Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,8,Mod(1,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("354.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.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: | \(110.584299021\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 103558 x^{6} + 5805883 x^{5} + 2559087821 x^{4} - 196601024266 x^{3} + \cdots - 22\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{7}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-299.356\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.1 |
$q$-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 | ||||||||
\(5\) | 319.148 | 1.14182 | 0.570909 | − | 0.821014i | \(-0.306591\pi\) | ||||
0.570909 | + | 0.821014i | \(0.306591\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | 134.129 | 0.147802 | 0.0739009 | − | 0.997266i | \(-0.476455\pi\) | ||||
0.0739009 | + | 0.997266i | \(0.476455\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 2553.18 | 0.807387 | ||||||||
\(11\) | 2917.38 | 0.660873 | 0.330437 | − | 0.943828i | \(-0.392804\pi\) | ||||
0.330437 | + | 0.943828i | \(0.392804\pi\) | |||||||
\(12\) | −1728.00 | −0.288675 | ||||||||
\(13\) | −10343.7 | −1.30579 | −0.652893 | − | 0.757450i | \(-0.726445\pi\) | ||||
−0.652893 | + | 0.757450i | \(0.726445\pi\) | |||||||
\(14\) | 1073.03 | 0.104512 | ||||||||
\(15\) | −8616.99 | −0.659229 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −9122.15 | −0.450325 | −0.225162 | − | 0.974321i | \(-0.572291\pi\) | ||||
−0.225162 | + | 0.974321i | \(0.572291\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | −32743.7 | −1.09519 | −0.547596 | − | 0.836743i | \(-0.684457\pi\) | ||||
−0.547596 | + | 0.836743i | \(0.684457\pi\) | |||||||
\(20\) | 20425.4 | 0.570909 | ||||||||
\(21\) | −3621.49 | −0.0853334 | ||||||||
\(22\) | 23339.0 | 0.467308 | ||||||||
\(23\) | −86624.7 | −1.48455 | −0.742274 | − | 0.670096i | \(-0.766253\pi\) | ||||
−0.742274 | + | 0.670096i | \(0.766253\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | 23730.2 | 0.303747 | ||||||||
\(26\) | −82749.2 | −0.923331 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 8584.26 | 0.0739009 | ||||||||
\(29\) | 14441.0 | 0.109952 | 0.0549762 | − | 0.998488i | \(-0.482492\pi\) | ||||
0.0549762 | + | 0.998488i | \(0.482492\pi\) | |||||||
\(30\) | −68935.9 | −0.466145 | ||||||||
\(31\) | −97822.8 | −0.589758 | −0.294879 | − | 0.955535i | \(-0.595279\pi\) | ||||
−0.294879 | + | 0.955535i | \(0.595279\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −78769.2 | −0.381555 | ||||||||
\(34\) | −72977.2 | −0.318428 | ||||||||
\(35\) | 42807.0 | 0.168763 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | −120168. | −0.390017 | −0.195009 | − | 0.980802i | \(-0.562473\pi\) | ||||
−0.195009 | + | 0.980802i | \(0.562473\pi\) | |||||||
\(38\) | −261950. | −0.774417 | ||||||||
\(39\) | 279279. | 0.753896 | ||||||||
\(40\) | 163404. | 0.403693 | ||||||||
\(41\) | 417584. | 0.946239 | 0.473119 | − | 0.880998i | \(-0.343128\pi\) | ||||
0.473119 | + | 0.880998i | \(0.343128\pi\) | |||||||
\(42\) | −28971.9 | −0.0603399 | ||||||||
\(43\) | −328583. | −0.630239 | −0.315120 | − | 0.949052i | \(-0.602045\pi\) | ||||
−0.315120 | + | 0.949052i | \(0.602045\pi\) | |||||||
\(44\) | 186712. | 0.330437 | ||||||||
\(45\) | 232659. | 0.380606 | ||||||||
\(46\) | −692998. | −1.04973 | ||||||||
\(47\) | 1.14848e6 | 1.61354 | 0.806772 | − | 0.590863i | \(-0.201212\pi\) | ||||
0.806772 | + | 0.590863i | \(0.201212\pi\) | |||||||
\(48\) | −110592. | −0.144338 | ||||||||
\(49\) | −805552. | −0.978155 | ||||||||
\(50\) | 189842. | 0.214781 | ||||||||
\(51\) | 246298. | 0.259995 | ||||||||
\(52\) | −661994. | −0.652893 | ||||||||
\(53\) | −1.09975e6 | −1.01468 | −0.507338 | − | 0.861747i | \(-0.669370\pi\) | ||||
−0.507338 | + | 0.861747i | \(0.669370\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | 931074. | 0.754597 | ||||||||
\(56\) | 68674.1 | 0.0522559 | ||||||||
\(57\) | 884080. | 0.632309 | ||||||||
\(58\) | 115528. | 0.0777481 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | −551487. | −0.329614 | ||||||||
\(61\) | −592942. | −0.334471 | −0.167235 | − | 0.985917i | \(-0.553484\pi\) | ||||
−0.167235 | + | 0.985917i | \(0.553484\pi\) | |||||||
\(62\) | −782582. | −0.417022 | ||||||||
\(63\) | 97780.1 | 0.0492673 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −3.30115e6 | −1.49097 | ||||||||
\(66\) | −630154. | −0.269800 | ||||||||
\(67\) | 115861. | 0.0470625 | 0.0235312 | − | 0.999723i | \(-0.492509\pi\) | ||||
0.0235312 | + | 0.999723i | \(0.492509\pi\) | |||||||
\(68\) | −583817. | −0.225162 | ||||||||
\(69\) | 2.33887e6 | 0.857105 | ||||||||
\(70\) | 342456. | 0.119333 | ||||||||
\(71\) | −968201. | −0.321042 | −0.160521 | − | 0.987032i | \(-0.551317\pi\) | ||||
−0.160521 | + | 0.987032i | \(0.551317\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | −3.88489e6 | −1.16882 | −0.584412 | − | 0.811457i | \(-0.698675\pi\) | ||||
−0.584412 | + | 0.811457i | \(0.698675\pi\) | |||||||
\(74\) | −961346. | −0.275784 | ||||||||
\(75\) | −640716. | −0.175368 | ||||||||
\(76\) | −2.09560e6 | −0.547596 | ||||||||
\(77\) | 391305. | 0.0976783 | ||||||||
\(78\) | 2.23423e6 | 0.533085 | ||||||||
\(79\) | −838845. | −0.191420 | −0.0957099 | − | 0.995409i | \(-0.530512\pi\) | ||||
−0.0957099 | + | 0.995409i | \(0.530512\pi\) | |||||||
\(80\) | 1.30723e6 | 0.285454 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 3.34068e6 | 0.669092 | ||||||||
\(83\) | 6.55543e6 | 1.25843 | 0.629213 | − | 0.777233i | \(-0.283377\pi\) | ||||
0.629213 | + | 0.777233i | \(0.283377\pi\) | |||||||
\(84\) | −231775. | −0.0426667 | ||||||||
\(85\) | −2.91131e6 | −0.514189 | ||||||||
\(86\) | −2.62866e6 | −0.445646 | ||||||||
\(87\) | −389908. | −0.0634811 | ||||||||
\(88\) | 1.49370e6 | 0.233654 | ||||||||
\(89\) | 6.86199e6 | 1.03178 | 0.515888 | − | 0.856656i | \(-0.327462\pi\) | ||||
0.515888 | + | 0.856656i | \(0.327462\pi\) | |||||||
\(90\) | 1.86127e6 | 0.269129 | ||||||||
\(91\) | −1.38739e6 | −0.192998 | ||||||||
\(92\) | −5.54398e6 | −0.742274 | ||||||||
\(93\) | 2.64122e6 | 0.340497 | ||||||||
\(94\) | 9.18784e6 | 1.14095 | ||||||||
\(95\) | −1.04501e7 | −1.25051 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | 6.68861e6 | 0.744106 | 0.372053 | − | 0.928212i | \(-0.378654\pi\) | ||||
0.372053 | + | 0.928212i | \(0.378654\pi\) | |||||||
\(98\) | −6.44442e6 | −0.691660 | ||||||||
\(99\) | 2.12677e6 | 0.220291 | ||||||||
\(100\) | 1.51873e6 | 0.151873 | ||||||||
\(101\) | 630861. | 0.0609269 | 0.0304634 | − | 0.999536i | \(-0.490302\pi\) | ||||
0.0304634 | + | 0.999536i | \(0.490302\pi\) | |||||||
\(102\) | 1.97038e6 | 0.183844 | ||||||||
\(103\) | −1.05376e7 | −0.950194 | −0.475097 | − | 0.879933i | \(-0.657587\pi\) | ||||
−0.475097 | + | 0.879933i | \(0.657587\pi\) | |||||||
\(104\) | −5.29595e6 | −0.461665 | ||||||||
\(105\) | −1.15579e6 | −0.0974352 | ||||||||
\(106\) | −8.79797e6 | −0.717484 | ||||||||
\(107\) | 8.36822e6 | 0.660374 | 0.330187 | − | 0.943916i | \(-0.392888\pi\) | ||||
0.330187 | + | 0.943916i | \(0.392888\pi\) | |||||||
\(108\) | −1.25971e6 | −0.0962250 | ||||||||
\(109\) | −1.38816e7 | −1.02671 | −0.513355 | − | 0.858176i | \(-0.671598\pi\) | ||||
−0.513355 | + | 0.858176i | \(0.671598\pi\) | |||||||
\(110\) | 7.44859e6 | 0.533580 | ||||||||
\(111\) | 3.24454e6 | 0.225177 | ||||||||
\(112\) | 549393. | 0.0369505 | ||||||||
