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: | \(2\) |
Coefficient field: | \(\Q(\sqrt{144169}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 36042 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-189.348\) 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 | ||||||||
\(3\) | 388445. | 1.26600 | 0.633002 | − | 0.774150i | \(-0.281823\pi\) | ||||
0.633002 | + | 0.774150i | \(0.281823\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.05062e8 | −0.962256 | −0.481128 | − | 0.876650i | \(-0.659773\pi\) | ||||
−0.481128 | + | 0.876650i | \(0.659773\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.81217e9 | −0.728693 | −0.364346 | − | 0.931263i | \(-0.618708\pi\) | ||||
−0.364346 | + | 0.931263i | \(0.618708\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.67462e10 | 0.602765 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.52200e11 | 0.266519 | 0.133260 | − | 0.991081i | \(-0.457456\pi\) | ||||
0.133260 | + | 0.991081i | \(0.457456\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.59099e12 | 0.555733 | 0.277867 | − | 0.960620i | \(-0.410373\pi\) | ||||
0.277867 | + | 0.960620i | \(0.410373\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.08108e13 | −1.21822 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.34190e14 | 1.65731 | 0.828657 | − | 0.559756i | \(-0.189105\pi\) | ||||
0.828657 | + | 0.559756i | \(0.189105\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.23086e14 | −1.22710 | −0.613552 | − | 0.789654i | \(-0.710260\pi\) | ||||
−0.613552 | + | 0.789654i | \(0.710260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.48082e15 | −0.922528 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.58786e15 | 0.785173 | 0.392587 | − | 0.919715i | \(-0.371580\pi\) | ||||
0.392587 | + | 0.919715i | \(0.371580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.82898e14 | −0.0740629 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.45267e16 | −0.502901 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.05923e16 | 0.313421 | 0.156710 | − | 0.987645i | \(-0.449911\pi\) | ||||
0.156710 | + | 0.987645i | \(0.449911\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.36357e17 | −0.963870 | −0.481935 | − | 0.876207i | \(-0.660066\pi\) | ||||
−0.481935 | + | 0.876207i | \(0.660066\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.79656e16 | 0.337414 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.00514e17 | 0.701189 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.23898e18 | 1.14484 | 0.572419 | − | 0.819961i | \(-0.306005\pi\) | ||||
0.572419 | + | 0.819961i | \(0.306005\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.39490e18 | 0.703560 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.40074e18 | 0.397506 | 0.198753 | − | 0.980050i | \(-0.436311\pi\) | ||||
0.198753 | + | 0.980050i | \(0.436311\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.18793e17 | 0.0359043 | 0.0179522 | − | 0.999839i | \(-0.494285\pi\) | ||||
0.0179522 | + | 0.999839i | \(0.494285\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.96187e18 | −0.580015 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.67836e18 | 0.512050 | 0.256025 | − | 0.966670i | \(-0.417587\pi\) | ||||
0.256025 | + | 0.966670i | \(0.417587\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.28361e19 | −0.469007 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.09698e19 | 2.09817 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.63436e19 | 1.13136 | 0.565679 | − | 0.824626i | \(-0.308614\pi\) | ||||
0.565679 | + | 0.824626i | \(0.308614\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.64966e19 | −0.256460 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.42034e20 | −1.55352 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.01862e18 | −0.00439760 | −0.00219880 | − | 0.999998i | \(-0.500700\pi\) | ||||
−0.00219880 | + | 0.999998i | \(0.500700\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.87337e20 | −0.845472 | −0.422736 | − | 0.906253i | \(-0.638930\pi\) | ||||
−0.422736 | + | 0.906253i | \(0.638930\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.16326e20 | −0.439231 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.77277e20 | −0.534758 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.47683e21 | 1.47730 | 0.738652 | − | 0.674088i | \(-0.235463\pi\) | ||||
0.738652 | + | 0.674088i | \(0.235463\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.39369e21 | 0.994032 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.64346e20 | −0.392481 | −0.196241 | − | 0.980556i | \(-0.562873\pi\) | ||||
−0.196241 | + | 0.980556i | \(0.562873\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.49433e21 | −1.30362 | −0.651810 | − | 0.758382i | \(-0.725990\pi\) | ||||
−0.651810 | + | 0.758382i | \(0.725990\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.42957e20 | −0.0937639 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.61427e20 | −0.194211 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.02350e22 | −1.53948 | −0.769742 | − | 0.638356i | \(-0.779615\pi\) | ||||
−0.769742 | + | 0.638356i | \(0.779615\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.09851e22 | −1.23944 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.71597e21 | −0.657646 | −0.328823 | − | 0.944392i | \(-0.606652\pi\) | ||||
−0.328823 | + | 0.944392i | \(0.606652\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.46044e22 | −1.59476 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.99897e21 | 0.396792 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.58518e21 | 0.175134 | 0.0875672 | − | 0.996159i | \(-0.472091\pi\) | ||||
0.0875672 | + | 0.996159i | \(0.472091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.36895e22 | −0.404959 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.29672e22 | −1.22026 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.54627e22 | 1.18079 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.13703e23 | −1.61398 | −0.806991 | − | 0.590564i | \(-0.798905\pi\) | ||||
−0.806991 | + | 0.590564i | \(0.798905\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.43114e22 | 0.160648 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.36243e23 | −1.21512 | −0.607558 | − | 0.794275i | \(-0.707851\pi\) | ||||
−0.607558 | + | 0.794275i | \(0.707851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.41401e22 | −0.100653 | −0.0503264 | − | 0.998733i | \(-0.516026\pi\) | ||||
−0.0503264 | + | 0.998733i | \(0.516026\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.55578e23 | 0.887708 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.02971e22 | 0.276938 | 0.138469 | − | 0.990367i | \(-0.455782\pi\) | ||||
