Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,5,Mod(15,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, 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("16.15");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.c (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: | \(1.65391940934\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 15.2 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.15 |
Dual form | 16.5.c.a.15.1 |
$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 13.8564i | 1.53960i | 0.638285 | + | 0.769800i | \(0.279644\pi\) | ||||
−0.638285 | + | 0.769800i | \(0.720356\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 18.0000 | 0.720000 | 0.360000 | − | 0.932952i | \(-0.382777\pi\) | ||||
0.360000 | + | 0.932952i | \(0.382777\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 27.7128i | − 0.565568i | −0.959184 | − | 0.282784i | \(-0.908742\pi\) | ||||
0.959184 | − | 0.282784i | \(-0.0912579\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −111.000 | −1.37037 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 124.708i | − 1.03064i | −0.856997 | − | 0.515321i | \(-0.827673\pi\) | ||||
0.856997 | − | 0.515321i | \(-0.172327\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 178.000 | 1.05325 | 0.526627 | − | 0.850096i | \(-0.323456\pi\) | ||||
0.526627 | + | 0.850096i | \(0.323456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 249.415i | 1.10851i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −126.000 | −0.435986 | −0.217993 | − | 0.975950i | \(-0.569951\pi\) | ||||
−0.217993 | + | 0.975950i | \(0.569951\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 401.836i | 1.11312i | 0.830808 | + | 0.556559i | \(0.187879\pi\) | ||||
−0.830808 | + | 0.556559i | \(0.812121\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 384.000 | 0.870748 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 748.246i | − 1.41445i | −0.706987 | − | 0.707227i | \(-0.749946\pi\) | ||||
0.706987 | − | 0.707227i | \(-0.250054\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −301.000 | −0.481600 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 415.692i | − 0.570222i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1422.00 | −1.69084 | −0.845422 | − | 0.534099i | \(-0.820651\pi\) | ||||
−0.845422 | + | 0.534099i | \(0.820651\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 332.554i | 0.346050i | 0.984917 | + | 0.173025i | \(0.0553541\pi\) | ||||
−0.984917 | + | 0.173025i | \(0.944646\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1728.00 | 1.58678 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 498.831i | − 0.407209i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 530.000 | 0.387144 | 0.193572 | − | 0.981086i | \(-0.437993\pi\) | ||||
0.193572 | + | 0.981086i | \(0.437993\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2466.44i | 1.62159i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 162.000 | 0.0963712 | 0.0481856 | − | 0.998838i | \(-0.484656\pi\) | ||||
0.0481856 | + | 0.998838i | \(0.484656\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1538.06i | 0.831834i | 0.909403 | + | 0.415917i | \(0.136539\pi\) | ||||
−0.909403 | + | 0.415917i | \(0.863461\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1998.00 | −0.986667 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 3491.81i | − 1.58072i | −0.612642 | − | 0.790361i | \(-0.709893\pi\) | ||||
0.612642 | − | 0.790361i | \(-0.290107\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1633.00 | 0.680133 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 1745.91i | − 0.671245i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 594.000 | 0.211463 | 0.105732 | − | 0.994395i | \(-0.466282\pi\) | ||||
0.105732 | + | 0.994395i | \(0.466282\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2244.74i | − 0.742062i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5568.00 | −1.71376 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2369.45i | 0.680680i | 0.940303 | + | 0.340340i | \(0.110542\pi\) | ||||
−0.940303 | + | 0.340340i | \(0.889458\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 626.000 | 0.168234 | 0.0841172 | − | 0.996456i | \(-0.473193\pi\) | ||||
0.0841172 | + | 0.996456i | \(0.473193\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3076.12i | 0.775037i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3204.00 | 0.758343 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1094.66i | − 0.243853i | −0.992539 | − | 0.121926i | \(-0.961093\pi\) | ||||
0.992539 | − | 0.121926i | \(-0.0389072\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10368.0 | 2.17769 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7731.87i | 1.53380i | 0.641768 | + | 0.766899i | \(0.278201\pi\) | ||||
−0.641768 | + | 0.766899i | \(0.721799\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6686.00 | −1.25464 | −0.627322 | − | 0.778760i | \(-0.715849\pi\) | ||||
−0.627322 | + | 0.778760i | \(0.715849\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 4170.78i | − 0.741472i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3456.00 | −0.582898 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 1385.64i | − 0.222022i | −0.993819 | − | 0.111011i | \(-0.964591\pi\) | ||||
0.993819 | − | 0.111011i | \(-0.0354089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3231.00 | −0.492455 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4614.18i | 0.669790i | 0.942255 | + | 0.334895i | \(0.108701\pi\) | ||||
−0.942255 | + | 0.334895i | \(0.891299\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2268.00 | −0.313910 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 19703.8i | − 2.60322i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8226.00 | 1.03851 | 0.519253 | − | 0.854621i | \(-0.326210\pi\) | ||||
0.519253 | + | 0.854621i | \(0.326210\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 4932.88i | − 0.595687i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4608.00 | −0.532778 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7233.04i | 0.801445i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1598.00 | −0.169837 | −0.0849187 | − | 0.996388i | \(-0.527063\pi\) | ||||
−0.0849187 | + | 0.996388i | \(0.527063\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13842.6i | 1.41236i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4590.00 | −0.449956 | −0.224978 | − | 0.974364i | \(-0.572231\pi\) | ||||
−0.224978 | + | 0.974364i | \(0.572231\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8951.24i | 0.843740i | 0.906656 | + | 0.421870i | \(0.138626\pi\) | ||||
−0.906656 | + | 0.421870i | \(0.861374\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6912.00 | 0.626939 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 3117.69i | − 0.272311i | −0.990687 | − | 0.136156i | \(-0.956525\pi\) | ||||
