Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,24,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(83.8010093363\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
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 | \(\chi\) | \(=\) | 25.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4016.35 | 1.38671 | 0.693357 | − | 0.720595i | \(-0.256131\pi\) | ||||
0.693357 | + | 0.720595i | \(0.256131\pi\) | |||||||
\(3\) | −388445. | −1.26600 | −0.633002 | − | 0.774150i | \(-0.718177\pi\) | ||||
−0.633002 | + | 0.774150i | \(0.718177\pi\) | |||||||
\(4\) | 7.74247e6 | 0.922974 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.56013e9 | −1.75558 | ||||||||
\(7\) | −3.81217e9 | −0.728693 | −0.364346 | − | 0.931263i | \(-0.618708\pi\) | ||||
−0.364346 | + | 0.931263i | \(0.618708\pi\) | |||||||
\(8\) | −2.59512e9 | −0.106813 | ||||||||
\(9\) | 5.67462e10 | 0.602765 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.52200e11 | 0.266519 | 0.133260 | − | 0.991081i | \(-0.457456\pi\) | ||||
0.133260 | + | 0.991081i | \(0.457456\pi\) | |||||||
\(12\) | −3.00752e12 | −1.16849 | ||||||||
\(13\) | 3.59099e12 | 0.555733 | 0.277867 | − | 0.960620i | \(-0.410373\pi\) | ||||
0.277867 | + | 0.960620i | \(0.410373\pi\) | |||||||
\(14\) | −1.53110e13 | −1.01049 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.53715e13 | −1.07109 | ||||||||
\(17\) | −2.34190e14 | −1.65731 | −0.828657 | − | 0.559756i | \(-0.810895\pi\) | ||||
−0.828657 | + | 0.559756i | \(0.810895\pi\) | |||||||
\(18\) | 2.27913e14 | 0.835863 | ||||||||
\(19\) | −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 | ||||||||
\(22\) | 1.01292e15 | 0.369586 | ||||||||
\(23\) | 3.58786e15 | 0.785173 | 0.392587 | − | 0.919715i | \(-0.371580\pi\) | ||||
0.392587 | + | 0.919715i | \(0.371580\pi\) | |||||||
\(24\) | 1.00806e15 | 0.135225 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.44227e16 | 0.770642 | ||||||||
\(27\) | 1.45267e16 | 0.502901 | ||||||||
\(28\) | −2.95156e16 | −0.672565 | ||||||||
\(29\) | −2.05923e16 | −0.313421 | −0.156710 | − | 0.987645i | \(-0.550089\pi\) | ||||
−0.156710 | + | 0.987645i | \(0.550089\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.36357e17 | 0.963870 | 0.481935 | − | 0.876207i | \(-0.339934\pi\) | ||||
0.481935 | + | 0.876207i | \(0.339934\pi\) | |||||||
\(32\) | −2.80949e17 | −1.37849 | ||||||||
\(33\) | −9.79656e16 | −0.337414 | ||||||||
\(34\) | −9.40588e17 | −2.29822 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.39356e17 | 0.556337 | ||||||||
\(37\) | 1.23898e18 | 1.14484 | 0.572419 | − | 0.819961i | \(-0.306005\pi\) | ||||
0.572419 | + | 0.819961i | \(0.306005\pi\) | |||||||
\(38\) | −2.50253e18 | −1.70164 | ||||||||
\(39\) | −1.39490e18 | −0.703560 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.40074e18 | 0.397506 | 0.198753 | − | 0.980050i | \(-0.436311\pi\) | ||||
0.198753 | + | 0.980050i | \(0.436311\pi\) | |||||||
\(42\) | 5.94748e18 | 1.27928 | ||||||||
\(43\) | −2.18793e17 | −0.0359043 | −0.0179522 | − | 0.999839i | \(-0.505715\pi\) | ||||
−0.0179522 | + | 0.999839i | \(0.505715\pi\) | |||||||
\(44\) | 1.95265e18 | 0.245990 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.44101e19 | 1.08881 | ||||||||
\(47\) | 8.67836e18 | 0.512050 | 0.256025 | − | 0.966670i | \(-0.417587\pi\) | ||||
0.256025 | + | 0.966670i | \(0.417587\pi\) | |||||||
\(48\) | 2.92777e19 | 1.35601 | ||||||||
\(49\) | −1.28361e19 | −0.469007 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.09698e19 | 2.09817 | ||||||||
\(52\) | 2.78032e19 | 0.512927 | ||||||||
\(53\) | 7.63436e19 | 1.13136 | 0.565679 | − | 0.824626i | \(-0.308614\pi\) | ||||
0.565679 | + | 0.824626i | \(0.308614\pi\) | |||||||
\(54\) | 5.83441e19 | 0.697379 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.89304e18 | 0.0778337 | ||||||||
\(57\) | 2.42034e20 | 1.55352 | ||||||||
\(58\) | −8.27059e19 | −0.434625 | ||||||||
\(59\) | −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 | \(-0.361070\pi\) | ||||
0.422736 | + | 0.906253i | \(0.361070\pi\) | |||||||
\(62\) | 5.47658e20 | 1.33661 | ||||||||
\(63\) | −2.16326e20 | −0.439231 | ||||||||
\(64\) | −4.96127e20 | −0.840472 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.93464e20 | −0.467897 | ||||||||
\(67\) | −1.47683e21 | −1.47730 | −0.738652 | − | 0.674088i | \(-0.764537\pi\) | ||||
−0.738652 | + | 0.674088i | \(0.764537\pi\) | |||||||
\(68\) | −1.81321e21 | −1.52966 | ||||||||
\(69\) | −1.39369e21 | −0.994032 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.64346e20 | 0.392481 | 0.196241 | − | 0.980556i | \(-0.437127\pi\) | ||||
0.196241 | + | 0.980556i | \(0.437127\pi\) | |||||||
\(72\) | −1.47263e20 | −0.0643830 | ||||||||
\(73\) | 3.49433e21 | 1.30362 | 0.651810 | − | 0.758382i | \(-0.274010\pi\) | ||||
0.651810 | + | 0.758382i | \(0.274010\pi\) | |||||||
\(74\) | 4.97617e21 | 1.58756 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.82422e21 | −1.13259 | ||||||||
\(77\) | −9.61427e20 | −0.194211 | ||||||||
\(78\) | −5.60242e21 | −0.975636 | ||||||||
\(79\) | 1.02350e22 | 1.53948 | 0.769742 | − | 0.638356i | \(-0.220385\pi\) | ||||
0.769742 | + | 0.638356i | \(0.220385\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.09851e22 | −1.23944 | ||||||||
\(82\) | 5.62587e21 | 0.551227 | ||||||||
\(83\) | 7.71597e21 | 0.657646 | 0.328823 | − | 0.944392i | \(-0.393348\pi\) | ||||
0.328823 | + | 0.944392i | \(0.393348\pi\) | |||||||
\(84\) | 1.14652e22 | 0.851469 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.78750e20 | −0.0497890 | ||||||||
\(87\) | 7.99897e21 | 0.396792 | ||||||||
\(88\) | −6.54489e20 | −0.0284676 | ||||||||
\(89\) | 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 | ||||||||
\(92\) | 2.77789e22 | 0.724695 | ||||||||
\(93\) | −5.29672e22 | −1.22026 | ||||||||
\(94\) | 3.48553e22 | 0.710067 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.09133e23 | 1.74517 | ||||||||
\(97\) | 1.13703e23 | 1.61398 | 0.806991 | − | 0.590564i | \(-0.201095\pi\) | ||||
0.806991 | + | 0.590564i | \(0.201095\pi\) | |||||||
\(98\) | −5.15544e22 | −0.650378 | ||||||||
\(99\) | 1.43114e22 | 0.160648 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.36243e23 | 1.21512 | 0.607558 | − | 0.794275i | \(-0.292149\pi\) | ||||
0.607558 | + | 0.794275i | \(0.292149\pi\) | |||||||
\(102\) | 3.65366e23 | 2.90956 | ||||||||
\(103\) | −1.41401e22 | −0.100653 | −0.0503264 | − | 0.998733i | \(-0.516026\pi\) | ||||
−0.0503264 | + | 0.998733i | \(0.516026\pi\) | |||||||
\(104\) | −9.31907e21 | −0.0593594 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.06623e23 | 1.56887 | ||||||||
\(107\) | −6.02971e22 | −0.276938 | −0.138469 | − | 0.990367i | \(-0.544218\pi\) | ||||
−0.138469 | + | 0.990367i | \(0.544218\pi\) | |||||||
\(108\) | 1.12472e23 | 0.464164 | ||||||||
\(109\) | −5.58169e22 | −0.207186 | −0.103593 | − | 0.994620i | \(-0.533034\pi\) | ||||
−0.103593 | + | 0.994620i | \(0.533034\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.81275e23 | −1.44937 | ||||||||
