Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,33,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.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: | \(25.9466620569\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 72511313626452 x^{12} + \cdots + 62\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{182}\cdot 3^{20}\cdot 5^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.12 | ||
Root | \(5.00408e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.33.b.b.3.11 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 46092.7 | + | 46587.9i | 0.703318 | + | 0.710875i | ||||
\(3\) | 8.00653e7i | 1.85996i | 0.367608 | + | 0.929981i | \(0.380177\pi\) | ||||
−0.367608 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(4\) | −4.59006e7 | + | 4.29472e9i | −0.0106871 | + | 0.999943i | ||||
\(5\) | −3.25403e10 | −0.213256 | −0.106628 | − | 0.994299i | \(-0.534005\pi\) | ||||
−0.106628 | + | 0.994299i | \(0.534005\pi\) | |||||||
\(6\) | −3.73007e12 | + | 3.69042e12i | −1.32220 | + | 1.30815i | ||||
\(7\) | − | 4.74477e13i | − | 1.42773i | −0.700283 | − | 0.713866i | \(-0.746943\pi\) | ||
0.700283 | − | 0.713866i | \(-0.253057\pi\) | |||||||
\(8\) | −2.02198e14 | + | 1.95817e14i | −0.718351 | + | 0.695681i | ||||
\(9\) | −4.55743e15 | −2.45946 | ||||||||
\(10\) | −1.49987e15 | − | 1.51599e15i | −0.149987 | − | 0.151599i | ||||
\(11\) | − | 1.35259e16i | − | 0.294362i | −0.989110 | − | 0.147181i | \(-0.952980\pi\) | ||
0.989110 | − | 0.147181i | \(-0.0470200\pi\) | |||||||
\(12\) | −3.43858e17 | − | 3.67504e15i | −1.85986 | − | 0.0198775i | ||||
\(13\) | 9.45442e16 | 0.142083 | 0.0710413 | − | 0.997473i | \(-0.477368\pi\) | ||||
0.0710413 | + | 0.997473i | \(0.477368\pi\) | |||||||
\(14\) | 2.21049e18 | − | 2.18699e18i | 1.01494 | − | 1.00415i | ||||
\(15\) | − | 2.60535e18i | − | 0.396648i | ||||||
\(16\) | −1.84425e19 | − | 3.94261e17i | −0.999772 | − | 0.0213729i | ||||
\(17\) | 6.35019e18 | 0.130498 | 0.0652491 | − | 0.997869i | \(-0.479216\pi\) | ||||
0.0652491 | + | 0.997869i | \(0.479216\pi\) | |||||||
\(18\) | −2.10064e20 | − | 2.12321e20i | −1.72978 | − | 1.74837i | ||||
\(19\) | 4.93031e20i | 1.70929i | 0.519210 | + | 0.854647i | \(0.326226\pi\) | ||||
−0.519210 | + | 0.854647i | \(0.673774\pi\) | |||||||
\(20\) | 1.49362e18 | − | 1.39752e20i | 0.00227908 | − | 0.213244i | ||||
\(21\) | 3.79891e21 | 2.65553 | ||||||||
\(22\) | 6.30141e20 | − | 6.23443e20i | 0.209255 | − | 0.207030i | ||||
\(23\) | 4.92552e21i | 0.803168i | 0.915822 | + | 0.401584i | \(0.131540\pi\) | ||||
−0.915822 | + | 0.401584i | \(0.868460\pi\) | |||||||
\(24\) | −1.56781e22 | − | 1.61890e22i | −1.29394 | − | 1.33611i | ||||
\(25\) | −2.22242e22 | −0.954522 | ||||||||
\(26\) | 4.35779e21 | + | 4.40461e21i | 0.0999293 | + | 0.101003i | ||||
\(27\) | − | 2.16529e23i | − | 2.71454i | ||||||
\(28\) | 2.03775e23 | + | 2.17788e21i | 1.42765 | + | 0.0152583i | ||||
\(29\) | −2.04879e23 | −0.818709 | −0.409355 | − | 0.912375i | \(-0.634246\pi\) | ||||
−0.409355 | + | 0.912375i | \(0.634246\pi\) | |||||||
\(30\) | 1.21378e23 | − | 1.20087e23i | 0.281967 | − | 0.278970i | ||||
\(31\) | − | 8.15726e23i | − | 1.12139i | −0.828022 | − | 0.560696i | \(-0.810534\pi\) | ||
0.828022 | − | 0.560696i | \(-0.189466\pi\) | |||||||
\(32\) | −8.31698e23 | − | 8.77372e23i | −0.687964 | − | 0.725745i | ||||
\(33\) | 1.08295e24 | 0.547502 | ||||||||
\(34\) | 2.92697e23 | + | 2.95842e23i | 0.0917817 | + | 0.0927679i | ||||
\(35\) | 1.54396e24i | 0.304473i | ||||||||
\(36\) | 2.09189e23 | − | 1.95729e25i | 0.0262844 | − | 2.45932i | ||||
\(37\) | 8.64253e24 | 0.700508 | 0.350254 | − | 0.936655i | \(-0.386095\pi\) | ||||
0.350254 | + | 0.936655i | \(0.386095\pi\) | |||||||
\(38\) | −2.29693e25 | + | 2.27251e25i | −1.21509 | + | 1.20218i | ||||
\(39\) | 7.56970e24i | 0.264268i | ||||||||
\(40\) | 6.57958e24 | − | 6.37194e24i | 0.153193 | − | 0.148358i | ||||
\(41\) | −9.37253e25 | −1.46999 | −0.734996 | − | 0.678071i | \(-0.762816\pi\) | ||||
−0.734996 | + | 0.678071i | \(0.762816\pi\) | |||||||
\(42\) | 1.75102e26 | + | 1.76983e26i | 1.86768 | + | 1.88775i | ||||
\(43\) | 9.13599e25i | 0.668744i | 0.942441 | + | 0.334372i | \(0.108524\pi\) | ||||
−0.942441 | + | 0.334372i | \(0.891476\pi\) | |||||||
\(44\) | 5.80898e25 | + | 6.20845e23i | 0.294345 | + | 0.00314587i | ||||
\(45\) | 1.48300e26 | 0.524495 | ||||||||
\(46\) | −2.29470e26 | + | 2.27030e26i | −0.570952 | + | 0.564883i | ||||
\(47\) | 4.69294e26i | 0.827712i | 0.910342 | + | 0.413856i | \(0.135818\pi\) | ||||
−0.910342 | + | 0.413856i | \(0.864182\pi\) | |||||||
\(48\) | 3.15666e25 | − | 1.47661e27i | 0.0397528 | − | 1.85954i | ||||
\(49\) | −1.14686e27 | −1.03842 | ||||||||
\(50\) | −1.02437e27 | − | 1.03538e27i | −0.671333 | − | 0.678546i | ||||
\(51\) | 5.08430e26i | 0.242722i | ||||||||
\(52\) | −4.33963e24 | + | 4.06041e26i | −0.00151845 | + | 0.142075i | ||||
\(53\) | 3.40698e27 | 0.878932 | 0.439466 | − | 0.898259i | \(-0.355168\pi\) | ||||
0.439466 | + | 0.898259i | \(0.355168\pi\) | |||||||
\(54\) | 1.00876e28 | − | 9.98040e27i | 1.92970 | − | 1.90918i | ||||
\(55\) | 4.40135e26i | 0.0627745i | ||||||||
\(56\) | 9.29106e27 | + | 9.59382e27i | 0.993246 | + | 1.02561i | ||||
\(57\) | −3.94747e28 | −3.17922 | ||||||||
\(58\) | −9.44342e27 | − | 9.54489e27i | −0.575813 | − | 0.582000i | ||||
\(59\) | − | 2.87556e27i | − | 0.133380i | −0.997774 | − | 0.0666898i | \(-0.978756\pi\) | ||
0.997774 | − | 0.0666898i | \(-0.0212438\pi\) | |||||||
\(60\) | 1.11892e28 | + | 1.19587e26i | 0.396626 | + | 0.00423901i | ||||
\(61\) | 7.72100e27 | 0.210086 | 0.105043 | − | 0.994468i | \(-0.466502\pi\) | ||||
0.105043 | + | 0.994468i | \(0.466502\pi\) | |||||||
\(62\) | 3.80030e28 | − | 3.75990e28i | 0.797169 | − | 0.788695i | ||||
\(63\) | 2.16239e29i | 3.51145i | ||||||||
\(64\) | 2.53976e27 | − | 7.91874e28i | 0.0320563 | − | 0.999486i | ||||
\(65\) | −3.07650e27 | −0.0303000 | ||||||||
\(66\) | 4.99161e28 | + | 5.04524e28i | 0.385068 | + | 0.389206i | ||||
\(67\) | 8.28696e28i | 0.502572i | 0.967913 | + | 0.251286i | \(0.0808534\pi\) | ||||
−0.967913 | + | 0.251286i | \(0.919147\pi\) | |||||||
\(68\) | −2.91478e26 | + | 2.72723e28i | −0.00139464 | + | 0.130491i | ||||
\(69\) | −3.94363e29 | −1.49386 | ||||||||
\(70\) | −7.19300e28 | + | 7.11654e28i | −0.216442 | + | 0.214141i | ||||
\(71\) | − | 2.37111e29i | − | 0.568615i | −0.958733 | − | 0.284307i | \(-0.908236\pi\) | ||
0.958733 | − | 0.284307i | \(-0.0917637\pi\) | |||||||
\(72\) | 9.21502e29 | − | 8.92420e29i | 1.76675 | − | 1.71100i | ||||
\(73\) | −4.61844e27 | −0.00710117 | −0.00355058 | − | 0.999994i | \(-0.501130\pi\) | ||||
−0.00355058 | + | 0.999994i | \(0.501130\pi\) | |||||||
\(74\) | 3.98357e29 | + | 4.02637e29i | 0.492680 | + | 0.497974i | ||||
\(75\) | − | 1.77939e30i | − | 1.77537i | ||||||
\(76\) | −2.11743e30 | − | 2.26304e28i | −1.70920 | − | 0.0182673i | ||||
\(77\) | −6.41771e29 | −0.420270 | ||||||||
\(78\) | −3.52657e29 | + | 3.48908e29i | −0.187862 | + | 0.185865i | ||||
\(79\) | 3.06260e30i | 1.33063i | 0.746563 | + | 0.665315i | \(0.231703\pi\) | ||||
−0.746563 | + | 0.665315i | \(0.768297\pi\) | |||||||
\(80\) | 6.00126e29 | + | 1.28294e28i | 0.213207 | + | 0.00455791i | ||||
\(81\) | 8.89145e30 | 2.58948 | ||||||||
\(82\) | −4.32005e30 | − | 4.36647e30i | −1.03387 | − | 1.04498i | ||||
\(83\) | − | 3.67153e29i | − | 0.0723764i | −0.999345 | − | 0.0361882i | \(-0.988478\pi\) | ||
0.999345 | − | 0.0361882i | \(-0.0115216\pi\) | |||||||
\(84\) | −1.74372e29 | + | 1.63153e31i | −0.0283798 | + | 2.65537i | ||||
\(85\) | −2.06637e29 | −0.0278295 | ||||||||
\(86\) | −4.25627e30 | + | 4.21102e30i | −0.475394 | + | 0.470340i | ||||
\(87\) | − | 1.64037e31i | − | 1.52277i | ||||||
\(88\) | 2.64859e30 | + | 2.73490e30i | 0.204782 | + | 0.211455i | ||||
\(89\) | −2.12166e31 | −1.36910 | −0.684550 | − | 0.728966i | \(-0.740001\pi\) | ||||
−0.684550 | + | 0.728966i | \(0.740001\pi\) | |||||||
\(90\) | 6.83554e30 | + | 6.90899e30i | 0.368887 | + | 0.372850i | ||||
\(91\) | − | 4.48590e30i | − | 0.202856i | ||||||
\(92\) | −2.11537e31 | − | 2.26084e29i | −0.803122 | − | 0.00858351i | ||||
\(93\) | 6.53113e31 | 2.08574 | ||||||||
\(94\) | −2.18634e31 | + | 2.16310e31i | −0.588400 | + | 0.582145i | ||||
\(95\) | − | 1.60434e31i | − | 0.364517i | ||||||
\(96\) | 7.02470e31 | − | 6.65901e31i | 1.34986 | − | 1.27959i | ||||
\(97\) | 2.45829e30 | 0.0400208 | 0.0200104 | − | 0.999800i | \(-0.493630\pi\) | ||||
0.0200104 | + | 0.999800i | \(0.493630\pi\) | |||||||
\(98\) | −5.28617e31 | − | 5.34297e31i | −0.730338 | − | 0.738185i | ||||
\(99\) | 6.16431e31i | 0.723971i | ||||||||
\(100\) | 1.02010e30 | − | 9.54467e31i | 0.0102010 | − | 0.954467i | ||||
\(101\) | −1.51581e32 | −1.29271 | −0.646356 | − | 0.763036i | \(-0.723708\pi\) | ||||
−0.646356 | + | 0.763036i | \(0.723708\pi\) | |||||||
\(102\) | −2.36867e31 | + | 2.34349e31i | −0.172545 | + | 0.170710i | ||||
\(103\) | 2.50065e30i | 0.0155833i | 0.999970 | + | 0.00779163i | \(0.00248018\pi\) | ||||
−0.999970 | + | 0.00779163i | \(0.997520\pi\) | |||||||
\(104\) | −1.91166e31 | + | 1.85133e31i | −0.102065 | + | 0.0988442i | ||||
\(105\) | −1.23618e32 | −0.566307 | ||||||||
\(106\) | 1.57037e32 | + | 1.58724e32i | 0.618169 | + | 0.624811i | ||||
\(107\) | 2.37982e32i | 0.806129i | 0.915172 | + | 0.403064i | \(0.132055\pi\) | ||||
−0.915172 | + | 0.403064i | \(0.867945\pi\) | |||||||
\(108\) | 9.29932e32 | + | 9.93881e30i | 2.71438 | + | 0.0290104i | ||||
\(109\) | −3.79577e32 | −0.956040 | −0.478020 | − | 0.878349i | \(-0.658645\pi\) | ||||
−0.478020 | + | 0.878349i | \(0.658645\pi\) | |||||||
