Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(197.773761087\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2070x^{2} - 13768x + 561570 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(14.0249\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-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 | ||||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2687.31 | −1.92288 | −0.961440 | − | 0.275016i | \(-0.911317\pi\) | ||||
−0.961440 | + | 0.275016i | \(0.911317\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −950.516 | −0.149630 | −0.0748149 | − | 0.997197i | \(-0.523837\pi\) | ||||
−0.0748149 | + | 0.997197i | \(0.523837\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −85357.5 | −1.75782 | −0.878911 | − | 0.476986i | \(-0.841729\pi\) | ||||
−0.878911 | + | 0.476986i | \(0.841729\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 124861. | 1.21250 | 0.606249 | − | 0.795275i | \(-0.292674\pi\) | ||||
0.606249 | + | 0.795275i | \(0.292674\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −217672. | −1.11017 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −21449.0 | −0.0622856 | −0.0311428 | − | 0.999515i | \(-0.509915\pi\) | ||||
−0.0311428 | + | 0.999515i | \(0.509915\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 243033. | 0.427832 | 0.213916 | − | 0.976852i | \(-0.431378\pi\) | ||||
0.213916 | + | 0.976852i | \(0.431378\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −76991.8 | −0.0863888 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 706695. | 0.526570 | 0.263285 | − | 0.964718i | \(-0.415194\pi\) | ||||
0.263285 | + | 0.964718i | \(0.415194\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.26849e6 | 2.69747 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.90211e6 | 1.02449 | 0.512246 | − | 0.858839i | \(-0.328814\pi\) | ||||
0.512246 | + | 0.858839i | \(0.328814\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.04528e6 | −1.56464 | −0.782319 | − | 0.622878i | \(-0.785963\pi\) | ||||
−0.782319 | + | 0.622878i | \(0.785963\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.91396e6 | −1.01488 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.55433e6 | 0.287720 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.67047e7 | 1.46531 | 0.732656 | − | 0.680599i | \(-0.238281\pi\) | ||||
0.732656 | + | 0.680599i | \(0.238281\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.01137e7 | 0.700036 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.31163e7 | −1.83027 | −0.915134 | − | 0.403149i | \(-0.867915\pi\) | ||||
−0.915134 | + | 0.403149i | \(0.867915\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.30635e7 | 1.47483 | 0.737413 | − | 0.675442i | \(-0.236047\pi\) | ||||
0.737413 | + | 0.675442i | \(0.236047\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.76314e7 | −0.640960 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.29633e7 | 0.985351 | 0.492675 | − | 0.870213i | \(-0.336019\pi\) | ||||
0.492675 | + | 0.870213i | \(0.336019\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.94501e7 | −0.977611 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.73737e6 | −0.0359606 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.61799e7 | 0.978001 | 0.489000 | − | 0.872284i | \(-0.337362\pi\) | ||||
0.489000 | + | 0.872284i | \(0.337362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.29382e8 | 3.38008 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.96857e7 | 0.247009 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.09356e7 | 0.117492 | 0.0587460 | − | 0.998273i | \(-0.481290\pi\) | ||||
0.0587460 | + | 0.998273i | \(0.481290\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.77590e7 | 0.349170 | 0.174585 | − | 0.984642i | \(-0.444142\pi\) | ||||
0.174585 | + | 0.984642i | \(0.444142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.23634e6 | −0.0498766 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.35539e8 | −2.33149 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.13783e7 | −0.553996 | −0.276998 | − | 0.960871i | \(-0.589340\pi\) | ||||
−0.276998 | + | 0.960871i | \(0.589340\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.72423e7 | 0.304016 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.44278e8 | −1.14083 | −0.570416 | − | 0.821356i | \(-0.693218\pi\) | ||||
−0.570416 | + | 0.821356i | \(0.693218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.30973e8 | 0.539795 | 0.269898 | − | 0.962889i | \(-0.413010\pi\) | ||||
0.269898 | + | 0.962889i | \(0.413010\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.26747e8 | 1.55738 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.11337e7 | 0.263023 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.26074e8 | 1.23073 | 0.615366 | − | 0.788241i | \(-0.289008\pi\) | ||||
0.615366 | + | 0.788241i | \(0.289008\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.32850e8 | 0.538547 | 0.269274 | − | 0.963064i | \(-0.413216\pi\) | ||||
0.269274 | + | 0.963064i | \(0.413216\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.76401e7 | 0.119768 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.16071e8 | 0.591490 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.89719e8 | −0.489465 | −0.244732 | − | 0.969591i | \(-0.578700\pi\) | ||||
−0.244732 | + | 0.969591i | \(0.578700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.18682e8 | −0.181426 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.51668e8 | −0.903344 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.53103e8 | −0.822670 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.74576e8 | −0.314912 | −0.157456 | − | 0.987526i | \(-0.550329\pi\) | ||||
−0.157456 | + | 0.987526i | \(0.550329\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.60031e8 | −0.585941 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.51816e8 | 0.432032 | 0.216016 | − | 0.976390i | \(-0.430694\pi\) | ||||
0.216016 | + | 0.976390i | \(0.430694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.90289e8 | −0.779405 | −0.389703 | − | 0.920941i | \(-0.627422\pi\) | ||||
−0.389703 | + | 0.920941i | \(0.627422\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.06901e8 | 0.166115 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.56017e9 | −1.88817 | −0.944087 | − | 0.329696i | \(-0.893054\pi\) | ||||
−0.944087 | + | 0.329696i | \(0.893054\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.33571e9 | −0.906345 | −0.453173 | − | 0.891423i | \(-0.649708\pi\) | ||||
−0.453173 | + | 0.891423i | \(0.649708\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.35308e9 | 0.845998 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.87335e9 | −1.65781 | −0.828906 | − | 0.559388i | \(-0.811036\pi\) | ||||
