Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,39,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, 39, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 39);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 39 \) |
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: | \(36.5853876134\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 9 x^{17} + \cdots + 98\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.5 | ||
Root | \(0.500000 + 7.90224e7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.39.b.a.3.6 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −306058. | − | 425684.i | −0.583759 | − | 0.811927i | ||||
\(3\) | − | 1.26436e9i | − | 1.08784i | −0.839136 | − | 0.543921i | \(-0.816939\pi\) | ||
0.839136 | − | 0.543921i | \(-0.183061\pi\) | |||||||
\(4\) | −8.75354e10 | + | 2.60567e11i | −0.318452 | + | 0.947939i | ||||
\(5\) | −4.90299e12 | −0.257058 | −0.128529 | − | 0.991706i | \(-0.541025\pi\) | ||||
−0.128529 | + | 0.991706i | \(0.541025\pi\) | |||||||
\(6\) | −5.38217e14 | + | 3.86966e14i | −0.883249 | + | 0.635038i | ||||
\(7\) | − | 1.75338e16i | − | 1.53820i | −0.639126 | − | 0.769102i | \(-0.720704\pi\) | ||
0.639126 | − | 0.769102i | \(-0.279296\pi\) | |||||||
\(8\) | 1.37710e17 | − | 4.24863e16i | 0.955557 | − | 0.294808i | ||||
\(9\) | −2.47749e17 | −0.183402 | ||||||||
\(10\) | 1.50060e18 | + | 2.08712e18i | 0.150060 | + | 0.208712i | ||||
\(11\) | − | 5.84750e19i | − | 0.956113i | −0.878329 | − | 0.478056i | \(-0.841341\pi\) | ||
0.878329 | − | 0.478056i | \(-0.158659\pi\) | |||||||
\(12\) | 3.29451e20 | + | 1.10676e20i | 1.03121 | + | 0.346426i | ||||
\(13\) | −2.66415e21 | −1.82236 | −0.911181 | − | 0.412007i | \(-0.864828\pi\) | ||||
−0.911181 | + | 0.412007i | \(0.864828\pi\) | |||||||
\(14\) | −7.46387e21 | + | 5.36636e21i | −1.24891 | + | 0.897940i | ||||
\(15\) | 6.19913e21i | 0.279638i | ||||||||
\(16\) | −6.02330e22 | − | 4.56178e22i | −0.797177 | − | 0.603746i | ||||
\(17\) | 3.72111e22 | 0.155648 | 0.0778239 | − | 0.996967i | \(-0.475203\pi\) | ||||
0.0778239 | + | 0.996967i | \(0.475203\pi\) | |||||||
\(18\) | 7.58254e22 | + | 1.05463e23i | 0.107062 | + | 0.148909i | ||||
\(19\) | − | 1.66958e24i | − | 0.843897i | −0.906620 | − | 0.421949i | \(-0.861346\pi\) | ||
0.906620 | − | 0.421949i | \(-0.138654\pi\) | |||||||
\(20\) | 4.29185e23 | − | 1.27756e24i | 0.0818605 | − | 0.243675i | ||||
\(21\) | −2.21690e25 | −1.67332 | ||||||||
\(22\) | −2.48918e25 | + | 1.78967e25i | −0.776294 | + | 0.558139i | ||||
\(23\) | − | 1.32941e25i | − | 0.178169i | −0.996024 | − | 0.0890843i | \(-0.971606\pi\) | ||
0.996024 | − | 0.0890843i | \(-0.0283940\pi\) | |||||||
\(24\) | −5.37179e25 | − | 1.74115e26i | −0.320704 | − | 1.03950i | ||||
\(25\) | −3.39759e26 | −0.933921 | ||||||||
\(26\) | 8.15382e26 | + | 1.13408e27i | 1.06382 | + | 1.47962i | ||||
\(27\) | − | 1.39472e27i | − | 0.888330i | ||||||
\(28\) | 4.56875e27 | + | 1.53483e27i | 1.45812 | + | 0.489844i | ||||
\(29\) | 4.91284e26 | 0.0804954 | 0.0402477 | − | 0.999190i | \(-0.487185\pi\) | ||||
0.0402477 | + | 0.999190i | \(0.487185\pi\) | |||||||
\(30\) | 2.63887e27 | − | 1.89729e27i | 0.227046 | − | 0.163241i | ||||
\(31\) | 3.21732e27i | 0.148464i | 0.997241 | + | 0.0742322i | \(0.0236506\pi\) | ||||
−0.997241 | + | 0.0742322i | \(0.976349\pi\) | |||||||
\(32\) | −9.83973e26 | + | 3.96019e28i | −0.0248390 | + | 0.999691i | ||||
\(33\) | −7.39333e28 | −1.04010 | ||||||||
\(34\) | −1.13887e28 | − | 1.58402e28i | −0.0908608 | − | 0.126375i | ||||
\(35\) | 8.59681e28i | 0.395407i | ||||||||
\(36\) | 2.16868e28 | − | 6.45553e28i | 0.0584047 | − | 0.173854i | ||||
\(37\) | 9.26858e29 | 1.48313 | 0.741567 | − | 0.670879i | \(-0.234083\pi\) | ||||
0.741567 | + | 0.670879i | \(0.234083\pi\) | |||||||
\(38\) | −7.10714e29 | + | 5.10989e29i | −0.685183 | + | 0.492632i | ||||
\(39\) | 3.36843e30i | 1.98244i | ||||||||
\(40\) | −6.75191e29 | + | 2.08310e29i | −0.245633 | + | 0.0757826i | ||||
\(41\) | 2.76483e30 | 0.629180 | 0.314590 | − | 0.949228i | \(-0.398133\pi\) | ||||
0.314590 | + | 0.949228i | \(0.398133\pi\) | |||||||
\(42\) | 6.78500e30 | + | 9.43700e30i | 0.976818 | + | 1.35862i | ||||
\(43\) | 8.54057e30i | 0.786296i | 0.919475 | + | 0.393148i | \(0.128614\pi\) | ||||
−0.919475 | + | 0.393148i | \(0.871386\pi\) | |||||||
\(44\) | 1.52367e31 | + | 5.11863e30i | 0.906336 | + | 0.304476i | ||||
\(45\) | 1.21471e30 | 0.0471448 | ||||||||
\(46\) | −5.65910e30 | + | 4.06877e30i | −0.144660 | + | 0.104007i | ||||
\(47\) | 1.63375e31i | 0.277540i | 0.990325 | + | 0.138770i | \(0.0443149\pi\) | ||||
−0.990325 | + | 0.138770i | \(0.955685\pi\) | |||||||
\(48\) | −5.76772e31 | + | 7.61560e31i | −0.656781 | + | 0.867203i | ||||
\(49\) | −1.77501e32 | −1.36607 | ||||||||
\(50\) | 1.03986e32 | + | 1.44630e32i | 0.545185 | + | 0.758276i | ||||
\(51\) | − | 4.70482e31i | − | 0.169320i | ||||||
\(52\) | 2.33207e32 | − | 6.94190e32i | 0.580334 | − | 1.72749i | ||||
\(53\) | 1.08629e33 | 1.88237 | 0.941187 | − | 0.337887i | \(-0.109712\pi\) | ||||
0.941187 | + | 0.337887i | \(0.109712\pi\) | |||||||
\(54\) | −5.93708e32 | + | 4.26864e32i | −0.721260 | + | 0.518570i | ||||
\(55\) | 2.86702e32i | 0.245776i | ||||||||
\(56\) | −7.44947e32 | − | 2.41459e33i | −0.453475 | − | 1.46984i | ||||
\(57\) | −2.11095e33 | −0.918028 | ||||||||
\(58\) | −1.50361e32 | − | 2.09132e32i | −0.0469899 | − | 0.0653564i | ||||
\(59\) | − | 6.34821e33i | − | 1.43371i | −0.697220 | − | 0.716857i | \(-0.745580\pi\) | ||
0.697220 | − | 0.716857i | \(-0.254420\pi\) | |||||||
\(60\) | −1.61529e33 | − | 5.42643e32i | −0.265080 | − | 0.0890513i | ||||
\(61\) | −9.47917e33 | −1.13633 | −0.568164 | − | 0.822916i | \(-0.692346\pi\) | ||||
−0.568164 | + | 0.822916i | \(0.692346\pi\) | |||||||
\(62\) | 1.36956e33 | − | 9.84686e32i | 0.120542 | − | 0.0866673i | ||||
\(63\) | 4.34398e33i | 0.282110i | ||||||||
\(64\) | 1.71590e34 | − | 1.17016e34i | 0.826177 | − | 0.563411i | ||||
\(65\) | 1.30623e34 | 0.468452 | ||||||||
\(66\) | 2.26278e34 | + | 3.14722e34i | 0.607167 | + | 0.844486i | ||||
\(67\) | 5.59969e34i | 1.12913i | 0.825389 | + | 0.564564i | \(0.190956\pi\) | ||||
−0.825389 | + | 0.564564i | \(0.809044\pi\) | |||||||
\(68\) | −3.25729e33 | + | 9.69601e33i | −0.0495663 | + | 0.147545i | ||||
\(69\) | −1.68085e34 | −0.193819 | ||||||||
\(70\) | 3.65952e34 | − | 2.63112e34i | 0.321042 | − | 0.230822i | ||||
\(71\) | 2.26917e35i | 1.52040i | 0.649689 | + | 0.760200i | \(0.274899\pi\) | ||||
−0.649689 | + | 0.760200i | \(0.725101\pi\) | |||||||
\(72\) | −3.41175e34 | + | 1.05259e34i | −0.175251 | + | 0.0540683i | ||||
\(73\) | 7.29274e34 | 0.288241 | 0.144121 | − | 0.989560i | \(-0.453965\pi\) | ||||
0.144121 | + | 0.989560i | \(0.453965\pi\) | |||||||
\(74\) | −2.83672e35 | − | 3.94548e35i | −0.865792 | − | 1.20420i | ||||
\(75\) | 4.29576e35i | 1.01596i | ||||||||
\(76\) | 4.35039e35 | + | 1.46148e35i | 0.799963 | + | 0.268741i | ||||
\(77\) | −1.02529e36 | −1.47070 | ||||||||
\(78\) | 1.43389e36 | − | 1.03093e36i | 1.60960 | − | 1.15727i | ||||
\(79\) | − | 7.48717e35i | − | 0.659786i | −0.944018 | − | 0.329893i | \(-0.892987\pi\) | ||
0.944018 | − | 0.329893i | \(-0.107013\pi\) | |||||||
\(80\) | 2.95321e35 | + | 2.23663e35i | 0.204920 | + | 0.155198i | ||||
\(81\) | −2.09809e36 | −1.14977 | ||||||||
\(82\) | −8.46197e35 | − | 1.17694e36i | −0.367289 | − | 0.510848i | ||||
\(83\) | 3.83632e36i | 1.32261i | 0.750118 | + | 0.661304i | \(0.229997\pi\) | ||||
−0.750118 | + | 0.661304i | \(0.770003\pi\) | |||||||
\(84\) | 1.94058e36 | − | 5.77653e36i | 0.532873 | − | 1.58621i | ||||
\(85\) | −1.82446e35 | −0.0400105 | ||||||||
\(86\) | 3.63558e36 | − | 2.61391e36i | 0.638415 | − | 0.459007i | ||||
\(87\) | − | 6.21159e35i | − | 0.0875663i | ||||||
\(88\) | −2.48438e36 | − | 8.05260e36i | −0.281869 | − | 0.913620i | ||||
\(89\) | −1.37441e37 | −1.25807 | −0.629036 | − | 0.777376i | \(-0.716550\pi\) | ||||
−0.629036 | + | 0.777376i | \(0.716550\pi\) | |||||||
\(90\) | −3.71771e35 | − | 5.17082e35i | −0.0275212 | − | 0.0382782i | ||||
\(91\) | 4.67127e37i | 2.80316i | ||||||||
\(92\) | 3.46402e36 | + | 1.16371e36i | 0.168893 | + | 0.0567381i | ||||
\(93\) | 4.06784e36 | 0.161506 | ||||||||
\(94\) | 6.95460e36 | − | 5.00021e36i | 0.225343 | − | 0.162017i | ||||
\(95\) | 8.18594e36i | 0.216930i | ||||||||
\(96\) | 5.00709e37 | + | 1.24409e36i | 1.08751 | + | 0.0270209i | ||||
\(97\) | 2.37702e37 | 0.424005 | 0.212002 | − | 0.977269i | \(-0.432002\pi\) | ||||
0.212002 | + | 0.977269i | \(0.432002\pi\) | |||||||
\(98\) | 5.43254e37 | + | 7.55591e37i | 0.797457 | + | 1.10915i | ||||
\(99\) | 1.44871e37i | 0.175353i | ||||||||
\(100\) | 2.97409e37 | − | 8.85301e37i | 0.297409 | − | 0.885301i | ||||
\(101\) | −1.83709e38 | −1.52064 | −0.760318 | − | 0.649551i | \(-0.774957\pi\) | ||||
−0.760318 | + | 0.649551i | \(0.774957\pi\) | |||||||
\(102\) | −2.00276e37 | + | 1.43994e37i | −0.137476 | + | 0.0988422i | ||||
\(103\) | − | 1.43454e38i | − | 0.818097i | −0.912513 | − | 0.409049i | \(-0.865861\pi\) | ||
0.912513 | − | 0.409049i | \(-0.134139\pi\) | |||||||
\(104\) | −3.66880e38 | + | 1.13190e38i | −1.74137 | + | 0.537246i | ||||
\(105\) | 1.08694e38 | 0.430141 | ||||||||
\(106\) | −3.32469e38 | − | 4.62418e38i | −1.09885 | − | 1.52835i | ||||
\(107\) | − | 1.34510e38i | − | 0.371932i | −0.982556 | − | 0.185966i | \(-0.940459\pi\) | ||
0.982556 | − | 0.185966i | \(-0.0595414\pi\) | |||||||
\(108\) | 3.63418e38 | + | 1.22087e38i | 0.842083 | + | 0.282890i | ||||
\(109\) | 9.17365e38 | 1.78418 | 0.892090 | − | 0.451857i | \(-0.149238\pi\) | ||||
