Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,24,Mod(1,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.1");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.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: | \(214.530583901\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 389656213x^{4} + 47522643058672215x^{2} - 1756479932541937262634975 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{71}\cdot 3^{6}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 32) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-11884.9\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 64.1 |
$q$-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 | ||||||||
\(3\) | −216966. | −0.707126 | −0.353563 | − | 0.935411i | \(-0.615030\pi\) | ||||
−0.353563 | + | 0.935411i | \(0.615030\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.90927e8 | −1.74869 | −0.874343 | − | 0.485308i | \(-0.838707\pi\) | ||||
−0.874343 | + | 0.485308i | \(0.838707\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.74240e9 | 1.86225 | 0.931126 | − | 0.364698i | \(-0.118828\pi\) | ||||
0.931126 | + | 0.364698i | \(0.118828\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.70690e10 | −0.499973 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.58624e11 | −1.01305 | −0.506527 | − | 0.862224i | \(-0.669071\pi\) | ||||
−0.506527 | + | 0.862224i | \(0.669071\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.14517e12 | 0.331981 | 0.165991 | − | 0.986127i | \(-0.446918\pi\) | ||||
0.165991 | + | 0.986127i | \(0.446918\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.14246e13 | 1.23654 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.65620e13 | 0.187974 | 0.0939872 | − | 0.995573i | \(-0.470039\pi\) | ||||
0.0939872 | + | 0.995573i | \(0.470039\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.63669e14 | −1.50397 | −0.751985 | − | 0.659181i | \(-0.770903\pi\) | ||||
−0.751985 | + | 0.659181i | \(0.770903\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.11377e15 | −1.31685 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.75905e15 | 0.822636 | 0.411318 | − | 0.911492i | \(-0.365069\pi\) | ||||
0.411318 | + | 0.911492i | \(0.365069\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.45321e16 | 2.05790 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.06382e16 | 1.06067 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.01247e16 | −0.762912 | −0.381456 | − | 0.924387i | \(-0.624577\pi\) | ||||
−0.381456 | + | 0.924387i | \(0.624577\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.90008e17 | −1.34311 | −0.671556 | − | 0.740954i | \(-0.734374\pi\) | ||||
−0.671556 | + | 0.740954i | \(0.734374\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.07989e17 | 0.716357 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.86008e18 | −3.25649 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.56774e18 | 1.44862 | 0.724311 | − | 0.689474i | \(-0.242158\pi\) | ||||
0.724311 | + | 0.689474i | \(0.242158\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.65429e17 | −0.234753 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.05851e18 | −0.867951 | −0.433975 | − | 0.900925i | \(-0.642890\pi\) | ||||
−0.433975 | + | 0.900925i | \(0.642890\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.07525e18 | −0.504653 | −0.252327 | − | 0.967642i | \(-0.581196\pi\) | ||||
−0.252327 | + | 0.967642i | \(0.581196\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.98674e18 | 0.874295 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.72401e18 | 0.160725 | 0.0803626 | − | 0.996766i | \(-0.474392\pi\) | ||||
0.0803626 | + | 0.996766i | \(0.474392\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.75455e19 | 2.46798 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.76305e18 | −0.132922 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.52631e19 | 0.374381 | 0.187191 | − | 0.982324i | \(-0.440062\pi\) | ||||
0.187191 | + | 0.982324i | \(0.440062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.83027e20 | 1.77151 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.65690e20 | 1.06350 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.29901e20 | 0.992527 | 0.496263 | − | 0.868172i | \(-0.334705\pi\) | ||||
0.496263 | + | 0.868172i | \(0.334705\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.13479e20 | 1.80512 | 0.902561 | − | 0.430562i | \(-0.141685\pi\) | ||||
0.902561 | + | 0.430562i | \(0.141685\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.58565e20 | −0.931075 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.09571e20 | −0.580531 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.20452e21 | 1.20491 | 0.602456 | − | 0.798152i | \(-0.294189\pi\) | ||||
0.602456 | + | 0.798152i | \(0.294189\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.15585e20 | −0.581707 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.43377e20 | −0.124971 | −0.0624854 | − | 0.998046i | \(-0.519903\pi\) | ||||
−0.0624854 | + | 0.998046i | \(0.519903\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.45063e20 | −0.128732 | −0.0643659 | − | 0.997926i | \(-0.520502\pi\) | ||||
−0.0643659 | + | 0.997926i | \(0.520502\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.32263e21 | −1.45520 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.33929e21 | −1.88656 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.08236e21 | 0.463630 | 0.231815 | − | 0.972760i | \(-0.425534\pi\) | ||||
0.231815 | + | 0.972760i | \(0.425534\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.21622e21 | −0.250055 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.36342e22 | 1.16207 | 0.581036 | − | 0.813878i | \(-0.302648\pi\) | ||||
0.581036 | + | 0.813878i | \(0.302648\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.07140e21 | −0.328708 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.08753e22 | 0.539475 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.67114e22 | −0.638303 | −0.319152 | − | 0.947704i | \(-0.603398\pi\) | ||||
−0.319152 | + | 0.947704i | \(0.603398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.08991e22 | 0.618232 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.12252e22 | 0.949749 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.45805e23 | 2.62997 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.71584e22 | 1.09524 | 0.547619 | − | 0.836728i | \(-0.315534\pi\) | ||||
0.547619 | + | 0.836728i | \(0.315534\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.51215e22 | 0.506499 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.31460e23 | −1.17246 | −0.586231 | − | 0.810144i | \(-0.699389\pi\) | ||||
