Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,5,Mod(197,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.197");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(91.1723074400\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-29})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 28x^{2} + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.3 | ||
Root | \(-3.80789 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.197 |
Dual form | 882.5.b.b.197.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | − 21.5407i | − 0.861626i | −0.902441 | − | 0.430813i | \(-0.858227\pi\) | ||||
0.902441 | − | 0.430813i | \(-0.141773\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 22.6274i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 60.9262 | 0.609262 | ||||||||
\(11\) | 57.9828i | 0.479196i | 0.970872 | + | 0.239598i | \(0.0770157\pi\) | ||||
−0.970872 | + | 0.239598i | \(0.922984\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 304.631 | 1.80255 | 0.901275 | − | 0.433248i | \(-0.142632\pi\) | ||||
0.901275 | + | 0.433248i | \(0.142632\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 323.110i | 1.11803i | 0.829158 | + | 0.559014i | \(0.188820\pi\) | ||||
−0.829158 | + | 0.559014i | \(0.811180\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −152.315 | −0.421926 | −0.210963 | − | 0.977494i | \(-0.567660\pi\) | ||||
−0.210963 | + | 0.977494i | \(0.567660\pi\) | |||||||
\(20\) | 172.325i | 0.430813i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −164.000 | −0.338843 | ||||||||
\(23\) | − 538.815i | − 1.01855i | −0.860602 | − | 0.509277i | \(-0.829913\pi\) | ||||
0.860602 | − | 0.509277i | \(-0.170087\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 161.000 | 0.257600 | ||||||||
\(26\) | 861.626i | 1.27460i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 83.4386i | 0.0992136i | 0.998769 | + | 0.0496068i | \(0.0157968\pi\) | ||||
−0.998769 | + | 0.0496068i | \(0.984203\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −761.577 | −0.792484 | −0.396242 | − | 0.918146i | \(-0.629686\pi\) | ||||
−0.396242 | + | 0.918146i | \(0.629686\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −913.893 | −0.790565 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −600.000 | −0.438276 | −0.219138 | − | 0.975694i | \(-0.570325\pi\) | ||||
−0.219138 | + | 0.975694i | \(0.570325\pi\) | |||||||
\(38\) | − 430.813i | − 0.298347i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −487.409 | −0.304631 | ||||||||
\(41\) | − 1615.55i | − 0.961065i | −0.876977 | − | 0.480532i | \(-0.840443\pi\) | ||||
0.876977 | − | 0.480532i | \(-0.159557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1160.00 | −0.627366 | −0.313683 | − | 0.949528i | \(-0.601563\pi\) | ||||
−0.313683 | + | 0.949528i | \(0.601563\pi\) | |||||||
\(44\) | − 463.862i | − 0.239598i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1524.00 | 0.720227 | ||||||||
\(47\) | 1077.03i | 0.487566i | 0.969830 | + | 0.243783i | \(0.0783884\pi\) | ||||
−0.969830 | + | 0.243783i | \(0.921612\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 455.377i | 0.182151i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2437.05 | −0.901275 | ||||||||
\(53\) | − 1104.50i | − 0.393201i | −0.980484 | − | 0.196600i | \(-0.937010\pi\) | ||||
0.980484 | − | 0.196600i | \(-0.0629902\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1248.99 | 0.412888 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −236.000 | −0.0701546 | ||||||||
\(59\) | 3661.91i | 1.05197i | 0.850493 | + | 0.525986i | \(0.176303\pi\) | ||||
−0.850493 | + | 0.525986i | \(0.823697\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2589.36 | −0.695878 | −0.347939 | − | 0.937517i | \(-0.613118\pi\) | ||||
−0.347939 | + | 0.937517i | \(0.613118\pi\) | |||||||
\(62\) | − 2154.07i | − 0.560371i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − 6561.95i | − 1.55312i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8278.00 | 1.84406 | 0.922032 | − | 0.387115i | \(-0.126528\pi\) | ||||
0.922032 | + | 0.387115i | \(0.126528\pi\) | |||||||
\(68\) | − 2584.88i | − 0.559014i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1839.89i | 0.364985i | 0.983207 | + | 0.182493i | \(0.0584166\pi\) | ||||
−0.983207 | + | 0.182493i | \(0.941583\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9291.24 | 1.74352 | 0.871762 | − | 0.489929i | \(-0.162977\pi\) | ||||
0.871762 | + | 0.489929i | \(0.162977\pi\) | |||||||
\(74\) | − 1697.06i | − 0.309908i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1218.52 | 0.210963 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3082.00 | 0.493831 | 0.246916 | − | 0.969037i | \(-0.420583\pi\) | ||||
0.246916 | + | 0.969037i | \(0.420583\pi\) | |||||||
\(80\) | − 1378.60i | − 0.215407i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4569.46 | 0.679575 | ||||||||
\(83\) | 13570.6i | 1.96990i | 0.172850 | + | 0.984948i | \(0.444702\pi\) | ||||
−0.172850 | + | 0.984948i | \(0.555298\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6960.00 | 0.963322 | ||||||||
\(86\) | − 3280.98i | − 0.443615i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1312.00 | 0.169421 | ||||||||
\(89\) | − 2046.36i | − 0.258347i | −0.991622 | − | 0.129173i | \(-0.958768\pi\) | ||||
0.991622 | − | 0.129173i | \(-0.0412323\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4310.52i | 0.509277i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3046.31 | −0.344761 | ||||||||
\(95\) | 3280.98i | 0.363543i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −761.577 | −0.0809414 | −0.0404707 | − | 0.999181i | \(-0.512886\pi\) | ||||
−0.0404707 | + | 0.999181i | \(0.512886\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1288.00 | −0.128800 | ||||||||
\(101\) | − 12816.7i | − 1.25642i | −0.778046 | − | 0.628208i | \(-0.783789\pi\) | ||||
0.778046 | − | 0.628208i | \(-0.216211\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5331.04 | 0.502502 | 0.251251 | − | 0.967922i | \(-0.419158\pi\) | ||||
0.251251 | + | 0.967922i | \(0.419158\pi\) | |||||||
\(104\) | − 6893.01i | − 0.637298i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3124.00 | 0.278035 | ||||||||
\(107\) | − 15611.5i | − 1.36357i | −0.731553 | − | 0.681785i | \(-0.761204\pi\) | ||||
0.731553 | − | 0.681785i | \(-0.238796\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17080.0 | 1.43759 | 0.718795 | − | 0.695222i | \(-0.244694\pi\) | ||||