0.990687 | − | 0.136156i | \(-0.0434747\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9394.00 | 0.790674 | 0.395337 | − | 0.918536i | \(-0.370628\pi\) | ||||
0.395337 | + | 0.918536i | \(0.370628\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7343.90i | 0.596047i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18882.0 | 1.47874 | 0.739369 | − | 0.673301i | \(-0.235124\pi\) | ||||
0.739369 | + | 0.673301i | \(0.235124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 13468.4i | − 1.01841i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19758.0 | −1.44335 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3491.81i | 0.246580i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −911.000 | −0.0622225 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2244.74i | 0.148373i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −16668.0 | −1.06675 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 14632.4i | − 0.907208i | −0.891203 | − | 0.453604i | \(-0.850138\pi\) | ||||
0.891203 | − | 0.453604i | \(-0.149862\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21312.0 | −1.28069 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 20826.2i | − 1.21358i | −0.794864 | − | 0.606788i | \(-0.792458\pi\) | ||||
0.794864 | − | 0.606788i | \(-0.207542\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11136.0 | 0.629544 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 7482.46i | − 0.410560i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8226.00 | 0.438276 | 0.219138 | − | 0.975694i | \(-0.429676\pi\) | ||||
0.219138 | + | 0.975694i | \(0.429676\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 28696.6i | 1.48526i | 0.669705 | + | 0.742628i | \(0.266421\pi\) | ||||
−0.669705 | + | 0.742628i | \(0.733579\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 48384.0 | 2.43368 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 22198.0i | − 1.08553i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −25596.0 | −1.21741 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 22627.5i | 1.04713i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −31662.0 | −1.42615 | −0.713076 | − | 0.701087i | \(-0.752699\pi\) | ||||
−0.713076 | + | 0.701087i | \(0.752699\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 39601.6i | 1.73684i | 0.495832 | + | 0.868418i | \(0.334863\pi\) | ||||
−0.495832 | + | 0.868418i | \(0.665137\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13986.0 | 0.597463 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5985.97i | 0.249156i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 29426.0 | 1.19380 | 0.596900 | − | 0.802315i | \(-0.296399\pi\) | ||||
0.596900 | + | 0.802315i | \(0.296399\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8230.71i | 0.325569i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20736.0 | −0.799969 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 18276.6i | − 0.687892i | −0.938989 | − | 0.343946i | \(-0.888236\pi\) | ||||
0.938989 | − | 0.343946i | \(-0.111764\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 31104.0 | 1.14248 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 15214.3i | − 0.545532i | −0.962080 | − | 0.272766i | \(-0.912062\pi\) | ||||
0.962080 | − | 0.272766i | \(-0.0879384\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3123.00 | 0.109345 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 44603.8i | − 1.52538i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20430.0 | −0.682616 | −0.341308 | − | 0.939952i | \(-0.610870\pi\) | ||||
−0.341308 | + | 0.939952i | \(0.610870\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8341.56i | 0.272377i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −32832.0 | −1.04797 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 22322.7i | − 0.696691i | −0.937366 | − | 0.348345i | \(-0.886744\pi\) | ||||
0.937366 | − | 0.348345i | \(-0.113256\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −37934.0 | −1.15790 | −0.578951 | − | 0.815363i | \(-0.696538\pi\) | ||||
−0.578951 | + | 0.815363i | \(0.696538\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8674.11i | 0.259014i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9540.00 | 0.278744 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15713.2i | 0.449346i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11520.0 | −0.322499 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 13967.3i | − 0.382864i | −0.981506 | − | 0.191432i | \(-0.938687\pi\) | ||||
0.981506 | − | 0.191432i | \(-0.0613131\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 35138.0 | 0.943327 | 0.471664 | − | 0.881779i | \(-0.343654\pi\) | ||||
0.471664 | + | 0.881779i | \(0.343654\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 44395.9i | 1.16755i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 46098.0 | 1.18782 | 0.593909 | − | 0.804532i | \(-0.297584\pi\) | ||||
0.593909 | + | 0.804532i | \(0.297584\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 77845.3i | − 1.96574i | −0.184299 | − | 0.982870i | \(-0.559001\pi\) | ||||
0.184299 | − | 0.982870i | \(-0.440999\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15168.0 | 0.375436 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 39407.6i | 0.956287i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2916.00 | 0.0693873 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 83055.3i | 1.93833i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 50112.0 | 1.14723 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 52058.5i | 1.16930i | 0.811285 | + | 0.584651i | \(0.198769\pi\) | ||||
−0.811285 | + | 0.584651i | \(0.801231\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −107136. | −2.36144 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27685.1i | 0.598920i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9216.00 | 0.195714 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 92643.9i | − 1.93165i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22428.0 | −0.459204 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 29597.3i | − 0.595172i | −0.954695 | − | 0.297586i | \(-0.903819\pi\) | ||||
0.954695 | − | 0.297586i | \(-0.0961814\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 33411.0 | 0.659970 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8106.00i | 0.157309i | 0.996902 | + | 0.0786547i | \(0.0250625\pi\) | ||||
−0.996902 | + | 0.0786547i | \(0.974938\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26770.0 | 0.510478 | 0.255239 | − | 0.966878i | \(-0.417846\pi\) | ||||
0.255239 | + | 0.966878i | \(0.417846\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 47887.7i | − 0.897430i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28062.0 | −0.516900 | −0.258450 | − | 0.966025i | \(-0.583212\pi\) | ||||