0.138469 | + | 0.990367i | \(0.455782\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.58169e22 | 0.207186 | 0.103593 | − | 0.994620i | \(-0.466966\pi\) | ||||
0.103593 | + | 0.994620i | \(0.466966\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.81275e23 | 1.44937 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.51523e23 | 0.862089 | 0.431044 | − | 0.902331i | \(-0.358145\pi\) | ||||
0.431044 | + | 0.902331i | \(0.358145\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.76948e23 | −0.755538 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.03775e23 | 0.334976 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.92770e23 | −1.20767 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.31826e23 | −0.928968 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.44111e23 | 0.503244 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.34520e24 | 1.03352 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.32044e24 | −1.48535 | −0.742674 | − | 0.669653i | \(-0.766443\pi\) | ||||
−0.742674 | + | 0.669653i | \(0.766443\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.49891e22 | 0.0454550 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.70825e23 | 0.390221 | 0.195111 | − | 0.980781i | \(-0.437493\pi\) | ||||
0.195111 | + | 0.980781i | \(0.437493\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.37531e24 | 0.894182 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.52620e24 | 0.483919 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.43869e24 | 1.18841 | 0.594207 | − | 0.804312i | \(-0.297466\pi\) | ||||
0.594207 | + | 0.804312i | \(0.297466\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.97229e23 | −0.112690 | −0.0563452 | − | 0.998411i | \(-0.517945\pi\) | ||||
−0.0563452 | + | 0.998411i | \(0.517945\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.37106e24 | 0.648257 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.05647e23 | 0.148114 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.16347e24 | −0.301591 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.98613e24 | −0.593764 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.10598e24 | −0.112748 | −0.0563738 | − | 0.998410i | \(-0.517954\pi\) | ||||
−0.0563738 | + | 0.998410i | \(0.517954\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.76304e24 | −0.329082 | −0.164541 | − | 0.986370i | \(-0.552614\pi\) | ||||
−0.164541 | + | 0.986370i | \(0.552614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.32894e25 | 0.998972 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.43260e25 | 0.927490 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.50090e25 | −0.838504 | −0.419252 | − | 0.907870i | \(-0.637708\pi\) | ||||
−0.419252 | + | 0.907870i | \(0.637708\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.96553e25 | 1.43230 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.36775e25 | −0.572150 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.61170e25 | −0.947907 | −0.473953 | − | 0.880550i | \(-0.657173\pi\) | ||||
−0.473953 | + | 0.880550i | \(0.657173\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.02925e25 | −0.324679 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.77408e25 | −0.487230 | −0.243615 | − | 0.969872i | \(-0.578333\pi\) | ||||
−0.243615 | + | 0.969872i | \(0.578333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.88587e25 | −0.691161 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.53578e25 | −0.739656 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.04109e26 | −1.90528 | −0.952640 | − | 0.304100i | \(-0.901644\pi\) | ||||
−0.952640 | + | 0.304100i | \(0.901644\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.36576e24 | 0.0539691 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.95679e23 | −0.00556737 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.00142e25 | −0.123824 | −0.0619122 | − | 0.998082i | \(-0.519720\pi\) | ||||
−0.0619122 | + | 0.998082i | \(0.519720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.17169e25 | 0.562768 | 0.281384 | − | 0.959595i | \(-0.409207\pi\) | ||||
0.281384 | + | 0.959595i | \(0.409207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.11615e26 | −1.07037 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.30170e26 | −1.10163 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.90625e25 | 0.441706 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.53780e25 | 0.366460 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.10126e26 | −1.81825 | −0.909127 | − | 0.416520i | \(-0.863250\pi\) | ||||
−0.909127 | + | 0.416520i | \(0.863250\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.28183e26 | −0.666687 | −0.333344 | − | 0.942805i | \(-0.608177\pi\) | ||||
−0.333344 | + | 0.942805i | \(0.608177\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.46551e26 | −0.677005 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.89967e26 | 1.60201 | 0.801007 | − | 0.598655i | \(-0.204298\pi\) | ||||
0.801007 | + | 0.598655i | \(0.204298\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.25611e26 | 0.459426 | 0.229713 | − | 0.973258i | \(-0.426221\pi\) | ||||
0.229713 | + | 0.973258i | \(0.426221\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.73666e26 | 1.87027 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.85013e25 | −0.228387 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.47165e26 | −0.382503 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.03598e26 | 0.473275 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.57142e26 | −0.327047 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.88286e26 | 1.09734 | 0.548669 | − | 0.836040i | \(-0.315135\pi\) | ||||
0.548669 | + | 0.836040i | \(0.315135\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.96906e26 | −0.496883 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.29869e25 | −0.0345491 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.19817e26 | 0.702365 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.35735e27 | −1.65039 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.40974e26 | 0.921025 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.38821e27 | −1.37072 | −0.685361 | − | 0.728203i | \(-0.740356\pi\) | ||||
−0.685361 | + | 0.728203i | \(0.740356\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.01012e25 | −0.0446425 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.14958e27 | −1.73004 | −0.865022 | − | 0.501734i | \(-0.832696\pi\) | ||||
−0.865022 | + | 0.501734i | \(0.832696\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.39851e26 | 0.465554 | 0.232777 | − | 0.972530i | \(-0.425219\pi\) | ||||
0.232777 | + | 0.972530i | \(0.425219\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.73461e26 | −0.245871 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.19149e27 | 1.30661 | 0.653306 | − | 0.757094i | \(-0.273381\pi\) | ||||
