Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,10,Mod(1,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.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: | \(13.9059675764\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.203942560.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 83x^{2} + 1440 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{8} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.96988\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −12.7978 | −0.565589 | −0.282794 | − | 0.959181i | \(-0.591261\pi\) | ||||
−0.282794 | + | 0.959181i | \(0.591261\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −348.216 | −0.680110 | ||||||||
\(5\) | −2019.77 | −1.44523 | −0.722615 | − | 0.691251i | \(-0.757060\pi\) | ||||
−0.722615 | + | 0.691251i | \(0.757060\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −665.864 | −0.104820 | −0.0524100 | − | 0.998626i | \(-0.516690\pi\) | ||||
−0.0524100 | + | 0.998626i | \(0.516690\pi\) | |||||||
\(8\) | 11008.9 | 0.950251 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 25848.6 | 0.817406 | ||||||||
\(11\) | −85435.1 | −1.75942 | −0.879709 | − | 0.475512i | \(-0.842263\pi\) | ||||
−0.879709 | + | 0.475512i | \(0.842263\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 84838.5 | 0.823850 | 0.411925 | − | 0.911218i | \(-0.364857\pi\) | ||||
0.411925 | + | 0.911218i | \(0.364857\pi\) | |||||||
\(14\) | 8521.60 | 0.0592851 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 37397.1 | 0.142658 | ||||||||
\(17\) | 139510. | 0.405122 | 0.202561 | − | 0.979270i | \(-0.435074\pi\) | ||||
0.202561 | + | 0.979270i | \(0.435074\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 993145. | 1.74832 | 0.874161 | − | 0.485636i | \(-0.161412\pi\) | ||||
0.874161 | + | 0.485636i | \(0.161412\pi\) | |||||||
\(20\) | 703317. | 0.982915 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.09338e6 | 0.995107 | ||||||||
\(23\) | −758529. | −0.565193 | −0.282597 | − | 0.959239i | \(-0.591196\pi\) | ||||
−0.282597 | + | 0.959239i | \(0.591196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.12635e6 | 1.08869 | ||||||||
\(26\) | −1.08575e6 | −0.465960 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 231865. | 0.0712891 | ||||||||
\(29\) | 4.04867e6 | 1.06297 | 0.531486 | − | 0.847067i | \(-0.321634\pi\) | ||||
0.531486 | + | 0.847067i | \(0.321634\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.01466e6 | −0.586288 | −0.293144 | − | 0.956068i | \(-0.594702\pi\) | ||||
−0.293144 | + | 0.956068i | \(0.594702\pi\) | |||||||
\(32\) | −6.11515e6 | −1.03094 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.78543e6 | −0.229133 | ||||||||
\(35\) | 1.34489e6 | 0.151489 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.04252e6 | 0.179168 | 0.0895838 | − | 0.995979i | \(-0.471446\pi\) | ||||
0.0895838 | + | 0.995979i | \(0.471446\pi\) | |||||||
\(38\) | −1.27101e7 | −0.988831 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.22354e7 | −1.37333 | ||||||||
\(41\) | 7.85245e6 | 0.433988 | 0.216994 | − | 0.976173i | \(-0.430375\pi\) | ||||
0.216994 | + | 0.976173i | \(0.430375\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.72306e7 | −1.21464 | −0.607322 | − | 0.794456i | \(-0.707756\pi\) | ||||
−0.607322 | + | 0.794456i | \(0.707756\pi\) | |||||||
\(44\) | 2.97499e7 | 1.19660 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.70751e6 | 0.319667 | ||||||||
\(47\) | 3.29865e7 | 0.986042 | 0.493021 | − | 0.870017i | \(-0.335893\pi\) | ||||
0.493021 | + | 0.870017i | \(0.335893\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.99102e7 | −0.989013 | ||||||||
\(50\) | −2.72126e7 | −0.615751 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.95421e7 | −0.560308 | ||||||||
\(53\) | −1.02265e8 | −1.78026 | −0.890131 | − | 0.455704i | \(-0.849388\pi\) | ||||
−0.890131 | + | 0.455704i | \(0.849388\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.72559e8 | 2.54276 | ||||||||
\(56\) | −7.33042e6 | −0.0996054 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.18141e7 | −0.601204 | ||||||||
\(59\) | 1.15657e8 | 1.24262 | 0.621308 | − | 0.783566i | \(-0.286601\pi\) | ||||
0.621308 | + | 0.783566i | \(0.286601\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.29214e8 | 1.19488 | 0.597439 | − | 0.801914i | \(-0.296185\pi\) | ||||
0.597439 | + | 0.801914i | \(0.296185\pi\) | |||||||
\(62\) | 3.85811e7 | 0.331598 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.91132e7 | 0.440428 | ||||||||
\(65\) | −1.71354e8 | −1.19065 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.95575e7 | −0.118570 | −0.0592852 | − | 0.998241i | \(-0.518882\pi\) | ||||
−0.0592852 | + | 0.998241i | \(0.518882\pi\) | |||||||
\(68\) | −4.85797e7 | −0.275528 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.72117e7 | −0.0856806 | ||||||||
\(71\) | 2.18178e8 | 1.01894 | 0.509471 | − | 0.860488i | \(-0.329841\pi\) | ||||
0.509471 | + | 0.860488i | \(0.329841\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.41427e8 | 1.81931 | 0.909653 | − | 0.415369i | \(-0.136347\pi\) | ||||
0.909653 | + | 0.415369i | \(0.136347\pi\) | |||||||
\(74\) | −2.61398e7 | −0.101335 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.45829e8 | −1.18905 | ||||||||
\(77\) | 5.68882e7 | 0.184422 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.09562e7 | −0.0316475 | −0.0158237 | − | 0.999875i | \(-0.505037\pi\) | ||||
−0.0158237 | + | 0.999875i | \(0.505037\pi\) | |||||||
\(80\) | −7.55335e7 | −0.206174 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.00494e8 | −0.245459 | ||||||||
\(83\) | 2.86843e8 | 0.663427 | 0.331714 | − | 0.943380i | \(-0.392373\pi\) | ||||
0.331714 | + | 0.943380i | \(0.392373\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.81779e8 | −0.585495 | ||||||||
\(86\) | 3.48492e8 | 0.686988 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.40544e8 | −1.67189 | ||||||||
\(89\) | −7.64398e8 | −1.29141 | −0.645706 | − | 0.763586i | \(-0.723437\pi\) | ||||
−0.645706 | + | 0.763586i | \(0.723437\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.64909e7 | −0.0863560 | ||||||||
\(92\) | 2.64132e8 | 0.384393 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.22154e8 | −0.557694 | ||||||||
\(95\) | −2.00593e9 | −2.52673 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 815669. | 0.000935494 0 | 0.000467747 | − | 1.00000i | \(-0.499851\pi\) | ||||
0.000467747 | 1.00000i | \(0.499851\pi\) | ||||||||
\(98\) | 5.10764e8 | 0.559374 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.40429e8 | −0.740429 | ||||||||
\(101\) | 8.80693e8 | 0.842129 | 0.421064 | − | 0.907031i | \(-0.361657\pi\) | ||||
0.421064 | + | 0.907031i | \(0.361657\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.47976e9 | 1.29546 | 0.647730 | − | 0.761870i | \(-0.275718\pi\) | ||||
0.647730 | + | 0.761870i | \(0.275718\pi\) | |||||||
\(104\) | 9.33977e8 | 0.782864 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.30876e9 | 1.00690 | ||||||||
\(107\) | 1.64812e9 | 1.21552 | 0.607759 | − | 0.794122i | \(-0.292069\pi\) | ||||