\(110\) | −2.05050e31 | + | 2.02870e31i | −0.0446248 | + | 0.0441505i | ||||
\(111\) | 6.91966e32i | 1.30292i | ||||||||
\(112\) | −1.87068e31 | + | 8.75056e32i | −0.0305148 | + | 1.42741i | ||||
\(113\) | 5.36449e32 | 0.759055 | 0.379527 | − | 0.925181i | \(-0.376087\pi\) | ||||
0.379527 | + | 0.925181i | \(0.376087\pi\) | |||||||
\(114\) | −1.81949e33 | − | 1.83904e33i | −2.23600 | − | 2.26003i | ||||
\(115\) | − | 1.60278e32i | − | 0.171281i | ||||||
\(116\) | 9.40407e30 | − | 8.79899e32i | 0.00874960 | − | 0.818662i | ||||
\(117\) | −4.30878e32 | −0.349446 | ||||||||
\(118\) | 1.33966e32 | − | 1.32542e32i | 0.0948163 | − | 0.0938084i | ||||
\(119\) | − | 3.01302e32i | − | 0.186316i | ||||||
\(120\) | 5.10171e32 | + | 5.26796e32i | 0.275941 | + | 0.284933i | ||||
\(121\) | 1.92843e33 | 0.913351 | ||||||||
\(122\) | 3.55882e32 | + | 3.59705e32i | 0.147757 | + | 0.149345i | ||||
\(123\) | − | 7.50414e33i | − | 2.73413i | ||||||
\(124\) | 3.50332e33 | + | 3.74423e31i | 1.12133 | + | 0.0119844i | ||||
\(125\) | 1.48082e33 | 0.416814 | ||||||||
\(126\) | −1.00741e34 | + | 9.96705e33i | −2.49620 | + | 2.46966i | ||||
\(127\) | 4.53645e33i | 0.990505i | 0.868749 | + | 0.495252i | \(0.164924\pi\) | ||||
−0.868749 | + | 0.495252i | \(0.835076\pi\) | |||||||
\(128\) | 3.80624e33 | − | 3.53164e33i | 0.733056 | − | 0.680169i | ||||
\(129\) | −7.31475e33 | −1.24384 | ||||||||
\(130\) | −1.41804e32 | − | 1.43328e32i | −0.0213105 | − | 0.0215395i | ||||
\(131\) | − | 3.62488e33i | − | 0.481896i | −0.970538 | − | 0.240948i | \(-0.922542\pi\) | ||
0.970538 | − | 0.240948i | \(-0.0774583\pi\) | |||||||
\(132\) | −4.97081e31 | + | 4.65097e33i | −0.00585119 | + | 0.547471i | ||||
\(133\) | 2.33932e34 | 2.44041 | ||||||||
\(134\) | −3.86072e33 | + | 3.81968e33i | −0.357266 | + | 0.353468i | ||||
\(135\) | 7.04592e33i | 0.578892i | ||||||||
\(136\) | −1.28400e33 | + | 1.24347e33i | −0.0937435 | + | 0.0907851i | ||||
\(137\) | −1.09766e33 | −0.0712753 | −0.0356376 | − | 0.999365i | \(-0.511346\pi\) | ||||
−0.0356376 | + | 0.999365i | \(0.511346\pi\) | |||||||
\(138\) | −1.81772e34 | − | 1.83725e34i | −1.05066 | − | 1.06195i | ||||
\(139\) | 1.65733e34i | 0.853439i | 0.904384 | + | 0.426719i | \(0.140331\pi\) | ||||
−0.904384 | + | 0.426719i | \(0.859669\pi\) | |||||||
\(140\) | −6.63089e33 | − | 7.08688e31i | −0.304455 | − | 0.00325392i | ||||
\(141\) | −3.75741e34 | −1.53951 | ||||||||
\(142\) | 1.10465e34 | − | 1.09291e34i | 0.404214 | − | 0.399917i | ||||
\(143\) | − | 1.27879e33i | − | 0.0418237i | ||||||
\(144\) | 8.40505e34 | + | 1.79681e33i | 2.45890 | + | 0.0525658i | ||||
\(145\) | 6.66683e33 | 0.174595 | ||||||||
\(146\) | −2.12876e32 | − | 2.15164e32i | −0.00499438 | − | 0.00504804i | ||||
\(147\) | − | 9.18234e34i | − | 1.93142i | ||||||
\(148\) | −3.96697e32 | + | 3.71172e34i | −0.00748638 | + | 0.700468i | ||||
\(149\) | −6.72732e34 | −1.13989 | −0.569944 | − | 0.821684i | \(-0.693035\pi\) | ||||
−0.569944 | + | 0.821684i | \(0.693035\pi\) | |||||||
\(150\) | 8.28979e34 | − | 8.20166e34i | 1.26207 | − | 1.24865i | ||||
\(151\) | 1.31684e35i | 1.80262i | 0.433178 | + | 0.901308i | \(0.357392\pi\) | ||||
−0.433178 | + | 0.901308i | \(0.642608\pi\) | |||||||
\(152\) | −9.65437e34 | − | 9.96898e34i | −1.18912 | − | 1.22787i | ||||
\(153\) | −2.89405e34 | −0.320955 | ||||||||
\(154\) | −2.95809e34 | − | 2.98988e34i | −0.295583 | − | 0.298759i | ||||
\(155\) | 2.65440e34i | 0.239144i | ||||||||
\(156\) | −3.25098e34 | − | 3.47454e32i | −0.264253 | − | 0.00282425i | ||||
\(157\) | 6.25240e34 | 0.458831 | 0.229415 | − | 0.973329i | \(-0.426319\pi\) | ||||
0.229415 | + | 0.973329i | \(0.426319\pi\) | |||||||
\(158\) | −1.42680e35 | + | 1.41164e35i | −0.945912 | + | 0.935856i | ||||
\(159\) | 2.72781e35i | 1.63478i | ||||||||
\(160\) | 2.70637e34 | + | 2.85499e34i | 0.146713 | + | 0.154770i | ||||
\(161\) | 2.33705e35 | 1.14671 | ||||||||
\(162\) | 4.09830e35 | + | 4.14234e35i | 1.82123 | + | 1.84080i | ||||
\(163\) | − | 3.41681e35i | − | 1.37600i | −0.725709 | − | 0.688001i | \(-0.758488\pi\) | ||
0.725709 | − | 0.688001i | \(-0.241512\pi\) | |||||||
\(164\) | 4.30205e33 | − | 4.02524e35i | 0.0157099 | − | 1.46991i | ||||
\(165\) | −3.52396e34 | −0.116758 | ||||||||
\(166\) | 1.71049e34 | − | 1.69230e34i | 0.0514506 | − | 0.0509037i | ||||
\(167\) | 2.40656e35i | 0.657557i | 0.944407 | + | 0.328779i | \(0.106637\pi\) | ||||
−0.944407 | + | 0.328779i | \(0.893363\pi\) | |||||||
\(168\) | −7.68132e35 | + | 7.43891e35i | −1.90760 | + | 1.84740i | ||||
\(169\) | −4.33841e35 | −0.979813 | ||||||||
\(170\) | −9.52446e33 | − | 9.62680e33i | −0.0195730 | − | 0.0197833i | ||||
\(171\) | − | 2.24695e36i | − | 4.20394i | ||||||
\(172\) | −3.92365e35 | − | 4.19347e33i | −0.668706 | − | 0.00714692i | ||||
\(173\) | 6.96522e35 | 1.08192 | 0.540962 | − | 0.841047i | \(-0.318060\pi\) | ||||
0.540962 | + | 0.841047i | \(0.318060\pi\) | |||||||
\(174\) | 7.64214e35 | − | 7.56090e35i | 1.08250 | − | 1.07099i | ||||
\(175\) | 1.05449e36i | 1.36280i | ||||||||
\(176\) | −5.33271e33 | + | 2.49451e35i | −0.00629137 | + | 0.294295i | ||||
\(177\) | 2.30232e35 | 0.248081 | ||||||||
\(178\) | −9.77929e35 | − | 9.88436e35i | −0.962913 | − | 0.973260i | ||||
\(179\) | 9.85163e35i | 0.886869i | 0.896307 | + | 0.443435i | \(0.146240\pi\) | ||||
−0.896307 | + | 0.443435i | \(0.853760\pi\) | |||||||
\(180\) | −6.80706e33 | + | 6.36907e35i | −0.00560531 | + | 0.524465i | ||||
\(181\) | 1.91175e36 | 1.44070 | 0.720349 | − | 0.693611i | \(-0.243982\pi\) | ||||
0.720349 | + | 0.693611i | \(0.243982\pi\) | |||||||
\(182\) | 2.08989e35 | − | 2.06767e35i | 0.144205 | − | 0.142672i | ||||
\(183\) | 6.18184e35i | 0.390751i | ||||||||
\(184\) | −9.64499e35 | − | 9.95929e35i | −0.558749 | − | 0.576957i | ||||
\(185\) | −2.81230e35 | −0.149388 | ||||||||
\(186\) | 3.01037e36 | + | 3.04272e36i | 1.46694 | + | 1.48270i | ||||
\(187\) | − | 8.58918e34i | − | 0.0384137i | ||||||
\(188\) | −2.01549e36 | − | 2.15409e34i | −0.827664 | − | 0.00884581i | ||||
\(189\) | −1.02738e37 | −3.87563 | ||||||||
\(190\) | 7.47428e35 | − | 7.39482e35i | 0.259126 | − | 0.256372i | ||||
\(191\) | 2.21443e36i | 0.705876i | 0.935647 | + | 0.352938i | \(0.114817\pi\) | ||||
−0.935647 | + | 0.352938i | \(0.885183\pi\) | |||||||
\(192\) | 6.34016e36 | + | 2.03347e35i | 1.85901 | + | 0.0596235i | ||||
\(193\) | 3.14662e36 | 0.849037 | 0.424519 | − | 0.905419i | \(-0.360443\pi\) | ||||
0.424519 | + | 0.905419i | \(0.360443\pi\) | |||||||
\(194\) | 1.13309e35 | + | 1.14527e35i | 0.0281473 | + | 0.0284498i | ||||
\(195\) | − | 2.46320e35i | − | 0.0563568i | ||||||
\(196\) | 5.26414e34 | − | 4.92543e36i | 0.0110976 | − | 1.03836i | ||||
\(197\) | 6.11775e36 | 1.18886 | 0.594432 | − | 0.804146i | \(-0.297377\pi\) | ||||
0.594432 | + | 0.804146i | \(0.297377\pi\) | |||||||
\(198\) | −2.87182e36 | + | 2.84129e36i | −0.514653 | + | 0.509182i | ||||
\(199\) | 1.63495e36i | 0.270306i | 0.990825 | + | 0.135153i | \(0.0431525\pi\) | ||||
−0.990825 | + | 0.135153i | \(0.956847\pi\) | |||||||
\(200\) | 4.49368e36 | − | 4.35187e36i | 0.685682 | − | 0.664043i | ||||
\(201\) | −6.63497e36 | −0.934765 | ||||||||
\(202\) | −6.98675e36 | − | 7.06182e36i | −0.909187 | − | 0.918956i | ||||
\(203\) | 9.72104e36i | 1.16890i | ||||||||
\(204\) | −2.18357e36 | − | 2.33372e34i | −0.242708 | − | 0.00259398i | ||||
\(205\) | 3.04985e36 | 0.313485 | ||||||||
\(206\) | −1.16500e35 | + | 1.15262e35i | −0.0110777 | + | 0.0109600i | ||||
\(207\) | − | 2.24477e37i | − | 1.97536i | ||||||
\(208\) | −1.74363e36 | − | 3.72750e34i | −0.142050 | − | 0.00303672i | ||||
\(209\) | 6.66867e36 | 0.503151 | ||||||||
\(210\) | −5.69787e36 | − | 5.75910e36i | −0.398294 | − | 0.402574i | ||||
\(211\) | − | 7.39921e36i | − | 0.479364i | −0.970851 | − | 0.239682i | \(-0.922957\pi\) | ||
0.970851 | − | 0.239682i | \(-0.0770432\pi\) | |||||||
\(212\) | −1.56382e35 | + | 1.46320e37i | −0.00939321 | + | 0.878882i | ||||
\(213\) | 1.89844e37 | 1.05760 | ||||||||
\(214\) | −1.10871e37 | + | 1.09692e37i | −0.573057 | + | 0.566965i | ||||
\(215\) | − | 2.97288e36i | − | 0.142614i | ||||||
\(216\) | 4.24000e37 | + | 4.37817e37i | 1.88845 | + | 1.94999i | ||||
\(217\) | −3.87043e37 | −1.60105 | ||||||||
\(218\) | −1.74957e37 | − | 1.76837e37i | −0.672400 | − | 0.679625i | ||||
\(219\) | − | 3.69777e35i | − | 0.0132079i | ||||||
\(220\) | −1.89026e36 | − | 2.02025e34i | −0.0627709 | − | 0.000670875i | ||||
\(221\) | 6.00374e35 | 0.0185415 | ||||||||
\(222\) | −3.22373e37 | + | 3.18946e37i | −0.926212 | + | 0.916366i | ||||
\(223\) | − | 5.90826e36i | − | 0.157973i | −0.996876 | − | 0.0789863i | \(-0.974832\pi\) | ||
0.996876 | − | 0.0789863i | \(-0.0251683\pi\) | |||||||
\(224\) | −4.16293e37 | + | 3.94621e37i | −1.03617 | + | 0.982228i | ||||
\(225\) | 1.01285e38 | 2.34761 | ||||||||
\(226\) | 2.47263e37 | + | 2.49920e37i | 0.533857 | + | 0.539593i | ||||
\(227\) | 8.07545e37i | 1.62462i | 0.583223 | + | 0.812312i | \(0.301791\pi\) | ||||
−0.583223 | + | 0.812312i | \(0.698209\pi\) | |||||||
\(228\) | 1.81191e36 | − | 1.69533e38i | 0.0339765 | − | 3.17904i | ||||
\(229\) | 2.52873e37 | 0.442115 | 0.221058 | − | 0.975261i | \(-0.429049\pi\) | ||||
0.221058 | + | 0.975261i | \(0.429049\pi\) | |||||||
\(230\) | 7.46701e36 | − | 7.38763e36i | 0.121759 | − | 0.120465i | ||||
\(231\) | − | 5.13835e37i | − | 0.781686i | ||||||
\(232\) | 4.14261e37 | − | 4.01188e37i | 0.588121 | − | 0.569560i | ||||
\(233\) | −9.45644e37 | −1.25324 | −0.626618 | − | 0.779326i | \(-0.715561\pi\) | ||||
−0.626618 | + | 0.779326i | \(0.715561\pi\) | |||||||
\(234\) | −1.98603e37 | − | 2.00737e37i | −0.245772 | − | 0.248413i | ||||
