | + | 0.0352795i | ||||
\(589\) | 1.39793e33 | 0.801867 | ||||||||
\(590\) | − | 2.15506e32i | − | 0.121125i | ||||||
\(591\) | 5.71696e32 | − | 1.37714e33i | 0.314859 | − | 0.758451i | ||||
\(592\) | 6.85723e32 | 0.370074 | ||||||||
\(593\) | − | 8.57869e32i | − | 0.453696i | −0.973930 | − | 0.226848i | \(-0.927158\pi\) | ||
0.973930 | − | 0.226848i | \(-0.0728420\pi\) | |||||||
\(594\) | 3.73273e32 | + | 9.07200e32i | 0.193459 | + | 0.470182i | ||||
\(595\) | −9.93025e32 | −0.504379 | ||||||||
\(596\) | − | 1.22326e32i | − | 0.0608923i | ||||||
\(597\) | −2.96540e33 | − | 1.23104e33i | −1.44674 | − | 0.600592i | ||||
\(598\) | −4.38288e32 | −0.209578 | ||||||||
\(599\) | 1.41388e33i | 0.662658i | 0.943515 | + | 0.331329i | \(0.107497\pi\) | ||||
−0.943515 | + | 0.331329i | \(0.892503\pi\) | |||||||
\(600\) | 2.18939e32 | − | 5.27394e32i | 0.100579 | − | 0.242282i | ||||
\(601\) | −1.65022e33 | −0.743103 | −0.371552 | − | 0.928412i | \(-0.621174\pi\) | ||||
−0.371552 | + | 0.928412i | \(0.621174\pi\) | |||||||
\(602\) | − | 2.64802e33i | − | 1.16886i | ||||||
\(603\) | 1.70077e33 | + | 1.70613e33i | 0.735934 | + | 0.738250i | ||||
\(604\) | −1.07821e33 | −0.457360 | ||||||||
\(605\) | 5.89990e32i | 0.245346i | ||||||||
\(606\) | 3.14102e33 | + | 1.30394e33i | 1.28056 | + | 0.531602i | ||||
\(607\) | −2.77181e33 | −1.10790 | −0.553948 | − | 0.832552i | \(-0.686879\pi\) | ||||
−0.553948 | + | 0.832552i | \(0.686879\pi\) | |||||||
\(608\) | 4.17054e32i | 0.163437i | ||||||||
\(609\) | −2.09365e33 | + | 5.04332e33i | −0.804446 | + | 1.93780i | ||||
\(610\) | 2.66606e31 | 0.0100441 | ||||||||
\(611\) | − | 5.47249e32i | − | 0.202158i | ||||||
\(612\) | 8.92073e32 | − | 8.89276e32i | 0.323135 | − | 0.322121i | ||||
\(613\) | 3.92257e33 | 1.39330 | 0.696651 | − | 0.717410i | \(-0.254673\pi\) | ||||
0.696651 | + | 0.717410i | \(0.254673\pi\) | |||||||
\(614\) | 2.78091e33i | 0.968649i | ||||||||
\(615\) | 1.16362e33 | + | 4.83057e32i | 0.397474 | + | 0.165005i | ||||
\(616\) | 8.25749e32 | 0.276617 | ||||||||
\(617\) | − | 2.49852e33i | − | 0.820844i | −0.911896 | − | 0.410422i | \(-0.865381\pi\) | ||
0.911896 | − | 0.410422i | \(-0.134619\pi\) | |||||||
\(618\) | −2.27695e32 | + | 5.48485e32i | −0.0733654 | + | 0.176727i | ||||
\(619\) | 3.36013e33 | 1.06186 | 0.530931 | − | 0.847415i | \(-0.321842\pi\) | ||||
0.530931 | + | 0.847415i | \(0.321842\pi\) | |||||||
\(620\) | 7.10683e32i | 0.220280i | ||||||||
\(621\) | −4.38732e33 | + | 1.80519e33i | −1.33383 | + | 0.548812i | ||||
\(622\) | 5.30935e32 | 0.158328 | ||||||||
\(623\) | 2.41527e33i | 0.706495i | ||||||||
\(624\) | −1.65359e32 | − | 6.86461e31i | −0.0474474 | − | 0.0196970i | ||||
\(625\) | 1.03921e33 | 0.292511 | ||||||||
\(626\) | − | 4.81764e33i | − | 1.33028i | ||||||
\(627\) | 9.40892e32 | − | 2.26648e33i | 0.254876 | − | 0.613962i | ||||
\(628\) | −1.64021e33 | −0.435898 | ||||||||
\(629\) | 5.18088e33i | 1.35082i | ||||||||
\(630\) | 1.07865e33 | + | 1.08205e33i | 0.275928 | + | 0.276796i | ||||
\(631\) | 4.71285e33 | 1.18285 | 0.591427 | − | 0.806359i | \(-0.298565\pi\) | ||||
0.591427 | + | 0.806359i | \(0.298565\pi\) | |||||||
\(632\) | 6.34729e32i | 0.156309i | ||||||||
\(633\) | −4.72485e33 | − | 1.96145e33i | −1.14168 | − | 0.473949i | ||||
\(634\) | −1.59547e33 | −0.378284 | ||||||||
\(635\) | − | 2.67622e33i | − | 0.622640i | ||||||
\(636\) | 8.91533e32 | − | 2.14758e33i | 0.203541 | − | 0.490302i | ||||
\(637\) | 1.68796e32 | 0.0378171 | ||||||||
\(638\) | 4.45892e33i | 0.980351i | ||||||||
\(639\) | 4.10285e33 | − | 4.08998e33i | 0.885269 | − | 0.882493i | ||||
\(640\) | −2.12023e32 | −0.0448976 | ||||||||
