Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [96,12,Mod(1,96)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(96, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("96.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 96 = 2^{5} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 96.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: | \(73.7609453337\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1945}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 486 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(22.5511\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 96.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3700.71 | −0.529603 | −0.264801 | − | 0.964303i | \(-0.585306\pi\) | ||||
−0.264801 | + | 0.964303i | \(0.585306\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 72358.6 | 1.62724 | 0.813619 | − | 0.581399i | \(-0.197494\pi\) | ||||
0.813619 | + | 0.581399i | \(0.197494\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.03599e6 | 1.93953 | 0.969764 | − | 0.244045i | \(-0.0784743\pi\) | ||||
0.969764 | + | 0.244045i | \(0.0784743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −447532. | −0.334300 | −0.167150 | − | 0.985932i | \(-0.553456\pi\) | ||||
−0.167150 | + | 0.985932i | \(0.553456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 899273. | 0.305766 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 966903. | 0.165163 | 0.0825817 | − | 0.996584i | \(-0.473683\pi\) | ||||
0.0825817 | + | 0.996584i | \(0.473683\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −180409. | −0.0167153 | −0.00835765 | − | 0.999965i | \(-0.502660\pi\) | ||||
−0.00835765 | + | 0.999965i | \(0.502660\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.75831e7 | −0.939486 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.67982e7 | −0.544202 | −0.272101 | − | 0.962269i | \(-0.587718\pi\) | ||||
−0.272101 | + | 0.962269i | \(0.587718\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.51329e7 | −0.719521 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.48887e8 | 1.34793 | 0.673967 | − | 0.738761i | \(-0.264589\pi\) | ||||
0.673967 | + | 0.738761i | \(0.264589\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.16841e8 | −1.36036 | −0.680178 | − | 0.733047i | \(-0.738098\pi\) | ||||
−0.680178 | + | 0.733047i | \(0.738098\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.51746e8 | −1.11979 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.67778e8 | −0.861789 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.70953e8 | 1.59068 | 0.795340 | − | 0.606164i | \(-0.207292\pi\) | ||||
0.795340 | + | 0.606164i | \(0.207292\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.08750e8 | 0.193008 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.72819e8 | −0.637358 | −0.318679 | − | 0.947863i | \(-0.603239\pi\) | ||||
−0.318679 | + | 0.947863i | \(0.603239\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.14447e9 | 1.18721 | 0.593607 | − | 0.804755i | \(-0.297703\pi\) | ||||
0.593607 | + | 0.804755i | \(0.297703\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.18523e8 | −0.176534 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.31669e7 | 0.00837425 | 0.00418712 | − | 0.999991i | \(-0.498667\pi\) | ||||
0.00418712 | + | 0.999991i | \(0.498667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.25844e9 | 1.64790 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.34957e8 | −0.0953572 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.04271e9 | −1.32787 | −0.663935 | − | 0.747791i | \(-0.731115\pi\) | ||||
−0.663935 | + | 0.747791i | \(0.731115\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.83390e9 | −1.02718 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.38395e7 | 0.00965059 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.23772e9 | −1.13590 | −0.567949 | − | 0.823064i | \(-0.692263\pi\) | ||||
−0.567949 | + | 0.823064i | \(0.692263\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.61870e9 | 1.00336 | 0.501682 | − | 0.865052i | \(-0.332715\pi\) | ||||
0.501682 | + | 0.865052i | \(0.332715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.27270e9 | 0.542412 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.65619e9 | 0.177046 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.97892e10 | 1.79067 | 0.895336 | − | 0.445391i | \(-0.146935\pi\) | ||||
0.895336 | + | 0.445391i | \(0.146935\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.08196e9 | 0.314195 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.10433e10 | 1.38418 | 0.692090 | − | 0.721811i | \(-0.256690\pi\) | ||||
0.692090 | + | 0.721811i | \(0.256690\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.27113e10 | −0.717652 | −0.358826 | − | 0.933404i | \(-0.616823\pi\) | ||||
−0.358826 | + | 0.933404i | \(0.616823\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.53729e9 | 0.415416 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.49628e10 | 3.15607 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.16162e10 | −0.424731 | −0.212365 | − | 0.977190i | \(-0.568117\pi\) | ||||
−0.212365 | + | 0.977190i | \(0.568117\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.54557e10 | −1.54531 | −0.772657 | − | 0.634824i | \(-0.781073\pi\) | ||||
−0.772657 | + | 0.634824i | \(0.781073\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.57823e9 | −0.0874710 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.61796e10 | −0.778230 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.43356e10 | 1.03143 | 0.515715 | − | 0.856760i | \(-0.327526\pi\) | ||||
0.515715 | + | 0.856760i | \(0.327526\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.23828e10 | −0.543985 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.26924e10 | 0.785402 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.67643e8 | 0.00885247 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.98530e10 | 1.06240 | 0.531200 | − | 0.847247i | \(-0.321741\pi\) | ||||
0.531200 | + | 0.847247i | \(0.321741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.11742e10 | 0.646509 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.25134e10 | −0.213144 | −0.106572 | − | 0.994305i | \(-0.533987\pi\) | ||||
−0.106572 | + | 0.994305i | \(0.533987\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.54872e9 | 0.0811597 | 0.0405798 | − | 0.999176i | \(-0.487079\pi\) | ||||
0.0405798 | + | 0.999176i | \(0.487079\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.50701e10 | 0.497554 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.38434e10 | 0.646835 | 0.323417 | − | 0.946256i | \(-0.395168\pi\) | ||||