−0.586231 | + | 0.810144i | \(0.699389\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.43701e23 | −1.73472 | −0.867361 | − | 0.497680i | \(-0.834185\pi\) | ||||
−0.867361 | + | 0.497680i | \(0.834185\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.03575e23 | 2.30275 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.04639e23 | 0.480598 | 0.240299 | − | 0.970699i | \(-0.422754\pi\) | ||||
0.240299 | + | 0.970699i | \(0.422754\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.91477e22 | −0.219550 | −0.109775 | − | 0.993956i | \(-0.535013\pi\) | ||||
−0.109775 | + | 0.993956i | \(0.535013\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.40147e23 | −1.02436 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.55264e23 | 0.380774 | 0.190387 | − | 0.981709i | \(-0.439026\pi\) | ||||
0.190387 | + | 0.981709i | \(0.439026\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.17703e23 | −1.43853 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00971e23 | −0.165981 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.58778e23 | 0.350056 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.35294e22 | 0.0262772 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.63591e23 | 0.613751 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.40781e24 | −1.84994 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.80213e24 | 1.79368 | 0.896841 | − | 0.442353i | \(-0.145856\pi\) | ||||
0.896841 | + | 0.442353i | \(0.145856\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.67224e23 | 0.356854 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.42927e23 | −0.198478 | −0.0992390 | − | 0.995064i | \(-0.531641\pi\) | ||||
−0.0992390 | + | 0.995064i | \(0.531641\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.43997e24 | −2.80077 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.84966e24 | −1.85478 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.28208e24 | 1.41423 | 0.707113 | − | 0.707101i | \(-0.249997\pi\) | ||||
0.707113 | + | 0.707101i | \(0.249997\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.03441e24 | −0.234435 | −0.117218 | − | 0.993106i | \(-0.537397\pi\) | ||||
−0.117218 | + | 0.993106i | \(0.537397\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.91018e23 | −0.113653 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.05641e24 | −0.336315 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.57014e24 | 1.33409 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.46551e25 | −1.74517 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.38525e23 | 0.0956762 | 0.0478381 | − | 0.998855i | \(-0.484767\pi\) | ||||
0.0478381 | + | 0.998855i | \(0.484767\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.67720e23 | 0.0583928 | 0.0291964 | − | 0.999574i | \(-0.490705\pi\) | ||||
0.0291964 | + | 0.999574i | \(0.490705\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.25025e24 | −0.0939820 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.62776e25 | 2.34868 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.43848e25 | 0.803635 | 0.401818 | − | 0.915720i | \(-0.368379\pi\) | ||||
0.401818 | + | 0.915720i | \(0.368379\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.48123e24 | −0.264735 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.66221e25 | 1.53195 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.39784e25 | −0.870289 | −0.435145 | − | 0.900361i | \(-0.643303\pi\) | ||||
−0.435145 | + | 0.900361i | \(0.643303\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.97106e25 | −1.25268 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.51560e25 | −0.416242 | −0.208121 | − | 0.978103i | \(-0.566735\pi\) | ||||
−0.208121 | + | 0.978103i | \(0.566735\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.71521e25 | −0.889788 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.59452e25 | 0.751943 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.92919e25 | −1.08509 | −0.542545 | − | 0.840027i | \(-0.682539\pi\) | ||||
−0.542545 | + | 0.840027i | \(0.682539\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.39002e26 | 3.83233 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.98806e25 | −0.701842 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.32487e24 | 0.0782063 | 0.0391031 | − | 0.999235i | \(-0.487550\pi\) | ||||
0.0391031 | + | 0.999235i | \(0.487550\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.91917e25 | 0.317655 | 0.158828 | − | 0.987306i | \(-0.449229\pi\) | ||||
0.158828 | + | 0.987306i | \(0.449229\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.33104e26 | −1.27645 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.99324e26 | −2.53318 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.54630e25 | −0.190428 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.98490e26 | 1.97523 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.38328e26 | −1.98360 | −0.991800 | − | 0.127796i | \(-0.959210\pi\) | ||||
−0.991800 | + | 0.127796i | \(0.959210\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.27890e26 | −0.665163 | −0.332581 | − | 0.943075i | \(-0.607920\pi\) | ||||
−0.332581 | + | 0.943075i | \(0.607920\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.88629e25 | 0.410509 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.48404e26 | −1.43127 | −0.715635 | − | 0.698474i | \(-0.753863\pi\) | ||||
−0.715635 | + | 0.698474i | \(0.753863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.41137e26 | 0.516214 | 0.258107 | − | 0.966116i | \(-0.416901\pi\) | ||||
0.258107 | + | 0.966116i | \(0.416901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.61341e26 | −0.852025 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.88334e26 | −1.42073 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.83951e26 | 1.51777 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.76935e26 | −0.411295 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.32072e26 | 1.52360 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.52456e26 | 0.843972 | 0.421986 | − | 0.906602i | \(-0.361333\pi\) | ||||
0.421986 | + | 0.906602i | \(0.361333\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.28045e25 | 0.0883701 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.87148e26 | 0.882480 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.85113e27 | −2.50121 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.48669e25 | 0.0910296 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.69801e25 | 0.0624040 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.10896e26 | −0.899421 | −0.449711 | − | 0.893174i | \(-0.648473\pi\) | ||||
−0.449711 | + | 0.893174i | \(0.648473\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.15470e27 | −1.02890 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.31344e26 | −0.347158 | −0.173579 | − | 0.984820i | \(-0.555533\pi\) | ||||
