Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,9,Mod(319,384)]
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([1, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.319");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(156.433386263\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 200x^{6} - 586x^{5} + 10949x^{4} - 20926x^{3} + 78946x^{2} - 68580x + 222900 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.5 | ||
Root | \(-0.366025 + 2.01178i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.9.b.a.319.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 46.7654 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 721.475i | − 1.15436i | −0.816617 | − | 0.577180i | \(-0.804153\pi\) | ||||
0.816617 | − | 0.577180i | \(-0.195847\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1935.65i | 0.806184i | 0.915159 | + | 0.403092i | \(0.132065\pi\) | ||||
−0.915159 | + | 0.403092i | \(0.867935\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2187.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14414.4 | −0.984521 | −0.492260 | − | 0.870448i | \(-0.663829\pi\) | ||||
−0.492260 | + | 0.870448i | \(0.663829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2280.40i | 0.0798431i | 0.999203 | + | 0.0399216i | \(0.0127108\pi\) | ||||
−0.999203 | + | 0.0399216i | \(0.987289\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 33740.1i | − 0.666470i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −78065.2 | −0.934678 | −0.467339 | − | 0.884078i | \(-0.654787\pi\) | ||||
−0.467339 | + | 0.884078i | \(0.654787\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 48459.6 | 0.371848 | 0.185924 | − | 0.982564i | \(-0.440472\pi\) | ||||
0.185924 | + | 0.982564i | \(0.440472\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 90521.3i | 0.465451i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 222858.i | 0.796375i | 0.917304 | + | 0.398187i | \(0.130361\pi\) | ||||
−0.917304 | + | 0.398187i | \(0.869639\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −129901. | −0.332548 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 102276. | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1.12756e6i | − 1.59422i | −0.603835 | − | 0.797109i | \(-0.706361\pi\) | ||||
0.603835 | − | 0.797109i | \(-0.293639\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 828931.i | 0.897576i | 0.893638 | + | 0.448788i | \(0.148144\pi\) | ||||
−0.893638 | + | 0.448788i | \(0.851856\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −674093. | −0.568413 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.39652e6 | 0.930627 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 931641.i | − 0.497097i | −0.968619 | − | 0.248549i | \(-0.920046\pi\) | ||||
0.968619 | − | 0.248549i | \(-0.0799536\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 106644.i | 0.0460974i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.58800e6 | 1.62363 | 0.811816 | − | 0.583913i | \(-0.198479\pi\) | ||||
0.811816 | + | 0.583913i | \(0.198479\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.91683e6 | −0.853174 | −0.426587 | − | 0.904447i | \(-0.640284\pi\) | ||||
−0.426587 | + | 0.904447i | \(0.640284\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1.57787e6i | − 0.384787i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.52086e6i | 1.54126i | 0.637282 | + | 0.770630i | \(0.280059\pi\) | ||||
−0.637282 | + | 0.770630i | \(0.719941\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.01807e6 | 0.350067 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.65075e6 | −0.539637 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.79808e6i | 0.608085i | 0.952659 | + | 0.304042i | \(0.0983364\pi\) | ||||
−0.952659 | + | 0.304042i | \(0.901664\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.03996e7i | 1.13649i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.26623e6 | 0.214686 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.36767e6 | 0.690552 | 0.345276 | − | 0.938501i | \(-0.387785\pi\) | ||||
0.345276 | + | 0.938501i | \(0.387785\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.86342e6i | 0.279031i | 0.990220 | + | 0.139515i | \(0.0445545\pi\) | ||||
−0.990220 | + | 0.139515i | \(0.955446\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.23326e6i | 0.268728i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.64525e6 | 0.0921677 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 352024. | 0.0174692 | 0.00873459 | − | 0.999962i | \(-0.497220\pi\) | ||||
0.00873459 | + | 0.999962i | \(0.497220\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.04220e7i | 0.459787i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 2.68851e7i | − 1.05798i | −0.848628 | − | 0.528990i | \(-0.822571\pi\) | ||||
0.848628 | − | 0.528990i | \(-0.177429\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.13722e6 | 0.286540 | 0.143270 | − | 0.989684i | \(-0.454238\pi\) | ||||
0.143270 | + | 0.989684i | \(0.454238\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.07489e6 | −0.191997 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.79011e7i | − 0.793705i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.31004e7i | 1.10655i | 0.832997 | + | 0.553277i | \(0.186623\pi\) | ||||
−0.832997 | + | 0.553277i | \(0.813377\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.58735e7 | 0.755896 | 0.377948 | − | 0.925827i | \(-0.376630\pi\) | ||||
0.377948 | + | 0.925827i | \(0.376630\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.63221e7i | 1.07896i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 5.27308e7i | − 0.920423i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.79238e7 | 0.445055 | 0.222528 | − | 0.974926i | \(-0.428569\pi\) | ||||
0.222528 | + | 0.974926i | \(0.428569\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.41405e6 | −0.0643683 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.87652e7i | 0.518216i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 3.49624e7i | − 0.429246i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.07429e8 | 1.21349 | 0.606745 | − | 0.794897i | \(-0.292475\pi\) | ||||
0.606745 | + | 0.794897i | \(0.292475\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.15242e7 | −0.328174 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.03404e8i | − 0.993696i | −0.867838 | − | 0.496848i | \(-0.834491\pi\) | ||||
0.867838 | − | 0.496848i | \(-0.165509\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.38564e8i | − 1.23112i | −0.788088 | − | 0.615562i | \(-0.788929\pi\) | ||||
0.788088 | − | 0.615562i | \(-0.211071\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.53089e7 | 0.537298 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.74166e7 | 0.438028 | 0.219014 | − | 0.975722i | \(-0.429716\pi\) | ||||