−0.258450 | + | 0.966025i | \(0.583212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 62852.7i | − 1.13812i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19200.0 | 0.341826 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14466.1i | 0.253253i | 0.991950 | + | 0.126627i | \(0.0404150\pi\) | ||||
−0.991950 | + | 0.126627i | \(0.959585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −58622.0 | −1.00931 | −0.504657 | − | 0.863320i | \(-0.668381\pi\) | ||||
−0.504657 | + | 0.863320i | \(0.668381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 78441.1i | − 1.32841i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 29394.0 | 0.489696 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 71526.8i | 1.17240i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −63936.0 | −1.03121 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 92159.0i | 1.46282i | 0.681939 | + | 0.731409i | \(0.261137\pi\) | ||||
−0.681939 | + | 0.731409i | \(0.738863\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −93312.0 | −1.45779 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 31426.3i | − 0.483296i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 47106.0 | 0.713198 | 0.356599 | − | 0.934258i | \(-0.383936\pi\) | ||||
0.356599 | + | 0.934258i | \(0.383936\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 14687.8i | − 0.218956i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 157842. | 2.31708 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 57614.9i | 0.832959i | 0.909145 | + | 0.416479i | \(0.136736\pi\) | ||||
−0.909145 | + | 0.416479i | \(0.863264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10692.0 | 0.152253 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 113983.i | 1.59888i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 44082.0 | 0.609196 | 0.304598 | − | 0.952481i | \(-0.401478\pi\) | ||||
0.304598 | + | 0.952481i | \(0.401478\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 79203.2i | − 1.07846i | −0.842158 | − | 0.539230i | \(-0.818715\pi\) | ||||
0.842158 | − | 0.539230i | \(-0.181285\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 68352.0 | 0.917120 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 37537.0i | 0.496357i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 40402.0 | 0.526554 | 0.263277 | − | 0.964720i | \(-0.415197\pi\) | ||||
0.263277 | + | 0.964720i | \(0.415197\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 36913.5i | − 0.474216i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −153054. | −1.93835 | −0.969175 | − | 0.246375i | \(-0.920761\pi\) | ||||
−0.969175 | + | 0.246375i | \(0.920761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29971.4i | 0.374226i | 0.982338 | + | 0.187113i | \(0.0599131\pi\) | ||||
−0.982338 | + | 0.187113i | \(0.940087\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −100224. | −1.23391 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 4489.48i | − 0.0545044i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −67645.0 | −0.809916 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 22142.5i | − 0.261482i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 100242. | 1.16765 | 0.583827 | − | 0.811878i | \(-0.301554\pi\) | ||||
0.583827 | + | 0.811878i | \(0.301554\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 42650.0i | 0.490089i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −51840.0 | −0.587695 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 133188.i | − 1.48978i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42624.0 | 0.470458 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 63600.9i | − 0.692752i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11268.0 | 0.121129 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 146033.i | − 1.54943i | −0.632308 | − | 0.774717i | \(-0.717892\pi\) | ||||
0.632308 | − | 0.774717i | \(-0.282108\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −124032. | −1.29902 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 53624.3i | − 0.554422i | −0.960809 | − | 0.277211i | \(-0.910590\pi\) | ||||
0.960809 | − | 0.277211i | \(-0.0894102\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 145634. | 1.48653 | 0.743266 | − | 0.668996i | \(-0.233276\pi\) | ||||
0.743266 | + | 0.668996i | \(0.233276\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 55370.2i | 0.558027i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9486.00 | −0.0943984 | −0.0471992 | − | 0.998885i | \(-0.515030\pi\) | ||||
−0.0471992 | + | 0.998885i | \(0.515030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 177334.i | 1.74265i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 43200.0 | 0.419251 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 50631.3i | − 0.485304i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −53578.0 | −0.507247 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 130167.i | 1.21732i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −96768.0 | −0.894005 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 94542.3i | 0.862919i | 0.902132 | + | 0.431459i | \(0.142001\pi\) | ||||
−0.902132 | + | 0.431459i | \(0.857999\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −58830.0 | −0.530531 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 19703.8i | − 0.175574i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 145474. | 1.28093 | 0.640465 | − | 0.767987i | \(-0.278742\pi\) | ||||
0.640465 | + | 0.767987i | \(0.278742\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 261637.i | 2.27667i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 41472.0 | 0.356653 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 111793.i | − 0.950229i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 186624. | 1.56794 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 182198.i | − 1.51316i | −0.653902 | − | 0.756579i | \(-0.726869\pi\) | ||||
0.653902 | − | 0.756579i | \(-0.273131\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 626.000 | 0.00513953 | 0.00256977 | − | 0.999997i | \(-0.499182\pi\) | ||||
0.00256977 | + | 0.999997i | \(0.499182\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 73993.2i | − 0.600589i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25218.0 | 0.202377 | 0.101189 | − | 0.994867i | \(-0.467735\pi\) | ||||
0.101189 | + | 0.994867i | \(0.467735\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 139174.i | 1.10433i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −48384.0 | −0.379634 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 45144.2i | − 0.350278i | −0.984544 | − | 0.175139i | \(-0.943963\pi\) | ||||
0.984544 | − | 0.175139i | \(-0.0560375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −31151.0 | −0.239033 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 12623.2i | − 0.0957978i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −120348. | −0.903344 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14022.7i | 0.104112i | 0.998644 | + | 0.0520558i | \(0.0165774\pi\) | ||||