−0.173579 | + | 0.984820i | \(0.555533\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.66792e27 | −1.21357 | −0.606787 | − | 0.794864i | \(-0.707542\pi\) | ||||
−0.606787 | + | 0.794864i | \(0.707542\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.02631e27 | 1.33404 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.01267e26 | −0.298866 | −0.149433 | − | 0.988772i | \(-0.547745\pi\) | ||||
−0.149433 | + | 0.988772i | \(0.547745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.20088e26 | −0.281058 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.68766e26 | −0.327845 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.25295e27 | −1.00271 | −0.501355 | − | 0.865241i | \(-0.667165\pi\) | ||||
−0.501355 | + | 0.865241i | \(0.667165\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.48722e26 | −0.262339 | −0.131169 | − | 0.991360i | \(-0.541873\pi\) | ||||
−0.131169 | + | 0.991360i | \(0.541873\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.40354e27 | −0.883850 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.28963e28 | −4.31572 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.63820e27 | −0.499290 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.95817e27 | −0.821732 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.85626e26 | 0.199053 | 0.0995264 | − | 0.995035i | \(-0.468267\pi\) | ||||
0.0995264 | + | 0.995035i | \(0.468267\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.60351e27 | −0.833374 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.10032e27 | 0.232438 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.31330e27 | 1.21906 | 0.609531 | − | 0.792762i | \(-0.291358\pi\) | ||||
0.609531 | + | 0.792762i | \(0.291358\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.52736e28 | 2.69770 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.35932e27 | 0.381435 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.63348e27 | 0.389977 | 0.194989 | − | 0.980806i | \(-0.437533\pi\) | ||||
0.194989 | + | 0.980806i | \(0.437533\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.82340e27 | −0.654675 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.62580e27 | 0.451361 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.67658e27 | −0.991282 | −0.495641 | − | 0.868527i | \(-0.665067\pi\) | ||||
−0.495641 | + | 0.868527i | \(0.665067\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.35097e28 | 1.41742 | 0.708711 | − | 0.705499i | \(-0.249277\pi\) | ||||
0.708711 | + | 0.705499i | \(0.249277\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.53439e27 | −0.437168 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.35171e28 | −2.08477 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.14474e27 | 0.174927 | 0.0874635 | − | 0.996168i | \(-0.472124\pi\) | ||||
0.0874635 | + | 0.996168i | \(0.472124\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.94348e27 | 0.671519 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.26495e28 | 0.874883 | 0.437441 | − | 0.899247i | \(-0.355885\pi\) | ||||
0.437441 | + | 0.899247i | \(0.355885\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.33583e27 | 0.212647 | 0.106324 | − | 0.994332i | \(-0.466092\pi\) | ||||
0.106324 | + | 0.994332i | \(0.466092\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.16347e28 | −1.85972 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.97972e28 | −1.61634 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.92620e28 | −0.964666 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.67407e28 | −0.774472 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.39590e28 | −1.02445 | −0.512225 | − | 0.858851i | \(-0.671179\pi\) | ||||
−0.512225 | + | 0.858851i | \(0.671179\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.38942e28 | −1.73562 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.93705e28 | −1.07452 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.06380e27 | 0.273100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.99603e28 | −0.939792 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.85224e28 | 0.829078 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.17130e29 | −3.15659 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.06329e28 | −1.01575 | −0.507874 | − | 0.861431i | \(-0.669569\pi\) | ||||
−0.507874 | + | 0.861431i | \(0.669569\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.28749e28 | 1.22667 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.40957e27 | −0.0519033 | −0.0259517 | − | 0.999663i | \(-0.508262\pi\) | ||||
−0.0259517 | + | 0.999663i | \(0.508262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.08964e28 | −0.618226 | −0.309113 | − | 0.951025i | \(-0.600032\pi\) | ||||
−0.309113 | + | 0.951025i | \(0.600032\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.75523e28 | 1.62816 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.47714e28 | 0.774140 | 0.387070 | − | 0.922050i | \(-0.373487\pi\) | ||||
0.387070 | + | 0.922050i | \(0.373487\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.80507e28 | 0.772871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.27032e28 | −0.339843 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.02846e28 | −0.282708 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.26256e28 | 0.683185 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.28330e28 | 0.155249 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.65384e28 | 0.299311 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.57485e28 | 0.586423 | 0.293212 | − | 0.956048i | \(-0.405276\pi\) | ||||
0.293212 | + | 0.956048i | \(0.405276\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.37921e28 | −0.724271 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.29976e29 | −2.10701 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.21767e28 | 0.531966 | 0.265983 | − | 0.963978i | \(-0.414303\pi\) | ||||
0.265983 | + | 0.963978i | \(0.414303\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.36869e28 | −0.269255 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.82146e29 | 1.36064 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.91418e29 | 2.73375 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.55717e29 | 1.01722 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.40504e29 | −0.858817 | −0.429409 | − | 0.903110i | \(-0.641278\pi\) | ||||
−0.429409 | + | 0.903110i | \(0.641278\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.62640e28 | 0.550772 | 0.275386 | − | 0.961334i | \(-0.411194\pi\) | ||||
0.275386 | + | 0.961334i | \(0.411194\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.57242e28 | 0.352122 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.84480e29 | −1.42772 | −0.713860 | − | 0.700288i | \(-0.753055\pi\) | ||||
