Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(209.608008215\) |
Analytic rank: | \(0\) |
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: | \( x^{8} - 2 x^{7} - 13701836 x^{6} + 201589162 x^{5} + 55078074399586 x^{4} + \cdots + 23\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{10}\cdot 5^{14}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(155.916\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −238.916 | −0.164979 | −0.0824897 | − | 0.996592i | \(-0.526287\pi\) | ||||
−0.0824897 | + | 0.996592i | \(0.526287\pi\) | |||||||
\(3\) | 59049.0 | 0.577350 | ||||||||
\(4\) | −2.04007e6 | −0.972782 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.41077e7 | −0.0952509 | ||||||||
\(7\) | −6.22955e8 | −0.833542 | −0.416771 | − | 0.909012i | \(-0.636838\pi\) | ||||
−0.416771 | + | 0.909012i | \(0.636838\pi\) | |||||||
\(8\) | 9.88448e8 | 0.325468 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.17658e10 | 0.136773 | 0.0683864 | − | 0.997659i | \(-0.478215\pi\) | ||||
0.0683864 | + | 0.997659i | \(0.478215\pi\) | |||||||
\(12\) | −1.20464e11 | −0.561636 | ||||||||
\(13\) | −6.64700e11 | −1.33727 | −0.668637 | − | 0.743589i | \(-0.733122\pi\) | ||||
−0.668637 | + | 0.743589i | \(0.733122\pi\) | |||||||
\(14\) | 1.48834e11 | 0.137517 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.04218e12 | 0.919086 | ||||||||
\(17\) | −1.24087e13 | −1.49284 | −0.746421 | − | 0.665474i | \(-0.768229\pi\) | ||||
−0.746421 | + | 0.665474i | \(0.768229\pi\) | |||||||
\(18\) | −8.33048e11 | −0.0549932 | ||||||||
\(19\) | 1.38702e13 | 0.519003 | 0.259502 | − | 0.965743i | \(-0.416442\pi\) | ||||
0.259502 | + | 0.965743i | \(0.416442\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.67849e13 | −0.481246 | ||||||||
\(22\) | −2.81105e12 | −0.0225647 | ||||||||
\(23\) | −2.44684e14 | −1.23158 | −0.615791 | − | 0.787910i | \(-0.711163\pi\) | ||||
−0.615791 | + | 0.787910i | \(0.711163\pi\) | |||||||
\(24\) | 5.83669e13 | 0.187909 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.58807e14 | 0.220623 | ||||||||
\(27\) | 2.05891e14 | 0.192450 | ||||||||
\(28\) | 1.27087e15 | 0.810854 | ||||||||
\(29\) | −2.45457e15 | −1.08342 | −0.541709 | − | 0.840566i | \(-0.682223\pi\) | ||||
−0.541709 | + | 0.840566i | \(0.682223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.56996e15 | 1.43968 | 0.719838 | − | 0.694142i | \(-0.244216\pi\) | ||||
0.719838 | + | 0.694142i | \(0.244216\pi\) | |||||||
\(32\) | −3.03867e15 | −0.477099 | ||||||||
\(33\) | 6.94761e14 | 0.0789658 | ||||||||
\(34\) | 2.96464e15 | 0.246288 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.11329e15 | −0.324261 | ||||||||
\(37\) | −8.38999e15 | −0.286842 | −0.143421 | − | 0.989662i | \(-0.545810\pi\) | ||||
−0.143421 | + | 0.989662i | \(0.545810\pi\) | |||||||
\(38\) | −3.31381e15 | −0.0856249 | ||||||||
\(39\) | −3.92499e16 | −0.772075 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.59593e16 | −0.185687 | −0.0928437 | − | 0.995681i | \(-0.529596\pi\) | ||||
−0.0928437 | + | 0.995681i | \(0.529596\pi\) | |||||||
\(42\) | 8.78849e15 | 0.0793956 | ||||||||
\(43\) | −1.03720e17 | −0.731890 | −0.365945 | − | 0.930637i | \(-0.619254\pi\) | ||||
−0.365945 | + | 0.930637i | \(0.619254\pi\) | |||||||
\(44\) | −2.40032e16 | −0.133050 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.84589e16 | 0.203186 | ||||||||
\(47\) | −6.98293e17 | −1.93647 | −0.968234 | − | 0.250047i | \(-0.919554\pi\) | ||||
−0.968234 | + | 0.250047i | \(0.919554\pi\) | |||||||
\(48\) | 2.38687e17 | 0.530635 | ||||||||
\(49\) | −1.70473e17 | −0.305208 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.32723e17 | −0.861892 | ||||||||
\(52\) | 1.35603e18 | 1.30088 | ||||||||
\(53\) | 1.25834e18 | 0.988331 | 0.494165 | − | 0.869368i | \(-0.335474\pi\) | ||||
0.494165 | + | 0.869368i | \(0.335474\pi\) | |||||||
\(54\) | −4.91906e16 | −0.0317503 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.15759e17 | −0.271292 | ||||||||
\(57\) | 8.19022e17 | 0.299647 | ||||||||
\(58\) | 5.86435e17 | 0.178742 | ||||||||
\(59\) | 2.40302e18 | 0.612084 | 0.306042 | − | 0.952018i | \(-0.400995\pi\) | ||||
0.306042 | + | 0.952018i | \(0.400995\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.88392e18 | −1.23558 | −0.617792 | − | 0.786342i | \(-0.711973\pi\) | ||||
−0.617792 | + | 0.786342i | \(0.711973\pi\) | |||||||
\(62\) | −1.56967e18 | −0.237517 | ||||||||
\(63\) | −2.17211e18 | −0.277847 | ||||||||
\(64\) | −7.75109e18 | −0.840375 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.65989e17 | −0.0130277 | ||||||||
\(67\) | −1.90793e19 | −1.27872 | −0.639361 | − | 0.768907i | \(-0.720801\pi\) | ||||
−0.639361 | + | 0.768907i | \(0.720801\pi\) | |||||||
\(68\) | 2.53147e19 | 1.45221 | ||||||||
\(69\) | −1.44483e19 | −0.711054 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.30232e18 | 0.229767 | 0.114884 | − | 0.993379i | \(-0.463351\pi\) | ||||
0.114884 | + | 0.993379i | \(0.463351\pi\) | |||||||
\(72\) | 3.44650e18 | 0.108489 | ||||||||
\(73\) | 3.72824e19 | 1.01534 | 0.507672 | − | 0.861550i | \(-0.330506\pi\) | ||||
0.507672 | + | 0.861550i | \(0.330506\pi\) | |||||||
\(74\) | 2.00450e18 | 0.0473231 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.82962e19 | −0.504877 | ||||||||
\(77\) | −7.32959e18 | −0.114006 | ||||||||
\(78\) | 9.37741e18 | 0.127377 | ||||||||
\(79\) | −9.29902e19 | −1.10498 | −0.552488 | − | 0.833521i | \(-0.686321\pi\) | ||||
−0.552488 | + | 0.833521i | \(0.686321\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 3.81292e18 | 0.0306346 | ||||||||
\(83\) | −5.72322e19 | −0.404875 | −0.202437 | − | 0.979295i | \(-0.564886\pi\) | ||||
−0.202437 | + | 0.979295i | \(0.564886\pi\) | |||||||
\(84\) | 7.50438e19 | 0.468147 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.47804e19 | 0.120747 | ||||||||
\(87\) | −1.44940e20 | −0.625512 | ||||||||
\(88\) | 1.16299e19 | 0.0445152 | ||||||||
\(89\) | −1.21048e20 | −0.411492 | −0.205746 | − | 0.978605i | \(-0.565962\pi\) | ||||
−0.205746 | + | 0.978605i | \(0.565962\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.14078e20 | 1.11467 | ||||||||
\(92\) | 4.99173e20 | 1.19806 | ||||||||
\(93\) | 3.87950e20 | 0.831198 | ||||||||
\(94\) | 1.66833e20 | 0.319477 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.79430e20 | −0.275453 | ||||||||
\(97\) | 7.43455e20 | 1.02365 | 0.511825 | − | 0.859090i | \(-0.328970\pi\) | ||||
0.511825 | + | 0.859090i | \(0.328970\pi\) | |||||||
\(98\) | 4.07286e19 | 0.0503530 | ||||||||
\(99\) | 4.10250e19 | 0.0455909 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.78527e21 | 1.60816 | 0.804079 | − | 0.594523i | \(-0.202659\pi\) | ||||
0.804079 | + | 0.594523i | \(0.202659\pi\) | |||||||
\(102\) | 1.75059e20 | 0.142195 | ||||||||
\(103\) | 2.03656e20 | 0.149316 | 0.0746578 | − | 0.997209i | \(-0.476214\pi\) | ||||
0.0746578 | + | 0.997209i | \(0.476214\pi\) | |||||||
\(104\) | −6.57021e20 | −0.435240 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.00638e20 | −0.163054 | ||||||||
\(107\) | −1.84578e20 | −0.0907090 | −0.0453545 | − | 0.998971i | \(-0.514442\pi\) | ||||
−0.0453545 | + | 0.998971i | \(0.514442\pi\) | |||||||
\(108\) | −4.20033e20 | −0.187212 | ||||||||
