Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,8,Mod(129,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, 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("256.129");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.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: | \(79.9705665239\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.50765497344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 101x^{4} + 2512x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 128) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.6 | ||
Root | \(-7.53231i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.129 |
Dual form | 256.8.b.l.129.1 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 62.2585i | 1.33130i | 0.746266 | + | 0.665648i | \(0.231845\pi\) | ||||
−0.746266 | + | 0.665648i | \(0.768155\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 203.009i | 0.726307i | 0.931729 | + | 0.363153i | \(0.118300\pi\) | ||||
−0.931729 | + | 0.363153i | \(0.881700\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 534.535 | 0.589024 | 0.294512 | − | 0.955648i | \(-0.404843\pi\) | ||||
0.294512 | + | 0.955648i | \(0.404843\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1689.12 | −0.772346 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1579.58i | − 0.357822i | −0.983865 | − | 0.178911i | \(-0.942743\pi\) | ||||
0.983865 | − | 0.178911i | \(-0.0572574\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1771.71i | − 0.223661i | −0.993727 | − | 0.111831i | \(-0.964329\pi\) | ||||
0.993727 | − | 0.111831i | \(-0.0356714\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −12639.0 | −0.966929 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 28985.6 | 1.43091 | 0.715453 | − | 0.698661i | \(-0.246220\pi\) | ||||
0.715453 | + | 0.698661i | \(0.246220\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 39214.3i | − 1.31162i | −0.754928 | − | 0.655808i | \(-0.772328\pi\) | ||||
0.754928 | − | 0.655808i | \(-0.227672\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 33279.3i | 0.784165i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 85265.7 | 1.46126 | 0.730629 | − | 0.682774i | \(-0.239227\pi\) | ||||
0.730629 | + | 0.682774i | \(0.239227\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 36912.4 | 0.472478 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 30997.2i | 0.303074i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 246207.i | − 1.87459i | −0.348531 | − | 0.937297i | \(-0.613319\pi\) | ||||
0.348531 | − | 0.937297i | \(-0.386681\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 54648.0 | 0.329464 | 0.164732 | − | 0.986338i | \(-0.447324\pi\) | ||||
0.164732 | + | 0.986338i | \(0.447324\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 98342.3 | 0.476367 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 108515.i | 0.427812i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 290027.i | − 0.941310i | −0.882317 | − | 0.470655i | \(-0.844018\pi\) | ||||
0.882317 | − | 0.470655i | \(-0.155982\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 110304. | 0.297759 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 725641. | 1.64429 | 0.822145 | − | 0.569278i | \(-0.192777\pi\) | ||||
0.822145 | + | 0.569278i | \(0.192777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 668406.i | − 1.28204i | −0.767525 | − | 0.641019i | \(-0.778512\pi\) | ||||
0.767525 | − | 0.641019i | \(-0.221488\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 342907.i | − 0.560961i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −429632. | −0.603607 | −0.301803 | − | 0.953370i | \(-0.597589\pi\) | ||||
−0.301803 | + | 0.953370i | \(0.597589\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −537815. | −0.653051 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.80460e6i | 1.90496i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 725328.i | − 0.669220i | −0.942357 | − | 0.334610i | \(-0.891395\pi\) | ||||
0.942357 | − | 0.334610i | \(-0.108605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 320669. | 0.259889 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.44142e6 | 1.74615 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 165981.i | − 0.105215i | −0.998615 | − | 0.0526073i | \(-0.983247\pi\) | ||||
0.998615 | − | 0.0526073i | \(-0.0167532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 2.66752e6i | − 1.50471i | −0.658758 | − | 0.752355i | \(-0.728918\pi\) | ||||
0.658758 | − | 0.752355i | \(-0.271082\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −902895. | −0.454931 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 359673. | 0.162447 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.16279e6i | 0.472322i | 0.971714 | + | 0.236161i | \(0.0758892\pi\) | ||||
−0.971714 | + | 0.236161i | \(0.924111\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.30852e6i | 1.94537i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.87428e6 | 1.28466 | 0.642328 | − | 0.766430i | \(-0.277969\pi\) | ||||
0.642328 | + | 0.766430i | \(0.277969\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −579226. | −0.174268 | −0.0871341 | − | 0.996197i | \(-0.527771\pi\) | ||||
−0.0871341 | + | 0.996197i | \(0.527771\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.29811e6i | 0.629008i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 844341.i | − 0.210766i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.92515e6 | −0.439308 | −0.219654 | − | 0.975578i | \(-0.570493\pi\) | ||||
−0.219654 | + | 0.975578i | \(0.570493\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.62395e6 | −1.17583 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.86286e6i | 0.933509i | 0.884387 | + | 0.466755i | \(0.154577\pi\) | ||||
−0.884387 | + | 0.466755i | \(0.845423\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.88434e6i | 1.03928i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.53285e7 | 2.49564 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.58660e6 | −0.689645 | −0.344823 | − | 0.938668i | \(-0.612061\pi\) | ||||
−0.344823 | + | 0.938668i | \(0.612061\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 947042.i | − 0.131742i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.40230e6i | 0.438614i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.96085e6 | 0.952636 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.18281e6 | −0.465336 | −0.232668 | − | 0.972556i | \(-0.574746\pi\) | ||||
−0.232668 | + | 0.972556i | \(0.574746\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.66810e6i | 0.276363i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 4.85215e6i | − 0.468608i | −0.972163 | − | 0.234304i | \(-0.924719\pi\) | ||||
0.972163 | − | 0.234304i | \(-0.0752811\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.31137e7 | −1.18249 | −0.591243 | − | 0.806494i | \(-0.701363\pi\) | ||||
