Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,21,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (of order \(4\), degree \(2\), 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: | \(12.6756882551\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 7326009 x^{16} + 21914129354136 x^{14} + \cdots + 79\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{48}\cdot 3^{16}\cdot 5^{32} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2.1 | ||
Root | \(1286.49i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.2 |
Dual form | 5.21.c.a.3.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1286.49 | − | 1286.49i | −1.25634 | − | 1.25634i | −0.952827 | − | 0.303515i | \(-0.901840\pi\) |
−0.303515 | − | 0.952827i | \(-0.598160\pi\) | |||||||
\(3\) | 59231.4 | − | 59231.4i | 1.00309 | − | 1.00309i | 0.00309291 | − | 0.999995i | \(-0.499015\pi\) |
0.999995 | − | 0.00309291i | \(-0.000984506\pi\) | |||||||
\(4\) | 2.26156e6i | 2.15679i | ||||||||
\(5\) | 2.84523e6 | − | 9.34195e6i | 0.291352 | − | 0.956616i | ||||
\(6\) | −1.52402e8 | −2.52044 | ||||||||
\(7\) | −2.38026e8 | − | 2.38026e8i | −0.842644 | − | 0.842644i | 0.146558 | − | 0.989202i | \(-0.453180\pi\) |
−0.989202 | + | 0.146558i | \(0.953180\pi\) | |||||||
\(8\) | 1.56049e9 | − | 1.56049e9i | 1.45332 | − | 1.45332i | ||||
\(9\) | − | 3.52992e9i | − | 1.01237i | ||||||
\(10\) | −1.56787e10 | + | 8.35799e9i | −1.56787 | + | 0.835799i | ||||
\(11\) | −2.64802e10 | −1.02093 | −0.510464 | − | 0.859899i | \(-0.670526\pi\) | ||||
−0.510464 | + | 0.859899i | \(0.670526\pi\) | |||||||
\(12\) | 1.33955e11 | + | 1.33955e11i | 2.16345 | + | 2.16345i | ||||
\(13\) | 1.86588e10 | − | 1.86588e10i | 0.135347 | − | 0.135347i | −0.636187 | − | 0.771535i | \(-0.719489\pi\) |
0.771535 | + | 0.636187i | \(0.219489\pi\) | |||||||
\(14\) | 6.12438e11i | 2.11730i | ||||||||
\(15\) | −3.84810e11 | − | 7.21863e11i | −0.667319 | − | 1.25182i | ||||
\(16\) | −1.64372e12 | −1.49495 | ||||||||
\(17\) | 2.00052e12 | + | 2.00052e12i | 0.992324 | + | 0.992324i | 0.999971 | − | 0.00764641i | \(-0.00243395\pi\) |
−0.00764641 | + | 0.999971i | \(0.502434\pi\) | |||||||
\(18\) | −4.54122e12 | + | 4.54122e12i | −1.27188 | + | 1.27188i | ||||
\(19\) | − | 5.99288e12i | − | 0.977461i | −0.872435 | − | 0.488731i | \(-0.837460\pi\) | ||
0.872435 | − | 0.488731i | \(-0.162540\pi\) | |||||||
\(20\) | 2.11274e13 | + | 6.43466e12i | 2.06322 | + | 0.628385i | ||||
\(21\) | −2.81972e13 | −1.69049 | ||||||||
\(22\) | 3.40667e13 | + | 3.40667e13i | 1.28263 | + | 1.28263i | ||||
\(23\) | −4.08127e12 | + | 4.08127e12i | −0.0985184 | + | 0.0985184i | −0.754648 | − | 0.656130i | \(-0.772192\pi\) |
0.656130 | + | 0.754648i | \(0.272192\pi\) | |||||||
\(24\) | − | 1.84860e14i | − | 2.91562i | ||||||
\(25\) | −7.91767e13 | − | 5.31601e13i | −0.830228 | − | 0.557424i | ||||
\(26\) | −4.80088e13 | −0.340085 | ||||||||
\(27\) | −2.55507e12 | − | 2.55507e12i | −0.0124098 | − | 0.0124098i | ||||
\(28\) | 5.38310e14 | − | 5.38310e14i | 1.81741 | − | 1.81741i | ||||
\(29\) | 4.65510e14i | 1.10649i | 0.833017 | + | 0.553247i | \(0.186611\pi\) | ||||
−0.833017 | + | 0.553247i | \(0.813389\pi\) | |||||||
\(30\) | −4.33618e14 | + | 1.42373e15i | −0.734336 | + | 2.41110i | ||||
\(31\) | −1.10651e14 | −0.135001 | −0.0675007 | − | 0.997719i | \(-0.521502\pi\) | ||||
−0.0675007 | + | 0.997719i | \(0.521502\pi\) | |||||||
\(32\) | 4.78335e14 | + | 4.78335e14i | 0.424847 | + | 0.424847i | ||||
\(33\) | −1.56846e15 | + | 1.56846e15i | −1.02408 | + | 1.02408i | ||||
\(34\) | − | 5.14731e15i | − | 2.49340i | ||||||
\(35\) | −2.90087e15 | + | 1.54639e15i | −1.05159 | + | 0.560581i | ||||
\(36\) | 7.98312e15 | 2.18347 | ||||||||
\(37\) | 1.51125e14 | + | 1.51125e14i | 0.0314281 | + | 0.0314281i | 0.722646 | − | 0.691218i | \(-0.242926\pi\) |
−0.691218 | + | 0.722646i | \(0.742926\pi\) | |||||||
\(38\) | −7.70980e15 | + | 7.70980e15i | −1.22803 | + | 1.22803i | ||||
\(39\) | − | 2.21037e15i | − | 0.271531i | ||||||
\(40\) | −1.01381e16 | − | 1.90180e16i | −0.966844 | − | 1.81370i | ||||
\(41\) | 6.70503e15 | 0.499530 | 0.249765 | − | 0.968306i | \(-0.419647\pi\) | ||||
0.249765 | + | 0.968306i | \(0.419647\pi\) | |||||||
\(42\) | 3.62755e16 | + | 3.62755e16i | 2.12384 | + | 2.12384i | ||||
\(43\) | 8.19546e15 | − | 8.19546e15i | 0.379218 | − | 0.379218i | −0.491602 | − | 0.870820i | \(-0.663589\pi\) |
0.870820 | + | 0.491602i | \(0.163589\pi\) | |||||||
\(44\) | − | 5.98866e16i | − | 2.20193i | ||||||
\(45\) | −3.29764e16 | − | 1.00434e16i | −0.968451 | − | 0.294956i | ||||
\(46\) | 1.05011e16 | 0.247545 | ||||||||
\(47\) | −5.57252e16 | − | 5.57252e16i | −1.05943 | − | 1.05943i | −0.998119 | − | 0.0613137i | \(-0.980471\pi\) |
−0.0613137 | − | 0.998119i | \(-0.519529\pi\) | |||||||
\(48\) | −9.73595e16 | + | 9.73595e16i | −1.49957 | + | 1.49957i | ||||
\(49\) | 3.35205e16i | 0.420098i | ||||||||
\(50\) | 3.34703e16 | + | 1.70250e17i | 0.342736 | + | 1.74336i | ||||
\(51\) | 2.36987e17 | 1.99078 | ||||||||
\(52\) | 4.21979e16 | + | 4.21979e16i | 0.291916 | + | 0.291916i | ||||
\(53\) | 8.91509e16 | − | 8.91509e16i | 0.509761 | − | 0.509761i | −0.404692 | − | 0.914453i | \(-0.632621\pi\) |
0.914453 | + | 0.404692i | \(0.132621\pi\) | |||||||
\(54\) | 6.57415e15i | 0.0311819i | ||||||||
\(55\) | −7.53424e16 | + | 2.47377e17i | −0.297449 | + | 0.976636i | ||||
\(56\) | −7.42876e17 | −2.44927 | ||||||||
\(57\) | −3.54966e17 | − | 3.54966e17i | −0.980480 | − | 0.980480i | ||||
\(58\) | 5.98876e17 | − | 5.98876e17i | 1.39013 | − | 1.39013i | ||||
\(59\) | 4.26601e16i | 0.0834645i | 0.999129 | + | 0.0417323i | \(0.0132876\pi\) | ||||
−0.999129 | + | 0.0417323i | \(0.986712\pi\) | |||||||
\(60\) | 1.63254e18 | − | 8.70269e17i | 2.69992 | − | 1.43927i | ||||
\(61\) | −1.01319e18 | −1.42034 | −0.710168 | − | 0.704032i | \(-0.751381\pi\) | ||||
−0.710168 | + | 0.704032i | \(0.751381\pi\) | |||||||
\(62\) | 1.42352e17 | + | 1.42352e17i | 0.169608 | + | 0.169608i | ||||
\(63\) | −8.40213e17 | + | 8.40213e17i | −0.853069 | + | 0.853069i | ||||
\(64\) | 4.92812e17i | 0.427446i | ||||||||
\(65\) | −1.21221e17 | − | 2.27398e17i | −0.0900417 | − | 0.168909i | ||||
\(66\) | 4.03563e18 | 2.57319 | ||||||||
\(67\) | −1.19643e18 | − | 1.19643e18i | −0.656355 | − | 0.656355i | 0.298160 | − | 0.954516i | \(-0.403627\pi\) |
−0.954516 | + | 0.298160i | \(0.903627\pi\) | |||||||
\(68\) | −4.52429e18 | + | 4.52429e18i | −2.14023 | + | 2.14023i | ||||
\(69\) | 4.83479e17i | 0.197645i | ||||||||
\(70\) | 5.72137e18 | + | 1.74253e18i | 2.02544 | + | 0.616879i | ||||
\(71\) | −4.52528e18 | −1.39015 | −0.695075 | − | 0.718937i | \(-0.744629\pi\) | ||||
−0.695075 | + | 0.718937i | \(0.744629\pi\) | |||||||
\(72\) | −5.50842e18 | − | 5.50842e18i | −1.47130 | − | 1.47130i | ||||
\(73\) | 3.34929e18 | − | 3.34929e18i | 0.779335 | − | 0.779335i | −0.200383 | − | 0.979718i | \(-0.564219\pi\) |
0.979718 | + | 0.200383i | \(0.0642186\pi\) | |||||||
\(74\) | − | 3.88842e17i | − | 0.0789689i | ||||||
\(75\) | −7.83849e18 | + | 1.54100e18i | −1.39194 | + | 0.273647i | ||||
\(76\) | 1.35532e19 | 2.10818 | ||||||||
\(77\) | 6.30299e18 | + | 6.30299e18i | 0.860279 | + | 0.860279i | ||||
\(78\) | −2.84363e18 | + | 2.84363e18i | −0.341135 | + | 0.341135i | ||||
\(79\) | − | 9.80914e18i | − | 1.03600i | −0.855381 | − | 0.518000i | \(-0.826677\pi\) | ||
0.855381 | − | 0.518000i | \(-0.173323\pi\) | |||||||
\(80\) | −4.67675e18 | + | 1.53555e19i | −0.435557 | + | 1.43009i | ||||
\(81\) | 1.20054e19 | 0.987475 | ||||||||
\(82\) | −8.62598e18 | − | 8.62598e18i | −0.627581 | − | 0.627581i | ||||
\(83\) | −1.34022e19 | + | 1.34022e19i | −0.863763 | + | 0.863763i | −0.991773 | − | 0.128010i | \(-0.959141\pi\) |
0.128010 | + | 0.991773i | \(0.459141\pi\) | |||||||
\(84\) | − | 6.37696e19i | − | 3.64604i | ||||||
\(85\) | 2.43807e19 | − | 1.29968e19i | 1.23839 | − | 0.660158i | ||||
\(86\) | −2.10868e19 | −0.952854 | ||||||||
\(87\) | 2.75728e19 | + | 2.75728e19i | 1.10991 | + | 1.10991i | ||||
\(88\) | −4.13222e19 | + | 4.13222e19i | −1.48374 | + | 1.48374i | ||||
\(89\) | − | 4.73439e19i | − | 1.51832i | −0.650903 | − | 0.759161i | \(-0.725609\pi\) | ||
0.650903 | − | 0.759161i | \(-0.274391\pi\) | |||||||
\(90\) | 2.95031e19 | + | 5.53447e19i | 0.846139 | + | 1.58727i | ||||
\(91\) | −8.88255e18 | −0.228099 | ||||||||
\(92\) | −9.23003e18 | − | 9.23003e18i | −0.212483 | − | 0.212483i | ||||
\(93\) | −6.55400e18 | + | 6.55400e18i | −0.135418 | + | 0.135418i | ||||
\(94\) | 1.43380e20i | 2.66202i | ||||||||
\(95\) | −5.59852e19 | − | 1.70511e19i | −0.935055 | − | 0.284785i | ||||
\(96\) | 5.66648e19 | 0.852317 | ||||||||
\(97\) | −1.75542e19 | − | 1.75542e19i | −0.238047 | − | 0.238047i | 0.577994 | − | 0.816041i | \(-0.303836\pi\) |
−0.816041 | + | 0.577994i | \(0.803836\pi\) | |||||||
\(98\) | 4.31240e19 | − | 4.31240e19i | 0.527786 | − | 0.527786i | ||||
\(99\) | 9.34732e19i | 1.03356i | ||||||||
\(100\) | 1.20225e20 | − | 1.79063e20i | 1.20225 | − | 1.79063i | ||||
\(101\) | 1.27364e20 | 1.15301 | 0.576506 | − | 0.817093i | \(-0.304416\pi\) | ||||
0.576506 | + | 0.817093i | \(0.304416\pi\) | |||||||
\(102\) | −3.04882e20 | − | 3.04882e20i | −2.50110 | − | 2.50110i | ||||
\(103\) | 3.91228e19 | − | 3.91228e19i | 0.291110 | − | 0.291110i | −0.546409 | − | 0.837519i | \(-0.684005\pi\) |
0.837519 | + | 0.546409i | \(0.184005\pi\) | |||||||
\(104\) | − | 5.82338e19i | − | 0.393407i | ||||||
\(105\) | −8.02276e19 | + | 2.63417e20i | −0.492528 | + | 1.61715i | ||||
\(106\) | −2.29384e20 | −1.28087 | ||||||||
\(107\) | 9.32958e19 | + | 9.32958e19i | 0.474269 | + | 0.474269i | 0.903293 | − | 0.429024i | \(-0.141143\pi\) |
−0.429024 | + | 0.903293i | \(0.641143\pi\) | |||||||
\(108\) | 5.77843e18 | − | 5.77843e18i | 0.0267653 | − | 0.0267653i | ||||
\(109\) | − | 8.91537e19i | − | 0.376595i | −0.982112 | − | 0.188297i | \(-0.939703\pi\) | ||
0.982112 | − | 0.188297i | \(-0.0602969\pi\) | |||||||