\(235\) | − | 1.52710e37i | − | 0.176515i | ||||||
\(236\) | 1.23497e37 | + | 1.31990e35i | 0.133372 | + | 0.00142544i | ||||
\(237\) | −2.45208e38 | −2.47492 | ||||||||
\(238\) | 1.40370e37 | − | 1.38878e37i | 0.132448 | − | 0.131040i | ||||
\(239\) | − | 1.78296e38i | − | 1.57317i | −0.617484 | − | 0.786584i | \(-0.711848\pi\) | ||
0.617484 | − | 0.786584i | \(-0.288152\pi\) | |||||||
\(240\) | −1.02719e36 | + | 4.80492e37i | −0.00847753 | + | 0.396558i | ||||
\(241\) | 8.20511e37 | 0.633595 | 0.316797 | − | 0.948493i | \(-0.397392\pi\) | ||||
0.316797 | + | 0.948493i | \(0.397392\pi\) | |||||||
\(242\) | 8.88864e37 | + | 8.98415e37i | 0.642376 | + | 0.649279i | ||||
\(243\) | 3.10664e38i | 2.10179i | ||||||||
\(244\) | −3.54399e35 | + | 3.31596e37i | −0.00224520 | + | 0.210074i | ||||
\(245\) | 3.73191e37 | 0.221449 | ||||||||
\(246\) | 3.49602e38 | − | 3.45886e38i | 1.94363 | − | 1.92296i | ||||
\(247\) | 4.66132e37i | 0.242861i | ||||||||
\(248\) | 1.59733e38 | + | 1.64938e38i | 0.780130 | + | 0.805552i | ||||
\(249\) | 2.93962e37 | 0.134617 | ||||||||
\(250\) | 6.82549e37 | + | 6.89883e37i | 0.293153 | + | 0.296303i | ||||
\(251\) | 2.58885e38i | 1.04310i | 0.853220 | + | 0.521551i | \(0.174646\pi\) | ||||
−0.853220 | + | 0.521551i | \(0.825354\pi\) | |||||||
\(252\) | −9.28688e38 | − | 9.92552e36i | −3.51125 | − | 0.0375271i | ||||
\(253\) | 6.66218e37 | 0.236422 | ||||||||
\(254\) | −2.11344e38 | + | 2.09097e38i | −0.704125 | + | 0.696640i | ||||
\(255\) | − | 1.65445e37i | − | 0.0517619i | ||||||
\(256\) | 3.39971e38 | + | 1.45423e37i | 0.999086 | + | 0.0427361i | ||||
\(257\) | −3.36333e38 | −0.928622 | −0.464311 | − | 0.885672i | \(-0.653698\pi\) | ||||
−0.464311 | + | 0.885672i | \(0.653698\pi\) | |||||||
\(258\) | −3.37156e38 | − | 3.40779e38i | −0.874815 | − | 0.884214i | ||||
\(259\) | − | 4.10068e38i | − | 1.00014i | ||||||
\(260\) | 1.41213e35 | − | 1.32127e37i | 0.000323818 | − | 0.0302983i | ||||
\(261\) | 9.33721e38 | 2.01358 | ||||||||
\(262\) | 1.68876e38 | − | 1.67080e38i | 0.342568 | − | 0.338926i | ||||
\(263\) | 3.51698e38i | 0.671239i | 0.941998 | + | 0.335620i | \(0.108946\pi\) | ||||
−0.941998 | + | 0.335620i | \(0.891054\pi\) | |||||||
\(264\) | −2.18970e38 | + | 2.12060e38i | −0.393299 | + | 0.380887i | ||||
\(265\) | −1.10864e38 | −0.187438 | ||||||||
\(266\) | 1.07825e39 | + | 1.08984e39i | 1.71639 | + | 1.73483i | ||||
\(267\) | − | 1.69871e39i | − | 2.54647i | ||||||
\(268\) | −3.55902e38 | − | 3.80376e36i | −0.502543 | − | 0.00537102i | ||||
\(269\) | −5.77334e37 | −0.0768052 | −0.0384026 | − | 0.999262i | \(-0.512227\pi\) | ||||
−0.0384026 | + | 0.999262i | \(0.512227\pi\) | |||||||
\(270\) | −3.28255e38 | + | 3.24765e38i | −0.411520 | + | 0.407145i | ||||
\(271\) | − | 1.07532e39i | − | 1.27066i | −0.772242 | − | 0.635328i | \(-0.780865\pi\) | ||
0.772242 | − | 0.635328i | \(-0.219135\pi\) | |||||||
\(272\) | −1.17114e38 | − | 2.50363e36i | −0.130468 | − | 0.00278913i | ||||
\(273\) | 3.59165e38 | 0.377304 | ||||||||
\(274\) | −5.05941e37 | − | 5.11377e37i | −0.0501292 | − | 0.0506678i | ||||
\(275\) | 3.00601e38i | 0.280975i | ||||||||
\(276\) | 1.81015e37 | − | 1.69368e39i | 0.0159650 | − | 1.49378i | ||||
\(277\) | −1.81603e39 | −1.51164 | −0.755819 | − | 0.654781i | \(-0.772761\pi\) | ||||
−0.755819 | + | 0.654781i | \(0.772761\pi\) | |||||||
\(278\) | −7.72116e38 | + | 7.63908e38i | −0.606688 | + | 0.600239i | ||||
\(279\) | 3.71761e39i | 2.75802i | ||||||||
\(280\) | −3.02334e38 | − | 3.12186e38i | −0.211816 | − | 0.218718i | ||||
\(281\) | 2.38762e39 | 1.58003 | 0.790014 | − | 0.613089i | \(-0.210073\pi\) | ||||
0.790014 | + | 0.613089i | \(0.210073\pi\) | |||||||
\(282\) | −1.73189e39 | − | 1.75050e39i | −1.08277 | − | 1.09440i | ||||
\(283\) | − | 2.42757e39i | − | 1.43413i | −0.697006 | − | 0.717065i | \(-0.745485\pi\) | ||
0.697006 | − | 0.717065i | \(-0.254515\pi\) | |||||||
\(284\) | 1.01833e39 | + | 1.08835e37i | 0.568583 | + | 0.00607683i | ||||
\(285\) | 1.28452e39 | 0.677988 | ||||||||
\(286\) | 5.95762e37 | − | 5.89428e37i | 0.0297315 | − | 0.0294154i | ||||
\(287\) | 4.44705e39i | 2.09875i | ||||||||
\(288\) | 3.79040e39 | + | 3.99856e39i | 1.69202 | + | 1.78494i | ||||
\(289\) | −2.32759e39 | −0.982970 | ||||||||
\(290\) | 3.07292e38 | + | 3.10594e38i | 0.122796 | + | 0.124115i | ||||
\(291\) | 1.96824e38i | 0.0744371i | ||||||||
\(292\) | 2.11989e35 | − | 1.98349e37i | 7.58907e−5 | − | 0.00710076i | ||||
\(293\) | −4.98153e39 | −1.68842 | −0.844210 | − | 0.536012i | \(-0.819930\pi\) | ||||
−0.844210 | + | 0.536012i | \(0.819930\pi\) | |||||||
\(294\) | 4.27786e39 | − | 4.23239e39i | 1.37300 | − | 1.35840i | ||||
\(295\) | 9.35715e37i | 0.0284440i | ||||||||
\(296\) | −1.74750e39 | + | 1.69235e39i | −0.503211 | + | 0.487330i | ||||
\(297\) | −2.92874e39 | −0.799057 | ||||||||
\(298\) | −3.10080e39 | − | 3.13412e39i | −0.801704 | − | 0.810318i | ||||
\(299\) | 4.65679e38i | 0.114116i | ||||||||
\(300\) | 7.64197e39 | + | 8.16749e37i | 1.77527 | + | 0.0189735i | ||||
\(301\) | 4.33482e39 | 0.954787 | ||||||||
\(302\) | −6.13490e39 | + | 6.06969e39i | −1.28144 | + | 1.26781i | ||||
\(303\) | − | 1.21363e40i | − | 2.40439i | ||||||
\(304\) | 1.94383e38 | − | 9.09274e39i | 0.0365326 | − | 1.70890i | ||||
\(305\) | −2.51244e38 | −0.0448021 | ||||||||
\(306\) | −1.33395e39 | − | 1.34828e39i | −0.225733 | − | 0.228159i | ||||
\(307\) | 4.44575e39i | 0.714055i | 0.934094 | + | 0.357027i | \(0.116210\pi\) | ||||
−0.934094 | + | 0.357027i | \(0.883790\pi\) | |||||||
\(308\) | 2.94577e37 | − | 2.75623e39i | 0.00449145 | − | 0.420246i | ||||
\(309\) | −2.00216e38 | −0.0289843 | ||||||||
\(310\) | −1.23663e39 | + | 1.22348e39i | −0.170001 | + | 0.168194i | ||||
\(311\) | 8.05331e39i | 1.05150i | 0.850640 | + | 0.525749i | \(0.176215\pi\) | ||||
−0.850640 | + | 0.525749i | \(0.823785\pi\) | |||||||
\(312\) | −1.48227e39 | − | 1.53058e39i | −0.183846 | − | 0.189837i | ||||
\(313\) | 1.22081e40 | 1.43859 | 0.719297 | − | 0.694703i | \(-0.244464\pi\) | ||||
0.719297 | + | 0.694703i | \(0.244464\pi\) | |||||||
\(314\) | 2.88190e39 | + | 2.91286e39i | 0.322704 | + | 0.326171i | ||||
\(315\) | − | 7.03650e39i | − | 0.748838i | ||||||
\(316\) | −1.31530e40 | − | 1.40575e38i | −1.33055 | − | 0.0142205i | ||||
\(317\) | 1.31141e40 | 1.26122 | 0.630608 | − | 0.776101i | \(-0.282806\pi\) | ||||
0.630608 | + | 0.776101i | \(0.282806\pi\) | |||||||
\(318\) | −1.27083e40 | + | 1.25732e40i | −1.16212 | + | 1.14977i | ||||
\(319\) | 2.77116e39i | 0.240997i | ||||||||
\(320\) | −8.26447e37 | + | 2.57678e39i | −0.00683621 | + | 0.213147i | ||||
\(321\) | −1.90541e40 | −1.49937 | ||||||||
\(322\) | 1.07721e40 | + | 1.08878e40i | 0.806501 | + | 0.815167i | ||||
\(323\) | 3.13084e39i | 0.223060i | ||||||||
\(324\) | −4.08123e38 | + | 3.81863e40i | −0.0276739 | + | 2.58933i | ||||
\(325\) | −2.10117e39 | −0.135621 | ||||||||
\(326\) | 1.59182e40 | − | 1.57490e40i | 0.978166 | − | 0.967768i | ||||
\(327\) | − | 3.03909e40i | − | 1.77820i | ||||||
\(328\) | 1.89511e40 | − | 1.83530e40i | 1.05597 | − | 1.02265i | ||||
\(329\) | 2.22669e40 | 1.18175 | ||||||||
\(330\) | −1.62429e39 | − | 1.64174e39i | −0.0821182 | − | 0.0830005i | ||||
\(331\) | 4.77499e39i | 0.229998i | 0.993366 | + | 0.114999i | \(0.0366866\pi\) | ||||
−0.993366 | + | 0.114999i | \(0.963313\pi\) | |||||||
\(332\) | 1.57682e39 | + | 1.68525e37i | 0.0723723 | + | 0.000773492i | ||||
\(333\) | −3.93877e40 | −1.72287 | ||||||||
\(334\) | −1.12117e40 | + | 1.10925e40i | −0.467441 | + | 0.462472i | ||||
\(335\) | − | 2.69660e39i | − | 0.107177i | ||||||
\(336\) | −7.00616e40 | − | 1.49776e39i | −2.65492 | − | 0.0567563i | ||||
\(337\) | 2.78352e40 | 1.00581 | 0.502906 | − | 0.864341i | \(-0.332264\pi\) | ||||
0.502906 | + | 0.864341i | \(0.332264\pi\) | |||||||
\(338\) | −1.99969e40 | − | 2.02117e40i | −0.689120 | − | 0.696524i | ||||
\(339\) | 4.29509e40i | 1.41181i | ||||||||
\(340\) | 9.48478e36 | − | 8.87450e38i | 0.000297416 | − | 0.0278279i | ||||
\(341\) | −1.10334e40 | −0.330095 | ||||||||
\(342\) | 1.04681e41 | − | 1.03568e41i | 2.98847 | − | 2.95670i | ||||
\(343\) | 2.01317e39i | 0.0548498i | ||||||||
\(344\) | −1.78898e40 | − | 1.84728e40i | −0.465233 | − | 0.480393i | ||||
\(345\) | 1.28327e40 | 0.318575 | ||||||||
\(346\) | 3.21045e40 | + | 3.24495e40i | 0.760937 | + | 0.769114i | ||||
\(347\) | 2.07944e40i | 0.470625i | 0.971920 | + | 0.235312i | \(0.0756113\pi\) | ||||
−0.971920 | + | 0.235312i | \(0.924389\pi\) | |||||||
\(348\) | 7.04493e40 | + | 7.52940e38i | 1.52268 | + | 0.0162739i | ||||
\(349\) | 2.76042e39 | 0.0569861 | 0.0284931 | − | 0.999594i | \(-0.490929\pi\) | ||||
0.0284931 | + | 0.999594i | \(0.490929\pi\) | |||||||
\(350\) | −4.91263e40 | + | 4.86041e40i | −0.968781 | + | 0.958483i | ||||
\(351\) | − | 2.04715e40i | − | 0.385689i | ||||||
\(352\) | −1.18672e40 | + | 1.12494e40i | −0.213632 | + | 0.202510i | ||||
\(353\) | −9.59897e40 | −1.65131 | −0.825656 | − | 0.564174i | \(-0.809195\pi\) | ||||
−0.825656 | + | 0.564174i | \(0.809195\pi\) | |||||||
\(354\) | 1.06120e40 | + | 1.07260e40i | 0.174480 | + | 0.176355i | ||||
\(355\) | 7.71567e39i | 0.121261i | ||||||||
\(356\) | 9.73854e38 | − | 9.11193e40i | 0.0146317 | − | 1.36902i | ||||
\(357\) | 2.41238e40 | 0.346541 | ||||||||
\(358\) | −4.58967e40 | + | 4.54088e40i | −0.630453 | + | 0.623751i | ||||
\(359\) | − | 6.27660e40i | − | 0.824543i | −0.911061 | − | 0.412271i | \(-0.864736\pi\) | ||
0.911061 | − | 0.412271i | \(-0.135264\pi\) | |||||||
\(360\) | −2.99859e40 | + | 2.90396e40i | −0.376771 | + | 0.364881i | ||||
\(361\) | −1.59881e41 | −1.92168 | ||||||||