−0.998644 | + | 0.0520558i | \(0.983423\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17982.0 | −0.132064 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 16461.4i | − 0.119597i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −203182. | −1.46039 | −0.730193 | − | 0.683241i | \(-0.760570\pi\) | ||||
−0.730193 | + | 0.683241i | \(0.760570\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 230959.i | − 1.64237i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −253116. | −1.78089 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 122892.i | − 0.855553i | −0.903885 | − | 0.427776i | \(-0.859297\pi\) | ||||
0.903885 | − | 0.427776i | \(-0.140703\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 202752. | 1.39674 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 131691.i | 0.897758i | 0.893592 | + | 0.448879i | \(0.148177\pi\) | ||||
−0.893592 | + | 0.448879i | \(0.851823\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −62208.0 | −0.419686 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 170725.i | − 1.13992i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 150930. | 0.997416 | 0.498708 | − | 0.866770i | \(-0.333808\pi\) | ||||
0.498708 | + | 0.866770i | \(0.333808\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 94279.0i | 0.616682i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 288576. | 1.86842 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 24941.5i | − 0.159856i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36146.0 | 0.229340 | 0.114670 | − | 0.993404i | \(-0.463419\pi\) | ||||
0.114670 | + | 0.993404i | \(0.463419\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 154305.i | 0.969246i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −156798. | −0.975106 | −0.487553 | − | 0.873093i | \(-0.662110\pi\) | ||||
−0.487553 | + | 0.873093i | \(0.662110\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 59194.6i | 0.364478i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −58158.0 | −0.354568 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 66095.1i | − 0.399007i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 254050. | 1.51870 | 0.759351 | − | 0.650681i | \(-0.225517\pi\) | ||||
0.759351 | + | 0.650681i | \(0.225517\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 113983.i | 0.674770i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 65664.0 | 0.384970 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 83055.3i | 0.482249i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −397632. | −2.28670 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 169727.i | 0.966770i | 0.875408 | + | 0.483385i | \(0.160593\pi\) | ||||
−0.875408 | + | 0.483385i | \(0.839407\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37742.0 | −0.212942 | −0.106471 | − | 0.994316i | \(-0.533955\pi\) | ||||
−0.106471 | + | 0.994316i | \(0.533955\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 387591.i | 2.16617i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 37926.0 | 0.209971 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 17348.2i | − 0.0951479i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 307584. | 1.67128 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 175090.i | − 0.942553i | −0.881986 | − | 0.471276i | \(-0.843793\pi\) | ||||
0.881986 | − | 0.471276i | \(-0.156207\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −165886. | −0.884777 | −0.442389 | − | 0.896823i | \(-0.645869\pi\) | ||||
−0.442389 | + | 0.896823i | \(0.645869\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 354669.i | − 1.87432i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 300672. | 1.57445 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 169353.i | − 0.878747i | −0.898304 | − | 0.439373i | \(-0.855200\pi\) | ||||
0.898304 | − | 0.439373i | \(-0.144800\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −181263. | −0.932034 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 317630.i | 1.61851i | 0.587460 | + | 0.809254i | \(0.300128\pi\) | ||||
−0.587460 | + | 0.809254i | \(0.699872\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 148068. | 0.747724 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 438722.i | − 2.19570i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 192834. | 0.956513 | 0.478257 | − | 0.878220i | \(-0.341269\pi\) | ||||
0.478257 | + | 0.878220i | \(0.341269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 20202.6i | − 0.0993242i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −548736. | −2.67403 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 88791.9i | − 0.428894i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −151262. | −0.724265 | −0.362132 | − | 0.932127i | \(-0.617951\pi\) | ||||
−0.362132 | + | 0.932127i | \(0.617951\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 52377.2i | 0.248609i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −119502. | −0.562307 | −0.281153 | − | 0.959663i | \(-0.590717\pi\) | ||||
−0.281153 | + | 0.959663i | \(0.590717\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 288269.i | − 1.34473i | −0.740219 | − | 0.672366i | \(-0.765278\pi\) | ||||
0.740219 | − | 0.672366i | \(-0.234722\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −82944.0 | −0.383600 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 96399.0i | 0.442017i | 0.975272 | + | 0.221008i | \(0.0709348\pi\) | ||||
−0.975272 | + | 0.221008i | \(0.929065\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30336.0 | −0.137915 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 407739.i | 1.83798i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 191808. | 0.857323 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 120953.i | − 0.536078i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −65934.0 | −0.289783 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 292315.i | 1.27403i | 0.770851 | + | 0.637015i | \(0.219831\pi\) | ||||
−0.770851 | + | 0.637015i | \(0.780169\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 94340.0 | 0.407761 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 287326.i | − 1.23163i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28764.0 | −0.122283 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 194572.i | − 0.820392i | −0.911997 | − | 0.410196i | \(-0.865460\pi\) | ||||
0.911997 | − | 0.410196i | \(-0.134540\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 253248. | 1.05908 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 39033.5i | − 0.161910i | −0.996718 | − | 0.0809551i | \(-0.974203\pi\) | ||||
0.996718 | − | 0.0809551i | \(-0.0257971\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 179172. | 0.737185 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 249166.i | 1.01690i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 214272. | 0.867466 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 159252.i | 0.639562i | 0.947491 | + | 0.319781i | \(0.103609\pi\) | ||||