0.219014 | + | 0.975722i | \(0.429716\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 6.98643e7i | − 0.494936i | −0.968896 | − | 0.247468i | \(-0.920401\pi\) | ||||
0.968896 | − | 0.247468i | \(-0.0795986\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 4.35685e7i | − 0.286999i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.79469e7 | −0.232735 | −0.116368 | − | 0.993206i | \(-0.537125\pi\) | ||||
−0.116368 | + | 0.993206i | \(0.537125\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.60787e8 | 0.919303 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.98723e6i | 0.0266144i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 1.51107e8i | − 0.753523i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.58494e6 | −0.0307193 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.14559e8 | 0.937405 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.88106e8i | − 0.770480i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.59422e8i | 1.38162i | 0.723035 | + | 0.690811i | \(0.242746\pi\) | ||||
−0.723035 | + | 0.690811i | \(0.757254\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.36407e8 | −0.492580 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.43800e8 | −0.827845 | −0.413923 | − | 0.910312i | \(-0.635842\pi\) | ||||
−0.413923 | + | 0.910312i | \(0.635842\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.38007e7i | 0.299778i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 7.37895e7i | − 0.222157i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.47050e8 | 0.701299 | 0.350650 | − | 0.936507i | \(-0.385961\pi\) | ||||
0.350650 | + | 0.936507i | \(0.385961\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.81853e7 | 0.0755029 | 0.0377515 | − | 0.999287i | \(-0.487980\pi\) | ||||
0.0377515 | + | 0.999287i | \(0.487980\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.51716e8i | 0.889847i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 3.28705e7i | − 0.0786072i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.13507e8 | −1.84030 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.43756e7 | 0.202111 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 7.49164e8i | − 1.51996i | −0.649947 | − | 0.759979i | \(-0.725209\pi\) | ||||
0.649947 | − | 0.759979i | \(-0.274791\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.67117e8i | 0.898500i | 0.893406 | + | 0.449250i | \(0.148309\pi\) | ||||
−0.893406 | + | 0.449250i | \(0.851691\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.70729e8 | −0.311559 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.98053e8 | 1.03613 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.89031e8i | 1.62784i | 0.580978 | + | 0.813919i | \(0.302670\pi\) | ||||
−0.580978 | + | 0.813919i | \(0.697330\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.24384e8i | 0.351078i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.31375e8 | −0.642025 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.27344e9 | 1.80397 | 0.901983 | − | 0.431772i | \(-0.142112\pi\) | ||||
0.901983 | + | 0.431772i | \(0.142112\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.86342e8i | 0.656154i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.11871e9i | 1.43831i | 0.694851 | + | 0.719154i | \(0.255470\pi\) | ||||
−0.694851 | + | 0.719154i | \(0.744530\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.10531e8 | 0.993625 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.05981e8 | 0.123949 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 3.83147e8i | − 0.427741i | −0.976862 | − | 0.213871i | \(-0.931393\pi\) | ||||
0.976862 | − | 0.213871i | \(-0.0686071\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 2.51444e8i | − 0.268095i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.91317e8 | 0.398691 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.05972e9 | 1.03224 | 0.516119 | − | 0.856517i | \(-0.327376\pi\) | ||||
0.516119 | + | 0.856517i | \(0.327376\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.48989e8i | 0.604676i | 0.953201 | + | 0.302338i | \(0.0977672\pi\) | ||||
−0.953201 | + | 0.302338i | \(0.902233\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.80674e8i | 0.161099i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.72156e8 | −0.573830 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.12526e9 | 0.920210 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.97970e8i | 0.155150i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 9.60451e8i | − 0.721675i | −0.932629 | − | 0.360838i | \(-0.882491\pi\) | ||||
0.932629 | − | 0.360838i | \(-0.117509\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.58783e8 | −0.258585 | −0.129292 | − | 0.991607i | \(-0.541271\pi\) | ||||
−0.129292 | + | 0.991607i | \(0.541271\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.69408e7 | 0.0532131 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4.30337e8i | − 0.285722i | −0.989743 | − | 0.142861i | \(-0.954370\pi\) | ||||
0.989743 | − | 0.142861i | \(-0.0456302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 1.29888e9i | − 0.828240i | −0.910222 | − | 0.414120i | \(-0.864089\pi\) | ||||
0.910222 | − | 0.414120i | \(-0.135911\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.64625e7 | 0.0100858 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.18256e9 | 1.28523 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 3.31013e9i | − 1.87426i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.87391e8i | 0.265458i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.98514e8 | −0.366092 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.04305e8 | −0.103074 | −0.0515371 | − | 0.998671i | \(-0.516412\pi\) | ||||
−0.0515371 | + | 0.998671i | \(0.516412\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.25729e9i | − 0.610826i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.10442e9i | 0.984870i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.60452e9 | −0.723612 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.80540e8 | 0.165434 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.78020e8i | − 0.0746276i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3.90139e9i | − 1.57761i | −0.614642 | − | 0.788806i | \(-0.710699\pi\) | ||||
0.614642 | − | 0.788806i | \(-0.289301\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.84095e8 | −0.110849 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.87794e9 | 1.46049 | 0.730243 | − | 0.683188i | \(-0.239407\pi\) | ||||
0.730243 | + | 0.683188i | \(0.239407\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.23158e9i | 1.53872i | 0.638813 | + | 0.769362i | \(0.279426\pi\) | ||||
−0.638813 | + | 0.769362i | \(0.720574\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 1.30481e9i | − 0.458246i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.60146e9 | 0.543367 | 0.271684 | − | 0.962387i | \(-0.412420\pi\) | ||||