\(362\) | 8.81175e40 | + | 8.90643e40i | 1.01327 | + | 1.02416i | ||||
\(363\) | 1.54400e41i | 1.69880i | ||||||||
\(364\) | 1.92657e40 | + | 2.05906e38i | 0.202844 | + | 0.00216793i | ||||
\(365\) | 1.50286e38 | 0.00151437 | ||||||||
\(366\) | −2.87999e40 | + | 2.84938e40i | −0.277775 | + | 0.274823i | ||||
\(367\) | 8.57201e39i | 0.0791454i | 0.999217 | + | 0.0395727i | \(0.0125997\pi\) | ||||
−0.999217 | + | 0.0395727i | \(0.987400\pi\) | |||||||
\(368\) | 1.94194e39 | − | 9.08390e40i | 0.0171660 | − | 0.802985i | ||||
\(369\) | 4.27146e41 | 3.61539 | ||||||||
\(370\) | −1.29627e40 | − | 1.31019e40i | −0.105067 | − | 0.106196i | ||||
\(371\) | − | 1.61653e41i | − | 1.25488i | ||||||
\(372\) | −2.99783e39 | + | 2.80494e41i | −0.0222905 | + | 2.08563i | ||||
\(373\) | 1.37825e41 | 0.981716 | 0.490858 | − | 0.871240i | \(-0.336683\pi\) | ||||
0.490858 | + | 0.871240i | \(0.336683\pi\) | |||||||
\(374\) | 4.00152e39 | − | 3.95898e39i | 0.0273073 | − | 0.0270170i | ||||
\(375\) | 1.18562e41i | 0.775258i | ||||||||
\(376\) | −9.18956e40 | − | 9.48902e40i | −0.575823 | − | 0.594588i | ||||
\(377\) | −1.93701e40 | −0.116324 | ||||||||
\(378\) | −4.73547e41 | − | 4.78635e41i | −2.72580 | − | 2.75509i | ||||
\(379\) | − | 1.50229e41i | − | 0.828946i | −0.910062 | − | 0.414473i | \(-0.863966\pi\) | ||
0.910062 | − | 0.414473i | \(-0.136034\pi\) | |||||||
\(380\) | 6.89019e40 | + | 7.36401e38i | 0.364497 | + | 0.00389562i | ||||
\(381\) | −3.63212e41 | −1.84230 | ||||||||
\(382\) | −1.03166e41 | + | 1.02069e41i | −0.501790 | + | 0.496455i | ||||
\(383\) | − | 2.19628e41i | − | 1.02449i | −0.858840 | − | 0.512244i | \(-0.828814\pi\) | ||
0.858840 | − | 0.512244i | \(-0.171186\pi\) | |||||||
\(384\) | 2.82762e41 | + | 3.04748e41i | 1.26509 | + | 1.36346i | ||||
\(385\) | 2.08834e40 | 0.0896251 | ||||||||
\(386\) | 1.45036e41 | + | 1.46594e41i | 0.597143 | + | 0.603560i | ||||
\(387\) | − | 4.16366e41i | − | 1.64475i | ||||||
\(388\) | −1.12837e38 | + | 1.05577e40i | −0.000427705 | + | 0.0400185i | ||||
\(389\) | 2.11359e40 | 0.0768826 | 0.0384413 | − | 0.999261i | \(-0.487761\pi\) | ||||
0.0384413 | + | 0.999261i | \(0.487761\pi\) | |||||||
\(390\) | 1.14756e40 | − | 1.13536e40i | 0.0400627 | − | 0.0396368i | ||||
\(391\) | 3.12780e40i | 0.104812i | ||||||||
\(392\) | 2.31892e41 | − | 2.24574e41i | 0.745948 | − | 0.722407i | ||||
\(393\) | 2.90227e41 | 0.896308 | ||||||||
\(394\) | 2.81983e41 | + | 2.85013e41i | 0.836150 | + | 0.845134i | ||||
\(395\) | − | 9.96581e40i | − | 0.283765i | ||||||
\(396\) | −2.64740e41 | − | 2.82945e39i | −0.723930 | − | 0.00773713i | ||||
\(397\) | −4.90660e41 | −1.28864 | −0.644322 | − | 0.764754i | \(-0.722860\pi\) | ||||
−0.644322 | + | 0.764754i | \(0.722860\pi\) | |||||||
\(398\) | −7.61689e40 | + | 7.53592e40i | −0.192154 | + | 0.190111i | ||||
\(399\) | 1.87298e42i | 4.53907i | ||||||||
\(400\) | 4.09870e41 | + | 8.76213e39i | 0.954304 | + | 0.0204009i | ||||
\(401\) | 1.99805e41 | 0.446989 | 0.223494 | − | 0.974705i | \(-0.428254\pi\) | ||||
0.223494 | + | 0.974705i | \(0.428254\pi\) | |||||||
\(402\) | −3.05824e41 | − | 3.09110e41i | −0.657437 | − | 0.664501i | ||||
\(403\) | − | 7.71221e40i | − | 0.159330i | ||||||
\(404\) | 6.95764e39 | − | 6.50996e41i | 0.0138153 | − | 1.29264i | ||||
\(405\) | −2.89330e41 | −0.552222 | ||||||||
\(406\) | −4.52883e41 | + | 4.48069e41i | −0.830940 | + | 0.822106i | ||||
\(407\) | − | 1.16898e41i | − | 0.206203i | ||||||
\(408\) | −9.95591e40 | − | 1.02803e41i | −0.168857 | − | 0.174359i | ||||
\(409\) | 3.16160e41 | 0.515625 | 0.257812 | − | 0.966195i | \(-0.416998\pi\) | ||||
0.257812 | + | 0.966195i | \(0.416998\pi\) | |||||||
\(410\) | 1.40576e41 | + | 1.42086e41i | 0.220480 | + | 0.222849i | ||||
\(411\) | − | 8.78845e40i | − | 0.132569i | ||||||
\(412\) | −1.07396e40 | − | 1.14782e38i | −0.0155824 | − | 0.000166539i | ||||
\(413\) | −1.36439e41 | −0.190430 | ||||||||
\(414\) | 1.04579e42 | − | 1.03467e42i | 1.40423 | − | 1.38931i | ||||
\(415\) | 1.19473e40i | 0.0154347i | ||||||||
\(416\) | −7.86321e40 | − | 8.29504e40i | −0.0977478 | − | 0.103116i | ||||
\(417\) | −1.32695e42 | −1.58736 | ||||||||
\(418\) | 3.07377e41 | + | 3.10679e41i | 0.353875 | + | 0.357678i | ||||
\(419\) | 2.27724e41i | 0.252338i | 0.992009 | + | 0.126169i | \(0.0402682\pi\) | ||||
−0.992009 | + | 0.126169i | \(0.959732\pi\) | |||||||
\(420\) | 5.67413e39 | − | 5.30904e41i | 0.00605216 | − | 0.566275i | ||||
\(421\) | 5.81964e41 | 0.597561 | 0.298781 | − | 0.954322i | \(-0.403420\pi\) | ||||
0.298781 | + | 0.954322i | \(0.403420\pi\) | |||||||
\(422\) | 3.44714e41 | − | 3.41049e41i | 0.340768 | − | 0.337146i | ||||
\(423\) | − | 2.13877e42i | − | 2.03572i | ||||||
\(424\) | −6.88883e41 | + | 6.67143e41i | −0.631382 | + | 0.611456i | ||||
\(425\) | −1.41128e41 | −0.124563 | ||||||||
\(426\) | 8.75040e41 | + | 8.84442e41i | 0.743831 | + | 0.751823i | ||||
\(427\) | − | 3.66344e41i | − | 0.299946i | ||||||
\(428\) | −1.02207e42 | − | 1.09235e40i | −0.806083 | − | 0.00861515i | ||||
\(429\) | 1.02387e41 | 0.0777905 | ||||||||
\(430\) | 1.38500e41 | − | 1.37028e41i | 0.101381 | − | 0.100303i | ||||
\(431\) | − | 6.23287e41i | − | 0.439594i | −0.975546 | − | 0.219797i | \(-0.929461\pi\) | ||
0.975546 | − | 0.219797i | \(-0.0705395\pi\) | |||||||
\(432\) | −8.53689e40 | + | 3.99334e42i | −0.0580176 | + | 2.71392i | ||||
\(433\) | 2.42979e42 | 1.59134 | 0.795669 | − | 0.605732i | \(-0.207120\pi\) | ||||
0.795669 | + | 0.605732i | \(0.207120\pi\) | |||||||
\(434\) | −1.78399e42 | − | 1.80315e42i | −1.12604 | − | 1.13814i | ||||
\(435\) | 5.33781e41i | 0.324740i | ||||||||
\(436\) | 1.74228e40 | − | 1.63018e42i | 0.0102173 | − | 0.955985i | ||||
\(437\) | −2.42843e42 | −1.37285 | ||||||||
\(438\) | 1.72271e40 | − | 1.70440e40i | 0.00938917 | − | 0.00928936i | ||||
\(439\) | 1.23596e42i | 0.649489i | 0.945802 | + | 0.324744i | \(0.105278\pi\) | ||||
−0.945802 | + | 0.324744i | \(0.894722\pi\) | |||||||
\(440\) | −8.61859e40 | − | 8.89944e40i | −0.0436710 | − | 0.0450941i | ||||
\(441\) | 5.22672e42 | 2.55394 | ||||||||
\(442\) | 2.76728e40 | + | 2.79702e40i | 0.0130406 | + | 0.0131807i | ||||
\(443\) | 3.70666e42i | 1.68470i | 0.538928 | + | 0.842352i | \(0.318830\pi\) | ||||
−0.538928 | + | 0.842352i | \(0.681170\pi\) | |||||||
\(444\) | −2.97180e42 | − | 3.17617e40i | −1.30284 | − | 0.0139244i | ||||
\(445\) | 6.90394e41 | 0.291969 | ||||||||
\(446\) | 2.75254e41 | − | 2.72327e41i | 0.112299 | − | 0.111105i | ||||
\(447\) | − | 5.38625e42i | − | 2.12015i | ||||||
\(448\) | −3.75726e42 | − | 1.20506e41i | −1.42700 | − | 0.0457678i | ||||
\(449\) | 1.53593e42 | 0.562898 | 0.281449 | − | 0.959576i | \(-0.409185\pi\) | ||||
0.281449 | + | 0.959576i | \(0.409185\pi\) | |||||||
\(450\) | 4.66850e42 | + | 4.71866e42i | 1.65111 | + | 1.66886i | ||||
\(451\) | 1.26771e42i | 0.432710i | ||||||||
\(452\) | −2.46233e40 | + | 2.30390e42i | −0.00811207 | + | 0.759011i | ||||
\(453\) | −1.05434e43 | −3.35280 | ||||||||
\(454\) | −3.76218e42 | + | 3.72219e42i | −1.15491 | + | 1.14263i | ||||
\(455\) | 1.45973e41i | 0.0432603i | ||||||||
\(456\) | 7.98169e42 | − | 7.72980e42i | 2.28380 | − | 2.21172i | ||||
\(457\) | 9.11690e41 | 0.251877 | 0.125938 | − | 0.992038i | \(-0.459806\pi\) | ||||
0.125938 | + | 0.992038i | \(0.459806\pi\) | |||||||
\(458\) | 1.16556e42 | + | 1.17808e42i | 0.310948 | + | 0.314289i | ||||
\(459\) | − | 1.37500e42i | − | 0.354242i | ||||||
\(460\) | 6.88349e41 | + | 7.35685e39i | 0.171271 | + | 0.00183049i | ||||
\(461\) | 2.18901e42 | 0.526057 | 0.263029 | − | 0.964788i | \(-0.415279\pi\) | ||||
0.263029 | + | 0.964788i | \(0.415279\pi\) | |||||||
\(462\) | 2.39385e42 | − | 2.36840e42i | 0.555681 | − | 0.549774i | ||||
\(463\) | − | 2.51512e42i | − | 0.563980i | −0.959417 | − | 0.281990i | \(-0.909006\pi\) | ||
0.959417 | − | 0.281990i | \(-0.0909945\pi\) | |||||||
\(464\) | 3.77849e42 | + | 8.07758e40i | 0.818522 | + | 0.0174982i | ||||
\(465\) | −2.12525e42 | −0.444798 | ||||||||
\(466\) | −4.35873e42 | − | 4.40556e42i | −0.881424 | − | 0.890895i | ||||
\(467\) | 4.49771e42i | 0.878864i | 0.898276 | + | 0.439432i | \(0.144820\pi\) | ||||
−0.898276 | + | 0.439432i | \(0.855180\pi\) | |||||||
\(468\) | 1.97776e40 | − | 1.85050e42i | 0.00373456 | − | 0.349426i | ||||
\(469\) | 3.93197e42 | 0.717538 | ||||||||
\(470\) | 7.11442e41 | − | 7.03879e41i | 0.125480 | − | 0.124146i | ||||
\(471\) | 5.00600e42i | 0.853408i | ||||||||
\(472\) | 5.63082e41 | + | 5.81431e41i | 0.0927897 | + | 0.0958134i | ||||
\(473\) | 1.23572e42 | 0.196853 | ||||||||
\(474\) | −1.13023e43 | − | 1.14237e43i | −1.74066 | − | 1.75936i | ||||
\(475\) | − | 1.09572e43i | − | 1.63156i | ||||||
\(476\) | 1.29401e42 | + | 1.38300e40i | 0.186306 | + | 0.00199117i | ||||
\(477\) | −1.55270e43 | −2.16170 | ||||||||
\(478\) | 8.30644e42 | − | 8.21813e42i | 1.11833 | − | 1.10644i | ||||
\(479\) | 1.36411e43i | 1.77616i | 0.459689 | + | 0.888080i | \(0.347961\pi\) | ||||
−0.459689 | + | 0.888080i | \(0.652039\pi\) | |||||||
\(480\) | −2.28586e42 | + | 2.16686e42i | −0.287865 | + | 0.272880i | ||||
\(481\) | 8.17100e41 | 0.0995300 | ||||||||
\(482\) | 3.78195e42 | + | 3.82259e42i | 0.445619 | + | 0.450407i | ||||
\(483\) | 1.87116e43i | 2.13283i | ||||||||
\(484\) | −8.85161e40 | + | 8.28207e42i | −0.00976104 | + | 0.913299i | ||||
\(485\) | −7.99935e40 | −0.00853468 | ||||||||
\(486\) | −1.44732e43 | + | 1.43193e43i | −1.49411 | + | 1.47823i | ||||
\(487\) | − | 1.93772e43i | − | 1.93565i | −0.251618 | − | 0.967827i | \(-0.580963\pi\) | ||
0.251618 | − | 0.967827i | \(-0.419037\pi\) | |||||||