−0.947491 | + | 0.319781i | \(0.896391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 210816. | 0.839901 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 363398.i | 1.43631i | 0.695886 | + | 0.718153i | \(0.255012\pi\) | ||||
−0.695886 | + | 0.718153i | \(0.744988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −82620.0 | −0.323968 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 43273.6i | 0.168348i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −259470. | −1.00150 | −0.500751 | − | 0.865592i | \(-0.666943\pi\) | ||||
−0.500751 | + | 0.865592i | \(0.666943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 185288.i | 0.709586i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 167040. | 0.634725 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 161122.i | 0.607493i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −435456. | −1.62916 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 283086.i | − 1.05096i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17442.0 | 0.0642571 | 0.0321285 | − | 0.999484i | \(-0.489771\pi\) | ||||
0.0321285 | + | 0.999484i | \(0.489771\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6969.77i | 0.0254809i | 0.999919 | + | 0.0127405i | \(0.00405553\pi\) | ||||
−0.999919 | + | 0.0127405i | \(0.995944\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −115584. | −0.419352 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 41901.8i | − 0.150873i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −280031. | −1.00068 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 263008.i | − 0.932783i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28836.0 | 0.101503 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 56118.4i | − 0.196064i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 309312. | 1.07263 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 203648.i | − 0.700974i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 231922. | 0.792405 | 0.396203 | − | 0.918163i | \(-0.370328\pi\) | ||||
0.396203 | + | 0.918163i | \(0.370328\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 525629.i | − 1.78271i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 169092. | 0.569285 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 233134.i | 0.779168i | 0.920991 | + | 0.389584i | \(0.127381\pi\) | ||||
−0.920991 | + | 0.389584i | \(0.872619\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −69486.0 | −0.230543 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 571410.i | − 1.88211i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −38400.0 | −0.125569 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 132190.i | 0.429154i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −552654. | −1.78132 | −0.890662 | − | 0.454666i | \(-0.849759\pi\) | ||||
−0.890662 | + | 0.454666i | \(0.849759\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 273775.i | 0.876133i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −217728. | −0.691813 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 101387.i | 0.319865i | 0.987128 | + | 0.159933i | \(0.0511277\pi\) | ||||
−0.987128 | + | 0.159933i | \(0.948872\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 339876. | 1.06469 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 89540.1i | 0.278517i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −483102. | −1.49216 | −0.746078 | − | 0.665858i | \(-0.768065\pi\) | ||||
−0.746078 | + | 0.665858i | \(0.768065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 221993.i | − 0.680876i | −0.940267 | − | 0.340438i | \(-0.889425\pi\) | ||||
0.940267 | − | 0.340438i | \(-0.110575\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 193536. | 0.589458 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 225222.i | 0.681201i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 176642. | 0.530570 | 0.265285 | − | 0.964170i | \(-0.414534\pi\) | ||||
0.265285 | + | 0.964170i | \(0.414534\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 486886.i | 1.45235i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 127872. | 0.378812 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 74076.3i | − 0.217943i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −355644. | −1.03921 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 209634.i | − 0.608394i | −0.952609 | − | 0.304197i | \(-0.901612\pi\) | ||||
0.952609 | − | 0.304197i | \(-0.0983880\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −133632. | −0.385194 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 638753.i | 1.82876i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 653634. | 1.85877 | 0.929384 | − | 0.369114i | \(-0.120339\pi\) | ||||
0.929384 | + | 0.369114i | \(0.120339\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 62852.7i | 0.177537i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.07866e6 | 3.02646 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5237.72i | 0.0145978i | 0.999973 | + | 0.00729892i | \(0.00232334\pi\) | ||||
−0.999973 | + | 0.00729892i | \(0.997677\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 77858.0 | 0.215553 | 0.107777 | − | 0.994175i | \(-0.465627\pi\) | ||||
0.107777 | + | 0.994175i | \(0.465627\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 121507.i | 0.334169i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16398.0 | −0.0448002 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 153529.i | 0.416690i | 0.978055 | + | 0.208345i | \(0.0668077\pi\) | ||||
−0.978055 | + | 0.208345i | \(0.933192\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −546048. | −1.47230 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 621543.i | − 1.66490i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 197522. | 0.525647 | 0.262824 | − | 0.964844i | \(-0.415346\pi\) | ||||
0.262824 | + | 0.964844i | \(0.415346\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 40405.3i | 0.106829i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −394398. | −1.03601 | −0.518006 | − | 0.855377i | \(-0.673325\pi\) | ||||
−0.518006 | + | 0.855377i | \(0.673325\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 262066.i | − 0.683958i | −0.939708 | − | 0.341979i | \(-0.888903\pi\) | ||||
0.939708 | − | 0.341979i | \(-0.111097\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −311040. | −0.806553 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 227966.i | − 0.587345i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −111899. | −0.286461 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 694372.i | 1.76627i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −66780.0 | −0.168789 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 659149.i | 1.65548i | 0.561109 | + | 0.827742i | \(0.310375\pi\) | ||||