0.653306 | + | 0.757094i | \(0.273381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.11766e26 | −0.492723 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.97572e27 | −1.94899 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.09944e27 | −0.489322 | −0.244661 | − | 0.969609i | \(-0.578677\pi\) | ||||
−0.244661 | + | 0.969609i | \(0.578677\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.44651e27 | −0.584961 | −0.292480 | − | 0.956272i | \(-0.594481\pi\) | ||||
−0.292480 | + | 0.956272i | \(0.594481\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.89951e27 | −1.06623 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.34859e27 | 0.451304 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.23750e27 | −0.681942 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.99723e27 | −0.832582 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.24453e26 | 0.0568693 | 0.0284346 | − | 0.999596i | \(-0.490948\pi\) | ||||
0.0284346 | + | 0.999596i | \(0.490948\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.04857e26 | 0.209264 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.55747e27 | −2.01897 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.95005e27 | −0.762732 | −0.381366 | − | 0.924424i | \(-0.624546\pi\) | ||||
−0.381366 | + | 0.924424i | \(0.624546\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.72320e27 | −0.834236 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.16853e27 | 0.188919 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.01521e27 | −0.298420 | −0.149210 | − | 0.988805i | \(-0.547673\pi\) | ||||
−0.149210 | + | 0.988805i | \(0.547673\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.02081e27 | −1.08866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.78109e27 | 0.221721 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.72063e27 | −0.653571 | −0.326785 | − | 0.945099i | \(-0.605965\pi\) | ||||
−0.326785 | + | 0.945099i | \(0.605965\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.18050e27 | −0.543531 | −0.271766 | − | 0.962363i | \(-0.587608\pi\) | ||||
−0.271766 | + | 0.962363i | \(0.587608\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.31761e27 | −0.512679 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.22667e26 | −0.0197392 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.29611e28 | −1.05712 | −0.528560 | − | 0.848896i | \(-0.677268\pi\) | ||||
−0.528560 | + | 0.848896i | \(0.677268\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.73776e27 | −0.580987 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.24154e28 | 0.858691 | 0.429346 | − | 0.903140i | \(-0.358744\pi\) | ||||
0.429346 | + | 0.903140i | \(0.358744\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.15031e28 | −1.37074 | −0.685372 | − | 0.728193i | \(-0.740360\pi\) | ||||
−0.685372 | + | 0.728193i | \(0.740360\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.54286e28 | 1.49488 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.33986e27 | −0.289660 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.48772e28 | 1.74669 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.41675e28 | −2.04331 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.20307e28 | 0.514416 | 0.257208 | − | 0.966356i | \(-0.417197\pi\) | ||||
0.257208 | + | 0.966356i | \(0.417197\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.07019e26 | 0.00423161 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.66362e27 | −0.134033 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.28840e28 | 0.436347 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.34076e26 | −0.0261632 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.29228e28 | −1.53834 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.01883e28 | 0.813560 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.70428e28 | −1.17598 | −0.587992 | − | 0.808867i | \(-0.700081\pi\) | ||||
−0.587992 | + | 0.808867i | \(0.700081\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.49267e27 | −0.127427 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.99672e26 | 0.0193794 | 0.00968968 | − | 0.999953i | \(-0.496916\pi\) | ||||
0.00968968 | + | 0.999953i | \(0.496916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.13525e28 | −0.227159 | −0.113579 | − | 0.993529i | \(-0.536232\pi\) | ||||
−0.113579 | + | 0.993529i | \(0.536232\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.27277e28 | 0.422653 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.37896e28 | −0.238436 | −0.119218 | − | 0.992868i | \(-0.538039\pi\) | ||||
−0.119218 | + | 0.992868i | \(0.538039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.19337e27 | 0.0835326 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.34221e28 | 0.350605 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.45920e29 | −2.03370 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.17048e27 | −0.0411592 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.16818e28 | 0.262298 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.30834e28 | −0.373127 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.62668e29 | 1.71112 | 0.855559 | − | 0.517706i | \(-0.173214\pi\) | ||||
0.855559 | + | 0.517706i | \(0.173214\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.03074e28 | 0.690069 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.55159e29 | −1.42154 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.64138e29 | −1.40432 | −0.702160 | − | 0.712019i | \(-0.747781\pi\) | ||||
−0.702160 | + | 0.712019i | \(0.747781\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.36547e29 | 1.09141 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.43892e28 | −0.256890 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.53268e29 | 1.07045 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.46424e29 | −0.956514 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.45586e29 | 0.889876 | 0.444938 | − | 0.895561i | \(-0.353226\pi\) | ||||
0.444938 | + | 0.895561i | \(0.353226\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.22110e28 | −0.127080 | −0.0635398 | − | 0.997979i | \(-0.520239\pi\) | ||||
−0.0635398 | + | 0.997979i | \(0.520239\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.21651e28 | −0.279479 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.57166e28 | 0.129064 | 0.0645320 | − | 0.997916i | \(-0.479445\pi\) | ||||
0.0645320 | + | 0.997916i | \(0.479445\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.03037e28 | 0.377668 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.46792e29 | −1.52892 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.34157e29 | 1.38154 | 0.690771 | − | 0.723074i | \(-0.257271\pi\) | ||||