\(109\) | −1.88509e19 | −0.00762701 | −0.00381351 | − | 0.999993i | \(-0.501214\pi\) | ||||
−0.00381351 | + | 0.999993i | \(0.501214\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.95420e20 | −0.165609 | ||||||||
\(112\) | −2.51810e21 | −0.766097 | ||||||||
\(113\) | −2.80252e21 | −0.776651 | −0.388325 | − | 0.921522i | \(-0.626946\pi\) | ||||
−0.388325 | + | 0.921522i | \(0.626946\pi\) | |||||||
\(114\) | −1.95677e20 | −0.0494356 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.00750e21 | 1.05393 | ||||||||
\(117\) | −2.31766e21 | −0.445758 | ||||||||
\(118\) | −5.74119e20 | −0.100981 | ||||||||
\(119\) | 7.73008e21 | 1.24435 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.26181e21 | −0.981293 | ||||||||
\(122\) | 1.64468e21 | 0.203846 | ||||||||
\(123\) | −9.42379e20 | −0.107207 | ||||||||
\(124\) | −1.34032e22 | −1.40049 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.18952e20 | 0.0458391 | ||||||||
\(127\) | −7.11473e21 | −0.578388 | −0.289194 | − | 0.957271i | \(-0.593387\pi\) | ||||
−0.289194 | + | 0.957271i | \(0.593387\pi\) | |||||||
\(128\) | 8.22440e21 | 0.615743 | ||||||||
\(129\) | −6.12459e21 | −0.422557 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.82556e21 | −0.518076 | −0.259038 | − | 0.965867i | \(-0.583406\pi\) | ||||
−0.259038 | + | 0.965867i | \(0.583406\pi\) | |||||||
\(132\) | −1.41736e21 | −0.0768165 | ||||||||
\(133\) | −8.64052e21 | −0.432611 | ||||||||
\(134\) | 4.55833e21 | 0.210963 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.22654e22 | −0.485873 | ||||||||
\(137\) | −1.39205e22 | −0.510611 | −0.255305 | − | 0.966860i | \(-0.582176\pi\) | ||||
−0.255305 | + | 0.966860i | \(0.582176\pi\) | |||||||
\(138\) | 3.45194e21 | 0.117309 | ||||||||
\(139\) | 4.93436e22 | 1.55445 | 0.777223 | − | 0.629225i | \(-0.216628\pi\) | ||||
0.777223 | + | 0.629225i | \(0.216628\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.12335e22 | −1.11802 | ||||||||
\(142\) | −1.50572e21 | −0.0379068 | ||||||||
\(143\) | −7.82075e21 | −0.182903 | ||||||||
\(144\) | 1.40942e22 | 0.306362 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.90735e21 | −0.167511 | ||||||||
\(147\) | −1.00662e22 | −0.176212 | ||||||||
\(148\) | 1.71162e22 | 0.279035 | ||||||||
\(149\) | −1.06667e23 | −1.62022 | −0.810108 | − | 0.586280i | \(-0.800592\pi\) | ||||
−0.810108 | + | 0.586280i | \(0.800592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.44371e22 | 0.850899 | 0.425449 | − | 0.904982i | \(-0.360116\pi\) | ||||
0.425449 | + | 0.904982i | \(0.360116\pi\) | |||||||
\(152\) | 1.37100e22 | 0.168919 | ||||||||
\(153\) | −4.32666e22 | −0.497614 | ||||||||
\(154\) | 1.75116e21 | 0.0188086 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 8.00725e22 | 0.751061 | ||||||||
\(157\) | −9.89402e22 | −0.867814 | −0.433907 | − | 0.900958i | \(-0.642865\pi\) | ||||
−0.433907 | + | 0.900958i | \(0.642865\pi\) | |||||||
\(158\) | 2.22168e22 | 0.182298 | ||||||||
\(159\) | 7.43039e22 | 0.570613 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.52427e23 | 1.02657 | ||||||||
\(162\) | −2.90466e21 | −0.0183311 | ||||||||
\(163\) | −1.08411e23 | −0.641360 | −0.320680 | − | 0.947188i | \(-0.603911\pi\) | ||||
−0.320680 | + | 0.947188i | \(0.603911\pi\) | |||||||
\(164\) | 3.25580e22 | 0.180633 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.36737e22 | 0.0667960 | ||||||||
\(167\) | 7.76750e22 | 0.356253 | 0.178127 | − | 0.984008i | \(-0.442996\pi\) | ||||
0.178127 | + | 0.984008i | \(0.442996\pi\) | |||||||
\(168\) | −3.63599e22 | −0.156630 | ||||||||
\(169\) | 1.94761e23 | 0.788301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.83624e22 | 0.173001 | ||||||||
\(172\) | 2.11597e23 | 0.711969 | ||||||||
\(173\) | 4.65341e23 | 1.47329 | 0.736643 | − | 0.676282i | \(-0.236410\pi\) | ||||
0.736643 | + | 0.676282i | \(0.236410\pi\) | |||||||
\(174\) | 3.46284e22 | 0.103197 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.75597e22 | 0.125706 | ||||||||
\(177\) | 1.41896e23 | 0.353387 | ||||||||
\(178\) | 2.89202e22 | 0.0678877 | ||||||||
\(179\) | 8.42823e22 | 0.186543 | 0.0932717 | − | 0.995641i | \(-0.470267\pi\) | ||||
0.0932717 | + | 0.995641i | \(0.470267\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.95022e21 | 0.0176282 | 0.00881412 | − | 0.999961i | \(-0.497194\pi\) | ||||
0.00881412 | + | 0.999961i | \(0.497194\pi\) | |||||||
\(182\) | −9.89298e22 | −0.183898 | ||||||||
\(183\) | −4.06488e23 | −0.713365 | ||||||||
\(184\) | −2.41857e23 | −0.400841 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.26873e22 | −0.137131 | ||||||||
\(187\) | −1.45999e23 | −0.204180 | ||||||||
\(188\) | 1.42457e24 | 1.88376 | ||||||||
\(189\) | −1.28261e23 | −0.160415 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.42464e23 | 0.271517 | 0.135759 | − | 0.990742i | \(-0.456653\pi\) | ||||
0.135759 | + | 0.990742i | \(0.456653\pi\) | |||||||
\(192\) | −4.57694e23 | −0.485191 | ||||||||
\(193\) | 4.05656e23 | 0.407199 | 0.203599 | − | 0.979054i | \(-0.434736\pi\) | ||||
0.203599 | + | 0.979054i | \(0.434736\pi\) | |||||||
\(194\) | −1.77623e23 | −0.168881 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.47776e23 | 0.296901 | ||||||||
\(197\) | −1.30868e23 | −0.105910 | −0.0529550 | − | 0.998597i | \(-0.516864\pi\) | ||||
−0.0529550 | + | 0.998597i | \(0.516864\pi\) | |||||||
\(198\) | −9.80151e21 | −0.00752157 | ||||||||
\(199\) | 2.06881e24 | 1.50579 | 0.752893 | − | 0.658143i | \(-0.228658\pi\) | ||||
0.752893 | + | 0.658143i | \(0.228658\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.12661e24 | −0.738270 | ||||||||
\(202\) | −4.26528e23 | −0.265313 | ||||||||
\(203\) | 1.52909e24 | 0.903075 | ||||||||
\(204\) | 1.49481e24 | 0.838433 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.86565e22 | −0.0246340 | ||||||||
\(207\) | −8.53160e23 | −0.410527 | ||||||||
\(208\) | −2.68684e24 | −1.22907 | ||||||||
\(209\) | 1.63195e23 | 0.0709856 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.07171e24 | −1.20897 | −0.604483 | − | 0.796618i | \(-0.706620\pi\) | ||||
−0.604483 | + | 0.796618i | \(0.706620\pi\) | |||||||
\(212\) | −2.56711e24 | −0.961430 | ||||||||
\(213\) | 3.72146e23 | 0.132656 | ||||||||
\(214\) | 4.40986e22 | 0.0149651 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.03513e23 | 0.0626364 | ||||||||
\(217\) | −4.09279e24 | −1.20003 | ||||||||
\(218\) | 4.50378e21 | 0.00125830 | ||||||||
\(219\) | 2.20149e24 | 0.586210 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.24808e24 | 1.99634 | ||||||||
\(222\) | 1.18364e23 | 0.0273220 | ||||||||
\(223\) | 7.14085e24 | 1.57235 | 0.786174 | − | 0.618005i | \(-0.212059\pi\) | ||||
0.786174 | + | 0.618005i | \(0.212059\pi\) | |||||||
\(224\) | 1.89295e24 | 0.397682 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.69567e23 | 0.128131 | ||||||||
\(227\) | 7.23862e24 | 1.32246 | 0.661232 | − | 0.750181i | \(-0.270034\pi\) | ||||
0.661232 | + | 0.750181i | \(0.270034\pi\) | |||||||
\(228\) | −1.67086e24 | −0.291491 | ||||||||
\(229\) | 9.22621e24 | 1.53727 | 0.768636 | − | 0.639686i | \(-0.220936\pi\) | ||||
0.768636 | + | 0.639686i | \(0.220936\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.32805e23 | −0.0658213 | ||||||||
\(232\) | −2.42621e24 | −0.352619 | ||||||||