0.892090 | + | 0.451857i | \(0.149238\pi\) | |||||||
\(110\) | 1.22044e38 | − | 8.77473e37i | 0.199552 | − | 0.143474i | ||||
\(111\) | − | 1.17188e39i | − | 1.61342i | ||||||
\(112\) | −7.99854e38 | + | 1.05612e39i | −0.928685 | + | 1.22622i | ||||
\(113\) | −2.82851e38 | −0.277375 | −0.138687 | − | 0.990336i | \(-0.544288\pi\) | ||||
−0.138687 | + | 0.990336i | \(0.544288\pi\) | |||||||
\(114\) | 6.46072e38 | + | 8.98597e38i | 0.535906 | + | 0.745372i | ||||
\(115\) | 6.51809e37i | 0.0457996i | ||||||||
\(116\) | −4.30048e37 | + | 1.28013e38i | −0.0256339 | + | 0.0763047i | ||||
\(117\) | 6.60039e38 | 0.334224 | ||||||||
\(118\) | −2.70233e39 | + | 1.94292e39i | −1.16407 | + | 0.836943i | ||||
\(119\) | − | 6.52453e38i | − | 0.239418i | ||||||
\(120\) | 2.63378e38 | + | 8.53683e38i | 0.0824395 | + | 0.267210i | ||||
\(121\) | 3.21112e38 | 0.0858487 | ||||||||
\(122\) | 2.90117e39 | + | 4.03513e39i | 0.663341 | + | 0.922615i | ||||
\(123\) | − | 3.49573e39i | − | 0.684449i | ||||||
\(124\) | −8.38329e38 | − | 2.81629e38i | −0.140735 | − | 0.0472787i | ||||
\(125\) | 3.44953e39 | 0.497129 | ||||||||
\(126\) | 1.84916e39 | − | 1.32951e39i | 0.229052 | − | 0.164684i | ||||
\(127\) | 1.29401e40i | 1.37932i | 0.724131 | + | 0.689662i | \(0.242241\pi\) | ||||
−0.724131 | + | 0.689662i | \(0.757759\pi\) | |||||||
\(128\) | −1.02328e40 | − | 3.72296e39i | −0.939737 | − | 0.341899i | ||||
\(129\) | 1.07983e40 | 0.855367 | ||||||||
\(130\) | −3.99781e39 | − | 5.56040e39i | −0.273463 | − | 0.380349i | ||||
\(131\) | − | 1.09909e40i | − | 0.649949i | −0.945723 | − | 0.324974i | \(-0.894644\pi\) | ||
0.945723 | − | 0.324974i | \(-0.105356\pi\) | |||||||
\(132\) | 6.47178e39 | − | 1.92646e40i | 0.331222 | − | 0.985952i | ||||
\(133\) | −2.92742e40 | −1.29809 | ||||||||
\(134\) | 2.38370e40 | − | 1.71383e40i | 0.916769 | − | 0.659138i | ||||
\(135\) | 6.83828e39i | 0.228352i | ||||||||
\(136\) | 5.12435e39 | − | 1.58096e39i | 0.148730 | − | 0.0458862i | ||||
\(137\) | −6.79802e40 | −1.71669 | −0.858345 | − | 0.513073i | \(-0.828507\pi\) | ||||
−0.858345 | + | 0.513073i | \(0.828507\pi\) | |||||||
\(138\) | 5.14438e39 | + | 7.15512e39i | 0.113144 | + | 0.157367i | ||||
\(139\) | − | 2.04964e40i | − | 0.393004i | −0.980503 | − | 0.196502i | \(-0.937042\pi\) | ||
0.980503 | − | 0.196502i | \(-0.0629582\pi\) | |||||||
\(140\) | −2.24005e40 | − | 7.52525e39i | −0.374822 | − | 0.125918i | ||||
\(141\) | 2.06564e40 | 0.301920 | ||||||||
\(142\) | 9.65948e40 | − | 6.94496e40i | 1.23445 | − | 0.887547i | ||||
\(143\) | 1.55786e41i | 1.74238i | ||||||||
\(144\) | 1.49226e40 | + | 1.13017e40i | 0.146204 | + | 0.110728i | ||||
\(145\) | −2.40876e39 | −0.0206919 | ||||||||
\(146\) | −2.23200e40 | − | 3.10440e40i | −0.168263 | − | 0.234031i | ||||
\(147\) | 2.24424e41i | 1.48607i | ||||||||
\(148\) | −8.11329e40 | + | 2.41509e41i | −0.472307 | + | 1.40592i | ||||
\(149\) | 1.44807e41 | 0.741737 | 0.370869 | − | 0.928685i | \(-0.379060\pi\) | ||||
0.370869 | + | 0.928685i | \(0.379060\pi\) | |||||||
\(150\) | 1.82864e41 | − | 1.31475e41i | 0.824885 | − | 0.593075i | ||||
\(151\) | − | 1.49687e41i | − | 0.595145i | −0.954699 | − | 0.297572i | \(-0.903823\pi\) | ||
0.954699 | − | 0.297572i | \(-0.0961769\pi\) | |||||||
\(152\) | −7.09344e40 | − | 2.29919e41i | −0.248788 | − | 0.806392i | ||||
\(153\) | −9.21900e39 | −0.0285461 | ||||||||
\(154\) | 3.13798e41 | + | 4.36450e41i | 0.858532 | + | 1.19410i | ||||
\(155\) | − | 1.57745e40i | − | 0.0381639i | ||||||
\(156\) | −8.77705e41 | − | 2.94857e41i | −1.87923 | − | 0.631312i | ||||
\(157\) | −1.37059e41 | −0.259905 | −0.129952 | − | 0.991520i | \(-0.541482\pi\) | ||||
−0.129952 | + | 0.991520i | \(0.541482\pi\) | |||||||
\(158\) | −3.18717e41 | + | 2.29151e41i | −0.535698 | + | 0.385156i | ||||
\(159\) | − | 1.37346e42i | − | 2.04773i | ||||||
\(160\) | 4.82441e39 | − | 1.94167e41i | 0.00638505 | − | 0.256978i | ||||
\(161\) | −2.33097e41 | −0.274060 | ||||||||
\(162\) | 6.42137e41 | + | 8.93124e41i | 0.671186 | + | 0.933526i | ||||
\(163\) | − | 7.67808e41i | − | 0.713984i | −0.934107 | − | 0.356992i | \(-0.883802\pi\) | ||
0.934107 | − | 0.356992i | \(-0.116198\pi\) | |||||||
\(164\) | −2.42020e41 | + | 7.20424e41i | −0.200364 | + | 0.596424i | ||||
\(165\) | 3.62494e41 | 0.267366 | ||||||||
\(166\) | 1.63306e42 | − | 1.17414e42i | 1.07386 | − | 0.772084i | ||||
\(167\) | − | 7.43939e41i | − | 0.436440i | −0.975900 | − | 0.218220i | \(-0.929975\pi\) | ||
0.975900 | − | 0.218220i | \(-0.0700250\pi\) | |||||||
\(168\) | −3.05290e42 | + | 9.41880e41i | −1.59896 | + | 0.493309i | ||||
\(169\) | 4.96047e42 | 2.32100 | ||||||||
\(170\) | 5.58388e40 | + | 7.76641e40i | 0.0233565 | + | 0.0324856i | ||||
\(171\) | 4.13637e41i | 0.154772i | ||||||||
\(172\) | −2.22539e42 | − | 7.47602e41i | −0.745361 | − | 0.250397i | ||||
\(173\) | −1.86001e42 | −0.558005 | −0.279003 | − | 0.960290i | \(-0.590004\pi\) | ||||
−0.279003 | + | 0.960290i | \(0.590004\pi\) | |||||||
\(174\) | −2.64417e41 | + | 1.90110e41i | −0.0710975 | + | 0.0511176i | ||||
\(175\) | 5.95727e42i | 1.43656i | ||||||||
\(176\) | −2.66750e42 | + | 3.52212e42i | −0.577249 | + | 0.762191i | ||||
\(177\) | −8.02640e42 | −1.55966 | ||||||||
\(178\) | 4.20648e42 | + | 5.85063e42i | 0.734410 | + | 1.02146i | ||||
\(179\) | − | 5.61184e42i | − | 0.880842i | −0.897791 | − | 0.440421i | \(-0.854829\pi\) | ||
0.897791 | − | 0.440421i | \(-0.145171\pi\) | |||||||
\(180\) | −1.06330e41 | + | 3.16513e41i | −0.0150134 | + | 0.0446904i | ||||
\(181\) | 8.57246e42 | 1.08946 | 0.544732 | − | 0.838610i | \(-0.316632\pi\) | ||||
0.544732 | + | 0.838610i | \(0.316632\pi\) | |||||||
\(182\) | 1.98848e43 | − | 1.42968e43i | 2.27597 | − | 1.63637i | ||||
\(183\) | 1.19851e43i | 1.23615i | ||||||||
\(184\) | −5.64818e41 | − | 1.83074e42i | −0.0525255 | − | 0.170250i | ||||
\(185\) | −4.54437e42 | −0.381251 | ||||||||
\(186\) | −1.24499e42 | − | 1.73162e42i | −0.0942804 | − | 0.131131i | ||||
\(187\) | − | 2.17592e42i | − | 0.148817i | ||||||
\(188\) | −4.25702e42 | − | 1.43011e42i | −0.263091 | − | 0.0883832i | ||||
\(189\) | −2.44547e43 | −1.36643 | ||||||||
\(190\) | 3.48462e42 | − | 2.50537e42i | 0.176132 | − | 0.126635i | ||||
\(191\) | 8.48625e42i | 0.388223i | 0.980979 | + | 0.194112i | \(0.0621824\pi\) | ||||
−0.980979 | + | 0.194112i | \(0.937818\pi\) | |||||||
\(192\) | −1.47950e43 | − | 2.16951e43i | −0.612903 | − | 0.898750i | ||||
\(193\) | −2.67677e42 | −0.100467 | −0.0502333 | − | 0.998738i | \(-0.515996\pi\) | ||||
−0.0502333 | + | 0.998738i | \(0.515996\pi\) | |||||||
\(194\) | −7.27506e42 | − | 1.01186e43i | −0.247516 | − | 0.344261i | ||||
\(195\) | − | 1.65154e43i | − | 0.509602i | ||||||
\(196\) | 1.55376e43 | − | 4.62509e43i | 0.435029 | − | 1.29495i | ||||
\(197\) | −9.67188e42 | −0.245840 | −0.122920 | − | 0.992417i | \(-0.539226\pi\) | ||||
−0.122920 | + | 0.992417i | \(0.539226\pi\) | |||||||
\(198\) | 6.16692e42 | − | 4.43389e42i | 0.142374 | − | 0.102364i | ||||
\(199\) | 4.54881e43i | 0.954309i | 0.878819 | + | 0.477155i | \(0.158332\pi\) | ||||
−0.878819 | + | 0.477155i | \(0.841668\pi\) | |||||||
\(200\) | −4.67882e43 | + | 1.44351e43i | −0.892415 | + | 0.275327i | ||||
\(201\) | 7.08002e43 | 1.22831 | ||||||||
\(202\) | 5.62257e43 | + | 7.82021e43i | 0.887685 | + | 1.23465i | ||||
\(203\) | − | 8.61410e42i | − | 0.123818i | ||||||
\(204\) | 1.22592e43 | + | 4.11838e42i | 0.160505 | + | 0.0539204i | ||||
\(205\) | −1.35559e43 | −0.161736 | ||||||||
\(206\) | −6.10660e43 | + | 4.39052e43i | −0.664236 | + | 0.477571i | ||||
\(207\) | 3.29360e42i | 0.0326764i | ||||||||
\(208\) | 1.60469e44 | + | 1.21532e44i | 1.45274 | + | 1.10024i | ||||
\(209\) | −9.76288e43 | −0.806861 | ||||||||
\(210\) | −3.32668e43 | − | 4.62695e43i | −0.251098 | − | 0.349243i | ||||
\(211\) | − | 1.63132e44i | − | 1.12505i | −0.826779 | − | 0.562526i | \(-0.809829\pi\) | ||
0.826779 | − | 0.562526i | \(-0.190171\pi\) | |||||||
\(212\) | −9.50891e43 | + | 2.83053e44i | −0.599445 | + | 1.78438i | ||||
\(213\) | 2.86904e44 | 1.65396 | ||||||||
\(214\) | −5.72588e43 | + | 4.11679e43i | −0.301982 | + | 0.217118i | ||||
\(215\) | − | 4.18743e43i | − | 0.202123i | ||||||
\(216\) | −5.92563e43 | − | 1.92067e44i | −0.261887 | − | 0.848850i | ||||
\(217\) | 5.64120e43 | 0.228369 | ||||||||
\(218\) | −2.80767e44 | − | 3.90508e44i | −1.04153 | − | 1.44863i | ||||
\(219\) | − | 9.22063e43i | − | 0.313561i | ||||||
\(220\) | −7.47052e43 | − | 2.50966e43i | −0.232981 | − | 0.0782678i | ||||
\(221\) | −9.91359e43 | −0.283647 | ||||||||
\(222\) | −4.98850e44 | + | 3.58663e44i | −1.30998 | + | 0.941846i | ||||
\(223\) | − | 1.45800e44i | − | 0.351532i | −0.984432 | − | 0.175766i | \(-0.943760\pi\) | ||
0.984432 | − | 0.175766i | \(-0.0562403\pi\) | |||||||
\(224\) | 6.94372e44 | + | 1.72528e43i | 1.53773 | + | 0.0382074i | ||||
\(225\) | 8.41747e43 | 0.171283 | ||||||||
\(226\) | 8.65686e43 | + | 1.20405e44i | 0.161920 | + | 0.225208i | ||||
\(227\) | − | 6.75172e44i | − | 1.16124i | −0.814174 | − | 0.580622i | \(-0.802810\pi\) | ||
0.814174 | − | 0.580622i | \(-0.197190\pi\) | |||||||
\(228\) | 1.84783e44 | − | 5.50045e44i | 0.292348 | − | 0.870234i | ||||
\(229\) | −1.19571e44 | −0.174082 | −0.0870408 | − | 0.996205i | \(-0.527741\pi\) | ||||
−0.0870408 | + | 0.996205i | \(0.527741\pi\) | |||||||
\(230\) | 2.77465e43 | − | 1.99491e43i | 0.0371859 | − | 0.0267359i | ||||
\(231\) | 1.29633e45i | 1.59989i | ||||||||
\(232\) | 6.76549e43 | − | 2.08728e43i | 0.0769179 | − | 0.0237307i | ||||
\(233\) | −2.07166e44 | −0.217048 | −0.108524 | − | 0.994094i | \(-0.534612\pi\) | ||||
