Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,22,Mod(1,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("24.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.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: | \(67.0745626289\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 12529199x - 17012391021 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{4}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2135.93\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 24.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 59049.0 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.51850e7 | −1.61128 | −0.805642 | − | 0.592403i | \(-0.798179\pi\) | ||||
−0.805642 | + | 0.592403i | \(0.798179\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.43346e8 | 0.325608 | 0.162804 | − | 0.986658i | \(-0.447946\pi\) | ||||
0.162804 | + | 0.986658i | \(0.447946\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.47083e9 | −0.0635961 | −0.0317980 | − | 0.999494i | \(-0.510123\pi\) | ||||
−0.0317980 | + | 0.999494i | \(0.510123\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.75801e11 | −0.554868 | −0.277434 | − | 0.960745i | \(-0.589484\pi\) | ||||
−0.277434 | + | 0.960745i | \(0.589484\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.07764e12 | −0.930275 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.88815e12 | −0.948990 | −0.474495 | − | 0.880258i | \(-0.657369\pi\) | ||||
−0.474495 | + | 0.880258i | \(0.657369\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.71614e13 | −0.642156 | −0.321078 | − | 0.947053i | \(-0.604045\pi\) | ||||
−0.321078 | + | 0.947053i | \(0.604045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.43693e13 | 0.187990 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.02245e14 | 0.514635 | 0.257318 | − | 0.966327i | \(-0.417161\pi\) | ||||
0.257318 | + | 0.966327i | \(0.417161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.61145e14 | 1.59624 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.05891e14 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.25807e15 | 1.43807 | 0.719037 | − | 0.694972i | \(-0.244583\pi\) | ||||
0.719037 | + | 0.694972i | \(0.244583\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.25673e15 | −1.15191 | −0.575954 | − | 0.817482i | \(-0.695369\pi\) | ||||
−0.575954 | + | 0.817482i | \(0.695369\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.23047e14 | −0.0367172 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.56212e15 | −0.524647 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.32886e15 | −0.0454319 | −0.0227160 | − | 0.999742i | \(-0.507231\pi\) | ||||
−0.0227160 | + | 0.999742i | \(0.507231\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.62857e16 | −0.320353 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.25989e17 | 1.46589 | 0.732944 | − | 0.680289i | \(-0.238146\pi\) | ||||
0.732944 | + | 0.680289i | \(0.238146\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.18452e16 | −0.577530 | −0.288765 | − | 0.957400i | \(-0.593245\pi\) | ||||
−0.288765 | + | 0.957400i | \(0.593245\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.22682e17 | −0.537095 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.29399e17 | 0.913471 | 0.456735 | − | 0.889603i | \(-0.349019\pi\) | ||||
0.456735 | + | 0.889603i | \(0.349019\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.99329e17 | −0.893980 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.65787e17 | −0.547899 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.26060e18 | 0.990103 | 0.495052 | − | 0.868864i | \(-0.335149\pi\) | ||||
0.495052 | + | 0.868864i | \(0.335149\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.92491e17 | 0.102471 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.01336e18 | −0.370749 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.01887e18 | 1.27838 | 0.639190 | − | 0.769049i | \(-0.279270\pi\) | ||||
0.639190 | + | 0.769049i | \(0.279270\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.90880e18 | 1.41954 | 0.709769 | − | 0.704434i | \(-0.248799\pi\) | ||||
0.709769 | + | 0.704434i | \(0.248799\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.48495e17 | 0.108536 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.70403e18 | 0.894050 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.13054e18 | −0.611943 | −0.305972 | − | 0.952041i | \(-0.598981\pi\) | ||||
−0.305972 | + | 0.952041i | \(0.598981\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.03746e18 | 0.297125 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.27073e19 | −1.19243 | −0.596215 | − | 0.802825i | \(-0.703329\pi\) | ||||
−0.596215 | + | 0.802825i | \(0.703329\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.66934e19 | 0.726966 | 0.363483 | − | 0.931601i | \(-0.381587\pi\) | ||||
0.363483 | + | 0.931601i | \(0.381587\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.49448e19 | 0.921587 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.33131e18 | −0.0207074 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.51094e20 | 1.79541 | 0.897706 | − | 0.440595i | \(-0.145232\pi\) | ||||
0.897706 | + | 0.440595i | \(0.145232\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.78125e20 | 1.96752 | 0.983761 | − | 0.179482i | \(-0.0574422\pi\) | ||||
0.983761 | + | 0.179482i | \(0.0574422\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.77544e20 | 1.52909 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.92386e20 | 0.830273 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.69366e20 | −0.575747 | −0.287873 | − | 0.957669i | \(-0.592948\pi\) | ||||
−0.287873 | + | 0.957669i | \(0.592948\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.71149e19 | −0.180669 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.10405e20 | −0.665055 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.03824e20 | 1.03470 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.36145e20 | 0.738209 | 0.369104 | − | 0.929388i | \(-0.379664\pi\) | ||||
0.369104 | + | 0.929388i | \(0.379664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.90756e19 | −0.0211987 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.66650e21 | 1.50117 | 0.750587 | − | 0.660771i | \(-0.229771\pi\) | ||||
0.750587 | + | 0.660771i | \(0.229771\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.73073e21 | −1.26893 | −0.634465 | − | 0.772952i | \(-0.718779\pi\) | ||||
−0.634465 | + | 0.772952i | \(0.718779\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.05585e20 | −0.302905 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.95507e21 | 0.960800 | 0.480400 | − | 0.877050i | \(-0.340492\pi\) | ||||