\(110\) | 4.15177e20 | − | 2.21322e20i | 1.60069 | − | 0.853291i | ||||
\(111\) | 1.79026e19 | 0.0630503 | ||||||||
\(112\) | 3.91247e20 | + | 3.91247e20i | 1.25971 | + | 1.25971i | ||||
\(113\) | 1.21796e20 | − | 1.21796e20i | 0.358796 | − | 0.358796i | −0.504573 | − | 0.863369i | \(-0.668350\pi\) |
0.863369 | + | 0.504573i | \(0.168350\pi\) | |||||||
\(114\) | 9.13324e20i | 2.46364i | ||||||||
\(115\) | 2.65149e19 | + | 4.97392e19i | 0.0655407 | + | 0.122948i | ||||
\(116\) | −1.05278e21 | −2.38647 | ||||||||
\(117\) | −6.58640e19 | − | 6.58640e19i | −0.137022 | − | 0.137022i | ||||
\(118\) | 5.48820e19 | − | 5.48820e19i | 0.104860 | − | 0.104860i | ||||
\(119\) | − | 9.52352e20i | − | 1.67235i | ||||||
\(120\) | −1.72696e21 | − | 5.25970e20i | −2.78913 | − | 0.849472i | ||||
\(121\) | 2.84529e19 | 0.0422935 | ||||||||
\(122\) | 1.30346e21 | + | 1.30346e21i | 1.78443 | + | 1.78443i | ||||
\(123\) | 3.97148e20 | − | 3.97148e20i | 0.501073 | − | 0.501073i | ||||
\(124\) | − | 2.50243e20i | − | 0.291169i | ||||||
\(125\) | −7.21895e20 | + | 5.88413e20i | −0.775129 | + | 0.631803i | ||||
\(126\) | 2.16186e21 | 2.14349 | ||||||||
\(127\) | 7.06445e20 | + | 7.06445e20i | 0.647204 | + | 0.647204i | 0.952316 | − | 0.305112i | \(-0.0986940\pi\) |
−0.305112 | + | 0.952316i | \(0.598694\pi\) | |||||||
\(128\) | 1.13557e21 | − | 1.13557e21i | 0.961865 | − | 0.961865i | ||||
\(129\) | − | 9.70856e20i | − | 0.760778i | ||||||
\(130\) | −1.36596e20 | + | 4.48496e20i | −0.0990844 | + | 0.325331i | ||||
\(131\) | −1.37131e21 | −0.921343 | −0.460672 | − | 0.887571i | \(-0.652391\pi\) | ||||
−0.460672 | + | 0.887571i | \(0.652391\pi\) | |||||||
\(132\) | −3.54716e21 | − | 3.54716e21i | −2.20873 | − | 2.20873i | ||||
\(133\) | −1.42646e21 | + | 1.42646e21i | −0.823652 | + | 0.823652i | ||||
\(134\) | 3.07840e21i | 1.64921i | ||||||||
\(135\) | −3.11391e19 | + | 1.65995e19i | −0.0154870 | + | 0.00825579i | ||||
\(136\) | 6.24360e21 | 2.88434 | ||||||||
\(137\) | 1.04913e20 | + | 1.04913e20i | 0.0450427 | + | 0.0450427i | 0.729269 | − | 0.684227i | \(-0.239860\pi\) |
−0.684227 | + | 0.729269i | \(0.739860\pi\) | |||||||
\(138\) | 6.21992e20 | − | 6.21992e20i | 0.248310 | − | 0.248310i | ||||
\(139\) | − | 1.71087e21i | − | 0.635434i | −0.948186 | − | 0.317717i | \(-0.897084\pi\) | ||
0.948186 | − | 0.317717i | \(-0.102916\pi\) | |||||||
\(140\) | −3.49725e21 | − | 6.56048e21i | −1.20905 | − | 2.26806i | ||||
\(141\) | −6.60136e21 | −2.12541 | ||||||||
\(142\) | 5.82174e21 | + | 5.82174e21i | 1.74650 | + | 1.74650i | ||||
\(143\) | −4.94089e20 | + | 4.94089e20i | −0.138180 | + | 0.138180i | ||||
\(144\) | 5.80219e21i | 1.51345i | ||||||||
\(145\) | 4.34877e21 | + | 1.32448e21i | 1.05849 | + | 0.322379i | ||||
\(146\) | −8.61768e21 | −1.95822 | ||||||||
\(147\) | 1.98547e21 | + | 1.98547e21i | 0.421395 | + | 0.421395i | ||||
\(148\) | −3.41777e20 | + | 3.41777e20i | −0.0677838 | + | 0.0677838i | ||||
\(149\) | 6.18077e21i | 1.14599i | 0.819560 | + | 0.572994i | \(0.194218\pi\) | ||||
−0.819560 | + | 0.572994i | \(0.805782\pi\) | |||||||
\(150\) | 1.20667e22 | + | 8.10168e21i | 2.09254 | + | 1.40495i | ||||
\(151\) | −1.28013e21 | −0.207724 | −0.103862 | − | 0.994592i | \(-0.533120\pi\) | ||||
−0.103862 | + | 0.994592i | \(0.533120\pi\) | |||||||
\(152\) | −9.35185e21 | − | 9.35185e21i | −1.42057 | − | 1.42057i | ||||
\(153\) | 7.06168e21 | − | 7.06168e21i | 1.00460 | − | 1.00460i | ||||
\(154\) | − | 1.62175e22i | − | 2.16161i | ||||||
\(155\) | −3.14828e20 | + | 1.03370e21i | −0.0393329 | + | 0.129144i | ||||
\(156\) | 4.99888e21 | 0.585634 | ||||||||
\(157\) | −8.25482e21 | − | 8.25482e21i | −0.907216 | − | 0.907216i | 0.0888303 | − | 0.996047i | \(-0.471687\pi\) |
−0.996047 | + | 0.0888303i | \(0.971687\pi\) | |||||||
\(158\) | −1.26194e22 | + | 1.26194e22i | −1.30157 | + | 1.30157i | ||||
\(159\) | − | 1.05611e22i | − | 1.02267i | ||||||
\(160\) | 5.82955e21 | − | 3.10761e21i | 0.530195 | − | 0.282635i | ||||
\(161\) | 1.94290e21 | 0.166032 | ||||||||
\(162\) | −1.54449e22 | − | 1.54449e22i | −1.24061 | − | 1.24061i | ||||
\(163\) | 1.65197e22 | − | 1.65197e22i | 1.24774 | − | 1.24774i | 0.291031 | − | 0.956714i | \(-0.406002\pi\) |
0.956714 | − | 0.291031i | \(-0.0939984\pi\) | |||||||
\(164\) | 1.51638e22i | 1.07738i | ||||||||
\(165\) | 1.01898e22 | + | 1.91151e22i | 0.681284 | + | 1.27802i | ||||
\(166\) | 3.44837e22 | 2.17036 | ||||||||
\(167\) | 1.72661e22 | + | 1.72661e22i | 1.02336 | + | 1.02336i | 0.999720 | + | 0.0236440i | \(0.00752682\pi\) |
0.0236440 | + | 0.999720i | \(0.492473\pi\) | |||||||
\(168\) | −4.40016e22 | + | 4.40016e22i | −2.45683 | + | 2.45683i | ||||
\(169\) | 1.83087e22i | 0.963362i | ||||||||
\(170\) | −4.80860e22 | − | 1.46453e22i | −2.38522 | − | 0.726456i | ||||
\(171\) | −2.11544e22 | −0.989554 | ||||||||
\(172\) | 1.85345e22 | + | 1.85345e22i | 0.817893 | + | 0.817893i | ||||
\(173\) | 2.99421e22 | − | 2.99421e22i | 1.24687 | − | 1.24687i | 0.289773 | − | 0.957095i | \(-0.406420\pi\) |
0.957095 | − | 0.289773i | \(-0.0935799\pi\) | |||||||
\(174\) | − | 7.09444e22i | − | 2.78885i | ||||||
\(175\) | 6.19265e21 | + | 3.14996e22i | 0.229877 | + | 1.16930i | ||||
\(176\) | 4.35260e22 | 1.52624 | ||||||||
\(177\) | 2.52682e21 | + | 2.52682e21i | 0.0837223 | + | 0.0837223i | ||||
\(178\) | −6.09076e22 | + | 6.09076e22i | −1.90753 | + | 1.90753i | ||||
\(179\) | − | 2.64440e22i | − | 0.783063i | −0.920165 | − | 0.391531i | \(-0.871945\pi\) | ||
0.920165 | − | 0.391531i | \(-0.128055\pi\) | |||||||
\(180\) | 2.27138e22 | − | 7.45779e22i | 0.636159 | − | 2.08874i | ||||
\(181\) | −2.29061e22 | −0.606968 | −0.303484 | − | 0.952837i | \(-0.598150\pi\) | ||||
−0.303484 | + | 0.952837i | \(0.598150\pi\) | |||||||
\(182\) | 1.14273e22 | + | 1.14273e22i | 0.286571 | + | 0.286571i | ||||
\(183\) | −6.00124e22 | + | 6.00124e22i | −1.42472 | + | 1.42472i | ||||
\(184\) | 1.27376e22i | 0.286358i | ||||||||
\(185\) | 1.84178e21 | − | 9.81815e20i | 0.0392213 | − | 0.0209080i | ||||
\(186\) | 1.68634e22 | 0.340263 | ||||||||
\(187\) | −5.29742e22 | − | 5.29742e22i | −1.01309 | − | 1.01309i | ||||
\(188\) | 1.26026e23 | − | 1.26026e23i | 2.28497 | − | 2.28497i | ||||
\(189\) | 1.21634e21i | 0.0209141i | ||||||||
\(190\) | 5.00884e22 | + | 9.39608e22i | 0.816961 | + | 1.53254i | ||||
\(191\) | −1.43936e22 | −0.222759 | −0.111379 | − | 0.993778i | \(-0.535527\pi\) | ||||
−0.111379 | + | 0.993778i | \(0.535527\pi\) | |||||||
\(192\) | 2.91899e22 | + | 2.91899e22i | 0.428766 | + | 0.428766i | ||||
\(193\) | 1.94187e22 | − | 1.94187e22i | 0.270798 | − | 0.270798i | −0.558623 | − | 0.829422i | \(-0.688670\pi\) |
0.829422 | + | 0.558623i | \(0.188670\pi\) | |||||||
\(194\) | 4.51667e22i | 0.598137i | ||||||||
\(195\) | −2.06492e22 | − | 6.28901e21i | −0.259750 | − | 0.0791109i | ||||
\(196\) | −7.58086e22 | −0.906062 | ||||||||
\(197\) | 6.12299e22 | + | 6.12299e22i | 0.695506 | + | 0.695506i | 0.963438 | − | 0.267932i | \(-0.0863401\pi\) |
−0.267932 | + | 0.963438i | \(0.586340\pi\) | |||||||
\(198\) | 1.20253e23 | − | 1.20253e23i | 1.29850 | − | 1.29850i | ||||
\(199\) | − | 6.79895e22i | − | 0.698089i | −0.937106 | − | 0.349045i | \(-0.886506\pi\) | ||
0.937106 | − | 0.349045i | \(-0.113494\pi\) | |||||||
\(200\) | −2.06511e23 | + | 4.05989e22i | −2.01671 | + | 0.396473i | ||||
\(201\) | −1.41732e23 | −1.31676 | ||||||||
\(202\) | −1.63853e23 | − | 1.63853e23i | −1.44858 | − | 1.44858i | ||||
\(203\) | 1.10803e23 | − | 1.10803e23i | 0.932380 | − | 0.932380i | ||||
\(204\) | 5.35960e23i | 4.29369i | ||||||||
\(205\) | 1.90774e22 | − | 6.26380e22i | 0.145539 | − | 0.477859i | ||||
\(206\) | −1.00662e23 | −0.731468 | ||||||||
\(207\) | 1.44066e22 | + | 1.44066e22i | 0.0997372 | + | 0.0997372i | ||||
\(208\) | −3.06697e22 | + | 3.06697e22i | −0.202338 | + | 0.202338i | ||||
\(209\) | 1.58693e23i | 0.997917i | ||||||||
\(210\) | 4.42097e23 | − | 2.35672e23i | 2.65048 | − | 1.41291i | ||||
\(211\) | 2.19229e23 | 1.25336 | 0.626678 | − | 0.779278i | \(-0.284414\pi\) | ||||
0.626678 | + | 0.779278i | \(0.284414\pi\) | |||||||
\(212\) | 2.01620e23 | + | 2.01620e23i | 1.09945 | + | 1.09945i | ||||
\(213\) | −2.68038e23 | + | 2.68038e23i | −1.39444 | + | 1.39444i | ||||
\(214\) | − | 2.40049e23i | − | 1.19169i | ||||||
\(215\) | −5.32436e22 | − | 9.98795e22i | −0.252280 | − | 0.473251i | ||||
\(216\) | −7.97433e21 | −0.0360709 | ||||||||
\(217\) | 2.63378e22 | + | 2.63378e22i | 0.113758 | + | 0.113758i | ||||
\(218\) | −1.14696e23 | + | 1.14696e23i | −0.473132 | + | 0.473132i | ||||
\(219\) | − | 3.96766e23i | − | 1.56348i | ||||||
\(220\) | −5.59458e23 | − | 1.70391e23i | −2.10640 | − | 0.641535i | ||||
\(221\) | 7.46545e22 | 0.268617 | ||||||||
\(222\) | −2.30316e22 | − | 2.30316e22i | −0.0792128 | − | 0.0792128i | ||||
\(223\) | 2.11342e23 | − | 2.11342e23i | 0.694924 | − | 0.694924i | −0.268387 | − | 0.963311i | \(-0.586491\pi\) |
0.963311 | + | 0.268387i | \(0.0864906\pi\) | |||||||
\(224\) | − | 2.27712e23i | − | 0.715989i | ||||||
\(225\) | −1.87651e23 | + | 2.79488e23i | −0.564320 | + | 0.840499i | ||||
\(226\) | −3.13379e23 | −0.901542 | ||||||||
\(227\) | −7.69430e22 | − | 7.69430e22i | −0.211793 | − | 0.211793i | 0.593236 | − | 0.805029i | \(-0.297850\pi\) |
−0.805029 | + | 0.593236i | \(0.797850\pi\) | |||||||
\(228\) | 8.02777e23 | − | 8.02777e23i | 2.11469 | − | 2.11469i | ||||
\(229\) | 9.53460e22i | 0.240407i | 0.992749 | + | 0.120204i | \(0.0383548\pi\) | ||||
−0.992749 | + | 0.120204i | \(0.961645\pi\) | |||||||
\(230\) | 2.98780e22 | − | 9.81004e22i | 0.0721228 | − | 0.236806i | ||||
\(231\) | 7.46669e23 | 1.72587 | ||||||||
\(232\) | 7.26425e23 | + | 7.26425e23i | 1.60809 | + | 1.60809i | ||||
\(233\) | −5.12339e23 | + | 5.12339e23i | −1.08642 | + | 1.08642i | −0.0905279 | + | 0.995894i | \(0.528855\pi\) |
−0.995894 | + | 0.0905279i | \(0.971145\pi\) | |||||||
\(234\) | 1.69467e23i | 0.344292i | ||||||||
\(235\) | −6.79134e23 | + | 3.62031e23i | −1.32214 | + | 0.704802i | ||||