−0.591243 | + | 0.806494i | \(0.701363\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.75600e6 | −0.569544 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.04501e6i | − 0.161381i | −0.996739 | − | 0.0806905i | \(-0.974287\pi\) | ||||
0.996739 | − | 0.0806905i | \(-0.0257126\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.15280e6i | 0.676957i | 0.940974 | + | 0.338479i | \(0.109912\pi\) | ||||
−0.940974 | + | 0.338479i | \(0.890088\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.80567e7 | 1.25316 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.75532e7 | −1.14441 | −0.572207 | − | 0.820110i | \(-0.693912\pi\) | ||||
−0.572207 | + | 0.820110i | \(0.693912\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.73097e7i | 1.06132i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.99264e6i | 0.172744i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.54938e7 | 0.842838 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.69921e7 | 0.871963 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.51773e7i | 2.18903i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.33536e7i | 1.06947i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.81077e7 | 1.65082 | 0.825410 | − | 0.564534i | \(-0.190944\pi\) | ||||
0.825410 | + | 0.564534i | \(0.190944\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.16140e7 | 1.70677 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.06882e7i | 0.804033i | 0.915633 | + | 0.402016i | \(0.131690\pi\) | ||||
−0.915633 | + | 0.402016i | \(0.868310\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.09614e7i | − 0.772573i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.29270e6 | −0.220125 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.98669e7 | −0.660099 | −0.330049 | − | 0.943964i | \(-0.607065\pi\) | ||||
−0.330049 | + | 0.943964i | \(0.607065\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.73872e7i | 1.81244i | 0.422808 | + | 0.906219i | \(0.361045\pi\) | ||||
−0.422808 | + | 0.906219i | \(0.638955\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.67482e7i | − 0.803578i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.79856e6 | −0.0800310 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.99822e7 | 1.36153 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 3.34836e7i | − 0.869403i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 5.61302e7i | − 1.39009i | −0.718964 | − | 0.695047i | \(-0.755383\pi\) | ||||
0.718964 | − | 0.695047i | \(-0.244617\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.71149e7 | 1.34999 | 0.674994 | − | 0.737823i | \(-0.264146\pi\) | ||||
0.674994 | + | 0.737823i | \(0.264146\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.89602e7 | −1.10516 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.10940e7i | 0.239292i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2.12835e7i | − 0.438928i | −0.975621 | − | 0.219464i | \(-0.929569\pi\) | ||||
0.975621 | − | 0.219464i | \(-0.0704309\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.51578e7 | 0.890929 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.55775e7 | 0.860716 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.30446e7i | 0.416785i | 0.978045 | + | 0.208393i | \(0.0668232\pi\) | ||||
−0.978045 | + | 0.208393i | \(0.933177\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.99644e7i | 0.345989i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.81864e7 | −1.13290 | −0.566448 | − | 0.824097i | \(-0.691683\pi\) | ||||
−0.566448 | + | 0.824097i | \(0.691683\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.96096e7 | 0.949976 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.62377e7i | 1.01302i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.37015e7i | − 0.201191i | −0.994927 | − | 0.100595i | \(-0.967925\pi\) | ||||
0.994927 | − | 0.100595i | \(-0.0320747\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.97309e7 | 0.278301 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.03337e7 | 0.140072 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3.41349e6i | − 0.0444849i | −0.999753 | − | 0.0222424i | \(-0.992919\pi\) | ||||
0.999753 | − | 0.0222424i | \(-0.00708057\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 6.65355e7i | − 0.834024i | −0.908901 | − | 0.417012i | \(-0.863077\pi\) | ||||
0.908901 | − | 0.417012i | \(-0.136923\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.66076e8 | 2.00321 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.88781e7 | 0.683680 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4.57851e7i | − 0.512010i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.65691e7i | 0.178518i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.69543e8 | 1.76061 | 0.880303 | − | 0.474413i | \(-0.157340\pi\) | ||||
0.880303 | + | 0.474413i | \(0.157340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.77620e8 | −1.77845 | −0.889226 | − | 0.457468i | \(-0.848757\pi\) | ||||
−0.889226 | + | 0.457468i | \(0.848757\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.23927e7i | 0.216265i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.47827e6i | 0.0696898i | 0.999393 | + | 0.0348449i | \(0.0110937\pi\) | ||||
−0.999393 | + | 0.0348449i | \(0.988906\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.63422e8 | −1.47003 | −0.735014 | − | 0.678052i | \(-0.762824\pi\) | ||||
−0.735014 | + | 0.678052i | \(0.762824\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.23933e7 | −0.628799 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.31606e8i | − 1.10418i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.47312e8i | 1.19426i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.44024e8 | −1.12860 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.19421e7 | −0.469325 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.12526e8i | 1.55749i | 0.627343 | + | 0.778743i | \(0.284143\pi\) | ||||
−0.627343 | + | 0.778743i | \(0.715857\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.41207e8i | 1.71026i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.35692e8 | 0.931153 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.92113e7 | 0.194062 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 3.60618e7i | − 0.232002i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 5.13541e7i | − 0.320039i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.42620e8 | −1.46507 | −0.732536 | − | 0.680728i | \(-0.761664\pi\) | ||||
−0.732536 | + | 0.680728i | \(0.761664\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.23495e7 | −0.364917 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.63844e7i | 0.0929695i | 0.998919 | + | 0.0464847i | \(0.0148019\pi\) | ||||