0.607759 | + | 0.794122i | \(0.292069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.21670e8 | −0.218268 | −0.109134 | − | 0.994027i | \(-0.534808\pi\) | ||||
−0.109134 | + | 0.994027i | \(0.534808\pi\) | |||||||
\(110\) | −2.20838e9 | −1.43816 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.49014e7 | −0.0149535 | ||||||||
\(113\) | 1.91951e9 | 1.10748 | 0.553741 | − | 0.832689i | \(-0.313200\pi\) | ||||
0.553741 | + | 0.832689i | \(0.313200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.53206e9 | 0.816835 | ||||||||
\(116\) | −1.40981e9 | −0.722937 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.48015e9 | −0.702810 | ||||||||
\(119\) | −9.28949e7 | −0.0424650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.94120e9 | 2.09555 | ||||||||
\(122\) | −1.65365e9 | −0.675810 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.04975e9 | 0.398740 | ||||||||
\(125\) | −3.49874e8 | −0.128179 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.81305e9 | −0.959535 | −0.479767 | − | 0.877396i | \(-0.659279\pi\) | ||||
−0.479767 | + | 0.877396i | \(0.659279\pi\) | |||||||
\(128\) | 2.37444e9 | 0.781836 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.19296e9 | 0.673419 | ||||||||
\(131\) | 7.34372e8 | 0.217869 | 0.108934 | − | 0.994049i | \(-0.465256\pi\) | ||||
0.108934 | + | 0.994049i | \(0.465256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.61300e8 | −0.183259 | ||||||||
\(134\) | 2.50293e8 | 0.0670621 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.53585e9 | 0.384968 | ||||||||
\(137\) | −1.00181e9 | −0.242964 | −0.121482 | − | 0.992594i | \(-0.538765\pi\) | ||||
−0.121482 | + | 0.992594i | \(0.538765\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.12304e9 | −0.482382 | −0.241191 | − | 0.970478i | \(-0.577538\pi\) | ||||
−0.241191 | + | 0.970478i | \(0.577538\pi\) | |||||||
\(140\) | −4.68313e8 | −0.103029 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.79221e9 | −0.576302 | ||||||||
\(143\) | −7.24818e9 | −1.44950 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.17739e9 | −1.53624 | ||||||||
\(146\) | −5.64930e9 | −1.02898 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.11240e8 | −0.121854 | ||||||||
\(149\) | 6.02059e9 | 1.00069 | 0.500346 | − | 0.865825i | \(-0.333206\pi\) | ||||
0.500346 | + | 0.865825i | \(0.333206\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.86951e9 | −1.38836 | −0.694182 | − | 0.719800i | \(-0.744234\pi\) | ||||
−0.694182 | + | 0.719800i | \(0.744234\pi\) | |||||||
\(152\) | 1.09334e10 | 1.66135 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.28044e8 | −0.104307 | ||||||||
\(155\) | 6.08893e9 | 0.847321 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.51721e9 | −0.330652 | −0.165326 | − | 0.986239i | \(-0.552868\pi\) | ||||
−0.165326 | + | 0.986239i | \(0.552868\pi\) | |||||||
\(158\) | 1.40216e8 | 0.0178994 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.23512e10 | 1.48994 | ||||||||
\(161\) | 5.05078e8 | 0.0592436 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.17153e8 | −0.0684776 | −0.0342388 | − | 0.999414i | \(-0.510901\pi\) | ||||
−0.0342388 | + | 0.999414i | \(0.510901\pi\) | |||||||
\(164\) | −2.73435e9 | −0.295160 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.67096e9 | −0.375227 | ||||||||
\(167\) | −1.06520e10 | −1.05976 | −0.529882 | − | 0.848072i | \(-0.677764\pi\) | ||||
−0.529882 | + | 0.848072i | \(0.677764\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.40693e9 | −0.321272 | ||||||||
\(170\) | 3.60615e9 | 0.331149 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.48212e9 | 0.826090 | ||||||||
\(173\) | −4.55410e8 | −0.0386540 | −0.0193270 | − | 0.999813i | \(-0.506152\pi\) | ||||
−0.0193270 | + | 0.999813i | \(0.506152\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.41586e9 | −0.114117 | ||||||||
\(176\) | −3.19502e9 | −0.250996 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.78262e9 | 0.730408 | ||||||||
\(179\) | −9.54934e9 | −0.695240 | −0.347620 | − | 0.937636i | \(-0.613010\pi\) | ||||
−0.347620 | + | 0.937636i | \(0.613010\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.10546e10 | 1.45812 | 0.729061 | − | 0.684449i | \(-0.239957\pi\) | ||||
0.729061 | + | 0.684449i | \(0.239957\pi\) | |||||||
\(182\) | 7.22960e8 | 0.0488420 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.35056e9 | −0.537075 | ||||||||
\(185\) | −4.12543e9 | −0.258938 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.19191e10 | −0.712779 | ||||||||
\(188\) | −1.14864e10 | −0.670617 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.56715e10 | 1.42909 | ||||||||
\(191\) | 2.71245e10 | 1.47473 | 0.737364 | − | 0.675496i | \(-0.236070\pi\) | ||||
0.737364 | + | 0.675496i | \(0.236070\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.06145e9 | 0.262583 | 0.131292 | − | 0.991344i | \(-0.458088\pi\) | ||||
0.131292 | + | 0.991344i | \(0.458088\pi\) | |||||||
\(194\) | −1.04388e7 | −0.000529105 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.38974e10 | 0.672637 | ||||||||
\(197\) | 1.23458e10 | 0.584010 | 0.292005 | − | 0.956417i | \(-0.405678\pi\) | ||||
0.292005 | + | 0.956417i | \(0.405678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.20900e10 | 0.546497 | 0.273249 | − | 0.961943i | \(-0.411902\pi\) | ||||
0.273249 | + | 0.961943i | \(0.411902\pi\) | |||||||
\(200\) | 2.34087e10 | 1.03453 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.12709e10 | −0.476299 | ||||||||
\(203\) | −2.69587e9 | −0.111421 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.58602e10 | −0.627213 | ||||||||
\(206\) | −1.89377e10 | −0.732698 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.17271e9 | 0.117529 | ||||||||
\(209\) | −8.48494e10 | −3.07603 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.72325e10 | −0.598516 | −0.299258 | − | 0.954172i | \(-0.596739\pi\) | ||||
−0.299258 | + | 0.954172i | \(0.596739\pi\) | |||||||
\(212\) | 3.56102e10 | 1.21077 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.10923e10 | −0.687483 | ||||||||
\(215\) | 5.49995e10 | 1.75544 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00736e9 | 0.0614548 | ||||||||
\(218\) | 4.11667e9 | 0.123450 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.00879e10 | −1.72936 | ||||||||
\(221\) | 1.18358e10 | 0.333760 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.12781e10 | −0.846972 | −0.423486 | − | 0.905903i | \(-0.639194\pi\) | ||||
−0.423486 | + | 0.905903i | \(0.639194\pi\) | |||||||
\(224\) | 4.07186e9 | 0.108063 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.45655e10 | −0.626379 | ||||||||
\(227\) | 9.86598e9 | 0.246617 | 0.123309 | − | 0.992368i | \(-0.460649\pi\) | ||||
0.123309 | + | 0.992368i | \(0.460649\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.08107e10 | 0.980651 | 0.490325 | − | 0.871539i | \(-0.336878\pi\) | ||||
0.490325 | + | 0.871539i | \(0.336878\pi\) | |||||||
\(230\) | −1.96070e10 | −0.461992 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.45713e10 | 1.01009 | ||||||||
