Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,8,Mod(1,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.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: | \(3.74862030581\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 12.1 |
$q$-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 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 270.000 | 0.965981 | 0.482991 | − | 0.875625i | \(-0.339550\pi\) | ||||
0.482991 | + | 0.875625i | \(0.339550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1112.00 | 1.22535 | 0.612677 | − | 0.790333i | \(-0.290093\pi\) | ||||
0.612677 | + | 0.790333i | \(0.290093\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5724.00 | −1.29666 | −0.648329 | − | 0.761361i | \(-0.724532\pi\) | ||||
−0.648329 | + | 0.761361i | \(0.724532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4570.00 | −0.576919 | −0.288459 | − | 0.957492i | \(-0.593143\pi\) | ||||
−0.288459 | + | 0.957492i | \(0.593143\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7290.00 | 0.557710 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −36558.0 | −1.80473 | −0.902363 | − | 0.430977i | \(-0.858169\pi\) | ||||
−0.902363 | + | 0.430977i | \(0.858169\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 51740.0 | 1.73057 | 0.865284 | − | 0.501281i | \(-0.167138\pi\) | ||||
0.865284 | + | 0.501281i | \(0.167138\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 30024.0 | 0.707459 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22248.0 | 0.381280 | 0.190640 | − | 0.981660i | \(-0.438944\pi\) | ||||
0.190640 | + | 0.981660i | \(0.438944\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5225.00 | −0.0668800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −157194. | −1.19686 | −0.598429 | − | 0.801175i | \(-0.704208\pi\) | ||||
−0.598429 | + | 0.801175i | \(0.704208\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −103936. | −0.626614 | −0.313307 | − | 0.949652i | \(-0.601437\pi\) | ||||
−0.313307 | + | 0.949652i | \(0.601437\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −154548. | −0.748625 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 300240. | 1.18367 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −94834.0 | −0.307793 | −0.153896 | − | 0.988087i | \(-0.549182\pi\) | ||||
−0.153896 | + | 0.988087i | \(0.549182\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −123390. | −0.333084 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 659610. | 1.49466 | 0.747332 | − | 0.664451i | \(-0.231334\pi\) | ||||
0.747332 | + | 0.664451i | \(0.231334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −75772.0 | −0.145335 | −0.0726673 | − | 0.997356i | \(-0.523151\pi\) | ||||
−0.0726673 | + | 0.997356i | \(0.523151\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 196830. | 0.321994 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 405648. | 0.569911 | 0.284955 | − | 0.958541i | \(-0.408021\pi\) | ||||
0.284955 | + | 0.958541i | \(0.408021\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 413001. | 0.501493 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −987066. | −1.04196 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.34627e6 | −1.24213 | −0.621066 | − | 0.783758i | \(-0.713300\pi\) | ||||
−0.621066 | + | 0.783758i | \(0.713300\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.54548e6 | −1.25255 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.39698e6 | 0.999144 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.30388e6 | −0.826527 | −0.413263 | − | 0.910612i | \(-0.635611\pi\) | ||||
−0.413263 | + | 0.910612i | \(0.635611\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.83378e6 | 1.03441 | 0.517206 | − | 0.855861i | \(-0.326972\pi\) | ||||
0.517206 | + | 0.855861i | \(0.326972\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 810648. | 0.408451 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.23390e6 | −0.557293 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.36939e6 | 0.556243 | 0.278122 | − | 0.960546i | \(-0.410288\pi\) | ||||
0.278122 | + | 0.960546i | \(0.410288\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 600696. | 0.220132 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.71404e6 | 0.899937 | 0.449968 | − | 0.893044i | \(-0.351435\pi\) | ||||
0.449968 | + | 0.893044i | \(0.351435\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.86879e6 | 0.863116 | 0.431558 | − | 0.902085i | \(-0.357964\pi\) | ||||
0.431558 | + | 0.902085i | \(0.357964\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −141075. | −0.0386132 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.36509e6 | −1.58886 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.12965e6 | −0.257779 | −0.128890 | − | 0.991659i | \(-0.541141\pi\) | ||||
−0.128890 | + | 0.991659i | \(0.541141\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.91203e6 | 1.13491 | 0.567457 | − | 0.823403i | \(-0.307927\pi\) | ||||
0.567457 | + | 0.823403i | \(0.307927\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.87066e6 | −1.74333 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.24424e6 | −0.691007 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −897750. | −0.134987 | −0.0674933 | − | 0.997720i | \(-0.521500\pi\) | ||||
−0.0674933 | + | 0.997720i | \(0.521500\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.08184e6 | −0.706930 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.80627e6 | −0.361776 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.39698e7 | 1.67170 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.37191e7 | 1.52624 | 0.763122 | − | 0.646255i | \(-0.223666\pi\) | ||||
0.763122 | + | 0.646255i | \(0.223666\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.17280e6 | −0.432219 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.93304e6 | 0.186688 | 0.0933438 | − | 0.995634i | \(-0.470244\pi\) | ||||
0.0933438 | + | 0.995634i | \(0.470244\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.76127e6 | 0.429331 | 0.214666 | − | 0.976688i | \(-0.431134\pi\) | ||||
0.214666 | + | 0.976688i | \(0.431134\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.10648e6 | 0.683392 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.21044e6 | 0.174435 | 0.0872177 | − | 0.996189i | \(-0.472202\pi\) | ||||
0.0872177 | + | 0.996189i | \(0.472202\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00929e7 | −1.48610 | −0.743052 | − | 0.669234i | \(-0.766622\pi\) | ||||
−0.743052 | + | 0.669234i | \(0.766622\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.56052e6 | −0.177704 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.94075e6 | 0.517711 | 0.258855 | − | 0.965916i | \(-0.416655\pi\) | ||||