−0.561109 | + | 0.827742i | \(0.689625\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −721344. | −1.80026 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 263383.i | − 0.653190i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 290674. | 0.716353 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 858238.i | − 2.10187i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 314946. | 0.766514 | 0.383257 | − | 0.923642i | \(-0.374802\pi\) | ||||
0.383257 | + | 0.923642i | \(0.374802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 563554.i | − 1.36306i | −0.731792 | − | 0.681528i | \(-0.761316\pi\) | ||||
0.731792 | − | 0.681528i | \(-0.238684\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −383616. | −0.922098 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 161871.i | − 0.386687i | −0.981131 | − | 0.193343i | \(-0.938067\pi\) | ||||
0.981131 | − | 0.193343i | \(-0.0619331\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 295488. | 0.701537 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 127701.i | 0.301322i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −472014. | −1.10695 | −0.553476 | − | 0.832865i | \(-0.686699\pi\) | ||||
−0.553476 | + | 0.832865i | \(0.686699\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 374871.i | − 0.873775i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 742146. | 1.71933 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 508184.i | − 1.17017i | −0.810971 | − | 0.585086i | \(-0.801061\pi\) | ||||
0.810971 | − | 0.585086i | \(-0.198939\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16558.0 | −0.0378970 | −0.0189485 | − | 0.999820i | \(-0.506032\pi\) | ||||
−0.0189485 | + | 0.999820i | \(0.506032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 310771.i | − 0.706991i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 200448. | 0.453272 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.06401e6i | 2.39162i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 410112. | 0.916326 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 78067.0i | − 0.173389i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −543550. | −1.20008 | −0.600039 | − | 0.799971i | \(-0.704848\pi\) | ||||
−0.600039 | + | 0.799971i | \(0.704848\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 125123.i | 0.274619i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −419310. | −0.914867 | −0.457433 | − | 0.889244i | \(-0.651231\pi\) | ||||
−0.457433 | + | 0.889244i | \(0.651231\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 44285.1i | 0.0960545i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −112320. | −0.242194 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 912735.i | 1.95661i | 0.207178 | + | 0.978303i | \(0.433572\pi\) | ||||
−0.207178 | + | 0.978303i | \(0.566428\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 148068. | 0.315559 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 370936.i | 0.785933i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 105732. | 0.222725 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 17001.8i | − 0.0356073i | −0.999842 | − | 0.0178037i | \(-0.994333\pi\) | ||||
0.999842 | − | 0.0178037i | \(-0.00566738\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 383616. | 0.798786 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 516539.i | 1.06938i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20412.0 | −0.0420165 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 388838.i | − 0.795820i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −462222. | −0.940621 | −0.470310 | − | 0.882501i | \(-0.655858\pi\) | ||||
−0.470310 | + | 0.882501i | \(0.655858\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 212973.i | 0.430937i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 870912. | 1.75225 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 127202.i | 0.254480i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −162158. | −0.322586 | −0.161293 | − | 0.986907i | \(-0.551566\pi\) | ||||
−0.161293 | + | 0.986907i | \(0.551566\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 153806.i | 0.304253i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 248832. | 0.489471 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 399563.i | − 0.781580i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −200448. | −0.389909 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 204022.i | − 0.394656i | −0.980338 | − | 0.197328i | \(-0.936774\pi\) | ||||
0.980338 | − | 0.197328i | \(-0.0632264\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 248064. | 0.477192 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 812290.i | − 1.55394i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 428022. | 0.814311 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 144910.i | 0.274177i | 0.990559 | + | 0.137088i | \(0.0437744\pi\) | ||||
−0.990559 | + | 0.137088i | \(0.956226\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 825201. | 1.55276 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 193796.i | − 0.362668i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −885902. | −1.64884 | −0.824419 | − | 0.565981i | \(-0.808498\pi\) | ||||
−0.824419 | + | 0.565981i | \(0.808498\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 407295.i | 0.753936i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −136512. | −0.251325 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 114274.i | − 0.209246i | −0.994512 | − | 0.104623i | \(-0.966636\pi\) | ||||
0.994512 | − | 0.104623i | \(-0.0333636\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −991104. | −1.80502 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 581387.i | 1.05314i | 0.850131 | + | 0.526572i | \(0.176523\pi\) | ||||
−0.850131 | + | 0.526572i | \(0.823477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −569916. | −1.02683 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 512174.i | − 0.917860i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −86400.0 | −0.154010 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1.11178e6i | − 1.97124i | −0.168970 | − | 0.985621i | \(-0.554044\pi\) | ||||
0.168970 | − | 0.985621i | \(-0.445956\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.27699e6 | −2.25215 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 712829.i | 1.25052i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 376786. | 0.657511 | 0.328755 | − | 0.944415i | \(-0.393371\pi\) | ||||
0.328755 | + | 0.944415i | \(0.393371\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 1.29297e6i | − 2.24442i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 307170. | 0.530407 | 0.265204 | − | 0.964192i | \(-0.414561\pi\) | ||||