0.718795 | + | 0.695222i | \(0.244694\pi\) | |||||||
\(110\) | 3532.67i | 0.291956i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18949.0i | 1.48399i | 0.670406 | + | 0.741994i | \(0.266120\pi\) | ||||
−0.670406 | + | 0.741994i | \(0.733880\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11606.4 | −0.877613 | ||||||||
\(116\) | − 667.509i | − 0.0496068i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10357.5 | −0.743856 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11279.0 | 0.770371 | ||||||||
\(122\) | − 7323.82i | − 0.492060i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6092.62 | 0.396242 | ||||||||
\(125\) | − 16931.0i | − 1.08358i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19958.0 | 1.23740 | 0.618699 | − | 0.785628i | \(-0.287660\pi\) | ||||
0.618699 | + | 0.785628i | \(0.287660\pi\) | |||||||
\(128\) | − 1448.15i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 18560.0 | 1.09822 | ||||||||
\(131\) | − 21971.5i | − 1.28031i | −0.768244 | − | 0.640157i | \(-0.778869\pi\) | ||||
0.768244 | − | 0.640157i | \(-0.221131\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 23413.7i | 1.30395i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7311.14 | 0.395282 | ||||||||
\(137\) | 11368.9i | 0.605726i | 0.953034 | + | 0.302863i | \(0.0979424\pi\) | ||||
−0.953034 | + | 0.302863i | \(0.902058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3655.57 | 0.189202 | 0.0946010 | − | 0.995515i | \(-0.469842\pi\) | ||||
0.0946010 | + | 0.995515i | \(0.469842\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5204.00 | −0.258084 | ||||||||
\(143\) | 17663.3i | 0.863775i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1797.32 | 0.0854850 | ||||||||
\(146\) | 26279.6i | 1.23286i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4800.00 | 0.219138 | ||||||||
\(149\) | − 13773.0i | − 0.620379i | −0.950675 | − | 0.310189i | \(-0.899608\pi\) | ||||
0.950675 | − | 0.310189i | \(-0.100392\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 29200.0 | 1.28065 | 0.640323 | − | 0.768106i | \(-0.278801\pi\) | ||||
0.640323 | + | 0.768106i | \(0.278801\pi\) | |||||||
\(152\) | 3446.51i | 0.149174i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16404.9i | 0.682825i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22695.0 | 0.920727 | 0.460364 | − | 0.887730i | \(-0.347719\pi\) | ||||
0.460364 | + | 0.887730i | \(0.347719\pi\) | |||||||
\(158\) | 8717.21i | 0.349191i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3899.28 | 0.152315 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23562.0 | −0.886823 | −0.443411 | − | 0.896318i | \(-0.646232\pi\) | ||||
−0.443411 | + | 0.896318i | \(0.646232\pi\) | |||||||
\(164\) | 12924.4i | 0.480532i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −38383.5 | −1.39293 | ||||||||
\(167\) | − 6246.79i | − 0.223988i | −0.993709 | − | 0.111994i | \(-0.964276\pi\) | ||||
0.993709 | − | 0.111994i | \(-0.0357237\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 64239.0 | 2.24919 | ||||||||
\(170\) | 19685.9i | 0.681171i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9280.00 | 0.313683 | ||||||||
\(173\) | 42542.8i | 1.42146i | 0.703466 | + | 0.710729i | \(0.251635\pi\) | ||||
−0.703466 | + | 0.710729i | \(0.748365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3710.90i | 0.119799i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5787.99 | 0.182679 | ||||||||
\(179\) | 46613.9i | 1.45482i | 0.686203 | + | 0.727410i | \(0.259276\pi\) | ||||
−0.686203 | + | 0.727410i | \(0.740724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6092.62 | 0.185972 | 0.0929858 | − | 0.995667i | \(-0.470359\pi\) | ||||
0.0929858 | + | 0.995667i | \(0.470359\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12192.0 | −0.360113 | ||||||||
\(185\) | 12924.4i | 0.377630i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18734.8 | −0.535755 | ||||||||
\(188\) | − 8616.26i | − 0.243783i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9280.00 | −0.257064 | ||||||||
\(191\) | − 45001.7i | − 1.23357i | −0.787134 | − | 0.616783i | \(-0.788436\pi\) | ||||
0.787134 | − | 0.616783i | \(-0.211564\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 54080.0 | 1.45185 | 0.725926 | − | 0.687773i | \(-0.241412\pi\) | ||||
0.725926 | + | 0.687773i | \(0.241412\pi\) | |||||||
\(194\) | − 2154.07i | − 0.0572342i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 16940.9i | − 0.436519i | −0.975891 | − | 0.218259i | \(-0.929962\pi\) | ||||
0.975891 | − | 0.218259i | \(-0.0700379\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −58793.8 | −1.48465 | −0.742327 | − | 0.670038i | \(-0.766278\pi\) | ||||
−0.742327 | + | 0.670038i | \(0.766278\pi\) | |||||||
\(200\) | − 3643.01i | − 0.0910754i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 36251.1 | 0.888420 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −34800.0 | −0.828079 | ||||||||
\(206\) | 15078.5i | 0.355322i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 19496.4 | 0.450637 | ||||||||
\(209\) | − 8831.67i | − 0.202186i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 65480.0 | 1.47077 | 0.735383 | − | 0.677651i | \(-0.237002\pi\) | ||||
0.735383 | + | 0.677651i | \(0.237002\pi\) | |||||||
\(212\) | 8836.01i | 0.196600i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 44156.0 | 0.964189 | ||||||||
\(215\) | 24987.2i | 0.540555i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 48309.5i | 1.01653i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9991.89 | −0.206444 | ||||||||
\(221\) | 98429.3i | 2.01530i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −49654.8 | −0.998509 | −0.499254 | − | 0.866455i | \(-0.666393\pi\) | ||||
−0.499254 | + | 0.866455i | \(0.666393\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −53596.0 | −1.04934 | ||||||||
\(227\) | − 68283.9i | − 1.32515i | −0.748994 | − | 0.662577i | \(-0.769463\pi\) | ||||
0.748994 | − | 0.662577i | \(-0.230537\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 49654.8 | 0.946871 | 0.473435 | − | 0.880829i | \(-0.343014\pi\) | ||||
0.473435 | + | 0.880829i | \(0.343014\pi\) | |||||||
\(230\) | − 32828.0i | − 0.620566i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1888.00 | 0.0350773 | ||||||||
\(233\) | 5488.56i | 0.101099i | 0.998722 | + | 0.0505495i | \(0.0160973\pi\) | ||||