−0.828906 | + | 0.559388i | \(0.811036\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.89910e9 | −1.01253 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.19211e8 | 0.404166 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.03876e7 | 0.00931978 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.92796e9 | 2.08994 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.68242e9 | −1.05671 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.90939e9 | −3.26402 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.49390e8 | −0.187397 | −0.0936987 | − | 0.995601i | \(-0.529869\pi\) | ||||
−0.0936987 | + | 0.995601i | \(0.529869\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.67815e9 | 0.851492 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.50142e8 | 0.103878 | 0.0519390 | − | 0.998650i | \(-0.483460\pi\) | ||||
0.0519390 | + | 0.998650i | \(0.483460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.31007e8 | −0.0640165 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.42814e9 | −0.370058 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.45719e9 | 0.595930 | 0.297965 | − | 0.954577i | \(-0.403692\pi\) | ||||
0.297965 | + | 0.954577i | \(0.403692\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.52695e9 | −0.801368 | −0.400684 | − | 0.916216i | \(-0.631228\pi\) | ||||
−0.400684 | + | 0.916216i | \(0.631228\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.67003e9 | 0.568893 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.06578e10 | −2.13135 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.04862e10 | −1.96997 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.19546e9 | −0.564424 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.64409e9 | 0.771903 | 0.385952 | − | 0.922519i | \(-0.373873\pi\) | ||||
0.385952 | + | 0.922519i | \(0.373873\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.68753e9 | 0.264152 | 0.132076 | − | 0.991240i | \(-0.457836\pi\) | ||||
0.132076 | + | 0.991240i | \(0.457836\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.40727e8 | −0.0207619 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.16201e10 | 3.00861 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.63799e9 | 0.740587 | 0.370294 | − | 0.928915i | \(-0.379257\pi\) | ||||
0.370294 | + | 0.928915i | \(0.379257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.55057e9 | 0.564649 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.71725e8 | −0.0787907 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.19678e9 | −0.687577 | −0.343789 | − | 0.939047i | \(-0.611710\pi\) | ||||
−0.343789 | + | 0.939047i | \(0.611710\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.85799e10 | 1.95149 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.41917e9 | 0.937106 | 0.468553 | − | 0.883435i | \(-0.344776\pi\) | ||||
0.468553 | + | 0.883435i | \(0.344776\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.98570e9 | 0.470149 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.59454e9 | 0.142611 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.18003e8 | −0.0100158 | −0.00500790 | − | 0.999987i | \(-0.501594\pi\) | ||||
−0.00500790 | + | 0.999987i | \(0.501594\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.00778e9 | −0.403621 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.85783e8 | 0.0678340 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.46326e9 | 0.688973 | 0.344486 | − | 0.938791i | \(-0.388053\pi\) | ||||
0.344486 | + | 0.938791i | \(0.388053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.75573e10 | 1.21592 | 0.607960 | − | 0.793967i | \(-0.291988\pi\) | ||||
0.607960 | + | 0.793967i | \(0.291988\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.05848e9 | 0.201593 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.48905e10 | −2.81762 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.83084e9 | 0.109487 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.05143e8 | −0.0287963 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.11901e10 | −0.608394 | −0.304197 | − | 0.952609i | \(-0.598388\pi\) | ||||
−0.304197 | + | 0.952609i | \(0.598388\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.78678e9 | −0.144575 | −0.0722877 | − | 0.997384i | \(-0.523030\pi\) | ||||
−0.0722877 | + | 0.997384i | \(0.523030\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.71787e10 | −1.34608 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.22790e10 | −1.52694 | −0.763470 | − | 0.645843i | \(-0.776506\pi\) | ||||
−0.763470 | + | 0.645843i | \(0.776506\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.55007e10 | 1.15269 | 0.576345 | − | 0.817206i | \(-0.304478\pi\) | ||||
0.576345 | + | 0.817206i | \(0.304478\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.40164e9 | −0.319850 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.70902e9 | −0.153294 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.89937e10 | 3.51939 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.63662e9 | 0.175523 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.07447e10 | −0.752053 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.47230e9 | −0.294259 | −0.147130 | − | 0.989117i | \(-0.547003\pi\) | ||||
−0.147130 | + | 0.989117i | \(0.547003\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.97865e10 | −0.658659 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.88518e10 | −2.83591 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.64717e9 | 0.234116 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.06088e10 | 0.311651 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.67814e9 | −0.0755211 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.56578e10 | −1.23636 | −0.618178 | − | 0.786038i | \(-0.712129\pi\) | ||||
−0.618178 | + | 0.786038i | \(0.712129\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.45665e10 | 0.899155 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.68244e10 | 0.920490 | 0.460245 | − | 0.887792i | \(-0.347762\pi\) | ||||
0.460245 | + | 0.887792i | \(0.347762\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.88405e10 | −0.693015 | −0.346507 | − | 0.938047i | \(-0.612632\pi\) | ||||
−0.346507 | + | 0.938047i | \(0.612632\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.57183e9 | 0.151856 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.88931e10 | −0.864513 | −0.432256 | − | 0.901751i | \(-0.642282\pi\) | ||||