\(233\) | 1.65552e24 | 0.229983 | 0.114992 | − | 0.993366i | \(-0.463316\pi\) | ||||
0.114992 | + | 0.993366i | \(0.463316\pi\) | |||||||
\(234\) | 5.53727e23 | 0.0735409 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.90233e24 | −0.595424 | ||||||||
\(237\) | −5.49098e24 | −0.637958 | ||||||||
\(238\) | −1.84684e24 | −0.205292 | ||||||||
\(239\) | 1.58345e25 | 1.68433 | 0.842165 | − | 0.539220i | \(-0.181281\pi\) | ||||
0.842165 | + | 0.539220i | \(0.181281\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.20116e24 | 0.799275 | 0.399637 | − | 0.916673i | \(-0.369136\pi\) | ||||
0.399637 | + | 0.916673i | \(0.369136\pi\) | |||||||
\(242\) | 1.73496e24 | 0.161893 | ||||||||
\(243\) | 7.17898e23 | 0.0641500 | ||||||||
\(244\) | 1.40437e25 | 1.20195 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.25149e23 | 0.0176869 | ||||||||
\(247\) | −9.21952e24 | −0.694049 | ||||||||
\(248\) | 6.49406e24 | 0.468569 | ||||||||
\(249\) | −3.37950e24 | −0.233754 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.56271e25 | 1.62976 | 0.814882 | − | 0.579627i | \(-0.196802\pi\) | ||||
0.814882 | + | 0.579627i | \(0.196802\pi\) | |||||||
\(252\) | 4.43126e24 | 0.270285 | ||||||||
\(253\) | −2.87891e24 | −0.168447 | ||||||||
\(254\) | 1.69982e24 | 0.0954221 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.42903e25 | 0.738790 | ||||||||
\(257\) | −3.92069e25 | −1.94565 | −0.972826 | − | 0.231537i | \(-0.925625\pi\) | ||||
−0.972826 | + | 0.231537i | \(0.925625\pi\) | |||||||
\(258\) | 1.46326e24 | 0.0697132 | ||||||||
\(259\) | 5.22659e24 | 0.239095 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.55855e24 | −0.361140 | ||||||||
\(262\) | 2.10857e24 | 0.0854719 | ||||||||
\(263\) | 4.53674e25 | 1.76689 | 0.883444 | − | 0.468538i | \(-0.155219\pi\) | ||||
0.883444 | + | 0.468538i | \(0.155219\pi\) | |||||||
\(264\) | 6.86735e23 | 0.0257009 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.06436e24 | 0.0713719 | ||||||||
\(267\) | −7.14774e24 | −0.237575 | ||||||||
\(268\) | 3.89230e25 | 1.24392 | ||||||||
\(269\) | 4.05174e25 | 1.24521 | 0.622605 | − | 0.782537i | \(-0.286075\pi\) | ||||
0.622605 | + | 0.782537i | \(0.286075\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.27979e25 | 0.363883 | 0.181941 | − | 0.983309i | \(-0.441762\pi\) | ||||
0.181941 | + | 0.983309i | \(0.441762\pi\) | |||||||
\(272\) | −5.01584e25 | −1.37205 | ||||||||
\(273\) | 2.44509e25 | 0.643557 | ||||||||
\(274\) | 3.32584e24 | 0.0842403 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.94756e25 | 0.691700 | ||||||||
\(277\) | −2.24981e25 | −0.508286 | −0.254143 | − | 0.967167i | \(-0.581793\pi\) | ||||
−0.254143 | + | 0.967167i | \(0.581793\pi\) | |||||||
\(278\) | −1.17890e25 | −0.256452 | ||||||||
\(279\) | 2.29080e25 | 0.479892 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.16732e25 | −1.39296 | −0.696482 | − | 0.717574i | \(-0.745253\pi\) | ||||
−0.696482 | + | 0.717574i | \(0.745253\pi\) | |||||||
\(282\) | 9.85134e24 | 0.184450 | ||||||||
\(283\) | 8.64233e25 | 1.55910 | 0.779548 | − | 0.626342i | \(-0.215449\pi\) | ||||
0.779548 | + | 0.626342i | \(0.215449\pi\) | |||||||
\(284\) | −1.28572e25 | −0.223513 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.86850e24 | 0.0301752 | ||||||||
\(287\) | 9.94191e24 | 0.154778 | ||||||||
\(288\) | −1.05952e25 | −0.159033 | ||||||||
\(289\) | 8.48847e25 | 1.22858 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.39003e25 | 0.591005 | ||||||||
\(292\) | −7.60587e25 | −0.987709 | ||||||||
\(293\) | −3.51471e25 | −0.440331 | −0.220166 | − | 0.975463i | \(-0.570660\pi\) | ||||
−0.220166 | + | 0.975463i | \(0.570660\pi\) | |||||||
\(294\) | 2.40498e24 | 0.0290713 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.29307e24 | −0.0933582 | ||||||||
\(297\) | 2.42248e24 | 0.0263219 | ||||||||
\(298\) | 2.54844e25 | 0.267302 | ||||||||
\(299\) | 1.62641e26 | 1.64696 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.46132e25 | 0.610061 | ||||||||
\(302\) | −1.53950e25 | −0.140381 | ||||||||
\(303\) | 1.05418e26 | 0.928470 | ||||||||
\(304\) | 5.60659e25 | 0.477009 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.03371e25 | 0.0820961 | ||||||||
\(307\) | 8.57923e25 | 0.658408 | 0.329204 | − | 0.944259i | \(-0.393220\pi\) | ||||
0.329204 | + | 0.944259i | \(0.393220\pi\) | |||||||
\(308\) | 1.49529e25 | 0.110903 | ||||||||
\(309\) | 1.20257e25 | 0.0862074 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.84449e24 | 0.0123564 | 0.00617822 | − | 0.999981i | \(-0.498033\pi\) | ||||
0.00617822 | + | 0.999981i | \(0.498033\pi\) | |||||||
\(312\) | −3.87964e25 | −0.251286 | ||||||||
\(313\) | −1.74224e26 | −1.09117 | −0.545586 | − | 0.838055i | \(-0.683693\pi\) | ||||
−0.545586 | + | 0.838055i | \(0.683693\pi\) | |||||||
\(314\) | 2.36384e25 | 0.143171 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.89707e26 | 1.07490 | ||||||||
\(317\) | −2.20674e26 | −1.20957 | −0.604783 | − | 0.796390i | \(-0.706740\pi\) | ||||
−0.604783 | + | 0.796390i | \(0.706740\pi\) | |||||||
\(318\) | −1.77524e25 | −0.0941394 | ||||||||
\(319\) | −2.88801e25 | −0.148182 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.08991e25 | −0.0523708 | ||||||||
\(322\) | −3.64172e25 | −0.169364 | ||||||||
\(323\) | −1.72112e26 | −0.774790 | ||||||||
\(324\) | −2.48025e25 | −0.108087 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.59010e25 | 0.105811 | ||||||||
\(327\) | −1.11313e24 | −0.00440346 | ||||||||
\(328\) | −1.57749e25 | −0.0604354 | ||||||||
\(329\) | 4.35005e26 | 1.61413 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.10750e26 | −0.385613 | −0.192806 | − | 0.981237i | \(-0.561759\pi\) | ||||
−0.192806 | + | 0.981237i | \(0.561759\pi\) | |||||||
\(332\) | 1.16758e26 | 0.393855 | ||||||||
\(333\) | −2.92541e25 | −0.0956141 | ||||||||
\(334\) | −1.85578e25 | −0.0587744 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.48691e26 | −0.442306 | ||||||||
\(337\) | 2.24462e26 | 0.647187 | 0.323593 | − | 0.946196i | \(-0.395109\pi\) | ||||
0.323593 | + | 0.946196i | \(0.395109\pi\) | |||||||
\(338\) | −4.65315e25 | −0.130053 | ||||||||
\(339\) | −1.65486e26 | −0.448399 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.73011e25 | 0.196909 | ||||||||
\(342\) | −1.15545e25 | −0.0285416 | ||||||||
\(343\) | 4.54146e26 | 1.08795 | ||||||||
\(344\) | −1.02522e26 | −0.238207 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.11177e26 | −0.243062 | ||||||||
\(347\) | 1.21672e26 | 0.258067 | 0.129033 | − | 0.991640i | \(-0.458813\pi\) | ||||
0.129033 | + | 0.991640i | \(0.458813\pi\) | |||||||
\(348\) | 2.95688e26 | 0.608487 | ||||||||
\(349\) | 3.00266e26 | 0.599570 | 0.299785 | − | 0.954007i | \(-0.403085\pi\) | ||||
0.299785 | + | 0.954007i | \(0.403085\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.36856e26 | −0.257358 | ||||||||
\(352\) | −3.57525e25 | −0.0652542 | ||||||||
\(353\) | 2.67970e26 | 0.474736 | 0.237368 | − | 0.971420i | \(-0.423715\pi\) | ||||
0.237368 | + | 0.971420i | \(0.423715\pi\) | |||||||
\(354\) | −3.39012e25 | −0.0583016 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.46946e26 | 0.400291 | ||||||||
\(357\) | 4.56454e26 | 0.718424 | ||||||||
\(358\) | −2.01364e25 | −0.0307758 | ||||||||
\(359\) | −1.26376e27 | −1.87574 | −0.937871 | − | 0.346983i | \(-0.887206\pi\) | ||||