0.323417 | + | 0.946256i | \(0.395168\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.91213e11 | 1.19034 | 0.595171 | − | 0.803599i | \(-0.297084\pi\) | ||||
0.595171 | + | 0.803599i | \(0.297084\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.63042e11 | −0.918379 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.95153e10 | 0.252818 | 0.126409 | − | 0.991978i | \(-0.459655\pi\) | ||||
0.126409 | + | 0.991978i | \(0.459655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.21653e10 | 0.288211 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.64263e10 | −0.111433 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.99637e10 | 0.268760 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.87965e11 | 2.76177 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.14895e11 | 0.367979 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.10715e11 | 0.910663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.97557e11 | −0.530607 | −0.265303 | − | 0.964165i | \(-0.585472\pi\) | ||||
−0.265303 | + | 0.964165i | \(0.585472\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.78107e11 | −0.685438 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.83115e11 | 0.414697 | 0.207348 | − | 0.978267i | \(-0.433517\pi\) | ||||
0.207348 | + | 0.978267i | \(0.433517\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.30542e10 | −0.0271998 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.31011e10 | 0.101922 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.28201e11 | 1.11208 | 0.556040 | − | 0.831156i | \(-0.312320\pi\) | ||||
0.556040 | + | 0.831156i | \(0.312320\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.54003e11 | 0.742125 | 0.371063 | − | 0.928608i | \(-0.378994\pi\) | ||||
0.371063 | + | 0.928608i | \(0.378994\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.19956e9 | −0.00483487 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.63639e11 | −0.648383 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.50989e11 | −0.713870 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.91800e11 | −0.951416 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.73907e10 | 0.0751753 | 0.0375877 | − | 0.999293i | \(-0.488033\pi\) | ||||
0.0375877 | + | 0.999293i | \(0.488033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.18702e11 | 0.123051 | 0.0615255 | − | 0.998106i | \(-0.480403\pi\) | ||||
0.0615255 | + | 0.998106i | \(0.480403\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.70947e10 | 0.0550545 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.02467e11 | 0.720448 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.26981e11 | −0.357240 | −0.178620 | − | 0.983918i | \(-0.557163\pi\) | ||||
−0.178620 | + | 0.983918i | \(0.557163\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.82379e11 | 0.766646 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.21549e12 | −0.885545 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.59306e12 | 1.08443 | 0.542213 | − | 0.840241i | \(-0.317587\pi\) | ||||
0.542213 | + | 0.840241i | \(0.317587\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.31638e11 | 0.593042 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.86964e12 | −1.70957 | −0.854784 | − | 0.518984i | \(-0.826310\pi\) | ||||
−0.854784 | + | 0.518984i | \(0.826310\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.59188e12 | −0.888244 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.06530e10 | −0.00557177 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.44648e11 | −0.463464 | −0.231732 | − | 0.972780i | \(-0.574439\pi\) | ||||
−0.231732 | + | 0.972780i | \(0.574439\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.54216e12 | −1.17083 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.51576e12 | 0.655811 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.03716e11 | −0.0421846 | −0.0210923 | − | 0.999778i | \(-0.506714\pi\) | ||||
−0.0210923 | + | 0.999778i | \(0.506714\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.88807e12 | −1.48765 | −0.743826 | − | 0.668373i | \(-0.766991\pi\) | ||||
−0.743826 | + | 0.668373i | \(0.766991\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.60835e12 | −0.579293 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.48300e12 | −0.842428 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.00170e12 | 0.320339 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.03827e12 | −0.313162 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.02318e12 | −1.42986 | −0.714932 | − | 0.699194i | \(-0.753543\pi\) | ||||
−0.714932 | + | 0.699194i | \(0.753543\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.75193e11 | 0.262135 | 0.131068 | − | 0.991373i | \(-0.458159\pi\) | ||||
0.131068 | + | 0.991373i | \(0.458159\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.02453e11 | −0.102217 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.81611e12 | −0.676216 | −0.338108 | − | 0.941107i | \(-0.609787\pi\) | ||||
−0.338108 | + | 0.941107i | \(0.609787\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.97846e12 | 1.35799 | 0.678996 | − | 0.734142i | \(-0.262415\pi\) | ||||
0.678996 | + | 0.734142i | \(0.262415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.80877e12 | −1.03385 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.07733e13 | 2.19341 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.74976e12 | 0.337546 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.91917e11 | −0.181401 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.86902e11 | −0.0324198 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.16625e13 | 1.91972 | 0.959862 | − | 0.280473i | \(-0.0904914\pi\) | ||||
0.959862 | + | 0.280473i | \(0.0904914\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.11352e12 | −0.799157 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.23536e12 | −0.628752 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.56903e13 | −2.21362 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.08884e12 | 0.414337 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.32720e11 | −0.0552141 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.47931e12 | −0.665348 | −0.332674 | − | 0.943042i | \(-0.607951\pi\) | ||||
−0.332674 | + | 0.943042i | \(0.607951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.07456e12 | −0.239840 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.92971e12 | −0.873203 | −0.436601 | − | 0.899655i | \(-0.643818\pi\) | ||||
−0.436601 | + | 0.899655i | \(0.643818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.43526e13 | 1.50604 | 0.753019 | − | 0.657998i | \(-0.228597\pi\) | ||||