0.480400 | + | 0.877050i | \(0.340492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.31264e21 | 0.935687 | 0.467844 | − | 0.883811i | \(-0.345031\pi\) | ||||
0.467844 | + | 0.883811i | \(0.345031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.84679e19 | −0.0262301 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.49465e21 | −1.52271 | −0.761354 | − | 0.648336i | \(-0.775465\pi\) | ||||
−0.761354 | + | 0.648336i | \(0.775465\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.59749e21 | −0.829224 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.61657e20 | −0.184956 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.91955e21 | −0.308998 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.37032e21 | −0.995956 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.43950e21 | 0.846331 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00033e22 | −0.960705 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.26429e21 | 0.671841 | 0.335921 | − | 0.941890i | \(-0.390953\pi\) | ||||
0.335921 | + | 0.941890i | \(0.390953\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.83288e21 | −0.333437 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.36696e22 | −0.802433 | −0.401216 | − | 0.915983i | \(-0.631412\pi\) | ||||
−0.401216 | + | 0.915983i | \(0.631412\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.17616e21 | −0.209091 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.24427e21 | −0.310092 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.55734e22 | −1.67165 | −0.835826 | − | 0.548994i | \(-0.815011\pi\) | ||||
−0.835826 | + | 0.548994i | \(0.815011\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.19577e22 | −0.376697 | −0.188349 | − | 0.982102i | \(-0.560314\pi\) | ||||
−0.188349 | + | 0.982102i | \(0.560314\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.94507e22 | 0.527393 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.50886e21 | 0.0352874 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.14635e23 | −2.31715 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.94849e22 | −0.516139 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.81889e22 | 1.49144 | 0.745721 | − | 0.666258i | \(-0.232105\pi\) | ||||
0.745721 | + | 0.666258i | \(0.232105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.19351e23 | 1.57605 | 0.788025 | − | 0.615644i | \(-0.211104\pi\) | ||||
0.788025 | + | 0.615644i | \(0.211104\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.75043e22 | −0.316330 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.84958e23 | 1.85605 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.47687e22 | −0.655803 | −0.327901 | − | 0.944712i | \(-0.606341\pi\) | ||||
−0.327901 | + | 0.944712i | \(0.606341\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.44372e22 | 0.571636 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.48809e22 | 0.167569 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.03663e23 | 1.20488 | 0.602438 | − | 0.798166i | \(-0.294196\pi\) | ||||
0.602438 | + | 0.798166i | \(0.294196\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.13664e22 | 0.0591619 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.50641e23 | 0.690907 | 0.345453 | − | 0.938436i | \(-0.387725\pi\) | ||||
0.345453 | + | 0.938436i | \(0.387725\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.70999e23 | −0.692121 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.98382e22 | −0.214052 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.13849e23 | −0.677054 | −0.338527 | − | 0.940957i | \(-0.609929\pi\) | ||||
−0.338527 | + | 0.940957i | \(0.609929\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.85221e23 | 0.519747 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.96359e23 | 0.738073 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.14152e22 | −0.0695318 | −0.0347659 | − | 0.999395i | \(-0.511069\pi\) | ||||
−0.0347659 | + | 0.999395i | \(0.511069\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.03303e22 | 0.118826 | 0.0594128 | − | 0.998233i | \(-0.481077\pi\) | ||||
0.0594128 | + | 0.998233i | \(0.481077\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.67007e23 | 0.819571 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.67559e22 | 0.0732038 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.31547e22 | 0.0603520 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.01028e22 | 0.0626632 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.09055e24 | 1.22123 | 0.610613 | − | 0.791929i | \(-0.290923\pi\) | ||||
0.610613 | + | 0.791929i | \(0.290923\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.10755e23 | 0.311936 | 0.155968 | − | 0.987762i | \(-0.450150\pi\) | ||||
0.155968 | + | 0.987762i | \(0.450150\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.73013e23 | 0.516180 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.68710e24 | −1.36535 | −0.682676 | − | 0.730721i | \(-0.739184\pi\) | ||||
−0.682676 | + | 0.730721i | \(0.739184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.51134e24 | −1.10003 | −0.550015 | − | 0.835155i | \(-0.685378\pi\) | ||||
−0.550015 | + | 0.835155i | \(0.685378\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.39149e23 | −0.353305 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.92838e23 | 0.468248 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.43291e24 | −2.36196 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.56506e23 | 0.171545 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.38872e22 | 0.0408386 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.04443e24 | −1.59181 | −0.795906 | − | 0.605420i | \(-0.793005\pi\) | ||||
−0.795906 | + | 0.605420i | \(0.793005\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.93134e24 | −0.688449 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.87972e24 | 0.930564 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.27920e24 | −0.375070 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.57622e24 | 0.419714 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.17556e24 | 0.526564 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.23296e24 | −0.711868 | −0.355934 | − | 0.934511i | \(-0.615837\pi\) | ||||
−0.355934 | + | 0.934511i | \(0.615837\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.65395e24 | 0.532079 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.71374e24 | −1.04388 | −0.521938 | − | 0.852983i | \(-0.674791\pi\) | ||||
−0.521938 | + | 0.852983i | \(0.674791\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.35658e24 | −0.226033 | −0.113016 | − | 0.993593i | \(-0.536051\pi\) | ||||