−0.713860 | + | 0.700288i | \(0.753055\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.64672e28 | 0.218535 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.61459e28 | −0.247533 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.00468e29 | −0.415376 | −0.207688 | − | 0.978195i | \(-0.566594\pi\) | ||||
−0.207688 | + | 0.978195i | \(0.566594\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.25361e29 | 1.26192 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.10508e27 | −0.0185813 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.58818e28 | 0.225112 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.45272e29 | −1.74966 | −0.874829 | − | 0.484431i | \(-0.839027\pi\) | ||||
−0.874829 | + | 0.484431i | \(0.839027\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.43961e29 | 0.433952 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.46123e29 | 0.697192 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.93840e29 | −0.516170 | −0.258085 | − | 0.966122i | \(-0.583091\pi\) | ||||
−0.258085 | + | 0.966122i | \(0.583091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.22413e29 | 1.30814 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.07526e29 | −0.253272 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.74346e29 | 0.608063 | 0.304031 | − | 0.952662i | \(-0.401667\pi\) | ||||
0.304031 | + | 0.952662i | \(0.401667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.07967e29 | −1.26836 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.18842e29 | −0.822744 | −0.411372 | − | 0.911468i | \(-0.634950\pi\) | ||||
−0.411372 | + | 0.911468i | \(0.634950\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.78312e30 | 3.29900 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.44749e29 | 0.252313 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.88162e29 | −0.801944 | −0.400972 | − | 0.916090i | \(-0.631328\pi\) | ||||
−0.400972 | + | 0.916090i | \(0.631328\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.98479e28 | 0.154634 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.61000e28 | 0.140349 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.88505e29 | −0.810743 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.29652e30 | 1.68535 | 0.842673 | − | 0.538425i | \(-0.180981\pi\) | ||||
0.842673 | + | 0.538425i | \(0.180981\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.61422e30 | 1.98050 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.12391e30 | 1.30188 | 0.650939 | − | 0.759130i | \(-0.274375\pi\) | ||||
0.650939 | + | 0.759130i | \(0.274375\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.07599e29 | −0.445888 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.23136e29 | 0.437267 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.50288e30 | −1.46753 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.82215e29 | 0.260472 | 0.130236 | − | 0.991483i | \(-0.458426\pi\) | ||||
0.130236 | + | 0.991483i | \(0.458426\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.14603e30 | −1.00004 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.23978e30 | 1.84833 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.60314e30 | −2.03210 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.24432e29 | 0.165775 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.72724e30 | −1.90661 | −0.953305 | − | 0.302009i | \(-0.902343\pi\) | ||||
−0.953305 | + | 0.302009i | \(0.902343\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.64535e30 | 1.08897 | 0.544484 | − | 0.838771i | \(-0.316726\pi\) | ||||
0.544484 | + | 0.838771i | \(0.316726\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.28217e29 | −0.0803582 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.51623e29 | 0.386833 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.97675e30 | 3.36159 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.46171e29 | 0.237817 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.50630e30 | 1.26632 | 0.633162 | − | 0.774020i | \(-0.281757\pi\) | ||||
0.633162 | + | 0.774020i | \(0.281757\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.04414e30 | 0.979262 | 0.489631 | − | 0.871930i | \(-0.337131\pi\) | ||||
0.489631 | + | 0.871930i | \(0.337131\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.07639e30 | −0.943373 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.87067e30 | −1.23722 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.46273e30 | 1.82498 | 0.912492 | − | 0.409095i | \(-0.134156\pi\) | ||||
0.912492 | + | 0.409095i | \(0.134156\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.17930e30 | −1.23392 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.66470e30 | 0.613330 | 0.306665 | − | 0.951817i | \(-0.400787\pi\) | ||||
0.306665 | + | 0.951817i | \(0.400787\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.19065e30 | 1.11619 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.03628e29 | −0.0676551 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.50605e30 | −1.10659 | −0.553293 | − | 0.832986i | \(-0.686629\pi\) | ||||
−0.553293 | + | 0.832986i | \(0.686629\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.93196e30 | 0.879281 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.44872e29 | −0.0412911 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.99020e30 | −1.08109 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.37923e30 | −1.38575 | −0.692873 | − | 0.721059i | \(-0.743655\pi\) | ||||
−0.692873 | + | 0.721059i | \(0.743655\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.13813e29 | 0.199379 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.22741e30 | −0.519086 | −0.259543 | − | 0.965731i | \(-0.583572\pi\) | ||||
−0.259543 | + | 0.965731i | \(0.583572\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.60053e29 | 0.0576608 | 0.0288304 | − | 0.999584i | \(-0.490822\pi\) | ||||
0.0288304 | + | 0.999584i | \(0.490822\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.87100e30 | −1.66081 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.02144e30 | 1.61105 | 0.805524 | − | 0.592563i | \(-0.201884\pi\) | ||||
0.805524 | + | 0.592563i | \(0.201884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.17350e31 | 2.24385 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.12102e30 | −0.568272 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.94801e30 | 0.511241 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.87344e31 | −3.09502 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.18911e30 | −0.187180 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.99745e30 | 1.49979 | 0.749896 | − | 0.661556i | \(-0.230104\pi\) | ||||