0.753019 | + | 0.657998i | \(0.228597\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.82160e13 | −1.82216 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.04880e13 | −1.00054 | −0.500270 | − | 0.865870i | \(-0.666766\pi\) | ||||
−0.500270 | + | 0.865870i | \(0.666766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.87269e10 | −0.00443502 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.82273e12 | 0.245218 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.19376e12 | −0.181971 | −0.0909853 | − | 0.995852i | \(-0.529002\pi\) | ||||
−0.0909853 | + | 0.995852i | \(0.529002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.67370e13 | 1.32612 | 0.663061 | − | 0.748566i | \(-0.269257\pi\) | ||||
0.663061 | + | 0.748566i | \(0.269257\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.20585e13 | −0.872732 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.07390e10 | 0.00558792 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.34757e13 | 0.892187 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.55537e11 | −0.0542043 | −0.0271021 | − | 0.999633i | \(-0.508628\pi\) | ||||
−0.0271021 | + | 0.999633i | \(0.508628\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.74028e13 | −1.05549 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.69509e11 | 0.0505014 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.35801e13 | 1.86831 | 0.934157 | − | 0.356863i | \(-0.116154\pi\) | ||||
0.934157 | + | 0.356863i | \(0.116154\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.85492e13 | 2.58841 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.79165e12 | 0.449311 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.27665e12 | 0.209579 | 0.104789 | − | 0.994494i | \(-0.466583\pi\) | ||||
0.104789 | + | 0.994494i | \(0.466583\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.49609e13 | 0.703243 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.32036e13 | −0.595496 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.98975e12 | 0.259281 | 0.129641 | − | 0.991561i | \(-0.458618\pi\) | ||||
0.129641 | + | 0.991561i | \(0.458618\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.73797e12 | −0.280026 | −0.140013 | − | 0.990150i | \(-0.544714\pi\) | ||||
−0.140013 | + | 0.990150i | \(0.544714\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.86902e12 | 0.314070 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.63973e13 | −1.39553 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.07764e13 | −0.397041 | −0.198520 | − | 0.980097i | \(-0.563614\pi\) | ||||
−0.198520 | + | 0.980097i | \(0.563614\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.28043e13 | −0.453452 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.69195e13 | 1.25710 | 0.628552 | − | 0.777768i | \(-0.283648\pi\) | ||||
0.628552 | + | 0.777768i | \(0.283648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.10491e13 | 1.01677 | 0.508386 | − | 0.861129i | \(-0.330242\pi\) | ||||
0.508386 | + | 0.861129i | \(0.330242\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.62237e11 | −0.00511098 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.42125e13 | −1.03713 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.33370e13 | −0.972721 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.18343e13 | −0.613377 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.52302e13 | 1.49419 | 0.747093 | − | 0.664720i | \(-0.231449\pi\) | ||||
0.747093 | + | 0.664720i | \(0.231449\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.30840e13 | 0.601575 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.48653e13 | −0.373262 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.51774e12 | 0.181926 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.28125e13 | 1.93188 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.47076e12 | 0.123059 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.44939e13 | −0.531385 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.43204e13 | 1.55542 | 0.777709 | − | 0.628624i | \(-0.216382\pi\) | ||||
0.777709 | + | 0.628624i | \(0.216382\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.32034e12 | −0.0468576 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.89430e13 | −0.759010 | −0.379505 | − | 0.925190i | \(-0.623906\pi\) | ||||
−0.379505 | + | 0.925190i | \(0.623906\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.90171e13 | 0.734110 | 0.367055 | − | 0.930199i | \(-0.380366\pi\) | ||||
0.367055 | + | 0.930199i | \(0.380366\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.58120e13 | −0.287263 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.65971e13 | 0.817585 | 0.408792 | − | 0.912627i | \(-0.365950\pi\) | ||||
0.408792 | + | 0.912627i | \(0.365950\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.54246e14 | 2.61436 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.28040e13 | −0.373450 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.74438e11 | −0.00276076 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.57231e13 | 0.240536 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.64648e13 | −0.687245 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.52739e11 | 0.0136269 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.99455e13 | −0.967623 | −0.483811 | − | 0.875172i | \(-0.660748\pi\) | ||||
−0.483811 | + | 0.875172i | \(0.660748\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.96191e13 | 0.530227 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.32340e13 | −0.948345 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.11801e14 | 1.40114 | 0.700569 | − | 0.713585i | \(-0.252930\pi\) | ||||
0.700569 | + | 0.713585i | \(0.252930\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.20322e13 | −0.145965 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.24646e14 | −2.63845 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.26994e13 | 1.05429 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.51062e13 | −0.166398 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.63901e13 | 0.388303 | 0.194152 | − | 0.980972i | \(-0.437805\pi\) | ||||
0.194152 | + | 0.980972i | \(0.437805\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.52083e12 | 0.0880932 | 0.0440466 | − | 0.999029i | \(-0.485975\pi\) | ||||
0.0440466 | + | 0.999029i | \(0.485975\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.42160e12 | 0.0643360 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.50603e13 | −0.437555 | −0.218778 | − | 0.975775i | \(-0.570207\pi\) | ||||
−0.218778 | + | 0.975775i | \(0.570207\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.78751e13 | −0.733065 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.70012e13 | −0.155169 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.06639e12 | 0.00943840 | 0.00471920 | − | 0.999989i | \(-0.498498\pi\) | ||||