−0.113016 | + | 0.993593i | \(0.536051\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.86122e22 | −0.0119554 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.19554e24 | 0.582842 | 0.291421 | − | 0.956595i | \(-0.405872\pi\) | ||||
0.291421 | + | 0.956595i | \(0.405872\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.15899e25 | −1.47186 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.92198e24 | 1.03658 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.83395e24 | −0.407820 | −0.203910 | − | 0.978990i | \(-0.565365\pi\) | ||||
−0.203910 | + | 0.978990i | \(0.565365\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.11880e24 | 0.109037 | 0.0545186 | − | 0.998513i | \(-0.482638\pi\) | ||||
0.0545186 | + | 0.998513i | \(0.482638\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.17898e23 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.75689e25 | 1.44045 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.73313e24 | 0.356312 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.64230e25 | 1.13595 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.18420e24 | 0.138905 | 0.0694527 | − | 0.997585i | \(-0.477875\pi\) | ||||
0.0694527 | + | 0.997585i | \(0.477875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.59365e23 | −0.0327288 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.63887e25 | 0.882821 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.30434e24 | 0.412105 | 0.206052 | − | 0.978541i | \(-0.433938\pi\) | ||||
0.206052 | + | 0.978541i | \(0.433938\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.23373e23 | −0.0147930 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.13602e25 | 0.479358 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.63856e25 | 1.02762 | 0.513809 | − | 0.857904i | \(-0.328234\pi\) | ||||
0.513809 | + | 0.857904i | \(0.328234\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.43542e25 | −1.59534 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.00009e25 | −0.332407 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.85272e25 | 1.18405 | 0.592023 | − | 0.805921i | \(-0.298330\pi\) | ||||
0.592023 | + | 0.805921i | \(0.298330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.43179e25 | −1.26009 | −0.630046 | − | 0.776558i | \(-0.716964\pi\) | ||||
−0.630046 | + | 0.776558i | \(0.716964\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.96307e24 | −0.104310 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.16410e24 | −0.101514 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.73390e24 | 0.129542 | 0.0647712 | − | 0.997900i | \(-0.479368\pi\) | ||||
0.0647712 | + | 0.997900i | \(0.479368\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.83291e25 | −0.383969 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.65196e25 | 0.904107 | 0.452054 | − | 0.891991i | \(-0.350692\pi\) | ||||
0.452054 | + | 0.891991i | \(0.350692\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.23171e25 | −0.402605 | −0.201303 | − | 0.979529i | \(-0.564517\pi\) | ||||
−0.201303 | + | 0.979529i | \(0.564517\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.56552e25 | 0.597381 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.06588e25 | 0.477305 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.86904e24 | −0.0994189 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.16588e25 | 0.426205 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.10928e25 | 0.514820 | 0.257410 | − | 0.966302i | \(-0.417131\pi\) | ||||
0.257410 | + | 0.966302i | \(0.417131\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.76589e26 | −2.05983 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.12640e24 | −0.0122391 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.81992e25 | −0.285555 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.99167e25 | −0.188048 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.84052e25 | 0.866704 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.78271e26 | −2.28728 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.68334e25 | −0.589654 | −0.294827 | − | 0.955551i | \(-0.595262\pi\) | ||||
−0.294827 | + | 0.955551i | \(0.595262\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.02198e26 | −0.732617 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.06898e25 | −0.473557 | −0.236779 | − | 0.971564i | \(-0.576092\pi\) | ||||
−0.236779 | + | 0.971564i | \(0.576092\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.82026e25 | −0.176634 | −0.0883168 | − | 0.996092i | \(-0.528149\pi\) | ||||
−0.0883168 | + | 0.996092i | \(0.528149\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.98543e25 | −0.174882 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.32837e26 | −1.27623 | −0.638115 | − | 0.769941i | \(-0.720286\pi\) | ||||
−0.638115 | + | 0.769941i | \(0.720286\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.78244e25 | −0.0914559 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.15445e26 | 0.554718 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.35372e26 | 0.609399 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.09924e26 | −0.885701 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.36559e26 | 0.540219 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.01579e25 | 0.297433 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.36145e26 | 1.86676 | 0.933379 | − | 0.358892i | \(-0.116845\pi\) | ||||
0.933379 | + | 0.358892i | \(0.116845\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.63345e24 | −0.0151440 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.21258e26 | 0.986014 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.24070e26 | 1.51104 | 0.755519 | − | 0.655126i | \(-0.227385\pi\) | ||||
0.755519 | + | 0.655126i | \(0.227385\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.24454e26 | −0.879136 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.87587e25 | 0.0732568 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.57429e26 | −0.616694 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.12428e26 | −0.478753 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.79992e26 | 0.805962 | 0.402981 | − | 0.915208i | \(-0.367974\pi\) | ||||
0.402981 | + | 0.915208i | \(0.367974\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.61472e26 | −0.522106 | −0.261053 | − | 0.965324i | \(-0.584070\pi\) | ||||
−0.261053 | + | 0.965324i | \(0.584070\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.67849e25 | −0.106784 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.68732e26 | 0.476086 | 0.238043 | − | 0.971255i | \(-0.423494\pi\) | ||||
0.238043 | + | 0.971255i | \(0.423494\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.15081e27 | 1.92134 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.13347e26 | −0.178400 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.16873e26 | 0.618745 | 0.309373 | − | 0.950941i | \(-0.399881\pi\) | ||||