\(488\) | −1.56117e42 | + | 1.51190e42i | −0.150915 | + | 0.146153i | ||||
\(489\) | 2.73568e43 | 2.55931 | ||||||||
\(490\) | 1.72014e42 | + | 1.73862e42i | 0.155749 | + | 0.157423i | ||||
\(491\) | − | 1.38022e41i | − | 0.0120960i | −0.999982 | − | 0.00604802i | \(-0.998075\pi\) | ||
0.999982 | − | 0.00604802i | \(-0.00192516\pi\) | |||||||
\(492\) | 3.22282e43 | + | 3.44445e41i | 2.73397 | + | 0.0292198i | ||||
\(493\) | −1.30102e42 | −0.106840 | ||||||||
\(494\) | −2.17161e42 | + | 2.14853e42i | −0.172644 | + | 0.170809i | ||||
\(495\) | − | 2.00588e42i | − | 0.154391i | ||||||
\(496\) | −3.21609e41 | + | 1.50440e43i | −0.0239674 | + | 1.12114i | ||||
\(497\) | −1.12504e43 | −0.811830 | ||||||||
\(498\) | 1.35495e42 | + | 1.36951e42i | 0.0946789 | + | 0.0956962i | ||||
\(499\) | − | 1.55609e43i | − | 1.05299i | −0.850177 | − | 0.526497i | \(-0.823505\pi\) | ||
0.850177 | − | 0.526497i | \(-0.176495\pi\) | |||||||
\(500\) | −6.79705e40 | + | 6.35971e42i | −0.00445452 | + | 0.416790i | ||||
\(501\) | −1.92682e43 | −1.22303 | ||||||||
\(502\) | −1.20609e43 | + | 1.19327e43i | −0.741515 | + | 0.733632i | ||||
\(503\) | 6.36940e42i | 0.379325i | 0.981849 | + | 0.189662i | \(0.0607393\pi\) | ||||
−0.981849 | + | 0.189662i | \(0.939261\pi\) | |||||||
\(504\) | −4.23433e43 | − | 4.37231e43i | −2.44285 | − | 2.52245i | ||||
\(505\) | 4.93248e42 | 0.275679 | ||||||||
\(506\) | 3.07078e42 | + | 3.10377e42i | 0.166280 | + | 0.168067i | ||||
\(507\) | − | 3.47356e43i | − | 1.82241i | ||||||
\(508\) | −1.94828e43 | − | 2.08226e41i | −0.990448 | − | 0.0105856i | ||||
\(509\) | −1.11048e43 | −0.547048 | −0.273524 | − | 0.961865i | \(-0.588189\pi\) | ||||
−0.273524 | + | 0.961865i | \(0.588189\pi\) | |||||||
\(510\) | 7.70772e41 | − | 7.62579e41i | 0.0367962 | − | 0.0364051i | ||||
\(511\) | 2.19134e41i | 0.0101386i | ||||||||
\(512\) | 1.49927e43 | + | 1.65089e43i | 0.672296 | + | 0.740283i | ||||
\(513\) | 1.06756e44 | 4.63994 | ||||||||
\(514\) | −1.55025e43 | − | 1.56690e43i | −0.653117 | − | 0.660134i | ||||
\(515\) | − | 8.13721e40i | − | 0.00332322i | ||||||
\(516\) | 3.35751e41 | − | 3.14148e43i | 0.0132930 | − | 1.24377i | ||||
\(517\) | 6.34760e42 | 0.243647 | ||||||||
\(518\) | 1.91042e43 | − | 1.89011e43i | 0.710973 | − | 0.703415i | ||||
\(519\) | 5.57672e43i | 2.01234i | ||||||||
\(520\) | 6.22061e41 | − | 6.02429e41i | 0.0217660 | − | 0.0210791i | ||||
\(521\) | −4.50656e43 | −1.52912 | −0.764560 | − | 0.644552i | \(-0.777044\pi\) | ||||
−0.764560 | + | 0.644552i | \(0.777044\pi\) | |||||||
\(522\) | 4.30377e43 | + | 4.35001e43i | 1.41619 | + | 1.43141i | ||||
\(523\) | − | 2.33715e43i | − | 0.745864i | −0.927859 | − | 0.372932i | \(-0.878352\pi\) | ||
0.927859 | − | 0.372932i | \(-0.121648\pi\) | |||||||
\(524\) | 1.55679e43 | + | 1.66384e41i | 0.481868 | + | 0.00515005i | ||||
\(525\) | −8.44278e43 | −2.53476 | ||||||||
\(526\) | −1.63849e43 | + | 1.62107e43i | −0.477167 | + | 0.472095i | ||||
\(527\) | − | 5.18002e42i | − | 0.146339i | ||||||
\(528\) | −1.99724e43 | − | 4.26965e41i | −0.547377 | − | 0.0117017i | ||||
\(529\) | 1.33482e43 | 0.354921 | ||||||||
\(530\) | −5.11002e42 | − | 5.16493e42i | −0.131828 | − | 0.133245i | ||||
\(531\) | 1.31051e43i | 0.328042i | ||||||||
\(532\) | −1.07376e42 | + | 1.00467e44i | −0.0260808 | + | 2.44027i | ||||
\(533\) | −8.86118e42 | −0.208860 | ||||||||
\(534\) | 7.91394e43 | − | 7.82981e43i | 1.81023 | − | 1.79098i | ||||
\(535\) | − | 7.74402e42i | − | 0.171912i | ||||||
\(536\) | −1.62272e43 | − | 1.67560e43i | −0.349630 | − | 0.361023i | ||||
\(537\) | −7.88773e43 | −1.64954 | ||||||||
\(538\) | −2.66108e42 | − | 2.68968e42i | −0.0540185 | − | 0.0545989i | ||||
\(539\) | 1.55122e43i | 0.305671i | ||||||||
\(540\) | −3.02603e43 | − | 3.23412e41i | −0.578859 | − | 0.00618666i | ||||
\(541\) | 6.53826e43 | 1.21424 | 0.607122 | − | 0.794609i | \(-0.292324\pi\) | ||||
0.607122 | + | 0.794609i | \(0.292324\pi\) | |||||||
\(542\) | 5.00968e43 | − | 4.95642e43i | 0.903278 | − | 0.893676i | ||||
\(543\) | 1.53065e44i | 2.67964i | ||||||||
\(544\) | −5.28144e42 | − | 5.57148e42i | −0.0897780 | − | 0.0947083i | ||||
\(545\) | 1.23516e43 | 0.203881 | ||||||||
\(546\) | 1.65549e43 | + | 1.67327e43i | 0.265365 | + | 0.268216i | ||||
\(547\) | − | 2.02527e43i | − | 0.315273i | −0.987497 | − | 0.157636i | \(-0.949613\pi\) | ||
0.987497 | − | 0.157636i | \(-0.0503874\pi\) | |||||||
\(548\) | 5.03833e40 | − | 4.71415e42i | 0.000761724 | − | 0.0712712i | ||||
\(549\) | −3.51879e43 | −0.516697 | ||||||||
\(550\) | −1.40044e43 | + | 1.38555e43i | −0.199738 | + | 0.197615i | ||||
\(551\) | − | 1.01012e44i | − | 1.39941i | ||||||
\(552\) | 7.97393e43 | − | 7.72229e43i | 1.07312 | − | 1.03925i | ||||
\(553\) | 1.45314e44 | 1.89978 | ||||||||
\(554\) | −8.37058e43 | − | 8.46052e43i | −1.06316 | − | 1.07459i | ||||
\(555\) | − | 2.25168e43i | − | 0.277855i | ||||||
\(556\) | −7.11777e43 | − | 7.60725e41i | −0.853390 | − | 0.00912075i | ||||
\(557\) | −8.56431e43 | −0.997722 | −0.498861 | − | 0.866682i | \(-0.666248\pi\) | ||||
−0.498861 | + | 0.866682i | \(0.666248\pi\) | |||||||
\(558\) | −1.73196e44 | + | 1.71355e44i | −1.96060 | + | 1.93976i | ||||
\(559\) | 8.63754e42i | 0.0950170i | ||||||||
\(560\) | 6.08724e41 | − | 2.84746e43i | 0.00650747 | − | 0.304403i | ||||
\(561\) | 6.87695e42 | 0.0714480 | ||||||||
\(562\) | 1.10052e44 | + | 1.11234e44i | 1.11126 | + | 1.12320i | ||||
\(563\) | 1.69794e44i | 1.66644i | 0.552945 | + | 0.833218i | \(0.313504\pi\) | ||||
−0.552945 | + | 0.833218i | \(0.686496\pi\) | |||||||
\(564\) | 1.72468e42 | − | 1.61370e44i | 0.0164529 | − | 1.53942i | ||||
\(565\) | −1.74562e43 | −0.161873 | ||||||||
\(566\) | 1.13095e44 | − | 1.11893e44i | 1.01949 | − | 1.00865i | ||||
\(567\) | − | 4.21879e44i | − | 3.69708i | ||||||
\(568\) | 4.64303e43 | + | 4.79433e43i | 0.395575 | + | 0.408465i | ||||
\(569\) | 1.73820e44 | 1.43981 | 0.719904 | − | 0.694074i | \(-0.244186\pi\) | ||||
0.719904 | + | 0.694074i | \(0.244186\pi\) | |||||||
\(570\) | 5.92068e43 | + | 5.98430e43i | 0.476842 | + | 0.481965i | ||||
\(571\) | − | 9.06850e43i | − | 0.710162i | −0.934835 | − | 0.355081i | \(-0.884453\pi\) | ||
0.934835 | − | 0.355081i | \(-0.115547\pi\) | |||||||
\(572\) | 5.49205e42 | + | 5.86972e40i | 0.0418213 | + | 0.000446973i | ||||
\(573\) | −1.77299e44 | −1.31290 | ||||||||
\(574\) | −2.07179e44 | + | 2.04976e44i | −1.49195 | + | 1.47609i | ||||
\(575\) | − | 1.09466e44i | − | 0.766642i | ||||||
\(576\) | −1.15748e43 | + | 3.60891e44i | −0.0788412 | + | 2.45819i | ||||
\(577\) | 5.56570e43 | 0.368728 | 0.184364 | − | 0.982858i | \(-0.440977\pi\) | ||||
0.184364 | + | 0.982858i | \(0.440977\pi\) | |||||||
\(578\) | −1.07285e44 | − | 1.08437e44i | −0.691341 | − | 0.698769i | ||||
\(579\) | 2.51935e44i | 1.57918i | ||||||||
\(580\) | −3.06011e41 | + | 2.86322e43i | −0.00186591 | + | 0.174585i | ||||
\(581\) | −1.74206e43 | −0.103334 | ||||||||
\(582\) | −9.16961e42 | + | 9.07213e42i | −0.0529155 | + | 0.0523530i | ||||
\(583\) | − | 4.60823e43i | − | 0.258724i | ||||||
\(584\) | 9.33839e41 | − | 9.04368e41i | 0.00510113 | − | 0.00494015i | ||||
\(585\) | 1.40209e43 | 0.0745216 | ||||||||
\(586\) | −2.29612e44 | − | 2.32079e44i | −1.18750 | − | 1.20026i | ||||
\(587\) | 2.62247e44i | 1.31978i | 0.751362 | + | 0.659890i | \(0.229397\pi\) | ||||
−0.751362 | + | 0.659890i | \(0.770603\pi\) | |||||||
\(588\) | 3.94356e44 | + | 4.21475e42i | 1.93131 | + | 0.0206412i | ||||
\(589\) | 4.02178e44 | 1.91679 | ||||||||
\(590\) | −4.35930e42 | + | 4.31296e42i | −0.0202202 | + | 0.0200052i | ||||
\(591\) | 4.89819e44i | 2.21124i | ||||||||
\(592\) | −1.59390e44 | − | 3.40741e42i | −0.700348 | − | 0.0149719i | ||||
\(593\) | −9.29311e43 | −0.397453 | −0.198727 | − | 0.980055i | \(-0.563681\pi\) | ||||
−0.198727 | + | 0.980055i | \(0.563681\pi\) | |||||||
\(594\) | −1.34993e44 | − | 1.36444e44i | −0.561991 | − | 0.568030i | ||||
\(595\) | 9.80447e42i | 0.0397331i | ||||||||
\(596\) | 3.08788e42 | − | 2.88920e44i | 0.0121821 | − | 1.13982i | ||||
\(597\) | −1.30903e44 | −0.502758 | ||||||||
\(598\) | −2.16950e43 | + | 2.14644e43i | −0.0811224 | + | 0.0802600i | ||||
\(599\) | − | 4.04496e44i | − | 1.47260i | −0.676655 | − | 0.736301i | \(-0.736571\pi\) | ||
0.676655 | − | 0.736301i | \(-0.263429\pi\) | |||||||
\(600\) | 3.48434e44 | + | 3.59788e44i | 1.23509 | + | 1.27534i | ||||
\(601\) | −3.28279e43 | −0.113305 | −0.0566527 | − | 0.998394i | \(-0.518043\pi\) | ||||
−0.0566527 | + | 0.998394i | \(0.518043\pi\) | |||||||
\(602\) | 1.99803e44 | + | 2.01950e44i | 0.671519 | + | 0.678735i | ||||
\(603\) | − | 3.77672e44i | − | 1.23605i | ||||||
\(604\) | −5.65548e44 | − | 6.04440e42i | −1.80251 | − | 0.0192647i | ||||
\(605\) | −6.27517e43 | −0.194778 | ||||||||
\(606\) | 5.65407e44 | − | 5.59396e44i | 1.70922 | − | 1.69105i | ||||
\(607\) | 2.42531e43i | 0.0714081i | 0.999362 | + | 0.0357041i | \(0.0113674\pi\) | ||||
−0.999362 | + | 0.0357041i | \(0.988633\pi\) | |||||||
\(608\) | 4.32571e44 | − | 4.10053e44i | 1.24051 | − | 1.17593i | ||||
\(609\) | −7.78318e44 | −2.17410 | ||||||||
\(610\) | −1.15805e43 | − | 1.17049e43i | −0.0315101 | − | 0.0318487i | ||||
\(611\) | 4.43690e43i | 0.117603i | ||||||||
\(612\) | 1.32839e42 | − | 1.24292e44i | 0.00343007 | − | 0.320936i | ||||
\(613\) | −3.90547e44 | −0.982440 | −0.491220 | − | 0.871035i | \(-0.663449\pi\) | ||||
−0.491220 | + | 0.871035i | \(0.663449\pi\) | |||||||
\(614\) | −2.07118e44 | + | 2.04917e44i | −0.507604 | + | 0.502208i | ||||
\(615\) | 2.44187e44i | 0.583070i | ||||||||
\(616\) | 1.29765e44 | − | 1.25669e44i | 0.301901 | − | 0.292374i | ||||