−0.998919 | + | 0.0464847i | \(0.985198\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.30425e8i | 1.26796i | 0.773350 | + | 0.633979i | \(0.218579\pi\) | ||||
−0.773350 | + | 0.633979i | \(0.781421\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.25674e7 | 0.280591 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.52807e7 | 0.493468 | 0.246734 | − | 0.969083i | \(-0.420643\pi\) | ||||
0.246734 | + | 0.969083i | \(0.420643\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 8.72191e7i | − 0.438404i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.19857e8i | − 0.584848i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.85841e8 | −0.880540 | −0.440270 | − | 0.897865i | \(-0.645117\pi\) | ||||
−0.440270 | + | 0.897865i | \(0.645117\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −105251. | −0.000484356 0 | −0.000242178 | − | 1.00000i | \(-0.500077\pi\) | ||||
−0.000242178 | 1.00000i | \(0.500077\pi\) | ||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 2.82348e8i | − 1.26230i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.09181e8i | − 0.474315i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.94764e7 | −0.293358 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.02755e8 | −1.24278 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.64315e7i | 0.145418i | 0.997353 | + | 0.0727092i | \(0.0231645\pi\) | ||||
−0.997353 | + | 0.0727092i | \(0.976836\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.34684e8i | − 0.522871i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.66350e8 | −1.38358 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.82041e8 | −1.03645 | −0.518223 | − | 0.855246i | \(-0.673406\pi\) | ||||
−0.518223 | + | 0.855246i | \(0.673406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.55030e8i | − 0.554454i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.15874e8i | 1.44784i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.38965e8 | −0.810008 | −0.405004 | − | 0.914315i | \(-0.632730\pi\) | ||||
−0.405004 | + | 0.914315i | \(0.632730\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.47248e8 | 0.486059 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2.85555e8i | − 0.918121i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 3.57893e8i | − 1.12104i | −0.828142 | − | 0.560519i | \(-0.810602\pi\) | ||||
0.828142 | − | 0.560519i | \(-0.189398\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.58788e8 | −0.484646 | −0.242323 | − | 0.970196i | \(-0.577909\pi\) | ||||
−0.242323 | + | 0.970196i | \(0.577909\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.89614e7 | 0.175387 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 5.83060e7i | − 0.169063i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4.11223e8i | − 1.16251i | −0.813720 | − | 0.581257i | \(-0.802561\pi\) | ||||
0.813720 | − | 0.581257i | \(-0.197439\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.23071e7 | −0.254460 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.05056e8 | 0.820177 | 0.410088 | − | 0.912046i | \(-0.365498\pi\) | ||||
0.410088 | + | 0.912046i | \(0.365498\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4.22725e8i | − 1.10868i | −0.832291 | − | 0.554340i | \(-0.812971\pi\) | ||||
0.832291 | − | 0.554340i | \(-0.187029\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.95631e8i | 1.26824i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.87880e8 | 0.968526 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.29827e8 | 1.04749 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 2.60415e8i | − 0.619500i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 4.27521e8i | − 0.992934i | −0.868056 | − | 0.496467i | \(-0.834630\pi\) | ||||
0.868056 | − | 0.496467i | \(-0.165370\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.36956e7 | 0.0764181 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.89625e7 | 0.108447 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.51066e8i | − 0.326827i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3.57286e8i | − 0.755151i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.02088e8 | 0.623855 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.41530e8 | 1.09288 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.51344e8i | 0.495775i | 0.968789 | + | 0.247888i | \(0.0797363\pi\) | ||||
−0.968789 | + | 0.247888i | \(0.920264\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 8.16441e8i | − 1.57424i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.95523e8 | −1.68817 | −0.844083 | − | 0.536212i | \(-0.819855\pi\) | ||||
−0.844083 | + | 0.536212i | \(0.819855\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.23000e8 | 0.964043 | 0.482021 | − | 0.876159i | \(-0.339903\pi\) | ||||
0.482021 | + | 0.876159i | \(0.339903\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1.83296e8i | − 0.330419i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.06111e8i | 1.24499i | 0.782624 | + | 0.622495i | \(0.213881\pi\) | ||||
−0.782624 | + | 0.622495i | \(0.786119\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.88904e8 | −0.670772 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.27319e8 | 0.214846 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.13665e9i | − 1.87680i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 6.53981e7i | − 0.105675i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.69840e8 | −0.901230 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.29653e8 | −0.355539 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.98152e8i | 0.300331i | 0.988661 | + | 0.150166i | \(0.0479807\pi\) | ||||
−0.988661 | + | 0.150166i | \(0.952019\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.89891e8i | 0.727018i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.36056e8 | −0.343050 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.39645e8 | −0.341086 | −0.170543 | − | 0.985350i | \(-0.554552\pi\) | ||||
−0.170543 | + | 0.985350i | \(0.554552\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.09284e9i | − 1.52355i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 8.63209e7i | − 0.117890i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.27694e8 | −0.973686 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.07768e9 | −1.41293 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.75125e8i | 0.353490i | 0.984257 | + | 0.176745i | \(0.0565568\pi\) | ||||
−0.984257 | + | 0.176745i | \(0.943443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.32765e9i | − 1.67184i | −0.548854 | − | 0.835918i | \(-0.684936\pi\) | ||||
0.548854 | − | 0.835918i | \(-0.315064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.49180e7 | 0.0677860 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.24065e9 | 1.50120 | 0.750598 | − | 0.660759i | \(-0.229765\pi\) | ||||