\(641\) | 4.12036e33i | 0.856326i | 0.903702 | + | 0.428163i | \(0.140839\pi\) | ||||
−0.903702 | + | 0.428163i | \(0.859161\pi\) | |||||||
\(642\) | −4.36529e33 | − | 1.81218e33i | −0.890415 | − | 0.369641i | ||||
\(643\) | −1.45104e33 | −0.290501 | −0.145250 | − | 0.989395i | \(-0.546399\pi\) | ||||
−0.145250 | + | 0.989395i | \(0.546399\pi\) | |||||||
\(644\) | 3.99341e33i | 0.784718i | ||||||||
\(645\) | 1.53392e33 | − | 3.69501e33i | 0.295861 | − | 0.712687i | ||||
\(646\) | −3.15099e33 | −0.596564 | ||||||||
\(647\) | − | 9.20942e33i | − | 1.71152i | −0.517377 | − | 0.855758i | \(-0.673091\pi\) | ||
0.517377 | − | 0.855758i | \(-0.326909\pi\) | |||||||
\(648\) | −1.93800e33 | − | 6.08757e30i | −0.353552 | − | 0.00111057i | ||||
\(649\) | −1.35394e33 | −0.242474 | ||||||||
\(650\) | − | 6.13247e32i | − | 0.107814i | ||||||
\(651\) | 5.05016e33 | + | 2.09649e33i | 0.871633 | + | 0.361844i | ||||
\(652\) | −1.21105e33 | −0.205206 | ||||||||
\(653\) | − | 3.83686e33i | − | 0.638289i | −0.947706 | − | 0.319144i | \(-0.896604\pi\) | ||
0.947706 | − | 0.319144i | \(-0.103396\pi\) | |||||||
\(654\) | −9.99018e32 | + | 2.40650e33i | −0.163170 | + | 0.393054i | ||||
\(655\) | 1.40941e33 | 0.226018 | ||||||||
\(656\) | 1.34522e33i | 0.211810i | ||||||||
\(657\) | −7.14826e33 | − | 7.17075e33i | −1.10514 | − | 1.10861i | ||||
\(658\) | −4.98619e33 | −0.756935 | ||||||||
\(659\) | 1.22388e34i | 1.82437i | 0.409774 | + | 0.912187i | \(0.365608\pi\) | ||||
−0.409774 | + | 0.912187i | \(0.634392\pi\) | |||||||
\(660\) | 1.15224e33 | + | 4.78333e32i | 0.168661 | + | 0.0700169i | ||||
\(661\) | 4.50499e33 | 0.647555 | 0.323777 | − | 0.946133i | \(-0.395047\pi\) | ||||
0.323777 | + | 0.946133i | \(0.395047\pi\) | |||||||
\(662\) | − | 7.31409e33i | − | 1.03244i | ||||||
\(663\) | 5.18646e32 | − | 1.24935e33i | 0.0718966 | − | 0.173189i | ||||
\(664\) | 2.85382e33 | 0.388516 | ||||||||
\(665\) | − | 3.82202e33i | − | 0.511015i | ||||||
\(666\) | 5.64534e33 | − | 5.62764e33i | 0.741309 | − | 0.738984i | ||||
\(667\) | −2.15638e34 | −2.78109 | ||||||||
\(668\) | 3.98213e33i | 0.504426i | ||||||||
\(669\) | 9.17176e33 | + | 3.80751e33i | 1.14114 | + | 0.473726i | ||||
\(670\) | 3.06371e33 | 0.374412 | ||||||||
\(671\) | − | 1.67499e32i | − | 0.0201068i | ||||||
\(672\) | −6.25460e32 | + | 1.50665e33i | −0.0737511 | + | 0.177656i | ||||
\(673\) | 1.47939e34 | 1.71356 | 0.856782 | − | 0.515678i | \(-0.172460\pi\) | ||||
0.856782 | + | 0.515678i | \(0.172460\pi\) | |||||||
\(674\) | − | 1.79160e33i | − | 0.203855i | ||||||
\(675\) | −2.52580e33 | − | 6.13867e33i | −0.282327 | − | 0.686166i | ||||
\(676\) | 4.36107e33 | 0.478886 | ||||||||
\(677\) | 9.47154e33i | 1.02178i | 0.859647 | + | 0.510889i | \(0.170684\pi\) | ||||
−0.859647 | + | 0.510889i | \(0.829316\pi\) | |||||||
\(678\) | −3.84944e33 | − | 1.59803e33i | −0.407982 | − | 0.169367i | ||||
\(679\) | −1.25346e33 | −0.130518 | ||||||||
\(680\) | − | 1.60191e33i | − | 0.163882i | ||||||
\(681\) | −3.67672e33 | + | 8.85670e33i | −0.369568 | + | 0.890239i | ||||
\(682\) | 4.46497e33 | 0.440967 | ||||||||
\(683\) | 1.32859e34i | 1.28927i | 0.764492 | + | 0.644633i | \(0.222990\pi\) | ||||
−0.764492 | + | 0.644633i | \(0.777010\pi\) | |||||||
\(684\) | 3.42270e33 | + | 3.43347e33i | 0.326359 | + | 0.327386i | ||||
\(685\) | 1.71507e33 | 0.160692 | ||||||||
\(686\) | 6.81914e33i | 0.627828i | ||||||||
\(687\) | 9.65261e33 | + | 4.00713e33i | 0.873301 | + | 0.362537i | ||||
\(688\) | 4.27168e33 | 0.379785 | ||||||||
\(689\) | − | 2.49718e33i | − | 0.218182i | ||||||
\(690\) | −2.31327e33 | + | 5.57234e33i | −0.198626 | + | 0.478463i | ||||