0.690771 | + | 0.723074i | \(0.257271\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.30406e29 | 0.505785 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.23118e29 | −1.17608 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.67122e29 | 1.25442 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.62664e29 | −0.521954 | −0.260977 | − | 0.965345i | \(-0.584045\pi\) | ||||
−0.260977 | + | 0.965345i | \(0.584045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.94868e28 | 0.239603 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.91034e29 | −0.824412 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.03540e29 | −0.275712 | −0.137856 | − | 0.990452i | \(-0.544021\pi\) | ||||
−0.137856 | + | 0.990452i | \(0.544021\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.22535e29 | 1.30844 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.39468e28 | 0.174178 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.62210e29 | 1.46772 | 0.733862 | − | 0.679298i | \(-0.237716\pi\) | ||||
0.733862 | + | 0.679298i | \(0.237716\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.01364e29 | −1.88046 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.96585e29 | −0.582591 | −0.291295 | − | 0.956633i | \(-0.594086\pi\) | ||||
−0.291295 | + | 0.956633i | \(0.594086\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.01010e29 | 0.186880 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.24157e28 | 0.0216419 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.06609e30 | 1.75134 | 0.875672 | − | 0.482906i | \(-0.160419\pi\) | ||||
0.875672 | + | 0.482906i | \(0.160419\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.40240e29 | 1.30128 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.38267e29 | 0.494021 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.07531e30 | 1.48138 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.67462e28 | −0.0217683 | −0.0108842 | − | 0.999941i | \(-0.503465\pi\) | ||||
−0.0108842 | + | 0.999941i | \(0.503465\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.22676e29 | 1.13204 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.87121e29 | 0.448421 | 0.224211 | − | 0.974541i | \(-0.428020\pi\) | ||||
0.224211 | + | 0.974541i | \(0.428020\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.89658e29 | −0.535654 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.15411e30 | 1.19266 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.12470e29 | 0.305121 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00511e29 | 0.461950 | 0.230975 | − | 0.972960i | \(-0.425808\pi\) | ||||
0.230975 | + | 0.972960i | \(0.425808\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.72418e30 | 1.50454 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.88316e27 | 0.00320450 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.10655e29 | 0.632824 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.93146e29 | −0.142666 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.70760e30 | 1.19378 | 0.596891 | − | 0.802322i | \(-0.296402\pi\) | ||||
0.596891 | + | 0.802322i | \(0.296402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.97218e29 | 0.395265 | 0.197633 | − | 0.980276i | \(-0.436675\pi\) | ||||
0.197633 | + | 0.980276i | \(0.436675\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.92464e29 | 0.308646 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.06766e29 | −0.122746 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.09538e30 | 0.616089 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.51794e29 | 0.187512 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.91854e30 | −0.969353 | −0.484676 | − | 0.874694i | \(-0.661063\pi\) | ||||
−0.484676 | + | 0.874694i | \(0.661063\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.68456e30 | −1.28606 | −0.643032 | − | 0.765839i | \(-0.722324\pi\) | ||||
−0.643032 | + | 0.765839i | \(0.722324\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.40388e29 | −0.381815 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.23555e30 | −0.963489 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.11168e29 | −0.0863549 | −0.0431775 | − | 0.999067i | \(-0.513748\pi\) | ||||
−0.0431775 | + | 0.999067i | \(0.513748\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.28401e29 | −0.282701 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.12623e29 | −0.299396 | −0.149698 | − | 0.988732i | \(-0.547830\pi\) | ||||
−0.149698 | + | 0.988732i | \(0.547830\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.81728e29 | −0.168524 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.29614e29 | −0.142739 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.76596e30 | −1.18862 | −0.594310 | − | 0.804236i | \(-0.702575\pi\) | ||||
−0.594310 | + | 0.804236i | \(0.702575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.53267e29 | 0.105943 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.46173e30 | −0.416619 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.43824e30 | 0.389674 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.14090e30 | 0.551518 | 0.275759 | − | 0.961227i | \(-0.411071\pi\) | ||||
0.275759 | + | 0.961227i | \(0.411071\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.40199e30 | −0.833465 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.76379e30 | −1.11018 | −0.555088 | − | 0.831792i | \(-0.687315\pi\) | ||||
−0.555088 | + | 0.831792i | \(0.687315\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.67574e30 | 1.70192 | 0.850959 | − | 0.525232i | \(-0.176021\pi\) | ||||
0.850959 | + | 0.525232i | \(0.176021\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.56485e30 | 1.17421 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.87884e30 | −0.578194 | −0.289097 | − | 0.957300i | \(-0.593355\pi\) | ||||
−0.289097 | + | 0.957300i | \(0.593355\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.62992e30 | −1.07650 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.83016e30 | −1.06155 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.51796e28 | 0.00956919 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.50121e29 | 0.0908829 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.33221e30 | 0.681943 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.82143e30 | −1.02333 | −0.511666 | − | 0.859184i | \(-0.670972\pi\) | ||||
−0.511666 | + | 0.859184i | \(0.670972\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.44917e30 | 0.636224 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.31297e30 | −0.724344 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.19459e31 | 1.55306 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.59361e29 | −0.106560 | −0.0532798 | − | 0.998580i | \(-0.516968\pi\) | ||||