0.00471920 | + | 0.999989i | \(0.498498\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.16458e14 | −0.999721 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.91475e14 | −1.59451 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.70408e13 | 0.380070 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.34488e14 | 1.83848 | 0.919238 | − | 0.393702i | \(-0.128806\pi\) | ||||
0.919238 | + | 0.393702i | \(0.128806\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.79195e13 | −0.212453 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.92525e14 | −2.16076 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.10203e14 | −1.50744 | −0.753721 | − | 0.657195i | \(-0.771743\pi\) | ||||
−0.753721 | + | 0.657195i | \(0.771743\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.55038e13 | −0.525771 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.66319e13 | −0.450614 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.01106e13 | 0.329165 | 0.164583 | − | 0.986363i | \(-0.447372\pi\) | ||||
0.164583 | + | 0.986363i | \(0.447372\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.80064e13 | 0.306346 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.72523e13 | −0.106968 | −0.0534839 | − | 0.998569i | \(-0.517033\pi\) | ||||
−0.0534839 | + | 0.998569i | \(0.517033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.77416e14 | −1.67146 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.75800e13 | 0.395738 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.19041e13 | 0.352368 | 0.176184 | − | 0.984357i | \(-0.443625\pi\) | ||||
0.176184 | + | 0.984357i | \(0.443625\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.62422e13 | −0.0898822 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.44968e13 | −0.239425 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.29881e13 | 0.224938 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.69202e14 | −0.861110 | −0.430555 | − | 0.902564i | \(-0.641682\pi\) | ||||
−0.430555 | + | 0.902564i | \(0.641682\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.17216e12 | 0.0157038 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.29537e14 | 1.58712 | 0.793560 | − | 0.608492i | \(-0.208225\pi\) | ||||
0.793560 | + | 0.608492i | \(0.208225\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.70435e13 | 0.454767 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.29036e13 | −0.0588447 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.95101e14 | 3.08517 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.14267e14 | −1.35775 | −0.678876 | − | 0.734253i | \(-0.737533\pi\) | ||||
−0.678876 | + | 0.734253i | \(0.737533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.52653e14 | −0.642059 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.51352e14 | −1.84838 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.05225e14 | 0.818402 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.10323e14 | −0.428466 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.34666e14 | −1.26600 | −0.633002 | − | 0.774150i | \(-0.718177\pi\) | ||||
−0.633002 | + | 0.774150i | \(0.718177\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.04256e14 | 0.752704 | 0.376352 | − | 0.926477i | \(-0.377178\pi\) | ||||
0.376352 | + | 0.926477i | \(0.377178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.77493e11 | 0.00279142 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.39701e13 | −0.118839 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.78920e14 | 1.63271 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.12664e14 | 0.374344 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.34783e14 | −1.08427 | −0.542136 | − | 0.840291i | \(-0.682384\pi\) | ||||
−0.542136 | + | 0.840291i | \(0.682384\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.97010e14 | 1.56921 | 0.784606 | − | 0.619995i | \(-0.212865\pi\) | ||||
0.784606 | + | 0.619995i | \(0.212865\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.33890e14 | 0.412153 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.03055e12 | 0.00909650 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.20500e14 | −1.52358 | −0.761791 | − | 0.647823i | \(-0.775680\pi\) | ||||
−0.761791 | + | 0.647823i | \(0.775680\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.92408e14 | 0.549300 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.95757e14 | −1.38054 | −0.690269 | − | 0.723553i | \(-0.742508\pi\) | ||||
−0.690269 | + | 0.723553i | \(0.742508\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.01080e14 | −0.546248 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.63759e13 | −0.0434025 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.58259e14 | −1.44371 | −0.721857 | − | 0.692042i | \(-0.756711\pi\) | ||||
−0.721857 | + | 0.692042i | \(0.756711\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.89836e14 | −1.23617 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.88446e13 | −0.0710436 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.19839e14 | 0.288096 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.01951e13 | 0.141261 | 0.0706305 | − | 0.997503i | \(-0.477499\pi\) | ||||
0.0706305 | + | 0.997503i | \(0.477499\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.38740e13 | −0.0317857 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.66904e14 | −1.26810 | −0.634051 | − | 0.773291i | \(-0.718609\pi\) | ||||
−0.634051 | + | 0.773291i | \(0.718609\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.23760e14 | 1.14403 | 0.572015 | − | 0.820243i | \(-0.306162\pi\) | ||||
0.572015 | + | 0.820243i | \(0.306162\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.94999e14 | −0.415951 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.49157e14 | 0.310743 | 0.155371 | − | 0.987856i | \(-0.450343\pi\) | ||||
0.155371 | + | 0.987856i | \(0.450343\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.43192e15 | 2.91385 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.03756e14 | 0.206253 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.18566e15 | 2.30264 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.33830e12 | 0.0120270 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.38718e14 | −0.442623 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.11276e14 | 0.745225 | 0.372613 | − | 0.927987i | \(-0.378462\pi\) | ||||
0.372613 | + | 0.927987i | \(0.378462\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.00273e14 | −0.531764 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.95365e14 | 0.511270 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.32520e14 | −0.562650 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.09682e14 | 0.181437 | 0.0907186 | − | 0.995877i | \(-0.471084\pi\) | ||||