\(112\) | 2.87329e23 | 0.780498 | ||||||||
\(113\) | −3.51523e23 | −0.862089 | −0.431044 | − | 0.902331i | \(-0.641855\pi\) | ||||
−0.431044 | + | 0.902331i | \(0.641855\pi\) | |||||||
\(114\) | 9.72095e23 | 2.15428 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.59435e23 | −0.289279 | ||||||||
\(117\) | 2.03775e23 | 0.334976 | ||||||||
\(118\) | −4.09115e21 | −0.00609821 | ||||||||
\(119\) | 8.92770e23 | 1.20767 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.31826e23 | −0.928968 | ||||||||
\(122\) | 1.15405e24 | 1.17243 | ||||||||
\(123\) | −5.44111e23 | −0.503244 | ||||||||
\(124\) | 1.05574e24 | 0.889627 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.68842e23 | −0.609087 | ||||||||
\(127\) | −2.32044e24 | −1.48535 | −0.742674 | − | 0.669653i | \(-0.766443\pi\) | ||||
−0.742674 | + | 0.669653i | \(0.766443\pi\) | |||||||
\(128\) | 3.64148e23 | 0.212992 | ||||||||
\(129\) | 8.49891e22 | 0.0454550 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.70825e23 | 0.390221 | 0.195111 | − | 0.980781i | \(-0.437493\pi\) | ||||
0.195111 | + | 0.980781i | \(0.437493\pi\) | |||||||
\(132\) | −7.58496e23 | −0.311425 | ||||||||
\(133\) | 2.37531e24 | 0.894182 | ||||||||
\(134\) | −5.93146e24 | −2.04860 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.07751e23 | 0.177022 | ||||||||
\(137\) | −4.43869e24 | −1.18841 | −0.594207 | − | 0.804312i | \(-0.702534\pi\) | ||||
−0.594207 | + | 0.804312i | \(0.702534\pi\) | |||||||
\(138\) | −5.59753e24 | −1.37844 | ||||||||
\(139\) | −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 | ||||||||
\(142\) | 3.06988e24 | 0.544259 | ||||||||
\(143\) | 9.05647e23 | 0.148114 | ||||||||
\(144\) | −4.27705e24 | −0.645617 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.40345e25 | 1.80775 | ||||||||
\(147\) | 4.98613e24 | 0.593764 | ||||||||
\(148\) | 9.59276e24 | 1.05666 | ||||||||
\(149\) | 1.10598e24 | 0.112748 | 0.0563738 | − | 0.998410i | \(-0.482046\pi\) | ||||
0.0563738 | + | 0.998410i | \(0.482046\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.76304e24 | 0.329082 | 0.164541 | − | 0.986370i | \(-0.447386\pi\) | ||||
0.164541 | + | 0.986370i | \(0.447386\pi\) | |||||||
\(152\) | 1.61698e24 | 0.131070 | ||||||||
\(153\) | −1.32894e25 | −0.998972 | ||||||||
\(154\) | −3.86143e24 | −0.269315 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.08000e25 | −0.649368 | ||||||||
\(157\) | −1.50090e25 | −0.838504 | −0.419252 | − | 0.907870i | \(-0.637708\pi\) | ||||
−0.419252 | + | 0.907870i | \(0.637708\pi\) | |||||||
\(158\) | 4.11072e25 | 2.13482 | ||||||||
\(159\) | −2.96553e25 | −1.43230 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.36775e25 | −0.572150 | ||||||||
\(162\) | −4.41199e25 | −1.71875 | ||||||||
\(163\) | 2.61170e25 | 0.947907 | 0.473953 | − | 0.880550i | \(-0.342827\pi\) | ||||
0.473953 | + | 0.880550i | \(0.342827\pi\) | |||||||
\(164\) | 1.08452e25 | 0.366888 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.09900e25 | 0.911967 | ||||||||
\(167\) | −1.77408e25 | −0.487230 | −0.243615 | − | 0.969872i | \(-0.578333\pi\) | ||||
−0.243615 | + | 0.969872i | \(0.578333\pi\) | |||||||
\(168\) | −3.84290e24 | −0.0985377 | ||||||||
\(169\) | −2.88587e25 | −0.691161 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.53578e25 | −0.739656 | ||||||||
\(172\) | −1.69400e24 | −0.0331387 | ||||||||
\(173\) | −1.04109e26 | −1.90528 | −0.952640 | − | 0.304100i | \(-0.901644\pi\) | ||||
−0.952640 | + | 0.304100i | \(0.901644\pi\) | |||||||
\(174\) | 3.21267e25 | 0.550237 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.90087e25 | −0.285467 | ||||||||
\(177\) | 3.95679e23 | 0.00556737 | ||||||||
\(178\) | 1.84157e25 | 0.242861 | ||||||||
\(179\) | −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 | \(-0.590793\pi\) | ||||
−0.281384 | + | 0.959595i | \(0.590793\pi\) | |||||||
\(182\) | −5.49817e25 | −0.561562 | ||||||||
\(183\) | −1.11615e26 | −1.07037 | ||||||||
\(184\) | −9.31094e24 | −0.0838665 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.12735e26 | −1.69216 | ||||||||
\(187\) | −5.90625e25 | −0.441706 | ||||||||
\(188\) | 6.71919e25 | 0.472609 | ||||||||
\(189\) | −5.53780e25 | −0.366460 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.10126e26 | 1.81825 | 0.909127 | − | 0.416520i | \(-0.136750\pi\) | ||||
0.909127 | + | 0.416520i | \(0.136750\pi\) | |||||||
\(192\) | 1.92718e26 | 1.06404 | ||||||||
\(193\) | 1.28183e26 | 0.666687 | 0.333344 | − | 0.942805i | \(-0.391823\pi\) | ||||
0.333344 | + | 0.942805i | \(0.391823\pi\) | |||||||
\(194\) | 4.56673e26 | 2.23813 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.93833e25 | −0.432881 | ||||||||
\(197\) | 3.89967e26 | 1.60201 | 0.801007 | − | 0.598655i | \(-0.204298\pi\) | ||||
0.801007 | + | 0.598655i | \(0.204298\pi\) | |||||||
\(198\) | 5.74795e25 | 0.222773 | ||||||||
\(199\) | −1.25611e26 | −0.459426 | −0.229713 | − | 0.973258i | \(-0.573779\pi\) | ||||
−0.229713 | + | 0.973258i | \(0.573779\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.73666e26 | 1.87027 | ||||||||
\(202\) | 5.47199e26 | 1.68502 | ||||||||
\(203\) | 7.85013e25 | 0.228387 | ||||||||
\(204\) | 7.04330e26 | 1.93655 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.67918e25 | −0.139577 | ||||||||
\(207\) | 2.03598e26 | 0.473275 | ||||||||
\(208\) | −2.70658e26 | −0.595242 | ||||||||
\(209\) | −1.57142e26 | −0.327047 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.88286e26 | 1.09734 | 0.548669 | − | 0.836040i | \(-0.315135\pi\) | ||||
0.548669 | + | 0.836040i | \(0.315135\pi\) | |||||||
\(212\) | 5.91088e26 | 1.04421 | ||||||||
\(213\) | −2.96906e26 | −0.496883 | ||||||||
\(214\) | −2.42174e26 | −0.384034 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.76984e25 | −0.0537162 | ||||||||
\(217\) | −5.19817e26 | −0.702365 | ||||||||
\(218\) | −2.24180e26 | −0.287308 | ||||||||
\(219\) | −1.35735e27 | −1.65039 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.40974e26 | −0.921025 | ||||||||
\(222\) | −1.93297e27 | −2.00986 | ||||||||
\(223\) | −1.38821e27 | −1.37072 | −0.685361 | − | 0.728203i | \(-0.740356\pi\) | ||||
−0.685361 | + | 0.728203i | \(0.740356\pi\) | |||||||
\(224\) | 1.07102e27 | 1.00449 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.41184e27 | −1.19547 | ||||||||
\(227\) | 2.14958e27 | 1.73004 | 0.865022 | − | 0.501734i | \(-0.167304\pi\) | ||||
0.865022 | + | 0.501734i | \(0.167304\pi\) | |||||||
\(228\) | 1.87394e27 | 1.43386 | ||||||||
\(229\) | −6.39851e26 | −0.465554 | −0.232777 | − | 0.972530i | \(-0.574781\pi\) | ||||
−0.232777 | + | 0.972530i | \(0.574781\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.73461e26 | 0.245871 | ||||||||
\(232\) | 5.34395e25 | 0.0334773 | ||||||||
\(233\) | −2.19149e27 | −1.30661 | −0.653306 | − | 0.757094i | \(-0.726619\pi\) | ||||
−0.653306 | + | 0.757094i | \(0.726619\pi\) | |||||||
