Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,8,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.a (trivial) |
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: | yes |
Analytic conductor: | \(178.059464526\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3046x^{2} + 50476x + 497070 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-6.96971\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −125.000 | −0.447214 | ||||||||
\(6\) | 216.000 | 0.408248 | ||||||||
\(7\) | −1119.70 | −1.23384 | −0.616918 | − | 0.787027i | \(-0.711619\pi\) | ||||
−0.616918 | + | 0.787027i | \(0.711619\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −1000.00 | −0.316228 | ||||||||
\(11\) | 1725.45 | 0.390866 | 0.195433 | − | 0.980717i | \(-0.437389\pi\) | ||||
0.195433 | + | 0.980717i | \(0.437389\pi\) | |||||||
\(12\) | 1728.00 | 0.288675 | ||||||||
\(13\) | 47.9718 | 0.00605598 | 0.00302799 | − | 0.999995i | \(-0.499036\pi\) | ||||
0.00302799 | + | 0.999995i | \(0.499036\pi\) | |||||||
\(14\) | −8957.58 | −0.872454 | ||||||||
\(15\) | −3375.00 | −0.258199 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 28333.6 | 1.39872 | 0.699360 | − | 0.714770i | \(-0.253468\pi\) | ||||
0.699360 | + | 0.714770i | \(0.253468\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | 6859.00 | 0.229416 | ||||||||
\(20\) | −8000.00 | −0.223607 | ||||||||
\(21\) | −30231.8 | −0.712356 | ||||||||
\(22\) | 13803.6 | 0.276384 | ||||||||
\(23\) | −85045.6 | −1.45749 | −0.728743 | − | 0.684788i | \(-0.759895\pi\) | ||||
−0.728743 | + | 0.684788i | \(0.759895\pi\) | |||||||
\(24\) | 13824.0 | 0.204124 | ||||||||
\(25\) | 15625.0 | 0.200000 | ||||||||
\(26\) | 383.775 | 0.00428223 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −71660.7 | −0.616918 | ||||||||
\(29\) | −17328.4 | −0.131936 | −0.0659682 | − | 0.997822i | \(-0.521014\pi\) | ||||
−0.0659682 | + | 0.997822i | \(0.521014\pi\) | |||||||
\(30\) | −27000.0 | −0.182574 | ||||||||
\(31\) | −185488. | −1.11828 | −0.559139 | − | 0.829074i | \(-0.688868\pi\) | ||||
−0.559139 | + | 0.829074i | \(0.688868\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | 46587.2 | 0.225667 | ||||||||
\(34\) | 226669. | 0.989044 | ||||||||
\(35\) | 139962. | 0.551789 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | 308884. | 1.00251 | 0.501255 | − | 0.865299i | \(-0.332872\pi\) | ||||
0.501255 | + | 0.865299i | \(0.332872\pi\) | |||||||
\(38\) | 54872.0 | 0.162221 | ||||||||
\(39\) | 1295.24 | 0.00349642 | ||||||||
\(40\) | −64000.0 | −0.158114 | ||||||||
\(41\) | 221162. | 0.501149 | 0.250575 | − | 0.968097i | \(-0.419380\pi\) | ||||
0.250575 | + | 0.968097i | \(0.419380\pi\) | |||||||
\(42\) | −241855. | −0.503712 | ||||||||
\(43\) | −237096. | −0.454762 | −0.227381 | − | 0.973806i | \(-0.573016\pi\) | ||||
−0.227381 | + | 0.973806i | \(0.573016\pi\) | |||||||
\(44\) | 110429. | 0.195433 | ||||||||
\(45\) | −91125.0 | −0.149071 | ||||||||
\(46\) | −680364. | −1.03060 | ||||||||
\(47\) | 666086. | 0.935811 | 0.467905 | − | 0.883779i | \(-0.345009\pi\) | ||||
0.467905 | + | 0.883779i | \(0.345009\pi\) | |||||||
\(48\) | 110592. | 0.144338 | ||||||||
\(49\) | 430180. | 0.522353 | ||||||||
\(50\) | 125000. | 0.141421 | ||||||||
\(51\) | 765008. | 0.807551 | ||||||||
\(52\) | 3070.20 | 0.00302799 | ||||||||
\(53\) | −1.91062e6 | −1.76282 | −0.881411 | − | 0.472351i | \(-0.843405\pi\) | ||||
−0.881411 | + | 0.472351i | \(0.843405\pi\) | |||||||
\(54\) | 157464. | 0.136083 | ||||||||
\(55\) | −215681. | −0.174801 | ||||||||
\(56\) | −573285. | −0.436227 | ||||||||
\(57\) | 185193. | 0.132453 | ||||||||
\(58\) | −138627. | −0.0932931 | ||||||||
\(59\) | 112866. | 0.0715452 | 0.0357726 | − | 0.999360i | \(-0.488611\pi\) | ||||
0.0357726 | + | 0.999360i | \(0.488611\pi\) | |||||||
\(60\) | −216000. | −0.129099 | ||||||||
\(61\) | −1.13216e6 | −0.638634 | −0.319317 | − | 0.947648i | \(-0.603453\pi\) | ||||
−0.319317 | + | 0.947648i | \(0.603453\pi\) | |||||||
\(62\) | −1.48390e6 | −0.790743 | ||||||||
\(63\) | −816260. | −0.411279 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −5996.48 | −0.00270832 | ||||||||
\(66\) | 372697. | 0.159571 | ||||||||
\(67\) | 142005. | 0.0576820 | 0.0288410 | − | 0.999584i | \(-0.490818\pi\) | ||||
0.0288410 | + | 0.999584i | \(0.490818\pi\) | |||||||
\(68\) | 1.81335e6 | 0.699360 | ||||||||
\(69\) | −2.29623e6 | −0.841480 | ||||||||
\(70\) | 1.11970e6 | 0.390173 | ||||||||
\(71\) | −2.61842e6 | −0.868232 | −0.434116 | − | 0.900857i | \(-0.642939\pi\) | ||||
−0.434116 | + | 0.900857i | \(0.642939\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | −1.27471e6 | −0.383513 | −0.191756 | − | 0.981443i | \(-0.561418\pi\) | ||||
−0.191756 | + | 0.981443i | \(0.561418\pi\) | |||||||
\(74\) | 2.47107e6 | 0.708882 | ||||||||
\(75\) | 421875. | 0.115470 | ||||||||
\(76\) | 438976. | 0.114708 | ||||||||
\(77\) | −1.93198e6 | −0.482265 | ||||||||
\(78\) | 10361.9 | 0.00247234 | ||||||||
\(79\) | 5.39395e6 | 1.23087 | 0.615434 | − | 0.788188i | \(-0.288981\pi\) | ||||
0.615434 | + | 0.788188i | \(0.288981\pi\) | |||||||
\(80\) | −512000. | −0.111803 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 1.76930e6 | 0.354366 | ||||||||
\(83\) | −2.72417e6 | −0.522951 | −0.261475 | − | 0.965210i | \(-0.584209\pi\) | ||||
−0.261475 | + | 0.965210i | \(0.584209\pi\) | |||||||
\(84\) | −1.93484e6 | −0.356178 | ||||||||
\(85\) | −3.54170e6 | −0.625527 | ||||||||
\(86\) | −1.89677e6 | −0.321566 | ||||||||
\(87\) | −467866. | −0.0761735 | ||||||||
\(88\) | 883431. | 0.138192 | ||||||||
\(89\) | −8.03487e6 | −1.20813 | −0.604065 | − | 0.796935i | \(-0.706453\pi\) | ||||
−0.604065 | + | 0.796935i | \(0.706453\pi\) | |||||||
\(90\) | −729000. | −0.105409 | ||||||||
\(91\) | −53714.0 | −0.00747209 | ||||||||
\(92\) | −5.44292e6 | −0.728743 | ||||||||
\(93\) | −5.00818e6 | −0.645639 | ||||||||
\(94\) | 5.32869e6 | 0.661718 | ||||||||
\(95\) | −857375. | −0.102598 | ||||||||
\(96\) | 884736. | 0.102062 | ||||||||
\(97\) | −9.96801e6 | −1.10894 | −0.554469 | − | 0.832204i | \(-0.687079\pi\) | ||||
−0.554469 | + | 0.832204i | \(0.687079\pi\) | |||||||
\(98\) | 3.44144e6 | 0.369359 | ||||||||
\(99\) | 1.25785e6 | 0.130289 | ||||||||
\(100\) | 1.00000e6 | 0.100000 | ||||||||
\(101\) | −1.36343e7 | −1.31677 | −0.658384 | − | 0.752682i | \(-0.728760\pi\) | ||||
−0.658384 | + | 0.752682i | \(0.728760\pi\) | |||||||
\(102\) | 6.12006e6 | 0.571025 | ||||||||
\(103\) | −1.13321e7 | −1.02183 | −0.510915 | − | 0.859631i | \(-0.670693\pi\) | ||||
−0.510915 | + | 0.859631i | \(0.670693\pi\) | |||||||
\(104\) | 24561.6 | 0.00214111 | ||||||||
\(105\) | 3.77898e6 | 0.318575 | ||||||||
\(106\) | −1.52849e7 | −1.24650 | ||||||||
\(107\) | −1.30823e7 | −1.03239 | −0.516193 | − | 0.856472i | \(-0.672651\pi\) | ||||
−0.516193 | + | 0.856472i | \(0.672651\pi\) | |||||||
\(108\) | 1.25971e6 | 0.0962250 | ||||||||
\(109\) | 364392. | 0.0269510 | 0.0134755 | − | 0.999909i | \(-0.495710\pi\) | ||||
0.0134755 | + | 0.999909i | \(0.495710\pi\) | |||||||
\(110\) | −1.72545e6 | −0.123603 | ||||||||
\(111\) | 8.33986e6 | 0.578800 | ||||||||
\(112\) | −4.58628e6 | −0.308459 | ||||||||
\(113\) | 7.56438e6 | 0.493173 | 0.246586 | − | 0.969121i | \(-0.420691\pi\) | ||||
0.246586 | + | 0.969121i | \(0.420691\pi\) | |||||||
\(114\) | 1.48154e6 | 0.0936586 | ||||||||
\(115\) | 1.06307e7 | 0.651807 | ||||||||
\(116\) | −1.10902e6 | −0.0659682 | ||||||||