\(236\) | −9.64783e22 | −0.180015 | ||||||||
\(237\) | −5.81008e23 | − | 5.81008e23i | −1.03920 | − | 1.03920i | ||||
\(238\) | −1.22519e24 | + | 1.22519e24i | −2.10105 | + | 2.10105i | ||||
\(239\) | 3.51188e23i | 0.577512i | 0.957403 | + | 0.288756i | \(0.0932416\pi\) | ||||
−0.957403 | + | 0.288756i | \(0.906758\pi\) | |||||||
\(240\) | 6.32518e23 | + | 1.18654e24i | 0.997609 | + | 1.87141i | ||||
\(241\) | 5.29836e23 | 0.801624 | 0.400812 | − | 0.916160i | \(-0.368728\pi\) | ||||
0.400812 | + | 0.916160i | \(0.368728\pi\) | |||||||
\(242\) | −3.66045e22 | − | 3.66045e22i | −0.0531351 | − | 0.0531351i | ||||
\(243\) | 7.20005e23 | − | 7.20005e23i | 1.00293 | − | 1.00293i | ||||
\(244\) | − | 2.29138e24i | − | 3.06337i | ||||||
\(245\) | 3.13147e23 | + | 9.53737e22i | 0.401872 | + | 0.122396i | ||||
\(246\) | −1.02186e24 | −1.25904 | ||||||||
\(247\) | −1.11820e23 | − | 1.11820e23i | −0.132297 | − | 0.132297i | ||||
\(248\) | −1.72670e23 | + | 1.72670e23i | −0.196201 | + | 0.196201i | ||||
\(249\) | 1.58766e24i | 1.73286i | ||||||||
\(250\) | 1.68570e24 | + | 1.71724e23i | 1.76759 | + | 0.180066i | ||||
\(251\) | 6.18463e23 | 0.623127 | 0.311564 | − | 0.950225i | \(-0.399147\pi\) | ||||
0.311564 | + | 0.950225i | \(0.399147\pi\) | |||||||
\(252\) | −1.90019e24 | − | 1.90019e24i | −1.83989 | − | 1.83989i | ||||
\(253\) | 1.08073e23 | − | 1.08073e23i | 0.100580 | − | 0.100580i | ||||
\(254\) | − | 1.81767e24i | − | 1.62622i | ||||||
\(255\) | 6.74283e23 | − | 2.21392e24i | 0.580017 | − | 1.90441i | ||||
\(256\) | −2.40506e24 | −1.98942 | ||||||||
\(257\) | 1.39844e24 | + | 1.39844e24i | 1.11253 | + | 1.11253i | 0.992807 | + | 0.119723i | \(0.0382006\pi\) |
0.119723 | + | 0.992807i | \(0.461799\pi\) | |||||||
\(258\) | −1.24900e24 | + | 1.24900e24i | −0.955797 | + | 0.955797i | ||||
\(259\) | − | 7.19432e22i | − | 0.0529654i | ||||||
\(260\) | 5.14274e23 | − | 2.74148e23i | 0.364301 | − | 0.194201i | ||||
\(261\) | 1.64321e24 | 1.12018 | ||||||||
\(262\) | 1.76418e24 | + | 1.76418e24i | 1.15752 | + | 1.15752i | ||||
\(263\) | −9.89553e23 | + | 9.89553e23i | −0.625002 | + | 0.625002i | −0.946806 | − | 0.321804i | \(-0.895711\pi\) |
0.321804 | + | 0.946806i | \(0.395711\pi\) | |||||||
\(264\) | 4.89514e24i | 2.97664i | ||||||||
\(265\) | −5.79188e23 | − | 1.08650e24i | −0.339126 | − | 0.636166i | ||||
\(266\) | 3.67027e24 | 2.06958 | ||||||||
\(267\) | −2.80424e24 | − | 2.80424e24i | −1.52301 | − | 1.52301i | ||||
\(268\) | 2.70579e24 | − | 2.70579e24i | 1.41562 | − | 1.41562i | ||||
\(269\) | 6.03707e23i | 0.304301i | 0.988357 | + | 0.152150i | \(0.0486198\pi\) | ||||
−0.988357 | + | 0.152150i | \(0.951380\pi\) | |||||||
\(270\) | 6.14154e22 | + | 1.87050e22i | 0.0298291 | + | 0.00908489i | ||||
\(271\) | −3.36780e24 | −1.57635 | −0.788177 | − | 0.615449i | \(-0.788975\pi\) | ||||
−0.788177 | + | 0.615449i | \(0.788975\pi\) | |||||||
\(272\) | −3.28829e24 | − | 3.28829e24i | −1.48348 | − | 1.48348i | ||||
\(273\) | −5.26125e23 | + | 5.26125e23i | −0.228804 | + | 0.228804i | ||||
\(274\) | − | 2.69940e23i | − | 0.113178i | ||||||
\(275\) | 2.09662e24 | + | 1.40769e24i | 0.847603 | + | 0.569089i | ||||
\(276\) | −1.09341e24 | −0.426279 | ||||||||
\(277\) | −1.99675e24 | − | 1.99675e24i | −0.750803 | − | 0.750803i | 0.223826 | − | 0.974629i | \(-0.428145\pi\) |
−0.974629 | + | 0.223826i | \(0.928145\pi\) | |||||||
\(278\) | −2.20103e24 | + | 2.20103e24i | −0.798322 | + | 0.798322i | ||||
\(279\) | 3.90589e23i | 0.136672i | ||||||||
\(280\) | −2.11366e24 | + | 6.93991e24i | −0.713599 | + | 2.34301i | ||||
\(281\) | 2.53470e24 | 0.825778 | 0.412889 | − | 0.910781i | \(-0.364520\pi\) | ||||
0.412889 | + | 0.910781i | \(0.364520\pi\) | |||||||
\(282\) | 8.49261e24 | + | 8.49261e24i | 2.67024 | + | 2.67024i | ||||
\(283\) | 1.97158e24 | − | 1.97158e24i | 0.598342 | − | 0.598342i | −0.341529 | − | 0.939871i | \(-0.610945\pi\) |
0.939871 | + | 0.341529i | \(0.110945\pi\) | |||||||
\(284\) | − | 1.02342e25i | − | 2.99826i | ||||||
\(285\) | −4.32604e24 | + | 2.30612e24i | −1.22361 | + | 0.652278i | ||||
\(286\) | 1.27128e24 | 0.347202 | ||||||||
\(287\) | −1.59597e24 | − | 1.59597e24i | −0.420926 | − | 0.420926i | ||||
\(288\) | 1.68848e24 | − | 1.68848e24i | 0.430103 | − | 0.430103i | ||||
\(289\) | 3.93993e24i | 0.969415i | ||||||||
\(290\) | −3.89073e24 | − | 7.29861e24i | −0.924806 | − | 1.73484i | ||||
\(291\) | −2.07951e24 | −0.477565 | ||||||||
\(292\) | 7.57461e24 | + | 7.57461e24i | 1.68086 | + | 1.68086i | ||||
\(293\) | −3.02579e24 | + | 3.02579e24i | −0.648878 | + | 0.648878i | −0.952722 | − | 0.303844i | \(-0.901730\pi\) |
0.303844 | + | 0.952722i | \(0.401730\pi\) | |||||||
\(294\) | − | 5.10858e24i | − | 1.05883i | ||||||
\(295\) | 3.98529e23 | + | 1.21378e23i | 0.0798435 | + | 0.0243175i | ||||
\(296\) | 4.71658e23 | 0.0913504 | ||||||||
\(297\) | 6.76587e22 | + | 6.76587e22i | 0.0126695 | + | 0.0126695i | ||||
\(298\) | 7.95152e24 | − | 7.95152e24i | 1.43975 | − | 1.43975i | ||||
\(299\) | 1.52303e23i | 0.0266684i | ||||||||
\(300\) | −3.48507e24 | − | 1.77272e25i | −0.590199 | − | 3.00212i | ||||
\(301\) | −3.90146e24 | −0.639091 | ||||||||
\(302\) | 1.64689e24 | + | 1.64689e24i | 0.260972 | + | 0.260972i | ||||
\(303\) | 7.54396e24 | − | 7.54396e24i | 1.15657 | − | 1.15657i | ||||
\(304\) | 9.85059e24i | 1.46126i | ||||||||
\(305\) | −2.88275e24 | + | 9.46514e24i | −0.413818 | + | 1.35872i | ||||
\(306\) | −1.81696e25 | −2.52424 | ||||||||
\(307\) | 4.93037e23 | + | 4.93037e23i | 0.0662973 | + | 0.0662973i | 0.739478 | − | 0.673181i | \(-0.235072\pi\) |
−0.673181 | + | 0.739478i | \(0.735072\pi\) | |||||||
\(308\) | −1.42546e25 | + | 1.42546e25i | −1.85544 | + | 1.85544i | ||||
\(309\) | − | 4.63459e24i | − | 0.584018i | ||||||
\(310\) | 1.73487e24 | − | 9.24820e23i | 0.211665 | − | 0.112834i | ||||
\(311\) | 1.51891e25 | 1.79444 | 0.897218 | − | 0.441588i | \(-0.145585\pi\) | ||||
0.897218 | + | 0.441588i | \(0.145585\pi\) | |||||||
\(312\) | −3.44927e24 | − | 3.44927e24i | −0.394622 | − | 0.394622i | ||||
\(313\) | 5.78929e24 | − | 5.78929e24i | 0.641479 | − | 0.641479i | −0.309440 | − | 0.950919i | \(-0.600142\pi\) |
0.950919 | + | 0.309440i | \(0.100142\pi\) | |||||||
\(314\) | 2.12395e25i | 2.27955i | ||||||||
\(315\) | 5.45863e24 | + | 1.02398e25i | 0.567516 | + | 1.06460i | ||||
\(316\) | 2.21839e25 | 2.23443 | ||||||||
\(317\) | −6.71778e24 | − | 6.71778e24i | −0.655591 | − | 0.655591i | 0.298743 | − | 0.954334i | \(-0.403433\pi\) |
−0.954334 | + | 0.298743i | \(0.903433\pi\) | |||||||
\(318\) | −1.35867e25 | + | 1.35867e25i | −1.28482 | + | 1.28482i | ||||
\(319\) | − | 1.23268e25i | − | 1.12965i | ||||||
\(320\) | 4.60382e24 | + | 1.40216e24i | 0.408902 | + | 0.124537i | ||||
\(321\) | 1.10521e25 | 0.951466 | ||||||||
\(322\) | −2.49953e24 | − | 2.49953e24i | −0.208593 | − | 0.208593i | ||||
\(323\) | 1.19889e25 | − | 1.19889e25i | 0.969959 | − | 0.969959i | ||||
\(324\) | 2.71509e25i | 2.12978i | ||||||||
\(325\) | −2.46924e24 | + | 4.85439e23i | −0.187815 | + | 0.0369234i | ||||
\(326\) | −4.25050e25 | −3.13519 | ||||||||
\(327\) | −5.28069e24 | − | 5.28069e24i | −0.377758 | − | 0.377758i | ||||
\(328\) | 1.04631e25 | − | 1.04631e25i | 0.725979 | − | 0.725979i | ||||
\(329\) | 2.65281e25i | 1.78545i | ||||||||
\(330\) | 1.14823e25 | − | 3.77007e25i | 0.749704 | − | 2.46155i | ||||
\(331\) | −2.32303e25 | −1.47155 | −0.735776 | − | 0.677225i | \(-0.763182\pi\) | ||||
−0.735776 | + | 0.677225i | \(0.763182\pi\) | |||||||
\(332\) | −3.03098e25 | − | 3.03098e25i | −1.86295 | − | 1.86295i | ||||
\(333\) | 5.33458e23 | − | 5.33458e23i | 0.0318169 | − | 0.0318169i | ||||
\(334\) | − | 4.44255e25i | − | 2.57139i | ||||||
\(335\) | −1.45811e25 | + | 7.77287e24i | −0.819110 | + | 0.436650i | ||||
\(336\) | 4.63482e25 | 2.52720 | ||||||||
\(337\) | 1.80258e25 | + | 1.80258e25i | 0.954105 | + | 0.954105i | 0.998992 | − | 0.0448872i | \(-0.0142928\pi\) |
−0.0448872 | + | 0.998992i | \(0.514293\pi\) | |||||||
\(338\) | 2.35540e25 | − | 2.35540e25i | 1.21031 | − | 1.21031i | ||||
\(339\) | − | 1.44283e25i | − | 0.719809i | ||||||
\(340\) | 2.93931e25 | + | 5.51384e25i | 1.42382 | + | 2.67094i | ||||
\(341\) | 2.93006e24 | 0.137827 | ||||||||
\(342\) | 2.72150e25 | + | 2.72150e25i | 1.24322 | + | 1.24322i | ||||
\(343\) | −1.10139e25 | + | 1.10139e25i | −0.488651 | + | 0.488651i | ||||
\(344\) | − | 2.55779e25i | − | 1.10225i | ||||||
\(345\) | 4.51663e24 | + | 1.37561e24i | 0.189071 | + | 0.0575843i | ||||
\(346\) | −7.70406e25 | −3.13299 | ||||||||
\(347\) | 3.26396e25 | + | 3.26396e25i | 1.28958 | + | 1.28958i | 0.935039 | + | 0.354544i | \(0.115364\pi\) |
0.354544 | + | 0.935039i | \(0.384636\pi\) | |||||||
\(348\) | −6.23574e25 | + | 6.23574e25i | −2.39384 | + | 2.39384i | ||||
\(349\) | − | 2.58898e25i | − | 0.965772i | −0.875683 | − | 0.482886i | \(-0.839589\pi\) | ||
0.875683 | − | 0.482886i | \(-0.160411\pi\) | |||||||
\(350\) | 3.25572e25 | − | 4.84909e25i | 1.18023 | − | 1.75784i | ||||
\(351\) | −9.53488e22 | −0.00335926 | ||||||||
\(352\) | −1.26664e25 | − | 1.26664e25i | −0.433738 | − | 0.433738i | ||||
\(353\) | −1.27154e25 | + | 1.27154e25i | −0.423235 | + | 0.423235i | −0.886316 | − | 0.463081i | \(-0.846744\pi\) |
0.463081 | + | 0.886316i | \(0.346744\pi\) | |||||||
\(354\) | − | 6.50147e24i | − | 0.210368i | ||||||
\(355\) | −1.28755e25 | + | 4.22749e25i | −0.405023 | + | 1.32984i | ||||
\(356\) | 1.07071e26 | 3.27470 | ||||||||
\(357\) | −5.64091e25 | − | 5.64091e25i | −1.67752 | − | 1.67752i | ||||
\(358\) | −3.40200e25 | + | 3.40200e25i | −0.983794 | + | 0.983794i | ||||
\(359\) | − | 1.64035e25i | − | 0.461310i | −0.973036 | − | 0.230655i | \(-0.925913\pi\) | ||
0.973036 | − | 0.230655i | \(-0.0740868\pi\) | |||||||
\(360\) | −6.71321e25 | + | 3.57867e25i | −1.83614 | + | 0.978805i | ||||
\(361\) | 1.67537e24 | 0.0445696 | ||||||||
\(362\) | 2.94686e25 | + | 2.94686e25i | 0.762559 | + | 0.762559i | ||||