\(617\) | −3.70500e44 | −0.839895 | −0.419948 | − | 0.907548i | \(-0.637952\pi\) | ||||
−0.419948 | + | 0.907548i | \(0.637952\pi\) | |||||||
\(618\) | −9.22847e42 | − | 9.32763e42i | −0.0203852 | − | 0.0206042i | ||||
\(619\) | − | 6.45166e44i | − | 1.38874i | −0.719618 | − | 0.694370i | \(-0.755683\pi\) | ||
0.719618 | − | 0.694370i | \(-0.244317\pi\) | |||||||
\(620\) | −1.13999e44 | − | 1.21838e42i | −0.239130 | − | 0.00255574i | ||||
\(621\) | 1.06652e45 | 2.18023 | ||||||||
\(622\) | −3.75187e44 | + | 3.71198e44i | −0.747483 | + | 0.739537i | ||||
\(623\) | 1.00668e45i | 1.95471i | ||||||||
\(624\) | 2.98444e42 | − | 1.39604e44i | 0.00564818 | − | 0.264208i | ||||
\(625\) | 4.69261e44 | 0.865634 | ||||||||
\(626\) | 5.62703e44 | + | 5.68750e44i | 1.01179 | + | 1.02266i | ||||
\(627\) | 5.33928e44i | 0.935842i | ||||||||
\(628\) | −2.86989e42 | + | 2.68523e44i | −0.00490355 | + | 0.458804i | ||||
\(629\) | 5.48817e43 | 0.0914150 | ||||||||
\(630\) | 3.27816e44 | − | 3.24331e44i | 0.532330 | − | 0.526671i | ||||
\(631\) | − | 3.80541e44i | − | 0.602465i | −0.953551 | − | 0.301233i | \(-0.902602\pi\) | ||
0.953551 | − | 0.301233i | \(-0.0973980\pi\) | |||||||
\(632\) | −5.99709e44 | − | 6.19252e44i | −0.925694 | − | 0.955860i | ||||
\(633\) | 5.92419e44 | 0.891600 | ||||||||
\(634\) | 6.04463e44 | + | 6.10958e44i | 0.887036 | + | 0.896567i | ||||
\(635\) | − | 1.47617e44i | − | 0.211231i | ||||||
\(636\) | −1.17152e45 | − | 1.25208e43i | −1.63469 | − | 0.0174710i | ||||
\(637\) | −1.08429e44 | −0.147541 | ||||||||
\(638\) | −1.29103e44 | + | 1.27730e44i | −0.171319 | + | 0.169497i | ||||
\(639\) | 1.08062e45i | 1.39848i | ||||||||
\(640\) | −1.23856e44 | + | 1.14921e44i | −0.156329 | + | 0.145050i | ||||
\(641\) | −3.15290e44 | −0.388134 | −0.194067 | − | 0.980988i | \(-0.562168\pi\) | ||||
−0.194067 | + | 0.980988i | \(0.562168\pi\) | |||||||
\(642\) | −8.78256e44 | − | 8.87692e44i | −1.05453 | − | 1.06586i | ||||
\(643\) | − | 6.19810e44i | − | 0.725910i | −0.931807 | − | 0.362955i | \(-0.881768\pi\) | ||
0.931807 | − | 0.362955i | \(-0.118232\pi\) | |||||||
\(644\) | −1.07272e43 | + | 1.00370e45i | −0.0122550 | + | 1.14664i | ||||
\(645\) | 2.38024e44 | 0.265256 | ||||||||
\(646\) | −1.45859e44 | + | 1.44309e44i | −0.158568 | + | 0.156882i | ||||
\(647\) | − | 1.08329e45i | − | 1.14888i | −0.818545 | − | 0.574442i | \(-0.805219\pi\) | ||
0.818545 | − | 0.574442i | \(-0.194781\pi\) | |||||||
\(648\) | −1.79783e45 | + | 1.74109e45i | −1.86015 | + | 1.80145i | ||||
\(649\) | −3.88944e43 | −0.0392619 | ||||||||
\(650\) | −9.68484e43 | − | 9.78890e43i | −0.0953847 | − | 0.0964096i | ||||
\(651\) | − | 3.09887e45i | − | 2.97788i | ||||||
\(652\) | 1.46743e45 | + | 1.56834e43i | 1.37592 | + | 0.0147054i | ||||
\(653\) | −8.28187e44 | −0.757735 | −0.378868 | − | 0.925451i | \(-0.623686\pi\) | ||||
−0.378868 | + | 0.925451i | \(0.623686\pi\) | |||||||
\(654\) | 1.41585e45 | − | 1.40080e45i | 1.26408 | − | 1.25064i | ||||
\(655\) | 1.17955e44i | 0.102767i | ||||||||
\(656\) | 1.72853e45 | + | 3.69522e43i | 1.46966 | + | 0.0314180i | ||||
\(657\) | 2.10482e43 | 0.0174650 | ||||||||
\(658\) | 1.02634e45 | + | 1.03737e45i | 0.831146 | + | 0.840077i | ||||
\(659\) | 1.81794e45i | 1.43686i | 0.695600 | + | 0.718429i | \(0.255138\pi\) | ||||
−0.695600 | + | 0.718429i | \(0.744862\pi\) | |||||||
\(660\) | 1.61752e42 | − | 1.51344e44i | 0.00124780 | − | 0.116752i | ||||
\(661\) | 2.20937e45 | 1.66359 | 0.831794 | − | 0.555085i | \(-0.187314\pi\) | ||||
0.831794 | + | 0.555085i | \(0.187314\pi\) | |||||||
\(662\) | −2.22457e44 | + | 2.20092e44i | −0.163500 | + | 0.161762i | ||||
\(663\) | 4.80691e43i | 0.0344865i | ||||||||
\(664\) | 7.18946e43 | + | 7.42375e43i | 0.0503509 | + | 0.0519917i | ||||
\(665\) | −7.61222e44 | −0.520433 | ||||||||
\(666\) | −1.81548e45 | − | 1.83499e45i | −1.21173 | − | 1.22475i | ||||
\(667\) | − | 1.00914e45i | − | 0.657561i | ||||||
\(668\) | −1.03355e45 | − | 1.10463e43i | −0.657520 | − | 0.00702736i | ||||
\(669\) | 4.73046e44 | 0.293823 | ||||||||
\(670\) | 1.25629e44 | − | 1.24294e44i | 0.0761891 | − | 0.0753792i | ||||
\(671\) | − | 1.04433e44i | − | 0.0618412i | ||||||
\(672\) | −3.15955e45 | − | 3.33306e45i | −1.82691 | − | 1.92723i | ||||
\(673\) | −2.06677e45 | −1.16695 | −0.583473 | − | 0.812132i | \(-0.698307\pi\) | ||||
−0.583473 | + | 0.812132i | \(0.698307\pi\) | |||||||
\(674\) | 1.28300e45 | + | 1.29679e45i | 0.707405 | + | 0.715006i | ||||
\(675\) | 4.81218e45i | 2.59109i | ||||||||
\(676\) | 1.99135e43 | − | 1.86323e45i | 0.0104713 | − | 0.979757i | ||||
\(677\) | 3.45773e45 | 1.77571 | 0.887856 | − | 0.460121i | \(-0.152194\pi\) | ||||
0.887856 | + | 0.460121i | \(0.152194\pi\) | |||||||
\(678\) | −2.00099e45 | + | 1.97972e45i | −1.00362 | + | 0.992954i | ||||
\(679\) | − | 1.16640e44i | − | 0.0571389i | ||||||
\(680\) | 4.17816e43 | − | 4.04630e43i | 0.0199914 | − | 0.0193605i | ||||
\(681\) | −6.46563e45 | −3.02174 | ||||||||
\(682\) | −5.08558e44 | − | 5.14023e44i | −0.232162 | − | 0.234656i | ||||
\(683\) | 3.98486e43i | 0.0177698i | 0.999961 | + | 0.00888488i | \(0.00282818\pi\) | ||||
−0.999961 | + | 0.00888488i | \(0.997172\pi\) | |||||||
\(684\) | 9.65004e45 | + | 1.03136e44i | 4.20370 | + | 0.0449278i | ||||
\(685\) | 3.57182e43 | 0.0151999 | ||||||||
\(686\) | −9.37895e43 | + | 9.27924e43i | −0.0389914 | + | 0.0385769i | ||||
\(687\) | 2.02464e45i | 0.822317i | ||||||||
\(688\) | 3.60196e43 | − | 1.68491e45i | 0.0142930 | − | 0.668592i | ||||
\(689\) | 3.22110e44 | 0.124881 | ||||||||
\(690\) | 5.91493e44 | + | 5.97848e44i | 0.224060 | + | 0.226467i | ||||
\(691\) | 1.35175e45i | 0.500319i | 0.968205 | + | 0.250159i | \(0.0804830\pi\) | ||||
−0.968205 | + | 0.250159i | \(0.919517\pi\) | |||||||
\(692\) | −3.19708e43 | + | 2.99137e45i | −0.0115626 | + | 1.08186i | ||||
\(693\) | 2.92482e45 | 1.03364 | ||||||||
\(694\) | −9.68768e44 | + | 9.58469e44i | −0.334555 | + | 0.330999i | ||||
\(695\) | − | 5.39300e44i | − | 0.182001i | ||||||
\(696\) | 3.21212e45 | + | 3.31679e45i | 1.05936 | + | 1.09388i | ||||
\(697\) | −5.95174e44 | −0.191831 | ||||||||
\(698\) | 1.27235e44 | + | 1.28602e44i | 0.0400794 | + | 0.0405100i | ||||
\(699\) | − | 7.57132e45i | − | 2.33097i | ||||||
\(700\) | −4.52873e45 | − | 4.84016e43i | −1.36272 | − | 0.0145643i | ||||
\(701\) | −5.09328e45 | −1.49799 | −0.748995 | − | 0.662575i | \(-0.769464\pi\) | ||||
−0.748995 | + | 0.662575i | \(0.769464\pi\) | |||||||
\(702\) | 9.53727e44 | − | 9.43588e44i | 0.274176 | − | 0.271262i | ||||
\(703\) | 4.26103e45i | 1.19737i | ||||||||
\(704\) | −1.07108e45 | − | 3.43525e43i | −0.294211 | − | 0.00943616i | ||||
\(705\) | 1.22267e45 | 0.328310 | ||||||||
\(706\) | −4.42442e45 | − | 4.47196e45i | −1.16140 | − | 1.17388i | ||||
\(707\) | 7.19215e45i | 1.84564i | ||||||||
\(708\) | −1.05678e43 | + | 9.88783e44i | −0.00265126 | + | 0.248067i | ||||
\(709\) | −3.07778e45 | −0.754915 | −0.377458 | − | 0.926027i | \(-0.623202\pi\) | ||||
−0.377458 | + | 0.926027i | \(0.623202\pi\) | |||||||
\(710\) | −3.59457e44 | + | 3.55636e44i | −0.0862012 | + | 0.0852848i | ||||
\(711\) | − | 1.39576e46i | − | 3.27263i | ||||||
\(712\) | 4.28995e45 | − | 4.15456e45i | 0.983495 | − | 0.952457i | ||||
\(713\) | 4.01787e45 | 0.900666 | ||||||||
\(714\) | 1.11193e45 | + | 1.12388e45i | 0.243729 | + | 0.246348i | ||||
\(715\) | 4.16122e43i | 0.00891917i | ||||||||
\(716\) | −4.23100e45 | − | 4.52196e43i | −0.886818 | − | 0.00947803i | ||||
\(717\) | 1.42753e46 | 2.92603 | ||||||||
\(718\) | 2.92414e45 | − | 2.89305e45i | 0.586147 | − | 0.579916i | ||||
\(719\) | − | 5.99920e45i | − | 1.17607i | −0.808837 | − | 0.588033i | \(-0.799903\pi\) | ||
0.808837 | − | 0.588033i | \(-0.200097\pi\) | |||||||
\(720\) | −2.73503e45 | − | 5.84689e43i | −0.524375 | − | 0.0112100i | ||||
\(721\) | 1.18650e44 | 0.0222487 | ||||||||
\(722\) | −7.36935e45 | − | 7.44853e45i | −1.35156 | − | 1.36608i | ||||
\(723\) | 6.56944e45i | 1.17846i | ||||||||
\(724\) | −8.77503e43 | + | 8.21042e45i | −0.0153968 | + | 1.44062i | ||||
\(725\) | 4.55327e45 | 0.781476 | ||||||||
\(726\) | −7.19318e45 | + | 7.11671e45i | −1.20763 | + | 1.19480i | ||||
\(727\) | − | 8.37590e44i | − | 0.137556i | −0.997632 | − | 0.0687782i | \(-0.978090\pi\) | ||
0.997632 | − | 0.0687782i | \(-0.0219101\pi\) | |||||||
\(728\) | 8.78415e44 | + | 9.07040e44i | 0.141123 | + | 0.145722i | ||||
\(729\) | −8.39733e45 | −1.31978 | ||||||||
\(730\) | 6.92706e42 | + | 7.00149e42i | 0.00106508 | + | 0.00107653i | ||||
\(731\) | 5.80153e44i | 0.0872699i | ||||||||
\(732\) | −2.65493e45 | − | 2.83750e43i | −0.390729 | − | 0.00417599i | ||||
\(733\) | −6.02634e45 | −0.867740 | −0.433870 | − | 0.900975i | \(-0.642852\pi\) | ||||
−0.433870 | + | 0.900975i | \(0.642852\pi\) | |||||||
\(734\) | −3.99352e44 | + | 3.95107e44i | −0.0562625 | + | 0.0556644i | ||||
\(735\) | 2.98796e45i | 0.411887i | ||||||||
\(736\) | 4.32151e45 | − | 4.09654e45i | 0.582895 | − | 0.552551i | ||||
\(737\) | 1.12088e45 | 0.147938 | ||||||||
\(738\) | 1.96883e46 | + | 1.98999e46i | 2.54277 | + | 2.57009i | ||||
\(739\) | − | 2.20478e45i | − | 0.278648i | −0.990247 | − | 0.139324i | \(-0.955507\pi\) | ||
0.990247 | − | 0.139324i | \(-0.0444929\pi\) | |||||||
\(740\) | 1.29086e43 | − | 1.20781e45i | 0.00159652 | − | 0.149379i | ||||
\(741\) | −3.73210e45 | −0.451712 | ||||||||
\(742\) | 7.53109e45 | − | 7.45103e45i | 0.892062 | − | 0.882579i | ||||
\(743\) | − | 6.54848e45i | − | 0.759135i | −0.925164 | − | 0.379568i | \(-0.876073\pi\) | ||
0.925164 | − | 0.379568i | \(-0.123927\pi\) | |||||||
\(744\) | −1.32058e46 | + | 1.27890e46i | −1.49830 | + | 1.45101i | ||||