0.749896 | + | 0.661556i | \(0.230104\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.36308e30 | 0.480915 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.94575e30 | −1.08329 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.47316e31 | −1.91523 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.15003e30 | −0.638597 | −0.319298 | − | 0.947654i | \(-0.603447\pi\) | ||||
−0.319298 | + | 0.947654i | \(0.603447\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.20250e30 | 0.615404 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.37446e30 | 0.719460 | 0.359730 | − | 0.933056i | \(-0.382869\pi\) | ||||
0.359730 | + | 0.933056i | \(0.382869\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.33141e30 | −0.143408 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.61490e30 | −0.885708 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.37108e30 | −0.232727 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.09248e30 | −0.852170 | −0.426085 | − | 0.904683i | \(-0.640108\pi\) | ||||
−0.426085 | + | 0.904683i | \(0.640108\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.28834e30 | 0.294335 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.41376e30 | 0.206377 | 0.103189 | − | 0.994662i | \(-0.467095\pi\) | ||||
0.103189 | + | 0.994662i | \(0.467095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.50993e31 | 2.05027 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.06075e30 | 0.629193 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.40043e31 | −1.79075 | −0.895376 | − | 0.445312i | \(-0.853093\pi\) | ||||
−0.895376 | + | 0.445312i | \(0.853093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.36174e30 | −0.239731 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.33975e31 | −1.59522 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.65291e31 | 3.03348 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.61131e30 | −0.162823 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.28643e31 | 0.767295 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.16451e31 | −1.80581 | −0.902907 | − | 0.429835i | \(-0.858572\pi\) | ||||
−0.902907 | + | 0.429835i | \(0.858572\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.09227e31 | −1.14248 | −0.571239 | − | 0.820784i | \(-0.693537\pi\) | ||||
−0.571239 | + | 0.820784i | \(0.693537\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.18552e31 | −2.70994 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.04699e30 | −0.252471 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.75004e30 | −0.323270 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.08212e31 | −0.496236 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.56102e30 | −0.288143 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.99785e31 | −0.840415 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.37228e30 | −0.0553017 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.47508e31 | −2.50020 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.40632e31 | −0.520375 | −0.260187 | − | 0.965558i | \(-0.583784\pi\) | ||||
−0.260187 | + | 0.965558i | \(0.583784\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.33360e30 | −0.224622 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.12929e31 | 0.383924 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.95880e31 | 0.964410 | 0.482205 | − | 0.876058i | \(-0.339836\pi\) | ||||
0.482205 | + | 0.876058i | \(0.339836\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.88758e31 | −0.902511 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.82787e31 | 1.14740 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.00295e31 | 0.863395 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.49431e31 | 1.79128 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.87490e30 | 0.208406 | 0.104203 | − | 0.994556i | \(-0.466771\pi\) | ||||
0.104203 | + | 0.994556i | \(0.466771\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.59694e30 | −0.167535 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.52460e30 | 0.134657 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.45515e31 | −1.04235 | −0.521177 | − | 0.853448i | \(-0.674507\pi\) | ||||
−0.521177 | + | 0.853448i | \(0.674507\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.96440e31 | −0.665854 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.15913e31 | −0.465665 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.59955e31 | −1.15974 | −0.579872 | − | 0.814708i | \(-0.696897\pi\) | ||||
−0.579872 | + | 0.814708i | \(0.696897\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.51176e29 | 0.0189211 | 0.00946053 | − | 0.999955i | \(-0.496989\pi\) | ||||
0.00946053 | + | 0.999955i | \(0.496989\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.34056e31 | 1.40266 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.22174e31 | 1.69290 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.28399e31 | −0.226485 | −0.113243 | − | 0.993567i | \(-0.536124\pi\) | ||||
−0.113243 | + | 0.993567i | \(0.536124\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.77478e31 | 0.470354 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.32830e32 | 2.16407 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.42178e31 | −0.379268 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.92781e31 | 0.290250 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.40632e31 | 1.07217 | 0.536086 | − | 0.844163i | \(-0.319902\pi\) | ||||
0.536086 | + | 0.844163i | \(0.319902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.45103e32 | 2.02000 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.55918e31 | 1.01209 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.21493e31 | −1.05797 | −0.528987 | − | 0.848630i | \(-0.677428\pi\) | ||||
−0.528987 | + | 0.848630i | \(0.677428\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.94076e31 | −0.612137 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.06218e31 | −0.365028 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.31000e32 | −1.50267 | −0.751333 | − | 0.659924i | \(-0.770589\pi\) | ||||
−0.751333 | + | 0.659924i | \(0.770589\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.05699e31 | 0.116685 | 0.0583424 | − | 0.998297i | \(-0.481418\pi\) | ||||
0.0583424 | + | 0.998297i | \(0.481418\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.66958e31 | −0.602423 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.49239e30 | −0.0459506 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.29237e31 | 0.127267 | 0.0636337 | − | 0.997973i | \(-0.479731\pi\) | ||||
0.0636337 | + | 0.997973i | \(0.479731\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.05952e32 | 1.00464 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.84348e30 | 0.0533578 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.92595e31 | −0.784981 | −0.392490 | − | 0.919756i | \(-0.628386\pi\) | ||||