−0.432256 | + | 0.901751i | \(0.642282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.85826e10 | −1.89471 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.45120e10 | 0.710564 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.42661e10 | −0.877568 | −0.438784 | − | 0.898593i | \(-0.644591\pi\) | ||||
−0.438784 | + | 0.898593i | \(0.644591\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.41867e10 | 1.79851 | 0.899255 | − | 0.437426i | \(-0.144110\pi\) | ||||
0.899255 | + | 0.437426i | \(0.144110\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.06015e11 | 1.87983 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.03452e10 | 0.518746 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.88608e10 | 0.310931 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.84495e10 | −0.452421 | −0.226211 | − | 0.974078i | \(-0.572634\pi\) | ||||
−0.226211 | + | 0.974078i | \(0.572634\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.03217e10 | −0.925617 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.66885e9 | 0.0691479 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.16667e10 | −0.166820 | −0.0834100 | − | 0.996515i | \(-0.526581\pi\) | ||||
−0.0834100 | + | 0.996515i | \(0.526581\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.58781e10 | −0.219254 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.56017e10 | 0.341497 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.37197e11 | −1.76825 | −0.884127 | − | 0.467247i | \(-0.845246\pi\) | ||||
−0.884127 | + | 0.467247i | \(0.845246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.50972e11 | −1.88058 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.34672e10 | −0.282593 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.76644e10 | 0.671463 | 0.335732 | − | 0.941958i | \(-0.391016\pi\) | ||||
0.335732 | + | 0.941958i | \(0.391016\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.16504e11 | −1.31213 | −0.656067 | − | 0.754703i | \(-0.727781\pi\) | ||||
−0.656067 | + | 0.754703i | \(0.727781\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.61325e9 | −0.104746 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.49705e11 | −4.74166 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.33146e10 | −0.135884 | −0.0679419 | − | 0.997689i | \(-0.521643\pi\) | ||||
−0.0679419 | + | 0.997689i | \(0.521643\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.27851e10 | −0.521546 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.34219e10 | −0.319781 | −0.159891 | − | 0.987135i | \(-0.551114\pi\) | ||||
−0.159891 | + | 0.987135i | \(0.551114\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.11954e10 | −0.474452 | −0.237226 | − | 0.971455i | \(-0.576238\pi\) | ||||
−0.237226 | + | 0.971455i | \(0.576238\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.29014e10 | −0.474969 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.14776e10 | 0.273863 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.18128e11 | −0.996121 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.22407e10 | −0.181815 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.69283e11 | −1.34187 | −0.670934 | − | 0.741517i | \(-0.734107\pi\) | ||||
−0.670934 | + | 0.741517i | \(0.734107\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.93873e10 | −0.225923 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.53625e10 | −0.338293 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.82384e10 | 0.638465 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.14274e10 | −0.220678 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.65971e10 | 0.249434 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.01470e11 | −0.671411 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.67510e11 | 1.07626 | 0.538130 | − | 0.842862i | \(-0.319131\pi\) | ||||
0.538130 | + | 0.842862i | \(0.319131\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.21134e10 | −0.449990 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.42940e11 | 1.47257 | 0.736287 | − | 0.676669i | \(-0.236577\pi\) | ||||
0.736287 | + | 0.676669i | \(0.236577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.59566e11 | −1.52862 | −0.764308 | − | 0.644851i | \(-0.776919\pi\) | ||||
−0.764308 | + | 0.644851i | \(0.776919\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.67589e10 | 0.0959067 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.98973e11 | 1.66290 | 0.831448 | − | 0.555603i | \(-0.187512\pi\) | ||||
0.831448 | + | 0.555603i | \(0.187512\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.33074e11 | −1.80087 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.07374e11 | −1.09014 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.21282e9 | −0.0266478 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.57827e11 | 3.27067 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.08193e11 | −0.523279 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.13322e10 | −0.147438 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.64913e11 | −1.67095 | −0.835475 | − | 0.549528i | \(-0.814807\pi\) | ||||
−0.835475 | + | 0.549528i | \(0.814807\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.09599e11 | 0.488437 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.45561e11 | 1.06527 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.45199e11 | −0.613237 | −0.306618 | − | 0.951833i | \(-0.599197\pi\) | ||||
−0.306618 | + | 0.951833i | \(0.599197\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.32741e11 | −0.957139 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.86725e11 | 2.75035 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.58547e10 | 0.295910 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.53827e11 | −0.584585 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.28543e10 | −0.0475955 | −0.0237978 | − | 0.999717i | \(-0.507576\pi\) | ||||
−0.0237978 | + | 0.999717i | \(0.507576\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.59013e11 | −0.573744 | −0.286872 | − | 0.957969i | \(-0.592615\pi\) | ||||
−0.286872 | + | 0.957969i | \(0.592615\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.63561e10 | 0.233345 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.03715e11 | 0.355512 | 0.177756 | − | 0.984075i | \(-0.443116\pi\) | ||||
0.177756 | + | 0.984075i | \(0.443116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.56449e11 | 2.19368 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.65140e9 | 0.00538078 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.16136e10 | 0.132224 | 0.0661120 | − | 0.997812i | \(-0.478941\pi\) | ||||