\(745\) | 2.18909e45 | 0.243088 | ||||||||
\(746\) | 6.35271e45 | + | 6.42097e45i | 0.690459 | + | 0.697877i | ||||
\(747\) | 1.67327e45i | 0.178007i | ||||||||
\(748\) | 3.68881e44 | + | 3.94249e42i | 0.0384115 | + | 0.000410530i | ||||
\(749\) | 1.12917e46 | 1.15094 | ||||||||
\(750\) | −5.52357e45 | + | 5.46485e45i | −0.551112 | + | 0.545253i | ||||
\(751\) | 1.64814e46i | 1.60974i | 0.593450 | + | 0.804871i | \(0.297765\pi\) | ||||
−0.593450 | + | 0.804871i | \(0.702235\pi\) | |||||||
\(752\) | 1.85024e44 | − | 8.65497e45i | 0.0176906 | − | 0.827523i | ||||
\(753\) | −2.07277e46 | −1.94013 | ||||||||
\(754\) | −8.92820e44 | − | 9.02414e44i | −0.0818130 | − | 0.0826921i | ||||
\(755\) | − | 4.28505e45i | − | 0.384419i | ||||||
\(756\) | 4.71574e44 | − | 4.41231e46i | 0.0414191 | − | 3.87541i | ||||
\(757\) | 3.89000e44 | 0.0334515 | 0.0167258 | − | 0.999860i | \(-0.494676\pi\) | ||||
0.0167258 | + | 0.999860i | \(0.494676\pi\) | |||||||
\(758\) | 6.99885e45 | − | 6.92445e45i | 0.589277 | − | 0.583013i | ||||
\(759\) | 5.33409e45i | 0.439736i | ||||||||
\(760\) | 3.14156e45 | + | 3.24394e45i | 0.253588 | + | 0.261851i | ||||
\(761\) | 6.29711e45 | 0.497722 | 0.248861 | − | 0.968539i | \(-0.419944\pi\) | ||||
0.248861 | + | 0.968539i | \(0.419944\pi\) | |||||||
\(762\) | −1.67414e46 | − | 1.69213e46i | −1.29572 | − | 1.30965i | ||||
\(763\) | 1.80101e46i | 1.36497i | ||||||||
\(764\) | −9.51037e45 | − | 1.01644e44i | −0.705835 | − | 0.00754374i | ||||
\(765\) | 9.41734e44 | 0.0684456 | ||||||||
\(766\) | 1.02320e46 | − | 1.01232e46i | 0.728283 | − | 0.720541i | ||||
\(767\) | − | 2.71867e44i | − | 0.0189509i | ||||||
\(768\) | −1.16434e45 | + | 2.72199e46i | −0.0794875 | + | 1.85826i | ||||
\(769\) | −1.79196e46 | −1.19814 | −0.599070 | − | 0.800696i | \(-0.704463\pi\) | ||||
−0.599070 | + | 0.800696i | \(0.704463\pi\) | |||||||
\(770\) | 9.62572e44 | + | 9.72915e44i | 0.0630350 | + | 0.0637123i | ||||
\(771\) | − | 2.69286e46i | − | 1.72720i | ||||||
\(772\) | −1.44432e44 | + | 1.35138e46i | −0.00907372 | + | 0.848989i | ||||
\(773\) | −7.75856e45 | −0.477430 | −0.238715 | − | 0.971090i | \(-0.576726\pi\) | ||||
−0.238715 | + | 0.971090i | \(0.576726\pi\) | |||||||
\(774\) | 1.93976e46 | − | 1.91914e46i | 1.16921 | − | 1.15678i | ||||
\(775\) | 1.81288e46i | 1.07039i | ||||||||
\(776\) | −4.97061e44 | + | 4.81374e44i | −0.0287490 | + | 0.0278417i | ||||
\(777\) | 3.28322e46 | 1.86022 | ||||||||
\(778\) | 9.74211e44 | + | 9.84679e44i | 0.0540729 | + | 0.0546539i | ||||
\(779\) | − | 4.62095e46i | − | 2.51265i | ||||||
\(780\) | 1.05788e45 | + | 1.13063e43i | 0.0563536 | + | 0.000602289i | ||||
\(781\) | −3.20713e45 | −0.167379 | ||||||||
\(782\) | −1.45718e45 | + | 1.44169e45i | −0.0745082 | + | 0.0737162i | ||||
\(783\) | 4.43623e46i | 2.22242i | ||||||||
\(784\) | 2.11509e46 | + | 4.52161e44i | 1.03818 | + | 0.0221940i | ||||
\(785\) | −2.03455e45 | −0.0978485 | ||||||||
\(786\) | 1.33773e46 | + | 1.35211e46i | 0.630390 | + | 0.637163i | ||||
\(787\) | − | 9.43901e43i | − | 0.00435844i | −0.999998 | − | 0.00217922i | \(-0.999306\pi\) | ||
0.999998 | − | 0.00217922i | \(-0.000693668\pi\) | |||||||
\(788\) | −2.80808e44 | + | 2.62740e46i | −0.0127055 | + | 1.18880i | ||||
\(789\) | −2.81588e46 | −1.24848 | ||||||||
\(790\) | 4.64286e45 | − | 4.59351e45i | 0.201722 | − | 0.199577i | ||||
\(791\) | − | 2.54533e46i | − | 1.08373i | ||||||
\(792\) | −1.20707e46 | − | 1.24641e46i | −0.503653 | − | 0.520065i | ||||
\(793\) | 7.29976e44 | 0.0298495 | ||||||||
\(794\) | −2.26158e46 | − | 2.28588e46i | −0.906327 | − | 0.916065i | ||||
\(795\) | − | 8.87636e45i | − | 0.348627i | ||||||
\(796\) | −7.02165e45 | − | 7.50452e43i | −0.270290 | − | 0.00288878i | ||||
\(797\) | −3.19696e46 | −1.20616 | −0.603079 | − | 0.797681i | \(-0.706060\pi\) | ||||
−0.603079 | + | 0.797681i | \(0.706060\pi\) | |||||||
\(798\) | −8.72583e46 | + | 8.63307e46i | −3.22672 | + | 3.19241i | ||||
\(799\) | 2.98011e45i | 0.108015i | ||||||||
\(800\) | 1.84838e46 | + | 1.94989e46i | 0.656677 | + | 0.692739i | ||||
\(801\) | 9.66930e46 | 3.36725 | ||||||||
\(802\) | 9.20955e45 | + | 9.30850e45i | 0.314375 | + | 0.317753i | ||||
\(803\) | 6.24684e43i | 0.00209031i | ||||||||
\(804\) | 3.04549e44 | − | 2.84954e46i | 0.00998989 | − | 0.934711i | ||||
\(805\) | −7.60482e45 | −0.244543 | ||||||||
\(806\) | 3.59296e45 | − | 3.55476e45i | 0.113264 | − | 0.112060i | ||||
\(807\) | − | 4.62244e45i | − | 0.142855i | ||||||
\(808\) | 3.06493e46 | − | 2.96820e46i | 0.928621 | − | 0.899315i | ||||
\(809\) | −9.61726e45 | −0.285677 | −0.142838 | − | 0.989746i | \(-0.545623\pi\) | ||||
−0.142838 | + | 0.989746i | \(0.545623\pi\) | |||||||
\(810\) | −1.33360e46 | − | 1.34793e46i | −0.388388 | − | 0.392561i | ||||
\(811\) | 3.33522e46i | 0.952337i | 0.879354 | + | 0.476169i | \(0.157975\pi\) | ||||
−0.879354 | + | 0.476169i | \(0.842025\pi\) | |||||||
\(812\) | −4.17492e46 | − | 4.46202e44i | −1.16883 | − | 0.0124921i | ||||
\(813\) | 8.60956e46 | 2.36337 | ||||||||
\(814\) | 5.44601e45 | − | 5.38812e45i | 0.146585 | − | 0.145026i | ||||
\(815\) | 1.11184e46i | 0.293441i | ||||||||
\(816\) | 2.00454e44 | − | 9.37674e45i | 0.00518767 | − | 0.242666i | ||||
\(817\) | −4.50432e46 | −1.14308 | ||||||||
\(818\) | 1.45726e46 | + | 1.47292e46i | 0.362648 | + | 0.366545i | ||||
\(819\) | 2.04442e46i | 0.498916i | ||||||||
\(820\) | −1.39990e44 | + | 1.30983e46i | −0.00335024 | + | 0.313467i | ||||
\(821\) | 4.76322e46 | 1.11792 | 0.558959 | − | 0.829195i | \(-0.311201\pi\) | ||||
0.558959 | + | 0.829195i | \(0.311201\pi\) | |||||||
\(822\) | 4.09435e45 | − | 4.05083e45i | 0.0942402 | − | 0.0932384i | ||||
\(823\) | − | 4.85340e46i | − | 1.09559i | −0.836612 | − | 0.547796i | \(-0.815467\pi\) | ||
0.836612 | − | 0.547796i | \(-0.184533\pi\) | |||||||
\(824\) | −4.89670e44 | − | 5.05627e44i | −0.0108410 | − | 0.0111942i | ||||
\(825\) | −2.40677e46 | −0.522603 | ||||||||
\(826\) | −6.28882e45 | − | 6.35639e45i | −0.133933 | − | 0.135372i | ||||
\(827\) | − | 3.23463e46i | − | 0.675674i | −0.941205 | − | 0.337837i | \(-0.890305\pi\) | ||
0.941205 | − | 0.337837i | \(-0.109695\pi\) | |||||||
\(828\) | 9.64066e46 | + | 1.03036e45i | 1.97525 | + | 0.0211108i | ||||
\(829\) | −8.22952e46 | −1.65387 | −0.826936 | − | 0.562296i | \(-0.809918\pi\) | ||||
−0.826936 | + | 0.562296i | \(0.809918\pi\) | |||||||
\(830\) | −5.56598e44 | + | 5.50681e44i | −0.0109722 | + | 0.0108555i | ||||
\(831\) | − | 1.45401e47i | − | 2.81159i | ||||||
\(832\) | 2.40120e44 | − | 7.48671e45i | 0.00455465 | − | 0.142010i | ||||
\(833\) | −7.28277e45 | −0.135512 | ||||||||
\(834\) | −6.11625e46 | − | 6.18196e46i | −1.11642 | − | 1.12842i | ||||
\(835\) | − | 7.83103e45i | − | 0.140228i | ||||||
\(836\) | −3.06096e44 | + | 2.86401e46i | −0.00537721 | + | 0.503122i | ||||
\(837\) | −1.76628e47 | −3.04406 | ||||||||
\(838\) | −1.06092e46 | + | 1.04964e46i | −0.179381 | + | 0.177474i | ||||
\(839\) | 1.12025e47i | 1.85834i | 0.369656 | + | 0.929169i | \(0.379475\pi\) | ||||
−0.369656 | + | 0.929169i | \(0.620525\pi\) | |||||||
\(840\) | 2.49952e46 | − | 2.42064e46i | 0.406807 | − | 0.393969i | ||||
\(841\) | −2.06479e46 | −0.329715 | ||||||||
\(842\) | 2.68243e46 | + | 2.71125e46i | 0.420276 | + | 0.424791i | ||||
\(843\) | 1.91166e47i | 2.93879i | ||||||||
\(844\) | 3.17775e46 | + | 3.39628e44i | 0.479337 | + | 0.00512300i | ||||
\(845\) | 1.41173e46 | 0.208951 | ||||||||
\(846\) | 9.96409e46 | − | 9.85817e46i | 1.44714 | − | 1.43176i | ||||
\(847\) | − | 9.14995e46i | − | 1.30402i | ||||||
\(848\) | −6.28333e46 | − | 1.34324e45i | −0.878731 | − | 0.0187853i | ||||
\(849\) | 1.94364e47 | 2.66743 | ||||||||
\(850\) | −6.50496e45 | − | 6.57486e45i | −0.0876076 | − | 0.0885490i | ||||
\(851\) | 4.25689e46i | 0.562626i | ||||||||
\(852\) | −8.71394e44 | + | 8.15326e46i | −0.0113027 | + | 1.05754i | ||||
\(853\) | 1.49776e47 | 1.90659 | 0.953295 | − | 0.302040i | \(-0.0976677\pi\) | ||||
0.953295 | + | 0.302040i | \(0.0976677\pi\) | |||||||
\(854\) | 1.70672e46 | − | 1.68858e46i | 0.213224 | − | 0.210957i | ||||
\(855\) | 7.31165e46i | 0.896515i | ||||||||
\(856\) | −4.66010e46 | − | 4.81195e46i | −0.560808 | − | 0.579084i | ||||
\(857\) | 6.71938e46 | 0.793662 | 0.396831 | − | 0.917892i | \(-0.370110\pi\) | ||||
0.396831 | + | 0.917892i | \(0.370110\pi\) | |||||||
\(858\) | 4.71927e45 | + | 4.76998e45i | 0.0547115 | + | 0.0552994i | ||||
\(859\) | 1.13231e47i | 1.28847i | 0.764828 | + | 0.644235i | \(0.222824\pi\) | ||||
−0.764828 | + | 0.644235i | \(0.777176\pi\) | |||||||
\(860\) | 1.27677e46 | + | 1.36457e44i | 0.142606 | + | 0.00152412i | ||||
\(861\) | −3.56054e47 | −3.90360 | ||||||||
\(862\) | 2.90376e46 | − | 2.87290e46i | 0.312496 | − | 0.309174i | ||||
\(863\) | 1.18796e47i | 1.25495i | 0.778635 | + | 0.627477i | \(0.215912\pi\) | ||||
−0.778635 | + | 0.627477i | \(0.784088\pi\) | |||||||
\(864\) | −1.89976e47 | + | 1.80087e47i | −1.97006 | + | 1.86750i | ||||
\(865\) | −2.26650e46 | −0.230727 | ||||||||
\(866\) | 1.11995e47 | + | 1.13199e47i | 1.11922 | + | 1.13124i | ||||
\(867\) | − | 1.86359e47i | − | 1.82829i | ||||||
\(868\) | 1.77655e45 | − | 1.66224e47i | 0.0171105 | − | 1.60095i | ||||
\(869\) | 4.14243e46 | 0.391687 | ||||||||
\(870\) | −2.48678e46 | + | 2.46034e46i | −0.230849 | + | 0.228395i | ||||
\(871\) | 7.83483e45i | 0.0714067i | ||||||||
\(872\) | 7.67496e46 | − | 7.43275e46i | 0.686772 | − | 0.665098i | ||||
\(873\) | −1.12035e46 | −0.0984294 | ||||||||
\(874\) | −1.11933e47 | − | 1.13136e47i | −0.965550 | − | 0.975925i | ||||
\(875\) | − | 7.02615e46i | − | 0.595098i | ||||||