−0.0532798 | + | 0.998580i | \(0.516968\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.01450e31 | −1.20005 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.15140e30 | −0.807149 | −0.403575 | − | 0.914947i | \(-0.632232\pi\) | ||||
−0.403575 | + | 0.914947i | \(0.632232\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.82250e30 | 0.519437 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.50358e30 | −0.154585 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.91382e30 | 0.285998 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.77913e31 | 1.66744 | 0.833722 | − | 0.552185i | \(-0.186206\pi\) | ||||
0.833722 | + | 0.552185i | \(0.186206\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.89133e30 | −0.616835 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.56155e30 | −0.561015 | −0.280507 | − | 0.959852i | \(-0.590503\pi\) | ||||
−0.280507 | + | 0.959852i | \(0.590503\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.43139e31 | 1.16925 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.12100e31 | −0.875012 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.19826e31 | 0.893917 | 0.446959 | − | 0.894555i | \(-0.352507\pi\) | ||||
0.446959 | + | 0.894555i | \(0.352507\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.33210e31 | 0.949939 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.05135e30 | 0.617112 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.48559e30 | 0.0968537 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.18868e30 | 0.136471 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.04407e31 | −2.41209 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.26240e31 | −1.29103 | −0.645514 | − | 0.763749i | \(-0.723357\pi\) | ||||
−0.645514 | + | 0.763749i | \(0.723357\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.41914e31 | −1.86702 | −0.933508 | − | 0.358557i | \(-0.883269\pi\) | ||||
−0.933508 | + | 0.358557i | \(0.883269\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.30741e30 | 0.0683251 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.19334e31 | −1.59744 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.00772e30 | −0.383503 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.78030e28 | −0.00265072 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.03006e30 | 0.220907 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.33494e30 | −0.266486 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.88996e30 | −0.156762 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.23726e30 | −0.124999 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.75024e30 | 0.101766 | 0.0508829 | − | 0.998705i | \(-0.483796\pi\) | ||||
0.0508829 | + | 0.998705i | \(0.483796\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.00892e31 | 0.712466 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.86424e30 | −0.199366 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.03197e31 | −0.336367 | −0.168184 | − | 0.985756i | \(-0.553790\pi\) | ||||
−0.168184 | + | 0.985756i | \(0.553790\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.63053e31 | −0.509621 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.28308e31 | −0.384600 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.90174e31 | 1.12181 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.05637e31 | −1.39466 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.36262e31 | −0.360613 | −0.180307 | − | 0.983610i | \(-0.557709\pi\) | ||||
−0.180307 | + | 0.983610i | \(0.557709\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.85685e29 | 0.0199532 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.29425e31 | 0.559202 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.09091e31 | 0.723169 | 0.361585 | − | 0.932339i | \(-0.382236\pi\) | ||||
0.361585 | + | 0.932339i | \(0.382236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.69317e31 | −0.829550 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.18769e31 | 0.903171 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.93051e31 | −1.43540 | −0.717702 | − | 0.696350i | \(-0.754806\pi\) | ||||
−0.717702 | + | 0.696350i | \(0.754806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.24961e30 | −0.124319 | −0.0621595 | − | 0.998066i | \(-0.519799\pi\) | ||||
−0.0621595 | + | 0.998066i | \(0.519799\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.20467e32 | −2.30192 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.16772e30 | −0.0581522 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.59740e31 | −0.281768 | −0.140884 | − | 0.990026i | \(-0.544994\pi\) | ||||
−0.140884 | + | 0.990026i | \(0.544994\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.97921e31 | −0.844029 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.94146e31 | 0.479222 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.92538e31 | 0.301529 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.14091e31 | −0.322333 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.16635e31 | 1.18220 | 0.591099 | − | 0.806599i | \(-0.298694\pi\) | ||||
0.591099 | + | 0.806599i | \(0.298694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.49622e31 | 1.18277 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.51481e32 | 2.02816 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.61370e30 | −0.0722970 | −0.0361485 | − | 0.999346i | \(-0.511509\pi\) | ||||
−0.0361485 | + | 0.999346i | \(0.511509\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.37963e31 | 1.16209 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.87928e31 | 0.581635 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.60231e32 | −1.83797 | −0.918985 | − | 0.394293i | \(-0.870990\pi\) | ||||
−0.918985 | + | 0.394293i | \(0.870990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.47641e31 | 0.935741 | 0.467870 | − | 0.883797i | \(-0.345021\pi\) | ||||
0.467870 | + | 0.883797i | \(0.345021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.38044e31 | 0.890467 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.73933e31 | 0.893905 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.63793e31 | 0.161296 | 0.0806481 | − | 0.996743i | \(-0.474301\pi\) | ||||
0.0806481 | + | 0.996743i | \(0.474301\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.04934e31 | −0.289139 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.11639e31 | 0.284563 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.93558e31 | −0.170222 | −0.0851110 | − | 0.996371i | \(-0.527124\pi\) | ||||
−0.0851110 | + | 0.996371i | \(0.527124\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.71654e31 | −0.484250 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.25618e31 | 0.428934 | 0.214467 | − | 0.976731i | \(-0.431199\pi\) | ||||