0.265204 | + | 0.964192i | \(0.414561\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 260334.i | − 0.447180i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 251748. | 0.430173 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 421761.i | 0.716929i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −110014. | −0.186035 | −0.0930176 | − | 0.995664i | \(-0.529651\pi\) | ||||
−0.0930176 | + | 0.995664i | \(0.529651\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 652720.i | 1.09804i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 685458. | 1.14715 | 0.573577 | − | 0.819152i | \(-0.305555\pi\) | ||||
0.573577 | + | 0.819152i | \(0.305555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 100099.i | − 0.166658i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 203520. | 0.337105 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 65097.4i | 0.107273i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 964224. | 1.58080 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 591114.i | 0.964157i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 529668. | 0.859537 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 382700.i | − 0.617887i | −0.951080 | − | 0.308944i | \(-0.900025\pi\) | ||||
0.951080 | − | 0.308944i | \(-0.0999754\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −798336. | −1.28242 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 523273.i | − 0.836326i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 111428. | 0.177194 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 148153.i | 0.234410i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 672498. | 1.05870 | 0.529352 | − | 0.848402i | \(-0.322435\pi\) | ||||
0.529352 | + | 0.848402i | \(0.322435\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 439969.i | 0.689173i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −913086. | −1.42314 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 833795.i | 1.29309i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −373248. | −0.575978 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 610818.i | 0.937918i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18594.0 | 0.0284103 | 0.0142051 | − | 0.999899i | \(-0.495478\pi\) | ||||
0.0142051 | + | 0.999899i | \(0.495478\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.05507e6i | 1.60413i | 0.597238 | + | 0.802064i | \(0.296265\pi\) | ||||
−0.597238 | + | 0.802064i | \(0.703735\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.09747e6 | 1.66040 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 328979.i | − 0.495282i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −618048. | −0.925930 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 547550.i | 0.816311i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −250542. | −0.371701 | −0.185851 | − | 0.982578i | \(-0.559504\pi\) | ||||
−0.185851 | + | 0.982578i | \(0.559504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 807413.i | − 1.19205i | −0.802964 | − | 0.596027i | \(-0.796745\pi\) | ||||
0.802964 | − | 0.596027i | \(-0.203255\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −520128. | −0.764192 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 316882.i | − 0.463326i | −0.972796 | − | 0.231663i | \(-0.925583\pi\) | ||||
0.972796 | − | 0.231663i | \(-0.0744167\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 428914. | 0.624110 | 0.312055 | − | 0.950064i | \(-0.398983\pi\) | ||||
0.312055 | + | 0.950064i | \(0.398983\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 559827.i | 0.810684i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −205758. | −0.296529 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 273858.i | − 0.392783i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 138240. | 0.197325 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 829805.i | 1.17883i | 0.807830 | + | 0.589416i | \(0.200642\pi\) | ||||
−0.807830 | + | 0.589416i | \(0.799358\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.31480e6 | 1.85895 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.12078e6i | − 2.98428i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 56214.0 | 0.0787283 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25246.4i | 0.0351910i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −415296. | −0.576159 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 396570.i | − 0.547597i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51502.0 | −0.0707825 | −0.0353913 | − | 0.999374i | \(-0.511268\pi\) | ||||
−0.0353913 | + | 0.999374i | \(0.511268\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 802868.i | − 1.09828i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −574110. | −0.781688 | −0.390844 | − | 0.920457i | \(-0.627817\pi\) | ||||
−0.390844 | + | 0.920457i | \(0.627817\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 173330.i | − 0.234902i | −0.993079 | − | 0.117451i | \(-0.962528\pi\) | ||||
0.993079 | − | 0.117451i | \(-0.0374723\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 62208.0 | 0.0839151 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 246422.i | − 0.330871i | −0.986221 | − | 0.165435i | \(-0.947097\pi\) | ||||
0.986221 | − | 0.165435i | \(-0.0529029\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −367740. | −0.491483 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 937317.i | − 1.24695i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −172800. | −0.228825 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 194849.i | − 0.256839i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 177378. | 0.232740 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 461917.i | 0.603320i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.39579e6 | −1.81477 | −0.907384 | − | 0.420304i | \(-0.861924\pi\) | ||||
−0.907384 | + | 0.420304i | \(0.861924\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.38899e6i | 1.79772i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −702270. | −0.904799 | −0.452400 | − | 0.891815i | \(-0.649432\pi\) | ||||
−0.452400 | + | 0.891815i | \(0.649432\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 776028.i | 0.995305i | 0.867377 | + | 0.497652i | \(0.165804\pi\) | ||||
−0.867377 | + | 0.497652i | \(0.834196\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −590976. | −0.754542 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 382853.i | − 0.486614i | −0.969949 | − | 0.243307i | \(-0.921768\pi\) | ||||
0.969949 | − | 0.243307i | \(-0.0782322\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −405504. | −0.513088 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 402930.i | 0.507545i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.40314e6 | 1.75953 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 401808.i | − 0.501617i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.84550e6 | 2.29367 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 472891.i | − 0.585116i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −74844.0 | −0.0921950 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 590615.i | 0.724318i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −682812. | −0.833689 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 66829.4i | 0.0812369i | 0.999175 | + | 0.0406184i | \(0.0129328\pi\) | ||||