0.750598 | + | 0.660759i | \(0.229765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.86513e8i | 0.933054i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.64622e8i | 1.12207i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.28760e9 | 1.46876 | 0.734381 | − | 0.678737i | \(-0.237472\pi\) | ||||
0.734381 | + | 0.678737i | \(0.237472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.43889e8 | −0.720338 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.05790e9i | 1.16084i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.17588e8i | − 0.126572i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.96596e8 | 0.524412 | 0.262206 | − | 0.965012i | \(-0.415550\pi\) | ||||
0.262206 | + | 0.965012i | \(0.415550\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.22570e9 | −1.26996 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3.87713e8i | − 0.394187i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5.27113e8i | − 0.525923i | −0.964806 | − | 0.262962i | \(-0.915301\pi\) | ||||
0.964806 | − | 0.262962i | \(-0.0846993\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.45396e9 | −1.42378 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.36208e8 | −0.419275 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.16631e9i | 1.10047i | 0.835011 | + | 0.550233i | \(0.185461\pi\) | ||||
−0.835011 | + | 0.550233i | \(0.814539\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.37253e9i | 2.19773i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.29099e8 | −0.754068 | −0.377034 | − | 0.926199i | \(-0.623056\pi\) | ||||
−0.377034 | + | 0.926199i | \(0.623056\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.71409e8 | 0.153081 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.12902e9i | 0.990177i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.52571e9i | 1.31416i | 0.753820 | + | 0.657081i | \(0.228209\pi\) | ||||
−0.753820 | + | 0.657081i | \(0.771791\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.47148e9 | 2.09092 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.28802e9 | −1.07040 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 3.90822e8i | − 0.319072i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.58821e7i | − 0.0368024i | −0.999831 | − | 0.0184012i | \(-0.994142\pi\) | ||||
0.999831 | − | 0.0184012i | \(-0.00585762\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.30503e9 | 1.02852 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.83043e8 | 0.296648 | 0.148324 | − | 0.988939i | \(-0.452612\pi\) | ||||
0.148324 | + | 0.988939i | \(0.452612\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9.68204e7i | − 0.0736884i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.14171e9i | − 0.854012i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.58121e8 | −0.336822 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.39912e9 | 1.01117 | 0.505585 | − | 0.862777i | \(-0.331277\pi\) | ||||
0.505585 | + | 0.862777i | \(0.331277\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.23689e9i | − 0.878786i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 8.87226e7i | − 0.0619740i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.87205e8 | −0.678014 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.57284e9 | −2.41289 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.40633e9i | 0.933984i | 0.884261 | + | 0.466992i | \(0.154662\pi\) | ||||
−0.884261 | + | 0.466992i | \(0.845338\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.69826e9i | 1.76237i | 0.472772 | + | 0.881185i | \(0.343253\pi\) | ||||
−0.472772 | + | 0.881185i | \(0.656747\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.25700e8 | 0.466193 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.06993e9 | 0.676072 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.42588e9i | − 0.886310i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1.74234e8i | − 0.106545i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.53153e9 | 0.921415 | 0.460707 | − | 0.887552i | \(-0.347596\pi\) | ||||
0.460707 | + | 0.887552i | \(0.347596\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.09800e9 | −0.649975 | −0.324987 | − | 0.945718i | \(-0.605360\pi\) | ||||
−0.324987 | + | 0.945718i | \(0.605360\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.11182e9i | 1.81260i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.34364e9i | − 1.91661i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.20920e9 | 1.24626 | 0.623132 | − | 0.782117i | \(-0.285860\pi\) | ||||
0.623132 | + | 0.782117i | \(0.285860\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.08436e8 | 0.504381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.92969e8i | 0.488004i | 0.969775 | + | 0.244002i | \(0.0784604\pi\) | ||||
−0.969775 | + | 0.244002i | \(0.921540\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 9.31120e8i | − 0.500894i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.49458e9 | 1.85063 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.50310e9 | 1.30502 | 0.652509 | − | 0.757781i | \(-0.273717\pi\) | ||||
0.652509 | + | 0.757781i | \(0.273717\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1.14621e9i | − 0.588363i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.55589e9i | 1.79723i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.92258e8 | 0.0956851 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.69849e9 | 1.81267 | 0.906333 | − | 0.422563i | \(-0.138870\pi\) | ||||
0.906333 | + | 0.422563i | \(0.138870\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.98471e8i | 0.433670i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1.58606e9i | − 0.753990i | −0.926215 | − | 0.376995i | \(-0.876957\pi\) | ||||
0.926215 | − | 0.376995i | \(-0.123043\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.21797e9 | −0.570298 | −0.285149 | − | 0.958483i | \(-0.592043\pi\) | ||||
−0.285149 | + | 0.958483i | \(0.592043\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.90698e8 | −0.318568 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.27823e9i | 0.580766i | 0.956911 | + | 0.290383i | \(0.0937826\pi\) | ||||
−0.956911 | + | 0.290383i | \(0.906217\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.21549e8i | 0.278209i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.32508e9 | 0.584343 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.05580e9 | −0.458741 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.44749e9i | − 0.619710i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.22517e9i | 0.516870i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.51593e9 | −1.04598 | −0.522991 | − | 0.852338i | \(-0.675184\pi\) | ||||
−0.522991 | + | 0.852338i | \(0.675184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.13845e8 | −0.210535 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.83759e9i | 1.14587i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 8.49147e8i | − 0.337977i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.49252e9 | 1.37021 | 0.685106 | − | 0.728443i | \(-0.259756\pi\) | ||||