−0.998722 | + | 0.0505495i | \(0.983903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23200.0 | 0.420100 | ||||||||
\(236\) | − 29295.3i | − 0.525986i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 38323.8i | − 0.670923i | −0.942054 | − | 0.335461i | \(-0.891108\pi\) | ||||
0.942054 | − | 0.335461i | \(-0.108892\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −53767.4 | −0.925731 | −0.462865 | − | 0.886429i | \(-0.653179\pi\) | ||||
−0.462865 | + | 0.886429i | \(0.653179\pi\) | |||||||
\(242\) | 31901.8i | 0.544734i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20714.9 | 0.347939 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −46400.0 | −0.760544 | ||||||||
\(248\) | 17232.5i | 0.280185i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 47888.0 | 0.766208 | ||||||||
\(251\) | 18525.0i | 0.294042i | 0.989133 | + | 0.147021i | \(0.0469686\pi\) | ||||
−0.989133 | + | 0.147021i | \(0.953031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31242.0 | 0.488088 | ||||||||
\(254\) | 56449.7i | 0.874973i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 10231.8i | 0.154912i | 0.996996 | + | 0.0774562i | \(0.0246798\pi\) | ||||
−0.996996 | + | 0.0774562i | \(0.975320\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 52495.6i | 0.776562i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 62144.7 | 0.905319 | ||||||||
\(263\) | 115823.i | 1.67449i | 0.546829 | + | 0.837244i | \(0.315835\pi\) | ||||
−0.546829 | + | 0.837244i | \(0.684165\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −23791.7 | −0.338792 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −66224.0 | −0.922032 | ||||||||
\(269\) | 38880.9i | 0.537318i | 0.963235 | + | 0.268659i | \(0.0865805\pi\) | ||||
−0.963235 | + | 0.268659i | \(0.913419\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −117131. | −1.59489 | −0.797447 | − | 0.603389i | \(-0.793817\pi\) | ||||
−0.797447 | + | 0.603389i | \(0.793817\pi\) | |||||||
\(272\) | 20679.0i | 0.279507i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −32156.0 | −0.428313 | ||||||||
\(275\) | 9335.22i | 0.123441i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2558.00 | −0.0333381 | −0.0166691 | − | 0.999861i | \(-0.505306\pi\) | ||||
−0.0166691 | + | 0.999861i | \(0.505306\pi\) | |||||||
\(278\) | 10339.5i | 0.133786i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 44857.4i | − 0.568096i | −0.958810 | − | 0.284048i | \(-0.908322\pi\) | ||||
0.958810 | − | 0.284048i | \(-0.0916775\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 152772. | 1.90753 | 0.953766 | − | 0.300549i | \(-0.0971698\pi\) | ||||
0.953766 | + | 0.300549i | \(0.0971698\pi\) | |||||||
\(284\) | − 14719.1i | − 0.182493i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −49959.5 | −0.610781 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20879.0 | −0.249985 | ||||||||
\(290\) | 5083.60i | 0.0604470i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −74329.9 | −0.871762 | ||||||||
\(293\) | 77223.3i | 0.899524i | 0.893148 | + | 0.449762i | \(0.148491\pi\) | ||||
−0.893148 | + | 0.449762i | \(0.851509\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 78880.0 | 0.906406 | ||||||||
\(296\) | 13576.5i | 0.154954i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 38956.0 | 0.438674 | ||||||||
\(299\) | − 164140.i | − 1.83600i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 82590.1i | 0.905553i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9748.19 | −0.105482 | ||||||||
\(305\) | 55776.6i | 0.599587i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 119872. | 1.27187 | 0.635934 | − | 0.771744i | \(-0.280615\pi\) | ||||
0.635934 | + | 0.771744i | \(0.280615\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −46400.0 | −0.482830 | ||||||||
\(311\) | − 82500.7i | − 0.852976i | −0.904493 | − | 0.426488i | \(-0.859751\pi\) | ||||
0.904493 | − | 0.426488i | \(-0.140249\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 170898. | 1.74441 | 0.872204 | − | 0.489142i | \(-0.162690\pi\) | ||||
0.872204 | + | 0.489142i | \(0.162690\pi\) | |||||||
\(314\) | 64191.2i | 0.651052i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24656.0 | −0.246916 | ||||||||
\(317\) | − 108472.i | − 1.07944i | −0.841845 | − | 0.539719i | \(-0.818531\pi\) | ||||
0.841845 | − | 0.539719i | \(-0.181469\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4838.00 | −0.0475428 | ||||||||
\(320\) | 11028.8i | 0.107703i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 49214.6i | − 0.471725i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 49045.6 | 0.464337 | ||||||||
\(326\) | − 66643.4i | − 0.627079i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −36555.7 | −0.339788 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 123320. | 1.12558 | 0.562792 | − | 0.826599i | \(-0.309727\pi\) | ||||
0.562792 | + | 0.826599i | \(0.309727\pi\) | |||||||
\(332\) | − 108565.i | − 0.984948i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17668.6 | 0.158383 | ||||||||
\(335\) | − 178314.i | − 1.58889i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 183920. | 1.61946 | 0.809728 | − | 0.586805i | \(-0.199615\pi\) | ||||
0.809728 | + | 0.586805i | \(0.199615\pi\) | |||||||
\(338\) | 181695.i | 1.59041i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −55680.0 | −0.481661 | ||||||||
\(341\) | − 44158.4i | − 0.379756i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 26247.8i | 0.221807i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −120329. | −1.00512 | ||||||||
\(347\) | 52383.9i | 0.435050i | 0.976055 | + | 0.217525i | \(0.0697983\pi\) | ||||
−0.976055 | + | 0.217525i | \(0.930202\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −105555. | −0.866615 | −0.433308 | − | 0.901246i | \(-0.642654\pi\) | ||||
−0.433308 | + | 0.901246i | \(0.642654\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10496.0 | −0.0847107 | ||||||||
\(353\) | 176095.i | 1.41318i | 0.707623 | + | 0.706590i | \(0.249767\pi\) | ||||
−0.707623 | + | 0.706590i | \(0.750233\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39632.5 | 0.314481 | ||||||||
\(356\) | 16370.9i | 0.129173i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −131844. | −1.02871 | ||||||||
\(359\) | 22767.4i | 0.176655i | 0.996092 | + | 0.0883273i | \(0.0281521\pi\) | ||||