0.309373 | + | 0.950941i | \(0.399881\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.19695e26 | −0.587636 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.35210e26 | −0.575015 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.39207e26 | −1.17135 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.62599e26 | 1.01582 | 0.507908 | − | 0.861411i | \(-0.330419\pi\) | ||||
0.507908 | + | 0.861411i | \(0.330419\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.39295e26 | 0.488630 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.06762e26 | 0.322385 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.44945e27 | 1.43966 | 0.719830 | − | 0.694151i | \(-0.244220\pi\) | ||||
0.719830 | + | 0.694151i | \(0.244220\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.90688e26 | −0.554664 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.98577e26 | −0.797942 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00826e27 | 0.846952 | 0.423476 | − | 0.905907i | \(-0.360810\pi\) | ||||
0.423476 | + | 0.905907i | \(0.360810\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.87998e26 | 0.387888 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.55682e26 | −0.117125 | −0.0585627 | − | 0.998284i | \(-0.518652\pi\) | ||||
−0.0585627 | + | 0.998284i | \(0.518652\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.68419e25 | 0.0333655 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.85376e26 | −0.192510 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.90693e26 | −0.185765 | −0.0928825 | − | 0.995677i | \(-0.529608\pi\) | ||||
−0.0928825 | + | 0.995677i | \(0.529608\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.06524e26 | −0.488384 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.07179e26 | −0.463285 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.31625e27 | −2.89292 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.52566e27 | 0.787331 | 0.393665 | − | 0.919254i | \(-0.371207\pi\) | ||||
0.393665 | + | 0.919254i | \(0.371207\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.46598e26 | −0.120719 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.96782e27 | −0.914048 | −0.457024 | − | 0.889454i | \(-0.651085\pi\) | ||||
−0.457024 | + | 0.889454i | \(0.651085\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.44981e27 | 0.639157 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.27767e26 | −0.179032 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.26998e24 | 0.00288929 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.91042e27 | 1.47615 | 0.738073 | − | 0.674721i | \(-0.235736\pi\) | ||||
0.738073 | + | 0.674721i | \(0.235736\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.69107e27 | −0.965129 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.22132e27 | 0.416250 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.78581e27 | −3.17024 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.06091e26 | −0.217486 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.38402e27 | 0.698334 | 0.349167 | − | 0.937060i | \(-0.386465\pi\) | ||||
0.349167 | + | 0.937060i | \(0.386465\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.54346e27 | 1.54461 | 0.772305 | − | 0.635252i | \(-0.219104\pi\) | ||||
0.772305 | + | 0.635252i | \(0.219104\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.14854e27 | 0.304490 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00402e27 | −1.51481 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.92457e27 | 0.462213 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.90966e25 | 0.0203732 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.83540e27 | 1.92404 | 0.962022 | − | 0.272971i | \(-0.0880063\pi\) | ||||
0.962022 | + | 0.272971i | \(0.0880063\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.01615e27 | −1.24794 | −0.623972 | − | 0.781446i | \(-0.714482\pi\) | ||||
−0.623972 | + | 0.781446i | \(0.714482\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.76909e27 | −1.33780 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.75467e27 | −0.330476 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.36549e27 | −0.963234 | −0.481617 | − | 0.876382i | \(-0.659950\pi\) | ||||
−0.481617 | + | 0.876382i | \(0.659950\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.74105e27 | −0.297993 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.01374e25 | 0.00328673 | 0.00164337 | − | 0.999999i | \(-0.499477\pi\) | ||||
0.00164337 | + | 0.999999i | \(0.499477\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.95914e27 | 0.927691 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.79796e27 | 0.861085 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.26698e27 | 0.604691 | 0.302346 | − | 0.953198i | \(-0.402230\pi\) | ||||
0.302346 | + | 0.953198i | \(0.402230\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.89263e26 | −0.0932248 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.04759e27 | 0.909933 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.36144e27 | 0.291110 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.37046e28 | 1.61341 | 0.806707 | − | 0.590952i | \(-0.201248\pi\) | ||||
0.806707 | + | 0.590952i | \(0.201248\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.62410e27 | −0.182633 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.95760e26 | 0.0425179 | 0.0212590 | − | 0.999774i | \(-0.493233\pi\) | ||||
0.0212590 | + | 0.999774i | \(0.493233\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.64489e28 | 1.68864 | 0.844320 | − | 0.535839i | \(-0.180005\pi\) | ||||
0.844320 | + | 0.535839i | \(0.180005\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.09216e28 | 1.07159 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.81167e27 | 0.451303 | 0.225651 | − | 0.974208i | \(-0.427549\pi\) | ||||
0.225651 | + | 0.974208i | \(0.427549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.22188e27 | −0.199253 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.41501e27 | −0.378628 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.47761e26 | 0.0367286 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.30623e28 | −1.02503 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.39544e27 | 0.330034 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.27968e27 | 0.594964 | 0.297482 | − | 0.954727i | \(-0.403853\pi\) | ||||