0.0661120 | + | 0.997812i | \(0.478941\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.63623e11 | −0.816959 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.99165e11 | 1.20663 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.51965e11 | −1.03796 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.78771e11 | −1.08988 | −0.544941 | − | 0.838474i | \(-0.683448\pi\) | ||||
−0.544941 | + | 0.838474i | \(0.683448\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.17276e11 | −0.610089 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.33999e10 | −0.146338 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.90824e10 | 0.211539 | 0.105769 | − | 0.994391i | \(-0.466269\pi\) | ||||
0.105769 | + | 0.994391i | \(0.466269\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.21661e11 | −1.88448 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.87220e11 | 1.24219 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.43207e11 | −1.35235 | −0.676175 | − | 0.736741i | \(-0.736364\pi\) | ||||
−0.676175 | + | 0.736741i | \(0.736364\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.45006e10 | −0.108194 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.88749e11 | 1.63556 | 0.817780 | − | 0.575531i | \(-0.195204\pi\) | ||||
0.817780 | + | 0.575531i | \(0.195204\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.18031e11 | −0.505761 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.16930e11 | 0.491609 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.70395e11 | 1.04157 | 0.520786 | − | 0.853687i | \(-0.325639\pi\) | ||||
0.520786 | + | 0.853687i | \(0.325639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.51579e10 | −0.0327977 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.83615e10 | 0.0599740 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.14499e12 | −2.36655 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.27728e11 | −1.06623 | −0.533117 | − | 0.846042i | \(-0.678979\pi\) | ||||
−0.533117 | + | 0.846042i | \(0.678979\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.87115e10 | −0.0369599 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.78849e11 | −0.345411 | −0.172705 | − | 0.984974i | \(-0.555251\pi\) | ||||
−0.172705 | + | 0.984974i | \(0.555251\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.00454e12 | −1.89712 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.15680e11 | −0.213653 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.42587e12 | −2.57576 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.40686e11 | 0.778707 | 0.389353 | − | 0.921088i | \(-0.372698\pi\) | ||||
0.389353 | + | 0.921088i | \(0.372698\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.99032e11 | 0.344061 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.03945e10 | −0.0175803 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.25738e11 | −1.03556 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.85683e11 | −0.462670 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.08642e10 | 0.0489207 | 0.0244603 | − | 0.999701i | \(-0.492213\pi\) | ||||
0.0244603 | + | 0.999701i | \(0.492213\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.60022e11 | 0.403405 | 0.201703 | − | 0.979447i | \(-0.435353\pi\) | ||||
0.201703 | + | 0.979447i | \(0.435353\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.16272e11 | 0.328450 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.13004e11 | −0.168013 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.58906e10 | −0.0522462 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.63282e11 | −1.23054 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.19190e11 | −0.724734 | −0.362367 | − | 0.932035i | \(-0.618031\pi\) | ||||
−0.362367 | + | 0.932035i | \(0.618031\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.00829e12 | 1.37844 | 0.689222 | − | 0.724550i | \(-0.257953\pi\) | ||||
0.689222 | + | 0.724550i | \(0.257953\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.49379e11 | −1.13736 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.71750e11 | 0.225284 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.62358e10 | 0.0337135 | 0.0168568 | − | 0.999858i | \(-0.494634\pi\) | ||||
0.0168568 | + | 0.999858i | \(0.494634\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.58832e11 | −0.325870 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.82095e10 | 0.0841450 | 0.0420725 | − | 0.999115i | \(-0.486604\pi\) | ||||
0.0420725 | + | 0.999115i | \(0.486604\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.78563e11 | 0.941182 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.76172e11 | 0.445658 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.23102e12 | 1.42941 | 0.714707 | − | 0.699424i | \(-0.246560\pi\) | ||||
0.714707 | + | 0.699424i | \(0.246560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.82673e12 | 3.21728 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.36690e11 | 0.152508 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.18935e11 | 0.348860 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.33313e11 | 0.250216 | 0.125108 | − | 0.992143i | \(-0.460072\pi\) | ||||
0.125108 | + | 0.992143i | \(0.460072\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.13989e10 | −0.0119869 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.98394e11 | −0.823310 | −0.411655 | − | 0.911340i | \(-0.635049\pi\) | ||||
−0.411655 | + | 0.911340i | \(0.635049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.46529e11 | −0.148186 | −0.0740931 | − | 0.997251i | \(-0.523606\pi\) | ||||
−0.0740931 | + | 0.997251i | \(0.523606\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.75123e12 | 1.73702 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.53277e12 | −1.49125 | −0.745627 | − | 0.666364i | \(-0.767850\pi\) | ||||
−0.745627 | + | 0.666364i | \(0.767850\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.68566e10 | 0.0828943 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.56677e11 | 0.427578 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.82222e12 | −2.59248 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.28041e12 | 1.15406 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.68596e11 | 0.326000 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.94475e11 | −0.689558 | −0.344779 | − | 0.938684i | \(-0.612046\pi\) | ||||
−0.344779 | + | 0.938684i | \(0.612046\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.08576e12 | 1.77669 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.44097e10 | −0.0454898 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.37870e11 | 0.605539 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.34532e12 | −1.08379 | −0.541893 | − | 0.840447i | \(-0.682292\pi\) | ||||