0.258855 | + | 0.965916i | \(0.416655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00696e6 | 0.368309 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.33153e6 | −0.192306 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.06525e7 | −2.21143 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.32770e7 | 0.681320 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.78095e7 | 0.862945 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.25045e7 | −1.03059 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.27395e7 | −0.985071 | −0.492536 | − | 0.870292i | \(-0.663930\pi\) | ||||
−0.492536 | + | 0.870292i | \(0.663930\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.04584e6 | −0.0839090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.27784e7 | −0.885265 | −0.442633 | − | 0.896703i | \(-0.645955\pi\) | ||||
−0.442633 | + | 0.896703i | \(0.645955\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.75349e7 | 2.12056 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.31441e6 | 0.185903 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.16987e7 | 1.38548 | 0.692741 | − | 0.721186i | \(-0.256403\pi\) | ||||
0.692741 | + | 0.721186i | \(0.256403\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.19472e6 | −0.195645 | −0.0978227 | − | 0.995204i | \(-0.531188\pi\) | ||||
−0.0978227 | + | 0.995204i | \(0.531188\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.09525e7 | 0.329038 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.61587e7 | 0.748066 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.24424e7 | −1.15614 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.11510e7 | 0.289537 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.41658e6 | −0.134145 | −0.0670723 | − | 0.997748i | \(-0.521366\pi\) | ||||
−0.0670723 | + | 0.997748i | \(0.521366\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.08444e7 | 1.67450 | 0.837252 | − | 0.546818i | \(-0.184161\pi\) | ||||
0.837252 | + | 0.546818i | \(0.184161\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.66508e7 | −0.601575 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.80627e7 | −0.605297 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.90801e7 | −1.63087 | −0.815433 | − | 0.578851i | \(-0.803501\pi\) | ||||
−0.815433 | + | 0.578851i | \(0.803501\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.63494e7 | −0.717146 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.47398e7 | 0.467203 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.44491e7 | −0.442188 | −0.221094 | − | 0.975253i | \(-0.570963\pi\) | ||||
−0.221094 | + | 0.975253i | \(0.570963\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.17280e7 | −0.723158 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.55538e7 | 0.590716 | 0.295358 | − | 0.955387i | \(-0.404561\pi\) | ||||
0.295358 | + | 0.955387i | \(0.404561\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.18636e7 | −0.667165 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.77185e7 | 0.576856 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.02794e8 | 1.50941 | 0.754704 | − | 0.656066i | \(-0.227781\pi\) | ||||
0.754704 | + | 0.656066i | \(0.227781\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.81020e6 | −0.0819517 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.52049e7 | −0.477195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.15587e7 | −0.541597 | −0.270799 | − | 0.962636i | \(-0.587288\pi\) | ||||
−0.270799 | + | 0.962636i | \(0.587288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.35013e7 | −0.419939 | −0.209969 | − | 0.977708i | \(-0.567336\pi\) | ||||
−0.209969 | + | 0.977708i | \(0.567336\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.95121e7 | 0.597218 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.56052e7 | −0.297322 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.09258e8 | 2.34011 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.18875e7 | 0.235820 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.90804e7 | 0.509672 | 0.254836 | − | 0.966984i | \(-0.417978\pi\) | ||||
0.254836 | + | 0.966984i | \(0.417978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.04483e7 | 0.605248 | 0.302624 | − | 0.953110i | \(-0.402137\pi\) | ||||
0.302624 | + | 0.953110i | \(0.402137\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.33153e7 | −0.321753 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00456e6 | 0.0466374 | 0.0233187 | − | 0.999728i | \(-0.492577\pi\) | ||||
0.0233187 | + | 0.999728i | \(0.492577\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.21135e8 | −1.98917 | −0.994584 | − | 0.103935i | \(-0.966857\pi\) | ||||
−0.994584 | + | 0.103935i | \(0.966857\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.69735e7 | 0.321147 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.74800e8 | −1.46658 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.78095e8 | 1.44382 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.62188e7 | 0.127093 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.96160e8 | −2.24395 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.16641e7 | −0.525186 | −0.262593 | − | 0.964907i | \(-0.584578\pi\) | ||||
−0.262593 | + | 0.964907i | \(0.584578\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.32791e7 | 0.519579 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.04584e7 | −0.140391 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.15577e8 | −0.767824 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.74574e7 | 0.498320 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.67070e8 | 1.04118 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.61440e7 | 0.157872 | 0.0789360 | − | 0.996880i | \(-0.474848\pi\) | ||||
0.0789360 | + | 0.996880i | \(0.474848\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.80902e6 | −0.0222933 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.40994e7 | −0.193489 | −0.0967444 | − | 0.995309i | \(-0.530843\pi\) | ||||
−0.0967444 | + | 0.995309i | \(0.530843\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.27428e8 | 1.25147 | 0.625734 | − | 0.780037i | \(-0.284800\pi\) | ||||
0.625734 | + | 0.780037i | \(0.284800\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.71857e8 | −0.917331 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.69060e7 | 0.294722 | 0.147361 | − | 0.989083i | \(-0.452922\pi\) | ||||
0.147361 | + | 0.989083i | \(0.452922\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.09525e8 | 0.550523 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.05005e7 | −0.148829 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.02716e8 | 1.43431 | 0.717154 | − | 0.696915i | \(-0.245444\pi\) | ||||
0.717154 | + | 0.696915i | \(0.245444\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.53696e7 | −0.116749 | −0.0583746 | − | 0.998295i | \(-0.518592\pi\) | ||||