−0.937871 | + | 0.346983i | \(0.887206\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.21827e26 | −0.730636 | ||||||||
\(362\) | −2.13835e24 | −0.00290830 | ||||||||
\(363\) | −4.28803e26 | −0.566550 | ||||||||
\(364\) | −8.44749e26 | −1.08433 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.71165e25 | 0.117691 | ||||||||
\(367\) | −2.61225e26 | −0.307625 | −0.153813 | − | 0.988100i | \(-0.549155\pi\) | ||||
−0.153813 | + | 0.988100i | \(0.549155\pi\) | |||||||
\(368\) | −9.89057e26 | −1.13193 | ||||||||
\(369\) | −5.56465e25 | −0.0618958 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.83891e26 | −0.823815 | ||||||||
\(372\) | −7.91445e26 | −0.808574 | ||||||||
\(373\) | −2.44037e26 | −0.242389 | −0.121194 | − | 0.992629i | \(-0.538672\pi\) | ||||
−0.121194 | + | 0.992629i | \(0.538672\pi\) | |||||||
\(374\) | 3.48815e25 | 0.0336855 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.90226e26 | −0.630259 | ||||||||
\(377\) | 1.63155e27 | 1.44883 | ||||||||
\(378\) | 3.06436e25 | 0.0264652 | ||||||||
\(379\) | −8.36662e26 | −0.702811 | −0.351405 | − | 0.936223i | \(-0.614296\pi\) | ||||
−0.351405 | + | 0.936223i | \(0.614296\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.20117e26 | −0.333932 | ||||||||
\(382\) | −5.79286e25 | −0.0447948 | ||||||||
\(383\) | 2.27339e27 | 1.71036 | 0.855180 | − | 0.518331i | \(-0.173447\pi\) | ||||
0.855180 | + | 0.518331i | \(0.173447\pi\) | |||||||
\(384\) | 4.85643e26 | 0.355500 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.69177e25 | −0.0671794 | ||||||||
\(387\) | −3.61651e26 | −0.243963 | ||||||||
\(388\) | −1.51670e27 | −0.995788 | ||||||||
\(389\) | −2.73112e27 | −1.74530 | −0.872650 | − | 0.488346i | \(-0.837600\pi\) | ||||
−0.872650 | + | 0.488346i | \(0.837600\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.03622e27 | 1.83856 | ||||||||
\(392\) | −1.68503e26 | −0.0993356 | ||||||||
\(393\) | −5.21140e26 | −0.299111 | ||||||||
\(394\) | 3.12663e25 | 0.0174730 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.36938e25 | −0.0443500 | ||||||||
\(397\) | 3.32220e27 | 1.71445 | 0.857225 | − | 0.514942i | \(-0.172186\pi\) | ||||
0.857225 | + | 0.514942i | \(0.172186\pi\) | |||||||
\(398\) | −4.94271e26 | −0.248424 | ||||||||
\(399\) | −5.10214e26 | −0.249768 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00698e25 | 0.00932238 | 0.00466119 | − | 0.999989i | \(-0.498516\pi\) | ||||
0.00466119 | + | 0.999989i | \(0.498516\pi\) | |||||||
\(402\) | 2.69165e26 | 0.121799 | ||||||||
\(403\) | −4.36705e27 | −1.92524 | ||||||||
\(404\) | −3.64207e27 | −1.56439 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.65323e26 | −0.148989 | ||||||||
\(407\) | −9.87153e25 | −0.0392322 | ||||||||
\(408\) | −7.24259e26 | −0.280519 | ||||||||
\(409\) | −7.78690e26 | −0.293948 | −0.146974 | − | 0.989140i | \(-0.546953\pi\) | ||||
−0.146974 | + | 0.989140i | \(0.546953\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.21994e26 | −0.294801 | ||||||||
\(412\) | −4.15472e26 | −0.145252 | ||||||||
\(413\) | −1.49697e27 | −0.510198 | ||||||||
\(414\) | 2.03833e26 | 0.0677286 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.01980e27 | 0.638012 | ||||||||
\(417\) | 2.91369e27 | 0.897460 | ||||||||
\(418\) | −3.89898e25 | −0.0117112 | ||||||||
\(419\) | 2.65635e27 | 0.778105 | 0.389053 | − | 0.921216i | \(-0.372802\pi\) | ||||
0.389053 | + | 0.921216i | \(0.372802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.30672e27 | −1.47865 | −0.739323 | − | 0.673351i | \(-0.764854\pi\) | ||||
−0.739323 | + | 0.673351i | \(0.764854\pi\) | |||||||
\(422\) | 7.33880e26 | 0.199455 | ||||||||
\(423\) | −2.43480e27 | −0.645489 | ||||||||
\(424\) | 1.24381e27 | 0.321670 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.89115e25 | −0.0218855 | ||||||||
\(427\) | 4.28837e27 | 1.02991 | ||||||||
\(428\) | 3.76552e26 | 0.0882400 | ||||||||
\(429\) | −4.61808e26 | −0.105599 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.05593e27 | −0.883240 | −0.441620 | − | 0.897202i | \(-0.645596\pi\) | ||||
−0.441620 | + | 0.897202i | \(0.645596\pi\) | |||||||
\(432\) | 8.32250e26 | 0.176878 | ||||||||
\(433\) | −4.54389e27 | −0.942551 | −0.471276 | − | 0.881986i | \(-0.656206\pi\) | ||||
−0.471276 | + | 0.881986i | \(0.656206\pi\) | |||||||
\(434\) | 9.77832e26 | 0.197980 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.84572e25 | 0.00741942 | ||||||||
\(437\) | −3.39382e27 | −0.639195 | ||||||||
\(438\) | −5.25970e26 | −0.0967126 | ||||||||
\(439\) | −8.75725e27 | −1.57214 | −0.786068 | − | 0.618139i | \(-0.787887\pi\) | ||||
−0.786068 | + | 0.618139i | \(0.787887\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.94401e26 | −0.101736 | ||||||||
\(442\) | −1.97060e27 | −0.329355 | ||||||||
\(443\) | −1.26129e27 | −0.205861 | −0.102931 | − | 0.994689i | \(-0.532822\pi\) | ||||
−0.102931 | + | 0.994689i | \(0.532822\pi\) | |||||||
\(444\) | 1.01069e27 | 0.161101 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.70606e27 | −0.259405 | ||||||||
\(447\) | −6.29856e27 | −0.935432 | ||||||||
\(448\) | 4.82858e27 | 0.700487 | ||||||||
\(449\) | −7.95388e27 | −1.12718 | −0.563589 | − | 0.826056i | \(-0.690580\pi\) | ||||
−0.563589 | + | 0.826056i | \(0.690580\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.87774e26 | −0.0253970 | ||||||||
\(452\) | 5.71735e27 | 0.755511 | ||||||||
\(453\) | 3.80495e27 | 0.491267 | ||||||||
\(454\) | −1.72942e27 | −0.218180 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.09560e26 | 0.0975256 | ||||||||
\(457\) | −4.40411e27 | −0.518487 | −0.259244 | − | 0.965812i | \(-0.583473\pi\) | ||||
−0.259244 | + | 0.965812i | \(0.583473\pi\) | |||||||
\(458\) | −2.20429e27 | −0.253618 | ||||||||
\(459\) | −2.55485e27 | −0.287297 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.56648e27 | 0.598027 | 0.299014 | − | 0.954249i | \(-0.403342\pi\) | ||||
0.299014 | + | 0.954249i | \(0.403342\pi\) | |||||||
\(462\) | 1.03404e26 | 0.0108592 | ||||||||
\(463\) | 5.57113e27 | 0.571930 | 0.285965 | − | 0.958240i | \(-0.407686\pi\) | ||||
0.285965 | + | 0.958240i | \(0.407686\pi\) | |||||||
\(464\) | −9.92182e27 | −0.995755 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.95529e26 | −0.0379425 | ||||||||
\(467\) | −9.37044e26 | −0.0878886 | −0.0439443 | − | 0.999034i | \(-0.513992\pi\) | ||||
−0.0439443 | + | 0.999034i | \(0.513992\pi\) | |||||||
\(468\) | 4.72820e27 | 0.433625 | ||||||||
\(469\) | 1.18855e28 | 1.06587 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.84232e27 | −0.501033 | ||||||||
\(472\) | 2.37526e27 | 0.199214 | ||||||||
\(473\) | −1.22036e27 | −0.100103 | ||||||||
\(474\) | 1.31188e27 | 0.105250 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.57699e28 | −1.21048 | ||||||||
\(477\) | 4.38757e27 | 0.329444 | ||||||||
\(478\) | −3.78312e27 | −0.277880 | ||||||||
\(479\) | 2.09902e28 | 1.50832 | 0.754160 | − | 0.656690i | \(-0.228044\pi\) | ||||
0.754160 | + | 0.656690i | \(0.228044\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.57682e27 | 0.383587 | ||||||||
\(482\) | −1.95939e27 | −0.131864 | ||||||||
\(483\) | 9.00067e27 | 0.592693 | ||||||||
\(484\) | 1.48146e28 | 0.954584 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.71517e26 | −0.0105834 | ||||||||