−0.108524 | + | 0.994094i | \(0.534612\pi\) | |||||||
\(234\) | −2.02010e44 | − | 2.80968e44i | −0.195106 | − | 0.271366i | ||||
\(235\) | − | 8.01025e43i | − | 0.0713439i | ||||||
\(236\) | 1.65414e45 | + | 5.55693e44i | 1.35907 | + | 0.456569i | ||||
\(237\) | −9.46646e44 | −0.717743 | ||||||||
\(238\) | −2.77739e44 | + | 1.99688e44i | −0.194390 | + | 0.139762i | ||||
\(239\) | 1.97531e45i | 1.27666i | 0.769762 | + | 0.638331i | \(0.220375\pi\) | ||||
−0.769762 | + | 0.638331i | \(0.779625\pi\) | |||||||
\(240\) | 2.82790e44 | − | 3.73392e44i | 0.168830 | − | 0.222921i | ||||
\(241\) | −1.80484e45 | −0.995670 | −0.497835 | − | 0.867272i | \(-0.665871\pi\) | ||||
−0.497835 | + | 0.867272i | \(0.665871\pi\) | |||||||
\(242\) | −9.82786e43 | − | 1.36692e44i | −0.0501149 | − | 0.0697029i | ||||
\(243\) | 7.68684e44i | 0.362434i | ||||||||
\(244\) | 8.29763e44 | − | 2.46996e45i | 0.361866 | − | 1.07717i | ||||
\(245\) | 8.70283e44 | 0.351160 | ||||||||
\(246\) | −1.48808e45 | + | 1.06990e45i | −0.555723 | + | 0.399553i | ||||
\(247\) | 4.44801e45i | 1.53789i | ||||||||
\(248\) | 1.36692e44 | + | 4.43058e44i | 0.0437684 | + | 0.141866i | ||||
\(249\) | 4.85048e45 | 1.43879 | ||||||||
\(250\) | −1.05575e45 | − | 1.46841e45i | −0.290203 | − | 0.403633i | ||||
\(251\) | − | 4.76316e45i | − | 1.21365i | −0.794834 | − | 0.606827i | \(-0.792442\pi\) | ||
0.794834 | − | 0.606827i | \(-0.207558\pi\) | |||||||
\(252\) | −1.13190e45 | − | 3.80252e44i | −0.267423 | − | 0.0898383i | ||||
\(253\) | −7.77374e44 | −0.170349 | ||||||||
\(254\) | 5.50838e45 | − | 3.96041e45i | 1.11991 | − | 0.805192i | ||||
\(255\) | 2.30676e44i | 0.0435251i | ||||||||
\(256\) | 1.54703e45 | + | 5.49539e45i | 0.270982 | + | 0.962584i | ||||
\(257\) | −6.75988e45 | −1.09954 | −0.549768 | − | 0.835317i | \(-0.685284\pi\) | ||||
−0.549768 | + | 0.835317i | \(0.685284\pi\) | |||||||
\(258\) | −3.30491e45 | − | 4.59668e45i | −0.499328 | − | 0.694496i | ||||
\(259\) | − | 1.62514e46i | − | 2.28136i | ||||||
\(260\) | −1.14341e45 | + | 3.40360e45i | −0.149179 | + | 0.444064i | ||||
\(261\) | −1.21715e44 | −0.0147630 | ||||||||
\(262\) | −4.67865e45 | + | 3.36385e45i | −0.527711 | + | 0.379413i | ||||
\(263\) | − | 6.31600e45i | − | 0.662648i | −0.943517 | − | 0.331324i | \(-0.892505\pi\) | ||
0.943517 | − | 0.331324i | \(-0.107495\pi\) | |||||||
\(264\) | −1.01814e46 | + | 3.14115e45i | −0.993875 | + | 0.306630i | ||||
\(265\) | −5.32608e45 | −0.483879 | ||||||||
\(266\) | 8.95959e45 | + | 1.24615e46i | 0.757769 | + | 1.05395i | ||||
\(267\) | 1.73774e46i | 1.36858i | ||||||||
\(268\) | −1.45910e46 | − | 4.90171e45i | −1.07034 | − | 0.359573i | ||||
\(269\) | 1.61772e46 | 1.10563 | 0.552817 | − | 0.833303i | \(-0.313553\pi\) | ||||
0.552817 | + | 0.833303i | \(0.313553\pi\) | |||||||
\(270\) | 2.91094e45 | − | 2.09291e45i | 0.185405 | − | 0.133303i | ||||
\(271\) | − | 1.77512e46i | − | 1.05393i | −0.849888 | − | 0.526963i | \(-0.823331\pi\) | ||
0.849888 | − | 0.526963i | \(-0.176669\pi\) | |||||||
\(272\) | −2.24134e45 | − | 1.69749e45i | −0.124079 | − | 0.0939718i | ||||
\(273\) | 5.90616e46 | 3.04940 | ||||||||
\(274\) | 2.08059e46 | + | 2.89381e46i | 1.00213 | + | 1.39383i | ||||
\(275\) | 1.98674e46i | 0.892934i | ||||||||
\(276\) | 1.47134e45 | − | 4.37976e45i | 0.0617221 | − | 0.183729i | ||||
\(277\) | −3.30297e46 | −1.29357 | −0.646783 | − | 0.762674i | \(-0.723886\pi\) | ||||
−0.646783 | + | 0.762674i | \(0.723886\pi\) | |||||||
\(278\) | −8.72499e45 | + | 6.27309e45i | −0.319091 | + | 0.229419i | ||||
\(279\) | − | 7.97087e44i | − | 0.0272286i | ||||||
\(280\) | 3.65247e45 | + | 1.18387e46i | 0.116569 | + | 0.377834i | ||||
\(281\) | −4.17143e46 | −1.24413 | −0.622063 | − | 0.782967i | \(-0.713705\pi\) | ||||
−0.622063 | + | 0.782967i | \(0.713705\pi\) | |||||||
\(282\) | −6.32206e45 | − | 8.79311e45i | −0.176248 | − | 0.245137i | ||||
\(283\) | 3.96827e46i | 1.03433i | 0.855886 | + | 0.517165i | \(0.173013\pi\) | ||||
−0.855886 | + | 0.517165i | \(0.826987\pi\) | |||||||
\(284\) | −5.91271e46 | − | 1.98632e46i | −1.44125 | − | 0.484174i | ||||
\(285\) | 1.03500e46 | 0.235986 | ||||||||
\(286\) | 6.63155e46 | − | 4.76795e46i | 1.41469 | − | 1.01713i | ||||
\(287\) | − | 4.84780e46i | − | 0.967808i | ||||||
\(288\) | 2.43778e44 | − | 9.81131e45i | 0.00455551 | − | 0.183345i | ||||
\(289\) | −5.57710e46 | −0.975774 | ||||||||
\(290\) | 7.37219e44 | + | 1.02537e45i | 0.0120791 | + | 0.0168004i | ||||
\(291\) | − | 3.00541e46i | − | 0.461250i | ||||||
\(292\) | −6.38373e45 | + | 1.90025e46i | −0.0917910 | + | 0.273235i | ||||
\(293\) | −1.90543e46 | −0.256748 | −0.128374 | − | 0.991726i | \(-0.540976\pi\) | ||||
−0.128374 | + | 0.991726i | \(0.540976\pi\) | |||||||
\(294\) | 9.55337e46 | − | 6.86867e46i | 1.20658 | − | 0.867508i | ||||
\(295\) | 3.11252e46i | 0.368547i | ||||||||
\(296\) | 1.27638e47 | − | 3.93788e46i | 1.41722 | − | 0.437240i | ||||
\(297\) | −8.15560e46 | −0.849344 | ||||||||
\(298\) | −4.43193e46 | − | 6.16419e46i | −0.432996 | − | 0.602237i | ||||
\(299\) | 3.54175e46i | 0.324687i | ||||||||
\(300\) | −1.11934e47 | − | 3.76031e46i | −0.963068 | − | 0.323534i | ||||
\(301\) | 1.49749e47 | 1.20948 | ||||||||
\(302\) | −6.37194e46 | + | 4.58129e46i | −0.483214 | + | 0.347421i | ||||
\(303\) | 2.32274e47i | 1.65421i | ||||||||
\(304\) | −7.61626e46 | + | 1.00564e47i | −0.509500 | + | 0.672735i | ||||
\(305\) | 4.64762e46 | 0.292102 | ||||||||
\(306\) | 2.82155e45 | + | 3.92438e45i | 0.0166640 | + | 0.0231774i | ||||
\(307\) | 1.32974e47i | 0.738138i | 0.929402 | + | 0.369069i | \(0.120323\pi\) | ||||
−0.929402 | + | 0.369069i | \(0.879677\pi\) | |||||||
\(308\) | 8.97492e46 | − | 2.67157e47i | 0.468346 | − | 1.39413i | ||||
\(309\) | −1.81377e47 | −0.889961 | ||||||||
\(310\) | −6.71494e45 | + | 4.82790e45i | −0.0309863 | + | 0.0222785i | ||||
\(311\) | − | 4.05175e47i | − | 1.75871i | −0.476164 | − | 0.879357i | \(-0.657973\pi\) | ||
0.476164 | − | 0.879357i | \(-0.342027\pi\) | |||||||
\(312\) | 1.43112e47 | + | 4.63868e47i | 0.584439 | + | 1.89434i | ||||
\(313\) | 3.46826e47 | 1.33281 | 0.666407 | − | 0.745589i | \(-0.267832\pi\) | ||||
0.666407 | + | 0.745589i | \(0.267832\pi\) | |||||||
\(314\) | 4.19480e46 | + | 5.83438e46i | 0.151722 | + | 0.211024i | ||||
\(315\) | − | 2.12985e46i | − | 0.0725184i | ||||||
\(316\) | 1.95091e47 | + | 6.55392e46i | 0.625437 | + | 0.210110i | ||||
\(317\) | −2.88485e47 | −0.870958 | −0.435479 | − | 0.900199i | \(-0.643421\pi\) | ||||
−0.435479 | + | 0.900199i | \(0.643421\pi\) | |||||||
\(318\) | −5.84661e47 | + | 4.20359e47i | −1.66260 | + | 1.19538i | ||||
\(319\) | − | 2.87278e46i | − | 0.0769626i | ||||||
\(320\) | −8.41304e46 | + | 5.73727e46i | −0.212375 | + | 0.144829i | ||||
\(321\) | −1.70069e47 | −0.404604 | ||||||||
\(322\) | 7.13411e46 | + | 9.92256e46i | 0.159985 | + | 0.222517i | ||||
\(323\) | − | 6.21270e46i | − | 0.131351i | ||||||
\(324\) | 1.83657e47 | − | 5.46695e47i | 0.366145 | − | 1.08991i | ||||
\(325\) | 9.05167e47 | 1.70194 | ||||||||
\(326\) | −3.26844e47 | + | 2.34994e47i | −0.579703 | + | 0.416794i | ||||
\(327\) | − | 1.15988e48i | − | 1.94091i | ||||||
\(328\) | 3.80745e47 | − | 1.17467e47i | 0.601217 | − | 0.185487i | ||||
\(329\) | 2.86459e47 | 0.426914 | ||||||||
\(330\) | −1.10944e47 | − | 1.54308e47i | −0.156077 | − | 0.217082i | ||||
\(331\) | 2.85500e47i | 0.379206i | 0.981861 | + | 0.189603i | \(0.0607200\pi\) | ||||
−0.981861 | + | 0.189603i | \(0.939280\pi\) | |||||||
\(332\) | −9.99621e47 | − | 3.35814e47i | −1.25375 | − | 0.421187i | ||||
\(333\) | −2.29628e47 | −0.272010 | ||||||||
\(334\) | −3.16683e47 | + | 2.27688e47i | −0.354358 | + | 0.254776i | ||||
\(335\) | − | 2.74552e47i | − | 0.290251i | ||||||
\(336\) | 1.33531e48 | + | 1.01130e48i | 1.33394 | + | 1.01026i | ||||
\(337\) | −8.12808e47 | −0.767397 | −0.383698 | − | 0.923458i | \(-0.625350\pi\) | ||||
−0.383698 | + | 0.923458i | \(0.625350\pi\) | |||||||
\(338\) | −1.51819e48 | − | 2.11159e48i | −1.35490 | − | 1.88448i | ||||
\(339\) | 3.57624e47i | 0.301740i | ||||||||
\(340\) | 1.59704e46 | − | 4.75394e46i | 0.0127414 | − | 0.0379275i | ||||
\(341\) | 1.88133e47 | 0.141949 | ||||||||
\(342\) | 1.76079e47 | − | 1.26597e47i | 0.125664 | − | 0.0903497i | ||||
\(343\) | 8.34010e47i | 0.563096i | ||||||||
\(344\) | 3.62857e47 | + | 1.17612e48i | 0.231806 | + | 0.751351i | ||||
\(345\) | 8.24120e46 | 0.0498228 | ||||||||
\(346\) | 5.69269e47 | + | 7.91774e47i | 0.325740 | + | 0.453060i | ||||
\(347\) | 1.12522e48i | 0.609505i | 0.952432 | + | 0.304752i | \(0.0985737\pi\) | ||||
−0.952432 | + | 0.304752i | \(0.901426\pi\) | |||||||
\(348\) | 1.61854e47 | + | 5.43734e46i | 0.0830075 | + | 0.0278856i | ||||
\(349\) | −1.77642e48 | −0.862707 | −0.431353 | − | 0.902183i | \(-0.641964\pi\) | ||||
−0.431353 | + | 0.902183i | \(0.641964\pi\) | |||||||
\(350\) | 2.53591e48 | − | 1.82327e48i | 1.16638 | − | 0.838606i | ||||
\(351\) | 3.71573e48i | 1.61886i | ||||||||
\(352\) | 2.31572e48 | + | 5.75378e46i | 0.955818 | + | 0.0237489i | ||||
\(353\) | −3.18465e46 | −0.0124549 | −0.00622747 | − | 0.999981i | \(-0.501982\pi\) | ||||
−0.00622747 | + | 0.999981i | \(0.501982\pi\) | |||||||
\(354\) | 2.45654e48 | + | 3.41671e48i | 0.910463 | + | 1.26633i | ||||
\(355\) | − | 1.11257e48i | − | 0.390831i | ||||||
\(356\) | 1.20309e48 | − | 3.58126e48i | 0.400635 | − | 1.19258i | ||||
\(357\) | −8.24935e47 | −0.260449 | ||||||||
\(358\) | −2.38887e48 | + | 1.71755e48i | −0.715180 | + | 0.514199i | ||||
\(359\) | − | 3.97930e46i | − | 0.0112983i | −0.999984 | − | 0.00564914i | \(-0.998202\pi\) | ||
0.999984 | − | 0.00564914i | \(-0.00179819\pi\) | |||||||