−0.0583746 | + | 0.998295i | \(0.518592\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.11510e8 | 0.484433 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.36452e8 | −0.998397 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.59625e8 | 0.655243 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.46544e7 | −0.0584939 | −0.0292469 | − | 0.999572i | \(-0.509311\pi\) | ||||
−0.0292469 | + | 0.999572i | \(0.509311\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.27348e8 | −0.494389 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.66508e8 | −1.00651 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.34652e7 | −0.0862300 | −0.0431150 | − | 0.999070i | \(-0.513728\pi\) | ||||
−0.0431150 | + | 0.999070i | \(0.513728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.05455e8 | −0.377155 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.14594e8 | −0.398953 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.25583e8 | 1.44258 | 0.721289 | − | 0.692634i | \(-0.243550\pi\) | ||||
0.721289 | + | 0.692634i | \(0.243550\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.63494e8 | −1.19988 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.42393e7 | −0.0779345 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.93062e8 | −1.23120 | −0.615599 | − | 0.788060i | \(-0.711086\pi\) | ||||
−0.615599 | + | 0.788060i | \(0.711086\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.89560e7 | 0.179943 | 0.0899716 | − | 0.995944i | \(-0.471322\pi\) | ||||
0.0899716 | + | 0.995944i | \(0.471322\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.37210e8 | −0.408146 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.99079e7 | 0.0867204 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.15973e7 | −0.0610550 | −0.0305275 | − | 0.999534i | \(-0.509719\pi\) | ||||
−0.0305275 | + | 0.999534i | \(0.509719\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.57693e7 | −0.208871 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.34718e8 | −0.899926 | −0.449963 | − | 0.893047i | \(-0.648563\pi\) | ||||
−0.449963 | + | 0.893047i | \(0.648563\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.26806e8 | 0.857113 | 0.428557 | − | 0.903515i | \(-0.359022\pi\) | ||||
0.428557 | + | 0.903515i | \(0.359022\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.77185e8 | 0.965155 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.33486e8 | 1.83149 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.26149e8 | 2.25703 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.70415e8 | 0.881177 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.28964e8 | −1.69305 | −0.846525 | − | 0.532350i | \(-0.821309\pi\) | ||||
−0.846525 | + | 0.532350i | \(0.821309\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.52049e8 | −0.798409 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.12665e8 | −0.249542 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.01673e8 | −0.219967 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.42585e7 | −0.178086 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.21920e7 | 0.107784 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.95121e8 | 0.999222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.26039e8 | −0.248612 | −0.124306 | − | 0.992244i | \(-0.539670\pi\) | ||||
−0.124306 | + | 0.992244i | \(0.539670\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.28554e8 | 0.247875 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.15768e8 | −1.34931 | −0.674654 | − | 0.738134i | \(-0.735707\pi\) | ||||
−0.674654 | + | 0.738134i | \(0.735707\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.91196e8 | −0.536760 | −0.268380 | − | 0.963313i | \(-0.586488\pi\) | ||||
−0.268380 | + | 0.963313i | \(0.586488\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.18875e8 | 0.394556 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.24285e7 | 0.0748084 | 0.0374042 | − | 0.999300i | \(-0.488091\pi\) | ||||
0.0374042 | + | 0.999300i | \(0.488091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.99778e8 | 1.55192 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.96818e7 | 0.100710 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.89151e9 | −3.12320 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.38782e7 | 0.0385843 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.42507e8 | −0.858002 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.51081e8 | 0.698343 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.47257e8 | −0.829455 | −0.414728 | − | 0.909946i | \(-0.636123\pi\) | ||||
−0.414728 | + | 0.909946i | \(0.636123\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.91340e7 | −0.102598 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.69735e8 | 0.537321 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.85332e8 | −0.263783 | −0.131891 | − | 0.991264i | \(-0.542105\pi\) | ||||
−0.131891 | + | 0.991264i | \(0.542105\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.14400e8 | 0.298900 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.94930e8 | 0.812504 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.56523e8 | −0.610848 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.62188e8 | 0.212643 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.29711e9 | 1.66657 | 0.833286 | − | 0.552842i | \(-0.186457\pi\) | ||||
0.833286 | + | 0.552842i | \(0.186457\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.22136e8 | −0.783423 | −0.391711 | − | 0.920088i | \(-0.628117\pi\) | ||||
−0.391711 | + | 0.920088i | \(0.628117\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.99513e7 | −0.111028 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.20687e8 | 0.751037 | 0.375519 | − | 0.926815i | \(-0.377465\pi\) | ||||
0.375519 | + | 0.926815i | \(0.377465\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.32791e8 | 0.869322 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.09762e9 | −1.27677 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.06882e8 | 0.692268 | 0.346134 | − | 0.938185i | \(-0.387494\pi\) | ||||
0.346134 | + | 0.938185i | \(0.387494\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.78316e9 | 1.99487 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.58479e8 | 0.393360 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.74574e8 | 0.833754 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.40538e9 | −1.48410 | −0.742051 | − | 0.670343i | \(-0.766147\pi\) | ||||
−0.742051 | + | 0.670343i | \(0.766147\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.80856e8 | 0.498222 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.49706e9 | −1.52205 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.12925e9 | −1.12670 | −0.563350 | − | 0.826218i | \(-0.690488\pi\) | ||||