\(487\) | 1.01659e28 | 0.613890 | 0.306945 | − | 0.951727i | \(-0.400693\pi\) | ||||
0.306945 | + | 0.951727i | \(0.400693\pi\) | |||||||
\(488\) | −6.80439e27 | −0.402144 | ||||||||
\(489\) | −6.40153e27 | −0.370289 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.39966e28 | 1.32982 | 0.664912 | − | 0.746922i | \(-0.268469\pi\) | ||||
0.664912 | + | 0.746922i | \(0.268469\pi\) | |||||||
\(492\) | 1.92252e27 | 0.104289 | ||||||||
\(493\) | 3.04581e28 | 1.61737 | ||||||||
\(494\) | 2.20269e27 | 0.114504 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.65570e28 | 1.32319 | ||||||||
\(497\) | −3.92606e27 | −0.191520 | ||||||||
\(498\) | 8.07417e26 | 0.0385647 | ||||||||
\(499\) | −1.36280e28 | −0.637347 | −0.318674 | − | 0.947865i | \(-0.603237\pi\) | ||||
−0.318674 | + | 0.947865i | \(0.603237\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.58663e27 | 0.205683 | ||||||||
\(502\) | −6.12271e27 | −0.268878 | ||||||||
\(503\) | −8.66833e27 | −0.372796 | −0.186398 | − | 0.982474i | \(-0.559681\pi\) | ||||
−0.186398 | + | 0.982474i | \(0.559681\pi\) | |||||||
\(504\) | −2.14702e27 | −0.0904305 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.87818e26 | 0.0277903 | ||||||||
\(507\) | 1.15005e28 | 0.455126 | ||||||||
\(508\) | 1.45145e28 | 0.562645 | ||||||||
\(509\) | 4.28603e28 | 1.62749 | 0.813746 | − | 0.581221i | \(-0.197425\pi\) | ||||
0.813746 | + | 0.581221i | \(0.197425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.32253e28 | −0.846333 | ||||||||
\(512\) | −2.06620e28 | −0.737628 | ||||||||
\(513\) | 2.85575e27 | 0.0998822 | ||||||||
\(514\) | 9.36716e27 | 0.320993 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.24946e28 | 0.411055 | ||||||||
\(517\) | −8.21601e27 | −0.264856 | ||||||||
\(518\) | −1.24871e27 | −0.0394458 | ||||||||
\(519\) | 2.74779e28 | 0.850602 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.43988e28 | 1.02270 | 0.511348 | − | 0.859374i | \(-0.329146\pi\) | ||||
0.511348 | + | 0.859374i | \(0.329146\pi\) | |||||||
\(522\) | 2.04477e27 | 0.0595806 | ||||||||
\(523\) | −1.93221e28 | −0.551805 | −0.275902 | − | 0.961186i | \(-0.588977\pi\) | ||||
−0.275902 | + | 0.961186i | \(0.588977\pi\) | |||||||
\(524\) | 1.80048e28 | 0.503975 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.08390e28 | −0.291500 | ||||||||
\(527\) | −8.15249e28 | −2.14921 | ||||||||
\(528\) | 2.80835e27 | 0.0725764 | ||||||||
\(529\) | 2.03986e28 | 0.516793 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.37881e27 | 0.204028 | ||||||||
\(532\) | 1.76273e28 | 0.420836 | ||||||||
\(533\) | 1.06081e28 | 0.248315 | ||||||||
\(534\) | 1.70771e27 | 0.0391950 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.88588e28 | −0.416183 | ||||||||
\(537\) | 4.97679e27 | 0.107701 | ||||||||
\(538\) | −9.68024e27 | −0.205434 | ||||||||
\(539\) | −2.00575e27 | −0.0417442 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.87852e28 | 1.57715 | 0.788576 | − | 0.614937i | \(-0.210819\pi\) | ||||
0.788576 | + | 0.614937i | \(0.210819\pi\) | |||||||
\(542\) | −3.05762e27 | −0.0600332 | ||||||||
\(543\) | 5.28502e26 | 0.0101777 | ||||||||
\(544\) | 3.77060e28 | 0.712233 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.84171e27 | −0.106174 | ||||||||
\(547\) | −7.58840e28 | −1.35295 | −0.676477 | − | 0.736463i | \(-0.736494\pi\) | ||||
−0.676477 | + | 0.736463i | \(0.736494\pi\) | |||||||
\(548\) | 2.83989e28 | 0.496713 | ||||||||
\(549\) | −2.40027e28 | −0.411861 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.40454e28 | −0.562298 | ||||||||
\(552\) | −1.42814e28 | −0.231426 | ||||||||
\(553\) | 5.79287e28 | 0.921043 | ||||||||
\(554\) | 5.37514e27 | 0.0838567 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00665e29 | −1.51214 | ||||||||
\(557\) | −2.99634e28 | −0.441684 | −0.220842 | − | 0.975310i | \(-0.570880\pi\) | ||||
−0.220842 | + | 0.975310i | \(0.570880\pi\) | |||||||
\(558\) | −5.47309e27 | −0.0791724 | ||||||||
\(559\) | 6.89429e28 | 0.978737 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.62111e27 | −0.117883 | ||||||||
\(562\) | 1.71238e28 | 0.229811 | ||||||||
\(563\) | 5.00310e28 | 0.659024 | 0.329512 | − | 0.944151i | \(-0.393116\pi\) | ||||
0.329512 | + | 0.944151i | \(0.393116\pi\) | |||||||
\(564\) | 8.41193e28 | 1.08759 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.06479e28 | −0.257219 | ||||||||
\(567\) | −7.57368e27 | −0.0926158 | ||||||||
\(568\) | 6.22951e27 | 0.0747819 | ||||||||
\(569\) | −7.22336e28 | −0.851257 | −0.425628 | − | 0.904898i | \(-0.639947\pi\) | ||||
−0.425628 | + | 0.904898i | \(0.639947\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.75601e28 | 0.540211 | 0.270105 | − | 0.962831i | \(-0.412941\pi\) | ||||
0.270105 | + | 0.962831i | \(0.412941\pi\) | |||||||
\(572\) | 1.59549e28 | 0.177924 | ||||||||
\(573\) | 1.43173e28 | 0.156761 | ||||||||
\(574\) | −2.37528e27 | −0.0255352 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.70264e28 | −0.280125 | ||||||||
\(577\) | 1.81982e28 | 0.185218 | 0.0926089 | − | 0.995703i | \(-0.470479\pi\) | ||||
0.0926089 | + | 0.995703i | \(0.470479\pi\) | |||||||
\(578\) | −2.02803e28 | −0.202690 | ||||||||
\(579\) | 2.39536e28 | 0.235096 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.56531e28 | 0.337480 | ||||||||
\(582\) | −1.04885e28 | −0.0975037 | ||||||||
\(583\) | 1.48055e28 | 0.135177 | ||||||||
\(584\) | 3.68517e28 | 0.330463 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.39719e27 | 0.0726456 | ||||||||
\(587\) | −1.43285e29 | −1.21759 | −0.608793 | − | 0.793329i | \(-0.708346\pi\) | ||||
−0.608793 | + | 0.793329i | \(0.708346\pi\) | |||||||
\(588\) | 2.05358e28 | 0.171416 | ||||||||
\(589\) | 9.11267e28 | 0.747197 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.72760e27 | −0.0611471 | ||||||||
\(592\) | −3.39139e28 | −0.263633 | ||||||||
\(593\) | −8.65845e27 | −0.0661250 | −0.0330625 | − | 0.999453i | \(-0.510526\pi\) | ||||
−0.0330625 | + | 0.999453i | \(0.510526\pi\) | |||||||
\(594\) | −5.78769e26 | −0.00434258 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.17608e29 | 1.57612 | ||||||||
\(597\) | 1.22161e29 | 0.869366 | ||||||||
\(598\) | −3.88576e28 | −0.271715 | ||||||||
\(599\) | −2.52821e29 | −1.73712 | −0.868562 | − | 0.495580i | \(-0.834956\pi\) | ||||
−0.868562 | + | 0.495580i | \(0.834956\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.34861e29 | −1.55822 | −0.779111 | − | 0.626886i | \(-0.784329\pi\) | ||||
−0.779111 | + | 0.626886i | \(0.784329\pi\) | |||||||
\(602\) | −1.54371e28 | −0.100647 | ||||||||
\(603\) | −6.65252e28 | −0.426240 | ||||||||
\(604\) | −1.31456e29 | −0.827739 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.51861e28 | −0.153178 | ||||||||
\(607\) | 1.40619e29 | 0.840551 | 0.420275 | − | 0.907397i | \(-0.361933\pi\) | ||||
0.420275 | + | 0.907397i | \(0.361933\pi\) | |||||||
\(608\) | −4.21469e28 | −0.247616 | ||||||||
\(609\) | 9.02911e28 | 0.521391 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.64155e29 | 2.58959 | ||||||||
\(612\) | 8.82669e28 | 0.484070 | ||||||||
\(613\) | 2.49046e27 | 0.0134259 | 0.00671297 | − | 0.999977i | \(-0.497863\pi\) | ||||
0.00671297 | + | 0.999977i | \(0.497863\pi\) | |||||||