\(233\) | −3.65168e10 | −0.811693 | −0.405846 | − | 0.913941i | \(-0.633023\pi\) | ||||
−0.405846 | + | 0.913941i | \(0.633023\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.66251e10 | −1.42506 | ||||||||
\(236\) | −4.02736e10 | −0.845115 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.18885e9 | 0.0240177 | ||||||||
\(239\) | −5.78935e9 | −0.114773 | −0.0573865 | − | 0.998352i | \(-0.518277\pi\) | ||||
−0.0573865 | + | 0.998352i | \(0.518277\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.33566e10 | 0.445998 | 0.222999 | − | 0.974819i | \(-0.428415\pi\) | ||||
0.222999 | + | 0.974819i | \(0.428415\pi\) | |||||||
\(242\) | −6.32366e10 | −1.18522 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.49942e10 | −0.812649 | ||||||||
\(245\) | 8.06095e10 | 1.42935 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.42570e10 | 1.44035 | ||||||||
\(248\) | −3.31881e10 | −0.557121 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.47761e9 | 0.0724964 | ||||||||
\(251\) | −1.44384e10 | −0.229608 | −0.114804 | − | 0.993388i | \(-0.536624\pi\) | ||||
−0.114804 | + | 0.993388i | \(0.536624\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.48050e10 | 0.994411 | ||||||||
\(254\) | 3.60009e10 | 0.542702 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.06535e10 | −0.882625 | ||||||||
\(257\) | 9.77486e10 | 1.39769 | 0.698846 | − | 0.715272i | \(-0.253697\pi\) | ||||
0.698846 | + | 0.715272i | \(0.253697\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.36004e9 | −0.0187804 | ||||||||
\(260\) | 5.96683e10 | 0.809774 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.39835e9 | −0.123224 | ||||||||
\(263\) | −2.94535e10 | −0.379609 | −0.189804 | − | 0.981822i | \(-0.560785\pi\) | ||||
−0.189804 | + | 0.981822i | \(0.560785\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.06551e11 | 2.57289 | ||||||||
\(266\) | 8.46319e9 | 0.103649 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.81023e9 | 0.0806409 | ||||||||
\(269\) | 6.86011e10 | 0.798814 | 0.399407 | − | 0.916774i | \(-0.369216\pi\) | ||||
0.399407 | + | 0.916774i | \(0.369216\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.74978e10 | −0.760200 | −0.380100 | − | 0.924945i | \(-0.624110\pi\) | ||||
−0.380100 | + | 0.924945i | \(0.624110\pi\) | |||||||
\(272\) | 5.21728e9 | 0.0577941 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.28209e10 | 0.137417 | ||||||||
\(275\) | −1.81665e11 | −1.91546 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.24779e10 | 0.637628 | 0.318814 | − | 0.947817i | \(-0.396715\pi\) | ||||
0.318814 | + | 0.947817i | \(0.396715\pi\) | |||||||
\(278\) | 2.71702e10 | 0.272830 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.48058e10 | 0.143953 | ||||||||
\(281\) | −8.68104e10 | −0.830603 | −0.415301 | − | 0.909684i | \(-0.636324\pi\) | ||||
−0.415301 | + | 0.909684i | \(0.636324\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.37271e11 | 1.27216 | 0.636078 | − | 0.771625i | \(-0.280556\pi\) | ||||
0.636078 | + | 0.771625i | \(0.280556\pi\) | |||||||
\(284\) | −7.59733e10 | −0.692992 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.27609e10 | 0.819818 | ||||||||
\(287\) | −5.22867e9 | −0.0454907 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.91248e10 | −0.835876 | ||||||||
\(290\) | 1.04653e11 | 0.868879 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.53712e11 | −1.23733 | ||||||||
\(293\) | 1.06733e11 | 0.846050 | 0.423025 | − | 0.906118i | \(-0.360968\pi\) | ||||
0.423025 | + | 0.906118i | \(0.360968\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.33600e11 | −1.79587 | ||||||||
\(296\) | 2.24859e10 | 0.170254 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.70503e10 | −0.565980 | ||||||||
\(299\) | −6.43525e10 | −0.465634 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.81319e10 | 0.127319 | ||||||||
\(302\) | 1.13510e11 | 0.785243 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.71407e10 | 0.249413 | ||||||||
\(305\) | −2.60982e11 | −1.72688 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.13729e11 | −0.730716 | −0.365358 | − | 0.930867i | \(-0.619054\pi\) | ||||
−0.365358 | + | 0.930867i | \(0.619054\pi\) | |||||||
\(308\) | −1.98094e10 | −0.125427 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.79249e10 | −0.479235 | ||||||||
\(311\) | 1.66986e9 | 0.0101218 | 0.00506091 | − | 0.999987i | \(-0.498389\pi\) | ||||
0.00506091 | + | 0.999987i | \(0.498389\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.22551e10 | 0.307736 | 0.153868 | − | 0.988091i | \(-0.450827\pi\) | ||||
0.153868 | + | 0.988091i | \(0.450827\pi\) | |||||||
\(314\) | 3.22148e10 | 0.187013 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.81513e9 | 0.0215237 | ||||||||
\(317\) | 1.76926e11 | 0.984070 | 0.492035 | − | 0.870575i | \(-0.336253\pi\) | ||||
0.492035 | + | 0.870575i | \(0.336253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.45898e11 | −1.87021 | ||||||||
\(320\) | −1.19395e11 | −0.636519 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.46389e9 | −0.0335075 | ||||||||
\(323\) | 1.38554e11 | 0.708284 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.80396e11 | 0.896918 | ||||||||
\(326\) | 7.89820e9 | 0.0387301 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.64467e10 | 0.412398 | ||||||||
\(329\) | −2.19645e10 | −0.103357 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.59523e11 | −0.730461 | −0.365231 | − | 0.930917i | \(-0.619010\pi\) | ||||
−0.365231 | + | 0.930917i | \(0.619010\pi\) | |||||||
\(332\) | −9.98834e10 | −0.451203 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.36323e11 | 0.599390 | ||||||||
\(335\) | 3.95017e10 | 0.171362 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.07204e11 | 0.452769 | 0.226384 | − | 0.974038i | \(-0.427309\pi\) | ||||
0.226384 | + | 0.974038i | \(0.427309\pi\) | |||||||
\(338\) | 4.36012e10 | 0.181708 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.81199e10 | 0.398201 | ||||||||
\(341\) | 2.57558e11 | 1.03153 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.34448e10 | 0.208489 | ||||||||
\(344\) | −2.99778e11 | −1.15422 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.82824e9 | 0.0218623 | ||||||||
\(347\) | 4.80474e11 | 1.77904 | 0.889522 | − | 0.456892i | \(-0.151037\pi\) | ||||
0.889522 | + | 0.456892i | \(0.151037\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.05930e11 | −0.743027 | −0.371514 | − | 0.928428i | \(-0.621161\pi\) | ||||
−0.371514 | + | 0.928428i | \(0.621161\pi\) | |||||||
\(350\) | 1.81199e10 | 0.0645431 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.22448e11 | 1.81385 | ||||||||
\(353\) | −2.84250e11 | −0.974348 | −0.487174 | − | 0.873305i | \(-0.661972\pi\) | ||||
−0.487174 | + | 0.873305i | \(0.661972\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.40671e11 | −1.47261 | ||||||||
\(356\) | 2.66176e11 | 0.878301 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.22211e11 | 0.393220 | ||||||||