\(234\) | 8.18434e26 | 0.464516 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.88666e24 | −0.00405887 | ||||||||
\(237\) | −3.97572e27 | −1.94899 | ||||||||
\(238\) | 3.58568e27 | 1.67470 | ||||||||
\(239\) | 1.09944e27 | 0.489322 | 0.244661 | − | 0.969609i | \(-0.421323\pi\) | ||||
0.244661 | + | 0.969609i | \(0.421323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.44651e27 | −0.584961 | −0.292480 | − | 0.956272i | \(-0.594481\pi\) | ||||
−0.292480 | + | 0.956272i | \(0.594481\pi\) | |||||||
\(242\) | −3.34090e27 | −1.28821 | ||||||||
\(243\) | 2.89951e27 | 1.06623 | ||||||||
\(244\) | 2.22470e27 | 0.780349 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.18534e27 | −0.697855 | ||||||||
\(247\) | −2.23750e27 | −0.681942 | ||||||||
\(248\) | −3.53864e26 | −0.102954 | ||||||||
\(249\) | −2.99723e27 | −0.832582 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.24453e26 | 0.0568693 | 0.0284346 | − | 0.999596i | \(-0.490948\pi\) | ||||
0.0284346 | + | 0.999596i | \(0.490948\pi\) | |||||||
\(252\) | −1.67490e27 | −0.405399 | ||||||||
\(253\) | 9.04857e26 | 0.209264 | ||||||||
\(254\) | −9.31972e27 | −2.05975 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.62436e27 | 1.13583 | ||||||||
\(257\) | 3.95005e27 | 0.762732 | 0.381366 | − | 0.924424i | \(-0.375454\pi\) | ||||
0.381366 | + | 0.924424i | \(0.375454\pi\) | |||||||
\(258\) | 3.41346e26 | 0.0630330 | ||||||||
\(259\) | −4.72320e27 | −0.834236 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.16853e27 | −0.188919 | ||||||||
\(262\) | 3.49754e27 | 0.541125 | ||||||||
\(263\) | −2.01521e27 | −0.298420 | −0.149210 | − | 0.988805i | \(-0.547673\pi\) | ||||
−0.149210 | + | 0.988805i | \(0.547673\pi\) | |||||||
\(264\) | 2.54233e26 | 0.0360401 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.54007e27 | 1.23997 | ||||||||
\(267\) | −1.78109e27 | −0.221721 | ||||||||
\(268\) | −1.14343e28 | −1.36351 | ||||||||
\(269\) | 5.72063e27 | 0.653571 | 0.326785 | − | 0.945099i | \(-0.394035\pi\) | ||||
0.326785 | + | 0.945099i | \(0.394035\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.18050e27 | 0.543531 | 0.271766 | − | 0.962363i | \(-0.412392\pi\) | ||||
0.271766 | + | 0.962363i | \(0.412392\pi\) | |||||||
\(272\) | 1.76512e28 | 1.77514 | ||||||||
\(273\) | 5.31761e27 | 0.512679 | ||||||||
\(274\) | −1.78273e28 | −1.64799 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.07906e28 | −0.917466 | ||||||||
\(277\) | −1.29611e28 | −1.05712 | −0.528560 | − | 0.848896i | \(-0.677268\pi\) | ||||
−0.528560 | + | 0.848896i | \(0.677268\pi\) | |||||||
\(278\) | −1.99705e27 | −0.156269 | ||||||||
\(279\) | 7.73776e27 | 0.580987 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.24154e28 | 0.858691 | 0.429346 | − | 0.903140i | \(-0.358744\pi\) | ||||
0.429346 | + | 0.903140i | \(0.358744\pi\) | |||||||
\(282\) | −1.35394e28 | −0.898947 | ||||||||
\(283\) | 2.15031e28 | 1.37074 | 0.685372 | − | 0.728193i | \(-0.259640\pi\) | ||||
0.685372 | + | 0.728193i | \(0.259640\pi\) | |||||||
\(284\) | 5.91792e27 | 0.362250 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.63740e27 | 0.205391 | ||||||||
\(287\) | −5.33986e27 | −0.289660 | ||||||||
\(288\) | −1.59428e28 | −0.830903 | ||||||||
\(289\) | 3.48772e28 | 1.74669 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.41675e28 | −2.04331 | ||||||||
\(292\) | 2.70547e28 | 1.20321 | ||||||||
\(293\) | 1.20307e28 | 0.514416 | 0.257208 | − | 0.966356i | \(-0.417197\pi\) | ||||
0.257208 | + | 0.966356i | \(0.417197\pi\) | |||||||
\(294\) | 2.00260e28 | 0.823380 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.21530e27 | −0.122283 | ||||||||
\(297\) | 3.66362e27 | 0.134033 | ||||||||
\(298\) | 4.44202e27 | 0.156349 | ||||||||
\(299\) | 1.28840e28 | 0.436347 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.34076e26 | 0.0261632 | ||||||||
\(302\) | 1.51137e28 | 0.456342 | ||||||||
\(303\) | −5.29228e28 | −1.53834 | ||||||||
\(304\) | 4.69629e28 | 1.31434 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.33748e28 | −1.38529 | ||||||||
\(307\) | 4.70428e28 | 1.17598 | 0.587992 | − | 0.808867i | \(-0.299919\pi\) | ||||
0.587992 | + | 0.808867i | \(0.299919\pi\) | |||||||
\(308\) | −7.44382e27 | −0.179251 | ||||||||
\(309\) | 5.49267e27 | 0.127427 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.99672e26 | −0.0193794 | −0.00968968 | − | 0.999953i | \(-0.503084\pi\) | ||||
−0.00968968 | + | 0.999953i | \(0.503084\pi\) | |||||||
\(312\) | 3.61994e27 | 0.0751492 | ||||||||
\(313\) | 1.13525e28 | 0.227159 | 0.113579 | − | 0.993529i | \(-0.463768\pi\) | ||||
0.113579 | + | 0.993529i | \(0.463768\pi\) | |||||||
\(314\) | −6.02814e28 | −1.16277 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.92439e28 | 1.42090 | ||||||||
\(317\) | −1.37896e28 | −0.238436 | −0.119218 | − | 0.992868i | \(-0.538039\pi\) | ||||
−0.119218 | + | 0.992868i | \(0.538039\pi\) | |||||||
\(318\) | −1.19106e29 | −1.98619 | ||||||||
\(319\) | −5.19337e27 | −0.0835326 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.34221e28 | 0.350605 | ||||||||
\(322\) | −5.49338e28 | −0.793408 | ||||||||
\(323\) | 1.45920e29 | 2.03370 | ||||||||
\(324\) | −8.50516e28 | −1.14397 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.04895e29 | 1.31448 | ||||||||
\(327\) | 2.16818e28 | 0.262298 | ||||||||
\(328\) | −3.63510e27 | −0.0424587 | ||||||||
\(329\) | −3.30834e28 | −0.373127 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.62668e29 | 1.71112 | 0.855559 | − | 0.517706i | \(-0.173214\pi\) | ||||
0.855559 | + | 0.517706i | \(0.173214\pi\) | |||||||
\(332\) | 5.97406e28 | 0.606990 | ||||||||
\(333\) | 7.03074e28 | 0.690069 | ||||||||
\(334\) | −7.12534e28 | −0.675649 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.11611e29 | −0.988113 | ||||||||
\(337\) | 1.64138e29 | 1.40432 | 0.702160 | − | 0.712019i | \(-0.252219\pi\) | ||||
0.702160 | + | 0.712019i | \(0.252219\pi\) | |||||||
\(338\) | −1.15907e29 | −0.958442 | ||||||||
\(339\) | 1.36547e29 | 1.09141 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.43892e28 | 0.256890 | ||||||||
\(342\) | −1.42009e29 | −1.02569 | ||||||||
\(343\) | 1.53268e29 | 1.07045 | ||||||||
\(344\) | 5.67795e26 | 0.00383504 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.18139e29 | −2.64208 | ||||||||
\(347\) | −1.45586e29 | −0.889876 | −0.444938 | − | 0.895561i | \(-0.646774\pi\) | ||||
−0.444938 | + | 0.895561i | \(0.646774\pi\) | |||||||
\(348\) | 6.19318e28 | 0.366229 | ||||||||
\(349\) | 2.22110e28 | 0.127080 | 0.0635398 | − | 0.997979i | \(-0.479761\pi\) | ||||
0.0635398 | + | 0.997979i | \(0.479761\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.21651e28 | 0.279479 | ||||||||
\(352\) | −7.08552e28 | −0.367393 | ||||||||
\(353\) | −2.57166e28 | −0.129064 | −0.0645320 | − | 0.997916i | \(-0.520555\pi\) | ||||
−0.0645320 | + | 0.997916i | \(0.520555\pi\) | |||||||
\(354\) | 1.58919e27 | 0.00772035 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.55006e28 | 0.161644 | ||||||||