\(614\) | −2.04971e28 | −0.108624 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.24492e27 | −0.0371053 | ||||||||
\(617\) | 3.02386e29 | 1.52253 | 0.761267 | − | 0.648439i | \(-0.224578\pi\) | ||||
0.761267 | + | 0.648439i | \(0.224578\pi\) | |||||||
\(618\) | −2.87312e27 | −0.0142225 | ||||||||
\(619\) | −1.15264e29 | −0.560972 | −0.280486 | − | 0.959858i | \(-0.590496\pi\) | ||||
−0.280486 | + | 0.959858i | \(0.590496\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.03782e28 | −0.237018 | ||||||||
\(622\) | −4.40679e26 | −0.00203856 | ||||||||
\(623\) | 7.54072e28 | 0.342995 | ||||||||
\(624\) | −1.58655e29 | −0.709604 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.16249e28 | 0.180021 | ||||||||
\(627\) | 9.63648e27 | 0.0409835 | ||||||||
\(628\) | 2.01845e29 | 0.844193 | ||||||||
\(629\) | 1.04109e29 | 0.428210 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.78376e28 | 0.150527 | 0.0752636 | − | 0.997164i | \(-0.476020\pi\) | ||||
0.0752636 | + | 0.997164i | \(0.476020\pi\) | |||||||
\(632\) | −9.19160e28 | −0.359635 | ||||||||
\(633\) | −1.81381e29 | −0.697997 | ||||||||
\(634\) | 5.27226e28 | 0.199554 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.51585e29 | −0.555082 | ||||||||
\(637\) | 1.13313e29 | 0.408146 | ||||||||
\(638\) | 6.89991e27 | 0.0244470 | ||||||||
\(639\) | 2.19748e28 | 0.0765890 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.77565e29 | −1.27345 | −0.636726 | − | 0.771090i | \(-0.719712\pi\) | ||||
−0.636726 | + | 0.771090i | \(0.719712\pi\) | |||||||
\(642\) | 2.60398e27 | 0.00864011 | ||||||||
\(643\) | −4.92823e29 | −1.60870 | −0.804351 | − | 0.594154i | \(-0.797487\pi\) | ||||
−0.804351 | + | 0.594154i | \(0.797487\pi\) | |||||||
\(644\) | −3.10962e29 | −0.998633 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.11202e28 | 0.127824 | ||||||||
\(647\) | −1.91254e29 | −0.584946 | −0.292473 | − | 0.956274i | \(-0.594478\pi\) | ||||
−0.292473 | + | 0.956274i | \(0.594478\pi\) | |||||||
\(648\) | 1.20172e28 | 0.0361632 | ||||||||
\(649\) | 2.82735e28 | 0.0837165 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.41675e29 | −0.692838 | ||||||||
\(652\) | 2.21165e29 | 0.623903 | ||||||||
\(653\) | −5.64626e29 | −1.56737 | −0.783686 | − | 0.621157i | \(-0.786663\pi\) | ||||
−0.783686 | + | 0.621157i | \(0.786663\pi\) | |||||||
\(654\) | 2.65944e26 | 0.000726480 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.45103e28 | −0.170663 | ||||||||
\(657\) | 1.29996e29 | 0.338448 | ||||||||
\(658\) | −1.03930e29 | −0.266298 | ||||||||
\(659\) | −7.36315e29 | −1.85681 | −0.928404 | − | 0.371573i | \(-0.878819\pi\) | ||||
−0.928404 | + | 0.371573i | \(0.878819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.28744e29 | −1.78016 | −0.890081 | − | 0.455802i | \(-0.849353\pi\) | ||||
−0.890081 | + | 0.455802i | \(0.849353\pi\) | |||||||
\(662\) | 2.64600e28 | 0.0636182 | ||||||||
\(663\) | 4.87041e29 | 1.15259 | ||||||||
\(664\) | −5.65711e28 | −0.131774 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.98926e27 | 0.0157744 | ||||||||
\(667\) | 6.00594e29 | 1.33432 | ||||||||
\(668\) | −1.58463e29 | −0.346556 | ||||||||
\(669\) | 4.21660e29 | 0.907795 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.09951e28 | −0.168994 | ||||||||
\(672\) | 1.11777e29 | 0.229602 | ||||||||
\(673\) | 5.49339e29 | 1.11092 | 0.555460 | − | 0.831543i | \(-0.312542\pi\) | ||||
0.555460 | + | 0.831543i | \(0.312542\pi\) | |||||||
\(674\) | −5.36276e28 | −0.106773 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.97327e29 | −0.766845 | ||||||||
\(677\) | −4.21550e29 | −0.801065 | −0.400533 | − | 0.916282i | \(-0.631175\pi\) | ||||
−0.400533 | + | 0.916282i | \(0.631175\pi\) | |||||||
\(678\) | 3.95373e28 | 0.0739767 | ||||||||
\(679\) | −4.63139e29 | −0.853256 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.27433e29 | 0.763525 | ||||||||
\(682\) | −1.84685e28 | −0.0324859 | ||||||||
\(683\) | −6.15920e29 | −1.06686 | −0.533430 | − | 0.845844i | \(-0.679097\pi\) | ||||
−0.533430 | + | 0.845844i | \(0.679097\pi\) | |||||||
\(684\) | −9.86628e28 | −0.168292 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.08503e29 | −0.179489 | ||||||||
\(687\) | 5.44799e29 | 0.887545 | ||||||||
\(688\) | −4.19257e29 | −0.672670 | ||||||||
\(689\) | −8.36420e29 | −1.32167 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.19456e29 | 0.489657 | 0.244829 | − | 0.969566i | \(-0.421268\pi\) | ||||
0.244829 | + | 0.969566i | \(0.421268\pi\) | |||||||
\(692\) | −9.49328e29 | −1.43319 | ||||||||
\(693\) | −2.55567e28 | −0.0380020 | ||||||||
\(694\) | −2.90694e28 | −0.0425757 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.43266e29 | −0.203584 | ||||||||
\(697\) | 1.98034e29 | 0.277202 | ||||||||
\(698\) | −7.17383e28 | −0.0989167 | ||||||||
\(699\) | 9.77565e28 | 0.132781 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.68402e29 | 0.485605 | 0.242802 | − | 0.970076i | \(-0.421933\pi\) | ||||
0.242802 | + | 0.970076i | \(0.421933\pi\) | |||||||
\(702\) | 3.26970e28 | 0.0424589 | ||||||||
\(703\) | −1.16371e29 | −0.148872 | ||||||||
\(704\) | −9.11981e28 | −0.114940 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.40224e28 | −0.0783218 | ||||||||
\(707\) | −1.11214e30 | −1.34047 | ||||||||
\(708\) | −2.89478e29 | −0.343768 | ||||||||
\(709\) | −2.65319e29 | −0.310444 | −0.155222 | − | 0.987880i | \(-0.549609\pi\) | ||||
−0.155222 | + | 0.987880i | \(0.549609\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.24237e29 | −0.368325 | ||||||||
\(712\) | −1.19649e29 | −0.133928 | ||||||||
\(713\) | −1.60756e30 | −1.77308 | ||||||||
\(714\) | −1.09054e29 | −0.118525 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.71942e29 | −0.181466 | ||||||||
\(717\) | 9.35013e29 | 0.972448 | ||||||||
\(718\) | 3.01932e29 | 0.309459 | ||||||||
\(719\) | −3.34469e28 | −0.0337833 | −0.0168916 | − | 0.999857i | \(-0.505377\pi\) | ||||
−0.0168916 | + | 0.999857i | \(0.505377\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.26868e29 | −0.124461 | ||||||||
\(722\) | 1.24673e29 | 0.120540 | ||||||||
\(723\) | 4.84270e29 | 0.461462 | ||||||||
\(724\) | −1.82591e28 | −0.0171484 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.02448e29 | 0.0934691 | ||||||||
\(727\) | 2.10941e30 | 1.89692 | 0.948461 | − | 0.316893i | \(-0.102640\pi\) | ||||
0.948461 | + | 0.316893i | \(0.102640\pi\) | |||||||
\(728\) | 4.09295e29 | 0.362791 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.28704e30 | 1.09260 | ||||||||
\(732\) | 8.29265e29 | 0.693948 | ||||||||
\(733\) | 7.89829e29 | 0.651540 | 0.325770 | − | 0.945449i | \(-0.394376\pi\) | ||||
0.325770 | + | 0.945449i | \(0.394376\pi\) | |||||||
\(734\) | 6.24109e28 | 0.0507518 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.43513e29 | 0.587586 | ||||||||
\(737\) | −2.24483e29 | −0.174894 | ||||||||
\(738\) | 1.32948e28 | 0.0102115 | ||||||||
\(739\) | 1.77434e30 | 1.34360 | 0.671801 | − | 0.740732i | \(-0.265521\pi\) | ||||
0.671801 | + | 0.740732i | \(0.265521\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.44404e29 | −0.400710 | ||||||||
\(742\) | 1.87284e29 | 0.135913 | ||||||||
\(743\) | 4.10542e29 | 0.293748 | 0.146874 | − | 0.989155i | \(-0.453079\pi\) | ||||
0.146874 | + | 0.989155i | \(0.453079\pi\) | |||||||