0.297482 | + | 0.954727i | \(0.403853\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.66500e26 | 0.0252087 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.46919e27 | 0.0967462 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.88642e28 | −1.18946 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.94208e28 | −1.77664 | −0.888321 | − | 0.459223i | \(-0.848128\pi\) | ||||
−0.888321 | + | 0.459223i | \(0.848128\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.20261e28 | 0.695635 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.03749e26 | −0.0279164 | −0.0139582 | − | 0.999903i | \(-0.504443\pi\) | ||||
−0.0139582 | + | 0.999903i | \(0.504443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.57001e28 | −1.36472 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.71175e26 | 0.0341571 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.95920e27 | −0.388264 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.85361e28 | 1.33456 | 0.667282 | − | 0.744805i | \(-0.267458\pi\) | ||||
0.667282 | + | 0.744805i | \(0.267458\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.89518e27 | 0.398895 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.16677e28 | 1.36192 | 0.680962 | − | 0.732319i | \(-0.261562\pi\) | ||||
0.680962 | + | 0.732319i | \(0.261562\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.86358e28 | −2.41882 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00973e28 | −0.399596 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.83426e27 | 0.221538 | 0.110769 | − | 0.993846i | \(-0.464669\pi\) | ||||
0.110769 | + | 0.993846i | \(0.464669\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.49574e27 | 0.236706 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.53338e27 | −0.123583 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.08955e28 | 2.04461 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.80209e27 | −0.0580932 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.26276e28 | −0.390897 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.34708e28 | −1.29241 | −0.646207 | − | 0.763162i | \(-0.723646\pi\) | ||||
−0.646207 | + | 0.763162i | \(0.723646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.35350e28 | −1.81445 | −0.907226 | − | 0.420644i | \(-0.861804\pi\) | ||||
−0.907226 | + | 0.420644i | \(0.861804\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.09371e28 | 0.300076 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.14659e28 | 1.09315 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.90175e28 | −0.735150 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.74997e28 | 0.426127 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.47477e28 | −0.813375 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.87891e28 | −1.54812 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.85504e27 | −0.0401442 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.73174e27 | 0.0568536 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.40153e28 | 0.280563 | 0.140281 | − | 0.990112i | \(-0.455199\pi\) | ||||
0.140281 | + | 0.990112i | \(0.455199\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.56244e27 | 0.0686040 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.13703e28 | −1.50766 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.55956e28 | −0.278058 | −0.139029 | − | 0.990288i | \(-0.544398\pi\) | ||||
−0.139029 | + | 0.990288i | \(0.544398\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.75763e28 | 0.473180 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.59131e28 | −0.923468 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.67682e28 | 0.584600 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.76089e27 | 0.0422642 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.80978e28 | 0.856406 | 0.428203 | − | 0.903682i | \(-0.359147\pi\) | ||||
0.428203 | + | 0.903682i | \(0.359147\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.25729e28 | 0.320453 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.54824e27 | 0.0348442 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.80401e28 | 1.15969 | 0.579846 | − | 0.814726i | \(-0.303113\pi\) | ||||
0.579846 | + | 0.814726i | \(0.303113\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.93329e29 | 2.45352 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.95852e27 | 0.0361786 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.11084e29 | −1.30910 | −0.654551 | − | 0.756018i | \(-0.727142\pi\) | ||||
−0.654551 | + | 0.756018i | \(0.727142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.41935e28 | −0.615557 | −0.307778 | − | 0.951458i | \(-0.599586\pi\) | ||||
−0.307778 | + | 0.951458i | \(0.599586\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.43961e28 | 0.705076 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.78232e28 | 0.821480 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.58822e27 | 0.0466980 | 0.0233490 | − | 0.999727i | \(-0.492567\pi\) | ||||
0.0233490 | + | 0.999727i | \(0.492567\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.83497e28 | 0.180096 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.76805e28 | 0.640641 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.89653e27 | −0.0629667 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.38359e28 | 0.298017 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.93390e28 | 0.844150 | 0.422075 | − | 0.906561i | \(-0.361302\pi\) | ||||
0.422075 | + | 0.906561i | \(0.361302\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.02129e28 | 0.739704 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.96214e28 | −0.788286 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.21696e28 | −0.474793 | −0.237396 | − | 0.971413i | \(-0.576294\pi\) | ||||
−0.237396 | + | 0.971413i | \(0.576294\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.75393e28 | 0.497884 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.92430e28 | −0.635102 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.21046e28 | −0.632849 | −0.316424 | − | 0.948618i | \(-0.602482\pi\) | ||||
−0.316424 | + | 0.948618i | \(0.602482\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.86893e28 | −0.389383 | −0.194691 | − | 0.980865i | \(-0.562371\pi\) | ||||
−0.194691 | + | 0.980865i | \(0.562371\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.18362e28 | −0.203981 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.59324e29 | 1.60477 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.82607e29 | 1.09153 | 0.545766 | − | 0.837938i | \(-0.316239\pi\) | ||||
0.545766 | + | 0.837938i | \(0.316239\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.68163e28 | 0.270343 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.08484e28 | −0.506856 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.99434e29 | 1.07514 | 0.537570 | − | 0.843219i | \(-0.319342\pi\) | ||||