−0.996092 | + | 0.0883273i | \(0.971848\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −107121. | −0.821978 | ||||||||
\(362\) | 17232.5i | 0.131502i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 200140.i | − 1.50227i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −210500. | −1.56286 | −0.781430 | − | 0.623993i | \(-0.785509\pi\) | ||||
−0.781430 | + | 0.623993i | \(0.785509\pi\) | |||||||
\(368\) | − 34484.2i | − 0.254639i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −36555.7 | −0.267025 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 45358.0 | 0.326014 | 0.163007 | − | 0.986625i | \(-0.447881\pi\) | ||||
0.163007 | + | 0.986625i | \(0.447881\pi\) | |||||||
\(374\) | − 52990.0i | − 0.378836i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24370.5 | 0.172381 | ||||||||
\(377\) | 25418.0i | 0.178837i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8520.00 | 0.0593145 | 0.0296573 | − | 0.999560i | \(-0.490558\pi\) | ||||
0.0296573 | + | 0.999560i | \(0.490558\pi\) | |||||||
\(380\) | − 26247.8i | − 0.181771i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 127284. | 0.872262 | ||||||||
\(383\) | 232639.i | 1.58593i | 0.609264 | + | 0.792967i | \(0.291465\pi\) | ||||
−0.609264 | + | 0.792967i | \(0.708535\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 152961.i | 1.02661i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6092.62 | 0.0404707 | ||||||||
\(389\) | − 220757.i | − 1.45887i | −0.684051 | − | 0.729434i | \(-0.739784\pi\) | ||||
0.684051 | − | 0.729434i | \(-0.260216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 174097. | 1.13877 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 47916.0 | 0.308666 | ||||||||
\(395\) | − 66388.3i | − 0.425498i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −106164. | −0.673590 | −0.336795 | − | 0.941578i | \(-0.609343\pi\) | ||||
−0.336795 | + | 0.941578i | \(0.609343\pi\) | |||||||
\(398\) | − 166294.i | − 1.04981i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10304.0 | 0.0644000 | ||||||||
\(401\) | − 79027.7i | − 0.491463i | −0.969338 | − | 0.245731i | \(-0.920972\pi\) | ||||
0.969338 | − | 0.245731i | \(-0.0790281\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −232000. | −1.42849 | ||||||||
\(404\) | 102534.i | 0.628208i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 34789.7i | − 0.210020i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 165872. | 0.991574 | 0.495787 | − | 0.868444i | \(-0.334880\pi\) | ||||
0.495787 | + | 0.868444i | \(0.334880\pi\) | |||||||
\(410\) | − 98429.3i | − 0.585540i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −42648.3 | −0.251251 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 292320. | 1.69731 | ||||||||
\(416\) | 55144.1i | 0.318649i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 24979.7 | 0.142967 | ||||||||
\(419\) | 293815.i | 1.67358i | 0.547527 | + | 0.836788i | \(0.315569\pi\) | ||||
−0.547527 | + | 0.836788i | \(0.684431\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −182082. | −1.02731 | −0.513657 | − | 0.857996i | \(-0.671709\pi\) | ||||
−0.513657 | + | 0.857996i | \(0.671709\pi\) | |||||||
\(422\) | 185205.i | 1.03999i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −24992.0 | −0.139017 | ||||||||
\(425\) | 52020.7i | 0.288004i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 124892.i | 0.681785i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −70674.4 | −0.382230 | ||||||||
\(431\) | − 192928.i | − 1.03858i | −0.854597 | − | 0.519292i | \(-0.826196\pi\) | ||||
0.854597 | − | 0.519292i | \(-0.173804\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16145.4 | −0.0861141 | −0.0430570 | − | 0.999073i | \(-0.513710\pi\) | ||||
−0.0430570 | + | 0.999073i | \(0.513710\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −136640. | −0.718795 | ||||||||
\(437\) | 82069.9i | 0.429755i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −305240. | −1.58384 | −0.791922 | − | 0.610622i | \(-0.790920\pi\) | ||||
−0.791922 | + | 0.610622i | \(0.790920\pi\) | |||||||
\(440\) | − 28261.3i | − 0.145978i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −278400. | −1.42503 | ||||||||
\(443\) | − 328266.i | − 1.67270i | −0.548195 | − | 0.836350i | \(-0.684685\pi\) | ||||
0.548195 | − | 0.836350i | \(-0.315315\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −44080.0 | −0.222598 | ||||||||
\(446\) | − 140445.i | − 0.706052i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 129091.i | − 0.640328i | −0.947362 | − | 0.320164i | \(-0.896262\pi\) | ||||
0.947362 | − | 0.320164i | \(-0.103738\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 93674.0 | 0.460539 | ||||||||
\(452\) | − 151592.i | − 0.741994i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 193136. | 0.937026 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 242240. | 1.15988 | 0.579941 | − | 0.814659i | \(-0.303076\pi\) | ||||
0.579941 | + | 0.814659i | \(0.303076\pi\) | |||||||
\(458\) | 140445.i | 0.669539i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 92851.5 | 0.438807 | ||||||||
\(461\) | − 57836.7i | − 0.272146i | −0.990699 | − | 0.136073i | \(-0.956552\pi\) | ||||
0.990699 | − | 0.136073i | \(-0.0434481\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −100438. | −0.468529 | −0.234264 | − | 0.972173i | \(-0.575268\pi\) | ||||
−0.234264 | + | 0.972173i | \(0.575268\pi\) | |||||||
\(464\) | 5340.07i | 0.0248034i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15524.0 | −0.0714878 | ||||||||
\(467\) | − 138722.i | − 0.636079i | −0.948077 | − | 0.318040i | \(-0.896976\pi\) | ||||
0.948077 | − | 0.318040i | \(-0.103024\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 65619.5i | 0.297055i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 82859.6 | 0.371928 | ||||||||
\(473\) | − 67260.0i | − 0.300632i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24522.8 | −0.108688 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 108396. | 0.474414 | ||||||||
\(479\) | 215837.i | 0.940710i | 0.882477 | + | 0.470355i | \(0.155874\pi\) | ||||
−0.882477 | + | 0.470355i | \(0.844126\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −182779. | −0.790015 | ||||||||
\(482\) | − 152077.i | − 0.654590i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −90232.0 | −0.385185 | ||||||||
\(485\) | 16404.9i | 0.0697412i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −356240. | −1.50205 | −0.751026 | − | 0.660273i | \(-0.770441\pi\) | ||||