0.214467 | + | 0.976731i | \(0.431199\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.42009e31 | −0.740650 | −0.370325 | − | 0.928902i | \(-0.620754\pi\) | ||||
−0.370325 | + | 0.928902i | \(0.620754\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.21196e31 | −0.394864 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.74795e31 | −0.127619 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.30804e32 | −0.920452 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.10410e31 | −0.414042 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.90156e32 | 1.89736 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.22784e32 | 1.40458 | 0.702288 | − | 0.711892i | \(-0.252162\pi\) | ||||
0.702288 | + | 0.711892i | \(0.252162\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.28517e32 | 1.38923 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.43790e32 | 1.42929 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.60944e31 | −0.260642 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.33738e31 | −0.236574 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.38602e32 | 0.729295 | 0.364648 | − | 0.931146i | \(-0.381189\pi\) | ||||
0.364648 | + | 0.931146i | \(0.381189\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.71401e31 | 0.188546 | 0.0942729 | − | 0.995546i | \(-0.469947\pi\) | ||||
0.0942729 | + | 0.995546i | \(0.469947\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.92913e30 | −0.0437393 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.77554e32 | 1.78476 | 0.892379 | − | 0.451286i | \(-0.149035\pi\) | ||||
0.892379 | + | 0.451286i | \(0.149035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.56896e29 | −0.00117204 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.01920e32 | 0.889197 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.58042e31 | 0.364760 | 0.182380 | − | 0.983228i | \(-0.441620\pi\) | ||||
0.182380 | + | 0.983228i | \(0.441620\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.14906e31 | −0.375493 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.98290e32 | −0.785777 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.46687e32 | 0.561319 | 0.280660 | − | 0.959807i | \(-0.409447\pi\) | ||||
0.280660 | + | 0.959807i | \(0.409447\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.02066e32 | −0.746752 | −0.373376 | − | 0.927680i | \(-0.621800\pi\) | ||||
−0.373376 | + | 0.927680i | \(0.621800\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.26672e32 | 1.16602 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.49555e32 | −0.860432 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.38823e31 | 0.246090 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.39243e32 | −1.73534 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.24664e31 | −0.225334 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.34692e32 | 1.60668 | 0.803341 | − | 0.595519i | \(-0.203053\pi\) | ||||
0.803341 | + | 0.595519i | \(0.203053\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.28256e31 | 0.0372463 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.10049e32 | −0.308899 | −0.154449 | − | 0.988001i | \(-0.549360\pi\) | ||||
−0.154449 | + | 0.988001i | \(0.549360\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.33457e32 | 1.17610 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.34995e32 | −2.19024 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.97297e32 | −0.753967 | −0.376983 | − | 0.926220i | \(-0.623039\pi\) | ||||
−0.376983 | + | 0.926220i | \(0.623039\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.66337e32 | −1.14356 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.48547e32 | 0.589394 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.74149e32 | 0.628733 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.18838e32 | −1.59453 | −0.797266 | − | 0.603628i | \(-0.793721\pi\) | ||||
−0.797266 | + | 0.603628i | \(0.793721\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.45574e31 | −0.117063 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.22399e31 | 0.108437 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.28039e32 | 0.658793 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.51274e32 | 1.65418 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.02832e33 | 1.93362 | 0.966810 | − | 0.255497i | \(-0.0822390\pi\) | ||||
0.966810 | + | 0.255497i | \(0.0822390\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.71990e32 | −1.40484 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.54171e32 | −0.623790 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.19380e32 | 0.885446 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.50942e32 | 0.414134 | 0.207067 | − | 0.978327i | \(-0.433608\pi\) | ||||
0.207067 | + | 0.978327i | \(0.433608\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.80796e32 | −0.927947 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.89231e32 | −0.756805 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.51492e31 | −0.142523 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.27071e32 | −0.619483 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.09247e32 | −0.996358 | −0.498179 | − | 0.867074i | \(-0.665998\pi\) | ||||
−0.498179 | + | 0.867074i | \(0.665998\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.39046e31 | 0.0733450 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.61891e32 | −0.740562 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.81809e31 | −0.0232128 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.63712e32 | −0.573591 | −0.286795 | − | 0.957992i | \(-0.592590\pi\) | ||||
−0.286795 | + | 0.957992i | \(0.592590\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.21300e31 | −0.110417 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.12391e31 | 0.0595047 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.54780e33 | 1.74188 | 0.870941 | − | 0.491387i | \(-0.163510\pi\) | ||||
0.870941 | + | 0.491387i | \(0.163510\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.23852e32 | 0.571353 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.72455e32 | 0.393730 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.49249e33 | −1.52932 | −0.764662 | − | 0.644431i | \(-0.777094\pi\) | ||||
−0.764662 | + | 0.644431i | \(0.777094\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.69144e32 | −0.863341 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.19934e32 | −0.115497 | −0.0577487 | − | 0.998331i | \(-0.518392\pi\) | ||||
−0.0577487 | + | 0.998331i | \(0.518392\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.16197e32 | 0.108492 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.37852e32 | −0.396406 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.29863e32 | −0.201803 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.42812e33 | −1.21592 | −0.607959 | − | 0.793969i | \(-0.708011\pi\) | ||||