0.537570 | + | 0.843219i | \(0.319342\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.61759e29 | −1.36368 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.61110e28 | 0.282523 | 0.141261 | − | 0.989972i | \(-0.454884\pi\) | ||||
0.141261 | + | 0.989972i | \(0.454884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.67515e29 | −1.30196 | −0.650978 | − | 0.759096i | \(-0.725641\pi\) | ||||
−0.650978 | + | 0.759096i | \(0.725641\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.10513e28 | 0.0990416 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.12146e28 | −0.187468 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.09746e28 | −0.0482667 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.54395e27 | 0.0235782 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.04823e28 | 0.0431144 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.36523e29 | 0.940948 | 0.470474 | − | 0.882414i | \(-0.344083\pi\) | ||||
0.470474 | + | 0.882414i | \(0.344083\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.38820e29 | −0.919033 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.90779e29 | −1.08253 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.37715e29 | 0.496041 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.14043e29 | −0.397476 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.06042e29 | −1.70678 | −0.853389 | − | 0.521274i | \(-0.825457\pi\) | ||||
−0.853389 | + | 0.521274i | \(0.825457\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.16614e29 | −0.380657 | −0.190329 | − | 0.981720i | \(-0.560955\pi\) | ||||
−0.190329 | + | 0.981720i | \(0.560955\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.70045e29 | 0.537262 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.16701e29 | −1.88616 | −0.943082 | − | 0.332561i | \(-0.892087\pi\) | ||||
−0.943082 | + | 0.332561i | \(0.892087\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.74574e28 | −0.0813000 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.55357e28 | −0.216547 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.77314e29 | −1.04741 | −0.523703 | − | 0.851901i | \(-0.675450\pi\) | ||||
−0.523703 | + | 0.851901i | \(0.675450\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.80966e29 | 1.29295 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.30742e28 | 0.242322 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.99810e29 | 0.756048 | 0.378024 | − | 0.925796i | \(-0.376604\pi\) | ||||
0.378024 | + | 0.925796i | \(0.376604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.87781e29 | −1.19154 | −0.595771 | − | 0.803154i | \(-0.703154\pi\) | ||||
−0.595771 | + | 0.803154i | \(0.703154\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.28464e29 | 0.304012 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.46938e29 | 0.336905 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.33121e29 | 0.740084 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.90903e29 | −0.410997 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.32677e28 | −0.0902771 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.88058e28 | 0.199813 | 0.0999066 | − | 0.994997i | \(-0.468146\pi\) | ||||
0.0999066 | + | 0.994997i | \(0.468146\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.56713e29 | 0.307196 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.03899e29 | −0.197438 | −0.0987189 | − | 0.995115i | \(-0.531474\pi\) | ||||
−0.0987189 | + | 0.995115i | \(0.531474\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.30469e29 | 0.240366 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.37391e29 | −0.602682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.77427e28 | 0.0307328 | 0.0153664 | − | 0.999882i | \(-0.495109\pi\) | ||||
0.0153664 | + | 0.999882i | \(0.495109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.60350e30 | 2.69351 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.01044e28 | −0.130500 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.47674e29 | −0.549377 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.85136e29 | −1.35672 | −0.678361 | − | 0.734729i | \(-0.737309\pi\) | ||||
−0.678361 | + | 0.734729i | \(0.737309\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.64197e27 | −0.00690246 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.20732e29 | 0.606966 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.93817e29 | −1.39111 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.47743e29 | 0.336504 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.01323e30 | 1.33558 | 0.667791 | − | 0.744349i | \(-0.267240\pi\) | ||||
0.667791 | + | 0.744349i | \(0.267240\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.28051e28 | 0.0291744 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.84371e29 | −0.849779 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.05536e29 | 0.488794 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.34197e27 | −0.00391036 | −0.00195518 | − | 0.999998i | \(-0.500622\pi\) | ||||
−0.00195518 | + | 0.999998i | \(0.500622\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.26834e29 | 0.598471 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.37474e29 | −0.592813 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.30891e28 | −0.0568581 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.26391e29 | −0.235455 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.99416e29 | 0.605445 | 0.302723 | − | 0.953079i | \(-0.402104\pi\) | ||||
0.302723 | + | 0.953079i | \(0.402104\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.21165e29 | −0.413173 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.60642e28 | 0.0629527 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.47986e30 | 2.29551 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.65266e30 | 1.48618 | 0.743092 | − | 0.669189i | \(-0.233358\pi\) | ||||
0.743092 | + | 0.669189i | \(0.233358\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.45607e29 | 0.548070 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.23430e29 | −0.349293 | −0.174646 | − | 0.984631i | \(-0.555878\pi\) | ||||
−0.174646 | + | 0.984631i | \(0.555878\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.03742e30 | 0.831647 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.99517e28 | 0.0389172 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.50879e30 | 1.89975 | 0.949877 | − | 0.312624i | \(-0.101208\pi\) | ||||
0.949877 | + | 0.312624i | \(0.101208\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.79486e29 | 0.205717 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.01564e30 | 0.726706 | 0.363353 | − | 0.931652i | \(-0.381632\pi\) | ||||