−0.751026 | + | 0.660273i | \(0.770441\pi\) | |||||||
\(488\) | 58590.6i | 0.246030i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 256540.i | − 1.06412i | −0.846706 | − | 0.532061i | \(-0.821418\pi\) | ||||
0.846706 | − | 0.532061i | \(-0.178582\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26959.8 | −0.110923 | ||||||||
\(494\) | − 131239.i | − 0.537785i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −48740.9 | −0.198121 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 118440. | 0.475661 | 0.237830 | − | 0.971307i | \(-0.423564\pi\) | ||||
0.237830 | + | 0.971307i | \(0.423564\pi\) | |||||||
\(500\) | 135448.i | 0.541791i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −52396.5 | −0.207919 | ||||||||
\(503\) | − 141953.i | − 0.561059i | −0.959845 | − | 0.280529i | \(-0.909490\pi\) | ||||
0.959845 | − | 0.280529i | \(-0.0905100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −276080. | −1.08256 | ||||||||
\(506\) | 88365.7i | 0.345130i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −159664. | −0.618699 | ||||||||
\(509\) | 119443.i | 0.461026i | 0.973069 | + | 0.230513i | \(0.0740403\pi\) | ||||
−0.973069 | + | 0.230513i | \(0.925960\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28939.9 | −0.109540 | ||||||||
\(515\) | − 114834.i | − 0.432969i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −62449.3 | −0.233640 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −148480. | −0.549112 | ||||||||
\(521\) | − 360698.i | − 1.32883i | −0.747365 | − | 0.664414i | \(-0.768681\pi\) | ||||
0.747365 | − | 0.664414i | \(-0.231319\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 523965. | 1.91557 | 0.957787 | − | 0.287478i | \(-0.0928168\pi\) | ||||
0.957787 | + | 0.287478i | \(0.0928168\pi\) | |||||||
\(524\) | 175772.i | 0.640157i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −327596. | −1.18404 | ||||||||
\(527\) | − 246073.i | − 0.886019i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10481.0 | −0.0374534 | ||||||||
\(530\) | − 67293.0i | − 0.239562i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 492146.i | − 1.73237i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −336282. | −1.17489 | ||||||||
\(536\) | − 187310.i | − 0.651975i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −109972. | −0.379941 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 397762. | 1.35903 | 0.679515 | − | 0.733662i | \(-0.262190\pi\) | ||||
0.679515 | + | 0.733662i | \(0.262190\pi\) | |||||||
\(542\) | − 331295.i | − 1.12776i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −58489.1 | −0.197641 | ||||||||
\(545\) | − 367914.i | − 1.23866i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −371318. | −1.24100 | −0.620499 | − | 0.784207i | \(-0.713070\pi\) | ||||
−0.620499 | + | 0.784207i | \(0.713070\pi\) | |||||||
\(548\) | − 90950.9i | − 0.302863i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −26404.0 | −0.0872860 | ||||||||
\(551\) | − 12709.0i | − 0.0418608i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 7235.12i | − 0.0235736i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −29244.6 | −0.0946010 | ||||||||
\(557\) | − 374002.i | − 1.20549i | −0.797935 | − | 0.602744i | \(-0.794074\pi\) | ||||
0.797935 | − | 0.602744i | \(-0.205926\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −353372. | −1.13086 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 126876. | 0.401705 | ||||||||
\(563\) | − 210452.i | − 0.663952i | −0.943288 | − | 0.331976i | \(-0.892285\pi\) | ||||
0.943288 | − | 0.331976i | \(-0.107715\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 408175. | 1.27864 | ||||||||
\(566\) | 432106.i | 1.34883i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 41632.0 | 0.129042 | ||||||||
\(569\) | − 126825.i | − 0.391725i | −0.980631 | − | 0.195862i | \(-0.937249\pi\) | ||||
0.980631 | − | 0.195862i | \(-0.0627506\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −119082. | −0.365236 | −0.182618 | − | 0.983184i | \(-0.558457\pi\) | ||||
−0.182618 | + | 0.983184i | \(0.558457\pi\) | |||||||
\(572\) | − 141307.i | − 0.431888i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 86749.3i | − 0.262380i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 89256.9 | 0.268096 | 0.134048 | − | 0.990975i | \(-0.457202\pi\) | ||||
0.134048 | + | 0.990975i | \(0.457202\pi\) | |||||||
\(578\) | − 59054.7i | − 0.176766i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −14378.6 | −0.0427425 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 64042.0 | 0.188420 | ||||||||
\(584\) | − 210237.i | − 0.616429i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −218420. | −0.636060 | ||||||||
\(587\) | 465063.i | 1.34969i | 0.737958 | + | 0.674847i | \(0.235790\pi\) | ||||
−0.737958 | + | 0.674847i | \(0.764210\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 116000. | 0.334370 | ||||||||
\(590\) | 223106.i | 0.640926i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −38400.0 | −0.109569 | ||||||||
\(593\) | − 232316.i | − 0.660647i | −0.943868 | − | 0.330324i | \(-0.892842\pi\) | ||||
0.943868 | − | 0.330324i | \(-0.107158\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 110184.i | 0.310189i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 464258. | 1.29824 | ||||||||
\(599\) | 38323.8i | 0.106811i | 0.998573 | + | 0.0534053i | \(0.0170075\pi\) | ||||
−0.998573 | + | 0.0534053i | \(0.982992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 340273. | 0.942059 | 0.471030 | − | 0.882117i | \(-0.343882\pi\) | ||||
0.471030 | + | 0.882117i | \(0.343882\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −233600. | −0.640323 | ||||||||
\(605\) | − 242957.i | − 0.663772i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4569.46 | −0.0124019 | −0.00620094 | − | 0.999981i | \(-0.501974\pi\) | ||||
−0.00620094 | + | 0.999981i | \(0.501974\pi\) | |||||||
\(608\) | − 27572.0i | − 0.0745868i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −157760. | −0.423972 | ||||||||
\(611\) | 328098.i | 0.878862i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −564562. | −1.50242 | −0.751209 | − | 0.660065i | \(-0.770529\pi\) | ||||
−0.751209 | + | 0.660065i | \(0.770529\pi\) | |||||||
\(614\) | 339050.i | 0.899346i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 346537.i | − 0.910290i | −0.890417 | − | 0.455145i | \(-0.849587\pi\) | ||||