−0.563350 | + | 0.826218i | \(0.690488\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.07622e8 | −0.595009 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.18377e8 | 0.690490 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.63515e9 | 1.54284 | 0.771419 | − | 0.636328i | \(-0.219547\pi\) | ||||
0.771419 | + | 0.636328i | \(0.219547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.13966e8 | −0.568731 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.27685e8 | −0.207080 | −0.103540 | − | 0.994625i | \(-0.533017\pi\) | ||||
−0.103540 | + | 0.994625i | \(0.533017\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.71857e9 | −1.53481 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.52378e7 | −0.0484449 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.23120e8 | −0.536720 | −0.268360 | − | 0.963319i | \(-0.586482\pi\) | ||||
−0.268360 | + | 0.963319i | \(0.586482\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.13342e8 | −0.688105 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.15016e8 | −0.511108 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.05005e8 | −0.249010 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.49583e6 | −0.00119982 | −0.000599911 | − | 1.00000i | \(-0.500191\pi\) | ||||
−0.000599911 | 1.00000i | \(0.500191\pi\) | ||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.55344e9 | 1.22431 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.06501e8 | −0.237370 | −0.118685 | − | 0.992932i | \(-0.537868\pi\) | ||||
−0.118685 | + | 0.992932i | \(0.537868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.74988e8 | 0.361505 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.43489e8 | 0.107331 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.42830e8 | 0.399101 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.56868e8 | 0.257915 | 0.128957 | − | 0.991650i | \(-0.458837\pi\) | ||||
0.128957 | + | 0.991650i | \(0.458837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.12587e9 | 0.799909 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.44992e9 | −1.01279 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.59625e9 | 1.09631 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.67257e8 | −0.112956 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.28428e9 | −1.51705 | −0.758526 | − | 0.651642i | \(-0.774080\pi\) | ||||
−0.758526 | + | 0.651642i | \(0.774080\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.63135e8 | 0.171866 | 0.0859332 | − | 0.996301i | \(-0.472613\pi\) | ||||
0.0859332 | + | 0.996301i | \(0.472613\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.95717e8 | 0.189970 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.91016e8 | 0.120700 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.03917e9 | 1.26752 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.06284e8 | 0.431896 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.49053e9 | 0.896747 | 0.448374 | − | 0.893846i | \(-0.352003\pi\) | ||||
0.448374 | + | 0.893846i | \(0.352003\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.10539e9 | 0.654347 | 0.327174 | − | 0.944964i | \(-0.393904\pi\) | ||||
0.327174 | + | 0.944964i | \(0.393904\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.14594e9 | −0.667500 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.15111e9 | 0.659830 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.96353e8 | 0.167180 | 0.0835898 | − | 0.996500i | \(-0.473361\pi\) | ||||
0.0835898 | + | 0.996500i | \(0.473361\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.01078e8 | 0.167164 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.58944e8 | 0.196162 | 0.0980808 | − | 0.995178i | \(-0.468730\pi\) | ||||
0.0980808 | + | 0.995178i | \(0.468730\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.42393e8 | −0.130394 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.46248e8 | −0.0774484 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.41948e9 | −1.78278 | −0.891391 | − | 0.453235i | \(-0.850270\pi\) | ||||
−0.891391 | + | 0.453235i | \(0.850270\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.77561e9 | −1.93807 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.91280e9 | 0.966775 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.37210e9 | −0.682881 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.85828e9 | −1.40087 | −0.700434 | − | 0.713717i | \(-0.747010\pi\) | ||||
−0.700434 | + | 0.713717i | \(0.747010\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.19571e8 | −0.347320 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.62700e8 | 0.457654 | 0.228827 | − | 0.973467i | \(-0.426511\pi\) | ||||
0.228827 | + | 0.973467i | \(0.426511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.01893e8 | 0.281829 | 0.140914 | − | 0.990022i | \(-0.454996\pi\) | ||||
0.140914 | + | 0.990022i | \(0.454996\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.57693e8 | −0.349469 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.72060e9 | 0.781755 | 0.390878 | − | 0.920443i | \(-0.372172\pi\) | ||||
0.390878 | + | 0.920443i | \(0.372172\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.52276e9 | 0.681595 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.13516e9 | −0.941581 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.33719e8 | 0.188449 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.70342e8 | −0.115740 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.81434e8 | −0.414044 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.37262e8 | −0.223363 | −0.111682 | − | 0.993744i | \(-0.535624\pi\) | ||||
−0.111682 | + | 0.993744i | \(0.535624\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.33391e8 | 0.177571 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.67974e8 | 0.269740 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.70415e9 | 1.47432 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.49621e9 | −1.76399 | −0.881993 | − | 0.471262i | \(-0.843799\pi\) | ||||
−0.881993 | + | 0.471262i | \(0.843799\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.60127e8 | −0.255297 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.32917e9 | 1.26926 | 0.634631 | − | 0.772815i | \(-0.281152\pi\) | ||||
0.634631 | + | 0.772815i | \(0.281152\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.74670e9 | 2.16000 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.12665e9 | −0.417516 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.01801e9 | 1.10274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.04986e9 | −0.738536 | −0.369268 | − | 0.929323i | \(-0.620392\pi\) | ||||
−0.369268 | + | 0.929323i | \(0.620392\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.59953e8 | 0.341050 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.76491e8 | 0.272050 | 0.136025 | − | 0.990705i | \(-0.456567\pi\) | ||||