\(359\) | −3.45110e11 | −1.09656 | −0.548280 | − | 0.836295i | \(-0.684717\pi\) | ||||
−0.548280 | + | 0.836295i | \(0.684717\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.63650e11 | 2.05663 | ||||||||
\(362\) | −2.69453e11 | −0.824697 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.96711e10 | 0.0587315 | ||||||||
\(365\) | −8.91581e11 | −2.62932 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.68807e10 | 0.221218 | 0.110609 | − | 0.993864i | \(-0.464720\pi\) | ||||
0.110609 | + | 0.993864i | \(0.464720\pi\) | |||||||
\(368\) | −2.83668e10 | −0.0806296 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.27965e10 | 0.146453 | ||||||||
\(371\) | 6.80944e10 | 0.186607 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.76354e11 | 1.00671 | 0.503357 | − | 0.864078i | \(-0.332098\pi\) | ||||
0.503357 | + | 0.864078i | \(0.332098\pi\) | |||||||
\(374\) | 1.52538e11 | 0.403140 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.63144e11 | 0.936987 | ||||||||
\(377\) | 3.43483e11 | 0.875728 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.18048e11 | −0.791801 | −0.395900 | − | 0.918294i | \(-0.629567\pi\) | ||||
−0.395900 | + | 0.918294i | \(0.629567\pi\) | |||||||
\(380\) | 6.98496e11 | 1.71845 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.47135e11 | −0.834089 | ||||||||
\(383\) | 1.21289e11 | 0.288023 | 0.144011 | − | 0.989576i | \(-0.454000\pi\) | ||||
0.144011 | + | 0.989576i | \(0.454000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.14901e11 | −0.266533 | ||||||||
\(386\) | −6.47755e10 | −0.148514 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.84029e8 | −0.000636239 0 | ||||||||
\(389\) | 7.63532e11 | 1.69065 | 0.845325 | − | 0.534252i | \(-0.179407\pi\) | ||||
0.845325 | + | 0.534252i | \(0.179407\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.05823e11 | −0.228972 | ||||||||
\(392\) | −4.39367e11 | −0.939810 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.57999e11 | −0.330309 | ||||||||
\(395\) | 2.21291e10 | 0.0457379 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.37941e11 | −1.08687 | −0.543435 | − | 0.839451i | \(-0.682876\pi\) | ||||
−0.543435 | + | 0.839451i | \(0.682876\pi\) | |||||||
\(398\) | −1.54726e11 | −0.309093 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.95192e10 | 0.155311 | ||||||||
\(401\) | −2.23876e11 | −0.432373 | −0.216187 | − | 0.976352i | \(-0.569362\pi\) | ||||
−0.216187 | + | 0.976352i | \(0.569362\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.55760e11 | −0.483013 | ||||||||
\(404\) | −3.06672e11 | −0.572740 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.45012e10 | 0.0630183 | ||||||||
\(407\) | −1.74503e11 | −0.315231 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.59201e11 | −1.69494 | −0.847471 | − | 0.530842i | \(-0.821876\pi\) | ||||
−0.847471 | + | 0.530842i | \(0.821876\pi\) | |||||||
\(410\) | 2.02975e11 | 0.354745 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.15277e11 | −0.881055 | ||||||||
\(413\) | −7.70117e10 | −0.130251 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.79358e11 | −0.958805 | ||||||||
\(416\) | −5.18800e11 | −0.849337 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.08589e12 | 1.73977 | ||||||||
\(419\) | 8.85619e11 | 1.40373 | 0.701865 | − | 0.712310i | \(-0.252351\pi\) | ||||
0.701865 | + | 0.712310i | \(0.252351\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.06418e12 | 1.65100 | 0.825498 | − | 0.564405i | \(-0.190894\pi\) | ||||
0.825498 | + | 0.564405i | \(0.190894\pi\) | |||||||
\(422\) | 2.20538e11 | 0.338514 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.12582e12 | −1.69170 | ||||||||
\(425\) | 2.96648e11 | 0.441053 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.60387e10 | −0.125247 | ||||||||
\(428\) | −5.73901e11 | −0.826685 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.03873e11 | −0.992857 | ||||||||
\(431\) | −4.41717e11 | −0.616589 | −0.308295 | − | 0.951291i | \(-0.599758\pi\) | ||||
−0.308295 | + | 0.951291i | \(0.599758\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.91127e11 | 1.21827 | 0.609136 | − | 0.793066i | \(-0.291516\pi\) | ||||
0.609136 | + | 0.793066i | \(0.291516\pi\) | |||||||
\(434\) | −2.56898e10 | −0.0347581 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.12011e11 | 0.148446 | ||||||||
\(437\) | −7.53330e11 | −0.988140 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.66122e11 | −0.470474 | −0.235237 | − | 0.971938i | \(-0.575587\pi\) | ||||
−0.235237 | + | 0.971938i | \(0.575587\pi\) | |||||||
\(440\) | 1.89968e12 | 2.41626 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.51473e11 | −0.188771 | ||||||||
\(443\) | −6.97003e11 | −0.859840 | −0.429920 | − | 0.902867i | \(-0.641458\pi\) | ||||
−0.429920 | + | 0.902867i | \(0.641458\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.54391e12 | 1.86639 | ||||||||
\(446\) | 4.00292e11 | 0.479038 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.93614e10 | −0.0461657 | ||||||||
\(449\) | −8.70295e11 | −1.01055 | −0.505275 | − | 0.862958i | \(-0.668609\pi\) | ||||
−0.505275 | + | 0.862958i | \(0.668609\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.70875e11 | −0.763567 | ||||||||
\(452\) | −6.68403e11 | −0.753208 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.26263e11 | −0.139484 | ||||||||
\(455\) | 1.14099e11 | 0.124804 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.32855e11 | 0.893195 | 0.446598 | − | 0.894735i | \(-0.352636\pi\) | ||||
0.446598 | + | 0.894735i | \(0.352636\pi\) | |||||||
\(458\) | −5.22287e11 | −0.554645 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.33486e11 | −0.555537 | ||||||||
\(461\) | −1.63782e11 | −0.168893 | −0.0844467 | − | 0.996428i | \(-0.526912\pi\) | ||||
−0.0844467 | + | 0.996428i | \(0.526912\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.51302e11 | 0.759801 | 0.379901 | − | 0.925027i | \(-0.375958\pi\) | ||||
0.379901 | + | 0.925027i | \(0.375958\pi\) | |||||||
\(464\) | 1.51408e11 | 0.151642 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.67336e11 | 0.459084 | ||||||||
\(467\) | −3.65892e11 | −0.355981 | −0.177991 | − | 0.984032i | \(-0.556960\pi\) | ||||
−0.177991 | + | 0.984032i | \(0.556960\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.30226e10 | 0.0124286 | ||||||||
\(470\) | 8.52655e11 | 0.805996 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.27325e12 | 1.18080 | ||||||||
\(473\) | 2.32645e12 | 2.13707 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.11177e12 | 1.90338 | ||||||||
\(476\) | 3.23475e10 | 0.0288808 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.40910e10 | 0.0649142 | ||||||||
\(479\) | 5.30846e11 | 0.460743 | 0.230371 | − | 0.973103i | \(-0.426006\pi\) | ||||
0.230371 | + | 0.973103i | \(0.426006\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.73285e11 | 0.147607 | ||||||||
\(482\) | −2.98913e11 | −0.252251 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.72061e12 | −1.42520 | ||||||||