\(113\) | −2.27659e6 | −0.148426 | −0.0742129 | − | 0.997242i | \(-0.523644\pi\) | ||||
−0.0742129 | + | 0.997242i | \(0.523644\pi\) | |||||||
\(114\) | 7.07264e6 | 0.447110 | ||||||||
\(115\) | −2.76461e7 | −1.69508 | ||||||||
\(116\) | 924225. | 0.0549762 | ||||||||
\(117\) | −7.54052e6 | −0.435262 | ||||||||
\(118\) | −1.64303e6 | −0.0920575 | ||||||||
\(119\) | −1.22355e6 | −0.0665589 | ||||||||
\(120\) | −4.41190e6 | −0.233072 | ||||||||
\(121\) | −1.09761e7 | −0.563246 | ||||||||
\(122\) | −4.74354e6 | −0.236506 | ||||||||
\(123\) | −1.12748e7 | −0.546311 | ||||||||
\(124\) | −6.26066e6 | −0.294879 | ||||||||
\(125\) | −1.73600e7 | −0.794994 | ||||||||
\(126\) | 782241. | 0.0348372 | ||||||||
\(127\) | −1.95434e7 | −0.846619 | −0.423309 | − | 0.905985i | \(-0.639132\pi\) | ||||
−0.423309 | + | 0.905985i | \(0.639132\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | 8.87174e6 | 0.363869 | ||||||||
\(130\) | −2.64092e7 | −1.05428 | ||||||||
\(131\) | −3.49073e7 | −1.35665 | −0.678323 | − | 0.734764i | \(-0.737293\pi\) | ||||
−0.678323 | + | 0.734764i | \(0.737293\pi\) | |||||||
\(132\) | −5.04123e6 | −0.190778 | ||||||||
\(133\) | −4.39188e6 | −0.161871 | ||||||||
\(134\) | 926887. | 0.0332782 | ||||||||
\(135\) | −6.28178e6 | −0.219743 | ||||||||
\(136\) | −4.67054e6 | −0.159214 | ||||||||
\(137\) | 1.88810e7 | 0.627341 | 0.313671 | − | 0.949532i | \(-0.398441\pi\) | ||||
0.313671 | + | 0.949532i | \(0.398441\pi\) | |||||||
\(138\) | 1.87109e7 | 0.606064 | ||||||||
\(139\) | −2.01690e7 | −0.636989 | −0.318495 | − | 0.947925i | \(-0.603177\pi\) | ||||
−0.318495 | + | 0.947925i | \(0.603177\pi\) | |||||||
\(140\) | 2.73965e6 | 0.0843814 | ||||||||
\(141\) | −3.10090e7 | −0.931580 | ||||||||
\(142\) | −7.74561e6 | −0.227011 | ||||||||
\(143\) | −3.01764e7 | −0.862960 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | 4.60882e6 | 0.125546 | ||||||||
\(146\) | −3.10792e7 | −0.826484 | ||||||||
\(147\) | 2.17499e7 | 0.564738 | ||||||||
\(148\) | −7.69077e6 | −0.195009 | ||||||||
\(149\) | −5.44713e6 | −0.134901 | −0.0674507 | − | 0.997723i | \(-0.521487\pi\) | ||||
−0.0674507 | + | 0.997723i | \(0.521487\pi\) | |||||||
\(150\) | −5.12573e6 | −0.124004 | ||||||||
\(151\) | −3.35678e7 | −0.793420 | −0.396710 | − | 0.917944i | \(-0.629848\pi\) | ||||
−0.396710 | + | 0.917944i | \(0.629848\pi\) | |||||||
\(152\) | −1.67648e7 | −0.387209 | ||||||||
\(153\) | −6.65005e6 | −0.150108 | ||||||||
\(154\) | 3.13044e6 | 0.0690690 | ||||||||
\(155\) | −3.12199e7 | −0.673396 | ||||||||
\(156\) | 1.78738e7 | 0.376948 | ||||||||
\(157\) | −1.87403e7 | −0.386481 | −0.193241 | − | 0.981151i | \(-0.561900\pi\) | ||||
−0.193241 | + | 0.981151i | \(0.561900\pi\) | |||||||
\(158\) | −6.71076e6 | −0.135354 | ||||||||
\(159\) | 2.96932e7 | 0.585823 | ||||||||
\(160\) | 1.04578e7 | 0.201847 | ||||||||
\(161\) | −1.16189e7 | −0.219419 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | 1.24638e7 | 0.225421 | 0.112711 | − | 0.993628i | \(-0.464047\pi\) | ||||
0.112711 | + | 0.993628i | \(0.464047\pi\) | |||||||
\(164\) | 2.67254e7 | 0.473119 | ||||||||
\(165\) | −2.51390e7 | −0.435667 | ||||||||
\(166\) | 5.24434e7 | 0.889842 | ||||||||
\(167\) | 5.38299e7 | 0.894367 | 0.447184 | − | 0.894442i | \(-0.352427\pi\) | ||||
0.447184 | + | 0.894442i | \(0.352427\pi\) | |||||||
\(168\) | −1.85420e6 | −0.0301699 | ||||||||
\(169\) | 4.42427e7 | 0.705079 | ||||||||
\(170\) | −2.32905e7 | −0.363586 | ||||||||
\(171\) | −2.38702e7 | −0.365064 | ||||||||
\(172\) | −2.10293e7 | −0.315120 | ||||||||
\(173\) | 777614. | 0.0114183 | 0.00570916 | − | 0.999984i | \(-0.498183\pi\) | ||||
0.00570916 | + | 0.999984i | \(0.498183\pi\) | |||||||
\(174\) | −3.11926e6 | −0.0448879 | ||||||||
\(175\) | 3.18291e6 | 0.0448943 | ||||||||
\(176\) | 1.19496e7 | 0.165218 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | 5.48959e7 | 0.729576 | ||||||||
\(179\) | −1.44464e8 | −1.88267 | −0.941336 | − | 0.337470i | \(-0.890429\pi\) | ||||
−0.941336 | + | 0.337470i | \(0.890429\pi\) | |||||||
\(180\) | 1.48902e7 | 0.190303 | ||||||||
\(181\) | −4.03624e7 | −0.505944 | −0.252972 | − | 0.967474i | \(-0.581408\pi\) | ||||
−0.252972 | + | 0.967474i | \(0.581408\pi\) | |||||||
\(182\) | −1.10991e7 | −0.136470 | ||||||||
\(183\) | 1.60094e7 | 0.193107 | ||||||||
\(184\) | −4.43519e7 | −0.524867 | ||||||||
\(185\) | −3.83514e7 | −0.445329 | ||||||||
\(186\) | 2.11297e7 | 0.240768 | ||||||||
\(187\) | −2.66128e7 | −0.297608 | ||||||||
\(188\) | 7.35027e7 | 0.806772 | ||||||||
\(189\) | −2.64006e6 | −0.0284445 | ||||||||
\(190\) | −8.36006e7 | −0.884243 | ||||||||
\(191\) | 1.39579e8 | 1.44945 | 0.724724 | − | 0.689039i | \(-0.241967\pi\) | ||||
0.724724 | + | 0.689039i | \(0.241967\pi\) | |||||||
\(192\) | −7.07789e6 | −0.0721688 | ||||||||
\(193\) | −1.83138e8 | −1.83370 | −0.916849 | − | 0.399233i | \(-0.869276\pi\) | ||||
−0.916849 | + | 0.399233i | \(0.869276\pi\) | |||||||
\(194\) | 5.35089e7 | 0.526162 | ||||||||
\(195\) | 8.91311e7 | 0.860812 | ||||||||
\(196\) | −5.15554e7 | −0.489077 | ||||||||
\(197\) | 8.56358e7 | 0.798038 | 0.399019 | − | 0.916943i | \(-0.369351\pi\) | ||||
0.399019 | + | 0.916943i | \(0.369351\pi\) | |||||||
\(198\) | 1.70141e7 | 0.155769 | ||||||||
\(199\) | 6.24126e6 | 0.0561418 | 0.0280709 | − | 0.999606i | \(-0.491064\pi\) | ||||
0.0280709 | + | 0.999606i | \(0.491064\pi\) | |||||||
\(200\) | 1.21499e7 | 0.107391 | ||||||||
\(201\) | −3.12824e6 | −0.0271715 | ||||||||
\(202\) | 5.04689e6 | 0.0430818 | ||||||||
\(203\) | 1.93696e6 | 0.0162512 | ||||||||
\(204\) | 1.57631e7 | 0.129998 | ||||||||
\(205\) | 1.33271e8 | 1.08043 | ||||||||
\(206\) | −8.43010e7 | −0.671889 | ||||||||
\(207\) | −6.31494e7 | −0.494850 | ||||||||
\(208\) | −4.23676e7 | −0.326447 | ||||||||
\(209\) | −9.55257e7 | −0.723783 | ||||||||
\(210\) | −9.24631e6 | −0.0688971 | ||||||||
\(211\) | 6.27202e7 | 0.459641 | 0.229821 | − | 0.973233i | \(-0.426186\pi\) | ||||
0.229821 | + | 0.973233i | \(0.426186\pi\) | |||||||
\(212\) | −7.03838e7 | −0.507338 | ||||||||
\(213\) | 2.61414e7 | 0.185353 | ||||||||
\(214\) | 6.69457e7 | 0.466955 | ||||||||
\(215\) | −1.04866e8 | −0.719618 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | −1.31209e7 | −0.0871674 | ||||||||
\(218\) | −1.11053e8 | −0.725994 | ||||||||
\(219\) | 1.04892e8 | 0.674821 | ||||||||
\(220\) | 5.95888e7 | 0.377298 | ||||||||
\(221\) | 9.43564e7 | 0.588028 | ||||||||
\(222\) | 2.59564e7 | 0.159224 | ||||||||
\(223\) | 7.41061e7 | 0.447494 | 0.223747 | − | 0.974647i | \(-0.428171\pi\) | ||||
0.223747 | + | 0.974647i | \(0.428171\pi\) | |||||||
\(224\) | 4.39514e6 | 0.0261279 | ||||||||
\(225\) | 1.72993e7 | 0.101249 | ||||||||
\(226\) | −1.82127e7 | −0.104953 | ||||||||
\(227\) | 1.73592e8 | 0.985009 | 0.492505 | − | 0.870310i | \(-0.336081\pi\) | ||||
0.492505 | + | 0.870310i | \(0.336081\pi\) | |||||||
\(228\) | 5.65811e7 | 0.316155 | ||||||||
\(229\) | 2.10444e7 | 0.115801 | 0.0579006 | − | 0.998322i | \(-0.481559\pi\) | ||||
0.0579006 | + | 0.998322i | \(0.481559\pi\) | |||||||
\(230\) | −2.21169e8 | −1.19860 | ||||||||
\(231\) | −1.05652e7 | −0.0563946 | ||||||||
\(232\) | 7.39380e6 | 0.0388741 | ||||||||
\(233\) | 7.90948e6 | 0.0409640 | 0.0204820 | − | 0.999790i | \(-0.493480\pi\) | ||||
0.0204820 | + | 0.999790i | \(0.493480\pi\) | |||||||
\(234\) | −6.03242e7 | −0.307777 | ||||||||
\(235\) | 3.66535e8 | 1.84237 | ||||||||