\(357\) | −3.46792e29 | −1.52892 | ||||||||
\(358\) | −4.02205e28 | −0.171709 | ||||||||
\(359\) | −3.34157e29 | −1.38154 | −0.690771 | − | 0.723074i | \(-0.742729\pi\) | ||||
−0.690771 | + | 0.723074i | \(0.742729\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.30406e29 | 0.505785 | ||||||||
\(362\) | −2.07713e29 | −0.780398 | ||||||||
\(363\) | 3.23118e29 | 1.17608 | ||||||||
\(364\) | −1.05990e29 | −0.373766 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.48284e29 | −1.48430 | ||||||||
\(367\) | −1.62664e29 | −0.521954 | −0.260977 | − | 0.965345i | \(-0.584045\pi\) | ||||
−0.260977 | + | 0.965345i | \(0.584045\pi\) | |||||||
\(368\) | −2.70422e29 | −0.840994 | ||||||||
\(369\) | 7.94868e28 | 0.239603 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.91034e29 | −0.824412 | ||||||||
\(372\) | −4.10097e29 | −1.12627 | ||||||||
\(373\) | −1.03540e29 | −0.275712 | −0.137856 | − | 0.990452i | \(-0.544021\pi\) | ||||
−0.137856 | + | 0.990452i | \(0.544021\pi\) | |||||||
\(374\) | −2.37216e29 | −0.612520 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.25214e28 | −0.0546935 | ||||||||
\(377\) | −7.39468e28 | −0.174178 | ||||||||
\(378\) | −2.22418e29 | −0.508175 | ||||||||
\(379\) | 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 | ||||||||
\(382\) | 1.24557e30 | 2.52140 | ||||||||
\(383\) | −2.96585e29 | −0.582591 | −0.291295 | − | 0.956633i | \(-0.594086\pi\) | ||||
−0.291295 | + | 0.956633i | \(0.594086\pi\) | |||||||
\(384\) | −1.41451e29 | −0.269648 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.14829e29 | 0.924504 | ||||||||
\(387\) | −1.24157e28 | −0.0216419 | ||||||||
\(388\) | 8.80345e29 | 1.48966 | ||||||||
\(389\) | −1.06609e30 | −1.75134 | −0.875672 | − | 0.482906i | \(-0.839581\pi\) | ||||
−0.875672 | + | 0.482906i | \(0.839581\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.40240e29 | −1.30128 | ||||||||
\(392\) | 3.33113e28 | 0.0500959 | ||||||||
\(393\) | −3.38267e29 | −0.494021 | ||||||||
\(394\) | 1.56624e30 | 2.22153 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.10805e29 | 0.148274 | ||||||||
\(397\) | −1.67462e28 | −0.0217683 | −0.0108842 | − | 0.999941i | \(-0.503465\pi\) | ||||
−0.0108842 | + | 0.999941i | \(0.503465\pi\) | |||||||
\(398\) | −5.04496e29 | −0.637093 | ||||||||
\(399\) | −9.22676e29 | −1.13204 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.87121e29 | 0.448421 | 0.224211 | − | 0.974541i | \(-0.428020\pi\) | ||||
0.224211 | + | 0.974541i | \(0.428020\pi\) | |||||||
\(402\) | 2.30404e30 | 2.59353 | ||||||||
\(403\) | 4.89658e29 | 0.535654 | ||||||||
\(404\) | 1.05486e30 | 1.12152 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.15289e29 | 0.316708 | ||||||||
\(407\) | 3.12470e29 | 0.305121 | ||||||||
\(408\) | −2.36078e29 | −0.224111 | ||||||||
\(409\) | 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 | ||||||||
\(412\) | −1.09480e29 | −0.0928999 | ||||||||
\(413\) | 3.88316e27 | 0.00320450 | ||||||||
\(414\) | 8.17719e29 | 0.656297 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00889e30 | −0.766070 | ||||||||
\(417\) | 1.93146e29 | 0.142666 | ||||||||
\(418\) | −6.31137e29 | −0.453520 | ||||||||
\(419\) | 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 | \(-0.563325\pi\) | ||||
−0.197633 | + | 0.980276i | \(0.563325\pi\) | |||||||
\(422\) | 2.36276e30 | 1.52169 | ||||||||
\(423\) | 4.92464e29 | 0.308646 | ||||||||
\(424\) | −1.98121e29 | −0.120843 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.19248e30 | −0.689034 | ||||||||
\(427\) | −1.09538e30 | −0.616089 | ||||||||
\(428\) | −4.66848e29 | −0.255607 | ||||||||
\(429\) | −3.51794e29 | −0.187512 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.91854e30 | 0.969353 | 0.484676 | − | 0.874694i | \(-0.338937\pi\) | ||||
0.484676 | + | 0.874694i | \(0.338937\pi\) | |||||||
\(432\) | −1.09490e30 | −0.538653 | ||||||||
\(433\) | 2.68456e30 | 1.28606 | 0.643032 | − | 0.765839i | \(-0.277676\pi\) | ||||
0.643032 | + | 0.765839i | \(0.277676\pi\) | |||||||
\(434\) | −2.08777e30 | −0.973980 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.32160e29 | −0.191228 | ||||||||
\(437\) | −2.23555e30 | −0.963489 | ||||||||
\(438\) | −5.45161e30 | −2.28862 | ||||||||
\(439\) | 2.11168e29 | 0.0863549 | 0.0431775 | − | 0.999067i | \(-0.486252\pi\) | ||||
0.0431775 | + | 0.999067i | \(0.486252\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.28401e29 | −0.282701 | ||||||||
\(442\) | −3.37765e30 | −1.27720 | ||||||||
\(443\) | 8.12623e29 | 0.299396 | 0.149698 | − | 0.988732i | \(-0.452170\pi\) | ||||
0.149698 | + | 0.988732i | \(0.452170\pi\) | |||||||
\(444\) | −3.72626e30 | −1.33773 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.57554e30 | −1.90080 | ||||||||
\(447\) | −4.29614e29 | −0.142739 | ||||||||
\(448\) | 1.89132e30 | 0.612446 | ||||||||
\(449\) | −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 | ||||||||
\(452\) | −2.72166e30 | −0.795686 | ||||||||
\(453\) | −1.46173e30 | −0.416619 | ||||||||
\(454\) | 8.63348e30 | 2.39907 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.28109e29 | −0.165936 | ||||||||
\(457\) | −2.14090e30 | −0.551518 | −0.275759 | − | 0.961227i | \(-0.588929\pi\) | ||||
−0.275759 | + | 0.961227i | \(0.588929\pi\) | |||||||
\(458\) | −2.56986e30 | −0.645591 | ||||||||
\(459\) | −3.40199e30 | −0.833465 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.76379e30 | 1.11018 | 0.555088 | − | 0.831792i | \(-0.312685\pi\) | ||||
0.555088 | + | 0.831792i | \(0.312685\pi\) | |||||||
\(462\) | 1.49995e30 | 0.340953 | ||||||||
\(463\) | 7.67574e30 | 1.70192 | 0.850959 | − | 0.525232i | \(-0.176021\pi\) | ||||
0.850959 | + | 0.525232i | \(0.176021\pi\) | |||||||
\(464\) | 1.55207e30 | 0.335703 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.80180e30 | −1.81190 | ||||||||
\(467\) | 2.87884e30 | 0.578194 | 0.289097 | − | 0.957300i | \(-0.406645\pi\) | ||||
0.289097 | + | 0.957300i | \(0.406645\pi\) | |||||||
\(468\) | 1.57772e30 | 0.309175 | ||||||||
\(469\) | 5.62992e30 | 1.07650 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.83016e30 | 1.06155 | ||||||||
\(472\) | 2.64345e27 | 0.000469719 0 | ||||||||
\(473\) | −5.51796e28 | −0.00956919 | ||||||||
\(474\) | −1.59679e31 | −2.70269 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.91225e30 | 1.11465 | ||||||||
\(477\) | 4.33221e30 | 0.681943 | ||||||||
\(478\) | 4.41573e30 | 0.678549 | ||||||||
\(479\) | 6.82143e30 | 1.02333 | 0.511666 | − | 0.859184i | \(-0.329028\pi\) | ||||
0.511666 | + | 0.859184i | \(0.329028\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.44917e30 | 0.636224 | ||||||||
\(482\) | −5.80971e30 | −0.811173 | ||||||||
\(483\) | 5.31297e30 | 0.724344 | ||||||||
\(484\) | −6.44038e30 | −0.857413 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.16455e31 | 1.47856 | ||||||||
\(487\) | −8.59361e29 | −0.106560 | −0.0532798 | − | 0.998580i | \(-0.516968\pi\) | ||||
−0.0532798 | + | 0.998580i | \(0.516968\pi\) | |||||||