−0.541893 | + | 0.840447i | \(0.682292\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.01939e11 | −0.396973 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.75188e12 | 1.36031 | 0.680154 | − | 0.733069i | \(-0.261913\pi\) | ||||
0.680154 | + | 0.733069i | \(0.261913\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.36964e10 | −0.0638110 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.50497e12 | 1.12669 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.32190e11 | 0.170702 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.66101e11 | −0.553138 | −0.276569 | − | 0.960994i | \(-0.589197\pi\) | ||||
−0.276569 | + | 0.960994i | \(0.589197\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.62953e11 | 0.541038 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.02872e12 | 1.41308 | 0.706540 | − | 0.707673i | \(-0.250255\pi\) | ||||
0.706540 | + | 0.707673i | \(0.250255\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.21417e12 | −0.830745 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.03842e11 | 0.271441 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.08049e11 | −0.203418 | −0.101709 | − | 0.994814i | \(-0.532431\pi\) | ||||
−0.101709 | + | 0.994814i | \(0.532431\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.24492e11 | −0.0807695 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.29158e11 | 0.0823364 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.39248e12 | 1.49870 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.81367e12 | −1.73207 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.55824e9 | −0.00578262 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.45259e12 | −1.45833 | −0.729165 | − | 0.684338i | \(-0.760091\pi\) | ||||
−0.729165 | + | 0.684338i | \(0.760091\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.41650e12 | −1.41231 | −0.706154 | − | 0.708059i | \(-0.749571\pi\) | ||||
−0.706154 | + | 0.708059i | \(0.749571\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.05630e11 | −0.233031 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.72564e11 | 0.0974543 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.30174e12 | −0.722724 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.17484e10 | 0.0391640 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.13493e12 | −2.21920 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.87996e12 | 3.63073 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.66524e11 | 0.397779 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.36737e12 | 1.71847 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.14349e12 | 0.573911 | 0.286955 | − | 0.957944i | \(-0.407357\pi\) | ||||
0.286955 | + | 0.957944i | \(0.407357\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.42215e12 | 0.702012 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.58947e12 | 1.74279 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.20917e12 | 0.577492 | 0.288746 | − | 0.957406i | \(-0.406762\pi\) | ||||
0.288746 | + | 0.957406i | \(0.406762\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.47737e11 | 0.116390 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.48340e11 | 0.438310 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.04991e11 | −0.184154 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.63613e12 | −1.62675 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.18500e12 | −0.961838 | −0.480919 | − | 0.876765i | \(-0.659697\pi\) | ||||
−0.480919 | + | 0.876765i | \(0.659697\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.12833e12 | 1.78822 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.48298e11 | 0.0632123 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.68753e11 | −0.0707886 | −0.0353943 | − | 0.999373i | \(-0.511269\pi\) | ||||
−0.0353943 | + | 0.999373i | \(0.511269\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.72157e12 | 3.18777 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.09166e10 | −0.0166255 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00268e12 | −1.20089 | −0.600446 | − | 0.799665i | \(-0.705010\pi\) | ||||
−0.600446 | + | 0.799665i | \(0.705010\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.51453e12 | 1.77726 | 0.888628 | − | 0.458628i | \(-0.151659\pi\) | ||||
0.888628 | + | 0.458628i | \(0.151659\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.06401e11 | −0.351257 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.72321e12 | 1.42041 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.10024e12 | 1.16441 | 0.582203 | − | 0.813044i | \(-0.302191\pi\) | ||||
0.582203 | + | 0.813044i | \(0.302191\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.25729e11 | −0.0834706 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.21327e11 | −0.0805828 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.79537e12 | −1.71915 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.20147e12 | −0.777162 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.50051e11 | 0.0869275 | 0.0434637 | − | 0.999055i | \(-0.486161\pi\) | ||||
0.0434637 | + | 0.999055i | \(0.486161\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.95527e12 | −0.669402 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.61460e12 | −0.881580 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.58185e12 | −0.525314 | −0.262657 | − | 0.964889i | \(-0.584599\pi\) | ||||
−0.262657 | + | 0.964889i | \(0.584599\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.47878e10 | −0.0179208 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.06555e12 | 0.665506 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.55230e12 | −1.44481 | −0.722404 | − | 0.691471i | \(-0.756963\pi\) | ||||
−0.722404 | + | 0.691471i | \(0.756963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.54016e12 | 1.73216 | 0.866079 | − | 0.499908i | \(-0.166633\pi\) | ||||
0.866079 | + | 0.499908i | \(0.166633\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.99533e11 | −0.184665 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.32429e13 | −4.01870 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.77998e12 | −0.831175 | −0.415587 | − | 0.909553i | \(-0.636424\pi\) | ||||
−0.415587 | + | 0.909553i | \(0.636424\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.00430e11 | −0.0885046 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.11583e12 | 1.19474 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.59888e11 | 0.0457346 | 0.0228673 | − | 0.999739i | \(-0.492720\pi\) | ||||
0.0228673 | + | 0.999739i | \(0.492720\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.20849e12 | 2.03192 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.35346e12 | 1.76493 | 0.882464 | − | 0.470380i | \(-0.155883\pi\) | ||||