\(117\) | 34971.5 | 0.00201866 | ||||||||
\(118\) | 902927. | 0.0505901 | ||||||||
\(119\) | −3.17251e7 | −1.72579 | ||||||||
\(120\) | −1.72800e6 | −0.0912871 | ||||||||
\(121\) | −1.65100e7 | −0.847224 | ||||||||
\(122\) | −9.05725e6 | −0.451582 | ||||||||
\(123\) | 5.97138e6 | 0.289339 | ||||||||
\(124\) | −1.18712e7 | −0.559139 | ||||||||
\(125\) | −1.95312e6 | −0.0894427 | ||||||||
\(126\) | −6.53008e6 | −0.290818 | ||||||||
\(127\) | −1.18095e7 | −0.511586 | −0.255793 | − | 0.966732i | \(-0.582337\pi\) | ||||
−0.255793 | + | 0.966732i | \(0.582337\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −6.40159e6 | −0.262557 | ||||||||
\(130\) | −47971.8 | −0.00191507 | ||||||||
\(131\) | 1.45149e7 | 0.564109 | 0.282055 | − | 0.959398i | \(-0.408984\pi\) | ||||
0.282055 | + | 0.959398i | \(0.408984\pi\) | |||||||
\(132\) | 2.98158e6 | 0.112833 | ||||||||
\(133\) | −7.68001e6 | −0.283062 | ||||||||
\(134\) | 1.13604e6 | 0.0407874 | ||||||||
\(135\) | −2.46038e6 | −0.0860663 | ||||||||
\(136\) | 1.45068e7 | 0.494522 | ||||||||
\(137\) | −5.09194e7 | −1.69185 | −0.845924 | − | 0.533304i | \(-0.820950\pi\) | ||||
−0.845924 | + | 0.533304i | \(0.820950\pi\) | |||||||
\(138\) | −1.83698e7 | −0.595016 | ||||||||
\(139\) | 1.66451e7 | 0.525695 | 0.262848 | − | 0.964837i | \(-0.415338\pi\) | ||||
0.262848 | + | 0.964837i | \(0.415338\pi\) | |||||||
\(140\) | 8.95758e6 | 0.275894 | ||||||||
\(141\) | 1.79843e7 | 0.540290 | ||||||||
\(142\) | −2.09474e7 | −0.613933 | ||||||||
\(143\) | 82773.1 | 0.00236708 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | 2.16605e6 | 0.0590038 | ||||||||
\(146\) | −1.01976e7 | −0.271185 | ||||||||
\(147\) | 1.16149e7 | 0.301581 | ||||||||
\(148\) | 1.97686e7 | 0.501255 | ||||||||
\(149\) | −1.37603e7 | −0.340782 | −0.170391 | − | 0.985377i | \(-0.554503\pi\) | ||||
−0.170391 | + | 0.985377i | \(0.554503\pi\) | |||||||
\(150\) | 3.37500e6 | 0.0816497 | ||||||||
\(151\) | 2.19402e7 | 0.518585 | 0.259293 | − | 0.965799i | \(-0.416511\pi\) | ||||
0.259293 | + | 0.965799i | \(0.416511\pi\) | |||||||
\(152\) | 3.51181e6 | 0.0811107 | ||||||||
\(153\) | 2.06552e7 | 0.466240 | ||||||||
\(154\) | −1.54559e7 | −0.341013 | ||||||||
\(155\) | 2.31860e7 | 0.500110 | ||||||||
\(156\) | 82895.3 | 0.00174821 | ||||||||
\(157\) | 5.42084e7 | 1.11794 | 0.558969 | − | 0.829189i | \(-0.311197\pi\) | ||||
0.558969 | + | 0.829189i | \(0.311197\pi\) | |||||||
\(158\) | 4.31516e7 | 0.870356 | ||||||||
\(159\) | −5.15867e7 | −1.01777 | ||||||||
\(160\) | −4.09600e6 | −0.0790569 | ||||||||
\(161\) | 9.52253e7 | 1.79830 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | 4.59104e7 | 0.830336 | 0.415168 | − | 0.909745i | \(-0.363723\pi\) | ||||
0.415168 | + | 0.909745i | \(0.363723\pi\) | |||||||
\(164\) | 1.41544e7 | 0.250575 | ||||||||
\(165\) | −5.82340e6 | −0.100921 | ||||||||
\(166\) | −2.17934e7 | −0.369782 | ||||||||
\(167\) | −2.68258e7 | −0.445703 | −0.222851 | − | 0.974852i | \(-0.571536\pi\) | ||||
−0.222851 | + | 0.974852i | \(0.571536\pi\) | |||||||
\(168\) | −1.54787e7 | −0.251856 | ||||||||
\(169\) | −6.27462e7 | −0.999963 | ||||||||
\(170\) | −2.83336e7 | −0.442314 | ||||||||
\(171\) | 5.00021e6 | 0.0764719 | ||||||||
\(172\) | −1.51741e7 | −0.227381 | ||||||||
\(173\) | −1.06963e6 | −0.0157063 | −0.00785314 | − | 0.999969i | \(-0.502500\pi\) | ||||
−0.00785314 | + | 0.999969i | \(0.502500\pi\) | |||||||
\(174\) | −3.74293e6 | −0.0538628 | ||||||||
\(175\) | −1.74953e7 | −0.246767 | ||||||||
\(176\) | 7.06745e6 | 0.0977166 | ||||||||
\(177\) | 3.04738e6 | 0.0413066 | ||||||||
\(178\) | −6.42789e7 | −0.854277 | ||||||||
\(179\) | −1.03267e8 | −1.34578 | −0.672892 | − | 0.739740i | \(-0.734948\pi\) | ||||
−0.672892 | + | 0.739740i | \(0.734948\pi\) | |||||||
\(180\) | −5.83200e6 | −0.0745356 | ||||||||
\(181\) | −1.56751e8 | −1.96488 | −0.982440 | − | 0.186577i | \(-0.940261\pi\) | ||||
−0.982440 | + | 0.186577i | \(0.940261\pi\) | |||||||
\(182\) | −429712. | −0.00528357 | ||||||||
\(183\) | −3.05682e7 | −0.368715 | ||||||||
\(184\) | −4.35433e7 | −0.515299 | ||||||||
\(185\) | −3.86105e7 | −0.448336 | ||||||||
\(186\) | −4.00654e7 | −0.456535 | ||||||||
\(187\) | 4.88883e7 | 0.546713 | ||||||||
\(188\) | 4.26295e7 | 0.467905 | ||||||||
\(189\) | −2.20390e7 | −0.237452 | ||||||||
\(190\) | −6.85900e6 | −0.0725476 | ||||||||
\(191\) | −7.99566e7 | −0.830305 | −0.415153 | − | 0.909752i | \(-0.636272\pi\) | ||||
−0.415153 | + | 0.909752i | \(0.636272\pi\) | |||||||
\(192\) | 7.07789e6 | 0.0721688 | ||||||||
\(193\) | 4.45266e7 | 0.445830 | 0.222915 | − | 0.974838i | \(-0.428443\pi\) | ||||
0.222915 | + | 0.974838i | \(0.428443\pi\) | |||||||
\(194\) | −7.97441e7 | −0.784138 | ||||||||
\(195\) | −161905. | −0.00156365 | ||||||||
\(196\) | 2.75315e7 | 0.261176 | ||||||||
\(197\) | 5.51428e7 | 0.513875 | 0.256937 | − | 0.966428i | \(-0.417287\pi\) | ||||
0.256937 | + | 0.966428i | \(0.417287\pi\) | |||||||
\(198\) | 1.00628e7 | 0.0921281 | ||||||||
\(199\) | −1.74844e7 | −0.157277 | −0.0786385 | − | 0.996903i | \(-0.525057\pi\) | ||||
−0.0786385 | + | 0.996903i | \(0.525057\pi\) | |||||||
\(200\) | 8.00000e6 | 0.0707107 | ||||||||
\(201\) | 3.83412e6 | 0.0333027 | ||||||||
\(202\) | −1.09075e8 | −0.931096 | ||||||||
\(203\) | 1.94025e7 | 0.162788 | ||||||||
\(204\) | 4.89605e7 | 0.403776 | ||||||||
\(205\) | −2.76453e7 | −0.224121 | ||||||||
\(206\) | −9.06566e7 | −0.722543 | ||||||||
\(207\) | −6.19982e7 | −0.485828 | ||||||||
\(208\) | 196493. | 0.00151400 | ||||||||
\(209\) | 1.18349e7 | 0.0896709 | ||||||||
\(210\) | 3.02318e7 | 0.225267 | ||||||||
\(211\) | 1.44125e8 | 1.05621 | 0.528107 | − | 0.849178i | \(-0.322902\pi\) | ||||
0.528107 | + | 0.849178i | \(0.322902\pi\) | |||||||
\(212\) | −1.22280e8 | −0.881411 | ||||||||
\(213\) | −7.06975e7 | −0.501274 | ||||||||
\(214\) | −1.04659e8 | −0.730007 | ||||||||
\(215\) | 2.96370e7 | 0.203376 | ||||||||
\(216\) | 1.00777e7 | 0.0680414 | ||||||||
\(217\) | 2.07691e8 | 1.37977 | ||||||||
\(218\) | 2.91513e6 | 0.0190573 | ||||||||
\(219\) | −3.44171e7 | −0.221421 | ||||||||
\(220\) | −1.38036e7 | −0.0874004 | ||||||||
\(221\) | 1.35922e6 | 0.00847062 | ||||||||
\(222\) | 6.67189e7 | 0.409273 | ||||||||
\(223\) | 2.00665e8 | 1.21173 | 0.605864 | − | 0.795568i | \(-0.292828\pi\) | ||||
0.605864 | + | 0.795568i | \(0.292828\pi\) | |||||||
\(224\) | −3.66903e7 | −0.218114 | ||||||||
\(225\) | 1.13906e7 | 0.0666667 | ||||||||
\(226\) | 6.05151e7 | 0.348726 | ||||||||
\(227\) | 2.62691e8 | 1.49058 | 0.745288 | − | 0.666742i | \(-0.232312\pi\) | ||||
0.745288 | + | 0.666742i | \(0.232312\pi\) | |||||||
\(228\) | 1.18524e7 | 0.0662266 | ||||||||
\(229\) | −3.03629e8 | −1.67078 | −0.835388 | − | 0.549660i | \(-0.814757\pi\) | ||||
−0.835388 | + | 0.549660i | \(0.814757\pi\) | |||||||
\(230\) | 8.50456e7 | 0.460897 | ||||||||
\(231\) | −5.21636e7 | −0.278436 | ||||||||
\(232\) | −8.87212e6 | −0.0466466 | ||||||||
\(233\) | 7.52452e7 | 0.389703 | 0.194851 | − | 0.980833i | \(-0.437578\pi\) | ||||
0.194851 | + | 0.980833i | \(0.437578\pi\) | |||||||
\(234\) | 279772. | 0.00142741 | ||||||||
\(235\) | −8.32608e7 | −0.418507 | ||||||||
\(236\) | 7.22341e6 | 0.0357726 | ||||||||
\(237\) | 1.45637e8 | 0.710642 | ||||||||
\(238\) | −2.53801e8 | −1.22032 | ||||||||
\(239\) | 1.17291e8 | 0.555741 | 0.277870 | − | 0.960619i | \(-0.410371\pi\) | ||||