0.685106 | + | 0.728443i | \(0.259756\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.43472e9 | −0.554864 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.34800e9i | 1.65769i | 0.559475 | + | 0.828847i | \(0.311003\pi\) | ||||
−0.559475 | + | 0.828847i | \(0.688997\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 7.13646e9i | − 2.68237i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.41649e8 | −0.200724 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.07094e9 | 0.756693 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.73130e9i | 0.623763i | 0.950121 | + | 0.311882i | \(0.100959\pi\) | ||||
−0.950121 | + | 0.311882i | \(0.899041\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 4.24519e9i | − 1.50822i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.79236e9 | 0.627967 | 0.313984 | − | 0.949428i | \(-0.398336\pi\) | ||||
0.313984 | + | 0.949428i | \(0.398336\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.85030e8 | 0.340353 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.71120e9i | 1.26470i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.51265e9i | − 0.508423i | −0.967149 | − | 0.254211i | \(-0.918184\pi\) | ||||
0.967149 | − | 0.254211i | \(-0.0818159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.09617e8 | −0.102648 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.21553e9 | 0.397517 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2.66220e9i | − 0.858847i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.78638e8i | 0.215984i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.53036e8 | 0.267844 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.48250e8 | 0.107884 | 0.0539422 | − | 0.998544i | \(-0.482821\pi\) | ||||
0.0539422 | + | 0.998544i | \(0.482821\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.73487e9i | − 0.835950i | −0.908458 | − | 0.417975i | \(-0.862740\pi\) | ||||
0.908458 | − | 0.417975i | \(-0.137260\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.22842e9i | 0.370501i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.58400e9 | 0.471432 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.86542e9 | 1.13528 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.80362e8i | 0.0812622i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.28563e9i | − 0.367764i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.15156e8 | 0.117212 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.12519e8 | 0.0592225 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.49523e8i | 0.233676i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.93847e9i | 0.797866i | 0.916980 | + | 0.398933i | \(0.130619\pi\) | ||||
−0.916980 | + | 0.398933i | \(0.869381\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.14240e9 | 1.11033 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.85810e9 | −0.491679 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.18061e9i | 1.35340i | 0.736260 | + | 0.676699i | \(0.236590\pi\) | ||||
−0.736260 | + | 0.676699i | \(0.763410\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.50576e9i | 1.16216i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.65483e9 | −2.45875 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.02906e9 | −0.258763 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.66566e9i | 0.910180i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.69427e9i | 0.660615i | 0.943873 | + | 0.330307i | \(0.107152\pi\) | ||||
−0.943873 | + | 0.330307i | \(0.892848\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.18422e9 | −0.286742 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.85051e9 | 0.681636 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 5.45741e9i | − 1.28886i | −0.764661 | − | 0.644432i | \(-0.777094\pi\) | ||||
0.764661 | − | 0.644432i | \(-0.222906\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 3.56347e9i | − 0.831195i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.00620e9 | −0.692590 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.17326e9 | −0.722125 | −0.361063 | − | 0.932542i | \(-0.617586\pi\) | ||||
−0.361063 | + | 0.932542i | \(0.617586\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 2.68017e8i | − 0.0602471i | −0.999546 | − | 0.0301236i | \(-0.990410\pi\) | ||||
0.999546 | − | 0.0301236i | \(-0.00959007\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.05555e10i | 2.34388i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.14736e9 | 0.690413 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.47388e9 | −1.83640 | −0.918199 | − | 0.396119i | \(-0.870357\pi\) | ||||
−0.918199 | + | 0.396119i | \(0.870357\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1.10584e10i | − 2.36764i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.59937e9i | 0.549859i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.14571e9 | −0.239462 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.07532e8 | −0.125465 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 8.85508e9i | − 1.80700i | −0.428584 | − | 0.903502i | \(-0.640987\pi\) | ||||
0.428584 | − | 0.903502i | \(-0.359013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 2.14298e9i | − 0.432131i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.65586e8 | −0.0927777 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.89886e9 | −0.767796 | −0.383898 | − | 0.923375i | \(-0.625419\pi\) | ||||
−0.383898 | + | 0.923375i | \(0.625419\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.14538e9i | 0.612159i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.01744e10i | − 1.95704i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.95793e9 | 0.372224 | 0.186112 | − | 0.982529i | \(-0.440411\pi\) | ||||
0.186112 | + | 0.982529i | \(0.440411\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.25172e8 | 0.0798920 | 0.0399460 | − | 0.999202i | \(-0.487281\pi\) | ||||
0.0399460 | + | 0.999202i | \(0.487281\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.96409e9i | − 0.364796i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.44955e9i | 0.633313i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.98918e9 | 0.905459 | 0.452729 | − | 0.891648i | \(-0.350450\pi\) | ||||
0.452729 | + | 0.891648i | \(0.350450\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.19361e9 | 1.46999 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.61183e8i | 0.135004i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.35346e9i | 1.64006i | 0.572318 | + | 0.820032i | \(0.306044\pi\) | ||||
−0.572318 | + | 0.820032i | \(0.693956\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.17140e9 | −1.58991 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.29392e9 | −0.735963 | −0.367982 | − | 0.929833i | \(-0.619951\pi\) | ||||