0.882464 | + | 0.470380i | \(0.155883\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.67188e12 | 0.457716 | 0.228858 | − | 0.973460i | \(-0.426501\pi\) | ||||
0.228858 | + | 0.973460i | \(0.426501\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.75566e11 | 0.101339 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.75382e11 | 0.0732386 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.36522e13 | 3.57885 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.68032e12 | −0.434198 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.58299e11 | −0.0912678 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.69214e12 | −0.927141 | −0.463571 | − | 0.886060i | \(-0.653432\pi\) | ||||
−0.463571 | + | 0.886060i | \(0.653432\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.86256e11 | −0.169891 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.47638e12 | 0.360343 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.92577e12 | −1.18535 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.60271e12 | −0.380277 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.43986e12 | −0.570826 | −0.285413 | − | 0.958405i | \(-0.592131\pi\) | ||||
−0.285413 | + | 0.958405i | \(0.592131\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.91171e12 | −0.441034 | −0.220517 | − | 0.975383i | \(-0.570774\pi\) | ||||
−0.220517 | + | 0.975383i | \(0.570774\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.19699e12 | −1.63732 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.33401e12 | 1.42105 | 0.710525 | − | 0.703672i | \(-0.248458\pi\) | ||||
0.710525 | + | 0.703672i | \(0.248458\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.33435e11 | −0.206530 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.19421e11 | 0.135167 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.21499e12 | −0.476718 | −0.238359 | − | 0.971177i | \(-0.576610\pi\) | ||||
−0.238359 | + | 0.971177i | \(0.576610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.40939e11 | −0.199745 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.59314e11 | 0.179932 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.59753e12 | −0.743054 | −0.371527 | − | 0.928422i | \(-0.621166\pi\) | ||||
−0.371527 | + | 0.928422i | \(0.621166\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.41730e12 | 0.492521 | 0.246260 | − | 0.969204i | \(-0.420798\pi\) | ||||
0.246260 | + | 0.969204i | \(0.420798\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.16929e11 | −0.0436021 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.20785e11 | 0.123096 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.75760e12 | 0.539467 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.69828e12 | −0.713810 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.22302e12 | −0.613778 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.32596e12 | −0.249152 | −0.124576 | − | 0.992210i | \(-0.539757\pi\) | ||||
−0.124576 | + | 0.992210i | \(0.539757\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.79989e12 | 0.519127 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.49781e12 | 0.456995 | 0.228497 | − | 0.973545i | \(-0.426619\pi\) | ||||
0.228497 | + | 0.973545i | \(0.426619\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.60989e11 | 0.0471203 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.98277e12 | 0.531445 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.02091e13 | −1.79512 | −0.897558 | − | 0.440895i | \(-0.854661\pi\) | ||||
−0.897558 | + | 0.440895i | \(0.854661\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.60321e12 | −1.14590 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.33608e12 | −0.400112 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.01466e12 | 1.18582 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.33760e12 | −0.890625 | −0.445313 | − | 0.895375i | \(-0.646907\pi\) | ||||
−0.445313 | + | 0.895375i | \(0.646907\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.32318e11 | 0.0876742 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.47798e12 | 1.54093 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.10313e11 | 0.113999 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.15034e12 | −0.499127 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.96175e12 | 1.08890 | 0.544449 | − | 0.838794i | \(-0.316739\pi\) | ||||
0.544449 | + | 0.838794i | \(0.316739\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.05978e12 | 0.626908 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.17519e12 | −1.09391 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.29459e11 | −0.0646449 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.14423e13 | 1.70061 | 0.850307 | − | 0.526287i | \(-0.176416\pi\) | ||||
0.850307 | + | 0.526287i | \(0.176416\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.79547e12 | 0.410244 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.68556e12 | −0.823892 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.86408e13 | 4.09834 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.58555e12 | −0.506664 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.43048e12 | −0.757806 | −0.378903 | − | 0.925436i | \(-0.623699\pi\) | ||||
−0.378903 | + | 0.925436i | \(0.623699\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.46234e11 | 0.116622 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.62912e12 | 1.03837 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.05582e13 | 2.76353 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.18258e12 | −0.820852 | −0.410426 | − | 0.911894i | \(-0.634620\pi\) | ||||
−0.410426 | + | 0.911894i | \(0.634620\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.09180e11 | −0.0918604 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.14558e13 | −1.46574 | −0.732870 | − | 0.680368i | \(-0.761820\pi\) | ||||
−0.732870 | + | 0.680368i | \(0.761820\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.58718e12 | 1.08532 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.79983e12 | 0.973826 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.13658e13 | 1.40184 | 0.700920 | − | 0.713240i | \(-0.252773\pi\) | ||||
0.700920 | + | 0.713240i | \(0.252773\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.45796e12 | 0.299498 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.42813e13 | 1.71917 | 0.859584 | − | 0.510995i | \(-0.170723\pi\) | ||||