\(363\) | 1.68531e24 | − | 1.68531e24i | 0.0424241 | − | 0.0424241i | ||||
\(364\) | − | 2.00884e25i | − | 0.491962i | ||||||
\(365\) | −2.17594e25 | − | 4.08184e25i | −0.518463 | − | 0.972585i | ||||
\(366\) | 1.54411e26 | 3.57988 | ||||||||
\(367\) | −2.08553e25 | − | 2.08553e25i | −0.470495 | − | 0.470495i | 0.431580 | − | 0.902075i | \(-0.357956\pi\) |
−0.902075 | + | 0.431580i | \(0.857956\pi\) | |||||||
\(368\) | 6.70845e24 | − | 6.70845e24i | 0.147280 | − | 0.147280i | ||||
\(369\) | − | 2.36682e25i | − | 0.505710i | ||||||
\(370\) | −3.63254e24 | − | 1.10635e24i | −0.0755429 | − | 0.0230077i | ||||
\(371\) | −4.24405e25 | −0.859095 | ||||||||
\(372\) | −1.48223e25 | − | 1.48223e25i | −0.292069 | − | 0.292069i | ||||
\(373\) | 5.98463e25 | − | 5.98463e25i | 1.14802 | − | 1.14802i | 0.161077 | − | 0.986942i | \(-0.448503\pi\) |
0.986942 | − | 0.161077i | \(-0.0514967\pi\) | |||||||
\(374\) | 1.36302e26i | 2.54558i | ||||||||
\(375\) | −7.90634e24 | + | 7.76113e25i | −0.143768 | + | 1.41128i | ||||
\(376\) | −1.73918e26 | −3.07939 | ||||||||
\(377\) | 8.68584e24 | + | 8.68584e24i | 0.149761 | + | 0.149761i | ||||
\(378\) | 1.56482e24 | − | 1.56482e24i | 0.0262752 | − | 0.0262752i | ||||
\(379\) | 8.22219e25i | 1.34461i | 0.740276 | + | 0.672303i | \(0.234695\pi\) | ||||
−0.740276 | + | 0.672303i | \(0.765305\pi\) | |||||||
\(380\) | 3.85621e25 | − | 1.26614e26i | 0.614221 | − | 2.01672i | ||||
\(381\) | 8.36874e25 | 1.29841 | ||||||||
\(382\) | 1.85172e25 | + | 1.85172e25i | 0.279861 | + | 0.279861i | ||||
\(383\) | 5.06387e25 | − | 5.06387e25i | 0.745581 | − | 0.745581i | −0.228065 | − | 0.973646i | \(-0.573240\pi\) |
0.973646 | + | 0.228065i | \(0.0732399\pi\) | |||||||
\(384\) | − | 1.34523e26i | − | 1.92967i | ||||||
\(385\) | 7.68157e25 | − | 4.09487e25i | 1.07360 | − | 0.572313i | ||||
\(386\) | −4.99640e25 | −0.680431 | ||||||||
\(387\) | −2.89293e25 | − | 2.89293e25i | −0.383909 | − | 0.383909i | ||||
\(388\) | 3.96998e25 | − | 3.96998e25i | 0.513418 | − | 0.513418i | ||||
\(389\) | 3.29273e25i | 0.415011i | 0.978234 | + | 0.207506i | \(0.0665345\pi\) | ||||
−0.978234 | + | 0.207506i | \(0.933465\pi\) | |||||||
\(390\) | 1.84742e25 | + | 3.46558e25i | 0.226945 | + | 0.425726i | ||||
\(391\) | −1.63293e25 | −0.195524 | ||||||||
\(392\) | 5.23086e25 | + | 5.23086e25i | 0.610537 | + | 0.610537i | ||||
\(393\) | −8.12243e25 | + | 8.12243e25i | −0.924188 | + | 0.924188i | ||||
\(394\) | − | 1.57544e26i | − | 1.74759i | ||||||
\(395\) | −9.16365e25 | − | 2.79093e25i | −0.991054 | − | 0.301841i | ||||
\(396\) | −2.11395e26 | −2.22917 | ||||||||
\(397\) | −9.96917e25 | − | 9.96917e25i | −1.02507 | − | 1.02507i | −0.999678 | − | 0.0253931i | \(-0.991916\pi\) |
−0.0253931 | − | 0.999678i | \(-0.508084\pi\) | |||||||
\(398\) | −8.74681e25 | + | 8.74681e25i | −0.877039 | + | 0.877039i | ||||
\(399\) | 1.68982e26i | 1.65239i | ||||||||
\(400\) | 1.30144e26 | + | 8.73800e25i | 1.24115 | + | 0.833321i | ||||
\(401\) | 1.33713e26 | 1.24374 | 0.621868 | − | 0.783122i | \(-0.286374\pi\) | ||||
0.621868 | + | 0.783122i | \(0.286374\pi\) | |||||||
\(402\) | 1.82338e26 | + | 1.82338e26i | 1.65431 | + | 1.65431i | ||||
\(403\) | −2.06461e24 | + | 2.06461e24i | −0.0182721 | + | 0.0182721i | ||||
\(404\) | 2.88042e26i | 2.48680i | ||||||||
\(405\) | 3.41581e25 | − | 1.12154e26i | 0.287703 | − | 0.944635i | ||||
\(406\) | −2.85096e26 | −2.34278 | ||||||||
\(407\) | −4.00182e24 | − | 4.00182e24i | −0.0320858 | − | 0.0320858i | ||||
\(408\) | 3.69817e26 | − | 3.69817e26i | 2.89324 | − | 2.89324i | ||||
\(409\) | 1.78296e26i | 1.36115i | 0.732676 | + | 0.680577i | \(0.238271\pi\) | ||||
−0.732676 | + | 0.680577i | \(0.761729\pi\) | |||||||
\(410\) | −1.05126e26 | + | 5.60406e25i | −0.783201 | + | 0.417507i | ||||
\(411\) | 1.24283e25 | 0.0903635 | ||||||||
\(412\) | 8.84784e25 | + | 8.84784e25i | 0.627863 | + | 0.627863i | ||||
\(413\) | 1.01542e25 | − | 1.01542e25i | 0.0703309 | − | 0.0703309i | ||||
\(414\) | − | 3.70679e25i | − | 0.250608i | ||||||
\(415\) | 8.70702e25 | + | 1.63335e26i | 0.574631 | + | 1.07795i | ||||
\(416\) | 1.78503e25 | 0.115004 | ||||||||
\(417\) | −1.01337e26 | − | 1.01337e26i | −0.637396 | − | 0.637396i | ||||
\(418\) | 2.04157e26 | − | 2.04157e26i | 1.25373 | − | 1.25373i | ||||
\(419\) | − | 2.35922e26i | − | 1.41458i | −0.706924 | − | 0.707290i | \(-0.749918\pi\) | ||
0.706924 | − | 0.707290i | \(-0.250082\pi\) | |||||||
\(420\) | −5.95733e26 | − | 1.81439e26i | −3.48786 | − | 1.06228i | ||||
\(421\) | 1.00758e26 | 0.576051 | 0.288025 | − | 0.957623i | \(-0.407001\pi\) | ||||
0.288025 | + | 0.957623i | \(0.407001\pi\) | |||||||
\(422\) | −2.82037e26 | − | 2.82037e26i | −1.57464 | − | 1.57464i | ||||
\(423\) | −1.96706e26 | + | 1.96706e26i | −1.07254 | + | 1.07254i | ||||
\(424\) | − | 2.78239e26i | − | 1.48170i | ||||||
\(425\) | −5.20469e25 | − | 2.64742e26i | −0.270711 | − | 1.37700i | ||||
\(426\) | 6.89659e26 | 3.50379 | ||||||||
\(427\) | 2.41165e26 | + | 2.41165e26i | 1.19684 | + | 1.19684i | ||||
\(428\) | −2.10994e26 | + | 2.10994e26i | −1.02290 | + | 1.02290i | ||||
\(429\) | 5.85311e25i | 0.277213i | ||||||||
\(430\) | −5.99969e25 | + | 1.96992e26i | −0.277616 | + | 0.911515i | ||||
\(431\) | −5.63826e25 | −0.254902 | −0.127451 | − | 0.991845i | \(-0.540679\pi\) | ||||
−0.127451 | + | 0.991845i | \(0.540679\pi\) | |||||||
\(432\) | 4.19980e24 | + | 4.19980e24i | 0.0185520 | + | 0.0185520i | ||||
\(433\) | −3.60490e25 | + | 3.60490e25i | −0.155602 | + | 0.155602i | −0.780614 | − | 0.625013i | \(-0.785094\pi\) |
0.625013 | + | 0.780614i | \(0.285094\pi\) | |||||||
\(434\) | − | 6.77669e25i | − | 0.285838i | ||||||
\(435\) | 3.36035e26 | − | 1.79133e26i | 1.38513 | − | 0.738384i | ||||
\(436\) | 2.01626e26 | 0.812236 | ||||||||
\(437\) | 2.44586e25 | + | 2.44586e25i | 0.0962979 | + | 0.0962979i | ||||
\(438\) | −5.10437e26 | + | 5.10437e26i | −1.96427 | + | 1.96427i | ||||
\(439\) | − | 2.47680e26i | − | 0.931636i | −0.884881 | − | 0.465818i | \(-0.845760\pi\) | ||
0.884881 | − | 0.465818i | \(-0.154240\pi\) | |||||||
\(440\) | 2.68459e26 | + | 5.03602e26i | 0.987077 | + | 1.85166i | ||||
\(441\) | 1.18325e26 | 0.425295 | ||||||||
\(442\) | −9.60426e25 | − | 9.60426e25i | −0.337475 | − | 0.337475i | ||||
\(443\) | 6.46778e25 | − | 6.46778e25i | 0.222187 | − | 0.222187i | −0.587232 | − | 0.809419i | \(-0.699782\pi\) |
0.809419 | + | 0.587232i | \(0.199782\pi\) | |||||||
\(444\) | 4.04879e25i | 0.135986i | ||||||||
\(445\) | −4.42284e26 | − | 1.34704e26i | −1.45245 | − | 0.442366i | ||||
\(446\) | −5.43781e26 | −1.74612 | ||||||||
\(447\) | 3.66095e26 | + | 3.66095e26i | 1.14953 | + | 1.14953i | ||||
\(448\) | 1.17302e26 | − | 1.17302e26i | 0.360185 | − | 0.360185i | ||||
\(449\) | − | 1.35248e26i | − | 0.406131i | −0.979165 | − | 0.203066i | \(-0.934910\pi\) | ||
0.979165 | − | 0.203066i | \(-0.0650905\pi\) | |||||||
\(450\) | 6.00971e26 | − | 1.18148e26i | 1.76493 | − | 0.346976i | ||||
\(451\) | −1.77551e26 | −0.509984 | ||||||||
\(452\) | 2.75448e26 | + | 2.75448e26i | 0.773848 | + | 0.773848i | ||||
\(453\) | −7.58241e25 | + | 7.58241e25i | −0.208365 | + | 0.208365i | ||||
\(454\) | 1.97973e26i | 0.532168i | ||||||||
\(455\) | −2.52729e25 | + | 8.29804e25i | −0.0664571 | + | 0.218203i | ||||
\(456\) | −1.10785e27 | −2.84991 | ||||||||
\(457\) | 1.50945e26 | + | 1.50945e26i | 0.379889 | + | 0.379889i | 0.871062 | − | 0.491173i | \(-0.163432\pi\) |
−0.491173 | + | 0.871062i | \(0.663432\pi\) | |||||||
\(458\) | 1.22662e26 | − | 1.22662e26i | 0.302034 | − | 0.302034i | ||||
\(459\) | − | 1.02229e25i | − | 0.0246291i | ||||||
\(460\) | −1.12488e26 | + | 5.99649e25i | −0.265172 | + | 0.141358i | ||||
\(461\) | 1.32819e26 | 0.306374 | 0.153187 | − | 0.988197i | \(-0.451046\pi\) | ||||
0.153187 | + | 0.988197i | \(0.451046\pi\) | |||||||
\(462\) | −9.60585e26 | − | 9.60585e26i | −2.16828 | − | 2.16828i | ||||
\(463\) | 1.91477e26 | − | 1.91477e26i | 0.422967 | − | 0.422967i | −0.463257 | − | 0.886224i | \(-0.653319\pi\) |
0.886224 | + | 0.463257i | \(0.153319\pi\) | |||||||
\(464\) | − | 7.65166e26i | − | 1.65415i | ||||||
\(465\) | 4.25795e25 | + | 7.98749e25i | 0.0900889 | + | 0.168998i | ||||
\(466\) | 1.31824e27 | 2.72983 | ||||||||
\(467\) | −6.02296e26 | − | 6.02296e26i | −1.22079 | − | 1.22079i | −0.967352 | − | 0.253438i | \(-0.918439\pi\) |
−0.253438 | − | 0.967352i | \(-0.581561\pi\) | |||||||
\(468\) | 1.48955e26 | − | 1.48955e26i | 0.295527 | − | 0.295527i | ||||
\(469\) | 5.69563e26i | 1.10615i | ||||||||
\(470\) | 1.33945e27 | + | 4.07950e26i | 2.54653 | + | 0.775584i | ||||
\(471\) | −9.77888e26 | −1.82004 | ||||||||
\(472\) | 6.65708e25 | + | 6.65708e25i | 0.121301 | + | 0.121301i | ||||
\(473\) | −2.17018e26 | + | 2.17018e26i | −0.387154 | + | 0.387154i | ||||
\(474\) | 1.49493e27i | 2.61118i | ||||||||
\(475\) | −3.18582e26 | + | 4.74497e26i | −0.544860 | + | 0.811516i | ||||
\(476\) | 2.15380e27 | 3.60691 | ||||||||
\(477\) | −3.14696e26 | − | 3.14696e26i | −0.516068 | − | 0.516068i | ||||
\(478\) | 4.51802e26 | − | 4.51802e26i | 0.725552 | − | 0.725552i | ||||
\(479\) | − | 5.87413e26i | − | 0.923822i | −0.886926 | − | 0.461911i | \(-0.847164\pi\) | ||
0.886926 | − | 0.461911i | \(-0.152836\pi\) | |||||||
\(480\) | 1.61225e26 | − | 5.29360e26i | 0.248324 | − | 0.815340i | ||||
\(481\) | 5.63960e24 | 0.00850742 | ||||||||
\(482\) | −6.81630e26 | − | 6.81630e26i | −1.00711 | − | 1.00711i | ||||
\(483\) | 1.15080e26 | − | 1.15080e26i | 0.166545 | − | 0.166545i | ||||
\(484\) | 6.43480e25i | 0.0912181i | ||||||||
\(485\) | −2.13936e26 | + | 1.14045e26i | −0.297075 | + | 0.158364i | ||||
\(486\) | −1.85256e27 | −2.52006 | ||||||||
\(487\) | 1.69794e26 | + | 1.69794e26i | 0.226273 | + | 0.226273i | 0.811134 | − | 0.584861i | \(-0.198851\pi\) |
−0.584861 | + | 0.811134i | \(0.698851\pi\) | |||||||
\(488\) | −1.58107e27 | + | 1.58107e27i | −2.06421 | + | 2.06421i | ||||