−0.367982 | + | 0.929833i | \(0.619951\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.13759e9i | 0.362249i | 0.983460 | + | 0.181124i | \(0.0579737\pi\) | ||||
−0.983460 | + | 0.181124i | \(0.942026\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.64300e9i | 0.442870i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.45170e9 | −0.406217 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.85721e9 | −0.304286 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 3.85642e9i | − 0.624811i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 8.40662e9i | − 1.34693i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.18683e10 | 1.88056 | 0.940279 | − | 0.340405i | \(-0.110564\pi\) | ||||
0.940279 | + | 0.340405i | \(0.110564\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.32316e10 | −2.07347 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.73620e9i | 1.19900i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.52854e8i | 0.146062i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.54413e9 | −0.992199 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.07897e9 | 0.461746 | 0.230873 | − | 0.972984i | \(-0.425842\pi\) | ||||
0.230873 | + | 0.972984i | \(0.425842\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.68440e9i | − 0.249866i | −0.992165 | − | 0.124933i | \(-0.960128\pi\) | ||||
0.992165 | − | 0.124933i | \(-0.0398716\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.44800e9i | 1.23964i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.22431e10 | −1.77717 | −0.888583 | − | 0.458717i | \(-0.848309\pi\) | ||||
−0.888583 | + | 0.458717i | \(0.848309\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.62180e8 | −0.0376481 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.81865e9i | 0.258354i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.42587e8i | 0.118418i | 0.998246 | + | 0.0592092i | \(0.0188579\pi\) | ||||
−0.998246 | + | 0.0592092i | \(0.981142\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.19989e9 | −0.583974 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.78384e8 | 0.134595 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.45717e10i | − 1.98341i | −0.128537 | − | 0.991705i | \(-0.541028\pi\) | ||||
0.128537 | − | 0.991705i | \(-0.458972\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.88432e9i | 0.523130i | 0.965186 | + | 0.261565i | \(0.0842386\pi\) | ||||
−0.965186 | + | 0.261565i | \(0.915761\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.19723e9 | 0.426066 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.25535e9 | 0.561125 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.09930e10i | − 2.73927i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.51051e10i | − 1.95044i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.21356e9 | −0.538418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.67232e9 | −0.211479 | −0.105739 | − | 0.994394i | \(-0.533721\pi\) | ||||
−0.105739 | + | 0.994394i | \(0.533721\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.14418e9i | 0.143196i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.25476e8i | 0.0279280i | 0.999902 | + | 0.0139640i | \(0.00444503\pi\) | ||||
−0.999902 | + | 0.0139640i | \(0.995555\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.23586e9 | −0.274094 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.02007e9 | −0.123770 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.61244e8i | 0.0553934i | 0.999616 | + | 0.0276967i | \(0.00881727\pi\) | ||||
−0.999616 | + | 0.0276967i | \(0.991183\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 4.03316e9i | − 0.479434i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.43459e10 | −1.68803 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.28507e9 | −0.149679 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.53967e9i | 0.408122i | 0.978958 | + | 0.204061i | \(0.0654141\pi\) | ||||
−0.978958 | + | 0.204061i | \(0.934586\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.42619e9i | 0.162784i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.16501e10 | −1.31639 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.10331e10 | 2.35282 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.93204e9i | 0.656952i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.06039e8i | 0.0774134i | 0.999251 | + | 0.0387067i | \(0.0123238\pi\) | ||||
−0.999251 | + | 0.0387067i | \(0.987676\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.13732e10 | −1.23464 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.43013e9 | 0.583644 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.59364e9i | − 0.276021i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.28048e9i | − 0.134931i | −0.997722 | − | 0.0674655i | \(-0.978509\pi\) | ||||
0.997722 | − | 0.0674655i | \(-0.0214912\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.25181e9 | 0.339298 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.65960e9 | 0.481432 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 5.68133e8i | − 0.0581271i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.15702e10i | − 1.17226i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.73237e9 | 0.173816 | 0.0869079 | − | 0.996216i | \(-0.472301\pi\) | ||||
0.0869079 | + | 0.996216i | \(0.472301\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.00975e9 | −0.696512 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6.55274e6i | 0 0.000644821i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 9.08808e9i | − 0.885705i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.24560e9 | −0.313274 | −0.156637 | − | 0.987656i | \(-0.550065\pi\) | ||||
−0.156637 | + | 0.987656i | \(0.550065\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.27898e9 | 0.504665 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.93741e10i | − 1.83447i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.80499e9i | 0.731996i | 0.930616 | + | 0.365998i | \(0.119272\pi\) | ||||
−0.930616 | + | 0.365998i | \(0.880728\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.79747e9 | 0.631454 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.83671e9 | 0.169007 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.03879e10i | 1.85831i | 0.369694 | + | 0.929154i | \(0.379463\pi\) | ||||
−0.369694 | + | 0.929154i | \(0.620537\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 4.32550e9i | − 0.390546i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.44304e9 | 0.576275 | 0.288137 | − | 0.957589i | \(-0.406964\pi\) | ||||
0.288137 | + | 0.957589i | \(0.406964\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.13949e10 | 1.00964 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 8.21397e9i | − 0.720993i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1.09313e9i | − 0.0950573i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.02921e8 | 0.0347120 | 0.0173560 | − | 0.999849i | \(-0.494475\pi\) | ||||