\(744\) | 3.83468e29 | 0.270529 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.83043e28 | 0.0399892 | ||||||||
\(747\) | −1.99556e29 | −0.134958 | ||||||||
\(748\) | 2.97849e29 | 0.198623 | ||||||||
\(749\) | 1.14984e29 | 0.0756097 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.69088e29 | 0.619647 | 0.309823 | − | 0.950794i | \(-0.399730\pi\) | ||||
0.309823 | + | 0.950794i | \(0.399730\pi\) | |||||||
\(752\) | −2.82263e30 | −1.77978 | ||||||||
\(753\) | 1.51325e30 | 0.940945 | ||||||||
\(754\) | −3.89803e29 | −0.239027 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.61662e29 | 0.156049 | ||||||||
\(757\) | 7.60535e29 | 0.447314 | 0.223657 | − | 0.974668i | \(-0.428200\pi\) | ||||
0.223657 | + | 0.974668i | \(0.428200\pi\) | |||||||
\(758\) | 1.99892e29 | 0.115949 | ||||||||
\(759\) | −1.69997e29 | −0.0972529 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.38436e30 | 1.32688 | 0.663442 | − | 0.748228i | \(-0.269095\pi\) | ||||
0.663442 | + | 0.748228i | \(0.269095\pi\) | |||||||
\(762\) | 1.00373e29 | 0.0550920 | ||||||||
\(763\) | 1.17433e28 | 0.00635743 | ||||||||
\(764\) | −4.94645e29 | −0.264127 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.43150e29 | −0.282174 | ||||||||
\(767\) | −1.59729e30 | −0.818524 | ||||||||
\(768\) | 8.43826e29 | 0.426540 | ||||||||
\(769\) | 1.52146e30 | 0.758636 | 0.379318 | − | 0.925266i | \(-0.376159\pi\) | ||||
0.379318 | + | 0.925266i | \(0.376159\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.31513e30 | −1.12332 | ||||||||
\(772\) | −8.27568e29 | −0.396116 | ||||||||
\(773\) | −1.63448e30 | −0.771783 | −0.385891 | − | 0.922544i | \(-0.626106\pi\) | ||||
−0.385891 | + | 0.922544i | \(0.626106\pi\) | |||||||
\(774\) | 8.64041e28 | 0.0402489 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.34867e29 | 0.333166 | ||||||||
\(777\) | 3.08625e29 | 0.138042 | ||||||||
\(778\) | 6.52508e29 | 0.287939 | ||||||||
\(779\) | −2.21358e29 | −0.0963724 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.41521e28 | 0.0314259 | ||||||||
\(782\) | −7.25400e29 | −0.303324 | ||||||||
\(783\) | −5.05374e29 | −0.208504 | ||||||||
\(784\) | −6.89082e29 | −0.280512 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.24509e29 | 0.0493472 | ||||||||
\(787\) | −1.59330e30 | −0.623109 | −0.311554 | − | 0.950228i | \(-0.600850\pi\) | ||||
−0.311554 | + | 0.950228i | \(0.600850\pi\) | |||||||
\(788\) | 2.66979e29 | 0.103027 | ||||||||
\(789\) | 2.67890e30 | 1.02011 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.74585e30 | 0.647371 | ||||||||
\(792\) | 4.05510e28 | 0.0148384 | ||||||||
\(793\) | 4.57574e30 | 1.65231 | ||||||||
\(794\) | −7.93725e29 | −0.282849 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.22052e30 | −1.46480 | ||||||||
\(797\) | −3.98384e30 | −1.36455 | −0.682276 | − | 0.731095i | \(-0.739010\pi\) | ||||
−0.682276 | + | 0.731095i | \(0.739010\pi\) | |||||||
\(798\) | 1.21898e29 | 0.0412066 | ||||||||
\(799\) | 8.66493e30 | 2.89084 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.22067e29 | −0.137164 | ||||||||
\(802\) | −4.79499e27 | −0.00153800 | ||||||||
\(803\) | 4.38659e29 | 0.138872 | ||||||||
\(804\) | 2.29837e30 | 0.718176 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.04336e30 | 0.317625 | ||||||||
\(807\) | 2.39251e30 | 0.718922 | ||||||||
\(808\) | 1.76464e30 | 0.523405 | ||||||||
\(809\) | −5.29166e30 | −1.54929 | −0.774645 | − | 0.632396i | \(-0.782071\pi\) | ||||
−0.774645 | + | 0.632396i | \(0.782071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.38103e30 | −0.679276 | −0.339638 | − | 0.940556i | \(-0.610305\pi\) | ||||
−0.339638 | + | 0.940556i | \(0.610305\pi\) | |||||||
\(812\) | −3.11945e30 | −0.878495 | ||||||||
\(813\) | 7.55704e29 | 0.210088 | ||||||||
\(814\) | 2.35846e28 | 0.00647252 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.96180e30 | −0.792153 | ||||||||
\(817\) | −1.43862e30 | −0.379853 | ||||||||
\(818\) | 1.86041e29 | 0.0484953 | ||||||||
\(819\) | 1.44380e30 | 0.371558 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.82391e30 | 1.71171 | 0.855855 | − | 0.517216i | \(-0.173031\pi\) | ||||
0.855855 | + | 0.517216i | \(0.173031\pi\) | |||||||
\(822\) | 1.96387e29 | 0.0486362 | ||||||||
\(823\) | −3.46830e30 | −0.848044 | −0.424022 | − | 0.905652i | \(-0.639382\pi\) | ||||
−0.424022 | + | 0.905652i | \(0.639382\pi\) | |||||||
\(824\) | 2.01303e29 | 0.0485975 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.57650e29 | 0.0841721 | ||||||||
\(827\) | −3.88117e30 | −0.901893 | −0.450946 | − | 0.892551i | \(-0.648913\pi\) | ||||
−0.450946 | + | 0.892551i | \(0.648913\pi\) | |||||||
\(828\) | 1.74051e30 | 0.399353 | ||||||||
\(829\) | 2.71415e30 | 0.614909 | 0.307454 | − | 0.951563i | \(-0.400523\pi\) | ||||
0.307454 | + | 0.951563i | \(0.400523\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.32849e30 | −0.293459 | ||||||||
\(832\) | 5.15215e30 | 1.12381 | ||||||||
\(833\) | 2.11535e30 | 0.455627 | ||||||||
\(834\) | −6.96127e29 | −0.148062 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.32929e29 | −0.0690535 | ||||||||
\(837\) | 1.35270e30 | 0.277066 | ||||||||
\(838\) | −6.34644e29 | −0.128371 | ||||||||
\(839\) | 7.41628e30 | 1.48144 | 0.740722 | − | 0.671811i | \(-0.234483\pi\) | ||||
0.740722 | + | 0.671811i | \(0.234483\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.92068e29 | 0.173796 | ||||||||
\(842\) | 1.26786e30 | 0.243946 | ||||||||
\(843\) | −4.23223e30 | −0.804229 | ||||||||
\(844\) | 6.26651e30 | 1.17606 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.81712e29 | 0.106492 | ||||||||
\(847\) | 4.52379e30 | 0.817949 | ||||||||
\(848\) | 5.08645e30 | 0.908361 | ||||||||
\(849\) | 5.10321e30 | 0.900145 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.05290e30 | 0.353270 | ||||||||
\(852\) | −7.59203e29 | −0.129045 | ||||||||
\(853\) | −1.13715e31 | −1.90920 | −0.954602 | − | 0.297885i | \(-0.903719\pi\) | ||||
−0.954602 | + | 0.297885i | \(0.903719\pi\) | |||||||
\(854\) | −1.02456e30 | −0.169914 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.82446e29 | −0.0295229 | ||||||||
\(857\) | −1.05299e31 | −1.68315 | −0.841577 | − | 0.540137i | \(-0.818372\pi\) | ||||
−0.841577 | + | 0.540137i | \(0.818372\pi\) | |||||||
\(858\) | 1.10333e29 | 0.0174217 | ||||||||
\(859\) | −7.09784e30 | −1.10713 | −0.553564 | − | 0.832806i | \(-0.686733\pi\) | ||||
−0.553564 | + | 0.832806i | \(0.686733\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.87060e29 | 0.0893613 | ||||||||
\(862\) | 9.69025e29 | 0.145716 | ||||||||
\(863\) | 3.54700e27 | 0.000526923 0 | 0.000263462 | − | 1.00000i | \(-0.499916\pi\) | ||||
0.000263462 | 1.00000i | \(0.499916\pi\) | ||||||||
\(864\) | −6.25635e29 | −0.0918177 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.08561e30 | 0.155502 | ||||||||
\(867\) | 5.01236e30 | 0.709319 | ||||||||
\(868\) | 8.34959e30 | 1.16737 | ||||||||
\(869\) | −1.09411e30 | −0.151131 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.26820e31 | 1.71000 | ||||||||
\(872\) | −1.86332e28 | −0.00248235 | ||||||||
\(873\) | 2.59227e30 | 0.341217 | ||||||||
\(874\) | 8.10836e29 | 0.105454 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.49119e30 | −0.570254 | ||||||||