0.0907186 | + | 0.995877i | \(0.471084\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.87113e14 | −0.626093 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.72537e14 | 0.747288 | 0.373644 | − | 0.927572i | \(-0.378108\pi\) | ||||
0.373644 | + | 0.927572i | \(0.378108\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.43960e14 | 0.222629 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.26388e14 | −0.342393 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.52266e15 | 2.25239 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.74148e14 | −0.830750 | −0.415375 | − | 0.909650i | \(-0.636350\pi\) | ||||
−0.415375 | + | 0.909650i | \(0.636350\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.97322e14 | 0.987020 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.08687e15 | −1.50505 | −0.752527 | − | 0.658562i | \(-0.771165\pi\) | ||||
−0.752527 | + | 0.658562i | \(0.771165\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.33156e13 | 0.112882 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.86826e14 | 0.512828 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.21857e15 | 1.58089 | 0.790444 | − | 0.612534i | \(-0.209850\pi\) | ||||
0.790444 | + | 0.612534i | \(0.209850\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.19771e14 | −1.16779 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.58868e12 | 0.00321686 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.53370e13 | −0.0429824 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.36408e13 | 0.0162421 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.29549e14 | 0.267581 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.69864e14 | 0.307990 | 0.153995 | − | 0.988072i | \(-0.450786\pi\) | ||||
0.153995 | + | 0.988072i | \(0.450786\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.16264e15 | −1.29922 | −0.649612 | − | 0.760266i | \(-0.725069\pi\) | ||||
−0.649612 | + | 0.760266i | \(0.725069\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.17746e14 | 0.675980 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.09665e14 | −0.224681 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.70630e14 | −0.703845 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.68331e14 | −0.378633 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.11602e14 | 0.213068 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.47287e14 | −0.342565 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.52030e13 | 0.0243553 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.37571e15 | 3.19615 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.25701e14 | 0.766016 | 0.383008 | − | 0.923745i | \(-0.374888\pi\) | ||||
0.383008 | + | 0.923745i | \(0.374888\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.44800e14 | 0.858896 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.07624e14 | −0.630408 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.74544e13 | 0.0501641 | 0.0250820 | − | 0.999685i | \(-0.492015\pi\) | ||||
0.0250820 | + | 0.999685i | \(0.492015\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.90828e14 | 0.334455 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.68607e13 | −0.0225311 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.40529e14 | −0.691138 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.03370e14 | 0.486376 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.26265e14 | −0.573973 | −0.286987 | − | 0.957935i | \(-0.592654\pi\) | ||||
−0.286987 | + | 0.957935i | \(0.592654\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.12188e14 | −0.396885 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.43414e14 | −0.184948 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.71049e15 | 1.27446 | 0.637228 | − | 0.770676i | \(-0.280081\pi\) | ||||
0.637228 | + | 0.770676i | \(0.280081\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.83242e14 | −0.133893 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.52299e14 | 0.180804 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.09455e15 | 0.769343 | 0.384671 | − | 0.923054i | \(-0.374315\pi\) | ||||
0.384671 | + | 0.923054i | \(0.374315\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.11533e15 | 0.768965 | 0.384482 | − | 0.923132i | \(-0.374380\pi\) | ||||
0.384482 | + | 0.923132i | \(0.374380\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.22063e15 | 0.825533 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.90169e14 | 0.391565 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.38973e14 | −0.155554 | −0.0777771 | − | 0.996971i | \(-0.524782\pi\) | ||||
−0.0777771 | + | 0.996971i | \(0.524782\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.36972e14 | −0.151344 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.01270e15 | −2.51459 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.18821e15 | −2.57544 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.77962e13 | 0.0590153 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.38562e15 | −0.820606 | −0.410303 | − | 0.911949i | \(-0.634577\pi\) | ||||
−0.410303 | + | 0.911949i | \(0.634577\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.91202e13 | 0.0227388 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.84315e14 | 0.390414 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.16303e15 | 0.651313 | 0.325656 | − | 0.945488i | \(-0.394415\pi\) | ||||
0.325656 | + | 0.945488i | \(0.394415\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.58916e14 | −0.142336 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.45277e15 | −0.784037 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.93685e15 | −1.02624 | −0.513119 | − | 0.858317i | \(-0.671510\pi\) | ||||
−0.513119 | + | 0.858317i | \(0.671510\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.80344e15 | 0.938194 | 0.469097 | − | 0.883147i | \(-0.344580\pi\) | ||||
0.469097 | + | 0.883147i | \(0.344580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.16853e15 | 0.596891 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.91603e15 | −1.46264 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.61637e15 | −1.78129 | −0.890646 | − | 0.454696i | \(-0.849748\pi\) | ||||
−0.890646 | + | 0.454696i | \(0.849748\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.61791e15 | −1.26637 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.89262e12 | −0.00279951 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.52906e15 | −0.713496 | −0.356748 | − | 0.934201i | \(-0.616114\pi\) | ||||