\(236\) | −1.31443e7 | −0.0650945 | ||||||||
\(237\) | 2.26488e7 | 0.110516 | ||||||||
\(238\) | −9.78837e6 | −0.0470642 | ||||||||
\(239\) | 2.40543e8 | 1.13973 | 0.569864 | − | 0.821739i | \(-0.306996\pi\) | ||||
0.569864 | + | 0.821739i | \(0.306996\pi\) | |||||||
\(240\) | −3.52952e7 | −0.164807 | ||||||||
\(241\) | 5.06740e7 | 0.233198 | 0.116599 | − | 0.993179i | \(-0.462801\pi\) | ||||
0.116599 | + | 0.993179i | \(0.462801\pi\) | |||||||
\(242\) | −8.78086e7 | −0.398275 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −3.79483e7 | −0.167235 | ||||||||
\(245\) | −2.57090e8 | −1.11687 | ||||||||
\(246\) | −9.01982e7 | −0.386300 | ||||||||
\(247\) | 3.38690e8 | 1.43009 | ||||||||
\(248\) | −5.00853e7 | −0.208511 | ||||||||
\(249\) | −1.76997e8 | −0.726553 | ||||||||
\(250\) | −1.38880e8 | −0.562146 | ||||||||
\(251\) | −1.14512e8 | −0.457083 | −0.228541 | − | 0.973534i | \(-0.573396\pi\) | ||||
−0.228541 | + | 0.973534i | \(0.573396\pi\) | |||||||
\(252\) | 6.25793e6 | 0.0246336 | ||||||||
\(253\) | −2.52717e8 | −0.981099 | ||||||||
\(254\) | −1.56347e8 | −0.598650 | ||||||||
\(255\) | 7.86054e7 | 0.296867 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −3.64177e8 | −1.33828 | −0.669139 | − | 0.743137i | \(-0.733337\pi\) | ||||
−0.669139 | + | 0.743137i | \(0.733337\pi\) | |||||||
\(258\) | 7.09739e7 | 0.257294 | ||||||||
\(259\) | −1.61181e7 | −0.0576453 | ||||||||
\(260\) | −2.11274e8 | −0.745485 | ||||||||
\(261\) | 1.05275e7 | 0.0366508 | ||||||||
\(262\) | −2.79258e8 | −0.959294 | ||||||||
\(263\) | 5.67871e8 | 1.92489 | 0.962443 | − | 0.271485i | \(-0.0875148\pi\) | ||||
0.962443 | + | 0.271485i | \(0.0875148\pi\) | |||||||
\(264\) | −4.03298e7 | −0.134900 | ||||||||
\(265\) | −3.50982e8 | −1.15857 | ||||||||
\(266\) | −3.51351e7 | −0.114460 | ||||||||
\(267\) | −1.85274e8 | −0.595696 | ||||||||
\(268\) | 7.41509e6 | 0.0235312 | ||||||||
\(269\) | 1.62135e7 | 0.0507858 | 0.0253929 | − | 0.999678i | \(-0.491916\pi\) | ||||
0.0253929 | + | 0.999678i | \(0.491916\pi\) | |||||||
\(270\) | −5.02543e7 | −0.155382 | ||||||||
\(271\) | −3.79912e8 | −1.15955 | −0.579777 | − | 0.814775i | \(-0.696860\pi\) | ||||
−0.579777 | + | 0.814775i | \(0.696860\pi\) | |||||||
\(272\) | −3.73643e7 | −0.112581 | ||||||||
\(273\) | 3.74594e7 | 0.111427 | ||||||||
\(274\) | 1.51048e8 | 0.443597 | ||||||||
\(275\) | 6.92300e7 | 0.200738 | ||||||||
\(276\) | 1.49688e8 | 0.428552 | ||||||||
\(277\) | 1.24053e8 | 0.350694 | 0.175347 | − | 0.984507i | \(-0.443895\pi\) | ||||
0.175347 | + | 0.984507i | \(0.443895\pi\) | |||||||
\(278\) | −1.61352e8 | −0.450419 | ||||||||
\(279\) | −7.13128e7 | −0.196586 | ||||||||
\(280\) | 2.19172e7 | 0.0596666 | ||||||||
\(281\) | −1.26772e8 | −0.340840 | −0.170420 | − | 0.985371i | \(-0.554512\pi\) | ||||
−0.170420 | + | 0.985371i | \(0.554512\pi\) | |||||||
\(282\) | −2.48072e8 | −0.658727 | ||||||||
\(283\) | −2.43240e8 | −0.637943 | −0.318972 | − | 0.947764i | \(-0.603337\pi\) | ||||
−0.318972 | + | 0.947764i | \(0.603337\pi\) | |||||||
\(284\) | −6.19649e7 | −0.160521 | ||||||||
\(285\) | 2.82152e8 | 0.721982 | ||||||||
\(286\) | −2.41411e8 | −0.610205 | ||||||||
\(287\) | 5.60102e7 | 0.139856 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | −3.27125e8 | −0.797208 | ||||||||
\(290\) | 3.68705e7 | 0.0887742 | ||||||||
\(291\) | −1.80592e8 | −0.429610 | ||||||||
\(292\) | −2.48633e8 | −0.584412 | ||||||||
\(293\) | 6.19586e8 | 1.43901 | 0.719507 | − | 0.694485i | \(-0.244368\pi\) | ||||
0.719507 | + | 0.694485i | \(0.244368\pi\) | |||||||
\(294\) | 1.73999e8 | 0.399330 | ||||||||
\(295\) | −6.55462e7 | −0.148652 | ||||||||
\(296\) | −6.15262e7 | −0.137892 | ||||||||
\(297\) | −5.74227e7 | −0.127185 | ||||||||
\(298\) | −4.35771e7 | −0.0953896 | ||||||||
\(299\) | 8.96016e8 | 1.93850 | ||||||||
\(300\) | −4.10058e7 | −0.0876841 | ||||||||
\(301\) | −4.40725e7 | −0.0931506 | ||||||||
\(302\) | −2.68542e8 | −0.561033 | ||||||||
\(303\) | −1.70332e7 | −0.0351761 | ||||||||
\(304\) | −1.34118e8 | −0.273798 | ||||||||
\(305\) | −1.89236e8 | −0.381904 | ||||||||
\(306\) | −5.32004e7 | −0.106143 | ||||||||
\(307\) | 9.81142e7 | 0.193530 | 0.0967648 | − | 0.995307i | \(-0.469151\pi\) | ||||
0.0967648 | + | 0.995307i | \(0.469151\pi\) | |||||||
\(308\) | 2.50435e7 | 0.0488392 | ||||||||
\(309\) | 2.84516e8 | 0.548595 | ||||||||
\(310\) | −2.49759e8 | −0.476163 | ||||||||
\(311\) | −8.04142e8 | −1.51590 | −0.757951 | − | 0.652311i | \(-0.773799\pi\) | ||||
−0.757951 | + | 0.652311i | \(0.773799\pi\) | |||||||
\(312\) | 1.42991e8 | 0.266543 | ||||||||
\(313\) | −1.80847e8 | −0.333354 | −0.166677 | − | 0.986012i | \(-0.553304\pi\) | ||||
−0.166677 | + | 0.986012i | \(0.553304\pi\) | |||||||
\(314\) | −1.49923e8 | −0.273283 | ||||||||
\(315\) | 3.12063e7 | 0.0562542 | ||||||||
\(316\) | −5.36861e7 | −0.0957099 | ||||||||
\(317\) | 2.56434e8 | 0.452135 | 0.226068 | − | 0.974112i | \(-0.427413\pi\) | ||||
0.226068 | + | 0.974112i | \(0.427413\pi\) | |||||||
\(318\) | 2.37545e8 | 0.414239 | ||||||||
\(319\) | 4.21299e7 | 0.0726647 | ||||||||
\(320\) | 8.36626e7 | 0.142727 | ||||||||
\(321\) | −2.25942e8 | −0.381267 | ||||||||
\(322\) | −9.29512e7 | −0.155153 | ||||||||
\(323\) | 2.98693e8 | 0.493192 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −2.45457e8 | −0.396629 | ||||||||
\(326\) | 9.97106e7 | 0.159397 | ||||||||
\(327\) | 3.74804e8 | 0.592772 | ||||||||
\(328\) | 2.13803e8 | 0.334546 | ||||||||
\(329\) | 1.54045e8 | 0.238485 | ||||||||
\(330\) | −2.01112e8 | −0.308063 | ||||||||
\(331\) | 7.23950e8 | 1.09726 | 0.548632 | − | 0.836064i | \(-0.315149\pi\) | ||||
0.548632 | + | 0.836064i | \(0.315149\pi\) | |||||||
\(332\) | 4.19548e8 | 0.629213 | ||||||||
\(333\) | −8.76027e7 | −0.130006 | ||||||||
\(334\) | 4.30639e8 | 0.632413 | ||||||||
\(335\) | 3.69767e7 | 0.0537368 | ||||||||
\(336\) | −1.48336e7 | −0.0213334 | ||||||||
\(337\) | 5.14260e8 | 0.731945 | 0.365972 | − | 0.930626i | \(-0.380736\pi\) | ||||
0.365972 | + | 0.930626i | \(0.380736\pi\) | |||||||
\(338\) | 3.53942e8 | 0.498566 | ||||||||
\(339\) | 6.14678e7 | 0.0856937 | ||||||||
\(340\) | −1.86324e8 | −0.257094 | ||||||||
\(341\) | −2.85386e8 | −0.389756 | ||||||||
\(342\) | −1.90961e8 | −0.258139 | ||||||||
\(343\) | −2.18509e8 | −0.292375 | ||||||||
\(344\) | −1.68234e8 | −0.222823 | ||||||||
\(345\) | 7.46444e8 | 0.978657 | ||||||||
\(346\) | 6.22091e6 | 0.00807398 | ||||||||
\(347\) | 1.80074e8 | 0.231365 | 0.115683 | − | 0.993286i | \(-0.463094\pi\) | ||||
0.115683 | + | 0.993286i | \(0.463094\pi\) | |||||||
\(348\) | −2.49541e7 | −0.0317405 | ||||||||
\(349\) | −9.22057e8 | −1.16110 | −0.580549 | − | 0.814226i | \(-0.697162\pi\) | ||||
−0.580549 | + | 0.814226i | \(0.697162\pi\) | |||||||
\(350\) | 2.54633e7 | 0.0317451 | ||||||||
\(351\) | 2.03594e8 | 0.251299 | ||||||||
\(352\) | 9.55966e7 | 0.116827 | ||||||||
\(353\) | 7.10394e8 | 0.859584 | 0.429792 | − | 0.902928i | \(-0.358587\pi\) | ||||
0.429792 | + | 0.902928i | \(0.358587\pi\) | |||||||
\(354\) | 4.43619e7 | 0.0531494 | ||||||||
\(355\) | −3.08999e8 | −0.366571 | ||||||||
\(356\) | 4.39168e8 | 0.515888 | ||||||||
\(357\) | 3.30357e7 | 0.0384278 | ||||||||
\(358\) | −1.15571e9 | −1.33125 | ||||||||
\(359\) | 1.68759e8 | 0.192503 | 0.0962514 | − | 0.995357i | \(-0.469315\pi\) | ||||
0.0962514 | + | 0.995357i | \(0.469315\pi\) | |||||||
\(360\) | 1.19121e8 | 0.134564 | ||||||||