\(877\) | 1.15261e31 | 1.44607 | 0.723033 | − | 0.690814i | \(-0.242748\pi\) | ||||
0.723033 | + | 0.690814i | \(0.242748\pi\) | |||||||
\(878\) | 2.09225e30 | 0.259370 | ||||||||
\(879\) | −2.07540e30 | −0.254225 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.58779e30 | 1.14676 | 0.573379 | − | 0.819291i | \(-0.305632\pi\) | ||||
0.573379 | + | 0.819291i | \(0.305632\pi\) | |||||||
\(882\) | 1.42012e29 | 0.0167843 | ||||||||
\(883\) | 5.46477e30 | 0.638241 | 0.319120 | − | 0.947714i | \(-0.396613\pi\) | ||||
0.319120 | + | 0.947714i | \(0.396613\pi\) | |||||||
\(884\) | −1.68267e31 | −1.94200 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.01341e29 | 0.0339629 | ||||||||
\(887\) | −1.25659e31 | −1.39957 | −0.699787 | − | 0.714352i | \(-0.746722\pi\) | ||||
−0.699787 | + | 0.714352i | \(0.746722\pi\) | |||||||
\(888\) | −4.89697e29 | −0.0539004 | ||||||||
\(889\) | 4.43216e30 | 0.482110 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.43045e29 | 0.0151970 | ||||||||
\(892\) | −1.45678e31 | −1.52955 | ||||||||
\(893\) | −9.68547e30 | −1.00503 | ||||||||
\(894\) | 1.50483e30 | 0.154327 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.12344e30 | −0.513248 | ||||||||
\(897\) | 9.60381e30 | 0.950874 | ||||||||
\(898\) | 1.90031e30 | 0.185961 | ||||||||
\(899\) | −1.61264e31 | −1.55977 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.56144e31 | −1.47542 | ||||||||
\(902\) | 4.48622e28 | 0.00418998 | ||||||||
\(903\) | 3.81534e30 | 0.352219 | ||||||||
\(904\) | −2.77015e30 | −0.252775 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.09061e29 | −0.0810489 | ||||||||
\(907\) | 1.10098e31 | 0.970292 | 0.485146 | − | 0.874433i | \(-0.338766\pi\) | ||||
0.485146 | + | 0.874433i | \(0.338766\pi\) | |||||||
\(908\) | −1.47673e31 | −1.28647 | ||||||||
\(909\) | 6.22484e30 | 0.536052 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.42131e30 | 0.119604 | 0.0598021 | − | 0.998210i | \(-0.480953\pi\) | ||||
0.0598021 | + | 0.998210i | \(0.480953\pi\) | |||||||
\(912\) | 3.31064e30 | 0.275401 | ||||||||
\(913\) | −6.73385e29 | −0.0553758 | ||||||||
\(914\) | 1.05221e30 | 0.0855398 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.88221e31 | −1.49543 | ||||||||
\(917\) | 5.49793e30 | 0.431838 | ||||||||
\(918\) | 6.10393e29 | 0.0473982 | ||||||||
\(919\) | −3.78618e30 | −0.290662 | −0.145331 | − | 0.989383i | \(-0.546425\pi\) | ||||
−0.145331 | + | 0.989383i | \(0.546425\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.06595e30 | 0.380132 | ||||||||
\(922\) | −1.32992e30 | −0.0986622 | ||||||||
\(923\) | −4.18915e30 | −0.307261 | ||||||||
\(924\) | 8.82953e29 | 0.0640298 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.33103e30 | −0.0943567 | ||||||||
\(927\) | 7.10103e29 | 0.0497719 | ||||||||
\(928\) | 7.45862e30 | 0.516898 | ||||||||
\(929\) | −2.18847e31 | −1.49960 | −0.749801 | − | 0.661664i | \(-0.769851\pi\) | ||||
−0.749801 | + | 0.661664i | \(0.769851\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.36449e30 | −0.158404 | ||||||||
\(932\) | −3.37737e30 | −0.223723 | ||||||||
\(933\) | 1.08916e29 | 0.00713399 | ||||||||
\(934\) | 2.23875e29 | 0.0144998 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.29089e30 | −0.145080 | ||||||||
\(937\) | 4.82022e30 | 0.301857 | 0.150928 | − | 0.988545i | \(-0.451774\pi\) | ||||
0.150928 | + | 0.988545i | \(0.451774\pi\) | |||||||
\(938\) | −2.83964e30 | −0.175846 | ||||||||
\(939\) | −1.02878e31 | −0.629988 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.95284e30 | 0.296594 | 0.148297 | − | 0.988943i | \(-0.452621\pi\) | ||||
0.148297 | + | 0.988943i | \(0.452621\pi\) | |||||||
\(942\) | 1.39582e30 | 0.0826601 | ||||||||
\(943\) | 3.90498e30 | 0.228689 | ||||||||
\(944\) | 9.71344e30 | 0.562558 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.91563e29 | 0.0165149 | ||||||||
\(947\) | −1.93524e30 | −0.108408 | −0.0542038 | − | 0.998530i | \(-0.517262\pi\) | ||||
−0.0542038 | + | 0.998530i | \(0.517262\pi\) | |||||||
\(948\) | 1.12020e31 | 0.620594 | ||||||||
\(949\) | −2.47816e31 | −1.35779 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.30306e31 | −0.698343 | ||||||||
\(952\) | 7.64079e30 | 0.404995 | ||||||||
\(953\) | −2.80007e31 | −1.46789 | −0.733946 | − | 0.679208i | \(-0.762323\pi\) | ||||
−0.733946 | + | 0.679208i | \(0.762323\pi\) | |||||||
\(954\) | −1.04826e30 | −0.0543514 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.23036e31 | −1.63849 | ||||||||
\(957\) | −1.70534e30 | −0.0855531 | ||||||||
\(958\) | −5.01489e30 | −0.248842 | ||||||||
\(959\) | 8.67187e30 | 0.425615 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.23389e31 | 1.07267 | ||||||||
\(962\) | −1.33239e30 | −0.0632839 | ||||||||
\(963\) | −6.43584e29 | −0.0302363 | ||||||||
\(964\) | −1.67309e31 | −0.777520 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.15040e30 | −0.0977822 | ||||||||
\(967\) | 3.92899e31 | 1.76727 | 0.883634 | − | 0.468177i | \(-0.155089\pi\) | ||||
0.883634 | + | 0.468177i | \(0.155089\pi\) | |||||||
\(968\) | −7.17793e30 | −0.319380 | ||||||||
\(969\) | −1.01630e31 | −0.447325 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.41965e31 | 1.47292 | 0.736462 | − | 0.676479i | \(-0.236495\pi\) | ||||
0.736462 | + | 0.676479i | \(0.236495\pi\) | |||||||
\(972\) | −1.46456e30 | −0.0624040 | ||||||||
\(973\) | −3.07389e31 | −1.29570 | ||||||||
\(974\) | −2.42879e30 | −0.101279 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.78261e31 | −1.13561 | ||||||||
\(977\) | 4.27738e30 | 0.172697 | 0.0863486 | − | 0.996265i | \(-0.472480\pi\) | ||||
0.0863486 | + | 0.996265i | \(0.472480\pi\) | |||||||
\(978\) | 1.52943e30 | 0.0610901 | ||||||||
\(979\) | −1.42423e30 | −0.0562809 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.57291e28 | −0.00254234 | ||||||||
\(982\) | −5.73317e30 | −0.219394 | ||||||||
\(983\) | −3.07553e31 | −1.16441 | −0.582207 | − | 0.813041i | \(-0.697811\pi\) | ||||
−0.582207 | + | 0.813041i | \(0.697811\pi\) | |||||||
\(984\) | −9.31492e29 | −0.0348924 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.27692e30 | −0.266833 | ||||||||
\(987\) | 2.56866e31 | 0.931917 | ||||||||
\(988\) | 1.88085e31 | 0.675159 | ||||||||
\(989\) | 2.53787e31 | 0.901382 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.50222e30 | 0.0522348 | 0.0261174 | − | 0.999659i | \(-0.491686\pi\) | ||||
0.0261174 | + | 0.999659i | \(0.491686\pi\) | |||||||
\(992\) | −1.99639e31 | −0.686868 | ||||||||
\(993\) | −6.53970e30 | −0.222634 | ||||||||
\(994\) | 9.37998e29 | 0.0315969 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.89443e30 | 0.227392 | ||||||||
\(997\) | −4.25981e31 | −1.39024 | −0.695122 | − | 0.718891i | \(-0.744650\pi\) | ||||
−0.695122 | + | 0.718891i | \(0.744650\pi\) | |||||||
\(998\) | 3.25594e30 | 0.105149 | ||||||||
\(999\) | −1.72742e30 | −0.0552028 |
(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 | 75.22.a.k.1.4 | ✓ | 8 | |
5.2 | odd | 4 | 75.22.b.j.49.7 | 16 | |||
5.3 | odd | 4 | 75.22.b.j.49.10 | 16 | |||
5.4 | even | 2 | 75.22.a.l.1.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.22.a.k.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
75.22.a.l.1.5 | yes | 8 | 5.4 | even | 2 | ||
75.22.b.j.49.7 | 16 | 5.2 | odd | 4 | |||
75.22.b.j.49.10 | 16 | 5.3 | odd | 4 |