\(485\) | −1.64746e9 | −0.00135200 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.23142e11 | 0.743684 | 0.371842 | − | 0.928296i | \(-0.378726\pi\) | ||||
0.371842 | + | 0.928296i | \(0.378726\pi\) | |||||||
\(488\) | 1.42250e12 | 1.13543 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.03163e12 | −0.808425 | ||||||||
\(491\) | −1.62628e12 | −1.26278 | −0.631391 | − | 0.775465i | \(-0.717516\pi\) | ||||
−0.631391 | + | 0.775465i | \(0.717516\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.64831e11 | 0.430633 | ||||||||
\(494\) | −1.07830e12 | −0.814648 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.12740e11 | −0.0836390 | ||||||||
\(497\) | −1.45277e11 | −0.106806 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.59222e11 | −0.475970 | −0.237985 | − | 0.971269i | \(-0.576487\pi\) | ||||
−0.237985 | + | 0.971269i | \(0.576487\pi\) | |||||||
\(500\) | 1.21832e11 | 0.0871756 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.84780e11 | 0.129864 | ||||||||
\(503\) | 6.69047e11 | 0.466016 | 0.233008 | − | 0.972475i | \(-0.425143\pi\) | ||||
0.233008 | + | 0.972475i | \(0.425143\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.77880e12 | −1.21707 | ||||||||
\(506\) | −8.29362e11 | −0.562428 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.79549e11 | 0.652589 | ||||||||
\(509\) | −4.58197e11 | −0.302568 | −0.151284 | − | 0.988490i | \(-0.548341\pi\) | ||||
−0.151284 | + | 0.988490i | \(0.548341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.93930e11 | −0.190700 | ||||||||
\(512\) | −4.39479e11 | −0.282633 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.25097e12 | −0.790518 | ||||||||
\(515\) | −2.98878e12 | −1.87224 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.81820e12 | −1.73486 | ||||||||
\(518\) | 1.74056e10 | 0.0106220 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.88642e12 | −1.13142 | ||||||||
\(521\) | 3.34551e12 | 1.98926 | 0.994632 | − | 0.103472i | \(-0.0329952\pi\) | ||||
0.994632 | + | 0.103472i | \(0.0329952\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.03945e12 | 1.19194 | 0.595970 | − | 0.803007i | \(-0.296768\pi\) | ||||
0.595970 | + | 0.803007i | \(0.296768\pi\) | |||||||
\(524\) | −2.55720e11 | −0.148175 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.76940e11 | 0.214702 | ||||||||
\(527\) | −4.20577e11 | −0.237518 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.22579e12 | −0.680556 | ||||||||
\(530\) | −2.64340e12 | −1.45520 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.30275e11 | 0.124636 | ||||||||
\(533\) | 6.66190e11 | 0.357541 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.32882e12 | −1.75670 | ||||||||
\(536\) | −2.15306e11 | −0.112672 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.77944e11 | −0.451800 | ||||||||
\(539\) | 3.40973e12 | 1.74009 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.69312e12 | 1.85355 | 0.926777 | − | 0.375612i | \(-0.122567\pi\) | ||||
0.926777 | + | 0.375612i | \(0.122567\pi\) | |||||||
\(542\) | 8.63825e11 | 0.429961 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.53126e11 | −0.417655 | ||||||||
\(545\) | 6.49699e11 | 0.315448 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.88944e11 | 0.281275 | 0.140637 | − | 0.990061i | \(-0.455085\pi\) | ||||
0.140637 | + | 0.990061i | \(0.455085\pi\) | |||||||
\(548\) | 3.48845e11 | 0.165242 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.32491e12 | 1.08336 | ||||||||
\(551\) | 4.02092e12 | 1.85842 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.29536e9 | 0.00331729 | ||||||||
\(554\) | −7.99580e11 | −0.360635 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.39275e11 | 0.328072 | ||||||||
\(557\) | −3.85457e12 | −1.69679 | −0.848394 | − | 0.529366i | \(-0.822430\pi\) | ||||
−0.848394 | + | 0.529366i | \(0.822430\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.31020e12 | −1.00068 | ||||||||
\(560\) | 5.02951e10 | 0.0216112 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.11098e12 | 0.469779 | ||||||||
\(563\) | −3.03834e12 | −1.27453 | −0.637264 | − | 0.770646i | \(-0.719934\pi\) | ||||
−0.637264 | + | 0.770646i | \(0.719934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.87696e12 | −1.60057 | ||||||||
\(566\) | −1.75677e12 | −0.719517 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.40190e12 | 0.968250 | ||||||||
\(569\) | −5.83227e11 | −0.233256 | −0.116628 | − | 0.993176i | \(-0.537208\pi\) | ||||
−0.116628 | + | 0.993176i | \(0.537208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.09092e12 | −0.823142 | −0.411571 | − | 0.911378i | \(-0.635020\pi\) | ||||
−0.411571 | + | 0.911378i | \(0.635020\pi\) | |||||||
\(572\) | 2.52393e12 | 0.985816 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.69155e10 | 0.0257290 | ||||||||
\(575\) | −1.61290e12 | −0.615321 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.05766e12 | 1.14841 | 0.574206 | − | 0.818711i | \(-0.305311\pi\) | ||||
0.574206 | + | 0.818711i | \(0.305311\pi\) | |||||||
\(578\) | 1.26858e12 | 0.472762 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.84750e12 | 1.04481 | ||||||||
\(581\) | −1.90999e11 | −0.0695405 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.73699e12 | 3.13223 | ||||||||
\(584\) | 4.85962e12 | 1.72880 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.36595e12 | −0.478516 | ||||||||
\(587\) | 1.81796e12 | 0.631995 | 0.315997 | − | 0.948760i | \(-0.397661\pi\) | ||||
0.315997 | + | 0.948760i | \(0.397661\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.99400e12 | −1.02502 | ||||||||
\(590\) | 2.98957e12 | 1.01572 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.63844e10 | 0.0255598 | ||||||||
\(593\) | −1.51787e12 | −0.504067 | −0.252034 | − | 0.967719i | \(-0.581099\pi\) | ||||
−0.252034 | + | 0.967719i | \(0.581099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.87626e11 | 0.0613716 | ||||||||
\(596\) | −2.09647e12 | −0.680581 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.23571e11 | 0.263357 | ||||||||
\(599\) | 2.38179e12 | 0.755932 | 0.377966 | − | 0.925819i | \(-0.376624\pi\) | ||||
0.377966 | + | 0.925819i | \(0.376624\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.56564e12 | −0.489506 | −0.244753 | − | 0.969586i | \(-0.578707\pi\) | ||||
−0.244753 | + | 0.969586i | \(0.578707\pi\) | |||||||
\(602\) | −2.32048e11 | −0.0720102 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.08851e12 | 0.944239 | ||||||||
\(605\) | −9.98009e12 | −3.02855 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.20030e12 | 1.25583 | 0.627915 | − | 0.778282i | \(-0.283908\pi\) | ||||
0.627915 | + | 0.778282i | \(0.283908\pi\) | |||||||
\(608\) | −6.07323e12 | −1.80241 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.34000e12 | 0.976701 | ||||||||
\(611\) | 2.79852e12 | 0.812350 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.01770e12 | −0.863186 | −0.431593 | − | 0.902068i | \(-0.642048\pi\) | ||||
−0.431593 | + | 0.902068i | \(0.642048\pi\) | |||||||
\(614\) | 1.45548e12 | 0.413285 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.26275e11 | 0.175247 | ||||||||