−0.356748 | + | 0.934201i | \(0.616114\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.25193e14 | −0.194882 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.55216e15 | 1.14905 | 0.574527 | − | 0.818486i | \(-0.305186\pi\) | ||||
0.574527 | + | 0.818486i | \(0.305186\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.80917e14 | 0.168474 | 0.0842368 | − | 0.996446i | \(-0.473155\pi\) | ||||
0.0842368 | + | 0.996446i | \(0.473155\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.41036e14 | 0.104732 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.93165e15 | 1.67838 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.65605e14 | 0.237232 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.54173e13 | 0.0187176 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.48747e14 | 0.262722 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.56890e14 | −0.142027 | −0.0710137 | − | 0.997475i | \(-0.522623\pi\) | ||||
−0.0710137 | + | 0.997475i | \(0.522623\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.83399e15 | −1.10835 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.31102e14 | 0.281011 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.45826e15 | −0.550892 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.24258e15 | 0.461393 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.54768e15 | −0.929877 | −0.464938 | − | 0.885343i | \(-0.653923\pi\) | ||||
−0.464938 | + | 0.885343i | \(0.653923\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.63356e15 | −0.586103 | −0.293052 | − | 0.956097i | \(-0.594671\pi\) | ||||
−0.293052 | + | 0.956097i | \(0.594671\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.02919e15 | 0.363010 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.25249e15 | −1.47458 | −0.737292 | − | 0.675574i | \(-0.763896\pi\) | ||||
−0.737292 | + | 0.675574i | \(0.763896\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.46221e15 | −2.20311 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.81275e15 | 1.27804 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.44142e15 | −0.804675 | −0.402337 | − | 0.915491i | \(-0.631802\pi\) | ||||
−0.402337 | + | 0.915491i | \(0.631802\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.77654e14 | −0.219625 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.50589e14 | −0.239217 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.38613e14 | −0.0747867 | −0.0373934 | − | 0.999301i | \(-0.511905\pi\) | ||||
−0.0373934 | + | 0.999301i | \(0.511905\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.87186e15 | 1.50171 | 0.750857 | − | 0.660465i | \(-0.229641\pi\) | ||||
0.750857 | + | 0.660465i | \(0.229641\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.05151e14 | 0.0318779 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.83097e13 | 0.0144051 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.50104e15 | −0.733548 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.33147e15 | 0.384139 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.85692e15 | 1.94605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.52255e15 | −0.983499 | −0.491749 | − | 0.870737i | \(-0.663642\pi\) | ||||
−0.491749 | + | 0.870737i | \(0.663642\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.04118e14 | 0.138472 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.58634e15 | −0.698952 | −0.349476 | − | 0.936945i | \(-0.613640\pi\) | ||||
−0.349476 | + | 0.936945i | \(0.613640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.50163e15 | 1.72878 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.92692e15 | 0.504144 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.30583e15 | −0.336180 | −0.168090 | − | 0.985772i | \(-0.553760\pi\) | ||||
−0.168090 | + | 0.985772i | \(0.553760\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.32479e15 | −0.588960 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.48769e15 | −0.869512 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.80924e15 | 0.443906 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.18257e15 | −0.285559 | −0.142780 | − | 0.989754i | \(-0.545604\pi\) | ||||
−0.142780 | + | 0.989754i | \(0.545604\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.42648e15 | 1.05202 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.68013e15 | −0.393031 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.57170e14 | −0.105268 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.54858e15 | 0.577662 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.03869e15 | −0.678012 | −0.339006 | − | 0.940784i | \(-0.610091\pi\) | ||||
−0.339006 | + | 0.940784i | \(0.610091\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.21046e14 | −0.0265887 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.18406e13 | 0.00256056 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.62904e15 | −0.346836 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.59417e15 | 0.543807 | 0.271903 | − | 0.962325i | \(-0.412347\pi\) | ||||
0.271903 | + | 0.962325i | \(0.412347\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.85923e14 | −0.141577 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.64255e15 | 0.740308 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.71579e15 | 0.343385 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.33084e14 | 0.105061 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.81042e15 | 0.933629 | 0.466815 | − | 0.884355i | \(-0.345402\pi\) | ||||
0.466815 | + | 0.884355i | \(0.345402\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.90932e14 | 0.132066 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.06708e15 | −0.765636 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.23084e15 | −0.969867 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.01188e15 | −1.46317 | −0.731586 | − | 0.681749i | \(-0.761219\pi\) | ||||
−0.731586 | + | 0.681749i | \(0.761219\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.10659e15 | 0.196084 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.63527e15 | 0.634549 | 0.317275 | − | 0.948334i | \(-0.397232\pi\) | ||||
0.317275 | + | 0.948334i | \(0.397232\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.93022e15 | 0.503872 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.05014e16 | 3.47306 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.07406e15 | −1.34756 | −0.673779 | − | 0.738933i | \(-0.735330\pi\) | ||||
−0.673779 | + | 0.738933i | \(0.735330\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.96196e13 | −0.00322619 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.46070e15 | −1.04675 | −0.523373 | − | 0.852104i | \(-0.675326\pi\) | ||||