\(360\) | 1.67278e47 | − | 5.16084e46i | 0.0450496 | − | 0.0138987i | ||||
\(361\) | 1.12664e48 | 0.287837 | ||||||||
\(362\) | −2.62367e48 | − | 3.64916e48i | −0.635983 | − | 0.884565i | ||||
\(363\) | − | 4.06000e47i | − | 0.0933899i | ||||||
\(364\) | −1.21718e49 | − | 4.08901e48i | −2.65723 | − | 0.892673i | ||||
\(365\) | −3.57562e47 | −0.0740947 | ||||||||
\(366\) | 5.10185e48 | − | 3.66812e48i | 1.00366 | − | 0.721610i | ||||
\(367\) | 8.45967e48i | 1.58015i | 0.613011 | + | 0.790075i | \(0.289958\pi\) | ||||
−0.613011 | + | 0.790075i | \(0.710042\pi\) | |||||||
\(368\) | −6.06448e47 | + | 8.00745e47i | −0.107569 | + | 0.142032i | ||||
\(369\) | −6.84983e47 | −0.115393 | ||||||||
\(370\) | 1.39084e48 | + | 1.93447e48i | 0.222559 | + | 0.309548i | ||||
\(371\) | − | 1.90469e49i | − | 2.89548i | ||||||
\(372\) | −3.56080e47 | + | 1.05995e48i | −0.0514318 | + | 0.153098i | ||||
\(373\) | −4.35741e47 | −0.0598082 | −0.0299041 | − | 0.999553i | \(-0.509520\pi\) | ||||
−0.0299041 | + | 0.999553i | \(0.509520\pi\) | |||||||
\(374\) | −9.26253e47 | + | 6.65957e47i | −0.120828 | + | 0.0868731i | ||||
\(375\) | − | 4.36144e48i | − | 0.540798i | ||||||
\(376\) | 6.94119e47 | + | 2.24984e48i | 0.0818210 | + | 0.265205i | ||||
\(377\) | −1.30885e48 | −0.146692 | ||||||||
\(378\) | 7.48456e48 | + | 1.04100e49i | 0.797668 | + | 1.10945i | ||||
\(379\) | 3.70147e48i | 0.375171i | 0.982248 | + | 0.187586i | \(0.0600662\pi\) | ||||
−0.982248 | + | 0.187586i | \(0.939934\pi\) | |||||||
\(380\) | −2.13299e48 | − | 7.16560e47i | −0.205637 | − | 0.0690818i | ||||
\(381\) | 1.63609e49 | 1.50049 | ||||||||
\(382\) | 3.61246e48 | − | 2.59728e48i | 0.315209 | − | 0.226629i | ||||
\(383\) | − | 4.28701e48i | − | 0.355941i | −0.984036 | − | 0.177971i | \(-0.943047\pi\) | ||
0.984036 | − | 0.177971i | \(-0.0569532\pi\) | |||||||
\(384\) | −4.70715e48 | + | 1.29380e49i | −0.371933 | + | 1.02229i | ||||
\(385\) | 5.02698e48 | 0.378054 | ||||||||
\(386\) | 8.19245e47 | + | 1.13946e48i | 0.0586483 | + | 0.0815716i | ||||
\(387\) | − | 2.11591e48i | − | 0.144208i | ||||||
\(388\) | −2.08074e48 | + | 6.19375e48i | −0.135025 | + | 0.401931i | ||||
\(389\) | −6.95989e48 | −0.430091 | −0.215045 | − | 0.976604i | \(-0.568990\pi\) | ||||
−0.215045 | + | 0.976604i | \(0.568990\pi\) | |||||||
\(390\) | −7.03033e48 | + | 5.05466e48i | −0.413760 | + | 0.297485i | ||||
\(391\) | − | 4.94689e47i | − | 0.0277316i | ||||||
\(392\) | −2.44436e49 | + | 7.54134e48i | −1.30536 | + | 0.402729i | ||||
\(393\) | −1.38964e49 | −0.707042 | ||||||||
\(394\) | 2.96015e48 | + | 4.11716e48i | 0.143511 | + | 0.199604i | ||||
\(395\) | 3.67095e48i | 0.169603i | ||||||||
\(396\) | −3.77487e48 | − | 1.26813e48i | −0.166224 | − | 0.0558414i | ||||
\(397\) | 9.66079e48 | 0.405502 | 0.202751 | − | 0.979230i | \(-0.435012\pi\) | ||||
0.202751 | + | 0.979230i | \(0.435012\pi\) | |||||||
\(398\) | 1.93635e49 | − | 1.39220e49i | 0.774830 | − | 0.557086i | ||||
\(399\) | 3.70131e49i | 1.41211i | ||||||||
\(400\) | 2.04647e49 | + | 1.54990e49i | 0.744500 | + | 0.563851i | ||||
\(401\) | 2.47391e49 | 0.858302 | 0.429151 | − | 0.903233i | \(-0.358813\pi\) | ||||
0.429151 | + | 0.903233i | \(0.358813\pi\) | |||||||
\(402\) | −2.16689e49 | − | 3.01385e49i | −0.717038 | − | 0.997301i | ||||
\(403\) | − | 8.57141e48i | − | 0.270556i | ||||||
\(404\) | 1.60811e49 | − | 4.78687e49i | 0.484250 | − | 1.44147i | ||||
\(405\) | 1.02869e49 | 0.295556 | ||||||||
\(406\) | −3.66688e48 | + | 2.63641e48i | −0.100531 | + | 0.0722800i | ||||
\(407\) | − | 5.41980e49i | − | 1.41804i | ||||||
\(408\) | −1.99890e48 | − | 6.47901e48i | −0.0499170 | − | 0.161795i | ||||
\(409\) | −1.71268e49 | −0.408257 | −0.204128 | − | 0.978944i | \(-0.565436\pi\) | ||||
−0.204128 | + | 0.978944i | \(0.565436\pi\) | |||||||
\(410\) | 4.14889e48 | + | 5.77053e48i | 0.0944145 | + | 0.131317i | ||||
\(411\) | 8.59513e49i | 1.86749i | ||||||||
\(412\) | 3.73794e49 | + | 1.25573e49i | 0.775507 | + | 0.260525i | ||||
\(413\) | −1.11308e50 | −2.20535 | ||||||||
\(414\) | 1.40203e48 | − | 1.00803e48i | 0.0265309 | − | 0.0190752i | ||||
\(415\) | − | 1.88094e49i | − | 0.339987i | ||||||
\(416\) | 2.62145e48 | − | 1.05505e50i | 0.0452656 | − | 1.82180i | ||||
\(417\) | −2.59148e49 | −0.427526 | ||||||||
\(418\) | 2.98800e49 | + | 4.15590e49i | 0.471012 | + | 0.655112i | ||||
\(419\) | − | 6.12828e49i | − | 0.923150i | −0.887101 | − | 0.461575i | \(-0.847284\pi\) | ||
0.887101 | − | 0.461575i | \(-0.152716\pi\) | |||||||
\(420\) | −9.51461e48 | + | 2.83222e49i | −0.136979 | + | 0.407747i | ||||
\(421\) | −1.14147e49 | −0.157074 | −0.0785371 | − | 0.996911i | \(-0.525025\pi\) | ||||
−0.0785371 | + | 0.996911i | \(0.525025\pi\) | |||||||
\(422\) | −6.94427e49 | + | 4.99278e49i | −0.913461 | + | 0.656759i | ||||
\(423\) | − | 4.04759e48i | − | 0.0509014i | ||||||
\(424\) | 1.49594e50 | − | 4.61526e49i | 1.79871 | − | 0.554938i | ||||
\(425\) | −1.26428e49 | −0.145363 | ||||||||
\(426\) | −8.78091e49 | − | 1.22130e50i | −0.965511 | − | 1.34289i | ||||
\(427\) | 1.66206e50i | 1.74790i | ||||||||
\(428\) | 3.50490e49 | + | 1.17744e49i | 0.352569 | + | 0.118442i | ||||
\(429\) | 1.96969e50 | 1.89544 | ||||||||
\(430\) | −1.78252e49 | + | 1.28159e49i | −0.164110 | + | 0.117991i | ||||
\(431\) | 6.33263e49i | 0.557848i | 0.960313 | + | 0.278924i | \(0.0899778\pi\) | ||||
−0.960313 | + | 0.278924i | \(0.910022\pi\) | |||||||
\(432\) | −6.36238e49 | + | 8.40079e49i | −0.536326 | + | 0.708156i | ||||
\(433\) | 2.92411e49 | 0.235898 | 0.117949 | − | 0.993020i | \(-0.462368\pi\) | ||||
0.117949 | + | 0.993020i | \(0.462368\pi\) | |||||||
\(434\) | −1.72653e49 | − | 2.40137e49i | −0.133312 | − | 0.185419i | ||||
\(435\) | 3.04553e48i | 0.0225096i | ||||||||
\(436\) | −8.03019e49 | + | 2.39036e50i | −0.568176 | + | 1.69129i | ||||
\(437\) | −2.21957e49 | −0.150356 | ||||||||
\(438\) | −3.92507e49 | + | 2.82204e49i | −0.254589 | + | 0.183044i | ||||
\(439\) | − | 5.86332e49i | − | 0.364181i | −0.983282 | − | 0.182091i | \(-0.941714\pi\) | ||
0.983282 | − | 0.182091i | \(-0.0582864\pi\) | |||||||
\(440\) | 1.21809e49 | + | 3.94818e49i | 0.0724567 | + | 0.234853i | ||||
\(441\) | 4.39755e49 | 0.250540 | ||||||||
\(442\) | 3.03413e49 | + | 4.22005e49i | 0.165581 | + | 0.230300i | ||||
\(443\) | − | 2.23210e50i | − | 1.16693i | −0.812139 | − | 0.583464i | \(-0.801697\pi\) | ||
0.812139 | − | 0.583464i | \(-0.198303\pi\) | |||||||
\(444\) | 3.05354e50 | + | 1.02581e50i | 1.52942 | + | 0.513796i | ||||
\(445\) | 6.73870e49 | 0.323397 | ||||||||
\(446\) | −6.20647e49 | + | 4.46232e49i | −0.285419 | + | 0.205210i | ||||
\(447\) | − | 1.83088e50i | − | 0.806894i | ||||||
\(448\) | −2.05174e50 | − | 3.00863e50i | −0.866641 | − | 1.27083i | ||||
\(449\) | 6.21641e49 | 0.251686 | 0.125843 | − | 0.992050i | \(-0.459836\pi\) | ||||
0.125843 | + | 0.992050i | \(0.459836\pi\) | |||||||
\(450\) | −2.57623e49 | − | 3.58318e49i | −0.0999879 | − | 0.139069i | ||||
\(451\) | − | 1.61673e50i | − | 0.601567i | ||||||
\(452\) | 2.47594e49 | − | 7.37017e49i | 0.0883304 | − | 0.262934i | ||||
\(453\) | −1.89258e50 | −0.647424 | ||||||||
\(454\) | −2.87410e50 | + | 2.06642e50i | −0.942845 | + | 0.677886i | ||||
\(455\) | − | 2.29032e50i | − | 0.720575i | ||||||
\(456\) | −2.90699e50 | + | 8.96864e49i | −0.877227 | + | 0.270642i | ||||
\(457\) | −6.07259e49 | −0.175779 | −0.0878893 | − | 0.996130i | \(-0.528012\pi\) | ||||
−0.0878893 | + | 0.996130i | \(0.528012\pi\) | |||||||
\(458\) | 3.65957e49 | + | 5.08995e49i | 0.101622 | + | 0.141342i | ||||
\(459\) | − | 5.18990e49i | − | 0.138267i | ||||||
\(460\) | −1.69840e49 | − | 5.70564e48i | −0.0434152 | − | 0.0145850i | ||||
\(461\) | −2.79239e50 | −0.684948 | −0.342474 | − | 0.939527i | \(-0.611265\pi\) | ||||
−0.342474 | + | 0.939527i | \(0.611265\pi\) | |||||||
\(462\) | 5.51828e50 | − | 3.96753e50i | 1.29899 | − | 0.933948i | ||||
\(463\) | − | 9.66146e49i | − | 0.218275i | −0.994027 | − | 0.109138i | \(-0.965191\pi\) | ||
0.994027 | − | 0.109138i | \(-0.0348089\pi\) | |||||||
\(464\) | −2.95915e49 | − | 2.24113e49i | −0.0641690 | − | 0.0485987i | ||||
\(465\) | −1.99446e49 | −0.0415163 | ||||||||
\(466\) | 6.34048e49 | + | 8.81873e49i | 0.126704 | + | 0.176227i | ||||
\(467\) | 9.06956e50i | 1.74007i | 0.492994 | + | 0.870033i | \(0.335902\pi\) | ||||
−0.492994 | + | 0.870033i | \(0.664098\pi\) | |||||||
\(468\) | −5.77767e49 | + | 1.71985e50i | −0.106434 | + | 0.316824i | ||||
\(469\) | 9.81841e50 | 1.73683 | ||||||||
\(470\) | −3.40983e49 | + | 2.45160e49i | −0.0579260 | + | 0.0416476i | ||||
\(471\) | 1.73292e50i | 0.282735i | ||||||||
\(472\) | −2.69712e50 | − | 8.74213e50i | −0.422670 | − | 1.37000i | ||||
\(473\) | 4.99410e50 | 0.751788 | ||||||||
\(474\) | 2.89728e50 | + | 4.02972e50i | 0.418989 | + | 0.582755i | ||||
\(475\) | 5.67255e50i | 0.788134i | ||||||||
\(476\) | 1.70008e50 | + | 5.71128e49i | 0.226954 | + | 0.0762432i | ||||
\(477\) | −2.69128e50 | −0.345231 | ||||||||
\(478\) | 8.40858e50 | − | 6.04559e50i | 1.03656 | − | 0.745262i | ||||
\(479\) | 8.82583e50i | 1.04564i | 0.852444 | + | 0.522819i | \(0.175119\pi\) | ||||
−0.852444 | + | 0.522819i | \(0.824881\pi\) | |||||||
\(480\) | −2.45497e50 | − | 6.09978e48i | −0.279552 | − | 0.00694593i | ||||
\(481\) | −2.46929e51 | −2.70281 | ||||||||
\(482\) | 5.52386e50 | + | 7.68292e50i | 0.581231 | + | 0.808412i | ||||
\(483\) | 2.94718e50i | 0.298134i | ||||||||
\(484\) | −2.81086e49 | + | 8.36712e49i | −0.0273387 | + | 0.0813794i | ||||
\(485\) | −1.16545e50 | −0.108994 | ||||||||
\(486\) | 3.27216e50 | − | 2.35262e50i | 0.294270 | − | 0.211574i | ||||