\(876\) | 1.58809e45 | + | 1.69730e43i | 0.0132071 | + | 0.000141154i | ||||
\(877\) | 4.86612e46 | 0.397365 | 0.198682 | − | 0.980064i | \(-0.436334\pi\) | ||||
0.198682 | + | 0.980064i | \(0.436334\pi\) | |||||||
\(878\) | −5.75807e46 | + | 5.69686e46i | −0.461705 | + | 0.456797i | ||||
\(879\) | − | 3.98847e47i | − | 3.14040i | ||||||
\(880\) | 1.73528e44 | − | 8.11721e45i | 0.00134167 | − | 0.0627602i | ||||
\(881\) | 1.38653e47 | 1.05273 | 0.526364 | − | 0.850259i | \(-0.323555\pi\) | ||||
0.526364 | + | 0.850259i | \(0.323555\pi\) | |||||||
\(882\) | 2.40913e47 | + | 2.43502e47i | 1.79624 | + | 1.81554i | ||||
\(883\) | − | 4.21902e46i | − | 0.308916i | −0.987999 | − | 0.154458i | \(-0.950637\pi\) | ||
0.987999 | − | 0.154458i | \(-0.0493631\pi\) | |||||||
\(884\) | −2.75575e43 | + | 2.57844e45i | −0.000198154 | + | 0.0185405i | ||||
\(885\) | −7.49183e45 | −0.0529048 | ||||||||
\(886\) | −1.72686e47 | + | 1.70850e47i | −1.19761 | + | 1.18488i | ||||
\(887\) | 1.47559e46i | 0.100505i | 0.998737 | + | 0.0502524i | \(0.0160026\pi\) | ||||
−0.998737 | + | 0.0502524i | \(0.983997\pi\) | |||||||
\(888\) | −1.35499e47 | − | 1.39914e47i | −0.906415 | − | 0.935953i | ||||
\(889\) | 2.15244e47 | 1.41417 | ||||||||
\(890\) | 3.18221e46 | + | 3.21640e46i | 0.205347 | + | 0.207554i | ||||
\(891\) | − | 1.20264e47i | − | 0.762244i | ||||||
\(892\) | 2.53743e46 | + | 2.71193e44i | 0.157964 | + | 0.00168826i | ||||
\(893\) | −2.31376e47 | −1.41480 | ||||||||
\(894\) | 2.50934e47 | − | 2.48267e47i | 1.50716 | − | 1.49114i | ||||
\(895\) | − | 3.20575e46i | − | 0.189130i | ||||||
\(896\) | −1.67568e47 | − | 1.80597e47i | −0.971098 | − | 1.04661i | ||||
\(897\) | −3.72847e46 | −0.212252 | ||||||||
\(898\) | 7.07951e46 | + | 7.15557e46i | 0.395896 | + | 0.400150i | ||||
\(899\) | 1.67125e47i | 0.918093i | ||||||||
\(900\) | −4.64905e45 | + | 4.34991e47i | −0.0250890 | + | 2.34747i | ||||
\(901\) | 2.16350e46 | 0.114699 | ||||||||
\(902\) | −5.90602e46 | + | 5.84323e46i | −0.307603 | + | 0.304333i | ||||
\(903\) | 3.47068e47i | 1.77587i | ||||||||
\(904\) | −1.08469e47 | + | 1.05046e47i | −0.545268 | + | 0.528060i | ||||
\(905\) | −6.22088e46 | −0.307238 | ||||||||
\(906\) | −4.85971e47 | − | 4.91193e47i | −2.35808 | − | 2.38342i | ||||
\(907\) | − | 7.24496e46i | − | 0.345398i | −0.984975 | − | 0.172699i | \(-0.944751\pi\) | ||
0.984975 | − | 0.172699i | \(-0.0552487\pi\) | |||||||
\(908\) | −3.46818e47 | − | 3.70668e45i | −1.62453 | − | 0.0173625i | ||||
\(909\) | 6.90817e47 | 3.17937 | ||||||||
\(910\) | −6.80056e45 | + | 6.72827e45i | −0.0307526 | + | 0.0304257i | ||||
\(911\) | 9.68720e46i | 0.430432i | 0.976566 | + | 0.215216i | \(0.0690455\pi\) | ||||
−0.976566 | + | 0.215216i | \(0.930954\pi\) | |||||||
\(912\) | 7.28013e47 | + | 1.55633e46i | 3.17849 | + | 0.0679492i | ||||
\(913\) | −4.96605e45 | −0.0213049 | ||||||||
\(914\) | 4.20222e46 | + | 4.24737e46i | 0.177149 | + | 0.179053i | ||||
\(915\) | − | 2.01159e46i | − | 0.0833301i | ||||||
\(916\) | −1.16070e45 | + | 1.08602e47i | −0.00472491 | + | 0.442090i | ||||
\(917\) | −1.71992e47 | −0.688018 | ||||||||
\(918\) | 6.40584e46 | − | 6.33775e46i | 0.251822 | − | 0.249145i | ||||
\(919\) | 3.03055e47i | 1.17077i | 0.810754 | + | 0.585386i | \(0.199057\pi\) | ||||
−0.810754 | + | 0.585386i | \(0.800943\pi\) | |||||||
\(920\) | 3.13851e46 | + | 3.24078e46i | 0.119157 | + | 0.123040i | ||||
\(921\) | −3.55951e47 | −1.32811 | ||||||||
\(922\) | 1.00897e47 | + | 1.01981e47i | 0.369986 | + | 0.373961i | ||||
\(923\) | − | 2.24175e46i | − | 0.0807903i | ||||||
\(924\) | 2.20678e47 | + | 2.35854e45i | 0.781641 | + | 0.00835393i | ||||
\(925\) | −1.92073e47 | −0.668650 | ||||||||
\(926\) | 1.17174e47 | − | 1.15929e47i | 0.400919 | − | 0.396657i | ||||
\(927\) | − | 1.13966e46i | − | 0.0383264i | ||||||
\(928\) | 1.70397e47 | + | 1.79755e47i | 0.563242 | + | 0.594174i | ||||
\(929\) | −5.44330e47 | −1.76852 | −0.884261 | − | 0.466993i | \(-0.845337\pi\) | ||||
−0.884261 | + | 0.466993i | \(0.845337\pi\) | |||||||
\(930\) | −9.79584e46 | − | 9.90110e46i | −0.312834 | − | 0.316196i | ||||
\(931\) | − | 5.65436e47i | − | 1.77496i | ||||||
\(932\) | 4.34056e45 | − | 4.06128e47i | 0.0133934 | − | 1.25316i | ||||
\(933\) | −6.44790e47 | −1.95575 | ||||||||
\(934\) | −2.09539e47 | + | 2.07311e47i | −0.624762 | + | 0.618121i | ||||
\(935\) | 2.79495e45i | 0.00819196i | ||||||||
\(936\) | 8.71226e46 | − | 8.43731e46i | 0.251025 | − | 0.243103i | ||||
\(937\) | 3.91148e47 | 1.10792 | 0.553958 | − | 0.832544i | \(-0.313117\pi\) | ||||
0.553958 | + | 0.832544i | \(0.313117\pi\) | |||||||
\(938\) | 1.81235e47 | + | 1.83182e47i | 0.504657 | + | 0.510080i | ||||
\(939\) | 9.77444e47i | 2.67573i | ||||||||
\(940\) | 6.55846e46 | + | 7.00947e44i | 0.176505 | + | 0.00188642i | ||||
\(941\) | 3.45260e47 | 0.913507 | 0.456753 | − | 0.889593i | \(-0.349012\pi\) | ||||
0.456753 | + | 0.889593i | \(0.349012\pi\) | |||||||
\(942\) | −2.33219e47 | + | 2.30740e47i | −0.606666 | + | 0.600217i | ||||
\(943\) | − | 4.61646e47i | − | 1.18065i | ||||||
\(944\) | −1.13372e45 | + | 5.30325e46i | −0.00285071 | + | 0.133349i | ||||
\(945\) | 3.34313e47 | 0.826502 | ||||||||
\(946\) | 5.69576e46 | + | 5.75696e46i | 0.138450 | + | 0.139938i | ||||
\(947\) | − | 6.77649e47i | − | 1.61959i | −0.586713 | − | 0.809795i | \(-0.699578\pi\) | ||
0.586713 | − | 0.809795i | \(-0.300422\pi\) | |||||||
\(948\) | 1.12552e46 | − | 1.05310e48i | 0.0264497 | − | 2.47478i | ||||
\(949\) | −4.36647e44 | −0.00100895 | ||||||||
\(950\) | 5.10474e47 | − | 5.05047e47i | 1.15983 | − | 1.14750i | ||||
\(951\) | 1.04998e48i | 2.34581i | ||||||||
\(952\) | 5.90000e46 | + | 6.09226e46i | 0.129617 | + | 0.133841i | ||||
\(953\) | 6.43964e47 | 1.39115 | 0.695577 | − | 0.718452i | \(-0.255149\pi\) | ||||
0.695577 | + | 0.718452i | \(0.255149\pi\) | |||||||
\(954\) | −7.15683e47 | − | 7.23373e47i | −1.52036 | − | 1.53670i | ||||
\(955\) | − | 7.20583e46i | − | 0.150532i | ||||||
\(956\) | 7.65731e47 | + | 8.18389e45i | 1.57308 | + | 0.0168125i | ||||
\(957\) | −2.21874e47 | −0.448245 | ||||||||
\(958\) | −6.35512e47 | + | 6.28756e47i | −1.26263 | + | 1.24921i | ||||
\(959\) | 5.20815e46i | 0.101762i | ||||||||
\(960\) | −2.06311e47 | − | 6.61697e45i | −0.396444 | − | 0.0127151i | ||||
\(961\) | −1.36264e47 | −0.257518 | ||||||||
\(962\) | 3.76623e46 | + | 3.80670e46i | 0.0700013 | + | 0.0707534i | ||||
\(963\) | − | 1.08459e48i | − | 1.98264i | ||||||
\(964\) | −3.76619e45 | + | 3.52387e47i | −0.00677127 | + | 0.633559i | ||||
\(965\) | −1.02392e47 | −0.181062 | ||||||||
\(966\) | −8.71735e47 | + | 8.62468e47i | −1.51618 | + | 1.50006i | ||||
\(967\) | 1.27943e46i | 0.0218874i | 0.999940 | + | 0.0109437i | \(0.00348355\pi\) | ||||
−0.999940 | + | 0.0109437i | \(0.996516\pi\) | |||||||
\(968\) | −3.89924e47 | + | 3.77619e47i | −0.656107 | + | 0.635401i | ||||
\(969\) | −2.50672e47 | −0.414882 | ||||||||
\(970\) | −3.68711e45 | − | 3.72673e45i | −0.00600259 | − | 0.00606709i | ||||
\(971\) | 1.02864e47i | 0.164724i | 0.996602 | + | 0.0823620i | \(0.0262464\pi\) | ||||
−0.996602 | + | 0.0823620i | \(0.973754\pi\) | |||||||
\(972\) | −1.33421e48 | − | 1.42596e46i | −2.10167 | − | 0.0224620i | ||||
\(973\) | 7.86365e47 | 1.21848 | ||||||||
\(974\) | 9.02743e47 | − | 8.93147e47i | 1.37601 | − | 1.36138i | ||||
\(975\) | − | 1.68231e47i | − | 0.252250i | ||||||
\(976\) | −1.42395e47 | − | 3.04409e45i | −0.210038 | − | 0.00449014i | ||||
\(977\) | −1.19273e48 | −1.73073 | −0.865363 | − | 0.501145i | \(-0.832912\pi\) | ||||
−0.865363 | + | 0.501145i | \(0.832912\pi\) | |||||||
\(978\) | 1.26095e48 | + | 1.27450e48i | 1.80001 | + | 1.81935i | ||||
\(979\) | 2.86972e47i | 0.403011i | ||||||||
\(980\) | −1.71297e45 | + | 1.60275e47i | −0.00236664 | + | 0.221436i | ||||
\(981\) | 1.72989e48 | 2.35134 | ||||||||
\(982\) | 6.43014e45 | − | 6.36178e45i | 0.00859878 | − | 0.00850737i | ||||
\(983\) | − | 7.70423e47i | − | 1.01362i | −0.862059 | − | 0.506808i | \(-0.830825\pi\) | ||
0.862059 | − | 0.506808i | \(-0.169175\pi\) | |||||||
\(984\) | 1.46944e48 | + | 1.51732e48i | 1.90208 | + | 1.96407i | ||||
\(985\) | −1.99073e47 | −0.253533 | ||||||||
\(986\) | −5.99676e46 | − | 6.06119e46i | −0.0751425 | − | 0.0759499i | ||||
\(987\) | 1.78281e48i | 2.19801i | ||||||||
\(988\) | −2.00191e47 | − | 2.13957e45i | −0.242847 | − | 0.00259547i | ||||
\(989\) | −4.49995e47 | −0.537114 | ||||||||
\(990\) | 9.34500e46 | − | 9.24566e46i | 0.109753 | − | 0.108586i | ||||
\(991\) | − | 1.05952e48i | − | 1.22442i | −0.790696 | − | 0.612209i | \(-0.790281\pi\) | ||
0.790696 | − | 0.612209i | \(-0.209719\pi\) | |||||||
\(992\) | −7.15695e47 | + | 6.78437e47i | −0.813844 | + | 0.771477i | ||||
\(993\) | −3.82311e47 | −0.427788 | ||||||||
\(994\) | −5.18560e47 | − | 5.24132e47i | −0.570974 | − | 0.577109i | ||||
\(995\) | − | 5.32018e46i | − | 0.0576444i | ||||||
\(996\) | −1.34930e45 | + | 1.26248e47i | −0.00143867 | + | 0.134610i | ||||
\(997\) | 1.16358e48 | 1.22088 | 0.610441 | − | 0.792062i | \(-0.290992\pi\) | ||||
0.610441 | + | 0.792062i | \(0.290992\pi\) | |||||||
\(998\) | 7.24950e47 | − | 7.17243e47i | 0.748548 | − | 0.740590i | ||||
\(999\) | − | 1.87136e48i | − | 1.90156i |
(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 | 4.33.b.b.3.12 | yes | 14 | |
3.2 | odd | 2 | 36.33.d.b.19.3 | 14 | |||
4.3 | odd | 2 | inner | 4.33.b.b.3.11 | ✓ | 14 | |
12.11 | even | 2 | 36.33.d.b.19.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.33.b.b.3.11 | ✓ | 14 | 4.3 | odd | 2 | inner | |
4.33.b.b.3.12 | yes | 14 | 1.1 | even | 1 | trivial | |
36.33.d.b.19.3 | 14 | 3.2 | odd | 2 | |||
36.33.d.b.19.4 | 14 | 12.11 | even | 2 |