−0.523373 | + | 0.852104i | \(0.675326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.49393e14 | −0.0398130 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.27460e15 | −0.515105 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.79038e15 | 1.05255 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.19982e16 | 1.83272 | 0.916360 | − | 0.400356i | \(-0.131114\pi\) | ||||
0.916360 | + | 0.400356i | \(0.131114\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.07896e14 | 0.0312948 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.39282e14 | −0.0651682 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.11408e14 | −0.118635 | −0.0593174 | − | 0.998239i | \(-0.518892\pi\) | ||||
−0.0593174 | + | 0.998239i | \(0.518892\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.22888e15 | 0.609390 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.21569e15 | −1.16689 | −0.583443 | − | 0.812154i | \(-0.698295\pi\) | ||||
−0.583443 | + | 0.812154i | \(0.698295\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.38359e16 | 1.93697 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.11291e14 | −0.0291570 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.79158e15 | 0.379730 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.70956e15 | 0.631518 | 0.315759 | − | 0.948839i | \(-0.397741\pi\) | ||||
0.315759 | + | 0.948839i | \(0.397741\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.15996e15 | −1.07867 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.17494e16 | 1.53118 | 0.765592 | − | 0.643327i | \(-0.222446\pi\) | ||||
0.765592 | + | 0.643327i | \(0.222446\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.61826e15 | 0.978805 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.17975e16 | −1.49442 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.53009e13 | 0.0106536 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.18006e16 | 2.68466 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.13637e15 | −0.259410 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.58013e15 | 0.189195 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.33025e16 | −1.57063 | −0.785314 | − | 0.619097i | \(-0.787499\pi\) | ||||
−0.785314 | + | 0.619097i | \(0.787499\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.03923e15 | −0.121000 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.58286e15 | 0.411395 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.96208e15 | −0.335424 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.63550e15 | −0.406018 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.20782e16 | −1.33040 | −0.665199 | − | 0.746666i | \(-0.731653\pi\) | ||||
−0.665199 | + | 0.746666i | \(0.731653\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.27311e13 | 0.00138312 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.20846e15 | 0.343810 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.31688e16 | −1.39191 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.49819e15 | 0.468987 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.45551e15 | −0.149696 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.02426e15 | 0.509748 | 0.254874 | − | 0.966974i | \(-0.417966\pi\) | ||||
0.254874 | + | 0.966974i | \(0.417966\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.39996e13 | 0.00340298 | 0.00170149 | − | 0.999999i | \(-0.499458\pi\) | ||||
0.00170149 | + | 0.999999i | \(0.499458\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.63733e15 | 0.161673 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.89544e15 | −0.574314 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.06474e14 | −0.0198446 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.91217e15 | −0.181328 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.80167e16 | −1.68573 | −0.842863 | − | 0.538129i | \(-0.819131\pi\) | ||||
−0.842863 | + | 0.538129i | \(0.819131\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.17666e15 | −0.477915 | −0.238957 | − | 0.971030i | \(-0.576806\pi\) | ||||
−0.238957 | + | 0.971030i | \(0.576806\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.84455e15 | 0.805710 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.37881e15 | −0.393619 | −0.196810 | − | 0.980442i | \(-0.563058\pi\) | ||||
−0.196810 | + | 0.980442i | \(0.563058\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.83589e15 | 0.162853 | 0.0814265 | − | 0.996679i | \(-0.474052\pi\) | ||||
0.0814265 | + | 0.996679i | \(0.474052\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.61867e15 | 0.229232 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.15059e15 | 0.272173 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.06197e16 | 0.905392 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.11144e15 | 0.261801 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.24026e15 | −0.352129 | −0.176064 | − | 0.984379i | \(-0.556337\pi\) | ||||
−0.176064 | + | 0.984379i | \(0.556337\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.96693e15 | 0.816927 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.97144e15 | −0.725789 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.89107e15 | 0.470416 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.70160e16 | 4.49405 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.54493e15 | −0.587033 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.12708e16 | −0.865651 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.06183e16 | −1.56327 | −0.781634 | − | 0.623737i | \(-0.785614\pi\) | ||||
−0.781634 | + | 0.623737i | \(0.785614\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.94236e13 | 0.00295082 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.18051e16 | 0.872316 | 0.436158 | − | 0.899870i | \(-0.356339\pi\) | ||||
0.436158 | + | 0.899870i | \(0.356339\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.58163e16 | 1.88335 | 0.941676 | − | 0.336522i | \(-0.109251\pi\) | ||||
0.941676 | + | 0.336522i | \(0.109251\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.31363e15 | 0.598789 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.55796e15 | 0.608570 | 0.304285 | − | 0.952581i | \(-0.401582\pi\) | ||||
0.304285 | + | 0.952581i | \(0.401582\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.49587e15 | 0.245452 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.10089e15 | 0.561601 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.20342e16 | −0.823777 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.85629e15 | −0.598621 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.30573e15 | 0.354133 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.24829e16 | 1.48186 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.91250e16 | −1.24481 | −0.622405 | − | 0.782695i | \(-0.713844\pi\) | ||||