0.136025 | + | 0.990705i | \(0.456567\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.21920e8 | 0.180337 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.13032e9 | −0.385188 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.56679e9 | −1.53497 | −0.767483 | − | 0.641069i | \(-0.778491\pi\) | ||||
−0.767483 | + | 0.641069i | \(0.778491\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.19010e9 | 1.05762 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.01840e9 | 0.333048 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.28554e9 | 0.414726 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.32193e9 | −0.738979 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.77544e9 | 0.871457 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.21159e9 | −0.685130 | −0.342565 | − | 0.939494i | \(-0.611296\pi\) | ||||
−0.342565 | + | 0.939494i | \(0.611296\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.34154e9 | −0.715724 | −0.357862 | − | 0.933774i | \(-0.616494\pi\) | ||||
−0.357862 | + | 0.933774i | \(0.616494\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.56875e8 | −0.0473148 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.79969e9 | 1.13087 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.90985e9 | −0.854626 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.50531e8 | −0.275509 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.01442e9 | −0.862300 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.96818e8 | 0.168501 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.12209e9 | −0.312691 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.36402e9 | −0.650265 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.35497e9 | 0.639433 | 0.319717 | − | 0.947513i | \(-0.396412\pi\) | ||||
0.319717 | + | 0.947513i | \(0.396412\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.04534e8 | −0.242452 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.42507e9 | −1.43555 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.41493e9 | 0.892127 | 0.446063 | − | 0.895001i | \(-0.352826\pi\) | ||||
0.446063 | + | 0.895001i | \(0.352826\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.33683e9 | 0.344804 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.13322e9 | −2.07125 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.25617e9 | −0.315871 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.91340e8 | −0.171659 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.79293e8 | −0.117519 | −0.0587595 | − | 0.998272i | \(-0.518715\pi\) | ||||
−0.0587595 | + | 0.998272i | \(0.518715\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.46278e8 | 0.0838462 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.64997e9 | 1.35106 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.50302e9 | 1.53580 | 0.767902 | − | 0.640567i | \(-0.221301\pi\) | ||||
0.767902 | + | 0.640567i | \(0.221301\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.14400e9 | 0.500099 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.90962e8 | 0.136150 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.51625e9 | −1.02774 | −0.513872 | − | 0.857867i | \(-0.671789\pi\) | ||||
−0.513872 | + | 0.857867i | \(0.671789\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.47375e9 | 0.556071 | 0.278035 | − | 0.960571i | \(-0.410317\pi\) | ||||
0.278035 | + | 0.960571i | \(0.410317\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.32517e9 | 0.294260 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.16246e8 | −0.0255000 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.31721e8 | −0.115231 | −0.0576154 | − | 0.998339i | \(-0.518350\pi\) | ||||
−0.0576154 | + | 0.998339i | \(0.518350\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.63210e9 | 0.349440 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.57418e9 | 1.39067 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.70607e9 | 1.61062 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.99513e8 | −0.185764 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.17110e9 | 1.66743 | 0.833715 | − | 0.552195i | \(-0.186210\pi\) | ||||
0.833715 | + | 0.552195i | \(0.186210\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.37765e9 | −1.08440 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.35123e8 | 0.0269261 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.59923e9 | −0.314934 | −0.157467 | − | 0.987524i | \(-0.550333\pi\) | ||||
−0.157467 | + | 0.987524i | \(0.550333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.09762e10 | −2.13620 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.97064e9 | −1.14845 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.80330e9 | −1.67360 | −0.836800 | − | 0.547509i | \(-0.815576\pi\) | ||||
−0.836800 | + | 0.547509i | \(0.815576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.21235e9 | 1.54314 | 0.771572 | − | 0.636142i | \(-0.219471\pi\) | ||||
0.771572 | + | 0.636142i | \(0.219471\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.98284e8 | 0.185414 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.58479e9 | 0.658143 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.09192e9 | 0.924105 | 0.462052 | − | 0.886853i | \(-0.347113\pi\) | ||||
0.462052 | + | 0.886853i | \(0.347113\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.71959e9 | −0.846728 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.85381e9 | −0.328792 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.01282e9 | −1.22965 | −0.614824 | − | 0.788664i | \(-0.710773\pi\) | ||||
−0.614824 | + | 0.788664i | \(0.710773\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.80856e9 | 0.833589 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.63714e9 | 0.794789 | 0.397394 | − | 0.917648i | \(-0.369914\pi\) | ||||
0.397394 | + | 0.917648i | \(0.369914\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.33917e9 | 0.226943 | 0.113472 | − | 0.993541i | \(-0.463803\pi\) | ||||
0.113472 | + | 0.993541i | \(0.463803\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.37907e8 | 0.0733773 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.98298e8 | −0.165406 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.66801e9 | −0.928647 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.99631e9 | −1.29555 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.46694e9 | 0.555481 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.12354e10 | −1.78027 | −0.890133 | − | 0.455700i | \(-0.849389\pi\) | ||||