\(617\) | 1.00060e12 | 0.277958 | 0.138979 | − | 0.990295i | \(-0.455618\pi\) | ||||
0.138979 | + | 0.990295i | \(0.455618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.40437e12 | −1.20580 | −0.602901 | − | 0.797816i | \(-0.705989\pi\) | ||||
−0.602901 | + | 0.797816i | \(0.705989\pi\) | |||||||
\(620\) | −2.12026e12 | −0.576271 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.13706e10 | −0.00572479 | ||||||||
\(623\) | 5.08985e11 | 0.135366 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.44636e12 | −0.903443 | ||||||||
\(626\) | −6.68750e11 | −0.174052 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.76534e11 | 0.224880 | ||||||||
\(629\) | 2.84953e11 | 0.0725848 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.71463e11 | −0.118390 | −0.0591950 | − | 0.998246i | \(-0.518853\pi\) | ||||
−0.0591950 | + | 0.998246i | \(0.518853\pi\) | |||||||
\(632\) | −1.20616e11 | −0.0300730 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.26427e12 | −0.556579 | ||||||||
\(635\) | 5.68172e12 | 1.38675 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.38592e12 | −0.814798 | ||||||||
\(638\) | 4.42674e12 | 1.05777 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.79582e12 | −1.12993 | ||||||||
\(641\) | 3.52736e12 | 0.825256 | 0.412628 | − | 0.910900i | \(-0.364611\pi\) | ||||
0.412628 | + | 0.910900i | \(0.364611\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.60256e12 | 1.06182 | 0.530909 | − | 0.847429i | \(-0.321851\pi\) | ||||
0.530909 | + | 0.847429i | \(0.321851\pi\) | |||||||
\(644\) | −1.75876e11 | −0.0402922 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.77319e12 | −0.400598 | ||||||||
\(647\) | −5.52821e12 | −1.24027 | −0.620134 | − | 0.784496i | \(-0.712922\pi\) | ||||
−0.620134 | + | 0.784496i | \(0.712922\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.88115e12 | −2.18628 | ||||||||
\(650\) | −2.30868e12 | −0.507286 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.14902e11 | 0.0465723 | ||||||||
\(653\) | 6.02691e12 | 1.29714 | 0.648568 | − | 0.761157i | \(-0.275368\pi\) | ||||
0.648568 | + | 0.761157i | \(0.275368\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.48326e12 | −0.314871 | ||||||||
\(656\) | 2.93659e11 | 0.0619121 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.81098e11 | 0.0584575 | ||||||||
\(659\) | 2.97106e11 | 0.0613658 | 0.0306829 | − | 0.999529i | \(-0.490232\pi\) | ||||
0.0306829 | + | 0.999529i | \(0.490232\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.47716e12 | 1.11596 | 0.557981 | − | 0.829854i | \(-0.311576\pi\) | ||||
0.557981 | + | 0.829854i | \(0.311576\pi\) | |||||||
\(662\) | 2.04154e12 | 0.413141 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.15782e12 | 0.630422 | ||||||||
\(665\) | 1.33567e12 | 0.264852 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.07103e12 | −0.600784 | ||||||||
\(668\) | 3.70921e12 | 0.720755 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.05535e11 | −0.0969202 | ||||||||
\(671\) | −1.10394e13 | −2.10229 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.06690e12 | −0.764180 | −0.382090 | − | 0.924125i | \(-0.624795\pi\) | ||||
−0.382090 | + | 0.924125i | \(0.624795\pi\) | |||||||
\(674\) | −1.37198e12 | −0.256081 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.18635e12 | 0.218500 | ||||||||
\(677\) | 4.84588e12 | 0.886591 | 0.443295 | − | 0.896376i | \(-0.353809\pi\) | ||||
0.443295 | + | 0.896376i | \(0.353809\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.43125e8 | −9.80586e−5 0 | ||||||||
\(680\) | −3.10207e12 | −0.556367 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.29618e12 | −0.583419 | ||||||||
\(683\) | −5.80468e12 | −1.02067 | −0.510334 | − | 0.859976i | \(-0.670478\pi\) | ||||
−0.510334 | + | 0.859976i | \(0.670478\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.02342e12 | 0.351138 | ||||||||
\(686\) | −6.83977e11 | −0.117919 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.01834e12 | −0.173279 | ||||||||
\(689\) | −8.67598e12 | −1.46667 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.46733e12 | 1.57971 | 0.789853 | − | 0.613296i | \(-0.210157\pi\) | ||||
0.789853 | + | 0.613296i | \(0.210157\pi\) | |||||||
\(692\) | 1.58581e11 | 0.0262890 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.14901e12 | −1.00621 | ||||||||
\(695\) | 4.28805e12 | 0.697153 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.09550e12 | 0.175818 | ||||||||
\(698\) | 2.63545e12 | 0.420248 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.93025e11 | 0.0776118 | ||||||||
\(701\) | 7.16819e12 | 1.12119 | 0.560594 | − | 0.828091i | \(-0.310573\pi\) | ||||
0.560594 | + | 0.828091i | \(0.310573\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.02852e12 | 0.313243 | ||||||||
\(704\) | −5.05034e12 | −0.774896 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.63778e12 | 0.551080 | ||||||||
\(707\) | −5.86422e11 | −0.0882720 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.05585e12 | 0.454175 | 0.227088 | − | 0.973874i | \(-0.427080\pi\) | ||||
0.227088 | + | 0.973874i | \(0.427080\pi\) | |||||||
\(710\) | 5.63962e12 | 0.832889 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.41517e12 | −1.22716 | ||||||||
\(713\) | 2.28671e12 | 0.331366 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.46397e13 | 2.09486 | ||||||||
\(716\) | 3.32523e12 | 0.472839 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.41665e12 | 0.620202 | ||||||||
\(719\) | −5.43142e12 | −0.757938 | −0.378969 | − | 0.925409i | \(-0.623721\pi\) | ||||
−0.378969 | + | 0.925409i | \(0.623721\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.85320e11 | −0.135790 | ||||||||
\(722\) | −8.49327e12 | −1.16321 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.33155e12 | −0.991682 | ||||||||
\(725\) | 8.60889e12 | 1.15725 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.25700e12 | 0.963502 | 0.481751 | − | 0.876308i | \(-0.340001\pi\) | ||||
0.481751 | + | 0.876308i | \(0.340001\pi\) | |||||||
\(728\) | −6.21902e11 | −0.0820599 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.14103e13 | 1.48711 | ||||||||
\(731\) | −3.79895e12 | −0.492079 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.75487e11 | 0.112016 | 0.0560082 | − | 0.998430i | \(-0.482163\pi\) | ||||
0.0560082 | + | 0.998430i | \(0.482163\pi\) | |||||||
\(734\) | −9.83905e11 | −0.125118 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.63852e12 | 0.582679 | ||||||||
\(737\) | 1.67090e12 | 0.208615 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.05185e12 | 0.376411 | 0.188206 | − | 0.982130i | \(-0.439733\pi\) | ||||
0.188206 | + | 0.982130i | \(0.439733\pi\) | |||||||
\(740\) | 1.43654e12 | 0.176106 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.71459e11 | −0.105543 | ||||||||
\(743\) | −8.89001e11 | −0.107017 | −0.0535085 | − | 0.998567i | \(-0.517040\pi\) | ||||
−0.0535085 | + | 0.998567i | \(0.517040\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.21602e13 | −1.44623 | ||||||||