0.363353 | + | 0.931652i | \(0.381632\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.45477e30 | −2.40314 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.69761e29 | 0.655841 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.75759e29 | 0.312844 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.34721e30 | −1.50083 | −0.750417 | − | 0.660964i | \(-0.770148\pi\) | ||||
−0.750417 | + | 0.660964i | \(0.770148\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.28975e29 | 0.0801970 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.19938e30 | −2.53946 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.29629e29 | 0.193874 | 0.0969369 | − | 0.995291i | \(-0.469095\pi\) | ||||
0.0969369 | + | 0.995291i | \(0.469095\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.30300e28 | −0.0188960 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.22786e30 | −1.23979 | −0.619896 | − | 0.784684i | \(-0.712825\pi\) | ||||
−0.619896 | + | 0.784684i | \(0.712825\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.62773e29 | 0.304667 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.67737e29 | 0.509697 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.38421e30 | −0.709333 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.41780e30 | −1.20557 | −0.602786 | − | 0.797903i | \(-0.705943\pi\) | ||||
−0.602786 | + | 0.797903i | \(0.705943\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.90363e29 | 0.237929 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.22170e30 | 0.576871 | 0.288435 | − | 0.957499i | \(-0.406865\pi\) | ||||
0.288435 | + | 0.957499i | \(0.406865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00113e30 | −1.83872 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.90948e28 | −0.00854074 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.16214e30 | −0.941329 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.78936e29 | 0.0758338 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.70808e29 | 0.276758 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.63073e30 | 1.05668 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.41643e29 | −0.133609 | −0.0668047 | − | 0.997766i | \(-0.521280\pi\) | ||||
−0.0668047 | + | 0.997766i | \(0.521280\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.55804e30 | 0.593296 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.33710e30 | −0.495806 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.18125e30 | −0.787657 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.61907e30 | −0.921069 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.47484e30 | 1.87525 | 0.937625 | − | 0.347648i | \(-0.113020\pi\) | ||||
0.937625 | + | 0.347648i | \(0.113020\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.59835e30 | −0.866874 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.90543e29 | −0.191916 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.46035e29 | −0.0462322 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.75434e29 | −0.270002 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.27499e30 | 0.683609 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.91242e30 | 1.73103 | 0.865517 | − | 0.500880i | \(-0.166990\pi\) | ||||
0.865517 | + | 0.500880i | \(0.166990\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.38545e30 | 0.680537 | 0.340269 | − | 0.940328i | \(-0.389482\pi\) | ||||
0.340269 | + | 0.940328i | \(0.389482\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.61693e30 | −0.727514 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.16588e30 | −1.94140 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.40458e30 | 0.370864 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.34015e29 | −0.0602231 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.05222e30 | −1.26730 | −0.633650 | − | 0.773620i | \(-0.718444\pi\) | ||||
−0.633650 | + | 0.773620i | \(0.718444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.68241e29 | 0.212296 | 0.106148 | − | 0.994350i | \(-0.466148\pi\) | ||||
0.106148 | + | 0.994350i | \(0.466148\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.45886e29 | −0.0586093 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.90101e30 | 0.906503 | 0.453251 | − | 0.891383i | \(-0.350264\pi\) | ||||
0.453251 | + | 0.891383i | \(0.350264\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.27365e30 | −1.19478 | −0.597391 | − | 0.801950i | \(-0.703796\pi\) | ||||
−0.597391 | + | 0.801950i | \(0.703796\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.38581e29 | 0.0747914 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.93878e30 | 0.848377 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.30029e30 | −1.11325 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.08231e30 | −0.221685 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.94809e30 | 1.78743 | 0.893716 | − | 0.448632i | \(-0.148089\pi\) | ||||
0.893716 | + | 0.448632i | \(0.148089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.48217e30 | 1.06806 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.74694e30 | 0.521987 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.01658e30 | 1.11520 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.79354e30 | −0.324291 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.31780e30 | −0.232444 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.35869e29 | −0.0233809 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.79287e30 | 0.972588 | 0.486294 | − | 0.873795i | \(-0.338348\pi\) | ||||
0.486294 | + | 0.873795i | \(0.338348\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.10540e30 | 0.344898 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.06465e31 | −1.70181 | −0.850903 | − | 0.525323i | \(-0.823944\pi\) | ||||
−0.850903 | + | 0.525323i | \(0.823944\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.06376e31 | 1.65927 | 0.829633 | − | 0.558309i | \(-0.188549\pi\) | ||||
0.829633 | + | 0.558309i | \(0.188549\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.81037e30 | 0.275572 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.39788e30 | −1.09899 | −0.549495 | − | 0.835497i | \(-0.685180\pi\) | ||||
−0.549495 | + | 0.835497i | \(0.685180\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.52427e30 | 1.09093 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.05610e29 | −0.0573995 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.26613e29 | −0.114181 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.51821e30 | 0.339548 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.86942e30 | 0.246070 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.43427e30 | −0.312813 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.08447e31 | 1.36057 | 0.680284 | − | 0.732949i | \(-0.261857\pi\) | ||||