\(489\) | − | 1.95697e27i | − | 2.50320i | ||||||
\(490\) | −2.80164e26 | − | 5.25560e26i | −0.351117 | − | 0.658660i | ||||
\(491\) | −7.03307e26 | −0.863634 | −0.431817 | − | 0.901961i | \(-0.642127\pi\) | ||||
−0.431817 | + | 0.901961i | \(0.642127\pi\) | |||||||
\(492\) | 8.98173e26 | + | 8.98173e26i | 1.08071 | + | 1.08071i | ||||
\(493\) | −9.31262e26 | + | 9.31262e26i | −1.09800 | + | 1.09800i | ||||
\(494\) | 2.87711e26i | 0.332420i | ||||||||
\(495\) | 8.73222e26 | + | 2.65953e26i | 0.988718 | + | 0.301129i | ||||
\(496\) | 1.81879e26 | 0.201820 | ||||||||
\(497\) | 1.07713e27 | + | 1.07713e27i | 1.17140 | + | 1.17140i | ||||
\(498\) | 2.04251e27 | − | 2.04251e27i | 2.17707 | − | 2.17707i | ||||
\(499\) | 1.55018e27i | 1.61949i | 0.586783 | + | 0.809744i | \(0.300394\pi\) | ||||
−0.586783 | + | 0.809744i | \(0.699606\pi\) | |||||||
\(500\) | −1.33073e27 | − | 1.63261e27i | −1.36267 | − | 1.67179i | ||||
\(501\) | 2.04539e27 | 2.05305 | ||||||||
\(502\) | −7.95650e26 | − | 7.95650e26i | −0.782861 | − | 0.782861i | ||||
\(503\) | 7.37100e26 | − | 7.37100e26i | 0.710962 | − | 0.710962i | −0.255774 | − | 0.966737i | \(-0.582330\pi\) |
0.966737 | + | 0.255774i | \(0.0823303\pi\) | |||||||
\(504\) | 2.62229e27i | 2.47957i | ||||||||
\(505\) | 3.62381e26 | − | 1.18983e27i | 0.335932 | − | 1.10299i | ||||
\(506\) | −2.78071e26 | −0.252726 | ||||||||
\(507\) | 1.08445e27 | + | 1.08445e27i | 0.966337 | + | 0.966337i | ||||
\(508\) | −1.59767e27 | + | 1.59767e27i | −1.39588 | + | 1.39588i | ||||
\(509\) | 4.37786e26i | 0.375046i | 0.982260 | + | 0.187523i | \(0.0600459\pi\) | ||||
−0.982260 | + | 0.187523i | \(0.939954\pi\) | |||||||
\(510\) | −3.71566e27 | + | 1.98074e27i | −3.12129 | + | 1.66389i | ||||
\(511\) | −1.59444e27 | −1.31340 | ||||||||
\(512\) | 1.90336e27 | + | 1.90336e27i | 1.53752 | + | 1.53752i | ||||
\(513\) | −1.53122e25 | + | 1.53122e25i | −0.0121301 | + | 0.0121301i | ||||
\(514\) | − | 3.59816e27i | − | 2.79544i | ||||||
\(515\) | −2.54170e26 | − | 4.76796e26i | −0.193665 | − | 0.363296i | ||||
\(516\) | 2.19565e27 | 1.64084 | ||||||||
\(517\) | 1.47562e27 | + | 1.47562e27i | 1.08160 | + | 1.08160i | ||||
\(518\) | −9.25545e25 | + | 9.25545e25i | −0.0665427 | + | 0.0665427i | ||||
\(519\) | − | 3.54702e27i | − | 2.50144i | ||||||
\(520\) | −5.44017e26 | − | 1.65689e26i | −0.376339 | − | 0.114620i | ||||
\(521\) | −2.74417e27 | −1.86223 | −0.931117 | − | 0.364721i | \(-0.881164\pi\) | ||||
−0.931117 | + | 0.364721i | \(0.881164\pi\) | |||||||
\(522\) | −2.11398e27 | − | 2.11398e27i | −1.40733 | − | 1.40733i | ||||
\(523\) | 1.64898e27 | − | 1.64898e27i | 1.07696 | − | 1.07696i | 0.0801793 | − | 0.996780i | \(-0.474451\pi\) |
0.996780 | − | 0.0801793i | \(-0.0255493\pi\) | |||||||
\(524\) | − | 3.10129e27i | − | 1.98714i | ||||||
\(525\) | 2.23256e27 | + | 1.49897e27i | 1.40349 | + | 0.942320i | ||||
\(526\) | 2.54611e27 | 1.57043 | ||||||||
\(527\) | −2.21359e26 | − | 2.21359e26i | −0.133965 | − | 0.133965i | ||||
\(528\) | 2.57810e27 | − | 2.57810e27i | 1.53095 | − | 1.53095i | ||||
\(529\) | 1.68284e27i | 0.980588i | ||||||||
\(530\) | −6.52651e26 | + | 2.14290e27i | −0.373184 | + | 1.22530i | ||||
\(531\) | 1.50587e26 | 0.0844971 | ||||||||
\(532\) | −3.22602e27 | − | 3.22602e27i | −1.77644 | − | 1.77644i | ||||
\(533\) | 1.25108e26 | − | 1.25108e26i | 0.0676101 | − | 0.0676101i | ||||
\(534\) | 7.21528e27i | 3.82684i | ||||||||
\(535\) | 1.13701e27 | − | 6.06117e26i | 0.591872 | − | 0.315514i | ||||
\(536\) | −3.73404e27 | −1.90779 | ||||||||
\(537\) | −1.56631e27 | − | 1.56631e27i | −0.785481 | − | 0.785481i | ||||
\(538\) | 7.76665e26 | − | 7.76665e26i | 0.382306 | − | 0.382306i | ||||
\(539\) | − | 8.87632e26i | − | 0.428889i | ||||||
\(540\) | −3.75408e25 | − | 7.04228e25i | −0.0178060 | − | 0.0334022i | ||||
\(541\) | −2.06020e27 | −0.959263 | −0.479631 | − | 0.877470i | \(-0.659230\pi\) | ||||
−0.479631 | + | 0.877470i | \(0.659230\pi\) | |||||||
\(542\) | 4.33266e27 | + | 4.33266e27i | 1.98044 | + | 1.98044i | ||||
\(543\) | −1.35676e27 | + | 1.35676e27i | −0.608842 | + | 0.608842i | ||||
\(544\) | 1.91384e27i | 0.843171i | ||||||||
\(545\) | −8.32870e26 | − | 2.53663e26i | −0.360257 | − | 0.109722i | ||||
\(546\) | 1.35371e27 | 0.574911 | ||||||||
\(547\) | 4.14511e26 | + | 4.14511e26i | 0.172847 | + | 0.172847i | 0.788229 | − | 0.615382i | \(-0.210998\pi\) |
−0.615382 | + | 0.788229i | \(0.710998\pi\) | |||||||
\(548\) | −2.37267e26 | + | 2.37267e26i | −0.0971476 | + | 0.0971476i | ||||
\(549\) | 3.57647e27i | 1.43791i | ||||||||
\(550\) | −8.86301e26 | − | 4.50827e27i | −0.349909 | − | 1.77985i | ||||
\(551\) | 2.78974e27 | 1.08155 | ||||||||
\(552\) | 7.54465e26 | + | 7.54465e26i | 0.287242 | + | 0.287242i | ||||
\(553\) | −2.33483e27 | + | 2.33483e27i | −0.872979 | + | 0.872979i | ||||
\(554\) | 5.13761e27i | 1.88653i | ||||||||
\(555\) | 5.09372e25 | − | 1.67246e26i | 0.0183698 | − | 0.0603149i | ||||
\(556\) | 3.86924e27 | 1.37050 | ||||||||
\(557\) | 6.05596e26 | + | 6.05596e26i | 0.210684 | + | 0.210684i | 0.804558 | − | 0.593874i | \(-0.202402\pi\) |
−0.593874 | + | 0.804558i | \(0.702402\pi\) | |||||||
\(558\) | 5.02491e26 | − | 5.02491e26i | 0.171706 | − | 0.171706i | ||||
\(559\) | − | 3.05834e26i | − | 0.102652i | ||||||
\(560\) | 4.76820e27 | − | 2.54182e27i | 1.57208 | − | 0.838041i | ||||
\(561\) | −6.27547e27 | −2.03244 | ||||||||
\(562\) | −3.26087e27 | − | 3.26087e27i | −1.03746 | − | 1.03746i | ||||
\(563\) | 2.05402e27 | − | 2.05402e27i | 0.641978 | − | 0.641978i | −0.309063 | − | 0.951042i | \(-0.600015\pi\) |
0.951042 | + | 0.309063i | \(0.100015\pi\) | |||||||
\(564\) | − | 1.49294e28i | − | 4.58406i | ||||||
\(565\) | −7.91273e26 | − | 1.48435e27i | −0.238694 | − | 0.447766i | ||||
\(566\) | −5.07285e27 | −1.50344 | ||||||||
\(567\) | −2.85760e27 | − | 2.85760e27i | −0.832090 | − | 0.832090i | ||||
\(568\) | −7.06166e27 | + | 7.06166e27i | −2.02034 | + | 2.02034i | ||||
\(569\) | 2.67189e27i | 0.751097i | 0.926803 | + | 0.375548i | \(0.122546\pi\) | ||||
−0.926803 | + | 0.375548i | \(0.877454\pi\) | |||||||
\(570\) | 8.53223e27 | + | 2.59862e27i | 2.35675 | + | 0.717785i | ||||
\(571\) | 2.12903e27 | 0.577857 | 0.288929 | − | 0.957351i | \(-0.406701\pi\) | ||||
0.288929 | + | 0.957351i | \(0.406701\pi\) | |||||||
\(572\) | −1.11741e27 | − | 1.11741e27i | −0.298025 | − | 0.298025i | ||||
\(573\) | −8.52551e26 | + | 8.52551e26i | −0.223447 | + | 0.223447i | ||||
\(574\) | 4.10641e27i | 1.05765i | ||||||||
\(575\) | 5.40102e26 | − | 1.06181e26i | 0.136709 | − | 0.0268763i | ||||
\(576\) | 1.73959e27 | 0.432734 | ||||||||
\(577\) | −1.47017e27 | − | 1.47017e27i | −0.359427 | − | 0.359427i | 0.504175 | − | 0.863602i | \(-0.331797\pi\) |
−0.863602 | + | 0.504175i | \(0.831797\pi\) | |||||||
\(578\) | 5.06869e27 | − | 5.06869e27i | 1.21792 | − | 1.21792i | ||||
\(579\) | − | 2.30039e27i | − | 0.543270i | ||||||
\(580\) | −2.99540e27 | + | 9.83499e27i | −0.695303 | + | 2.28294i | ||||
\(581\) | 6.38014e27 | 1.45569 | ||||||||
\(582\) | 2.67528e27 | + | 2.67528e27i | 0.599984 | + | 0.599984i | ||||
\(583\) | −2.36074e27 | + | 2.36074e27i | −0.520430 | + | 0.520430i | ||||
\(584\) | − | 1.04531e28i | − | 2.26525i | ||||||
\(585\) | −8.02697e26 | + | 4.27900e26i | −0.170999 | + | 0.0911557i | ||||
\(586\) | 7.78532e27 | 1.63042 | ||||||||
\(587\) | 4.17034e26 | + | 4.17034e26i | 0.0858600 | + | 0.0858600i | 0.748732 | − | 0.662872i | \(-0.230663\pi\) |
−0.662872 | + | 0.748732i | \(0.730663\pi\) | |||||||
\(588\) | −4.49025e27 | + | 4.49025e27i | −0.908860 | + | 0.908860i | ||||
\(589\) | 6.63118e26i | 0.131959i | ||||||||
\(590\) | −3.56553e26 | − | 6.68857e26i | −0.0697596 | − | 0.130862i | ||||
\(591\) | 7.25346e27 | 1.39531 | ||||||||
\(592\) | −2.48406e26 | − | 2.48406e26i | −0.0469835 | − | 0.0469835i | ||||
\(593\) | 5.98664e27 | − | 5.98664e27i | 1.11336 | − | 1.11336i | 0.120669 | − | 0.992693i | \(-0.461496\pi\) |
0.992693 | − | 0.120669i | \(-0.0385040\pi\) | |||||||
\(594\) | − | 1.74085e26i | − | 0.0318344i | ||||||
\(595\) | −8.89682e27 | − | 2.70966e27i | −1.59980 | − | 0.487243i | ||||
\(596\) | −1.39782e28 | −2.47165 | ||||||||
\(597\) | −4.02711e27 | − | 4.02711e27i | −0.700245 | − | 0.700245i | ||||
\(598\) | 1.95937e26 | − | 1.95937e26i | 0.0335046 | − | 0.0335046i | ||||
\(599\) | 4.93475e27i | 0.829846i | 0.909857 | + | 0.414923i | \(0.136191\pi\) | ||||
−0.909857 | + | 0.414923i | \(0.863809\pi\) | |||||||
\(600\) | −9.82718e27 | + | 1.46366e28i | −1.62524 | + | 2.42063i | ||||
\(601\) | 8.84404e27 | 1.43849 | 0.719244 | − | 0.694758i | \(-0.244488\pi\) | ||||
0.719244 | + | 0.694758i | \(0.244488\pi\) | |||||||
\(602\) | 5.01921e27 | + | 5.01921e27i | 0.802917 | + | 0.802917i | ||||
\(603\) | −4.22330e27 | + | 4.22330e27i | −0.664475 | + | 0.664475i | ||||
\(604\) | − | 2.89510e27i | − | 0.448016i | ||||||
\(605\) | 8.09552e25 | − | 2.65806e26i | 0.0123223 | − | 0.0404586i | ||||
\(606\) | −1.94105e28 | −2.90610 | ||||||||
\(607\) | −2.47176e27 | − | 2.47176e27i | −0.364015 | − | 0.364015i | 0.501274 | − | 0.865289i | \(-0.332865\pi\) |
−0.865289 | + | 0.501274i | \(0.832865\pi\) | |||||||
\(608\) | 2.86660e27 | − | 2.86660e27i | 0.415271 | − | 0.415271i | ||||
\(609\) | − | 1.31261e28i | − | 1.87052i | ||||||
\(610\) | 1.58855e28 | − | 8.46821e27i | 2.22691 | − | 1.18712i | ||||
\(611\) | −2.07953e27 | −0.286783 | ||||||||
\(612\) | 1.59704e28 | + | 1.59704e28i | 2.16671 | + | 2.16671i | ||||
\(613\) | −3.58716e27 | + | 3.58716e27i | −0.478791 | + | 0.478791i | −0.904745 | − | 0.425954i | \(-0.859939\pi\) |
0.425954 | + | 0.904745i | \(0.359939\pi\) | |||||||
\(614\) | − | 1.26858e27i | − | 0.166584i | ||||||
\(615\) | −2.58016e27 | − | 4.84011e27i | −0.333346 | − | 0.625323i | ||||
\(616\) | 1.96715e28 | 2.50053 | ||||||||
\(617\) | 8.29805e27 | + | 8.29805e27i | 1.03783 | + | 1.03783i | 0.999256 | + | 0.0385691i | \(0.0122800\pi\) |
0.0385691 | + | 0.999256i | \(0.487720\pi\) | |||||||