−0.890133 | + | 0.455700i | \(0.849389\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.93493e9 | −0.303216 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.13966e9 | −0.951561 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.88741e9 | −0.289321 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.97854e9 | 0.299979 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.82380e9 | 1.47325 | 0.736625 | − | 0.676301i | \(-0.236418\pi\) | ||||
0.736625 | + | 0.676301i | \(0.236418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.56240e9 | 0.528450 | 0.264225 | − | 0.964461i | \(-0.414884\pi\) | ||||
0.264225 | + | 0.964461i | \(0.414884\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.52378e8 | −0.0810545 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.91119e9 | 0.858045 | 0.429022 | − | 0.903294i | \(-0.358858\pi\) | ||||
0.429022 | + | 0.903294i | \(0.358858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.46343e9 | 1.07172 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.12057e9 | −0.443303 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.70538e8 | −0.108292 | −0.0541462 | − | 0.998533i | \(-0.517244\pi\) | ||||
−0.0541462 | + | 0.998533i | \(0.517244\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.15016e9 | −0.855150 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.09135e9 | 0.287705 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.95271e9 | 0.674130 | 0.337065 | − | 0.941481i | \(-0.390566\pi\) | ||||
0.337065 | + | 0.941481i | \(0.390566\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.20319e9 | −0.162042 | −0.0810210 | − | 0.996712i | \(-0.525818\pi\) | ||||
−0.0810210 | + | 0.996712i | \(0.525818\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.51089e9 | 0.601125 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.55344e10 | 2.04842 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.49725e9 | −0.456338 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.05888e8 | 0.0911474 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.04966e10 | −1.34128 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.30823e10 | 1.65436 | 0.827181 | − | 0.561936i | \(-0.189943\pi\) | ||||
0.827181 | + | 0.561936i | \(0.189943\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.02844e8 | −0.0128711 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.49380e10 | −1.85025 | −0.925126 | − | 0.379660i | \(-0.876041\pi\) | ||||
−0.925126 | + | 0.379660i | \(0.876041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.52556e10 | 1.87019 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.20683e8 | −0.111711 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.50415e9 | −1.14141 | −0.570704 | − | 0.821156i | \(-0.693330\pi\) | ||||
−0.570704 | + | 0.821156i | \(0.693330\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.12587e10 | 1.33835 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.14055e9 | 0.722535 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.15247e9 | 0.716609 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.87893e9 | 0.216639 | 0.108320 | − | 0.994116i | \(-0.465453\pi\) | ||||
0.108320 | + | 0.994116i | \(0.465453\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.64015e9 | −0.529622 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.67257e9 | −0.188990 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.41140e10 | −2.69746 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.53646e9 | 0.170158 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.06591e10 | −1.16872 | −0.584359 | − | 0.811496i | \(-0.698654\pi\) | ||||
−0.584359 | + | 0.811496i | \(0.698654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.90671e9 | −0.532656 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.95717e9 | 0.317845 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.14954e9 | 0.228758 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.58464e10 | −1.66982 | −0.834911 | − | 0.550385i | \(-0.814481\pi\) | ||||
−0.834911 | + | 0.550385i | \(0.814481\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.23513e8 | −0.0859265 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.31237e9 | −0.238915 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.06284e9 | 0.722617 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.17333e9 | 0.828098 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.78482e10 | −1.79079 | −0.895394 | − | 0.445274i | \(-0.853106\pi\) | ||||
−0.895394 | + | 0.445274i | \(0.853106\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.29453e9 | 0.526083 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.84979e8 | −0.0674051 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.21339e8 | 0.0800459 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.41123e10 | 1.36216 | 0.681081 | − | 0.732208i | \(-0.261510\pi\) | ||||
0.681081 | + | 0.732208i | \(0.261510\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.77007e9 | 0.262289 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.55324e9 | −0.520814 | −0.260407 | − | 0.965499i | \(-0.583857\pi\) | ||||
−0.260407 | + | 0.965499i | \(0.583857\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.01078e9 | 0.279687 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.83838e9 | −0.721257 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.72614e9 | 0.886513 | 0.443256 | − | 0.896395i | \(-0.353823\pi\) | ||||
0.443256 | + | 0.896395i | \(0.353823\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.38420e9 | −0.576425 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.37462e8 | 0.0749038 | 0.0374519 | − | 0.999298i | \(-0.488076\pi\) | ||||
0.0374519 | + | 0.999298i | \(0.488076\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.46248e9 | −0.129581 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.30987e9 | 0.378305 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.45800e9 | 0.213745 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.05422e9 | −0.263124 | −0.131562 | − | 0.991308i | \(-0.541999\pi\) | ||||
−0.131562 | + | 0.991308i | \(0.541999\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.95669e8 | −0.0337715 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.91280e10 | 1.61754 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.77250e10 | 1.48508 | 0.742541 | − | 0.669800i | \(-0.233620\pi\) | ||||
0.742541 | + | 0.669800i | \(0.233620\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.43838e9 | −0.285436 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.28268e9 | 0.105505 | 0.0527524 | − | 0.998608i | \(-0.483201\pi\) | ||||
0.0527524 | + | 0.998608i | \(0.483201\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.23433e10 | −1.82100 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.19571e9 | −0.581110 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.95875e9 | 0.476839 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.50778e10 | 1.19562 | 0.597812 | − | 0.801636i | \(-0.296037\pi\) | ||||