\(746\) | −4.81650e12 | −0.569386 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.15041e12 | 0.484768 | ||||||||
\(749\) | −1.09742e12 | −0.127411 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.97996e12 | 0.800707 | 0.400353 | − | 0.916361i | \(-0.368887\pi\) | ||||
0.400353 | + | 0.916361i | \(0.368887\pi\) | |||||||
\(752\) | 1.23360e12 | 0.140667 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.39583e12 | −0.495302 | ||||||||
\(755\) | 1.79144e13 | 2.00651 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.54121e13 | 1.70581 | 0.852905 | − | 0.522066i | \(-0.174838\pi\) | ||||
0.852905 | + | 0.522066i | \(0.174838\pi\) | |||||||
\(758\) | 4.07031e12 | 0.447833 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.20830e13 | −2.40103 | ||||||||
\(761\) | −8.97482e12 | −0.970052 | −0.485026 | − | 0.874500i | \(-0.661190\pi\) | ||||
−0.485026 | + | 0.874500i | \(0.661190\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.14188e11 | 0.0228789 | ||||||||
\(764\) | −9.44520e12 | −1.00298 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.55223e12 | −0.162902 | ||||||||
\(767\) | 9.81215e12 | 1.02373 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.29561e12 | 0.236718 | 0.118359 | − | 0.992971i | \(-0.462237\pi\) | ||||
0.118359 | + | 0.992971i | \(0.462237\pi\) | |||||||
\(770\) | 1.47048e12 | 0.150748 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.76248e12 | −0.178585 | ||||||||
\(773\) | −4.85355e12 | −0.488936 | −0.244468 | − | 0.969657i | \(-0.578613\pi\) | ||||
−0.244468 | + | 0.969657i | \(0.578613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.41023e12 | −0.638287 | ||||||||
\(776\) | 8.97960e9 | 0.000888954 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.77154e12 | −0.956213 | ||||||||
\(779\) | 7.79863e12 | 0.758752 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.86401e13 | −1.79274 | ||||||||
\(782\) | 1.35430e12 | 0.129504 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.49253e12 | −0.141091 | ||||||||
\(785\) | 5.08419e12 | 0.477869 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.25927e13 | −1.17013 | −0.585063 | − | 0.810987i | \(-0.698930\pi\) | ||||
−0.585063 | + | 0.810987i | \(0.698930\pi\) | |||||||
\(788\) | −4.29899e12 | −0.397191 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.83203e11 | −0.0258688 | ||||||||
\(791\) | −1.27813e12 | −0.116086 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.09623e13 | 0.984400 | ||||||||
\(794\) | 6.88447e12 | 0.614721 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.20994e12 | −0.371678 | ||||||||
\(797\) | 5.33654e12 | 0.468487 | 0.234243 | − | 0.972178i | \(-0.424739\pi\) | ||||
0.234243 | + | 0.972178i | \(0.424739\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.60195e12 | 0.399468 | ||||||||
\(800\) | −1.30029e13 | −1.12237 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.86513e12 | 0.244545 | ||||||||
\(803\) | −3.77133e13 | −3.20092 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.02014e12 | −0.0856207 | ||||||||
\(806\) | 3.27316e12 | 0.273187 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.69545e12 | 0.800234 | ||||||||
\(809\) | −2.28889e13 | −1.87870 | −0.939348 | − | 0.342964i | \(-0.888569\pi\) | ||||
−0.939348 | + | 0.342964i | \(0.888569\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.01947e11 | −0.0732128 | −0.0366064 | − | 0.999330i | \(-0.511655\pi\) | ||||
−0.0366064 | + | 0.999330i | \(0.511655\pi\) | |||||||
\(812\) | 9.38744e11 | 0.0757783 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.23326e12 | 0.178291 | ||||||||
\(815\) | 1.24651e12 | 0.0989659 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.70439e13 | −2.12359 | ||||||||
\(818\) | 1.22757e13 | 0.958640 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.52276e12 | 0.426574 | ||||||||
\(821\) | −7.51091e12 | −0.576963 | −0.288482 | − | 0.957485i | \(-0.593150\pi\) | ||||
−0.288482 | + | 0.957485i | \(0.593150\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.53129e13 | −1.16348 | −0.581738 | − | 0.813377i | \(-0.697627\pi\) | ||||
−0.581738 | + | 0.813377i | \(0.697627\pi\) | |||||||
\(824\) | 1.62905e13 | 1.23101 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.85582e11 | 0.0736686 | ||||||||
\(827\) | 1.24239e13 | 0.923602 | 0.461801 | − | 0.886984i | \(-0.347203\pi\) | ||||
0.461801 | + | 0.886984i | \(0.347203\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.14034e12 | 0.525078 | 0.262539 | − | 0.964921i | \(-0.415440\pi\) | ||||
0.262539 | + | 0.964921i | \(0.415440\pi\) | |||||||
\(830\) | 7.41451e12 | 0.542289 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.01508e12 | 0.362846 | ||||||||
\(833\) | −5.56789e12 | −0.400671 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.15147e13 | 1.53160 | ||||||||
\(836\) | 2.95459e13 | 2.09204 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.13340e13 | −0.793934 | ||||||||
\(839\) | 1.84306e13 | 1.28414 | 0.642068 | − | 0.766648i | \(-0.278077\pi\) | ||||
0.642068 | + | 0.766648i | \(0.278077\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.88459e12 | 0.129907 | ||||||||
\(842\) | −1.36192e13 | −0.933785 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.00062e12 | 0.407057 | ||||||||
\(845\) | 6.88121e12 | 0.464312 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.29017e12 | −0.219656 | ||||||||
\(848\) | −3.82440e12 | −0.253970 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.79644e12 | −0.249455 | ||||||||
\(851\) | −1.54931e12 | −0.101264 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.76438e12 | 0.372805 | 0.186403 | − | 0.982473i | \(-0.440317\pi\) | ||||
0.186403 | + | 0.982473i | \(0.440317\pi\) | |||||||
\(854\) | 1.10111e12 | 0.0708385 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.81439e13 | 1.15505 | ||||||||
\(857\) | 4.75199e12 | 0.300927 | 0.150464 | − | 0.988616i | \(-0.451923\pi\) | ||||
0.150464 | + | 0.988616i | \(0.451923\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.45715e12 | 0.279311 | 0.139656 | − | 0.990200i | \(-0.455400\pi\) | ||||
0.139656 | + | 0.990200i | \(0.455400\pi\) | |||||||
\(860\) | −1.91517e13 | −1.19389 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.65301e12 | 0.348736 | ||||||||
\(863\) | −1.65466e13 | −1.01545 | −0.507727 | − | 0.861518i | \(-0.669514\pi\) | ||||
−0.507727 | + | 0.861518i | \(0.669514\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.19823e11 | 0.0558640 | ||||||||
\(866\) | −1.14045e13 | −0.689041 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.98994e11 | −0.0417960 | ||||||||
\(869\) | 9.36045e11 | 0.0556811 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.65923e12 | −0.0976842 | ||||||||
\(872\) | −3.54122e12 | −0.207410 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.64097e12 | 0.558881 | ||||||||
\(875\) | 2.32968e11 | 0.0134357 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.05493e13 | 1.74382 | 0.871912 | − | 0.489663i | \(-0.162880\pi\) | ||||
0.871912 | + | 0.489663i | \(0.162880\pi\) | |||||||