0.277870 | + | 0.960619i | \(0.410371\pi\) | |||||||
\(240\) | −1.38240e7 | −0.0645497 | ||||||||
\(241\) | −1.81339e8 | −0.834509 | −0.417254 | − | 0.908790i | \(-0.637008\pi\) | ||||
−0.417254 | + | 0.908790i | \(0.637008\pi\) | |||||||
\(242\) | −1.32080e8 | −0.599077 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −7.24580e7 | −0.319317 | ||||||||
\(245\) | −5.37725e7 | −0.233603 | ||||||||
\(246\) | 4.77710e7 | 0.204593 | ||||||||
\(247\) | 329039. | 0.00138934 | ||||||||
\(248\) | −9.49699e7 | −0.395371 | ||||||||
\(249\) | −7.35526e7 | −0.301926 | ||||||||
\(250\) | −1.56250e7 | −0.0632456 | ||||||||
\(251\) | 2.98853e8 | 1.19289 | 0.596445 | − | 0.802654i | \(-0.296579\pi\) | ||||
0.596445 | + | 0.802654i | \(0.296579\pi\) | |||||||
\(252\) | −5.22406e7 | −0.205639 | ||||||||
\(253\) | −1.46742e8 | −0.569682 | ||||||||
\(254\) | −9.44761e7 | −0.361746 | ||||||||
\(255\) | −9.56260e7 | −0.361148 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −3.78646e8 | −1.39145 | −0.695725 | − | 0.718308i | \(-0.744917\pi\) | ||||
−0.695725 | + | 0.718308i | \(0.744917\pi\) | |||||||
\(258\) | −5.12127e7 | −0.185656 | ||||||||
\(259\) | −3.45856e8 | −1.23693 | ||||||||
\(260\) | −383775. | −0.00135416 | ||||||||
\(261\) | −1.26324e7 | −0.0439788 | ||||||||
\(262\) | 1.16119e8 | 0.398885 | ||||||||
\(263\) | 5.17351e8 | 1.75364 | 0.876819 | − | 0.480821i | \(-0.159661\pi\) | ||||
0.876819 | + | 0.480821i | \(0.159661\pi\) | |||||||
\(264\) | 2.38526e7 | 0.0797853 | ||||||||
\(265\) | 2.38827e8 | 0.788358 | ||||||||
\(266\) | −6.14401e7 | −0.200155 | ||||||||
\(267\) | −2.16941e8 | −0.697514 | ||||||||
\(268\) | 9.08829e6 | 0.0288410 | ||||||||
\(269\) | 1.92975e8 | 0.604461 | 0.302230 | − | 0.953235i | \(-0.402269\pi\) | ||||
0.302230 | + | 0.953235i | \(0.402269\pi\) | |||||||
\(270\) | −1.96830e7 | −0.0608581 | ||||||||
\(271\) | −2.99352e8 | −0.913669 | −0.456835 | − | 0.889552i | \(-0.651017\pi\) | ||||
−0.456835 | + | 0.889552i | \(0.651017\pi\) | |||||||
\(272\) | 1.16055e8 | 0.349680 | ||||||||
\(273\) | −1.45028e6 | −0.00431402 | ||||||||
\(274\) | −4.07355e8 | −1.19632 | ||||||||
\(275\) | 2.69602e7 | 0.0781733 | ||||||||
\(276\) | −1.46959e8 | −0.420740 | ||||||||
\(277\) | −5.02737e8 | −1.42122 | −0.710610 | − | 0.703586i | \(-0.751581\pi\) | ||||
−0.710610 | + | 0.703586i | \(0.751581\pi\) | |||||||
\(278\) | 1.33161e8 | 0.371723 | ||||||||
\(279\) | −1.35221e8 | −0.372760 | ||||||||
\(280\) | 7.16607e7 | 0.195087 | ||||||||
\(281\) | 3.05398e8 | 0.821095 | 0.410548 | − | 0.911839i | \(-0.365338\pi\) | ||||
0.410548 | + | 0.911839i | \(0.365338\pi\) | |||||||
\(282\) | 1.43875e8 | 0.382043 | ||||||||
\(283\) | −5.40221e8 | −1.41683 | −0.708417 | − | 0.705795i | \(-0.750590\pi\) | ||||
−0.708417 | + | 0.705795i | \(0.750590\pi\) | |||||||
\(284\) | −1.67579e8 | −0.434116 | ||||||||
\(285\) | −2.31491e7 | −0.0592349 | ||||||||
\(286\) | 662184. | 0.00167378 | ||||||||
\(287\) | −2.47635e8 | −0.618337 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | 3.92455e8 | 0.956418 | ||||||||
\(290\) | 1.73284e7 | 0.0417220 | ||||||||
\(291\) | −2.69136e8 | −0.640246 | ||||||||
\(292\) | −8.15812e7 | −0.191756 | ||||||||
\(293\) | −2.78333e8 | −0.646440 | −0.323220 | − | 0.946324i | \(-0.604765\pi\) | ||||
−0.323220 | + | 0.946324i | \(0.604765\pi\) | |||||||
\(294\) | 9.29189e7 | 0.213250 | ||||||||
\(295\) | −1.41082e7 | −0.0319960 | ||||||||
\(296\) | 1.58148e8 | 0.354441 | ||||||||
\(297\) | 3.39621e7 | 0.0752223 | ||||||||
\(298\) | −1.10082e8 | −0.240969 | ||||||||
\(299\) | −4.07979e6 | −0.00882651 | ||||||||
\(300\) | 2.70000e7 | 0.0577350 | ||||||||
\(301\) | 2.65476e8 | 0.561102 | ||||||||
\(302\) | 1.75521e8 | 0.366695 | ||||||||
\(303\) | −3.68127e8 | −0.760237 | ||||||||
\(304\) | 2.80945e7 | 0.0573539 | ||||||||
\(305\) | 1.41520e8 | 0.285606 | ||||||||
\(306\) | 1.65242e8 | 0.329681 | ||||||||
\(307\) | 4.49571e8 | 0.886777 | 0.443388 | − | 0.896330i | \(-0.353776\pi\) | ||||
0.443388 | + | 0.896330i | \(0.353776\pi\) | |||||||
\(308\) | −1.23647e8 | −0.241133 | ||||||||
\(309\) | −3.05966e8 | −0.589954 | ||||||||
\(310\) | 1.85488e8 | 0.353631 | ||||||||
\(311\) | −7.75155e8 | −1.46126 | −0.730629 | − | 0.682775i | \(-0.760773\pi\) | ||||
−0.730629 | + | 0.682775i | \(0.760773\pi\) | |||||||
\(312\) | 663163. | 0.00123617 | ||||||||
\(313\) | 1.99952e8 | 0.368570 | 0.184285 | − | 0.982873i | \(-0.441003\pi\) | ||||
0.184285 | + | 0.982873i | \(0.441003\pi\) | |||||||
\(314\) | 4.33667e8 | 0.790502 | ||||||||
\(315\) | 1.02032e8 | 0.183930 | ||||||||
\(316\) | 3.45213e8 | 0.615434 | ||||||||
\(317\) | −7.21290e8 | −1.27175 | −0.635876 | − | 0.771791i | \(-0.719361\pi\) | ||||
−0.635876 | + | 0.771791i | \(0.719361\pi\) | |||||||
\(318\) | −4.12693e8 | −0.719669 | ||||||||
\(319\) | −2.98993e7 | −0.0515695 | ||||||||
\(320\) | −3.27680e7 | −0.0559017 | ||||||||
\(321\) | −3.53223e8 | −0.596048 | ||||||||
\(322\) | 7.61803e8 | 1.27159 | ||||||||
\(323\) | 1.94340e8 | 0.320888 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | 749560. | 0.00121120 | ||||||||
\(326\) | 3.67283e8 | 0.587136 | ||||||||
\(327\) | 9.83857e6 | 0.0155602 | ||||||||
\(328\) | 1.13235e8 | 0.177183 | ||||||||
\(329\) | −7.45815e8 | −1.15464 | ||||||||
\(330\) | −4.65872e7 | −0.0713621 | ||||||||
\(331\) | 2.46711e8 | 0.373930 | 0.186965 | − | 0.982367i | \(-0.440135\pi\) | ||||
0.186965 | + | 0.982367i | \(0.440135\pi\) | |||||||
\(332\) | −1.74347e8 | −0.261475 | ||||||||
\(333\) | 2.25176e8 | 0.334170 | ||||||||
\(334\) | −2.14607e8 | −0.315160 | ||||||||
\(335\) | −1.77506e7 | −0.0257962 | ||||||||
\(336\) | −1.23830e8 | −0.178089 | ||||||||
\(337\) | 8.10307e8 | 1.15331 | 0.576654 | − | 0.816989i | \(-0.304358\pi\) | ||||
0.576654 | + | 0.816989i | \(0.304358\pi\) | |||||||
\(338\) | −5.01970e8 | −0.707081 | ||||||||
\(339\) | 2.04238e8 | 0.284733 | ||||||||
\(340\) | −2.26669e8 | −0.312763 | ||||||||
\(341\) | −3.20051e8 | −0.437098 | ||||||||
\(342\) | 4.00017e7 | 0.0540738 | ||||||||
\(343\) | 4.40448e8 | 0.589338 | ||||||||
\(344\) | −1.21393e8 | −0.160783 | ||||||||
\(345\) | 2.87029e8 | 0.376321 | ||||||||
\(346\) | −8.55706e6 | −0.0111060 | ||||||||
\(347\) | −1.29901e9 | −1.66901 | −0.834503 | − | 0.551004i | \(-0.814245\pi\) | ||||
−0.834503 | + | 0.551004i | \(0.814245\pi\) | |||||||
\(348\) | −2.99434e7 | −0.0380868 | ||||||||
\(349\) | 1.12893e7 | 0.0142160 | 0.00710802 | − | 0.999975i | \(-0.497737\pi\) | ||||
0.00710802 | + | 0.999975i | \(0.497737\pi\) | |||||||
\(350\) | −1.39962e8 | −0.174491 | ||||||||
\(351\) | 944230. | 0.00116547 | ||||||||
\(352\) | 5.65396e7 | 0.0690961 | ||||||||
\(353\) | −2.91341e8 | −0.352525 | −0.176262 | − | 0.984343i | \(-0.556401\pi\) | ||||
−0.176262 | + | 0.984343i | \(0.556401\pi\) | |||||||
\(354\) | 2.43790e7 | 0.0292082 | ||||||||
\(355\) | 3.27303e8 | 0.388285 | ||||||||
\(356\) | −5.14231e8 | −0.604065 | ||||||||
\(357\) | −8.56577e8 | −0.996387 | ||||||||
\(358\) | −8.26135e8 | −0.951614 | ||||||||
\(359\) | 1.27308e9 | 1.45219 | 0.726097 | − | 0.687593i | \(-0.241332\pi\) | ||||
0.726097 | + | 0.687593i | \(0.241332\pi\) | |||||||
\(360\) | −4.66560e7 | −0.0527046 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | −1.25401e9 | −1.38938 | ||||||||
\(363\) | −4.45770e8 | −0.489145 | ||||||||
\(364\) | −3.43769e6 | −0.00373605 | ||||||||
\(365\) | 1.59338e8 | 0.171512 | ||||||||