\(488\) | −7.45676e29 | −0.0903071 | ||||||||
\(489\) | −1.01450e31 | −1.20005 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.15140e30 | −0.807149 | −0.403575 | − | 0.914947i | \(-0.632232\pi\) | ||||
−0.403575 | + | 0.914947i | \(0.632232\pi\) | |||||||
\(492\) | −4.21276e30 | −0.464481 | ||||||||
\(493\) | 4.82250e30 | 0.519437 | ||||||||
\(494\) | −8.98658e30 | −0.945659 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.02774e31 | −1.03239 | ||||||||
\(497\) | −2.91382e30 | −0.285998 | ||||||||
\(498\) | −1.20379e31 | −1.15455 | ||||||||
\(499\) | 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 | ||||||||
\(502\) | 9.01483e29 | 0.0788614 | ||||||||
\(503\) | −6.56155e30 | −0.561015 | −0.280507 | − | 0.959852i | \(-0.590503\pi\) | ||||
−0.280507 | + | 0.959852i | \(0.590503\pi\) | |||||||
\(504\) | 5.61393e29 | 0.0469154 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.63422e30 | 0.290189 | ||||||||
\(507\) | 1.12100e31 | 0.875012 | ||||||||
\(508\) | −1.79660e31 | −1.37094 | ||||||||
\(509\) | −1.19826e31 | −0.893917 | −0.446959 | − | 0.894555i | \(-0.647493\pi\) | ||||
−0.446959 | + | 0.894555i | \(0.647493\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.33210e31 | −0.949939 | ||||||||
\(512\) | 1.95347e31 | 1.36208 | ||||||||
\(513\) | −9.05135e30 | −0.617112 | ||||||||
\(514\) | 1.58648e31 | 1.05769 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.58025e29 | 0.0419538 | ||||||||
\(517\) | 2.18868e30 | 0.136471 | ||||||||
\(518\) | −1.89700e31 | −1.15685 | ||||||||
\(519\) | 4.04407e31 | 2.41209 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.26240e31 | −1.29103 | −0.645514 | − | 0.763749i | \(-0.723357\pi\) | ||||
−0.645514 | + | 0.763749i | \(0.723357\pi\) | |||||||
\(522\) | −4.69325e30 | −0.261977 | ||||||||
\(523\) | 3.41914e31 | 1.86702 | 0.933508 | − | 0.358557i | \(-0.116731\pi\) | ||||
0.933508 | + | 0.358557i | \(0.116731\pi\) | |||||||
\(524\) | 6.74233e30 | 0.360164 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.09378e30 | −0.413824 | ||||||||
\(527\) | −3.19334e31 | −1.59744 | ||||||||
\(528\) | 7.38381e30 | 0.361402 | ||||||||
\(529\) | −8.00772e30 | −0.383503 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.78030e28 | −0.00265072 | ||||||||
\(532\) | 1.83907e31 | 0.825307 | ||||||||
\(533\) | 5.03006e30 | 0.220907 | ||||||||
\(534\) | −7.15348e30 | −0.307463 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.83255e30 | 0.157795 | ||||||||
\(537\) | 3.88996e30 | 0.156762 | ||||||||
\(538\) | 2.29761e31 | 0.906315 | ||||||||
\(539\) | −3.23726e30 | −0.124999 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.75024e30 | −0.101766 | −0.0508829 | − | 0.998705i | \(-0.516204\pi\) | ||||
−0.0508829 | + | 0.998705i | \(0.516204\pi\) | |||||||
\(542\) | 2.08067e31 | 0.753722 | ||||||||
\(543\) | 2.00892e31 | 0.712466 | ||||||||
\(544\) | 6.57953e31 | 2.28459 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.13574e31 | 0.710939 | ||||||||
\(547\) | 1.03197e31 | 0.336367 | 0.168184 | − | 0.985756i | \(-0.446210\pi\) | ||||
0.168184 | + | 0.985756i | \(0.446210\pi\) | |||||||
\(548\) | −3.43664e31 | −1.09688 | ||||||||
\(549\) | 1.63053e31 | 0.509621 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.28308e31 | 0.384600 | ||||||||
\(552\) | 3.61679e30 | 0.106175 | ||||||||
\(553\) | −3.90174e31 | −1.12181 | ||||||||
\(554\) | −5.20563e31 | −1.46592 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.84978e30 | −0.104010 | ||||||||
\(557\) | −1.36262e31 | −0.360613 | −0.180307 | − | 0.983610i | \(-0.557709\pi\) | ||||
−0.180307 | + | 0.983610i | \(0.557709\pi\) | |||||||
\(558\) | 3.10775e31 | 0.805663 | ||||||||
\(559\) | −7.85685e29 | −0.0199532 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.29425e31 | 0.559202 | ||||||||
\(562\) | 4.98645e31 | 1.19076 | ||||||||
\(563\) | −3.09091e31 | −0.723169 | −0.361585 | − | 0.932339i | \(-0.617764\pi\) | ||||
−0.361585 | + | 0.932339i | \(0.617764\pi\) | |||||||
\(564\) | −2.61004e31 | −0.598325 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.63638e31 | 1.90083 | ||||||||
\(567\) | 4.18769e31 | 0.903171 | ||||||||
\(568\) | −1.98357e30 | −0.0419220 | ||||||||
\(569\) | −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 | \(0.519799\pi\) | |||||||
\(572\) | 7.01195e30 | 0.136705 | ||||||||
\(573\) | −1.20467e32 | −2.30192 | ||||||||
\(574\) | −2.14468e31 | −0.401675 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.81534e31 | −0.506607 | ||||||||
\(577\) | 1.59740e31 | 0.281768 | 0.140884 | − | 0.990026i | \(-0.455006\pi\) | ||||
0.140884 | + | 0.990026i | \(0.455006\pi\) | |||||||
\(578\) | 1.40079e32 | 2.42216 | ||||||||
\(579\) | −4.97921e31 | −0.844029 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.94146e31 | −0.479222 | ||||||||
\(582\) | −1.77392e32 | −2.83348 | ||||||||
\(583\) | 1.92538e31 | 0.301529 | ||||||||
\(584\) | −9.06822e30 | −0.139243 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.83197e31 | 0.713348 | ||||||||
\(587\) | −8.16635e31 | −1.18220 | −0.591099 | − | 0.806599i | \(-0.701306\pi\) | ||||
−0.591099 | + | 0.806599i | \(0.701306\pi\) | |||||||
\(588\) | 3.86049e31 | 0.548029 | ||||||||
\(589\) | −8.49622e31 | −1.18277 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.51481e32 | −2.02816 | ||||||||
\(592\) | −9.33837e31 | −1.22623 | ||||||||
\(593\) | 5.61370e30 | 0.0722970 | 0.0361485 | − | 0.999346i | \(-0.488491\pi\) | ||||
0.0361485 | + | 0.999346i | \(0.488491\pi\) | |||||||
\(594\) | 1.47144e31 | 0.185865 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.56305e30 | 0.104063 | ||||||||
\(597\) | 4.87928e31 | 0.581635 | ||||||||
\(598\) | 5.17466e31 | 0.605088 | ||||||||
\(599\) | 1.60231e32 | 1.83797 | 0.918985 | − | 0.394293i | \(-0.129010\pi\) | ||||
0.918985 | + | 0.394293i | \(0.129010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.47641e31 | 0.935741 | 0.467870 | − | 0.883797i | \(-0.345021\pi\) | ||||
0.467870 | + | 0.883797i | \(0.345021\pi\) | |||||||
\(602\) | 3.34994e30 | 0.0362809 | ||||||||
\(603\) | −8.38044e31 | −0.890467 | ||||||||
\(604\) | 2.91352e31 | 0.303734 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.12557e32 | −2.13324 | ||||||||
\(607\) | 1.63793e31 | 0.161296 | 0.0806481 | − | 0.996743i | \(-0.474301\pi\) | ||||
0.0806481 | + | 0.996743i | \(0.474301\pi\) | |||||||
\(608\) | 1.75055e32 | 1.69155 | ||||||||
\(609\) | −3.04934e31 | −0.289139 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.11639e31 | 0.284563 | ||||||||
\(612\) | −1.02893e32 | −0.922025 | ||||||||
\(613\) | −1.93558e31 | −0.170222 | −0.0851110 | − | 0.996371i | \(-0.527124\pi\) | ||||
−0.0851110 | + | 0.996371i | \(0.527124\pi\) | |||||||
\(614\) | 1.88940e32 | 1.63075 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.49502e30 | 0.0207442 | ||||||||
\(617\) | −5.25618e31 | −0.428934 | −0.214467 | − | 0.976731i | \(-0.568801\pi\) | ||||
−0.214467 | + | 0.976731i | \(0.568801\pi\) | |||||||