\(361\) | 1.78278e8 | 0.199445 | ||||||||
\(362\) | −3.22900e8 | −0.357756 | ||||||||
\(363\) | 2.96354e8 | 0.325190 | ||||||||
\(364\) | −8.87927e7 | −0.0964989 | ||||||||
\(365\) | −1.23985e9 | −1.33458 | ||||||||
\(366\) | 1.28076e8 | 0.136547 | ||||||||
\(367\) | 1.63146e9 | 1.72284 | 0.861419 | − | 0.507895i | \(-0.169576\pi\) | ||||
0.861419 | + | 0.507895i | \(0.169576\pi\) | |||||||
\(368\) | −3.54815e8 | −0.371137 | ||||||||
\(369\) | 3.04419e8 | 0.315413 | ||||||||
\(370\) | −3.06811e8 | −0.314895 | ||||||||
\(371\) | −1.47508e8 | −0.149971 | ||||||||
\(372\) | 1.69038e8 | 0.170249 | ||||||||
\(373\) | 1.08661e9 | 1.08416 | 0.542078 | − | 0.840328i | \(-0.317638\pi\) | ||||
0.542078 | + | 0.840328i | \(0.317638\pi\) | |||||||
\(374\) | −2.12902e8 | −0.210440 | ||||||||
\(375\) | 4.68719e8 | 0.458990 | ||||||||
\(376\) | 5.88022e8 | 0.570474 | ||||||||
\(377\) | −1.49373e8 | −0.143574 | ||||||||
\(378\) | −2.11205e7 | −0.0201133 | ||||||||
\(379\) | −3.15599e8 | −0.297782 | −0.148891 | − | 0.988854i | \(-0.547570\pi\) | ||||
−0.148891 | + | 0.988854i | \(0.547570\pi\) | |||||||
\(380\) | −6.68805e8 | −0.625254 | ||||||||
\(381\) | 5.27673e8 | 0.488796 | ||||||||
\(382\) | 1.11663e9 | 1.02491 | ||||||||
\(383\) | 7.06697e8 | 0.642743 | 0.321372 | − | 0.946953i | \(-0.395856\pi\) | ||||
0.321372 | + | 0.946953i | \(0.395856\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | 1.24884e8 | 0.111531 | ||||||||
\(386\) | −1.46510e9 | −1.29662 | ||||||||
\(387\) | −2.39537e8 | −0.210080 | ||||||||
\(388\) | 4.28071e8 | 0.372053 | ||||||||
\(389\) | 3.95928e8 | 0.341030 | 0.170515 | − | 0.985355i | \(-0.445457\pi\) | ||||
0.170515 | + | 0.985355i | \(0.445457\pi\) | |||||||
\(390\) | 7.13049e8 | 0.608686 | ||||||||
\(391\) | 7.90204e8 | 0.668529 | ||||||||
\(392\) | −4.12443e8 | −0.345830 | ||||||||
\(393\) | 9.42497e8 | 0.783260 | ||||||||
\(394\) | 6.85086e8 | 0.564298 | ||||||||
\(395\) | −2.67715e8 | −0.218566 | ||||||||
\(396\) | 1.36113e8 | 0.110146 | ||||||||
\(397\) | −1.69179e9 | −1.35700 | −0.678500 | − | 0.734601i | \(-0.737369\pi\) | ||||
−0.678500 | + | 0.734601i | \(0.737369\pi\) | |||||||
\(398\) | 4.99300e7 | 0.0396982 | ||||||||
\(399\) | 1.18581e8 | 0.0934565 | ||||||||
\(400\) | 9.71990e7 | 0.0759367 | ||||||||
\(401\) | −1.31847e9 | −1.02110 | −0.510548 | − | 0.859849i | \(-0.670557\pi\) | ||||
−0.510548 | + | 0.859849i | \(0.670557\pi\) | |||||||
\(402\) | −2.50259e7 | −0.0192132 | ||||||||
\(403\) | 1.01185e9 | 0.770099 | ||||||||
\(404\) | 4.03751e7 | 0.0304634 | ||||||||
\(405\) | 1.69608e8 | 0.126869 | ||||||||
\(406\) | 1.54957e7 | 0.0114913 | ||||||||
\(407\) | −3.50576e8 | −0.257752 | ||||||||
\(408\) | 1.26105e8 | 0.0919222 | ||||||||
\(409\) | 7.65102e8 | 0.552952 | 0.276476 | − | 0.961021i | \(-0.410833\pi\) | ||||
0.276476 | + | 0.961021i | \(0.410833\pi\) | |||||||
\(410\) | 1.06617e9 | 0.763981 | ||||||||
\(411\) | −5.09788e8 | −0.362196 | ||||||||
\(412\) | −6.74408e8 | −0.475097 | ||||||||
\(413\) | −2.75473e7 | −0.0192422 | ||||||||
\(414\) | −5.05195e8 | −0.349911 | ||||||||
\(415\) | 2.09215e9 | 1.43689 | ||||||||
\(416\) | −3.38941e8 | −0.230833 | ||||||||
\(417\) | 5.44562e8 | 0.367766 | ||||||||
\(418\) | −7.64206e8 | −0.511792 | ||||||||
\(419\) | −2.00535e9 | −1.33180 | −0.665902 | − | 0.746039i | \(-0.731953\pi\) | ||||
−0.665902 | + | 0.746039i | \(0.731953\pi\) | |||||||
\(420\) | −7.39705e7 | −0.0487176 | ||||||||
\(421\) | 1.17061e9 | 0.764582 | 0.382291 | − | 0.924042i | \(-0.375135\pi\) | ||||
0.382291 | + | 0.924042i | \(0.375135\pi\) | |||||||
\(422\) | 5.01762e8 | 0.325016 | ||||||||
\(423\) | 8.37242e8 | 0.537848 | ||||||||
\(424\) | −5.63070e8 | −0.358742 | ||||||||
\(425\) | −2.16471e8 | −0.136785 | ||||||||
\(426\) | 2.09131e8 | 0.131065 | ||||||||
\(427\) | −7.95308e7 | −0.0494354 | ||||||||
\(428\) | 5.35566e8 | 0.330187 | ||||||||
\(429\) | 8.14761e8 | 0.498230 | ||||||||
\(430\) | −8.38932e8 | −0.508847 | ||||||||
\(431\) | 2.19094e9 | 1.31814 | 0.659069 | − | 0.752083i | \(-0.270951\pi\) | ||||
0.659069 | + | 0.752083i | \(0.270951\pi\) | |||||||
\(432\) | −8.06216e7 | −0.0481125 | ||||||||
\(433\) | −2.07257e9 | −1.22688 | −0.613438 | − | 0.789743i | \(-0.710214\pi\) | ||||
−0.613438 | + | 0.789743i | \(0.710214\pi\) | |||||||
\(434\) | −1.04967e8 | −0.0616367 | ||||||||
\(435\) | −1.24438e8 | −0.0724838 | ||||||||
\(436\) | −8.88425e8 | −0.513355 | ||||||||
\(437\) | 2.83641e9 | 1.62587 | ||||||||
\(438\) | 8.39137e8 | 0.477170 | ||||||||
\(439\) | −7.57095e8 | −0.427095 | −0.213547 | − | 0.976933i | \(-0.568502\pi\) | ||||
−0.213547 | + | 0.976933i | \(0.568502\pi\) | |||||||
\(440\) | 4.76710e8 | 0.266790 | ||||||||
\(441\) | −5.87248e8 | −0.326052 | ||||||||
\(442\) | 7.54851e8 | 0.415799 | ||||||||
\(443\) | 1.63901e9 | 0.895710 | 0.447855 | − | 0.894106i | \(-0.352188\pi\) | ||||
0.447855 | + | 0.894106i | \(0.352188\pi\) | |||||||
\(444\) | 2.07651e8 | 0.112588 | ||||||||
\(445\) | 2.18999e9 | 1.17810 | ||||||||
\(446\) | 5.92849e8 | 0.316426 | ||||||||
\(447\) | 1.47073e8 | 0.0778853 | ||||||||
\(448\) | 3.51611e7 | 0.0184752 | ||||||||
\(449\) | −4.36670e8 | −0.227663 | −0.113831 | − | 0.993500i | \(-0.536312\pi\) | ||||
−0.113831 | + | 0.993500i | \(0.536312\pi\) | |||||||
\(450\) | 1.38395e8 | 0.0715938 | ||||||||
\(451\) | 1.21825e9 | 0.625344 | ||||||||
\(452\) | −1.45701e8 | −0.0742129 | ||||||||
\(453\) | 9.06330e8 | 0.458081 | ||||||||
\(454\) | 1.38874e9 | 0.696507 | ||||||||
\(455\) | −4.42781e8 | −0.220368 | ||||||||
\(456\) | 4.52649e8 | 0.223555 | ||||||||
\(457\) | 2.88443e9 | 1.41369 | 0.706844 | − | 0.707369i | \(-0.250118\pi\) | ||||
0.706844 | + | 0.707369i | \(0.250118\pi\) | |||||||
\(458\) | 1.68356e8 | 0.0818839 | ||||||||
\(459\) | 1.79551e8 | 0.0866651 | ||||||||
\(460\) | −1.76935e9 | −0.847542 | ||||||||
\(461\) | −2.73090e9 | −1.29823 | −0.649117 | − | 0.760688i | \(-0.724862\pi\) | ||||
−0.649117 | + | 0.760688i | \(0.724862\pi\) | |||||||
\(462\) | −8.45219e7 | −0.0398770 | ||||||||
\(463\) | 1.90108e9 | 0.890158 | 0.445079 | − | 0.895491i | \(-0.353176\pi\) | ||||
0.445079 | + | 0.895491i | \(0.353176\pi\) | |||||||
\(464\) | 5.91504e7 | 0.0274881 | ||||||||
\(465\) | 8.42938e8 | 0.388786 | ||||||||
\(466\) | 6.32758e7 | 0.0289659 | ||||||||
\(467\) | 2.16043e9 | 0.981594 | 0.490797 | − | 0.871274i | \(-0.336706\pi\) | ||||
0.490797 | + | 0.871274i | \(0.336706\pi\) | |||||||
\(468\) | −4.82594e8 | −0.217631 | ||||||||
\(469\) | 1.55403e7 | 0.00695592 | ||||||||
\(470\) | 2.93228e9 | 1.30275 | ||||||||
\(471\) | 5.05989e8 | 0.223135 | ||||||||
\(472\) | −1.05154e8 | −0.0460287 | ||||||||
\(473\) | −9.58601e8 | −0.416508 | ||||||||
\(474\) | 1.81190e8 | 0.0781468 | ||||||||
\(475\) | −7.77015e8 | −0.332661 | ||||||||
\(476\) | −7.83069e7 | −0.0332794 | ||||||||
\(477\) | −8.01715e8 | −0.338225 | ||||||||
\(478\) | 1.92435e9 | 0.805909 | ||||||||
\(479\) | −2.39817e9 | −0.997022 | −0.498511 | − | 0.866883i | \(-0.666120\pi\) | ||||
−0.498511 | + | 0.866883i | \(0.666120\pi\) | |||||||
\(480\) | −2.82361e8 | −0.116536 | ||||||||
\(481\) | 1.24298e9 | 0.509280 | ||||||||
\(482\) | 4.05392e8 | 0.164896 | ||||||||
\(483\) | 3.13710e8 | 0.126682 | ||||||||
\(484\) | −7.02469e8 | −0.281623 | ||||||||
\(485\) | 2.13465e9 | 0.849633 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | 2.94508e9 | 1.15544 | 0.577718 | − | 0.816236i | \(-0.303943\pi\) | ||||