−0.607959 | + | 0.793969i | \(0.708011\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.71877e31 | 0.0719967 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.95352e32 | 0.316661 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.56208e33 | 1.21367 | 0.606835 | − | 0.794828i | \(-0.292439\pi\) | ||||
0.606835 | + | 0.794828i | \(0.292439\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.51487e32 | 0.264929 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.92115e33 | 1.40488 | 0.702439 | − | 0.711744i | \(-0.252094\pi\) | ||||
0.702439 | + | 0.711744i | \(0.252094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.12783e32 | −0.150975 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.39621e33 | −0.961267 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.65787e30 | −0.00244389 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.22615e33 | 0.795044 | 0.397522 | − | 0.917593i | \(-0.369870\pi\) | ||||
0.397522 | + | 0.917593i | \(0.369870\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.53438e33 | −0.965621 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.43914e32 | 0.515507 | 0.257753 | − | 0.966211i | \(-0.417018\pi\) | ||||
0.257753 | + | 0.966211i | \(0.417018\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.20390e32 | 0.0713870 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.83470e33 | −1.05615 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.72782e32 | −0.487781 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.92768e32 | −0.104604 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.99137e32 | −0.157620 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.57687e33 | 0.806856 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.37027e33 | 0.680919 | 0.340460 | − | 0.940259i | \(-0.389417\pi\) | ||||
0.340460 | + | 0.940259i | \(0.389417\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.82797e32 | −0.377801 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.34007e33 | −0.628198 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.03183e33 | −0.469857 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.11564e33 | −1.37824 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.57462e33 | −0.676714 | −0.338357 | − | 0.941018i | \(-0.609871\pi\) | ||||
−0.338357 | + | 0.941018i | \(0.609871\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.03238e33 | 0.848628 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.60192e32 | 0.105565 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.81269e32 | −0.347440 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.43699e33 | 0.550555 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.22215e33 | −0.827423 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.56942e33 | −0.929882 | −0.464941 | − | 0.885342i | \(-0.653924\pi\) | ||||
−0.464941 | + | 0.885342i | \(0.653924\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.25770e33 | 0.442423 | 0.221212 | − | 0.975226i | \(-0.428999\pi\) | ||||
0.221212 | + | 0.975226i | \(0.428999\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.01234e33 | −0.688112 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.74390e33 | 0.912129 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.36327e32 | −0.0440583 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.76826e32 | −0.244095 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.38117e32 | 0.0727519 | 0.0363759 | − | 0.999338i | \(-0.488419\pi\) | ||||
0.0363759 | + | 0.999338i | \(0.488419\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.82453e33 | −1.73047 | −0.865233 | − | 0.501370i | \(-0.832830\pi\) | ||||
−0.865233 | + | 0.501370i | \(0.832830\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.64937e31 | −0.0249899 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.61128e33 | −1.01472 | −0.507362 | − | 0.861733i | \(-0.669379\pi\) | ||||
−0.507362 | + | 0.861733i | \(0.669379\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.27935e33 | −1.71608 | −0.858040 | − | 0.513584i | \(-0.828318\pi\) | ||||
−0.858040 | + | 0.513584i | \(0.828318\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.03467e33 | −1.33832 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.00609e33 | −0.777292 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.86389e33 | 0.468841 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.98081e33 | 0.484731 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.51696e32 | −0.178970 | −0.0894849 | − | 0.995988i | \(-0.528522\pi\) | ||||
−0.0894849 | + | 0.995988i | \(0.528522\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.89268e33 | −0.901767 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.82269e33 | 1.08711 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.03195e33 | 0.665074 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.17106e33 | 0.676932 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.35275e33 | −1.73537 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.44528e33 | 0.898896 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.11290e33 | 1.79367 | 0.896836 | − | 0.442364i | \(-0.145860\pi\) | ||||
0.896836 | + | 0.442364i | \(0.145860\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.71476e33 | 0.711738 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.17423e33 | 1.15160 | 0.575802 | − | 0.817589i | \(-0.304690\pi\) | ||||
0.575802 | + | 0.817589i | \(0.304690\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.86175e33 | −0.338065 | −0.169033 | − | 0.985610i | \(-0.554064\pi\) | ||||
−0.169033 | + | 0.985610i | \(0.554064\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.07424e33 | −0.366710 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.22144e33 | 0.898806 | 0.449403 | − | 0.893329i | \(-0.351637\pi\) | ||||
0.449403 | + | 0.893329i | \(0.351637\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.09379e34 | 1.83337 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.35479e34 | 2.21132 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.58126e33 | −0.410302 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.30328e33 | 0.820986 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.45224e33 | −0.972852 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.12811e33 | −0.753121 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.73800e32 | 0.0963908 | 0.0481954 | − | 0.998838i | \(-0.484653\pi\) | ||||
0.0481954 | + | 0.998838i | \(0.484653\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.67328e33 | 0.651253 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.36978e34 | 1.85963 | 0.929815 | − | 0.368028i | \(-0.119967\pi\) | ||||