0.890417 | − | 0.455145i | \(-0.150413\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 164196. | 0.428530 | 0.214265 | − | 0.976776i | \(-0.431264\pi\) | ||||
0.214265 | + | 0.976776i | \(0.431264\pi\) | |||||||
\(620\) | − 131239.i | − 0.341413i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 233347. | 0.603145 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −264079. | −0.676042 | ||||||||
\(626\) | 483372.i | 1.23348i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −181560. | −0.460364 | ||||||||
\(629\) | − 193866.i | − 0.490005i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −394122. | −0.989856 | −0.494928 | − | 0.868934i | \(-0.664806\pi\) | ||||
−0.494928 | + | 0.868934i | \(0.664806\pi\) | |||||||
\(632\) | − 69737.7i | − 0.174596i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 306804. | 0.763278 | ||||||||
\(635\) | − 429908.i | − 1.06618i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 13683.9i | − 0.0336178i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −31194.2 | −0.0761577 | ||||||||
\(641\) | − 346368.i | − 0.842988i | −0.906831 | − | 0.421494i | \(-0.861506\pi\) | ||||
0.906831 | − | 0.421494i | \(-0.138494\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −54376.6 | −0.131520 | −0.0657598 | − | 0.997835i | \(-0.520947\pi\) | ||||
−0.0657598 | + | 0.997835i | \(0.520947\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 139200. | 0.333560 | ||||||||
\(647\) | 730875.i | 1.74596i | 0.487756 | + | 0.872980i | \(0.337816\pi\) | ||||
−0.487756 | + | 0.872980i | \(0.662184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −212328. | −0.504101 | ||||||||
\(650\) | 138722.i | 0.328336i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 188496. | 0.443411 | ||||||||
\(653\) | 488836.i | 1.14640i | 0.819415 | + | 0.573200i | \(0.194298\pi\) | ||||
−0.819415 | + | 0.573200i | \(0.805702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −473280. | −1.10315 | ||||||||
\(656\) | − 103395.i | − 0.240266i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6560.54i | 0.0151067i | 0.999971 | + | 0.00755333i | \(0.00240432\pi\) | ||||
−0.999971 | + | 0.00755333i | \(0.997596\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −198467. | −0.454240 | −0.227120 | − | 0.973867i | \(-0.572931\pi\) | ||||
−0.227120 | + | 0.973867i | \(0.572931\pi\) | |||||||
\(662\) | 348802.i | 0.795907i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 307068. | 0.696464 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44958.0 | 0.101054 | ||||||||
\(668\) | 49974.3i | 0.111994i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 504347. | 1.12352 | ||||||||
\(671\) | − 150138.i | − 0.333462i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 224240. | 0.495089 | 0.247544 | − | 0.968877i | \(-0.420376\pi\) | ||||
0.247544 | + | 0.968877i | \(0.420376\pi\) | |||||||
\(674\) | 520204.i | 1.14513i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −513912. | −1.12459 | ||||||||
\(677\) | 213576.i | 0.465988i | 0.972478 | + | 0.232994i | \(0.0748522\pi\) | ||||
−0.972478 | + | 0.232994i | \(0.925148\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 157487.i | − 0.340586i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 124899. | 0.268528 | ||||||||
\(683\) | 433031.i | 0.928277i | 0.885763 | + | 0.464138i | \(0.153636\pi\) | ||||
−0.885763 | + | 0.464138i | \(0.846364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 244893. | 0.521909 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −74240.0 | −0.156842 | ||||||||
\(689\) | − 336465.i | − 0.708764i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9443.56 | −0.0197779 | −0.00988894 | − | 0.999951i | \(-0.503148\pi\) | ||||
−0.00988894 | + | 0.999951i | \(0.503148\pi\) | |||||||
\(692\) | − 340342.i | − 0.710729i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −148164. | −0.307627 | ||||||||
\(695\) | − 78743.4i | − 0.163021i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 522000. | 1.07450 | ||||||||
\(698\) | − 298554.i | − 0.612790i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 458232.i | 0.932501i | 0.884653 | + | 0.466251i | \(0.154396\pi\) | ||||
−0.884653 | + | 0.466251i | \(0.845604\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 91389.3 | 0.184920 | ||||||||
\(704\) | − 29687.2i | − 0.0598995i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −498072. | −0.999269 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −84920.0 | −0.168934 | −0.0844671 | − | 0.996426i | \(-0.526919\pi\) | ||||
−0.0844671 | + | 0.996426i | \(0.526919\pi\) | |||||||
\(710\) | 112098.i | 0.222372i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −46303.9 | −0.0913393 | ||||||||
\(713\) | 410350.i | 0.807188i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 380480. | 0.744252 | ||||||||
\(716\) | − 372911.i | − 0.727410i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −64396.0 | −0.124914 | ||||||||
\(719\) | 469156.i | 0.907526i | 0.891122 | + | 0.453763i | \(0.149919\pi\) | ||||
−0.891122 | + | 0.453763i | \(0.850081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 302984.i | − 0.581226i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −48740.9 | −0.0929858 | ||||||||
\(725\) | 13433.6i | 0.0255574i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −755028. | −1.42855 | −0.714273 | − | 0.699867i | \(-0.753242\pi\) | ||||
−0.714273 | + | 0.699867i | \(0.753242\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 566080. | 1.06226 | ||||||||
\(731\) | − 374807.i | − 0.701412i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −829205. | −1.54331 | −0.771657 | − | 0.636039i | \(-0.780572\pi\) | ||||
−0.771657 | + | 0.636039i | \(0.780572\pi\) | |||||||
\(734\) | − 595384.i | − 1.10511i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 97536.0 | 0.180057 | ||||||||
\(737\) | 479981.i | 0.883668i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −396758. | −0.726502 | −0.363251 | − | 0.931691i | \(-0.618333\pi\) | ||||
−0.363251 | + | 0.931691i | \(0.618333\pi\) | |||||||
\(740\) | − 103395.i | − 0.188815i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 335818.i | 0.608311i | 0.952622 | + | 0.304156i | \(0.0983743\pi\) | ||||
−0.952622 | + | 0.304156i | \(0.901626\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −296680. | −0.534535 | ||||||||