\(691\) | −1.22829e34 | −1.03649 | −0.518246 | − | 0.855232i | \(-0.673415\pi\) | ||||
−0.518246 | + | 0.855232i | \(0.673415\pi\) | |||||||
\(692\) | − | 6.61206e33i | − | 0.548357i | ||||||
\(693\) | 6.79813e33 | − | 6.77681e33i | 0.554103 | − | 0.552365i | ||||
\(694\) | 9.49647e33 | 0.760761 | ||||||||
\(695\) | 8.57040e33i | 0.674813i | ||||||||
\(696\) | −8.13567e33 | − | 3.37739e33i | −0.629626 | − | 0.261379i | ||||
\(697\) | −1.01636e34 | −0.773134 | ||||||||
\(698\) | 3.57025e33i | 0.266952i | ||||||||
\(699\) | −7.95506e33 | + | 1.91626e34i | −0.584679 | + | 1.40841i | ||||
\(700\) | −5.58752e33 | −0.403685 | ||||||||
\(701\) | − | 2.57975e34i | − | 1.83215i | −0.401007 | − | 0.916075i | \(-0.631340\pi\) | ||
0.401007 | − | 0.916075i | \(-0.368660\pi\) | |||||||
\(702\) | −1.92472e33 | + | 7.91937e32i | −0.134376 | + | 0.0552898i | ||||
\(703\) | −1.99405e34 | −1.36859 | ||||||||
\(704\) | 1.33206e33i | 0.0898779i | ||||||||
\(705\) | −6.95766e33 | − | 2.88836e33i | −0.461523 | − | 0.191594i | ||||
\(706\) | 1.52091e34 | 0.991854 | ||||||||
\(707\) | − | 3.32778e34i | − | 2.13364i | ||||||
\(708\) | 1.02554e33 | − | 2.47038e33i | 0.0646478 | − | 0.155728i | ||||
\(709\) | 1.67711e34 | 1.03946 | 0.519728 | − | 0.854332i | \(-0.326033\pi\) | ||||
0.519728 | + | 0.854332i | \(0.326033\pi\) | |||||||
\(710\) | − | 7.36754e33i | − | 0.448975i | ||||||
\(711\) | 5.20913e33 | + | 5.22552e33i | 0.312126 | + | 0.313108i | ||||
\(712\) | −3.89621e33 | −0.229553 | ||||||||
\(713\) | 2.15931e34i | 1.25095i | ||||||||
\(714\) | −1.13833e34 | − | 4.72557e33i | −0.648467 | − | 0.269201i | ||||
\(715\) | 1.33981e33 | 0.0750532 | ||||||||
\(716\) | − | 1.44008e34i | − | 0.793287i | ||||||
\(717\) | 2.34120e33 | − | 5.63961e33i | 0.126826 | − | 0.305506i | ||||
\(718\) | 8.99482e33 | 0.479181 | ||||||||
\(719\) | − | 1.42987e34i | − | 0.749115i | −0.927204 | − | 0.374558i | \(-0.877795\pi\) | ||
0.927204 | − | 0.374558i | \(-0.122205\pi\) | |||||||
\(720\) | −1.74552e33 | + | 1.74004e33i | −0.0899360 | + | 0.0896540i | ||||
\(721\) | 5.81097e33 | 0.294459 | ||||||||
\(722\) | 2.06058e33i | 0.102694i | ||||||||
\(723\) | 1.11285e34 | + | 4.61981e33i | 0.545477 | + | 0.226446i | ||||
\(724\) | 5.53623e33 | 0.266902 | ||||||||
\(725\) | − | 3.01718e34i | − | 1.43069i | ||||||
\(726\) | −2.80762e33 | + | 6.76317e33i | −0.130948 | + | 0.315436i | ||||
\(727\) | −1.19847e34 | −0.549813 | −0.274907 | − | 0.961471i | \(-0.588647\pi\) | ||||
−0.274907 | + | 0.961471i | \(0.588647\pi\) | |||||||
\(728\) | 1.75191e33i | 0.0790561i | ||||||||
\(729\) | −1.60049e34 | + | 1.58547e34i | −0.710431 | + | 0.703767i | ||||
\(730\) | −1.28766e34 | −0.562246 | ||||||||
\(731\) | 3.22740e34i | 1.38626i | ||||||||
\(732\) | 3.05616e32 | + | 1.26872e32i | 0.0129135 | + | 0.00536083i | ||||
\(733\) | 3.29541e34 | 1.36981 | 0.684906 | − | 0.728631i | \(-0.259843\pi\) | ||||
0.684906 | + | 0.728631i | \(0.259843\pi\) | |||||||
\(734\) | 4.47421e33i | 0.182963i | ||||||||
\(735\) | 8.90897e32 | − | 2.14605e33i | 0.0358410 | − | 0.0863359i | ||||
\(736\) | −6.44200e33 | −0.254969 | ||||||||
\(737\) | − | 1.92482e34i | − | 0.749515i | ||||||
\(738\) | 1.10400e34 | + | 1.10748e34i | 0.422955 | + | 0.424286i | ||||
\(739\) | −1.97092e34 | −0.742909 | −0.371455 | − | 0.928451i | \(-0.621141\pi\) | ||||
−0.371455 | + | 0.928451i | \(0.621141\pi\) | |||||||
\(740\) | − | 1.01374e34i | − | 0.375964i | ||||||
\(741\) | 4.80857e33 | + | 1.99620e33i | 0.175468 | + | 0.0728426i | ||||
\(742\) | −2.27527e34 | −0.816933 | ||||||||
\(743\) | − | 1.02403e34i | − | 0.361780i | −0.983503 | − | 0.180890i | \(-0.942102\pi\) | ||