0.929815 | + | 0.368028i | \(0.119967\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.49590e33 | 0.197859 | 0.0989294 | − | 0.995094i | \(-0.468458\pi\) | ||||
0.0989294 | + | 0.995094i | \(0.468458\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.15708e31 | 0.00535724 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.44904e33 | 0.809792 | 0.404896 | − | 0.914363i | \(-0.367308\pi\) | ||||
0.404896 | + | 0.914363i | \(0.367308\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.84592e33 | 1.08236 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.77043e33 | −0.330334 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.40736e33 | −0.628339 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.05211e33 | 0.119151 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.00472e33 | 0.552417 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.80791e33 | −0.302097 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.78789e34 | 1.87502 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.23993e32 | −0.0331227 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.43349e33 | −0.541527 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.42282e33 | 0.624083 | 0.312041 | − | 0.950069i | \(-0.398987\pi\) | ||||
0.312041 | + | 0.950069i | \(0.398987\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.73126e33 | −0.732430 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.48932e34 | 1.37571 | 0.687855 | − | 0.725848i | \(-0.258553\pi\) | ||||
0.687855 | + | 0.725848i | \(0.258553\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.94596e33 | −0.175275 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.17265e34 | 1.02997 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.31973e33 | −0.284351 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.10701e33 | −0.259546 | −0.129773 | − | 0.991544i | \(-0.541425\pi\) | ||||
−0.129773 | + | 0.991544i | \(0.541425\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.82735e34 | −1.48880 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.74476e33 | −0.218115 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.09389e33 | −0.0847900 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.02400e32 | −0.0606700 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.72846e34 | 1.27490 | 0.637452 | − | 0.770490i | \(-0.279988\pi\) | ||||
0.637452 | + | 0.770490i | \(0.279988\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.99801e33 | 0.575520 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.49473e32 | 0.0245343 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.20523e33 | −0.425035 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.61548e34 | −1.07969 | −0.539843 | − | 0.841766i | \(-0.681516\pi\) | ||||
−0.539843 | + | 0.841766i | \(0.681516\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.40980e33 | −0.287584 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.69275e33 | −0.489554 | −0.244777 | − | 0.969579i | \(-0.578715\pi\) | ||||
−0.244777 | + | 0.969579i | \(0.578715\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.02567e33 | 0.312111 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.81813e33 | −0.352629 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.94332e34 | −1.74106 | −0.870528 | − | 0.492119i | \(-0.836222\pi\) | ||||
−0.870528 | + | 0.492119i | \(0.836222\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.25481e34 | −0.724465 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.35651e33 | −0.301860 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.97292e34 | 1.08528 | 0.542641 | − | 0.839965i | \(-0.317425\pi\) | ||||
0.542641 | + | 0.839965i | \(0.317425\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.25825e34 | 1.74963 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.01734e33 | 0.105753 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.69210e34 | −0.865989 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.42003e33 | −0.0709542 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.42163e33 | 0.166929 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.34672e34 | 0.641524 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.03266e34 | 0.945496 | 0.472748 | − | 0.881198i | \(-0.343262\pi\) | ||||
0.472748 | + | 0.881198i | \(0.343262\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.66820e34 | −2.57467 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.40470e34 | 1.51028 | 0.755141 | − | 0.655563i | \(-0.227569\pi\) | ||||
0.755141 | + | 0.655563i | \(0.227569\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.89552e33 | 0.0821166 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.23156e33 | −0.0521077 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.68167e32 | −0.0152145 | −0.00760725 | − | 0.999971i | \(-0.502421\pi\) | ||||
−0.00760725 | + | 0.999971i | \(0.502421\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.15638e33 | 0.0466767 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.16740e33 | 0.124885 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.23724e33 | 0.317261 | 0.158630 | − | 0.987338i | \(-0.449292\pi\) | ||||
0.158630 | + | 0.987338i | \(0.449292\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.09707e34 | −1.54155 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.28511e34 | −0.472380 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.85000e32 | 0.0281911 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.70349e33 | −0.0948590 | −0.0474295 | − | 0.998875i | \(-0.515103\pi\) | ||||
−0.0474295 | + | 0.998875i | \(0.515103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.31875e34 | 2.16628 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.31969e34 | −0.442086 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.64692e33 | 0.152115 | 0.0760573 | − | 0.997103i | \(-0.475767\pi\) | ||||
0.0760573 | + | 0.997103i | \(0.475767\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.79982e34 | −0.575740 |
(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.g.1.2 | 2 | ||
4.3 | odd | 2 | 64.24.a.d.1.1 | 2 | |||
8.3 | odd | 2 | 1.24.a.a.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 16.24.a.b.1.1 | 2 | |||
24.11 | even | 2 | 9.24.a.b.1.2 | 2 | |||
40.3 | even | 4 | 25.24.b.a.24.3 | 4 | |||
40.19 | odd | 2 | 25.24.a.a.1.2 | 2 | |||
40.27 | even | 4 | 25.24.b.a.24.2 | 4 | |||
56.27 | even | 2 | 49.24.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.24.a.a.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
9.24.a.b.1.2 | 2 | 24.11 | even | 2 | |||
16.24.a.b.1.1 | 2 | 8.5 | even | 2 | |||
25.24.a.a.1.2 | 2 | 40.19 | odd | 2 | |||
25.24.b.a.24.2 | 4 | 40.27 | even | 4 | |||
25.24.b.a.24.3 | 4 | 40.3 | even | 4 | |||
49.24.a.b.1.1 | 2 | 56.27 | even | 2 | |||
64.24.a.d.1.1 | 2 | 4.3 | odd | 2 | |||
64.24.a.g.1.2 | 2 | 1.1 | even | 1 | trivial |