\(487\) | − | 5.11024e50i | − | 0.441968i | −0.975277 | − | 0.220984i | \(-0.929073\pi\) | ||
0.975277 | − | 0.220984i | \(-0.0709268\pi\) | |||||||
\(488\) | −1.30538e51 | + | 4.02735e50i | −1.08583 | + | 0.334998i | ||||
\(489\) | −9.70784e50 | −0.776702 | ||||||||
\(490\) | −2.66357e50 | − | 3.70465e50i | −0.204992 | − | 0.285116i | ||||
\(491\) | − | 1.05732e51i | − | 0.782810i | −0.920218 | − | 0.391405i | \(-0.871989\pi\) | ||
0.920218 | − | 0.391405i | \(-0.128011\pi\) | |||||||
\(492\) | 9.10874e50 | + | 3.06000e50i | 0.648816 | + | 0.217964i | ||||
\(493\) | 1.82812e49 | 0.0125289 | ||||||||
\(494\) | 1.89345e51 | − | 1.36135e51i | 1.24865 | − | 0.897754i | ||||
\(495\) | − | 7.10300e49i | − | 0.0450758i | ||||||
\(496\) | 1.46767e50 | − | 1.93789e50i | 0.0896347 | − | 0.118352i | ||||
\(497\) | 3.97872e51 | 2.33869 | ||||||||
\(498\) | −1.48453e51 | − | 2.06477e51i | −0.839906 | − | 1.16819i | ||||
\(499\) | − | 1.29283e51i | − | 0.704095i | −0.935982 | − | 0.352048i | \(-0.885486\pi\) | ||
0.935982 | − | 0.352048i | \(-0.114514\pi\) | |||||||
\(500\) | −3.01956e50 | + | 8.98835e50i | −0.158312 | + | 0.471248i | ||||
\(501\) | −9.40605e50 | −0.474778 | ||||||||
\(502\) | −2.02760e51 | + | 1.45780e51i | −0.985399 | + | 0.708481i | ||||
\(503\) | 3.84626e51i | 1.79989i | 0.436002 | + | 0.899946i | \(0.356394\pi\) | ||||
−0.436002 | + | 0.899946i | \(0.643606\pi\) | |||||||
\(504\) | 1.84560e50 | + | 5.98211e50i | 0.0831681 | + | 0.269572i | ||||
\(505\) | 9.00725e50 | 0.390891 | ||||||||
\(506\) | 2.37921e50 | + | 3.30915e50i | 0.0994428 | + | 0.138311i | ||||
\(507\) | − | 6.27180e51i | − | 2.52488i | ||||||
\(508\) | −3.37176e51 | − | 1.13271e51i | −1.30751 | − | 0.439248i | ||||
\(509\) | 1.54984e51 | 0.578960 | 0.289480 | − | 0.957184i | \(-0.406518\pi\) | ||||
0.289480 | + | 0.957184i | \(0.406518\pi\) | |||||||
\(510\) | 9.81952e49 | − | 7.06003e49i | 0.0353392 | − | 0.0254082i | ||||
\(511\) | − | 1.27870e51i | − | 0.443374i | ||||||
\(512\) | 1.86582e51 | − | 2.34045e51i | 0.623361 | − | 0.781934i | ||||
\(513\) | −2.32860e51 | −0.749660 | ||||||||
\(514\) | 2.06891e51 | + | 2.87757e51i | 0.641864 | + | 0.892744i | ||||
\(515\) | 7.03352e50i | 0.210298i | ||||||||
\(516\) | −9.45236e50 | + | 2.81370e51i | −0.272393 | + | 0.810835i | ||||
\(517\) | 9.55334e50 | 0.265360 | ||||||||
\(518\) | −6.91795e51 | + | 4.97386e51i | −1.85230 | + | 1.33177i | ||||
\(519\) | 2.35171e51i | 0.607022i | ||||||||
\(520\) | 1.79881e51 | − | 5.54967e50i | 0.447632 | − | 0.138103i | ||||
\(521\) | −3.81868e51 | −0.916214 | −0.458107 | − | 0.888897i | \(-0.651472\pi\) | ||||
−0.458107 | + | 0.888897i | \(0.651472\pi\) | |||||||
\(522\) | 3.72518e49 | + | 5.18121e49i | 0.00861803 | + | 0.0119865i | ||||
\(523\) | − | 2.36519e51i | − | 0.527636i | −0.964572 | − | 0.263818i | \(-0.915018\pi\) | ||
0.964572 | − | 0.263818i | \(-0.0849818\pi\) | |||||||
\(524\) | 2.86388e51 | + | 9.62094e50i | 0.616112 | + | 0.206977i | ||||
\(525\) | 7.53212e51 | 1.56275 | ||||||||
\(526\) | −2.68862e51 | + | 1.93306e51i | −0.538022 | + | 0.386826i | ||||
\(527\) | 1.19720e50i | 0.0231082i | ||||||||
\(528\) | 4.45322e51 | + | 3.37267e51i | 0.829144 | + | 0.627956i | ||||
\(529\) | 5.39073e51 | 0.968256 | ||||||||
\(530\) | 1.63009e51 | + | 2.26723e51i | 0.282468 | + | 0.392874i | ||||
\(531\) | 1.57276e51i | 0.262946i | ||||||||
\(532\) | 2.56253e51 | − | 7.62790e51i | 0.413378 | − | 1.23051i | ||||
\(533\) | −7.36591e51 | −1.14659 | ||||||||
\(534\) | 7.39729e51 | − | 5.31849e51i | 1.11119 | − | 0.798923i | ||||
\(535\) | 6.59502e50i | 0.0956080i | ||||||||
\(536\) | 2.37910e51 | + | 7.71135e51i | 0.332876 | + | 1.07895i | ||||
\(537\) | −7.09538e51 | −0.958218 | ||||||||
\(538\) | −4.95117e51 | − | 6.88639e51i | −0.645423 | − | 0.897694i | ||||
\(539\) | 1.03793e52i | 1.30612i | ||||||||
\(540\) | −1.78183e51 | − | 5.98591e50i | −0.216464 | − | 0.0727192i | ||||
\(541\) | 5.02770e51 | 0.589687 | 0.294843 | − | 0.955546i | \(-0.404733\pi\) | ||||
0.294843 | + | 0.955546i | \(0.404733\pi\) | |||||||
\(542\) | −7.55638e51 | + | 5.43288e51i | −0.855711 | + | 0.615238i | ||||
\(543\) | − | 1.08387e52i | − | 1.18516i | ||||||
\(544\) | −3.66147e49 | + | 1.47363e51i | −0.00386613 | + | 0.155600i | ||||
\(545\) | −4.49783e51 | −0.458637 | ||||||||
\(546\) | −1.80762e52 | − | 2.51416e52i | −1.78011 | − | 2.47589i | ||||
\(547\) | 1.20514e52i | 1.14625i | 0.819468 | + | 0.573125i | \(0.194269\pi\) | ||||
−0.819468 | + | 0.573125i | \(0.805731\pi\) | |||||||
\(548\) | 5.95067e51 | − | 1.77134e52i | 0.546683 | − | 1.62732i | ||||
\(549\) | 2.34845e51 | 0.208405 | ||||||||
\(550\) | 8.45722e51 | − | 6.08056e51i | 0.724997 | − | 0.521258i | ||||
\(551\) | − | 8.20240e50i | − | 0.0679298i | ||||||
\(552\) | −2.31471e51 | + | 7.14132e50i | −0.185205 | + | 0.0571395i | ||||
\(553\) | −1.31279e52 | −1.01489 | ||||||||
\(554\) | 1.01090e52 | + | 1.40602e52i | 0.755130 | + | 1.05028i | ||||
\(555\) | 5.74571e51i | 0.414741i | ||||||||
\(556\) | 5.34070e51 | + | 1.79416e51i | 0.372544 | + | 0.125153i | ||||
\(557\) | −4.26713e51 | −0.287665 | −0.143833 | − | 0.989602i | \(-0.545943\pi\) | ||||
−0.143833 | + | 0.989602i | \(0.545943\pi\) | |||||||
\(558\) | −3.39307e50 | + | 2.43955e50i | −0.0221077 | + | 0.0158949i | ||||
\(559\) | − | 2.27533e52i | − | 1.43292i | ||||||
\(560\) | 3.92167e51 | − | 5.17812e51i | 0.238726 | − | 0.315210i | ||||
\(561\) | −2.75114e51 | −0.161889 | ||||||||
\(562\) | 1.27670e52 | + | 1.77571e52i | 0.726270 | + | 1.01014i | ||||
\(563\) | − | 2.39954e51i | − | 0.131968i | −0.997821 | − | 0.0659841i | \(-0.978981\pi\) | ||
0.997821 | − | 0.0659841i | \(-0.0210187\pi\) | |||||||
\(564\) | −1.80817e51 | + | 5.38239e51i | −0.0961470 | + | 0.286202i | ||||
\(565\) | 1.38681e51 | 0.0713012 | ||||||||
\(566\) | 1.68923e52 | − | 1.21452e52i | 0.839801 | − | 0.603799i | ||||
\(567\) | 3.67876e52i | 1.76857i | ||||||||
\(568\) | 9.64085e51 | + | 3.12488e52i | 0.448226 | + | 1.45283i | ||||
\(569\) | 1.00752e52 | 0.453023 | 0.226512 | − | 0.974008i | \(-0.427268\pi\) | ||||
0.226512 | + | 0.974008i | \(0.427268\pi\) | |||||||
\(570\) | −3.16768e51 | − | 4.40581e51i | −0.137759 | − | 0.191603i | ||||
\(571\) | − | 3.72705e50i | − | 0.0156776i | −0.999969 | − | 0.00783880i | \(-0.997505\pi\) | ||
0.999969 | − | 0.00783880i | \(-0.00249519\pi\) | |||||||
\(572\) | −4.05927e52 | − | 1.36368e52i | −1.65167 | − | 0.554865i | ||||
\(573\) | 1.07297e52 | 0.422326 | ||||||||
\(574\) | −2.06363e52 | + | 1.48371e52i | −0.785789 | + | 0.564966i | ||||
\(575\) | 4.51680e51i | 0.166395i | ||||||||
\(576\) | −4.25112e51 | + | 2.89905e51i | −0.151522 | + | 0.103331i | ||||
\(577\) | −9.17812e51 | −0.316529 | −0.158264 | − | 0.987397i | \(-0.550590\pi\) | ||||
−0.158264 | + | 0.987397i | \(0.550590\pi\) | |||||||
\(578\) | 1.70691e52 | + | 2.37408e52i | 0.569616 | + | 0.792257i | ||||
\(579\) | 3.38439e51i | 0.109292i | ||||||||
\(580\) | 2.10852e50 | − | 6.27644e50i | 0.00658939 | − | 0.0196147i | ||||
\(581\) | 6.72654e52 | 2.03444 | ||||||||
\(582\) | −1.27935e52 | + | 9.19828e51i | −0.374502 | + | 0.269259i | ||||
\(583\) | − | 6.35210e52i | − | 1.79976i | ||||||
\(584\) | 1.00428e52 | − | 3.09841e51i | 0.275431 | − | 0.0849758i | ||||
\(585\) | −3.23616e51 | −0.0859149 | ||||||||
\(586\) | 5.83171e51 | + | 8.11110e51i | 0.149879 | + | 0.208461i | ||||
\(587\) | − | 2.86552e52i | − | 0.712983i | −0.934299 | − | 0.356491i | \(-0.883973\pi\) | ||
0.934299 | − | 0.356491i | \(-0.116027\pi\) | |||||||
\(588\) | −5.84776e52 | − | 1.96451e52i | −1.40871 | − | 0.473243i | ||||
\(589\) | 5.37158e51 | 0.125289 | ||||||||
\(590\) | 1.32495e52 | − | 9.52609e51i | 0.299234 | − | 0.215143i | ||||
\(591\) | 1.22287e52i | 0.267435i | ||||||||
\(592\) | −5.58274e52 | − | 4.22812e52i | −1.18232 | − | 0.895436i | ||||
\(593\) | −8.79157e52 | −1.80313 | −0.901565 | − | 0.432643i | \(-0.857581\pi\) | ||||
−0.901565 | + | 0.432643i | \(0.857581\pi\) | |||||||
\(594\) | 2.49608e52 | + | 3.47171e52i | 0.495812 | + | 0.689605i | ||||
\(595\) | 3.19897e51i | 0.0615443i | ||||||||
\(596\) | −1.26757e52 | + | 3.77320e52i | −0.236208 | + | 0.703122i | ||||
\(597\) | 5.75132e52 | 1.03814 | ||||||||
\(598\) | 1.50767e52 | − | 1.08398e52i | 0.263623 | − | 0.189539i | ||||
\(599\) | − | 5.80821e52i | − | 0.983858i | −0.870635 | − | 0.491929i | \(-0.836292\pi\) | ||
0.870635 | − | 0.491929i | \(-0.163708\pi\) | |||||||
\(600\) | 1.82511e52 | + | 5.91571e52i | 0.299513 | + | 0.970807i | ||||
\(601\) | 1.87927e51 | 0.0298796 | 0.0149398 | − | 0.999888i | \(-0.495244\pi\) | ||||
0.0149398 | + | 0.999888i | \(0.495244\pi\) | |||||||
\(602\) | −4.58318e52 | − | 6.37457e52i | −0.706047 | − | 0.982014i | ||||
\(603\) | − | 1.38732e52i | − | 0.207084i | ||||||
\(604\) | 3.90036e52 | + | 1.31029e52i | 0.564161 | + | 0.189525i | ||||
\(605\) | −1.57441e51 | −0.0220681 | ||||||||
\(606\) | 9.88755e52 | − | 7.10894e52i | 1.34310 | − | 0.965661i | ||||
\(607\) | 5.89099e52i | 0.775538i | 0.921757 | + | 0.387769i | \(0.126754\pi\) | ||||
−0.921757 | + | 0.387769i | \(0.873246\pi\) | |||||||
\(608\) | 6.61186e52 | + | 1.64283e51i | 0.843637 | + | 0.0209615i | ||||
\(609\) | −1.08913e52 | −0.134695 | ||||||||
\(610\) | −1.42244e52 | − | 1.97842e52i | −0.170517 | − | 0.237165i | ||||
\(611\) | − | 4.35255e52i | − | 0.505779i | ||||||
\(612\) | 8.06989e50 | − | 2.40217e51i | 0.00909056 | − | 0.0270600i | ||||
\(613\) | −4.69520e52 | −0.512749 | −0.256374 | − | 0.966578i | \(-0.582528\pi\) | ||||
−0.256374 | + | 0.966578i | \(0.582528\pi\) | |||||||