−0.392490 | + | 0.919756i | \(0.628386\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.26697e32 | −1.07326 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.18347e32 | −0.965777 | −0.482889 | − | 0.875682i | \(-0.660412\pi\) | ||||
−0.482889 | + | 0.875682i | \(0.660412\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.35060e32 | 1.84815 | 0.924073 | − | 0.382217i | \(-0.124839\pi\) | ||||
0.924073 | + | 0.382217i | \(0.124839\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.15170e32 | 0.872545 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.62809e32 | −1.18868 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.67271e32 | 1.17706 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.58835e32 | −1.07738 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.16424e31 | 0.272304 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.77460e32 | 1.11883 | 0.559415 | − | 0.828888i | \(-0.311026\pi\) | ||||
0.559415 | + | 0.828888i | \(0.311026\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.81674e31 | −0.596795 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.35002e32 | −3.13659 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.44897e32 | 0.819323 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.14555e31 | 0.0624820 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.82879e32 | 0.962270 | 0.481135 | − | 0.876646i | \(-0.340225\pi\) | ||||
0.481135 | + | 0.876646i | \(0.340225\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.51276e32 | −0.767971 | −0.383986 | − | 0.923339i | \(-0.625449\pi\) | ||||
−0.383986 | + | 0.923339i | \(0.625449\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.27391e32 | −0.624025 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.45858e32 | 0.689495 | 0.344747 | − | 0.938695i | \(-0.387965\pi\) | ||||
0.344747 | + | 0.938695i | \(0.387965\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.20388e32 | −1.00548 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.01632e32 | 1.76867 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.02823e32 | 0.862216 | 0.431108 | − | 0.902300i | \(-0.358123\pi\) | ||||
0.431108 | + | 0.902300i | \(0.358123\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.45666e31 | 0.347076 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.62418e31 | 0.0643624 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.26709e32 | 1.25020 | 0.625099 | − | 0.780545i | \(-0.285058\pi\) | ||||
0.625099 | + | 0.780545i | \(0.285058\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.26703e31 | 0.194648 | 0.0973238 | − | 0.995253i | \(-0.468972\pi\) | ||||
0.0973238 | + | 0.995253i | \(0.468972\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.23627e31 | −0.0441275 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.42049e33 | 4.89767 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.88421e32 | −0.627599 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.97633e32 | 0.636004 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.88095e32 | −1.82868 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.50043e32 | 0.751349 | 0.375675 | − | 0.926752i | \(-0.377411\pi\) | ||||
0.375675 | + | 0.926752i | \(0.377411\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.51620e32 | 2.18276 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.88330e31 | 0.0528627 | 0.0264313 | − | 0.999651i | \(-0.491586\pi\) | ||||
0.0264313 | + | 0.999651i | \(0.491586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.51708e32 | 2.03961 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.35870e31 | 0.245484 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.97248e32 | 0.500236 | 0.250118 | − | 0.968215i | \(-0.419531\pi\) | ||||
0.250118 | + | 0.968215i | \(0.419531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.00849e33 | −2.47304 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.61881e32 | 0.858150 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.41937e31 | 0.124288 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.10523e32 | −1.13245 | −0.566223 | − | 0.824252i | \(-0.691596\pi\) | ||||
−0.566223 | + | 0.824252i | \(0.691596\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.39591e32 | 0.943228 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.97497e32 | 0.409954 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.12402e31 | −0.163153 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.08758e32 | 0.211336 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.10061e32 | −0.959103 | −0.479551 | − | 0.877514i | \(-0.659201\pi\) | ||||
−0.479551 | + | 0.877514i | \(0.659201\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.19724e33 | −2.17868 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.12841e32 | 0.198743 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.28074e33 | −2.18342 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.56920e32 | 0.424000 | 0.212000 | − | 0.977270i | \(-0.432002\pi\) | ||||
0.212000 | + | 0.977270i | \(0.432002\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.45083e32 | −0.231802 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.14248e32 | −1.10489 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.92624e32 | 0.588109 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.88813e32 | 0.709043 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.23870e32 | −0.876419 | −0.438209 | − | 0.898873i | \(-0.644387\pi\) | ||||
−0.438209 | + | 0.898873i | \(0.644387\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.37423e33 | −3.23049 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.40750e32 | 0.185507 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.22966e33 | −1.57000 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.55385e32 | 0.192205 | 0.0961024 | − | 0.995371i | \(-0.469362\pi\) | ||||
0.0961024 | + | 0.995371i | \(0.469362\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.30127e32 | 0.875048 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.16849e31 | −0.0948619 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.32529e32 | −0.711844 | −0.355922 | − | 0.934516i | \(-0.615833\pi\) | ||||
−0.355922 | + | 0.934516i | \(0.615833\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.79805e33 | 3.05176 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.15469e33 | −1.22064 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.11960e33 | 1.14723 | 0.573615 | − | 0.819125i | \(-0.305541\pi\) | ||||
0.573615 | + | 0.819125i | \(0.305541\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.55434e32 | 0.353061 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.97216e32 | −0.960325 | −0.480162 | − | 0.877180i | \(-0.659422\pi\) | ||||