0.983503 | − | 0.180890i | \(-0.0578979\pi\) | |||||||
\(744\) | −3.38198e33 | + | 8.14671e33i | −0.117570 | + | 0.283209i | ||||
\(745\) | −1.80840e33 | −0.0618614 | ||||||||
\(746\) | 2.36663e34i | 0.796646i | ||||||||
\(747\) | 2.34946e34 | − | 2.34209e34i | 0.778252 | − | 0.775811i | ||||
\(748\) | −1.00642e34 | −0.328065 | ||||||||
\(749\) | 4.62484e34i | 1.48359i | ||||||||
\(750\) | −1.83048e34 | − | 7.59894e33i | −0.577869 | − | 0.239893i | ||||
\(751\) | −1.34386e34 | −0.417519 | −0.208759 | − | 0.977967i | \(-0.566943\pi\) | ||||
−0.208759 | + | 0.977967i | \(0.566943\pi\) | |||||||
\(752\) | − | 8.04352e33i | − | 0.245942i | ||||||
\(753\) | 5.60299e32 | − | 1.34968e33i | 0.0168609 | − | 0.0406155i | ||||
\(754\) | −9.46005e33 | −0.280180 | ||||||||
\(755\) | 1.59397e34i | 0.464639i | ||||||||
\(756\) | 7.21563e33 | + | 1.75368e34i | 0.207020 | + | 0.503140i | ||||
\(757\) | 5.51041e34 | 1.55608 | 0.778042 | − | 0.628212i | \(-0.216213\pi\) | ||||
0.778042 | + | 0.628212i | \(0.216213\pi\) | |||||||
\(758\) | 3.94290e34i | 1.09594i | ||||||||
\(759\) | 3.50090e34 | + | 1.45334e34i | 0.957809 | + | 0.397619i | ||||
\(760\) | 6.16553e33 | 0.166038 | ||||||||
\(761\) | 4.30641e34i | 1.14156i | 0.821102 | + | 0.570781i | \(0.193360\pi\) | ||||
−0.821102 | + | 0.570781i | \(0.806640\pi\) | |||||||
\(762\) | 1.27355e34 | − | 3.06781e34i | 0.332320 | − | 0.800513i | ||||
\(763\) | 2.54958e34 | 0.654900 | ||||||||
\(764\) | 7.38812e33i | 0.186816i | ||||||||
\(765\) | −1.31466e34 | − | 1.31880e34i | −0.327248 | − | 0.328278i | ||||
\(766\) | 6.20260e32 | 0.0151995 | ||||||||
\(767\) | − | 2.87253e33i | − | 0.0692980i | ||||||
\(768\) | −2.43046e33 | − | 1.00897e33i | −0.0577237 | − | 0.0239631i | ||||
\(769\) | −3.03466e34 | −0.709567 | −0.354784 | − | 0.934948i | \(-0.615445\pi\) | ||||
−0.354784 | + | 0.934948i | \(0.615445\pi\) | |||||||
\(770\) | − | 1.22075e34i | − | 0.281020i | ||||||
\(771\) | 2.34207e34 | − | 5.64171e34i | 0.530819 | − | 1.27867i | ||||
\(772\) | 1.39249e34 | 0.310730 | ||||||||
\(773\) | − | 1.67755e34i | − | 0.368571i | −0.982873 | − | 0.184286i | \(-0.941003\pi\) | ||
0.982873 | − | 0.184286i | \(-0.0589972\pi\) | |||||||
\(774\) | 3.51674e34 | − | 3.50571e34i | 0.760761 | − | 0.758375i | ||||
\(775\) | −3.02127e34 | −0.643531 | ||||||||
\(776\) | − | 2.02202e33i | − | 0.0424077i | ||||||
\(777\) | −7.20371e34 | − | 2.99050e34i | −1.48766 | − | 0.617578i | ||||
\(778\) | 7.14350e33 | 0.145263 | ||||||||
\(779\) | − | 3.91184e34i | − | 0.783307i | ||||||
\(780\) | −1.01483e33 | + | 2.44459e33i | −0.0200105 | + | 0.0482026i | ||||
\(781\) | −4.62876e34 | −0.898778 | ||||||||
\(782\) | − | 4.86716e34i | − | 0.930667i | ||||||
\(783\) | −9.46962e34 | + | 3.89633e34i | −1.78316 | + | 0.733694i | ||||
\(784\) | 2.48098e33 | 0.0460076 | ||||||||
\(785\) | 2.42481e34i | 0.442835i | ||||||||
\(786\) | 1.61564e34 | + | 6.70708e33i | 0.290586 | + | 0.120632i | ||||
\(787\) | 3.01739e34 | 0.534484 | 0.267242 | − | 0.963629i | \(-0.413888\pi\) | ||||
0.267242 | + | 0.963629i | \(0.413888\pi\) | |||||||
\(788\) | − | 2.35363e34i | − | 0.410604i | ||||||
\(789\) | 3.42290e33 | − | 8.24530e33i | 0.0588126 | − | 0.141671i | ||||
\(790\) | 9.38352e33 | 0.158796 | ||||||||
\(791\) | 4.07832e34i | 0.679773i | ||||||||
\(792\) | 1.09321e34 | + | 1.09665e34i | 0.179473 | + | 0.180038i | ||||
\(793\) | 3.55367e32 | 0.00574644 | ||||||||
\(794\) | 3.48857e34i | 0.555651i | ||||||||
\(795\) | −3.17488e34 | − | 1.31800e34i | −0.498106 | − | 0.206781i | ||||
\(796\) | −5.06809e34 | −0.783226 | ||||||||
\(797\) | − | 7.59723e34i | − | 1.15653i | −0.815850 | − | 0.578263i | \(-0.803731\pi\) | ||