\(614\) | 5.66049e52 | − | 4.06977e52i | 0.599315 | − | 0.430895i | ||||
\(615\) | 1.71395e52i | 0.175943i | ||||||||
\(616\) | −1.41193e53 | + | 4.35608e52i | −1.40533 | + | 0.433573i | ||||
\(617\) | −8.74221e52 | −0.843730 | −0.421865 | − | 0.906659i | \(-0.638624\pi\) | ||||
−0.421865 | + | 0.906659i | \(0.638624\pi\) | |||||||
\(618\) | 5.55118e52 | + | 7.72093e52i | 0.519523 | + | 0.722584i | ||||
\(619\) | 1.44865e53i | 1.31474i | 0.753568 | + | 0.657370i | \(0.228331\pi\) | ||||
−0.753568 | + | 0.657370i | \(0.771669\pi\) | |||||||
\(620\) | 4.11032e51 | + | 1.38082e51i | 0.0361770 | + | 0.0121534i | ||||
\(621\) | −1.85415e52 | −0.158273 | ||||||||
\(622\) | −1.72476e53 | + | 1.24007e53i | −1.42795 | + | 1.02666i | ||||
\(623\) | 2.40986e53i | 1.93517i | ||||||||
\(624\) | 1.53660e53 | − | 2.02891e53i | 1.19689 | − | 1.58036i | ||||
\(625\) | 1.06690e53 | 0.806130 | ||||||||
\(626\) | −1.06149e53 | − | 1.47638e53i | −0.778041 | − | 1.08215i | ||||
\(627\) | 1.23438e53i | 0.877738i | ||||||||
\(628\) | 1.19975e52 | − | 3.57131e52i | 0.0827671 | − | 0.246374i | ||||
\(629\) | 3.44894e52 | 0.230847 | ||||||||
\(630\) | −9.06642e51 | + | 6.51857e51i | −0.0588797 | + | 0.0423332i | ||||
\(631\) | − | 5.15579e52i | − | 0.324891i | −0.986718 | − | 0.162445i | \(-0.948062\pi\) | ||
0.986718 | − | 0.162445i | \(-0.0519381\pi\) | |||||||
\(632\) | −3.18102e52 | − | 1.03106e53i | −0.194510 | − | 0.630463i | ||||
\(633\) | −2.06257e53 | −1.22388 | ||||||||
\(634\) | 8.82930e52 | + | 1.22803e53i | 0.508429 | + | 0.707155i | ||||
\(635\) | − | 6.34450e52i | − | 0.354566i | ||||||
\(636\) | 3.57880e53 | + | 1.20227e53i | 1.94112 | + | 0.652102i | ||||
\(637\) | 4.72887e53 | 2.48948 | ||||||||
\(638\) | −1.22290e52 | + | 8.79237e51i | −0.0624881 | + | 0.0449276i | ||||
\(639\) | − | 5.62183e52i | − | 0.278844i | ||||||
\(640\) | 5.01714e52 | + | 1.82536e52i | 0.241566 | + | 0.0878879i | ||||
\(641\) | −3.57878e53 | −1.67275 | −0.836377 | − | 0.548154i | \(-0.815331\pi\) | ||||
−0.836377 | + | 0.548154i | \(0.815331\pi\) | |||||||
\(642\) | 5.20509e52 | + | 7.23956e52i | 0.236191 | + | 0.328509i | ||||
\(643\) | − | 3.39613e53i | − | 1.49615i | −0.663612 | − | 0.748077i | \(-0.730977\pi\) | ||
0.663612 | − | 0.748077i | \(-0.269023\pi\) | |||||||
\(644\) | 2.04042e52 | − | 6.07375e52i | 0.0872748 | − | 0.259792i | ||||
\(645\) | −5.29441e52 | −0.219879 | ||||||||
\(646\) | −2.64465e52 | + | 1.90145e52i | −0.106647 | + | 0.0766772i | ||||
\(647\) | − | 1.31557e53i | − | 0.515147i | −0.966259 | − | 0.257573i | \(-0.917077\pi\) | ||
0.966259 | − | 0.257573i | \(-0.0829229\pi\) | |||||||
\(648\) | −2.88929e53 | + | 8.91401e52i | −1.09867 | + | 0.338960i | ||||
\(649\) | −3.71211e53 | −1.37079 | ||||||||
\(650\) | −2.77033e53 | − | 3.85315e53i | −0.993523 | − | 1.38185i | ||||
\(651\) | − | 7.13249e52i | − | 0.248429i | ||||||
\(652\) | 2.00066e53 | + | 6.72104e52i | 0.676813 | + | 0.227369i | ||||
\(653\) | 4.19492e53 | 1.37839 | 0.689196 | − | 0.724575i | \(-0.257964\pi\) | ||||
0.689196 | + | 0.724575i | \(0.257964\pi\) | |||||||
\(654\) | −4.93741e53 | + | 3.54989e53i | −1.57588 | + | 1.13302i | ||||
\(655\) | 5.38883e52i | 0.167074i | ||||||||
\(656\) | −1.66534e53 | − | 1.26125e53i | −0.501568 | − | 0.379865i | ||||
\(657\) | −1.80677e52 | −0.0528640 | ||||||||
\(658\) | −8.76729e52 | − | 1.21941e53i | −0.249215 | − | 0.346623i | ||||
\(659\) | − | 5.59855e53i | − | 1.54615i | −0.634313 | − | 0.773076i | \(-0.718717\pi\) | ||
0.634313 | − | 0.773076i | \(-0.281283\pi\) | |||||||
\(660\) | −3.17310e52 | + | 9.44541e52i | −0.0851431 | + | 0.253446i | ||||
\(661\) | 3.67571e53 | 0.958326 | 0.479163 | − | 0.877726i | \(-0.340940\pi\) | ||||
0.479163 | + | 0.877726i | \(0.340940\pi\) | |||||||
\(662\) | 1.21533e53 | − | 8.73796e52i | 0.307887 | − | 0.221365i | ||||
\(663\) | 1.25343e53i | 0.308563i | ||||||||
\(664\) | 1.62991e53 | + | 5.28301e53i | 0.389915 | + | 1.26383i | ||||
\(665\) | 1.43531e53 | 0.333683 | ||||||||
\(666\) | 7.02794e52 | + | 9.77488e52i | 0.158788 | + | 0.220852i | ||||
\(667\) | − | 6.53120e51i | − | 0.0143417i | ||||||
\(668\) | 1.93846e53 | + | 6.51210e52i | 0.413718 | + | 0.138985i | ||||
\(669\) | −1.84343e53 | −0.382412 | ||||||||
\(670\) | −1.16872e53 | + | 8.40288e52i | −0.235663 | + | 0.169436i | ||||
\(671\) | 5.54294e53i | 1.08646i | ||||||||
\(672\) | 2.18137e52 | − | 8.77935e53i | 0.0415637 | − | 1.67281i | ||||
\(673\) | 6.30791e53 | 1.16842 | 0.584210 | − | 0.811602i | \(-0.301404\pi\) | ||||
0.584210 | + | 0.811602i | \(0.301404\pi\) | |||||||
\(674\) | 2.48766e53 | + | 3.45999e53i | 0.447974 | + | 0.623070i | ||||
\(675\) | 4.73867e53i | 0.829631i | ||||||||
\(676\) | −4.34216e53 | + | 1.29254e54i | −0.739127 | + | 2.20017i | ||||
\(677\) | 8.12445e53 | 1.34465 | 0.672325 | − | 0.740256i | \(-0.265296\pi\) | ||||
0.672325 | + | 0.740256i | \(0.265296\pi\) | |||||||
\(678\) | 1.52235e53 | − | 1.09454e53i | 0.244991 | − | 0.176143i | ||||
\(679\) | − | 4.16783e53i | − | 0.652206i | ||||||
\(680\) | −2.51246e52 | + | 7.75143e51i | −0.0382323 | + | 0.0117954i | ||||
\(681\) | −8.53659e53 | −1.26325 | ||||||||
\(682\) | −5.75795e52 | − | 8.00851e52i | −0.0828637 | − | 0.115252i | ||||
\(683\) | 2.65341e53i | 0.371373i | 0.982609 | + | 0.185687i | \(0.0594509\pi\) | ||||
−0.982609 | + | 0.185687i | \(0.940549\pi\) | |||||||
\(684\) | −1.07780e53 | − | 3.62079e52i | −0.146715 | − | 0.0492875i | ||||
\(685\) | 3.33306e53 | 0.441288 | ||||||||
\(686\) | 3.55024e53 | − | 2.55255e53i | 0.457193 | − | 0.328712i | ||||
\(687\) | 1.51181e53i | 0.189373i | ||||||||
\(688\) | 3.89602e53 | − | 5.14424e53i | 0.474723 | − | 0.626817i | ||||
\(689\) | −2.89405e54 | −3.43036 | ||||||||
\(690\) | −2.52228e52 | − | 3.50815e52i | −0.0290845 | − | 0.0404525i | ||||
\(691\) | − | 3.44958e53i | − | 0.386976i | −0.981103 | − | 0.193488i | \(-0.938020\pi\) | ||
0.981103 | − | 0.193488i | \(-0.0619800\pi\) | |||||||
\(692\) | 1.62816e53 | − | 4.84657e53i | 0.177698 | − | 0.528955i | ||||
\(693\) | 2.54014e53 | 0.269728 | ||||||||
\(694\) | 4.78987e53 | − | 3.44382e53i | 0.494873 | − | 0.355804i | ||||
\(695\) | 1.00494e53i | 0.101025i | ||||||||
\(696\) | −2.63907e52 | − | 8.55399e52i | −0.0258152 | − | 0.0836745i | ||||
\(697\) | 1.02882e53 | 0.0979305 | ||||||||
\(698\) | 5.43688e53 | + | 7.56194e53i | 0.503613 | + | 0.700455i | ||||
\(699\) | 2.61932e53i | 0.236114i | ||||||||
\(700\) | −1.55227e54 | − | 5.21472e53i | −1.36177 | − | 0.457476i | ||||
\(701\) | 2.07439e52 | 0.0177112 | 0.00885560 | − | 0.999961i | \(-0.497181\pi\) | ||||
0.00885560 | + | 0.999961i | \(0.497181\pi\) | |||||||
\(702\) | 1.58173e54 | − | 1.13723e54i | 1.31440 | − | 0.945023i | ||||
\(703\) | − | 1.54747e54i | − | 1.25161i | ||||||
\(704\) | −6.84250e53 | − | 1.00337e54i | −0.538684 | − | 0.789918i | ||||
\(705\) | −1.01278e53 | −0.0776109 | ||||||||
\(706\) | 9.74685e51 | + | 1.35565e52i | 0.00727068 | + | 0.0101125i | ||||
\(707\) | 3.22113e54i | 2.33905i | ||||||||
\(708\) | 7.02594e53 | − | 2.09142e54i | 0.496675 | − | 1.47846i | ||||
\(709\) | 9.61703e53 | 0.661854 | 0.330927 | − | 0.943656i | \(-0.392639\pi\) | ||||
0.330927 | + | 0.943656i | \(0.392639\pi\) | |||||||
\(710\) | −4.73603e53 | + | 3.40510e53i | −0.317326 | + | 0.228151i | ||||
\(711\) | 1.85494e53i | 0.121006i | ||||||||
\(712\) | −1.89270e54 | + | 5.83934e53i | −1.20216 | + | 0.370889i | ||||
\(713\) | 4.27715e52 | 0.0264517 | ||||||||
\(714\) | 2.52478e53 | + | 3.51161e53i | 0.152040 | + | 0.211466i | ||||
\(715\) | − | 7.63816e53i | − | 0.447893i | ||||||
\(716\) | 1.46226e54 | + | 4.91235e53i | 0.834985 | + | 0.280506i | ||||
\(717\) | 2.49750e54 | 1.38881 | ||||||||
\(718\) | −1.69392e52 | + | 1.21789e52i | −0.00917337 | + | 0.00659546i | ||||
\(719\) | − | 9.39009e53i | − | 0.495246i | −0.968856 | − | 0.247623i | \(-0.920351\pi\) | ||
0.968856 | − | 0.247623i | \(-0.0796494\pi\) | |||||||
\(720\) | −7.31655e52 | − | 5.54123e52i | −0.0375828 | − | 0.0284635i | ||||
\(721\) | −2.51530e54 | −1.25840 | ||||||||
\(722\) | −3.44816e53 | − | 4.79591e53i | −0.168027 | − | 0.233703i | ||||
\(723\) | 2.28197e54i | 1.08313i | ||||||||
\(724\) | −7.50394e53 | + | 2.23370e54i | −0.346942 | + | 1.03274i | ||||
\(725\) | −1.66918e53 | −0.0751763 | ||||||||
\(726\) | −1.72828e53 | + | 1.24259e53i | −0.0758258 | + | 0.0545172i | ||||
\(727\) | − | 2.50321e54i | − | 1.06990i | −0.844884 | − | 0.534950i | \(-0.820331\pi\) | ||
0.844884 | − | 0.534950i | \(-0.179669\pi\) | |||||||
\(728\) | 1.98465e54 | + | 6.43282e54i | 0.826395 | + | 2.67858i | ||||
\(729\) | −1.86232e54 | −0.755495 | ||||||||
\(730\) | 1.09435e53 | + | 1.52208e53i | 0.0432534 | + | 0.0601595i | ||||
\(731\) | 3.17804e53i | 0.122385i | ||||||||
\(732\) | −3.12292e54 | − | 1.04912e54i | −1.17179 | − | 0.393653i | ||||
\(733\) | −1.03311e53 | −0.0377719 | −0.0188860 | − | 0.999822i | \(-0.506012\pi\) | ||||
−0.0188860 | + | 0.999822i | \(0.506012\pi\) | |||||||
\(734\) | 3.60114e54 | − | 2.58915e54i | 1.28297 | − | 0.922426i | ||||
\(735\) | − | 1.10035e54i | − | 0.382007i | ||||||
\(736\) | 5.26472e53 | + | 1.30811e52i | 0.178114 | + | 0.00442553i | ||||
\(737\) | 3.27442e54 | 1.07957 | ||||||||
\(738\) | 2.09644e53 | + | 2.91586e53i | 0.0673615 | + | 0.0936905i | ||||
\(739\) | − | 4.25818e54i | − | 1.33346i | −0.745300 | − | 0.666729i | \(-0.767694\pi\) | ||
0.745300 | − | 0.666729i | \(-0.232306\pi\) | |||||||
\(740\) | 3.97793e53 | − | 1.18412e54i | 0.121410 | − | 0.361403i | ||||
\(741\) | 5.62388e54 | 1.67298 | ||||||||
\(742\) | −8.10795e54 | + | 5.82945e54i | −2.35092 | + | 1.69026i | ||||