0.0173560 | + | 0.999849i | \(0.494475\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.26817e9 | −0.193595 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.15948e10i | 0.980505i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.77299e9i | 0.316119i | 0.987430 | + | 0.158059i | \(0.0505237\pi\) | ||||
−0.987430 | + | 0.158059i | \(0.949476\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.38523e9 | 0.696095 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.52431e9 | −0.207633 | −0.103817 | − | 0.994596i | \(-0.533106\pi\) | ||||
−0.103817 | + | 0.994596i | \(0.533106\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.89249e9i | 0.398744i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 9.93936e9i | − 0.802682i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.94070e8 | −0.0235325 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.59413e9 | −0.443599 | −0.221799 | − | 0.975092i | \(-0.571193\pi\) | ||||
−0.221799 | + | 0.975092i | \(0.571193\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1.75595e10i | − 1.37982i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.30520e9i | 0.724599i | 0.932062 | + | 0.362299i | \(0.118008\pi\) | ||||
−0.932062 | + | 0.362299i | \(0.881992\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.01719e9 | 0.155665 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.65192e9 | 0.738142 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 2.84555e10i | − 2.15668i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 6.11974e9i | − 0.459678i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.63172e9 | 0.568141 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.32073e9 | 0.318797 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.70711e9i | 0.563612i | 0.959471 | + | 0.281806i | \(0.0909334\pi\) | ||||
−0.959471 | + | 0.281806i | \(0.909067\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1.48776e10i | − 1.07836i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.38282e9 | −0.674087 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.72607e9 | −0.336546 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.16745e9i | 0.647088i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.88557e10i | 1.31928i | 0.751581 | + | 0.659641i | \(0.229292\pi\) | ||||
−0.751581 | + | 0.659641i | \(0.770708\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.24531e10 | −0.863704 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.74732e9 | 0.532645 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.14934e8i | 0.0623570i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.25264e9i | 0.625144i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.22819e10 | 1.49243 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.30677e9 | −0.485183 | −0.242591 | − | 0.970129i | \(-0.577997\pi\) | ||||
−0.242591 | + | 0.970129i | \(0.577997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.71333e10i | 1.12789i | 0.825812 | + | 0.563945i | \(0.190717\pi\) | ||||
−0.825812 | + | 0.563945i | \(0.809283\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 9.88588e9i | − 0.645206i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.67826e9 | −0.302714 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.62111e10 | −1.68154 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.59967e9i | 0.101750i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.36575e10i | 0.861331i | 0.902512 | + | 0.430666i | \(0.141721\pi\) | ||||
−0.902512 | + | 0.430666i | \(0.858279\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.25803e9 | 0.453858 | 0.226929 | − | 0.973911i | \(-0.427132\pi\) | ||||
0.226929 | + | 0.973911i | \(0.427132\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.63005e9 | 0.225073 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.25663e10i | 1.38736i | 0.720281 | + | 0.693682i | \(0.244013\pi\) | ||||
−0.720281 | + | 0.693682i | \(0.755987\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1.61901e10i | − 0.986979i | −0.869752 | − | 0.493490i | \(-0.835721\pi\) | ||||
0.869752 | − | 0.493490i | \(-0.164279\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.56021e10 | 1.54765 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.55889e10 | −0.934454 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1.38425e10i | − 0.822831i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.69393e9i | 0.0998520i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.41622e9 | 0.491983 | 0.245992 | − | 0.969272i | \(-0.420886\pi\) | ||||
0.245992 | + | 0.969272i | \(0.420886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.33680e10 | −2.51410 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.89923e10i | 1.09190i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.21013e10i | 0.689974i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.08287e9 | 0.513607 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.63183e10 | 1.47598 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 2.47294e10i | − 1.37550i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.31544e10i | 0.725687i | 0.931850 | + | 0.362844i | \(0.118194\pi\) | ||||
−0.931850 | + | 0.362844i | \(0.881806\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.34469e10 | −0.735765 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.19572e10 | −1.73435 | −0.867174 | − | 0.498006i | \(-0.834066\pi\) | ||||
−0.867174 | + | 0.498006i | \(0.834066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.50626e9i | 0.0810821i | 0.999178 | + | 0.0405410i | \(0.0129082\pi\) | ||||
−0.999178 | + | 0.0405410i | \(0.987092\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.41489e10i | 1.28939i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.34154e10 | −0.710504 | −0.355252 | − | 0.934771i | \(-0.615605\pi\) | ||||
−0.355252 | + | 0.934771i | \(0.615605\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.78153e9 | 0.146126 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.67604e10i | 1.39452i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.04092e9i | 0.157194i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.06012e9 | 0.105640 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.06527e9 | 0.359401 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.24833e10i | 0.629944i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.79535e10i | 0.898775i | 0.893337 | + | 0.449387i | \(0.148358\pi\) | ||||
−0.893337 | + | 0.449387i | \(0.851642\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.66168e10 | 1.32189 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.94700e9 | 0.391550 | 0.195775 | − | 0.980649i | \(-0.437278\pi\) | ||||