0.815850 | − | 0.578263i | \(-0.196269\pi\) | |||||||
\(798\) | 1.81881e34 | − | 4.38126e34i | 0.272743 | − | 0.656999i | ||||
\(799\) | 6.07716e34 | 0.897717 | ||||||||
\(800\) | − | 9.01356e33i | − | 0.131165i | ||||||
\(801\) | −3.20763e34 | + | 3.19757e34i | −0.459826 | + | 0.458384i | ||||
\(802\) | −1.41381e34 | −0.199664 | ||||||||
\(803\) | 8.08990e34i | 1.12553i | ||||||||
\(804\) | 3.51199e34 | + | 1.45795e34i | 0.481372 | + | 0.199834i | ||||
\(805\) | 5.90366e34 | 0.797207 | ||||||||
\(806\) | 9.47289e33i | 0.126027i | ||||||||
\(807\) | 1.45001e34 | − | 3.49287e34i | 0.190059 | − | 0.457826i | ||||
\(808\) | 5.36823e34 | 0.693258 | ||||||||
\(809\) | 5.59731e33i | 0.0712192i | 0.999366 | + | 0.0356096i | \(0.0113373\pi\) | ||||
−0.999366 | + | 0.0356096i | \(0.988663\pi\) | |||||||
\(810\) | −8.99958e31 | + | 2.86504e34i | −0.00112824 | + | 0.359179i | ||||
\(811\) | 3.95151e34 | 0.488104 | 0.244052 | − | 0.969762i | \(-0.421523\pi\) | ||||
0.244052 | + | 0.969762i | \(0.421523\pi\) | |||||||
\(812\) | 8.61941e34i | 1.04907i | ||||||||
\(813\) | 4.09991e34 | + | 1.70201e34i | 0.491686 | + | 0.204115i | ||||
\(814\) | −6.36897e34 | −0.752621 | ||||||||
\(815\) | 1.79036e34i | 0.208472i | ||||||||
\(816\) | 7.62310e33 | − | 1.83630e34i | 0.0874681 | − | 0.210699i | ||||
\(817\) | −1.24219e35 | −1.40450 | ||||||||
\(818\) | − | 6.20093e34i | − | 0.690904i | ||||||
\(819\) | 1.43777e34 | + | 1.44229e34i | 0.157864 | + | 0.158360i | ||||
\(820\) | 1.98871e34 | 0.215182 | ||||||||
\(821\) | 9.13276e33i | 0.0973832i | 0.998814 | + | 0.0486916i | \(0.0155051\pi\) | ||||
−0.998814 | + | 0.0486916i | \(0.984495\pi\) | |||||||
\(822\) | 1.96602e34 | + | 8.16161e33i | 0.206598 | + | 0.0857657i | ||||
\(823\) | 1.85735e34 | 0.192352 | 0.0961760 | − | 0.995364i | \(-0.469339\pi\) | ||||
0.0961760 | + | 0.995364i | \(0.469339\pi\) | |||||||
\(824\) | 9.37401e33i | 0.0956751i | ||||||||
\(825\) | −2.03350e34 | + | 4.89842e34i | −0.204549 | + | 0.492729i | ||||
\(826\) | −2.61727e34 | −0.259471 | ||||||||
\(827\) | − | 1.06740e35i | − | 1.04295i | −0.853267 | − | 0.521474i | \(-0.825382\pi\) | ||
0.853267 | − | 0.521474i | \(-0.174618\pi\) | |||||||
\(828\) | −5.30349e34 | + | 5.28686e34i | −0.510738 | + | 0.509136i | ||||
\(829\) | 1.82567e35 | 1.73288 | 0.866440 | − | 0.499281i | \(-0.166403\pi\) | ||||
0.866440 | + | 0.499281i | \(0.166403\pi\) | |||||||
\(830\) | − | 4.21895e34i | − | 0.394700i | ||||||
\(831\) | 7.37553e34 | + | 3.06183e34i | 0.680113 | + | 0.282338i | ||||
\(832\) | −2.82611e33 | −0.0256867 | ||||||||
\(833\) | 1.87447e34i | 0.167933i | ||||||||
\(834\) | −4.07845e34 | + | 9.82443e34i | −0.360166 | + | 0.867591i | ||||
\(835\) | 5.88699e34 | 0.512454 | ||||||||
\(836\) | − | 3.87358e34i | − | 0.332382i | ||||||
\(837\) | 3.90162e34 | + | 9.48247e34i | 0.330019 | + | 0.802077i | ||||
\(838\) | −2.86747e32 | −0.00239095 | ||||||||
\(839\) | 1.68970e34i | 0.138888i | 0.997586 | + | 0.0694442i | \(0.0221226\pi\) | ||||
−0.997586 | + | 0.0694442i | \(0.977877\pi\) | |||||||
\(840\) | 2.22736e34 | + | 9.24651e33i | 0.180484 | + | 0.0749249i | ||||
\(841\) | −3.40250e35 | −2.71798 | ||||||||
\(842\) | 4.02009e34i | 0.316586i | ||||||||
\(843\) | −2.80465e34 | + | 6.75601e34i | −0.217745 | + | 0.524517i | ||||
\(844\) | −8.07512e34 | −0.618073 | ||||||||
\(845\) | − | 6.44719e34i | − | 0.486508i | ||||||
\(846\) | −6.60120e34 | − | 6.62197e34i | −0.491110 | − | 0.492655i | ||||
\(847\) | 7.16530e34 | 0.525574 | ||||||||
\(848\) | − | 3.67037e34i | − | 0.265436i | ||||||
\(849\) | 2.10042e34 | + | 8.71957e33i | 0.149766 | + | 0.0621731i | ||||