0.859584 | + | 0.510995i | \(0.170723\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.24801e13 | −1.48428 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.52773e12 | 0.179516 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.43348e12 | 0.282527 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.50025e12 | 0.286816 | 0.143408 | − | 0.989664i | \(-0.454194\pi\) | ||||
0.143408 | + | 0.989664i | \(0.454194\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.30441e12 | −0.261205 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.53490e12 | −0.507933 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.03072e13 | 1.14080 | 0.570402 | − | 0.821366i | \(-0.306787\pi\) | ||||
0.570402 | + | 0.821366i | \(0.306787\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.88606e12 | −0.534405 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.02116e12 | −0.866974 | −0.433487 | − | 0.901160i | \(-0.642717\pi\) | ||||
−0.433487 | + | 0.901160i | \(0.642717\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.26962e12 | 0.135616 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.78177e11 | 0.0399226 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.36543e12 | 0.142459 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.09614e13 | 1.13031 | 0.565154 | − | 0.824985i | \(-0.308817\pi\) | ||||
0.565154 | + | 0.824985i | \(0.308817\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.45001e11 | −0.0963136 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.65013e12 | −0.770657 | −0.385329 | − | 0.922779i | \(-0.625912\pi\) | ||||
−0.385329 | + | 0.922779i | \(0.625912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.23865e13 | −4.22055 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.28612e12 | −0.126587 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.04835e12 | −0.783048 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.08509e13 | 2.00538 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.07374e12 | 0.197163 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.51510e13 | −1.42406 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.07846e13 | 1.93133 | 0.965663 | − | 0.259797i | \(-0.0836556\pi\) | ||||
0.965663 | + | 0.259797i | \(0.0836556\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.11130e13 | −1.02090 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.73116e12 | 0.248058 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.71462e12 | 0.423367 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.22288e13 | −1.08575 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.87904e12 | 0.516112 | 0.258056 | − | 0.966130i | \(-0.416918\pi\) | ||||
0.258056 | + | 0.966130i | \(0.416918\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.07032e11 | −0.0613731 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.90084e12 | −0.163155 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.11795e13 | −0.948863 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.80513e12 | 0.151505 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.67081e12 | 0.387669 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.17127e13 | 0.961363 | 0.480682 | − | 0.876895i | \(-0.340389\pi\) | ||||
0.480682 | + | 0.876895i | \(0.340389\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.27415e12 | −0.184597 | −0.0922987 | − | 0.995731i | \(-0.529421\pi\) | ||||
−0.0922987 | + | 0.995731i | \(0.529421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.43681e12 | −0.757561 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.66526e13 | 1.32213 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.03552e12 | 0.630979 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.78673e11 | −0.0604753 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.39279e12 | 0.644707 | 0.322353 | − | 0.946619i | \(-0.395526\pi\) | ||||
0.322353 | + | 0.946619i | \(0.395526\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.70938e12 | 0.281839 | 0.140920 | − | 0.990021i | \(-0.454994\pi\) | ||||
0.140920 | + | 0.990021i | \(0.454994\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.64261e13 | −2.73760 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.53080e13 | −1.88141 | −0.940706 | − | 0.339224i | \(-0.889836\pi\) | ||||
−0.940706 | + | 0.339224i | \(0.889836\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.59061e13 | 1.16968 | 0.584842 | − | 0.811147i | \(-0.301156\pi\) | ||||
0.584842 | + | 0.811147i | \(0.301156\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.07848e12 | −0.0784525 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.46167e11 | 0.0608911 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.53122e13 | −1.80194 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.27559e12 | −0.301115 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.57050e12 | 0.179097 | 0.0895487 | − | 0.995982i | \(-0.471458\pi\) | ||||
0.0895487 | + | 0.995982i | \(0.471458\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.19297e11 | 0.0495822 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.70718e12 | −0.184626 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.33981e13 | −0.904041 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.68411e12 | −0.312717 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.14683e12 | −0.273925 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.18051e13 | 0.771590 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.41468e12 | −0.414863 | −0.207431 | − | 0.978250i | \(-0.566510\pi\) | ||||
−0.207431 | + | 0.978250i | \(0.566510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.28501e12 | −0.274223 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.31074e13 | −0.830046 | −0.415023 | − | 0.909811i | \(-0.636226\pi\) | ||||
−0.415023 | + | 0.909811i | \(0.636226\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.06234e13 | −0.665723 | −0.332861 | − | 0.942976i | \(-0.608014\pi\) | ||||
−0.332861 | + | 0.942976i | \(0.608014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.54969e12 | 0.158115 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.71438e12 | 0.289318 | 0.144659 | − | 0.989482i | \(-0.453791\pi\) | ||||
0.144659 | + | 0.989482i | \(0.453791\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.17110e11 | 0.0192592 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.56835e12 | −0.575110 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.63687e13 | −2.16341 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.14096e13 | −0.671719 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.80149e12 | −0.104971 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.46852e12 | 0.488395 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.59207e12 | −0.262126 | −0.131063 | − | 0.991374i | \(-0.541839\pi\) | ||||