0.597812 | + | 0.801636i | \(0.296037\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.33561e8 | −0.0497849 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.26737e10 | 0.986902 | 0.493451 | − | 0.869774i | \(-0.335735\pi\) | ||||
0.493451 | + | 0.869774i | \(0.335735\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.43066e8 | 0.0419079 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.84730e9 | −0.217750 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.41282e10 | 2.58662 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.55352e10 | −1.16691 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.09405e9 | −0.230336 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.13516e10 | −1.57539 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.46684e9 | −0.107268 | −0.0536342 | − | 0.998561i | \(-0.517081\pi\) | ||||
−0.0536342 | + | 0.998561i | \(0.517081\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.14907e10 | 0.832873 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.83012e9 | 0.634379 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.38038e9 | −0.596771 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.81434e9 | −0.692749 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.49629e10 | −1.04692 | −0.523459 | − | 0.852051i | \(-0.675359\pi\) | ||||
−0.523459 | + | 0.852051i | \(0.675359\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.48297e10 | −1.02853 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.54460e8 | −0.0449955 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.64210e10 | −1.11917 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.67974e9 | 0.451309 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.06127e10 | −0.710832 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.06263e10 | 0.705606 | 0.352803 | − | 0.935698i | \(-0.385229\pi\) | ||||
0.352803 | + | 0.935698i | \(0.385229\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.44306e10 | −1.60828 | −0.804139 | − | 0.594442i | \(-0.797373\pi\) | ||||
−0.804139 | + | 0.594442i | \(0.797373\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.59181e9 | 0.103890 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.60127e9 | −0.427145 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.92044e9 | −0.251512 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.70466e9 | −0.235643 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.68568e10 | 1.69376 | 0.846882 | − | 0.531781i | \(-0.178477\pi\) | ||||
0.846882 | + | 0.531781i | \(0.178477\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.82914e9 | 0.364506 | 0.182253 | − | 0.983252i | \(-0.441661\pi\) | ||||
0.182253 | + | 0.983252i | \(0.441661\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.07513e8 | 0.0500681 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.31761e10 | −0.810062 | −0.405031 | − | 0.914303i | \(-0.632739\pi\) | ||||
−0.405031 | + | 0.914303i | \(0.632739\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.99634e10 | 1.21701 | 0.608504 | − | 0.793551i | \(-0.291770\pi\) | ||||
0.608504 | + | 0.793551i | \(0.291770\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.83128e8 | −0.0352501 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.50985e10 | −0.905057 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.59953e9 | 0.570620 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.04577e9 | −0.120592 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.19433e10 | 1.28273 | 0.641365 | − | 0.767236i | \(-0.278368\pi\) | ||||
0.641365 | + | 0.767236i | \(0.278368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.46008e9 | 0.432471 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.03739e9 | −0.519573 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.13032e10 | −0.644469 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.47640e10 | 0.834859 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.82378e9 | 0.494854 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.10987e9 | −0.117355 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.13102e10 | −1.17562 | −0.587808 | − | 0.809000i | \(-0.700009\pi\) | ||||
−0.587808 | + | 0.809000i | \(0.700009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.01840e10 | 0.557232 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.65996e9 | 0.252900 | 0.126450 | − | 0.991973i | \(-0.459642\pi\) | ||||
0.126450 | + | 0.991973i | \(0.459642\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.68420e9 | −0.0906606 | −0.0453303 | − | 0.998972i | \(-0.514434\pi\) | ||||
−0.0453303 | + | 0.998972i | \(0.514434\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.98041e10 | 1.05741 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.08632e9 | 0.0575336 | 0.0287668 | − | 0.999586i | \(-0.490842\pi\) | ||||
0.0287668 | + | 0.999586i | \(0.490842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.77544e10 | 1.45806 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.50060e10 | 1.30310 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.46611e9 | 0.334252 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.25810e9 | −0.320907 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.00012e10 | 0.508748 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.50250e10 | −1.26283 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.11443e10 | 0.557897 | 0.278948 | − | 0.960306i | \(-0.410014\pi\) | ||||
0.278948 | + | 0.960306i | \(0.410014\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.96820e10 | −0.977482 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.78845e10 | −1.86658 | −0.933288 | − | 0.359130i | \(-0.883074\pi\) | ||||
−0.933288 | + | 0.359130i | \(0.883074\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.58131e10 | 0.772956 | 0.386478 | − | 0.922299i | \(-0.373692\pi\) | ||||
0.386478 | + | 0.922299i | \(0.373692\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.50531e9 | −0.460962 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.52171e10 | −0.732148 | −0.366074 | − | 0.930586i | \(-0.619298\pi\) | ||||
−0.366074 | + | 0.930586i | \(0.619298\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.52863e10 | −1.20706 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.04197e9 | −0.144073 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.09882e10 | 0.986270 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.12209e10 | −0.523173 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.74518e9 | −0.126998 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.63381e10 | 0.749969 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.92171e10 | 2.24171 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.27498e9 | −0.102818 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.04534e9 | −0.405653 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.52395e10 | −0.678181 | −0.339091 | − | 0.940754i | \(-0.610119\pi\) | ||||