\(618\) | −5.96237e27 | + | 5.96237e27i | −0.733726 | + | 0.733726i | ||||
\(619\) | 4.81099e27i | 0.582543i | 0.956640 | + | 0.291271i | \(0.0940783\pi\) | ||||
−0.956640 | + | 0.291271i | \(0.905922\pi\) | |||||||
\(620\) | −2.33776e27 | − | 7.12001e26i | −0.278537 | − | 0.0848328i | ||||
\(621\) | 2.08558e25 | 0.00244518 | ||||||||
\(622\) | −1.95407e28 | − | 1.95407e28i | −2.25442 | − | 2.25442i | ||||
\(623\) | −1.12691e28 | + | 1.12691e28i | −1.27941 | + | 1.27941i | ||||
\(624\) | 3.63322e27i | 0.405925i | ||||||||
\(625\) | 3.44296e27 | + | 8.41808e27i | 0.378558 | + | 0.925578i | ||||
\(626\) | −1.48958e28 | −1.61183 | ||||||||
\(627\) | 9.39959e27 | + | 9.39959e27i | 1.00100 | + | 1.00100i | ||||
\(628\) | 1.86687e28 | − | 1.86687e28i | 1.95667 | − | 1.95667i | ||||
\(629\) | 6.04656e26i | 0.0623738i | ||||||||
\(630\) | 6.15099e27 | − | 2.01960e28i | 0.624510 | − | 2.05050i | ||||
\(631\) | 2.89091e26 | 0.0288895 | 0.0144448 | − | 0.999896i | \(-0.495402\pi\) | ||||
0.0144448 | + | 0.999896i | \(0.495402\pi\) | |||||||
\(632\) | −1.53071e28 | − | 1.53071e28i | −1.50564 | − | 1.50564i | ||||
\(633\) | 1.29853e28 | − | 1.29853e28i | 1.25723 | − | 1.25723i | ||||
\(634\) | 1.72848e28i | 1.64729i | ||||||||
\(635\) | 8.60958e27 | − | 4.58958e27i | 0.807690 | − | 0.430562i | ||||
\(636\) | 2.38844e28 | 2.20569 | ||||||||
\(637\) | 6.25452e26 | + | 6.25452e26i | 0.0568591 | + | 0.0568591i | ||||
\(638\) | −1.58584e28 | + | 1.58584e28i | −1.41923 | + | 1.41923i | ||||
\(639\) | 1.59739e28i | 1.40735i | ||||||||
\(640\) | −7.37748e27 | − | 1.38394e28i | −0.639894 | − | 1.20038i | ||||
\(641\) | −7.88928e27 | −0.673686 | −0.336843 | − | 0.941561i | \(-0.609359\pi\) | ||||
−0.336843 | + | 0.941561i | \(0.609359\pi\) | |||||||
\(642\) | −1.42184e28 | − | 1.42184e28i | −1.19537 | − | 1.19537i | ||||
\(643\) | 1.35996e27 | − | 1.35996e27i | 0.112569 | − | 0.112569i | −0.648579 | − | 0.761147i | \(-0.724636\pi\) |
0.761147 | + | 0.648579i | \(0.224636\pi\) | |||||||
\(644\) | 4.39398e27i | 0.358096i | ||||||||
\(645\) | −9.06969e27 | − | 2.76231e27i | −0.727772 | − | 0.221654i | ||||
\(646\) | −3.08472e28 | −2.43720 | ||||||||
\(647\) | −1.13173e28 | − | 1.13173e28i | −0.880444 | − | 0.880444i | 0.113136 | − | 0.993580i | \(-0.463911\pi\) |
−0.993580 | + | 0.113136i | \(0.963911\pi\) | |||||||
\(648\) | 1.87343e28 | − | 1.87343e28i | 1.43512 | − | 1.43512i | ||||
\(649\) | − | 1.12965e27i | − | 0.0852112i | ||||||
\(650\) | 3.80118e27 | + | 2.55215e27i | 0.282348 | + | 0.189571i | ||||
\(651\) | 3.12005e27 | 0.228219 | ||||||||
\(652\) | 3.73602e28 | + | 3.73602e28i | 2.69112 | + | 2.69112i | ||||
\(653\) | 6.02418e27 | − | 6.02418e27i | 0.427333 | − | 0.427333i | −0.460386 | − | 0.887719i | \(-0.652289\pi\) |
0.887719 | + | 0.460386i | \(0.152289\pi\) | |||||||
\(654\) | 1.35872e28i | 0.949186i | ||||||||
\(655\) | −3.90168e27 | + | 1.28107e28i | −0.268435 | + | 0.881372i | ||||
\(656\) | −1.10212e28 | −0.746773 | ||||||||
\(657\) | −1.18227e28 | − | 1.18227e28i | −0.788976 | − | 0.788976i | ||||
\(658\) | 3.41283e28 | − | 3.41283e28i | 2.24313 | − | 2.24313i | ||||
\(659\) | − | 2.19924e26i | − | 0.0142370i | −0.999975 | − | 0.00711851i | \(-0.997734\pi\) | ||
0.999975 | − | 0.00711851i | \(-0.00226591\pi\) | |||||||
\(660\) | −4.32299e28 | + | 2.30449e28i | −2.75642 | + | 1.46939i | ||||
\(661\) | 6.20388e27 | 0.389627 | 0.194813 | − | 0.980840i | \(-0.437590\pi\) | ||||
0.194813 | + | 0.980840i | \(0.437590\pi\) | |||||||
\(662\) | 2.98857e28 | + | 2.98857e28i | 1.84877 | + | 1.84877i | ||||
\(663\) | 4.42189e27 | − | 4.42189e27i | 0.269446 | − | 0.269446i | ||||
\(664\) | 4.18280e28i | 2.51065i | ||||||||
\(665\) | 9.26732e27 | + | 1.73846e28i | 0.547946 | + | 1.02789i | ||||
\(666\) | −1.37258e27 | −0.0799459 | ||||||||
\(667\) | −1.89987e27 | − | 1.89987e27i | −0.109010 | − | 0.109010i | ||||
\(668\) | −3.90483e28 | + | 3.90483e28i | −2.20718 | + | 2.20718i | ||||
\(669\) | − | 2.50362e28i | − | 1.39414i | ||||||
\(670\) | 2.87583e28 | + | 8.75876e27i | 1.57766 | + | 0.480501i | ||||
\(671\) | 2.68294e28 | 1.45006 | ||||||||
\(672\) | −1.34877e28 | − | 1.34877e28i | −0.718200 | − | 0.718200i | ||||
\(673\) | −4.47258e26 | + | 4.47258e26i | −0.0234643 | + | 0.0234643i | −0.718742 | − | 0.695277i | \(-0.755282\pi\) |
0.695277 | + | 0.718742i | \(0.255282\pi\) | |||||||
\(674\) | − | 4.63802e28i | − | 2.39736i | ||||||
\(675\) | 6.64743e25 | + | 3.38129e26i | 0.00338545 | + | 0.0172205i | ||||
\(676\) | −4.14061e28 | −2.07777 | ||||||||
\(677\) | −2.32780e28 | − | 2.32780e28i | −1.15096 | − | 1.15096i | −0.986361 | − | 0.164597i | \(-0.947368\pi\) |
−0.164597 | − | 0.986361i | \(-0.552632\pi\) | |||||||
\(678\) | −1.85619e28 | + | 1.85619e28i | −0.904326 | + | 0.904326i | ||||
\(679\) | 8.35670e27i | 0.401178i | ||||||||
\(680\) | 1.77645e28 | − | 5.83274e28i | 0.840356 | − | 2.75920i | ||||
\(681\) | −9.11488e27 | −0.424893 | ||||||||
\(682\) | −3.76951e27 | − | 3.76951e27i | −0.173157 | − | 0.173157i | ||||
\(683\) | 4.46628e27 | − | 4.46628e27i | 0.202180 | − | 0.202180i | −0.598753 | − | 0.800934i | \(-0.704337\pi\) |
0.800934 | + | 0.598753i | \(0.204337\pi\) | |||||||
\(684\) | − | 4.78419e28i | − | 2.13426i | ||||||
\(685\) | 1.27860e27 | − | 6.81591e26i | 0.0562118 | − | 0.0299653i | ||||
\(686\) | 2.83386e28 | 1.22783 | ||||||||
\(687\) | 5.64747e27 | + | 5.64747e27i | 0.241150 | + | 0.241150i | ||||
\(688\) | −1.34710e28 | + | 1.34710e28i | −0.566912 | + | 0.566912i | ||||
\(689\) | − | 3.32689e27i | − | 0.137990i | ||||||
\(690\) | −4.04091e27 | − | 7.58033e27i | −0.165192 | − | 0.309883i | ||||
\(691\) | −8.29432e27 | −0.334195 | −0.167098 | − | 0.985940i | \(-0.553440\pi\) | ||||
−0.167098 | + | 0.985940i | \(0.553440\pi\) | |||||||
\(692\) | 6.77157e28 | + | 6.77157e28i | 2.68923 | + | 2.68923i | ||||
\(693\) | 2.22490e28 | − | 2.22490e28i | 0.870922 | − | 0.870922i | ||||
\(694\) | − | 8.39812e28i | − | 3.24032i | ||||||
\(695\) | −1.59829e28 | − | 4.86784e27i | −0.607866 | − | 0.185135i | ||||
\(696\) | 8.60543e28 | 3.22612 | ||||||||
\(697\) | 1.34135e28 | + | 1.34135e28i | 0.495696 | + | 0.495696i | ||||
\(698\) | −3.33071e28 | + | 3.33071e28i | −1.21334 | + | 1.21334i | ||||
\(699\) | 6.06931e28i | 2.17955i | ||||||||
\(700\) | −7.12382e28 | + | 1.40050e28i | −2.52193 | + | 0.495797i | ||||
\(701\) | −4.44091e28 | −1.54986 | −0.774929 | − | 0.632049i | \(-0.782214\pi\) | ||||
−0.774929 | + | 0.632049i | \(0.782214\pi\) | |||||||
\(702\) | 1.22666e26 | + | 1.22666e26i | 0.00422038 | + | 0.00422038i | ||||
\(703\) | 9.05672e26 | − | 9.05672e26i | 0.0307198 | − | 0.0307198i | ||||
\(704\) | − | 1.30498e28i | − | 0.436391i | ||||||
\(705\) | −1.87824e28 | + | 6.16696e28i | −0.619241 | + | 2.03320i | ||||
\(706\) | 3.27165e28 | 1.06346 | ||||||||
\(707\) | −3.03160e28 | − | 3.03160e28i | −0.971579 | − | 0.971579i | ||||
\(708\) | −5.71454e27 | + | 5.71454e27i | −0.180571 | + | 0.180571i | ||||
\(709\) | − | 8.23820e27i | − | 0.256667i | −0.991731 | − | 0.128333i | \(-0.959037\pi\) | ||
0.991731 | − | 0.128333i | \(-0.0409628\pi\) | |||||||
\(710\) | 7.09506e28 | − | 3.78222e28i | 2.17958 | − | 1.16189i | ||||
\(711\) | −3.46255e28 | −1.04882 | ||||||||
\(712\) | −7.38798e28 | − | 7.38798e28i | −2.20661 | − | 2.20661i | ||||
\(713\) | 4.51597e26 | − | 4.51597e26i | 0.0133001 | − | 0.0133001i | ||||
\(714\) | 1.45140e29i | 4.21507i | ||||||||
\(715\) | 3.20996e27 | + | 6.02155e27i | 0.0919261 | + | 0.172444i | ||||
\(716\) | 5.98046e28 | 1.68890 | ||||||||
\(717\) | 2.08014e28 | + | 2.08014e28i | 0.579295 | + | 0.579295i | ||||
\(718\) | −2.11030e28 | + | 2.11030e28i | −0.579563 | + | 0.579563i | ||||
\(719\) | − | 9.86614e27i | − | 0.267214i | −0.991034 | − | 0.133607i | \(-0.957344\pi\) | ||
0.991034 | − | 0.133607i | \(-0.0426559\pi\) | |||||||
\(720\) | 5.42038e28 | + | 1.65086e28i | 1.44779 | + | 0.440945i | ||||
\(721\) | −1.86245e28 | −0.490604 | ||||||||
\(722\) | −2.15535e27 | − | 2.15535e27i | −0.0559946 | − | 0.0559946i | ||||
\(723\) | 3.13829e28 | − | 3.13829e28i | 0.804100 | − | 0.804100i | ||||
\(724\) | − | 5.18035e28i | − | 1.30910i | ||||||
\(725\) | 2.47465e28 | − | 3.68575e28i | 0.616786 | − | 0.918642i | ||||
\(726\) | −4.33627e27 | −0.106598 | ||||||||
\(727\) | −2.04991e28 | − | 2.04991e28i | −0.497040 | − | 0.497040i | 0.413475 | − | 0.910515i | \(-0.364315\pi\) |
−0.910515 | + | 0.413475i | \(0.864315\pi\) | |||||||
\(728\) | −1.38612e28 | + | 1.38612e28i | −0.331502 | + | 0.331502i | ||||
\(729\) | − | 4.34335e28i | − | 1.02459i | ||||||
\(730\) | −2.45193e28 | + | 8.05060e28i | −0.570531 | + | 1.87327i | ||||
\(731\) | 3.27903e28 | 0.752614 | ||||||||
\(732\) | −1.35722e29 | − | 1.35722e29i | −3.07283 | − | 3.07283i | ||||
\(733\) | −3.34359e28 | + | 3.34359e28i | −0.746748 | + | 0.746748i | −0.973867 | − | 0.227119i | \(-0.927069\pi\) |
0.227119 | + | 0.973867i | \(0.427069\pi\) | |||||||
\(734\) | 5.36603e28i | 1.18220i | ||||||||
\(735\) | 2.41973e28 | − | 1.28990e28i | 0.525887 | − | 0.280339i | ||||
\(736\) | −3.90443e27 | −0.0837104 | ||||||||
\(737\) | 3.16817e28 | + | 3.16817e28i | 0.670091 | + | 0.670091i | ||||
\(738\) | −3.04490e28 | + | 3.04490e28i | −0.635345 | + | 0.635345i | ||||
\(739\) | − | 1.03645e28i | − | 0.213356i | −0.994294 | − | 0.106678i | \(-0.965979\pi\) | ||
0.994294 | − | 0.106678i | \(-0.0340214\pi\) | |||||||
\(740\) | 2.22043e27 | + | 4.16530e27i | 0.0450941 | + | 0.0845920i | ||||
\(741\) | −1.32465e28 | −0.265411 | ||||||||
\(742\) | 5.45994e28 | + | 5.45994e28i | 1.07932 | + | 1.07932i | ||||
\(743\) | −2.84193e28 | + | 2.84193e28i | −0.554275 | + | 0.554275i | −0.927672 | − | 0.373397i | \(-0.878193\pi\) |
0.373397 | + | 0.927672i | \(0.378193\pi\) | |||||||
\(744\) | 2.04550e28i | 0.393613i | ||||||||
\(745\) | 5.77405e28 | + | 1.75857e28i | 1.09627 | + | 0.333886i | ||||
\(746\) | −1.53984e29 | −2.88461 | ||||||||
\(747\) | 4.73086e28 | + | 4.73086e28i | 0.874449 | + | 0.874449i | ||||