−0.131063 | + | 0.991374i | \(0.541839\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.37119e13 | −0.774728 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.82236e13 | 1.01916 | 0.509580 | − | 0.860423i | \(-0.329801\pi\) | ||||
0.509580 | + | 0.860423i | \(0.329801\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.47414e12 | 0.192320 | 0.0961598 | − | 0.995366i | \(-0.469344\pi\) | ||||
0.0961598 | + | 0.995366i | \(0.469344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.38037e12 | −0.130437 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.73676e12 | −0.419665 | −0.209833 | − | 0.977737i | \(-0.567292\pi\) | ||||
−0.209833 | + | 0.977737i | \(0.567292\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.22204e11 | 0.0280403 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.67436e12 | −0.195314 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.01117e12 | 0.421565 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.54307e13 | −1.32481 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.14731e12 | 0.368618 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.13936e13 | −1.60296 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.20500e12 | −0.0609153 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.54562e12 | −0.127409 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.71820e13 | −2.33807 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.47553e13 | −1.21461 | −0.607303 | − | 0.794470i | \(-0.707749\pi\) | ||||
−0.607303 | + | 0.794470i | \(0.707749\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.96437e12 | 0.144011 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.49811e13 | −1.68268 | −0.841339 | − | 0.540508i | \(-0.818232\pi\) | ||||
−0.841339 | + | 0.540508i | \(0.818232\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.98755e13 | −0.946670 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.21907e12 | −0.387639 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.32816e11 | −0.0155432 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.70135e13 | −0.786816 | −0.393408 | − | 0.919364i | \(-0.628704\pi\) | ||||
−0.393408 | + | 0.919364i | \(0.628704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.35683e13 | 0.621379 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.05007e13 | −1.38325 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.80083e13 | 3.95263 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.84118e12 | −0.259802 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.63520e12 | 0.336318 | 0.168159 | − | 0.985760i | \(-0.446218\pi\) | ||||
0.168159 | + | 0.985760i | \(0.446218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.58767e12 | −0.418254 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.96781e13 | 0.850191 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.92002e12 | −0.210530 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.23096e12 | −0.136932 | −0.0684658 | − | 0.997653i | \(-0.521810\pi\) | ||||
−0.0684658 | + | 0.997653i | \(0.521810\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.10249e13 | −0.882547 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.68554e13 | −1.53232 | −0.766158 | − | 0.642652i | \(-0.777834\pi\) | ||||
−0.766158 | + | 0.642652i | \(0.777834\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.34031e13 | −0.963765 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.35747e12 | 0.0553718 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.16984e13 | 0.876703 | 0.438352 | − | 0.898804i | \(-0.355563\pi\) | ||||
0.438352 | + | 0.898804i | \(0.355563\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.63534e13 | 0.654500 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.42168e13 | 0.960073 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.33996e12 | −0.366798 | −0.183399 | − | 0.983039i | \(-0.558710\pi\) | ||||
−0.183399 | + | 0.983039i | \(0.558710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.00713e13 | 1.16987 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.69790e13 | −1.03973 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.33560e12 | −0.0891690 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.82869e13 | 1.44809 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.67973e13 | −0.629392 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.48892e12 | 0.278001 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.17891e12 | 0.227244 | 0.113622 | − | 0.993524i | \(-0.463755\pi\) | ||||
0.113622 | + | 0.993524i | \(0.463755\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.22238e11 | −0.0153851 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.66682e13 | 1.68475 | 0.842373 | − | 0.538894i | \(-0.181158\pi\) | ||||
0.842373 | + | 0.538894i | \(0.181158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.35242e12 | 0.119909 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.32840e13 | 1.88832 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.66780e13 | −1.63903 | −0.819515 | − | 0.573058i | \(-0.805757\pi\) | ||||
−0.819515 | + | 0.573058i | \(0.805757\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.47297e13 | 0.860392 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.76361e12 | −0.302115 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.93231e13 | −1.34325 | −0.671625 | − | 0.740891i | \(-0.734404\pi\) | ||||
−0.671625 | + | 0.740891i | \(0.734404\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.67436e13 | 2.93612 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.53791e12 | −0.0851233 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.33658e13 | 0.776600 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.82257e13 | −0.600280 | −0.300140 | − | 0.953895i | \(-0.597033\pi\) | ||||
−0.300140 | + | 0.953895i | \(0.597033\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.95580e13 | −0.964724 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.85281e13 | −2.21648 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.16514e13 | 1.01453 | 0.507264 | − | 0.861791i | \(-0.330657\pi\) | ||||
0.507264 | + | 0.861791i | \(0.330657\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.87754e12 | 0.281999 |
(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 | 384.10.a.g.1.1 | yes | 4 | |
4.3 | odd | 2 | 384.10.a.c.1.1 | yes | 4 | ||
8.3 | odd | 2 | 384.10.a.f.1.4 | yes | 4 | ||
8.5 | even | 2 | 384.10.a.b.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.a.b.1.4 | ✓ | 4 | 8.5 | even | 2 | ||
384.10.a.c.1.1 | yes | 4 | 4.3 | odd | 2 | ||
384.10.a.f.1.4 | yes | 4 | 8.3 | odd | 2 | ||
384.10.a.g.1.1 | yes | 4 | 1.1 | even | 1 | trivial |