−0.480162 | + | 0.877180i | \(0.659422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.79190e32 | −0.167308 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.41750e32 | −0.581004 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.01944e33 | 0.894994 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.68302e32 | −0.398719 | −0.199359 | − | 0.979926i | \(-0.563886\pi\) | ||||
−0.199359 | + | 0.979926i | \(0.563886\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.70454e32 | −0.140755 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.27486e32 | −0.102111 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.06644e33 | −0.828576 | −0.414288 | − | 0.910146i | \(-0.635969\pi\) | ||||
−0.414288 | + | 0.910146i | \(0.635969\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.81839e32 | 0.589301 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.10705e33 | 0.809550 | 0.404775 | − | 0.914416i | \(-0.367350\pi\) | ||||
0.404775 | + | 0.914416i | \(0.367350\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.76240e32 | −0.408857 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.38706e32 | 0.164345 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.93177e32 | 0.329500 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.85970e32 | −0.639309 | −0.319655 | − | 0.947534i | \(-0.603567\pi\) | ||||
−0.319655 | + | 0.947534i | \(0.603567\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.36977e33 | −0.862030 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.87456e33 | 1.75593 | 0.877965 | − | 0.478725i | \(-0.158901\pi\) | ||||
0.877965 | + | 0.478725i | \(0.158901\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.66129e33 | −2.76399 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.31384e33 | −1.90761 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.33569e33 | 1.30537 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.33307e32 | 0.126602 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.53573e33 | −0.809198 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.74645e33 | −1.40531 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.82813e32 | −0.388999 | −0.194500 | − | 0.980903i | \(-0.562308\pi\) | ||||
−0.194500 | + | 0.980903i | \(0.562308\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.71375e32 | −0.275763 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.51264e33 | 0.709097 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.31602e33 | 0.599266 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.04651e33 | 0.462938 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.46880e33 | 0.631235 | 0.315617 | − | 0.948887i | \(-0.397788\pi\) | ||||
0.315617 | + | 0.948887i | \(0.397788\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.23554e31 | 0.0302122 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.86588e32 | 0.319134 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.30786e32 | 0.130412 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.99214e33 | −2.67891 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.88252e33 | 0.700962 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.87756e33 | −1.40330 | −0.701650 | − | 0.712522i | \(-0.747553\pi\) | ||||
−0.701650 | + | 0.712522i | \(0.747553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.25547e33 | −1.14518 | −0.572591 | − | 0.819841i | \(-0.694062\pi\) | ||||
−0.572591 | + | 0.819841i | \(0.694062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.93115e33 | −1.00230 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.57813e33 | 1.52186 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.34847e33 | 0.758983 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.83700e32 | −0.309099 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.90085e33 | −1.19183 | −0.595914 | − | 0.803049i | \(-0.703210\pi\) | ||||
−0.595914 | + | 0.803049i | \(0.703210\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.74515e33 | 0.518482 | 0.259241 | − | 0.965813i | \(-0.416528\pi\) | ||||
0.259241 | + | 0.965813i | \(0.416528\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.10240e33 | 1.47419 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.60301e33 | 1.29339 | 0.646694 | − | 0.762749i | \(-0.276151\pi\) | ||||
0.646694 | + | 0.762749i | \(0.276151\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.40688e31 | −0.0202422 | −0.0101211 | − | 0.999949i | \(-0.503222\pi\) | ||||
−0.0101211 | + | 0.999949i | \(0.503222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.65335e32 | −0.123695 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.79415e33 | 0.463917 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.89369e33 | 0.727876 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.82150e33 | −1.42460 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.97493e33 | 0.708294 | 0.354147 | − | 0.935190i | \(-0.384771\pi\) | ||||
0.354147 | + | 0.935190i | \(0.384771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.80424e33 | −0.417965 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.74450e33 | −0.618652 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.09334e33 | 1.55596 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.29233e32 | 0.0489348 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.23761e32 | −0.150368 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.89322e33 | 1.19169 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.32152e32 | 0.104742 | 0.0523711 | − | 0.998628i | \(-0.483322\pi\) | ||||
0.0523711 | + | 0.998628i | \(0.483322\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.86290e33 | −1.31491 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.39595e33 | 1.19296 | 0.596480 | − | 0.802628i | \(-0.296566\pi\) | ||||
0.596480 | + | 0.802628i | \(0.296566\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.22319e32 | 0.0948450 | 0.0474225 | − | 0.998875i | \(-0.484899\pi\) | ||||
0.0474225 | + | 0.998875i | \(0.484899\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.46497e33 | 1.14296 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.61664e33 | −1.31111 | −0.655555 | − | 0.755147i | \(-0.727565\pi\) | ||||
−0.655555 | + | 0.755147i | \(0.727565\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.13204e34 | 1.89748 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.17920e33 | 0.682140 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.95482e33 | −0.469682 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.58391e33 | 0.400008 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.63177e33 | −0.547589 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.34579e34 | −3.44506 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.20154e33 | 0.744109 | 0.372055 | − | 0.928211i | \(-0.378653\pi\) | ||||