\(743\) | 3.69716e54i | 1.04491i | 0.852666 | + | 0.522457i | \(0.174984\pi\) | ||||
−0.852666 | + | 0.522457i | \(0.825016\pi\) | |||||||
\(744\) | 5.60184e53 | − | 1.72828e53i | 0.154328 | − | 0.0476132i | ||||
\(745\) | −7.09986e53 | −0.190669 | ||||||||
\(746\) | 1.33362e53 | + | 1.85488e53i | 0.0349135 | + | 0.0485599i | ||||
\(747\) | − | 9.50444e53i | − | 0.242569i | ||||||
\(748\) | 5.66974e53 | + | 1.90470e53i | 0.141069 | + | 0.0473910i | ||||
\(749\) | −2.35848e54 | −0.572108 | ||||||||
\(750\) | −1.85659e54 | + | 1.33485e54i | −0.439089 | + | 0.315696i | ||||
\(751\) | − | 3.10593e54i | − | 0.716197i | −0.933684 | − | 0.358098i | \(-0.883425\pi\) | ||
0.933684 | − | 0.358098i | \(-0.116575\pi\) | |||||||
\(752\) | 7.45280e53 | − | 9.84056e53i | 0.167564 | − | 0.221249i | ||||
\(753\) | −6.02234e54 | −1.32026 | ||||||||
\(754\) | 4.00584e53 | + | 5.57158e53i | 0.0856325 | + | 0.119103i | ||||
\(755\) | 7.33914e53i | 0.152986i | ||||||||
\(756\) | 2.14065e54 | − | 6.37211e54i | 0.435143 | − | 1.29530i | ||||
\(757\) | 8.97740e54 | 1.77963 | 0.889814 | − | 0.456324i | \(-0.150834\pi\) | ||||
0.889814 | + | 0.456324i | \(0.150834\pi\) | |||||||
\(758\) | 1.57566e54 | − | 1.13286e54i | 0.304612 | − | 0.219010i | ||||
\(759\) | 9.82879e53i | 0.185313i | ||||||||
\(760\) | 3.47790e53 | + | 1.12729e54i | 0.0639527 | + | 0.207289i | ||||
\(761\) | 2.14256e54 | 0.384260 | 0.192130 | − | 0.981369i | \(-0.438460\pi\) | ||||
0.192130 | + | 0.981369i | \(0.438460\pi\) | |||||||
\(762\) | −5.00737e54 | − | 6.96456e54i | −0.875922 | − | 1.21829i | ||||
\(763\) | − | 1.60849e55i | − | 2.74444i | ||||||
\(764\) | −2.21124e54 | − | 7.42847e53i | −0.368012 | − | 0.123630i | ||||
\(765\) | 4.52006e52 | 0.00733799 | ||||||||
\(766\) | −1.82491e54 | + | 1.31207e54i | −0.288998 | + | 0.207784i | ||||
\(767\) | 1.69125e55i | 2.61275i | ||||||||
\(768\) | 6.94813e54 | − | 1.95600e54i | 1.04714 | − | 0.294786i | ||||
\(769\) | −4.13582e54 | −0.608081 | −0.304041 | − | 0.952659i | \(-0.598336\pi\) | ||||
−0.304041 | + | 0.952659i | \(0.598336\pi\) | |||||||
\(770\) | −1.53855e54 | − | 2.13991e54i | −0.220692 | − | 0.306952i | ||||
\(771\) | 8.54691e54i | 1.19612i | ||||||||
\(772\) | 2.34312e53 | − | 6.97479e53i | 0.0319938 | − | 0.0952363i | ||||
\(773\) | −9.18697e54 | −1.22395 | −0.611973 | − | 0.790879i | \(-0.709624\pi\) | ||||
−0.611973 | + | 0.790879i | \(0.709624\pi\) | |||||||
\(774\) | −9.00710e53 | + | 6.47592e53i | −0.117087 | + | 0.0841827i | ||||
\(775\) | − | 1.09311e54i | − | 0.138654i | ||||||
\(776\) | 3.27340e54 | − | 1.00991e54i | 0.405160 | − | 0.125000i | ||||
\(777\) | −2.05476e55 | −2.48177 | ||||||||
\(778\) | 2.13013e54 | + | 2.96271e54i | 0.251069 | + | 0.349202i | ||||
\(779\) | − | 4.61611e54i | − | 0.530963i | ||||||
\(780\) | 4.30337e54 | + | 1.44568e54i | 0.483072 | + | 0.162284i | ||||
\(781\) | 1.32690e55 | 1.45367 | ||||||||
\(782\) | −2.10581e53 | + | 1.51403e53i | −0.0225160 | + | 0.0161885i | ||||
\(783\) | − | 6.85202e53i | − | 0.0715065i | ||||||
\(784\) | 1.06914e55 | + | 8.09718e54i | 1.08900 | + | 0.824761i | ||||
\(785\) | 6.71998e53 | 0.0668105 | ||||||||
\(786\) | 4.25311e54 | + | 5.91549e54i | 0.412742 | + | 0.574067i | ||||
\(787\) | 1.88649e55i | 1.78704i | 0.449019 | + | 0.893522i | \(0.351774\pi\) | ||||
−0.449019 | + | 0.893522i | \(0.648226\pi\) | |||||||
\(788\) | 8.46632e53 | − | 2.52018e54i | 0.0782882 | − | 0.233041i | ||||
\(789\) | −7.98568e54 | −0.720856 | ||||||||
\(790\) | 1.56266e54 | − | 1.12352e54i | 0.137705 | − | 0.0990072i | ||||
\(791\) | 4.95945e54i | 0.426659i | ||||||||
\(792\) | 6.15503e53 | + | 1.99502e54i | 0.0516954 | + | 0.167560i | ||||
\(793\) | 2.52539e55 | 2.07080 | ||||||||
\(794\) | −2.95676e54 | − | 4.11244e54i | −0.236715 | − | 0.329238i | ||||
\(795\) | 6.73407e54i | 0.526384i | ||||||||
\(796\) | −1.18527e55 | − | 3.98182e54i | −0.904627 | − | 0.303901i | ||||
\(797\) | 4.64822e54 | 0.346401 | 0.173200 | − | 0.984887i | \(-0.444589\pi\) | ||||
0.173200 | + | 0.984887i | \(0.444589\pi\) | |||||||
\(798\) | 1.57559e55 | − | 1.13281e55i | 1.14653 | − | 0.824334i | ||||
\(799\) | 6.07936e53i | 0.0431986i | ||||||||
\(800\) | 3.34313e53 | − | 1.34551e55i | 0.0231977 | − | 0.933633i | ||||
\(801\) | 3.40508e54 | 0.230733 | ||||||||
\(802\) | −7.57157e54 | − | 1.05310e55i | −0.501041 | − | 0.696879i | ||||
\(803\) | − | 4.26443e54i | − | 0.275591i | ||||||
\(804\) | −6.19752e54 | + | 1.84482e55i | −0.391159 | + | 1.16437i | ||||
\(805\) | 1.14287e54 | 0.0704492 | ||||||||
\(806\) | −3.64871e54 | + | 2.62335e54i | −0.219672 | + | 0.157939i | ||||
\(807\) | − | 2.04538e55i | − | 1.20276i | ||||||
\(808\) | −2.52987e55 | + | 7.80513e54i | −1.45305 | + | 0.448295i | ||||
\(809\) | −2.35673e55 | −1.32217 | −0.661087 | − | 0.750309i | \(-0.729905\pi\) | ||||
−0.661087 | + | 0.750309i | \(0.729905\pi\) | |||||||
\(810\) | −3.14839e54 | − | 4.37897e54i | −0.172533 | − | 0.239970i | ||||
\(811\) | − | 1.74153e55i | − | 0.932256i | −0.884717 | − | 0.466128i | \(-0.845649\pi\) | ||
0.884717 | − | 0.466128i | \(-0.154351\pi\) | |||||||
\(812\) | 2.24455e54 | + | 7.54038e53i | 0.117372 | + | 0.0394302i | ||||
\(813\) | −2.24438e55 | −1.14651 | ||||||||
\(814\) | −2.30712e55 | + | 1.65877e55i | −1.15135 | + | 0.827795i | ||||
\(815\) | 3.76455e54i | 0.183535i | ||||||||
\(816\) | −2.14623e54 | + | 2.83385e54i | −0.102226 | + | 0.134978i | ||||
\(817\) | 1.42592e55 | 0.663553 | ||||||||
\(818\) | 5.24179e54 | + | 7.29060e54i | 0.238323 | + | 0.331475i | ||||
\(819\) | − | 1.15730e55i | − | 0.514105i | ||||||
\(820\) | 1.18662e54 | − | 3.53223e54i | 0.0515050 | − | 0.153315i | ||||
\(821\) | 5.44852e54 | 0.231078 | 0.115539 | − | 0.993303i | \(-0.463140\pi\) | ||||
0.115539 | + | 0.993303i | \(0.463140\pi\) | |||||||
\(822\) | 3.65881e55 | − | 2.63061e55i | 1.51626 | − | 1.09016i | ||||
\(823\) | − | 4.31927e55i | − | 1.74910i | −0.484938 | − | 0.874548i | \(-0.661158\pi\) | ||
0.484938 | − | 0.874548i | \(-0.338842\pi\) | |||||||
\(824\) | −6.09482e54 | − | 1.97551e55i | −0.241181 | − | 0.781738i | ||||
\(825\) | 2.51195e55 | 0.971372 | ||||||||
\(826\) | 3.40668e55 | + | 4.73822e55i | 1.28739 | + | 1.79058i | ||||
\(827\) | − | 3.19468e55i | − | 1.17984i | −0.807462 | − | 0.589919i | \(-0.799160\pi\) | ||
0.807462 | − | 0.589919i | \(-0.200840\pi\) | |||||||
\(828\) | −8.58206e53 | − | 2.88307e53i | −0.0309753 | − | 0.0104059i | ||||
\(829\) | 3.55499e55 | 1.25401 | 0.627007 | − | 0.779013i | \(-0.284280\pi\) | ||||
0.627007 | + | 0.779013i | \(0.284280\pi\) | |||||||
\(830\) | −8.00687e54 | + | 5.75677e54i | −0.276044 | + | 0.198470i | ||||
\(831\) | 4.17613e55i | 1.40720i | ||||||||
\(832\) | −4.57141e55 | + | 3.11747e55i | −1.50559 | + | 1.02674i | ||||
\(833\) | −6.60499e54 | −0.212626 | ||||||||
\(834\) | 7.93142e54 | + | 1.10315e55i | 0.249572 | + | 0.347120i | ||||
\(835\) | 3.64752e54i | 0.112190i | ||||||||
\(836\) | 8.54598e54 | − | 2.54389e55i | 0.256946 | − | 0.764855i | ||||
\(837\) | 4.48725e54 | 0.131885 | ||||||||
\(838\) | −2.60871e55 | + | 1.87561e55i | −0.749531 | + | 0.538897i | ||||
\(839\) | 2.45001e55i | 0.688162i | 0.938940 | + | 0.344081i | \(0.111809\pi\) | ||||
−0.938940 | + | 0.344081i | \(0.888191\pi\) | |||||||
\(840\) | 1.49683e55 | − | 4.61802e54i | 0.411024 | − | 0.126809i | ||||
\(841\) | −3.70084e55 | −0.993520 | ||||||||
\(842\) | 3.49356e54 | + | 4.85906e54i | 0.0916934 | + | 0.127533i | ||||
\(843\) | 5.27418e55i | 1.35341i | ||||||||
\(844\) | 4.25069e55 | + | 1.42798e55i | 1.06648 | + | 0.358275i | ||||
\(845\) | −2.43211e55 | −0.596631 | ||||||||
\(846\) | −1.72299e54 | + | 1.23880e54i | −0.0413282 | + | 0.0297141i | ||||
\(847\) | − | 5.63032e54i | − | 0.132053i | ||||||
\(848\) | −6.54307e55 | − | 4.95543e55i | −1.50058 | − | 1.13648i | ||||
\(849\) | 5.01732e55 | 1.12519 | ||||||||
\(850\) | 3.86942e54 | + | 5.38183e54i | 0.0848568 | + | 0.118024i | ||||
\(851\) | − | 1.23218e55i | − | 0.264248i | ||||||
\(852\) | −2.51142e55 | + | 7.47578e55i | −0.526706 | + | 1.56785i | ||||
\(853\) | −4.60031e55 | −0.943530 | −0.471765 | − | 0.881724i | \(-0.656383\pi\) | ||||
−0.471765 | + | 0.881724i | \(0.656383\pi\) | |||||||
\(854\) | 7.07513e55 | − | 5.08687e55i | 1.41917 | − | 1.02035i | ||||
\(855\) | − | 2.02806e54i | − | 0.0397854i | ||||||
\(856\) | −5.71484e54 | − | 1.85234e55i | −0.109648 | − | 0.355402i | ||||
\(857\) | 6.69827e55 | 1.25698 | 0.628488 | − | 0.777819i | \(-0.283674\pi\) | ||||
0.628488 | + | 0.777819i | \(0.283674\pi\) | |||||||
\(858\) | −6.02839e55 | − | 8.38466e55i | −1.10648 | − | 1.53896i | ||||
\(859\) | 5.14374e55i | 0.923441i | 0.887025 | + | 0.461720i | \(0.152768\pi\) | ||||
−0.887025 | + | 0.461720i | \(0.847232\pi\) | |||||||
\(860\) | 1.09111e55 | + | 3.66548e54i | 0.191601 | + | 0.0643666i | ||||
\(861\) | −6.12936e55 | −1.05282 | ||||||||
\(862\) | 2.69570e55 | − | 1.93815e55i | 0.452932 | − | 0.325649i | ||||
\(863\) | 3.93612e55i | 0.646940i | 0.946239 | + | 0.323470i | \(0.104849\pi\) | ||||
−0.946239 | + | 0.323470i | \(0.895151\pi\) | |||||||
\(864\) | 5.52334e55 | + | 1.37236e54i | 0.888056 | + | 0.0220652i | ||||
\(865\) | 9.11958e54 | 0.143440 | ||||||||
\(866\) | −8.94948e54 | − | 1.24475e55i | −0.137708 | − | 0.191532i | ||||
\(867\) | 7.05144e55i | 1.06149i | ||||||||
\(868\) | −4.93804e54 | + | 1.46991e55i | −0.0727244 | + | 0.216479i | ||||
\(869\) | −4.37812e55 | −0.630830 | ||||||||
\(870\) | 1.29643e54 | − | 9.32109e53i | 0.0182761 | − | 0.0131402i | ||||
\(871\) | − | 1.49184e56i | − | 2.05768i | ||||||
\(872\) | 1.26331e56 | − | 3.89754e55i | 1.70489 | − | 0.525990i | ||||
\(873\) | −5.88904e54 | −0.0777632 | ||||||||