\(850\) | 6.81006e34 | 0.478767 | ||||||||
\(851\) | − | 3.08010e35i | − | 2.13506i | ||||||
\(852\) | 3.50604e34 | − | 8.44556e34i | 0.239630 | − | 0.577236i | ||||
\(853\) | −5.01848e34 | −0.338208 | −0.169104 | − | 0.985598i | \(-0.554087\pi\) | ||||
−0.169104 | + | 0.985598i | \(0.554087\pi\) | |||||||
\(854\) | − | 3.23788e33i | − | 0.0215162i | ||||||
\(855\) | 5.07588e34 | − | 5.05996e34i | 0.332597 | − | 0.331554i | ||||
\(856\) | −7.46060e34 | −0.482046 | ||||||||
\(857\) | 1.02720e35i | 0.654465i | 0.944944 | + | 0.327233i | \(0.106116\pi\) | ||||
−0.944944 | + | 0.327233i | \(0.893884\pi\) | |||||||
\(858\) | 1.53585e34 | + | 6.37582e33i | 0.0964941 | + | 0.0400580i | ||||
\(859\) | 1.27721e35 | 0.791304 | 0.395652 | − | 0.918400i | \(-0.370519\pi\) | ||||
0.395652 | + | 0.918400i | \(0.370519\pi\) | |||||||
\(860\) | − | 6.31504e34i | − | 0.385829i | ||||||
\(861\) | 5.86663e34 | − | 1.41319e35i | 0.353469 | − | 0.851457i | ||||
\(862\) | −1.32770e35 | −0.788883 | ||||||||
\(863\) | − | 2.40446e35i | − | 1.40893i | −0.709740 | − | 0.704463i | \(-0.751188\pi\) | ||
0.709740 | − | 0.704463i | \(-0.248812\pi\) | |||||||
\(864\) | −2.82897e34 | + | 1.16400e34i | −0.163479 | + | 0.0672646i | ||||
\(865\) | −9.77495e34 | −0.557085 | ||||||||
\(866\) | 1.75100e35i | 0.984173i | ||||||||
\(867\) | −2.78719e34 | − | 1.15706e34i | −0.154503 | − | 0.0641395i | ||||
\(868\) | 8.63110e34 | 0.471878 | ||||||||
\(869\) | − | 5.89533e34i | − | 0.317886i | ||||||
\(870\) | −4.99297e34 | + | 1.20274e35i | −0.265539 | + | 0.639647i | ||||
\(871\) | 4.08370e34 | 0.214208 | ||||||||
\(872\) | 4.11288e34i | 0.212789i | ||||||||
\(873\) | −1.65944e34 | − | 1.66467e34i | −0.0846822 | − | 0.0849486i | ||||
\(874\) | 1.87331e35 | 0.942912 | ||||||||
\(875\) | 1.93932e35i | 0.962835i | ||||||||
\(876\) | −1.47607e35 | − | 6.12767e34i | −0.722866 | − | 0.300086i | ||||
\(877\) | 1.99000e35 | 0.961300 | 0.480650 | − | 0.876912i | \(-0.340401\pi\) | ||||
0.480650 | + | 0.876912i | \(0.340401\pi\) | |||||||
\(878\) | − | 1.17180e35i | − | 0.558368i | ||||||
\(879\) | −3.49442e34 | + | 8.41758e34i | −0.164251 | + | 0.395659i | ||||
\(880\) | 1.96926e34 | 0.0913084 | ||||||||
\(881\) | 1.97792e35i | 0.904684i | 0.891845 | + | 0.452342i | \(0.149411\pi\) | ||||
−0.891845 | + | 0.452342i | \(0.850589\pi\) | |||||||
\(882\) | 2.04251e34 | − | 2.03610e34i | 0.0921597 | − | 0.0918706i | ||||
\(883\) | −1.50399e35 | −0.669446 | −0.334723 | − | 0.942317i | \(-0.608643\pi\) | ||||
−0.334723 | + | 0.942317i | \(0.608643\pi\) | |||||||
\(884\) | − | 2.13522e34i | − | 0.0937597i | ||||||
\(885\) | −3.65210e34 | − | 1.51611e34i | −0.158206 | − | 0.0656767i | ||||
\(886\) | 3.00265e35 | 1.28322 | ||||||||
\(887\) | 3.11037e35i | 1.31138i | 0.755031 | + | 0.655689i | \(0.227622\pi\) | ||||
−0.755031 | + | 0.655689i | \(0.772378\pi\) | |||||||
\(888\) | 4.82415e34 | − | 1.16207e35i | 0.200662 | − | 0.483367i | ||||
\(889\) | −3.25021e35 | −1.33380 | ||||||||
\(890\) | 5.75997e34i | 0.233206i | ||||||||
\(891\) | 1.80000e35 | + | 5.65411e32i | 0.719020 | + | 0.00225856i | ||||
\(892\) | 1.56752e35 | 0.617782 | ||||||||
\(893\) | 2.33902e35i | 0.909529i | ||||||||
\(894\) | −2.07301e34 | − | 8.60576e33i | −0.0795337 | − | 0.0330171i | ||||
\(895\) | −2.12895e35 | −0.805913 | ||||||||
\(896\) | 2.57497e34i | 0.0961782i | ||||||||
\(897\) | −3.08342e34 | + | 7.42752e34i | −0.113638 | + | 0.273738i | ||||
\(898\) | 1.56467e35 | 0.568993 | ||||||||
\(899\) | 4.66067e35i | 1.67237i | ||||||||
\(900\) | −7.39730e34 | − | 7.42058e34i | −0.261917 | − | 0.262741i | ||||
\(901\) | 2.77310e35 | 0.968874 | ||||||||