0.680284 | + | 0.732949i | \(0.261857\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.42649e30 | 0.297231 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.94287e30 | 0.471591 | 0.235796 | − | 0.971803i | \(-0.424230\pi\) | ||||
0.235796 | + | 0.971803i | \(0.424230\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.16137e30 | 0.135638 | 0.0678191 | − | 0.997698i | \(-0.478396\pi\) | ||||
0.0678191 | + | 0.997698i | \(0.478396\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.04274e31 | −1.18925 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.66393e29 | −0.0853599 | −0.0426799 | − | 0.999089i | \(-0.513590\pi\) | ||||
−0.0426799 | + | 0.999089i | \(0.513590\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.01108e30 | 0.218757 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.65126e28 | −0.00706623 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.65295e30 | −0.586590 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.10534e30 | 0.112035 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.66514e30 | −0.164865 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.71268e31 | −1.65653 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.94380e30 | −0.939598 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.17606e30 | −0.108570 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.12272e30 | −0.191462 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.52281e31 | 1.34205 | 0.671027 | − | 0.741432i | \(-0.265853\pi\) | ||||
0.671027 | + | 0.741432i | \(0.265853\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.81073e30 | 0.500392 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.10597e31 | 1.77218 | 0.886092 | − | 0.463510i | \(-0.153410\pi\) | ||||
0.886092 | + | 0.463510i | \(0.153410\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.52157e30 | −0.125127 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.64316e31 | −1.32056 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.32645e30 | −0.261278 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.82307e29 | 0.0754109 | 0.0377055 | − | 0.999289i | \(-0.487995\pi\) | ||||
0.0377055 | + | 0.999289i | \(0.487995\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.53693e30 | −0.340437 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.02070e30 | 0.661641 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.01146e30 | −0.0725201 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.03467e30 | −0.422976 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.88415e31 | −1.29107 | −0.645535 | − | 0.763731i | \(-0.723365\pi\) | ||||
−0.645535 | + | 0.763731i | \(0.723365\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.56919e30 | 0.574074 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.17416e30 | −0.273408 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.51840e30 | −0.0972442 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.47039e31 | −1.54703 | −0.773516 | − | 0.633777i | \(-0.781504\pi\) | ||||
−0.773516 | + | 0.633777i | \(0.781504\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.66533e30 | −0.101979 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.65576e31 | −0.991530 | −0.495765 | − | 0.868457i | \(-0.665112\pi\) | ||||
−0.495765 | + | 0.868457i | \(0.665112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.28817e31 | 0.754398 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.76286e30 | −0.100968 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.58984e30 | 0.481183 | 0.240592 | − | 0.970626i | \(-0.422659\pi\) | ||||
0.240592 | + | 0.970626i | \(0.422659\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.36206e30 | −0.403370 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.37488e31 | −0.736832 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.50226e30 | −0.183600 | −0.0918000 | − | 0.995777i | \(-0.529262\pi\) | ||||
−0.0918000 | + | 0.995777i | \(0.529262\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.83711e31 | −1.96774 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.05251e30 | −0.0528021 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.10901e31 | −0.544303 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.80771e30 | 0.326893 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.81691e30 | 0.320267 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.09339e31 | −0.502618 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.62968e31 | 1.18284 | 0.591419 | − | 0.806364i | \(-0.298568\pi\) | ||||
0.591419 | + | 0.806364i | \(0.298568\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.99357e30 | 0.351837 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.10311e30 | −0.305947 | −0.152974 | − | 0.988230i | \(-0.548885\pi\) | ||||
−0.152974 | + | 0.988230i | \(0.548885\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.90986e30 | −0.122656 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.23958e31 | −0.511360 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.54851e30 | 0.183644 | 0.0918218 | − | 0.995775i | \(-0.470731\pi\) | ||||
0.0918218 | + | 0.995775i | \(0.470731\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.26574e29 | 0.0366152 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.06369e30 | 0.311896 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.59763e30 | 0.325512 | 0.162756 | − | 0.986666i | \(-0.447962\pi\) | ||||
0.162756 | + | 0.986666i | \(0.447962\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.93604e31 | 2.19997 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.73324e30 | 0.171723 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.36826e30 | −0.297217 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.32226e31 | 1.15521 | 0.577604 | − | 0.816317i | \(-0.303988\pi\) | ||||
0.577604 | + | 0.816317i | \(0.303988\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.16588e31 | 1.07777 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.31764e31 | 1.77246 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.79911e30 | −0.287170 | −0.143585 | − | 0.989638i | \(-0.545863\pi\) | ||||
−0.143585 | + | 0.989638i | \(0.545863\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.73601e29 | −0.00874338 |
(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 | 24.22.a.d.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 72.22.a.c.1.3 | 3 | |||
4.3 | odd | 2 | 48.22.a.j.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.22.a.d.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
48.22.a.j.1.1 | 3 | 4.3 | odd | 2 | |||
72.22.a.c.1.3 | 3 | 3.2 | odd | 2 |