0.195775 | + | 0.980649i | \(0.437278\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.90736e10i | 0.932329i | 0.884698 | + | 0.466165i | \(0.154365\pi\) | ||||
−0.884698 | + | 0.466165i | \(0.845635\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.09784e9i | 0.101735i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.73840e10 | −0.836406 | −0.418203 | − | 0.908354i | \(-0.637340\pi\) | ||||
−0.418203 | + | 0.908354i | \(0.637340\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.03699e10 | 0.972372 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.88347e9i | 0.420737i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.68477e10i | 0.791700i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.92968e8 | 0.0323097 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.40516e9 | 0.435104 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.34547e10i | − 0.617612i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2.10241e10i | − 0.957591i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.22441e10 | 1.00533 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.35073e10 | 0.605757 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.37564e10i | 0.612180i | 0.952003 | + | 0.306090i | \(0.0990208\pi\) | ||||
−0.952003 | + | 0.306090i | \(0.900979\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.19587e9i | 0.361928i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.97126e9 | 0.305490 | 0.152745 | − | 0.988266i | \(-0.451189\pi\) | ||||
0.152745 | + | 0.988266i | \(0.451189\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.68128e9 | 0.334030 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.37148e10i | 1.45495i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.10586e10i | 0.473594i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.22655e9 | −0.179631 | −0.0898156 | − | 0.995958i | \(-0.528628\pi\) | ||||
−0.0898156 | + | 0.995958i | \(0.528628\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.56483e10 | −0.660023 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 6.86410e9i | − 0.287328i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1.07056e10i | − 0.444749i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.21507e10 | 0.913289 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.34132e9 | −0.0548881 | −0.0274441 | − | 0.999623i | \(-0.508737\pi\) | ||||
−0.0274441 | + | 0.999623i | \(0.508737\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.10901e10i | 0.856552i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 5.57539e10i | − 2.24745i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.29478e9 | 0.371876 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.84420e10 | −0.732353 | −0.366176 | − | 0.930545i | \(-0.619333\pi\) | ||||
−0.366176 | + | 0.930545i | \(0.619333\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.25612e10i | 1.28343i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.73596e10i | 1.07040i | 0.844725 | + | 0.535201i | \(0.179764\pi\) | ||||
−0.844725 | + | 0.535201i | \(0.820236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.18723e10 | 2.40273 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.36367e9 | −0.129659 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 9.65273e9i | − 0.369339i | −0.982801 | − | 0.184670i | \(-0.940879\pi\) | ||||
0.982801 | − | 0.184670i | \(-0.0591215\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.02622e9i | 0.0389771i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.39614e10 | −1.65745 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.34107e10 | −0.876170 | −0.438085 | − | 0.898934i | \(-0.644343\pi\) | ||||
−0.438085 | + | 0.898934i | \(0.644343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.44187e10i | 1.27874i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.42126e10i | − 0.892995i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.06196e10 | −0.388814 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.45262e10 | −0.891453 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.45427e9i | 0.124642i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 3.60585e10i | − 1.29170i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.12588e10 | 1.46732 | 0.733658 | − | 0.679519i | \(-0.237812\pi\) | ||||
0.733658 | + | 0.679519i | \(0.237812\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.07661e10 | 2.49857 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 2.00506e10i | − 0.702846i | −0.936217 | − | 0.351423i | \(-0.885698\pi\) | ||||
0.936217 | − | 0.351423i | \(-0.114302\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.06755e10i | 1.06757i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.07159e9 | 0.140685 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.24784e10 | 0.428084 | 0.214042 | − | 0.976824i | \(-0.431337\pi\) | ||||
0.214042 | + | 0.976824i | \(0.431337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.24490e9i | 0.246770i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.54602e10i | − 0.522846i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.76481e9 | −0.260732 | −0.130366 | − | 0.991466i | \(-0.541615\pi\) | ||||
−0.130366 | + | 0.991466i | \(0.541615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.51816e9 | −0.0506162 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.42979e10i | − 0.473327i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 5.69921e10i | − 1.87339i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.53111e9 | 0.213171 | 0.106586 | − | 0.994304i | \(-0.466008\pi\) | ||||
0.106586 | + | 0.994304i | \(0.466008\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.23366e10 | −0.399829 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 3.31762e10i | − 1.06769i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.43782e10i | 1.41820i | 0.705110 | + | 0.709098i | \(0.250898\pi\) | ||||
−0.705110 | + | 0.709098i | \(0.749102\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.99002e9 | 0.285287 |
(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 | 256.8.b.l.129.6 | 6 | ||
4.3 | odd | 2 | 256.8.b.k.129.1 | 6 | |||
8.3 | odd | 2 | 256.8.b.k.129.6 | 6 | |||
8.5 | even | 2 | inner | 256.8.b.l.129.1 | 6 | ||
16.3 | odd | 4 | 128.8.a.c.1.3 | yes | 3 | ||
16.5 | even | 4 | 128.8.a.d.1.3 | yes | 3 | ||
16.11 | odd | 4 | 128.8.a.b.1.1 | yes | 3 | ||
16.13 | even | 4 | 128.8.a.a.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.8.a.a.1.1 | ✓ | 3 | 16.13 | even | 4 | ||
128.8.a.b.1.1 | yes | 3 | 16.11 | odd | 4 | ||
128.8.a.c.1.3 | yes | 3 | 16.3 | odd | 4 | ||
128.8.a.d.1.3 | yes | 3 | 16.5 | even | 4 | ||
256.8.b.k.129.1 | 6 | 4.3 | odd | 2 | |||
256.8.b.k.129.6 | 6 | 8.3 | odd | 2 | |||
256.8.b.l.129.1 | 6 | 8.5 | even | 2 | inner | ||
256.8.b.l.129.6 | 6 | 1.1 | even | 1 | trivial |