\(746\) | 128292.i | 0.230527i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 149878. | 0.267877 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −223680. | −0.396595 | −0.198298 | − | 0.980142i | \(-0.563541\pi\) | ||||
−0.198298 | + | 0.980142i | \(0.563541\pi\) | |||||||
\(752\) | 68930.1i | 0.121891i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −71892.9 | −0.126457 | ||||||||
\(755\) | − 628987.i | − 1.10344i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 721720. | 1.25944 | 0.629719 | − | 0.776823i | \(-0.283170\pi\) | ||||
0.629719 | + | 0.776823i | \(0.283170\pi\) | |||||||
\(758\) | 24098.2i | 0.0419417i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 74240.0 | 0.128532 | ||||||||
\(761\) | 773633.i | 1.33587i | 0.744218 | + | 0.667937i | \(0.232822\pi\) | ||||
−0.744218 | + | 0.667937i | \(0.767178\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 360014.i | 0.616783i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −658003. | −1.12142 | ||||||||
\(767\) | 1.11553e6i | 1.89623i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −170593. | −0.288476 | −0.144238 | − | 0.989543i | \(-0.546073\pi\) | ||||
−0.144238 | + | 0.989543i | \(0.546073\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −432640. | −0.725926 | ||||||||
\(773\) | 189019.i | 0.316335i | 0.987412 | + | 0.158167i | \(0.0505586\pi\) | ||||
−0.987412 | + | 0.158167i | \(0.949441\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −122614. | −0.204144 | ||||||||
\(776\) | 17232.5i | 0.0286171i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 624396. | 1.03158 | ||||||||
\(779\) | 246073.i | 0.405499i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −106682. | −0.174900 | ||||||||
\(782\) | 492419.i | 0.805233i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 488865.i | − 0.793323i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −262592. | −0.423967 | −0.211983 | − | 0.977273i | \(-0.567992\pi\) | ||||
−0.211983 | + | 0.977273i | \(0.567992\pi\) | |||||||
\(788\) | 135527.i | 0.218259i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 187775. | 0.300872 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −788800. | −1.25436 | ||||||||
\(794\) | − 300277.i | − 0.476300i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 470350. | 0.742327 | ||||||||
\(797\) | 870135.i | 1.36984i | 0.728618 | + | 0.684920i | \(0.240163\pi\) | ||||
−0.728618 | + | 0.684920i | \(0.759837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −348000. | −0.545112 | ||||||||
\(800\) | 29144.1i | 0.0455377i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 223524. | 0.347516 | ||||||||
\(803\) | 538732.i | 0.835491i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 656195.i | − 1.01010i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −290009. | −0.444210 | ||||||||
\(809\) | − 99672.4i | − 0.152292i | −0.997097 | − | 0.0761461i | \(-0.975738\pi\) | ||||
0.997097 | − | 0.0761461i | \(-0.0242615\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 524879. | 0.798027 | 0.399013 | − | 0.916945i | \(-0.369353\pi\) | ||||
0.399013 | + | 0.916945i | \(0.369353\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 98400.0 | 0.148507 | ||||||||
\(815\) | 507541.i | 0.764110i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 176686. | 0.264702 | ||||||||
\(818\) | 469156.i | 0.701149i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 278400. | 0.414039 | ||||||||
\(821\) | 382490.i | 0.567457i | 0.958905 | + | 0.283729i | \(0.0915715\pi\) | ||||
−0.958905 | + | 0.283729i | \(0.908428\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.00724e6 | 1.48708 | 0.743540 | − | 0.668692i | \(-0.233145\pi\) | ||||
0.743540 | + | 0.668692i | \(0.233145\pi\) | |||||||
\(824\) | − 120628.i | − 0.177661i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.29576e6i | 1.89458i | 0.320379 | + | 0.947290i | \(0.396190\pi\) | ||||
−0.320379 | + | 0.947290i | \(0.603810\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −61535.4 | −0.0895398 | −0.0447699 | − | 0.998997i | \(-0.514255\pi\) | ||||
−0.0447699 | + | 0.998997i | \(0.514255\pi\) | |||||||
\(830\) | 826806.i | 1.20018i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −155971. | −0.225319 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −134560. | −0.192994 | ||||||||
\(836\) | 70653.4i | 0.101093i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −831033. | −1.18340 | ||||||||
\(839\) | − 600984.i | − 0.853767i | −0.904307 | − | 0.426883i | \(-0.859611\pi\) | ||||
0.904307 | − | 0.426883i | \(-0.140389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 700319. | 0.990157 | ||||||||
\(842\) | − 515006.i | − 0.726420i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −523840. | −0.735383 | ||||||||
\(845\) | − 1.38375e6i | − 1.93796i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 70688.1i | − 0.0983002i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −147137. | −0.203649 | ||||||||
\(851\) | 323289.i | 0.446408i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 974971. | 1.33997 | 0.669983 | − | 0.742376i | \(-0.266301\pi\) | ||||
0.669983 | + | 0.742376i | \(0.266301\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −353248. | −0.482095 | ||||||||
\(857\) | 914078.i | 1.24458i | 0.782788 | + | 0.622288i | \(0.213797\pi\) | ||||
−0.782788 | + | 0.622288i | \(0.786203\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 918005. | 1.24411 | 0.622055 | − | 0.782973i | \(-0.286298\pi\) | ||||
0.622055 | + | 0.782973i | \(0.286298\pi\) | |||||||
\(860\) | − 199897.i | − 0.270278i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 545684. | 0.734390 | ||||||||
\(863\) | 420331.i | 0.564378i | 0.959359 | + | 0.282189i | \(0.0910605\pi\) | ||||
−0.959359 | + | 0.282189i | \(0.908939\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 916400. | 1.22477 | ||||||||
\(866\) | − 45666.2i | − 0.0608918i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 178703.i | 0.236642i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.52173e6 | 3.32402 | ||||||||
\(872\) | − 386476.i | − 0.508265i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −232129. | −0.303883 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −886158. | −1.15216 | −0.576079 | − | 0.817394i | \(-0.695418\pi\) | ||||
−0.576079 | + | 0.817394i | \(0.695418\pi\) | |||||||