\(618\) | 2.20605e31 | 0.176704 | ||||||||
\(619\) | −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 | ||||||||
\(622\) | −3.61340e30 | −0.0268736 | ||||||||
\(623\) | −1.74795e31 | −0.127619 | ||||||||
\(624\) | 1.05136e32 | 0.753578 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.55954e31 | 0.315004 | ||||||||
\(627\) | 6.10410e31 | 0.414042 | ||||||||
\(628\) | −1.16207e32 | −0.773918 | ||||||||
\(629\) | −2.90156e32 | −1.89736 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.22784e32 | −1.40458 | −0.702288 | − | 0.711892i | \(-0.747838\pi\) | ||||
−0.702288 | + | 0.711892i | \(0.747838\pi\) | |||||||
\(632\) | −2.65610e31 | −0.164436 | ||||||||
\(633\) | −2.28517e32 | −1.38923 | ||||||||
\(634\) | −5.53840e31 | −0.330642 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.29605e32 | −1.32198 | ||||||||
\(637\) | −4.60944e31 | −0.260642 | ||||||||
\(638\) | −2.08584e31 | −0.115836 | ||||||||
\(639\) | 4.33738e31 | 0.236574 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.38602e32 | 0.729295 | 0.364648 | − | 0.931146i | \(-0.381189\pi\) | ||||
0.364648 | + | 0.931146i | \(0.381189\pi\) | |||||||
\(642\) | 9.40714e31 | 0.486188 | ||||||||
\(643\) | −3.71401e31 | −0.188546 | −0.0942729 | − | 0.995546i | \(-0.530053\pi\) | ||||
−0.0942729 | + | 0.995546i | \(0.530053\pi\) | |||||||
\(644\) | −1.05898e32 | −0.528080 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.86067e32 | 2.82016 | ||||||||
\(647\) | 3.77554e32 | 1.78476 | 0.892379 | − | 0.451286i | \(-0.149035\pi\) | ||||
0.892379 | + | 0.451286i | \(0.149035\pi\) | |||||||
\(648\) | 2.85076e31 | 0.132388 | ||||||||
\(649\) | −2.56896e29 | −0.00117204 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.01920e32 | 0.889197 | ||||||||
\(652\) | 2.02210e32 | 0.874893 | ||||||||
\(653\) | 8.58042e31 | 0.364760 | 0.182380 | − | 0.983228i | \(-0.441620\pi\) | ||||
0.182380 | + | 0.983228i | \(0.441620\pi\) | |||||||
\(654\) | 8.70816e31 | 0.363733 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.05576e32 | −0.425766 | ||||||||
\(657\) | 1.98290e32 | 0.785777 | ||||||||
\(658\) | −1.32874e32 | −0.517421 | ||||||||
\(659\) | 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 | \(-0.378200\pi\) | ||||
0.373376 | + | 0.927680i | \(0.378200\pi\) | |||||||
\(662\) | 6.53331e32 | 2.37283 | ||||||||
\(663\) | 3.26672e32 | 1.16602 | ||||||||
\(664\) | −2.00239e31 | −0.0702450 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.82379e32 | 0.956927 | ||||||||
\(667\) | −7.38823e31 | −0.246090 | ||||||||
\(668\) | −1.37358e32 | −0.449701 | ||||||||
\(669\) | 5.39243e32 | 1.73534 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.24664e31 | 0.225334 | ||||||||
\(672\) | −4.16034e32 | −1.27169 | ||||||||
\(673\) | −5.34692e32 | −1.60668 | −0.803341 | − | 0.595519i | \(-0.796947\pi\) | ||||
−0.803341 | + | 0.595519i | \(0.796947\pi\) | |||||||
\(674\) | 6.59237e32 | 1.94739 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.23437e32 | −0.637924 | ||||||||
\(677\) | −1.10049e32 | −0.308899 | −0.154449 | − | 0.988001i | \(-0.549360\pi\) | ||||
−0.154449 | + | 0.988001i | \(0.549360\pi\) | |||||||
\(678\) | 5.48422e32 | 1.51347 | ||||||||
\(679\) | −4.33457e32 | −1.17610 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.34995e32 | −2.19024 | ||||||||
\(682\) | 1.38119e32 | 0.356233 | ||||||||
\(683\) | 2.97297e32 | 0.753967 | 0.376983 | − | 0.926220i | \(-0.376961\pi\) | ||||
0.376983 | + | 0.926220i | \(0.376961\pi\) | |||||||
\(684\) | −2.73756e32 | −0.682683 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.15577e32 | 1.48441 | ||||||||
\(687\) | 2.48547e32 | 0.589394 | ||||||||
\(688\) | 1.64908e31 | 0.0384568 | ||||||||
\(689\) | 2.74149e32 | 0.628733 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.18838e32 | −1.59453 | −0.797266 | − | 0.603628i | \(-0.793721\pi\) | ||||
−0.797266 | + | 0.603628i | \(0.793721\pi\) | |||||||
\(692\) | −8.06062e32 | −1.75852 | ||||||||
\(693\) | −5.45574e31 | −0.117063 | ||||||||
\(694\) | −5.84723e32 | −1.23400 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.07583e31 | −0.0423824 | ||||||||
\(697\) | −3.28039e32 | −0.658793 | ||||||||
\(698\) | 8.92072e31 | 0.176223 | ||||||||
\(699\) | 8.51274e32 | 1.65418 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.02832e33 | −1.93362 | −0.966810 | − | 0.255497i | \(-0.917761\pi\) | ||||
−0.966810 | + | 0.255497i | \(0.917761\pi\) | |||||||
\(702\) | 2.09513e32 | 0.387557 | ||||||||
\(703\) | −7.71990e32 | −1.40484 | ||||||||
\(704\) | −1.25123e32 | −0.224002 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.03287e32 | −0.178975 | ||||||||
\(707\) | −5.19380e32 | −0.885446 | ||||||||
\(708\) | 3.06353e30 | 0.00513854 | ||||||||
\(709\) | −2.50942e32 | −0.414134 | −0.207067 | − | 0.978327i | \(-0.566392\pi\) | ||||
−0.207067 | + | 0.978327i | \(0.566392\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.80796e32 | 0.927947 | ||||||||
\(712\) | −1.18991e31 | −0.0187066 | ||||||||
\(713\) | 4.89231e32 | 0.756805 | ||||||||
\(714\) | −1.39284e33 | −2.12017 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.75346e31 | −0.114287 | ||||||||
\(717\) | −4.27071e32 | −0.619483 | ||||||||
\(718\) | −1.34209e33 | −1.91580 | ||||||||
\(719\) | 7.09247e32 | 0.996358 | 0.498179 | − | 0.867074i | \(-0.334002\pi\) | ||||
0.498179 | + | 0.867074i | \(0.334002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.39046e31 | 0.0733450 | ||||||||
\(722\) | 5.23757e32 | 0.701378 | ||||||||
\(723\) | 5.61891e32 | 0.740562 | ||||||||
\(724\) | −4.00417e32 | −0.519420 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.29776e33 | 1.63088 | ||||||||
\(727\) | −4.63712e32 | −0.573591 | −0.286795 | − | 0.957992i | \(-0.592590\pi\) | ||||
−0.286795 | + | 0.957992i | \(0.592590\pi\) | |||||||
\(728\) | 3.55259e31 | 0.0432547 | ||||||||
\(729\) | −9.21300e31 | −0.110417 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.12391e31 | 0.0595047 | ||||||||
\(732\) | −8.64174e32 | −0.987924 | ||||||||
\(733\) | 1.54780e33 | 1.74188 | 0.870941 | − | 0.491387i | \(-0.163510\pi\) | ||||
0.870941 | + | 0.491387i | \(0.163510\pi\) | |||||||
\(734\) | −6.53317e32 | −0.723801 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00801e33 | −1.08235 | ||||||||
\(737\) | −3.72455e32 | −0.393730 | ||||||||
\(738\) | 3.19247e32 | 0.332260 | ||||||||
\(739\) | −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 | ||||||||
\(742\) | −1.16890e33 | −1.14322 | ||||||||
\(743\) | −1.19934e32 | −0.115497 | −0.0577487 | − | 0.998331i | \(-0.518392\pi\) | ||||
−0.0577487 | + | 0.998331i | \(0.518392\pi\) | |||||||
\(744\) | 1.37456e32 | 0.130340 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.15852e32 | −0.382334 | ||||||||
\(747\) | 4.37852e32 | 0.396406 | ||||||||
\(748\) | −4.57290e32 | −0.407683 | ||||||||
\(749\) | 2.29863e32 | 0.201803 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.42812e33 | 1.21592 | 0.607959 | − | 0.793969i | \(-0.291989\pi\) | ||||