0.271684 | + | 0.962387i | \(0.412420\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.42612e9 | 1.77917 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.01561e9i | 0.638870i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 4.56209e9i | − 1.39821i | −0.715020 | − | 0.699104i | \(-0.753582\pi\) | ||||
0.715020 | − | 0.699104i | \(-0.246418\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.07036e9 | 0.317293 | 0.158646 | − | 0.987335i | \(-0.449287\pi\) | ||||
0.158646 | + | 0.987335i | \(0.449287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.23677e8 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.45598e9i | − 0.404103i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.10507e8i | 0.0296895i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.67764e9 | 0.436417 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.33963e9 | 1.84918 | 0.924591 | − | 0.380962i | \(-0.124407\pi\) | ||||
0.924591 | + | 0.380962i | \(0.124407\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 3.21236e9i | − 0.784047i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.63393e9i | 0.622935i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.12468e9 | 0.716263 | 0.358131 | − | 0.933671i | \(-0.383414\pi\) | ||||
0.358131 | + | 0.933671i | \(0.383414\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.80333e9 | 0.400752 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 2.46598e9i | − 0.531406i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 1.11900e9i | − 0.233888i | −0.993138 | − | 0.116944i | \(-0.962690\pi\) | ||||
0.993138 | − | 0.116944i | \(-0.0373099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.46170e9 | 0.701949 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.30587e9 | 0.256953 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.46571e9i | 1.42581i | 0.701260 | + | 0.712905i | \(0.252621\pi\) | ||||
−0.701260 | + | 0.712905i | \(0.747379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.57691e9i | 1.03399i | 0.855988 | + | 0.516996i | \(0.172950\pi\) | ||||
−0.855988 | + | 0.516996i | \(0.827050\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.06425e8 | −0.0371630 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.87245e9 | 0.327400 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3.93505e8i | − 0.0668392i | −0.999441 | − | 0.0334196i | \(-0.989360\pi\) | ||||
0.999441 | − | 0.0334196i | \(-0.0106398\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.81287e9i | 0.299192i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.79797e9 | 0.929931 | 0.464965 | − | 0.885329i | \(-0.346067\pi\) | ||||
0.464965 | + | 0.885329i | \(0.346067\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.02243e10 | 1.59400 | 0.797000 | − | 0.603979i | \(-0.206419\pi\) | ||||
0.797000 | + | 0.603979i | \(0.206419\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.63503e9i | − 0.247825i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.88075e9i | 1.30895i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.81576e8 | −0.126377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.02397e9 | 0.700609 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.81507e9i | 1.19607i | 0.801471 | + | 0.598033i | \(0.204051\pi\) | ||||
−0.801471 | + | 0.598033i | \(0.795949\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 6.03707e9i | − 0.797146i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.47424e9 | −0.189471 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.08206e8 | −0.0635850 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 5.64596e9i | − 0.687815i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 4.83574e9i | − 0.573710i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.78736e9 | 0.322102 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.21061e9 | 0.361438 | 0.180719 | − | 0.983535i | \(-0.442157\pi\) | ||||
0.180719 | + | 0.983535i | \(0.442157\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 6.48001e9i | − 0.710790i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.08177e9i | 0.543218i | 0.962408 | + | 0.271609i | \(0.0875557\pi\) | ||||
−0.962408 | + | 0.271609i | \(0.912444\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.25663e10 | −1.30927 | −0.654635 | − | 0.755945i | \(-0.727178\pi\) | ||||
−0.654635 | + | 0.755945i | \(0.727178\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.05419e9 | 0.310209 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.32195e10i | 1.30911i | 0.756012 | + | 0.654557i | \(0.227145\pi\) | ||||
−0.756012 | + | 0.654557i | \(0.772855\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.62531e10i | 1.56954i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.68511e9 | 0.252896 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.78301e9 | −0.347558 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2.96227e8i | − 0.0265517i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 3.26723e9i | − 0.285752i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.45577e10 | −1.24254 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.19088e10 | 1.82519 | 0.912594 | − | 0.408867i | \(-0.134076\pi\) | ||||
0.912594 | + | 0.408867i | \(0.134076\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2.03750e9i | − 0.165699i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 2.53976e8i | − 0.0201657i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.12340e9 | 0.629823 | 0.314911 | − | 0.949121i | \(-0.398025\pi\) | ||||
0.314911 | + | 0.949121i | \(0.398025\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.77460e9 | −0.134370 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1.19485e10i | − 0.883682i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.50649e10i | 1.08840i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.51925e9 | 0.530760 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.53179e10 | 1.05653 | 0.528265 | − | 0.849080i | \(-0.322843\pi\) | ||||
0.528265 | + | 0.849080i | \(0.322843\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.16917e10i | − 0.788087i | −0.919092 | − | 0.394044i | \(-0.871076\pi\) | ||||
0.919092 | − | 0.394044i | \(-0.128924\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.33230e8i | 0.0153658i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.62886e9 | −0.298109 | −0.149055 | − | 0.988829i | \(-0.547623\pi\) | ||||
−0.149055 | + | 0.988829i | \(0.547623\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.93969e10 | −1.22129 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 7.06657e9i | − 0.435047i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 3.20147e10i | − 1.92740i | −0.266988 | − | 0.963700i | \(-0.586028\pi\) | ||||
0.266988 | − | 0.963700i | \(-0.413972\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.46352e10 | −0.861729 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.07947e8 | −0.0177358 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 5.87080e9i | − 0.330770i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.27393e10i | − 0.702236i | −0.936331 | − | 0.351118i | \(-0.885802\pi\) | ||||
0.936331 | − | 0.351118i | \(-0.114198\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.00340e10 | 0.541211 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.28740e9 | −0.490228 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.72758e9i | 0.347555i | 0.984785 | + | 0.173777i | \(0.0555974\pi\) | ||||
−0.984785 | + | 0.173777i | \(0.944403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 8.79683e9i | − 0.444837i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.57129e9 | 0.127287 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.22538e10 | −0.593900 | −0.296950 | − | 0.954893i | \(-0.595969\pi\) | ||||
−0.296950 | + | 0.954893i | \(0.595969\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.68085e10i | 0.797680i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 5.30566e9i | − 0.246572i | −0.992371 | − | 0.123286i | \(-0.960657\pi\) | ||||
0.992371 | − | 0.123286i | \(-0.0393433\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.01300e10 | −0.916222 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.37911e9 | −0.284391 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 7.15446e8i | − 0.0312449i | −0.999878 | − | 0.0156224i | \(-0.995027\pi\) | ||||
0.999878 | − | 0.0156224i | \(-0.00497298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 1.73975e10i | − 0.744354i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.14014e10 | −0.477957 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.10959e10 | 1.27736 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3.32363e9i | − 0.133798i | −0.997760 | − | 0.0668992i | \(-0.978689\pi\) | ||||
0.997760 | − | 0.0668992i | \(-0.0213106\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.38662e9i | 0.173077i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.67738e10 | 1.03546 | 0.517728 | − | 0.855545i | \(-0.326778\pi\) | ||||
0.517728 | + | 0.855545i | \(0.326778\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.89029e9 | −0.0716653 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 3.45079e9i | − 0.128262i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.34290e10i | 0.489403i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.94258e9 | −0.355309 | −0.177654 | − | 0.984093i | \(-0.556851\pi\) | ||||
−0.177654 | + | 0.984093i | \(0.556851\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.15534e10 | 0.404895 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.61969e10i | 0.556712i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 2.58819e10i | − 0.872576i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.31810e9 | 0.0435916 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.71310e10 | −1.52915 | −0.764576 | − | 0.644534i | \(-0.777051\pi\) | ||||
−0.764576 | + | 0.644534i | \(0.777051\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.18839e10i | 1.33327i | 0.745383 | + | 0.666636i | \(0.232267\pi\) | ||||
−0.745383 | + | 0.666636i | \(0.767733\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.64481e10i | 0.513754i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.01408e10 | 0.310825 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.47822e9 | −0.224950 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1.53720e9i | − 0.0453839i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 6.88707e9i | − 0.199584i | −0.995008 | − | 0.0997919i | \(-0.968182\pi\) | ||||
0.995008 | − | 0.0997919i | \(-0.0318177\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.00742e10 | −1.70898 | −0.854489 | − | 0.519470i | \(-0.826129\pi\) | ||||
−0.854489 | + | 0.519470i | \(0.826129\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.80440e10 | −1.06250 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.07996e10i | 0.296130i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.83040e10i | 1.30054i | 0.759702 | + | 0.650272i | \(0.225345\pi\) | ||||
−0.759702 | + | 0.650272i | \(0.774655\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.41351e9 | 0.116689 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.58299e10 | 0.411020 | 0.205510 | − | 0.978655i | \(-0.434115\pi\) | ||||
0.205510 | + | 0.978655i | \(0.434115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.01463e10i | − 0.513754i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 3.50349e10i | − 0.877548i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.96933e10 | −0.484543 | −0.242272 | − | 0.970208i | \(-0.577893\pi\) | ||||
−0.242272 | + | 0.970208i | \(0.577893\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.61331e10 | −1.59850 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.18449e10i | 0.518749i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.18463e9i | 0.0743042i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.00151e10 | 0.229609 | 0.114804 | − | 0.993388i | \(-0.463376\pi\) | ||||
0.114804 | + | 0.993388i | \(0.463376\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.98419e9 | −0.179879 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 6.66757e10i | − 1.47626i | −0.674656 | − | 0.738132i | \(-0.735708\pi\) | ||||
0.674656 | − | 0.738132i | \(-0.264292\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2.84891e10i | − 0.619947i | −0.950745 | − | 0.309974i | \(-0.899680\pi\) | ||||
0.950745 | − | 0.309974i | \(-0.100320\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.79682e10 | 0.598208 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.61916e10 | −1.60192 | −0.800958 | − | 0.598721i | \(-0.795676\pi\) | ||||
−0.800958 | + | 0.598721i | \(0.795676\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.81394e8i | 0.0140834i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.62524e10i | 0.939833i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.20443e10 | 0.839967 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.29497e9 | −0.123657 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.04934e10i | 0.202695i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.65203e10i | 1.64352i | 0.569832 | + | 0.821761i | \(0.307008\pi\) | ||||
−0.569832 | + | 0.821761i | \(0.692992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.12451e9 | 0.0396898 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.01734e10 | −0.370673 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 7.75076e10i | − 1.40080i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 6.89487e9i | − 0.122577i | −0.998120 | − | 0.0612886i | \(-0.980479\pi\) | ||||
0.998120 | − | 0.0612886i | \(-0.0195210\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.95529e10 | 1.04152 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.99344e10 | −0.687103 | −0.343551 | − | 0.939134i | \(-0.611630\pi\) | ||||
−0.343551 | + | 0.939134i | \(0.611630\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.80233e10i | 1.49008i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.27439e10i | 0.378830i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.20401e10 | 0.852928 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.20114e11 | −1.93727 | −0.968636 | − | 0.248484i | \(-0.920068\pi\) | ||||
−0.968636 | + | 0.248484i | \(0.920068\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.23169e10i | 0.830407i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.58763e10i | 0.872882i | 0.899733 | + | 0.436441i | \(0.143761\pi\) | ||||
−0.899733 | + | 0.436441i | \(0.856239\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.46037e10 | −1.14708 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.79048e10 | 0.573670 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 8.15450e10i | − 1.21486i | −0.794373 | − | 0.607430i | \(-0.792201\pi\) | ||||
0.794373 | − | 0.607430i | \(-0.207799\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.57508e10i | 0.231004i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.95624e9 | 0.0715621 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.99706e10 | −1.42116 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1.08408e11i | − 1.51740i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 1.79180e10i | − 0.246957i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.07597e11 | 1.46033 | 0.730164 | − | 0.683272i | \(-0.239444\pi\) | ||||
0.730164 | + | 0.683272i | \(0.239444\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.80227e10 | 1.31015 | 0.655074 | − | 0.755565i | \(-0.272638\pi\) | ||||
0.655074 | + | 0.755565i | \(0.272638\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1.17589e10i | − 0.154785i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 6.47107e10i | − 0.838945i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.86452e10 | 0.365787 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.83001e10 | 0.230184 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.04625e10i | 0.129636i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 4.14246e10i | − 0.505642i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.95583e10 | 0.595963 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.90891e10 | −0.344648 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.58826e10i | 0.769098i | 0.923105 | + | 0.384549i | \(0.125643\pi\) | ||||
−0.923105 | + | 0.384549i | \(0.874357\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.03502e10i | 0.349110i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.04054e10 | −0.571335 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.39006e10 | −0.602066 | −0.301033 | − | 0.953614i | \(-0.597332\pi\) | ||||
−0.301033 | + | 0.953614i | \(0.597332\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.44930e9i | 0.0930103i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 5.46411e10i | − 0.592807i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.34272e10 | −0.892087 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.14336e10 | −0.331301 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.99973e10i | 1.03888i | 0.854506 | + | 0.519442i | \(0.173860\pi\) | ||||
−0.854506 | + | 0.519442i | \(0.826140\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 6.65154e9i | − 0.0681200i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.26232e10 | 0.531283 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.53496e11 | −1.52779 | −0.763894 | − | 0.645342i | \(-0.776715\pi\) | ||||
−0.763894 | + | 0.645342i | \(0.776715\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.73777e10i | 0.268661i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.25815e9i | 0.0895760i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.48473e10 | −0.332445 | −0.166223 | − | 0.986088i | \(-0.553157\pi\) | ||||
−0.166223 | + | 0.986088i | \(0.553157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.37057e11 | −1.28931 | −0.644653 | − | 0.764475i | \(-0.722998\pi\) | ||||
−0.644653 | + | 0.764475i | \(0.722998\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 4.49159e10i | − 0.416659i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 2.89496e10i | − 0.264833i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.95056e11 | −1.75977 | −0.879886 | − | 0.475184i | \(-0.842381\pi\) | ||||
−0.879886 | + | 0.475184i | \(0.842381\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.67786e10 | −0.149294 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.94386e10i | 0.609391i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 6.91613e10i | − 0.598672i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.59817e9 | 0.0307226 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.06974e10 | 0.0901000 | 0.0450500 | − | 0.998985i | \(-0.485655\pi\) | ||||
0.0450500 | + | 0.998985i | \(0.485655\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.01696e10i | 0.333762i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 2.01249e10i | − 0.164962i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.88202e9 | 0.0637410 | 0.0318705 | − | 0.999492i | \(-0.489854\pi\) | ||||
0.0318705 | + | 0.999492i | \(0.489854\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.09020e11 | −0.869837 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 6.07426e10i | − 0.478185i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1.53927e11i | − 1.19566i | −0.801623 | − | 0.597829i | \(-0.796030\pi\) | ||||
0.801623 | − | 0.597829i | \(-0.203970\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.29745e11 | −0.994474 | −0.497237 | − | 0.867615i | \(-0.665652\pi\) | ||||
−0.497237 | + | 0.867615i | \(0.665652\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.69876e8 | 0.00582306 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.75087e9i | 0.0354611i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.20655e10i | 0.530851i | 0.964131 | + | 0.265425i | \(0.0855124\pi\) | ||||
−0.964131 | + | 0.265425i | \(0.914488\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.02068e11 | 0.742030 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.71506e10 | −0.123059 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.45320e11i | − 1.02916i | −0.857441 | − | 0.514582i | \(-0.827947\pi\) | ||||
0.857441 | − | 0.514582i | \(-0.172053\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 1.54799e11i | − 1.08210i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.45016e11 | 1.69065 | 0.845326 | − | 0.534250i | \(-0.179406\pi\) | ||||
0.845326 | + | 0.534250i | \(0.179406\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.98540e11 | 1.35234 | 0.676168 | − | 0.736747i | \(-0.263639\pi\) | ||||
0.676168 | + | 0.736747i | \(0.263639\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.27930e10i | 0.153262i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.40506e10i | 0.358797i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.86456e11 | −1.22196 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.26663e10 | −0.211363 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.27287e10i | 0.464626i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 4.07591e10i | − 0.257103i | −0.991703 | − | 0.128552i | \(-0.958967\pi\) | ||||
0.991703 | − | 0.128552i | \(-0.0410328\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.55441e9 | −0.0595099 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.59314e11 | 1.59489 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.60199e9i | 0.0279504i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 5.87977e10i | − 0.352660i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.31764e11 | 0.780484 | 0.390242 | − | 0.920712i | \(-0.372391\pi\) | ||||
0.390242 | + | 0.920712i | \(0.372391\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.05733e11 | −1.78854 | −0.894269 | − | 0.447529i | \(-0.852304\pi\) | ||||
−0.894269 | + | 0.447529i | \(0.852304\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.84140e10i | 0.568615i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.54416e11i | 0.881200i | 0.897704 | + | 0.440600i | \(0.145234\pi\) | ||||
−0.897704 | + | 0.440600i | \(0.854766\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.20615e11 | −0.679863 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.50359e10 | −0.417778 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.78985e10i | − 0.0984385i | −0.998788 | − | 0.0492192i | \(-0.984327\pi\) | ||||
0.998788 | − | 0.0492192i | \(-0.0156733\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.75896e11i | 0.955632i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.77961e10 | 0.0955132 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.97373e10 | 0.104652 | 0.0523259 | − | 0.998630i | \(-0.483337\pi\) | ||||
0.0523259 | + | 0.998630i | \(0.483337\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.60626e10i | 0.398442i | 0.979955 | + | 0.199221i | \(0.0638412\pi\) | ||||
−0.979955 | + | 0.199221i | \(0.936159\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 8.32517e9i | − 0.0430863i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.76749e10 | 0.346052 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.51286e11 | 1.26960 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.82450e11i | − 0.910835i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 5.56887e10i | − 0.274712i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.07843e11 | −1.98807 | −0.994037 | − | 0.109048i | \(-0.965220\pi\) | ||||
−0.994037 | + | 0.109048i | \(0.965220\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.32858e10 | −0.0639989 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.18653e11i | 1.04088i | 0.853898 | + | 0.520441i | \(0.174232\pi\) | ||||
−0.853898 | + | 0.520441i | \(0.825768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.07946e11i | 0.978297i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.81353e11 | 0.843212 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.94065e10 | −0.227039 | −0.113520 | − | 0.993536i | \(-0.536213\pi\) | ||||
−0.113520 | + | 0.993536i | \(0.536213\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.78241e11i | − 0.809552i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.97891e11i | 0.888382i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.09415e10 | −0.0485514 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.61217e11 | 1.14575 | 0.572875 | − | 0.819643i | \(-0.305828\pi\) | ||||
0.572875 | + | 0.819643i | \(0.305828\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 6.10198e10i | − 0.264568i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 2.03350e10i | − 0.0871576i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.58163e11 | −1.51757 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.48931e10 | 0.313713 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 3.02799e10i | − 0.125396i | −0.998033 | − | 0.0626978i | \(-0.980030\pi\) | ||||
0.998033 | − | 0.0626978i | \(-0.0199704\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 4.51469e10i | − 0.184844i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.53754e11 | 1.02720 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.00155e11 | 0.801102 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 4.16090e11i | − 1.64665i | −0.567569 | − | 0.823326i | \(-0.692116\pi\) | ||||
0.567569 | − | 0.823326i | \(-0.307884\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.42606e10i | 0.368852i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.84734e11 | −0.714807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.37153e10 | −0.0907410 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.13348e11i | − 0.807256i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1.05973e11i | − 0.396533i | −0.980148 | − | 0.198266i | \(-0.936469\pi\) | ||||
0.980148 | − | 0.198266i | \(-0.0635311\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.68212e11 | 0.992514 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.00556e10 | 0.183189 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.46472e11i | 0.530154i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.26439e11i | 0.452631i | 0.974054 | + | 0.226316i | \(0.0726680\pi\) | ||||
−0.974054 | + | 0.226316i | \(0.927332\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.04604e10 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.27703e11 | 0.797443 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.65523e11i | 0.573380i | 0.958023 | + | 0.286690i | \(0.0925550\pi\) | ||||
−0.958023 | + | 0.286690i | \(0.907445\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 6.80896e10i | − 0.233309i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.07420e9 | −0.0171988 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.19272e11 | 0.399908 | 0.199954 | − | 0.979805i | \(-0.435921\pi\) | ||||
0.199954 | + | 0.979805i | \(0.435921\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.16791e9i | 0.0171412i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.81265e11i | 1.25104i | 0.780207 | + | 0.625521i | \(0.215114\pi\) | ||||
−0.780207 | + | 0.625521i | \(0.784886\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.40503e11 | −1.75458 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.84554e10 | 0.251965 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.11138e11i | 0.353131i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.41653e11i | 0.445314i | 0.974897 | + | 0.222657i | \(0.0714730\pi\) | ||||
−0.974897 | + | 0.222657i | \(0.928527\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.43241e11 | 1.06763 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.37014e11 | 1.03719 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 5.57665e10i | − 0.169820i | −0.996389 | − | 0.0849102i | \(-0.972940\pi\) | ||||
0.996389 | − | 0.0849102i | \(-0.0270603\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 1.50227e11i | − 0.452670i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.13907e11 | 0.637802 | 0.318901 | − | 0.947788i | \(-0.396686\pi\) | ||||
0.318901 | + | 0.947788i | \(0.396686\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.35233e11 | 0.399010 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.23177e11i | 0.359652i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.90816e10i | 0.0551358i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.63198e11 | −0.752622 | −0.376311 | − | 0.926493i | \(-0.622808\pi\) | ||||
−0.376311 | + | 0.926493i | \(0.622808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.46127e11 | 0.413535 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.77626e11i | 0.777576i | 0.921327 | + | 0.388788i | \(0.127106\pi\) | ||||
−0.921327 | + | 0.388788i | \(0.872894\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1.07679e11i | − 0.298487i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.43333e10 | 0.231374 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.22332e11 | 0.603744 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.87531e11i | 1.04160i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 1.15322e11i | − 0.306808i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.13562e11 | 1.87911 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.72082e11 | 1.49128 | 0.745640 | − | 0.666349i | \(-0.232144\pi\) | ||||
0.745640 | + | 0.666349i | \(0.232144\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 5.23306e10i | − 0.135035i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 7.34519e10i | − 0.187628i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.81014e9 | −0.0222787 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.61887e11 | 0.405270 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.56832e11i | 0.636525i | 0.948003 | + | 0.318263i | \(0.103099\pi\) | ||||
−0.948003 | + | 0.318263i | \(0.896901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 5.87118e11i | − 1.44058i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.10693e10 | 0.148352 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.17293e11 | −0.282104 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.11227e11i | 0.741128i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.49137e11i | 0.823192i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.79597e11 | 1.82002 | 0.910010 | − | 0.414587i | \(-0.136074\pi\) | ||||
0.910010 | + | 0.414587i | \(0.136074\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.07882e10 | −0.0711706 | −0.0355853 | − | 0.999367i | \(-0.511330\pi\) | ||||
−0.0355853 | + | 0.999367i | \(0.511330\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.60806e11i | 0.596975i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 9.18756e11i | − 2.08243i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.41348e11 | −0.317251 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.65353e9 | −0.0214561 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 7.99169e11i | − 1.75900i | −0.475897 | − | 0.879501i | \(-0.657877\pi\) | ||||
0.475897 | − | 0.879501i | \(-0.342123\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 6.70207e11i | − 1.46086i | −0.682986 | − | 0.730432i | \(-0.739319\pi\) | ||||
0.682986 | − | 0.730432i | \(-0.260681\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.75657e10 | 0.189025 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.99262e11 | −0.639778 | −0.319889 | − | 0.947455i | \(-0.603646\pi\) | ||||
−0.319889 | + | 0.947455i | \(0.603646\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 5.98250e11i | − 1.26667i | −0.773876 | − | 0.633337i | \(-0.781685\pi\) | ||||
0.773876 | − | 0.633337i | \(-0.218315\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 1.84024e10i | − 0.0385896i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.57541e11 | −0.327200 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.07122e11 | 1.66032 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.47796e10i | 0.172739i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.61857e11i | 1.33572i | 0.744286 | + | 0.667862i | \(0.232790\pi\) | ||||
−0.744286 | + | 0.667862i | \(0.767210\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.71147e11 | −1.54153 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.71144e11 | 0.536896 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 5.84778e11i | − 1.14700i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.27461e10i | − 0.0247654i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.78144e11 | 0.920296 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.07624e11 | 0.395876 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.28630e11i | 1.75407i | 0.480429 | + | 0.877034i | \(0.340481\pi\) | ||||
−0.480429 | + | 0.877034i | \(0.659519\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 7.64627e10i | − 0.143082i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.18265e11 | 1.14618 | 0.573088 | − | 0.819494i | \(-0.305745\pi\) | ||||
0.573088 | + | 0.819494i | \(0.305745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.65298e11 | 0.303595 | 0.151797 | − | 0.988412i | \(-0.451494\pi\) | ||||
0.151797 | + | 0.988412i | \(0.451494\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.15312e11i | 0.755721i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.18737e11i | 1.47605i | 0.674773 | + | 0.738025i | \(0.264241\pi\) | ||||
−0.674773 | + | 0.738025i | \(0.735759\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.76431e11 | −0.493768 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.12272e10 | −0.0729638 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 6.21265e11i | − 1.08943i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.02755e8i | 0.00139479i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.34948e11 | 0.404497 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.64106e11 | 0.621149 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.52430e11i | − 0.426719i | −0.976974 | − | 0.213360i | \(-0.931559\pi\) | ||||
0.976974 | − | 0.213360i | \(-0.0684406\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.12240e11i | 0.690550i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.66961e11 | −0.775135 | −0.387567 | − | 0.921841i | \(-0.626685\pi\) | ||||
−0.387567 | + | 0.921841i | \(0.626685\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.96639e11 | 0.816955 | 0.408478 | − | 0.912768i | \(-0.366060\pi\) | ||||
0.408478 | + | 0.912768i | \(0.366060\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2.82326e11i | − 0.460233i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1.11639e12i | − 1.80352i | −0.432241 | − | 0.901758i | \(-0.642277\pi\) | ||||
0.432241 | − | 0.901758i | \(-0.357723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.95714e11 | −1.11384 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.89435e10 | −0.109391 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.64458e11i | 0.573114i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 7.64564e11i | − 1.19158i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.37664e10 | −0.0367108 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.34670e11 | 1.43093 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 3.74563e11i | − 0.568363i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 2.64035e11i | − 0.397110i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.68229e11 | 0.698014 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.12696e11 | −0.757583 | −0.378792 | − | 0.925482i | \(-0.623660\pi\) | ||||
−0.378792 | + | 0.925482i | \(0.623660\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 2.26145e11i | − 0.331232i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.66460e11i | 1.25798i | 0.777412 | + | 0.628992i | \(0.216532\pi\) | ||||
−0.777412 | + | 0.628992i | \(0.783468\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.17094e11 | −0.744195 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.30352e11 | 0.185966 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.71912e11i | − 0.667396i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.36874e11i | 1.17327i | 0.809851 | + | 0.586635i | \(0.199548\pi\) | ||||
−0.809851 | + | 0.586635i | \(0.800452\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.50145e11 | 0.208677 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.13087e10 | 0.0844725 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.21021e11i | 0.165309i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 3.03040e11i | − 0.410375i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.54104e11 | −0.743924 | −0.371962 | − | 0.928248i | \(-0.621315\pi\) | ||||
−0.371962 | + | 0.928248i | \(0.621315\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.77945e10 | 0.130171 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.37651e11i | 0.313627i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 8.11848e11i | − 1.06225i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.88881e11 | −0.893687 | −0.446844 | − | 0.894612i | \(-0.647452\pi\) | ||||
−0.446844 | + | 0.894612i | \(0.647452\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.87666e11 | −0.755907 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 5.89653e10i | − 0.0752035i | −0.999293 | − | 0.0376018i | \(-0.988028\pi\) | ||||
0.999293 | − | 0.0376018i | \(-0.0119718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.02247e12i | 1.29302i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.42831e11 | 0.179099 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.00015e12 | 1.24355 | 0.621776 | − | 0.783195i | \(-0.286412\pi\) | ||||
0.621776 | + | 0.783195i | \(0.286412\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.85561e10i | 0.0228782i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.18214e11i | 0.755818i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.67568e11 | 0.566856 | 0.283428 | − | 0.958993i | \(-0.408528\pi\) | ||||
0.283428 | + | 0.958993i | \(0.408528\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.92942e11 | −0.833073 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.60081e11i | 0.906175i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.78203e11i | 0.565377i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.65765e11 | 0.194357 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.25570e11 | 0.146009 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.58853e11i | 0.298500i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.44768e11i | 1.08049i | 0.841509 | + | 0.540243i | \(0.181668\pi\) | ||||
−0.841509 | + | 0.540243i | \(0.818332\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.76914e11 | −0.200663 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.80297e11 | −1.10276 | −0.551380 | − | 0.834255i | \(-0.685898\pi\) | ||||
−0.551380 | + | 0.834255i | \(0.685898\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.45569e10i | 0.0608693i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 1.38532e10i | − 0.0153296i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.82458e11 | −0.200256 | −0.100128 | − | 0.994975i | \(-0.531925\pi\) | ||||
−0.100128 | + | 0.994975i | \(0.531925\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.02504e11 | −0.438166 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.52793e11i | − 0.164979i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.08194e11i | 0.544271i | 0.962259 | + | 0.272136i | \(0.0877299\pi\) | ||||
−0.962259 | + | 0.272136i | \(0.912270\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.10478e11 | −0.329826 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.80798e11 | −0.717381 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 6.50040e11i | − 0.679446i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.63948e11i | 0.895762i | 0.894093 | + | 0.447881i | \(0.147821\pi\) | ||||
−0.894093 | + | 0.447881i | \(0.852179\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.02458e12 | 1.05377 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.37109e11 | −0.956088 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.83564e12i | 1.85783i | 0.370293 | + | 0.928915i | \(0.379257\pi\) | ||||
−0.370293 | + | 0.928915i | \(0.620743\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 9.52843e10i | − 0.0956664i |
(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 | 384.9.b.a.319.5 | yes | 8 | |
4.3 | odd | 2 | inner | 384.9.b.a.319.1 | ✓ | 8 | |
8.3 | odd | 2 | inner | 384.9.b.a.319.8 | yes | 8 | |
8.5 | even | 2 | inner | 384.9.b.a.319.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.9.b.a.319.1 | ✓ | 8 | 4.3 | odd | 2 | inner | |
384.9.b.a.319.4 | yes | 8 | 8.5 | even | 2 | inner | |
384.9.b.a.319.5 | yes | 8 | 1.1 | even | 1 | trivial | |
384.9.b.a.319.8 | yes | 8 | 8.3 | odd | 2 | inner |