\(878\) | − 863350.i | − 1.11995i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 79935.2 | 0.103222 | ||||||||
\(881\) | 341958.i | 0.440576i | 0.975435 | + | 0.220288i | \(0.0706997\pi\) | ||||
−0.975435 | + | 0.220288i | \(0.929300\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −671720. | −0.861523 | −0.430761 | − | 0.902466i | \(-0.641755\pi\) | ||||
−0.430761 | + | 0.902466i | \(0.641755\pi\) | |||||||
\(884\) | − 787434.i | − 1.00765i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 928476. | 1.18278 | ||||||||
\(887\) | − 327633.i | − 0.416429i | −0.978083 | − | 0.208214i | \(-0.933235\pi\) | ||||
0.978083 | − | 0.208214i | \(-0.0667652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 124677.i | − 0.157401i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 397239. | 0.499254 | ||||||||
\(893\) | − 164049.i | − 0.205717i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.00409e6 | 1.25351 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 365124. | 0.452780 | ||||||||
\(899\) | − 63544.9i | − 0.0786252i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 356875. | 0.439609 | ||||||||
\(902\) | 264950.i | 0.325650i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 428768. | 0.524669 | ||||||||
\(905\) | − 131239.i | − 0.160238i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 762760. | 0.927200 | 0.463600 | − | 0.886045i | \(-0.346558\pi\) | ||||
0.463600 | + | 0.886045i | \(0.346558\pi\) | |||||||
\(908\) | 546271.i | 0.662577i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 529059.i | 0.637481i | 0.947842 | + | 0.318740i | \(0.103260\pi\) | ||||
−0.947842 | + | 0.318740i | \(0.896740\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −786862. | −0.943967 | ||||||||
\(914\) | 685158.i | 0.820160i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −397239. | −0.473435 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −422880. | −0.500710 | −0.250355 | − | 0.968154i | \(-0.580547\pi\) | ||||
−0.250355 | + | 0.968154i | \(0.580547\pi\) | |||||||
\(920\) | 262624.i | 0.310283i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 163587. | 0.192436 | ||||||||
\(923\) | 560488.i | 0.657905i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −96600.0 | −0.112900 | ||||||||
\(926\) | − 284082.i | − 0.331300i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15104.0 | −0.0175386 | ||||||||
\(929\) | − 1.68631e6i | − 1.95392i | −0.213429 | − | 0.976959i | \(-0.568463\pi\) | ||||
0.213429 | − | 0.976959i | \(-0.431537\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 43908.5i | − 0.0505495i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 392365. | 0.449776 | ||||||||
\(935\) | 403560.i | 0.461620i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.31235e6 | −1.49476 | −0.747378 | − | 0.664399i | \(-0.768688\pi\) | ||||
−0.747378 | + | 0.664399i | \(0.768688\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −185600. | −0.210050 | ||||||||
\(941\) | − 362852.i | − 0.409780i | −0.978785 | − | 0.204890i | \(-0.934316\pi\) | ||||
0.978785 | − | 0.204890i | \(-0.0656837\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −870483. | −0.978897 | ||||||||
\(944\) | 234362.i | 0.262993i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 190240. | 0.212579 | ||||||||
\(947\) | − 1.05772e6i | − 1.17942i | −0.807614 | − | 0.589712i | \(-0.799241\pi\) | ||||
0.807614 | − | 0.589712i | \(-0.200759\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.83040e6 | 3.14279 | ||||||||
\(950\) | − 69360.9i | − 0.0768542i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.55377e6i | 1.71081i | 0.517963 | + | 0.855403i | \(0.326691\pi\) | ||||
−0.517963 | + | 0.855403i | \(0.673309\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −969366. | −1.06287 | ||||||||
\(956\) | 306590.i | 0.335461i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −610480. | −0.665182 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −343521. | −0.371969 | ||||||||
\(962\) | − 516976.i | − 0.558625i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 430139. | 0.462865 | ||||||||
\(965\) | − 1.16492e6i | − 1.25095i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.09892e6 | 1.17521 | 0.587603 | − | 0.809149i | \(-0.300072\pi\) | ||||
0.587603 | + | 0.809149i | \(0.300072\pi\) | |||||||
\(968\) | − 255215.i | − 0.272367i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −46400.0 | −0.0493145 | ||||||||
\(971\) | 1.63472e6i | 1.73382i | 0.498461 | + | 0.866912i | \(0.333899\pi\) | ||||
−0.498461 | + | 0.866912i | \(0.666101\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 1.00760e6i | − 1.06211i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −165719. | −0.173970 | ||||||||
\(977\) | 82025.8i | 0.0859333i | 0.999077 | + | 0.0429666i | \(0.0136809\pi\) | ||||
−0.999077 | + | 0.0429666i | \(0.986319\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 118654. | 0.123799 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 725604. | 0.752448 | ||||||||
\(983\) | − 1.51883e6i | − 1.57182i | −0.618341 | − | 0.785910i | \(-0.712195\pi\) | ||||
0.618341 | − | 0.785910i | \(-0.287805\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −364917. | −0.376116 | ||||||||
\(986\) | − 76253.9i | − 0.0784347i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 371200. | 0.380272 | ||||||||
\(989\) | 625026.i | 0.639007i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −497680. | −0.506761 | −0.253380 | − | 0.967367i | \(-0.581542\pi\) | ||||
−0.253380 | + | 0.967367i | \(0.581542\pi\) | |||||||
\(992\) | − 137860.i | − 0.140093i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.26646e6i | 1.27922i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −203950. | −0.205180 | −0.102590 | − | 0.994724i | \(-0.532713\pi\) | ||||
−0.102590 | + | 0.994724i | \(0.532713\pi\) | |||||||
\(998\) | 334999.i | 0.336343i | ||||||||
\(999\) | 0 | 0 |
(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 | 882.5.b.b.197.3 | yes | 4 | |
3.2 | odd | 2 | inner | 882.5.b.b.197.2 | yes | 4 | |
7.6 | odd | 2 | inner | 882.5.b.b.197.4 | yes | 4 | |
21.20 | even | 2 | inner | 882.5.b.b.197.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.5.b.b.197.1 | ✓ | 4 | 21.20 | even | 2 | inner | |
882.5.b.b.197.2 | yes | 4 | 3.2 | odd | 2 | inner | |
882.5.b.b.197.3 | yes | 4 | 1.1 | even | 1 | trivial | |
882.5.b.b.197.4 | yes | 4 | 7.6 | odd | 2 | inner |