0.607959 | + | 0.793969i | \(0.291989\pi\) | |||||||
\(752\) | −6.54101e32 | −0.548453 | ||||||||
\(753\) | −8.71877e31 | −0.0719967 | ||||||||
\(754\) | −2.96996e32 | −0.241535 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.28763e32 | −0.338233 | ||||||||
\(757\) | 1.56208e33 | 1.21367 | 0.606835 | − | 0.794828i | \(-0.292439\pi\) | ||||
0.606835 | + | 0.794828i | \(0.292439\pi\) | |||||||
\(758\) | 2.65967e33 | 2.03531 | ||||||||
\(759\) | −3.51487e32 | −0.264929 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.92115e33 | 1.40488 | 0.702439 | − | 0.711744i | \(-0.252094\pi\) | ||||
0.702439 | + | 0.711744i | \(0.252094\pi\) | |||||||
\(762\) | 3.62020e33 | 2.60765 | ||||||||
\(763\) | 2.12783e32 | 0.150975 | ||||||||
\(764\) | 2.40114e33 | 1.67820 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.19119e33 | −0.807886 | ||||||||
\(767\) | −3.65787e30 | −0.00244389 | ||||||||
\(768\) | −2.18475e33 | −1.43797 | ||||||||
\(769\) | 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 | ||||||||
\(772\) | 9.92455e32 | 0.615335 | ||||||||
\(773\) | 8.43914e32 | 0.515507 | 0.257753 | − | 0.966211i | \(-0.417018\pi\) | ||||
0.257753 | + | 0.966211i | \(0.417018\pi\) | |||||||
\(774\) | −4.98658e31 | −0.0300111 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.95074e32 | −0.172394 | ||||||||
\(777\) | 1.83470e33 | 1.05615 | ||||||||
\(778\) | −4.28177e33 | −2.42861 | ||||||||
\(779\) | −8.72782e32 | −0.487781 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.92768e32 | 0.104604 | ||||||||
\(782\) | −3.37470e33 | −1.80450 | ||||||||
\(783\) | −2.99137e32 | −0.157620 | ||||||||
\(784\) | 9.67477e32 | 0.502350 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.35860e33 | −0.685066 | ||||||||
\(787\) | −1.37027e33 | −0.680919 | −0.340460 | − | 0.940259i | \(-0.610583\pi\) | ||||
−0.340460 | + | 0.940259i | \(0.610583\pi\) | |||||||
\(788\) | 3.01931e33 | 1.47862 | ||||||||
\(789\) | 7.82797e32 | 0.377801 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.34007e33 | 0.628198 | ||||||||
\(792\) | −3.71398e31 | −0.0171593 | ||||||||
\(793\) | 1.03183e33 | 0.469857 | ||||||||
\(794\) | −6.72586e31 | −0.0301865 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.72536e32 | −0.424039 | ||||||||
\(797\) | −1.57462e33 | −0.676714 | −0.338357 | − | 0.941018i | \(-0.609871\pi\) | ||||
−0.338357 | + | 0.941018i | \(0.609871\pi\) | |||||||
\(798\) | −3.70579e33 | −1.56981 | ||||||||
\(799\) | −2.03238e33 | −0.848628 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.60192e32 | 0.105565 | ||||||||
\(802\) | 1.55481e33 | 0.621832 | ||||||||
\(803\) | 8.81269e32 | 0.347440 | ||||||||
\(804\) | 4.44159e33 | 1.72621 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.96664e33 | 0.742799 | ||||||||
\(807\) | −2.22215e33 | −0.827423 | ||||||||
\(808\) | −3.53567e32 | −0.129790 | ||||||||
\(809\) | −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 | \(0.428999\pi\) | |||||||
\(812\) | 6.07794e32 | 0.210796 | ||||||||
\(813\) | −2.01234e33 | −0.688112 | ||||||||
\(814\) | 1.25499e33 | 0.423116 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.85652e33 | −2.24733 | ||||||||
\(817\) | 1.36327e32 | 0.0440583 | ||||||||
\(818\) | 2.01023e33 | 0.640593 | ||||||||
\(819\) | −7.76826e32 | −0.244095 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.38117e32 | −0.0727519 | −0.0363759 | − | 0.999338i | \(-0.511581\pi\) | ||||
−0.0363759 | + | 0.999338i | \(0.511581\pi\) | |||||||
\(822\) | 6.92493e33 | 2.08636 | ||||||||
\(823\) | −5.82453e33 | −1.73047 | −0.865233 | − | 0.501370i | \(-0.832830\pi\) | ||||
−0.865233 | + | 0.501370i | \(0.832830\pi\) | |||||||
\(824\) | 3.66954e31 | 0.0107510 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.55961e31 | 0.00444372 | ||||||||
\(827\) | 3.61128e33 | 1.01472 | 0.507362 | − | 0.861733i | \(-0.330621\pi\) | ||||
0.507362 | + | 0.861733i | \(0.330621\pi\) | |||||||
\(828\) | 1.57635e33 | 0.436821 | ||||||||
\(829\) | 6.27935e33 | 1.71608 | 0.858040 | − | 0.513584i | \(-0.171682\pi\) | ||||
0.858040 | + | 0.513584i | \(0.171682\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.03467e33 | 1.33832 | ||||||||
\(832\) | −1.78159e33 | −0.467078 | ||||||||
\(833\) | 3.00609e33 | 0.777292 | ||||||||
\(834\) | 7.75743e32 | 0.197837 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.21667e33 | −0.301856 | ||||||||
\(837\) | 1.98081e33 | 0.484731 | ||||||||
\(838\) | 6.85832e33 | 1.65543 | ||||||||
\(839\) | 7.51696e32 | 0.178970 | 0.0894849 | − | 0.995988i | \(-0.471478\pi\) | ||||
0.0894849 | + | 0.995988i | \(0.471478\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.89268e33 | −0.901767 | ||||||||
\(842\) | −2.39864e33 | −0.548120 | ||||||||
\(843\) | −4.82269e33 | −1.08711 | ||||||||
\(844\) | 4.55478e33 | 1.01281 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.97791e33 | 0.428003 | ||||||||
\(847\) | 3.17106e33 | 0.676932 | ||||||||
\(848\) | −5.75412e33 | −1.21179 | ||||||||
\(849\) | −8.35275e33 | −1.73537 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.44528e33 | 0.898896 | ||||||||
\(852\) | −2.29879e33 | −0.458610 | ||||||||
\(853\) | 9.11290e33 | 1.79367 | 0.896836 | − | 0.442364i | \(-0.145860\pi\) | ||||
0.896836 | + | 0.442364i | \(0.145860\pi\) | |||||||
\(854\) | −4.39943e33 | −0.854339 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.56478e32 | 0.0295805 | ||||||||
\(857\) | −6.17423e33 | −1.15160 | −0.575802 | − | 0.817589i | \(-0.695310\pi\) | ||||
−0.575802 | + | 0.817589i | \(0.695310\pi\) | |||||||
\(858\) | −1.41293e33 | −0.260026 | ||||||||
\(859\) | −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 | ||||||||
\(862\) | 7.70552e33 | 1.34421 | ||||||||
\(863\) | 5.22144e33 | 0.898806 | 0.449403 | − | 0.893329i | \(-0.351637\pi\) | ||||
0.449403 | + | 0.893329i | \(0.351637\pi\) | |||||||
\(864\) | −4.08125e33 | −0.693242 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.07821e34 | 1.78340 | ||||||||
\(867\) | −1.35479e34 | −2.21132 | ||||||||
\(868\) | −4.02466e33 | −0.648265 | ||||||||
\(869\) | 2.58126e33 | 0.410302 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.30328e33 | −0.820986 | ||||||||
\(872\) | 1.44852e32 | 0.0221301 | ||||||||
\(873\) | 6.45224e33 | 0.972852 | ||||||||
\(874\) | −8.97874e33 | −1.33608 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.05093e34 | −1.52327 | ||||||||
\(877\) | 6.73800e32 | 0.0963908 | 0.0481954 | − | 0.998838i | \(-0.484653\pi\) | ||||
0.0481954 | + | 0.998838i | \(0.484653\pi\) | |||||||
\(878\) | 8.48127e32 | 0.119750 | ||||||||
\(879\) | −4.67328e33 | −0.651253 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.36978e34 | 1.85963 | 0.929815 | − | 0.368028i | \(-0.119967\pi\) | ||||
0.929815 | + | 0.368028i | \(0.119967\pi\) | |||||||
\(882\) | −2.92552e33 | −0.392025 | ||||||||
\(883\) | −1.49590e33 | −0.197859 | −0.0989294 | − | 0.995094i | \(-0.531542\pi\) | ||||
−0.0989294 | + | 0.995094i | \(0.531542\pi\) | |||||||