\(874\) | 6.79315e54 | + | 9.44833e54i | 0.0877716 | + | 0.122078i | ||||
\(875\) | − | 6.04834e55i | − | 0.764687i | ||||||
\(876\) | 2.40260e55 | + | 8.07132e54i | 0.297237 | + | 0.0998542i | ||||
\(877\) | −9.57785e55 | −1.15951 | −0.579757 | − | 0.814790i | \(-0.696852\pi\) | ||||
−0.579757 | + | 0.814790i | \(0.696852\pi\) | |||||||
\(878\) | −2.49592e55 | + | 1.79451e55i | −0.295689 | + | 0.212594i | ||||
\(879\) | 2.40914e55i | 0.279302i | ||||||||
\(880\) | 1.30787e55 | − | 1.72689e55i | 0.148386 | − | 0.195927i | ||||
\(881\) | −1.25845e56 | −1.39731 | −0.698656 | − | 0.715458i | \(-0.746218\pi\) | ||||
−0.698656 | + | 0.715458i | \(0.746218\pi\) | |||||||
\(882\) | −1.34590e55 | − | 1.87197e55i | −0.146255 | − | 0.203421i | ||||
\(883\) | 3.62248e55i | 0.385259i | 0.981272 | + | 0.192629i | \(0.0617015\pi\) | ||||
−0.981272 | + | 0.192629i | \(0.938299\pi\) | |||||||
\(884\) | 8.67790e54 | − | 2.58316e55i | 0.0903278 | − | 0.268880i | ||||
\(885\) | 3.93533e55 | 0.400922 | ||||||||
\(886\) | −9.50171e55 | + | 6.83153e55i | −0.947460 | + | 0.681204i | ||||
\(887\) | − | 7.17047e55i | − | 0.699840i | −0.936780 | − | 0.349920i | \(-0.886209\pi\) | ||
0.936780 | − | 0.349920i | \(-0.113791\pi\) | |||||||
\(888\) | −4.97888e55 | − | 1.61380e56i | −0.475648 | − | 1.54171i | ||||
\(889\) | 2.26889e56 | 2.12168 | ||||||||
\(890\) | −2.06243e55 | − | 2.86855e55i | −0.188786 | − | 0.262575i | ||||
\(891\) | 1.22686e56i | 1.09931i | ||||||||
\(892\) | 3.79908e55 | + | 1.27627e55i | 0.333231 | + | 0.111946i | ||||
\(893\) | 2.72768e55 | 0.234216 | ||||||||
\(894\) | −7.79375e55 | + | 5.60354e55i | −0.655139 | + | 0.471031i | ||||
\(895\) | 2.75148e55i | 0.226427i | ||||||||
\(896\) | −6.52777e55 | + | 1.79421e56i | −0.525911 | + | 1.44551i | ||||
\(897\) | 4.47804e55 | 0.353209 | ||||||||
\(898\) | −1.90258e55 | − | 2.64622e55i | −0.146924 | − | 0.204351i | ||||
\(899\) | 1.58062e54i | 0.0119507i | ||||||||
\(900\) | −7.36827e54 | + | 2.19332e55i | −0.0545454 | + | 0.162366i | ||||
\(901\) | 4.04222e55 | 0.292987 | ||||||||
\(902\) | −6.88217e55 | + | 4.94813e55i | −0.488429 | + | 0.351170i | ||||
\(903\) | − | 1.89336e56i | − | 1.31573i | ||||||
\(904\) | −3.89514e55 | + | 1.20173e55i | −0.265047 | + | 0.0817722i | ||||
\(905\) | −4.20306e55 | −0.280055 | ||||||||
\(906\) | 5.79239e55 | + | 8.05641e55i | 0.377939 | + | 0.525661i | ||||
\(907\) | − | 8.50893e55i | − | 0.543671i | −0.962344 | − | 0.271836i | \(-0.912369\pi\) | ||
0.962344 | − | 0.271836i | \(-0.0876307\pi\) | |||||||
\(908\) | 1.75928e56 | + | 5.91015e55i | 1.10079 | + | 0.369800i | ||||
\(909\) | 4.55138e55 | 0.278888 | ||||||||
\(910\) | −9.74951e55 | + | 7.00969e55i | −0.585054 | + | 0.420642i | ||||
\(911\) | 3.16761e56i | 1.86158i | 0.365550 | + | 0.930792i | \(0.380881\pi\) | ||||
−0.365550 | + | 0.930792i | \(0.619119\pi\) | |||||||
\(912\) | 1.27149e56 | + | 9.62968e55i | 0.731830 | + | 0.554255i | ||||
\(913\) | 2.24329e56 | 1.26456 | ||||||||
\(914\) | 1.85856e55 | + | 2.58500e55i | 0.102612 | + | 0.142719i | ||||
\(915\) | − | 5.87626e55i | − | 0.317761i | ||||||
\(916\) | 1.04667e55 | − | 3.11564e55i | 0.0554366 | − | 0.165019i | ||||
\(917\) | −1.92713e56 | −0.999755 | ||||||||
\(918\) | −2.20925e55 | + | 1.58841e55i | −0.112263 | + | 0.0807144i | ||||
\(919\) | 1.03826e55i | 0.0516787i | 0.999666 | + | 0.0258394i | \(0.00822584\pi\) | ||||
−0.999666 | + | 0.0258394i | \(0.991774\pi\) | |||||||
\(920\) | 2.76930e54 | + | 8.97608e54i | 0.0135021 | + | 0.0437641i | ||||
\(921\) | 1.68127e56 | 0.802978 | ||||||||
\(922\) | 8.54631e55 | + | 1.18867e56i | 0.399844 | + | 0.556128i | ||||
\(923\) | − | 6.04540e56i | − | 2.77072i | ||||||
\(924\) | −3.37783e56 | − | 1.13475e56i | −1.51660 | − | 0.509487i | ||||
\(925\) | −3.14908e56 | −1.38513 | ||||||||
\(926\) | −4.11273e55 | + | 2.95696e55i | −0.177223 | + | 0.127420i | ||||
\(927\) | 3.55405e55i | 0.150041i | ||||||||
\(928\) | −4.83411e53 | + | 1.94558e55i | −0.00199942 | + | 0.0804705i | ||||
\(929\) | 4.61993e56 | 1.87213 | 0.936066 | − | 0.351824i | \(-0.114439\pi\) | ||||
0.936066 | + | 0.351824i | \(0.114439\pi\) | |||||||
\(930\) | 6.10419e54 | + | 8.49008e54i | 0.0242355 | + | 0.0337082i | ||||
\(931\) | 2.96352e56i | 1.15283i | ||||||||
\(932\) | 1.81344e55 | − | 5.39808e55i | 0.0691194 | − | 0.205749i | ||||
\(933\) | −5.12286e56 | −1.91320 | ||||||||
\(934\) | 3.86076e56 | − | 2.77581e56i | 1.41281 | − | 1.01578i | ||||
\(935\) | 1.06685e55i | 0.0382545i | ||||||||
\(936\) | 9.08941e55 | − | 2.80426e55i | 0.319370 | − | 0.0985319i | ||||
\(937\) | −3.24881e56 | −1.11859 | −0.559297 | − | 0.828967i | \(-0.688929\pi\) | ||||
−0.559297 | + | 0.828967i | \(0.688929\pi\) | |||||||
\(938\) | −3.00500e56 | − | 4.17954e56i | −1.01389 | − | 1.41018i | ||||
\(939\) | − | 4.38512e56i | − | 1.44989i | ||||||
\(940\) | 2.08721e55 | + | 7.01180e54i | 0.0676296 | + | 0.0227196i | ||||
\(941\) | 2.13347e56 | 0.677461 | 0.338730 | − | 0.940884i | \(-0.390003\pi\) | ||||
0.338730 | + | 0.940884i | \(0.390003\pi\) | |||||||
\(942\) | 7.37674e55 | − | 5.30372e55i | 0.229561 | − | 0.165049i | ||||
\(943\) | − | 3.67560e55i | − | 0.112100i | ||||||
\(944\) | −2.89591e56 | + | 3.82371e56i | −0.865599 | + | 1.14292i | ||||
\(945\) | 1.19901e56 | 0.351252 | ||||||||
\(946\) | −1.52848e56 | − | 2.12591e56i | −0.438863 | − | 0.610397i | ||||
\(947\) | 4.92826e56i | 1.38690i | 0.720507 | + | 0.693448i | \(0.243909\pi\) | ||||
−0.720507 | + | 0.693448i | \(0.756091\pi\) | |||||||
\(948\) | 8.28650e55 | − | 2.46665e56i | 0.228567 | − | 0.680377i | ||||
\(949\) | −1.94289e56 | −0.525280 | ||||||||
\(950\) | 2.41471e56 | − | 1.73613e56i | 0.639907 | − | 0.460080i | ||||
\(951\) | 3.64748e56i | 0.947465i | ||||||||
\(952\) | −2.77203e55 | − | 8.98495e55i | −0.0705824 | − | 0.228778i | ||||
\(953\) | −4.13229e55 | −0.103140 | −0.0515699 | − | 0.998669i | \(-0.516422\pi\) | ||||
−0.0515699 | + | 0.998669i | \(0.516422\pi\) | |||||||
\(954\) | 8.23686e55 | + | 1.14563e56i | 0.201531 | + | 0.280302i | ||||
\(955\) | − | 4.16080e55i | − | 0.0997958i | ||||||
\(956\) | −5.14702e56 | − | 1.72910e56i | −1.21020 | − | 0.406555i | ||||
\(957\) | −3.63223e55 | −0.0837232 | ||||||||
\(958\) | 3.75701e56 | − | 2.70121e56i | 0.848981 | − | 0.610400i | ||||
\(959\) | 1.19195e57i | 2.64062i | ||||||||
\(960\) | 7.25396e55 | + | 1.06371e56i | 0.157551 | + | 0.231031i | ||||
\(961\) | 4.59266e56 | 0.977958 | ||||||||
\(962\) | 7.55744e56 | + | 1.05113e57i | 1.57779 | + | 2.19448i | ||||
\(963\) | 3.33247e55i | 0.0682130i | ||||||||
\(964\) | 1.57988e56 | − | 4.70283e56i | 0.317073 | − | 0.943834i | ||||
\(965\) | 1.31242e55 | 0.0258257 | ||||||||
\(966\) | 1.25457e56 | − | 9.02007e55i | 0.242063 | − | 0.174038i | ||||
\(967\) | − | 1.86519e56i | − | 0.352874i | −0.984312 | − | 0.176437i | \(-0.943543\pi\) | ||
0.984312 | − | 0.176437i | \(-0.0564571\pi\) | |||||||
\(968\) | 4.42203e55 | − | 1.36428e55i | 0.0820333 | − | 0.0253089i | ||||
\(969\) | −7.85508e55 | −0.142889 | ||||||||
\(970\) | 3.56695e55 | + | 4.96114e55i | 0.0636260 | + | 0.0884949i | ||||
\(971\) | − | 2.84061e56i | − | 0.496873i | −0.968648 | − | 0.248437i | \(-0.920083\pi\) | ||
0.968648 | − | 0.248437i | \(-0.0799168\pi\) | |||||||
\(972\) | −2.00294e56 | − | 6.72870e55i | −0.343565 | − | 0.115418i | ||||
\(973\) | −3.59381e56 | −0.604520 | ||||||||
\(974\) | −2.17534e56 | + | 1.56403e56i | −0.358846 | + | 0.258003i | ||||
\(975\) | − | 1.14445e57i | − | 1.85145i | ||||||
\(976\) | 5.70959e56 | + | 4.32418e56i | 0.905854 | + | 0.686053i | ||||
\(977\) | −5.09703e56 | −0.793087 | −0.396544 | − | 0.918016i | \(-0.629790\pi\) | ||||
−0.396544 | + | 0.918016i | \(0.629790\pi\) | |||||||
\(978\) | 2.97116e56 | + | 4.13247e56i | 0.453407 | + | 0.630626i | ||||
\(979\) | 8.03684e56i | 1.20286i | ||||||||
\(980\) | −7.61805e55 | + | 2.26767e56i | −0.111827 | + | 0.332878i | ||||
\(981\) | −2.27276e56 | −0.327222 | ||||||||
\(982\) | −4.50082e56 | + | 3.23600e56i | −0.635585 | + | 0.456972i | ||||
\(983\) | − | 1.19102e56i | − | 0.164969i | −0.996592 | − | 0.0824845i | \(-0.973715\pi\) | ||
0.996592 | − | 0.0824845i | \(-0.0262855\pi\) | |||||||
\(984\) | −1.48521e56 | − | 4.81398e56i | −0.201781 | − | 0.654030i | ||||
\(985\) | 4.74211e55 | 0.0631951 | ||||||||
\(986\) | −5.59511e54 | − | 7.78202e54i | −0.00731387 | − | 0.0101726i | ||||
\(987\) | − | 3.62186e56i | − | 0.464415i | ||||||
\(988\) | −1.15901e57 | − | 3.89359e56i | −1.45782 | − | 0.489743i | ||||
\(989\) | 1.13539e56 | 0.140093 | ||||||||
\(990\) | −3.02363e55 | + | 2.17393e55i | −0.0365983 | + | 0.0263134i | ||||
\(991\) | 2.37717e56i | 0.282268i | 0.989991 | + | 0.141134i | \(0.0450748\pi\) | ||||
−0.989991 | + | 0.141134i | \(0.954925\pi\) | |||||||
\(992\) | −1.27412e56 | − | 3.16576e54i | −0.148419 | − | 0.00368770i | ||||
\(993\) | 3.60975e56 | 0.412516 | ||||||||
\(994\) | −1.21772e57 | − | 1.69368e57i | −1.36523 | − | 1.89884i | ||||
\(995\) | − | 2.23027e56i | − | 0.245312i | ||||||
\(996\) | −4.24589e56 | + | 1.26388e57i | −0.458185 | + | 1.36389i | ||||
\(997\) | 6.97114e56 | 0.738067 | 0.369034 | − | 0.929416i | \(-0.379689\pi\) | ||||
0.369034 | + | 0.929416i | \(0.379689\pi\) | |||||||
\(998\) | −5.50337e56 | + | 3.95681e56i | −0.571674 | + | 0.411022i | ||||
\(999\) | − | 1.29270e57i | − | 1.31751i |
(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 | 4.39.b.a.3.5 | ✓ | 18 | |
4.3 | odd | 2 | inner | 4.39.b.a.3.6 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.39.b.a.3.5 | ✓ | 18 | 1.1 | even | 1 | trivial | |
4.39.b.a.3.6 | yes | 18 | 4.3 | odd | 2 | inner |