0.372055 | + | 0.928211i | \(0.378653\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.19828e33 | 0.724415 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.52401e33 | −0.342664 | −0.171332 | − | 0.985213i | \(-0.554807\pi\) | ||||
−0.171332 | + | 0.985213i | \(0.554807\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.17998e33 | −0.685141 | −0.342570 | − | 0.939492i | \(-0.611298\pi\) | ||||
−0.342570 | + | 0.939492i | \(0.611298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.52355e33 | 1.22730 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.35171e34 | −1.69731 | −0.848654 | − | 0.528948i | \(-0.822587\pi\) | ||||
−0.848654 | + | 0.528948i | \(0.822587\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.72995e34 | 3.34029 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.12452e33 | 0.253319 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.08025e33 | −0.241726 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.20759e33 | −0.136758 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.74957e33 | −0.193116 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.52408e33 | 1.02468 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.71039e32 | 0.0703741 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.50036e33 | 0.664551 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.57348e33 | −0.555479 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.97097e32 | 0.0483011 | 0.0241505 | − | 0.999708i | \(-0.492312\pi\) | ||||
0.0241505 | + | 0.999708i | \(0.492312\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.18770e33 | 0.586199 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.11942e33 | −0.750004 | −0.375002 | − | 0.927024i | \(-0.622358\pi\) | ||||
−0.375002 | + | 0.927024i | \(0.622358\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.30701e34 | −1.17724 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.54131e34 | 2.23211 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.31517e33 | −0.369616 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.62024e34 | 1.35348 | 0.676741 | − | 0.736221i | \(-0.263392\pi\) | ||||
0.676741 | + | 0.736221i | \(0.263392\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.81595e33 | 0.718262 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.22086e32 | −0.0414880 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.84600e34 | 2.98112 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.14708e34 | 0.867313 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.55887e34 | −1.14982 | −0.574910 | − | 0.818216i | \(-0.694963\pi\) | ||||
−0.574910 | + | 0.818216i | \(0.694963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.15825e34 | −3.71177 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.22795e32 | 0.0367022 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.86157e33 | 0.332999 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.49867e33 | −0.300662 | −0.150331 | − | 0.988636i | \(-0.548034\pi\) | ||||
−0.150331 | + | 0.988636i | \(0.548034\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.70345e33 | 0.437164 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.17928e32 | −0.0329601 | −0.0164801 | − | 0.999864i | \(-0.505246\pi\) | ||||
−0.0164801 | + | 0.999864i | \(0.505246\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.14971e34 | −0.714007 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.69897e34 | −3.45406 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.30688e33 | −0.254764 | −0.127382 | − | 0.991854i | \(-0.540657\pi\) | ||||
−0.127382 | + | 0.991854i | \(0.540657\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.40220e32 | −0.0427365 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.71387e33 | −0.547414 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.71314e34 | 1.49246 | 0.746231 | − | 0.665687i | \(-0.231862\pi\) | ||||
0.746231 | + | 0.665687i | \(0.231862\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.45959e34 | 3.46870 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.04254e34 | −0.546517 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.14601e34 | 2.63364 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.60897e34 | 0.803948 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.92528e33 | −0.240286 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.44176e34 | 1.16316 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.19669e34 | −1.95210 | −0.976050 | − | 0.217547i | \(-0.930194\pi\) | ||||
−0.976050 | + | 0.217547i | \(0.930194\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.40107e33 | 0.199910 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.05790e34 | −0.912857 | −0.456428 | − | 0.889760i | \(-0.650871\pi\) | ||||
−0.456428 | + | 0.889760i | \(0.650871\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.00776e34 | −0.436577 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.14180e34 | −0.483098 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.04532e34 | 0.431979 | 0.215989 | − | 0.976396i | \(-0.430702\pi\) | ||||
0.215989 | + | 0.976396i | \(0.430702\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.60199e34 | 0.646635 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.78402e33 | 0.109769 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.14322e34 | −1.21063 | −0.605313 | − | 0.795988i | \(-0.706952\pi\) | ||||
−0.605313 | + | 0.795988i | \(0.706952\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.65197e34 | 2.50284 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.75793e33 | −0.211651 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.15600e34 | −0.415146 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.36431e34 | −0.478704 | −0.239352 | − | 0.970933i | \(-0.576935\pi\) | ||||
−0.239352 | + | 0.970933i | \(0.576935\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.20955e34 | −0.414675 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.69468e34 | −0.902696 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.61404e34 | −0.855693 | −0.427847 | − | 0.903851i | \(-0.640728\pi\) | ||||
−0.427847 | + | 0.903851i | \(0.640728\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.80328e34 | 1.53651 |
(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 | 64.24.a.n.1.2 | 6 | ||
4.3 | odd | 2 | inner | 64.24.a.n.1.5 | 6 | ||
8.3 | odd | 2 | 32.24.a.d.1.2 | ✓ | 6 | ||
8.5 | even | 2 | 32.24.a.d.1.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.24.a.d.1.2 | ✓ | 6 | 8.3 | odd | 2 | ||
32.24.a.d.1.5 | yes | 6 | 8.5 | even | 2 | ||
64.24.a.n.1.2 | 6 | 1.1 | even | 1 | trivial | ||
64.24.a.n.1.5 | 6 | 4.3 | odd | 2 | inner |