−0.999175 | + | 0.0406184i | \(0.987067\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 509490. | 0.616606 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.43115e6i | − 1.72444i | −0.506538 | − | 0.862218i | \(-0.669075\pi\) | ||||
0.506538 | − | 0.862218i | \(-0.330925\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 575424. | 0.690314 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 156134.i | 0.186490i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −577152. | −0.686359 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.45584e6i | 1.72378i | 0.507095 | + | 0.861890i | \(0.330719\pi\) | ||||
−0.507095 | + | 0.861890i | \(0.669281\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.02349e6 | 2.38551 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.37627e6i | 1.61548i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −159530. | −0.186449 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 993587.i | − 1.15624i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −582462. | −0.674895 | −0.337447 | − | 0.941344i | \(-0.609564\pi\) | ||||
−0.337447 | + | 0.941344i | \(0.609564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 656198.i | 0.757069i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 743040. | 0.853589 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 282837.i | 0.323529i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 887138. | 1.01044 | 0.505222 | − | 0.862990i | \(-0.331411\pi\) | ||||
0.505222 | + | 0.862990i | \(0.331411\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.01796e6i | 2.28866i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −777294. | −0.877821 | −0.438911 | − | 0.898531i | \(-0.644636\pi\) | ||||
−0.438911 | + | 0.898531i | \(0.644636\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 121216.i | − 0.136313i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −207360. | −0.232200 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.44299e6i | − 1.60903i | −0.593933 | − | 0.804515i | \(-0.702425\pi\) | ||||
0.593933 | − | 0.804515i | \(-0.297575\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.19011e6 | −1.32146 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 131442.i | − 0.145336i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −584478. | −0.643550 | −0.321775 | − | 0.946816i | \(-0.604279\pi\) | ||||
−0.321775 | + | 0.946816i | \(0.604279\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 251411.i | − 0.275662i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.45722e6 | −2.68299 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 227966.i | − 0.247875i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 812929. | 0.880250 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 346064.i | 0.373167i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 632484. | 0.679196 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 316785.i | 0.338775i | 0.985549 | + | 0.169388i | \(0.0541790\pi\) | ||||
−0.985549 | + | 0.169388i | \(0.945821\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 701568. | 0.747175 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.18734e6i | − 1.25932i | −0.776870 | − | 0.629662i | \(-0.783194\pi\) | ||||
0.776870 | − | 0.629662i | \(-0.216806\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 795264. | 0.840012 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 742399.i | − 0.780958i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −665982. | −0.697707 | −0.348854 | − | 0.937177i | \(-0.613429\pi\) | ||||
−0.348854 | + | 0.937177i | \(0.613429\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.02585e6i | − 1.07033i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.04273e6 | −1.08352 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 73078.7i | 0.0756282i | 0.999285 | + | 0.0378141i | \(0.0120395\pi\) | ||||
−0.999285 | + | 0.0378141i | \(0.987961\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 829764. | 0.855228 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.34086e6i | − 1.37641i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.15085e6 | 1.17659 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 764098.i | 0.778039i | 0.921229 | + | 0.389020i | \(0.127186\pi\) | ||||
−0.921229 | + | 0.389020i | \(0.872814\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.31002e6 | −1.32855 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.40122e6i | − 1.41533i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 979730. | 0.985635 | 0.492817 | − | 0.870133i | \(-0.335967\pi\) | ||||
0.492817 | + | 0.870133i | \(0.335967\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 220317.i | − 0.220758i |
(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 | 16.5.c.a.15.2 | yes | 2 | |
3.2 | odd | 2 | 144.5.g.c.127.1 | 2 | |||
4.3 | odd | 2 | inner | 16.5.c.a.15.1 | ✓ | 2 | |
5.2 | odd | 4 | 400.5.h.b.399.3 | 4 | |||
5.3 | odd | 4 | 400.5.h.b.399.1 | 4 | |||
5.4 | even | 2 | 400.5.b.d.351.1 | 2 | |||
7.6 | odd | 2 | 784.5.d.a.687.1 | 2 | |||
8.3 | odd | 2 | 64.5.c.c.63.2 | 2 | |||
8.5 | even | 2 | 64.5.c.c.63.1 | 2 | |||
12.11 | even | 2 | 144.5.g.c.127.2 | 2 | |||
16.3 | odd | 4 | 256.5.d.f.127.3 | 4 | |||
16.5 | even | 4 | 256.5.d.f.127.4 | 4 | |||
16.11 | odd | 4 | 256.5.d.f.127.2 | 4 | |||
16.13 | even | 4 | 256.5.d.f.127.1 | 4 | |||
20.3 | even | 4 | 400.5.h.b.399.4 | 4 | |||
20.7 | even | 4 | 400.5.h.b.399.2 | 4 | |||
20.19 | odd | 2 | 400.5.b.d.351.2 | 2 | |||
24.5 | odd | 2 | 576.5.g.h.127.1 | 2 | |||
24.11 | even | 2 | 576.5.g.h.127.2 | 2 | |||
28.27 | even | 2 | 784.5.d.a.687.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.c.a.15.1 | ✓ | 2 | 4.3 | odd | 2 | inner | |
16.5.c.a.15.2 | yes | 2 | 1.1 | even | 1 | trivial | |
64.5.c.c.63.1 | 2 | 8.5 | even | 2 | |||
64.5.c.c.63.2 | 2 | 8.3 | odd | 2 | |||
144.5.g.c.127.1 | 2 | 3.2 | odd | 2 | |||
144.5.g.c.127.2 | 2 | 12.11 | even | 2 | |||
256.5.d.f.127.1 | 4 | 16.13 | even | 4 | |||
256.5.d.f.127.2 | 4 | 16.11 | odd | 4 | |||
256.5.d.f.127.3 | 4 | 16.3 | odd | 4 | |||
256.5.d.f.127.4 | 4 | 16.5 | even | 4 | |||
400.5.b.d.351.1 | 2 | 5.4 | even | 2 | |||
400.5.b.d.351.2 | 2 | 20.19 | odd | 2 | |||
400.5.h.b.399.1 | 4 | 5.3 | odd | 4 | |||
400.5.h.b.399.2 | 4 | 20.7 | even | 4 | |||
400.5.h.b.399.3 | 4 | 5.2 | odd | 4 | |||
400.5.h.b.399.4 | 4 | 20.3 | even | 4 | |||
576.5.g.h.127.1 | 2 | 24.5 | odd | 2 | |||
576.5.g.h.127.2 | 2 | 24.11 | even | 2 | |||
784.5.d.a.687.1 | 2 | 7.6 | odd | 2 | |||
784.5.d.a.687.2 | 2 | 28.27 | even | 2 |