\(748\) | 1.19804e29 | − | 1.19804e29i | 2.18502 | − | 2.18502i | ||||
\(749\) | − | 4.44137e28i | − | 0.799279i | ||||||
\(750\) | 1.10018e29 | − | 8.96750e28i | 1.95367 | − | 1.59242i | ||||
\(751\) | −5.17262e28 | −0.906381 | −0.453191 | − | 0.891414i | \(-0.649714\pi\) | ||||
−0.453191 | + | 0.891414i | \(0.649714\pi\) | |||||||
\(752\) | 9.15964e28 | + | 9.15964e28i | 1.58380 | + | 1.58380i | ||||
\(753\) | 3.66324e28 | − | 3.66324e28i | 0.625052 | − | 0.625052i | ||||
\(754\) | − | 2.23486e28i | − | 0.376302i | ||||||
\(755\) | −3.64228e27 | + | 1.19590e28i | −0.0605207 | + | 0.198712i | ||||
\(756\) | −2.75083e27 | −0.0451072 | ||||||||
\(757\) | 2.90311e28 | + | 2.90311e28i | 0.469791 | + | 0.469791i | 0.901847 | − | 0.432056i | \(-0.142212\pi\) |
−0.432056 | + | 0.901847i | \(0.642212\pi\) | |||||||
\(758\) | 1.05778e29 | − | 1.05778e29i | 1.68929 | − | 1.68929i | ||||
\(759\) | − | 1.28026e28i | − | 0.201781i | ||||||
\(760\) | −1.13973e29 | + | 6.07564e28i | −1.77282 | + | 0.945052i | ||||
\(761\) | 5.55850e28 | 0.853318 | 0.426659 | − | 0.904413i | \(-0.359690\pi\) | ||||
0.426659 | + | 0.904413i | \(0.359690\pi\) | |||||||
\(762\) | −1.07663e29 | − | 1.07663e29i | −1.63124 | − | 1.63124i | ||||
\(763\) | −2.12209e28 | + | 2.12209e28i | −0.317335 | + | 0.317335i | ||||
\(764\) | − | 3.25519e28i | − | 0.480444i | ||||||
\(765\) | −4.58777e28 | − | 8.60620e28i | −0.668325 | − | 1.25371i | ||||
\(766\) | −1.30293e29 | −1.87341 | ||||||||
\(767\) | 7.95986e26 | + | 7.95986e26i | 0.0112967 | + | 0.0112967i | ||||
\(768\) | −1.42455e29 | + | 1.42455e29i | −1.99556 | + | 1.99556i | ||||
\(769\) | 8.46303e28i | 1.17021i | 0.810959 | + | 0.585103i | \(0.198946\pi\) | ||||
−0.810959 | + | 0.585103i | \(0.801054\pi\) | |||||||
\(770\) | −1.51503e29 | − | 4.61426e28i | −2.06783 | − | 0.629788i | ||||
\(771\) | 1.65663e29 | 2.23193 | ||||||||
\(772\) | 4.39164e28 | + | 4.39164e28i | 0.584055 | + | 0.584055i | ||||
\(773\) | 1.26889e27 | − | 1.26889e27i | 0.0166583 | − | 0.0166583i | −0.698729 | − | 0.715387i | \(-0.746250\pi\) |
0.715387 | + | 0.698729i | \(0.246250\pi\) | |||||||
\(774\) | 7.44348e28i | 0.964642i | ||||||||
\(775\) | 8.76098e27 | + | 5.88221e27i | 0.112082 | + | 0.0752529i | ||||
\(776\) | −5.47863e28 | −0.691919 | ||||||||
\(777\) | −4.26130e27 | − | 4.26130e27i | −0.0531290 | − | 0.0531290i | ||||
\(778\) | 4.23607e28 | − | 4.23607e28i | 0.521396 | − | 0.521396i | ||||
\(779\) | − | 4.01824e28i | − | 0.488272i | ||||||
\(780\) | 1.42230e28 | − | 4.66993e28i | 0.170626 | − | 0.560227i | ||||
\(781\) | 1.19830e29 | 1.41924 | ||||||||
\(782\) | 2.10076e28 | + | 2.10076e28i | 0.245645 | + | 0.245645i | ||||
\(783\) | 1.18941e27 | − | 1.18941e27i | 0.0137313 | − | 0.0137313i | ||||
\(784\) | − | 5.50983e28i | − | 0.628025i | ||||||
\(785\) | −1.00603e29 | + | 5.36292e28i | −1.13218 | + | 0.603539i | ||||
\(786\) | 2.08989e29 | 2.32219 | ||||||||
\(787\) | −7.82439e27 | − | 7.82439e27i | −0.0858427 | − | 0.0858427i | 0.662882 | − | 0.748724i | \(-0.269333\pi\) |
−0.748724 | + | 0.662882i | \(0.769333\pi\) | |||||||
\(788\) | −1.38475e29 | + | 1.38475e29i | −1.50006 | + | 1.50006i | ||||
\(789\) | 1.17225e29i | 1.25386i | ||||||||
\(790\) | 8.19847e28 | + | 1.53795e29i | 0.865888 | + | 1.62432i | ||||
\(791\) | −5.79812e28 | −0.604675 | ||||||||
\(792\) | 1.45864e29 | + | 1.45864e29i | 1.50209 | + | 1.50209i | ||||
\(793\) | −1.89048e28 | + | 1.89048e28i | −0.192239 | + | 0.192239i | ||||
\(794\) | 2.56505e29i | 2.57568i | ||||||||
\(795\) | −9.86609e28 | − | 3.00487e28i | −0.978304 | − | 0.297957i | ||||
\(796\) | 1.53762e29 | 1.50563 | ||||||||
\(797\) | −9.35158e28 | − | 9.35158e28i | −0.904278 | − | 0.904278i | 0.0915249 | − | 0.995803i | \(-0.470826\pi\) |
−0.995803 | + | 0.0915249i | \(0.970826\pi\) | |||||||
\(798\) | 2.17395e29 | − | 2.17395e29i | 2.07597 | − | 2.07597i | ||||
\(799\) | − | 2.22959e29i | − | 2.10260i | ||||||
\(800\) | −1.24447e28 | − | 6.33013e28i | −0.115900 | − | 0.589539i | ||||
\(801\) | −1.67120e29 | −1.53711 | ||||||||
\(802\) | −1.72020e29 | − | 1.72020e29i | −1.56256 | − | 1.56256i | ||||
\(803\) | −8.86900e28 | + | 8.86900e28i | −0.795644 | + | 0.795644i | ||||
\(804\) | − | 3.20536e29i | − | 2.83998i | ||||||
\(805\) | 5.52800e27 | − | 1.81505e28i | 0.0483737 | − | 0.158829i | ||||
\(806\) | 5.31222e27 | 0.0459119 | ||||||||
\(807\) | 3.57584e28 | + | 3.57584e28i | 0.305241 | + | 0.305241i | ||||
\(808\) | 1.98751e29 | − | 1.98751e29i | 1.67570 | − | 1.67570i | ||||
\(809\) | 7.84858e28i | 0.653590i | 0.945095 | + | 0.326795i | \(0.105969\pi\) | ||||
−0.945095 | + | 0.326795i | \(0.894031\pi\) | |||||||
\(810\) | −1.88229e29 | + | 1.00341e29i | −1.54824 | + | 0.825331i | ||||
\(811\) | 7.38021e27 | 0.0599598 | 0.0299799 | − | 0.999551i | \(-0.490456\pi\) | ||||
0.0299799 | + | 0.999551i | \(0.490456\pi\) | |||||||
\(812\) | 2.50588e29 | + | 2.50588e29i | 2.01095 | + | 2.01095i | ||||
\(813\) | −1.99480e29 | + | 1.99480e29i | −1.58122 | + | 1.58122i | ||||
\(814\) | 1.02966e28i | 0.0806215i | ||||||||
\(815\) | −1.07324e29 | − | 2.01328e29i | −0.830080 | − | 1.55715i | ||||
\(816\) | −3.89539e29 | −2.97611 | ||||||||
\(817\) | −4.91144e28 | − | 4.91144e28i | −0.370671 | − | 0.370671i | ||||
\(818\) | 2.29376e29 | − | 2.29376e29i | 1.71008 | − | 1.71008i | ||||
\(819\) | 3.13547e28i | 0.230921i | ||||||||
\(820\) | 1.41660e29 | + | 4.31445e28i | 1.03064 | + | 0.313897i | ||||
\(821\) | 1.98234e29 | 1.42478 | 0.712389 | − | 0.701785i | \(-0.247613\pi\) | ||||
0.712389 | + | 0.701785i | \(0.247613\pi\) | |||||||
\(822\) | −1.59889e28 | − | 1.59889e28i | −0.113527 | − | 0.113527i | ||||
\(823\) | 9.57142e28 | − | 9.57142e28i | 0.671395 | − | 0.671395i | −0.286643 | − | 0.958037i | \(-0.592539\pi\) |
0.958037 | + | 0.286643i | \(0.0925393\pi\) | |||||||
\(824\) | − | 1.22102e29i | − | 0.846154i | ||||||
\(825\) | 2.07565e29 | − | 4.08061e28i | 1.42107 | − | 0.279374i | ||||
\(826\) | −2.61267e28 | −0.176719 | ||||||||
\(827\) | 8.77185e28 | + | 8.77185e28i | 0.586187 | + | 0.586187i | 0.936597 | − | 0.350410i | \(-0.113958\pi\) |
−0.350410 | + | 0.936597i | \(0.613958\pi\) | |||||||
\(828\) | −3.25813e28 | + | 3.25813e28i | −0.215112 | + | 0.215112i | ||||
\(829\) | 2.13178e29i | 1.39058i | 0.718728 | + | 0.695291i | \(0.244724\pi\) | ||||
−0.718728 | + | 0.695291i | \(0.755276\pi\) | |||||||
\(830\) | 9.81140e28 | − | 3.22145e29i | 0.632339 | − | 2.07620i | ||||
\(831\) | −2.36540e29 | −1.50624 | ||||||||
\(832\) | 9.19526e27 | + | 9.19526e27i | 0.0578537 | + | 0.0578537i | ||||
\(833\) | −6.70585e28 | + | 6.70585e28i | −0.416873 | + | 0.416873i | ||||
\(834\) | 2.60740e29i | 1.60157i | ||||||||
\(835\) | 2.10426e29 | − | 1.12173e29i | 1.27713 | − | 0.680808i | ||||
\(836\) | −3.58893e29 | −2.15230 | ||||||||
\(837\) | 2.82720e26 | + | 2.82720e26i | 0.00167534 | + | 0.00167534i | ||||
\(838\) | −3.03512e29 | + | 3.03512e29i | −1.77720 | + | 1.77720i | ||||
\(839\) | − | 6.36044e28i | − | 0.368017i | −0.982925 | − | 0.184008i | \(-0.941093\pi\) | ||
0.982925 | − | 0.184008i | \(-0.0589073\pi\) | |||||||
\(840\) | 2.85866e29 | + | 5.36255e29i | 1.63444 | + | 3.06605i | ||||
\(841\) | −3.97048e28 | −0.224328 | ||||||||
\(842\) | −1.29625e29 | − | 1.29625e29i | −0.723717 | − | 0.723717i | ||||
\(843\) | 1.50134e29 | − | 1.50134e29i | 0.828328 | − | 0.828328i | ||||
\(844\) | 4.95800e29i | 2.70322i | ||||||||
\(845\) | 1.71039e29 | + | 5.20924e28i | 0.921568 | + | 0.280677i | ||||
\(846\) | 5.06121e29 | 2.69495 | ||||||||
\(847\) | −6.77254e27 | − | 6.77254e27i | −0.0356383 | − | 0.0356383i | ||||
\(848\) | −1.46539e29 | + | 1.46539e29i | −0.762068 | + | 0.762068i | ||||
\(849\) | − | 2.33558e29i | − | 1.20038i | ||||||
\(850\) | −2.73631e29 | + | 4.07547e29i | −1.38988 | + | 2.07009i | ||||
\(851\) | −1.23356e27 | −0.00619249 | ||||||||
\(852\) | −6.06184e29 | − | 6.06184e29i | −3.00752 | − | 3.00752i | ||||
\(853\) | −1.38791e29 | + | 1.38791e29i | −0.680568 | + | 0.680568i | −0.960128 | − | 0.279560i | \(-0.909811\pi\) |
0.279560 | + | 0.960128i | \(0.409811\pi\) | |||||||
\(854\) | − | 6.20514e29i | − | 3.00727i | ||||||
\(855\) | −6.01892e28 | + | 1.97623e29i | −0.288308 | + | 0.946623i | ||||
\(856\) | 2.91175e29 | 1.37853 | ||||||||
\(857\) | 7.58343e27 | + | 7.58343e27i | 0.0354860 | + | 0.0354860i | 0.724627 | − | 0.689141i | \(-0.242012\pi\) |
−0.689141 | + | 0.724627i | \(0.742012\pi\) | |||||||
\(858\) | 7.52999e28 | − | 7.52999e28i | 0.348274 | − | 0.348274i | ||||
\(859\) | − | 1.12132e29i | − | 0.512622i | −0.966594 | − | 0.256311i | \(-0.917493\pi\) | ||
0.966594 | − | 0.256311i | \(-0.0825071\pi\) | |||||||
\(860\) | 2.25883e29 | − | 1.20413e29i | 1.02070 | − | 0.544115i | ||||
\(861\) | −1.89063e29 | −0.844452 | ||||||||
\(862\) | 7.25359e28 | + | 7.25359e28i | 0.320244 | + | 0.320244i | ||||
\(863\) | 1.95303e29 | − | 1.95303e29i | 0.852319 | − | 0.852319i | −0.138100 | − | 0.990418i | \(-0.544099\pi\) |
0.990418 | + | 0.138100i | \(0.0440994\pi\) | |||||||
\(864\) | − | 2.44435e27i | − | 0.0105445i | ||||||
\(865\) | −1.94525e29 | − | 3.64909e29i | −0.829497 | − | 1.55605i | ||||
\(866\) | 9.27536e28 | 0.390977 | ||||||||
\(867\) | 2.33367e29 | + | 2.33367e29i | 0.972409 | + | 0.972409i | ||||
\(868\) | −5.95645e28 | + | 5.95645e28i | −0.245352 | + | 0.245352i | ||||
\(869\) | 2.59748e29i | 1.05768i | ||||||||
\(870\) | −6.62759e29 | − | 2.01853e29i | −2.66786 | − | 0.812538i | ||||
\(871\) | −4.46478e28 | −0.177672 | ||||||||
\(872\) | −1.39124e29 | − | 1.39124e29i | −0.547314 | − | 0.547314i | ||||
\(873\) | −6.19648e28 | + | 6.19648e28i | −0.240992 | + | 0.240992i | ||||
\(874\) | − | 6.29316e28i | − | 0.241966i | ||||||
\(875\) | 3.11887e29 | + | 3.17723e28i | 1.18554 | + | 0.120772i | ||||
\(876\) | 8.97309e29 | 3.37210 | ||||||||
\(877\) | 4.06067e28 | + | 4.06067e28i | 0.150870 | + | 0.150870i | 0.778506 | − | 0.627637i | \(-0.215978\pi\) |