0.577718 | + | 0.816236i | \(0.303943\pi\) | |||||||
\(488\) | −3.03586e8 | −0.118253 | ||||||||
\(489\) | −3.36523e8 | −0.130147 | ||||||||
\(490\) | −2.05672e9 | −0.789749 | ||||||||
\(491\) | −2.47730e9 | −0.944481 | −0.472241 | − | 0.881470i | \(-0.656555\pi\) | ||||
−0.472241 | + | 0.881470i | \(0.656555\pi\) | |||||||
\(492\) | −7.21586e8 | −0.273156 | ||||||||
\(493\) | −1.31733e8 | −0.0495143 | ||||||||
\(494\) | 2.70952e9 | 1.01122 | ||||||||
\(495\) | 6.78753e8 | 0.251532 | ||||||||
\(496\) | −4.00682e8 | −0.147440 | ||||||||
\(497\) | −1.29864e8 | −0.0474506 | ||||||||
\(498\) | −1.41597e9 | −0.513750 | ||||||||
\(499\) | 2.09171e9 | 0.753617 | 0.376808 | − | 0.926291i | \(-0.377022\pi\) | ||||
0.376808 | + | 0.926291i | \(0.377022\pi\) | |||||||
\(500\) | −1.11104e9 | −0.397497 | ||||||||
\(501\) | −1.45341e9 | −0.516363 | ||||||||
\(502\) | −9.16100e8 | −0.323206 | ||||||||
\(503\) | −2.28640e9 | −0.801058 | −0.400529 | − | 0.916284i | \(-0.631174\pi\) | ||||
−0.400529 | + | 0.916284i | \(0.631174\pi\) | |||||||
\(504\) | 5.00634e7 | 0.0174186 | ||||||||
\(505\) | 2.01338e8 | 0.0695673 | ||||||||
\(506\) | −2.02174e9 | −0.693742 | ||||||||
\(507\) | −1.19455e9 | −0.407078 | ||||||||
\(508\) | −1.25078e9 | −0.423309 | ||||||||
\(509\) | −1.86659e9 | −0.627389 | −0.313695 | − | 0.949524i | \(-0.601567\pi\) | ||||
−0.313695 | + | 0.949524i | \(0.601567\pi\) | |||||||
\(510\) | 6.28843e8 | 0.209917 | ||||||||
\(511\) | −5.21077e8 | −0.172754 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 6.44494e8 | 0.210770 | ||||||||
\(514\) | −2.91341e9 | −0.946305 | ||||||||
\(515\) | −3.36306e9 | −1.08495 | ||||||||
\(516\) | 5.67791e8 | 0.181934 | ||||||||
\(517\) | 3.35055e9 | 1.06635 | ||||||||
\(518\) | −1.28945e8 | −0.0407614 | ||||||||
\(519\) | −2.09956e7 | −0.00659238 | ||||||||
\(520\) | −1.69019e9 | −0.527138 | ||||||||
\(521\) | 5.27830e9 | 1.63517 | 0.817583 | − | 0.575811i | \(-0.195314\pi\) | ||||
0.817583 | + | 0.575811i | \(0.195314\pi\) | |||||||
\(522\) | 8.42200e7 | 0.0259160 | ||||||||
\(523\) | 4.76478e9 | 1.45642 | 0.728210 | − | 0.685354i | \(-0.240352\pi\) | ||||
0.728210 | + | 0.685354i | \(0.240352\pi\) | |||||||
\(524\) | −2.23407e9 | −0.678323 | ||||||||
\(525\) | −8.59387e7 | −0.0259198 | ||||||||
\(526\) | 4.54297e9 | 1.36110 | ||||||||
\(527\) | 8.92354e8 | 0.265583 | ||||||||
\(528\) | −3.22639e8 | −0.0953889 | ||||||||
\(529\) | 4.09902e9 | 1.20388 | ||||||||
\(530\) | −2.80785e9 | −0.819235 | ||||||||
\(531\) | −1.49721e8 | −0.0433963 | ||||||||
\(532\) | −2.81081e8 | −0.0809357 | ||||||||
\(533\) | −4.31935e9 | −1.23559 | ||||||||
\(534\) | −1.48219e9 | −0.421221 | ||||||||
\(535\) | 2.67070e9 | 0.754026 | ||||||||
\(536\) | 5.93208e7 | 0.0166391 | ||||||||
\(537\) | 3.90053e9 | 1.08696 | ||||||||
\(538\) | 1.29708e8 | 0.0359110 | ||||||||
\(539\) | −2.35010e9 | −0.646436 | ||||||||
\(540\) | −4.02034e8 | −0.109871 | ||||||||
\(541\) | −2.56129e9 | −0.695454 | −0.347727 | − | 0.937596i | \(-0.613046\pi\) | ||||
−0.347727 | + | 0.937596i | \(0.613046\pi\) | |||||||
\(542\) | −3.03930e9 | −0.819928 | ||||||||
\(543\) | 1.08979e9 | 0.292107 | ||||||||
\(544\) | −2.98915e8 | −0.0796069 | ||||||||
\(545\) | −4.43029e9 | −1.17232 | ||||||||
\(546\) | 2.99675e8 | 0.0787910 | ||||||||
\(547\) | 1.83572e9 | 0.479568 | 0.239784 | − | 0.970826i | \(-0.422923\pi\) | ||||
0.239784 | + | 0.970826i | \(0.422923\pi\) | |||||||
\(548\) | 1.20839e9 | 0.313671 | ||||||||
\(549\) | −4.32255e8 | −0.111490 | ||||||||
\(550\) | 5.53840e8 | 0.141943 | ||||||||
\(551\) | −4.72852e8 | −0.120419 | ||||||||
\(552\) | 1.19750e9 | 0.303032 | ||||||||
\(553\) | −1.12514e8 | −0.0282922 | ||||||||
\(554\) | 9.92423e8 | 0.247978 | ||||||||
\(555\) | 1.03549e9 | 0.257111 | ||||||||
\(556\) | −1.29081e9 | −0.318495 | ||||||||
\(557\) | −2.68214e9 | −0.657641 | −0.328820 | − | 0.944392i | \(-0.606651\pi\) | ||||
−0.328820 | + | 0.944392i | \(0.606651\pi\) | |||||||
\(558\) | −5.70503e8 | −0.139007 | ||||||||
\(559\) | 3.39875e9 | 0.822958 | ||||||||
\(560\) | 1.75337e8 | 0.0421907 | ||||||||
\(561\) | 7.18544e8 | 0.171824 | ||||||||
\(562\) | −1.01418e9 | −0.241010 | ||||||||
\(563\) | −7.19760e9 | −1.69984 | −0.849921 | − | 0.526910i | \(-0.823350\pi\) | ||||
−0.849921 | + | 0.526910i | \(0.823350\pi\) | |||||||
\(564\) | −1.98457e9 | −0.465790 | ||||||||
\(565\) | −7.26567e8 | −0.169475 | ||||||||
\(566\) | −1.94592e9 | −0.451094 | ||||||||
\(567\) | 7.12817e7 | 0.0164224 | ||||||||
\(568\) | −4.95719e8 | −0.113505 | ||||||||
\(569\) | −8.54848e9 | −1.94534 | −0.972671 | − | 0.232189i | \(-0.925411\pi\) | ||||
−0.972671 | + | 0.232189i | \(0.925411\pi\) | |||||||
\(570\) | 2.25722e9 | 0.510518 | ||||||||
\(571\) | 7.25047e9 | 1.62982 | 0.814911 | − | 0.579587i | \(-0.196786\pi\) | ||||
0.814911 | + | 0.579587i | \(0.196786\pi\) | |||||||
\(572\) | −1.93129e9 | −0.431480 | ||||||||
\(573\) | −3.76863e9 | −0.836839 | ||||||||
\(574\) | 4.48082e8 | 0.0988930 | ||||||||
\(575\) | −2.05562e9 | −0.450927 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | −5.68024e9 | −1.23098 | −0.615490 | − | 0.788145i | \(-0.711042\pi\) | ||||
−0.615490 | + | 0.788145i | \(0.711042\pi\) | |||||||
\(578\) | −2.61700e9 | −0.563711 | ||||||||
\(579\) | 4.94473e9 | 1.05869 | ||||||||
\(580\) | 2.94964e8 | 0.0627728 | ||||||||
\(581\) | 8.79274e8 | 0.185998 | ||||||||
\(582\) | −1.44474e9 | −0.303780 | ||||||||
\(583\) | −3.20838e9 | −0.670572 | ||||||||
\(584\) | −1.98907e9 | −0.413242 | ||||||||
\(585\) | −2.40654e9 | −0.496990 | ||||||||
\(586\) | 4.95669e9 | 1.01754 | ||||||||
\(587\) | 2.80625e9 | 0.572655 | 0.286327 | − | 0.958132i | \(-0.407566\pi\) | ||||
0.286327 | + | 0.958132i | \(0.407566\pi\) | |||||||
\(588\) | 1.39199e9 | 0.282369 | ||||||||
\(589\) | 3.20308e9 | 0.645899 | ||||||||
\(590\) | −5.24370e8 | −0.105113 | ||||||||
\(591\) | −2.31217e9 | −0.460747 | ||||||||
\(592\) | −4.92209e8 | −0.0975043 | ||||||||
\(593\) | −9.23383e9 | −1.81840 | −0.909202 | − | 0.416355i | \(-0.863307\pi\) | ||||
−0.909202 | + | 0.416355i | \(0.863307\pi\) | |||||||
\(594\) | −4.59382e8 | −0.0899335 | ||||||||
\(595\) | −3.90492e8 | −0.0759980 | ||||||||
\(596\) | −3.48617e8 | −0.0674507 | ||||||||
\(597\) | −1.68514e8 | −0.0324135 | ||||||||
\(598\) | 7.16813e9 | 1.37073 | ||||||||
\(599\) | −2.65856e9 | −0.505420 | −0.252710 | − | 0.967542i | \(-0.581322\pi\) | ||||
−0.252710 | + | 0.967542i | \(0.581322\pi\) | |||||||
\(600\) | −3.28047e8 | −0.0620021 | ||||||||
\(601\) | −7.40132e8 | −0.139075 | −0.0695374 | − | 0.997579i | \(-0.522152\pi\) | ||||
−0.0695374 | + | 0.997579i | \(0.522152\pi\) | |||||||
\(602\) | −3.52580e8 | −0.0658674 | ||||||||
\(603\) | 8.44626e7 | 0.0156875 | ||||||||
\(604\) | −2.14834e9 | −0.396710 | ||||||||
\(605\) | −3.50299e9 | −0.643124 | ||||||||
\(606\) | −1.36266e8 | −0.0248733 | ||||||||
\(607\) | −5.21369e9 | −0.946204 | −0.473102 | − | 0.881008i | \(-0.656866\pi\) | ||||
−0.473102 | + | 0.881008i | \(0.656866\pi\) | |||||||
\(608\) | −1.07295e9 | −0.193604 | ||||||||
\(609\) | −5.22980e7 | −0.00938262 | ||||||||
\(610\) | −1.51389e9 | −0.270047 | ||||||||
\(611\) | −1.18795e10 | −2.10695 | ||||||||
\(612\) | −4.25603e8 | −0.0750541 | ||||||||
\(613\) | −4.36241e9 | −0.764919 | −0.382459 | − | 0.923972i | \(-0.624923\pi\) | ||||
−0.382459 | + | 0.923972i | \(0.624923\pi\) | |||||||
\(614\) | 7.84914e8 | 0.136846 | ||||||||