\(902\) | − | 1.24944e35i | − | 0.430760i | ||||||
\(903\) | −4.48751e35 | − | 1.86292e35i | −1.52670 | − | 0.633783i | ||||
\(904\) | −6.57898e34 | −0.220870 | ||||||||
\(905\) | − | 8.18450e34i | − | 0.271150i | ||||||
\(906\) | −7.58532e34 | + | 1.82720e35i | −0.247991 | + | 0.597375i | ||||
\(907\) | −1.62862e35 | −0.525450 | −0.262725 | − | 0.964871i | \(-0.584621\pi\) | ||||
−0.262725 | + | 0.964871i | \(0.584621\pi\) | |||||||
\(908\) | 1.51368e35i | 0.481951i | ||||||||
\(909\) | 4.41949e35 | − | 4.40563e35i | 1.38869 | − | 1.38434i | ||||
\(910\) | 2.58994e34 | 0.0803143 | ||||||||
\(911\) | − | 1.31582e35i | − | 0.402695i | −0.979520 | − | 0.201347i | \(-0.935468\pi\) | ||
0.979520 | − | 0.201347i | \(-0.0645320\pi\) | |||||||
\(912\) | 7.06767e34 | + | 2.93403e34i | 0.213471 | + | 0.0886189i | ||||
\(913\) | −2.65061e35 | −0.790128 | ||||||||
\(914\) | − | 1.67963e35i | − | 0.494150i | ||||||
\(915\) | 1.87561e33 | − | 4.51809e33i | 0.00544615 | − | 0.0131190i | ||||
\(916\) | 1.64970e35 | 0.472781 | ||||||||
\(917\) | − | 1.71171e35i | − | 0.484169i | ||||||
\(918\) | −8.79440e34 | − | 2.13738e35i | −0.245524 | − | 0.596720i | ||||
\(919\) | −1.38423e35 | −0.381435 | −0.190718 | − | 0.981645i | \(-0.561081\pi\) | ||||
−0.190718 | + | 0.981645i | \(0.561081\pi\) | |||||||
\(920\) | 9.52354e34i | 0.259027i | ||||||||
\(921\) | 4.71271e35 | + | 1.95641e35i | 1.26519 | + | 0.525223i | ||||
\(922\) | −1.51309e35 | −0.400954 | ||||||||
\(923\) | − | 9.82039e34i | − | 0.256867i | ||||||
\(924\) | 5.80925e34 | − | 1.39937e35i | 0.149988 | − | 0.361300i | ||||
\(925\) | 4.30964e35 | 1.09835 | ||||||||
\(926\) | 6.10853e34i | 0.153676i | ||||||||
\(927\) | 7.69312e34 | + | 7.71732e34i | 0.191049 | + | 0.191650i | ||||
\(928\) | −1.39045e35 | −0.340862 | ||||||||
\(929\) | − | 5.79667e35i | − | 1.40278i | −0.712776 | − | 0.701391i | \(-0.752563\pi\) | ||
0.712776 | − | 0.701391i | \(-0.247437\pi\) | |||||||
\(930\) | 1.20437e35 | + | 4.99975e34i | 0.287716 | + | 0.119441i | ||||
\(931\) | −7.21457e34 | −0.170143 | ||||||||
\(932\) | 3.27504e35i | 0.762474i | ||||||||
\(933\) | 3.73520e34 | − | 8.99758e34i | 0.0858488 | − | 0.206798i | ||||
\(934\) | −4.71783e35 | −1.07048 | ||||||||
\(935\) | 1.48784e35i | 0.333287i | ||||||||
\(936\) | −2.32664e34 | + | 2.31935e34i | −0.0514541 | + | 0.0512927i | ||||
\(937\) | −2.61380e35 | −0.570685 | −0.285343 | − | 0.958426i | \(-0.592107\pi\) | ||||
−0.285343 | + | 0.958426i | \(0.592107\pi\) | |||||||
\(938\) | − | 3.72081e35i | − | 0.802054i | ||||||
\(939\) | −8.16428e35 | − | 3.38927e35i | −1.73752 | − | 0.721305i | ||||
\(940\) | −1.18912e35 | −0.249856 | ||||||||
\(941\) | − | 2.84502e35i | − | 0.590215i | −0.955464 | − | 0.295107i | \(-0.904645\pi\) | ||
0.955464 | − | 0.295107i | \(-0.0953554\pi\) | |||||||
\(942\) | −1.15391e35 | + | 2.77961e35i | −0.236353 | + | 0.569343i | ||||
\(943\) | 6.04240e35 | 1.22200 | ||||||||
\(944\) | − | 4.22207e34i | − | 0.0843066i | ||||||
\(945\) | 2.59256e35 | − | 1.06672e35i | 0.511148 | − | 0.210315i | ||||
\(946\) | −3.96752e35 | −0.772370 | ||||||||
\(947\) | 2.03824e35i | 0.391792i | 0.980625 | + | 0.195896i | \(0.0627615\pi\) | ||||
−0.980625 | + | 0.195896i | \(0.937239\pi\) | |||||||
\(948\) | 1.07565e35 | + | 4.46540e34i | 0.204161 | + | 0.0847540i | ||||
\(949\) | −1.71636e35 | −0.321672 | ||||||||
\(950\) | 2.62110e35i | 0.485066i | ||||||||
\(951\) | −1.12244e35 | + | 2.70379e35i | −0.205114 | + | 0.494091i | ||||
\(952\) | −1.94548e35 | −0.351062 | ||||||||
\(953\) | 1.97399e35i | 0.351746i | 0.984413 | + | 0.175873i | \(0.0562748\pi\) | ||||
−0.984413 | + | 0.175873i | \(0.943725\pi\) | |||||||