\(878\) | 4.68556e12 | 0.266095 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.45321e12 | 0.362747 | ||||||||
\(881\) | 6.84641e12 | 0.382887 | 0.191444 | − | 0.981504i | \(-0.438683\pi\) | ||||
0.191444 | + | 0.981504i | \(0.438683\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.29262e13 | −1.26914 | −0.634570 | − | 0.772865i | \(-0.718823\pi\) | ||||
−0.634570 | + | 0.772865i | \(0.718823\pi\) | |||||||
\(884\) | −4.12143e12 | −0.226993 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.92011e12 | 0.486316 | ||||||||
\(887\) | 2.46814e13 | 1.33879 | 0.669397 | − | 0.742905i | \(-0.266553\pi\) | ||||
0.669397 | + | 0.742905i | \(0.266553\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.87311e12 | 0.100578 | ||||||||
\(890\) | −1.97587e13 | −1.05561 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.08916e13 | 0.576034 | ||||||||
\(893\) | 3.27604e13 | 1.72392 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.92875e13 | 1.00478 | ||||||||
\(896\) | −1.58105e12 | −0.0819521 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.11379e13 | 0.571556 | ||||||||
\(899\) | −1.22054e13 | −0.623207 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.42670e13 | −0.721224 | ||||||||
\(902\) | 8.58573e12 | 0.431865 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.11316e13 | 1.05238 | ||||||||
\(905\) | −4.25255e13 | −2.10732 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.45774e13 | −1.20588 | −0.602938 | − | 0.797788i | \(-0.706003\pi\) | ||||
−0.602938 | + | 0.797788i | \(0.706003\pi\) | |||||||
\(908\) | −3.43549e12 | −0.167727 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.46021e12 | −0.0705879 | ||||||||
\(911\) | 5.71188e12 | 0.274756 | 0.137378 | − | 0.990519i | \(-0.456133\pi\) | ||||
0.137378 | + | 0.990519i | \(0.456133\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.45065e13 | −1.16725 | ||||||||
\(914\) | −1.06587e13 | −0.505181 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.42109e13 | −0.666950 | ||||||||
\(917\) | −4.88992e11 | −0.0228370 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.90767e13 | −0.882231 | −0.441116 | − | 0.897450i | \(-0.645417\pi\) | ||||
−0.441116 | + | 0.897450i | \(0.645417\pi\) | |||||||
\(920\) | 1.68662e13 | 0.776198 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.09605e12 | 0.0955242 | ||||||||
\(923\) | 1.85099e13 | 0.839455 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.34312e12 | 0.195058 | ||||||||
\(926\) | −9.61502e12 | −0.429735 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.47582e13 | −1.09586 | ||||||||
\(929\) | −2.72807e13 | −1.20167 | −0.600835 | − | 0.799373i | \(-0.705165\pi\) | ||||
−0.600835 | + | 0.799373i | \(0.705165\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.96367e13 | −1.72911 | ||||||||
\(932\) | 1.27158e13 | 0.552040 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.68261e12 | 0.201339 | ||||||||
\(935\) | 2.40738e13 | 1.03013 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.38541e13 | 0.587152 | 0.293576 | − | 0.955936i | \(-0.405155\pi\) | ||||
0.293576 | + | 0.955936i | \(0.405155\pi\) | |||||||
\(938\) | −1.66661e11 | −0.00702946 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.31999e13 | 0.969195 | ||||||||
\(941\) | 1.33886e12 | 0.0556648 | 0.0278324 | − | 0.999613i | \(-0.491140\pi\) | ||||
0.0278324 | + | 0.999613i | \(0.491140\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.95632e12 | −0.245287 | ||||||||
\(944\) | 4.32522e12 | 0.177270 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.97734e13 | −1.20870 | ||||||||
\(947\) | −4.26511e13 | −1.72328 | −0.861639 | − | 0.507521i | \(-0.830562\pi\) | ||||
−0.861639 | + | 0.507521i | \(0.830562\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.74500e13 | 1.49883 | ||||||||
\(950\) | −2.70261e13 | −1.07653 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.02267e12 | −0.0403524 | ||||||||
\(953\) | 2.62256e13 | 1.02993 | 0.514964 | − | 0.857212i | \(-0.327805\pi\) | ||||
0.514964 | + | 0.857212i | \(0.327805\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.47853e13 | −2.13132 | ||||||||
\(956\) | 2.01595e12 | 0.0780581 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.79366e12 | −0.260591 | ||||||||
\(959\) | 6.67067e11 | 0.0254675 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.73514e13 | −0.656266 | ||||||||
\(962\) | −2.21766e12 | −0.0834849 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.13314e12 | −0.303328 | ||||||||
\(965\) | −1.02230e13 | −0.379493 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.79584e11 | −0.00660463 | −0.00330232 | − | 0.999995i | \(-0.501051\pi\) | ||||
−0.00330232 | + | 0.999995i | \(0.501051\pi\) | |||||||
\(968\) | 5.43971e13 | 1.99130 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.10839e10 | 0.000764679 0 | ||||||||
\(971\) | 2.95293e13 | 1.06602 | 0.533012 | − | 0.846108i | \(-0.321060\pi\) | ||||
0.533012 | + | 0.846108i | \(0.321060\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.41365e12 | 0.0505633 | ||||||||
\(974\) | −1.18142e13 | −0.420619 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.83221e12 | 0.170460 | ||||||||
\(977\) | 4.93042e13 | 1.73124 | 0.865622 | − | 0.500699i | \(-0.166924\pi\) | ||||
0.865622 | + | 0.500699i | \(0.166924\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.53064e13 | 2.27213 | ||||||||
\(980\) | −2.80695e13 | −0.972115 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.08128e13 | 0.714215 | ||||||||
\(983\) | −8.89206e12 | −0.303747 | −0.151873 | − | 0.988400i | \(-0.548531\pi\) | ||||
−0.151873 | + | 0.988400i | \(0.548531\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.49356e13 | −0.844029 | ||||||||
\(986\) | −7.22860e12 | −0.243561 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.93396e13 | −0.979599 | ||||||||
\(989\) | 2.06552e13 | 0.686508 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.67054e13 | −0.550207 | −0.275103 | − | 0.961415i | \(-0.588712\pi\) | ||||
−0.275103 | + | 0.961415i | \(0.588712\pi\) | |||||||
\(992\) | 1.84351e13 | 0.604426 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.85923e12 | 0.0604080 | ||||||||
\(995\) | −2.44191e13 | −0.789814 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.62911e12 | 0.0842714 | 0.0421357 | − | 0.999112i | \(-0.486584\pi\) | ||||
0.0421357 | + | 0.999112i | \(0.486584\pi\) | |||||||
\(998\) | 8.43660e12 | 0.269203 | ||||||||
\(999\) | 0 | 0 |
(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 | 27.10.a.d.1.2 | ✓ | 4 | |
3.2 | odd | 2 | inner | 27.10.a.d.1.3 | yes | 4 | |
9.2 | odd | 6 | 81.10.c.j.28.2 | 8 | |||
9.4 | even | 3 | 81.10.c.j.55.3 | 8 | |||
9.5 | odd | 6 | 81.10.c.j.55.2 | 8 | |||
9.7 | even | 3 | 81.10.c.j.28.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.10.a.d.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
27.10.a.d.1.3 | yes | 4 | 3.2 | odd | 2 | inner | |
81.10.c.j.28.2 | 8 | 9.2 | odd | 6 | |||
81.10.c.j.28.3 | 8 | 9.7 | even | 3 | |||
81.10.c.j.55.2 | 8 | 9.5 | odd | 6 | |||
81.10.c.j.55.3 | 8 | 9.4 | even | 3 |