−0.627637 | + | 0.778506i | \(0.715978\pi\) | |||||||
\(878\) | −3.18639e29 | + | 3.18639e29i | −1.17045 | + | 1.17045i | ||||
\(879\) | 3.58443e29i | 1.30176i | ||||||||
\(880\) | 1.23842e29 | − | 4.06618e29i | 0.444672 | − | 1.46002i | ||||
\(881\) | 1.52098e29 | 0.539962 | 0.269981 | − | 0.962866i | \(-0.412983\pi\) | ||||
0.269981 | + | 0.962866i | \(0.412983\pi\) | |||||||
\(882\) | −1.52224e29 | − | 1.52224e29i | −0.534316 | − | 0.534316i | ||||
\(883\) | 2.56486e29 | − | 2.56486e29i | 0.890137 | − | 0.890137i | −0.104399 | − | 0.994536i | \(-0.533292\pi\) |
0.994536 | + | 0.104399i | \(0.0332918\pi\) | |||||||
\(884\) | 1.68835e29i | 0.579350i | ||||||||
\(885\) | 3.07948e28 | − | 1.64160e28i | 0.104483 | − | 0.0556974i | ||||
\(886\) | −1.66415e29 | −0.558285 | ||||||||
\(887\) | 6.78026e28 | + | 6.78026e28i | 0.224911 | + | 0.224911i | 0.810563 | − | 0.585652i | \(-0.199161\pi\) |
−0.585652 | + | 0.810563i | \(0.699161\pi\) | |||||||
\(888\) | 2.79370e28 | − | 2.79370e28i | 0.0916325 | − | 0.0916325i | ||||
\(889\) | − | 3.36305e29i | − | 1.09072i | ||||||
\(890\) | 3.95700e29 | + | 7.42293e29i | 1.26901 | + | 2.38054i | ||||
\(891\) | −3.17906e29 | −1.00814 | ||||||||
\(892\) | 4.77962e29 | + | 4.77962e29i | 1.49881 | + | 1.49881i | ||||
\(893\) | −3.33955e29 | + | 3.33955e29i | −1.03555 | + | 1.03555i | ||||
\(894\) | − | 9.41959e29i | − | 2.88840i | ||||||
\(895\) | −2.47038e29 | − | 7.52393e28i | −0.749090 | − | 0.228147i | ||||
\(896\) | −5.40590e29 | −1.62102 | ||||||||
\(897\) | 9.02112e27 | + | 9.02112e27i | 0.0267507 | + | 0.0267507i | ||||
\(898\) | −1.73995e29 | + | 1.73995e29i | −0.510239 | + | 0.510239i | ||||
\(899\) | − | 5.15091e28i | − | 0.149378i | ||||||
\(900\) | −6.32077e29 | − | 4.24383e29i | −1.81278 | − | 1.21712i | ||||
\(901\) | 3.56696e29 | 1.01170 | ||||||||
\(902\) | 2.28418e29 | + | 2.28418e29i | 0.640715 | + | 0.640715i | ||||
\(903\) | −2.31089e29 | + | 2.31089e29i | −0.641065 | + | 0.641065i | ||||
\(904\) | − | 3.80123e29i | − | 1.04289i | ||||||
\(905\) | −6.51732e28 | + | 2.13988e29i | −0.176841 | + | 0.580635i | ||||
\(906\) | 1.95095e29 | 0.523556 | ||||||||
\(907\) | −3.21925e29 | − | 3.21925e29i | −0.854442 | − | 0.854442i | 0.136235 | − | 0.990677i | \(-0.456500\pi\) |
−0.990677 | + | 0.136235i | \(0.956500\pi\) | |||||||
\(908\) | 1.74011e29 | − | 1.74011e29i | 0.456792 | − | 0.456792i | ||||
\(909\) | − | 4.49586e29i | − | 1.16728i | ||||||
\(910\) | 1.39267e29 | − | 7.42403e28i | 0.357631 | − | 0.190645i | ||||
\(911\) | −5.89230e29 | −1.49658 | −0.748292 | − | 0.663370i | \(-0.769126\pi\) | ||||
−0.748292 | + | 0.663370i | \(0.769126\pi\) | |||||||
\(912\) | 5.83464e29 | + | 5.83464e29i | 1.46577 | + | 1.46577i | ||||
\(913\) | 3.54893e29 | − | 3.54893e29i | 0.881840 | − | 0.881840i | ||||
\(914\) | − | 3.88379e29i | − | 0.954540i | ||||||
\(915\) | 3.89884e29 | + | 7.31382e29i | 0.947817 | + | 1.77801i | ||||
\(916\) | −2.15630e29 | −0.518508 | ||||||||
\(917\) | 3.26407e29 | + | 3.26407e29i | 0.776364 | + | 0.776364i | ||||
\(918\) | −1.31517e28 | + | 1.31517e28i | −0.0309425 | + | 0.0309425i | ||||
\(919\) | 5.18713e29i | 1.20718i | 0.797295 | + | 0.603590i | \(0.206264\pi\) | ||||
−0.797295 | + | 0.603590i | \(0.793736\pi\) | |||||||
\(920\) | 1.18994e29 | + | 3.62414e28i | 0.273935 | + | 0.0834309i | ||||
\(921\) | 5.84065e28 | 0.133004 | ||||||||
\(922\) | −1.70871e29 | − | 1.70871e29i | −0.384910 | − | 0.384910i | ||||
\(923\) | −8.44361e28 | + | 8.44361e28i | −0.188153 | + | 0.188153i | ||||
\(924\) | 1.68863e30i | 3.72234i | ||||||||
\(925\) | −3.93176e27 | − | 1.99994e28i | −0.00857373 | − | 0.0436113i | ||||
\(926\) | −4.92667e29 | −1.06278 | ||||||||
\(927\) | −1.38100e29 | − | 1.38100e29i | −0.294712 | − | 0.294712i | ||||
\(928\) | −2.22670e29 | + | 2.22670e29i | −0.470090 | + | 0.470090i | ||||
\(929\) | 9.59557e28i | 0.200407i | 0.994967 | + | 0.100204i | \(0.0319495\pi\) | ||||
−0.994967 | + | 0.100204i | \(0.968051\pi\) | |||||||
\(930\) | 4.79802e28 | − | 1.57537e29i | 0.0991363 | − | 0.325501i | ||||
\(931\) | 2.00885e29 | 0.410629 | ||||||||
\(932\) | −1.15868e30 | − | 1.15868e30i | −2.34318 | − | 2.34318i | ||||
\(933\) | 8.99671e29 | − | 8.99671e29i | 1.79998 | − | 1.79998i | ||||
\(934\) | 1.54970e30i | 3.06746i | ||||||||
\(935\) | −6.45607e29 | + | 3.44159e29i | −1.26431 | + | 0.673973i | ||||
\(936\) | −2.05561e29 | −0.398274 | ||||||||
\(937\) | −2.24886e29 | − | 2.24886e29i | −0.431089 | − | 0.431089i | 0.457910 | − | 0.888999i | \(-0.348598\pi\) |
−0.888999 | + | 0.457910i | \(0.848598\pi\) | |||||||
\(938\) | 7.32739e29 | − | 7.32739e29i | 1.38970 | − | 1.38970i | ||||
\(939\) | − | 6.85815e29i | − | 1.28692i | ||||||
\(940\) | −8.18754e29 | − | 1.53590e30i | −1.52011 | − | 2.85157i | ||||
\(941\) | 9.61795e29 | 1.76679 | 0.883397 | − | 0.468625i | \(-0.155250\pi\) | ||||
0.883397 | + | 0.468625i | \(0.155250\pi\) | |||||||
\(942\) | 1.25805e30 | + | 1.25805e30i | 2.28659 | + | 2.28659i | ||||
\(943\) | −2.73650e28 | + | 2.73650e28i | −0.0492129 | + | 0.0492129i | ||||
\(944\) | − | 7.01211e28i | − | 0.124775i | ||||||
\(945\) | 1.13630e28 | + | 3.46078e27i | 0.0200067 | + | 0.00609335i | ||||
\(946\) | 5.58384e29 | 0.972795 | ||||||||
\(947\) | 5.36645e29 | + | 5.36645e29i | 0.925097 | + | 0.925097i | 0.997384 | − | 0.0722867i | \(-0.0230297\pi\) |
−0.0722867 | + | 0.997384i | \(0.523030\pi\) | |||||||
\(948\) | 1.31398e30 | − | 1.31398e30i | 2.24133 | − | 2.24133i | ||||
\(949\) | − | 1.24987e29i | − | 0.210962i | ||||||
\(950\) | 1.02029e30 | − | 2.00583e29i | 1.70407 | − | 0.335011i | ||||
\(951\) | −7.95806e29 | −1.31523 | ||||||||
\(952\) | −1.48614e30 | − | 1.48614e30i | −2.43047 | − | 2.43047i | ||||
\(953\) | −3.99557e29 | + | 3.99557e29i | −0.646621 | + | 0.646621i | −0.952175 | − | 0.305554i | \(-0.901158\pi\) |
0.305554 | + | 0.952175i | \(0.401158\pi\) | |||||||
\(954\) | 8.09708e29i | 1.29672i | ||||||||
\(955\) | −4.09531e28 | + | 1.34464e29i | −0.0649012 | + | 0.213095i | ||||
\(956\) | −7.94232e29 | −1.24557 | ||||||||
\(957\) | −7.30134e29 | − | 7.30134e29i | −1.13314 | − | 1.13314i | ||||
\(958\) | −7.55703e29 | + | 7.55703e29i | −1.16064 | + | 1.16064i | ||||
\(959\) | − | 4.99441e28i | − | 0.0759099i | ||||||
\(960\) | 3.55743e29 | − | 1.89639e29i | 0.535086 | − | 0.285243i | ||||
\(961\) | −6.59547e29 | −0.981775 | ||||||||
\(962\) | −7.25532e27 | − | 7.25532e27i | −0.0106882 | − | 0.0106882i | ||||
\(963\) | 3.29327e29 | − | 3.29327e29i | 0.480136 | − | 0.480136i | ||||
\(964\) | 1.19825e30i | 1.72893i | ||||||||
\(965\) | −1.26158e29 | − | 2.36659e29i | −0.180153 | − | 0.337948i | ||||
\(966\) | −2.96101e29 | −0.418474 | ||||||||
\(967\) | −4.84629e29 | − | 4.84629e29i | −0.677867 | − | 0.677867i | 0.281650 | − | 0.959517i | \(-0.409118\pi\) |
−0.959517 | + | 0.281650i | \(0.909118\pi\) | |||||||
\(968\) | 4.44006e28 | − | 4.44006e28i | 0.0614661 | − | 0.0614661i | ||||
\(969\) | − | 1.42023e30i | − | 1.94591i | ||||||
\(970\) | 4.21945e29 | + | 1.28510e29i | 0.572188 | + | 0.174268i | ||||
\(971\) | −1.49540e29 | −0.200709 | −0.100354 | − | 0.994952i | \(-0.531998\pi\) | ||||
−0.100354 | + | 0.994952i | \(0.531998\pi\) | |||||||
\(972\) | 1.62833e30 | + | 1.62833e30i | 2.16312 | + | 2.16312i | ||||
\(973\) | −4.07233e29 | + | 4.07233e29i | −0.535444 | + | 0.535444i | ||||
\(974\) | − | 4.36877e29i | − | 0.568552i | ||||||
\(975\) | −1.17503e29 | + | 1.75010e29i | −0.151358 | + | 0.225432i | ||||
\(976\) | 1.66539e30 | 2.12333 | ||||||||
\(977\) | 1.07442e29 | + | 1.07442e29i | 0.135590 | + | 0.135590i | 0.771644 | − | 0.636054i | \(-0.219435\pi\) |
−0.636054 | + | 0.771644i | \(0.719435\pi\) | |||||||
\(978\) | −2.51763e30 | + | 2.51763e30i | −3.14487 | + | 3.14487i | ||||
\(979\) | 1.25368e30i | 1.55010i | ||||||||
\(980\) | −2.15693e29 | + | 7.08201e29i | −0.263983 | + | 0.866754i | ||||
\(981\) | −3.14706e29 | −0.381254 | ||||||||
\(982\) | 9.04800e29 | + | 9.04800e29i | 1.08502 | + | 1.08502i | ||||
\(983\) | 2.34164e29 | − | 2.34164e29i | 0.277962 | − | 0.277962i | −0.554333 | − | 0.832295i | \(-0.687027\pi\) |
0.832295 | + | 0.554333i | \(0.187027\pi\) | |||||||
\(984\) | − | 1.23949e30i | − | 1.45644i | ||||||
\(985\) | 7.46220e29 | − | 3.97793e29i | 0.867970 | − | 0.462696i | ||||
\(986\) | 2.39612e30 | 2.75893 | ||||||||
\(987\) | 1.57130e30 | + | 1.57130e30i | 1.79096 | + | 1.79096i | ||||
\(988\) | 2.52887e29 | − | 2.52887e29i | 0.285336 | − | 0.285336i | ||||
\(989\) | 6.68958e28i | 0.0747198i | ||||||||
\(990\) | −7.81248e29 | − | 1.46554e30i | −0.863847 | − | 1.62049i | ||||
\(991\) | 4.79836e29 | 0.525238 | 0.262619 | − | 0.964900i | \(-0.415414\pi\) | ||||
0.262619 | + | 0.964900i | \(0.415414\pi\) | |||||||
\(992\) | −5.29282e28 | − | 5.29282e28i | −0.0573549 | − | 0.0573549i | ||||
\(993\) | −1.37596e30 | + | 1.37596e30i | −1.47610 | + | 1.47610i | ||||
\(994\) | − | 2.77145e30i | − | 2.94336i | ||||||
\(995\) | −6.35155e29 | − | 1.93446e29i | −0.667803 | − | 0.203390i | ||||
\(996\) | −3.59058e30 | −3.73742 | ||||||||
\(997\) | −9.92132e28 | − | 9.92132e28i | −0.102239 | − | 0.102239i | 0.654137 | − | 0.756376i | \(-0.273032\pi\) |
−0.756376 | + | 0.654137i | \(0.773032\pi\) | |||||||
\(998\) | 1.99430e30 | − | 1.99430e30i | 2.03463 | − | 2.03463i | ||||
\(999\) | − | 7.72267e26i | − | 0.000780032i |
(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 | 5.21.c.a.2.1 | ✓ | 18 | |
3.2 | odd | 2 | 45.21.g.a.37.9 | 18 | |||
5.2 | odd | 4 | 25.21.c.b.18.9 | 18 | |||
5.3 | odd | 4 | inner | 5.21.c.a.3.1 | yes | 18 | |
5.4 | even | 2 | 25.21.c.b.7.9 | 18 | |||
15.8 | even | 4 | 45.21.g.a.28.9 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.21.c.a.2.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
5.21.c.a.3.1 | yes | 18 | 5.3 | odd | 4 | inner | |
25.21.c.b.7.9 | 18 | 5.4 | even | 2 | |||
25.21.c.b.18.9 | 18 | 5.2 | odd | 4 | |||
45.21.g.a.28.9 | 18 | 15.8 | even | 4 | |||
45.21.g.a.37.9 | 18 | 3.2 | odd | 2 |