\(615\) | −3.59832e9 | −0.623788 | ||||||||
\(616\) | 2.00348e8 | 0.0345345 | ||||||||
\(617\) | −2.10920e9 | −0.361510 | −0.180755 | − | 0.983528i | \(-0.557854\pi\) | ||||
−0.180755 | + | 0.983528i | \(0.557854\pi\) | |||||||
\(618\) | 2.27613e9 | 0.387915 | ||||||||
\(619\) | −6.07418e9 | −1.02937 | −0.514684 | − | 0.857380i | \(-0.672091\pi\) | ||||
−0.514684 | + | 0.857380i | \(0.672091\pi\) | |||||||
\(620\) | −1.99807e9 | −0.336698 | ||||||||
\(621\) | 1.70503e9 | 0.285702 | ||||||||
\(622\) | −6.43313e9 | −1.07190 | ||||||||
\(623\) | 9.20393e8 | 0.152498 | ||||||||
\(624\) | 1.14393e9 | 0.188474 | ||||||||
\(625\) | −7.39432e9 | −1.21148 | ||||||||
\(626\) | −1.44677e9 | −0.235717 | ||||||||
\(627\) | 2.57919e9 | 0.417876 | ||||||||
\(628\) | −1.19938e9 | −0.193241 | ||||||||
\(629\) | 1.09619e9 | 0.175634 | ||||||||
\(630\) | 2.49650e8 | 0.0397778 | ||||||||
\(631\) | 2.61613e9 | 0.414531 | 0.207266 | − | 0.978285i | \(-0.433544\pi\) | ||||
0.207266 | + | 0.978285i | \(0.433544\pi\) | |||||||
\(632\) | −4.29489e8 | −0.0676771 | ||||||||
\(633\) | −1.69345e9 | −0.265374 | ||||||||
\(634\) | 2.05147e9 | 0.319708 | ||||||||
\(635\) | −6.23724e9 | −0.966684 | ||||||||
\(636\) | 1.90036e9 | 0.292912 | ||||||||
\(637\) | 8.33236e9 | 1.27726 | ||||||||
\(638\) | 3.37039e8 | 0.0513817 | ||||||||
\(639\) | −7.05819e8 | −0.107014 | ||||||||
\(640\) | 6.69301e8 | 0.100923 | ||||||||
\(641\) | 6.44130e9 | 0.965985 | 0.482992 | − | 0.875625i | \(-0.339550\pi\) | ||||
0.482992 | + | 0.875625i | \(0.339550\pi\) | |||||||
\(642\) | −1.80753e9 | −0.269596 | ||||||||
\(643\) | 6.42061e9 | 0.952441 | 0.476220 | − | 0.879326i | \(-0.342006\pi\) | ||||
0.476220 | + | 0.879326i | \(0.342006\pi\) | |||||||
\(644\) | −7.43609e8 | −0.109710 | ||||||||
\(645\) | 2.83140e9 | 0.415472 | ||||||||
\(646\) | 2.38954e9 | 0.348739 | ||||||||
\(647\) | 5.79769e9 | 0.841570 | 0.420785 | − | 0.907160i | \(-0.361755\pi\) | ||||
0.420785 | + | 0.907160i | \(0.361755\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | −5.99168e8 | −0.0860384 | ||||||||
\(650\) | −1.96366e9 | −0.280459 | ||||||||
\(651\) | 3.54264e8 | 0.0503261 | ||||||||
\(652\) | 7.97685e8 | 0.112711 | ||||||||
\(653\) | −5.29082e9 | −0.743578 | −0.371789 | − | 0.928317i | \(-0.621256\pi\) | ||||
−0.371789 | + | 0.928317i | \(0.621256\pi\) | |||||||
\(654\) | 2.99843e9 | 0.419153 | ||||||||
\(655\) | −1.11406e10 | −1.54904 | ||||||||
\(656\) | 1.71043e9 | 0.236560 | ||||||||
\(657\) | −2.83209e9 | −0.389608 | ||||||||
\(658\) | 1.23236e9 | 0.168634 | ||||||||
\(659\) | 6.58899e9 | 0.896850 | 0.448425 | − | 0.893820i | \(-0.351985\pi\) | ||||
0.448425 | + | 0.893820i | \(0.351985\pi\) | |||||||
\(660\) | −1.60890e9 | −0.217833 | ||||||||
\(661\) | 3.86916e9 | 0.521089 | 0.260545 | − | 0.965462i | \(-0.416098\pi\) | ||||
0.260545 | + | 0.965462i | \(0.416098\pi\) | |||||||
\(662\) | 5.79160e9 | 0.775882 | ||||||||
\(663\) | −2.54762e9 | −0.339498 | ||||||||
\(664\) | 3.35638e9 | 0.444921 | ||||||||
\(665\) | −1.40166e9 | −0.184828 | ||||||||
\(666\) | −7.00822e8 | −0.0919280 | ||||||||
\(667\) | −1.25095e9 | −0.163230 | ||||||||
\(668\) | 3.44511e9 | 0.447184 | ||||||||
\(669\) | −2.00086e9 | −0.258361 | ||||||||
\(670\) | 2.95814e8 | 0.0379976 | ||||||||
\(671\) | −1.72984e9 | −0.221043 | ||||||||
\(672\) | −1.18669e8 | −0.0150850 | ||||||||
\(673\) | −4.55131e9 | −0.575550 | −0.287775 | − | 0.957698i | \(-0.592916\pi\) | ||||
−0.287775 | + | 0.957698i | \(0.592916\pi\) | |||||||
\(674\) | 4.11408e9 | 0.517563 | ||||||||
\(675\) | −4.67082e8 | −0.0584561 | ||||||||
\(676\) | 2.83153e9 | 0.352540 | ||||||||
\(677\) | 3.14550e9 | 0.389609 | 0.194805 | − | 0.980842i | \(-0.437593\pi\) | ||||
0.194805 | + | 0.980842i | \(0.437593\pi\) | |||||||
\(678\) | 4.91742e8 | 0.0605946 | ||||||||
\(679\) | 8.97137e8 | 0.109980 | ||||||||
\(680\) | −1.49059e9 | −0.181793 | ||||||||
\(681\) | −4.68700e9 | −0.568695 | ||||||||
\(682\) | −2.28309e9 | −0.275599 | ||||||||
\(683\) | −1.39868e10 | −1.67976 | −0.839879 | − | 0.542774i | \(-0.817374\pi\) | ||||
−0.839879 | + | 0.542774i | \(0.817374\pi\) | |||||||
\(684\) | −1.52769e9 | −0.182532 | ||||||||
\(685\) | 6.02584e9 | 0.716309 | ||||||||
\(686\) | −1.74807e9 | −0.206740 | ||||||||
\(687\) | −5.68200e8 | −0.0668579 | ||||||||
\(688\) | −1.34588e9 | −0.157560 | ||||||||
\(689\) | 1.13754e10 | 1.32495 | ||||||||
\(690\) | 5.97155e9 | 0.692015 | ||||||||
\(691\) | −3.62313e9 | −0.417745 | −0.208872 | − | 0.977943i | \(-0.566979\pi\) | ||||
−0.208872 | + | 0.977943i | \(0.566979\pi\) | |||||||
\(692\) | 4.97673e7 | 0.00570916 | ||||||||
\(693\) | 2.85262e8 | 0.0325594 | ||||||||
\(694\) | 1.44059e9 | 0.163600 | ||||||||
\(695\) | −6.43688e9 | −0.727325 | ||||||||
\(696\) | −1.99633e8 | −0.0224439 | ||||||||
\(697\) | −3.80927e9 | −0.426115 | ||||||||
\(698\) | −7.37645e9 | −0.821020 | ||||||||
\(699\) | −2.13556e8 | −0.0236506 | ||||||||
\(700\) | 2.03706e8 | 0.0224472 | ||||||||
\(701\) | 2.11707e9 | 0.232126 | 0.116063 | − | 0.993242i | \(-0.462973\pi\) | ||||
0.116063 | + | 0.993242i | \(0.462973\pi\) | |||||||
\(702\) | 1.62875e9 | 0.177695 | ||||||||
\(703\) | 3.93475e9 | 0.427144 | ||||||||
\(704\) | 7.64773e8 | 0.0826092 | ||||||||
\(705\) | −9.89644e9 | −1.06369 | ||||||||
\(706\) | 5.68316e9 | 0.607817 | ||||||||
\(707\) | 8.46168e7 | 0.00900510 | ||||||||
\(708\) | 3.54895e8 | 0.0375823 | ||||||||
\(709\) | 6.94371e9 | 0.731694 | 0.365847 | − | 0.930675i | \(-0.380779\pi\) | ||||
0.365847 | + | 0.930675i | \(0.380779\pi\) | |||||||
\(710\) | −2.47199e9 | −0.259205 | ||||||||
\(711\) | −6.11518e8 | −0.0638066 | ||||||||
\(712\) | 3.51334e9 | 0.364788 | ||||||||
\(713\) | 8.47387e9 | 0.875525 | ||||||||
\(714\) | 2.64286e8 | 0.0271725 | ||||||||
\(715\) | −9.63071e9 | −0.985342 | ||||||||
\(716\) | −9.24571e9 | −0.941336 | ||||||||
\(717\) | −6.49467e9 | −0.658022 | ||||||||
\(718\) | 1.35007e9 | 0.136120 | ||||||||
\(719\) | 2.10736e9 | 0.211441 | 0.105720 | − | 0.994396i | \(-0.466285\pi\) | ||||
0.105720 | + | 0.994396i | \(0.466285\pi\) | |||||||
\(720\) | 9.52970e8 | 0.0951514 | ||||||||
\(721\) | −1.41340e9 | −0.140440 | ||||||||
\(722\) | 1.42622e9 | 0.141029 | ||||||||
\(723\) | −1.36820e9 | −0.134637 | ||||||||
\(724\) | −2.58320e9 | −0.252972 | ||||||||
\(725\) | 3.42689e8 | 0.0333977 | ||||||||
\(726\) | 2.37083e9 | 0.229944 | ||||||||
\(727\) | 1.52446e10 | 1.47145 | 0.735725 | − | 0.677281i | \(-0.236842\pi\) | ||||
0.735725 | + | 0.677281i | \(0.236842\pi\) | |||||||
\(728\) | −7.10341e8 | −0.0682350 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −9.91884e9 | −0.943693 | ||||||||
\(731\) | 2.99738e9 | 0.283812 | ||||||||
\(732\) | 1.02460e9 | 0.0965534 | ||||||||
\(733\) | −8.80231e9 | −0.825530 | −0.412765 | − | 0.910838i | \(-0.635437\pi\) | ||||
−0.412765 | + | 0.910838i | \(0.635437\pi\) | |||||||
\(734\) | 1.30517e10 | 1.21823 | ||||||||
\(735\) | 6.94143e9 | 0.644827 | ||||||||
\(736\) | −2.83852e9 | −0.262434 | ||||||||
\(737\) | 3.38010e8 | 0.0311023 | ||||||||
\(738\) | 2.43535e9 | 0.223031 | ||||||||
\(739\) | 1.46818e10 | 1.33820 | 0.669102 | − | 0.743170i | \(-0.266679\pi\) | ||||
0.669102 | + | 0.743170i | \(0.266679\pi\) | |||||||
\(740\) | −2.45449e9 | −0.222664 | ||||||||
\(741\) | −9.14462e9 | −0.825661 | ||||||||
\(742\) | −1.18006e9 | −0.106045 | ||||||||
\(743\) | 1.31756e9 | 0.117845 | 0.0589224 | − | 0.998263i | \(-0.481234\pi\) | ||||