−0.622405 | + | 0.782695i | \(0.713844\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.34209e16 | −0.862669 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.10140e16 | −1.33395 | −0.666977 | − | 0.745079i | \(-0.732412\pi\) | ||||
−0.666977 | + | 0.745079i | \(0.732412\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.22222e16 | −1.39317 | −0.696585 | − | 0.717474i | \(-0.745298\pi\) | ||||
−0.696585 | + | 0.717474i | \(0.745298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.60941e15 | −0.347319 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.18293e15 | −0.133494 | −0.0667469 | − | 0.997770i | \(-0.521262\pi\) | ||||
−0.0667469 | + | 0.997770i | \(0.521262\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.42950e16 | −0.863423 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.61228e15 | 0.215503 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.37543e12 | −0.000139978 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.83823e14 | 0.0223411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.82681e15 | −0.105035 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.22849e16 | −1.83367 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.90891e15 | −0.219315 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.01234e16 | −1.11537 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.43886e16 | 0.787864 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.06657e16 | 1.11792 | 0.558959 | − | 0.829195i | \(-0.311201\pi\) | ||||
0.558959 | + | 0.829195i | \(0.311201\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.32939e15 | −0.0710481 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.53802e16 | −1.86814 | −0.934069 | − | 0.357093i | \(-0.883768\pi\) | ||||
−0.934069 | + | 0.357093i | \(0.883768\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.74516e16 | −2.99718 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.95202e15 | 0.306795 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.32499e16 | 0.674810 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.42662e16 | −0.717916 | −0.358958 | − | 0.933354i | \(-0.616868\pi\) | ||||
−0.358958 | + | 0.933354i | \(0.616868\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.80599e16 | −0.898021 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.41754e15 | −0.462731 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.35725e16 | −1.14453 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.63842e14 | 0.0270532 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.33625e16 | −0.633581 | −0.316791 | − | 0.948495i | \(-0.602605\pi\) | ||||
−0.316791 | + | 0.948495i | \(0.602605\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.87853e14 | −0.0275452 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.46315e15 | 0.438215 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.70701e15 | −0.169652 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.55253e16 | 1.15452 | 0.577262 | − | 0.816559i | \(-0.304121\pi\) | ||||
0.577262 | + | 0.816559i | \(0.304121\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.48115e15 | −0.423838 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.09251e15 | 0.357553 | 0.178776 | − | 0.983890i | \(-0.442786\pi\) | ||||
0.178776 | + | 0.983890i | \(0.442786\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.94251e15 | 0.346851 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.84232e15 | 0.165851 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.57497e16 | 0.671965 | 0.335983 | − | 0.941868i | \(-0.390932\pi\) | ||||
0.335983 | + | 0.941868i | \(0.390932\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.68871e15 | 0.239911 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.13231e16 | −0.472033 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.17771e16 | −1.72158 | −0.860791 | − | 0.508958i | \(-0.830031\pi\) | ||||
−0.860791 | + | 0.508958i | \(0.830031\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.85893e16 | 0.757260 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.74818e16 | −1.50940 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.54558e16 | 1.80962 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.16117e16 | 0.850570 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.54136e15 | 0.215612 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.60891e15 | −0.138827 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.23895e16 | −0.471205 | −0.235602 | − | 0.971850i | \(-0.575706\pi\) | ||||
−0.235602 | + | 0.971850i | \(0.575706\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.23885e13 | 0.00159392 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.25057e16 | 0.464945 | 0.232473 | − | 0.972603i | \(-0.425318\pi\) | ||||
0.232473 | + | 0.972603i | \(0.425318\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.28510e16 | 1.20761 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.82071e15 | −0.138873 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.22032e16 | −0.797988 | −0.398994 | − | 0.916954i | \(-0.630641\pi\) | ||||
−0.398994 | + | 0.916954i | \(0.630641\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.62912e16 | 2.00049 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.12909e16 | 0.396781 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.91680e16 | −0.666090 | −0.333045 | − | 0.942911i | \(-0.608076\pi\) | ||||
−0.333045 | + | 0.942911i | \(0.608076\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.04216e16 | 0.358126 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.31516e14 | −0.00786749 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.92251e16 | −0.646084 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.50183e16 | −0.831482 | −0.415741 | − | 0.909483i | \(-0.636478\pi\) | ||||
−0.415741 | + | 0.909483i | \(0.636478\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.69968e16 | 0.558657 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.21245e16 | −0.719196 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.15404e16 | 0.371019 | 0.185510 | − | 0.982642i | \(-0.440606\pi\) | ||||
0.185510 | + | 0.982642i | \(0.440606\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.62745e15 | −0.306126 |
(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 | 96.12.a.d.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 96.12.a.f.1.1 | yes | 2 | ||
8.3 | odd | 2 | 192.12.a.u.1.2 | 2 | |||
8.5 | even | 2 | 192.12.a.x.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.12.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
96.12.a.f.1.1 | yes | 2 | 4.3 | odd | 2 | ||
192.12.a.u.1.2 | 2 | 8.3 | odd | 2 | |||
192.12.a.x.1.2 | 2 | 8.5 | even | 2 |