\(954\) | −3.01222e35 | − | 3.02170e35i | −0.530038 | − | 0.531705i | ||||
\(955\) | 1.09222e35 | 0.189789 | ||||||||
\(956\) | − | 9.63852e34i | − | 0.165392i | ||||||
\(957\) | 7.55638e35 | + | 3.13691e35i | 1.28047 | + | 0.531568i | ||||
\(958\) | 5.07312e35 | 0.848963 | ||||||||
\(959\) | − | 2.08291e35i | − | 0.344230i | ||||||
\(960\) | −1.49161e34 | + | 3.59308e34i | −0.0243444 | + | 0.0586424i | ||||
\(961\) | −1.53714e35 | −0.247760 | ||||||||
\(962\) | − | 1.35124e35i | − | 0.215096i | ||||||
\(963\) | −6.14207e35 | + | 6.12281e35i | −0.965605 | + | 0.962576i | ||||
\(964\) | 1.90194e35 | 0.295306 | ||||||||
\(965\) | − | 2.05859e35i | − | 0.315676i | ||||||
\(966\) | 6.76749e35 | + | 2.80942e35i | 1.02495 | + | 0.425491i | ||||
\(967\) | 6.81298e35 | 1.01911 | 0.509553 | − | 0.860439i | \(-0.329811\pi\) | ||||
0.509553 | + | 0.860439i | \(0.329811\pi\) | |||||||
\(968\) | 1.15588e35i | 0.170768i | ||||||||
\(969\) | −2.21676e35 | + | 5.33988e35i | −0.323470 | + | 0.779194i | ||||
\(970\) | −2.98926e34 | −0.0430827 | ||||||||
\(971\) | − | 4.00910e35i | − | 0.570711i | −0.958422 | − | 0.285355i | \(-0.907888\pi\) | ||
0.958422 | − | 0.285355i | \(-0.0921117\pi\) | |||||||
\(972\) | −1.37372e35 | + | 3.27997e35i | −0.193154 | + | 0.461185i | ||||
\(973\) | 1.04086e36 | 1.44556 | ||||||||
\(974\) | 2.09530e35i | 0.287435i | ||||||||
\(975\) | −1.03925e35 | − | 4.31428e34i | −0.140820 | − | 0.0584591i | ||||
\(976\) | 5.22321e33 | 0.00699101 | ||||||||
\(977\) | 1.43289e36i | 1.89443i | 0.320600 | + | 0.947215i | \(0.396116\pi\) | ||||
−0.320600 | + | 0.947215i | \(0.603884\pi\) | |||||||
\(978\) | −8.51990e34 | + | 2.05233e35i | −0.111267 | + | 0.268028i | ||||
\(979\) | 3.61878e35 | 0.466843 | ||||||||
\(980\) | − | 3.66776e34i | − | 0.0467399i | ||||||
\(981\) | 3.37539e35 | + | 3.38600e35i | 0.424908 | + | 0.426245i | ||||
\(982\) | −3.02085e35 | −0.375657 | ||||||||
\(983\) | − | 8.32748e35i | − | 1.02299i | −0.859286 | − | 0.511495i | \(-0.829092\pi\) | ||
0.859286 | − | 0.511495i | \(-0.170908\pi\) | |||||||
\(984\) | 2.27970e35 | + | 9.46380e34i | 0.276654 | + | 0.114848i | ||||
\(985\) | −3.47949e35 | −0.417139 | ||||||||
\(986\) | − | 1.05053e36i | − | 1.24419i | ||||||
\(987\) | −3.50785e35 | + | 8.44993e35i | −0.410427 | + | 0.988661i | ||||
\(988\) | 8.21820e34 | 0.0949934 | ||||||||
\(989\) | − | 1.91873e36i | − | 2.19109i | ||||||
\(990\) | 1.62123e35 | − | 1.61614e35i | 0.182903 | − | 0.182330i | ||||
\(991\) | −2.31096e35 | −0.257578 | −0.128789 | − | 0.991672i | \(-0.541109\pi\) | ||||
−0.128789 | + | 0.991672i | \(0.541109\pi\) | |||||||
\(992\) | 1.39233e35i | 0.153322i | ||||||||
\(993\) | −1.23949e36 | − | 5.14556e35i | −1.34851 | − | 0.559811i | ||||
\(994\) | −8.94772e35 | −0.961780 | ||||||||
\(995\) | 7.49241e35i | 0.795692i | ||||||||
\(996\) | 2.00770e35 | − | 4.83627e35i | 0.210662 | − | 0.507456i | ||||
\(997\) | −8.99382e35 | −0.932400 | −0.466200 | − | 0.884679i | \(-0.654377\pi\) | ||||
−0.466200 | + | 0.884679i | \(0.654377\pi\) | |||||||
\(998\) | 4.54875e35i | 0.465935i | ||||||||
\(999\) | −5.56539e35 | − | 1.35261e36i | −0.563261 | − | 1.36895i |
(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 | 6.25.b.a.5.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 6.25.b.a.5.5 | yes | 8 | |
4.3 | odd | 2 | 48.25.e.d.17.8 | 8 | |||
12.11 | even | 2 | 48.25.e.d.17.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.25.b.a.5.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
6.25.b.a.5.5 | yes | 8 | 3.2 | odd | 2 | inner | |
48.25.e.d.17.7 | 8 | 12.11 | even | 2 | |||
48.25.e.d.17.8 | 8 | 4.3 | odd | 2 |