\(366\) | −2.44546e8 | −0.260721 | ||||||||
\(367\) | −5.18592e8 | −0.547640 | −0.273820 | − | 0.961781i | \(-0.588287\pi\) | ||||
−0.273820 | + | 0.961781i | \(0.588287\pi\) | |||||||
\(368\) | −3.48347e8 | −0.364371 | ||||||||
\(369\) | 1.61227e8 | 0.167050 | ||||||||
\(370\) | −3.08884e8 | −0.317022 | ||||||||
\(371\) | 2.13931e9 | 2.17503 | ||||||||
\(372\) | −3.20523e8 | −0.322819 | ||||||||
\(373\) | 1.45203e9 | 1.44876 | 0.724379 | − | 0.689402i | \(-0.242127\pi\) | ||||
0.724379 | + | 0.689402i | \(0.242127\pi\) | |||||||
\(374\) | 3.91106e8 | 0.386584 | ||||||||
\(375\) | −5.27344e7 | −0.0516398 | ||||||||
\(376\) | 3.41036e8 | 0.330859 | ||||||||
\(377\) | −831274. | −0.000799005 0 | ||||||||
\(378\) | −1.76312e8 | −0.167904 | ||||||||
\(379\) | 9.42327e8 | 0.889128 | 0.444564 | − | 0.895747i | \(-0.353359\pi\) | ||||
0.444564 | + | 0.895747i | \(0.353359\pi\) | |||||||
\(380\) | −5.48720e7 | −0.0512989 | ||||||||
\(381\) | −3.18857e8 | −0.295365 | ||||||||
\(382\) | −6.39653e8 | −0.587114 | ||||||||
\(383\) | −1.39307e8 | −0.126700 | −0.0633502 | − | 0.997991i | \(-0.520178\pi\) | ||||
−0.0633502 | + | 0.997991i | \(0.520178\pi\) | |||||||
\(384\) | 5.66231e7 | 0.0510310 | ||||||||
\(385\) | 2.41498e8 | 0.215676 | ||||||||
\(386\) | 3.56213e8 | 0.315249 | ||||||||
\(387\) | −1.72843e8 | −0.151587 | ||||||||
\(388\) | −6.37953e8 | −0.554469 | ||||||||
\(389\) | −1.31288e9 | −1.13084 | −0.565421 | − | 0.824803i | \(-0.691286\pi\) | ||||
−0.565421 | + | 0.824803i | \(0.691286\pi\) | |||||||
\(390\) | −1.29524e6 | −0.00110567 | ||||||||
\(391\) | −2.40965e9 | −2.03861 | ||||||||
\(392\) | 2.20252e8 | 0.184680 | ||||||||
\(393\) | 3.91901e8 | 0.325689 | ||||||||
\(394\) | 4.41143e8 | 0.363364 | ||||||||
\(395\) | −6.74243e8 | −0.550461 | ||||||||
\(396\) | 8.05027e7 | 0.0651444 | ||||||||
\(397\) | 1.47480e8 | 0.118295 | 0.0591475 | − | 0.998249i | \(-0.481162\pi\) | ||||
0.0591475 | + | 0.998249i | \(0.481162\pi\) | |||||||
\(398\) | −1.39875e8 | −0.111212 | ||||||||
\(399\) | −2.07360e8 | −0.163426 | ||||||||
\(400\) | 6.40000e7 | 0.0500000 | ||||||||
\(401\) | −1.79473e9 | −1.38994 | −0.694968 | − | 0.719041i | \(-0.744581\pi\) | ||||
−0.694968 | + | 0.719041i | \(0.744581\pi\) | |||||||
\(402\) | 3.06730e7 | 0.0235486 | ||||||||
\(403\) | −8.89821e6 | −0.00677228 | ||||||||
\(404\) | −8.72598e8 | −0.658384 | ||||||||
\(405\) | −6.64301e7 | −0.0496904 | ||||||||
\(406\) | 1.55220e8 | 0.115108 | ||||||||
\(407\) | 5.32964e8 | 0.391848 | ||||||||
\(408\) | 3.91684e8 | 0.285513 | ||||||||
\(409\) | −1.25791e8 | −0.0909111 | −0.0454556 | − | 0.998966i | \(-0.514474\pi\) | ||||
−0.0454556 | + | 0.998966i | \(0.514474\pi\) | |||||||
\(410\) | −2.21162e8 | −0.158477 | ||||||||
\(411\) | −1.37482e9 | −0.976788 | ||||||||
\(412\) | −7.25252e8 | −0.510915 | ||||||||
\(413\) | −1.26376e8 | −0.0882751 | ||||||||
\(414\) | −4.95986e8 | −0.343533 | ||||||||
\(415\) | 3.40521e8 | 0.233871 | ||||||||
\(416\) | 1.57194e6 | 0.00107056 | ||||||||
\(417\) | 4.49417e8 | 0.303510 | ||||||||
\(418\) | 9.46790e7 | 0.0634069 | ||||||||
\(419\) | −8.86373e8 | −0.588664 | −0.294332 | − | 0.955703i | \(-0.595097\pi\) | ||||
−0.294332 | + | 0.955703i | \(0.595097\pi\) | |||||||
\(420\) | 2.41855e8 | 0.159288 | ||||||||
\(421\) | −1.84141e9 | −1.20272 | −0.601360 | − | 0.798979i | \(-0.705374\pi\) | ||||
−0.601360 | + | 0.798979i | \(0.705374\pi\) | |||||||
\(422\) | 1.15300e9 | 0.746856 | ||||||||
\(423\) | 4.85577e8 | 0.311937 | ||||||||
\(424\) | −9.78236e8 | −0.623251 | ||||||||
\(425\) | 4.42713e8 | 0.279744 | ||||||||
\(426\) | −5.65580e8 | −0.354454 | ||||||||
\(427\) | 1.26767e9 | 0.787970 | ||||||||
\(428\) | −8.37269e8 | −0.516193 | ||||||||
\(429\) | 2.23487e6 | 0.00136663 | ||||||||
\(430\) | 2.37096e8 | 0.143808 | ||||||||
\(431\) | 1.87364e9 | 1.12724 | 0.563620 | − | 0.826034i | \(-0.309408\pi\) | ||||
0.563620 | + | 0.826034i | \(0.309408\pi\) | |||||||
\(432\) | 8.06216e7 | 0.0481125 | ||||||||
\(433\) | 7.91307e7 | 0.0468422 | 0.0234211 | − | 0.999726i | \(-0.492544\pi\) | ||||
0.0234211 | + | 0.999726i | \(0.492544\pi\) | |||||||
\(434\) | 1.66153e9 | 0.975647 | ||||||||
\(435\) | 5.84832e7 | 0.0340658 | ||||||||
\(436\) | 2.33211e7 | 0.0134755 | ||||||||
\(437\) | −5.83327e8 | −0.334370 | ||||||||
\(438\) | −2.75336e8 | −0.156568 | ||||||||
\(439\) | 1.65113e9 | 0.931439 | 0.465720 | − | 0.884932i | \(-0.345796\pi\) | ||||
0.465720 | + | 0.884932i | \(0.345796\pi\) | |||||||
\(440\) | −1.10429e8 | −0.0618014 | ||||||||
\(441\) | 3.13601e8 | 0.174118 | ||||||||
\(442\) | 1.08737e7 | 0.00598964 | ||||||||
\(443\) | −6.31651e8 | −0.345195 | −0.172597 | − | 0.984992i | \(-0.555216\pi\) | ||||
−0.172597 | + | 0.984992i | \(0.555216\pi\) | |||||||
\(444\) | 5.33751e8 | 0.289400 | ||||||||
\(445\) | 1.00436e9 | 0.540292 | ||||||||
\(446\) | 1.60532e9 | 0.856821 | ||||||||
\(447\) | −3.71528e8 | −0.196750 | ||||||||
\(448\) | −2.93522e8 | −0.154230 | ||||||||
\(449\) | 1.33505e9 | 0.696042 | 0.348021 | − | 0.937487i | \(-0.386854\pi\) | ||||
0.348021 | + | 0.937487i | \(0.386854\pi\) | |||||||
\(450\) | 9.11250e7 | 0.0471405 | ||||||||
\(451\) | 3.81604e8 | 0.195882 | ||||||||
\(452\) | 4.84121e8 | 0.246586 | ||||||||
\(453\) | 5.92384e8 | 0.299405 | ||||||||
\(454\) | 2.10153e9 | 1.05400 | ||||||||
\(455\) | 6.71424e6 | 0.00334162 | ||||||||
\(456\) | 9.48188e7 | 0.0468293 | ||||||||
\(457\) | 1.49804e9 | 0.734205 | 0.367103 | − | 0.930180i | \(-0.380350\pi\) | ||||
0.367103 | + | 0.930180i | \(0.380350\pi\) | |||||||
\(458\) | −2.42903e9 | −1.18142 | ||||||||
\(459\) | 5.57691e8 | 0.269184 | ||||||||
\(460\) | 6.80364e8 | 0.325904 | ||||||||
\(461\) | −1.75477e9 | −0.834195 | −0.417098 | − | 0.908862i | \(-0.636953\pi\) | ||||
−0.417098 | + | 0.908862i | \(0.636953\pi\) | |||||||
\(462\) | −4.17309e8 | −0.196884 | ||||||||
\(463\) | −4.17524e8 | −0.195500 | −0.0977502 | − | 0.995211i | \(-0.531165\pi\) | ||||
−0.0977502 | + | 0.995211i | \(0.531165\pi\) | |||||||
\(464\) | −7.09770e7 | −0.0329841 | ||||||||
\(465\) | 6.26022e8 | 0.288738 | ||||||||
\(466\) | 6.01962e8 | 0.275561 | ||||||||
\(467\) | 2.65812e9 | 1.20772 | 0.603858 | − | 0.797092i | \(-0.293629\pi\) | ||||
0.603858 | + | 0.797092i | \(0.293629\pi\) | |||||||
\(468\) | 2.23817e6 | 0.00100933 | ||||||||
\(469\) | −1.59002e8 | −0.0711702 | ||||||||
\(470\) | −6.66086e8 | −0.295929 | ||||||||
\(471\) | 1.46363e9 | 0.645442 | ||||||||
\(472\) | 5.77873e7 | 0.0252950 | ||||||||
\(473\) | −4.09097e8 | −0.177751 | ||||||||
\(474\) | 1.16509e9 | 0.502500 | ||||||||
\(475\) | 1.07172e8 | 0.0458831 | ||||||||
\(476\) | −2.03041e9 | −0.862896 | ||||||||
\(477\) | −1.39284e9 | −0.587607 | ||||||||
\(478\) | 9.38329e8 | 0.392968 | ||||||||
\(479\) | −1.77848e9 | −0.739391 | −0.369696 | − | 0.929153i | \(-0.620538\pi\) | ||||
−0.369696 | + | 0.929153i | \(0.620538\pi\) | |||||||
\(480\) | −1.10592e8 | −0.0456435 | ||||||||
\(481\) | 1.48177e7 | 0.00607119 | ||||||||
\(482\) | −1.45071e9 | −0.590087 | ||||||||
\(483\) | 2.57108e9 | 1.03825 | ||||||||
\(484\) | −1.05664e9 | −0.423612 | ||||||||
\(485\) | 1.24600e9 | 0.495932 | ||||||||
\(486\) | 1.14791e8 | 0.0453609 | ||||||||
\(487\) | −1.46602e9 | −0.575161 | −0.287580 | − | 0.957756i | \(-0.592851\pi\) | ||||
−0.287580 | + | 0.957756i | \(0.592851\pi\) | |||||||
\(488\) | −5.79664e8 | −0.225791 | ||||||||
\(489\) | 1.23958e9 | 0.479395 | ||||||||
\(490\) | −4.30180e8 | −0.165183 | ||||||||
\(491\) | 2.85504e9 | 1.08850 | 0.544248 | − | 0.838924i | \(-0.316815\pi\) | ||||
0.544248 | + | 0.838924i | \(0.316815\pi\) | |||||||
\(492\) | 3.82168e8 | 0.144669 | ||||||||
\(493\) | −4.90975e8 | −0.184542 | ||||||||
\(494\) | 2.63231e6 | 0.000982410 0 | ||||||||
\(495\) | −1.57232e8 | −0.0582669 | ||||||||
\(496\) | −7.59759e8 | −0.279570 | ||||||||
\(497\) | 2.93184e9 | 1.07126 | ||||||||
\(498\) | −5.88421e8 | −0.213494 | ||||||||
\(499\) | −3.21188e8 | −0.115720 | −0.0578599 | − | 0.998325i | \(-0.518428\pi\) | ||||
−0.0578599 | + | 0.998325i | \(0.518428\pi\) | |||||||
\(500\) | −1.25000e8 | −0.0447214 | ||||||||
\(501\) | −7.24297e8 | −0.257327 | ||||||||
\(502\) | 2.39083e9 | 0.843500 | ||||||||
\(503\) | −3.27732e9 | −1.14823 | −0.574117 | − | 0.818773i | \(-0.694655\pi\) | ||||
−0.574117 | + | 0.818773i | \(0.694655\pi\) | |||||||
\(504\) | −4.17925e8 | −0.145409 | ||||||||
\(505\) | 1.70429e9 | 0.588877 | ||||||||
\(506\) | −1.17394e9 | −0.402826 | ||||||||
\(507\) | −1.69415e9 | −0.577329 | ||||||||
\(508\) | −7.55809e8 | −0.255793 | ||||||||
\(509\) | 8.75728e8 | 0.294345 | 0.147173 | − | 0.989111i | \(-0.452983\pi\) | ||||
0.147173 | + | 0.989111i | \(0.452983\pi\) | |||||||
\(510\) | −7.65008e8 | −0.255370 | ||||||||
\(511\) | 1.42729e9 | 0.473192 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 1.35006e8 | 0.0441511 | ||||||||
\(514\) | −3.02917e9 | −0.983904 | ||||||||
\(515\) | 1.41651e9 | 0.456977 | ||||||||
\(516\) | −4.09702e8 | −0.131279 | ||||||||
\(517\) | 1.14930e9 | 0.365777 | ||||||||
\(518\) | −2.76685e9 | −0.874645 | ||||||||
\(519\) | −2.88801e7 | −0.00906803 | ||||||||
\(520\) | −3.07020e6 | −0.000957535 0 | ||||||||
\(521\) | 5.04023e9 | 1.56141 | 0.780707 | − | 0.624897i | \(-0.214859\pi\) | ||||
0.780707 | + | 0.624897i | \(0.214859\pi\) | |||||||
\(522\) | −1.01059e8 | −0.0310977 | ||||||||
\(523\) | −3.57359e9 | −1.09232 | −0.546158 | − | 0.837682i | \(-0.683910\pi\) | ||||
−0.546158 | + | 0.837682i | \(0.683910\pi\) | |||||||
\(524\) | 9.28951e8 | 0.282055 | ||||||||
\(525\) | −4.72372e8 | −0.142471 | ||||||||
\(526\) | 4.13880e9 | 1.24001 | ||||||||
\(527\) | −5.25555e9 | −1.56416 | ||||||||
\(528\) | 1.90821e8 | 0.0564167 | ||||||||
\(529\) | 3.82792e9 | 1.12426 | ||||||||
\(530\) | 1.91062e9 | 0.557453 | ||||||||
\(531\) | 8.22792e7 | 0.0238484 | ||||||||
\(532\) | −4.91520e8 | −0.141531 | ||||||||
\(533\) | 1.06096e7 | 0.00303495 | ||||||||
\(534\) | −1.73553e9 | −0.493217 | ||||||||
\(535\) | 1.63529e9 | 0.461697 | ||||||||
\(536\) | 7.27064e7 | 0.0203937 | ||||||||
\(537\) | −2.78821e9 | −0.776989 | ||||||||
\(538\) | 1.54380e9 | 0.427418 | ||||||||
\(539\) | 7.42255e8 | 0.204170 | ||||||||
\(540\) | −1.57464e8 | −0.0430331 | ||||||||
\(541\) | −7.01044e9 | −1.90351 | −0.951755 | − | 0.306860i | \(-0.900722\pi\) | ||||
−0.951755 | + | 0.306860i | \(0.900722\pi\) | |||||||
\(542\) | −2.39481e9 | −0.646062 | ||||||||
\(543\) | −4.23229e9 | −1.13442 | ||||||||
\(544\) | 9.28436e8 | 0.247261 | ||||||||
\(545\) | −4.55490e7 | −0.0120529 | ||||||||
\(546\) | −1.16022e7 | −0.00305047 | ||||||||
\(547\) | 1.11829e9 | 0.292146 | 0.146073 | − | 0.989274i | \(-0.453336\pi\) | ||||
0.146073 | + | 0.989274i | \(0.453336\pi\) | |||||||
\(548\) | −3.25884e9 | −0.845924 | ||||||||
\(549\) | −8.25342e8 | −0.212878 | ||||||||
\(550\) | 2.15681e8 | 0.0552768 | ||||||||
\(551\) | −1.18855e8 | −0.0302683 | ||||||||
\(552\) | −1.17567e9 | −0.297508 | ||||||||
\(553\) | −6.03959e9 | −1.51869 | ||||||||
\(554\) | −4.02190e9 | −1.00495 | ||||||||
\(555\) | −1.04248e9 | −0.258847 | ||||||||
\(556\) | 1.06529e9 | 0.262848 | ||||||||
\(557\) | 4.38631e9 | 1.07549 | 0.537744 | − | 0.843108i | \(-0.319277\pi\) | ||||
0.537744 | + | 0.843108i | \(0.319277\pi\) | |||||||
\(558\) | −1.08177e9 | −0.263581 | ||||||||
\(559\) | −1.13739e7 | −0.00275403 | ||||||||
\(560\) | 5.73285e8 | 0.137947 | ||||||||
\(561\) | 1.31998e9 | 0.315645 | ||||||||
\(562\) | 2.44318e9 | 0.580602 | ||||||||
\(563\) | 3.15070e9 | 0.744093 | 0.372046 | − | 0.928214i | \(-0.378656\pi\) | ||||
0.372046 | + | 0.928214i | \(0.378656\pi\) | |||||||
\(564\) | 1.15100e9 | 0.270145 | ||||||||
\(565\) | −9.45548e8 | −0.220554 | ||||||||
\(566\) | −4.32177e9 | −1.00185 | ||||||||
\(567\) | −5.95053e8 | −0.137093 | ||||||||
\(568\) | −1.34063e9 | −0.306966 | ||||||||
\(569\) | −1.19494e9 | −0.271929 | −0.135964 | − | 0.990714i | \(-0.543413\pi\) | ||||
−0.135964 | + | 0.990714i | \(0.543413\pi\) | |||||||
\(570\) | −1.85193e8 | −0.0418854 | ||||||||
\(571\) | 7.01962e9 | 1.57793 | 0.788964 | − | 0.614440i | \(-0.210618\pi\) | ||||
0.788964 | + | 0.614440i | \(0.210618\pi\) | |||||||
\(572\) | 5.29748e6 | 0.00118354 | ||||||||
\(573\) | −2.15883e9 | −0.479377 | ||||||||
\(574\) | −1.98108e9 | −0.437230 | ||||||||
\(575\) | −1.32884e9 | −0.291497 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | 4.83242e9 | 1.04725 | 0.523624 | − | 0.851950i | \(-0.324580\pi\) | ||||
0.523624 | + | 0.851950i | \(0.324580\pi\) | |||||||
\(578\) | 3.13964e9 | 0.676290 | ||||||||
\(579\) | 1.20222e9 | 0.257400 | ||||||||
\(580\) | 1.38627e8 | 0.0295019 | ||||||||
\(581\) | 3.05025e9 | 0.645236 | ||||||||
\(582\) | −2.15309e9 | −0.452722 | ||||||||
\(583\) | −3.29668e9 | −0.689027 | ||||||||
\(584\) | −6.52649e8 | −0.135592 | ||||||||
\(585\) | −4.37143e6 | −0.000902773 0 | ||||||||
\(586\) | −2.22667e9 | −0.457102 | ||||||||
\(587\) | −3.82091e9 | −0.779711 | −0.389855 | − | 0.920876i | \(-0.627475\pi\) | ||||
−0.389855 | + | 0.920876i | \(0.627475\pi\) | |||||||
\(588\) | 7.43351e8 | 0.150790 | ||||||||
\(589\) | −1.27226e9 | −0.256551 | ||||||||
\(590\) | −1.12866e8 | −0.0226246 | ||||||||
\(591\) | 1.48886e9 | 0.296686 | ||||||||
\(592\) | 1.26519e9 | 0.250628 | ||||||||
\(593\) | 8.54084e9 | 1.68193 | 0.840967 | − | 0.541086i | \(-0.181987\pi\) | ||||
0.840967 | + | 0.541086i | \(0.181987\pi\) | |||||||
\(594\) | 2.71696e8 | 0.0531902 | ||||||||
\(595\) | 3.96564e9 | 0.771798 | ||||||||
\(596\) | −8.80659e8 | −0.170391 | ||||||||
\(597\) | −4.72079e8 | −0.0908040 | ||||||||
\(598\) | −3.26383e7 | −0.00624128 | ||||||||
\(599\) | 5.83250e8 | 0.110882 | 0.0554409 | − | 0.998462i | \(-0.482344\pi\) | ||||
0.0554409 | + | 0.998462i | \(0.482344\pi\) | |||||||
\(600\) | 2.16000e8 | 0.0408248 | ||||||||
\(601\) | 2.26108e9 | 0.424869 | 0.212435 | − | 0.977175i | \(-0.431861\pi\) | ||||
0.212435 | + | 0.977175i | \(0.431861\pi\) | |||||||
\(602\) | 2.12381e9 | 0.396759 | ||||||||
\(603\) | 1.03521e8 | 0.0192273 | ||||||||
\(604\) | 1.40417e9 | 0.259293 | ||||||||
\(605\) | 2.06375e9 | 0.378890 | ||||||||
\(606\) | −2.94502e9 | −0.537568 | ||||||||
\(607\) | −6.08814e9 | −1.10490 | −0.552452 | − | 0.833545i | \(-0.686308\pi\) | ||||
−0.552452 | + | 0.833545i | \(0.686308\pi\) | |||||||
\(608\) | 2.24756e8 | 0.0405554 | ||||||||
\(609\) | 5.23868e8 | 0.0939857 | ||||||||
\(610\) | 1.13216e9 | 0.201954 | ||||||||
\(611\) | 3.19534e7 | 0.00566725 | ||||||||
\(612\) | 1.32193e9 | 0.233120 | ||||||||
\(613\) | 4.36248e9 | 0.764929 | 0.382465 | − | 0.923970i | \(-0.375075\pi\) | ||||
0.382465 | + | 0.923970i | \(0.375075\pi\) | |||||||
\(614\) | 3.59657e9 | 0.627046 | ||||||||
\(615\) | −7.46422e8 | −0.129396 | ||||||||
\(616\) | −9.89176e8 | −0.170507 | ||||||||
\(617\) | −4.74419e9 | −0.813138 | −0.406569 | − | 0.913620i | \(-0.633275\pi\) | ||||
−0.406569 | + | 0.913620i | \(0.633275\pi\) | |||||||
\(618\) | −2.44773e9 | −0.417161 | ||||||||
\(619\) | 5.39704e9 | 0.914615 | 0.457307 | − | 0.889309i | \(-0.348814\pi\) | ||||
0.457307 | + | 0.889309i | \(0.348814\pi\) | |||||||
\(620\) | 1.48390e9 | 0.250055 | ||||||||
\(621\) | −1.67395e9 | −0.280493 | ||||||||
\(622\) | −6.20124e9 | −1.03327 | ||||||||
\(623\) | 8.99662e9 | 1.49064 | ||||||||
\(624\) | 5.30530e6 | 0.000874106 0 | ||||||||
\(625\) | 2.44141e8 | 0.0400000 | ||||||||
\(626\) | 1.59961e9 | 0.260618 | ||||||||
\(627\) | 3.19541e8 | 0.0517715 | ||||||||
\(628\) | 3.46934e9 | 0.558969 | ||||||||
\(629\) | 8.75179e9 | 1.40223 | ||||||||
\(630\) | 8.16260e8 | 0.130058 | ||||||||
\(631\) | −5.46391e9 | −0.865767 | −0.432884 | − | 0.901450i | \(-0.642504\pi\) | ||||
−0.432884 | + | 0.901450i | \(0.642504\pi\) | |||||||
\(632\) | 2.76170e9 | 0.435178 | ||||||||
\(633\) | 3.89139e9 | 0.609806 | ||||||||
\(634\) | −5.77032e9 | −0.899265 | ||||||||
\(635\) | 1.47619e9 | 0.228788 | ||||||||
\(636\) | −3.30155e9 | −0.508883 | ||||||||
\(637\) | 2.06365e7 | 0.00316336 | ||||||||
\(638\) | −2.39194e8 | −0.0364651 | ||||||||
\(639\) | −1.90883e9 | −0.289411 | ||||||||
\(640\) | −2.62144e8 | −0.0395285 | ||||||||
\(641\) | −4.72360e8 | −0.0708386 | −0.0354193 | − | 0.999373i | \(-0.511277\pi\) | ||||
−0.0354193 | + | 0.999373i | \(0.511277\pi\) | |||||||
\(642\) | −2.82578e9 | −0.421470 | ||||||||
\(643\) | 2.26551e8 | 0.0336069 | 0.0168034 | − | 0.999859i | \(-0.494651\pi\) | ||||
0.0168034 | + | 0.999859i | \(0.494651\pi\) | |||||||
\(644\) | 6.09442e9 | 0.899149 | ||||||||
\(645\) | 8.00199e8 | 0.117419 | ||||||||
\(646\) | 1.55472e9 | 0.226902 | ||||||||
\(647\) | 3.86399e9 | 0.560882 | 0.280441 | − | 0.959871i | \(-0.409519\pi\) | ||||
0.280441 | + | 0.959871i | \(0.409519\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | 1.94744e8 | 0.0279646 | ||||||||
\(650\) | 5.99648e6 | 0.000856445 0 | ||||||||
\(651\) | 5.60765e9 | 0.796613 | ||||||||
\(652\) | 2.93826e9 | 0.415168 | ||||||||
\(653\) | 7.63350e9 | 1.07282 | 0.536411 | − | 0.843957i | \(-0.319780\pi\) | ||||
0.536411 | + | 0.843957i | \(0.319780\pi\) | |||||||
\(654\) | 7.87086e7 | 0.0110027 | ||||||||
\(655\) | −1.81436e9 | −0.252277 | ||||||||
\(656\) | 9.05880e8 | 0.125287 | ||||||||
\(657\) | −9.29260e8 | −0.127838 | ||||||||
\(658\) | −5.96652e9 | −0.816452 | ||||||||
\(659\) | 9.98595e9 | 1.35922 | 0.679611 | − | 0.733573i | \(-0.262149\pi\) | ||||
0.679611 | + | 0.733573i | \(0.262149\pi\) | |||||||
\(660\) | −3.72697e8 | −0.0504606 | ||||||||
\(661\) | 3.98575e9 | 0.536791 | 0.268395 | − | 0.963309i | \(-0.413507\pi\) | ||||
0.268395 | + | 0.963309i | \(0.413507\pi\) | |||||||
\(662\) | 1.97369e9 | 0.264408 | ||||||||
\(663\) | 3.66988e7 | 0.00489052 | ||||||||
\(664\) | −1.39478e9 | −0.184891 | ||||||||
\(665\) | 9.60001e8 | 0.126589 | ||||||||
\(666\) | 1.80141e9 | 0.236294 | ||||||||
\(667\) | 1.47370e9 | 0.192295 | ||||||||
\(668\) | −1.71685e9 | −0.222851 | ||||||||
\(669\) | 5.41796e9 | 0.699591 | ||||||||
\(670\) | −1.42005e8 | −0.0182407 | ||||||||
\(671\) | −1.95348e9 | −0.249620 | ||||||||
\(672\) | −9.90637e8 | −0.125928 | ||||||||
\(673\) | 1.74903e9 | 0.221180 | 0.110590 | − | 0.993866i | \(-0.464726\pi\) | ||||
0.110590 | + | 0.993866i | \(0.464726\pi\) | |||||||
\(674\) | 6.48246e9 | 0.815512 | ||||||||
\(675\) | 3.07547e8 | 0.0384900 | ||||||||
\(676\) | −4.01576e9 | −0.499982 | ||||||||
\(677\) | 3.50541e9 | 0.434189 | 0.217094 | − | 0.976151i | \(-0.430342\pi\) | ||||
0.217094 | + | 0.976151i | \(0.430342\pi\) | |||||||
\(678\) | 1.63391e9 | 0.201337 | ||||||||
\(679\) | 1.11612e10 | 1.36825 | ||||||||
\(680\) | −1.81335e9 | −0.221157 | ||||||||
\(681\) | 7.09265e9 | 0.860585 | ||||||||
\(682\) | −2.56041e9 | −0.309075 | ||||||||
\(683\) | 3.54964e8 | 0.0426297 | 0.0213148 | − | 0.999773i | \(-0.493215\pi\) | ||||
0.0213148 | + | 0.999773i | \(0.493215\pi\) | |||||||
\(684\) | 3.20014e8 | 0.0382360 | ||||||||
\(685\) | 6.36492e9 | 0.756617 | ||||||||
\(686\) | 3.52358e9 | 0.416725 | ||||||||
\(687\) | −8.19797e9 | −0.964624 | ||||||||
\(688\) | −9.71145e8 | −0.113691 | ||||||||
\(689\) | −9.16558e7 | −0.0106756 | ||||||||
\(690\) | 2.29623e9 | 0.266099 | ||||||||
\(691\) | −5.81392e9 | −0.670342 | −0.335171 | − | 0.942157i | \(-0.608794\pi\) | ||||
−0.335171 | + | 0.942157i | \(0.608794\pi\) | |||||||
\(692\) | −6.84565e7 | −0.00785314 | ||||||||
\(693\) | −1.40842e9 | −0.160755 | ||||||||
\(694\) | −1.03920e10 | −1.18016 | ||||||||
\(695\) | −2.08064e9 | −0.235098 | ||||||||
\(696\) | −2.39547e8 | −0.0269314 | ||||||||
\(697\) | 6.26632e9 | 0.700968 | ||||||||
\(698\) | 9.03145e7 | 0.0100523 | ||||||||
\(699\) | 2.03162e9 | 0.224995 | ||||||||
\(700\) | −1.11970e9 | −0.123384 | ||||||||
\(701\) | 1.45880e10 | 1.59949 | 0.799747 | − | 0.600338i | \(-0.204967\pi\) | ||||
0.799747 | + | 0.600338i | \(0.204967\pi\) | |||||||
\(702\) | 7.55384e6 | 0.000824115 0 | ||||||||
\(703\) | 2.11863e9 | 0.229992 | ||||||||
\(704\) | 4.52317e8 | 0.0488583 | ||||||||
\(705\) | −2.24804e9 | −0.241625 | ||||||||
\(706\) | −2.33073e9 | −0.249273 | ||||||||
\(707\) | 1.52663e10 | 1.62468 | ||||||||
\(708\) | 1.95032e8 | 0.0206533 | ||||||||
\(709\) | −1.06100e10 | −1.11803 | −0.559015 | − | 0.829158i | \(-0.688821\pi\) | ||||
−0.559015 | + | 0.829158i | \(0.688821\pi\) | |||||||
\(710\) | 2.61842e9 | 0.274559 | ||||||||
\(711\) | 3.93219e9 | 0.410290 | ||||||||
\(712\) | −4.11385e9 | −0.427138 | ||||||||
\(713\) | 1.57749e10 | 1.62988 | ||||||||
\(714\) | −6.85262e9 | −0.704552 | ||||||||
\(715\) | −1.03466e7 | −0.00105859 | ||||||||
\(716\) | −6.60908e9 | −0.672892 | ||||||||
\(717\) | 3.16686e9 | 0.320857 | ||||||||
\(718\) | 1.01846e10 | 1.02686 | ||||||||
\(719\) | 1.40920e10 | 1.41391 | 0.706955 | − | 0.707259i | \(-0.250068\pi\) | ||||
0.706955 | + | 0.707259i | \(0.250068\pi\) | |||||||
\(720\) | −3.73248e8 | −0.0372678 | ||||||||
\(721\) | 1.26885e10 | 1.26077 | ||||||||
\(722\) | 3.76367e8 | 0.0372161 | ||||||||
\(723\) | −4.89614e9 | −0.481804 | ||||||||
\(724\) | −1.00321e10 | −0.982440 | ||||||||
\(725\) | −2.70756e8 | −0.0263873 | ||||||||
\(726\) | −3.56616e9 | −0.345878 | ||||||||
\(727\) | −8.87157e9 | −0.856308 | −0.428154 | − | 0.903706i | \(-0.640836\pi\) | ||||
−0.428154 | + | 0.903706i | \(0.640836\pi\) | |||||||
\(728\) | −2.75015e7 | −0.00264178 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 1.27471e9 | 0.121277 | ||||||||
\(731\) | −6.71778e9 | −0.636085 | ||||||||
\(732\) | −1.95637e9 | −0.184358 | ||||||||
\(733\) | 9.54110e7 | 0.00894818 | 0.00447409 | − | 0.999990i | \(-0.498576\pi\) | ||||
0.00447409 | + | 0.999990i | \(0.498576\pi\) | |||||||
\(734\) | −4.14874e9 | −0.387240 | ||||||||
\(735\) | −1.45186e9 | −0.134871 | ||||||||
\(736\) | −2.78677e9 | −0.257649 | ||||||||
\(737\) | 2.45022e8 | 0.0225460 | ||||||||
\(738\) | 1.28982e9 | 0.118122 | ||||||||
\(739\) | 1.27194e10 | 1.15934 | 0.579671 | − | 0.814851i | \(-0.303181\pi\) | ||||
0.579671 | + | 0.814851i | \(0.303181\pi\) | |||||||
\(740\) | −2.47107e9 | −0.224168 | ||||||||
\(741\) | 8.88405e6 | 0.000802134 0 | ||||||||
\(742\) | 1.71145e10 | 1.53798 | ||||||||
\(743\) | −1.15304e10 | −1.03130 | −0.515650 | − | 0.856799i | \(-0.672450\pi\) | ||||
−0.515650 | + | 0.856799i | \(0.672450\pi\) | |||||||
\(744\) | −2.56419e9 | −0.228268 | ||||||||
\(745\) | 1.72004e9 | 0.152402 | ||||||||
\(746\) | 1.16163e10 | 1.02443 | ||||||||
\(747\) | −1.98592e9 | −0.174317 | ||||||||
\(748\) | 3.12885e9 | 0.273356 | ||||||||
\(749\) | 1.46483e10 | 1.27380 | ||||||||
\(750\) | −4.21875e8 | −0.0365148 | ||||||||
\(751\) | −1.90878e9 | −0.164443 | −0.0822216 | − | 0.996614i | \(-0.526202\pi\) | ||||
−0.0822216 | + | 0.996614i | \(0.526202\pi\) | |||||||
\(752\) | 2.72829e9 | 0.233953 | ||||||||
\(753\) | 8.06904e9 | 0.688715 | ||||||||
\(754\) | −6.65019e6 | −0.000564982 0 | ||||||||
\(755\) | −2.74252e9 | −0.231918 | ||||||||
\(756\) | −1.41050e9 | −0.118726 | ||||||||
\(757\) | 7.08476e9 | 0.593594 | 0.296797 | − | 0.954941i | \(-0.404082\pi\) | ||||
0.296797 | + | 0.954941i | \(0.404082\pi\) | |||||||
\(758\) | 7.53862e9 | 0.628709 | ||||||||
\(759\) | −3.96203e9 | −0.328906 | ||||||||
\(760\) | −4.38976e8 | −0.0362738 | ||||||||
\(761\) | 2.32756e10 | 1.91450 | 0.957249 | − | 0.289264i | \(-0.0934106\pi\) | ||||
0.957249 | + | 0.289264i | \(0.0934106\pi\) | |||||||
\(762\) | −2.55086e9 | −0.208854 | ||||||||
\(763\) | −4.08008e8 | −0.0332532 | ||||||||
\(764\) | −5.11723e9 | −0.415153 | ||||||||
\(765\) | −2.58190e9 | −0.208509 | ||||||||
\(766\) | −1.11446e9 | −0.0895907 | ||||||||
\(767\) | 5.41438e6 | 0.000433276 0 | ||||||||
\(768\) | 4.52985e8 | 0.0360844 | ||||||||
\(769\) | −2.51570e10 | −1.99488 | −0.997441 | − | 0.0714999i | \(-0.977221\pi\) | ||||
−0.997441 | + | 0.0714999i | \(0.977221\pi\) | |||||||
\(770\) | 1.93198e9 | 0.152506 | ||||||||
\(771\) | −1.02234e10 | −0.803354 | ||||||||
\(772\) | 2.84970e9 | 0.222915 | ||||||||
\(773\) | 1.03014e10 | 0.802170 | 0.401085 | − | 0.916041i | \(-0.368633\pi\) | ||||
0.401085 | + | 0.916041i | \(0.368633\pi\) | |||||||
\(774\) | −1.38274e9 | −0.107189 | ||||||||
\(775\) | −2.89825e9 | −0.223656 | ||||||||
\(776\) | −5.10362e9 | −0.392069 | ||||||||
\(777\) | −9.33812e9 | −0.714144 | ||||||||
\(778\) | −1.05030e10 | −0.799625 | ||||||||
\(779\) | 1.51695e9 | 0.114972 | ||||||||
\(780\) | −1.03619e7 | −0.000781824 0 | ||||||||
\(781\) | −4.51796e9 | −0.339363 | ||||||||
\(782\) | −1.92772e10 | −1.44152 | ||||||||
\(783\) | −3.41074e8 | −0.0253912 | ||||||||
\(784\) | 1.76202e9 | 0.130588 | ||||||||
\(785\) | −6.77605e9 | −0.499957 | ||||||||
\(786\) | 3.13521e9 | 0.230297 | ||||||||
\(787\) | −2.63516e10 | −1.92706 | −0.963529 | − | 0.267604i | \(-0.913768\pi\) | ||||
−0.963529 | + | 0.267604i | \(0.913768\pi\) | |||||||
\(788\) | 3.52914e9 | 0.256937 | ||||||||
\(789\) | 1.39685e10 | 1.01246 | ||||||||
\(790\) | −5.39395e9 | −0.389235 | ||||||||
\(791\) | −8.46982e9 | −0.608495 | ||||||||
\(792\) | 6.44021e8 | 0.0460640 | ||||||||
\(793\) | −5.43116e7 | −0.00386755 | ||||||||
\(794\) | 1.17984e9 | 0.0836472 | ||||||||
\(795\) | 6.44833e9 | 0.455158 | ||||||||
\(796\) | −1.11900e9 | −0.0786385 | ||||||||
\(797\) | 2.63384e10 | 1.84283 | 0.921416 | − | 0.388579i | \(-0.127034\pi\) | ||||
0.921416 | + | 0.388579i | \(0.127034\pi\) | |||||||
\(798\) | −1.65888e9 | −0.115559 | ||||||||
\(799\) | 1.88726e10 | 1.30894 | ||||||||
\(800\) | 5.12000e8 | 0.0353553 | ||||||||
\(801\) | −5.85742e9 | −0.402710 | ||||||||
\(802\) | −1.43579e10 | −0.982833 | ||||||||
\(803\) | −2.19944e9 | −0.149902 | ||||||||
\(804\) | 2.45384e8 | 0.0166514 | ||||||||
\(805\) | −1.19032e10 | −0.804224 | ||||||||
\(806\) | −7.11856e7 | −0.00478872 | ||||||||
\(807\) | 5.21032e9 | 0.348986 | ||||||||
\(808\) | −6.98078e9 | −0.465548 | ||||||||
\(809\) | 4.24126e9 | 0.281628 | 0.140814 | − | 0.990036i | \(-0.455028\pi\) | ||||
0.140814 | + | 0.990036i | \(0.455028\pi\) | |||||||
\(810\) | −5.31441e8 | −0.0351364 | ||||||||
\(811\) | 5.56399e9 | 0.366280 | 0.183140 | − | 0.983087i | \(-0.441374\pi\) | ||||
0.183140 | + | 0.983087i | \(0.441374\pi\) | |||||||
\(812\) | 1.24176e9 | 0.0813940 | ||||||||
\(813\) | −8.08249e9 | −0.527507 | ||||||||
\(814\) | 4.26371e9 | 0.277078 | ||||||||
\(815\) | −5.73879e9 | −0.371338 | ||||||||
\(816\) | 3.13347e9 | 0.201888 | ||||||||
\(817\) | −1.62624e9 | −0.104330 | ||||||||
\(818\) | −1.00633e9 | −0.0642839 | ||||||||
\(819\) | −3.91575e7 | −0.00249070 | ||||||||
\(820\) | −1.76930e9 | −0.112060 | ||||||||
\(821\) | −2.99915e9 | −0.189146 | −0.0945729 | − | 0.995518i | \(-0.530149\pi\) | ||||
−0.0945729 | + | 0.995518i | \(0.530149\pi\) | |||||||
\(822\) | −1.09986e10 | −0.690694 | ||||||||
\(823\) | 1.82277e10 | 1.13981 | 0.569904 | − | 0.821711i | \(-0.306980\pi\) | ||||
0.569904 | + | 0.821711i | \(0.306980\pi\) | |||||||
\(824\) | −5.80202e9 | −0.361272 | ||||||||
\(825\) | 7.27925e8 | 0.0451334 | ||||||||
\(826\) | −1.01100e9 | −0.0624199 | ||||||||
\(827\) | −3.03052e10 | −1.86315 | −0.931576 | − | 0.363546i | \(-0.881566\pi\) | ||||
−0.931576 | + | 0.363546i | \(0.881566\pi\) | |||||||
\(828\) | −3.96789e9 | −0.242914 | ||||||||
\(829\) | −9.22068e9 | −0.562111 | −0.281055 | − | 0.959692i | \(-0.590684\pi\) | ||||
−0.281055 | + | 0.959692i | \(0.590684\pi\) | |||||||
\(830\) | 2.72417e9 | 0.165372 | ||||||||
\(831\) | −1.35739e10 | −0.820542 | ||||||||
\(832\) | 1.25755e7 | 0.000756998 0 | ||||||||
\(833\) | 1.21886e10 | 0.730626 | ||||||||
\(834\) | 3.59534e9 | 0.214614 | ||||||||
\(835\) | 3.35323e9 | 0.199324 | ||||||||
\(836\) | 7.57432e8 | 0.0448354 | ||||||||
\(837\) | −3.65096e9 | −0.215213 | ||||||||
\(838\) | −7.09098e9 | −0.416248 | ||||||||
\(839\) | 2.26505e9 | 0.132407 | 0.0662034 | − | 0.997806i | \(-0.478911\pi\) | ||||
0.0662034 | + | 0.997806i | \(0.478911\pi\) | |||||||
\(840\) | 1.93484e9 | 0.112633 | ||||||||
\(841\) | −1.69496e10 | −0.982593 | ||||||||
\(842\) | −1.47313e10 | −0.850451 | ||||||||
\(843\) | 8.24574e9 | 0.474060 | ||||||||
\(844\) | 9.22403e9 | 0.528107 | ||||||||
\(845\) | 7.84328e9 | 0.447197 | ||||||||
\(846\) | 3.88461e9 | 0.220573 | ||||||||
\(847\) | 1.84862e10 | 1.04534 | ||||||||
\(848\) | −7.82589e9 | −0.440705 | ||||||||
\(849\) | −1.45860e10 | −0.818009 | ||||||||
\(850\) | 3.54170e9 | 0.197809 | ||||||||
\(851\) | −2.62692e10 | −1.46114 | ||||||||
\(852\) | −4.52464e9 | −0.250637 | ||||||||
\(853\) | 7.21996e9 | 0.398303 | 0.199151 | − | 0.979969i | \(-0.436181\pi\) | ||||
0.199151 | + | 0.979969i | \(0.436181\pi\) | |||||||
\(854\) | 1.01414e10 | 0.557179 | ||||||||
\(855\) | −6.25026e8 | −0.0341993 | ||||||||
\(856\) | −6.69815e9 | −0.365003 | ||||||||
\(857\) | −1.16026e10 | −0.629685 | −0.314842 | − | 0.949144i | \(-0.601952\pi\) | ||||
−0.314842 | + | 0.949144i | \(0.601952\pi\) | |||||||
\(858\) | 1.78790e7 | 0.000966356 0 | ||||||||
\(859\) | −2.98667e9 | −0.160772 | −0.0803861 | − | 0.996764i | \(-0.525615\pi\) | ||||
−0.0803861 | + | 0.996764i | \(0.525615\pi\) | |||||||
\(860\) | 1.89677e9 | 0.101688 | ||||||||
\(861\) | −6.68614e9 | −0.356997 | ||||||||
\(862\) | 1.49891e10 | 0.797079 | ||||||||
\(863\) | 1.27942e10 | 0.677604 | 0.338802 | − | 0.940858i | \(-0.389978\pi\) | ||||
0.338802 | + | 0.940858i | \(0.389978\pi\) | |||||||
\(864\) | 6.44973e8 | 0.0340207 | ||||||||
\(865\) | 1.33704e8 | 0.00702406 | ||||||||
\(866\) | 6.33046e8 | 0.0331224 | ||||||||
\(867\) | 1.05963e10 | 0.552188 | ||||||||
\(868\) | 1.32922e10 | 0.689887 | ||||||||
\(869\) | 9.30699e9 | 0.481105 | ||||||||
\(870\) | 4.67866e8 | 0.0240882 | ||||||||
\(871\) | 6.81222e6 | 0.000349321 0 | ||||||||
\(872\) | 1.86569e8 | 0.00952863 | ||||||||
\(873\) | −7.26668e9 | −0.369646 | ||||||||
\(874\) | −4.66662e9 | −0.236435 | ||||||||
\(875\) | 2.18691e9 | 0.110358 | ||||||||
\(876\) | −2.20269e9 | −0.110711 | ||||||||
\(877\) | 2.24309e9 | 0.112292 | 0.0561459 | − | 0.998423i | \(-0.482119\pi\) | ||||
0.0561459 | + | 0.998423i | \(0.482119\pi\) | |||||||
\(878\) | 1.32090e10 | 0.658627 | ||||||||
\(879\) | −7.51500e9 | −0.373222 | ||||||||
\(880\) | −8.83431e8 | −0.0437002 | ||||||||
\(881\) | 1.15239e10 | 0.567787 | 0.283893 | − | 0.958856i | \(-0.408374\pi\) | ||||
0.283893 | + | 0.958856i | \(0.408374\pi\) | |||||||
\(882\) | 2.50881e9 | 0.123120 | ||||||||
\(883\) | −9.27109e9 | −0.453177 | −0.226589 | − | 0.973991i | \(-0.572757\pi\) | ||||
−0.226589 | + | 0.973991i | \(0.572757\pi\) | |||||||
\(884\) | 8.69898e7 | 0.00423531 | ||||||||
\(885\) | −3.80922e8 | −0.0184729 | ||||||||
\(886\) | −5.05321e9 | −0.244089 | ||||||||
\(887\) | −2.13154e10 | −1.02556 | −0.512779 | − | 0.858521i | \(-0.671384\pi\) | ||||
−0.512779 | + | 0.858521i | \(0.671384\pi\) | |||||||
\(888\) | 4.27001e9 | 0.204637 | ||||||||
\(889\) | 1.32231e10 | 0.631214 | ||||||||
\(890\) | 8.03487e9 | 0.382044 | ||||||||
\(891\) | 9.16976e8 | 0.0434296 | ||||||||
\(892\) | 1.28426e10 | 0.605864 | ||||||||
\(893\) | 4.56869e9 | 0.214690 | ||||||||
\(894\) | −2.97223e9 | −0.139123 | ||||||||
\(895\) | 1.29084e10 | 0.601853 | ||||||||
\(896\) | −2.34818e9 | −0.109057 | ||||||||
\(897\) | −1.10154e8 | −0.00509599 | ||||||||
\(898\) | 1.06804e10 | 0.492176 | ||||||||
\(899\) | 3.21421e9 | 0.147542 | ||||||||
\(900\) | 7.29000e8 | 0.0333333 | ||||||||
\(901\) | −5.41347e10 | −2.46569 | ||||||||
\(902\) | 3.05284e9 | 0.138510 | ||||||||
\(903\) | 7.16785e9 | 0.323953 | ||||||||
\(904\) | 3.87296e9 | 0.174363 | ||||||||
\(905\) | 1.95939e10 | 0.878721 | ||||||||
\(906\) | 4.73907e9 | 0.211712 | ||||||||
\(907\) | −4.13216e8 | −0.0183887 | −0.00919435 | − | 0.999958i | \(-0.502927\pi\) | ||||
−0.00919435 | + | 0.999958i | \(0.502927\pi\) | |||||||
\(908\) | 1.68122e10 | 0.745288 | ||||||||
\(909\) | −9.93944e9 | −0.438923 | ||||||||
\(910\) | 5.37140e7 | 0.00236288 | ||||||||
\(911\) | 3.46681e9 | 0.151920 | 0.0759602 | − | 0.997111i | \(-0.475798\pi\) | ||||
0.0759602 | + | 0.997111i | \(0.475798\pi\) | |||||||
\(912\) | 7.58551e8 | 0.0331133 | ||||||||
\(913\) | −4.70042e9 | −0.204404 | ||||||||
\(914\) | 1.19843e10 | 0.519161 | ||||||||
\(915\) | 3.82103e9 | 0.164895 | ||||||||
\(916\) | −1.94322e10 | −0.835388 | ||||||||
\(917\) | −1.62522e10 | −0.696018 | ||||||||
\(918\) | 4.46152e9 | 0.190342 | ||||||||
\(919\) | −2.19386e10 | −0.932406 | −0.466203 | − | 0.884678i | \(-0.654378\pi\) | ||||
−0.466203 | + | 0.884678i | \(0.654378\pi\) | |||||||
\(920\) | 5.44292e9 | 0.230449 | ||||||||
\(921\) | 1.21384e10 | 0.511981 | ||||||||
\(922\) | −1.40382e10 | −0.589865 | ||||||||
\(923\) | −1.25611e8 | −0.00525800 | ||||||||
\(924\) | −3.33847e9 | −0.139218 | ||||||||
\(925\) | 4.82631e9 | 0.200502 | ||||||||
\(926\) | −3.34019e9 | −0.138240 | ||||||||
\(927\) | −8.26108e9 | −0.340610 | ||||||||
\(928\) | −5.67816e8 | −0.0233233 | ||||||||
\(929\) | 1.61947e10 | 0.662703 | 0.331352 | − | 0.943507i | \(-0.392495\pi\) | ||||
0.331352 | + | 0.943507i | \(0.392495\pi\) | |||||||
\(930\) | 5.00818e9 | 0.204169 | ||||||||
\(931\) | 2.95061e9 | 0.119836 | ||||||||
\(932\) | 4.81569e9 | 0.194851 | ||||||||
\(933\) | −2.09292e10 | −0.843658 | ||||||||
\(934\) | 2.12649e10 | 0.853985 | ||||||||
\(935\) | −6.11103e9 | −0.244497 | ||||||||
\(936\) | 1.79054e7 | 0.000713704 0 | ||||||||
\(937\) | 9.44456e9 | 0.375053 | 0.187527 | − | 0.982260i | \(-0.439953\pi\) | ||||
0.187527 | + | 0.982260i | \(0.439953\pi\) | |||||||
\(938\) | −1.27202e9 | −0.0503249 | ||||||||
\(939\) | 5.39870e9 | 0.212794 | ||||||||
\(940\) | −5.32869e9 | −0.209254 | ||||||||
\(941\) | −2.59333e10 | −1.01460 | −0.507299 | − | 0.861770i | \(-0.669356\pi\) | ||||
−0.507299 | + | 0.861770i | \(0.669356\pi\) | |||||||
\(942\) | 1.17090e10 | 0.456396 | ||||||||
\(943\) | −1.88089e10 | −0.730418 | ||||||||
\(944\) | 4.62298e8 | 0.0178863 | ||||||||
\(945\) | 2.75488e9 | 0.106192 | ||||||||
\(946\) | −3.27278e9 | −0.125689 | ||||||||
\(947\) | 2.40537e9 | 0.0920359 | 0.0460180 | − | 0.998941i | \(-0.485347\pi\) | ||||
0.0460180 | + | 0.998941i | \(0.485347\pi\) | |||||||
\(948\) | 9.32074e9 | 0.355321 | ||||||||
\(949\) | −6.11500e7 | −0.00232255 | ||||||||
\(950\) | 8.57375e8 | 0.0324443 | ||||||||
\(951\) | −1.94748e10 | −0.734246 | ||||||||
\(952\) | −1.62432e10 | −0.610160 | ||||||||
\(953\) | −3.83728e10 | −1.43614 | −0.718072 | − | 0.695969i | \(-0.754975\pi\) | ||||
−0.718072 | + | 0.695969i | \(0.754975\pi\) | |||||||
\(954\) | −1.11427e10 | −0.415501 | ||||||||
\(955\) | 9.99458e9 | 0.371324 | ||||||||
\(956\) | 7.50663e9 | 0.277870 | ||||||||
\(957\) | −8.07280e8 | −0.0297737 | ||||||||
\(958\) | −1.42278e10 | −0.522829 | ||||||||
\(959\) | 5.70143e10 | 2.08746 | ||||||||
\(960\) | −8.84736e8 | −0.0322749 | ||||||||
\(961\) | 6.89323e9 | 0.250548 | ||||||||
\(962\) | 1.18542e8 | 0.00429298 | ||||||||
\(963\) | −9.53702e9 | −0.344129 | ||||||||
\(964\) | −1.16057e10 | −0.417254 | ||||||||
\(965\) | −5.56583e9 | −0.199381 | ||||||||
\(966\) | 2.05687e10 | 0.734152 | ||||||||
\(967\) | 1.51477e10 | 0.538707 | 0.269353 | − | 0.963041i | \(-0.413190\pi\) | ||||
0.269353 | + | 0.963041i | \(0.413190\pi\) | |||||||
\(968\) | −8.45311e9 | −0.299539 | ||||||||
\(969\) | 5.24719e9 | 0.185265 | ||||||||
\(970\) | 9.96801e9 | 0.350677 | ||||||||
\(971\) | −5.97035e9 | −0.209282 | −0.104641 | − | 0.994510i | \(-0.533369\pi\) | ||||
−0.104641 | + | 0.994510i | \(0.533369\pi\) | |||||||
\(972\) | 9.18330e8 | 0.0320750 | ||||||||
\(973\) | −1.86375e10 | −0.648622 | ||||||||
\(974\) | −1.17282e10 | −0.406700 | ||||||||
\(975\) | 2.02381e7 | 0.000699285 0 | ||||||||
\(976\) | −4.63731e9 | −0.159658 | ||||||||
\(977\) | 2.54311e10 | 0.872436 | 0.436218 | − | 0.899841i | \(-0.356318\pi\) | ||||
0.436218 | + | 0.899841i | \(0.356318\pi\) | |||||||
\(978\) | 9.91664e9 | 0.338983 | ||||||||
\(979\) | −1.38638e10 | −0.472217 | ||||||||
\(980\) | −3.44144e9 | −0.116802 | ||||||||
\(981\) | 2.65641e8 | 0.00898368 | ||||||||
\(982\) | 2.28403e10 | 0.769683 | ||||||||
\(983\) | 2.08515e10 | 0.700163 | 0.350082 | − | 0.936719i | \(-0.386154\pi\) | ||||
0.350082 | + | 0.936719i | \(0.386154\pi\) | |||||||
\(984\) | 3.05735e9 | 0.102297 | ||||||||
\(985\) | −6.89285e9 | −0.229812 | ||||||||
\(986\) | −3.92780e9 | −0.130491 | ||||||||
\(987\) | −2.01370e10 | −0.666630 | ||||||||
\(988\) | 2.10585e7 | 0.000694669 0 | ||||||||
\(989\) | 2.01640e10 | 0.662809 | ||||||||
\(990\) | −1.25785e9 | −0.0412009 | ||||||||
\(991\) | −4.40793e10 | −1.43872 | −0.719360 | − | 0.694637i | \(-0.755565\pi\) | ||||
−0.719360 | + | 0.694637i | \(0.755565\pi\) | |||||||
\(992\) | −6.07807e9 | −0.197686 | ||||||||
\(993\) | 6.66119e9 | 0.215889 | ||||||||
\(994\) | 2.34548e10 | 0.757493 | ||||||||
\(995\) | 2.18555e9 | 0.0703364 | ||||||||
\(996\) | −4.70737e9 | −0.150963 | ||||||||
\(997\) | −3.76004e10 | −1.20160 | −0.600800 | − | 0.799400i | \(-0.705151\pi\) | ||||
−0.600800 | + | 0.799400i | \(0.705151\pi\) | |||||||
\(998\) | −2.56950e9 | −0.0818262 | ||||||||
\(999\) | 6.07976e9 | 0.192933 |
(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 | 570.8.a.b.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.8.a.b.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |