Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,8,Mod(17,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.17");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.b (of order \(2\), degree \(1\), not 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: | \(9.99632081549\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 10x^{4} - 24x^{3} - 320x^{2} - 3072x + 32768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 17.5 | ||
Root | \(-4.85268 - 2.90715i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 32.17 |
Dual form | 32.8.b.a.17.2 |
$q$-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 \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 40.2163i | 0.859959i | 0.902839 | + | 0.429979i | \(0.141479\pi\) | ||||
−0.902839 | + | 0.429979i | \(0.858521\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 324.492i | − 1.16094i | −0.814283 | − | 0.580468i | \(-0.802870\pi\) | ||||
0.814283 | − | 0.580468i | \(-0.197130\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 956.960 | 1.05451 | 0.527255 | − | 0.849707i | \(-0.323221\pi\) | ||||
0.527255 | + | 0.849707i | \(0.323221\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 569.651 | 0.260471 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5452.20i | 1.23509i | 0.786537 | + | 0.617544i | \(0.211872\pi\) | ||||
−0.786537 | + | 0.617544i | \(0.788128\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6289.38i | 0.793973i | 0.917824 | + | 0.396987i | \(0.129944\pi\) | ||||
−0.917824 | + | 0.396987i | \(0.870056\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13049.8 | 0.998357 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 34587.3 | 1.70744 | 0.853720 | − | 0.520733i | \(-0.174341\pi\) | ||||
0.853720 | + | 0.520733i | \(0.174341\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 14595.6i | − 0.488186i | −0.969752 | − | 0.244093i | \(-0.921510\pi\) | ||||
0.969752 | − | 0.244093i | \(-0.0784903\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 38485.4i | 0.906835i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24667.5 | 0.422743 | 0.211372 | − | 0.977406i | \(-0.432207\pi\) | ||||
0.211372 | + | 0.977406i | \(0.432207\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −27169.8 | −0.347774 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 110862.i | 1.08395i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 171116.i | − 1.30286i | −0.758710 | − | 0.651429i | \(-0.774170\pi\) | ||||
0.758710 | − | 0.651429i | \(-0.225830\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −111688. | −0.673352 | −0.336676 | − | 0.941620i | \(-0.609303\pi\) | ||||
−0.336676 | + | 0.941620i | \(0.609303\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −219267. | −1.06212 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 310526.i | − 1.22422i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 103636.i | 0.336360i | 0.985756 | + | 0.168180i | \(0.0537890\pi\) | ||||
−0.985756 | + | 0.168180i | \(0.946211\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −252935. | −0.682784 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 71691.3 | 0.162451 | 0.0812256 | − | 0.996696i | \(-0.474117\pi\) | ||||
0.0812256 | + | 0.996696i | \(0.474117\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 328419.i | − 0.629925i | −0.949104 | − | 0.314962i | \(-0.898008\pi\) | ||||
0.949104 | − | 0.314962i | \(-0.101992\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 184847.i | − 0.302391i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −119043. | −0.167248 | −0.0836241 | − | 0.996497i | \(-0.526650\pi\) | ||||
−0.0836241 | + | 0.996497i | \(0.526650\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 92230.3 | 0.111992 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.39097e6i | 1.46833i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.04011e6i | 0.959648i | 0.877365 | + | 0.479824i | \(0.159300\pi\) | ||||
−0.877365 | + | 0.479824i | \(0.840700\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.76919e6 | 1.43386 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 586982. | 0.419820 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 225984.i | − 0.143250i | −0.997432 | − | 0.0716250i | \(-0.977182\pi\) | ||||
0.997432 | − | 0.0716250i | \(-0.0228185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.55268e6i | − 0.875843i | −0.899013 | − | 0.437922i | \(-0.855715\pi\) | ||||
0.899013 | − | 0.437922i | \(-0.144285\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 545133. | 0.274670 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.04085e6 | 0.921753 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 316375.i | 0.128511i | 0.997933 | + | 0.0642555i | \(0.0204673\pi\) | ||||
−0.997933 | + | 0.0642555i | \(0.979533\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 992033.i | 0.363542i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −538965. | −0.178713 | −0.0893566 | − | 0.996000i | \(-0.528481\pi\) | ||||
−0.0893566 | + | 0.996000i | \(0.528481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.68512e6 | −0.807856 | −0.403928 | − | 0.914791i | \(-0.632355\pi\) | ||||
−0.403928 | + | 0.914791i | \(0.632355\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 1.09267e6i | − 0.299071i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.21754e6i | 1.30241i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.22632e6 | −1.87720 | −0.938600 | − | 0.345007i | \(-0.887877\pi\) | ||||
−0.938600 | + | 0.345007i | \(0.887877\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.21264e6 | −0.671684 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 5.89510e6i | − 1.13167i | −0.824520 | − | 0.565833i | \(-0.808555\pi\) | ||||
0.824520 | − | 0.565833i | \(-0.191445\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 1.12233e7i | − 1.98223i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.88164e6 | 1.12040 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 437005. | 0.0657085 | 0.0328542 | − | 0.999460i | \(-0.489540\pi\) | ||||
0.0328542 | + | 0.999460i | \(0.489540\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.01868e6i | 0.837253i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.49169e6i | − 0.579055i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.73616e6 | −0.566753 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.84322e6 | −0.872556 | −0.436278 | − | 0.899812i | \(-0.643704\pi\) | ||||
−0.436278 | + | 0.899812i | \(0.643704\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.10585e6i | 0.321705i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.19757e6i | 0.598545i | 0.954168 | + | 0.299272i | \(0.0967439\pi\) | ||||
−0.954168 | + | 0.299272i | \(0.903256\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.59816e6 | 0.594966 | 0.297483 | − | 0.954727i | \(-0.403853\pi\) | ||||
0.297483 | + | 0.954727i | \(0.403853\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.24882e7 | 1.05278 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 512845.i | 0.0404709i | 0.999795 | + | 0.0202354i | \(0.00644158\pi\) | ||||
−0.999795 | + | 0.0202354i | \(0.993558\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.95882e7i | 1.44878i | 0.689393 | + | 0.724388i | \(0.257877\pi\) | ||||
−0.689393 | + | 0.724388i | \(0.742123\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.16785e6 | −0.289256 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.88876e7 | 1.23141 | 0.615705 | − | 0.787977i | \(-0.288871\pi\) | ||||
0.615705 | + | 0.787977i | \(0.288871\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 8.00438e6i | − 0.490778i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.58275e6i | 0.206807i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.30987e7 | 1.80051 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.02394e7 | −0.525441 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.88316e6i | 0.139701i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.65345e7i | − 0.757193i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.96314e7 | −1.71683 | −0.858413 | − | 0.512959i | \(-0.828549\pi\) | ||||
−0.858413 | + | 0.512959i | \(0.828549\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.32078e7 | 0.541709 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.65337e7i | 1.41986i | 0.704274 | + | 0.709928i | \(0.251273\pi\) | ||||
−0.704274 | + | 0.709928i | \(0.748727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.39675e7i | − 0.514797i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.59739e7 | 1.25840 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.56967e7 | −0.853799 | −0.426899 | − | 0.904299i | \(-0.640394\pi\) | ||||
−0.426899 | + | 0.904299i | \(0.640394\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 5.23001e7i | − 1.65177i | −0.563836 | − | 0.825886i | \(-0.690675\pi\) | ||||
0.563836 | − | 0.825886i | \(-0.309325\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 4.78747e6i | − 0.143827i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.42910e7 | −0.980626 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.55256e7 | −1.51254 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.70916e6i | 0.0963085i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.80406e7i | 0.446785i | 0.974729 | + | 0.223392i | \(0.0717131\pi\) | ||||
−0.974729 | + | 0.223392i | \(0.928287\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.87385e7 | −0.915637 | −0.457818 | − | 0.889046i | \(-0.651369\pi\) | ||||
−0.457818 | + | 0.889046i | \(0.651369\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.97027e7 | 0.444739 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.62420e7i | 0.781719i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 5.12341e7i | − 1.05660i | −0.849058 | − | 0.528300i | \(-0.822830\pi\) | ||||
0.849058 | − | 0.528300i | \(-0.177170\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.18292e7 | −0.825258 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.36058e7 | 0.445787 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.57572e7i | − 1.55101i | −0.631343 | − | 0.775504i | \(-0.717496\pi\) | ||||
0.631343 | − | 0.775504i | \(-0.282504\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.11504e7i | 1.23306i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.05871e8 | 1.75901 | 0.879503 | − | 0.475893i | \(-0.157875\pi\) | ||||
0.879503 | + | 0.475893i | \(0.157875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.31923e7 | 0.369606 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 8.31441e6i | − 0.127158i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.98148e7i | − 0.290956i | −0.989361 | − | 0.145478i | \(-0.953528\pi\) | ||||
0.989361 | − | 0.145478i | \(-0.0464720\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.60005e7 | −0.366731 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.08822e6 | 0.123189 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.97800e7i | 0.388096i | 0.980992 | + | 0.194048i | \(0.0621618\pi\) | ||||
−0.980992 | + | 0.194048i | \(0.937838\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3.96227e6i | − 0.0496671i | −0.999692 | − | 0.0248335i | \(-0.992094\pi\) | ||||
0.999692 | − | 0.0248335i | \(-0.00790558\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.24429e7 | 0.753189 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.36290e7 | 0.390493 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.88577e8i | 2.10884i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.06091e8i | 1.14304i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.80105e7 | 0.498562 | 0.249281 | − | 0.968431i | \(-0.419806\pi\) | ||||
0.249281 | + | 0.968431i | \(0.419806\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.72502e6 | −0.0473100 | −0.0236550 | − | 0.999720i | \(-0.507530\pi\) | ||||
−0.0236550 | + | 0.999720i | \(0.507530\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.20754e7i | 0.792669i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.14882e8i | − 1.07058i | −0.844668 | − | 0.535290i | \(-0.820202\pi\) | ||||
0.844668 | − | 0.535290i | \(-0.179798\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.20933e7 | −0.108782 | −0.0543911 | − | 0.998520i | \(-0.517322\pi\) | ||||
−0.0543911 | + | 0.998520i | \(0.517322\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.27234e7 | −0.110514 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.63751e8i | − 1.37388i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 2.32632e7i | − 0.188596i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.40518e7 | 0.110112 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.95784e7 | 0.602953 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.95850e8i | − 1.43527i | −0.696418 | − | 0.717636i | \(-0.745224\pi\) | ||||
0.696418 | − | 0.717636i | \(-0.254776\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 2.16752e7i | − 0.153686i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.06569e8 | −0.731302 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.06881e8 | −0.710057 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1.07986e8i | − 0.694723i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.17532e8i | 1.35566i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.08024e8 | −0.652311 | −0.326156 | − | 0.945316i | \(-0.605753\pi\) | ||||
−0.326156 | + | 0.945316i | \(0.605753\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.54773e7 | −0.0905851 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.61144e8i | 0.914374i | 0.889371 | + | 0.457187i | \(0.151143\pi\) | ||||
−0.889371 | + | 0.457187i | \(0.848857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 5.27173e7i | − 0.290088i | −0.989425 | − | 0.145044i | \(-0.953668\pi\) | ||||
0.989425 | − | 0.145044i | \(-0.0463323\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.09830e8 | −1.12002 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.79423e8 | −0.929249 | −0.464625 | − | 0.885508i | \(-0.653811\pi\) | ||||
−0.464625 | + | 0.885508i | \(0.653811\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.86285e7i | 0.194165i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3.30832e8i | − 1.61431i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.42441e7 | 0.399160 | 0.199580 | − | 0.979882i | \(-0.436042\pi\) | ||||
0.199580 | + | 0.979882i | \(0.436042\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.12302e8 | −0.977000 | −0.488500 | − | 0.872564i | \(-0.662456\pi\) | ||||
−0.488500 | + | 0.872564i | \(0.662456\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.13255e8i | 0.506333i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2.99280e7i | − 0.130016i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.17975e7 | 0.387607 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.37079e8 | 0.973186 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1.18102e8i | − 0.471411i | −0.971825 | − | 0.235706i | \(-0.924260\pi\) | ||||
0.971825 | − | 0.235706i | \(-0.0757401\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.34492e8i | 0.522125i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.51359e8 | 1.70463 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.27463e8 | 0.468402 | 0.234201 | − | 0.972188i | \(-0.424753\pi\) | ||||
0.234201 | + | 0.972188i | \(0.424753\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.91755e7i | 0.354695i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 9.74762e7i | − 0.339357i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.33125e8 | −1.46814 | −0.734071 | − | 0.679073i | \(-0.762382\pi\) | ||||
−0.734071 | + | 0.679073i | \(0.762382\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.37506e8 | 1.11409 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.75747e7i | 0.0565066i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.44748e8i | 1.07986i | 0.841709 | + | 0.539931i | \(0.181550\pi\) | ||||
−0.841709 | + | 0.539931i | \(0.818450\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.42513e8 | 1.35062 | 0.675311 | − | 0.737533i | \(-0.264010\pi\) | ||||
0.675311 | + | 0.737533i | \(0.264010\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.42049e8 | −0.720003 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1.48135e8i | − 0.429531i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.18148e8i | 0.899395i | 0.893181 | + | 0.449697i | \(0.148468\pi\) | ||||
−0.893181 | + | 0.449697i | \(0.851532\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.36234e7 | −0.175389 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.28497e8 | 0.345478 | 0.172739 | − | 0.984968i | \(-0.444738\pi\) | ||||
0.172739 | + | 0.984968i | \(0.444738\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.98970e8i | 1.04637i | 0.852218 | + | 0.523187i | \(0.175257\pi\) | ||||
−0.852218 | + | 0.523187i | \(0.824743\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.90471e8i | − 0.487384i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.86057e7 | 0.171306 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.85942e8 | 1.91535 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 3.15425e8i | − 0.750362i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.00958e8i | 0.466732i | 0.972389 | + | 0.233366i | \(0.0749741\pi\) | ||||
−0.972389 | + | 0.233366i | \(0.925026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.33298e7 | −0.166304 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.04444e8 | −1.33878 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.55143e8i | 0.335647i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3.14284e8i | − 0.664262i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.49243e8 | −0.514724 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.03830e8 | −1.01680 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.58918e7i | − 0.0313465i | −0.999877 | − | 0.0156733i | \(-0.995011\pi\) | ||||
0.999877 | − | 0.0156733i | \(-0.00498916\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.65353e8i | 0.511646i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.87710e8 | −0.919391 | −0.459695 | − | 0.888077i | \(-0.652041\pi\) | ||||
−0.459695 | + | 0.888077i | \(0.652041\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.24731e8 | −0.598576 | −0.299288 | − | 0.954163i | \(-0.596749\pi\) | ||||
−0.299288 | + | 0.954163i | \(0.596749\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1.76891e8i | − 0.318874i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.06084e9i | − 1.87043i | −0.354086 | − | 0.935213i | \(-0.615208\pi\) | ||||
0.354086 | − | 0.935213i | \(-0.384792\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.32958e8 | 1.60914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.06247e7 | −0.0348033 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 5.04824e8i | − 0.833548i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1.70881e8i | − 0.276123i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.87763e8 | −1.24589 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.13919e8 | −0.176365 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.88487e8i | 0.437249i | 0.975809 | + | 0.218624i | \(0.0701569\pi\) | ||||
−0.975809 | + | 0.218624i | \(0.929843\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.90363e7i | 0.0876121i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.02661e8 | 0.149193 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.10595e8 | −0.157410 | −0.0787051 | − | 0.996898i | \(-0.525079\pi\) | ||||
−0.0787051 | + | 0.996898i | \(0.525079\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.59590e8i | 1.05896i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 6.08948e8i | − 0.831649i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.99837e8 | −0.936414 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.21907e8 | 0.422049 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.10651e9i | − 1.42168i | −0.703352 | − | 0.710841i | \(-0.748314\pi\) | ||||
0.703352 | − | 0.710841i | \(-0.251686\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.38337e9i | 1.74201i | 0.491278 | + | 0.871003i | \(0.336530\pi\) | ||||
−0.491278 | + | 0.871003i | \(0.663470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.97254e8 | −0.860630 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.47617e8 | −0.299618 | −0.149809 | − | 0.988715i | \(-0.547866\pi\) | ||||
−0.149809 | + | 0.988715i | \(0.547866\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.74890e8i | 0.207475i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.33111e9i | 1.54837i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.38641e9 | 1.58148 | 0.790738 | − | 0.612155i | \(-0.209697\pi\) | ||||
0.790738 | + | 0.612155i | \(0.209697\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.80839e8 | 0.761674 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 4.11789e8i | − 0.451858i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.71299e8i | 0.937869i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.49367e8 | 0.791341 | 0.395670 | − | 0.918393i | \(-0.370512\pi\) | ||||
0.395670 | + | 0.918393i | \(0.370512\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.08390e7 | 0.0423139 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.95340e8i | 1.01196i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1.49519e9i | − 1.49181i | −0.666051 | − | 0.745906i | \(-0.732017\pi\) | ||||
0.666051 | − | 0.745906i | \(-0.267983\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.64957e8 | 0.651155 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.07621e9 | 1.03443 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 7.92096e7i | − 0.0747379i | −0.999302 | − | 0.0373689i | \(-0.988102\pi\) | ||||
0.999302 | − | 0.0373689i | \(-0.0118977\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 1.59383e9i | − 1.47640i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.80285e8 | −0.436820 | −0.218410 | − | 0.975857i | \(-0.570087\pi\) | ||||
−0.218410 | + | 0.975857i | \(0.570087\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.69305e9 | 1.51202 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.87084e8i | − 0.164077i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 1.07150e9i | − 0.922928i | −0.887159 | − | 0.461464i | \(-0.847324\pi\) | ||||
0.887159 | − | 0.461464i | \(-0.152676\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.53180e8 | 0.721809 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.46925e9 | −1.22102 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.66937e9i | 2.17931i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.03185e9i | 1.62976i | 0.579627 | + | 0.814882i | \(0.303198\pi\) | ||||
−0.579627 | + | 0.814882i | \(0.696802\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.61719e8 | 0.442705 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.57759e9 | −1.99622 | −0.998111 | − | 0.0614301i | \(-0.980434\pi\) | ||||
−0.998111 | + | 0.0614301i | \(0.980434\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 7.02451e8i | − 0.534624i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.04248e9i | 0.779782i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.65044e8 | −0.415434 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.30242e8 | 0.238672 | 0.119336 | − | 0.992854i | \(-0.461923\pi\) | ||||
0.119336 | + | 0.992854i | \(0.461923\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.03343e9i | − 0.734232i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.16257e8i | − 0.151059i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.91291e9 | −1.31379 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.10331e9 | 1.42046 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 5.80021e7i | − 0.0385207i | −0.999815 | − | 0.0192604i | \(-0.993869\pi\) | ||||
0.999815 | − | 0.0192604i | \(-0.00613114\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.90609e8i | 0.124496i | 0.998061 | + | 0.0622480i | \(0.0198270\pi\) | ||||
−0.998061 | + | 0.0622480i | \(0.980173\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.78129e7 | −0.0435633 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.39731e8 | −0.593803 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.48585e9i | − 0.923586i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1.37906e9i | − 0.843298i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.42923e9 | −1.46150 | −0.730749 | − | 0.682646i | \(-0.760829\pi\) | ||||
−0.730749 | + | 0.682646i | \(0.760829\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.37902e9 | −1.40828 | −0.704141 | − | 0.710060i | \(-0.748668\pi\) | ||||
−0.704141 | + | 0.710060i | \(0.748668\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 2.23303e9i | − 1.30072i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.60037e8i | − 0.206378i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.33161e9 | 0.751194 | 0.375597 | − | 0.926783i | \(-0.377438\pi\) | ||||
0.375597 | + | 0.926783i | \(0.377438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.25390e7 | 0.0291707 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 5.02643e8i | − 0.274692i | −0.990523 | − | 0.137346i | \(-0.956143\pi\) | ||||
0.990523 | − | 0.137346i | \(-0.0438573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.41805e8i | − 0.0762834i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.25525e8 | −0.384217 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.14785e9 | 1.64116 | 0.820580 | − | 0.571531i | \(-0.193650\pi\) | ||||
0.820580 | + | 0.571531i | \(0.193650\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.90876e8i | 0.200641i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.55792e9i | − 0.787410i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.95301e9 | 0.971998 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.68422e9 | −1.31556 | −0.657782 | − | 0.753209i | \(-0.728505\pi\) | ||||
−0.657782 | + | 0.753209i | \(0.728505\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.83442e9i | 1.85078i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.30434e9i | 0.620065i | 0.950726 | + | 0.310033i | \(0.100340\pi\) | ||||
−0.950726 | + | 0.310033i | \(0.899660\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.86853e9 | −1.34315 | −0.671577 | − | 0.740934i | \(-0.734383\pi\) | ||||
−0.671577 | + | 0.740934i | \(0.734383\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.45752e9 | −0.672246 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 5.96519e8i | − 0.271029i | −0.990775 | − | 0.135514i | \(-0.956731\pi\) | ||||
0.990775 | − | 0.135514i | \(-0.0432687\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.02758e8i | 0.135516i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.06045e9 | 0.908632 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.79061e9 | 0.778012 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.96561e8i | 0.169778i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.92497e8i | 0.249961i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.16068e9 | 0.898289 | 0.449144 | − | 0.893459i | \(-0.351729\pi\) | ||||
0.449144 | + | 0.893459i | \(0.351729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.51805e8 | −0.267061 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.49337e8i | 0.383359i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.54506e9i | 1.01298i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.41934e8 | −0.0556847 | −0.0278424 | − | 0.999612i | \(-0.508864\pi\) | ||||
−0.0278424 | + | 0.999612i | \(0.508864\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.44884e9 | 1.33380 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 2.38677e9i | − 0.909966i | −0.890500 | − | 0.454983i | \(-0.849645\pi\) | ||||
0.890500 | − | 0.454983i | \(-0.150355\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.91843e9i | − 2.22455i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.00782e9 | 0.373479 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.15769e8 | −0.188455 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.23900e9i | 1.88754i | 0.330601 | + | 0.943771i | \(0.392749\pi\) | ||||
−0.330601 | + | 0.943771i | \(0.607251\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.25772e9i | 1.51267i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.63292e9 | 1.27282 | 0.636411 | − | 0.771350i | \(-0.280418\pi\) | ||||
0.636411 | + | 0.771350i | \(0.280418\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.01106e9 | 0.694872 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.32706e8i | 0.317846i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.58693e9i | 0.869505i | 0.900550 | + | 0.434753i | \(0.143164\pi\) | ||||
−0.900550 | + | 0.434753i | \(0.856836\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.56955e9 | −0.851892 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.61811e9 | 0.529171 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2.14105e9i | − 0.690718i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 6.49047e8i | − 0.206566i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.96876e8 | 0.250210 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.08542e8 | 0.0336253 | 0.0168127 | − | 0.999859i | \(-0.494648\pi\) | ||||
0.0168127 | + | 0.999859i | \(0.494648\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 6.10725e9i | − 1.86676i | −0.358884 | − | 0.933382i | \(-0.616843\pi\) | ||||
0.358884 | − | 0.933382i | \(-0.383157\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1.04564e9i | − 0.315374i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.86300e9 | −1.14971 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.79634e9 | −0.821288 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1.28732e8i | − 0.0373125i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.50894e8i | 0.128982i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.66414e8 | 0.0469841 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.19764e9 | −0.333747 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.02858e8i | 0.138320i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.39345e8i | 0.146445i | 0.997316 | + | 0.0732227i | \(0.0233284\pi\) | ||||
−0.997316 | + | 0.0732227i | \(0.976672\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.59348e8 | 0.0427116 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.35620e9 | 1.68194 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 8.82287e7i | − 0.0230491i | −0.999934 | − | 0.0115246i | \(-0.996332\pi\) | ||||
0.999934 | − | 0.0115246i | \(-0.00366846\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 8.84483e8i | − 0.228132i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.49754e9 | −0.636037 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.87226e9 | −1.97953 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.35243e9i | 0.335807i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5.57233e8i | − 0.136629i | −0.997664 | − | 0.0683147i | \(-0.978238\pi\) | ||||
0.997664 | − | 0.0683147i | \(-0.0217622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.06555e9 | 0.500143 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.58386e9 | −1.81351 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.17012e9i | 0.276344i | 0.990408 | + | 0.138172i | \(0.0441227\pi\) | ||||
−0.990408 | + | 0.138172i | \(0.955877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 6.12887e9i | − 1.42959i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.07437e9 | −0.708297 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.39181e9 | −0.544295 | −0.272147 | − | 0.962256i | \(-0.587734\pi\) | ||||
−0.272147 | + | 0.962256i | \(0.587734\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.15823e9i | 0.709933i | 0.934879 | + | 0.354966i | \(0.115508\pi\) | ||||
−0.934879 | + | 0.354966i | \(0.884492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.93080e9i | 0.428743i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.70211e8 | −0.147019 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.03435e9 | 0.874296 | 0.437148 | − | 0.899390i | \(-0.355989\pi\) | ||||
0.437148 | + | 0.899390i | \(0.355989\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1.90023e8i | − 0.0406846i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 5.64138e9i | − 1.19335i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.67087e9 | −1.18525 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.16257e9 | 0.240090 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.72240e9i | 0.555544i | 0.960647 | + | 0.277772i | \(0.0895960\pi\) | ||||
−0.960647 | + | 0.277772i | \(0.910404\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.63016e9i | 0.328721i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.62012e9 | 0.920655 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.29251e9 | −0.451460 | −0.225730 | − | 0.974190i | \(-0.572477\pi\) | ||||
−0.225730 | + | 0.974190i | \(0.572477\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.07402e10i | − 2.09028i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 4.86346e8i | − 0.0935482i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.58734e9 | 0.681991 | 0.340995 | − | 0.940065i | \(-0.389236\pi\) | ||||
0.340995 | + | 0.940065i | \(0.389236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.20369e9 | 1.54152 | 0.770759 | − | 0.637127i | \(-0.219877\pi\) | ||||
0.770759 | + | 0.637127i | \(0.219877\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.80223e8i | 0.0334734i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.32259e9i | 0.610004i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.60087e9 | 0.834986 | 0.417493 | − | 0.908680i | \(-0.362909\pi\) | ||||
0.417493 | + | 0.908680i | \(0.362909\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.58546e9 | 1.18148 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 7.48707e8i | − 0.132791i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.55728e9i | 1.50046i | 0.661178 | + | 0.750229i | \(0.270057\pi\) | ||||
−0.661178 | + | 0.750229i | \(0.729943\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.35561e8 | 0.162184 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.58089e9 | −0.442355 | −0.221178 | − | 0.975234i | \(-0.570990\pi\) | ||||
−0.221178 | + | 0.975234i | \(0.570990\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 5.26641e9i | − 0.892478i | −0.894914 | − | 0.446239i | \(-0.852763\pi\) | ||||
0.894914 | − | 0.446239i | \(-0.147237\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.73469e9i | 0.458234i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.18197e8 | 0.0692903 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.48796e9 | −1.22683 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.20035e9i | 0.518514i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.58449e9i | 0.574314i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.32515e9 | −1.31914 | −0.659568 | − | 0.751645i | \(-0.729261\pi\) | ||||
−0.659568 | + | 0.751645i | \(0.729261\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.87635e9 | 1.23428 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.28601e10i | 1.99313i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.80071e8i | 0.0889187i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.07022e8 | −0.0465496 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.26190e9 | 0.639146 | 0.319573 | − | 0.947562i | \(-0.396460\pi\) | ||||
0.319573 | + | 0.947562i | \(0.396460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.26588e10i | 1.87782i | 0.344167 | + | 0.938908i | \(0.388161\pi\) | ||||
−0.344167 | + | 0.938908i | \(0.611839\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 4.28582e9i | − 0.628890i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.38061e9 | 1.07134 | 0.535670 | − | 0.844427i | \(-0.320059\pi\) | ||||
0.535670 | + | 0.844427i | \(0.320059\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.23211e9 | 0.176926 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 4.29837e9i | − 0.610620i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 3.21579e9i | − 0.451951i | −0.974133 | − | 0.225975i | \(-0.927443\pi\) | ||||
0.974133 | − | 0.225975i | \(-0.0725569\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.18549e10 | 1.64836 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.52958e9 | −0.210423 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 5.17004e9i | − 0.703711i | −0.936054 | − | 0.351856i | \(-0.885551\pi\) | ||||
0.936054 | − | 0.351856i | \(-0.114449\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1.95604e9i | − 0.263435i | −0.991287 | − | 0.131717i | \(-0.957951\pi\) | ||||
0.991287 | − | 0.131717i | \(-0.0420491\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.74835e9 | −1.16581 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.53232e9 | −0.597647 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.22099e9i | − 0.550775i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 4.34434e9i | − 0.560961i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.46551e9 | 1.08174 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.54679e9 | 0.195605 | 0.0978024 | − | 0.995206i | \(-0.468819\pi\) | ||||
0.0978024 | + | 0.995206i | \(0.468819\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 3.01211e9i | − 0.376971i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 8.55209e9i | − 1.05928i | −0.848222 | − | 0.529642i | \(-0.822326\pi\) | ||||
0.848222 | − | 0.529642i | \(-0.177674\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.50565e9 | −0.920119 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.48061e9 | −0.786323 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 7.26976e9i | − 0.873067i | −0.899688 | − | 0.436534i | \(-0.856206\pi\) | ||||
0.899688 | − | 0.436534i | \(-0.143794\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.33837e9i | 0.991206i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.12010e9 | 0.249463 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.54162e9 | −0.761935 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.19893e9i | 0.599434i | 0.954028 | + | 0.299717i | \(0.0968922\pi\) | ||||
−0.954028 | + | 0.299717i | \(0.903108\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.97218e9i | 0.339241i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.69709e10 | −1.91760 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.47961e9 | 0.277376 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 7.21572e9i | − 0.799116i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.35221e10i | − 1.48262i | −0.671163 | − | 0.741310i | \(-0.734205\pi\) | ||||
0.671163 | − | 0.741310i | \(-0.265795\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.51263e9 | 0.164206 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.55349e9 | −0.166974 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.93083e9i | 0.631172i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.05901e10i | 1.11594i | 0.829862 | + | 0.557969i | \(0.188419\pi\) | ||||
−0.829862 | + | 0.557969i | \(0.811581\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.68613e9 | −0.488957 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.75507e9 | −0.284655 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.11271e10i | 1.13845i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.38799e9i | 0.343261i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.49161e10 | −1.49659 | −0.748297 | − | 0.663363i | \(-0.769128\pi\) | ||||
−0.748297 | + | 0.663363i | \(0.769128\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.31417e9 | 0.627398 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 8.53800e9i | − 0.840180i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.64919e9i | 0.453100i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.90159e9 | 0.859206 | 0.429603 | − | 0.903018i | \(-0.358654\pi\) | ||||
0.429603 | + | 0.903018i | \(0.358654\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.15808e10 | −1.10711 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.13591e10i | − 1.07556i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 7.99792e9i | − 0.750090i | −0.927007 | − | 0.375045i | \(-0.877627\pi\) | ||||
0.927007 | − | 0.375045i | \(-0.122373\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.20359e9 | 0.111808 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.72494e9 | −0.158722 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.03852e10i | − 0.946588i | −0.880905 | − | 0.473294i | \(-0.843065\pi\) | ||||
0.880905 | − | 0.473294i | \(-0.156935\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.69175e9i | 0.333326i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.73477e9 | 0.334044 | 0.167022 | − | 0.985953i | \(-0.446585\pi\) | ||||
0.167022 | + | 0.985953i | \(0.446585\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.85402e9 | 0.518689 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 3.35815e9i | − 0.294766i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.90772e8i | 0.0426770i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.34330e10 | 1.15726 | 0.578631 | − | 0.815589i | \(-0.303587\pi\) | ||||
0.578631 | + | 0.815589i | \(0.303587\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.74963e9 | 0.405394 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.25703e10i | 1.06300i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 6.78007e9i | − 0.568065i | −0.958815 | − | 0.284033i | \(-0.908328\pi\) | ||||
0.958815 | − | 0.284033i | \(-0.0916724\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.40877e9 | −0.449006 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.01137e9 | 0.658962 | 0.329481 | − | 0.944162i | \(-0.393126\pi\) | ||||
0.329481 | + | 0.944162i | \(0.393126\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.87451e10i | 1.52775i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 6.39335e9i | − 0.516314i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.42130e9 | 0.113737 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.46553e10 | 1.16213 | 0.581063 | − | 0.813858i | \(-0.302637\pi\) | ||||
0.581063 | + | 0.813858i | \(0.302637\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.12609e9i | 0.402806i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.33296e10i | 1.81668i | 0.418233 | + | 0.908340i | \(0.362650\pi\) | ||||
−0.418233 | + | 0.908340i | \(0.637350\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.03456e9 | 0.234174 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.98847e9 | −0.305023 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.04638e9i | − 0.0793064i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 2.93855e9i | − 0.220726i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.89703e10 | 1.41224 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.66250e10 | −1.22664 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.27740e8i | 0.0385930i | 0.999814 | + | 0.0192965i | \(0.00614264\pi\) | ||||
−0.999814 | + | 0.0192965i | \(0.993857\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1.74187e10i | − 1.26254i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.80747e10 | 1.29853 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.76536e9 | 0.695396 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.35732e10i | 0.958072i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.41514e9i | 0.168981i | 0.996424 | + | 0.0844907i | \(0.0269263\pi\) | ||||
−0.996424 | + | 0.0844907i | \(0.973074\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.11738e9 | −0.285566 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.48940e8 | 0.0171152 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.46398e10i | − 0.997773i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 7.65988e9i | − 0.517531i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.38645e10 | −0.928636 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.16364e10 | 0.772679 | 0.386340 | − | 0.922357i | \(-0.373739\pi\) | ||||
0.386340 | + | 0.922357i | \(0.373739\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.44359e10i | 0.950320i | 0.879899 | + | 0.475160i | \(0.157610\pi\) | ||||
−0.879899 | + | 0.475160i | \(0.842390\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.77962e10i | 1.16148i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.78275e10 | −1.80062 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.79348e9 | −0.307521 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.42855e9i | 0.218080i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.63805e9i | 0.481706i | 0.970562 | + | 0.240853i | \(0.0774271\pi\) | ||||
−0.970562 | + | 0.240853i | \(0.922573\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.16446e10 | 1.35348 | 0.676738 | − | 0.736224i | \(-0.263393\pi\) | ||||
0.676738 | + | 0.736224i | \(0.263393\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.95746e9 | 0.369379 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1.57823e10i | − 0.970288i | −0.874434 | − | 0.485144i | \(-0.838767\pi\) | ||||
0.874434 | − | 0.485144i | \(-0.161233\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.63296e10i | 1.60510i | 0.596582 | + | 0.802552i | \(0.296525\pi\) | ||||
−0.596582 | + | 0.802552i | \(0.703475\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.27947e10 | −0.773442 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.19000e9 | 0.191220 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 3.43541e10i | − 2.04210i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.23820e10i | − 0.729882i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.84995e9 | 0.108142 | 0.0540710 | − | 0.998537i | \(-0.482780\pi\) | ||||
0.0540710 | + | 0.998537i | \(0.482780\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.20307e10 | −0.697438 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.16767e9i | 0.297097i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 7.52569e9i | − 0.429090i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.79866e9 | −0.554083 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.60451e10 | −0.899839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.55643e9i | 0.142194i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.28088e7i | 0.00346496i | 0.999998 | + | 0.00173248i | \(0.000551466\pi\) | ||||
−0.999998 | + | 0.00173248i | \(0.999449\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.69796e9 | −0.147623 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.25595e9 | −0.339516 | −0.169758 | − | 0.985486i | \(-0.554299\pi\) | ||||
−0.169758 | + | 0.985486i | \(0.554299\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 2.48119e10i | − 1.33562i | −0.744331 | − | 0.667811i | \(-0.767231\pi\) | ||||
0.744331 | − | 0.667811i | \(-0.232769\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.75907e9i | 0.147316i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.28944e10 | −0.682909 | −0.341455 | − | 0.939898i | \(-0.610920\pi\) | ||||
−0.341455 | + | 0.939898i | \(0.610920\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.42973e9 | −0.337782 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.16077e10i | 1.64712i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 4.48516e10i | − 2.31851i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.98980e9 | −0.102034 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.46789e9 | −0.227276 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.58229e10i | − 0.798468i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.75670e10i | − 1.38004i | −0.723792 | − | 0.690018i | \(-0.757603\pi\) | ||||
0.723792 | − | 0.690018i | \(-0.242397\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.08177e9 | −0.401371 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.74343e10 | 1.35169 | 0.675847 | − | 0.737042i | \(-0.263778\pi\) | ||||
0.675847 | + | 0.737042i | \(0.263778\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.09906e10i | 1.02604i | 0.858378 | + | 0.513018i | \(0.171473\pi\) | ||||
−0.858378 | + | 0.513018i | \(0.828527\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2.94905e9i | − 0.143015i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.39134e10 | 1.15056 | 0.575280 | − | 0.817957i | \(-0.304893\pi\) | ||||
0.575280 | + | 0.817957i | \(0.304893\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.79257e10 | −1.81041 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.75160e10i | − 0.829588i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.73751e9i | 0.0816483i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.66337e9 | 0.450555 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.23927e9 | −0.288643 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.91117e10i | 0.877282i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.59744e10i | 1.63854i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.26393e10 | 0.571238 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.28572e9 | −0.0576603 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.84425e10i | 1.71075i | 0.518012 | + | 0.855373i | \(0.326672\pi\) | ||||
−0.518012 | + | 0.855373i | \(0.673328\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.53045e9i | 0.155904i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.64507e10 | −1.59732 | −0.798660 | − | 0.601783i | \(-0.794457\pi\) | ||||
−0.798660 | + | 0.601783i | \(0.794457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.21413e10 | 1.39771 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 2.02622e10i | − 0.874405i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.49613e10i | 1.49725i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.37343e10 | −1.00872 | −0.504361 | − | 0.863493i | \(-0.668272\pi\) | ||||
−0.504361 | + | 0.863493i | \(0.668272\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.39111e8 | 0.0269567 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.38976e9i | − 0.141894i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 2.81577e9i | − 0.116977i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.75864e9 | 0.154972 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.23952e10 | −1.73485 | −0.867424 | − | 0.497570i | \(-0.834226\pi\) | ||||
−0.867424 | + | 0.497570i | \(0.834226\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.34616e9i | − 0.0546730i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.96139e10i | − 0.790638i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.11916e10 | 2.44823 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.70014e10 | 1.46937 | 0.734683 | − | 0.678411i | \(-0.237331\pi\) | ||||
0.734683 | + | 0.678411i | \(0.237331\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 1.30595e10i | − 0.514750i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.10617e10i | 0.824005i | 0.911183 | + | 0.412003i | \(0.135171\pi\) | ||||
−0.911183 | + | 0.412003i | \(0.864829\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.76844e9 | 0.0686752 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.44256e10 | 1.32700 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.35146e10i | − 0.517104i | −0.965997 | − | 0.258552i | \(-0.916755\pi\) | ||||
0.965997 | − | 0.258552i | \(-0.0832454\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.68877e10i | − 0.641416i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.26628e10 | 1.60849 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.26831e10 | 1.59746 | 0.798731 | − | 0.601688i | \(-0.205505\pi\) | ||||
0.798731 | + | 0.601688i | \(0.205505\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1.55790e10i | − 0.578799i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.75201e10i | 1.38380i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.45907e10 | −0.900340 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.50383e10 | −0.546597 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.92142e8i | 0.0105415i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.53323e9i | 0.0549239i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.32274e10 | −0.826053 | −0.413026 | − | 0.910719i | \(-0.635528\pi\) | ||||
−0.413026 | + | 0.910719i | \(0.635528\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.03021e10 | 0.716817 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.85678e10i | 1.70248i | 0.524780 | + | 0.851238i | \(0.324148\pi\) | ||||
−0.524780 | + | 0.851238i | \(0.675852\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 5.00491e10i | − 1.74181i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.87221e9 | 0.237454 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.54549e10 | 0.530193 | 0.265096 | − | 0.964222i | \(-0.414596\pi\) | ||||
0.265096 | + | 0.964222i | \(0.414596\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.38264e9i | 0.0811557i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.11584e10i | 0.377364i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.59192e10 | 0.534546 | 0.267273 | − | 0.963621i | \(-0.413877\pi\) | ||||
0.267273 | + | 0.963621i | \(0.413877\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.72782e10 | −1.24288 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 4.58142e9i | − 0.151667i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 8.10126e9i | − 0.266296i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.49883e10 | −0.489208 | −0.244604 | − | 0.969623i | \(-0.578658\pi\) | ||||
−0.244604 | + | 0.969623i | \(0.578658\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.16019e10 | −0.376016 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.92416e9i | 0.126289i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.44101e10i | 1.09965i | 0.835281 | + | 0.549824i | \(0.185305\pi\) | ||||
−0.835281 | + | 0.549824i | \(0.814695\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.14893e10 | −0.364598 |
(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 | 32.8.b.a.17.5 | 6 | ||
3.2 | odd | 2 | 288.8.d.b.145.5 | 6 | |||
4.3 | odd | 2 | 8.8.b.a.5.2 | yes | 6 | ||
8.3 | odd | 2 | 8.8.b.a.5.1 | ✓ | 6 | ||
8.5 | even | 2 | inner | 32.8.b.a.17.2 | 6 | ||
12.11 | even | 2 | 72.8.d.b.37.5 | 6 | |||
16.3 | odd | 4 | 256.8.a.r.1.5 | 6 | |||
16.5 | even | 4 | 256.8.a.q.1.5 | 6 | |||
16.11 | odd | 4 | 256.8.a.r.1.2 | 6 | |||
16.13 | even | 4 | 256.8.a.q.1.2 | 6 | |||
24.5 | odd | 2 | 288.8.d.b.145.2 | 6 | |||
24.11 | even | 2 | 72.8.d.b.37.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.8.b.a.5.1 | ✓ | 6 | 8.3 | odd | 2 | ||
8.8.b.a.5.2 | yes | 6 | 4.3 | odd | 2 | ||
32.8.b.a.17.2 | 6 | 8.5 | even | 2 | inner | ||
32.8.b.a.17.5 | 6 | 1.1 | even | 1 | trivial | ||
72.8.d.b.37.5 | 6 | 12.11 | even | 2 | |||
72.8.d.b.37.6 | 6 | 24.11 | even | 2 | |||
256.8.a.q.1.2 | 6 | 16.13 | even | 4 | |||
256.8.a.q.1.5 | 6 | 16.5 | even | 4 | |||
256.8.a.r.1.2 | 6 | 16.11 | odd | 4 | |||
256.8.a.r.1.5 | 6 | 16.3 | odd | 4 | |||
288.8.d.b.145.2 | 6 | 24.5 | odd | 2 | |||
288.8.d.b.145.5 | 6 | 3.2 | odd | 2 |