−0.339091 | + | 0.940754i | \(0.610119\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.40918e9 | 0.0622292 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.49447e10 | −0.654895 | −0.327448 | − | 0.944869i | \(-0.606189\pi\) | ||||
−0.327448 | + | 0.944869i | \(0.606189\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.38404e10 | −1.47160 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.33683e10 | 0.576901 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.53296e10 | −1.08476 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.65291e10 | −0.702500 | −0.351250 | − | 0.936282i | \(-0.614243\pi\) | ||||
−0.351250 | + | 0.936282i | \(0.614243\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.40306e9 | −0.143536 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.24032e10 | −0.519190 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.95508e8 | 0.0205852 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.47097e9 | 0.143110 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.58170e10 | −1.05646 | −0.528228 | − | 0.849102i | \(-0.677143\pi\) | ||||
−0.528228 | + | 0.849102i | \(0.677143\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.13687e10 | 0.867868 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.93257e10 | −0.779023 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.64997e10 | 2.26050 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.83428e10 | −0.728411 | −0.364206 | − | 0.931319i | \(-0.618659\pi\) | ||||
−0.364206 | + | 0.931319i | \(0.618659\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.86229e9 | −0.309899 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.33346e9 | −0.247786 | −0.123893 | − | 0.992296i | \(-0.539538\pi\) | ||||
−0.123893 | + | 0.992296i | \(0.539538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.46750e10 | 0.569885 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.90962e9 | 0.227797 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.01958e10 | 0.772744 | 0.386372 | − | 0.922343i | \(-0.373728\pi\) | ||||
0.386372 | + | 0.922343i | \(0.373728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.31104e10 | −0.497948 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.14557e9 | 0.0431906 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.86172e10 | 1.81955 | 0.909777 | − | 0.415096i | \(-0.136252\pi\) | ||||
0.909777 | + | 0.415096i | \(0.136252\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.32517e10 | 0.492334 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.42940e10 | 0.895999 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.63690e10 | 1.69771 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.67099e10 | −0.607355 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.61141e9 | 0.0581451 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.63210e10 | 0.584659 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.23778e10 | 0.440201 | 0.220100 | − | 0.975477i | \(-0.429362\pi\) | ||||
0.220100 | + | 0.975477i | \(0.429362\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.10708e10 | −1.80318 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.70597e10 | −0.598003 | −0.299001 | − | 0.954253i | \(-0.596654\pi\) | ||||
−0.299001 | + | 0.954253i | \(0.596654\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.88852e9 | −0.239735 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.44713e8 | 0.0222767 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.96945e10 | 1.36176 | 0.680878 | − | 0.732397i | \(-0.261598\pi\) | ||||
0.680878 | + | 0.732397i | \(0.261598\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.13872e9 | 0.175031 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.46477e10 | −0.495368 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.55397e7 | −0.00253652 | −0.00126826 | − | 0.999999i | \(-0.500404\pi\) | ||||
−0.00126826 | + | 0.999999i | \(0.500404\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.35123e9 | 0.0450508 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.21792e10 | 0.403188 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.68578e9 | −0.0554131 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.99026e10 | −0.976002 | −0.488001 | − | 0.872843i | \(-0.662274\pi\) | ||||
−0.488001 | + | 0.872843i | \(0.662274\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.47759e10 | −0.478886 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.97064e10 | −1.92150 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.24254e10 | 0.397081 | 0.198540 | − | 0.980093i | \(-0.436380\pi\) | ||||
0.198540 | + | 0.980093i | \(0.436380\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.86662e9 | −0.0592347 |
(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 | 12.8.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 36.8.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 48.8.a.d.1.1 | 1 | |||
5.2 | odd | 4 | 300.8.d.a.49.1 | 2 | |||
5.3 | odd | 4 | 300.8.d.a.49.2 | 2 | |||
5.4 | even | 2 | 300.8.a.a.1.1 | 1 | |||
7.2 | even | 3 | 588.8.i.b.361.1 | 2 | |||
7.3 | odd | 6 | 588.8.i.g.373.1 | 2 | |||
7.4 | even | 3 | 588.8.i.b.373.1 | 2 | |||
7.5 | odd | 6 | 588.8.i.g.361.1 | 2 | |||
7.6 | odd | 2 | 588.8.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 192.8.a.j.1.1 | 1 | |||
8.5 | even | 2 | 192.8.a.b.1.1 | 1 | |||
9.2 | odd | 6 | 324.8.e.e.109.1 | 2 | |||
9.4 | even | 3 | 324.8.e.b.217.1 | 2 | |||
9.5 | odd | 6 | 324.8.e.e.217.1 | 2 | |||
9.7 | even | 3 | 324.8.e.b.109.1 | 2 | |||
12.11 | even | 2 | 144.8.a.c.1.1 | 1 | |||
24.5 | odd | 2 | 576.8.a.v.1.1 | 1 | |||
24.11 | even | 2 | 576.8.a.u.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.8.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
36.8.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
48.8.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
144.8.a.c.1.1 | 1 | 12.11 | even | 2 | |||
192.8.a.b.1.1 | 1 | 8.5 | even | 2 | |||
192.8.a.j.1.1 | 1 | 8.3 | odd | 2 | |||
300.8.a.a.1.1 | 1 | 5.4 | even | 2 | |||
300.8.d.a.49.1 | 2 | 5.2 | odd | 4 | |||
300.8.d.a.49.2 | 2 | 5.3 | odd | 4 | |||
324.8.e.b.109.1 | 2 | 9.7 | even | 3 | |||
324.8.e.b.217.1 | 2 | 9.4 | even | 3 | |||
324.8.e.e.109.1 | 2 | 9.2 | odd | 6 | |||
324.8.e.e.217.1 | 2 | 9.5 | odd | 6 | |||
576.8.a.u.1.1 | 1 | 24.11 | even | 2 | |||
576.8.a.v.1.1 | 1 | 24.5 | odd | 2 | |||
588.8.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
588.8.i.b.361.1 | 2 | 7.2 | even | 3 | |||
588.8.i.b.373.1 | 2 | 7.4 | even | 3 | |||
588.8.i.g.361.1 | 2 | 7.5 | odd | 6 | |||
588.8.i.g.373.1 | 2 | 7.3 | odd | 6 |