\(884\) | −6.51121e33 | −0.850082 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.26378e33 | 0.415177 | ||||||||
\(887\) | 6.44904e33 | 0.809792 | 0.404896 | − | 0.914363i | \(-0.367308\pi\) | ||||
0.404896 | + | 0.914363i | \(0.367308\pi\) | |||||||
\(888\) | 1.24897e33 | 0.154811 | ||||||||
\(889\) | 8.84592e33 | 1.08236 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.77043e33 | −0.330334 | ||||||||
\(892\) | −1.07482e34 | −1.26514 | ||||||||
\(893\) | −5.40736e33 | −0.628339 | ||||||||
\(894\) | −1.72548e33 | −0.197938 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.38819e33 | −0.155206 | ||||||||
\(897\) | −5.00472e33 | −0.552417 | ||||||||
\(898\) | −1.51254e34 | −1.64827 | ||||||||
\(899\) | −2.80791e33 | −0.302097 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.78789e34 | −1.87502 | ||||||||
\(902\) | 1.41884e33 | 0.146913 | ||||||||
\(903\) | −3.23993e32 | −0.0331227 | ||||||||
\(904\) | 9.12246e32 | 0.0920820 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.87083e33 | −0.577731 | ||||||||
\(907\) | −6.42282e33 | −0.624083 | −0.312041 | − | 0.950069i | \(-0.601013\pi\) | ||||
−0.312041 | + | 0.950069i | \(0.601013\pi\) | |||||||
\(908\) | 1.66431e34 | 1.59679 | ||||||||
\(909\) | 7.73126e33 | 0.732430 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.48932e34 | −1.37571 | −0.687855 | − | 0.725848i | \(-0.741447\pi\) | ||||
−0.687855 | + | 0.725848i | \(0.741447\pi\) | |||||||
\(912\) | −1.82425e34 | −1.66396 | ||||||||
\(913\) | 1.94596e33 | 0.175275 | ||||||||
\(914\) | −8.59859e33 | −0.764797 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.95402e33 | −0.429695 | ||||||||
\(917\) | −3.31973e33 | −0.284351 | ||||||||
\(918\) | −1.36636e34 | −1.15578 | ||||||||
\(919\) | 3.10701e33 | 0.259546 | 0.129773 | − | 0.991544i | \(-0.458575\pi\) | ||||
0.129773 | + | 0.991544i | \(0.458575\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.82735e34 | −1.48880 | ||||||||
\(922\) | 1.91330e34 | 1.53950 | ||||||||
\(923\) | 2.74476e33 | 0.218115 | ||||||||
\(924\) | 2.89151e33 | 0.226933 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.08285e34 | 2.36007 | ||||||||
\(927\) | −8.02400e32 | −0.0606700 | ||||||||
\(928\) | 5.78538e33 | 0.432046 | ||||||||
\(929\) | 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 | ||||||||
\(932\) | −1.69676e34 | −1.20597 | ||||||||
\(933\) | 3.49473e32 | 0.0245343 | ||||||||
\(934\) | 1.15624e34 | 0.801790 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.28822e32 | −0.0357797 | ||||||||
\(937\) | 1.61548e34 | 1.07969 | 0.539843 | − | 0.841766i | \(-0.318484\pi\) | ||||
0.539843 | + | 0.841766i | \(0.318484\pi\) | |||||||
\(938\) | 2.26117e34 | 1.49280 | ||||||||
\(939\) | −4.40980e33 | −0.287584 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.69275e33 | 0.489554 | 0.244777 | − | 0.969579i | \(-0.421285\pi\) | ||||
0.244777 | + | 0.969579i | \(0.421285\pi\) | |||||||
\(942\) | 2.34160e34 | 1.47206 | ||||||||
\(943\) | 5.02567e33 | 0.312111 | ||||||||
\(944\) | 7.67751e31 | 0.00471023 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.21620e32 | −0.0132697 | ||||||||
\(947\) | 2.94332e34 | 1.74106 | 0.870528 | − | 0.492119i | \(-0.163778\pi\) | ||||
0.870528 | + | 0.492119i | \(0.163778\pi\) | |||||||
\(948\) | −3.07819e34 | −1.79887 | ||||||||
\(949\) | 1.25481e34 | 0.724465 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.35651e33 | 0.301860 | ||||||||
\(952\) | −2.31685e33 | −0.128995 | ||||||||
\(953\) | −1.97292e34 | −1.08528 | −0.542641 | − | 0.839965i | \(-0.682575\pi\) | ||||
−0.542641 | + | 0.839965i | \(0.682575\pi\) | |||||||
\(954\) | 1.73997e34 | 0.945659 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.51236e33 | 0.451632 | ||||||||
\(957\) | 2.01734e33 | 0.105753 | ||||||||
\(958\) | 2.73973e34 | 1.41907 | ||||||||
\(959\) | 1.69210e34 | 0.865989 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.42003e33 | −0.0709542 | ||||||||
\(962\) | 1.78694e34 | 0.882261 | ||||||||
\(963\) | −3.42163e33 | −0.166929 | ||||||||
\(964\) | −1.11996e34 | −0.539904 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.13387e34 | 1.00446 | ||||||||
\(967\) | 2.03266e34 | 0.945496 | 0.472748 | − | 0.881198i | \(-0.343262\pi\) | ||||
0.472748 | + | 0.881198i | \(0.343262\pi\) | |||||||
\(968\) | 2.15869e33 | 0.0992255 | ||||||||
\(969\) | −5.66820e34 | −2.57467 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.40470e34 | 1.51028 | 0.755141 | − | 0.655563i | \(-0.227569\pi\) | ||||
0.755141 | + | 0.655563i | \(0.227569\pi\) | |||||||
\(972\) | 2.24494e34 | 0.984106 | ||||||||
\(973\) | 1.89552e33 | 0.0821166 | ||||||||
\(974\) | −3.45150e33 | −0.147768 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.16570e34 | −0.905579 | ||||||||
\(977\) | 3.68167e32 | 0.0152145 | 0.00760725 | − | 0.999971i | \(-0.497579\pi\) | ||||
0.00760725 | + | 0.999971i | \(0.497579\pi\) | |||||||
\(978\) | −4.07459e34 | −1.66413 | ||||||||
\(979\) | 1.15638e33 | 0.0466767 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.16740e33 | −0.124885 | ||||||||
\(982\) | −2.87225e34 | −1.11928 | ||||||||
\(983\) | 8.23724e33 | 0.317261 | 0.158630 | − | 0.987338i | \(-0.449292\pi\) | ||||
0.158630 | + | 0.987338i | \(0.449292\pi\) | |||||||
\(984\) | 1.41203e33 | 0.0537529 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.93689e34 | 0.720310 | ||||||||
\(987\) | 1.28511e34 | 0.472380 | ||||||||
\(988\) | −1.73238e34 | −0.629415 | ||||||||
\(989\) | −7.85000e32 | −0.0281911 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.70349e33 | 0.0948590 | 0.0474295 | − | 0.998875i | \(-0.484897\pi\) | ||||
0.0474295 | + | 0.998875i | \(0.484897\pi\) | |||||||
\(992\) | −3.83094e34 | −1.32868 | ||||||||
\(993\) | −6.31875e34 | −2.16628 | ||||||||
\(994\) | −1.17029e34 | −0.396598 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.32059e34 | −0.768452 | ||||||||
\(997\) | 4.64692e33 | 0.152115 | 0.0760573 | − | 0.997103i | \(-0.475767\pi\) | ||||
0.0760573 | + | 0.997103i | \(0.475767\pi\) | |||||||
\(998\) | 7.14561e34 | 2.31227 | ||||||||
\(999\) | 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 | 25.24.a.a.1.2 | 2 | ||
5.2 | odd | 4 | 25.24.b.a.24.3 | 4 | |||
5.3 | odd | 4 | 25.24.b.a.24.2 | 4 | |||
5.4 | even | 2 | 1.24.a.a.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 9.24.a.b.1.2 | 2 | |||
20.19 | odd | 2 | 16.24.a.b.1.1 | 2 | |||
35.34 | odd | 2 | 49.24.a.b.1.1 | 2 | |||
40.19 | odd | 2 | 64.24.a.g.1.2 | 2 | |||
40.29 | even | 2 | 64.24.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.24.a.a.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
9.24.a.b.1.2 | 2 | 15.14 | odd | 2 | |||
16.24.a.b.1.1 | 2 | 20.19 | odd | 2 | |||
25.24.a.a.1.2 | 2 | 1.1 | even | 1 | trivial | ||
25.24.b.a.24.2 | 4 | 5.3 | odd | 4 | |||
25.24.b.a.24.3 | 4 | 5.2 | odd | 4 | |||
49.24.a.b.1.1 | 2 | 35.34 | odd | 2 | |||
64.24.a.d.1.1 | 2 | 40.29 | even | 2 | |||
64.24.a.g.1.2 | 2 | 40.19 | odd | 2 |