0.0589224 | + | 0.998263i | \(0.481234\pi\) | |||||||
\(744\) | 1.35230e9 | 0.120384 | ||||||||
\(745\) | −1.73844e9 | −0.154033 | ||||||||
\(746\) | 8.69286e9 | 0.766614 | ||||||||
\(747\) | 4.77891e9 | 0.419476 | ||||||||
\(748\) | −1.70322e9 | −0.148804 | ||||||||
\(749\) | 1.12242e9 | 0.0976045 | ||||||||
\(750\) | 3.74975e9 | 0.324555 | ||||||||
\(751\) | −6.26370e9 | −0.539624 | −0.269812 | − | 0.962913i | \(-0.586962\pi\) | ||||
−0.269812 | + | 0.962913i | \(0.586962\pi\) | |||||||
\(752\) | 4.70417e9 | 0.403386 | ||||||||
\(753\) | 3.09184e9 | 0.263897 | ||||||||
\(754\) | −1.19498e9 | −0.101522 | ||||||||
\(755\) | −1.07131e10 | −0.905941 | ||||||||
\(756\) | −1.68964e8 | −0.0142222 | ||||||||
\(757\) | 8.13983e9 | 0.681993 | 0.340997 | − | 0.940065i | \(-0.389236\pi\) | ||||
0.340997 | + | 0.940065i | \(0.389236\pi\) | |||||||
\(758\) | −2.52479e9 | −0.210564 | ||||||||
\(759\) | 6.82336e9 | 0.566438 | ||||||||
\(760\) | −5.35044e9 | −0.442122 | ||||||||
\(761\) | −8.43213e9 | −0.693571 | −0.346786 | − | 0.937944i | \(-0.612727\pi\) | ||||
−0.346786 | + | 0.937944i | \(0.612727\pi\) | |||||||
\(762\) | 4.22138e9 | 0.345631 | ||||||||
\(763\) | −1.86193e9 | −0.151750 | ||||||||
\(764\) | 8.93304e9 | 0.724724 | ||||||||
\(765\) | −2.12235e9 | −0.171396 | ||||||||
\(766\) | 5.65358e9 | 0.454488 | ||||||||
\(767\) | 2.12437e9 | 0.169999 | ||||||||
\(768\) | −4.52985e8 | −0.0360844 | ||||||||
\(769\) | −1.10963e10 | −0.879902 | −0.439951 | − | 0.898022i | \(-0.645004\pi\) | ||||
−0.439951 | + | 0.898022i | \(0.645004\pi\) | |||||||
\(770\) | 9.99073e8 | 0.0788642 | ||||||||
\(771\) | 9.83277e9 | 0.772655 | ||||||||
\(772\) | −1.17208e10 | −0.916849 | ||||||||
\(773\) | −8.97205e9 | −0.698656 | −0.349328 | − | 0.937000i | \(-0.613590\pi\) | ||||
−0.349328 | + | 0.937000i | \(0.613590\pi\) | |||||||
\(774\) | −1.91630e9 | −0.148549 | ||||||||
\(775\) | −2.32136e9 | −0.179137 | ||||||||
\(776\) | 3.42457e9 | 0.263081 | ||||||||
\(777\) | 4.35188e8 | 0.0332815 | ||||||||
\(778\) | 3.16743e9 | 0.241145 | ||||||||
\(779\) | −1.36733e10 | −1.03631 | ||||||||
\(780\) | 5.70439e9 | 0.430406 | ||||||||
\(781\) | −2.82461e9 | −0.212168 | ||||||||
\(782\) | 6.32163e9 | 0.472721 | ||||||||
\(783\) | −2.84243e8 | −0.0211604 | ||||||||
\(784\) | −3.29954e9 | −0.244539 | ||||||||
\(785\) | −5.98093e9 | −0.441291 | ||||||||
\(786\) | 7.53998e9 | 0.553849 | ||||||||
\(787\) | −7.29218e9 | −0.533268 | −0.266634 | − | 0.963798i | \(-0.585912\pi\) | ||||
−0.266634 | + | 0.963798i | \(0.585912\pi\) | |||||||
\(788\) | 5.48069e9 | 0.399019 | ||||||||
\(789\) | −1.53325e10 | −1.11133 | ||||||||
\(790\) | −2.14172e9 | −0.154550 | ||||||||
\(791\) | −3.05356e8 | −0.0219376 | ||||||||
\(792\) | 1.08891e9 | 0.0778847 | ||||||||
\(793\) | 6.13319e9 | 0.436747 | ||||||||
\(794\) | −1.35343e10 | −0.959543 | ||||||||
\(795\) | 9.47650e9 | 0.668903 | ||||||||
\(796\) | 3.99440e8 | 0.0280709 | ||||||||
\(797\) | −6.90636e9 | −0.483220 | −0.241610 | − | 0.970373i | \(-0.577675\pi\) | ||||
−0.241610 | + | 0.970373i | \(0.577675\pi\) | |||||||
\(798\) | 9.48647e8 | 0.0660837 | ||||||||
\(799\) | −1.04766e10 | −0.726619 | ||||||||
\(800\) | 7.77592e8 | 0.0536954 | ||||||||
\(801\) | 5.00239e9 | 0.343925 | ||||||||
\(802\) | −1.05478e10 | −0.722024 | ||||||||
\(803\) | −1.13337e10 | −0.772445 | ||||||||
\(804\) | −2.00208e8 | −0.0135858 | ||||||||
\(805\) | −3.70814e9 | −0.250536 | ||||||||
\(806\) | 8.09476e9 | 0.544542 | ||||||||
\(807\) | −4.37763e8 | −0.0293212 | ||||||||
\(808\) | 3.23001e8 | 0.0215409 | ||||||||
\(809\) | 3.14663e9 | 0.208942 | 0.104471 | − | 0.994528i | \(-0.466685\pi\) | ||||
0.104471 | + | 0.994528i | \(0.466685\pi\) | |||||||
\(810\) | 1.35687e9 | 0.0897096 | ||||||||
\(811\) | 7.96292e9 | 0.524203 | 0.262101 | − | 0.965040i | \(-0.415584\pi\) | ||||
0.262101 | + | 0.965040i | \(0.415584\pi\) | |||||||
\(812\) | 1.23966e8 | 0.00812559 | ||||||||
\(813\) | 1.02576e10 | 0.669469 | ||||||||
\(814\) | −2.80461e9 | −0.182258 | ||||||||
\(815\) | 3.97780e9 | 0.257390 | ||||||||
\(816\) | 1.00884e9 | 0.0649988 | ||||||||
\(817\) | 1.07590e10 | 0.690233 | ||||||||
\(818\) | 6.12081e9 | 0.390996 | ||||||||
\(819\) | −1.01140e9 | −0.0643326 | ||||||||
\(820\) | 8.52935e9 | 0.540216 | ||||||||
\(821\) | 3.29660e9 | 0.207905 | 0.103952 | − | 0.994582i | \(-0.466851\pi\) | ||||
0.103952 | + | 0.994582i | \(0.466851\pi\) | |||||||
\(822\) | −4.07830e9 | −0.256111 | ||||||||
\(823\) | −1.24257e10 | −0.776999 | −0.388500 | − | 0.921449i | \(-0.627007\pi\) | ||||
−0.388500 | + | 0.921449i | \(0.627007\pi\) | |||||||
\(824\) | −5.39526e9 | −0.335944 | ||||||||
\(825\) | −1.86921e9 | −0.115896 | ||||||||
\(826\) | −2.20378e8 | −0.0136063 | ||||||||
\(827\) | 4.41350e9 | 0.271340 | 0.135670 | − | 0.990754i | \(-0.456681\pi\) | ||||
0.135670 | + | 0.990754i | \(0.456681\pi\) | |||||||
\(828\) | −4.04156e9 | −0.247425 | ||||||||
\(829\) | 8.72723e9 | 0.532029 | 0.266015 | − | 0.963969i | \(-0.414293\pi\) | ||||
0.266015 | + | 0.963969i | \(0.414293\pi\) | |||||||
\(830\) | 1.67372e10 | 1.01604 | ||||||||
\(831\) | −3.34943e9 | −0.202473 | ||||||||
\(832\) | −2.71153e9 | −0.163223 | ||||||||
\(833\) | 7.34837e9 | 0.440487 | ||||||||
\(834\) | 4.35650e9 | 0.260050 | ||||||||
\(835\) | 1.71797e10 | 1.02120 | ||||||||
\(836\) | −6.11365e9 | −0.361892 | ||||||||
\(837\) | 1.92545e9 | 0.113499 | ||||||||
\(838\) | −1.60428e10 | −0.941727 | ||||||||
\(839\) | −2.17827e10 | −1.27334 | −0.636671 | − | 0.771136i | \(-0.719689\pi\) | ||||
−0.636671 | + | 0.771136i | \(0.719689\pi\) | |||||||
\(840\) | −5.91764e8 | −0.0344485 | ||||||||
\(841\) | −1.70413e10 | −0.987910 | ||||||||
\(842\) | 9.36486e9 | 0.540641 | ||||||||
\(843\) | 3.42284e9 | 0.196784 | ||||||||
\(844\) | 4.01410e9 | 0.229821 | ||||||||
\(845\) | 1.41200e10 | 0.805072 | ||||||||
\(846\) | 6.69794e9 | 0.380316 | ||||||||
\(847\) | −1.47221e9 | −0.0832489 | ||||||||
\(848\) | −4.50456e9 | −0.253669 | ||||||||
\(849\) | 6.56747e9 | 0.368317 | ||||||||
\(850\) | −1.73176e9 | −0.0967214 | ||||||||
\(851\) | 1.04095e10 | 0.579000 | ||||||||
\(852\) | 1.67305e9 | 0.0926767 | ||||||||
\(853\) | 1.58424e10 | 0.873975 | 0.436988 | − | 0.899467i | \(-0.356045\pi\) | ||||
0.436988 | + | 0.899467i | \(0.356045\pi\) | |||||||
\(854\) | −6.36247e8 | −0.0349561 | ||||||||
\(855\) | −7.61810e9 | −0.416836 | ||||||||
\(856\) | 4.28453e9 | 0.233477 | ||||||||
\(857\) | 2.86266e10 | 1.55359 | 0.776795 | − | 0.629754i | \(-0.216844\pi\) | ||||
0.776795 | + | 0.629754i | \(0.216844\pi\) | |||||||
\(858\) | 6.51809e9 | 0.352302 | ||||||||
\(859\) | −2.17783e10 | −1.17233 | −0.586164 | − | 0.810193i | \(-0.699362\pi\) | ||||
−0.586164 | + | 0.810193i | \(0.699362\pi\) | |||||||
\(860\) | −6.71146e9 | −0.359809 | ||||||||
\(861\) | −1.51228e9 | −0.0807458 | ||||||||
\(862\) | 1.75275e10 | 0.932064 | ||||||||
\(863\) | 2.85634e10 | 1.51277 | 0.756384 | − | 0.654128i | \(-0.226964\pi\) | ||||
0.756384 | + | 0.654128i | \(0.226964\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | 2.48174e8 | 0.0130376 | ||||||||
\(866\) | −1.65805e10 | −0.867533 | ||||||||
\(867\) | 8.83238e9 | 0.460268 | ||||||||
\(868\) | −8.39737e8 | −0.0435837 | ||||||||
\(869\) | −2.44723e9 | −0.126504 | ||||||||
\(870\) | −9.95505e8 | −0.0512538 | ||||||||
\(871\) | −1.19842e9 | −0.0614536 | ||||||||
\(872\) | −7.10740e9 | −0.362997 | ||||||||
\(873\) | 4.87600e9 | 0.248035 | ||||||||
\(874\) | 2.26913e10 | 1.14966 | ||||||||
\(875\) | −2.32848e9 | −0.117502 | ||||||||
\(876\) | 6.71310e9 | 0.337410 | ||||||||
\(877\) | −2.74548e10 | −1.37442 | −0.687211 | − | 0.726458i | \(-0.741165\pi\) | ||||
−0.687211 | + | 0.726458i | \(0.741165\pi\) | |||||||
\(878\) | −6.05676e9 | −0.302002 | ||||||||
\(879\) | −1.67288e10 | −0.830816 | ||||||||
\(880\) | 3.81368e9 | 0.188649 | ||||||||
\(881\) | 1.02452e10 | 0.504782 | 0.252391 | − | 0.967625i | \(-0.418783\pi\) | ||||
0.252391 | + | 0.967625i | \(0.418783\pi\) | |||||||
\(882\) | −4.69798e9 | −0.230553 | ||||||||
\(883\) | 3.23693e10 | 1.58223 | 0.791116 | − | 0.611666i | \(-0.209500\pi\) | ||||
0.791116 | + | 0.611666i | \(0.209500\pi\) | |||||||
\(884\) | 6.03881e9 | 0.294014 | ||||||||
\(885\) | 1.76975e9 | 0.0858242 | ||||||||
\(886\) | 1.31120e10 | 0.633363 | ||||||||
\(887\) | −9.60511e9 | −0.462136 | −0.231068 | − | 0.972938i | \(-0.574222\pi\) | ||||
−0.231068 | + | 0.972938i | \(0.574222\pi\) | |||||||
\(888\) | 1.66121e9 | 0.0796120 | ||||||||
\(889\) | −2.62134e9 | −0.125132 | ||||||||
\(890\) | 1.75199e10 | 0.833042 | ||||||||
\(891\) | 1.55041e9 | 0.0734304 | ||||||||
\(892\) | 4.74279e9 | 0.223747 | ||||||||
\(893\) | −3.76055e10 | −1.76714 | ||||||||
\(894\) | 1.17658e9 | 0.0550732 | ||||||||
\(895\) | −4.61054e10 | −2.14967 | ||||||||
\(896\) | 2.81289e8 | 0.0130640 | ||||||||
\(897\) | −2.41924e10 | −1.11920 | ||||||||
\(898\) | −3.49336e9 | −0.160982 | ||||||||
\(899\) | −1.41266e9 | −0.0648454 | ||||||||
\(900\) | 1.10716e9 | 0.0506245 | ||||||||
\(901\) | 1.00321e10 | 0.456933 | ||||||||
\(902\) | 9.74601e9 | 0.442185 | ||||||||
\(903\) | 1.18996e9 | 0.0537805 | ||||||||
\(904\) | −1.16561e9 | −0.0524764 | ||||||||
\(905\) | −1.28816e10 | −0.577696 | ||||||||
\(906\) | 7.25064e9 | 0.323912 | ||||||||
\(907\) | 1.72814e10 | 0.769049 | 0.384524 | − | 0.923115i | \(-0.374365\pi\) | ||||
0.384524 | + | 0.923115i | \(0.374365\pi\) | |||||||
\(908\) | 1.11099e10 | 0.492505 | ||||||||
\(909\) | 4.59898e8 | 0.0203090 | ||||||||
\(910\) | −3.54225e9 | −0.155824 | ||||||||
\(911\) | 6.29595e9 | 0.275897 | 0.137949 | − | 0.990439i | \(-0.455949\pi\) | ||||
0.137949 | + | 0.990439i | \(0.455949\pi\) | |||||||
\(912\) | 3.62119e9 | 0.158077 | ||||||||
\(913\) | 1.91247e10 | 0.831661 | ||||||||
\(914\) | 2.30755e10 | 0.999629 | ||||||||
\(915\) | 5.10938e9 | 0.220493 | ||||||||
\(916\) | 1.34684e9 | 0.0579006 | ||||||||
\(917\) | −4.68208e9 | −0.200515 | ||||||||
\(918\) | 1.43641e9 | 0.0612814 | ||||||||
\(919\) | 1.91283e10 | 0.812967 | 0.406484 | − | 0.913658i | \(-0.366755\pi\) | ||||
0.406484 | + | 0.913658i | \(0.366755\pi\) | |||||||
\(920\) | −1.41548e10 | −0.599302 | ||||||||
\(921\) | −2.64908e9 | −0.111734 | ||||||||
\(922\) | −2.18472e10 | −0.917990 | ||||||||
\(923\) | 1.00147e10 | 0.419212 | ||||||||
\(924\) | −6.76176e8 | −0.0281973 | ||||||||
\(925\) | −2.85162e9 | −0.118467 | ||||||||
\(926\) | 1.52087e10 | 0.629437 | ||||||||
\(927\) | −7.68193e9 | −0.316731 | ||||||||
\(928\) | 4.73203e8 | 0.0194370 | ||||||||
\(929\) | 1.91374e10 | 0.783120 | 0.391560 | − | 0.920153i | \(-0.371936\pi\) | ||||
0.391560 | + | 0.920153i | \(0.371936\pi\) | |||||||
\(930\) | 6.74350e9 | 0.274913 | ||||||||
\(931\) | 2.63768e10 | 1.07127 | ||||||||
\(932\) | 5.06207e8 | 0.0204820 | ||||||||
\(933\) | 2.17118e10 | 0.875206 | ||||||||
\(934\) | 1.72835e10 | 0.694092 | ||||||||
\(935\) | −8.49340e9 | −0.339814 | ||||||||
\(936\) | −3.86075e9 | −0.153888 | ||||||||
\(937\) | 1.89347e10 | 0.751917 | 0.375959 | − | 0.926636i | \(-0.377313\pi\) | ||||
0.375959 | + | 0.926636i | \(0.377313\pi\) | |||||||
\(938\) | 1.24323e8 | 0.00491858 | ||||||||
\(939\) | 4.88286e9 | 0.192462 | ||||||||
\(940\) | 2.34582e10 | 0.921187 | ||||||||
\(941\) | 2.68365e10 | 1.04994 | 0.524968 | − | 0.851122i | \(-0.324077\pi\) | ||||
0.524968 | + | 0.851122i | \(0.324077\pi\) | |||||||
\(942\) | 4.04791e9 | 0.157780 | ||||||||
\(943\) | −3.61731e10 | −1.40474 | ||||||||
\(944\) | −8.41232e8 | −0.0325472 | ||||||||
\(945\) | −8.42570e8 | −0.0324784 | ||||||||
\(946\) | −7.66881e9 | −0.294516 | ||||||||
\(947\) | −2.07924e10 | −0.795573 | −0.397786 | − | 0.917478i | \(-0.630221\pi\) | ||||
−0.397786 | + | 0.917478i | \(0.630221\pi\) | |||||||
\(948\) | 1.44952e9 | 0.0552581 | ||||||||
\(949\) | 4.01840e10 | 1.52624 | ||||||||
\(950\) | −6.21612e9 | −0.235227 | ||||||||
\(951\) | −6.92372e9 | −0.261040 | ||||||||
\(952\) | −6.26455e8 | −0.0235321 | ||||||||
\(953\) | 2.94329e10 | 1.10156 | 0.550781 | − | 0.834650i | \(-0.314330\pi\) | ||||
0.550781 | + | 0.834650i | \(0.314330\pi\) | |||||||
\(954\) | −6.41372e9 | −0.239161 | ||||||||
\(955\) | 4.45462e10 | 1.65500 | ||||||||
\(956\) | 1.53948e10 | 0.569864 | ||||||||
\(957\) | −1.13751e9 | −0.0419530 | ||||||||
\(958\) | −1.91853e10 | −0.705001 | ||||||||
\(959\) | 2.53250e9 | 0.0927222 | ||||||||
\(960\) | −2.25889e9 | −0.0824036 | ||||||||
\(961\) | −1.79433e10 | −0.652185 | ||||||||
\(962\) | 9.94384e9 | 0.360115 | ||||||||
\(963\) | 6.10043e9 | 0.220125 | ||||||||
\(964\) | 3.24314e9 | 0.116599 | ||||||||
\(965\) | −5.84481e10 | −2.09375 | ||||||||
\(966\) | 2.50968e9 | 0.0895775 | ||||||||
\(967\) | 3.07634e10 | 1.09406 | 0.547031 | − | 0.837113i | \(-0.315758\pi\) | ||||
0.547031 | + | 0.837113i | \(0.315758\pi\) | |||||||
\(968\) | −5.61975e9 | −0.199138 | ||||||||
\(969\) | −8.06471e9 | −0.284745 | ||||||||
\(970\) | 1.70772e10 | 0.600781 | ||||||||
\(971\) | 1.82869e10 | 0.641020 | 0.320510 | − | 0.947245i | \(-0.396146\pi\) | ||||
0.320510 | + | 0.947245i | \(0.396146\pi\) | |||||||
\(972\) | −9.18330e8 | −0.0320750 | ||||||||
\(973\) | −2.70525e9 | −0.0941482 | ||||||||
\(974\) | 2.35607e10 | 0.817017 | ||||||||
\(975\) | 6.62734e9 | 0.228994 | ||||||||
\(976\) | −2.42869e9 | −0.0836177 | ||||||||
\(977\) | −7.33555e9 | −0.251653 | −0.125826 | − | 0.992052i | \(-0.540158\pi\) | ||||
−0.125826 | + | 0.992052i | \(0.540158\pi\) | |||||||
\(978\) | −2.69219e9 | −0.0920278 | ||||||||
\(979\) | 2.00190e10 | 0.681873 | ||||||||
\(980\) | −1.64538e10 | −0.558437 | ||||||||
\(981\) | −1.01197e10 | −0.342237 | ||||||||
\(982\) | −1.98184e10 | −0.667849 | ||||||||
\(983\) | 2.08551e10 | 0.700285 | 0.350142 | − | 0.936696i | \(-0.386133\pi\) | ||||
0.350142 | + | 0.936696i | \(0.386133\pi\) | |||||||
\(984\) | −5.77269e9 | −0.193150 | ||||||||
\(985\) | 2.73305e10 | 0.911214 | ||||||||
\(986\) | −1.05387e9 | −0.0350119 | ||||||||
\(987\) | −4.15920e9 | −0.137689 | ||||||||
\(988\) | 2.16761e10 | 0.715043 | ||||||||
\(989\) | 2.84634e10 | 0.935621 | ||||||||
\(990\) | 5.43003e9 | 0.177860 | ||||||||
\(991\) | 5.03707e10 | 1.64407 | 0.822034 | − | 0.569438i | \(-0.192839\pi\) | ||||
0.822034 | + | 0.569438i | \(0.192839\pi\) | |||||||
\(992\) | −3.20546e9 | −0.104256 | ||||||||
\(993\) | −1.95467e10 | −0.633505 | ||||||||
\(994\) | −1.03891e9 | −0.0335526 | ||||||||
\(995\) | 1.99188e9 | 0.0641037 | ||||||||
\(996\) | −1.13278e10 | −0.363276 | ||||||||
\(997\) | −5.54924e10 | −1.77337 | −0.886687 | − | 0.462371i | \(-0.846999\pi\) | ||||
−0.886687 | + | 0.462371i | \(0.846999\pi\) | |||||||
\(998\) | 1.67337e10 | 0.532887 | ||||||||
\(999\) | 2.36527e9 | 0.0750589 |
(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 | 354.8.a.d.1.8 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.8.a.d.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial |